Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1245 conjugacy classes of subgroups.
The subgroup lattice has 776 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #62637 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #61106 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #33539 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#2193 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #33523 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #24296 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #13338 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #13334 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #13312 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #13311 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #13068 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #13035 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #13021 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #12979 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #12747 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #3585 | — | 2 | 1 | no | — |
| 17 | #3584 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#578 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | C2×#576 | C22 | 1 | 1 | yes | characteristic |
| 20 | #3417 | — | 2 | 2 | no | — |
| 21 | #3417 | — | 2 | 2 | no | — |
| 22 | #3416 | — | 2 | 2 | no | — |
| 23 | #3416 | — | 2 | 2 | no | — |
| 24 | #3414 | — | 2 | 2 | no | — |
| 25 | #3414 | C22 | 1 | 1 | yes | characteristic |
| 26 | #3414 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | C2×#510 | — | 2 | 2 | no | — |
| 28 | C2×#510 | C22 | 1 | 1 | yes | characteristic |
| 29 | C2×#510 | C22 | 1 | 1 | yes | characteristic, complemented |
| 30 | C2×#509 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | C22×SD32 | C22 | 1 | 1 | yes | characteristic, complemented |
| 32 | #3407 | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | #3292 | — | 2 | 2 | no | — |
| 34 | #3290 | — | 2 | 2 | no | — |
| 35 | #3288 | — | 2 | 4 | no | — |
| 36 | #3155 | C22 | 1 | 1 | yes | characteristic |
| 37 | #3068 | — | 2 | 1 | no | — |
| 38 | #3067 | C22 | 1 | 1 | yes | characteristic |
| 39 | #3067 | C22 | 1 | 1 | yes | characteristic, complemented |
| 40 | C2×#472 | C22 | 1 | 1 | yes | characteristic |
| 41 | #3059 | C22 | 1 | 1 | yes | characteristic, complemented |
| 42 | #3021 | — | 2 | 1 | no | — |
| 43 | #3020 | — | 2 | 1 | no | — |
| 44 | #3019 | — | 2 | 1 | no | — |
| 45 | #2957 | C22 | 1 | 1 | yes | characteristic |
| 46 | #2955 | C22 | 1 | 1 | yes | characteristic |
| 47 | #2194 | — | 2 | 2 | no | — |
| 48 | #2193 | — | 2 | 4 | no | — |
| 49 | #2192 | — | 2 | 2 | no | — |
| 50 | #2189 | — | 2 | 2 | no | — |
| 51 | #2187 | — | 2 | 2 | no | — |
| 52 | C2×#362 | C22 | 1 | 1 | yes | characteristic, complemented |
| 53 | C2×#361 | C22 | 1 | 1 | yes | characteristic, complemented |
| 54 | #2145 | C22 | 1 | 1 | yes | characteristic, complemented |
| 55 | #2143 | C22 | 1 | 1 | yes | characteristic |
| 56 | C2×#359 | C22 | 1 | 1 | yes | characteristic, complemented |
| 57 | C2×#359 | C22 | 1 | 1 | yes | characteristic, complemented |
| 58 | #2140 | C22 | 1 | 1 | yes | characteristic, complemented |
| 59 | #2138 | C22 | 1 | 1 | yes | characteristic |
| 60 | #2117 | C22 | 1 | 1 | yes | characteristic, complemented |
| 61 | C2×#350 | C22 | 1 | 1 | yes | characteristic, complemented |
| 62 | #2113 | C22 | 1 | 1 | yes | characteristic, complemented |
| 63 | #2049 | — | 2 | 1 | no | — |
| 64 | #2009 | — | 2 | 1 | no | — |
| 65 | #1979 | C22 | 1 | 1 | yes | characteristic, complemented |
| 66 | #1976 | C22 | 1 | 1 | yes | characteristic, complemented |
| 67 | #1814 | C22 | 1 | 1 | yes | characteristic, complemented |
| 68 | #1796 | — | 2 | 1 | no | — |
| 69 | #1389 | C22 | 1 | 1 | yes | characteristic, complemented |
| 70 | #1385 | C22 | 1 | 1 | yes | characteristic, complemented |
| 71 | #1379 | C22 | 1 | 1 | yes | characteristic, complemented |
| 72 | #1378 | C22 | 1 | 1 | yes | characteristic, complemented |
| 73 | #585 | — | 2 | 1 | no | — |
| 74 | C2×2−1+4 | — | 2 | 1 | no | — |
| 75 | C2×H(5,𝔽2) | — | 2 | 1 | no | — |
| 76 | #578 | — | 2 | 1 | no | — |
| 77 | #578 | — | 2 | 2 | no | — |
| 78 | #578 | — | 2 | 2 | no | — |
| 79 | #578 | — | 2 | 2 | no | — |
| 80 | #578 | — | 4 | 1 | no | — |
| 81 | #578 | D4 | 1 | 2 | yes | — |
| 82 | #577 | — | 2 | 4 | no | — |
| 83 | #577 | — | 2 | 2 | no | — |
| 84 | #577 | — | 4 | 1 | no | — |
| 85 | #577 | — | 4 | 2 | no | — |
| 86 | #576 | — | 2 | 1 | no | — |
| 87 | #576 | — | 2 | 4 | no | — |
| 88 | #576 | — | 2 | 2 | no | — |
| 89 | #576 | — | 2 | 2 | no | — |
| 90 | #576 | — | 2 | 2 | no | — |
| 91 | #576 | — | 4 | 1 | no | — |
| 92 | #576 | — | 4 | 2 | no | — |
| 93 | #576 | D4 | 1 | 2 | yes | — |
| 94 | #575 | — | 2 | 1 | no | — |
| 95 | #575 | — | 2 | 1 | no | — |
| 96 | #575 | — | 2 | 1 | no | — |
| 97 | #575 | — | 4 | 1 | no | — |
| 98 | #575 | — | 4 | 2 | no | — |
| 99 | #575 | D4 | 1 | 1 | yes | characteristic |
| 100 | C2×#137 | — | 2 | 1 | no | — |
| 101 | C2×#137 | — | 4 | 1 | no | — |
| 102 | C2×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 103 | C2×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 104 | C2×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 105 | C2×AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 106 | C2×AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 107 | C2×#135 | — | 2 | 2 | no | — |
| 108 | C2×#135 | — | 2 | 1 | no | — |
| 109 | C2×#135 | — | 2 | 1 | no | — |
| 110 | C2×#135 | C23 | 1 | 1 | yes | characteristic |
| 111 | C2×#135 | C23 | 1 | 1 | yes | characteristic |
| 112 | C2×#135 | C23 | 1 | 1 | yes | characteristic |
| 113 | C22×Q16 | — | 2 | 1 | no | — |
| 114 | C22×Q16 | C23 | 1 | 1 | yes | characteristic |
| 115 | C22×D8 | — | 2 | 1 | no | — |
| 116 | C22×D8 | C23 | 1 | 1 | yes | characteristic |
| 117 | #568 | — | 2 | 1 | no | — |
| 118 | C2×#131 | C23 | 1 | 1 | yes | characteristic |
| 119 | C2×#131 | C23 | 1 | 1 | yes | characteristic |
| 120 | #536 | — | 2 | 1 | no | — |
| 121 | #535 | — | 2 | 1 | no | — |
| 122 | #510 | — | 2 | 4 | no | — |
| 123 | #510 | — | 2 | 4 | no | — |
| 124 | #510 | — | 2 | 4 | no | — |
| 125 | #510 | — | 2 | 2 | no | — |
| 126 | #510 | — | 2 | 2 | no | — |
| 127 | #510 | — | 2 | 1 | no | — |
| 128 | #510 | — | 2 | 2 | no | — |
| 129 | #510 | — | 2 | 1 | no | — |
| 130 | #510 | — | 2 | 1 | no | — |
| 131 | #510 | — | 2 | 2 | no | — |
| 132 | #510 | D4 | 1 | 2 | yes | complemented |
| 133 | #509 | — | 2 | 4 | no | — |
| 134 | #509 | — | 2 | 1 | no | — |
| 135 | #509 | — | 2 | 1 | no | — |
| 136 | #509 | — | 2 | 1 | no | — |
| 137 | #509 | — | 2 | 2 | no | — |
| 138 | #509 | — | 4 | 1 | no | — |
| 139 | #509 | D4 | 1 | 2 | yes | complemented |
| 140 | #508 | — | 2 | 4 | no | — |
| 141 | #508 | — | 2 | 4 | no | — |
| 142 | #508 | — | 2 | 2 | no | — |
| 143 | #508 | — | 2 | 2 | no | — |
| 144 | C2×Q32 | — | 2 | 4 | no | — |
| 145 | C2×Q32 | — | 2 | 1 | no | — |
| 146 | C2×Q32 | D4 | 1 | 2 | yes | complemented |
| 147 | C2×SD32 | — | 2 | 4 | no | — |
| 148 | C2×SD32 | — | 2 | 1 | no | — |
| 149 | C2×SD32 | — | 2 | 2 | no | — |
| 150 | C2×SD32 | — | 2 | 1 | no | — |
| 151 | C2×SD32 | — | 2 | 2 | no | — |
| 152 | C2×SD32 | — | 4 | 1 | no | — |
| 153 | C2×SD32 | D4 | 1 | 2 | yes | complemented |
| 154 | C2×D16 | — | 2 | 1 | no | — |
| 155 | #504 | — | 2 | 2 | no | — |
| 156 | #504 | — | 2 | 2 | no | — |
| 157 | C2×M32 | — | 2 | 2 | no | — |
| 158 | C2×M32 | C23 | 1 | 1 | yes | characteristic |
| 159 | C2×M32 | C23 | 1 | 1 | yes | characteristic |
| 160 | C2×M32 | C23 | 1 | 1 | yes | characteristic |
| 161 | C22×C16 | C23 | 1 | 1 | yes | characteristic |
| 162 | #496 | — | 2 | 2 | no | — |
| 163 | #495 | — | 2 | 1 | no | — |
| 164 | #493 | — | 2 | 1 | no | — |
| 165 | #473 | — | 2 | 1 | no | — |
| 166 | #473 | — | 2 | 1 | no | — |
| 167 | #472 | — | 2 | 4 | no | — |
| 168 | #472 | — | 2 | 1 | no | — |
| 169 | #472 | — | 2 | 2 | no | — |
| 170 | #472 | — | 2 | 1 | no | — |
| 171 | #472 | D4 | 1 | 4 | yes | — |
| 172 | #471 | — | 2 | 4 | no | — |
| 173 | #471 | — | 2 | 2 | no | — |
| 174 | #471 | — | 4 | 1 | no | — |
| 175 | #470 | — | 4 | 1 | no | — |
| 176 | #467 | — | 2 | 2 | no | — |
| 177 | #456 | — | 4 | 2 | no | — |
| 178 | #455 | — | 2 | 4 | no | — |
| 179 | #454 | — | 2 | 4 | no | — |
| 180 | #454 | — | 4 | 2 | no | — |
| 181 | #453 | — | 2 | 4 | no | — |
| 182 | #453 | — | 2 | 4 | no | — |
| 183 | #444 | — | 2 | 2 | no | — |
| 184 | #444 | — | 2 | 2 | no | — |
| 185 | #443 | — | 2 | 2 | no | — |
| 186 | #443 | — | 2 | 2 | no | — |
| 187 | #430 | D4 | 1 | 1 | yes | characteristic |
| 188 | C2×#108 | C23 | 1 | 1 | yes | characteristic |
| 189 | C2×#108 | C23 | 1 | 1 | yes | characteristic |
| 190 | #427 | C23 | 1 | 1 | yes | characteristic |
| 191 | #421 | — | 2 | 1 | no | — |
| 192 | #421 | — | 2 | 1 | no | — |
| 193 | #421 | — | 2 | 1 | no | — |
| 194 | #421 | D4 | 1 | 1 | yes | characteristic |
| 195 | #421 | D4 | 1 | 1 | yes | characteristic |
| 196 | #419 | — | 2 | 1 | no | — |
| 197 | #419 | — | 2 | 1 | no | — |
| 198 | #413 | — | 2 | 1 | no | — |
| 199 | #413 | — | 2 | 1 | no | — |
| 200 | C2×#101 | — | 2 | 1 | no | — |
| 201 | C2×#100 | — | 2 | 1 | no | — |
| 202 | #410 | — | 2 | 1 | no | — |
| 203 | #405 | C23 | 1 | 1 | yes | characteristic |
| 204 | #362 | — | 2 | 2 | no | — |
| 205 | #361 | — | 2 | 2 | no | — |
| 206 | #360 | — | 4 | 1 | no | — |
| 207 | #359 | — | 2 | 2 | no | — |
| 208 | #359 | — | 2 | 2 | no | — |
| 209 | #359 | — | 4 | 1 | no | — |
| 210 | #358 | — | 2 | 1 | no | — |
| 211 | #357 | — | 2 | 1 | no | — |
| 212 | #357 | — | 2 | 2 | no | — |
| 213 | #350 | — | 2 | 2 | no | — |
| 214 | #350 | — | 2 | 2 | no | — |
| 215 | C22⋊C16 | — | 2 | 2 | no | — |
| 216 | #344 | — | 2 | 1 | no | — |
| 217 | 2−1+4 | — | 2 | 2 | no | — |
| 218 | 2−1+4 | — | 4 | 1 | no | — |
| 219 | 2−1+4 | — | 4 | 2 | no | — |
| 220 | 2−1+4 | — | 4 | 2 | no | — |
| 221 | 2−1+4 | — | 4 | 1 | no | — |
| 222 | 2−1+4 | — | 4 | 2 | no | — |
| 223 | 2−1+4 | — | 8 | 1 | no | — |
| 224 | H(5,𝔽2) | — | 2 | 4 | no | — |
| 225 | H(5,𝔽2) | — | 2 | 2 | no | — |
| 226 | H(5,𝔽2) | — | 4 | 1 | no | — |
| 227 | H(5,𝔽2) | — | 4 | 2 | no | — |
| 228 | H(5,𝔽2) | — | 4 | 2 | no | — |
| 229 | H(5,𝔽2) | — | 4 | 1 | no | — |
| 230 | H(5,𝔽2) | — | 8 | 1 | no | — |
| 231 | H(5,𝔽2) | — | 8 | 1 | no | — |
| 232 | C2×#41 | — | 2 | 1 | no | — |
| 233 | C2×#41 | — | 2 | 1 | no | — |
| 234 | C2×#41 | — | 2 | 1 | no | — |
| 235 | C2×#41 | — | 4 | 1 | no | — |
| 236 | C2×#41 | — | 4 | 1 | no | — |
| 237 | C2×#41 | — | 4 | 2 | no | — |
| 238 | C2×#41 | — | 4 | 2 | no | — |
| 239 | C2×#41 | — | 4 | 1 | no | — |
| 240 | C2×#41 | — | 4 | 1 | no | — |
| 241 | C2×#41 | — | 8 | 1 | no | — |
| 242 | C2×#41 | — | 8 | 1 | no | — |
| 243 | C2×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 244 | C2×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 245 | C22×Q8 | — | 2 | 1 | no | — |
| 246 | C22×Q8 | — | 4 | 1 | no | — |
| 247 | C22×Q8 | — | 4 | 1 | no | — |
| 248 | C22×D4 | — | 2 | 1 | no | — |
| 249 | C22×D4 | — | 4 | 1 | no | — |
| 250 | C22×D4 | — | 4 | 1 | no | — |
| 251 | C22×D4 | — | 8 | 1 | no | — |
| 252 | #137 | — | 2 | 1 | no | — |
| 253 | #137 | — | 2 | 2 | no | — |
| 254 | #137 | — | 2 | 2 | no | — |
| 255 | #137 | — | 4 | 2 | no | — |
| 256 | #137 | — | 4 | 4 | no | — |
| 257 | #137 | — | 4 | 2 | no | — |
| 258 | #137 | — | 4 | 2 | no | — |
| 259 | #137 | — | 4 | 1 | no | — |
| 260 | #137 | — | 4 | 4 | no | — |
| 261 | #137 | — | 4 | 4 | no | — |
| 262 | #137 | — | 4 | 1 | no | — |
| 263 | #137 | — | 4 | 1 | no | — |
| 264 | #137 | — | 4 | 1 | no | — |
| 265 | #137 | — | 4 | 2 | no | — |
| 266 | #137 | D8 | 1 | 2 | yes | — |
| 267 | AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 268 | AGL(1,ℤ/8) | — | 2 | 4 | no | — |
| 269 | AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 270 | AGL(1,ℤ/8) | — | 2 | 4 | no | — |
| 271 | AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 272 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 273 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 274 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 275 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 276 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 277 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 278 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 279 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 280 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 281 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 282 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 283 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 284 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 285 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 286 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 287 | AGL(1,ℤ/8) | D8 | 1 | 2 | yes | — |
| 288 | #135 | — | 2 | 2 | no | — |
| 289 | #135 | — | 2 | 4 | no | — |
| 290 | #135 | — | 2 | 2 | no | — |
| 291 | #135 | — | 2 | 2 | no | — |
| 292 | #135 | — | 2 | 1 | no | — |
| 293 | #135 | — | 2 | 1 | no | — |
| 294 | #135 | — | 2 | 1 | no | — |
| 295 | #135 | — | 2 | 1 | no | — |
| 296 | #135 | — | 2 | 1 | no | — |
| 297 | #135 | — | 2 | 1 | no | — |
| 298 | #135 | — | 2 | 1 | no | — |
| 299 | #135 | — | 2 | 1 | no | — |
| 300 | #135 | — | 2 | 1 | no | — |
| 301 | #135 | — | 2 | 1 | no | — |
| 302 | #135 | — | 4 | 2 | no | — |
| 303 | #135 | — | 4 | 2 | no | — |
| 304 | #135 | — | 4 | 2 | no | — |
| 305 | #135 | — | 4 | 2 | no | — |
| 306 | #135 | — | 4 | 4 | no | — |
| 307 | #135 | — | 4 | 4 | no | — |
| 308 | #135 | — | 4 | 2 | no | — |
| 309 | #135 | — | 4 | 2 | no | — |
| 310 | #135 | — | 8 | 1 | no | — |
| 311 | #135 | C2×D4 | 1 | 2 | yes | — |
| 312 | #135 | C2×D4 | 1 | 2 | yes | — |
| 313 | C2×Q16 | — | 2 | 4 | no | — |
| 314 | C2×Q16 | — | 2 | 2 | no | — |
| 315 | C2×Q16 | — | 2 | 1 | no | — |
| 316 | C2×Q16 | — | 2 | 1 | no | — |
| 317 | C2×Q16 | — | 2 | 1 | no | — |
| 318 | C2×Q16 | — | 2 | 1 | no | — |
| 319 | C2×Q16 | — | 2 | 1 | no | — |
| 320 | C2×Q16 | — | 4 | 2 | no | — |
| 321 | C2×Q16 | — | 4 | 1 | no | — |
| 322 | C2×Q16 | C2×D4 | 1 | 1 | yes | characteristic |
| 323 | C2×Q16 | C2×D4 | 1 | 2 | yes | — |
| 324 | C2×Q16 | C2×D4 | 1 | 1 | yes | characteristic |
| 325 | C2×Q16 | C2×D4 | 1 | 1 | yes | characteristic |
| 326 | C2×SD16 | — | 2 | 2 | no | — |
| 327 | C2×SD16 | — | 2 | 1 | no | — |
| 328 | C2×SD16 | — | 2 | 1 | no | — |
| 329 | C2×SD16 | — | 2 | 1 | no | — |
| 330 | C2×SD16 | — | 4 | 2 | no | — |
| 331 | C2×SD16 | — | 4 | 1 | no | — |
| 332 | C2×SD16 | — | 4 | 1 | no | — |
| 333 | C2×SD16 | — | 4 | 4 | no | — |
| 334 | C2×SD16 | — | 4 | 1 | no | — |
| 335 | C2×D8 | — | 2 | 2 | no | — |
| 336 | C2×D8 | — | 2 | 2 | no | — |
| 337 | C2×D8 | — | 2 | 1 | no | — |
| 338 | C2×D8 | — | 2 | 1 | no | — |
| 339 | C2×D8 | — | 2 | 1 | no | — |
| 340 | C2×D8 | — | 2 | 1 | no | — |
| 341 | C2×D8 | — | 2 | 1 | no | — |
| 342 | C2×D8 | — | 4 | 1 | no | — |
| 343 | C2×D8 | — | 4 | 2 | no | — |
| 344 | C2×D8 | — | 4 | 4 | no | — |
| 345 | C2×D8 | — | 4 | 1 | no | — |
| 346 | C2×D8 | — | 4 | 2 | no | — |
| 347 | C2×D8 | C2×D4 | 1 | 2 | yes | — |
| 348 | C2×D8 | C2×D4 | 1 | 1 | yes | characteristic |
| 349 | C2×D8 | C2×D4 | 1 | 1 | yes | characteristic |
| 350 | C2×D8 | C2×D4 | 1 | 1 | yes | characteristic |
| 351 | #131 | — | 2 | 1 | no | — |
| 352 | #131 | — | 2 | 1 | no | — |
| 353 | #131 | — | 2 | 4 | no | — |
| 354 | #131 | — | 2 | 1 | no | — |
| 355 | #131 | — | 2 | 1 | no | — |
| 356 | #131 | — | 2 | 1 | no | — |
| 357 | #131 | — | 2 | 1 | no | — |
| 358 | #131 | — | 4 | 2 | no | — |
| 359 | #131 | C2×D4 | 1 | 2 | yes | — |
| 360 | #131 | C2×D4 | 1 | 2 | yes | — |
| 361 | C2×M16 | — | 2 | 1 | no | — |
| 362 | C2×M16 | — | 2 | 1 | no | — |
| 363 | C2×M16 | — | 2 | 1 | no | — |
| 364 | C2×M16 | — | 2 | 1 | no | — |
| 365 | C2×M16 | — | 4 | 2 | no | — |
| 366 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 367 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 368 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 369 | C22×C8 | — | 2 | 1 | no | — |
| 370 | C22×C8 | — | 2 | 1 | no | — |
| 371 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 372 | C4⋊Q8 | — | 4 | 1 | no | — |
| 373 | #127 | — | 2 | 2 | no | — |
| 374 | #124 | — | 2 | 2 | no | — |
| 375 | #124 | — | 4 | 1 | no | — |
| 376 | #123 | — | 8 | 1 | no | — |
| 377 | C22⋊Q8 | — | 4 | 2 | no | — |
| 378 | #121 | — | 8 | 1 | no | — |
| 379 | #120 | — | 8 | 1 | no | — |
| 380 | #117 | — | 2 | 1 | no | — |
| 381 | #117 | C2×D4 | 1 | 1 | yes | characteristic |
| 382 | Q32 | — | 2 | 4 | no | — |
| 383 | Q32 | — | 2 | 2 | no | — |
| 384 | Q32 | — | 2 | 2 | no | — |
| 385 | Q32 | — | 2 | 4 | no | — |
| 386 | SD32 | — | 2 | 4 | no | — |
| 387 | SD32 | — | 2 | 2 | no | — |
| 388 | SD32 | — | 2 | 2 | no | — |
| 389 | SD32 | — | 2 | 2 | no | — |
| 390 | SD32 | — | 2 | 2 | no | — |
| 391 | SD32 | — | 2 | 4 | no | — |
| 392 | SD32 | — | 4 | 4 | no | — |
| 393 | SD32 | — | 4 | 2 | no | — |
| 394 | D16 | — | 2 | 2 | no | — |
| 395 | D16 | — | 2 | 2 | no | — |
| 396 | D16 | — | 4 | 2 | no | — |
| 397 | M32 | — | 2 | 4 | no | — |
| 398 | M32 | — | 2 | 1 | no | — |
| 399 | M32 | — | 2 | 1 | no | — |
| 400 | M32 | — | 2 | 1 | no | — |
| 401 | M32 | — | 2 | 1 | no | — |
| 402 | M32 | — | 2 | 1 | no | — |
| 403 | M32 | C2×D4 | 1 | 2 | yes | — |
| 404 | C2×C16 | — | 2 | 4 | no | — |
| 405 | C2×C16 | — | 2 | 1 | no | — |
| 406 | C2×C16 | — | 2 | 1 | no | — |
| 407 | C2×C16 | — | 2 | 1 | no | — |
| 408 | C2×C16 | — | 2 | 1 | no | — |
| 409 | C2×C16 | — | 2 | 1 | no | — |
| 410 | C2×C16 | C2×D4 | 1 | 2 | yes | — |
| 411 | #108 | — | 2 | 2 | no | — |
| 412 | #108 | — | 2 | 1 | no | — |
| 413 | #108 | — | 2 | 1 | no | — |
| 414 | #108 | — | 2 | 1 | no | — |
| 415 | #108 | C2×D4 | 1 | 2 | yes | — |
| 416 | #107 | — | 2 | 1 | no | — |
| 417 | #106 | — | 2 | 1 | no | — |
| 418 | #104 | — | 2 | 4 | no | — |
| 419 | #104 | — | 2 | 2 | no | — |
| 420 | #104 | — | 2 | 2 | no | — |
| 421 | #104 | — | 4 | 2 | no | — |
| 422 | #104 | — | 4 | 2 | no | — |
| 423 | #103 | — | 4 | 2 | no | — |
| 424 | #103 | — | 8 | 1 | no | — |
| 425 | #101 | — | 2 | 2 | no | — |
| 426 | #101 | — | 4 | 1 | no | — |
| 427 | #101 | — | 4 | 2 | no | — |
| 428 | #100 | — | 2 | 2 | no | — |
| 429 | #100 | — | 2 | 4 | no | — |
| 430 | #100 | — | 4 | 1 | no | — |
| 431 | #99 | — | 8 | 1 | no | — |
| 432 | #97 | — | 2 | 1 | no | — |
| 433 | C4×C8 | — | 2 | 1 | no | — |
| 434 | C24 | — | 4 | 1 | no | — |
| 435 | C24 | — | 8 | 1 | no | — |
| 436 | #41 | — | 2 | 1 | no | — |
| 437 | #41 | — | 2 | 1 | no | — |
| 438 | #41 | — | 2 | 1 | no | — |
| 439 | #41 | — | 2 | 2 | no | — |
| 440 | #41 | — | 2 | 1 | no | — |
| 441 | #41 | — | 2 | 2 | no | — |
| 442 | #41 | — | 2 | 1 | no | — |
| 443 | #41 | — | 2 | 1 | no | — |
| 444 | #41 | — | 4 | 2 | no | — |
| 445 | #41 | — | 4 | 2 | no | — |
| 446 | #41 | — | 4 | 4 | no | — |
| 447 | #41 | — | 4 | 1 | no | — |
| 448 | #41 | — | 4 | 1 | no | — |
| 449 | #41 | — | 4 | 4 | no | — |
| 450 | #41 | — | 4 | 4 | no | — |
| 451 | #41 | — | 4 | 2 | no | — |
| 452 | #41 | — | 4 | 2 | no | — |
| 453 | #41 | — | 4 | 1 | no | — |
| 454 | #41 | — | 4 | 1 | no | — |
| 455 | #41 | — | 4 | 1 | no | — |
| 456 | #41 | — | 4 | 1 | no | — |
| 457 | #41 | — | 4 | 1 | no | — |
| 458 | #41 | — | 4 | 1 | no | — |
| 459 | #41 | — | 4 | 1 | no | — |
| 460 | #41 | — | 4 | 1 | no | — |
| 461 | #41 | — | 8 | 2 | no | — |
| 462 | #41 | — | 8 | 2 | no | — |
| 463 | #41 | — | 8 | 2 | no | — |
| 464 | #41 | — | 8 | 2 | no | — |
| 465 | #41 | — | 8 | 2 | no | — |
| 466 | #41 | — | 8 | 4 | no | — |
| 467 | #41 | — | 8 | 2 | no | — |
| 468 | #41 | — | 8 | 2 | no | — |
| 469 | #41 | — | 8 | 2 | no | — |
| 470 | #41 | — | 8 | 1 | no | — |
| 471 | #41 | — | 8 | 4 | no | — |
| 472 | #41 | — | 8 | 1 | no | — |
| 473 | #41 | — | 8 | 2 | no | — |
| 474 | #41 | #120 | 1 | 2 | yes | — |
| 475 | #41 | C2×D8 | 1 | 2 | yes | — |
| 476 | C2×Q8 | — | 2 | 1 | no | — |
| 477 | C2×Q8 | — | 2 | 1 | no | — |
| 478 | C2×Q8 | — | 2 | 1 | no | — |
| 479 | C2×Q8 | — | 2 | 2 | no | — |
| 480 | C2×Q8 | — | 4 | 2 | no | — |
| 481 | C2×Q8 | — | 4 | 4 | no | — |
| 482 | C2×Q8 | — | 4 | 1 | no | — |
| 483 | C2×Q8 | — | 4 | 2 | no | — |
| 484 | C2×Q8 | — | 4 | 1 | no | — |
| 485 | C2×Q8 | — | 4 | 1 | no | — |
| 486 | C2×Q8 | — | 4 | 1 | no | — |
| 487 | C2×Q8 | — | 4 | 1 | no | — |
| 488 | C2×Q8 | — | 8 | 1 | no | — |
| 489 | C2×Q8 | — | 8 | 2 | no | — |
| 490 | C2×Q8 | — | 8 | 2 | no | — |
| 491 | C2×Q8 | — | 8 | 1 | no | — |
| 492 | C2×Q8 | — | 8 | 2 | no | — |
| 493 | C2×Q8 | C2×D8 | 1 | 1 | yes | characteristic |
| 494 | C2×Q8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 495 | C2×D4 | — | 2 | 1 | no | — |
| 496 | C2×D4 | — | 2 | 1 | no | — |
| 497 | C2×D4 | — | 2 | 2 | no | — |
| 498 | C2×D4 | — | 2 | 1 | no | — |
| 499 | C2×D4 | — | 2 | 1 | no | — |
| 500 | C2×D4 | — | 2 | 1 | no | — |
| 501 | C2×D4 | — | 4 | 2 | no | — |
| 502 | C2×D4 | — | 4 | 4 | no | — |
| 503 | C2×D4 | — | 4 | 4 | no | — |
| 504 | C2×D4 | — | 4 | 1 | no | — |
| 505 | C2×D4 | — | 4 | 2 | no | — |
| 506 | C2×D4 | — | 4 | 1 | no | — |
| 507 | C2×D4 | — | 4 | 1 | no | — |
| 508 | C2×D4 | — | 4 | 1 | no | — |
| 509 | C2×D4 | — | 4 | 1 | no | — |
| 510 | C2×D4 | — | 4 | 1 | no | — |
| 511 | C2×D4 | — | 4 | 1 | no | — |
| 512 | C2×D4 | — | 4 | 1 | no | — |
| 513 | C2×D4 | — | 8 | 1 | no | — |
| 514 | C2×D4 | — | 8 | 2 | no | — |
| 515 | C2×D4 | — | 8 | 2 | no | — |
| 516 | C2×D4 | — | 8 | 1 | no | — |
| 517 | C2×D4 | — | 8 | 2 | no | — |
| 518 | C2×D4 | — | 8 | 2 | no | — |
| 519 | C2×D4 | — | 8 | 1 | no | — |
| 520 | C2×D4 | — | 8 | 2 | no | — |
| 521 | C2×D4 | — | 8 | 4 | no | — |
| 522 | C2×D4 | — | 8 | 4 | no | — |
| 523 | C2×D4 | — | 8 | 2 | no | — |
| 524 | C2×D4 | — | 8 | 1 | no | — |
| 525 | C2×D4 | C2×D8 | 1 | 1 | yes | characteristic |
| 526 | C2×D4 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 527 | C22×C4 | — | 2 | 1 | no | — |
| 528 | C22×C4 | — | 2 | 1 | no | — |
| 529 | C22×C4 | — | 4 | 1 | no | — |
| 530 | C22×C4 | — | 4 | 1 | no | — |
| 531 | C22×C4 | — | 4 | 1 | no | — |
| 532 | C22×C4 | — | 4 | 1 | no | — |
| 533 | C22×C4 | — | 8 | 1 | no | — |
| 534 | C22×C4 | — | 8 | 2 | no | — |
| 535 | C22×C4 | — | 8 | 1 | no | — |
| 536 | C22×C4 | — | 8 | 1 | no | — |
| 537 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 538 | Q16 | — | 2 | 2 | no | — |
| 539 | Q16 | — | 2 | 1 | no | — |
| 540 | Q16 | — | 2 | 2 | no | — |
| 541 | Q16 | — | 2 | 1 | no | — |
| 542 | Q16 | — | 2 | 1 | no | — |
| 543 | Q16 | — | 2 | 1 | no | — |
| 544 | Q16 | — | 2 | 2 | no | — |
| 545 | Q16 | — | 2 | 1 | no | — |
| 546 | Q16 | — | 4 | 2 | no | — |
| 547 | Q16 | — | 4 | 4 | no | — |
| 548 | Q16 | — | 4 | 2 | no | — |
| 549 | Q16 | — | 4 | 1 | no | — |
| 550 | Q16 | — | 4 | 1 | no | — |
| 551 | Q16 | — | 8 | 1 | no | — |
| 552 | Q16 | #120 | 1 | 2 | yes | — |
| 553 | SD16 | — | 2 | 2 | no | — |
| 554 | SD16 | — | 2 | 2 | no | — |
| 555 | SD16 | — | 2 | 2 | no | — |
| 556 | SD16 | — | 2 | 2 | no | — |
| 557 | SD16 | — | 4 | 2 | no | — |
| 558 | SD16 | — | 4 | 2 | no | — |
| 559 | SD16 | — | 4 | 4 | no | — |
| 560 | SD16 | — | 4 | 4 | no | — |
| 561 | SD16 | — | 4 | 2 | no | — |
| 562 | SD16 | — | 4 | 4 | no | — |
| 563 | SD16 | — | 4 | 2 | no | — |
| 564 | SD16 | — | 4 | 4 | no | — |
| 565 | SD16 | — | 4 | 1 | no | — |
| 566 | SD16 | — | 4 | 1 | no | — |
| 567 | SD16 | — | 4 | 1 | no | — |
| 568 | SD16 | — | 4 | 1 | no | — |
| 569 | SD16 | — | 8 | 1 | no | — |
| 570 | SD16 | — | 8 | 1 | no | — |
| 571 | D8 | — | 2 | 2 | no | — |
| 572 | D8 | — | 2 | 1 | no | — |
| 573 | D8 | — | 2 | 1 | no | — |
| 574 | D8 | — | 2 | 1 | no | — |
| 575 | D8 | — | 2 | 1 | no | — |
| 576 | D8 | — | 2 | 1 | no | — |
| 577 | D8 | — | 2 | 2 | no | — |
| 578 | D8 | — | 2 | 2 | no | — |
| 579 | D8 | — | 4 | 2 | no | — |
| 580 | D8 | — | 4 | 4 | no | — |
| 581 | D8 | — | 4 | 4 | no | — |
| 582 | D8 | — | 4 | 2 | no | — |
| 583 | D8 | — | 4 | 4 | no | — |
| 584 | D8 | — | 4 | 1 | no | — |
| 585 | D8 | — | 4 | 1 | no | — |
| 586 | D8 | — | 8 | 1 | no | — |
| 587 | D8 | #120 | 1 | 2 | yes | — |
| 588 | M16 | — | 2 | 1 | no | — |
| 589 | M16 | — | 2 | 1 | no | — |
| 590 | M16 | — | 2 | 2 | no | — |
| 591 | M16 | — | 2 | 2 | no | — |
| 592 | M16 | — | 2 | 2 | no | — |
| 593 | M16 | — | 2 | 1 | no | — |
| 594 | M16 | — | 2 | 1 | no | — |
| 595 | M16 | — | 4 | 4 | no | — |
| 596 | M16 | — | 4 | 1 | no | — |
| 597 | M16 | — | 4 | 1 | no | — |
| 598 | M16 | — | 4 | 1 | no | — |
| 599 | M16 | — | 4 | 1 | no | — |
| 600 | M16 | — | 4 | 1 | no | — |
| 601 | M16 | #120 | 1 | 2 | yes | — |
| 602 | M16 | C2×D8 | 1 | 2 | yes | — |
| 603 | C2×C8 | — | 2 | 1 | no | — |
| 604 | C2×C8 | — | 2 | 1 | no | — |
| 605 | C2×C8 | — | 2 | 2 | no | — |
| 606 | C2×C8 | — | 2 | 2 | no | — |
| 607 | C2×C8 | — | 2 | 1 | no | — |
| 608 | C2×C8 | — | 4 | 4 | no | — |
| 609 | C2×C8 | — | 4 | 1 | no | — |
| 610 | C2×C8 | — | 4 | 1 | no | — |
| 611 | C2×C8 | — | 4 | 1 | no | — |
| 612 | C2×C8 | — | 4 | 1 | no | — |
| 613 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 614 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 615 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 616 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 617 | C2×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 618 | C2×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 619 | C4⋊C4 | — | 2 | 1 | no | — |
| 620 | C4⋊C4 | — | 4 | 1 | no | — |
| 621 | C4⋊C4 | — | 8 | 2 | no | — |
| 622 | C22⋊C4 | — | 2 | 1 | no | — |
| 623 | C22⋊C4 | — | 4 | 1 | no | — |
| 624 | C22⋊C4 | — | 8 | 2 | no | — |
| 625 | C22⋊C4 | — | 8 | 2 | no | — |
| 626 | C42 | — | 2 | 1 | no | — |
| 627 | C42 | — | 4 | 1 | no | — |
| 628 | C16 | — | 2 | 2 | no | — |
| 629 | C16 | — | 2 | 2 | no | — |
| 630 | C16 | — | 4 | 1 | no | — |
| 631 | C16 | — | 4 | 1 | no | — |
| 632 | C23 | — | 2 | 1 | no | — |
| 633 | C23 | — | 2 | 1 | no | — |
| 634 | C23 | — | 4 | 1 | no | — |
| 635 | C23 | — | 4 | 2 | no | — |
| 636 | C23 | — | 4 | 1 | no | — |
| 637 | C23 | — | 4 | 1 | no | — |
| 638 | C23 | — | 8 | 2 | no | — |
| 639 | C23 | — | 8 | 4 | no | — |
| 640 | C23 | — | 8 | 1 | no | — |
| 641 | C23 | — | 8 | 1 | no | — |
| 642 | C23 | — | 32 | 1 | no | — |
| 643 | C23 | — | 32 | 2 | no | — |
| 644 | C23 | #576 | 1 | 1 | yes | characteristic |
| 645 | Q8 | — | 2 | 1 | no | — |
| 646 | Q8 | — | 2 | 2 | no | — |
| 647 | Q8 | — | 2 | 1 | no | — |
| 648 | Q8 | — | 2 | 1 | no | — |
| 649 | Q8 | — | 4 | 1 | no | — |
| 650 | Q8 | — | 4 | 1 | no | — |
| 651 | Q8 | — | 4 | 2 | no | — |
| 652 | Q8 | — | 4 | 1 | no | — |
| 653 | Q8 | — | 4 | 1 | no | — |
| 654 | Q8 | — | 4 | 2 | no | — |
| 655 | Q8 | — | 4 | 1 | no | — |
| 656 | Q8 | — | 8 | 2 | no | — |
| 657 | Q8 | — | 8 | 4 | no | — |
| 658 | Q8 | — | 8 | 1 | no | — |
| 659 | Q8 | — | 8 | 1 | no | — |
| 660 | Q8 | #447 | 1 | 2 | yes | — |
| 661 | D4 | — | 2 | 2 | no | — |
| 662 | D4 | — | 2 | 2 | no | — |
| 663 | D4 | — | 2 | 2 | no | — |
| 664 | D4 | — | 2 | 1 | no | — |
| 665 | D4 | — | 2 | 1 | no | — |
| 666 | D4 | — | 2 | 1 | no | — |
| 667 | D4 | — | 4 | 1 | no | — |
| 668 | D4 | — | 4 | 2 | no | — |
| 669 | D4 | — | 4 | 1 | no | — |
| 670 | D4 | — | 4 | 2 | no | — |
| 671 | D4 | — | 4 | 2 | no | — |
| 672 | D4 | — | 4 | 1 | no | — |
| 673 | D4 | — | 4 | 1 | no | — |
| 674 | D4 | — | 4 | 1 | no | — |
| 675 | D4 | — | 4 | 2 | no | — |
| 676 | D4 | — | 4 | 1 | no | — |
| 677 | D4 | — | 4 | 1 | no | — |
| 678 | D4 | — | 8 | 2 | no | — |
| 679 | D4 | — | 8 | 2 | no | — |
| 680 | D4 | — | 8 | 4 | no | — |
| 681 | D4 | — | 8 | 4 | no | — |
| 682 | D4 | — | 8 | 2 | no | — |
| 683 | D4 | — | 8 | 4 | no | — |
| 684 | D4 | — | 8 | 1 | no | — |
| 685 | D4 | — | 8 | 1 | no | — |
| 686 | D4 | — | 8 | 1 | no | — |
| 687 | D4 | — | 8 | 1 | no | — |
| 688 | D4 | — | 8 | 1 | no | — |
| 689 | D4 | — | 8 | 1 | no | — |
| 690 | D4 | — | 32 | 2 | no | — |
| 691 | D4 | #447 | 1 | 2 | yes | — |
| 692 | C2×C4 | — | 2 | 1 | no | — |
| 693 | C2×C4 | — | 2 | 2 | no | — |
| 694 | C2×C4 | — | 2 | 2 | no | — |
| 695 | C2×C4 | — | 2 | 1 | no | — |
| 696 | C2×C4 | — | 4 | 1 | no | — |
| 697 | C2×C4 | — | 4 | 1 | no | — |
| 698 | C2×C4 | — | 4 | 2 | no | — |
| 699 | C2×C4 | — | 4 | 1 | no | — |
| 700 | C2×C4 | — | 4 | 2 | no | — |
| 701 | C2×C4 | — | 4 | 1 | no | — |
| 702 | C2×C4 | — | 4 | 1 | no | — |
| 703 | C2×C4 | — | 4 | 1 | no | — |
| 704 | C2×C4 | — | 4 | 2 | no | — |
| 705 | C2×C4 | — | 8 | 2 | no | — |
| 706 | C2×C4 | — | 8 | 2 | no | — |
| 707 | C2×C4 | — | 8 | 4 | no | — |
| 708 | C2×C4 | — | 8 | 4 | no | — |
| 709 | C2×C4 | — | 8 | 2 | no | — |
| 710 | C2×C4 | — | 8 | 4 | no | — |
| 711 | C2×C4 | — | 8 | 1 | no | — |
| 712 | C2×C4 | — | 8 | 1 | no | — |
| 713 | C2×C4 | — | 8 | 1 | no | — |
| 714 | C2×C4 | — | 8 | 1 | no | — |
| 715 | C2×C4 | — | 8 | 1 | no | — |
| 716 | C2×C4 | — | 8 | 1 | no | — |
| 717 | C2×C4 | — | 8 | 1 | no | — |
| 718 | C2×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 719 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 720 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 721 | C2×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 722 | C2×C4 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 723 | C2×C4 | #576 | 1 | 1 | yes | characteristic |
| 724 | C8 | — | 2 | 2 | no | — |
| 725 | C8 | — | 2 | 2 | no | — |
| 726 | C8 | — | 4 | 1 | no | — |
| 727 | C8 | — | 4 | 2 | no | — |
| 728 | C8 | — | 8 | 1 | no | — |
| 729 | C8 | C2×#120 | 1 | 1 | yes | characteristic |
| 730 | C8 | #534 | 1 | 1 | yes | characteristic |
| 731 | C8 | D42 | 1 | 1 | yes | characteristic |
| 732 | C8 | D42 | 1 | 1 | yes | characteristic |
| 733 | C22 | — | 2 | 2 | no | — |
| 734 | C22 | — | 4 | 1 | no | — |
| 735 | C22 | — | 4 | 2 | no | — |
| 736 | C22 | — | 4 | 2 | no | — |
| 737 | C22 | — | 4 | 1 | no | — |
| 738 | C22 | — | 8 | 1 | no | — |
| 739 | C22 | — | 8 | 1 | no | — |
| 740 | C22 | — | 8 | 1 | no | — |
| 741 | C22 | — | 8 | 2 | no | — |
| 742 | C22 | — | 16 | 1 | no | — |
| 743 | C22 | — | 16 | 1 | no | — |
| 744 | C22 | — | 16 | 2 | no | — |
| 745 | C22 | — | 16 | 1 | no | — |
| 746 | C22 | — | 16 | 2 | no | — |
| 747 | C22 | — | 32 | 1 | no | — |
| 748 | C22 | — | 32 | 2 | no | — |
| 749 | C22 | — | 32 | 4 | no | — |
| 750 | C22 | #3008 | 1 | 1 | yes | characteristic |
| 751 | C22 | #3264 | 1 | 1 | yes | characteristic |
| 752 | C22 | D4×D8 | 1 | 1 | yes | characteristic |
| 753 | C4 | — | 2 | 2 | no | — |
| 754 | C4 | — | 4 | 1 | no | — |
| 755 | C4 | — | 4 | 2 | no | — |
| 756 | C4 | — | 8 | 1 | no | — |
| 757 | C4 | — | 8 | 1 | no | — |
| 758 | C4 | — | 8 | 1 | no | — |
| 759 | C4 | — | 8 | 2 | no | — |
| 760 | C4 | — | 16 | 1 | no | — |
| 761 | C4 | #2403 | 1 | 1 | yes | characteristic |
| 762 | C4 | C2×#447 | 1 | 1 | yes | characteristic |
| 763 | C4 | #3264 | 1 | 1 | yes | characteristic |
| 764 | C4 | D4×D8 | 1 | 1 | yes | characteristic |
| 765 | C2 | — | 2 | 1 | no | — |
| 766 | C2 | — | 2 | 1 | no | — |
| 767 | C2 | — | 2 | 1 | no | — |
| 768 | C2 | — | 4 | 2 | no | — |
| 769 | C2 | — | 8 | 1 | no | — |
| 770 | C2 | — | 8 | 2 | no | — |
| 771 | C2 | — | 16 | 1 | no | — |
| 772 | C2 | — | 16 | 2 | no | — |
| 773 | C2 | — | 16 | 1 | no | — |
| 774 | C2 | #23848 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #23848 |
| commutator, Frattini, cosocle | C22×C8 | C24 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #2955 ◁ G | |
| LECS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #62637 | C2 | semidirect |
| 2. #61106 | C2 | semidirect |
| 3. #33539 | C2 | semidirect |
| 4. C2×#2193 | C2 | semidirect |
| 5. #33523 | C2 | semidirect |
| 6. #24296 | C2 | semidirect |
| 7. #13338 | C2 | semidirect |
| 8. #13334 | C2 | semidirect |
| 9. #13312 | C2 | semidirect |
| 10. #13311 | C2 | semidirect |
| 11. #13068 | C2 | semidirect |
| 12. #13035 | C2 | semidirect |
| 13. #13021 | C2 | semidirect |
| 14. #12979 | C2 | semidirect |
| 15. #12747 | C2 | semidirect |
| 18. C2×#578 | C22 | semidirect |
| 26. #3414 | C22 | semidirect |
| 29. C2×#510 | C22 | semidirect |
| 30. C2×#509 | C22 | semidirect |
| 31. C22×SD32 | C22 | semidirect |
| 32. #3407 | C22 | semidirect |
| 39. #3067 | C22 | semidirect |
| 41. #3059 | C22 | semidirect |
| 52. C2×#362 | C22 | semidirect |
| 53. C2×#361 | C22 | semidirect |
| 54. #2145 | C22 | semidirect |
| 56. C2×#359 | C22 | semidirect |
| 57. C2×#359 | C22 | semidirect |
| 58. #2140 | C22 | semidirect |
| 60. #2117 | C22 | semidirect |
| 61. C2×#350 | C22 | semidirect |
| 62. #2113 | C22 | semidirect |
| 65. #1979 | C22 | semidirect |
| 66. #1976 | C22 | semidirect |
| 67. #1814 | C22 | semidirect |
| 69. #1389 | C22 | semidirect |
| 70. #1385 | C22 | semidirect |
| 71. #1379 | C22 | semidirect |
| 72. #1378 | C22 | semidirect |
| 132. #510 | D4 | semidirect |
| 139. #509 | D4 | semidirect |
| 146. C2×Q32 | D4 | semidirect |
| 153. C2×SD32 | D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #62637 | 2 |
| #61106 | 2 |
| #33539 | 2 |
| C2×#2193 | 2 |
| #33523 | 2 |
| #24296 | 2 |
| #13338 | 2 |
| #13334 | 2 |
| #13312 | 2 |
| #13311 | 2 |
| #13068 | 2 |
| #13035 | 2 |
| #13021 | 2 |
| #12979 | 2 |
| #12747 | 2 |