Subgroups — C₂×C₁₁×D₆₄ #14590931

Order 2816.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×D₃₂	C₂	1	2	yes	maximal, complemented
2	C₁₁×D₆₄	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₁×C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₁×D₁₆	—	2	2	no	—
5	C₁₁×D₃₂	—	2	2	no	—
6	C₁₁×D₃₂	C₂²	1	4	yes	complemented
7	C₂×C₁₁×C₃₂	C₂²	1	1	yes	characteristic
8	C₁₁×C₆₄	C₂²	1	2	yes	complemented
9	C₂×C₁₁×D₈	—	4	2	no	—
10	C₁₁×D₁₆	—	2	4	no	—
11	C₁₁×D₁₆	—	4	2	no	—
12	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
13	C₁₁×C₃₂	D₄	1	1	yes	characteristic
14	C₁₁×C₃₂	C₂³	1	1	yes	characteristic
15	C₂×D₆₄	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₂×D₄×C₁₁	—	8	2	no	—
17	C₁₁×D₈	—	4	4	no	—
18	C₁₁×D₈	—	8	2	no	—
19	C₂×C₈×C₁₁	D₈	1	1	yes	characteristic
20	C₁₁×C₁₆	D₈	1	1	yes	characteristic
21	C₁₁×C₁₆	C₂×D₄	1	1	yes	characteristic
22	C₂×D₃₂	C₂×C₁₁	1	2	yes	complemented
23	D₆₄	C₂×C₁₁	1	4	yes	direct product factor
24	C₂×C₆₄	C₂×C₁₁	1	1	yes	characteristic, complemented
25	C₂³×C₁₁	—	16	2	no	—
26	D₄×C₁₁	—	8	4	no	—
27	D₄×C₁₁	—	16	2	no	—
28	C₂×C₄×C₁₁	D₁₆	1	1	yes	characteristic
29	C₈×C₁₁	D₁₆	1	1	yes	characteristic
30	C₈×C₁₁	C₂×D₈	1	1	yes	characteristic
31	C₂×D₁₆	—	2	2	no	—
32	D₃₂	—	2	2	no	—
33	D₃₂	C₂²×C₁₁	1	4	yes	complemented
34	C₂×C₃₂	C₂²×C₁₁	1	1	yes	characteristic
35	C₆₄	C₂²×C₁₁	1	2	yes	complemented
36	C₂²×C₁₁	—	16	4	no	—
37	C₂²×C₁₁	—	32	4	no	—
38	C₂²×C₁₁	D₃₂	1	1	yes	characteristic
39	C₄×C₁₁	D₃₂	1	1	yes	characteristic
40	C₄×C₁₁	C₂×D₁₆	1	1	yes	characteristic
41	C₂×D₈	—	4	2	no	—
42	D₁₆	—	2	4	no	—
43	D₁₆	—	4	2	no	—
44	C₂×C₁₆	D₄×C₁₁	1	1	yes	characteristic
45	C₃₂	D₄×C₁₁	1	1	yes	characteristic
46	C₃₂	C₂³×C₁₁	1	1	yes	characteristic
47	C₂×C₁₁	—	32	4	no	—
48	C₂×C₁₁	D₆₄	1	2	yes	direct product factor
49	C₂×C₁₁	C₂×D₃₂	1	1	yes	characteristic
50	C₂×D₄	—	8	2	no	—
51	D₈	—	4	4	no	—
52	D₈	—	8	2	no	—
53	C₂×C₈	C₁₁×D₈	1	1	yes	characteristic
54	C₁₆	C₁₁×D₈	1	1	yes	characteristic
55	C₁₆	C₂×D₄×C₁₁	1	1	yes	characteristic
56	C₁₁	C₂×D₆₄	1	1	yes	characteristic, direct product factor, Sylow
57	C₂³	—	16	2	no	—
58	D₄	—	8	4	no	—
59	D₄	—	16	2	no	—
60	C₂×C₄	C₁₁×D₁₆	1	1	yes	characteristic
61	C₈	C₁₁×D₁₆	1	1	yes	characteristic
62	C₈	C₂×C₁₁×D₈	1	1	yes	characteristic
63	C₂²	—	16	4	no	—
64	C₂²	—	32	4	no	—
65	C₂²	C₁₁×D₃₂	1	1	yes	characteristic
66	C₄	C₁₁×D₃₂	1	1	yes	characteristic
67	C₄	C₂×C₁₁×D₁₆	1	1	yes	characteristic
68	C₂	—	32	4	no	—
69	C₂	C₁₁×D₆₄	1	2	yes	direct product factor
70	C₂	C₂×C₁₁×D₃₂	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁	D₃₂
commutator, Frattini, cosocle	C₃₂	C₂³×C₁₁
LCS	G ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₈×C₁₁ ◁ C₂×C₁₁×C₁₆ ◁ C₂×C₁₁×C₃₂ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₁×D₃₂	C₂	semidirect
2. C₁₁×D₆₄	C₂	direct (N × H)
3. C₂×C₁₁×C₆₄	C₂	semidirect
6. C₁₁×D₃₂	C₂²	semidirect
8. C₁₁×C₆₄	C₂²	semidirect
15. C₂×D₆₄	C₁₁	direct (N × H)
22. C₂×D₃₂	C₂×C₁₁	semidirect
23. D₆₄	C₂×C₁₁	direct (N × H)
24. C₂×C₆₄	C₂×C₁₁	semidirect
33. D₃₂	C₂²×C₁₁	semidirect
35. C₆₄	C₂²×C₁₁	semidirect
48. C₂×C₁₁	D₆₄	direct (N × H)
56. C₁₁	C₂×D₆₄	direct (N × H)
69. C₂	C₁₁×D₆₄	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×D₃₂	2
C₁₁×D₆₄	2
C₂×C₁₁×C₆₄	2
C₂×D₆₄	11

Subgroups — C2×C11×D64 #14590931

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×D₆₄ #14590931