Subgroups — #23758136

Order 10048.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11929441	C₂	1	2	yes	maximal
2	C₈×Dic₁₅₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#11929441	—	2	2	no	—
4	C₂×#11929434	C₄	1	1	yes	characteristic
5	C₄×Dic₁₅₇	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₁₅₇	C₄	1	1	yes	characteristic
7	#11929441	—	4	2	no	—
8	C₂×Dic₁₅₇	D₄	1	1	yes	characteristic
9	C₂×Dic₁₅₇	Q₈	1	1	yes	characteristic
10	#11929434	—	2	1	no	—
11	C₂×C₄×C₁₅₇	C₂×C₄	1	1	yes	characteristic
12	C₈×C₁₅₇	C₈	1	2	yes	complemented
13	C₂²×C₁₅₇	C₄⋊C₄	1	1	yes	characteristic
14	C₄×C₁₅₇	C₂×C₈	1	1	yes	characteristic
15	C₄×C₁₅₇	M₁₆	1	1	yes	characteristic
16	Dic₁₅₇	—	2	1	no	—
17	Dic₁₅₇	D₈	1	1	yes	characteristic
18	Dic₁₅₇	Q₁₆	1	1	yes	characteristic
19	C₂×C₁₅₇	C₄⋊C₈	1	1	yes	characteristic
20	C₂×C₁₅₇	#107	1	1	yes	characteristic
21	C₂×C₁₅₇	#108	1	1	yes	characteristic
22	C₁₅₇	#335	1	1	yes	characteristic, complemented, Sylow
23	#335	—	157	1	no	maximal, Sylow
24	C₄⋊C₈	—	157	2	no	—
25	C₄×C₈	—	157	1	no	—
26	C₂×C₈	—	314	2	no	—
27	C₂×C₈	—	157	1	no	—
28	C₂×C₈	#10597845	1	1	yes	characteristic
29	C₄²	—	157	1	no	—
30	C₂×C₄	—	157	1	no	—
31	C₂×C₄	—	157	1	no	—
32	C₂×C₄	C₂×#10597845	1	1	yes	characteristic
33	C₈	—	314	1	no	—
34	C₈	—	628	2	no	—
35	C₈	#11929441	1	2	yes	complemented
36	C₂²	C₄⋊#10597845	1	1	yes	characteristic
37	C₄	—	314	1	no	—
38	C₄	—	157	1	no	—
39	C₄	—	157	1	no	—
40	C₄	C₂×#11929441	1	1	yes	characteristic
41	C₄	#14578964	1	1	yes	characteristic
42	C₂	C₄⋊#11929441	1	1	yes	characteristic
43	C₂	#19097840	1	1	yes	characteristic
44	C₂	#19097842	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₄⋊#10597845
commutator	C₄×C₁₅₇	C₂×C₈
Frattini	C₂×C₄	C₂×#10597845
Fitting	C₂×C₈×C₁₅₇	C₄
socle, prime radical	C₂²×C₁₅₇	C₄⋊C₄
cosocle	C₄×Dic₁₅₇	C₂²
hypercenter	C₂×C₈	#10597845
hypocenter	C₁₅₇	#335
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
12. C₈×C₁₅₇	C₈	semidirect
22. C₁₅₇	#335	semidirect
35. C₈	#11929441	semidirect