The suffix for words like pedagogue and demagogue derives from the Greek -agogos (to lead); the suffix for words like analogue, catalogue, dialogue, and epilogue derives from the Greek -logos (speech, word). While the traditional suffixes -agogue and -logue remain generally more popular than their modern variants -agog and -log, the modern forms have been rising in popularity and may someday become standard and preferred. However, for now and for some time, the traditional spellings remain stronger in most cases.
Do not confuse the -agogue suffix with the adverb agog, which is etymologically unrelated.