Subgroups — #92201

Order 486.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6859	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃⋊((C₃⋊D₃)⋊C₃)	—	3	1	no	maximal
3	#4169	—	3	1	no	maximal
4	#4169	—	3	2	no	maximal
5	C₃×H(3,𝔽₃)	D₃	1	1	yes	characteristic
6	C₃²⋊C₉	D₃	1	1	yes	characteristic, complemented
7	C₃²⋊C₉	D₃	1	2	yes	complemented
8	C₃⋊(C₃⋊D₃)	—	3	1	no	—
9	C₃×C₃⋊D₃	—	9	1	no	—
10	C₃⋊D₉	—	3	1	no	—
11	C₃⋊D₉	—	3	2	no	—
12	(C₃⋊D₃)⋊C₃	—	9	3	no	—
13	C₃³	—	3	1	no	—
14	C₃³	C₃⋊D₃	1	1	yes	characteristic
15	H(3,𝔽₃)	—	3	3	no	—
16	C₃×C₉	—	3	1	no	—
17	C₃×C₉	—	3	2	no	—
18	C₃⋊D₃	—	9	1	no	—
19	C₃⋊D₃	—	9	3	no	—
20	C₃⋊D₃	—	27	2	no	—
21	C₃⋊D₃	—	27	1	no	—
22	C₃×D₃	—	27	1	no	—
23	C₃×D₃	—	27	2	no	—
24	C₃×D₃	—	27	1	no	—
25	D₉	—	27	1	no	—
26	D₉	—	27	2	no	—
27	C₃²	—	3	1	no	—
28	C₃²	—	3	3	no	—
29	C₃²	—	3	2	no	—
30	C₃²	—	3	1	no	—
31	C₃²	—	9	2	no	—
32	C₃²	—	9	1	no	—
33	C₃²	#272	1	1	yes	characteristic
34	C₉	—	9	1	no	—
35	C₉	—	9	2	no	—
36	C₂×C₃	—	81	1	no	—
37	D₃	—	27	1	no	—
38	D₃	—	27	2	no	—
39	D₃	—	27	1	no	—
40	D₃	—	81	3	no	—
41	C₃	—	9	3	no	—
42	C₃	—	9	1	no	—
43	C₃	#4183	1	1	yes	characteristic
44	C₃	#4184	1	2	yes	—
45	C₃	#4185	1	1	yes	characteristic
46	C₂	—	81	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	#6859	C₂
Frattini	C₃³	C₃⋊D₃
socle	C₃²	#272
LCS	G ▷ #6859
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.