Subgroups — C₃²×C₁₃×C₉⋊C₉ #23745008

Order 9477.

1484 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₉×C₁₃	C₃	1	3	yes	maximal
2	C₃³×C₉×C₁₃	C₃	1	1	yes	maximal, characteristic
3	C₃×C₁₃×C₉⋊C₉	C₃	1	36	yes	maximal, direct product factor
4	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
5	C₃²×C₉×C₁₃	—	3	27	no	—
6	C₃²×C₉×C₁₃	C₉	1	27	yes	complemented
7	C₃²×C₉×C₁₃	C₃²	1	36	yes	—
8	C₃²×C₉×C₁₃	C₃²	1	12	yes	—
9	C₁₃×C₉⋊C₉	C₃²	1	81	yes	direct product factor
10	C₃²×C₉⋊C₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₃³×C₁₃	C₃×C₉	1	9	yes	—
12	C₃³×C₁₃	3₋¹⁺²	1	27	yes	—
13	C₃³×C₁₃	C₃³	1	4	yes	—
14	C₃×C₉×C₁₃	—	3	108	no	—
15	C₃×C₉×C₁₃	C₃×C₉	1	108	yes	complemented
16	C₃×C₉×C₁₃	C₃³	1	27	yes	—
17	C₃×C₉×C₁₃	C₃³	1	9	yes	—
18	C₃³×C₉	C₃×C₁₃	1	3	yes	—
19	C₃³×C₉	C₃×C₁₃	1	1	yes	characteristic
20	C₃×C₉⋊C₉	C₃×C₁₃	1	36	yes	direct product factor
21	C₃²×C₁₃	C₉⋊C₉	1	81	yes	direct product factor
22	C₃²×C₁₃	C₃²×C₉	1	12	yes	—
23	C₃²×C₁₃	C₃×3₋¹⁺²	1	36	yes	—
24	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
25	C₉×C₁₃	—	3	27	no	—
26	C₉×C₁₃	C₃²×C₉	1	27	yes	complemented
27	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
28	C₃²×C₉	—	3	27	no	—
29	C₃²×C₉	C₉×C₁₃	1	27	yes	complemented
30	C₃²×C₉	C₃²×C₁₃	1	36	yes	—
31	C₃²×C₉	C₃²×C₁₃	1	12	yes	—
32	C₉⋊C₉	C₃²×C₁₃	1	81	yes	direct product factor
33	C₃×C₁₃	C₃×C₉⋊C₉	1	36	yes	direct product factor
34	C₃×C₁₃	C₃³×C₉	1	1	yes	characteristic
35	C₃×C₁₃	C₃²×3₋¹⁺²	1	3	yes	—
36	C₃³	C₃×C₉×C₁₃	1	9	yes	—
37	C₃³	C₁₃×3₋¹⁺²	1	27	yes	—
38	C₃³	C₃³×C₁₃	1	4	yes	—
39	C₃×C₉	—	3	108	no	—
40	C₃×C₉	C₃×C₉×C₁₃	1	108	yes	complemented
41	C₃×C₉	C₃³×C₁₃	1	27	yes	—
42	C₃×C₉	C₃³×C₁₃	1	9	yes	—
43	C₁₃	C₃²×C₉⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
44	C₃²	C₁₃×C₉⋊C₉	1	81	yes	direct product factor
45	C₃²	C₃²×C₉×C₁₃	1	12	yes	—
46	C₃²	C₃×C₁₃×3₋¹⁺²	1	36	yes	—
47	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
48	C₉	—	3	27	no	—
49	C₉	C₃²×C₉×C₁₃	1	27	yes	complemented
50	C₃	C₃×C₁₃×C₉⋊C₉	1	36	yes	direct product factor
51	C₃	C₃³×C₉×C₁₃	1	1	yes	characteristic
52	C₃	C₃²×C₁₃×3₋¹⁺²	1	3	yes	—

	subgroup	G/H
center, socle, prime radical	C₃⁴×C₁₃	C₃²
commutator	C₃	C₃³×C₉×C₁₃
Frattini, cosocle	C₃²	C₃⁴×C₁₃
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃×C₁₃×C₉⋊C₉	C₃	direct (N × H)
6. C₃²×C₉×C₁₃	C₉	semidirect
9. C₁₃×C₉⋊C₉	C₃²	direct (N × H)
10. C₃²×C₉⋊C₉	C₁₃	direct (N × H)
15. C₃×C₉×C₁₃	C₃×C₉	semidirect
20. C₃×C₉⋊C₉	C₃×C₁₃	direct (N × H)
21. C₃²×C₁₃	C₉⋊C₉	direct (N × H)
26. C₉×C₁₃	C₃²×C₉	semidirect
29. C₃²×C₉	C₉×C₁₃	semidirect
32. C₉⋊C₉	C₃²×C₁₃	direct (N × H)
33. C₃×C₁₃	C₃×C₉⋊C₉	direct (N × H)
40. C₃×C₉	C₃×C₉×C₁₃	semidirect
43. C₁₃	C₃²×C₉⋊C₉	direct (N × H)
44. C₃²	C₁₃×C₉⋊C₉	direct (N × H)
49. C₉	C₃²×C₉×C₁₃	semidirect
50. C₃	C₃×C₁₃×C₉⋊C₉	direct (N × H)

Subgroups — C32×C13×C9⋊C9 #23745008

Conjugacy classes of subgroups

Complements

Subgroups — C₃²×C₁₃×C₉⋊C₉ #23745008