Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
6889 conjugacy classes of subgroups.
The subgroup lattice has 758 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#3503 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#3480 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #42944 | C2 | 1 | 6 | yes | maximal, complemented |
| 4 | #42918 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | #42682 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #42678 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #39343 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | #38911 | C2 | 1 | 6 | yes | maximal, complemented |
| 9 | #37622 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #37615 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | #36577 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #36445 | C2 | 1 | 2 | yes | maximal, complemented |
| 13 | #36076 | C2 | 1 | 2 | yes | maximal, complemented |
| 14 | #35996 | C2 | 1 | 2 | yes | maximal, complemented |
| 15 | #35948 | C2 | 1 | 2 | yes | maximal, complemented |
| 16 | #35937 | C2 | 1 | 2 | yes | maximal, complemented |
| 17 | #35316 | C2 | 1 | 3 | yes | maximal, complemented |
| 18 | #34627 | C2 | 1 | 3 | yes | maximal, complemented |
| 19 | #34193 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 20 | #3503 | — | 2 | 16 | no | — |
| 21 | #3480 | — | 2 | 16 | no | — |
| 22 | C2×#559 | C22 | 1 | 3 | yes | — |
| 23 | C2×Q82 | C22 | 1 | 2 | yes | — |
| 24 | C2×#557 | C22 | 1 | 2 | yes | — |
| 25 | C2×#557 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×#556 | C22 | 1 | 3 | yes | — |
| 27 | C2×#554 | C22 | 1 | 6 | yes | — |
| 28 | C2×#553 | C22 | 1 | 3 | yes | — |
| 29 | C2×#553 | C22 | 1 | 3 | yes | — |
| 30 | C2×#550 | C22 | 1 | 1 | yes | characteristic |
| 31 | C2×D4×Q8 | C22 | 1 | 6 | yes | — |
| 32 | C2×#548 | C22 | 1 | 1 | yes | characteristic |
| 33 | C2×#548 | C22 | 1 | 1 | yes | characteristic |
| 34 | C2×#544 | C22 | 1 | 6 | yes | — |
| 35 | C2×#536 | C22 | 1 | 6 | yes | — |
| 36 | C2×#533 | C22 | 1 | 3 | yes | — |
| 37 | C2×#532 | C22 | 1 | 3 | yes | — |
| 38 | C22×C4⋊Q8 | C22 | 1 | 3 | yes | — |
| 39 | C2×#529 | C22 | 1 | 3 | yes | — |
| 40 | C2×#529 | C22 | 1 | 3 | yes | — |
| 41 | C2×#520 | C22 | 1 | 2 | yes | — |
| 42 | C2×C4×#41 | C22 | 1 | 3 | yes | — |
| 43 | C2×C4×#41 | C22 | 1 | 1 | yes | characteristic |
| 44 | C2×C4×#41 | C22 | 1 | 1 | yes | characteristic |
| 45 | C22×C4×Q8 | C22 | 1 | 1 | yes | characteristic |
| 46 | #2857 | C22 | 1 | 6 | yes | — |
| 47 | #2857 | C22 | 1 | 6 | yes | — |
| 48 | #2821 | C22 | 1 | 12 | yes | — |
| 49 | #2814 | C22 | 1 | 12 | yes | — |
| 50 | #2689 | C22 | 1 | 24 | yes | — |
| 51 | #2687 | C22 | 1 | 24 | yes | — |
| 52 | #2674 | C22 | 1 | 24 | yes | — |
| 53 | #2672 | C22 | 1 | 24 | yes | — |
| 54 | #2664 | C22 | 1 | 12 | yes | — |
| 55 | #2660 | C22 | 1 | 6 | yes | — |
| 56 | #2640 | C22 | 1 | 6 | yes | — |
| 57 | #2638 | C22 | 1 | 6 | yes | — |
| 58 | #2638 | C22 | 1 | 6 | yes | — |
| 59 | #2634 | C22 | 1 | 6 | yes | — |
| 60 | #2633 | C22 | 1 | 6 | yes | — |
| 61 | #2628 | C22 | 1 | 1 | yes | characteristic |
| 62 | #2628 | C22 | 1 | 3 | yes | — |
| 63 | #2625 | C22 | 1 | 6 | yes | — |
| 64 | #2625 | C22 | 1 | 6 | yes | — |
| 65 | #2624 | C22 | 1 | 6 | yes | — |
| 66 | #2623 | C22 | 1 | 12 | yes | — |
| 67 | #2621 | C22 | 1 | 3 | yes | — |
| 68 | #2621 | C22 | 1 | 3 | yes | — |
| 69 | #2621 | C22 | 1 | 6 | yes | — |
| 70 | #2616 | C22 | 1 | 6 | yes | — |
| 71 | #2592 | C22 | 1 | 6 | yes | — |
| 72 | #2584 | C22 | 1 | 6 | yes | — |
| 73 | #2582 | C22 | 1 | 6 | yes | — |
| 74 | #2568 | C22 | 1 | 6 | yes | — |
| 75 | #2551 | C22 | 1 | 12 | yes | — |
| 76 | #2550 | C22 | 1 | 12 | yes | — |
| 77 | #2547 | C22 | 1 | 6 | yes | — |
| 78 | #2547 | C22 | 1 | 6 | yes | — |
| 79 | #2546 | C22 | 1 | 6 | yes | — |
| 80 | #2546 | C22 | 1 | 6 | yes | — |
| 81 | #2542 | C22 | 1 | 6 | yes | — |
| 82 | #2538 | C22 | 1 | 6 | yes | — |
| 83 | #2504 | C22 | 1 | 6 | yes | — |
| 84 | #2502 | C22 | 1 | 6 | yes | — |
| 85 | #2492 | C22 | 1 | 12 | yes | — |
| 86 | #2491 | C22 | 1 | 12 | yes | — |
| 87 | #2486 | C22 | 1 | 6 | yes | — |
| 88 | #2486 | C22 | 1 | 6 | yes | — |
| 89 | #2486 | C22 | 1 | 6 | yes | — |
| 90 | #2486 | C22 | 1 | 6 | yes | — |
| 91 | #2454 | C22 | 1 | 12 | yes | — |
| 92 | #2453 | C22 | 1 | 12 | yes | — |
| 93 | #2447 | C22 | 1 | 12 | yes | — |
| 94 | #2445 | C22 | 1 | 12 | yes | — |
| 95 | #2442 | C22 | 1 | 12 | yes | — |
| 96 | #2441 | C22 | 1 | 12 | yes | — |
| 97 | #2422 | C22 | 1 | 12 | yes | — |
| 98 | #2420 | C22 | 1 | 12 | yes | — |
| 99 | #2415 | C22 | 1 | 12 | yes | — |
| 100 | #2409 | C22 | 1 | 12 | yes | — |
| 101 | #2399 | C22 | 1 | 6 | yes | — |
| 102 | #2398 | C22 | 1 | 6 | yes | — |
| 103 | #2395 | C22 | 1 | 6 | yes | — |
| 104 | #2395 | C22 | 1 | 6 | yes | — |
| 105 | #2354 | C22 | 1 | 6 | yes | — |
| 106 | #2351 | C22 | 1 | 4 | yes | — |
| 107 | Q8×C4⋊C4 | C22 | 1 | 4 | yes | — |
| 108 | Q8×C4⋊C4 | C22 | 1 | 2 | yes | — |
| 109 | #2347 | C22 | 1 | 6 | yes | — |
| 110 | #2341 | C22 | 1 | 4 | yes | — |
| 111 | #2341 | C22 | 1 | 2 | yes | — |
| 112 | Q8×C22⋊C4 | C22 | 1 | 4 | yes | — |
| 113 | #2319 | C22 | 1 | 6 | yes | — |
| 114 | #2310 | C22 | 1 | 6 | yes | — |
| 115 | C4×C22⋊Q8 | C22 | 1 | 6 | yes | — |
| 116 | C4×C22⋊Q8 | C22 | 1 | 6 | yes | — |
| 117 | #2285 | C22 | 1 | 3 | yes | — |
| 118 | #2283 | C22 | 1 | 3 | yes | — |
| 119 | #2276 | C22 | 1 | 2 | yes | — |
| 120 | C22×#41 | C23 | 1 | 1 | yes | characteristic |
| 121 | C22×#41 | C23 | 1 | 3 | yes | — |
| 122 | C22×#41 | C23 | 1 | 1 | yes | characteristic |
| 123 | C23×Q8 | C23 | 1 | 1 | yes | characteristic |
| 124 | C23×Q8 | C23 | 1 | 6 | yes | — |
| 125 | #559 | — | 2 | 24 | no | — |
| 126 | Q82 | — | 2 | 16 | no | — |
| 127 | #557 | — | 2 | 8 | no | — |
| 128 | #557 | — | 2 | 16 | no | — |
| 129 | #556 | — | 2 | 24 | no | — |
| 130 | #554 | — | 2 | 48 | no | — |
| 131 | #553 | — | 2 | 24 | no | — |
| 132 | #553 | — | 2 | 24 | no | — |
| 133 | #550 | — | 2 | 8 | no | — |
| 134 | D4×Q8 | — | 2 | 48 | no | — |
| 135 | #548 | — | 2 | 8 | no | — |
| 136 | #548 | — | 2 | 8 | no | — |
| 137 | #544 | — | 2 | 48 | no | — |
| 138 | #536 | — | 4 | 24 | no | — |
| 139 | #533 | — | 2 | 24 | no | — |
| 140 | #532 | — | 2 | 24 | no | — |
| 141 | C2×C4⋊Q8 | — | 2 | 24 | no | — |
| 142 | C2×C4⋊Q8 | C23 | 1 | 6 | yes | — |
| 143 | C2×C4⋊Q8 | C23 | 1 | 6 | yes | — |
| 144 | C2×C4⋊Q8 | C23 | 1 | 3 | yes | — |
| 145 | C2×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 146 | C2×C4⋊Q8 | C23 | 1 | 6 | yes | — |
| 147 | C2×C4⋊Q8 | C23 | 1 | 3 | yes | — |
| 148 | C2×C4⋊Q8 | C23 | 1 | 12 | yes | — |
| 149 | C2×C4⋊Q8 | C23 | 1 | 12 | yes | — |
| 150 | C2×#127 | C23 | 1 | 3 | yes | — |
| 151 | #529 | — | 2 | 24 | no | — |
| 152 | #529 | — | 2 | 24 | no | — |
| 153 | C2×#126 | C23 | 1 | 6 | yes | — |
| 154 | C2×#126 | C23 | 1 | 6 | yes | — |
| 155 | C2×#125 | C23 | 1 | 3 | yes | — |
| 156 | C2×#125 | C23 | 1 | 6 | yes | — |
| 157 | C2×#125 | C23 | 1 | 3 | yes | — |
| 158 | C2×#125 | C23 | 1 | 12 | yes | — |
| 159 | C2×#124 | C23 | 1 | 3 | yes | — |
| 160 | C2×#124 | C23 | 1 | 3 | yes | — |
| 161 | C2×#124 | C23 | 1 | 6 | yes | — |
| 162 | C2×#124 | C23 | 1 | 12 | yes | — |
| 163 | C2×#123 | C23 | 1 | 6 | yes | — |
| 164 | C2×#123 | C23 | 1 | 6 | yes | — |
| 165 | C2×#123 | C23 | 1 | 12 | yes | — |
| 166 | C2×#123 | C23 | 1 | 12 | yes | — |
| 167 | C2×C22⋊Q8 | C23 | 1 | 6 | yes | — |
| 168 | C2×C22⋊Q8 | C23 | 1 | 6 | yes | — |
| 169 | C2×C22⋊Q8 | C23 | 1 | 3 | yes | — |
| 170 | C2×C22⋊Q8 | C23 | 1 | 6 | yes | — |
| 171 | C2×C22⋊Q8 | C23 | 1 | 3 | yes | — |
| 172 | C2×C22⋊Q8 | C23 | 1 | 24 | yes | — |
| 173 | C2×C22⋊Q8 | C23 | 1 | 12 | yes | — |
| 174 | C2×C22⋊Q8 | C23 | 1 | 6 | yes | — |
| 175 | C2×#121 | C23 | 1 | 3 | yes | — |
| 176 | C2×#121 | C23 | 1 | 3 | yes | — |
| 177 | C2×#121 | C23 | 1 | 6 | yes | — |
| 178 | C2×#121 | C23 | 1 | 3 | yes | — |
| 179 | C2×#121 | C23 | 1 | 3 | yes | — |
| 180 | #520 | — | 2 | 16 | no | — |
| 181 | C4×#41 | — | 2 | 8 | no | — |
| 182 | C4×#41 | — | 2 | 24 | no | — |
| 183 | C4×#41 | D4 | 1 | 16 | yes | — |
| 184 | C2×C4×Q8 | — | 2 | 8 | no | — |
| 185 | C2×C4×Q8 | C23 | 1 | 3 | yes | — |
| 186 | C2×C4×Q8 | C23 | 1 | 6 | yes | — |
| 187 | C2×C4×Q8 | C23 | 1 | 6 | yes | — |
| 188 | C2×C4×Q8 | C23 | 1 | 4 | yes | — |
| 189 | C2×C4×Q8 | C23 | 1 | 4 | yes | — |
| 190 | C2×C4×Q8 | C23 | 1 | 1 | yes | characteristic |
| 191 | C2×C4×Q8 | C23 | 1 | 1 | yes | characteristic |
| 192 | C2×C4×Q8 | C23 | 1 | 3 | yes | — |
| 193 | C2×C4×Q8 | C23 | 1 | 3 | yes | — |
| 194 | C2×C4×Q8 | C23 | 1 | 3 | yes | — |
| 195 | C2×C4×Q8 | C23 | 1 | 1 | yes | characteristic |
| 196 | C2×C4×Q8 | C23 | 1 | 1 | yes | characteristic |
| 197 | C2×C4×D4 | C23 | 1 | 3 | yes | — |
| 198 | C2×C4×D4 | C23 | 1 | 3 | yes | — |
| 199 | C2×C4×D4 | C23 | 1 | 3 | yes | — |
| 200 | C2×C4×D4 | C23 | 1 | 3 | yes | — |
| 201 | C2×C4×D4 | C23 | 1 | 3 | yes | — |
| 202 | C2×C4×D4 | C23 | 1 | 3 | yes | — |
| 203 | C2×C4×D4 | C23 | 1 | 3 | yes | — |
| 204 | C2×C4×D4 | C23 | 1 | 3 | yes | — |
| 205 | C2×C4×D4 | C23 | 1 | 12 | yes | — |
| 206 | C2×C4×D4 | C23 | 1 | 6 | yes | — |
| 207 | C2×C4×D4 | C23 | 1 | 3 | yes | — |
| 208 | C2×C4×D4 | C23 | 1 | 3 | yes | — |
| 209 | C2×#117 | C23 | 1 | 3 | yes | — |
| 210 | C2×#117 | C23 | 1 | 1 | yes | characteristic |
| 211 | C2×#117 | C23 | 1 | 3 | yes | — |
| 212 | C2×#117 | C23 | 1 | 6 | yes | — |
| 213 | C2×#117 | C23 | 1 | 3 | yes | — |
| 214 | C2×#117 | C23 | 1 | 6 | yes | — |
| 215 | C2×#117 | C23 | 1 | 3 | yes | — |
| 216 | C22×C4⋊C4 | C23 | 1 | 6 | yes | — |
| 217 | C22×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 218 | C22×C4⋊C4 | C23 | 1 | 6 | yes | — |
| 219 | C22×C42 | C23 | 1 | 3 | yes | — |
| 220 | C22×C42 | C23 | 1 | 3 | yes | — |
| 221 | C22×C42 | C23 | 1 | 3 | yes | — |
| 222 | #400 | C23 | 1 | 24 | yes | — |
| 223 | #400 | C23 | 1 | 6 | yes | — |
| 224 | #400 | C23 | 1 | 12 | yes | — |
| 225 | #400 | C23 | 1 | 2 | yes | — |
| 226 | #399 | C23 | 1 | 24 | yes | — |
| 227 | #399 | C23 | 1 | 6 | yes | — |
| 228 | #399 | C23 | 1 | 2 | yes | — |
| 229 | #398 | C23 | 1 | 6 | yes | — |
| 230 | #398 | C23 | 1 | 12 | yes | — |
| 231 | #398 | C23 | 1 | 24 | yes | — |
| 232 | #398 | C23 | 1 | 12 | yes | — |
| 233 | #398 | C23 | 1 | 6 | yes | — |
| 234 | #398 | C23 | 1 | 6 | yes | — |
| 235 | #398 | C23 | 1 | 6 | yes | — |
| 236 | #398 | C23 | 1 | 12 | yes | — |
| 237 | #397 | C23 | 1 | 6 | yes | — |
| 238 | #397 | C23 | 1 | 12 | yes | — |
| 239 | #397 | C23 | 1 | 12 | yes | — |
| 240 | #397 | C23 | 1 | 6 | yes | — |
| 241 | #397 | C23 | 1 | 6 | yes | — |
| 242 | #397 | C23 | 1 | 6 | yes | — |
| 243 | #397 | C23 | 1 | 12 | yes | — |
| 244 | #397 | C23 | 1 | 12 | yes | — |
| 245 | #397 | C23 | 1 | 24 | yes | — |
| 246 | #396 | C23 | 1 | 24 | yes | — |
| 247 | #395 | C23 | 1 | 24 | yes | — |
| 248 | #395 | C23 | 1 | 6 | yes | — |
| 249 | #395 | C23 | 1 | 12 | yes | — |
| 250 | #395 | C23 | 1 | 2 | yes | — |
| 251 | #394 | C23 | 1 | 12 | yes | — |
| 252 | #394 | C23 | 1 | 12 | yes | — |
| 253 | #394 | C23 | 1 | 12 | yes | — |
| 254 | #394 | C23 | 1 | 24 | yes | — |
| 255 | #393 | C23 | 1 | 24 | yes | — |
| 256 | #393 | C23 | 1 | 6 | yes | — |
| 257 | #393 | C23 | 1 | 2 | yes | — |
| 258 | #391 | C23 | 1 | 6 | yes | — |
| 259 | #391 | C23 | 1 | 12 | yes | — |
| 260 | #391 | C23 | 1 | 12 | yes | — |
| 261 | #391 | C23 | 1 | 12 | yes | — |
| 262 | #391 | C23 | 1 | 6 | yes | — |
| 263 | #391 | C23 | 1 | 12 | yes | — |
| 264 | #391 | C23 | 1 | 12 | yes | — |
| 265 | #390 | C23 | 1 | 12 | yes | — |
| 266 | #390 | C23 | 1 | 12 | yes | — |
| 267 | #390 | C23 | 1 | 12 | yes | — |
| 268 | #389 | C23 | 1 | 12 | yes | — |
| 269 | #389 | C23 | 1 | 6 | yes | — |
| 270 | #389 | C23 | 1 | 12 | yes | — |
| 271 | #389 | C23 | 1 | 12 | yes | — |
| 272 | #389 | C23 | 1 | 24 | yes | — |
| 273 | #389 | C23 | 1 | 12 | yes | — |
| 274 | #389 | C23 | 1 | 12 | yes | — |
| 275 | #389 | C23 | 1 | 12 | yes | — |
| 276 | #389 | C23 | 1 | 12 | yes | — |
| 277 | #389 | C23 | 1 | 2 | yes | — |
| 278 | #388 | C23 | 1 | 24 | yes | — |
| 279 | #388 | C23 | 1 | 24 | yes | — |
| 280 | #387 | C23 | 1 | 12 | yes | — |
| 281 | #387 | C23 | 1 | 12 | yes | — |
| 282 | #386 | C23 | 1 | 24 | yes | — |
| 283 | #385 | C23 | 1 | 24 | yes | — |
| 284 | #385 | C23 | 1 | 12 | yes | — |
| 285 | #385 | C23 | 1 | 12 | yes | — |
| 286 | #384 | C23 | 1 | 6 | yes | — |
| 287 | #384 | C23 | 1 | 12 | yes | — |
| 288 | #383 | C23 | 1 | 6 | yes | — |
| 289 | #382 | C23 | 1 | 12 | yes | — |
| 290 | #382 | C23 | 1 | 1 | yes | characteristic |
| 291 | #382 | C23 | 1 | 3 | yes | — |
| 292 | #381 | C23 | 1 | 12 | yes | — |
| 293 | #381 | C23 | 1 | 12 | yes | — |
| 294 | #381 | C23 | 1 | 6 | yes | — |
| 295 | #380 | C23 | 1 | 6 | yes | — |
| 296 | #380 | C23 | 1 | 12 | yes | — |
| 297 | #380 | C23 | 1 | 12 | yes | — |
| 298 | #380 | C23 | 1 | 6 | yes | — |
| 299 | #380 | C23 | 1 | 12 | yes | — |
| 300 | #380 | C23 | 1 | 12 | yes | — |
| 301 | #380 | C23 | 1 | 6 | yes | — |
| 302 | #380 | C23 | 1 | 2 | yes | — |
| 303 | #380 | C23 | 1 | 6 | yes | — |
| 304 | C4×C4⋊C4 | C23 | 1 | 6 | yes | — |
| 305 | C4×C4⋊C4 | C23 | 1 | 6 | yes | — |
| 306 | C4×C4⋊C4 | C23 | 1 | 6 | yes | — |
| 307 | C4×C4⋊C4 | C23 | 1 | 12 | yes | — |
| 308 | C4×C4⋊C4 | C23 | 1 | 12 | yes | — |
| 309 | C4×C4⋊C4 | C23 | 1 | 12 | yes | — |
| 310 | C4×C22⋊C4 | C23 | 1 | 12 | yes | — |
| 311 | C4×C22⋊C4 | C23 | 1 | 6 | yes | — |
| 312 | C4×C22⋊C4 | C23 | 1 | 12 | yes | — |
| 313 | #376 | C23 | 1 | 6 | yes | — |
| 314 | C2×#41 | — | 2 | 4 | no | — |
| 315 | C2×#41 | — | 2 | 8 | no | — |
| 316 | C2×#41 | — | 2 | 8 | no | — |
| 317 | C2×#41 | — | 2 | 12 | no | — |
| 318 | C2×#41 | — | 2 | 12 | no | — |
| 319 | C2×#41 | — | 4 | 6 | no | — |
| 320 | C2×#41 | C2×D4 | 1 | 8 | yes | — |
| 321 | C22×Q8 | — | 2 | 4 | no | — |
| 322 | C22×Q8 | — | 2 | 8 | no | — |
| 323 | C22×Q8 | — | 2 | 24 | no | — |
| 324 | C22×Q8 | — | 4 | 12 | no | — |
| 325 | C22×Q8 | — | 4 | 12 | no | — |
| 326 | C22×Q8 | C24 | 1 | 3 | yes | — |
| 327 | C22×Q8 | C24 | 1 | 6 | yes | — |
| 328 | C22×Q8 | C24 | 1 | 3 | yes | — |
| 329 | C22×Q8 | C24 | 1 | 2 | yes | — |
| 330 | C22×Q8 | C24 | 1 | 12 | yes | — |
| 331 | C22×Q8 | C24 | 1 | 1 | yes | characteristic |
| 332 | C22×D4 | C24 | 1 | 3 | yes | — |
| 333 | C22×D4 | C24 | 1 | 3 | yes | — |
| 334 | C22×D4 | C24 | 1 | 3 | yes | — |
| 335 | C22×D4 | C24 | 1 | 3 | yes | — |
| 336 | C22×D4 | C24 | 1 | 3 | yes | — |
| 337 | C22×D4 | C24 | 1 | 6 | yes | — |
| 338 | C23×C4 | C24 | 1 | 3 | yes | — |
| 339 | C23×C4 | C24 | 1 | 3 | yes | — |
| 340 | C23×C4 | C24 | 1 | 3 | yes | — |
| 341 | C23×C4 | C24 | 1 | 3 | yes | — |
| 342 | C23×C4 | C24 | 1 | 3 | yes | — |
| 343 | C23×C4 | C24 | 1 | 1 | yes | characteristic |
| 344 | C23×C4 | C24 | 1 | 3 | yes | — |
| 345 | C23×C4 | C24 | 1 | 12 | yes | — |
| 346 | C23×C4 | C24 | 1 | 3 | yes | — |
| 347 | C23×C4 | C24 | 1 | 3 | yes | — |
| 348 | C4⋊Q8 | — | 2 | 12 | no | — |
| 349 | C4⋊Q8 | — | 2 | 48 | no | — |
| 350 | C4⋊Q8 | — | 2 | 12 | no | — |
| 351 | C4⋊Q8 | — | 2 | 24 | no | — |
| 352 | C4⋊Q8 | — | 2 | 24 | no | — |
| 353 | C4⋊Q8 | — | 2 | 24 | no | — |
| 354 | C4⋊Q8 | — | 2 | 4 | no | — |
| 355 | C4⋊Q8 | — | 4 | 24 | no | — |
| 356 | #127 | — | 2 | 12 | no | — |
| 357 | #126 | — | 2 | 24 | no | — |
| 358 | #126 | — | 2 | 24 | no | — |
| 359 | #125 | — | 2 | 12 | no | — |
| 360 | #125 | — | 2 | 48 | no | — |
| 361 | #125 | — | 2 | 12 | no | — |
| 362 | #125 | — | 2 | 24 | no | — |
| 363 | #124 | — | 2 | 12 | no | — |
| 364 | #124 | — | 2 | 24 | no | — |
| 365 | #124 | — | 2 | 12 | no | — |
| 366 | #124 | — | 4 | 24 | no | — |
| 367 | #123 | — | 2 | 24 | no | — |
| 368 | #123 | — | 2 | 24 | no | — |
| 369 | #123 | — | 4 | 24 | no | — |
| 370 | #123 | — | 4 | 24 | no | — |
| 371 | C22⋊Q8 | — | 2 | 12 | no | — |
| 372 | C22⋊Q8 | — | 2 | 24 | no | — |
| 373 | C22⋊Q8 | — | 2 | 24 | no | — |
| 374 | C22⋊Q8 | — | 2 | 24 | no | — |
| 375 | C22⋊Q8 | — | 2 | 12 | no | — |
| 376 | C22⋊Q8 | — | 2 | 96 | no | — |
| 377 | C22⋊Q8 | — | 4 | 12 | no | — |
| 378 | C22⋊Q8 | — | 4 | 24 | no | — |
| 379 | #121 | — | 2 | 12 | no | — |
| 380 | #121 | — | 2 | 12 | no | — |
| 381 | #121 | — | 2 | 12 | no | — |
| 382 | #121 | — | 2 | 12 | no | — |
| 383 | #121 | — | 2 | 24 | no | — |
| 384 | C4×Q8 | — | 2 | 4 | no | — |
| 385 | C4×Q8 | — | 2 | 4 | no | — |
| 386 | C4×Q8 | — | 2 | 16 | no | — |
| 387 | C4×Q8 | — | 2 | 16 | no | — |
| 388 | C4×Q8 | — | 2 | 12 | no | — |
| 389 | C4×Q8 | — | 2 | 12 | no | — |
| 390 | C4×Q8 | — | 2 | 12 | no | — |
| 391 | C4×Q8 | — | 2 | 12 | no | — |
| 392 | C4×Q8 | — | 2 | 24 | no | — |
| 393 | C4×Q8 | — | 2 | 24 | no | — |
| 394 | C4×Q8 | C2×D4 | 1 | 8 | yes | — |
| 395 | C4×Q8 | C2×D4 | 1 | 8 | yes | — |
| 396 | C4×D4 | — | 2 | 48 | no | — |
| 397 | C4×D4 | — | 2 | 12 | no | — |
| 398 | C4×D4 | — | 2 | 12 | no | — |
| 399 | C4×D4 | — | 2 | 12 | no | — |
| 400 | C4×D4 | — | 2 | 12 | no | — |
| 401 | C4×D4 | — | 2 | 24 | no | — |
| 402 | C4×D4 | — | 2 | 12 | no | — |
| 403 | C4×D4 | — | 2 | 12 | no | — |
| 404 | C4×D4 | — | 2 | 12 | no | — |
| 405 | C4×D4 | — | 2 | 12 | no | — |
| 406 | C4×D4 | C2×D4 | 1 | 24 | yes | — |
| 407 | C4×D4 | C2×D4 | 1 | 24 | yes | — |
| 408 | #117 | — | 2 | 12 | no | — |
| 409 | #117 | — | 2 | 24 | no | — |
| 410 | #117 | — | 2 | 12 | no | — |
| 411 | #117 | — | 2 | 4 | no | — |
| 412 | #117 | — | 2 | 12 | no | — |
| 413 | #117 | — | 4 | 12 | no | — |
| 414 | #117 | C2×D4 | 1 | 24 | yes | — |
| 415 | C2×C4⋊C4 | — | 2 | 24 | no | — |
| 416 | C2×C4⋊C4 | — | 2 | 24 | no | — |
| 417 | C2×C4⋊C4 | — | 2 | 12 | no | — |
| 418 | C2×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 419 | C2×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 420 | C2×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 421 | C2×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 422 | C2×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 423 | C2×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 424 | C2×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 425 | C2×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 426 | C2×C4⋊C4 | C24 | 1 | 1 | yes | characteristic |
| 427 | C2×C4⋊C4 | C24 | 1 | 1 | yes | characteristic |
| 428 | C2×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 429 | C2×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 430 | C2×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 431 | C2×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 432 | C2×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 433 | C2×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 434 | C2×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 435 | C2×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 436 | C2×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 437 | C2×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 438 | C2×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 439 | C2×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 440 | C2×C4⋊C4 | C24 | 1 | 24 | yes | — |
| 441 | C2×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 442 | C2×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 443 | C2×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 444 | C2×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 445 | C2×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 446 | C2×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 447 | C2×C22⋊C4 | C24 | 1 | 1 | yes | characteristic |
| 448 | C2×C22⋊C4 | C24 | 1 | 1 | yes | characteristic |
| 449 | C2×C22⋊C4 | C24 | 1 | 3 | yes | — |
| 450 | C2×C22⋊C4 | C24 | 1 | 3 | yes | — |
| 451 | C2×C22⋊C4 | C24 | 1 | 6 | yes | — |
| 452 | C2×C22⋊C4 | C24 | 1 | 12 | yes | — |
| 453 | C2×C22⋊C4 | C24 | 1 | 3 | yes | — |
| 454 | C2×C22⋊C4 | C24 | 1 | 3 | yes | — |
| 455 | C2×C22⋊C4 | C24 | 1 | 6 | yes | — |
| 456 | C2×C22⋊C4 | C24 | 1 | 6 | yes | — |
| 457 | C2×C22⋊C4 | C24 | 1 | 12 | yes | — |
| 458 | C2×C22⋊C4 | C24 | 1 | 12 | yes | — |
| 459 | C2×C22⋊C4 | C24 | 1 | 24 | yes | — |
| 460 | C2×C22⋊C4 | C24 | 1 | 12 | yes | — |
| 461 | C2×C22⋊C4 | C24 | 1 | 4 | yes | — |
| 462 | C2×C22⋊C4 | C24 | 1 | 12 | yes | — |
| 463 | C2×C22⋊C4 | C24 | 1 | 12 | yes | — |
| 464 | C2×C22⋊C4 | C24 | 1 | 6 | yes | — |
| 465 | C2×C42 | — | 2 | 12 | no | — |
| 466 | C2×C42 | — | 2 | 12 | no | — |
| 467 | C2×C42 | C2×D4 | 1 | 24 | yes | — |
| 468 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 469 | C2×C42 | C24 | 1 | 3 | yes | — |
| 470 | C2×C42 | C24 | 1 | 3 | yes | — |
| 471 | C2×C42 | C24 | 1 | 12 | yes | — |
| 472 | C2×C42 | C24 | 1 | 3 | yes | — |
| 473 | C2×C42 | C24 | 1 | 3 | yes | — |
| 474 | C2×C42 | C24 | 1 | 3 | yes | — |
| 475 | C2×C42 | C24 | 1 | 12 | yes | — |
| 476 | C2×C42 | C24 | 1 | 12 | yes | — |
| 477 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 478 | C2×C42 | C24 | 1 | 3 | yes | — |
| 479 | C2×C42 | C24 | 1 | 3 | yes | — |
| 480 | C2×C42 | C24 | 1 | 3 | yes | — |
| 481 | #95 | C24 | 1 | 2 | yes | — |
| 482 | #95 | C24 | 1 | 6 | yes | — |
| 483 | #95 | C24 | 1 | 12 | yes | — |
| 484 | #95 | C24 | 1 | 2 | yes | — |
| 485 | #95 | C24 | 1 | 4 | yes | — |
| 486 | #95 | C24 | 1 | 6 | yes | — |
| 487 | #95 | C24 | 1 | 12 | yes | — |
| 488 | #95 | C24 | 1 | 12 | yes | — |
| 489 | #95 | C24 | 1 | 12 | yes | — |
| 490 | #95 | C24 | 1 | 4 | yes | — |
| 491 | #95 | C24 | 1 | 12 | yes | — |
| 492 | #95 | C24 | 1 | 12 | yes | — |
| 493 | #95 | C24 | 1 | 12 | yes | — |
| 494 | #95 | C24 | 1 | 12 | yes | — |
| 495 | #95 | C24 | 1 | 24 | yes | — |
| 496 | #95 | C24 | 1 | 24 | yes | — |
| 497 | C24 | C25 | 1 | 3 | yes | — |
| 498 | C24 | C25 | 1 | 3 | yes | — |
| 499 | C24 | C25 | 1 | 1 | yes | characteristic |
| 500 | #41 | — | 2 | 32 | no | — |
| 501 | #41 | — | 4 | 48 | no | — |
| 502 | #41 | — | 4 | 16 | no | — |
| 503 | C2×Q8 | — | 2 | 4 | no | — |
| 504 | C2×Q8 | — | 2 | 6 | no | — |
| 505 | C2×Q8 | — | 2 | 6 | no | — |
| 506 | C2×Q8 | — | 2 | 12 | no | — |
| 507 | C2×Q8 | — | 2 | 24 | no | — |
| 508 | C2×Q8 | — | 2 | 12 | no | — |
| 509 | C2×Q8 | — | 2 | 6 | no | — |
| 510 | C2×Q8 | — | 2 | 12 | no | — |
| 511 | C2×Q8 | — | 2 | 12 | no | — |
| 512 | C2×Q8 | — | 4 | 4 | no | — |
| 513 | C2×Q8 | — | 4 | 3 | no | — |
| 514 | C2×Q8 | — | 4 | 12 | no | — |
| 515 | C2×Q8 | — | 4 | 12 | no | — |
| 516 | C2×Q8 | — | 4 | 16 | no | — |
| 517 | C2×Q8 | — | 8 | 48 | no | — |
| 518 | C2×Q8 | C22×D4 | 1 | 4 | yes | — |
| 519 | C2×Q8 | 2−1+4 | 1 | 8 | yes | — |
| 520 | C2×D4 | — | 2 | 6 | no | — |
| 521 | C2×D4 | — | 2 | 6 | no | — |
| 522 | C2×D4 | — | 2 | 6 | no | — |
| 523 | C2×D4 | — | 2 | 6 | no | — |
| 524 | C2×D4 | — | 2 | 12 | no | — |
| 525 | C2×D4 | — | 2 | 6 | no | — |
| 526 | C2×D4 | — | 2 | 6 | no | — |
| 527 | C2×D4 | — | 2 | 6 | no | — |
| 528 | C2×D4 | — | 2 | 12 | no | — |
| 529 | C2×D4 | — | 2 | 12 | no | — |
| 530 | C2×D4 | — | 4 | 3 | no | — |
| 531 | C2×D4 | — | 4 | 3 | no | — |
| 532 | C2×D4 | — | 4 | 3 | no | — |
| 533 | C2×D4 | — | 4 | 12 | no | — |
| 534 | C2×D4 | C22×D4 | 1 | 12 | yes | — |
| 535 | C22×C4 | — | 2 | 2 | no | — |
| 536 | C22×C4 | — | 2 | 6 | no | — |
| 537 | C22×C4 | — | 2 | 12 | no | — |
| 538 | C22×C4 | — | 2 | 6 | no | — |
| 539 | C22×C4 | — | 2 | 2 | no | — |
| 540 | C22×C4 | — | 2 | 24 | no | — |
| 541 | C22×C4 | — | 2 | 6 | no | — |
| 542 | C22×C4 | — | 2 | 6 | no | — |
| 543 | C22×C4 | — | 2 | 6 | no | — |
| 544 | C22×C4 | — | 2 | 6 | no | — |
| 545 | C22×C4 | — | 2 | 12 | no | — |
| 546 | C22×C4 | — | 2 | 12 | no | — |
| 547 | C22×C4 | — | 2 | 6 | no | — |
| 548 | C22×C4 | — | 2 | 6 | no | — |
| 549 | C22×C4 | — | 2 | 6 | no | — |
| 550 | C22×C4 | — | 4 | 6 | no | — |
| 551 | C22×C4 | — | 4 | 12 | no | — |
| 552 | C22×C4 | — | 4 | 6 | no | — |
| 553 | C22×C4 | — | 4 | 6 | no | — |
| 554 | C22×C4 | — | 4 | 12 | no | — |
| 555 | C22×C4 | C22×D4 | 1 | 12 | yes | — |
| 556 | C22×C4 | C22×D4 | 1 | 12 | yes | — |
| 557 | C22×C4 | C22×D4 | 1 | 12 | yes | — |
| 558 | C22×C4 | H(5,𝔽2) | 1 | 4 | yes | — |
| 559 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 560 | C22×C4 | C25 | 1 | 4 | yes | — |
| 561 | C22×C4 | C25 | 1 | 3 | yes | — |
| 562 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 563 | C22×C4 | C25 | 1 | 12 | yes | — |
| 564 | C22×C4 | C25 | 1 | 3 | yes | — |
| 565 | C22×C4 | C25 | 1 | 4 | yes | — |
| 566 | C22×C4 | C25 | 1 | 12 | yes | — |
| 567 | C22×C4 | C25 | 1 | 3 | yes | — |
| 568 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 569 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 570 | C22×C4 | C25 | 1 | 3 | yes | — |
| 571 | C22×C4 | C25 | 1 | 3 | yes | — |
| 572 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 573 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 574 | C22×C4 | C25 | 1 | 3 | yes | — |
| 575 | C4⋊C4 | — | 2 | 12 | no | — |
| 576 | C4⋊C4 | — | 2 | 12 | no | — |
| 577 | C4⋊C4 | — | 2 | 24 | no | — |
| 578 | C4⋊C4 | — | 2 | 6 | no | — |
| 579 | C4⋊C4 | — | 2 | 12 | no | — |
| 580 | C4⋊C4 | — | 2 | 24 | no | — |
| 581 | C4⋊C4 | — | 2 | 4 | no | — |
| 582 | C4⋊C4 | — | 2 | 2 | no | — |
| 583 | C4⋊C4 | — | 2 | 2 | no | — |
| 584 | C4⋊C4 | — | 2 | 6 | no | — |
| 585 | C4⋊C4 | — | 2 | 6 | no | — |
| 586 | C4⋊C4 | — | 2 | 6 | no | — |
| 587 | C4⋊C4 | — | 2 | 6 | no | — |
| 588 | C4⋊C4 | — | 2 | 6 | no | — |
| 589 | C4⋊C4 | — | 2 | 12 | no | — |
| 590 | C4⋊C4 | — | 2 | 4 | no | — |
| 591 | C4⋊C4 | — | 2 | 24 | no | — |
| 592 | C4⋊C4 | — | 2 | 24 | no | — |
| 593 | C4⋊C4 | — | 2 | 12 | no | — |
| 594 | C4⋊C4 | — | 2 | 24 | no | — |
| 595 | C4⋊C4 | — | 2 | 24 | no | — |
| 596 | C4⋊C4 | — | 2 | 4 | no | — |
| 597 | C4⋊C4 | — | 4 | 12 | no | — |
| 598 | C4⋊C4 | — | 4 | 4 | no | — |
| 599 | C4⋊C4 | — | 4 | 12 | no | — |
| 600 | C4⋊C4 | — | 4 | 12 | no | — |
| 601 | C4⋊C4 | — | 4 | 24 | no | — |
| 602 | C4⋊C4 | C22×D4 | 1 | 12 | yes | — |
| 603 | C4⋊C4 | C22×D4 | 1 | 12 | yes | — |
| 604 | C22⋊C4 | — | 2 | 6 | no | — |
| 605 | C22⋊C4 | — | 2 | 24 | no | — |
| 606 | C22⋊C4 | — | 2 | 6 | no | — |
| 607 | C22⋊C4 | — | 2 | 12 | no | — |
| 608 | C22⋊C4 | — | 2 | 24 | no | — |
| 609 | C22⋊C4 | — | 2 | 2 | no | — |
| 610 | C22⋊C4 | — | 2 | 2 | no | — |
| 611 | C22⋊C4 | — | 2 | 6 | no | — |
| 612 | C22⋊C4 | — | 2 | 12 | no | — |
| 613 | C22⋊C4 | — | 2 | 6 | no | — |
| 614 | C22⋊C4 | — | 2 | 12 | no | — |
| 615 | C22⋊C4 | — | 4 | 4 | no | — |
| 616 | C22⋊C4 | — | 4 | 12 | no | — |
| 617 | C22⋊C4 | — | 4 | 12 | no | — |
| 618 | C22⋊C4 | — | 4 | 12 | no | — |
| 619 | C22⋊C4 | — | 4 | 12 | no | — |
| 620 | C22⋊C4 | — | 4 | 24 | no | — |
| 621 | C22⋊C4 | C22×D4 | 1 | 24 | yes | — |
| 622 | C42 | — | 2 | 2 | no | — |
| 623 | C42 | — | 2 | 6 | no | — |
| 624 | C42 | — | 2 | 6 | no | — |
| 625 | C42 | — | 2 | 6 | no | — |
| 626 | C42 | — | 2 | 6 | no | — |
| 627 | C42 | — | 2 | 6 | no | — |
| 628 | C42 | — | 2 | 24 | no | — |
| 629 | C42 | — | 2 | 24 | no | — |
| 630 | C42 | — | 4 | 12 | no | — |
| 631 | C42 | C22×D4 | 1 | 12 | yes | — |
| 632 | C42 | C22×D4 | 1 | 4 | yes | — |
| 633 | C42 | C22×D4 | 1 | 12 | yes | — |
| 634 | C42 | C22×D4 | 1 | 12 | yes | — |
| 635 | C23 | — | 2 | 1 | no | — |
| 636 | C23 | — | 2 | 3 | no | — |
| 637 | C23 | — | 2 | 2 | no | — |
| 638 | C23 | — | 2 | 6 | no | — |
| 639 | C23 | — | 2 | 3 | no | — |
| 640 | C23 | — | 2 | 1 | no | — |
| 641 | C23 | — | 2 | 2 | no | — |
| 642 | C23 | — | 2 | 6 | no | — |
| 643 | C23 | — | 2 | 3 | no | — |
| 644 | C23 | — | 2 | 3 | no | — |
| 645 | C23 | — | 2 | 6 | no | — |
| 646 | C23 | — | 2 | 3 | no | — |
| 647 | C23 | — | 2 | 6 | no | — |
| 648 | C23 | C23×D4 | 1 | 6 | yes | — |
| 649 | C23 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 650 | C23 | C26 | 1 | 1 | yes | characteristic |
| 651 | Q8 | — | 4 | 12 | no | — |
| 652 | Q8 | — | 4 | 8 | no | — |
| 653 | Q8 | — | 4 | 12 | no | — |
| 654 | Q8 | — | 4 | 24 | no | — |
| 655 | Q8 | — | 8 | 24 | no | — |
| 656 | Q8 | #536 | 1 | 16 | yes | complemented |
| 657 | D4 | — | 2 | 24 | no | — |
| 658 | D4 | — | 4 | 12 | no | — |
| 659 | D4 | — | 4 | 12 | no | — |
| 660 | D4 | — | 4 | 12 | no | — |
| 661 | D4 | — | 4 | 12 | no | — |
| 662 | D4 | — | 8 | 12 | no | — |
| 663 | C2×C4 | — | 2 | 1 | no | — |
| 664 | C2×C4 | — | 2 | 3 | no | — |
| 665 | C2×C4 | — | 2 | 2 | no | — |
| 666 | C2×C4 | — | 2 | 1 | no | — |
| 667 | C2×C4 | — | 2 | 3 | no | — |
| 668 | C2×C4 | — | 2 | 6 | no | — |
| 669 | C2×C4 | — | 2 | 2 | no | — |
| 670 | C2×C4 | — | 2 | 24 | no | — |
| 671 | C2×C4 | — | 2 | 24 | no | — |
| 672 | C2×C4 | — | 2 | 8 | no | — |
| 673 | C2×C4 | — | 2 | 1 | no | — |
| 674 | C2×C4 | — | 2 | 1 | no | — |
| 675 | C2×C4 | — | 2 | 4 | no | — |
| 676 | C2×C4 | — | 2 | 3 | no | — |
| 677 | C2×C4 | — | 2 | 3 | no | — |
| 678 | C2×C4 | — | 2 | 3 | no | — |
| 679 | C2×C4 | — | 2 | 12 | no | — |
| 680 | C2×C4 | — | 2 | 12 | no | — |
| 681 | C2×C4 | — | 2 | 12 | no | — |
| 682 | C2×C4 | — | 2 | 3 | no | — |
| 683 | C2×C4 | — | 2 | 4 | no | — |
| 684 | C2×C4 | — | 2 | 12 | no | — |
| 685 | C2×C4 | — | 2 | 2 | no | — |
| 686 | C2×C4 | — | 2 | 6 | no | — |
| 687 | C2×C4 | — | 2 | 4 | no | — |
| 688 | C2×C4 | — | 2 | 12 | no | — |
| 689 | C2×C4 | — | 2 | 3 | no | — |
| 690 | C2×C4 | — | 2 | 4 | no | — |
| 691 | C2×C4 | — | 2 | 4 | no | — |
| 692 | C2×C4 | — | 2 | 12 | no | — |
| 693 | C2×C4 | — | 2 | 4 | no | — |
| 694 | C2×C4 | — | 2 | 2 | no | — |
| 695 | C2×C4 | — | 2 | 6 | no | — |
| 696 | C2×C4 | — | 4 | 12 | no | — |
| 697 | C2×C4 | — | 4 | 12 | no | — |
| 698 | C2×C4 | — | 4 | 12 | no | — |
| 699 | C2×C4 | — | 4 | 12 | no | — |
| 700 | C2×C4 | — | 8 | 6 | no | — |
| 701 | C2×C4 | — | 8 | 6 | no | — |
| 702 | C2×C4 | — | 8 | 24 | no | — |
| 703 | C2×C4 | C23×D4 | 1 | 6 | yes | — |
| 704 | C2×C4 | C23×D4 | 1 | 2 | yes | — |
| 705 | C2×C4 | C23×D4 | 1 | 2 | yes | — |
| 706 | C2×C4 | C23×D4 | 1 | 6 | yes | — |
| 707 | C2×C4 | C23×D4 | 1 | 6 | yes | — |
| 708 | C2×C4 | C23×D4 | 1 | 2 | yes | — |
| 709 | C2×C4 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 710 | C2×C4 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 711 | C2×C4 | C2×2−1+4 | 1 | 12 | yes | — |
| 712 | C2×C4 | #585 | 1 | 2 | yes | — |
| 713 | C22 | — | 2 | 6 | no | — |
| 714 | C22 | — | 2 | 2 | no | — |
| 715 | C22 | — | 2 | 6 | no | — |
| 716 | C22 | — | 2 | 6 | no | — |
| 717 | C22 | — | 2 | 4 | no | — |
| 718 | C22 | — | 4 | 1 | no | — |
| 719 | C22 | — | 4 | 1 | no | — |
| 720 | C22 | — | 4 | 6 | no | — |
| 721 | C22 | — | 4 | 2 | no | — |
| 722 | C22 | — | 4 | 6 | no | — |
| 723 | C22 | — | 4 | 3 | no | — |
| 724 | C22 | — | 4 | 3 | no | — |
| 725 | C22 | — | 4 | 3 | no | — |
| 726 | C22 | — | 4 | 6 | no | — |
| 727 | C22 | — | 4 | 6 | no | — |
| 728 | C22 | C24×D4 | 1 | 1 | yes | characteristic |
| 729 | C22 | C22×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 730 | C22 | C22×2−1+4 | 1 | 2 | yes | — |
| 731 | C22 | C2×#585 | 1 | 1 | yes | characteristic |
| 732 | C22 | 2−1+6 | 1 | 2 | yes | — |
| 733 | C4 | — | 2 | 6 | no | — |
| 734 | C4 | — | 2 | 2 | no | — |
| 735 | C4 | — | 2 | 2 | no | — |
| 736 | C4 | — | 2 | 6 | no | — |
| 737 | C4 | — | 2 | 2 | no | — |
| 738 | C4 | — | 4 | 3 | no | — |
| 739 | C4 | — | 4 | 12 | no | — |
| 740 | C4 | — | 4 | 1 | no | — |
| 741 | C4 | — | 4 | 3 | no | — |
| 742 | C4 | — | 4 | 4 | no | — |
| 743 | C4 | — | 4 | 1 | no | — |
| 744 | C4 | — | 4 | 3 | no | — |
| 745 | C4 | — | 4 | 12 | no | — |
| 746 | C4 | — | 4 | 4 | no | — |
| 747 | C4 | C2×#536 | 1 | 12 | yes | — |
| 748 | C4 | #3488 | 1 | 4 | yes | — |
| 749 | C2 | — | 4 | 6 | no | — |
| 750 | C2 | — | 4 | 2 | no | — |
| 751 | C2 | — | 8 | 3 | no | — |
| 752 | C2 | C22×#536 | 1 | 1 | yes | characteristic |
| 753 | C2 | C2×#3488 | 1 | 1 | yes | characteristic |
| 754 | C2 | #62859 | 1 | 1 | yes | characteristic |
| 755 | C2 | #62946 | 1 | 2 | yes | — |
| 756 | C2 | #62953 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C23 | C26 |
| prime radical | C2×#3480 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#3503 | C2 | semidirect |
| 3. #42944 | C2 | semidirect |
| 4. #42918 | C2 | semidirect |
| 5. #42682 | C2 | semidirect |
| 6. #42678 | C2 | semidirect |
| 7. #39343 | C2 | semidirect |
| 8. #38911 | C2 | semidirect |
| 9. #37622 | C2 | semidirect |
| 10. #37615 | C2 | semidirect |
| 11. #36577 | C2 | semidirect |
| 12. #36445 | C2 | semidirect |
| 13. #36076 | C2 | semidirect |
| 14. #35996 | C2 | semidirect |
| 15. #35948 | C2 | semidirect |
| 16. #35937 | C2 | semidirect |
| 17. #35316 | C2 | semidirect |
| 18. #34627 | C2 | semidirect |
| 19. #34193 | C2 | semidirect |
| 656. Q8 | #536 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3503 | 2 |
| C2×#3480 | 2 |
| #42944 | 2 |
| #42918 | 2 |
| #42682 | 2 |
| #42678 | 2 |
| #39343 | 2 |
| #38911 | 2 |
| #37622 | 2 |
| #37615 | 2 |
| #36577 | 2 |
| #36445 | 2 |
| #36076 | 2 |
| #35996 | 2 |
| #35948 | 2 |
| #35937 | 2 |
| #35316 | 2 |
| #34627 | 2 |
| #34193 | 2 |