Subgroups — C₇×C₁₁×D₇×C₂₃ #37613541

Order 24794.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₁₁×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×D₇×C₂₃	C₇	1	1	yes	maximal, characteristic, direct product factor
3	C₂×C₇×C₁₁×C₂₃	—	7	1	no	maximal
4	C₇×D₇×C₂₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×C₁₁×C₂₃	—	2	3	no	—
6	C₇×C₁₁×C₂₃	D₇	1	1	yes	characteristic, direct product factor
7	C₇×C₁₁×C₂₃	C₂×C₇	1	1	yes	characteristic, complemented
8	C₇²×C₂₃	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
9	C₇×C₁₁×D₇	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₇²×C₁₁	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₁₁×C₂₃	—	7	1	no	Hall
12	C₂×C₇×C₂₃	—	7	1	no	—
13	D₇×C₂₃	C₇×C₁₁	1	1	yes	characteristic, direct product factor
14	C₁₁×C₂₃	C₇×D₇	1	1	yes	characteristic, direct product factor, Hall
15	C₇×C₂₃	—	2	3	no	—
16	C₇×C₂₃	C₁₁×D₇	1	1	yes	characteristic, direct product factor
17	C₇×C₂₃	C₂×C₇×C₁₁	1	1	yes	characteristic, complemented
18	C₂×C₇×C₁₁	—	7	1	no	—
19	C₁₁×D₇	C₇×C₂₃	1	1	yes	characteristic, direct product factor
20	C₇×D₇	C₁₁×C₂₃	1	1	yes	characteristic, direct product factor, Hall
21	C₇×C₁₁	—	2	3	no	—
22	C₇×C₁₁	D₇×C₂₃	1	1	yes	characteristic, direct product factor
23	C₇×C₁₁	C₂×C₇×C₂₃	1	1	yes	characteristic, complemented
24	C₇²	C₂×C₁₁×C₂₃	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₂₃	—	7	1	no	Hall
26	C₂₃	C₇×C₁₁×D₇	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₁₁	—	7	1	no	Hall
28	C₂×C₇	—	7	1	no	—
29	D₇	C₇×C₁₁×C₂₃	1	1	yes	characteristic, direct product factor
30	C₁₁	C₇×D₇×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
31	C₇	—	2	3	no	—
32	C₇	C₂×C₇×C₁₁×C₂₃	1	1	yes	characteristic, complemented
33	C₇	C₁₁×D₇×C₂₃	1	1	yes	characteristic, direct product factor
34	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₁₁×C₂₃	D₇
commutator, cosocle, hypocenter	C₇	C₂×C₇×C₁₁×C₂₃
Frattini	C₁	G
Fitting, socle	C₇²×C₁₁×C₂₃	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₇×C₁₁×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₇²×C₁₁×C₂₃	C₂	semidirect
2. C₁₁×D₇×C₂₃	C₇	direct (N × H)
4. C₇×D₇×C₂₃	C₁₁	direct (N × H)
6. C₇×C₁₁×C₂₃	D₇	direct (N × H)
7. C₇×C₁₁×C₂₃	C₂×C₇	semidirect
8. C₇²×C₂₃	C₂×C₁₁	semidirect
9. C₇×C₁₁×D₇	C₂₃	direct (N × H)
10. C₇²×C₁₁	C₂×C₂₃	semidirect
13. D₇×C₂₃	C₇×C₁₁	direct (N × H)
14. C₁₁×C₂₃	C₇×D₇	direct (N × H)
16. C₇×C₂₃	C₁₁×D₇	direct (N × H)
17. C₇×C₂₃	C₂×C₇×C₁₁	semidirect
19. C₁₁×D₇	C₇×C₂₃	direct (N × H)
20. C₇×D₇	C₁₁×C₂₃	direct (N × H)
22. C₇×C₁₁	D₇×C₂₃	direct (N × H)
23. C₇×C₁₁	C₂×C₇×C₂₃	semidirect
24. C₇²	C₂×C₁₁×C₂₃	semidirect
26. C₂₃	C₇×C₁₁×D₇	direct (N × H)
29. D₇	C₇×C₁₁×C₂₃	direct (N × H)
30. C₁₁	C₇×D₇×C₂₃	direct (N × H)
32. C₇	C₂×C₇×C₁₁×C₂₃	semidirect
33. C₇	C₁₁×D₇×C₂₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇²×C₁₁×C₂₃	2
C₁₁×D₇×C₂₃	7
C₂×C₇×C₁₁×C₂₃	7
C₇×D₇×C₂₃	11
C₇×C₁₁×D₇	23

Subgroups — C7×C11×D7×C23 #37613541

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₁₁×D₇×C₂₃ #37613541