Subgroups — C₂×D₅₆₉₆ #36475471

Order 22784.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₈₄₈	C₂	1	2	yes	maximal, complemented
2	D₅₆₉₆	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₆₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₄₂₄	—	2	2	no	—
5	D₂₈₄₈	—	2	2	no	—
6	D₂₈₄₈	C₂²	1	4	yes	complemented
7	C₂×C₃₂×C₈₉	C₂²	1	1	yes	characteristic
8	C₆₄×C₈₉	C₂²	1	2	yes	complemented
9	C₂×D₇₁₂	—	4	2	no	—
10	D₁₄₂₄	—	2	4	no	—
11	D₁₄₂₄	—	4	2	no	—
12	C₂×C₁₆×C₈₉	D₄	1	1	yes	characteristic
13	C₃₂×C₈₉	D₄	1	1	yes	characteristic
14	C₃₂×C₈₉	C₂³	1	1	yes	characteristic
15	C₂×D₃₅₆	—	8	2	no	—
16	D₇₁₂	—	4	4	no	—
17	D₇₁₂	—	8	2	no	—
18	C₂×C₈×C₈₉	D₈	1	1	yes	characteristic
19	C₁₆×C₈₉	D₈	1	1	yes	characteristic
20	C₁₆×C₈₉	C₂×D₄	1	1	yes	characteristic
21	C₂²×D₈₉	—	16	2	no	—
22	C₂×C₄×C₈₉	D₁₆	1	1	yes	characteristic
23	D₃₅₆	—	8	4	no	—
24	D₃₅₆	—	16	2	no	—
25	C₈×C₈₉	D₁₆	1	1	yes	characteristic
26	C₈×C₈₉	C₂×D₈	1	1	yes	characteristic
27	C₂²×C₈₉	D₃₂	1	1	yes	characteristic
28	C₂×D₈₉	—	16	4	no	—
29	C₂×D₈₉	—	32	4	no	—
30	C₄×C₈₉	D₃₂	1	1	yes	characteristic
31	C₄×C₈₉	C₂×D₁₆	1	1	yes	characteristic
32	C₂×D₆₄	—	89	1	no	maximal, Sylow
33	C₂×C₈₉	D₆₄	1	2	yes	complemented
34	C₂×C₈₉	C₂×D₃₂	1	1	yes	characteristic
35	D₈₉	—	32	4	no	—
36	C₂×D₃₂	—	89	2	no	—
37	D₆₄	—	89	4	no	—
38	C₂×C₆₄	D₈₉	1	1	yes	characteristic, complemented
39	C₈₉	C₂×D₆₄	1	1	yes	characteristic, complemented, Sylow
40	C₂×D₁₆	—	178	2	no	—
41	D₃₂	—	89	4	no	—
42	D₃₂	—	178	2	no	—
43	C₂×C₃₂	C₂×D₈₉	1	1	yes	characteristic
44	C₆₄	C₂×D₈₉	1	2	yes	complemented
45	C₂×D₈	—	356	2	no	—
46	D₁₆	—	356	2	no	—
47	D₁₆	—	178	4	no	—
48	C₂×C₁₆	D₃₅₆	1	1	yes	characteristic
49	C₃₂	D₃₅₆	1	1	yes	characteristic
50	C₃₂	C₂²×D₈₉	1	1	yes	characteristic
51	C₂×D₄	—	712	2	no	—
52	D₈	—	356	4	no	—
53	D₈	—	712	2	no	—
54	C₂×C₈	D₇₁₂	1	1	yes	characteristic
55	C₁₆	D₇₁₂	1	1	yes	characteristic
56	C₁₆	C₂×D₃₅₆	1	1	yes	characteristic
57	C₂³	—	1424	2	no	—
58	D₄	—	1424	2	no	—
59	D₄	—	712	4	no	—
60	C₂×C₄	D₁₄₂₄	1	1	yes	characteristic
61	C₈	D₁₄₂₄	1	1	yes	characteristic
62	C₈	C₂×D₇₁₂	1	1	yes	characteristic
63	C₂²	—	2848	4	no	—
64	C₂²	—	1424	4	no	—
65	C₂²	D₂₈₄₈	1	1	yes	characteristic
66	C₄	D₂₈₄₈	1	1	yes	characteristic
67	C₄	C₂×D₁₄₂₄	1	1	yes	characteristic
68	C₂	—	2848	4	no	—
69	C₂	D₅₆₉₆	1	2	yes	direct product factor
70	C₂	C₂×D₂₈₄₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₂₈₄₈
commutator, cosocle	C₃₂×C₈₉	C₂³
Frattini	C₃₂	C₂²×D₈₉
Fitting	C₂×C₆₄×C₈₉	C₂
socle	C₂²×C₈₉	D₃₂
hypercenter	C₂×C₆₄	D₈₉
hypocenter	C₈₉	C₂×D₆₄
LCS	G ▷ C₃₂×C₈₉ ▷ C₁₆×C₈₉ ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
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×D₂₈₄₈	C₂	semidirect
2. D₅₆₉₆	C₂	direct (N × H)
3. C₂×C₆₄×C₈₉	C₂	semidirect
6. D₂₈₄₈	C₂²	semidirect
8. C₆₄×C₈₉	C₂²	semidirect
33. C₂×C₈₉	D₆₄	semidirect
38. C₂×C₆₄	D₈₉	semidirect
39. C₈₉	C₂×D₆₄	semidirect
44. C₆₄	C₂×D₈₉	semidirect
69. C₂	D₅₆₉₆	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×D₂₈₄₈	2
D₅₆₉₆	2
C₂×C₆₄×C₈₉	2
C₂×D₆₄	89

Subgroups — C2×D5696 #36475471

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₅₆₉₆ #36475471