Subgroups — #23758183

Order 10048.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19097832	C₂	1	2	yes	maximal
2	#19097769	C₂	1	1	yes	maximal, characteristic
3	#14578963	—	2	2	no	—
4	C₂×Dic₃₁₄	C₂²	1	1	yes	characteristic
5	#14578933	—	2	2	no	—
6	C₄×Dic₁₅₇	C₄	1	1	yes	characteristic
7	C₂×Q₈×C₁₅₇	C₄	1	1	yes	characteristic
8	#11929441	—	4	2	no	—
9	Dic₃₁₄	—	4	1	no	—
10	C₂×Dic₁₅₇	—	2	1	no	—
11	C₂×Dic₁₅₇	D₄	1	2	yes	—
12	Q₈×C₁₅₇	—	4	1	no	—
13	C₂×C₄×C₁₅₇	—	2	1	no	—
14	C₂×C₄×C₁₅₇	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₁₅₇	C₂²⋊C₄	1	1	yes	characteristic
16	C₄×C₁₅₇	—	2	1	no	—
17	C₄×C₁₅₇	—	4	1	no	—
18	Dic₁₅₇	—	2	2	no	—
19	Dic₁₅₇	—	2	2	no	—
20	C₂×C₁₅₇	—	2	1	no	—
21	C₂×C₁₅₇	#99	1	1	yes	characteristic
22	C₁₅₇	#356	1	1	yes	characteristic, complemented, Sylow
23	#356	—	157	1	no	maximal, Sylow
24	C₄⋊Q₈	—	157	1	no	—
25	#101	—	157	2	no	—
26	C₂×Q₈	—	157	1	no	—
27	C₂×Q₈	#10597845	1	1	yes	characteristic
28	M₁₆	—	314	2	no	—
29	C₄⋊C₄	—	314	2	no	—
30	C₄²	—	157	1	no	—
31	Q₈	—	4	1	no	—
32	Q₈	—	628	1	no	—
33	C₂×C₄	—	2	1	no	—
34	C₂×C₄	—	314	1	no	—
35	C₂×C₄	—	157	2	no	—
36	C₂×C₄	C₂×#10597845	1	1	yes	characteristic
37	C₈	—	628	2	no	—
38	C₂²	C₂²⋊#10597845	1	1	yes	characteristic
39	C₄	—	2	1	no	—
40	C₄	—	4	1	no	—
41	C₄	—	314	2	no	—
42	C₄	—	314	2	no	—
43	C₂	—	2	1	no	—
44	C₂	#19097829	1	1	yes	characteristic

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

N	H ≅ G/N	type
22. C₁₅₇	#356	semidirect