How many subalgebras are there in $sl_3$?

Question

The Lie algebra $sl_3$ is 8 dimensional and $B=\{h_1, h_2, e_1, e_2, [e_1, e_2], f_1, f_2, [f_1, f_2]\}$ is a basis of $sl_3$. For every $x \in B$, $\text{Span}\{x\}$ is a one-dimensional subalgebra of $sl_3$. There are three 3-dimensional subalgebras of $sl_3$: $\text{Span}\{h_1, e_1, f_1\}$, $\text{Span}\{h_2, e_2, f_2\}$, $\text{Span}\{h_1+h_2, [e_1, e_2], [f_1, f_2]\}$. Fix $k_1, k_2 \in \mathbb{C}$, $\text{Span}\{k_1 h_1 + k_2 h_2\}$ is also a 1-dimensional subalgebra of $sl_3$. The algebras $\text{Span}\{h_1, e_1\}$, $\text{Span}\{h_1, e_2\}$ are 2-dimensional subalgebras of $sl_3$. My question is: are $\text{Span}\{h_1, e_1, f_1\}$, $\text{Span}\{h_2, e_2, f_2\}$, $\text{Span}\{h_1+h_2, [e_1, e_2], [f_1, f_2]\}$ maximal subalgebras of $sl_3$? How to write down all maximal subalgebras of $sl_3$? Thank you very much.