  By an old result of Cohn (1965), a Hadamard matrix of order n has no proper
Hadamard submatrices of order m > n/2. We generalise this result to maximal
determinant submatrices of Hadamard matrices, and show that an interval of
length asymptotically equal to n/2 is excluded from the allowable orders. We
make a conjecture regarding a lower bound for sums of squares of minors of
maximal determinant matrices, and give evidence in support of the conjecture.
We give tables of the values taken by the minors of all maximal determinant
matrices of orders up to and including 21 and make some observations on the
data. Finally, we describe the algorithms that were used to compute the tables.
