Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
1307 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 1307 conjugacy classes of subgroups — too many to draw. Only its 87 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 | #6357224 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #153536 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #153535 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #153528 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #153524 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #152056 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #152056 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #62525 | — | 2 | 1 | no | — |
| 9 | #62413 | — | 2 | 1 | no | — |
| 10 | #60665 | C4 | 1 | 1 | yes | characteristic, complemented |
| 11 | #60647 | C22 | 1 | 1 | yes | characteristic |
| 12 | #19654 | — | 2 | 1 | no | — |
| 13 | #19654 | C22 | 1 | 1 | yes | characteristic |
| 14 | #19652 | — | 2 | 1 | no | — |
| 15 | #19652 | C4 | 1 | 1 | yes | characteristic, complemented |
| 16 | #19623 | — | 2 | 2 | no | — |
| 17 | #19623 | — | 2 | 1 | no | — |
| 18 | #19621 | — | 2 | 2 | no | — |
| 19 | #19621 | — | 2 | 1 | no | — |
| 20 | #19608 | — | 2 | 1 | no | — |
| 21 | #19608 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#1715 | — | 2 | 1 | no | — |
| 23 | C2×#1715 | C4 | 1 | 1 | yes | characteristic, complemented |
| 24 | #17316 | C4 | 1 | 1 | yes | characteristic, complemented |
| 25 | #13589 | C22 | 1 | 1 | yes | characteristic |
| 26 | #13589 | C22 | 1 | 1 | yes | characteristic |
| 27 | #13583 | C22 | 1 | 1 | yes | characteristic |
| 28 | #13583 | C22 | 1 | 1 | yes | characteristic |
| 29 | #13579 | — | 2 | 1 | no | — |
| 30 | #13579 | — | 2 | 1 | no | — |
| 31 | #12718 | — | 2 | 1 | no | — |
| 32 | #12718 | — | 2 | 1 | no | — |
| 33 | #7536 | — | 2 | 2 | no | — |
| 34 | #7535 | — | 2 | 2 | no | — |
| 35 | #7534 | — | 2 | 1 | no | — |
| 36 | #7534 | — | 2 | 1 | no | — |
| 37 | #7533 | — | 2 | 1 | no | — |
| 38 | #7533 | — | 2 | 1 | no | — |
| 39 | C2×#576 | — | 4 | 1 | no | — |
| 40 | #3503 | — | 2 | 1 | no | — |
| 41 | #3498 | D4 | 1 | 1 | yes | characteristic |
| 42 | #3498 | D4 | 1 | 1 | yes | characteristic |
| 43 | #3392 | — | 4 | 2 | no | — |
| 44 | #3362 | — | 4 | 2 | no | — |
| 45 | #3295 | — | 4 | 4 | no | — |
| 46 | #3295 | — | 4 | 2 | no | — |
| 47 | D4×SD16 | — | 4 | 4 | no | — |
| 48 | D4×SD16 | — | 4 | 2 | no | — |
| 49 | #3227 | — | 2 | 2 | no | — |
| 50 | #3227 | — | 2 | 1 | no | — |
| 51 | #3208 | — | 2 | 2 | no | — |
| 52 | #3208 | — | 2 | 2 | no | — |
| 53 | #3208 | — | 2 | 1 | no | — |
| 54 | #3208 | — | 2 | 1 | no | — |
| 55 | #3206 | — | 2 | 2 | no | — |
| 56 | #3206 | — | 2 | 1 | no | — |
| 57 | #3167 | — | 2 | 2 | no | — |
| 58 | #3167 | — | 2 | 2 | no | — |
| 59 | #3167 | — | 2 | 1 | no | — |
| 60 | #3167 | — | 2 | 1 | no | — |
| 61 | #3165 | — | 2 | 2 | no | — |
| 62 | #3165 | — | 2 | 1 | no | — |
| 63 | #3163 | — | 4 | 2 | no | — |
| 64 | #3163 | — | 4 | 1 | no | — |
| 65 | #3160 | — | 2 | 1 | no | — |
| 66 | #3160 | C2×C4 | 1 | 1 | yes | characteristic |
| 67 | C2×#498 | — | 2 | 1 | no | — |
| 68 | C2×#498 | C2×C4 | 1 | 1 | yes | characteristic |
| 69 | #3155 | — | 4 | 1 | no | — |
| 70 | #3155 | — | 4 | 2 | no | — |
| 71 | #3151 | — | 2 | 1 | no | — |
| 72 | #3151 | — | 2 | 1 | no | — |
| 73 | #3151 | D4 | 1 | 1 | yes | characteristic |
| 74 | #3151 | D4 | 1 | 1 | yes | characteristic |
| 75 | #3147 | — | 2 | 1 | no | — |
| 76 | #3147 | C23 | 1 | 1 | yes | characteristic |
| 77 | C2×#493 | — | 2 | 1 | no | — |
| 78 | C2×#493 | C2×C4 | 1 | 1 | yes | characteristic |
| 79 | C2×#492 | — | 2 | 2 | no | — |
| 80 | C2×#492 | — | 2 | 1 | no | — |
| 81 | C2×#486 | — | 2 | 2 | no | — |
| 82 | C2×#486 | — | 2 | 1 | no | — |
| 83 | C8×#41 | — | 2 | 1 | no | — |
| 84 | #2912 | — | 4 | 1 | no | — |
| 85 | C4×#131 | C2×C4 | 1 | 1 | yes | characteristic |
| 86 | #2132 | — | 2 | 1 | no | — |
| 87 | #2132 | — | 2 | 1 | no | — |
| 88 | #2126 | — | 2 | 1 | no | — |
| 89 | #2126 | — | 2 | 1 | no | — |
| 90 | #2122 | — | 4 | 1 | no | — |
| 91 | #2122 | — | 4 | 1 | no | — |
| 92 | #1795 | — | 4 | 1 | no | — |
| 93 | #1795 | — | 4 | 1 | no | — |
| 94 | #1716 | — | 2 | 1 | no | — |
| 95 | #1716 | D4 | 1 | 1 | yes | characteristic |
| 96 | #1716 | D4 | 1 | 1 | yes | characteristic |
| 97 | #1715 | — | 2 | 2 | no | — |
| 98 | #1715 | — | 2 | 2 | no | — |
| 99 | #1715 | — | 2 | 1 | no | — |
| 100 | #1715 | — | 2 | 2 | no | — |
| 101 | #1715 | — | 2 | 1 | no | — |
| 102 | #1715 | — | 2 | 1 | no | — |
| 103 | #1715 | — | 2 | 1 | no | — |
| 104 | #1715 | — | 2 | 1 | no | — |
| 105 | #1715 | D4 | 1 | 1 | yes | characteristic |
| 106 | #1715 | D4 | 1 | 1 | yes | characteristic |
| 107 | #1714 | — | 2 | 2 | no | — |
| 108 | #1714 | — | 2 | 2 | no | — |
| 109 | #1714 | — | 2 | 1 | no | — |
| 110 | #1714 | — | 2 | 1 | no | — |
| 111 | #1708 | — | 2 | 2 | no | — |
| 112 | #1708 | D4 | 1 | 2 | yes | — |
| 113 | #1706 | — | 2 | 2 | no | — |
| 114 | #1706 | — | 2 | 2 | no | — |
| 115 | #1706 | — | 2 | 2 | no | — |
| 116 | #1705 | — | 2 | 2 | no | — |
| 117 | #1705 | D4 | 1 | 2 | yes | — |
| 118 | #1450 | — | 2 | 1 | no | — |
| 119 | #1450 | C2×C4 | 1 | 1 | yes | characteristic |
| 120 | C8×M16 | — | 2 | 1 | no | — |
| 121 | C8×M16 | — | 2 | 2 | no | — |
| 122 | C2×#322 | — | 2 | 1 | no | — |
| 123 | C2×#322 | C2×C4 | 1 | 1 | yes | characteristic |
| 124 | #1411 | — | 2 | 1 | no | — |
| 125 | #1411 | — | 2 | 1 | no | — |
| 126 | #1410 | — | 2 | 1 | no | — |
| 127 | #1410 | — | 2 | 1 | no | — |
| 128 | #1409 | — | 2 | 1 | no | — |
| 129 | #1409 | — | 2 | 1 | no | — |
| 130 | #1408 | — | 2 | 1 | no | — |
| 131 | #1408 | — | 2 | 1 | no | — |
| 132 | #1406 | — | 4 | 2 | no | — |
| 133 | #1406 | — | 4 | 2 | no | — |
| 134 | C2×H(5,𝔽2) | — | 2 | 1 | no | — |
| 135 | C2×H(5,𝔽2) | — | 2 | 1 | no | — |
| 136 | #576 | — | 8 | 4 | no | — |
| 137 | #576 | — | 8 | 4 | no | — |
| 138 | C2×AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 139 | C2×AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 140 | C2×AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 141 | C2×AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 142 | C2×#135 | — | 4 | 1 | no | — |
| 143 | C2×#135 | — | 4 | 2 | no | — |
| 144 | C22×SD16 | — | 4 | 2 | no | — |
| 145 | C22×SD16 | — | 4 | 4 | no | — |
| 146 | C22×D8 | — | 4 | 1 | no | — |
| 147 | C22×D8 | — | 4 | 2 | no | — |
| 148 | C2×#131 | — | 2 | 1 | no | — |
| 149 | Q82 | — | 4 | 1 | no | — |
| 150 | #557 | — | 4 | 1 | no | — |
| 151 | #554 | — | 4 | 1 | no | — |
| 152 | #554 | — | 4 | 2 | no | — |
| 153 | #550 | — | 4 | 1 | no | — |
| 154 | #550 | — | 4 | 1 | no | — |
| 155 | D4×Q8 | — | 4 | 1 | no | — |
| 156 | D4×Q8 | — | 4 | 2 | no | — |
| 157 | D42 | — | 4 | 2 | no | — |
| 158 | D42 | — | 4 | 2 | no | — |
| 159 | D42 | — | 4 | 1 | no | — |
| 160 | D42 | — | 4 | 1 | no | — |
| 161 | #544 | — | 4 | 2 | no | — |
| 162 | #544 | — | 4 | 1 | no | — |
| 163 | #535 | — | 2 | 1 | no | — |
| 164 | #535 | — | 2 | 1 | no | — |
| 165 | #535 | — | 4 | 1 | no | — |
| 166 | #535 | — | 4 | 1 | no | — |
| 167 | #533 | — | 2 | 2 | no | — |
| 168 | #533 | — | 2 | 1 | no | — |
| 169 | #532 | — | 2 | 1 | no | — |
| 170 | #532 | — | 2 | 1 | no | — |
| 171 | #532 | C2×D4 | 1 | 1 | yes | characteristic |
| 172 | #532 | C2×D4 | 1 | 1 | yes | characteristic |
| 173 | C2×C4⋊Q8 | — | 2 | 2 | no | — |
| 174 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 175 | C2×#127 | — | 2 | 1 | no | — |
| 176 | C2×#127 | — | 2 | 1 | no | — |
| 177 | C2×#127 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 178 | C2×#127 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 179 | #520 | — | 4 | 1 | no | — |
| 180 | C4×#41 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 181 | #501 | — | 4 | 4 | no | — |
| 182 | #501 | — | 4 | 2 | no | — |
| 183 | #500 | — | 2 | 2 | no | — |
| 184 | #500 | — | 2 | 1 | no | — |
| 185 | #499 | — | 4 | 1 | no | — |
| 186 | #499 | — | 4 | 2 | no | — |
| 187 | #498 | — | 2 | 2 | no | — |
| 188 | #498 | — | 2 | 1 | no | — |
| 189 | #498 | — | 2 | 1 | no | — |
| 190 | #498 | — | 2 | 2 | no | — |
| 191 | #498 | — | 2 | 1 | no | — |
| 192 | #498 | — | 4 | 1 | no | — |
| 193 | #498 | — | 4 | 2 | no | — |
| 194 | #498 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 195 | #498 | C22⋊C4 | 1 | 2 | yes | — |
| 196 | #498 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 197 | #496 | — | 2 | 2 | no | — |
| 198 | #496 | — | 2 | 2 | no | — |
| 199 | #496 | — | 4 | 2 | no | — |
| 200 | #496 | — | 4 | 2 | no | — |
| 201 | #495 | — | 4 | 1 | no | — |
| 202 | #495 | — | 4 | 2 | no | — |
| 203 | #494 | C2×D4 | 1 | 1 | yes | characteristic |
| 204 | #493 | — | 2 | 1 | no | — |
| 205 | #493 | — | 2 | 1 | no | — |
| 206 | #493 | — | 2 | 1 | no | — |
| 207 | #493 | — | 2 | 1 | no | — |
| 208 | #493 | — | 4 | 1 | no | — |
| 209 | #493 | — | 4 | 2 | no | — |
| 210 | #493 | C2×D4 | 1 | 1 | yes | characteristic |
| 211 | #492 | — | 2 | 2 | no | — |
| 212 | #492 | — | 2 | 2 | no | — |
| 213 | #492 | — | 2 | 2 | no | — |
| 214 | #492 | — | 2 | 2 | no | — |
| 215 | #492 | — | 2 | 1 | no | — |
| 216 | #492 | — | 2 | 1 | no | — |
| 217 | #492 | — | 2 | 1 | no | — |
| 218 | #492 | — | 2 | 2 | no | — |
| 219 | #492 | — | 2 | 1 | no | — |
| 220 | #492 | — | 4 | 2 | no | — |
| 221 | #492 | — | 4 | 4 | no | — |
| 222 | #492 | C2×D4 | 1 | 1 | yes | characteristic |
| 223 | #492 | C2×D4 | 1 | 1 | yes | characteristic |
| 224 | #487 | — | 2 | 1 | no | — |
| 225 | #487 | — | 2 | 1 | no | — |
| 226 | #487 | — | 2 | 2 | no | — |
| 227 | #486 | — | 2 | 2 | no | — |
| 228 | #486 | — | 2 | 2 | no | — |
| 229 | #486 | — | 2 | 2 | no | — |
| 230 | #486 | — | 2 | 2 | no | — |
| 231 | #486 | — | 2 | 1 | no | — |
| 232 | #486 | — | 2 | 2 | no | — |
| 233 | #486 | — | 2 | 1 | no | — |
| 234 | #486 | — | 4 | 2 | no | — |
| 235 | #486 | — | 4 | 4 | no | — |
| 236 | #481 | — | 4 | 2 | no | — |
| 237 | #481 | — | 4 | 4 | no | — |
| 238 | #476 | — | 4 | 2 | no | — |
| 239 | #476 | — | 4 | 4 | no | — |
| 240 | #465 | — | 4 | 2 | no | — |
| 241 | #465 | — | 4 | 4 | no | — |
| 242 | #465 | — | 4 | 2 | no | — |
| 243 | #465 | — | 4 | 4 | no | — |
| 244 | #461 | — | 4 | 2 | no | — |
| 245 | #461 | — | 4 | 4 | no | — |
| 246 | #460 | — | 4 | 2 | no | — |
| 247 | #460 | — | 4 | 4 | no | — |
| 248 | #460 | — | 4 | 2 | no | — |
| 249 | #460 | — | 4 | 4 | no | — |
| 250 | #450 | — | 4 | 2 | no | — |
| 251 | #450 | — | 4 | 4 | no | — |
| 252 | #450 | — | 4 | 2 | no | — |
| 253 | #450 | — | 4 | 4 | no | — |
| 254 | #448 | — | 4 | 2 | no | — |
| 255 | #448 | — | 4 | 4 | no | — |
| 256 | C8×Q8 | — | 2 | 2 | no | — |
| 257 | C4×SD16 | — | 4 | 2 | no | — |
| 258 | C4×SD16 | — | 4 | 4 | no | — |
| 259 | C4×SD16 | — | 4 | 2 | no | — |
| 260 | C4×SD16 | — | 4 | 4 | no | — |
| 261 | C8×D4 | — | 2 | 2 | no | — |
| 262 | C8×D4 | — | 2 | 4 | no | — |
| 263 | #431 | — | 2 | 2 | no | — |
| 264 | #431 | — | 2 | 1 | no | — |
| 265 | #428 | — | 4 | 2 | no | — |
| 266 | #428 | — | 4 | 4 | no | — |
| 267 | #427 | — | 4 | 2 | no | — |
| 268 | #427 | — | 4 | 1 | no | — |
| 269 | C2×#106 | — | 4 | 2 | no | — |
| 270 | C2×#106 | — | 4 | 1 | no | — |
| 271 | #421 | — | 8 | 1 | no | — |
| 272 | #421 | — | 8 | 1 | no | — |
| 273 | #418 | — | 8 | 1 | no | — |
| 274 | #418 | — | 8 | 1 | no | — |
| 275 | C2×#102 | — | 4 | 2 | no | — |
| 276 | C2×#102 | — | 4 | 4 | no | — |
| 277 | #413 | — | 4 | 1 | no | — |
| 278 | #413 | — | 4 | 1 | no | — |
| 279 | #410 | — | 4 | 1 | no | — |
| 280 | #410 | — | 4 | 1 | no | — |
| 281 | #405 | — | 2 | 1 | no | — |
| 282 | #405 | — | 2 | 2 | no | — |
| 283 | C4×M16 | — | 2 | 1 | no | — |
| 284 | C4×M16 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 285 | C2×C4×C8 | — | 2 | 2 | no | — |
| 286 | C2×C4×C8 | — | 2 | 1 | no | — |
| 287 | C2×C4×C8 | — | 2 | 1 | no | — |
| 288 | C2×C4×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 289 | #356 | — | 4 | 1 | no | — |
| 290 | #356 | — | 4 | 1 | no | — |
| 291 | #355 | — | 4 | 1 | no | — |
| 292 | #355 | — | 4 | 1 | no | — |
| 293 | #354 | — | 4 | 1 | no | — |
| 294 | #354 | — | 4 | 1 | no | — |
| 295 | #353 | — | 4 | 1 | no | — |
| 296 | #353 | — | 4 | 1 | no | — |
| 297 | AΣL(1,𝔽16) | — | 8 | 2 | no | — |
| 298 | AΣL(1,𝔽16) | — | 8 | 2 | no | — |
| 299 | #322 | — | 2 | 2 | no | — |
| 300 | #322 | — | 2 | 1 | no | — |
| 301 | #322 | — | 2 | 1 | no | — |
| 302 | #322 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 303 | #322 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 304 | C82 | — | 2 | 2 | no | — |
| 305 | C82 | C22⋊C4 | 1 | 2 | yes | — |
| 306 | H(5,𝔽2) | — | 8 | 2 | no | — |
| 307 | H(5,𝔽2) | — | 8 | 2 | no | — |
| 308 | H(5,𝔽2) | — | 8 | 2 | no | — |
| 309 | H(5,𝔽2) | — | 8 | 2 | no | — |
| 310 | C2×#41 | — | 2 | 1 | no | — |
| 311 | C2×#41 | — | 2 | 1 | no | — |
| 312 | C2×#41 | — | 4 | 1 | no | — |
| 313 | C2×#41 | — | 4 | 1 | no | — |
| 314 | C2×#41 | — | 4 | 1 | no | — |
| 315 | C2×#41 | — | 4 | 1 | no | — |
| 316 | C2×#41 | #99 | 1 | 1 | yes | characteristic |
| 317 | C22×Q8 | — | 4 | 2 | no | — |
| 318 | C22×Q8 | — | 4 | 1 | no | — |
| 319 | C22×D4 | — | 2 | 1 | no | — |
| 320 | C22×D4 | — | 2 | 1 | no | — |
| 321 | C22×D4 | — | 4 | 1 | no | — |
| 322 | C22×D4 | — | 4 | 1 | no | — |
| 323 | C22×D4 | — | 4 | 1 | no | — |
| 324 | C22×D4 | — | 4 | 1 | no | — |
| 325 | C22×D4 | — | 4 | 2 | no | — |
| 326 | C22×D4 | — | 4 | 2 | no | — |
| 327 | C22×D4 | — | 4 | 1 | no | — |
| 328 | C22×D4 | — | 4 | 1 | no | — |
| 329 | C22×D4 | — | 8 | 1 | no | — |
| 330 | C22×D4 | — | 8 | 1 | no | — |
| 331 | AGL(1,ℤ/8) | — | 8 | 2 | no | — |
| 332 | AGL(1,ℤ/8) | — | 8 | 2 | no | — |
| 333 | AGL(1,ℤ/8) | — | 8 | 2 | no | — |
| 334 | AGL(1,ℤ/8) | — | 8 | 2 | no | — |
| 335 | AGL(1,ℤ/8) | — | 8 | 8 | no | — |
| 336 | AGL(1,ℤ/8) | — | 8 | 8 | no | — |
| 337 | #135 | — | 8 | 2 | no | — |
| 338 | #135 | — | 8 | 2 | no | — |
| 339 | #135 | — | 8 | 8 | no | — |
| 340 | C2×Q16 | — | 4 | 1 | no | — |
| 341 | C2×SD16 | — | 4 | 1 | no | — |
| 342 | C2×SD16 | — | 4 | 1 | no | — |
| 343 | C2×SD16 | — | 4 | 2 | no | — |
| 344 | C2×SD16 | — | 4 | 2 | no | — |
| 345 | C2×SD16 | — | 4 | 2 | no | — |
| 346 | C2×SD16 | — | 4 | 4 | no | — |
| 347 | C2×SD16 | — | 4 | 4 | no | — |
| 348 | C2×SD16 | — | 4 | 4 | no | — |
| 349 | C2×SD16 | — | 4 | 4 | no | — |
| 350 | C2×SD16 | — | 4 | 2 | no | — |
| 351 | C2×SD16 | — | 4 | 4 | no | — |
| 352 | C2×SD16 | — | 16 | 4 | no | — |
| 353 | C2×SD16 | — | 16 | 8 | no | — |
| 354 | C2×D8 | — | 4 | 1 | no | — |
| 355 | C2×D8 | — | 4 | 2 | no | — |
| 356 | C2×D8 | — | 4 | 2 | no | — |
| 357 | C2×D8 | — | 4 | 2 | no | — |
| 358 | C2×D8 | — | 4 | 2 | no | — |
| 359 | C2×D8 | — | 8 | 2 | no | — |
| 360 | C2×D8 | — | 8 | 2 | no | — |
| 361 | C2×D8 | — | 8 | 8 | no | — |
| 362 | #131 | — | 2 | 4 | no | — |
| 363 | #131 | — | 2 | 4 | no | — |
| 364 | C2×M16 | — | 2 | 2 | no | — |
| 365 | C2×M16 | — | 2 | 1 | no | — |
| 366 | C2×M16 | — | 8 | 1 | no | — |
| 367 | C2×M16 | — | 8 | 1 | no | — |
| 368 | C22×C8 | — | 2 | 2 | no | — |
| 369 | C22×C8 | — | 2 | 1 | no | — |
| 370 | C22×C8 | — | 2 | 4 | no | — |
| 371 | C22×C8 | — | 2 | 2 | no | — |
| 372 | C4⋊Q8 | — | 2 | 1 | no | — |
| 373 | C4⋊Q8 | — | 2 | 2 | no | — |
| 374 | C4⋊Q8 | — | 2 | 1 | no | — |
| 375 | C4⋊Q8 | — | 4 | 2 | no | — |
| 376 | C4⋊Q8 | — | 4 | 2 | no | — |
| 377 | C4⋊Q8 | — | 4 | 1 | no | — |
| 378 | C4⋊Q8 | — | 4 | 2 | no | — |
| 379 | C4⋊Q8 | — | 4 | 1 | no | — |
| 380 | C4⋊Q8 | — | 4 | 1 | no | — |
| 381 | C4⋊Q8 | — | 8 | 2 | no | — |
| 382 | C4⋊Q8 | — | 8 | 1 | no | — |
| 383 | C4⋊Q8 | #120 | 1 | 1 | yes | characteristic |
| 384 | C4⋊Q8 | #120 | 1 | 1 | yes | characteristic |
| 385 | #127 | — | 2 | 1 | no | — |
| 386 | #127 | — | 2 | 1 | no | — |
| 387 | #127 | — | 2 | 1 | no | — |
| 388 | #127 | — | 2 | 1 | no | — |
| 389 | #127 | — | 4 | 1 | no | — |
| 390 | #127 | — | 4 | 1 | no | — |
| 391 | #127 | — | 4 | 1 | no | — |
| 392 | #127 | — | 4 | 1 | no | — |
| 393 | #127 | — | 4 | 2 | no | — |
| 394 | #127 | — | 4 | 2 | no | — |
| 395 | #127 | #120 | 1 | 1 | yes | characteristic |
| 396 | #127 | #120 | 1 | 1 | yes | characteristic |
| 397 | #125 | — | 4 | 2 | no | — |
| 398 | #125 | — | 4 | 1 | no | — |
| 399 | #125 | — | 8 | 2 | no | — |
| 400 | #125 | — | 8 | 1 | no | — |
| 401 | #124 | — | 2 | 1 | no | — |
| 402 | #124 | — | 2 | 1 | no | — |
| 403 | #124 | — | 4 | 1 | no | — |
| 404 | #124 | — | 4 | 1 | no | — |
| 405 | C22⋊Q8 | — | 4 | 2 | no | — |
| 406 | C22⋊Q8 | — | 4 | 1 | no | — |
| 407 | C22⋊Q8 | — | 4 | 2 | no | — |
| 408 | C22⋊Q8 | — | 4 | 1 | no | — |
| 409 | C22⋊Q8 | — | 8 | 2 | no | — |
| 410 | C22⋊Q8 | — | 8 | 2 | no | — |
| 411 | C22⋊Q8 | — | 8 | 2 | no | — |
| 412 | #121 | — | 4 | 1 | no | — |
| 413 | #121 | — | 4 | 1 | no | — |
| 414 | #121 | — | 4 | 2 | no | — |
| 415 | #121 | — | 4 | 2 | no | — |
| 416 | #121 | — | 8 | 1 | no | — |
| 417 | #121 | — | 8 | 1 | no | — |
| 418 | #121 | — | 8 | 2 | no | — |
| 419 | #121 | — | 8 | 2 | no | — |
| 420 | #120 | — | 4 | 2 | no | — |
| 421 | #120 | — | 4 | 2 | no | — |
| 422 | #120 | — | 8 | 2 | no | — |
| 423 | #120 | — | 8 | 2 | no | — |
| 424 | C4×Q8 | — | 2 | 1 | no | — |
| 425 | C4×Q8 | — | 4 | 2 | no | — |
| 426 | C4×Q8 | — | 4 | 1 | no | — |
| 427 | C4×Q8 | — | 4 | 2 | no | — |
| 428 | C4×Q8 | — | 4 | 1 | no | — |
| 429 | C4×Q8 | — | 8 | 1 | no | — |
| 430 | C4×D4 | — | 2 | 1 | no | — |
| 431 | C4×D4 | — | 2 | 2 | no | — |
| 432 | C4×D4 | — | 4 | 1 | no | — |
| 433 | C4×D4 | — | 4 | 1 | no | — |
| 434 | C4×D4 | — | 4 | 2 | no | — |
| 435 | C4×D4 | — | 4 | 2 | no | — |
| 436 | C4×D4 | — | 8 | 2 | no | — |
| 437 | C4×D4 | — | 8 | 1 | no | — |
| 438 | #117 | — | 2 | 1 | no | — |
| 439 | #117 | — | 4 | 2 | no | — |
| 440 | #117 | — | 4 | 1 | no | — |
| 441 | #117 | — | 8 | 1 | no | — |
| 442 | #117 | — | 8 | 1 | no | — |
| 443 | #117 | #99 | 1 | 1 | yes | characteristic |
| 444 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 445 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 446 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 447 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 448 | C2×C42 | — | 2 | 1 | no | — |
| 449 | C2×C42 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 450 | #107 | — | 4 | 4 | no | — |
| 451 | #107 | — | 4 | 2 | no | — |
| 452 | #106 | — | 4 | 2 | no | — |
| 453 | #106 | — | 4 | 4 | no | — |
| 454 | #106 | — | 4 | 2 | no | — |
| 455 | #106 | — | 4 | 2 | no | — |
| 456 | #106 | — | 4 | 4 | no | — |
| 457 | #106 | — | 4 | 1 | no | — |
| 458 | #106 | — | 4 | 2 | no | — |
| 459 | #106 | — | 4 | 1 | no | — |
| 460 | C4⋊C8 | — | 2 | 4 | no | — |
| 461 | C4⋊C8 | — | 2 | 2 | no | — |
| 462 | #104 | — | 16 | 2 | no | — |
| 463 | #104 | — | 16 | 2 | no | — |
| 464 | #103 | — | 4 | 2 | no | — |
| 465 | #103 | — | 4 | 2 | no | — |
| 466 | #103 | — | 4 | 4 | no | — |
| 467 | #102 | — | 4 | 2 | no | — |
| 468 | #102 | — | 4 | 4 | no | — |
| 469 | #102 | — | 4 | 4 | no | — |
| 470 | #102 | — | 4 | 4 | no | — |
| 471 | #102 | — | 4 | 4 | no | — |
| 472 | #102 | — | 4 | 2 | no | — |
| 473 | #102 | — | 4 | 4 | no | — |
| 474 | #102 | — | 16 | 2 | no | — |
| 475 | #102 | — | 16 | 2 | no | — |
| 476 | #101 | — | 8 | 1 | no | — |
| 477 | #101 | — | 8 | 1 | no | — |
| 478 | #100 | — | 8 | 1 | no | — |
| 479 | #100 | — | 8 | 1 | no | — |
| 480 | #99 | — | 8 | 1 | no | — |
| 481 | #99 | — | 8 | 1 | no | — |
| 482 | #99 | — | 8 | 1 | no | — |
| 483 | #99 | — | 8 | 1 | no | — |
| 484 | C22⋊C8 | — | 2 | 4 | no | — |
| 485 | C22⋊C8 | — | 2 | 2 | no | — |
| 486 | #97 | — | 2 | 2 | no | — |
| 487 | #97 | #99 | 1 | 2 | yes | — |
| 488 | C4×C8 | — | 2 | 2 | no | — |
| 489 | C4×C8 | — | 2 | 4 | no | — |
| 490 | C4×C8 | — | 2 | 2 | no | — |
| 491 | C4×C8 | — | 2 | 1 | no | — |
| 492 | C4×C8 | — | 2 | 1 | no | — |
| 493 | C4×C8 | — | 2 | 2 | no | — |
| 494 | C4×C8 | — | 2 | 1 | no | — |
| 495 | C4×C8 | — | 2 | 1 | no | — |
| 496 | C4×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 497 | C4×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 498 | C24 | — | 4 | 1 | no | — |
| 499 | C24 | — | 4 | 1 | no | — |
| 500 | C24 | — | 8 | 1 | no | — |
| 501 | C24 | — | 8 | 1 | no | — |
| 502 | #41 | — | 2 | 2 | no | — |
| 503 | #41 | — | 2 | 2 | no | — |
| 504 | #41 | — | 8 | 1 | no | — |
| 505 | #41 | — | 8 | 1 | no | — |
| 506 | #41 | — | 8 | 1 | no | — |
| 507 | #41 | — | 8 | 1 | no | — |
| 508 | #41 | — | 8 | 4 | no | — |
| 509 | #41 | — | 8 | 4 | no | — |
| 510 | #41 | — | 8 | 2 | no | — |
| 511 | #41 | — | 8 | 2 | no | — |
| 512 | #41 | — | 16 | 1 | no | — |
| 513 | #41 | — | 16 | 1 | no | — |
| 514 | C2×Q8 | — | 2 | 1 | no | — |
| 515 | C2×Q8 | — | 2 | 1 | no | — |
| 516 | C2×Q8 | — | 4 | 1 | no | — |
| 517 | C2×Q8 | — | 4 | 2 | no | — |
| 518 | C2×Q8 | — | 4 | 1 | no | — |
| 519 | C2×Q8 | — | 8 | 2 | no | — |
| 520 | C2×Q8 | — | 8 | 1 | no | — |
| 521 | C2×Q8 | — | 16 | 2 | no | — |
| 522 | C2×Q8 | — | 16 | 4 | no | — |
| 523 | C2×Q8 | #353 | 1 | 1 | yes | characteristic |
| 524 | C2×D4 | — | 2 | 1 | no | — |
| 525 | C2×D4 | — | 2 | 1 | no | — |
| 526 | C2×D4 | — | 2 | 1 | no | — |
| 527 | C2×D4 | — | 4 | 1 | no | — |
| 528 | C2×D4 | — | 4 | 1 | no | — |
| 529 | C2×D4 | — | 4 | 2 | no | — |
| 530 | C2×D4 | — | 4 | 2 | no | — |
| 531 | C2×D4 | — | 4 | 1 | no | — |
| 532 | C2×D4 | — | 4 | 1 | no | — |
| 533 | C2×D4 | — | 4 | 1 | no | — |
| 534 | C2×D4 | — | 4 | 1 | no | — |
| 535 | C2×D4 | — | 4 | 1 | no | — |
| 536 | C2×D4 | — | 4 | 1 | no | — |
| 537 | C2×D4 | — | 8 | 1 | no | — |
| 538 | C2×D4 | — | 8 | 1 | no | — |
| 539 | C2×D4 | — | 8 | 1 | no | — |
| 540 | C2×D4 | — | 8 | 1 | no | — |
| 541 | C2×D4 | — | 8 | 4 | no | — |
| 542 | C2×D4 | — | 8 | 4 | no | — |
| 543 | C2×D4 | — | 8 | 1 | no | — |
| 544 | C2×D4 | — | 8 | 1 | no | — |
| 545 | C2×D4 | — | 8 | 2 | no | — |
| 546 | C2×D4 | — | 8 | 2 | no | — |
| 547 | C2×D4 | — | 8 | 1 | no | — |
| 548 | C2×D4 | — | 8 | 1 | no | — |
| 549 | C2×D4 | — | 8 | 1 | no | — |
| 550 | C2×D4 | — | 8 | 1 | no | — |
| 551 | C2×D4 | — | 8 | 2 | no | — |
| 552 | C2×D4 | — | 8 | 2 | no | — |
| 553 | C2×D4 | — | 16 | 2 | no | — |
| 554 | C2×D4 | — | 16 | 4 | no | — |
| 555 | C2×D4 | — | 16 | 2 | no | — |
| 556 | C2×D4 | — | 16 | 4 | no | — |
| 557 | C2×D4 | — | 16 | 1 | no | — |
| 558 | C2×D4 | — | 16 | 1 | no | — |
| 559 | C2×D4 | — | 16 | 4 | no | — |
| 560 | C2×D4 | — | 16 | 4 | no | — |
| 561 | C2×D4 | #353 | 1 | 1 | yes | characteristic |
| 562 | C22×C4 | — | 2 | 1 | no | — |
| 563 | C22×C4 | — | 2 | 2 | no | — |
| 564 | C22×C4 | — | 2 | 1 | no | — |
| 565 | C22×C4 | — | 4 | 1 | no | — |
| 566 | C22×C4 | — | 4 | 1 | no | — |
| 567 | C22×C4 | — | 8 | 1 | no | — |
| 568 | C22×C4 | — | 8 | 1 | no | — |
| 569 | C22×C4 | — | 8 | 2 | no | — |
| 570 | C22×C4 | — | 8 | 1 | no | — |
| 571 | C22×C4 | C2×#99 | 1 | 1 | yes | characteristic |
| 572 | Q16 | — | 8 | 2 | no | — |
| 573 | SD16 | — | 8 | 2 | no | — |
| 574 | SD16 | — | 8 | 2 | no | — |
| 575 | SD16 | — | 8 | 4 | no | — |
| 576 | SD16 | — | 8 | 4 | no | — |
| 577 | SD16 | — | 8 | 4 | no | — |
| 578 | SD16 | — | 8 | 8 | no | — |
| 579 | SD16 | — | 16 | 2 | no | — |
| 580 | SD16 | — | 16 | 4 | no | — |
| 581 | SD16 | — | 16 | 4 | no | — |
| 582 | SD16 | — | 16 | 4 | no | — |
| 583 | SD16 | — | 16 | 4 | no | — |
| 584 | D8 | — | 8 | 2 | no | — |
| 585 | D8 | — | 8 | 4 | no | — |
| 586 | D8 | — | 8 | 4 | no | — |
| 587 | D8 | — | 8 | 4 | no | — |
| 588 | D8 | — | 8 | 4 | no | — |
| 589 | M16 | — | 2 | 8 | no | — |
| 590 | M16 | — | 2 | 2 | no | — |
| 591 | M16 | — | 2 | 2 | no | — |
| 592 | M16 | — | 16 | 1 | no | — |
| 593 | M16 | — | 16 | 1 | no | — |
| 594 | M16 | — | 16 | 1 | no | — |
| 595 | M16 | — | 16 | 1 | no | — |
| 596 | C2×C8 | — | 2 | 8 | no | — |
| 597 | C2×C8 | — | 2 | 2 | no | — |
| 598 | C2×C8 | — | 2 | 2 | no | — |
| 599 | C2×C8 | — | 2 | 1 | no | — |
| 600 | C2×C8 | — | 2 | 2 | no | — |
| 601 | C2×C8 | — | 2 | 1 | no | — |
| 602 | C2×C8 | — | 2 | 2 | no | — |
| 603 | C2×C8 | — | 2 | 2 | no | — |
| 604 | C2×C8 | — | 2 | 4 | no | — |
| 605 | C2×C8 | — | 8 | 2 | no | — |
| 606 | C2×C8 | — | 8 | 4 | no | — |
| 607 | C2×C8 | — | 16 | 1 | no | — |
| 608 | C2×C8 | — | 16 | 1 | no | — |
| 609 | C4⋊C4 | — | 2 | 2 | no | — |
| 610 | C4⋊C4 | — | 2 | 1 | no | — |
| 611 | C4⋊C4 | — | 4 | 1 | no | — |
| 612 | C4⋊C4 | — | 4 | 1 | no | — |
| 613 | C4⋊C4 | — | 4 | 2 | no | — |
| 614 | C4⋊C4 | — | 4 | 1 | no | — |
| 615 | C4⋊C4 | — | 4 | 1 | no | — |
| 616 | C4⋊C4 | — | 4 | 2 | no | — |
| 617 | C4⋊C4 | — | 4 | 1 | no | — |
| 618 | C4⋊C4 | — | 4 | 1 | no | — |
| 619 | C4⋊C4 | — | 8 | 2 | no | — |
| 620 | C4⋊C4 | — | 8 | 2 | no | — |
| 621 | C4⋊C4 | — | 8 | 1 | no | — |
| 622 | C4⋊C4 | — | 8 | 2 | no | — |
| 623 | C4⋊C4 | — | 8 | 1 | no | — |
| 624 | C4⋊C4 | — | 8 | 2 | no | — |
| 625 | C4⋊C4 | — | 8 | 1 | no | — |
| 626 | C4⋊C4 | — | 8 | 1 | no | — |
| 627 | C4⋊C4 | — | 16 | 1 | no | — |
| 628 | C4⋊C4 | — | 16 | 1 | no | — |
| 629 | C22⋊C4 | — | 2 | 2 | no | — |
| 630 | C22⋊C4 | — | 8 | 1 | no | — |
| 631 | C22⋊C4 | — | 8 | 1 | no | — |
| 632 | C22⋊C4 | — | 8 | 2 | no | — |
| 633 | C22⋊C4 | — | 8 | 2 | no | — |
| 634 | C22⋊C4 | — | 8 | 2 | no | — |
| 635 | C22⋊C4 | — | 8 | 1 | no | — |
| 636 | C22⋊C4 | — | 16 | 1 | no | — |
| 637 | C22⋊C4 | — | 16 | 1 | no | — |
| 638 | C22⋊C4 | #353 | 1 | 2 | yes | — |
| 639 | C42 | — | 2 | 2 | no | — |
| 640 | C42 | — | 2 | 1 | no | — |
| 641 | C42 | — | 2 | 1 | no | — |
| 642 | C42 | — | 8 | 2 | no | — |
| 643 | C42 | — | 8 | 1 | no | — |
| 644 | C42 | — | 16 | 1 | no | — |
| 645 | C42 | — | 16 | 1 | no | — |
| 646 | C42 | #379 | 1 | 1 | yes | characteristic |
| 647 | C42 | C2×#99 | 1 | 1 | yes | characteristic |
| 648 | C23 | — | 2 | 1 | no | — |
| 649 | C23 | — | 4 | 1 | no | — |
| 650 | C23 | — | 4 | 1 | no | — |
| 651 | C23 | — | 8 | 1 | no | — |
| 652 | C23 | — | 8 | 1 | no | — |
| 653 | C23 | — | 16 | 2 | no | — |
| 654 | C23 | — | 16 | 2 | no | — |
| 655 | C23 | — | 16 | 1 | no | — |
| 656 | C23 | — | 16 | 1 | no | — |
| 657 | C23 | — | 32 | 1 | no | — |
| 658 | C23 | — | 32 | 1 | no | — |
| 659 | C23 | — | 32 | 2 | no | — |
| 660 | C23 | — | 32 | 2 | no | — |
| 661 | C23 | C2×#353 | 1 | 1 | yes | characteristic |
| 662 | Q8 | — | 2 | 1 | no | — |
| 663 | Q8 | — | 8 | 1 | no | — |
| 664 | Q8 | — | 8 | 1 | no | — |
| 665 | Q8 | — | 8 | 4 | no | — |
| 666 | Q8 | — | 8 | 2 | no | — |
| 667 | Q8 | — | 8 | 2 | no | — |
| 668 | Q8 | — | 32 | 2 | no | — |
| 669 | Q8 | — | 32 | 1 | no | — |
| 670 | Q8 | #1409 | 1 | 2 | yes | — |
| 671 | D4 | — | 2 | 4 | no | — |
| 672 | D4 | — | 2 | 1 | no | — |
| 673 | D4 | — | 8 | 1 | no | — |
| 674 | D4 | — | 8 | 1 | no | — |
| 675 | D4 | — | 8 | 2 | no | — |
| 676 | D4 | — | 8 | 2 | no | — |
| 677 | D4 | — | 8 | 2 | no | — |
| 678 | D4 | — | 8 | 4 | no | — |
| 679 | D4 | — | 8 | 2 | no | — |
| 680 | D4 | — | 8 | 4 | no | — |
| 681 | D4 | — | 8 | 1 | no | — |
| 682 | D4 | — | 8 | 1 | no | — |
| 683 | D4 | — | 8 | 1 | no | — |
| 684 | D4 | — | 8 | 1 | no | — |
| 685 | D4 | — | 16 | 2 | no | — |
| 686 | D4 | — | 16 | 2 | no | — |
| 687 | D4 | — | 16 | 1 | no | — |
| 688 | D4 | — | 16 | 1 | no | — |
| 689 | D4 | — | 16 | 2 | no | — |
| 690 | D4 | — | 16 | 2 | no | — |
| 691 | D4 | — | 32 | 2 | no | — |
| 692 | D4 | — | 32 | 2 | no | — |
| 693 | D4 | — | 32 | 1 | no | — |
| 694 | D4 | — | 32 | 1 | no | — |
| 695 | D4 | #1409 | 1 | 2 | yes | — |
| 696 | C2×C4 | — | 2 | 4 | no | — |
| 697 | C2×C4 | — | 2 | 1 | no | — |
| 698 | C2×C4 | — | 2 | 1 | no | — |
| 699 | C2×C4 | — | 2 | 1 | no | — |
| 700 | C2×C4 | — | 2 | 1 | no | — |
| 701 | C2×C4 | — | 2 | 2 | no | — |
| 702 | C2×C4 | — | 2 | 1 | no | — |
| 703 | C2×C4 | — | 4 | 2 | no | — |
| 704 | C2×C4 | — | 4 | 4 | no | — |
| 705 | C2×C4 | — | 4 | 1 | no | — |
| 706 | C2×C4 | — | 4 | 1 | no | — |
| 707 | C2×C4 | — | 8 | 1 | no | — |
| 708 | C2×C4 | — | 8 | 1 | no | — |
| 709 | C2×C4 | — | 8 | 1 | no | — |
| 710 | C2×C4 | — | 8 | 1 | no | — |
| 711 | C2×C4 | — | 8 | 1 | no | — |
| 712 | C2×C4 | — | 8 | 2 | no | — |
| 713 | C2×C4 | — | 8 | 1 | no | — |
| 714 | C2×C4 | — | 16 | 2 | no | — |
| 715 | C2×C4 | — | 16 | 2 | no | — |
| 716 | C2×C4 | — | 32 | 1 | no | — |
| 717 | C2×C4 | — | 32 | 2 | no | — |
| 718 | C2×C4 | — | 32 | 1 | no | — |
| 719 | C2×C4 | — | 32 | 1 | no | — |
| 720 | C2×C4 | #1781 | 1 | 1 | yes | characteristic |
| 721 | C2×C4 | C2×#353 | 1 | 1 | yes | characteristic |
| 722 | C8 | — | 2 | 2 | no | — |
| 723 | C8 | — | 2 | 4 | no | — |
| 724 | C8 | — | 2 | 2 | no | — |
| 725 | C8 | — | 4 | 2 | no | — |
| 726 | C8 | — | 4 | 2 | no | — |
| 727 | C8 | — | 4 | 4 | no | — |
| 728 | C8 | — | 32 | 1 | no | — |
| 729 | C8 | — | 32 | 1 | no | — |
| 730 | C22 | — | 2 | 1 | no | — |
| 731 | C22 | — | 2 | 2 | no | — |
| 732 | C22 | — | 4 | 1 | no | — |
| 733 | C22 | — | 4 | 2 | no | — |
| 734 | C22 | — | 8 | 1 | no | — |
| 735 | C22 | — | 8 | 1 | no | — |
| 736 | C22 | — | 16 | 1 | no | — |
| 737 | C22 | — | 16 | 1 | no | — |
| 738 | C22 | — | 16 | 2 | no | — |
| 739 | C22 | — | 16 | 2 | no | — |
| 740 | C22 | — | 16 | 1 | no | — |
| 741 | C22 | — | 16 | 1 | no | — |
| 742 | C22 | — | 64 | 2 | no | — |
| 743 | C22 | — | 64 | 2 | no | — |
| 744 | C22 | — | 64 | 1 | no | — |
| 745 | C22 | — | 64 | 1 | no | — |
| 746 | C22 | #12693 | 1 | 1 | yes | characteristic |
| 747 | C4 | — | 2 | 2 | no | — |
| 748 | C4 | — | 2 | 1 | no | — |
| 749 | C4 | — | 2 | 2 | no | — |
| 750 | C4 | — | 4 | 2 | no | — |
| 751 | C4 | — | 4 | 1 | no | — |
| 752 | C4 | — | 8 | 1 | no | — |
| 753 | C4 | — | 8 | 1 | no | — |
| 754 | C4 | — | 16 | 2 | no | — |
| 755 | C4 | — | 16 | 1 | no | — |
| 756 | C4 | — | 16 | 1 | no | — |
| 757 | C4 | — | 64 | 1 | no | — |
| 758 | C4 | — | 64 | 1 | no | — |
| 759 | C4 | C2×#1409 | 1 | 1 | yes | characteristic |
| 760 | C4 | C2×#1409 | 1 | 1 | yes | characteristic |
| 761 | C2 | — | 2 | 1 | no | — |
| 762 | C2 | — | 4 | 2 | no | — |
| 763 | C2 | — | 4 | 1 | no | — |
| 764 | C2 | — | 16 | 1 | no | — |
| 765 | C2 | — | 16 | 1 | no | — |
| 766 | C2 | — | 32 | 1 | no | — |
| 767 | C2 | — | 32 | 1 | no | — |
| 768 | C2 | #152036 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #152036 |
| commutator | C2×C4×C8 | C22×C4 |
| Frattini, cosocle | #3147 | C23 |
| prime radical | #60647 | C22 |
| LCS | G ▷ C2×C4×C8 ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ C4×#41 ◁ #60647 ◁ G | |
| LECS | G ▷ #3147 ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #153536 | C2 | semidirect |
| 3. #153535 | C2 | semidirect |
| 4. #153528 | C2 | semidirect |
| 5. #153524 | C2 | semidirect |
| 10. #60665 | C4 | semidirect |
| 15. #19652 | C4 | semidirect |
| 23. C2×#1715 | C4 | semidirect |
| 24. #17316 | C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #6357224 | 2 |
| #153536 | 2 |
| #153535 | 2 |
| #153528 | 2 |
| #153524 | 2 |
| #152056 | 2 |