We analyzed data in the mass/charge group 12-16 amu/e from the High Intensity Sensor (HIS) of the Ion Mass Spectrometer IMS on board the spacecraft Giotto during the comet Halley flyby. The most abundant ion in this mass/charge range is CH3+. Its parent molecules are either CH2, CH3 or CH4. Hereby, the methane abundance serves as an important clue as to the origin of comets, and has already been discussed several times. Detailed analysis of the radial density profiles from the HIS instrument lead to an upper limit for the methane production of 1% in comet Halley during the Giotto encounter. Even no methane at all is compatible with our data. We find, however, experimental evidence for a quasi-point source of the CH2 radical with a source strength of 0.27% compared to water. CH2 could be due to the presence of heavy organic molecules which undergo very fast photodissociation or it could be present in the cometary ice as a free radical.