Subgroups — C₂×D₃₃₉₂ #27305135

Order 13568.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₆₉₆	C₂	1	2	yes	maximal, complemented
2	D₃₃₉₂	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₅₃×C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₈₄₈	—	2	2	no	—
5	D₁₆₉₆	—	2	2	no	—
6	D₁₆₉₆	C₂²	1	4	yes	complemented
7	C₂×C₃₂×C₅₃	C₂²	1	1	yes	characteristic
8	C₅₃×C₆₄	C₂²	1	2	yes	complemented
9	C₂×D₄₂₄	—	4	2	no	—
10	D₈₄₈	—	2	4	no	—
11	D₈₄₈	—	4	2	no	—
12	C₂×C₁₆×C₅₃	D₄	1	1	yes	characteristic
13	C₃₂×C₅₃	D₄	1	1	yes	characteristic
14	C₃₂×C₅₃	C₂³	1	1	yes	characteristic
15	C₂×D₂₁₂	—	8	2	no	—
16	C₂×C₈×C₅₃	D₈	1	1	yes	characteristic
17	D₄₂₄	—	4	4	no	—
18	D₄₂₄	—	8	2	no	—
19	C₁₆×C₅₃	D₈	1	1	yes	characteristic
20	C₁₆×C₅₃	C₂×D₄	1	1	yes	characteristic
21	C₂²×D₅₃	—	16	2	no	—
22	C₂×C₄×C₅₃	D₁₆	1	1	yes	characteristic
23	D₂₁₂	—	8	4	no	—
24	D₂₁₂	—	16	2	no	—
25	C₈×C₅₃	D₁₆	1	1	yes	characteristic
26	C₈×C₅₃	C₂×D₈	1	1	yes	characteristic
27	C₂×D₆₄	—	53	1	no	maximal, Sylow
28	C₂²×C₅₃	D₃₂	1	1	yes	characteristic
29	C₂×D₅₃	—	16	4	no	—
30	C₂×D₅₃	—	32	4	no	—
31	C₄×C₅₃	D₃₂	1	1	yes	characteristic
32	C₄×C₅₃	C₂×D₁₆	1	1	yes	characteristic
33	C₂×D₃₂	—	53	2	no	—
34	D₆₄	—	53	4	no	—
35	C₂×C₆₄	D₅₃	1	1	yes	characteristic, complemented
36	C₂×C₅₃	D₆₄	1	2	yes	complemented
37	C₂×C₅₃	C₂×D₃₂	1	1	yes	characteristic
38	D₅₃	—	32	4	no	—
39	C₂×D₁₆	—	106	2	no	—
40	D₃₂	—	53	4	no	—
41	D₃₂	—	106	2	no	—
42	C₂×C₃₂	C₂×D₅₃	1	1	yes	characteristic
43	C₆₄	C₂×D₅₃	1	2	yes	complemented
44	C₅₃	C₂×D₆₄	1	1	yes	characteristic, complemented, Sylow
45	C₂×D₈	—	212	2	no	—
46	D₁₆	—	106	4	no	—
47	D₁₆	—	212	2	no	—
48	C₂×C₁₆	D₂₁₂	1	1	yes	characteristic
49	C₃₂	D₂₁₂	1	1	yes	characteristic
50	C₃₂	C₂²×D₅₃	1	1	yes	characteristic
51	C₂×D₄	—	424	2	no	—
52	D₈	—	424	2	no	—
53	D₈	—	212	4	no	—
54	C₂×C₈	D₄₂₄	1	1	yes	characteristic
55	C₁₆	D₄₂₄	1	1	yes	characteristic
56	C₁₆	C₂×D₂₁₂	1	1	yes	characteristic
57	C₂³	—	848	2	no	—
58	D₄	—	848	2	no	—
59	D₄	—	424	4	no	—
60	C₂×C₄	D₈₄₈	1	1	yes	characteristic
61	C₈	D₈₄₈	1	1	yes	characteristic
62	C₈	C₂×D₄₂₄	1	1	yes	characteristic
63	C₂²	—	848	4	no	—
64	C₂²	—	1696	4	no	—
65	C₂²	D₁₆₉₆	1	1	yes	characteristic
66	C₄	D₁₆₉₆	1	1	yes	characteristic
67	C₄	C₂×D₈₄₈	1	1	yes	characteristic
68	C₂	—	1696	4	no	—
69	C₂	D₃₃₉₂	1	2	yes	direct product factor
70	C₂	C₂×D₁₆₉₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₁₆₉₆
commutator, cosocle	C₃₂×C₅₃	C₂³
Frattini	C₃₂	C₂²×D₅₃
Fitting	C₂×C₅₃×C₆₄	C₂
socle	C₂²×C₅₃	D₃₂
hypercenter	C₂×C₆₄	D₅₃
hypocenter	C₅₃	C₂×D₆₄
LCS	G ▷ C₃₂×C₅₃ ▷ C₁₆×C₅₃ ▷ C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
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×D₁₆₉₆	C₂	semidirect
2. D₃₃₉₂	C₂	direct (N × H)
3. C₂×C₅₃×C₆₄	C₂	semidirect
6. D₁₆₉₆	C₂²	semidirect
8. C₅₃×C₆₄	C₂²	semidirect
35. C₂×C₆₄	D₅₃	semidirect
36. C₂×C₅₃	D₆₄	semidirect
43. C₆₄	C₂×D₅₃	semidirect
44. C₅₃	C₂×D₆₄	semidirect
69. C₂	D₃₃₉₂	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×D₁₆₉₆	2
D₃₃₉₂	2
C₂×C₅₃×C₆₄	2
C₂×D₆₄	53

Subgroups — C2×D3392 #27305135

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃₃₉₂ #27305135