Subgroups — C₂×D₄₅₆ #14269741

Order 1824.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₂₈	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄₅₆	C₂	1	4	yes	maximal, direct product factor
4	C₂×D₁₅₂	—	3	1	no	maximal, Hall
5	C₂²×D₅₇	—	2	2	no	—
6	C₂×C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
7	D₂₂₈	—	2	2	no	—
8	D₂₂₈	C₂²	1	4	yes	complemented
9	C₃×C₈×C₁₉	C₂²	1	2	yes	complemented
10	C₂×D₇₆	—	3	2	no	—
11	C₂×C₈×C₁₉	D₃	1	1	yes	characteristic, complemented
12	D₁₅₂	—	3	4	no	—
13	C₂²×C₃×C₁₉	D₄	1	1	yes	characteristic
14	C₂×D₅₇	—	2	4	no	—
15	C₂×D₅₇	—	4	4	no	—
16	C₃×C₄×C₁₉	D₄	1	1	yes	characteristic
17	C₃×C₄×C₁₉	C₂³	1	1	yes	characteristic
18	C₂²×D₁₉	—	6	2	no	—
19	C₂×C₄×C₁₉	C₂×D₃	1	1	yes	characteristic
20	D₇₆	—	3	4	no	—
21	D₇₆	—	6	2	no	—
22	C₈×C₁₉	C₂×D₃	1	2	yes	complemented
23	C₂×C₃×C₁₉	D₈	1	2	yes	complemented
24	C₂×C₃×C₁₉	C₂×D₄	1	1	yes	characteristic
25	D₅₇	—	4	4	no	—
26	C₂×D₂₄	—	19	1	no	maximal, Hall
27	C₂²×C₁₉	D₁₂	1	1	yes	characteristic
28	C₂×D₁₉	—	6	4	no	—
29	C₂×D₁₉	—	12	4	no	—
30	C₄×C₁₉	D₁₂	1	1	yes	characteristic
31	C₄×C₁₉	C₂²×D₃	1	1	yes	characteristic
32	C₃×C₁₉	C₂×D₈	1	1	yes	characteristic, complemented, Hall
33	C₂×D₁₂	—	19	2	no	—
34	C₂×C₃×C₈	D₁₉	1	1	yes	characteristic, complemented
35	D₂₄	—	19	4	no	—
36	C₂×C₁₉	D₂₄	1	2	yes	complemented
37	C₂×C₁₉	C₂×D₁₂	1	1	yes	characteristic
38	D₁₉	—	12	4	no	—
39	C₂×D₈	—	57	1	no	Sylow
40	C₂²×D₃	—	38	2	no	—
41	C₂×C₃×C₄	C₂×D₁₉	1	1	yes	characteristic
42	D₁₂	—	19	4	no	—
43	D₁₂	—	38	2	no	—
44	C₃×C₈	C₂×D₁₉	1	2	yes	complemented
45	C₁₉	C₂×D₂₄	1	1	yes	characteristic, complemented, Sylow
46	C₂×D₄	—	57	2	no	—
47	D₈	—	57	4	no	—
48	C₂×C₈	D₅₇	1	1	yes	characteristic, complemented
49	C₂²×C₃	D₇₆	1	1	yes	characteristic
50	C₂×D₃	—	38	4	no	—
51	C₂×D₃	—	76	4	no	—
52	C₃×C₄	D₇₆	1	1	yes	characteristic
53	C₃×C₄	C₂²×D₁₉	1	1	yes	characteristic
54	C₂³	—	114	2	no	—
55	D₄	—	57	4	no	—
56	D₄	—	114	2	no	—
57	C₂×C₄	C₂×D₅₇	1	1	yes	characteristic
58	C₈	C₂×D₅₇	1	2	yes	complemented
59	C₂×C₃	D₁₅₂	1	2	yes	complemented
60	C₂×C₃	C₂×D₇₆	1	1	yes	characteristic
61	D₃	—	76	4	no	—
62	C₂²	—	114	4	no	—
63	C₂²	—	228	4	no	—
64	C₂²	D₂₂₈	1	1	yes	characteristic
65	C₄	D₂₂₈	1	1	yes	characteristic
66	C₄	C₂²×D₅₇	1	1	yes	characteristic
67	C₃	C₂×D₁₅₂	1	1	yes	characteristic, complemented, Sylow
68	C₂	—	228	4	no	—
69	C₂	D₄₅₆	1	2	yes	direct product factor
70	C₂	C₂×D₂₂₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₂₂₈
commutator, cosocle	C₃×C₄×C₁₉	C₂³
Frattini	C₄	C₂²×D₅₇
Fitting	C₂×C₃×C₈×C₁₉	C₂
socle	C₂²×C₃×C₁₉	D₄
hypercenter	C₂×C₈	D₅₇
hypocenter	C₃×C₁₉	C₂×D₈
LCS	G ▷ C₃×C₄×C₁₉ ▷ C₂×C₃×C₁₉ ▷ C₃×C₁₉
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×D₂₂₈	C₂	semidirect
2. C₂×C₃×C₈×C₁₉	C₂	semidirect
3. D₄₅₆	C₂	direct (N × H)
8. D₂₂₈	C₂²	semidirect
9. C₃×C₈×C₁₉	C₂²	semidirect
11. C₂×C₈×C₁₉	D₃	semidirect
22. C₈×C₁₉	C₂×D₃	semidirect
23. C₂×C₃×C₁₉	D₈	semidirect
32. C₃×C₁₉	C₂×D₈	semidirect
34. C₂×C₃×C₈	D₁₉	semidirect
36. C₂×C₁₉	D₂₄	semidirect
44. C₃×C₈	C₂×D₁₉	semidirect
45. C₁₉	C₂×D₂₄	semidirect
48. C₂×C₈	D₅₇	semidirect
58. C₈	C₂×D₅₇	semidirect
59. C₂×C₃	D₁₅₂	semidirect
67. C₃	C₂×D₁₅₂	semidirect
69. C₂	D₄₅₆	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×D₂₂₈	2
C₂×C₃×C₈×C₁₉	2
D₄₅₆	2
C₂×D₁₅₂	3
C₂×D₂₄	19

Subgroups — C2×D456 #14269741

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₄₅₆ #14269741