Haagerup Symmetry in (E_{8})_{1}?

We suggest that the chiral (e_{8})_{1} theory-in many senses the simplest vertex operator algebra-may have Haagerup symmetry H_{i} for i=1, 2, 3. Likewise, we suggest that the nonchiral (E_{8})_{1} Wess-Zumino-Witten model may have H_{i}×H_{i}^{op} symmetry, and that gauging the diagonal symmetry gives a c=8 theory with Z(H_{3}) symmetry, which is the theory predicted in Evans and Gannon [Commun. Math. Phys. 307, 463 (2011)CMPHAY0010-361610.1007/s00220-011-1329-3]. Along the way, we show that (E_{8})_{1} also has a Fib×Fib^{op} symmetry, and that gauging the diagonal symmetry gives the (G_{2})_{1}×(F_{4})_{1} Wess-Zumino-Witten model, explaining the well-known conformal embedding (G_{2})_{1}×(F_{4})_{1}⊂(E_{8})_{1}. Finally, we suggest a relation to theories with H_{3} symmetry at c=2, 6, complimenting the discussion with new modular bootstrap results.