Subgroups — C₂×D₃×D₉ #6264

Order 216.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⋊D₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₃×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×D₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×D₉	C₂	1	4	yes	maximal, direct product factor
5	C₂×D₃²	—	3	1	no	maximal
6	C₂²×D₉	—	3	1	no	maximal
7	C₂×C₃×C₉	C₂²	1	1	yes	characteristic, complemented
8	C₃⋊D₉	C₂²	1	2	yes	complemented
9	D₃×C₉	C₂²	1	2	yes	complemented
10	C₃×D₉	C₂²	1	2	yes	complemented
11	C₂×C₃⋊D₃	—	3	1	no	—
12	C₂×C₃×D₃	—	3	1	no	—
13	C₂×C₃×D₃	D₃	1	1	yes	characteristic
14	D₃²	—	3	4	no	—
15	C₂²×C₉	—	3	1	no	—
16	C₂×D₉	—	3	1	no	—
17	C₂×D₉	—	3	4	no	—
18	C₂×D₉	—	6	1	no	—
19	C₂×D₉	D₃	1	1	yes	characteristic, direct product factor
20	C₃×C₉	C₂³	1	1	yes	characteristic, complemented, Sylow
21	C₂²×D₃	—	9	1	no	—
22	C₂²×D₃	—	9	1	no	—
23	C₂×C₃²	C₂×D₃	1	1	yes	characteristic
24	C₃⋊D₃	—	3	2	no	—
25	C₃×D₃	—	3	2	no	—
26	C₃×D₃	C₂×D₃	1	2	yes	—
27	C₂×C₉	—	2	1	no	—
28	C₂×C₉	—	3	2	no	—
29	C₂×C₉	C₂×D₃	1	1	yes	characteristic, complemented
30	D₉	—	3	2	no	—
31	D₉	—	6	2	no	—
32	D₉	C₂×D₃	1	2	yes	direct product factor
33	C₂²×C₃	—	3	1	no	—
34	C₂²×C₃	—	9	1	no	—
35	C₂×D₃	—	3	1	no	—
36	C₂×D₃	—	9	4	no	—
37	C₂×D₃	—	9	1	no	—
38	C₂×D₃	—	9	1	no	—
39	C₂×D₃	—	9	4	no	—
40	C₂×D₃	—	18	1	no	—
41	C₂×D₃	D₉	1	1	yes	characteristic, direct product factor
42	C₃²	C₂²×D₃	1	1	yes	characteristic
43	C₉	—	2	1	no	—
44	C₉	C₂²×D₃	1	1	yes	characteristic, complemented
45	C₂³	—	27	1	no	Sylow
46	C₂×C₃	—	2	1	no	—
47	C₂×C₃	—	3	2	no	—
48	C₂×C₃	—	9	2	no	—
49	C₂×C₃	C₂×D₉	1	1	yes	characteristic, complemented
50	C₂×C₃	D₃²	1	1	yes	characteristic
51	D₃	—	3	2	no	—
52	D₃	—	9	2	no	—
53	D₃	—	9	2	no	—
54	D₃	—	18	2	no	—
55	D₃	C₂×D₉	1	2	yes	direct product factor
56	C₂²	—	3	1	no	—
57	C₂²	—	9	1	no	—
58	C₂²	—	27	4	no	—
59	C₂²	—	27	1	no	—
60	C₃	—	2	1	no	—
61	C₃	C₂²×D₉	1	1	yes	characteristic, complemented
62	C₃	C₂×D₃²	1	1	yes	characteristic
63	C₂	—	3	2	no	—
64	C₂	—	9	2	no	—
65	C₂	—	27	2	no	—
66	C₂	D₃×D₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₃×D₉
commutator, cosocle, hypocenter	C₃×C₉	C₂³
Frattini	C₃	C₂×D₃²
Fitting	C₂×C₃×C₉	C₂²
socle	C₂×C₃²	C₂×D₃
LCS	G ▷ C₃×C₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₃⋊D₉	C₂	semidirect
2. C₂×D₃×C₉	C₂	semidirect
3. C₂×C₃×D₉	C₂	semidirect
4. D₃×D₉	C₂	direct (N × H)
7. C₂×C₃×C₉	C₂²	semidirect
8. C₃⋊D₉	C₂²	semidirect
9. D₃×C₉	C₂²	semidirect
10. C₃×D₉	C₂²	semidirect
19. C₂×D₉	D₃	direct (N × H)
20. C₃×C₉	C₂³	semidirect
29. C₂×C₉	C₂×D₃	semidirect
32. D₉	C₂×D₃	direct (N × H)
41. C₂×D₃	D₉	direct (N × H)
44. C₉	C₂²×D₃	semidirect
49. C₂×C₃	C₂×D₉	semidirect
55. D₃	C₂×D₉	direct (N × H)
61. C₃	C₂²×D₉	semidirect
66. C₂	D₃×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×C₃⋊D₉	2
C₂×D₃×C₉	2
C₂×C₃×D₉	2
D₃×D₉	2
C₂×D₃²	3
C₂²×D₉	3

Subgroups — C2×D3×D9 #6264

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃×D₉ #6264