Assembly and budding of the influenza C virus is mediated by three membrane proteins: the hemagglutinin-esterase-fusion glycoprotein (HEF), the matrix protein (CM1), and the ion channel (CM2). Here we investigated whether the formation of the hexagonal HEF arrangement, a distinctive feature of influenza C virions is important for virus budding. We used super resolution microscopy and found 250-nm sized HEF clusters at the plasma membrane of transfected cells, which were insensitive to cholesterol extraction and cytochalasin treatment. Overexpression of either CM1, CM2, or HEF caused the release of membrane-enveloped particles. Cryo-electron microscopy of the latter revealed spherical vesicles exhibiting the hexagonal HEF clusters. We subsequently used reverse genetics to identify elements in HEF required for this clustering. We found that deletion of the short cytoplasmic tail of HEF reduced virus titer and hexagonal HEF arrays, suggesting that an interaction with CM1 stabilizes the HEF clusters. In addition, we substituted amino acids at the surface of the closed HEF conformation and identified specific mutations that prevented virus rescue, others reduced virus titers and the number of HEF clusters in virions. Finally, mutation of two regions that mediate contacts between trimers in the in-situ structure of HEF was shown to prevent rescue of infectious virus particles. Mutations at residues thought to mediate lateral interactions were revealed to promote intracellular trafficking defects. Taken together, we propose that lateral interactions between the ectodomains of HEF trimers are a driving force for virus budding, although CM2 and CM1 also play important roles in this process.