Subgroups — #23757885

Order 10048.

192 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	#19097764	C₂	1	4	yes	maximal
3	#19097763	C₂	1	1	yes	maximal, characteristic, complemented
4	#19097761	C₂	1	4	yes	maximal, complemented
5	#19097750	C₂	1	2	yes	maximal
6	C₄×Dic₃₁₄	C₂	1	2	yes	maximal, complemented
7	#117×C₁₅₇	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₃₁₄	C₂²	1	2	yes	—
9	C₄⋊Dic₁₅₇	C₂²	1	2	yes	—
10	C₄⋊Dic₁₅₇	C₂²	1	4	yes	—
11	#14578933	C₂²	1	4	yes	—
12	#14578933	C₂²	1	4	yes	—
13	#14578933	C₂²	1	4	yes	—
14	C₂²⋊Dic₁₅₇	C₂²	1	4	yes	—
15	C₄×Dic₁₅₇	C₂²	1	4	yes	—
16	C₂²×C₄×C₁₅₇	C₂²	1	1	yes	characteristic
17	C₄⋊C₄×C₁₅₇	C₂²	1	2	yes	—
18	C₂²⋊C₄×C₁₅₇	C₂²	1	2	yes	—
19	C₄²×C₁₅₇	C₂²	1	1	yes	characteristic
20	C₄²×C₁₅₇	C₂²	1	1	yes	characteristic
21	Dic₃₁₄	—	2	4	no	—
22	C₂×Dic₁₅₇	C₂³	1	4	yes	—
23	C₂×Dic₁₅₇	C₂³	1	4	yes	—
24	C₂³×C₁₅₇	C₂³	1	1	yes	characteristic
25	C₂×C₄×C₁₅₇	—	2	2	no	—
26	C₂×C₄×C₁₅₇	C₂³	1	2	yes	—
27	C₂×C₄×C₁₅₇	C₂³	1	2	yes	—
28	C₂×C₄×C₁₅₇	C₂³	1	1	yes	characteristic
29	C₂×C₄×C₁₅₇	C₂³	1	1	yes	characteristic
30	C₂²×C₁₅₇	—	2	1	no	—
31	C₂²×C₁₅₇	—	2	2	no	—
32	C₂²×C₁₅₇	C₂⁴	1	1	yes	characteristic
33	C₄×C₁₅₇	—	2	1	no	—
34	C₄×C₁₅₇	—	2	2	no	—
35	C₄×C₁₅₇	—	2	2	no	—
36	C₄×C₁₅₇	#41	1	2	yes	—
37	Dic₁₅₇	—	2	4	no	—
38	Dic₁₅₇	—	2	4	no	—
39	C₂×C₁₅₇	—	4	1	no	—
40	C₂×C₁₅₇	C₂×#41	1	1	yes	characteristic
41	C₂×C₁₅₇	2₋¹⁺⁴	1	2	yes	—
42	C₁₅₇	#541	1	1	yes	characteristic, complemented, Sylow
43	#541	—	157	1	no	maximal, Sylow
44	C₄⋊Q₈	—	157	1	no	—
45	#126	—	157	4	no	—
46	#125	—	157	4	no	—
47	#125	—	157	1	no	—
48	C₂²⋊Q₈	—	157	2	no	—
49	C₄×Q₈	—	157	2	no	—
50	#117	D₁₅₇	1	1	yes	characteristic
51	C₂×Q₈	—	157	2	no	—
52	C₂²×C₄	C₂×D₁₅₇	1	1	yes	characteristic
53	C₄⋊C₄	—	157	2	no	—
54	C₄⋊C₄	—	157	4	no	—
55	C₄⋊C₄	—	157	4	no	—
56	C₄⋊C₄	—	157	4	no	—
57	C₄⋊C₄	—	157	4	no	—
58	C₄⋊C₄	C₂×D₁₅₇	1	2	yes	—
59	C₂²⋊C₄	—	157	4	no	—
60	C₂²⋊C₄	C₂×D₁₅₇	1	2	yes	—
61	C₄²	—	157	4	no	—
62	C₄²	C₂×D₁₅₇	1	1	yes	characteristic
63	C₄²	C₂×D₁₅₇	1	1	yes	characteristic
64	C₂³	C₂²×D₁₅₇	1	1	yes	characteristic
65	Q₈	—	314	4	no	—
66	C₂×C₄	—	2	2	no	—
67	C₂×C₄	—	157	4	no	—
68	C₂×C₄	—	157	4	no	—
69	C₂×C₄	C₂²×D₁₅₇	1	2	yes	—
70	C₂×C₄	C₂²×D₁₅₇	1	2	yes	—
71	C₂×C₄	C₂²×D₁₅₇	1	1	yes	characteristic
72	C₂×C₄	C₂²×D₁₅₇	1	1	yes	characteristic
73	C₂²	—	2	1	no	—
74	C₂²	—	2	2	no	—
75	C₂²	C₂³×D₁₅₇	1	1	yes	characteristic
76	C₄	—	2	1	no	—
77	C₄	—	2	2	no	—
78	C₄	—	2	2	no	—
79	C₄	—	314	4	no	—
80	C₄	—	314	4	no	—
81	C₄	#14578954	1	2	yes	—
82	C₂	—	4	1	no	—
83	C₂	C₂×#14578954	1	1	yes	characteristic
84	C₂	#19097818	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₁₅₇
commutator, socle, cosocle	C₂²×C₁₅₇	C₂⁴
Fitting	#117×C₁₅₇	C₂
prime radical	C₂³×C₁₅₇	C₂³
hypercenter	#117	D₁₅₇
hypocenter	C₁₅₇	#541
LCS	G ▷ C₂²×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂² ◁ #117

Complements

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

N	H ≅ G/N	type
1. #19097771	C₂	semidirect
3. #19097763	C₂	semidirect
4. #19097761	C₂	semidirect
6. C₄×Dic₃₁₄	C₂	semidirect
42. C₁₅₇	#541	semidirect