Subgroups — #23758148

Order 10048.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₅₇⋊M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×D₁₅₇⋊C₈	C₂	1	1	yes	maximal, characteristic
3	M₁₆×D₁₅₇	C₂	1	1	yes	maximal, characteristic
4	#14578964	C₄	1	2	yes	—
5	#14578963	—	2	1	no	—
6	D₁₅₇⋊C₈	—	2	1	no	—
7	D₁₅₇⋊C₈	—	2	1	no	—
8	D₁₅₇⋊C₈	C₄	1	2	yes	—
9	C₂×#11929441	—	2	1	no	—
10	C₂×C₄×D₁₅₇	C₂²	1	1	yes	characteristic
11	#14578938	C₄	1	1	yes	characteristic
12	#14578937	—	2	1	no	—
13	C₈×D₁₅₇	—	2	1	no	—
14	M₁₆×C₁₅₇	C₄	1	1	yes	characteristic
15	#11929441	—	2	2	no	—
16	#11929441	—	2	2	no	—
17	C₂²×D₁₅₇	Q₈	1	1	yes	characteristic
18	C₂×Dic₁₅₇	D₄	1	1	yes	characteristic
19	C₄×D₁₅₇	C₂×C₄	1	1	yes	characteristic
20	C₄×D₁₅₇	C₂×C₄	1	1	yes	characteristic
21	C₄×D₁₅₇	D₄	1	1	yes	characteristic
22	C₄×D₁₅₇	D₄	1	1	yes	characteristic
23	#11929434	—	2	1	no	—
24	C₂×C₄×C₁₅₇	C₂×C₄	1	1	yes	characteristic
25	C₈×C₁₅₇	—	2	1	no	—
26	C₂²×C₁₅₇	C₄⋊C₄	1	1	yes	characteristic
27	C₂×D₁₅₇	—	2	2	no	—
28	C₂×D₁₅₇	C₄⋊C₄	1	1	yes	characteristic
29	C₂×D₁₅₇	C₄⋊C₄	1	1	yes	characteristic
30	C₄×C₁₅₇	C₄²	1	1	yes	characteristic
31	C₄×C₁₅₇	C₂²⋊C₄	1	1	yes	characteristic
32	Dic₁₅₇	C₂²⋊C₄	1	1	yes	characteristic
33	Dic₁₅₇	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₁₅₇	—	2	1	no	—
35	C₂×C₁₅₇	#95	1	1	yes	characteristic
36	D₁₅₇	—	2	1	no	—
37	D₁₅₇	#108	1	2	yes	—
38	C₁₅₇	#341	1	1	yes	characteristic, complemented, Sylow
39	#341	—	157	1	no	maximal, Sylow
40	C₂×M₁₆	—	157	1	no	—
41	C₂×M₁₆	—	157	1	no	—
42	C₂²×C₈	—	157	1	no	—
43	C₂²×C₄	—	157	1	no	—
44	M₁₆	—	314	1	no	—
45	M₁₆	—	314	1	no	—
46	M₁₆	—	157	2	no	—
47	M₁₆	—	157	1	no	—
48	M₁₆	#10597845	1	1	yes	characteristic
49	C₂×C₈	—	314	1	no	—
50	C₂×C₈	—	314	1	no	—
51	C₂×C₈	—	314	1	no	—
52	C₂×C₈	—	314	1	no	—
53	C₂×C₈	—	157	2	no	—
54	C₂³	—	157	1	no	—
55	C₂×C₄	—	157	1	no	—
56	C₂×C₄	—	157	1	no	—
57	C₂×C₄	—	157	1	no	—
58	C₂×C₄	—	157	1	no	—
59	C₂×C₄	—	157	1	no	—
60	C₂×C₄	C₂×#10597845	1	1	yes	characteristic
61	C₈	—	2	1	no	—
62	C₈	—	314	2	no	—
63	C₈	—	314	2	no	—
64	C₈	—	314	1	no	—
65	C₂²	—	314	2	no	—
66	C₂²	—	157	1	no	—
67	C₂²	—	157	1	no	—
68	C₂²	C₄⋊#10597845	1	1	yes	characteristic
69	C₄	—	157	1	no	—
70	C₄	—	157	1	no	—
71	C₄	C₄×#10597845	1	1	yes	characteristic
72	C₄	C₂²⋊#10597845	1	1	yes	characteristic
73	C₂	—	2	1	no	—
74	C₂	—	314	1	no	—
75	C₂	—	157	2	no	—
76	C₂	(C₂×#10597845)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊#10597845
commutator	C₄×C₁₅₇	C₄²
Frattini	C₂×C₄	C₂×#10597845
Fitting	M₁₆×C₁₅₇	C₄
socle	C₂×C₁₅₇	#95
prime radical	C₂²×D₁₅₇	Q₈
cosocle	C₂×C₄×D₁₅₇	C₂²
hypercenter	M₁₆	#10597845
hypocenter	C₁₅₇	#341
LCS	G ▷ C₄×C₁₅₇ ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
38. C₁₅₇	#341	semidirect