The powerful p-star-central subgroup conjecture

Let $G$ be a finite $p$-group of fixed rank $r$. A subgroup $K$ is powerful $p^*$-central with the $\Omega$EP if it has those properties. The powerful $p^*$-central subgroup conjecture. There exists a subgroup $K$ of bounded index, with the bound depending only on $p$ and $r$, that is powerful $p^*$-central with the $\Omega$EP. For $p\geq 5$, the corresponding subgroup is known to exist; the conjecture concerns the remaining primes $p=2$ and $p=3$.