Subgroups — #23758313

Order 10048.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#10597845	C₂	1	2	yes	maximal
2	#19097839	C₂	1	1	yes	maximal, characteristic
3	#19097834	C₂	1	2	yes	maximal
4	#19097825	C₂	1	1	yes	maximal, characteristic
5	Q₁₆×D₁₅₇	C₂	1	1	yes	maximal, characteristic
6	D₁₅₇⋊C₈	C₂²	1	1	yes	characteristic
7	C₄⋊#10597845	—	2	2	no	—
8	C₄⋊#10597845	C₂²	1	2	yes	—
9	C₄×#10597845	—	2	2	no	—
10	C₄×#10597845	C₂²	1	1	yes	characteristic
11	Q₈×D₁₅₇	C₂²	1	2	yes	—
12	Dic₆₂₈	C₄	1	1	yes	characteristic, complemented
13	#14578944	C₄	1	2	yes	complemented
14	C₈×D₁₅₇	C₂²	1	1	yes	characteristic
15	Q₁₆×C₁₅₇	C₄	1	1	yes	characteristic, complemented
16	C₂×#10597845	—	2	2	no	—
17	C₂×#10597845	D₄	1	2	yes	—
18	#11929441	—	2	1	no	—
19	Dic₃₁₄	—	2	2	no	—
20	Dic₃₁₄	C₂×C₄	1	2	yes	—
21	C₄×D₁₅₇	—	2	2	no	—
22	C₄×D₁₅₇	C₂³	1	1	yes	characteristic
23	#11929434	C₂×C₄	1	1	yes	characteristic
24	Q₈×C₁₅₇	C₂×C₄	1	2	yes	—
25	C₈×C₁₅₇	C₂×C₄	1	1	yes	characteristic
26	C₂×D₁₅₇	C₂×D₄	1	1	yes	characteristic
27	#10597845	—	2	2	no	—
28	#10597845	—	4	2	no	—
29	C₄×C₁₅₇	—	2	2	no	—
30	C₄×C₁₅₇	C₂²×C₄	1	1	yes	characteristic
31	Dic₁₅₇	—	2	2	no	—
32	Dic₁₅₇	#41	1	1	yes	characteristic
33	C₂×C₁₅₇	C₄×D₄	1	1	yes	characteristic
34	D₁₅₇	#137	1	2	yes	—
35	C₁₅₇	#441	1	1	yes	characteristic, complemented, Sylow
36	#441	—	157	1	no	maximal, Sylow
37	C₂×Q₁₆	—	157	1	no	—
38	C₄×Q₈	—	157	2	no	—
39	#106	—	157	1	no	—
40	#103	—	157	2	no	—
41	#97	—	157	1	no	—
42	C₂×Q₈	—	157	2	no	—
43	Q₁₆	—	157	2	no	—
44	Q₁₆	—	157	1	no	—
45	Q₁₆	#10597845	1	1	yes	characteristic, complemented
46	C₂×C₈	—	157	1	no	—
47	C₂×C₈	—	157	1	no	—
48	C₄⋊C₄	—	314	2	no	—
49	C₄⋊C₄	—	157	2	no	—
50	C₄²	—	314	2	no	—
51	C₄²	—	157	1	no	—
52	Q₈	—	314	2	no	—
53	Q₈	—	157	2	no	—
54	Q₈	C₂×#10597845	1	2	yes	—
55	C₂×C₄	—	314	2	no	—
56	C₂×C₄	—	314	2	no	—
57	C₂×C₄	—	157	2	no	—
58	C₂×C₄	—	157	1	no	—
59	C₈	—	314	1	no	—
60	C₈	—	157	1	no	—
61	C₈	C₂×#10597845	1	1	yes	characteristic
62	C₂²	—	157	1	no	—
63	C₄	—	2	2	no	—
64	C₄	—	314	2	no	—
65	C₄	—	314	2	no	—
66	C₄	—	628	2	no	—
67	C₄	—	157	1	no	—
68	C₄	C₂²×#10597845	1	1	yes	characteristic
69	C₂	—	157	2	no	—
70	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	C₂×D₁₅₇	C₂×D₄
cosocle	C₄×D₁₅₇	C₂³
hypercenter	Q₁₆	#10597845
hypocenter	C₁₅₇	#441
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
12. Dic₆₂₈	C₄	semidirect
13. #14578944	C₄	semidirect
15. Q₁₆×C₁₅₇	C₄	semidirect
35. C₁₅₇	#441	semidirect
45. Q₁₆	#10597845	semidirect