Subgroups — C₃⋊AGL(1,ℤ/9) #4206

Order 162.

49 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃×C₃⋊D₃	—	3	1	no	maximal
3	C₃⋊D₉	C₃	1	1	yes	maximal, characteristic, complemented
4	AGL(1,ℤ/9)	—	3	3	no	maximal
5	C₃³	D₃	1	1	yes	characteristic
6	3₋¹⁺²	—	2	3	no	—
7	3₋¹⁺²	D₃	1	3	yes	complemented
8	C₃×C₉	—	2	1	no	—
9	C₃×C₉	C₂×C₃	1	1	yes	characteristic, complemented
10	C₃⋊D₃	—	3	1	no	—
11	C₃×D₃	—	9	3	no	—
12	C₃×D₃	—	9	1	no	—
13	D₉	—	3	3	no	—
14	C₃²	—	2	1	no	—
15	C₃²	—	3	3	no	—
16	C₃²	C₃×D₃	1	1	yes	characteristic
17	C₃²	C₃⋊D₃	1	1	yes	characteristic
18	C₉	—	2	3	no	—
19	C₉	C₃×D₃	1	3	yes	complemented
20	C₂×C₃	—	27	1	no	—
21	D₃	—	9	3	no	—
22	D₃	—	9	1	no	—
23	C₃	—	3	1	no	—
24	C₃	—	6	1	no	—
25	C₃	AGL(1,ℤ/9)	1	3	yes	complemented
26	C₃	C₃×C₃⋊D₃	1	1	yes	characteristic
27	C₂	—	27	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₃×C₉	C₂×C₃
Frattini	C₃	C₃×C₃⋊D₃
Fitting	C₃×3₋¹⁺²	C₂
socle	C₃²	C₃×D₃
LCS	G ▷ C₃×C₉
UCS	C₁

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.