Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1424 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 1424 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #41×S4 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#5919 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | A4×#137 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #85513 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #85499 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #85465 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #85464 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #85462 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #85460 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #85443 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | M16×S4 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #61068 | — | 3 | 1 | no | maximal, Sylow |
| 13 | A4×#41 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×Q8×A4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | #5919 | — | 2 | 1 | no | — |
| 16 | #5919 | — | 2 | 1 | no | — |
| 17 | #5919 | C22 | 1 | 2 | yes | — |
| 18 | #5919 | C22 | 1 | 2 | yes | complemented |
| 19 | #5919 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | Q8×S4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | #5914 | — | 2 | 1 | no | — |
| 22 | #5914 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | D4×S4 | — | 2 | 1 | no | — |
| 24 | D4×S4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | #5912 | — | 2 | 1 | no | — |
| 26 | #5912 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×C4⋊S4 | — | 2 | 1 | no | — |
| 28 | C2×C4⋊S4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | C2×C4×S4 | — | 2 | 1 | no | — |
| 30 | C2×C4×S4 | — | 2 | 1 | no | — |
| 31 | C2×C4×S4 | C22 | 1 | 1 | yes | characteristic |
| 32 | #5777 | — | 4 | 1 | no | maximal |
| 33 | A4×Q16 | C22 | 1 | 2 | yes | complemented |
| 34 | A4×SD16 | C22 | 1 | 2 | yes | complemented |
| 35 | A4×M16 | C22 | 1 | 1 | yes | characteristic, complemented |
| 36 | #5417 | C22 | 1 | 2 | yes | complemented |
| 37 | #5417 | C22 | 1 | 2 | yes | complemented |
| 38 | #5416 | C22 | 1 | 2 | yes | complemented |
| 39 | #5415 | C22 | 1 | 2 | yes | complemented |
| 40 | #5409 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | #5402 | C22 | 1 | 2 | yes | complemented |
| 42 | #5401 | C22 | 1 | 2 | yes | complemented |
| 43 | #5400 | C22 | 1 | 2 | yes | complemented |
| 44 | C8×S4 | C22 | 1 | 2 | yes | complemented |
| 45 | C2×#575 | — | 3 | 1 | no | — |
| 46 | C22×#137 | D3 | 1 | 1 | yes | characteristic, complemented |
| 47 | D4×#41 | — | 3 | 1 | no | — |
| 48 | C2×#548 | — | 3 | 1 | no | — |
| 49 | #3285 | — | 3 | 2 | no | — |
| 50 | #3282 | — | 3 | 2 | no | — |
| 51 | #3277 | — | 3 | 2 | no | — |
| 52 | #3275 | — | 3 | 2 | no | — |
| 53 | #3271 | — | 3 | 2 | no | — |
| 54 | #3270 | — | 3 | 2 | no | — |
| 55 | #3269 | — | 3 | 2 | no | — |
| 56 | #3265 | — | 3 | 2 | no | — |
| 57 | #3153 | — | 3 | 1 | no | — |
| 58 | #3056 | — | 3 | 1 | no | — |
| 59 | #3055 | — | 3 | 1 | no | — |
| 60 | #3040 | — | 3 | 1 | no | — |
| 61 | #3037 | — | 3 | 1 | no | — |
| 62 | #3007 | — | 3 | 1 | no | — |
| 63 | #3006 | — | 3 | 1 | no | — |
| 64 | #3005 | — | 3 | 1 | no | — |
| 65 | #3004 | — | 3 | 1 | no | — |
| 66 | C4×#137 | — | 3 | 1 | no | — |
| 67 | D4×M16 | — | 3 | 1 | no | — |
| 68 | C22×S4 | — | 2 | 1 | no | — |
| 69 | C22×S4 | — | 2 | 1 | no | — |
| 70 | C22×S4 | D4 | 1 | 1 | yes | characteristic |
| 71 | D3×#41 | — | 4 | 1 | no | — |
| 72 | C2×#239 | — | 4 | 1 | no | — |
| 73 | Q8×A4 | — | 2 | 1 | no | — |
| 74 | Q8×A4 | C23 | 1 | 1 | yes | characteristic |
| 75 | Q8×A4 | C23 | 1 | 2 | yes | — |
| 76 | D4×A4 | — | 2 | 1 | no | — |
| 77 | D4×A4 | C23 | 1 | 1 | yes | characteristic |
| 78 | C2×C4×A4 | — | 2 | 1 | no | — |
| 79 | C2×C4×A4 | — | 2 | 1 | no | — |
| 80 | C2×C4×A4 | C23 | 1 | 1 | yes | characteristic |
| 81 | GL(2,ℤ/4) | — | 2 | 1 | no | — |
| 82 | GL(2,ℤ/4) | — | 2 | 1 | no | — |
| 83 | GL(2,ℤ/4) | — | 2 | 1 | no | — |
| 84 | C2×SL(2,ℤ/4) | — | 2 | 1 | no | — |
| 85 | C2×SL(2,ℤ/4) | D4 | 1 | 1 | yes | characteristic |
| 86 | C4⋊S4 | — | 2 | 2 | no | — |
| 87 | C4⋊S4 | — | 2 | 2 | no | — |
| 88 | C4⋊S4 | — | 2 | 1 | no | — |
| 89 | C4⋊S4 | — | 2 | 1 | no | — |
| 90 | C4⋊S4 | C23 | 1 | 2 | yes | — |
| 91 | C4⋊S4 | C23 | 1 | 1 | yes | characteristic |
| 92 | C4×S4 | — | 2 | 1 | no | — |
| 93 | C4×S4 | — | 2 | 1 | no | — |
| 94 | C4×S4 | — | 2 | 1 | no | — |
| 95 | C4×S4 | — | 2 | 2 | no | — |
| 96 | C4×S4 | — | 2 | 2 | no | — |
| 97 | C4×S4 | D4 | 1 | 1 | yes | characteristic |
| 98 | C4×S4 | D4 | 1 | 1 | yes | characteristic |
| 99 | C4×S4 | C23 | 1 | 1 | yes | characteristic |
| 100 | C4×S4 | C23 | 1 | 1 | yes | characteristic |
| 101 | A4⋊Q8 | — | 2 | 1 | no | — |
| 102 | A4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 103 | C3×#137 | — | 4 | 1 | no | — |
| 104 | #949 | — | 4 | 1 | no | — |
| 105 | #942 | — | 4 | 1 | no | — |
| 106 | #919 | — | 4 | 2 | no | — |
| 107 | #918 | — | 4 | 2 | no | — |
| 108 | #916 | — | 4 | 2 | no | — |
| 109 | #914 | — | 4 | 2 | no | — |
| 110 | #908 | — | 4 | 1 | no | — |
| 111 | D3×M16 | — | 4 | 1 | no | — |
| 112 | C8×A4 | C23 | 1 | 2 | yes | — |
| 113 | A4⋊C8 | C23 | 1 | 2 | yes | — |
| 114 | C22×#41 | — | 3 | 1 | no | — |
| 115 | C22×#41 | — | 3 | 1 | no | — |
| 116 | C22×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 117 | C23×Q8 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 118 | #575 | — | 6 | 1 | no | — |
| 119 | #575 | — | 6 | 1 | no | — |
| 120 | #575 | — | 6 | 2 | no | — |
| 121 | #575 | — | 6 | 2 | no | — |
| 122 | #575 | — | 6 | 1 | no | — |
| 123 | #575 | — | 6 | 1 | no | — |
| 124 | C2×#137 | — | 3 | 1 | no | — |
| 125 | C2×#137 | — | 3 | 1 | no | — |
| 126 | C2×#137 | — | 3 | 1 | no | — |
| 127 | C2×#137 | — | 3 | 1 | no | — |
| 128 | C2×#137 | — | 3 | 2 | no | — |
| 129 | C2×#137 | — | 3 | 2 | no | — |
| 130 | C2×#137 | — | 3 | 1 | no | — |
| 131 | C2×#137 | — | 3 | 2 | no | — |
| 132 | C2×#137 | — | 3 | 1 | no | — |
| 133 | C2×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 134 | C2×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 135 | C2×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 136 | C2×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 137 | C2×#135 | — | 3 | 2 | no | — |
| 138 | C2×#135 | — | 3 | 2 | no | — |
| 139 | C22×Q16 | C2×D3 | 1 | 2 | yes | complemented |
| 140 | C22×SD16 | C2×D3 | 1 | 2 | yes | complemented |
| 141 | C22×M16 | — | 3 | 1 | no | — |
| 142 | C22×M16 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 143 | #550 | — | 3 | 1 | no | — |
| 144 | D4×Q8 | — | 3 | 1 | no | — |
| 145 | #548 | — | 3 | 2 | no | — |
| 146 | #548 | — | 3 | 2 | no | — |
| 147 | #548 | — | 3 | 1 | no | — |
| 148 | #548 | — | 3 | 2 | no | — |
| 149 | #548 | — | 3 | 2 | no | — |
| 150 | #548 | — | 3 | 1 | no | — |
| 151 | #548 | — | 6 | 1 | no | — |
| 152 | #548 | — | 6 | 1 | no | — |
| 153 | #548 | — | 6 | 1 | no | — |
| 154 | #548 | — | 6 | 1 | no | — |
| 155 | #547 | — | 3 | 1 | no | — |
| 156 | #547 | — | 6 | 1 | no | — |
| 157 | #546 | — | 3 | 1 | no | — |
| 158 | #546 | — | 3 | 1 | no | — |
| 159 | #546 | — | 6 | 1 | no | — |
| 160 | #546 | — | 6 | 1 | no | — |
| 161 | D42 | — | 3 | 1 | no | — |
| 162 | D42 | — | 6 | 1 | no | — |
| 163 | #532 | — | 3 | 1 | no | — |
| 164 | #532 | — | 6 | 1 | no | — |
| 165 | C2×#124 | — | 3 | 1 | no | — |
| 166 | C2×#124 | — | 6 | 1 | no | — |
| 167 | #525 | — | 3 | 1 | no | — |
| 168 | #525 | — | 3 | 1 | no | — |
| 169 | #525 | — | 6 | 1 | no | — |
| 170 | #525 | — | 6 | 1 | no | — |
| 171 | C2×C22⋊Q8 | — | 3 | 1 | no | — |
| 172 | C2×C22⋊Q8 | — | 6 | 1 | no | — |
| 173 | C2×#121 | — | 3 | 1 | no | — |
| 174 | C2×#121 | — | 6 | 1 | no | — |
| 175 | C4×#41 | — | 3 | 1 | no | — |
| 176 | C2×C4×Q8 | — | 3 | 1 | no | — |
| 177 | C2×C4×D4 | — | 3 | 1 | no | — |
| 178 | C2×C4×D4 | — | 6 | 1 | no | — |
| 179 | C2×C4×D4 | — | 6 | 1 | no | — |
| 180 | #497 | — | 3 | 2 | no | — |
| 181 | #496 | — | 3 | 2 | no | — |
| 182 | #495 | — | 3 | 2 | no | — |
| 183 | #495 | — | 3 | 2 | no | — |
| 184 | #470 | — | 3 | 2 | no | — |
| 185 | #469 | — | 3 | 2 | no | — |
| 186 | #468 | — | 3 | 2 | no | — |
| 187 | #468 | — | 3 | 2 | no | — |
| 188 | #467 | — | 3 | 2 | no | — |
| 189 | #466 | — | 3 | 2 | no | — |
| 190 | #465 | — | 3 | 2 | no | — |
| 191 | #465 | — | 3 | 2 | no | — |
| 192 | #464 | — | 3 | 2 | no | — |
| 193 | #464 | — | 3 | 2 | no | — |
| 194 | #464 | — | 3 | 2 | no | — |
| 195 | #464 | — | 3 | 2 | no | — |
| 196 | #463 | — | 3 | 2 | no | — |
| 197 | #463 | — | 3 | 2 | no | — |
| 198 | #462 | — | 3 | 2 | no | — |
| 199 | #460 | — | 3 | 2 | no | — |
| 200 | #452 | — | 3 | 2 | no | — |
| 201 | #452 | — | 3 | 2 | no | — |
| 202 | #452 | — | 3 | 2 | no | — |
| 203 | #452 | — | 3 | 2 | no | — |
| 204 | #451 | — | 3 | 2 | no | — |
| 205 | #451 | — | 3 | 2 | no | — |
| 206 | #451 | — | 3 | 2 | no | — |
| 207 | #450 | — | 3 | 2 | no | — |
| 208 | #449 | — | 3 | 2 | no | — |
| 209 | #449 | — | 3 | 2 | no | — |
| 210 | #449 | — | 3 | 2 | no | — |
| 211 | #449 | — | 3 | 2 | no | — |
| 212 | #448 | — | 3 | 2 | no | — |
| 213 | #448 | — | 3 | 2 | no | — |
| 214 | #448 | — | 3 | 2 | no | — |
| 215 | #447 | — | 3 | 2 | no | — |
| 216 | #441 | — | 3 | 2 | no | — |
| 217 | #440 | — | 3 | 2 | no | — |
| 218 | C4×Q16 | — | 3 | 2 | no | — |
| 219 | C4×SD16 | — | 3 | 2 | no | — |
| 220 | #436 | — | 3 | 2 | no | — |
| 221 | #435 | — | 3 | 2 | no | — |
| 222 | #435 | — | 3 | 2 | no | — |
| 223 | C8×D4 | — | 3 | 2 | no | — |
| 224 | #428 | — | 3 | 1 | no | — |
| 225 | #423 | — | 3 | 1 | no | — |
| 226 | #419 | — | 3 | 1 | no | — |
| 227 | #419 | — | 3 | 1 | no | — |
| 228 | #418 | — | 3 | 1 | no | — |
| 229 | #417 | — | 3 | 1 | no | — |
| 230 | #417 | — | 3 | 1 | no | — |
| 231 | #417 | — | 3 | 1 | no | — |
| 232 | #407 | — | 3 | 1 | no | — |
| 233 | #407 | — | 3 | 1 | no | — |
| 234 | C4×M16 | — | 3 | 1 | no | — |
| 235 | C22×A4 | — | 2 | 1 | no | — |
| 236 | C22×A4 | C2×D4 | 1 | 1 | yes | characteristic |
| 237 | C2×S4 | — | 2 | 2 | no | — |
| 238 | C2×S4 | — | 2 | 1 | no | — |
| 239 | C2×S4 | — | 4 | 1 | no | — |
| 240 | C2×S4 | — | 4 | 2 | no | — |
| 241 | C2×S4 | — | 4 | 2 | no | — |
| 242 | C2×S4 | C2×D4 | 1 | 1 | yes | characteristic |
| 243 | C2×S4 | C2×D4 | 1 | 1 | yes | characteristic |
| 244 | C3×#41 | — | 4 | 1 | no | — |
| 245 | C2×C3×Q8 | — | 4 | 1 | no | — |
| 246 | #239 | — | 4 | 2 | no | — |
| 247 | #239 | — | 4 | 2 | no | — |
| 248 | #239 | — | 4 | 1 | no | — |
| 249 | #239 | — | 8 | 1 | no | — |
| 250 | #239 | — | 8 | 1 | no | — |
| 251 | D3×Q8 | — | 4 | 1 | no | — |
| 252 | #237 | — | 4 | 1 | no | — |
| 253 | #237 | — | 8 | 1 | no | — |
| 254 | D3×D4 | — | 4 | 1 | no | — |
| 255 | D3×D4 | — | 8 | 1 | no | — |
| 256 | #235 | — | 4 | 1 | no | — |
| 257 | #235 | — | 8 | 1 | no | — |
| 258 | C2×D12 | — | 4 | 1 | no | — |
| 259 | C2×D12 | — | 8 | 1 | no | — |
| 260 | C2×C4×D3 | — | 4 | 1 | no | — |
| 261 | C2×C4×D3 | — | 8 | 1 | no | — |
| 262 | C2×C4×D3 | — | 8 | 1 | no | — |
| 263 | C4×A4 | — | 2 | 1 | no | — |
| 264 | C4×A4 | — | 2 | 2 | no | — |
| 265 | C4×A4 | C2×D4 | 1 | 1 | yes | characteristic |
| 266 | C4×A4 | C24 | 1 | 1 | yes | characteristic |
| 267 | SL(2,ℤ/4) | — | 2 | 1 | no | — |
| 268 | SL(2,ℤ/4) | C2×D4 | 1 | 1 | yes | characteristic |
| 269 | SL(2,ℤ/4) | C2×D4 | 1 | 1 | yes | characteristic |
| 270 | C3×Q16 | — | 4 | 2 | no | — |
| 271 | C3×SD16 | — | 4 | 2 | no | — |
| 272 | C3×M16 | — | 4 | 1 | no | — |
| 273 | #216 | — | 4 | 2 | no | — |
| 274 | #215 | — | 4 | 2 | no | — |
| 275 | #215 | — | 4 | 2 | no | — |
| 276 | #213 | — | 4 | 2 | no | — |
| 277 | #208 | — | 4 | 1 | no | — |
| 278 | D24 | — | 4 | 2 | no | — |
| 279 | #204 | — | 4 | 2 | no | — |
| 280 | ΓL(1,𝔽25) | — | 4 | 2 | no | — |
| 281 | D3×C8 | — | 4 | 2 | no | — |
| 282 | C2×#41 | — | 3 | 1 | no | — |
| 283 | C2×#41 | — | 3 | 1 | no | — |
| 284 | C2×#41 | — | 3 | 1 | no | — |
| 285 | C2×#41 | — | 3 | 1 | no | — |
| 286 | C2×#41 | — | 3 | 1 | no | — |
| 287 | C2×#41 | — | 3 | 1 | no | — |
| 288 | C2×#41 | — | 3 | 2 | no | — |
| 289 | C2×#41 | — | 3 | 2 | no | — |
| 290 | C2×#41 | — | 3 | 1 | no | — |
| 291 | C2×#41 | — | 6 | 1 | no | — |
| 292 | C2×#41 | — | 6 | 1 | no | — |
| 293 | C2×#41 | — | 6 | 1 | no | — |
| 294 | C2×#41 | — | 6 | 1 | no | — |
| 295 | C2×#41 | — | 6 | 1 | no | — |
| 296 | C2×#41 | — | 6 | 1 | no | — |
| 297 | C2×#41 | — | 6 | 2 | no | — |
| 298 | C2×#41 | — | 6 | 1 | no | — |
| 299 | C2×#41 | — | 6 | 1 | no | — |
| 300 | C2×#41 | — | 6 | 1 | no | — |
| 301 | C2×#41 | — | 6 | 1 | no | — |
| 302 | C2×#41 | — | 6 | 1 | no | — |
| 303 | C2×#41 | — | 6 | 1 | no | — |
| 304 | C2×#41 | — | 12 | 1 | no | — |
| 305 | C2×#41 | — | 12 | 1 | no | — |
| 306 | C2×#41 | — | 12 | 1 | no | — |
| 307 | C2×#41 | — | 12 | 1 | no | — |
| 308 | C22×Q8 | — | 2 | 1 | no | — |
| 309 | C22×Q8 | — | 3 | 1 | no | — |
| 310 | C22×Q8 | — | 3 | 1 | no | — |
| 311 | C22×Q8 | — | 3 | 2 | no | — |
| 312 | C22×Q8 | — | 3 | 1 | no | — |
| 313 | C22×Q8 | — | 6 | 1 | no | — |
| 314 | C22×Q8 | — | 6 | 1 | no | — |
| 315 | C22×Q8 | C22×D3 | 1 | 2 | yes | — |
| 316 | C22×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 317 | C22×D4 | — | 2 | 1 | no | — |
| 318 | C22×D4 | — | 3 | 1 | no | — |
| 319 | C22×D4 | — | 3 | 1 | no | — |
| 320 | C22×D4 | — | 3 | 1 | no | — |
| 321 | C22×D4 | — | 6 | 1 | no | — |
| 322 | C22×D4 | — | 6 | 1 | no | — |
| 323 | C22×D4 | — | 6 | 1 | no | — |
| 324 | C22×D4 | — | 6 | 1 | no | — |
| 325 | C22×D4 | C22×D3 | 1 | 1 | yes | characteristic |
| 326 | C23×C4 | — | 2 | 1 | no | — |
| 327 | C23×C4 | — | 2 | 1 | no | — |
| 328 | C23×C4 | — | 3 | 1 | no | — |
| 329 | C23×C4 | — | 6 | 1 | no | — |
| 330 | C23×C4 | — | 6 | 1 | no | — |
| 331 | C23×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 332 | #137 | — | 3 | 1 | no | — |
| 333 | #137 | — | 3 | 1 | no | — |
| 334 | #137 | — | 3 | 2 | no | — |
| 335 | #137 | — | 3 | 2 | no | — |
| 336 | #137 | — | 3 | 1 | no | — |
| 337 | #137 | — | 6 | 2 | no | — |
| 338 | #137 | — | 6 | 1 | no | — |
| 339 | #137 | — | 6 | 1 | no | — |
| 340 | #137 | — | 6 | 2 | no | — |
| 341 | #137 | — | 6 | 1 | no | — |
| 342 | #137 | — | 6 | 2 | no | — |
| 343 | #137 | — | 6 | 2 | no | — |
| 344 | #137 | — | 6 | 2 | no | — |
| 345 | #137 | — | 6 | 2 | no | — |
| 346 | #137 | — | 6 | 1 | no | — |
| 347 | #137 | — | 6 | 1 | no | — |
| 348 | #137 | — | 6 | 2 | no | — |
| 349 | #137 | — | 12 | 1 | no | — |
| 350 | #137 | — | 12 | 1 | no | — |
| 351 | #137 | S4 | 1 | 1 | yes | characteristic, complemented |
| 352 | AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 353 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 354 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 355 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 356 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 357 | AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 358 | AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 359 | AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 360 | AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 361 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 362 | AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 363 | AGL(1,ℤ/8) | — | 12 | 1 | no | — |
| 364 | AGL(1,ℤ/8) | — | 12 | 1 | no | — |
| 365 | #135 | — | 6 | 2 | no | — |
| 366 | #135 | — | 6 | 2 | no | — |
| 367 | #135 | — | 6 | 2 | no | — |
| 368 | #135 | — | 6 | 2 | no | — |
| 369 | #135 | — | 6 | 2 | no | — |
| 370 | #135 | — | 6 | 2 | no | — |
| 371 | #135 | — | 6 | 2 | no | — |
| 372 | #135 | — | 6 | 2 | no | — |
| 373 | C2×Q16 | — | 3 | 2 | no | — |
| 374 | C2×Q16 | — | 3 | 2 | no | — |
| 375 | C2×Q16 | — | 3 | 2 | no | — |
| 376 | C2×Q16 | — | 3 | 2 | no | — |
| 377 | C2×Q16 | — | 3 | 2 | no | — |
| 378 | C2×Q16 | — | 3 | 2 | no | — |
| 379 | C2×SD16 | — | 3 | 2 | no | — |
| 380 | C2×SD16 | — | 3 | 2 | no | — |
| 381 | C2×SD16 | — | 3 | 2 | no | — |
| 382 | C2×SD16 | — | 3 | 2 | no | — |
| 383 | C2×SD16 | — | 3 | 2 | no | — |
| 384 | C2×SD16 | — | 3 | 2 | no | — |
| 385 | C2×SD16 | — | 3 | 2 | no | — |
| 386 | C2×SD16 | — | 3 | 2 | no | — |
| 387 | C2×SD16 | — | 3 | 2 | no | — |
| 388 | C2×D8 | — | 3 | 2 | no | — |
| 389 | C2×D8 | — | 3 | 2 | no | — |
| 390 | C2×D8 | — | 3 | 2 | no | — |
| 391 | C2×M16 | — | 3 | 1 | no | — |
| 392 | C2×M16 | — | 3 | 1 | no | — |
| 393 | C2×M16 | — | 3 | 2 | no | — |
| 394 | C2×M16 | — | 3 | 1 | no | — |
| 395 | C2×M16 | — | 3 | 2 | no | — |
| 396 | C2×M16 | — | 3 | 1 | no | — |
| 397 | C2×M16 | — | 6 | 1 | no | — |
| 398 | C2×M16 | — | 6 | 2 | no | — |
| 399 | C2×M16 | — | 6 | 1 | no | — |
| 400 | C22×C8 | — | 3 | 2 | no | — |
| 401 | C22×C8 | C22×D3 | 1 | 2 | yes | — |
| 402 | C4⋊Q8 | — | 3 | 1 | no | — |
| 403 | C4⋊Q8 | — | 6 | 1 | no | — |
| 404 | #127 | — | 3 | 1 | no | — |
| 405 | #127 | — | 6 | 1 | no | — |
| 406 | #124 | — | 3 | 2 | no | — |
| 407 | #124 | — | 3 | 2 | no | — |
| 408 | #124 | — | 3 | 1 | no | — |
| 409 | #124 | — | 3 | 1 | no | — |
| 410 | #124 | — | 6 | 1 | no | — |
| 411 | #124 | — | 6 | 1 | no | — |
| 412 | #124 | — | 6 | 2 | no | — |
| 413 | #124 | — | 6 | 2 | no | — |
| 414 | #124 | — | 6 | 2 | no | — |
| 415 | #124 | — | 6 | 2 | no | — |
| 416 | #124 | — | 6 | 1 | no | — |
| 417 | #124 | — | 6 | 1 | no | — |
| 418 | #123 | — | 6 | 1 | no | — |
| 419 | #123 | — | 6 | 1 | no | — |
| 420 | #123 | — | 6 | 1 | no | — |
| 421 | #123 | — | 6 | 1 | no | — |
| 422 | #123 | — | 6 | 1 | no | — |
| 423 | #123 | — | 6 | 1 | no | — |
| 424 | C22⋊Q8 | — | 3 | 2 | no | — |
| 425 | C22⋊Q8 | — | 3 | 2 | no | — |
| 426 | C22⋊Q8 | — | 3 | 1 | no | — |
| 427 | C22⋊Q8 | — | 3 | 1 | no | — |
| 428 | C22⋊Q8 | — | 3 | 1 | no | — |
| 429 | C22⋊Q8 | — | 3 | 1 | no | — |
| 430 | C22⋊Q8 | — | 6 | 1 | no | — |
| 431 | C22⋊Q8 | — | 6 | 1 | no | — |
| 432 | C22⋊Q8 | — | 6 | 2 | no | — |
| 433 | C22⋊Q8 | — | 6 | 2 | no | — |
| 434 | C22⋊Q8 | — | 6 | 2 | no | — |
| 435 | C22⋊Q8 | — | 6 | 2 | no | — |
| 436 | C22⋊Q8 | — | 6 | 1 | no | — |
| 437 | C22⋊Q8 | — | 6 | 1 | no | — |
| 438 | C22⋊Q8 | — | 6 | 1 | no | — |
| 439 | C22⋊Q8 | — | 6 | 1 | no | — |
| 440 | #121 | — | 3 | 2 | no | — |
| 441 | #121 | — | 3 | 1 | no | — |
| 442 | #121 | — | 3 | 1 | no | — |
| 443 | #121 | — | 3 | 1 | no | — |
| 444 | #121 | — | 3 | 2 | no | — |
| 445 | #121 | — | 3 | 1 | no | — |
| 446 | #121 | — | 6 | 1 | no | — |
| 447 | #121 | — | 6 | 1 | no | — |
| 448 | #121 | — | 6 | 1 | no | — |
| 449 | #121 | — | 6 | 1 | no | — |
| 450 | #121 | — | 6 | 1 | no | — |
| 451 | #121 | — | 6 | 2 | no | — |
| 452 | #121 | — | 6 | 2 | no | — |
| 453 | #121 | — | 6 | 1 | no | — |
| 454 | #121 | — | 6 | 1 | no | — |
| 455 | #121 | — | 6 | 1 | no | — |
| 456 | #121 | — | 6 | 1 | no | — |
| 457 | #121 | — | 6 | 2 | no | — |
| 458 | #121 | — | 6 | 2 | no | — |
| 459 | #121 | — | 6 | 1 | no | — |
| 460 | #121 | — | 6 | 1 | no | — |
| 461 | #121 | — | 6 | 1 | no | — |
| 462 | #120 | — | 6 | 1 | no | — |
| 463 | #120 | — | 6 | 1 | no | — |
| 464 | #120 | — | 6 | 1 | no | — |
| 465 | #120 | — | 6 | 1 | no | — |
| 466 | #120 | — | 6 | 1 | no | — |
| 467 | #120 | — | 6 | 1 | no | — |
| 468 | C4×Q8 | — | 3 | 2 | no | — |
| 469 | C4×Q8 | — | 3 | 2 | no | — |
| 470 | C4×Q8 | — | 3 | 1 | no | — |
| 471 | C4×Q8 | — | 3 | 1 | no | — |
| 472 | C4×Q8 | — | 6 | 1 | no | — |
| 473 | C4×Q8 | — | 6 | 1 | no | — |
| 474 | C4×D4 | — | 3 | 1 | no | — |
| 475 | C4×D4 | — | 3 | 1 | no | — |
| 476 | C4×D4 | — | 3 | 1 | no | — |
| 477 | C4×D4 | — | 3 | 1 | no | — |
| 478 | C4×D4 | — | 3 | 1 | no | — |
| 479 | C4×D4 | — | 3 | 1 | no | — |
| 480 | C4×D4 | — | 3 | 1 | no | — |
| 481 | C4×D4 | — | 3 | 1 | no | — |
| 482 | C4×D4 | — | 3 | 1 | no | — |
| 483 | C4×D4 | — | 3 | 1 | no | — |
| 484 | C4×D4 | — | 6 | 1 | no | — |
| 485 | C4×D4 | — | 6 | 1 | no | — |
| 486 | C4×D4 | — | 6 | 1 | no | — |
| 487 | C4×D4 | — | 6 | 2 | no | — |
| 488 | C4×D4 | — | 6 | 2 | no | — |
| 489 | C4×D4 | — | 6 | 1 | no | — |
| 490 | C4×D4 | — | 6 | 2 | no | — |
| 491 | C4×D4 | — | 6 | 2 | no | — |
| 492 | C4×D4 | — | 6 | 1 | no | — |
| 493 | C4×D4 | — | 6 | 1 | no | — |
| 494 | C4×D4 | — | 6 | 1 | no | — |
| 495 | C4×D4 | — | 6 | 1 | no | — |
| 496 | C4×D4 | — | 6 | 1 | no | — |
| 497 | C4×D4 | — | 6 | 1 | no | — |
| 498 | C4×D4 | — | 6 | 1 | no | — |
| 499 | C4×D4 | — | 6 | 1 | no | — |
| 500 | #117 | — | 3 | 1 | no | — |
| 501 | #117 | — | 6 | 1 | no | — |
| 502 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 503 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 504 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 505 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 506 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 507 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 508 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 509 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 510 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 511 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 512 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 513 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 514 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 515 | C2×C42 | — | 3 | 1 | no | — |
| 516 | C2×C42 | — | 6 | 1 | no | — |
| 517 | C2×C42 | — | 6 | 1 | no | — |
| 518 | #107 | — | 3 | 2 | no | — |
| 519 | #106 | — | 3 | 2 | no | — |
| 520 | C4⋊C8 | — | 3 | 2 | no | — |
| 521 | C4⋊C8 | — | 3 | 2 | no | — |
| 522 | #103 | — | 3 | 2 | no | — |
| 523 | #103 | — | 3 | 2 | no | — |
| 524 | #103 | — | 3 | 2 | no | — |
| 525 | #103 | — | 3 | 2 | no | — |
| 526 | #103 | — | 3 | 2 | no | — |
| 527 | #103 | — | 3 | 2 | no | — |
| 528 | #103 | — | 3 | 2 | no | — |
| 529 | #102 | — | 3 | 2 | no | — |
| 530 | #102 | — | 3 | 2 | no | — |
| 531 | #102 | — | 3 | 2 | no | — |
| 532 | #102 | — | 3 | 2 | no | — |
| 533 | #102 | — | 3 | 2 | no | — |
| 534 | C22⋊C8 | — | 3 | 2 | no | — |
| 535 | C22⋊C8 | — | 3 | 2 | no | — |
| 536 | C22⋊C8 | — | 3 | 2 | no | — |
| 537 | C22⋊C8 | — | 3 | 2 | no | — |
| 538 | #97 | — | 3 | 2 | no | — |
| 539 | C4×C8 | — | 3 | 2 | no | — |
| 540 | C22×D3 | — | 4 | 1 | no | — |
| 541 | C22×D3 | — | 8 | 1 | no | — |
| 542 | C22×D3 | — | 8 | 1 | no | — |
| 543 | C2×A4 | — | 2 | 1 | no | — |
| 544 | C2×A4 | — | 4 | 1 | no | — |
| 545 | C2×A4 | C22×D4 | 1 | 1 | yes | characteristic |
| 546 | S4 | — | 2 | 1 | no | — |
| 547 | S4 | — | 2 | 1 | no | — |
| 548 | S4 | — | 4 | 2 | no | — |
| 549 | S4 | — | 4 | 1 | no | — |
| 550 | C3×Q8 | — | 4 | 1 | no | — |
| 551 | C3×Q8 | — | 4 | 2 | no | — |
| 552 | C3×Q8 | — | 8 | 1 | no | — |
| 553 | C3×D4 | — | 4 | 1 | no | — |
| 554 | C3×D4 | — | 8 | 1 | no | — |
| 555 | C2×C3×C4 | — | 4 | 1 | no | — |
| 556 | C2×C3×C4 | — | 8 | 1 | no | — |
| 557 | C2×C3×C4 | — | 8 | 1 | no | — |
| 558 | #67 | — | 8 | 1 | no | — |
| 559 | #67 | — | 8 | 1 | no | — |
| 560 | #67 | — | 8 | 1 | no | — |
| 561 | C2×Dic3 | — | 4 | 1 | no | — |
| 562 | C2×Dic3 | — | 8 | 1 | no | — |
| 563 | D12 | — | 4 | 2 | no | — |
| 564 | D12 | — | 4 | 1 | no | — |
| 565 | D12 | — | 8 | 1 | no | — |
| 566 | D12 | — | 8 | 2 | no | — |
| 567 | D12 | — | 8 | 2 | no | — |
| 568 | D12 | — | 8 | 1 | no | — |
| 569 | C4×D3 | — | 4 | 1 | no | — |
| 570 | C4×D3 | — | 4 | 1 | no | — |
| 571 | C4×D3 | — | 4 | 1 | no | — |
| 572 | C4×D3 | — | 4 | 1 | no | — |
| 573 | C4×D3 | — | 8 | 1 | no | — |
| 574 | C4×D3 | — | 8 | 2 | no | — |
| 575 | C4×D3 | — | 8 | 2 | no | — |
| 576 | C4×D3 | — | 8 | 1 | no | — |
| 577 | C4×D3 | — | 8 | 1 | no | — |
| 578 | Dic6 | — | 4 | 1 | no | — |
| 579 | Dic6 | — | 8 | 1 | no | — |
| 580 | C3×C8 | — | 4 | 2 | no | — |
| 581 | C3⋊C8 | — | 4 | 2 | no | — |
| 582 | C24 | — | 2 | 1 | no | — |
| 583 | C24 | — | 3 | 1 | no | — |
| 584 | C24 | — | 6 | 1 | no | — |
| 585 | C24 | — | 6 | 1 | no | — |
| 586 | C24 | D3×D4 | 1 | 1 | yes | characteristic |
| 587 | #41 | — | 3 | 1 | no | — |
| 588 | #41 | — | 3 | 1 | no | — |
| 589 | #41 | — | 3 | 1 | no | — |
| 590 | #41 | — | 6 | 1 | no | — |
| 591 | #41 | — | 6 | 1 | no | — |
| 592 | #41 | — | 6 | 1 | no | — |
| 593 | #41 | — | 6 | 1 | no | — |
| 594 | #41 | — | 6 | 1 | no | — |
| 595 | #41 | — | 6 | 1 | no | — |
| 596 | #41 | — | 6 | 1 | no | — |
| 597 | #41 | — | 6 | 1 | no | — |
| 598 | #41 | — | 6 | 1 | no | — |
| 599 | #41 | — | 6 | 2 | no | — |
| 600 | #41 | — | 6 | 1 | no | — |
| 601 | #41 | — | 6 | 2 | no | — |
| 602 | #41 | — | 6 | 2 | no | — |
| 603 | #41 | — | 6 | 1 | no | — |
| 604 | #41 | — | 6 | 2 | no | — |
| 605 | #41 | — | 6 | 1 | no | — |
| 606 | #41 | — | 6 | 1 | no | — |
| 607 | #41 | — | 12 | 1 | no | — |
| 608 | #41 | — | 12 | 1 | no | — |
| 609 | #41 | — | 12 | 1 | no | — |
| 610 | #41 | — | 12 | 1 | no | — |
| 611 | #41 | — | 12 | 1 | no | — |
| 612 | #41 | — | 12 | 1 | no | — |
| 613 | #41 | — | 12 | 1 | no | — |
| 614 | #41 | — | 12 | 2 | no | — |
| 615 | #41 | — | 12 | 2 | no | — |
| 616 | #41 | — | 12 | 1 | no | — |
| 617 | #41 | — | 12 | 1 | no | — |
| 618 | #41 | — | 12 | 1 | no | — |
| 619 | #41 | — | 12 | 1 | no | — |
| 620 | #41 | — | 12 | 1 | no | — |
| 621 | #41 | — | 12 | 1 | no | — |
| 622 | #41 | — | 12 | 1 | no | — |
| 623 | #41 | — | 12 | 2 | no | — |
| 624 | #41 | — | 12 | 2 | no | — |
| 625 | #41 | — | 12 | 1 | no | — |
| 626 | #41 | — | 12 | 1 | no | — |
| 627 | #41 | C2×S4 | 1 | 1 | yes | characteristic |
| 628 | C2×Q8 | — | 3 | 2 | no | — |
| 629 | C2×Q8 | — | 3 | 1 | no | — |
| 630 | C2×Q8 | — | 3 | 2 | no | — |
| 631 | C2×Q8 | — | 3 | 1 | no | — |
| 632 | C2×Q8 | — | 3 | 2 | no | — |
| 633 | C2×Q8 | — | 3 | 1 | no | — |
| 634 | C2×Q8 | — | 3 | 1 | no | — |
| 635 | C2×Q8 | — | 6 | 1 | no | — |
| 636 | C2×Q8 | — | 6 | 1 | no | — |
| 637 | C2×Q8 | — | 6 | 1 | no | — |
| 638 | C2×Q8 | — | 6 | 2 | no | — |
| 639 | C2×Q8 | — | 6 | 1 | no | — |
| 640 | C2×Q8 | — | 6 | 1 | no | — |
| 641 | C2×Q8 | — | 6 | 2 | no | — |
| 642 | C2×Q8 | — | 6 | 1 | no | — |
| 643 | C2×Q8 | — | 6 | 1 | no | — |
| 644 | C2×Q8 | — | 6 | 1 | no | — |
| 645 | C2×Q8 | — | 6 | 1 | no | — |
| 646 | C2×Q8 | — | 6 | 1 | no | — |
| 647 | C2×Q8 | — | 6 | 1 | no | — |
| 648 | C2×Q8 | — | 12 | 2 | no | — |
| 649 | C2×Q8 | — | 12 | 1 | no | — |
| 650 | C2×Q8 | C2×S4 | 1 | 1 | yes | characteristic, complemented |
| 651 | C2×D4 | — | 3 | 1 | no | — |
| 652 | C2×D4 | — | 3 | 1 | no | — |
| 653 | C2×D4 | — | 3 | 1 | no | — |
| 654 | C2×D4 | — | 3 | 1 | no | — |
| 655 | C2×D4 | — | 3 | 2 | no | — |
| 656 | C2×D4 | — | 3 | 1 | no | — |
| 657 | C2×D4 | — | 3 | 1 | no | — |
| 658 | C2×D4 | — | 3 | 1 | no | — |
| 659 | C2×D4 | — | 6 | 1 | no | — |
| 660 | C2×D4 | — | 6 | 1 | no | — |
| 661 | C2×D4 | — | 6 | 1 | no | — |
| 662 | C2×D4 | — | 6 | 1 | no | — |
| 663 | C2×D4 | — | 6 | 1 | no | — |
| 664 | C2×D4 | — | 6 | 1 | no | — |
| 665 | C2×D4 | — | 6 | 1 | no | — |
| 666 | C2×D4 | — | 6 | 1 | no | — |
| 667 | C2×D4 | — | 6 | 1 | no | — |
| 668 | C2×D4 | — | 6 | 1 | no | — |
| 669 | C2×D4 | — | 6 | 1 | no | — |
| 670 | C2×D4 | — | 6 | 1 | no | — |
| 671 | C2×D4 | — | 6 | 1 | no | — |
| 672 | C2×D4 | — | 6 | 1 | no | — |
| 673 | C2×D4 | — | 6 | 1 | no | — |
| 674 | C2×D4 | — | 6 | 2 | no | — |
| 675 | C2×D4 | — | 6 | 1 | no | — |
| 676 | C2×D4 | — | 6 | 1 | no | — |
| 677 | C2×D4 | — | 6 | 2 | no | — |
| 678 | C2×D4 | — | 6 | 2 | no | — |
| 679 | C2×D4 | — | 6 | 1 | no | — |
| 680 | C2×D4 | — | 6 | 1 | no | — |
| 681 | C2×D4 | — | 6 | 2 | no | — |
| 682 | C2×D4 | — | 6 | 1 | no | — |
| 683 | C2×D4 | — | 6 | 1 | no | — |
| 684 | C2×D4 | — | 6 | 1 | no | — |
| 685 | C2×D4 | — | 12 | 1 | no | — |
| 686 | C2×D4 | — | 12 | 1 | no | — |
| 687 | C2×D4 | — | 12 | 2 | no | — |
| 688 | C2×D4 | — | 12 | 1 | no | — |
| 689 | C2×D4 | — | 12 | 1 | no | — |
| 690 | C2×D4 | — | 12 | 1 | no | — |
| 691 | C2×D4 | — | 12 | 1 | no | — |
| 692 | C2×D4 | — | 12 | 2 | no | — |
| 693 | C2×D4 | — | 12 | 1 | no | — |
| 694 | C2×D4 | — | 12 | 1 | no | — |
| 695 | C2×D4 | — | 12 | 1 | no | — |
| 696 | C2×D4 | — | 12 | 2 | no | — |
| 697 | C2×D4 | — | 12 | 2 | no | — |
| 698 | C2×D4 | — | 12 | 2 | no | — |
| 699 | C22×C4 | — | 2 | 2 | no | — |
| 700 | C22×C4 | — | 2 | 1 | no | — |
| 701 | C22×C4 | — | 3 | 1 | no | — |
| 702 | C22×C4 | — | 3 | 1 | no | — |
| 703 | C22×C4 | — | 3 | 1 | no | — |
| 704 | C22×C4 | — | 3 | 1 | no | — |
| 705 | C22×C4 | — | 3 | 1 | no | — |
| 706 | C22×C4 | — | 3 | 1 | no | — |
| 707 | C22×C4 | — | 3 | 1 | no | — |
| 708 | C22×C4 | — | 3 | 1 | no | — |
| 709 | C22×C4 | — | 3 | 1 | no | — |
| 710 | C22×C4 | — | 3 | 1 | no | — |
| 711 | C22×C4 | — | 3 | 1 | no | — |
| 712 | C22×C4 | — | 6 | 1 | no | — |
| 713 | C22×C4 | — | 6 | 1 | no | — |
| 714 | C22×C4 | — | 6 | 1 | no | — |
| 715 | C22×C4 | — | 6 | 1 | no | — |
| 716 | C22×C4 | — | 6 | 1 | no | — |
| 717 | C22×C4 | — | 6 | 1 | no | — |
| 718 | C22×C4 | — | 6 | 1 | no | — |
| 719 | C22×C4 | — | 6 | 1 | no | — |
| 720 | C22×C4 | — | 6 | 1 | no | — |
| 721 | C22×C4 | — | 6 | 1 | no | — |
| 722 | C22×C4 | — | 6 | 1 | no | — |
| 723 | C22×C4 | — | 6 | 1 | no | — |
| 724 | C22×C4 | — | 6 | 2 | no | — |
| 725 | C22×C4 | — | 6 | 2 | no | — |
| 726 | C22×C4 | — | 6 | 1 | no | — |
| 727 | C22×C4 | — | 6 | 1 | no | — |
| 728 | C22×C4 | — | 6 | 1 | no | — |
| 729 | C22×C4 | — | 6 | 2 | no | — |
| 730 | C22×C4 | — | 6 | 1 | no | — |
| 731 | C22×C4 | — | 6 | 1 | no | — |
| 732 | C22×C4 | — | 12 | 1 | no | — |
| 733 | C22×C4 | — | 12 | 1 | no | — |
| 734 | C22×C4 | — | 12 | 1 | no | — |
| 735 | C22×C4 | — | 12 | 2 | no | — |
| 736 | C22×C4 | — | 12 | 1 | no | — |
| 737 | C22×C4 | — | 12 | 1 | no | — |
| 738 | C22×C4 | — | 12 | 1 | no | — |
| 739 | C22×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 740 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 741 | Q16 | — | 3 | 2 | no | — |
| 742 | Q16 | — | 3 | 2 | no | — |
| 743 | Q16 | — | 3 | 2 | no | — |
| 744 | Q16 | — | 6 | 2 | no | — |
| 745 | Q16 | — | 6 | 2 | no | — |
| 746 | Q16 | — | 6 | 2 | no | — |
| 747 | Q16 | — | 12 | 2 | no | — |
| 748 | Q16 | C2×S4 | 1 | 2 | yes | complemented |
| 749 | SD16 | — | 3 | 2 | no | — |
| 750 | SD16 | — | 3 | 2 | no | — |
| 751 | SD16 | — | 3 | 2 | no | — |
| 752 | SD16 | — | 6 | 2 | no | — |
| 753 | SD16 | — | 6 | 2 | no | — |
| 754 | SD16 | — | 6 | 2 | no | — |
| 755 | SD16 | — | 6 | 2 | no | — |
| 756 | SD16 | — | 6 | 2 | no | — |
| 757 | SD16 | — | 6 | 2 | no | — |
| 758 | SD16 | — | 6 | 2 | no | — |
| 759 | SD16 | — | 12 | 2 | no | — |
| 760 | SD16 | — | 12 | 2 | no | — |
| 761 | SD16 | C2×S4 | 1 | 2 | yes | complemented |
| 762 | D8 | — | 6 | 2 | no | — |
| 763 | D8 | — | 6 | 2 | no | — |
| 764 | D8 | — | 6 | 2 | no | — |
| 765 | D8 | — | 6 | 2 | no | — |
| 766 | D8 | — | 12 | 2 | no | — |
| 767 | M16 | — | 3 | 1 | no | — |
| 768 | M16 | — | 3 | 2 | no | — |
| 769 | M16 | — | 6 | 1 | no | — |
| 770 | M16 | — | 6 | 2 | no | — |
| 771 | M16 | — | 6 | 1 | no | — |
| 772 | M16 | — | 6 | 1 | no | — |
| 773 | M16 | — | 6 | 1 | no | — |
| 774 | M16 | — | 6 | 1 | no | — |
| 775 | M16 | — | 6 | 2 | no | — |
| 776 | M16 | C2×S4 | 1 | 1 | yes | characteristic, complemented |
| 777 | C2×C8 | — | 3 | 2 | no | — |
| 778 | C2×C8 | — | 3 | 2 | no | — |
| 779 | C2×C8 | — | 3 | 2 | no | — |
| 780 | C2×C8 | — | 3 | 2 | no | — |
| 781 | C2×C8 | — | 6 | 2 | no | — |
| 782 | C2×C8 | — | 6 | 2 | no | — |
| 783 | C4⋊C4 | — | 3 | 1 | no | — |
| 784 | C4⋊C4 | — | 3 | 1 | no | — |
| 785 | C4⋊C4 | — | 3 | 1 | no | — |
| 786 | C4⋊C4 | — | 3 | 1 | no | — |
| 787 | C4⋊C4 | — | 3 | 2 | no | — |
| 788 | C4⋊C4 | — | 3 | 1 | no | — |
| 789 | C4⋊C4 | — | 3 | 1 | no | — |
| 790 | C4⋊C4 | — | 6 | 1 | no | — |
| 791 | C4⋊C4 | — | 6 | 1 | no | — |
| 792 | C4⋊C4 | — | 6 | 2 | no | — |
| 793 | C4⋊C4 | — | 6 | 2 | no | — |
| 794 | C4⋊C4 | — | 6 | 1 | no | — |
| 795 | C4⋊C4 | — | 6 | 1 | no | — |
| 796 | C4⋊C4 | — | 6 | 2 | no | — |
| 797 | C4⋊C4 | — | 6 | 2 | no | — |
| 798 | C4⋊C4 | — | 6 | 1 | no | — |
| 799 | C4⋊C4 | — | 6 | 1 | no | — |
| 800 | C4⋊C4 | — | 6 | 1 | no | — |
| 801 | C4⋊C4 | — | 6 | 1 | no | — |
| 802 | C4⋊C4 | — | 6 | 1 | no | — |
| 803 | C22⋊C4 | — | 3 | 1 | no | — |
| 804 | C22⋊C4 | — | 3 | 1 | no | — |
| 805 | C22⋊C4 | — | 3 | 1 | no | — |
| 806 | C22⋊C4 | — | 3 | 1 | no | — |
| 807 | C22⋊C4 | — | 3 | 1 | no | — |
| 808 | C22⋊C4 | — | 3 | 1 | no | — |
| 809 | C22⋊C4 | — | 3 | 1 | no | — |
| 810 | C22⋊C4 | — | 3 | 1 | no | — |
| 811 | C22⋊C4 | — | 6 | 1 | no | — |
| 812 | C22⋊C4 | — | 6 | 1 | no | — |
| 813 | C22⋊C4 | — | 6 | 1 | no | — |
| 814 | C22⋊C4 | — | 6 | 1 | no | — |
| 815 | C22⋊C4 | — | 6 | 2 | no | — |
| 816 | C22⋊C4 | — | 6 | 2 | no | — |
| 817 | C22⋊C4 | — | 6 | 2 | no | — |
| 818 | C22⋊C4 | — | 6 | 2 | no | — |
| 819 | C22⋊C4 | — | 6 | 2 | no | — |
| 820 | C22⋊C4 | — | 6 | 2 | no | — |
| 821 | C22⋊C4 | — | 6 | 1 | no | — |
| 822 | C22⋊C4 | — | 6 | 1 | no | — |
| 823 | C22⋊C4 | — | 6 | 1 | no | — |
| 824 | C22⋊C4 | — | 6 | 1 | no | — |
| 825 | C22⋊C4 | — | 6 | 1 | no | — |
| 826 | C22⋊C4 | — | 6 | 1 | no | — |
| 827 | C22⋊C4 | — | 6 | 1 | no | — |
| 828 | C22⋊C4 | — | 6 | 2 | no | — |
| 829 | C22⋊C4 | — | 6 | 2 | no | — |
| 830 | C22⋊C4 | — | 6 | 1 | no | — |
| 831 | C22⋊C4 | — | 6 | 1 | no | — |
| 832 | C22⋊C4 | — | 6 | 1 | no | — |
| 833 | C22⋊C4 | — | 6 | 1 | no | — |
| 834 | C42 | — | 3 | 1 | no | — |
| 835 | C42 | — | 3 | 1 | no | — |
| 836 | C42 | — | 3 | 1 | no | — |
| 837 | C42 | — | 3 | 1 | no | — |
| 838 | C42 | — | 6 | 1 | no | — |
| 839 | C42 | — | 6 | 1 | no | — |
| 840 | C42 | — | 6 | 1 | no | — |
| 841 | C42 | — | 6 | 2 | no | — |
| 842 | C42 | — | 6 | 2 | no | — |
| 843 | C22×C3 | — | 4 | 1 | no | — |
| 844 | C22×C3 | — | 8 | 1 | no | — |
| 845 | C2×D3 | — | 4 | 1 | no | — |
| 846 | C2×D3 | — | 4 | 1 | no | — |
| 847 | C2×D3 | — | 8 | 2 | no | — |
| 848 | C2×D3 | — | 8 | 1 | no | — |
| 849 | C2×D3 | — | 16 | 1 | no | — |
| 850 | C2×D3 | — | 16 | 2 | no | — |
| 851 | C2×D3 | — | 16 | 2 | no | — |
| 852 | A4 | #575 | 1 | 1 | yes | characteristic, complemented |
| 853 | C3×C4 | — | 4 | 1 | no | — |
| 854 | C3×C4 | — | 4 | 1 | no | — |
| 855 | C3×C4 | — | 8 | 1 | no | — |
| 856 | C3×C4 | — | 8 | 2 | no | — |
| 857 | Dic3 | — | 4 | 1 | no | — |
| 858 | Dic3 | — | 4 | 1 | no | — |
| 859 | Dic3 | — | 8 | 1 | no | — |
| 860 | C23 | — | 2 | 1 | no | — |
| 861 | C23 | — | 3 | 1 | no | — |
| 862 | C23 | — | 3 | 1 | no | — |
| 863 | C23 | — | 3 | 1 | no | — |
| 864 | C23 | — | 3 | 1 | no | — |
| 865 | C23 | — | 4 | 1 | no | — |
| 866 | C23 | — | 6 | 1 | no | — |
| 867 | C23 | — | 6 | 1 | no | — |
| 868 | C23 | — | 6 | 1 | no | — |
| 869 | C23 | — | 6 | 1 | no | — |
| 870 | C23 | — | 6 | 2 | no | — |
| 871 | C23 | — | 6 | 1 | no | — |
| 872 | C23 | — | 6 | 1 | no | — |
| 873 | C23 | — | 12 | 1 | no | — |
| 874 | C23 | — | 12 | 1 | no | — |
| 875 | C23 | — | 12 | 1 | no | — |
| 876 | C23 | — | 12 | 1 | no | — |
| 877 | C23 | — | 12 | 1 | no | — |
| 878 | C23 | — | 12 | 1 | no | — |
| 879 | C23 | — | 12 | 2 | no | — |
| 880 | C23 | — | 12 | 2 | no | — |
| 881 | C23 | — | 12 | 2 | no | — |
| 882 | C23 | — | 12 | 1 | no | — |
| 883 | C23 | — | 24 | 1 | no | — |
| 884 | C23 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 885 | Q8 | — | 2 | 1 | no | — |
| 886 | Q8 | — | 3 | 2 | no | — |
| 887 | Q8 | — | 3 | 1 | no | — |
| 888 | Q8 | — | 6 | 2 | no | — |
| 889 | Q8 | — | 6 | 2 | no | — |
| 890 | Q8 | — | 6 | 1 | no | — |
| 891 | Q8 | — | 6 | 1 | no | — |
| 892 | Q8 | — | 6 | 2 | no | — |
| 893 | Q8 | — | 6 | 1 | no | — |
| 894 | Q8 | — | 6 | 1 | no | — |
| 895 | Q8 | — | 6 | 1 | no | — |
| 896 | Q8 | — | 12 | 1 | no | — |
| 897 | Q8 | — | 12 | 1 | no | — |
| 898 | Q8 | — | 12 | 1 | no | — |
| 899 | Q8 | C22×S4 | 1 | 2 | yes | — |
| 900 | Q8 | C22×S4 | 1 | 1 | yes | characteristic |
| 901 | D4 | — | 2 | 1 | no | — |
| 902 | D4 | — | 3 | 1 | no | — |
| 903 | D4 | — | 6 | 1 | no | — |
| 904 | D4 | — | 6 | 1 | no | — |
| 905 | D4 | — | 6 | 1 | no | — |
| 906 | D4 | — | 6 | 2 | no | — |
| 907 | D4 | — | 6 | 1 | no | — |
| 908 | D4 | — | 6 | 1 | no | — |
| 909 | D4 | — | 6 | 1 | no | — |
| 910 | D4 | — | 6 | 1 | no | — |
| 911 | D4 | — | 6 | 1 | no | — |
| 912 | D4 | — | 6 | 1 | no | — |
| 913 | D4 | — | 6 | 1 | no | — |
| 914 | D4 | — | 6 | 1 | no | — |
| 915 | D4 | — | 6 | 2 | no | — |
| 916 | D4 | — | 12 | 1 | no | — |
| 917 | D4 | — | 12 | 2 | no | — |
| 918 | D4 | — | 12 | 2 | no | — |
| 919 | D4 | — | 12 | 1 | no | — |
| 920 | D4 | — | 12 | 1 | no | — |
| 921 | D4 | — | 12 | 1 | no | — |
| 922 | D4 | — | 12 | 1 | no | — |
| 923 | D4 | — | 12 | 1 | no | — |
| 924 | D4 | — | 12 | 1 | no | — |
| 925 | D4 | — | 12 | 1 | no | — |
| 926 | D4 | — | 12 | 2 | no | — |
| 927 | D4 | — | 12 | 2 | no | — |
| 928 | D4 | — | 12 | 2 | no | — |
| 929 | D4 | — | 12 | 1 | no | — |
| 930 | D4 | — | 12 | 1 | no | — |
| 931 | D4 | — | 12 | 2 | no | — |
| 932 | D4 | — | 12 | 1 | no | — |
| 933 | D4 | — | 12 | 1 | no | — |
| 934 | D4 | — | 12 | 4 | no | — |
| 935 | D4 | — | 12 | 2 | no | — |
| 936 | D4 | — | 12 | 1 | no | — |
| 937 | D4 | — | 12 | 1 | no | — |
| 938 | D4 | — | 12 | 2 | no | — |
| 939 | D4 | — | 12 | 1 | no | — |
| 940 | D4 | — | 24 | 1 | no | — |
| 941 | D4 | — | 24 | 1 | no | — |
| 942 | D4 | — | 24 | 1 | no | — |
| 943 | D4 | C22×S4 | 1 | 1 | yes | characteristic |
| 944 | C2×C4 | — | 2 | 1 | no | — |
| 945 | C2×C4 | — | 2 | 1 | no | — |
| 946 | C2×C4 | — | 3 | 1 | no | — |
| 947 | C2×C4 | — | 3 | 1 | no | — |
| 948 | C2×C4 | — | 3 | 1 | no | — |
| 949 | C2×C4 | — | 3 | 1 | no | — |
| 950 | C2×C4 | — | 3 | 1 | no | — |
| 951 | C2×C4 | — | 3 | 1 | no | — |
| 952 | C2×C4 | — | 3 | 1 | no | — |
| 953 | C2×C4 | — | 3 | 1 | no | — |
| 954 | C2×C4 | — | 3 | 1 | no | — |
| 955 | C2×C4 | — | 3 | 1 | no | — |
| 956 | C2×C4 | — | 3 | 1 | no | — |
| 957 | C2×C4 | — | 3 | 1 | no | — |
| 958 | C2×C4 | — | 3 | 1 | no | — |
| 959 | C2×C4 | — | 6 | 1 | no | — |
| 960 | C2×C4 | — | 6 | 1 | no | — |
| 961 | C2×C4 | — | 6 | 2 | no | — |
| 962 | C2×C4 | — | 6 | 2 | no | — |
| 963 | C2×C4 | — | 6 | 1 | no | — |
| 964 | C2×C4 | — | 6 | 1 | no | — |
| 965 | C2×C4 | — | 6 | 1 | no | — |
| 966 | C2×C4 | — | 6 | 1 | no | — |
| 967 | C2×C4 | — | 6 | 1 | no | — |
| 968 | C2×C4 | — | 6 | 1 | no | — |
| 969 | C2×C4 | — | 6 | 1 | no | — |
| 970 | C2×C4 | — | 6 | 1 | no | — |
| 971 | C2×C4 | — | 6 | 1 | no | — |
| 972 | C2×C4 | — | 6 | 1 | no | — |
| 973 | C2×C4 | — | 6 | 1 | no | — |
| 974 | C2×C4 | — | 6 | 1 | no | — |
| 975 | C2×C4 | — | 6 | 1 | no | — |
| 976 | C2×C4 | — | 6 | 1 | no | — |
| 977 | C2×C4 | — | 6 | 2 | no | — |
| 978 | C2×C4 | — | 6 | 1 | no | — |
| 979 | C2×C4 | — | 6 | 1 | no | — |
| 980 | C2×C4 | — | 6 | 1 | no | — |
| 981 | C2×C4 | — | 6 | 2 | no | — |
| 982 | C2×C4 | — | 6 | 1 | no | — |
| 983 | C2×C4 | — | 12 | 1 | no | — |
| 984 | C2×C4 | — | 12 | 2 | no | — |
| 985 | C2×C4 | — | 12 | 2 | no | — |
| 986 | C2×C4 | — | 12 | 1 | no | — |
| 987 | C2×C4 | — | 12 | 1 | no | — |
| 988 | C2×C4 | — | 12 | 1 | no | — |
| 989 | C2×C4 | — | 12 | 1 | no | — |
| 990 | C2×C4 | — | 12 | 1 | no | — |
| 991 | C2×C4 | — | 12 | 1 | no | — |
| 992 | C2×C4 | — | 12 | 1 | no | — |
| 993 | C2×C4 | — | 12 | 2 | no | — |
| 994 | C2×C4 | — | 12 | 2 | no | — |
| 995 | C2×C4 | — | 12 | 1 | no | — |
| 996 | C2×C4 | — | 12 | 1 | no | — |
| 997 | C2×C4 | — | 12 | 1 | no | — |
| 998 | C2×C4 | — | 12 | 2 | no | — |
| 999 | C2×C4 | — | 12 | 2 | no | — |
| 1000 | C2×C4 | — | 12 | 1 | no | — |
| 1001 | C2×C4 | — | 24 | 1 | no | — |
| 1002 | C2×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 1003 | C8 | — | 3 | 2 | no | — |
| 1004 | C8 | — | 6 | 2 | no | — |
| 1005 | C8 | — | 6 | 2 | no | — |
| 1006 | C8 | C22×S4 | 1 | 2 | yes | — |
| 1007 | C2×C3 | — | 4 | 1 | no | — |
| 1008 | C2×C3 | — | 8 | 1 | no | — |
| 1009 | C2×C3 | — | 16 | 1 | no | — |
| 1010 | D3 | — | 8 | 1 | no | — |
| 1011 | D3 | — | 8 | 1 | no | — |
| 1012 | D3 | — | 16 | 2 | no | — |
| 1013 | D3 | — | 16 | 1 | no | — |
| 1014 | C22 | — | 2 | 1 | no | — |
| 1015 | C22 | — | 3 | 1 | no | — |
| 1016 | C22 | — | 3 | 1 | no | — |
| 1017 | C22 | — | 3 | 1 | no | — |
| 1018 | C22 | — | 6 | 1 | no | — |
| 1019 | C22 | — | 6 | 1 | no | — |
| 1020 | C22 | — | 6 | 1 | no | — |
| 1021 | C22 | — | 6 | 1 | no | — |
| 1022 | C22 | — | 6 | 1 | no | — |
| 1023 | C22 | — | 6 | 1 | no | — |
| 1024 | C22 | — | 6 | 1 | no | — |
| 1025 | C22 | — | 6 | 1 | no | — |
| 1026 | C22 | — | 6 | 1 | no | — |
| 1027 | C22 | — | 6 | 1 | no | — |
| 1028 | C22 | — | 6 | 1 | no | — |
| 1029 | C22 | — | 12 | 1 | no | — |
| 1030 | C22 | — | 12 | 1 | no | — |
| 1031 | C22 | — | 12 | 1 | no | — |
| 1032 | C22 | — | 12 | 1 | no | — |
| 1033 | C22 | — | 12 | 1 | no | — |
| 1034 | C22 | — | 12 | 2 | no | — |
| 1035 | C22 | — | 12 | 1 | no | — |
| 1036 | C22 | — | 12 | 2 | no | — |
| 1037 | C22 | — | 12 | 2 | no | — |
| 1038 | C22 | — | 12 | 1 | no | — |
| 1039 | C22 | — | 24 | 1 | no | — |
| 1040 | C22 | — | 24 | 2 | no | — |
| 1041 | C22 | — | 24 | 2 | no | — |
| 1042 | C22 | — | 24 | 1 | no | — |
| 1043 | C22 | — | 24 | 2 | no | — |
| 1044 | C22 | — | 24 | 2 | no | — |
| 1045 | C22 | #5777 | 1 | 1 | yes | characteristic, complemented |
| 1046 | C22 | D4×S4 | 1 | 1 | yes | characteristic |
| 1047 | C4 | — | 2 | 1 | no | — |
| 1048 | C4 | — | 2 | 2 | no | — |
| 1049 | C4 | — | 3 | 1 | no | — |
| 1050 | C4 | — | 3 | 1 | no | — |
| 1051 | C4 | — | 6 | 1 | no | — |
| 1052 | C4 | — | 6 | 1 | no | — |
| 1053 | C4 | — | 6 | 1 | no | — |
| 1054 | C4 | — | 6 | 1 | no | — |
| 1055 | C4 | — | 6 | 1 | no | — |
| 1056 | C4 | — | 6 | 1 | no | — |
| 1057 | C4 | — | 6 | 1 | no | — |
| 1058 | C4 | — | 6 | 2 | no | — |
| 1059 | C4 | — | 12 | 1 | no | — |
| 1060 | C4 | — | 12 | 2 | no | — |
| 1061 | C4 | — | 12 | 1 | no | — |
| 1062 | C4 | — | 12 | 1 | no | — |
| 1063 | C4 | D4×S4 | 1 | 1 | yes | characteristic |
| 1064 | C4 | C23×S4 | 1 | 1 | yes | characteristic |
| 1065 | C3 | — | 4 | 1 | no | Sylow |
| 1066 | C2 | — | 2 | 1 | no | — |
| 1067 | C2 | — | 3 | 1 | no | — |
| 1068 | C2 | — | 3 | 1 | no | — |
| 1069 | C2 | — | 4 | 1 | no | — |
| 1070 | C2 | — | 6 | 1 | no | — |
| 1071 | C2 | — | 12 | 1 | no | — |
| 1072 | C2 | — | 12 | 1 | no | — |
| 1073 | C2 | — | 12 | 1 | no | — |
| 1074 | C2 | — | 24 | 1 | no | — |
| 1075 | C2 | — | 24 | 2 | no | — |
| 1076 | C2 | C2×D4×S4 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×D4×S4 |
| commutator, cosocle | C4×A4 | C24 |
| Frattini | C4 | C23×S4 |
| Fitting | C22×#137 | D3 |
| socle | C23 | C2×D3×D4 |
| hypercenter | #137 | S4 |
| hypocenter | A4 | #575 |
| LCS | G ▷ C4×A4 ▷ C2×A4 ▷ A4 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #137 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #41×S4 | C2 | semidirect |
| 2. C2×#5919 | C2 | semidirect |
| 3. A4×#137 | C2 | semidirect |
| 4. #85513 | C2 | semidirect |
| 5. #85499 | C2 | semidirect |
| 6. #85465 | C2 | semidirect |
| 7. #85464 | C2 | semidirect |
| 8. #85462 | C2 | semidirect |
| 9. #85460 | C2 | semidirect |
| 10. #85443 | C2 | semidirect |
| 11. M16×S4 | C2 | semidirect |
| 14. C2×Q8×A4 | C22 | semidirect |
| 18. #5919 | C22 | semidirect |
| 19. #5919 | C22 | semidirect |
| 20. Q8×S4 | C22 | semidirect |
| 22. #5914 | C22 | semidirect |
| 24. D4×S4 | C22 | semidirect |
| 28. C2×C4⋊S4 | C22 | semidirect |
| 33. A4×Q16 | C22 | semidirect |
| 34. A4×SD16 | C22 | semidirect |
| 35. A4×M16 | C22 | semidirect |
| 36. #5417 | C22 | semidirect |
| 37. #5417 | C22 | semidirect |
| 38. #5416 | C22 | semidirect |
| 39. #5415 | C22 | semidirect |
| 40. #5409 | C22 | semidirect |
| 41. #5402 | C22 | semidirect |
| 42. #5401 | C22 | semidirect |
| 43. #5400 | C22 | semidirect |
| 44. C8×S4 | C22 | semidirect |
| 46. C22×#137 | D3 | semidirect |
| 117. C23×Q8 | C2×D3 | semidirect |
| 139. C22×Q16 | C2×D3 | semidirect |
| 140. C22×SD16 | C2×D3 | semidirect |
| 142. C22×M16 | C2×D3 | semidirect |
| 351. #137 | S4 | semidirect |
| 650. C2×Q8 | C2×S4 | semidirect |
| 748. Q16 | C2×S4 | semidirect |
| 761. SD16 | C2×S4 | semidirect |
| 776. M16 | C2×S4 | semidirect |
| 852. A4 | #575 | semidirect |
| 1045. C22 | #5777 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×S4 | 2 |
| C2×#5919 | 2 |
| A4×#137 | 2 |
| #85513 | 2 |
| #85499 | 2 |
| #85465 | 2 |
| #85464 | 2 |
| #85462 | 2 |
| #85460 | 2 |
| #85443 | 2 |
| M16×S4 | 2 |
| #61068 | 3 |
| #5777 | 4 |