Subgroups — C₂×D₇₀₄ #14674816

Order 2816.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂²	D₃₅₂
commutator, cosocle	C₁₁×C₃₂	C₂³
Frattini	C₃₂	C₂²×D₁₁
Fitting	C₂×C₁₁×C₆₄	C₂
socle	C₂²×C₁₁	D₃₂
hypercenter	C₂×C₆₄	D₁₁
hypocenter	C₁₁	C₂×D₆₄
LCS	G ▷ C₁₁×C₃₂ ▷ C₁₁×C₁₆ ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ C₂×C₆₄

Complements

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

N	H ≅ G/N	type
1. C₂×D₃₅₂	C₂	semidirect
2. D₇₀₄	C₂	direct (N × H)
3. C₂×C₁₁×C₆₄	C₂	semidirect
7. D₃₅₂	C₂²	semidirect
8. C₁₁×C₆₄	C₂²	semidirect
24. C₂×C₆₄	D₁₁	semidirect
35. C₆₄	C₂×D₁₁	semidirect
47. C₂×C₁₁	D₆₄	semidirect
56. C₁₁	C₂×D₆₄	semidirect
69. C₂	D₇₀₄	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×D₃₅₂	2
D₇₀₄	2
C₂×C₁₁×C₆₄	2
C₂×D₆₄	11

Subgroups — C2×D704 #14674816

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₇₀₄ #14674816