Subgroups — C₄²×#11929639 #35204157

Order 20288.

258 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#11929639	C₂	1	6	yes	maximal
2	C₄²×D₃₁₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×#11929639	C₂²	1	4	yes	—
4	C₄×#11929639	C₄	1	24	yes	direct product factor
5	C₂×C₄×D₃₁₇	C₂²	1	3	yes	—
6	C₄×Dic₃₁₇	C₄	1	3	yes	complemented
7	C₄²×C₃₁₇	C₄	1	1	yes	characteristic, complemented
8	C₂×#11929639	C₂×C₄	1	24	yes	—
9	C₂²×D₃₁₇	C₂³	1	1	yes	characteristic
10	C₂×Dic₃₁₇	C₂×C₄	1	3	yes	—
11	C₄×D₃₁₇	C₂×C₄	1	12	yes	—
12	C₂×C₄×C₃₁₇	C₂×C₄	1	3	yes	—
13	C₂²×C₃₁₇	C₂²×C₄	1	1	yes	characteristic
14	C₂×D₃₁₇	C₂²×C₄	1	6	yes	—
15	#11929639	C₄²	1	16	yes	direct product factor
16	C₄×C₃₁₇	C₄²	1	6	yes	complemented
17	Dic₃₁₇	C₄²	1	6	yes	complemented
18	C₂×C₃₁₇	C₂×C₄²	1	3	yes	—
19	D₃₁₇	C₂×C₄²	1	4	yes	—
20	C₃₁₇	C₄³	1	1	yes	characteristic, complemented, Sylow
21	C₄³	—	317	1	no	maximal, Sylow
22	C₂×C₄²	—	317	6	no	—
23	C₂×C₄²	—	317	1	no	—
24	C₂²×C₄	—	317	4	no	—
25	C₂²×C₄	—	317	3	no	—
26	C₄²	—	317	24	no	—
27	C₄²	—	317	3	no	—
28	C₄²	#11929639	1	1	yes	characteristic, direct product factor
29	C₂³	—	317	1	no	—
30	C₂×C₄	—	317	24	no	—
31	C₂×C₄	—	317	3	no	—
32	C₂×C₄	—	317	12	no	—
33	C₂×C₄	C₂×#11929639	1	3	yes	—
34	C₂²	—	317	6	no	—
35	C₂²	C₂²×#11929639	1	1	yes	characteristic
36	C₄	—	317	16	no	—
37	C₄	—	317	6	no	—
38	C₄	C₄×#11929639	1	6	yes	direct product factor
39	C₂	—	317	4	no	—
40	C₂	C₂×C₄×#11929639	1	3	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.