Magento upgrade from 2.4.3p1 to 2.4.4

I tried to upgrade my Magento 2.4.3p1 site to 2.4.4 using the regular composer commands, but there are some dependency issues. I need someone who can tell me which commands I have to execute to get the upgrade done. If your commands do not work I will send you the error reportings. This mini project is finished when the upgrade has been done.

I will take care of extensions, customization etc myself.