References:
The Soviet Air Force Since 1918 by Alexander Boyd.

Close Support Bomber Regiments (August 1941)

2 x Bomber Squadrons
1 x Fighter Squadron

Shturmovik Regiments (August 1941)

2 x Shturmovik Squadrons
1 x Fighter Squadron

Army Composite Air Division (1940)

Army Headquarters

HQ Composite Air Division

Fighter Regiment (45 x I-16)
Fighter Regiment (45 x I-153)
Fast Bomber Regiment (36 x SB)
Fast Bomber Regiment (36 x SB)
Light Bomber Regiment (45 x R-5)

Shturmovik Regiment (Late 1941)

Regimental Headquarters

Formation Leader Zveno (3 x Su-2)
3 x Shturmovik Squadrons (10 Il-2 each)
      3 x Zvenos (3 Il-2 each)
      1 x Reserve Il-2
1 x Fighter Squadron (6 x I-16 and 4 x LaGG-3)

Air Army (circa 1943) (original drawing)

Air Army HQ

Sub Divisional Units Attached to Air Army HQ
      1 x GVF Transport Regiment
      1 x Reconnaisance Regiment
      1 x Special Liason Squadron
      1 x Communications Regiment
      1 x Artillery Spotting Regiment
      1 x Recovery & Ambulance Squadron
      1 x Training Regiment

Normal Subordinates
      1 x Night Bomber Division with 5 Regiments (135 x LNB)
      1 x Fighter Division with 3 Regiments (90 x Yak-7B)
      1 x Shturmovik Division with 3 Regiments (90 x Il-2)

Subordinates via GKO Reserve Allocation
      1 x Shturmovik Division with 2 Regiments (60 x Il-2)

      1 x Fighter Corps

1 x Fighter Division with 3 Regiments (100 x Yak-9)
1 x Fighter Division with 2 Regiments (60 x La-5)

      1 x Bomber Corps

1 x Bomber Division with 3 Regiments (80 x Pe-2)
1 x Bomber Division with 2 Regiments (45 x Pe-2)

Cold War Tactical Air Force (FA) Fighter Division (Original Drawing)

Divisional HQ

1 x Transport Squadron (1 x An-12, 1 x An-26, 2 x Mi-8, 2 x An-2)
1 x Fighter Regiment (36 x Su-17)
1 x Fighter Regiment (36 x Su-17)
1 x Fighter Regiment

1 x Communications Flight (2 x Mi-4, 1 x Aero-45)
1 x Squadron (12 x MiG-23)
1 x Squadron (12 x MiG-23)
1 x Squadron (8 x MiG-23, 4 x MiG-23U)