of a Klein 4-group 210+16.O10+(2) 22+11+22.(M24 × S3) normalizer of a Klein 4-group; contains the normalizer (23:11) × S4 of a Sylow 23-subgroup 31+12.2Suz.2 normalizer of a subgroup of order 3 25+10+20.(S3 × L5(2)) S3 × Th normalizer of a subgroup of order 3; contains the normalizer (31:15) × S3 of a Sylow 31-subgroup 23+6+12+18.(L3(2) × 3S6) 38.O8− (3).23 (D10 × HN).2 normalizer of a subgroup of order 5 (32:2 × O8+(3)).S4 32+5+10.(M11 × 2S4) 33+2+6+6:(L3(3) × SD16) 51+6:2J2:4 normalizer of a subgroup of order 5 (7:3 × He):2 normalizer of a subgroup of order 7 (A5 × A12):2 53+3.(2 × L3(5)) (A6 × A6 × A6).(2 × S4) (A5 × U3(8):31):2 contains the normalizer ((19:9) × A5):2 of a Sylow 19-subgroup 52+2+4:(S3 × GL2(5)) (L3(2) × S4(4):2).2 contains the normalizer ((17:8) × L3(2)).2 of a Sylow 17-subgroup 71+4:(3 × 2S7) normalizer of a subgroup of order 7 (52:4.22 × U3(5)).S3 (L2(11) × M12):2 contains the normalizer (11:5 × M12):2 of a subgroup of order 11 (A7 × (A5 × A5):22):2 54:(3 × 2L2(25)):22 72+1+2:GL2(7) M11 × A6.22 (S5 × S5 × S5):S3 (L2(11) × L2(11)):4 132:2L2(13).4 (72:(3 × 2A4) × L2(7)):2 (13:6 × L3(3)).2 normalizer of a subgroup of order 13 131+2:(3 × 4S4) normalizer of a subgroup of order 13; normalizer of a Sylow 13-subgroup L2(71) contains the normalizer 71:35 of a Sylow 71-subgroup L2(59) contains the normalizer 59:29 of a Sylow 59-subgroup 112:(5 × 2A5) normalizer of a Sylow 11-subgroup. L2(41) Norton and Wilson found a maximal subgroup of this form; due to a subtle error pointed out by Zavarnitsine some previous lists and papers stated that no such maximal subgroup existed L2(29):2 72:SL2(7) this was accidentally omitted from some previous lists of 7-local subgroups L2(19):2 41:40 normalizer of a Sylow 41-subgroup See also Supersingular prime, the prime numbers that divide the order of the monster Citations Sources Further reading published in the US by HarperCollins as Symmetry, ). External links What is... The Monster? by Richard E. Borcherds, Notices of the American Mathematical Society, October 2002 1077 MathWorld: Monster Group Atlas of Finite Group Representations: Monster group Scientific American June 1980 Issue: The capture of the monster: a mathematical group with a ridiculous number of elements Moonshine theory Sporadic groups