Subgroups — C₉⋊D₂₇ #92205

Order 486.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₂₇	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃⋊D₂₇	—	3	3	no	maximal
3	C₉⋊D₉	—	3	1	no	maximal
4	C₃×C₂₇	D₃	1	3	yes	—
5	C₉²	D₃	1	1	yes	characteristic
6	C₃⋊D₉	—	9	3	no	—
7	C₃⋊D₉	—	9	1	no	—
8	D₂₇	—	9	9	no	—
9	C₃×C₉	D₉	1	3	yes	—
10	C₃×C₉	C₃⋊D₃	1	1	yes	characteristic
11	C₂₇	D₉	1	9	yes	complemented
12	C₃⋊D₃	—	27	1	no	—
13	D₉	—	27	9	no	—
14	D₉	—	27	3	no	—
15	C₃²	C₃⋊D₉	1	1	yes	characteristic
16	C₉	D₂₇	1	9	yes	complemented
17	C₉	C₃⋊D₉	1	3	yes	—
18	D₃	—	81	1	no	—
19	D₃	—	81	3	no	—
20	C₃	C₉⋊D₉	1	1	yes	characteristic
21	C₃	C₃⋊D₂₇	1	3	yes	—
22	C₂	—	243	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₂₇	C₂
Frattini	C₃×C₉	C₃⋊D₃
socle	C₃²	C₃⋊D₉
LCS	G ▷ C₉×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.