Subgroups — #92302

Order 486.

147 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6891	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃²×C₃⋊D₃	—	3	1	no	maximal
3	C₃×AGL(1,ℤ/9)	—	3	3	no	maximal
4	#4181	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃⁴	D₃	1	1	yes	characteristic
6	C₃×3₋¹⁺²	D₃	1	3	yes	complemented
7	C₃²⋊C₉	—	2	1	no	—
8	C₃²⋊C₉	—	2	3	no	—
9	C₃²⋊C₉	C₂×C₃	1	1	yes	characteristic, complemented
10	C₃×C₃⋊D₃	—	3	3	no	—
11	C₃×C₃⋊D₃	—	3	1	no	—
12	C₃²×D₃	—	9	3	no	—
13	C₃²×D₃	—	9	1	no	—
14	AGL(1,ℤ/9)	—	3	9	no	—
15	C₃×D₉	—	3	3	no	—
16	C₃³	—	2	1	no	—
17	C₃³	—	3	3	no	—
18	C₃³	—	3	3	no	—
19	C₃³	—	6	3	no	—
20	C₃³	C₃×D₃	1	1	yes	characteristic
21	C₃³	C₃⋊D₃	1	1	yes	characteristic
22	3₋¹⁺²	—	3	9	no	—
23	C₃×C₉	—	2	3	no	—
24	C₃×C₉	C₃×D₃	1	3	yes	complemented
25	C₂×C₃²	—	27	1	no	—
26	C₃⋊D₃	—	3	1	no	—
27	C₃×D₃	—	9	9	no	—
28	C₃×D₃	—	9	3	no	—
29	C₃×D₃	—	9	3	no	—
30	C₃×D₃	—	9	1	no	—
31	D₉	—	3	3	no	—
32	C₃²	—	2	3	no	—
33	C₃²	—	3	1	no	—
34	C₃²	—	3	1	no	—
35	C₃²	—	3	9	no	—
36	C₃²	—	6	1	no	—
37	C₃²	—	6	1	no	—
38	C₃²	—	6	1	no	—
39	C₃²	—	6	9	no	—
40	C₃²	—	6	1	no	—
41	C₃²	—	6	1	no	—
42	C₃²	AGL(1,ℤ/9)	1	3	yes	complemented
43	C₃²	#272	1	3	yes	—
44	C₃²	C₃×C₃⋊D₃	1	1	yes	characteristic
45	C₉	—	3	3	no	—
46	C₉	—	6	3	no	—
47	C₂×C₃	—	27	3	no	—
48	C₂×C₃	—	27	1	no	—
49	D₃	—	9	3	no	—
50	D₃	—	9	1	no	—
51	C₃	—	2	1	no	—
52	C₃	—	3	3	no	—
53	C₃	—	3	3	no	—
54	C₃	—	6	3	no	—
55	C₃	C₃×#272	1	1	yes	characteristic
56	C₃	C₃⋊AGL(1,ℤ/9)	1	1	yes	characteristic
57	C₂	—	27	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	C₃⋊AGL(1,ℤ/9)
commutator, cosocle, hypocenter	C₃²⋊C₉	C₂×C₃
Frattini, socle	C₃²	C₃×C₃⋊D₃
Fitting	#6891	C₂
LCS	G ▷ C₃²⋊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.