Subgroups — C₉×C₄₃×C₉⋊C₉ #44531483

Order 31347.

482 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₃×C₉⋊C₉	C₃	1	3	yes	maximal
2	C₃×C₉²×C₄₃	C₃	1	3	yes	maximal
3	C₃×C₉²×C₄₃	C₃	1	1	yes	maximal, characteristic
4	C₄₃×#6855	C₃	1	6	yes	maximal
5	C₃²×C₉×C₄₃	C₃²	1	2	yes	—
6	C₃²×C₉×C₄₃	C₃²	1	9	yes	—
7	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
8	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
9	C₄₃×C₉⋊C₉	C₉	1	27	yes	direct product factor
10	C₉²×C₄₃	—	3	9	no	—
11	C₉²×C₄₃	C₉	1	9	yes	complemented
12	C₃³×C₄₃	C₃³	1	1	yes	characteristic
13	C₃×C₉×C₄₃	—	3	9	no	—
14	C₃×C₉×C₄₃	—	3	6	no	—
15	C₃×C₉×C₄₃	—	3	18	no	—
16	C₃×C₉×C₄₃	C₃×C₉	1	6	yes	—
17	C₃×C₉×C₄₃	C₃×C₉	1	27	yes	—
18	C₃×C₉×C₄₃	C₃×C₉	1	3	yes	—
19	C₃×C₉×C₄₃	C₃×C₉	1	9	yes	—
20	C₃×C₉×C₄₃	C₃×C₉	1	3	yes	—
21	C₃×C₉×C₄₃	3₋¹⁺²	1	9	yes	—
22	C₉×C₉⋊C₉	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
23	C₃²×C₄₃	C₃²×C₉	1	1	yes	characteristic
24	C₃²×C₄₃	C₃²×C₉	1	3	yes	—
25	C₃²×C₄₃	C₃×3₋¹⁺²	1	3	yes	—
26	C₃²×C₄₃	#737	1	6	yes	—
27	C₉×C₄₃	—	3	6	no	—
28	C₉×C₄₃	—	3	27	no	—
29	C₉×C₄₃	C₉²	1	9	yes	complemented
30	C₉×C₄₃	C₉⋊C₉	1	9	yes	direct product factor
31	C₃×C₉⋊C₉	C₃×C₄₃	1	3	yes	—
32	C₃×C₉²	C₃×C₄₃	1	3	yes	—
33	C₃×C₉²	C₃×C₄₃	1	1	yes	characteristic
34	#6855	C₃×C₄₃	1	6	yes	—
35	C₃×C₄₃	C₃×C₉²	1	1	yes	characteristic
36	C₃×C₄₃	C₃×C₉⋊C₉	1	1	yes	characteristic
37	C₃×C₄₃	#6887	1	2	yes	—
38	C₃×C₄₃	C₉×3₋¹⁺²	1	9	yes	—
39	C₃²×C₉	C₃²×C₄₃	1	2	yes	—
40	C₃²×C₉	C₃²×C₄₃	1	9	yes	—
41	C₃²×C₉	C₃²×C₄₃	1	1	yes	characteristic
42	C₃²×C₉	C₃²×C₄₃	1	1	yes	characteristic
43	C₉⋊C₉	C₉×C₄₃	1	27	yes	direct product factor
44	C₉²	—	3	9	no	—
45	C₉²	C₉×C₄₃	1	9	yes	complemented
46	C₄₃	C₉×C₉⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
47	C₃³	C₃³×C₄₃	1	1	yes	characteristic
48	C₃×C₉	—	3	9	no	—
49	C₃×C₉	—	3	6	no	—
50	C₃×C₉	—	3	18	no	—
51	C₃×C₉	C₃×C₉×C₄₃	1	6	yes	—
52	C₃×C₉	C₃×C₉×C₄₃	1	27	yes	—
53	C₃×C₉	C₃×C₉×C₄₃	1	3	yes	—
54	C₃×C₉	C₃×C₉×C₄₃	1	9	yes	—
55	C₃×C₉	C₃×C₉×C₄₃	1	3	yes	—
56	C₃×C₉	3₋¹⁺²×C₄₃	1	9	yes	—
57	C₃²	C₃²×C₉×C₄₃	1	1	yes	characteristic
58	C₃²	C₃²×C₉×C₄₃	1	3	yes	—
59	C₃²	C₃×3₋¹⁺²×C₄₃	1	3	yes	—
60	C₃²	C₄₃×#737	1	6	yes	—
61	C₉	—	3	6	no	—
62	C₉	—	3	27	no	—
63	C₉	C₉²×C₄₃	1	9	yes	complemented
64	C₉	C₄₃×C₉⋊C₉	1	9	yes	direct product factor
65	C₃	C₃×C₉²×C₄₃	1	1	yes	characteristic
66	C₃	C₃×C₄₃×C₉⋊C₉	1	1	yes	characteristic
67	C₃	C₄₃×#6887	1	2	yes	—
68	C₃	C₉×3₋¹⁺²×C₄₃	1	9	yes	—

	subgroup	G/H
center	C₃²×C₉×C₄₃	C₃²
commutator	C₃	C₃×C₉²×C₄₃
Frattini, cosocle	C₃³	C₃³×C₄₃
socle, prime radical	C₃³×C₄₃	C₃³
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₉×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
9. C₄₃×C₉⋊C₉	C₉	direct (N × H)
11. C₉²×C₄₃	C₉	semidirect
22. C₉×C₉⋊C₉	C₄₃	direct (N × H)
29. C₉×C₄₃	C₉²	semidirect
30. C₉×C₄₃	C₉⋊C₉	direct (N × H)
43. C₉⋊C₉	C₉×C₄₃	direct (N × H)
45. C₉²	C₉×C₄₃	semidirect
46. C₄₃	C₉×C₉⋊C₉	direct (N × H)
63. C₉	C₉²×C₄₃	semidirect
64. C₉	C₄₃×C₉⋊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
C₃×C₄₃×C₉⋊C₉	3
C₃×C₉²×C₄₃	3
C₄₃×#6855	3
C₉×C₉⋊C₉	43

Subgroups — C9×C43×C9⋊C9 #44531483

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×C₄₃×C₉⋊C₉ #44531483