Subgroups — C₇⋊#16811784 #37558866

Order 23870.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#13133723	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₂₃₈₇	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	#16811784	—	7	1	no	maximal, Hall
4	C₇×C₁₁×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
5	C₇⋊(D₃₁⋊C₅)	—	11	1	no	maximal, Hall
6	#13133723	D₇	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	D₃₄₁	—	7	1	no	Hall
10	D₂₁₇	—	55	1	no	Hall
11	C₇×C₁₁⋊C₅	—	31	1	no	Hall
12	C₁₁×C₃₁	C₅×D₇	1	1	yes	characteristic, complemented, Hall
13	D₃₁⋊C₅	—	77	1	no	Hall
14	C₇×C₃₁	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Hall
15	ΓL(1,𝔽₃₂)	—	11	1	no	Hall
16	D₇₇	—	155	1	no	Hall
17	AGL(1,𝔽₁₁)	—	217	1	no	Hall
18	C₇×C₁₁	D₃₁⋊C₅	1	1	yes	characteristic, complemented, Hall
19	C₅×D₇	—	341	1	no	Hall
20	D₃₁	—	385	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	—	1085	1	no	Hall
25	D₇	—	1705	1	no	Hall
26	C₁₁	C₇⋊(D₃₁⋊C₅)	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₅	—	2387	1	no	Hall
28	C₇	#16811784	1	1	yes	characteristic, complemented, Sylow
29	C₅	—	341	1	no	Sylow
30	C₂	—	11935	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₁×C₃₁	C₂×C₅
LCS	G ▷ C₇×C₁₁×C₃₁
UCS	C₁

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

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