Subgroups — C₂²⋊(C₁₁⋊C₆₄) #14641582

Order 2816.

98 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, complemented
2	C₂²×C₁₁×C₃₂	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₁×C₁₆	C₄	1	1	yes	characteristic
4	C₂×C₁₁×C₃₂	—	2	2	no	—
5	C₂×C₁₁×C₃₂	C₄	1	1	yes	characteristic
6	C₂×C₁₁×C₃₂	C₂²	1	1	yes	characteristic
7	C₁₁⋊C₆₄	—	2	2	no	—
8	C₂²×C₈×C₁₁	C₈	1	1	yes	characteristic
9	C₂×C₁₁×C₁₆	—	2	1	no	—
10	C₂×C₁₁×C₁₆	—	2	1	no	—
11	C₂×C₁₁×C₁₆	C₈	1	1	yes	characteristic
12	C₂×C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
13	C₁₁×C₃₂	—	2	1	no	—
14	C₁₁×C₃₂	D₄	1	2	yes	—
15	C₂²⋊C₆₄	—	11	1	no	maximal, Sylow
16	C₂²×C₄×C₁₁	C₁₆	1	1	yes	characteristic
17	C₂×C₈×C₁₁	—	2	1	no	—
18	C₂×C₈×C₁₁	—	2	1	no	—
19	C₂×C₈×C₁₁	C₁₆	1	1	yes	characteristic
20	C₂×C₈×C₁₁	C₂×C₈	1	1	yes	characteristic
21	C₁₁×C₁₆	—	2	1	no	—
22	C₁₁×C₁₆	C₂²⋊C₄	1	1	yes	characteristic
23	C₁₁×C₁₆	M₁₆	1	1	yes	characteristic
24	C₂²×C₃₂	D₁₁	1	1	yes	characteristic
25	C₂×C₆₄	—	11	2	no	—
26	C₂³×C₁₁	C₃₂	1	1	yes	characteristic
27	C₂×C₄×C₁₁	—	2	1	no	—
28	C₂×C₄×C₁₁	—	2	1	no	—
29	C₂×C₄×C₁₁	C₃₂	1	1	yes	characteristic
30	C₂×C₄×C₁₁	C₂×C₁₆	1	1	yes	characteristic
31	C₈×C₁₁	—	2	1	no	—
32	C₈×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
33	C₈×C₁₁	M₃₂	1	1	yes	characteristic
34	C₂²×C₁₆	Dic₁₁	1	1	yes	characteristic
35	C₂×C₃₂	—	2	2	no	—
36	C₂×C₃₂	Dic₁₁	1	1	yes	characteristic
37	C₂×C₃₂	C₂×D₁₁	1	1	yes	characteristic
38	C₆₄	—	22	2	no	—
39	C₂²×C₁₁	—	2	1	no	—
40	C₂²×C₁₁	—	2	1	no	—
41	C₂²×C₁₁	C₆₄	1	2	yes	complemented
42	C₂²×C₁₁	C₂×C₃₂	1	1	yes	characteristic
43	C₄×C₁₁	—	2	1	no	—
44	C₄×C₁₁	C₂²⋊C₁₆	1	1	yes	characteristic
45	C₄×C₁₁	M₆₄	1	1	yes	characteristic
46	C₂²×C₈	C₁₁⋊C₈	1	1	yes	characteristic
47	C₂×C₁₆	—	2	1	no	—
48	C₂×C₁₆	—	2	1	no	—
49	C₂×C₁₆	C₁₁⋊C₈	1	1	yes	characteristic
50	C₂×C₁₆	C₂×Dic₁₁	1	1	yes	characteristic
51	C₃₂	—	2	1	no	—
52	C₃₂	C₂²⋊D₁₁	1	2	yes	—
53	C₂×C₁₁	—	2	2	no	—
54	C₂×C₁₁	C₂²⋊C₃₂	1	1	yes	characteristic
55	C₂×C₁₁	C₂×C₆₄	1	1	yes	characteristic
56	C₂×C₁₁	M₁₂₈	1	1	yes	characteristic
57	C₂²×C₄	C₁₁⋊C₁₆	1	1	yes	characteristic
58	C₂×C₈	—	2	1	no	—
59	C₂×C₈	—	2	1	no	—
60	C₂×C₈	C₁₁⋊C₁₆	1	1	yes	characteristic
61	C₂×C₈	C₂×C₁₁⋊C₈	1	1	yes	characteristic
62	C₁₆	—	2	1	no	—
63	C₁₆	#4318	1	1	yes	characteristic
64	C₁₆	C₂²⋊Dic₁₁	1	1	yes	characteristic
65	C₁₁	C₂²⋊C₆₄	1	1	yes	characteristic, complemented, Sylow
66	C₂³	C₁₁⋊C₃₂	1	1	yes	characteristic
67	C₂×C₄	—	2	1	no	—
68	C₂×C₄	—	2	1	no	—
69	C₂×C₄	C₁₁⋊C₃₂	1	1	yes	characteristic
70	C₂×C₄	C₂×C₁₁⋊C₁₆	1	1	yes	characteristic
71	C₈	—	2	1	no	—
72	C₈	#66876	1	1	yes	characteristic
73	C₈	C₂²⋊(C₁₁⋊C₈)	1	1	yes	characteristic
74	C₂²	—	2	1	no	—
75	C₂²	—	2	1	no	—
76	C₂²	C₁₁⋊C₆₄	1	2	yes	complemented
77	C₂²	C₂×C₁₁⋊C₃₂	1	1	yes	characteristic
78	C₄	—	2	1	no	—
79	C₄	#10622137	1	1	yes	characteristic
80	C₄	C₂²⋊(C₁₁⋊C₁₆)	1	1	yes	characteristic
81	C₂	—	2	2	no	—
82	C₂	C₂²⋊(C₁₁⋊C₃₂)	1	1	yes	characteristic
83	C₂	C₂×C₁₁⋊C₆₄	1	1	yes	characteristic
84	C₂	#13066827	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₃₂	C₂×D₁₁
commutator	C₂×C₁₁	C₂×C₆₄
Fitting	C₂²×C₁₁×C₃₂	C₂
socle	C₂²×C₁₁	C₂×C₃₂
prime radical	C₂³×C₁₁	C₃₂
cosocle	C₂×C₁₁×C₃₂	C₂²
hypercenter	C₂²×C₃₂	D₁₁
hypocenter	C₁₁	C₂²⋊C₆₄
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₃₂ ◁ C₂²×C₃₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₁⋊C₆₄	C₂	semidirect
41. C₂²×C₁₁	C₆₄	semidirect
65. C₁₁	C₂²⋊C₆₄	semidirect
76. C₂²	C₁₁⋊C₆₄	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
C₂²×C₁₁×C₃₂	2
C₂²⋊C₆₄	11

Subgroups — C22⋊(C11⋊C64) #14641582

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²⋊(C₁₁⋊C₆₄) #14641582