The coefficient of $x^{11}$ in the expansion of ${(1+x^2)}^4{(1+x^3)}^7{(1+x^4)}^{12}$  is equal to ____

$$\begin{gathered} (1+{}^4{c}_1{x}^2+{}^4{c}_2{x}^4+{}^4{c}_3{x}^6+{}^4{c}_4{x}^8)(1+{}^7{c}_1{x}^3+{}^7{c}_2{x}^6+{}^7{c}_3{x}^9+{}^7{c}_4{x}^{12})\times \\ (1+{}^{12}{c}_1{x}^4+{}^{12}{c}_2{x}^8+\mathrm{...}) \end{gathered}$$

coefficient of $x^{11}=({}^7{c}_1\times {}^{12}{c}_2)+{(}^4{c}_1\times {}^7{c}_3)+({}^7{c}_1\times {}^{12}{c}_1{\times }^4{c}_2)+({}^4{c}_4\times {}^7{c}_1)$

$=462+140+504+7=1113$