theorem: Let $ G $ be solvable with $ \Phi(G)=1 $ and assume that each minimal normal subgroup has prime order or order $ 4 $. Then every chief factor of $ G $ has prime order or is $ G $-isomorphic to a minimal normal subgroup of $ G $ of order $ 4 $.
For proof: Let $ K/L $ be a chief factor of $ G $. We proceed by induction on $ \vert K \vert $. Let $ M $ be the smallest normal subgroup of $ K $ such that $ K/M $ is nilpotent, and so $ M \lhd G $ and $ M \leq L $.
What's mean smallest normal subgroup and $ G $-isomorphis ?