Prime Orders All of Whose Prime Suborders Are Selfdual

Let P be an order on a set V. A subset A of V is autonomous in P if every element of V not in A is either less than or greater than or incomparable to all elements of A. The empty set, the singletons from V and the set V are autonomous sets and are called trivial. Call an order prime if all its autonomous sets are trivial. We give the complete list of all finite prime orders all of whose prime suborders are selfdual.