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The switching of behavior, from the hyperchaotic to controlled magnetoconvection model, is studied by a feedback control technique. The magnetoconvection model shows hyperchaotic oscillations for different values of parameters: Rayleigh number r, Chandrasekhar number Q, and diffusivity ratio l. Chaotic responses of the magnetoconvection model are considered through boundedness and Lyapunov exponents to specify the place where the controller needs to be applied. The controller for the magnetoconvection model is calculated by using the concept of the Lie derivative, which is the most significant facet of control analytical techniques. Speed and dislocated feedback techniques are also utilized with the consideration of stability analysis through feedback gains. To show the advantages of the feedback control technique, we give a comparison with other control techniques such as speed and dislocated feedback techniques. Simulation results indicate that the analytical strategy for controlling the oscillation is effective and controlled within a small duration of time.