The orlicz norm of maximum sub-gaussian random variable

Question

For $K$ sub-guassian random vectors ${\bf a}_1,\dots, {\bf a}_K$, we have $||{\bf a}_i||_{\psi_2}\leq C,i=1\dots, K$ where $C$ is a constant. If we want to bound $||\max_i{\bf a}_i^H{\bf X}{\bf a}_i||_{\psi_1}\leq \|{\bf X}\|_F\|\max_i{\bf a}_i\|_{\psi_2}$, how do I bound $||\max_{i=1,\dots,K}{\bf a}_i||_{\psi_2}$?