The Tits group, if regarded as a sporadic group, would belong in this generation: there is a subgroup S4 ×2F4(2)′ normalising a 2C2 subgroup of "B", giving rise to a subgroup 2·S4 ×2F4(2)′ normalising a certain Q8 subgroup of the Monster. 2F4(2)′ is also a subquotient of the Fischer group "Fi"22, and thus also of "Fi"23 and "Fi"24′, and of the Baby Monster "B". 2F4(2)′ is also a subquotient of the (pariah) Rudvalis group "Ru", and has no involvements in sporadic simple groups except the ones already mentioned.