Here is part of the OOB of TASK FORCE 58 during the Battle of the Phillipine Sea. You can get an idea from it what the escorts for both a Carrier Task Group and a Battleship Task Group would be made of.
------------------------------------------------------------
United States Naval Forces (USN)
5th Fleet
Admiral Raymond Spruance
Task Force 58 (TF58)
Vice Admiral Marc Mitscher
TF 58.1
Rear Admiral Joseph J. (‘Jocko’) Clark
CV12 Hornet
41 - F6F, 33 - SB2C, 18 - TBF
CV10 Yorktown (F)
46 - F6F, 40 - SB2C, 17 - TBF, 4 - SBD
CVL24 Belleau Wood
26 - F6F, 9 - TBF
CVL29 Bataan
24 - F6F, 9 - TBF
CA68 Baltimore
CA69 Boston
CA70 Canberra
CL95 Oakland
Desron 46
DD589 Izard
DD581 Charrette
DD582 Conner
DD587 Bell
DD588 Burns
DD544 Boyd
DD545 Bradford
DD546 Brown
DD547 Cowell
TF 58.2
Rear Admiral Alfred E. Montgomery
CV17 Bunker Hill (F)
42 - F6F, 33 - SB2C, 18 - TBF
CV18 Wasp
39 - F6F, 32 - SB2C, 18 - TBF
CVL28 Cabot
26 - F6F, 9 - TBF
CVL26 Monterey
21 - F6F, 8 - TBF
CL60 Santa Fe
CL63 Mobile
CL80 Biloxi
CL54 San Juan
Desron 52
DD536 Owen
DD535 Miller
DD537 The Sullivans
DD538 Stephen Potter
DD539 Tingey
DD673 Hickox
DD674 Hunt
DD675 Lewis Hancock
DD676 Marshall
TF 58.3
Rear Admiral John W. Reeves
CV6 Enterprise (F)
Captain Matthais B Gardner
31 - F6F, 3 - F4U, 21 - SBD, 14 - TBF
CV16 Lexington (F) - Task Force 58 Flagship
Vice Admiral Marc Mitscher
41 - F6F, 34 - SBD, 18 - TBF
CVL30 San Jacinto
24 - F6F, 8 - TBF
CVL23 Princeton
24 - F6F, 9 - TBF
CA 35 Indianapolis (F) - 5th Fleet Flagship
Admiral Raymond Spruance
CL96 Reno
CL57 Montpelier
CL55 Cleveland
CL62 Birmingham
Desron 50
DD668 Clarence K. Bronson
DD669 Cotten
DD670 Dortch
DD671 Gatling
DD672 Healy
DD651 Cogswell
DD650 Caperton
DD652 Ingersoll
DD653 Knapp
DD515 Anthony
DD516 Wadsworth
DD513 Terry
DD630 Braine
TF 58.4
Rear Admiral William K. Harrill
CV9 Essex
Captain R. A. Ofstie
42 - F6F, 36 - SB2C, 20 - TBF
CVL27 Langley
23 - F6F, 9 - TBF
CVL25 Cowpens
23 - F6F, 9 - TBF
CL53 San Diego
CL64 Vincennes
CL81 Houston
CL89 Miami
DD486 Lansdowne
DD487 Lardner
DD488 McCalla
DD399 Lang
DD407 Sterett
DD408 Wilson
DD370 Case
DD398 Ellet
DD570 Charles Ausburne
DD478 Stanly
DD509 Converse
DD512 Spence
DD514 Thatcher
TF 58.7
Vice Admiral Willis A. Lee
BB56 Washington (F)
Captain Thomas R. Cooley
Battleship Division 8
Rear Admiral Glenn B. Davis
BB55 North Carolina
Captain Frank B. Thomas
BB58 Indiana (F)
Captain Jennings
Battleship Division 7
Rear Admiral O. M. Hustvedt
BB61 Iowa
Captain John L. McCrea
BB62 New Jersey
Captain Carl F. Holden
Battleship Division 9
Rear Admiral E. W. Hanson
BB57 South Dakota
BB60 Alabama
Captain Fred D. Kirtland
CA45 Wichita
CA36 Minneapolis
CA32 New Orleans
CA38 San Francisco
DD389 Mugford
DD371 Conyngham
DD392 Patterson
DD386 Bagley
DD357 Selfridge
DD480 Halford
DD472 Guest
DD473 Bennett
DD474 Fullam
DD475 Hudson
DD540 Twining
DD798 Monssen
DD541 Yarnall (Radar Pickett)
DD683 Stockham (Radar Pickett)