Subgroups — #23758317

Order 10048.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19097859	C₂	1	2	yes	maximal, complemented
2	#19097842	C₂	1	1	yes	maximal, characteristic, complemented
3	#19097836	C₂	1	2	yes	maximal, complemented
4	C₈×#10597845	C₂	1	1	yes	maximal, characteristic, complemented
5	#19097794	C₂	1	1	yes	maximal, characteristic
6	#14578964	—	2	2	no	—
7	#14578964	C₂²	1	2	yes	—
8	D₁₅₇⋊C₈	—	2	2	no	—
9	D₁₅₇⋊C₈	C₂²	1	1	yes	characteristic
10	C₄×#10597845	C₂²	1	1	yes	characteristic
11	#14578955	C₂²	1	2	yes	—
12	#14578941	C₄	1	2	yes	complemented
13	D₁₂₅₆	C₄	1	1	yes	characteristic, complemented
14	C₈×D₁₅₇	C₂²	1	1	yes	characteristic
15	Q₁₆×C₁₅₇	C₄	1	1	yes	characteristic, complemented
16	C₂×#10597845	—	2	1	no	—
17	#11929441	—	2	2	no	—
18	#11929441	D₄	1	1	yes	characteristic
19	#11929441	D₄	1	1	yes	characteristic
20	D₆₂₈	—	2	2	no	—
21	D₆₂₈	C₂×C₄	1	2	yes	—
22	C₄×D₁₅₇	—	2	2	no	—
23	C₄×D₁₅₇	C₂³	1	1	yes	characteristic
24	#11929434	C₂×C₄	1	1	yes	characteristic
25	Q₈×C₁₅₇	C₂×C₄	1	2	yes	—
26	C₈×C₁₅₇	C₂×C₄	1	1	yes	characteristic
27	C₂×D₁₅₇	—	2	2	no	—
28	C₂×D₁₅₇	#41	1	1	yes	characteristic
29	#10597845	—	2	2	no	—
30	C₄×C₁₅₇	—	2	2	no	—
31	C₄×C₁₅₇	C₂²×C₄	1	1	yes	characteristic
32	Dic₁₅₇	C₂×D₄	1	1	yes	characteristic
33	C₂×C₁₅₇	C₄×D₄	1	1	yes	characteristic
34	D₁₅₇	—	2	1	no	—
35	D₁₅₇	—	4	2	no	—
36	C₁₅₇	#443	1	1	yes	characteristic, complemented, Sylow
37	#443	—	157	1	no	maximal, Sylow
38	#135	—	157	1	no	—
39	#131	—	157	2	no	—
40	#108	—	157	1	no	—
41	#104	—	157	2	no	—
42	C₄×C₈	—	157	1	no	—
43	#41	—	157	2	no	—
44	Q₁₆	#10597845	1	1	yes	characteristic, complemented
45	SD₁₆	—	157	2	no	—
46	D₈	—	157	1	no	—
47	M₁₆	—	314	2	no	—
48	M₁₆	—	157	2	no	—
49	C₂×C₈	—	314	2	no	—
50	C₂×C₈	—	157	1	no	—
51	C₂×C₈	—	157	1	no	—
52	C₄²	—	157	1	no	—
53	Q₈	C₂×#10597845	1	2	yes	—
54	D₄	—	314	2	no	—
55	D₄	—	157	2	no	—
56	C₂×C₄	—	314	2	no	—
57	C₂×C₄	—	314	1	no	—
58	C₂×C₄	—	157	1	no	—
59	C₈	—	314	2	no	—
60	C₈	—	157	1	no	—
61	C₈	—	157	1	no	—
62	C₈	—	157	1	no	—
63	C₈	C₂×#10597845	1	1	yes	characteristic
64	C₂²	—	314	2	no	—
65	C₂²	—	157	1	no	—
66	C₄	—	2	2	no	—
67	C₄	—	314	2	no	—
68	C₄	—	157	1	no	—
69	C₄	C₂²×#10597845	1	1	yes	characteristic
70	C₂	—	314	1	no	—
71	C₂	—	628	2	no	—
72	C₂	D₄×#10597845	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×#10597845
commutator	C₄×C₁₅₇	C₂²×C₄
Frattini	C₄	C₂²×#10597845
Fitting	Q₁₆×C₁₅₇	C₄
socle	C₂×C₁₅₇	C₄×D₄
prime radical	#19097794	C₂
cosocle	C₄×D₁₅₇	C₂³
hypercenter	Q₁₆	#10597845
hypocenter	C₁₅₇	#443
LCS	G ▷ C₄×C₁₅₇ ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
1. #19097859	C₂	semidirect
2. #19097842	C₂	semidirect
3. #19097836	C₂	semidirect
4. C₈×#10597845	C₂	semidirect
12. #14578941	C₄	semidirect
13. D₁₂₅₆	C₄	semidirect
15. Q₁₆×C₁₅₇	C₄	semidirect
36. C₁₅₇	#443	semidirect
44. Q₁₆	#10597845	semidirect