Subgroups — D₃×C₂²⋊C₉ #6261

Order 216.

45 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂²⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×D₃	C₃	1	1	yes	maximal, characteristic
3	C₂×C₂²⋊C₉	—	3	1	no	maximal
4	D₃×C₉	—	4	1	no	maximal
5	C₂²×C₃²	C₂×C₃	1	1	yes	characteristic
6	C₂×C₃×D₃	—	3	1	no	—
7	C₂×C₃×D₃	—	3	1	no	—
8	C₂²⋊C₉	—	2	1	no	—
9	C₂²⋊C₉	D₃	1	1	yes	characteristic, direct product factor
10	C₃×C₉	—	4	1	no	Sylow
11	C₂³×C₃	—	3	1	no	—
12	C₂²×D₃	C₉	1	1	yes	characteristic, complemented
13	C₂×C₃²	—	3	1	no	—
14	C₃×D₃	—	3	1	no	—
15	C₃×D₃	A₄	1	1	yes	characteristic
16	C₂×C₉	—	12	1	no	—
17	C₂²×C₃	—	2	1	no	—
18	C₂²×C₃	—	9	1	no	—
19	C₂²×C₃	—	9	1	no	—
20	C₂²×C₃	C₂×C₉	1	1	yes	characteristic, complemented
21	C₂²×C₃	C₃×D₃	1	1	yes	characteristic
22	C₂×D₃	—	3	1	no	—
23	C₂×D₃	—	3	1	no	—
24	C₃²	C₂×A₄	1	1	yes	characteristic
25	C₉	—	4	1	no	—
26	C₉	—	8	1	no	—
27	C₂³	—	3	1	no	Sylow
28	C₂×C₃	—	3	1	no	—
29	C₂×C₃	—	3	1	no	—
30	C₂×C₃	—	3	1	no	—
31	C₂×C₃	—	6	1	no	—
32	C₂×C₃	—	9	1	no	—
33	D₃	—	3	1	no	—
34	D₃	C₂²⋊C₉	1	1	yes	characteristic, direct product factor
35	C₂²	—	9	1	no	—
36	C₂²	—	9	1	no	—
37	C₂²	D₃×C₉	1	1	yes	characteristic, complemented
38	C₃	—	2	1	no	—
39	C₃	C₂×C₂²⋊C₉	1	1	yes	characteristic, complemented
40	C₃	D₃×A₄	1	1	yes	characteristic
41	C₂	—	3	1	no	—
42	C₂	—	3	1	no	—
43	C₂	—	9	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	D₃×A₄
commutator, hypocenter	C₂²×C₃	C₂×C₉
Fitting, socle, cosocle	C₂²×C₃²	C₂×C₃
prime radical	C₂²×C₃×D₃	C₃
LCS	G ▷ C₂²×C₃
UCS	C₁ ◁ C₃

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.