Subgroups — C₁₃₁×SD₂₅₆ #45693436

Order 33536.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₁₂₈×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	D₆₄×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	C₁₂₈×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₆₄×C₁₃₁	—	2	1	no	—
5	D₃₂×C₁₃₁	—	2	1	no	—
6	C₆₄×C₁₃₁	C₂²	1	1	yes	characteristic
7	Q₃₂×C₁₃₁	—	4	1	no	—
8	D₁₆×C₁₃₁	—	4	1	no	—
9	C₃₂×C₁₃₁	D₄	1	1	yes	characteristic
10	Q₁₆×C₁₃₁	—	8	1	no	—
11	D₈×C₁₃₁	—	8	1	no	—
12	C₁₆×C₁₃₁	D₈	1	1	yes	characteristic
13	Q₈×C₁₃₁	—	16	1	no	—
14	D₄×C₁₃₁	—	16	1	no	—
15	C₈×C₁₃₁	D₁₆	1	1	yes	characteristic
16	C₂²×C₁₃₁	—	32	1	no	—
17	C₄×C₁₃₁	—	32	1	no	—
18	C₄×C₁₃₁	D₃₂	1	1	yes	characteristic
19	C₂×C₁₃₁	—	64	1	no	—
20	C₂×C₁₃₁	D₆₄	1	1	yes	characteristic
21	SD₂₅₆	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
22	C₁₃₁	SD₂₅₆	1	1	yes	characteristic, direct product factor, Sylow
23	Q₁₂₈	C₂×C₁₃₁	1	1	yes	characteristic, complemented
24	D₆₄	C₂×C₁₃₁	1	1	yes	characteristic
25	C₁₂₈	C₂×C₁₃₁	1	1	yes	characteristic, complemented
26	Q₆₄	—	2	1	no	—
27	D₃₂	—	2	1	no	—
28	C₆₄	C₂²×C₁₃₁	1	1	yes	characteristic
29	Q₃₂	—	4	1	no	—
30	D₁₆	—	4	1	no	—
31	C₃₂	D₄×C₁₃₁	1	1	yes	characteristic
32	Q₁₆	—	8	1	no	—
33	D₈	—	8	1	no	—
34	C₁₆	D₈×C₁₃₁	1	1	yes	characteristic
35	Q₈	—	16	1	no	—
36	D₄	—	16	1	no	—
37	C₈	D₁₆×C₁₃₁	1	1	yes	characteristic
38	C₂²	—	32	1	no	—
39	C₄	—	32	1	no	—
40	C₄	D₃₂×C₁₃₁	1	1	yes	characteristic
41	C₂	—	64	1	no	—
42	C₂	D₆₄×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃₁	D₆₄
commutator, Frattini, cosocle	C₆₄	C₂²×C₁₃₁
prime radical	D₆₄×C₁₃₁	C₂
LCS	G ▷ C₆₄ ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃₁ ◁ C₄×C₁₃₁ ◁ C₈×C₁₃₁ ◁ C₁₆×C₁₃₁ ◁ C₃₂×C₁₃₁ ◁ C₆₄×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. Q₁₂₈×C₁₃₁	C₂	semidirect
3. C₁₂₈×C₁₃₁	C₂	semidirect
21. SD₂₅₆	C₁₃₁	direct (N × H)
22. C₁₃₁	SD₂₅₆	direct (N × H)
23. Q₁₂₈	C₂×C₁₃₁	semidirect
25. C₁₂₈	C₂×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
Q₁₂₈×C₁₃₁	2
D₆₄×C₁₃₁	2
C₁₂₈×C₁₃₁	2
SD₂₅₆	131

Subgroups — C131×SD256 #45693436

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×SD₂₅₆ #45693436