Subgroups — C₁₆×#11929639 #35204107

Order 20288.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₁₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₈×#11929639	C₂	1	1	yes	maximal, characteristic
3	C₁₆×D₃₁₇	C₂	1	1	yes	maximal, characteristic
4	D₃₁₇⋊C₈	C₄	1	1	yes	characteristic
5	C₄×#11929639	C₄	1	1	yes	characteristic
6	#19099577	C₄	1	2	yes	complemented
7	C₈×D₃₁₇	C₂²	1	1	yes	characteristic
8	#19099549	C₄	1	1	yes	characteristic, complemented
9	C₁₆×C₃₁₇	C₄	1	1	yes	characteristic, complemented
10	C₂×#11929639	C₈	1	2	yes	—
11	#14579268	C₈	1	2	yes	—
12	C₄×D₃₁₇	C₂×C₄	1	1	yes	characteristic
13	#14579261	C₂×C₄	1	1	yes	characteristic
14	C₈×C₃₁₇	C₂×C₄	1	1	yes	characteristic
15	C₂×D₃₁₇	C₂×C₈	1	1	yes	characteristic
16	#11929639	C₁₆	1	4	yes	direct product factor
17	C₄×C₃₁₇	C₄²	1	1	yes	characteristic
18	Dic₃₁₇	C₂×C₈	1	1	yes	characteristic
19	C₂×C₃₁₇	C₄×C₈	1	1	yes	characteristic
20	D₃₁₇	C₂×C₁₆	1	2	yes	—
21	C₃₁₇	C₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
22	C₄×C₁₆	—	317	1	no	maximal, Sylow
23	C₂×C₁₆	—	317	1	no	—
24	C₂×C₁₆	—	317	1	no	—
25	C₄×C₈	—	317	1	no	—
26	C₂×C₈	—	317	1	no	—
27	C₂×C₈	—	317	1	no	—
28	C₄²	—	317	1	no	—
29	C₁₆	—	317	2	no	—
30	C₁₆	—	317	1	no	—
31	C₁₆	#11929639	1	1	yes	characteristic, direct product factor
32	C₂×C₄	—	317	2	no	—
33	C₂×C₄	—	317	1	no	—
34	C₈	—	317	2	no	—
35	C₈	—	317	1	no	—
36	C₈	C₂×#11929639	1	1	yes	characteristic
37	C₂²	—	317	1	no	—
38	C₄	—	317	4	no	—
39	C₄	—	317	1	no	—
40	C₄	C₄×#11929639	1	1	yes	characteristic
41	C₂	—	317	2	no	—
42	C₂	C₈×#11929639	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₁₆	#11929639
commutator, hypocenter	C₃₁₇	C₄×C₁₆
Frattini	C₈	C₂×#11929639
Fitting	C₁₆×C₃₁₇	C₄
socle	C₂×C₃₁₇	C₄×C₈
prime radical	C₂×D₃₁₇	C₂×C₈
cosocle	C₈×D₃₁₇	C₂²
LCS	G ▷ C₃₁₇
UCS	C₁ ◁ C₁₆

Complements

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

N	H ≅ G/N	type
6. #19099577	C₄	semidirect
8. #19099549	C₄	semidirect
9. C₁₆×C₃₁₇	C₄	semidirect
16. #11929639	C₁₆	direct (N × H)
21. C₃₁₇	C₄×C₁₆	semidirect
31. C₁₆	#11929639	direct (N × H)

Maximal subgroups

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

subgroup	index
D₃₁₇⋊C₁₆	2
C₈×#11929639	2
C₁₆×D₃₁₇	2
C₄×C₁₆	317

Subgroups — C16×#11929639 #35204107

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₆×#11929639 #35204107