Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1618 conjugacy classes of subgroups.
The subgroup lattice has 459 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #61409 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #61375 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #60883 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #33248 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #31180 | C2 | 1 | 8 | yes | maximal, complemented |
| 6 | #29861 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #28763 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #28701 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #26504 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #26274 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | #25928 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #25690 | C2 | 1 | 2 | yes | maximal, complemented |
| 13 | #21737 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #21295 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #3508 | C22 | 1 | 2 | yes | — |
| 16 | #3504 | C22 | 1 | 2 | yes | — |
| 17 | #3399 | — | 2 | 4 | no | — |
| 18 | #3396 | — | 2 | 2 | no | — |
| 19 | #3391 | — | 2 | 2 | no | — |
| 20 | #3390 | — | 2 | 2 | no | — |
| 21 | #3389 | — | 2 | 2 | no | — |
| 22 | #3381 | — | 2 | 4 | no | — |
| 23 | #3241 | — | 2 | 8 | no | — |
| 24 | #3235 | — | 2 | 4 | no | — |
| 25 | #3234 | — | 2 | 4 | no | — |
| 26 | #3166 | C22 | 1 | 2 | yes | — |
| 27 | #3163 | C22 | 1 | 2 | yes | — |
| 28 | #3162 | C22 | 1 | 1 | yes | characteristic |
| 29 | C2×#499 | C22 | 1 | 1 | yes | characteristic |
| 30 | #3155 | C22 | 1 | 2 | yes | — |
| 31 | C2×#493 | C22 | 1 | 1 | yes | characteristic |
| 32 | #3138 | C22 | 1 | 2 | yes | — |
| 33 | C2×#490 | C22 | 1 | 2 | yes | — |
| 34 | #3096 | C22 | 1 | 8 | yes | — |
| 35 | #3083 | C22 | 1 | 4 | yes | — |
| 36 | #3081 | C22 | 1 | 8 | yes | — |
| 37 | #3080 | C22 | 1 | 2 | yes | — |
| 38 | #3041 | C22 | 1 | 4 | yes | — |
| 39 | #3038 | C22 | 1 | 2 | yes | — |
| 40 | #2960 | C22 | 1 | 1 | yes | characteristic |
| 41 | #2960 | C22 | 1 | 1 | yes | characteristic |
| 42 | #2952 | C22 | 1 | 2 | yes | — |
| 43 | #2948 | C22 | 1 | 2 | yes | — |
| 44 | C4×#135 | C22 | 1 | 1 | yes | characteristic |
| 45 | #2923 | C22 | 1 | 2 | yes | — |
| 46 | #2641 | C22 | 1 | 2 | yes | — |
| 47 | #2089 | C22 | 1 | 4 | yes | — |
| 48 | #2063 | C22 | 1 | 8 | yes | — |
| 49 | #2051 | C22 | 1 | 8 | yes | — |
| 50 | #2045 | C22 | 1 | 4 | yes | — |
| 51 | #2037 | C22 | 1 | 8 | yes | — |
| 52 | #2027 | C22 | 1 | 8 | yes | — |
| 53 | #1998 | C22 | 1 | 2 | yes | — |
| 54 | #1995 | C22 | 1 | 1 | yes | characteristic |
| 55 | #1995 | C22 | 1 | 1 | yes | characteristic |
| 56 | #1978 | C22 | 1 | 4 | yes | — |
| 57 | #1975 | C22 | 1 | 2 | yes | — |
| 58 | #1972 | C22 | 1 | 4 | yes | — |
| 59 | #1970 | C22 | 1 | 4 | yes | — |
| 60 | #1965 | C22 | 1 | 2 | yes | — |
| 61 | #1951 | C22 | 1 | 4 | yes | — |
| 62 | #1946 | C22 | 1 | 2 | yes | — |
| 63 | #1945 | C22 | 1 | 4 | yes | — |
| 64 | #1937 | C22 | 1 | 4 | yes | — |
| 65 | #1883 | C22 | 1 | 8 | yes | — |
| 66 | #1856 | C22 | 1 | 8 | yes | — |
| 67 | #1849 | C22 | 1 | 1 | yes | characteristic |
| 68 | C4×#108 | C22 | 1 | 1 | yes | characteristic |
| 69 | #1773 | C22 | 1 | 4 | yes | — |
| 70 | #1759 | C22 | 1 | 2 | yes | — |
| 71 | #1726 | C22 | 1 | 1 | yes | characteristic |
| 72 | C2×AGL(1,ℤ/8) | C23 | 1 | 4 | yes | — |
| 73 | C2×#135 | C23 | 1 | 1 | yes | characteristic |
| 74 | C22×D8 | C23 | 1 | 2 | yes | — |
| 75 | C22×D8 | C23 | 1 | 2 | yes | — |
| 76 | #559 | — | 2 | 4 | no | — |
| 77 | #557 | — | 2 | 4 | no | — |
| 78 | #554 | — | 2 | 4 | no | — |
| 79 | #554 | — | 4 | 4 | no | — |
| 80 | #550 | — | 2 | 4 | no | — |
| 81 | #546 | — | 4 | 4 | no | — |
| 82 | #544 | — | 2 | 4 | no | — |
| 83 | #544 | C23 | 1 | 4 | yes | — |
| 84 | #540 | — | 2 | 4 | no | — |
| 85 | #535 | C23 | 1 | 4 | yes | — |
| 86 | #533 | — | 2 | 2 | no | — |
| 87 | #533 | C23 | 1 | 1 | yes | characteristic |
| 88 | #533 | C23 | 1 | 1 | yes | characteristic |
| 89 | #532 | — | 2 | 4 | no | — |
| 90 | C2×#127 | C23 | 1 | 2 | yes | — |
| 91 | C2×#125 | — | 2 | 2 | no | — |
| 92 | C2×#125 | C23 | 1 | 2 | yes | — |
| 93 | #520 | C23 | 1 | 4 | yes | — |
| 94 | #518 | C23 | 1 | 4 | yes | — |
| 95 | C4×#41 | C23 | 1 | 2 | yes | — |
| 96 | #501 | — | 2 | 4 | no | — |
| 97 | #501 | — | 2 | 4 | no | — |
| 98 | #501 | D4 | 1 | 4 | yes | — |
| 99 | #501 | D4 | 1 | 4 | yes | — |
| 100 | #499 | — | 2 | 4 | no | — |
| 101 | #499 | — | 2 | 2 | no | — |
| 102 | #499 | — | 2 | 2 | no | — |
| 103 | #499 | — | 2 | 2 | no | — |
| 104 | #498 | — | 2 | 2 | no | — |
| 105 | #496 | — | 2 | 4 | no | — |
| 106 | #495 | — | 2 | 2 | no | — |
| 107 | #493 | — | 2 | 2 | no | — |
| 108 | #493 | — | 2 | 2 | no | — |
| 109 | #493 | — | 2 | 2 | no | — |
| 110 | #490 | — | 2 | 2 | no | — |
| 111 | #490 | — | 2 | 2 | no | — |
| 112 | #490 | — | 2 | 4 | no | — |
| 113 | #490 | — | 2 | 4 | no | — |
| 114 | #486 | — | 2 | 4 | no | — |
| 115 | #482 | — | 2 | 8 | no | — |
| 116 | #482 | — | 2 | 8 | no | — |
| 117 | #481 | — | 2 | 8 | no | — |
| 118 | #480 | — | 2 | 8 | no | — |
| 119 | #479 | — | 2 | 4 | no | — |
| 120 | #479 | — | 2 | 4 | no | — |
| 121 | #478 | — | 2 | 4 | no | — |
| 122 | #478 | — | 2 | 8 | no | — |
| 123 | #478 | — | 2 | 8 | no | — |
| 124 | #478 | — | 2 | 4 | no | — |
| 125 | #477 | — | 2 | 4 | no | — |
| 126 | #476 | — | 2 | 8 | no | — |
| 127 | #474 | — | 2 | 8 | no | — |
| 128 | #474 | — | 2 | 4 | no | — |
| 129 | #463 | — | 2 | 8 | no | — |
| 130 | #460 | — | 2 | 4 | no | — |
| 131 | #459 | — | 2 | 4 | no | — |
| 132 | #459 | — | 2 | 8 | no | — |
| 133 | #446 | — | 2 | 2 | no | — |
| 134 | #446 | — | 2 | 2 | no | — |
| 135 | C8×Q8 | — | 2 | 2 | no | — |
| 136 | C8×Q8 | — | 2 | 2 | no | — |
| 137 | #442 | — | 2 | 2 | no | — |
| 138 | #442 | — | 2 | 4 | no | — |
| 139 | #441 | — | 2 | 2 | no | — |
| 140 | C4×Q16 | D4 | 1 | 2 | yes | — |
| 141 | C4×SD16 | — | 2 | 4 | no | — |
| 142 | C4×SD16 | D4 | 1 | 4 | yes | — |
| 143 | C4×D8 | — | 2 | 4 | no | — |
| 144 | C4×D8 | D4 | 1 | 2 | yes | — |
| 145 | #433 | — | 2 | 4 | no | — |
| 146 | #432 | — | 2 | 4 | no | — |
| 147 | C2×#108 | C23 | 1 | 2 | yes | — |
| 148 | C2×#108 | C23 | 1 | 4 | yes | — |
| 149 | #428 | C23 | 1 | 4 | yes | — |
| 150 | #428 | C23 | 1 | 8 | yes | — |
| 151 | #427 | C23 | 1 | 4 | yes | — |
| 152 | #427 | C23 | 1 | 1 | yes | characteristic |
| 153 | C2×#107 | C23 | 1 | 2 | yes | — |
| 154 | C2×#106 | C23 | 1 | 2 | yes | — |
| 155 | #424 | C23 | 1 | 4 | yes | — |
| 156 | #424 | C23 | 1 | 2 | yes | — |
| 157 | #424 | C23 | 1 | 2 | yes | — |
| 158 | #423 | C23 | 1 | 1 | yes | characteristic |
| 159 | #423 | C23 | 1 | 1 | yes | characteristic |
| 160 | C2×#104 | C23 | 1 | 4 | yes | — |
| 161 | #418 | C23 | 1 | 8 | yes | — |
| 162 | #418 | C23 | 1 | 4 | yes | — |
| 163 | #417 | C23 | 1 | 4 | yes | — |
| 164 | #416 | C23 | 1 | 2 | yes | — |
| 165 | C2×#102 | C23 | 1 | 8 | yes | — |
| 166 | C2×#100 | C23 | 1 | 8 | yes | — |
| 167 | #408 | C23 | 1 | 4 | yes | — |
| 168 | #405 | C23 | 1 | 2 | yes | — |
| 169 | #405 | C23 | 1 | 2 | yes | — |
| 170 | C4×M16 | C23 | 1 | 2 | yes | — |
| 171 | C2×#97 | C23 | 1 | 2 | yes | — |
| 172 | C2×#97 | C23 | 1 | 1 | yes | characteristic |
| 173 | C2×C4×C8 | C23 | 1 | 2 | yes | — |
| 174 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 175 | #394 | — | 4 | 4 | no | — |
| 176 | #390 | C23 | 1 | 8 | yes | — |
| 177 | #376 | C23 | 1 | 1 | yes | characteristic |
| 178 | #343 | C23 | 1 | 8 | yes | — |
| 179 | #341 | C23 | 1 | 2 | yes | — |
| 180 | #339 | C23 | 1 | 4 | yes | — |
| 181 | #339 | C23 | 1 | 4 | yes | — |
| 182 | #339 | C23 | 1 | 4 | yes | — |
| 183 | C2×#41 | — | 4 | 4 | no | — |
| 184 | C2×#41 | C24 | 1 | 2 | yes | — |
| 185 | C22×D4 | — | 2 | 4 | no | — |
| 186 | C22×D4 | C24 | 1 | 4 | yes | — |
| 187 | AGL(1,ℤ/8) | — | 4 | 8 | no | — |
| 188 | #135 | — | 2 | 4 | no | — |
| 189 | C2×Q16 | C2×D4 | 1 | 1 | yes | characteristic |
| 190 | C2×SD16 | — | 2 | 4 | no | — |
| 191 | C2×SD16 | C2×D4 | 1 | 2 | yes | — |
| 192 | C2×D8 | — | 2 | 4 | no | — |
| 193 | C2×D8 | — | 2 | 2 | no | — |
| 194 | C2×D8 | — | 2 | 2 | no | — |
| 195 | C2×D8 | — | 2 | 4 | no | — |
| 196 | C2×D8 | — | 2 | 8 | no | — |
| 197 | C2×D8 | — | 4 | 4 | no | — |
| 198 | C2×D8 | C2×D4 | 1 | 1 | yes | characteristic |
| 199 | C2×M16 | C24 | 1 | 2 | yes | — |
| 200 | C2×M16 | C24 | 1 | 2 | yes | — |
| 201 | C2×M16 | C24 | 1 | 4 | yes | — |
| 202 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 203 | C22×C8 | C24 | 1 | 2 | yes | — |
| 204 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 205 | C4⋊Q8 | — | 2 | 4 | no | — |
| 206 | C4⋊Q8 | — | 2 | 4 | no | — |
| 207 | C4⋊Q8 | — | 4 | 4 | no | — |
| 208 | C4⋊Q8 | C2×D4 | 1 | 2 | yes | — |
| 209 | C4⋊Q8 | C2×D4 | 1 | 2 | yes | — |
| 210 | #127 | — | 2 | 4 | no | — |
| 211 | #127 | — | 2 | 2 | no | — |
| 212 | #127 | — | 2 | 2 | no | — |
| 213 | #127 | — | 2 | 4 | no | — |
| 214 | #125 | — | 2 | 4 | no | — |
| 215 | #125 | — | 2 | 4 | no | — |
| 216 | #125 | — | 2 | 2 | no | — |
| 217 | #125 | — | 2 | 2 | no | — |
| 218 | #125 | — | 2 | 4 | no | — |
| 219 | #125 | — | 4 | 4 | no | — |
| 220 | #125 | — | 4 | 4 | no | — |
| 221 | #125 | C2×D4 | 1 | 2 | yes | — |
| 222 | #125 | C2×D4 | 1 | 2 | yes | — |
| 223 | #124 | — | 2 | 4 | no | — |
| 224 | #124 | — | 4 | 4 | no | — |
| 225 | #123 | — | 4 | 8 | no | — |
| 226 | C22⋊Q8 | — | 2 | 2 | no | — |
| 227 | C22⋊Q8 | — | 2 | 2 | no | — |
| 228 | C22⋊Q8 | — | 4 | 4 | no | — |
| 229 | C22⋊Q8 | — | 4 | 4 | no | — |
| 230 | C22⋊Q8 | — | 4 | 4 | no | — |
| 231 | C22⋊Q8 | — | 4 | 4 | no | — |
| 232 | #121 | — | 2 | 8 | no | — |
| 233 | #121 | — | 4 | 8 | no | — |
| 234 | #121 | — | 4 | 4 | no | — |
| 235 | #120 | — | 4 | 4 | no | — |
| 236 | C4×Q8 | — | 2 | 2 | no | — |
| 237 | C4×Q8 | — | 2 | 2 | no | — |
| 238 | C4×Q8 | — | 2 | 4 | no | — |
| 239 | C4×Q8 | — | 4 | 4 | no | — |
| 240 | C4×Q8 | C2×D4 | 1 | 4 | yes | — |
| 241 | C4×D4 | — | 2 | 4 | no | — |
| 242 | C4×D4 | — | 2 | 4 | no | — |
| 243 | C4×D4 | — | 2 | 8 | no | — |
| 244 | C4×D4 | — | 2 | 8 | no | — |
| 245 | C4×D4 | — | 4 | 4 | no | — |
| 246 | C4×D4 | — | 4 | 4 | no | — |
| 247 | C4×D4 | C2×D4 | 1 | 4 | yes | — |
| 248 | #117 | — | 2 | 2 | no | — |
| 249 | #117 | — | 2 | 4 | no | — |
| 250 | #117 | C24 | 1 | 2 | yes | — |
| 251 | #117 | C24 | 1 | 2 | yes | — |
| 252 | #117 | C24 | 1 | 2 | yes | — |
| 253 | C2×C4⋊C4 | — | 2 | 4 | no | — |
| 254 | C2×C4⋊C4 | — | 2 | 4 | no | — |
| 255 | C2×C4⋊C4 | — | 4 | 4 | no | — |
| 256 | C2×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 257 | C2×C22⋊C4 | — | 4 | 4 | no | — |
| 258 | C2×C22⋊C4 | — | 4 | 8 | no | — |
| 259 | C2×C42 | — | 2 | 2 | no | — |
| 260 | C2×C42 | C24 | 1 | 2 | yes | — |
| 261 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 262 | #108 | — | 2 | 4 | no | — |
| 263 | #108 | — | 4 | 4 | no | — |
| 264 | #107 | — | 2 | 2 | no | — |
| 265 | #107 | — | 2 | 2 | no | — |
| 266 | #107 | — | 2 | 4 | no | — |
| 267 | #107 | — | 2 | 8 | no | — |
| 268 | #107 | C2×D4 | 1 | 2 | yes | — |
| 269 | #107 | C2×D4 | 1 | 8 | yes | — |
| 270 | #106 | — | 2 | 2 | no | — |
| 271 | #106 | — | 2 | 2 | no | — |
| 272 | #106 | — | 2 | 8 | no | — |
| 273 | #106 | — | 2 | 4 | no | — |
| 274 | #106 | C2×D4 | 1 | 2 | yes | — |
| 275 | #106 | C2×D4 | 1 | 8 | yes | — |
| 276 | C4⋊C8 | — | 2 | 8 | no | — |
| 277 | C4⋊C8 | — | 2 | 4 | no | — |
| 278 | C4⋊C8 | — | 2 | 4 | no | — |
| 279 | C4⋊C8 | — | 2 | 2 | no | — |
| 280 | C4⋊C8 | — | 2 | 2 | no | — |
| 281 | #104 | — | 4 | 4 | no | — |
| 282 | #103 | — | 2 | 4 | no | — |
| 283 | #103 | C2×D4 | 1 | 4 | yes | — |
| 284 | #102 | — | 2 | 4 | no | — |
| 285 | #102 | — | 2 | 8 | no | — |
| 286 | #102 | — | 2 | 8 | no | — |
| 287 | #102 | — | 2 | 8 | no | — |
| 288 | #102 | — | 2 | 8 | no | — |
| 289 | #102 | — | 2 | 8 | no | — |
| 290 | #102 | C2×D4 | 1 | 4 | yes | — |
| 291 | #100 | — | 4 | 8 | no | — |
| 292 | C22⋊C8 | — | 2 | 8 | no | — |
| 293 | #97 | — | 2 | 2 | no | — |
| 294 | #97 | — | 2 | 2 | no | — |
| 295 | #97 | — | 2 | 4 | no | — |
| 296 | #97 | — | 2 | 2 | no | — |
| 297 | #97 | C2×D4 | 1 | 2 | yes | — |
| 298 | #97 | C2×D4 | 1 | 2 | yes | — |
| 299 | C4×C8 | — | 2 | 2 | no | — |
| 300 | C4×C8 | — | 2 | 2 | no | — |
| 301 | C4×C8 | — | 2 | 2 | no | — |
| 302 | C4×C8 | — | 4 | 2 | no | — |
| 303 | C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 304 | C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 305 | #95 | — | 2 | 2 | no | — |
| 306 | C24 | — | 2 | 4 | no | — |
| 307 | #41 | — | 2 | 4 | no | — |
| 308 | #41 | — | 2 | 4 | no | — |
| 309 | #41 | — | 16 | 8 | no | — |
| 310 | C2×Q8 | — | 2 | 2 | no | — |
| 311 | C2×Q8 | — | 2 | 2 | no | — |
| 312 | C2×Q8 | — | 4 | 4 | no | — |
| 313 | C2×Q8 | C22×D4 | 1 | 2 | yes | — |
| 314 | C2×D4 | — | 2 | 2 | no | — |
| 315 | C2×D4 | — | 2 | 4 | no | — |
| 316 | C2×D4 | — | 2 | 4 | no | — |
| 317 | C2×D4 | — | 2 | 8 | no | — |
| 318 | C2×D4 | — | 2 | 8 | no | — |
| 319 | C2×D4 | — | 4 | 8 | no | — |
| 320 | C2×D4 | — | 4 | 4 | no | — |
| 321 | C2×D4 | — | 4 | 4 | no | — |
| 322 | C2×D4 | — | 16 | 4 | no | — |
| 323 | C2×D4 | C22×D4 | 1 | 2 | yes | — |
| 324 | C22×C4 | — | 2 | 2 | no | — |
| 325 | C22×C4 | — | 2 | 4 | no | — |
| 326 | C22×C4 | — | 2 | 2 | no | — |
| 327 | C22×C4 | — | 2 | 4 | no | — |
| 328 | C22×C4 | — | 4 | 8 | no | — |
| 329 | C22×C4 | — | 4 | 4 | no | — |
| 330 | C22×C4 | H(5,𝔽2) | 1 | 2 | yes | — |
| 331 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 332 | Q16 | — | 2 | 2 | no | — |
| 333 | SD16 | — | 2 | 4 | no | — |
| 334 | SD16 | — | 8 | 4 | no | — |
| 335 | D8 | — | 2 | 2 | no | — |
| 336 | D8 | — | 4 | 4 | no | — |
| 337 | D8 | — | 4 | 4 | no | — |
| 338 | D8 | — | 8 | 4 | no | — |
| 339 | D8 | — | 8 | 4 | no | — |
| 340 | M16 | — | 2 | 4 | no | — |
| 341 | M16 | — | 2 | 4 | no | — |
| 342 | M16 | — | 2 | 4 | no | — |
| 343 | M16 | — | 2 | 4 | no | — |
| 344 | C2×C8 | — | 2 | 2 | no | — |
| 345 | C2×C8 | — | 2 | 2 | no | — |
| 346 | C2×C8 | — | 2 | 2 | no | — |
| 347 | C2×C8 | — | 2 | 4 | no | — |
| 348 | C2×C8 | — | 2 | 2 | no | — |
| 349 | C2×C8 | — | 2 | 2 | no | — |
| 350 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 351 | C2×C8 | C22×D4 | 1 | 4 | yes | — |
| 352 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 353 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 354 | C2×C8 | 2−1+4 | 1 | 4 | yes | — |
| 355 | C4⋊C4 | — | 2 | 4 | no | — |
| 356 | C4⋊C4 | — | 2 | 4 | no | — |
| 357 | C4⋊C4 | — | 2 | 2 | no | — |
| 358 | C4⋊C4 | — | 2 | 4 | no | — |
| 359 | C4⋊C4 | — | 2 | 2 | no | — |
| 360 | C4⋊C4 | — | 2 | 4 | no | — |
| 361 | C4⋊C4 | — | 2 | 4 | no | — |
| 362 | C4⋊C4 | — | 4 | 4 | no | — |
| 363 | C4⋊C4 | — | 4 | 4 | no | — |
| 364 | C4⋊C4 | — | 4 | 4 | no | — |
| 365 | C4⋊C4 | — | 4 | 4 | no | — |
| 366 | C4⋊C4 | — | 4 | 4 | no | — |
| 367 | C4⋊C4 | — | 4 | 4 | no | — |
| 368 | C4⋊C4 | C22×D4 | 1 | 4 | yes | — |
| 369 | C4⋊C4 | C22×D4 | 1 | 4 | yes | — |
| 370 | C4⋊C4 | C22×D4 | 1 | 4 | yes | — |
| 371 | C22⋊C4 | — | 2 | 2 | no | — |
| 372 | C22⋊C4 | — | 2 | 2 | no | — |
| 373 | C22⋊C4 | — | 2 | 2 | no | — |
| 374 | C22⋊C4 | — | 2 | 4 | no | — |
| 375 | C22⋊C4 | — | 4 | 8 | no | — |
| 376 | C22⋊C4 | — | 4 | 8 | no | — |
| 377 | C22⋊C4 | — | 4 | 4 | no | — |
| 378 | C22⋊C4 | — | 16 | 8 | no | — |
| 379 | C42 | — | 2 | 4 | no | — |
| 380 | C42 | — | 2 | 2 | no | — |
| 381 | C42 | — | 2 | 2 | no | — |
| 382 | C42 | — | 2 | 2 | no | — |
| 383 | C42 | — | 2 | 2 | no | — |
| 384 | C42 | — | 2 | 2 | no | — |
| 385 | C42 | — | 4 | 4 | no | — |
| 386 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 387 | C42 | C22×D4 | 1 | 2 | yes | — |
| 388 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 389 | C23 | — | 2 | 2 | no | — |
| 390 | C23 | — | 4 | 4 | no | — |
| 391 | C23 | — | 4 | 8 | no | — |
| 392 | C23 | — | 8 | 8 | no | — |
| 393 | C23 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 394 | Q8 | — | 2 | 2 | no | — |
| 395 | Q8 | — | 2 | 2 | no | — |
| 396 | Q8 | — | 4 | 4 | no | — |
| 397 | Q8 | — | 8 | 2 | no | — |
| 398 | Q8 | — | 16 | 4 | no | — |
| 399 | D4 | — | 2 | 2 | no | — |
| 400 | D4 | — | 2 | 2 | no | — |
| 401 | D4 | — | 4 | 4 | no | — |
| 402 | D4 | — | 4 | 4 | no | — |
| 403 | D4 | — | 4 | 8 | no | — |
| 404 | D4 | — | 4 | 4 | no | — |
| 405 | D4 | — | 8 | 8 | no | — |
| 406 | D4 | — | 16 | 4 | no | — |
| 407 | D4 | — | 16 | 8 | no | — |
| 408 | C2×C4 | — | 2 | 2 | no | — |
| 409 | C2×C4 | — | 2 | 4 | no | — |
| 410 | C2×C4 | — | 2 | 4 | no | — |
| 411 | C2×C4 | — | 2 | 4 | no | — |
| 412 | C2×C4 | — | 4 | 2 | no | — |
| 413 | C2×C4 | — | 4 | 4 | no | — |
| 414 | C2×C4 | — | 4 | 4 | no | — |
| 415 | C2×C4 | — | 4 | 4 | no | — |
| 416 | C2×C4 | — | 4 | 2 | no | — |
| 417 | C2×C4 | — | 8 | 4 | no | — |
| 418 | C2×C4 | — | 8 | 4 | no | — |
| 419 | C2×C4 | — | 16 | 8 | no | — |
| 420 | C2×C4 | — | 16 | 4 | no | — |
| 421 | C2×C4 | D42 | 1 | 2 | yes | — |
| 422 | C2×C4 | D42 | 1 | 2 | yes | — |
| 423 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 424 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 425 | C2×C4 | C2×2−1+4 | 1 | 2 | yes | — |
| 426 | C2×C4 | #585 | 1 | 2 | yes | — |
| 427 | C8 | — | 2 | 4 | no | — |
| 428 | C8 | — | 2 | 2 | no | — |
| 429 | C8 | — | 4 | 4 | no | — |
| 430 | C8 | — | 4 | 2 | no | — |
| 431 | C8 | — | 4 | 2 | no | — |
| 432 | C8 | #536 | 1 | 2 | yes | — |
| 433 | C8 | #536 | 1 | 2 | yes | — |
| 434 | C22 | — | 2 | 2 | no | — |
| 435 | C22 | — | 4 | 4 | no | — |
| 436 | C22 | — | 4 | 2 | no | — |
| 437 | C22 | — | 8 | 8 | no | — |
| 438 | C22 | — | 8 | 4 | no | — |
| 439 | C22 | — | 16 | 8 | no | — |
| 440 | C22 | C2×D42 | 1 | 1 | yes | characteristic |
| 441 | C22 | #3554 | 1 | 2 | yes | — |
| 442 | C4 | — | 2 | 2 | no | — |
| 443 | C4 | — | 2 | 2 | no | — |
| 444 | C4 | — | 4 | 4 | no | — |
| 445 | C4 | — | 4 | 4 | no | — |
| 446 | C4 | — | 4 | 4 | no | — |
| 447 | C4 | — | 4 | 2 | no | — |
| 448 | C4 | — | 8 | 2 | no | — |
| 449 | C4 | — | 8 | 4 | no | — |
| 450 | C4 | C2×#536 | 1 | 1 | yes | characteristic |
| 451 | C4 | #3497 | 1 | 2 | yes | — |
| 452 | C4 | #3500 | 1 | 1 | yes | characteristic |
| 453 | C2 | — | 2 | 2 | no | — |
| 454 | C2 | — | 8 | 2 | no | — |
| 455 | C2 | — | 16 | 4 | no | — |
| 456 | C2 | #39363 | 1 | 1 | yes | characteristic |
| 457 | C2 | #61106 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C2×D42 |
| commutator, Frattini, cosocle | C22×C4 | C25 |
| prime radical | #61409 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #61375 | C2 | semidirect |
| 3. #60883 | C2 | semidirect |
| 4. #33248 | C2 | semidirect |
| 5. #31180 | C2 | semidirect |
| 6. #29861 | C2 | semidirect |
| 7. #28763 | C2 | semidirect |
| 8. #28701 | C2 | semidirect |
| 9. #26504 | C2 | semidirect |
| 10. #26274 | C2 | semidirect |
| 11. #25928 | C2 | semidirect |
| 12. #25690 | C2 | semidirect |
| 13. #21737 | C2 | semidirect |
| 14. #21295 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #61409 | 2 |
| #61375 | 2 |
| #60883 | 2 |
| #33248 | 2 |
| #31180 | 2 |
| #29861 | 2 |
| #28763 | 2 |
| #28701 | 2 |
| #26504 | 2 |
| #26274 | 2 |
| #25928 | 2 |
| #25690 | 2 |
| #21737 | 2 |
| #21295 | 2 |