Subgroups — C₃³×C₃⋊(C₃⋊D₃) #13091724

Order 1458.

29492 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⁶	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃²×C₃⋊(C₃⋊D₃)	C₃	1	13	yes	maximal, direct product factor
3	C₃³×C₃⋊D₃	—	3	13	no	maximal
4	C₃⁵	—	2	169	no	—
5	C₃⁵	D₃	1	13	yes	complemented
6	C₃⁵	C₂×C₃	1	13	yes	complemented
7	C₃×C₃⋊(C₃⋊D₃)	C₃²	1	13	yes	direct product factor
8	C₃²×C₃⋊D₃	—	3	169	no	—
9	C₃³×D₃	—	9	13	no	—
10	C₃⁴	—	2	4056	no	—
11	C₃⁴	—	2	676	no	—
12	C₃⁴	—	2	676	no	—
13	C₃⁴	C₃×D₃	1	169	yes	complemented
14	C₃⁴	C₃⋊D₃	1	13	yes	complemented
15	C₃⁴	C₂×C₃²	1	13	yes	complemented
16	C₂×C₃³	—	27	1	no	—
17	C₃⋊(C₃⋊D₃)	C₃³	1	1	yes	characteristic, direct product factor
18	C₃×C₃⋊D₃	—	3	169	no	—
19	C₃²×D₃	—	9	169	no	—
20	C₃³	—	2	5616	no	—
21	C₃³	—	2	4056	no	—
22	C₃³	—	2	4056	no	—
23	C₃³	—	2	169	no	—
24	C₃³	—	2	2704	no	—
25	C₃³	—	2	169	no	—
26	C₃³	C₃²×D₃	1	169	yes	complemented
27	C₃³	C₃×C₃⋊D₃	1	169	yes	complemented
28	C₃³	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, direct product factor
29	C₃³	C₂×C₃³	1	1	yes	characteristic, complemented
30	C₂×C₃²	—	27	13	no	—
31	C₃⋊D₃	—	3	13	no	—
32	C₃×D₃	—	9	169	no	—
33	C₃²	—	2	4056	no	—
34	C₃²	—	2	676	no	—
35	C₃²	—	2	676	no	—
36	C₃²	C₃³×D₃	1	13	yes	complemented
37	C₃²	C₃²×C₃⋊D₃	1	169	yes	complemented
38	C₃²	C₃×C₃⋊(C₃⋊D₃)	1	13	yes	direct product factor
39	C₂×C₃	—	27	13	no	—
40	D₃	—	9	13	no	—
41	C₃	—	2	169	no	—
42	C₃	C₃³×C₃⋊D₃	1	13	yes	complemented
43	C₃	C₃²×C₃⋊(C₃⋊D₃)	1	13	yes	direct product factor
44	C₂	—	27	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃³	C₃⋊(C₃⋊D₃)
commutator, cosocle, hypocenter	C₃³	C₂×C₃³
Frattini	C₁	G
Fitting, socle	C₃⁶	C₂
LCS	G ▷ C₃³
UCS	C₁ ◁ C₃³

Complements

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

N	H ≅ G/N	type
1. C₃⁶	C₂	semidirect
2. C₃²×C₃⋊(C₃⋊D₃)	C₃	direct (N × H)
5. C₃⁵	D₃	semidirect
6. C₃⁵	C₂×C₃	semidirect
7. C₃×C₃⋊(C₃⋊D₃)	C₃²	direct (N × H)
13. C₃⁴	C₃×D₃	semidirect
14. C₃⁴	C₃⋊D₃	semidirect
15. C₃⁴	C₂×C₃²	semidirect
17. C₃⋊(C₃⋊D₃)	C₃³	direct (N × H)
26. C₃³	C₃²×D₃	semidirect
27. C₃³	C₃×C₃⋊D₃	semidirect
28. C₃³	C₃⋊(C₃⋊D₃)	direct (N × H)
29. C₃³	C₂×C₃³	semidirect
36. C₃²	C₃³×D₃	semidirect
37. C₃²	C₃²×C₃⋊D₃	semidirect
38. C₃²	C₃×C₃⋊(C₃⋊D₃)	direct (N × H)
42. C₃	C₃³×C₃⋊D₃	semidirect
43. C₃	C₃²×C₃⋊(C₃⋊D₃)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃⁶	2
C₃²×C₃⋊(C₃⋊D₃)	3
C₃³×C₃⋊D₃	3

Subgroups — C33×C3⋊(C3⋊D3) #13091724

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃³×C₃⋊(C₃⋊D₃) #13091724