-agogue In the US often -agog.
Leading or promoting.
[Greek agōgos, leading.]
A demagogue (Greek demos, the people) is a political leader who seeks support by appealing to popular desires and prejudices; a pedagogue is a teacher, especially a strict or pedantic one (originally from Greek paidagōgos, a slave who accompanied a child to school).
The ending appears in medical terms for a substance that induces expulsion or secretion: cholagogue (Greek cholē, bile), something that promotes the flow of bile; emmenagogue (Greek emmēna, menses), one that stimulates or increases menstrual flow; secretagogue, a substance which promotes secretion.
However, synagogue comes from the Greek word for a meeting, from sun-, together, plus the related agein, bring.