Subgroups — C₂²×C₃×D₉ #6271

Order 216.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₉	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₃×D₃	—	3	1	no	maximal
4	C₂²×D₉	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₂×C₃×C₉	C₂²	1	3	yes	complemented
6	C₃×D₉	C₂²	1	4	yes	direct product factor
7	C₂²×C₃²	D₃	1	1	yes	characteristic
8	C₂×C₃×D₃	—	3	6	no	—
9	C₂²×C₉	—	2	1	no	—
10	C₂²×C₉	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂×D₉	C₂×C₃	1	6	yes	direct product factor
12	C₃×C₉	C₂³	1	1	yes	characteristic, complemented, Sylow
13	C₂³×C₃	—	9	1	no	—
14	C₂²×D₃	—	3	1	no	—
15	C₂×C₃²	C₂×D₃	1	3	yes	—
16	C₃×D₃	—	3	4	no	—
17	C₂×C₉	—	2	3	no	—
18	C₂×C₉	C₂²×C₃	1	3	yes	complemented
19	D₉	C₂²×C₃	1	4	yes	direct product factor
20	C₂²×C₃	—	2	1	no	—
21	C₂²×C₃	—	9	6	no	—
22	C₂²×C₃	D₉	1	1	yes	characteristic, direct product factor
23	C₂²×C₃	C₃×D₃	1	1	yes	characteristic
24	C₂×D₃	—	3	6	no	—
25	C₃²	C₂²×D₃	1	1	yes	characteristic
26	C₉	—	2	1	no	—
27	C₉	C₂³×C₃	1	1	yes	characteristic, complemented
28	C₂³	—	9	1	no	Sylow
29	C₂×C₃	—	2	3	no	—
30	C₂×C₃	—	9	4	no	—
31	C₂×C₃	C₂×D₉	1	3	yes	direct product factor
32	C₂×C₃	C₂×C₃×D₃	1	3	yes	—
33	D₃	—	3	4	no	—
34	C₂²	—	9	6	no	—
35	C₂²	C₃×D₉	1	1	yes	characteristic, direct product factor
36	C₃	—	2	1	no	—
37	C₃	C₂²×D₉	1	1	yes	characteristic, direct product factor
38	C₃	C₂²×C₃×D₃	1	1	yes	characteristic
39	C₂	—	9	4	no	—
40	C₂	C₂×C₃×D₉	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₃	D₉
commutator, cosocle, hypocenter	C₉	C₂³×C₃
Frattini	C₃	C₂²×C₃×D₃
Fitting	C₂²×C₃×C₉	C₂
socle	C₂²×C₃²	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₂²×C₃

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₉	C₂	semidirect
2. C₂×C₃×D₉	C₂	direct (N × H)
4. C₂²×D₉	C₃	direct (N × H)
5. C₂×C₃×C₉	C₂²	semidirect
6. C₃×D₉	C₂²	direct (N × H)
10. C₂²×C₉	C₂×C₃	semidirect
11. C₂×D₉	C₂×C₃	direct (N × H)
12. C₃×C₉	C₂³	semidirect
18. C₂×C₉	C₂²×C₃	semidirect
19. D₉	C₂²×C₃	direct (N × H)
22. C₂²×C₃	D₉	direct (N × H)
27. C₉	C₂³×C₃	semidirect
31. C₂×C₃	C₂×D₉	direct (N × H)
35. C₂²	C₃×D₉	direct (N × H)
37. C₃	C₂²×D₉	direct (N × H)
40. C₂	C₂×C₃×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
C₂²×C₃×C₉	2
C₂×C₃×D₉	2
C₂²×C₃×D₃	3
C₂²×D₉	3

Subgroups — C22×C3×D9 #6271

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×D₉ #6271