Subgroups — C₃₁₇⋊#401 #35203166

Order 20288.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23778687	C₂	1	3	yes	maximal
2	#23778687	C₂	1	3	yes	maximal
3	#95×C₃₁₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×Dic₃₁₇	C₂²	1	3	yes	—
5	C₂²×Dic₃₁₇	C₂²	1	1	yes	characteristic
6	C₂²×C₄×C₃₁₇	C₂²	1	3	yes	—
7	C₂×Dic₃₁₇	—	2	3	no	—
8	C₂×Dic₃₁₇	—	2	3	no	—
9	C₂×Dic₃₁₇	—	2	3	no	—
10	C₂×Dic₃₁₇	—	2	3	no	—
11	C₂³×C₃₁₇	C₂³	1	1	yes	characteristic
12	C₂×C₄×C₃₁₇	—	2	6	no	—
13	C₂×C₄×C₃₁₇	—	2	3	no	—
14	C₂²×C₃₁₇	#41	1	3	yes	—
15	C₂²×C₃₁₇	#41	1	3	yes	—
16	C₂²×C₃₁₇	#41	1	1	yes	characteristic
17	C₄×C₃₁₇	—	4	3	no	—
18	Dic₃₁₇	—	4	1	no	—
19	Dic₃₁₇	—	4	3	no	—
20	C₂×C₃₁₇	#126	1	3	yes	—
21	C₂×C₃₁₇	#126	1	1	yes	characteristic
22	C₂×C₃₁₇	#126	1	3	yes	—
23	C₃₁₇	#401	1	1	yes	characteristic, complemented, Sylow
24	#401	—	317	1	no	maximal, Sylow
25	#95	—	317	3	no	—
26	#95	—	317	3	no	—
27	#95	D₃₁₇	1	1	yes	characteristic
28	C₂²×C₄	—	317	3	no	—
29	C₂²×C₄	—	317	1	no	—
30	C₂²×C₄	C₂×D₃₁₇	1	3	yes	—
31	C₂³	C₂²×D₃₁₇	1	1	yes	characteristic
32	C₂×C₄	—	2	6	no	—
33	C₂×C₄	—	2	3	no	—
34	C₂×C₄	—	634	3	no	—
35	C₂×C₄	—	634	3	no	—
36	C₂×C₄	—	634	3	no	—
37	C₂×C₄	—	634	3	no	—
38	C₂²	#19099573	1	3	yes	—
39	C₂²	#19099574	1	3	yes	—
40	C₂²	#19099575	1	1	yes	characteristic
41	C₄	—	4	3	no	—
42	C₄	—	1268	1	no	—
43	C₄	—	1268	3	no	—
44	C₂	#23778773	1	3	yes	—
45	C₂	#23778774	1	1	yes	characteristic
46	C₂	#23778775	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₃₁₇
commutator, socle, prime radical, cosocle	C₂³×C₃₁₇	C₂³
Fitting	#95×C₃₁₇	C₂
hypercenter	#95	D₃₁₇
hypocenter	C₃₁₇	#401
LCS	G ▷ C₂³×C₃₁₇ ▷ C₃₁₇
UCS	C₁ ◁ C₂³ ◁ #95

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

N	H ≅ G/N	type
23. C₃₁₇	#401	semidirect

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