Subgroups — C₂×C₉⋊D₉ #66382

Order 324.

115 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉²	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉⋊D₉	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃⋊D₉	—	3	4	no	maximal
4	C₉²	C₂²	1	1	yes	characteristic, complemented, Sylow
5	C₂×C₃×C₉	D₃	1	4	yes	—
6	C₃⋊D₉	—	3	8	no	—
7	C₂×C₃⋊D₃	—	9	1	no	—
8	C₂×D₉	—	9	12	no	—
9	C₃×C₉	C₂×D₃	1	4	yes	—
10	C₂×C₃²	C₃⋊D₃	1	1	yes	characteristic
11	C₃⋊D₃	—	9	2	no	—
12	C₂×C₉	D₉	1	12	yes	complemented
13	D₉	—	9	24	no	—
14	C₂×D₃	—	27	4	no	—
15	C₃²	C₂×C₃⋊D₃	1	1	yes	characteristic
16	C₉	C₂×D₉	1	12	yes	complemented
17	C₂×C₃	C₃⋊D₉	1	4	yes	—
18	D₃	—	27	8	no	—
19	C₂²	—	81	1	no	Sylow
20	C₃	C₂×C₃⋊D₉	1	4	yes	—
21	C₂	—	81	2	no	—
22	C₂	C₉⋊D₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₉⋊D₉
commutator, cosocle, hypocenter	C₉²	C₂²
Frattini	C₃²	C₂×C₃⋊D₃
Fitting	C₂×C₉²	C₂
socle	C₂×C₃²	C₃⋊D₃
LCS	G ▷ C₉²
UCS	C₁ ◁ C₂

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.