Subgroups — #23758188

Order 10048.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₅₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	#19097842	C₂	1	1	yes	maximal, characteristic, complemented
3	#19097794	C₂	1	1	yes	maximal, characteristic
4	#14578964	—	2	1	no	—
5	#14578957	—	2	1	no	—
6	#14578955	—	2	1	no	—
7	#14578941	—	2	1	no	—
8	D₁₂₅₆	C₄	1	1	yes	characteristic
9	C₈×D₁₅₇	C₂²	1	1	yes	characteristic
10	Q₁₆×C₁₅₇	C₄	1	1	yes	characteristic
11	#11929441	—	4	1	no	—
12	D₆₂₈	—	2	1	no	—
13	D₆₂₈	—	4	1	no	—
14	C₄×D₁₅₇	—	4	1	no	—
15	C₄×D₁₅₇	D₄	1	1	yes	characteristic
16	#11929434	D₄	1	1	yes	characteristic
17	Q₈×C₁₅₇	—	2	1	no	—
18	C₈×C₁₅₇	C₂×C₄	1	1	yes	characteristic
19	C₂×D₁₅₇	—	4	1	no	—
20	C₂×D₁₅₇	SD₁₆	1	1	yes	characteristic
21	C₄×C₁₅₇	—	4	1	no	—
22	C₄×C₁₅₇	C₂²⋊C₄	1	1	yes	characteristic
23	Dic₁₅₇	D₈	1	1	yes	characteristic
24	C₂×C₁₅₇	#102	1	1	yes	characteristic
25	D₁₅₇	—	2	1	no	—
26	D₁₅₇	—	8	1	no	—
27	C₁₅₇	#359	1	1	yes	characteristic, complemented, Sylow
28	#359	—	157	1	no	maximal, Sylow
29	#135	—	157	1	no	—
30	C₂×C₁₆	—	157	1	no	—
31	#108	—	157	1	no	—
32	#41	—	314	1	no	—
33	Q₁₆	#10597845	1	1	yes	characteristic
34	SD₁₆	—	314	1	no	—
35	D₈	—	157	1	no	—
36	M₁₆	—	314	1	no	—
37	C₂×C₈	—	157	1	no	—
38	C₁₆	—	314	1	no	—
39	Q₈	—	2	1	no	—
40	D₄	—	314	1	no	—
41	D₄	—	628	1	no	—
42	C₂×C₄	—	628	1	no	—
43	C₂×C₄	—	157	1	no	—
44	C₈	—	628	1	no	—
45	C₈	—	157	1	no	—
46	C₈	C₂×#10597845	1	1	yes	characteristic
47	C₂²	—	628	1	no	—
48	C₂²	—	157	1	no	—
49	C₄	—	4	1	no	—
50	C₄	—	157	1	no	—
51	C₄	C₂²⋊#10597845	1	1	yes	characteristic
52	C₂	—	314	1	no	—
53	C₂	—	1256	1	no	—
54	C₂	#19097833	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#19097833
commutator	C₈×C₁₅₇	C₂×C₄
Frattini	C₈	C₂×#10597845
Fitting	Q₁₆×C₁₅₇	C₄
socle	C₂×C₁₅₇	#102
prime radical	#19097794	C₂
cosocle	C₈×D₁₅₇	C₂²
hypercenter	Q₁₆	#10597845
hypocenter	C₁₅₇	#359
LCS	G ▷ C₈×C₁₅₇ ▷ C₄×C₁₅₇ ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
1. D₁₅₇⋊C₁₆	C₂	semidirect
2. #19097842	C₂	semidirect
27. C₁₅₇	#359	semidirect