Subgroups — C₂×C₉×C₃⋊D₃ #66451

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

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×C₉	C₂	semidirect
2. C₉×C₃⋊D₃	C₂	direct (N × H)
5. C₃²×C₉	C₂²	semidirect
9. C₂×C₃×C₉	D₃	semidirect
11. C₂×C₃⋊D₃	C₉	direct (N × H)
16. C₃×C₉	C₂×D₃	semidirect
18. C₂×C₃²	C₂×C₉	semidirect
20. C₃⋊D₃	C₂×C₉	direct (N × H)
24. C₂×C₉	C₃⋊D₃	direct (N × H)
28. C₃²	C₂²×C₉	semidirect
31. C₉	C₂×C₃⋊D₃	direct (N × H)
34. C₂×C₃	D₃×C₉	semidirect
39. C₃	C₂×D₃×C₉	semidirect
42. C₂	C₉×C₃⋊D₃	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
C₉×C₃⋊D₃	2
C₂×C₃×C₃⋊D₃	3
C₂×D₃×C₉	3

Subgroups — C2×C9×C3⋊D3 #66451

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×C₃⋊D₃ #66451