Subgroups — C₃²×#16812499 #44534639

Order 31347.

1484 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₄₃⋊C₉	C₃	1	3	yes	maximal
2	C₃×#16812499	C₃	1	36	yes	maximal, direct product factor
3	C₃³×C₉×C₄₃	C₃	1	1	yes	maximal, characteristic
4	C₃²×C₄₃⋊C₉	—	3	27	no	—
5	C₃²×C₄₃⋊C₉	C₃²	1	36	yes	—
6	#16812499	C₃²	1	81	yes	direct product factor
7	C₃⁴×C₄₃	C₃²	1	1	yes	characteristic
8	C₃²×C₉×C₄₃	C₉	1	27	yes	complemented
9	C₃²×C₉×C₄₃	C₃²	1	12	yes	—
10	C₃×C₄₃⋊C₉	—	3	108	no	—
11	C₃×C₄₃⋊C₉	C₃³	1	27	yes	—
12	C₃³×C₄₃	C₃×C₉	1	9	yes	—
13	C₃³×C₄₃	3₋¹⁺²	1	27	yes	—
14	C₃³×C₄₃	C₃³	1	4	yes	—
15	C₃×C₉×C₄₃	C₃×C₉	1	108	yes	complemented
16	C₃×C₉×C₄₃	C₃³	1	9	yes	—
17	C₃²×C₉⋊C₉	—	43	1	no	maximal, Sylow
18	C₃²×C₄₃	C₉⋊C₉	1	81	yes	complemented
19	C₃²×C₄₃	C₃²×C₉	1	12	yes	—
20	C₃²×C₄₃	C₃×3₋¹⁺²	1	36	yes	—
21	C₃²×C₄₃	C₃⁴	1	1	yes	characteristic
22	C₉×C₄₃	C₃²×C₉	1	27	yes	complemented
23	C₄₃⋊C₉	—	3	27	no	—
24	C₃³×C₉	—	43	3	no	—
25	C₃³×C₉	C₄₃⋊C₃	1	1	yes	characteristic
26	C₃×C₉⋊C₉	—	43	36	no	—
27	C₃×C₄₃	C₃×C₉⋊C₉	1	36	yes	complemented
28	C₃×C₄₃	C₃³×C₉	1	1	yes	characteristic
29	C₃×C₄₃	C₃²×3₋¹⁺²	1	3	yes	—
30	C₃⁴	C₃×C₄₃⋊C₃	1	1	yes	characteristic
31	C₃²×C₉	—	43	36	no	—
32	C₃²×C₉	—	129	27	no	—
33	C₃²×C₉	C₄₃⋊C₉	1	27	yes	complemented
34	C₃²×C₉	C₃×C₄₃⋊C₃	1	12	yes	—
35	C₉⋊C₉	—	43	81	no	—
36	C₄₃	C₃²×C₉⋊C₉	1	1	yes	characteristic, complemented, Sylow
37	C₃³	C₃×C₄₃⋊C₉	1	9	yes	—
38	C₃³	#11923957	1	27	yes	—
39	C₃³	C₃²×C₄₃⋊C₃	1	4	yes	—
40	C₃×C₉	—	43	27	no	—
41	C₃×C₉	—	129	108	no	—
42	C₃×C₉	C₃×C₄₃⋊C₉	1	108	yes	complemented
43	C₃×C₉	C₃²×C₄₃⋊C₃	1	9	yes	—
44	C₃²	#16812499	1	81	yes	direct product factor
45	C₃²	C₃²×C₄₃⋊C₉	1	12	yes	—
46	C₃²	C₃×#11923957	1	36	yes	—
47	C₃²	C₃³×C₄₃⋊C₃	1	1	yes	characteristic
48	C₉	—	129	27	no	—
49	C₉	C₃²×C₄₃⋊C₉	1	27	yes	complemented
50	C₃	C₃×#16812499	1	36	yes	direct product factor
51	C₃	C₃³×C₄₃⋊C₉	1	1	yes	characteristic
52	C₃	C₃²×#11923957	1	3	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₃×#16812499	C₃	direct (N × H)
6. #16812499	C₃²	direct (N × H)
8. C₃²×C₉×C₄₃	C₉	semidirect
15. C₃×C₉×C₄₃	C₃×C₉	semidirect
18. C₃²×C₄₃	C₉⋊C₉	semidirect
22. C₉×C₄₃	C₃²×C₉	semidirect
27. C₃×C₄₃	C₃×C₉⋊C₉	semidirect
33. C₃²×C₉	C₄₃⋊C₉	semidirect
36. C₄₃	C₃²×C₉⋊C₉	semidirect
42. C₃×C₉	C₃×C₄₃⋊C₉	semidirect
44. C₃²	#16812499	direct (N × H)
49. C₉	C₃²×C₄₃⋊C₉	semidirect
50. C₃	C₃×#16812499	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃³×C₄₃⋊C₉	3
C₃×#16812499	3
C₃³×C₉×C₄₃	3
C₃²×C₉⋊C₉	43

Subgroups — C32×#16812499 #44534639

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#16812499 #44534639