Subgroups — Dic₁₁⋊C₆₄ #14641668

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	1	yes	maximal, characteristic
2	C₃₂×Dic₁₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₁×C₆₄	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₁×C₃₂	C₂²	1	1	yes	characteristic
5	C₁₆×Dic₁₁	C₄	1	1	yes	characteristic
6	C₂×C₁₁⋊C₃₂	C₄	1	1	yes	characteristic
7	C₁₁×C₆₄	—	2	1	no	—
8	C₁₁⋊C₆₄	—	2	1	no	—
9	C₂×C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
10	C₈×Dic₁₁	C₈	1	1	yes	characteristic
11	C₂×C₁₁⋊C₁₆	C₈	1	1	yes	characteristic
12	C₁₁×C₃₂	D₄	1	1	yes	characteristic
13	C₁₁×C₃₂	Q₈	1	1	yes	characteristic
14	C₁₁⋊C₃₂	—	2	1	no	—
15	C₄⋊C₆₄	—	11	1	no	maximal, Sylow
16	C₂×C₈×C₁₁	C₂×C₈	1	1	yes	characteristic
17	C₄×Dic₁₁	C₁₆	1	1	yes	characteristic
18	C₂×C₁₁⋊C₈	C₁₆	1	1	yes	characteristic
19	C₁₁×C₁₆	C₄⋊C₄	1	1	yes	characteristic
20	C₁₁×C₁₆	M₁₆	1	1	yes	characteristic
21	C₁₁⋊C₁₆	—	2	1	no	—
22	C₂×C₆₄	—	11	1	no	—
23	C₂×C₆₄	D₁₁	1	1	yes	characteristic
24	C₄×C₃₂	—	11	1	no	—
25	C₂×C₄×C₁₁	C₂×C₁₆	1	1	yes	characteristic
26	C₂×Dic₁₁	C₃₂	1	1	yes	characteristic
27	C₂×Dic₁₁	C₃₂	1	1	yes	characteristic
28	C₈×C₁₁	C₄⋊C₈	1	1	yes	characteristic
29	C₈×C₁₁	M₃₂	1	1	yes	characteristic
30	C₁₁⋊C₈	—	2	1	no	—
31	C₂×C₃₂	—	11	1	no	—
32	C₂×C₃₂	C₂×D₁₁	1	1	yes	characteristic
33	C₄×C₁₆	—	11	1	no	—
34	C₆₄	—	2	1	no	—
35	C₆₄	—	22	1	no	—
36	C₂²×C₁₁	C₂×C₃₂	1	1	yes	characteristic
37	C₄×C₁₁	C₄⋊C₁₆	1	1	yes	characteristic
38	C₄×C₁₁	M₆₄	1	1	yes	characteristic
39	Dic₁₁	—	2	1	no	—
40	Dic₁₁	C₆₄	1	2	yes	complemented
41	C₂×C₁₆	—	11	1	no	—
42	C₂×C₁₆	C₄×D₁₁	1	1	yes	characteristic
43	C₄×C₈	—	11	1	no	—
44	C₃₂	—	22	1	no	—
45	C₃₂	Dic₂₂	1	1	yes	characteristic
46	C₃₂	C₂²⋊D₁₁	1	1	yes	characteristic
47	C₂×C₁₁	C₄⋊C₃₂	1	1	yes	characteristic
48	C₂×C₁₁	C₂×C₆₄	1	1	yes	characteristic
49	C₂×C₁₁	M₁₂₈	1	1	yes	characteristic
50	C₂×C₈	—	11	1	no	—
51	C₂×C₈	C₈×D₁₁	1	1	yes	characteristic
52	C₄²	—	11	1	no	—
53	C₁₆	—	22	1	no	—
54	C₁₆	#4313	1	1	yes	characteristic
55	C₁₆	Dic₁₁⋊C₄	1	1	yes	characteristic
56	C₁₁	C₄⋊C₆₄	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₄	—	11	1	no	—
58	C₂×C₄	—	11	1	no	—
59	C₂×C₄	C₁₆×D₁₁	1	1	yes	characteristic
60	C₈	—	22	1	no	—
61	C₈	#66862	1	1	yes	characteristic
62	C₈	Dic₁₁⋊C₈	1	1	yes	characteristic
63	C₂²	D₁₁×C₃₂	1	1	yes	characteristic
64	C₄	—	11	2	no	—
65	C₄	—	22	1	no	—
66	C₄	#10622085	1	1	yes	characteristic
67	C₄	Dic₁₁⋊C₁₆	1	1	yes	characteristic
68	C₂	Dic₁₁⋊C₃₂	1	1	yes	characteristic
69	C₂	D₁₁×C₆₄	1	1	yes	characteristic
70	C₂	#13066826	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₃₂	C₂×D₁₁
commutator	C₂×C₁₁	C₂×C₆₄
Fitting	C₂×C₁₁×C₆₄	C₂
socle, prime radical	C₂²×C₁₁	C₂×C₃₂
cosocle	C₂×C₁₁×C₃₂	C₂²
hypercenter	C₂×C₆₄	D₁₁
hypocenter	C₁₁	C₄⋊C₆₄
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₃₂ ◁ C₂×C₆₄

Complements

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

N	H ≅ G/N	type
40. Dic₁₁	C₆₄	semidirect
56. C₁₁	C₄⋊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
C₃₂×Dic₁₁	2
C₂×C₁₁×C₆₄	2
C₄⋊C₆₄	11

Subgroups — Dic11⋊C64 #14641668

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₁₁⋊C₆₄ #14641668