Subgroups — #23782890

Order 10449.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#11923956	C₃	1	1	yes	maximal, characteristic, complemented
2	H(3,𝔽₃)×C₄₃⋊C₃	C₃	1	3	yes	maximal, 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	#11923956	—	3	3	no	—
9	C₃²⋊(C₄₃⋊C₃)	—	3	6	no	—
10	C₃²⋊(C₄₃⋊C₃)	C₃²	1	6	yes	complemented
11	C₃×C₄₃⋊C₉	C₃²	1	2	yes	complemented
12	H(3,𝔽₃)×C₄₃	C₃²	1	3	yes	complemented
13	C₃×C₉×C₄₃	C₃²	1	1	yes	characteristic, complemented
14	C₃²×C₄₃	—	3	3	no	—
15	C₃²×C₄₃	C₃³	1	1	yes	characteristic
16	C₃×C₄₃⋊C₃	—	3	6	no	—
17	C₃×C₄₃⋊C₃	—	9	1	no	—
18	C₃×C₄₃⋊C₃	—	9	9	no	—
19	C₃×C₄₃⋊C₃	H(3,𝔽₃)	1	3	yes	—
20	C₉×C₄₃	—	3	1	no	—
21	C₄₃⋊C₉	—	3	2	no	—
22	#6911	—	43	1	no	maximal, Sylow
23	C₃×C₄₃	—	3	1	no	—
24	C₃×C₄₃	—	9	3	no	—
25	C₃×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
26	C₄₃⋊C₃	—	3	3	no	—
27	C₄₃⋊C₃	—	9	6	no	—
28	C₃×3₋¹⁺²	—	43	1	no	—
29	C₃×H(3,𝔽₃)	—	43	3	no	—
30	#732	—	43	6	no	—
31	#732	—	43	2	no	—
32	#732	C₄₃⋊C₃	1	1	yes	characteristic, complemented
33	C₄₃	#6911	1	1	yes	characteristic, complemented, Sylow
34	C₃³	—	43	1	no	—
35	C₃³	—	129	3	no	—
36	3₋¹⁺²	—	129	3	no	—
37	H(3,𝔽₃)	—	43	6	no	—
38	H(3,𝔽₃)	—	129	6	no	—
39	H(3,𝔽₃)	C₃×C₄₃⋊C₃	1	3	yes	complemented
40	C₃×C₉	—	43	2	no	—
41	C₃×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic, complemented
42	C₃²	—	3	3	no	—
43	C₃²	—	43	3	no	—
44	C₃²	—	129	6	no	—
45	C₃²	—	387	1	no	—
46	C₃²	—	387	9	no	—
47	C₃²	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
48	C₉	—	3	1	no	—
49	C₉	—	129	2	no	—
50	C₃	—	3	1	no	—
51	C₃	—	9	3	no	—
52	C₃	—	129	3	no	—
53	C₃	—	387	6	no	—
54	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	#6911
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. C₃×#11923956	C₃	semidirect
2. H(3,𝔽₃)×C₄₃⋊C₃	C₃	semidirect
3. #16812513	C₃	semidirect
4. #16812512	C₃	semidirect
5. C₄₃×#732	C₃	semidirect
10. C₃²⋊(C₄₃⋊C₃)	C₃²	semidirect
11. C₃×C₄₃⋊C₉	C₃²	semidirect
12. H(3,𝔽₃)×C₄₃	C₃²	semidirect
13. C₃×C₉×C₄₃	C₃²	semidirect
32. #732	C₄₃⋊C₃	semidirect
33. C₄₃	#6911	semidirect
39. H(3,𝔽₃)	C₃×C₄₃⋊C₃	semidirect
41. C₃×C₉	C₃×C₄₃⋊C₃	semidirect