Subgroups — #23758199

Order 10048.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19097840	C₂	1	2	yes	maximal
2	C₁₆×D₁₅₇	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#10597845	—	2	2	no	—
4	C₈×D₁₅₇	C₂²	1	1	yes	characteristic
5	#14578929	C₄	1	1	yes	characteristic, complemented
6	C₁₆×C₁₅₇	C₄	1	1	yes	characteristic, complemented
7	C₂×#10597845	—	4	2	no	—
8	C₄×D₁₅₇	D₄	1	1	yes	characteristic
9	#11929434	Q₈	1	1	yes	characteristic
10	C₈×C₁₅₇	C₂×C₄	1	1	yes	characteristic
11	C₂×D₁₅₇	D₈	1	1	yes	characteristic
12	#10597845	—	8	2	no	—
13	C₄×C₁₅₇	C₄⋊C₄	1	1	yes	characteristic
14	Dic₁₅₇	Q₁₆	1	1	yes	characteristic
15	C₂×C₁₅₇	#107	1	1	yes	characteristic
16	D₁₅₇	D₁₆	1	1	yes	characteristic
17	D₁₅₇	Q₃₂	1	1	yes	characteristic
18	C₁₅₇	#366	1	1	yes	characteristic, complemented, Sylow
19	#366	—	157	1	no	maximal, Sylow
20	C₂×C₁₆	—	157	1	no	—
21	#107	—	157	2	no	—
22	C₂×C₈	—	157	1	no	—
23	C₄⋊C₄	—	314	2	no	—
24	C₁₆	—	157	1	no	—
25	C₁₆	#10597845	1	1	yes	characteristic, complemented
26	C₂×C₄	—	628	2	no	—
27	C₂×C₄	—	157	1	no	—
28	C₈	—	157	1	no	—
29	C₈	C₂×#10597845	1	1	yes	characteristic
30	C₂²	—	157	1	no	—
31	C₄	—	157	1	no	—
32	C₄	—	1256	2	no	—
33	C₄	C₄⋊#10597845	1	1	yes	characteristic
34	C₂	—	157	1	no	—
35	C₂	—	157	1	no	—
36	C₂	#19097840	1	1	yes	characteristic

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