Oh...be a little careful here! If you have a filter centered at 44MHz
and 1MHz wide, even with perfect "brick wall" attenuation below 43.5
and above 44.5, it would be very bad to sample at 4MHz, or any
frequency whose harmonic landed in the passband. That is because you
will not be able to distinguish (with 4MHz sampling) between a signal
in your IF at 44.1MHz or 43.9MHz. Both will come out aliased by the
sampling to 0.1MHz.

For a more practical example, let's say you manage to find or build a
filter with acceptable flatness from 43.5 to 44.5, and acceptable
attenuation below 42.5 and above 45.5. (Acceptable means that whatever
signals appear there will be attenuated enough to not cause trouble if
they alias into the ADC's output in the desired 1MHz passband.) Then
you can, at best, use a sampling frequency whose harmonic is at
43.0MHz, and whose sampling frequency is at large enough so that the
sampling freq harmonic which lies on the other side of the IF filter
passband won't let signals alias into the output passband. So maybe
you could use 3.071429Mhz sampling, which has a harmonic at 43MHz,
alisaing 43.5-44.5 down to 0.5-1.5, and the the next harmonic at
46.07MHz is more than 1.5MHz above upper frequency where the filter
gives good enough attenuation to prevent aliases. (Good luck building
a filter like that with acceptable performance from practical inductors
and capacitors, unless you don't need much alias protection!)

If you have trouble seeing this, draw some pictures of what goes on in
the frequency domain. Remember that you get nominally the same ADC
response from a signal x kHz above the effective sampling rate
(harmonic of the ADC sample rate) as you do from a signal x kHz below,
and remember that you get response from signals x kHz away (above or
below) the 11th harmonic just the same as the 10th harmonic or the 12th
harmonic, with perfect sampling. So, do NOT let in frequencies that
would let you see the same response from two different inputs...be sure
to filter out those freqs that would give you the same response. (That
applies to noise, too...don't let multiple copies of amplifier noise
alias all down to the ADC output.)

Yes, you WILL end up with your desired passband aliased to something
like 0.5MHz to 1.5MHz. But you can do whatever you want to that with
digital signal processing. (You can also do I and Q sampling
[quadrature sampling] just like you can do I and Q mixing, but you'll
have the same problems with sideband rejection degraded by imperfect
quadrature phase and amplitude matching.)

Cheers,
Tom