Subgroups — C₁₁×M₂₅₆ #14584743

Order 2816.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×C₆₄	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₁₂₈	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₁×C₃₂	C₄	1	1	yes	characteristic
4	C₁₁×C₆₄	C₄	1	1	yes	characteristic
5	C₁₁×C₆₄	C₂²	1	1	yes	characteristic
6	C₂×C₁₁×C₁₆	C₈	1	1	yes	characteristic
7	C₁₁×C₃₂	C₈	1	1	yes	characteristic
8	C₁₁×C₃₂	C₂×C₄	1	1	yes	characteristic
9	M₂₅₆	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂×C₈×C₁₁	C₁₆	1	1	yes	characteristic
11	C₁₁×C₁₆	C₁₆	1	1	yes	characteristic
12	C₁₁×C₁₆	C₂×C₈	1	1	yes	characteristic
13	C₂×C₆₄	C₂×C₁₁	1	1	yes	characteristic
14	C₁₂₈	C₂×C₁₁	1	2	yes	complemented
15	C₂×C₄×C₁₁	C₃₂	1	1	yes	characteristic
16	C₈×C₁₁	C₃₂	1	1	yes	characteristic
17	C₈×C₁₁	C₂×C₁₆	1	1	yes	characteristic
18	C₂×C₃₂	C₄×C₁₁	1	1	yes	characteristic
19	C₆₄	C₄×C₁₁	1	1	yes	characteristic
20	C₆₄	C₂²×C₁₁	1	1	yes	characteristic
21	C₂²×C₁₁	C₆₄	1	1	yes	characteristic
22	C₄×C₁₁	C₆₄	1	1	yes	characteristic
23	C₄×C₁₁	C₂×C₃₂	1	1	yes	characteristic
24	C₂×C₁₆	C₈×C₁₁	1	1	yes	characteristic
25	C₃₂	C₈×C₁₁	1	1	yes	characteristic
26	C₃₂	C₂×C₄×C₁₁	1	1	yes	characteristic
27	C₂×C₁₁	—	2	1	no	—
28	C₂×C₁₁	C₂×C₆₄	1	1	yes	characteristic
29	C₂×C₈	C₁₁×C₁₆	1	1	yes	characteristic
30	C₁₆	C₁₁×C₁₆	1	1	yes	characteristic
31	C₁₆	C₂×C₈×C₁₁	1	1	yes	characteristic
32	C₁₁	M₂₅₆	1	1	yes	characteristic, direct product factor, Sylow
33	C₂×C₄	C₁₁×C₃₂	1	1	yes	characteristic
34	C₈	C₁₁×C₃₂	1	1	yes	characteristic
35	C₈	C₂×C₁₁×C₁₆	1	1	yes	characteristic
36	C₂²	C₁₁×C₆₄	1	1	yes	characteristic
37	C₄	C₁₁×C₆₄	1	1	yes	characteristic
38	C₄	C₂×C₁₁×C₃₂	1	1	yes	characteristic
39	C₂	—	2	1	no	—
40	C₂	C₂×C₁₁×C₆₄	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₁₁×C₁₂₈	C₂	semidirect
9. M₂₅₆	C₁₁	direct (N × H)
14. C₁₂₈	C₂×C₁₁	semidirect
32. C₁₁	M₂₅₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₁×C₆₄	2
C₁₁×C₁₂₈	2
M₂₅₆	11

Subgroups — C11×M256 #14584743

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×M₂₅₆ #14584743