The present paper is devoted to the group classification of
magnetogasdynamics equations in which dependent variables in Euler coordinates
depend on time and two spatial coordinates. It is assumed that the continuum is
inviscid and nonthermal polytropic gas with infinite electrical conductivity.
The equations are considered in mass Lagrangian coordinates. Use of Lagrangian
coordinates allows reducing number of dependent variables. The analysis
presented in this article gives complete group classification of the studied
equations. This analysis is necessary for constructing invariant solutions and
conservation laws on the base of Noether's theorem