On irreducible supersingular representations of ${\mathrm{G}\mathrm{L}}_2(F)$

Let $F$ be a non-archimedean local field of residual characteristic $p>3$ and residue degree $f>1$. We study a certain type of diagram, called \emph{cyclic diagrams}, and use them to show that the universal supersingular modules of ${\mathrm{G}\mathrm{L}}_2(F)$ admit infinitely many non-isomorphic irreducible admissible quotients.