Subgroups — #14641578

Order 2816.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁⋊C₆₄	C₂	1	2	yes	maximal
2	C₄×C₁₁×C₃₂	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₁×C₃₂	C₄	1	1	yes	characteristic
4	C₂×C₁₁×C₃₂	C₂²	1	1	yes	characteristic
5	C₄×C₁₁×C₁₆	C₄	1	1	yes	characteristic
6	C₁₁⋊C₆₄	C₄	1	4	yes	complemented
7	C₂×C₁₁×C₁₆	C₈	1	1	yes	characteristic
8	C₂×C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
9	C₄×C₈×C₁₁	C₈	1	1	yes	characteristic
10	C₁₁×C₃₂	C₈	1	2	yes	—
11	C₁₁×C₃₂	C₂×C₄	1	2	yes	—
12	#7510	—	11	1	no	maximal, Sylow
13	C₂×C₈×C₁₁	C₁₆	1	1	yes	characteristic
14	C₂×C₈×C₁₁	C₂×C₈	1	1	yes	characteristic
15	C₄²×C₁₁	C₁₆	1	1	yes	characteristic
16	C₁₁×C₁₆	C₁₆	1	2	yes	—
17	C₁₁×C₁₆	C₄²	1	1	yes	characteristic
18	C₁₁×C₁₆	C₂×C₈	1	1	yes	characteristic
19	C₂×C₆₄	—	11	2	no	—
20	C₄×C₃₂	D₁₁	1	1	yes	characteristic
21	C₂×C₄×C₁₁	C₃₂	1	2	yes	—
22	C₂×C₄×C₁₁	C₂×C₁₆	1	1	yes	characteristic
23	C₈×C₁₁	C₃₂	1	2	yes	—
24	C₈×C₁₁	C₄×C₈	1	1	yes	characteristic
25	C₈×C₁₁	C₂×C₁₆	1	1	yes	characteristic
26	C₂×C₃₂	Dic₁₁	1	1	yes	characteristic
27	C₂×C₃₂	C₂×D₁₁	1	1	yes	characteristic
28	C₄×C₁₆	Dic₁₁	1	1	yes	characteristic
29	C₆₄	—	11	4	no	—
30	C₂²×C₁₁	C₂×C₃₂	1	1	yes	characteristic
31	C₄×C₁₁	—	2	2	no	—
32	C₄×C₁₁	C₄×C₁₆	1	1	yes	characteristic
33	C₄×C₁₁	C₂×C₃₂	1	1	yes	characteristic
34	C₂×C₁₆	C₁₁⋊C₈	1	1	yes	characteristic
35	C₂×C₁₆	C₂×Dic₁₁	1	1	yes	characteristic
36	C₄×C₈	C₁₁⋊C₈	1	1	yes	characteristic
37	C₃₂	C₁₁⋊C₈	1	2	yes	—
38	C₃₂	C₄×D₁₁	1	2	yes	—
39	C₂×C₁₁	C₄×C₃₂	1	1	yes	characteristic
40	C₂×C₁₁	M₁₂₈	1	2	yes	—
41	C₂×C₈	C₁₁⋊C₁₆	1	1	yes	characteristic
42	C₂×C₈	C₂×C₁₁⋊C₈	1	1	yes	characteristic
43	C₄²	C₁₁⋊C₁₆	1	1	yes	characteristic
44	C₁₆	C₁₁⋊C₁₆	1	2	yes	—
45	C₁₆	C₂×C₁₁⋊C₈	1	1	yes	characteristic
46	C₁₆	C₄×Dic₁₁	1	1	yes	characteristic
47	C₁₁	#7510	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₄	C₁₁⋊C₃₂	1	2	yes	—
49	C₂×C₄	C₂×C₁₁⋊C₁₆	1	1	yes	characteristic
50	C₈	C₁₁⋊C₃₂	1	2	yes	—
51	C₈	C₄×C₁₁⋊C₈	1	1	yes	characteristic
52	C₈	C₂×C₁₁⋊C₁₆	1	1	yes	characteristic
53	C₂²	C₂×C₁₁⋊C₃₂	1	1	yes	characteristic
54	C₄	—	2	2	no	—
55	C₄	C₄×C₁₁⋊C₁₆	1	1	yes	characteristic
56	C₄	C₂×C₁₁⋊C₃₂	1	1	yes	characteristic
57	C₂	C₄×C₁₁⋊C₃₂	1	1	yes	characteristic
58	C₂	#13066827	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₃₂	C₂×D₁₁
commutator	C₂×C₁₁	C₄×C₃₂
Fitting	C₄×C₁₁×C₃₂	C₂
socle, prime radical	C₂²×C₁₁	C₂×C₃₂
cosocle	C₂×C₁₁×C₃₂	C₂²
hypercenter	C₄×C₃₂	D₁₁
hypocenter	C₁₁	#7510
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₃₂ ◁ C₄×C₃₂

Complements

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

N	H ≅ G/N	type
6. C₁₁⋊C₆₄	C₄	semidirect
47. C₁₁	#7510	semidirect

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
C₄×C₁₁×C₃₂	2
#7510	11