Subgroups — #92305

Order 486.

96 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⋊#272	C₃	1	1	yes	maximal, characteristic
3	C₉×C₃⋊D₃	—	3	1	no	maximal
4	(C₃⋊D₃)⋊C₉	—	3	3	no	maximal
5	C₃×3₋¹⁺²	—	2	1	no	—
6	C₃×H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic
7	C₃²×C₉	D₃	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	—	3	3	no	—
12	#272	—	9	3	no	—
13	D₃×C₉	—	9	3	no	—
14	D₃×C₉	—	9	1	no	—
15	C₃³	C₃×D₃	1	3	yes	—
16	C₃³	C₃×D₃	1	1	yes	characteristic
17	3₋¹⁺²	—	6	3	no	—
18	H(3,𝔽₃)	—	3	3	no	—
19	C₃×C₉	—	2	1	no	—
20	C₃×C₉	—	2	3	no	—
21	C₃×C₉	—	3	3	no	—
22	C₃×C₉	C₃⋊D₃	1	1	yes	characteristic
23	C₃⋊D₃	—	3	1	no	—
24	C₃⋊D₃	—	3	3	no	—
25	C₃×D₃	—	9	3	no	—
26	C₃×D₃	—	9	1	no	—
27	C₃×D₃	—	27	3	no	—
28	C₂×C₉	—	27	1	no	—
29	C₃²	—	3	1	no	—
30	C₃²	—	3	3	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	1	no	—
37	C₉	—	6	1	no	—
38	C₉	—	6	3	no	—
39	C₂×C₃	—	27	1	no	—
40	D₃	—	9	3	no	—
41	D₃	—	9	1	no	—
42	D₃	—	27	3	no	—
43	C₃	—	2	1	no	—
44	C₃	—	3	3	no	—
45	C₃	—	9	3	no	—
46	C₃	C₃⋊((C₃⋊D₃)⋊C₃)	1	1	yes	characteristic
47	C₃	#4208	1	1	yes	characteristic
48	C₂	—	27	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	C₃⋊((C₃⋊D₃)⋊C₃)
commutator, cosocle, hypocenter	C₃×H(3,𝔽₃)	C₂×C₃
Frattini, socle	C₃²	C₃×C₃⋊D₃
Fitting	#6893	C₂
prime radical	C₃⋊#272	C₃
LCS	G ▷ C₃×H(3,𝔽₃)
UCS	C₁ ◁ C₃

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.