Subgroups — D₇₇×ΓL(1,𝔽₃₂) #37558857

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	C₃₁×D₇₇	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	D₁₁×ΓL(1,𝔽₃₂)	—	7	1	no	maximal, Hall
4	C₇×C₁₁×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
5	D₇×ΓL(1,𝔽₃₂)	—	11	1	no	maximal, Hall
6	C₁₁×ΓL(1,𝔽₃₂)	D₇	1	1	yes	characteristic, complemented, Hall
7	C₇×ΓL(1,𝔽₃₂)	D₁₁	1	1	yes	characteristic, complemented, Hall
8	C₅×D₇₇	—	31	1	no	maximal, Hall
9	D₁₁×C₃₁	—	7	1	no	Hall
10	D₇×C₃₁	—	11	1	no	Hall
11	C₅×C₇×C₁₁	—	31	1	no	Hall
12	C₁₁×C₃₁	C₅×D₇	1	1	yes	characteristic, complemented, Hall
13	C₂×ΓL(1,𝔽₃₂)	—	77	1	no	Hall
14	C₇×C₃₁	C₅×D₁₁	1	1	yes	characteristic, complemented, Hall
15	ΓL(1,𝔽₃₂)	D₇₇	1	1	yes	characteristic, direct product factor, Hall
16	D₇₇	ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor, Hall
17	C₅×D₁₁	—	217	1	no	Hall
18	C₇×C₁₁	C₂×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented, Hall
19	C₅×D₇	—	341	1	no	Hall
20	C₂×C₃₁	—	77	1	no	Hall
21	C₅×C₁₁	—	31	1	no	Hall
22	C₅×C₇	—	31	1	no	Hall
23	C₃₁	C₅×D₇₇	1	1	yes	characteristic, complemented, Sylow
24	D₁₁	—	7	1	no	Hall
25	D₇	—	11	1	no	Hall
26	C₁₁	D₇×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₅	—	2387	1	no	Hall
28	C₇	D₁₁×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented, Sylow
29	C₅	—	31	1	no	Sylow
30	C₂	—	77	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.