Subgroups — #92308

Order 486.

63 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6896	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	#4181	C₃	1	1	yes	maximal, characteristic
3	D₉⋊C₉	—	3	2	no	maximal
4	(C₃⋊D₃)⋊C₉	—	3	1	no	maximal
5	C₉×D₉	—	3	1	no	maximal
6	C₃×3₋¹⁺²	—	2	1	no	—
7	C₉⋊C₉	—	2	2	no	—
8	C₉⋊C₉	—	2	1	no	—
9	C₉⋊C₉	D₃	1	2	yes	complemented
10	C₃²⋊C₉	D₃	1	1	yes	characteristic
11	C₃²⋊C₉	C₂×C₃	1	1	yes	characteristic
12	C₉²	D₃	1	1	yes	characteristic, complemented
13	C₃×C₃⋊D₃	—	3	1	no	—
14	D₃×C₉	—	9	1	no	—
15	C₃×D₉	—	3	1	no	—
16	C₃×D₉	—	3	2	no	—
17	C₃³	C₃×D₃	1	1	yes	characteristic
18	3₋¹⁺²	—	6	3	no	—
19	C₃×C₉	—	2	1	no	—
20	C₃×C₉	—	2	1	no	—
21	C₃×C₉	—	2	2	no	—
22	C₃×C₉	C₃×D₃	1	1	yes	characteristic
23	C₃×C₉	C₃×D₃	1	2	yes	—
24	C₃×C₉	C₃⋊D₃	1	1	yes	characteristic
25	C₃⋊D₃	—	3	1	no	—
26	C₃×D₃	—	9	1	no	—
27	C₃×D₃	—	27	1	no	—
28	C₂×C₉	—	27	1	no	—
29	D₉	—	3	1	no	—
30	D₉	—	3	2	no	—
31	C₃²	—	3	1	no	—
32	C₃²	—	3	1	no	—
33	C₃²	—	6	1	no	—
34	C₃²	C₃×C₃⋊D₃	1	1	yes	characteristic
35	C₉	—	2	3	no	—
36	C₉	—	3	1	no	—
37	C₉	—	3	1	no	—
38	C₉	—	3	2	no	—
39	C₉	—	6	2	no	—
40	C₉	—	6	1	no	—
41	C₂×C₃	—	27	1	no	—
42	D₃	—	9	1	no	—
43	D₃	—	27	1	no	—
44	C₃	—	2	1	no	—
45	C₃	—	9	1	no	—
46	C₃	#4207	1	1	yes	characteristic
47	C₃	#4208	1	1	yes	characteristic
48	C₂	—	27	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	#4207
commutator, cosocle, hypocenter	C₃²⋊C₉	C₂×C₃
Frattini, socle	C₃²	C₃×C₃⋊D₃
Fitting	#6896	C₂
prime radical	#4181	C₃
LCS	G ▷ C₃²⋊C₉
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.