Subgroups — C₇×ΓL(1,𝔽₃₂)⋊D₁₁ #37558839

Order 23870.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₁×ΓL(1,𝔽₃₂)	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₃₄₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	ΓL(1,𝔽₃₂)⋊D₁₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₇×C₁₁×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
5	C₇×D₃₁⋊C₅	—	11	1	no	maximal, Hall
6	C₁₁×ΓL(1,𝔽₃₂)	C₂×C₇	1	1	yes	characteristic, complemented, Hall
7	C₇×ΓL(1,𝔽₃₂)	D₁₁	1	1	yes	characteristic, complemented, Hall
8	C₅×C₇×D₁₁	—	31	1	no	maximal, Hall
9	D₃₄₁	C₅×C₇	1	1	yes	characteristic, complemented, Hall
10	C₇×D₃₁	—	11	1	no	Hall
11	C₅×C₇×C₁₁	—	31	1	no	Hall
12	C₁₁×C₃₁	C₂×C₅×C₇	1	1	yes	characteristic, complemented, Hall
13	D₃₁⋊C₅	—	11	1	no	Hall
14	C₇×C₃₁	C₅×D₁₁	1	1	yes	characteristic, complemented, Hall
15	ΓL(1,𝔽₃₂)	C₇×D₁₁	1	1	yes	characteristic, complemented, Hall
16	C₇×D₁₁	—	31	1	no	Hall
17	C₅×D₁₁	—	31	1	no	Hall
18	C₇×C₁₁	D₃₁⋊C₅	1	1	yes	characteristic, complemented, Hall
19	C₂×C₅×C₇	—	341	1	no	Hall
20	D₃₁	—	11	1	no	Hall
21	C₅×C₁₁	—	31	1	no	Hall
22	C₅×C₇	—	31	1	no	Hall
23	C₃₁	C₅×C₇×D₁₁	1	1	yes	characteristic, complemented, Sylow
24	D₁₁	—	31	1	no	Hall
25	C₂×C₇	—	341	1	no	Hall
26	C₁₁	C₇×D₃₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₅	—	341	1	no	Hall
28	C₇	ΓL(1,𝔽₃₂)⋊D₁₁	1	1	yes	characteristic, direct product factor, Sylow
29	C₅	—	31	1	no	Sylow
30	C₂	—	341	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	ΓL(1,𝔽₃₂)⋊D₁₁
commutator, cosocle, hypocenter	C₁₁×C₃₁	C₂×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₇×C₁₁×C₃₁	C₂×C₅
LCS	G ▷ C₁₁×C₃₁
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₁×ΓL(1,𝔽₃₂)	C₂	semidirect
2. C₇×D₃₄₁	C₅	semidirect
3. ΓL(1,𝔽₃₂)⋊D₁₁	C₇	direct (N × H)
4. C₇×C₁₁×C₃₁	C₂×C₅	semidirect
6. C₁₁×ΓL(1,𝔽₃₂)	C₂×C₇	semidirect
7. C₇×ΓL(1,𝔽₃₂)	D₁₁	semidirect
9. D₃₄₁	C₅×C₇	semidirect
12. C₁₁×C₃₁	C₂×C₅×C₇	semidirect
14. C₇×C₃₁	C₅×D₁₁	semidirect
15. ΓL(1,𝔽₃₂)	C₇×D₁₁	semidirect
18. C₇×C₁₁	D₃₁⋊C₅	semidirect
23. C₃₁	C₅×C₇×D₁₁	semidirect
26. C₁₁	C₇×D₃₁⋊C₅	semidirect
28. C₇	ΓL(1,𝔽₃₂)⋊D₁₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×C₁₁×ΓL(1,𝔽₃₂)	2
C₇×D₃₄₁	5
ΓL(1,𝔽₃₂)⋊D₁₁	7
C₇×D₃₁⋊C₅	11
C₅×C₇×D₁₁	31

Subgroups — C7×ΓL(1,𝔽32)⋊D11 #37558839

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×ΓL(1,𝔽₃₂)⋊D₁₁ #37558839