Subgroups — #92306

Order 486.

99 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6893	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃⋊(C₃⋊D₉)	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃⋊((C₃⋊D₃)⋊C₃)	—	3	1	no	maximal
4	#4169	—	3	3	no	maximal
5	C₃×3₋¹⁺²	—	2	1	no	—
6	C₃×H(3,𝔽₃)	D₃	1	1	yes	characteristic
7	C₃²×C₉	C₂×C₃	1	1	yes	characteristic, complemented
8	C₃²⋊C₉	—	2	3	no	—
9	C₃²⋊C₉	D₃	1	3	yes	complemented
10	C₃⋊(C₃⋊D₃)	—	3	1	no	—
11	C₃×C₃⋊D₃	—	9	1	no	—
12	C₃⋊D₉	—	3	3	no	—
13	C₃⋊D₉	—	9	3	no	—
14	(C₃⋊D₃)⋊C₃	—	9	3	no	—
15	C₃³	—	2	1	no	—
16	C₃³	C₃×D₃	1	1	yes	characteristic
17	C₃³	C₃⋊D₃	1	1	yes	characteristic
18	3₋¹⁺²	—	6	3	no	—
19	H(3,𝔽₃)	—	3	3	no	—
20	C₃×C₉	—	2	3	no	—
21	C₃×C₉	—	3	3	no	—
22	C₃×C₉	C₃×D₃	1	3	yes	—
23	C₃⋊D₃	—	9	1	no	—
24	C₃⋊D₃	—	9	3	no	—
25	C₃⋊D₃	—	27	3	no	—
26	C₃×D₃	—	27	1	no	—
27	C₃×D₃	—	27	3	no	—
28	D₉	—	27	3	no	—
29	C₃²	—	3	3	no	—
30	C₃²	—	3	1	no	—
31	C₃²	—	3	3	no	—
32	C₃²	—	6	1	no	—
33	C₃²	—	6	3	no	—
34	C₃²	(C₃⋊D₃)⋊C₃	1	3	yes	—
35	C₃²	C₃×C₃⋊D₃	1	1	yes	characteristic
36	C₉	—	3	3	no	—
37	C₉	—	6	3	no	—
38	C₂×C₃	—	81	1	no	—
39	D₃	—	27	1	no	—
40	D₃	—	27	3	no	—
41	D₃	—	81	3	no	—
42	C₃	—	3	3	no	—
43	C₃	—	9	1	no	—
44	C₃	—	18	1	no	—
45	C₃	C₃⋊((C₃⋊D₃)⋊C₃)	1	1	yes	characteristic
46	C₃	#4207	1	3	yes	—
47	C₂	—	81	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₃²×C₉	C₂×C₃
Frattini, socle	C₃²	C₃×C₃⋊D₃
Fitting	#6893	C₂
LCS	G ▷ C₃²×C₉
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.