Subgroups — #23782905

Order 10449.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812525	C₃	1	3	yes	maximal, complemented
2	#16812515	C₃	1	2	yes	maximal, complemented
3	#16812513	C₃	1	1	yes	maximal, characteristic, complemented
4	#16812510	C₃	1	3	yes	maximal, complemented
5	#16812507	C₃	1	3	yes	maximal, complemented
6	C₃×3₋¹⁺²×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented
7	#11923958	C₃²	1	6	yes	—
8	#11923957	—	3	3	no	—
9	#11923956	—	3	3	no	—
10	C₃²⋊(C₄₃⋊C₃)	C₃²	1	3	yes	—
11	C₉×C₄₃⋊C₃	—	3	3	no	—
12	C₃³×C₄₃	C₃²	1	1	yes	characteristic
13	3₋¹⁺²×C₄₃	—	3	3	no	—
14	C₃×C₉×C₄₃	C₃²	1	1	yes	characteristic
15	C₃×C₉×C₄₃	C₃²	1	1	yes	characteristic
16	C₃×C₉×C₄₃	C₃²	1	1	yes	characteristic
17	C₃²×C₄₃	—	3	1	no	—
18	C₃²×C₄₃	—	9	1	no	—
19	C₃²×C₄₃	C₃³	1	1	yes	characteristic
20	C₃×C₄₃⋊C₃	—	3	3	no	—
21	C₉×C₄₃	—	3	1	no	—
22	C₉×C₄₃	—	3	1	no	—
23	C₉×C₄₃	H(3,𝔽₃)	1	3	yes	—
24	C₄₃⋊C₉	—	3	6	no	—
25	#6913	—	43	1	no	maximal, Sylow
26	C₃×C₄₃	—	3	1	no	—
27	C₃×C₄₃	—	9	1	no	—
28	C₃×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
29	C₄₃⋊C₃	—	9	3	no	—
30	#737	—	43	3	no	—
31	C₃×3₋¹⁺²	C₄₃⋊C₃	1	1	yes	characteristic, complemented
32	#733	—	43	2	no	—
33	#732	—	43	1	no	—
34	#731	—	43	3	no	—
35	AΣL(1,𝔽₂₇)	—	43	3	no	—
36	C₄₃	#6913	1	1	yes	characteristic, complemented, Sylow
37	C₃³	C₃×C₄₃⋊C₃	1	1	yes	characteristic
38	3₋¹⁺²	—	3	3	no	—
39	3₋¹⁺²	—	43	6	no	—
40	3₋¹⁺²	—	129	3	no	—
41	3₋¹⁺²	—	129	3	no	—
42	H(3,𝔽₃)	—	43	3	no	—
43	C₃×C₉	—	129	3	no	—
44	C₃×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
45	C₃×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
46	C₃×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
47	C₃²	—	3	1	no	—
48	C₃²	—	9	1	no	—
49	C₃²	—	129	3	no	—
50	C₃²	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
51	C₉	—	3	1	no	—
52	C₉	—	3	1	no	—
53	C₉	—	129	6	no	—
54	C₉	C₃²⋊(C₄₃⋊C₃)	1	3	yes	—
55	C₃	—	3	1	no	—
56	C₃	—	9	1	no	—
57	C₃	—	387	3	no	—
58	C₃	C₃×C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₃	C₃×C₃²⋊(C₄₃⋊C₃)
commutator, cosocle	C₃²×C₄₃	C₃³
Frattini	C₃²	C₃²×C₄₃⋊C₃
Fitting	C₃×3₋¹⁺²×C₄₃	C₃
socle	C₃×C₄₃	C₃×H(3,𝔽₃)
hypercenter	C₃×3₋¹⁺²	C₄₃⋊C₃
hypocenter	C₄₃	#6913
LCS	G ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃ ◁ C₃×C₉ ◁ C₃×3₋¹⁺²

Complements

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

N	H ≅ G/N	type
1. #16812525	C₃	semidirect
2. #16812515	C₃	semidirect
3. #16812513	C₃	semidirect
4. #16812510	C₃	semidirect
5. #16812507	C₃	semidirect
6. C₃×3₋¹⁺²×C₄₃	C₃	semidirect
31. C₃×3₋¹⁺²	C₄₃⋊C₃	semidirect
36. C₄₃	#6913	semidirect