Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1104 conjugacy classes of subgroups.
The subgroup lattice has 845 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #61105 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #33719 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#2212 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #33542 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #33541 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #33532 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #33531 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #28503 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #13324 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #13323 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #13311 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #13310 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #13259 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #13197 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #12646 | 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 | C2×#509 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#509 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | C2×#509 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | #3293 | — | 2 | 1 | no | — |
| 26 | #3292 | — | 2 | 1 | no | — |
| 27 | #3291 | — | 2 | 2 | no | — |
| 28 | #3290 | — | 2 | 1 | no | — |
| 29 | #3290 | — | 2 | 1 | no | — |
| 30 | #3290 | — | 2 | 2 | no | — |
| 31 | #3154 | — | 2 | 1 | no | — |
| 32 | #3147 | C22 | 1 | 1 | yes | characteristic |
| 33 | C2×#495 | C22 | 1 | 1 | yes | characteristic, complemented |
| 34 | #3067 | — | 2 | 1 | no | — |
| 35 | #3067 | C22 | 1 | 1 | yes | characteristic |
| 36 | #3067 | C22 | 1 | 1 | yes | characteristic |
| 37 | C2×#473 | C22 | 1 | 1 | yes | characteristic, complemented |
| 38 | C2×#472 | C22 | 1 | 1 | yes | characteristic, complemented |
| 39 | #3059 | C22 | 1 | 1 | yes | characteristic, complemented |
| 40 | #3058 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | #3018 | — | 2 | 1 | no | — |
| 42 | #3018 | — | 2 | 1 | no | — |
| 43 | C2×#443 | C22 | 1 | 1 | yes | characteristic |
| 44 | C2×#443 | C22 | 1 | 1 | yes | characteristic |
| 45 | #2251 | — | 2 | 1 | no | — |
| 46 | #2250 | — | 2 | 1 | no | — |
| 47 | #2249 | — | 2 | 1 | no | — |
| 48 | #2249 | — | 2 | 1 | no | — |
| 49 | #2212 | — | 2 | 2 | no | — |
| 50 | #2212 | — | 2 | 2 | no | — |
| 51 | #2195 | — | 2 | 2 | no | — |
| 52 | #2194 | — | 2 | 2 | no | — |
| 53 | #2193 | — | 2 | 2 | no | — |
| 54 | #2192 | — | 2 | 2 | no | — |
| 55 | #2191 | — | 2 | 4 | no | — |
| 56 | #2190 | — | 2 | 4 | no | — |
| 57 | C2×#364 | C22 | 1 | 1 | yes | characteristic, complemented |
| 58 | #2148 | C22 | 1 | 1 | yes | characteristic |
| 59 | C2×#362 | C22 | 1 | 1 | yes | characteristic, complemented |
| 60 | C2×#361 | C22 | 1 | 1 | yes | characteristic, complemented |
| 61 | #2145 | C22 | 1 | 1 | yes | characteristic |
| 62 | #2145 | C22 | 1 | 1 | yes | characteristic, complemented |
| 63 | #2145 | C22 | 1 | 1 | yes | characteristic, complemented |
| 64 | #2143 | C22 | 1 | 1 | yes | characteristic, complemented |
| 65 | #2143 | C22 | 1 | 1 | yes | characteristic, complemented |
| 66 | #2117 | C22 | 1 | 1 | yes | characteristic, complemented |
| 67 | #2117 | C22 | 1 | 1 | yes | characteristic, complemented |
| 68 | #2115 | C22 | 1 | 1 | yes | characteristic, complemented |
| 69 | #2115 | C22 | 1 | 1 | yes | characteristic, complemented |
| 70 | C4×M32 | C22 | 1 | 1 | yes | characteristic, complemented |
| 71 | #2004 | — | 2 | 1 | no | — |
| 72 | #2003 | — | 2 | 1 | no | — |
| 73 | #1977 | — | 2 | 1 | no | — |
| 74 | #1772 | C22 | 1 | 1 | yes | characteristic, complemented |
| 75 | #1389 | C22 | 1 | 1 | yes | characteristic, complemented |
| 76 | #1388 | C22 | 1 | 1 | yes | characteristic, complemented |
| 77 | #585 | — | 2 | 1 | no | — |
| 78 | #585 | — | 2 | 1 | no | — |
| 79 | #578 | — | 2 | 2 | no | — |
| 80 | #578 | — | 2 | 1 | no | — |
| 81 | #578 | — | 2 | 1 | no | — |
| 82 | #578 | — | 2 | 1 | no | — |
| 83 | #578 | — | 2 | 1 | no | — |
| 84 | #578 | — | 4 | 1 | no | — |
| 85 | #577 | — | 2 | 2 | no | — |
| 86 | #577 | — | 2 | 2 | no | — |
| 87 | #577 | — | 2 | 2 | no | — |
| 88 | #577 | — | 2 | 2 | no | — |
| 89 | #577 | — | 4 | 1 | no | — |
| 90 | #577 | — | 4 | 1 | no | — |
| 91 | #577 | — | 4 | 1 | no | — |
| 92 | #577 | — | 4 | 1 | no | — |
| 93 | #576 | — | 2 | 2 | no | — |
| 94 | #576 | — | 2 | 1 | no | — |
| 95 | #576 | — | 2 | 1 | no | — |
| 96 | #576 | — | 2 | 1 | no | — |
| 97 | #576 | — | 2 | 1 | no | — |
| 98 | #576 | — | 4 | 1 | no | — |
| 99 | #575 | — | 2 | 2 | no | — |
| 100 | #575 | — | 2 | 2 | no | — |
| 101 | #575 | — | 2 | 1 | no | — |
| 102 | #575 | — | 2 | 1 | no | — |
| 103 | #575 | — | 2 | 1 | no | — |
| 104 | #575 | — | 2 | 1 | no | — |
| 105 | #575 | — | 4 | 2 | no | — |
| 106 | C2×#137 | — | 2 | 1 | no | — |
| 107 | C2×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 108 | C2×#135 | — | 2 | 1 | no | — |
| 109 | C2×#135 | — | 4 | 1 | no | — |
| 110 | C2×#135 | — | 4 | 1 | no | — |
| 111 | C2×#135 | — | 4 | 2 | no | — |
| 112 | C2×#135 | D4 | 1 | 1 | yes | characteristic |
| 113 | C2×#135 | C23 | 1 | 1 | yes | characteristic |
| 114 | C2×#135 | C23 | 1 | 1 | yes | characteristic |
| 115 | C2×#135 | C23 | 1 | 1 | yes | characteristic |
| 116 | C22×Q16 | C23 | 1 | 1 | yes | characteristic |
| 117 | C22×SD16 | — | 2 | 1 | no | — |
| 118 | C22×D8 | C23 | 1 | 1 | yes | characteristic |
| 119 | C2×#131 | — | 2 | 1 | no | — |
| 120 | C2×#131 | C23 | 1 | 1 | yes | characteristic |
| 121 | C2×#131 | C23 | 1 | 1 | yes | characteristic |
| 122 | #536 | — | 2 | 1 | no | — |
| 123 | #535 | — | 2 | 1 | no | — |
| 124 | #532 | — | 2 | 1 | no | — |
| 125 | C2×#124 | — | 2 | 1 | no | — |
| 126 | #510 | — | 2 | 2 | no | — |
| 127 | #510 | — | 2 | 2 | no | — |
| 128 | #510 | — | 2 | 2 | no | — |
| 129 | #510 | — | 2 | 2 | no | — |
| 130 | #510 | — | 4 | 1 | no | — |
| 131 | #510 | — | 4 | 1 | no | — |
| 132 | #509 | — | 2 | 2 | no | — |
| 133 | #509 | — | 2 | 2 | no | — |
| 134 | #509 | — | 2 | 2 | no | — |
| 135 | #509 | — | 2 | 2 | no | — |
| 136 | #509 | — | 4 | 1 | no | — |
| 137 | #509 | — | 4 | 1 | no | — |
| 138 | C2×Q32 | — | 2 | 1 | no | — |
| 139 | C2×Q32 | — | 2 | 1 | no | — |
| 140 | C2×Q32 | — | 2 | 1 | no | — |
| 141 | C2×SD32 | — | 2 | 1 | no | — |
| 142 | C2×SD32 | — | 2 | 1 | no | — |
| 143 | C2×SD32 | — | 2 | 1 | no | — |
| 144 | C2×SD32 | — | 2 | 1 | no | — |
| 145 | C2×SD32 | — | 2 | 1 | no | — |
| 146 | C2×SD32 | — | 2 | 1 | no | — |
| 147 | C2×D16 | — | 2 | 1 | no | — |
| 148 | C2×D16 | — | 2 | 1 | no | — |
| 149 | C2×D16 | — | 2 | 1 | no | — |
| 150 | C2×M32 | C23 | 1 | 1 | yes | characteristic |
| 151 | C2×M32 | C23 | 1 | 1 | yes | characteristic |
| 152 | C2×M32 | C23 | 1 | 1 | yes | characteristic |
| 153 | C2×M32 | C23 | 1 | 1 | yes | characteristic |
| 154 | #497 | — | 4 | 1 | no | — |
| 155 | #496 | — | 4 | 1 | no | — |
| 156 | #495 | — | 2 | 1 | no | — |
| 157 | #495 | — | 2 | 1 | no | — |
| 158 | #495 | — | 2 | 1 | no | — |
| 159 | #495 | — | 2 | 1 | no | — |
| 160 | #495 | — | 2 | 1 | no | — |
| 161 | #495 | — | 4 | 1 | no | — |
| 162 | #495 | D4 | 1 | 1 | yes | characteristic, complemented |
| 163 | #495 | D4 | 1 | 1 | yes | characteristic, complemented |
| 164 | #494 | D4 | 1 | 1 | yes | characteristic, complemented |
| 165 | #493 | D4 | 1 | 1 | yes | characteristic, complemented |
| 166 | #492 | — | 2 | 1 | no | — |
| 167 | #492 | — | 4 | 1 | no | — |
| 168 | #473 | — | 2 | 2 | no | — |
| 169 | #473 | — | 2 | 1 | no | — |
| 170 | #473 | — | 2 | 1 | no | — |
| 171 | #473 | — | 2 | 2 | no | — |
| 172 | #473 | — | 4 | 1 | no | — |
| 173 | #472 | — | 2 | 2 | no | — |
| 174 | #472 | — | 2 | 1 | no | — |
| 175 | #472 | — | 2 | 1 | no | — |
| 176 | #472 | — | 2 | 2 | no | — |
| 177 | #472 | — | 4 | 1 | no | — |
| 178 | #471 | — | 2 | 2 | no | — |
| 179 | #471 | — | 2 | 2 | no | — |
| 180 | #471 | — | 2 | 2 | no | — |
| 181 | #471 | — | 2 | 2 | no | — |
| 182 | #470 | — | 2 | 2 | no | — |
| 183 | #469 | — | 2 | 2 | no | — |
| 184 | #467 | — | 4 | 1 | no | — |
| 185 | #466 | — | 4 | 1 | no | — |
| 186 | #456 | — | 2 | 2 | no | — |
| 187 | #456 | — | 2 | 2 | no | — |
| 188 | #455 | — | 2 | 2 | no | — |
| 189 | #455 | — | 2 | 2 | no | — |
| 190 | #454 | — | 2 | 2 | no | — |
| 191 | #454 | — | 2 | 2 | no | — |
| 192 | #453 | — | 2 | 2 | no | — |
| 193 | #453 | — | 2 | 2 | no | — |
| 194 | #443 | — | 2 | 1 | no | — |
| 195 | #443 | — | 2 | 1 | no | — |
| 196 | #443 | — | 2 | 1 | no | — |
| 197 | #443 | — | 2 | 1 | no | — |
| 198 | #443 | — | 2 | 1 | no | — |
| 199 | #443 | — | 2 | 1 | no | — |
| 200 | #443 | D4 | 1 | 2 | yes | complemented |
| 201 | #443 | D4 | 1 | 2 | yes | complemented |
| 202 | C2×#108 | D4 | 1 | 1 | yes | characteristic |
| 203 | C2×#108 | C23 | 1 | 1 | yes | characteristic |
| 204 | C2×#108 | C23 | 1 | 1 | yes | characteristic |
| 205 | #427 | C23 | 1 | 1 | yes | characteristic |
| 206 | C2×#104 | — | 2 | 1 | no | — |
| 207 | C2×#104 | D4 | 1 | 1 | yes | characteristic |
| 208 | C2×#104 | D4 | 1 | 1 | yes | characteristic |
| 209 | #419 | — | 2 | 1 | no | — |
| 210 | #418 | — | 2 | 1 | no | — |
| 211 | #413 | — | 2 | 1 | no | — |
| 212 | #413 | — | 2 | 1 | no | — |
| 213 | C2×#101 | — | 2 | 1 | no | — |
| 214 | C2×#100 | — | 2 | 1 | no | — |
| 215 | #405 | — | 2 | 1 | no | — |
| 216 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 217 | #364 | — | 2 | 1 | no | — |
| 218 | #364 | — | 2 | 1 | no | — |
| 219 | #362 | — | 2 | 2 | no | — |
| 220 | #362 | D4 | 1 | 2 | yes | complemented |
| 221 | #361 | — | 2 | 2 | no | — |
| 222 | #361 | D4 | 1 | 2 | yes | complemented |
| 223 | #360 | — | 2 | 2 | no | — |
| 224 | #360 | — | 2 | 2 | no | — |
| 225 | #360 | D4 | 1 | 4 | yes | complemented |
| 226 | #359 | — | 2 | 2 | no | — |
| 227 | #359 | — | 2 | 2 | no | — |
| 228 | #350 | — | 2 | 2 | no | — |
| 229 | #350 | — | 2 | 2 | no | — |
| 230 | #349 | — | 2 | 2 | no | — |
| 231 | #349 | — | 2 | 2 | no | — |
| 232 | #346 | — | 2 | 1 | no | — |
| 233 | C4×C16 | — | 2 | 1 | no | — |
| 234 | #339 | — | 2 | 1 | no | — |
| 235 | 2−1+4 | — | 2 | 2 | no | — |
| 236 | 2−1+4 | — | 2 | 2 | no | — |
| 237 | 2−1+4 | — | 4 | 1 | no | — |
| 238 | 2−1+4 | — | 4 | 1 | no | — |
| 239 | 2−1+4 | — | 4 | 1 | no | — |
| 240 | 2−1+4 | — | 4 | 1 | no | — |
| 241 | H(5,𝔽2) | — | 2 | 2 | no | — |
| 242 | H(5,𝔽2) | — | 2 | 2 | no | — |
| 243 | H(5,𝔽2) | — | 4 | 1 | no | — |
| 244 | H(5,𝔽2) | — | 4 | 1 | no | — |
| 245 | H(5,𝔽2) | — | 4 | 1 | no | — |
| 246 | H(5,𝔽2) | — | 4 | 1 | no | — |
| 247 | H(5,𝔽2) | — | 8 | 1 | no | — |
| 248 | H(5,𝔽2) | — | 8 | 1 | no | — |
| 249 | C2×#41 | — | 2 | 1 | no | — |
| 250 | C2×#41 | — | 2 | 1 | no | — |
| 251 | C2×#41 | — | 2 | 1 | no | — |
| 252 | C2×#41 | — | 4 | 2 | no | — |
| 253 | C2×#41 | — | 4 | 2 | no | — |
| 254 | C2×#41 | — | 4 | 2 | no | — |
| 255 | C2×#41 | — | 4 | 2 | no | — |
| 256 | C2×#41 | — | 8 | 1 | no | — |
| 257 | C2×#41 | — | 8 | 1 | no | — |
| 258 | C2×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 259 | C2×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 260 | C22×Q8 | — | 2 | 1 | no | — |
| 261 | C22×D4 | — | 2 | 1 | no | — |
| 262 | #137 | — | 2 | 2 | no | — |
| 263 | #137 | — | 2 | 2 | no | — |
| 264 | #137 | — | 2 | 2 | no | — |
| 265 | #137 | — | 2 | 2 | no | — |
| 266 | #137 | — | 4 | 1 | no | — |
| 267 | #137 | — | 4 | 1 | no | — |
| 268 | #137 | — | 4 | 2 | no | — |
| 269 | #137 | — | 4 | 2 | no | — |
| 270 | #137 | — | 4 | 2 | no | — |
| 271 | #137 | — | 4 | 2 | no | — |
| 272 | #137 | — | 4 | 2 | no | — |
| 273 | #137 | — | 4 | 2 | no | — |
| 274 | #137 | — | 4 | 2 | no | — |
| 275 | #137 | — | 4 | 1 | no | — |
| 276 | #137 | — | 4 | 1 | no | — |
| 277 | #137 | — | 4 | 2 | no | — |
| 278 | #137 | — | 4 | 2 | no | — |
| 279 | #137 | — | 8 | 1 | no | — |
| 280 | AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 281 | AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 282 | AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 283 | AGL(1,ℤ/8) | — | 2 | 2 | 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) | — | 4 | 2 | no | — |
| 288 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 289 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 290 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 291 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 292 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 293 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 294 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 295 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 296 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 297 | AGL(1,ℤ/8) | — | 8 | 1 | no | — |
| 298 | #135 | — | 2 | 1 | no | — |
| 299 | #135 | — | 2 | 1 | no | — |
| 300 | #135 | — | 2 | 1 | no | — |
| 301 | #135 | — | 2 | 1 | no | — |
| 302 | #135 | — | 2 | 1 | no | — |
| 303 | #135 | — | 2 | 1 | no | — |
| 304 | #135 | — | 2 | 1 | no | — |
| 305 | #135 | — | 2 | 1 | no | — |
| 306 | #135 | — | 2 | 1 | no | — |
| 307 | #135 | — | 2 | 1 | no | — |
| 308 | #135 | — | 2 | 1 | no | — |
| 309 | #135 | — | 2 | 1 | no | — |
| 310 | #135 | — | 2 | 1 | no | — |
| 311 | #135 | — | 2 | 1 | no | — |
| 312 | #135 | — | 4 | 2 | no | — |
| 313 | #135 | — | 4 | 2 | no | — |
| 314 | #135 | — | 4 | 1 | no | — |
| 315 | #135 | — | 4 | 1 | no | — |
| 316 | #135 | — | 4 | 1 | no | — |
| 317 | #135 | — | 4 | 1 | no | — |
| 318 | #135 | — | 4 | 2 | no | — |
| 319 | #135 | — | 4 | 2 | no | — |
| 320 | #135 | — | 4 | 2 | no | — |
| 321 | #135 | — | 4 | 2 | no | — |
| 322 | #135 | — | 4 | 2 | no | — |
| 323 | #135 | — | 4 | 2 | no | — |
| 324 | #135 | — | 4 | 2 | no | — |
| 325 | #135 | — | 4 | 2 | no | — |
| 326 | #135 | — | 4 | 1 | no | — |
| 327 | #135 | — | 4 | 1 | no | — |
| 328 | #135 | — | 4 | 1 | no | — |
| 329 | #135 | — | 4 | 1 | no | — |
| 330 | #135 | C2×D4 | 1 | 2 | yes | — |
| 331 | #135 | C2×D4 | 1 | 2 | yes | — |
| 332 | C2×Q16 | — | 2 | 1 | no | — |
| 333 | C2×Q16 | — | 2 | 1 | no | — |
| 334 | C2×Q16 | — | 2 | 1 | no | — |
| 335 | C2×Q16 | — | 2 | 1 | no | — |
| 336 | C2×Q16 | — | 2 | 1 | no | — |
| 337 | C2×Q16 | — | 2 | 1 | no | — |
| 338 | C2×Q16 | — | 2 | 1 | no | — |
| 339 | C2×Q16 | — | 4 | 1 | no | — |
| 340 | C2×Q16 | — | 4 | 1 | no | — |
| 341 | C2×Q16 | — | 4 | 2 | no | — |
| 342 | C2×Q16 | — | 4 | 1 | no | — |
| 343 | C2×Q16 | D8 | 1 | 1 | yes | characteristic |
| 344 | C2×Q16 | C2×D4 | 1 | 1 | yes | characteristic |
| 345 | C2×Q16 | C2×D4 | 1 | 1 | yes | characteristic |
| 346 | C2×Q16 | C2×D4 | 1 | 1 | yes | characteristic |
| 347 | C2×SD16 | — | 2 | 1 | no | — |
| 348 | C2×SD16 | — | 2 | 1 | no | — |
| 349 | C2×SD16 | — | 2 | 1 | no | — |
| 350 | C2×SD16 | — | 2 | 1 | no | — |
| 351 | C2×SD16 | — | 2 | 1 | no | — |
| 352 | C2×SD16 | — | 4 | 2 | no | — |
| 353 | C2×SD16 | — | 4 | 2 | no | — |
| 354 | C2×SD16 | — | 4 | 2 | no | — |
| 355 | C2×SD16 | — | 4 | 2 | no | — |
| 356 | C2×SD16 | — | 4 | 1 | no | — |
| 357 | C2×SD16 | — | 4 | 1 | no | — |
| 358 | C2×SD16 | — | 4 | 1 | no | — |
| 359 | C2×SD16 | — | 4 | 1 | no | — |
| 360 | C2×SD16 | — | 4 | 1 | no | — |
| 361 | C2×SD16 | — | 4 | 1 | no | — |
| 362 | C2×SD16 | — | 4 | 1 | no | — |
| 363 | C2×SD16 | — | 4 | 1 | no | — |
| 364 | C2×SD16 | D8 | 1 | 1 | yes | characteristic |
| 365 | C2×SD16 | D8 | 1 | 1 | yes | characteristic |
| 366 | C2×D8 | — | 2 | 1 | no | — |
| 367 | C2×D8 | — | 2 | 1 | no | — |
| 368 | C2×D8 | — | 2 | 1 | no | — |
| 369 | C2×D8 | — | 2 | 1 | no | — |
| 370 | C2×D8 | — | 2 | 1 | no | — |
| 371 | C2×D8 | — | 2 | 1 | no | — |
| 372 | C2×D8 | — | 2 | 1 | no | — |
| 373 | C2×D8 | — | 4 | 1 | no | — |
| 374 | C2×D8 | — | 4 | 1 | no | — |
| 375 | C2×D8 | — | 4 | 2 | no | — |
| 376 | C2×D8 | — | 4 | 1 | no | — |
| 377 | C2×D8 | D8 | 1 | 1 | yes | characteristic |
| 378 | C2×D8 | C2×D4 | 1 | 1 | yes | characteristic |
| 379 | C2×D8 | C2×D4 | 1 | 1 | yes | characteristic |
| 380 | C2×D8 | C2×D4 | 1 | 1 | yes | characteristic |
| 381 | #131 | — | 2 | 2 | no | — |
| 382 | #131 | — | 2 | 2 | no | — |
| 383 | #131 | — | 2 | 1 | no | — |
| 384 | #131 | — | 2 | 1 | no | — |
| 385 | #131 | — | 2 | 1 | no | — |
| 386 | #131 | — | 2 | 1 | no | — |
| 387 | #131 | — | 2 | 1 | no | — |
| 388 | #131 | — | 2 | 1 | no | — |
| 389 | #131 | — | 2 | 1 | no | — |
| 390 | #131 | — | 2 | 1 | no | — |
| 391 | #131 | — | 4 | 1 | no | — |
| 392 | #131 | — | 4 | 1 | no | — |
| 393 | C2×M16 | — | 2 | 1 | no | — |
| 394 | C2×M16 | — | 2 | 1 | no | — |
| 395 | C2×M16 | — | 2 | 1 | no | — |
| 396 | C2×M16 | — | 2 | 1 | no | — |
| 397 | C2×M16 | — | 4 | 1 | no | — |
| 398 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 399 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 400 | C22×C8 | — | 2 | 1 | no | — |
| 401 | C22×C8 | — | 2 | 1 | no | — |
| 402 | C22×C8 | — | 4 | 1 | no | — |
| 403 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 404 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 405 | C4⋊Q8 | — | 2 | 1 | no | — |
| 406 | C4⋊Q8 | — | 4 | 1 | no | — |
| 407 | #127 | — | 2 | 1 | no | — |
| 408 | #127 | — | 4 | 1 | no | — |
| 409 | #124 | — | 2 | 1 | no | — |
| 410 | #124 | — | 2 | 1 | no | — |
| 411 | #124 | — | 4 | 1 | no | — |
| 412 | #124 | — | 4 | 1 | no | — |
| 413 | #124 | — | 4 | 1 | no | — |
| 414 | #124 | — | 4 | 1 | no | — |
| 415 | #124 | — | 8 | 1 | no | — |
| 416 | #123 | — | 8 | 1 | no | — |
| 417 | C22⋊Q8 | — | 4 | 2 | no | — |
| 418 | #121 | — | 4 | 2 | no | — |
| 419 | #121 | — | 8 | 1 | no | — |
| 420 | #120 | — | 8 | 1 | no | — |
| 421 | C4×D4 | — | 8 | 1 | no | — |
| 422 | #117 | — | 2 | 1 | no | — |
| 423 | C2×C22⋊C4 | — | 8 | 1 | no | — |
| 424 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 425 | Q32 | — | 4 | 2 | no | — |
| 426 | Q32 | — | 4 | 2 | no | — |
| 427 | Q32 | — | 4 | 2 | no | — |
| 428 | SD32 | — | 4 | 2 | no | — |
| 429 | SD32 | — | 4 | 2 | no | — |
| 430 | SD32 | — | 4 | 2 | no | — |
| 431 | SD32 | — | 4 | 2 | no | — |
| 432 | SD32 | — | 4 | 2 | no | — |
| 433 | SD32 | — | 4 | 2 | no | — |
| 434 | D16 | — | 4 | 2 | no | — |
| 435 | D16 | — | 4 | 2 | no | — |
| 436 | D16 | — | 4 | 2 | no | — |
| 437 | M32 | — | 2 | 1 | no | — |
| 438 | M32 | — | 2 | 1 | no | — |
| 439 | M32 | — | 2 | 1 | no | — |
| 440 | M32 | — | 2 | 1 | no | — |
| 441 | M32 | — | 2 | 1 | no | — |
| 442 | M32 | — | 2 | 1 | no | — |
| 443 | M32 | C2×D4 | 1 | 2 | yes | — |
| 444 | M32 | C2×D4 | 1 | 2 | yes | — |
| 445 | C2×C16 | — | 2 | 1 | no | — |
| 446 | C2×C16 | — | 2 | 1 | no | — |
| 447 | C2×C16 | — | 2 | 1 | no | — |
| 448 | C2×C16 | — | 2 | 1 | no | — |
| 449 | #108 | — | 2 | 1 | no | — |
| 450 | #108 | — | 2 | 1 | no | — |
| 451 | #108 | — | 2 | 1 | no | — |
| 452 | #108 | — | 2 | 1 | no | — |
| 453 | #108 | C2×D4 | 1 | 2 | yes | — |
| 454 | #108 | C2×D4 | 1 | 2 | yes | — |
| 455 | #107 | — | 2 | 1 | no | — |
| 456 | #106 | C2×D4 | 1 | 2 | yes | — |
| 457 | #104 | — | 2 | 2 | no | — |
| 458 | #104 | — | 2 | 2 | no | — |
| 459 | #104 | — | 2 | 1 | no | — |
| 460 | #104 | — | 2 | 1 | no | — |
| 461 | #104 | — | 2 | 1 | no | — |
| 462 | #104 | — | 2 | 1 | no | — |
| 463 | #103 | — | 4 | 2 | no | — |
| 464 | #102 | — | 4 | 2 | no | — |
| 465 | #101 | — | 2 | 2 | no | — |
| 466 | #101 | — | 2 | 2 | no | — |
| 467 | #101 | — | 4 | 2 | no | — |
| 468 | #100 | — | 2 | 2 | no | — |
| 469 | #100 | — | 2 | 2 | no | — |
| 470 | #100 | — | 4 | 2 | no | — |
| 471 | #97 | — | 4 | 1 | no | — |
| 472 | C4×C8 | — | 4 | 1 | no | — |
| 473 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 474 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 475 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 476 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 477 | C24 | — | 4 | 1 | no | — |
| 478 | #41 | — | 2 | 1 | no | — |
| 479 | #41 | — | 2 | 1 | no | — |
| 480 | #41 | — | 2 | 2 | no | — |
| 481 | #41 | — | 2 | 1 | no | — |
| 482 | #41 | — | 2 | 1 | no | — |
| 483 | #41 | — | 2 | 2 | no | — |
| 484 | #41 | — | 2 | 1 | no | — |
| 485 | #41 | — | 2 | 1 | no | — |
| 486 | #41 | — | 2 | 1 | no | — |
| 487 | #41 | — | 2 | 1 | no | — |
| 488 | #41 | — | 4 | 1 | no | — |
| 489 | #41 | — | 4 | 1 | no | — |
| 490 | #41 | — | 4 | 2 | no | — |
| 491 | #41 | — | 4 | 2 | no | — |
| 492 | #41 | — | 4 | 2 | no | — |
| 493 | #41 | — | 4 | 2 | no | — |
| 494 | #41 | — | 4 | 2 | no | — |
| 495 | #41 | — | 4 | 2 | no | — |
| 496 | #41 | — | 4 | 2 | no | — |
| 497 | #41 | — | 4 | 2 | no | — |
| 498 | #41 | — | 4 | 1 | no | — |
| 499 | #41 | — | 4 | 1 | no | — |
| 500 | #41 | — | 4 | 1 | no | — |
| 501 | #41 | — | 4 | 1 | no | — |
| 502 | #41 | — | 4 | 1 | no | — |
| 503 | #41 | — | 4 | 1 | no | — |
| 504 | #41 | — | 4 | 1 | no | — |
| 505 | #41 | — | 4 | 1 | no | — |
| 506 | #41 | — | 8 | 2 | no | — |
| 507 | #41 | — | 8 | 2 | no | — |
| 508 | #41 | — | 8 | 2 | no | — |
| 509 | #41 | — | 8 | 2 | no | — |
| 510 | #41 | — | 8 | 2 | no | — |
| 511 | #41 | — | 8 | 2 | no | — |
| 512 | #41 | — | 8 | 2 | no | — |
| 513 | #41 | — | 8 | 2 | no | — |
| 514 | #41 | — | 8 | 1 | no | — |
| 515 | #41 | — | 8 | 1 | no | — |
| 516 | #41 | — | 8 | 1 | no | — |
| 517 | #41 | — | 8 | 1 | no | — |
| 518 | C2×Q8 | — | 2 | 1 | no | — |
| 519 | C2×Q8 | — | 2 | 1 | no | — |
| 520 | C2×Q8 | — | 2 | 1 | no | — |
| 521 | C2×Q8 | — | 4 | 2 | no | — |
| 522 | C2×Q8 | — | 4 | 2 | no | — |
| 523 | C2×Q8 | — | 4 | 2 | no | — |
| 524 | C2×Q8 | — | 4 | 2 | no | — |
| 525 | C2×Q8 | — | 4 | 1 | no | — |
| 526 | C2×Q8 | — | 4 | 1 | no | — |
| 527 | C2×Q8 | — | 4 | 1 | no | — |
| 528 | C2×Q8 | — | 4 | 1 | no | — |
| 529 | C2×Q8 | — | 4 | 1 | no | — |
| 530 | C2×Q8 | — | 4 | 1 | no | — |
| 531 | C2×Q8 | — | 8 | 1 | no | — |
| 532 | C2×Q8 | — | 8 | 1 | no | — |
| 533 | C2×Q8 | C2×D8 | 1 | 1 | yes | characteristic |
| 534 | C2×Q8 | C2×D8 | 1 | 1 | yes | characteristic |
| 535 | C2×D4 | — | 2 | 1 | no | — |
| 536 | C2×D4 | — | 2 | 1 | no | — |
| 537 | C2×D4 | — | 2 | 1 | no | — |
| 538 | C2×D4 | — | 2 | 1 | no | — |
| 539 | C2×D4 | — | 2 | 1 | no | — |
| 540 | C2×D4 | — | 4 | 2 | no | — |
| 541 | C2×D4 | — | 4 | 2 | no | — |
| 542 | C2×D4 | — | 4 | 2 | no | — |
| 543 | C2×D4 | — | 4 | 2 | no | — |
| 544 | C2×D4 | — | 4 | 1 | no | — |
| 545 | C2×D4 | — | 4 | 1 | no | — |
| 546 | C2×D4 | — | 4 | 1 | no | — |
| 547 | C2×D4 | — | 4 | 1 | no | — |
| 548 | C2×D4 | — | 4 | 1 | no | — |
| 549 | C2×D4 | — | 4 | 1 | no | — |
| 550 | C2×D4 | — | 4 | 1 | no | — |
| 551 | C2×D4 | — | 4 | 1 | no | — |
| 552 | C2×D4 | — | 4 | 1 | no | — |
| 553 | C2×D4 | — | 8 | 1 | no | — |
| 554 | C2×D4 | — | 8 | 2 | no | — |
| 555 | C2×D4 | — | 8 | 1 | no | — |
| 556 | C2×D4 | — | 8 | 1 | no | — |
| 557 | C2×D4 | — | 8 | 2 | no | — |
| 558 | C2×D4 | — | 8 | 2 | no | — |
| 559 | C2×D4 | — | 8 | 2 | no | — |
| 560 | C2×D4 | — | 8 | 2 | no | — |
| 561 | C2×D4 | — | 8 | 2 | no | — |
| 562 | C2×D4 | — | 8 | 2 | no | — |
| 563 | C2×D4 | C2×D8 | 1 | 1 | yes | characteristic |
| 564 | C2×D4 | C2×D8 | 1 | 1 | yes | characteristic |
| 565 | C22×C4 | — | 2 | 1 | no | — |
| 566 | C22×C4 | — | 2 | 1 | no | — |
| 567 | C22×C4 | — | 2 | 1 | no | — |
| 568 | C22×C4 | — | 4 | 1 | no | — |
| 569 | C22×C4 | — | 4 | 1 | no | — |
| 570 | C22×C4 | — | 4 | 1 | no | — |
| 571 | C22×C4 | — | 4 | 1 | no | — |
| 572 | C22×C4 | — | 8 | 2 | no | — |
| 573 | C22×C4 | — | 8 | 2 | no | — |
| 574 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 575 | Q16 | — | 2 | 1 | no | — |
| 576 | Q16 | — | 2 | 1 | no | — |
| 577 | Q16 | — | 2 | 1 | no | — |
| 578 | Q16 | — | 2 | 1 | no | — |
| 579 | Q16 | — | 2 | 1 | no | — |
| 580 | Q16 | — | 2 | 1 | no | — |
| 581 | Q16 | — | 2 | 1 | no | — |
| 582 | Q16 | — | 4 | 2 | no | — |
| 583 | Q16 | — | 4 | 2 | no | — |
| 584 | Q16 | — | 4 | 2 | no | — |
| 585 | Q16 | — | 4 | 2 | no | — |
| 586 | Q16 | — | 4 | 1 | no | — |
| 587 | Q16 | — | 4 | 1 | no | — |
| 588 | Q16 | — | 4 | 1 | no | — |
| 589 | Q16 | — | 4 | 1 | no | — |
| 590 | Q16 | — | 4 | 1 | no | — |
| 591 | Q16 | — | 4 | 1 | no | — |
| 592 | Q16 | — | 8 | 2 | no | — |
| 593 | Q16 | #127 | 1 | 2 | yes | — |
| 594 | SD16 | — | 2 | 2 | no | — |
| 595 | SD16 | — | 2 | 2 | no | — |
| 596 | SD16 | — | 2 | 1 | no | — |
| 597 | SD16 | — | 2 | 1 | no | — |
| 598 | SD16 | — | 2 | 1 | no | — |
| 599 | SD16 | — | 2 | 1 | no | — |
| 600 | SD16 | — | 4 | 2 | no | — |
| 601 | SD16 | — | 4 | 2 | no | — |
| 602 | SD16 | — | 4 | 2 | no | — |
| 603 | SD16 | — | 4 | 2 | no | — |
| 604 | SD16 | — | 4 | 2 | no | — |
| 605 | SD16 | — | 4 | 2 | no | — |
| 606 | SD16 | — | 4 | 2 | no | — |
| 607 | SD16 | — | 4 | 2 | no | — |
| 608 | SD16 | — | 4 | 1 | no | — |
| 609 | SD16 | — | 4 | 1 | no | — |
| 610 | SD16 | — | 4 | 1 | no | — |
| 611 | SD16 | — | 4 | 1 | no | — |
| 612 | SD16 | — | 4 | 1 | no | — |
| 613 | SD16 | — | 4 | 1 | no | — |
| 614 | SD16 | — | 4 | 1 | no | — |
| 615 | SD16 | — | 4 | 1 | no | — |
| 616 | SD16 | — | 8 | 2 | no | — |
| 617 | SD16 | — | 8 | 2 | no | — |
| 618 | SD16 | — | 8 | 1 | no | — |
| 619 | SD16 | — | 8 | 1 | no | — |
| 620 | SD16 | — | 8 | 1 | no | — |
| 621 | SD16 | — | 8 | 1 | no | — |
| 622 | D8 | — | 2 | 1 | no | — |
| 623 | D8 | — | 2 | 1 | no | — |
| 624 | D8 | — | 2 | 1 | no | — |
| 625 | D8 | — | 2 | 1 | no | — |
| 626 | D8 | — | 2 | 1 | no | — |
| 627 | D8 | — | 2 | 1 | no | — |
| 628 | D8 | — | 2 | 1 | no | — |
| 629 | D8 | — | 4 | 2 | no | — |
| 630 | D8 | — | 4 | 2 | no | — |
| 631 | D8 | — | 4 | 2 | no | — |
| 632 | D8 | — | 4 | 2 | no | — |
| 633 | D8 | — | 4 | 1 | no | — |
| 634 | D8 | — | 4 | 1 | no | — |
| 635 | D8 | — | 4 | 1 | no | — |
| 636 | D8 | — | 4 | 1 | no | — |
| 637 | D8 | — | 4 | 1 | no | — |
| 638 | D8 | — | 4 | 1 | no | — |
| 639 | D8 | — | 8 | 2 | no | — |
| 640 | D8 | #127 | 1 | 2 | yes | — |
| 641 | M16 | — | 2 | 1 | no | — |
| 642 | M16 | — | 2 | 1 | no | — |
| 643 | M16 | — | 2 | 2 | no | — |
| 644 | M16 | — | 2 | 1 | no | — |
| 645 | M16 | — | 2 | 2 | no | — |
| 646 | M16 | — | 2 | 1 | no | — |
| 647 | M16 | — | 4 | 1 | no | — |
| 648 | M16 | — | 4 | 1 | no | — |
| 649 | M16 | — | 4 | 1 | no | — |
| 650 | M16 | — | 4 | 1 | no | — |
| 651 | M16 | — | 4 | 1 | no | — |
| 652 | M16 | — | 4 | 1 | no | — |
| 653 | M16 | — | 4 | 2 | no | — |
| 654 | M16 | — | 4 | 2 | no | — |
| 655 | C2×C8 | — | 2 | 1 | no | — |
| 656 | C2×C8 | — | 2 | 1 | no | — |
| 657 | C2×C8 | — | 4 | 1 | no | — |
| 658 | C2×C8 | — | 4 | 1 | no | — |
| 659 | C2×C8 | — | 4 | 1 | no | — |
| 660 | C2×C8 | — | 4 | 1 | no | — |
| 661 | C2×C8 | — | 4 | 1 | no | — |
| 662 | C2×C8 | — | 4 | 1 | no | — |
| 663 | C2×C8 | — | 4 | 2 | no | — |
| 664 | C2×C8 | — | 4 | 2 | no | — |
| 665 | C2×C8 | #120 | 1 | 1 | yes | characteristic |
| 666 | C2×C8 | #120 | 1 | 1 | yes | characteristic |
| 667 | C2×C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 668 | C2×C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 669 | C2×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 670 | C2×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 671 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 672 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 673 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 674 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 675 | C2×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 676 | C2×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 677 | C4⋊C4 | — | 2 | 2 | no | — |
| 678 | C4⋊C4 | — | 8 | 1 | no | — |
| 679 | C4⋊C4 | — | 8 | 2 | no | — |
| 680 | C22⋊C4 | — | 4 | 1 | no | — |
| 681 | C22⋊C4 | — | 8 | 1 | no | — |
| 682 | C22⋊C4 | — | 8 | 1 | no | — |
| 683 | C22⋊C4 | — | 8 | 2 | no | — |
| 684 | C22⋊C4 | — | 8 | 2 | no | — |
| 685 | C22⋊C4 | — | 8 | 2 | no | — |
| 686 | C22⋊C4 | — | 8 | 2 | no | — |
| 687 | C42 | — | 2 | 1 | no | — |
| 688 | C42 | — | 4 | 1 | no | — |
| 689 | C42 | #120 | 1 | 1 | yes | characteristic |
| 690 | C42 | #120 | 1 | 1 | yes | characteristic |
| 691 | C16 | — | 2 | 2 | no | — |
| 692 | C16 | — | 2 | 2 | no | — |
| 693 | C16 | — | 4 | 1 | no | — |
| 694 | C16 | — | 4 | 1 | no | — |
| 695 | C23 | — | 2 | 1 | no | — |
| 696 | C23 | — | 2 | 1 | no | — |
| 697 | C23 | — | 4 | 1 | no | — |
| 698 | C23 | — | 4 | 1 | no | — |
| 699 | C23 | — | 4 | 1 | no | — |
| 700 | C23 | — | 8 | 2 | no | — |
| 701 | C23 | — | 8 | 2 | no | — |
| 702 | C23 | — | 8 | 1 | no | — |
| 703 | C23 | — | 8 | 1 | no | — |
| 704 | C23 | — | 8 | 1 | no | — |
| 705 | C23 | — | 16 | 2 | no | — |
| 706 | C23 | #576 | 1 | 1 | yes | characteristic |
| 707 | Q8 | — | 2 | 2 | no | — |
| 708 | Q8 | — | 2 | 1 | no | — |
| 709 | Q8 | — | 2 | 1 | no | — |
| 710 | Q8 | — | 2 | 1 | no | — |
| 711 | Q8 | — | 2 | 1 | no | — |
| 712 | Q8 | — | 4 | 1 | no | — |
| 713 | Q8 | — | 4 | 1 | no | — |
| 714 | Q8 | — | 4 | 1 | no | — |
| 715 | Q8 | — | 4 | 1 | no | — |
| 716 | Q8 | — | 4 | 1 | no | — |
| 717 | Q8 | — | 8 | 2 | no | — |
| 718 | Q8 | — | 8 | 2 | no | — |
| 719 | Q8 | — | 8 | 1 | no | — |
| 720 | Q8 | — | 8 | 1 | no | — |
| 721 | Q8 | — | 8 | 1 | no | — |
| 722 | Q8 | — | 8 | 1 | no | — |
| 723 | D4 | — | 2 | 2 | no | — |
| 724 | D4 | — | 2 | 1 | no | — |
| 725 | D4 | — | 2 | 1 | no | — |
| 726 | D4 | — | 2 | 1 | no | — |
| 727 | D4 | — | 2 | 1 | no | — |
| 728 | D4 | — | 4 | 1 | no | — |
| 729 | D4 | — | 4 | 1 | no | — |
| 730 | D4 | — | 4 | 2 | no | — |
| 731 | D4 | — | 4 | 1 | no | — |
| 732 | D4 | — | 4 | 1 | no | — |
| 733 | D4 | — | 4 | 2 | no | — |
| 734 | D4 | — | 4 | 1 | no | — |
| 735 | D4 | — | 4 | 1 | no | — |
| 736 | D4 | — | 4 | 1 | no | — |
| 737 | D4 | — | 4 | 1 | no | — |
| 738 | D4 | — | 4 | 1 | no | — |
| 739 | D4 | — | 8 | 2 | no | — |
| 740 | D4 | — | 8 | 2 | no | — |
| 741 | D4 | — | 8 | 2 | no | — |
| 742 | D4 | — | 8 | 2 | no | — |
| 743 | D4 | — | 8 | 2 | no | — |
| 744 | D4 | — | 8 | 2 | no | — |
| 745 | D4 | — | 8 | 1 | no | — |
| 746 | D4 | — | 8 | 1 | no | — |
| 747 | D4 | — | 8 | 1 | no | — |
| 748 | D4 | — | 8 | 1 | no | — |
| 749 | D4 | — | 8 | 1 | no | — |
| 750 | D4 | — | 8 | 1 | no | — |
| 751 | D4 | — | 8 | 1 | no | — |
| 752 | D4 | — | 8 | 1 | no | — |
| 753 | D4 | — | 16 | 2 | no | — |
| 754 | D4 | — | 32 | 2 | no | — |
| 755 | C2×C4 | — | 2 | 1 | no | — |
| 756 | C2×C4 | — | 2 | 1 | no | — |
| 757 | C2×C4 | — | 2 | 1 | no | — |
| 758 | C2×C4 | — | 2 | 1 | no | — |
| 759 | C2×C4 | — | 4 | 1 | no | — |
| 760 | C2×C4 | — | 4 | 1 | no | — |
| 761 | C2×C4 | — | 4 | 1 | no | — |
| 762 | C2×C4 | — | 4 | 2 | no | — |
| 763 | C2×C4 | — | 4 | 1 | no | — |
| 764 | C2×C4 | — | 4 | 1 | no | — |
| 765 | C2×C4 | — | 4 | 2 | no | — |
| 766 | C2×C4 | — | 4 | 1 | no | — |
| 767 | C2×C4 | — | 4 | 1 | no | — |
| 768 | C2×C4 | — | 4 | 2 | no | — |
| 769 | C2×C4 | — | 8 | 1 | no | — |
| 770 | C2×C4 | — | 8 | 2 | no | — |
| 771 | C2×C4 | — | 8 | 2 | no | — |
| 772 | C2×C4 | — | 8 | 2 | no | — |
| 773 | C2×C4 | — | 8 | 2 | no | — |
| 774 | C2×C4 | — | 8 | 2 | no | — |
| 775 | C2×C4 | — | 8 | 2 | no | — |
| 776 | C2×C4 | — | 8 | 1 | no | — |
| 777 | C2×C4 | — | 8 | 1 | no | — |
| 778 | C2×C4 | — | 8 | 1 | no | — |
| 779 | C2×C4 | — | 8 | 1 | no | — |
| 780 | C2×C4 | — | 8 | 1 | no | — |
| 781 | C2×C4 | — | 8 | 1 | no | — |
| 782 | C2×C4 | — | 8 | 1 | no | — |
| 783 | C2×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 784 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 785 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 786 | C2×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 787 | C2×C4 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 788 | C2×C4 | #576 | 1 | 1 | yes | characteristic |
| 789 | C8 | — | 4 | 1 | no | — |
| 790 | C8 | — | 4 | 1 | no | — |
| 791 | C8 | — | 4 | 2 | no | — |
| 792 | C8 | — | 4 | 2 | no | — |
| 793 | C8 | #447 | 1 | 1 | yes | characteristic |
| 794 | C8 | #447 | 1 | 1 | yes | characteristic |
| 795 | C8 | #447 | 1 | 1 | yes | characteristic |
| 796 | C8 | #447 | 1 | 1 | yes | characteristic |
| 797 | C8 | C2×#127 | 1 | 1 | yes | characteristic |
| 798 | C8 | #535 | 1 | 1 | yes | characteristic |
| 799 | C8 | D42 | 1 | 1 | yes | characteristic |
| 800 | C8 | D42 | 1 | 1 | yes | characteristic |
| 801 | C22 | — | 4 | 1 | no | — |
| 802 | C22 | — | 4 | 1 | no | — |
| 803 | C22 | — | 4 | 1 | no | — |
| 804 | C22 | — | 4 | 2 | no | — |
| 805 | C22 | — | 8 | 1 | no | — |
| 806 | C22 | — | 8 | 1 | no | — |
| 807 | C22 | — | 8 | 1 | no | — |
| 808 | C22 | — | 8 | 1 | no | — |
| 809 | C22 | — | 16 | 1 | no | — |
| 810 | C22 | — | 16 | 1 | no | — |
| 811 | C22 | — | 16 | 1 | no | — |
| 812 | C22 | — | 16 | 2 | no | — |
| 813 | C22 | — | 16 | 2 | no | — |
| 814 | C22 | — | 16 | 1 | no | — |
| 815 | C22 | — | 32 | 1 | no | — |
| 816 | C22 | — | 32 | 2 | no | — |
| 817 | C22 | — | 32 | 2 | no | — |
| 818 | C22 | #3008 | 1 | 1 | yes | characteristic |
| 819 | C22 | #3274 | 1 | 1 | yes | characteristic |
| 820 | C22 | D4×D8 | 1 | 1 | yes | characteristic |
| 821 | C4 | — | 4 | 1 | no | — |
| 822 | C4 | — | 4 | 1 | no | — |
| 823 | C4 | — | 4 | 1 | no | — |
| 824 | C4 | — | 4 | 1 | no | — |
| 825 | C4 | — | 4 | 2 | no | — |
| 826 | C4 | — | 8 | 2 | no | — |
| 827 | C4 | — | 8 | 1 | no | — |
| 828 | C4 | — | 8 | 1 | no | — |
| 829 | C4 | — | 16 | 1 | no | — |
| 830 | C4 | #2433 | 1 | 1 | yes | characteristic |
| 831 | C4 | C2×#447 | 1 | 1 | yes | characteristic |
| 832 | C4 | #3274 | 1 | 1 | yes | characteristic |
| 833 | C4 | D4×D8 | 1 | 1 | yes | characteristic |
| 834 | C2 | — | 2 | 1 | no | — |
| 835 | C2 | — | 2 | 1 | no | — |
| 836 | C2 | — | 2 | 1 | no | — |
| 837 | C2 | — | 8 | 1 | no | — |
| 838 | C2 | — | 8 | 1 | no | — |
| 839 | C2 | — | 8 | 2 | no | — |
| 840 | C2 | — | 16 | 1 | no | — |
| 841 | C2 | — | 16 | 1 | no | — |
| 842 | C2 | — | 32 | 1 | no | — |
| 843 | C2 | #25757 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #25757 |
| commutator, Frattini, cosocle | C22×C8 | C24 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ C2×#443 ◁ G | |
| LECS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #61105 | C2 | semidirect |
| 2. #33719 | C2 | semidirect |
| 3. C2×#2212 | C2 | semidirect |
| 4. #33542 | C2 | semidirect |
| 5. #33541 | C2 | semidirect |
| 6. #33532 | C2 | semidirect |
| 7. #33531 | C2 | semidirect |
| 8. #28503 | C2 | semidirect |
| 9. #13324 | C2 | semidirect |
| 10. #13323 | C2 | semidirect |
| 11. #13311 | C2 | semidirect |
| 12. #13310 | C2 | semidirect |
| 13. #13259 | C2 | semidirect |
| 14. #13197 | C2 | semidirect |
| 15. #12646 | C2 | semidirect |
| 20. C2×#510 | C22 | semidirect |
| 21. C2×#510 | C22 | semidirect |
| 23. C2×#509 | C22 | semidirect |
| 24. C2×#509 | C22 | semidirect |
| 33. C2×#495 | C22 | semidirect |
| 37. C2×#473 | C22 | semidirect |
| 38. C2×#472 | C22 | semidirect |
| 39. #3059 | C22 | semidirect |
| 40. #3058 | C22 | semidirect |
| 57. C2×#364 | C22 | semidirect |
| 59. C2×#362 | C22 | semidirect |
| 60. C2×#361 | C22 | semidirect |
| 62. #2145 | C22 | semidirect |
| 63. #2145 | C22 | semidirect |
| 64. #2143 | C22 | semidirect |
| 65. #2143 | C22 | semidirect |
| 66. #2117 | C22 | semidirect |
| 67. #2117 | C22 | semidirect |
| 68. #2115 | C22 | semidirect |
| 69. #2115 | C22 | semidirect |
| 70. C4×M32 | C22 | semidirect |
| 74. #1772 | C22 | semidirect |
| 75. #1389 | C22 | semidirect |
| 76. #1388 | C22 | semidirect |
| 162. #495 | D4 | semidirect |
| 163. #495 | D4 | semidirect |
| 164. #494 | D4 | semidirect |
| 165. #493 | D4 | semidirect |
| 200. #443 | D4 | semidirect |
| 201. #443 | D4 | semidirect |
| 220. #362 | D4 | semidirect |
| 222. #361 | D4 | semidirect |
| 225. #360 | D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #61105 | 2 |
| #33719 | 2 |
| C2×#2212 | 2 |
| #33542 | 2 |
| #33541 | 2 |
| #33532 | 2 |
| #33531 | 2 |
| #28503 | 2 |
| #13324 | 2 |
| #13323 | 2 |
| #13311 | 2 |
| #13310 | 2 |
| #13259 | 2 |
| #13197 | 2 |
| #12646 | 2 |