Hojman conserved quantities deduced from the special Liesymmetry, the Noether symmetry and the form invariance for a nonholonomic system of the unilateral non-Chetaev type in the event space are investigated. The differential equations of motion of the system above are established. The criteria of the Lie symmetry, the Noether symmetry and the form invariance are given and the relations between them are obtained. The Hojman conserved quantities are gained by which the Hojman theorem is extended and applied to the nonholonomic system of the unilateral non-Chetaev type in the event space. An example is given to illustrate the application of the result.