Subgroups — C₃₁×SD₂₅₆ #21464311

Order 7936.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×Q₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×D₆₄	C₂	1	1	yes	maximal, characteristic
3	C₃₁×C₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×Q₆₄	—	2	1	no	—
5	C₃₁×D₃₂	—	2	1	no	—
6	C₃₁×C₆₄	C₂²	1	1	yes	characteristic
7	C₃₁×Q₃₂	—	4	1	no	—
8	C₃₁×D₁₆	—	4	1	no	—
9	C₃₁×C₃₂	D₄	1	1	yes	characteristic
10	Q₁₆×C₃₁	—	8	1	no	—
11	D₈×C₃₁	—	8	1	no	—
12	C₁₆×C₃₁	D₈	1	1	yes	characteristic
13	SD₂₅₆	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	Q₈×C₃₁	—	16	1	no	—
15	D₄×C₃₁	—	16	1	no	—
16	C₈×C₃₁	D₁₆	1	1	yes	characteristic
17	Q₁₂₈	C₂×C₃₁	1	1	yes	characteristic, complemented
18	D₆₄	C₂×C₃₁	1	1	yes	characteristic
19	C₁₂₈	C₂×C₃₁	1	1	yes	characteristic, complemented
20	C₂²×C₃₁	—	32	1	no	—
21	C₄×C₃₁	—	32	1	no	—
22	C₄×C₃₁	D₃₂	1	1	yes	characteristic
23	Q₆₄	—	2	1	no	—
24	D₃₂	—	2	1	no	—
25	C₆₄	C₂²×C₃₁	1	1	yes	characteristic
26	C₂×C₃₁	—	64	1	no	—
27	C₂×C₃₁	D₆₄	1	1	yes	characteristic
28	Q₃₂	—	4	1	no	—
29	D₁₆	—	4	1	no	—
30	C₃₂	D₄×C₃₁	1	1	yes	characteristic
31	C₃₁	SD₂₅₆	1	1	yes	characteristic, direct product factor, Sylow
32	Q₁₆	—	8	1	no	—
33	D₈	—	8	1	no	—
34	C₁₆	D₈×C₃₁	1	1	yes	characteristic
35	Q₈	—	16	1	no	—
36	D₄	—	16	1	no	—
37	C₈	C₃₁×D₁₆	1	1	yes	characteristic
38	C₂²	—	32	1	no	—
39	C₄	—	32	1	no	—
40	C₄	C₃₁×D₃₂	1	1	yes	characteristic
41	C₂	—	64	1	no	—
42	C₂	C₃₁×D₆₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃₁	D₆₄
commutator, Frattini, cosocle	C₆₄	C₂²×C₃₁
prime radical	C₃₁×D₆₄	C₂
LCS	G ▷ C₆₄ ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃₁ ◁ C₄×C₃₁ ◁ C₈×C₃₁ ◁ C₁₆×C₃₁ ◁ C₃₁×C₃₂ ◁ C₃₁×C₆₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×Q₁₂₈	C₂	semidirect
3. C₃₁×C₁₂₈	C₂	semidirect
13. SD₂₅₆	C₃₁	direct (N × H)
17. Q₁₂₈	C₂×C₃₁	semidirect
19. C₁₂₈	C₂×C₃₁	semidirect
31. C₃₁	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
C₃₁×Q₁₂₈	2
C₃₁×D₆₄	2
C₃₁×C₁₂₈	2
SD₂₅₆	31

Subgroups — C31×SD256 #21464311

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×SD₂₅₆ #21464311