Subgroups — #23758140

Order 10048.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₅₇⋊M₁₆	C₂	1	1	yes	maximal, characteristic
2	#19097850	C₂	1	1	yes	maximal, characteristic
3	#19097728	C₂	1	1	yes	maximal, characteristic
4	#14578964	—	2	1	no	—
5	#14578963	—	2	1	no	—
6	D₁₅₇⋊C₈	C₄	1	2	yes	complemented
7	C₄⋊#10597845	—	2	1	no	—
8	C₂²⋊#10597845	—	2	1	no	—
9	C₄×#10597845	C₄	1	2	yes	complemented
10	C₂×C₄×D₁₅₇	C₂²	1	1	yes	characteristic
11	#14578933	—	2	1	no	—
12	#14578931	—	2	1	no	—
13	C₄×Dic₁₅₇	C₄	1	1	yes	characteristic, complemented
14	C₄²×C₁₅₇	C₄	1	1	yes	characteristic, complemented
15	C₂×#10597845	—	2	2	no	—
16	#11929441	—	2	2	no	—
17	C₂²×D₁₅₇	D₄	1	1	yes	characteristic
18	C₂×Dic₁₅₇	—	2	1	no	—
19	C₂×Dic₁₅₇	D₄	1	1	yes	characteristic
20	C₄×D₁₅₇	C₂×C₄	1	1	yes	characteristic
21	C₄×D₁₅₇	C₂×C₄	1	1	yes	characteristic
22	C₄×D₁₅₇	D₄	1	1	yes	characteristic
23	C₄×D₁₅₇	Q₈	1	1	yes	characteristic
24	C₂×C₄×C₁₅₇	—	2	1	no	—
25	C₂×C₄×C₁₅₇	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₁₅₇	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×D₁₅₇	—	4	1	no	—
28	C₂×D₁₅₇	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×D₁₅₇	C₄⋊C₄	1	1	yes	characteristic
30	#10597845	—	4	2	no	—
31	C₄×C₁₅₇	—	4	1	no	—
32	C₄×C₁₅₇	C₄²	1	1	yes	characteristic
33	C₄×C₁₅₇	C₄⋊C₄	1	1	yes	characteristic
34	Dic₁₅₇	—	4	1	no	—
35	Dic₁₅₇	C₂²⋊C₄	1	1	yes	characteristic
36	Dic₁₅₇	C₄⋊C₄	1	1	yes	characteristic
37	C₂×C₁₅₇	—	2	1	no	—
38	C₂×C₁₅₇	#95	1	1	yes	characteristic
39	D₁₅₇	—	2	1	no	—
40	D₁₅₇	—	2	1	no	—
41	C₁₅₇	H(3,ℤ/4)	1	1	yes	characteristic, complemented, Sylow
42	H(3,ℤ/4)	—	157	1	no	maximal, Sylow
43	C₂×M₁₆	—	157	1	no	—
44	#117	—	157	1	no	—
45	#117	—	157	1	no	—
46	C₂²×C₄	—	157	1	no	—
47	M₁₆	—	314	1	no	—
48	M₁₆	—	314	1	no	—
49	C₂×C₈	—	157	2	no	—
50	C₄⋊C₄	—	314	1	no	—
51	C₄⋊C₄	—	314	1	no	—
52	C₂²⋊C₄	—	314	1	no	—
53	C₂²⋊C₄	—	314	1	no	—
54	C₄²	—	157	2	no	—
55	C₄²	—	157	1	no	—
56	C₄²	#10597845	1	1	yes	characteristic, complemented
57	C₂³	—	157	1	no	—
58	C₂×C₄	—	2	1	no	—
59	C₂×C₄	—	314	2	no	—
60	C₂×C₄	—	314	1	no	—
61	C₂×C₄	—	157	1	no	—
62	C₂×C₄	—	157	1	no	—
63	C₂×C₄	—	157	1	no	—
64	C₂×C₄	—	157	1	no	—
65	C₂×C₄	—	157	1	no	—
66	C₂×C₄	C₂×#10597845	1	1	yes	characteristic
67	C₈	—	314	2	no	—
68	C₂²	—	628	1	no	—
69	C₂²	—	157	1	no	—
70	C₂²	—	157	1	no	—
71	C₂²	C₂²⋊#10597845	1	1	yes	characteristic
72	C₄	—	4	1	no	—
73	C₄	—	628	1	no	—
74	C₄	—	628	2	no	—
75	C₄	—	157	1	no	—
76	C₄	—	157	1	no	—
77	C₄	C₄×#10597845	1	1	yes	characteristic
78	C₄	C₄⋊#10597845	1	1	yes	characteristic
79	C₂	—	2	1	no	—
80	C₂	—	314	1	no	—
81	C₂	—	314	1	no	—
82	C₂	(C₂×#10597845)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄×#10597845
commutator	C₄×C₁₅₇	C₄²
Frattini	C₂×C₄	C₂×#10597845
Fitting	C₄²×C₁₅₇	C₄
socle	C₂×C₁₅₇	#95
prime radical	C₂²×D₁₅₇	D₄
cosocle	C₂×C₄×D₁₅₇	C₂²
hypercenter	C₄²	#10597845
hypocenter	C₁₅₇	H(3,ℤ/4)
LCS	G ▷ C₄×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
6. D₁₅₇⋊C₈	C₄	semidirect
9. C₄×#10597845	C₄	semidirect
13. C₄×Dic₁₅₇	C₄	semidirect
14. C₄²×C₁₅₇	C₄	semidirect
41. C₁₅₇	H(3,ℤ/4)	semidirect
56. C₄²	#10597845	semidirect