Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1909 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 | #60916 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #60860 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#3152 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #60210 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #19377 | C2 | 1 | 8 | yes | maximal, complemented |
| 6 | #19293 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #19291 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #19268 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #19266 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #19239 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | #19231 | C2 | 1 | 4 | yes | maximal, complemented |
| 12 | #17796 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #17717 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | C2×#1549 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C22×#137 | — | 2 | 2 | no | — |
| 16 | #3444 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×#532 | C22 | 1 | 1 | yes | characteristic |
| 18 | C22×C4⋊Q8 | C22 | 1 | 1 | yes | characteristic |
| 19 | #3254 | — | 2 | 1 | no | — |
| 20 | #3253 | — | 2 | 1 | no | — |
| 21 | #3251 | C22 | 1 | 4 | yes | — |
| 22 | #3247 | — | 2 | 2 | no | — |
| 23 | #3246 | C22 | 1 | 2 | yes | — |
| 24 | #3245 | C22 | 1 | 2 | yes | — |
| 25 | #3239 | C22 | 1 | 4 | yes | complemented |
| 26 | #3238 | — | 2 | 2 | no | — |
| 27 | #3230 | — | 2 | 1 | no | — |
| 28 | #3229 | C22 | 1 | 2 | yes | complemented |
| 29 | #3227 | — | 2 | 1 | no | — |
| 30 | #3226 | C22 | 1 | 2 | yes | complemented |
| 31 | #3165 | — | 2 | 1 | no | — |
| 32 | #3152 | — | 2 | 1 | no | — |
| 33 | #3152 | — | 2 | 1 | no | — |
| 34 | #3152 | — | 2 | 2 | no | — |
| 35 | #3152 | C22 | 1 | 4 | yes | — |
| 36 | #3152 | C22 | 1 | 4 | yes | — |
| 37 | C2×#497 | — | 2 | 2 | no | — |
| 38 | C2×#494 | C22 | 1 | 2 | yes | — |
| 39 | C2×#492 | C22 | 1 | 2 | yes | — |
| 40 | #3141 | — | 2 | 1 | no | — |
| 41 | #3092 | — | 2 | 2 | no | — |
| 42 | #3079 | C22 | 1 | 2 | yes | — |
| 43 | #3079 | C22 | 1 | 2 | yes | — |
| 44 | #3079 | C22 | 1 | 2 | yes | — |
| 45 | #3077 | — | 2 | 1 | no | — |
| 46 | #3055 | — | 2 | 2 | no | — |
| 47 | #3038 | C22 | 1 | 2 | yes | — |
| 48 | #3036 | — | 2 | 1 | no | — |
| 49 | #2969 | C22 | 1 | 4 | yes | complemented |
| 50 | #2968 | — | 2 | 2 | no | — |
| 51 | #2965 | — | 2 | 2 | no | — |
| 52 | #2965 | C22 | 1 | 2 | yes | — |
| 53 | C8×#41 | C22 | 1 | 2 | yes | — |
| 54 | #2962 | C22 | 1 | 2 | yes | complemented |
| 55 | #2935 | C22 | 1 | 2 | yes | complemented |
| 56 | #2933 | — | 2 | 2 | no | — |
| 57 | #2922 | — | 2 | 1 | no | — |
| 58 | #2920 | C22 | 1 | 1 | yes | characteristic |
| 59 | C2×#431 | C22 | 1 | 1 | yes | characteristic |
| 60 | C2×#423 | C22 | 1 | 1 | yes | characteristic |
| 61 | C4×#131 | — | 2 | 1 | no | — |
| 62 | C2×C4×M16 | C22 | 1 | 1 | yes | characteristic |
| 63 | #1690 | C22 | 1 | 8 | yes | complemented |
| 64 | #1689 | C22 | 1 | 8 | yes | complemented |
| 65 | #1686 | C22 | 1 | 8 | yes | complemented |
| 66 | #1685 | C22 | 1 | 8 | yes | complemented |
| 67 | #1670 | C22 | 1 | 8 | yes | complemented |
| 68 | #1669 | C22 | 1 | 8 | yes | complemented |
| 69 | #1666 | C22 | 1 | 8 | yes | complemented |
| 70 | #1665 | C22 | 1 | 8 | yes | complemented |
| 71 | #1569 | C22 | 1 | 4 | yes | complemented |
| 72 | #1567 | C22 | 1 | 2 | yes | — |
| 73 | #1566 | C22 | 1 | 2 | yes | — |
| 74 | #1565 | C22 | 1 | 4 | yes | complemented |
| 75 | #1553 | C22 | 1 | 4 | yes | — |
| 76 | #1549 | C22 | 1 | 2 | yes | — |
| 77 | #1549 | C22 | 1 | 2 | yes | — |
| 78 | #1549 | C22 | 1 | 1 | yes | characteristic |
| 79 | #1549 | C22 | 1 | 1 | yes | characteristic |
| 80 | #1549 | C22 | 1 | 4 | yes | complemented |
| 81 | #1545 | C22 | 1 | 1 | yes | characteristic |
| 82 | #1545 | C22 | 1 | 1 | yes | characteristic |
| 83 | #1540 | C22 | 1 | 4 | yes | — |
| 84 | C2×#332 | C22 | 1 | 4 | yes | complemented |
| 85 | C22×#41 | — | 2 | 1 | no | — |
| 86 | C23×Q8 | — | 2 | 1 | no | — |
| 87 | C2×#137 | — | 2 | 4 | no | — |
| 88 | C2×#137 | — | 2 | 8 | no | — |
| 89 | C2×#137 | — | 2 | 4 | no | — |
| 90 | C2×#137 | — | 4 | 16 | no | — |
| 91 | C2×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 92 | C22×Q16 | — | 2 | 4 | no | — |
| 93 | C22×SD16 | — | 2 | 4 | no | — |
| 94 | C2×#131 | — | 2 | 2 | no | — |
| 95 | C22×M16 | — | 2 | 1 | no | — |
| 96 | C22×M16 | D4 | 1 | 2 | yes | — |
| 97 | #533 | D4 | 1 | 1 | yes | characteristic |
| 98 | #533 | D4 | 1 | 1 | yes | characteristic |
| 99 | #533 | C23 | 1 | 1 | yes | characteristic |
| 100 | #532 | — | 2 | 1 | no | — |
| 101 | #532 | — | 2 | 1 | no | — |
| 102 | #532 | — | 2 | 1 | no | — |
| 103 | #532 | — | 2 | 1 | no | — |
| 104 | #532 | — | 2 | 1 | no | — |
| 105 | #532 | — | 2 | 1 | no | — |
| 106 | #532 | D4 | 1 | 1 | yes | characteristic |
| 107 | #532 | D4 | 1 | 1 | yes | characteristic |
| 108 | #532 | C23 | 1 | 2 | yes | — |
| 109 | #532 | C23 | 1 | 2 | yes | — |
| 110 | #532 | C23 | 1 | 1 | yes | characteristic |
| 111 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 112 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 113 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 114 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 115 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 116 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 117 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 118 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 119 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 120 | C2×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 121 | C2×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 122 | C2×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 123 | C2×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 124 | C2×#127 | C23 | 1 | 1 | yes | characteristic |
| 125 | #529 | — | 2 | 1 | no | — |
| 126 | #529 | — | 2 | 1 | no | — |
| 127 | #529 | — | 2 | 1 | no | — |
| 128 | #529 | — | 2 | 1 | no | — |
| 129 | #529 | D4 | 1 | 2 | yes | — |
| 130 | #529 | C23 | 1 | 2 | yes | — |
| 131 | C2×#124 | — | 2 | 1 | no | — |
| 132 | #525 | — | 2 | 1 | no | — |
| 133 | #525 | — | 2 | 1 | no | — |
| 134 | #525 | D4 | 1 | 2 | yes | — |
| 135 | C2×#121 | — | 2 | 1 | no | — |
| 136 | C2×#121 | — | 2 | 1 | no | — |
| 137 | C4×#41 | — | 2 | 1 | no | — |
| 138 | C4×#41 | — | 2 | 1 | no | — |
| 139 | C4×#41 | C23 | 1 | 2 | yes | — |
| 140 | C2×C4×D4 | — | 2 | 1 | no | — |
| 141 | C2×C4×D4 | — | 2 | 1 | no | — |
| 142 | C22×C4⋊C4 | — | 2 | 1 | no | — |
| 143 | C22×C4⋊C4 | — | 2 | 1 | no | — |
| 144 | C22×C42 | C23 | 1 | 1 | yes | characteristic |
| 145 | #501 | — | 2 | 4 | no | — |
| 146 | #500 | — | 2 | 2 | no | — |
| 147 | #498 | — | 2 | 2 | no | — |
| 148 | #497 | — | 2 | 4 | no | — |
| 149 | #497 | — | 2 | 4 | no | — |
| 150 | #497 | — | 2 | 8 | no | — |
| 151 | #494 | — | 2 | 2 | no | — |
| 152 | #494 | — | 2 | 2 | no | — |
| 153 | #494 | C23 | 1 | 8 | yes | — |
| 154 | #492 | — | 2 | 2 | no | — |
| 155 | #492 | — | 2 | 2 | no | — |
| 156 | #492 | C23 | 1 | 8 | yes | — |
| 157 | #489 | — | 2 | 4 | no | — |
| 158 | #487 | — | 2 | 2 | no | — |
| 159 | #486 | — | 2 | 2 | no | — |
| 160 | #484 | — | 2 | 4 | no | — |
| 161 | #483 | — | 2 | 4 | no | — |
| 162 | #481 | — | 2 | 4 | no | — |
| 163 | #480 | — | 2 | 4 | no | — |
| 164 | #478 | — | 2 | 4 | no | — |
| 165 | #477 | — | 2 | 2 | no | — |
| 166 | #477 | — | 2 | 2 | no | — |
| 167 | #477 | — | 2 | 2 | no | — |
| 168 | #476 | — | 2 | 2 | no | — |
| 169 | #476 | — | 2 | 2 | no | — |
| 170 | #476 | — | 2 | 2 | no | — |
| 171 | #476 | — | 2 | 2 | no | — |
| 172 | #475 | C23 | 1 | 4 | yes | — |
| 173 | #475 | C23 | 1 | 4 | yes | — |
| 174 | #475 | C23 | 1 | 4 | yes | — |
| 175 | #474 | — | 2 | 2 | no | — |
| 176 | #474 | C23 | 1 | 4 | yes | — |
| 177 | #474 | C23 | 1 | 4 | yes | — |
| 178 | #474 | C23 | 1 | 4 | yes | — |
| 179 | #469 | — | 2 | 4 | no | — |
| 180 | #468 | — | 2 | 4 | no | — |
| 181 | #466 | — | 2 | 4 | no | — |
| 182 | #465 | — | 2 | 4 | no | — |
| 183 | #463 | — | 2 | 4 | no | — |
| 184 | #461 | — | 2 | 2 | no | — |
| 185 | #460 | — | 2 | 2 | no | — |
| 186 | #460 | C23 | 1 | 4 | yes | — |
| 187 | #459 | — | 2 | 2 | no | — |
| 188 | #459 | — | 2 | 2 | no | — |
| 189 | #459 | C23 | 1 | 4 | yes | — |
| 190 | #446 | — | 2 | 4 | no | — |
| 191 | #446 | C23 | 1 | 4 | yes | — |
| 192 | C8×Q8 | C23 | 1 | 4 | yes | — |
| 193 | #436 | — | 2 | 4 | no | — |
| 194 | #436 | C23 | 1 | 4 | yes | — |
| 195 | #435 | — | 2 | 4 | no | — |
| 196 | #435 | — | 2 | 4 | no | — |
| 197 | #435 | — | 2 | 4 | no | — |
| 198 | C8×D4 | — | 2 | 4 | no | — |
| 199 | C8×D4 | C23 | 1 | 4 | yes | — |
| 200 | #433 | — | 2 | 4 | no | — |
| 201 | #432 | — | 2 | 1 | no | — |
| 202 | #432 | C23 | 1 | 2 | yes | — |
| 203 | #431 | — | 2 | 1 | no | — |
| 204 | #431 | — | 2 | 1 | no | — |
| 205 | #431 | — | 2 | 1 | no | — |
| 206 | #431 | — | 2 | 2 | no | — |
| 207 | #431 | — | 2 | 2 | no | — |
| 208 | #431 | C23 | 1 | 2 | yes | — |
| 209 | #431 | C23 | 1 | 1 | yes | characteristic |
| 210 | #431 | C23 | 1 | 1 | yes | characteristic |
| 211 | #431 | C23 | 1 | 2 | yes | — |
| 212 | #428 | — | 2 | 2 | no | — |
| 213 | #428 | — | 2 | 2 | no | — |
| 214 | #428 | — | 2 | 2 | no | — |
| 215 | #424 | — | 2 | 2 | no | — |
| 216 | #423 | — | 2 | 1 | no | — |
| 217 | #423 | — | 2 | 1 | no | — |
| 218 | #423 | C23 | 1 | 1 | yes | characteristic |
| 219 | #423 | C23 | 1 | 1 | yes | characteristic |
| 220 | #423 | C23 | 1 | 2 | yes | — |
| 221 | #423 | C23 | 1 | 2 | yes | — |
| 222 | C2×C4⋊C8 | — | 2 | 1 | no | — |
| 223 | C2×C4⋊C8 | C23 | 1 | 2 | yes | — |
| 224 | C2×C4⋊C8 | C23 | 1 | 2 | yes | — |
| 225 | #418 | — | 2 | 2 | no | — |
| 226 | #417 | — | 2 | 2 | no | — |
| 227 | #417 | — | 2 | 2 | no | — |
| 228 | #417 | — | 2 | 2 | no | — |
| 229 | #408 | — | 2 | 2 | no | — |
| 230 | #407 | — | 2 | 1 | no | — |
| 231 | C2×C22⋊C8 | — | 2 | 1 | no | — |
| 232 | #405 | — | 2 | 2 | no | — |
| 233 | #405 | — | 2 | 4 | no | — |
| 234 | C4×M16 | — | 2 | 1 | no | — |
| 235 | C4×M16 | — | 2 | 2 | no | — |
| 236 | C4×M16 | D4 | 1 | 1 | yes | characteristic |
| 237 | C4×M16 | D4 | 1 | 1 | yes | characteristic |
| 238 | C4×M16 | D4 | 1 | 2 | yes | — |
| 239 | C4×M16 | C23 | 1 | 2 | yes | — |
| 240 | C4×M16 | C23 | 1 | 2 | yes | — |
| 241 | C2×#97 | D4 | 1 | 2 | yes | — |
| 242 | C2×C4×C8 | — | 2 | 1 | no | — |
| 243 | C2×C4×C8 | — | 2 | 2 | no | — |
| 244 | C2×C4×C8 | C23 | 1 | 2 | yes | — |
| 245 | #335 | C23 | 1 | 8 | yes | — |
| 246 | #334 | C23 | 1 | 8 | yes | — |
| 247 | #332 | C23 | 1 | 8 | yes | — |
| 248 | #332 | C23 | 1 | 8 | yes | — |
| 249 | #332 | C23 | 1 | 4 | yes | — |
| 250 | #332 | C23 | 1 | 4 | yes | — |
| 251 | #331 | C23 | 1 | 4 | yes | — |
| 252 | #331 | C23 | 1 | 4 | yes | — |
| 253 | C2×#41 | — | 2 | 1 | no | — |
| 254 | C2×#41 | — | 2 | 1 | no | — |
| 255 | C2×#41 | — | 2 | 2 | no | — |
| 256 | C2×#41 | — | 2 | 2 | no | — |
| 257 | C2×#41 | — | 4 | 8 | no | — |
| 258 | C2×#41 | — | 4 | 1 | no | — |
| 259 | C2×#41 | — | 4 | 1 | no | — |
| 260 | C2×#41 | C2×D4 | 1 | 2 | yes | — |
| 261 | C22×Q8 | — | 2 | 1 | no | — |
| 262 | C22×Q8 | — | 2 | 2 | no | — |
| 263 | C22×Q8 | — | 2 | 2 | no | — |
| 264 | C22×Q8 | — | 2 | 2 | no | — |
| 265 | C22×Q8 | — | 4 | 8 | no | — |
| 266 | C22×Q8 | — | 4 | 1 | no | — |
| 267 | C22×Q8 | — | 4 | 1 | no | — |
| 268 | C22×Q8 | — | 4 | 1 | no | — |
| 269 | C22×D4 | — | 2 | 1 | no | — |
| 270 | C22×D4 | — | 2 | 1 | no | — |
| 271 | C22×D4 | — | 2 | 1 | no | — |
| 272 | C22×D4 | — | 4 | 1 | no | — |
| 273 | C23×C4 | — | 4 | 1 | no | — |
| 274 | C23×C4 | — | 4 | 1 | no | — |
| 275 | C23×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 276 | C23×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 277 | C23×C4 | #41 | 1 | 1 | yes | characteristic |
| 278 | #137 | — | 4 | 16 | no | — |
| 279 | #137 | — | 4 | 32 | no | — |
| 280 | #137 | — | 4 | 16 | no | — |
| 281 | AGL(1,ℤ/8) | — | 8 | 4 | no | — |
| 282 | C2×Q16 | — | 2 | 8 | no | — |
| 283 | C2×Q16 | — | 2 | 8 | no | — |
| 284 | C2×Q16 | — | 4 | 16 | no | — |
| 285 | C2×SD16 | — | 2 | 4 | no | — |
| 286 | C2×SD16 | — | 2 | 8 | no | — |
| 287 | C2×SD16 | — | 2 | 8 | no | — |
| 288 | C2×SD16 | — | 4 | 16 | no | — |
| 289 | C2×D8 | — | 2 | 4 | no | — |
| 290 | #131 | — | 4 | 8 | no | — |
| 291 | C2×M16 | — | 2 | 8 | no | — |
| 292 | C2×M16 | — | 2 | 2 | no | — |
| 293 | C2×M16 | — | 2 | 1 | no | — |
| 294 | C2×M16 | — | 2 | 1 | no | — |
| 295 | C2×M16 | — | 2 | 2 | no | — |
| 296 | C2×M16 | — | 2 | 4 | no | — |
| 297 | C2×M16 | — | 8 | 2 | no | — |
| 298 | C2×M16 | C2×D4 | 1 | 2 | yes | — |
| 299 | C2×M16 | C2×D4 | 1 | 4 | yes | — |
| 300 | C2×M16 | C2×D4 | 1 | 2 | yes | — |
| 301 | C22×C8 | — | 2 | 2 | no | — |
| 302 | C22×C8 | — | 2 | 2 | no | — |
| 303 | C22×C8 | — | 2 | 4 | no | — |
| 304 | C22×C8 | C2×D4 | 1 | 4 | yes | — |
| 305 | C4⋊Q8 | — | 2 | 2 | no | — |
| 306 | C4⋊Q8 | — | 2 | 2 | no | — |
| 307 | C4⋊Q8 | — | 2 | 2 | no | — |
| 308 | C4⋊Q8 | — | 2 | 1 | no | — |
| 309 | C4⋊Q8 | — | 2 | 2 | no | — |
| 310 | C4⋊Q8 | — | 2 | 2 | no | — |
| 311 | C4⋊Q8 | — | 2 | 2 | no | — |
| 312 | C4⋊Q8 | — | 2 | 1 | no | — |
| 313 | C4⋊Q8 | — | 2 | 2 | no | — |
| 314 | C4⋊Q8 | — | 2 | 2 | no | — |
| 315 | C4⋊Q8 | — | 2 | 2 | no | — |
| 316 | C4⋊Q8 | — | 2 | 1 | no | — |
| 317 | C4⋊Q8 | — | 4 | 1 | no | — |
| 318 | C4⋊Q8 | — | 4 | 1 | no | — |
| 319 | C4⋊Q8 | — | 4 | 1 | no | — |
| 320 | C4⋊Q8 | — | 4 | 1 | no | — |
| 321 | C4⋊Q8 | — | 4 | 1 | no | — |
| 322 | C4⋊Q8 | — | 4 | 1 | no | — |
| 323 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 324 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 325 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 326 | C4⋊Q8 | C24 | 1 | 4 | yes | — |
| 327 | C4⋊Q8 | C24 | 1 | 2 | yes | — |
| 328 | #127 | — | 2 | 1 | no | — |
| 329 | #127 | — | 2 | 1 | no | — |
| 330 | #127 | — | 2 | 1 | no | — |
| 331 | #127 | C2×D4 | 1 | 1 | yes | characteristic |
| 332 | #127 | C24 | 1 | 2 | yes | — |
| 333 | #126 | — | 2 | 2 | no | — |
| 334 | #126 | — | 2 | 2 | no | — |
| 335 | #125 | — | 2 | 1 | no | — |
| 336 | #125 | — | 2 | 1 | no | — |
| 337 | #125 | C2×D4 | 1 | 2 | yes | — |
| 338 | #124 | — | 2 | 1 | no | — |
| 339 | #124 | — | 2 | 2 | no | — |
| 340 | #124 | — | 2 | 2 | no | — |
| 341 | #124 | — | 2 | 1 | no | — |
| 342 | #124 | — | 4 | 1 | no | — |
| 343 | #124 | — | 4 | 1 | no | — |
| 344 | #124 | C2×D4 | 1 | 2 | yes | — |
| 345 | #123 | — | 2 | 2 | no | — |
| 346 | #123 | — | 2 | 2 | no | — |
| 347 | #123 | — | 2 | 2 | no | — |
| 348 | C22⋊Q8 | — | 2 | 1 | no | — |
| 349 | C22⋊Q8 | — | 2 | 1 | no | — |
| 350 | C22⋊Q8 | — | 2 | 1 | no | — |
| 351 | C22⋊Q8 | — | 2 | 1 | no | — |
| 352 | C22⋊Q8 | C2×D4 | 1 | 2 | yes | — |
| 353 | C22⋊Q8 | C2×D4 | 1 | 2 | yes | — |
| 354 | #121 | — | 2 | 1 | no | — |
| 355 | #121 | — | 2 | 1 | no | — |
| 356 | #121 | — | 2 | 1 | no | — |
| 357 | #121 | — | 2 | 1 | no | — |
| 358 | #121 | — | 2 | 2 | no | — |
| 359 | #121 | — | 2 | 2 | no | — |
| 360 | #121 | — | 2 | 2 | no | — |
| 361 | #121 | — | 2 | 2 | no | — |
| 362 | #121 | — | 4 | 1 | no | — |
| 363 | #121 | — | 4 | 1 | no | — |
| 364 | #121 | — | 4 | 1 | no | — |
| 365 | #121 | — | 4 | 1 | no | — |
| 366 | #121 | C2×D4 | 1 | 2 | yes | — |
| 367 | #121 | C2×D4 | 1 | 2 | yes | — |
| 368 | #120 | — | 2 | 2 | no | — |
| 369 | C4×Q8 | — | 2 | 1 | no | — |
| 370 | C4×Q8 | — | 2 | 1 | no | — |
| 371 | C4×Q8 | — | 2 | 1 | no | — |
| 372 | C4×Q8 | — | 2 | 1 | no | — |
| 373 | C4×Q8 | C2×D4 | 1 | 2 | yes | — |
| 374 | C4×Q8 | C24 | 1 | 2 | yes | — |
| 375 | C4×D4 | — | 2 | 2 | no | — |
| 376 | C4×D4 | — | 2 | 2 | no | — |
| 377 | C4×D4 | — | 2 | 2 | no | — |
| 378 | C4×D4 | — | 2 | 2 | no | — |
| 379 | C4×D4 | — | 2 | 2 | no | — |
| 380 | C4×D4 | — | 2 | 2 | no | — |
| 381 | C4×D4 | — | 2 | 1 | no | — |
| 382 | C4×D4 | — | 2 | 1 | no | — |
| 383 | C4×D4 | — | 2 | 1 | no | — |
| 384 | C4×D4 | — | 2 | 1 | no | — |
| 385 | C4×D4 | — | 2 | 2 | no | — |
| 386 | C4×D4 | — | 2 | 2 | no | — |
| 387 | C4×D4 | — | 2 | 2 | no | — |
| 388 | C4×D4 | — | 2 | 2 | no | — |
| 389 | C4×D4 | — | 4 | 1 | no | — |
| 390 | C4×D4 | — | 4 | 1 | no | — |
| 391 | C4×D4 | — | 4 | 1 | no | — |
| 392 | C4×D4 | — | 4 | 1 | no | — |
| 393 | C4×D4 | C2×D4 | 1 | 2 | yes | — |
| 394 | C4×D4 | C24 | 1 | 2 | yes | — |
| 395 | #117 | — | 2 | 1 | no | — |
| 396 | #117 | — | 2 | 1 | no | — |
| 397 | #117 | — | 2 | 2 | no | — |
| 398 | #117 | — | 2 | 2 | no | — |
| 399 | #117 | — | 2 | 2 | no | — |
| 400 | #117 | C2×D4 | 1 | 2 | yes | — |
| 401 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 402 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 403 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 404 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 405 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 406 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 407 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 408 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 409 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 410 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 411 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 412 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 413 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 414 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 415 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 416 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 417 | C2×C42 | — | 2 | 2 | no | — |
| 418 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 419 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 420 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 421 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 422 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 423 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 424 | C2×C42 | #41 | 1 | 1 | yes | characteristic |
| 425 | C2×C42 | #41 | 1 | 1 | yes | characteristic |
| 426 | C2×C42 | #41 | 1 | 1 | yes | characteristic |
| 427 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 428 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 429 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 430 | #107 | — | 2 | 4 | no | — |
| 431 | #107 | — | 2 | 4 | no | — |
| 432 | #107 | — | 2 | 4 | no | — |
| 433 | #106 | — | 2 | 4 | no | — |
| 434 | #106 | — | 2 | 4 | no | — |
| 435 | #106 | — | 2 | 4 | no | — |
| 436 | C4⋊C8 | — | 2 | 4 | no | — |
| 437 | C4⋊C8 | — | 2 | 4 | no | — |
| 438 | C4⋊C8 | — | 2 | 2 | no | — |
| 439 | C4⋊C8 | — | 2 | 2 | no | — |
| 440 | C4⋊C8 | — | 2 | 2 | no | — |
| 441 | C4⋊C8 | — | 2 | 2 | no | — |
| 442 | C4⋊C8 | — | 2 | 1 | no | — |
| 443 | C4⋊C8 | — | 2 | 1 | no | — |
| 444 | C4⋊C8 | C24 | 1 | 2 | yes | — |
| 445 | C4⋊C8 | C24 | 1 | 2 | yes | — |
| 446 | C4⋊C8 | C24 | 1 | 2 | yes | — |
| 447 | C4⋊C8 | C24 | 1 | 2 | yes | — |
| 448 | C4⋊C8 | C24 | 1 | 4 | yes | — |
| 449 | #103 | — | 2 | 4 | no | — |
| 450 | #103 | — | 2 | 4 | no | — |
| 451 | #103 | — | 2 | 4 | no | — |
| 452 | #102 | — | 2 | 4 | no | — |
| 453 | #102 | — | 2 | 4 | no | — |
| 454 | #102 | — | 2 | 4 | no | — |
| 455 | #102 | — | 2 | 4 | no | — |
| 456 | #102 | — | 2 | 4 | no | — |
| 457 | C22⋊C8 | — | 2 | 1 | no | — |
| 458 | C22⋊C8 | — | 2 | 1 | no | — |
| 459 | C22⋊C8 | — | 2 | 2 | no | — |
| 460 | C22⋊C8 | — | 2 | 2 | no | — |
| 461 | C22⋊C8 | — | 2 | 2 | no | — |
| 462 | C22⋊C8 | — | 2 | 4 | no | — |
| 463 | C22⋊C8 | — | 2 | 4 | no | — |
| 464 | #97 | — | 2 | 4 | no | — |
| 465 | #97 | — | 2 | 2 | no | — |
| 466 | #97 | C2×D4 | 1 | 2 | yes | — |
| 467 | #97 | C2×D4 | 1 | 2 | yes | — |
| 468 | #97 | C2×D4 | 1 | 4 | yes | — |
| 469 | C4×C8 | — | 2 | 4 | no | — |
| 470 | C4×C8 | — | 2 | 1 | no | — |
| 471 | C4×C8 | — | 2 | 1 | no | — |
| 472 | C4×C8 | — | 2 | 2 | no | — |
| 473 | C4×C8 | — | 2 | 2 | no | — |
| 474 | C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 475 | C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 476 | C4×C8 | C24 | 1 | 4 | yes | — |
| 477 | C24 | — | 4 | 1 | no | — |
| 478 | C24 | #121 | 1 | 1 | yes | characteristic |
| 479 | #41 | — | 2 | 4 | no | — |
| 480 | #41 | — | 2 | 4 | no | — |
| 481 | #41 | — | 4 | 8 | no | — |
| 482 | #41 | — | 4 | 4 | no | — |
| 483 | #41 | — | 4 | 8 | no | — |
| 484 | #41 | — | 8 | 2 | no | — |
| 485 | #41 | — | 8 | 4 | no | — |
| 486 | #41 | — | 8 | 4 | no | — |
| 487 | C2×Q8 | — | 2 | 1 | no | — |
| 488 | C2×Q8 | — | 2 | 1 | no | — |
| 489 | C2×Q8 | — | 2 | 2 | no | — |
| 490 | C2×Q8 | — | 2 | 4 | no | — |
| 491 | C2×Q8 | — | 4 | 8 | no | — |
| 492 | C2×Q8 | — | 4 | 4 | no | — |
| 493 | C2×Q8 | — | 4 | 8 | no | — |
| 494 | C2×Q8 | — | 4 | 1 | no | — |
| 495 | C2×Q8 | — | 4 | 2 | no | — |
| 496 | C2×Q8 | — | 4 | 2 | no | — |
| 497 | C2×Q8 | — | 4 | 2 | no | — |
| 498 | C2×Q8 | — | 4 | 8 | no | — |
| 499 | C2×Q8 | — | 8 | 4 | no | — |
| 500 | C2×Q8 | — | 8 | 4 | no | — |
| 501 | C2×Q8 | — | 8 | 4 | no | — |
| 502 | C2×Q8 | C22×D4 | 1 | 2 | yes | — |
| 503 | C2×D4 | — | 2 | 2 | no | — |
| 504 | C2×D4 | — | 2 | 2 | no | — |
| 505 | C2×D4 | — | 2 | 2 | no | — |
| 506 | C2×D4 | — | 2 | 1 | no | — |
| 507 | C2×D4 | — | 2 | 1 | no | — |
| 508 | C2×D4 | — | 2 | 2 | no | — |
| 509 | C2×D4 | — | 2 | 2 | no | — |
| 510 | C2×D4 | — | 2 | 2 | no | — |
| 511 | C2×D4 | — | 4 | 4 | no | — |
| 512 | C2×D4 | — | 4 | 2 | no | — |
| 513 | C2×D4 | — | 4 | 2 | no | — |
| 514 | C2×D4 | — | 4 | 1 | no | — |
| 515 | C2×D4 | — | 4 | 1 | no | — |
| 516 | C2×D4 | — | 4 | 1 | no | — |
| 517 | C2×D4 | — | 4 | 2 | no | — |
| 518 | C2×D4 | — | 4 | 2 | no | — |
| 519 | C2×D4 | — | 8 | 2 | no | — |
| 520 | C2×D4 | — | 8 | 4 | no | — |
| 521 | C2×D4 | C22×D4 | 1 | 2 | yes | — |
| 522 | C22×C4 | — | 2 | 4 | no | — |
| 523 | C22×C4 | — | 2 | 2 | no | — |
| 524 | C22×C4 | — | 2 | 2 | no | — |
| 525 | C22×C4 | — | 2 | 2 | no | — |
| 526 | C22×C4 | — | 2 | 2 | no | — |
| 527 | C22×C4 | — | 2 | 2 | no | — |
| 528 | C22×C4 | — | 4 | 2 | no | — |
| 529 | C22×C4 | — | 4 | 1 | no | — |
| 530 | C22×C4 | — | 4 | 2 | no | — |
| 531 | C22×C4 | — | 4 | 2 | no | — |
| 532 | C22×C4 | — | 4 | 2 | no | — |
| 533 | C22×C4 | — | 4 | 2 | no | — |
| 534 | C22×C4 | — | 4 | 2 | no | — |
| 535 | C22×C4 | — | 8 | 4 | no | — |
| 536 | C22×C4 | — | 8 | 4 | no | — |
| 537 | C22×C4 | #121 | 1 | 1 | yes | characteristic |
| 538 | C22×C4 | #121 | 1 | 1 | yes | characteristic |
| 539 | C22×C4 | #121 | 1 | 1 | yes | characteristic |
| 540 | C22×C4 | #121 | 1 | 1 | yes | characteristic |
| 541 | C22×C4 | #121 | 1 | 1 | yes | characteristic |
| 542 | C22×C4 | #121 | 1 | 1 | yes | characteristic |
| 543 | C22×C4 | #121 | 1 | 1 | yes | characteristic |
| 544 | C22×C4 | #121 | 1 | 1 | yes | characteristic |
| 545 | C22×C4 | #121 | 1 | 1 | yes | characteristic |
| 546 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 547 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 548 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 549 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 550 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 551 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 552 | C22×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 553 | C22×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 554 | C22×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 555 | Q16 | — | 4 | 16 | no | — |
| 556 | Q16 | — | 4 | 16 | no | — |
| 557 | SD16 | — | 4 | 16 | no | — |
| 558 | SD16 | — | 4 | 16 | no | — |
| 559 | SD16 | — | 8 | 4 | no | — |
| 560 | D8 | — | 8 | 4 | no | — |
| 561 | M16 | — | 2 | 4 | no | — |
| 562 | M16 | — | 2 | 8 | no | — |
| 563 | M16 | — | 4 | 2 | no | — |
| 564 | M16 | — | 4 | 4 | no | — |
| 565 | M16 | — | 4 | 2 | no | — |
| 566 | M16 | — | 4 | 8 | no | — |
| 567 | M16 | — | 8 | 2 | no | — |
| 568 | M16 | AGL(1,ℤ/8) | 1 | 8 | yes | complemented |
| 569 | C2×C8 | — | 2 | 8 | no | — |
| 570 | C2×C8 | — | 2 | 2 | no | — |
| 571 | C2×C8 | — | 2 | 2 | no | — |
| 572 | C2×C8 | — | 2 | 2 | no | — |
| 573 | C2×C8 | — | 2 | 2 | no | — |
| 574 | C2×C8 | — | 2 | 4 | no | — |
| 575 | C2×C8 | — | 4 | 4 | no | — |
| 576 | C2×C8 | — | 4 | 8 | no | — |
| 577 | C2×C8 | — | 8 | 2 | no | — |
| 578 | C2×C8 | C22×D4 | 1 | 4 | yes | — |
| 579 | C2×C8 | C22×D4 | 1 | 4 | yes | — |
| 580 | C4⋊C4 | — | 2 | 1 | no | — |
| 581 | C4⋊C4 | — | 2 | 1 | no | — |
| 582 | C4⋊C4 | — | 2 | 1 | no | — |
| 583 | C4⋊C4 | — | 2 | 1 | no | — |
| 584 | C4⋊C4 | — | 2 | 2 | no | — |
| 585 | C4⋊C4 | — | 2 | 2 | no | — |
| 586 | C4⋊C4 | — | 2 | 2 | no | — |
| 587 | C4⋊C4 | — | 2 | 2 | no | — |
| 588 | C4⋊C4 | — | 2 | 2 | no | — |
| 589 | C4⋊C4 | — | 2 | 2 | no | — |
| 590 | C4⋊C4 | — | 2 | 4 | no | — |
| 591 | C4⋊C4 | — | 2 | 2 | no | — |
| 592 | C4⋊C4 | — | 2 | 4 | no | — |
| 593 | C4⋊C4 | — | 2 | 2 | no | — |
| 594 | C4⋊C4 | — | 4 | 2 | no | — |
| 595 | C4⋊C4 | — | 4 | 2 | no | — |
| 596 | C4⋊C4 | — | 4 | 2 | no | — |
| 597 | C4⋊C4 | — | 4 | 2 | no | — |
| 598 | C4⋊C4 | — | 4 | 2 | no | — |
| 599 | C4⋊C4 | — | 4 | 2 | no | — |
| 600 | C4⋊C4 | — | 4 | 1 | no | — |
| 601 | C4⋊C4 | — | 4 | 1 | no | — |
| 602 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 603 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 604 | C22⋊C4 | — | 2 | 2 | no | — |
| 605 | C22⋊C4 | — | 2 | 2 | no | — |
| 606 | C22⋊C4 | — | 2 | 2 | no | — |
| 607 | C22⋊C4 | — | 2 | 2 | no | — |
| 608 | C22⋊C4 | — | 2 | 2 | no | — |
| 609 | C22⋊C4 | — | 2 | 2 | no | — |
| 610 | C22⋊C4 | — | 2 | 2 | no | — |
| 611 | C22⋊C4 | — | 2 | 2 | no | — |
| 612 | C22⋊C4 | — | 2 | 2 | no | — |
| 613 | C22⋊C4 | — | 4 | 2 | no | — |
| 614 | C22⋊C4 | — | 4 | 2 | no | — |
| 615 | C22⋊C4 | — | 4 | 2 | no | — |
| 616 | C22⋊C4 | — | 4 | 2 | no | — |
| 617 | C42 | — | 2 | 2 | no | — |
| 618 | C42 | — | 2 | 2 | no | — |
| 619 | C42 | — | 2 | 2 | no | — |
| 620 | C42 | #121 | 1 | 1 | yes | characteristic |
| 621 | C42 | #121 | 1 | 1 | yes | characteristic |
| 622 | C42 | #121 | 1 | 1 | yes | characteristic |
| 623 | C42 | #121 | 1 | 1 | yes | characteristic |
| 624 | C42 | #121 | 1 | 1 | yes | characteristic |
| 625 | C42 | #121 | 1 | 1 | yes | characteristic |
| 626 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 627 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 628 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 629 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 630 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 631 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 632 | C42 | C2×#41 | 1 | 1 | yes | characteristic |
| 633 | C42 | C2×#41 | 1 | 1 | yes | characteristic |
| 634 | C42 | C2×#41 | 1 | 1 | yes | characteristic |
| 635 | C42 | C25 | 1 | 1 | yes | characteristic |
| 636 | C23 | — | 2 | 2 | no | — |
| 637 | C23 | — | 2 | 2 | no | — |
| 638 | C23 | — | 2 | 2 | no | — |
| 639 | C23 | — | 4 | 1 | no | — |
| 640 | C23 | — | 4 | 2 | no | — |
| 641 | C23 | — | 8 | 2 | no | — |
| 642 | C23 | — | 8 | 2 | no | — |
| 643 | C23 | — | 8 | 2 | no | — |
| 644 | C23 | C2×#121 | 1 | 1 | yes | characteristic |
| 645 | C23 | C2×#121 | 1 | 1 | yes | characteristic |
| 646 | C23 | C2×#121 | 1 | 1 | yes | characteristic |
| 647 | Q8 | — | 2 | 2 | no | — |
| 648 | Q8 | — | 2 | 2 | no | — |
| 649 | Q8 | — | 4 | 2 | no | — |
| 650 | Q8 | — | 4 | 8 | no | — |
| 651 | Q8 | — | 4 | 4 | no | — |
| 652 | Q8 | — | 8 | 1 | no | — |
| 653 | Q8 | — | 8 | 4 | no | — |
| 654 | Q8 | — | 8 | 4 | no | — |
| 655 | Q8 | — | 8 | 2 | no | — |
| 656 | Q8 | — | 8 | 4 | no | — |
| 657 | D4 | — | 2 | 2 | no | — |
| 658 | D4 | — | 2 | 2 | no | — |
| 659 | D4 | — | 4 | 4 | no | — |
| 660 | D4 | — | 4 | 4 | no | — |
| 661 | D4 | — | 4 | 2 | no | — |
| 662 | D4 | — | 4 | 4 | no | — |
| 663 | D4 | — | 4 | 2 | no | — |
| 664 | D4 | — | 4 | 2 | no | — |
| 665 | D4 | — | 8 | 1 | no | — |
| 666 | D4 | — | 8 | 2 | no | — |
| 667 | D4 | — | 8 | 2 | no | — |
| 668 | D4 | — | 8 | 2 | no | — |
| 669 | D4 | — | 8 | 4 | no | — |
| 670 | D4 | — | 8 | 4 | no | — |
| 671 | D4 | — | 8 | 2 | no | — |
| 672 | D4 | — | 8 | 2 | no | — |
| 673 | C2×C4 | — | 2 | 2 | no | — |
| 674 | C2×C4 | — | 2 | 2 | no | — |
| 675 | C2×C4 | — | 2 | 2 | no | — |
| 676 | C2×C4 | — | 2 | 2 | no | — |
| 677 | C2×C4 | — | 2 | 2 | no | — |
| 678 | C2×C4 | — | 2 | 2 | no | — |
| 679 | C2×C4 | — | 2 | 2 | no | — |
| 680 | C2×C4 | — | 2 | 2 | no | — |
| 681 | C2×C4 | — | 2 | 2 | no | — |
| 682 | C2×C4 | — | 2 | 2 | no | — |
| 683 | C2×C4 | — | 2 | 2 | no | — |
| 684 | C2×C4 | — | 2 | 1 | no | — |
| 685 | C2×C4 | — | 2 | 1 | no | — |
| 686 | C2×C4 | — | 2 | 1 | no | — |
| 687 | C2×C4 | — | 2 | 1 | no | — |
| 688 | C2×C4 | — | 2 | 2 | no | — |
| 689 | C2×C4 | — | 2 | 2 | no | — |
| 690 | C2×C4 | — | 2 | 2 | no | — |
| 691 | C2×C4 | — | 4 | 1 | no | — |
| 692 | C2×C4 | — | 4 | 1 | no | — |
| 693 | C2×C4 | — | 4 | 1 | no | — |
| 694 | C2×C4 | — | 4 | 4 | no | — |
| 695 | C2×C4 | — | 4 | 4 | no | — |
| 696 | C2×C4 | — | 4 | 4 | no | — |
| 697 | C2×C4 | — | 4 | 2 | no | — |
| 698 | C2×C4 | — | 4 | 4 | no | — |
| 699 | C2×C4 | — | 8 | 4 | no | — |
| 700 | C2×C4 | — | 8 | 2 | no | — |
| 701 | C2×C4 | — | 8 | 4 | no | — |
| 702 | C2×C4 | — | 8 | 4 | no | — |
| 703 | C2×C4 | — | 8 | 4 | no | — |
| 704 | C2×C4 | — | 8 | 4 | no | — |
| 705 | C2×C4 | C2×#121 | 1 | 1 | yes | characteristic |
| 706 | C2×C4 | C2×#121 | 1 | 1 | yes | characteristic |
| 707 | C2×C4 | C2×#121 | 1 | 1 | yes | characteristic |
| 708 | C2×C4 | C2×#121 | 1 | 1 | yes | characteristic |
| 709 | C2×C4 | C2×#121 | 1 | 1 | yes | characteristic |
| 710 | C2×C4 | C2×#121 | 1 | 1 | yes | characteristic |
| 711 | C2×C4 | C2×#121 | 1 | 1 | yes | characteristic |
| 712 | C2×C4 | C2×#121 | 1 | 1 | yes | characteristic |
| 713 | C2×C4 | C2×#121 | 1 | 1 | yes | characteristic |
| 714 | C2×C4 | C2×AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 715 | C2×C4 | #577 | 1 | 2 | yes | — |
| 716 | C2×C4 | #578 | 1 | 2 | yes | — |
| 717 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 718 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 719 | C2×C4 | C22×#41 | 1 | 1 | yes | characteristic |
| 720 | C8 | — | 2 | 4 | no | — |
| 721 | C8 | — | 4 | 2 | no | — |
| 722 | C8 | — | 4 | 2 | no | — |
| 723 | C8 | — | 4 | 4 | no | — |
| 724 | C8 | — | 4 | 2 | no | — |
| 725 | C8 | — | 4 | 2 | no | — |
| 726 | C8 | C2×AGL(1,ℤ/8) | 1 | 8 | yes | — |
| 727 | C22 | — | 2 | 1 | no | — |
| 728 | C22 | — | 2 | 1 | no | — |
| 729 | C22 | — | 2 | 1 | no | — |
| 730 | C22 | — | 2 | 1 | no | — |
| 731 | C22 | — | 2 | 1 | no | — |
| 732 | C22 | — | 2 | 1 | no | — |
| 733 | C22 | — | 2 | 1 | no | — |
| 734 | C22 | — | 4 | 4 | no | — |
| 735 | C22 | — | 4 | 2 | no | — |
| 736 | C22 | — | 4 | 2 | no | — |
| 737 | C22 | — | 4 | 2 | no | — |
| 738 | C22 | — | 8 | 2 | no | — |
| 739 | C22 | — | 8 | 2 | no | — |
| 740 | C22 | — | 8 | 2 | no | — |
| 741 | C22 | — | 16 | 4 | no | — |
| 742 | C22 | #3038 | 1 | 2 | yes | — |
| 743 | C22 | #3063 | 1 | 2 | yes | — |
| 744 | C22 | C22×#121 | 1 | 1 | yes | characteristic |
| 745 | C4 | — | 2 | 1 | no | — |
| 746 | C4 | — | 2 | 1 | no | — |
| 747 | C4 | — | 2 | 1 | no | — |
| 748 | C4 | — | 2 | 1 | no | — |
| 749 | C4 | — | 2 | 1 | no | — |
| 750 | C4 | — | 2 | 1 | no | — |
| 751 | C4 | — | 2 | 1 | no | — |
| 752 | C4 | — | 4 | 2 | no | — |
| 753 | C4 | — | 4 | 2 | no | — |
| 754 | C4 | — | 4 | 2 | no | — |
| 755 | C4 | — | 8 | 2 | no | — |
| 756 | C4 | — | 8 | 4 | no | — |
| 757 | C4 | #3038 | 1 | 2 | yes | — |
| 758 | C4 | #3063 | 1 | 2 | yes | — |
| 759 | C4 | #3069 | 1 | 2 | yes | — |
| 760 | C4 | C22×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 761 | C4 | C2×#577 | 1 | 1 | yes | characteristic |
| 762 | C4 | C2×#578 | 1 | 1 | yes | characteristic |
| 763 | C2 | — | 2 | 2 | no | — |
| 764 | C2 | — | 2 | 2 | no | — |
| 765 | C2 | — | 4 | 1 | no | — |
| 766 | C2 | — | 8 | 2 | no | — |
| 767 | C2 | — | 16 | 2 | no | — |
| 768 | C2 | C2×#3038 | 1 | 1 | yes | characteristic |
| 769 | C2 | C2×#3063 | 1 | 1 | yes | characteristic |
| 770 | C2 | C2×#3069 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C22×#121 |
| commutator, Frattini, cosocle | C42 | C25 |
| prime radical | #60916 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C22×C42 ◁ G | |
| LECS | G ▷ C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #60860 | C2 | semidirect |
| 3. C2×#3152 | C2 | semidirect |
| 4. #60210 | C2 | semidirect |
| 5. #19377 | C2 | semidirect |
| 6. #19293 | C2 | semidirect |
| 7. #19291 | C2 | semidirect |
| 8. #19268 | C2 | semidirect |
| 9. #19266 | C2 | semidirect |
| 10. #19239 | C2 | semidirect |
| 11. #19231 | C2 | semidirect |
| 12. #17796 | C2 | semidirect |
| 13. #17717 | C2 | semidirect |
| 14. C2×#1549 | C2 | semidirect |
| 25. #3239 | C22 | semidirect |
| 28. #3229 | C22 | semidirect |
| 30. #3226 | C22 | semidirect |
| 49. #2969 | C22 | semidirect |
| 54. #2962 | C22 | semidirect |
| 55. #2935 | C22 | semidirect |
| 63. #1690 | C22 | semidirect |
| 64. #1689 | C22 | semidirect |
| 65. #1686 | C22 | semidirect |
| 66. #1685 | C22 | semidirect |
| 67. #1670 | C22 | semidirect |
| 68. #1669 | C22 | semidirect |
| 69. #1666 | C22 | semidirect |
| 70. #1665 | C22 | semidirect |
| 71. #1569 | C22 | semidirect |
| 74. #1565 | C22 | semidirect |
| 80. #1549 | C22 | semidirect |
| 84. C2×#332 | C22 | semidirect |
| 568. M16 | AGL(1,ℤ/8) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #60916 | 2 |
| #60860 | 2 |
| C2×#3152 | 2 |
| #60210 | 2 |
| #19377 | 2 |
| #19293 | 2 |
| #19291 | 2 |
| #19268 | 2 |
| #19266 | 2 |
| #19239 | 2 |
| #19231 | 2 |
| #17796 | 2 |
| #17717 | 2 |
| C2×#1549 | 2 |