Subgroups — C₄⋊(C₁₁⋊C₆₄) #14641669

Order 2816.

74 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	—	2	2	no	—
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	—	2	1	no	—
11	C₁₁×C₃₂	D₄	1	1	yes	characteristic
12	C₁₁×C₃₂	Q₈	1	1	yes	characteristic
13	C₄⋊C₆₄	—	11	1	no	maximal, Sylow
14	C₂×C₈×C₁₁	C₁₆	1	1	yes	characteristic
15	C₂×C₈×C₁₁	C₂×C₈	1	1	yes	characteristic
16	C₄²×C₁₁	C₁₆	1	1	yes	characteristic
17	C₁₁×C₁₆	—	2	1	no	—
18	C₁₁×C₁₆	C₄⋊C₄	1	1	yes	characteristic
19	C₁₁×C₁₆	M₁₆	1	1	yes	characteristic
20	C₂×C₆₄	—	11	2	no	—
21	C₄×C₃₂	D₁₁	1	1	yes	characteristic
22	C₂×C₄×C₁₁	C₃₂	1	1	yes	characteristic
23	C₂×C₄×C₁₁	C₃₂	1	1	yes	characteristic
24	C₂×C₄×C₁₁	C₂×C₁₆	1	1	yes	characteristic
25	C₈×C₁₁	—	2	1	no	—
26	C₈×C₁₁	C₄⋊C₈	1	1	yes	characteristic
27	C₈×C₁₁	M₃₂	1	1	yes	characteristic
28	C₂×C₃₂	Dic₁₁	1	1	yes	characteristic
29	C₂×C₃₂	C₂×D₁₁	1	1	yes	characteristic
30	C₄×C₁₆	Dic₁₁	1	1	yes	characteristic
31	C₆₄	—	22	2	no	—
32	C₂²×C₁₁	C₂×C₃₂	1	1	yes	characteristic
33	C₄×C₁₁	—	2	1	no	—
34	C₄×C₁₁	C₆₄	1	2	yes	complemented
35	C₄×C₁₁	C₄⋊C₁₆	1	1	yes	characteristic
36	C₄×C₁₁	M₆₄	1	1	yes	characteristic
37	C₂×C₁₆	C₁₁⋊C₈	1	1	yes	characteristic
38	C₂×C₁₆	C₂×Dic₁₁	1	1	yes	characteristic
39	C₄×C₈	C₁₁⋊C₈	1	1	yes	characteristic
40	C₃₂	—	2	1	no	—
41	C₃₂	Dic₂₂	1	1	yes	characteristic
42	C₃₂	D₄₄	1	1	yes	characteristic
43	C₂×C₁₁	C₄⋊C₃₂	1	1	yes	characteristic
44	C₂×C₁₁	C₂×C₆₄	1	1	yes	characteristic
45	C₂×C₁₁	M₁₂₈	1	1	yes	characteristic
46	C₂×C₈	C₁₁⋊C₁₆	1	1	yes	characteristic
47	C₂×C₈	C₂×C₁₁⋊C₈	1	1	yes	characteristic
48	C₄²	C₁₁⋊C₁₆	1	1	yes	characteristic
49	C₁₆	—	2	1	no	—
50	C₁₆	#4318	1	1	yes	characteristic
51	C₁₆	C₄⋊Dic₁₁	1	1	yes	characteristic
52	C₁₁	C₄⋊C₆₄	1	1	yes	characteristic, complemented, Sylow
53	C₂×C₄	C₁₁⋊C₃₂	1	1	yes	characteristic
54	C₂×C₄	C₁₁⋊C₃₂	1	1	yes	characteristic
55	C₂×C₄	C₂×C₁₁⋊C₁₆	1	1	yes	characteristic
56	C₈	—	2	1	no	—
57	C₈	C₄⋊(C₁₁⋊C₈)	1	1	yes	characteristic
58	C₈	#66876	1	1	yes	characteristic
59	C₂²	C₂×C₁₁⋊C₃₂	1	1	yes	characteristic
60	C₄	—	2	1	no	—
61	C₄	C₁₁⋊C₆₄	1	2	yes	complemented
62	C₄	C₄⋊(C₁₁⋊C₁₆)	1	1	yes	characteristic
63	C₄	#10622137	1	1	yes	characteristic
64	C₂	C₄⋊(C₁₁⋊C₃₂)	1	1	yes	characteristic
65	C₂	C₂×C₁₁⋊C₆₄	1	1	yes	characteristic
66	C₂	#13066827	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₃₂	C₂×D₁₁
commutator	C₂×C₁₁	C₂×C₆₄
Fitting	C₄×C₁₁×C₃₂	C₂
socle, prime radical	C₂²×C₁₁	C₂×C₃₂
cosocle	C₂×C₁₁×C₃₂	C₂²
hypercenter	C₄×C₃₂	D₁₁
hypocenter	C₁₁	C₄⋊C₆₄
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
34. C₄×C₁₁	C₆₄	semidirect
52. C₁₁	C₄⋊C₆₄	semidirect
61. C₄	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
C₄×C₁₁×C₃₂	2
C₄⋊C₆₄	11

Subgroups — C4⋊(C11⋊C64) #14641669

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊(C₁₁⋊C₆₄) #14641669