Subgroups — #23757670

Order 10048.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19097770	C₂	1	2	yes	maximal
2	#19097703	C₂	1	1	yes	maximal, characteristic
3	#19097702	C₂	1	2	yes	maximal
4	C₈×Dic₁₅₇	C₂	1	1	yes	maximal, characteristic
5	#106×C₁₅₇	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₃₁₄	—	2	2	no	—
7	C₂×#11929434	C₂²	1	1	yes	characteristic
8	C₄⋊Dic₁₅₇	C₂²	1	2	yes	—
9	#14578933	—	2	2	no	—
10	C₄×Dic₁₅₇	C₂²	1	1	yes	characteristic
11	C₂×C₈×C₁₅₇	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₁₅₇	C₂²	1	2	yes	—
13	Dic₃₁₄	—	4	4	no	—
14	C₂×Dic₁₅₇	—	2	2	no	—
15	C₂×Dic₁₅₇	D₄	1	2	yes	—
16	#11929434	Q₈	1	2	yes	complemented
17	C₂×C₄×C₁₅₇	—	2	2	no	—
18	C₂×C₄×C₁₅₇	C₂³	1	1	yes	characteristic
19	C₈×C₁₅₇	Q₈	1	2	yes	complemented
20	C₂²×C₁₅₇	C₂×D₄	1	1	yes	characteristic
21	C₄×C₁₅₇	—	4	2	no	—
22	C₄×C₁₅₇	C₂×Q₈	1	1	yes	characteristic
23	C₄×C₁₅₇	C₂×Q₈	1	1	yes	characteristic
24	Dic₁₅₇	—	4	2	no	—
25	Dic₁₅₇	SD₁₆	1	4	yes	—
26	C₂×C₁₅₇	C₄⋊Q₈	1	1	yes	characteristic
27	C₂×C₁₅₇	C₂×SD₁₆	1	2	yes	—
28	C₁₅₇	#498	1	1	yes	characteristic, complemented, Sylow
29	#498	—	157	1	no	maximal, Sylow
30	C₄⋊Q₈	—	157	2	no	—
31	#106	—	157	1	no	—
32	#106	—	157	2	no	—
33	#106	D₁₅₇	1	1	yes	characteristic
34	C₄×C₈	—	157	1	no	—
35	C₂×Q₈	—	314	2	no	—
36	C₂×C₈	—	157	1	no	—
37	C₂×C₈	C₂×D₁₅₇	1	1	yes	characteristic
38	C₄⋊C₄	—	314	2	no	—
39	C₄⋊C₄	—	157	2	no	—
40	C₄⋊C₄	C₂×D₁₅₇	1	2	yes	—
41	C₄²	—	157	1	no	—
42	Q₈	—	628	4	no	—
43	C₂×C₄	—	2	2	no	—
44	C₂×C₄	—	314	2	no	—
45	C₂×C₄	—	157	2	no	—
46	C₂×C₄	C₂²×D₁₅₇	1	1	yes	characteristic
47	C₈	—	157	2	no	—
48	C₈	Dic₃₁₄	1	2	yes	complemented
49	C₂²	D₄×D₁₅₇	1	1	yes	characteristic
50	C₄	—	4	2	no	—
51	C₄	—	628	2	no	—
52	C₄	—	157	4	no	—
53	C₄	Q₈×D₁₅₇	1	1	yes	characteristic
54	C₄	C₂×Dic₃₁₄	1	1	yes	characteristic
55	C₂	#19097770	1	1	yes	characteristic
56	C₂	SD₁₆×D₁₅₇	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₁₅₇
commutator, cosocle	C₂×C₄×C₁₅₇	C₂³
Frattini	C₂×C₄	C₂²×D₁₅₇
Fitting	#106×C₁₅₇	C₂
socle, prime radical	C₂²×C₁₅₇	C₂×D₄
hypercenter	#106	D₁₅₇
hypocenter	C₁₅₇	#498
LCS	G ▷ C₂×C₄×C₁₅₇ ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
16. #11929434	Q₈	semidirect
19. C₈×C₁₅₇	Q₈	semidirect
28. C₁₅₇	#498	semidirect
48. C₈	Dic₃₁₄	semidirect