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The database currently contains 99,426 $p$-adic fields, including all with $p < 200$ and degree $n < 16$. Here are some further statistics.

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The table gives for each $p$ and $n$ shown, the number of degree $n$ extension fields of $\Q_p$ up to isomorphism.

$p$ \ $n$ 2 3 4 5 6 7 8 9 10 11 12 13 14 15
2 7 2 59 2 47 2 1823 3 158 2 5493 2 590 4
3 3 10 5 2 75 2 8 795 6 2 785 2 6 1172
5 3 2 7 26 7 2 11 3 258 2 17 2 6 1012
7 3 4 5 2 12 50 8 7 6 2 20 2 654 8
11 3 2 5 6 7 2 8 3 18 122 13 2 6 12
13 3 4 7 2 12 2 11 7 6 2 28 170 9 8
17 3 2 7 2 7 2 15 3 6 2 17 2 6 4
19 3 4 5 2 12 2 8 13 8 2 20 2 6 8
23 3 2 5 2 7 2 8 3 6 12 13 2 6 4

Some interesting $p$-adic fields or a random $p$-adic field

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Degree e.g. 6, or a range like 3..5 Residue field characteristic e.g. 3, or a range like 3..7
Ramification index e.g. 3, or a range like 2..6 Residue field degree e.g. 3, or a range like 2..6
Discriminant exponent e.g. 8, or a range like 2..6 Top slope e.g. 4/3, or a range like 3..5
Galois unramified degree e.g. 3, or a range like 1..4 Galois tame degree e.g. 2, or a range like 2..3
Wild slopes e.g. [2,2,3] or [3,7/2,4] Visible slopes e.g. [2,2,3] or [2,3,17/4]
Ind. of insep. e.g. [1,1,0] or [18,10,4,0] Assoc. Inertia e.g. [1,2,1] or [1,1,1,1]
Galois group e.g. [8,3], 8.3, C5 or 7T2 Inertia subgroup e.g. e.g. [8,3], 8.3, C5 or 7T2
Wild inertia subgroup e.g. e.g. [8,3], 8.3, C5 or 7T2
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e.g. 2.4.6.7