Subgroups — #733×C₄₃⋊C₃ #23782870

Order 10449.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	3₋¹⁺²×C₄₃⋊C₃	C₃	1	3	yes	maximal
2	C₃×C₉×C₄₃⋊C₃	C₃	1	1	yes	maximal, characteristic
3	#16812515	C₃	1	2	yes	maximal, complemented
4	#16812514	C₃	1	6	yes	maximal, complemented
5	C₄₃×#733	C₃	1	1	yes	maximal, characteristic, complemented
6	C₃²×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
7	#11923958	C₃²	1	6	yes	—
8	#11923957	—	3	3	no	—
9	#11923956	—	3	3	no	—
10	C₃×C₄₃⋊C₉	C₃²	1	2	yes	—
11	C₉×C₄₃⋊C₃	—	3	1	no	—
12	C₉×C₄₃⋊C₃	—	3	1	no	—
13	C₉×C₄₃⋊C₃	—	3	1	no	—
14	C₉×C₄₃⋊C₃	—	3	3	no	—
15	3₋¹⁺²×C₄₃	C₃²	1	3	yes	—
16	C₃×C₉×C₄₃	C₃²	1	1	yes	characteristic
17	C₃²×C₄₃	C₃³	1	1	yes	characteristic
18	C₃×C₄₃⋊C₃	—	3	3	no	—
19	C₃×C₄₃⋊C₃	H(3,𝔽₃)	1	1	yes	characteristic
20	C₃×C₄₃⋊C₃	H(3,𝔽₃)	1	1	yes	characteristic
21	C₃×C₄₃⋊C₃	H(3,𝔽₃)	1	1	yes	characteristic
22	C₉×C₄₃	—	3	1	no	—
23	C₉×C₄₃	—	3	3	no	—
24	C₄₃⋊C₉	—	3	2	no	—
25	C₄₃⋊C₉	—	3	6	no	—
26	C₃×#733	—	43	1	no	maximal, Sylow
27	C₃×C₄₃	—	3	1	no	—
28	C₃×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
29	C₄₃⋊C₃	—	3	1	no	—
30	C₄₃⋊C₃	—	3	1	no	—
31	C₄₃⋊C₃	#733	1	3	yes	direct product factor
32	C₃×3₋¹⁺²	—	43	3	no	—
33	C₃²×C₉	—	43	1	no	—
34	#733	—	43	6	no	—
35	#733	—	43	2	no	—
36	#733	C₄₃⋊C₃	1	1	yes	characteristic, direct product factor
37	C₄₃	C₃×#733	1	1	yes	characteristic, complemented, Sylow
38	C₃³	—	43	1	no	—
39	3₋¹⁺²	—	43	6	no	—
40	3₋¹⁺²	—	129	3	no	—
41	3₋¹⁺²	—	129	3	no	—
42	3₋¹⁺²	C₃×C₄₃⋊C₃	1	3	yes	—
43	C₃×C₉	—	43	2	no	—
44	C₃×C₉	—	129	1	no	—
45	C₃×C₉	—	129	1	no	—
46	C₃×C₉	—	129	1	no	—
47	C₃×C₉	—	129	3	no	—
48	C₃×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
49	C₃²	—	43	1	no	—
50	C₃²	—	43	1	no	—
51	C₃²	—	43	1	no	—
52	C₃²	—	129	3	no	—
53	C₃²	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
54	C₉	—	3	1	no	—
55	C₉	—	3	3	no	—
56	C₉	—	129	2	no	—
57	C₉	—	129	6	no	—
58	C₃	—	3	1	no	—
59	C₃	—	43	3	no	—
60	C₃	—	129	1	no	—
61	C₃	—	129	1	no	—
62	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×#733	C₃
socle	C₃×C₄₃	C₃×H(3,𝔽₃)
prime radical	C₃²×C₄₃⋊C₃	C₃²
hypercenter	#733	C₄₃⋊C₃
hypocenter	C₄₃	C₃×#733
LCS	G ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃ ◁ C₃² ◁ #733

Complements

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

N	H ≅ G/N	type
3. #16812515	C₃	semidirect
4. #16812514	C₃	semidirect
5. C₄₃×#733	C₃	semidirect
31. C₄₃⋊C₃	#733	direct (N × H)
36. #733	C₄₃⋊C₃	direct (N × H)
37. C₄₃	C₃×#733	semidirect

Subgroups — #733×C43⋊C3 #23782870

Conjugacy classes of subgroups

Complements

Subgroups — #733×C₄₃⋊C₃ #23782870