  Let $G$ be a group and let $\mathcal{F}$ be a family of subgroups of $G$
closed under conjugation. For a positive integer $n$, let $C_n$ denote a cyclic
group of order $n$. We show that if there exists an integer $n$ such that every
group in $\mathcal{F}$ is $C_n$-cellular and has finite exponent diving $n$,
then the active sum $S$ of $\mathcal{F}$ is $C_n$-cellular. We obtain a couple
of interesting consequences of this result, using results about cellularity.
Finally, we give different proofs of the facts that Coxeter groups are
$C_2$-cellular and that many groups of the form $\mathrm{SL}(n,\,q)$ for
$n\geq3$ are $C_3$-cellular.
