Subgroups — #23758195

Order 10048.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19097845	C₂	1	2	yes	maximal
2	C₈×Dic₁₅₇	C₂	1	1	yes	maximal, characteristic
3	#14578957	—	2	2	no	—
4	C₂×#11929434	C₂²	1	1	yes	characteristic
5	C₄×Dic₁₅₇	C₄	1	1	yes	characteristic
6	C₂×C₈×C₁₅₇	C₄	1	1	yes	characteristic
7	C₂×Dic₁₅₇	—	2	1	no	—
8	#11929434	D₄	1	1	yes	characteristic
9	#11929434	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₁₅₇	C₂×C₄	1	1	yes	characteristic
11	C₈×C₁₅₇	C₈	1	2	yes	—
12	C₂²×C₁₅₇	M₁₆	1	1	yes	characteristic
13	C₄×C₁₅₇	C₄⋊C₄	1	1	yes	characteristic
14	C₄×C₁₅₇	C₂×C₈	1	1	yes	characteristic
15	Dic₁₅₇	—	2	2	no	—
16	C₂×C₁₅₇	—	2	1	no	—
17	C₂×C₁₅₇	C₄⋊C₈	1	1	yes	characteristic
18	C₁₅₇	#364	1	1	yes	characteristic, complemented, Sylow
19	#364	—	157	1	no	maximal, Sylow
20	M₃₂	—	157	2	no	—
21	C₄×C₈	—	157	1	no	—
22	C₂×C₈	—	157	1	no	—
23	C₂×C₈	#10597845	1	1	yes	characteristic
24	C₄²	—	157	1	no	—
25	C₁₆	—	314	2	no	—
26	C₂×C₄	—	314	1	no	—
27	C₂×C₄	C₂×#10597845	1	1	yes	characteristic
28	C₈	—	157	1	no	—
29	C₈	—	157	1	no	—
30	C₈	#11929441	1	2	yes	—
31	C₂²	#14578964	1	1	yes	characteristic
32	C₄	—	314	2	no	—
33	C₄	C₄⋊#10597845	1	1	yes	characteristic
34	C₄	C₂×#11929441	1	1	yes	characteristic
35	C₂	—	2	1	no	—
36	C₂	C₄⋊#11929441	1	1	yes	characteristic

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

N	H ≅ G/N	type
18. C₁₅₇	#364	semidirect