Subgroups — #23758126

Order 10048.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19097828	C₂	1	1	yes	maximal, characteristic
2	(C₂×#10597845)⋊C₄	C₂	1	1	yes	maximal, characteristic
3	#19097751	C₂	1	1	yes	maximal, characteristic
4	C₂²×#10597845	—	2	1	no	—
5	C₂×#11929441	—	2	1	no	—
6	C₂×Dic₃₁₄	C₄	1	1	yes	characteristic, complemented
7	C₂×C₄×D₁₅₇	C₂²	1	1	yes	characteristic
8	C₄⋊Dic₁₅₇	—	2	1	no	—
9	#14578931	—	2	1	no	—
10	C₄⋊C₄×C₁₅₇	C₄	1	1	yes	characteristic, complemented
11	C₂×#10597845	—	2	2	no	—
12	C₂×#10597845	—	4	1	no	—
13	C₂×#10597845	—	4	1	no	—
14	#11929441	—	4	1	no	—
15	C₂²×D₁₅₇	D₄	1	1	yes	characteristic
16	Dic₃₁₄	—	4	1	no	—
17	C₂×Dic₁₅₇	—	2	1	no	—
18	C₂×Dic₁₅₇	D₄	1	1	yes	characteristic
19	C₄×D₁₅₇	—	4	1	no	—
20	C₂×C₄×C₁₅₇	—	2	1	no	—
21	C₂×C₄×C₁₅₇	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₁₅₇	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×D₁₅₇	—	2	1	no	—
24	C₂×D₁₅₇	—	2	1	no	—
25	C₂×D₁₅₇	SD₁₆	1	1	yes	characteristic
26	C₂×D₁₅₇	Q₁₆	1	1	yes	characteristic
27	#10597845	—	4	2	no	—
28	C₄×C₁₅₇	—	2	1	no	—
29	C₄×C₁₅₇	—	4	1	no	—
30	Dic₁₅₇	—	2	1	no	—
31	Dic₁₅₇	—	4	1	no	—
32	C₂×C₁₅₇	#99	1	1	yes	characteristic
33	C₂×C₁₅₇	#103	1	1	yes	characteristic
34	C₂×C₁₅₇	#104	1	1	yes	characteristic
35	D₁₅₇	—	2	1	no	—
36	D₁₅₇	—	2	1	no	—
37	C₁₅₇	#328	1	1	yes	characteristic, complemented, Sylow
38	#328	—	157	1	no	maximal, Sylow
39	C₂²⋊Q₈	—	157	1	no	—
40	C₂²⋊C₈	—	157	1	no	—
41	#95	—	157	1	no	—
42	C₂×Q₈	—	157	1	no	—
43	C₂²×C₄	—	314	1	no	—
44	C₂²×C₄	—	157	1	no	—
45	C₂×C₈	—	314	1	no	—
46	C₄⋊C₄	—	314	1	no	—
47	C₄⋊C₄	#10597845	1	1	yes	characteristic, complemented
48	C₂²⋊C₄	—	314	1	no	—
49	C₂³	—	157	1	no	—
50	Q₈	—	628	1	no	—
51	C₂×C₄	—	2	1	no	—
52	C₂×C₄	—	314	2	no	—
53	C₂×C₄	—	314	1	no	—
54	C₂×C₄	—	628	1	no	—
55	C₂×C₄	—	628	1	no	—
56	C₂×C₄	—	628	1	no	—
57	C₂×C₄	—	157	1	no	—
58	C₂×C₄	C₂×#10597845	1	1	yes	characteristic
59	C₈	—	628	1	no	—
60	C₂²	—	314	1	no	—
61	C₂²	—	314	1	no	—
62	C₂²	—	157	1	no	—
63	C₂²	—	157	1	no	—
64	C₂²	C₂²⋊#10597845	1	1	yes	characteristic
65	C₄	—	2	1	no	—
66	C₄	—	4	1	no	—
67	C₄	—	314	1	no	—
68	C₄	—	628	2	no	—
69	C₄	—	628	1	no	—
70	C₂	—	314	1	no	—
71	C₂	—	314	1	no	—
72	C₂	#19097830	1	1	yes	characteristic
73	C₂	#19097834	1	1	yes	characteristic
74	C₂	#19097835	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#10597845
commutator	C₂×C₄×C₁₅₇	C₂×C₄
Frattini	C₂×C₄	C₂×#10597845
Fitting	C₄⋊C₄×C₁₅₇	C₄
socle	C₂²×C₁₅₇	C₂²⋊C₄
prime radical	C₂²×D₁₅₇	D₄
cosocle	C₂×C₄×D₁₅₇	C₂²
hypercenter	C₄⋊C₄	#10597845
hypocenter	C₁₅₇	#328
LCS	G ▷ C₂×C₄×C₁₅₇ ▷ C₂²×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
6. C₂×Dic₃₁₄	C₄	semidirect
10. C₄⋊C₄×C₁₅₇	C₄	semidirect
37. C₁₅₇	#328	semidirect
47. C₄⋊C₄	#10597845	semidirect