Subgroups — #92333

Order 486.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6911	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃×AGL(1,ℤ/9)	—	3	1	no	maximal
3	C₃×(C₃⋊D₃)⋊C₃	—	3	3	no	maximal
4	#4185	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃×3₋¹⁺²	D₃	1	1	yes	characteristic, complemented
6	C₃×H(3,𝔽₃)	D₃	1	3	yes	complemented
7	#732	—	2	3	no	—
8	#732	—	2	1	no	—
9	#732	C₂×C₃	1	1	yes	characteristic, complemented
10	C₃×C₃⋊D₃	—	3	3	no	—
11	C₃²×D₃	—	9	1	no	—
12	AGL(1,ℤ/9)	—	3	3	no	—
13	(C₃⋊D₃)⋊C₃	—	3	6	no	—
14	(C₃⋊D₃)⋊C₃	—	3	3	no	—
15	C₃×D₉	—	3	1	no	—
16	C₃³	—	3	3	no	—
17	C₃³	C₃⋊D₃	1	1	yes	characteristic
18	3₋¹⁺²	—	3	3	no	—
19	H(3,𝔽₃)	—	2	3	no	—
20	H(3,𝔽₃)	—	3	6	no	—
21	H(3,𝔽₃)	C₃×D₃	1	3	yes	complemented
22	C₃×C₉	—	2	1	no	—
23	C₃×C₉	C₃×D₃	1	1	yes	characteristic, complemented
24	C₂×C₃²	—	27	1	no	—
25	C₃⋊D₃	—	3	3	no	—
26	C₃×D₃	—	9	3	no	—
27	C₃×D₃	—	9	1	no	—
28	C₃×D₃	—	27	3	no	—
29	D₉	—	3	1	no	—
30	C₃²	—	3	3	no	—
31	C₃²	—	6	3	no	—
32	C₃²	—	9	1	no	—
33	C₃²	—	9	3	no	—
34	C₃²	—	18	3	no	—
35	C₃²	#272	1	3	yes	—
36	C₃²	C₃×C₃⋊D₃	1	1	yes	characteristic
37	C₉	—	3	1	no	—
38	C₉	—	6	1	no	—
39	C₂×C₃	—	27	3	no	—
40	C₂×C₃	—	27	1	no	—
41	D₃	—	9	1	no	—
42	D₃	—	27	3	no	—
43	C₃	—	3	3	no	—
44	C₃	—	3	1	no	—
45	C₃	—	9	3	no	—
46	C₃	—	18	3	no	—
47	C₃	C₃×#272	1	1	yes	characteristic
48	C₂	—	27	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	#732	C₂×C₃
Frattini	C₃²	C₃×C₃⋊D₃
Fitting	#6911	C₂
socle	C₃	C₃×#272
LCS	G ▷ #732
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.