In this research, we propose modified subgradient extragradient method to find the common solution of split variational inequality problem and common fixed point problem of a finite family of demicontractive mappings without knowing norm of bounded linear operator and Lipschitz constants of the associated pseudomonotone operators. We obtain the strong convergence result for the proposed method under certain mild conditions. This result extends and generalizes many recent results in this direction. Furthermore, we demonstrate how our findings may be used to solve a generalized Nash equilibrium problem and LASSO problem. Finally, we give numerical experiments to validate the performance of our algorithm and compare it with other existing methods.