Subgroups — C₂×C₃⋊D₉ #1100

Order 108.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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