Subgroups — #23778849

Order 10144.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11929639	C₂	1	2	yes	maximal
2	C₈×D₃₁₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#11929639	—	2	2	no	—
4	C₄×D₃₁₇	C₂²	1	1	yes	characteristic
5	#14579261	C₄	1	1	yes	characteristic, complemented
6	C₈×C₃₁₇	C₄	1	1	yes	characteristic, complemented
7	C₂×D₃₁₇	D₄	1	1	yes	characteristic
8	#11929639	—	4	2	no	—
9	C₄×C₃₁₇	C₂×C₄	1	1	yes	characteristic
10	Dic₃₁₇	Q₈	1	1	yes	characteristic
11	C₂×C₃₁₇	C₄⋊C₄	1	1	yes	characteristic
12	D₃₁₇	D₈	1	1	yes	characteristic
13	D₃₁₇	Q₁₆	1	1	yes	characteristic
14	C₃₁₇	#107	1	1	yes	characteristic, complemented, Sylow
15	#107	—	317	1	no	maximal, Sylow
16	C₂×C₈	—	317	1	no	—
17	C₄⋊C₄	—	317	2	no	—
18	C₂×C₄	—	317	1	no	—
19	C₂×C₄	—	634	2	no	—
20	C₈	—	317	1	no	—
21	C₈	#11929639	1	1	yes	characteristic, complemented
22	C₂²	—	317	1	no	—
23	C₄	—	317	1	no	—
24	C₄	—	1268	2	no	—
25	C₄	C₂×#11929639	1	1	yes	characteristic
26	C₂	—	317	1	no	—
27	C₂	—	317	1	no	—
28	C₂	C₄⋊#11929639	1	1	yes	characteristic

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