Subgroups — #14641684

Order 2816.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁⋊C₁₂₈	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₁×C₆₄	C₂	1	1	yes	maximal, characteristic
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	—	11	1	no	maximal, 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	D₁₁	1	1	yes	characteristic
14	C₁₂₈	—	11	2	no	—
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	Dic₁₁	1	1	yes	characteristic
19	C₆₄	Dic₁₁	1	1	yes	characteristic
20	C₆₄	C₂×D₁₁	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	C₁₁⋊C₈	1	1	yes	characteristic
25	C₃₂	C₁₁⋊C₈	1	1	yes	characteristic
26	C₃₂	C₂×Dic₁₁	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×C₁₁⋊C₈	1	1	yes	characteristic
32	C₁₁	M₂₅₆	1	1	yes	characteristic, complemented, 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, Frattini	C₆₄	C₂×D₁₁
commutator, socle	C₂×C₁₁	C₂×C₆₄
Fitting	C₂×C₁₁×C₆₄	C₂
prime radical	C₂²×C₁₁	C₆₄
cosocle	C₁₁×C₆₄	C₂²
hypercenter	C₂×C₆₄	D₁₁
hypocenter	C₁₁	M₂₅₆
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₆₄ ◁ C₂×C₆₄

Complements

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

N	H ≅ G/N	type
1. C₁₁⋊C₁₂₈	C₂	semidirect
32. C₁₁	M₂₅₆	semidirect

Maximal subgroups

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

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