Subgroups — #35204109

Order 20288.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19099577	C₂	1	2	yes	maximal
2	C₈×Dic₃₁₇	C₂	1	1	yes	maximal, characteristic
3	#19099577	C₄	1	4	yes	complemented
4	C₂×#14579261	C₂²	1	1	yes	characteristic
5	C₄×Dic₃₁₇	C₄	1	1	yes	characteristic
6	C₂×C₈×C₃₁₇	C₄	1	1	yes	characteristic
7	C₂×Dic₃₁₇	C₈	1	2	yes	—
8	#14579261	C₂×C₄	1	2	yes	—
9	C₂×C₄×C₃₁₇	C₂×C₄	1	1	yes	characteristic
10	C₈×C₃₁₇	C₈	1	2	yes	—
11	C₂²×C₃₁₇	C₂×C₈	1	1	yes	characteristic
12	C₄×C₃₁₇	C₄²	1	1	yes	characteristic
13	C₄×C₃₁₇	C₂×C₈	1	1	yes	characteristic
14	Dic₃₁₇	C₁₆	1	4	yes	complemented
15	C₂×C₃₁₇	C₄×C₈	1	1	yes	characteristic
16	C₂×C₃₁₇	C₂×C₁₆	1	2	yes	—
17	C₃₁₇	C₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
18	C₄×C₁₆	—	317	1	no	maximal, Sylow
19	C₂×C₁₆	—	317	2	no	—
20	C₄×C₈	—	317	1	no	—
21	C₂×C₈	—	317	1	no	—
22	C₂×C₈	#11929639	1	1	yes	characteristic
23	C₄²	—	317	1	no	—
24	C₁₆	—	317	4	no	—
25	C₂×C₄	—	317	2	no	—
26	C₂×C₄	C₂×#11929639	1	1	yes	characteristic
27	C₈	—	317	2	no	—
28	C₈	#14579268	1	2	yes	—
29	C₂²	D₃₁₇⋊C₈	1	1	yes	characteristic
30	C₄	—	317	4	no	—
31	C₄	C₄×#11929639	1	1	yes	characteristic
32	C₄	C₂×#14579268	1	1	yes	characteristic
33	C₂	C₄×#14579268	1	1	yes	characteristic
34	C₂	D₃₁₇⋊C₁₆	1	2	yes	—

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

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.