What is the max score for ASVAB for each section?

The ASVAB isn't a score, it's a percentile. So having a 99 means top 1 percentile. I have seen the line scores go as high as the low 150s

The ASVAB (Armed Services Vocational Aptitude Battery) consists of several sections, each with its own scoring range. The maximum scores for each section is 99.
https://asvab-prep.com/asvab-scores
The overall scores, known as the Armed Forces Qualification Test (AFQT) scores, are derived from the combination of specific sections:
AFQT Scores: 1 to 99 (based on a combination of AR, MK, WK, and PC)
Each section is scored based on the number of correct answers, with scores then converted to a standard scale.

320 per area. However a 99 AFQT score DOES NOT mean you scored better than 99% of the people who took the test.

A 99 means you scored in the 99 range on the percentile chart. The 99 could be the top 99.99999 percent of those that took the test. The 99 could also be in the top 95% of the people that took the test. Technically a guy who scored an 80 AFQT could have a better percentage of questions right on the test than a guy that scored a 95 AFQT.

The percentile score has nothing to do with the population who took the test in the inital test group or prior test takers. It is a percentile on a chart that was calculated from your overall test score which is somewhat of a mystery because only the DoD knows the weighted score of each question and you cannot get that information. But you can get the overall top score before it goes to the percentile chart. I do think a 240 will get you in the 99 range for the percentile chart. Below 240 it starts to drop 98, 97,96,95 and so on. Most people score over 200 and between 240.

The highest score is a 320. 254-320 is the 99 AFQT range.

125-127 = 3%; 128-131 = 4%; 132-134 =5%; 135-137 = 6%; 138-139 = 7%; 140-142 = 8%; 143-144 = 9%; 145-146 = 10%; 147-148 = 11%; 149-150 = 12%; 151-153 = 13%; 154 = 14%; 155-156 = 15%; 157-158 = 16%; 159-160 = 17%; 161-162 = 18%; 163-164 = 19%; 165 = 20%; 166-167 = 21%; 168-169 = 22%; 170-171 = 23%; 172 = 24%; 173-174 = 25%; 175 = 26%; 176-177 = 27%; 178 = 28%; 179-180 = 29%; 181 = 30%; 182 = 31%; 183-184 = 32%; 185 = 33%; 186 = 34%; 187-188 = 35%; 189 = 36%; 190 = 37%; 191 = 38%; 192 = 39%; 193 = 40%; 194 = 41%; 195-196 = 42%; 197 = 43%; 198 = 44%; 199 = 45%; 200 = 46%; 201 = 47%; 202 = 48%; 203 = 49%; 204 = 50%; 205 = 51%; 206 = 52%; 207-208 = 53%; 209 = 54%; 210 = 55%; 211 = 56%; 212 = 57%; 213 = 58%; 214 = 59%; 215 = 61%; 216 = 62%; 217 = 63%; 218 = 64%; 219 = 65%; 220 = 66%; 221 = 67%; 222 = 68%; 223 = 69%; 224 = 70%; 225 = 71%; 226 = 72%; 227 = 73%; 228 = 74%; 229 = 75%; 230 = 76%; 231 = 77%; 232 = 78%; 233 = 79%; 234 = 80%; 235 = 81%; 236 = 82%; 237 = 83%; 238-239 = 84%; 240 = 85%; 241 = 86%; 242 = 87%; 243 = 88%; 244 = 89%; 245 = 90%; 246 = 91%; 247 = 92%; 248 = 93%; 249 = 94%; 250 = 95%; 251 = 96%; 252 = 97%; 253 = 98%;

254-320 = 99%. (The questions are weighted and this is how you get a score as high as 320)