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More precisely, we classify those nilpotent elements with a simple 3-dimensional Lie overalgebra in $\\mathfrak{g} := \\text{Lie}(G)$ and also those with overalgebras isomorphic to the algebras $\\text{Lie}(\\text{SL}_2)$ and $\\text{Lie}(\\text{PGL}_2)$. 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