Subgroups — #23758170

Order 10048.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19097845	C₂	1	2	yes	maximal, complemented
2	C₂×#14578937	C₂	1	1	yes	maximal, characteristic
3	#14578957	—	2	2	no	—
4	C₂×C₄×D₁₅₇	C₄	1	1	yes	characteristic
5	#14578937	—	2	2	no	—
6	C₂×#11929434	C₂²	1	1	yes	characteristic
7	C₂×C₈×C₁₅₇	C₄	1	1	yes	characteristic
8	C₂²×D₁₅₇	C₈	1	1	yes	characteristic
9	C₂×Dic₁₅₇	C₈	1	1	yes	characteristic
10	C₄×D₁₅₇	—	2	1	no	—
11	C₄×D₁₅₇	—	2	1	no	—
12	#11929434	D₄	1	2	yes	—
13	C₂×C₄×C₁₅₇	C₂×C₄	1	1	yes	characteristic
14	C₈×C₁₅₇	—	2	1	no	—
15	C₂²×C₁₅₇	C₂×C₈	1	1	yes	characteristic
16	C₂×D₁₅₇	—	2	1	no	—
17	C₂×D₁₅₇	—	4	1	no	—
18	C₄×C₁₅₇	C₂²⋊C₄	1	1	yes	characteristic
19	C₄×C₁₅₇	M₁₆	1	1	yes	characteristic
20	Dic₁₅₇	—	2	1	no	—
21	C₂×C₁₅₇	—	2	1	no	—
22	C₂×C₁₅₇	C₂²⋊C₈	1	1	yes	characteristic
23	D₁₅₇	—	4	1	no	—
24	C₁₅₇	#349	1	1	yes	characteristic, complemented, Sylow
25	#349	—	157	1	no	maximal, Sylow
26	C₂×M₁₆	—	157	1	no	—
27	M₃₂	—	157	2	no	—
28	C₂²×C₄	—	157	1	no	—
29	M₁₆	—	314	2	no	—
30	C₂×C₈	—	157	1	no	—
31	C₂×C₈	#10597845	1	1	yes	characteristic
32	C₁₆	—	314	2	no	—
33	C₂³	—	157	1	no	—
34	C₂×C₄	—	314	1	no	—
35	C₂×C₄	—	314	1	no	—
36	C₂×C₄	—	157	1	no	—
37	C₂×C₄	C₂×#10597845	1	1	yes	characteristic
38	C₈	—	2	1	no	—
39	C₈	—	157	2	no	—
40	C₂²	—	314	1	no	—
41	C₂²	—	628	1	no	—
42	C₂²	D₁₅₇⋊C₈	1	1	yes	characteristic
43	C₄	—	314	1	no	—
44	C₄	C₂²⋊#10597845	1	1	yes	characteristic
45	C₄	#14578964	1	1	yes	characteristic
46	C₂	—	2	1	no	—
47	C₂	—	628	1	no	—
48	C₂	#19097828	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊#10597845
commutator	C₂²×C₁₅₇	C₂×C₈
Frattini	C₂×C₄	C₂×#10597845
Fitting	C₂×C₈×C₁₅₇	C₄
socle	C₂×C₁₅₇	C₂²⋊C₈
prime radical	C₂²×D₁₅₇	C₈
cosocle	C₂×#11929434	C₂²
hypercenter	C₂×C₈	#10597845
hypocenter	C₁₅₇	#349
LCS	G ▷ C₂²×C₁₅₇ ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
1. #19097845	C₂	semidirect
24. C₁₅₇	#349	semidirect