Subgroups — #92309

Order 486.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6896	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃⋊AGL(1,ℤ/9)	—	3	2	no	maximal
3	C₉⋊D₉	C₃	1	1	yes	maximal, characteristic, complemented
4	#4169	—	3	2	no	maximal
5	C₃×3₋¹⁺²	D₃	1	2	yes	—
6	C₉⋊C₉	—	2	2	no	—
7	C₉⋊C₉	—	2	2	no	—
8	C₃²⋊C₉	D₃	1	2	yes	—
9	C₉²	C₂×C₃	1	1	yes	characteristic, complemented
10	C₃×C₃⋊D₃	—	9	1	no	—
11	C₃⋊D₉	—	3	2	no	—
12	C₃⋊D₉	—	3	2	no	—
13	AGL(1,ℤ/9)	—	9	6	no	—
14	C₃³	C₃⋊D₃	1	1	yes	characteristic
15	3₋¹⁺²	—	3	6	no	—
16	C₃×C₉	—	2	2	no	—
17	C₃×C₉	—	2	2	no	—
18	C₃×C₉	C₃×D₃	1	2	yes	—
19	C₃×C₉	C₃×D₃	1	2	yes	—
20	C₃⋊D₃	—	9	1	no	—
21	C₃×D₃	—	27	2	no	—
22	C₃×D₃	—	27	2	no	—
23	D₉	—	9	6	no	—
24	D₉	—	27	2	no	—
25	C₃²	—	3	2	no	—
26	C₃²	—	3	2	no	—
27	C₃²	C₃×C₃⋊D₃	1	1	yes	characteristic
28	C₉	—	3	2	no	—
29	C₉	—	6	2	no	—
30	C₉	—	6	2	no	—
31	C₉	AGL(1,ℤ/9)	1	6	yes	complemented
32	C₂×C₃	—	81	1	no	—
33	D₃	—	27	2	no	—
34	D₃	—	27	2	no	—
35	C₃	—	9	1	no	—
36	C₃	C₃⋊AGL(1,ℤ/9)	1	2	yes	—
37	C₃	#4207	1	2	yes	—
38	C₂	—	81	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₉²	C₂×C₃
Frattini, socle	C₃²	C₃×C₃⋊D₃
Fitting	#6896	C₂
LCS	G ▷ C₉²
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.