Subgroups — C₃×AGL(1,ℤ/9) #4200

Order 162.

46 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	C₃²×D₃	—	3	1	no	maximal
3	AGL(1,ℤ/9)	C₃	1	3	yes	maximal, direct product factor
4	C₃×D₉	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃³	D₃	1	1	yes	characteristic
6	3₋¹⁺²	—	2	3	no	—
7	3₋¹⁺²	C₂×C₃	1	3	yes	complemented
8	C₃×C₉	—	2	1	no	—
9	C₃×C₉	C₂×C₃	1	1	yes	characteristic, complemented
10	C₂×C₃²	—	9	1	no	—
11	C₃×D₃	—	3	1	no	—
12	C₃×D₃	—	3	3	no	—
13	D₉	C₃²	1	1	yes	characteristic, complemented
14	C₃²	—	3	1	no	—
15	C₃²	—	6	1	no	—
16	C₃²	C₃×D₃	1	1	yes	characteristic
17	C₃²	C₃×D₃	1	3	yes	—
18	C₉	—	2	3	no	—
19	C₉	—	2	1	no	—
20	C₉	C₂×C₃²	1	1	yes	characteristic, complemented
21	C₂×C₃	—	9	3	no	—
22	C₂×C₃	—	9	1	no	—
23	D₃	—	3	1	no	—
24	C₃	—	2	1	no	—
25	C₃	—	3	3	no	—
26	C₃	AGL(1,ℤ/9)	1	1	yes	characteristic, direct product factor
27	C₃	C₃²×D₃	1	1	yes	characteristic
28	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	AGL(1,ℤ/9)
commutator, cosocle, hypocenter	C₉	C₂×C₃²
Frattini	C₃	C₃²×D₃
Fitting	C₃×3₋¹⁺²	C₂
socle	C₃²	C₃×D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₃

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.