For the hybrid environment, we can synchronize distribution groups and mail-enabled security groups to the cloud with AAD. In this case, however, these groups need to be managed from on-premises. Additionally, on-premises security groups must be mail-enabled before being synced to Exchange Online. For your reference: On-premises security groups are not synced to Exchange Online in a hybrid deployment.
If you want to manage these groups from O365, we have to re-create distribution groups and security groups in the cloud manually. Then add the membership, x500 addresses, and remove the on-premises groups. You can check these blogs for more details:
Migrate Distribution Groups from Exchange On-Premise to Exchange Online,
Migrating Distribution Groups to Office 365.
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