Subgroups — #23758191

Order 10048.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19097846	C₂	1	1	yes	maximal, characteristic, complemented
2	#19097841	C₂	1	1	yes	maximal, characteristic, complemented
3	D₈×D₁₅₇	C₂	1	1	yes	maximal, characteristic
4	#14578964	—	2	1	no	—
5	#14578957	—	2	1	no	—
6	D₄×D₁₅₇	—	2	1	no	—
7	D₁₂₅₆	C₄	1	1	yes	characteristic
8	#14578939	—	2	1	no	—
9	C₈×D₁₅₇	C₂²	1	1	yes	characteristic
10	D₈×C₁₅₇	C₄	1	1	yes	characteristic
11	#11929441	—	4	1	no	—
12	C₂²×D₁₅₇	—	4	1	no	—
13	D₆₂₈	—	2	1	no	—
14	C₂²⋊D₁₅₇	—	4	1	no	—
15	C₄×D₁₅₇	D₄	1	1	yes	characteristic
16	#11929434	D₄	1	1	yes	characteristic
17	D₄×C₁₅₇	—	2	1	no	—
18	C₈×C₁₅₇	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₁₅₇	—	4	1	no	—
20	C₂×D₁₅₇	—	4	1	no	—
21	C₂×D₁₅₇	—	8	2	no	—
22	C₂×D₁₅₇	SD₁₆	1	1	yes	characteristic
23	C₄×C₁₅₇	C₂²⋊C₄	1	1	yes	characteristic
24	Dic₁₅₇	D₈	1	1	yes	characteristic
25	C₂×C₁₅₇	—	8	1	no	—
26	C₂×C₁₅₇	#102	1	1	yes	characteristic
27	D₁₅₇	—	2	1	no	—
28	D₁₅₇	—	8	1	no	—
29	C₁₅₇	#361	1	1	yes	characteristic, complemented, Sylow
30	#361	—	157	1	no	maximal, Sylow
31	C₂×D₈	—	157	1	no	—
32	M₃₂	—	157	1	no	—
33	#108	—	157	1	no	—
34	C₂×D₄	—	314	1	no	—
35	D₈	—	314	1	no	—
36	D₈	—	157	1	no	—
37	D₈	#10597845	1	1	yes	characteristic
38	M₁₆	—	314	1	no	—
39	C₂×C₈	—	157	1	no	—
40	C₁₆	—	314	1	no	—
41	C₂³	—	628	1	no	—
42	D₄	—	2	1	no	—
43	D₄	—	314	1	no	—
44	D₄	—	628	1	no	—
45	C₂×C₄	—	157	1	no	—
46	C₈	—	628	1	no	—
47	C₈	—	157	1	no	—
48	C₈	C₂×#10597845	1	1	yes	characteristic
49	C₂²	—	4	1	no	—
50	C₂²	—	628	1	no	—
51	C₂²	—	157	1	no	—
52	C₂²	—	1256	2	no	—
53	C₄	—	157	1	no	—
54	C₄	C₂²⋊#10597845	1	1	yes	characteristic
55	C₂	—	8	1	no	—
56	C₂	—	314	1	no	—
57	C₂	—	1256	1	no	—
58	C₂	#19097833	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#19097833
commutator	C₈×C₁₅₇	C₂×C₄
Frattini	C₈	C₂×#10597845
Fitting	D₈×C₁₅₇	C₄
socle	C₂×C₁₅₇	#102
prime radical	D₈×D₁₅₇	C₂
cosocle	C₈×D₁₅₇	C₂²
hypercenter	D₈	#10597845
hypocenter	C₁₅₇	#361
LCS	G ▷ C₈×C₁₅₇ ▷ C₄×C₁₅₇ ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. #19097846	C₂	semidirect
2. #19097841	C₂	semidirect
29. C₁₅₇	#361	semidirect