Subgroups — C₃×C₄₃×#6887 #44531795

Order 31347.

1052 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₉×C₄₃	C₃	1	1	yes	maximal, characteristic
2	C₄₃×#6887	C₃	1	27	yes	maximal, direct product factor
3	C₃×C₄₃×C₉⋊C₉	C₃	1	6	yes	maximal, complemented
4	C₃×C₄₃×C₃²⋊C₉	C₃	1	3	yes	maximal
5	C₃×C₉²×C₄₃	C₃	1	3	yes	maximal, complemented
6	C₃⁴×C₄₃	C₃²	1	1	yes	characteristic
7	C₃²×C₉×C₄₃	C₉	1	27	yes	complemented
8	C₃²×C₉×C₄₃	C₃²	1	9	yes	—
9	C₃²×C₉×C₄₃	C₃²	1	2	yes	—
10	C₃²×C₉×C₄₃	C₃²	1	9	yes	—
11	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
12	C₄₃×C₉⋊C₉	C₃²	1	54	yes	complemented
13	C₄₃×C₃²⋊C₉	C₃²	1	27	yes	—
14	C₉²×C₄₃	C₃²	1	27	yes	complemented
15	C₃³×C₄₃	—	3	9	no	—
16	C₃³×C₄₃	C₃×C₉	1	9	yes	—
17	C₃³×C₄₃	C₃³	1	3	yes	—
18	C₃³×C₄₃	C₃³	1	1	yes	characteristic
19	C₃×C₉×C₄₃	—	3	27	no	—
20	C₃×C₉×C₄₃	C₃×C₉	1	18	yes	—
21	C₃×C₉×C₄₃	C₃×C₉	1	9	yes	—
22	C₃×C₉×C₄₃	C₃×C₉	1	81	yes	complemented
23	C₃×C₉×C₄₃	C₃³	1	27	yes	—
24	C₃×C₉×C₄₃	C₃³	1	3	yes	—
25	C₃×C₉×C₄₃	C₃³	1	6	yes	—
26	C₃×#6887	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
27	C₃²×C₄₃	—	3	9	no	—
28	C₃²×C₄₃	—	3	27	no	—
29	C₃²×C₄₃	C₃²×C₉	1	9	yes	—
30	C₃²×C₄₃	C₃²×C₉	1	3	yes	—
31	C₃²×C₄₃	#737	1	9	yes	—
32	C₃²×C₄₃	C₃⁴	1	1	yes	characteristic
33	C₉×C₄₃	—	3	27	no	—
34	C₉×C₄₃	C₃²×C₉	1	18	yes	—
35	C₉×C₄₃	C₃²×C₉	1	9	yes	—
36	C₃³×C₉	C₃×C₄₃	1	1	yes	characteristic
37	#6887	C₃×C₄₃	1	27	yes	direct product factor
38	C₃×C₉⋊C₉	C₃×C₄₃	1	6	yes	complemented
39	C₃×C₃²⋊C₉	C₃×C₄₃	1	3	yes	—
40	C₃×C₉²	C₃×C₄₃	1	3	yes	complemented
41	C₃×C₄₃	—	3	9	no	—
42	C₃×C₄₃	#6887	1	9	yes	direct product factor
43	C₃×C₄₃	C₃³×C₉	1	1	yes	characteristic
44	C₃×C₄₃	C₃×#737	1	3	yes	—
45	C₃⁴	C₃²×C₄₃	1	1	yes	characteristic
46	C₃²×C₉	C₉×C₄₃	1	27	yes	complemented
47	C₃²×C₉	C₃²×C₄₃	1	9	yes	—
48	C₃²×C₉	C₃²×C₄₃	1	2	yes	—
49	C₃²×C₉	C₃²×C₄₃	1	1	yes	characteristic
50	C₃²×C₉	C₃²×C₄₃	1	9	yes	—
51	C₉⋊C₉	C₃²×C₄₃	1	54	yes	complemented
52	C₃²⋊C₉	C₃²×C₄₃	1	27	yes	—
53	C₉²	C₃²×C₄₃	1	27	yes	complemented
54	C₄₃	C₃×#6887	1	1	yes	characteristic, direct product factor, Sylow
55	C₃³	—	3	9	no	—
56	C₃³	C₃×C₉×C₄₃	1	9	yes	—
57	C₃³	C₃³×C₄₃	1	3	yes	—
58	C₃³	C₃³×C₄₃	1	1	yes	characteristic
59	C₃×C₉	—	3	27	no	—
60	C₃×C₉	C₃×C₉×C₄₃	1	18	yes	—
61	C₃×C₉	C₃×C₉×C₄₃	1	9	yes	—
62	C₃×C₉	C₃×C₉×C₄₃	1	81	yes	complemented
63	C₃×C₉	C₃³×C₄₃	1	27	yes	—
64	C₃×C₉	C₃³×C₄₃	1	3	yes	—
65	C₃×C₉	C₃³×C₄₃	1	6	yes	—
66	C₃²	—	3	9	no	—
67	C₃²	—	3	27	no	—
68	C₃²	C₃²×C₉×C₄₃	1	9	yes	—
69	C₃²	C₃²×C₉×C₄₃	1	3	yes	—
70	C₃²	C₄₃×#737	1	9	yes	—
71	C₃²	C₃⁴×C₄₃	1	1	yes	characteristic
72	C₉	—	3	27	no	—
73	C₉	C₃²×C₉×C₄₃	1	9	yes	—
74	C₉	C₃²×C₉×C₄₃	1	18	yes	—
75	C₃	—	3	9	no	—
76	C₃	C₄₃×#6887	1	9	yes	direct product factor
77	C₃	C₃³×C₉×C₄₃	1	1	yes	characteristic
78	C₃	C₃×C₄₃×#737	1	3	yes	—

	subgroup	G/H
center	C₃²×C₉×C₄₃	C₃²
commutator	C₃	C₃³×C₉×C₄₃
Frattini, cosocle	C₃²	C₃⁴×C₄₃
socle	C₃³×C₄₃	C₃³
prime radical	C₃⁴×C₄₃	C₃²
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
2. C₄₃×#6887	C₃	direct (N × H)
3. C₃×C₄₃×C₉⋊C₉	C₃	semidirect
5. C₃×C₉²×C₄₃	C₃	semidirect
7. C₃²×C₉×C₄₃	C₉	semidirect
12. C₄₃×C₉⋊C₉	C₃²	semidirect
14. C₉²×C₄₃	C₃²	semidirect
22. C₃×C₉×C₄₃	C₃×C₉	semidirect
26. C₃×#6887	C₄₃	direct (N × H)
37. #6887	C₃×C₄₃	direct (N × H)
38. C₃×C₉⋊C₉	C₃×C₄₃	semidirect
40. C₃×C₉²	C₃×C₄₃	semidirect
42. C₃×C₄₃	#6887	direct (N × H)
46. C₃²×C₉	C₉×C₄₃	semidirect
51. C₉⋊C₉	C₃²×C₄₃	semidirect
53. C₉²	C₃²×C₄₃	semidirect
54. C₄₃	C₃×#6887	direct (N × H)
62. C₃×C₉	C₃×C₉×C₄₃	semidirect
76. C₃	C₄₃×#6887	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×C₉×C₄₃	3
C₄₃×#6887	3
C₃×C₄₃×C₉⋊C₉	3
C₃×C₄₃×C₃²⋊C₉	3
C₃×C₉²×C₄₃	3
C₃×#6887	43

Subgroups — C3×C43×#6887 #44531795

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄₃×#6887 #44531795