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We consider a twelve-dimensional Lie algebra L12 admitted by the gas dynamic equations with equation of state of a special form. Lie algebra L12 is a direct sum of two ideals L11 and Y1. For Lie algebra L11 admitted by gas dynamic equations with an arbitrary equation of state, the optimal system of non-similar subalgebras is built up to inner automorphisms. Using the optimal system for Lie algebra L11, in the article we obtain an optimal system for non-similar subalgebras of the sum of two ideals for L11 and Y1 and the rule of construction of such subalgebras.

Optimal system of non-similar subalgebras of sum of two ideals