It is odd that Adolfo Suárez González was entitled Duque de Suárez, since there is nowhere of that name in Spain (though many places elsewhere in the Hispanic world). I suppose he might have been given the title Duque de Cebreros, his birthplace, but perhaps he did not wish to be associated with a zebra.
Arms of Cebreros:

The reason why the 1st Duke's granddaughter now holds the title although his eldest son is still alive, is that under the 2006 "Ley de Igualdad para la Sucesión de Títulos Nobiliarios" succession is to the first-born. The 1st Duke's eldest child was a daughter who died in 2004, so the title passed to her eldest child, also a daughter. The child's uncle, disinherited by the 2006 law, petitioned the King but was unsuccessful.