Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
10354 conjugacy classes of subgroups.
The subgroup lattice has 807 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#3584 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #62853 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #61086 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #61084 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #61080 | C2 | 1 | 8 | yes | maximal, complemented |
| 6 | #61062 | C2 | 1 | 16 | yes | maximal, complemented |
| 7 | #61057 | C2 | 1 | 8 | yes | maximal, complemented |
| 8 | #61056 | C2 | 1 | 8 | yes | maximal, complemented |
| 9 | #60643 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C2×#3061 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #60425 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #60371 | C2 | 1 | 4 | yes | maximal, complemented |
| 13 | C2×#2951 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #60140 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C2×#585 | C22 | 1 | 4 | yes | complemented |
| 16 | #3584 | — | 2 | 32 | no | — |
| 17 | C2×#578 | C22 | 1 | 4 | yes | complemented |
| 18 | C2×#578 | C22 | 1 | 4 | yes | complemented |
| 19 | C2×#577 | C22 | 1 | 8 | yes | complemented |
| 20 | C2×#577 | C22 | 1 | 8 | yes | complemented |
| 21 | C2×#576 | C22 | 1 | 4 | yes | complemented |
| 22 | C2×#576 | C22 | 1 | 4 | yes | complemented |
| 23 | C2×#575 | C22 | 1 | 4 | yes | complemented |
| 24 | C2×#575 | C22 | 1 | 8 | yes | complemented |
| 25 | C2×#575 | C22 | 1 | 2 | yes | complemented |
| 26 | C22×#135 | C22 | 1 | 1 | yes | characteristic |
| 27 | C22×#135 | C22 | 1 | 2 | yes | complemented |
| 28 | C22×#135 | C22 | 1 | 8 | yes | complemented |
| 29 | C22×#131 | C22 | 1 | 2 | yes | complemented |
| 30 | #3497 | C22 | 1 | 8 | yes | complemented |
| 31 | #3496 | — | 2 | 8 | no | — |
| 32 | #3496 | C22 | 1 | 8 | yes | complemented |
| 33 | #3489 | — | 2 | 8 | no | — |
| 34 | #3489 | C22 | 1 | 16 | yes | complemented |
| 35 | #3488 | — | 2 | 8 | no | — |
| 36 | #3488 | C22 | 1 | 16 | yes | complemented |
| 37 | #3449 | — | 2 | 4 | no | — |
| 38 | #3449 | C22 | 1 | 1 | yes | characteristic |
| 39 | #3449 | C22 | 1 | 2 | yes | complemented |
| 40 | C2×#537 | — | 2 | 4 | no | — |
| 41 | C2×#537 | C22 | 1 | 4 | yes | complemented |
| 42 | C2×#520 | C22 | 1 | 2 | yes | complemented |
| 43 | #3287 | C22 | 1 | 8 | yes | complemented |
| 44 | D4×Q16 | C22 | 1 | 8 | yes | complemented |
| 45 | #3285 | C22 | 1 | 16 | yes | complemented |
| 46 | #3283 | C22 | 1 | 8 | yes | complemented |
| 47 | #3280 | C22 | 1 | 16 | yes | complemented |
| 48 | D4×D8 | C22 | 1 | 8 | yes | complemented |
| 49 | #3278 | C22 | 1 | 16 | yes | complemented |
| 50 | #3277 | C22 | 1 | 16 | yes | complemented |
| 51 | #3273 | C22 | 1 | 16 | yes | complemented |
| 52 | #3272 | C22 | 1 | 16 | yes | complemented |
| 53 | #3269 | C22 | 1 | 32 | yes | complemented |
| 54 | #3268 | C22 | 1 | 32 | yes | complemented |
| 55 | #3266 | C22 | 1 | 32 | yes | complemented |
| 56 | #3265 | C22 | 1 | 32 | yes | complemented |
| 57 | #3156 | C22 | 1 | 4 | yes | complemented |
| 58 | #3155 | C22 | 1 | 4 | yes | complemented |
| 59 | #3154 | C22 | 1 | 8 | yes | complemented |
| 60 | #3150 | C22 | 1 | 4 | yes | complemented |
| 61 | #3147 | C22 | 1 | 4 | yes | complemented |
| 62 | #3061 | C22 | 1 | 8 | yes | complemented |
| 63 | #3061 | C22 | 1 | 8 | yes | complemented |
| 64 | #3061 | C22 | 1 | 8 | yes | complemented |
| 65 | #3061 | C22 | 1 | 8 | yes | complemented |
| 66 | C2×#468 | C22 | 1 | 8 | yes | complemented |
| 67 | C2×#467 | C22 | 1 | 4 | yes | complemented |
| 68 | C2×#466 | C22 | 1 | 4 | yes | complemented |
| 69 | #3046 | C22 | 1 | 16 | yes | complemented |
| 70 | #3045 | C22 | 1 | 16 | yes | complemented |
| 71 | #3037 | C22 | 1 | 8 | yes | complemented |
| 72 | #3036 | C22 | 1 | 8 | yes | complemented |
| 73 | #3013 | C22 | 1 | 16 | yes | complemented |
| 74 | #3013 | C22 | 1 | 16 | yes | complemented |
| 75 | #3012 | C22 | 1 | 16 | yes | complemented |
| 76 | #3012 | C22 | 1 | 16 | yes | complemented |
| 77 | #3007 | C22 | 1 | 16 | yes | complemented |
| 78 | #3006 | C22 | 1 | 16 | yes | complemented |
| 79 | #2951 | C22 | 1 | 8 | yes | complemented |
| 80 | #2951 | C22 | 1 | 8 | yes | complemented |
| 81 | C2×#440 | C22 | 1 | 4 | yes | complemented |
| 82 | C2×C4×Q16 | C22 | 1 | 2 | yes | complemented |
| 83 | C2×C4×D8 | C22 | 1 | 2 | yes | complemented |
| 84 | #2932 | C22 | 1 | 4 | yes | complemented |
| 85 | #2931 | C22 | 1 | 4 | yes | complemented |
| 86 | #2930 | C22 | 1 | 8 | yes | complemented |
| 87 | #2929 | C22 | 1 | 8 | yes | complemented |
| 88 | C22×#107 | C22 | 1 | 1 | yes | characteristic, complemented |
| 89 | #2905 | C22 | 1 | 1 | yes | characteristic, complemented |
| 90 | C2×#417 | C22 | 1 | 2 | yes | complemented |
| 91 | C2×#417 | C22 | 1 | 4 | yes | complemented |
| 92 | #2879 | C22 | 1 | 2 | yes | complemented |
| 93 | C2×#405 | C22 | 1 | 1 | yes | characteristic, complemented |
| 94 | #585 | — | 2 | 32 | no | — |
| 95 | #585 | — | 4 | 16 | no | — |
| 96 | C2×2−1+4 | — | 2 | 4 | no | — |
| 97 | C2×2−1+4 | C23 | 1 | 8 | yes | — |
| 98 | C2×2−1+4 | C23 | 1 | 8 | yes | — |
| 99 | C2×H(5,𝔽2) | — | 2 | 4 | no | — |
| 100 | C2×H(5,𝔽2) | — | 2 | 8 | no | — |
| 101 | C2×H(5,𝔽2) | C23 | 1 | 8 | yes | — |
| 102 | C2×H(5,𝔽2) | C23 | 1 | 8 | yes | — |
| 103 | C22×#41 | — | 2 | 8 | no | — |
| 104 | C22×#41 | — | 2 | 8 | no | — |
| 105 | C22×#41 | C23 | 1 | 4 | yes | — |
| 106 | C22×#41 | C23 | 1 | 16 | yes | — |
| 107 | C22×#41 | C23 | 1 | 2 | yes | — |
| 108 | C22×#41 | C23 | 1 | 2 | yes | — |
| 109 | #578 | — | 2 | 32 | no | — |
| 110 | #578 | — | 2 | 32 | no | — |
| 111 | #577 | — | 2 | 64 | no | — |
| 112 | #577 | — | 2 | 64 | no | — |
| 113 | #576 | — | 2 | 32 | no | — |
| 114 | #576 | — | 2 | 32 | no | — |
| 115 | #575 | — | 2 | 32 | no | — |
| 116 | #575 | — | 2 | 64 | no | — |
| 117 | #575 | — | 4 | 8 | no | — |
| 118 | C2×#137 | C23 | 1 | 8 | yes | — |
| 119 | C2×#137 | C23 | 1 | 16 | yes | — |
| 120 | C2×#137 | C23 | 1 | 8 | yes | — |
| 121 | C2×#137 | C23 | 1 | 16 | yes | — |
| 122 | C2×#137 | C23 | 1 | 8 | yes | — |
| 123 | C2×AGL(1,ℤ/8) | C23 | 1 | 8 | yes | — |
| 124 | C2×AGL(1,ℤ/8) | C23 | 1 | 16 | yes | — |
| 125 | C2×AGL(1,ℤ/8) | C23 | 1 | 8 | yes | — |
| 126 | C2×AGL(1,ℤ/8) | C23 | 1 | 16 | yes | — |
| 127 | C2×AGL(1,ℤ/8) | C23 | 1 | 8 | yes | — |
| 128 | C2×#135 | — | 2 | 64 | no | — |
| 129 | C2×#135 | — | 2 | 16 | no | — |
| 130 | C2×#135 | D4 | 1 | 16 | yes | complemented |
| 131 | C2×#135 | C23 | 1 | 4 | yes | — |
| 132 | C2×#135 | C23 | 1 | 4 | yes | — |
| 133 | C2×#135 | C23 | 1 | 4 | yes | — |
| 134 | C2×#135 | C23 | 1 | 4 | yes | — |
| 135 | C2×#135 | C23 | 1 | 16 | yes | — |
| 136 | C2×#135 | C23 | 1 | 16 | yes | — |
| 137 | C2×#135 | C23 | 1 | 8 | yes | — |
| 138 | C2×#135 | C23 | 1 | 8 | yes | — |
| 139 | C2×#135 | C23 | 1 | 8 | yes | — |
| 140 | C2×#135 | C23 | 1 | 4 | yes | — |
| 141 | C2×#135 | C23 | 1 | 4 | yes | — |
| 142 | C22×Q16 | C23 | 1 | 2 | yes | — |
| 143 | C22×Q16 | C23 | 1 | 8 | yes | — |
| 144 | C22×Q16 | C23 | 1 | 1 | yes | characteristic |
| 145 | C22×SD16 | C23 | 1 | 4 | yes | — |
| 146 | C22×SD16 | C23 | 1 | 16 | yes | — |
| 147 | C22×SD16 | C23 | 1 | 2 | yes | — |
| 148 | C22×D8 | C23 | 1 | 2 | yes | — |
| 149 | C22×D8 | C23 | 1 | 8 | yes | — |
| 150 | C22×D8 | C23 | 1 | 1 | yes | characteristic |
| 151 | C2×#131 | — | 2 | 16 | no | — |
| 152 | C2×#131 | C23 | 1 | 4 | yes | — |
| 153 | C2×#131 | C23 | 1 | 4 | yes | — |
| 154 | C2×#131 | C23 | 1 | 4 | yes | — |
| 155 | C2×#131 | C23 | 1 | 4 | yes | — |
| 156 | C22×M16 | C23 | 1 | 1 | yes | characteristic |
| 157 | C22×M16 | C23 | 1 | 2 | yes | — |
| 158 | C22×M16 | C23 | 1 | 4 | yes | — |
| 159 | C23×C8 | C23 | 1 | 4 | yes | — |
| 160 | C23×C8 | C23 | 1 | 1 | yes | characteristic |
| 161 | #550 | — | 2 | 8 | no | — |
| 162 | #550 | C23 | 1 | 16 | yes | — |
| 163 | D4×Q8 | — | 2 | 8 | no | — |
| 164 | D4×Q8 | C23 | 1 | 16 | yes | — |
| 165 | #548 | — | 2 | 16 | no | — |
| 166 | #548 | C23 | 1 | 32 | yes | — |
| 167 | #547 | — | 2 | 8 | no | — |
| 168 | #547 | — | 2 | 32 | no | — |
| 169 | #547 | C23 | 1 | 16 | yes | — |
| 170 | #546 | — | 2 | 16 | no | — |
| 171 | #546 | — | 2 | 32 | no | — |
| 172 | #546 | — | 2 | 32 | no | — |
| 173 | #546 | C23 | 1 | 32 | yes | — |
| 174 | D42 | — | 2 | 8 | no | — |
| 175 | D42 | — | 2 | 32 | no | — |
| 176 | D42 | C23 | 1 | 16 | yes | — |
| 177 | #537 | — | 2 | 8 | no | — |
| 178 | #537 | — | 2 | 8 | no | — |
| 179 | #537 | — | 2 | 16 | no | — |
| 180 | #537 | — | 2 | 16 | no | — |
| 181 | #537 | — | 2 | 16 | no | — |
| 182 | #537 | — | 2 | 2 | no | — |
| 183 | #537 | — | 2 | 2 | no | — |
| 184 | #537 | D4 | 1 | 2 | yes | — |
| 185 | #537 | D4 | 1 | 2 | yes | — |
| 186 | #537 | C23 | 1 | 16 | yes | — |
| 187 | #537 | C23 | 1 | 16 | yes | — |
| 188 | #536 | — | 2 | 16 | no | — |
| 189 | #536 | D4 | 1 | 4 | yes | — |
| 190 | #536 | C23 | 1 | 8 | yes | — |
| 191 | #535 | — | 2 | 16 | no | — |
| 192 | #535 | D4 | 1 | 4 | yes | — |
| 193 | #535 | C23 | 1 | 8 | yes | — |
| 194 | #534 | — | 2 | 16 | no | — |
| 195 | #534 | — | 2 | 4 | no | — |
| 196 | #534 | D4 | 1 | 4 | yes | — |
| 197 | #532 | — | 2 | 16 | no | — |
| 198 | #532 | C23 | 1 | 8 | yes | — |
| 199 | #532 | C23 | 1 | 4 | yes | — |
| 200 | #525 | — | 2 | 16 | no | — |
| 201 | #525 | — | 2 | 16 | no | — |
| 202 | #525 | — | 2 | 8 | no | — |
| 203 | #525 | C23 | 1 | 8 | yes | — |
| 204 | C2×C22⋊Q8 | — | 2 | 4 | no | — |
| 205 | C2×C22⋊Q8 | — | 2 | 16 | no | — |
| 206 | C2×C22⋊Q8 | C23 | 1 | 8 | yes | — |
| 207 | C2×#121 | — | 2 | 4 | no | — |
| 208 | C2×#121 | — | 2 | 8 | no | — |
| 209 | C2×#121 | — | 2 | 16 | no | — |
| 210 | C2×#121 | — | 2 | 16 | no | — |
| 211 | C2×#121 | C23 | 1 | 8 | yes | — |
| 212 | #520 | — | 2 | 8 | no | — |
| 213 | #520 | C23 | 1 | 16 | yes | — |
| 214 | C2×C4×Q8 | C23 | 1 | 4 | yes | — |
| 215 | C2×C4×D4 | — | 2 | 4 | no | — |
| 216 | C2×C4×D4 | C23 | 1 | 4 | yes | — |
| 217 | C2×#117 | — | 2 | 2 | no | — |
| 218 | C2×#117 | C23 | 1 | 1 | yes | characteristic |
| 219 | C22×C4⋊C4 | — | 2 | 2 | no | — |
| 220 | C22×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 221 | #497 | C23 | 1 | 16 | yes | — |
| 222 | #496 | C23 | 1 | 16 | yes | — |
| 223 | #495 | C23 | 1 | 8 | yes | — |
| 224 | #495 | C23 | 1 | 8 | yes | — |
| 225 | #494 | C23 | 1 | 4 | yes | — |
| 226 | #493 | C23 | 1 | 4 | yes | — |
| 227 | #492 | C23 | 1 | 8 | yes | — |
| 228 | #468 | C23 | 1 | 32 | yes | — |
| 229 | #468 | C23 | 1 | 32 | yes | — |
| 230 | #467 | C23 | 1 | 16 | yes | — |
| 231 | #467 | C23 | 1 | 16 | yes | — |
| 232 | #466 | C23 | 1 | 16 | yes | — |
| 233 | #466 | C23 | 1 | 16 | yes | — |
| 234 | #464 | C23 | 1 | 32 | yes | — |
| 235 | #463 | C23 | 1 | 32 | yes | — |
| 236 | #462 | C23 | 1 | 16 | yes | — |
| 237 | #461 | C23 | 1 | 16 | yes | — |
| 238 | #460 | C23 | 1 | 16 | yes | — |
| 239 | #459 | C23 | 1 | 16 | yes | — |
| 240 | #452 | C23 | 1 | 32 | yes | — |
| 241 | #452 | C23 | 1 | 32 | yes | — |
| 242 | #451 | C23 | 1 | 32 | yes | — |
| 243 | #450 | C23 | 1 | 32 | yes | — |
| 244 | #449 | C23 | 1 | 32 | yes | — |
| 245 | #449 | C23 | 1 | 32 | yes | — |
| 246 | #448 | C23 | 1 | 32 | yes | — |
| 247 | #447 | C23 | 1 | 32 | yes | — |
| 248 | #440 | C23 | 1 | 32 | yes | — |
| 249 | C4×Q16 | C23 | 1 | 8 | yes | — |
| 250 | C4×Q16 | C23 | 1 | 8 | yes | — |
| 251 | C4×D8 | C23 | 1 | 8 | yes | — |
| 252 | C4×D8 | C23 | 1 | 8 | yes | — |
| 253 | #436 | C23 | 1 | 8 | yes | — |
| 254 | #436 | C23 | 1 | 8 | yes | — |
| 255 | #435 | C23 | 1 | 16 | yes | — |
| 256 | #435 | C23 | 1 | 16 | yes | — |
| 257 | C8×D4 | C23 | 1 | 8 | yes | — |
| 258 | C8×D4 | C23 | 1 | 8 | yes | — |
| 259 | C2×#107 | C23 | 1 | 2 | yes | — |
| 260 | C2×#107 | C23 | 1 | 2 | yes | — |
| 261 | C2×#107 | C23 | 1 | 4 | yes | — |
| 262 | C2×#107 | C23 | 1 | 4 | yes | — |
| 263 | #424 | C23 | 1 | 8 | yes | — |
| 264 | #423 | C23 | 1 | 4 | yes | — |
| 265 | #417 | C23 | 1 | 16 | yes | — |
| 266 | #417 | C23 | 1 | 16 | yes | — |
| 267 | #417 | C23 | 1 | 16 | yes | — |
| 268 | C2×#103 | C23 | 1 | 4 | yes | — |
| 269 | C2×#103 | C23 | 1 | 8 | yes | — |
| 270 | C2×#102 | C23 | 1 | 4 | yes | — |
| 271 | C2×#102 | C23 | 1 | 8 | yes | — |
| 272 | #408 | C23 | 1 | 8 | yes | — |
| 273 | #408 | C23 | 1 | 8 | yes | — |
| 274 | #407 | C23 | 1 | 8 | yes | — |
| 275 | #405 | C23 | 1 | 4 | yes | — |
| 276 | #405 | C23 | 1 | 4 | yes | — |
| 277 | C2×#97 | C23 | 1 | 2 | yes | — |
| 278 | C2×C4×C8 | C23 | 1 | 2 | yes | — |
| 279 | 2−1+4 | — | 2 | 32 | no | — |
| 280 | 2−1+4 | — | 2 | 32 | no | — |
| 281 | 2−1+4 | — | 4 | 16 | no | — |
| 282 | 2−1+4 | — | 4 | 16 | no | — |
| 283 | 2−1+4 | — | 4 | 32 | no | — |
| 284 | H(5,𝔽2) | — | 2 | 32 | no | — |
| 285 | H(5,𝔽2) | — | 2 | 32 | no | — |
| 286 | H(5,𝔽2) | — | 4 | 64 | no | — |
| 287 | H(5,𝔽2) | — | 4 | 16 | no | — |
| 288 | H(5,𝔽2) | — | 4 | 16 | no | — |
| 289 | H(5,𝔽2) | — | 4 | 32 | no | — |
| 290 | C2×#41 | — | 2 | 8 | no | — |
| 291 | C2×#41 | — | 2 | 8 | no | — |
| 292 | C2×#41 | — | 2 | 8 | no | — |
| 293 | C2×#41 | — | 2 | 16 | no | — |
| 294 | C2×#41 | — | 2 | 16 | no | — |
| 295 | C2×#41 | — | 2 | 8 | no | — |
| 296 | C2×#41 | — | 2 | 4 | no | — |
| 297 | C2×#41 | — | 2 | 8 | no | — |
| 298 | C2×#41 | — | 2 | 4 | no | — |
| 299 | C2×#41 | — | 2 | 16 | no | — |
| 300 | C2×#41 | — | 2 | 4 | no | — |
| 301 | C2×#41 | — | 2 | 16 | no | — |
| 302 | C2×#41 | — | 2 | 8 | no | — |
| 303 | C2×#41 | — | 2 | 8 | no | — |
| 304 | C2×#41 | — | 2 | 64 | no | — |
| 305 | C2×#41 | — | 2 | 16 | no | — |
| 306 | C2×#41 | — | 2 | 16 | no | — |
| 307 | C2×#41 | — | 4 | 32 | no | — |
| 308 | C2×#41 | — | 4 | 64 | no | — |
| 309 | C2×#41 | — | 4 | 64 | no | — |
| 310 | C2×#41 | C2×D4 | 1 | 4 | yes | — |
| 311 | C2×#41 | C2×D4 | 1 | 4 | yes | — |
| 312 | C2×#41 | C2×D4 | 1 | 16 | yes | complemented |
| 313 | C2×#41 | C24 | 1 | 8 | yes | — |
| 314 | C2×#41 | C24 | 1 | 8 | yes | — |
| 315 | C2×#41 | C24 | 1 | 16 | yes | — |
| 316 | C2×#41 | C24 | 1 | 16 | yes | — |
| 317 | C2×#41 | C24 | 1 | 8 | yes | — |
| 318 | C2×#41 | C24 | 1 | 4 | yes | — |
| 319 | C2×#41 | C24 | 1 | 4 | yes | — |
| 320 | C22×Q8 | — | 2 | 8 | no | — |
| 321 | C22×Q8 | — | 2 | 8 | no | — |
| 322 | C22×Q8 | C2×D4 | 1 | 2 | yes | — |
| 323 | C22×Q8 | C24 | 1 | 4 | yes | — |
| 324 | C22×Q8 | C24 | 1 | 16 | yes | — |
| 325 | C22×Q8 | C24 | 1 | 2 | yes | — |
| 326 | C22×D4 | — | 2 | 2 | no | — |
| 327 | C22×D4 | — | 2 | 4 | no | — |
| 328 | C22×D4 | — | 2 | 16 | no | — |
| 329 | C22×D4 | — | 2 | 8 | no | — |
| 330 | C22×D4 | — | 2 | 16 | no | — |
| 331 | C22×D4 | — | 2 | 8 | no | — |
| 332 | C22×D4 | — | 2 | 16 | no | — |
| 333 | C22×D4 | — | 2 | 8 | no | — |
| 334 | C22×D4 | — | 2 | 16 | no | — |
| 335 | C22×D4 | C2×D4 | 1 | 4 | yes | — |
| 336 | C22×D4 | C2×D4 | 1 | 2 | yes | — |
| 337 | C22×D4 | C24 | 1 | 4 | yes | — |
| 338 | C22×D4 | C24 | 1 | 16 | yes | — |
| 339 | C22×D4 | C24 | 1 | 2 | yes | — |
| 340 | C23×C4 | — | 2 | 2 | no | — |
| 341 | C23×C4 | — | 2 | 2 | no | — |
| 342 | C23×C4 | — | 2 | 16 | no | — |
| 343 | C23×C4 | — | 2 | 4 | no | — |
| 344 | C23×C4 | — | 2 | 4 | no | — |
| 345 | C23×C4 | C24 | 1 | 4 | yes | — |
| 346 | C23×C4 | C24 | 1 | 1 | yes | characteristic |
| 347 | #137 | — | 2 | 32 | no | — |
| 348 | #137 | — | 2 | 32 | no | — |
| 349 | #137 | — | 2 | 64 | no | — |
| 350 | #137 | — | 2 | 64 | no | — |
| 351 | #137 | — | 4 | 16 | no | — |
| 352 | AGL(1,ℤ/8) | — | 2 | 32 | no | — |
| 353 | AGL(1,ℤ/8) | — | 2 | 32 | no | — |
| 354 | AGL(1,ℤ/8) | — | 2 | 64 | no | — |
| 355 | AGL(1,ℤ/8) | — | 2 | 64 | no | — |
| 356 | AGL(1,ℤ/8) | — | 4 | 16 | no | — |
| 357 | #135 | — | 2 | 64 | no | — |
| 358 | #135 | — | 2 | 32 | no | — |
| 359 | #135 | — | 2 | 64 | no | — |
| 360 | #135 | — | 2 | 32 | no | — |
| 361 | #135 | — | 2 | 16 | no | — |
| 362 | #135 | — | 2 | 16 | no | — |
| 363 | #135 | — | 2 | 16 | no | — |
| 364 | #135 | — | 2 | 16 | no | — |
| 365 | #135 | — | 4 | 16 | no | — |
| 366 | #135 | C2×D4 | 1 | 32 | yes | complemented |
| 367 | #135 | C2×D4 | 1 | 32 | yes | complemented |
| 368 | C2×Q16 | — | 2 | 32 | no | — |
| 369 | C2×Q16 | — | 2 | 8 | no | — |
| 370 | C2×Q16 | C2×D4 | 1 | 8 | yes | complemented |
| 371 | C2×Q16 | C24 | 1 | 4 | yes | — |
| 372 | C2×Q16 | C24 | 1 | 16 | yes | — |
| 373 | C2×Q16 | C24 | 1 | 4 | yes | — |
| 374 | C2×Q16 | C24 | 1 | 8 | yes | — |
| 375 | C2×Q16 | C24 | 1 | 2 | yes | — |
| 376 | C2×Q16 | C24 | 1 | 2 | yes | — |
| 377 | C2×SD16 | — | 2 | 64 | no | — |
| 378 | C2×SD16 | — | 2 | 16 | no | — |
| 379 | C2×SD16 | C2×D4 | 1 | 16 | yes | complemented |
| 380 | C2×SD16 | C24 | 1 | 8 | yes | — |
| 381 | C2×SD16 | C24 | 1 | 16 | yes | — |
| 382 | C2×SD16 | C24 | 1 | 16 | yes | — |
| 383 | C2×SD16 | C24 | 1 | 8 | yes | — |
| 384 | C2×SD16 | C24 | 1 | 16 | yes | — |
| 385 | C2×SD16 | C24 | 1 | 8 | yes | — |
| 386 | C2×D8 | — | 2 | 32 | no | — |
| 387 | C2×D8 | — | 2 | 8 | no | — |
| 388 | C2×D8 | C2×D4 | 1 | 8 | yes | complemented |
| 389 | C2×D8 | C24 | 1 | 4 | yes | — |
| 390 | C2×D8 | C24 | 1 | 16 | yes | — |
| 391 | C2×D8 | C24 | 1 | 4 | yes | — |
| 392 | C2×D8 | C24 | 1 | 8 | yes | — |
| 393 | C2×D8 | C24 | 1 | 2 | yes | — |
| 394 | C2×D8 | C24 | 1 | 2 | yes | — |
| 395 | #131 | — | 2 | 16 | no | — |
| 396 | #131 | — | 2 | 16 | no | — |
| 397 | #131 | — | 2 | 16 | no | — |
| 398 | #131 | — | 2 | 16 | no | — |
| 399 | C2×M16 | — | 2 | 8 | no | — |
| 400 | C2×M16 | — | 2 | 4 | no | — |
| 401 | C2×M16 | — | 2 | 16 | no | — |
| 402 | C2×M16 | C24 | 1 | 4 | yes | — |
| 403 | C2×M16 | C24 | 1 | 4 | yes | — |
| 404 | C2×M16 | C24 | 1 | 8 | yes | — |
| 405 | C2×M16 | C24 | 1 | 8 | yes | — |
| 406 | C2×M16 | C24 | 1 | 4 | yes | — |
| 407 | C22×C8 | — | 2 | 16 | no | — |
| 408 | C22×C8 | C2×D4 | 1 | 8 | yes | complemented |
| 409 | C22×C8 | C24 | 1 | 4 | yes | — |
| 410 | C22×C8 | C24 | 1 | 8 | yes | — |
| 411 | C22×C8 | C24 | 1 | 8 | yes | — |
| 412 | C22×C8 | C24 | 1 | 2 | yes | — |
| 413 | C22×C8 | C24 | 1 | 2 | yes | — |
| 414 | C22×C8 | C24 | 1 | 2 | yes | — |
| 415 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 416 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 417 | C4⋊Q8 | — | 2 | 16 | no | — |
| 418 | C4⋊Q8 | C2×D4 | 1 | 4 | yes | — |
| 419 | C4⋊Q8 | C24 | 1 | 8 | yes | — |
| 420 | #127 | — | 2 | 16 | no | — |
| 421 | #127 | C2×D4 | 1 | 4 | yes | — |
| 422 | #127 | C24 | 1 | 8 | yes | — |
| 423 | #124 | — | 2 | 32 | no | — |
| 424 | #124 | C2×D4 | 1 | 8 | yes | — |
| 425 | #124 | C24 | 1 | 16 | yes | — |
| 426 | #123 | — | 2 | 32 | no | — |
| 427 | #123 | — | 2 | 32 | no | — |
| 428 | #123 | — | 2 | 16 | no | — |
| 429 | #123 | C2×D4 | 1 | 16 | yes | — |
| 430 | C22⋊Q8 | — | 2 | 16 | no | — |
| 431 | C22⋊Q8 | — | 2 | 16 | no | — |
| 432 | C22⋊Q8 | — | 2 | 16 | no | — |
| 433 | C22⋊Q8 | — | 2 | 8 | no | — |
| 434 | C22⋊Q8 | — | 2 | 32 | no | — |
| 435 | C22⋊Q8 | — | 2 | 8 | no | — |
| 436 | C22⋊Q8 | — | 2 | 32 | no | — |
| 437 | C22⋊Q8 | C2×D4 | 1 | 8 | yes | — |
| 438 | C22⋊Q8 | C2×D4 | 1 | 8 | yes | — |
| 439 | C22⋊Q8 | C24 | 1 | 32 | yes | — |
| 440 | #121 | — | 2 | 16 | no | — |
| 441 | #121 | — | 2 | 32 | no | — |
| 442 | #121 | — | 2 | 16 | no | — |
| 443 | #121 | — | 2 | 32 | no | — |
| 444 | #121 | — | 2 | 32 | no | — |
| 445 | #121 | — | 2 | 16 | no | — |
| 446 | #121 | — | 2 | 8 | no | — |
| 447 | #121 | — | 2 | 16 | no | — |
| 448 | #121 | — | 2 | 8 | no | — |
| 449 | #121 | — | 2 | 8 | no | — |
| 450 | #121 | — | 2 | 16 | no | — |
| 451 | #121 | — | 2 | 8 | no | — |
| 452 | #121 | — | 2 | 32 | no | — |
| 453 | #121 | — | 2 | 32 | no | — |
| 454 | #121 | C2×D4 | 1 | 8 | yes | — |
| 455 | #121 | C2×D4 | 1 | 8 | yes | — |
| 456 | #121 | C2×D4 | 1 | 8 | yes | — |
| 457 | #121 | C2×D4 | 1 | 8 | yes | — |
| 458 | #121 | C24 | 1 | 32 | yes | — |
| 459 | #120 | — | 2 | 32 | no | — |
| 460 | #120 | — | 2 | 32 | no | — |
| 461 | #120 | — | 2 | 16 | no | — |
| 462 | #120 | C2×D4 | 1 | 16 | yes | — |
| 463 | C4×Q8 | — | 2 | 8 | no | — |
| 464 | C4×Q8 | C24 | 1 | 16 | yes | — |
| 465 | C4×D4 | — | 2 | 16 | no | — |
| 466 | C4×D4 | — | 2 | 16 | no | — |
| 467 | C4×D4 | — | 2 | 32 | no | — |
| 468 | C4×D4 | — | 2 | 32 | no | — |
| 469 | C4×D4 | — | 2 | 8 | no | — |
| 470 | C4×D4 | — | 2 | 8 | no | — |
| 471 | C4×D4 | — | 2 | 8 | no | — |
| 472 | C4×D4 | C24 | 1 | 16 | yes | — |
| 473 | C4×D4 | C24 | 1 | 8 | yes | — |
| 474 | C4×D4 | C24 | 1 | 8 | yes | — |
| 475 | #117 | — | 2 | 16 | no | — |
| 476 | #117 | C2×D4 | 1 | 4 | yes | — |
| 477 | #117 | C24 | 1 | 4 | yes | — |
| 478 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 479 | C2×C4⋊C4 | — | 2 | 4 | no | — |
| 480 | C2×C4⋊C4 | — | 2 | 4 | no | — |
| 481 | C2×C4⋊C4 | — | 2 | 8 | no | — |
| 482 | C2×C4⋊C4 | — | 2 | 16 | no | — |
| 483 | C2×C4⋊C4 | — | 2 | 16 | no | — |
| 484 | C2×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 485 | C2×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 486 | C2×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 487 | C2×C4⋊C4 | C24 | 1 | 8 | yes | — |
| 488 | C2×C22⋊C4 | — | 2 | 8 | no | — |
| 489 | C2×C22⋊C4 | — | 2 | 4 | no | — |
| 490 | C2×C22⋊C4 | — | 2 | 8 | no | — |
| 491 | C2×C22⋊C4 | — | 2 | 32 | no | — |
| 492 | C2×C22⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 493 | C2×C42 | — | 2 | 4 | no | — |
| 494 | C2×C42 | C24 | 1 | 2 | yes | — |
| 495 | #107 | C24 | 1 | 4 | yes | — |
| 496 | #107 | C24 | 1 | 4 | yes | — |
| 497 | #107 | C24 | 1 | 8 | yes | — |
| 498 | C4⋊C8 | C24 | 1 | 8 | yes | — |
| 499 | C4⋊C8 | C24 | 1 | 8 | yes | — |
| 500 | #103 | C24 | 1 | 16 | yes | — |
| 501 | #103 | C24 | 1 | 32 | yes | — |
| 502 | #102 | C24 | 1 | 16 | yes | — |
| 503 | #102 | C24 | 1 | 32 | yes | — |
| 504 | C22⋊C8 | C24 | 1 | 16 | yes | — |
| 505 | C22⋊C8 | C24 | 1 | 16 | yes | — |
| 506 | #97 | C24 | 1 | 8 | yes | — |
| 507 | C4×C8 | C24 | 1 | 4 | yes | — |
| 508 | C4×C8 | C24 | 1 | 4 | yes | — |
| 509 | C24 | — | 2 | 2 | no | — |
| 510 | C24 | — | 2 | 16 | no | — |
| 511 | C24 | — | 2 | 4 | no | — |
| 512 | C24 | C22×D4 | 1 | 4 | yes | — |
| 513 | C24 | C22×D4 | 1 | 1 | yes | characteristic |
| 514 | #41 | — | 2 | 16 | no | — |
| 515 | #41 | — | 2 | 16 | no | — |
| 516 | #41 | — | 2 | 32 | no | — |
| 517 | #41 | — | 2 | 8 | no | — |
| 518 | #41 | — | 2 | 8 | no | — |
| 519 | #41 | — | 2 | 16 | no | — |
| 520 | #41 | — | 2 | 8 | no | — |
| 521 | #41 | — | 2 | 8 | no | — |
| 522 | #41 | — | 2 | 32 | no | — |
| 523 | #41 | — | 2 | 32 | no | — |
| 524 | #41 | — | 2 | 16 | no | — |
| 525 | #41 | — | 2 | 16 | no | — |
| 526 | #41 | — | 2 | 16 | no | — |
| 527 | #41 | — | 2 | 16 | no | — |
| 528 | #41 | — | 4 | 64 | no | — |
| 529 | #41 | — | 4 | 16 | no | — |
| 530 | #41 | — | 4 | 16 | no | — |
| 531 | #41 | — | 4 | 64 | no | — |
| 532 | #41 | — | 4 | 64 | no | — |
| 533 | #41 | — | 4 | 32 | no | — |
| 534 | #41 | — | 4 | 32 | no | — |
| 535 | #41 | — | 4 | 64 | no | — |
| 536 | #41 | — | 4 | 32 | no | — |
| 537 | #41 | — | 4 | 32 | no | — |
| 538 | #41 | — | 4 | 16 | no | — |
| 539 | #41 | — | 4 | 16 | no | — |
| 540 | #41 | C22×D4 | 1 | 32 | yes | — |
| 541 | C2×Q8 | — | 2 | 8 | no | — |
| 542 | C2×Q8 | — | 2 | 2 | no | — |
| 543 | C2×Q8 | — | 2 | 4 | no | — |
| 544 | C2×Q8 | — | 2 | 16 | no | — |
| 545 | C2×Q8 | — | 2 | 4 | no | — |
| 546 | C2×Q8 | — | 2 | 32 | no | — |
| 547 | C2×Q8 | — | 2 | 8 | no | — |
| 548 | C2×Q8 | — | 2 | 8 | no | — |
| 549 | C2×Q8 | — | 4 | 16 | no | — |
| 550 | C2×Q8 | — | 4 | 32 | no | — |
| 551 | C2×Q8 | — | 4 | 32 | no | — |
| 552 | C2×Q8 | C22×D4 | 1 | 8 | yes | — |
| 553 | C2×Q8 | C22×D4 | 1 | 4 | yes | — |
| 554 | C2×Q8 | C22×D4 | 1 | 4 | yes | — |
| 555 | C2×Q8 | C25 | 1 | 8 | yes | — |
| 556 | C2×Q8 | C25 | 1 | 4 | yes | — |
| 557 | C2×D4 | — | 2 | 16 | no | — |
| 558 | C2×D4 | — | 2 | 16 | no | — |
| 559 | C2×D4 | — | 2 | 8 | no | — |
| 560 | C2×D4 | — | 2 | 32 | no | — |
| 561 | C2×D4 | — | 2 | 16 | no | — |
| 562 | C2×D4 | — | 2 | 8 | no | — |
| 563 | C2×D4 | — | 2 | 8 | no | — |
| 564 | C2×D4 | — | 2 | 16 | no | — |
| 565 | C2×D4 | — | 2 | 32 | no | — |
| 566 | C2×D4 | — | 2 | 8 | no | — |
| 567 | C2×D4 | — | 2 | 2 | no | — |
| 568 | C2×D4 | — | 2 | 8 | no | — |
| 569 | C2×D4 | — | 2 | 16 | no | — |
| 570 | C2×D4 | — | 2 | 4 | no | — |
| 571 | C2×D4 | — | 2 | 8 | no | — |
| 572 | C2×D4 | — | 2 | 8 | no | — |
| 573 | C2×D4 | — | 2 | 4 | no | — |
| 574 | C2×D4 | — | 2 | 8 | no | — |
| 575 | C2×D4 | — | 4 | 16 | no | — |
| 576 | C2×D4 | — | 4 | 32 | no | — |
| 577 | C2×D4 | — | 4 | 64 | no | — |
| 578 | C2×D4 | — | 4 | 32 | no | — |
| 579 | C2×D4 | — | 4 | 64 | no | — |
| 580 | C2×D4 | — | 4 | 64 | no | — |
| 581 | C2×D4 | — | 4 | 16 | no | — |
| 582 | C2×D4 | — | 16 | 16 | no | — |
| 583 | C2×D4 | — | 16 | 8 | no | — |
| 584 | C2×D4 | C22×D4 | 1 | 8 | yes | — |
| 585 | C2×D4 | C22×D4 | 1 | 8 | yes | — |
| 586 | C2×D4 | C22×D4 | 1 | 4 | yes | — |
| 587 | C2×D4 | C22×D4 | 1 | 4 | yes | — |
| 588 | C2×D4 | C22×D4 | 1 | 8 | yes | — |
| 589 | C2×D4 | C22×D4 | 1 | 8 | yes | — |
| 590 | C2×D4 | C22×D4 | 1 | 8 | yes | — |
| 591 | C2×D4 | C25 | 1 | 8 | yes | — |
| 592 | C2×D4 | C25 | 1 | 4 | yes | — |
| 593 | C22×C4 | — | 2 | 2 | no | — |
| 594 | C22×C4 | — | 2 | 16 | no | — |
| 595 | C22×C4 | — | 2 | 8 | no | — |
| 596 | C22×C4 | — | 2 | 8 | no | — |
| 597 | C22×C4 | — | 2 | 8 | no | — |
| 598 | C22×C4 | — | 2 | 4 | no | — |
| 599 | C22×C4 | — | 2 | 16 | no | — |
| 600 | C22×C4 | — | 2 | 4 | no | — |
| 601 | C22×C4 | — | 2 | 8 | no | — |
| 602 | C22×C4 | — | 2 | 16 | no | — |
| 603 | C22×C4 | — | 2 | 16 | no | — |
| 604 | C22×C4 | — | 2 | 8 | no | — |
| 605 | C22×C4 | — | 2 | 8 | no | — |
| 606 | C22×C4 | — | 2 | 16 | no | — |
| 607 | C22×C4 | — | 4 | 64 | no | — |
| 608 | C22×C4 | — | 4 | 16 | no | — |
| 609 | C22×C4 | — | 16 | 4 | no | — |
| 610 | C22×C4 | — | 16 | 2 | no | — |
| 611 | C22×C4 | C22×D4 | 1 | 4 | yes | — |
| 612 | C22×C4 | C22×D4 | 1 | 8 | yes | — |
| 613 | C22×C4 | C22×D4 | 1 | 2 | yes | — |
| 614 | C22×C4 | C22×D4 | 1 | 2 | yes | — |
| 615 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 616 | C22×C4 | C22×D4 | 1 | 2 | yes | — |
| 617 | C22×C4 | C22×D4 | 1 | 4 | yes | — |
| 618 | C22×C4 | H(5,𝔽2) | 1 | 4 | yes | — |
| 619 | C22×C4 | C25 | 1 | 8 | yes | — |
| 620 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 621 | C22×C4 | C25 | 1 | 2 | yes | — |
| 622 | Q16 | — | 2 | 32 | no | — |
| 623 | Q16 | — | 2 | 8 | no | — |
| 624 | Q16 | — | 2 | 8 | no | — |
| 625 | Q16 | — | 4 | 8 | no | — |
| 626 | Q16 | C22×D4 | 1 | 8 | yes | — |
| 627 | Q16 | C22×D4 | 1 | 8 | yes | — |
| 628 | SD16 | — | 2 | 32 | no | — |
| 629 | SD16 | — | 2 | 32 | no | — |
| 630 | SD16 | — | 2 | 16 | no | — |
| 631 | SD16 | — | 2 | 16 | no | — |
| 632 | SD16 | — | 4 | 16 | no | — |
| 633 | SD16 | C22×D4 | 1 | 32 | yes | — |
| 634 | D8 | — | 2 | 32 | no | — |
| 635 | D8 | — | 2 | 8 | no | — |
| 636 | D8 | — | 2 | 8 | no | — |
| 637 | D8 | — | 4 | 8 | no | — |
| 638 | D8 | C22×D4 | 1 | 8 | yes | — |
| 639 | D8 | C22×D4 | 1 | 8 | yes | — |
| 640 | M16 | — | 2 | 8 | no | — |
| 641 | M16 | — | 2 | 8 | no | — |
| 642 | M16 | — | 2 | 8 | no | — |
| 643 | M16 | — | 2 | 16 | no | — |
| 644 | M16 | — | 2 | 16 | no | — |
| 645 | C2×C8 | — | 2 | 8 | no | — |
| 646 | C2×C8 | — | 2 | 4 | no | — |
| 647 | C2×C8 | — | 2 | 16 | no | — |
| 648 | C2×C8 | — | 2 | 16 | no | — |
| 649 | C2×C8 | C22×D4 | 1 | 8 | yes | — |
| 650 | C2×C8 | C22×D4 | 1 | 8 | yes | — |
| 651 | C2×C8 | C22×D4 | 1 | 4 | yes | — |
| 652 | C2×C8 | C22×D4 | 1 | 4 | yes | — |
| 653 | C2×C8 | C25 | 1 | 4 | yes | — |
| 654 | C2×C8 | C25 | 1 | 8 | yes | — |
| 655 | C2×C8 | C25 | 1 | 1 | yes | characteristic |
| 656 | C2×C8 | C25 | 1 | 1 | yes | characteristic |
| 657 | C2×C8 | C25 | 1 | 2 | yes | — |
| 658 | C4⋊C4 | — | 2 | 8 | no | — |
| 659 | C4⋊C4 | — | 2 | 16 | no | — |
| 660 | C4⋊C4 | — | 2 | 4 | no | — |
| 661 | C4⋊C4 | — | 2 | 8 | no | — |
| 662 | C4⋊C4 | — | 2 | 32 | no | — |
| 663 | C4⋊C4 | — | 2 | 8 | no | — |
| 664 | C4⋊C4 | C22×D4 | 1 | 4 | yes | — |
| 665 | C4⋊C4 | C22×D4 | 1 | 8 | yes | — |
| 666 | C4⋊C4 | C22×D4 | 1 | 4 | yes | — |
| 667 | C4⋊C4 | C22×D4 | 1 | 8 | yes | — |
| 668 | C4⋊C4 | C25 | 1 | 8 | yes | — |
| 669 | C22⋊C4 | — | 2 | 32 | no | — |
| 670 | C22⋊C4 | — | 2 | 16 | no | — |
| 671 | C22⋊C4 | — | 2 | 32 | no | — |
| 672 | C22⋊C4 | — | 2 | 16 | no | — |
| 673 | C22⋊C4 | — | 2 | 16 | no | — |
| 674 | C22⋊C4 | C22×D4 | 1 | 16 | yes | — |
| 675 | C22⋊C4 | C22×D4 | 1 | 8 | yes | — |
| 676 | C22⋊C4 | C22×D4 | 1 | 16 | yes | — |
| 677 | C42 | — | 2 | 16 | no | — |
| 678 | C42 | C22×D4 | 1 | 4 | yes | — |
| 679 | C42 | C25 | 1 | 4 | yes | — |
| 680 | C23 | — | 2 | 4 | no | — |
| 681 | C23 | — | 2 | 8 | no | — |
| 682 | C23 | — | 2 | 8 | no | — |
| 683 | C23 | — | 2 | 8 | no | — |
| 684 | C23 | — | 4 | 1 | no | — |
| 685 | C23 | — | 4 | 1 | no | — |
| 686 | C23 | — | 4 | 4 | no | — |
| 687 | C23 | — | 4 | 4 | no | — |
| 688 | C23 | — | 4 | 32 | no | — |
| 689 | C23 | — | 4 | 8 | no | — |
| 690 | C23 | — | 8 | 2 | no | — |
| 691 | C23 | — | 8 | 2 | no | — |
| 692 | C23 | — | 8 | 4 | no | — |
| 693 | C23 | — | 8 | 16 | no | — |
| 694 | C23 | — | 8 | 4 | no | — |
| 695 | C23 | — | 8 | 16 | no | — |
| 696 | C23 | D42 | 1 | 4 | yes | — |
| 697 | C23 | C23×D4 | 1 | 8 | yes | — |
| 698 | C23 | C23×D4 | 1 | 2 | yes | — |
| 699 | C23 | C23×D4 | 1 | 1 | yes | characteristic |
| 700 | Q8 | — | 2 | 4 | no | — |
| 701 | Q8 | — | 2 | 8 | no | — |
| 702 | Q8 | — | 2 | 8 | no | — |
| 703 | Q8 | — | 2 | 8 | no | — |
| 704 | Q8 | — | 2 | 8 | no | — |
| 705 | Q8 | — | 2 | 8 | no | — |
| 706 | Q8 | — | 4 | 32 | no | — |
| 707 | Q8 | — | 4 | 8 | no | — |
| 708 | Q8 | C23×D4 | 1 | 8 | yes | — |
| 709 | D4 | — | 2 | 32 | no | — |
| 710 | D4 | — | 2 | 16 | no | — |
| 711 | D4 | — | 2 | 16 | no | — |
| 712 | D4 | — | 2 | 8 | no | — |
| 713 | D4 | — | 2 | 4 | no | — |
| 714 | D4 | — | 2 | 8 | no | — |
| 715 | D4 | — | 2 | 8 | no | — |
| 716 | D4 | — | 2 | 8 | no | — |
| 717 | D4 | — | 2 | 8 | no | — |
| 718 | D4 | — | 4 | 8 | no | — |
| 719 | D4 | — | 4 | 8 | no | — |
| 720 | D4 | — | 4 | 32 | no | — |
| 721 | D4 | — | 4 | 32 | no | — |
| 722 | D4 | — | 4 | 32 | no | — |
| 723 | D4 | — | 4 | 16 | no | — |
| 724 | D4 | — | 4 | 16 | no | — |
| 725 | D4 | — | 4 | 8 | no | — |
| 726 | D4 | — | 8 | 8 | no | — |
| 727 | D4 | — | 8 | 8 | no | — |
| 728 | D4 | — | 8 | 32 | no | — |
| 729 | D4 | C23×D4 | 1 | 8 | yes | — |
| 730 | C2×C4 | — | 2 | 4 | no | — |
| 731 | C2×C4 | — | 2 | 8 | no | — |
| 732 | C2×C4 | — | 2 | 8 | no | — |
| 733 | C2×C4 | — | 2 | 8 | no | — |
| 734 | C2×C4 | — | 2 | 8 | no | — |
| 735 | C2×C4 | — | 2 | 32 | no | — |
| 736 | C2×C4 | — | 2 | 16 | no | — |
| 737 | C2×C4 | — | 2 | 8 | no | — |
| 738 | C2×C4 | — | 2 | 8 | no | — |
| 739 | C2×C4 | — | 4 | 2 | no | — |
| 740 | C2×C4 | — | 4 | 2 | no | — |
| 741 | C2×C4 | — | 4 | 32 | no | — |
| 742 | C2×C4 | — | 4 | 32 | no | — |
| 743 | C2×C4 | — | 4 | 32 | no | — |
| 744 | C2×C4 | — | 4 | 8 | no | — |
| 745 | C2×C4 | — | 4 | 16 | no | — |
| 746 | C2×C4 | — | 4 | 16 | no | — |
| 747 | C2×C4 | — | 8 | 16 | no | — |
| 748 | C2×C4 | — | 8 | 4 | no | — |
| 749 | C2×C4 | — | 8 | 8 | no | — |
| 750 | C2×C4 | D42 | 1 | 4 | yes | — |
| 751 | C2×C4 | D42 | 1 | 8 | yes | — |
| 752 | C2×C4 | C23×D4 | 1 | 4 | yes | — |
| 753 | C2×C4 | C23×D4 | 1 | 4 | yes | — |
| 754 | C2×C4 | C23×D4 | 1 | 8 | yes | — |
| 755 | C2×C4 | C23×D4 | 1 | 4 | yes | — |
| 756 | C2×C4 | C23×D4 | 1 | 2 | yes | — |
| 757 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 758 | C2×C4 | C23×D4 | 1 | 2 | yes | — |
| 759 | C2×C4 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 760 | C2×C4 | C2×H(5,𝔽2) | 1 | 4 | yes | — |
| 761 | C2×C4 | C26 | 1 | 1 | yes | characteristic |
| 762 | C8 | — | 2 | 8 | no | — |
| 763 | C8 | — | 2 | 4 | no | — |
| 764 | C8 | C23×D4 | 1 | 2 | yes | — |
| 765 | C8 | C23×D4 | 1 | 4 | yes | — |
| 766 | C8 | C23×D4 | 1 | 2 | yes | — |
| 767 | C22 | — | 2 | 1 | no | — |
| 768 | C22 | — | 2 | 2 | no | — |
| 769 | C22 | — | 2 | 1 | no | — |
| 770 | C22 | — | 2 | 2 | no | — |
| 771 | C22 | — | 2 | 8 | no | — |
| 772 | C22 | — | 2 | 8 | no | — |
| 773 | C22 | — | 2 | 8 | no | — |
| 774 | C22 | — | 2 | 8 | no | — |
| 775 | C22 | — | 4 | 4 | no | — |
| 776 | C22 | — | 4 | 4 | no | — |
| 777 | C22 | — | 4 | 4 | no | — |
| 778 | C22 | — | 4 | 8 | no | — |
| 779 | C22 | — | 4 | 8 | no | — |
| 780 | C22 | — | 4 | 8 | no | — |
| 781 | C22 | — | 8 | 8 | no | — |
| 782 | C22 | — | 8 | 8 | no | — |
| 783 | C22 | — | 16 | 8 | no | — |
| 784 | C22 | — | 16 | 32 | no | — |
| 785 | C22 | C2×D42 | 1 | 2 | yes | — |
| 786 | C22 | C2×D42 | 1 | 4 | yes | — |
| 787 | C22 | C24×D4 | 1 | 1 | yes | characteristic |
| 788 | C4 | — | 2 | 4 | no | — |
| 789 | C4 | — | 2 | 4 | no | — |
| 790 | C4 | — | 2 | 8 | no | — |
| 791 | C4 | — | 2 | 8 | no | — |
| 792 | C4 | — | 4 | 8 | no | — |
| 793 | C4 | — | 4 | 8 | no | — |
| 794 | C4 | C2×D42 | 1 | 4 | yes | — |
| 795 | C4 | C2×D42 | 1 | 2 | yes | — |
| 796 | C4 | C24×D4 | 1 | 1 | yes | characteristic |
| 797 | C4 | C22×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 798 | C2 | — | 2 | 2 | no | — |
| 799 | C2 | — | 2 | 4 | no | — |
| 800 | C2 | — | 4 | 8 | no | — |
| 801 | C2 | — | 4 | 8 | no | — |
| 802 | C2 | — | 8 | 8 | no | — |
| 803 | C2 | C22×D42 | 1 | 1 | yes | characteristic |
| 804 | C2 | #63091 | 1 | 1 | yes | characteristic |
| 805 | C2 | #63093 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C24×D4 |
| commutator, Frattini, cosocle | C2×C4 | C26 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ #3449 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#3584 | C2 | semidirect |
| 2. #62853 | C2 | semidirect |
| 3. #61086 | C2 | semidirect |
| 4. #61084 | C2 | semidirect |
| 5. #61080 | C2 | semidirect |
| 6. #61062 | C2 | semidirect |
| 7. #61057 | C2 | semidirect |
| 8. #61056 | C2 | semidirect |
| 9. #60643 | C2 | semidirect |
| 10. C2×#3061 | C2 | semidirect |
| 11. #60425 | C2 | semidirect |
| 12. #60371 | C2 | semidirect |
| 13. C2×#2951 | C2 | semidirect |
| 14. #60140 | C2 | semidirect |
| 15. C2×#585 | C22 | semidirect |
| 17. C2×#578 | C22 | semidirect |
| 18. C2×#578 | C22 | semidirect |
| 19. C2×#577 | C22 | semidirect |
| 20. C2×#577 | C22 | semidirect |
| 21. C2×#576 | C22 | semidirect |
| 22. C2×#576 | C22 | semidirect |
| 23. C2×#575 | C22 | semidirect |
| 24. C2×#575 | C22 | semidirect |
| 25. C2×#575 | C22 | semidirect |
| 27. C22×#135 | C22 | semidirect |
| 28. C22×#135 | C22 | semidirect |
| 29. C22×#131 | C22 | semidirect |
| 30. #3497 | C22 | semidirect |
| 32. #3496 | C22 | semidirect |
| 34. #3489 | C22 | semidirect |
| 36. #3488 | C22 | semidirect |
| 39. #3449 | C22 | semidirect |
| 41. C2×#537 | C22 | semidirect |
| 42. C2×#520 | C22 | semidirect |
| 43. #3287 | C22 | semidirect |
| 44. D4×Q16 | C22 | semidirect |
| 45. #3285 | C22 | semidirect |
| 46. #3283 | C22 | semidirect |
| 47. #3280 | C22 | semidirect |
| 48. D4×D8 | C22 | semidirect |
| 49. #3278 | C22 | semidirect |
| 50. #3277 | C22 | semidirect |
| 51. #3273 | C22 | semidirect |
| 52. #3272 | C22 | semidirect |
| 53. #3269 | C22 | semidirect |
| 54. #3268 | C22 | semidirect |
| 55. #3266 | C22 | semidirect |
| 56. #3265 | C22 | semidirect |
| 57. #3156 | C22 | semidirect |
| 58. #3155 | C22 | semidirect |
| 59. #3154 | C22 | semidirect |
| 60. #3150 | C22 | semidirect |
| 61. #3147 | C22 | semidirect |
| 62. #3061 | C22 | semidirect |
| 63. #3061 | C22 | semidirect |
| 64. #3061 | C22 | semidirect |
| 65. #3061 | C22 | semidirect |
| 66. C2×#468 | C22 | semidirect |
| 67. C2×#467 | C22 | semidirect |
| 68. C2×#466 | C22 | semidirect |
| 69. #3046 | C22 | semidirect |
| 70. #3045 | C22 | semidirect |
| 71. #3037 | C22 | semidirect |
| 72. #3036 | C22 | semidirect |
| 73. #3013 | C22 | semidirect |
| 74. #3013 | C22 | semidirect |
| 75. #3012 | C22 | semidirect |
| 76. #3012 | C22 | semidirect |
| 77. #3007 | C22 | semidirect |
| 78. #3006 | C22 | semidirect |
| 79. #2951 | C22 | semidirect |
| 80. #2951 | C22 | semidirect |
| 81. C2×#440 | C22 | semidirect |
| 82. C2×C4×Q16 | C22 | semidirect |
| 83. C2×C4×D8 | C22 | semidirect |
| 84. #2932 | C22 | semidirect |
| 85. #2931 | C22 | semidirect |
| 86. #2930 | C22 | semidirect |
| 87. #2929 | C22 | semidirect |
| 88. C22×#107 | C22 | semidirect |
| 89. #2905 | C22 | semidirect |
| 90. C2×#417 | C22 | semidirect |
| 91. C2×#417 | C22 | semidirect |
| 92. #2879 | C22 | semidirect |
| 93. C2×#405 | C22 | semidirect |
| 130. C2×#135 | D4 | semidirect |
| 312. C2×#41 | C2×D4 | semidirect |
| 366. #135 | C2×D4 | semidirect |
| 367. #135 | C2×D4 | semidirect |
| 370. C2×Q16 | C2×D4 | semidirect |
| 379. C2×SD16 | C2×D4 | semidirect |
| 388. C2×D8 | C2×D4 | semidirect |
| 408. C22×C8 | C2×D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3584 | 2 |
| #62853 | 2 |
| #61086 | 2 |
| #61084 | 2 |
| #61080 | 2 |
| #61062 | 2 |
| #61057 | 2 |
| #61056 | 2 |
| #60643 | 2 |
| C2×#3061 | 2 |
| #60425 | 2 |
| #60371 | 2 |
| C2×#2951 | 2 |
| #60140 | 2 |