In other threads people have talked about the minimum number of people for a generation starship or to repopulate the earth. Here are a couple of real world examples: Tristan da Cunha (current population 264) was populated from eight men and seven women. Pitcairn (current population 50 after extensive emmigration) did the same with 15 men and 12 women. Both islands are extremely isolated and survived for 200 years. Only Tristan da Cunha had problems with inbreeding and they were relatively mild.