Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
5181 conjugacy classes of subgroups.
The subgroup lattice has 431 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #59935 | C2 | 1 | 6 | yes | maximal, complemented |
| 2 | #58998 | C2 | 1 | 6 | yes | maximal, complemented |
| 3 | #51601 | C2 | 1 | 12 | yes | maximal, complemented |
| 4 | #48838 | C2 | 1 | 12 | yes | maximal, complemented |
| 5 | #46152 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #46004 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #39616 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | #39594 | C2 | 1 | 6 | yes | maximal, complemented |
| 9 | #36562 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #34524 | C2 | 1 | 2 | yes | maximal |
| 11 | C4×H(3,𝔽4) | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | C2×H(3,𝔽4) | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#557 | C22 | 1 | 3 | yes | complemented |
| 14 | C2×#554 | C22 | 1 | 3 | yes | — |
| 15 | C2×D4×Q8 | C22 | 1 | 6 | yes | — |
| 16 | C22×C22⋊Q8 | C22 | 1 | 6 | yes | complemented |
| 17 | #2868 | C22 | 1 | 2 | yes | complemented |
| 18 | #2862 | C22 | 1 | 3 | yes | complemented |
| 19 | #2859 | C22 | 1 | 6 | yes | complemented |
| 20 | #2848 | C22 | 1 | 2 | yes | complemented |
| 21 | #2844 | C22 | 1 | 6 | yes | complemented |
| 22 | #2811 | C22 | 1 | 6 | yes | complemented |
| 23 | #2809 | C22 | 1 | 12 | yes | complemented |
| 24 | #2804 | C22 | 1 | 6 | yes | — |
| 25 | #2784 | C22 | 1 | 12 | yes | — |
| 26 | #2763 | C22 | 1 | 24 | yes | complemented |
| 27 | #2720 | C22 | 1 | 24 | yes | complemented |
| 28 | #2720 | C22 | 1 | 24 | yes | complemented |
| 29 | #2720 | C22 | 1 | 24 | yes | complemented |
| 30 | #2692 | C22 | 1 | 24 | yes | — |
| 31 | #2683 | C22 | 1 | 12 | yes | — |
| 32 | #2677 | C22 | 1 | 12 | yes | complemented |
| 33 | #2660 | C22 | 1 | 12 | yes | complemented |
| 34 | #2626 | C22 | 1 | 12 | yes | complemented |
| 35 | #2612 | C22 | 1 | 12 | yes | complemented |
| 36 | #2574 | C22 | 1 | 24 | yes | complemented |
| 37 | #2568 | C22 | 1 | 6 | yes | complemented |
| 38 | #2567 | C22 | 1 | 3 | yes | complemented |
| 39 | #2567 | C22 | 1 | 12 | yes | complemented |
| 40 | #2566 | C22 | 1 | 12 | yes | — |
| 41 | #2566 | C22 | 1 | 6 | yes | — |
| 42 | #2565 | C22 | 1 | 6 | yes | complemented |
| 43 | #2556 | C22 | 1 | 24 | yes | complemented |
| 44 | #2542 | C22 | 1 | 3 | yes | — |
| 45 | #2542 | C22 | 1 | 6 | yes | — |
| 46 | #2502 | C22 | 1 | 12 | yes | complemented |
| 47 | #2497 | C22 | 1 | 24 | yes | complemented |
| 48 | #2492 | C22 | 1 | 12 | yes | complemented |
| 49 | #2487 | C22 | 1 | 12 | yes | — |
| 50 | #2449 | C22 | 1 | 24 | yes | — |
| 51 | #2440 | C22 | 1 | 24 | yes | complemented |
| 52 | #2437 | C22 | 1 | 12 | yes | complemented |
| 53 | #2434 | C22 | 1 | 12 | yes | complemented |
| 54 | #2434 | C22 | 1 | 6 | yes | complemented |
| 55 | #2429 | C22 | 1 | 12 | yes | complemented |
| 56 | #2429 | C22 | 1 | 12 | yes | complemented |
| 57 | #2417 | C22 | 1 | 12 | yes | — |
| 58 | #2409 | C22 | 1 | 6 | yes | — |
| 59 | #2379 | C22 | 1 | 3 | yes | — |
| 60 | #2379 | C22 | 1 | 6 | yes | — |
| 61 | #2379 | C22 | 1 | 6 | yes | — |
| 62 | #2375 | C22 | 1 | 6 | yes | — |
| 63 | #2372 | C22 | 1 | 12 | yes | — |
| 64 | #2360 | C22 | 1 | 12 | yes | complemented |
| 65 | #2358 | C22 | 1 | 12 | yes | — |
| 66 | #2345 | C22 | 1 | 6 | yes | complemented |
| 67 | #2326 | C22 | 1 | 12 | yes | — |
| 68 | #2321 | C22 | 1 | 12 | yes | — |
| 69 | C4×#124 | C22 | 1 | 6 | yes | — |
| 70 | C4×#124 | C22 | 1 | 3 | yes | — |
| 71 | C4×#124 | C22 | 1 | 6 | yes | — |
| 72 | C4×#120 | C22 | 1 | 6 | yes | — |
| 73 | #2295 | C22 | 1 | 6 | yes | complemented |
| 74 | C42×Q8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 75 | C23×Q8 | C23 | 1 | 6 | yes | — |
| 76 | C24×C4 | C23 | 1 | 2 | yes | — |
| 77 | H(3,𝔽4) | Q8 | 1 | 16 | yes | complemented |
| 78 | #557 | — | 4 | 12 | no | — |
| 79 | #554 | — | 4 | 12 | no | — |
| 80 | D4×Q8 | — | 4 | 24 | no | — |
| 81 | C2×C4⋊Q8 | C23 | 1 | 3 | yes | — |
| 82 | C2×C4⋊Q8 | C23 | 1 | 12 | yes | — |
| 83 | C2×C4⋊Q8 | C23 | 1 | 6 | yes | — |
| 84 | C2×C4⋊Q8 | C23 | 1 | 3 | yes | — |
| 85 | C2×C4⋊Q8 | C23 | 1 | 6 | yes | — |
| 86 | C2×#125 | C23 | 1 | 6 | yes | — |
| 87 | C2×#125 | C23 | 1 | 6 | yes | — |
| 88 | C2×#125 | C23 | 1 | 12 | yes | — |
| 89 | C2×#124 | C23 | 1 | 6 | yes | — |
| 90 | C2×#124 | C23 | 1 | 3 | yes | — |
| 91 | C2×C22⋊Q8 | — | 4 | 24 | no | — |
| 92 | C2×C22⋊Q8 | C23 | 1 | 12 | yes | — |
| 93 | C2×C22⋊Q8 | C23 | 1 | 6 | yes | — |
| 94 | C2×C22⋊Q8 | C23 | 1 | 12 | yes | — |
| 95 | C2×C22⋊Q8 | C23 | 1 | 12 | yes | — |
| 96 | C2×C22⋊Q8 | C23 | 1 | 24 | yes | — |
| 97 | C2×C22⋊Q8 | C23 | 1 | 24 | yes | — |
| 98 | C2×#120 | C23 | 1 | 6 | yes | — |
| 99 | C2×C4×Q8 | C23 | 1 | 6 | yes | — |
| 100 | C2×C4×Q8 | C23 | 1 | 3 | yes | — |
| 101 | C2×C4×Q8 | C23 | 1 | 6 | yes | — |
| 102 | C2×C4×Q8 | C23 | 1 | 3 | yes | — |
| 103 | C2×C4×D4 | C23 | 1 | 6 | yes | — |
| 104 | C2×C4×D4 | C23 | 1 | 12 | yes | — |
| 105 | C2×C4×D4 | C23 | 1 | 3 | yes | — |
| 106 | C2×C4×D4 | C23 | 1 | 6 | yes | — |
| 107 | C22×C4⋊C4 | C23 | 1 | 6 | yes | — |
| 108 | C22×C4⋊C4 | C23 | 1 | 12 | yes | — |
| 109 | C22×C22⋊C4 | C23 | 1 | 12 | yes | — |
| 110 | #400 | C23 | 1 | 12 | yes | — |
| 111 | #400 | C23 | 1 | 12 | yes | — |
| 112 | #400 | C23 | 1 | 24 | yes | — |
| 113 | #399 | C23 | 1 | 24 | yes | — |
| 114 | #399 | C23 | 1 | 12 | yes | — |
| 115 | #398 | C23 | 1 | 24 | yes | — |
| 116 | #398 | C23 | 1 | 24 | yes | — |
| 117 | #398 | C23 | 1 | 24 | yes | — |
| 118 | #396 | C23 | 1 | 24 | yes | — |
| 119 | #396 | C23 | 1 | 24 | yes | — |
| 120 | #396 | C23 | 1 | 24 | yes | — |
| 121 | #395 | C23 | 1 | 12 | yes | — |
| 122 | #395 | C23 | 1 | 24 | yes | — |
| 123 | #395 | C23 | 1 | 24 | yes | — |
| 124 | #395 | C23 | 1 | 12 | yes | — |
| 125 | #395 | C23 | 1 | 24 | yes | — |
| 126 | #393 | C23 | 1 | 24 | yes | — |
| 127 | #393 | C23 | 1 | 12 | yes | — |
| 128 | #391 | C23 | 1 | 3 | yes | — |
| 129 | #391 | C23 | 1 | 6 | yes | — |
| 130 | #391 | C23 | 1 | 6 | yes | — |
| 131 | #391 | C23 | 1 | 12 | yes | — |
| 132 | #391 | C23 | 1 | 12 | yes | — |
| 133 | #391 | C23 | 1 | 12 | yes | — |
| 134 | #391 | C23 | 1 | 24 | yes | — |
| 135 | #391 | C23 | 1 | 12 | yes | — |
| 136 | #390 | C23 | 1 | 6 | yes | — |
| 137 | #390 | C23 | 1 | 3 | yes | — |
| 138 | #390 | C23 | 1 | 12 | yes | — |
| 139 | #390 | C23 | 1 | 6 | yes | — |
| 140 | #389 | C23 | 1 | 12 | yes | — |
| 141 | #389 | C23 | 1 | 24 | yes | — |
| 142 | #389 | C23 | 1 | 24 | yes | — |
| 143 | #389 | C23 | 1 | 24 | yes | — |
| 144 | #388 | C23 | 1 | 12 | yes | — |
| 145 | #388 | C23 | 1 | 24 | yes | — |
| 146 | #388 | C23 | 1 | 24 | yes | — |
| 147 | #388 | C23 | 1 | 24 | yes | — |
| 148 | #388 | C23 | 1 | 12 | yes | — |
| 149 | #388 | C23 | 1 | 12 | yes | — |
| 150 | #387 | C23 | 1 | 24 | yes | — |
| 151 | #387 | C23 | 1 | 24 | yes | — |
| 152 | #387 | C23 | 1 | 24 | yes | — |
| 153 | #386 | C23 | 1 | 24 | yes | — |
| 154 | #386 | C23 | 1 | 12 | yes | — |
| 155 | #386 | C23 | 1 | 6 | yes | — |
| 156 | #386 | C23 | 1 | 12 | yes | — |
| 157 | #385 | C23 | 1 | 12 | yes | — |
| 158 | #385 | C23 | 1 | 24 | yes | — |
| 159 | #385 | C23 | 1 | 24 | yes | — |
| 160 | #385 | C23 | 1 | 12 | yes | — |
| 161 | #385 | C23 | 1 | 24 | yes | — |
| 162 | #385 | C23 | 1 | 12 | yes | — |
| 163 | #385 | C23 | 1 | 12 | yes | — |
| 164 | #385 | C23 | 1 | 6 | yes | — |
| 165 | #385 | C23 | 1 | 12 | yes | — |
| 166 | #384 | C23 | 1 | 6 | yes | — |
| 167 | #384 | C23 | 1 | 6 | yes | — |
| 168 | #384 | C23 | 1 | 12 | yes | — |
| 169 | #384 | C23 | 1 | 12 | yes | — |
| 170 | #384 | C23 | 1 | 4 | yes | — |
| 171 | #382 | C23 | 1 | 6 | yes | — |
| 172 | #382 | C23 | 1 | 12 | yes | — |
| 173 | #382 | C23 | 1 | 3 | yes | — |
| 174 | #382 | C23 | 1 | 6 | yes | — |
| 175 | #382 | C23 | 1 | 6 | yes | — |
| 176 | #380 | C23 | 1 | 24 | yes | — |
| 177 | #380 | C23 | 1 | 6 | yes | — |
| 178 | #380 | C23 | 1 | 12 | yes | — |
| 179 | #379 | C23 | 1 | 4 | yes | — |
| 180 | #379 | C23 | 1 | 6 | yes | — |
| 181 | C4×C4⋊C4 | C23 | 1 | 6 | yes | — |
| 182 | C4×C4⋊C4 | C23 | 1 | 12 | yes | — |
| 183 | C4×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 184 | C4×C4⋊C4 | C23 | 1 | 6 | yes | — |
| 185 | C4×C22⋊C4 | C23 | 1 | 12 | yes | — |
| 186 | C4×C22⋊C4 | C23 | 1 | 6 | yes | — |
| 187 | C4×C22⋊C4 | C23 | 1 | 24 | yes | — |
| 188 | C4×C22⋊C4 | C23 | 1 | 12 | yes | — |
| 189 | #376 | C23 | 1 | 12 | yes | — |
| 190 | C43 | C23 | 1 | 2 | yes | — |
| 191 | C43 | C23 | 1 | 1 | yes | characteristic |
| 192 | C43 | C23 | 1 | 2 | yes | — |
| 193 | C25 | C24 | 1 | 2 | yes | — |
| 194 | C22×Q8 | — | 4 | 12 | no | — |
| 195 | C22×Q8 | — | 4 | 24 | no | — |
| 196 | C22×Q8 | C24 | 1 | 1 | yes | characteristic |
| 197 | C22×Q8 | C24 | 1 | 6 | yes | — |
| 198 | C22×Q8 | C24 | 1 | 12 | yes | — |
| 199 | C22×Q8 | C24 | 1 | 6 | yes | — |
| 200 | C22×Q8 | C24 | 1 | 3 | yes | — |
| 201 | C22×D4 | C24 | 1 | 3 | yes | — |
| 202 | C22×D4 | C24 | 1 | 6 | yes | — |
| 203 | C23×C4 | — | 4 | 12 | no | — |
| 204 | C23×C4 | C24 | 1 | 6 | yes | — |
| 205 | C23×C4 | C24 | 1 | 12 | yes | — |
| 206 | C23×C4 | C24 | 1 | 12 | yes | — |
| 207 | C23×C4 | C24 | 1 | 6 | yes | — |
| 208 | C4⋊Q8 | — | 4 | 24 | no | — |
| 209 | C4⋊Q8 | — | 4 | 6 | no | — |
| 210 | C4⋊Q8 | — | 4 | 12 | no | — |
| 211 | C4⋊Q8 | — | 4 | 12 | no | — |
| 212 | C4⋊Q8 | — | 4 | 6 | no | — |
| 213 | #125 | — | 4 | 12 | no | — |
| 214 | #125 | — | 4 | 12 | no | — |
| 215 | #125 | — | 4 | 24 | no | — |
| 216 | #124 | C2×Q8 | 1 | 48 | yes | complemented |
| 217 | #124 | C2×Q8 | 1 | 24 | yes | complemented |
| 218 | C22⋊Q8 | — | 2 | 48 | no | — |
| 219 | C22⋊Q8 | — | 4 | 48 | no | — |
| 220 | C22⋊Q8 | — | 4 | 48 | no | — |
| 221 | C22⋊Q8 | — | 4 | 24 | no | — |
| 222 | C22⋊Q8 | — | 4 | 24 | no | — |
| 223 | C22⋊Q8 | — | 4 | 12 | no | — |
| 224 | #120 | C2×Q8 | 1 | 48 | yes | complemented |
| 225 | C4×Q8 | — | 2 | 24 | no | — |
| 226 | C4×Q8 | — | 2 | 12 | no | — |
| 227 | C4×Q8 | — | 4 | 12 | no | — |
| 228 | C4×Q8 | — | 4 | 6 | no | — |
| 229 | C4×D4 | — | 4 | 24 | no | — |
| 230 | C4×D4 | — | 4 | 12 | no | — |
| 231 | C4×D4 | — | 4 | 12 | no | — |
| 232 | C4×D4 | — | 4 | 6 | no | — |
| 233 | C2×C4⋊C4 | — | 2 | 24 | no | — |
| 234 | C2×C4⋊C4 | — | 4 | 24 | no | — |
| 235 | C2×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 236 | C2×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 237 | C2×C4⋊C4 | C24 | 1 | 24 | yes | — |
| 238 | C2×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 239 | C2×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 240 | C2×C4⋊C4 | C24 | 1 | 24 | yes | — |
| 241 | C2×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 242 | C2×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 243 | C2×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 244 | C2×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 245 | C2×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 246 | C2×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 247 | C2×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 248 | C2×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 249 | C2×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 250 | C2×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 251 | C2×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 252 | C2×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 253 | C2×C4⋊C4 | C24 | 1 | 24 | yes | — |
| 254 | C2×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 255 | C2×C22⋊C4 | — | 4 | 24 | no | — |
| 256 | C2×C22⋊C4 | C24 | 1 | 24 | yes | — |
| 257 | C2×C22⋊C4 | C24 | 1 | 24 | yes | — |
| 258 | C2×C22⋊C4 | C24 | 1 | 12 | yes | — |
| 259 | C2×C22⋊C4 | C24 | 1 | 6 | yes | — |
| 260 | C2×C22⋊C4 | C24 | 1 | 12 | yes | — |
| 261 | C2×C22⋊C4 | C24 | 1 | 12 | yes | — |
| 262 | C2×C22⋊C4 | C24 | 1 | 6 | yes | — |
| 263 | C2×C22⋊C4 | C24 | 1 | 12 | yes | — |
| 264 | C2×C22⋊C4 | C24 | 1 | 6 | yes | — |
| 265 | C2×C22⋊C4 | C24 | 1 | 12 | yes | — |
| 266 | C2×C42 | C24 | 1 | 6 | yes | — |
| 267 | C2×C42 | C24 | 1 | 12 | yes | — |
| 268 | C2×C42 | C24 | 1 | 6 | yes | — |
| 269 | C2×C42 | C24 | 1 | 3 | yes | — |
| 270 | C2×C42 | C24 | 1 | 6 | yes | — |
| 271 | C2×C42 | C24 | 1 | 3 | yes | — |
| 272 | C2×C42 | C24 | 1 | 6 | yes | — |
| 273 | C2×C42 | C24 | 1 | 12 | yes | — |
| 274 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 275 | C2×C42 | C24 | 1 | 2 | yes | — |
| 276 | #95 | C24 | 1 | 24 | yes | — |
| 277 | #95 | C24 | 1 | 24 | yes | — |
| 278 | #95 | C24 | 1 | 12 | yes | — |
| 279 | #95 | C24 | 1 | 12 | yes | — |
| 280 | #95 | C24 | 1 | 12 | yes | — |
| 281 | #95 | C24 | 1 | 24 | yes | — |
| 282 | #95 | C24 | 1 | 6 | yes | — |
| 283 | #95 | C24 | 1 | 12 | yes | — |
| 284 | #95 | C24 | 1 | 24 | yes | — |
| 285 | #95 | C24 | 1 | 12 | yes | — |
| 286 | #95 | C24 | 1 | 24 | yes | — |
| 287 | C24 | — | 4 | 6 | no | — |
| 288 | C24 | — | 4 | 6 | no | — |
| 289 | C24 | C22×Q8 | 1 | 8 | yes | — |
| 290 | C24 | C25 | 1 | 6 | yes | — |
| 291 | C2×Q8 | — | 2 | 6 | no | — |
| 292 | C2×Q8 | — | 2 | 12 | no | — |
| 293 | C2×Q8 | — | 2 | 24 | no | — |
| 294 | C2×Q8 | — | 4 | 3 | no | — |
| 295 | C2×Q8 | — | 4 | 3 | no | — |
| 296 | C2×Q8 | — | 4 | 12 | no | — |
| 297 | C2×Q8 | — | 4 | 24 | no | — |
| 298 | C2×Q8 | — | 4 | 6 | no | — |
| 299 | C2×Q8 | — | 4 | 12 | no | — |
| 300 | C2×Q8 | — | 8 | 48 | no | — |
| 301 | C2×Q8 | C22×Q8 | 1 | 12 | yes | — |
| 302 | C2×D4 | — | 4 | 6 | no | — |
| 303 | C2×D4 | — | 4 | 3 | no | — |
| 304 | C2×D4 | — | 4 | 3 | no | — |
| 305 | C2×D4 | — | 4 | 6 | no | — |
| 306 | C2×D4 | C22×Q8 | 1 | 24 | yes | — |
| 307 | C2×D4 | C22×Q8 | 1 | 12 | yes | — |
| 308 | C22×C4 | — | 2 | 12 | no | — |
| 309 | C22×C4 | — | 2 | 24 | no | — |
| 310 | C22×C4 | — | 2 | 24 | no | — |
| 311 | C22×C4 | — | 4 | 12 | no | — |
| 312 | C22×C4 | — | 4 | 6 | no | — |
| 313 | C22×C4 | — | 4 | 24 | no | — |
| 314 | C22×C4 | — | 4 | 12 | no | — |
| 315 | C22×C4 | — | 4 | 24 | no | — |
| 316 | C22×C4 | — | 8 | 16 | no | — |
| 317 | C22×C4 | C25 | 1 | 3 | yes | — |
| 318 | C22×C4 | C25 | 1 | 12 | yes | — |
| 319 | C22×C4 | C25 | 1 | 6 | yes | — |
| 320 | C22×C4 | C25 | 1 | 12 | yes | — |
| 321 | C22×C4 | C25 | 1 | 6 | yes | — |
| 322 | C22×C4 | C25 | 1 | 2 | yes | — |
| 323 | C22×C4 | C25 | 1 | 6 | yes | — |
| 324 | C22×C4 | C25 | 1 | 3 | yes | — |
| 325 | C22×C4 | C25 | 1 | 6 | yes | — |
| 326 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 327 | C4⋊C4 | — | 2 | 24 | no | — |
| 328 | C4⋊C4 | — | 2 | 12 | no | — |
| 329 | C4⋊C4 | — | 2 | 48 | no | — |
| 330 | C4⋊C4 | — | 2 | 24 | no | — |
| 331 | C4⋊C4 | — | 2 | 12 | no | — |
| 332 | C4⋊C4 | — | 4 | 24 | no | — |
| 333 | C4⋊C4 | — | 4 | 24 | no | — |
| 334 | C4⋊C4 | — | 4 | 3 | no | — |
| 335 | C4⋊C4 | — | 4 | 6 | no | — |
| 336 | C4⋊C4 | — | 4 | 12 | no | — |
| 337 | C4⋊C4 | — | 4 | 6 | no | — |
| 338 | C4⋊C4 | — | 4 | 3 | no | — |
| 339 | C4⋊C4 | — | 4 | 6 | no | — |
| 340 | C4⋊C4 | — | 4 | 12 | no | — |
| 341 | C4⋊C4 | — | 4 | 6 | no | — |
| 342 | C4⋊C4 | — | 4 | 12 | no | — |
| 343 | C4⋊C4 | — | 4 | 12 | no | — |
| 344 | C4⋊C4 | — | 4 | 12 | no | — |
| 345 | C4⋊C4 | — | 4 | 6 | no | — |
| 346 | C4⋊C4 | H(5,𝔽2) | 1 | 12 | yes | — |
| 347 | C22⋊C4 | — | 2 | 48 | no | — |
| 348 | C22⋊C4 | — | 4 | 24 | no | — |
| 349 | C22⋊C4 | — | 4 | 6 | no | — |
| 350 | C22⋊C4 | — | 4 | 12 | no | — |
| 351 | C22⋊C4 | — | 4 | 12 | no | — |
| 352 | C22⋊C4 | — | 4 | 12 | no | — |
| 353 | C22⋊C4 | — | 4 | 6 | no | — |
| 354 | C22⋊C4 | — | 4 | 12 | no | — |
| 355 | C22⋊C4 | C22×Q8 | 1 | 24 | yes | — |
| 356 | C22⋊C4 | C22×Q8 | 1 | 48 | yes | — |
| 357 | C42 | — | 2 | 12 | no | — |
| 358 | C42 | — | 2 | 24 | no | — |
| 359 | C42 | — | 2 | 12 | no | — |
| 360 | C42 | — | 2 | 6 | no | — |
| 361 | C42 | — | 4 | 6 | no | — |
| 362 | C42 | — | 4 | 6 | no | — |
| 363 | C42 | — | 4 | 3 | no | — |
| 364 | C42 | — | 4 | 12 | no | — |
| 365 | C42 | C22×Q8 | 1 | 4 | yes | — |
| 366 | C42 | C22×Q8 | 1 | 8 | yes | — |
| 367 | C23 | — | 2 | 12 | no | — |
| 368 | C23 | — | 2 | 6 | no | — |
| 369 | C23 | — | 2 | 6 | no | — |
| 370 | C23 | — | 2 | 12 | no | — |
| 371 | C23 | — | 4 | 24 | no | — |
| 372 | C23 | — | 8 | 4 | no | — |
| 373 | C23 | — | 8 | 12 | no | — |
| 374 | C23 | C23×Q8 | 1 | 12 | yes | — |
| 375 | C23 | C26 | 1 | 1 | yes | characteristic |
| 376 | Q8 | — | 4 | 12 | no | — |
| 377 | Q8 | — | 4 | 4 | no | — |
| 378 | Q8 | — | 4 | 24 | no | — |
| 379 | Q8 | — | 8 | 24 | no | — |
| 380 | Q8 | — | 16 | 6 | no | — |
| 381 | D4 | — | 4 | 24 | no | — |
| 382 | D4 | — | 4 | 12 | no | — |
| 383 | C2×C4 | — | 2 | 3 | no | — |
| 384 | C2×C4 | — | 2 | 6 | no | — |
| 385 | C2×C4 | — | 2 | 3 | no | — |
| 386 | C2×C4 | — | 2 | 6 | no | — |
| 387 | C2×C4 | — | 2 | 12 | no | — |
| 388 | C2×C4 | — | 2 | 6 | no | — |
| 389 | C2×C4 | — | 2 | 3 | no | — |
| 390 | C2×C4 | — | 2 | 6 | no | — |
| 391 | C2×C4 | — | 2 | 12 | no | — |
| 392 | C2×C4 | — | 2 | 24 | no | — |
| 393 | C2×C4 | — | 2 | 12 | no | — |
| 394 | C2×C4 | — | 2 | 6 | no | — |
| 395 | C2×C4 | — | 2 | 12 | no | — |
| 396 | C2×C4 | — | 2 | 12 | no | — |
| 397 | C2×C4 | — | 2 | 6 | no | — |
| 398 | C2×C4 | — | 2 | 24 | no | — |
| 399 | C2×C4 | — | 4 | 24 | no | — |
| 400 | C2×C4 | — | 8 | 24 | no | — |
| 401 | C2×C4 | — | 8 | 12 | no | — |
| 402 | C2×C4 | — | 8 | 24 | no | — |
| 403 | C2×C4 | C23×Q8 | 1 | 6 | yes | — |
| 404 | C2×C4 | C23×Q8 | 1 | 12 | yes | — |
| 405 | C2×C4 | C2×H(5,𝔽2) | 1 | 12 | yes | — |
| 406 | C2×C4 | C2×H(5,𝔽2) | 1 | 6 | yes | — |
| 407 | C22 | — | 2 | 24 | no | — |
| 408 | C22 | — | 2 | 12 | no | — |
| 409 | C22 | — | 4 | 6 | no | — |
| 410 | C22 | — | 4 | 6 | no | — |
| 411 | C22 | — | 4 | 12 | no | — |
| 412 | C22 | — | 8 | 16 | no | — |
| 413 | C22 | C24×Q8 | 1 | 1 | yes | characteristic |
| 414 | C22 | C22×H(5,𝔽2) | 1 | 3 | yes | — |
| 415 | C22 | 2−1+6 | 1 | 3 | yes | — |
| 416 | C4 | — | 2 | 6 | no | — |
| 417 | C4 | — | 2 | 12 | no | — |
| 418 | C4 | — | 2 | 12 | no | — |
| 419 | C4 | — | 4 | 6 | no | — |
| 420 | C4 | — | 4 | 12 | no | — |
| 421 | C4 | — | 4 | 2 | no | — |
| 422 | C4 | — | 4 | 6 | no | — |
| 423 | C4 | — | 4 | 12 | no | — |
| 424 | C4 | — | 4 | 3 | no | — |
| 425 | C4 | #3549 | 1 | 4 | yes | — |
| 426 | C2 | — | 4 | 12 | no | — |
| 427 | C2 | C2×#3549 | 1 | 1 | yes | characteristic |
| 428 | C2 | Q8×H(5,𝔽2) | 1 | 3 | yes | — |
| 429 | C2 | #63063 | 1 | 3 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C23 | C26 |
| prime radical | C2×H(3,𝔽4) | C22 |
| 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. #59935 | C2 | semidirect |
| 2. #58998 | C2 | semidirect |
| 3. #51601 | C2 | semidirect |
| 4. #48838 | C2 | semidirect |
| 5. #46152 | C2 | semidirect |
| 6. #46004 | C2 | semidirect |
| 7. #39616 | C2 | semidirect |
| 8. #39594 | C2 | semidirect |
| 9. #36562 | C2 | semidirect |
| 13. C2×#557 | C22 | semidirect |
| 16. C22×C22⋊Q8 | C22 | semidirect |
| 17. #2868 | C22 | semidirect |
| 18. #2862 | C22 | semidirect |
| 19. #2859 | C22 | semidirect |
| 20. #2848 | C22 | semidirect |
| 21. #2844 | C22 | semidirect |
| 22. #2811 | C22 | semidirect |
| 23. #2809 | C22 | semidirect |
| 26. #2763 | C22 | semidirect |
| 27. #2720 | C22 | semidirect |
| 28. #2720 | C22 | semidirect |
| 29. #2720 | C22 | semidirect |
| 32. #2677 | C22 | semidirect |
| 33. #2660 | C22 | semidirect |
| 34. #2626 | C22 | semidirect |
| 35. #2612 | C22 | semidirect |
| 36. #2574 | C22 | semidirect |
| 37. #2568 | C22 | semidirect |
| 38. #2567 | C22 | semidirect |
| 39. #2567 | C22 | semidirect |
| 42. #2565 | C22 | semidirect |
| 43. #2556 | C22 | semidirect |
| 46. #2502 | C22 | semidirect |
| 47. #2497 | C22 | semidirect |
| 48. #2492 | C22 | semidirect |
| 51. #2440 | C22 | semidirect |
| 52. #2437 | C22 | semidirect |
| 53. #2434 | C22 | semidirect |
| 54. #2434 | C22 | semidirect |
| 55. #2429 | C22 | semidirect |
| 56. #2429 | C22 | semidirect |
| 64. #2360 | C22 | semidirect |
| 66. #2345 | C22 | semidirect |
| 73. #2295 | C22 | semidirect |
| 74. C42×Q8 | C22 | semidirect |
| 77. H(3,𝔽4) | Q8 | semidirect |
| 216. #124 | C2×Q8 | semidirect |
| 217. #124 | C2×Q8 | semidirect |
| 224. #120 | C2×Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #59935 | 2 |
| #58998 | 2 |
| #51601 | 2 |
| #48838 | 2 |
| #46152 | 2 |
| #46004 | 2 |
| #39616 | 2 |
| #39594 | 2 |
| #36562 | 2 |
| #34524 | 2 |
| C4×H(3,𝔽4) | 2 |