Finite groups of non-prime-power order with exactly four character codegrees

For an irreducible complex character $\chi$ of a finite group $G$, the \emph{codegree} of $\chi$ is defined as the ratio $\mathrm{\mid }G:\ker (\chi )\mathrm{\mid }\mathrm{/}\chi (1)$, where $\ker (\chi )$ represents the kernel of $\chi$. In this paper, we provide a detailed characterization of finite groups of non-prime power order that have exactly four irreducible character co-degrees.