Which programs can break subroutines on a trap?
Traps generally do not have one of the 3 usual subtypes (Barrier, Code Gate, or Sentry). So they cannot be broken by breakers for those types of ice. In general you need an AI breaker like Crypsis, Overmind, Knight, or any of the other AI breakers. However traps can still be bypassed with Femme, just like any other ice.

Note that some traps DO have a breakable subtypes. Such as data mine. Because this trap is AP it can be broken with Deus Ex.