Subgroups — #23757633

Order 10048.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19097771	C₂	1	1	yes	maximal, characteristic, complemented
2	#19097759	C₂	1	1	yes	maximal, characteristic
3	#19097696	C₂	1	2	yes	maximal, complemented
4	#19097693	C₂	1	2	yes	maximal
5	#97×C₁₅₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₃₁₄	—	2	1	no	—
7	C₂×Dic₃₁₄	C₂²	1	1	yes	characteristic
8	C₂×D₆₂₈	C₂²	1	1	yes	characteristic
9	C₄⋊Dic₁₅₇	—	2	1	no	—
10	C₄⋊Dic₁₅₇	C₂²	1	2	yes	—
11	#14578931	—	2	1	no	—
12	#14578931	—	2	1	no	—
13	C₂×C₈×C₁₅₇	C₂²	1	2	yes	—
14	C₄²×C₁₅₇	C₂²	1	1	yes	characteristic
15	C₂²×D₁₅₇	—	2	1	no	—
16	Dic₃₁₄	—	2	2	no	—
17	Dic₃₁₄	—	4	2	no	—
18	D₆₂₈	—	2	2	no	—
19	C₂×Dic₁₅₇	—	2	2	no	—
20	C₂×Dic₁₅₇	—	2	1	no	—
21	C₂×C₄×C₁₅₇	D₄	1	1	yes	characteristic
22	C₂×C₄×C₁₅₇	D₄	1	1	yes	characteristic
23	C₂×C₄×C₁₅₇	C₂³	1	1	yes	characteristic
24	C₈×C₁₅₇	—	2	2	no	—
25	C₂²×C₁₅₇	C₂×D₄	1	1	yes	characteristic
26	C₂×D₁₅₇	—	4	1	no	—
27	C₂×D₁₅₇	—	4	1	no	—
28	C₂×D₁₅₇	—	4	1	no	—
29	C₄×C₁₅₇	—	2	1	no	—
30	C₄×C₁₅₇	—	2	1	no	—
31	C₄×C₁₅₇	#41	1	2	yes	—
32	Dic₁₅₇	—	4	1	no	—
33	Dic₁₅₇	—	4	2	no	—
34	C₂×C₁₅₇	#124	1	1	yes	characteristic
35	C₂×C₁₅₇	AGL(1,ℤ/8)	1	1	yes	characteristic
36	C₂×C₁₅₇	#137	1	1	yes	characteristic
37	D₁₅₇	—	8	1	no	—
38	C₁₅₇	#489	1	1	yes	characteristic, complemented, Sylow
39	#489	—	157	1	no	maximal, Sylow
40	C₄⋊Q₈	—	157	1	no	—
41	#124	—	157	1	no	—
42	#103	—	157	2	no	—
43	#102	—	157	2	no	—
44	#97	D₁₅₇	1	1	yes	characteristic, complemented
45	C₂×Q₈	—	314	1	no	—
46	C₂×Q₈	—	157	1	no	—
47	C₂×D₄	—	157	1	no	—
48	C₂×C₈	C₂×D₁₅₇	1	2	yes	—
49	C₄⋊C₄	—	314	1	no	—
50	C₄⋊C₄	—	157	2	no	—
51	C₂²⋊C₄	—	314	1	no	—
52	C₂²⋊C₄	—	314	1	no	—
53	C₄²	C₂×D₁₅₇	1	1	yes	characteristic
54	C₂³	—	314	1	no	—
55	Q₈	—	314	2	no	—
56	Q₈	—	628	2	no	—
57	D₄	—	314	2	no	—
58	C₂×C₄	—	314	1	no	—
59	C₂×C₄	—	314	2	no	—
60	C₂×C₄	D₆₂₈	1	1	yes	characteristic
61	C₂×C₄	D₆₂₈	1	1	yes	characteristic
62	C₂×C₄	C₂²×D₁₅₇	1	1	yes	characteristic
63	C₈	—	2	2	no	—
64	C₂²	—	628	1	no	—
65	C₂²	—	628	1	no	—
66	C₂²	—	628	1	no	—
67	C₂²	C₂×D₆₂₈	1	1	yes	characteristic
68	C₄	—	2	1	no	—
69	C₄	—	2	1	no	—
70	C₄	—	628	1	no	—
71	C₄	—	628	2	no	—
72	C₄	#14578954	1	2	yes	—
73	C₂	—	1256	1	no	—
74	C₂	#19097759	1	1	yes	characteristic
75	C₂	#19097799	1	1	yes	characteristic
76	C₂	#19097804	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₆₂₈
commutator, cosocle	C₂×C₄×C₁₅₇	C₂³
Frattini	C₂×C₄	C₂²×D₁₅₇
Fitting	#97×C₁₅₇	C₂
socle	C₂²×C₁₅₇	C₂×D₄
prime radical	C₂×D₆₂₈	C₂²
hypercenter	#97	D₁₅₇
hypocenter	C₁₅₇	#489
LCS	G ▷ C₂×C₄×C₁₅₇ ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

Complements

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

N	H ≅ G/N	type
1. #19097771	C₂	semidirect
3. #19097696	C₂	semidirect
5. #97×C₁₅₇	C₂	semidirect
38. C₁₅₇	#489	semidirect
44. #97	D₁₅₇	semidirect