Defect of subnormality in unit groups of modular group algebras

Question

Let $p$ be a prime number, $G$ a finite p-Group and $K$ a finite field with $char(K)=p$. It is well-known that the group $1+rad(KG)$ is a p-group containing $G$. $G$ is normal in $1+rad(KG)$ if and only if $G$ is abelian. As $1+rad(KG)$ is nilpotent, the group $G$ is subnormal in $1+rad(KG)$. Is the defect of subnormality known for $G$ in $1+rad(KG)$?