Subgroups — #92184

Order 486.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6873	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	#4207	—	3	1	no	maximal
3	C₃⋊D₂₇	C₃	1	1	yes	maximal, characteristic, complemented
4	#737	D₃	1	1	yes	characteristic
5	C₂₇⋊C₃	—	2	1	no	—
6	C₃×C₂₇	C₂×C₃	1	1	yes	characteristic, complemented
7	C₃⋊D₉	—	3	1	no	—
8	AGL(1,ℤ/9)	—	9	2	no	—
9	(C₃⋊D₃)⋊C₃	—	9	1	no	—
10	C₃×D₉	—	9	1	no	—
11	D₂₇	—	9	1	no	—
12	3₋¹⁺²	—	2	1	no	—
13	3₋¹⁺²	—	3	2	no	—
14	H(3,𝔽₃)	D₉	1	1	yes	characteristic
15	C₃×C₉	—	3	1	no	—
16	C₃×C₉	C₃×D₃	1	1	yes	characteristic
17	C₂₇	—	3	1	no	—
18	C₂₇	—	6	1	no	—
19	C₃⋊D₃	—	9	1	no	—
20	C₃×D₃	—	27	1	no	—
21	D₉	—	9	1	no	—
22	D₉	—	9	2	no	—
23	C₃²	—	3	1	no	—
24	C₃²	C₃×D₉	1	1	yes	characteristic
25	C₉	—	6	1	no	—
26	C₉	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
27	C₉	AGL(1,ℤ/9)	1	2	yes	—
28	C₂×C₃	—	81	1	no	—
29	D₃	—	27	1	no	—
30	D₃	—	81	1	no	—
31	C₃	—	3	1	no	—
32	C₃	—	9	1	no	—
33	C₃	#4169	1	1	yes	characteristic
34	C₂	—	81	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₃×C₂₇	C₂×C₃
Frattini	C₃×C₉	C₃×D₃
Fitting	#6873	C₂
socle	C₃	#4169
LCS	G ▷ C₃×C₂₇
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.