In Spanish, "could have [done something]" is expressed in 3 different ways. They all refer to when someone had a chance to do something in the past but missed the opportunity:
Poder in El Pretérito Indefinido + El Infinitivo Compuesto
Poder in El Pretérito Imperfecto + El Infinitivo Compuesto
Poder in El Condicional Simple + El Infinitivo Compuesto
Have a look at the following example with the 3 different tenses but all referring to the same thing:
Gabriela pudo haber ido a la universidad de Exeter pero no fue.Gabriela could have gone to Exeter university but she didn't go.
The three different tenses are interchangeable, the meaning does not change no matter which one you use. They all refer to what could have happened in the past (but didn't).
Here are more examples:
Me podrías haber avisado para ir a recogerte a la estación.You could have told me so I could go pick you up at the station.
Pudimos haber ido a la playa en vez de a la montaña.We could have gone to the beach instead of the mountains.
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