Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
10133 conjugacy classes of subgroups.
The subgroup lattice has 864 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #63093 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #63092 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #61111 | C2 | 1 | 6 | yes | maximal, complemented |
| 4 | #61109 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | #61108 | C2 | 1 | 12 | yes | maximal, complemented |
| 6 | #61107 | C2 | 1 | 12 | yes | maximal, complemented |
| 7 | #61100 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | C2×#3289 | C2 | 1 | 6 | yes | maximal, complemented |
| 9 | #60651 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #60472 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #60470 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #60391 | C2 | 1 | 2 | yes | maximal, complemented |
| 13 | #60390 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #60389 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #60184 | C2 | 1 | 2 | yes | maximal, complemented |
| 16 | 2−1+6 | C22 | 1 | 2 | yes | complemented |
| 17 | 2−1+6 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | H(7,𝔽2) | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | #3586 | — | 2 | 8 | no | — |
| 20 | #3586 | — | 2 | 8 | no | — |
| 21 | #3586 | — | 2 | 8 | no | — |
| 22 | #3586 | C22 | 1 | 12 | yes | complemented |
| 23 | #3586 | C22 | 1 | 2 | yes | complemented |
| 24 | #3586 | C22 | 1 | 2 | yes | complemented |
| 25 | #3586 | C22 | 1 | 2 | yes | complemented |
| 26 | #3586 | C22 | 1 | 12 | yes | complemented |
| 27 | #3586 | C22 | 1 | 12 | yes | complemented |
| 28 | #3585 | — | 2 | 8 | no | — |
| 29 | #3585 | C22 | 1 | 12 | yes | complemented |
| 30 | #3585 | C22 | 1 | 2 | yes | complemented |
| 31 | #3584 | — | 2 | 8 | no | — |
| 32 | #3584 | — | 2 | 8 | no | — |
| 33 | #3584 | C22 | 1 | 2 | yes | — |
| 34 | #3584 | C22 | 1 | 12 | yes | complemented |
| 35 | #3584 | C22 | 1 | 12 | yes | complemented |
| 36 | C2×#578 | — | 2 | 8 | no | — |
| 37 | C2×#578 | C22 | 1 | 2 | yes | complemented |
| 38 | C2×#578 | C22 | 1 | 12 | yes | complemented |
| 39 | C2×#577 | — | 2 | 8 | no | — |
| 40 | C2×#577 | C22 | 1 | 12 | yes | complemented |
| 41 | C2×#577 | C22 | 1 | 2 | yes | complemented |
| 42 | #3573 | C22 | 1 | 2 | yes | complemented |
| 43 | #3573 | C22 | 1 | 2 | yes | complemented |
| 44 | #3500 | C22 | 1 | 1 | yes | characteristic, complemented |
| 45 | #3499 | C22 | 1 | 1 | yes | characteristic, complemented |
| 46 | #3293 | C22 | 1 | 24 | yes | complemented |
| 47 | #3291 | C22 | 1 | 24 | yes | complemented |
| 48 | #3290 | C22 | 1 | 48 | yes | complemented |
| 49 | #3289 | C22 | 1 | 12 | yes | complemented |
| 50 | #3289 | C22 | 1 | 48 | yes | complemented |
| 51 | #3289 | C22 | 1 | 24 | yes | complemented |
| 52 | #3289 | C22 | 1 | 24 | yes | complemented |
| 53 | #3289 | C22 | 1 | 12 | yes | complemented |
| 54 | #3288 | C22 | 1 | 12 | yes | complemented |
| 55 | #3288 | C22 | 1 | 24 | yes | complemented |
| 56 | #3288 | C22 | 1 | 4 | yes | complemented |
| 57 | #3156 | C22 | 1 | 6 | yes | complemented |
| 58 | #3154 | C22 | 1 | 6 | yes | complemented |
| 59 | #3153 | C22 | 1 | 3 | yes | complemented |
| 60 | #3152 | C22 | 1 | 3 | yes | complemented |
| 61 | #3150 | C22 | 1 | 3 | yes | complemented |
| 62 | C2×#497 | C22 | 1 | 3 | yes | complemented |
| 63 | #3069 | C22 | 1 | 12 | yes | complemented |
| 64 | #3069 | C22 | 1 | 12 | yes | complemented |
| 65 | #3069 | C22 | 1 | 12 | yes | complemented |
| 66 | #3068 | C22 | 1 | 12 | yes | complemented |
| 67 | #3067 | C22 | 1 | 12 | yes | complemented |
| 68 | #3067 | C22 | 1 | 12 | yes | complemented |
| 69 | C2×#473 | C22 | 1 | 12 | yes | complemented |
| 70 | C2×#471 | C22 | 1 | 12 | yes | complemented |
| 71 | #3022 | C22 | 1 | 6 | yes | complemented |
| 72 | #3022 | C22 | 1 | 12 | yes | complemented |
| 73 | #3021 | C22 | 1 | 6 | yes | complemented |
| 74 | #3020 | C22 | 1 | 6 | yes | complemented |
| 75 | #3020 | C22 | 1 | 12 | yes | complemented |
| 76 | #3019 | C22 | 1 | 6 | yes | complemented |
| 77 | #3018 | C22 | 1 | 6 | yes | complemented |
| 78 | #3018 | C22 | 1 | 6 | yes | complemented |
| 79 | #3018 | C22 | 1 | 12 | yes | complemented |
| 80 | C2×#456 | C22 | 1 | 12 | yes | complemented |
| 81 | C2×#454 | C22 | 1 | 6 | yes | complemented |
| 82 | C2×#455 | C22 | 1 | 6 | yes | complemented |
| 83 | #2957 | C22 | 1 | 12 | yes | complemented |
| 84 | #2956 | C22 | 1 | 12 | yes | complemented |
| 85 | #2955 | C22 | 1 | 12 | yes | complemented |
| 86 | C2×#444 | C22 | 1 | 12 | yes | complemented |
| 87 | #2916 | C22 | 1 | 2 | yes | complemented |
| 88 | #2901 | C22 | 1 | 2 | yes | complemented |
| 89 | #2901 | C22 | 1 | 2 | yes | complemented |
| 90 | #2889 | C22 | 1 | 2 | yes | complemented |
| 91 | #2889 | C22 | 1 | 1 | yes | characteristic, complemented |
| 92 | #2888 | C22 | 1 | 1 | yes | characteristic, complemented |
| 93 | #2875 | C22 | 1 | 1 | yes | characteristic, complemented |
| 94 | #585 | — | 2 | 8 | no | — |
| 95 | #585 | — | 2 | 8 | no | — |
| 96 | #585 | — | 2 | 8 | no | — |
| 97 | #585 | — | 2 | 8 | no | — |
| 98 | #585 | — | 4 | 3 | no | — |
| 99 | #585 | — | 4 | 6 | no | — |
| 100 | #585 | — | 4 | 1 | no | — |
| 101 | #585 | C23 | 1 | 12 | yes | — |
| 102 | #585 | C23 | 1 | 6 | yes | — |
| 103 | #585 | C23 | 1 | 2 | yes | — |
| 104 | #585 | C23 | 1 | 2 | yes | — |
| 105 | #585 | C23 | 1 | 6 | yes | complemented |
| 106 | C2×2−1+4 | — | 2 | 8 | no | — |
| 107 | C2×2−1+4 | — | 2 | 8 | no | — |
| 108 | C2×2−1+4 | — | 2 | 8 | no | — |
| 109 | C2×2−1+4 | — | 4 | 1 | no | — |
| 110 | C2×2−1+4 | — | 4 | 2 | no | — |
| 111 | C2×2−1+4 | C23 | 1 | 12 | yes | — |
| 112 | C2×2−1+4 | C23 | 1 | 2 | yes | — |
| 113 | C2×2−1+4 | C23 | 1 | 1 | yes | characteristic |
| 114 | C2×2−1+4 | C23 | 1 | 6 | yes | complemented |
| 115 | C2×H(5,𝔽2) | — | 2 | 8 | no | — |
| 116 | C2×H(5,𝔽2) | — | 4 | 3 | no | — |
| 117 | C2×H(5,𝔽2) | C23 | 1 | 1 | yes | characteristic |
| 118 | C2×H(5,𝔽2) | C23 | 1 | 6 | yes | — |
| 119 | #578 | — | 2 | 8 | no | — |
| 120 | #578 | — | 2 | 8 | no | — |
| 121 | #578 | — | 2 | 8 | no | — |
| 122 | #578 | — | 2 | 24 | no | — |
| 123 | #578 | — | 2 | 24 | no | — |
| 124 | #578 | — | 2 | 24 | no | — |
| 125 | #578 | — | 2 | 24 | no | — |
| 126 | #578 | — | 2 | 24 | no | — |
| 127 | #578 | — | 2 | 12 | no | — |
| 128 | #578 | — | 2 | 12 | no | — |
| 129 | #578 | — | 2 | 8 | no | — |
| 130 | #578 | — | 2 | 8 | no | — |
| 131 | #578 | D4 | 1 | 8 | yes | complemented |
| 132 | #578 | C23 | 1 | 24 | yes | — |
| 133 | #578 | C23 | 1 | 24 | yes | complemented |
| 134 | #578 | C23 | 1 | 48 | yes | complemented |
| 135 | #577 | — | 2 | 8 | no | — |
| 136 | #577 | — | 2 | 8 | no | — |
| 137 | #577 | — | 2 | 8 | no | — |
| 138 | #577 | — | 2 | 8 | no | — |
| 139 | #577 | — | 2 | 24 | no | — |
| 140 | #577 | — | 2 | 24 | no | — |
| 141 | #577 | — | 2 | 24 | no | — |
| 142 | #577 | — | 2 | 24 | no | — |
| 143 | #577 | — | 2 | 24 | no | — |
| 144 | #577 | — | 2 | 24 | no | — |
| 145 | #577 | — | 2 | 12 | no | — |
| 146 | #577 | — | 2 | 12 | no | — |
| 147 | #577 | — | 2 | 12 | no | — |
| 148 | #577 | — | 2 | 12 | no | — |
| 149 | #577 | — | 2 | 8 | no | — |
| 150 | #577 | — | 2 | 8 | no | — |
| 151 | #577 | D4 | 1 | 8 | yes | complemented |
| 152 | #577 | D4 | 1 | 8 | yes | complemented |
| 153 | #577 | C23 | 1 | 8 | yes | — |
| 154 | #577 | C23 | 1 | 24 | yes | — |
| 155 | #577 | C23 | 1 | 48 | yes | — |
| 156 | #577 | C23 | 1 | 24 | yes | complemented |
| 157 | #577 | C23 | 1 | 24 | yes | complemented |
| 158 | #576 | — | 2 | 8 | no | — |
| 159 | #576 | — | 2 | 24 | no | — |
| 160 | #576 | — | 2 | 12 | no | — |
| 161 | #576 | — | 2 | 12 | no | — |
| 162 | #576 | D4 | 1 | 8 | yes | complemented |
| 163 | #576 | C23 | 1 | 24 | yes | — |
| 164 | #576 | C23 | 1 | 8 | yes | complemented |
| 165 | #575 | — | 2 | 24 | no | — |
| 166 | #575 | — | 2 | 24 | no | — |
| 167 | #575 | — | 2 | 24 | no | — |
| 168 | #575 | — | 2 | 24 | no | — |
| 169 | #575 | — | 2 | 24 | no | — |
| 170 | #575 | — | 2 | 24 | no | — |
| 171 | #575 | C23 | 1 | 12 | yes | — |
| 172 | #575 | C23 | 1 | 12 | yes | — |
| 173 | #575 | C23 | 1 | 12 | yes | — |
| 174 | #575 | C23 | 1 | 12 | yes | — |
| 175 | #575 | C23 | 1 | 12 | yes | complemented |
| 176 | C2×#137 | — | 2 | 24 | no | — |
| 177 | C2×#137 | — | 2 | 24 | no | — |
| 178 | C2×#137 | — | 2 | 24 | no | — |
| 179 | C2×#137 | — | 2 | 12 | no | — |
| 180 | C2×#137 | — | 2 | 12 | no | — |
| 181 | C2×#137 | — | 2 | 12 | no | — |
| 182 | C2×#137 | C23 | 1 | 12 | yes | — |
| 183 | C2×#137 | C23 | 1 | 12 | yes | — |
| 184 | C2×#137 | C23 | 1 | 6 | yes | — |
| 185 | C2×#137 | C23 | 1 | 12 | yes | complemented |
| 186 | C2×#137 | C23 | 1 | 6 | yes | complemented |
| 187 | C2×#137 | C23 | 1 | 6 | yes | complemented |
| 188 | C2×AGL(1,ℤ/8) | — | 2 | 24 | no | — |
| 189 | C2×AGL(1,ℤ/8) | — | 2 | 12 | no | — |
| 190 | C2×AGL(1,ℤ/8) | C23 | 1 | 12 | yes | — |
| 191 | C2×AGL(1,ℤ/8) | C23 | 1 | 6 | yes | — |
| 192 | C2×#135 | — | 2 | 24 | no | — |
| 193 | C2×#135 | — | 2 | 24 | no | — |
| 194 | C2×#135 | — | 2 | 12 | no | — |
| 195 | C2×#135 | — | 2 | 12 | no | — |
| 196 | C2×#135 | C23 | 1 | 12 | yes | — |
| 197 | C2×#135 | C23 | 1 | 6 | yes | — |
| 198 | C2×#135 | C23 | 1 | 6 | yes | complemented |
| 199 | C22×Q16 | — | 2 | 12 | no | — |
| 200 | C22×Q16 | C23 | 1 | 6 | yes | complemented |
| 201 | C22×SD16 | — | 2 | 12 | no | — |
| 202 | C22×SD16 | C23 | 1 | 6 | yes | — |
| 203 | #568 | — | 2 | 8 | no | — |
| 204 | #568 | — | 2 | 8 | no | — |
| 205 | #568 | C23 | 1 | 12 | yes | — |
| 206 | #568 | C23 | 1 | 2 | yes | — |
| 207 | #568 | C23 | 1 | 2 | yes | — |
| 208 | #568 | C23 | 1 | 12 | yes | complemented |
| 209 | C2×#131 | — | 2 | 8 | no | — |
| 210 | C2×#131 | — | 2 | 8 | no | — |
| 211 | C2×#131 | C23 | 1 | 12 | yes | — |
| 212 | C2×#131 | C23 | 1 | 2 | yes | — |
| 213 | C2×#131 | C23 | 1 | 12 | yes | complemented |
| 214 | D4×Q8 | — | 4 | 1 | no | — |
| 215 | #548 | — | 4 | 1 | no | — |
| 216 | #547 | — | 4 | 3 | no | — |
| 217 | #546 | — | 4 | 3 | no | — |
| 218 | #536 | C23 | 1 | 3 | yes | — |
| 219 | #536 | C23 | 1 | 6 | yes | complemented |
| 220 | #535 | C23 | 1 | 3 | yes | — |
| 221 | #532 | C23 | 1 | 3 | yes | — |
| 222 | #532 | C23 | 1 | 3 | yes | complemented |
| 223 | C2×C4⋊Q8 | C23 | 1 | 3 | yes | complemented |
| 224 | C2×#124 | C23 | 1 | 3 | yes | — |
| 225 | C4×#41 | C23 | 1 | 1 | yes | characteristic |
| 226 | #497 | C23 | 1 | 3 | yes | complemented |
| 227 | #497 | C23 | 1 | 6 | yes | complemented |
| 228 | #497 | C23 | 1 | 12 | yes | complemented |
| 229 | #497 | C23 | 1 | 3 | yes | complemented |
| 230 | #497 | C23 | 1 | 6 | yes | complemented |
| 231 | #496 | C23 | 1 | 1 | yes | characteristic, complemented |
| 232 | #496 | C23 | 1 | 3 | yes | complemented |
| 233 | #496 | C23 | 1 | 6 | yes | complemented |
| 234 | #495 | C23 | 1 | 12 | yes | complemented |
| 235 | #494 | C23 | 1 | 6 | yes | complemented |
| 236 | #492 | C23 | 1 | 6 | yes | complemented |
| 237 | #473 | C23 | 1 | 24 | yes | complemented |
| 238 | #473 | C23 | 1 | 48 | yes | complemented |
| 239 | #473 | C23 | 1 | 24 | yes | complemented |
| 240 | #472 | C23 | 1 | 8 | yes | complemented |
| 241 | #472 | C23 | 1 | 24 | yes | complemented |
| 242 | #471 | C23 | 1 | 24 | yes | complemented |
| 243 | #471 | C23 | 1 | 8 | yes | complemented |
| 244 | #471 | C23 | 1 | 24 | yes | complemented |
| 245 | #471 | C23 | 1 | 24 | yes | complemented |
| 246 | #471 | C23 | 1 | 48 | yes | complemented |
| 247 | #456 | C23 | 1 | 12 | yes | — |
| 248 | #456 | C23 | 1 | 24 | yes | complemented |
| 249 | #456 | C23 | 1 | 48 | yes | complemented |
| 250 | #456 | C23 | 1 | 12 | yes | complemented |
| 251 | #455 | C23 | 1 | 12 | yes | — |
| 252 | #455 | C23 | 1 | 24 | yes | — |
| 253 | #455 | C23 | 1 | 4 | yes | complemented |
| 254 | #455 | C23 | 1 | 24 | yes | complemented |
| 255 | #454 | C23 | 1 | 4 | yes | — |
| 256 | #454 | C23 | 1 | 12 | yes | complemented |
| 257 | #454 | C23 | 1 | 24 | yes | complemented |
| 258 | #454 | C23 | 1 | 24 | yes | complemented |
| 259 | #453 | C23 | 1 | 12 | yes | — |
| 260 | #453 | C23 | 1 | 8 | yes | complemented |
| 261 | #453 | C23 | 1 | 12 | yes | complemented |
| 262 | #444 | C23 | 1 | 8 | yes | complemented |
| 263 | #444 | C23 | 1 | 24 | yes | complemented |
| 264 | #444 | C23 | 1 | 24 | yes | complemented |
| 265 | #444 | C23 | 1 | 24 | yes | complemented |
| 266 | #443 | C23 | 1 | 48 | yes | complemented |
| 267 | #430 | C23 | 1 | 12 | yes | complemented |
| 268 | C2×#108 | C23 | 1 | 12 | yes | complemented |
| 269 | #421 | C23 | 1 | 12 | yes | — |
| 270 | #421 | C23 | 1 | 12 | yes | complemented |
| 271 | C2×#104 | C23 | 1 | 12 | yes | — |
| 272 | C2×#104 | C23 | 1 | 12 | yes | complemented |
| 273 | #413 | C23 | 1 | 6 | yes | — |
| 274 | #413 | C23 | 1 | 6 | yes | complemented |
| 275 | #413 | C23 | 1 | 12 | yes | complemented |
| 276 | C2×#101 | C23 | 1 | 6 | yes | complemented |
| 277 | C2×#101 | C23 | 1 | 12 | yes | complemented |
| 278 | C2×#100 | C23 | 1 | 6 | yes | — |
| 279 | #405 | C23 | 1 | 6 | yes | complemented |
| 280 | C4×M16 | C23 | 1 | 3 | yes | complemented |
| 281 | C2×#97 | C23 | 1 | 3 | yes | complemented |
| 282 | 2−1+4 | — | 2 | 2 | no | — |
| 283 | 2−1+4 | — | 2 | 2 | no | — |
| 284 | 2−1+4 | — | 2 | 24 | no | — |
| 285 | 2−1+4 | — | 2 | 8 | no | — |
| 286 | 2−1+4 | — | 2 | 24 | no | — |
| 287 | 2−1+4 | — | 2 | 8 | no | — |
| 288 | 2−1+4 | — | 2 | 8 | no | — |
| 289 | 2−1+4 | — | 2 | 24 | no | — |
| 290 | 2−1+4 | — | 2 | 12 | no | — |
| 291 | 2−1+4 | — | 2 | 12 | no | — |
| 292 | 2−1+4 | — | 2 | 12 | no | — |
| 293 | 2−1+4 | — | 2 | 12 | no | — |
| 294 | 2−1+4 | — | 4 | 4 | no | — |
| 295 | 2−1+4 | — | 4 | 12 | no | — |
| 296 | 2−1+4 | — | 4 | 6 | no | — |
| 297 | 2−1+4 | — | 4 | 8 | no | — |
| 298 | 2−1+4 | — | 4 | 8 | no | — |
| 299 | 2−1+4 | — | 4 | 8 | no | — |
| 300 | 2−1+4 | — | 4 | 24 | no | — |
| 301 | 2−1+4 | — | 4 | 12 | no | — |
| 302 | 2−1+4 | C2×D4 | 1 | 8 | yes | — |
| 303 | 2−1+4 | C2×D4 | 1 | 8 | yes | — |
| 304 | 2−1+4 | C24 | 1 | 24 | yes | — |
| 305 | 2−1+4 | C24 | 1 | 4 | yes | — |
| 306 | 2−1+4 | C24 | 1 | 12 | yes | — |
| 307 | H(5,𝔽2) | — | 2 | 6 | no | — |
| 308 | H(5,𝔽2) | — | 2 | 6 | no | — |
| 309 | H(5,𝔽2) | — | 2 | 24 | no | — |
| 310 | H(5,𝔽2) | — | 2 | 8 | no | — |
| 311 | H(5,𝔽2) | — | 2 | 12 | no | — |
| 312 | H(5,𝔽2) | — | 2 | 12 | no | — |
| 313 | H(5,𝔽2) | — | 2 | 12 | no | — |
| 314 | H(5,𝔽2) | — | 2 | 12 | no | — |
| 315 | H(5,𝔽2) | — | 4 | 6 | no | — |
| 316 | H(5,𝔽2) | — | 4 | 12 | no | — |
| 317 | H(5,𝔽2) | — | 4 | 6 | no | — |
| 318 | H(5,𝔽2) | — | 4 | 24 | no | — |
| 319 | H(5,𝔽2) | — | 4 | 12 | no | — |
| 320 | H(5,𝔽2) | — | 4 | 6 | no | — |
| 321 | H(5,𝔽2) | — | 4 | 24 | no | — |
| 322 | H(5,𝔽2) | — | 4 | 4 | no | — |
| 323 | H(5,𝔽2) | C2×D4 | 1 | 8 | yes | — |
| 324 | H(5,𝔽2) | C2×D4 | 1 | 8 | yes | — |
| 325 | H(5,𝔽2) | C24 | 1 | 8 | yes | — |
| 326 | H(5,𝔽2) | C24 | 1 | 12 | yes | — |
| 327 | H(5,𝔽2) | C24 | 1 | 4 | yes | — |
| 328 | C2×#41 | — | 2 | 8 | no | — |
| 329 | C2×#41 | — | 2 | 8 | no | — |
| 330 | C2×#41 | — | 2 | 1 | no | — |
| 331 | C2×#41 | — | 2 | 3 | no | — |
| 332 | C2×#41 | — | 2 | 6 | no | — |
| 333 | C2×#41 | — | 2 | 24 | no | — |
| 334 | C2×#41 | — | 2 | 24 | no | — |
| 335 | C2×#41 | — | 2 | 24 | no | — |
| 336 | C2×#41 | — | 2 | 24 | no | — |
| 337 | C2×#41 | — | 2 | 12 | no | — |
| 338 | C2×#41 | — | 2 | 12 | no | — |
| 339 | C2×#41 | — | 2 | 12 | no | — |
| 340 | C2×#41 | — | 2 | 12 | no | — |
| 341 | C2×#41 | — | 4 | 12 | no | — |
| 342 | C2×#41 | — | 4 | 6 | no | — |
| 343 | C2×#41 | — | 4 | 6 | no | — |
| 344 | C2×#41 | — | 4 | 12 | no | — |
| 345 | C2×#41 | — | 4 | 6 | no | — |
| 346 | C2×#41 | — | 4 | 24 | no | — |
| 347 | C2×#41 | — | 4 | 24 | no | — |
| 348 | C2×#41 | — | 4 | 24 | no | — |
| 349 | C2×#41 | — | 4 | 8 | no | — |
| 350 | C2×#41 | — | 4 | 12 | no | — |
| 351 | C2×#41 | — | 4 | 8 | no | — |
| 352 | C2×#41 | — | 4 | 4 | no | — |
| 353 | C2×#41 | C24 | 1 | 12 | yes | — |
| 354 | C2×#41 | C24 | 1 | 12 | yes | — |
| 355 | C2×#41 | C24 | 1 | 3 | yes | — |
| 356 | C2×#41 | C24 | 1 | 3 | yes | — |
| 357 | C2×#41 | C24 | 1 | 6 | yes | — |
| 358 | C2×#41 | C24 | 1 | 1 | yes | characteristic |
| 359 | C22×Q8 | — | 2 | 1 | no | — |
| 360 | C22×Q8 | — | 2 | 2 | no | — |
| 361 | C22×Q8 | — | 2 | 12 | no | — |
| 362 | C22×Q8 | — | 2 | 12 | no | — |
| 363 | C22×Q8 | — | 2 | 12 | no | — |
| 364 | C22×Q8 | — | 4 | 4 | no | — |
| 365 | C22×Q8 | — | 4 | 8 | no | — |
| 366 | C22×Q8 | C24 | 1 | 3 | yes | — |
| 367 | C22×Q8 | C24 | 1 | 6 | yes | — |
| 368 | C22×D4 | — | 2 | 12 | no | — |
| 369 | C22×D4 | — | 2 | 3 | no | — |
| 370 | C22×D4 | — | 4 | 6 | no | — |
| 371 | C22×D4 | — | 4 | 12 | no | — |
| 372 | C22×D4 | C24 | 1 | 3 | yes | — |
| 373 | #137 | — | 2 | 24 | no | — |
| 374 | #137 | — | 2 | 24 | no | — |
| 375 | #137 | — | 2 | 24 | no | — |
| 376 | #137 | — | 2 | 12 | no | — |
| 377 | #137 | — | 2 | 12 | no | — |
| 378 | #137 | — | 2 | 12 | no | — |
| 379 | #137 | — | 2 | 12 | no | — |
| 380 | #137 | — | 2 | 24 | no | — |
| 381 | #137 | — | 2 | 48 | no | — |
| 382 | #137 | — | 2 | 24 | no | — |
| 383 | #137 | — | 2 | 24 | no | — |
| 384 | #137 | — | 2 | 8 | no | — |
| 385 | #137 | — | 2 | 24 | no | — |
| 386 | #137 | — | 2 | 24 | no | — |
| 387 | #137 | — | 2 | 48 | no | — |
| 388 | #137 | — | 2 | 24 | no | — |
| 389 | #137 | — | 2 | 48 | no | — |
| 390 | #137 | — | 2 | 24 | no | — |
| 391 | #137 | — | 2 | 24 | no | — |
| 392 | #137 | — | 2 | 24 | no | — |
| 393 | #137 | — | 2 | 24 | no | — |
| 394 | #137 | C2×D4 | 1 | 24 | yes | — |
| 395 | #137 | C2×D4 | 1 | 24 | yes | — |
| 396 | #137 | C24 | 1 | 24 | yes | — |
| 397 | #137 | C24 | 1 | 24 | yes | — |
| 398 | #137 | C24 | 1 | 24 | yes | — |
| 399 | #137 | C24 | 1 | 8 | yes | — |
| 400 | AGL(1,ℤ/8) | — | 2 | 24 | no | — |
| 401 | AGL(1,ℤ/8) | — | 2 | 12 | no | — |
| 402 | AGL(1,ℤ/8) | — | 2 | 12 | no | — |
| 403 | AGL(1,ℤ/8) | — | 2 | 12 | no | — |
| 404 | AGL(1,ℤ/8) | — | 2 | 12 | no | — |
| 405 | AGL(1,ℤ/8) | — | 2 | 24 | no | — |
| 406 | AGL(1,ℤ/8) | — | 2 | 24 | no | — |
| 407 | AGL(1,ℤ/8) | — | 2 | 8 | no | — |
| 408 | AGL(1,ℤ/8) | — | 2 | 8 | no | — |
| 409 | AGL(1,ℤ/8) | — | 2 | 24 | no | — |
| 410 | AGL(1,ℤ/8) | — | 2 | 48 | no | — |
| 411 | AGL(1,ℤ/8) | — | 2 | 8 | no | — |
| 412 | AGL(1,ℤ/8) | — | 2 | 24 | no | — |
| 413 | AGL(1,ℤ/8) | — | 2 | 24 | no | — |
| 414 | AGL(1,ℤ/8) | — | 2 | 24 | no | — |
| 415 | AGL(1,ℤ/8) | C2×D4 | 1 | 24 | yes | — |
| 416 | AGL(1,ℤ/8) | C2×D4 | 1 | 24 | yes | — |
| 417 | AGL(1,ℤ/8) | C24 | 1 | 24 | yes | — |
| 418 | AGL(1,ℤ/8) | C24 | 1 | 8 | yes | — |
| 419 | AGL(1,ℤ/8) | C24 | 1 | 8 | yes | — |
| 420 | AGL(1,ℤ/8) | C24 | 1 | 8 | yes | — |
| 421 | #135 | — | 2 | 24 | no | — |
| 422 | #135 | — | 2 | 24 | no | — |
| 423 | #135 | — | 2 | 24 | no | — |
| 424 | #135 | — | 2 | 24 | no | — |
| 425 | #135 | — | 2 | 8 | no | — |
| 426 | #135 | — | 2 | 24 | no | — |
| 427 | #135 | — | 2 | 24 | no | — |
| 428 | #135 | — | 2 | 8 | no | — |
| 429 | #135 | — | 2 | 48 | no | — |
| 430 | #135 | — | 2 | 24 | no | — |
| 431 | #135 | — | 2 | 24 | no | — |
| 432 | #135 | — | 2 | 24 | no | — |
| 433 | #135 | — | 2 | 24 | no | — |
| 434 | #135 | — | 2 | 48 | no | — |
| 435 | #135 | — | 2 | 12 | no | — |
| 436 | #135 | — | 2 | 12 | no | — |
| 437 | #135 | — | 2 | 12 | no | — |
| 438 | #135 | — | 2 | 12 | no | — |
| 439 | #135 | C2×D4 | 1 | 24 | yes | — |
| 440 | #135 | C2×D4 | 1 | 24 | yes | — |
| 441 | #135 | C24 | 1 | 8 | yes | — |
| 442 | #135 | C24 | 1 | 24 | yes | — |
| 443 | C2×Q16 | — | 2 | 12 | no | — |
| 444 | C2×Q16 | — | 2 | 12 | no | — |
| 445 | C2×Q16 | — | 2 | 12 | no | — |
| 446 | C2×Q16 | — | 2 | 24 | no | — |
| 447 | C2×Q16 | — | 2 | 48 | no | — |
| 448 | C2×Q16 | — | 2 | 24 | no | — |
| 449 | C2×Q16 | — | 2 | 12 | no | — |
| 450 | C2×Q16 | — | 2 | 12 | no | — |
| 451 | C2×Q16 | C2×D4 | 1 | 12 | yes | — |
| 452 | C2×Q16 | C24 | 1 | 6 | yes | — |
| 453 | C2×Q16 | C24 | 1 | 12 | yes | — |
| 454 | C2×Q16 | C24 | 1 | 6 | yes | — |
| 455 | C2×SD16 | — | 2 | 12 | no | — |
| 456 | C2×SD16 | — | 2 | 12 | no | — |
| 457 | C2×SD16 | — | 2 | 12 | no | — |
| 458 | C2×SD16 | — | 2 | 12 | no | — |
| 459 | C2×SD16 | — | 2 | 24 | no | — |
| 460 | C2×SD16 | — | 2 | 48 | no | — |
| 461 | C2×SD16 | — | 2 | 8 | no | — |
| 462 | C2×SD16 | — | 2 | 24 | no | — |
| 463 | C2×SD16 | — | 2 | 24 | no | — |
| 464 | C2×SD16 | — | 2 | 12 | no | — |
| 465 | C2×SD16 | — | 2 | 12 | no | — |
| 466 | C2×SD16 | C2×D4 | 1 | 12 | yes | — |
| 467 | C2×SD16 | C2×D4 | 1 | 12 | yes | — |
| 468 | C2×SD16 | C24 | 1 | 6 | yes | — |
| 469 | C2×SD16 | C24 | 1 | 12 | yes | — |
| 470 | C2×SD16 | C24 | 1 | 2 | yes | — |
| 471 | C2×SD16 | C24 | 1 | 6 | yes | — |
| 472 | C2×SD16 | C24 | 1 | 6 | yes | — |
| 473 | C2×D8 | — | 2 | 12 | no | — |
| 474 | C2×D8 | — | 2 | 8 | no | — |
| 475 | C2×D8 | — | 2 | 24 | no | — |
| 476 | C2×D8 | C2×D4 | 1 | 12 | yes | — |
| 477 | C2×D8 | C24 | 1 | 6 | yes | — |
| 478 | C2×D8 | C24 | 1 | 2 | yes | — |
| 479 | #131 | — | 2 | 8 | no | — |
| 480 | #131 | — | 2 | 8 | no | — |
| 481 | #131 | — | 2 | 24 | no | — |
| 482 | #131 | — | 2 | 24 | no | — |
| 483 | #131 | — | 2 | 12 | no | — |
| 484 | #131 | — | 2 | 12 | no | — |
| 485 | #131 | — | 2 | 12 | no | — |
| 486 | #131 | — | 2 | 12 | no | — |
| 487 | #131 | C2×D4 | 1 | 8 | yes | — |
| 488 | #131 | C2×D4 | 1 | 8 | yes | — |
| 489 | #131 | C24 | 1 | 8 | yes | — |
| 490 | #131 | C24 | 1 | 24 | yes | — |
| 491 | #131 | C24 | 1 | 8 | yes | — |
| 492 | #131 | C24 | 1 | 24 | yes | — |
| 493 | C2×M16 | — | 2 | 24 | no | — |
| 494 | C2×M16 | — | 2 | 24 | no | — |
| 495 | C2×M16 | — | 2 | 12 | no | — |
| 496 | C2×M16 | — | 2 | 12 | no | — |
| 497 | C2×M16 | C24 | 1 | 12 | yes | — |
| 498 | C2×M16 | C24 | 1 | 12 | yes | — |
| 499 | C2×M16 | C24 | 1 | 6 | yes | — |
| 500 | C22×C8 | — | 2 | 12 | no | — |
| 501 | C22×C8 | — | 2 | 12 | no | — |
| 502 | C22×C8 | C24 | 1 | 6 | yes | — |
| 503 | C4⋊Q8 | — | 4 | 3 | no | — |
| 504 | C4⋊Q8 | C24 | 1 | 3 | yes | — |
| 505 | C4⋊Q8 | C24 | 1 | 6 | yes | — |
| 506 | C4⋊Q8 | C24 | 1 | 3 | yes | — |
| 507 | #127 | C24 | 1 | 3 | yes | — |
| 508 | #127 | C24 | 1 | 1 | yes | characteristic |
| 509 | #124 | — | 4 | 3 | no | — |
| 510 | #124 | C24 | 1 | 3 | yes | — |
| 511 | #124 | C24 | 1 | 6 | yes | — |
| 512 | #124 | C24 | 1 | 1 | yes | characteristic |
| 513 | #124 | C24 | 1 | 6 | yes | — |
| 514 | #123 | — | 4 | 3 | no | — |
| 515 | #123 | — | 4 | 6 | no | — |
| 516 | C22⋊Q8 | — | 4 | 3 | no | — |
| 517 | C22⋊Q8 | — | 4 | 6 | no | — |
| 518 | #121 | — | 4 | 3 | no | — |
| 519 | #121 | — | 4 | 3 | no | — |
| 520 | #121 | — | 4 | 3 | no | — |
| 521 | #120 | — | 4 | 3 | no | — |
| 522 | C4×Q8 | — | 2 | 1 | no | — |
| 523 | C4×D4 | — | 2 | 3 | no | — |
| 524 | C4×D4 | — | 4 | 3 | no | — |
| 525 | C4×D4 | — | 4 | 3 | no | — |
| 526 | #117 | C24 | 1 | 3 | yes | — |
| 527 | C2×C4⋊C4 | — | 4 | 3 | no | — |
| 528 | C2×C22⋊C4 | — | 4 | 3 | no | — |
| 529 | C2×C42 | C24 | 1 | 3 | yes | — |
| 530 | #108 | C24 | 1 | 8 | yes | — |
| 531 | #108 | C24 | 1 | 24 | yes | — |
| 532 | #104 | C24 | 1 | 8 | yes | — |
| 533 | #104 | C24 | 1 | 24 | yes | — |
| 534 | #104 | C24 | 1 | 8 | yes | — |
| 535 | #104 | C24 | 1 | 24 | yes | — |
| 536 | #101 | C24 | 1 | 12 | yes | — |
| 537 | #101 | C24 | 1 | 24 | yes | — |
| 538 | #101 | C24 | 1 | 4 | yes | — |
| 539 | #100 | C24 | 1 | 12 | yes | — |
| 540 | #100 | C24 | 1 | 4 | yes | — |
| 541 | #100 | C24 | 1 | 8 | yes | — |
| 542 | #97 | C24 | 1 | 1 | yes | characteristic |
| 543 | #97 | C24 | 1 | 3 | yes | — |
| 544 | #97 | C24 | 1 | 6 | yes | — |
| 545 | C4×C8 | C24 | 1 | 6 | yes | — |
| 546 | C24 | — | 2 | 3 | no | — |
| 547 | C24 | — | 4 | 6 | no | — |
| 548 | #41 | — | 2 | 8 | no | — |
| 549 | #41 | — | 2 | 8 | no | — |
| 550 | #41 | — | 2 | 24 | no | — |
| 551 | #41 | — | 2 | 24 | no | — |
| 552 | #41 | — | 2 | 12 | no | — |
| 553 | #41 | — | 2 | 12 | no | — |
| 554 | #41 | — | 2 | 12 | no | — |
| 555 | #41 | — | 2 | 12 | no | — |
| 556 | #41 | — | 2 | 8 | no | — |
| 557 | #41 | — | 2 | 24 | no | — |
| 558 | #41 | — | 2 | 8 | no | — |
| 559 | #41 | — | 2 | 8 | no | — |
| 560 | #41 | — | 2 | 24 | no | — |
| 561 | #41 | — | 2 | 8 | no | — |
| 562 | #41 | — | 2 | 24 | no | — |
| 563 | #41 | — | 2 | 24 | no | — |
| 564 | #41 | — | 2 | 12 | no | — |
| 565 | #41 | — | 2 | 12 | no | — |
| 566 | #41 | — | 2 | 12 | no | — |
| 567 | #41 | — | 2 | 12 | no | — |
| 568 | #41 | — | 4 | 12 | no | — |
| 569 | #41 | — | 4 | 24 | no | — |
| 570 | #41 | — | 4 | 12 | no | — |
| 571 | #41 | — | 4 | 4 | no | — |
| 572 | #41 | — | 4 | 12 | no | — |
| 573 | #41 | — | 4 | 24 | no | — |
| 574 | #41 | — | 4 | 24 | no | — |
| 575 | #41 | — | 4 | 24 | no | — |
| 576 | #41 | — | 4 | 24 | no | — |
| 577 | #41 | — | 4 | 24 | no | — |
| 578 | #41 | — | 4 | 24 | no | — |
| 579 | #41 | — | 4 | 24 | no | — |
| 580 | #41 | — | 4 | 24 | no | — |
| 581 | #41 | — | 4 | 24 | no | — |
| 582 | #41 | — | 4 | 48 | no | — |
| 583 | #41 | — | 4 | 24 | no | — |
| 584 | #41 | — | 4 | 12 | no | — |
| 585 | #41 | — | 4 | 12 | no | — |
| 586 | #41 | — | 4 | 12 | no | — |
| 587 | #41 | — | 4 | 12 | no | — |
| 588 | #41 | — | 4 | 4 | no | — |
| 589 | #41 | — | 4 | 12 | no | — |
| 590 | #41 | — | 4 | 24 | no | — |
| 591 | #41 | C22×D4 | 1 | 24 | yes | — |
| 592 | #41 | C22×D4 | 1 | 24 | yes | — |
| 593 | #41 | C22×D4 | 1 | 8 | yes | — |
| 594 | #41 | C25 | 1 | 8 | yes | — |
| 595 | #41 | C25 | 1 | 8 | yes | — |
| 596 | C2×Q8 | — | 2 | 8 | no | — |
| 597 | C2×Q8 | — | 2 | 8 | no | — |
| 598 | C2×Q8 | — | 2 | 3 | no | — |
| 599 | C2×Q8 | — | 2 | 6 | no | — |
| 600 | C2×Q8 | — | 2 | 24 | no | — |
| 601 | C2×Q8 | — | 2 | 24 | no | — |
| 602 | C2×Q8 | — | 2 | 24 | no | — |
| 603 | C2×Q8 | — | 2 | 8 | no | — |
| 604 | C2×Q8 | — | 2 | 12 | no | — |
| 605 | C2×Q8 | — | 2 | 12 | no | — |
| 606 | C2×Q8 | — | 2 | 12 | no | — |
| 607 | C2×Q8 | — | 4 | 12 | no | — |
| 608 | C2×Q8 | — | 4 | 6 | no | — |
| 609 | C2×Q8 | — | 4 | 24 | no | — |
| 610 | C2×Q8 | — | 4 | 24 | no | — |
| 611 | C2×Q8 | — | 4 | 24 | no | — |
| 612 | C2×Q8 | — | 4 | 6 | no | — |
| 613 | C2×Q8 | — | 4 | 12 | no | — |
| 614 | C2×Q8 | — | 4 | 6 | no | — |
| 615 | C2×Q8 | — | 4 | 4 | no | — |
| 616 | C2×Q8 | — | 4 | 8 | no | — |
| 617 | C2×Q8 | C22×D4 | 1 | 12 | yes | — |
| 618 | C2×Q8 | C22×D4 | 1 | 12 | yes | — |
| 619 | C2×Q8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 620 | C2×Q8 | C25 | 1 | 3 | yes | — |
| 621 | C2×Q8 | C25 | 1 | 6 | yes | — |
| 622 | C2×Q8 | C25 | 1 | 1 | yes | characteristic |
| 623 | C2×D4 | — | 2 | 12 | no | — |
| 624 | C2×D4 | — | 2 | 12 | no | — |
| 625 | C2×D4 | — | 2 | 24 | no | — |
| 626 | C2×D4 | — | 2 | 24 | no | — |
| 627 | C2×D4 | — | 2 | 8 | no | — |
| 628 | C2×D4 | — | 2 | 24 | no | — |
| 629 | C2×D4 | — | 2 | 8 | no | — |
| 630 | C2×D4 | — | 2 | 8 | no | — |
| 631 | C2×D4 | — | 2 | 3 | no | — |
| 632 | C2×D4 | — | 2 | 3 | no | — |
| 633 | C2×D4 | — | 2 | 6 | no | — |
| 634 | C2×D4 | — | 2 | 12 | no | — |
| 635 | C2×D4 | — | 2 | 3 | no | — |
| 636 | C2×D4 | — | 4 | 24 | no | — |
| 637 | C2×D4 | — | 4 | 12 | no | — |
| 638 | C2×D4 | — | 4 | 1 | no | — |
| 639 | C2×D4 | — | 4 | 3 | no | — |
| 640 | C2×D4 | — | 4 | 12 | no | — |
| 641 | C2×D4 | — | 4 | 8 | no | — |
| 642 | C2×D4 | — | 4 | 4 | no | — |
| 643 | C2×D4 | — | 4 | 24 | no | — |
| 644 | C2×D4 | — | 4 | 6 | no | — |
| 645 | C2×D4 | — | 4 | 12 | no | — |
| 646 | C2×D4 | — | 4 | 6 | no | — |
| 647 | C2×D4 | — | 4 | 24 | no | — |
| 648 | C2×D4 | — | 4 | 24 | no | — |
| 649 | C2×D4 | — | 4 | 24 | no | — |
| 650 | C2×D4 | — | 4 | 24 | no | — |
| 651 | C2×D4 | — | 4 | 6 | no | — |
| 652 | C2×D4 | — | 4 | 12 | no | — |
| 653 | C2×D4 | — | 4 | 12 | no | — |
| 654 | C2×D4 | C22×D4 | 1 | 12 | yes | — |
| 655 | C2×D4 | C22×D4 | 1 | 12 | yes | — |
| 656 | C2×D4 | H(5,𝔽2) | 1 | 3 | yes | — |
| 657 | C2×D4 | C25 | 1 | 2 | yes | — |
| 658 | C2×D4 | C25 | 1 | 3 | yes | — |
| 659 | C2×D4 | C25 | 1 | 1 | yes | characteristic |
| 660 | C22×C4 | — | 2 | 12 | no | — |
| 661 | C22×C4 | — | 2 | 12 | no | — |
| 662 | C22×C4 | — | 2 | 3 | no | — |
| 663 | C22×C4 | — | 2 | 6 | no | — |
| 664 | C22×C4 | — | 2 | 3 | no | — |
| 665 | C22×C4 | — | 2 | 3 | no | — |
| 666 | C22×C4 | — | 2 | 3 | no | — |
| 667 | C22×C4 | — | 2 | 6 | no | — |
| 668 | C22×C4 | — | 4 | 6 | no | — |
| 669 | C22×C4 | — | 4 | 12 | no | — |
| 670 | C22×C4 | — | 4 | 24 | no | — |
| 671 | C22×C4 | — | 4 | 12 | no | — |
| 672 | C22×C4 | — | 4 | 12 | no | — |
| 673 | C22×C4 | — | 4 | 12 | no | — |
| 674 | C22×C4 | — | 4 | 12 | no | — |
| 675 | C22×C4 | C25 | 1 | 3 | yes | — |
| 676 | Q16 | — | 2 | 24 | no | — |
| 677 | Q16 | — | 2 | 24 | no | — |
| 678 | Q16 | — | 2 | 24 | no | — |
| 679 | Q16 | — | 2 | 8 | no | — |
| 680 | Q16 | — | 2 | 6 | no | — |
| 681 | Q16 | — | 2 | 6 | no | — |
| 682 | Q16 | — | 2 | 24 | no | — |
| 683 | Q16 | — | 2 | 12 | no | — |
| 684 | Q16 | C22×D4 | 1 | 8 | yes | — |
| 685 | Q16 | C22×D4 | 1 | 24 | yes | — |
| 686 | SD16 | — | 2 | 24 | no | — |
| 687 | SD16 | — | 2 | 8 | no | — |
| 688 | SD16 | — | 2 | 8 | no | — |
| 689 | SD16 | — | 2 | 8 | no | — |
| 690 | SD16 | — | 2 | 24 | no | — |
| 691 | SD16 | — | 2 | 24 | no | — |
| 692 | SD16 | — | 2 | 24 | no | — |
| 693 | SD16 | — | 2 | 8 | no | — |
| 694 | SD16 | — | 2 | 6 | no | — |
| 695 | SD16 | — | 2 | 2 | no | — |
| 696 | SD16 | — | 2 | 6 | no | — |
| 697 | SD16 | — | 2 | 24 | no | — |
| 698 | SD16 | — | 2 | 12 | no | — |
| 699 | SD16 | — | 2 | 12 | no | — |
| 700 | SD16 | — | 2 | 2 | no | — |
| 701 | SD16 | C22×D4 | 1 | 8 | yes | — |
| 702 | SD16 | C22×D4 | 1 | 24 | yes | — |
| 703 | SD16 | C22×D4 | 1 | 8 | yes | — |
| 704 | SD16 | C22×D4 | 1 | 24 | yes | — |
| 705 | D8 | — | 2 | 8 | no | — |
| 706 | D8 | — | 2 | 24 | no | — |
| 707 | D8 | — | 2 | 8 | no | — |
| 708 | D8 | — | 2 | 8 | no | — |
| 709 | D8 | — | 2 | 2 | no | — |
| 710 | D8 | — | 2 | 12 | no | — |
| 711 | D8 | — | 2 | 2 | no | — |
| 712 | D8 | C22×D4 | 1 | 8 | yes | — |
| 713 | D8 | C22×D4 | 1 | 24 | yes | — |
| 714 | M16 | — | 2 | 12 | no | — |
| 715 | M16 | — | 2 | 12 | no | — |
| 716 | M16 | — | 2 | 8 | no | — |
| 717 | M16 | — | 2 | 24 | no | — |
| 718 | M16 | — | 2 | 8 | no | — |
| 719 | M16 | — | 2 | 24 | no | — |
| 720 | M16 | C22×D4 | 1 | 24 | yes | — |
| 721 | M16 | C25 | 1 | 8 | yes | — |
| 722 | M16 | C25 | 1 | 8 | yes | — |
| 723 | C2×C8 | — | 2 | 12 | no | — |
| 724 | C2×C8 | — | 2 | 12 | no | — |
| 725 | C2×C8 | — | 2 | 8 | no | — |
| 726 | C2×C8 | — | 2 | 8 | no | — |
| 727 | C2×C8 | — | 2 | 24 | no | — |
| 728 | C2×C8 | — | 2 | 24 | no | — |
| 729 | C2×C8 | C22×D4 | 1 | 12 | yes | — |
| 730 | C2×C8 | C22×D4 | 1 | 12 | yes | — |
| 731 | C2×C8 | C25 | 1 | 6 | yes | — |
| 732 | C2×C8 | C25 | 1 | 2 | yes | — |
| 733 | C4⋊C4 | — | 2 | 3 | no | — |
| 734 | C4⋊C4 | — | 4 | 3 | no | — |
| 735 | C4⋊C4 | — | 4 | 6 | no | — |
| 736 | C4⋊C4 | — | 4 | 3 | no | — |
| 737 | C22⋊C4 | — | 2 | 3 | no | — |
| 738 | C22⋊C4 | — | 4 | 3 | no | — |
| 739 | C22⋊C4 | — | 4 | 6 | no | — |
| 740 | C22⋊C4 | — | 4 | 1 | no | — |
| 741 | C22⋊C4 | — | 4 | 6 | no | — |
| 742 | C42 | — | 2 | 3 | no | — |
| 743 | C42 | C25 | 1 | 3 | yes | — |
| 744 | C42 | C25 | 1 | 1 | yes | characteristic |
| 745 | C23 | — | 2 | 12 | no | — |
| 746 | C23 | — | 2 | 12 | no | — |
| 747 | C23 | — | 2 | 2 | no | — |
| 748 | C23 | — | 2 | 3 | no | — |
| 749 | C23 | — | 2 | 1 | no | — |
| 750 | C23 | — | 4 | 4 | no | — |
| 751 | C23 | — | 4 | 8 | no | — |
| 752 | C23 | — | 4 | 12 | no | — |
| 753 | C23 | — | 4 | 6 | no | — |
| 754 | C23 | — | 16 | 3 | no | — |
| 755 | C23 | — | 32 | 6 | no | — |
| 756 | C23 | C2×H(5,𝔽2) | 1 | 3 | yes | — |
| 757 | Q8 | — | 2 | 12 | no | — |
| 758 | Q8 | — | 2 | 12 | no | — |
| 759 | Q8 | — | 2 | 6 | no | — |
| 760 | Q8 | — | 2 | 6 | no | — |
| 761 | Q8 | — | 2 | 6 | no | — |
| 762 | Q8 | — | 2 | 2 | no | — |
| 763 | Q8 | — | 4 | 24 | no | — |
| 764 | Q8 | — | 4 | 12 | no | — |
| 765 | Q8 | — | 4 | 4 | no | — |
| 766 | Q8 | — | 4 | 6 | no | — |
| 767 | Q8 | — | 4 | 12 | no | — |
| 768 | Q8 | D42 | 1 | 4 | yes | — |
| 769 | Q8 | C23×D4 | 1 | 8 | yes | — |
| 770 | Q8 | C23×D4 | 1 | 8 | yes | — |
| 771 | D4 | — | 2 | 8 | no | — |
| 772 | D4 | — | 2 | 8 | no | — |
| 773 | D4 | — | 2 | 24 | no | — |
| 774 | D4 | — | 2 | 24 | no | — |
| 775 | D4 | — | 2 | 2 | no | — |
| 776 | D4 | — | 2 | 6 | no | — |
| 777 | D4 | — | 2 | 2 | no | — |
| 778 | D4 | — | 2 | 2 | no | — |
| 779 | D4 | — | 2 | 12 | no | — |
| 780 | D4 | — | 2 | 12 | no | — |
| 781 | D4 | — | 4 | 24 | no | — |
| 782 | D4 | — | 4 | 8 | no | — |
| 783 | D4 | — | 4 | 8 | no | — |
| 784 | D4 | — | 4 | 8 | no | — |
| 785 | D4 | — | 4 | 4 | no | — |
| 786 | D4 | — | 4 | 12 | no | — |
| 787 | D4 | — | 4 | 24 | no | — |
| 788 | D4 | — | 4 | 6 | no | — |
| 789 | D4 | — | 4 | 6 | no | — |
| 790 | D4 | — | 4 | 12 | no | — |
| 791 | D4 | — | 4 | 6 | no | — |
| 792 | D4 | — | 8 | 2 | no | — |
| 793 | D4 | — | 16 | 3 | no | — |
| 794 | D4 | D42 | 1 | 12 | yes | — |
| 795 | D4 | C23×D4 | 1 | 8 | yes | — |
| 796 | D4 | C23×D4 | 1 | 8 | yes | — |
| 797 | C2×C4 | — | 2 | 12 | no | — |
| 798 | C2×C4 | — | 2 | 12 | no | — |
| 799 | C2×C4 | — | 2 | 8 | no | — |
| 800 | C2×C4 | — | 2 | 8 | no | — |
| 801 | C2×C4 | — | 2 | 24 | no | — |
| 802 | C2×C4 | — | 2 | 24 | no | — |
| 803 | C2×C4 | — | 2 | 1 | no | — |
| 804 | C2×C4 | — | 2 | 3 | no | — |
| 805 | C2×C4 | — | 2 | 3 | no | — |
| 806 | C2×C4 | — | 2 | 1 | no | — |
| 807 | C2×C4 | — | 2 | 6 | no | — |
| 808 | C2×C4 | — | 4 | 12 | no | — |
| 809 | C2×C4 | — | 4 | 8 | no | — |
| 810 | C2×C4 | — | 4 | 4 | no | — |
| 811 | C2×C4 | — | 4 | 8 | no | — |
| 812 | C2×C4 | — | 4 | 24 | no | — |
| 813 | C2×C4 | — | 4 | 24 | no | — |
| 814 | C2×C4 | — | 4 | 24 | no | — |
| 815 | C2×C4 | — | 4 | 6 | no | — |
| 816 | C2×C4 | — | 4 | 12 | no | — |
| 817 | C2×C4 | — | 4 | 6 | no | — |
| 818 | C2×C4 | — | 4 | 6 | no | — |
| 819 | C2×C4 | — | 4 | 12 | no | — |
| 820 | C2×C4 | — | 8 | 3 | no | — |
| 821 | C2×C4 | C23×D4 | 1 | 12 | yes | — |
| 822 | C2×C4 | C2×H(5,𝔽2) | 1 | 3 | yes | — |
| 823 | C2×C4 | C26 | 1 | 1 | yes | characteristic |
| 824 | C8 | — | 2 | 8 | no | — |
| 825 | C8 | — | 2 | 8 | no | — |
| 826 | C8 | C23×D4 | 1 | 2 | yes | — |
| 827 | C8 | C23×D4 | 1 | 2 | yes | — |
| 828 | C8 | C23×D4 | 1 | 12 | yes | — |
| 829 | C22 | — | 2 | 8 | no | — |
| 830 | C22 | — | 2 | 8 | no | — |
| 831 | C22 | — | 4 | 3 | no | — |
| 832 | C22 | — | 4 | 2 | no | — |
| 833 | C22 | — | 4 | 1 | no | — |
| 834 | C22 | — | 4 | 3 | no | — |
| 835 | C22 | — | 8 | 12 | no | — |
| 836 | C22 | — | 8 | 12 | no | — |
| 837 | C22 | — | 8 | 2 | no | — |
| 838 | C22 | — | 8 | 1 | no | — |
| 839 | C22 | — | 8 | 3 | no | — |
| 840 | C22 | — | 16 | 6 | no | — |
| 841 | C22 | — | 16 | 4 | no | — |
| 842 | C22 | — | 16 | 8 | no | — |
| 843 | C22 | — | 16 | 12 | no | — |
| 844 | C22 | C2×D42 | 1 | 6 | yes | — |
| 845 | C22 | C22×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 846 | C4 | — | 2 | 8 | no | — |
| 847 | C4 | — | 2 | 8 | no | — |
| 848 | C4 | — | 4 | 1 | no | — |
| 849 | C4 | — | 4 | 3 | no | — |
| 850 | C4 | — | 4 | 1 | no | — |
| 851 | C4 | — | 4 | 3 | no | — |
| 852 | C4 | — | 4 | 6 | no | — |
| 853 | C4 | C2×D42 | 1 | 6 | yes | — |
| 854 | C4 | C24×D4 | 1 | 2 | yes | — |
| 855 | C2 | — | 2 | 1 | no | — |
| 856 | C2 | — | 2 | 6 | no | — |
| 857 | C2 | — | 4 | 8 | no | — |
| 858 | C2 | — | 4 | 8 | no | — |
| 859 | C2 | — | 8 | 2 | no | — |
| 860 | C2 | — | 8 | 1 | no | — |
| 861 | C2 | — | 8 | 3 | no | — |
| 862 | C2 | C22×D42 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | C22×D42 |
| commutator, Frattini, cosocle | C2×C4 | C26 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C2×#41 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #63093 | C2 | semidirect |
| 2. #63092 | C2 | semidirect |
| 3. #61111 | C2 | semidirect |
| 4. #61109 | C2 | semidirect |
| 5. #61108 | C2 | semidirect |
| 6. #61107 | C2 | semidirect |
| 7. #61100 | C2 | semidirect |
| 8. C2×#3289 | C2 | semidirect |
| 9. #60651 | C2 | semidirect |
| 10. #60472 | C2 | semidirect |
| 11. #60470 | C2 | semidirect |
| 12. #60391 | C2 | semidirect |
| 13. #60390 | C2 | semidirect |
| 14. #60389 | C2 | semidirect |
| 15. #60184 | C2 | semidirect |
| 16. 2−1+6 | C22 | semidirect |
| 17. 2−1+6 | C22 | semidirect |
| 18. H(7,𝔽2) | C22 | semidirect |
| 22. #3586 | C22 | semidirect |
| 23. #3586 | C22 | semidirect |
| 24. #3586 | C22 | semidirect |
| 25. #3586 | C22 | semidirect |
| 26. #3586 | C22 | semidirect |
| 27. #3586 | C22 | semidirect |
| 29. #3585 | C22 | semidirect |
| 30. #3585 | C22 | semidirect |
| 34. #3584 | C22 | semidirect |
| 35. #3584 | C22 | semidirect |
| 37. C2×#578 | C22 | semidirect |
| 38. C2×#578 | C22 | semidirect |
| 40. C2×#577 | C22 | semidirect |
| 41. C2×#577 | C22 | semidirect |
| 42. #3573 | C22 | semidirect |
| 43. #3573 | C22 | semidirect |
| 44. #3500 | C22 | semidirect |
| 45. #3499 | C22 | semidirect |
| 46. #3293 | C22 | semidirect |
| 47. #3291 | C22 | semidirect |
| 48. #3290 | C22 | semidirect |
| 49. #3289 | C22 | semidirect |
| 50. #3289 | C22 | semidirect |
| 51. #3289 | C22 | semidirect |
| 52. #3289 | C22 | semidirect |
| 53. #3289 | C22 | semidirect |
| 54. #3288 | C22 | semidirect |
| 55. #3288 | C22 | semidirect |
| 56. #3288 | C22 | semidirect |
| 57. #3156 | C22 | semidirect |
| 58. #3154 | C22 | semidirect |
| 59. #3153 | C22 | semidirect |
| 60. #3152 | C22 | semidirect |
| 61. #3150 | C22 | semidirect |
| 62. C2×#497 | C22 | semidirect |
| 63. #3069 | C22 | semidirect |
| 64. #3069 | C22 | semidirect |
| 65. #3069 | C22 | semidirect |
| 66. #3068 | C22 | semidirect |
| 67. #3067 | C22 | semidirect |
| 68. #3067 | C22 | semidirect |
| 69. C2×#473 | C22 | semidirect |
| 70. C2×#471 | C22 | semidirect |
| 71. #3022 | C22 | semidirect |
| 72. #3022 | C22 | semidirect |
| 73. #3021 | C22 | semidirect |
| 74. #3020 | C22 | semidirect |
| 75. #3020 | C22 | semidirect |
| 76. #3019 | C22 | semidirect |
| 77. #3018 | C22 | semidirect |
| 78. #3018 | C22 | semidirect |
| 79. #3018 | C22 | semidirect |
| 80. C2×#456 | C22 | semidirect |
| 81. C2×#454 | C22 | semidirect |
| 82. C2×#455 | C22 | semidirect |
| 83. #2957 | C22 | semidirect |
| 84. #2956 | C22 | semidirect |
| 85. #2955 | C22 | semidirect |
| 86. C2×#444 | C22 | semidirect |
| 87. #2916 | C22 | semidirect |
| 88. #2901 | C22 | semidirect |
| 89. #2901 | C22 | semidirect |
| 90. #2889 | C22 | semidirect |
| 91. #2889 | C22 | semidirect |
| 92. #2888 | C22 | semidirect |
| 93. #2875 | C22 | semidirect |
| 105. #585 | C23 | semidirect |
| 114. C2×2−1+4 | C23 | semidirect |
| 131. #578 | D4 | semidirect |
| 133. #578 | C23 | semidirect |
| 134. #578 | C23 | semidirect |
| 151. #577 | D4 | semidirect |
| 152. #577 | D4 | semidirect |
| 156. #577 | C23 | semidirect |
| 157. #577 | C23 | semidirect |
| 162. #576 | D4 | semidirect |
| 164. #576 | C23 | semidirect |
| 175. #575 | C23 | semidirect |
| 185. C2×#137 | C23 | semidirect |
| 186. C2×#137 | C23 | semidirect |
| 187. C2×#137 | C23 | semidirect |
| 198. C2×#135 | C23 | semidirect |
| 200. C22×Q16 | C23 | semidirect |
| 208. #568 | C23 | semidirect |
| 213. C2×#131 | C23 | semidirect |
| 219. #536 | C23 | semidirect |
| 222. #532 | C23 | semidirect |
| 223. C2×C4⋊Q8 | C23 | semidirect |
| 226. #497 | C23 | semidirect |
| 227. #497 | C23 | semidirect |
| 228. #497 | C23 | semidirect |
| 229. #497 | C23 | semidirect |
| 230. #497 | C23 | semidirect |
| 231. #496 | C23 | semidirect |
| 232. #496 | C23 | semidirect |
| 233. #496 | C23 | semidirect |
| 234. #495 | C23 | semidirect |
| 235. #494 | C23 | semidirect |
| 236. #492 | C23 | semidirect |
| 237. #473 | C23 | semidirect |
| 238. #473 | C23 | semidirect |
| 239. #473 | C23 | semidirect |
| 240. #472 | C23 | semidirect |
| 241. #472 | C23 | semidirect |
| 242. #471 | C23 | semidirect |
| 243. #471 | C23 | semidirect |
| 244. #471 | C23 | semidirect |
| 245. #471 | C23 | semidirect |
| 246. #471 | C23 | semidirect |
| 248. #456 | C23 | semidirect |
| 249. #456 | C23 | semidirect |
| 250. #456 | C23 | semidirect |
| 253. #455 | C23 | semidirect |
| 254. #455 | C23 | semidirect |
| 256. #454 | C23 | semidirect |
| 257. #454 | C23 | semidirect |
| 258. #454 | C23 | semidirect |
| 260. #453 | C23 | semidirect |
| 261. #453 | C23 | semidirect |
| 262. #444 | C23 | semidirect |
| 263. #444 | C23 | semidirect |
| 264. #444 | C23 | semidirect |
| 265. #444 | C23 | semidirect |
| 266. #443 | C23 | semidirect |
| 267. #430 | C23 | semidirect |
| 268. C2×#108 | C23 | semidirect |
| 270. #421 | C23 | semidirect |
| 272. C2×#104 | C23 | semidirect |
| 274. #413 | C23 | semidirect |
| 275. #413 | C23 | semidirect |
| 276. C2×#101 | C23 | semidirect |
| 277. C2×#101 | C23 | semidirect |
| 279. #405 | C23 | semidirect |
| 280. C4×M16 | C23 | semidirect |
| 281. C2×#97 | C23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63093 | 2 |
| #63092 | 2 |
| #61111 | 2 |
| #61109 | 2 |
| #61108 | 2 |
| #61107 | 2 |
| #61100 | 2 |
| C2×#3289 | 2 |
| #60651 | 2 |
| #60472 | 2 |
| #60470 | 2 |
| #60391 | 2 |
| #60390 | 2 |
| #60389 | 2 |
| #60184 | 2 |