Subgroups — C₃₇×SD₂₅₆ #22628805

Order 9472.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×Q₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₇×D₆₄	C₂	1	1	yes	maximal, characteristic
3	C₃₇×C₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×Q₆₄	—	2	1	no	—
5	C₃₇×D₃₂	—	2	1	no	—
6	C₃₇×C₆₄	C₂²	1	1	yes	characteristic
7	Q₃₂×C₃₇	—	4	1	no	—
8	D₁₆×C₃₇	—	4	1	no	—
9	C₃₂×C₃₇	D₄	1	1	yes	characteristic
10	Q₁₆×C₃₇	—	8	1	no	—
11	D₈×C₃₇	—	8	1	no	—
12	C₁₆×C₃₇	D₈	1	1	yes	characteristic
13	Q₈×C₃₇	—	16	1	no	—
14	D₄×C₃₇	—	16	1	no	—
15	C₈×C₃₇	D₁₆	1	1	yes	characteristic
16	SD₂₅₆	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂²×C₃₇	—	32	1	no	—
18	C₄×C₃₇	—	32	1	no	—
19	C₄×C₃₇	D₃₂	1	1	yes	characteristic
20	Q₁₂₈	C₂×C₃₇	1	1	yes	characteristic, complemented
21	D₆₄	C₂×C₃₇	1	1	yes	characteristic
22	C₁₂₈	C₂×C₃₇	1	1	yes	characteristic, complemented
23	C₂×C₃₇	—	64	1	no	—
24	C₂×C₃₇	D₆₄	1	1	yes	characteristic
25	Q₆₄	—	2	1	no	—
26	D₃₂	—	2	1	no	—
27	C₆₄	C₂²×C₃₇	1	1	yes	characteristic
28	C₃₇	SD₂₅₆	1	1	yes	characteristic, direct product factor, Sylow
29	Q₃₂	—	4	1	no	—
30	D₁₆	—	4	1	no	—
31	C₃₂	D₄×C₃₇	1	1	yes	characteristic
32	Q₁₆	—	8	1	no	—
33	D₈	—	8	1	no	—
34	C₁₆	D₈×C₃₇	1	1	yes	characteristic
35	Q₈	—	16	1	no	—
36	D₄	—	16	1	no	—
37	C₈	D₁₆×C₃₇	1	1	yes	characteristic
38	C₂²	—	32	1	no	—
39	C₄	—	32	1	no	—
40	C₄	C₃₇×D₃₂	1	1	yes	characteristic
41	C₂	—	64	1	no	—
42	C₂	C₃₇×D₆₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃₇	D₆₄
commutator, Frattini, cosocle	C₆₄	C₂²×C₃₇
prime radical	C₃₇×D₆₄	C₂
LCS	G ▷ C₆₄ ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃₇ ◁ C₄×C₃₇ ◁ C₈×C₃₇ ◁ C₁₆×C₃₇ ◁ C₃₂×C₃₇ ◁ C₃₇×C₆₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₇×Q₁₂₈	C₂	semidirect
3. C₃₇×C₁₂₈	C₂	semidirect
16. SD₂₅₆	C₃₇	direct (N × H)
20. Q₁₂₈	C₂×C₃₇	semidirect
22. C₁₂₈	C₂×C₃₇	semidirect
28. C₃₇	SD₂₅₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₇×Q₁₂₈	2
C₃₇×D₆₄	2
C₃₇×C₁₂₈	2
SD₂₅₆	37

Subgroups — C37×SD256 #22628805

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×SD₂₅₆ #22628805