Subgroups — C₂²×C₁₁⋊C₆₄ #14674807

Order 2816.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁⋊C₆₄	C₂	1	6	yes	maximal, direct product factor
2	C₂²×C₁₁×C₃₂	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₁×C₁₆	C₄	1	1	yes	characteristic
4	C₂×C₁₁×C₃₂	C₄	1	3	yes	—
5	C₂×C₁₁×C₃₂	C₂²	1	3	yes	—
6	C₁₁⋊C₆₄	C₂²	1	4	yes	direct product factor
7	C₂²×C₈×C₁₁	C₈	1	1	yes	characteristic
8	C₂×C₁₁×C₁₆	C₈	1	3	yes	—
9	C₂×C₁₁×C₁₆	C₂×C₄	1	3	yes	—
10	C₁₁×C₃₂	C₂×C₄	1	3	yes	—
11	C₁₁×C₃₂	C₂³	1	1	yes	characteristic
12	C₂²×C₆₄	—	11	1	no	maximal, Sylow
13	C₂²×C₄×C₁₁	C₁₆	1	1	yes	characteristic
14	C₂×C₈×C₁₁	C₁₆	1	3	yes	—
15	C₂×C₈×C₁₁	C₂×C₈	1	3	yes	—
16	C₁₁×C₁₆	C₂×C₈	1	3	yes	—
17	C₁₁×C₁₆	C₂²×C₄	1	1	yes	characteristic
18	C₂²×C₃₂	D₁₁	1	1	yes	characteristic
19	C₂×C₆₄	—	11	6	no	—
20	C₂³×C₁₁	C₃₂	1	1	yes	characteristic
21	C₂×C₄×C₁₁	C₃₂	1	3	yes	—
22	C₂×C₄×C₁₁	C₂×C₁₆	1	3	yes	—
23	C₈×C₁₁	C₂×C₁₆	1	3	yes	—
24	C₈×C₁₁	C₂²×C₈	1	1	yes	characteristic
25	C₂²×C₁₆	Dic₁₁	1	1	yes	characteristic
26	C₂×C₃₂	Dic₁₁	1	3	yes	—
27	C₂×C₃₂	C₂×D₁₁	1	3	yes	—
28	C₆₄	—	11	4	no	—
29	C₂²×C₁₁	C₆₄	1	4	yes	complemented
30	C₂²×C₁₁	C₂×C₃₂	1	3	yes	—
31	C₄×C₁₁	C₂×C₃₂	1	3	yes	—
32	C₄×C₁₁	C₂²×C₁₆	1	1	yes	characteristic
33	C₂²×C₈	C₁₁⋊C₈	1	1	yes	characteristic
34	C₂×C₁₆	C₁₁⋊C₈	1	3	yes	—
35	C₂×C₁₆	C₂×Dic₁₁	1	3	yes	—
36	C₃₂	C₂×Dic₁₁	1	3	yes	—
37	C₃₂	C₂²×D₁₁	1	1	yes	characteristic
38	C₂×C₁₁	C₂×C₆₄	1	6	yes	complemented
39	C₂×C₁₁	C₂²×C₃₂	1	1	yes	characteristic
40	C₂²×C₄	C₁₁⋊C₁₆	1	1	yes	characteristic
41	C₂×C₈	C₁₁⋊C₁₆	1	3	yes	—
42	C₂×C₈	C₂×C₁₁⋊C₈	1	3	yes	—
43	C₁₆	C₂×C₁₁⋊C₈	1	3	yes	—
44	C₁₆	C₂²×Dic₁₁	1	1	yes	characteristic
45	C₁₁	C₂²×C₆₄	1	1	yes	characteristic, complemented, Sylow
46	C₂³	C₁₁⋊C₃₂	1	1	yes	characteristic
47	C₂×C₄	C₁₁⋊C₃₂	1	3	yes	—
48	C₂×C₄	C₂×C₁₁⋊C₁₆	1	3	yes	—
49	C₈	C₂×C₁₁⋊C₁₆	1	3	yes	—
50	C₈	C₂²×C₁₁⋊C₈	1	1	yes	characteristic
51	C₂²	C₁₁⋊C₆₄	1	4	yes	direct product factor
52	C₂²	C₂×C₁₁⋊C₃₂	1	3	yes	—
53	C₄	C₂×C₁₁⋊C₃₂	1	3	yes	—
54	C₄	C₂²×C₁₁⋊C₁₆	1	1	yes	characteristic
55	C₂	C₂×C₁₁⋊C₆₄	1	6	yes	direct product factor
56	C₂	C₂²×C₁₁⋊C₃₂	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₁⋊C₆₄	C₂	direct (N × H)
6. C₁₁⋊C₆₄	C₂²	direct (N × H)
29. C₂²×C₁₁	C₆₄	semidirect
38. C₂×C₁₁	C₂×C₆₄	semidirect
45. C₁₁	C₂²×C₆₄	semidirect
51. C₂²	C₁₁⋊C₆₄	direct (N × H)
55. C₂	C₂×C₁₁⋊C₆₄	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
C₂²×C₁₁×C₃₂	2
C₂²×C₆₄	11

Subgroups — C22×C11⋊C64 #14674807

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₁⋊C₆₄ #14674807