Subgroups — C₈×#11929441 #23758113

Order 10048.

74 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	C₄	1	4	yes	—
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	C₈	1	8	yes	direct product factor
8	C₂×Dic₁₅₇	C₂×C₄	1	2	yes	—
9	#11929434	C₈	1	2	yes	complemented
10	C₂×C₄×C₁₅₇	C₂×C₄	1	1	yes	characteristic
11	C₈×C₁₅₇	C₈	1	2	yes	complemented
12	C₂²×C₁₅₇	C₄²	1	1	yes	characteristic
13	C₄×C₁₅₇	C₂×C₈	1	1	yes	characteristic
14	C₄×C₁₅₇	C₂×C₈	1	1	yes	characteristic
15	Dic₁₅₇	C₂×C₈	1	4	yes	—
16	C₂×C₁₅₇	C₄×C₈	1	2	yes	—
17	C₂×C₁₅₇	C₄×C₈	1	1	yes	characteristic
18	C₁₅₇	C₈²	1	1	yes	characteristic, complemented, Sylow
19	C₈²	—	157	1	no	maximal, Sylow
20	C₄×C₈	—	157	2	no	—
21	C₄×C₈	—	157	1	no	—
22	C₂×C₈	—	157	4	no	—
23	C₂×C₈	—	157	1	no	—
24	C₂×C₈	#10597845	1	1	yes	characteristic
25	C₄²	—	157	1	no	—
26	C₂×C₄	—	157	2	no	—
27	C₂×C₄	C₂×#10597845	1	1	yes	characteristic
28	C₈	—	157	8	no	—
29	C₈	—	157	2	no	—
30	C₈	#11929441	1	2	yes	direct product factor
31	C₂²	C₄×#10597845	1	1	yes	characteristic
32	C₄	—	157	4	no	—
33	C₄	C₂×#11929441	1	1	yes	characteristic
34	C₄	D₁₅₇⋊C₈	1	1	yes	characteristic
35	C₂	C₈×#10597845	1	2	yes	—
36	C₂	C₄×#11929441	1	1	yes	characteristic

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