Subdirectly Irreducible Nil Semigroups of order 4 

list:=[
[# 1
[ 0, 0, 0, 0 ],
[ 0, 0, 0, 0 ],
[ 0, 0, 0, 1 ],
[ 0, 0, 1, 0 ]
],
[# 2
[ 0, 0, 0, 0 ],
[ 0, 0, 0, 0 ],
[ 0, 0, 0, 1 ],
[ 0, 0, 1, 1 ]
],
[# 3
[ 0, 0, 0, 0 ],
[ 0, 0, 0, 0 ],
[ 0, 0, 0, 1 ],
[ 0, 0, 1, 2 ]
],
[# 4
[ 0, 0, 0, 0 ],
[ 0, 0, 0, 0 ],
[ 0, 0, 1, 0 ],
[ 0, 0, 0, 1 ]
]
];
Computed by Peter Jipsen using GAP 3.4 (this list can be copied and read into GAP)