Subgroups — C₃×C₉×C₉⋊C₉ #14552012

Order 2187.

2114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₉⋊C₉	C₃	1	3	yes	maximal
2	C₃²×C₉²	C₃	1	3	yes	maximal
3	C₃²×C₉²	C₃	1	1	yes	maximal, characteristic
4	C₉×C₉⋊C₉	C₃	1	27	yes	maximal, direct product factor
5	C₃×#6855	C₃	1	6	yes	maximal
6	C₃³×C₉	C₃²	1	2	yes	—
7	C₃³×C₉	C₃²	1	9	yes	—
8	C₃³×C₉	C₃²	1	1	yes	characteristic
9	C₃³×C₉	C₃²	1	1	yes	characteristic
10	C₃×C₉⋊C₉	C₉	1	81	yes	direct product factor
11	C₃×C₉⋊C₉	C₃²	1	27	yes	—
12	C₃×C₉²	—	3	27	no	—
13	C₃×C₉²	C₉	1	27	yes	complemented
14	C₃×C₉²	C₃²	1	27	yes	—
15	C₃×C₉²	C₃²	1	9	yes	—
16	#6855	C₃²	1	54	yes	—
17	C₃⁴	C₃³	1	1	yes	characteristic
18	C₃²×C₉	—	3	27	no	—
19	C₃²×C₉	—	3	18	no	—
20	C₃²×C₉	—	3	54	no	—
21	C₃²×C₉	C₃×C₉	1	18	yes	—
22	C₃²×C₉	C₃×C₉	1	81	yes	—
23	C₃²×C₉	C₃×C₉	1	9	yes	—
24	C₃²×C₉	C₃×C₉	1	27	yes	—
25	C₃²×C₉	C₃×C₉	1	9	yes	—
26	C₃²×C₉	3₋¹⁺²	1	27	yes	—
27	C₃²×C₉	C₃³	1	6	yes	—
28	C₃²×C₉	C₃³	1	27	yes	—
29	C₃²×C₉	C₃³	1	3	yes	—
30	C₃²×C₉	C₃³	1	3	yes	—
31	C₉⋊C₉	C₃×C₉	1	243	yes	direct product factor
32	C₉²	—	3	81	no	—
33	C₉²	C₃×C₉	1	81	yes	complemented
34	C₃³	C₃²×C₉	1	3	yes	—
35	C₃³	C₃²×C₉	1	9	yes	—
36	C₃³	C₃×3₋¹⁺²	1	9	yes	—
37	C₃³	#737	1	18	yes	—
38	C₃³	C₃⁴	1	1	yes	characteristic
39	C₃×C₉	—	3	27	no	—
40	C₃×C₉	—	3	18	no	—
41	C₃×C₉	—	3	54	no	—
42	C₃×C₉	—	3	54	no	—
43	C₃×C₉	—	3	243	no	—
44	C₃×C₉	C₉²	1	81	yes	complemented
45	C₃×C₉	C₉⋊C₉	1	81	yes	direct product factor
46	C₃×C₉	C₃²×C₉	1	18	yes	—
47	C₃×C₉	C₃²×C₉	1	81	yes	—
48	C₃×C₉	C₃²×C₉	1	9	yes	—
49	C₃×C₉	C₃²×C₉	1	27	yes	—
50	C₃×C₉	C₃²×C₉	1	9	yes	—
51	C₃×C₉	C₃×3₋¹⁺²	1	27	yes	—
52	C₃²	C₃×C₉²	1	9	yes	—
53	C₃²	C₃×C₉⋊C₉	1	9	yes	—
54	C₃²	#6887	1	18	yes	—
55	C₃²	C₉×3₋¹⁺²	1	81	yes	—
56	C₃²	C₃³×C₉	1	1	yes	characteristic
57	C₃²	C₃³×C₉	1	3	yes	—
58	C₃²	C₃²×3₋¹⁺²	1	3	yes	—
59	C₃²	C₃×#737	1	6	yes	—
60	C₉	—	3	18	no	—
61	C₉	—	3	81	no	—
62	C₉	C₃×C₉²	1	27	yes	complemented
63	C₉	C₃×C₉⋊C₉	1	27	yes	direct product factor
64	C₃	C₉×C₉⋊C₉	1	27	yes	direct product factor
65	C₃	C₃²×C₉²	1	1	yes	characteristic
66	C₃	C₃²×C₉⋊C₉	1	1	yes	characteristic
67	C₃	C₃×#6887	1	2	yes	—
68	C₃	C₃×C₉×3₋¹⁺²	1	9	yes	—

	subgroup	G/H
center	C₃³×C₉	C₃²
commutator	C₃	C₃²×C₉²
Frattini, cosocle	C₃³	C₃⁴
socle, prime radical	C₃⁴	C₃³
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃³×C₉ ◁ G
LECS	G ▷ C₃³ ▷ C₁

Complements

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

N	H ≅ G/N	type
4. C₉×C₉⋊C₉	C₃	direct (N × H)
10. C₃×C₉⋊C₉	C₉	direct (N × H)
13. C₃×C₉²	C₉	semidirect
31. C₉⋊C₉	C₃×C₉	direct (N × H)
33. C₉²	C₃×C₉	semidirect
44. C₃×C₉	C₉²	semidirect
45. C₃×C₉	C₉⋊C₉	direct (N × H)
62. C₉	C₃×C₉²	semidirect
63. C₉	C₃×C₉⋊C₉	direct (N × H)
64. C₃	C₉×C₉⋊C₉	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃²×C₉⋊C₉	3
C₃²×C₉²	3
C₉×C₉⋊C₉	3
C₃×#6855	3

Subgroups — C3×C9×C9⋊C9 #14552012

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₉×C₉⋊C₉ #14552012