Subgroups — C₄₁×D₂₃₁ #34038824

Order 18942.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₁×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₄₁×D₇₇	—	3	1	no	maximal, Hall
3	C₇×C₁₁×C₄₁	D₃	1	1	yes	characteristic, complemented, Hall
4	C₄₁×D₃₃	—	7	1	no	maximal, Hall
5	C₄₁×D₂₁	—	11	1	no	maximal, Hall
6	C₃×C₁₁×C₄₁	D₇	1	1	yes	characteristic, complemented, Hall
7	D₁₁×C₄₁	—	21	1	no	Hall
8	C₃×C₇×C₄₁	D₁₁	1	1	yes	characteristic, complemented, Hall
9	D₇×C₄₁	—	33	1	no	Hall
10	D₂₃₁	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₁₁×C₄₁	D₂₁	1	1	yes	characteristic, complemented, Hall
12	C₇×C₄₁	D₃₃	1	1	yes	characteristic, complemented, Hall
13	D₃×C₄₁	—	77	1	no	Hall
14	C₃×C₇×C₁₁	C₂×C₄₁	1	1	yes	characteristic, complemented, Hall
15	D₇₇	—	3	1	no	Hall
16	C₃×C₄₁	D₇₇	1	1	yes	characteristic, complemented, Hall
17	C₂×C₄₁	—	231	1	no	Hall
18	C₇×C₁₁	D₃×C₄₁	1	1	yes	characteristic, complemented, Hall
19	D₃₃	—	7	1	no	Hall
20	D₂₁	—	11	1	no	Hall
21	C₄₁	D₂₃₁	1	1	yes	characteristic, direct product factor, Sylow
22	C₃×C₁₁	D₇×C₄₁	1	1	yes	characteristic, complemented, Hall
23	D₁₁	—	21	1	no	Hall
24	C₃×C₇	D₁₁×C₄₁	1	1	yes	characteristic, complemented, Hall
25	D₇	—	33	1	no	Hall
26	C₁₁	C₄₁×D₂₁	1	1	yes	characteristic, complemented, Sylow
27	C₇	C₄₁×D₃₃	1	1	yes	characteristic, complemented, Sylow
28	D₃	—	77	1	no	Hall
29	C₃	C₄₁×D₇₇	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	231	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₄₁	D₂₃₁
commutator, cosocle, hypocenter	C₃×C₇×C₁₁	C₂×C₄₁
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₁×C₄₁	C₂
LCS	G ▷ C₃×C₇×C₁₁
UCS	C₁ ◁ C₄₁

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.