Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
2785720 conjugacy classes of subgroups.
The subgroup lattice has 628 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #72236365 | C2 | 1 | 42 | yes | maximal, complemented |
| 2 | #72218920 | C2 | 1 | 168 | yes | maximal, complemented |
| 3 | C23×#2846 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #72217511 | C2 | 1 | 42 | yes | maximal, complemented |
| 5 | C29 | C22 | 1 | 1 | yes | characteristic, complemented |
| 6 | C2×#62817 | C22 | 1 | 14 | yes | complemented |
| 7 | C24×#120 | C22 | 1 | 21 | yes | complemented |
| 8 | #8108058 | C22 | 1 | 1344 | yes | complemented |
| 9 | #8108057 | C22 | 1 | 1344 | yes | complemented |
| 10 | #8093108 | C22 | 1 | 56 | yes | complemented |
| 11 | #8093107 | C22 | 1 | 168 | yes | complemented |
| 12 | #7708352 | C22 | 1 | 2016 | yes | complemented |
| 13 | #7708349 | C22 | 1 | 2016 | yes | complemented |
| 14 | #7670230 | C22 | 1 | 504 | yes | complemented |
| 15 | #7670206 | C22 | 1 | 1008 | yes | complemented |
| 16 | #7670203 | C22 | 1 | 504 | yes | complemented |
| 17 | #7642273 | C22 | 1 | 252 | yes | complemented |
| 18 | #7642247 | C22 | 1 | 504 | yes | complemented |
| 19 | #7642244 | C22 | 1 | 252 | yes | complemented |
| 20 | #7641846 | C22 | 1 | 14 | yes | complemented |
| 21 | #7641845 | C22 | 1 | 42 | yes | complemented |
| 22 | C22×#2846 | C22 | 1 | 84 | yes | complemented |
| 23 | C22×#2846 | C22 | 1 | 252 | yes | complemented |
| 24 | #7630944 | C22 | 1 | 252 | yes | complemented |
| 25 | #7630939 | C22 | 1 | 84 | yes | complemented |
| 26 | #7626202 | C22 | 1 | 42 | yes | complemented |
| 27 | C23×#379 | C22 | 1 | 21 | yes | complemented |
| 28 | C28 | — | 4 | 112 | no | — |
| 29 | C28 | C23 | 1 | 21 | yes | — |
| 30 | C28 | C23 | 1 | 42 | yes | — |
| 31 | C25×D4 | C23 | 1 | 21 | yes | complemented |
| 32 | #62817 | — | 4 | 224 | no | — |
| 33 | C2×#3490 | C23 | 1 | 252 | yes | complemented |
| 34 | C2×#3484 | C23 | 1 | 252 | yes | complemented |
| 35 | C2×#3532 | C23 | 1 | 336 | yes | complemented |
| 36 | C23×#120 | — | 4 | 336 | no | — |
| 37 | C23×#120 | C23 | 1 | 42 | yes | — |
| 38 | C23×#120 | C23 | 1 | 504 | yes | complemented |
| 39 | C23×#120 | C23 | 1 | 126 | yes | complemented |
| 40 | C23×#120 | C23 | 1 | 504 | yes | complemented |
| 41 | C24×C22⋊C4 | C23 | 1 | 63 | yes | complemented |
| 42 | #59192 | C23 | 1 | 1344 | yes | complemented |
| 43 | #59006 | C23 | 1 | 4032 | yes | complemented |
| 44 | #58991 | C23 | 1 | 4032 | yes | complemented |
| 45 | #58990 | C23 | 1 | 1344 | yes | complemented |
| 46 | #53169 | C23 | 1 | 384 | yes | complemented |
| 47 | #53158 | C23 | 1 | 2688 | yes | complemented |
| 48 | #45458 | C23 | 1 | 1344 | yes | complemented |
| 49 | #45457 | C23 | 1 | 4032 | yes | complemented |
| 50 | #45439 | C23 | 1 | 1344 | yes | complemented |
| 51 | #45438 | C23 | 1 | 4032 | yes | complemented |
| 52 | #37848 | C23 | 1 | 8064 | yes | complemented |
| 53 | #37833 | C23 | 1 | 4032 | yes | complemented |
| 54 | #37832 | C23 | 1 | 4032 | yes | complemented |
| 55 | #37660 | C23 | 1 | 8064 | yes | complemented |
| 56 | #37645 | C23 | 1 | 4032 | yes | complemented |
| 57 | #37644 | C23 | 1 | 4032 | yes | complemented |
| 58 | #37475 | C23 | 1 | 336 | yes | complemented |
| 59 | #37436 | C23 | 1 | 1008 | yes | complemented |
| 60 | #36725 | C23 | 1 | 4032 | yes | complemented |
| 61 | #36714 | C23 | 1 | 1008 | yes | complemented |
| 62 | #36703 | C23 | 1 | 2016 | yes | complemented |
| 63 | #36702 | C23 | 1 | 1008 | yes | complemented |
| 64 | #36614 | C23 | 1 | 168 | yes | complemented |
| 65 | C2×#2846 | C23 | 1 | 504 | yes | — |
| 66 | C2×#2846 | C23 | 1 | 168 | yes | complemented |
| 67 | C2×#2846 | C23 | 1 | 504 | yes | complemented |
| 68 | C2×#2846 | C23 | 1 | 2016 | yes | complemented |
| 69 | C2×#2846 | C23 | 1 | 2016 | yes | complemented |
| 70 | C2×#2846 | C23 | 1 | 168 | yes | complemented |
| 71 | C2×#2846 | C23 | 1 | 24 | yes | complemented |
| 72 | #36158 | C23 | 1 | 4032 | yes | complemented |
| 73 | #36152 | C23 | 1 | 1344 | yes | complemented |
| 74 | #36098 | C23 | 1 | 4032 | yes | complemented |
| 75 | D4×#120 | C23 | 1 | 1344 | yes | complemented |
| 76 | #35390 | C23 | 1 | 168 | yes | complemented |
| 77 | #35369 | C23 | 1 | 336 | yes | complemented |
| 78 | #35367 | C23 | 1 | 504 | yes | complemented |
| 79 | #35350 | C23 | 1 | 504 | yes | complemented |
| 80 | #35348 | C23 | 1 | 1008 | yes | complemented |
| 81 | #35346 | C23 | 1 | 168 | yes | complemented |
| 82 | #35222 | C23 | 1 | 504 | yes | complemented |
| 83 | #35050 | C23 | 1 | 1008 | yes | complemented |
| 84 | #34992 | C23 | 1 | 504 | yes | complemented |
| 85 | #34988 | C23 | 1 | 2016 | yes | complemented |
| 86 | #34982 | C23 | 1 | 504 | yes | complemented |
| 87 | #34981 | C23 | 1 | 504 | yes | complemented |
| 88 | #34980 | C23 | 1 | 504 | yes | complemented |
| 89 | #34980 | C23 | 1 | 504 | yes | complemented |
| 90 | #34356 | C23 | 1 | 1008 | yes | complemented |
| 91 | #34198 | C23 | 1 | 1008 | yes | complemented |
| 92 | #34176 | C23 | 1 | 252 | yes | complemented |
| 93 | #34171 | C23 | 1 | 252 | yes | complemented |
| 94 | C22×#379 | C23 | 1 | 42 | yes | — |
| 95 | C22×#379 | C23 | 1 | 504 | yes | complemented |
| 96 | C22×#379 | C23 | 1 | 126 | yes | complemented |
| 97 | C22×#379 | C23 | 1 | 504 | yes | complemented |
| 98 | C27 | — | 2 | 336 | no | — |
| 99 | C27 | — | 4 | 1008 | no | — |
| 100 | C27 | — | 4 | 1008 | no | — |
| 101 | C27 | — | 4 | 1344 | no | — |
| 102 | C27 | — | 4 | 7168 | no | — |
| 103 | C27 | C24 | 1 | 21 | yes | — |
| 104 | C27 | C24 | 1 | 126 | yes | — |
| 105 | C27 | C24 | 1 | 252 | yes | — |
| 106 | C27 | C24 | 1 | 63 | yes | — |
| 107 | C27 | C24 | 1 | 14 | yes | — |
| 108 | C27 | C24 | 1 | 168 | yes | — |
| 109 | C27 | C24 | 1 | 7 | yes | — |
| 110 | C27 | C24 | 1 | 3 | yes | complemented |
| 111 | C22×H(5,𝔽2) | C24 | 1 | 28 | yes | complemented |
| 112 | C24×D4 | — | 4 | 504 | no | — |
| 113 | C24×D4 | C24 | 1 | 126 | yes | — |
| 114 | C24×D4 | C24 | 1 | 336 | yes | complemented |
| 115 | C24×D4 | C24 | 1 | 126 | yes | complemented |
| 116 | C25×C4 | C24 | 1 | 21 | yes | complemented |
| 117 | #3532 | — | 4 | 2688 | no | — |
| 118 | C2×H(3,𝔽4) | C24 | 1 | 112 | yes | complemented |
| 119 | C2×#560 | C24 | 1 | 336 | yes | complemented |
| 120 | #3490 | — | 4 | 2016 | no | — |
| 121 | #3484 | — | 4 | 2016 | no | — |
| 122 | C2×#551 | C24 | 1 | 1008 | yes | complemented |
| 123 | C2×#546 | C24 | 1 | 2016 | yes | complemented |
| 124 | C2×D42 | C24 | 1 | 1008 | yes | complemented |
| 125 | C2×#543 | C24 | 1 | 84 | yes | complemented |
| 126 | C2×#538 | C24 | 1 | 1008 | yes | complemented |
| 127 | C2×#535 | C24 | 1 | 504 | yes | complemented |
| 128 | C2×#534 | C24 | 1 | 252 | yes | complemented |
| 129 | C2×#534 | C24 | 1 | 504 | yes | complemented |
| 130 | C2×#525 | C24 | 1 | 504 | yes | complemented |
| 131 | C22×#120 | — | 2 | 672 | no | — |
| 132 | C22×#120 | — | 4 | 1008 | no | — |
| 133 | C22×#120 | — | 4 | 4032 | no | — |
| 134 | C22×#120 | — | 4 | 4032 | no | — |
| 135 | C22×#120 | C24 | 1 | 504 | yes | — |
| 136 | C22×#120 | C24 | 1 | 504 | yes | — |
| 137 | C22×#120 | C24 | 1 | 504 | yes | — |
| 138 | C22×#120 | C24 | 1 | 2016 | yes | — |
| 139 | C22×#120 | C24 | 1 | 672 | yes | complemented |
| 140 | C22×#120 | C24 | 1 | 2016 | yes | complemented |
| 141 | C22×#120 | C24 | 1 | 2016 | yes | complemented |
| 142 | C22×#120 | C24 | 1 | 504 | yes | complemented |
| 143 | C22×#120 | C24 | 1 | 672 | yes | complemented |
| 144 | C22×#120 | C24 | 1 | 168 | yes | complemented |
| 145 | C2×#518 | C24 | 1 | 252 | yes | complemented |
| 146 | C23×C22⋊C4 | — | 4 | 504 | no | — |
| 147 | C23×C22⋊C4 | C24 | 1 | 126 | yes | — |
| 148 | C23×C22⋊C4 | C24 | 1 | 252 | yes | — |
| 149 | C23×C22⋊C4 | C24 | 1 | 1008 | yes | complemented |
| 150 | C23×C22⋊C4 | C24 | 1 | 252 | yes | complemented |
| 151 | C23×C22⋊C4 | C24 | 1 | 126 | yes | complemented |
| 152 | #2849 | C24 | 1 | 1008 | yes | complemented |
| 153 | #2848 | C24 | 1 | 672 | yes | complemented |
| 154 | #2847 | C24 | 1 | 672 | yes | complemented |
| 155 | #2846 | C24 | 1 | 1344 | yes | — |
| 156 | #2846 | C24 | 1 | 4032 | yes | — |
| 157 | #2846 | C24 | 1 | 48 | yes | complemented |
| 158 | #2846 | C24 | 1 | 2016 | yes | complemented |
| 159 | #2846 | C24 | 1 | 2688 | yes | complemented |
| 160 | #2846 | C24 | 1 | 1008 | yes | complemented |
| 161 | #2846 | C24 | 1 | 1152 | yes | complemented |
| 162 | #2846 | C24 | 1 | 336 | yes | complemented |
| 163 | #2842 | C24 | 1 | 336 | yes | complemented |
| 164 | #2840 | C24 | 1 | 112 | yes | complemented |
| 165 | #2812 | C24 | 1 | 1344 | yes | complemented |
| 166 | #2736 | C24 | 1 | 1344 | yes | complemented |
| 167 | #2735 | C24 | 1 | 4032 | yes | complemented |
| 168 | #2697 | C24 | 1 | 4032 | yes | complemented |
| 169 | #2685 | C24 | 1 | 8064 | yes | complemented |
| 170 | #2684 | C24 | 1 | 4032 | yes | complemented |
| 171 | #2679 | C24 | 1 | 1344 | yes | complemented |
| 172 | #2678 | C24 | 1 | 8064 | yes | complemented |
| 173 | #2670 | C24 | 1 | 4032 | yes | complemented |
| 174 | #2669 | C24 | 1 | 4032 | yes | complemented |
| 175 | #2668 | C24 | 1 | 4032 | yes | complemented |
| 176 | #2626 | C24 | 1 | 2016 | yes | complemented |
| 177 | #2622 | C24 | 1 | 2016 | yes | complemented |
| 178 | #2617 | C24 | 1 | 2016 | yes | complemented |
| 179 | #2613 | C24 | 1 | 2016 | yes | complemented |
| 180 | #2561 | C24 | 1 | 2016 | yes | complemented |
| 181 | #2539 | C24 | 1 | 2016 | yes | complemented |
| 182 | #2534 | C24 | 1 | 4032 | yes | complemented |
| 183 | #2483 | C24 | 1 | 1008 | yes | complemented |
| 184 | #2482 | C24 | 1 | 2016 | yes | complemented |
| 185 | #2480 | C24 | 1 | 8064 | yes | complemented |
| 186 | #2472 | C24 | 1 | 8064 | yes | complemented |
| 187 | #2437 | C24 | 1 | 4032 | yes | complemented |
| 188 | #2435 | C24 | 1 | 2016 | yes | complemented |
| 189 | #2433 | C24 | 1 | 2016 | yes | complemented |
| 190 | #2424 | C24 | 1 | 8064 | yes | complemented |
| 191 | #2418 | C24 | 1 | 8064 | yes | complemented |
| 192 | #2412 | C24 | 1 | 4032 | yes | complemented |
| 193 | #2411 | C24 | 1 | 4032 | yes | complemented |
| 194 | #2410 | C24 | 1 | 4032 | yes | complemented |
| 195 | #2410 | C24 | 1 | 4032 | yes | complemented |
| 196 | #2408 | C24 | 1 | 4032 | yes | complemented |
| 197 | #2405 | C24 | 1 | 2016 | yes | complemented |
| 198 | #2405 | C24 | 1 | 2016 | yes | complemented |
| 199 | #2404 | C24 | 1 | 2016 | yes | complemented |
| 200 | #2403 | C24 | 1 | 2016 | yes | complemented |
| 201 | #2403 | C24 | 1 | 1008 | yes | complemented |
| 202 | #2375 | C24 | 1 | 1344 | yes | complemented |
| 203 | #2358 | C24 | 1 | 4032 | yes | complemented |
| 204 | #2342 | C24 | 1 | 4032 | yes | complemented |
| 205 | D4×C22⋊C4 | C24 | 1 | 4032 | yes | complemented |
| 206 | #2321 | C24 | 1 | 4032 | yes | complemented |
| 207 | #2315 | C24 | 1 | 504 | yes | complemented |
| 208 | #2312 | C24 | 1 | 1008 | yes | complemented |
| 209 | #2309 | C24 | 1 | 504 | yes | complemented |
| 210 | #2308 | C24 | 1 | 504 | yes | complemented |
| 211 | #2308 | C24 | 1 | 504 | yes | complemented |
| 212 | C4×#120 | C24 | 1 | 1344 | yes | complemented |
| 213 | #2280 | C24 | 1 | 504 | yes | complemented |
| 214 | C2×#379 | C24 | 1 | 504 | yes | — |
| 215 | C2×#379 | C24 | 1 | 504 | yes | — |
| 216 | C2×#379 | C24 | 1 | 2016 | yes | — |
| 217 | C2×#379 | C24 | 1 | 504 | yes | — |
| 218 | C2×#379 | C24 | 1 | 2016 | yes | complemented |
| 219 | C2×#379 | C24 | 1 | 672 | yes | complemented |
| 220 | C2×#379 | C24 | 1 | 504 | yes | complemented |
| 221 | C2×#379 | C24 | 1 | 672 | yes | complemented |
| 222 | C2×#379 | C24 | 1 | 2016 | yes | complemented |
| 223 | C2×#379 | C24 | 1 | 168 | yes | complemented |
| 224 | #2273 | C24 | 1 | 168 | yes | complemented |
| 225 | C26 | — | 2 | 504 | no | — |
| 226 | C26 | — | 2 | 2016 | no | — |
| 227 | C26 | — | 2 | 2016 | no | — |
| 228 | C26 | — | 2 | 504 | no | — |
| 229 | C26 | — | 4 | 336 | no | — |
| 230 | C26 | — | 4 | 168 | no | — |
| 231 | C26 | — | 4 | 504 | no | — |
| 232 | C26 | — | 4 | 2016 | no | — |
| 233 | C26 | — | 4 | 4032 | no | — |
| 234 | C26 | — | 4 | 1008 | no | — |
| 235 | C26 | — | 4 | 1008 | no | — |
| 236 | C26 | — | 4 | 504 | no | — |
| 237 | C26 | — | 4 | 1008 | no | — |
| 238 | C26 | — | 4 | 2016 | no | — |
| 239 | C26 | — | 4 | 2016 | no | — |
| 240 | C26 | — | 4 | 224 | no | — |
| 241 | C26 | — | 4 | 672 | no | — |
| 242 | C26 | — | 4 | 168 | no | — |
| 243 | C26 | — | 4 | 84 | no | — |
| 244 | C26 | — | 4 | 16128 | no | — |
| 245 | C26 | — | 4 | 10752 | no | — |
| 246 | C26 | — | 4 | 21504 | no | — |
| 247 | C26 | — | 4 | 64512 | no | — |
| 248 | C26 | — | 4 | 65536 | no | — |
| 249 | C26 | H(5,𝔽2) | 1 | 112 | yes | complemented |
| 250 | C26 | C25 | 1 | 3 | yes | — |
| 251 | C26 | C25 | 1 | 168 | yes | — |
| 252 | C26 | C25 | 1 | 63 | yes | — |
| 253 | C26 | C25 | 1 | 42 | yes | — |
| 254 | C26 | C25 | 1 | 168 | yes | — |
| 255 | C26 | C25 | 1 | 504 | yes | — |
| 256 | C26 | C25 | 1 | 63 | yes | — |
| 257 | C26 | C25 | 1 | 42 | yes | — |
| 258 | C26 | C25 | 1 | 168 | yes | — |
| 259 | C26 | C25 | 1 | 126 | yes | — |
| 260 | C26 | C25 | 1 | 48 | yes | — |
| 261 | C26 | C25 | 1 | 42 | yes | — |
| 262 | C2×H(5,𝔽2) | — | 4 | 336 | no | — |
| 263 | C22×#41 | C25 | 1 | 168 | yes | complemented |
| 264 | C23×D4 | — | 2 | 1008 | no | — |
| 265 | C23×D4 | — | 4 | 504 | no | — |
| 266 | C23×D4 | — | 4 | 1008 | no | — |
| 267 | C23×D4 | — | 4 | 1008 | no | — |
| 268 | C23×D4 | — | 4 | 4032 | no | — |
| 269 | C23×D4 | — | 8 | 2688 | no | — |
| 270 | C23×D4 | C25 | 1 | 84 | yes | — |
| 271 | C23×D4 | C25 | 1 | 252 | yes | — |
| 272 | C23×D4 | C25 | 1 | 1008 | yes | — |
| 273 | C23×D4 | C25 | 1 | 1008 | yes | — |
| 274 | C23×D4 | C25 | 1 | 168 | yes | complemented |
| 275 | C24×C4 | — | 4 | 252 | no | — |
| 276 | C24×C4 | C25 | 1 | 126 | yes | — |
| 277 | C24×C4 | C25 | 1 | 168 | yes | — |
| 278 | H(3,𝔽4) | — | 4 | 448 | no | — |
| 279 | #560 | — | 4 | 1344 | no | — |
| 280 | #551 | — | 4 | 4032 | no | — |
| 281 | #546 | — | 4 | 8064 | no | — |
| 282 | D42 | — | 4 | 4032 | no | — |
| 283 | #543 | — | 4 | 336 | no | — |
| 284 | #538 | — | 4 | 4032 | no | — |
| 285 | #535 | — | 4 | 2016 | no | — |
| 286 | #534 | — | 4 | 1008 | no | — |
| 287 | #534 | — | 4 | 2016 | no | — |
| 288 | C2×#127 | C25 | 1 | 336 | yes | complemented |
| 289 | C2×#126 | C25 | 1 | 672 | yes | complemented |
| 290 | C2×#124 | C25 | 1 | 1008 | yes | complemented |
| 291 | #525 | — | 4 | 2016 | no | — |
| 292 | C2×#123 | C25 | 1 | 1008 | yes | complemented |
| 293 | C2×#123 | C25 | 1 | 1008 | yes | complemented |
| 294 | C2×C22⋊Q8 | C25 | 1 | 1008 | yes | complemented |
| 295 | C2×#121 | C25 | 1 | 2016 | yes | complemented |
| 296 | C2×#121 | C25 | 1 | 1008 | yes | complemented |
| 297 | C2×#120 | — | 2 | 4032 | no | — |
| 298 | C2×#120 | — | 2 | 4032 | no | — |
| 299 | C2×#120 | — | 4 | 2016 | no | — |
| 300 | C2×#120 | — | 4 | 2016 | no | — |
| 301 | C2×#120 | — | 4 | 8064 | no | — |
| 302 | C2×#120 | — | 4 | 8064 | no | — |
| 303 | C2×#120 | — | 4 | 2688 | no | — |
| 304 | C2×#120 | — | 4 | 8064 | no | — |
| 305 | C2×#120 | — | 4 | 2688 | no | — |
| 306 | C2×#120 | — | 4 | 672 | no | — |
| 307 | C2×#120 | C25 | 1 | 1008 | yes | — |
| 308 | C2×#120 | C25 | 1 | 1008 | yes | — |
| 309 | C2×#120 | C25 | 1 | 336 | yes | — |
| 310 | C2×#120 | C25 | 1 | 336 | yes | — |
| 311 | C2×#120 | C25 | 1 | 4032 | yes | — |
| 312 | C2×#120 | C25 | 1 | 4032 | yes | — |
| 313 | C2×#120 | C25 | 1 | 1008 | yes | complemented |
| 314 | C2×#120 | C25 | 1 | 336 | yes | complemented |
| 315 | #518 | — | 4 | 1008 | no | — |
| 316 | C2×C4×D4 | C25 | 1 | 2016 | yes | complemented |
| 317 | C2×#117 | C25 | 1 | 504 | yes | complemented |
| 318 | C22×C22⋊C4 | — | 2 | 1008 | no | — |
| 319 | C22×C22⋊C4 | — | 4 | 1008 | no | — |
| 320 | C22×C22⋊C4 | — | 4 | 1008 | no | — |
| 321 | C22×C22⋊C4 | — | 4 | 4032 | no | — |
| 322 | C22×C22⋊C4 | — | 4 | 504 | no | — |
| 323 | C22×C22⋊C4 | C25 | 1 | 252 | yes | — |
| 324 | C22×C22⋊C4 | C25 | 1 | 252 | yes | — |
| 325 | C22×C22⋊C4 | C25 | 1 | 1008 | yes | — |
| 326 | C22×C22⋊C4 | C25 | 1 | 1008 | yes | — |
| 327 | C22×C22⋊C4 | C25 | 1 | 504 | yes | — |
| 328 | C22×C22⋊C4 | C25 | 1 | 2016 | yes | — |
| 329 | C22×C22⋊C4 | C25 | 1 | 2016 | yes | — |
| 330 | C22×C22⋊C4 | C25 | 1 | 504 | yes | complemented |
| 331 | #399 | C25 | 1 | 1344 | yes | complemented |
| 332 | #397 | C25 | 1 | 4032 | yes | complemented |
| 333 | #396 | C25 | 1 | 2688 | yes | complemented |
| 334 | #394 | C25 | 1 | 8064 | yes | complemented |
| 335 | #393 | C25 | 1 | 1344 | yes | complemented |
| 336 | #392 | C25 | 1 | 4032 | yes | complemented |
| 337 | #390 | C25 | 1 | 4032 | yes | complemented |
| 338 | #388 | C25 | 1 | 8064 | yes | complemented |
| 339 | #386 | C25 | 1 | 4032 | yes | complemented |
| 340 | #386 | C25 | 1 | 4032 | yes | complemented |
| 341 | #385 | C25 | 1 | 4032 | yes | complemented |
| 342 | #381 | C25 | 1 | 1008 | yes | complemented |
| 343 | #380 | C25 | 1 | 2016 | yes | complemented |
| 344 | #379 | C25 | 1 | 4032 | yes | — |
| 345 | #379 | C25 | 1 | 1008 | yes | — |
| 346 | #379 | C25 | 1 | 336 | yes | — |
| 347 | #379 | C25 | 1 | 1008 | yes | — |
| 348 | #379 | C25 | 1 | 336 | yes | — |
| 349 | #379 | C25 | 1 | 4032 | yes | — |
| 350 | #379 | C25 | 1 | 1008 | yes | complemented |
| 351 | C4×C22⋊C4 | C25 | 1 | 2016 | yes | complemented |
| 352 | C25 | — | 2 | 84 | no | — |
| 353 | C25 | — | 2 | 2688 | no | — |
| 354 | C25 | — | 2 | 2016 | no | — |
| 355 | C25 | — | 2 | 504 | no | — |
| 356 | C25 | — | 2 | 504 | no | — |
| 357 | C25 | — | 2 | 252 | no | — |
| 358 | C25 | — | 2 | 672 | no | — |
| 359 | C25 | — | 2 | 2016 | no | — |
| 360 | C25 | — | 2 | 2016 | no | — |
| 361 | C25 | — | 2 | 672 | no | — |
| 362 | C25 | — | 2 | 2016 | no | — |
| 363 | C25 | — | 2 | 504 | no | — |
| 364 | C25 | — | 2 | 504 | no | — |
| 365 | C25 | — | 2 | 168 | no | — |
| 366 | C25 | — | 4 | 1344 | no | — |
| 367 | C25 | — | 4 | 504 | no | — |
| 368 | C25 | — | 4 | 1008 | no | — |
| 369 | C25 | — | 4 | 504 | no | — |
| 370 | C25 | — | 4 | 504 | no | — |
| 371 | C25 | — | 4 | 1008 | no | — |
| 372 | C25 | — | 4 | 336 | no | — |
| 373 | C25 | — | 4 | 336 | no | — |
| 374 | C25 | — | 4 | 1008 | no | — |
| 375 | C25 | — | 4 | 2016 | no | — |
| 376 | C25 | — | 4 | 2016 | no | — |
| 377 | C25 | — | 4 | 1008 | no | — |
| 378 | C25 | — | 4 | 1008 | no | — |
| 379 | C25 | — | 4 | 1008 | no | — |
| 380 | C25 | — | 4 | 504 | no | — |
| 381 | C25 | — | 4 | 672 | no | — |
| 382 | C25 | — | 4 | 504 | no | — |
| 383 | C25 | — | 4 | 8064 | no | — |
| 384 | C25 | — | 4 | 8064 | no | — |
| 385 | C25 | — | 4 | 32256 | no | — |
| 386 | C25 | — | 4 | 32256 | no | — |
| 387 | C25 | — | 4 | 8064 | no | — |
| 388 | C25 | — | 4 | 16128 | no | — |
| 389 | C25 | — | 4 | 4032 | no | — |
| 390 | C25 | — | 4 | 32256 | no | — |
| 391 | C25 | — | 4 | 32256 | no | — |
| 392 | C25 | — | 4 | 1792 | no | — |
| 393 | C25 | — | 4 | 16128 | no | — |
| 394 | C25 | — | 4 | 16128 | no | — |
| 395 | C25 | — | 4 | 32256 | no | — |
| 396 | C25 | — | 4 | 5376 | no | — |
| 397 | C25 | — | 4 | 32256 | no | — |
| 398 | C25 | — | 4 | 10752 | no | — |
| 399 | C25 | — | 4 | 172032 | no | — |
| 400 | C25 | — | 4 | 344064 | no | — |
| 401 | C25 | — | 4 | 896 | no | — |
| 402 | C25 | — | 8 | 672 | no | — |
| 403 | C25 | C2×H(5,𝔽2) | 1 | 504 | yes | — |
| 404 | C25 | C2×H(5,𝔽2) | 1 | 336 | yes | — |
| 405 | C25 | C26 | 1 | 21 | yes | — |
| 406 | C25 | C26 | 1 | 252 | yes | — |
| 407 | C25 | C26 | 1 | 126 | yes | — |
| 408 | C25 | C26 | 1 | 84 | yes | — |
| 409 | C25 | C26 | 1 | 168 | yes | — |
| 410 | C25 | C26 | 1 | 63 | yes | — |
| 411 | C25 | C26 | 1 | 14 | yes | — |
| 412 | C25 | C26 | 1 | 7 | yes | — |
| 413 | C25 | C26 | 1 | 8 | yes | complemented |
| 414 | H(5,𝔽2) | — | 16 | 448 | no | — |
| 415 | C2×#41 | — | 4 | 1008 | no | — |
| 416 | C22×Q8 | C26 | 1 | 56 | yes | complemented |
| 417 | C22×D4 | — | 2 | 1008 | no | — |
| 418 | C22×D4 | — | 2 | 1008 | no | — |
| 419 | C22×D4 | — | 2 | 4032 | no | — |
| 420 | C22×D4 | — | 4 | 1008 | no | — |
| 421 | C22×D4 | — | 4 | 2016 | no | — |
| 422 | C22×D4 | — | 4 | 4032 | no | — |
| 423 | C22×D4 | — | 4 | 4032 | no | — |
| 424 | C22×D4 | — | 4 | 1008 | no | — |
| 425 | C22×D4 | — | 8 | 4032 | no | — |
| 426 | C22×D4 | — | 8 | 4032 | no | — |
| 427 | C22×D4 | — | 8 | 10752 | no | — |
| 428 | C22×D4 | C26 | 1 | 336 | yes | — |
| 429 | C22×D4 | C26 | 1 | 1008 | yes | — |
| 430 | C22×D4 | C26 | 1 | 168 | yes | complemented |
| 431 | C23×C4 | — | 2 | 504 | no | — |
| 432 | C23×C4 | — | 4 | 504 | no | — |
| 433 | C23×C4 | — | 4 | 1008 | no | — |
| 434 | C23×C4 | — | 8 | 672 | no | — |
| 435 | C23×C4 | C26 | 1 | 84 | yes | — |
| 436 | C23×C4 | C26 | 1 | 504 | yes | — |
| 437 | C23×C4 | C26 | 1 | 168 | yes | complemented |
| 438 | #127 | — | 4 | 672 | no | — |
| 439 | #126 | — | 4 | 1344 | no | — |
| 440 | #124 | — | 4 | 2016 | no | — |
| 441 | #123 | — | 4 | 2016 | no | — |
| 442 | #123 | — | 4 | 2016 | no | — |
| 443 | C22⋊Q8 | — | 4 | 2016 | no | — |
| 444 | #121 | — | 4 | 4032 | no | — |
| 445 | #121 | — | 4 | 2016 | no | — |
| 446 | #120 | — | 2 | 1344 | no | — |
| 447 | #120 | — | 2 | 4032 | no | — |
| 448 | #120 | — | 2 | 4032 | no | — |
| 449 | #120 | — | 2 | 1344 | no | — |
| 450 | #120 | — | 4 | 8064 | no | — |
| 451 | #120 | — | 4 | 8064 | no | — |
| 452 | #120 | — | 4 | 2016 | no | — |
| 453 | #120 | — | 4 | 672 | no | — |
| 454 | C4×D4 | — | 4 | 4032 | no | — |
| 455 | #117 | — | 4 | 1008 | no | — |
| 456 | C2×C4⋊C4 | C26 | 1 | 1008 | yes | complemented |
| 457 | C2×C22⋊C4 | — | 2 | 1008 | no | — |
| 458 | C2×C22⋊C4 | — | 2 | 1008 | no | — |
| 459 | C2×C22⋊C4 | — | 2 | 4032 | no | — |
| 460 | C2×C22⋊C4 | — | 4 | 4032 | no | — |
| 461 | C2×C22⋊C4 | — | 4 | 4032 | no | — |
| 462 | C2×C22⋊C4 | — | 4 | 1008 | no | — |
| 463 | C2×C22⋊C4 | — | 4 | 2016 | no | — |
| 464 | C2×C22⋊C4 | — | 4 | 1008 | no | — |
| 465 | C2×C22⋊C4 | C26 | 1 | 1008 | yes | — |
| 466 | C2×C22⋊C4 | C26 | 1 | 1008 | yes | — |
| 467 | C2×C22⋊C4 | C26 | 1 | 2016 | yes | — |
| 468 | C2×C22⋊C4 | C26 | 1 | 1008 | yes | complemented |
| 469 | C2×C42 | C26 | 1 | 336 | yes | complemented |
| 470 | #95 | C26 | 1 | 1344 | yes | complemented |
| 471 | C24 | — | 2 | 672 | no | — |
| 472 | C24 | — | 2 | 252 | no | — |
| 473 | C24 | — | 2 | 5376 | no | — |
| 474 | C24 | — | 2 | 2016 | no | — |
| 475 | C24 | — | 2 | 2016 | no | — |
| 476 | C24 | — | 2 | 1008 | no | — |
| 477 | C24 | — | 2 | 1008 | no | — |
| 478 | C24 | — | 2 | 504 | no | — |
| 479 | C24 | — | 2 | 252 | no | — |
| 480 | C24 | — | 2 | 1008 | no | — |
| 481 | C24 | — | 2 | 1008 | no | — |
| 482 | C24 | — | 2 | 504 | no | — |
| 483 | C24 | — | 4 | 2016 | no | — |
| 484 | C24 | — | 4 | 2016 | no | — |
| 485 | C24 | — | 4 | 28 | no | — |
| 486 | C24 | — | 4 | 252 | no | — |
| 487 | C24 | — | 4 | 252 | no | — |
| 488 | C24 | — | 4 | 504 | no | — |
| 489 | C24 | — | 4 | 84 | no | — |
| 490 | C24 | — | 4 | 504 | no | — |
| 491 | C24 | — | 4 | 168 | no | — |
| 492 | C24 | — | 4 | 336 | no | — |
| 493 | C24 | — | 4 | 56 | no | — |
| 494 | C24 | — | 4 | 8064 | no | — |
| 495 | C24 | — | 4 | 8064 | no | — |
| 496 | C24 | — | 4 | 8064 | no | — |
| 497 | C24 | — | 4 | 4032 | no | — |
| 498 | C24 | — | 4 | 8064 | no | — |
| 499 | C24 | — | 4 | 4032 | no | — |
| 500 | C24 | — | 4 | 21504 | no | — |
| 501 | C24 | — | 4 | 2016 | no | — |
| 502 | C24 | — | 4 | 4032 | no | — |
| 503 | C24 | — | 4 | 8064 | no | — |
| 504 | C24 | — | 4 | 8064 | no | — |
| 505 | C24 | — | 4 | 16128 | no | — |
| 506 | C24 | — | 4 | 4032 | no | — |
| 507 | C24 | — | 4 | 8064 | no | — |
| 508 | C24 | — | 4 | 8064 | no | — |
| 509 | C24 | — | 4 | 2016 | no | — |
| 510 | C24 | — | 4 | 2688 | no | — |
| 511 | C24 | — | 4 | 2688 | no | — |
| 512 | C24 | — | 4 | 16128 | no | — |
| 513 | C24 | — | 4 | 8064 | no | — |
| 514 | C24 | — | 4 | 8064 | no | — |
| 515 | C24 | — | 4 | 5376 | no | — |
| 516 | C24 | — | 4 | 7168 | no | — |
| 517 | C24 | — | 4 | 129024 | no | — |
| 518 | C24 | — | 4 | 64512 | no | — |
| 519 | C24 | — | 4 | 258048 | no | — |
| 520 | C24 | — | 4 | 14336 | no | — |
| 521 | C24 | — | 4 | 172032 | no | — |
| 522 | C24 | — | 4 | 2688 | no | — |
| 523 | C24 | — | 4 | 672 | no | — |
| 524 | C24 | — | 8 | 1008 | no | — |
| 525 | C24 | — | 8 | 1344 | no | — |
| 526 | C24 | — | 16 | 768 | no | — |
| 527 | C24 | C22×H(5,𝔽2) | 1 | 84 | yes | — |
| 528 | C24 | C22×H(5,𝔽2) | 1 | 504 | yes | — |
| 529 | C24 | C22×H(5,𝔽2) | 1 | 252 | yes | — |
| 530 | C24 | C22×H(5,𝔽2) | 1 | 56 | yes | — |
| 531 | C24 | C22×H(5,𝔽2) | 1 | 84 | yes | — |
| 532 | C24 | C27 | 1 | 24 | yes | — |
| 533 | C24 | C27 | 1 | 42 | yes | — |
| 534 | C24 | C27 | 1 | 21 | yes | — |
| 535 | #41 | — | 16 | 672 | no | — |
| 536 | C2×Q8 | — | 4 | 168 | no | — |
| 537 | C2×D4 | — | 2 | 2016 | no | — |
| 538 | C2×D4 | — | 2 | 2016 | no | — |
| 539 | C2×D4 | — | 4 | 2016 | no | — |
| 540 | C2×D4 | — | 4 | 504 | no | — |
| 541 | C2×D4 | — | 4 | 1344 | no | — |
| 542 | C2×D4 | — | 8 | 2016 | no | — |
| 543 | C2×D4 | — | 8 | 8064 | no | — |
| 544 | C2×D4 | — | 8 | 8064 | no | — |
| 545 | C2×D4 | — | 16 | 672 | no | — |
| 546 | C22×C4 | — | 2 | 504 | no | — |
| 547 | C22×C4 | — | 2 | 1008 | no | — |
| 548 | C22×C4 | — | 4 | 1008 | no | — |
| 549 | C22×C4 | — | 4 | 504 | no | — |
| 550 | C22×C4 | — | 8 | 1008 | no | — |
| 551 | C22×C4 | — | 8 | 1344 | no | — |
| 552 | C22×C4 | C27 | 1 | 168 | yes | — |
| 553 | C4⋊C4 | — | 4 | 1008 | no | — |
| 554 | C22⋊C4 | — | 2 | 2016 | no | — |
| 555 | C22⋊C4 | — | 2 | 2016 | no | — |
| 556 | C22⋊C4 | — | 4 | 2016 | no | — |
| 557 | C22⋊C4 | — | 4 | 1008 | no | — |
| 558 | C42 | — | 4 | 336 | no | — |
| 559 | C23 | — | 2 | 672 | no | — |
| 560 | C23 | — | 2 | 768 | no | — |
| 561 | C23 | — | 2 | 504 | no | — |
| 562 | C23 | — | 2 | 84 | no | — |
| 563 | C23 | — | 2 | 2016 | no | — |
| 564 | C23 | — | 2 | 2016 | no | — |
| 565 | C23 | — | 2 | 504 | no | — |
| 566 | C23 | — | 2 | 252 | no | — |
| 567 | C23 | — | 2 | 168 | no | — |
| 568 | C23 | — | 4 | 168 | no | — |
| 569 | C23 | — | 4 | 504 | no | — |
| 570 | C23 | — | 4 | 504 | no | — |
| 571 | C23 | — | 4 | 168 | no | — |
| 572 | C23 | — | 4 | 2016 | no | — |
| 573 | C23 | — | 4 | 4032 | no | — |
| 574 | C23 | — | 4 | 2016 | no | — |
| 575 | C23 | — | 4 | 8064 | no | — |
| 576 | C23 | — | 4 | 21504 | no | — |
| 577 | C23 | — | 4 | 8064 | no | — |
| 578 | C23 | — | 4 | 1008 | no | — |
| 579 | C23 | — | 4 | 1008 | no | — |
| 580 | C23 | — | 4 | 2016 | no | — |
| 581 | C23 | — | 4 | 5376 | no | — |
| 582 | C23 | — | 4 | 5376 | no | — |
| 583 | C23 | — | 4 | 21504 | no | — |
| 584 | C23 | — | 4 | 64512 | no | — |
| 585 | C23 | — | 4 | 21504 | no | — |
| 586 | C23 | — | 4 | 16128 | no | — |
| 587 | C23 | — | 4 | 6144 | no | — |
| 588 | C23 | — | 4 | 224 | no | — |
| 589 | C23 | — | 4 | 672 | no | — |
| 590 | C23 | — | 4 | 1008 | no | — |
| 591 | C23 | — | 4 | 336 | no | — |
| 592 | C23 | — | 8 | 1008 | no | — |
| 593 | C23 | — | 16 | 1344 | no | — |
| 594 | C23 | — | 16 | 56 | no | — |
| 595 | C23 | #62817 | 1 | 112 | yes | complemented |
| 596 | C23 | C23×H(5,𝔽2) | 1 | 84 | yes | — |
| 597 | C23 | C23×H(5,𝔽2) | 1 | 126 | yes | — |
| 598 | C23 | C28 | 1 | 1 | yes | characteristic |
| 599 | Q8 | — | 16 | 56 | no | — |
| 600 | D4 | — | 4 | 1344 | no | — |
| 601 | D4 | — | 8 | 2016 | no | — |
| 602 | D4 | — | 16 | 168 | no | — |
| 603 | C2×C4 | — | 2 | 504 | no | — |
| 604 | C2×C4 | — | 4 | 336 | no | — |
| 605 | C2×C4 | — | 8 | 1008 | no | — |
| 606 | C2×C4 | — | 16 | 168 | no | — |
| 607 | C22 | — | 2 | 672 | no | — |
| 608 | C22 | — | 2 | 252 | no | — |
| 609 | C22 | — | 2 | 252 | no | — |
| 610 | C22 | — | 4 | 112 | no | — |
| 611 | C22 | — | 4 | 2016 | no | — |
| 612 | C22 | — | 4 | 4032 | no | — |
| 613 | C22 | — | 4 | 1008 | no | — |
| 614 | C22 | — | 4 | 224 | no | — |
| 615 | C22 | — | 4 | 2688 | no | — |
| 616 | C22 | — | 4 | 168 | no | — |
| 617 | C22 | — | 4 | 168 | no | — |
| 618 | C22 | — | 16 | 336 | no | — |
| 619 | C22 | — | 64 | 8 | no | — |
| 620 | C22 | C2×#62817 | 1 | 84 | yes | — |
| 621 | C22 | C24×H(5,𝔽2) | 1 | 7 | yes | — |
| 622 | C4 | — | 4 | 168 | no | — |
| 623 | C2 | — | 2 | 84 | no | — |
| 624 | C2 | — | 4 | 84 | no | — |
| 625 | C2 | — | 8 | 24 | no | — |
| 626 | C2 | C22×#62817 | 1 | 7 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C23 | C28 |
| 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. #72236365 | C2 | semidirect |
| 2. #72218920 | C2 | semidirect |
| 3. C23×#2846 | C2 | semidirect |
| 4. #72217511 | C2 | semidirect |
| 5. C29 | C22 | semidirect |
| 6. C2×#62817 | C22 | semidirect |
| 7. C24×#120 | C22 | semidirect |
| 8. #8108058 | C22 | semidirect |
| 9. #8108057 | C22 | semidirect |
| 10. #8093108 | C22 | semidirect |
| 11. #8093107 | C22 | semidirect |
| 12. #7708352 | C22 | semidirect |
| 13. #7708349 | C22 | semidirect |
| 14. #7670230 | C22 | semidirect |
| 15. #7670206 | C22 | semidirect |
| 16. #7670203 | C22 | semidirect |
| 17. #7642273 | C22 | semidirect |
| 18. #7642247 | C22 | semidirect |
| 19. #7642244 | C22 | semidirect |
| 20. #7641846 | C22 | semidirect |
| 21. #7641845 | C22 | semidirect |
| 22. C22×#2846 | C22 | semidirect |
| 23. C22×#2846 | C22 | semidirect |
| 24. #7630944 | C22 | semidirect |
| 25. #7630939 | C22 | semidirect |
| 26. #7626202 | C22 | semidirect |
| 27. C23×#379 | C22 | semidirect |
| 31. C25×D4 | C23 | semidirect |
| 33. C2×#3490 | C23 | semidirect |
| 34. C2×#3484 | C23 | semidirect |
| 35. C2×#3532 | C23 | semidirect |
| 38. C23×#120 | C23 | semidirect |
| 39. C23×#120 | C23 | semidirect |
| 40. C23×#120 | C23 | semidirect |
| 41. C24×C22⋊C4 | C23 | semidirect |
| 42. #59192 | C23 | semidirect |
| 43. #59006 | C23 | semidirect |
| 44. #58991 | C23 | semidirect |
| 45. #58990 | C23 | semidirect |
| 46. #53169 | C23 | semidirect |
| 47. #53158 | C23 | semidirect |
| 48. #45458 | C23 | semidirect |
| 49. #45457 | C23 | semidirect |
| 50. #45439 | C23 | semidirect |
| 51. #45438 | C23 | semidirect |
| 52. #37848 | C23 | semidirect |
| 53. #37833 | C23 | semidirect |
| 54. #37832 | C23 | semidirect |
| 55. #37660 | C23 | semidirect |
| 56. #37645 | C23 | semidirect |
| 57. #37644 | C23 | semidirect |
| 58. #37475 | C23 | semidirect |
| 59. #37436 | C23 | semidirect |
| 60. #36725 | C23 | semidirect |
| 61. #36714 | C23 | semidirect |
| 62. #36703 | C23 | semidirect |
| 63. #36702 | C23 | semidirect |
| 64. #36614 | C23 | semidirect |
| 66. C2×#2846 | C23 | semidirect |
| 67. C2×#2846 | C23 | semidirect |
| 68. C2×#2846 | C23 | semidirect |
| 69. C2×#2846 | C23 | semidirect |
| 70. C2×#2846 | C23 | semidirect |
| 71. C2×#2846 | C23 | semidirect |
| 72. #36158 | C23 | semidirect |
| 73. #36152 | C23 | semidirect |
| 74. #36098 | C23 | semidirect |
| 75. D4×#120 | C23 | semidirect |
| 76. #35390 | C23 | semidirect |
| 77. #35369 | C23 | semidirect |
| 78. #35367 | C23 | semidirect |
| 79. #35350 | C23 | semidirect |
| 80. #35348 | C23 | semidirect |
| 81. #35346 | C23 | semidirect |
| 82. #35222 | C23 | semidirect |
| 83. #35050 | C23 | semidirect |
| 84. #34992 | C23 | semidirect |
| 85. #34988 | C23 | semidirect |
| 86. #34982 | C23 | semidirect |
| 87. #34981 | C23 | semidirect |
| 88. #34980 | C23 | semidirect |
| 89. #34980 | C23 | semidirect |
| 90. #34356 | C23 | semidirect |
| 91. #34198 | C23 | semidirect |
| 92. #34176 | C23 | semidirect |
| 93. #34171 | C23 | semidirect |
| 95. C22×#379 | C23 | semidirect |
| 96. C22×#379 | C23 | semidirect |
| 97. C22×#379 | C23 | semidirect |
| 110. C27 | C24 | semidirect |
| 111. C22×H(5,𝔽2) | C24 | semidirect |
| 114. C24×D4 | C24 | semidirect |
| 115. C24×D4 | C24 | semidirect |
| 116. C25×C4 | C24 | semidirect |
| 118. C2×H(3,𝔽4) | C24 | semidirect |
| 119. C2×#560 | C24 | semidirect |
| 122. C2×#551 | C24 | semidirect |
| 123. C2×#546 | C24 | semidirect |
| 124. C2×D42 | C24 | semidirect |
| 125. C2×#543 | C24 | semidirect |
| 126. C2×#538 | C24 | semidirect |
| 127. C2×#535 | C24 | semidirect |
| 128. C2×#534 | C24 | semidirect |
| 129. C2×#534 | C24 | semidirect |
| 130. C2×#525 | C24 | semidirect |
| 139. C22×#120 | C24 | semidirect |
| 140. C22×#120 | C24 | semidirect |
| 141. C22×#120 | C24 | semidirect |
| 142. C22×#120 | C24 | semidirect |
| 143. C22×#120 | C24 | semidirect |
| 144. C22×#120 | C24 | semidirect |
| 145. C2×#518 | C24 | semidirect |
| 149. C23×C22⋊C4 | C24 | semidirect |
| 150. C23×C22⋊C4 | C24 | semidirect |
| 151. C23×C22⋊C4 | C24 | semidirect |
| 152. #2849 | C24 | semidirect |
| 153. #2848 | C24 | semidirect |
| 154. #2847 | C24 | semidirect |
| 157. #2846 | C24 | semidirect |
| 158. #2846 | C24 | semidirect |
| 159. #2846 | C24 | semidirect |
| 160. #2846 | C24 | semidirect |
| 161. #2846 | C24 | semidirect |
| 162. #2846 | C24 | semidirect |
| 163. #2842 | C24 | semidirect |
| 164. #2840 | C24 | semidirect |
| 165. #2812 | C24 | semidirect |
| 166. #2736 | C24 | semidirect |
| 167. #2735 | C24 | semidirect |
| 168. #2697 | C24 | semidirect |
| 169. #2685 | C24 | semidirect |
| 170. #2684 | C24 | semidirect |
| 171. #2679 | C24 | semidirect |
| 172. #2678 | C24 | semidirect |
| 173. #2670 | C24 | semidirect |
| 174. #2669 | C24 | semidirect |
| 175. #2668 | C24 | semidirect |
| 176. #2626 | C24 | semidirect |
| 177. #2622 | C24 | semidirect |
| 178. #2617 | C24 | semidirect |
| 179. #2613 | C24 | semidirect |
| 180. #2561 | C24 | semidirect |
| 181. #2539 | C24 | semidirect |
| 182. #2534 | C24 | semidirect |
| 183. #2483 | C24 | semidirect |
| 184. #2482 | C24 | semidirect |
| 185. #2480 | C24 | semidirect |
| 186. #2472 | C24 | semidirect |
| 187. #2437 | C24 | semidirect |
| 188. #2435 | C24 | semidirect |
| 189. #2433 | C24 | semidirect |
| 190. #2424 | C24 | semidirect |
| 191. #2418 | C24 | semidirect |
| 192. #2412 | C24 | semidirect |
| 193. #2411 | C24 | semidirect |
| 194. #2410 | C24 | semidirect |
| 195. #2410 | C24 | semidirect |
| 196. #2408 | C24 | semidirect |
| 197. #2405 | C24 | semidirect |
| 198. #2405 | C24 | semidirect |
| 199. #2404 | C24 | semidirect |
| 200. #2403 | C24 | semidirect |
| 201. #2403 | C24 | semidirect |
| 202. #2375 | C24 | semidirect |
| 203. #2358 | C24 | semidirect |
| 204. #2342 | C24 | semidirect |
| 205. D4×C22⋊C4 | C24 | semidirect |
| 206. #2321 | C24 | semidirect |
| 207. #2315 | C24 | semidirect |
| 208. #2312 | C24 | semidirect |
| 209. #2309 | C24 | semidirect |
| 210. #2308 | C24 | semidirect |
| 211. #2308 | C24 | semidirect |
| 212. C4×#120 | C24 | semidirect |
| 213. #2280 | C24 | semidirect |
| 218. C2×#379 | C24 | semidirect |
| 219. C2×#379 | C24 | semidirect |
| 220. C2×#379 | C24 | semidirect |
| 221. C2×#379 | C24 | semidirect |
| 222. C2×#379 | C24 | semidirect |
| 223. C2×#379 | C24 | semidirect |
| 224. #2273 | C24 | semidirect |
| 249. C26 | H(5,𝔽2) | semidirect |
| 263. C22×#41 | C25 | semidirect |
| 274. C23×D4 | C25 | semidirect |
| 288. C2×#127 | C25 | semidirect |
| 289. C2×#126 | C25 | semidirect |
| 290. C2×#124 | C25 | semidirect |
| 292. C2×#123 | C25 | semidirect |
| 293. C2×#123 | C25 | semidirect |
| 294. C2×C22⋊Q8 | C25 | semidirect |
| 295. C2×#121 | C25 | semidirect |
| 296. C2×#121 | C25 | semidirect |
| 313. C2×#120 | C25 | semidirect |
| 314. C2×#120 | C25 | semidirect |
| 316. C2×C4×D4 | C25 | semidirect |
| 317. C2×#117 | C25 | semidirect |
| 330. C22×C22⋊C4 | C25 | semidirect |
| 331. #399 | C25 | semidirect |
| 332. #397 | C25 | semidirect |
| 333. #396 | C25 | semidirect |
| 334. #394 | C25 | semidirect |
| 335. #393 | C25 | semidirect |
| 336. #392 | C25 | semidirect |
| 337. #390 | C25 | semidirect |
| 338. #388 | C25 | semidirect |
| 339. #386 | C25 | semidirect |
| 340. #386 | C25 | semidirect |
| 341. #385 | C25 | semidirect |
| 342. #381 | C25 | semidirect |
| 343. #380 | C25 | semidirect |
| 350. #379 | C25 | semidirect |
| 351. C4×C22⋊C4 | C25 | semidirect |
| 413. C25 | C26 | semidirect |
| 416. C22×Q8 | C26 | semidirect |
| 430. C22×D4 | C26 | semidirect |
| 437. C23×C4 | C26 | semidirect |
| 456. C2×C4⋊C4 | C26 | semidirect |
| 468. C2×C22⋊C4 | C26 | semidirect |
| 469. C2×C42 | C26 | semidirect |
| 470. #95 | C26 | semidirect |
| 595. C23 | #62817 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72236365 | 2 |
| #72218920 | 2 |
| C23×#2846 | 2 |
| #72217511 | 2 |