Subgroups — C₃×D₁₅₈₁ #23748688

Order 9486.

36 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	D₁₅₈₁	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×D₅₂₇	—	3	1	no	maximal
4	C₃×C₁₇×C₃₁	—	2	1	no	—
5	C₃×C₁₇×C₃₁	D₃	1	1	yes	characteristic, complemented
6	C₃×C₁₇×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented
7	D₅₂₇	—	3	1	no	Hall
8	C₃×D₉₃	—	17	1	no	maximal, Hall
9	C₁₇×C₃₁	C₃×D₃	1	1	yes	characteristic, complemented, Hall
10	C₃×D₅₁	—	31	1	no	maximal, Hall
11	C₃²×C₃₁	D₁₇	1	1	yes	characteristic, complemented, Hall
12	D₉₃	—	17	1	no	—
13	C₃×D₃₁	—	51	1	no	—
14	C₃²×C₁₇	D₃₁	1	1	yes	characteristic, complemented, Hall
15	D₅₁	—	31	1	no	—
16	C₃×D₁₇	—	93	1	no	—
17	C₃×C₃₁	—	2	1	no	—
18	C₃×C₃₁	C₃×D₁₇	1	1	yes	characteristic, complemented
19	C₃×C₃₁	D₅₁	1	1	yes	characteristic, complemented
20	D₃₁	—	51	1	no	Hall
21	C₃×C₁₇	—	2	1	no	—
22	C₃×C₁₇	C₃×D₃₁	1	1	yes	characteristic, complemented
23	C₃×C₁₇	D₉₃	1	1	yes	characteristic, complemented
24	D₁₇	—	93	1	no	Hall
25	C₃₁	C₃×D₅₁	1	1	yes	characteristic, complemented, Sylow
26	C₃×D₃	—	527	1	no	Hall
27	C₁₇	C₃×D₉₃	1	1	yes	characteristic, complemented, Sylow
28	C₃²	D₅₂₇	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃	—	1581	1	no	—
30	D₃	—	527	1	no	—
31	C₃	—	2	1	no	—
32	C₃	C₃×D₅₂₇	1	1	yes	characteristic, complemented
33	C₃	D₁₅₈₁	1	1	yes	characteristic, direct product factor
34	C₂	—	1581	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	D₁₅₈₁
commutator, cosocle, hypocenter	C₃×C₁₇×C₃₁	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₇×C₃₁	C₂
LCS	G ▷ C₃×C₁₇×C₃₁
UCS	C₁ ◁ C₃

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