Subgroups — H(3,𝔽₃)⋊(C₄₃⋊C₉) #23782720

Order 10449.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₄₃⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
2	C₃²⋊(C₄₃⋊C₉)	C₃	1	2	yes	maximal, complemented
3	C₃×H(3,𝔽₃)×C₄₃	C₃	1	1	yes	maximal, characteristic
4	C₃×C₄₃⋊C₉	—	3	1	no	—
5	C₃×C₄₃⋊C₉	—	3	3	no	—
6	C₃×C₄₃⋊C₉	—	3	2	no	—
7	C₃³×C₄₃	—	3	1	no	—
8	C₃³×C₄₃	C₃²	1	1	yes	characteristic
9	H(3,𝔽₃)×C₄₃	—	3	2	no	—
10	H(3,𝔽₃)×C₄₃	C₉	1	3	yes	complemented
11	C₃²×C₄₃	—	3	1	no	—
12	C₃²×C₄₃	—	3	1	no	—
13	C₃²×C₄₃	—	3	1	no	—
14	C₃²×C₄₃	—	3	3	no	—
15	C₃²×C₄₃	—	9	1	no	—
16	C₃²×C₄₃	—	9	1	no	—
17	C₃²×C₄₃	—	9	1	no	—
18	C₃²×C₄₃	C₃×C₉	1	1	yes	characteristic
19	C₃²×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
20	C₃²×C₄₃	3₋¹⁺²	1	2	yes	—
21	C₄₃⋊C₉	—	3	3	no	—
22	C₄₃⋊C₉	—	9	2	no	—
23	H(3,𝔽₃)⋊C₉	—	43	1	no	maximal, Sylow
24	C₃×C₄₃	—	3	1	no	—
25	C₃×C₄₃	—	3	2	no	—
26	C₃×C₄₃	—	9	3	no	—
27	C₃×C₄₃	C₃²⋊C₉	1	1	yes	characteristic
28	C₃×C₄₃	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
29	C₃×C₄₃	#731	1	1	yes	characteristic
30	C₃×C₄₃	#732	1	1	yes	characteristic
31	C₃×H(3,𝔽₃)	C₄₃⋊C₃	1	1	yes	characteristic
32	C₃²×C₉	—	43	1	no	—
33	C₃²⋊C₉	—	43	2	no	—
34	C₄₃	H(3,𝔽₃)⋊C₉	1	1	yes	characteristic, complemented, Sylow
35	C₃³	—	3	1	no	—
36	C₃³	C₃×C₄₃⋊C₃	1	1	yes	characteristic
37	H(3,𝔽₃)	—	3	2	no	—
38	H(3,𝔽₃)	C₄₃⋊C₉	1	3	yes	complemented
39	C₃×C₉	—	129	1	no	—
40	C₃×C₉	—	129	3	no	—
41	C₃×C₉	—	129	2	no	—
42	C₃²	—	3	1	no	—
43	C₃²	—	3	1	no	—
44	C₃²	—	3	1	no	—
45	C₃²	—	3	3	no	—
46	C₃²	—	9	1	no	—
47	C₃²	—	9	1	no	—
48	C₃²	—	9	1	no	—
49	C₃²	C₃×C₄₃⋊C₉	1	1	yes	characteristic
50	C₃²	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
51	C₃²	#11923958	1	2	yes	—
52	C₉	—	129	3	no	—
53	C₉	—	387	2	no	—
54	C₃	—	3	1	no	—
55	C₃	—	3	2	no	—
56	C₃	—	9	3	no	—
57	C₃	C₃²⋊(C₄₃⋊C₉)	1	1	yes	characteristic
58	C₃	#16812506	1	1	yes	characteristic
59	C₃	#16812509	1	1	yes	characteristic
60	C₃	#16812512	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₃²×C₄₃⋊C₉	C₃	semidirect
2. C₃²⋊(C₄₃⋊C₉)	C₃	semidirect
10. H(3,𝔽₃)×C₄₃	C₉	semidirect
34. C₄₃	H(3,𝔽₃)⋊C₉	semidirect
38. H(3,𝔽₃)	C₄₃⋊C₉	semidirect

Subgroups — H(3,𝔽3)⋊(C43⋊C9) #23782720

Conjugacy classes of subgroups

Complements

Subgroups — H(3,𝔽₃)⋊(C₄₃⋊C₉) #23782720