Subgroups — C₁₁⋊((C₃₇⋊C₃)⋊D₁₃) #44540832

Order 31746.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₃×C₃₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₂₉₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁×C₁₃×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	(C₃₇⋊C₃)⋊D₁₃	—	11	1	no	maximal, Hall
5	C₁₁⋊(D₃₇⋊C₃)	—	13	1	no	maximal, Hall
6	C₁₃×C₃₇⋊C₃	D₁₁	1	1	yes	characteristic, complemented, Hall
7	C₁₁×C₃₇⋊C₃	D₁₃	1	1	yes	characteristic, complemented, Hall
8	D₄₈₁	—	11	1	no	Hall
9	C₃×D₁₄₃	—	37	1	no	maximal, Hall
10	D₄₀₇	—	13	1	no	Hall
11	C₁₃×C₃₇	C₃×D₁₁	1	1	yes	characteristic, complemented, Hall
12	C₃×C₁₁×C₁₃	—	37	1	no	Hall
13	C₁₁×C₃₇	C₃×D₁₃	1	1	yes	characteristic, complemented, Hall
14	D₁₄₃	—	37	1	no	Hall
15	D₃₇⋊C₃	—	143	1	no	Hall
16	C₁₁×C₁₃	D₃₇⋊C₃	1	1	yes	characteristic, complemented, Hall
17	C₃₇⋊C₃	D₁₄₃	1	1	yes	characteristic, complemented, Hall
18	C₃×D₁₃	—	407	1	no	Hall
19	D₃₇	—	143	1	no	Hall
20	C₃×D₁₁	—	481	1	no	Hall
21	C₃×C₁₃	—	37	1	no	Hall
22	C₃₇	C₃×D₁₄₃	1	1	yes	characteristic, complemented, Sylow
23	C₃×C₁₁	—	37	1	no	Hall
24	D₁₃	—	407	1	no	Hall
25	D₁₁	—	481	1	no	Hall
26	C₁₃	C₁₁⋊(D₃₇⋊C₃)	1	1	yes	characteristic, complemented, Sylow
27	C₁₁	(C₃₇⋊C₃)⋊D₁₃	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	5291	1	no	Hall
29	C₃	—	37	1	no	Sylow
30	C₂	—	5291	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₁×C₁₃×C₃₇	C₂×C₃
LCS	G ▷ C₁₁×C₁₃×C₃₇
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.