A Sugihara algebra is any algebra belonging to the variety \({\mathcal S}\) generated by the following algebra: \({\mathfrak S}=(Z,\wedge,\vee,\to,^-)\), where Z is the set of integers with the usual ordering, \(\bar x=-x\) and \(x\to y=\bar x\vee y\) if \(x\leq y\), \(x\to y=\bar x\wedge y\) otherwise. The authors characterize the directly indecomposable finite algebras of \({\mathcal S}\). Then they prove that the lattice \(\Lambda\) (\({\mathcal K})\) of subquasivarieties of a subquasivariety \({\mathcal K}\) of \({\mathcal S}\) is finite if and only if \({\mathcal K}\) is generated by a finite set of finite algebras. Also, \(\Lambda\) (\({\mathcal K})\) is not modular. The relevance of these results to logic is discussed.