Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1959 conjugacy classes of subgroups.
The subgroup lattice has 941 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #60664 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #60489 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#3081 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #60168 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #26504 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #26503 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #26501 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #26500 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #23601 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C2×#2063 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #23463 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #23462 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #21249 | C2 | 1 | 1 | yes | maximal, characteristic |
| 14 | #21235 | C2 | 1 | 1 | yes | maximal, characteristic |
| 15 | #21182 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #21164 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 17 | #20858 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 18 | #20856 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 19 | #20446 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 20 | C22×AGL(1,ℤ/8) | C22 | 1 | 1 | yes | characteristic |
| 21 | #3458 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#544 | C22 | 1 | 1 | yes | characteristic |
| 23 | #3428 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×#518 | C22 | 1 | 1 | yes | characteristic |
| 25 | #3166 | — | 2 | 2 | no | — |
| 26 | #3165 | — | 2 | 2 | no | — |
| 27 | #3164 | — | 2 | 2 | no | — |
| 28 | #3164 | C22 | 1 | 4 | yes | complemented |
| 29 | #3163 | — | 2 | 2 | no | — |
| 30 | #3163 | C22 | 1 | 4 | yes | complemented |
| 31 | #3084 | — | 2 | 1 | no | — |
| 32 | #3084 | — | 2 | 1 | no | — |
| 33 | #3083 | — | 2 | 1 | no | — |
| 34 | #3083 | — | 2 | 1 | no | — |
| 35 | #3082 | C22 | 1 | 2 | yes | complemented |
| 36 | #3082 | C22 | 1 | 2 | yes | complemented |
| 37 | #3081 | — | 2 | 2 | no | — |
| 38 | #3081 | — | 2 | 2 | no | — |
| 39 | #3081 | C22 | 1 | 4 | yes | — |
| 40 | #3081 | C22 | 1 | 4 | yes | — |
| 41 | #3081 | C22 | 1 | 2 | yes | complemented |
| 42 | #3081 | C22 | 1 | 2 | yes | complemented |
| 43 | #3076 | — | 2 | 2 | no | — |
| 44 | #3076 | — | 2 | 2 | no | — |
| 45 | C2×#478 | — | 2 | 1 | no | — |
| 46 | C2×#478 | — | 2 | 1 | no | — |
| 47 | C2×#476 | — | 2 | 1 | no | — |
| 48 | C2×#474 | — | 2 | 1 | no | — |
| 49 | #2949 | C22 | 1 | 4 | yes | — |
| 50 | #2948 | C22 | 1 | 4 | yes | — |
| 51 | #2946 | — | 2 | 2 | no | — |
| 52 | #2946 | — | 2 | 2 | no | — |
| 53 | C4×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 54 | C4×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 55 | C2×#430 | C22 | 1 | 1 | yes | characteristic |
| 56 | C22×#108 | C22 | 1 | 1 | yes | characteristic |
| 57 | #2911 | C22 | 1 | 1 | yes | characteristic |
| 58 | #2911 | C22 | 1 | 1 | yes | characteristic |
| 59 | #2911 | C22 | 1 | 1 | yes | characteristic |
| 60 | C2×#428 | C22 | 1 | 1 | yes | characteristic |
| 61 | C2×#428 | C22 | 1 | 1 | yes | characteristic |
| 62 | C2×#428 | C22 | 1 | 1 | yes | characteristic |
| 63 | C2×#427 | C22 | 1 | 1 | yes | characteristic |
| 64 | C2×#424 | C22 | 1 | 1 | yes | characteristic |
| 65 | C2×#424 | C22 | 1 | 1 | yes | characteristic |
| 66 | #2896 | C22 | 1 | 1 | yes | characteristic |
| 67 | #2896 | C22 | 1 | 1 | yes | characteristic |
| 68 | C2×#418 | C22 | 1 | 1 | yes | characteristic |
| 69 | C2×#418 | C22 | 1 | 1 | yes | characteristic |
| 70 | C2×#416 | C22 | 1 | 1 | yes | characteristic |
| 71 | C22×#102 | C22 | 1 | 1 | yes | characteristic |
| 72 | C2×#413 | C22 | 1 | 1 | yes | characteristic |
| 73 | C22×#100 | C22 | 1 | 1 | yes | characteristic |
| 74 | #2873 | C22 | 1 | 1 | yes | characteristic |
| 75 | #2873 | C22 | 1 | 1 | yes | characteristic |
| 76 | C2×#405 | C22 | 1 | 1 | yes | characteristic |
| 77 | #2311 | C22 | 1 | 1 | yes | characteristic |
| 78 | #2309 | C22 | 1 | 1 | yes | characteristic |
| 79 | #2064 | C22 | 1 | 2 | yes | complemented |
| 80 | #2064 | C22 | 1 | 2 | yes | complemented |
| 81 | #2063 | C22 | 1 | 4 | yes | — |
| 82 | #2063 | C22 | 1 | 4 | yes | — |
| 83 | #2063 | C22 | 1 | 2 | yes | complemented |
| 84 | #2063 | C22 | 1 | 2 | yes | complemented |
| 85 | #2028 | C22 | 1 | 4 | yes | complemented |
| 86 | #2027 | C22 | 1 | 4 | yes | — |
| 87 | #2027 | C22 | 1 | 4 | yes | — |
| 88 | #2027 | C22 | 1 | 4 | yes | complemented |
| 89 | #1978 | C22 | 1 | 4 | yes | — |
| 90 | #1977 | C22 | 1 | 4 | yes | — |
| 91 | #1973 | C22 | 1 | 2 | yes | — |
| 92 | #1972 | C22 | 1 | 2 | yes | — |
| 93 | #1970 | C22 | 1 | 2 | yes | — |
| 94 | #1968 | C22 | 1 | 2 | yes | — |
| 95 | #1952 | C22 | 1 | 4 | yes | complemented |
| 96 | #1951 | C22 | 1 | 4 | yes | complemented |
| 97 | #1946 | C22 | 1 | 4 | yes | complemented |
| 98 | #1945 | C22 | 1 | 4 | yes | complemented |
| 99 | #1857 | C22 | 1 | 4 | yes | complemented |
| 100 | #1856 | C22 | 1 | 4 | yes | — |
| 101 | #1856 | C22 | 1 | 4 | yes | — |
| 102 | #1856 | C22 | 1 | 4 | yes | complemented |
| 103 | #1773 | C22 | 1 | 4 | yes | complemented |
| 104 | #1772 | C22 | 1 | 4 | yes | complemented |
| 105 | #1742 | C22 | 1 | 1 | yes | characteristic |
| 106 | C2×#343 | C22 | 1 | 1 | yes | characteristic |
| 107 | #1733 | C22 | 1 | 1 | yes | characteristic |
| 108 | #1733 | C22 | 1 | 1 | yes | characteristic |
| 109 | #1733 | C22 | 1 | 1 | yes | characteristic |
| 110 | #1733 | C22 | 1 | 1 | yes | characteristic |
| 111 | C22×#41 | C23 | 1 | 1 | yes | characteristic |
| 112 | C23×D4 | C23 | 1 | 1 | yes | characteristic |
| 113 | C2×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 114 | C2×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 115 | C2×AGL(1,ℤ/8) | — | 2 | 4 | no | — |
| 116 | C2×AGL(1,ℤ/8) | Q8 | 1 | 8 | yes | complemented |
| 117 | C22×SD16 | C23 | 1 | 2 | yes | — |
| 118 | C22×D8 | C23 | 1 | 2 | yes | — |
| 119 | C22×M16 | C23 | 1 | 1 | yes | characteristic |
| 120 | C22×M16 | C23 | 1 | 1 | yes | characteristic |
| 121 | C22×M16 | C23 | 1 | 1 | yes | characteristic |
| 122 | C22×M16 | C23 | 1 | 1 | yes | characteristic |
| 123 | C22×M16 | C23 | 1 | 1 | yes | characteristic |
| 124 | C23×C8 | C23 | 1 | 1 | yes | characteristic |
| 125 | #544 | — | 2 | 2 | no | — |
| 126 | #544 | — | 2 | 2 | no | — |
| 127 | #544 | — | 2 | 1 | no | — |
| 128 | #544 | — | 2 | 1 | no | — |
| 129 | #544 | — | 2 | 1 | no | — |
| 130 | #544 | — | 2 | 1 | no | — |
| 131 | #544 | — | 4 | 1 | no | — |
| 132 | #544 | C23 | 1 | 4 | yes | — |
| 133 | #544 | C23 | 1 | 2 | yes | — |
| 134 | #544 | C23 | 1 | 2 | yes | — |
| 135 | #543 | — | 4 | 1 | no | — |
| 136 | #533 | — | 2 | 2 | no | — |
| 137 | #533 | — | 2 | 2 | no | — |
| 138 | #533 | — | 4 | 1 | no | — |
| 139 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 140 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 141 | C2×#125 | — | 2 | 1 | no | — |
| 142 | C2×#125 | — | 2 | 1 | no | — |
| 143 | C2×C22⋊Q8 | — | 4 | 1 | no | — |
| 144 | #520 | — | 2 | 1 | no | — |
| 145 | #520 | — | 2 | 1 | no | — |
| 146 | #520 | — | 2 | 1 | no | — |
| 147 | #520 | — | 2 | 1 | no | — |
| 148 | #519 | C23 | 1 | 2 | yes | — |
| 149 | #518 | — | 2 | 2 | no | — |
| 150 | #518 | — | 2 | 2 | no | — |
| 151 | #518 | — | 4 | 1 | no | — |
| 152 | #518 | — | 4 | 1 | no | — |
| 153 | #518 | C23 | 1 | 4 | yes | — |
| 154 | #518 | C23 | 1 | 2 | yes | — |
| 155 | C4×#41 | — | 2 | 2 | no | — |
| 156 | C4×#41 | — | 2 | 2 | no | — |
| 157 | C2×C4×D4 | — | 2 | 1 | no | — |
| 158 | C2×C4×D4 | — | 2 | 1 | no | — |
| 159 | C2×C4×D4 | — | 2 | 1 | no | — |
| 160 | C2×C4×D4 | — | 2 | 1 | no | — |
| 161 | C2×#117 | — | 4 | 1 | no | — |
| 162 | C2×#117 | C23 | 1 | 1 | yes | characteristic |
| 163 | C2×#117 | C23 | 1 | 1 | yes | characteristic |
| 164 | C2×#117 | C23 | 1 | 1 | yes | characteristic |
| 165 | C2×#117 | C23 | 1 | 1 | yes | characteristic |
| 166 | C2×#117 | C23 | 1 | 1 | yes | characteristic |
| 167 | C2×#117 | C23 | 1 | 1 | yes | characteristic |
| 168 | C22×C4⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 169 | C22×C22⋊C4 | — | 4 | 1 | no | — |
| 170 | #501 | — | 2 | 4 | no | — |
| 171 | #501 | — | 2 | 4 | no | — |
| 172 | #501 | — | 2 | 4 | no | — |
| 173 | #501 | — | 2 | 4 | no | — |
| 174 | #500 | — | 2 | 4 | no | — |
| 175 | #499 | — | 2 | 4 | no | — |
| 176 | #499 | — | 2 | 4 | no | — |
| 177 | #498 | — | 2 | 4 | no | — |
| 178 | #479 | — | 2 | 2 | no | — |
| 179 | #479 | — | 2 | 2 | no | — |
| 180 | #479 | — | 2 | 2 | no | — |
| 181 | #479 | — | 2 | 2 | no | — |
| 182 | #478 | — | 2 | 4 | no | — |
| 183 | #478 | — | 2 | 4 | no | — |
| 184 | #478 | — | 2 | 2 | no | — |
| 185 | #478 | — | 2 | 2 | no | — |
| 186 | #478 | — | 2 | 4 | no | — |
| 187 | #478 | — | 2 | 4 | no | — |
| 188 | #478 | — | 2 | 2 | no | — |
| 189 | #478 | — | 2 | 2 | no | — |
| 190 | #477 | — | 2 | 2 | no | — |
| 191 | #477 | — | 2 | 2 | no | — |
| 192 | #476 | — | 2 | 2 | no | — |
| 193 | #476 | — | 2 | 2 | no | — |
| 194 | #476 | — | 2 | 4 | no | — |
| 195 | #476 | — | 2 | 4 | no | — |
| 196 | #475 | — | 2 | 2 | no | — |
| 197 | #475 | — | 2 | 2 | no | — |
| 198 | #474 | — | 2 | 2 | no | — |
| 199 | #474 | — | 2 | 2 | no | — |
| 200 | #474 | — | 2 | 4 | no | — |
| 201 | #474 | — | 2 | 4 | no | — |
| 202 | #442 | — | 2 | 4 | no | — |
| 203 | #442 | — | 2 | 4 | no | — |
| 204 | #440 | — | 2 | 4 | no | — |
| 205 | #440 | — | 2 | 4 | no | — |
| 206 | C4×SD16 | — | 2 | 4 | no | — |
| 207 | C4×SD16 | — | 2 | 4 | no | — |
| 208 | C4×D8 | — | 2 | 4 | no | — |
| 209 | C4×D8 | — | 2 | 4 | no | — |
| 210 | #430 | — | 2 | 4 | no | — |
| 211 | C2×#108 | — | 2 | 4 | no | — |
| 212 | C2×#108 | C23 | 1 | 2 | yes | — |
| 213 | C2×#108 | C23 | 1 | 2 | yes | — |
| 214 | C2×#108 | C23 | 1 | 4 | yes | — |
| 215 | #428 | — | 2 | 2 | no | — |
| 216 | #428 | — | 2 | 2 | no | — |
| 217 | #428 | — | 2 | 2 | no | — |
| 218 | #428 | — | 2 | 2 | no | — |
| 219 | #428 | — | 2 | 1 | no | — |
| 220 | #428 | — | 2 | 1 | no | — |
| 221 | #428 | — | 2 | 1 | no | — |
| 222 | #428 | — | 2 | 1 | no | — |
| 223 | #428 | D4 | 1 | 2 | yes | — |
| 224 | #428 | D4 | 1 | 2 | yes | — |
| 225 | #428 | D4 | 1 | 2 | yes | — |
| 226 | #428 | D4 | 1 | 2 | yes | — |
| 227 | #428 | C23 | 1 | 4 | yes | — |
| 228 | #428 | C23 | 1 | 2 | yes | — |
| 229 | #428 | C23 | 1 | 2 | yes | — |
| 230 | #428 | C23 | 1 | 4 | yes | — |
| 231 | #428 | C23 | 1 | 2 | yes | — |
| 232 | #428 | C23 | 1 | 2 | yes | — |
| 233 | #427 | — | 2 | 2 | no | — |
| 234 | #427 | — | 2 | 2 | no | — |
| 235 | #427 | D4 | 1 | 2 | yes | — |
| 236 | #427 | D4 | 1 | 2 | yes | — |
| 237 | #427 | C23 | 1 | 2 | yes | — |
| 238 | #427 | C23 | 1 | 2 | yes | — |
| 239 | #427 | C23 | 1 | 4 | yes | — |
| 240 | C2×#107 | — | 2 | 1 | no | — |
| 241 | C2×#107 | — | 2 | 1 | no | — |
| 242 | C2×#107 | D4 | 1 | 1 | yes | characteristic |
| 243 | C2×#107 | D4 | 1 | 1 | yes | characteristic |
| 244 | C2×#107 | C23 | 1 | 2 | yes | — |
| 245 | C2×#106 | — | 2 | 1 | no | — |
| 246 | C2×#106 | — | 2 | 1 | no | — |
| 247 | C2×#106 | D4 | 1 | 1 | yes | characteristic |
| 248 | C2×#106 | D4 | 1 | 1 | yes | characteristic |
| 249 | C2×#106 | C23 | 1 | 2 | yes | — |
| 250 | #424 | — | 2 | 1 | no | — |
| 251 | #424 | — | 2 | 1 | no | — |
| 252 | #424 | — | 2 | 1 | no | — |
| 253 | #424 | — | 2 | 1 | no | — |
| 254 | #424 | C23 | 1 | 2 | yes | — |
| 255 | #424 | C23 | 1 | 2 | yes | — |
| 256 | #424 | C23 | 1 | 2 | yes | — |
| 257 | #424 | C23 | 1 | 2 | yes | — |
| 258 | C2×C4⋊C8 | — | 2 | 1 | no | — |
| 259 | C2×C4⋊C8 | — | 2 | 1 | no | — |
| 260 | C2×C4⋊C8 | — | 2 | 1 | no | — |
| 261 | C2×C4⋊C8 | — | 2 | 1 | no | — |
| 262 | #419 | C23 | 1 | 2 | yes | — |
| 263 | #419 | C23 | 1 | 2 | yes | — |
| 264 | #418 | — | 2 | 2 | no | — |
| 265 | #418 | — | 2 | 2 | no | — |
| 266 | #418 | C23 | 1 | 4 | yes | — |
| 267 | #418 | C23 | 1 | 2 | yes | — |
| 268 | #418 | C23 | 1 | 4 | yes | — |
| 269 | #418 | C23 | 1 | 2 | yes | — |
| 270 | #417 | — | 2 | 1 | no | — |
| 271 | #417 | — | 2 | 1 | no | — |
| 272 | #417 | — | 2 | 1 | no | — |
| 273 | #417 | — | 2 | 1 | no | — |
| 274 | #416 | — | 2 | 1 | no | — |
| 275 | #416 | — | 2 | 1 | no | — |
| 276 | #416 | — | 2 | 1 | no | — |
| 277 | #416 | — | 2 | 1 | no | — |
| 278 | #416 | — | 2 | 2 | no | — |
| 279 | #416 | — | 2 | 2 | no | — |
| 280 | C2×#103 | C23 | 1 | 1 | yes | characteristic |
| 281 | C2×#103 | C23 | 1 | 1 | yes | characteristic |
| 282 | C2×#102 | — | 2 | 1 | no | — |
| 283 | C2×#102 | — | 2 | 1 | no | — |
| 284 | C2×#102 | — | 2 | 1 | no | — |
| 285 | C2×#102 | — | 2 | 1 | no | — |
| 286 | C2×#102 | — | 2 | 1 | no | — |
| 287 | C2×#102 | — | 2 | 1 | no | — |
| 288 | C2×#102 | — | 2 | 1 | no | — |
| 289 | C2×#102 | — | 2 | 1 | no | — |
| 290 | C2×#102 | C23 | 1 | 2 | yes | — |
| 291 | C2×#102 | C23 | 1 | 2 | yes | — |
| 292 | C2×#102 | C23 | 1 | 1 | yes | characteristic |
| 293 | C2×#102 | C23 | 1 | 1 | yes | characteristic |
| 294 | #413 | — | 2 | 4 | no | — |
| 295 | C2×#101 | C23 | 1 | 2 | yes | — |
| 296 | C2×#100 | — | 2 | 4 | no | — |
| 297 | C2×#100 | C23 | 1 | 4 | yes | — |
| 298 | C2×#100 | C23 | 1 | 2 | yes | — |
| 299 | #405 | — | 2 | 2 | no | — |
| 300 | #405 | — | 2 | 2 | no | — |
| 301 | #405 | — | 2 | 4 | no | — |
| 302 | #405 | C23 | 1 | 4 | yes | — |
| 303 | #405 | C23 | 1 | 4 | yes | — |
| 304 | C4×M16 | — | 2 | 2 | no | — |
| 305 | C4×M16 | — | 2 | 2 | no | — |
| 306 | C2×#97 | C23 | 1 | 2 | yes | — |
| 307 | C2×C4×C8 | C23 | 1 | 2 | yes | — |
| 308 | #391 | C23 | 1 | 2 | yes | — |
| 309 | #390 | — | 4 | 1 | no | — |
| 310 | #390 | C23 | 1 | 2 | yes | — |
| 311 | #390 | C23 | 1 | 2 | yes | — |
| 312 | #390 | C23 | 1 | 2 | yes | — |
| 313 | #386 | — | 4 | 1 | no | — |
| 314 | #380 | — | 4 | 1 | no | — |
| 315 | #379 | — | 4 | 1 | no | — |
| 316 | #343 | C23 | 1 | 4 | yes | — |
| 317 | #343 | C23 | 1 | 2 | yes | — |
| 318 | #343 | C23 | 1 | 2 | yes | — |
| 319 | #339 | C23 | 1 | 4 | yes | — |
| 320 | #339 | C23 | 1 | 4 | yes | — |
| 321 | #339 | C23 | 1 | 4 | yes | — |
| 322 | #339 | C23 | 1 | 4 | yes | — |
| 323 | C25 | — | 2 | 1 | no | — |
| 324 | C2×#41 | — | 2 | 2 | no | — |
| 325 | C2×#41 | — | 2 | 1 | no | — |
| 326 | C2×#41 | — | 2 | 1 | no | — |
| 327 | C2×#41 | — | 2 | 1 | no | — |
| 328 | C2×#41 | — | 2 | 1 | no | — |
| 329 | C2×#41 | — | 2 | 2 | no | — |
| 330 | C2×#41 | — | 2 | 2 | no | — |
| 331 | C2×#41 | C2×Q8 | 1 | 4 | yes | — |
| 332 | C22×Q8 | — | 4 | 1 | no | — |
| 333 | C22×Q8 | C24 | 1 | 1 | yes | characteristic |
| 334 | C22×D4 | — | 2 | 1 | no | — |
| 335 | C22×D4 | — | 2 | 1 | no | — |
| 336 | C22×D4 | — | 2 | 1 | no | — |
| 337 | C22×D4 | — | 2 | 1 | no | — |
| 338 | C22×D4 | — | 2 | 1 | no | — |
| 339 | C22×D4 | — | 2 | 2 | no | — |
| 340 | C22×D4 | — | 2 | 2 | no | — |
| 341 | C22×D4 | — | 2 | 1 | no | — |
| 342 | C22×D4 | — | 2 | 2 | no | — |
| 343 | C22×D4 | C2×Q8 | 1 | 4 | yes | — |
| 344 | C22×D4 | C24 | 1 | 1 | yes | characteristic |
| 345 | C22×D4 | C24 | 1 | 2 | yes | — |
| 346 | C23×C4 | — | 2 | 1 | no | — |
| 347 | C23×C4 | — | 2 | 1 | no | — |
| 348 | C23×C4 | — | 4 | 1 | no | — |
| 349 | C23×C4 | — | 4 | 1 | no | — |
| 350 | C23×C4 | C24 | 1 | 1 | yes | characteristic |
| 351 | AGL(1,ℤ/8) | — | 2 | 16 | no | — |
| 352 | AGL(1,ℤ/8) | — | 2 | 16 | no | — |
| 353 | C2×SD16 | — | 2 | 4 | no | — |
| 354 | C2×SD16 | — | 2 | 4 | no | — |
| 355 | C2×SD16 | C2×Q8 | 1 | 8 | yes | complemented |
| 356 | C2×D8 | — | 2 | 4 | no | — |
| 357 | C2×D8 | — | 2 | 4 | no | — |
| 358 | C2×D8 | C2×Q8 | 1 | 8 | yes | complemented |
| 359 | C2×M16 | — | 2 | 1 | no | — |
| 360 | C2×M16 | — | 2 | 2 | no | — |
| 361 | C2×M16 | — | 2 | 1 | no | — |
| 362 | C2×M16 | — | 2 | 1 | no | — |
| 363 | C2×M16 | — | 2 | 1 | no | — |
| 364 | C2×M16 | — | 2 | 2 | no | — |
| 365 | C2×M16 | — | 2 | 2 | no | — |
| 366 | C2×M16 | — | 2 | 2 | no | — |
| 367 | C2×M16 | — | 2 | 2 | no | — |
| 368 | C2×M16 | — | 2 | 2 | no | — |
| 369 | C2×M16 | — | 2 | 2 | no | — |
| 370 | C2×M16 | C2×D4 | 1 | 2 | yes | — |
| 371 | C2×M16 | C2×D4 | 1 | 2 | yes | — |
| 372 | C2×M16 | C2×Q8 | 1 | 4 | yes | — |
| 373 | C2×M16 | #41 | 1 | 4 | yes | — |
| 374 | C2×M16 | #41 | 1 | 4 | yes | — |
| 375 | C2×M16 | C24 | 1 | 2 | yes | — |
| 376 | C2×M16 | C24 | 1 | 2 | yes | — |
| 377 | C2×M16 | C24 | 1 | 2 | yes | — |
| 378 | C2×M16 | C24 | 1 | 2 | yes | — |
| 379 | C22×C8 | — | 2 | 1 | no | — |
| 380 | C22×C8 | — | 2 | 2 | no | — |
| 381 | C22×C8 | — | 2 | 2 | no | — |
| 382 | C22×C8 | — | 2 | 1 | no | — |
| 383 | C22×C8 | — | 2 | 1 | no | — |
| 384 | C22×C8 | — | 2 | 1 | no | — |
| 385 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 386 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 387 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 388 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 389 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 390 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 391 | C22×C8 | C24 | 1 | 2 | yes | — |
| 392 | C4⋊Q8 | — | 2 | 4 | no | — |
| 393 | C4⋊Q8 | — | 2 | 4 | no | — |
| 394 | C4⋊Q8 | — | 2 | 2 | no | — |
| 395 | C4⋊Q8 | — | 2 | 2 | no | — |
| 396 | C4⋊Q8 | — | 2 | 2 | no | — |
| 397 | C4⋊Q8 | — | 2 | 2 | no | — |
| 398 | C4⋊Q8 | — | 4 | 2 | no | — |
| 399 | C4⋊Q8 | — | 4 | 2 | no | — |
| 400 | C4⋊Q8 | — | 4 | 1 | no | — |
| 401 | C4⋊Q8 | — | 4 | 1 | no | — |
| 402 | #125 | — | 2 | 4 | no | — |
| 403 | #125 | — | 2 | 4 | no | — |
| 404 | #125 | — | 2 | 2 | no | — |
| 405 | #125 | — | 2 | 2 | no | — |
| 406 | #125 | — | 2 | 2 | no | — |
| 407 | #125 | — | 2 | 2 | no | — |
| 408 | #125 | — | 4 | 2 | no | — |
| 409 | #125 | — | 4 | 2 | no | — |
| 410 | #125 | — | 4 | 1 | no | — |
| 411 | #125 | — | 4 | 1 | no | — |
| 412 | C22⋊Q8 | — | 4 | 4 | no | — |
| 413 | C22⋊Q8 | — | 4 | 2 | no | — |
| 414 | C22⋊Q8 | — | 4 | 2 | no | — |
| 415 | C22⋊Q8 | — | 4 | 4 | no | — |
| 416 | C22⋊Q8 | — | 4 | 2 | no | — |
| 417 | C22⋊Q8 | — | 4 | 2 | no | — |
| 418 | C22⋊Q8 | — | 4 | 2 | no | — |
| 419 | C22⋊Q8 | — | 4 | 2 | no | — |
| 420 | C4×Q8 | — | 2 | 2 | no | — |
| 421 | C4×Q8 | — | 2 | 2 | no | — |
| 422 | C4×Q8 | — | 2 | 2 | no | — |
| 423 | C4×Q8 | — | 2 | 2 | no | — |
| 424 | C4×Q8 | — | 4 | 2 | no | — |
| 425 | C4×Q8 | — | 4 | 2 | no | — |
| 426 | C4×D4 | — | 2 | 4 | no | — |
| 427 | C4×D4 | — | 2 | 4 | no | — |
| 428 | C4×D4 | — | 2 | 4 | no | — |
| 429 | C4×D4 | — | 2 | 4 | no | — |
| 430 | C4×D4 | — | 2 | 2 | no | — |
| 431 | C4×D4 | — | 2 | 2 | no | — |
| 432 | C4×D4 | — | 2 | 2 | no | — |
| 433 | C4×D4 | — | 2 | 2 | no | — |
| 434 | C4×D4 | — | 4 | 2 | no | — |
| 435 | C4×D4 | — | 4 | 2 | no | — |
| 436 | C4×D4 | — | 4 | 2 | no | — |
| 437 | C4×D4 | — | 4 | 2 | no | — |
| 438 | C4×D4 | — | 4 | 2 | no | — |
| 439 | C4×D4 | — | 4 | 2 | no | — |
| 440 | C4×D4 | — | 4 | 2 | no | — |
| 441 | C4×D4 | — | 4 | 2 | no | — |
| 442 | #117 | — | 2 | 1 | no | — |
| 443 | #117 | — | 2 | 1 | no | — |
| 444 | #117 | — | 2 | 1 | no | — |
| 445 | #117 | — | 2 | 1 | no | — |
| 446 | #117 | — | 2 | 1 | no | — |
| 447 | #117 | — | 2 | 1 | no | — |
| 448 | #117 | — | 2 | 1 | no | — |
| 449 | #117 | — | 2 | 1 | no | — |
| 450 | #117 | — | 2 | 2 | no | — |
| 451 | #117 | — | 2 | 2 | no | — |
| 452 | #117 | — | 2 | 1 | no | — |
| 453 | #117 | — | 2 | 1 | no | — |
| 454 | #117 | — | 2 | 1 | no | — |
| 455 | #117 | — | 2 | 1 | no | — |
| 456 | #117 | — | 4 | 2 | no | — |
| 457 | #117 | — | 4 | 2 | no | — |
| 458 | #117 | — | 4 | 1 | no | — |
| 459 | #117 | — | 4 | 1 | no | — |
| 460 | #117 | C2×D4 | 1 | 2 | yes | — |
| 461 | #117 | C2×D4 | 1 | 2 | yes | — |
| 462 | #117 | C2×D4 | 1 | 2 | yes | — |
| 463 | #117 | C2×D4 | 1 | 2 | yes | — |
| 464 | #117 | C24 | 1 | 2 | yes | — |
| 465 | #117 | C24 | 1 | 2 | yes | — |
| 466 | #117 | C24 | 1 | 2 | yes | — |
| 467 | #117 | C24 | 1 | 2 | yes | — |
| 468 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 469 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 470 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 471 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 472 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 473 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 474 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 475 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 476 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 477 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 478 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 479 | C2×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 480 | C2×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 481 | C2×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 482 | C2×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 483 | C2×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 484 | C2×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 485 | C2×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 486 | C2×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 487 | C2×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 488 | C2×C4⋊C4 | C24 | 1 | 1 | yes | characteristic |
| 489 | C2×C4⋊C4 | C24 | 1 | 1 | yes | characteristic |
| 490 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 491 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 492 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 493 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 494 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 495 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 496 | C2×C22⋊C4 | — | 4 | 4 | no | — |
| 497 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 498 | C2×C22⋊C4 | — | 4 | 4 | no | — |
| 499 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 500 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 501 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 502 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 503 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 504 | C2×C42 | — | 2 | 1 | no | — |
| 505 | C2×C42 | — | 2 | 1 | no | — |
| 506 | C2×C42 | — | 2 | 1 | no | — |
| 507 | C2×C42 | — | 2 | 1 | no | — |
| 508 | C2×C42 | — | 2 | 1 | no | — |
| 509 | C2×C42 | — | 4 | 2 | no | — |
| 510 | C2×C42 | C24 | 1 | 2 | yes | — |
| 511 | #108 | — | 2 | 4 | no | — |
| 512 | #108 | — | 2 | 4 | no | — |
| 513 | #108 | — | 2 | 8 | no | — |
| 514 | #107 | — | 2 | 4 | no | — |
| 515 | #107 | — | 2 | 4 | no | — |
| 516 | #107 | — | 2 | 4 | no | — |
| 517 | #107 | — | 2 | 2 | no | — |
| 518 | #107 | — | 2 | 2 | no | — |
| 519 | #107 | — | 2 | 2 | no | — |
| 520 | #107 | — | 2 | 2 | no | — |
| 521 | #107 | C2×D4 | 1 | 2 | yes | — |
| 522 | #107 | C2×D4 | 1 | 2 | yes | — |
| 523 | #107 | C2×D4 | 1 | 2 | yes | — |
| 524 | #107 | C2×D4 | 1 | 2 | yes | — |
| 525 | #107 | C2×D4 | 1 | 4 | yes | — |
| 526 | #107 | C2×D4 | 1 | 4 | yes | — |
| 527 | #106 | — | 2 | 4 | no | — |
| 528 | #106 | — | 2 | 4 | no | — |
| 529 | #106 | — | 2 | 4 | no | — |
| 530 | #106 | — | 2 | 2 | no | — |
| 531 | #106 | — | 2 | 2 | no | — |
| 532 | #106 | — | 2 | 2 | no | — |
| 533 | #106 | — | 2 | 2 | no | — |
| 534 | #106 | C2×D4 | 1 | 2 | yes | — |
| 535 | #106 | C2×D4 | 1 | 2 | yes | — |
| 536 | #106 | C2×D4 | 1 | 2 | yes | — |
| 537 | #106 | C2×D4 | 1 | 2 | yes | — |
| 538 | #106 | C2×D4 | 1 | 4 | yes | — |
| 539 | #106 | C2×D4 | 1 | 4 | yes | — |
| 540 | C4⋊C8 | — | 2 | 2 | no | — |
| 541 | C4⋊C8 | — | 2 | 2 | no | — |
| 542 | C4⋊C8 | — | 2 | 2 | no | — |
| 543 | C4⋊C8 | — | 2 | 2 | no | — |
| 544 | C4⋊C8 | — | 2 | 2 | no | — |
| 545 | C4⋊C8 | — | 2 | 2 | no | — |
| 546 | C4⋊C8 | — | 2 | 2 | no | — |
| 547 | C4⋊C8 | — | 2 | 2 | no | — |
| 548 | #103 | — | 2 | 1 | no | — |
| 549 | #103 | — | 2 | 1 | no | — |
| 550 | #103 | — | 2 | 1 | no | — |
| 551 | #103 | — | 2 | 1 | no | — |
| 552 | #103 | — | 2 | 2 | no | — |
| 553 | #103 | — | 2 | 2 | no | — |
| 554 | #103 | — | 2 | 2 | no | — |
| 555 | #103 | — | 2 | 2 | no | — |
| 556 | #102 | — | 2 | 2 | no | — |
| 557 | #102 | — | 2 | 2 | no | — |
| 558 | #102 | — | 2 | 2 | no | — |
| 559 | #102 | — | 2 | 2 | no | — |
| 560 | #102 | — | 2 | 1 | no | — |
| 561 | #102 | — | 2 | 1 | no | — |
| 562 | #102 | — | 2 | 1 | no | — |
| 563 | #102 | — | 2 | 1 | no | — |
| 564 | #102 | — | 2 | 4 | no | — |
| 565 | #102 | — | 2 | 4 | no | — |
| 566 | #102 | — | 2 | 4 | no | — |
| 567 | #102 | — | 2 | 4 | no | — |
| 568 | #102 | — | 2 | 2 | no | — |
| 569 | #102 | — | 2 | 2 | no | — |
| 570 | #102 | — | 2 | 2 | no | — |
| 571 | #102 | — | 2 | 2 | no | — |
| 572 | #101 | — | 2 | 4 | no | — |
| 573 | #100 | — | 2 | 8 | no | — |
| 574 | #100 | — | 2 | 4 | no | — |
| 575 | #97 | — | 2 | 4 | no | — |
| 576 | #97 | — | 2 | 4 | no | — |
| 577 | #97 | — | 2 | 4 | no | — |
| 578 | C4×C8 | — | 2 | 4 | no | — |
| 579 | C4×C8 | — | 2 | 4 | no | — |
| 580 | C4×C8 | — | 2 | 4 | no | — |
| 581 | #95 | — | 4 | 2 | no | — |
| 582 | C24 | — | 2 | 1 | no | — |
| 583 | C24 | — | 2 | 2 | no | — |
| 584 | C24 | — | 2 | 4 | no | — |
| 585 | C24 | — | 4 | 1 | no | — |
| 586 | C24 | — | 4 | 2 | no | — |
| 587 | C24 | — | 4 | 1 | no | — |
| 588 | C24 | — | 16 | 1 | no | — |
| 589 | C24 | — | 16 | 1 | no | — |
| 590 | C24 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 591 | #41 | — | 2 | 4 | no | — |
| 592 | #41 | — | 2 | 4 | no | — |
| 593 | #41 | — | 2 | 4 | no | — |
| 594 | #41 | — | 2 | 4 | no | — |
| 595 | #41 | — | 4 | 2 | no | — |
| 596 | #41 | — | 4 | 2 | no | — |
| 597 | #41 | — | 4 | 2 | no | — |
| 598 | #41 | — | 4 | 2 | no | — |
| 599 | C2×Q8 | — | 2 | 1 | no | — |
| 600 | C2×Q8 | — | 2 | 1 | no | — |
| 601 | C2×Q8 | — | 2 | 1 | no | — |
| 602 | C2×Q8 | — | 2 | 1 | no | — |
| 603 | C2×Q8 | — | 2 | 1 | no | — |
| 604 | C2×Q8 | — | 4 | 2 | no | — |
| 605 | C2×Q8 | — | 4 | 2 | no | — |
| 606 | C2×Q8 | — | 4 | 4 | no | — |
| 607 | C2×Q8 | — | 16 | 2 | no | — |
| 608 | C2×Q8 | C22×Q8 | 1 | 2 | yes | — |
| 609 | C2×D4 | — | 2 | 4 | no | — |
| 610 | C2×D4 | — | 2 | 4 | no | — |
| 611 | C2×D4 | — | 2 | 4 | no | — |
| 612 | C2×D4 | — | 2 | 4 | no | — |
| 613 | C2×D4 | — | 2 | 4 | no | — |
| 614 | C2×D4 | — | 2 | 4 | no | — |
| 615 | C2×D4 | — | 2 | 2 | no | — |
| 616 | C2×D4 | — | 2 | 1 | no | — |
| 617 | C2×D4 | — | 2 | 1 | no | — |
| 618 | C2×D4 | — | 2 | 2 | no | — |
| 619 | C2×D4 | — | 2 | 1 | no | — |
| 620 | C2×D4 | — | 2 | 2 | no | — |
| 621 | C2×D4 | — | 2 | 2 | no | — |
| 622 | C2×D4 | — | 2 | 1 | no | — |
| 623 | C2×D4 | — | 2 | 2 | no | — |
| 624 | C2×D4 | — | 2 | 1 | no | — |
| 625 | C2×D4 | — | 4 | 2 | no | — |
| 626 | C2×D4 | — | 4 | 1 | no | — |
| 627 | C2×D4 | — | 4 | 1 | no | — |
| 628 | C2×D4 | — | 4 | 2 | no | — |
| 629 | C2×D4 | — | 4 | 2 | no | — |
| 630 | C2×D4 | — | 4 | 2 | no | — |
| 631 | C2×D4 | — | 4 | 1 | no | — |
| 632 | C2×D4 | — | 4 | 1 | no | — |
| 633 | C2×D4 | — | 4 | 2 | no | — |
| 634 | C2×D4 | — | 4 | 2 | no | — |
| 635 | C2×D4 | C22×Q8 | 1 | 2 | yes | — |
| 636 | C2×D4 | C22×Q8 | 1 | 4 | yes | — |
| 637 | C22×C4 | — | 2 | 1 | no | — |
| 638 | C22×C4 | — | 2 | 1 | no | — |
| 639 | C22×C4 | — | 2 | 1 | no | — |
| 640 | C22×C4 | — | 2 | 1 | no | — |
| 641 | C22×C4 | — | 2 | 1 | no | — |
| 642 | C22×C4 | — | 2 | 1 | no | — |
| 643 | C22×C4 | — | 2 | 1 | no | — |
| 644 | C22×C4 | — | 2 | 1 | no | — |
| 645 | C22×C4 | — | 2 | 1 | no | — |
| 646 | C22×C4 | — | 2 | 4 | no | — |
| 647 | C22×C4 | — | 2 | 2 | no | — |
| 648 | C22×C4 | — | 2 | 2 | no | — |
| 649 | C22×C4 | — | 2 | 1 | no | — |
| 650 | C22×C4 | — | 2 | 1 | no | — |
| 651 | C22×C4 | — | 4 | 2 | no | — |
| 652 | C22×C4 | — | 4 | 2 | no | — |
| 653 | C22×C4 | — | 4 | 4 | no | — |
| 654 | C22×C4 | — | 4 | 4 | no | — |
| 655 | C22×C4 | — | 4 | 2 | no | — |
| 656 | C22×C4 | — | 4 | 1 | no | — |
| 657 | C22×C4 | — | 4 | 1 | no | — |
| 658 | C22×C4 | — | 4 | 1 | no | — |
| 659 | C22×C4 | — | 4 | 1 | no | — |
| 660 | C22×C4 | — | 16 | 2 | no | — |
| 661 | C22×C4 | — | 16 | 2 | no | — |
| 662 | C22×C4 | — | 16 | 1 | no | — |
| 663 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 664 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 665 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 666 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 667 | C22×C4 | C22×Q8 | 1 | 2 | yes | — |
| 668 | C22×C4 | C2×#41 | 1 | 2 | yes | — |
| 669 | C22×C4 | C2×#41 | 1 | 2 | yes | — |
| 670 | C22×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 671 | C22×C4 | 2−1+4 | 1 | 2 | yes | — |
| 672 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 673 | SD16 | — | 2 | 16 | no | — |
| 674 | D8 | — | 2 | 16 | no | — |
| 675 | M16 | — | 2 | 4 | no | — |
| 676 | M16 | — | 2 | 2 | no | — |
| 677 | M16 | — | 2 | 2 | no | — |
| 678 | M16 | — | 2 | 2 | no | — |
| 679 | M16 | — | 2 | 2 | no | — |
| 680 | M16 | — | 2 | 2 | no | — |
| 681 | M16 | — | 2 | 2 | no | — |
| 682 | M16 | — | 2 | 2 | no | — |
| 683 | M16 | — | 4 | 2 | no | — |
| 684 | M16 | — | 4 | 2 | no | — |
| 685 | M16 | — | 4 | 2 | no | — |
| 686 | M16 | C22⋊Q8 | 1 | 8 | yes | — |
| 687 | M16 | C22⋊Q8 | 1 | 8 | yes | — |
| 688 | M16 | C2×#41 | 1 | 4 | yes | — |
| 689 | C2×C8 | — | 2 | 2 | no | — |
| 690 | C2×C8 | — | 2 | 2 | no | — |
| 691 | C2×C8 | — | 2 | 2 | no | — |
| 692 | C2×C8 | — | 2 | 2 | no | — |
| 693 | C2×C8 | — | 2 | 4 | no | — |
| 694 | C2×C8 | — | 2 | 2 | no | — |
| 695 | C2×C8 | — | 2 | 1 | no | — |
| 696 | C2×C8 | — | 2 | 1 | no | — |
| 697 | C2×C8 | — | 2 | 1 | no | — |
| 698 | C2×C8 | — | 2 | 1 | no | — |
| 699 | C2×C8 | — | 2 | 2 | no | — |
| 700 | C2×C8 | — | 2 | 2 | no | — |
| 701 | C2×C8 | — | 2 | 2 | no | — |
| 702 | C2×C8 | — | 4 | 2 | no | — |
| 703 | C2×C8 | — | 4 | 2 | no | — |
| 704 | C2×C8 | — | 4 | 2 | no | — |
| 705 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 706 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 707 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 708 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 709 | C2×C8 | C22×D4 | 1 | 4 | yes | — |
| 710 | C2×C8 | C22×Q8 | 1 | 4 | yes | — |
| 711 | C2×C8 | C2×#41 | 1 | 4 | yes | — |
| 712 | C4⋊C4 | — | 2 | 1 | no | — |
| 713 | C4⋊C4 | — | 2 | 1 | no | — |
| 714 | C4⋊C4 | — | 2 | 1 | no | — |
| 715 | C4⋊C4 | — | 2 | 1 | no | — |
| 716 | C4⋊C4 | — | 2 | 1 | no | — |
| 717 | C4⋊C4 | — | 2 | 1 | no | — |
| 718 | C4⋊C4 | — | 2 | 1 | no | — |
| 719 | C4⋊C4 | — | 2 | 1 | no | — |
| 720 | C4⋊C4 | — | 2 | 2 | no | — |
| 721 | C4⋊C4 | — | 2 | 1 | no | — |
| 722 | C4⋊C4 | — | 2 | 1 | no | — |
| 723 | C4⋊C4 | — | 2 | 1 | no | — |
| 724 | C4⋊C4 | — | 2 | 2 | no | — |
| 725 | C4⋊C4 | — | 2 | 1 | no | — |
| 726 | C4⋊C4 | — | 4 | 2 | no | — |
| 727 | C4⋊C4 | — | 4 | 2 | no | — |
| 728 | C4⋊C4 | — | 4 | 4 | no | — |
| 729 | C4⋊C4 | — | 4 | 4 | no | — |
| 730 | C4⋊C4 | — | 4 | 4 | no | — |
| 731 | C4⋊C4 | — | 4 | 2 | no | — |
| 732 | C4⋊C4 | — | 4 | 2 | no | — |
| 733 | C4⋊C4 | — | 4 | 2 | no | — |
| 734 | C4⋊C4 | — | 4 | 2 | no | — |
| 735 | C4⋊C4 | — | 4 | 2 | no | — |
| 736 | C4⋊C4 | — | 4 | 2 | no | — |
| 737 | C4⋊C4 | — | 4 | 2 | no | — |
| 738 | C4⋊C4 | — | 4 | 1 | no | — |
| 739 | C4⋊C4 | — | 4 | 1 | no | — |
| 740 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 741 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 742 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 743 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 744 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 745 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 746 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 747 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 748 | C22⋊C4 | — | 2 | 2 | no | — |
| 749 | C22⋊C4 | — | 2 | 2 | no | — |
| 750 | C22⋊C4 | — | 2 | 2 | no | — |
| 751 | C22⋊C4 | — | 2 | 2 | no | — |
| 752 | C22⋊C4 | — | 2 | 2 | no | — |
| 753 | C22⋊C4 | — | 2 | 2 | no | — |
| 754 | C22⋊C4 | — | 2 | 2 | no | — |
| 755 | C22⋊C4 | — | 2 | 2 | no | — |
| 756 | C22⋊C4 | — | 4 | 4 | no | — |
| 757 | C22⋊C4 | — | 4 | 4 | no | — |
| 758 | C22⋊C4 | — | 4 | 2 | no | — |
| 759 | C22⋊C4 | — | 4 | 2 | no | — |
| 760 | C22⋊C4 | — | 4 | 2 | no | — |
| 761 | C22⋊C4 | — | 4 | 1 | no | — |
| 762 | C22⋊C4 | — | 4 | 1 | no | — |
| 763 | C22⋊C4 | — | 16 | 2 | no | — |
| 764 | C22⋊C4 | — | 16 | 2 | no | — |
| 765 | C22⋊C4 | — | 16 | 2 | no | — |
| 766 | C42 | — | 2 | 2 | no | — |
| 767 | C42 | — | 2 | 2 | no | — |
| 768 | C42 | — | 2 | 2 | no | — |
| 769 | C42 | — | 2 | 2 | no | — |
| 770 | C42 | — | 2 | 2 | no | — |
| 771 | C42 | — | 2 | 2 | no | — |
| 772 | C42 | — | 2 | 2 | no | — |
| 773 | C42 | — | 2 | 2 | no | — |
| 774 | C42 | — | 2 | 2 | no | — |
| 775 | C42 | — | 2 | 2 | no | — |
| 776 | C42 | — | 4 | 2 | no | — |
| 777 | C42 | — | 4 | 2 | no | — |
| 778 | C42 | — | 4 | 1 | no | — |
| 779 | C42 | — | 4 | 1 | no | — |
| 780 | C23 | — | 2 | 2 | no | — |
| 781 | C23 | — | 2 | 4 | no | — |
| 782 | C23 | — | 4 | 1 | no | — |
| 783 | C23 | — | 4 | 1 | no | — |
| 784 | C23 | — | 4 | 1 | no | — |
| 785 | C23 | — | 4 | 2 | no | — |
| 786 | C23 | — | 4 | 4 | no | — |
| 787 | C23 | — | 4 | 1 | no | — |
| 788 | C23 | — | 4 | 2 | no | — |
| 789 | C23 | — | 4 | 4 | no | — |
| 790 | C23 | — | 8 | 2 | no | — |
| 791 | C23 | — | 8 | 2 | no | — |
| 792 | C23 | — | 8 | 1 | no | — |
| 793 | C23 | — | 8 | 2 | no | — |
| 794 | C23 | — | 8 | 2 | no | — |
| 795 | C23 | — | 8 | 1 | no | — |
| 796 | C23 | — | 16 | 1 | no | — |
| 797 | C23 | — | 16 | 1 | no | — |
| 798 | C23 | — | 16 | 4 | no | — |
| 799 | C23 | — | 16 | 4 | no | — |
| 800 | C23 | #542 | 1 | 2 | yes | — |
| 801 | C23 | D42 | 1 | 1 | yes | characteristic |
| 802 | C23 | D42 | 1 | 1 | yes | characteristic |
| 803 | C23 | #554 | 1 | 2 | yes | — |
| 804 | C23 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 805 | Q8 | — | 2 | 2 | no | — |
| 806 | Q8 | — | 2 | 2 | no | — |
| 807 | Q8 | — | 4 | 1 | no | — |
| 808 | Q8 | — | 4 | 1 | no | — |
| 809 | Q8 | — | 16 | 2 | no | — |
| 810 | Q8 | — | 16 | 2 | no | — |
| 811 | Q8 | — | 16 | 4 | no | — |
| 812 | D4 | — | 2 | 2 | no | — |
| 813 | D4 | — | 2 | 4 | no | — |
| 814 | D4 | — | 2 | 4 | no | — |
| 815 | D4 | — | 2 | 2 | no | — |
| 816 | D4 | — | 4 | 4 | no | — |
| 817 | D4 | — | 4 | 4 | no | — |
| 818 | D4 | — | 4 | 2 | no | — |
| 819 | D4 | — | 4 | 1 | no | — |
| 820 | D4 | — | 4 | 2 | no | — |
| 821 | D4 | — | 4 | 1 | no | — |
| 822 | D4 | — | 4 | 4 | no | — |
| 823 | D4 | — | 4 | 4 | no | — |
| 824 | C2×C4 | — | 2 | 2 | no | — |
| 825 | C2×C4 | — | 2 | 2 | no | — |
| 826 | C2×C4 | — | 2 | 2 | no | — |
| 827 | C2×C4 | — | 2 | 2 | no | — |
| 828 | C2×C4 | — | 2 | 2 | no | — |
| 829 | C2×C4 | — | 2 | 2 | no | — |
| 830 | C2×C4 | — | 2 | 2 | no | — |
| 831 | C2×C4 | — | 2 | 2 | no | — |
| 832 | C2×C4 | — | 2 | 2 | no | — |
| 833 | C2×C4 | — | 4 | 2 | no | — |
| 834 | C2×C4 | — | 4 | 2 | no | — |
| 835 | C2×C4 | — | 4 | 1 | no | — |
| 836 | C2×C4 | — | 4 | 1 | no | — |
| 837 | C2×C4 | — | 4 | 4 | no | — |
| 838 | C2×C4 | — | 4 | 4 | no | — |
| 839 | C2×C4 | — | 4 | 2 | no | — |
| 840 | C2×C4 | — | 4 | 2 | no | — |
| 841 | C2×C4 | — | 4 | 2 | no | — |
| 842 | C2×C4 | — | 4 | 1 | no | — |
| 843 | C2×C4 | — | 4 | 1 | no | — |
| 844 | C2×C4 | — | 4 | 2 | no | — |
| 845 | C2×C4 | — | 8 | 1 | no | — |
| 846 | C2×C4 | — | 8 | 1 | no | — |
| 847 | C2×C4 | — | 8 | 1 | no | — |
| 848 | C2×C4 | — | 8 | 1 | no | — |
| 849 | C2×C4 | — | 8 | 1 | no | — |
| 850 | C2×C4 | — | 8 | 1 | no | — |
| 851 | C2×C4 | — | 8 | 2 | no | — |
| 852 | C2×C4 | — | 8 | 1 | no | — |
| 853 | C2×C4 | — | 8 | 1 | no | — |
| 854 | C2×C4 | — | 8 | 2 | no | — |
| 855 | C2×C4 | — | 16 | 2 | no | — |
| 856 | C2×C4 | — | 16 | 2 | no | — |
| 857 | C2×C4 | — | 16 | 4 | no | — |
| 858 | C2×C4 | — | 16 | 4 | no | — |
| 859 | C2×C4 | — | 16 | 1 | no | — |
| 860 | C2×C4 | C2×C22⋊Q8 | 1 | 2 | yes | — |
| 861 | C2×C4 | C2×C22⋊Q8 | 1 | 2 | yes | — |
| 862 | C2×C4 | #532 | 1 | 2 | yes | — |
| 863 | C2×C4 | #532 | 1 | 2 | yes | — |
| 864 | C2×C4 | #542 | 1 | 2 | yes | — |
| 865 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 866 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 867 | C2×C4 | #548 | 1 | 2 | yes | — |
| 868 | C2×C4 | #548 | 1 | 2 | yes | — |
| 869 | C2×C4 | D4×Q8 | 1 | 2 | yes | — |
| 870 | C2×C4 | D4×Q8 | 1 | 2 | yes | — |
| 871 | C2×C4 | #554 | 1 | 2 | yes | — |
| 872 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 873 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 874 | C2×C4 | C23×Q8 | 1 | 1 | yes | characteristic |
| 875 | C2×C4 | C22×#41 | 1 | 1 | yes | characteristic |
| 876 | C2×C4 | C22×#41 | 1 | 1 | yes | characteristic |
| 877 | C2×C4 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 878 | C8 | — | 2 | 1 | no | — |
| 879 | C8 | — | 2 | 1 | no | — |
| 880 | C8 | — | 2 | 1 | no | — |
| 881 | C8 | — | 2 | 1 | no | — |
| 882 | C8 | — | 2 | 4 | no | — |
| 883 | C8 | — | 4 | 2 | no | — |
| 884 | C8 | — | 4 | 2 | no | — |
| 885 | C8 | — | 4 | 2 | no | — |
| 886 | C8 | C2×C22⋊Q8 | 1 | 8 | yes | — |
| 887 | C22 | — | 2 | 1 | no | — |
| 888 | C22 | — | 2 | 1 | no | — |
| 889 | C22 | — | 2 | 1 | no | — |
| 890 | C22 | — | 2 | 1 | no | — |
| 891 | C22 | — | 2 | 1 | no | — |
| 892 | C22 | — | 2 | 1 | no | — |
| 893 | C22 | — | 4 | 2 | no | — |
| 894 | C22 | — | 4 | 2 | no | — |
| 895 | C22 | — | 4 | 2 | no | — |
| 896 | C22 | — | 4 | 4 | no | — |
| 897 | C22 | — | 8 | 2 | no | — |
| 898 | C22 | — | 8 | 4 | no | — |
| 899 | C22 | — | 8 | 8 | no | — |
| 900 | C22 | — | 8 | 1 | no | — |
| 901 | C22 | — | 8 | 2 | no | — |
| 902 | C22 | — | 8 | 1 | no | — |
| 903 | C22 | — | 8 | 2 | no | — |
| 904 | C22 | — | 16 | 1 | no | — |
| 905 | C22 | — | 16 | 2 | no | — |
| 906 | C22 | — | 16 | 4 | no | — |
| 907 | C22 | #2452 | 1 | 2 | yes | — |
| 908 | C22 | #2452 | 1 | 2 | yes | — |
| 909 | C22 | C2×#542 | 1 | 1 | yes | characteristic |
| 910 | C22 | C2×D42 | 1 | 1 | yes | characteristic |
| 911 | C22 | C2×#554 | 1 | 1 | yes | characteristic |
| 912 | C4 | — | 4 | 2 | no | — |
| 913 | C4 | — | 4 | 2 | no | — |
| 914 | C4 | — | 4 | 2 | no | — |
| 915 | C4 | — | 4 | 2 | no | — |
| 916 | C4 | — | 4 | 2 | no | — |
| 917 | C4 | — | 4 | 2 | no | — |
| 918 | C4 | — | 4 | 2 | no | — |
| 919 | C4 | — | 4 | 2 | no | — |
| 920 | C4 | — | 4 | 2 | no | — |
| 921 | C4 | — | 8 | 2 | no | — |
| 922 | C4 | — | 8 | 2 | no | — |
| 923 | C4 | — | 8 | 1 | no | — |
| 924 | C4 | — | 8 | 1 | no | — |
| 925 | C4 | #2452 | 1 | 2 | yes | — |
| 926 | C4 | #2452 | 1 | 2 | yes | — |
| 927 | C4 | C22×C22⋊Q8 | 1 | 1 | yes | characteristic |
| 928 | C4 | C2×#532 | 1 | 1 | yes | characteristic |
| 929 | C4 | C2×#548 | 1 | 1 | yes | characteristic |
| 930 | C4 | C2×D4×Q8 | 1 | 1 | yes | characteristic |
| 931 | C2 | — | 2 | 1 | no | — |
| 932 | C2 | — | 2 | 1 | no | — |
| 933 | C2 | — | 2 | 2 | no | — |
| 934 | C2 | — | 2 | 2 | no | — |
| 935 | C2 | — | 8 | 4 | no | — |
| 936 | C2 | — | 8 | 2 | no | — |
| 937 | C2 | C2×#2452 | 1 | 1 | yes | characteristic |
| 938 | C2 | #61106 | 1 | 1 | yes | characteristic |
| 939 | C2 | #61107 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C2×D42 |
| commutator, Frattini, cosocle | C22×C4 | C25 |
| prime radical | C22×AGL(1,ℤ/8) | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C23×C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #60664 | C2 | semidirect |
| 2. #60489 | C2 | semidirect |
| 3. C2×#3081 | C2 | semidirect |
| 5. #26504 | C2 | semidirect |
| 6. #26503 | C2 | semidirect |
| 7. #26501 | C2 | semidirect |
| 8. #26500 | C2 | semidirect |
| 9. #23601 | C2 | semidirect |
| 10. C2×#2063 | C2 | semidirect |
| 11. #23463 | C2 | semidirect |
| 12. #23462 | C2 | semidirect |
| 15. #21182 | C2 | semidirect |
| 16. #21164 | C2 | semidirect |
| 17. #20858 | C2 | semidirect |
| 18. #20856 | C2 | semidirect |
| 19. #20446 | C2 | semidirect |
| 28. #3164 | C22 | semidirect |
| 30. #3163 | C22 | semidirect |
| 35. #3082 | C22 | semidirect |
| 36. #3082 | C22 | semidirect |
| 41. #3081 | C22 | semidirect |
| 42. #3081 | C22 | semidirect |
| 79. #2064 | C22 | semidirect |
| 80. #2064 | C22 | semidirect |
| 83. #2063 | C22 | semidirect |
| 84. #2063 | C22 | semidirect |
| 85. #2028 | C22 | semidirect |
| 88. #2027 | C22 | semidirect |
| 95. #1952 | C22 | semidirect |
| 96. #1951 | C22 | semidirect |
| 97. #1946 | C22 | semidirect |
| 98. #1945 | C22 | semidirect |
| 99. #1857 | C22 | semidirect |
| 102. #1856 | C22 | semidirect |
| 103. #1773 | C22 | semidirect |
| 104. #1772 | C22 | semidirect |
| 116. C2×AGL(1,ℤ/8) | Q8 | semidirect |
| 355. C2×SD16 | C2×Q8 | semidirect |
| 358. C2×D8 | C2×Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #60664 | 2 |
| #60489 | 2 |
| C2×#3081 | 2 |
| #60168 | 2 |
| #26504 | 2 |
| #26503 | 2 |
| #26501 | 2 |
| #26500 | 2 |
| #23601 | 2 |
| C2×#2063 | 2 |
| #23463 | 2 |
| #23462 | 2 |
| #21249 | 2 |
| #21235 | 2 |
| #21182 | 2 |
| #21164 | 2 |
| #20858 | 2 |
| #20856 | 2 |
| #20446 | 2 |