I'm not sure from your post if you purchased coins from coinbase and paid the fee? Or if you used the GDAX?

If you PURCHASE COINS from Coinbase, they charge you a somewhat small fee.

But something kinda cool(in case others may not know), is that if you link a bank account with Coinbase, you can deposit hard cash directly to your wallet. Once you deposit the cash, you can then purchase whatever coin you want on the GDAX EXCHANGE directly with your cash, and avoid ALL/ANY fees!!!

Once you do that, you can transfer from your GDAX wallets to wallets on any other exchange you want to trade on (BitTrex for example).

NOTE: You automatically have A GDAX Account if you have a Coinbase account.