Nikon D3400 has a Nikon F lens mount and currently there are 305 native lenses available for this mount. Beware that Nikon D3400 doesn't have an internal focus motor so it will not auto focus with old-style screw-drive autofocus (AF) lenses. It still works well with modern Nikon AF-S, AF-I and G lenses but lenses form 1980s may not autofocus on Nikon D3400.
Nikon D3400 doesn't have a sensor based image stabilization system but 101 of these lenses already comes with optical image stabilization.
Since Nikon D3400 has a APS-C sensor, it has a focal length multiplier of 1.5x so you have to multiply lenses original focal length with this multiplier to find the Full Frame equivalent focal length of the lens when mounted on D3400.
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Nikon D3400 Lenses with Image Stabilization
Nikon D3400 Lenses with Weather Sealings