Subgroups — #95×D₃₁₇ #35203066

Order 20288.

330 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₃₁₇	C₂	1	3	yes	maximal
2	#23778687	C₂	1	3	yes	maximal, complemented
3	#95×C₃₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×D₃₁₇	C₂²	1	1	yes	characteristic
5	C₂²×Dic₃₁₇	C₂²	1	3	yes	—
6	C₂×C₄×D₃₁₇	—	2	12	no	—
7	C₂×C₄×D₃₁₇	C₄	1	12	yes	complemented
8	C₂²×C₄×C₃₁₇	C₂²	1	3	yes	—
9	C₂²×D₃₁₇	C₂×C₄	1	6	yes	—
10	C₂²×D₃₁₇	D₄	1	6	yes	—
11	C₂²×D₃₁₇	Q₈	1	2	yes	—
12	C₂×Dic₃₁₇	—	2	6	no	—
13	C₂×Dic₃₁₇	C₂×C₄	1	6	yes	complemented
14	C₄×D₃₁₇	—	2	24	no	—
15	C₂³×C₃₁₇	C₂³	1	1	yes	characteristic
16	C₂×C₄×C₃₁₇	—	2	6	no	—
17	C₂×C₄×C₃₁₇	C₂×C₄	1	6	yes	complemented
18	C₂²×C₃₁₇	C₂²×C₄	1	3	yes	—
19	C₂²×C₃₁₇	C₂×D₄	1	3	yes	—
20	C₂²×C₃₁₇	C₂×Q₈	1	1	yes	characteristic
21	C₂×D₃₁₇	C₄²	1	4	yes	—
22	C₂×D₃₁₇	C₂²⋊C₄	1	12	yes	—
23	C₂×D₃₁₇	C₄⋊C₄	1	12	yes	—
24	C₄×C₃₁₇	—	2	6	no	—
25	Dic₃₁₇	—	2	6	no	—
26	C₂×C₃₁₇	C₂×C₄²	1	1	yes	characteristic
27	C₂×C₃₁₇	C₂×C₂²⋊C₄	1	3	yes	—
28	C₂×C₃₁₇	C₂×C₄⋊C₄	1	3	yes	—
29	D₃₁₇	#95	1	8	yes	direct product factor
30	C₃₁₇	C₂×#95	1	1	yes	characteristic, complemented, Sylow
31	C₂×#95	—	317	1	no	maximal, Sylow
32	C₂³×C₄	—	317	3	no	—
33	#95	—	317	3	no	—
34	#95	D₃₁₇	1	1	yes	characteristic, direct product factor
35	C₂⁴	—	317	1	no	—
36	C₂²×C₄	—	317	3	no	—
37	C₂²×C₄	—	317	12	no	—
38	C₂²×C₄	—	634	12	no	—
39	C₂²×C₄	C₂×D₃₁₇	1	3	yes	—
40	C₂³	—	317	6	no	—
41	C₂³	—	317	6	no	—
42	C₂³	—	317	2	no	—
43	C₂³	C₂²×D₃₁₇	1	1	yes	characteristic
44	C₂×C₄	—	2	6	no	—
45	C₂×C₄	—	317	6	no	—
46	C₂×C₄	—	634	24	no	—
47	C₂×C₄	—	634	6	no	—
48	C₂×C₄	C₄×D₃₁₇	1	6	yes	complemented
49	C₂²	—	317	4	no	—
50	C₂²	—	317	12	no	—
51	C₂²	—	317	12	no	—
52	C₂²	C₂×C₄×D₃₁₇	1	3	yes	—
53	C₂²	D₄×D₃₁₇	1	3	yes	—
54	C₂²	Q₈×D₃₁₇	1	1	yes	characteristic
55	C₄	—	2	6	no	—
56	C₄	—	634	6	no	—
57	C₂	—	317	8	no	—
58	C₂	C₄²×D₃₁₇	1	1	yes	characteristic
59	C₂	C₂²⋊C₄×D₃₁₇	1	3	yes	—
60	C₂	C₄⋊C₄×D₃₁₇	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₃₁₇
commutator	C₂×C₃₁₇	C₂×C₄²
Fitting	#95×C₃₁₇	C₂
socle, cosocle	C₂³×C₃₁₇	C₂³
prime radical	C₂³×D₃₁₇	C₂²
hypercenter	#95	D₃₁₇
hypocenter	C₃₁₇	C₂×#95
LCS	G ▷ C₂×C₃₁₇ ▷ C₃₁₇
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
2. #23778687	C₂	semidirect
3. #95×C₃₁₇	C₂	semidirect
7. C₂×C₄×D₃₁₇	C₄	semidirect
13. C₂×Dic₃₁₇	C₂×C₄	semidirect
17. C₂×C₄×C₃₁₇	C₂×C₄	semidirect
29. D₃₁₇	#95	direct (N × H)
30. C₃₁₇	C₂×#95	semidirect
34. #95	D₃₁₇	direct (N × H)
48. C₂×C₄	C₄×D₃₁₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₃₁₇	2
#23778687	2
#95×C₃₁₇	2
C₂×#95	317

Subgroups — #95×D317 #35203066

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #95×D₃₁₇ #35203066