I'm not sure it's very subsidised in a cash sense - when I look at the breakdown on a cheap flight about half seems to be taxes. Whereas most countries railways receive direct cash from the taxpayer subsidies (https://en.wikipedia.org/wiki/Rail_subsidies).
eg in the UK
>Air Passenger Duty (APD) for flights leaving the United Kingdom, and not for inbound flights. You are charged £26 per person on short haul economy flights to most of Europe, and £150 per person on long haul flights
Though you could argue that air-travel is not billed for the damage to the environment it causes in CO2 which is an indirect kind of subsidy.
eg in the UK
>Air Passenger Duty (APD) for flights leaving the United Kingdom, and not for inbound flights. You are charged £26 per person on short haul economy flights to most of Europe, and £150 per person on long haul flights
Though you could argue that air-travel is not billed for the damage to the environment it causes in CO2 which is an indirect kind of subsidy.
An interesting future tech may be electric airliners eg https://en.wikipedia.org/wiki/Zunum_Aero which could be cheaper than both and greenish.