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Degree $n$ Residue characteristic $p$ Discriminant exponent $c$ Galois group
Ramification index $e$ Residue field degree $f$ Galois tame degree $t$ Galois unram. degree $u$
Num. automorphisms Inertia subgroup Indices Assoc. Inertia Jump Set
Top Artin slope Galois Artin Visible Artin Wild inertia subgroup
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Label Polynomial $p$ $f$ $e$ $c$ Galois group $u$ $t$ Visible Artin slopes Visible Swan slopes Artin slope content Swan slope content Hidden Artin slopes Hidden Swan slopes Unram. Ext. Eisen. Poly. Ind. of Insep. Assoc. Inertia Resid. Poly Jump Set
2.4.4.44a1.175 $( x^{4} + x + 1 )^{4} + 4 x^{2} ( x^{4} + x + 1 )^{3} + 4 x^{3} ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + \left(8 t^{3} + 8 t^{2} + 8 t\right) x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t\right) x + 16 t^{3} + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.176 $( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2}\right) ( x^{4} + x + 1 )^{3} + 4 x^{3} ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + \left(8 t^{2} + 8 t\right) x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t\right) x + 16 t^{3} + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.177 $( x^{4} + x + 1 )^{4} + 12 x^{2} ( x^{4} + x + 1 )^{3} + 4 x^{3} ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + \left(8 t^{3} + 8 t\right) x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t\right) x + 16 t^{3} + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.178 $( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 12 x^{2}\right) ( x^{4} + x + 1 )^{3} + 4 x^{3} ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + 8 t x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t\right) x + 16 t^{3} + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.179 $( x^{4} + x + 1 )^{4} + \left(4 x^{2} + 8 x\right) ( x^{4} + x + 1 )^{3} + 4 x^{3} ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + \left(8 t^{3} + 8 t^{2}\right) x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t\right) x + 16 t^{3} + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.180 $( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2} + 8 x\right) ( x^{4} + x + 1 )^{3} + 4 x^{3} ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + 8 t^{2} x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t\right) x + 16 t^{3} + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.181 $( x^{4} + x + 1 )^{4} + \left(12 x^{2} + 8 x\right) ( x^{4} + x + 1 )^{3} + 4 x^{3} ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + 8 t^{3} x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t\right) x + 16 t^{3} + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.182 $( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 12 x^{2} + 8 x\right) ( x^{4} + x + 1 )^{3} + 4 x^{3} ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t\right) x + 16 t^{3} + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.511 $( x^{4} + x + 1 )^{4} + 4 x^{2} ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2}\right) ( x^{4} + x + 1 )^{2} + 8 x^{3} ( x^{4} + x + 1 ) + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + \left(8 t^{3} + 8 t\right) x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t\right) x + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.512 $( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2}\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2}\right) ( x^{4} + x + 1 )^{2} + 8 x^{3} ( x^{4} + x + 1 ) + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t\right) x + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.513 $( x^{4} + x + 1 )^{4} + 12 x^{2} ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2}\right) ( x^{4} + x + 1 )^{2} + 8 x^{3} ( x^{4} + x + 1 ) + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + 8 t^{3} x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t\right) x + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.514 $( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 12 x^{2}\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2}\right) ( x^{4} + x + 1 )^{2} + 8 x^{3} ( x^{4} + x + 1 ) + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + 8 t x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t\right) x + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.515 $( x^{4} + x + 1 )^{4} + \left(4 x^{2} + 8 x\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2}\right) ( x^{4} + x + 1 )^{2} + 8 x^{3} ( x^{4} + x + 1 ) + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + \left(8 t^{3} + 8 t^{2} + 8 t\right) x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t\right) x + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.516 $( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2} + 8 x\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2}\right) ( x^{4} + x + 1 )^{2} + 8 x^{3} ( x^{4} + x + 1 ) + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + 8 t^{2} x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t\right) x + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.517 $( x^{4} + x + 1 )^{4} + \left(12 x^{2} + 8 x\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2}\right) ( x^{4} + x + 1 )^{2} + 8 x^{3} ( x^{4} + x + 1 ) + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + \left(8 t^{3} + 8 t^{2}\right) x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t\right) x + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.518 $( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 12 x^{2} + 8 x\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2}\right) ( x^{4} + x + 1 )^{2} + 8 x^{3} ( x^{4} + x + 1 ) + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + \left(8 t^{2} + 8 t\right) x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t\right) x + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.871 $( x^{4} + x + 1 )^{4} + \left(4 x^{2} + 4\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t\right) x + 8 t^{3} + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.872 $( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2} + 4\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + \left(8 t^{3} + 8 t^{2}\right) x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t\right) x + 8 t^{3} + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.873 $( x^{4} + x + 1 )^{4} + \left(12 x^{2} + 4\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + 8 t x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t\right) x + 8 t^{3} + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.874 $( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 12 x^{2} + 4\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + \left(8 t^{3} + 8 t^{2} + 8 t\right) x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t\right) x + 8 t^{3} + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.875 $( x^{4} + x + 1 )^{4} + \left(4 x^{2} + 8 x + 4\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + 8 t^{2} x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t\right) x + 8 t^{3} + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.876 $( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2} + 8 x + 4\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + 8 t^{3} x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t\right) x + 8 t^{3} + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.877 $( x^{4} + x + 1 )^{4} + \left(12 x^{2} + 8 x + 4\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + \left(8 t^{2} + 8 t\right) x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t\right) x + 8 t^{3} + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.878 $( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 12 x^{2} + 8 x + 4\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + \left(8 t^{3} + 8 t\right) x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t\right) x + 8 t^{3} + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.1139 $( x^{4} + x + 1 )^{4} + \left(4 x^{2} + 4\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2} + 4 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + \left(8 t^{3} + 8 t^{2} + 8 t\right) x^{3} + \left(4 t^{3} + 4\right) x^{2} + \left(8 t^{3} + 8 t + 8\right) x + 24 t^{3} + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.1140 $( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2} + 4\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2} + 4 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + \left(4 t^{3} + 4\right) x^{2} + \left(8 t^{3} + 8 t + 8\right) x + 24 t^{3} + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.1141 $( x^{4} + x + 1 )^{4} + \left(12 x^{2} + 4\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2} + 4 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + \left(8 t^{3} + 8 t\right) x^{3} + \left(4 t^{3} + 4\right) x^{2} + \left(8 t^{3} + 8 t + 8\right) x + 24 t^{3} + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.1142 $( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 12 x^{2} + 4\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2} + 4 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + 8 t^{2} x^{3} + \left(4 t^{3} + 4\right) x^{2} + \left(8 t^{3} + 8 t + 8\right) x + 24 t^{3} + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.1143 $( x^{4} + x + 1 )^{4} + \left(4 x^{2} + 8 x + 4\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2} + 4 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + \left(8 t^{3} + 8 t^{2}\right) x^{3} + \left(4 t^{3} + 4\right) x^{2} + \left(8 t^{3} + 8 t + 8\right) x + 24 t^{3} + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.1144 $( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2} + 8 x + 4\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2} + 4 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + 8 t x^{3} + \left(4 t^{3} + 4\right) x^{2} + \left(8 t^{3} + 8 t + 8\right) x + 24 t^{3} + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.1145 $( x^{4} + x + 1 )^{4} + \left(12 x^{2} + 8 x + 4\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2} + 4 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + 8 t^{3} x^{3} + \left(4 t^{3} + 4\right) x^{2} + \left(8 t^{3} + 8 t + 8\right) x + 24 t^{3} + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.1146 $( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 12 x^{2} + 8 x + 4\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2} + 4 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + \left(8 t^{2} + 8 t\right) x^{3} + \left(4 t^{3} + 4\right) x^{2} + \left(8 t^{3} + 8 t + 8\right) x + 24 t^{3} + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.1387 $( x^{4} + x + 1 )^{4} + 4 x^{2} ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x + 8\right) ( x^{4} + x + 1 ) + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + \left(8 t^{3} + 8 t^{2} + 8 t\right) x^{3} + \left(4 t^{3} + 4\right) x^{2} + \left(8 t^{3} + 8 t + 8\right) x + 16 t^{3} + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.1388 $( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2}\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x + 8\right) ( x^{4} + x + 1 ) + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + \left(8 t^{2} + 8 t\right) x^{3} + \left(4 t^{3} + 4\right) x^{2} + \left(8 t^{3} + 8 t + 8\right) x + 16 t^{3} + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.1389 $( x^{4} + x + 1 )^{4} + 12 x^{2} ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x + 8\right) ( x^{4} + x + 1 ) + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + \left(8 t^{3} + 8 t\right) x^{3} + \left(4 t^{3} + 4\right) x^{2} + \left(8 t^{3} + 8 t + 8\right) x + 16 t^{3} + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.1390 $( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 12 x^{2}\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x + 8\right) ( x^{4} + x + 1 ) + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + 8 t x^{3} + \left(4 t^{3} + 4\right) x^{2} + \left(8 t^{3} + 8 t + 8\right) x + 16 t^{3} + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.1391 $( x^{4} + x + 1 )^{4} + \left(4 x^{2} + 8 x\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x + 8\right) ( x^{4} + x + 1 ) + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + \left(8 t^{3} + 8 t^{2}\right) x^{3} + \left(4 t^{3} + 4\right) x^{2} + \left(8 t^{3} + 8 t + 8\right) x + 16 t^{3} + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.1392 $( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2} + 8 x\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x + 8\right) ( x^{4} + x + 1 ) + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + 8 t^{2} x^{3} + \left(4 t^{3} + 4\right) x^{2} + \left(8 t^{3} + 8 t + 8\right) x + 16 t^{3} + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.1393 $( x^{4} + x + 1 )^{4} + \left(12 x^{2} + 8 x\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x + 8\right) ( x^{4} + x + 1 ) + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + 8 t^{3} x^{3} + \left(4 t^{3} + 4\right) x^{2} + \left(8 t^{3} + 8 t + 8\right) x + 16 t^{3} + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.1394 $( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 12 x^{2} + 8 x\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x + 8\right) ( x^{4} + x + 1 ) + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + \left(4 t^{3} + 4\right) x^{2} + \left(8 t^{3} + 8 t + 8\right) x + 16 t^{3} + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.1611 $( x^{4} + x + 1 )^{4} + 4 x^{2} ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2} + 4\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 ) + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + \left(8 t^{3} + 8 t\right) x^{3} + \left(4 t^{3} + 4\right) x^{2} + \left(8 t^{3} + 8 t + 8\right) x + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.1612 $( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2}\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2} + 4\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 ) + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + \left(4 t^{3} + 4\right) x^{2} + \left(8 t^{3} + 8 t + 8\right) x + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.1613 $( x^{4} + x + 1 )^{4} + 12 x^{2} ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2} + 4\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 ) + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + 8 t^{3} x^{3} + \left(4 t^{3} + 4\right) x^{2} + \left(8 t^{3} + 8 t + 8\right) x + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.1614 $( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 12 x^{2}\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2} + 4\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 ) + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + 8 t x^{3} + \left(4 t^{3} + 4\right) x^{2} + \left(8 t^{3} + 8 t + 8\right) x + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.1615 $( x^{4} + x + 1 )^{4} + \left(4 x^{2} + 8 x\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2} + 4\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 ) + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + \left(8 t^{3} + 8 t^{2} + 8 t\right) x^{3} + \left(4 t^{3} + 4\right) x^{2} + \left(8 t^{3} + 8 t + 8\right) x + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.1616 $( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2} + 8 x\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2} + 4\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 ) + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + 8 t^{2} x^{3} + \left(4 t^{3} + 4\right) x^{2} + \left(8 t^{3} + 8 t + 8\right) x + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.1617 $( x^{4} + x + 1 )^{4} + \left(12 x^{2} + 8 x\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2} + 4\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 ) + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + \left(8 t^{3} + 8 t^{2}\right) x^{3} + \left(4 t^{3} + 4\right) x^{2} + \left(8 t^{3} + 8 t + 8\right) x + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.1618 $( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 12 x^{2} + 8 x\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2} + 4\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 ) + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + \left(8 t^{2} + 8 t\right) x^{3} + \left(4 t^{3} + 4\right) x^{2} + \left(8 t^{3} + 8 t + 8\right) x + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.1907 $( x^{4} + x + 1 )^{4} + \left(4 x^{2} + 4\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x + 4\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + \left(4 t^{3} + 4\right) x^{2} + \left(8 t^{3} + 8 t + 8\right) x + 8 t^{3} + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.4.4.44a1.1908 $( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2} + 4\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x + 4\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ $2$ $4$ $4$ $44$ $C_4^3.(C_2^2\times C_4)$ (as 16T1186) $4$ $1$ $[3, 4]$ $[2,3]$ $[2, 2, 2, 2, 3, 3, 3, 4]^{4}$ $[1,1,1,1,2,2,2,3]^{4}$ $[2,2,2,2,3,3]$ $[1,1,1,1,2,2]$ $t^{4} + t + 1$ $x^{4} + \left(8 t^{3} + 8 t^{2}\right) x^{3} + \left(4 t^{3} + 4\right) x^{2} + \left(8 t^{3} + 8 t + 8\right) x + 8 t^{3} + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
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