Subgroups — #23782725

Order 10449.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#11923958	C₃	1	1	yes	maximal, characteristic
2	C₃²×C₄₃⋊C₉	C₃	1	1	yes	maximal, characteristic
3	C₃²⋊(C₄₃⋊C₉)	C₃	1	1	yes	maximal, characteristic
4	C₄₃×C₃²⋊C₉	C₃	1	1	yes	maximal, characteristic
5	#11923958	—	3	1	no	—
6	#11923958	—	3	1	no	—
7	#11923958	C₉	1	3	yes	complemented
8	C₃×C₄₃⋊C₉	—	3	1	no	—
9	C₃×C₄₃⋊C₉	—	3	1	no	—
10	C₃×C₄₃⋊C₉	—	3	3	no	—
11	C₃×C₄₃⋊C₉	—	3	1	no	—
12	C₃³×C₄₃	C₃²	1	1	yes	characteristic
13	C₃×C₉×C₄₃	—	3	1	no	—
14	C₃²×C₄₃	—	3	1	no	—
15	C₃²×C₄₃	—	3	1	no	—
16	C₃²×C₄₃	—	3	1	no	—
17	C₃²×C₄₃	C₃×C₉	1	1	yes	characteristic
18	C₃²×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
19	C₃²×C₄₃	3₋¹⁺²	1	1	yes	characteristic
20	C₃²×C₄₃	3₋¹⁺²	1	1	yes	characteristic
21	C₉×C₄₃	—	9	1	no	—
22	C₄₃⋊C₉	—	3	3	no	—
23	C₄₃⋊C₉	—	3	3	no	—
24	C₄₃⋊C₉	—	9	1	no	—
25	3₋¹⁺²⋊C₉	—	43	1	no	maximal, Sylow
26	C₃×C₄₃	—	3	1	no	—
27	C₃×C₄₃	—	3	1	no	—
28	C₃×C₄₃	—	3	1	no	—
29	C₃×C₄₃	C₃²⋊C₉	1	1	yes	characteristic
30	C₃×C₄₃	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
31	C₃×C₄₃	#731	1	1	yes	characteristic
32	C₃×C₄₃	#733	1	1	yes	characteristic
33	C₃×3₋¹⁺²	—	43	1	no	—
34	C₃²×C₉	—	43	1	no	—
35	C₃²⋊C₉	—	43	1	no	—
36	C₃²⋊C₉	C₄₃⋊C₃	1	1	yes	characteristic
37	C₄₃	3₋¹⁺²⋊C₉	1	1	yes	characteristic, complemented, Sylow
38	C₃³	C₃×C₄₃⋊C₃	1	1	yes	characteristic
39	3₋¹⁺²	—	43	3	no	—
40	3₋¹⁺²	—	129	1	no	—
41	3₋¹⁺²	—	129	1	no	—
42	C₃×C₉	—	3	1	no	—
43	C₃×C₉	—	129	1	no	—
44	C₃×C₉	—	129	1	no	—
45	C₃×C₉	—	129	3	no	—
46	C₃×C₉	—	129	1	no	—
47	C₃²	—	3	1	no	—
48	C₃²	—	3	1	no	—
49	C₃²	—	3	1	no	—
50	C₃²	C₉×C₄₃⋊C₃	1	1	yes	characteristic
51	C₃²	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
52	C₃²	#11923956	1	1	yes	characteristic
53	C₃²	#11923957	1	1	yes	characteristic
54	C₉	—	9	1	no	—
55	C₉	—	129	3	no	—
56	C₉	—	129	3	no	—
57	C₉	—	387	1	no	—
58	C₃	—	3	1	no	—
59	C₃	—	3	1	no	—
60	C₃	—	3	1	no	—
61	C₃	(C₃×C₄₃⋊C₃)⋊C₉	1	1	yes	characteristic
62	C₃	#16812508	1	1	yes	characteristic
63	C₃	#16812509	1	1	yes	characteristic
64	C₃	#16812514	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
7. #11923958	C₉	semidirect
37. C₄₃	3₋¹⁺²⋊C₉	semidirect