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8 letter words:

illogics11,

7 letter words:

illogic10,

6 letter words:

logics9, sigloi7,

5 letter words:

clogs8, logic8, coils7, gills6, sigil6, lilos5,

4 letter words:

cigs7, clog7, cogs7, coil6, cols6, loci6, gill5, logs5, slog5, ills4, lilo4, oils4, sill4, silo4, soil4, soli4,

3 letter words:

cig6, cog6, cis5, col5, cos5, sic5, gos4, log4, ill3, lis3, oil3, sol3,

2 letter words:

go3, is2, li2, lo2, oi2, os2, si2, so2,