Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1026 conjugacy classes of subgroups.
The subgroup lattice has 772 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #61100 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #33619 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #33542 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #33532 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #33388 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #24800 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #13416 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #13391 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #13342 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #13311 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #13039 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #13005 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #12986 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #12944 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #12752 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #3584 | — | 2 | 1 | no | — |
| 17 | #3584 | C22 | 1 | 1 | yes | characteristic |
| 18 | #3584 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#510 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#510 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | C2×#510 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | #3407 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | #3289 | — | 2 | 2 | no | — |
| 24 | #3289 | — | 2 | 2 | no | — |
| 25 | #3288 | — | 2 | 2 | no | — |
| 26 | #3288 | — | 2 | 2 | no | — |
| 27 | #3150 | C22 | 1 | 1 | yes | characteristic |
| 28 | #3067 | — | 2 | 1 | no | — |
| 29 | #3067 | C22 | 1 | 1 | yes | characteristic |
| 30 | #3067 | C22 | 1 | 1 | yes | characteristic |
| 31 | C2×#473 | C22 | 1 | 1 | yes | characteristic, complemented |
| 32 | #3059 | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | #3046 | — | 2 | 1 | no | — |
| 34 | #3018 | — | 2 | 1 | no | — |
| 35 | #3018 | — | 2 | 1 | no | — |
| 36 | C2×#444 | C22 | 1 | 1 | yes | characteristic |
| 37 | C2×#444 | C22 | 1 | 1 | yes | characteristic |
| 38 | #2912 | C22 | 1 | 1 | yes | characteristic, complemented |
| 39 | #2223 | — | 2 | 2 | no | — |
| 40 | #2222 | — | 2 | 2 | no | — |
| 41 | #2195 | — | 2 | 2 | no | — |
| 42 | #2194 | — | 2 | 2 | no | — |
| 43 | #2191 | — | 2 | 2 | no | — |
| 44 | #2191 | — | 2 | 2 | no | — |
| 45 | #2161 | C22 | 1 | 1 | yes | characteristic, complemented |
| 46 | #2148 | C22 | 1 | 1 | yes | characteristic, complemented |
| 47 | #2148 | C22 | 1 | 1 | yes | characteristic, complemented |
| 48 | C2×#362 | C22 | 1 | 1 | yes | characteristic, complemented |
| 49 | #2145 | — | 2 | 2 | no | — |
| 50 | #2145 | C22 | 1 | 1 | yes | characteristic |
| 51 | #2145 | C22 | 1 | 1 | yes | characteristic, complemented |
| 52 | #2145 | C22 | 1 | 1 | yes | characteristic, complemented |
| 53 | C2×#360 | — | 2 | 2 | no | — |
| 54 | C2×#360 | C22 | 1 | 1 | yes | characteristic |
| 55 | C2×#360 | C22 | 1 | 1 | yes | characteristic, complemented |
| 56 | C2×#360 | C22 | 1 | 1 | yes | characteristic, complemented |
| 57 | #2143 | C22 | 1 | 1 | yes | characteristic |
| 58 | #2117 | C22 | 1 | 1 | yes | characteristic, complemented |
| 59 | #2117 | C22 | 1 | 1 | yes | characteristic, complemented |
| 60 | #2115 | C22 | 1 | 1 | yes | characteristic, complemented |
| 61 | #2064 | — | 2 | 1 | no | — |
| 62 | #2038 | — | 2 | 1 | no | — |
| 63 | #1971 | C22 | 1 | 1 | yes | characteristic, complemented |
| 64 | #1946 | C22 | 1 | 1 | yes | characteristic, complemented |
| 65 | #1882 | — | 2 | 1 | no | — |
| 66 | #1815 | C22 | 1 | 1 | yes | characteristic, complemented |
| 67 | #1389 | C22 | 1 | 1 | yes | characteristic, complemented |
| 68 | #1383 | C22 | 1 | 1 | yes | characteristic, complemented |
| 69 | #1377 | C22 | 1 | 1 | yes | characteristic, complemented |
| 70 | #1375 | C22 | 1 | 1 | yes | characteristic, complemented |
| 71 | #585 | — | 2 | 1 | no | — |
| 72 | #585 | — | 2 | 1 | no | — |
| 73 | #578 | — | 2 | 1 | no | — |
| 74 | #578 | — | 2 | 2 | no | — |
| 75 | #578 | — | 2 | 1 | no | — |
| 76 | #578 | — | 2 | 1 | no | — |
| 77 | #578 | — | 4 | 1 | no | — |
| 78 | #578 | D4 | 1 | 2 | yes | — |
| 79 | #577 | — | 2 | 2 | no | — |
| 80 | #577 | — | 2 | 2 | no | — |
| 81 | #577 | — | 2 | 2 | no | — |
| 82 | #577 | — | 2 | 2 | no | — |
| 83 | #577 | — | 4 | 1 | no | — |
| 84 | #577 | — | 4 | 1 | no | — |
| 85 | #577 | — | 4 | 1 | no | — |
| 86 | #577 | — | 4 | 1 | no | — |
| 87 | #576 | — | 2 | 1 | no | — |
| 88 | #576 | — | 2 | 2 | no | — |
| 89 | #576 | — | 2 | 1 | no | — |
| 90 | #576 | — | 2 | 1 | no | — |
| 91 | #576 | — | 4 | 1 | no | — |
| 92 | #576 | D4 | 1 | 2 | yes | — |
| 93 | #575 | — | 2 | 2 | no | — |
| 94 | #575 | — | 2 | 1 | no | — |
| 95 | #575 | — | 2 | 1 | no | — |
| 96 | #575 | — | 2 | 1 | no | — |
| 97 | #575 | — | 2 | 1 | no | — |
| 98 | #575 | — | 4 | 1 | no | — |
| 99 | #575 | — | 4 | 2 | no | — |
| 100 | C2×#137 | — | 2 | 1 | no | — |
| 101 | C2×#135 | — | 2 | 2 | no | — |
| 102 | C2×#135 | — | 2 | 1 | no | — |
| 103 | C2×#135 | — | 4 | 1 | no | — |
| 104 | C2×#135 | — | 4 | 2 | no | — |
| 105 | C2×#135 | D4 | 1 | 1 | yes | characteristic |
| 106 | C2×#135 | C23 | 1 | 1 | yes | characteristic |
| 107 | C2×#135 | C23 | 1 | 1 | yes | characteristic |
| 108 | C2×#135 | C23 | 1 | 1 | yes | characteristic |
| 109 | C22×Q16 | C23 | 1 | 1 | yes | characteristic |
| 110 | C2×#131 | — | 2 | 1 | no | — |
| 111 | C2×#131 | C23 | 1 | 1 | yes | characteristic |
| 112 | C2×#131 | C23 | 1 | 1 | yes | characteristic |
| 113 | #536 | — | 2 | 1 | no | — |
| 114 | #532 | — | 2 | 1 | no | — |
| 115 | #520 | — | 2 | 1 | no | — |
| 116 | #510 | — | 2 | 2 | no | — |
| 117 | #510 | — | 2 | 2 | no | — |
| 118 | #510 | — | 2 | 2 | no | — |
| 119 | #510 | — | 4 | 1 | no | — |
| 120 | #510 | — | 4 | 1 | no | — |
| 121 | #510 | — | 4 | 1 | no | — |
| 122 | C2×Q32 | — | 2 | 1 | no | — |
| 123 | C2×Q32 | — | 2 | 1 | no | — |
| 124 | C2×Q32 | — | 2 | 1 | no | — |
| 125 | C2×SD32 | — | 2 | 1 | no | — |
| 126 | C2×SD32 | — | 2 | 1 | no | — |
| 127 | C2×SD32 | — | 2 | 1 | no | — |
| 128 | #504 | — | 2 | 2 | no | — |
| 129 | #504 | — | 4 | 1 | no | — |
| 130 | C2×M32 | — | 2 | 2 | no | — |
| 131 | C2×M32 | C23 | 1 | 1 | yes | characteristic |
| 132 | C2×M32 | C23 | 1 | 1 | yes | characteristic |
| 133 | C2×M32 | C23 | 1 | 1 | yes | characteristic |
| 134 | C2×M32 | C23 | 1 | 1 | yes | characteristic |
| 135 | #497 | — | 2 | 1 | no | — |
| 136 | #497 | — | 2 | 1 | no | — |
| 137 | #496 | — | 2 | 1 | no | — |
| 138 | #496 | — | 2 | 1 | no | — |
| 139 | #473 | — | 2 | 2 | no | — |
| 140 | #473 | — | 2 | 1 | no | — |
| 141 | #473 | — | 2 | 2 | no | — |
| 142 | #473 | — | 2 | 2 | no | — |
| 143 | #473 | D4 | 1 | 2 | yes | — |
| 144 | #472 | — | 2 | 2 | no | — |
| 145 | #472 | — | 2 | 1 | no | — |
| 146 | #472 | D4 | 1 | 2 | yes | — |
| 147 | #471 | — | 2 | 2 | no | — |
| 148 | #471 | — | 2 | 2 | no | — |
| 149 | #471 | — | 2 | 2 | no | — |
| 150 | #471 | — | 2 | 2 | no | — |
| 151 | #470 | — | 2 | 1 | no | — |
| 152 | #470 | — | 2 | 1 | no | — |
| 153 | #467 | — | 4 | 1 | no | — |
| 154 | #464 | — | 4 | 1 | no | — |
| 155 | #463 | — | 4 | 1 | no | — |
| 156 | #462 | — | 4 | 1 | no | — |
| 157 | #461 | — | 4 | 1 | no | — |
| 158 | #456 | — | 2 | 2 | no | — |
| 159 | #456 | — | 2 | 2 | no | — |
| 160 | #455 | — | 2 | 2 | no | — |
| 161 | #455 | — | 2 | 2 | no | — |
| 162 | #454 | — | 2 | 2 | no | — |
| 163 | #454 | — | 2 | 2 | no | — |
| 164 | #453 | — | 2 | 2 | no | — |
| 165 | #453 | — | 2 | 2 | no | — |
| 166 | #444 | — | 2 | 2 | no | — |
| 167 | #444 | — | 2 | 2 | no | — |
| 168 | #444 | — | 2 | 2 | no | — |
| 169 | #444 | — | 2 | 2 | no | — |
| 170 | C2×#108 | D4 | 1 | 1 | yes | characteristic |
| 171 | C2×#108 | C23 | 1 | 1 | yes | characteristic |
| 172 | C2×#108 | C23 | 1 | 1 | yes | characteristic |
| 173 | #428 | — | 2 | 1 | no | — |
| 174 | #428 | — | 4 | 1 | no | — |
| 175 | #427 | — | 2 | 1 | no | — |
| 176 | #427 | C23 | 1 | 1 | yes | characteristic |
| 177 | C2×#106 | — | 2 | 1 | no | — |
| 178 | C2×#106 | C23 | 1 | 1 | yes | characteristic |
| 179 | #424 | — | 2 | 1 | no | — |
| 180 | C2×#104 | — | 2 | 1 | no | — |
| 181 | C2×#104 | D4 | 1 | 1 | yes | characteristic |
| 182 | C2×#104 | D4 | 1 | 1 | yes | characteristic |
| 183 | #419 | — | 2 | 1 | no | — |
| 184 | #417 | — | 2 | 1 | no | — |
| 185 | C2×#103 | — | 2 | 1 | no | — |
| 186 | #413 | — | 2 | 1 | no | — |
| 187 | #413 | — | 2 | 1 | no | — |
| 188 | C2×#101 | — | 2 | 1 | no | — |
| 189 | C2×#97 | C23 | 1 | 1 | yes | characteristic |
| 190 | #391 | — | 2 | 1 | no | — |
| 191 | #368 | — | 2 | 2 | no | — |
| 192 | #362 | — | 2 | 1 | no | — |
| 193 | #362 | — | 2 | 1 | no | — |
| 194 | #362 | — | 2 | 2 | no | — |
| 195 | #361 | — | 2 | 1 | no | — |
| 196 | #361 | — | 2 | 1 | no | — |
| 197 | #360 | — | 2 | 2 | no | — |
| 198 | #360 | — | 2 | 2 | no | — |
| 199 | #360 | — | 2 | 1 | no | — |
| 200 | #360 | — | 2 | 1 | no | — |
| 201 | #360 | — | 2 | 1 | no | — |
| 202 | #360 | — | 2 | 1 | no | — |
| 203 | #360 | — | 4 | 1 | no | — |
| 204 | #360 | D4 | 1 | 2 | yes | complemented |
| 205 | #360 | D4 | 1 | 2 | yes | complemented |
| 206 | #359 | — | 2 | 2 | no | — |
| 207 | #350 | — | 2 | 2 | no | — |
| 208 | #350 | — | 4 | 1 | no | — |
| 209 | #349 | — | 2 | 2 | no | — |
| 210 | #343 | — | 2 | 1 | no | — |
| 211 | #339 | — | 2 | 1 | no | — |
| 212 | 2−1+4 | — | 2 | 2 | no | — |
| 213 | 2−1+4 | — | 2 | 2 | no | — |
| 214 | 2−1+4 | — | 4 | 1 | no | — |
| 215 | 2−1+4 | — | 4 | 1 | no | — |
| 216 | 2−1+4 | — | 4 | 1 | no | — |
| 217 | 2−1+4 | — | 4 | 1 | no | — |
| 218 | H(5,𝔽2) | — | 2 | 2 | no | — |
| 219 | H(5,𝔽2) | — | 2 | 2 | no | — |
| 220 | H(5,𝔽2) | — | 4 | 1 | no | — |
| 221 | H(5,𝔽2) | — | 4 | 1 | no | — |
| 222 | H(5,𝔽2) | — | 4 | 1 | no | — |
| 223 | H(5,𝔽2) | — | 4 | 1 | no | — |
| 224 | H(5,𝔽2) | — | 8 | 1 | no | — |
| 225 | H(5,𝔽2) | — | 8 | 1 | no | — |
| 226 | C2×#41 | — | 2 | 1 | no | — |
| 227 | C2×#41 | — | 2 | 1 | no | — |
| 228 | C2×#41 | — | 2 | 1 | no | — |
| 229 | C2×#41 | — | 4 | 2 | no | — |
| 230 | C2×#41 | — | 4 | 2 | no | — |
| 231 | C2×#41 | — | 4 | 2 | no | — |
| 232 | C2×#41 | — | 4 | 2 | no | — |
| 233 | C2×#41 | — | 8 | 1 | no | — |
| 234 | C2×#41 | — | 8 | 1 | no | — |
| 235 | C2×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 236 | C2×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 237 | C22×Q8 | — | 2 | 1 | no | — |
| 238 | #137 | — | 2 | 2 | no | — |
| 239 | #137 | — | 2 | 2 | no | — |
| 240 | #137 | — | 2 | 2 | no | — |
| 241 | #137 | — | 2 | 2 | no | — |
| 242 | #137 | — | 4 | 2 | no | — |
| 243 | #137 | — | 4 | 2 | no | — |
| 244 | #137 | — | 4 | 1 | no | — |
| 245 | #137 | — | 4 | 1 | no | — |
| 246 | #137 | — | 4 | 2 | no | — |
| 247 | #137 | — | 4 | 2 | no | — |
| 248 | #137 | — | 4 | 2 | no | — |
| 249 | #137 | — | 4 | 2 | no | — |
| 250 | #137 | — | 4 | 2 | no | — |
| 251 | #137 | — | 4 | 1 | no | — |
| 252 | #137 | — | 4 | 1 | no | — |
| 253 | #137 | — | 4 | 2 | no | — |
| 254 | #137 | — | 4 | 2 | no | — |
| 255 | #137 | — | 4 | 2 | no | — |
| 256 | AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 257 | AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 258 | AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 259 | AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 260 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 261 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 262 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 263 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 264 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 265 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 266 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 267 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 268 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 269 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 270 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 271 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 272 | #135 | — | 2 | 2 | no | — |
| 273 | #135 | — | 2 | 2 | no | — |
| 274 | #135 | — | 2 | 2 | no | — |
| 275 | #135 | — | 2 | 2 | no | — |
| 276 | #135 | — | 2 | 1 | no | — |
| 277 | #135 | — | 2 | 1 | no | — |
| 278 | #135 | — | 2 | 1 | no | — |
| 279 | #135 | — | 2 | 1 | no | — |
| 280 | #135 | — | 2 | 1 | no | — |
| 281 | #135 | — | 2 | 1 | no | — |
| 282 | #135 | — | 2 | 1 | no | — |
| 283 | #135 | — | 2 | 1 | no | — |
| 284 | #135 | — | 2 | 1 | no | — |
| 285 | #135 | — | 2 | 1 | no | — |
| 286 | #135 | — | 4 | 2 | no | — |
| 287 | #135 | — | 4 | 2 | no | — |
| 288 | #135 | — | 4 | 2 | no | — |
| 289 | #135 | — | 4 | 1 | no | — |
| 290 | #135 | — | 4 | 1 | no | — |
| 291 | #135 | — | 4 | 1 | no | — |
| 292 | #135 | — | 4 | 1 | no | — |
| 293 | #135 | — | 4 | 2 | no | — |
| 294 | #135 | — | 4 | 2 | no | — |
| 295 | #135 | — | 4 | 2 | no | — |
| 296 | #135 | — | 4 | 2 | no | — |
| 297 | #135 | — | 4 | 2 | no | — |
| 298 | #135 | — | 4 | 2 | no | — |
| 299 | #135 | — | 4 | 2 | no | — |
| 300 | #135 | — | 4 | 1 | no | — |
| 301 | #135 | — | 4 | 1 | no | — |
| 302 | #135 | C2×D4 | 1 | 2 | yes | — |
| 303 | #135 | C2×D4 | 1 | 2 | yes | — |
| 304 | C2×Q16 | — | 2 | 2 | no | — |
| 305 | C2×Q16 | — | 2 | 1 | no | — |
| 306 | C2×Q16 | — | 2 | 1 | no | — |
| 307 | C2×Q16 | — | 2 | 1 | no | — |
| 308 | C2×Q16 | — | 2 | 1 | no | — |
| 309 | C2×Q16 | — | 2 | 1 | no | — |
| 310 | C2×Q16 | — | 2 | 1 | no | — |
| 311 | C2×Q16 | — | 2 | 1 | no | — |
| 312 | C2×Q16 | — | 4 | 1 | no | — |
| 313 | C2×Q16 | — | 4 | 2 | no | — |
| 314 | C2×Q16 | — | 4 | 1 | no | — |
| 315 | C2×Q16 | D8 | 1 | 1 | yes | characteristic |
| 316 | C2×Q16 | C2×D4 | 1 | 1 | yes | characteristic |
| 317 | C2×Q16 | C2×D4 | 1 | 1 | yes | characteristic |
| 318 | C2×Q16 | #41 | 1 | 1 | yes | characteristic |
| 319 | C2×SD16 | — | 2 | 1 | no | — |
| 320 | C2×SD16 | — | 2 | 1 | no | — |
| 321 | C2×SD16 | — | 2 | 1 | no | — |
| 322 | C2×SD16 | — | 2 | 1 | no | — |
| 323 | C2×SD16 | — | 2 | 1 | no | — |
| 324 | C2×SD16 | — | 4 | 2 | no | — |
| 325 | C2×SD16 | — | 4 | 2 | no | — |
| 326 | C2×SD16 | — | 4 | 2 | no | — |
| 327 | C2×SD16 | — | 4 | 2 | no | — |
| 328 | C2×SD16 | — | 4 | 1 | no | — |
| 329 | C2×SD16 | D8 | 1 | 1 | yes | characteristic |
| 330 | C2×SD16 | D8 | 1 | 1 | yes | characteristic |
| 331 | C2×D8 | — | 2 | 2 | no | — |
| 332 | C2×D8 | — | 2 | 1 | no | — |
| 333 | C2×D8 | — | 4 | 1 | no | — |
| 334 | C2×D8 | — | 4 | 2 | no | — |
| 335 | C2×D8 | D8 | 1 | 1 | yes | characteristic |
| 336 | C2×D8 | C2×D4 | 1 | 1 | yes | characteristic |
| 337 | C2×D8 | C2×D4 | 1 | 1 | yes | characteristic |
| 338 | C2×D8 | #41 | 1 | 1 | yes | characteristic |
| 339 | #131 | — | 2 | 1 | no | — |
| 340 | #131 | — | 2 | 1 | no | — |
| 341 | #131 | — | 2 | 2 | no | — |
| 342 | #131 | — | 2 | 2 | no | — |
| 343 | #131 | — | 2 | 1 | no | — |
| 344 | #131 | — | 2 | 1 | no | — |
| 345 | #131 | — | 2 | 1 | no | — |
| 346 | #131 | — | 2 | 1 | no | — |
| 347 | #131 | — | 4 | 1 | no | — |
| 348 | #131 | — | 4 | 1 | no | — |
| 349 | #131 | C2×D4 | 1 | 2 | yes | — |
| 350 | #131 | C2×D4 | 1 | 2 | yes | — |
| 351 | C2×M16 | — | 2 | 1 | no | — |
| 352 | C2×M16 | — | 2 | 1 | no | — |
| 353 | C2×M16 | — | 2 | 1 | no | — |
| 354 | C2×M16 | — | 2 | 1 | no | — |
| 355 | C2×M16 | — | 4 | 1 | no | — |
| 356 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 357 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 358 | C22×C8 | — | 2 | 1 | no | — |
| 359 | C22×C8 | — | 2 | 1 | no | — |
| 360 | C22×C8 | — | 4 | 1 | no | — |
| 361 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 362 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 363 | C4⋊Q8 | — | 2 | 1 | no | — |
| 364 | C4⋊Q8 | — | 4 | 1 | no | — |
| 365 | #127 | — | 2 | 1 | no | — |
| 366 | #124 | — | 2 | 1 | no | — |
| 367 | #124 | — | 2 | 1 | no | — |
| 368 | #124 | — | 4 | 1 | no | — |
| 369 | #123 | — | 8 | 1 | no | — |
| 370 | C22⋊Q8 | — | 4 | 1 | no | — |
| 371 | C22⋊Q8 | — | 4 | 1 | no | — |
| 372 | #121 | — | 8 | 1 | no | — |
| 373 | C4×Q8 | — | 4 | 1 | no | — |
| 374 | C4×D4 | — | 4 | 1 | no | — |
| 375 | C4×D4 | — | 8 | 1 | no | — |
| 376 | C4×D4 | — | 8 | 1 | no | — |
| 377 | #117 | — | 2 | 1 | no | — |
| 378 | #117 | — | 4 | 1 | no | — |
| 379 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 380 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 381 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 382 | Q32 | — | 4 | 2 | no | — |
| 383 | Q32 | — | 4 | 2 | no | — |
| 384 | Q32 | — | 4 | 2 | no | — |
| 385 | SD32 | — | 4 | 2 | no | — |
| 386 | SD32 | — | 4 | 2 | no | — |
| 387 | SD32 | — | 4 | 2 | no | — |
| 388 | M32 | — | 2 | 1 | no | — |
| 389 | M32 | — | 2 | 1 | no | — |
| 390 | M32 | — | 2 | 1 | no | — |
| 391 | M32 | — | 2 | 1 | no | — |
| 392 | M32 | — | 2 | 1 | no | — |
| 393 | M32 | — | 2 | 1 | no | — |
| 394 | M32 | — | 2 | 1 | no | — |
| 395 | M32 | — | 4 | 2 | no | — |
| 396 | M32 | C2×D4 | 1 | 2 | yes | — |
| 397 | C2×C16 | — | 2 | 1 | no | — |
| 398 | C2×C16 | — | 2 | 1 | no | — |
| 399 | C2×C16 | — | 2 | 1 | no | — |
| 400 | C2×C16 | — | 2 | 1 | no | — |
| 401 | C2×C16 | — | 4 | 2 | no | — |
| 402 | #108 | — | 2 | 2 | no | — |
| 403 | #108 | — | 2 | 1 | no | — |
| 404 | #108 | — | 2 | 1 | no | — |
| 405 | #108 | — | 2 | 1 | no | — |
| 406 | #108 | C2×D4 | 1 | 2 | yes | — |
| 407 | #107 | — | 2 | 1 | no | — |
| 408 | #107 | — | 4 | 1 | no | — |
| 409 | #106 | — | 2 | 1 | no | — |
| 410 | #106 | — | 2 | 1 | no | — |
| 411 | #106 | — | 4 | 1 | no | — |
| 412 | #106 | C2×D4 | 1 | 1 | yes | characteristic |
| 413 | #106 | C2×D4 | 1 | 1 | yes | characteristic |
| 414 | C4⋊C8 | — | 4 | 1 | no | — |
| 415 | C4⋊C8 | — | 4 | 1 | no | — |
| 416 | #104 | — | 2 | 2 | no | — |
| 417 | #104 | — | 2 | 2 | no | — |
| 418 | #104 | — | 2 | 2 | no | — |
| 419 | #104 | — | 2 | 2 | no | — |
| 420 | #103 | — | 4 | 1 | no | — |
| 421 | #103 | — | 4 | 1 | no | — |
| 422 | #103 | — | 4 | 1 | no | — |
| 423 | #103 | — | 4 | 1 | no | — |
| 424 | #103 | — | 4 | 1 | no | — |
| 425 | #102 | — | 4 | 1 | no | — |
| 426 | #101 | — | 2 | 2 | no | — |
| 427 | #101 | — | 2 | 2 | no | — |
| 428 | #101 | — | 4 | 2 | no | — |
| 429 | #100 | — | 2 | 2 | no | — |
| 430 | #100 | — | 2 | 2 | no | — |
| 431 | #97 | — | 2 | 1 | no | — |
| 432 | #97 | — | 2 | 1 | no | — |
| 433 | #95 | — | 8 | 1 | no | — |
| 434 | #41 | — | 2 | 1 | no | — |
| 435 | #41 | — | 2 | 1 | no | — |
| 436 | #41 | — | 2 | 1 | no | — |
| 437 | #41 | — | 2 | 2 | no | — |
| 438 | #41 | — | 2 | 2 | no | — |
| 439 | #41 | — | 2 | 1 | no | — |
| 440 | #41 | — | 2 | 1 | no | — |
| 441 | #41 | — | 2 | 1 | no | — |
| 442 | #41 | — | 4 | 2 | no | — |
| 443 | #41 | — | 4 | 2 | no | — |
| 444 | #41 | — | 4 | 1 | no | — |
| 445 | #41 | — | 4 | 1 | no | — |
| 446 | #41 | — | 4 | 2 | no | — |
| 447 | #41 | — | 4 | 2 | no | — |
| 448 | #41 | — | 4 | 2 | no | — |
| 449 | #41 | — | 4 | 2 | no | — |
| 450 | #41 | — | 4 | 2 | no | — |
| 451 | #41 | — | 4 | 2 | no | — |
| 452 | #41 | — | 4 | 1 | 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 | — | 8 | 2 | 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 | 2 | no | — |
| 467 | #41 | — | 8 | 2 | no | — |
| 468 | #41 | — | 8 | 1 | no | — |
| 469 | #41 | — | 8 | 1 | no | — |
| 470 | #41 | — | 8 | 1 | no | — |
| 471 | #41 | — | 8 | 1 | no | — |
| 472 | #41 | #120 | 1 | 2 | yes | — |
| 473 | #41 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 474 | C2×Q8 | — | 2 | 1 | no | — |
| 475 | C2×Q8 | — | 2 | 1 | no | — |
| 476 | C2×Q8 | — | 2 | 1 | no | — |
| 477 | C2×Q8 | — | 4 | 2 | no | — |
| 478 | C2×Q8 | — | 4 | 2 | no | — |
| 479 | C2×Q8 | — | 4 | 2 | no | — |
| 480 | C2×Q8 | — | 4 | 2 | no | — |
| 481 | C2×Q8 | — | 4 | 1 | no | — |
| 482 | C2×Q8 | — | 4 | 1 | no | — |
| 483 | C2×Q8 | — | 4 | 1 | no | — |
| 484 | C2×Q8 | — | 4 | 1 | no | — |
| 485 | C2×Q8 | — | 4 | 1 | no | — |
| 486 | C2×Q8 | — | 4 | 1 | no | — |
| 487 | C2×Q8 | — | 8 | 1 | no | — |
| 488 | C2×Q8 | — | 8 | 1 | no | — |
| 489 | C2×Q8 | C2×D8 | 1 | 1 | yes | characteristic |
| 490 | C2×Q8 | C2×D8 | 1 | 1 | yes | characteristic |
| 491 | C2×D4 | — | 2 | 1 | no | — |
| 492 | C2×D4 | — | 2 | 1 | no | — |
| 493 | C2×D4 | — | 2 | 1 | no | — |
| 494 | C2×D4 | — | 2 | 1 | no | — |
| 495 | C2×D4 | — | 2 | 1 | no | — |
| 496 | C2×D4 | — | 4 | 2 | no | — |
| 497 | C2×D4 | — | 4 | 2 | no | — |
| 498 | C2×D4 | — | 4 | 2 | no | — |
| 499 | C2×D4 | — | 4 | 1 | no | — |
| 500 | C2×D4 | — | 4 | 2 | no | — |
| 501 | C2×D4 | — | 4 | 1 | no | — |
| 502 | C2×D4 | — | 4 | 1 | no | — |
| 503 | C2×D4 | — | 8 | 1 | no | — |
| 504 | C2×D4 | — | 8 | 2 | no | — |
| 505 | C2×D4 | — | 8 | 1 | no | — |
| 506 | C2×D4 | — | 8 | 1 | no | — |
| 507 | C2×D4 | — | 8 | 2 | no | — |
| 508 | C2×D4 | — | 8 | 2 | no | — |
| 509 | C2×D4 | — | 8 | 2 | no | — |
| 510 | C2×D4 | — | 8 | 2 | no | — |
| 511 | C2×D4 | — | 8 | 2 | no | — |
| 512 | C2×D4 | C2×D8 | 1 | 1 | yes | characteristic |
| 513 | C2×D4 | C2×D8 | 1 | 1 | yes | characteristic |
| 514 | C22×C4 | — | 2 | 1 | no | — |
| 515 | C22×C4 | — | 2 | 1 | no | — |
| 516 | C22×C4 | — | 2 | 1 | no | — |
| 517 | C22×C4 | — | 4 | 1 | no | — |
| 518 | C22×C4 | — | 4 | 1 | no | — |
| 519 | C22×C4 | — | 4 | 1 | no | — |
| 520 | C22×C4 | — | 4 | 1 | no | — |
| 521 | C22×C4 | — | 4 | 1 | no | — |
| 522 | C22×C4 | — | 8 | 2 | no | — |
| 523 | C22×C4 | — | 8 | 2 | no | — |
| 524 | C22×C4 | — | 8 | 1 | no | — |
| 525 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 526 | Q16 | — | 2 | 2 | no | — |
| 527 | Q16 | — | 2 | 1 | no | — |
| 528 | Q16 | — | 2 | 1 | no | — |
| 529 | Q16 | — | 2 | 1 | no | — |
| 530 | Q16 | — | 2 | 1 | no | — |
| 531 | Q16 | — | 2 | 1 | no | — |
| 532 | Q16 | — | 4 | 2 | no | — |
| 533 | Q16 | — | 4 | 1 | no | — |
| 534 | Q16 | — | 4 | 1 | no | — |
| 535 | Q16 | — | 4 | 2 | no | — |
| 536 | Q16 | — | 4 | 2 | no | — |
| 537 | Q16 | — | 4 | 2 | no | — |
| 538 | Q16 | — | 4 | 1 | no | — |
| 539 | Q16 | — | 4 | 1 | no | — |
| 540 | Q16 | — | 4 | 1 | no | — |
| 541 | Q16 | — | 4 | 1 | no | — |
| 542 | Q16 | — | 8 | 2 | no | — |
| 543 | Q16 | #121 | 1 | 2 | yes | — |
| 544 | SD16 | — | 2 | 2 | no | — |
| 545 | SD16 | — | 2 | 2 | no | — |
| 546 | SD16 | — | 2 | 2 | no | — |
| 547 | SD16 | — | 2 | 2 | no | — |
| 548 | SD16 | — | 4 | 2 | no | — |
| 549 | SD16 | — | 4 | 2 | no | — |
| 550 | SD16 | — | 4 | 1 | no | — |
| 551 | SD16 | — | 4 | 1 | no | — |
| 552 | SD16 | — | 4 | 1 | no | — |
| 553 | SD16 | — | 4 | 1 | no | — |
| 554 | SD16 | — | 4 | 2 | no | — |
| 555 | SD16 | — | 4 | 2 | no | — |
| 556 | SD16 | — | 4 | 2 | no | — |
| 557 | SD16 | — | 4 | 2 | no | — |
| 558 | SD16 | — | 4 | 2 | no | — |
| 559 | SD16 | — | 4 | 2 | no | — |
| 560 | SD16 | — | 4 | 1 | no | — |
| 561 | SD16 | — | 4 | 1 | no | — |
| 562 | SD16 | — | 4 | 1 | no | — |
| 563 | SD16 | — | 4 | 1 | no | — |
| 564 | SD16 | — | 8 | 2 | no | — |
| 565 | D8 | — | 2 | 2 | no | — |
| 566 | D8 | — | 2 | 1 | no | — |
| 567 | D8 | — | 2 | 1 | no | — |
| 568 | D8 | — | 2 | 1 | no | — |
| 569 | D8 | — | 2 | 1 | no | — |
| 570 | D8 | — | 2 | 1 | no | — |
| 571 | D8 | — | 4 | 2 | no | — |
| 572 | D8 | — | 4 | 1 | no | — |
| 573 | D8 | — | 4 | 1 | no | — |
| 574 | D8 | — | 4 | 2 | no | — |
| 575 | D8 | — | 4 | 2 | no | — |
| 576 | D8 | — | 4 | 2 | no | — |
| 577 | D8 | #121 | 1 | 2 | yes | — |
| 578 | M16 | — | 2 | 1 | no | — |
| 579 | M16 | — | 2 | 2 | no | — |
| 580 | M16 | — | 2 | 2 | no | — |
| 581 | M16 | — | 2 | 1 | no | — |
| 582 | M16 | — | 2 | 2 | no | — |
| 583 | M16 | — | 2 | 1 | no | — |
| 584 | M16 | — | 4 | 2 | no | — |
| 585 | M16 | — | 4 | 2 | no | — |
| 586 | M16 | — | 4 | 1 | no | — |
| 587 | M16 | — | 4 | 1 | no | — |
| 588 | M16 | — | 4 | 1 | no | — |
| 589 | M16 | — | 4 | 1 | no | — |
| 590 | M16 | — | 4 | 1 | no | — |
| 591 | M16 | #120 | 1 | 2 | yes | — |
| 592 | C2×C8 | — | 2 | 1 | no | — |
| 593 | C2×C8 | — | 2 | 1 | no | — |
| 594 | C2×C8 | — | 2 | 1 | no | — |
| 595 | C2×C8 | — | 2 | 2 | no | — |
| 596 | C2×C8 | — | 2 | 2 | no | — |
| 597 | C2×C8 | — | 2 | 1 | no | — |
| 598 | C2×C8 | — | 4 | 2 | no | — |
| 599 | C2×C8 | — | 4 | 2 | no | — |
| 600 | C2×C8 | — | 4 | 1 | no | — |
| 601 | C2×C8 | — | 4 | 1 | no | — |
| 602 | C2×C8 | — | 4 | 1 | no | — |
| 603 | C2×C8 | — | 4 | 1 | no | — |
| 604 | C2×C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 605 | C2×C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 606 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 607 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 608 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 609 | C2×C8 | C2×#41 | 1 | 1 | yes | characteristic |
| 610 | C2×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 611 | C2×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 612 | C4⋊C4 | — | 2 | 1 | no | — |
| 613 | C4⋊C4 | — | 2 | 1 | no | — |
| 614 | C4⋊C4 | — | 4 | 1 | no | — |
| 615 | C4⋊C4 | — | 4 | 1 | no | — |
| 616 | C4⋊C4 | — | 8 | 1 | no | — |
| 617 | C4⋊C4 | — | 8 | 1 | no | — |
| 618 | C4⋊C4 | — | 8 | 1 | no | — |
| 619 | C4⋊C4 | — | 8 | 1 | no | — |
| 620 | C22⋊C4 | — | 4 | 1 | no | — |
| 621 | C22⋊C4 | — | 8 | 1 | no | — |
| 622 | C22⋊C4 | — | 8 | 1 | no | — |
| 623 | C22⋊C4 | — | 8 | 1 | no | — |
| 624 | C22⋊C4 | — | 8 | 1 | no | — |
| 625 | C22⋊C4 | — | 8 | 1 | no | — |
| 626 | C42 | — | 2 | 1 | no | — |
| 627 | C42 | — | 2 | 1 | no | — |
| 628 | C42 | — | 4 | 1 | no | — |
| 629 | C42 | — | 8 | 1 | no | — |
| 630 | C16 | — | 2 | 2 | no | — |
| 631 | C16 | — | 4 | 1 | no | — |
| 632 | C16 | — | 4 | 1 | no | — |
| 633 | C16 | — | 4 | 1 | no | — |
| 634 | C23 | — | 2 | 1 | no | — |
| 635 | C23 | — | 2 | 1 | no | — |
| 636 | C23 | — | 4 | 1 | no | — |
| 637 | C23 | — | 4 | 1 | no | — |
| 638 | C23 | — | 4 | 1 | no | — |
| 639 | C23 | — | 8 | 2 | no | — |
| 640 | C23 | — | 8 | 2 | no | — |
| 641 | C23 | #576 | 1 | 1 | yes | characteristic |
| 642 | Q8 | — | 2 | 1 | no | — |
| 643 | Q8 | — | 2 | 2 | no | — |
| 644 | Q8 | — | 2 | 1 | no | — |
| 645 | Q8 | — | 2 | 1 | no | — |
| 646 | Q8 | — | 4 | 1 | no | — |
| 647 | Q8 | — | 4 | 1 | no | — |
| 648 | Q8 | — | 4 | 1 | no | — |
| 649 | Q8 | — | 4 | 1 | no | — |
| 650 | Q8 | — | 4 | 1 | no | — |
| 651 | Q8 | — | 8 | 2 | no | — |
| 652 | Q8 | — | 8 | 2 | no | — |
| 653 | Q8 | — | 8 | 1 | no | — |
| 654 | Q8 | — | 8 | 1 | no | — |
| 655 | Q8 | — | 8 | 1 | no | — |
| 656 | Q8 | — | 8 | 1 | no | — |
| 657 | Q8 | #447 | 1 | 2 | yes | — |
| 658 | D4 | — | 2 | 2 | no | — |
| 659 | D4 | — | 2 | 2 | no | — |
| 660 | D4 | — | 2 | 2 | no | — |
| 661 | D4 | — | 2 | 1 | no | — |
| 662 | D4 | — | 2 | 1 | no | — |
| 663 | D4 | — | 2 | 1 | no | — |
| 664 | D4 | — | 4 | 1 | no | — |
| 665 | D4 | — | 4 | 2 | no | — |
| 666 | D4 | — | 4 | 2 | no | — |
| 667 | D4 | — | 4 | 1 | no | — |
| 668 | D4 | — | 4 | 1 | no | — |
| 669 | D4 | — | 4 | 1 | no | — |
| 670 | D4 | — | 4 | 1 | no | — |
| 671 | D4 | — | 4 | 1 | no | — |
| 672 | D4 | — | 4 | 1 | no | — |
| 673 | D4 | — | 8 | 2 | no | — |
| 674 | D4 | — | 8 | 2 | no | — |
| 675 | D4 | — | 8 | 2 | no | — |
| 676 | D4 | — | 8 | 2 | no | — |
| 677 | D4 | — | 8 | 2 | no | — |
| 678 | D4 | — | 8 | 2 | no | — |
| 679 | D4 | — | 8 | 1 | no | — |
| 680 | D4 | — | 8 | 1 | no | — |
| 681 | D4 | — | 8 | 1 | no | — |
| 682 | D4 | — | 8 | 1 | no | — |
| 683 | D4 | — | 16 | 2 | no | — |
| 684 | D4 | #447 | 1 | 2 | yes | — |
| 685 | C2×C4 | — | 2 | 1 | no | — |
| 686 | C2×C4 | — | 2 | 2 | no | — |
| 687 | C2×C4 | — | 2 | 2 | no | — |
| 688 | C2×C4 | — | 2 | 1 | no | — |
| 689 | C2×C4 | — | 4 | 1 | no | — |
| 690 | C2×C4 | — | 4 | 1 | no | — |
| 691 | C2×C4 | — | 4 | 2 | no | — |
| 692 | C2×C4 | — | 4 | 1 | no | — |
| 693 | C2×C4 | — | 4 | 2 | no | — |
| 694 | C2×C4 | — | 4 | 1 | no | — |
| 695 | C2×C4 | — | 4 | 1 | no | — |
| 696 | C2×C4 | — | 4 | 1 | no | — |
| 697 | C2×C4 | — | 4 | 1 | no | — |
| 698 | C2×C4 | — | 4 | 1 | no | — |
| 699 | C2×C4 | — | 8 | 2 | no | — |
| 700 | C2×C4 | — | 8 | 2 | no | — |
| 701 | C2×C4 | — | 8 | 2 | no | — |
| 702 | C2×C4 | — | 8 | 2 | no | — |
| 703 | C2×C4 | — | 8 | 2 | no | — |
| 704 | C2×C4 | — | 8 | 2 | no | — |
| 705 | C2×C4 | — | 8 | 1 | no | — |
| 706 | C2×C4 | — | 8 | 1 | no | — |
| 707 | C2×C4 | — | 8 | 1 | no | — |
| 708 | C2×C4 | — | 8 | 1 | no | — |
| 709 | C2×C4 | — | 8 | 1 | no | — |
| 710 | C2×C4 | — | 8 | 1 | no | — |
| 711 | C2×C4 | — | 8 | 1 | no | — |
| 712 | C2×C4 | — | 8 | 1 | no | — |
| 713 | C2×C4 | — | 8 | 1 | no | — |
| 714 | C2×C4 | — | 16 | 1 | no | — |
| 715 | C2×C4 | — | 32 | 1 | no | — |
| 716 | C2×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 717 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 718 | C2×C4 | #546 | 1 | 1 | yes | characteristic |
| 719 | C2×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 720 | C2×C4 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 721 | C2×C4 | #577 | 1 | 1 | yes | characteristic |
| 722 | C8 | — | 2 | 2 | no | — |
| 723 | C8 | — | 2 | 1 | no | — |
| 724 | C8 | — | 2 | 1 | no | — |
| 725 | C8 | — | 4 | 1 | no | — |
| 726 | C8 | — | 4 | 2 | no | — |
| 727 | C8 | — | 8 | 1 | no | — |
| 728 | C8 | C2×#121 | 1 | 1 | yes | characteristic |
| 729 | C8 | #534 | 1 | 1 | yes | characteristic |
| 730 | C8 | D42 | 1 | 1 | yes | characteristic |
| 731 | C8 | #546 | 1 | 1 | yes | characteristic |
| 732 | C22 | — | 2 | 2 | no | — |
| 733 | C22 | — | 4 | 1 | no | — |
| 734 | C22 | — | 4 | 1 | no | — |
| 735 | C22 | — | 4 | 2 | no | — |
| 736 | C22 | — | 8 | 1 | no | — |
| 737 | C22 | — | 8 | 1 | no | — |
| 738 | C22 | — | 8 | 1 | no | — |
| 739 | C22 | — | 8 | 1 | no | — |
| 740 | C22 | — | 16 | 1 | no | — |
| 741 | C22 | — | 16 | 1 | no | — |
| 742 | C22 | — | 16 | 1 | no | — |
| 743 | C22 | — | 32 | 2 | no | — |
| 744 | C22 | — | 32 | 2 | no | — |
| 745 | C22 | #3012 | 1 | 1 | yes | characteristic |
| 746 | C22 | D4×D8 | 1 | 1 | yes | characteristic |
| 747 | C22 | #3318 | 1 | 1 | yes | characteristic |
| 748 | C4 | — | 2 | 2 | no | — |
| 749 | C4 | — | 4 | 1 | no | — |
| 750 | C4 | — | 4 | 2 | no | — |
| 751 | C4 | — | 8 | 1 | no | — |
| 752 | C4 | — | 8 | 1 | no | — |
| 753 | C4 | — | 8 | 1 | no | — |
| 754 | C4 | — | 8 | 1 | no | — |
| 755 | C4 | — | 8 | 1 | no | — |
| 756 | C4 | — | 16 | 1 | no | — |
| 757 | C4 | — | 16 | 1 | no | — |
| 758 | C4 | #2410 | 1 | 1 | yes | characteristic |
| 759 | C4 | C2×#447 | 1 | 1 | yes | characteristic |
| 760 | C4 | #3265 | 1 | 1 | yes | characteristic |
| 761 | C4 | #3294 | 1 | 1 | yes | characteristic |
| 762 | C2 | — | 2 | 1 | no | — |
| 763 | C2 | — | 2 | 1 | no | — |
| 764 | C2 | — | 2 | 1 | no | — |
| 765 | C2 | — | 4 | 2 | no | — |
| 766 | C2 | — | 8 | 1 | no | — |
| 767 | C2 | — | 8 | 2 | no | — |
| 768 | C2 | — | 16 | 1 | no | — |
| 769 | C2 | — | 16 | 1 | no | — |
| 770 | C2 | #24424 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #24424 |
| commutator, Frattini, cosocle | C22×C8 | C24 |
| prime radical | #61100 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ C2×#444 ◁ G | |
| LECS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #33619 | C2 | semidirect |
| 3. #33542 | C2 | semidirect |
| 4. #33532 | C2 | semidirect |
| 5. #33388 | C2 | semidirect |
| 6. #24800 | C2 | semidirect |
| 7. #13416 | C2 | semidirect |
| 8. #13391 | C2 | semidirect |
| 9. #13342 | C2 | semidirect |
| 10. #13311 | C2 | semidirect |
| 11. #13039 | C2 | semidirect |
| 12. #13005 | C2 | semidirect |
| 13. #12986 | C2 | semidirect |
| 14. #12944 | C2 | semidirect |
| 15. #12752 | C2 | semidirect |
| 20. C2×#510 | C22 | semidirect |
| 21. C2×#510 | C22 | semidirect |
| 22. #3407 | C22 | semidirect |
| 31. C2×#473 | C22 | semidirect |
| 32. #3059 | C22 | semidirect |
| 38. #2912 | C22 | semidirect |
| 45. #2161 | C22 | semidirect |
| 46. #2148 | C22 | semidirect |
| 47. #2148 | C22 | semidirect |
| 48. C2×#362 | C22 | semidirect |
| 51. #2145 | C22 | semidirect |
| 52. #2145 | C22 | semidirect |
| 55. C2×#360 | C22 | semidirect |
| 56. C2×#360 | C22 | semidirect |
| 58. #2117 | C22 | semidirect |
| 59. #2117 | C22 | semidirect |
| 60. #2115 | C22 | semidirect |
| 63. #1971 | C22 | semidirect |
| 64. #1946 | C22 | semidirect |
| 66. #1815 | C22 | semidirect |
| 67. #1389 | C22 | semidirect |
| 68. #1383 | C22 | semidirect |
| 69. #1377 | C22 | semidirect |
| 70. #1375 | C22 | semidirect |
| 204. #360 | D4 | semidirect |
| 205. #360 | D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #61100 | 2 |
| #33619 | 2 |
| #33542 | 2 |
| #33532 | 2 |
| #33388 | 2 |
| #24800 | 2 |
| #13416 | 2 |
| #13391 | 2 |
| #13342 | 2 |
| #13311 | 2 |
| #13039 | 2 |
| #13005 | 2 |
| #12986 | 2 |
| #12944 | 2 |
| #12752 | 2 |