Subgroups — #23778708

Order 10144.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19099574	C₂	1	1	yes	maximal, characteristic
2	#19099558	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄²×C₃₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₆₃₄	C₄	1	1	yes	characteristic, complemented
5	D₁₂₆₈	C₄	1	1	yes	characteristic, complemented
6	C₂²⋊D₃₁₇	—	2	1	no	—
7	C₄×D₃₁₇	—	2	1	no	—
8	#14579261	—	2	1	no	—
9	C₂×C₄×C₃₁₇	—	2	1	no	—
10	C₂×C₄×C₃₁₇	C₂²	1	1	yes	characteristic
11	C₂²×C₃₁₇	D₄	1	1	yes	characteristic
12	C₂×D₃₁₇	—	2	1	no	—
13	C₄×C₃₁₇	—	2	2	no	—
14	C₄×C₃₁₇	C₂×C₄	1	1	yes	characteristic
15	C₄×C₃₁₇	D₄	1	1	yes	characteristic
16	Dic₃₁₇	—	2	1	no	—
17	C₂×C₃₁₇	—	2	1	no	—
18	C₂×C₃₁₇	C₂²⋊C₄	1	1	yes	characteristic
19	D₃₁₇	—	4	1	no	—
20	C₃₁₇	#104	1	1	yes	characteristic, complemented, Sylow
21	#104	—	317	1	no	maximal, Sylow
22	#41	—	317	1	no	—
23	M₁₆	—	317	1	no	—
24	C₄²	D₃₁₇	1	1	yes	characteristic, complemented
25	Q₈	—	317	1	no	—
26	D₄	—	317	1	no	—
27	D₄	—	634	1	no	—
28	C₂×C₄	—	2	1	no	—
29	C₂×C₄	—	634	1	no	—
30	C₂×C₄	C₂×D₃₁₇	1	1	yes	characteristic
31	C₈	—	634	1	no	—
32	C₂²	—	634	1	no	—
33	C₂²	C₂²⋊D₃₁₇	1	1	yes	characteristic
34	C₄	—	2	2	no	—
35	C₄	—	634	1	no	—
36	C₄	C₄×D₃₁₇	1	1	yes	characteristic
37	C₄	D₁₂₆₈	1	1	yes	characteristic
38	C₂	—	2	1	no	—
39	C₂	—	1268	1	no	—
40	C₂	#19099551	1	1	yes	characteristic

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