Subgroups — C₃×C₁₃×C₃²⋊H(3,𝔽₃) #23745016

Order 9477.

3824 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⁵×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented
2	C₃²×C₁₃×H(3,𝔽₃)	C₃	1	12	yes	maximal, complemented
3	C₁₃×C₃²⋊H(3,𝔽₃)	C₃	1	27	yes	maximal, direct product factor
4	C₃⁴×C₁₃	—	3	36	no	—
5	C₃⁴×C₁₃	C₃²	1	4	yes	—
6	C₃⁴×C₁₃	C₃²	1	9	yes	complemented
7	C₃⁴×C₁₃	C₃²	1	9	yes	complemented
8	C₃×C₁₃×H(3,𝔽₃)	—	3	108	no	—
9	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	108	yes	complemented
10	C₃×C₃²⋊H(3,𝔽₃)	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₃³×C₁₃	—	3	243	no	—
12	C₃³×C₁₃	—	3	36	no	—
13	C₃³×C₁₃	—	3	108	no	—
14	C₃³×C₁₃	—	3	108	no	—
15	C₃³×C₁₃	H(3,𝔽₃)	1	36	yes	complemented
16	C₃³×C₁₃	C₃³	1	12	yes	—
17	C₃³×C₁₃	C₃³	1	1	yes	characteristic
18	C₃³×C₁₃	C₃³	1	27	yes	complemented
19	C₁₃×H(3,𝔽₃)	—	3	324	no	—
20	C₃⁵	C₃×C₁₃	1	1	yes	characteristic, complemented
21	C₃²×H(3,𝔽₃)	C₃×C₁₃	1	12	yes	complemented
22	C₃²⋊H(3,𝔽₃)	C₃×C₁₃	1	27	yes	direct product factor
23	C₃²×C₁₃	—	3	243	no	—
24	C₃²×C₁₃	—	3	36	no	—
25	C₃²×C₁₃	—	3	108	no	—
26	C₃²×C₁₃	—	3	108	no	—
27	C₃²×C₁₃	—	9	81	no	—
28	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	12	yes	—
29	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	36	yes	complemented
30	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
31	C₃⁴	—	3	36	no	—
32	C₃⁴	C₃²×C₁₃	1	4	yes	—
33	C₃⁴	C₃²×C₁₃	1	9	yes	complemented
34	C₃⁴	C₃²×C₁₃	1	9	yes	complemented
35	C₃×H(3,𝔽₃)	—	3	108	no	—
36	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	108	yes	complemented
37	C₃×C₁₃	—	3	36	no	—
38	C₃×C₁₃	—	9	27	no	—
39	C₃×C₁₃	C₃²⋊H(3,𝔽₃)	1	9	yes	direct product factor
40	C₃×C₁₃	C₃²×H(3,𝔽₃)	1	4	yes	—
41	C₃³	—	3	243	no	—
42	C₃³	—	3	36	no	—
43	C₃³	—	3	108	no	—
44	C₃³	—	3	108	no	—
45	C₃³	C₁₃×H(3,𝔽₃)	1	36	yes	complemented
46	C₃³	C₃³×C₁₃	1	12	yes	—
47	C₃³	C₃³×C₁₃	1	1	yes	characteristic
48	C₃³	C₃³×C₁₃	1	27	yes	complemented
49	H(3,𝔽₃)	—	3	324	no	—
50	C₁₃	C₃×C₃²⋊H(3,𝔽₃)	1	1	yes	characteristic, direct product factor, Sylow
51	C₃²	—	3	243	no	—
52	C₃²	—	3	108	no	—
53	C₃²	—	3	36	no	—
54	C₃²	—	3	108	no	—
55	C₃²	—	9	81	no	—
56	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	12	yes	—
57	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	36	yes	complemented
58	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
59	C₃	—	3	36	no	—
60	C₃	—	9	27	no	—
61	C₃	C₁₃×C₃²⋊H(3,𝔽₃)	1	9	yes	direct product factor
62	C₃	C₃²×C₁₃×H(3,𝔽₃)	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₃⁵×C₁₃	C₃	semidirect
2. C₃²×C₁₃×H(3,𝔽₃)	C₃	semidirect
3. C₁₃×C₃²⋊H(3,𝔽₃)	C₃	direct (N × H)
6. C₃⁴×C₁₃	C₃²	semidirect
7. C₃⁴×C₁₃	C₃²	semidirect
9. C₃×C₁₃×H(3,𝔽₃)	C₃²	semidirect
10. C₃×C₃²⋊H(3,𝔽₃)	C₁₃	direct (N × H)
15. C₃³×C₁₃	H(3,𝔽₃)	semidirect
18. C₃³×C₁₃	C₃³	semidirect
20. C₃⁵	C₃×C₁₃	semidirect
21. C₃²×H(3,𝔽₃)	C₃×C₁₃	semidirect
22. C₃²⋊H(3,𝔽₃)	C₃×C₁₃	direct (N × H)
29. C₃²×C₁₃	C₃×H(3,𝔽₃)	semidirect
33. C₃⁴	C₃²×C₁₃	semidirect
34. C₃⁴	C₃²×C₁₃	semidirect
36. C₃×H(3,𝔽₃)	C₃²×C₁₃	semidirect
39. C₃×C₁₃	C₃²⋊H(3,𝔽₃)	direct (N × H)
45. C₃³	C₁₃×H(3,𝔽₃)	semidirect
48. C₃³	C₃³×C₁₃	semidirect
50. C₁₃	C₃×C₃²⋊H(3,𝔽₃)	direct (N × H)
57. C₃²	C₃×C₁₃×H(3,𝔽₃)	semidirect
61. C₃	C₁₃×C₃²⋊H(3,𝔽₃)	direct (N × H)

Subgroups — C3×C13×C32⋊H(3,𝔽3) #23745016

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₁₃×C₃²⋊H(3,𝔽₃) #23745016