Subgroups — (C₂×#10597845)⋊C₈ #23758138

Order 10048.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₅₇⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#10597845	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×D₁₅₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×#10597845	C₄	1	2	yes	—
5	D₁₅₇⋊C₈	—	2	1	no	—
6	D₁₅₇⋊C₈	—	2	1	no	—
7	C₂×#11929441	C₄	1	2	yes	complemented
8	C₄×#10597845	—	2	1	no	—
9	C₄×#10597845	—	2	1	no	—
10	C₂×C₄×D₁₅₇	C₂²	1	1	yes	characteristic
11	C₂×#11929434	C₄	1	1	yes	characteristic, complemented
12	C₈×D₁₅₇	—	2	1	no	—
13	C₈×D₁₅₇	—	2	1	no	—
14	C₂×C₈×C₁₅₇	C₄	1	1	yes	characteristic, complemented
15	C₂×#10597845	—	2	2	no	—
16	C₂×#10597845	—	2	2	no	—
17	C₂×#10597845	C₈	1	4	yes	complemented
18	#11929441	—	2	2	no	—
19	C₂²×D₁₅₇	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₁₅₇	C₂×C₄	1	1	yes	characteristic
21	C₄×D₁₅₇	D₄	1	1	yes	characteristic
22	C₄×D₁₅₇	D₄	1	1	yes	characteristic
23	C₄×D₁₅₇	D₄	1	1	yes	characteristic
24	C₄×D₁₅₇	Q₈	1	1	yes	characteristic
25	#11929434	—	2	1	no	—
26	C₂×C₄×C₁₅₇	C₂×C₄	1	1	yes	characteristic
27	C₈×C₁₅₇	—	2	1	no	—
28	C₂²×C₁₅₇	C₄²	1	1	yes	characteristic
29	C₂×D₁₅₇	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×D₁₅₇	C₄⋊C₄	1	1	yes	characteristic
31	C₂×D₁₅₇	C₂×C₈	1	2	yes	—
32	C₂×D₁₅₇	M₁₆	1	2	yes	—
33	#10597845	—	2	4	no	—
34	C₄×C₁₅₇	C₂²⋊C₄	1	1	yes	characteristic
35	C₄×C₁₅₇	C₄⋊C₄	1	1	yes	characteristic
36	Dic₁₅₇	C₂²⋊C₄	1	1	yes	characteristic
37	Dic₁₅₇	C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₁₅₇	#95	1	1	yes	characteristic
39	C₂×C₁₅₇	C₄×C₈	1	1	yes	characteristic
40	C₂×C₁₅₇	#97	1	1	yes	characteristic
41	D₁₅₇	C₂²⋊C₈	1	2	yes	—
42	D₁₅₇	C₄⋊C₈	1	2	yes	—
43	C₁₅₇	#336	1	1	yes	characteristic, complemented, Sylow
44	#336	—	157	1	no	maximal, Sylow
45	C₂²×C₈	—	157	1	no	—
46	C₂²×C₈	—	157	1	no	—
47	C₂×C₄²	—	157	1	no	—
48	C₂²×C₄	—	157	2	no	—
49	C₂²×C₄	—	157	1	no	—
50	C₂×C₈	—	314	1	no	—
51	C₂×C₈	—	314	1	no	—
52	C₂×C₈	—	314	1	no	—
53	C₂×C₈	—	314	1	no	—
54	C₂×C₈	—	157	2	no	—
55	C₂×C₈	—	157	1	no	—
56	C₂×C₈	#10597845	1	1	yes	characteristic, complemented
57	C₄²	—	314	1	no	—
58	C₄²	—	314	1	no	—
59	C₂³	—	157	1	no	—
60	C₂×C₄	—	314	2	no	—
61	C₂×C₄	—	314	2	no	—
62	C₂×C₄	—	157	4	no	—
63	C₂×C₄	—	157	1	no	—
64	C₂×C₄	—	157	1	no	—
65	C₂×C₄	—	157	1	no	—
66	C₂×C₄	—	157	1	no	—
67	C₂×C₄	—	157	1	no	—
68	C₂×C₄	C₂×#10597845	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₈	—	314	2	no	—
71	C₈	—	314	1	no	—
72	C₂²	—	157	1	no	—
73	C₂²	—	157	1	no	—
74	C₂²	—	157	2	no	—
75	C₂²	—	157	2	no	—
76	C₂²	C₄×#10597845	1	1	yes	characteristic
77	C₄	—	314	4	no	—
78	C₄	—	157	1	no	—
79	C₄	—	157	1	no	—
80	C₄	C₂²⋊#10597845	1	1	yes	characteristic
81	C₄	C₄⋊#10597845	1	1	yes	characteristic
82	C₂	—	157	2	no	—
83	C₂	—	157	2	no	—
84	C₂	(C₂×#10597845)⋊C₄	1	1	yes	characteristic
85	C₂	C₈×#10597845	1	1	yes	characteristic
86	C₂	#19097825	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×#10597845
commutator	C₂×C₁₅₇	C₄×C₈
Fitting	C₂×C₈×C₁₅₇	C₄
socle	C₂²×C₁₅₇	C₄²
prime radical	C₂²×D₁₅₇	C₂×C₄
cosocle	C₂×C₄×D₁₅₇	C₂²
hypercenter	C₂×C₈	#10597845
hypocenter	C₁₅₇	#336
LCS	G ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
7. C₂×#11929441	C₄	semidirect
11. C₂×#11929434	C₄	semidirect
14. C₂×C₈×C₁₅₇	C₄	semidirect
17. C₂×#10597845	C₈	semidirect
43. C₁₅₇	#336	semidirect
56. C₂×C₈	#10597845	semidirect

Subgroups — (C2×#10597845)⋊C8 #23758138

Conjugacy classes of subgroups

Complements

Subgroups — (C₂×#10597845)⋊C₈ #23758138