Subgroups — C₃³×C₃²⋊(C₄₃⋊C₃) #44535391

Order 31347.

11744 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⁴×C₄₃⋊C₃	C₃	1	3	yes	maximal, complemented
2	C₃²×C₃²⋊(C₄₃⋊C₃)	C₃	1	117	yes	maximal, direct product factor
3	C₃⁵×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃³×C₄₃⋊C₃	—	3	81	no	—
5	C₃³×C₄₃⋊C₃	C₃²	1	117	yes	complemented
6	C₃×C₃²⋊(C₄₃⋊C₃)	C₃²	1	1053	yes	direct product factor
7	C₃⁴×C₄₃	—	3	27	no	—
8	C₃⁴×C₄₃	C₃²	1	1	yes	characteristic
9	C₃⁴×C₄₃	C₃²	1	39	yes	complemented
10	C₃²×C₄₃⋊C₃	—	3	1053	no	—
11	C₃²×C₄₃⋊C₃	C₃³	1	351	yes	complemented
12	C₃²⋊(C₄₃⋊C₃)	C₃³	1	729	yes	direct product factor
13	C₃³×C₄₃	—	3	351	no	—
14	C₃³×C₄₃	H(3,𝔽₃)	1	27	yes	complemented
15	C₃³×C₄₃	C₃³	1	13	yes	—
16	C₃³×C₄₃	C₃³	1	117	yes	complemented
17	C₃³×H(3,𝔽₃)	—	43	1	no	maximal, Sylow
18	C₃²×C₄₃	—	3	351	no	—
19	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	117	yes	complemented
20	C₃²×C₄₃	C₃⁴	1	13	yes	—
21	C₃²×C₄₃	C₃⁴	1	27	yes	complemented
22	C₃×C₄₃⋊C₃	—	3	1053	no	—
23	C₃×C₄₃⋊C₃	C₃⁴	1	81	yes	complemented
24	C₃⁵	—	43	3	no	—
25	C₃⁵	C₄₃⋊C₃	1	1	yes	characteristic, complemented
26	C₃²×H(3,𝔽₃)	—	43	117	no	—
27	C₃×C₄₃	—	3	27	no	—
28	C₃×C₄₃	C₃²×H(3,𝔽₃)	1	39	yes	complemented
29	C₃×C₄₃	C₃⁵	1	1	yes	characteristic
30	C₄₃⋊C₃	—	3	81	no	—
31	C₃⁴	—	3	27	no	—
32	C₃⁴	—	43	117	no	—
33	C₃⁴	—	129	81	no	—
34	C₃⁴	C₃×C₄₃⋊C₃	1	1	yes	characteristic
35	C₃⁴	C₃×C₄₃⋊C₃	1	39	yes	complemented
36	C₃×H(3,𝔽₃)	—	43	1053	no	—
37	C₄₃	C₃³×H(3,𝔽₃)	1	1	yes	characteristic, complemented, Sylow
38	C₃³	—	3	351	no	—
39	C₃³	—	43	351	no	—
40	C₃³	—	129	1053	no	—
41	C₃³	C₃²⋊(C₄₃⋊C₃)	1	27	yes	direct product factor
42	C₃³	C₃²×C₄₃⋊C₃	1	13	yes	—
43	C₃³	C₃²×C₄₃⋊C₃	1	117	yes	complemented
44	H(3,𝔽₃)	—	43	729	no	—
45	C₃²	—	3	351	no	—
46	C₃²	—	43	81	no	—
47	C₃²	—	129	1053	no	—
48	C₃²	C₃×C₃²⋊(C₄₃⋊C₃)	1	117	yes	direct product factor
49	C₃²	C₃³×C₄₃⋊C₃	1	13	yes	—
50	C₃²	C₃³×C₄₃⋊C₃	1	27	yes	complemented
51	C₃	—	3	27	no	—
52	C₃	—	129	81	no	—
53	C₃	C₃²×C₃²⋊(C₄₃⋊C₃)	1	39	yes	direct product factor
54	C₃	C₃⁴×C₄₃⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃⁴	C₃×C₄₃⋊C₃
commutator, cosocle	C₃×C₄₃	C₃⁵
Frattini	C₃	C₃⁴×C₄₃⋊C₃
Fitting	C₃⁵×C₄₃	C₃
socle	C₃⁴×C₄₃	C₃²
hypercenter	C₃⁵	C₄₃⋊C₃
hypocenter	C₄₃	C₃³×H(3,𝔽₃)
LCS	G ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃⁴ ◁ C₃⁵

Complements

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

N	H ≅ G/N	type
1. C₃⁴×C₄₃⋊C₃	C₃	semidirect
2. C₃²×C₃²⋊(C₄₃⋊C₃)	C₃	direct (N × H)
3. C₃⁵×C₄₃	C₃	semidirect
5. C₃³×C₄₃⋊C₃	C₃²	semidirect
6. C₃×C₃²⋊(C₄₃⋊C₃)	C₃²	direct (N × H)
9. C₃⁴×C₄₃	C₃²	semidirect
11. C₃²×C₄₃⋊C₃	C₃³	semidirect
12. C₃²⋊(C₄₃⋊C₃)	C₃³	direct (N × H)
14. C₃³×C₄₃	H(3,𝔽₃)	semidirect
16. C₃³×C₄₃	C₃³	semidirect
19. C₃²×C₄₃	C₃×H(3,𝔽₃)	semidirect
21. C₃²×C₄₃	C₃⁴	semidirect
23. C₃×C₄₃⋊C₃	C₃⁴	semidirect
25. C₃⁵	C₄₃⋊C₃	semidirect
28. C₃×C₄₃	C₃²×H(3,𝔽₃)	semidirect
35. C₃⁴	C₃×C₄₃⋊C₃	semidirect
37. C₄₃	C₃³×H(3,𝔽₃)	semidirect
41. C₃³	C₃²⋊(C₄₃⋊C₃)	direct (N × H)
43. C₃³	C₃²×C₄₃⋊C₃	semidirect
48. C₃²	C₃×C₃²⋊(C₄₃⋊C₃)	direct (N × H)
50. C₃²	C₃³×C₄₃⋊C₃	semidirect
53. C₃	C₃²×C₃²⋊(C₄₃⋊C₃)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃⁴×C₄₃⋊C₃	3
C₃²×C₃²⋊(C₄₃⋊C₃)	3
C₃⁵×C₄₃	3
C₃³×H(3,𝔽₃)	43

Subgroups — C33×C32⋊(C43⋊C3) #44535391

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃³×C₃²⋊(C₄₃⋊C₃) #44535391