Subgroups — C₂×D₁₆₉₆ #20277013

Order 6784.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₈₄₈	C₂	1	2	yes	maximal, complemented
2	D₁₆₉₆	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₃₂×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄₂₄	—	2	2	no	—
5	D₈₄₈	—	2	2	no	—
6	D₈₄₈	C₂²	1	4	yes	complemented
7	C₂×C₁₆×C₅₃	C₂²	1	1	yes	characteristic
8	C₃₂×C₅₃	C₂²	1	2	yes	complemented
9	C₂×D₂₁₂	—	4	2	no	—
10	C₂×C₈×C₅₃	D₄	1	1	yes	characteristic
11	D₄₂₄	—	2	4	no	—
12	D₄₂₄	—	4	2	no	—
13	C₁₆×C₅₃	D₄	1	1	yes	characteristic
14	C₁₆×C₅₃	C₂³	1	1	yes	characteristic
15	C₂²×D₅₃	—	8	2	no	—
16	C₂×C₄×C₅₃	D₈	1	1	yes	characteristic
17	D₂₁₂	—	4	4	no	—
18	D₂₁₂	—	8	2	no	—
19	C₈×C₅₃	D₈	1	1	yes	characteristic
20	C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
21	C₂²×C₅₃	D₁₆	1	1	yes	characteristic
22	C₂×D₅₃	—	8	4	no	—
23	C₂×D₅₃	—	16	4	no	—
24	C₄×C₅₃	D₁₆	1	1	yes	characteristic
25	C₄×C₅₃	C₂×D₈	1	1	yes	characteristic
26	C₂×D₃₂	—	53	1	no	maximal, Sylow
27	C₂×C₅₃	D₃₂	1	2	yes	complemented
28	C₂×C₅₃	C₂×D₁₆	1	1	yes	characteristic
29	D₅₃	—	16	4	no	—
30	C₂×D₁₆	—	53	2	no	—
31	D₃₂	—	53	4	no	—
32	C₂×C₃₂	D₅₃	1	1	yes	characteristic, complemented
33	C₅₃	C₂×D₃₂	1	1	yes	characteristic, complemented, Sylow
34	C₂×D₈	—	106	2	no	—
35	D₁₆	—	53	4	no	—
36	D₁₆	—	106	2	no	—
37	C₂×C₁₆	C₂×D₅₃	1	1	yes	characteristic
38	C₃₂	C₂×D₅₃	1	2	yes	complemented
39	C₂×D₄	—	212	2	no	—
40	D₈	—	106	4	no	—
41	D₈	—	212	2	no	—
42	C₂×C₈	D₂₁₂	1	1	yes	characteristic
43	C₁₆	D₂₁₂	1	1	yes	characteristic
44	C₁₆	C₂²×D₅₃	1	1	yes	characteristic
45	C₂³	—	424	2	no	—
46	D₄	—	424	2	no	—
47	D₄	—	212	4	no	—
48	C₂×C₄	D₄₂₄	1	1	yes	characteristic
49	C₈	D₄₂₄	1	1	yes	characteristic
50	C₈	C₂×D₂₁₂	1	1	yes	characteristic
51	C₂²	—	848	4	no	—
52	C₂²	—	424	4	no	—
53	C₂²	D₈₄₈	1	1	yes	characteristic
54	C₄	D₈₄₈	1	1	yes	characteristic
55	C₄	C₂×D₄₂₄	1	1	yes	characteristic
56	C₂	—	848	4	no	—
57	C₂	D₁₆₉₆	1	2	yes	direct product factor
58	C₂	C₂×D₈₄₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₈₄₈
commutator	C₁₆×C₅₃	C₂³
Frattini	C₁₆	C₂²×D₅₃
Fitting	C₂×C₃₂×C₅₃	C₂
socle	C₂²×C₅₃	D₁₆
hypercenter	C₂×C₃₂	D₅₃
hypocenter	C₅₃	C₂×D₃₂
LCS	G ▷ C₁₆×C₅₃ ▷ C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
1. C₂×D₈₄₈	C₂	semidirect
2. D₁₆₉₆	C₂	direct (N × H)
3. C₂×C₃₂×C₅₃	C₂	semidirect
6. D₈₄₈	C₂²	semidirect
8. C₃₂×C₅₃	C₂²	semidirect
27. C₂×C₅₃	D₃₂	semidirect
32. C₂×C₃₂	D₅₃	semidirect
33. C₅₃	C₂×D₃₂	semidirect
38. C₃₂	C₂×D₅₃	semidirect
57. C₂	D₁₆₉₆	direct (N × H)

Subgroups — C2×D1696 #20277013

Conjugacy classes of subgroups

Complements

Subgroups — C₂×D₁₆₉₆ #20277013