Subgroups — C₂×D₃₁₂ #11928965

Order 1248.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₅₆	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃₁₂	C₂	1	4	yes	maximal, direct product factor
4	C₂×D₁₀₄	—	3	1	no	maximal, Hall
5	C₂²×D₃₉	—	2	2	no	—
6	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
7	D₁₅₆	—	2	2	no	—
8	D₁₅₆	C₂²	1	4	yes	complemented
9	C₃×C₈×C₁₃	C₂²	1	2	yes	complemented
10	C₂×D₅₂	—	3	2	no	—
11	C₂×C₈×C₁₃	D₃	1	1	yes	characteristic, complemented
12	D₁₀₄	—	3	4	no	—
13	C₂²×C₃×C₁₃	D₄	1	1	yes	characteristic
14	C₂×D₃₉	—	2	4	no	—
15	C₂×D₃₉	—	4	4	no	—
16	C₃×C₄×C₁₃	D₄	1	1	yes	characteristic
17	C₃×C₄×C₁₃	C₂³	1	1	yes	characteristic
18	C₂²×D₁₃	—	6	2	no	—
19	C₂×C₄×C₁₃	C₂×D₃	1	1	yes	characteristic
20	D₅₂	—	3	4	no	—
21	D₅₂	—	6	2	no	—
22	C₈×C₁₃	C₂×D₃	1	2	yes	complemented
23	C₂×D₂₄	—	13	1	no	maximal, Hall
24	C₂×C₃×C₁₃	D₈	1	2	yes	complemented
25	C₂×C₃×C₁₃	C₂×D₄	1	1	yes	characteristic
26	D₃₉	—	4	4	no	—
27	C₂²×C₁₃	D₁₂	1	1	yes	characteristic
28	C₂×D₁₃	—	6	4	no	—
29	C₂×D₁₃	—	12	4	no	—
30	C₄×C₁₃	D₁₂	1	1	yes	characteristic
31	C₄×C₁₃	C₂²×D₃	1	1	yes	characteristic
32	C₂×D₁₂	—	13	2	no	—
33	C₂×C₃×C₈	D₁₃	1	1	yes	characteristic, complemented
34	D₂₄	—	13	4	no	—
35	C₃×C₁₃	C₂×D₈	1	1	yes	characteristic, complemented, Hall
36	C₂×D₈	—	39	1	no	Sylow
37	C₂×C₁₃	D₂₄	1	2	yes	complemented
38	C₂×C₁₃	C₂×D₁₂	1	1	yes	characteristic
39	D₁₃	—	12	4	no	—
40	C₂²×D₃	—	26	2	no	—
41	C₂×C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
42	D₁₂	—	13	4	no	—
43	D₁₂	—	26	2	no	—
44	C₃×C₈	C₂×D₁₃	1	2	yes	complemented
45	C₂×D₄	—	39	2	no	—
46	D₈	—	39	4	no	—
47	C₂×C₈	D₃₉	1	1	yes	characteristic, complemented
48	C₁₃	C₂×D₂₄	1	1	yes	characteristic, complemented, Sylow
49	C₂²×C₃	D₅₂	1	1	yes	characteristic
50	C₂×D₃	—	26	4	no	—
51	C₂×D₃	—	52	4	no	—
52	C₃×C₄	D₅₂	1	1	yes	characteristic
53	C₃×C₄	C₂²×D₁₃	1	1	yes	characteristic
54	C₂³	—	78	2	no	—
55	D₄	—	39	4	no	—
56	D₄	—	78	2	no	—
57	C₂×C₄	C₂×D₃₉	1	1	yes	characteristic
58	C₈	C₂×D₃₉	1	2	yes	complemented
59	C₂×C₃	D₁₀₄	1	2	yes	complemented
60	C₂×C₃	C₂×D₅₂	1	1	yes	characteristic
61	D₃	—	52	4	no	—
62	C₂²	—	78	4	no	—
63	C₂²	—	156	4	no	—
64	C₂²	D₁₅₆	1	1	yes	characteristic
65	C₄	D₁₅₆	1	1	yes	characteristic
66	C₄	C₂²×D₃₉	1	1	yes	characteristic
67	C₃	C₂×D₁₀₄	1	1	yes	characteristic, complemented, Sylow
68	C₂	—	156	4	no	—
69	C₂	D₃₁₂	1	2	yes	direct product factor
70	C₂	C₂×D₁₅₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₁₅₆
commutator, cosocle	C₃×C₄×C₁₃	C₂³
Frattini	C₄	C₂²×D₃₉
Fitting	C₂×C₃×C₈×C₁₃	C₂
socle	C₂²×C₃×C₁₃	D₄
hypercenter	C₂×C₈	D₃₉
hypocenter	C₃×C₁₃	C₂×D₈
LCS	G ▷ C₃×C₄×C₁₃ ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×D₁₅₆	C₂	semidirect
2. C₂×C₃×C₈×C₁₃	C₂	semidirect
3. D₃₁₂	C₂	direct (N × H)
8. D₁₅₆	C₂²	semidirect
9. C₃×C₈×C₁₃	C₂²	semidirect
11. C₂×C₈×C₁₃	D₃	semidirect
22. C₈×C₁₃	C₂×D₃	semidirect
24. C₂×C₃×C₁₃	D₈	semidirect
33. C₂×C₃×C₈	D₁₃	semidirect
35. C₃×C₁₃	C₂×D₈	semidirect
37. C₂×C₁₃	D₂₄	semidirect
44. C₃×C₈	C₂×D₁₃	semidirect
47. C₂×C₈	D₃₉	semidirect
48. C₁₃	C₂×D₂₄	semidirect
58. C₈	C₂×D₃₉	semidirect
59. C₂×C₃	D₁₀₄	semidirect
67. C₃	C₂×D₁₀₄	semidirect
69. C₂	D₃₁₂	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×D₁₅₆	2
C₂×C₃×C₈×C₁₃	2
D₃₁₂	2
C₂×D₁₀₄	3
C₂×D₂₄	13

Subgroups — C2×D312 #11928965

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃₁₂ #11928965