  Italiano-Martelli-Migliorini recently constructed hyperbolic groups which
have non-hyperbolic subgroups of finite type. Using a closely related
construction, Llosa Isenrich-Martelli-Py constructed hyperbolic groups with
subgroups of type $F_3$ but not $F_4$. We observe that these hyperbolic groups
can be chosen to be special in the sense of Haglund-Wise.
