I figured there must have been some way, because they could travel in groups. How could they communicate without the allied navies knowing they were there?
The German navy, in both world wars, used radio systems to communicate with their U-boats. These were similarly used to communicate between U-boats. During WWII, very low-frequency radio systems, operating in the 15-25 KHz waveband, were used to communicate with submerged submarines - the systems could reach a submarine that was up to 30m underwater, depending on distance from the transmitter. However, U-boats could only receive messages this way as to send them required a huge antenna, that was impractical for a submarine. More common were radios in the high-frequency band, from ~1-30 MHz. The ship-to-shore system used by WWII-era boats was the Telefunken E-437S, which operated at frequencies between 1.5-25 MHz. During WWII, VHF systems were used for close-range communication between surfaced subs, or for communication with surface ships. With the exception of the VHF system, these all used Morse code, while the VHF waveband allowed for voice transmission. To prevent anyone eavesdropping, the transmissions were also encoded. During WWI, book codes were used, while in WWII the famous Enigma machine was used. Subs also carried signal lamps and flags for communication on the surface, but these were line-of-sight limited.
As you note, however, these radio systems did give the Allies a way to track and locate U-boats. Radio Direction Finding was developed during WWI as a way to track radio signals from U-boats and the German surface fleet. During the interwar years, this developed into High Frequency Direction Finding (HF/DF or Huff-Duff), which could more accurately home in on a signal. These systems used several directional antennae to triangulate a U-boat's signals. To avoid this, some attempts were made to shorten the duration of signals, as a longer signal was much easier to detect and track. During WWII, a code book was introduced, giving much condensed versions of typical signals, such as 'Convoy sighted in Area X'. Radio intercepts also provided a vulnerability should the codes used be broken, as happened to those used in both world wars.