Subgroups — #23757052

Order 10048.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₁₅₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#14578929	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₆×C₁₅₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×D₁₅₇	C₄	1	1	yes	characteristic
5	C₂×#11929434	C₄	1	1	yes	characteristic
6	C₈×D₁₅₇	—	2	1	no	—
7	C₈×D₁₅₇	—	2	1	no	—
8	#14578929	—	2	1	no	—
9	C₂×C₈×C₁₅₇	C₂²	1	1	yes	characteristic
10	C₁₆×C₁₅₇	—	2	1	no	—
11	C₂²×D₁₅₇	C₈	1	1	yes	characteristic
12	C₂×Dic₁₅₇	C₈	1	1	yes	characteristic
13	C₄×D₁₅₇	—	2	1	no	—
14	C₄×D₁₅₇	—	2	1	no	—
15	#11929434	—	2	1	no	—
16	C₂×C₄×C₁₅₇	C₂×C₄	1	1	yes	characteristic
17	C₈×C₁₅₇	D₄	1	1	yes	characteristic
18	C₈×C₁₅₇	D₄	1	1	yes	characteristic
19	C₂²×C₁₅₇	C₂×C₈	1	1	yes	characteristic
20	C₂×D₁₅₇	—	2	1	no	—
21	C₂×D₁₅₇	—	2	1	no	—
22	C₂×D₁₅₇	C₁₆	1	2	yes	complemented
23	C₄×C₁₅₇	C₂²⋊C₄	1	1	yes	characteristic
24	C₄×C₁₅₇	M₁₆	1	1	yes	characteristic
25	Dic₁₅₇	—	2	1	no	—
26	C₂×C₁₅₇	C₂²⋊C₈	1	1	yes	characteristic
27	C₂×C₁₅₇	C₂×C₁₆	1	1	yes	characteristic
28	C₂×C₁₅₇	M₃₂	1	1	yes	characteristic
29	D₁₅₇	—	2	2	no	—
30	C₁₅₇	C₂²⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
31	C₂²⋊C₁₆	—	157	1	no	maximal, Sylow
32	C₂²×C₈	—	157	1	no	—
33	C₂×C₁₆	—	157	1	no	—
34	C₂×C₁₆	D₁₅₇	1	1	yes	characteristic, complemented
35	C₂²×C₄	—	157	1	no	—
36	C₂×C₈	—	314	1	no	—
37	C₂×C₈	—	314	1	no	—
38	C₂×C₈	—	157	1	no	—
39	C₂×C₈	C₂×D₁₅₇	1	1	yes	characteristic
40	C₁₆	—	2	1	no	—
41	C₁₆	—	314	1	no	—
42	C₂³	—	157	1	no	—
43	C₂×C₄	—	314	1	no	—
44	C₂×C₄	—	314	1	no	—
45	C₂×C₄	—	157	1	no	—
46	C₂×C₄	C₄×D₁₅₇	1	1	yes	characteristic
47	C₈	—	314	1	no	—
48	C₈	C₂²⋊D₁₅₇	1	1	yes	characteristic
49	C₈	D₆₂₈	1	1	yes	characteristic
50	C₂²	—	314	1	no	—
51	C₂²	—	314	1	no	—
52	C₂²	—	157	2	no	—
53	C₂²	C₈×D₁₅₇	1	1	yes	characteristic
54	C₄	—	314	1	no	—
55	C₄	#14578931	1	1	yes	characteristic
56	C₄	#14578937	1	1	yes	characteristic
57	C₂	—	314	2	no	—
58	C₂	#19097683	1	1	yes	characteristic
59	C₂	C₁₆×D₁₅₇	1	1	yes	characteristic
60	C₂	#19097710	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×D₁₅₇
commutator	C₂×C₁₅₇	C₂×C₁₆
Fitting	C₂×C₁₆×C₁₅₇	C₂
socle	C₂²×C₁₅₇	C₂×C₈
prime radical	C₂²×D₁₅₇	C₈
cosocle	C₂×C₈×C₁₅₇	C₂²
hypercenter	C₂×C₁₆	D₁₅₇
hypocenter	C₁₅₇	C₂²⋊C₁₆
LCS	G ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×#14578929	C₂	semidirect
3. C₂×C₁₆×C₁₅₇	C₂	semidirect
22. C₂×D₁₅₇	C₁₆	semidirect
30. C₁₅₇	C₂²⋊C₁₆	semidirect
34. C₂×C₁₆	D₁₅₇	semidirect