What other ships were with USS Saratoga when it was hit by a torpedo on 1942 Jan 11?

To me it seems unlikely that a submarine would be able to get a "free shot" at a carrier. Normally the big ships are screened by a protective force of cruisers and destroyers.

Excellent answers have already been given, but I want to address the assumption made here, that this is extremely unusual.

Look at the list of sunk carriers - sinking by subs is not exceptional. Caveat: many of these are light "escort carriers", and wouldn't rate a full on destroyer screen. Some sinkings will be finishing shots, after the carrier is already dead in the water. But on the flip side, these are sunk carriers, i.e. Saratoga's attack here doesn't even make the list.

WW2 antisub combat, especially early on before radar, was a probability game and escorts were not guaranteed to sink or suppress subs. Even the radar often helped to spot or sink subs that were surfaced, reloading their batteries in "safe time", rather than at periscope depths during combat periods. Depth charges were deadly, but only to a point - determined submariners could press an attack.

Let's look at a famous action, that of Nautilus at Midway, against an enemy fully at battle stations:

At 07:55, 4 June, while approaching the northern boundary of her patrol area near Midway Island, she sighted masts on the horizon. Japanese planes sighted the submarine at the same time and began strafing. After diving to 100 feet (30 m), she continued observation. At 08:00, a formation of four enemy ships was sighted: the battleship Kirishima,[15] the cruiser Nagara,[16] and two destroyers (misidentified, as they often were early in the war, as cruisers)[17] in company. Within minutes the submarine was again sighted from the air and was bombed. Two of the "cruisers" closed for a kill and nine depth charges were dropped at a distance of about 1,000 yards (910 m).

When the attack ceased, Nautilus rose to periscope depth. Ships surrounded her. Sighting on Kirishima, she fired two bow tubes; one misfired, one missed. At 08:30, a destroyer immediately headed for the boat, which dived to 150 feet (46 m) to wait out the depth charge attack. At 08:46, periscope depth was again ordered. The cruiser and two of the destroyers were now out of range; echo ranging by the third appeared too accurate for comfort. At 09:00, the periscope was raised again and an aircraft carrier was sighted. Nautilus changed course to close for an attack. The enemy destroyer followed suit and at 09:18 attacked with six depth charges.

By 09:55 echo ranging ceased and Nautilus raised her periscope. The carrier, her escorts, and the attacking destroyer had disappeared. (Unbeknownst to her skipper at the time, the counter-attacking Japanese destroyer Arashi, in her rush to rejoin the carrier, was tracked by Enterprise's VB-6, led by Wade McClusky, back to the Japanese task force.) At 12:53, a damaged aircraft carrier with two escorts was sighted. The carrier was identified as Sōryū, but later research suggests it was probably Kaga. An hour later, Nautilus had moved into attack position. Between 13:59 and 14:05, after the battle was largely over, Nautilus launched four torpedoes at the carrier from less than 3,000 yards (2,700 m). One failed to run, two ran erratically, and the fourth was a dud (a familiar problem for the Mark XIV), impacting amidships and breaking in half.[18] Nautilus reported flames appeared along the length of the ship as the first hit, and the skeleton crew which had been aboard (survivors of which reported no torpedo hit) began going over the side, with the air flask of the dud torpedo acting as a life preserver for Japanese sailors

Nautilus went to 300 feet (91 m) as a prolonged depth charge attack commenced. At 16:10, the submarine rose to periscope depth. The carrier, burning along her entire length, had been abandoned. At 19:41, Nautilus resumed her patrol, having expended five torpedoes and survived 42 depth charges, but accomplished little of substance. (Not until much later was the importance of her attack on the battleship, and its connection to McClusky, recognized.)[19] Her commanding officer was awarded a Navy Cross for his actions.

And to clear up the TF-11 / TF-14 issue, CinCPac clearly defines them in a message of 4 Jan 1942. We know which carrier is associated with what task force simply by knowing the TF commanders' names:

• TF-8 - Halsey - therefore ENTERPRISE
• TF-11 - Brown = LEXINGTON
• TF-14 - Leary = SARATOGA
• TF-17 - Fletcher = YORKTOWN

A wikipedia page cites G. E. Wheeler's Kinkaid of the Seventh Fleet: A Biography of Admiral Thomas C. Kinkaid p. 143 as saying

TF–14 consisted of the fleet carrier Saratoga, the fleet oiler Neches, the seaplane tender Tangier, three heavy cruisers (Astoria, Minneapolis, and San Francisco), and 8 destroyers (Selfridge, Mugford, Jarvis, Patterson, Ralph Talbot, Henley, Blue, and Helm).

And to lend a little humanity to the issue, from USS SARATOGA War History page 2:

“11 Jan 42 – At 1915 on a clear night, excellent visibility, with SARATOGA outlined by Venus low on the Starboard quarter, position 19°N-155°15’W, SARATOGA torpedoed on the Starboard side amidships, approximately 18 feet below the waterline. Shell fractured from frame 104 to 111, a distance of 28 feet, and from bottom of inner belt to the outboard docking keel. Shell indented for sixty feet with plating dished between frames. The explosion was dull and muffled, with possibly a reverberation rather than a single sound. A column of oil and water rose as high as the stack. Some observers reported a splattering flash (as when steel is poured) while others saw only a glow or reflection. Three firerooms were flooded. Six men were killed in the engine rooms – RAINWATER, Osborn Keith, F1c., 1404 Sycamore St., North Little Rock Ark.; JOHNSON, Arthur Weller, WT2c., 111 E. 10th St., Howard, Ill.; HORNSBY, Marshall Thomas, WT2c., Pinson Tenn.; PRYMULA, Aloysius Walter, F2c., 4551 Melvina Ave., Chicago, Ill.; TAYLOR, Thomas Russell, WT1c., Woodston, Kansas.”

For some reason the sixth sailor was not listed.

However, from the 31 Jan 1942 muster roll for SARATOGA we can find the sixth on page 19:

MOLTHEN, Victor R., 3302899, F2c., last enlistment 24 Dec 1940 at Chicago, Ill., USN, DIED 1-11-42 in line of duty not misconduct.

The same wording, ". . . in line of duty not misconduct . . ." was used to describe the deaths of the five mentioned in the war history.

'Sara' had the shield up, in less than full alert but mere standard fashion, with a focus on looking up for planes, not so much down for submarines, but then one from I-6 got through, since no screen ever is perfect:

That’s exactly what happened on January 11, 1942, at 1915. Saratoga was zigzagging at a leisurely twelve knots, 420 miles southwest of Pearl Harbor. Flight operations had been secured for the day and most of the crew were sitting down to dinner.

From 4,700 yards away, the Japanese submarine I-6 fired three torpedoes at three-second intervals. One of the torpedoes slammed into Sara, port side, amidships. The big carrier wobbled, heeled sideways, and began listing to port. Three fire rooms were blown open and flooded, and six firemen were killed. The I-6 turned away and dove to 330 feet. A short time later, the sonar operator of the I-6 heard two loud explosions followed by several smaller ones. The excited submarine captain interpreted those noises as the sounds of the carrier breaking up and sinking. In actuality, the booms were depth charges from destroyers on a frantic search for the enemy sub. The I-6 boasted to her command authority in Guam that she had sunk a “Lexington-type” carrier.

Saratoga was wounded, badly, but swift damage-control measures and appropriate counter-flooding saved the ship. She limped back to Pearl but could not be fully repaired there. She headed to Puget Sound, where she was dry-docked and out of action for six months.

— Keith, Philip A: "Stay the rising sun: the true story of USS Lexington, her valiant crew, and changing the course of World War II", Zenith Press:Minneapolis, 2015.

More explicitly:

On January 11, a month after Pearl Harbor, the Saratoga was operating near Johnston Island five hundred miles southwest of Hawaii in seas so rough that Leary cancelled flight operations for the day. Waves broke over the bow and washed the flight deck. At 7:00 that evening, in the midst of the storm, a terrific explosion jolted the big carrier. A pilot on board said, “It felt like the whole ship had been moved about five feet.” A Japanese submarine, the I-6, had slipped through the screen of cruisers and destroyers and delivered a deadly Type 95 torpedo. The blast killed six men and flooded three fire rooms. Though the Japanese submarine skipper reported to Tokyo that he had sunk a Saratoga-class carrier, the big flattop managed to stay afloat and steam back to Pearl Harbor under her own power, arriving on January 15. Nimitz saw that the necessary repairs could not be completed in Hawaii and two days later reluctantly ordered her back to Bremerton, Washington.

— Craig L. Symonds: "The Battle of Midway", Oxford University Press: Oxford, New York, 2011.

The actual composition for the Task Force may rely on which Task Force is meant. Wikipedia makes it seem as if 'Task Force 14' is meant for the unlucky day, but in some narrations it seems by then it was actually 'Task Force 11'?:

16 Dec 1941 —— USN Task Force 14, centered around USS Saratoga, departed Pearl Harbor, US Territory of Hawaii to relieve Wake Island.
25 Dec 1941 —— Carrier USS Saratoga launched F2A Buffalo aircraft of Marine Fighter Squadron 221, originally intended to relieve Wake Atoll, to Midway Atoll. They became the first fighters to be based in Midway, and they immediately began a daily patrol schedule.
27 Dec 1941 —— USS Saratoga arrived at Pearl Harbor, US Territory of Hawaii.
31 Dec 1941 —— US Navy Task Force 11 with USS Saratoga departed Pearl Harbor, US Territory of Hawaii for patrol.
12 Jan 1942 —— USS Saratoga was damaged by a torpedo from Japanese submarine I-6 about 500 miles southwest of US Territory of Hawaii; she returned to Pearl Harbor under own power.

— World War II Database: Home » Equipment » Ships » Saratoga

The actual confusion may be enlightened by this explanation of numbers:

[…] Guam fell on 10 December, and Wake was under virtual siege from Japanese aircraft based in the Marshalls. Carrier task forces were to intercept and destroy Japanese raiding forces penetrating the area east of the 180th meridian as well.

The Pacific Fleet considered its first course of action to be the reinforcement of the Wake Island garrison. On 12 December Admiral Kimmel decided to employ the Lexington and the Saratoga in the operation.21 As refined, the plan was for Vice Admiral Brown’s Task Force 11 (designation changed from Task Force 12) with the Lexington to raid the island of Jaluit in the Marshalls, while Task Force 14 under Rear Admiral Frank Jack Fletcher would reinforce Wake with aircraft and equipment. Fletcher based his force around the Saratoga, with Rear Admiral Fitch as air commander. Brown sailed on 14 December, and Fletcher left Oahu two days later. Vice Admiral Halsey with the Enterprise (Task Force 8) was to be used in general reserve in the Midway area. He was scheduled to sail from Pearl Harbor on 19 December.

[…]

[…] Mid-January 1942 found the beginning of an intense debate between Navy and Army planners over basic American strategy in the Pacific.

Meanwhile Admiral Nimitz proceeded with the reinforcement of Samoa. At the end of December, Admiral Stark suggested that CinCPac plan a diversionary or covering raid into the Gilberts to coincide with the passage of the Samoa convoy south from the West Coast. Admiral King vigorously seconded that proposal on 2 January. In response to this, the staff worked on a plan which would have Vice Admiral Brown’s Task Force 11 attack positions in the Marshalls sometime around 13 and 14 January, while Task Force 8 raided the Gilberts three or four days later. Task Force 14 with the Saratoga, under the command of Rear Admiral Herbert Fairfax Leary, was to support the attacks from a central position. Rear Admiral Fletcher received orders to fly to San Diego and organize the new Task Force 17 around the Yorktown. The Samoa convoy with Task Force 17 in escort sailed from the West Coast on 6 January.

By 8 January, it was evident that the Samoa reinforcement would be the primary task of the Pacific Fleet in January. CinCPac decided to hold off on the raids until after the landing of the troops at Samoa, expected to be about 20 January. Then Task Force 8 and Task Force 17 could combine for simultaneous strikes against Japanese positions in the Gilberts, timed for the first week of February. Task Force 11 and Task Force 14 would remain in the Central Pacific to cover Hawaii. Unfortunately the Pacific Fleet lost the services of a carrier, when on 11 January the Japanese submarine 1-6 torpedoed the Saratoga in the vicinity of Johnston Island. The Saratoga returned on 13 January to Oahu, and two days later Admiral Nimitz decided to return her to the West Coast for repairs and modernization. The Saratoga remained inactive until the end of May. It was a very serious blow to the striking power of the Pacific Fleet.

— John B Lundstrom: "The First South Pacific Campaign: Pacific Fleet Strategy December 1941–June 1942", Naval Institute Press: Annapolis, 2014.

Another database lists this Task Force 11 composition:

1941/12/30 - 1942/01/11

CV Saratoga
CA Astoria, Minneapolis
DD Benham, Ellet
DesRon4: Selfridge, Bagley, Henley, Patterson

41/12/31 departed P.H.
42/01/07 refuel from Neches
42/01/11 500 miles SW of Oahu - Saratoga disabled by I-6 (19-00N, 165-00W) -> retired to P.H.
42/01/13 arrived back to P.H.

Wikipedia describes Task Force 11 as:

During World War II, Task Force 11 was a United States Navy aircraft carrier task force in the Pacific theater. After the attack on Pearl Harbor in December 1941, Destroyer Squadron 1 was attached to the task force, which was under the command of Vice Admiral Wilson Brown, made up of the aircraft carrier USS Lexington (CV-2) and the heavy cruisers USS Indianapolis (CA-35), USS Chicago (CA-29), and USS Portland (CA-33). On 14 December 1941, after delays due to bad weather, the task force cleared Pearl Harbor, Hawaii, as a diversion for an expedition under Rear Admiral Frank J. Fletcher in the aircraft carrier USS Saratoga (CV-3) to relieve Wake Island. Originally formed around Lexington, TF 11 then was formed around her sister ship Saratoga until Saratoga was torpedoed and disabled by the Imperial Japanese Navy submarine I-6 on 11 January 1942. It then was formed around Lexington again for the Battle of the Coral Sea in which Lexington was sunk in early May 1942, then again around Saratoga after her repairs were completed.

TF 11 – as part of Task Force 61 along with Task Force 16 – was involved in the Battle of the Eastern Solomons in late August 1942, but Saratoga was again crippled by a submarine, and the task force shrank to just the carrier and some destroyers.

Turning that perspective around, we see for I-6 and its commander Michimune Inaba that the carrier Saratoga was certainly not out on its own alone:

I-6 departs her patrol area to join the hunt for USS LEXINGTON (CV-2), detected by I-18. After I-1 develops a diesel trouble, I-6 replaces her in the picket line NE of Johnston Island. 10 January 1942: Throughout the day, the lookouts sight US aircraft patrolling in the area on five separate occasions. Plotting their courses, the navigator of I-6 calculates the enemy carrier's probable position. 11 January 1942: At 1841, while patrolling 270 miles NE of Johnston Island, I-6 sights a destroyer and crash-dives. Soon thereafter, a LEXINGTON-class carrier, one heavy cruiser and another destroyer appear on a southeasterly course at 19N, 165W. The carrier is USS SARATOGA (CV-3) of TF 14 under Rear Admiral Herbert F. Leary, steaming at 15 knots to rendezvous with USS ENTERPRISE (CV-6). LtCdr Inaba fires three Type 89 torpedoes with three-second intervals from 4,700 yards. At 1915, one of them hits SARATOGA port amidships, flooding three of her boiler rooms and killing six firemen. The carrier heels first to starboard, then to port, taking on 1,100 tons of water and losing headway. Seven minutes after the hit the escorting destroyers commence a counterattack, but fail to locate the submarine, escaping at 330-feet depth. The soundman of I-6 reports two loud explosions, followed by a series of smaller detonations, interpreted as breaking-up noises. After 2200, LtCdr Inaba reports two hits on a LEXINGTON-class carrier, claiming her as probably sunk. 1 SARATOGA is soon able to increase her speed to 16 knots and make it back to Pearl Harbor under her own power. As a result of subsequent repairs she is put out of the war for six months.

— Bob Hackett & Sander Kingsepp: "SENSUIKAN!, (Type J2 submarine), IJN Submarine I-6: Tabular Record of Movement", 2012.

And even more detail on the blowback that I-6 had to evade:

Submarine Attack on the USS Saratoga

The USS Saratoga (CV-3) became the victim of a hastily formed submarine picket line a month after the Pearl Harbor attack. Three submarines of the earlier special attack midget submarine mission, the 1-18, 1-22, and 1-24, were ordered to return to Hawaiian waters after they were resupplied at Kwajalein. They sortied on 3 January 1942. On the morning of 9 January, the 1-18 sighted a Lexington-class carrier and a cruiser steaming westward near Johnston Island. Rear Adm. Shigeaki Yamazaki, commander of Submarine Squadron 2, immediately ordered all available submarines in the area to establish a north-south picket line and to commence reconnaissance operations westward.

At 1740 (local time) on 11 January, Comdr. Michimune Inaba, in the 1-6, the third boat from the north in the extended picket line, sighted a Lexington-class carrier, one cruiser, and two destroyers about 270 miles from Johnston Island. Some time later, after maneuvering for a firing position, Inaba fired three torpedoes at the carrier target with an 80-degree angle on the bow and at a range of 4,700 yards. He heard two explosions and estimated that a large U.S. Navy aircraft carrier was sunk. The 1-6 survived a heavy depth-charge attack and surfaced at 2200, but no enemy ships were then in sight.

— Carl Boyd & Akihiko Yoshida: "The Japanese Submarine Force and World War II", Bluejacket Books, Naval Institute Press: Annapolis, 2002, p64.

The big mystery of "whose Task Force is it anyway" arises from not just bad information copied around books, the net etc, but also actually from a basis in fact that is confusing: Saratoga torpedoed twice in 1942, first by I-6 then by I-26, and a few re-organisations within the fleet, including renamings and regroupings, with both Task Forces ordered operating together at times:

Shortly before the torpedo-incident, Saratoga was tasked to go to Wake with these conditions as part of Task Force 14:

Against this background Kimmel's staff completed the final plans for the relief of Wake Island and organized the task forces to do the job. These first plans called for Vice Admiral Wilson Brown's Lexington task force (TF 12) to escort the seaplane tender-transport Tangier (AV 8), which would carry about 300 Marines of the Fourth Defense Battalion, ground personnel of VMF-221, plus additional guns, munitions, provisions, and radar sets. The plans also called for TF 14, commanded by Rear Admiral Aubrey W. (Jake) Fitch in Saratoga, to make a diversionary raid against Jaluit, a Japanese air base in the Marshall Islands. Expected to arrive on 14 December, Saratoga would be bringing VMF-221 from San Diego with its eighteen F2A-3 Buffalo fighter planes. Once dockside in Pearl these planes were to be loaded onto Lexington. Finally, Vice Admiral William F. (Bull) Halsey's TF 8, built around the carrier Enterprise, would enter Pearl Harbor for refueling once Task Forces 11 and 14 had sortied and then steam in the area southwest of Midway, positioning itself to assist the Wake Island force should it need support.

Because of delays in bringing Lexington and Saratoga into Pearl for refueling and sending them on their way, the operation order for the Wake Island expedition was changed and more delays followed. Admiral Brown's TF 12 was renumbered TF 11 and given the Jaluit raid mission. Lexington and its cruisers and destroyers finally cleared Pearl Harbor in the afternoon of 14 December. Because Saratoga was slow to arrive, Tangier, Neches (AO 5), and a division of destroyers headed west on the 15th, expecting the faster ships of TF 14 to overtake them en route to Wake. At 1115 on 16 December, TF 14 stood out of Pearl Harbor and turned west. In changing the carrier in the relief task force from Lexington to Saratoga, Admiral Kimmel had created a problem in command. The commander of CRUDIV 6, Rear Admiral Frank Jack Fletcher, was senior to Rear Admiral Fitch. The command was therefore placed with Fletcher, a non-aviator, who was on board Astoria. CINCPAC could have given the command of TF 14 to Fitch by simply asking Fletcher to stand aside, but Pye chose to follow regulation practice. Of course Fitch's carrier division command experience was not lost to TF 14; he simply did not command it. It should be noted that had Lexington remained with the Wake Island task force, Admiral Brown, also a non-aviator, would have had the task force command and no aviation flag officer would have been in the force. Once TF 14 overtook Tangier and Neches, it consisted of Saratoga; CRUDIV 6 heavy cruisers Astoria (F), Minneapolis (CA 36), and San Francisco (CA 38); and DESRON 4 destroyers Selfridge (DD 357) (F), Mugford (DD 389), Jarvis (DD 393), Patterson (DD 392), Ralph Talbot (DD 390), Henley (DD 391), Blue (DD 387) and Helm (DD 388).

After that was called off:

While these estimates were being drafted, a message came from the CNO about Pye's decision to recall TF 11 from the Jaluit raid and have it move to support TF 14. […]
Not willing to chance the possibility of losing TF 14, and uncertain (due to radio silence) of the exact location of Admiral Brown's Lexington TF 11, Pye reluctantly recalled Task Forces 14 and 11 and ordered Halsey's TF 8 to continue its operations in the vicinity of Midway. […]

Task Force 14 took a week to return to Pearl Harbor. During the return a swing north was made and on Christmas Day Saratoga launched VMF-221 to its new home on Midway. The task force finally entered Pearl on 29 December. The next day Kinkaid relieved his friend Frank Jack Fletcher of command of CRUDIV 6. The ceremony was brief and held on board Astoria. […]

The day after relieving Rear Admiral Fletcher, Kinkaid and a few of his cruisers and destroyers departed Pearl with TF 14 for several weeks of "covering operations" along a line from Midway to Johnston Island. Rear Admiral Herbert Fairfax Leary commanded the task force from Saratoga. […]

Saratoga had another task to complete during this cruise. The task force was slowly working its way south to meet Enterprise and TF 8. […]

A covering operation was despised by almost all involved because it was boring, but it did have some value for those participating. The scouting and bombing squadrons' pilots flew 200- to 300-mile sector searches from Saratoga as a part of their daily operations. Although the risk of losing a plane and crew was always present, the discipline of carrier operations developed competence and confidence in the pilots that would prove invaluable in the months ahead. Kinkaid's cruisers carried out their share of the task force's flight operations by launching their Seagulls for close-in antisubmarine surveillance. Were it not for the presence of the cruiser pilots, this inner patrol would have been flown by carrier fighter pilots, a task they truly detested. The fighter role during flight operations was to provide a continuous combat air patrol (CAP) over the task force and to investigate every "bogey" (unknown-identity aircraft) that appeared in the vicinity of the force.

Throughout the working day the cruisers exercised their gun crews with simulated and live firing of their antiaircraft weapons. But after a few days of "conforming to the movements of the flagship" as Saratoga launched and recovered its planes, exercising the gun crews at general quarters, and having pilots bore holes in the clouds, the covering operations became tedious. […]

The tedium of this cruise ended abruptly at 1915 on 11 January when a torpedo struck Saratoga forward on the port side. Belching smoke, the carrier turned hard to starboard and increased speed. With everyone in the task force at general quarters and the destroyers combing the area for the Japanese I-boat, Captain Archibald H. Douglas got the fire under control and the ship's trim restored.

— Gerald E. Wheeler: "Kinkaid of the Seventh Fleet. A Biography of Admiral Thomas C. Kinkaid, U.S. Navy", Naval Historical Center Department of the Navy: Washington, 1995. (PDF)

Note that for example an obituary for Saratoga's captain Douglas prolongs his commend until the second torpedo incident later in 1942 (certainly untrue), and even an official Navy history site gives the designation of the Japanese submarine as indeed "I-16" instead of I-6.

An interesting opinion on what happened why on that day, albeit for the later unlucky day:

— Quora: How was Task Force 11 unable to detect the submarine I-26 when it torpedoed USS Saratoga (CV-3) on August 31, 1942? — Answered by: Stephen Cipolla, Navy Veteran, Naval Historian, USS Constitution Crew-member. mAnswered Apr 5, 2022