Subgroups — C₈×D₆₂₈ #23757340

Order 10048.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₁₅₇	C₂	1	2	yes	maximal, complemented
2	C₄×D₆₂₈	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#11929434	C₂	1	1	yes	maximal, characteristic, complemented
4	#19097683	C₂	1	2	yes	maximal, complemented
5	C₄×C₈×C₁₅₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₆₂₈	C₄	1	1	yes	characteristic
7	C₂×C₄×D₁₅₇	C₂²	1	2	yes	—
8	C₂×#11929434	C₂²	1	2	yes	—
9	C₈×D₁₅₇	—	2	4	no	—
10	C₄⋊Dic₁₅₇	C₄	1	1	yes	characteristic
11	#14578931	C₄	1	2	yes	—
12	C₂×C₈×C₁₅₇	C₂²	1	1	yes	characteristic
13	C₂×C₈×C₁₅₇	C₂²	1	1	yes	characteristic
14	C₄²×C₁₅₇	C₂²	1	1	yes	characteristic
15	C₂²×D₁₅₇	C₂×C₄	1	2	yes	—
16	D₆₂₈	C₈	1	4	yes	direct product factor
17	C₂×Dic₁₅₇	C₂×C₄	1	2	yes	—
18	C₄×D₁₅₇	—	2	2	no	—
19	C₄×D₁₅₇	—	2	2	no	—
20	#11929434	—	2	2	no	—
21	C₂×C₄×C₁₅₇	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄×C₁₅₇	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄×C₁₅₇	C₂³	1	1	yes	characteristic
24	C₈×C₁₅₇	—	2	1	no	—
25	C₈×C₁₅₇	D₄	1	2	yes	complemented
26	C₂²×C₁₅₇	C₂²×C₄	1	1	yes	characteristic
27	C₂×D₁₅₇	—	2	2	no	—
28	C₂×D₁₅₇	—	2	2	no	—
29	C₂×D₁₅₇	C₂×C₈	1	4	yes	complemented
30	C₄×C₁₅₇	—	2	1	no	—
31	C₄×C₁₅₇	C₂×C₈	1	2	yes	complemented
32	C₄×C₁₅₇	C₂×D₄	1	1	yes	characteristic
33	C₄×C₁₅₇	#41	1	1	yes	characteristic
34	Dic₁₅₇	—	2	2	no	—
35	C₂×C₁₅₇	C₄×D₄	1	1	yes	characteristic
36	C₂×C₁₅₇	C₂²×C₈	1	1	yes	characteristic
37	C₂×C₁₅₇	#131	1	1	yes	characteristic
38	D₁₅₇	—	2	4	no	—
39	C₁₅₇	C₈×D₄	1	1	yes	characteristic, complemented, Sylow
40	C₈×D₄	—	157	1	no	maximal, Sylow
41	C₂²×C₈	—	157	2	no	—
42	C₄×D₄	—	157	1	no	—
43	C₄⋊C₈	—	157	1	no	—
44	C₂²⋊C₈	—	157	2	no	—
45	C₄×C₈	D₁₅₇	1	1	yes	characteristic, complemented
46	C₂×D₄	—	157	1	no	—
47	C₂²×C₄	—	157	2	no	—
48	C₂×C₈	—	314	4	no	—
49	C₂×C₈	—	157	2	no	—
50	C₂×C₈	C₂×D₁₅₇	1	1	yes	characteristic
51	C₂×C₈	C₂×D₁₅₇	1	1	yes	characteristic
52	C₄⋊C₄	—	157	1	no	—
53	C₂²⋊C₄	—	157	2	no	—
54	C₄²	C₂×D₁₅₇	1	1	yes	characteristic
55	C₂³	—	157	2	no	—
56	D₄	—	157	4	no	—
57	C₂×C₄	—	314	2	no	—
58	C₂×C₄	—	314	2	no	—
59	C₂×C₄	—	157	2	no	—
60	C₂×C₄	C₄×D₁₅₇	1	1	yes	characteristic
61	C₂×C₄	C₄×D₁₅₇	1	1	yes	characteristic
62	C₂×C₄	C₂²×D₁₅₇	1	1	yes	characteristic
63	C₈	—	2	1	no	—
64	C₈	—	314	2	no	—
65	C₈	D₆₂₈	1	2	yes	direct product factor
66	C₂²	—	314	2	no	—
67	C₂²	—	314	2	no	—
68	C₂²	—	157	4	no	—
69	C₂²	C₂×C₄×D₁₅₇	1	1	yes	characteristic
70	C₄	—	2	1	no	—
71	C₄	—	314	2	no	—
72	C₄	C₈×D₁₅₇	1	2	yes	complemented
73	C₄	C₂×D₆₂₈	1	1	yes	characteristic
74	C₄	#14578954	1	1	yes	characteristic
75	C₂	—	314	4	no	—
76	C₂	C₄×D₆₂₈	1	1	yes	characteristic
77	C₂	C₂×C₈×D₁₅₇	1	1	yes	characteristic
78	C₂	#19097777	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₁₅₇
commutator	C₂×C₁₅₇	C₂²×C₈
Frattini	C₂×C₄	C₂²×D₁₅₇
Fitting	C₄×C₈×C₁₅₇	C₂
socle	C₂²×C₁₅₇	C₂²×C₄
prime radical	C₂×D₆₂₈	C₄
cosocle	C₂×C₄×C₁₅₇	C₂³
hypercenter	C₄×C₈	D₁₅₇
hypocenter	C₁₅₇	C₈×D₄
LCS	G ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₈×D₁₅₇	C₂	semidirect
3. C₄⋊#11929434	C₂	semidirect
4. #19097683	C₂	semidirect
5. C₄×C₈×C₁₅₇	C₂	semidirect
16. D₆₂₈	C₈	direct (N × H)
25. C₈×C₁₅₇	D₄	semidirect
29. C₂×D₁₅₇	C₂×C₈	semidirect
31. C₄×C₁₅₇	C₂×C₈	semidirect
39. C₁₅₇	C₈×D₄	semidirect
45. C₄×C₈	D₁₅₇	semidirect
65. C₈	D₆₂₈	direct (N × H)
72. C₄	C₈×D₁₅₇	semidirect

Subgroups — C8×D628 #23757340

Conjugacy classes of subgroups

Complements

Subgroups — C₈×D₆₂₈ #23757340