Subgroups — C₁₁×SD₂₅₆ #14584745

Order 2816.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×Q₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×D₆₄	C₂	1	1	yes	maximal, characteristic
3	C₁₁×C₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×Q₆₄	—	2	1	no	—
5	C₁₁×D₃₂	—	2	1	no	—
6	C₁₁×C₆₄	C₂²	1	1	yes	characteristic
7	C₁₁×Q₃₂	—	4	1	no	—
8	C₁₁×D₁₆	—	4	1	no	—
9	C₁₁×C₃₂	D₄	1	1	yes	characteristic
10	SD₂₅₆	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₁₁×Q₁₆	—	8	1	no	—
12	C₁₁×D₈	—	8	1	no	—
13	C₁₁×C₁₆	D₈	1	1	yes	characteristic
14	Q₁₂₈	C₂×C₁₁	1	1	yes	characteristic, complemented
15	D₆₄	C₂×C₁₁	1	1	yes	characteristic
16	C₁₂₈	C₂×C₁₁	1	1	yes	characteristic, complemented
17	Q₈×C₁₁	—	16	1	no	—
18	D₄×C₁₁	—	16	1	no	—
19	C₈×C₁₁	D₁₆	1	1	yes	characteristic
20	Q₆₄	—	2	1	no	—
21	D₃₂	—	2	1	no	—
22	C₆₄	C₂²×C₁₁	1	1	yes	characteristic
23	C₂²×C₁₁	—	32	1	no	—
24	C₄×C₁₁	—	32	1	no	—
25	C₄×C₁₁	D₃₂	1	1	yes	characteristic
26	Q₃₂	—	4	1	no	—
27	D₁₆	—	4	1	no	—
28	C₃₂	D₄×C₁₁	1	1	yes	characteristic
29	C₂×C₁₁	—	64	1	no	—
30	C₂×C₁₁	D₆₄	1	1	yes	characteristic
31	Q₁₆	—	8	1	no	—
32	D₈	—	8	1	no	—
33	C₁₆	C₁₁×D₈	1	1	yes	characteristic
34	C₁₁	SD₂₅₆	1	1	yes	characteristic, direct product factor, Sylow
35	Q₈	—	16	1	no	—
36	D₄	—	16	1	no	—
37	C₈	C₁₁×D₁₆	1	1	yes	characteristic
38	C₂²	—	32	1	no	—
39	C₄	—	32	1	no	—
40	C₄	C₁₁×D₃₂	1	1	yes	characteristic
41	C₂	—	64	1	no	—
42	C₂	C₁₁×D₆₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₁	D₆₄
commutator, Frattini, cosocle	C₆₄	C₂²×C₁₁
prime radical	C₁₁×D₆₄	C₂
LCS	G ▷ C₆₄ ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₄×C₁₁ ◁ C₈×C₁₁ ◁ C₁₁×C₁₆ ◁ C₁₁×C₃₂ ◁ C₁₁×C₆₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₁×Q₁₂₈	C₂	semidirect
3. C₁₁×C₁₂₈	C₂	semidirect
10. SD₂₅₆	C₁₁	direct (N × H)
14. Q₁₂₈	C₂×C₁₁	semidirect
16. C₁₂₈	C₂×C₁₁	semidirect
34. C₁₁	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
C₁₁×Q₁₂₈	2
C₁₁×D₆₄	2
C₁₁×C₁₂₈	2
SD₂₅₆	11

Subgroups — C11×SD256 #14584745

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×SD₂₅₆ #14584745