Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1291 conjugacy classes of subgroups.
The subgroup lattice has 835 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #23612 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#2064 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#2051 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #23487 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×#2003 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #21235 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #21205 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#1958 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C2×#1937 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C2×#1772 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #11339 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #11079 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #10977 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #10943 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #10942 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C22×AGL(1,ℤ/8) | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×#536 | C22 | 1 | 1 | yes | characteristic |
| 18 | C22×#124 | C22 | 1 | 1 | yes | characteristic |
| 19 | C22×#108 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#428 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×#427 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#424 | C22 | 1 | 1 | yes | characteristic |
| 23 | C22×#104 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×#417 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×#419 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×#419 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×#418 | C22 | 1 | 1 | yes | characteristic |
| 28 | C2×#416 | C22 | 1 | 1 | yes | characteristic |
| 29 | C22×#103 | C22 | 1 | 1 | yes | characteristic |
| 30 | C22×#103 | C22 | 1 | 1 | yes | characteristic |
| 31 | C22×#102 | C22 | 1 | 1 | yes | characteristic |
| 32 | C22×#102 | C22 | 1 | 1 | yes | characteristic |
| 33 | C22×#101 | C22 | 1 | 1 | yes | characteristic |
| 34 | C22×#100 | C22 | 1 | 1 | yes | characteristic |
| 35 | C2×#408 | C22 | 1 | 1 | yes | characteristic |
| 36 | C2×#405 | C22 | 1 | 1 | yes | characteristic |
| 37 | C2×#405 | C22 | 1 | 1 | yes | characteristic |
| 38 | C22×C4×C8 | C22 | 1 | 1 | yes | characteristic |
| 39 | #2317 | C22 | 1 | 1 | yes | characteristic |
| 40 | #2311 | C22 | 1 | 1 | yes | characteristic |
| 41 | #2309 | C22 | 1 | 1 | yes | characteristic |
| 42 | C2×#382 | C22 | 1 | 1 | yes | characteristic |
| 43 | #2067 | — | 2 | 2 | no | — |
| 44 | #2065 | — | 2 | 2 | no | — |
| 45 | #2064 | — | 2 | 4 | no | — |
| 46 | #2051 | — | 2 | 4 | no | — |
| 47 | #2036 | — | 2 | 2 | no | — |
| 48 | #2035 | — | 2 | 2 | no | — |
| 49 | #2003 | — | 2 | 4 | no | — |
| 50 | #1973 | — | 2 | 1 | no | — |
| 51 | #1972 | — | 2 | 1 | no | — |
| 52 | #1970 | — | 2 | 1 | no | — |
| 53 | #1968 | — | 2 | 1 | no | — |
| 54 | #1960 | — | 2 | 1 | no | — |
| 55 | #1959 | — | 2 | 1 | no | — |
| 56 | #1958 | — | 2 | 1 | no | — |
| 57 | #1958 | — | 2 | 4 | no | — |
| 58 | #1956 | — | 2 | 1 | no | — |
| 59 | #1937 | — | 2 | 4 | no | — |
| 60 | #1772 | — | 2 | 4 | no | — |
| 61 | C2×#343 | C22 | 1 | 1 | yes | characteristic |
| 62 | C2×#343 | C22 | 1 | 1 | yes | characteristic |
| 63 | C2×#341 | C22 | 1 | 1 | yes | characteristic |
| 64 | #1736 | C22 | 1 | 1 | yes | characteristic |
| 65 | #1736 | C22 | 1 | 1 | yes | characteristic |
| 66 | C2×#339 | C22 | 1 | 1 | yes | characteristic |
| 67 | C2×#339 | C22 | 1 | 1 | yes | characteristic |
| 68 | C2×#339 | C22 | 1 | 1 | yes | characteristic |
| 69 | C22×#41 | C23 | 1 | 1 | yes | characteristic |
| 70 | C23×Q8 | C23 | 1 | 1 | yes | characteristic |
| 71 | C23×D4 | C23 | 1 | 1 | yes | characteristic |
| 72 | C2×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 73 | C2×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 74 | C2×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 75 | C2×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 76 | C2×AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 77 | C2×AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 78 | C22×SD16 | — | 2 | 1 | no | — |
| 79 | C22×D8 | — | 2 | 1 | no | — |
| 80 | C22×M16 | C23 | 1 | 1 | yes | characteristic |
| 81 | C22×M16 | C23 | 1 | 1 | yes | characteristic |
| 82 | C22×M16 | C23 | 1 | 1 | yes | characteristic |
| 83 | C22×M16 | C23 | 1 | 1 | yes | characteristic |
| 84 | C23×C8 | C23 | 1 | 1 | yes | characteristic |
| 85 | C23×C8 | C23 | 1 | 1 | yes | characteristic |
| 86 | #536 | — | 2 | 2 | no | — |
| 87 | #536 | — | 2 | 2 | no | — |
| 88 | #536 | — | 2 | 2 | no | — |
| 89 | #536 | — | 4 | 1 | no | — |
| 90 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 91 | C2×#124 | — | 2 | 2 | no | — |
| 92 | C2×#124 | — | 2 | 1 | no | — |
| 93 | C2×#124 | — | 2 | 2 | no | — |
| 94 | C2×#124 | — | 2 | 2 | no | — |
| 95 | C2×#124 | — | 2 | 2 | no | — |
| 96 | C2×#124 | — | 2 | 2 | no | — |
| 97 | C2×#124 | — | 4 | 1 | no | — |
| 98 | C2×#123 | — | 4 | 1 | no | — |
| 99 | C2×C22⋊Q8 | — | 2 | 2 | no | — |
| 100 | C2×#117 | C23 | 1 | 1 | yes | characteristic |
| 101 | C2×#117 | C23 | 1 | 1 | yes | characteristic |
| 102 | C2×#117 | C23 | 1 | 1 | yes | characteristic |
| 103 | C22×C4⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 104 | C22×C4⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 105 | C22×C22⋊C4 | — | 4 | 1 | no | — |
| 106 | C22×C42 | C23 | 1 | 1 | yes | characteristic |
| 107 | C2×#108 | — | 2 | 2 | no | — |
| 108 | C2×#108 | — | 2 | 2 | no | — |
| 109 | C2×#108 | D4 | 1 | 4 | yes | — |
| 110 | #428 | — | 2 | 2 | no | — |
| 111 | #428 | — | 4 | 1 | no | — |
| 112 | #427 | — | 2 | 2 | no | — |
| 113 | #427 | — | 2 | 2 | no | — |
| 114 | C2×#107 | — | 2 | 1 | no | — |
| 115 | C2×#107 | D4 | 1 | 2 | yes | — |
| 116 | C2×#106 | — | 2 | 1 | no | — |
| 117 | C2×#106 | D4 | 1 | 2 | yes | — |
| 118 | #424 | — | 2 | 2 | no | — |
| 119 | #424 | — | 2 | 2 | no | — |
| 120 | C2×C4⋊C8 | — | 2 | 1 | no | — |
| 121 | C2×C4⋊C8 | — | 2 | 1 | no | — |
| 122 | C2×#104 | — | 2 | 2 | no | — |
| 123 | C2×#104 | — | 2 | 2 | no | — |
| 124 | C2×#104 | — | 2 | 2 | no | — |
| 125 | #419 | — | 2 | 2 | no | — |
| 126 | #419 | — | 2 | 2 | no | — |
| 127 | #419 | — | 4 | 1 | no | — |
| 128 | #419 | — | 4 | 1 | no | — |
| 129 | #418 | — | 2 | 2 | no | — |
| 130 | #418 | — | 2 | 2 | no | — |
| 131 | #417 | — | 2 | 2 | no | — |
| 132 | #417 | — | 4 | 1 | no | — |
| 133 | #416 | — | 2 | 2 | no | — |
| 134 | #416 | — | 2 | 2 | no | — |
| 135 | C2×#103 | — | 2 | 1 | no | — |
| 136 | C2×#103 | — | 2 | 2 | no | — |
| 137 | C2×#103 | — | 2 | 1 | no | — |
| 138 | C2×#103 | — | 2 | 2 | no | — |
| 139 | C2×#103 | — | 2 | 2 | no | — |
| 140 | C2×#103 | — | 2 | 1 | no | — |
| 141 | C2×#103 | — | 2 | 1 | no | — |
| 142 | C2×#103 | — | 2 | 1 | no | — |
| 143 | C2×#103 | — | 2 | 2 | no | — |
| 144 | C2×#103 | — | 2 | 1 | no | — |
| 145 | C2×#103 | — | 2 | 1 | no | — |
| 146 | C2×#103 | — | 2 | 2 | no | — |
| 147 | C2×#103 | D4 | 1 | 1 | yes | characteristic |
| 148 | C2×#103 | D4 | 1 | 1 | yes | characteristic |
| 149 | C2×#102 | — | 2 | 1 | no | — |
| 150 | C2×#102 | — | 2 | 2 | no | — |
| 151 | C2×#102 | — | 2 | 1 | no | — |
| 152 | C2×#102 | — | 2 | 1 | no | — |
| 153 | C2×#102 | — | 2 | 2 | no | — |
| 154 | C2×#102 | — | 2 | 2 | no | — |
| 155 | C2×#102 | — | 2 | 1 | no | — |
| 156 | C2×#102 | — | 2 | 1 | no | — |
| 157 | C2×#102 | — | 2 | 2 | no | — |
| 158 | C2×#102 | — | 2 | 2 | no | — |
| 159 | C2×#102 | D4 | 1 | 1 | yes | characteristic |
| 160 | C2×#102 | D4 | 1 | 1 | yes | characteristic |
| 161 | C2×#101 | — | 2 | 2 | no | — |
| 162 | C2×#101 | — | 2 | 2 | no | — |
| 163 | C2×#101 | — | 2 | 2 | no | — |
| 164 | C2×#100 | — | 2 | 2 | no | — |
| 165 | C2×#100 | — | 2 | 2 | no | — |
| 166 | C2×#100 | — | 4 | 1 | no | — |
| 167 | #408 | — | 2 | 2 | no | — |
| 168 | #408 | — | 2 | 2 | no | — |
| 169 | C2×C22⋊C8 | — | 2 | 1 | no | — |
| 170 | C2×C22⋊C8 | — | 2 | 1 | no | — |
| 171 | #405 | — | 2 | 2 | no | — |
| 172 | #405 | — | 2 | 2 | no | — |
| 173 | #405 | — | 4 | 1 | no | — |
| 174 | #405 | — | 4 | 1 | no | — |
| 175 | C2×#97 | — | 2 | 1 | no | — |
| 176 | C2×#97 | — | 2 | 1 | no | — |
| 177 | C2×C4×C8 | — | 2 | 2 | no | — |
| 178 | C2×C4×C8 | — | 2 | 2 | no | — |
| 179 | C2×C4×C8 | — | 2 | 1 | no | — |
| 180 | C2×C4×C8 | — | 2 | 1 | no | — |
| 181 | C2×C4×C8 | D4 | 1 | 4 | yes | — |
| 182 | #391 | — | 2 | 1 | no | — |
| 183 | #390 | — | 2 | 1 | no | — |
| 184 | #390 | — | 2 | 2 | no | — |
| 185 | #390 | — | 2 | 1 | no | — |
| 186 | #390 | — | 2 | 1 | no | — |
| 187 | #389 | — | 2 | 2 | no | — |
| 188 | #386 | — | 4 | 1 | no | — |
| 189 | #385 | — | 4 | 1 | no | — |
| 190 | #384 | — | 2 | 1 | no | — |
| 191 | #382 | — | 2 | 1 | no | — |
| 192 | #382 | — | 2 | 2 | no | — |
| 193 | #382 | — | 4 | 1 | no | — |
| 194 | #380 | — | 2 | 2 | no | — |
| 195 | #379 | — | 4 | 1 | no | — |
| 196 | C2×#95 | — | 4 | 1 | no | — |
| 197 | #343 | — | 2 | 2 | no | — |
| 198 | #343 | — | 2 | 2 | no | — |
| 199 | #341 | — | 2 | 2 | no | — |
| 200 | #340 | — | 2 | 2 | no | — |
| 201 | #340 | — | 2 | 2 | no | — |
| 202 | #339 | — | 2 | 2 | no | — |
| 203 | #339 | — | 2 | 2 | no | — |
| 204 | #339 | D4 | 1 | 4 | yes | — |
| 205 | C25 | — | 2 | 1 | no | — |
| 206 | C2×#41 | — | 2 | 1 | no | — |
| 207 | C2×#41 | — | 2 | 1 | no | — |
| 208 | C2×#41 | — | 2 | 1 | no | — |
| 209 | C2×#41 | — | 2 | 1 | no | — |
| 210 | C2×#41 | — | 2 | 1 | no | — |
| 211 | C2×#41 | — | 2 | 1 | no | — |
| 212 | C2×#41 | — | 2 | 1 | no | — |
| 213 | C2×#41 | — | 2 | 1 | no | — |
| 214 | C2×#41 | — | 2 | 1 | no | — |
| 215 | C2×#41 | — | 2 | 1 | no | — |
| 216 | C2×#41 | — | 2 | 1 | no | — |
| 217 | C2×#41 | — | 2 | 1 | no | — |
| 218 | C22×Q8 | — | 2 | 1 | no | — |
| 219 | C22×Q8 | — | 2 | 1 | no | — |
| 220 | C22×Q8 | — | 2 | 1 | no | — |
| 221 | C22×Q8 | — | 2 | 1 | no | — |
| 222 | C22×Q8 | — | 2 | 1 | no | — |
| 223 | C22×Q8 | — | 2 | 1 | no | — |
| 224 | C22×Q8 | — | 2 | 1 | no | — |
| 225 | C22×Q8 | — | 2 | 1 | no | — |
| 226 | C22×Q8 | — | 2 | 1 | no | — |
| 227 | C22×Q8 | — | 2 | 1 | no | — |
| 228 | C22×Q8 | — | 2 | 1 | no | — |
| 229 | C22×Q8 | — | 2 | 1 | no | — |
| 230 | C22×Q8 | — | 2 | 1 | no | — |
| 231 | C22×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 232 | C22×Q8 | #41 | 1 | 2 | yes | — |
| 233 | C22×D4 | — | 2 | 1 | no | — |
| 234 | C22×D4 | — | 2 | 1 | no | — |
| 235 | C22×D4 | — | 2 | 1 | no | — |
| 236 | C22×D4 | — | 2 | 1 | no | — |
| 237 | C22×D4 | — | 2 | 1 | no | — |
| 238 | C22×D4 | — | 2 | 1 | no | — |
| 239 | C22×D4 | — | 2 | 1 | no | — |
| 240 | C22×D4 | — | 2 | 1 | no | — |
| 241 | C22×D4 | — | 2 | 1 | no | — |
| 242 | C22×D4 | — | 2 | 1 | no | — |
| 243 | C22×D4 | — | 2 | 1 | no | — |
| 244 | C22×D4 | — | 2 | 1 | no | — |
| 245 | C22×D4 | — | 2 | 1 | no | — |
| 246 | C22×D4 | — | 2 | 1 | no | — |
| 247 | C22×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 248 | C22×D4 | #41 | 1 | 2 | yes | — |
| 249 | C23×C4 | — | 2 | 1 | no | — |
| 250 | C23×C4 | — | 2 | 1 | no | — |
| 251 | C23×C4 | — | 2 | 1 | no | — |
| 252 | C23×C4 | — | 2 | 1 | no | — |
| 253 | C23×C4 | — | 2 | 1 | no | — |
| 254 | C23×C4 | C24 | 1 | 1 | yes | characteristic |
| 255 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 256 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 257 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 258 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 259 | C2×SD16 | — | 2 | 4 | no | — |
| 260 | C2×SD16 | — | 4 | 2 | no | — |
| 261 | C2×SD16 | — | 4 | 2 | no | — |
| 262 | C2×D8 | — | 2 | 4 | no | — |
| 263 | C2×D8 | — | 4 | 2 | no | — |
| 264 | C2×D8 | — | 4 | 2 | no | — |
| 265 | C2×M16 | — | 2 | 1 | no | — |
| 266 | C2×M16 | — | 2 | 1 | no | — |
| 267 | C2×M16 | — | 2 | 1 | no | — |
| 268 | C2×M16 | — | 2 | 1 | no | — |
| 269 | C2×M16 | — | 2 | 1 | no | — |
| 270 | C2×M16 | — | 2 | 1 | no | — |
| 271 | C2×M16 | — | 2 | 1 | no | — |
| 272 | C2×M16 | — | 2 | 1 | no | — |
| 273 | C2×M16 | — | 2 | 1 | no | — |
| 274 | C2×M16 | — | 2 | 1 | no | — |
| 275 | C2×M16 | — | 2 | 1 | no | — |
| 276 | C2×M16 | — | 2 | 1 | no | — |
| 277 | C2×M16 | — | 2 | 1 | no | — |
| 278 | C2×M16 | — | 2 | 1 | no | — |
| 279 | C2×M16 | — | 2 | 1 | no | — |
| 280 | C2×M16 | — | 2 | 1 | no | — |
| 281 | C2×M16 | — | 2 | 1 | no | — |
| 282 | C2×M16 | — | 2 | 1 | no | — |
| 283 | C2×M16 | — | 2 | 1 | no | — |
| 284 | C2×M16 | — | 2 | 1 | no | — |
| 285 | C2×M16 | C2×D4 | 1 | 2 | yes | — |
| 286 | C2×M16 | C2×D4 | 1 | 2 | yes | — |
| 287 | C2×M16 | C2×D4 | 1 | 2 | yes | — |
| 288 | C2×M16 | #41 | 1 | 2 | yes | — |
| 289 | C22×C8 | — | 2 | 1 | no | — |
| 290 | C22×C8 | — | 2 | 1 | no | — |
| 291 | C22×C8 | — | 2 | 1 | no | — |
| 292 | C22×C8 | — | 2 | 1 | no | — |
| 293 | C22×C8 | — | 2 | 1 | no | — |
| 294 | C22×C8 | — | 2 | 1 | no | — |
| 295 | C22×C8 | — | 2 | 1 | no | — |
| 296 | C22×C8 | — | 2 | 1 | no | — |
| 297 | C22×C8 | — | 2 | 1 | no | — |
| 298 | C22×C8 | — | 2 | 1 | no | — |
| 299 | C22×C8 | — | 2 | 1 | no | — |
| 300 | C22×C8 | — | 2 | 1 | no | — |
| 301 | C22×C8 | C2×D4 | 1 | 2 | yes | — |
| 302 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 303 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 304 | C22×C8 | C2×D4 | 1 | 2 | yes | — |
| 305 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 306 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 307 | C22×C8 | C2×D4 | 1 | 2 | yes | — |
| 308 | C22×C8 | #41 | 1 | 2 | yes | — |
| 309 | C4⋊Q8 | — | 2 | 4 | no | — |
| 310 | C4⋊Q8 | — | 4 | 2 | no | — |
| 311 | #124 | — | 2 | 8 | no | — |
| 312 | #124 | — | 2 | 4 | no | — |
| 313 | #124 | — | 4 | 4 | no | — |
| 314 | #124 | — | 4 | 2 | no | — |
| 315 | #124 | — | 4 | 4 | no | — |
| 316 | #124 | — | 4 | 4 | no | — |
| 317 | #123 | — | 4 | 4 | no | — |
| 318 | #123 | — | 4 | 4 | no | — |
| 319 | C22⋊Q8 | — | 4 | 4 | no | — |
| 320 | C22⋊Q8 | — | 4 | 4 | no | — |
| 321 | #117 | — | 2 | 1 | no | — |
| 322 | #117 | — | 2 | 1 | no | — |
| 323 | #117 | — | 2 | 1 | no | — |
| 324 | #117 | — | 2 | 1 | no | — |
| 325 | #117 | — | 2 | 1 | no | — |
| 326 | #117 | — | 2 | 1 | no | — |
| 327 | #117 | — | 2 | 1 | no | — |
| 328 | #117 | — | 2 | 1 | no | — |
| 329 | #117 | — | 2 | 1 | no | — |
| 330 | #117 | — | 2 | 1 | no | — |
| 331 | #117 | C2×D4 | 1 | 2 | yes | — |
| 332 | #117 | #41 | 1 | 2 | yes | — |
| 333 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 334 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 335 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 336 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 337 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 338 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 339 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 340 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 341 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 342 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 343 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 344 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 345 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 346 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 347 | C2×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 348 | C2×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 349 | C2×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 350 | C2×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 351 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 352 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 353 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 354 | C2×C22⋊C4 | — | 4 | 4 | no | — |
| 355 | C2×C22⋊C4 | — | 4 | 4 | no | — |
| 356 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 357 | C2×C22⋊C4 | — | 4 | 4 | no | — |
| 358 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 359 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 360 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 361 | C2×C42 | — | 2 | 1 | no | — |
| 362 | C2×C42 | — | 2 | 1 | no | — |
| 363 | C2×C42 | — | 2 | 1 | no | — |
| 364 | C2×C42 | — | 2 | 1 | no | — |
| 365 | C2×C42 | — | 2 | 1 | no | — |
| 366 | C2×C42 | — | 2 | 1 | no | — |
| 367 | C2×C42 | C2×D4 | 1 | 2 | yes | — |
| 368 | C2×C42 | C2×D4 | 1 | 2 | yes | — |
| 369 | C2×C42 | #41 | 1 | 2 | yes | — |
| 370 | #108 | — | 2 | 8 | no | — |
| 371 | #107 | — | 2 | 4 | no | — |
| 372 | #107 | — | 4 | 2 | no | — |
| 373 | #106 | — | 2 | 4 | no | — |
| 374 | #106 | — | 4 | 2 | no | — |
| 375 | C4⋊C8 | — | 4 | 2 | no | — |
| 376 | C4⋊C8 | — | 4 | 2 | no | — |
| 377 | #104 | — | 4 | 4 | no | — |
| 378 | #103 | — | 2 | 2 | no | — |
| 379 | #103 | — | 2 | 2 | no | — |
| 380 | #103 | — | 4 | 2 | no | — |
| 381 | #103 | — | 4 | 2 | no | — |
| 382 | #103 | — | 4 | 4 | no | — |
| 383 | #103 | — | 4 | 2 | no | — |
| 384 | #103 | — | 4 | 2 | no | — |
| 385 | #103 | — | 4 | 2 | no | — |
| 386 | #103 | — | 4 | 2 | no | — |
| 387 | #103 | — | 4 | 2 | no | — |
| 388 | #102 | — | 2 | 2 | no | — |
| 389 | #102 | — | 2 | 2 | no | — |
| 390 | #102 | — | 4 | 2 | no | — |
| 391 | #102 | — | 4 | 2 | no | — |
| 392 | #102 | — | 4 | 2 | no | — |
| 393 | #102 | — | 4 | 2 | no | — |
| 394 | #102 | — | 4 | 2 | no | — |
| 395 | #102 | — | 4 | 4 | no | — |
| 396 | #101 | — | 4 | 4 | no | — |
| 397 | #100 | — | 4 | 4 | no | — |
| 398 | C22⋊C8 | — | 4 | 2 | no | — |
| 399 | C22⋊C8 | — | 4 | 2 | no | — |
| 400 | #97 | — | 4 | 2 | no | — |
| 401 | #97 | — | 4 | 2 | no | — |
| 402 | C4×C8 | — | 2 | 8 | no | — |
| 403 | C4×C8 | — | 4 | 2 | no | — |
| 404 | C4×C8 | — | 4 | 2 | no | — |
| 405 | #95 | — | 4 | 2 | no | — |
| 406 | #95 | — | 4 | 2 | no | — |
| 407 | #95 | — | 4 | 4 | no | — |
| 408 | C24 | — | 2 | 1 | no | — |
| 409 | C24 | — | 2 | 2 | no | — |
| 410 | C24 | — | 4 | 1 | no | — |
| 411 | C24 | — | 4 | 1 | no | — |
| 412 | C24 | — | 4 | 1 | no | — |
| 413 | C24 | — | 4 | 1 | no | — |
| 414 | C24 | — | 4 | 1 | no | — |
| 415 | C24 | — | 4 | 1 | no | — |
| 416 | C24 | — | 8 | 2 | no | — |
| 417 | C24 | — | 8 | 2 | no | — |
| 418 | C24 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 419 | #41 | — | 4 | 1 | no | — |
| 420 | #41 | — | 4 | 1 | no | — |
| 421 | #41 | — | 4 | 1 | no | — |
| 422 | #41 | — | 4 | 1 | no | — |
| 423 | #41 | — | 4 | 1 | no | — |
| 424 | #41 | — | 4 | 1 | no | — |
| 425 | #41 | — | 4 | 1 | no | — |
| 426 | #41 | — | 4 | 1 | no | — |
| 427 | #41 | — | 4 | 1 | no | — |
| 428 | #41 | — | 4 | 1 | no | — |
| 429 | #41 | — | 4 | 1 | no | — |
| 430 | #41 | — | 4 | 1 | no | — |
| 431 | #41 | — | 4 | 1 | no | — |
| 432 | #41 | — | 4 | 1 | no | — |
| 433 | #41 | — | 4 | 1 | no | — |
| 434 | #41 | — | 4 | 1 | no | — |
| 435 | C2×Q8 | — | 2 | 1 | no | — |
| 436 | C2×Q8 | — | 2 | 2 | no | — |
| 437 | C2×Q8 | — | 2 | 2 | no | — |
| 438 | C2×Q8 | — | 2 | 1 | no | — |
| 439 | C2×Q8 | — | 2 | 1 | no | — |
| 440 | C2×Q8 | — | 2 | 2 | no | — |
| 441 | C2×Q8 | — | 2 | 1 | no | — |
| 442 | C2×Q8 | — | 2 | 1 | no | — |
| 443 | C2×Q8 | — | 2 | 2 | no | — |
| 444 | C2×Q8 | — | 2 | 1 | no | — |
| 445 | C2×Q8 | — | 2 | 2 | no | — |
| 446 | C2×Q8 | — | 2 | 2 | no | — |
| 447 | C2×Q8 | — | 4 | 1 | no | — |
| 448 | C2×Q8 | — | 4 | 1 | no | — |
| 449 | C2×Q8 | — | 4 | 1 | no | — |
| 450 | C2×Q8 | — | 4 | 1 | no | — |
| 451 | C2×Q8 | — | 4 | 1 | no | — |
| 452 | C2×Q8 | — | 4 | 1 | no | — |
| 453 | C2×Q8 | — | 4 | 1 | no | — |
| 454 | C2×Q8 | — | 4 | 1 | no | — |
| 455 | C2×Q8 | — | 4 | 1 | no | — |
| 456 | C2×Q8 | — | 4 | 1 | no | — |
| 457 | C2×Q8 | — | 4 | 1 | no | — |
| 458 | C2×Q8 | — | 4 | 1 | no | — |
| 459 | C2×Q8 | — | 4 | 1 | no | — |
| 460 | C2×Q8 | — | 4 | 1 | no | — |
| 461 | C2×Q8 | — | 4 | 1 | no | — |
| 462 | C2×Q8 | — | 4 | 1 | no | — |
| 463 | C2×Q8 | — | 4 | 1 | no | — |
| 464 | C2×Q8 | — | 4 | 1 | no | — |
| 465 | C2×Q8 | — | 4 | 1 | no | — |
| 466 | C2×Q8 | — | 4 | 1 | no | — |
| 467 | C2×Q8 | — | 4 | 1 | no | — |
| 468 | C2×Q8 | — | 4 | 1 | no | — |
| 469 | C2×D4 | — | 2 | 1 | no | — |
| 470 | C2×D4 | — | 2 | 2 | no | — |
| 471 | C2×D4 | — | 2 | 1 | no | — |
| 472 | C2×D4 | — | 2 | 1 | no | — |
| 473 | C2×D4 | — | 2 | 2 | no | — |
| 474 | C2×D4 | — | 2 | 2 | no | — |
| 475 | C2×D4 | — | 2 | 1 | no | — |
| 476 | C2×D4 | — | 2 | 1 | no | — |
| 477 | C2×D4 | — | 2 | 2 | no | — |
| 478 | C2×D4 | — | 2 | 2 | no | — |
| 479 | C2×D4 | — | 2 | 1 | no | — |
| 480 | C2×D4 | — | 2 | 2 | no | — |
| 481 | C2×D4 | — | 4 | 1 | no | — |
| 482 | C2×D4 | — | 4 | 1 | no | — |
| 483 | C2×D4 | — | 4 | 1 | no | — |
| 484 | C2×D4 | — | 4 | 1 | no | — |
| 485 | C2×D4 | — | 4 | 1 | no | — |
| 486 | C2×D4 | — | 4 | 1 | no | — |
| 487 | C2×D4 | — | 4 | 1 | no | — |
| 488 | C2×D4 | — | 4 | 1 | no | — |
| 489 | C2×D4 | — | 4 | 1 | no | — |
| 490 | C2×D4 | — | 4 | 1 | no | — |
| 491 | C2×D4 | — | 4 | 1 | no | — |
| 492 | C2×D4 | — | 4 | 1 | no | — |
| 493 | C2×D4 | — | 4 | 1 | no | — |
| 494 | C2×D4 | — | 4 | 1 | no | — |
| 495 | C2×D4 | — | 4 | 1 | no | — |
| 496 | C2×D4 | — | 4 | 1 | no | — |
| 497 | C2×D4 | — | 4 | 1 | no | — |
| 498 | C2×D4 | — | 4 | 1 | no | — |
| 499 | C2×D4 | — | 4 | 1 | no | — |
| 500 | C2×D4 | — | 4 | 1 | no | — |
| 501 | C2×D4 | — | 4 | 1 | no | — |
| 502 | C2×D4 | — | 4 | 1 | no | — |
| 503 | C2×D4 | — | 4 | 1 | no | — |
| 504 | C2×D4 | — | 4 | 1 | no | — |
| 505 | C2×D4 | — | 4 | 1 | no | — |
| 506 | C2×D4 | — | 4 | 1 | no | — |
| 507 | C2×D4 | — | 4 | 1 | no | — |
| 508 | C2×D4 | — | 4 | 1 | no | — |
| 509 | C22×C4 | — | 2 | 2 | no | — |
| 510 | C22×C4 | — | 2 | 2 | no | — |
| 511 | C22×C4 | — | 2 | 2 | no | — |
| 512 | C22×C4 | — | 2 | 2 | no | — |
| 513 | C22×C4 | — | 2 | 1 | no | — |
| 514 | C22×C4 | — | 2 | 1 | no | — |
| 515 | C22×C4 | — | 2 | 2 | no | — |
| 516 | C22×C4 | — | 2 | 1 | no | — |
| 517 | C22×C4 | — | 2 | 2 | no | — |
| 518 | C22×C4 | — | 4 | 2 | no | — |
| 519 | C22×C4 | — | 4 | 2 | no | — |
| 520 | C22×C4 | — | 4 | 1 | no | — |
| 521 | C22×C4 | — | 4 | 1 | no | — |
| 522 | C22×C4 | — | 4 | 1 | no | — |
| 523 | C22×C4 | — | 4 | 1 | no | — |
| 524 | C22×C4 | — | 4 | 1 | no | — |
| 525 | C22×C4 | — | 4 | 1 | no | — |
| 526 | C22×C4 | — | 4 | 1 | no | — |
| 527 | C22×C4 | — | 4 | 1 | no | — |
| 528 | C22×C4 | — | 4 | 1 | no | — |
| 529 | C22×C4 | — | 4 | 1 | no | — |
| 530 | C22×C4 | — | 4 | 1 | no | — |
| 531 | C22×C4 | — | 4 | 1 | no | — |
| 532 | C22×C4 | — | 4 | 1 | no | — |
| 533 | C22×C4 | — | 4 | 1 | no | — |
| 534 | C22×C4 | — | 4 | 1 | no | — |
| 535 | C22×C4 | — | 4 | 1 | no | — |
| 536 | C22×C4 | — | 4 | 1 | no | — |
| 537 | C22×C4 | — | 4 | 1 | no | — |
| 538 | C22×C4 | — | 8 | 2 | no | — |
| 539 | C22×C4 | — | 8 | 2 | no | — |
| 540 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 541 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 542 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 543 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 544 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 545 | C22×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 546 | C22×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 547 | C22×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 548 | C22×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 549 | C22×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 550 | C22×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 551 | C22×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 552 | C22×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 553 | C22×C4 | 2−1+4 | 1 | 1 | yes | characteristic |
| 554 | SD16 | — | 4 | 8 | no | — |
| 555 | D8 | — | 4 | 8 | no | — |
| 556 | M16 | — | 2 | 2 | no | — |
| 557 | M16 | — | 2 | 2 | no | — |
| 558 | M16 | — | 2 | 2 | no | — |
| 559 | M16 | — | 2 | 2 | no | — |
| 560 | M16 | — | 2 | 2 | no | — |
| 561 | M16 | — | 4 | 1 | no | — |
| 562 | M16 | — | 4 | 1 | no | — |
| 563 | M16 | — | 4 | 1 | no | — |
| 564 | M16 | — | 4 | 1 | no | — |
| 565 | M16 | — | 4 | 1 | no | — |
| 566 | M16 | — | 4 | 1 | no | — |
| 567 | M16 | — | 4 | 1 | no | — |
| 568 | M16 | — | 4 | 1 | no | — |
| 569 | M16 | — | 4 | 1 | no | — |
| 570 | M16 | — | 4 | 1 | no | — |
| 571 | M16 | #121 | 1 | 4 | yes | — |
| 572 | C2×C8 | — | 2 | 2 | no | — |
| 573 | C2×C8 | — | 2 | 2 | no | — |
| 574 | C2×C8 | — | 2 | 1 | no | — |
| 575 | C2×C8 | — | 2 | 1 | no | — |
| 576 | C2×C8 | — | 2 | 2 | no | — |
| 577 | C2×C8 | — | 2 | 2 | no | — |
| 578 | C2×C8 | — | 2 | 2 | no | — |
| 579 | C2×C8 | — | 2 | 2 | no | — |
| 580 | C2×C8 | — | 2 | 1 | no | — |
| 581 | C2×C8 | — | 2 | 1 | no | — |
| 582 | C2×C8 | — | 2 | 2 | no | — |
| 583 | C2×C8 | — | 2 | 1 | no | — |
| 584 | C2×C8 | — | 2 | 2 | no | — |
| 585 | C2×C8 | — | 2 | 1 | no | — |
| 586 | C2×C8 | — | 2 | 2 | no | — |
| 587 | C2×C8 | — | 2 | 1 | no | — |
| 588 | C2×C8 | — | 2 | 1 | no | — |
| 589 | C2×C8 | — | 2 | 2 | no | — |
| 590 | C2×C8 | — | 2 | 2 | no | — |
| 591 | C2×C8 | — | 2 | 2 | no | — |
| 592 | C2×C8 | — | 4 | 1 | no | — |
| 593 | C2×C8 | — | 4 | 1 | no | — |
| 594 | C2×C8 | — | 4 | 1 | no | — |
| 595 | C2×C8 | — | 4 | 1 | no | — |
| 596 | C2×C8 | — | 4 | 1 | no | — |
| 597 | C2×C8 | — | 4 | 1 | no | — |
| 598 | C2×C8 | — | 4 | 1 | no | — |
| 599 | C2×C8 | — | 4 | 1 | no | — |
| 600 | C2×C8 | #121 | 1 | 2 | yes | — |
| 601 | C2×C8 | #121 | 1 | 2 | yes | — |
| 602 | C2×C8 | #127 | 1 | 2 | yes | — |
| 603 | C2×C8 | #127 | 1 | 2 | yes | — |
| 604 | C4⋊C4 | — | 2 | 2 | no | — |
| 605 | C4⋊C4 | — | 2 | 1 | no | — |
| 606 | C4⋊C4 | — | 2 | 1 | no | — |
| 607 | C4⋊C4 | — | 2 | 2 | no | — |
| 608 | C4⋊C4 | — | 2 | 1 | no | — |
| 609 | C4⋊C4 | — | 2 | 1 | no | — |
| 610 | C4⋊C4 | — | 2 | 2 | no | — |
| 611 | C4⋊C4 | — | 4 | 8 | no | — |
| 612 | C4⋊C4 | — | 4 | 1 | no | — |
| 613 | C4⋊C4 | — | 4 | 1 | no | — |
| 614 | C4⋊C4 | — | 4 | 1 | no | — |
| 615 | C4⋊C4 | — | 4 | 1 | no | — |
| 616 | C4⋊C4 | — | 4 | 1 | no | — |
| 617 | C4⋊C4 | — | 4 | 1 | no | — |
| 618 | C4⋊C4 | — | 4 | 1 | no | — |
| 619 | C4⋊C4 | — | 4 | 1 | no | — |
| 620 | C4⋊C4 | — | 16 | 2 | no | — |
| 621 | C4⋊C4 | #121 | 1 | 4 | yes | — |
| 622 | C22⋊C4 | — | 2 | 2 | no | — |
| 623 | C22⋊C4 | — | 2 | 2 | no | — |
| 624 | C22⋊C4 | — | 4 | 16 | no | — |
| 625 | C22⋊C4 | — | 4 | 8 | no | — |
| 626 | C22⋊C4 | — | 4 | 1 | no | — |
| 627 | C22⋊C4 | — | 4 | 1 | no | — |
| 628 | C22⋊C4 | — | 4 | 1 | no | — |
| 629 | C22⋊C4 | — | 4 | 1 | no | — |
| 630 | C22⋊C4 | — | 16 | 2 | no | — |
| 631 | C22⋊C4 | — | 16 | 2 | no | — |
| 632 | C22⋊C4 | — | 16 | 2 | no | — |
| 633 | C42 | — | 2 | 2 | no | — |
| 634 | C42 | — | 2 | 2 | no | — |
| 635 | C42 | — | 2 | 2 | no | — |
| 636 | C42 | — | 2 | 2 | no | — |
| 637 | C42 | — | 2 | 2 | no | — |
| 638 | C42 | — | 4 | 1 | no | — |
| 639 | C42 | — | 4 | 1 | no | — |
| 640 | C42 | — | 4 | 1 | no | — |
| 641 | C42 | — | 4 | 1 | no | — |
| 642 | C42 | #121 | 1 | 4 | yes | — |
| 643 | C23 | — | 2 | 2 | no | — |
| 644 | C23 | — | 2 | 2 | no | — |
| 645 | C23 | — | 4 | 2 | no | — |
| 646 | C23 | — | 4 | 1 | no | — |
| 647 | C23 | — | 4 | 1 | no | — |
| 648 | C23 | — | 4 | 2 | no | — |
| 649 | C23 | — | 4 | 2 | no | — |
| 650 | C23 | — | 4 | 2 | no | — |
| 651 | C23 | — | 4 | 1 | no | — |
| 652 | C23 | — | 4 | 2 | no | — |
| 653 | C23 | — | 8 | 4 | no | — |
| 654 | C23 | — | 8 | 2 | no | — |
| 655 | C23 | — | 8 | 2 | no | — |
| 656 | C23 | — | 8 | 4 | no | — |
| 657 | C23 | — | 8 | 1 | no | — |
| 658 | C23 | — | 8 | 1 | no | — |
| 659 | C23 | — | 8 | 1 | no | — |
| 660 | C23 | — | 8 | 2 | no | — |
| 661 | C23 | — | 8 | 2 | no | — |
| 662 | C23 | — | 8 | 1 | no | — |
| 663 | C23 | — | 16 | 2 | no | — |
| 664 | C23 | — | 16 | 1 | no | — |
| 665 | C23 | — | 16 | 1 | no | — |
| 666 | C23 | — | 16 | 2 | no | — |
| 667 | C23 | #535 | 1 | 1 | yes | characteristic |
| 668 | C23 | #538 | 1 | 1 | yes | characteristic |
| 669 | C23 | #542 | 1 | 1 | yes | characteristic |
| 670 | C23 | D42 | 1 | 1 | yes | characteristic |
| 671 | C23 | #546 | 1 | 1 | yes | characteristic |
| 672 | C23 | #550 | 1 | 1 | yes | characteristic |
| 673 | C23 | #551 | 1 | 1 | yes | characteristic |
| 674 | Q8 | — | 4 | 2 | no | — |
| 675 | Q8 | — | 4 | 1 | no | — |
| 676 | Q8 | — | 4 | 1 | no | — |
| 677 | Q8 | — | 4 | 1 | no | — |
| 678 | Q8 | — | 4 | 2 | no | — |
| 679 | Q8 | — | 4 | 1 | no | — |
| 680 | Q8 | — | 4 | 2 | no | — |
| 681 | Q8 | — | 4 | 2 | no | — |
| 682 | Q8 | — | 8 | 1 | no | — |
| 683 | Q8 | — | 8 | 1 | no | — |
| 684 | Q8 | — | 8 | 1 | no | — |
| 685 | Q8 | — | 8 | 1 | no | — |
| 686 | D4 | — | 4 | 2 | no | — |
| 687 | D4 | — | 4 | 1 | no | — |
| 688 | D4 | — | 4 | 1 | no | — |
| 689 | D4 | — | 4 | 1 | no | — |
| 690 | D4 | — | 4 | 2 | no | — |
| 691 | D4 | — | 4 | 2 | no | — |
| 692 | D4 | — | 4 | 1 | no | — |
| 693 | D4 | — | 4 | 2 | no | — |
| 694 | D4 | — | 8 | 1 | no | — |
| 695 | D4 | — | 8 | 1 | no | — |
| 696 | D4 | — | 8 | 1 | no | — |
| 697 | D4 | — | 8 | 1 | no | — |
| 698 | D4 | — | 8 | 1 | no | — |
| 699 | D4 | — | 8 | 1 | no | — |
| 700 | D4 | — | 8 | 1 | no | — |
| 701 | D4 | — | 8 | 1 | no | — |
| 702 | C2×C4 | — | 2 | 4 | no | — |
| 703 | C2×C4 | — | 2 | 4 | no | — |
| 704 | C2×C4 | — | 4 | 2 | no | — |
| 705 | C2×C4 | — | 4 | 2 | no | — |
| 706 | C2×C4 | — | 4 | 4 | no | — |
| 707 | C2×C4 | — | 4 | 4 | no | — |
| 708 | C2×C4 | — | 4 | 2 | no | — |
| 709 | C2×C4 | — | 4 | 2 | no | — |
| 710 | C2×C4 | — | 4 | 2 | no | — |
| 711 | C2×C4 | — | 4 | 2 | no | — |
| 712 | C2×C4 | — | 4 | 2 | no | — |
| 713 | C2×C4 | — | 4 | 1 | no | — |
| 714 | C2×C4 | — | 4 | 2 | no | — |
| 715 | C2×C4 | — | 4 | 1 | no | — |
| 716 | C2×C4 | — | 4 | 2 | no | — |
| 717 | C2×C4 | — | 4 | 2 | no | — |
| 718 | C2×C4 | — | 4 | 2 | no | — |
| 719 | C2×C4 | — | 4 | 2 | no | — |
| 720 | C2×C4 | — | 4 | 1 | no | — |
| 721 | C2×C4 | — | 4 | 1 | no | — |
| 722 | C2×C4 | — | 4 | 1 | no | — |
| 723 | C2×C4 | — | 8 | 1 | no | — |
| 724 | C2×C4 | — | 8 | 1 | no | — |
| 725 | C2×C4 | — | 8 | 1 | no | — |
| 726 | C2×C4 | — | 8 | 1 | no | — |
| 727 | C2×C4 | — | 8 | 1 | no | — |
| 728 | C2×C4 | — | 8 | 1 | no | — |
| 729 | C2×C4 | — | 8 | 1 | no | — |
| 730 | C2×C4 | — | 8 | 1 | no | — |
| 731 | C2×C4 | — | 8 | 2 | no | — |
| 732 | C2×C4 | — | 8 | 2 | no | — |
| 733 | C2×C4 | — | 8 | 2 | no | — |
| 734 | C2×C4 | — | 8 | 2 | no | — |
| 735 | C2×C4 | — | 8 | 1 | no | — |
| 736 | C2×C4 | — | 8 | 1 | no | — |
| 737 | C2×C4 | — | 16 | 1 | no | — |
| 738 | C2×C4 | — | 16 | 1 | no | — |
| 739 | C2×C4 | C2×#121 | 1 | 1 | yes | characteristic |
| 740 | C2×C4 | C2×#121 | 1 | 1 | yes | characteristic |
| 741 | C2×C4 | C2×#121 | 1 | 1 | yes | characteristic |
| 742 | C2×C4 | C2×#121 | 1 | 1 | yes | characteristic |
| 743 | C2×C4 | #525 | 1 | 1 | yes | characteristic |
| 744 | C2×C4 | #525 | 1 | 1 | yes | characteristic |
| 745 | C2×C4 | #525 | 1 | 1 | yes | characteristic |
| 746 | C2×C4 | #529 | 1 | 1 | yes | characteristic |
| 747 | C2×C4 | #529 | 1 | 1 | yes | characteristic |
| 748 | C2×C4 | C2×#127 | 1 | 1 | yes | characteristic |
| 749 | C2×C4 | #532 | 1 | 1 | yes | characteristic |
| 750 | C2×C4 | #532 | 1 | 1 | yes | characteristic |
| 751 | C2×C4 | #532 | 1 | 1 | yes | characteristic |
| 752 | C2×C4 | #537 | 1 | 1 | yes | characteristic |
| 753 | C2×C4 | #538 | 1 | 1 | yes | characteristic |
| 754 | C2×C4 | #542 | 1 | 1 | yes | characteristic |
| 755 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 756 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 757 | C2×C4 | #546 | 1 | 1 | yes | characteristic |
| 758 | C2×C4 | #546 | 1 | 1 | yes | characteristic |
| 759 | C2×C4 | #546 | 1 | 1 | yes | characteristic |
| 760 | C2×C4 | #547 | 1 | 1 | yes | characteristic |
| 761 | C2×C4 | #548 | 1 | 1 | yes | characteristic |
| 762 | C2×C4 | #548 | 1 | 1 | yes | characteristic |
| 763 | C2×C4 | #548 | 1 | 1 | yes | characteristic |
| 764 | C2×C4 | #550 | 1 | 1 | yes | characteristic |
| 765 | C2×C4 | #551 | 1 | 1 | yes | characteristic |
| 766 | C2×C4 | #553 | 1 | 1 | yes | characteristic |
| 767 | C8 | — | 2 | 2 | no | — |
| 768 | C8 | — | 2 | 2 | no | — |
| 769 | C8 | — | 2 | 2 | no | — |
| 770 | C8 | — | 2 | 2 | no | — |
| 771 | C8 | — | 2 | 4 | no | — |
| 772 | C8 | — | 4 | 2 | no | — |
| 773 | C8 | — | 8 | 1 | no | — |
| 774 | C8 | — | 8 | 1 | no | — |
| 775 | C22 | — | 2 | 1 | no | — |
| 776 | C22 | — | 2 | 1 | no | — |
| 777 | C22 | — | 2 | 1 | no | — |
| 778 | C22 | — | 2 | 1 | no | — |
| 779 | C22 | — | 2 | 2 | no | — |
| 780 | C22 | — | 2 | 2 | no | — |
| 781 | C22 | — | 2 | 2 | no | — |
| 782 | C22 | — | 2 | 2 | no | — |
| 783 | C22 | — | 8 | 4 | no | — |
| 784 | C22 | — | 8 | 1 | no | — |
| 785 | C22 | — | 8 | 1 | no | — |
| 786 | C22 | — | 8 | 2 | no | — |
| 787 | C22 | — | 8 | 1 | no | — |
| 788 | C22 | — | 8 | 2 | no | — |
| 789 | C22 | — | 8 | 2 | no | — |
| 790 | C22 | — | 8 | 4 | no | — |
| 791 | C22 | — | 16 | 2 | no | — |
| 792 | C22 | — | 16 | 2 | no | — |
| 793 | C22 | — | 16 | 2 | no | — |
| 794 | C22 | — | 16 | 1 | no | — |
| 795 | C22 | — | 16 | 1 | no | — |
| 796 | C22 | — | 16 | 2 | no | — |
| 797 | C22 | #2411 | 1 | 1 | yes | characteristic |
| 798 | C22 | #2424 | 1 | 1 | yes | characteristic |
| 799 | C22 | #2426 | 1 | 1 | yes | characteristic |
| 800 | C22 | #2461 | 1 | 1 | yes | characteristic |
| 801 | C22 | #2541 | 1 | 1 | yes | characteristic |
| 802 | C22 | #2554 | 1 | 1 | yes | characteristic |
| 803 | C22 | #2662 | 1 | 1 | yes | characteristic |
| 804 | C22 | #3290 | 1 | 2 | yes | — |
| 805 | C22 | #3290 | 1 | 2 | yes | — |
| 806 | C4 | — | 4 | 4 | no | — |
| 807 | C4 | — | 4 | 4 | no | — |
| 808 | C4 | — | 8 | 1 | no | — |
| 809 | C4 | — | 8 | 1 | no | — |
| 810 | C4 | — | 8 | 2 | no | — |
| 811 | C4 | — | 8 | 1 | no | — |
| 812 | C4 | — | 8 | 2 | no | — |
| 813 | C4 | — | 16 | 1 | no | — |
| 814 | C4 | — | 16 | 1 | no | — |
| 815 | C4 | #2392 | 1 | 1 | yes | characteristic |
| 816 | C4 | #2416 | 1 | 1 | yes | characteristic |
| 817 | C4 | #2424 | 1 | 1 | yes | characteristic |
| 818 | C4 | #2426 | 1 | 1 | yes | characteristic |
| 819 | C4 | #2461 | 1 | 1 | yes | characteristic |
| 820 | C4 | #2540 | 1 | 1 | yes | characteristic |
| 821 | C4 | #2554 | 1 | 1 | yes | characteristic |
| 822 | C4 | #2856 | 1 | 1 | yes | characteristic |
| 823 | C2 | — | 2 | 1 | no | — |
| 824 | C2 | — | 2 | 1 | no | — |
| 825 | C2 | — | 2 | 1 | no | — |
| 826 | C2 | — | 2 | 1 | no | — |
| 827 | C2 | — | 16 | 1 | no | — |
| 828 | C2 | — | 16 | 2 | no | — |
| 829 | C2 | #14815 | 1 | 1 | yes | characteristic |
| 830 | C2 | #25189 | 1 | 2 | yes | — |
| 831 | C2 | #26851 | 1 | 2 | yes | — |
| 832 | C2 | #28501 | 1 | 1 | yes | characteristic |
| 833 | C2 | #28503 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | D42 |
| commutator, Frattini, cosocle | C23×C4 | C24 |
| prime radical | C22×AGL(1,ℤ/8) | C22 |
| LCS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C23×C4 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #23612 | C2 | semidirect |
| 2. C2×#2064 | C2 | semidirect |
| 4. #23487 | C2 | semidirect |
| 7. #21205 | C2 | semidirect |
| 8. C2×#1958 | C2 | semidirect |
| 9. C2×#1937 | C2 | semidirect |
| 10. C2×#1772 | C2 | semidirect |
| 11. #11339 | C2 | semidirect |
| 12. #11079 | C2 | semidirect |
| 13. #10977 | C2 | semidirect |
| 14. #10943 | C2 | semidirect |
| 15. #10942 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23612 | 2 |
| C2×#2064 | 2 |
| C2×#2051 | 2 |
| #23487 | 2 |
| C2×#2003 | 2 |
| #21235 | 2 |
| #21205 | 2 |
| C2×#1958 | 2 |
| C2×#1937 | 2 |
| C2×#1772 | 2 |
| #11339 | 2 |
| #11079 | 2 |
| #10977 | 2 |
| #10943 | 2 |
| #10942 | 2 |