Subgroups — C₃²×C₃²⋊(C₄₃⋊C₉) #44534636

Order 31347.

2996 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, complemented
2	C₃×C₃²⋊(C₄₃⋊C₉)	C₃	1	36	yes	maximal, direct product factor
3	C₃⁵×C₄₃	C₃	1	1	yes	maximal, characteristic
4	C₃²×C₄₃⋊C₉	—	3	27	no	—
5	C₃²×C₄₃⋊C₉	C₃²	1	36	yes	complemented
6	C₃²⋊(C₄₃⋊C₉)	C₃²	1	81	yes	direct product factor
7	C₃⁴×C₄₃	—	3	9	no	—
8	C₃⁴×C₄₃	—	3	18	no	—
9	C₃⁴×C₄₃	C₉	1	27	yes	complemented
10	C₃⁴×C₄₃	C₃²	1	12	yes	—
11	C₃⁴×C₄₃	C₃²	1	1	yes	characteristic
12	C₃×C₄₃⋊C₉	—	3	108	no	—
13	C₃×C₄₃⋊C₉	C₃³	1	27	yes	complemented
14	C₃³×C₄₃	—	3	243	no	—
15	C₃³×C₄₃	—	3	36	no	—
16	C₃³×C₄₃	—	3	72	no	—
17	C₃³×C₄₃	C₃×C₉	1	9	yes	—
18	C₃³×C₄₃	C₃×C₉	1	108	yes	complemented
19	C₃³×C₄₃	H(3,𝔽₃)	1	9	yes	—
20	C₃³×C₄₃	3₋¹⁺²	1	18	yes	—
21	C₃³×C₄₃	C₃³	1	9	yes	—
22	C₃³×C₄₃	C₃³	1	4	yes	—
23	C₃²×C₃²⋊C₉	—	43	1	no	maximal, Sylow
24	C₃²×C₄₃	—	3	9	no	—
25	C₃²×C₄₃	—	3	18	no	—
26	C₃²×C₄₃	—	3	324	no	—
27	C₃²×C₄₃	C₃²⋊C₉	1	81	yes	complemented
28	C₃²×C₄₃	C₃²×C₉	1	12	yes	—
29	C₃²×C₄₃	C₃²×C₉	1	27	yes	complemented
30	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	12	yes	—
31	C₃²×C₄₃	C₃×3₋¹⁺²	1	24	yes	—
32	C₃²×C₄₃	C₃⁴	1	1	yes	characteristic
33	C₄₃⋊C₉	—	3	27	no	—
34	C₃⁵	C₄₃⋊C₃	1	1	yes	characteristic
35	C₃³×C₉	—	43	3	no	—
36	C₃×C₃²⋊C₉	—	43	36	no	—
37	C₃×C₄₃	—	3	27	no	—
38	C₃×C₄₃	C₃×C₃²⋊C₉	1	36	yes	complemented
39	C₃×C₄₃	C₃³×C₉	1	1	yes	characteristic
40	C₃×C₄₃	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
41	C₃×C₄₃	C₃²×3₋¹⁺²	1	2	yes	—
42	C₃⁴	—	3	9	no	—
43	C₃⁴	—	3	18	no	—
44	C₃⁴	C₄₃⋊C₉	1	27	yes	complemented
45	C₃⁴	C₃×C₄₃⋊C₃	1	12	yes	—
46	C₃⁴	C₃×C₄₃⋊C₃	1	1	yes	characteristic
47	C₃²×C₉	—	43	36	no	—
48	C₃²×C₉	—	129	27	no	—
49	C₃²⋊C₉	—	43	81	no	—
50	C₄₃	C₃²×C₃²⋊C₉	1	1	yes	characteristic, complemented, Sylow
51	C₃³	—	3	243	no	—
52	C₃³	—	3	36	no	—
53	C₃³	—	3	72	no	—
54	C₃³	C₃×C₄₃⋊C₉	1	9	yes	—
55	C₃³	C₃×C₄₃⋊C₉	1	108	yes	complemented
56	C₃³	C₃²⋊(C₄₃⋊C₃)	1	9	yes	—
57	C₃³	#11923958	1	18	yes	—
58	C₃³	C₃²×C₄₃⋊C₃	1	9	yes	—
59	C₃³	C₃²×C₄₃⋊C₃	1	4	yes	—
60	C₃×C₉	—	43	27	no	—
61	C₃×C₉	—	129	108	no	—
62	C₃²	—	3	18	no	—
63	C₃²	—	3	324	no	—
64	C₃²	—	3	9	no	—
65	C₃²	C₃²⋊(C₄₃⋊C₉)	1	81	yes	direct product factor
66	C₃²	C₃²×C₄₃⋊C₉	1	12	yes	—
67	C₃²	C₃²×C₄₃⋊C₉	1	27	yes	complemented
68	C₃²	C₃×C₃²⋊(C₄₃⋊C₃)	1	12	yes	—
69	C₃²	C₃×#11923958	1	24	yes	—
70	C₃²	C₃³×C₄₃⋊C₃	1	1	yes	characteristic
71	C₉	—	129	27	no	—
72	C₃	—	3	27	no	—
73	C₃	C₃×C₃²⋊(C₄₃⋊C₉)	1	36	yes	direct product factor
74	C₃	C₃³×C₄₃⋊C₉	1	1	yes	characteristic
75	C₃	C₃²×C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
76	C₃	C₃²×#11923958	1	2	yes	—

	subgroup	G/H
center	C₃⁴	C₃×C₄₃⋊C₃
commutator	C₃×C₄₃	C₃³×C₉
Frattini	C₃²	C₃³×C₄₃⋊C₃
Fitting, prime radical	C₃⁵×C₄₃	C₃
socle	C₃⁴×C₄₃	C₃²
cosocle	C₃²×C₄₃	C₃⁴
hypercenter	C₃⁵	C₄₃⋊C₃
hypocenter	C₄₃	C₃²×C₃²⋊C₉
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. C₃³×C₄₃⋊C₉	C₃	semidirect
2. C₃×C₃²⋊(C₄₃⋊C₉)	C₃	direct (N × H)
5. C₃²×C₄₃⋊C₉	C₃²	semidirect
6. C₃²⋊(C₄₃⋊C₉)	C₃²	direct (N × H)
9. C₃⁴×C₄₃	C₉	semidirect
13. C₃×C₄₃⋊C₉	C₃³	semidirect
18. C₃³×C₄₃	C₃×C₉	semidirect
27. C₃²×C₄₃	C₃²⋊C₉	semidirect
29. C₃²×C₄₃	C₃²×C₉	semidirect
38. C₃×C₄₃	C₃×C₃²⋊C₉	semidirect
44. C₃⁴	C₄₃⋊C₉	semidirect
50. C₄₃	C₃²×C₃²⋊C₉	semidirect
55. C₃³	C₃×C₄₃⋊C₉	semidirect
65. C₃²	C₃²⋊(C₄₃⋊C₉)	direct (N × H)
67. C₃²	C₃²×C₄₃⋊C₉	semidirect
73. C₃	C₃×C₃²⋊(C₄₃⋊C₉)	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×C₃²⋊(C₄₃⋊C₉)	3
C₃⁵×C₄₃	3
C₃²×C₃²⋊C₉	43

Subgroups — C32×C32⋊(C43⋊C9) #44534636

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₃²⋊(C₄₃⋊C₉) #44534636