Subgroups — C₃²×C₃₁×D₁₇ #23748683

Order 9486.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₇×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₃₁×D₁₇	C₃	1	4	yes	maximal, direct product factor
3	C₃×C₁₇×C₃₁	C₂×C₃	1	4	yes	complemented
4	C₃₁×D₁₇	C₃²	1	1	yes	characteristic, direct product factor, Hall
5	C₂×C₃²×C₃₁	—	17	1	no	maximal, Hall
6	C₁₇×C₃₁	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
7	C₃²×D₁₇	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₃²×C₃₁	D₁₇	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₃×C₃₁	—	17	4	no	—
10	C₃²×C₁₇	C₂×C₃₁	1	1	yes	characteristic, complemented, Hall
11	C₃×D₁₇	C₃×C₃₁	1	4	yes	direct product factor
12	C₃×C₃₁	C₃×D₁₇	1	4	yes	direct product factor
13	C₂×C₃₁	—	17	1	no	Hall
14	C₃×C₁₇	C₂×C₃×C₃₁	1	4	yes	complemented
15	D₁₇	C₃²×C₃₁	1	1	yes	characteristic, direct product factor, Hall
16	C₃₁	C₃²×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
17	C₂×C₃²	—	17	1	no	Hall
18	C₁₇	C₂×C₃²×C₃₁	1	1	yes	characteristic, complemented, Sylow
19	C₃²	C₃₁×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃	—	17	4	no	—
21	C₃	C₃×C₃₁×D₁₇	1	4	yes	direct product factor
22	C₂	—	17	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²×C₃₁	D₁₇
commutator, cosocle, hypocenter	C₁₇	C₂×C₃²×C₃₁
Frattini	C₁	G
Fitting, socle	C₃²×C₁₇×C₃₁	C₂
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₃²×C₃₁

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