Finite Group DatabasebetaFinite Group DatabasebetaOrder 1536.
1735 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 1735 conjugacy classes of subgroups — too many to draw. Only its 62 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 | #9634946 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Sylow |
| 2 | C2×#5465 | — | 4 | 1 | no | maximal |
| 3 | C2×Q8⋊SL(2,𝔽3) | — | 4 | 1 | no | maximal |
| 4 | C2×#543⋊C3 | — | 4 | 2 | no | maximal |
| 5 | C2×#543⋊C3 | — | 4 | 1 | no | maximal |
| 6 | C2×#543⋊C3 | — | 4 | 1 | no | maximal |
| 7 | #73293 | — | 4 | 2 | no | maximal |
| 8 | #73293 | — | 4 | 1 | no | maximal |
| 9 | #73293 | — | 4 | 1 | no | maximal |
| 10 | #73291 | — | 4 | 2 | no | maximal |
| 11 | #73291 | — | 4 | 2 | no | maximal |
| 12 | #73291 | — | 4 | 2 | no | maximal |
| 13 | #73291 | — | 4 | 2 | no | maximal |
| 14 | #73291 | — | 4 | 2 | no | maximal |
| 15 | #73291 | — | 4 | 1 | no | maximal |
| 16 | #58037 | — | 3 | 2 | no | — |
| 17 | #57433 | — | 3 | 2 | no | — |
| 18 | #55326 | — | 3 | 2 | no | — |
| 19 | #54799 | — | 3 | 2 | no | — |
| 20 | #54670 | — | 3 | 2 | no | — |
| 21 | #53978 | — | 3 | 1 | no | — |
| 22 | #52941 | — | 3 | 1 | no | — |
| 23 | #51679 | — | 3 | 2 | no | — |
| 24 | #48812 | — | 3 | 1 | no | — |
| 25 | #48779 | — | 3 | 1 | no | — |
| 26 | #43493 | — | 3 | 1 | no | — |
| 27 | #42813 | — | 3 | 1 | no | — |
| 28 | #41616 | — | 3 | 1 | no | — |
| 29 | #40511 | — | 3 | 2 | no | — |
| 30 | #5465 | — | 4 | 1 | no | — |
| 31 | Q8⋊SL(2,𝔽3) | — | 4 | 1 | no | — |
| 32 | #543⋊C3 | — | 4 | 2 | no | — |
| 33 | #543⋊C3 | — | 4 | 1 | no | — |
| 34 | #543⋊C3 | — | 4 | 1 | no | — |
| 35 | C2×H(3,𝔽4) | A4 | 1 | 1 | yes | characteristic |
| 36 | C2×Q82 | A4 | 1 | 1 | yes | characteristic, complemented |
| 37 | C2×#552 | — | 3 | 1 | no | — |
| 38 | C2×#551 | — | 3 | 1 | no | — |
| 39 | C2×#543 | A4 | 1 | 2 | yes | complemented |
| 40 | C2×#543 | A4 | 1 | 1 | yes | characteristic, complemented |
| 41 | C2×#543 | A4 | 1 | 1 | yes | characteristic, complemented |
| 42 | #2841 | — | 3 | 1 | no | — |
| 43 | #2840 | A4 | 1 | 2 | yes | complemented |
| 44 | #2840 | A4 | 1 | 1 | yes | characteristic, complemented |
| 45 | #2840 | A4 | 1 | 1 | yes | characteristic, complemented |
| 46 | #2835 | — | 3 | 1 | no | — |
| 47 | #2833 | — | 3 | 1 | no | — |
| 48 | #2831 | — | 3 | 2 | no | — |
| 49 | #2831 | — | 3 | 2 | no | — |
| 50 | #2831 | — | 3 | 2 | no | — |
| 51 | #2821 | — | 3 | 2 | no | — |
| 52 | #2817 | — | 3 | 2 | no | — |
| 53 | #2814 | — | 3 | 2 | no | — |
| 54 | #2811 | A4 | 1 | 2 | yes | complemented |
| 55 | #2811 | A4 | 1 | 2 | yes | complemented |
| 56 | #2811 | A4 | 1 | 2 | yes | complemented |
| 57 | #2811 | A4 | 1 | 2 | yes | complemented |
| 58 | #2811 | A4 | 1 | 1 | yes | characteristic, complemented |
| 59 | #2811 | A4 | 1 | 2 | yes | complemented |
| 60 | #2799 | — | 3 | 1 | no | — |
| 61 | #2798 | — | 3 | 2 | no | — |
| 62 | #2798 | — | 3 | 2 | no | — |
| 63 | #2788 | — | 3 | 2 | no | — |
| 64 | #2775 | — | 3 | 2 | no | — |
| 65 | #2775 | — | 3 | 2 | no | — |
| 66 | #2774 | — | 3 | 2 | no | — |
| 67 | #2764 | — | 3 | 1 | no | — |
| 68 | #2764 | — | 3 | 2 | no | — |
| 69 | #2763 | — | 3 | 2 | no | — |
| 70 | #2762 | — | 3 | 2 | no | — |
| 71 | #2759 | — | 3 | 2 | no | — |
| 72 | #2758 | — | 3 | 2 | no | — |
| 73 | #2755 | — | 3 | 2 | no | — |
| 74 | #2755 | — | 3 | 2 | no | — |
| 75 | #2754 | — | 3 | 2 | no | — |
| 76 | #2751 | — | 3 | 2 | no | — |
| 77 | #2745 | — | 3 | 2 | no | — |
| 78 | #2745 | — | 3 | 2 | no | — |
| 79 | #2737 | — | 3 | 2 | no | — |
| 80 | #2735 | — | 3 | 1 | no | — |
| 81 | #2728 | — | 3 | 2 | no | — |
| 82 | #2723 | — | 3 | 2 | no | — |
| 83 | #2720 | — | 3 | 2 | no | — |
| 84 | #2717 | — | 3 | 2 | no | — |
| 85 | #2717 | — | 3 | 1 | no | — |
| 86 | #2715 | — | 3 | 2 | no | — |
| 87 | #2713 | — | 3 | 2 | no | — |
| 88 | #2713 | — | 3 | 2 | no | — |
| 89 | #2704 | — | 3 | 2 | no | — |
| 90 | #2700 | — | 3 | 2 | no | — |
| 91 | #2700 | — | 3 | 2 | no | — |
| 92 | #2698 | — | 3 | 2 | no | — |
| 93 | #2698 | — | 3 | 2 | no | — |
| 94 | #2697 | — | 3 | 2 | no | — |
| 95 | #2690 | — | 3 | 2 | no | — |
| 96 | #2690 | — | 3 | 2 | no | — |
| 97 | #2690 | — | 3 | 2 | no | — |
| 98 | #2689 | — | 3 | 2 | no | — |
| 99 | #2689 | — | 3 | 2 | no | — |
| 100 | #2689 | — | 3 | 2 | no | — |
| 101 | #2687 | — | 3 | 2 | no | — |
| 102 | #2684 | — | 3 | 1 | no | — |
| 103 | #2680 | — | 3 | 2 | no | — |
| 104 | #2674 | — | 3 | 2 | no | — |
| 105 | #2674 | — | 3 | 2 | no | — |
| 106 | #2666 | — | 3 | 2 | no | — |
| 107 | #2666 | — | 3 | 2 | no | — |
| 108 | #2663 | — | 3 | 2 | no | — |
| 109 | #2660 | — | 3 | 1 | no | — |
| 110 | #2653 | — | 3 | 2 | no | — |
| 111 | #2638 | — | 3 | 2 | no | — |
| 112 | #2638 | — | 3 | 1 | no | — |
| 113 | #2637 | — | 3 | 2 | no | — |
| 114 | #2625 | — | 3 | 1 | no | — |
| 115 | #2625 | — | 3 | 2 | no | — |
| 116 | #2622 | — | 3 | 2 | no | — |
| 117 | #2621 | — | 3 | 2 | no | — |
| 118 | #2599 | — | 3 | 2 | no | — |
| 119 | #2588 | — | 3 | 2 | no | — |
| 120 | #2586 | — | 3 | 1 | no | — |
| 121 | #2584 | — | 3 | 1 | no | — |
| 122 | #2574 | — | 3 | 2 | no | — |
| 123 | #2572 | — | 3 | 2 | no | — |
| 124 | #2564 | — | 3 | 1 | no | — |
| 125 | #2560 | — | 3 | 2 | no | — |
| 126 | #2549 | — | 3 | 2 | no | — |
| 127 | #2547 | — | 3 | 1 | no | — |
| 128 | #2534 | — | 3 | 1 | no | — |
| 129 | #2532 | — | 3 | 2 | no | — |
| 130 | #2527 | — | 3 | 2 | no | — |
| 131 | #2523 | — | 3 | 1 | no | — |
| 132 | #2523 | — | 3 | 2 | no | — |
| 133 | #2521 | — | 3 | 2 | no | — |
| 134 | #2511 | — | 3 | 2 | no | — |
| 135 | #2503 | — | 3 | 1 | no | — |
| 136 | #2499 | — | 3 | 2 | no | — |
| 137 | #2489 | — | 3 | 2 | no | — |
| 138 | #2488 | — | 3 | 2 | no | — |
| 139 | #2488 | — | 3 | 2 | no | — |
| 140 | #2488 | — | 3 | 2 | no | — |
| 141 | #2483 | — | 3 | 1 | no | — |
| 142 | #2482 | — | 3 | 1 | no | — |
| 143 | #2480 | — | 3 | 2 | no | — |
| 144 | #2477 | — | 3 | 2 | no | — |
| 145 | #2477 | — | 3 | 2 | no | — |
| 146 | #2474 | — | 3 | 2 | no | — |
| 147 | #2474 | — | 3 | 2 | no | — |
| 148 | #2450 | — | 3 | 2 | no | — |
| 149 | #2449 | — | 3 | 2 | no | — |
| 150 | #2447 | — | 3 | 2 | no | — |
| 151 | #2440 | — | 3 | 2 | no | — |
| 152 | #2439 | — | 3 | 2 | no | — |
| 153 | #2438 | — | 3 | 2 | no | — |
| 154 | #2438 | — | 3 | 2 | no | — |
| 155 | #2438 | — | 3 | 2 | no | — |
| 156 | #2423 | — | 3 | 2 | no | — |
| 157 | #2421 | — | 3 | 2 | no | — |
| 158 | #2418 | — | 3 | 2 | no | — |
| 159 | #2415 | — | 3 | 2 | no | — |
| 160 | #2412 | — | 3 | 2 | no | — |
| 161 | #2398 | — | 3 | 1 | no | — |
| 162 | C2×#397 | — | 3 | 1 | no | — |
| 163 | #2378 | — | 3 | 1 | no | — |
| 164 | #2368 | — | 3 | 1 | no | — |
| 165 | #2342 | — | 3 | 2 | no | — |
| 166 | #2321 | — | 3 | 1 | no | — |
| 167 | #2320 | — | 3 | 1 | no | — |
| 168 | C23×A4 | — | 16 | 1 | no | — |
| 169 | C23×A4 | — | 16 | 1 | no | — |
| 170 | C22×SL(2,𝔽3) | — | 16 | 2 | no | — |
| 171 | C22×SL(2,𝔽3) | — | 16 | 2 | no | — |
| 172 | C22×SL(2,𝔽3) | — | 16 | 1 | no | — |
| 173 | C22×SL(2,𝔽3) | — | 16 | 1 | no | — |
| 174 | C22×SL(2,𝔽3) | — | 16 | 2 | no | — |
| 175 | C22×SL(2,𝔽3) | — | 16 | 2 | no | — |
| 176 | C22×SL(2,𝔽3) | — | 16 | 2 | no | — |
| 177 | C22×SL(2,𝔽3) | — | 16 | 2 | no | — |
| 178 | C22×SL(2,𝔽3) | — | 16 | 1 | no | — |
| 179 | C22×SL(2,𝔽3) | — | 16 | 1 | no | — |
| 180 | C22×SL(2,𝔽3) | — | 16 | 2 | no | — |
| 181 | C22×SL(2,𝔽3) | — | 16 | 1 | no | — |
| 182 | H(3,𝔽4) | — | 4 | 1 | no | — |
| 183 | H(3,𝔽4) | — | 12 | 1 | no | — |
| 184 | Q82 | — | 4 | 1 | no | — |
| 185 | Q82 | — | 12 | 1 | no | — |
| 186 | #552 | — | 12 | 2 | no | — |
| 187 | #552 | — | 12 | 1 | no | — |
| 188 | #552 | — | 12 | 1 | no | — |
| 189 | #551 | — | 12 | 2 | no | — |
| 190 | #551 | — | 12 | 1 | no | — |
| 191 | #551 | — | 12 | 1 | no | — |
| 192 | #543 | — | 4 | 2 | no | — |
| 193 | #543 | — | 4 | 1 | no | — |
| 194 | #543 | — | 4 | 1 | no | — |
| 195 | #543 | — | 12 | 2 | no | — |
| 196 | #543 | — | 12 | 1 | no | — |
| 197 | #543 | — | 12 | 1 | no | — |
| 198 | C2×C4⋊Q8 | — | 3 | 2 | no | — |
| 199 | C2×C4⋊Q8 | — | 3 | 1 | no | — |
| 200 | C2×#126 | — | 3 | 2 | no | — |
| 201 | C2×#126 | — | 3 | 2 | no | — |
| 202 | C2×#125 | — | 3 | 1 | no | — |
| 203 | C2×#125 | — | 3 | 2 | no | — |
| 204 | C2×#124 | — | 3 | 1 | no | — |
| 205 | C2×#124 | — | 3 | 1 | no | — |
| 206 | C2×#124 | — | 3 | 2 | no | — |
| 207 | C2×#123 | — | 3 | 2 | no | — |
| 208 | C2×#123 | — | 3 | 2 | no | — |
| 209 | C2×#123 | — | 3 | 1 | no | — |
| 210 | C2×C22⋊Q8 | — | 3 | 1 | no | — |
| 211 | C2×C22⋊Q8 | — | 3 | 1 | no | — |
| 212 | C2×C22⋊Q8 | — | 3 | 2 | no | — |
| 213 | C2×C22⋊Q8 | — | 3 | 1 | no | — |
| 214 | C2×C22⋊Q8 | — | 3 | 2 | no | — |
| 215 | C2×C22⋊Q8 | — | 3 | 2 | no | — |
| 216 | C2×C22⋊Q8 | — | 3 | 1 | no | — |
| 217 | C2×C22⋊Q8 | — | 3 | 2 | no | — |
| 218 | C2×C22⋊Q8 | — | 3 | 2 | no | — |
| 219 | C2×C22⋊Q8 | — | 3 | 2 | no | — |
| 220 | C2×C22⋊Q8 | — | 3 | 2 | no | — |
| 221 | C2×#120 | — | 3 | 1 | no | — |
| 222 | C2×#120 | — | 3 | 1 | no | — |
| 223 | C2×C4×Q8 | — | 3 | 1 | no | — |
| 224 | C2×C4×Q8 | — | 3 | 1 | no | — |
| 225 | C2×C4×D4 | — | 3 | 1 | no | — |
| 226 | C2×C4×D4 | — | 3 | 2 | no | — |
| 227 | C2×#117 | — | 3 | 2 | no | — |
| 228 | C2×#117 | — | 3 | 2 | no | — |
| 229 | C2×#117 | — | 3 | 1 | no | — |
| 230 | C22×C4⋊C4 | — | 3 | 1 | no | — |
| 231 | C22×C22⋊C4 | — | 3 | 2 | no | — |
| 232 | C22×C22⋊C4 | — | 3 | 1 | no | — |
| 233 | C22×C22⋊C4 | — | 3 | 1 | no | — |
| 234 | #401 | — | 3 | 2 | no | — |
| 235 | #400 | — | 3 | 2 | no | — |
| 236 | #400 | — | 3 | 2 | no | — |
| 237 | #400 | — | 3 | 2 | no | — |
| 238 | #400 | — | 3 | 2 | no | — |
| 239 | #400 | — | 3 | 1 | no | — |
| 240 | #400 | — | 3 | 2 | no | — |
| 241 | #400 | — | 3 | 2 | no | — |
| 242 | #400 | — | 3 | 2 | no | — |
| 243 | #400 | — | 3 | 2 | no | — |
| 244 | #400 | — | 3 | 2 | no | — |
| 245 | #400 | — | 3 | 2 | no | — |
| 246 | #400 | — | 3 | 2 | no | — |
| 247 | #400 | — | 3 | 2 | no | — |
| 248 | #400 | — | 3 | 2 | no | — |
| 249 | #400 | — | 3 | 2 | no | — |
| 250 | #400 | — | 3 | 2 | no | — |
| 251 | #400 | — | 3 | 2 | no | — |
| 252 | #399 | — | 3 | 1 | no | — |
| 253 | #399 | — | 3 | 2 | no | — |
| 254 | #399 | — | 3 | 2 | no | — |
| 255 | #398 | — | 3 | 2 | no | — |
| 256 | #398 | — | 3 | 2 | no | — |
| 257 | #398 | — | 3 | 2 | no | — |
| 258 | #398 | — | 3 | 2 | no | — |
| 259 | #398 | — | 3 | 2 | no | — |
| 260 | #398 | — | 3 | 2 | no | — |
| 261 | #398 | — | 3 | 2 | no | — |
| 262 | #398 | — | 3 | 1 | no | — |
| 263 | #398 | — | 3 | 2 | no | — |
| 264 | #398 | — | 3 | 2 | no | — |
| 265 | #398 | — | 3 | 2 | no | — |
| 266 | #398 | — | 3 | 2 | no | — |
| 267 | #398 | — | 3 | 2 | no | — |
| 268 | #398 | — | 3 | 2 | no | — |
| 269 | #397 | — | 3 | 2 | no | — |
| 270 | #397 | — | 3 | 2 | no | — |
| 271 | #397 | — | 3 | 2 | no | — |
| 272 | #397 | — | 3 | 2 | no | — |
| 273 | #397 | — | 3 | 1 | no | — |
| 274 | #397 | — | 3 | 2 | no | — |
| 275 | #397 | — | 3 | 2 | no | — |
| 276 | #397 | — | 3 | 2 | no | — |
| 277 | #397 | — | 3 | 2 | no | — |
| 278 | #397 | — | 3 | 2 | no | — |
| 279 | #397 | — | 3 | 2 | no | — |
| 280 | #397 | — | 3 | 2 | no | — |
| 281 | #397 | — | 3 | 2 | no | — |
| 282 | #397 | — | 3 | 2 | no | — |
| 283 | #397 | — | 3 | 1 | no | — |
| 284 | #397 | — | 3 | 2 | no | — |
| 285 | #397 | — | 3 | 1 | no | — |
| 286 | #397 | — | 3 | 2 | no | — |
| 287 | #397 | — | 3 | 2 | no | — |
| 288 | #397 | — | 3 | 2 | no | — |
| 289 | #397 | — | 3 | 2 | no | — |
| 290 | #397 | — | 3 | 2 | no | — |
| 291 | #397 | — | 3 | 2 | no | — |
| 292 | #396 | — | 3 | 2 | no | — |
| 293 | #396 | — | 3 | 2 | no | — |
| 294 | #396 | — | 3 | 2 | no | — |
| 295 | #396 | — | 3 | 2 | no | — |
| 296 | #396 | — | 3 | 2 | no | — |
| 297 | #395 | — | 3 | 2 | no | — |
| 298 | #395 | — | 3 | 2 | no | — |
| 299 | #395 | — | 3 | 2 | no | — |
| 300 | #395 | — | 3 | 2 | no | — |
| 301 | #395 | — | 3 | 1 | no | — |
| 302 | #395 | — | 3 | 2 | no | — |
| 303 | #395 | — | 3 | 2 | no | — |
| 304 | #395 | — | 3 | 2 | no | — |
| 305 | #395 | — | 3 | 2 | no | — |
| 306 | #395 | — | 3 | 2 | no | — |
| 307 | #395 | — | 3 | 2 | no | — |
| 308 | #395 | — | 3 | 1 | no | — |
| 309 | #395 | — | 3 | 2 | no | — |
| 310 | #395 | — | 3 | 2 | no | — |
| 311 | #394 | — | 3 | 2 | no | — |
| 312 | #394 | — | 3 | 2 | no | — |
| 313 | #394 | — | 3 | 2 | no | — |
| 314 | #394 | — | 3 | 2 | no | — |
| 315 | #394 | — | 3 | 2 | no | — |
| 316 | #394 | — | 3 | 2 | no | — |
| 317 | #393 | — | 3 | 2 | no | — |
| 318 | #393 | — | 3 | 1 | no | — |
| 319 | #393 | — | 3 | 2 | no | — |
| 320 | #393 | — | 3 | 2 | no | — |
| 321 | #393 | — | 3 | 2 | no | — |
| 322 | #393 | — | 3 | 2 | no | — |
| 323 | #393 | — | 3 | 2 | no | — |
| 324 | #393 | — | 3 | 1 | no | — |
| 325 | #393 | — | 3 | 1 | no | — |
| 326 | #393 | — | 3 | 1 | no | — |
| 327 | #393 | — | 3 | 2 | no | — |
| 328 | #391 | — | 3 | 1 | no | — |
| 329 | #391 | — | 3 | 2 | no | — |
| 330 | #391 | — | 3 | 2 | no | — |
| 331 | #391 | — | 3 | 2 | no | — |
| 332 | #391 | — | 3 | 2 | no | — |
| 333 | #391 | — | 3 | 2 | no | — |
| 334 | #391 | — | 3 | 2 | no | — |
| 335 | #391 | — | 3 | 2 | no | — |
| 336 | #391 | — | 3 | 1 | no | — |
| 337 | #391 | — | 3 | 2 | no | — |
| 338 | #391 | — | 3 | 2 | no | — |
| 339 | #391 | — | 3 | 2 | no | — |
| 340 | #391 | — | 3 | 2 | no | — |
| 341 | #391 | — | 3 | 2 | no | — |
| 342 | #391 | — | 3 | 2 | no | — |
| 343 | #391 | — | 3 | 2 | no | — |
| 344 | #391 | — | 3 | 2 | no | — |
| 345 | #391 | — | 3 | 2 | no | — |
| 346 | #391 | — | 3 | 2 | no | — |
| 347 | #390 | — | 3 | 2 | no | — |
| 348 | #389 | — | 3 | 2 | no | — |
| 349 | #389 | — | 3 | 2 | no | — |
| 350 | #389 | — | 3 | 2 | no | — |
| 351 | #389 | — | 3 | 2 | no | — |
| 352 | #389 | — | 3 | 2 | no | — |
| 353 | #389 | — | 3 | 2 | no | — |
| 354 | #389 | — | 3 | 2 | no | — |
| 355 | #389 | — | 3 | 2 | no | — |
| 356 | #389 | — | 3 | 2 | no | — |
| 357 | #388 | — | 3 | 2 | no | — |
| 358 | #388 | — | 3 | 2 | no | — |
| 359 | #388 | — | 3 | 2 | no | — |
| 360 | #388 | — | 3 | 2 | no | — |
| 361 | #388 | — | 3 | 2 | no | — |
| 362 | #388 | — | 3 | 2 | no | — |
| 363 | #388 | — | 3 | 2 | no | — |
| 364 | #388 | — | 3 | 2 | no | — |
| 365 | #388 | — | 3 | 2 | no | — |
| 366 | #388 | — | 3 | 2 | no | — |
| 367 | #388 | — | 3 | 2 | no | — |
| 368 | #388 | — | 3 | 2 | no | — |
| 369 | #388 | — | 3 | 2 | no | — |
| 370 | #388 | — | 3 | 2 | no | — |
| 371 | #388 | — | 3 | 2 | no | — |
| 372 | #388 | — | 3 | 2 | no | — |
| 373 | #388 | — | 3 | 2 | no | — |
| 374 | #388 | — | 3 | 2 | no | — |
| 375 | #388 | — | 3 | 2 | no | — |
| 376 | #388 | — | 3 | 2 | no | — |
| 377 | #387 | — | 3 | 2 | no | — |
| 378 | #387 | — | 3 | 2 | no | — |
| 379 | #387 | — | 3 | 2 | no | — |
| 380 | #387 | — | 3 | 2 | no | — |
| 381 | #387 | — | 3 | 2 | no | — |
| 382 | #387 | — | 3 | 2 | no | — |
| 383 | #387 | — | 3 | 2 | no | — |
| 384 | #387 | — | 3 | 2 | no | — |
| 385 | #387 | — | 3 | 2 | no | — |
| 386 | #387 | — | 3 | 2 | no | — |
| 387 | #387 | — | 3 | 2 | no | — |
| 388 | #387 | — | 3 | 2 | no | — |
| 389 | #387 | — | 3 | 2 | no | — |
| 390 | #387 | — | 3 | 2 | no | — |
| 391 | #387 | — | 3 | 2 | no | — |
| 392 | #387 | — | 3 | 2 | no | — |
| 393 | #387 | — | 3 | 2 | no | — |
| 394 | #387 | — | 3 | 2 | no | — |
| 395 | #387 | — | 3 | 2 | no | — |
| 396 | #387 | — | 3 | 2 | no | — |
| 397 | #387 | — | 3 | 2 | no | — |
| 398 | #387 | — | 3 | 2 | no | — |
| 399 | #386 | — | 3 | 2 | no | — |
| 400 | #386 | — | 3 | 2 | no | — |
| 401 | #386 | — | 3 | 2 | no | — |
| 402 | #386 | — | 3 | 2 | no | — |
| 403 | #386 | — | 3 | 1 | no | — |
| 404 | #386 | — | 3 | 2 | no | — |
| 405 | #386 | — | 3 | 2 | no | — |
| 406 | #385 | — | 3 | 2 | no | — |
| 407 | #385 | — | 3 | 1 | no | — |
| 408 | #385 | — | 3 | 2 | no | — |
| 409 | #385 | — | 3 | 2 | no | — |
| 410 | #385 | — | 3 | 2 | no | — |
| 411 | #385 | — | 3 | 2 | no | — |
| 412 | #385 | — | 3 | 2 | no | — |
| 413 | #385 | — | 3 | 2 | no | — |
| 414 | #385 | — | 3 | 2 | no | — |
| 415 | #385 | — | 3 | 2 | no | — |
| 416 | #385 | — | 3 | 2 | no | — |
| 417 | #385 | — | 3 | 2 | no | — |
| 418 | #384 | — | 3 | 2 | no | — |
| 419 | #383 | — | 3 | 2 | no | — |
| 420 | #383 | — | 3 | 2 | no | — |
| 421 | #383 | — | 3 | 2 | no | — |
| 422 | #382 | — | 3 | 2 | no | — |
| 423 | #382 | — | 3 | 2 | no | — |
| 424 | #382 | — | 3 | 2 | no | — |
| 425 | #382 | — | 3 | 2 | no | — |
| 426 | #381 | — | 3 | 2 | no | — |
| 427 | #381 | — | 3 | 1 | no | — |
| 428 | #381 | — | 3 | 2 | no | — |
| 429 | #381 | — | 3 | 1 | no | — |
| 430 | #381 | — | 3 | 2 | no | — |
| 431 | #381 | — | 3 | 2 | no | — |
| 432 | #380 | — | 3 | 2 | no | — |
| 433 | #380 | — | 3 | 1 | no | — |
| 434 | #380 | — | 3 | 2 | no | — |
| 435 | #380 | — | 3 | 2 | no | — |
| 436 | #380 | — | 3 | 2 | no | — |
| 437 | #380 | — | 3 | 2 | no | — |
| 438 | #379 | — | 3 | 1 | no | — |
| 439 | #379 | — | 3 | 2 | no | — |
| 440 | #379 | — | 3 | 1 | no | — |
| 441 | C4×C4⋊C4 | — | 3 | 2 | no | — |
| 442 | C4×C4⋊C4 | — | 3 | 1 | no | — |
| 443 | C4×C4⋊C4 | — | 3 | 2 | no | — |
| 444 | C4×C22⋊C4 | — | 3 | 2 | no | — |
| 445 | C4×C22⋊C4 | — | 3 | 2 | no | — |
| 446 | C4×C22⋊C4 | — | 3 | 2 | no | — |
| 447 | C4×C22⋊C4 | — | 3 | 1 | no | — |
| 448 | C4×C22⋊C4 | — | 3 | 2 | no | — |
| 449 | #376 | — | 3 | 1 | no | — |
| 450 | C2×#95 | — | 3 | 1 | no | — |
| 451 | C2×#95 | — | 3 | 2 | no | — |
| 452 | C22×A4 | — | 16 | 1 | no | — |
| 453 | C22×A4 | — | 16 | 1 | no | — |
| 454 | C22×A4 | — | 16 | 1 | no | — |
| 455 | C22×A4 | — | 16 | 2 | no | — |
| 456 | C22×A4 | — | 16 | 2 | no | — |
| 457 | C22×A4 | — | 16 | 2 | no | — |
| 458 | C22×A4 | — | 16 | 1 | no | — |
| 459 | C22×A4 | — | 16 | 2 | no | — |
| 460 | C22×A4 | — | 16 | 1 | no | — |
| 461 | C22×A4 | — | 16 | 1 | no | — |
| 462 | C2×SL(2,𝔽3) | — | 16 | 2 | no | — |
| 463 | C2×SL(2,𝔽3) | — | 16 | 2 | no | — |
| 464 | C2×SL(2,𝔽3) | — | 16 | 1 | no | — |
| 465 | C2×SL(2,𝔽3) | — | 16 | 2 | no | — |
| 466 | C2×SL(2,𝔽3) | — | 16 | 1 | no | — |
| 467 | C2×SL(2,𝔽3) | — | 16 | 2 | no | — |
| 468 | C2×SL(2,𝔽3) | — | 16 | 2 | no | — |
| 469 | C2×SL(2,𝔽3) | — | 16 | 2 | no | — |
| 470 | C2×SL(2,𝔽3) | — | 16 | 1 | no | — |
| 471 | C2×SL(2,𝔽3) | — | 16 | 1 | no | — |
| 472 | C2×SL(2,𝔽3) | — | 16 | 2 | no | — |
| 473 | C2×SL(2,𝔽3) | — | 16 | 2 | no | — |
| 474 | C2×SL(2,𝔽3) | — | 16 | 1 | no | — |
| 475 | C2×SL(2,𝔽3) | — | 16 | 2 | no | — |
| 476 | C2×SL(2,𝔽3) | — | 16 | 2 | no | — |
| 477 | C2×SL(2,𝔽3) | — | 16 | 2 | no | — |
| 478 | C2×SL(2,𝔽3) | — | 16 | 2 | no | — |
| 479 | C2×SL(2,𝔽3) | — | 16 | 2 | no | — |
| 480 | C2×SL(2,𝔽3) | — | 16 | 2 | no | — |
| 481 | C2×SL(2,𝔽3) | — | 16 | 2 | no | — |
| 482 | C2×SL(2,𝔽3) | — | 16 | 2 | no | — |
| 483 | C2×SL(2,𝔽3) | — | 16 | 2 | no | — |
| 484 | C2×SL(2,𝔽3) | — | 16 | 2 | no | — |
| 485 | C2×SL(2,𝔽3) | — | 16 | 2 | no | — |
| 486 | C2×SL(2,𝔽3) | — | 16 | 2 | no | — |
| 487 | C2×SL(2,𝔽3) | — | 16 | 2 | no | — |
| 488 | C2×SL(2,𝔽3) | — | 16 | 2 | no | — |
| 489 | C2×SL(2,𝔽3) | — | 16 | 2 | no | — |
| 490 | C2×SL(2,𝔽3) | — | 16 | 2 | no | — |
| 491 | C2×SL(2,𝔽3) | — | 16 | 1 | no | — |
| 492 | C2×SL(2,𝔽3) | — | 16 | 2 | no | — |
| 493 | C2×SL(2,𝔽3) | — | 16 | 1 | no | — |
| 494 | C25 | C22⋊A4 | 1 | 1 | yes | characteristic |
| 495 | C25 | C22⋊A4 | 1 | 1 | yes | characteristic |
| 496 | C22×Q8 | — | 3 | 1 | no | — |
| 497 | C22×Q8 | C22⋊A4 | 1 | 1 | yes | characteristic |
| 498 | C22×Q8 | C22⋊A4 | 1 | 1 | yes | characteristic |
| 499 | C22×Q8 | C22⋊A4 | 1 | 2 | yes | — |
| 500 | C22×Q8 | C22⋊A4 | 1 | 2 | yes | — |
| 501 | C22×Q8 | C22⋊A4 | 1 | 1 | yes | characteristic |
| 502 | C22×Q8 | C22⋊A4 | 1 | 1 | yes | characteristic |
| 503 | C22×Q8 | C22⋊A4 | 1 | 2 | yes | — |
| 504 | C22×Q8 | C22⋊A4 | 1 | 2 | yes | — |
| 505 | C22×Q8 | C22⋊A4 | 1 | 2 | yes | — |
| 506 | C22×Q8 | C22⋊A4 | 1 | 1 | yes | characteristic |
| 507 | C22×Q8 | C22⋊A4 | 1 | 2 | yes | — |
| 508 | C22×Q8 | C22⋊A4 | 1 | 2 | yes | — |
| 509 | C22×D4 | — | 3 | 1 | no | — |
| 510 | C22×D4 | — | 3 | 2 | no | — |
| 511 | C23×C4 | — | 3 | 2 | no | — |
| 512 | C23×C4 | — | 3 | 1 | no | — |
| 513 | C23×C4 | — | 3 | 1 | no | — |
| 514 | C23×C4 | — | 3 | 2 | no | — |
| 515 | C23×C4 | — | 3 | 1 | no | — |
| 516 | C23×C4 | — | 3 | 1 | no | — |
| 517 | C4⋊Q8 | — | 12 | 2 | no | — |
| 518 | C4⋊Q8 | — | 12 | 1 | no | — |
| 519 | C4⋊Q8 | — | 12 | 2 | no | — |
| 520 | C4⋊Q8 | — | 12 | 1 | no | — |
| 521 | #126 | — | 12 | 2 | no | — |
| 522 | #126 | — | 12 | 2 | no | — |
| 523 | #126 | — | 12 | 2 | no | — |
| 524 | #126 | — | 12 | 2 | no | — |
| 525 | #125 | — | 12 | 1 | no | — |
| 526 | #125 | — | 12 | 1 | no | — |
| 527 | #125 | — | 12 | 2 | no | — |
| 528 | #125 | — | 12 | 2 | no | — |
| 529 | #124 | — | 12 | 1 | no | — |
| 530 | #124 | — | 12 | 2 | no | — |
| 531 | #124 | — | 12 | 1 | no | — |
| 532 | #124 | — | 12 | 2 | no | — |
| 533 | #124 | — | 12 | 1 | no | — |
| 534 | #124 | — | 12 | 1 | no | — |
| 535 | #123 | — | 12 | 2 | no | — |
| 536 | #123 | — | 12 | 2 | no | — |
| 537 | #123 | — | 12 | 1 | no | — |
| 538 | #123 | — | 12 | 1 | no | — |
| 539 | #123 | — | 12 | 2 | no | — |
| 540 | #123 | — | 12 | 2 | no | — |
| 541 | C22⋊Q8 | — | 6 | 1 | no | — |
| 542 | C22⋊Q8 | — | 6 | 2 | no | — |
| 543 | C22⋊Q8 | — | 6 | 1 | no | — |
| 544 | C22⋊Q8 | — | 6 | 2 | no | — |
| 545 | C22⋊Q8 | — | 6 | 1 | no | — |
| 546 | C22⋊Q8 | — | 6 | 1 | no | — |
| 547 | C22⋊Q8 | — | 12 | 2 | no | — |
| 548 | C22⋊Q8 | — | 12 | 2 | no | — |
| 549 | C22⋊Q8 | — | 12 | 2 | no | — |
| 550 | C22⋊Q8 | — | 12 | 2 | no | — |
| 551 | C22⋊Q8 | — | 12 | 2 | no | — |
| 552 | C22⋊Q8 | — | 12 | 2 | no | — |
| 553 | C22⋊Q8 | — | 12 | 2 | no | — |
| 554 | C22⋊Q8 | — | 12 | 2 | no | — |
| 555 | C22⋊Q8 | — | 12 | 2 | no | — |
| 556 | C22⋊Q8 | — | 12 | 2 | no | — |
| 557 | C22⋊Q8 | — | 12 | 2 | no | — |
| 558 | C22⋊Q8 | — | 12 | 2 | no | — |
| 559 | C22⋊Q8 | — | 12 | 2 | no | — |
| 560 | C22⋊Q8 | — | 12 | 2 | no | — |
| 561 | C22⋊Q8 | — | 12 | 1 | no | — |
| 562 | C22⋊Q8 | — | 12 | 1 | no | — |
| 563 | C22⋊Q8 | — | 12 | 1 | no | — |
| 564 | C22⋊Q8 | — | 12 | 1 | no | — |
| 565 | #120 | — | 6 | 1 | no | — |
| 566 | #120 | — | 6 | 2 | no | — |
| 567 | #120 | — | 6 | 1 | no | — |
| 568 | #120 | — | 12 | 1 | no | — |
| 569 | #120 | — | 12 | 1 | no | — |
| 570 | C4×Q8 | — | 6 | 1 | no | — |
| 571 | C4×Q8 | — | 6 | 2 | no | — |
| 572 | C4×Q8 | — | 6 | 1 | no | — |
| 573 | C4×Q8 | — | 12 | 1 | no | — |
| 574 | C4×Q8 | — | 12 | 1 | no | — |
| 575 | C4×D4 | — | 12 | 1 | no | — |
| 576 | C4×D4 | — | 12 | 1 | no | — |
| 577 | C4×D4 | — | 12 | 2 | no | — |
| 578 | C4×D4 | — | 12 | 2 | no | — |
| 579 | #117 | — | 12 | 2 | no | — |
| 580 | #117 | — | 12 | 2 | no | — |
| 581 | #117 | — | 12 | 2 | no | — |
| 582 | #117 | — | 12 | 2 | no | — |
| 583 | #117 | — | 12 | 1 | no | — |
| 584 | #117 | — | 12 | 1 | no | — |
| 585 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 586 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 587 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 588 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 589 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 590 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 591 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 592 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 593 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 594 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 595 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 596 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 597 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 598 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 599 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 600 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 601 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 602 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 603 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 604 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 605 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 606 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 607 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 608 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 609 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 610 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 611 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 612 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 613 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 614 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 615 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 616 | C2×C4⋊C4 | — | 12 | 1 | no | — |
| 617 | C2×C4⋊C4 | — | 12 | 1 | no | — |
| 618 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 619 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 620 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 621 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 622 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 623 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 624 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 625 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 626 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 627 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 628 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 629 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 630 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 631 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 632 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 633 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 634 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 635 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 636 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 637 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 638 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 639 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 640 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 641 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 642 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 643 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 644 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 645 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 646 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 647 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 648 | C2×C22⋊C4 | — | 12 | 1 | no | — |
| 649 | C2×C22⋊C4 | — | 12 | 1 | no | — |
| 650 | C2×C22⋊C4 | — | 12 | 1 | no | — |
| 651 | C2×C22⋊C4 | — | 12 | 1 | no | — |
| 652 | C2×C42 | — | 3 | 2 | no | — |
| 653 | C2×C42 | — | 3 | 1 | no | — |
| 654 | C2×C42 | — | 3 | 1 | no | — |
| 655 | C2×C42 | — | 3 | 2 | no | — |
| 656 | C2×C42 | — | 3 | 2 | no | — |
| 657 | C2×C42 | — | 3 | 1 | no | — |
| 658 | C2×C42 | — | 3 | 2 | no | — |
| 659 | C2×C42 | — | 3 | 2 | no | — |
| 660 | C2×C42 | — | 3 | 2 | no | — |
| 661 | #95 | — | 3 | 1 | no | — |
| 662 | #95 | — | 3 | 2 | no | — |
| 663 | #95 | — | 3 | 2 | no | — |
| 664 | #95 | — | 3 | 2 | no | — |
| 665 | #95 | — | 3 | 2 | no | — |
| 666 | #95 | — | 3 | 1 | no | — |
| 667 | #95 | — | 3 | 2 | no | — |
| 668 | #95 | — | 3 | 1 | no | — |
| 669 | #95 | — | 3 | 1 | no | — |
| 670 | #95 | — | 3 | 2 | no | — |
| 671 | #95 | — | 3 | 2 | no | — |
| 672 | #95 | — | 3 | 2 | no | — |
| 673 | #95 | — | 3 | 2 | no | — |
| 674 | #95 | — | 3 | 2 | no | — |
| 675 | #95 | — | 3 | 2 | no | — |
| 676 | #95 | — | 3 | 2 | no | — |
| 677 | #95 | — | 3 | 2 | no | — |
| 678 | #95 | — | 3 | 2 | no | — |
| 679 | #95 | — | 3 | 2 | no | — |
| 680 | #95 | — | 3 | 2 | no | — |
| 681 | #95 | — | 3 | 2 | no | — |
| 682 | #95 | — | 3 | 2 | no | — |
| 683 | #95 | — | 3 | 2 | no | — |
| 684 | #95 | — | 3 | 2 | no | — |
| 685 | #95 | — | 3 | 2 | no | — |
| 686 | #95 | — | 3 | 2 | no | — |
| 687 | #95 | — | 3 | 2 | no | — |
| 688 | #95 | — | 3 | 2 | no | — |
| 689 | #95 | — | 3 | 2 | no | — |
| 690 | #95 | — | 3 | 1 | no | — |
| 691 | #95 | — | 3 | 2 | no | — |
| 692 | #95 | — | 3 | 2 | no | — |
| 693 | #95 | — | 3 | 2 | no | — |
| 694 | #95 | — | 3 | 2 | no | — |
| 695 | #95 | — | 3 | 1 | no | — |
| 696 | #95 | — | 3 | 2 | no | — |
| 697 | #95 | — | 3 | 2 | no | — |
| 698 | #95 | — | 3 | 2 | no | — |
| 699 | #95 | — | 3 | 2 | no | — |
| 700 | #95 | — | 3 | 2 | no | — |
| 701 | #95 | — | 3 | 2 | no | — |
| 702 | #95 | — | 3 | 2 | no | — |
| 703 | #95 | — | 3 | 2 | no | — |
| 704 | #95 | — | 3 | 2 | no | — |
| 705 | C23×C3 | — | 64 | 1 | no | — |
| 706 | C2×A4 | — | 16 | 2 | no | — |
| 707 | C2×A4 | — | 16 | 1 | no | — |
| 708 | C2×A4 | — | 16 | 1 | no | — |
| 709 | C2×A4 | — | 16 | 1 | no | — |
| 710 | C2×A4 | — | 16 | 1 | no | — |
| 711 | C2×A4 | — | 16 | 2 | no | — |
| 712 | C2×A4 | — | 16 | 1 | no | — |
| 713 | C2×A4 | — | 16 | 2 | no | — |
| 714 | C2×A4 | — | 16 | 2 | no | — |
| 715 | C2×A4 | — | 16 | 1 | no | — |
| 716 | SL(2,𝔽3) | — | 16 | 1 | no | — |
| 717 | SL(2,𝔽3) | — | 16 | 1 | no | — |
| 718 | SL(2,𝔽3) | — | 16 | 1 | no | — |
| 719 | SL(2,𝔽3) | — | 16 | 1 | no | — |
| 720 | SL(2,𝔽3) | — | 16 | 2 | no | — |
| 721 | SL(2,𝔽3) | — | 16 | 2 | no | — |
| 722 | SL(2,𝔽3) | — | 16 | 2 | no | — |
| 723 | SL(2,𝔽3) | — | 16 | 2 | no | — |
| 724 | SL(2,𝔽3) | — | 16 | 2 | no | — |
| 725 | SL(2,𝔽3) | — | 16 | 1 | no | — |
| 726 | SL(2,𝔽3) | — | 16 | 2 | no | — |
| 727 | SL(2,𝔽3) | — | 16 | 2 | no | — |
| 728 | C24 | — | 3 | 1 | no | — |
| 729 | C24 | — | 3 | 1 | no | — |
| 730 | C24 | — | 3 | 1 | no | — |
| 731 | C24 | — | 4 | 1 | no | — |
| 732 | C24 | — | 4 | 1 | no | — |
| 733 | C24 | — | 4 | 2 | no | — |
| 734 | C24 | — | 4 | 2 | no | — |
| 735 | C24 | — | 4 | 1 | no | — |
| 736 | C24 | — | 4 | 2 | no | — |
| 737 | C24 | — | 4 | 1 | no | — |
| 738 | C24 | — | 4 | 2 | no | — |
| 739 | C24 | — | 4 | 1 | no | — |
| 740 | C24 | #997 | 1 | 1 | yes | characteristic |
| 741 | C2×Q8 | — | 3 | 1 | no | — |
| 742 | C2×Q8 | — | 4 | 1 | no | — |
| 743 | C2×Q8 | — | 4 | 2 | no | — |
| 744 | C2×Q8 | — | 4 | 2 | no | — |
| 745 | C2×Q8 | — | 4 | 2 | no | — |
| 746 | C2×Q8 | — | 4 | 1 | no | — |
| 747 | C2×Q8 | — | 4 | 2 | no | — |
| 748 | C2×Q8 | — | 4 | 2 | no | — |
| 749 | C2×Q8 | — | 4 | 2 | no | — |
| 750 | C2×Q8 | — | 4 | 2 | no | — |
| 751 | C2×Q8 | — | 4 | 2 | no | — |
| 752 | C2×Q8 | — | 4 | 1 | no | — |
| 753 | C2×Q8 | — | 4 | 2 | no | — |
| 754 | C2×Q8 | — | 4 | 1 | no | — |
| 755 | C2×Q8 | — | 4 | 2 | no | — |
| 756 | C2×Q8 | — | 4 | 1 | no | — |
| 757 | C2×Q8 | — | 4 | 2 | no | — |
| 758 | C2×Q8 | — | 4 | 2 | no | — |
| 759 | C2×Q8 | — | 4 | 2 | no | — |
| 760 | C2×Q8 | — | 4 | 2 | no | — |
| 761 | C2×Q8 | — | 4 | 2 | no | — |
| 762 | C2×Q8 | — | 4 | 2 | no | — |
| 763 | C2×Q8 | — | 4 | 2 | no | — |
| 764 | C2×Q8 | — | 4 | 2 | no | — |
| 765 | C2×Q8 | — | 4 | 2 | no | — |
| 766 | C2×Q8 | — | 4 | 2 | no | — |
| 767 | C2×Q8 | — | 4 | 2 | no | — |
| 768 | C2×Q8 | — | 4 | 2 | no | — |
| 769 | C2×Q8 | — | 4 | 2 | no | — |
| 770 | C2×Q8 | — | 4 | 2 | no | — |
| 771 | C2×Q8 | — | 4 | 2 | no | — |
| 772 | C2×Q8 | — | 4 | 1 | no | — |
| 773 | C2×Q8 | — | 12 | 1 | no | — |
| 774 | C2×Q8 | — | 12 | 1 | no | — |
| 775 | C2×Q8 | — | 12 | 1 | no | — |
| 776 | C2×Q8 | #997 | 1 | 1 | yes | characteristic |
| 777 | C2×D4 | — | 6 | 2 | no | — |
| 778 | C2×D4 | — | 6 | 2 | no | — |
| 779 | C2×D4 | — | 6 | 1 | no | — |
| 780 | C2×D4 | — | 6 | 1 | no | — |
| 781 | C2×D4 | — | 12 | 1 | no | — |
| 782 | C2×D4 | — | 12 | 2 | no | — |
| 783 | C2×D4 | — | 12 | 2 | no | — |
| 784 | C2×D4 | — | 12 | 1 | no | — |
| 785 | C22×C4 | — | 3 | 1 | no | — |
| 786 | C22×C4 | — | 3 | 2 | no | — |
| 787 | C22×C4 | — | 3 | 2 | no | — |
| 788 | C22×C4 | — | 3 | 2 | no | — |
| 789 | C22×C4 | — | 3 | 1 | no | — |
| 790 | C22×C4 | — | 3 | 2 | no | — |
| 791 | C22×C4 | — | 3 | 2 | no | — |
| 792 | C22×C4 | — | 3 | 1 | no | — |
| 793 | C22×C4 | — | 3 | 1 | no | — |
| 794 | C22×C4 | — | 3 | 1 | no | — |
| 795 | C22×C4 | — | 3 | 2 | no | — |
| 796 | C22×C4 | — | 3 | 2 | no | — |
| 797 | C22×C4 | — | 6 | 1 | no | — |
| 798 | C22×C4 | — | 6 | 1 | no | — |
| 799 | C22×C4 | — | 6 | 1 | no | — |
| 800 | C22×C4 | — | 6 | 1 | no | — |
| 801 | C22×C4 | — | 6 | 2 | no | — |
| 802 | C22×C4 | — | 6 | 2 | no | — |
| 803 | C22×C4 | — | 6 | 2 | no | — |
| 804 | C22×C4 | — | 6 | 2 | no | — |
| 805 | C22×C4 | — | 12 | 2 | no | — |
| 806 | C22×C4 | — | 12 | 2 | no | — |
| 807 | C22×C4 | — | 12 | 2 | no | — |
| 808 | C22×C4 | — | 12 | 2 | no | — |
| 809 | C22×C4 | — | 12 | 2 | no | — |
| 810 | C22×C4 | — | 12 | 2 | no | — |
| 811 | C22×C4 | — | 12 | 1 | no | — |
| 812 | C22×C4 | — | 12 | 1 | no | — |
| 813 | C22×C4 | — | 12 | 1 | no | — |
| 814 | C22×C4 | — | 12 | 2 | no | — |
| 815 | C22×C4 | — | 12 | 1 | no | — |
| 816 | C4⋊C4 | — | 6 | 1 | no | — |
| 817 | C4⋊C4 | — | 6 | 1 | no | — |
| 818 | C4⋊C4 | — | 6 | 1 | no | — |
| 819 | C4⋊C4 | — | 6 | 1 | no | — |
| 820 | C4⋊C4 | — | 6 | 2 | no | — |
| 821 | C4⋊C4 | — | 6 | 1 | no | — |
| 822 | C4⋊C4 | — | 6 | 2 | no | — |
| 823 | C4⋊C4 | — | 6 | 1 | no | — |
| 824 | C4⋊C4 | — | 6 | 2 | no | — |
| 825 | C4⋊C4 | — | 6 | 2 | no | — |
| 826 | C4⋊C4 | — | 6 | 2 | no | — |
| 827 | C4⋊C4 | — | 6 | 2 | no | — |
| 828 | C4⋊C4 | — | 12 | 2 | no | — |
| 829 | C4⋊C4 | — | 12 | 2 | no | — |
| 830 | C4⋊C4 | — | 12 | 2 | no | — |
| 831 | C4⋊C4 | — | 12 | 2 | no | — |
| 832 | C4⋊C4 | — | 12 | 2 | no | — |
| 833 | C4⋊C4 | — | 12 | 2 | no | — |
| 834 | C4⋊C4 | — | 12 | 2 | no | — |
| 835 | C4⋊C4 | — | 12 | 2 | no | — |
| 836 | C4⋊C4 | — | 12 | 2 | no | — |
| 837 | C4⋊C4 | — | 12 | 2 | no | — |
| 838 | C4⋊C4 | — | 12 | 2 | no | — |
| 839 | C4⋊C4 | — | 12 | 2 | no | — |
| 840 | C4⋊C4 | — | 12 | 2 | no | — |
| 841 | C4⋊C4 | — | 12 | 2 | no | — |
| 842 | C4⋊C4 | — | 12 | 1 | no | — |
| 843 | C4⋊C4 | — | 12 | 1 | no | — |
| 844 | C4⋊C4 | — | 12 | 2 | no | — |
| 845 | C4⋊C4 | — | 12 | 2 | no | — |
| 846 | C4⋊C4 | — | 12 | 2 | no | — |
| 847 | C4⋊C4 | — | 12 | 2 | no | — |
| 848 | C4⋊C4 | — | 12 | 1 | no | — |
| 849 | C4⋊C4 | — | 12 | 2 | no | — |
| 850 | C4⋊C4 | — | 12 | 1 | no | — |
| 851 | C4⋊C4 | — | 12 | 2 | no | — |
| 852 | C4⋊C4 | — | 12 | 2 | no | — |
| 853 | C22⋊C4 | — | 6 | 2 | no | — |
| 854 | C22⋊C4 | — | 6 | 2 | no | — |
| 855 | C22⋊C4 | — | 6 | 2 | no | — |
| 856 | C22⋊C4 | — | 6 | 2 | no | — |
| 857 | C22⋊C4 | — | 6 | 2 | no | — |
| 858 | C22⋊C4 | — | 6 | 2 | no | — |
| 859 | C22⋊C4 | — | 6 | 2 | no | — |
| 860 | C22⋊C4 | — | 6 | 2 | no | — |
| 861 | C22⋊C4 | — | 6 | 2 | no | — |
| 862 | C22⋊C4 | — | 6 | 2 | no | — |
| 863 | C22⋊C4 | — | 6 | 2 | no | — |
| 864 | C22⋊C4 | — | 6 | 2 | no | — |
| 865 | C22⋊C4 | — | 6 | 2 | no | — |
| 866 | C22⋊C4 | — | 6 | 2 | no | — |
| 867 | C22⋊C4 | — | 6 | 1 | no | — |
| 868 | C22⋊C4 | — | 6 | 1 | no | — |
| 869 | C22⋊C4 | — | 12 | 2 | no | — |
| 870 | C22⋊C4 | — | 12 | 2 | no | — |
| 871 | C22⋊C4 | — | 12 | 2 | no | — |
| 872 | C22⋊C4 | — | 12 | 2 | no | — |
| 873 | C22⋊C4 | — | 12 | 2 | no | — |
| 874 | C22⋊C4 | — | 12 | 2 | no | — |
| 875 | C22⋊C4 | — | 12 | 2 | no | — |
| 876 | C22⋊C4 | — | 12 | 1 | no | — |
| 877 | C22⋊C4 | — | 12 | 2 | no | — |
| 878 | C22⋊C4 | — | 12 | 2 | no | — |
| 879 | C22⋊C4 | — | 12 | 2 | no | — |
| 880 | C22⋊C4 | — | 12 | 1 | no | — |
| 881 | C22⋊C4 | — | 12 | 2 | no | — |
| 882 | C22⋊C4 | — | 12 | 2 | no | — |
| 883 | C22⋊C4 | — | 12 | 1 | no | — |
| 884 | C22⋊C4 | — | 12 | 1 | no | — |
| 885 | C22⋊C4 | — | 12 | 2 | no | — |
| 886 | C22⋊C4 | — | 12 | 1 | no | — |
| 887 | C42 | — | 6 | 2 | no | — |
| 888 | C42 | — | 6 | 2 | no | — |
| 889 | C42 | — | 6 | 1 | no | — |
| 890 | C42 | — | 6 | 1 | no | — |
| 891 | C42 | — | 12 | 2 | no | — |
| 892 | C42 | — | 12 | 2 | no | — |
| 893 | C42 | — | 12 | 2 | no | — |
| 894 | C42 | — | 12 | 1 | no | — |
| 895 | C42 | — | 12 | 2 | no | — |
| 896 | C42 | — | 12 | 2 | no | — |
| 897 | C42 | — | 12 | 1 | no | — |
| 898 | C22×C3 | — | 64 | 1 | no | — |
| 899 | C22×C3 | — | 64 | 1 | no | — |
| 900 | C22×C3 | — | 64 | 2 | no | — |
| 901 | C22×C3 | — | 64 | 2 | no | — |
| 902 | C22×C3 | — | 64 | 1 | no | — |
| 903 | A4 | — | 16 | 1 | no | — |
| 904 | A4 | — | 16 | 1 | no | — |
| 905 | C23 | — | 3 | 1 | no | — |
| 906 | C23 | — | 3 | 1 | no | — |
| 907 | C23 | — | 4 | 2 | no | — |
| 908 | C23 | — | 4 | 1 | no | — |
| 909 | C23 | — | 4 | 1 | no | — |
| 910 | C23 | — | 6 | 1 | no | — |
| 911 | C23 | — | 6 | 2 | no | — |
| 912 | C23 | — | 6 | 2 | no | — |
| 913 | C23 | — | 6 | 1 | no | — |
| 914 | C23 | — | 6 | 1 | no | — |
| 915 | C23 | — | 6 | 1 | no | — |
| 916 | C23 | — | 6 | 2 | no | — |
| 917 | C23 | — | 6 | 2 | no | — |
| 918 | C23 | — | 6 | 1 | no | — |
| 919 | C23 | — | 12 | 2 | no | — |
| 920 | C23 | — | 12 | 1 | no | — |
| 921 | C23 | — | 12 | 1 | no | — |
| 922 | C23 | — | 16 | 1 | no | — |
| 923 | C23 | — | 16 | 2 | no | — |
| 924 | C23 | — | 16 | 1 | no | — |
| 925 | C23 | — | 16 | 1 | no | — |
| 926 | C23 | — | 16 | 2 | no | — |
| 927 | C23 | — | 16 | 1 | no | — |
| 928 | C23 | — | 16 | 2 | no | — |
| 929 | C23 | C22⋊(C22⋊A4) | 1 | 1 | yes | characteristic |
| 930 | Q8 | — | 4 | 1 | no | — |
| 931 | Q8 | — | 4 | 1 | no | — |
| 932 | Q8 | — | 12 | 1 | no | — |
| 933 | Q8 | — | 12 | 1 | no | — |
| 934 | Q8 | — | 16 | 1 | no | — |
| 935 | Q8 | — | 16 | 1 | no | — |
| 936 | Q8 | — | 16 | 2 | no | — |
| 937 | Q8 | — | 16 | 2 | no | — |
| 938 | Q8 | — | 16 | 2 | no | — |
| 939 | Q8 | — | 16 | 2 | no | — |
| 940 | Q8 | — | 16 | 2 | no | — |
| 941 | Q8 | — | 16 | 1 | no | — |
| 942 | Q8 | — | 16 | 2 | no | — |
| 943 | Q8 | — | 16 | 2 | no | — |
| 944 | Q8 | — | 48 | 1 | no | — |
| 945 | D4 | — | 24 | 2 | no | — |
| 946 | D4 | — | 24 | 2 | no | — |
| 947 | D4 | — | 24 | 1 | no | — |
| 948 | D4 | — | 24 | 1 | no | — |
| 949 | C2×C4 | — | 3 | 1 | no | — |
| 950 | C2×C4 | — | 3 | 1 | no | — |
| 951 | C2×C4 | — | 6 | 2 | no | — |
| 952 | C2×C4 | — | 6 | 1 | no | — |
| 953 | C2×C4 | — | 6 | 2 | no | — |
| 954 | C2×C4 | — | 6 | 1 | no | — |
| 955 | C2×C4 | — | 6 | 2 | no | — |
| 956 | C2×C4 | — | 6 | 1 | no | — |
| 957 | C2×C4 | — | 6 | 2 | no | — |
| 958 | C2×C4 | — | 6 | 1 | no | — |
| 959 | C2×C4 | — | 6 | 2 | no | — |
| 960 | C2×C4 | — | 6 | 2 | no | — |
| 961 | C2×C4 | — | 6 | 2 | no | — |
| 962 | C2×C4 | — | 6 | 2 | no | — |
| 963 | C2×C4 | — | 6 | 2 | no | — |
| 964 | C2×C4 | — | 6 | 1 | no | — |
| 965 | C2×C4 | — | 6 | 2 | no | — |
| 966 | C2×C4 | — | 6 | 2 | no | — |
| 967 | C2×C4 | — | 6 | 2 | no | — |
| 968 | C2×C4 | — | 6 | 2 | no | — |
| 969 | C2×C4 | — | 6 | 2 | no | — |
| 970 | C2×C4 | — | 6 | 2 | no | — |
| 971 | C2×C4 | — | 6 | 2 | no | — |
| 972 | C2×C4 | — | 6 | 2 | no | — |
| 973 | C2×C4 | — | 6 | 2 | no | — |
| 974 | C2×C4 | — | 6 | 2 | no | — |
| 975 | C2×C4 | — | 6 | 2 | no | — |
| 976 | C2×C4 | — | 6 | 2 | no | — |
| 977 | C2×C4 | — | 6 | 2 | no | — |
| 978 | C2×C4 | — | 6 | 2 | no | — |
| 979 | C2×C4 | — | 6 | 2 | no | — |
| 980 | C2×C4 | — | 6 | 2 | no | — |
| 981 | C2×C4 | — | 6 | 1 | no | — |
| 982 | C2×C4 | — | 24 | 1 | no | — |
| 983 | C2×C4 | — | 24 | 1 | no | — |
| 984 | C2×C4 | — | 24 | 1 | no | — |
| 985 | C2×C4 | — | 24 | 1 | no | — |
| 986 | C2×C4 | — | 24 | 2 | no | — |
| 987 | C2×C4 | — | 24 | 2 | no | — |
| 988 | C2×C4 | — | 24 | 2 | no | — |
| 989 | C2×C4 | — | 24 | 2 | no | — |
| 990 | C2×C4 | — | 48 | 1 | no | — |
| 991 | C2×C4 | — | 48 | 1 | no | — |
| 992 | C2×C3 | — | 64 | 1 | no | — |
| 993 | C2×C3 | — | 64 | 2 | no | — |
| 994 | C2×C3 | — | 64 | 1 | no | — |
| 995 | C2×C3 | — | 64 | 2 | no | — |
| 996 | C2×C3 | — | 64 | 1 | no | — |
| 997 | C22 | — | 6 | 2 | no | — |
| 998 | C22 | — | 6 | 2 | no | — |
| 999 | C22 | — | 6 | 1 | no | — |
| 1000 | C22 | — | 6 | 1 | no | — |
| 1001 | C22 | — | 12 | 1 | no | — |
| 1002 | C22 | — | 12 | 2 | no | — |
| 1003 | C22 | — | 12 | 1 | no | — |
| 1004 | C22 | — | 12 | 1 | no | — |
| 1005 | C22 | — | 12 | 2 | no | — |
| 1006 | C22 | — | 12 | 1 | no | — |
| 1007 | C22 | — | 12 | 2 | no | — |
| 1008 | C22 | — | 12 | 1 | no | — |
| 1009 | C22 | — | 16 | 1 | no | — |
| 1010 | C22 | — | 16 | 1 | no | — |
| 1011 | C22 | — | 48 | 1 | no | — |
| 1012 | C22 | — | 48 | 1 | no | — |
| 1013 | C22 | C22⋊#997 | 1 | 1 | yes | characteristic |
| 1014 | C22 | C22⋊#997 | 1 | 1 | yes | characteristic |
| 1015 | C22 | #87551 | 1 | 2 | yes | — |
| 1016 | C22 | #87551 | 1 | 2 | yes | — |
| 1017 | C22 | #87551 | 1 | 1 | yes | characteristic |
| 1018 | C4 | — | 6 | 1 | no | — |
| 1019 | C4 | — | 6 | 1 | no | — |
| 1020 | C4 | — | 12 | 1 | no | — |
| 1021 | C4 | — | 12 | 1 | no | — |
| 1022 | C4 | — | 12 | 2 | no | — |
| 1023 | C4 | — | 12 | 2 | no | — |
| 1024 | C4 | — | 12 | 2 | no | — |
| 1025 | C4 | — | 12 | 2 | no | — |
| 1026 | C4 | — | 12 | 2 | no | — |
| 1027 | C4 | — | 12 | 1 | no | — |
| 1028 | C4 | — | 12 | 2 | no | — |
| 1029 | C4 | — | 12 | 2 | no | — |
| 1030 | C4 | — | 12 | 1 | no | — |
| 1031 | C3 | — | 64 | 1 | no | Sylow |
| 1032 | C2 | — | 12 | 1 | no | — |
| 1033 | C2 | — | 12 | 1 | no | — |
| 1034 | C2 | — | 24 | 1 | no | — |
| 1035 | C2 | #62871⋊C3 | 1 | 1 | yes | characteristic |
| 1036 | C2 | #62871⋊C3 | 1 | 2 | yes | — |
| 1037 | C2 | #11710758 | 1 | 1 | yes | characteristic |
| 1038 | C2 | #11710780 | 1 | 2 | yes | — |
| 1039 | C2 | #11710852 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, hypercenter | C23 | C22⋊(C22⋊A4) |
| commutator, Fitting, cosocle, hypocenter | #9634946 | C3 |
| LCS | G ▷ #9634946 | |
| UCS | C1 ◁ C23 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #9634946 | C3 | semidirect |
| 36. C2×Q82 | A4 | semidirect |
| 39. C2×#543 | A4 | semidirect |
| 40. C2×#543 | A4 | semidirect |
| 41. C2×#543 | A4 | semidirect |
| 43. #2840 | A4 | semidirect |
| 44. #2840 | A4 | semidirect |
| 45. #2840 | A4 | semidirect |
| 54. #2811 | A4 | semidirect |
| 55. #2811 | A4 | semidirect |
| 56. #2811 | A4 | semidirect |
| 57. #2811 | A4 | semidirect |
| 58. #2811 | A4 | semidirect |
| 59. #2811 | A4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #9634946 | 3 |
| C2×#5465 | 4 |
| C2×Q8⋊SL(2,𝔽3) | 4 |
| C2×#543⋊C3 | 4 |
| #73293 | 4 |
| #73291 | 4 |