Subgroups — #23782878

Order 10449.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812526	C₃	1	3	yes	maximal, complemented
2	C₃×C₉×C₄₃⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
3	#16812515	C₃	1	1	yes	maximal, characteristic, complemented
4	#16812513	C₃	1	1	yes	maximal, characteristic, complemented
5	#16812511	C₃	1	3	yes	maximal, complemented
6	#16812508	C₃	1	3	yes	maximal, complemented
7	C₄₃×#733	C₃	1	1	yes	maximal, characteristic, complemented
8	C₃²×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
9	#11923958	C₃²	1	3	yes	—
10	#11923957	—	3	3	no	—
11	#11923956	—	3	3	no	—
12	C₃²⋊(C₄₃⋊C₃)	C₃²	1	3	yes	—
13	C₃×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
14	C₃×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
15	C₉×C₄₃⋊C₃	—	3	1	no	—
16	C₉×C₄₃⋊C₃	—	3	1	no	—
17	C₉×C₄₃⋊C₃	—	3	1	no	—
18	C₉×C₄₃⋊C₃	—	3	3	no	—
19	3₋¹⁺²×C₄₃	C₃²	1	3	yes	—
20	C₃×C₉×C₄₃	C₃²	1	1	yes	characteristic
21	C₃²×C₄₃	C₃³	1	1	yes	characteristic
22	C₃×C₄₃⋊C₃	—	3	1	no	—
23	C₃×C₄₃⋊C₃	—	3	3	no	—
24	C₃×C₄₃⋊C₃	—	3	3	no	—
25	C₉×C₄₃	—	3	1	no	—
26	C₉×C₄₃	—	3	3	no	—
27	C₄₃⋊C₉	—	3	1	no	—
28	C₄₃⋊C₉	—	3	3	no	—
29	C₄₃⋊C₉	H(3,𝔽₃)	1	1	yes	characteristic
30	C₄₃⋊C₉	H(3,𝔽₃)	1	1	yes	characteristic
31	C₄₃⋊C₉	H(3,𝔽₃)	1	1	yes	characteristic
32	#6908	—	43	1	no	maximal, Sylow
33	C₃×C₄₃	—	3	1	no	—
34	C₃×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
35	C₄₃⋊C₃	—	3	3	no	—
36	C₄₃⋊C₃	—	9	3	no	—
37	#737	—	43	3	no	—
38	C₃²×C₉	—	43	1	no	—
39	#733	—	43	1	no	—
40	#733	C₄₃⋊C₃	1	1	yes	characteristic, complemented
41	#732	—	43	1	no	—
42	#731	—	43	3	no	—
43	AΣL(1,𝔽₂₇)	—	43	3	no	—
44	C₄₃	#6908	1	1	yes	characteristic, complemented, Sylow
45	C₃³	—	43	1	no	—
46	3₋¹⁺²	—	43	3	no	—
47	3₋¹⁺²	—	129	3	no	—
48	3₋¹⁺²	—	129	3	no	—
49	3₋¹⁺²	C₃×C₄₃⋊C₃	1	3	yes	—
50	H(3,𝔽₃)	—	43	3	no	—
51	C₃×C₉	—	43	1	no	—
52	C₃×C₉	—	43	1	no	—
53	C₃×C₉	—	129	1	no	—
54	C₃×C₉	—	129	1	no	—
55	C₃×C₉	—	129	1	no	—
56	C₃×C₉	—	129	3	no	—
57	C₃×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
58	C₃²	—	129	3	no	—
59	C₃²	—	129	1	no	—
60	C₃²	—	129	3	no	—
61	C₃²	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
62	C₉	—	3	1	no	—
63	C₉	—	3	3	no	—
64	C₉	—	43	1	no	—
65	C₉	—	43	1	no	—
66	C₉	—	43	1	no	—
67	C₉	—	129	1	no	—
68	C₉	—	129	3	no	—
69	C₃	—	3	1	no	—
70	C₃	—	129	3	no	—
71	C₃	—	387	3	no	—
72	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)
hypercenter	#733	C₄₃⋊C₃
hypocenter	C₄₃	#6908
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
1. #16812526	C₃	semidirect
2. C₃×C₉×C₄₃⋊C₃	C₃	semidirect
3. #16812515	C₃	semidirect
4. #16812513	C₃	semidirect
5. #16812511	C₃	semidirect
6. #16812508	C₃	semidirect
7. C₄₃×#733	C₃	semidirect
40. #733	C₄₃⋊C₃	semidirect
44. C₄₃	#6908	semidirect