Subgroups — C₂³×#11929639 #23778869

Order 10144.

236 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#11929639	C₂	1	14	yes	maximal, direct product factor
2	C₂³×D₃₁₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#11929639	C₂²	1	28	yes	direct product factor
4	C₂²×D₃₁₇	C₄	1	7	yes	complemented
5	C₂²×D₃₁₇	C₂²	1	7	yes	—
6	C₂³×C₃₁₇	C₄	1	1	yes	characteristic, complemented
7	C₂²×C₃₁₇	C₂×C₄	1	7	yes	complemented
8	C₂×D₃₁₇	C₂×C₄	1	21	yes	complemented
9	C₂×D₃₁₇	C₂³	1	7	yes	—
10	#11929639	C₂³	1	8	yes	direct product factor
11	C₂×C₃₁₇	C₂²×C₄	1	7	yes	complemented
12	D₃₁₇	C₂²×C₄	1	7	yes	complemented
13	D₃₁₇	C₂⁴	1	1	yes	characteristic
14	C₃₁₇	C₂³×C₄	1	1	yes	characteristic, complemented, Sylow
15	C₂³×C₄	—	317	1	no	maximal, Sylow
16	C₂⁴	—	317	1	no	—
17	C₂²×C₄	—	317	14	no	—
18	C₂³	—	317	7	no	—
19	C₂³	—	317	7	no	—
20	C₂³	#11929639	1	1	yes	characteristic, direct product factor
21	C₂×C₄	—	317	28	no	—
22	C₂²	—	317	7	no	—
23	C₂²	—	317	21	no	—
24	C₂²	C₂×#11929639	1	7	yes	direct product factor
25	C₄	—	317	8	no	—
26	C₂	—	317	1	no	—
27	C₂	—	317	7	no	—
28	C₂	C₂²×#11929639	1	7	yes	direct product factor

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