You left out detachment, which can be smaller than a flight (and larger too, I suppose). Also, between wing and numbered air force, there can be (used to be, in SAC, at least) air divisions. Also, larger than numbered air forces are Major Commands (like AMC, formerly MAC, etc). I know you already know all this. Just felt like talking.
When I was in the 509th BMW at Pease, we were in the same Air Division (maybe it was the 42d, but no longer remember for certain) with the folks at Plattsburgh AFB. And we were all part of 8th Air Force, which came under SAC (MajCom).
I remember for the flying portion of ORIs at Pease the F-111s and KC-135s would taxi out as close together as regulations allowed. The roar of the engines was phenomenal as they roared out in MITO (minimum interval take off)! (The F-111s put out a terrific plume on take off, as well, which was particularly impressive at night.)
Pease is now only a reserve base; Plattsburgh is closed. Alas, the 42d Air Division is no more!