Subgroups — D₁₁×D₆₄ #14674814

Order 2816.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₁×D₃₂	C₂	1	2	yes	maximal, complemented
2	D₇₀₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#13066828	C₂	1	2	yes	maximal, complemented
4	D₁₁×C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×D₆₄	C₂	1	1	yes	maximal, characteristic, complemented
6	D₁₁×D₁₆	—	2	2	no	—
7	C₁₁×D₃₂	C₂²	1	2	yes	complemented
8	#10622157	—	2	2	no	—
9	D₃₅₂	C₂²	1	2	yes	complemented
10	D₁₁×C₃₂	C₂²	1	1	yes	characteristic
11	C₁₁×C₆₄	C₂²	1	1	yes	characteristic, complemented
12	C₁₁⋊C₆₄	C₂²	1	1	yes	characteristic, complemented
13	D₈×D₁₁	—	4	2	no	—
14	C₁₁×D₁₆	—	2	2	no	—
15	#66890	—	4	2	no	—
16	D₁₇₆	—	2	2	no	—
17	C₁₆×D₁₁	D₄	1	1	yes	characteristic
18	C₁₁×C₃₂	C₂³	1	1	yes	characteristic
19	C₁₁⋊C₃₂	D₄	1	1	yes	characteristic
20	C₂×D₆₄	—	11	1	no	maximal, Sylow
21	D₄×D₁₁	—	8	2	no	—
22	C₁₁×D₈	—	4	2	no	—
23	#4323	—	8	2	no	—
24	D₈₈	—	4	2	no	—
25	C₈×D₁₁	D₈	1	1	yes	characteristic
26	C₁₁×C₁₆	C₂×D₄	1	1	yes	characteristic
27	C₁₁⋊C₁₆	D₈	1	1	yes	characteristic
28	C₂×D₃₂	—	11	2	no	—
29	D₆₄	—	11	2	no	—
30	D₆₄	—	11	1	no	—
31	D₆₄	D₁₁	1	1	yes	characteristic, direct product factor
32	C₂×C₆₄	—	11	1	no	—
33	C₂²×D₁₁	—	16	2	no	—
34	D₄×C₁₁	—	8	2	no	—
35	C₂²⋊D₁₁	—	16	2	no	—
36	D₄₄	—	8	2	no	—
37	C₄×D₁₁	D₁₆	1	1	yes	characteristic
38	C₈×C₁₁	C₂×D₈	1	1	yes	characteristic
39	C₁₁⋊C₈	D₁₆	1	1	yes	characteristic
40	C₂×D₁₆	—	22	2	no	—
41	D₃₂	—	11	2	no	—
42	D₃₂	—	22	2	no	—
43	D₃₂	C₂×D₁₁	1	2	yes	complemented
44	C₂×C₃₂	—	11	1	no	—
45	C₆₄	—	11	1	no	—
46	C₆₄	C₂×D₁₁	1	1	yes	characteristic, complemented
47	C₂²×C₁₁	—	16	2	no	—
48	C₂×D₁₁	—	16	2	no	—
49	C₂×D₁₁	—	32	4	no	—
50	C₂×D₁₁	D₃₂	1	1	yes	characteristic
51	C₄×C₁₁	C₂×D₁₆	1	1	yes	characteristic
52	Dic₁₁	D₃₂	1	1	yes	characteristic
53	C₂×D₈	—	44	2	no	—
54	D₁₆	—	2	2	no	—
55	D₁₆	—	22	2	no	—
56	D₁₆	—	44	2	no	—
57	C₂×C₁₆	—	11	1	no	—
58	C₃₂	—	11	1	no	—
59	C₃₂	C₂²×D₁₁	1	1	yes	characteristic
60	C₂×C₁₁	—	32	2	no	—
61	C₂×C₁₁	C₂×D₃₂	1	1	yes	characteristic
62	D₁₁	—	32	2	no	—
63	D₁₁	D₆₄	1	2	yes	direct product factor
64	C₂×D₄	—	88	2	no	—
65	D₈	—	4	2	no	—
66	D₈	—	44	2	no	—
67	D₈	—	88	2	no	—
68	C₂×C₈	—	11	1	no	—
69	C₁₆	—	11	1	no	—
70	C₁₆	D₄×D₁₁	1	1	yes	characteristic
71	C₁₁	C₂×D₆₄	1	1	yes	characteristic, complemented, Sylow
72	C₂³	—	176	2	no	—
73	D₄	—	8	2	no	—
74	D₄	—	88	2	no	—
75	D₄	—	176	2	no	—
76	C₂×C₄	—	11	1	no	—
77	C₈	—	11	1	no	—
78	C₈	D₈×D₁₁	1	1	yes	characteristic
79	C₂²	—	11	1	no	—
80	C₂²	—	16	2	no	—
81	C₂²	—	352	4	no	—
82	C₂²	—	176	2	no	—
83	C₄	—	11	1	no	—
84	C₄	D₁₁×D₁₆	1	1	yes	characteristic
85	C₂	—	11	2	no	—
86	C₂	—	32	2	no	—
87	C₂	—	352	2	no	—
88	C₂	D₁₁×D₃₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₁×D₃₂
commutator, cosocle	C₁₁×C₃₂	C₂³
Frattini	C₃₂	C₂²×D₁₁
Fitting	C₁₁×D₆₄	C₂
socle	C₂×C₁₁	C₂×D₃₂
hypercenter	D₆₄	D₁₁
hypocenter	C₁₁	C₂×D₆₄
LCS	G ▷ C₁₁×C₃₂ ▷ C₁₁×C₁₆ ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂ ◁ D₆₄

Complements

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

N	H ≅ G/N	type
1. D₁₁×D₃₂	C₂	semidirect
2. D₇₀₄	C₂	semidirect
3. #13066828	C₂	semidirect
4. D₁₁×C₆₄	C₂	semidirect
5. C₁₁×D₆₄	C₂	semidirect
7. C₁₁×D₃₂	C₂²	semidirect
9. D₃₅₂	C₂²	semidirect
11. C₁₁×C₆₄	C₂²	semidirect
12. C₁₁⋊C₆₄	C₂²	semidirect
31. D₆₄	D₁₁	direct (N × H)
43. D₃₂	C₂×D₁₁	semidirect
46. C₆₄	C₂×D₁₁	semidirect
63. D₁₁	D₆₄	direct (N × H)
71. C₁₁	C₂×D₆₄	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
D₁₁×D₃₂	2
D₇₀₄	2
#13066828	2
D₁₁×C₆₄	2
C₁₁×D₆₄	2
C₂×D₆₄	11

Subgroups — D11×D64 #14674814

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₁×D₆₄ #14674814