Can my network administrator figure out that i am running portableapps???

Yes, your administrator can see what you are running. He can access keys in the registry (remotely if he wishes) that will list off all the apps that you've run.

He can also, if he suspects anything, remotely dump a complete list of the processes and appliations currently running on the PC you are using.

There are some ways that you could remove the recently-run lists, but unless you know what you are doing they can really mess up the machine. Also, a completely clean list scrams that someone is hiding something. It would be the equivalent of coming back from a weekend away, where you'd left your teenager in the house with a "no parties" rule, to find the one of the rooms had been redecorated and recarpeted in almost exactly the original style.

And the only way to stop the administrator from monitoring what you are doing is to remove his admin rights from the PC, which, unless you are a co-admin of the network, is likely to get you fired.

So, why do you want to hide that you are running Mozilla suite applications?

As the network admin here, I've preinstalled firefox on all the PCs, though we frown on people using personal email clients.

Have you considered just asking his permission?