Subgroups — C₂×AGL(1,ℤ/9) #1099

Order 108.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic, complemented
2	AGL(1,ℤ/9)	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×D₃	—	3	1	no	maximal
4	C₂×D₉	C₃	1	1	yes	maximal, characteristic, complemented
5	3₋¹⁺²	C₂²	1	1	yes	characteristic, complemented, Sylow
6	C₂×C₃²	D₃	1	1	yes	characteristic
7	C₃×D₃	—	3	2	no	—
8	C₂×C₉	—	2	1	no	—
9	C₂×C₉	C₂×C₃	1	1	yes	characteristic, complemented
10	D₉	C₂×C₃	1	2	yes	complemented
11	C₂²×C₃	—	9	1	no	—
12	C₂×D₃	—	3	1	no	—
13	C₃²	C₂×D₃	1	1	yes	characteristic
14	C₉	—	2	1	no	—
15	C₉	C₂²×C₃	1	1	yes	characteristic, complemented
16	C₂×C₃	—	3	1	no	—
17	C₂×C₃	—	9	2	no	—
18	C₂×C₃	C₃×D₃	1	1	yes	characteristic
19	D₃	—	3	2	no	—
20	C₂²	—	9	1	no	Sylow
21	C₃	—	3	1	no	—
22	C₃	C₂×C₃×D₃	1	1	yes	characteristic
23	C₂	—	9	2	no	—
24	C₂	AGL(1,ℤ/9)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	AGL(1,ℤ/9)
commutator, cosocle, hypocenter	C₉	C₂²×C₃
Frattini	C₃	C₂×C₃×D₃
Fitting	C₂×3₋¹⁺²	C₂
socle	C₂×C₃	C₃×D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₂

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.