We employ the symmetry principle to obtain rate-independent hysteresis operators associated with a nonlinear diffusion equation. The direct Lie approach to this problem leads to an overdetermined system of equations for symmetries that are extremely difficult to analyze. To mitigate this problem, we employ the classification of low-dimensional Lie algebra following the suggestion of Lahno \textit{et al.} (Journal of Physics A: Mathematical and General \textbf{32} (42) (1999): 7405). After excluding linear models, we obtain a one-dimensional principal symmetry Lie algebra, seven symmetry Lie algebras of dimension two, twenty-six symmetry Lie algebras of dimension three, and two symmetry Lie algebras of dimension four. The curves of invariant solutions for symmetry Lie algebras of dimensions three and four are exhibited in three forms. Under appropriate selection of parameters, all invariant solutions show one-to-many relationships between inputs and outputs, except for one in dimension three.