Subgroups — C₃²×D₉ #4196

Order 162.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₉	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃²×D₃	—	3	1	no	maximal
3	C₃×D₉	C₃	1	4	yes	maximal, direct product factor
4	C₃³	D₃	1	1	yes	characteristic
5	C₃×C₉	—	2	4	no	—
6	C₃×C₉	C₂×C₃	1	4	yes	complemented
7	C₂×C₃²	—	9	1	no	—
8	C₃×D₃	—	3	4	no	—
9	D₉	C₃²	1	1	yes	characteristic, direct product factor
10	C₃²	—	2	4	no	—
11	C₃²	D₉	1	1	yes	characteristic, direct product factor
12	C₃²	C₃×D₃	1	4	yes	—
13	C₉	—	2	4	no	—
14	C₉	C₂×C₃²	1	1	yes	characteristic, complemented
15	C₂×C₃	—	9	4	no	—
16	D₃	—	3	1	no	—
17	C₃	—	2	4	no	—
18	C₃	C₃×D₉	1	4	yes	direct product factor
19	C₃	C₃²×D₃	1	1	yes	characteristic
20	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²	D₉
commutator, cosocle, hypocenter	C₉	C₂×C₃²
Frattini	C₃	C₃²×D₃
Fitting	C₃²×C₉	C₂
socle	C₃³	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₃²

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

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