← C23×#62842 #72324522
Subgroups — C23×#62842 #72324522
Order 2048.
16771240 conjugacy classes of subgroups.
The subgroup lattice has 736 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C23×#3449 | C2 | 1 | 4 | yes | maximal, complemented |
| 2 | C23×#3485 | C2 | 1 | 16 | yes | maximal, complemented |
| 3 | C24×#518 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C24×#534 | C2 | 1 | 8 | yes | maximal, complemented |
| 5 | C23×#3496 | C2 | 1 | 16 | yes | maximal, complemented |
| 6 | C22×#62842 | C2 | 1 | 448 | yes | maximal, direct product factor |
| 7 | C25×H(5,𝔽2) | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | C23×#3484 | C2 | 1 | 16 | yes | maximal, complemented |
| 9 | C24×H(5,𝔽2) | — | 2 | 256 | no | — |
| 10 | C24×H(5,𝔽2) | C22 | 1 | 16 | yes | complemented |
| 11 | C24×H(5,𝔽2) | C22 | 1 | 448 | yes | complemented |
| 12 | C24×H(5,𝔽2) | C22 | 1 | 16 | yes | complemented |
| 13 | C25×#41 | C22 | 1 | 4 | yes | complemented |
| 14 | C25×#41 | C22 | 1 | 8 | yes | complemented |
| 15 | C26×D4 | C22 | 1 | 1 | yes | characteristic |
| 16 | C26×D4 | C22 | 1 | 8 | yes | complemented |
| 17 | C26×D4 | C22 | 1 | 8 | yes | complemented |
| 18 | C2×#62842 | C22 | 1 | 28672 | yes | direct product factor |
| 19 | C22×#3485 | C22 | 1 | 3584 | yes | complemented |
| 20 | C22×#3496 | C22 | 1 | 3584 | yes | complemented |
| 21 | C22×#3484 | C22 | 1 | 3584 | yes | complemented |
| 22 | C23×#547 | C22 | 1 | 64 | yes | complemented |
| 23 | C23×#546 | C22 | 1 | 128 | yes | complemented |
| 24 | C23×D42 | C22 | 1 | 64 | yes | complemented |
| 25 | C22×#3449 | C22 | 1 | 896 | yes | complemented |
| 26 | C23×#536 | C22 | 1 | 16 | yes | complemented |
| 27 | C23×#537 | C22 | 1 | 16 | yes | complemented |
| 28 | C23×#535 | C22 | 1 | 16 | yes | complemented |
| 29 | C23×#534 | C22 | 1 | 16 | yes | complemented |
| 30 | C23×#534 | C22 | 1 | 64 | yes | complemented |
| 31 | C23×#534 | C22 | 1 | 1792 | yes | complemented |
| 32 | C23×#534 | C22 | 1 | 32 | yes | complemented |
| 33 | C23×#532 | C22 | 1 | 16 | yes | complemented |
| 34 | C23×#525 | C22 | 1 | 32 | yes | complemented |
| 35 | C24×#123 | C22 | 1 | 32 | yes | complemented |
| 36 | C24×#121 | C22 | 1 | 32 | yes | complemented |
| 37 | C24×#120 | C22 | 1 | 32 | yes | complemented |
| 38 | C23×#518 | C22 | 1 | 16 | yes | complemented |
| 39 | C23×#518 | C22 | 1 | 224 | yes | complemented |
| 40 | C24×C4×D4 | C22 | 1 | 8 | yes | complemented |
| 41 | C24×#117 | C22 | 1 | 2 | yes | complemented |
| 42 | C25×C22⋊C4 | C22 | 1 | 4 | yes | complemented |
| 43 | C28 | C23 | 1 | 2 | yes | — |
| 44 | C28 | C23 | 1 | 8 | yes | complemented |
| 45 | C23×H(5,𝔽2) | — | 2 | 1024 | no | — |
| 46 | C23×H(5,𝔽2) | — | 2 | 1024 | no | — |
| 47 | C23×H(5,𝔽2) | — | 2 | 28672 | no | — |
| 48 | C23×H(5,𝔽2) | C23 | 1 | 1792 | yes | complemented |
| 49 | C23×H(5,𝔽2) | C23 | 1 | 1792 | yes | complemented |
| 50 | C23×H(5,𝔽2) | C23 | 1 | 14336 | yes | complemented |
| 51 | C24×#41 | — | 2 | 512 | no | — |
| 52 | C24×#41 | — | 2 | 256 | no | — |
| 53 | C24×#41 | C23 | 1 | 16 | yes | — |
| 54 | C24×#41 | C23 | 1 | 16 | yes | complemented |
| 55 | C24×#41 | C23 | 1 | 64 | yes | complemented |
| 56 | C24×#41 | C23 | 1 | 448 | yes | complemented |
| 57 | C24×#41 | C23 | 1 | 896 | yes | complemented |
| 58 | C25×Q8 | C23 | 1 | 4 | yes | complemented |
| 59 | C25×D4 | — | 2 | 512 | no | — |
| 60 | C25×D4 | — | 2 | 512 | no | — |
| 61 | C25×D4 | D4 | 1 | 128 | yes | complemented |
| 62 | C25×D4 | C23 | 1 | 32 | yes | — |
| 63 | C25×D4 | C23 | 1 | 8 | yes | — |
| 64 | C25×D4 | C23 | 1 | 4 | yes | — |
| 65 | C25×D4 | C23 | 1 | 8 | yes | — |
| 66 | C25×D4 | C23 | 1 | 112 | yes | — |
| 67 | C25×D4 | C23 | 1 | 32 | yes | complemented |
| 68 | C25×D4 | C23 | 1 | 16 | yes | complemented |
| 69 | C25×D4 | C23 | 1 | 4 | yes | complemented |
| 70 | C25×D4 | C23 | 1 | 64 | yes | complemented |
| 71 | C25×D4 | C23 | 1 | 32 | yes | complemented |
| 72 | C25×D4 | C23 | 1 | 896 | yes | complemented |
| 73 | C25×D4 | C23 | 1 | 896 | yes | complemented |
| 74 | C26×C4 | C23 | 1 | 1 | yes | characteristic |
| 75 | C26×C4 | C23 | 1 | 8 | yes | complemented |
| 76 | C26×C4 | C23 | 1 | 8 | yes | complemented |
| 77 | C26×C4 | C23 | 1 | 8 | yes | complemented |
| 78 | #62842 | C23 | 1 | 262144 | yes | direct product factor |
| 79 | C2×#3485 | C23 | 1 | 114688 | yes | complemented |
| 80 | C2×#3496 | C23 | 1 | 114688 | yes | complemented |
| 81 | C2×#3484 | C23 | 1 | 114688 | yes | complemented |
| 82 | C22×#547 | C23 | 1 | 7168 | yes | complemented |
| 83 | C22×#546 | C23 | 1 | 14336 | yes | complemented |
| 84 | C22×D42 | C23 | 1 | 7168 | yes | complemented |
| 85 | C2×#3449 | C23 | 1 | 28672 | yes | complemented |
| 86 | C22×#536 | C23 | 1 | 1792 | yes | complemented |
| 87 | C22×#537 | C23 | 1 | 1792 | yes | complemented |
| 88 | C22×#535 | C23 | 1 | 1792 | yes | complemented |
| 89 | C22×#534 | C23 | 1 | 1792 | yes | complemented |
| 90 | C22×#534 | C23 | 1 | 7168 | yes | complemented |
| 91 | C22×#534 | C23 | 1 | 3584 | yes | complemented |
| 92 | C22×#534 | C23 | 1 | 57344 | yes | complemented |
| 93 | C22×#532 | C23 | 1 | 1792 | yes | complemented |
| 94 | C23×C4⋊Q8 | C23 | 1 | 16 | yes | complemented |
| 95 | C23×#127 | C23 | 1 | 16 | yes | complemented |
| 96 | C23×#124 | C23 | 1 | 32 | yes | complemented |
| 97 | C22×#525 | C23 | 1 | 3584 | yes | complemented |
| 98 | C23×#123 | C23 | 1 | 64 | yes | complemented |
| 99 | C23×#123 | C23 | 1 | 128 | yes | complemented |
| 100 | C23×#123 | C23 | 1 | 3584 | yes | complemented |
| 101 | C23×C22⋊Q8 | C23 | 1 | 64 | yes | complemented |
| 102 | C23×#121 | C23 | 1 | 64 | yes | complemented |
| 103 | C23×#121 | C23 | 1 | 128 | yes | complemented |
| 104 | C23×#121 | C23 | 1 | 64 | yes | complemented |
| 105 | C23×#121 | C23 | 1 | 3584 | yes | complemented |
| 106 | C23×#120 | C23 | 1 | 64 | yes | complemented |
| 107 | C23×#120 | C23 | 1 | 128 | yes | complemented |
| 108 | C23×#120 | C23 | 1 | 3584 | yes | complemented |
| 109 | C22×#518 | C23 | 1 | 1792 | yes | complemented |
| 110 | C22×#518 | C23 | 1 | 7168 | yes | complemented |
| 111 | C23×C4×D4 | C23 | 1 | 64 | yes | complemented |
| 112 | C23×C4×D4 | C23 | 1 | 64 | yes | complemented |
| 113 | C23×C4×D4 | C23 | 1 | 896 | yes | complemented |
| 114 | C23×#117 | C23 | 1 | 16 | yes | complemented |
| 115 | C23×#117 | C23 | 1 | 224 | yes | complemented |
| 116 | C24×C4⋊C4 | C23 | 1 | 4 | yes | complemented |
| 117 | C24×C4⋊C4 | C23 | 1 | 32 | yes | complemented |
| 118 | C24×C22⋊C4 | C23 | 1 | 4 | yes | — |
| 119 | C24×C22⋊C4 | C23 | 1 | 8 | yes | complemented |
| 120 | C24×C22⋊C4 | C23 | 1 | 32 | yes | complemented |
| 121 | C24×C22⋊C4 | C23 | 1 | 64 | yes | complemented |
| 122 | C24×C22⋊C4 | C23 | 1 | 448 | yes | complemented |
| 123 | C24×C42 | C23 | 1 | 4 | yes | complemented |
| 124 | C27 | — | 2 | 256 | no | — |
| 125 | C27 | — | 8 | 32 | no | — |
| 126 | C27 | — | 8 | 128 | no | — |
| 127 | C27 | C2×D4 | 1 | 128 | yes | complemented |
| 128 | C27 | C24 | 1 | 8 | yes | — |
| 129 | C27 | C24 | 1 | 32 | yes | — |
| 130 | C27 | C24 | 1 | 1 | yes | characteristic |
| 131 | C27 | C24 | 1 | 4 | yes | — |
| 132 | C27 | C24 | 1 | 8 | yes | — |
| 133 | C27 | C24 | 1 | 112 | yes | — |
| 134 | C27 | C24 | 1 | 448 | yes | complemented |
| 135 | C22×H(5,𝔽2) | — | 2 | 57344 | no | — |
| 136 | C22×H(5,𝔽2) | — | 2 | 57344 | no | — |
| 137 | C22×H(5,𝔽2) | — | 2 | 458752 | no | — |
| 138 | C22×H(5,𝔽2) | C24 | 1 | 28672 | yes | complemented |
| 139 | C22×H(5,𝔽2) | C24 | 1 | 28672 | yes | complemented |
| 140 | C22×H(5,𝔽2) | C24 | 1 | 65536 | yes | complemented |
| 141 | C23×#41 | — | 2 | 2048 | no | — |
| 142 | C23×#41 | — | 2 | 28672 | no | — |
| 143 | C23×#41 | — | 2 | 512 | no | — |
| 144 | C23×#41 | — | 2 | 512 | no | — |
| 145 | C23×#41 | — | 2 | 14336 | no | — |
| 146 | C23×#41 | C24 | 1 | 896 | yes | — |
| 147 | C23×#41 | C24 | 1 | 896 | yes | complemented |
| 148 | C23×#41 | C24 | 1 | 3584 | yes | complemented |
| 149 | C23×#41 | C24 | 1 | 7168 | yes | complemented |
| 150 | C23×#41 | C24 | 1 | 14336 | yes | complemented |
| 151 | C24×Q8 | — | 2 | 128 | no | — |
| 152 | C24×Q8 | C24 | 1 | 16 | yes | — |
| 153 | C24×Q8 | C24 | 1 | 224 | yes | complemented |
| 154 | C24×D4 | — | 2 | 256 | no | — |
| 155 | C24×D4 | — | 2 | 512 | no | — |
| 156 | C24×D4 | — | 2 | 1024 | no | — |
| 157 | C24×D4 | — | 2 | 1024 | no | — |
| 158 | C24×D4 | — | 2 | 28672 | no | — |
| 159 | C24×D4 | — | 2 | 2048 | no | — |
| 160 | C24×D4 | — | 2 | 28672 | no | — |
| 161 | C24×D4 | — | 2 | 128 | no | — |
| 162 | C24×D4 | — | 8 | 256 | no | — |
| 163 | C24×D4 | C2×D4 | 1 | 512 | yes | complemented |
| 164 | C24×D4 | C2×D4 | 1 | 256 | yes | complemented |
| 165 | C24×D4 | C2×D4 | 1 | 7168 | yes | complemented |
| 166 | C24×D4 | C24 | 1 | 16 | yes | — |
| 167 | C24×D4 | C24 | 1 | 64 | yes | — |
| 168 | C24×D4 | C24 | 1 | 16 | yes | — |
| 169 | C24×D4 | C24 | 1 | 448 | yes | — |
| 170 | C24×D4 | C24 | 1 | 1792 | yes | — |
| 171 | C24×D4 | C24 | 1 | 16 | yes | — |
| 172 | C24×D4 | C24 | 1 | 64 | yes | — |
| 173 | C24×D4 | C24 | 1 | 16 | yes | — |
| 174 | C24×D4 | C24 | 1 | 448 | yes | — |
| 175 | C24×D4 | C24 | 1 | 224 | yes | — |
| 176 | C24×D4 | C24 | 1 | 1792 | yes | — |
| 177 | C24×D4 | C24 | 1 | 896 | yes | complemented |
| 178 | C24×D4 | C24 | 1 | 224 | yes | complemented |
| 179 | C24×D4 | C24 | 1 | 1792 | yes | complemented |
| 180 | C24×D4 | C24 | 1 | 3584 | yes | complemented |
| 181 | C24×D4 | C24 | 1 | 1792 | yes | complemented |
| 182 | C24×D4 | C24 | 1 | 14336 | yes | complemented |
| 183 | C24×D4 | C24 | 1 | 14336 | yes | complemented |
| 184 | C25×C4 | — | 2 | 256 | no | — |
| 185 | C25×C4 | — | 2 | 256 | no | — |
| 186 | C25×C4 | — | 8 | 64 | no | — |
| 187 | C25×C4 | C2×D4 | 1 | 64 | yes | complemented |
| 188 | C25×C4 | C24 | 1 | 8 | yes | — |
| 189 | C25×C4 | C24 | 1 | 32 | yes | — |
| 190 | C25×C4 | C24 | 1 | 32 | yes | — |
| 191 | C25×C4 | C24 | 1 | 8 | yes | — |
| 192 | C25×C4 | C24 | 1 | 32 | yes | — |
| 193 | C25×C4 | C24 | 1 | 4 | yes | — |
| 194 | C25×C4 | C24 | 1 | 2 | yes | — |
| 195 | C25×C4 | C24 | 1 | 56 | yes | — |
| 196 | C25×C4 | C24 | 1 | 448 | yes | complemented |
| 197 | C25×C4 | C24 | 1 | 448 | yes | complemented |
| 198 | C25×C4 | C24 | 1 | 448 | yes | complemented |
| 199 | #3496 | C24 | 1 | 524288 | yes | complemented |
| 200 | #3485 | C24 | 1 | 524288 | yes | complemented |
| 201 | #3484 | C24 | 1 | 524288 | yes | complemented |
| 202 | C2×#547 | C24 | 1 | 114688 | yes | complemented |
| 203 | C2×#546 | C24 | 1 | 229376 | yes | complemented |
| 204 | C2×D42 | C24 | 1 | 114688 | yes | complemented |
| 205 | #3449 | C24 | 1 | 131072 | yes | complemented |
| 206 | C2×#537 | C24 | 1 | 28672 | yes | complemented |
| 207 | C2×#536 | C24 | 1 | 28672 | yes | complemented |
| 208 | C2×#535 | C24 | 1 | 28672 | yes | complemented |
| 209 | C2×#534 | C24 | 1 | 28672 | yes | complemented |
| 210 | C2×#534 | C24 | 1 | 114688 | yes | complemented |
| 211 | C2×#534 | C24 | 1 | 57344 | yes | complemented |
| 212 | C2×#534 | C24 | 1 | 262144 | yes | complemented |
| 213 | C2×#532 | C24 | 1 | 28672 | yes | complemented |
| 214 | C22×C4⋊Q8 | C24 | 1 | 896 | yes | complemented |
| 215 | C22×#127 | C24 | 1 | 896 | yes | complemented |
| 216 | C22×#124 | C24 | 1 | 1792 | yes | complemented |
| 217 | C2×#525 | C24 | 1 | 57344 | yes | complemented |
| 218 | C22×#123 | C24 | 1 | 3584 | yes | complemented |
| 219 | C22×#123 | C24 | 1 | 7168 | yes | complemented |
| 220 | C22×#123 | C24 | 1 | 57344 | yes | complemented |
| 221 | C22×C22⋊Q8 | C24 | 1 | 3584 | yes | complemented |
| 222 | C22×#121 | C24 | 1 | 3584 | yes | complemented |
| 223 | C22×#121 | C24 | 1 | 7168 | yes | complemented |
| 224 | C22×#121 | C24 | 1 | 3584 | yes | complemented |
| 225 | C22×#121 | C24 | 1 | 57344 | yes | complemented |
| 226 | C22×#120 | C24 | 1 | 3584 | yes | complemented |
| 227 | C22×#120 | C24 | 1 | 7168 | yes | complemented |
| 228 | C22×#120 | C24 | 1 | 57344 | yes | complemented |
| 229 | C2×#518 | C24 | 1 | 28672 | yes | complemented |
| 230 | C2×#518 | C24 | 1 | 32768 | yes | complemented |
| 231 | C22×C4×D4 | C24 | 1 | 3584 | yes | complemented |
| 232 | C22×C4×D4 | C24 | 1 | 3584 | yes | complemented |
| 233 | C22×C4×D4 | C24 | 1 | 14336 | yes | complemented |
| 234 | C22×#117 | C24 | 1 | 896 | yes | complemented |
| 235 | C22×#117 | C24 | 1 | 3584 | yes | complemented |
| 236 | C23×C4⋊C4 | C24 | 1 | 64 | yes | — |
| 237 | C23×C4⋊C4 | C24 | 1 | 16 | yes | — |
| 238 | C23×C4⋊C4 | C24 | 1 | 224 | yes | complemented |
| 239 | C23×C4⋊C4 | C24 | 1 | 1792 | yes | complemented |
| 240 | C23×C22⋊C4 | C24 | 1 | 16 | yes | — |
| 241 | C23×C22⋊C4 | C24 | 1 | 224 | yes | — |
| 242 | C23×C22⋊C4 | C24 | 1 | 32 | yes | — |
| 243 | C23×C22⋊C4 | C24 | 1 | 128 | yes | — |
| 244 | C23×C22⋊C4 | C24 | 1 | 448 | yes | complemented |
| 245 | C23×C22⋊C4 | C24 | 1 | 1792 | yes | complemented |
| 246 | C23×C22⋊C4 | C24 | 1 | 3584 | yes | complemented |
| 247 | C23×C22⋊C4 | C24 | 1 | 7168 | yes | complemented |
| 248 | C23×C42 | C24 | 1 | 16 | yes | — |
| 249 | C23×C42 | C24 | 1 | 224 | yes | complemented |
| 250 | C26 | — | 2 | 128 | no | — |
| 251 | C26 | — | 2 | 512 | no | — |
| 252 | C26 | — | 2 | 7168 | no | — |
| 253 | C26 | — | 4 | 64 | no | — |
| 254 | C26 | — | 4 | 16 | no | — |
| 255 | C26 | — | 4 | 128 | no | — |
| 256 | C26 | — | 4 | 128 | no | — |
| 257 | C26 | — | 4 | 512 | no | — |
| 258 | C26 | — | 8 | 1024 | no | — |
| 259 | C26 | — | 8 | 896 | no | — |
| 260 | C26 | — | 8 | 3584 | no | — |
| 261 | C26 | — | 8 | 4096 | no | — |
| 262 | C26 | C22×D4 | 1 | 256 | yes | — |
| 263 | C26 | C22×D4 | 1 | 32 | yes | — |
| 264 | C26 | C22×D4 | 1 | 128 | yes | — |
| 265 | C26 | C22×D4 | 1 | 3584 | yes | complemented |
| 266 | C26 | C25 | 1 | 16 | yes | — |
| 267 | C26 | C25 | 1 | 1 | yes | characteristic |
| 268 | C26 | C25 | 1 | 8 | yes | — |
| 269 | C26 | C25 | 1 | 2 | yes | — |
| 270 | C26 | C25 | 1 | 224 | yes | — |
| 271 | C26 | C25 | 1 | 896 | yes | — |
| 272 | C26 | C25 | 1 | 28 | yes | — |
| 273 | C26 | C25 | 1 | 112 | yes | — |
| 274 | C26 | C25 | 1 | 224 | yes | — |
| 275 | C26 | C25 | 1 | 896 | yes | — |
| 276 | C26 | C25 | 1 | 3584 | yes | complemented |
| 277 | C2×H(5,𝔽2) | — | 2 | 458752 | no | — |
| 278 | C2×H(5,𝔽2) | — | 2 | 458752 | no | — |
| 279 | C2×H(5,𝔽2) | — | 2 | 1048576 | no | — |
| 280 | C2×H(5,𝔽2) | C25 | 1 | 65536 | yes | complemented |
| 281 | C2×H(5,𝔽2) | C25 | 1 | 65536 | yes | complemented |
| 282 | C22×#41 | — | 2 | 57344 | no | — |
| 283 | C22×#41 | — | 2 | 229376 | no | — |
| 284 | C22×#41 | — | 2 | 14336 | no | — |
| 285 | C22×#41 | — | 2 | 14336 | no | — |
| 286 | C22×#41 | — | 2 | 114688 | no | — |
| 287 | C22×#41 | C25 | 1 | 7168 | yes | — |
| 288 | C22×#41 | C25 | 1 | 7168 | yes | complemented |
| 289 | C22×#41 | C25 | 1 | 28672 | yes | complemented |
| 290 | C22×#41 | C25 | 1 | 16384 | yes | complemented |
| 291 | C22×#41 | C25 | 1 | 32768 | yes | complemented |
| 292 | C23×Q8 | — | 2 | 256 | no | — |
| 293 | C23×Q8 | — | 2 | 3584 | no | — |
| 294 | C23×Q8 | C25 | 1 | 448 | yes | — |
| 295 | C23×Q8 | C25 | 1 | 1792 | yes | complemented |
| 296 | C23×D4 | — | 2 | 256 | no | — |
| 297 | C23×D4 | — | 2 | 1024 | no | — |
| 298 | C23×D4 | — | 2 | 256 | no | — |
| 299 | C23×D4 | — | 2 | 7168 | no | — |
| 300 | C23×D4 | — | 2 | 14336 | no | — |
| 301 | C23×D4 | — | 2 | 28672 | no | — |
| 302 | C23×D4 | — | 2 | 28672 | no | — |
| 303 | C23×D4 | — | 2 | 229376 | no | — |
| 304 | C23×D4 | — | 2 | 57344 | no | — |
| 305 | C23×D4 | — | 2 | 229376 | no | — |
| 306 | C23×D4 | — | 2 | 256 | no | — |
| 307 | C23×D4 | — | 2 | 3584 | no | — |
| 308 | C23×D4 | — | 4 | 512 | no | — |
| 309 | C23×D4 | — | 8 | 7168 | no | — |
| 310 | C23×D4 | C22×D4 | 1 | 512 | yes | — |
| 311 | C23×D4 | C22×D4 | 1 | 14336 | yes | complemented |
| 312 | C23×D4 | C22×D4 | 1 | 7168 | yes | complemented |
| 313 | C23×D4 | C22×D4 | 1 | 57344 | yes | complemented |
| 314 | C23×D4 | C25 | 1 | 448 | yes | — |
| 315 | C23×D4 | C25 | 1 | 1792 | yes | — |
| 316 | C23×D4 | C25 | 1 | 448 | yes | — |
| 317 | C23×D4 | C25 | 1 | 3584 | yes | — |
| 318 | C23×D4 | C25 | 1 | 14336 | yes | — |
| 319 | C23×D4 | C25 | 1 | 448 | yes | — |
| 320 | C23×D4 | C25 | 1 | 1792 | yes | — |
| 321 | C23×D4 | C25 | 1 | 448 | yes | — |
| 322 | C23×D4 | C25 | 1 | 3584 | yes | — |
| 323 | C23×D4 | C25 | 1 | 1792 | yes | — |
| 324 | C23×D4 | C25 | 1 | 4096 | yes | — |
| 325 | C23×D4 | C25 | 1 | 7168 | yes | complemented |
| 326 | C23×D4 | C25 | 1 | 1792 | yes | complemented |
| 327 | C23×D4 | C25 | 1 | 14336 | yes | complemented |
| 328 | C23×D4 | C25 | 1 | 28672 | yes | complemented |
| 329 | C23×D4 | C25 | 1 | 14336 | yes | complemented |
| 330 | C23×D4 | C25 | 1 | 32768 | yes | complemented |
| 331 | C23×D4 | C25 | 1 | 32768 | yes | complemented |
| 332 | C24×C4 | — | 2 | 128 | no | — |
| 333 | C24×C4 | — | 2 | 512 | no | — |
| 334 | C24×C4 | — | 2 | 7168 | no | — |
| 335 | C24×C4 | — | 2 | 512 | no | — |
| 336 | C24×C4 | — | 2 | 7168 | no | — |
| 337 | C24×C4 | — | 4 | 64 | no | — |
| 338 | C24×C4 | — | 4 | 256 | no | — |
| 339 | C24×C4 | — | 8 | 1792 | no | — |
| 340 | C24×C4 | C22×D4 | 1 | 128 | yes | — |
| 341 | C24×C4 | C22×D4 | 1 | 64 | yes | — |
| 342 | C24×C4 | C22×D4 | 1 | 1792 | yes | complemented |
| 343 | C24×C4 | C25 | 1 | 224 | yes | — |
| 344 | C24×C4 | C25 | 1 | 896 | yes | — |
| 345 | C24×C4 | C25 | 1 | 896 | yes | — |
| 346 | C24×C4 | C25 | 1 | 16 | yes | — |
| 347 | C24×C4 | C25 | 1 | 16 | yes | — |
| 348 | C24×C4 | C25 | 1 | 224 | yes | — |
| 349 | C24×C4 | C25 | 1 | 896 | yes | — |
| 350 | C24×C4 | C25 | 1 | 112 | yes | — |
| 351 | C24×C4 | C25 | 1 | 56 | yes | — |
| 352 | C24×C4 | C25 | 1 | 4 | yes | — |
| 353 | C24×C4 | C25 | 1 | 448 | yes | — |
| 354 | C24×C4 | C25 | 1 | 3584 | yes | complemented |
| 355 | C24×C4 | C25 | 1 | 3584 | yes | complemented |
| 356 | C24×C4 | C25 | 1 | 3584 | yes | complemented |
| 357 | #547 | C25 | 1 | 262144 | yes | complemented |
| 358 | #546 | C25 | 1 | 524288 | yes | complemented |
| 359 | D42 | C25 | 1 | 262144 | yes | complemented |
| 360 | #537 | C25 | 1 | 65536 | yes | complemented |
| 361 | #536 | C25 | 1 | 65536 | yes | complemented |
| 362 | #535 | C25 | 1 | 65536 | yes | complemented |
| 363 | #534 | C25 | 1 | 65536 | yes | complemented |
| 364 | #534 | C25 | 1 | 262144 | yes | complemented |
| 365 | #534 | C25 | 1 | 131072 | yes | complemented |
| 366 | #532 | C25 | 1 | 65536 | yes | complemented |
| 367 | C2×C4⋊Q8 | C25 | 1 | 7168 | yes | complemented |
| 368 | C2×#127 | C25 | 1 | 7168 | yes | complemented |
| 369 | C2×#124 | C25 | 1 | 14336 | yes | complemented |
| 370 | #525 | C25 | 1 | 131072 | yes | complemented |
| 371 | C2×#123 | C25 | 1 | 28672 | yes | complemented |
| 372 | C2×#123 | C25 | 1 | 57344 | yes | complemented |
| 373 | C2×#123 | C25 | 1 | 131072 | yes | complemented |
| 374 | C2×C22⋊Q8 | C25 | 1 | 28672 | yes | complemented |
| 375 | C2×#121 | C25 | 1 | 28672 | yes | complemented |
| 376 | C2×#121 | C25 | 1 | 57344 | yes | complemented |
| 377 | C2×#121 | C25 | 1 | 28672 | yes | complemented |
| 378 | C2×#121 | C25 | 1 | 131072 | yes | complemented |
| 379 | C2×#120 | C25 | 1 | 28672 | yes | complemented |
| 380 | C2×#120 | C25 | 1 | 57344 | yes | complemented |
| 381 | C2×#120 | C25 | 1 | 131072 | yes | complemented |
| 382 | #518 | C25 | 1 | 65536 | yes | complemented |
| 383 | C2×C4×D4 | C25 | 1 | 28672 | yes | complemented |
| 384 | C2×C4×D4 | C25 | 1 | 28672 | yes | complemented |
| 385 | C2×C4×D4 | C25 | 1 | 32768 | yes | complemented |
| 386 | C2×#117 | C25 | 1 | 7168 | yes | complemented |
| 387 | C2×#117 | C25 | 1 | 8192 | yes | complemented |
| 388 | C22×C4⋊C4 | C25 | 1 | 1792 | yes | — |
| 389 | C22×C4⋊C4 | C25 | 1 | 448 | yes | — |
| 390 | C22×C4⋊C4 | C25 | 1 | 1792 | yes | complemented |
| 391 | C22×C4⋊C4 | C25 | 1 | 14336 | yes | complemented |
| 392 | C22×C22⋊C4 | C25 | 1 | 448 | yes | — |
| 393 | C22×C22⋊C4 | C25 | 1 | 1792 | yes | — |
| 394 | C22×C22⋊C4 | C25 | 1 | 896 | yes | — |
| 395 | C22×C22⋊C4 | C25 | 1 | 3584 | yes | — |
| 396 | C22×C22⋊C4 | C25 | 1 | 3584 | yes | complemented |
| 397 | C22×C22⋊C4 | C25 | 1 | 14336 | yes | complemented |
| 398 | C22×C22⋊C4 | C25 | 1 | 28672 | yes | complemented |
| 399 | C22×C22⋊C4 | C25 | 1 | 16384 | yes | complemented |
| 400 | C22×C42 | C25 | 1 | 448 | yes | — |
| 401 | C22×C42 | C25 | 1 | 1792 | yes | complemented |
| 402 | C25 | — | 2 | 16 | no | — |
| 403 | C25 | — | 2 | 128 | no | — |
| 404 | C25 | — | 2 | 32 | no | — |
| 405 | C25 | — | 2 | 1792 | no | — |
| 406 | C25 | — | 2 | 128 | no | — |
| 407 | C25 | — | 2 | 256 | no | — |
| 408 | C25 | — | 2 | 7168 | no | — |
| 409 | C25 | — | 2 | 28672 | no | — |
| 410 | C25 | — | 4 | 896 | no | — |
| 411 | C25 | — | 4 | 256 | no | — |
| 412 | C25 | — | 4 | 2048 | no | — |
| 413 | C25 | — | 4 | 224 | no | — |
| 414 | C25 | — | 4 | 1792 | no | — |
| 415 | C25 | — | 4 | 1792 | no | — |
| 416 | C25 | — | 4 | 1024 | no | — |
| 417 | C25 | — | 4 | 7168 | no | — |
| 418 | C25 | — | 4 | 2048 | no | — |
| 419 | C25 | — | 8 | 4096 | no | — |
| 420 | C25 | — | 8 | 14336 | no | — |
| 421 | C25 | — | 8 | 3584 | no | — |
| 422 | C25 | — | 8 | 14336 | no | — |
| 423 | C25 | — | 8 | 57344 | no | — |
| 424 | C25 | C23×D4 | 1 | 32 | yes | — |
| 425 | C25 | C23×D4 | 1 | 128 | yes | — |
| 426 | C25 | C23×D4 | 1 | 16 | yes | — |
| 427 | C25 | C23×D4 | 1 | 3584 | yes | — |
| 428 | C25 | C23×D4 | 1 | 448 | yes | — |
| 429 | C25 | C23×D4 | 1 | 1792 | yes | — |
| 430 | C25 | C23×D4 | 1 | 14336 | yes | complemented |
| 431 | C25 | C26 | 1 | 224 | yes | — |
| 432 | C25 | C26 | 1 | 28 | yes | — |
| 433 | C25 | C26 | 1 | 112 | yes | — |
| 434 | C25 | C26 | 1 | 14 | yes | — |
| 435 | C25 | C26 | 1 | 3584 | yes | — |
| 436 | C25 | C26 | 1 | 896 | yes | — |
| 437 | C25 | C26 | 1 | 112 | yes | — |
| 438 | C25 | C26 | 1 | 896 | yes | — |
| 439 | C25 | C26 | 1 | 448 | yes | — |
| 440 | C25 | C26 | 1 | 1024 | yes | — |
| 441 | C25 | C26 | 1 | 1 | yes | characteristic |
| 442 | C25 | C26 | 1 | 4096 | yes | complemented |
| 443 | H(5,𝔽2) | — | 2 | 524288 | no | — |
| 444 | H(5,𝔽2) | — | 2 | 524288 | no | — |
| 445 | C2×#41 | — | 2 | 229376 | no | — |
| 446 | C2×#41 | — | 2 | 262144 | no | — |
| 447 | C2×#41 | — | 2 | 57344 | no | — |
| 448 | C2×#41 | — | 2 | 57344 | no | — |
| 449 | C2×#41 | — | 2 | 131072 | no | — |
| 450 | C2×#41 | C26 | 1 | 8192 | yes | — |
| 451 | C2×#41 | C26 | 1 | 8192 | yes | complemented |
| 452 | C2×#41 | C26 | 1 | 32768 | yes | complemented |
| 453 | C22×Q8 | — | 2 | 3584 | no | — |
| 454 | C22×Q8 | — | 2 | 14336 | no | — |
| 455 | C22×Q8 | C26 | 1 | 1792 | yes | — |
| 456 | C22×Q8 | C26 | 1 | 2048 | yes | complemented |
| 457 | C22×D4 | — | 2 | 3584 | no | — |
| 458 | C22×D4 | — | 2 | 14336 | no | — |
| 459 | C22×D4 | — | 2 | 3584 | no | — |
| 460 | C22×D4 | — | 2 | 28672 | no | — |
| 461 | C22×D4 | — | 2 | 57344 | no | — |
| 462 | C22×D4 | — | 2 | 114688 | no | — |
| 463 | C22×D4 | — | 2 | 114688 | no | — |
| 464 | C22×D4 | — | 2 | 262144 | no | — |
| 465 | C22×D4 | — | 2 | 229376 | no | — |
| 466 | C22×D4 | — | 2 | 262144 | no | — |
| 467 | C22×D4 | — | 2 | 3584 | no | — |
| 468 | C22×D4 | — | 2 | 14336 | no | — |
| 469 | C22×D4 | — | 4 | 7168 | no | — |
| 470 | C22×D4 | — | 8 | 28672 | no | — |
| 471 | C22×D4 | C23×D4 | 1 | 7168 | yes | — |
| 472 | C22×D4 | C23×D4 | 1 | 57344 | yes | complemented |
| 473 | C22×D4 | C23×D4 | 1 | 28672 | yes | complemented |
| 474 | C22×D4 | C23×D4 | 1 | 65536 | yes | complemented |
| 475 | C22×D4 | C26 | 1 | 1792 | yes | — |
| 476 | C22×D4 | C26 | 1 | 7168 | yes | — |
| 477 | C22×D4 | C26 | 1 | 16384 | yes | — |
| 478 | C22×D4 | C26 | 1 | 1792 | yes | — |
| 479 | C22×D4 | C26 | 1 | 1792 | yes | — |
| 480 | C22×D4 | C26 | 1 | 4096 | yes | — |
| 481 | C22×D4 | C26 | 1 | 7168 | yes | — |
| 482 | C22×D4 | C26 | 1 | 1792 | yes | — |
| 483 | C22×D4 | C26 | 1 | 2048 | yes | — |
| 484 | C22×D4 | C26 | 1 | 4096 | yes | — |
| 485 | C22×D4 | C26 | 1 | 16384 | yes | complemented |
| 486 | C22×D4 | C26 | 1 | 8192 | yes | complemented |
| 487 | C22×D4 | C26 | 1 | 2048 | yes | complemented |
| 488 | C22×D4 | C26 | 1 | 32768 | yes | complemented |
| 489 | C22×D4 | C26 | 1 | 16384 | yes | complemented |
| 490 | C23×C4 | — | 2 | 1792 | no | — |
| 491 | C23×C4 | — | 2 | 128 | no | — |
| 492 | C23×C4 | — | 2 | 7168 | no | — |
| 493 | C23×C4 | — | 2 | 28672 | no | — |
| 494 | C23×C4 | — | 2 | 128 | no | — |
| 495 | C23×C4 | — | 2 | 7168 | no | — |
| 496 | C23×C4 | — | 2 | 28672 | no | — |
| 497 | C23×C4 | — | 4 | 896 | no | — |
| 498 | C23×C4 | — | 4 | 3584 | no | — |
| 499 | C23×C4 | — | 8 | 7168 | no | — |
| 500 | C23×C4 | C23×D4 | 1 | 64 | yes | — |
| 501 | C23×C4 | C23×D4 | 1 | 1792 | yes | — |
| 502 | C23×C4 | C23×D4 | 1 | 896 | yes | — |
| 503 | C23×C4 | C23×D4 | 1 | 7168 | yes | complemented |
| 504 | C23×C4 | C26 | 1 | 224 | yes | — |
| 505 | C23×C4 | C26 | 1 | 224 | yes | — |
| 506 | C23×C4 | C26 | 1 | 3584 | yes | — |
| 507 | C23×C4 | C26 | 1 | 3584 | yes | — |
| 508 | C23×C4 | C26 | 1 | 896 | yes | — |
| 509 | C23×C4 | C26 | 1 | 896 | yes | — |
| 510 | C23×C4 | C26 | 1 | 3584 | yes | — |
| 511 | C23×C4 | C26 | 1 | 56 | yes | — |
| 512 | C23×C4 | C26 | 1 | 224 | yes | — |
| 513 | C23×C4 | C26 | 1 | 448 | yes | — |
| 514 | C23×C4 | C26 | 1 | 512 | yes | — |
| 515 | C23×C4 | C26 | 1 | 4096 | yes | complemented |
| 516 | C23×C4 | C26 | 1 | 4096 | yes | complemented |
| 517 | C23×C4 | C26 | 1 | 4096 | yes | complemented |
| 518 | C4⋊Q8 | C26 | 1 | 8192 | yes | complemented |
| 519 | #127 | C26 | 1 | 8192 | yes | complemented |
| 520 | #124 | C26 | 1 | 16384 | yes | complemented |
| 521 | #123 | C26 | 1 | 32768 | yes | complemented |
| 522 | #123 | C26 | 1 | 65536 | yes | complemented |
| 523 | C22⋊Q8 | C26 | 1 | 32768 | yes | complemented |
| 524 | #121 | C26 | 1 | 32768 | yes | complemented |
| 525 | #121 | C26 | 1 | 65536 | yes | complemented |
| 526 | #121 | C26 | 1 | 32768 | yes | complemented |
| 527 | #120 | C26 | 1 | 32768 | yes | complemented |
| 528 | #120 | C26 | 1 | 65536 | yes | complemented |
| 529 | C4×D4 | C26 | 1 | 32768 | yes | complemented |
| 530 | C4×D4 | C26 | 1 | 32768 | yes | complemented |
| 531 | #117 | C26 | 1 | 8192 | yes | complemented |
| 532 | C2×C4⋊C4 | C26 | 1 | 7168 | yes | — |
| 533 | C2×C4⋊C4 | C26 | 1 | 1792 | yes | — |
| 534 | C2×C4⋊C4 | C26 | 1 | 2048 | yes | complemented |
| 535 | C2×C4⋊C4 | C26 | 1 | 16384 | yes | complemented |
| 536 | C2×C22⋊C4 | C26 | 1 | 1792 | yes | — |
| 537 | C2×C22⋊C4 | C26 | 1 | 2048 | yes | — |
| 538 | C2×C22⋊C4 | C26 | 1 | 3584 | yes | — |
| 539 | C2×C22⋊C4 | C26 | 1 | 14336 | yes | — |
| 540 | C2×C22⋊C4 | C26 | 1 | 4096 | yes | complemented |
| 541 | C2×C22⋊C4 | C26 | 1 | 16384 | yes | complemented |
| 542 | C2×C22⋊C4 | C26 | 1 | 32768 | yes | complemented |
| 543 | C2×C42 | C26 | 1 | 1792 | yes | — |
| 544 | C2×C42 | C26 | 1 | 2048 | yes | complemented |
| 545 | C24 | — | 2 | 256 | no | — |
| 546 | C24 | — | 2 | 128 | no | — |
| 547 | C24 | — | 2 | 1024 | no | — |
| 548 | C24 | — | 2 | 112 | no | — |
| 549 | C24 | — | 2 | 896 | no | — |
| 550 | C24 | — | 2 | 224 | no | — |
| 551 | C24 | — | 2 | 3584 | no | — |
| 552 | C24 | — | 2 | 896 | no | — |
| 553 | C24 | — | 2 | 1792 | no | — |
| 554 | C24 | — | 2 | 14336 | no | — |
| 555 | C24 | — | 2 | 16384 | no | — |
| 556 | C24 | — | 4 | 1792 | no | — |
| 557 | C24 | — | 4 | 1792 | no | — |
| 558 | C24 | — | 4 | 14336 | no | — |
| 559 | C24 | — | 4 | 448 | no | — |
| 560 | C24 | — | 4 | 3584 | no | — |
| 561 | C24 | — | 4 | 3584 | no | — |
| 562 | C24 | — | 4 | 7168 | no | — |
| 563 | C24 | — | 4 | 14336 | no | — |
| 564 | C24 | — | 4 | 14336 | no | — |
| 565 | C24 | — | 4 | 1024 | no | — |
| 566 | C24 | — | 8 | 28672 | no | — |
| 567 | C24 | — | 8 | 28672 | no | — |
| 568 | C24 | — | 8 | 2048 | no | — |
| 569 | C24 | — | 8 | 8192 | no | — |
| 570 | C24 | — | 8 | 114688 | no | — |
| 571 | C24 | C24×D4 | 1 | 224 | yes | — |
| 572 | C24 | C24×D4 | 1 | 896 | yes | — |
| 573 | C24 | C24×D4 | 1 | 112 | yes | — |
| 574 | C24 | C24×D4 | 1 | 7168 | yes | — |
| 575 | C24 | C24×D4 | 1 | 896 | yes | — |
| 576 | C24 | C24×D4 | 1 | 3584 | yes | — |
| 577 | C24 | C24×D4 | 1 | 8 | yes | — |
| 578 | C24 | C24×D4 | 1 | 8192 | yes | complemented |
| 579 | C24 | H(7,𝔽2) | 1 | 16 | yes | — |
| 580 | C24 | C27 | 1 | 448 | yes | — |
| 581 | C24 | C27 | 1 | 56 | yes | — |
| 582 | C24 | C27 | 1 | 224 | yes | — |
| 583 | C24 | C27 | 1 | 28 | yes | — |
| 584 | C24 | C27 | 1 | 2048 | yes | — |
| 585 | C24 | C27 | 1 | 512 | yes | — |
| 586 | C24 | C27 | 1 | 64 | yes | — |
| 587 | C24 | C27 | 1 | 512 | yes | — |
| 588 | C24 | C27 | 1 | 256 | yes | — |
| 589 | C24 | C27 | 1 | 7 | yes | — |
| 590 | #41 | — | 2 | 131072 | no | — |
| 591 | #41 | — | 2 | 32768 | no | — |
| 592 | #41 | — | 2 | 32768 | no | — |
| 593 | C2×Q8 | — | 2 | 7168 | no | — |
| 594 | C2×Q8 | — | 2 | 8192 | no | — |
| 595 | C2×Q8 | C27 | 1 | 1024 | yes | — |
| 596 | C2×D4 | — | 2 | 7168 | no | — |
| 597 | C2×D4 | — | 2 | 28672 | no | — |
| 598 | C2×D4 | — | 2 | 7168 | no | — |
| 599 | C2×D4 | — | 2 | 16384 | no | — |
| 600 | C2×D4 | — | 2 | 32768 | no | — |
| 601 | C2×D4 | — | 2 | 65536 | no | — |
| 602 | C2×D4 | — | 2 | 65536 | no | — |
| 603 | C2×D4 | — | 2 | 131072 | no | — |
| 604 | C2×D4 | — | 2 | 7168 | no | — |
| 605 | C2×D4 | — | 2 | 8192 | no | — |
| 606 | C2×D4 | — | 4 | 14336 | no | — |
| 607 | C2×D4 | — | 8 | 16384 | no | — |
| 608 | C2×D4 | C24×D4 | 1 | 14336 | yes | — |
| 609 | C2×D4 | C24×D4 | 1 | 32768 | yes | complemented |
| 610 | C2×D4 | C24×D4 | 1 | 16384 | yes | complemented |
| 611 | C2×D4 | C27 | 1 | 1024 | yes | — |
| 612 | C2×D4 | C27 | 1 | 4096 | yes | — |
| 613 | C2×D4 | C27 | 1 | 1024 | yes | — |
| 614 | C2×D4 | C27 | 1 | 1024 | yes | — |
| 615 | C2×D4 | C27 | 1 | 4096 | yes | — |
| 616 | C2×D4 | C27 | 1 | 1024 | yes | — |
| 617 | C22×C4 | — | 2 | 3584 | no | — |
| 618 | C22×C4 | — | 2 | 896 | no | — |
| 619 | C22×C4 | — | 2 | 14336 | no | — |
| 620 | C22×C4 | — | 2 | 16384 | no | — |
| 621 | C22×C4 | — | 2 | 896 | no | — |
| 622 | C22×C4 | — | 2 | 14336 | no | — |
| 623 | C22×C4 | — | 2 | 16384 | no | — |
| 624 | C22×C4 | — | 4 | 1792 | no | — |
| 625 | C22×C4 | — | 4 | 7168 | no | — |
| 626 | C22×C4 | — | 8 | 4096 | no | — |
| 627 | C22×C4 | C24×D4 | 1 | 448 | yes | — |
| 628 | C22×C4 | C24×D4 | 1 | 3584 | yes | — |
| 629 | C22×C4 | C24×D4 | 1 | 1792 | yes | — |
| 630 | C22×C4 | C24×D4 | 1 | 4096 | yes | complemented |
| 631 | C22×C4 | C27 | 1 | 448 | yes | — |
| 632 | C22×C4 | C27 | 1 | 448 | yes | — |
| 633 | C22×C4 | C27 | 1 | 2048 | yes | — |
| 634 | C22×C4 | C27 | 1 | 2048 | yes | — |
| 635 | C22×C4 | C27 | 1 | 512 | yes | — |
| 636 | C22×C4 | C27 | 1 | 512 | yes | — |
| 637 | C22×C4 | C27 | 1 | 2048 | yes | — |
| 638 | C22×C4 | C27 | 1 | 112 | yes | — |
| 639 | C22×C4 | C27 | 1 | 128 | yes | — |
| 640 | C22×C4 | C27 | 1 | 256 | yes | — |
| 641 | C4⋊C4 | C27 | 1 | 4096 | yes | — |
| 642 | C4⋊C4 | C27 | 1 | 1024 | yes | — |
| 643 | C22⋊C4 | C27 | 1 | 1024 | yes | — |
| 644 | C22⋊C4 | C27 | 1 | 2048 | yes | — |
| 645 | C22⋊C4 | C27 | 1 | 8192 | yes | — |
| 646 | C42 | C27 | 1 | 1024 | yes | — |
| 647 | C23 | — | 2 | 112 | no | — |
| 648 | C23 | — | 2 | 896 | no | — |
| 649 | C23 | — | 2 | 224 | no | — |
| 650 | C23 | — | 2 | 896 | no | — |
| 651 | C23 | — | 2 | 448 | no | — |
| 652 | C23 | — | 2 | 3584 | no | — |
| 653 | C23 | — | 2 | 1024 | no | — |
| 654 | C23 | — | 2 | 896 | no | — |
| 655 | C23 | — | 2 | 1792 | no | — |
| 656 | C23 | — | 2 | 4096 | no | — |
| 657 | C23 | — | 4 | 512 | no | — |
| 658 | C23 | — | 4 | 1792 | no | — |
| 659 | C23 | — | 4 | 14336 | no | — |
| 660 | C23 | — | 4 | 128 | no | — |
| 661 | C23 | — | 4 | 1024 | no | — |
| 662 | C23 | — | 4 | 1024 | no | — |
| 663 | C23 | — | 4 | 7168 | no | — |
| 664 | C23 | — | 4 | 4096 | no | — |
| 665 | C23 | — | 4 | 14336 | no | — |
| 666 | C23 | — | 4 | 3584 | no | — |
| 667 | C23 | — | 8 | 28672 | no | — |
| 668 | C23 | — | 8 | 8192 | no | — |
| 669 | C23 | — | 8 | 32768 | no | — |
| 670 | C23 | #62842 | 1 | 64 | yes | direct product factor |
| 671 | C23 | C25×D4 | 1 | 224 | yes | — |
| 672 | C23 | C25×D4 | 1 | 896 | yes | — |
| 673 | C23 | C25×D4 | 1 | 112 | yes | — |
| 674 | C23 | C25×D4 | 1 | 2048 | yes | — |
| 675 | C23 | C25×D4 | 1 | 256 | yes | — |
| 676 | C23 | C25×D4 | 1 | 1024 | yes | — |
| 677 | C23 | C25×D4 | 1 | 28 | yes | — |
| 678 | C23 | C2×H(7,𝔽2) | 1 | 56 | yes | — |
| 679 | C23 | C28 | 1 | 128 | yes | — |
| 680 | C23 | C28 | 1 | 16 | yes | — |
| 681 | C23 | C28 | 1 | 64 | yes | — |
| 682 | C23 | C28 | 1 | 8 | yes | — |
| 683 | C23 | C28 | 1 | 7 | yes | — |
| 684 | Q8 | — | 2 | 2048 | no | — |
| 685 | D4 | — | 2 | 2048 | no | — |
| 686 | D4 | — | 2 | 8192 | no | — |
| 687 | D4 | — | 2 | 2048 | no | — |
| 688 | D4 | — | 2 | 2048 | no | — |
| 689 | D4 | — | 4 | 4096 | no | — |
| 690 | D4 | C25×D4 | 1 | 4096 | yes | — |
| 691 | C2×C4 | — | 2 | 1024 | no | — |
| 692 | C2×C4 | — | 2 | 896 | no | — |
| 693 | C2×C4 | — | 2 | 4096 | no | — |
| 694 | C2×C4 | — | 2 | 896 | no | — |
| 695 | C2×C4 | — | 2 | 4096 | no | — |
| 696 | C2×C4 | — | 4 | 512 | no | — |
| 697 | C2×C4 | — | 4 | 2048 | no | — |
| 698 | C2×C4 | C25×D4 | 1 | 448 | yes | — |
| 699 | C2×C4 | C25×D4 | 1 | 1024 | yes | — |
| 700 | C2×C4 | C25×D4 | 1 | 512 | yes | — |
| 701 | C2×C4 | C28 | 1 | 128 | yes | — |
| 702 | C2×C4 | C28 | 1 | 128 | yes | — |
| 703 | C2×C4 | C28 | 1 | 32 | yes | — |
| 704 | C22 | — | 2 | 448 | no | — |
| 705 | C22 | — | 2 | 224 | no | — |
| 706 | C22 | — | 2 | 1792 | no | — |
| 707 | C22 | — | 2 | 16 | no | — |
| 708 | C22 | — | 2 | 128 | no | — |
| 709 | C22 | — | 2 | 32 | no | — |
| 710 | C22 | — | 2 | 256 | no | — |
| 711 | C22 | — | 2 | 128 | no | — |
| 712 | C22 | — | 4 | 256 | no | — |
| 713 | C22 | — | 4 | 2048 | no | — |
| 714 | C22 | — | 4 | 1024 | no | — |
| 715 | C22 | — | 4 | 2048 | no | — |
| 716 | C22 | — | 4 | 1792 | no | — |
| 717 | C22 | — | 8 | 4096 | no | — |
| 718 | C22 | C2×#62842 | 1 | 112 | yes | direct product factor |
| 719 | C22 | C26×D4 | 1 | 32 | yes | — |
| 720 | C22 | C26×D4 | 1 | 128 | yes | — |
| 721 | C22 | C26×D4 | 1 | 16 | yes | — |
| 722 | C22 | C26×D4 | 1 | 14 | yes | — |
| 723 | C22 | C22×H(7,𝔽2) | 1 | 28 | yes | — |
| 724 | C22 | C29 | 1 | 1 | yes | characteristic |
| 725 | C4 | — | 2 | 128 | no | — |
| 726 | C4 | — | 2 | 128 | no | — |
| 727 | C4 | C26×D4 | 1 | 64 | yes | — |
| 728 | C2 | — | 2 | 32 | no | — |
| 729 | C2 | — | 2 | 16 | no | — |
| 730 | C2 | — | 2 | 128 | no | — |
| 731 | C2 | — | 4 | 128 | no | — |
| 732 | C2 | C23×H(7,𝔽2) | 1 | 2 | yes | — |
| 733 | C2 | C22×#62842 | 1 | 28 | yes | direct product factor |
| 734 | C2 | C27×D4 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|
| 1. C23×#3449 | C2 | semidirect |
| 2. C23×#3485 | C2 | semidirect |
| 3. C24×#518 | C2 | semidirect |
| 4. C24×#534 | C2 | semidirect |
| 5. C23×#3496 | C2 | semidirect |
| 6. C22×#62842 | C2 | direct (N × H) |
| 7. C25×H(5,𝔽2) | C2 | semidirect |
| 8. C23×#3484 | C2 | semidirect |
| 10. C24×H(5,𝔽2) | C22 | semidirect |
| 11. C24×H(5,𝔽2) | C22 | semidirect |
| 12. C24×H(5,𝔽2) | C22 | semidirect |
| 13. C25×#41 | C22 | semidirect |
| 14. C25×#41 | C22 | semidirect |
| 16. C26×D4 | C22 | semidirect |
| 17. C26×D4 | C22 | semidirect |
| 18. C2×#62842 | C22 | direct (N × H) |
| 19. C22×#3485 | C22 | semidirect |
| 20. C22×#3496 | C22 | semidirect |
| 21. C22×#3484 | C22 | semidirect |
| 22. C23×#547 | C22 | semidirect |
| 23. C23×#546 | C22 | semidirect |
| 24. C23×D42 | C22 | semidirect |
| 25. C22×#3449 | C22 | semidirect |
| 26. C23×#536 | C22 | semidirect |
| 27. C23×#537 | C22 | semidirect |
| 28. C23×#535 | C22 | semidirect |
| 29. C23×#534 | C22 | semidirect |
| 30. C23×#534 | C22 | semidirect |
| 31. C23×#534 | C22 | semidirect |
| 32. C23×#534 | C22 | semidirect |
| 33. C23×#532 | C22 | semidirect |
| 34. C23×#525 | C22 | semidirect |
| 35. C24×#123 | C22 | semidirect |
| 36. C24×#121 | C22 | semidirect |
| 37. C24×#120 | C22 | semidirect |
| 38. C23×#518 | C22 | semidirect |
| 39. C23×#518 | C22 | semidirect |
| 40. C24×C4×D4 | C22 | semidirect |
| 41. C24×#117 | C22 | semidirect |
| 42. C25×C22⋊C4 | C22 | semidirect |
| 44. C28 | C23 | semidirect |
| 48. C23×H(5,𝔽2) | C23 | semidirect |
| 49. C23×H(5,𝔽2) | C23 | semidirect |
| 50. C23×H(5,𝔽2) | C23 | semidirect |
| 54. C24×#41 | C23 | semidirect |
| 55. C24×#41 | C23 | semidirect |
| 56. C24×#41 | C23 | semidirect |
| 57. C24×#41 | C23 | semidirect |
| 58. C25×Q8 | C23 | semidirect |
| 61. C25×D4 | D4 | semidirect |
| 67. C25×D4 | C23 | semidirect |
| 68. C25×D4 | C23 | semidirect |
| 69. C25×D4 | C23 | semidirect |
| 70. C25×D4 | C23 | semidirect |
| 71. C25×D4 | C23 | semidirect |
| 72. C25×D4 | C23 | semidirect |
| 73. C25×D4 | C23 | semidirect |
| 75. C26×C4 | C23 | semidirect |
| 76. C26×C4 | C23 | semidirect |
| 77. C26×C4 | C23 | semidirect |
| 78. #62842 | C23 | direct (N × H) |
| 79. C2×#3485 | C23 | semidirect |
| 80. C2×#3496 | C23 | semidirect |
| 81. C2×#3484 | C23 | semidirect |
| 82. C22×#547 | C23 | semidirect |
| 83. C22×#546 | C23 | semidirect |
| 84. C22×D42 | C23 | semidirect |
| 85. C2×#3449 | C23 | semidirect |
| 86. C22×#536 | C23 | semidirect |
| 87. C22×#537 | C23 | semidirect |
| 88. C22×#535 | C23 | semidirect |
| 89. C22×#534 | C23 | semidirect |
| 90. C22×#534 | C23 | semidirect |
| 91. C22×#534 | C23 | semidirect |
| 92. C22×#534 | C23 | semidirect |
| 93. C22×#532 | C23 | semidirect |
| 94. C23×C4⋊Q8 | C23 | semidirect |
| 95. C23×#127 | C23 | semidirect |
| 96. C23×#124 | C23 | semidirect |
| 97. C22×#525 | C23 | semidirect |
| 98. C23×#123 | C23 | semidirect |
| 99. C23×#123 | C23 | semidirect |
| 100. C23×#123 | C23 | semidirect |
| 101. C23×C22⋊Q8 | C23 | semidirect |
| 102. C23×#121 | C23 | semidirect |
| 103. C23×#121 | C23 | semidirect |
| 104. C23×#121 | C23 | semidirect |
| 105. C23×#121 | C23 | semidirect |
| 106. C23×#120 | C23 | semidirect |
| 107. C23×#120 | C23 | semidirect |
| 108. C23×#120 | C23 | semidirect |
| 109. C22×#518 | C23 | semidirect |
| 110. C22×#518 | C23 | semidirect |
| 111. C23×C4×D4 | C23 | semidirect |
| 112. C23×C4×D4 | C23 | semidirect |
| 113. C23×C4×D4 | C23 | semidirect |
| 114. C23×#117 | C23 | semidirect |
| 115. C23×#117 | C23 | semidirect |
| 116. C24×C4⋊C4 | C23 | semidirect |
| 117. C24×C4⋊C4 | C23 | semidirect |
| 119. C24×C22⋊C4 | C23 | semidirect |
| 120. C24×C22⋊C4 | C23 | semidirect |
| 121. C24×C22⋊C4 | C23 | semidirect |
| 122. C24×C22⋊C4 | C23 | semidirect |
| 123. C24×C42 | C23 | semidirect |
| 127. C27 | C2×D4 | semidirect |
| 134. C27 | C24 | semidirect |
| 138. C22×H(5,𝔽2) | C24 | semidirect |
| 139. C22×H(5,𝔽2) | C24 | semidirect |
| 140. C22×H(5,𝔽2) | C24 | semidirect |
| 147. C23×#41 | C24 | semidirect |
| 148. C23×#41 | C24 | semidirect |
| 149. C23×#41 | C24 | semidirect |
| 150. C23×#41 | C24 | semidirect |
| 153. C24×Q8 | C24 | semidirect |
| 163. C24×D4 | C2×D4 | semidirect |
| 164. C24×D4 | C2×D4 | semidirect |
| 165. C24×D4 | C2×D4 | semidirect |
| 177. C24×D4 | C24 | semidirect |
| 178. C24×D4 | C24 | semidirect |
| 179. C24×D4 | C24 | semidirect |
| 180. C24×D4 | C24 | semidirect |
| 181. C24×D4 | C24 | semidirect |
| 182. C24×D4 | C24 | semidirect |
| 183. C24×D4 | C24 | semidirect |
| 187. C25×C4 | C2×D4 | semidirect |
| 196. C25×C4 | C24 | semidirect |
| 197. C25×C4 | C24 | semidirect |
| 198. C25×C4 | C24 | semidirect |
| 199. #3496 | C24 | semidirect |
| 200. #3485 | C24 | semidirect |
| 201. #3484 | C24 | semidirect |
| 202. C2×#547 | C24 | semidirect |
| 203. C2×#546 | C24 | semidirect |
| 204. C2×D42 | C24 | semidirect |
| 205. #3449 | C24 | semidirect |
| 206. C2×#537 | C24 | semidirect |
| 207. C2×#536 | C24 | semidirect |
| 208. C2×#535 | C24 | semidirect |
| 209. C2×#534 | C24 | semidirect |
| 210. C2×#534 | C24 | semidirect |
| 211. C2×#534 | C24 | semidirect |
| 212. C2×#534 | C24 | semidirect |
| 213. C2×#532 | C24 | semidirect |
| 214. C22×C4⋊Q8 | C24 | semidirect |
| 215. C22×#127 | C24 | semidirect |
| 216. C22×#124 | C24 | semidirect |
| 217. C2×#525 | C24 | semidirect |
| 218. C22×#123 | C24 | semidirect |
| 219. C22×#123 | C24 | semidirect |
| 220. C22×#123 | C24 | semidirect |
| 221. C22×C22⋊Q8 | C24 | semidirect |
| 222. C22×#121 | C24 | semidirect |
| 223. C22×#121 | C24 | semidirect |
| 224. C22×#121 | C24 | semidirect |
| 225. C22×#121 | C24 | semidirect |
| 226. C22×#120 | C24 | semidirect |
| 227. C22×#120 | C24 | semidirect |
| 228. C22×#120 | C24 | semidirect |
| 229. C2×#518 | C24 | semidirect |
| 230. C2×#518 | C24 | semidirect |
| 231. C22×C4×D4 | C24 | semidirect |
| 232. C22×C4×D4 | C24 | semidirect |
| 233. C22×C4×D4 | C24 | semidirect |
| 234. C22×#117 | C24 | semidirect |
| 235. C22×#117 | C24 | semidirect |
| 238. C23×C4⋊C4 | C24 | semidirect |
| 239. C23×C4⋊C4 | C24 | semidirect |
| 244. C23×C22⋊C4 | C24 | semidirect |
| 245. C23×C22⋊C4 | C24 | semidirect |
| 246. C23×C22⋊C4 | C24 | semidirect |
| 247. C23×C22⋊C4 | C24 | semidirect |
| 249. C23×C42 | C24 | semidirect |
| 265. C26 | C22×D4 | semidirect |
| 276. C26 | C25 | semidirect |
| 280. C2×H(5,𝔽2) | C25 | semidirect |
| 281. C2×H(5,𝔽2) | C25 | semidirect |
| 288. C22×#41 | C25 | semidirect |
| 289. C22×#41 | C25 | semidirect |
| 290. C22×#41 | C25 | semidirect |
| 291. C22×#41 | C25 | semidirect |
| 295. C23×Q8 | C25 | semidirect |
| 311. C23×D4 | C22×D4 | semidirect |
| 312. C23×D4 | C22×D4 | semidirect |
| 313. C23×D4 | C22×D4 | semidirect |
| 325. C23×D4 | C25 | semidirect |
| 326. C23×D4 | C25 | semidirect |
| 327. C23×D4 | C25 | semidirect |
| 328. C23×D4 | C25 | semidirect |
| 329. C23×D4 | C25 | semidirect |
| 330. C23×D4 | C25 | semidirect |
| 331. C23×D4 | C25 | semidirect |
| 342. C24×C4 | C22×D4 | semidirect |
| 354. C24×C4 | C25 | semidirect |
| 355. C24×C4 | C25 | semidirect |
| 356. C24×C4 | C25 | semidirect |
| 357. #547 | C25 | semidirect |
| 358. #546 | C25 | semidirect |
| 359. D42 | C25 | semidirect |
| 360. #537 | C25 | semidirect |
| 361. #536 | C25 | semidirect |
| 362. #535 | C25 | semidirect |
| 363. #534 | C25 | semidirect |
| 364. #534 | C25 | semidirect |
| 365. #534 | C25 | semidirect |
| 366. #532 | C25 | semidirect |
| 367. C2×C4⋊Q8 | C25 | semidirect |
| 368. C2×#127 | C25 | semidirect |
| 369. C2×#124 | C25 | semidirect |
| 370. #525 | C25 | semidirect |
| 371. C2×#123 | C25 | semidirect |
| 372. C2×#123 | C25 | semidirect |
| 373. C2×#123 | C25 | semidirect |
| 374. C2×C22⋊Q8 | C25 | semidirect |
| 375. C2×#121 | C25 | semidirect |
| 376. C2×#121 | C25 | semidirect |
| 377. C2×#121 | C25 | semidirect |
| 378. C2×#121 | C25 | semidirect |
| 379. C2×#120 | C25 | semidirect |
| 380. C2×#120 | C25 | semidirect |
| 381. C2×#120 | C25 | semidirect |
| 382. #518 | C25 | semidirect |
| 383. C2×C4×D4 | C25 | semidirect |
| 384. C2×C4×D4 | C25 | semidirect |
| 385. C2×C4×D4 | C25 | semidirect |
| 386. C2×#117 | C25 | semidirect |
| 387. C2×#117 | C25 | semidirect |
| 390. C22×C4⋊C4 | C25 | semidirect |
| 391. C22×C4⋊C4 | C25 | semidirect |
| 396. C22×C22⋊C4 | C25 | semidirect |
| 397. C22×C22⋊C4 | C25 | semidirect |
| 398. C22×C22⋊C4 | C25 | semidirect |
| 399. C22×C22⋊C4 | C25 | semidirect |
| 401. C22×C42 | C25 | semidirect |
| 430. C25 | C23×D4 | semidirect |
| 442. C25 | C26 | semidirect |
| 451. C2×#41 | C26 | semidirect |
| 452. C2×#41 | C26 | semidirect |
| 456. C22×Q8 | C26 | semidirect |
| 472. C22×D4 | C23×D4 | semidirect |
| 473. C22×D4 | C23×D4 | semidirect |
| 474. C22×D4 | C23×D4 | semidirect |
| 485. C22×D4 | C26 | semidirect |
| 486. C22×D4 | C26 | semidirect |
| 487. C22×D4 | C26 | semidirect |
| 488. C22×D4 | C26 | semidirect |
| 489. C22×D4 | C26 | semidirect |
| 503. C23×C4 | C23×D4 | semidirect |
| 515. C23×C4 | C26 | semidirect |
| 516. C23×C4 | C26 | semidirect |
| 517. C23×C4 | C26 | semidirect |
| 518. C4⋊Q8 | C26 | semidirect |
| 519. #127 | C26 | semidirect |
| 520. #124 | C26 | semidirect |
| 521. #123 | C26 | semidirect |
| 522. #123 | C26 | semidirect |
| 523. C22⋊Q8 | C26 | semidirect |
| 524. #121 | C26 | semidirect |
| 525. #121 | C26 | semidirect |
| 526. #121 | C26 | semidirect |
| 527. #120 | C26 | semidirect |
| 528. #120 | C26 | semidirect |
| 529. C4×D4 | C26 | semidirect |
| 530. C4×D4 | C26 | semidirect |
| 531. #117 | C26 | semidirect |
| 534. C2×C4⋊C4 | C26 | semidirect |
| 535. C2×C4⋊C4 | C26 | semidirect |
| 540. C2×C22⋊C4 | C26 | semidirect |
| 541. C2×C22⋊C4 | C26 | semidirect |
| 542. C2×C22⋊C4 | C26 | semidirect |
| 544. C2×C42 | C26 | semidirect |
| 578. C24 | C24×D4 | semidirect |
| 609. C2×D4 | C24×D4 | semidirect |
| 610. C2×D4 | C24×D4 | semidirect |
| 630. C22×C4 | C24×D4 | semidirect |
| 670. C23 | #62842 | direct (N × H) |
| 718. C22 | C2×#62842 | direct (N × H) |
| 733. C2 | C22×#62842 | 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