Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
22088 conjugacy classes of subgroups.
The subgroup lattice has 911 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C22×#585 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#3584 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #62811 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #60377 | C2 | 1 | 8 | yes | maximal, complemented |
| 5 | #60376 | C2 | 1 | 8 | yes | maximal, complemented |
| 6 | #60375 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #60374 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #60373 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #60372 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #60366 | C2 | 1 | 12 | yes | maximal, complemented |
| 11 | #60359 | C2 | 1 | 6 | yes | maximal, complemented |
| 12 | C2×#3002 | C2 | 1 | 6 | yes | maximal, complemented |
| 13 | #60086 | C2 | 1 | 2 | yes | maximal, complemented |
| 14 | C2×#2880 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C2×#585 | — | 2 | 32 | no | — |
| 16 | C2×#585 | — | 2 | 4 | no | — |
| 17 | C2×#585 | — | 2 | 3 | no | — |
| 18 | C2×#585 | — | 2 | 1 | no | — |
| 19 | C2×#585 | C22 | 1 | 2 | yes | — |
| 20 | C2×#585 | C22 | 1 | 6 | yes | complemented |
| 21 | C2×#585 | C22 | 1 | 8 | yes | complemented |
| 22 | C2×#585 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | C22×2−1+4 | — | 2 | 1 | no | — |
| 24 | C22×2−1+4 | C22 | 1 | 4 | yes | complemented |
| 25 | C22×H(5,𝔽2) | — | 2 | 3 | no | — |
| 26 | C22×H(5,𝔽2) | C22 | 1 | 4 | yes | complemented |
| 27 | C23×#41 | — | 2 | 4 | no | — |
| 28 | C23×#41 | C22 | 1 | 1 | yes | characteristic |
| 29 | C23×#41 | C22 | 1 | 6 | yes | complemented |
| 30 | #3584 | — | 2 | 32 | no | — |
| 31 | C2×#578 | C22 | 1 | 8 | yes | complemented |
| 32 | C2×#577 | C22 | 1 | 8 | yes | complemented |
| 33 | C2×#577 | C22 | 1 | 8 | yes | complemented |
| 34 | C2×#576 | C22 | 1 | 8 | yes | complemented |
| 35 | C2×#575 | C22 | 1 | 12 | yes | complemented |
| 36 | C22×#135 | C22 | 1 | 12 | yes | complemented |
| 37 | C22×#131 | C22 | 1 | 2 | yes | complemented |
| 38 | #3489 | C22 | 1 | 4 | yes | complemented |
| 39 | #3489 | C22 | 1 | 4 | yes | complemented |
| 40 | #3488 | C22 | 1 | 4 | yes | complemented |
| 41 | #3488 | C22 | 1 | 4 | yes | complemented |
| 42 | #3487 | — | 2 | 1 | no | — |
| 43 | #3486 | — | 2 | 1 | no | — |
| 44 | #3485 | — | 2 | 3 | no | — |
| 45 | #3484 | — | 2 | 3 | no | — |
| 46 | D4×#41 | — | 2 | 4 | no | — |
| 47 | D4×#41 | — | 2 | 4 | no | — |
| 48 | #3449 | C22 | 1 | 6 | yes | complemented |
| 49 | C2×#525 | C22 | 1 | 6 | yes | complemented |
| 50 | #3428 | C22 | 1 | 1 | yes | characteristic, complemented |
| 51 | #3013 | C22 | 1 | 24 | yes | complemented |
| 52 | #3013 | C22 | 1 | 24 | yes | complemented |
| 53 | #3012 | C22 | 1 | 24 | yes | complemented |
| 54 | #3012 | C22 | 1 | 24 | yes | complemented |
| 55 | #3011 | C22 | 1 | 24 | yes | complemented |
| 56 | #3010 | C22 | 1 | 24 | yes | complemented |
| 57 | #3009 | C22 | 1 | 24 | yes | complemented |
| 58 | #3008 | C22 | 1 | 24 | yes | complemented |
| 59 | #3007 | C22 | 1 | 12 | yes | complemented |
| 60 | #3007 | C22 | 1 | 12 | yes | complemented |
| 61 | #3006 | C22 | 1 | 12 | yes | complemented |
| 62 | #3006 | C22 | 1 | 12 | yes | complemented |
| 63 | #3005 | C22 | 1 | 24 | yes | complemented |
| 64 | #3004 | C22 | 1 | 12 | yes | complemented |
| 65 | #3003 | C22 | 1 | 12 | yes | complemented |
| 66 | #3002 | C22 | 1 | 4 | yes | complemented |
| 67 | #3002 | C22 | 1 | 12 | yes | complemented |
| 68 | #3002 | C22 | 1 | 12 | yes | complemented |
| 69 | #3002 | C22 | 1 | 12 | yes | complemented |
| 70 | #3002 | C22 | 1 | 24 | yes | complemented |
| 71 | #3002 | C22 | 1 | 24 | yes | complemented |
| 72 | #3002 | C22 | 1 | 24 | yes | complemented |
| 73 | C2×#452 | C22 | 1 | 12 | yes | complemented |
| 74 | C2×#449 | C22 | 1 | 12 | yes | complemented |
| 75 | C2×#451 | C22 | 1 | 6 | yes | complemented |
| 76 | C2×#448 | C22 | 1 | 6 | yes | complemented |
| 77 | C2×#450 | C22 | 1 | 6 | yes | complemented |
| 78 | C2×#447 | C22 | 1 | 6 | yes | complemented |
| 79 | #2898 | C22 | 1 | 8 | yes | complemented |
| 80 | #2898 | C22 | 1 | 8 | yes | complemented |
| 81 | #2897 | C22 | 1 | 8 | yes | complemented |
| 82 | #2897 | C22 | 1 | 8 | yes | complemented |
| 83 | #2896 | C22 | 1 | 12 | yes | complemented |
| 84 | C2×#416 | C22 | 1 | 12 | yes | complemented |
| 85 | #2880 | C22 | 1 | 4 | yes | complemented |
| 86 | #2880 | C22 | 1 | 4 | yes | complemented |
| 87 | #2880 | C22 | 1 | 8 | yes | complemented |
| 88 | C2×#408 | C22 | 1 | 6 | yes | complemented |
| 89 | C2×#407 | C22 | 1 | 3 | yes | complemented |
| 90 | C22×C22⋊C8 | C22 | 1 | 3 | yes | complemented |
| 91 | #585 | — | 2 | 32 | no | — |
| 92 | #585 | — | 2 | 96 | no | — |
| 93 | #585 | — | 2 | 128 | no | — |
| 94 | #585 | — | 2 | 64 | no | — |
| 95 | #585 | — | 2 | 64 | no | — |
| 96 | #585 | — | 2 | 16 | no | — |
| 97 | #585 | — | 2 | 96 | no | — |
| 98 | #585 | — | 2 | 16 | no | — |
| 99 | #585 | D4 | 1 | 32 | yes | complemented |
| 100 | C2×2−1+4 | — | 2 | 32 | no | — |
| 101 | C2×2−1+4 | — | 2 | 64 | no | — |
| 102 | C2×2−1+4 | — | 2 | 12 | no | — |
| 103 | C2×2−1+4 | — | 2 | 4 | no | — |
| 104 | C2×2−1+4 | — | 2 | 2 | no | — |
| 105 | C2×2−1+4 | — | 2 | 6 | no | — |
| 106 | C2×2−1+4 | — | 2 | 8 | no | — |
| 107 | C2×2−1+4 | — | 2 | 1 | no | — |
| 108 | C2×2−1+4 | C23 | 1 | 24 | yes | — |
| 109 | C2×2−1+4 | C23 | 1 | 8 | yes | — |
| 110 | C2×2−1+4 | C23 | 1 | 4 | yes | complemented |
| 111 | C2×H(5,𝔽2) | — | 2 | 96 | no | — |
| 112 | C2×H(5,𝔽2) | — | 2 | 64 | no | — |
| 113 | C2×H(5,𝔽2) | — | 2 | 12 | no | — |
| 114 | C2×H(5,𝔽2) | — | 2 | 4 | no | — |
| 115 | C2×H(5,𝔽2) | — | 2 | 6 | no | — |
| 116 | C2×H(5,𝔽2) | — | 2 | 12 | no | — |
| 117 | C2×H(5,𝔽2) | — | 2 | 6 | no | — |
| 118 | C2×H(5,𝔽2) | — | 2 | 24 | no | — |
| 119 | C2×H(5,𝔽2) | — | 2 | 3 | no | — |
| 120 | C2×H(5,𝔽2) | C23 | 1 | 24 | yes | — |
| 121 | C2×H(5,𝔽2) | C23 | 1 | 8 | yes | — |
| 122 | C2×H(5,𝔽2) | C23 | 1 | 4 | yes | complemented |
| 123 | C22×#41 | — | 2 | 128 | no | — |
| 124 | C22×#41 | — | 2 | 8 | no | — |
| 125 | C22×#41 | — | 2 | 24 | no | — |
| 126 | C22×#41 | — | 2 | 24 | no | — |
| 127 | C22×#41 | — | 2 | 8 | no | — |
| 128 | C22×#41 | — | 2 | 16 | no | — |
| 129 | C22×#41 | — | 2 | 96 | no | — |
| 130 | C22×#41 | — | 2 | 4 | no | — |
| 131 | C22×#41 | — | 2 | 4 | no | — |
| 132 | C22×#41 | — | 2 | 12 | no | — |
| 133 | C22×#41 | — | 2 | 6 | no | — |
| 134 | C22×#41 | — | 2 | 6 | no | — |
| 135 | C22×#41 | — | 2 | 6 | no | — |
| 136 | C22×#41 | — | 2 | 6 | no | — |
| 137 | C22×#41 | — | 2 | 6 | no | — |
| 138 | C22×#41 | — | 2 | 6 | no | — |
| 139 | C22×#41 | D4 | 1 | 4 | yes | — |
| 140 | C22×#41 | D4 | 1 | 4 | yes | — |
| 141 | C22×#41 | D4 | 1 | 3 | yes | — |
| 142 | C22×#41 | D4 | 1 | 1 | yes | characteristic |
| 143 | C22×#41 | C23 | 1 | 4 | yes | — |
| 144 | C22×#41 | C23 | 1 | 12 | yes | — |
| 145 | C22×#41 | C23 | 1 | 12 | yes | — |
| 146 | C22×#41 | C23 | 1 | 12 | yes | — |
| 147 | C22×#41 | C23 | 1 | 12 | yes | — |
| 148 | C22×#41 | C23 | 1 | 12 | yes | — |
| 149 | C22×#41 | C23 | 1 | 4 | yes | — |
| 150 | C22×#41 | C23 | 1 | 3 | yes | — |
| 151 | C22×#41 | C23 | 1 | 4 | yes | — |
| 152 | C22×#41 | C23 | 1 | 1 | yes | characteristic |
| 153 | C22×#41 | C23 | 1 | 6 | yes | complemented |
| 154 | C23×Q8 | — | 2 | 4 | no | — |
| 155 | C23×Q8 | D4 | 1 | 1 | yes | characteristic |
| 156 | C23×Q8 | C23 | 1 | 6 | yes | — |
| 157 | C23×D4 | — | 2 | 6 | no | — |
| 158 | C23×D4 | — | 2 | 12 | no | — |
| 159 | C23×D4 | D4 | 1 | 3 | yes | — |
| 160 | C23×D4 | C23 | 1 | 6 | yes | — |
| 161 | C24×C4 | — | 2 | 6 | no | — |
| 162 | C24×C4 | C23 | 1 | 3 | yes | — |
| 163 | #578 | — | 2 | 64 | no | — |
| 164 | #577 | — | 2 | 64 | no | — |
| 165 | #577 | — | 2 | 64 | no | — |
| 166 | #576 | — | 2 | 64 | no | — |
| 167 | #575 | — | 2 | 96 | no | — |
| 168 | C2×#137 | C23 | 1 | 24 | yes | complemented |
| 169 | C2×#137 | C23 | 1 | 24 | yes | complemented |
| 170 | C2×AGL(1,ℤ/8) | C23 | 1 | 24 | yes | complemented |
| 171 | C2×AGL(1,ℤ/8) | C23 | 1 | 24 | yes | complemented |
| 172 | C2×#135 | — | 2 | 96 | no | — |
| 173 | C2×#135 | C23 | 1 | 8 | yes | complemented |
| 174 | C2×#135 | C23 | 1 | 24 | yes | complemented |
| 175 | C2×#135 | C23 | 1 | 24 | yes | complemented |
| 176 | C2×#135 | C23 | 1 | 24 | yes | complemented |
| 177 | C22×Q16 | C23 | 1 | 12 | yes | complemented |
| 178 | C22×SD16 | C23 | 1 | 12 | yes | complemented |
| 179 | C22×SD16 | C23 | 1 | 12 | yes | complemented |
| 180 | C22×D8 | C23 | 1 | 12 | yes | complemented |
| 181 | C2×#131 | — | 2 | 16 | no | — |
| 182 | C2×#131 | C23 | 1 | 8 | yes | complemented |
| 183 | C2×#131 | C23 | 1 | 8 | yes | complemented |
| 184 | C22×M16 | C23 | 1 | 6 | yes | complemented |
| 185 | C23×C8 | C23 | 1 | 6 | yes | complemented |
| 186 | #550 | — | 2 | 4 | no | — |
| 187 | #550 | — | 2 | 4 | no | — |
| 188 | D4×Q8 | — | 2 | 4 | no | — |
| 189 | D4×Q8 | — | 2 | 4 | no | — |
| 190 | #548 | — | 2 | 4 | no | — |
| 191 | #548 | — | 2 | 4 | no | — |
| 192 | #548 | — | 2 | 4 | no | — |
| 193 | #548 | — | 2 | 4 | no | — |
| 194 | #547 | — | 2 | 12 | no | — |
| 195 | #547 | — | 2 | 12 | no | — |
| 196 | #546 | — | 2 | 12 | no | — |
| 197 | #546 | — | 2 | 12 | no | — |
| 198 | #546 | — | 2 | 12 | no | — |
| 199 | #546 | — | 2 | 12 | no | — |
| 200 | D42 | — | 2 | 12 | no | — |
| 201 | D42 | — | 2 | 12 | no | — |
| 202 | #537 | C23 | 1 | 12 | yes | complemented |
| 203 | #537 | C23 | 1 | 12 | yes | complemented |
| 204 | #536 | — | 2 | 6 | no | — |
| 205 | #536 | C23 | 1 | 12 | yes | complemented |
| 206 | #535 | — | 2 | 6 | no | — |
| 207 | #535 | C23 | 1 | 12 | yes | complemented |
| 208 | #534 | — | 2 | 12 | no | — |
| 209 | #532 | — | 2 | 12 | no | — |
| 210 | #525 | — | 2 | 12 | no | — |
| 211 | #525 | — | 2 | 6 | no | — |
| 212 | #525 | — | 2 | 6 | no | — |
| 213 | #525 | — | 2 | 6 | no | — |
| 214 | #525 | — | 2 | 6 | no | — |
| 215 | #525 | C23 | 1 | 4 | yes | — |
| 216 | #525 | C23 | 1 | 12 | yes | — |
| 217 | #525 | C23 | 1 | 12 | yes | complemented |
| 218 | #525 | C23 | 1 | 12 | yes | complemented |
| 219 | C2×#123 | — | 2 | 6 | no | — |
| 220 | C2×C22⋊Q8 | C23 | 1 | 6 | yes | — |
| 221 | C2×C22⋊Q8 | C23 | 1 | 6 | yes | complemented |
| 222 | C2×#121 | C23 | 1 | 6 | yes | — |
| 223 | C2×#121 | C23 | 1 | 6 | yes | complemented |
| 224 | C2×#120 | — | 2 | 6 | no | — |
| 225 | #520 | C23 | 1 | 4 | yes | complemented |
| 226 | #520 | C23 | 1 | 4 | yes | complemented |
| 227 | #519 | — | 2 | 1 | no | — |
| 228 | #518 | — | 2 | 3 | no | — |
| 229 | C4×#41 | — | 2 | 4 | no | — |
| 230 | C2×C4×D4 | — | 2 | 6 | no | — |
| 231 | C2×C4×D4 | — | 2 | 6 | no | — |
| 232 | C2×#117 | C23 | 1 | 6 | yes | complemented |
| 233 | #452 | C23 | 1 | 8 | yes | complemented |
| 234 | #452 | C23 | 1 | 24 | yes | complemented |
| 235 | #452 | C23 | 1 | 24 | yes | complemented |
| 236 | #452 | C23 | 1 | 24 | yes | complemented |
| 237 | #452 | C23 | 1 | 48 | yes | complemented |
| 238 | #451 | C23 | 1 | 4 | yes | — |
| 239 | #451 | C23 | 1 | 12 | yes | — |
| 240 | #451 | C23 | 1 | 24 | yes | complemented |
| 241 | #451 | C23 | 1 | 24 | yes | complemented |
| 242 | #450 | C23 | 1 | 4 | yes | — |
| 243 | #450 | C23 | 1 | 12 | yes | — |
| 244 | #450 | C23 | 1 | 24 | yes | complemented |
| 245 | #450 | C23 | 1 | 24 | yes | complemented |
| 246 | #449 | C23 | 1 | 8 | yes | complemented |
| 247 | #449 | C23 | 1 | 24 | yes | complemented |
| 248 | #449 | C23 | 1 | 24 | yes | complemented |
| 249 | #449 | C23 | 1 | 24 | yes | complemented |
| 250 | #449 | C23 | 1 | 48 | yes | complemented |
| 251 | #448 | C23 | 1 | 4 | yes | — |
| 252 | #448 | C23 | 1 | 12 | yes | — |
| 253 | #448 | C23 | 1 | 24 | yes | complemented |
| 254 | #448 | C23 | 1 | 24 | yes | complemented |
| 255 | #447 | C23 | 1 | 4 | yes | — |
| 256 | #447 | C23 | 1 | 12 | yes | — |
| 257 | #447 | C23 | 1 | 24 | yes | complemented |
| 258 | #447 | C23 | 1 | 24 | yes | complemented |
| 259 | #419 | C23 | 1 | 24 | yes | complemented |
| 260 | #418 | C23 | 1 | 24 | yes | complemented |
| 261 | #417 | C23 | 1 | 24 | yes | complemented |
| 262 | #417 | C23 | 1 | 24 | yes | complemented |
| 263 | #416 | C23 | 1 | 8 | yes | complemented |
| 264 | #416 | C23 | 1 | 24 | yes | complemented |
| 265 | #416 | C23 | 1 | 24 | yes | complemented |
| 266 | #416 | C23 | 1 | 24 | yes | complemented |
| 267 | C2×#103 | C23 | 1 | 12 | yes | complemented |
| 268 | C2×#103 | C23 | 1 | 12 | yes | complemented |
| 269 | C2×#102 | C23 | 1 | 12 | yes | complemented |
| 270 | C2×#102 | C23 | 1 | 12 | yes | complemented |
| 271 | #408 | C23 | 1 | 24 | yes | complemented |
| 272 | #408 | C23 | 1 | 24 | yes | complemented |
| 273 | #407 | C23 | 1 | 12 | yes | — |
| 274 | #407 | C23 | 1 | 12 | yes | complemented |
| 275 | C2×C22⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 276 | C2×C22⋊C8 | C23 | 1 | 3 | yes | — |
| 277 | C2×C22⋊C8 | C23 | 1 | 6 | yes | — |
| 278 | C2×C22⋊C8 | C23 | 1 | 6 | yes | — |
| 279 | C2×C22⋊C8 | C23 | 1 | 6 | yes | complemented |
| 280 | C2×C22⋊C8 | C23 | 1 | 12 | yes | complemented |
| 281 | C2×C22⋊C8 | C23 | 1 | 6 | yes | complemented |
| 282 | C25 | — | 2 | 6 | no | — |
| 283 | C25 | C2×D4 | 1 | 3 | yes | — |
| 284 | 2−1+4 | — | 2 | 192 | no | — |
| 285 | 2−1+4 | — | 2 | 96 | no | — |
| 286 | 2−1+4 | — | 2 | 64 | no | — |
| 287 | 2−1+4 | — | 2 | 128 | no | — |
| 288 | 2−1+4 | — | 2 | 96 | no | — |
| 289 | 2−1+4 | — | 2 | 32 | no | — |
| 290 | 2−1+4 | — | 2 | 32 | no | — |
| 291 | 2−1+4 | — | 2 | 96 | no | — |
| 292 | 2−1+4 | — | 2 | 32 | no | — |
| 293 | 2−1+4 | — | 4 | 8 | no | — |
| 294 | 2−1+4 | C2×D4 | 1 | 64 | yes | complemented |
| 295 | H(5,𝔽2) | — | 2 | 64 | no | — |
| 296 | H(5,𝔽2) | — | 2 | 96 | no | — |
| 297 | H(5,𝔽2) | — | 2 | 192 | no | — |
| 298 | H(5,𝔽2) | — | 2 | 384 | no | — |
| 299 | H(5,𝔽2) | — | 2 | 192 | no | — |
| 300 | H(5,𝔽2) | — | 2 | 96 | no | — |
| 301 | H(5,𝔽2) | — | 2 | 32 | no | — |
| 302 | H(5,𝔽2) | — | 2 | 96 | no | — |
| 303 | H(5,𝔽2) | — | 2 | 96 | no | — |
| 304 | H(5,𝔽2) | — | 2 | 32 | no | — |
| 305 | H(5,𝔽2) | — | 4 | 24 | no | — |
| 306 | H(5,𝔽2) | C2×D4 | 1 | 64 | yes | complemented |
| 307 | C2×#41 | — | 2 | 96 | no | — |
| 308 | C2×#41 | — | 2 | 64 | no | — |
| 309 | C2×#41 | — | 2 | 192 | no | — |
| 310 | C2×#41 | — | 2 | 96 | no | — |
| 311 | C2×#41 | — | 2 | 128 | no | — |
| 312 | C2×#41 | — | 2 | 384 | no | — |
| 313 | C2×#41 | — | 2 | 96 | no | — |
| 314 | C2×#41 | — | 2 | 384 | no | — |
| 315 | C2×#41 | — | 2 | 96 | no | — |
| 316 | C2×#41 | — | 2 | 96 | no | — |
| 317 | C2×#41 | — | 2 | 96 | no | — |
| 318 | C2×#41 | — | 2 | 32 | no | — |
| 319 | C2×#41 | — | 2 | 128 | no | — |
| 320 | C2×#41 | — | 2 | 32 | no | — |
| 321 | C2×#41 | — | 2 | 32 | no | — |
| 322 | C2×#41 | — | 2 | 96 | no | — |
| 323 | C2×#41 | — | 2 | 32 | no | — |
| 324 | C2×#41 | — | 2 | 96 | no | — |
| 325 | C2×#41 | — | 2 | 96 | no | — |
| 326 | C2×#41 | — | 2 | 32 | no | — |
| 327 | C2×#41 | — | 2 | 8 | no | — |
| 328 | C2×#41 | — | 2 | 24 | no | — |
| 329 | C2×#41 | — | 2 | 8 | no | — |
| 330 | C2×#41 | — | 2 | 48 | no | — |
| 331 | C2×#41 | — | 2 | 4 | no | — |
| 332 | C2×#41 | — | 2 | 24 | no | — |
| 333 | C2×#41 | — | 2 | 48 | no | — |
| 334 | C2×#41 | — | 2 | 24 | no | — |
| 335 | C2×#41 | — | 2 | 24 | no | — |
| 336 | C2×#41 | — | 2 | 48 | no | — |
| 337 | C2×#41 | — | 2 | 12 | no | — |
| 338 | C2×#41 | — | 2 | 12 | no | — |
| 339 | C2×#41 | — | 2 | 12 | no | — |
| 340 | C2×#41 | — | 2 | 4 | no | — |
| 341 | C2×#41 | — | 2 | 12 | no | — |
| 342 | C2×#41 | — | 2 | 4 | no | — |
| 343 | C2×#41 | — | 2 | 12 | no | — |
| 344 | C2×#41 | — | 2 | 12 | no | — |
| 345 | C2×#41 | — | 2 | 12 | no | — |
| 346 | C2×#41 | — | 2 | 12 | no | — |
| 347 | C2×#41 | — | 2 | 12 | no | — |
| 348 | C2×#41 | — | 2 | 12 | no | — |
| 349 | C2×#41 | — | 2 | 12 | no | — |
| 350 | C2×#41 | — | 2 | 48 | no | — |
| 351 | C2×#41 | — | 2 | 24 | no | — |
| 352 | C2×#41 | — | 2 | 6 | no | — |
| 353 | C2×#41 | — | 2 | 6 | no | — |
| 354 | C2×#41 | — | 2 | 48 | no | — |
| 355 | C2×#41 | — | 4 | 32 | no | — |
| 356 | C2×#41 | C2×D4 | 1 | 16 | yes | — |
| 357 | C2×#41 | C2×D4 | 1 | 12 | yes | — |
| 358 | C2×#41 | C2×D4 | 1 | 12 | yes | — |
| 359 | C2×#41 | C2×D4 | 1 | 12 | yes | — |
| 360 | C2×#41 | C2×D4 | 1 | 4 | yes | — |
| 361 | C2×#41 | C2×D4 | 1 | 4 | yes | — |
| 362 | C2×#41 | C2×D4 | 1 | 4 | yes | — |
| 363 | C2×#41 | C2×D4 | 1 | 96 | yes | complemented |
| 364 | C2×#41 | C24 | 1 | 4 | yes | — |
| 365 | C2×#41 | C24 | 1 | 12 | yes | — |
| 366 | C2×#41 | C24 | 1 | 8 | yes | — |
| 367 | C2×#41 | C24 | 1 | 24 | yes | — |
| 368 | C2×#41 | C24 | 1 | 8 | yes | — |
| 369 | C2×#41 | C24 | 1 | 24 | yes | — |
| 370 | C2×#41 | C24 | 1 | 12 | yes | — |
| 371 | C2×#41 | C24 | 1 | 4 | yes | — |
| 372 | C22×Q8 | — | 2 | 64 | no | — |
| 373 | C22×Q8 | — | 2 | 8 | no | — |
| 374 | C22×Q8 | — | 2 | 24 | no | — |
| 375 | C22×Q8 | — | 2 | 8 | no | — |
| 376 | C22×Q8 | — | 2 | 48 | no | — |
| 377 | C22×Q8 | — | 2 | 4 | no | — |
| 378 | C22×Q8 | — | 2 | 6 | no | — |
| 379 | C22×Q8 | — | 2 | 6 | no | — |
| 380 | C22×Q8 | — | 2 | 6 | no | — |
| 381 | C22×Q8 | C2×D4 | 1 | 3 | yes | — |
| 382 | C22×Q8 | C2×D4 | 1 | 4 | yes | — |
| 383 | C22×Q8 | C2×D4 | 1 | 4 | yes | — |
| 384 | C22×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 385 | C22×Q8 | C24 | 1 | 6 | yes | — |
| 386 | C22×Q8 | C24 | 1 | 4 | yes | — |
| 387 | C22×Q8 | C24 | 1 | 12 | yes | — |
| 388 | C22×Q8 | C24 | 1 | 12 | yes | — |
| 389 | C22×D4 | — | 2 | 96 | no | — |
| 390 | C22×D4 | — | 2 | 192 | no | — |
| 391 | C22×D4 | — | 2 | 12 | no | — |
| 392 | C22×D4 | — | 2 | 4 | no | — |
| 393 | C22×D4 | — | 2 | 12 | no | — |
| 394 | C22×D4 | — | 2 | 12 | no | — |
| 395 | C22×D4 | — | 2 | 12 | no | — |
| 396 | C22×D4 | — | 2 | 12 | no | — |
| 397 | C22×D4 | — | 2 | 24 | no | — |
| 398 | C22×D4 | — | 2 | 48 | no | — |
| 399 | C22×D4 | — | 2 | 24 | no | — |
| 400 | C22×D4 | — | 2 | 24 | no | — |
| 401 | C22×D4 | — | 2 | 48 | no | — |
| 402 | C22×D4 | — | 2 | 6 | no | — |
| 403 | C22×D4 | — | 2 | 6 | no | — |
| 404 | C22×D4 | — | 2 | 6 | no | — |
| 405 | C22×D4 | — | 2 | 12 | no | — |
| 406 | C22×D4 | — | 2 | 6 | no | — |
| 407 | C22×D4 | — | 2 | 6 | no | — |
| 408 | C22×D4 | — | 2 | 6 | no | — |
| 409 | C22×D4 | C2×D4 | 1 | 6 | yes | — |
| 410 | C22×D4 | C2×D4 | 1 | 3 | yes | — |
| 411 | C22×D4 | C2×D4 | 1 | 12 | yes | — |
| 412 | C22×D4 | C2×D4 | 1 | 12 | yes | — |
| 413 | C22×D4 | C2×D4 | 1 | 3 | yes | — |
| 414 | C22×D4 | C24 | 1 | 6 | yes | — |
| 415 | C22×D4 | C24 | 1 | 4 | yes | — |
| 416 | C22×D4 | C24 | 1 | 12 | yes | — |
| 417 | C22×D4 | C24 | 1 | 12 | yes | — |
| 418 | C23×C4 | — | 2 | 96 | no | — |
| 419 | C23×C4 | — | 2 | 6 | no | — |
| 420 | C23×C4 | — | 2 | 4 | no | — |
| 421 | C23×C4 | — | 2 | 12 | no | — |
| 422 | C23×C4 | — | 2 | 12 | no | — |
| 423 | C23×C4 | — | 2 | 12 | no | — |
| 424 | C23×C4 | — | 2 | 12 | no | — |
| 425 | C23×C4 | — | 2 | 12 | no | — |
| 426 | C23×C4 | — | 2 | 24 | no | — |
| 427 | C23×C4 | — | 2 | 6 | no | — |
| 428 | C23×C4 | C2×D4 | 1 | 6 | yes | — |
| 429 | C23×C4 | C2×D4 | 1 | 6 | yes | — |
| 430 | C23×C4 | C2×D4 | 1 | 3 | yes | — |
| 431 | C23×C4 | C2×D4 | 1 | 3 | yes | — |
| 432 | C23×C4 | C2×D4 | 1 | 3 | yes | — |
| 433 | C23×C4 | C24 | 1 | 6 | yes | — |
| 434 | C23×C4 | C24 | 1 | 6 | yes | — |
| 435 | C23×C4 | C24 | 1 | 1 | yes | characteristic |
| 436 | C23×C4 | C24 | 1 | 3 | yes | — |
| 437 | C23×C4 | C24 | 1 | 3 | yes | — |
| 438 | #137 | — | 2 | 96 | no | — |
| 439 | #137 | — | 2 | 96 | no | — |
| 440 | AGL(1,ℤ/8) | — | 2 | 96 | no | — |
| 441 | AGL(1,ℤ/8) | — | 2 | 96 | no | — |
| 442 | #135 | — | 2 | 32 | no | — |
| 443 | #135 | — | 2 | 96 | no | — |
| 444 | #135 | — | 2 | 96 | no | — |
| 445 | #135 | — | 2 | 96 | no | — |
| 446 | C2×Q16 | — | 2 | 48 | no | — |
| 447 | C2×Q16 | C24 | 1 | 8 | yes | — |
| 448 | C2×Q16 | C24 | 1 | 24 | yes | — |
| 449 | C2×SD16 | — | 2 | 48 | no | — |
| 450 | C2×SD16 | — | 2 | 48 | no | — |
| 451 | C2×SD16 | C24 | 1 | 8 | yes | — |
| 452 | C2×SD16 | C24 | 1 | 8 | yes | — |
| 453 | C2×SD16 | C24 | 1 | 24 | yes | — |
| 454 | C2×SD16 | C24 | 1 | 24 | yes | — |
| 455 | C2×D8 | — | 2 | 48 | no | — |
| 456 | C2×D8 | C24 | 1 | 8 | yes | — |
| 457 | C2×D8 | C24 | 1 | 24 | yes | — |
| 458 | #131 | — | 2 | 32 | no | — |
| 459 | #131 | — | 2 | 32 | no | — |
| 460 | C2×M16 | — | 2 | 24 | no | — |
| 461 | C2×M16 | C24 | 1 | 24 | yes | — |
| 462 | C22×C8 | — | 2 | 24 | no | — |
| 463 | C22×C8 | C24 | 1 | 2 | yes | — |
| 464 | C22×C8 | C24 | 1 | 6 | yes | — |
| 465 | C22×C8 | C24 | 1 | 12 | yes | — |
| 466 | C22×C8 | C24 | 1 | 12 | yes | — |
| 467 | C4⋊Q8 | — | 2 | 12 | no | — |
| 468 | #127 | — | 2 | 12 | no | — |
| 469 | #124 | — | 2 | 12 | no | — |
| 470 | #124 | — | 2 | 12 | no | — |
| 471 | #123 | — | 2 | 24 | no | — |
| 472 | #123 | — | 2 | 4 | no | — |
| 473 | #123 | — | 2 | 12 | no | — |
| 474 | #123 | — | 2 | 12 | no | — |
| 475 | #123 | — | 2 | 12 | no | — |
| 476 | C22⋊Q8 | — | 2 | 12 | no | — |
| 477 | C22⋊Q8 | — | 2 | 12 | no | — |
| 478 | C22⋊Q8 | — | 2 | 6 | no | — |
| 479 | C22⋊Q8 | — | 2 | 6 | no | — |
| 480 | C22⋊Q8 | — | 2 | 6 | no | — |
| 481 | C22⋊Q8 | — | 2 | 6 | no | — |
| 482 | C22⋊Q8 | C24 | 1 | 4 | yes | — |
| 483 | C22⋊Q8 | C24 | 1 | 12 | yes | — |
| 484 | C22⋊Q8 | C24 | 1 | 4 | yes | — |
| 485 | C22⋊Q8 | C24 | 1 | 12 | yes | — |
| 486 | #121 | — | 2 | 12 | no | — |
| 487 | #121 | — | 2 | 12 | no | — |
| 488 | #121 | — | 2 | 24 | no | — |
| 489 | #121 | — | 2 | 24 | no | — |
| 490 | #121 | — | 2 | 6 | no | — |
| 491 | #121 | — | 2 | 6 | no | — |
| 492 | #121 | — | 2 | 6 | no | — |
| 493 | #121 | — | 2 | 6 | no | — |
| 494 | #121 | C24 | 1 | 4 | yes | — |
| 495 | #121 | C24 | 1 | 12 | yes | — |
| 496 | #121 | C24 | 1 | 4 | yes | — |
| 497 | #121 | C24 | 1 | 12 | yes | — |
| 498 | #120 | — | 2 | 4 | no | — |
| 499 | #120 | — | 2 | 12 | no | — |
| 500 | #120 | — | 2 | 12 | no | — |
| 501 | #120 | — | 2 | 12 | no | — |
| 502 | #120 | — | 2 | 24 | no | — |
| 503 | C4×Q8 | — | 2 | 4 | no | — |
| 504 | C4×Q8 | — | 2 | 4 | no | — |
| 505 | C4×D4 | — | 2 | 12 | no | — |
| 506 | C4×D4 | — | 2 | 12 | no | — |
| 507 | C4×D4 | — | 2 | 4 | no | — |
| 508 | C4×D4 | — | 2 | 4 | no | — |
| 509 | C4×D4 | — | 2 | 12 | no | — |
| 510 | C4×D4 | — | 2 | 12 | no | — |
| 511 | C4×D4 | — | 2 | 12 | no | — |
| 512 | C4×D4 | — | 2 | 12 | no | — |
| 513 | C4×D4 | — | 2 | 12 | no | — |
| 514 | C4×D4 | — | 2 | 12 | no | — |
| 515 | #117 | — | 2 | 6 | no | — |
| 516 | #117 | — | 2 | 6 | no | — |
| 517 | #117 | C24 | 1 | 4 | yes | — |
| 518 | #117 | C24 | 1 | 12 | yes | — |
| 519 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 520 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 521 | C2×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 522 | C2×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 523 | C2×C22⋊C4 | — | 2 | 6 | no | — |
| 524 | C2×C22⋊C4 | — | 2 | 6 | no | — |
| 525 | C2×C22⋊C4 | — | 2 | 6 | no | — |
| 526 | C2×C22⋊C4 | — | 2 | 6 | no | — |
| 527 | C2×C22⋊C4 | — | 2 | 6 | no | — |
| 528 | C2×C42 | — | 2 | 6 | no | — |
| 529 | #103 | C24 | 1 | 8 | yes | — |
| 530 | #103 | C24 | 1 | 8 | yes | — |
| 531 | #103 | C24 | 1 | 24 | yes | — |
| 532 | #103 | C24 | 1 | 24 | yes | — |
| 533 | #102 | C24 | 1 | 8 | yes | — |
| 534 | #102 | C24 | 1 | 8 | yes | — |
| 535 | #102 | C24 | 1 | 24 | yes | — |
| 536 | #102 | C24 | 1 | 24 | yes | — |
| 537 | C22⋊C8 | C24 | 1 | 1 | yes | characteristic |
| 538 | C22⋊C8 | C24 | 1 | 1 | yes | characteristic |
| 539 | C22⋊C8 | C24 | 1 | 6 | yes | — |
| 540 | C22⋊C8 | C24 | 1 | 2 | yes | — |
| 541 | C22⋊C8 | C24 | 1 | 6 | yes | — |
| 542 | C22⋊C8 | C24 | 1 | 12 | yes | — |
| 543 | C22⋊C8 | C24 | 1 | 12 | yes | — |
| 544 | C22⋊C8 | C24 | 1 | 24 | yes | — |
| 545 | C24 | — | 2 | 48 | no | — |
| 546 | C24 | — | 2 | 4 | no | — |
| 547 | C24 | — | 2 | 12 | no | — |
| 548 | C24 | — | 2 | 12 | no | — |
| 549 | C24 | — | 2 | 12 | no | — |
| 550 | C24 | — | 2 | 6 | no | — |
| 551 | C24 | — | 4 | 6 | no | — |
| 552 | C24 | — | 8 | 12 | no | — |
| 553 | C24 | — | 8 | 3 | no | — |
| 554 | C24 | — | 8 | 12 | no | — |
| 555 | C24 | C22×D4 | 1 | 6 | yes | — |
| 556 | C24 | C22×D4 | 1 | 1 | yes | characteristic |
| 557 | C24 | C22×D4 | 1 | 6 | yes | — |
| 558 | C24 | C22×D4 | 1 | 3 | yes | — |
| 559 | C24 | C22×D4 | 1 | 3 | yes | — |
| 560 | #41 | — | 2 | 96 | no | — |
| 561 | #41 | — | 2 | 32 | no | — |
| 562 | #41 | — | 2 | 96 | no | — |
| 563 | #41 | — | 2 | 96 | no | — |
| 564 | #41 | — | 2 | 32 | no | — |
| 565 | #41 | — | 2 | 384 | no | — |
| 566 | #41 | — | 2 | 96 | no | — |
| 567 | #41 | — | 2 | 96 | no | — |
| 568 | #41 | — | 2 | 192 | no | — |
| 569 | #41 | — | 2 | 192 | no | — |
| 570 | #41 | — | 2 | 96 | no | — |
| 571 | #41 | — | 2 | 96 | no | — |
| 572 | #41 | — | 2 | 96 | no | — |
| 573 | #41 | — | 2 | 16 | no | — |
| 574 | #41 | — | 2 | 64 | no | — |
| 575 | #41 | — | 2 | 16 | no | — |
| 576 | #41 | — | 2 | 16 | no | — |
| 577 | #41 | — | 2 | 48 | no | — |
| 578 | #41 | — | 2 | 48 | no | — |
| 579 | #41 | — | 2 | 192 | no | — |
| 580 | #41 | — | 2 | 48 | no | — |
| 581 | #41 | — | 2 | 16 | no | — |
| 582 | #41 | — | 2 | 48 | no | — |
| 583 | #41 | — | 2 | 48 | no | — |
| 584 | #41 | — | 2 | 96 | no | — |
| 585 | #41 | — | 2 | 96 | no | — |
| 586 | #41 | — | 2 | 16 | no | — |
| 587 | #41 | — | 2 | 48 | no | — |
| 588 | #41 | — | 2 | 48 | no | — |
| 589 | #41 | — | 2 | 16 | no | — |
| 590 | #41 | — | 2 | 48 | no | — |
| 591 | #41 | — | 4 | 16 | no | — |
| 592 | #41 | — | 4 | 48 | no | — |
| 593 | #41 | — | 4 | 24 | no | — |
| 594 | #41 | — | 4 | 24 | no | — |
| 595 | #41 | #120 | 1 | 32 | yes | — |
| 596 | #41 | C22×D4 | 1 | 32 | yes | — |
| 597 | #41 | C22×D4 | 1 | 96 | yes | — |
| 598 | #41 | C22×D4 | 1 | 32 | yes | — |
| 599 | C2×Q8 | — | 2 | 48 | no | — |
| 600 | C2×Q8 | — | 2 | 192 | no | — |
| 601 | C2×Q8 | — | 2 | 48 | no | — |
| 602 | C2×Q8 | — | 2 | 48 | no | — |
| 603 | C2×Q8 | — | 2 | 16 | no | — |
| 604 | C2×Q8 | — | 2 | 64 | no | — |
| 605 | C2×Q8 | — | 2 | 16 | no | — |
| 606 | C2×Q8 | — | 2 | 16 | no | — |
| 607 | C2×Q8 | — | 2 | 48 | no | — |
| 608 | C2×Q8 | — | 2 | 12 | no | — |
| 609 | C2×Q8 | — | 2 | 12 | no | — |
| 610 | C2×Q8 | — | 2 | 4 | no | — |
| 611 | C2×Q8 | — | 2 | 12 | no | — |
| 612 | C2×Q8 | — | 2 | 24 | no | — |
| 613 | C2×Q8 | — | 2 | 6 | no | — |
| 614 | C2×Q8 | — | 2 | 24 | no | — |
| 615 | C2×Q8 | — | 4 | 16 | no | — |
| 616 | C2×Q8 | #120 | 1 | 8 | yes | — |
| 617 | C2×Q8 | C22×D4 | 1 | 48 | yes | — |
| 618 | C2×Q8 | C22×D4 | 1 | 12 | yes | — |
| 619 | C2×Q8 | C22×D4 | 1 | 4 | yes | — |
| 620 | C2×Q8 | C25 | 1 | 4 | yes | — |
| 621 | C2×Q8 | C25 | 1 | 8 | yes | — |
| 622 | C2×D4 | — | 2 | 96 | no | — |
| 623 | C2×D4 | — | 2 | 32 | no | — |
| 624 | C2×D4 | — | 2 | 48 | no | — |
| 625 | C2×D4 | — | 2 | 96 | no | — |
| 626 | C2×D4 | — | 2 | 96 | no | — |
| 627 | C2×D4 | — | 2 | 384 | no | — |
| 628 | C2×D4 | — | 2 | 96 | no | — |
| 629 | C2×D4 | — | 2 | 48 | no | — |
| 630 | C2×D4 | — | 2 | 192 | no | — |
| 631 | C2×D4 | — | 2 | 48 | no | — |
| 632 | C2×D4 | — | 2 | 96 | no | — |
| 633 | C2×D4 | — | 2 | 24 | no | — |
| 634 | C2×D4 | — | 2 | 24 | no | — |
| 635 | C2×D4 | — | 2 | 8 | no | — |
| 636 | C2×D4 | — | 2 | 8 | no | — |
| 637 | C2×D4 | — | 2 | 24 | no | — |
| 638 | C2×D4 | — | 2 | 48 | no | — |
| 639 | C2×D4 | — | 2 | 192 | no | — |
| 640 | C2×D4 | — | 2 | 48 | no | — |
| 641 | C2×D4 | — | 2 | 16 | no | — |
| 642 | C2×D4 | — | 2 | 48 | no | — |
| 643 | C2×D4 | — | 2 | 4 | no | — |
| 644 | C2×D4 | — | 2 | 4 | no | — |
| 645 | C2×D4 | — | 2 | 4 | no | — |
| 646 | C2×D4 | — | 2 | 12 | no | — |
| 647 | C2×D4 | — | 2 | 12 | no | — |
| 648 | C2×D4 | — | 2 | 12 | no | — |
| 649 | C2×D4 | — | 2 | 12 | no | — |
| 650 | C2×D4 | — | 2 | 12 | no | — |
| 651 | C2×D4 | — | 2 | 4 | no | — |
| 652 | C2×D4 | — | 2 | 12 | no | — |
| 653 | C2×D4 | — | 2 | 24 | no | — |
| 654 | C2×D4 | — | 2 | 24 | no | — |
| 655 | C2×D4 | — | 2 | 6 | no | — |
| 656 | C2×D4 | — | 4 | 24 | no | — |
| 657 | C2×D4 | — | 4 | 48 | no | — |
| 658 | C2×D4 | — | 8 | 12 | no | — |
| 659 | C2×D4 | — | 8 | 12 | no | — |
| 660 | C2×D4 | #120 | 1 | 24 | yes | — |
| 661 | C2×D4 | C22×D4 | 1 | 24 | yes | — |
| 662 | C2×D4 | C22×D4 | 1 | 12 | yes | — |
| 663 | C2×D4 | C22×D4 | 1 | 48 | yes | — |
| 664 | C2×D4 | C22×D4 | 1 | 12 | yes | — |
| 665 | C2×D4 | C25 | 1 | 4 | yes | — |
| 666 | C2×D4 | C25 | 1 | 8 | yes | — |
| 667 | C22×C4 | — | 2 | 32 | no | — |
| 668 | C22×C4 | — | 2 | 48 | no | — |
| 669 | C22×C4 | — | 2 | 96 | no | — |
| 670 | C22×C4 | — | 2 | 96 | no | — |
| 671 | C22×C4 | — | 2 | 96 | no | — |
| 672 | C22×C4 | — | 2 | 96 | no | — |
| 673 | C22×C4 | — | 2 | 12 | no | — |
| 674 | C22×C4 | — | 2 | 4 | no | — |
| 675 | C22×C4 | — | 2 | 12 | no | — |
| 676 | C22×C4 | — | 2 | 12 | no | — |
| 677 | C22×C4 | — | 2 | 24 | no | — |
| 678 | C22×C4 | — | 2 | 96 | no | — |
| 679 | C22×C4 | — | 2 | 12 | no | — |
| 680 | C22×C4 | — | 2 | 12 | no | — |
| 681 | C22×C4 | — | 2 | 24 | no | — |
| 682 | C22×C4 | — | 2 | 8 | no | — |
| 683 | C22×C4 | — | 2 | 4 | no | — |
| 684 | C22×C4 | — | 2 | 24 | no | — |
| 685 | C22×C4 | — | 2 | 24 | no | — |
| 686 | C22×C4 | — | 2 | 24 | no | — |
| 687 | C22×C4 | — | 2 | 24 | no | — |
| 688 | C22×C4 | — | 2 | 12 | no | — |
| 689 | C22×C4 | — | 2 | 8 | no | — |
| 690 | C22×C4 | — | 2 | 6 | no | — |
| 691 | C22×C4 | — | 2 | 6 | no | — |
| 692 | C22×C4 | — | 2 | 6 | no | — |
| 693 | C22×C4 | — | 2 | 12 | no | — |
| 694 | C22×C4 | — | 2 | 4 | no | — |
| 695 | C22×C4 | — | 4 | 24 | no | — |
| 696 | C22×C4 | C22×D4 | 1 | 6 | yes | — |
| 697 | C22×C4 | C22×D4 | 1 | 6 | yes | — |
| 698 | C22×C4 | C22×D4 | 1 | 6 | yes | — |
| 699 | C22×C4 | C22×D4 | 1 | 6 | yes | — |
| 700 | C22×C4 | C22×D4 | 1 | 6 | yes | — |
| 701 | C22×C4 | C22×D4 | 1 | 6 | yes | — |
| 702 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 703 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 704 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 705 | C22×C4 | C22×D4 | 1 | 6 | yes | — |
| 706 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 707 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 708 | C22×C4 | C22×D4 | 1 | 6 | yes | — |
| 709 | C22×C4 | C22×D4 | 1 | 24 | yes | — |
| 710 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 711 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 712 | C22×C4 | C25 | 1 | 6 | yes | — |
| 713 | C22×C4 | C25 | 1 | 6 | yes | — |
| 714 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 715 | Q16 | — | 2 | 16 | no | — |
| 716 | Q16 | — | 2 | 48 | no | — |
| 717 | SD16 | — | 2 | 16 | no | — |
| 718 | SD16 | — | 2 | 48 | no | — |
| 719 | SD16 | — | 2 | 16 | no | — |
| 720 | SD16 | — | 2 | 48 | no | — |
| 721 | D8 | — | 2 | 16 | no | — |
| 722 | D8 | — | 2 | 48 | no | — |
| 723 | M16 | — | 2 | 48 | no | — |
| 724 | C2×C8 | — | 2 | 4 | no | — |
| 725 | C2×C8 | — | 2 | 12 | no | — |
| 726 | C2×C8 | — | 2 | 24 | no | — |
| 727 | C2×C8 | — | 2 | 24 | no | — |
| 728 | C2×C8 | C25 | 1 | 2 | yes | — |
| 729 | C2×C8 | C25 | 1 | 2 | yes | — |
| 730 | C2×C8 | C25 | 1 | 12 | yes | — |
| 731 | C4⋊C4 | — | 2 | 4 | no | — |
| 732 | C4⋊C4 | — | 2 | 4 | no | — |
| 733 | C4⋊C4 | — | 2 | 12 | no | — |
| 734 | C4⋊C4 | — | 2 | 12 | no | — |
| 735 | C4⋊C4 | — | 2 | 6 | no | — |
| 736 | C4⋊C4 | — | 2 | 6 | no | — |
| 737 | C4⋊C4 | C25 | 1 | 4 | yes | — |
| 738 | C4⋊C4 | C25 | 1 | 4 | yes | — |
| 739 | C22⋊C4 | — | 2 | 4 | no | — |
| 740 | C22⋊C4 | — | 2 | 4 | no | — |
| 741 | C22⋊C4 | — | 2 | 4 | no | — |
| 742 | C22⋊C4 | — | 2 | 12 | no | — |
| 743 | C22⋊C4 | — | 2 | 12 | no | — |
| 744 | C22⋊C4 | — | 2 | 12 | no | — |
| 745 | C22⋊C4 | — | 2 | 4 | no | — |
| 746 | C22⋊C4 | — | 2 | 4 | no | — |
| 747 | C22⋊C4 | — | 2 | 12 | no | — |
| 748 | C22⋊C4 | — | 2 | 12 | no | — |
| 749 | C42 | — | 2 | 12 | no | — |
| 750 | C42 | — | 2 | 4 | no | — |
| 751 | C23 | — | 2 | 16 | no | — |
| 752 | C23 | — | 2 | 48 | no | — |
| 753 | C23 | — | 2 | 12 | no | — |
| 754 | C23 | — | 2 | 2 | no | — |
| 755 | C23 | — | 2 | 8 | no | — |
| 756 | C23 | — | 2 | 12 | no | — |
| 757 | C23 | — | 2 | 2 | no | — |
| 758 | C23 | — | 2 | 12 | no | — |
| 759 | C23 | — | 2 | 6 | no | — |
| 760 | C23 | — | 2 | 48 | no | — |
| 761 | C23 | — | 2 | 4 | no | — |
| 762 | C23 | — | 4 | 3 | no | — |
| 763 | C23 | — | 4 | 6 | no | — |
| 764 | C23 | — | 4 | 1 | no | — |
| 765 | C23 | — | 4 | 3 | no | — |
| 766 | C23 | — | 4 | 6 | no | — |
| 767 | C23 | — | 4 | 6 | no | — |
| 768 | C23 | — | 4 | 3 | no | — |
| 769 | C23 | — | 4 | 3 | no | — |
| 770 | C23 | — | 4 | 8 | no | — |
| 771 | C23 | — | 4 | 8 | no | — |
| 772 | C23 | — | 4 | 12 | no | — |
| 773 | C23 | — | 8 | 12 | no | — |
| 774 | C23 | — | 8 | 12 | no | — |
| 775 | C23 | — | 8 | 12 | no | — |
| 776 | C23 | — | 8 | 12 | no | — |
| 777 | C23 | — | 8 | 6 | no | — |
| 778 | C23 | — | 8 | 6 | no | — |
| 779 | C23 | — | 8 | 24 | no | — |
| 780 | C23 | — | 8 | 96 | no | — |
| 781 | C23 | C2×#120 | 1 | 12 | yes | — |
| 782 | C23 | C23×D4 | 1 | 6 | yes | — |
| 783 | C23 | C23×D4 | 1 | 1 | yes | characteristic |
| 784 | C23 | C23×D4 | 1 | 1 | yes | characteristic |
| 785 | C23 | C23×D4 | 1 | 1 | yes | characteristic |
| 786 | C23 | C23×D4 | 1 | 6 | yes | — |
| 787 | Q8 | — | 2 | 48 | no | — |
| 788 | Q8 | — | 2 | 16 | no | — |
| 789 | Q8 | — | 2 | 8 | no | — |
| 790 | Q8 | — | 2 | 48 | no | — |
| 791 | Q8 | — | 2 | 24 | no | — |
| 792 | Q8 | — | 2 | 8 | no | — |
| 793 | Q8 | — | 4 | 12 | no | — |
| 794 | Q8 | C2×#120 | 1 | 16 | yes | — |
| 795 | Q8 | C23×D4 | 1 | 16 | yes | — |
| 796 | D4 | — | 2 | 96 | no | — |
| 797 | D4 | — | 2 | 32 | no | — |
| 798 | D4 | — | 2 | 48 | no | — |
| 799 | D4 | — | 2 | 16 | no | — |
| 800 | D4 | — | 2 | 96 | no | — |
| 801 | D4 | — | 2 | 32 | no | — |
| 802 | D4 | — | 2 | 48 | no | — |
| 803 | D4 | — | 2 | 8 | no | — |
| 804 | D4 | — | 2 | 8 | no | — |
| 805 | D4 | — | 2 | 24 | no | — |
| 806 | D4 | — | 2 | 48 | no | — |
| 807 | D4 | — | 4 | 8 | no | — |
| 808 | D4 | — | 4 | 8 | no | — |
| 809 | D4 | — | 4 | 24 | no | — |
| 810 | D4 | — | 4 | 8 | no | — |
| 811 | D4 | — | 4 | 12 | no | — |
| 812 | D4 | — | 8 | 12 | no | — |
| 813 | D4 | — | 8 | 12 | no | — |
| 814 | D4 | C2×#120 | 1 | 48 | yes | — |
| 815 | D4 | C23×D4 | 1 | 16 | yes | — |
| 816 | C2×C4 | — | 2 | 16 | no | — |
| 817 | C2×C4 | — | 2 | 32 | no | — |
| 818 | C2×C4 | — | 2 | 48 | no | — |
| 819 | C2×C4 | — | 2 | 96 | no | — |
| 820 | C2×C4 | — | 2 | 8 | no | — |
| 821 | C2×C4 | — | 2 | 12 | no | — |
| 822 | C2×C4 | — | 2 | 2 | no | — |
| 823 | C2×C4 | — | 2 | 48 | no | — |
| 824 | C2×C4 | — | 2 | 12 | no | — |
| 825 | C2×C4 | — | 2 | 6 | no | — |
| 826 | C2×C4 | — | 2 | 2 | no | — |
| 827 | C2×C4 | — | 2 | 2 | no | — |
| 828 | C2×C4 | — | 2 | 12 | no | — |
| 829 | C2×C4 | — | 2 | 2 | no | — |
| 830 | C2×C4 | — | 2 | 32 | no | — |
| 831 | C2×C4 | — | 2 | 12 | no | — |
| 832 | C2×C4 | — | 2 | 12 | no | — |
| 833 | C2×C4 | — | 2 | 12 | no | — |
| 834 | C2×C4 | — | 2 | 2 | no | — |
| 835 | C2×C4 | — | 2 | 96 | no | — |
| 836 | C2×C4 | — | 2 | 12 | no | — |
| 837 | C2×C4 | — | 2 | 12 | no | — |
| 838 | C2×C4 | — | 2 | 4 | no | — |
| 839 | C2×C4 | — | 2 | 4 | no | — |
| 840 | C2×C4 | — | 2 | 4 | no | — |
| 841 | C2×C4 | — | 4 | 12 | no | — |
| 842 | C2×C4 | — | 4 | 8 | no | — |
| 843 | C2×C4 | — | 4 | 24 | no | — |
| 844 | C2×C4 | — | 8 | 6 | no | — |
| 845 | C2×C4 | — | 8 | 6 | no | — |
| 846 | C2×C4 | C2×#120 | 1 | 24 | yes | — |
| 847 | C2×C4 | C2×#120 | 1 | 12 | yes | — |
| 848 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 849 | C2×C4 | C23×D4 | 1 | 6 | yes | — |
| 850 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 851 | C2×C4 | C23×D4 | 1 | 4 | yes | — |
| 852 | C2×C4 | C23×D4 | 1 | 24 | yes | — |
| 853 | C2×C4 | C23×D4 | 1 | 6 | yes | — |
| 854 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 855 | C2×C4 | C26 | 1 | 1 | yes | characteristic |
| 856 | C8 | — | 2 | 2 | no | — |
| 857 | C8 | — | 2 | 2 | no | — |
| 858 | C8 | — | 2 | 12 | no | — |
| 859 | C22 | — | 2 | 6 | no | — |
| 860 | C22 | — | 2 | 1 | no | — |
| 861 | C22 | — | 2 | 6 | no | — |
| 862 | C22 | — | 2 | 1 | no | — |
| 863 | C22 | — | 2 | 1 | no | — |
| 864 | C22 | — | 2 | 1 | no | — |
| 865 | C22 | — | 2 | 6 | no | — |
| 866 | C22 | — | 2 | 1 | no | — |
| 867 | C22 | — | 2 | 1 | no | — |
| 868 | C22 | — | 2 | 6 | no | — |
| 869 | C22 | — | 2 | 6 | no | — |
| 870 | C22 | — | 2 | 1 | no | — |
| 871 | C22 | — | 2 | 16 | no | — |
| 872 | C22 | — | 4 | 12 | no | — |
| 873 | C22 | — | 4 | 4 | no | — |
| 874 | C22 | — | 4 | 24 | no | — |
| 875 | C22 | — | 4 | 32 | no | — |
| 876 | C22 | — | 4 | 8 | no | — |
| 877 | C22 | — | 4 | 8 | no | — |
| 878 | C22 | — | 4 | 4 | no | — |
| 879 | C22 | — | 4 | 4 | no | — |
| 880 | C22 | — | 4 | 4 | no | — |
| 881 | C22 | — | 8 | 6 | no | — |
| 882 | C22 | — | 8 | 12 | no | — |
| 883 | C22 | — | 8 | 48 | no | — |
| 884 | C22 | — | 8 | 48 | no | — |
| 885 | C22 | — | 16 | 12 | no | — |
| 886 | C22 | C22×#120 | 1 | 12 | yes | — |
| 887 | C22 | C22×#120 | 1 | 2 | yes | — |
| 888 | C22 | #3584 | 1 | 2 | yes | complemented |
| 889 | C22 | C24×D4 | 1 | 1 | yes | characteristic |
| 890 | C4 | — | 2 | 1 | no | — |
| 891 | C4 | — | 2 | 16 | no | — |
| 892 | C4 | — | 2 | 6 | no | — |
| 893 | C4 | — | 2 | 1 | no | — |
| 894 | C4 | — | 4 | 4 | no | — |
| 895 | C4 | — | 4 | 4 | no | — |
| 896 | C4 | — | 4 | 4 | no | — |
| 897 | C4 | C22×#120 | 1 | 2 | yes | — |
| 898 | C4 | C22×#120 | 1 | 12 | yes | — |
| 899 | C4 | C24×D4 | 1 | 2 | yes | — |
| 900 | C2 | — | 2 | 2 | no | — |
| 901 | C2 | — | 2 | 2 | no | — |
| 902 | C2 | — | 2 | 12 | no | — |
| 903 | C2 | — | 4 | 6 | no | — |
| 904 | C2 | — | 4 | 1 | no | — |
| 905 | C2 | — | 4 | 16 | no | — |
| 906 | C2 | — | 8 | 4 | no | — |
| 907 | C2 | C23×#120 | 1 | 1 | yes | characteristic |
| 908 | C2 | C2×#3584 | 1 | 1 | yes | characteristic |
| 909 | C2 | #63090 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C26 |
| socle | C22 | C24×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C23×#41 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#585 | C2 | semidirect |
| 2. C2×#3584 | C2 | semidirect |
| 3. #62811 | C2 | semidirect |
| 4. #60377 | C2 | semidirect |
| 5. #60376 | C2 | semidirect |
| 6. #60375 | C2 | semidirect |
| 7. #60374 | C2 | semidirect |
| 8. #60373 | C2 | semidirect |
| 9. #60372 | C2 | semidirect |
| 10. #60366 | C2 | semidirect |
| 11. #60359 | C2 | semidirect |
| 12. C2×#3002 | C2 | semidirect |
| 13. #60086 | C2 | semidirect |
| 14. C2×#2880 | C2 | semidirect |
| 20. C2×#585 | C22 | semidirect |
| 21. C2×#585 | C22 | semidirect |
| 22. C2×#585 | C22 | semidirect |
| 24. C22×2−1+4 | C22 | semidirect |
| 26. C22×H(5,𝔽2) | C22 | semidirect |
| 29. C23×#41 | C22 | semidirect |
| 31. C2×#578 | C22 | semidirect |
| 32. C2×#577 | C22 | semidirect |
| 33. C2×#577 | C22 | semidirect |
| 34. C2×#576 | C22 | semidirect |
| 35. C2×#575 | C22 | semidirect |
| 36. C22×#135 | C22 | semidirect |
| 37. C22×#131 | C22 | semidirect |
| 38. #3489 | C22 | semidirect |
| 39. #3489 | C22 | semidirect |
| 40. #3488 | C22 | semidirect |
| 41. #3488 | C22 | semidirect |
| 48. #3449 | C22 | semidirect |
| 49. C2×#525 | C22 | semidirect |
| 50. #3428 | C22 | semidirect |
| 51. #3013 | C22 | semidirect |
| 52. #3013 | C22 | semidirect |
| 53. #3012 | C22 | semidirect |
| 54. #3012 | C22 | semidirect |
| 55. #3011 | C22 | semidirect |
| 56. #3010 | C22 | semidirect |
| 57. #3009 | C22 | semidirect |
| 58. #3008 | C22 | semidirect |
| 59. #3007 | C22 | semidirect |
| 60. #3007 | C22 | semidirect |
| 61. #3006 | C22 | semidirect |
| 62. #3006 | C22 | semidirect |
| 63. #3005 | C22 | semidirect |
| 64. #3004 | C22 | semidirect |
| 65. #3003 | C22 | semidirect |
| 66. #3002 | C22 | semidirect |
| 67. #3002 | C22 | semidirect |
| 68. #3002 | C22 | semidirect |
| 69. #3002 | C22 | semidirect |
| 70. #3002 | C22 | semidirect |
| 71. #3002 | C22 | semidirect |
| 72. #3002 | C22 | semidirect |
| 73. C2×#452 | C22 | semidirect |
| 74. C2×#449 | C22 | semidirect |
| 75. C2×#451 | C22 | semidirect |
| 76. C2×#448 | C22 | semidirect |
| 77. C2×#450 | C22 | semidirect |
| 78. C2×#447 | C22 | semidirect |
| 79. #2898 | C22 | semidirect |
| 80. #2898 | C22 | semidirect |
| 81. #2897 | C22 | semidirect |
| 82. #2897 | C22 | semidirect |
| 83. #2896 | C22 | semidirect |
| 84. C2×#416 | C22 | semidirect |
| 85. #2880 | C22 | semidirect |
| 86. #2880 | C22 | semidirect |
| 87. #2880 | C22 | semidirect |
| 88. C2×#408 | C22 | semidirect |
| 89. C2×#407 | C22 | semidirect |
| 90. C22×C22⋊C8 | C22 | semidirect |
| 99. #585 | D4 | semidirect |
| 110. C2×2−1+4 | C23 | semidirect |
| 122. C2×H(5,𝔽2) | C23 | semidirect |
| 153. C22×#41 | C23 | semidirect |
| 168. C2×#137 | C23 | semidirect |
| 169. C2×#137 | C23 | semidirect |
| 170. C2×AGL(1,ℤ/8) | C23 | semidirect |
| 171. C2×AGL(1,ℤ/8) | C23 | semidirect |
| 173. C2×#135 | C23 | semidirect |
| 174. C2×#135 | C23 | semidirect |
| 175. C2×#135 | C23 | semidirect |
| 176. C2×#135 | C23 | semidirect |
| 177. C22×Q16 | C23 | semidirect |
| 178. C22×SD16 | C23 | semidirect |
| 179. C22×SD16 | C23 | semidirect |
| 180. C22×D8 | C23 | semidirect |
| 182. C2×#131 | C23 | semidirect |
| 183. C2×#131 | C23 | semidirect |
| 184. C22×M16 | C23 | semidirect |
| 185. C23×C8 | C23 | semidirect |
| 202. #537 | C23 | semidirect |
| 203. #537 | C23 | semidirect |
| 205. #536 | C23 | semidirect |
| 207. #535 | C23 | semidirect |
| 217. #525 | C23 | semidirect |
| 218. #525 | C23 | semidirect |
| 221. C2×C22⋊Q8 | C23 | semidirect |
| 223. C2×#121 | C23 | semidirect |
| 225. #520 | C23 | semidirect |
| 226. #520 | C23 | semidirect |
| 232. C2×#117 | C23 | semidirect |
| 233. #452 | C23 | semidirect |
| 234. #452 | C23 | semidirect |
| 235. #452 | C23 | semidirect |
| 236. #452 | C23 | semidirect |
| 237. #452 | C23 | semidirect |
| 240. #451 | C23 | semidirect |
| 241. #451 | C23 | semidirect |
| 244. #450 | C23 | semidirect |
| 245. #450 | C23 | semidirect |
| 246. #449 | C23 | semidirect |
| 247. #449 | C23 | semidirect |
| 248. #449 | C23 | semidirect |
| 249. #449 | C23 | semidirect |
| 250. #449 | C23 | semidirect |
| 253. #448 | C23 | semidirect |
| 254. #448 | C23 | semidirect |
| 257. #447 | C23 | semidirect |
| 258. #447 | C23 | semidirect |
| 259. #419 | C23 | semidirect |
| 260. #418 | C23 | semidirect |
| 261. #417 | C23 | semidirect |
| 262. #417 | C23 | semidirect |
| 263. #416 | C23 | semidirect |
| 264. #416 | C23 | semidirect |
| 265. #416 | C23 | semidirect |
| 266. #416 | C23 | semidirect |
| 267. C2×#103 | C23 | semidirect |
| 268. C2×#103 | C23 | semidirect |
| 269. C2×#102 | C23 | semidirect |
| 270. C2×#102 | C23 | semidirect |
| 271. #408 | C23 | semidirect |
| 272. #408 | C23 | semidirect |
| 274. #407 | C23 | semidirect |
| 279. C2×C22⋊C8 | C23 | semidirect |
| 280. C2×C22⋊C8 | C23 | semidirect |
| 281. C2×C22⋊C8 | C23 | semidirect |
| 294. 2−1+4 | C2×D4 | semidirect |
| 306. H(5,𝔽2) | C2×D4 | semidirect |
| 363. C2×#41 | C2×D4 | semidirect |
| 888. C22 | #3584 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#585 | 2 |
| C2×#3584 | 2 |
| #62811 | 2 |
| #60377 | 2 |
| #60376 | 2 |
| #60375 | 2 |
| #60374 | 2 |
| #60373 | 2 |
| #60372 | 2 |
| #60366 | 2 |
| #60359 | 2 |
| C2×#3002 | 2 |
| #60086 | 2 |
| C2×#2880 | 2 |