Subgroups — #23757572

Order 10048.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19097762	C₂	1	1	yes	maximal, characteristic, complemented
2	#19097733	C₂	1	1	yes	maximal, characteristic
3	#19097704	C₂	1	1	yes	maximal, characteristic, complemented
4	#19097700	C₂	1	1	yes	maximal, characteristic, complemented
5	#19097693	C₂	1	1	yes	maximal, characteristic
6	#19097691	C₂	1	1	yes	maximal, characteristic
7	#106×C₁₅₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₆₂₈	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₁₅₇	—	2	1	no	—
10	C₂×#11929434	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₁₅₇	—	2	1	no	—
12	C₄⋊Dic₁₅₇	C₂²	1	1	yes	characteristic
13	#14578933	—	2	1	no	—
14	#14578931	—	2	1	no	—
15	C₄×Dic₁₅₇	C₂²	1	1	yes	characteristic
16	C₂×C₈×C₁₅₇	C₂²	1	1	yes	characteristic
17	C₄⋊C₄×C₁₅₇	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₁₅₇	C₂²	1	1	yes	characteristic
19	C₂²×D₁₅₇	—	2	1	no	—
20	D₆₂₈	—	2	1	no	—
21	D₆₂₈	Q₈	1	2	yes	—
22	C₂×Dic₁₅₇	—	2	1	no	—
23	C₂×Dic₁₅₇	D₄	1	1	yes	characteristic
24	C₂×Dic₁₅₇	D₄	1	1	yes	characteristic
25	C₄×D₁₅₇	—	4	2	no	—
26	#11929434	—	2	1	no	—
27	C₂×C₄×C₁₅₇	—	2	1	no	—
28	C₂×C₄×C₁₅₇	—	2	1	no	—
29	C₂×C₄×C₁₅₇	C₂³	1	1	yes	characteristic
30	C₈×C₁₅₇	—	2	1	no	—
31	C₂²×C₁₅₇	C₂×D₄	1	1	yes	characteristic
32	C₂×D₁₅₇	—	2	2	no	—
33	C₂×D₁₅₇	—	4	1	no	—
34	C₂×D₁₅₇	—	4	1	no	—
35	C₄×C₁₅₇	—	4	1	no	—
36	C₄×C₁₅₇	—	4	1	no	—
37	C₄×C₁₅₇	C₂×Q₈	1	1	yes	characteristic
38	C₄×C₁₅₇	#41	1	1	yes	characteristic
39	Dic₁₅₇	—	2	1	no	—
40	Dic₁₅₇	—	2	1	no	—
41	Dic₁₅₇	—	4	1	no	—
42	C₂×C₁₅₇	C₂²⋊Q₈	1	1	yes	characteristic
43	C₂×C₁₅₇	#135	1	1	yes	characteristic
44	C₂×C₁₅₇	AGL(1,ℤ/8)	1	1	yes	characteristic
45	D₁₅₇	—	4	2	no	—
46	C₁₅₇	#478	1	1	yes	characteristic, complemented, Sylow
47	#478	—	157	1	no	maximal, Sylow
48	#125	—	157	1	no	—
49	C₄×D₄	—	157	1	no	—
50	#107	—	157	1	no	—
51	#106	D₁₅₇	1	1	yes	characteristic, complemented
52	C₄⋊C₈	—	157	1	no	—
53	#102	—	157	1	no	—
54	#102	—	157	1	no	—
55	C₂×D₄	—	157	1	no	—
56	C₂²×C₄	—	314	1	no	—
57	C₂×C₈	—	157	1	no	—
58	C₂×C₈	C₂×D₁₅₇	1	1	yes	characteristic
59	C₄⋊C₄	—	314	1	no	—
60	C₄⋊C₄	—	314	1	no	—
61	C₄⋊C₄	—	157	1	no	—
62	C₄⋊C₄	C₂×D₁₅₇	1	1	yes	characteristic
63	C₄⋊C₄	C₂×D₁₅₇	1	1	yes	characteristic
64	C₂²⋊C₄	—	314	1	no	—
65	C₄²	—	157	1	no	—
66	C₂³	—	314	1	no	—
67	D₄	—	314	1	no	—
68	D₄	—	157	2	no	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	314	1	no	—
72	C₂×C₄	—	628	2	no	—
73	C₂×C₄	—	157	1	no	—
74	C₂×C₄	—	157	1	no	—
75	C₂×C₄	C₂²×D₁₅₇	1	1	yes	characteristic
76	C₈	—	2	1	no	—
77	C₈	—	314	1	no	—
78	C₂²	—	314	2	no	—
79	C₂²	—	628	1	no	—
80	C₂²	—	628	1	no	—
81	C₂²	D₄×D₁₅₇	1	1	yes	characteristic
82	C₄	—	4	1	no	—
83	C₄	—	4	1	no	—
84	C₄	—	314	1	no	—
85	C₄	—	314	1	no	—
86	C₄	—	628	1	no	—
87	C₄	Q₈×D₁₅₇	1	1	yes	characteristic
88	C₄	#14578954	1	1	yes	characteristic
89	C₂	—	628	2	no	—
90	C₂	#19097749	1	1	yes	characteristic
91	C₂	#19097792	1	1	yes	characteristic
92	C₂	#19097798	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₅₇
commutator, cosocle	C₂×C₄×C₁₅₇	C₂³
Frattini	C₂×C₄	C₂²×D₁₅₇
Fitting	#106×C₁₅₇	C₂
socle	C₂²×C₁₅₇	C₂×D₄
prime radical	C₂×D₆₂₈	C₂²
hypercenter	#106	D₁₅₇
hypocenter	C₁₅₇	#478
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
1. #19097762	C₂	semidirect
3. #19097704	C₂	semidirect
4. #19097700	C₂	semidirect
7. #106×C₁₅₇	C₂	semidirect
46. C₁₅₇	#478	semidirect
51. #106	D₁₅₇	semidirect