Subgroups — C₃×H(3,𝔽₃)×C₄₃⋊C₉ #44534649

Order 31347.

1688 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₄₃⋊C₉	C₃	1	4	yes	maximal, complemented
2	H(3,𝔽₃)×C₄₃⋊C₉	C₃	1	27	yes	maximal, direct product factor
3	C₃×C₃²⋊(C₄₃⋊C₉)	C₃	1	8	yes	maximal, complemented
4	C₃²×H(3,𝔽₃)×C₄₃	C₃	1	1	yes	maximal, characteristic
5	C₃²×C₄₃⋊C₉	—	3	36	no	—
6	C₃²×C₄₃⋊C₉	C₃²	1	8	yes	—
7	C₃²×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
8	C₃²×C₄₃⋊C₉	C₃²	1	36	yes	complemented
9	C₃²⋊(C₄₃⋊C₉)	C₃²	1	72	yes	complemented
10	C₃⁴×C₄₃	C₃²	1	4	yes	—
11	C₃×H(3,𝔽₃)×C₄₃	C₉	1	27	yes	complemented
12	C₃×H(3,𝔽₃)×C₄₃	C₃²	1	9	yes	—
13	C₃×C₄₃⋊C₉	—	3	24	no	—
14	C₃×C₄₃⋊C₉	—	3	108	no	—
15	C₃×C₄₃⋊C₉	H(3,𝔽₃)	1	9	yes	direct product factor
16	C₃×C₄₃⋊C₉	C₃³	1	24	yes	—
17	C₃×C₄₃⋊C₉	C₃³	1	3	yes	—
18	C₃³×C₄₃	—	3	12	no	—
19	C₃³×C₄₃	—	3	24	no	—
20	C₃³×C₄₃	C₃×C₉	1	36	yes	complemented
21	C₃³×C₄₃	C₃³	1	12	yes	—
22	C₃³×C₄₃	C₃³	1	1	yes	characteristic
23	H(3,𝔽₃)×C₄₃	C₃×C₉	1	81	yes	complemented
24	C₃×C₉×H(3,𝔽₃)	—	43	1	no	maximal, Sylow
25	C₃²×C₄₃	—	3	12	no	—
26	C₃²×C₄₃	—	3	24	no	—
27	C₃²×C₄₃	—	3	108	no	—
28	C₃²×C₄₃	C₃²×C₉	1	3	yes	—
29	C₃²×C₄₃	C₃²×C₉	1	36	yes	complemented
30	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	3	yes	—
31	C₃²×C₄₃	#737	1	6	yes	—
32	C₃²×C₄₃	C₃⁴	1	1	yes	characteristic
33	C₄₃⋊C₉	—	3	24	no	—
34	C₄₃⋊C₉	C₃×H(3,𝔽₃)	1	9	yes	direct product factor
35	C₃²×H(3,𝔽₃)	C₄₃⋊C₃	1	1	yes	characteristic
36	C₃³×C₉	—	43	4	no	—
37	C₉×H(3,𝔽₃)	—	43	27	no	—
38	C₃×C₃²⋊C₉	—	43	8	no	—
39	C₃×C₄₃	—	3	36	no	—
40	C₃×C₄₃	C₉×H(3,𝔽₃)	1	9	yes	complemented
41	C₃×C₄₃	C₃³×C₉	1	1	yes	characteristic
42	C₃×C₄₃	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
43	C₃×C₄₃	C₃×#737	1	2	yes	—
44	C₃⁴	C₃×C₄₃⋊C₃	1	4	yes	—
45	C₃×H(3,𝔽₃)	C₄₃⋊C₉	1	27	yes	direct product factor
46	C₃×H(3,𝔽₃)	C₃×C₄₃⋊C₃	1	9	yes	—
47	C₃²×C₉	—	43	1	no	—
48	C₃²×C₉	—	43	36	no	—
49	C₃²×C₉	—	43	8	no	—
50	C₃²×C₉	—	129	36	no	—
51	C₃²⋊C₉	—	43	72	no	—
52	C₄₃	C₃×C₉×H(3,𝔽₃)	1	1	yes	characteristic, complemented, Sylow
53	C₃³	—	3	12	no	—
54	C₃³	—	3	24	no	—
55	C₃³	C₃×C₄₃⋊C₉	1	36	yes	complemented
56	C₃³	C₃²×C₄₃⋊C₃	1	12	yes	—
57	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
58	H(3,𝔽₃)	C₃×C₄₃⋊C₉	1	81	yes	direct product factor
59	C₃×C₉	—	43	9	no	—
60	C₃×C₉	—	43	3	no	—
61	C₃×C₉	—	43	24	no	—
62	C₃×C₉	—	129	108	no	—
63	C₃×C₉	—	129	24	no	—
64	C₃²	—	3	24	no	—
65	C₃²	—	3	108	no	—
66	C₃²	—	3	12	no	—
67	C₃²	C₃²×C₄₃⋊C₉	1	3	yes	—
68	C₃²	C₃²×C₄₃⋊C₉	1	36	yes	complemented
69	C₃²	H(3,𝔽₃)×C₄₃⋊C₃	1	3	yes	—
70	C₃²	#16812524	1	6	yes	—
71	C₃²	C₃³×C₄₃⋊C₃	1	1	yes	characteristic
72	C₉	—	43	9	no	—
73	C₉	—	129	24	no	—
74	C₃	—	3	36	no	—
75	C₃	H(3,𝔽₃)×C₄₃⋊C₉	1	9	yes	direct product factor
76	C₃	C₃³×C₄₃⋊C₉	1	1	yes	characteristic
77	C₃	C₃×H(3,𝔽₃)×C₄₃⋊C₃	1	1	yes	characteristic
78	C₃	C₃×#16812524	1	2	yes	—

	subgroup	G/H
center	C₃³	C₃²×C₄₃⋊C₃
commutator	C₃×C₄₃	C₃³×C₉
Frattini	C₃²	C₃³×C₄₃⋊C₃
Fitting, prime radical	C₃²×H(3,𝔽₃)×C₄₃	C₃
socle	C₃³×C₄₃	C₃³
cosocle	C₃²×C₄₃	C₃⁴
hypercenter	C₃²×H(3,𝔽₃)	C₄₃⋊C₃
hypocenter	C₄₃	C₃×C₉×H(3,𝔽₃)
LCS	G ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃³ ◁ C₃²×H(3,𝔽₃)

Complements

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

N	H ≅ G/N	type
1. C₃³×C₄₃⋊C₉	C₃	semidirect
2. H(3,𝔽₃)×C₄₃⋊C₉	C₃	direct (N × H)
3. C₃×C₃²⋊(C₄₃⋊C₉)	C₃	semidirect
8. C₃²×C₄₃⋊C₉	C₃²	semidirect
9. C₃²⋊(C₄₃⋊C₉)	C₃²	semidirect
11. C₃×H(3,𝔽₃)×C₄₃	C₉	semidirect
15. C₃×C₄₃⋊C₉	H(3,𝔽₃)	direct (N × H)
20. C₃³×C₄₃	C₃×C₉	semidirect
23. H(3,𝔽₃)×C₄₃	C₃×C₉	semidirect
29. C₃²×C₄₃	C₃²×C₉	semidirect
34. C₄₃⋊C₉	C₃×H(3,𝔽₃)	direct (N × H)
40. C₃×C₄₃	C₉×H(3,𝔽₃)	semidirect
45. C₃×H(3,𝔽₃)	C₄₃⋊C₉	direct (N × H)
52. C₄₃	C₃×C₉×H(3,𝔽₃)	semidirect
55. C₃³	C₃×C₄₃⋊C₉	semidirect
58. H(3,𝔽₃)	C₃×C₄₃⋊C₉	direct (N × H)
68. C₃²	C₃²×C₄₃⋊C₉	semidirect
75. C₃	H(3,𝔽₃)×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
H(3,𝔽₃)×C₄₃⋊C₉	3
C₃×C₃²⋊(C₄₃⋊C₉)	3
C₃²×H(3,𝔽₃)×C₄₃	3
C₃×C₉×H(3,𝔽₃)	43

Subgroups — C3×H(3,𝔽3)×C43⋊C9 #44534649

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×H(3,𝔽₃)×C₄₃⋊C₉ #44534649