Subgroups — #23757829

Order 10048.

222 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19097770	C₂	1	2	yes	maximal, complemented
2	#19097763	C₂	1	1	yes	maximal, characteristic, complemented
3	#19097749	C₂	1	4	yes	maximal
4	#19097736	C₂	1	4	yes	maximal, complemented
5	#19097729	C₂	1	2	yes	maximal
6	C₄²×D₁₅₇	C₂	1	1	yes	maximal, characteristic
7	#125×C₁₅₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Dic₃₁₄	C₂²	1	4	yes	—
9	C₂×C₄×D₁₅₇	C₂²	1	2	yes	—
10	C₂×C₄×D₁₅₇	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₁₅₇	C₂²	1	2	yes	—
12	#14578933	C₂²	1	4	yes	—
13	#14578933	C₂²	1	4	yes	—
14	#14578931	C₂²	1	4	yes	—
15	C₄×Dic₁₅₇	C₂²	1	2	yes	—
16	C₄×Dic₁₅₇	C₂²	1	1	yes	characteristic
17	C₄×Dic₁₅₇	C₂²	1	4	yes	—
18	C₄⋊C₄×C₁₅₇	C₂²	1	2	yes	—
19	C₄⋊C₄×C₁₅₇	C₂²	1	4	yes	—
20	C₄²×C₁₅₇	C₂²	1	1	yes	characteristic
21	C₂²×D₁₅₇	C₂³	1	1	yes	characteristic
22	Dic₃₁₄	—	2	8	no	—
23	C₂×Dic₁₅₇	C₂³	1	4	yes	—
24	C₂×Dic₁₅₇	C₂³	1	1	yes	characteristic
25	C₂×Dic₁₅₇	C₂³	1	2	yes	—
26	C₄×D₁₅₇	—	2	4	no	—
27	C₄×D₁₅₇	Q₈	1	4	yes	complemented
28	C₂×C₄×C₁₅₇	C₂³	1	2	yes	—
29	C₂×C₄×C₁₅₇	C₂³	1	4	yes	—
30	C₂×C₄×C₁₅₇	C₂³	1	1	yes	characteristic
31	C₂²×C₁₅₇	C₂⁴	1	1	yes	characteristic
32	C₂×D₁₅₇	—	2	2	no	—
33	C₂×D₁₅₇	C₂×Q₈	1	2	yes	—
34	C₄×C₁₅₇	—	2	2	no	—
35	C₄×C₁₅₇	—	2	4	no	—
36	C₄×C₁₅₇	C₂×Q₈	1	2	yes	—
37	Dic₁₅₇	—	2	4	no	—
38	Dic₁₅₇	C₂×Q₈	1	2	yes	—
39	Dic₁₅₇	#41	1	4	yes	—
40	C₂×C₁₅₇	C₂²×Q₈	1	1	yes	characteristic
41	C₂×C₁₅₇	C₂×#41	1	2	yes	—
42	D₁₅₇	—	2	2	no	—
43	C₁₅₇	#533	1	1	yes	characteristic, complemented, Sylow
44	#533	—	157	1	no	maximal, Sylow
45	C₄⋊Q₈	—	157	2	no	—
46	#125	—	157	1	no	—
47	#125	D₁₅₇	1	1	yes	characteristic, complemented
48	C₂²⋊Q₈	—	157	4	no	—
49	C₄×Q₈	—	157	4	no	—
50	#117	—	157	2	no	—
51	C₂×C₄²	—	157	1	no	—
52	C₂×Q₈	—	157	4	no	—
53	C₂²×C₄	—	157	2	no	—
54	C₂²×C₄	—	157	1	no	—
55	C₄⋊C₄	—	157	2	no	—
56	C₄⋊C₄	—	157	4	no	—
57	C₄⋊C₄	—	157	4	no	—
58	C₄⋊C₄	C₂×D₁₅₇	1	2	yes	—
59	C₄⋊C₄	C₂×D₁₅₇	1	4	yes	—
60	C₂²⋊C₄	—	157	4	no	—
61	C₄²	—	157	2	no	—
62	C₄²	—	157	1	no	—
63	C₄²	—	157	4	no	—
64	C₄²	C₂×D₁₅₇	1	1	yes	characteristic
65	C₂³	—	157	1	no	—
66	Q₈	—	314	8	no	—
67	C₂×C₄	—	314	4	no	—
68	C₂×C₄	—	157	4	no	—
69	C₂×C₄	—	157	1	no	—
70	C₂×C₄	—	157	2	no	—
71	C₂×C₄	—	157	4	no	—
72	C₂×C₄	C₂²×D₁₅₇	1	2	yes	—
73	C₂×C₄	C₂²×D₁₅₇	1	4	yes	—
74	C₂×C₄	C₂²×D₁₅₇	1	1	yes	characteristic
75	C₂²	—	314	2	no	—
76	C₂²	—	157	2	no	—
77	C₂²	C₂³×D₁₅₇	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	2	4	no	—
80	C₄	—	314	4	no	—
81	C₄	—	157	2	no	—
82	C₄	—	157	4	no	—
83	C₄	Q₈×D₁₅₇	1	2	yes	—
84	C₂	—	314	2	no	—
85	C₂	C₂×Q₈×D₁₅₇	1	1	yes	characteristic
86	C₂	#41×D₁₅₇	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₁₅₇
commutator, socle, cosocle	C₂²×C₁₅₇	C₂⁴
Fitting	#125×C₁₅₇	C₂
prime radical	C₂²×D₁₅₇	C₂³
hypercenter	#125	D₁₅₇
hypocenter	C₁₅₇	#533
LCS	G ▷ C₂²×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂² ◁ #125

Complements

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

N	H ≅ G/N	type
1. #19097770	C₂	semidirect
2. #19097763	C₂	semidirect
4. #19097736	C₂	semidirect
7. #125×C₁₅₇	C₂	semidirect
27. C₄×D₁₅₇	Q₈	semidirect
43. C₁₅₇	#533	semidirect
47. #125	D₁₅₇	semidirect