Subgroups — #732×C₄₃⋊C₃ #23782867

Order 10449.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	H(3,𝔽₃)×C₄₃⋊C₃	C₃	1	3	yes	maximal, complemented
2	C₃×C₉×C₄₃⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
3	#16812513	C₃	1	2	yes	maximal, complemented
4	#16812512	C₃	1	6	yes	maximal, complemented
5	C₄₃×#732	C₃	1	1	yes	maximal, characteristic, complemented
6	C₃²×C₄₃⋊C₃	—	3	3	no	—
7	C₃²×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
8	C₃²⋊(C₄₃⋊C₃)	—	3	6	no	—
9	C₃²⋊(C₄₃⋊C₃)	C₃²	1	6	yes	complemented
10	C₃×C₄₃⋊C₉	C₃²	1	2	yes	complemented
11	C₉×C₄₃⋊C₃	—	3	2	no	—
12	C₉×C₄₃⋊C₃	—	3	1	no	—
13	H(3,𝔽₃)×C₄₃	C₃²	1	3	yes	complemented
14	C₃×C₉×C₄₃	C₃²	1	1	yes	characteristic, complemented
15	C₃²×C₄₃	—	3	3	no	—
16	C₃²×C₄₃	C₃³	1	1	yes	characteristic
17	C₃×C₄₃⋊C₃	—	3	3	no	—
18	C₃×C₄₃⋊C₃	—	3	6	no	—
19	C₃×C₄₃⋊C₃	—	9	9	no	—
20	C₃×C₄₃⋊C₃	H(3,𝔽₃)	1	2	yes	—
21	C₃×C₄₃⋊C₃	H(3,𝔽₃)	1	1	yes	characteristic
22	C₉×C₄₃	—	3	1	no	—
23	C₄₃⋊C₉	—	3	2	no	—
24	C₃×#732	—	43	1	no	maximal, Sylow
25	C₃×C₄₃	—	3	1	no	—
26	C₃×C₄₃	—	9	3	no	—
27	C₃×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
28	C₄₃⋊C₃	—	3	2	no	—
29	C₄₃⋊C₃	—	9	6	no	—
30	C₄₃⋊C₃	#732	1	3	yes	direct product factor
31	C₃×H(3,𝔽₃)	—	43	3	no	—
32	C₃²×C₉	—	43	1	no	—
33	#732	—	43	6	no	—
34	#732	—	43	2	no	—
35	#732	C₄₃⋊C₃	1	1	yes	characteristic, direct product factor
36	C₄₃	C₃×#732	1	1	yes	characteristic, complemented, Sylow
37	C₃³	—	43	1	no	—
38	C₃³	—	129	3	no	—
39	H(3,𝔽₃)	—	43	6	no	—
40	H(3,𝔽₃)	—	129	6	no	—
41	H(3,𝔽₃)	C₃×C₄₃⋊C₃	1	3	yes	complemented
42	C₃×C₉	—	43	2	no	—
43	C₃×C₉	—	129	1	no	—
44	C₃×C₉	—	129	2	no	—
45	C₃×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic, complemented
46	C₃²	—	3	3	no	—
47	C₃²	—	43	1	no	—
48	C₃²	—	43	2	no	—
49	C₃²	—	129	3	no	—
50	C₃²	—	129	6	no	—
51	C₃²	—	387	9	no	—
52	C₃²	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
53	C₉	—	3	1	no	—
54	C₉	—	129	2	no	—
55	C₃	—	3	1	no	—
56	C₃	—	9	3	no	—
57	C₃	—	43	3	no	—
58	C₃	—	129	2	no	—
59	C₃	—	387	6	no	—
60	C₃	H(3,𝔽₃)×C₄₃⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃	H(3,𝔽₃)×C₄₃⋊C₃
commutator, cosocle	C₃²×C₄₃	C₃³
Frattini	C₃²	C₃²×C₄₃⋊C₃
Fitting	C₄₃×#732	C₃
socle	C₃×C₄₃	C₃×H(3,𝔽₃)
hypercenter	#732	C₄₃⋊C₃
hypocenter	C₄₃	C₃×#732
LCS	G ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃ ◁ C₃² ◁ #732

Complements

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

N	H ≅ G/N	type
1. H(3,𝔽₃)×C₄₃⋊C₃	C₃	semidirect
2. C₃×C₉×C₄₃⋊C₃	C₃	semidirect
3. #16812513	C₃	semidirect
4. #16812512	C₃	semidirect
5. C₄₃×#732	C₃	semidirect
9. C₃²⋊(C₄₃⋊C₃)	C₃²	semidirect
10. C₃×C₄₃⋊C₉	C₃²	semidirect
13. H(3,𝔽₃)×C₄₃	C₃²	semidirect
14. C₃×C₉×C₄₃	C₃²	semidirect
30. C₄₃⋊C₃	#732	direct (N × H)
35. #732	C₄₃⋊C₃	direct (N × H)
36. C₄₃	C₃×#732	semidirect
41. H(3,𝔽₃)	C₃×C₄₃⋊C₃	semidirect
45. C₃×C₉	C₃×C₄₃⋊C₃	semidirect

Subgroups — #732×C43⋊C3 #23782867

Conjugacy classes of subgroups

Complements

Subgroups — #732×C₄₃⋊C₃ #23782867