Subgroups — C₃³×C₉×C₄₃⋊C₃ #44535388

Order 31347.

10232 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⁴×C₄₃⋊C₃	C₃	1	1	yes	maximal, characteristic
2	C₃³×C₄₃⋊C₉	C₃	1	2	yes	maximal, complemented
3	C₃²×C₉×C₄₃⋊C₃	C₃	1	117	yes	maximal, direct product factor
4	C₃³×C₉×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃³×C₄₃⋊C₃	C₉	1	81	yes	direct product factor
6	C₃³×C₄₃⋊C₃	C₃²	1	39	yes	—
7	C₃²×C₄₃⋊C₉	C₃²	1	78	yes	complemented
8	C₃×C₉×C₄₃⋊C₃	C₃²	1	1053	yes	direct product factor
9	C₃⁴×C₄₃	C₃²	1	1	yes	characteristic
10	C₃²×C₉×C₄₃	C₃²	1	39	yes	complemented
11	C₃²×C₄₃⋊C₃	C₃×C₉	1	1053	yes	direct product factor
12	C₃²×C₄₃⋊C₃	C₃³	1	117	yes	—
13	C₃×C₄₃⋊C₉	C₃³	1	234	yes	complemented
14	C₉×C₄₃⋊C₃	C₃³	1	729	yes	direct product factor
15	C₃³×C₄₃	C₃×C₉	1	27	yes	complemented
16	C₃³×C₄₃	C₃³	1	13	yes	—
17	C₃×C₉×C₄₃	C₃³	1	117	yes	complemented
18	C₃⁴×C₉	—	43	1	no	maximal, Sylow
19	C₃²×C₄₃	C₃²×C₉	1	117	yes	complemented
20	C₃²×C₄₃	C₃⁴	1	13	yes	—
21	C₃×C₄₃⋊C₃	C₃²×C₉	1	1053	yes	direct product factor
22	C₃×C₄₃⋊C₃	C₃⁴	1	27	yes	—
23	C₉×C₄₃	C₃⁴	1	27	yes	complemented
24	C₄₃⋊C₉	C₃⁴	1	54	yes	complemented
25	C₃⁵	—	43	1	no	—
26	C₃³×C₉	—	43	2	no	—
27	C₃³×C₉	—	43	117	no	—
28	C₃³×C₉	C₄₃⋊C₃	1	1	yes	characteristic, direct product factor
29	C₃×C₄₃	C₃³×C₉	1	39	yes	complemented
30	C₃×C₄₃	C₃⁵	1	1	yes	characteristic
31	C₄₃⋊C₃	C₃³×C₉	1	81	yes	direct product factor
32	C₃⁴	—	43	81	no	—
33	C₃⁴	—	43	39	no	—
34	C₃⁴	C₃×C₄₃⋊C₃	1	1	yes	characteristic
35	C₃²×C₉	—	43	78	no	—
36	C₃²×C₉	—	43	1053	no	—
37	C₃²×C₉	C₃×C₄₃⋊C₃	1	39	yes	direct product factor
38	C₄₃	C₃⁴×C₉	1	1	yes	characteristic, complemented, Sylow
39	C₃³	—	43	1053	no	—
40	C₃³	—	43	117	no	—
41	C₃³	C₉×C₄₃⋊C₃	1	27	yes	direct product factor
42	C₃³	C₃²×C₄₃⋊C₃	1	13	yes	—
43	C₃×C₉	—	43	234	no	—
44	C₃×C₉	—	43	729	no	—
45	C₃×C₉	C₃²×C₄₃⋊C₃	1	117	yes	direct product factor
46	C₃²	—	43	27	no	—
47	C₃²	—	43	1053	no	—
48	C₃²	C₃×C₉×C₄₃⋊C₃	1	117	yes	direct product factor
49	C₃²	C₃³×C₄₃⋊C₃	1	13	yes	—
50	C₉	—	43	54	no	—
51	C₉	C₃³×C₄₃⋊C₃	1	27	yes	direct product factor
52	C₃	—	43	81	no	—
53	C₃	C₃²×C₉×C₄₃⋊C₃	1	39	yes	direct product factor
54	C₃	C₃⁴×C₄₃⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃³×C₉	C₄₃⋊C₃
commutator, hypocenter	C₄₃	C₃⁴×C₉
Frattini	C₃	C₃⁴×C₄₃⋊C₃
Fitting	C₃³×C₉×C₄₃	C₃
socle	C₃⁴×C₄₃	C₃²
prime radical	C₃⁴×C₄₃⋊C₃	C₃
cosocle	C₃×C₄₃	C₃⁵
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₃³×C₉

Complements

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

N	H ≅ G/N	type
2. C₃³×C₄₃⋊C₉	C₃	semidirect
3. C₃²×C₉×C₄₃⋊C₃	C₃	direct (N × H)
4. C₃³×C₉×C₄₃	C₃	semidirect
5. C₃³×C₄₃⋊C₃	C₉	direct (N × H)
7. C₃²×C₄₃⋊C₉	C₃²	semidirect
8. C₃×C₉×C₄₃⋊C₃	C₃²	direct (N × H)
10. C₃²×C₉×C₄₃	C₃²	semidirect
11. C₃²×C₄₃⋊C₃	C₃×C₉	direct (N × H)
13. C₃×C₄₃⋊C₉	C₃³	semidirect
14. C₉×C₄₃⋊C₃	C₃³	direct (N × H)
15. C₃³×C₄₃	C₃×C₉	semidirect
17. C₃×C₉×C₄₃	C₃³	semidirect
19. C₃²×C₄₃	C₃²×C₉	semidirect
21. C₃×C₄₃⋊C₃	C₃²×C₉	direct (N × H)
23. C₉×C₄₃	C₃⁴	semidirect
24. C₄₃⋊C₉	C₃⁴	semidirect
28. C₃³×C₉	C₄₃⋊C₃	direct (N × H)
29. C₃×C₄₃	C₃³×C₉	semidirect
31. C₄₃⋊C₃	C₃³×C₉	direct (N × H)
37. C₃²×C₉	C₃×C₄₃⋊C₃	direct (N × H)
38. C₄₃	C₃⁴×C₉	semidirect
41. C₃³	C₉×C₄₃⋊C₃	direct (N × H)
45. C₃×C₉	C₃²×C₄₃⋊C₃	direct (N × H)
48. C₃²	C₃×C₉×C₄₃⋊C₃	direct (N × H)
51. C₉	C₃³×C₄₃⋊C₃	direct (N × H)
53. C₃	C₃²×C₉×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
C₃³×C₄₃⋊C₉	3
C₃²×C₉×C₄₃⋊C₃	3
C₃³×C₉×C₄₃	3
C₃⁴×C₉	43

Subgroups — C33×C9×C43⋊C3 #44535388

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃³×C₉×C₄₃⋊C₃ #44535388