Subgroups — #92207

Order 486.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6866	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃×C₃⋊(C₃⋊D₃)	—	3	1	no	maximal
3	#4169	—	3	3	no	maximal
4	C₃⁴	D₃	1	1	yes	characteristic
5	C₃²⋊C₉	D₃	1	3	yes	complemented
6	C₃⋊(C₃⋊D₃)	—	3	1	no	—
7	C₃×C₃⋊D₃	—	9	9	no	—
8	C₃×C₃⋊D₃	—	9	3	no	—
9	C₃×C₃⋊D₃	—	9	1	no	—
10	C₃⋊D₉	—	3	3	no	—
11	C₃³	—	3	1	no	—
12	C₃³	—	3	9	no	—
13	C₃³	—	6	1	no	—
14	C₃³	D₉	1	3	yes	complemented
15	C₃³	C₃⋊D₃	1	1	yes	characteristic
16	C₃×C₉	—	3	3	no	—
17	C₃⋊D₃	—	9	3	no	—
18	C₃⋊D₃	—	9	9	no	—
19	C₃⋊D₃	—	9	1	no	—
20	C₃×D₃	—	27	9	no	—
21	C₃×D₃	—	27	3	no	—
22	C₃×D₃	—	27	1	no	—
23	D₉	—	27	3	no	—
24	C₃²	—	2	1	no	—
25	C₃²	—	3	9	no	—
26	C₃²	—	3	3	no	—
27	C₃²	—	3	9	no	—
28	C₃²	—	3	3	no	—
29	C₃²	—	6	9	no	—
30	C₃²	C₃⋊D₉	1	1	yes	characteristic
31	C₃²	#272	1	1	yes	characteristic
32	C₉	—	9	3	no	—
33	C₂×C₃	—	81	1	no	—
34	D₃	—	27	9	no	—
35	D₃	—	27	1	no	—
36	D₃	—	27	3	no	—
37	C₃	—	3	9	no	—
38	C₃	—	3	1	no	—
39	C₃	—	6	1	no	—
40	C₃	#4181	1	1	yes	characteristic
41	C₃	#4183	1	3	yes	—
42	C₂	—	81	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	#6866	C₂
Frattini	C₃³	C₃⋊D₃
socle	C₃²	#272
LCS	G ▷ #6866
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.