Subgroups — C₂×C₃²×D₉ #66444

Order 324.

122 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, complemented
2	C₃²×D₉	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃²×D₃	—	3	1	no	maximal
4	C₂×C₃×D₉	C₃	1	4	yes	maximal, direct product factor
5	C₃²×C₉	C₂²	1	1	yes	characteristic, complemented, Sylow
6	C₂×C₃³	D₃	1	1	yes	characteristic
7	C₃²×D₃	—	3	2	no	—
8	C₂×C₃×C₉	—	2	4	no	—
9	C₂×C₃×C₉	C₂×C₃	1	4	yes	complemented
10	C₃×D₉	C₂×C₃	1	8	yes	direct product factor
11	C₂²×C₃²	—	9	1	no	—
12	C₂×C₃×D₃	—	3	4	no	—
13	C₂×D₉	C₃²	1	1	yes	characteristic, direct product factor
14	C₃³	C₂×D₃	1	1	yes	characteristic
15	C₃×C₉	—	2	4	no	—
16	C₃×C₉	C₂²×C₃	1	4	yes	complemented
17	C₂×C₃²	—	2	4	no	—
18	C₂×C₃²	—	9	2	no	—
19	C₂×C₃²	D₉	1	1	yes	characteristic, direct product factor
20	C₂×C₃²	C₃×D₃	1	4	yes	—
21	C₃×D₃	—	3	8	no	—
22	C₂×C₉	—	2	4	no	—
23	C₂×C₉	C₂×C₃²	1	1	yes	characteristic, complemented
24	D₉	C₂×C₃²	1	2	yes	direct product factor
25	C₂²×C₃	—	9	4	no	—
26	C₂×D₃	—	3	1	no	—
27	C₃²	—	2	4	no	—
28	C₃²	C₂×D₉	1	1	yes	characteristic, direct product factor
29	C₃²	C₂×C₃×D₃	1	4	yes	—
30	C₉	—	2	4	no	—
31	C₉	C₂²×C₃²	1	1	yes	characteristic, complemented
32	C₂×C₃	—	2	4	no	—
33	C₂×C₃	—	9	8	no	—
34	C₂×C₃	C₃×D₉	1	4	yes	direct product factor
35	C₂×C₃	C₃²×D₃	1	1	yes	characteristic
36	D₃	—	3	2	no	—
37	C₂²	—	9	1	no	Sylow
38	C₃	—	2	4	no	—
39	C₃	C₂×C₃×D₉	1	4	yes	direct product factor
40	C₃	C₂×C₃²×D₃	1	1	yes	characteristic
41	C₂	—	9	2	no	—
42	C₂	C₃²×D₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²	D₉
commutator, cosocle, hypocenter	C₉	C₂²×C₃²
Frattini	C₃	C₂×C₃²×D₃
Fitting	C₂×C₃²×C₉	C₂
socle	C₂×C₃³	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₂×C₃²

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×C₉	C₂	semidirect
2. C₃²×D₉	C₂	direct (N × H)
4. C₂×C₃×D₉	C₃	direct (N × H)
5. C₃²×C₉	C₂²	semidirect
9. C₂×C₃×C₉	C₂×C₃	semidirect
10. C₃×D₉	C₂×C₃	direct (N × H)
13. C₂×D₉	C₃²	direct (N × H)
16. C₃×C₉	C₂²×C₃	semidirect
19. C₂×C₃²	D₉	direct (N × H)
23. C₂×C₉	C₂×C₃²	semidirect
24. D₉	C₂×C₃²	direct (N × H)
28. C₃²	C₂×D₉	direct (N × H)
31. C₉	C₂²×C₃²	semidirect
34. C₂×C₃	C₃×D₉	direct (N × H)
39. C₃	C₂×C₃×D₉	direct (N × H)
42. C₂	C₃²×D₉	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
C₃²×D₉	2
C₂×C₃²×D₃	3
C₂×C₃×D₉	3

Subgroups — C2×C32×D9 #66444

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×D₉ #66444