In the EU AI Act, the European Commission has detailed a number of specific penalties that will apply to organisations that fail to comply with the regulatory requirements. This is detailed in Chapter XII of the Act, and details different types of penalties for different types of violations. In any case, the fines can be substantial:

• Non-compliance with the prohibition of the AI practices referred to in the EU AI Act will be subject to administrative fines of up to 35 Million Euro or, if the offender is a corporate entity, up to 7% of its total worldwide annual turnover for the preceding financial year, whichever is higher.
• Non-compliance with any of the other provisions than the ones prohibiting specific types of AI, will be subject to administrative fines of up to 15 million Euro or, if the offender is a corporate entity, up to 3% of its total worldwide annual turnover for the preceding financial year, whichever is higher
• The supply of incorrect, incomplete or misleading information to notified bodies or national competent authorities in reply to a request will be subject to administrative fines of up to 7,5 million Euro or, if the offender is a corporation, up to 1% of its total worldwide annual turnover for the preceding financial year, whichever is higher.

As you can tell, these penalties are quite high, and not to be disregarded lightly. It is therefore very much advisable to make sure that compliance is achieved as soon as possible.