We perform numerical calculations to study coherent control of multisubband wavepackets by means of pairs of subpicosecond terahertz laser pulses in suitably designed quantum well structures. We employ a single-particle, effective-mass model of the semiconductor structures. Our purpose is to explore the applicability of the ideas of coherent control and wavepacket interferometry to a new physical system (multisubband wavepackets in doped semiconductor quantum wells) and in a new frequency range (terahertz radiation). Similar ideas have been successfully demonstrated in recent years in atomic, molecular, and excitonic systems, in the optical or near-infrared spectrum. We analyze in detail four quantum well structures, with emphasis on the wavepacket dynamics and interference, and demonstrate numerically the possibility of measurable coherent control of the population of the excited electrons. These wavepacket-interference effects could be used to study decoherence times in doped semiconductor structures. Also, due to the sensitivity of the interference effects to the potential energy, the scheme could be employed to detect defects in the sample. The article also presents a study to determine whether an absorption experiment in a quantum well can be used to determine the shape of a subcycle laser pulse. We show that it is difficult to distinguish pulses with a Gaussian envelope of the vector potential from pulses in which the electric field envelope is Gaussian.