Subgroups — #35204152

Order 20288.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23778851	C₂	1	2	yes	maximal
2	C₁₆×D₃₁₇	C₂	1	1	yes	maximal, characteristic
3	#19099584	—	2	2	no	—
4	C₈×D₃₁₇	C₂²	1	1	yes	characteristic
5	#19099549	C₄	1	1	yes	characteristic
6	C₁₆×C₃₁₇	C₄	1	1	yes	characteristic
7	#14579268	—	4	2	no	—
8	C₄×D₃₁₇	D₄	1	1	yes	characteristic
9	#14579261	Q₈	1	1	yes	characteristic
10	C₈×C₃₁₇	C₂×C₄	1	1	yes	characteristic
11	C₂×D₃₁₇	Q₁₆	1	1	yes	characteristic
12	C₄×C₃₁₇	C₄⋊C₄	1	1	yes	characteristic
13	Dic₃₁₇	D₈	1	1	yes	characteristic
14	C₂×C₃₁₇	#107	1	1	yes	characteristic
15	D₃₁₇	—	2	1	no	—
16	C₃₁₇	#368	1	1	yes	characteristic, complemented, Sylow
17	#368	—	317	1	no	maximal, Sylow
18	C₂×C₁₆	—	317	1	no	—
19	#108	—	317	2	no	—
20	M₁₆	—	634	2	no	—
21	C₂×C₈	—	317	1	no	—
22	C₁₆	—	317	1	no	—
23	C₁₆	#11929639	1	1	yes	characteristic
24	C₂×C₄	—	317	1	no	—
25	C₈	—	317	1	no	—
26	C₈	—	1268	2	no	—
27	C₈	C₂×#11929639	1	1	yes	characteristic
28	C₂²	—	317	1	no	—
29	C₄	—	317	1	no	—
30	C₄	C₄⋊#11929639	1	1	yes	characteristic
31	C₂	—	634	1	no	—
32	C₂	#23778849	1	1	yes	characteristic

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

N	H ≅ G/N	type
16. C₃₁₇	#368	semidirect

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