Subgroups — (C₁₁⋊C₅)⋊Dic₃₇ #22550776

Order 8140.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	C₃₇×C₁₁⋊C₅	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₄₀₇	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂×C₁₁×C₃₇	C₂×C₅	1	1	yes	characteristic
5	C₅×Dic₃₇	—	11	1	no	maximal, Hall
6	C₁₁×C₃₇	C₄×C₅	1	1	yes	characteristic, complemented, Hall
7	C₂×C₅×C₃₇	—	11	1	no	—
8	Dic₁₁⋊C₅	—	37	1	no	maximal, Hall
9	C₅×C₃₇	—	11	1	no	Hall
10	Dic₃₇	—	11	1	no	Hall
11	C₂×C₁₁⋊C₅	D₃₇	1	1	yes	characteristic
12	C₂×C₃₇	AGL(1,𝔽₁₁)	1	1	yes	characteristic
13	C₁₁⋊C₅	Dic₃₇	1	1	yes	characteristic, complemented, Hall
14	Dic₁₁	—	37	1	no	Hall
15	C₃₇	Dic₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₁₁	C₅×D₃₇	1	1	yes	characteristic
17	C₄×C₅	—	407	1	no	Hall
18	C₁₁	C₅×Dic₃₇	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₅	—	11	1	no	—
20	C₅	—	11	1	no	Sylow
21	C₄	—	407	1	no	Sylow
22	C₂	C₃₇⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃₇⋊AGL(1,𝔽₁₁)
commutator, hypocenter	C₁₁×C₃₇	C₄×C₅
Fitting, socle	C₂×C₁₁×C₃₇	C₂×C₅
LCS	G ▷ C₁₁×C₃₇
UCS	C₁ ◁ C₂

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