Subgroups — #23757102

Order 10048.

40 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	#19097707	C₂	1	1	yes	maximal, characteristic
3	#108×C₁₅₇	C₂	1	1	yes	maximal, characteristic
4	#14578938	—	2	1	no	—
5	#14578929	C₄	1	2	yes	—
6	M₁₆×C₁₅₇	—	2	1	no	—
7	C₂×C₈×C₁₅₇	C₂²	1	1	yes	characteristic
8	#11929434	—	4	1	no	—
9	C₂×C₄×C₁₅₇	D₄	1	1	yes	characteristic
10	C₈×C₁₅₇	—	4	1	no	—
11	C₈×C₁₅₇	C₂×C₄	1	1	yes	characteristic
12	C₈×C₁₅₇	Q₈	1	1	yes	characteristic
13	C₂²×C₁₅₇	Q₁₆	1	1	yes	characteristic
14	C₄×C₁₅₇	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₁₅₇	D₈	1	1	yes	characteristic
16	C₂×C₁₅₇	—	2	1	no	—
17	C₂×C₁₅₇	#107	1	1	yes	characteristic
18	C₁₅₇	#368	1	1	yes	characteristic, complemented, Sylow
19	#368	—	157	1	no	maximal, Sylow
20	C₂×C₁₆	—	157	1	no	—
21	#108	—	157	1	no	—
22	#108	D₁₅₇	1	1	yes	characteristic
23	M₁₆	—	2	1	no	—
24	M₁₆	—	314	1	no	—
25	C₂×C₈	C₂×D₁₅₇	1	1	yes	characteristic
26	C₁₆	—	157	2	no	—
27	C₂×C₄	C₂²⋊D₁₅₇	1	1	yes	characteristic
28	C₈	—	4	1	no	—
29	C₈	—	628	1	no	—
30	C₈	C₄×D₁₅₇	1	1	yes	characteristic
31	C₈	Dic₃₁₄	1	1	yes	characteristic
32	C₂²	#14578944	1	1	yes	characteristic
33	C₄	#14578933	1	1	yes	characteristic
34	C₄	#14578939	1	1	yes	characteristic
35	C₂	—	2	1	no	—
36	C₂	#19097704	1	1	yes	characteristic

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

N	H ≅ G/N	type
18. C₁₅₇	#368	semidirect