Was XXII TAC part of Twelfth Air Force?

[Lagarto]

Thank you Schenck, this info casts some light.
The movement of MTO Thunderbolts was somewhat erratic and I've been finding conflicting info. Again, correct me, if I'm wrong:
In July 1944 there were five P-47 outfits serving with 12th AF in MTO: 27th, 57th, 79th, 86th and 324th FGs (350th FG converted to P-47 in August/September 1944).
In mid-August, 27th, 79th and 324th FGs moved to France to support the American drive up the Rhone Valley. 324th FG stayed in France and in November was incorporated into the 1st Franco-American TAF. 27th and 79th FGs returned to Italy in October, whereupon 79th FG was attached to the British Desert Air Foirce until VE-Day. In February 1945, 27th and 86th FGs were transferred out of Italy to join 1st TAF.