Subgroups — #23778843

Order 10144.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₁₇⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#11929639	C₂	1	1	yes	maximal, characteristic
3	Q₈×D₃₁₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#11929639	—	2	1	no	—
5	#14579268	—	2	1	no	—
6	Dic₆₃₄	—	2	1	no	—
7	Dic₆₃₄	C₄	1	1	yes	characteristic, complemented
8	C₄×D₃₁₇	—	2	1	no	—
9	C₄×D₃₁₇	C₂²	1	1	yes	characteristic
10	Q₈×C₃₁₇	C₄	1	1	yes	characteristic, complemented
11	C₂×D₃₁₇	D₄	1	1	yes	characteristic
12	#11929639	—	4	1	no	—
13	C₄×C₃₁₇	—	2	1	no	—
14	C₄×C₃₁₇	C₂×C₄	1	1	yes	characteristic
15	Dic₃₁₇	—	2	1	no	—
16	Dic₃₁₇	D₄	1	1	yes	characteristic
17	C₂×C₃₁₇	C₂²⋊C₄	1	1	yes	characteristic
18	D₃₁₇	SD₁₆	1	1	yes	characteristic
19	D₃₁₇	Q₁₆	1	1	yes	characteristic
20	C₃₁₇	#103	1	1	yes	characteristic, complemented, Sylow
21	#103	—	317	1	no	maximal, Sylow
22	C₂×Q₈	—	317	1	no	—
23	C₂×C₈	—	317	1	no	—
24	C₄⋊C₄	—	317	1	no	—
25	Q₈	—	317	1	no	—
26	Q₈	—	634	1	no	—
27	Q₈	#11929639	1	1	yes	characteristic, complemented
28	C₂×C₄	—	317	1	no	—
29	C₂×C₄	—	634	1	no	—
30	C₂×C₄	—	634	1	no	—
31	C₈	—	634	1	no	—
32	C₂²	—	317	1	no	—
33	C₄	—	2	1	no	—
34	C₄	—	317	1	no	—
35	C₄	—	634	1	no	—
36	C₄	—	1268	1	no	—
37	C₄	C₂×#11929639	1	1	yes	characteristic
38	C₂	—	317	1	no	—
39	C₂	—	317	1	no	—
40	C₂	C₂²⋊#11929639	1	1	yes	characteristic

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