Subgroups — D₃×D₉ #1089

Order 108.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₉	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃²	—	3	1	no	maximal
5	C₂×D₉	—	3	1	no	maximal
6	C₃×C₉	C₂²	1	1	yes	characteristic, complemented, Sylow
7	C₃⋊D₃	—	3	1	no	—
8	C₃×D₃	—	3	1	no	—
9	C₃×D₃	D₃	1	1	yes	characteristic
10	C₂×C₉	—	3	1	no	—
11	D₉	—	3	1	no	—
12	D₉	—	6	1	no	—
13	D₉	D₃	1	1	yes	characteristic, direct product factor
14	C₂×D₃	—	9	1	no	—
15	C₂×D₃	—	9	1	no	—
16	C₃²	C₂×D₃	1	1	yes	characteristic
17	C₉	—	2	1	no	—
18	C₉	C₂×D₃	1	1	yes	characteristic, complemented
19	C₂×C₃	—	3	1	no	—
20	C₂×C₃	—	9	1	no	—
21	D₃	—	3	1	no	—
22	D₃	—	9	1	no	—
23	D₃	—	9	1	no	—
24	D₃	—	18	1	no	—
25	D₃	D₉	1	1	yes	characteristic, direct product factor
26	C₂²	—	27	1	no	Sylow
27	C₃	—	2	1	no	—
28	C₃	C₂×D₉	1	1	yes	characteristic, complemented
29	C₃	D₃²	1	1	yes	characteristic
30	C₂	—	3	1	no	—
31	C₂	—	9	1	no	—
32	C₂	—	27	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃×C₉	C₂²
Frattini	C₃	D₃²
socle	C₃²	C₂×D₃
LCS	G ▷ C₃×C₉
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.