Symmetry plays great importance role in modern physics. The symmetry analysis in electrodynamics is not only useful for solving specific excises，but can also provide us profound understanding of basic concepts.In this paper，we briefly summarize the general symmetry properties of electromagnetic fields in its non-relativity form. We address that gauge invariance is the fundamental symmetry classic electromagnetic field and governs the electromagnetic interaction. The broken of duality in electromagnetic field is an example of this governance. Based on these understanding，two confusing concepts，that magnetic charge and magnetic monopole，are further discussed.