Subgroups — C₃₁₇⋊#564 #35203978

Order 20288.

172 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23778772	C₂	1	2	yes	maximal
2	#23778771	C₂	1	4	yes	maximal
3	#23778770	C₂	1	4	yes	maximal
4	#23778770	C₂	1	4	yes	maximal
5	#125×C₃₁₇	C₂	1	1	yes	maximal, characteristic
6	C₄⋊Dic₃₁₇	C₂²	1	2	yes	—
7	C₄⋊Dic₃₁₇	C₂²	1	4	yes	—
8	C₄⋊Dic₃₁₇	C₂²	1	2	yes	—
9	#19099553	C₂²	1	4	yes	—
10	#19099553	C₂²	1	4	yes	—
11	#19099553	C₂²	1	4	yes	—
12	#19099553	C₂²	1	4	yes	—
13	C₄×Dic₃₁₇	C₂²	1	4	yes	—
14	C₄⋊C₄×C₃₁₇	C₂²	1	2	yes	—
15	C₄⋊C₄×C₃₁₇	C₂²	1	4	yes	—
16	C₄²×C₃₁₇	C₂²	1	1	yes	characteristic
17	C₂×Dic₃₁₇	C₂³	1	4	yes	—
18	C₂×Dic₃₁₇	C₂³	1	4	yes	—
19	C₂×C₄×C₃₁₇	C₂³	1	1	yes	characteristic
20	C₂×C₄×C₃₁₇	C₂³	1	2	yes	—
21	C₂×C₄×C₃₁₇	C₂³	1	4	yes	—
22	C₂²×C₃₁₇	C₂⁴	1	1	yes	characteristic
23	C₄×C₃₁₇	—	2	2	no	—
24	C₄×C₃₁₇	—	2	4	no	—
25	C₄×C₃₁₇	—	2	1	no	—
26	Dic₃₁₇	—	2	4	no	—
27	Dic₃₁₇	—	2	4	no	—
28	C₂×C₃₁₇	2₋¹⁺⁴	1	2	yes	—
29	C₂×C₃₁₇	2₋¹⁺⁴	1	1	yes	characteristic
30	C₃₁₇	#564	1	1	yes	characteristic, complemented, Sylow
31	#564	—	317	1	no	maximal, Sylow
32	#125	—	317	4	no	—
33	#125	—	317	4	no	—
34	#125	—	317	4	no	—
35	#125	—	317	2	no	—
36	#125	D₃₁₇	1	1	yes	characteristic
37	C₄⋊C₄	—	317	4	no	—
38	C₄⋊C₄	—	317	4	no	—
39	C₄⋊C₄	—	317	4	no	—
40	C₄⋊C₄	—	317	4	no	—
41	C₄⋊C₄	—	317	4	no	—
42	C₄⋊C₄	—	317	2	no	—
43	C₄⋊C₄	—	317	2	no	—
44	C₄⋊C₄	C₂×D₃₁₇	1	2	yes	—
45	C₄⋊C₄	C₂×D₃₁₇	1	4	yes	—
46	C₄²	—	317	4	no	—
47	C₄²	C₂×D₃₁₇	1	1	yes	characteristic
48	C₂×C₄	—	317	4	no	—
49	C₂×C₄	—	317	4	no	—
50	C₂×C₄	C₂²×D₃₁₇	1	4	yes	—
51	C₂×C₄	C₂²×D₃₁₇	1	2	yes	—
52	C₂×C₄	C₂²×D₃₁₇	1	1	yes	characteristic
53	C₂²	C₂³×D₃₁₇	1	1	yes	characteristic
54	C₄	—	2	4	no	—
55	C₄	—	2	2	no	—
56	C₄	—	2	1	no	—
57	C₄	—	634	4	no	—
58	C₄	—	634	4	no	—
59	C₂	#23778827	1	2	yes	—
60	C₂	#23778828	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₃₁₇
commutator, socle, prime radical, cosocle	C₂²×C₃₁₇	C₂⁴
Fitting	#125×C₃₁₇	C₂
hypercenter	#125	D₃₁₇
hypocenter	C₃₁₇	#564
LCS	G ▷ C₂²×C₃₁₇ ▷ C₃₁₇
UCS	C₁ ◁ C₂² ◁ #125

Complements

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

N	H ≅ G/N	type
30. C₃₁₇	#564	semidirect

Maximal subgroups

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

subgroup	index
#23778772	2
#23778771	2
#23778770	2
#125×C₃₁₇	2
#564	317

Subgroups — C317⋊#564 #35203978

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁₇⋊#564 #35203978