What is the the maximum and minimum of a sequence of $n$ random variables having Chi-squared distribution with $k$ degrees of freedom?

Question

Say we have a sequence of $n$ random variables $[X_1,X_2,\ldots,X_n]$, identically distributed, having Chi-squared distribution with $k$ degrees of freedom. Then, what is the upper bound of $\underset{1\leq i\leq n}{\max}\{X_i\}$ and lower bound of $\underset{1\leq i\leq n}{\min} \{X_i\}$. For example, we know that if $X_i$ is Gaussian distributed with zero mean and variance $\sigma^2$, then $\underset{1\leq i\leq n}{\max}\{X_i\}\leq \sigma\sqrt{2\log n}$. Are there similar results (upper and lower bounds) when $X_i$ is chi-squared distributed? Any help or reference to existing theory would be highly appreciated.