Subgroups — C₃×C₃⋊Dic₉ #66404

Order 324.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₃⋊Dic₃	—	3	1	no	maximal
3	C₃⋊Dic₉	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₃×Dic₉	—	3	3	no	maximal
5	C₃²×C₉	C₄	1	1	yes	characteristic, complemented, Sylow
6	C₂×C₃³	D₃	1	1	yes	characteristic
7	C₂×C₃×C₉	—	2	1	no	—
8	C₂×C₃×C₉	—	2	3	no	—
9	C₂×C₃×C₉	D₃	1	3	yes	—
10	C₂×C₃×C₉	C₂×C₃	1	1	yes	characteristic
11	C₃⋊Dic₃	—	3	1	no	—
12	C₃×Dic₃	—	9	3	no	—
13	C₃×Dic₃	—	9	1	no	—
14	Dic₉	—	3	3	no	—
15	C₃³	Dic₃	1	1	yes	characteristic
16	C₃×C₉	—	2	1	no	—
17	C₃×C₉	—	2	3	no	—
18	C₃×C₉	Dic₃	1	3	yes	complemented
19	C₃×C₉	C₃×C₄	1	1	yes	characteristic, complemented
20	C₂×C₃²	—	2	3	no	—
21	C₂×C₃²	—	2	1	no	—
22	C₂×C₃²	D₉	1	3	yes	—
23	C₂×C₃²	C₃×D₃	1	1	yes	characteristic
24	C₂×C₃²	C₃⋊D₃	1	1	yes	characteristic
25	C₂×C₉	—	2	3	no	—
26	C₂×C₉	C₃×D₃	1	3	yes	—
27	C₃×C₄	—	27	1	no	—
28	Dic₃	—	9	3	no	—
29	Dic₃	—	9	1	no	—
30	C₃²	—	2	3	no	—
31	C₃²	—	2	1	no	—
32	C₃²	Dic₉	1	3	yes	complemented
33	C₃²	C₃×Dic₃	1	1	yes	characteristic
34	C₃²	C₃⋊Dic₃	1	1	yes	characteristic
35	C₉	—	2	3	no	—
36	C₉	C₃×Dic₃	1	3	yes	complemented
37	C₂×C₃	—	2	3	no	—
38	C₂×C₃	—	2	1	no	—
39	C₂×C₃	C₃×D₉	1	3	yes	—
40	C₂×C₃	C₃⋊D₉	1	1	yes	characteristic
41	C₂×C₃	C₃×C₃⋊D₃	1	1	yes	characteristic
42	C₄	—	27	1	no	Sylow
43	C₃	—	2	3	no	—
44	C₃	—	2	1	no	—
45	C₃	C₃×Dic₉	1	3	yes	complemented
46	C₃	C₃⋊Dic₉	1	1	yes	characteristic, direct product factor
47	C₃	C₃×C₃⋊Dic₃	1	1	yes	characteristic
48	C₂	C₃×C₃⋊D₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	C₃⋊D₉
commutator, hypocenter	C₃×C₉	C₃×C₄
Frattini	C₂×C₃	C₃×C₃⋊D₃
Fitting	C₂×C₃²×C₉	C₂
socle, prime radical	C₂×C₃³	D₃
cosocle	C₂×C₃×C₉	C₂×C₃
LCS	G ▷ C₃×C₉
UCS	C₁ ◁ C₂×C₃

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. C₃⋊Dic₉	C₃	direct (N × H)
5. C₃²×C₉	C₄	semidirect
18. C₃×C₉	Dic₃	semidirect
19. C₃×C₉	C₃×C₄	semidirect
32. C₃²	Dic₉	semidirect
36. C₉	C₃×Dic₃	semidirect
45. C₃	C₃×Dic₉	semidirect
46. C₃	C₃⋊Dic₉	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃²×C₉	2
C₃×C₃⋊Dic₃	3
C₃⋊Dic₉	3
C₃×Dic₉	3

Subgroups — C3×C3⋊Dic9 #66404

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₃⋊Dic₉ #66404