Subgroups — #23758142

Order 10048.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₅₇⋊M₁₆	C₂	1	2	yes	maximal
2	C₂×#14578937	C₂	1	1	yes	maximal, characteristic
3	#14578964	—	2	2	no	—
4	#14578963	—	2	2	no	—
5	D₁₅₇⋊C₈	C₄	1	4	yes	—
6	C₂×C₄×D₁₅₇	C₂²	1	1	yes	characteristic
7	#14578937	—	2	2	no	—
8	C₂×#11929434	C₄	1	1	yes	characteristic
9	C₂×C₈×C₁₅₇	C₄	1	1	yes	characteristic
10	#11929441	—	2	4	no	—
11	C₂²×D₁₅₇	Q₈	1	1	yes	characteristic
12	C₂×Dic₁₅₇	D₄	1	1	yes	characteristic
13	C₄×D₁₅₇	C₂×C₄	1	2	yes	—
14	C₄×D₁₅₇	D₄	1	2	yes	—
15	#11929434	—	2	1	no	—
16	C₂×C₄×C₁₅₇	C₂×C₄	1	1	yes	characteristic
17	C₈×C₁₅₇	—	2	1	no	—
18	C₂²×C₁₅₇	C₄⋊C₄	1	1	yes	characteristic
19	C₂×D₁₅₇	—	4	1	no	—
20	C₂×D₁₅₇	C₄⋊C₄	1	2	yes	—
21	C₄×C₁₅₇	C₄²	1	1	yes	characteristic
22	C₄×C₁₅₇	C₂²⋊C₄	1	1	yes	characteristic
23	Dic₁₅₇	C₂²⋊C₄	1	2	yes	—
24	C₂×C₁₅₇	—	2	1	no	—
25	C₂×C₁₅₇	#95	1	1	yes	characteristic
26	D₁₅₇	—	2	2	no	—
27	C₁₅₇	#338	1	1	yes	characteristic, complemented, Sylow
28	#338	—	157	1	no	maximal, Sylow
29	C₂×M₁₆	—	157	2	no	—
30	C₂×M₁₆	—	157	1	no	—
31	C₂²×C₄	—	157	1	no	—
32	M₁₆	—	314	2	no	—
33	M₁₆	—	314	2	no	—
34	M₁₆	—	314	2	no	—
35	C₂×C₈	—	157	4	no	—
36	C₂×C₈	—	157	1	no	—
37	C₂×C₈	#10597845	1	1	yes	characteristic
38	C₂³	—	157	1	no	—
39	C₂×C₄	—	157	1	no	—
40	C₂×C₄	—	157	2	no	—
41	C₂×C₄	—	157	2	no	—
42	C₂×C₄	C₂×#10597845	1	1	yes	characteristic
43	C₈	—	2	1	no	—
44	C₈	—	314	4	no	—
45	C₈	—	314	1	no	—
46	C₂²	—	628	1	no	—
47	C₂²	—	157	2	no	—
48	C₂²	C₄⋊#10597845	1	1	yes	characteristic
49	C₄	—	157	2	no	—
50	C₄	C₄×#10597845	1	1	yes	characteristic
51	C₄	C₂²⋊#10597845	1	1	yes	characteristic
52	C₂	—	2	1	no	—
53	C₂	—	314	2	no	—
54	C₂	(C₂×#10597845)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄×#10597845
commutator	C₄×C₁₅₇	C₄²
Frattini	C₂×C₄	C₂×#10597845
Fitting	C₂×C₈×C₁₅₇	C₄
socle	C₂×C₁₅₇	#95
prime radical	C₂²×D₁₅₇	Q₈
cosocle	C₂×C₄×D₁₅₇	C₂²
hypercenter	C₂×C₈	#10597845
hypocenter	C₁₅₇	#338
LCS	G ▷ C₄×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
27. C₁₅₇	#338	semidirect