Subgroups — C₇×#16811779 #37558837

Order 23870.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#13133722	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₁₁×C₃₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	#16811779	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₇×C₁₁×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
5	C₂×C₇×ΓL(1,𝔽₃₂)	—	11	1	no	maximal, Hall
6	#13133722	C₂×C₇	1	1	yes	characteristic, complemented, Hall
7	C₇×ΓL(1,𝔽₃₂)	—	11	1	no	Hall
8	C₇×AGL(1,𝔽₁₁)	—	31	1	no	maximal, Hall
9	D₁₁×C₃₁	C₅×C₇	1	1	yes	characteristic, complemented, Hall
10	C₂×C₇×C₃₁	—	11	1	no	Hall
11	C₇×C₁₁⋊C₅	—	31	1	no	Hall
12	C₁₁×C₃₁	C₂×C₅×C₇	1	1	yes	characteristic, complemented, Hall
13	C₂×ΓL(1,𝔽₃₂)	—	11	1	no	Hall
14	C₇×C₃₁	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Hall
15	ΓL(1,𝔽₃₂)	—	11	1	no	Hall
16	C₇×D₁₁	ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented, Hall
17	AGL(1,𝔽₁₁)	—	31	1	no	Hall
18	C₇×C₁₁	C₂×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented, Hall
19	C₂×C₅×C₇	—	341	1	no	Hall
20	C₂×C₃₁	—	11	1	no	Hall
21	C₁₁⋊C₅	—	31	1	no	Hall
22	C₅×C₇	—	341	1	no	Hall
23	C₃₁	C₇×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Sylow
24	D₁₁	C₇×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented, Hall
25	C₂×C₇	—	11	1	no	Hall
26	C₁₁	C₂×C₇×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₅	—	341	1	no	Hall
28	C₇	#16811779	1	1	yes	characteristic, direct product factor, Sylow
29	C₅	—	341	1	no	Sylow
30	C₂	—	11	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	#16811779
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×#13133722	C₂	semidirect
2. C₇×D₁₁×C₃₁	C₅	semidirect
3. #16811779	C₇	direct (N × H)
4. C₇×C₁₁×C₃₁	C₂×C₅	semidirect
6. #13133722	C₂×C₇	semidirect
9. D₁₁×C₃₁	C₅×C₇	semidirect
12. C₁₁×C₃₁	C₂×C₅×C₇	semidirect
14. C₇×C₃₁	AGL(1,𝔽₁₁)	semidirect
16. C₇×D₁₁	ΓL(1,𝔽₃₂)	semidirect
18. C₇×C₁₁	C₂×ΓL(1,𝔽₃₂)	semidirect
23. C₃₁	C₇×AGL(1,𝔽₁₁)	semidirect
24. D₁₁	C₇×ΓL(1,𝔽₃₂)	semidirect
26. C₁₁	C₂×C₇×ΓL(1,𝔽₃₂)	semidirect
28. C₇	#16811779	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×#13133722	2
C₇×D₁₁×C₃₁	5
#16811779	7
C₂×C₇×ΓL(1,𝔽₃₂)	11
C₇×AGL(1,𝔽₁₁)	31

Subgroups — C7×#16811779 #37558837

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#16811779 #37558837