Subgroups — C₂²×AGL(1,ℤ/9) #6274

Order 216.

101 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×AGL(1,ℤ/9)	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₃×D₃	—	3	1	no	maximal
4	C₂²×D₉	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂×3₋¹⁺²	C₂²	1	3	yes	complemented
6	AGL(1,ℤ/9)	C₂²	1	4	yes	direct product factor
7	C₂²×C₃²	D₃	1	1	yes	characteristic
8	C₂×C₃×D₃	—	3	6	no	—
9	C₂²×C₉	—	2	1	no	—
10	C₂²×C₉	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂×D₉	C₂×C₃	1	6	yes	complemented
12	3₋¹⁺²	C₂³	1	1	yes	characteristic, complemented, Sylow
13	C₂³×C₃	—	9	1	no	—
14	C₂²×D₃	—	3	1	no	—
15	C₂×C₃²	C₂×D₃	1	3	yes	—
16	C₃×D₃	—	3	4	no	—
17	C₂×C₉	—	2	3	no	—
18	C₂×C₉	C₂²×C₃	1	3	yes	complemented
19	D₉	C₂²×C₃	1	4	yes	complemented
20	C₂²×C₃	—	3	1	no	—
21	C₂²×C₃	—	9	6	no	—
22	C₂²×C₃	C₃×D₃	1	1	yes	characteristic
23	C₂×D₃	—	3	6	no	—
24	C₃²	C₂²×D₃	1	1	yes	characteristic
25	C₉	—	2	1	no	—
26	C₉	C₂³×C₃	1	1	yes	characteristic, complemented
27	C₂³	—	9	1	no	Sylow
28	C₂×C₃	—	3	3	no	—
29	C₂×C₃	—	9	4	no	—
30	C₂×C₃	C₂×C₃×D₃	1	3	yes	—
31	D₃	—	3	4	no	—
32	C₂²	—	9	6	no	—
33	C₂²	AGL(1,ℤ/9)	1	1	yes	characteristic, direct product factor
34	C₃	—	3	1	no	—
35	C₃	C₂²×C₃×D₃	1	1	yes	characteristic
36	C₂	—	9	4	no	—
37	C₂	C₂×AGL(1,ℤ/9)	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²	AGL(1,ℤ/9)
commutator, cosocle, hypocenter	C₉	C₂³×C₃
Frattini	C₃	C₂²×C₃×D₃
Fitting	C₂²×3₋¹⁺²	C₂
socle	C₂²×C₃	C₃×D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₂²

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.