To answer your question, yes, she can have male friends, just as you can have female friends. When you are in a committed relationship, you make a promise to each other to be faithful. If you can't be faithful, you should end the relationship. Granted, that's the simplified version and if more people would do that, it would make life easier, but instead they choose to get sneaky, and some do eventually cheat.
My BF has a female friend that he initially hid from me for fear that me knowing about her would make me jealous. He didn't realize that I am not the jealous type, but I certainly had an issue with him hiding it from me because that makes it so much worse. It's all out now - I have met her (sooooooo not jealous of her), she is married, she was his friend through a very rough spot in his life, and he knows that I am not like his first wife and won't over react when she texts because she's having an issue. We have worked to rebuild the trust and it's made our relationship even stronger.
However, if your GF continues to sneak around and lie to you, even against your wishes...well, that's a huge red flag. Sorry.