You can't start the Admin Server from the Administration Console because the Admin Server must be started before you can access it; however, you can shut down the Admin Server from the console. When you shut down the Admin Server from the Administration Console, you lose the connection to the console right away, as shown here on the web page that was hosting the console prior to the shutting down of the Admin Server:
The administration server is shutting down, and the console is no longer
available. You will have to manually start the Administration Server using the
node manager or a command line to continue administering this domain.
Once the server is restarted return to the ...