Was ist eine Untergruppe?

This video first explains what is meant by a subgroup of a group. Then, all subgroups of the dihedral group D4 are identified, and finally, we discover a brilliant insight about subgroups. Related videos: What is a group? - Introduction to Group Theory:    • Was ist eine Gruppe? - Einführung in die G...   Dihedral group D4 - Symmetry group of a square:    • Diedergruppe D4 - Symmetriegruppe eines Qu...   Group Theory - Simple laws and calculation rules for groups:    • Gruppentheorie - Einfache Sätze und Rechen...   Isomorphism of groups:    • Isomorphie von Gruppen   Cyclic groups:    • Zyklische Gruppen   Dihedral groups/Symmetry groups:    • Diedergruppen/ Symmetriegruppen   Lagrange's theorem - Pearl of group theory:    • Satz von Lagrange - Perle der Gruppentheorie