Subgroups — C₃×C₄₃×#6899 #44531813

Order 31347.

788 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×3₋¹⁺²×C₄₃	C₃	1	1	yes	maximal, characteristic
2	C₄₃×#6899	C₃	1	27	yes	maximal, direct product factor
3	C₃×C₄₃×C₉⋊C₉	C₃	1	6	yes	maximal, complemented
4	C₃×C₄₃×C₉⋊C₉	C₃	1	2	yes	maximal, complemented
5	C₃×C₄₃×C₃²⋊C₉	C₃	1	3	yes	maximal
6	C₃×C₉²×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented
7	C₃⁴×C₄₃	C₃²	1	1	yes	characteristic
8	C₃×3₋¹⁺²×C₄₃	—	3	9	no	—
9	C₃×3₋¹⁺²×C₄₃	C₃²	1	9	yes	—
10	C₃²×C₉×C₄₃	C₃²	1	2	yes	—
11	C₃²×C₉×C₄₃	C₃²	1	3	yes	—
12	C₃²×C₉×C₄₃	C₃²	1	6	yes	—
13	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
14	C₄₃×C₉⋊C₉	C₃²	1	54	yes	complemented
15	C₄₃×C₉⋊C₉	C₃²	1	18	yes	complemented
16	C₄₃×C₃²⋊C₉	C₃²	1	27	yes	—
17	C₉²×C₄₃	C₃²	1	9	yes	complemented
18	C₃³×C₄₃	—	3	3	no	—
19	C₃³×C₄₃	—	3	9	no	—
20	C₃³×C₄₃	C₃³	1	3	yes	—
21	C₃³×C₄₃	C₃³	1	1	yes	characteristic
22	3₋¹⁺²×C₄₃	—	3	27	no	—
23	C₃×C₉×C₄₃	—	3	6	no	—
24	C₃×C₉×C₄₃	—	3	9	no	—
25	C₃×C₉×C₄₃	—	3	18	no	—
26	C₃×C₉×C₄₃	3₋¹⁺²	1	9	yes	—
27	C₃×C₉×C₄₃	C₃³	1	9	yes	—
28	C₃×C₉×C₄₃	C₃³	1	18	yes	—
29	C₃×C₉×C₄₃	C₃³	1	6	yes	—
30	C₃×C₉×C₄₃	C₃³	1	3	yes	—
31	C₃×#6899	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
32	C₃²×C₄₃	—	3	3	no	—
33	C₃²×C₄₃	—	3	9	no	—
34	C₃²×C₄₃	—	9	9	no	—
35	C₃²×C₄₃	C₃×3₋¹⁺²	1	3	yes	—
36	C₃²×C₄₃	#737	1	9	yes	—
37	C₃²×C₄₃	C₃⁴	1	1	yes	characteristic
38	C₉×C₄₃	—	3	6	no	—
39	C₉×C₄₃	—	3	9	no	—
40	C₉×C₄₃	—	3	18	no	—
41	C₉×C₄₃	C₃×3₋¹⁺²	1	9	yes	—
42	C₃²×3₋¹⁺²	C₃×C₄₃	1	1	yes	characteristic
43	#6899	C₃×C₄₃	1	27	yes	direct product factor
44	C₃×C₉⋊C₉	C₃×C₄₃	1	6	yes	complemented
45	C₃×C₉⋊C₉	C₃×C₄₃	1	2	yes	complemented
46	C₃×C₃²⋊C₉	C₃×C₄₃	1	3	yes	—
47	C₃×C₉²	C₃×C₄₃	1	1	yes	characteristic, complemented
48	C₃×C₄₃	—	9	3	no	—
49	C₃×C₄₃	#6899	1	9	yes	direct product factor
50	C₃×C₄₃	C₃²×3₋¹⁺²	1	1	yes	characteristic
51	C₃×C₄₃	C₃×#737	1	3	yes	—
52	C₃⁴	C₃²×C₄₃	1	1	yes	characteristic
53	C₃×3₋¹⁺²	—	3	9	no	—
54	C₃×3₋¹⁺²	C₃²×C₄₃	1	9	yes	—
55	C₃²×C₉	C₃²×C₄₃	1	2	yes	—
56	C₃²×C₉	C₃²×C₄₃	1	3	yes	—
57	C₃²×C₉	C₃²×C₄₃	1	6	yes	—
58	C₃²×C₉	C₃²×C₄₃	1	1	yes	characteristic
59	C₉⋊C₉	C₃²×C₄₃	1	54	yes	complemented
60	C₉⋊C₉	C₃²×C₄₃	1	18	yes	complemented
61	C₃²⋊C₉	C₃²×C₄₃	1	27	yes	—
62	C₉²	C₃²×C₄₃	1	9	yes	complemented
63	C₄₃	C₃×#6899	1	1	yes	characteristic, direct product factor, Sylow
64	C₃³	—	3	3	no	—
65	C₃³	—	3	9	no	—
66	C₃³	C₃³×C₄₃	1	3	yes	—
67	C₃³	C₃³×C₄₃	1	1	yes	characteristic
68	3₋¹⁺²	—	3	27	no	—
69	C₃×C₉	—	3	6	no	—
70	C₃×C₉	—	3	9	no	—
71	C₃×C₉	—	3	18	no	—
72	C₃×C₉	3₋¹⁺²×C₄₃	1	9	yes	—
73	C₃×C₉	C₃³×C₄₃	1	9	yes	—
74	C₃×C₉	C₃³×C₄₃	1	18	yes	—
75	C₃×C₉	C₃³×C₄₃	1	6	yes	—
76	C₃×C₉	C₃³×C₄₃	1	3	yes	—
77	C₃²	—	3	3	no	—
78	C₃²	—	3	9	no	—
79	C₃²	—	9	9	no	—
80	C₃²	C₃×3₋¹⁺²×C₄₃	1	3	yes	—
81	C₃²	C₄₃×#737	1	9	yes	—
82	C₃²	C₃⁴×C₄₃	1	1	yes	characteristic
83	C₉	—	3	6	no	—
84	C₉	—	3	9	no	—
85	C₉	—	3	18	no	—
86	C₉	C₃×3₋¹⁺²×C₄₃	1	9	yes	—
87	C₃	—	9	3	no	—
88	C₃	C₄₃×#6899	1	9	yes	direct product factor
89	C₃	C₃²×3₋¹⁺²×C₄₃	1	1	yes	characteristic
90	C₃	C₃×C₄₃×#737	1	3	yes	—

	subgroup	G/H
center, socle	C₃³×C₄₃	C₃³
commutator, Frattini, cosocle	C₃²	C₃⁴×C₄₃
prime radical	C₃⁴×C₄₃	C₃²
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃³×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₃×#6899	C₃	direct (N × H)
3. C₃×C₄₃×C₉⋊C₉	C₃	semidirect
4. C₃×C₄₃×C₉⋊C₉	C₃	semidirect
6. C₃×C₉²×C₄₃	C₃	semidirect
14. C₄₃×C₉⋊C₉	C₃²	semidirect
15. C₄₃×C₉⋊C₉	C₃²	semidirect
17. C₉²×C₄₃	C₃²	semidirect
31. C₃×#6899	C₄₃	direct (N × H)
43. #6899	C₃×C₄₃	direct (N × H)
44. C₃×C₉⋊C₉	C₃×C₄₃	semidirect
45. C₃×C₉⋊C₉	C₃×C₄₃	semidirect
47. C₃×C₉²	C₃×C₄₃	semidirect
49. C₃×C₄₃	#6899	direct (N × H)
59. C₉⋊C₉	C₃²×C₄₃	semidirect
60. C₉⋊C₉	C₃²×C₄₃	semidirect
62. C₉²	C₃²×C₄₃	semidirect
63. C₄₃	C₃×#6899	direct (N × H)
88. C₃	C₄₃×#6899	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×3₋¹⁺²×C₄₃	3
C₄₃×#6899	3
C₃×C₄₃×C₉⋊C₉	3
C₃×C₄₃×C₃²⋊C₉	3
C₃×C₉²×C₄₃	3
C₃×#6899	43

Subgroups — C3×C43×#6899 #44531813

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄₃×#6899 #44531813