Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
3456616 conjugacy classes of subgroups.
The subgroup lattice has 867 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C22×#34176 | C2 | 1 | 6 | yes | maximal, complemented |
| 2 | C22×#34356 | C2 | 1 | 24 | yes | maximal, complemented |
| 3 | C22×#34198 | C2 | 1 | 24 | yes | maximal, complemented |
| 4 | C22×#34171 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | C2×#7626202 | C2 | 1 | 192 | yes | maximal, direct product factor |
| 6 | C24×#379 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | C25×#120 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C29 | C22 | 1 | 1 | yes | characteristic |
| 9 | C26×D4 | C22 | 1 | 3 | yes | — |
| 10 | C24×#120 | C4 | 1 | 128 | yes | complemented |
| 11 | C24×#120 | C22 | 1 | 12 | yes | — |
| 12 | C24×#120 | C22 | 1 | 96 | yes | — |
| 13 | C24×#120 | C22 | 1 | 12 | yes | — |
| 14 | C23×#518 | C22 | 1 | 12 | yes | complemented |
| 15 | C25×C22⋊C4 | C22 | 1 | 3 | yes | — |
| 16 | C25×C22⋊C4 | C22 | 1 | 12 | yes | complemented |
| 17 | #7626202 | C22 | 1 | 4096 | yes | direct product factor |
| 18 | C2×#34356 | C22 | 1 | 2304 | yes | complemented |
| 19 | C22×#2375 | C22 | 1 | 32 | yes | complemented |
| 20 | C2×#34198 | C22 | 1 | 2304 | yes | complemented |
| 21 | C2×#34176 | C22 | 1 | 576 | yes | complemented |
| 22 | C2×#34171 | C22 | 1 | 576 | yes | complemented |
| 23 | C22×#2358 | C22 | 1 | 96 | yes | complemented |
| 24 | C22×#2342 | C22 | 1 | 96 | yes | complemented |
| 25 | C22×D4×C22⋊C4 | C22 | 1 | 96 | yes | complemented |
| 26 | C22×#2321 | C22 | 1 | 96 | yes | complemented |
| 27 | C22×#2309 | C22 | 1 | 12 | yes | complemented |
| 28 | C22×#2312 | C22 | 1 | 24 | yes | complemented |
| 29 | C22×#2315 | C22 | 1 | 12 | yes | complemented |
| 30 | C22×#2308 | C22 | 1 | 12 | yes | complemented |
| 31 | C22×#2308 | C22 | 1 | 12 | yes | complemented |
| 32 | C22×C4×#120 | C22 | 1 | 32 | yes | complemented |
| 33 | C22×#2280 | C22 | 1 | 12 | yes | complemented |
| 34 | C23×#379 | C22 | 1 | 12 | yes | — |
| 35 | C23×#379 | C22 | 1 | 24 | yes | complemented |
| 36 | C23×#379 | C22 | 1 | 12 | yes | complemented |
| 37 | C23×#379 | C22 | 1 | 192 | yes | complemented |
| 38 | C23×#379 | C22 | 1 | 4 | yes | complemented |
| 39 | C22×#2273 | C22 | 1 | 12 | yes | complemented |
| 40 | C28 | — | 4 | 96 | no | — |
| 41 | C28 | C2×C4 | 1 | 64 | yes | complemented |
| 42 | C28 | C23 | 1 | 3 | yes | — |
| 43 | C28 | C23 | 1 | 6 | yes | — |
| 44 | C28 | C23 | 1 | 6 | yes | — |
| 45 | C28 | C23 | 1 | 48 | yes | — |
| 46 | C28 | C23 | 1 | 1 | yes | characteristic |
| 47 | C25×D4 | — | 4 | 96 | no | — |
| 48 | C25×D4 | C2×C4 | 1 | 192 | yes | complemented |
| 49 | C25×D4 | C23 | 1 | 6 | yes | — |
| 50 | C25×D4 | C23 | 1 | 6 | yes | — |
| 51 | C25×D4 | C23 | 1 | 24 | yes | — |
| 52 | C25×D4 | C23 | 1 | 144 | yes | — |
| 53 | C26×C4 | C23 | 1 | 3 | yes | — |
| 54 | C26×C4 | C23 | 1 | 8 | yes | complemented |
| 55 | C23×#120 | C2×C4 | 1 | 768 | yes | complemented |
| 56 | C23×#120 | C2×C4 | 1 | 768 | yes | complemented |
| 57 | C23×#120 | C2×C4 | 1 | 6144 | yes | complemented |
| 58 | C23×#120 | C23 | 1 | 24 | yes | — |
| 59 | C23×#120 | C23 | 1 | 8 | yes | — |
| 60 | C23×#120 | C23 | 1 | 24 | yes | — |
| 61 | C23×#120 | C23 | 1 | 8 | yes | — |
| 62 | C23×#120 | C23 | 1 | 576 | yes | — |
| 63 | C23×#120 | C23 | 1 | 1024 | yes | — |
| 64 | C23×#120 | C23 | 1 | 576 | yes | — |
| 65 | C22×#518 | — | 4 | 192 | no | — |
| 66 | C22×#518 | C23 | 1 | 576 | yes | complemented |
| 67 | C23×C4×D4 | C23 | 1 | 96 | yes | complemented |
| 68 | C23×#117 | C23 | 1 | 24 | yes | complemented |
| 69 | C24×C22⋊C4 | — | 4 | 192 | no | — |
| 70 | C24×C22⋊C4 | C2×C4 | 1 | 192 | yes | complemented |
| 71 | C24×C22⋊C4 | C23 | 1 | 24 | yes | — |
| 72 | C24×C22⋊C4 | C23 | 1 | 48 | yes | — |
| 73 | C24×C22⋊C4 | C23 | 1 | 6 | yes | — |
| 74 | C24×C22⋊C4 | C23 | 1 | 6 | yes | — |
| 75 | C24×C22⋊C4 | C23 | 1 | 24 | yes | — |
| 76 | C24×C22⋊C4 | C23 | 1 | 144 | yes | — |
| 77 | C24×C22⋊C4 | C23 | 1 | 24 | yes | complemented |
| 78 | C24×C22⋊C4 | C23 | 1 | 48 | yes | complemented |
| 79 | C24×C22⋊C4 | C23 | 1 | 576 | yes | complemented |
| 80 | C24×C22⋊C4 | C23 | 1 | 24 | yes | complemented |
| 81 | #34356 | C23 | 1 | 24576 | yes | complemented |
| 82 | C2×#2375 | C23 | 1 | 1536 | yes | complemented |
| 83 | #34198 | C23 | 1 | 24576 | yes | complemented |
| 84 | #34176 | C23 | 1 | 6144 | yes | complemented |
| 85 | #34171 | C23 | 1 | 6144 | yes | complemented |
| 86 | C2×#2358 | C23 | 1 | 4608 | yes | complemented |
| 87 | C2×#2342 | C23 | 1 | 4608 | yes | complemented |
| 88 | C2×D4×C22⋊C4 | C23 | 1 | 4608 | yes | complemented |
| 89 | C2×#2321 | C23 | 1 | 4608 | yes | complemented |
| 90 | C2×#2315 | C23 | 1 | 576 | yes | complemented |
| 91 | C2×#2312 | C23 | 1 | 1152 | yes | complemented |
| 92 | C2×#2309 | C23 | 1 | 576 | yes | complemented |
| 93 | C2×#2308 | C23 | 1 | 576 | yes | complemented |
| 94 | C2×#2308 | C23 | 1 | 576 | yes | complemented |
| 95 | C2×C4×#120 | C23 | 1 | 1536 | yes | complemented |
| 96 | C22×#390 | C23 | 1 | 96 | yes | complemented |
| 97 | C22×#388 | C23 | 1 | 192 | yes | complemented |
| 98 | C22×#386 | C23 | 1 | 96 | yes | complemented |
| 99 | C22×#386 | C23 | 1 | 96 | yes | complemented |
| 100 | C22×#385 | C23 | 1 | 96 | yes | complemented |
| 101 | C2×#2280 | C23 | 1 | 576 | yes | complemented |
| 102 | C22×#381 | C23 | 1 | 24 | yes | complemented |
| 103 | C22×#380 | C23 | 1 | 48 | yes | complemented |
| 104 | C22×#379 | C23 | 1 | 8 | yes | — |
| 105 | C22×#379 | C23 | 1 | 24 | yes | — |
| 106 | C22×#379 | C23 | 1 | 48 | yes | — |
| 107 | C22×#379 | C23 | 1 | 576 | yes | — |
| 108 | C22×#379 | C23 | 1 | 8 | yes | complemented |
| 109 | C22×#379 | C23 | 1 | 24 | yes | complemented |
| 110 | C22×#379 | C23 | 1 | 16 | yes | complemented |
| 111 | C22×#379 | C23 | 1 | 1152 | yes | complemented |
| 112 | C22×#379 | C23 | 1 | 576 | yes | complemented |
| 113 | C22×#379 | C23 | 1 | 24 | yes | complemented |
| 114 | C22×#379 | C23 | 1 | 2048 | yes | complemented |
| 115 | C22×#379 | C23 | 1 | 192 | yes | complemented |
| 116 | C2×#2273 | C23 | 1 | 576 | yes | complemented |
| 117 | C22×C4×C22⋊C4 | C23 | 1 | 48 | yes | complemented |
| 118 | C22×C4×C22⋊C4 | C23 | 1 | 96 | yes | complemented |
| 119 | C27 | — | 2 | 96 | no | — |
| 120 | C27 | — | 2 | 192 | no | — |
| 121 | C27 | — | 4 | 3072 | no | — |
| 122 | C27 | — | 4 | 192 | no | — |
| 123 | C27 | — | 4 | 96 | no | — |
| 124 | C27 | — | 4 | 192 | no | — |
| 125 | C27 | — | 4 | 96 | no | — |
| 126 | C27 | — | 4 | 2304 | no | — |
| 127 | C27 | — | 4 | 48 | no | — |
| 128 | C27 | — | 4 | 4096 | no | — |
| 129 | C27 | C22×C4 | 1 | 96 | yes | — |
| 130 | C27 | C22×C4 | 1 | 192 | yes | — |
| 131 | C27 | C22×C4 | 1 | 192 | yes | — |
| 132 | C27 | C22×C4 | 1 | 1536 | yes | complemented |
| 133 | C27 | C22×C4 | 1 | 32 | yes | complemented |
| 134 | C27 | C24 | 1 | 1 | yes | characteristic |
| 135 | C27 | C24 | 1 | 2 | yes | — |
| 136 | C27 | C24 | 1 | 12 | yes | — |
| 137 | C27 | C24 | 1 | 6 | yes | — |
| 138 | C27 | C24 | 1 | 6 | yes | — |
| 139 | C27 | C24 | 1 | 3 | yes | — |
| 140 | C27 | C24 | 1 | 72 | yes | — |
| 141 | C27 | C24 | 1 | 6 | yes | — |
| 142 | C27 | C24 | 1 | 144 | yes | — |
| 143 | C27 | C24 | 1 | 2 | yes | — |
| 144 | C27 | C24 | 1 | 144 | yes | — |
| 145 | C27 | C24 | 1 | 24 | yes | — |
| 146 | C27 | C24 | 1 | 256 | yes | — |
| 147 | C27 | C24 | 1 | 3 | yes | — |
| 148 | C24×D4 | — | 2 | 192 | no | — |
| 149 | C24×D4 | — | 4 | 96 | no | — |
| 150 | C24×D4 | — | 4 | 3072 | no | — |
| 151 | C24×D4 | — | 4 | 384 | no | — |
| 152 | C24×D4 | — | 4 | 2304 | no | — |
| 153 | C24×D4 | C22×C4 | 1 | 192 | yes | — |
| 154 | C24×D4 | C22×C4 | 1 | 192 | yes | complemented |
| 155 | C24×D4 | C22×C4 | 1 | 768 | yes | complemented |
| 156 | C24×D4 | C22×C4 | 1 | 4608 | yes | complemented |
| 157 | C24×D4 | C24 | 1 | 24 | yes | — |
| 158 | C24×D4 | C24 | 1 | 144 | yes | — |
| 159 | C24×D4 | C24 | 1 | 24 | yes | — |
| 160 | C24×D4 | C24 | 1 | 576 | yes | — |
| 161 | C24×D4 | C24 | 1 | 768 | yes | — |
| 162 | C24×D4 | C24 | 1 | 144 | yes | — |
| 163 | C25×C4 | — | 4 | 48 | no | — |
| 164 | C25×C4 | — | 4 | 192 | no | — |
| 165 | C25×C4 | C22×C4 | 1 | 96 | yes | complemented |
| 166 | C25×C4 | C24 | 1 | 6 | yes | — |
| 167 | C25×C4 | C24 | 1 | 48 | yes | — |
| 168 | C25×C4 | C24 | 1 | 12 | yes | — |
| 169 | C25×C4 | C24 | 1 | 72 | yes | — |
| 170 | C25×C4 | C24 | 1 | 192 | yes | complemented |
| 171 | C25×C4 | C24 | 1 | 16 | yes | complemented |
| 172 | C22×#120 | C22×C4 | 1 | 768 | yes | — |
| 173 | C22×#120 | C22×C4 | 1 | 256 | yes | complemented |
| 174 | C22×#120 | C22×C4 | 1 | 768 | yes | complemented |
| 175 | C22×#120 | C22×C4 | 1 | 256 | yes | complemented |
| 176 | C22×#120 | C22×C4 | 1 | 18432 | yes | complemented |
| 177 | C22×#120 | C22×C4 | 1 | 18432 | yes | complemented |
| 178 | C22×#120 | C22×C4 | 1 | 32768 | yes | complemented |
| 179 | C22×#120 | C24 | 1 | 576 | yes | — |
| 180 | C22×#120 | C24 | 1 | 576 | yes | — |
| 181 | C22×#120 | C24 | 1 | 192 | yes | — |
| 182 | C22×#120 | C24 | 1 | 3072 | yes | — |
| 183 | C22×#120 | C24 | 1 | 3072 | yes | — |
| 184 | C22×#120 | C24 | 1 | 192 | yes | — |
| 185 | C2×#518 | — | 4 | 4608 | no | — |
| 186 | C2×#518 | C24 | 1 | 3072 | yes | complemented |
| 187 | C22×C4×D4 | — | 4 | 768 | no | — |
| 188 | C22×C4×D4 | C24 | 1 | 2304 | yes | complemented |
| 189 | C22×#117 | — | 4 | 192 | no | — |
| 190 | C22×#117 | C24 | 1 | 576 | yes | complemented |
| 191 | C23×C4⋊C4 | C24 | 1 | 48 | yes | complemented |
| 192 | C23×C22⋊C4 | — | 2 | 384 | no | — |
| 193 | C23×C22⋊C4 | — | 4 | 384 | no | — |
| 194 | C23×C22⋊C4 | — | 4 | 384 | no | — |
| 195 | C23×C22⋊C4 | — | 4 | 4608 | no | — |
| 196 | C23×C22⋊C4 | — | 4 | 192 | no | — |
| 197 | C23×C22⋊C4 | — | 4 | 192 | no | — |
| 198 | C23×C22⋊C4 | C22×C4 | 1 | 192 | yes | — |
| 199 | C23×C22⋊C4 | C22×C4 | 1 | 768 | yes | complemented |
| 200 | C23×C22⋊C4 | C22×C4 | 1 | 192 | yes | complemented |
| 201 | C23×C22⋊C4 | C22×C4 | 1 | 4608 | yes | complemented |
| 202 | C23×C22⋊C4 | C24 | 1 | 576 | yes | — |
| 203 | C23×C22⋊C4 | C24 | 1 | 48 | yes | — |
| 204 | C23×C22⋊C4 | C24 | 1 | 48 | yes | — |
| 205 | C23×C22⋊C4 | C24 | 1 | 1152 | yes | — |
| 206 | C23×C22⋊C4 | C24 | 1 | 96 | yes | — |
| 207 | C23×C22⋊C4 | C24 | 1 | 144 | yes | — |
| 208 | C23×C22⋊C4 | C24 | 1 | 24 | yes | — |
| 209 | C23×C22⋊C4 | C24 | 1 | 24 | yes | — |
| 210 | C23×C22⋊C4 | C24 | 1 | 576 | yes | — |
| 211 | C23×C22⋊C4 | C24 | 1 | 768 | yes | — |
| 212 | C23×C22⋊C4 | C24 | 1 | 144 | yes | — |
| 213 | C23×C22⋊C4 | C24 | 1 | 3072 | yes | complemented |
| 214 | C23×C22⋊C4 | C24 | 1 | 576 | yes | complemented |
| 215 | C23×C22⋊C4 | C24 | 1 | 1152 | yes | complemented |
| 216 | C23×C22⋊C4 | C24 | 1 | 576 | yes | complemented |
| 217 | C23×C22⋊C4 | C24 | 1 | 48 | yes | complemented |
| 218 | C23×C42 | C24 | 1 | 48 | yes | complemented |
| 219 | #2375 | C24 | 1 | 8192 | yes | complemented |
| 220 | #2358 | C24 | 1 | 24576 | yes | complemented |
| 221 | #2342 | C24 | 1 | 24576 | yes | complemented |
| 222 | D4×C22⋊C4 | C24 | 1 | 24576 | yes | complemented |
| 223 | #2321 | C24 | 1 | 24576 | yes | complemented |
| 224 | #2315 | C24 | 1 | 3072 | yes | complemented |
| 225 | #2312 | C24 | 1 | 6144 | yes | complemented |
| 226 | #2309 | C24 | 1 | 3072 | yes | complemented |
| 227 | #2308 | C24 | 1 | 3072 | yes | complemented |
| 228 | #2308 | C24 | 1 | 3072 | yes | complemented |
| 229 | C4×#120 | C24 | 1 | 8192 | yes | complemented |
| 230 | C2×#390 | C24 | 1 | 2304 | yes | complemented |
| 231 | C2×#388 | C24 | 1 | 4608 | yes | complemented |
| 232 | C2×#386 | C24 | 1 | 2304 | yes | complemented |
| 233 | C2×#386 | C24 | 1 | 2304 | yes | complemented |
| 234 | C2×#385 | C24 | 1 | 2304 | yes | complemented |
| 235 | #2280 | C24 | 1 | 3072 | yes | complemented |
| 236 | C2×#381 | C24 | 1 | 576 | yes | complemented |
| 237 | C2×#380 | C24 | 1 | 1152 | yes | complemented |
| 238 | C2×#379 | C24 | 1 | 1152 | yes | — |
| 239 | C2×#379 | C24 | 1 | 3072 | yes | — |
| 240 | C2×#379 | C24 | 1 | 192 | yes | — |
| 241 | C2×#379 | C24 | 1 | 576 | yes | — |
| 242 | C2×#379 | C24 | 1 | 576 | yes | complemented |
| 243 | C2×#379 | C24 | 1 | 384 | yes | complemented |
| 244 | C2×#379 | C24 | 1 | 192 | yes | complemented |
| 245 | C2×#379 | C24 | 1 | 6144 | yes | complemented |
| 246 | C2×#379 | C24 | 1 | 3072 | yes | complemented |
| 247 | C2×#379 | C24 | 1 | 576 | yes | complemented |
| 248 | C2×#379 | C24 | 1 | 1024 | yes | complemented |
| 249 | #2273 | C24 | 1 | 3072 | yes | complemented |
| 250 | C2×C4×C22⋊C4 | C24 | 1 | 2304 | yes | complemented |
| 251 | C2×C4×C22⋊C4 | C24 | 1 | 1152 | yes | complemented |
| 252 | C22×#95 | C24 | 1 | 96 | yes | complemented |
| 253 | C26 | — | 2 | 96 | no | — |
| 254 | C26 | — | 2 | 48 | no | — |
| 255 | C26 | — | 2 | 1536 | no | — |
| 256 | C26 | — | 2 | 3072 | no | — |
| 257 | C26 | — | 2 | 192 | no | — |
| 258 | C26 | — | 2 | 1152 | no | — |
| 259 | C26 | — | 2 | 48 | no | — |
| 260 | C26 | — | 2 | 192 | no | — |
| 261 | C26 | — | 2 | 192 | no | — |
| 262 | C26 | — | 2 | 2304 | no | — |
| 263 | C26 | — | 2 | 96 | no | — |
| 264 | C26 | — | 2 | 96 | no | — |
| 265 | C26 | — | 4 | 1536 | no | — |
| 266 | C26 | — | 4 | 3072 | no | — |
| 267 | C26 | — | 4 | 3072 | no | — |
| 268 | C26 | — | 4 | 1536 | no | — |
| 269 | C26 | — | 4 | 36864 | no | — |
| 270 | C26 | — | 4 | 48 | no | — |
| 271 | C26 | — | 4 | 48 | no | — |
| 272 | C26 | — | 4 | 96 | no | — |
| 273 | C26 | — | 4 | 2304 | no | — |
| 274 | C26 | — | 4 | 96 | no | — |
| 275 | C26 | — | 4 | 1152 | no | — |
| 276 | C26 | — | 4 | 48 | no | — |
| 277 | C26 | — | 4 | 1152 | no | — |
| 278 | C26 | — | 4 | 2304 | no | — |
| 279 | C26 | — | 4 | 48 | no | — |
| 280 | C26 | — | 4 | 6144 | no | — |
| 281 | C26 | — | 4 | 768 | no | — |
| 282 | C26 | — | 4 | 96 | no | — |
| 283 | C26 | — | 4 | 576 | no | — |
| 284 | C26 | — | 4 | 6144 | no | — |
| 285 | C26 | — | 4 | 3072 | no | — |
| 286 | C26 | — | 4 | 6144 | no | — |
| 287 | C26 | — | 4 | 65536 | no | — |
| 288 | C26 | — | 4 | 49152 | no | — |
| 289 | C26 | — | 8 | 512 | no | — |
| 290 | C26 | C23×C4 | 1 | 16 | yes | — |
| 291 | C26 | C23×C4 | 1 | 32 | yes | — |
| 292 | C26 | C23×C4 | 1 | 192 | yes | — |
| 293 | C26 | C23×C4 | 1 | 96 | yes | — |
| 294 | C26 | C23×C4 | 1 | 96 | yes | — |
| 295 | C26 | C23×C4 | 1 | 48 | yes | — |
| 296 | C26 | C23×C4 | 1 | 1152 | yes | — |
| 297 | C26 | C23×C4 | 1 | 96 | yes | — |
| 298 | C26 | C23×C4 | 1 | 2304 | yes | — |
| 299 | C26 | C23×C4 | 1 | 32 | yes | — |
| 300 | C26 | C23×C4 | 1 | 2304 | yes | — |
| 301 | C26 | C23×C4 | 1 | 48 | yes | — |
| 302 | C26 | C23×C4 | 1 | 4096 | yes | complemented |
| 303 | C26 | C23×C4 | 1 | 384 | yes | complemented |
| 304 | C26 | H(5,𝔽2) | 1 | 96 | yes | — |
| 305 | C26 | C25 | 1 | 12 | yes | — |
| 306 | C26 | C25 | 1 | 24 | yes | — |
| 307 | C26 | C25 | 1 | 4 | yes | — |
| 308 | C26 | C25 | 1 | 6 | yes | — |
| 309 | C26 | C25 | 1 | 144 | yes | — |
| 310 | C26 | C25 | 1 | 72 | yes | — |
| 311 | C26 | C25 | 1 | 6 | yes | — |
| 312 | C26 | C25 | 1 | 3 | yes | — |
| 313 | C26 | C25 | 1 | 72 | yes | — |
| 314 | C26 | C25 | 1 | 36 | yes | — |
| 315 | C26 | C25 | 1 | 192 | yes | — |
| 316 | C26 | C25 | 1 | 72 | yes | — |
| 317 | C26 | C25 | 1 | 384 | yes | — |
| 318 | C26 | C25 | 1 | 24 | yes | — |
| 319 | C26 | C25 | 1 | 384 | yes | — |
| 320 | C26 | C25 | 1 | 64 | yes | — |
| 321 | C26 | C25 | 1 | 36 | yes | — |
| 322 | C23×D4 | — | 2 | 3072 | no | — |
| 323 | C23×D4 | — | 2 | 384 | no | — |
| 324 | C23×D4 | — | 2 | 2304 | no | — |
| 325 | C23×D4 | — | 4 | 1536 | no | — |
| 326 | C23×D4 | — | 4 | 192 | no | — |
| 327 | C23×D4 | — | 4 | 1152 | no | — |
| 328 | C23×D4 | — | 4 | 6144 | no | — |
| 329 | C23×D4 | — | 4 | 36864 | no | — |
| 330 | C23×D4 | — | 4 | 4608 | no | — |
| 331 | C23×D4 | — | 4 | 6144 | no | — |
| 332 | C23×D4 | C23×C4 | 1 | 384 | yes | — |
| 333 | C23×D4 | C23×C4 | 1 | 2304 | yes | — |
| 334 | C23×D4 | C23×C4 | 1 | 384 | yes | — |
| 335 | C23×D4 | C23×C4 | 1 | 2304 | yes | complemented |
| 336 | C23×D4 | C23×C4 | 1 | 9216 | yes | complemented |
| 337 | C23×D4 | C23×C4 | 1 | 12288 | yes | complemented |
| 338 | C23×D4 | C25 | 1 | 384 | yes | — |
| 339 | C23×D4 | C25 | 1 | 288 | yes | — |
| 340 | C23×D4 | C25 | 1 | 288 | yes | — |
| 341 | C23×D4 | C25 | 1 | 384 | yes | — |
| 342 | C23×D4 | C25 | 1 | 1536 | yes | — |
| 343 | C24×C4 | — | 2 | 96 | no | — |
| 344 | C24×C4 | — | 2 | 384 | no | — |
| 345 | C24×C4 | — | 4 | 768 | no | — |
| 346 | C24×C4 | — | 4 | 96 | no | — |
| 347 | C24×C4 | — | 4 | 576 | no | — |
| 348 | C24×C4 | — | 4 | 384 | no | — |
| 349 | C24×C4 | — | 4 | 2304 | no | — |
| 350 | C24×C4 | — | 4 | 192 | no | — |
| 351 | C24×C4 | — | 8 | 1024 | no | — |
| 352 | C24×C4 | C23×C4 | 1 | 96 | yes | — |
| 353 | C24×C4 | C23×C4 | 1 | 192 | yes | — |
| 354 | C24×C4 | C23×C4 | 1 | 1152 | yes | complemented |
| 355 | C24×C4 | C25 | 1 | 32 | yes | — |
| 356 | C24×C4 | C25 | 1 | 72 | yes | — |
| 357 | C24×C4 | C25 | 1 | 12 | yes | — |
| 358 | C24×C4 | C25 | 1 | 576 | yes | — |
| 359 | C24×C4 | C25 | 1 | 144 | yes | — |
| 360 | C24×C4 | C25 | 1 | 192 | yes | — |
| 361 | C24×C4 | C25 | 1 | 512 | yes | complemented |
| 362 | C24×C4 | C25 | 1 | 192 | yes | complemented |
| 363 | C2×#120 | C23×C4 | 1 | 9216 | yes | — |
| 364 | C2×#120 | C23×C4 | 1 | 3072 | yes | complemented |
| 365 | C2×#120 | C23×C4 | 1 | 9216 | yes | complemented |
| 366 | C2×#120 | C23×C4 | 1 | 3072 | yes | complemented |
| 367 | C2×#120 | C23×C4 | 1 | 49152 | yes | complemented |
| 368 | C2×#120 | C23×C4 | 1 | 49152 | yes | complemented |
| 369 | C2×#120 | C25 | 1 | 1536 | yes | — |
| 370 | C2×#120 | C25 | 1 | 1536 | yes | — |
| 371 | C2×#120 | C25 | 1 | 512 | yes | — |
| 372 | C2×#120 | C25 | 1 | 512 | yes | — |
| 373 | #518 | — | 4 | 12288 | no | — |
| 374 | C2×C4×D4 | — | 4 | 9216 | no | — |
| 375 | C2×C4×D4 | C25 | 1 | 6144 | yes | complemented |
| 376 | C2×#117 | — | 4 | 2304 | no | — |
| 377 | C2×#117 | C25 | 1 | 1536 | yes | complemented |
| 378 | C22×C4⋊C4 | — | 4 | 192 | no | — |
| 379 | C22×C4⋊C4 | C25 | 1 | 576 | yes | complemented |
| 380 | C22×C22⋊C4 | — | 2 | 384 | no | — |
| 381 | C22×C22⋊C4 | — | 2 | 384 | no | — |
| 382 | C22×C22⋊C4 | — | 2 | 4608 | no | — |
| 383 | C22×C22⋊C4 | — | 4 | 4608 | no | — |
| 384 | C22×C22⋊C4 | — | 4 | 4608 | no | — |
| 385 | C22×C22⋊C4 | — | 4 | 12288 | no | — |
| 386 | C22×C22⋊C4 | — | 4 | 2304 | no | — |
| 387 | C22×C22⋊C4 | — | 4 | 384 | no | — |
| 388 | C22×C22⋊C4 | — | 4 | 2304 | no | — |
| 389 | C22×C22⋊C4 | — | 4 | 192 | no | — |
| 390 | C22×C22⋊C4 | C23×C4 | 1 | 384 | yes | — |
| 391 | C22×C22⋊C4 | C23×C4 | 1 | 2304 | yes | — |
| 392 | C22×C22⋊C4 | C23×C4 | 1 | 384 | yes | — |
| 393 | C22×C22⋊C4 | C23×C4 | 1 | 9216 | yes | complemented |
| 394 | C22×C22⋊C4 | C23×C4 | 1 | 2304 | yes | complemented |
| 395 | C22×C22⋊C4 | C23×C4 | 1 | 12288 | yes | complemented |
| 396 | C22×C22⋊C4 | C25 | 1 | 1536 | yes | — |
| 397 | C22×C22⋊C4 | C25 | 1 | 576 | yes | — |
| 398 | C22×C22⋊C4 | C25 | 1 | 576 | yes | — |
| 399 | C22×C22⋊C4 | C25 | 1 | 3072 | yes | — |
| 400 | C22×C22⋊C4 | C25 | 1 | 1152 | yes | — |
| 401 | C22×C22⋊C4 | C25 | 1 | 384 | yes | — |
| 402 | C22×C22⋊C4 | C25 | 1 | 288 | yes | — |
| 403 | C22×C22⋊C4 | C25 | 1 | 288 | yes | — |
| 404 | C22×C22⋊C4 | C25 | 1 | 384 | yes | — |
| 405 | C22×C22⋊C4 | C25 | 1 | 1536 | yes | — |
| 406 | C22×C22⋊C4 | C25 | 1 | 1536 | yes | complemented |
| 407 | C22×C22⋊C4 | C25 | 1 | 3072 | yes | complemented |
| 408 | C22×C22⋊C4 | C25 | 1 | 1536 | yes | complemented |
| 409 | C22×C22⋊C4 | C25 | 1 | 576 | yes | complemented |
| 410 | C22×C42 | — | 4 | 192 | no | — |
| 411 | C22×C42 | C25 | 1 | 576 | yes | complemented |
| 412 | #390 | C25 | 1 | 6144 | yes | complemented |
| 413 | #388 | C25 | 1 | 12288 | yes | complemented |
| 414 | #386 | C25 | 1 | 6144 | yes | complemented |
| 415 | #386 | C25 | 1 | 6144 | yes | complemented |
| 416 | #385 | C25 | 1 | 6144 | yes | complemented |
| 417 | #381 | C25 | 1 | 1536 | yes | complemented |
| 418 | #380 | C25 | 1 | 3072 | yes | complemented |
| 419 | #379 | C25 | 1 | 1536 | yes | — |
| 420 | #379 | C25 | 1 | 3072 | yes | — |
| 421 | #379 | C25 | 1 | 512 | yes | — |
| 422 | #379 | C25 | 1 | 1536 | yes | complemented |
| 423 | #379 | C25 | 1 | 1024 | yes | complemented |
| 424 | #379 | C25 | 1 | 512 | yes | complemented |
| 425 | #379 | C25 | 1 | 1536 | yes | complemented |
| 426 | C4×C22⋊C4 | C25 | 1 | 3072 | yes | complemented |
| 427 | C4×C22⋊C4 | C25 | 1 | 6144 | yes | complemented |
| 428 | C2×#95 | C25 | 1 | 1152 | yes | complemented |
| 429 | C25 | — | 2 | 1024 | no | — |
| 430 | C25 | — | 2 | 512 | no | — |
| 431 | C25 | — | 2 | 576 | no | — |
| 432 | C25 | — | 2 | 96 | no | — |
| 433 | C25 | — | 2 | 288 | no | — |
| 434 | C25 | — | 2 | 48 | no | — |
| 435 | C25 | — | 2 | 384 | no | — |
| 436 | C25 | — | 2 | 768 | no | — |
| 437 | C25 | — | 2 | 1152 | no | — |
| 438 | C25 | — | 2 | 1152 | no | — |
| 439 | C25 | — | 2 | 3072 | no | — |
| 440 | C25 | — | 2 | 576 | no | — |
| 441 | C25 | — | 2 | 96 | no | — |
| 442 | C25 | — | 2 | 96 | no | — |
| 443 | C25 | — | 2 | 1152 | no | — |
| 444 | C25 | — | 2 | 1536 | no | — |
| 445 | C25 | — | 2 | 288 | no | — |
| 446 | C25 | — | 2 | 48 | no | — |
| 447 | C25 | — | 2 | 1536 | no | — |
| 448 | C25 | — | 2 | 384 | no | — |
| 449 | C25 | — | 2 | 1536 | no | — |
| 450 | C25 | — | 2 | 1536 | no | — |
| 451 | C25 | — | 2 | 768 | no | — |
| 452 | C25 | — | 2 | 9216 | no | — |
| 453 | C25 | — | 2 | 18432 | no | — |
| 454 | C25 | — | 2 | 576 | no | — |
| 455 | C25 | — | 2 | 768 | no | — |
| 456 | C25 | — | 4 | 384 | no | — |
| 457 | C25 | — | 4 | 768 | no | — |
| 458 | C25 | — | 4 | 384 | no | — |
| 459 | C25 | — | 4 | 9216 | no | — |
| 460 | C25 | — | 4 | 384 | no | — |
| 461 | C25 | — | 4 | 768 | no | — |
| 462 | C25 | — | 4 | 18432 | no | — |
| 463 | C25 | — | 4 | 384 | no | — |
| 464 | C25 | — | 4 | 18432 | no | — |
| 465 | C25 | — | 4 | 9216 | no | — |
| 466 | C25 | — | 4 | 49152 | no | — |
| 467 | C25 | — | 4 | 768 | no | — |
| 468 | C25 | — | 4 | 288 | no | — |
| 469 | C25 | — | 4 | 288 | no | — |
| 470 | C25 | — | 4 | 576 | no | — |
| 471 | C25 | — | 4 | 3072 | no | — |
| 472 | C25 | — | 4 | 576 | no | — |
| 473 | C25 | — | 4 | 1536 | no | — |
| 474 | C25 | — | 4 | 288 | no | — |
| 475 | C25 | — | 4 | 1536 | no | — |
| 476 | C25 | — | 4 | 3072 | no | — |
| 477 | C25 | — | 4 | 288 | no | — |
| 478 | C25 | — | 4 | 768 | no | — |
| 479 | C25 | — | 4 | 4608 | no | — |
| 480 | C25 | — | 4 | 576 | no | — |
| 481 | C25 | — | 4 | 768 | no | — |
| 482 | C25 | — | 4 | 1536 | no | — |
| 483 | C25 | — | 4 | 3072 | no | — |
| 484 | C25 | — | 4 | 36864 | no | — |
| 485 | C25 | — | 4 | 49152 | no | — |
| 486 | C25 | — | 4 | 24576 | no | — |
| 487 | C25 | — | 4 | 18432 | no | — |
| 488 | C25 | — | 4 | 1536 | no | — |
| 489 | C25 | — | 4 | 768 | no | — |
| 490 | C25 | — | 4 | 49152 | no | — |
| 491 | C25 | — | 4 | 36864 | no | — |
| 492 | C25 | — | 4 | 393216 | no | — |
| 493 | C25 | — | 4 | 65536 | no | — |
| 494 | C25 | — | 4 | 512 | no | — |
| 495 | C25 | — | 8 | 768 | no | — |
| 496 | C25 | — | 8 | 4096 | no | — |
| 497 | C25 | — | 8 | 3072 | no | — |
| 498 | C25 | #518 | 1 | 768 | yes | complemented |
| 499 | C25 | C24×C4 | 1 | 48 | yes | — |
| 500 | C25 | C24×C4 | 1 | 192 | yes | — |
| 501 | C25 | C24×C4 | 1 | 96 | yes | — |
| 502 | C25 | C24×C4 | 1 | 32 | yes | — |
| 503 | C25 | C24×C4 | 1 | 1152 | yes | — |
| 504 | C25 | C24×C4 | 1 | 576 | yes | — |
| 505 | C25 | C24×C4 | 1 | 48 | yes | — |
| 506 | C25 | C24×C4 | 1 | 24 | yes | — |
| 507 | C25 | C24×C4 | 1 | 288 | yes | — |
| 508 | C25 | C24×C4 | 1 | 1536 | yes | — |
| 509 | C25 | C24×C4 | 1 | 576 | yes | — |
| 510 | C25 | C24×C4 | 1 | 3072 | yes | — |
| 511 | C25 | C24×C4 | 1 | 576 | yes | — |
| 512 | C25 | C24×C4 | 1 | 192 | yes | — |
| 513 | C25 | C24×C4 | 1 | 3072 | yes | — |
| 514 | C25 | C24×C4 | 1 | 288 | yes | — |
| 515 | C25 | C24×C4 | 1 | 512 | yes | complemented |
| 516 | C25 | C2×H(5,𝔽2) | 1 | 48 | yes | — |
| 517 | C25 | C2×H(5,𝔽2) | 1 | 96 | yes | — |
| 518 | C25 | C2×H(5,𝔽2) | 1 | 576 | yes | — |
| 519 | C25 | C26 | 1 | 36 | yes | — |
| 520 | C25 | C26 | 1 | 24 | yes | — |
| 521 | C25 | C26 | 1 | 32 | yes | — |
| 522 | C25 | C26 | 1 | 16 | yes | — |
| 523 | C25 | C26 | 1 | 192 | yes | — |
| 524 | C25 | C26 | 1 | 96 | yes | — |
| 525 | C25 | C26 | 1 | 18 | yes | — |
| 526 | C25 | C26 | 1 | 36 | yes | — |
| 527 | C25 | C26 | 1 | 48 | yes | — |
| 528 | C25 | C26 | 1 | 96 | yes | — |
| 529 | C25 | C26 | 1 | 96 | yes | — |
| 530 | C25 | C26 | 1 | 32 | yes | — |
| 531 | C25 | C26 | 1 | 48 | yes | — |
| 532 | C25 | C26 | 1 | 1 | yes | characteristic |
| 533 | C22×D4 | — | 2 | 2304 | no | — |
| 534 | C22×D4 | — | 2 | 3072 | no | — |
| 535 | C22×D4 | — | 2 | 3072 | no | — |
| 536 | C22×D4 | — | 2 | 18432 | no | — |
| 537 | C22×D4 | — | 4 | 1536 | no | — |
| 538 | C22×D4 | — | 4 | 9216 | no | — |
| 539 | C22×D4 | — | 4 | 1152 | no | — |
| 540 | C22×D4 | — | 4 | 1536 | no | — |
| 541 | C22×D4 | — | 4 | 36864 | no | — |
| 542 | C22×D4 | — | 4 | 49152 | no | — |
| 543 | C22×D4 | — | 4 | 6144 | no | — |
| 544 | C22×D4 | C24×C4 | 1 | 2304 | yes | — |
| 545 | C22×D4 | C24×C4 | 1 | 3072 | yes | — |
| 546 | C22×D4 | C24×C4 | 1 | 2304 | yes | — |
| 547 | C22×D4 | C24×C4 | 1 | 3072 | yes | complemented |
| 548 | C22×D4 | C24×C4 | 1 | 12288 | yes | complemented |
| 549 | C22×D4 | C26 | 1 | 384 | yes | — |
| 550 | C22×D4 | C26 | 1 | 384 | yes | — |
| 551 | C23×C4 | — | 2 | 96 | no | — |
| 552 | C23×C4 | — | 2 | 576 | no | — |
| 553 | C23×C4 | — | 2 | 768 | no | — |
| 554 | C23×C4 | — | 2 | 384 | no | — |
| 555 | C23×C4 | — | 2 | 2304 | no | — |
| 556 | C23×C4 | — | 4 | 768 | no | — |
| 557 | C23×C4 | — | 4 | 4608 | no | — |
| 558 | C23×C4 | — | 4 | 576 | no | — |
| 559 | C23×C4 | — | 4 | 768 | no | — |
| 560 | C23×C4 | — | 4 | 2304 | no | — |
| 561 | C23×C4 | — | 4 | 3072 | no | — |
| 562 | C23×C4 | — | 4 | 1152 | no | — |
| 563 | C23×C4 | — | 8 | 1536 | no | — |
| 564 | C23×C4 | — | 8 | 6144 | no | — |
| 565 | C23×C4 | — | 16 | 256 | no | — |
| 566 | C23×C4 | C24×C4 | 1 | 96 | yes | — |
| 567 | C23×C4 | C24×C4 | 1 | 576 | yes | — |
| 568 | C23×C4 | C24×C4 | 1 | 1152 | yes | — |
| 569 | C23×C4 | C24×C4 | 1 | 1536 | yes | complemented |
| 570 | C23×C4 | C26 | 1 | 192 | yes | — |
| 571 | C23×C4 | C26 | 1 | 72 | yes | — |
| 572 | C23×C4 | C26 | 1 | 96 | yes | — |
| 573 | C23×C4 | C26 | 1 | 768 | yes | — |
| 574 | C23×C4 | C26 | 1 | 192 | yes | — |
| 575 | C23×C4 | C26 | 1 | 256 | yes | complemented |
| 576 | #120 | C24×C4 | 1 | 12288 | yes | — |
| 577 | #120 | C24×C4 | 1 | 4096 | yes | complemented |
| 578 | #120 | C24×C4 | 1 | 12288 | yes | complemented |
| 579 | #120 | C24×C4 | 1 | 4096 | yes | complemented |
| 580 | C4×D4 | — | 4 | 12288 | no | — |
| 581 | #117 | — | 4 | 3072 | no | — |
| 582 | C2×C4⋊C4 | — | 4 | 1152 | no | — |
| 583 | C2×C4⋊C4 | C26 | 1 | 768 | yes | complemented |
| 584 | C2×C22⋊C4 | — | 2 | 2304 | no | — |
| 585 | C2×C22⋊C4 | — | 2 | 2304 | no | — |
| 586 | C2×C22⋊C4 | — | 2 | 6144 | no | — |
| 587 | C2×C22⋊C4 | — | 4 | 6144 | no | — |
| 588 | C2×C22⋊C4 | — | 4 | 6144 | no | — |
| 589 | C2×C22⋊C4 | — | 4 | 3072 | no | — |
| 590 | C2×C22⋊C4 | — | 4 | 2304 | no | — |
| 591 | C2×C22⋊C4 | — | 4 | 3072 | no | — |
| 592 | C2×C22⋊C4 | — | 4 | 1152 | no | — |
| 593 | C2×C22⋊C4 | C24×C4 | 1 | 2304 | yes | — |
| 594 | C2×C22⋊C4 | C24×C4 | 1 | 3072 | yes | — |
| 595 | C2×C22⋊C4 | C24×C4 | 1 | 2304 | yes | — |
| 596 | C2×C22⋊C4 | C24×C4 | 1 | 12288 | yes | complemented |
| 597 | C2×C22⋊C4 | C24×C4 | 1 | 3072 | yes | complemented |
| 598 | C2×C22⋊C4 | C26 | 1 | 768 | yes | — |
| 599 | C2×C22⋊C4 | C26 | 1 | 768 | yes | — |
| 600 | C2×C22⋊C4 | C26 | 1 | 1536 | yes | — |
| 601 | C2×C22⋊C4 | C26 | 1 | 384 | yes | — |
| 602 | C2×C22⋊C4 | C26 | 1 | 384 | yes | — |
| 603 | C2×C22⋊C4 | C26 | 1 | 768 | yes | complemented |
| 604 | C2×C42 | — | 4 | 1152 | no | — |
| 605 | C2×C42 | C26 | 1 | 768 | yes | complemented |
| 606 | #95 | C26 | 1 | 1536 | yes | complemented |
| 607 | C24 | — | 2 | 3072 | no | — |
| 608 | C24 | — | 2 | 4096 | no | — |
| 609 | C24 | — | 2 | 1536 | no | — |
| 610 | C24 | — | 2 | 2048 | no | — |
| 611 | C24 | — | 2 | 768 | no | — |
| 612 | C24 | — | 2 | 384 | no | — |
| 613 | C24 | — | 2 | 384 | no | — |
| 614 | C24 | — | 2 | 288 | no | — |
| 615 | C24 | — | 2 | 192 | no | — |
| 616 | C24 | — | 2 | 144 | no | — |
| 617 | C24 | — | 2 | 1152 | no | — |
| 618 | C24 | — | 2 | 192 | no | — |
| 619 | C24 | — | 2 | 2304 | no | — |
| 620 | C24 | — | 2 | 384 | no | — |
| 621 | C24 | — | 2 | 768 | no | — |
| 622 | C24 | — | 2 | 768 | no | — |
| 623 | C24 | — | 2 | 384 | no | — |
| 624 | C24 | — | 2 | 288 | no | — |
| 625 | C24 | — | 2 | 288 | no | — |
| 626 | C24 | — | 2 | 768 | no | — |
| 627 | C24 | — | 2 | 192 | no | — |
| 628 | C24 | — | 2 | 144 | no | — |
| 629 | C24 | — | 2 | 384 | no | — |
| 630 | C24 | — | 2 | 4608 | no | — |
| 631 | C24 | — | 2 | 1152 | no | — |
| 632 | C24 | — | 2 | 192 | no | — |
| 633 | C24 | — | 2 | 4608 | no | — |
| 634 | C24 | — | 2 | 4608 | no | — |
| 635 | C24 | — | 2 | 2304 | no | — |
| 636 | C24 | — | 2 | 384 | no | — |
| 637 | C24 | — | 2 | 6144 | no | — |
| 638 | C24 | — | 2 | 12288 | no | — |
| 639 | C24 | — | 2 | 384 | no | — |
| 640 | C24 | — | 2 | 2304 | no | — |
| 641 | C24 | — | 4 | 3072 | no | — |
| 642 | C24 | — | 4 | 1152 | no | — |
| 643 | C24 | — | 4 | 2304 | no | — |
| 644 | C24 | — | 4 | 1152 | no | — |
| 645 | C24 | — | 4 | 6144 | no | — |
| 646 | C24 | — | 4 | 1152 | no | — |
| 647 | C24 | — | 4 | 2304 | no | — |
| 648 | C24 | — | 4 | 12288 | no | — |
| 649 | C24 | — | 4 | 1152 | no | — |
| 650 | C24 | — | 4 | 12288 | no | — |
| 651 | C24 | — | 4 | 6144 | no | — |
| 652 | C24 | — | 4 | 2304 | no | — |
| 653 | C24 | — | 4 | 192 | no | — |
| 654 | C24 | — | 4 | 192 | no | — |
| 655 | C24 | — | 4 | 384 | no | — |
| 656 | C24 | — | 4 | 384 | no | — |
| 657 | C24 | — | 4 | 192 | no | — |
| 658 | C24 | — | 4 | 192 | no | — |
| 659 | C24 | — | 4 | 2304 | no | — |
| 660 | C24 | — | 4 | 3072 | no | — |
| 661 | C24 | — | 4 | 384 | no | — |
| 662 | C24 | — | 4 | 4608 | no | — |
| 663 | C24 | — | 4 | 9216 | no | — |
| 664 | C24 | — | 4 | 12288 | no | — |
| 665 | C24 | — | 4 | 6144 | no | — |
| 666 | C24 | — | 4 | 24576 | no | — |
| 667 | C24 | — | 4 | 147456 | no | — |
| 668 | C24 | — | 4 | 12288 | no | — |
| 669 | C24 | — | 4 | 73728 | no | — |
| 670 | C24 | — | 4 | 4608 | no | — |
| 671 | C24 | — | 4 | 2304 | no | — |
| 672 | C24 | — | 4 | 3072 | no | — |
| 673 | C24 | — | 4 | 6144 | no | — |
| 674 | C24 | — | 4 | 147456 | no | — |
| 675 | C24 | — | 4 | 24576 | no | — |
| 676 | C24 | — | 4 | 262144 | no | — |
| 677 | C24 | — | 4 | 1536 | no | — |
| 678 | C24 | — | 4 | 2048 | no | — |
| 679 | C24 | — | 4 | 256 | no | — |
| 680 | C24 | — | 4 | 384 | no | — |
| 681 | C24 | — | 8 | 2304 | no | — |
| 682 | C24 | — | 8 | 3072 | no | — |
| 683 | C24 | — | 8 | 12288 | no | — |
| 684 | C24 | — | 8 | 2048 | no | — |
| 685 | C24 | C2×#518 | 1 | 192 | yes | — |
| 686 | C24 | C2×#518 | 1 | 384 | yes | — |
| 687 | C24 | C2×#518 | 1 | 2304 | yes | complemented |
| 688 | C24 | C25×C4 | 1 | 144 | yes | — |
| 689 | C24 | C25×C4 | 1 | 128 | yes | — |
| 690 | C24 | C25×C4 | 1 | 64 | yes | — |
| 691 | C24 | C25×C4 | 1 | 96 | yes | — |
| 692 | C24 | C25×C4 | 1 | 768 | yes | — |
| 693 | C24 | C25×C4 | 1 | 384 | yes | — |
| 694 | C24 | C25×C4 | 1 | 144 | yes | — |
| 695 | C24 | C25×C4 | 1 | 72 | yes | — |
| 696 | C24 | C25×C4 | 1 | 192 | yes | — |
| 697 | C24 | C25×C4 | 1 | 384 | yes | — |
| 698 | C24 | C25×C4 | 1 | 384 | yes | — |
| 699 | C24 | C25×C4 | 1 | 128 | yes | — |
| 700 | C24 | C25×C4 | 1 | 192 | yes | — |
| 701 | C24 | C25×C4 | 1 | 4 | yes | — |
| 702 | C24 | C22×H(5,𝔽2) | 1 | 144 | yes | — |
| 703 | C24 | C22×H(5,𝔽2) | 1 | 288 | yes | — |
| 704 | C24 | C22×H(5,𝔽2) | 1 | 384 | yes | — |
| 705 | C24 | C22×H(5,𝔽2) | 1 | 24 | yes | — |
| 706 | C24 | C27 | 1 | 24 | yes | — |
| 707 | C24 | C27 | 1 | 16 | yes | — |
| 708 | C24 | C27 | 1 | 12 | yes | — |
| 709 | C24 | C27 | 1 | 24 | yes | — |
| 710 | C24 | C27 | 1 | 3 | yes | — |
| 711 | C2×D4 | — | 2 | 1536 | no | — |
| 712 | C2×D4 | — | 2 | 9216 | no | — |
| 713 | C2×D4 | — | 2 | 12288 | no | — |
| 714 | C2×D4 | — | 4 | 4608 | no | — |
| 715 | C2×D4 | — | 4 | 6144 | no | — |
| 716 | C2×D4 | — | 4 | 768 | no | — |
| 717 | C2×D4 | — | 4 | 24576 | no | — |
| 718 | C2×D4 | C25×C4 | 1 | 1536 | yes | — |
| 719 | C2×D4 | C25×C4 | 1 | 1536 | yes | — |
| 720 | C22×C4 | — | 2 | 288 | no | — |
| 721 | C22×C4 | — | 2 | 384 | no | — |
| 722 | C22×C4 | — | 2 | 2304 | no | — |
| 723 | C22×C4 | — | 2 | 384 | no | — |
| 724 | C22×C4 | — | 2 | 1152 | no | — |
| 725 | C22×C4 | — | 2 | 1536 | no | — |
| 726 | C22×C4 | — | 4 | 2304 | no | — |
| 727 | C22×C4 | — | 4 | 3072 | no | — |
| 728 | C22×C4 | — | 4 | 384 | no | — |
| 729 | C22×C4 | — | 4 | 1536 | no | — |
| 730 | C22×C4 | — | 4 | 768 | no | — |
| 731 | C22×C4 | — | 4 | 512 | no | — |
| 732 | C22×C4 | — | 8 | 4608 | no | — |
| 733 | C22×C4 | — | 8 | 4096 | no | — |
| 734 | C22×C4 | — | 16 | 768 | no | — |
| 735 | C22×C4 | C25×C4 | 1 | 288 | yes | — |
| 736 | C22×C4 | C25×C4 | 1 | 384 | yes | — |
| 737 | C22×C4 | C25×C4 | 1 | 768 | yes | — |
| 738 | C22×C4 | C27 | 1 | 128 | yes | — |
| 739 | C22×C4 | C27 | 1 | 48 | yes | — |
| 740 | C4⋊C4 | — | 4 | 768 | no | — |
| 741 | C22⋊C4 | — | 2 | 1536 | no | — |
| 742 | C22⋊C4 | — | 2 | 1536 | no | — |
| 743 | C22⋊C4 | — | 4 | 1536 | no | — |
| 744 | C22⋊C4 | — | 4 | 768 | no | — |
| 745 | C22⋊C4 | C25×C4 | 1 | 1536 | yes | — |
| 746 | C22⋊C4 | C25×C4 | 1 | 1536 | yes | — |
| 747 | C42 | — | 4 | 768 | no | — |
| 748 | C23 | — | 2 | 1024 | no | — |
| 749 | C23 | — | 2 | 6144 | no | — |
| 750 | C23 | — | 2 | 3072 | no | — |
| 751 | C23 | — | 2 | 512 | no | — |
| 752 | C23 | — | 2 | 384 | no | — |
| 753 | C23 | — | 2 | 288 | no | — |
| 754 | C23 | — | 2 | 768 | no | — |
| 755 | C23 | — | 2 | 576 | no | — |
| 756 | C23 | — | 2 | 1152 | no | — |
| 757 | C23 | — | 2 | 576 | no | — |
| 758 | C23 | — | 2 | 96 | no | — |
| 759 | C23 | — | 2 | 48 | no | — |
| 760 | C23 | — | 2 | 768 | no | — |
| 761 | C23 | — | 2 | 1536 | no | — |
| 762 | C23 | — | 2 | 576 | no | — |
| 763 | C23 | — | 2 | 1536 | no | — |
| 764 | C23 | — | 2 | 384 | no | — |
| 765 | C23 | — | 2 | 288 | no | — |
| 766 | C23 | — | 2 | 1536 | no | — |
| 767 | C23 | — | 2 | 1536 | no | — |
| 768 | C23 | — | 2 | 768 | no | — |
| 769 | C23 | — | 2 | 576 | no | — |
| 770 | C23 | — | 2 | 96 | no | — |
| 771 | C23 | — | 2 | 96 | no | — |
| 772 | C23 | — | 2 | 48 | no | — |
| 773 | C23 | — | 2 | 768 | no | — |
| 774 | C23 | — | 4 | 384 | no | — |
| 775 | C23 | — | 4 | 768 | no | — |
| 776 | C23 | — | 4 | 384 | no | — |
| 777 | C23 | — | 4 | 384 | no | — |
| 778 | C23 | — | 4 | 768 | no | — |
| 779 | C23 | — | 4 | 384 | no | — |
| 780 | C23 | — | 4 | 768 | no | — |
| 781 | C23 | — | 4 | 4608 | no | — |
| 782 | C23 | — | 4 | 768 | no | — |
| 783 | C23 | — | 4 | 18432 | no | — |
| 784 | C23 | — | 4 | 9216 | no | — |
| 785 | C23 | — | 4 | 1536 | no | — |
| 786 | C23 | — | 4 | 3072 | no | — |
| 787 | C23 | — | 4 | 49152 | no | — |
| 788 | C23 | — | 4 | 24576 | no | — |
| 789 | C23 | — | 4 | 4608 | no | — |
| 790 | C23 | — | 4 | 9216 | no | — |
| 791 | C23 | — | 4 | 1536 | no | — |
| 792 | C23 | — | 4 | 768 | no | — |
| 793 | C23 | — | 4 | 49152 | no | — |
| 794 | C23 | — | 4 | 3072 | no | — |
| 795 | C23 | — | 4 | 512 | no | — |
| 796 | C23 | — | 4 | 384 | no | — |
| 797 | C23 | — | 4 | 576 | no | — |
| 798 | C23 | — | 4 | 768 | no | — |
| 799 | C23 | — | 4 | 512 | no | — |
| 800 | C23 | — | 8 | 4608 | no | — |
| 801 | C23 | — | 8 | 768 | no | — |
| 802 | C23 | — | 8 | 4096 | no | — |
| 803 | C23 | C22×#518 | 1 | 288 | yes | — |
| 804 | C23 | C22×#518 | 1 | 576 | yes | — |
| 805 | C23 | C22×#518 | 1 | 48 | yes | — |
| 806 | C23 | C22×#518 | 1 | 768 | yes | complemented |
| 807 | C23 | #62817 | 1 | 64 | yes | — |
| 808 | C23 | C26×C4 | 1 | 48 | yes | — |
| 809 | C23 | C26×C4 | 1 | 32 | yes | — |
| 810 | C23 | C26×C4 | 1 | 48 | yes | — |
| 811 | C23 | C26×C4 | 1 | 24 | yes | — |
| 812 | C23 | C26×C4 | 1 | 6 | yes | — |
| 813 | C23 | C23×H(5,𝔽2) | 1 | 48 | yes | — |
| 814 | C23 | C23×H(5,𝔽2) | 1 | 96 | yes | — |
| 815 | C23 | C23×H(5,𝔽2) | 1 | 36 | yes | — |
| 816 | C23 | C28 | 1 | 1 | yes | characteristic |
| 817 | D4 | — | 2 | 3072 | no | — |
| 818 | D4 | — | 4 | 1536 | no | — |
| 819 | C2×C4 | — | 2 | 768 | no | — |
| 820 | C2×C4 | — | 2 | 576 | no | — |
| 821 | C2×C4 | — | 2 | 96 | no | — |
| 822 | C2×C4 | — | 2 | 384 | no | — |
| 823 | C2×C4 | — | 4 | 768 | no | — |
| 824 | C2×C4 | — | 4 | 768 | no | — |
| 825 | C2×C4 | — | 8 | 1536 | no | — |
| 826 | C2×C4 | — | 16 | 256 | no | — |
| 827 | C2×C4 | C26×C4 | 1 | 96 | yes | — |
| 828 | C22 | — | 2 | 1024 | no | — |
| 829 | C22 | — | 2 | 512 | no | — |
| 830 | C22 | — | 2 | 48 | no | — |
| 831 | C22 | — | 2 | 96 | no | — |
| 832 | C22 | — | 2 | 576 | no | — |
| 833 | C22 | — | 2 | 1152 | no | — |
| 834 | C22 | — | 2 | 192 | no | — |
| 835 | C22 | — | 2 | 96 | no | — |
| 836 | C22 | — | 2 | 96 | no | — |
| 837 | C22 | — | 2 | 48 | no | — |
| 838 | C22 | — | 2 | 96 | no | — |
| 839 | C22 | — | 4 | 768 | no | — |
| 840 | C22 | — | 4 | 3072 | no | — |
| 841 | C22 | — | 4 | 1536 | no | — |
| 842 | C22 | — | 4 | 768 | no | — |
| 843 | C22 | — | 4 | 1536 | no | — |
| 844 | C22 | — | 4 | 512 | no | — |
| 845 | C22 | — | 4 | 576 | no | — |
| 846 | C22 | — | 4 | 384 | no | — |
| 847 | C22 | — | 4 | 64 | no | — |
| 848 | C22 | — | 4 | 96 | no | — |
| 849 | C22 | — | 8 | 768 | no | — |
| 850 | C22 | #7626202 | 1 | 64 | yes | direct product factor |
| 851 | C22 | C23×#518 | 1 | 48 | yes | — |
| 852 | C22 | C23×#518 | 1 | 96 | yes | — |
| 853 | C22 | C23×#518 | 1 | 36 | yes | — |
| 854 | C22 | C2×#62817 | 1 | 48 | yes | — |
| 855 | C22 | C27×C4 | 1 | 1 | yes | characteristic |
| 856 | C22 | C24×H(5,𝔽2) | 1 | 6 | yes | — |
| 857 | C4 | — | 2 | 96 | no | — |
| 858 | C4 | — | 4 | 128 | no | — |
| 859 | C2 | — | 2 | 48 | no | — |
| 860 | C2 | — | 2 | 96 | no | — |
| 861 | C2 | — | 4 | 48 | no | — |
| 862 | C2 | — | 4 | 32 | no | — |
| 863 | C2 | C22×#62817 | 1 | 4 | yes | — |
| 864 | C2 | C2×#7626202 | 1 | 24 | yes | direct product factor |
| 865 | C2 | C24×#518 | 1 | 3 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C25 | C26 |
| commutator | C22 | C27×C4 |
| Frattini, cosocle | C23 | C28 |
| prime radical | C25×#120 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C25 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#34176 | C2 | semidirect |
| 2. C22×#34356 | C2 | semidirect |
| 3. C22×#34198 | C2 | semidirect |
| 4. C22×#34171 | C2 | semidirect |
| 5. C2×#7626202 | C2 | direct (N × H) |
| 6. C24×#379 | C2 | semidirect |
| 10. C24×#120 | C4 | semidirect |
| 14. C23×#518 | C22 | semidirect |
| 16. C25×C22⋊C4 | C22 | semidirect |
| 17. #7626202 | C22 | direct (N × H) |
| 18. C2×#34356 | C22 | semidirect |
| 19. C22×#2375 | C22 | semidirect |
| 20. C2×#34198 | C22 | semidirect |
| 21. C2×#34176 | C22 | semidirect |
| 22. C2×#34171 | C22 | semidirect |
| 23. C22×#2358 | C22 | semidirect |
| 24. C22×#2342 | C22 | semidirect |
| 25. C22×D4×C22⋊C4 | C22 | semidirect |
| 26. C22×#2321 | C22 | semidirect |
| 27. C22×#2309 | C22 | semidirect |
| 28. C22×#2312 | C22 | semidirect |
| 29. C22×#2315 | C22 | semidirect |
| 30. C22×#2308 | C22 | semidirect |
| 31. C22×#2308 | C22 | semidirect |
| 32. C22×C4×#120 | C22 | semidirect |
| 33. C22×#2280 | C22 | semidirect |
| 35. C23×#379 | C22 | semidirect |
| 36. C23×#379 | C22 | semidirect |
| 37. C23×#379 | C22 | semidirect |
| 38. C23×#379 | C22 | semidirect |
| 39. C22×#2273 | C22 | semidirect |
| 41. C28 | C2×C4 | semidirect |
| 48. C25×D4 | C2×C4 | semidirect |
| 54. C26×C4 | C23 | semidirect |
| 55. C23×#120 | C2×C4 | semidirect |
| 56. C23×#120 | C2×C4 | semidirect |
| 57. C23×#120 | C2×C4 | semidirect |
| 66. C22×#518 | C23 | semidirect |
| 67. C23×C4×D4 | C23 | semidirect |
| 68. C23×#117 | C23 | semidirect |
| 70. C24×C22⋊C4 | C2×C4 | semidirect |
| 77. C24×C22⋊C4 | C23 | semidirect |
| 78. C24×C22⋊C4 | C23 | semidirect |
| 79. C24×C22⋊C4 | C23 | semidirect |
| 80. C24×C22⋊C4 | C23 | semidirect |
| 81. #34356 | C23 | semidirect |
| 82. C2×#2375 | C23 | semidirect |
| 83. #34198 | C23 | semidirect |
| 84. #34176 | C23 | semidirect |
| 85. #34171 | C23 | semidirect |
| 86. C2×#2358 | C23 | semidirect |
| 87. C2×#2342 | C23 | semidirect |
| 88. C2×D4×C22⋊C4 | C23 | semidirect |
| 89. C2×#2321 | C23 | semidirect |
| 90. C2×#2315 | C23 | semidirect |
| 91. C2×#2312 | C23 | semidirect |
| 92. C2×#2309 | C23 | semidirect |
| 93. C2×#2308 | C23 | semidirect |
| 94. C2×#2308 | C23 | semidirect |
| 95. C2×C4×#120 | C23 | semidirect |
| 96. C22×#390 | C23 | semidirect |
| 97. C22×#388 | C23 | semidirect |
| 98. C22×#386 | C23 | semidirect |
| 99. C22×#386 | C23 | semidirect |
| 100. C22×#385 | C23 | semidirect |
| 101. C2×#2280 | C23 | semidirect |
| 102. C22×#381 | C23 | semidirect |
| 103. C22×#380 | C23 | semidirect |
| 108. C22×#379 | C23 | semidirect |
| 109. C22×#379 | C23 | semidirect |
| 110. C22×#379 | C23 | semidirect |
| 111. C22×#379 | C23 | semidirect |
| 112. C22×#379 | C23 | semidirect |
| 113. C22×#379 | C23 | semidirect |
| 114. C22×#379 | C23 | semidirect |
| 115. C22×#379 | C23 | semidirect |
| 116. C2×#2273 | C23 | semidirect |
| 117. C22×C4×C22⋊C4 | C23 | semidirect |
| 118. C22×C4×C22⋊C4 | C23 | semidirect |
| 132. C27 | C22×C4 | semidirect |
| 133. C27 | C22×C4 | semidirect |
| 154. C24×D4 | C22×C4 | semidirect |
| 155. C24×D4 | C22×C4 | semidirect |
| 156. C24×D4 | C22×C4 | semidirect |
| 165. C25×C4 | C22×C4 | semidirect |
| 170. C25×C4 | C24 | semidirect |
| 171. C25×C4 | C24 | semidirect |
| 173. C22×#120 | C22×C4 | semidirect |
| 174. C22×#120 | C22×C4 | semidirect |
| 175. C22×#120 | C22×C4 | semidirect |
| 176. C22×#120 | C22×C4 | semidirect |
| 177. C22×#120 | C22×C4 | semidirect |
| 178. C22×#120 | C22×C4 | semidirect |
| 186. C2×#518 | C24 | semidirect |
| 188. C22×C4×D4 | C24 | semidirect |
| 190. C22×#117 | C24 | semidirect |
| 191. C23×C4⋊C4 | C24 | semidirect |
| 199. C23×C22⋊C4 | C22×C4 | semidirect |
| 200. C23×C22⋊C4 | C22×C4 | semidirect |
| 201. C23×C22⋊C4 | C22×C4 | semidirect |
| 213. C23×C22⋊C4 | C24 | semidirect |
| 214. C23×C22⋊C4 | C24 | semidirect |
| 215. C23×C22⋊C4 | C24 | semidirect |
| 216. C23×C22⋊C4 | C24 | semidirect |
| 217. C23×C22⋊C4 | C24 | semidirect |
| 218. C23×C42 | C24 | semidirect |
| 219. #2375 | C24 | semidirect |
| 220. #2358 | C24 | semidirect |
| 221. #2342 | C24 | semidirect |
| 222. D4×C22⋊C4 | C24 | semidirect |
| 223. #2321 | C24 | semidirect |
| 224. #2315 | C24 | semidirect |
| 225. #2312 | C24 | semidirect |
| 226. #2309 | C24 | semidirect |
| 227. #2308 | C24 | semidirect |
| 228. #2308 | C24 | semidirect |
| 229. C4×#120 | C24 | semidirect |
| 230. C2×#390 | C24 | semidirect |
| 231. C2×#388 | C24 | semidirect |
| 232. C2×#386 | C24 | semidirect |
| 233. C2×#386 | C24 | semidirect |
| 234. C2×#385 | C24 | semidirect |
| 235. #2280 | C24 | semidirect |
| 236. C2×#381 | C24 | semidirect |
| 237. C2×#380 | C24 | semidirect |
| 242. C2×#379 | C24 | semidirect |
| 243. C2×#379 | C24 | semidirect |
| 244. C2×#379 | C24 | semidirect |
| 245. C2×#379 | C24 | semidirect |
| 246. C2×#379 | C24 | semidirect |
| 247. C2×#379 | C24 | semidirect |
| 248. C2×#379 | C24 | semidirect |
| 249. #2273 | C24 | semidirect |
| 250. C2×C4×C22⋊C4 | C24 | semidirect |
| 251. C2×C4×C22⋊C4 | C24 | semidirect |
| 252. C22×#95 | C24 | semidirect |
| 302. C26 | C23×C4 | semidirect |
| 303. C26 | C23×C4 | semidirect |
| 335. C23×D4 | C23×C4 | semidirect |
| 336. C23×D4 | C23×C4 | semidirect |
| 337. C23×D4 | C23×C4 | semidirect |
| 354. C24×C4 | C23×C4 | semidirect |
| 361. C24×C4 | C25 | semidirect |
| 362. C24×C4 | C25 | semidirect |
| 364. C2×#120 | C23×C4 | semidirect |
| 365. C2×#120 | C23×C4 | semidirect |
| 366. C2×#120 | C23×C4 | semidirect |
| 367. C2×#120 | C23×C4 | semidirect |
| 368. C2×#120 | C23×C4 | semidirect |
| 375. C2×C4×D4 | C25 | semidirect |
| 377. C2×#117 | C25 | semidirect |
| 379. C22×C4⋊C4 | C25 | semidirect |
| 393. C22×C22⋊C4 | C23×C4 | semidirect |
| 394. C22×C22⋊C4 | C23×C4 | semidirect |
| 395. C22×C22⋊C4 | C23×C4 | semidirect |
| 406. C22×C22⋊C4 | C25 | semidirect |
| 407. C22×C22⋊C4 | C25 | semidirect |
| 408. C22×C22⋊C4 | C25 | semidirect |
| 409. C22×C22⋊C4 | C25 | semidirect |
| 411. C22×C42 | C25 | semidirect |
| 412. #390 | C25 | semidirect |
| 413. #388 | C25 | semidirect |
| 414. #386 | C25 | semidirect |
| 415. #386 | C25 | semidirect |
| 416. #385 | C25 | semidirect |
| 417. #381 | C25 | semidirect |
| 418. #380 | C25 | semidirect |
| 422. #379 | C25 | semidirect |
| 423. #379 | C25 | semidirect |
| 424. #379 | C25 | semidirect |
| 425. #379 | C25 | semidirect |
| 426. C4×C22⋊C4 | C25 | semidirect |
| 427. C4×C22⋊C4 | C25 | semidirect |
| 428. C2×#95 | C25 | semidirect |
| 498. C25 | #518 | semidirect |
| 515. C25 | C24×C4 | semidirect |
| 547. C22×D4 | C24×C4 | semidirect |
| 548. C22×D4 | C24×C4 | semidirect |
| 569. C23×C4 | C24×C4 | semidirect |
| 575. C23×C4 | C26 | semidirect |
| 577. #120 | C24×C4 | semidirect |
| 578. #120 | C24×C4 | semidirect |
| 579. #120 | C24×C4 | semidirect |
| 583. C2×C4⋊C4 | C26 | semidirect |
| 596. C2×C22⋊C4 | C24×C4 | semidirect |
| 597. C2×C22⋊C4 | C24×C4 | semidirect |
| 603. C2×C22⋊C4 | C26 | semidirect |
| 605. C2×C42 | C26 | semidirect |
| 606. #95 | C26 | semidirect |
| 687. C24 | C2×#518 | semidirect |
| 806. C23 | C22×#518 | semidirect |
| 850. C22 | #7626202 | direct (N × H) |
| 864. C2 | C2×#7626202 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#34176 | 2 |
| C22×#34356 | 2 |
| C22×#34198 | 2 |
| C22×#34171 | 2 |
| C2×#7626202 | 2 |
| C24×#379 | 2 |
| C25×#120 | 2 |