I'm only counting base forms. Otherwise, Arceus and Silvally count for everything, and Rotom counts for quite a few types as well.
Normal:
11 (Arceus, Ditto, Maushold, Meloetta, Porygon, Porygon-Z, Porygon2, Regigigas, Silvally, Tandemaus, Type: Null)
Fire:
9 (Blacephalon, Chi-Yu, Ho-Oh, Iron Moth, Moltres, Reshiram, Victini, Volcanion)
Water:
14 (Arctovish, Dracovish, Iron Bundle, Keldeo, Kyogre, Manaphy, Palkia, Phione, Starmie, Staryu, Suicune, Tapu Fini, Volcanion, Walking Wake)
Electric:
17 (Arctozolt, Dracozolt, Electrode, Iron Hands, Iron Thorns, Magnemite, Magneton, Magnezone, Miraidon, Raikou, Regieleki, Rotom, Sandy Shocks, Tapu Koko, Zapdos, Zekrom, Zeraora)
Grass:
13 (Brute Bonnet, Calyrex, Celebi, Dhelmise, Iron Leaves, Kartana, Poltchageist, Shaymin, Sinistcha, Tapu Bulu, Virizion, Wo-Chien, Zarude)
Ice:
8 (Arctovish, Arctozolt, Articuno, Chien-Pao, Cryogonal, Iron Bundle, Kyurem, Regice, Glastrier)
Fighting:
14 (Buzzwole, Cobalion, Falinks, Great Tusk, Iron Hands, Iron Valiant, Keldeo, Koraidon, Marshadow, Pheromosa, Slither Wing, Terrakion, Virizion, Zamazenta)
Poison:
6 (Eternatus, Iron Moth, Naganadel, Nihilego, Pecharunt, Poipole)
Ground:
9 (Baltoy, Claydol, Golett, Golurk, Great Tusk, Iron Treads, Sandy Shocks, Ting-Lu, Zygarde)
Flying:
10 (Articuno, Celesteela, Ho-Oh, Iron Jugulis, Lugia, Minior, Moltres, Rayquaza, Yveltal, Zapdos)
Psychic:
33 (Azelf, Baltoy, Beldum, Bronzong, Bronzor, Calyrex, Celebi, Claydol, Cosmoem, Cosmog, Deoxys, Hoopa, Iron Boulder, Iron Crown, Iron Leaves, Jirachi, Lugia, Lunala, Lunatone, Mesprit, Metagross, Metang, Mew, Mewtwo, Necrozma, Scream Tail, Solgaleo, Solrock, Starmie, Tapu Lele, Unown, Uxie, Victini)
Bug:
5 (Buzzwole, Genesect, Pheromosa, Shedinja, Slither Wing)
Rock:
11 (Carbink, Diancie, Iron Boulder, Iron Thorns, Lunatone, Minior, Nihilego, Regirock, Solrock, Stakataka, Terrakion)
Ghost:
18 (Dhelmise, Flutter Mane, Gholdengo, Gimmighoul, Giratina, Golett, Golurk, Hoopa, Lunala, Marshadow, Pecharunt, Poltchageist, Polteageist, Rotom, Shedinja, Sinistcha, Sinistea, Spectrier)
Dragon:
21 (Dialga, Dracovish, Dracozolt, Eternatus, Giratina, Gouging Fire, Guzzlord, Koraidon, Kyurem, Miraidon, Naganadel, Palkia, Poipole, Raging Bolt, Rayquaza, Regidrago, Reshiram, Roaring Moon, Walking Wake, Zekrom, Zygarde)
Dark:
11 (Brute Bonnet, Chi-Yu, Chien-Pao, Darkrai, Guzzlord, Iron Jugulis, Roaring Moon, Ting-Lu, Wo-Chien, Yveltal, Zarude)
Steel:
22 (Beldum, Bronzong, Bronzor, Celesteela, Dialga, Genesect, Iron Crown, Iron Treads, Jirachi, Kartana, Klang, Klink, Klinklang, Magearna, Magnemite, Magneton, Magnezone, Melmetal, Meltan, Metagross, Metang, Registeel)
Fairy:
12 (Carbink, Diancie, Flutter Mane, Iron Valiant, Magearna, Scream Tail, Tapu Bulu, Tapu Fini, Tapu Koko, Tapu Lele, Xerneas, Zacian)
Psychic has the most, with Steel in second.
Gender unknown Pokemon (Bulbapedia)
