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For each natural number $d$ we construct a $3$-generated group $H_d$, whichis a subdirect product of free groups, such that the cohomological dimension of$H_d$ is $d$. Given a group $F$ and a normal subgroup $N \lhd F$ we prove thatany right angled Artin group containing the special HNN-extension of $F$ withrespect to $N$ must also contain $F/N$. We apply this to construct, for every$d \in \mathbb{N}$, a $4$-generated group $G_d$, embeddable into a right angledArtin group, such that the cohomological dimension of $G_d$ is $2$ but thecohomological dimension of any right angled Artin group, containing $G_d$, isat least $d$. These examples are used to show the non-existence of certain"universal" right angled Artin groups.  We also investigate finitely presented subgroups of direct products of limitgroups. In particular we show that for every $n\in \mathbb{N}$ there exists$\delta(n) \in \mathbb{N}$ such that any $n$-generated finitely presentedsubgroup of a direct product of finitely many free groups embeds into the$\delta(n)$-th direct power of the free group of rank $2$. As another corollarywe derive that any $n$-generated finitely presented residually free groupembeds into the direct product of at most $\delta(n)$ limit groups.

On subgroups of right angled Artin groups with few generators