  In this paper we characterize the genera of those quotient curves
$\mathcal{H}_q/G$ of the $\mathbb{F}_{q^2}$-maximal Hermitian curve
$\mathcal{H}_q$ for which $G$ is contained in the maximal subgroup
$\mathcal{M}_1$ of ${\rm Aut}(\mathcal{H}_q)$ fixing a self-polar triangle, or
$q$ is even and $G$ is contained in the maximal subgroup $\mathcal{M}_2$ of
${\rm Aut}(\mathcal{H}_q)$ fixing a pole-polar pair $(P,\ell)$ with respect to
the unitary polarity associated to $\mathcal{H}_q(\mathbb{F}_{q^2})$. In this
way several new values for the genus of a maximal curve over a finite field are
obtained. Together with what is known in the literature, our results leave just
two open cases to provide the complete list of genera of Galois subcovers of
the Hermitian curve; namely, the open cases in [Bassa-Ma-Xing-Yeo, J. Combin.
Theory Ser. A, 2013] when $G$ fixes a point $P \in
\mathcal{H}_q(\mathbb{F}_{q^2})$ and $q$ is even, and the open cases in
[Montanucci-Zini, Comm. Algebra, 2018] when $G\leq\mathcal{M}_2$ and $q$ is
odd.
