Subgroups — #10624863

Order 729.

472 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic
2	C₉×3₋¹⁺²	C₃	1	27	yes	maximal, complemented
3	#6887	C₃	1	9	yes	maximal, complemented
4	C₃×C₃²⋊C₉	C₃	1	3	yes	maximal
5	C₃⁴	C₃²	1	1	yes	characteristic
6	C₃×3₋¹⁺²	C₉	1	27	yes	complemented
7	C₃×3₋¹⁺²	C₃²	1	9	yes	—
8	C₃²×C₉	C₃²	1	9	yes	—
9	C₃²×C₉	C₃²	1	3	yes	—
10	C₉⋊C₉	C₃²	1	54	yes	complemented
11	C₃²⋊C₉	C₃²	1	9	yes	—
12	C₃²⋊C₉	C₃²	1	18	yes	—
13	C₉²	C₃²	1	27	yes	complemented
14	C₃³	—	9	3	no	—
15	C₃³	C₃×C₉	1	9	yes	—
16	C₃³	C₃³	1	1	yes	characteristic
17	C₃³	C₃³	1	3	yes	—
18	3₋¹⁺²	C₃×C₉	1	81	yes	complemented
19	C₃×C₉	—	9	9	no	—
20	C₃×C₉	C₃×C₉	1	27	yes	complemented
21	C₃×C₉	C₃³	1	27	yes	—
22	C₃×C₉	C₃³	1	9	yes	—
23	C₃²	—	3	3	no	—
24	C₃²	—	3	3	no	—
25	C₃²	—	3	6	no	—
26	C₃²	—	9	9	no	—
27	C₃²	C₃²×C₉	1	3	yes	—
28	C₃²	C₃²×C₉	1	9	yes	—
29	C₃²	C₃⁴	1	1	yes	characteristic
30	C₉	—	3	27	no	—
31	C₉	C₃²×C₉	1	27	yes	—
32	C₃	—	3	9	no	—
33	C₃	—	3	3	no	—
34	C₃	C₃³×C₉	1	1	yes	characteristic
35	C₃	3₋¹⁺⁴	1	3	yes	—

	subgroup	G/H
center, Frattini, socle, cosocle	C₃²	C₃⁴
commutator	C₃	C₃³×C₉
prime radical	C₃⁴	C₃²
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃² ◁ G
LECS	G ▷ C₃² ▷ 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.