← C24×#62817 #72301870
Subgroups — C24×#62817 #72301870
Order 4096.
319431739 conjugacy classes of subgroups.
The subgroup lattice has 645 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C24×#3490 | C2 | 1 | 18 | yes | maximal, complemented |
| 2 | C24×#543 | C22 | 1 | 6 | yes | complemented |
| 3 | C24×#3532 | C2 | 1 | 24 | yes | maximal, complemented |
| 4 | C24×H(3,𝔽4) | C22 | 1 | 8 | yes | complemented |
| 5 | C24×#560 | C22 | 1 | 24 | yes | complemented |
| 6 | C24×#538 | C22 | 1 | 72 | yes | complemented |
| 7 | C24×#551 | C22 | 1 | 72 | yes | complemented |
| 8 | C24×#3484 | C2 | 1 | 18 | yes | maximal, complemented |
| 9 | C24×#535 | C22 | 1 | 36 | yes | complemented |
| 10 | C24×#518 | C22 | 1 | 18 | yes | complemented |
| 11 | C24×#546 | C22 | 1 | 144 | yes | complemented |
| 12 | C24×#534 | C22 | 1 | 18 | yes | complemented |
| 13 | C24×#534 | C22 | 1 | 36 | yes | complemented |
| 14 | C26×#120 | C2 | 1 | 3 | yes | maximal, complemented |
| 15 | C26×C22⋊C4 | C22 | 1 | 9 | yes | complemented |
| 16 | C27×D4 | C22 | 1 | 9 | yes | complemented |
| 17 | C24×#525 | C22 | 1 | 36 | yes | complemented |
| 18 | C23×#62817 | C2 | 1 | 960 | yes | maximal, direct product factor |
| 19 | C23×#3490 | C22 | 1 | 8640 | yes | complemented |
| 20 | C25×#120 | C22 | 1 | 36 | yes | complemented |
| 21 | C25×#120 | C22 | 1 | 36 | yes | complemented |
| 22 | C25×#120 | C22 | 1 | 1440 | yes | complemented |
| 23 | C25×#120 | C22 | 1 | 12 | yes | complemented |
| 24 | C25×H(5,𝔽2) | C22 | 1 | 6 | yes | complemented |
| 25 | C23×#3532 | C22 | 1 | 11520 | yes | complemented |
| 26 | C23×#3484 | C22 | 1 | 8640 | yes | complemented |
| 27 | C24×D42 | C22 | 1 | 72 | yes | complemented |
| 28 | C22×#62817 | C22 | 1 | 143360 | yes | direct product factor |
| 29 | C210 | C22 | 1 | 1 | yes | characteristic, complemented |
| 30 | C29 | — | 4 | 192 | no | — |
| 31 | C29 | C23 | 1 | 9 | yes | — |
| 32 | C29 | C23 | 1 | 6 | yes | — |
| 33 | C29 | C23 | 1 | 240 | yes | complemented |
| 34 | C29 | C23 | 1 | 3 | yes | complemented |
| 35 | C24×H(5,𝔽2) | — | 4 | 384 | no | — |
| 36 | C24×H(5,𝔽2) | C23 | 1 | 1440 | yes | complemented |
| 37 | C25×#41 | C23 | 1 | 36 | yes | complemented |
| 38 | C26×D4 | — | 4 | 576 | no | — |
| 39 | C26×D4 | C23 | 1 | 18 | yes | — |
| 40 | C26×D4 | C23 | 1 | 72 | yes | complemented |
| 41 | C26×D4 | C23 | 1 | 18 | yes | complemented |
| 42 | C26×D4 | C23 | 1 | 36 | yes | complemented |
| 43 | C26×D4 | C23 | 1 | 2160 | yes | complemented |
| 44 | C27×C4 | C23 | 1 | 9 | yes | complemented |
| 45 | C2×#62817 | C23 | 1 | 3932160 | yes | direct product factor |
| 46 | C22×#3532 | C23 | 1 | 860160 | yes | complemented |
| 47 | C23×H(3,𝔽4) | C23 | 1 | 1920 | yes | complemented |
| 48 | C23×#560 | C23 | 1 | 5760 | yes | complemented |
| 49 | C22×#3490 | C23 | 1 | 645120 | yes | complemented |
| 50 | C22×#3484 | C23 | 1 | 645120 | yes | complemented |
| 51 | C23×#551 | C23 | 1 | 17280 | yes | complemented |
| 52 | C23×#546 | C23 | 1 | 34560 | yes | complemented |
| 53 | C23×D42 | C23 | 1 | 17280 | yes | complemented |
| 54 | C23×#535 | C23 | 1 | 8640 | yes | complemented |
| 55 | C23×#538 | C23 | 1 | 17280 | yes | complemented |
| 56 | C23×#543 | C23 | 1 | 1440 | yes | complemented |
| 57 | C23×#534 | C23 | 1 | 4320 | yes | complemented |
| 58 | C23×#534 | C23 | 1 | 8640 | yes | complemented |
| 59 | C24×#127 | C23 | 1 | 24 | yes | complemented |
| 60 | C24×#126 | C23 | 1 | 48 | yes | complemented |
| 61 | C24×#124 | C23 | 1 | 72 | yes | complemented |
| 62 | C23×#525 | C23 | 1 | 8640 | yes | complemented |
| 63 | C24×#123 | C23 | 1 | 72 | yes | complemented |
| 64 | C24×#123 | C23 | 1 | 72 | yes | complemented |
| 65 | C24×C22⋊Q8 | C23 | 1 | 72 | yes | complemented |
| 66 | C24×#121 | C23 | 1 | 72 | yes | complemented |
| 67 | C24×#121 | C23 | 1 | 144 | yes | complemented |
| 68 | C24×#120 | C23 | 1 | 72 | yes | — |
| 69 | C24×#120 | C23 | 1 | 72 | yes | complemented |
| 70 | C24×#120 | C23 | 1 | 24 | yes | complemented |
| 71 | C24×#120 | C23 | 1 | 24 | yes | complemented |
| 72 | C24×#120 | C23 | 1 | 24 | yes | complemented |
| 73 | C24×#120 | C23 | 1 | 8640 | yes | complemented |
| 74 | C24×#120 | C23 | 1 | 72 | yes | complemented |
| 75 | C24×#120 | C23 | 1 | 8640 | yes | complemented |
| 76 | C24×#120 | C23 | 1 | 2880 | yes | complemented |
| 77 | C24×#120 | C23 | 1 | 107520 | yes | complemented |
| 78 | C23×#518 | C23 | 1 | 4320 | yes | complemented |
| 79 | C24×C4×D4 | C23 | 1 | 144 | yes | complemented |
| 80 | C24×#117 | C23 | 1 | 36 | yes | complemented |
| 81 | C25×C22⋊C4 | C23 | 1 | 18 | yes | — |
| 82 | C25×C22⋊C4 | C23 | 1 | 72 | yes | complemented |
| 83 | C25×C22⋊C4 | C23 | 1 | 18 | yes | complemented |
| 84 | C25×C22⋊C4 | C23 | 1 | 2160 | yes | complemented |
| 85 | C25×C22⋊C4 | C23 | 1 | 36 | yes | complemented |
| 86 | C28 | — | 2 | 576 | no | — |
| 87 | C28 | — | 4 | 576 | no | — |
| 88 | C28 | — | 4 | 576 | no | — |
| 89 | C28 | — | 4 | 23040 | no | — |
| 90 | C28 | — | 4 | 288 | no | — |
| 91 | C28 | — | 4 | 16384 | no | — |
| 92 | C28 | C24 | 1 | 3 | yes | — |
| 93 | C28 | C24 | 1 | 18 | yes | — |
| 94 | C28 | C24 | 1 | 9 | yes | — |
| 95 | C28 | C24 | 1 | 1080 | yes | — |
| 96 | C28 | C24 | 1 | 18 | yes | — |
| 97 | C28 | C24 | 1 | 2 | yes | — |
| 98 | C28 | C24 | 1 | 720 | yes | — |
| 99 | C28 | C24 | 1 | 3 | yes | — |
| 100 | C28 | C24 | 1 | 8960 | yes | complemented |
| 101 | C28 | C24 | 1 | 360 | yes | complemented |
| 102 | C28 | C24 | 1 | 4 | yes | complemented |
| 103 | C23×H(5,𝔽2) | — | 4 | 46080 | no | — |
| 104 | C23×H(5,𝔽2) | C24 | 1 | 53760 | yes | complemented |
| 105 | C24×#41 | — | 4 | 1152 | no | — |
| 106 | C24×#41 | C24 | 1 | 4320 | yes | complemented |
| 107 | C25×Q8 | C24 | 1 | 12 | yes | complemented |
| 108 | C25×D4 | — | 2 | 1152 | no | — |
| 109 | C25×D4 | — | 4 | 576 | no | — |
| 110 | C25×D4 | — | 4 | 2304 | no | — |
| 111 | C25×D4 | — | 4 | 69120 | no | — |
| 112 | C25×D4 | — | 4 | 1152 | no | — |
| 113 | C25×D4 | C24 | 1 | 72 | yes | — |
| 114 | C25×D4 | C24 | 1 | 2160 | yes | — |
| 115 | C25×D4 | C24 | 1 | 72 | yes | — |
| 116 | C25×D4 | C24 | 1 | 2160 | yes | complemented |
| 117 | C25×D4 | C24 | 1 | 8640 | yes | complemented |
| 118 | C25×D4 | C24 | 1 | 36 | yes | complemented |
| 119 | C25×D4 | C24 | 1 | 80640 | yes | complemented |
| 120 | C25×D4 | C24 | 1 | 4320 | yes | complemented |
| 121 | C26×C4 | — | 4 | 288 | no | — |
| 122 | C26×C4 | C24 | 1 | 18 | yes | — |
| 123 | C26×C4 | C24 | 1 | 36 | yes | — |
| 124 | C26×C4 | C24 | 1 | 1080 | yes | complemented |
| 125 | C26×C4 | C24 | 1 | 36 | yes | complemented |
| 126 | #62817 | C24 | 1 | 16777216 | yes | direct product factor |
| 127 | C2×#3490 | C24 | 1 | 8847360 | yes | complemented |
| 128 | C2×#3484 | C24 | 1 | 8847360 | yes | complemented |
| 129 | C2×#3532 | C24 | 1 | 11796480 | yes | complemented |
| 130 | C22×#551 | C24 | 1 | 645120 | yes | complemented |
| 131 | C22×#546 | C24 | 1 | 1290240 | yes | complemented |
| 132 | C22×D42 | C24 | 1 | 645120 | yes | complemented |
| 133 | C22×H(3,𝔽4) | C24 | 1 | 71680 | yes | complemented |
| 134 | C22×#560 | C24 | 1 | 215040 | yes | complemented |
| 135 | C22×#535 | C24 | 1 | 322560 | yes | complemented |
| 136 | C22×#538 | C24 | 1 | 645120 | yes | complemented |
| 137 | C22×#543 | C24 | 1 | 53760 | yes | complemented |
| 138 | C22×#534 | C24 | 1 | 161280 | yes | complemented |
| 139 | C22×#534 | C24 | 1 | 322560 | yes | complemented |
| 140 | C23×#127 | C24 | 1 | 2880 | yes | complemented |
| 141 | C23×#126 | C24 | 1 | 5760 | yes | complemented |
| 142 | C23×#124 | C24 | 1 | 8640 | yes | complemented |
| 143 | C22×#525 | C24 | 1 | 322560 | yes | complemented |
| 144 | C23×#123 | C24 | 1 | 8640 | yes | complemented |
| 145 | C23×#123 | C24 | 1 | 8640 | yes | complemented |
| 146 | C23×C22⋊Q8 | C24 | 1 | 8640 | yes | complemented |
| 147 | C23×#121 | C24 | 1 | 8640 | yes | complemented |
| 148 | C23×#121 | C24 | 1 | 17280 | yes | complemented |
| 149 | C23×#120 | C24 | 1 | 8640 | yes | — |
| 150 | C23×#120 | C24 | 1 | 2880 | yes | complemented |
| 151 | C23×#120 | C24 | 1 | 8640 | yes | complemented |
| 152 | C23×#120 | C24 | 1 | 2880 | yes | complemented |
| 153 | C23×#120 | C24 | 1 | 2880 | yes | complemented |
| 154 | C23×#120 | C24 | 1 | 322560 | yes | complemented |
| 155 | C23×#120 | C24 | 1 | 8640 | yes | complemented |
| 156 | C23×#120 | C24 | 1 | 322560 | yes | complemented |
| 157 | C23×#120 | C24 | 1 | 1474560 | yes | complemented |
| 158 | C23×#120 | C24 | 1 | 107520 | yes | complemented |
| 159 | C22×#518 | C24 | 1 | 161280 | yes | complemented |
| 160 | C23×C4×D4 | C24 | 1 | 17280 | yes | complemented |
| 161 | C23×#117 | C24 | 1 | 4320 | yes | complemented |
| 162 | C24×C4⋊C4 | C24 | 1 | 72 | yes | complemented |
| 163 | C24×C22⋊C4 | C24 | 1 | 72 | yes | — |
| 164 | C24×C22⋊C4 | C24 | 1 | 2160 | yes | — |
| 165 | C24×C22⋊C4 | C24 | 1 | 72 | yes | — |
| 166 | C24×C22⋊C4 | C24 | 1 | 2160 | yes | complemented |
| 167 | C24×C22⋊C4 | C24 | 1 | 8640 | yes | complemented |
| 168 | C24×C22⋊C4 | C24 | 1 | 72 | yes | complemented |
| 169 | C24×C22⋊C4 | C24 | 1 | 80640 | yes | complemented |
| 170 | C24×C22⋊C4 | C24 | 1 | 4320 | yes | complemented |
| 171 | C24×C42 | C24 | 1 | 24 | yes | complemented |
| 172 | C27 | — | 2 | 288 | no | — |
| 173 | C27 | — | 2 | 1152 | no | — |
| 174 | C27 | — | 2 | 288 | no | — |
| 175 | C27 | — | 2 | 34560 | no | — |
| 176 | C27 | — | 2 | 576 | no | — |
| 177 | C27 | — | 4 | 96 | no | — |
| 178 | C27 | — | 4 | 288 | no | — |
| 179 | C27 | — | 4 | 288 | no | — |
| 180 | C27 | — | 4 | 34560 | no | — |
| 181 | C27 | — | 4 | 96 | no | — |
| 182 | C27 | — | 4 | 34560 | no | — |
| 183 | C27 | — | 4 | 430080 | no | — |
| 184 | C27 | — | 4 | 576 | no | — |
| 185 | C27 | — | 4 | 17280 | no | — |
| 186 | C27 | — | 4 | 192 | no | — |
| 187 | C27 | — | 4 | 36864 | no | — |
| 188 | C27 | — | 4 | 24576 | no | — |
| 189 | C27 | — | 4 | 983040 | no | — |
| 190 | C27 | — | 8 | 6144 | no | — |
| 191 | C27 | H(5,𝔽2) | 1 | 192 | yes | complemented |
| 192 | C27 | C25 | 1 | 180 | yes | — |
| 193 | C27 | C25 | 1 | 12 | yes | — |
| 194 | C27 | C25 | 1 | 6 | yes | — |
| 195 | C27 | C25 | 1 | 1080 | yes | — |
| 196 | C27 | C25 | 1 | 9 | yes | — |
| 197 | C27 | C25 | 1 | 1080 | yes | — |
| 198 | C27 | C25 | 1 | 540 | yes | — |
| 199 | C27 | C25 | 1 | 20160 | yes | — |
| 200 | C27 | C25 | 1 | 120 | yes | — |
| 201 | C27 | C25 | 1 | 13440 | yes | — |
| 202 | C27 | C25 | 1 | 180 | yes | — |
| 203 | C27 | C25 | 1 | 61440 | yes | complemented |
| 204 | C27 | C25 | 1 | 6720 | yes | complemented |
| 205 | C27 | C25 | 1 | 240 | yes | complemented |
| 206 | C22×H(5,𝔽2) | — | 4 | 860160 | no | — |
| 207 | C22×H(5,𝔽2) | C25 | 1 | 368640 | yes | complemented |
| 208 | C23×#41 | — | 4 | 69120 | no | — |
| 209 | C23×#41 | C25 | 1 | 80640 | yes | complemented |
| 210 | C24×Q8 | — | 4 | 192 | no | — |
| 211 | C24×Q8 | C25 | 1 | 720 | yes | complemented |
| 212 | C24×D4 | — | 2 | 2304 | no | — |
| 213 | C24×D4 | — | 2 | 69120 | no | — |
| 214 | C24×D4 | — | 4 | 1152 | no | — |
| 215 | C24×D4 | — | 4 | 34560 | no | — |
| 216 | C24×D4 | — | 4 | 576 | no | — |
| 217 | C24×D4 | — | 4 | 138240 | no | — |
| 218 | C24×D4 | — | 4 | 1290240 | no | — |
| 219 | C24×D4 | — | 4 | 69120 | no | — |
| 220 | C24×D4 | C25 | 1 | 4320 | yes | — |
| 221 | C24×D4 | C25 | 1 | 40320 | yes | — |
| 222 | C24×D4 | C25 | 1 | 4320 | yes | — |
| 223 | C24×D4 | C25 | 1 | 40320 | yes | complemented |
| 224 | C24×D4 | C25 | 1 | 161280 | yes | complemented |
| 225 | C24×D4 | C25 | 1 | 2160 | yes | complemented |
| 226 | C24×D4 | C25 | 1 | 552960 | yes | complemented |
| 227 | C24×D4 | C25 | 1 | 80640 | yes | complemented |
| 228 | C25×C4 | — | 2 | 576 | no | — |
| 229 | C25×C4 | — | 4 | 576 | no | — |
| 230 | C25×C4 | — | 4 | 17280 | no | — |
| 231 | C25×C4 | — | 4 | 576 | no | — |
| 232 | C25×C4 | C25 | 1 | 1080 | yes | — |
| 233 | C25×C4 | C25 | 1 | 36 | yes | — |
| 234 | C25×C4 | C25 | 1 | 2160 | yes | — |
| 235 | C25×C4 | C25 | 1 | 20160 | yes | complemented |
| 236 | C25×C4 | C25 | 1 | 2160 | yes | complemented |
| 237 | #3532 | C25 | 1 | 25165824 | yes | complemented |
| 238 | C2×H(3,𝔽4) | C25 | 1 | 491520 | yes | complemented |
| 239 | C2×#560 | C25 | 1 | 1474560 | yes | complemented |
| 240 | #3490 | C25 | 1 | 18874368 | yes | complemented |
| 241 | #3484 | C25 | 1 | 18874368 | yes | complemented |
| 242 | C2×#551 | C25 | 1 | 4423680 | yes | complemented |
| 243 | C2×#546 | C25 | 1 | 8847360 | yes | complemented |
| 244 | C2×D42 | C25 | 1 | 4423680 | yes | complemented |
| 245 | C2×#543 | C25 | 1 | 368640 | yes | complemented |
| 246 | C2×#538 | C25 | 1 | 4423680 | yes | complemented |
| 247 | C2×#535 | C25 | 1 | 2211840 | yes | complemented |
| 248 | C2×#534 | C25 | 1 | 1105920 | yes | complemented |
| 249 | C2×#534 | C25 | 1 | 2211840 | yes | complemented |
| 250 | C22×#127 | C25 | 1 | 53760 | yes | complemented |
| 251 | C22×#126 | C25 | 1 | 107520 | yes | complemented |
| 252 | C22×#124 | C25 | 1 | 161280 | yes | complemented |
| 253 | C2×#525 | C25 | 1 | 2211840 | yes | complemented |
| 254 | C22×#123 | C25 | 1 | 161280 | yes | complemented |
| 255 | C22×#123 | C25 | 1 | 161280 | yes | complemented |
| 256 | C22×C22⋊Q8 | C25 | 1 | 161280 | yes | complemented |
| 257 | C22×#121 | C25 | 1 | 322560 | yes | complemented |
| 258 | C22×#121 | C25 | 1 | 161280 | yes | complemented |
| 259 | C22×#120 | C25 | 1 | 161280 | yes | — |
| 260 | C22×#120 | C25 | 1 | 53760 | yes | complemented |
| 261 | C22×#120 | C25 | 1 | 161280 | yes | complemented |
| 262 | C22×#120 | C25 | 1 | 53760 | yes | complemented |
| 263 | C22×#120 | C25 | 1 | 2211840 | yes | complemented |
| 264 | C22×#120 | C25 | 1 | 161280 | yes | complemented |
| 265 | C22×#120 | C25 | 1 | 2211840 | yes | complemented |
| 266 | C22×#120 | C25 | 1 | 53760 | yes | complemented |
| 267 | C22×#120 | C25 | 1 | 737280 | yes | complemented |
| 268 | C22×#120 | C25 | 1 | 3145728 | yes | complemented |
| 269 | C2×#518 | C25 | 1 | 1105920 | yes | complemented |
| 270 | C22×C4×D4 | C25 | 1 | 322560 | yes | complemented |
| 271 | C22×#117 | C25 | 1 | 80640 | yes | complemented |
| 272 | C23×C4⋊C4 | C25 | 1 | 4320 | yes | complemented |
| 273 | C23×C22⋊C4 | C25 | 1 | 4320 | yes | — |
| 274 | C23×C22⋊C4 | C25 | 1 | 40320 | yes | — |
| 275 | C23×C22⋊C4 | C25 | 1 | 4320 | yes | — |
| 276 | C23×C22⋊C4 | C25 | 1 | 40320 | yes | complemented |
| 277 | C23×C22⋊C4 | C25 | 1 | 161280 | yes | complemented |
| 278 | C23×C22⋊C4 | C25 | 1 | 552960 | yes | complemented |
| 279 | C23×C22⋊C4 | C25 | 1 | 80640 | yes | complemented |
| 280 | C23×C22⋊C4 | C25 | 1 | 4320 | yes | complemented |
| 281 | C23×C42 | C25 | 1 | 1440 | yes | complemented |
| 282 | C26 | — | 2 | 6144 | no | — |
| 283 | C26 | — | 2 | 8640 | no | — |
| 284 | C26 | — | 2 | 288 | no | — |
| 285 | C26 | — | 2 | 576 | no | — |
| 286 | C26 | — | 2 | 34560 | no | — |
| 287 | C26 | — | 2 | 8640 | no | — |
| 288 | C26 | — | 2 | 288 | no | — |
| 289 | C26 | — | 2 | 322560 | no | — |
| 290 | C26 | — | 2 | 17280 | no | — |
| 291 | C26 | — | 4 | 3072 | no | — |
| 292 | C26 | — | 4 | 2880 | no | — |
| 293 | C26 | — | 4 | 8640 | no | — |
| 294 | C26 | — | 4 | 8640 | no | — |
| 295 | C26 | — | 4 | 322560 | no | — |
| 296 | C26 | — | 4 | 2880 | no | — |
| 297 | C26 | — | 4 | 322560 | no | — |
| 298 | C26 | — | 4 | 1474560 | no | — |
| 299 | C26 | — | 4 | 17280 | no | — |
| 300 | C26 | — | 4 | 161280 | no | — |
| 301 | C26 | — | 4 | 5760 | no | — |
| 302 | C26 | — | 4 | 18432 | no | — |
| 303 | C26 | — | 4 | 1105920 | no | — |
| 304 | C26 | — | 4 | 9216 | no | — |
| 305 | C26 | — | 4 | 737280 | no | — |
| 306 | C26 | — | 4 | 9175040 | no | — |
| 307 | C26 | — | 4 | 2048 | no | — |
| 308 | C26 | — | 8 | 9216 | no | — |
| 309 | C26 | — | 8 | 184320 | no | — |
| 310 | C26 | — | 16 | 1024 | no | — |
| 311 | C26 | C2×H(5,𝔽2) | 1 | 288 | yes | — |
| 312 | C26 | C2×H(5,𝔽2) | 1 | 5760 | yes | complemented |
| 313 | C26 | C26 | 1 | 1680 | yes | — |
| 314 | C26 | C26 | 1 | 360 | yes | — |
| 315 | C26 | C26 | 1 | 180 | yes | — |
| 316 | C26 | C26 | 1 | 10080 | yes | — |
| 317 | C26 | C26 | 1 | 270 | yes | — |
| 318 | C26 | C26 | 1 | 10080 | yes | — |
| 319 | C26 | C26 | 1 | 5040 | yes | — |
| 320 | C26 | C26 | 1 | 69120 | yes | — |
| 321 | C26 | C26 | 1 | 1120 | yes | — |
| 322 | C26 | C26 | 1 | 46080 | yes | — |
| 323 | C26 | C26 | 1 | 1680 | yes | — |
| 324 | C26 | C26 | 1 | 1 | yes | characteristic |
| 325 | C26 | C26 | 1 | 65536 | yes | complemented |
| 326 | C26 | C26 | 1 | 23040 | yes | complemented |
| 327 | C26 | C26 | 1 | 2240 | yes | complemented |
| 328 | C2×H(5,𝔽2) | — | 4 | 2949120 | no | — |
| 329 | C2×H(5,𝔽2) | C26 | 1 | 393216 | yes | complemented |
| 330 | C22×#41 | — | 4 | 645120 | no | — |
| 331 | C22×#41 | C26 | 1 | 276480 | yes | complemented |
| 332 | C23×Q8 | — | 4 | 5760 | no | — |
| 333 | C23×Q8 | C26 | 1 | 6720 | yes | complemented |
| 334 | C23×D4 | — | 2 | 69120 | no | — |
| 335 | C23×D4 | — | 2 | 645120 | no | — |
| 336 | C23×D4 | — | 4 | 34560 | no | — |
| 337 | C23×D4 | — | 4 | 322560 | no | — |
| 338 | C23×D4 | — | 4 | 17280 | no | — |
| 339 | C23×D4 | — | 4 | 1290240 | no | — |
| 340 | C23×D4 | — | 4 | 4423680 | no | — |
| 341 | C23×D4 | — | 4 | 645120 | no | — |
| 342 | C23×D4 | C26 | 1 | 40320 | yes | — |
| 343 | C23×D4 | C26 | 1 | 138240 | yes | — |
| 344 | C23×D4 | C26 | 1 | 40320 | yes | — |
| 345 | C23×D4 | C26 | 1 | 138240 | yes | complemented |
| 346 | C23×D4 | C26 | 1 | 552960 | yes | complemented |
| 347 | C23×D4 | C26 | 1 | 20160 | yes | complemented |
| 348 | C23×D4 | C26 | 1 | 589824 | yes | complemented |
| 349 | C23×D4 | C26 | 1 | 276480 | yes | complemented |
| 350 | C24×C4 | — | 2 | 576 | no | — |
| 351 | C24×C4 | — | 2 | 17280 | no | — |
| 352 | C24×C4 | — | 4 | 17280 | no | — |
| 353 | C24×C4 | — | 4 | 161280 | no | — |
| 354 | C24×C4 | — | 4 | 17280 | no | — |
| 355 | C24×C4 | C26 | 1 | 1080 | yes | — |
| 356 | C24×C4 | C26 | 1 | 10080 | yes | — |
| 357 | C24×C4 | C26 | 1 | 20160 | yes | — |
| 358 | C24×C4 | C26 | 1 | 69120 | yes | complemented |
| 359 | C24×C4 | C26 | 1 | 20160 | yes | complemented |
| 360 | H(3,𝔽4) | C26 | 1 | 524288 | yes | complemented |
| 361 | #560 | C26 | 1 | 1572864 | yes | complemented |
| 362 | #551 | C26 | 1 | 4718592 | yes | complemented |
| 363 | #546 | C26 | 1 | 9437184 | yes | complemented |
| 364 | D42 | C26 | 1 | 4718592 | yes | complemented |
| 365 | #543 | C26 | 1 | 393216 | yes | complemented |
| 366 | #538 | C26 | 1 | 4718592 | yes | complemented |
| 367 | #535 | C26 | 1 | 2359296 | yes | complemented |
| 368 | #534 | C26 | 1 | 1179648 | yes | complemented |
| 369 | #534 | C26 | 1 | 2359296 | yes | complemented |
| 370 | C2×#127 | C26 | 1 | 184320 | yes | complemented |
| 371 | C2×#126 | C26 | 1 | 368640 | yes | complemented |
| 372 | C2×#124 | C26 | 1 | 552960 | yes | complemented |
| 373 | #525 | C26 | 1 | 2359296 | yes | complemented |
| 374 | C2×#123 | C26 | 1 | 552960 | yes | complemented |
| 375 | C2×#123 | C26 | 1 | 552960 | yes | complemented |
| 376 | C2×C22⋊Q8 | C26 | 1 | 552960 | yes | complemented |
| 377 | C2×#121 | C26 | 1 | 1105920 | yes | complemented |
| 378 | C2×#121 | C26 | 1 | 552960 | yes | complemented |
| 379 | C2×#120 | C26 | 1 | 552960 | yes | — |
| 380 | C2×#120 | C26 | 1 | 184320 | yes | complemented |
| 381 | C2×#120 | C26 | 1 | 552960 | yes | complemented |
| 382 | C2×#120 | C26 | 1 | 184320 | yes | complemented |
| 383 | C2×#120 | C26 | 1 | 2359296 | yes | complemented |
| 384 | C2×#120 | C26 | 1 | 552960 | yes | complemented |
| 385 | C2×#120 | C26 | 1 | 2359296 | yes | complemented |
| 386 | C2×#120 | C26 | 1 | 184320 | yes | complemented |
| 387 | C2×#120 | C26 | 1 | 786432 | yes | complemented |
| 388 | #518 | C26 | 1 | 1179648 | yes | complemented |
| 389 | C2×C4×D4 | C26 | 1 | 1105920 | yes | complemented |
| 390 | C2×#117 | C26 | 1 | 276480 | yes | complemented |
| 391 | C22×C4⋊C4 | C26 | 1 | 40320 | yes | complemented |
| 392 | C22×C22⋊C4 | C26 | 1 | 40320 | yes | — |
| 393 | C22×C22⋊C4 | C26 | 1 | 138240 | yes | — |
| 394 | C22×C22⋊C4 | C26 | 1 | 40320 | yes | — |
| 395 | C22×C22⋊C4 | C26 | 1 | 138240 | yes | complemented |
| 396 | C22×C22⋊C4 | C26 | 1 | 552960 | yes | complemented |
| 397 | C22×C22⋊C4 | C26 | 1 | 589824 | yes | complemented |
| 398 | C22×C22⋊C4 | C26 | 1 | 276480 | yes | complemented |
| 399 | C22×C22⋊C4 | C26 | 1 | 40320 | yes | complemented |
| 400 | C22×C42 | C26 | 1 | 13440 | yes | complemented |
| 401 | C25 | — | 2 | 92160 | no | — |
| 402 | C25 | — | 2 | 4608 | no | — |
| 403 | C25 | — | 2 | 40320 | no | — |
| 404 | C25 | — | 2 | 4320 | no | — |
| 405 | C25 | — | 2 | 8640 | no | — |
| 406 | C25 | — | 2 | 161280 | no | — |
| 407 | C25 | — | 2 | 40320 | no | — |
| 408 | C25 | — | 2 | 4320 | no | — |
| 409 | C25 | — | 2 | 552960 | no | — |
| 410 | C25 | — | 2 | 80640 | no | — |
| 411 | C25 | — | 4 | 46080 | no | — |
| 412 | C25 | — | 4 | 13440 | no | — |
| 413 | C25 | — | 4 | 40320 | no | — |
| 414 | C25 | — | 4 | 40320 | no | — |
| 415 | C25 | — | 4 | 552960 | no | — |
| 416 | C25 | — | 4 | 13440 | no | — |
| 417 | C25 | — | 4 | 552960 | no | — |
| 418 | C25 | — | 4 | 786432 | no | — |
| 419 | C25 | — | 4 | 80640 | no | — |
| 420 | C25 | — | 4 | 276480 | no | — |
| 421 | C25 | — | 4 | 26880 | no | — |
| 422 | C25 | — | 4 | 276480 | no | — |
| 423 | C25 | — | 4 | 5160960 | no | — |
| 424 | C25 | — | 4 | 138240 | no | — |
| 425 | C25 | — | 4 | 3440640 | no | — |
| 426 | C25 | — | 4 | 15728640 | no | — |
| 427 | C25 | — | 4 | 30720 | no | — |
| 428 | C25 | — | 4 | 1536 | no | — |
| 429 | C25 | — | 4 | 3072 | no | — |
| 430 | C25 | — | 8 | 138240 | no | — |
| 431 | C25 | — | 8 | 860160 | no | — |
| 432 | C25 | — | 16 | 15360 | no | — |
| 433 | C25 | C22×H(5,𝔽2) | 1 | 4320 | yes | — |
| 434 | C25 | C22×H(5,𝔽2) | 1 | 48 | yes | — |
| 435 | C25 | C22×H(5,𝔽2) | 1 | 26880 | yes | complemented |
| 436 | C25 | C27 | 1 | 840 | yes | — |
| 437 | C25 | C27 | 1 | 1680 | yes | — |
| 438 | C25 | C27 | 1 | 2880 | yes | — |
| 439 | C25 | C27 | 1 | 17280 | yes | — |
| 440 | C25 | C27 | 1 | 1260 | yes | — |
| 441 | C25 | C27 | 1 | 8640 | yes | — |
| 442 | C25 | C27 | 1 | 36864 | yes | — |
| 443 | C25 | C27 | 1 | 17280 | yes | — |
| 444 | C25 | C27 | 1 | 1920 | yes | — |
| 445 | C25 | C27 | 1 | 24576 | yes | — |
| 446 | C25 | C27 | 1 | 2880 | yes | — |
| 447 | C25 | C27 | 1 | 15 | yes | — |
| 448 | C25 | C27 | 1 | 12288 | yes | complemented |
| 449 | C25 | C27 | 1 | 3840 | yes | complemented |
| 450 | H(5,𝔽2) | — | 4 | 1572864 | no | — |
| 451 | C2×#41 | — | 4 | 1105920 | no | — |
| 452 | C2×#41 | C27 | 1 | 147456 | yes | complemented |
| 453 | C22×Q8 | — | 4 | 26880 | no | — |
| 454 | C22×Q8 | C27 | 1 | 11520 | yes | complemented |
| 455 | C22×D4 | — | 2 | 322560 | no | — |
| 456 | C22×D4 | — | 2 | 1105920 | no | — |
| 457 | C22×D4 | — | 4 | 161280 | no | — |
| 458 | C22×D4 | — | 4 | 552960 | no | — |
| 459 | C22×D4 | — | 4 | 80640 | no | — |
| 460 | C22×D4 | — | 4 | 2211840 | no | — |
| 461 | C22×D4 | — | 4 | 2359296 | no | — |
| 462 | C22×D4 | — | 4 | 1105920 | no | — |
| 463 | C22×D4 | C27 | 1 | 69120 | yes | — |
| 464 | C22×D4 | C27 | 1 | 73728 | yes | — |
| 465 | C22×D4 | C27 | 1 | 69120 | yes | — |
| 466 | C22×D4 | C27 | 1 | 73728 | yes | complemented |
| 467 | C22×D4 | C27 | 1 | 294912 | yes | complemented |
| 468 | C22×D4 | C27 | 1 | 34560 | yes | complemented |
| 469 | C22×D4 | C27 | 1 | 147456 | yes | complemented |
| 470 | C23×C4 | — | 2 | 8640 | no | — |
| 471 | C23×C4 | — | 2 | 80640 | no | — |
| 472 | C23×C4 | — | 4 | 80640 | no | — |
| 473 | C23×C4 | — | 4 | 276480 | no | — |
| 474 | C23×C4 | — | 4 | 80640 | no | — |
| 475 | C23×C4 | C27 | 1 | 5040 | yes | — |
| 476 | C23×C4 | C27 | 1 | 17280 | yes | — |
| 477 | C23×C4 | C27 | 1 | 34560 | yes | — |
| 478 | C23×C4 | C27 | 1 | 36864 | yes | complemented |
| 479 | C23×C4 | C27 | 1 | 34560 | yes | complemented |
| 480 | #127 | C27 | 1 | 98304 | yes | complemented |
| 481 | #126 | C27 | 1 | 196608 | yes | complemented |
| 482 | #124 | C27 | 1 | 294912 | yes | complemented |
| 483 | #123 | C27 | 1 | 294912 | yes | complemented |
| 484 | #123 | C27 | 1 | 294912 | yes | complemented |
| 485 | C22⋊Q8 | C27 | 1 | 294912 | yes | complemented |
| 486 | #121 | C27 | 1 | 589824 | yes | complemented |
| 487 | #121 | C27 | 1 | 294912 | yes | complemented |
| 488 | #120 | C27 | 1 | 294912 | yes | — |
| 489 | #120 | C27 | 1 | 98304 | yes | complemented |
| 490 | #120 | C27 | 1 | 294912 | yes | complemented |
| 491 | #120 | C27 | 1 | 98304 | yes | complemented |
| 492 | #120 | C27 | 1 | 294912 | yes | complemented |
| 493 | #120 | C27 | 1 | 98304 | yes | complemented |
| 494 | C4×D4 | C27 | 1 | 589824 | yes | complemented |
| 495 | #117 | C27 | 1 | 147456 | yes | complemented |
| 496 | C2×C4⋊C4 | C27 | 1 | 69120 | yes | complemented |
| 497 | C2×C22⋊C4 | C27 | 1 | 69120 | yes | — |
| 498 | C2×C22⋊C4 | C27 | 1 | 73728 | yes | — |
| 499 | C2×C22⋊C4 | C27 | 1 | 69120 | yes | — |
| 500 | C2×C22⋊C4 | C27 | 1 | 73728 | yes | complemented |
| 501 | C2×C22⋊C4 | C27 | 1 | 294912 | yes | complemented |
| 502 | C2×C22⋊C4 | C27 | 1 | 147456 | yes | complemented |
| 503 | C2×C22⋊C4 | C27 | 1 | 69120 | yes | complemented |
| 504 | C2×C42 | C27 | 1 | 23040 | yes | complemented |
| 505 | C24 | — | 2 | 215040 | no | — |
| 506 | C24 | — | 2 | 34560 | no | — |
| 507 | C24 | — | 2 | 34560 | no | — |
| 508 | C24 | — | 2 | 10080 | no | — |
| 509 | C24 | — | 2 | 20160 | no | — |
| 510 | C24 | — | 2 | 138240 | no | — |
| 511 | C24 | — | 2 | 34560 | no | — |
| 512 | C24 | — | 2 | 10080 | no | — |
| 513 | C24 | — | 2 | 147456 | no | — |
| 514 | C24 | — | 2 | 69120 | no | — |
| 515 | C24 | — | 4 | 107520 | no | — |
| 516 | C24 | — | 4 | 11520 | no | — |
| 517 | C24 | — | 4 | 34560 | no | — |
| 518 | C24 | — | 4 | 34560 | no | — |
| 519 | C24 | — | 4 | 147456 | no | — |
| 520 | C24 | — | 4 | 11520 | no | — |
| 521 | C24 | — | 4 | 147456 | no | — |
| 522 | C24 | — | 4 | 69120 | no | — |
| 523 | C24 | — | 4 | 73728 | no | — |
| 524 | C24 | — | 4 | 23040 | no | — |
| 525 | C24 | — | 4 | 645120 | no | — |
| 526 | C24 | — | 4 | 4423680 | no | — |
| 527 | C24 | — | 4 | 322560 | no | — |
| 528 | C24 | — | 4 | 2949120 | no | — |
| 529 | C24 | — | 4 | 4194304 | no | — |
| 530 | C24 | — | 4 | 71680 | no | — |
| 531 | C24 | — | 4 | 11520 | no | — |
| 532 | C24 | — | 4 | 23040 | no | — |
| 533 | C24 | — | 8 | 322560 | no | — |
| 534 | C24 | — | 8 | 737280 | no | — |
| 535 | C24 | — | 16 | 35840 | no | — |
| 536 | C24 | #62817 | 1 | 256 | yes | direct product factor |
| 537 | C24 | C23×H(5,𝔽2) | 1 | 10080 | yes | — |
| 538 | C24 | C23×H(5,𝔽2) | 1 | 360 | yes | — |
| 539 | C24 | C23×H(5,𝔽2) | 1 | 23040 | yes | complemented |
| 540 | C24 | C28 | 1 | 720 | yes | — |
| 541 | C24 | C28 | 1 | 1440 | yes | — |
| 542 | C24 | C28 | 1 | 768 | yes | — |
| 543 | C24 | C28 | 1 | 4608 | yes | — |
| 544 | C24 | C28 | 1 | 1080 | yes | — |
| 545 | C24 | C28 | 1 | 2304 | yes | — |
| 546 | C24 | C28 | 1 | 4608 | yes | — |
| 547 | C24 | C28 | 1 | 512 | yes | — |
| 548 | C24 | C28 | 1 | 768 | yes | — |
| 549 | C24 | C28 | 1 | 35 | yes | — |
| 550 | C24 | C28 | 1 | 1024 | yes | complemented |
| 551 | #41 | — | 4 | 294912 | no | — |
| 552 | C2×Q8 | — | 4 | 23040 | no | — |
| 553 | C2×Q8 | C28 | 1 | 3072 | yes | complemented |
| 554 | C2×D4 | — | 2 | 276480 | no | — |
| 555 | C2×D4 | — | 2 | 294912 | no | — |
| 556 | C2×D4 | — | 4 | 138240 | no | — |
| 557 | C2×D4 | — | 4 | 147456 | no | — |
| 558 | C2×D4 | — | 4 | 69120 | no | — |
| 559 | C2×D4 | — | 4 | 589824 | no | — |
| 560 | C2×D4 | — | 4 | 294912 | no | — |
| 561 | C2×D4 | C28 | 1 | 18432 | yes | — |
| 562 | C2×D4 | C28 | 1 | 18432 | yes | — |
| 563 | C2×D4 | C28 | 1 | 9216 | yes | complemented |
| 564 | C22×C4 | — | 2 | 20160 | no | — |
| 565 | C22×C4 | — | 2 | 69120 | no | — |
| 566 | C22×C4 | — | 4 | 69120 | no | — |
| 567 | C22×C4 | — | 4 | 73728 | no | — |
| 568 | C22×C4 | — | 4 | 69120 | no | — |
| 569 | C22×C4 | C28 | 1 | 4320 | yes | — |
| 570 | C22×C4 | C28 | 1 | 4608 | yes | — |
| 571 | C22×C4 | C28 | 1 | 9216 | yes | — |
| 572 | C22×C4 | C28 | 1 | 9216 | yes | complemented |
| 573 | C4⋊C4 | C28 | 1 | 18432 | yes | complemented |
| 574 | C22⋊C4 | C28 | 1 | 18432 | yes | — |
| 575 | C22⋊C4 | C28 | 1 | 18432 | yes | — |
| 576 | C22⋊C4 | C28 | 1 | 18432 | yes | complemented |
| 577 | C42 | C28 | 1 | 6144 | yes | complemented |
| 578 | C23 | — | 2 | 92160 | no | — |
| 579 | C23 | — | 2 | 4608 | no | — |
| 580 | C23 | — | 2 | 4320 | no | — |
| 581 | C23 | — | 2 | 40320 | no | — |
| 582 | C23 | — | 2 | 8640 | no | — |
| 583 | C23 | — | 2 | 18432 | no | — |
| 584 | C23 | — | 2 | 4608 | no | — |
| 585 | C23 | — | 2 | 4320 | no | — |
| 586 | C23 | — | 2 | 9216 | no | — |
| 587 | C23 | — | 4 | 46080 | no | — |
| 588 | C23 | — | 4 | 1536 | no | — |
| 589 | C23 | — | 4 | 4608 | no | — |
| 590 | C23 | — | 4 | 4608 | no | — |
| 591 | C23 | — | 4 | 1536 | no | — |
| 592 | C23 | — | 4 | 9216 | no | — |
| 593 | C23 | — | 4 | 3072 | no | — |
| 594 | C23 | — | 4 | 276480 | no | — |
| 595 | C23 | — | 4 | 589824 | no | — |
| 596 | C23 | — | 4 | 138240 | no | — |
| 597 | C23 | — | 4 | 393216 | no | — |
| 598 | C23 | — | 4 | 30720 | no | — |
| 599 | C23 | — | 4 | 13440 | no | — |
| 600 | C23 | — | 4 | 26880 | no | — |
| 601 | C23 | — | 8 | 138240 | no | — |
| 602 | C23 | — | 8 | 98304 | no | — |
| 603 | C23 | — | 16 | 15360 | no | — |
| 604 | C23 | C2×#62817 | 1 | 960 | yes | direct product factor |
| 605 | C23 | C24×H(5,𝔽2) | 1 | 4320 | yes | — |
| 606 | C23 | C24×H(5,𝔽2) | 1 | 420 | yes | — |
| 607 | C23 | C24×H(5,𝔽2) | 1 | 3072 | yes | complemented |
| 608 | C23 | C29 | 1 | 96 | yes | — |
| 609 | C23 | C29 | 1 | 192 | yes | — |
| 610 | C23 | C29 | 1 | 144 | yes | — |
| 611 | C23 | C29 | 1 | 15 | yes | — |
| 612 | Q8 | — | 4 | 3072 | no | — |
| 613 | D4 | — | 2 | 36864 | no | — |
| 614 | D4 | — | 4 | 18432 | no | — |
| 615 | D4 | — | 4 | 9216 | no | — |
| 616 | C2×C4 | — | 2 | 8640 | no | — |
| 617 | C2×C4 | — | 2 | 9216 | no | — |
| 618 | C2×C4 | — | 4 | 9216 | no | — |
| 619 | C2×C4 | — | 4 | 9216 | no | — |
| 620 | C2×C4 | C29 | 1 | 576 | yes | — |
| 621 | C22 | — | 2 | 6144 | no | — |
| 622 | C22 | — | 2 | 8640 | no | — |
| 623 | C22 | — | 2 | 288 | no | — |
| 624 | C22 | — | 2 | 576 | no | — |
| 625 | C22 | — | 2 | 288 | no | — |
| 626 | C22 | — | 4 | 3072 | no | — |
| 627 | C22 | — | 4 | 18432 | no | — |
| 628 | C22 | — | 4 | 9216 | no | — |
| 629 | C22 | — | 4 | 2048 | no | — |
| 630 | C22 | — | 4 | 2880 | no | — |
| 631 | C22 | — | 4 | 5760 | no | — |
| 632 | C22 | — | 8 | 9216 | no | — |
| 633 | C22 | — | 16 | 1024 | no | — |
| 634 | C22 | C210 | 1 | 1 | yes | characteristic |
| 635 | C22 | C22×#62817 | 1 | 560 | yes | direct product factor |
| 636 | C22 | C25×H(5,𝔽2) | 1 | 288 | yes | — |
| 637 | C22 | C25×H(5,𝔽2) | 1 | 90 | yes | — |
| 638 | C4 | — | 2 | 576 | no | — |
| 639 | C2 | — | 2 | 288 | no | — |
| 640 | C2 | — | 4 | 96 | no | — |
| 641 | C2 | — | 4 | 192 | no | — |
| 642 | C2 | C23×#62817 | 1 | 60 | yes | direct product factor |
| 643 | C2 | C26×H(5,𝔽2) | 1 | 3 | yes | — |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|
| 1. C24×#3490 | C2 | semidirect |
| 2. C24×#543 | C22 | semidirect |
| 3. C24×#3532 | C2 | semidirect |
| 4. C24×H(3,𝔽4) | C22 | semidirect |
| 5. C24×#560 | C22 | semidirect |
| 6. C24×#538 | C22 | semidirect |
| 7. C24×#551 | C22 | semidirect |
| 8. C24×#3484 | C2 | semidirect |
| 9. C24×#535 | C22 | semidirect |
| 10. C24×#518 | C22 | semidirect |
| 11. C24×#546 | C22 | semidirect |
| 12. C24×#534 | C22 | semidirect |
| 13. C24×#534 | C22 | semidirect |
| 14. C26×#120 | C2 | semidirect |
| 15. C26×C22⋊C4 | C22 | semidirect |
| 16. C27×D4 | C22 | semidirect |
| 17. C24×#525 | C22 | semidirect |
| 18. C23×#62817 | C2 | direct (N × H) |
| 19. C23×#3490 | C22 | semidirect |
| 20. C25×#120 | C22 | semidirect |
| 21. C25×#120 | C22 | semidirect |
| 22. C25×#120 | C22 | semidirect |
| 23. C25×#120 | C22 | semidirect |
| 24. C25×H(5,𝔽2) | C22 | semidirect |
| 25. C23×#3532 | C22 | semidirect |
| 26. C23×#3484 | C22 | semidirect |
| 27. C24×D42 | C22 | semidirect |
| 28. C22×#62817 | C22 | direct (N × H) |
| 29. C210 | C22 | semidirect |
| 33. C29 | C23 | semidirect |
| 34. C29 | C23 | semidirect |
| 36. C24×H(5,𝔽2) | C23 | semidirect |
| 37. C25×#41 | C23 | semidirect |
| 40. C26×D4 | C23 | semidirect |
| 41. C26×D4 | C23 | semidirect |
| 42. C26×D4 | C23 | semidirect |
| 43. C26×D4 | C23 | semidirect |
| 44. C27×C4 | C23 | semidirect |
| 45. C2×#62817 | C23 | direct (N × H) |
| 46. C22×#3532 | C23 | semidirect |
| 47. C23×H(3,𝔽4) | C23 | semidirect |
| 48. C23×#560 | C23 | semidirect |
| 49. C22×#3490 | C23 | semidirect |
| 50. C22×#3484 | C23 | semidirect |
| 51. C23×#551 | C23 | semidirect |
| 52. C23×#546 | C23 | semidirect |
| 53. C23×D42 | C23 | semidirect |
| 54. C23×#535 | C23 | semidirect |
| 55. C23×#538 | C23 | semidirect |
| 56. C23×#543 | C23 | semidirect |
| 57. C23×#534 | C23 | semidirect |
| 58. C23×#534 | C23 | semidirect |
| 59. C24×#127 | C23 | semidirect |
| 60. C24×#126 | C23 | semidirect |
| 61. C24×#124 | C23 | semidirect |
| 62. C23×#525 | C23 | semidirect |
| 63. C24×#123 | C23 | semidirect |
| 64. C24×#123 | C23 | semidirect |
| 65. C24×C22⋊Q8 | C23 | semidirect |
| 66. C24×#121 | C23 | semidirect |
| 67. C24×#121 | C23 | semidirect |
| 69. C24×#120 | C23 | semidirect |
| 70. C24×#120 | C23 | semidirect |
| 71. C24×#120 | C23 | semidirect |
| 72. C24×#120 | C23 | semidirect |
| 73. C24×#120 | C23 | semidirect |
| 74. C24×#120 | C23 | semidirect |
| 75. C24×#120 | C23 | semidirect |
| 76. C24×#120 | C23 | semidirect |
| 77. C24×#120 | C23 | semidirect |
| 78. C23×#518 | C23 | semidirect |
| 79. C24×C4×D4 | C23 | semidirect |
| 80. C24×#117 | C23 | semidirect |
| 82. C25×C22⋊C4 | C23 | semidirect |
| 83. C25×C22⋊C4 | C23 | semidirect |
| 84. C25×C22⋊C4 | C23 | semidirect |
| 85. C25×C22⋊C4 | C23 | semidirect |
| 100. C28 | C24 | semidirect |
| 101. C28 | C24 | semidirect |
| 102. C28 | C24 | semidirect |
| 104. C23×H(5,𝔽2) | C24 | semidirect |
| 106. C24×#41 | C24 | semidirect |
| 107. C25×Q8 | C24 | semidirect |
| 116. C25×D4 | C24 | semidirect |
| 117. C25×D4 | C24 | semidirect |
| 118. C25×D4 | C24 | semidirect |
| 119. C25×D4 | C24 | semidirect |
| 120. C25×D4 | C24 | semidirect |
| 124. C26×C4 | C24 | semidirect |
| 125. C26×C4 | C24 | semidirect |
| 126. #62817 | C24 | direct (N × H) |
| 127. C2×#3490 | C24 | semidirect |
| 128. C2×#3484 | C24 | semidirect |
| 129. C2×#3532 | C24 | semidirect |
| 130. C22×#551 | C24 | semidirect |
| 131. C22×#546 | C24 | semidirect |
| 132. C22×D42 | C24 | semidirect |
| 133. C22×H(3,𝔽4) | C24 | semidirect |
| 134. C22×#560 | C24 | semidirect |
| 135. C22×#535 | C24 | semidirect |
| 136. C22×#538 | C24 | semidirect |
| 137. C22×#543 | C24 | semidirect |
| 138. C22×#534 | C24 | semidirect |
| 139. C22×#534 | C24 | semidirect |
| 140. C23×#127 | C24 | semidirect |
| 141. C23×#126 | C24 | semidirect |
| 142. C23×#124 | C24 | semidirect |
| 143. C22×#525 | C24 | semidirect |
| 144. C23×#123 | C24 | semidirect |
| 145. C23×#123 | C24 | semidirect |
| 146. C23×C22⋊Q8 | C24 | semidirect |
| 147. C23×#121 | C24 | semidirect |
| 148. C23×#121 | C24 | semidirect |
| 150. C23×#120 | C24 | semidirect |
| 151. C23×#120 | C24 | semidirect |
| 152. C23×#120 | C24 | semidirect |
| 153. C23×#120 | C24 | semidirect |
| 154. C23×#120 | C24 | semidirect |
| 155. C23×#120 | C24 | semidirect |
| 156. C23×#120 | C24 | semidirect |
| 157. C23×#120 | C24 | semidirect |
| 158. C23×#120 | C24 | semidirect |
| 159. C22×#518 | C24 | semidirect |
| 160. C23×C4×D4 | C24 | semidirect |
| 161. C23×#117 | C24 | semidirect |
| 162. C24×C4⋊C4 | C24 | semidirect |
| 166. C24×C22⋊C4 | C24 | semidirect |
| 167. C24×C22⋊C4 | C24 | semidirect |
| 168. C24×C22⋊C4 | C24 | semidirect |
| 169. C24×C22⋊C4 | C24 | semidirect |
| 170. C24×C22⋊C4 | C24 | semidirect |
| 171. C24×C42 | C24 | semidirect |
| 191. C27 | H(5,𝔽2) | semidirect |
| 203. C27 | C25 | semidirect |
| 204. C27 | C25 | semidirect |
| 205. C27 | C25 | semidirect |
| 207. C22×H(5,𝔽2) | C25 | semidirect |
| 209. C23×#41 | C25 | semidirect |
| 211. C24×Q8 | C25 | semidirect |
| 223. C24×D4 | C25 | semidirect |
| 224. C24×D4 | C25 | semidirect |
| 225. C24×D4 | C25 | semidirect |
| 226. C24×D4 | C25 | semidirect |
| 227. C24×D4 | C25 | semidirect |
| 235. C25×C4 | C25 | semidirect |
| 236. C25×C4 | C25 | semidirect |
| 237. #3532 | C25 | semidirect |
| 238. C2×H(3,𝔽4) | C25 | semidirect |
| 239. C2×#560 | C25 | semidirect |
| 240. #3490 | C25 | semidirect |
| 241. #3484 | C25 | semidirect |
| 242. C2×#551 | C25 | semidirect |
| 243. C2×#546 | C25 | semidirect |
| 244. C2×D42 | C25 | semidirect |
| 245. C2×#543 | C25 | semidirect |
| 246. C2×#538 | C25 | semidirect |
| 247. C2×#535 | C25 | semidirect |
| 248. C2×#534 | C25 | semidirect |
| 249. C2×#534 | C25 | semidirect |
| 250. C22×#127 | C25 | semidirect |
| 251. C22×#126 | C25 | semidirect |
| 252. C22×#124 | C25 | semidirect |
| 253. C2×#525 | C25 | semidirect |
| 254. C22×#123 | C25 | semidirect |
| 255. C22×#123 | C25 | semidirect |
| 256. C22×C22⋊Q8 | C25 | semidirect |
| 257. C22×#121 | C25 | semidirect |
| 258. C22×#121 | C25 | semidirect |
| 260. C22×#120 | C25 | semidirect |
| 261. C22×#120 | C25 | semidirect |
| 262. C22×#120 | C25 | semidirect |
| 263. C22×#120 | C25 | semidirect |
| 264. C22×#120 | C25 | semidirect |
| 265. C22×#120 | C25 | semidirect |
| 266. C22×#120 | C25 | semidirect |
| 267. C22×#120 | C25 | semidirect |
| 268. C22×#120 | C25 | semidirect |
| 269. C2×#518 | C25 | semidirect |
| 270. C22×C4×D4 | C25 | semidirect |
| 271. C22×#117 | C25 | semidirect |
| 272. C23×C4⋊C4 | C25 | semidirect |
| 276. C23×C22⋊C4 | C25 | semidirect |
| 277. C23×C22⋊C4 | C25 | semidirect |
| 278. C23×C22⋊C4 | C25 | semidirect |
| 279. C23×C22⋊C4 | C25 | semidirect |
| 280. C23×C22⋊C4 | C25 | semidirect |
| 281. C23×C42 | C25 | semidirect |
| 312. C26 | C2×H(5,𝔽2) | semidirect |
| 325. C26 | C26 | semidirect |
| 326. C26 | C26 | semidirect |
| 327. C26 | C26 | semidirect |
| 329. C2×H(5,𝔽2) | C26 | semidirect |
| 331. C22×#41 | C26 | semidirect |
| 333. C23×Q8 | C26 | semidirect |
| 345. C23×D4 | C26 | semidirect |
| 346. C23×D4 | C26 | semidirect |
| 347. C23×D4 | C26 | semidirect |
| 348. C23×D4 | C26 | semidirect |
| 349. C23×D4 | C26 | semidirect |
| 358. C24×C4 | C26 | semidirect |
| 359. C24×C4 | C26 | semidirect |
| 360. H(3,𝔽4) | C26 | semidirect |
| 361. #560 | C26 | semidirect |
| 362. #551 | C26 | semidirect |
| 363. #546 | C26 | semidirect |
| 364. D42 | C26 | semidirect |
| 365. #543 | C26 | semidirect |
| 366. #538 | C26 | semidirect |
| 367. #535 | C26 | semidirect |
| 368. #534 | C26 | semidirect |
| 369. #534 | C26 | semidirect |
| 370. C2×#127 | C26 | semidirect |
| 371. C2×#126 | C26 | semidirect |
| 372. C2×#124 | C26 | semidirect |
| 373. #525 | C26 | semidirect |
| 374. C2×#123 | C26 | semidirect |
| 375. C2×#123 | C26 | semidirect |
| 376. C2×C22⋊Q8 | C26 | semidirect |
| 377. C2×#121 | C26 | semidirect |
| 378. C2×#121 | C26 | semidirect |
| 380. C2×#120 | C26 | semidirect |
| 381. C2×#120 | C26 | semidirect |
| 382. C2×#120 | C26 | semidirect |
| 383. C2×#120 | C26 | semidirect |
| 384. C2×#120 | C26 | semidirect |
| 385. C2×#120 | C26 | semidirect |
| 386. C2×#120 | C26 | semidirect |
| 387. C2×#120 | C26 | semidirect |
| 388. #518 | C26 | semidirect |
| 389. C2×C4×D4 | C26 | semidirect |
| 390. C2×#117 | C26 | semidirect |
| 391. C22×C4⋊C4 | C26 | semidirect |
| 395. C22×C22⋊C4 | C26 | semidirect |
| 396. C22×C22⋊C4 | C26 | semidirect |
| 397. C22×C22⋊C4 | C26 | semidirect |
| 398. C22×C22⋊C4 | C26 | semidirect |
| 399. C22×C22⋊C4 | C26 | semidirect |
| 400. C22×C42 | C26 | semidirect |
| 435. C25 | C22×H(5,𝔽2) | semidirect |
| 448. C25 | C27 | semidirect |
| 449. C25 | C27 | semidirect |
| 452. C2×#41 | C27 | semidirect |
| 454. C22×Q8 | C27 | semidirect |
| 466. C22×D4 | C27 | semidirect |
| 467. C22×D4 | C27 | semidirect |
| 468. C22×D4 | C27 | semidirect |
| 469. C22×D4 | C27 | semidirect |
| 478. C23×C4 | C27 | semidirect |
| 479. C23×C4 | C27 | semidirect |
| 480. #127 | C27 | semidirect |
| 481. #126 | C27 | semidirect |
| 482. #124 | C27 | semidirect |
| 483. #123 | C27 | semidirect |
| 484. #123 | C27 | semidirect |
| 485. C22⋊Q8 | C27 | semidirect |
| 486. #121 | C27 | semidirect |
| 487. #121 | C27 | semidirect |
| 489. #120 | C27 | semidirect |
| 490. #120 | C27 | semidirect |
| 491. #120 | C27 | semidirect |
| 492. #120 | C27 | semidirect |
| 493. #120 | C27 | semidirect |
| 494. C4×D4 | C27 | semidirect |
| 495. #117 | C27 | semidirect |
| 496. C2×C4⋊C4 | C27 | semidirect |
| 500. C2×C22⋊C4 | C27 | semidirect |
| 501. C2×C22⋊C4 | C27 | semidirect |
| 502. C2×C22⋊C4 | C27 | semidirect |
| 503. C2×C22⋊C4 | C27 | semidirect |
| 504. C2×C42 | C27 | semidirect |
| 536. C24 | #62817 | direct (N × H) |
| 539. C24 | C23×H(5,𝔽2) | semidirect |
| 550. C24 | C28 | semidirect |
| 553. C2×Q8 | C28 | semidirect |
| 563. C2×D4 | C28 | semidirect |
| 572. C22×C4 | C28 | semidirect |
| 573. C4⋊C4 | C28 | semidirect |
| 576. C22⋊C4 | C28 | semidirect |
| 577. C42 | C28 | semidirect |
| 604. C23 | C2×#62817 | direct (N × H) |
| 607. C23 | C24×H(5,𝔽2) | semidirect |
| 635. C22 | C22×#62817 | direct (N × H) |
| 642. C2 | C23×#62817 | direct (N × H) |
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta