Finite Group DatabasebetaFinite Group DatabasebetaOrder 4096.
1529 conjugacy classes of subgroups.
The subgroup lattice has 955 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #72225506 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #72225504 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #72225502 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #72225500 | — | 2 | 4 | no | — |
| 5 | #72225499 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #72225487 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #72225485 | C22 | 1 | 2 | yes | — |
| 8 | #72225484 | C22 | 1 | 2 | yes | — |
| 9 | #72225472 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #72225470 | C22 | 1 | 2 | yes | — |
| 11 | #72225468 | C22 | 1 | 2 | yes | — |
| 12 | #72225455 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #72225453 | C22 | 1 | 2 | yes | — |
| 14 | #72225452 | C22 | 1 | 2 | yes | — |
| 15 | #72225430 | C2 | 1 | 1 | yes | maximal, characteristic |
| 16 | #72225427 | C22 | 1 | 2 | yes | — |
| 17 | #72225425 | C4 | 1 | 4 | yes | complemented |
| 18 | #72225424 | C22 | 1 | 2 | yes | — |
| 19 | #72225423 | C4 | 1 | 2 | yes | complemented |
| 20 | #72225422 | C4 | 1 | 2 | yes | complemented |
| 21 | #72225408 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 22 | #72225405 | C22 | 1 | 2 | yes | — |
| 23 | #72225404 | C22 | 1 | 2 | yes | — |
| 24 | #72225395 | C22 | 1 | 1 | yes | characteristic |
| 25 | #72225395 | C22 | 1 | 1 | yes | characteristic |
| 26 | #72225315 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 27 | #72225314 | C22 | 1 | 1 | yes | characteristic |
| 28 | #72225313 | C22 | 1 | 1 | yes | characteristic |
| 29 | #72225312 | — | 2 | 1 | no | — |
| 30 | #72225311 | — | 2 | 1 | no | — |
| 31 | #72225310 | C22 | 1 | 1 | yes | characteristic |
| 32 | #72225308 | C22 | 1 | 1 | yes | characteristic |
| 33 | #72225305 | C22 | 1 | 1 | yes | characteristic |
| 34 | #72225304 | — | 2 | 1 | no | — |
| 35 | #72224652 | — | 2 | 4 | no | — |
| 36 | #72223679 | C22 | 1 | 1 | yes | characteristic |
| 37 | #72216316 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 38 | #72216311 | — | 2 | 1 | no | — |
| 39 | #72216311 | C22 | 1 | 2 | yes | — |
| 40 | #72216305 | — | 2 | 1 | no | — |
| 41 | #72216305 | C22 | 1 | 2 | yes | — |
| 42 | #72216296 | C22 | 1 | 1 | yes | characteristic |
| 43 | #72216283 | — | 2 | 1 | no | — |
| 44 | #72216261 | C22 | 1 | 1 | yes | characteristic |
| 45 | #72216241 | — | 2 | 1 | no | — |
| 46 | C8×#1398 | C22 | 1 | 1 | yes | characteristic |
| 47 | #72216211 | — | 2 | 1 | no | — |
| 48 | #513082 | — | 2 | 1 | no | — |
| 49 | #513082 | C23 | 1 | 2 | yes | — |
| 50 | #512778 | — | 2 | 1 | no | — |
| 51 | #512773 | C23 | 1 | 1 | yes | characteristic |
| 52 | #493242 | — | 2 | 1 | no | — |
| 53 | #493217 | — | 4 | 1 | no | — |
| 54 | #491485 | — | 2 | 1 | no | — |
| 55 | #483943 | — | 2 | 2 | no | — |
| 56 | #483943 | — | 4 | 1 | no | — |
| 57 | C2×#12047 | — | 2 | 1 | no | — |
| 58 | C2×#12046 | — | 2 | 1 | no | — |
| 59 | #213237 | — | 4 | 1 | no | — |
| 60 | #153681 | — | 2 | 2 | no | — |
| 61 | #153674 | C2×C4 | 1 | 4 | yes | — |
| 62 | #153656 | C2×C4 | 1 | 4 | yes | — |
| 63 | #153607 | — | 2 | 2 | no | — |
| 64 | #153598 | — | 2 | 4 | no | — |
| 65 | #153582 | C23 | 1 | 2 | yes | — |
| 66 | #153582 | C23 | 1 | 2 | yes | — |
| 67 | #151999 | — | 2 | 1 | no | — |
| 68 | #151998 | C23 | 1 | 1 | yes | characteristic |
| 69 | #151973 | — | 2 | 1 | no | — |
| 70 | #151971 | — | 2 | 1 | no | — |
| 71 | #151968 | — | 2 | 1 | no | — |
| 72 | C4×#1398 | D4 | 1 | 1 | yes | characteristic |
| 73 | C4×#1398 | C23 | 1 | 1 | yes | characteristic |
| 74 | #151732 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 75 | #151724 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 76 | #151718 | — | 2 | 1 | no | — |
| 77 | #151715 | — | 2 | 1 | no | — |
| 78 | #151715 | C2×C4 | 1 | 2 | yes | complemented |
| 79 | #151129 | — | 2 | 2 | no | — |
| 80 | #151129 | — | 2 | 2 | no | — |
| 81 | #151129 | — | 4 | 2 | no | — |
| 82 | #151086 | — | 2 | 1 | no | — |
| 83 | #151086 | — | 2 | 1 | no | — |
| 84 | #151086 | D4 | 1 | 2 | yes | — |
| 85 | #151086 | D4 | 1 | 2 | yes | — |
| 86 | #151085 | — | 2 | 2 | no | — |
| 87 | #151085 | — | 2 | 2 | no | — |
| 88 | #151085 | — | 4 | 2 | no | — |
| 89 | #151082 | — | 2 | 1 | no | — |
| 90 | #151082 | C2×C4 | 1 | 2 | yes | — |
| 91 | #151081 | — | 2 | 1 | no | — |
| 92 | #151081 | C2×C4 | 1 | 2 | yes | — |
| 93 | #151055 | — | 2 | 1 | no | — |
| 94 | #151055 | C23 | 1 | 2 | yes | — |
| 95 | #151040 | C23 | 1 | 1 | yes | characteristic |
| 96 | #151035 | C23 | 1 | 1 | yes | characteristic |
| 97 | #150160 | — | 2 | 2 | no | — |
| 98 | #150160 | — | 2 | 2 | no | — |
| 99 | #150069 | — | 2 | 1 | no | — |
| 100 | #150067 | — | 2 | 1 | no | — |
| 101 | #149495 | D4 | 1 | 1 | yes | characteristic |
| 102 | #149495 | C23 | 1 | 1 | yes | characteristic |
| 103 | C8×M64 | D4 | 1 | 1 | yes | characteristic |
| 104 | C8×M64 | C23 | 1 | 1 | yes | characteristic |
| 105 | #141812 | — | 4 | 1 | no | — |
| 106 | #141786 | — | 2 | 2 | no | — |
| 107 | #141786 | — | 4 | 1 | no | — |
| 108 | #135796 | — | 2 | 1 | no | — |
| 109 | #129143 | — | 2 | 1 | no | — |
| 110 | #129142 | — | 2 | 1 | no | — |
| 111 | #129101 | — | 2 | 1 | no | — |
| 112 | #128674 | — | 4 | 1 | no | — |
| 113 | #128673 | — | 4 | 1 | no | — |
| 114 | C4×#1335 | — | 4 | 1 | no | — |
| 115 | C8×#346 | D4 | 1 | 1 | yes | characteristic |
| 116 | #94754 | — | 2 | 4 | no | — |
| 117 | #94748 | — | 2 | 1 | no | — |
| 118 | #94748 | C2×C4 | 1 | 2 | yes | complemented |
| 119 | #94746 | — | 2 | 1 | no | — |
| 120 | #94746 | C2×C4 | 1 | 2 | yes | complemented |
| 121 | #94743 | C2×C4 | 1 | 4 | yes | complemented |
| 122 | #94738 | C2×C4 | 1 | 4 | yes | complemented |
| 123 | #94696 | — | 2 | 2 | no | — |
| 124 | #94694 | — | 2 | 2 | no | — |
| 125 | #94614 | — | 2 | 4 | no | — |
| 126 | #94613 | — | 2 | 4 | no | — |
| 127 | #94509 | — | 2 | 2 | no | — |
| 128 | #94506 | — | 2 | 2 | no | — |
| 129 | #94054 | — | 2 | 1 | no | — |
| 130 | #94053 | — | 2 | 1 | no | — |
| 131 | #94029 | — | 2 | 1 | no | — |
| 132 | #33981 | #41 | 1 | 1 | yes | characteristic |
| 133 | #33733 | — | 2 | 2 | no | — |
| 134 | #33733 | — | 4 | 1 | no | — |
| 135 | C2×#2179 | — | 2 | 1 | no | — |
| 136 | C2×#2178 | — | 2 | 1 | no | — |
| 137 | #33451 | — | 2 | 1 | no | — |
| 138 | C2×#2170 | — | 4 | 1 | no | — |
| 139 | C2×#2170 | — | 4 | 1 | no | — |
| 140 | #33326 | — | 8 | 1 | no | — |
| 141 | #21705 | — | 8 | 1 | no | — |
| 142 | C4×#443 | — | 4 | 1 | no | — |
| 143 | #19603 | — | 4 | 1 | no | — |
| 144 | #17956 | — | 4 | 2 | no | — |
| 145 | #17956 | — | 8 | 1 | no | — |
| 146 | #13742 | — | 2 | 4 | no | — |
| 147 | #13733 | — | 2 | 1 | no | — |
| 148 | #13733 | C22×C4 | 1 | 2 | yes | — |
| 149 | #13725 | — | 2 | 1 | no | — |
| 150 | #13725 | C22×C4 | 1 | 2 | yes | — |
| 151 | #13719 | — | 2 | 2 | no | — |
| 152 | #13719 | — | 2 | 2 | no | — |
| 153 | #13697 | — | 2 | 2 | no | — |
| 154 | #13697 | — | 2 | 2 | no | — |
| 155 | #13697 | — | 4 | 2 | no | — |
| 156 | #13658 | — | 2 | 4 | no | — |
| 157 | #13657 | — | 2 | 4 | no | — |
| 158 | #13656 | — | 2 | 1 | no | — |
| 159 | #13656 | C2×D4 | 1 | 2 | yes | — |
| 160 | #13655 | — | 2 | 1 | no | — |
| 161 | #13655 | C22×C4 | 1 | 2 | yes | — |
| 162 | #13654 | — | 2 | 2 | no | — |
| 163 | #13654 | — | 2 | 2 | no | — |
| 164 | #13654 | — | 4 | 2 | no | — |
| 165 | #13638 | — | 2 | 1 | no | — |
| 166 | #13636 | #41 | 1 | 1 | yes | characteristic |
| 167 | #13625 | — | 2 | 1 | no | — |
| 168 | #13622 | — | 2 | 1 | no | — |
| 169 | #13620 | — | 2 | 1 | no | — |
| 170 | C2×#1398 | — | 2 | 1 | no | — |
| 171 | C2×#1398 | — | 2 | 1 | no | — |
| 172 | C2×#1398 | — | 4 | 1 | no | — |
| 173 | C4×M64 | C2×D4 | 1 | 1 | yes | characteristic |
| 174 | C4×M64 | C2×D4 | 1 | 1 | yes | characteristic |
| 175 | C4×M64 | C2×D4 | 1 | 1 | yes | characteristic |
| 176 | C4×M64 | C24 | 1 | 1 | yes | characteristic |
| 177 | #12676 | — | 2 | 1 | no | — |
| 178 | #12671 | — | 2 | 1 | no | — |
| 179 | #12670 | — | 2 | 1 | no | — |
| 180 | #12664 | — | 4 | 1 | no | — |
| 181 | #12664 | — | 4 | 1 | no | — |
| 182 | C4×#364 | — | 4 | 1 | no | — |
| 183 | #12642 | — | 4 | 1 | no | — |
| 184 | #12641 | — | 4 | 1 | no | — |
| 185 | #12640 | — | 4 | 1 | no | — |
| 186 | #12615 | — | 8 | 1 | no | — |
| 187 | #12615 | — | 8 | 1 | no | — |
| 188 | #12604 | — | 8 | 1 | no | — |
| 189 | C4×#346 | D8 | 1 | 1 | yes | characteristic |
| 190 | C4×#346 | C2×D4 | 1 | 1 | yes | characteristic |
| 191 | #12521 | — | 2 | 1 | no | — |
| 192 | #12515 | — | 2 | 1 | no | — |
| 193 | #12509 | — | 4 | 1 | no | — |
| 194 | #12503 | — | 2 | 2 | no | — |
| 195 | #12503 | — | 4 | 1 | no | — |
| 196 | #12086 | — | 4 | 2 | no | — |
| 197 | #12086 | — | 4 | 2 | no | — |
| 198 | #12086 | — | 8 | 1 | no | — |
| 199 | #12086 | — | 8 | 1 | no | — |
| 200 | #12047 | — | 2 | 2 | no | — |
| 201 | #12047 | — | 2 | 2 | no | — |
| 202 | #12047 | — | 4 | 1 | no | — |
| 203 | #12047 | — | 4 | 1 | no | — |
| 204 | #12046 | — | 2 | 2 | no | — |
| 205 | #12046 | — | 2 | 2 | no | — |
| 206 | #12046 | — | 4 | 1 | no | — |
| 207 | #12046 | — | 4 | 1 | no | — |
| 208 | #12045 | — | 4 | 2 | no | — |
| 209 | #12045 | — | 4 | 2 | no | — |
| 210 | #12045 | — | 8 | 1 | no | — |
| 211 | #12045 | — | 8 | 1 | no | — |
| 212 | #12023 | — | 2 | 2 | no | — |
| 213 | #12023 | — | 4 | 1 | no | — |
| 214 | C2×#1373 | — | 2 | 1 | no | — |
| 215 | C2×#1373 | — | 2 | 1 | no | — |
| 216 | #11671 | — | 4 | 2 | no | — |
| 217 | #11671 | — | 4 | 2 | no | — |
| 218 | C2×#1335 | — | 4 | 1 | no | — |
| 219 | C2×#1335 | — | 4 | 1 | no | — |
| 220 | C2×#1311 | D8 | 1 | 1 | yes | characteristic |
| 221 | C2×#1311 | C2×D4 | 1 | 1 | yes | characteristic |
| 222 | C2×C8×C16 | D8 | 1 | 1 | yes | characteristic |
| 223 | C2×C8×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 224 | #9856 | — | 8 | 1 | no | — |
| 225 | #9844 | — | 4 | 2 | no | — |
| 226 | #9844 | — | 8 | 1 | no | — |
| 227 | #8823 | — | 4 | 1 | no | — |
| 228 | C4×C82 | D8 | 1 | 1 | yes | characteristic |
| 229 | #7548 | — | 2 | 4 | no | — |
| 230 | #7544 | — | 2 | 2 | no | — |
| 231 | #7544 | C22×C4 | 1 | 4 | yes | — |
| 232 | #7541 | — | 2 | 4 | no | — |
| 233 | #7540 | — | 2 | 4 | no | — |
| 234 | #7513 | — | 2 | 2 | no | — |
| 235 | #7513 | — | 2 | 2 | no | — |
| 236 | #7511 | — | 2 | 2 | no | — |
| 237 | #7511 | — | 2 | 2 | no | — |
| 238 | #7480 | — | 2 | 1 | no | — |
| 239 | #7479 | — | 2 | 1 | no | — |
| 240 | #7476 | #41 | 1 | 1 | yes | characteristic |
| 241 | #7475 | #41 | 1 | 1 | yes | characteristic |
| 242 | #7464 | — | 2 | 1 | no | — |
| 243 | #7464 | C2×D4 | 1 | 2 | yes | — |
| 244 | #7463 | — | 2 | 2 | no | — |
| 245 | #7463 | — | 2 | 2 | no | — |
| 246 | #7463 | — | 4 | 2 | no | — |
| 247 | #7462 | — | 2 | 1 | no | — |
| 248 | #7462 | C22×C4 | 1 | 2 | yes | — |
| 249 | #7388 | — | 2 | 2 | no | — |
| 250 | #7388 | — | 2 | 2 | no | — |
| 251 | #7387 | — | 2 | 2 | no | — |
| 252 | #7387 | — | 2 | 2 | no | — |
| 253 | #7385 | — | 4 | 4 | no | — |
| 254 | #7385 | — | 4 | 2 | no | — |
| 255 | #7385 | — | 4 | 2 | no | — |
| 256 | #7330 | — | 2 | 1 | no | — |
| 257 | #7330 | — | 2 | 1 | no | — |
| 258 | #7330 | C2×D4 | 1 | 1 | yes | characteristic |
| 259 | #7330 | C2×D4 | 1 | 1 | yes | characteristic |
| 260 | #7330 | #41 | 1 | 1 | yes | characteristic |
| 261 | #7330 | #41 | 1 | 1 | yes | characteristic |
| 262 | #7329 | — | 2 | 1 | no | — |
| 263 | #7329 | C22×C4 | 1 | 1 | yes | characteristic |
| 264 | #7329 | #41 | 1 | 1 | yes | characteristic |
| 265 | C8×C32 | — | 2 | 1 | no | — |
| 266 | C8×C32 | C22×C4 | 1 | 1 | yes | characteristic |
| 267 | C8×C32 | #41 | 1 | 1 | yes | characteristic |
| 268 | #7179 | — | 4 | 1 | no | — |
| 269 | #7179 | — | 4 | 1 | no | — |
| 270 | #7160 | — | 4 | 1 | no | — |
| 271 | C2×#508 | — | 2 | 1 | no | — |
| 272 | C2×#504 | — | 8 | 1 | no | — |
| 273 | C2×#504 | — | 8 | 1 | no | — |
| 274 | #3169 | — | 4 | 2 | no | — |
| 275 | #3169 | — | 8 | 1 | no | — |
| 276 | #3147 | — | 8 | 1 | no | — |
| 277 | C2×#443 | — | 4 | 1 | no | — |
| 278 | C2×#443 | — | 4 | 1 | no | — |
| 279 | C2×#443 | — | 16 | 2 | no | — |
| 280 | C4×#135 | — | 4 | 1 | no | — |
| 281 | #2931 | — | 8 | 2 | no | — |
| 282 | C4×#131 | — | 8 | 1 | no | — |
| 283 | #2264 | — | 2 | 2 | no | — |
| 284 | #2263 | — | 2 | 2 | no | — |
| 285 | #2262 | — | 2 | 1 | no | — |
| 286 | #2262 | C4×D4 | 1 | 2 | yes | — |
| 287 | C2×D32 | — | 2 | 2 | no | — |
| 288 | C2×D32 | — | 2 | 2 | no | — |
| 289 | C2×D32 | — | 4 | 2 | no | — |
| 290 | C2×M64 | — | 2 | 1 | no | — |
| 291 | C2×M64 | — | 2 | 1 | no | — |
| 292 | C2×M64 | — | 2 | 1 | no | — |
| 293 | C2×M64 | C2×#41 | 1 | 1 | yes | characteristic |
| 294 | C2×M64 | C2×#41 | 1 | 1 | yes | characteristic |
| 295 | #2252 | — | 2 | 2 | no | — |
| 296 | #2252 | — | 4 | 1 | no | — |
| 297 | #2246 | — | 2 | 2 | no | — |
| 298 | #2246 | — | 4 | 1 | no | — |
| 299 | #2240 | — | 4 | 2 | no | — |
| 300 | #2240 | — | 4 | 2 | no | — |
| 301 | #2215 | — | 4 | 2 | no | — |
| 302 | #2215 | — | 4 | 2 | no | — |
| 303 | #2215 | — | 8 | 1 | no | — |
| 304 | #2215 | — | 8 | 1 | no | — |
| 305 | #2179 | — | 2 | 4 | no | — |
| 306 | #2179 | — | 4 | 2 | no | — |
| 307 | #2178 | — | 2 | 2 | no | — |
| 308 | #2178 | — | 2 | 2 | no | — |
| 309 | #2178 | — | 4 | 1 | no | — |
| 310 | #2178 | — | 4 | 1 | no | — |
| 311 | #2177 | — | 2 | 2 | no | — |
| 312 | #2176 | — | 2 | 2 | no | — |
| 313 | #2175 | — | 4 | 2 | no | — |
| 314 | C4×D16 | — | 4 | 2 | no | — |
| 315 | C4×D16 | — | 4 | 2 | no | — |
| 316 | C4×D16 | — | 8 | 1 | no | — |
| 317 | C4×D16 | — | 8 | 1 | no | — |
| 318 | #2170 | — | 4 | 2 | no | — |
| 319 | #2170 | — | 4 | 2 | no | — |
| 320 | #2170 | — | 4 | 2 | no | — |
| 321 | #2170 | — | 4 | 2 | no | — |
| 322 | #2170 | — | 8 | 1 | no | — |
| 323 | #2170 | — | 8 | 1 | no | — |
| 324 | #2170 | — | 8 | 1 | no | — |
| 325 | #2170 | — | 8 | 1 | no | — |
| 326 | C2×#368 | — | 2 | 1 | no | — |
| 327 | C2×#368 | — | 2 | 1 | no | — |
| 328 | #2158 | — | 2 | 1 | no | — |
| 329 | C2×#364 | — | 4 | 1 | no | — |
| 330 | C2×#364 | — | 4 | 1 | no | — |
| 331 | C2×#359 | — | 4 | 1 | no | — |
| 332 | C2×#359 | — | 4 | 1 | no | — |
| 333 | #2138 | — | 4 | 1 | no | — |
| 334 | C2×#350 | — | 8 | 1 | no | — |
| 335 | C2×#350 | — | 8 | 1 | no | — |
| 336 | #2108 | — | 8 | 1 | no | — |
| 337 | #2108 | — | 8 | 1 | no | — |
| 338 | #2108 | — | 16 | 1 | no | — |
| 339 | #2108 | — | 16 | 1 | no | — |
| 340 | C4×M32 | — | 8 | 1 | no | — |
| 341 | C4×M32 | — | 16 | 1 | no | — |
| 342 | C2×#346 | — | 2 | 1 | no | — |
| 343 | C2×#346 | — | 2 | 1 | no | — |
| 344 | C2×#346 | — | 2 | 1 | no | — |
| 345 | C2×#346 | — | 2 | 1 | no | — |
| 346 | C2×#346 | — | 16 | 1 | no | — |
| 347 | C2×C4×C16 | C2×D8 | 1 | 1 | yes | characteristic |
| 348 | C2×C4×C16 | C2×D8 | 1 | 1 | yes | characteristic |
| 349 | C2×C4×C16 | C2×D8 | 1 | 1 | yes | characteristic |
| 350 | C2×C4×C16 | C22×D4 | 1 | 1 | yes | characteristic |
| 351 | #1974 | — | 16 | 2 | no | — |
| 352 | #1962 | — | 8 | 2 | no | — |
| 353 | #1848 | — | 8 | 1 | no | — |
| 354 | C4×#108 | — | 4 | 1 | no | — |
| 355 | #1772 | — | 4 | 1 | no | — |
| 356 | #1772 | — | 4 | 1 | no | — |
| 357 | #1764 | — | 8 | 1 | no | — |
| 358 | #1764 | — | 8 | 1 | no | — |
| 359 | C4×#104 | — | 8 | 1 | no | — |
| 360 | C42×C8 | — | 2 | 1 | no | — |
| 361 | C42×C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 362 | #1713 | — | 4 | 1 | no | — |
| 363 | #1712 | — | 4 | 1 | no | — |
| 364 | #1709 | — | 8 | 1 | no | — |
| 365 | #1706 | — | 4 | 2 | no | — |
| 366 | #1706 | — | 8 | 1 | no | — |
| 367 | #1589 | — | 8 | 2 | no | — |
| 368 | #1589 | — | 8 | 2 | no | — |
| 369 | #1589 | — | 16 | 2 | no | — |
| 370 | C8×D8 | — | 8 | 2 | no | — |
| 371 | C8×D8 | — | 8 | 2 | no | — |
| 372 | C8×D8 | — | 16 | 2 | no | — |
| 373 | #1567 | — | 4 | 2 | no | — |
| 374 | #1567 | — | 8 | 1 | no | — |
| 375 | #1492 | — | 8 | 2 | no | — |
| 376 | #1492 | — | 8 | 2 | no | — |
| 377 | C2×C82 | — | 2 | 1 | no | — |
| 378 | C2×C82 | C2×D8 | 1 | 1 | yes | characteristic |
| 379 | C2×C82 | C2×D8 | 1 | 1 | yes | characteristic |
| 380 | SD128 | — | 4 | 4 | no | — |
| 381 | D64 | — | 4 | 4 | no | — |
| 382 | M128 | — | 2 | 4 | no | — |
| 383 | M128 | — | 4 | 2 | no | — |
| 384 | #1426 | — | 2 | 4 | no | — |
| 385 | #1425 | — | 2 | 1 | no | — |
| 386 | #1425 | C4×D4 | 1 | 2 | yes | — |
| 387 | #1424 | — | 2 | 2 | no | — |
| 388 | #1424 | — | 2 | 2 | no | — |
| 389 | #1424 | — | 4 | 2 | no | — |
| 390 | #1420 | — | 2 | 2 | no | — |
| 391 | #1419 | — | 2 | 2 | no | — |
| 392 | #1418 | — | 2 | 4 | no | — |
| 393 | #1417 | — | 2 | 2 | no | — |
| 394 | #1417 | — | 2 | 2 | no | — |
| 395 | #1415 | — | 4 | 4 | no | — |
| 396 | #1415 | — | 4 | 2 | no | — |
| 397 | #1415 | — | 4 | 2 | no | — |
| 398 | #1398 | — | 2 | 4 | no | — |
| 399 | #1398 | — | 4 | 2 | no | — |
| 400 | #1398 | — | 4 | 4 | no | — |
| 401 | #1397 | — | 2 | 1 | no | — |
| 402 | #1397 | — | 2 | 1 | no | — |
| 403 | #1397 | #121 | 1 | 1 | yes | characteristic |
| 404 | #1397 | #121 | 1 | 1 | yes | characteristic |
| 405 | #1397 | C22×D4 | 1 | 1 | yes | characteristic |
| 406 | #1397 | C2×#41 | 1 | 1 | yes | characteristic |
| 407 | C4×C32 | — | 2 | 1 | no | — |
| 408 | C4×C32 | — | 2 | 1 | no | — |
| 409 | C4×C32 | C4×D4 | 1 | 1 | yes | characteristic |
| 410 | C4×C32 | C4×D4 | 1 | 1 | yes | characteristic |
| 411 | C4×C32 | C23×C4 | 1 | 1 | yes | characteristic |
| 412 | C4×C32 | C2×#41 | 1 | 1 | yes | characteristic |
| 413 | #1382 | — | 4 | 1 | no | — |
| 414 | #1382 | — | 4 | 1 | no | — |
| 415 | #1381 | — | 4 | 1 | no | — |
| 416 | #1379 | — | 8 | 1 | no | — |
| 417 | #1379 | — | 8 | 1 | no | — |
| 418 | #1376 | — | 8 | 1 | no | — |
| 419 | #1373 | — | 2 | 2 | no | — |
| 420 | #1373 | — | 2 | 2 | no | — |
| 421 | #1373 | — | 4 | 1 | no | — |
| 422 | #1373 | — | 4 | 1 | no | — |
| 423 | #1372 | — | 4 | 2 | no | — |
| 424 | #1372 | — | 4 | 2 | no | — |
| 425 | #1372 | — | 8 | 1 | no | — |
| 426 | #1372 | — | 8 | 1 | no | — |
| 427 | #1335 | — | 4 | 2 | no | — |
| 428 | #1335 | — | 4 | 2 | no | — |
| 429 | #1335 | — | 4 | 2 | no | — |
| 430 | #1335 | — | 4 | 2 | no | — |
| 431 | #1331 | — | 8 | 2 | no | — |
| 432 | #1331 | — | 8 | 2 | no | — |
| 433 | #1331 | — | 8 | 2 | no | — |
| 434 | #1331 | — | 8 | 2 | no | — |
| 435 | #1311 | — | 2 | 1 | no | — |
| 436 | #1311 | — | 2 | 1 | no | — |
| 437 | #1311 | #121 | 1 | 1 | yes | characteristic |
| 438 | #1311 | #121 | 1 | 1 | yes | characteristic |
| 439 | #1311 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 440 | #1311 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 441 | C8×C16 | — | 4 | 1 | no | — |
| 442 | C8×C16 | C4×D4 | 1 | 1 | yes | characteristic |
| 443 | C8×C16 | C4×D4 | 1 | 1 | yes | characteristic |
| 444 | C8×C16 | #135 | 1 | 1 | yes | characteristic |
| 445 | C8×C16 | #135 | 1 | 1 | yes | characteristic |
| 446 | C2×#135 | — | 4 | 1 | no | — |
| 447 | C2×#135 | — | 16 | 2 | no | — |
| 448 | C2×#131 | — | 8 | 1 | no | — |
| 449 | C2×#131 | — | 8 | 1 | no | — |
| 450 | C2×#131 | — | 16 | 2 | no | — |
| 451 | #532 | — | 8 | 2 | no | — |
| 452 | C4×#41 | — | 8 | 1 | no | — |
| 453 | #508 | — | 2 | 2 | no | — |
| 454 | #508 | — | 2 | 2 | no | — |
| 455 | #508 | — | 4 | 1 | no | — |
| 456 | #508 | — | 4 | 1 | no | — |
| 457 | C2×Q32 | — | 2 | 1 | no | — |
| 458 | C2×SD32 | — | 4 | 1 | no | — |
| 459 | C2×D16 | — | 2 | 1 | no | — |
| 460 | C2×D16 | — | 4 | 2 | no | — |
| 461 | C2×D16 | — | 4 | 2 | no | — |
| 462 | C2×D16 | — | 8 | 1 | no | — |
| 463 | C2×D16 | — | 8 | 1 | no | — |
| 464 | #504 | — | 8 | 2 | no | — |
| 465 | #504 | — | 8 | 2 | no | — |
| 466 | #504 | — | 8 | 2 | no | — |
| 467 | #504 | — | 8 | 2 | no | — |
| 468 | #504 | — | 16 | 1 | no | — |
| 469 | #504 | — | 16 | 1 | no | — |
| 470 | #504 | — | 16 | 1 | no | — |
| 471 | #504 | — | 16 | 1 | no | — |
| 472 | C2×M32 | — | 8 | 1 | no | — |
| 473 | C2×M32 | — | 8 | 1 | no | — |
| 474 | C2×M32 | — | 16 | 1 | no | — |
| 475 | C2×M32 | — | 16 | 1 | no | — |
| 476 | C22×C16 | — | 2 | 1 | no | — |
| 477 | C22×C16 | — | 2 | 1 | no | — |
| 478 | C22×C16 | — | 16 | 1 | no | — |
| 479 | C22×C16 | — | 16 | 1 | no | — |
| 480 | C22×C16 | #509 | 1 | 1 | yes | characteristic |
| 481 | C22×C16 | #509 | 1 | 1 | yes | characteristic |
| 482 | C22×C16 | #525 | 1 | 1 | yes | characteristic |
| 483 | C22×C16 | #575 | 1 | 1 | yes | characteristic |
| 484 | #500 | — | 4 | 2 | no | — |
| 485 | #500 | — | 8 | 1 | no | — |
| 486 | #495 | — | 16 | 2 | no | — |
| 487 | #494 | — | 8 | 1 | no | — |
| 488 | #493 | — | 4 | 2 | no | — |
| 489 | #493 | — | 8 | 1 | no | — |
| 490 | #493 | — | 8 | 1 | no | — |
| 491 | #492 | — | 8 | 2 | no | — |
| 492 | #486 | — | 8 | 2 | no | — |
| 493 | #486 | — | 8 | 2 | no | — |
| 494 | #466 | — | 8 | 2 | no | — |
| 495 | #466 | — | 8 | 2 | no | — |
| 496 | #466 | — | 16 | 2 | no | — |
| 497 | #443 | — | 4 | 4 | no | — |
| 498 | #443 | — | 4 | 2 | no | — |
| 499 | #443 | — | 4 | 2 | no | — |
| 500 | #443 | — | 8 | 2 | no | — |
| 501 | #443 | — | 8 | 1 | no | — |
| 502 | #443 | — | 8 | 1 | no | — |
| 503 | #443 | — | 32 | 8 | no | — |
| 504 | C4×Q16 | — | 4 | 2 | no | — |
| 505 | C4×SD16 | — | 8 | 2 | no | — |
| 506 | C4×D8 | — | 4 | 2 | no | — |
| 507 | C4×D8 | — | 8 | 2 | no | — |
| 508 | C4×D8 | — | 8 | 2 | no | — |
| 509 | C4×D8 | — | 16 | 2 | no | — |
| 510 | #436 | — | 16 | 2 | no | — |
| 511 | #436 | — | 16 | 2 | no | — |
| 512 | C8×D4 | — | 16 | 2 | no | — |
| 513 | C8×D4 | — | 16 | 2 | no | — |
| 514 | C2×#108 | — | 4 | 1 | no | — |
| 515 | C2×#108 | — | 4 | 1 | no | — |
| 516 | C2×#108 | — | 16 | 2 | no | — |
| 517 | #427 | — | 4 | 1 | no | — |
| 518 | #423 | — | 8 | 2 | no | — |
| 519 | C2×#104 | — | 8 | 1 | no | — |
| 520 | C2×#104 | — | 8 | 1 | no | — |
| 521 | C2×#104 | — | 16 | 4 | no | — |
| 522 | #416 | — | 8 | 1 | no | — |
| 523 | #408 | — | 16 | 2 | no | — |
| 524 | #405 | — | 8 | 1 | no | — |
| 525 | #405 | — | 8 | 1 | no | — |
| 526 | #405 | — | 16 | 1 | no | — |
| 527 | #405 | — | 16 | 1 | no | — |
| 528 | C4×M16 | — | 8 | 1 | no | — |
| 529 | C4×M16 | — | 16 | 1 | no | — |
| 530 | C2×C4×C8 | — | 2 | 1 | no | — |
| 531 | C2×C4×C8 | — | 2 | 1 | no | — |
| 532 | C2×C4×C8 | — | 2 | 1 | no | — |
| 533 | C2×C4×C8 | — | 2 | 1 | no | — |
| 534 | C2×C4×C8 | — | 4 | 2 | no | — |
| 535 | C2×C4×C8 | — | 16 | 1 | no | — |
| 536 | C2×C4×C8 | #509 | 1 | 1 | yes | characteristic |
| 537 | C2×C4×C8 | C22×D8 | 1 | 1 | yes | characteristic |
| 538 | C43 | #509 | 1 | 1 | yes | characteristic |
| 539 | Q64 | — | 2 | 1 | no | — |
| 540 | Q64 | #443 | 1 | 2 | yes | complemented |
| 541 | SD64 | — | 2 | 2 | no | — |
| 542 | SD64 | — | 2 | 2 | no | — |
| 543 | D32 | — | 2 | 1 | no | — |
| 544 | D32 | — | 4 | 4 | no | — |
| 545 | D32 | — | 8 | 2 | no | — |
| 546 | D32 | — | 8 | 4 | no | — |
| 547 | D32 | #443 | 1 | 2 | yes | complemented |
| 548 | M64 | — | 2 | 2 | no | — |
| 549 | M64 | — | 2 | 2 | no | — |
| 550 | M64 | — | 4 | 1 | no | — |
| 551 | M64 | — | 4 | 2 | no | — |
| 552 | M64 | — | 4 | 2 | no | — |
| 553 | M64 | — | 4 | 1 | no | — |
| 554 | C2×C32 | — | 2 | 1 | no | — |
| 555 | C2×C32 | — | 2 | 1 | no | — |
| 556 | C2×C32 | — | 2 | 1 | no | — |
| 557 | C2×C32 | — | 2 | 1 | no | — |
| 558 | C2×C32 | — | 4 | 1 | no | — |
| 559 | C2×C32 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 560 | C2×C32 | C4×#41 | 1 | 1 | yes | characteristic |
| 561 | C2×C32 | #529 | 1 | 1 | yes | characteristic |
| 562 | C2×C32 | #532 | 1 | 1 | yes | characteristic |
| 563 | #368 | — | 2 | 2 | no | — |
| 564 | #368 | — | 2 | 2 | no | — |
| 565 | #368 | — | 4 | 1 | no | — |
| 566 | #368 | — | 4 | 1 | no | — |
| 567 | #367 | — | 2 | 2 | no | — |
| 568 | #366 | — | 4 | 1 | no | — |
| 569 | #366 | — | 4 | 2 | no | — |
| 570 | #366 | — | 4 | 2 | no | — |
| 571 | #366 | — | 8 | 1 | no | — |
| 572 | #366 | — | 8 | 1 | no | — |
| 573 | #364 | — | 4 | 2 | no | — |
| 574 | #364 | — | 4 | 2 | no | — |
| 575 | #364 | — | 8 | 1 | no | — |
| 576 | #364 | — | 8 | 1 | no | — |
| 577 | #359 | — | 4 | 4 | no | — |
| 578 | #359 | — | 4 | 2 | no | — |
| 579 | #359 | — | 4 | 2 | no | — |
| 580 | #358 | — | 4 | 2 | no | — |
| 581 | #357 | — | 4 | 2 | no | — |
| 582 | #357 | — | 8 | 2 | no | — |
| 583 | #357 | — | 8 | 2 | no | — |
| 584 | #357 | — | 8 | 2 | no | — |
| 585 | #357 | — | 8 | 2 | no | — |
| 586 | #350 | — | 8 | 2 | no | — |
| 587 | #350 | — | 8 | 2 | no | — |
| 588 | #350 | — | 8 | 2 | no | — |
| 589 | #350 | — | 8 | 2 | no | — |
| 590 | #346 | — | 2 | 2 | no | — |
| 591 | #346 | — | 2 | 2 | no | — |
| 592 | #346 | — | 4 | 2 | no | — |
| 593 | #346 | — | 4 | 1 | no | — |
| 594 | #346 | — | 4 | 1 | no | — |
| 595 | #346 | — | 8 | 1 | no | — |
| 596 | #346 | — | 16 | 1 | no | — |
| 597 | #346 | — | 16 | 1 | no | — |
| 598 | #346 | — | 16 | 1 | no | — |
| 599 | C4×C16 | — | 2 | 1 | no | — |
| 600 | C4×C16 | — | 2 | 1 | no | — |
| 601 | C4×C16 | — | 2 | 1 | no | — |
| 602 | C4×C16 | — | 16 | 1 | no | — |
| 603 | C4×C16 | — | 16 | 1 | no | — |
| 604 | C4×C16 | — | 16 | 1 | no | — |
| 605 | C4×C16 | C4×D8 | 1 | 1 | yes | characteristic |
| 606 | C4×C16 | C4×D8 | 1 | 1 | yes | characteristic |
| 607 | C4×C16 | #459 | 1 | 1 | yes | characteristic |
| 608 | C4×C16 | #459 | 1 | 1 | yes | characteristic |
| 609 | C4×C16 | #509 | 1 | 1 | yes | characteristic |
| 610 | C4×C16 | #509 | 1 | 1 | yes | characteristic |
| 611 | C4×C16 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 612 | C4×C16 | C2×#121 | 1 | 1 | yes | characteristic |
| 613 | C4×C16 | C2×#135 | 1 | 1 | yes | characteristic |
| 614 | C4×C16 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 615 | #341 | — | 8 | 1 | no | — |
| 616 | #339 | — | 8 | 1 | no | — |
| 617 | #339 | — | 8 | 1 | no | — |
| 618 | #335 | — | 8 | 2 | no | — |
| 619 | #335 | — | 8 | 2 | no | — |
| 620 | #335 | — | 16 | 2 | no | — |
| 621 | D4⋊C8 | — | 16 | 2 | no | — |
| 622 | D4⋊C8 | — | 16 | 2 | no | — |
| 623 | D4⋊C8 | — | 16 | 4 | no | — |
| 624 | C82 | — | 2 | 1 | no | — |
| 625 | C82 | — | 2 | 1 | no | — |
| 626 | C82 | — | 4 | 2 | no | — |
| 627 | C82 | C4×D8 | 1 | 1 | yes | characteristic |
| 628 | C82 | C4×D8 | 1 | 1 | yes | characteristic |
| 629 | C82 | #459 | 1 | 1 | yes | characteristic |
| 630 | C82 | #459 | 1 | 1 | yes | characteristic |
| 631 | C64 | — | 4 | 4 | no | — |
| 632 | C64 | — | 8 | 2 | no | — |
| 633 | C2×#41 | — | 8 | 1 | no | — |
| 634 | C2×#41 | — | 16 | 2 | no | — |
| 635 | #135 | — | 4 | 2 | no | — |
| 636 | #135 | — | 4 | 2 | no | — |
| 637 | #135 | — | 8 | 1 | no | — |
| 638 | #135 | — | 8 | 1 | no | — |
| 639 | #135 | — | 32 | 4 | no | — |
| 640 | #135 | — | 32 | 4 | no | — |
| 641 | C2×Q16 | — | 4 | 1 | no | — |
| 642 | C2×Q16 | — | 16 | 2 | no | — |
| 643 | C2×SD16 | — | 8 | 1 | no | — |
| 644 | C2×SD16 | — | 16 | 4 | no | — |
| 645 | C2×D8 | — | 4 | 1 | no | — |
| 646 | C2×D8 | — | 8 | 2 | no | — |
| 647 | C2×D8 | — | 8 | 2 | no | — |
| 648 | C2×D8 | — | 16 | 2 | no | — |
| 649 | C2×D8 | — | 16 | 2 | no | — |
| 650 | #131 | — | 8 | 4 | no | — |
| 651 | #131 | — | 8 | 2 | no | — |
| 652 | #131 | — | 8 | 2 | no | — |
| 653 | #131 | — | 16 | 1 | no | — |
| 654 | #131 | — | 16 | 1 | no | — |
| 655 | #131 | — | 16 | 2 | no | — |
| 656 | #131 | — | 32 | 8 | no | — |
| 657 | C2×M16 | — | 8 | 1 | no | — |
| 658 | C2×M16 | — | 8 | 1 | no | — |
| 659 | C2×M16 | — | 16 | 1 | no | — |
| 660 | C2×M16 | — | 16 | 1 | no | — |
| 661 | C2×M16 | — | 16 | 2 | no | — |
| 662 | C2×M16 | — | 32 | 2 | no | — |
| 663 | C22×C8 | — | 2 | 2 | no | — |
| 664 | C22×C8 | — | 2 | 1 | no | — |
| 665 | C22×C8 | — | 4 | 1 | no | — |
| 666 | C22×C8 | — | 16 | 1 | no | — |
| 667 | C22×C8 | — | 16 | 1 | no | — |
| 668 | C22×C8 | — | 32 | 2 | no | — |
| 669 | C22×C8 | #3100 | 1 | 1 | yes | characteristic |
| 670 | C22×C8 | C2×#509 | 1 | 1 | yes | characteristic |
| 671 | C4⋊Q8 | — | 8 | 2 | no | — |
| 672 | #127 | — | 8 | 2 | no | — |
| 673 | #124 | — | 16 | 2 | no | — |
| 674 | #121 | — | 16 | 2 | no | — |
| 675 | #121 | — | 16 | 2 | no | — |
| 676 | C4×Q8 | — | 8 | 2 | no | — |
| 677 | C4×D4 | — | 8 | 2 | no | — |
| 678 | C4×D4 | — | 16 | 2 | no | — |
| 679 | C4×D4 | — | 16 | 2 | no | — |
| 680 | C4×D4 | — | 16 | 2 | no | — |
| 681 | #117 | — | 8 | 1 | no | — |
| 682 | #117 | — | 16 | 1 | no | — |
| 683 | C2×C42 | — | 2 | 1 | no | — |
| 684 | C2×C42 | — | 4 | 1 | no | — |
| 685 | C2×C42 | — | 16 | 1 | no | — |
| 686 | C2×C42 | C2×#509 | 1 | 1 | yes | characteristic |
| 687 | Q32 | — | 2 | 2 | no | — |
| 688 | Q32 | — | 4 | 1 | no | — |
| 689 | SD32 | — | 4 | 2 | no | — |
| 690 | SD32 | — | 4 | 2 | no | — |
| 691 | D16 | — | 2 | 2 | no | — |
| 692 | D16 | — | 4 | 1 | no | — |
| 693 | D16 | — | 8 | 4 | no | — |
| 694 | D16 | — | 8 | 2 | no | — |
| 695 | D16 | — | 8 | 2 | no | — |
| 696 | D16 | — | 16 | 2 | no | — |
| 697 | D16 | — | 16 | 1 | no | — |
| 698 | D16 | — | 16 | 1 | no | — |
| 699 | M32 | — | 8 | 2 | no | — |
| 700 | M32 | — | 8 | 2 | no | — |
| 701 | M32 | — | 16 | 2 | no | — |
| 702 | M32 | — | 16 | 2 | no | — |
| 703 | M32 | — | 16 | 2 | no | — |
| 704 | M32 | — | 16 | 1 | no | — |
| 705 | M32 | — | 16 | 1 | no | — |
| 706 | M32 | — | 16 | 2 | no | — |
| 707 | C2×C16 | — | 2 | 1 | no | — |
| 708 | C2×C16 | — | 2 | 1 | no | — |
| 709 | C2×C16 | — | 2 | 1 | no | — |
| 710 | C2×C16 | — | 2 | 1 | no | — |
| 711 | C2×C16 | — | 2 | 2 | no | — |
| 712 | C2×C16 | — | 2 | 1 | no | — |
| 713 | C2×C16 | — | 2 | 1 | no | — |
| 714 | C2×C16 | — | 4 | 1 | no | — |
| 715 | C2×C16 | — | 4 | 1 | no | — |
| 716 | C2×C16 | — | 4 | 1 | no | — |
| 717 | C2×C16 | — | 4 | 1 | no | — |
| 718 | C2×C16 | — | 4 | 1 | no | — |
| 719 | C2×C16 | — | 4 | 1 | no | — |
| 720 | C2×C16 | — | 16 | 2 | no | — |
| 721 | C2×C16 | — | 16 | 2 | no | — |
| 722 | C2×C16 | — | 16 | 2 | no | — |
| 723 | C2×C16 | — | 16 | 1 | no | — |
| 724 | C2×C16 | — | 16 | 1 | no | — |
| 725 | C2×C16 | — | 16 | 2 | no | — |
| 726 | C2×C16 | #2177 | 1 | 1 | yes | characteristic |
| 727 | C2×C16 | #2177 | 1 | 1 | yes | characteristic |
| 728 | C2×C16 | #2177 | 1 | 1 | yes | characteristic |
| 729 | C2×C16 | #2177 | 1 | 1 | yes | characteristic |
| 730 | C2×C16 | C4×#121 | 1 | 1 | yes | characteristic |
| 731 | C2×C16 | C4×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 732 | C2×C16 | #3035 | 1 | 1 | yes | characteristic |
| 733 | C2×C16 | #3106 | 1 | 1 | yes | characteristic |
| 734 | #108 | — | 4 | 2 | no | — |
| 735 | #108 | — | 4 | 2 | no | — |
| 736 | #108 | — | 8 | 1 | no | — |
| 737 | #108 | — | 8 | 1 | no | — |
| 738 | #108 | — | 32 | 4 | no | — |
| 739 | #107 | — | 4 | 2 | no | — |
| 740 | #107 | — | 8 | 2 | no | — |
| 741 | #107 | — | 8 | 2 | no | — |
| 742 | #107 | — | 16 | 2 | no | — |
| 743 | #106 | — | 8 | 1 | no | — |
| 744 | C4⋊C8 | — | 16 | 2 | no | — |
| 745 | C4⋊C8 | — | 16 | 2 | no | — |
| 746 | #104 | — | 8 | 4 | no | — |
| 747 | #104 | — | 8 | 2 | no | — |
| 748 | #104 | — | 8 | 2 | no | — |
| 749 | #104 | — | 32 | 8 | no | — |
| 750 | #103 | — | 8 | 2 | no | — |
| 751 | #102 | — | 8 | 2 | no | — |
| 752 | #102 | — | 16 | 4 | no | — |
| 753 | #102 | — | 16 | 2 | no | — |
| 754 | #102 | — | 16 | 2 | no | — |
| 755 | C22⋊C8 | — | 32 | 2 | no | — |
| 756 | C22⋊C8 | — | 32 | 2 | no | — |
| 757 | #97 | — | 16 | 1 | no | — |
| 758 | #97 | — | 16 | 1 | no | — |
| 759 | #97 | — | 16 | 1 | no | — |
| 760 | C4×C8 | — | 2 | 2 | no | — |
| 761 | C4×C8 | — | 2 | 2 | no | — |
| 762 | C4×C8 | — | 2 | 2 | no | — |
| 763 | C4×C8 | — | 2 | 1 | no | — |
| 764 | C4×C8 | — | 2 | 1 | no | — |
| 765 | C4×C8 | — | 2 | 1 | no | — |
| 766 | C4×C8 | — | 2 | 1 | no | — |
| 767 | C4×C8 | — | 4 | 1 | no | — |
| 768 | C4×C8 | — | 4 | 1 | no | — |
| 769 | C4×C8 | — | 4 | 1 | no | — |
| 770 | C4×C8 | — | 4 | 1 | no | — |
| 771 | C4×C8 | — | 8 | 4 | no | — |
| 772 | C4×C8 | — | 16 | 1 | no | — |
| 773 | C4×C8 | — | 16 | 1 | no | — |
| 774 | C4×C8 | — | 16 | 1 | no | — |
| 775 | C4×C8 | C2×C4×D8 | 1 | 1 | yes | characteristic |
| 776 | C4×C8 | C2×#459 | 1 | 1 | yes | characteristic |
| 777 | C4×C8 | C2×#509 | 1 | 1 | yes | characteristic |
| 778 | C4×C8 | #3414 | 1 | 1 | yes | characteristic |
| 779 | C32 | — | 2 | 2 | no | — |
| 780 | C32 | — | 2 | 2 | no | — |
| 781 | C32 | — | 2 | 1 | no | — |
| 782 | C32 | — | 2 | 1 | no | — |
| 783 | C32 | — | 2 | 1 | no | — |
| 784 | C32 | — | 4 | 1 | no | — |
| 785 | C32 | — | 4 | 1 | no | — |
| 786 | C32 | — | 4 | 2 | no | — |
| 787 | C32 | C2×#443 | 1 | 2 | yes | — |
| 788 | #41 | — | 8 | 2 | no | — |
| 789 | #41 | — | 8 | 2 | no | — |
| 790 | #41 | — | 16 | 1 | no | — |
| 791 | #41 | — | 16 | 1 | no | — |
| 792 | #41 | — | 32 | 4 | no | — |
| 793 | #41 | — | 32 | 4 | no | — |
| 794 | C2×Q8 | — | 8 | 1 | no | — |
| 795 | C2×Q8 | — | 16 | 2 | no | — |
| 796 | C2×D4 | — | 8 | 1 | no | — |
| 797 | C2×D4 | — | 16 | 2 | no | — |
| 798 | C2×D4 | — | 16 | 2 | no | — |
| 799 | C2×D4 | — | 16 | 1 | no | — |
| 800 | C2×D4 | — | 16 | 2 | no | — |
| 801 | C2×D4 | — | 32 | 2 | no | — |
| 802 | C22×C4 | — | 2 | 1 | no | — |
| 803 | C22×C4 | — | 4 | 1 | no | — |
| 804 | C22×C4 | — | 16 | 1 | no | — |
| 805 | C22×C4 | — | 16 | 2 | no | — |
| 806 | C22×C4 | — | 32 | 2 | no | — |
| 807 | C22×C4 | #33669 | 1 | 1 | yes | characteristic |
| 808 | Q16 | — | 4 | 2 | no | — |
| 809 | Q16 | — | 8 | 1 | no | — |
| 810 | Q16 | — | 32 | 4 | no | — |
| 811 | SD16 | — | 8 | 2 | no | — |
| 812 | SD16 | — | 8 | 2 | no | — |
| 813 | SD16 | — | 32 | 8 | no | — |
| 814 | D8 | — | 4 | 2 | no | — |
| 815 | D8 | — | 8 | 1 | no | — |
| 816 | D8 | — | 16 | 2 | no | — |
| 817 | D8 | — | 16 | 2 | no | — |
| 818 | D8 | — | 16 | 2 | no | — |
| 819 | D8 | — | 16 | 2 | no | — |
| 820 | D8 | — | 32 | 4 | no | — |
| 821 | D8 | — | 32 | 4 | no | — |
| 822 | M16 | — | 8 | 2 | no | — |
| 823 | M16 | — | 8 | 2 | no | — |
| 824 | M16 | — | 16 | 2 | no | — |
| 825 | M16 | — | 16 | 4 | no | — |
| 826 | M16 | — | 16 | 1 | no | — |
| 827 | M16 | — | 16 | 1 | no | — |
| 828 | M16 | — | 16 | 2 | no | — |
| 829 | M16 | — | 32 | 4 | no | — |
| 830 | M16 | — | 64 | 4 | no | — |
| 831 | C2×C8 | — | 2 | 2 | no | — |
| 832 | C2×C8 | — | 2 | 1 | no | — |
| 833 | C2×C8 | — | 2 | 1 | no | — |
| 834 | C2×C8 | — | 2 | 1 | no | — |
| 835 | C2×C8 | — | 2 | 1 | no | — |
| 836 | C2×C8 | — | 2 | 2 | no | — |
| 837 | C2×C8 | — | 2 | 2 | no | — |
| 838 | C2×C8 | — | 4 | 4 | no | — |
| 839 | C2×C8 | — | 4 | 1 | no | — |
| 840 | C2×C8 | — | 4 | 1 | no | — |
| 841 | C2×C8 | — | 4 | 1 | no | — |
| 842 | C2×C8 | — | 4 | 1 | no | — |
| 843 | C2×C8 | — | 8 | 2 | no | — |
| 844 | C2×C8 | — | 16 | 2 | no | — |
| 845 | C2×C8 | — | 16 | 4 | no | — |
| 846 | C2×C8 | — | 16 | 1 | no | — |
| 847 | C2×C8 | — | 16 | 1 | no | — |
| 848 | C2×C8 | — | 16 | 2 | no | — |
| 849 | C2×C8 | — | 32 | 2 | no | — |
| 850 | C2×C8 | — | 64 | 4 | no | — |
| 851 | C2×C8 | C4×#459 | 1 | 1 | yes | characteristic |
| 852 | C2×C8 | C2×#2177 | 1 | 1 | yes | characteristic |
| 853 | C2×C8 | #33580 | 1 | 1 | yes | characteristic |
| 854 | C2×C8 | #33675 | 1 | 1 | yes | characteristic |
| 855 | C4⋊C4 | — | 8 | 2 | no | — |
| 856 | C4⋊C4 | — | 16 | 2 | no | — |
| 857 | C4⋊C4 | — | 16 | 2 | no | — |
| 858 | C4⋊C4 | — | 16 | 2 | no | — |
| 859 | C22⋊C4 | — | 16 | 2 | no | — |
| 860 | C22⋊C4 | — | 16 | 1 | no | — |
| 861 | C22⋊C4 | — | 32 | 2 | no | — |
| 862 | C22⋊C4 | — | 32 | 2 | no | — |
| 863 | C42 | — | 2 | 1 | no | — |
| 864 | C42 | — | 2 | 2 | no | — |
| 865 | C42 | — | 4 | 1 | no | — |
| 866 | C42 | — | 8 | 2 | no | — |
| 867 | C42 | — | 16 | 1 | no | — |
| 868 | C42 | — | 16 | 2 | no | — |
| 869 | C42 | C4×#509 | 1 | 1 | yes | characteristic |
| 870 | C42 | #33582 | 1 | 1 | yes | characteristic |
| 871 | C16 | — | 2 | 1 | no | — |
| 872 | C16 | — | 2 | 1 | no | — |
| 873 | C16 | — | 2 | 1 | no | — |
| 874 | C16 | — | 2 | 1 | no | — |
| 875 | C16 | — | 2 | 1 | no | — |
| 876 | C16 | — | 2 | 1 | no | — |
| 877 | C16 | — | 4 | 2 | no | — |
| 878 | C16 | — | 4 | 1 | no | — |
| 879 | C16 | — | 4 | 1 | no | — |
| 880 | C16 | — | 16 | 2 | no | — |
| 881 | C16 | — | 16 | 2 | no | — |
| 882 | C16 | #13658 | 1 | 1 | yes | characteristic |
| 883 | C16 | #13658 | 1 | 1 | yes | characteristic |
| 884 | C16 | #21544 | 1 | 1 | yes | characteristic |
| 885 | C16 | #21558 | 1 | 1 | yes | characteristic |
| 886 | C23 | — | 16 | 1 | no | — |
| 887 | C23 | — | 32 | 2 | no | — |
| 888 | C23 | #513022 | 1 | 1 | yes | characteristic |
| 889 | Q8 | — | 8 | 2 | no | — |
| 890 | Q8 | — | 16 | 1 | no | — |
| 891 | Q8 | — | 32 | 4 | no | — |
| 892 | D4 | — | 8 | 2 | no | — |
| 893 | D4 | — | 16 | 1 | no | — |
| 894 | D4 | — | 16 | 2 | no | — |
| 895 | D4 | — | 16 | 2 | no | — |
| 896 | D4 | — | 32 | 4 | no | — |
| 897 | D4 | — | 32 | 4 | no | — |
| 898 | D4 | — | 32 | 2 | no | — |
| 899 | D4 | — | 32 | 2 | no | — |
| 900 | D4 | — | 64 | 4 | no | — |
| 901 | C2×C4 | — | 2 | 1 | no | — |
| 902 | C2×C4 | — | 2 | 1 | no | — |
| 903 | C2×C4 | — | 2 | 1 | no | — |
| 904 | C2×C4 | — | 2 | 1 | no | — |
| 905 | C2×C4 | — | 4 | 2 | no | — |
| 906 | C2×C4 | — | 4 | 2 | no | — |
| 907 | C2×C4 | — | 16 | 2 | no | — |
| 908 | C2×C4 | — | 16 | 1 | no | — |
| 909 | C2×C4 | — | 16 | 1 | no | — |
| 910 | C2×C4 | — | 16 | 2 | no | — |
| 911 | C2×C4 | — | 16 | 2 | no | — |
| 912 | C2×C4 | — | 32 | 2 | no | — |
| 913 | C2×C4 | — | 64 | 2 | no | — |
| 914 | C2×C4 | — | 64 | 2 | no | — |
| 915 | C2×C4 | — | 64 | 2 | no | — |
| 916 | C2×C4 | #495812 | 1 | 1 | yes | characteristic |
| 917 | C2×C4 | #513022 | 1 | 1 | yes | characteristic |
| 918 | C8 | — | 2 | 4 | no | — |
| 919 | C8 | — | 2 | 1 | no | — |
| 920 | C8 | — | 2 | 1 | no | — |
| 921 | C8 | — | 4 | 2 | no | — |
| 922 | C8 | — | 4 | 2 | no | — |
| 923 | C8 | — | 8 | 1 | no | — |
| 924 | C8 | — | 8 | 1 | no | — |
| 925 | C8 | — | 16 | 2 | no | — |
| 926 | C8 | — | 16 | 2 | no | — |
| 927 | C8 | — | 64 | 2 | no | — |
| 928 | C8 | #211692 | 1 | 1 | yes | characteristic |
| 929 | C8 | #495835 | 1 | 1 | yes | characteristic |
| 930 | C8 | C2×#13658 | 1 | 1 | yes | characteristic |
| 931 | C8 | #512778 | 1 | 1 | yes | characteristic |
| 932 | C22 | — | 2 | 1 | no | — |
| 933 | C22 | — | 4 | 1 | no | — |
| 934 | C22 | — | 16 | 2 | no | — |
| 935 | C22 | — | 32 | 2 | no | — |
| 936 | C22 | — | 64 | 2 | no | — |
| 937 | C22 | — | 64 | 2 | no | — |
| 938 | C22 | — | 64 | 2 | no | — |
| 939 | C22 | #72216258 | 1 | 1 | yes | characteristic |
| 940 | C4 | — | 2 | 2 | no | — |
| 941 | C4 | — | 2 | 1 | no | — |
| 942 | C4 | — | 4 | 1 | no | — |
| 943 | C4 | — | 8 | 2 | no | — |
| 944 | C4 | — | 16 | 2 | no | — |
| 945 | C4 | — | 32 | 2 | no | — |
| 946 | C4 | — | 64 | 2 | no | — |
| 947 | C4 | #72225507 | 1 | 1 | yes | characteristic |
| 948 | C4 | #72225508 | 1 | 1 | yes | characteristic |
| 949 | C2 | — | 2 | 1 | no | — |
| 950 | C2 | — | 4 | 1 | no | — |
| 951 | C2 | — | 32 | 2 | no | — |
| 952 | C2 | — | 128 | 2 | no | — |
| 953 | C2 | #72225509 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #72225509 |
| commutator | C4×C32 | C23×C4 |
| Frattini, cosocle | C4×M64 | C24 |
| prime radical | #72225430 | C2 |
| LCS | G ▷ C4×C32 ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ C2×C4×C8 ◁ C8×#346 ◁ C8×#1398 ◁ G | |
| LECS | G ▷ C4×M64 ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72225506 | C2 | semidirect |
| 2. #72225504 | C2 | semidirect |
| 3. #72225502 | C2 | semidirect |
| 5. #72225499 | C2 | semidirect |
| 6. #72225487 | C2 | semidirect |
| 9. #72225472 | C2 | semidirect |
| 12. #72225455 | C2 | semidirect |
| 17. #72225425 | C4 | semidirect |
| 19. #72225423 | C4 | semidirect |
| 20. #72225422 | C4 | semidirect |
| 21. #72225408 | C2 | semidirect |
| 26. #72225315 | C2 | semidirect |
| 37. #72216316 | C2 | semidirect |
| 74. #151732 | C2×C4 | semidirect |
| 75. #151724 | C2×C4 | semidirect |
| 78. #151715 | C2×C4 | semidirect |
| 118. #94748 | C2×C4 | semidirect |
| 120. #94746 | C2×C4 | semidirect |
| 121. #94743 | C2×C4 | semidirect |
| 122. #94738 | C2×C4 | semidirect |
| 540. Q64 | #443 | semidirect |
| 547. D32 | #443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72225506 | 2 |
| #72225504 | 2 |
| #72225502 | 2 |
| #72225499 | 2 |
| #72225487 | 2 |
| #72225472 | 2 |
| #72225455 | 2 |
| #72225430 | 2 |
| #72225408 | 2 |
| #72225315 | 2 |
| #72216316 | 2 |