Subgroups — C₃²×#66848 #15691688

Order 3159.

576 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₁₃⋊C₃	C₃	1	1	yes	maximal, characteristic
2	C₃×#66848	C₃	1	36	yes	maximal, direct product factor
3	C₃²×C₁₃⋊C₉	C₃	1	2	yes	maximal, complemented
4	C₃²×C₉×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃³×C₁₃	C₃²	1	1	yes	characteristic
6	C₃²×C₁₃⋊C₃	—	3	9	no	—
7	C₃²×C₁₃⋊C₃	C₃²	1	12	yes	—
8	C₃×C₉×C₁₃	C₃²	1	12	yes	complemented
9	C₃×C₁₃⋊C₉	C₃²	1	24	yes	complemented
10	#66848	C₃²	1	81	yes	direct product factor
11	C₃²×3₋¹⁺²	—	13	1	no	maximal, Sylow
12	C₃²×C₁₃	3₋¹⁺²	1	9	yes	complemented
13	C₃²×C₁₃	C₃³	1	4	yes	—
14	C₃×C₁₃⋊C₃	—	3	36	no	—
15	C₃×C₁₃⋊C₃	C₃³	1	9	yes	—
16	C₉×C₁₃	C₃³	1	9	yes	complemented
17	C₁₃⋊C₉	C₃³	1	18	yes	complemented
18	C₃⁴	—	13	1	no	—
19	C₃×3₋¹⁺²	—	13	36	no	—
20	C₃²×C₉	—	13	2	no	—
21	C₃²×C₉	C₁₃⋊C₃	1	1	yes	characteristic, complemented
22	C₃×C₁₃	C₃×3₋¹⁺²	1	12	yes	complemented
23	C₃×C₁₃	C₃⁴	1	1	yes	characteristic
24	C₁₃⋊C₃	—	3	9	no	—
25	C₃³	—	13	12	no	—
26	C₃³	—	39	9	no	—
27	C₃³	C₃×C₁₃⋊C₃	1	1	yes	characteristic
28	3₋¹⁺²	—	13	81	no	—
29	C₃×C₉	—	13	24	no	—
30	C₃×C₉	C₃×C₁₃⋊C₃	1	12	yes	complemented
31	C₁₃	C₃²×3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
32	C₃²	—	13	9	no	—
33	C₃²	—	39	36	no	—
34	C₃²	#66848	1	9	yes	direct product factor
35	C₃²	C₃²×C₁₃⋊C₃	1	4	yes	—
36	C₉	—	13	18	no	—
37	C₉	C₃²×C₁₃⋊C₃	1	9	yes	complemented
38	C₃	—	39	9	no	—
39	C₃	C₃×#66848	1	12	yes	direct product factor
40	C₃	C₃³×C₁₃⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃³	C₃×C₁₃⋊C₃
commutator, cosocle	C₃×C₁₃	C₃⁴
Frattini	C₃	C₃³×C₁₃⋊C₃
Fitting	C₃²×C₉×C₁₃	C₃
socle	C₃³×C₁₃	C₃²
prime radical	C₃³×C₁₃⋊C₃	C₃
hypercenter	C₃²×C₉	C₁₃⋊C₃
hypocenter	C₁₃	C₃²×3₋¹⁺²
LCS	G ▷ C₃×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₃³ ◁ C₃²×C₉

Complements

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

N	H ≅ G/N	type
2. C₃×#66848	C₃	direct (N × H)
3. C₃²×C₁₃⋊C₉	C₃	semidirect
4. C₃²×C₉×C₁₃	C₃	semidirect
8. C₃×C₉×C₁₃	C₃²	semidirect
9. C₃×C₁₃⋊C₉	C₃²	semidirect
10. #66848	C₃²	direct (N × H)
12. C₃²×C₁₃	3₋¹⁺²	semidirect
16. C₉×C₁₃	C₃³	semidirect
17. C₁₃⋊C₉	C₃³	semidirect
21. C₃²×C₉	C₁₃⋊C₃	semidirect
22. C₃×C₁₃	C₃×3₋¹⁺²	semidirect
30. C₃×C₉	C₃×C₁₃⋊C₃	semidirect
31. C₁₃	C₃²×3₋¹⁺²	semidirect
34. C₃²	#66848	direct (N × H)
37. C₉	C₃²×C₁₃⋊C₃	semidirect
39. C₃	C₃×#66848	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃³×C₁₃⋊C₃	3
C₃×#66848	3
C₃²×C₁₃⋊C₉	3
C₃²×C₉×C₁₃	3
C₃²×3₋¹⁺²	13

Subgroups — C32×#66848 #15691688

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#66848 #15691688