Subgroups — #23778803

Order 10144.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19099575	C₂	1	2	yes	maximal, complemented
2	#19099561	C₂	1	2	yes	maximal, complemented
3	D₂₅₃₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈×D₃₁₇	C₂	1	1	yes	maximal, characteristic, complemented
5	Q₁₆×C₃₁₇	C₂	1	1	yes	maximal, characteristic, complemented
6	D₁₂₆₈	—	2	2	no	—
7	D₁₂₆₈	C₂²	1	2	yes	—
8	C₄×D₃₁₇	—	2	2	no	—
9	C₄×D₃₁₇	C₂²	1	1	yes	characteristic
10	#14579261	C₂²	1	1	yes	characteristic
11	Q₈×C₃₁₇	C₂²	1	2	yes	—
12	C₈×C₃₁₇	C₂²	1	1	yes	characteristic
13	C₂×D₃₁₇	—	2	2	no	—
14	C₂×D₃₁₇	D₄	1	1	yes	characteristic
15	C₄×C₃₁₇	—	2	2	no	—
16	C₄×C₃₁₇	C₂³	1	1	yes	characteristic
17	Dic₃₁₇	D₄	1	1	yes	characteristic
18	C₂×C₃₁₇	C₂×D₄	1	1	yes	characteristic
19	D₃₁₇	—	2	1	no	—
20	D₃₁₇	—	4	2	no	—
21	C₃₁₇	#135	1	1	yes	characteristic, complemented, Sylow
22	#135	—	317	1	no	maximal, Sylow
23	#41	—	317	2	no	—
24	Q₁₆	D₃₁₇	1	1	yes	characteristic, complemented
25	SD₁₆	—	317	2	no	—
26	D₈	—	317	1	no	—
27	C₂×C₈	—	317	1	no	—
28	Q₈	C₂×D₃₁₇	1	2	yes	—
29	D₄	—	317	2	no	—
30	D₄	—	634	2	no	—
31	C₂×C₄	—	317	1	no	—
32	C₂×C₄	—	634	2	no	—
33	C₈	—	317	1	no	—
34	C₈	C₂×D₃₁₇	1	1	yes	characteristic
35	C₂²	—	317	1	no	—
36	C₂²	—	634	2	no	—
37	C₄	—	2	2	no	—
38	C₄	—	317	1	no	—
39	C₄	C₂²×D₃₁₇	1	1	yes	characteristic
40	C₂	—	634	1	no	—
41	C₂	—	1268	2	no	—
42	C₂	D₄×D₃₁₇	1	1	yes	characteristic

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