Let $p$ be a prime number, $G=:G_1$ a (non-Abelian) finite p-Group and $K$ a finite field with $\operatorname{char}(K)=p$. It is well-known that the group $G_2:=1+\operatorname{rad}(KG)$ is a p-group containing $G$.

My questions are:

1.) On what terms the derived length of $G_2$ is equal to the derived length of $G_1$?

2.) On what terms the Lie derived length of $KG_2$ is equal to the Lie derived length of $KG_1$?

Conjecture: If the length are equal, then the size of the derived subgroup of $G$ is bounded.