Subgroups — #23758149

Order 10048.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14578964	C₂	1	2	yes	maximal
2	C₂×C₈×D₁₅₇	C₂	1	1	yes	maximal, characteristic
3	#14578964	—	2	2	no	—
4	#14578964	C₄	1	4	yes	—
5	C₂×#11929441	—	2	2	no	—
6	C₂×C₄×D₁₅₇	C₂²	1	1	yes	characteristic
7	C₂×#11929434	C₄	1	1	yes	characteristic
8	C₈×D₁₅₇	—	2	2	no	—
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	—	2	1	no	—
20	C₂×D₁₅₇	—	2	1	no	—
21	C₂×D₁₅₇	C₄⋊C₄	1	2	yes	—
22	C₄×C₁₅₇	C₄²	1	1	yes	characteristic
23	C₄×C₁₅₇	C₂²⋊C₄	1	1	yes	characteristic
24	Dic₁₅₇	C₂²⋊C₄	1	2	yes	—
25	C₂×C₁₅₇	#95	1	1	yes	characteristic
26	C₂×C₁₅₇	#108	1	1	yes	characteristic
27	C₂×C₁₅₇	#108	1	1	yes	characteristic
28	D₁₅₇	—	2	2	no	—
29	C₁₅₇	#341	1	1	yes	characteristic, complemented, Sylow
30	#341	—	157	1	no	maximal, Sylow
31	C₂×M₁₆	—	157	2	no	—
32	C₂²×C₈	—	157	1	no	—
33	C₂²×C₄	—	157	1	no	—
34	M₁₆	—	314	2	no	—
35	M₁₆	—	157	4	no	—
36	C₂×C₈	—	314	2	no	—
37	C₂×C₈	—	314	2	no	—
38	C₂×C₈	—	157	1	no	—
39	C₂×C₈	#10597845	1	1	yes	characteristic
40	C₂³	—	157	1	no	—
41	C₂×C₄	—	157	1	no	—
42	C₂×C₄	—	157	2	no	—
43	C₂×C₄	—	157	2	no	—
44	C₂×C₄	C₂×#10597845	1	1	yes	characteristic
45	C₈	—	2	1	no	—
46	C₈	—	314	4	no	—
47	C₈	—	314	1	no	—
48	C₂²	—	314	1	no	—
49	C₂²	—	314	1	no	—
50	C₂²	—	157	2	no	—
51	C₂²	C₄⋊#10597845	1	1	yes	characteristic
52	C₄	—	157	2	no	—
53	C₄	C₄×#10597845	1	1	yes	characteristic
54	C₄	C₂²⋊#10597845	1	1	yes	characteristic
55	C₂	—	314	2	no	—
56	C₂	(C₂×#10597845)⋊C₄	1	1	yes	characteristic
57	C₂	#19097841	1	1	yes	characteristic
58	C₂	#19097842	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₄⋊#10597845
commutator	C₄×C₁₅₇	C₄²
Frattini	C₂×C₄	C₂×#10597845
Fitting	C₂×C₈×C₁₅₇	C₄
socle	C₂²×C₁₅₇	C₄⋊C₄
prime radical	C₂²×D₁₅₇	Q₈
cosocle	C₂×C₄×D₁₅₇	C₂²
hypercenter	C₂×C₈	#10597845
hypocenter	C₁₅₇	#341
LCS	G ▷ C₄×C₁₅₇ ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

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