The maximum number of dots an electron dot diagram can have is eight. The maximum number of dots drawn on a side of a chemical symbol in an electron dot diagram is two.
This is because the electron dot diagrams, also known as Lewis dot structures, represent the valence electrons of an atom, and since electrons occupy orbitals in pairs, each side of the chemical symbol can hold up to two dots, representing up to two valence electrons. The eight-dot maximum reflects the octet rule, where atoms tend to prefer having eight valence electrons, achieving a stable electron configuration similar to that of noble gases.