Subgroups — C₃×H(3,𝔽₃)×C₄₃⋊C₃ #23782910

Order 10449.

900 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₄₃⋊C₃	C₃	1	4	yes	maximal, complemented
2	C₃×C₃²⋊(C₄₃⋊C₃)	C₃	1	8	yes	maximal, complemented
3	H(3,𝔽₃)×C₄₃⋊C₃	C₃	1	27	yes	maximal, direct product factor
4	C₃×H(3,𝔽₃)×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃²×C₄₃⋊C₃	—	3	36	no	—
6	C₃²×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
7	C₃²×C₄₃⋊C₃	C₃²	1	36	yes	complemented
8	C₃²×C₄₃⋊C₃	C₃²	1	8	yes	complemented
9	C₃²⋊(C₄₃⋊C₃)	C₃²	1	72	yes	complemented
10	C₃³×C₄₃	C₃²	1	4	yes	complemented
11	H(3,𝔽₃)×C₄₃	C₃²	1	9	yes	complemented
12	C₃²×C₄₃	—	3	12	no	—
13	C₃²×C₄₃	C₃³	1	1	yes	characteristic
14	C₃²×C₄₃	C₃³	1	12	yes	complemented
15	C₃×C₄₃⋊C₃	—	3	24	no	—
16	C₃×C₄₃⋊C₃	—	3	108	no	—
17	C₃×C₄₃⋊C₃	H(3,𝔽₃)	1	9	yes	direct product factor
18	C₃×C₄₃⋊C₃	C₃³	1	3	yes	—
19	C₃×C₄₃⋊C₃	C₃³	1	24	yes	complemented
20	C₃²×H(3,𝔽₃)	—	43	1	no	maximal, Sylow
21	C₃×C₄₃	—	3	12	no	—
22	C₃×C₄₃	C₃×H(3,𝔽₃)	1	3	yes	complemented
23	C₃×C₄₃	C₃⁴	1	1	yes	characteristic
24	C₄₃⋊C₃	—	3	24	no	—
25	C₄₃⋊C₃	C₃×H(3,𝔽₃)	1	9	yes	direct product factor
26	C₃⁴	—	43	4	no	—
27	C₃×H(3,𝔽₃)	—	43	8	no	—
28	C₃×H(3,𝔽₃)	—	43	27	no	—
29	C₃×H(3,𝔽₃)	C₄₃⋊C₃	1	1	yes	characteristic, direct product factor
30	C₄₃	C₃²×H(3,𝔽₃)	1	1	yes	characteristic, complemented, Sylow
31	C₃³	—	43	1	no	—
32	C₃³	—	43	8	no	—
33	C₃³	—	43	36	no	—
34	C₃³	—	129	36	no	—
35	C₃³	C₃×C₄₃⋊C₃	1	4	yes	complemented
36	H(3,𝔽₃)	—	43	72	no	—
37	H(3,𝔽₃)	C₃×C₄₃⋊C₃	1	9	yes	direct product factor
38	C₃²	—	3	12	no	—
39	C₃²	—	43	9	no	—
40	C₃²	—	43	3	no	—
41	C₃²	—	43	24	no	—
42	C₃²	—	129	108	no	—
43	C₃²	—	129	24	no	—
44	C₃²	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
45	C₃²	C₃²×C₄₃⋊C₃	1	12	yes	complemented
46	C₃	—	3	12	no	—
47	C₃	—	43	9	no	—
48	C₃	—	129	24	no	—
49	C₃	H(3,𝔽₃)×C₄₃⋊C₃	1	3	yes	direct product factor
50	C₃	C₃³×C₄₃⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	C₃²×C₄₃⋊C₃
commutator, cosocle	C₃×C₄₃	C₃⁴
Frattini	C₃	C₃³×C₄₃⋊C₃
Fitting	C₃×H(3,𝔽₃)×C₄₃	C₃
socle	C₃²×C₄₃	C₃³
hypercenter	C₃×H(3,𝔽₃)	C₄₃⋊C₃
hypocenter	C₄₃	C₃²×H(3,𝔽₃)
LCS	G ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃² ◁ C₃×H(3,𝔽₃)

Complements

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

N	H ≅ G/N	type
1. C₃³×C₄₃⋊C₃	C₃	semidirect
2. C₃×C₃²⋊(C₄₃⋊C₃)	C₃	semidirect
3. H(3,𝔽₃)×C₄₃⋊C₃	C₃	direct (N × H)
4. C₃×H(3,𝔽₃)×C₄₃	C₃	semidirect
7. C₃²×C₄₃⋊C₃	C₃²	semidirect
8. C₃²×C₄₃⋊C₃	C₃²	semidirect
9. C₃²⋊(C₄₃⋊C₃)	C₃²	semidirect
10. C₃³×C₄₃	C₃²	semidirect
11. H(3,𝔽₃)×C₄₃	C₃²	semidirect
14. C₃²×C₄₃	C₃³	semidirect
17. C₃×C₄₃⋊C₃	H(3,𝔽₃)	direct (N × H)
19. C₃×C₄₃⋊C₃	C₃³	semidirect
22. C₃×C₄₃	C₃×H(3,𝔽₃)	semidirect
25. C₄₃⋊C₃	C₃×H(3,𝔽₃)	direct (N × H)
29. C₃×H(3,𝔽₃)	C₄₃⋊C₃	direct (N × H)
30. C₄₃	C₃²×H(3,𝔽₃)	semidirect
35. C₃³	C₃×C₄₃⋊C₃	semidirect
37. H(3,𝔽₃)	C₃×C₄₃⋊C₃	direct (N × H)
45. C₃²	C₃²×C₄₃⋊C₃	semidirect
49. C₃	H(3,𝔽₃)×C₄₃⋊C₃	direct (N × H)

Subgroups — C3×H(3,𝔽3)×C43⋊C3 #23782910

Conjugacy classes of subgroups

Complements

Subgroups — C₃×H(3,𝔽₃)×C₄₃⋊C₃ #23782910