Subgroups — #23757091

Order 10048.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14578929	C₂	1	1	yes	maximal, characteristic
2	C₈×Dic₁₅₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₁₅₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#11929434	C₄	1	1	yes	characteristic
5	C₄×Dic₁₅₇	C₄	1	1	yes	characteristic
6	#14578929	—	2	1	no	—
7	C₂×C₈×C₁₅₇	C₂²	1	1	yes	characteristic
8	C₁₆×C₁₅₇	—	2	1	no	—
9	C₂×Dic₁₅₇	C₈	1	1	yes	characteristic
10	C₂×Dic₁₅₇	C₈	1	1	yes	characteristic
11	#11929434	—	2	1	no	—
12	C₂×C₄×C₁₅₇	C₂×C₄	1	1	yes	characteristic
13	C₈×C₁₅₇	D₄	1	1	yes	characteristic
14	C₈×C₁₅₇	Q₈	1	1	yes	characteristic
15	C₂²×C₁₅₇	C₂×C₈	1	1	yes	characteristic
16	C₄×C₁₅₇	C₄⋊C₄	1	1	yes	characteristic
17	C₄×C₁₅₇	M₁₆	1	1	yes	characteristic
18	Dic₁₅₇	—	2	1	no	—
19	Dic₁₅₇	C₁₆	1	2	yes	complemented
20	C₂×C₁₅₇	C₄⋊C₈	1	1	yes	characteristic
21	C₂×C₁₅₇	C₂×C₁₆	1	1	yes	characteristic
22	C₂×C₁₅₇	M₃₂	1	1	yes	characteristic
23	C₁₅₇	C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
24	C₄⋊C₁₆	—	157	1	no	maximal, Sylow
25	C₂×C₁₆	—	157	1	no	—
26	C₂×C₁₆	D₁₅₇	1	1	yes	characteristic
27	C₄×C₈	—	157	1	no	—
28	C₂×C₈	—	157	1	no	—
29	C₂×C₈	C₂×D₁₅₇	1	1	yes	characteristic
30	C₄²	—	157	1	no	—
31	C₁₆	—	2	1	no	—
32	C₁₆	—	314	1	no	—
33	C₂×C₄	—	157	1	no	—
34	C₂×C₄	—	157	1	no	—
35	C₂×C₄	C₄×D₁₅₇	1	1	yes	characteristic
36	C₈	—	314	1	no	—
37	C₈	C₂²⋊D₁₅₇	1	1	yes	characteristic
38	C₈	Dic₃₁₄	1	1	yes	characteristic
39	C₂²	C₈×D₁₅₇	1	1	yes	characteristic
40	C₄	—	314	1	no	—
41	C₄	—	157	2	no	—
42	C₄	#14578933	1	1	yes	characteristic
43	C₄	#14578937	1	1	yes	characteristic
44	C₂	#19097700	1	1	yes	characteristic
45	C₂	C₁₆×D₁₅₇	1	1	yes	characteristic
46	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, prime radical	C₂²×C₁₅₇	C₂×C₈
cosocle	C₂×C₈×C₁₅₇	C₂²
hypercenter	C₂×C₁₆	D₁₅₇
hypocenter	C₁₅₇	C₄⋊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
19. Dic₁₅₇	C₁₆	semidirect
23. C₁₅₇	C₄⋊C₁₆	semidirect