Subgroups — C₃²×C₁₁²×D₇ #29503913

Order 15246.

336 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×C₁₁²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₁₁²×D₇	C₃	1	4	yes	maximal, direct product factor
3	C₃×C₇×C₁₁²	C₂×C₃	1	4	yes	complemented
4	C₂×C₃²×C₁₁²	—	7	1	no	maximal, Hall
5	C₁₁²×D₇	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃²×C₁₁×D₇	C₁₁	1	12	yes	maximal, direct product factor
7	C₃²×C₁₁²	D₇	1	1	yes	characteristic, direct product factor, Hall
8	C₇×C₁₁²	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃×C₁₁²	—	7	4	no	—
10	C₃²×C₇×C₁₁	C₂×C₁₁	1	12	yes	complemented
11	C₃×C₁₁×D₇	C₃×C₁₁	1	48	yes	direct product factor
12	C₃×C₁₁²	C₃×D₇	1	4	yes	direct product factor
13	C₂×C₁₁²	—	7	1	no	Hall
14	C₃×C₇×C₁₁	C₂×C₃×C₁₁	1	48	yes	complemented
15	C₂×C₃²×C₁₁	—	7	12	no	—
16	C₁₁×D₇	C₃²×C₁₁	1	12	yes	direct product factor
17	C₃²×D₇	C₁₁²	1	1	yes	characteristic, direct product factor, Hall
18	C₁₁²	C₃²×D₇	1	1	yes	characteristic, direct product factor, Sylow
19	C₃²×C₁₁	C₁₁×D₇	1	12	yes	direct product factor
20	C₇×C₁₁	C₂×C₃²×C₁₁	1	12	yes	complemented
21	C₂×C₃×C₁₁	—	7	48	no	—
22	C₃²×C₇	C₂×C₁₁²	1	1	yes	characteristic, complemented, Hall
23	C₃×D₇	C₃×C₁₁²	1	4	yes	direct product factor
24	C₃×C₁₁	C₃×C₁₁×D₇	1	48	yes	direct product factor
25	C₂×C₁₁	—	7	12	no	—
26	C₃×C₇	C₂×C₃×C₁₁²	1	4	yes	complemented
27	C₂×C₃²	—	7	1	no	Hall
28	D₇	C₃²×C₁₁²	1	1	yes	characteristic, direct product factor, Hall
29	C₁₁	C₃²×C₁₁×D₇	1	12	yes	direct product factor
30	C₃²	C₁₁²×D₇	1	1	yes	characteristic, direct product factor, Sylow
31	C₇	C₂×C₃²×C₁₁²	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₃	—	7	4	no	—
33	C₃	C₃×C₁₁²×D₇	1	4	yes	direct product factor
34	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²×C₁₁²	D₇
commutator, cosocle, hypocenter	C₇	C₂×C₃²×C₁₁²
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₁₁²	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₃²×C₁₁²

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃²×C₇×C₁₁²	C₂	semidirect
2. C₃×C₁₁²×D₇	C₃	direct (N × H)
3. C₃×C₇×C₁₁²	C₂×C₃	semidirect
5. C₁₁²×D₇	C₃²	direct (N × H)
6. C₃²×C₁₁×D₇	C₁₁	direct (N × H)
7. C₃²×C₁₁²	D₇	direct (N × H)
8. C₇×C₁₁²	C₂×C₃²	semidirect
10. C₃²×C₇×C₁₁	C₂×C₁₁	semidirect
11. C₃×C₁₁×D₇	C₃×C₁₁	direct (N × H)
12. C₃×C₁₁²	C₃×D₇	direct (N × H)
14. C₃×C₇×C₁₁	C₂×C₃×C₁₁	semidirect
16. C₁₁×D₇	C₃²×C₁₁	direct (N × H)
17. C₃²×D₇	C₁₁²	direct (N × H)
18. C₁₁²	C₃²×D₇	direct (N × H)
19. C₃²×C₁₁	C₁₁×D₇	direct (N × H)
20. C₇×C₁₁	C₂×C₃²×C₁₁	semidirect
22. C₃²×C₇	C₂×C₁₁²	semidirect
23. C₃×D₇	C₃×C₁₁²	direct (N × H)
24. C₃×C₁₁	C₃×C₁₁×D₇	direct (N × H)
26. C₃×C₇	C₂×C₃×C₁₁²	semidirect
28. D₇	C₃²×C₁₁²	direct (N × H)
29. C₁₁	C₃²×C₁₁×D₇	direct (N × H)
30. C₃²	C₁₁²×D₇	direct (N × H)
31. C₇	C₂×C₃²×C₁₁²	semidirect
33. C₃	C₃×C₁₁²×D₇	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃²×C₇×C₁₁²	2
C₃×C₁₁²×D₇	3
C₂×C₃²×C₁₁²	7
C₃²×C₁₁×D₇	11

Subgroups — C32×C112×D7 #29503913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₁₁²×D₇ #29503913