Subgroups — C₃×C₉×D₉ #92246

Order 486.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉²	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃×D₃×C₉	—	3	1	no	maximal
3	C₃²×D₉	C₃	1	1	yes	maximal, characteristic
4	C₉×D₉	C₃	1	3	yes	maximal, direct product factor
5	C₃²×C₉	—	2	1	no	—
6	C₃²×C₉	D₃	1	1	yes	characteristic
7	C₃²×C₉	C₂×C₃	1	1	yes	characteristic
8	C₉²	—	2	3	no	—
9	C₉²	C₂×C₃	1	3	yes	complemented
10	C₃²×D₃	—	3	1	no	—
11	C₂×C₃×C₉	—	9	1	no	—
12	D₃×C₉	—	3	3	no	—
13	C₃×D₉	C₉	1	3	yes	direct product factor
14	C₃×D₉	C₃²	1	1	yes	characteristic
15	C₃³	C₃×D₃	1	1	yes	characteristic
16	C₃×C₉	—	2	9	no	—
17	C₃×C₉	—	2	1	no	—
18	C₃×C₉	—	2	3	no	—
19	C₃×C₉	—	2	1	no	—
20	C₃×C₉	—	2	3	no	—
21	C₃×C₉	—	2	3	no	—
22	C₃×C₉	D₉	1	1	yes	characteristic, direct product factor
23	C₃×C₉	C₂×C₉	1	3	yes	complemented
24	C₃×C₉	C₃×D₃	1	3	yes	—
25	C₃×C₉	C₂×C₃²	1	1	yes	characteristic
26	C₂×C₃²	—	9	1	no	—
27	C₃×D₃	—	3	3	no	—
28	C₃×D₃	—	3	1	no	—
29	C₂×C₉	—	9	3	no	—
30	D₉	C₃×C₉	1	1	yes	characteristic, direct product factor
31	C₃²	—	2	3	no	—
32	C₃²	—	2	1	no	—
33	C₃²	C₃×D₉	1	1	yes	characteristic
34	C₃²	D₃×C₉	1	3	yes	—
35	C₃²	C₃²×D₃	1	1	yes	characteristic
36	C₉	—	2	9	no	—
37	C₉	—	2	3	no	—
38	C₉	—	2	3	no	—
39	C₉	—	2	1	no	—
40	C₉	C₃×D₉	1	3	yes	direct product factor
41	C₉	C₂×C₃×C₉	1	1	yes	characteristic, complemented
42	C₂×C₃	—	9	3	no	—
43	C₂×C₃	—	9	1	no	—
44	D₃	—	3	1	no	—
45	C₃	—	2	1	no	—
46	C₃	—	2	3	no	—
47	C₃	C₉×D₉	1	3	yes	direct product factor
48	C₃	C₃²×D₉	1	1	yes	characteristic
49	C₃	C₃×D₃×C₉	1	1	yes	characteristic
50	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₉	D₉
commutator, hypocenter	C₉	C₂×C₃×C₉
Frattini	C₃²	C₃²×D₃
Fitting	C₃×C₉²	C₂
socle	C₃³	C₃×D₃
prime radical	C₃²×D₉	C₃
cosocle	C₃×C₉	C₂×C₃²
LCS	G ▷ C₉
UCS	C₁ ◁ C₃×C₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₉²	C₂	semidirect
4. C₉×D₉	C₃	direct (N × H)
9. C₉²	C₂×C₃	semidirect
13. C₃×D₉	C₉	direct (N × H)
22. C₃×C₉	D₉	direct (N × H)
23. C₃×C₉	C₂×C₉	semidirect
30. D₉	C₃×C₉	direct (N × H)
40. C₉	C₃×D₉	direct (N × H)
41. C₉	C₂×C₃×C₉	semidirect
47. C₃	C₉×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
C₃×C₉²	2
C₃×D₃×C₉	3
C₃²×D₉	3
C₉×D₉	3

Subgroups — C3×C9×D9 #92246

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₉×D₉ #92246