Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
1589 conjugacy classes of subgroups.
The subgroup lattice has 773 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #72322647 | C2 | 1 | 4 | yes | maximal, complemented |
| 2 | #72322645 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #72321739 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #72321119 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #72320649 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×#94614 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #72232007 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C2×#33982 | C4 | 1 | 1 | yes | characteristic |
| 9 | C4×#3415 | — | 2 | 1 | no | — |
| 10 | #512770 | C4 | 1 | 1 | yes | characteristic |
| 11 | #512770 | C22 | 1 | 2 | yes | — |
| 12 | #512766 | C4 | 1 | 1 | yes | characteristic |
| 13 | #512766 | C22 | 1 | 2 | yes | — |
| 14 | #512764 | — | 2 | 2 | no | — |
| 15 | #512764 | — | 2 | 1 | no | — |
| 16 | C4×#2263 | — | 2 | 1 | no | — |
| 17 | C4×#2263 | — | 2 | 2 | no | — |
| 18 | #512761 | C4 | 1 | 2 | yes | — |
| 19 | #512761 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#13654 | C4 | 1 | 2 | yes | — |
| 21 | C2×#13654 | C22 | 1 | 1 | yes | characteristic |
| 22 | #512720 | C4 | 1 | 1 | yes | characteristic |
| 23 | #512691 | — | 2 | 1 | no | — |
| 24 | #512545 | C22 | 1 | 1 | yes | characteristic |
| 25 | #483413 | — | 2 | 1 | no | — |
| 26 | #153583 | C22 | 1 | 4 | yes | complemented |
| 27 | #153582 | — | 2 | 2 | no | — |
| 28 | #153570 | — | 2 | 1 | no | — |
| 29 | #153430 | — | 2 | 1 | no | — |
| 30 | C2×#7511 | C22 | 1 | 2 | yes | complemented |
| 31 | #151058 | C22 | 1 | 4 | yes | complemented |
| 32 | #151057 | — | 2 | 2 | no | — |
| 33 | C2×#7464 | C22 | 1 | 2 | yes | complemented |
| 34 | #151035 | — | 2 | 1 | no | — |
| 35 | #94615 | C22 | 1 | 4 | yes | complemented |
| 36 | #94614 | C22 | 1 | 8 | yes | complemented |
| 37 | #94614 | C22 | 1 | 4 | yes | complemented |
| 38 | C2×#3415 | — | 2 | 1 | no | — |
| 39 | C4×#576 | — | 4 | 1 | no | — |
| 40 | #33982 | — | 2 | 4 | no | — |
| 41 | #33982 | — | 2 | 4 | no | — |
| 42 | C2×#2263 | — | 2 | 2 | no | — |
| 43 | C2×#2263 | — | 2 | 1 | no | — |
| 44 | C2×#2262 | C2×C4 | 1 | 2 | yes | — |
| 45 | C2×#2262 | C2×C4 | 1 | 1 | yes | characteristic |
| 46 | C22×D32 | C2×C4 | 1 | 2 | yes | — |
| 47 | C22×D32 | C2×C4 | 1 | 1 | yes | characteristic |
| 48 | C2×#2258 | C2×C4 | 1 | 1 | yes | characteristic |
| 49 | C2×#2258 | D4 | 1 | 1 | yes | characteristic |
| 50 | #33459 | — | 2 | 1 | no | — |
| 51 | #33459 | — | 2 | 2 | no | — |
| 52 | #33456 | — | 2 | 1 | no | — |
| 53 | #33456 | — | 2 | 2 | no | — |
| 54 | #33454 | — | 4 | 2 | no | — |
| 55 | #33454 | — | 4 | 1 | no | — |
| 56 | C4×#509 | — | 4 | 1 | no | — |
| 57 | C4×#509 | — | 4 | 2 | no | — |
| 58 | C4×#508 | — | 2 | 2 | no | — |
| 59 | C4×#508 | — | 2 | 1 | no | — |
| 60 | C2×C4×D16 | — | 2 | 2 | no | — |
| 61 | C2×C4×D16 | — | 2 | 1 | no | — |
| 62 | #33428 | — | 4 | 1 | no | — |
| 63 | #33410 | — | 2 | 1 | no | — |
| 64 | #33381 | — | 4 | 1 | no | — |
| 65 | C4×#504 | D4 | 1 | 1 | yes | characteristic |
| 66 | C2×M128 | — | 2 | 2 | no | — |
| 67 | #13654 | — | 2 | 2 | no | — |
| 68 | #13654 | — | 2 | 2 | no | — |
| 69 | #13654 | — | 2 | 1 | no | — |
| 70 | #13654 | — | 2 | 1 | no | — |
| 71 | #13654 | C2×C4 | 1 | 2 | yes | — |
| 72 | #13654 | C2×C4 | 1 | 2 | yes | — |
| 73 | #13654 | C2×C4 | 1 | 1 | yes | characteristic |
| 74 | #13654 | C2×C4 | 1 | 2 | yes | — |
| 75 | #13654 | C2×C4 | 1 | 2 | yes | — |
| 76 | #13654 | C23 | 1 | 2 | yes | — |
| 77 | #13654 | C23 | 1 | 1 | yes | characteristic |
| 78 | #13653 | C2×C4 | 1 | 2 | yes | — |
| 79 | #13653 | C2×C4 | 1 | 1 | yes | characteristic |
| 80 | #13653 | C23 | 1 | 1 | yes | characteristic |
| 81 | #13652 | — | 2 | 2 | no | — |
| 82 | #13652 | — | 2 | 2 | no | — |
| 83 | #13652 | — | 2 | 1 | no | — |
| 84 | #13652 | — | 2 | 1 | no | — |
| 85 | C4×SD64 | — | 2 | 2 | no | — |
| 86 | C4×SD64 | — | 2 | 2 | no | — |
| 87 | C4×SD64 | — | 2 | 2 | no | — |
| 88 | C4×D32 | — | 2 | 2 | no | — |
| 89 | C4×D32 | — | 2 | 2 | no | — |
| 90 | C4×D32 | — | 2 | 2 | no | — |
| 91 | #13634 | — | 2 | 2 | no | — |
| 92 | #13634 | — | 2 | 1 | no | — |
| 93 | #13633 | C2×C4 | 1 | 2 | yes | — |
| 94 | #13633 | C2×C4 | 1 | 1 | yes | characteristic |
| 95 | C2×#1424 | C2×C4 | 1 | 1 | yes | characteristic |
| 96 | C2×#1424 | C2×C4 | 1 | 2 | yes | — |
| 97 | #13617 | — | 2 | 1 | no | — |
| 98 | #13617 | — | 2 | 2 | no | — |
| 99 | #13616 | — | 2 | 1 | no | — |
| 100 | #13616 | — | 2 | 2 | no | — |
| 101 | #13615 | — | 2 | 2 | no | — |
| 102 | #13615 | — | 2 | 1 | no | — |
| 103 | C2×#1415 | — | 2 | 2 | no | — |
| 104 | C2×#1415 | — | 2 | 1 | no | — |
| 105 | #13549 | C2×C4 | 1 | 1 | yes | characteristic |
| 106 | #13549 | D4 | 1 | 1 | yes | characteristic |
| 107 | #13549 | D4 | 1 | 2 | yes | — |
| 108 | #13549 | C23 | 1 | 2 | yes | — |
| 109 | C4×M64 | D4 | 1 | 2 | yes | — |
| 110 | C4×M64 | D4 | 1 | 1 | yes | characteristic |
| 111 | C2×#1397 | C2×C4 | 1 | 2 | yes | — |
| 112 | C2×#1397 | C23 | 1 | 1 | yes | characteristic |
| 113 | #12027 | — | 2 | 4 | no | — |
| 114 | #12026 | — | 4 | 2 | no | — |
| 115 | C2×#1373 | — | 2 | 2 | no | — |
| 116 | #12002 | — | 4 | 1 | no | — |
| 117 | #7544 | — | 2 | 4 | no | — |
| 118 | #7513 | — | 2 | 4 | no | — |
| 119 | #7511 | — | 2 | 2 | no | — |
| 120 | #7511 | C23 | 1 | 4 | yes | — |
| 121 | #7464 | — | 2 | 2 | no | — |
| 122 | #7464 | C23 | 1 | 4 | yes | — |
| 123 | #7462 | — | 2 | 4 | no | — |
| 124 | C2×#576 | — | 4 | 1 | no | — |
| 125 | C4×H(5,𝔽2) | — | 8 | 1 | no | — |
| 126 | #3415 | — | 2 | 8 | no | — |
| 127 | #3415 | — | 4 | 4 | no | — |
| 128 | C2×#509 | — | 4 | 1 | no | — |
| 129 | C2×#509 | — | 4 | 2 | no | — |
| 130 | C2×#508 | — | 2 | 2 | no | — |
| 131 | C2×#508 | — | 2 | 1 | no | — |
| 132 | C22×D16 | — | 2 | 2 | no | — |
| 133 | C22×D16 | — | 2 | 1 | no | — |
| 134 | C2×#504 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 135 | C2×#504 | SD16 | 1 | 1 | yes | characteristic |
| 136 | #2951 | — | 4 | 1 | no | — |
| 137 | #2951 | — | 4 | 2 | no | — |
| 138 | #2948 | — | 4 | 1 | no | — |
| 139 | #2948 | — | 4 | 2 | no | — |
| 140 | #2946 | — | 8 | 1 | no | — |
| 141 | #2946 | — | 8 | 2 | no | — |
| 142 | C4×AGL(1,ℤ/8) | — | 8 | 2 | no | — |
| 143 | C4×AGL(1,ℤ/8) | — | 8 | 1 | no | — |
| 144 | C4×#135 | — | 4 | 2 | no | — |
| 145 | C4×#135 | — | 4 | 1 | no | — |
| 146 | C2×C4×D8 | — | 4 | 2 | no | — |
| 147 | C2×C4×D8 | — | 4 | 1 | no | — |
| 148 | #2913 | — | 4 | 1 | no | — |
| 149 | #2897 | — | 8 | 1 | no | — |
| 150 | C4×#131 | D8 | 1 | 1 | yes | characteristic |
| 151 | #2263 | — | 2 | 8 | no | — |
| 152 | #2263 | — | 2 | 16 | no | — |
| 153 | #2262 | — | 2 | 4 | no | — |
| 154 | #2262 | — | 2 | 4 | no | — |
| 155 | #2262 | — | 2 | 2 | no | — |
| 156 | #2262 | M16 | 1 | 4 | yes | — |
| 157 | C2×Q64 | C22×C4 | 1 | 1 | yes | characteristic |
| 158 | C2×SD64 | — | 2 | 2 | no | — |
| 159 | C2×SD64 | — | 2 | 1 | no | — |
| 160 | C2×D32 | — | 2 | 4 | no | — |
| 161 | C2×D32 | — | 2 | 4 | no | — |
| 162 | C2×D32 | — | 2 | 2 | no | — |
| 163 | C2×D32 | — | 2 | 1 | no | — |
| 164 | C2×D32 | — | 2 | 2 | no | — |
| 165 | C2×D32 | M16 | 1 | 4 | yes | — |
| 166 | C2×D32 | C22×C4 | 1 | 1 | yes | characteristic |
| 167 | C2×D32 | C22×C4 | 1 | 2 | yes | — |
| 168 | #2258 | — | 2 | 2 | no | — |
| 169 | #2258 | — | 2 | 2 | no | — |
| 170 | #2258 | — | 4 | 2 | no | — |
| 171 | C2×M64 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 172 | C2×M64 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 173 | C2×M64 | C22⋊C4 | 1 | 2 | yes | — |
| 174 | C2×M64 | C2×D4 | 1 | 2 | yes | — |
| 175 | C22×C32 | C22⋊C4 | 1 | 2 | yes | — |
| 176 | C22×C32 | C22×C4 | 1 | 2 | yes | — |
| 177 | C22×C32 | C22×C4 | 1 | 1 | yes | characteristic |
| 178 | C22×C32 | C2×D4 | 1 | 1 | yes | characteristic |
| 179 | #2177 | — | 4 | 2 | no | — |
| 180 | #2177 | — | 4 | 2 | no | — |
| 181 | #2177 | — | 4 | 2 | no | — |
| 182 | #2175 | — | 4 | 2 | no | — |
| 183 | #2175 | — | 4 | 2 | no | — |
| 184 | #2175 | — | 4 | 2 | no | — |
| 185 | C4×Q32 | — | 2 | 2 | no | — |
| 186 | C4×Q32 | — | 2 | 1 | no | — |
| 187 | C4×Q32 | — | 2 | 1 | no | — |
| 188 | C4×SD32 | — | 4 | 2 | no | — |
| 189 | C4×SD32 | — | 4 | 2 | no | — |
| 190 | C4×SD32 | — | 4 | 1 | no | — |
| 191 | C4×SD32 | — | 4 | 1 | no | — |
| 192 | C4×D16 | — | 2 | 2 | no | — |
| 193 | C4×D16 | — | 2 | 2 | no | — |
| 194 | C4×D16 | — | 2 | 2 | no | — |
| 195 | C4×D16 | — | 2 | 2 | no | — |
| 196 | C4×D16 | — | 2 | 1 | no | — |
| 197 | C4×D16 | — | 2 | 1 | no | — |
| 198 | C4×D16 | — | 2 | 2 | no | — |
| 199 | C4×D16 | — | 4 | 2 | no | — |
| 200 | C4×D16 | — | 4 | 2 | no | — |
| 201 | C4×D16 | — | 4 | 1 | no | — |
| 202 | C4×D16 | — | 4 | 1 | no | — |
| 203 | #2166 | — | 4 | 4 | no | — |
| 204 | #2165 | — | 8 | 2 | no | — |
| 205 | #2159 | — | 4 | 1 | no | — |
| 206 | #2159 | — | 4 | 2 | no | — |
| 207 | #2158 | — | 2 | 2 | no | — |
| 208 | #2158 | — | 2 | 1 | no | — |
| 209 | C2×#366 | — | 2 | 2 | no | — |
| 210 | C2×#366 | — | 2 | 1 | no | — |
| 211 | C2×#364 | — | 4 | 2 | no | — |
| 212 | #2140 | — | 4 | 1 | no | — |
| 213 | #2140 | — | 4 | 2 | no | — |
| 214 | #2139 | — | 4 | 1 | no | — |
| 215 | #2139 | — | 4 | 2 | no | — |
| 216 | #2138 | — | 4 | 2 | no | — |
| 217 | #2138 | — | 4 | 1 | no | — |
| 218 | C2×#357 | — | 4 | 2 | no | — |
| 219 | C2×#357 | — | 4 | 1 | no | — |
| 220 | #2115 | — | 8 | 1 | no | — |
| 221 | #2110 | — | 8 | 1 | no | — |
| 222 | #2108 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 223 | #2108 | D8 | 1 | 2 | yes | — |
| 224 | #2108 | SD16 | 1 | 1 | yes | characteristic |
| 225 | #2108 | C2×D4 | 1 | 2 | yes | — |
| 226 | C4×M32 | D8 | 1 | 1 | yes | characteristic |
| 227 | C4×M32 | SD16 | 1 | 2 | yes | — |
| 228 | C2×C4×C16 | C22⋊C4 | 1 | 2 | yes | — |
| 229 | C2×C4×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 230 | M128 | — | 2 | 4 | no | — |
| 231 | M128 | — | 4 | 2 | no | — |
| 232 | C2×C64 | — | 4 | 2 | no | — |
| 233 | #1424 | — | 2 | 2 | no | — |
| 234 | #1424 | — | 2 | 1 | no | — |
| 235 | #1424 | C22×C4 | 1 | 2 | yes | — |
| 236 | #1424 | C22×C4 | 1 | 1 | yes | characteristic |
| 237 | #1424 | C22×C4 | 1 | 1 | yes | characteristic |
| 238 | #1423 | — | 2 | 2 | no | — |
| 239 | #1423 | — | 2 | 1 | no | — |
| 240 | #1416 | — | 2 | 1 | no | — |
| 241 | #1416 | — | 2 | 2 | no | — |
| 242 | #1416 | — | 2 | 1 | no | — |
| 243 | #1415 | — | 2 | 1 | no | — |
| 244 | #1415 | — | 2 | 2 | no | — |
| 245 | #1415 | — | 2 | 2 | no | — |
| 246 | #1415 | — | 2 | 2 | no | — |
| 247 | #1415 | — | 2 | 2 | no | — |
| 248 | #1415 | — | 2 | 2 | no | — |
| 249 | #1415 | — | 2 | 1 | no | — |
| 250 | #1397 | C22⋊C4 | 1 | 2 | yes | — |
| 251 | #1397 | C22⋊C4 | 1 | 2 | yes | — |
| 252 | #1397 | C22×C4 | 1 | 1 | yes | characteristic |
| 253 | #1397 | C22×C4 | 1 | 2 | yes | — |
| 254 | #1397 | C2×D4 | 1 | 1 | yes | characteristic |
| 255 | #1397 | C2×D4 | 1 | 1 | yes | characteristic |
| 256 | #1397 | C24 | 1 | 1 | yes | characteristic |
| 257 | C4×C32 | C22⋊C4 | 1 | 2 | yes | — |
| 258 | C4×C32 | C2×D4 | 1 | 2 | yes | — |
| 259 | C4×C32 | C2×D4 | 1 | 2 | yes | — |
| 260 | #1373 | — | 2 | 4 | no | — |
| 261 | #1373 | — | 4 | 2 | no | — |
| 262 | #1369 | — | 4 | 4 | no | — |
| 263 | C2×H(5,𝔽2) | — | 8 | 1 | no | — |
| 264 | #576 | — | 4 | 8 | no | — |
| 265 | #576 | — | 8 | 4 | no | — |
| 266 | C2×AGL(1,ℤ/8) | — | 8 | 2 | no | — |
| 267 | C2×AGL(1,ℤ/8) | — | 8 | 1 | no | — |
| 268 | C2×#135 | — | 4 | 2 | no | — |
| 269 | C2×#135 | — | 4 | 1 | no | — |
| 270 | C22×D8 | — | 4 | 2 | no | — |
| 271 | C22×D8 | — | 4 | 1 | no | — |
| 272 | C2×#131 | #102 | 1 | 1 | yes | characteristic |
| 273 | C2×#131 | D16 | 1 | 1 | yes | characteristic |
| 274 | #520 | — | 8 | 1 | no | — |
| 275 | #520 | — | 8 | 1 | no | — |
| 276 | #520 | — | 8 | 2 | no | — |
| 277 | #520 | — | 16 | 1 | no | — |
| 278 | #518 | — | 8 | 1 | no | — |
| 279 | #518 | — | 8 | 2 | no | — |
| 280 | #518 | — | 16 | 2 | no | — |
| 281 | #518 | — | 16 | 1 | no | — |
| 282 | C4×#41 | — | 8 | 2 | no | — |
| 283 | C4×#41 | — | 8 | 1 | no | — |
| 284 | C4×#41 | — | 16 | 1 | no | — |
| 285 | C4×#41 | SD32 | 1 | 1 | yes | characteristic |
| 286 | C2×C4×D4 | — | 8 | 2 | no | — |
| 287 | C2×C4×D4 | — | 8 | 1 | no | — |
| 288 | C2×C4×D4 | — | 16 | 2 | no | — |
| 289 | C2×C4×D4 | — | 16 | 1 | no | — |
| 290 | #509 | — | 4 | 8 | no | — |
| 291 | #509 | — | 4 | 16 | no | — |
| 292 | #508 | — | 2 | 8 | no | — |
| 293 | #508 | — | 2 | 4 | no | — |
| 294 | #508 | — | 4 | 4 | no | — |
| 295 | #508 | — | 4 | 2 | no | — |
| 296 | C2×Q32 | — | 2 | 1 | no | — |
| 297 | C2×SD32 | — | 4 | 2 | no | — |
| 298 | C2×SD32 | — | 4 | 1 | no | — |
| 299 | C2×D16 | — | 2 | 8 | no | — |
| 300 | C2×D16 | — | 2 | 2 | no | — |
| 301 | C2×D16 | — | 2 | 1 | no | — |
| 302 | C2×D16 | — | 2 | 4 | no | — |
| 303 | C2×D16 | — | 4 | 4 | no | — |
| 304 | C2×D16 | — | 4 | 2 | no | — |
| 305 | C2×D16 | — | 4 | 1 | no | — |
| 306 | C2×D16 | — | 4 | 2 | no | — |
| 307 | #504 | — | 2 | 2 | no | — |
| 308 | #504 | — | 2 | 2 | no | — |
| 309 | #504 | — | 4 | 2 | no | — |
| 310 | C2×M32 | — | 8 | 2 | no | — |
| 311 | C2×M32 | #102 | 1 | 1 | yes | characteristic |
| 312 | C2×M32 | #102 | 1 | 1 | yes | characteristic |
| 313 | C2×M32 | #102 | 1 | 2 | yes | — |
| 314 | C2×M32 | C2×SD16 | 1 | 2 | yes | — |
| 315 | C22×C16 | #102 | 1 | 2 | yes | — |
| 316 | C22×C16 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 317 | C22×C16 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 318 | C22×C16 | C2×SD16 | 1 | 1 | yes | characteristic |
| 319 | #442 | — | 8 | 2 | no | — |
| 320 | #442 | — | 8 | 2 | no | — |
| 321 | #442 | — | 8 | 2 | no | — |
| 322 | #440 | — | 8 | 2 | no | — |
| 323 | #440 | — | 8 | 2 | no | — |
| 324 | #440 | — | 8 | 2 | no | — |
| 325 | C4×Q16 | — | 4 | 1 | no | — |
| 326 | C4×Q16 | — | 4 | 1 | no | — |
| 327 | C4×Q16 | — | 4 | 2 | no | — |
| 328 | C4×SD16 | — | 8 | 2 | no | — |
| 329 | C4×SD16 | — | 8 | 2 | no | — |
| 330 | C4×SD16 | — | 8 | 1 | no | — |
| 331 | C4×SD16 | — | 8 | 1 | no | — |
| 332 | C4×D8 | — | 4 | 2 | no | — |
| 333 | C4×D8 | — | 4 | 1 | no | — |
| 334 | C4×D8 | — | 4 | 1 | no | — |
| 335 | C4×D8 | — | 4 | 2 | no | — |
| 336 | C4×D8 | — | 4 | 2 | no | — |
| 337 | C4×D8 | — | 4 | 2 | no | — |
| 338 | C4×D8 | — | 4 | 2 | no | — |
| 339 | C4×D8 | — | 8 | 2 | no | — |
| 340 | C4×D8 | — | 8 | 2 | no | — |
| 341 | C4×D8 | — | 8 | 1 | no | — |
| 342 | C4×D8 | — | 8 | 1 | no | — |
| 343 | #428 | — | 8 | 2 | no | — |
| 344 | #428 | — | 8 | 1 | no | — |
| 345 | #427 | — | 4 | 2 | no | — |
| 346 | #427 | — | 4 | 1 | no | — |
| 347 | C2×#107 | — | 4 | 2 | no | — |
| 348 | C2×#107 | — | 4 | 1 | no | — |
| 349 | #418 | — | 8 | 1 | no | — |
| 350 | #418 | — | 8 | 2 | no | — |
| 351 | #417 | — | 8 | 1 | no | — |
| 352 | #417 | — | 8 | 2 | no | — |
| 353 | #416 | — | 8 | 2 | no | — |
| 354 | #416 | — | 8 | 1 | no | — |
| 355 | C2×#102 | — | 8 | 2 | no | — |
| 356 | C2×#102 | — | 8 | 1 | no | — |
| 357 | #405 | #102 | 1 | 1 | yes | characteristic |
| 358 | #405 | D16 | 1 | 1 | yes | characteristic |
| 359 | #405 | SD32 | 1 | 2 | yes | — |
| 360 | #405 | C2×D8 | 1 | 2 | yes | — |
| 361 | C4×M16 | D16 | 1 | 2 | yes | — |
| 362 | C4×M16 | SD32 | 1 | 1 | yes | characteristic |
| 363 | C2×C4×C8 | #102 | 1 | 2 | yes | — |
| 364 | C2×C4×C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 365 | Q64 | — | 2 | 1 | no | — |
| 366 | Q64 | C2×M16 | 1 | 2 | yes | — |
| 367 | SD64 | — | 2 | 8 | no | — |
| 368 | SD64 | — | 2 | 4 | no | — |
| 369 | D32 | — | 2 | 8 | no | — |
| 370 | D32 | — | 2 | 2 | no | — |
| 371 | D32 | — | 2 | 1 | no | — |
| 372 | D32 | — | 2 | 4 | no | — |
| 373 | D32 | C2×M16 | 1 | 2 | yes | — |
| 374 | D32 | C2×M16 | 1 | 4 | yes | — |
| 375 | M64 | — | 2 | 2 | no | — |
| 376 | M64 | — | 2 | 2 | no | — |
| 377 | M64 | — | 2 | 4 | no | — |
| 378 | M64 | — | 4 | 2 | no | — |
| 379 | C2×C32 | — | 2 | 2 | no | — |
| 380 | C2×C32 | — | 2 | 2 | no | — |
| 381 | C2×C32 | — | 2 | 2 | no | — |
| 382 | C2×C32 | — | 4 | 2 | no | — |
| 383 | C2×C32 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 384 | C2×C32 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 385 | C2×C32 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 386 | C2×C32 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 387 | C2×C32 | C2×M16 | 1 | 2 | yes | — |
| 388 | C2×C32 | C2×M16 | 1 | 2 | yes | — |
| 389 | C2×C32 | C23×C4 | 1 | 1 | yes | characteristic |
| 390 | C2×C32 | C22×D4 | 1 | 1 | yes | characteristic |
| 391 | #367 | — | 4 | 2 | no | — |
| 392 | #367 | — | 4 | 1 | no | — |
| 393 | #366 | — | 2 | 1 | no | — |
| 394 | #366 | — | 2 | 2 | no | — |
| 395 | #366 | — | 2 | 1 | no | — |
| 396 | #366 | — | 4 | 2 | no | — |
| 397 | #366 | — | 4 | 1 | no | — |
| 398 | #364 | — | 4 | 4 | no | — |
| 399 | #364 | — | 8 | 2 | no | — |
| 400 | #358 | — | 4 | 1 | no | — |
| 401 | #358 | — | 4 | 1 | no | — |
| 402 | #358 | — | 4 | 2 | no | — |
| 403 | #357 | — | 4 | 2 | no | — |
| 404 | #357 | — | 4 | 1 | no | — |
| 405 | #357 | — | 4 | 1 | no | — |
| 406 | #357 | — | 4 | 2 | no | — |
| 407 | #357 | — | 4 | 2 | no | — |
| 408 | #357 | — | 4 | 2 | no | — |
| 409 | #357 | — | 4 | 2 | no | — |
| 410 | #349 | — | 8 | 4 | no | — |
| 411 | #347 | — | 8 | 4 | no | — |
| 412 | #346 | #102 | 1 | 2 | yes | — |
| 413 | #346 | C2×D8 | 1 | 2 | yes | — |
| 414 | #346 | C2×SD16 | 1 | 2 | yes | — |
| 415 | C4×C16 | #102 | 1 | 2 | yes | — |
| 416 | C4×C16 | #102 | 1 | 2 | yes | — |
| 417 | C4×C16 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 418 | C4×C16 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 419 | C4×C16 | C2×D8 | 1 | 1 | yes | characteristic |
| 420 | C4×C16 | C2×SD16 | 1 | 1 | yes | characteristic |
| 421 | C4×C16 | C22×D4 | 1 | 1 | yes | characteristic |
| 422 | C64 | — | 4 | 4 | no | — |
| 423 | H(5,𝔽2) | — | 8 | 8 | no | — |
| 424 | H(5,𝔽2) | — | 16 | 4 | no | — |
| 425 | C2×#41 | — | 8 | 2 | no | — |
| 426 | C2×#41 | — | 8 | 1 | no | — |
| 427 | C2×#41 | — | 16 | 1 | no | — |
| 428 | C2×#41 | #357 | 1 | 1 | yes | characteristic |
| 429 | C22×D4 | — | 8 | 2 | no | — |
| 430 | C22×D4 | — | 8 | 1 | no | — |
| 431 | C22×D4 | — | 16 | 2 | no | — |
| 432 | C22×D4 | — | 16 | 1 | no | — |
| 433 | C23×C4 | — | 16 | 2 | no | — |
| 434 | C23×C4 | — | 16 | 1 | no | — |
| 435 | AGL(1,ℤ/8) | — | 8 | 8 | no | — |
| 436 | AGL(1,ℤ/8) | — | 8 | 16 | no | — |
| 437 | #135 | — | 4 | 8 | no | — |
| 438 | #135 | — | 4 | 4 | no | — |
| 439 | #135 | — | 8 | 4 | no | — |
| 440 | #135 | — | 8 | 2 | no | — |
| 441 | C2×Q16 | — | 4 | 1 | no | — |
| 442 | C2×SD16 | — | 8 | 2 | no | — |
| 443 | C2×SD16 | — | 8 | 1 | no | — |
| 444 | C2×D8 | — | 4 | 8 | no | — |
| 445 | C2×D8 | — | 4 | 2 | no | — |
| 446 | C2×D8 | — | 4 | 1 | no | — |
| 447 | C2×D8 | — | 4 | 4 | no | — |
| 448 | C2×D8 | — | 8 | 4 | no | — |
| 449 | C2×D8 | — | 8 | 2 | no | — |
| 450 | C2×D8 | — | 8 | 1 | no | — |
| 451 | C2×D8 | — | 8 | 2 | no | — |
| 452 | #131 | — | 2 | 2 | no | — |
| 453 | #131 | — | 2 | 2 | no | — |
| 454 | #131 | — | 4 | 2 | no | — |
| 455 | C2×M16 | #357 | 1 | 2 | yes | — |
| 456 | C2×M16 | #357 | 1 | 1 | yes | characteristic |
| 457 | C2×M16 | #357 | 1 | 1 | yes | characteristic |
| 458 | C2×M16 | C2×D16 | 1 | 2 | yes | — |
| 459 | C22×C8 | #357 | 1 | 2 | yes | — |
| 460 | C22×C8 | C2×#102 | 1 | 2 | yes | — |
| 461 | C22×C8 | C2×#102 | 1 | 1 | yes | characteristic |
| 462 | C22×C8 | C2×D16 | 1 | 1 | yes | characteristic |
| 463 | C4×Q8 | — | 2 | 1 | no | — |
| 464 | C4×Q8 | — | 8 | 1 | no | — |
| 465 | C4×Q8 | — | 8 | 1 | no | — |
| 466 | C4×Q8 | — | 8 | 2 | no | — |
| 467 | C4×Q8 | — | 16 | 1 | no | — |
| 468 | C4×D4 | — | 2 | 2 | no | — |
| 469 | C4×D4 | — | 2 | 1 | no | — |
| 470 | C4×D4 | — | 8 | 2 | no | — |
| 471 | C4×D4 | — | 8 | 1 | no | — |
| 472 | C4×D4 | — | 8 | 1 | no | — |
| 473 | C4×D4 | — | 8 | 2 | no | — |
| 474 | C4×D4 | — | 8 | 2 | no | — |
| 475 | C4×D4 | — | 8 | 2 | no | — |
| 476 | C4×D4 | — | 8 | 2 | no | — |
| 477 | C4×D4 | — | 16 | 2 | no | — |
| 478 | C4×D4 | — | 16 | 1 | no | — |
| 479 | C4×D4 | — | 16 | 2 | no | — |
| 480 | C4×D4 | — | 16 | 1 | no | — |
| 481 | C4×D4 | — | 16 | 2 | no | — |
| 482 | C4×D4 | — | 16 | 2 | no | — |
| 483 | C4×D4 | — | 16 | 2 | no | — |
| 484 | C4×D4 | — | 16 | 1 | no | — |
| 485 | C4×D4 | — | 16 | 2 | no | — |
| 486 | C4×D4 | — | 16 | 1 | no | — |
| 487 | C4×D4 | — | 16 | 2 | no | — |
| 488 | C4×D4 | — | 16 | 2 | no | — |
| 489 | C4×D4 | — | 16 | 1 | no | — |
| 490 | C4×D4 | — | 16 | 2 | no | — |
| 491 | C4×D4 | — | 16 | 1 | no | — |
| 492 | C4×D4 | — | 16 | 2 | no | — |
| 493 | C4×D4 | — | 16 | 1 | no | — |
| 494 | #117 | — | 8 | 2 | no | — |
| 495 | #117 | — | 8 | 1 | no | — |
| 496 | #117 | — | 16 | 2 | no | — |
| 497 | #117 | — | 16 | 1 | no | — |
| 498 | #117 | — | 16 | 1 | no | — |
| 499 | #117 | — | 16 | 2 | no | — |
| 500 | #117 | #357 | 1 | 1 | yes | characteristic |
| 501 | #117 | C2×SD32 | 1 | 2 | yes | — |
| 502 | C2×C4⋊C4 | — | 8 | 2 | no | — |
| 503 | C2×C4⋊C4 | — | 8 | 1 | no | — |
| 504 | C2×C4⋊C4 | — | 16 | 1 | no | — |
| 505 | C2×C4⋊C4 | — | 16 | 2 | no | — |
| 506 | C2×C22⋊C4 | — | 16 | 2 | no | — |
| 507 | C2×C22⋊C4 | — | 16 | 2 | no | — |
| 508 | C2×C22⋊C4 | — | 16 | 2 | no | — |
| 509 | C2×C22⋊C4 | — | 16 | 2 | no | — |
| 510 | C2×C22⋊C4 | — | 16 | 1 | no | — |
| 511 | C2×C42 | — | 16 | 2 | no | — |
| 512 | C2×C42 | — | 16 | 1 | no | — |
| 513 | C2×C42 | #357 | 1 | 2 | yes | — |
| 514 | C2×C42 | C2×SD32 | 1 | 1 | yes | characteristic |
| 515 | Q32 | — | 2 | 2 | no | — |
| 516 | Q32 | — | 4 | 1 | no | — |
| 517 | SD32 | — | 4 | 8 | no | — |
| 518 | SD32 | — | 4 | 4 | no | — |
| 519 | D16 | — | 2 | 2 | no | — |
| 520 | D16 | — | 2 | 4 | no | — |
| 521 | D16 | — | 4 | 8 | no | — |
| 522 | D16 | — | 4 | 1 | no | — |
| 523 | D16 | — | 4 | 2 | no | — |
| 524 | D16 | — | 4 | 4 | no | — |
| 525 | M32 | — | 2 | 2 | no | — |
| 526 | M32 | — | 2 | 2 | no | — |
| 527 | M32 | — | 2 | 4 | no | — |
| 528 | M32 | — | 4 | 2 | no | — |
| 529 | M32 | — | 8 | 4 | no | — |
| 530 | M32 | — | 16 | 2 | no | — |
| 531 | C2×C16 | — | 2 | 2 | no | — |
| 532 | C2×C16 | — | 2 | 2 | no | — |
| 533 | C2×C16 | — | 2 | 2 | no | — |
| 534 | C2×C16 | — | 4 | 2 | no | — |
| 535 | C2×C16 | — | 16 | 2 | no | — |
| 536 | C2×C16 | #407 | 1 | 2 | yes | — |
| 537 | C2×C16 | C2×#102 | 1 | 1 | yes | characteristic |
| 538 | C2×C16 | C2×#102 | 1 | 2 | yes | — |
| 539 | C2×C16 | C2×#102 | 1 | 2 | yes | — |
| 540 | C2×C16 | C2×#102 | 1 | 1 | yes | characteristic |
| 541 | C2×C16 | #421 | 1 | 2 | yes | — |
| 542 | C2×C16 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 543 | C2×C16 | C22×SD16 | 1 | 1 | yes | characteristic |
| 544 | #107 | — | 4 | 2 | no | — |
| 545 | #107 | — | 4 | 1 | no | — |
| 546 | #107 | — | 4 | 1 | no | — |
| 547 | #107 | — | 8 | 2 | no | — |
| 548 | #107 | — | 8 | 1 | no | — |
| 549 | #106 | — | 8 | 2 | no | — |
| 550 | #106 | — | 8 | 1 | no | — |
| 551 | #103 | — | 8 | 1 | no | — |
| 552 | #103 | — | 8 | 1 | no | — |
| 553 | #103 | — | 8 | 2 | no | — |
| 554 | #102 | — | 8 | 2 | no | — |
| 555 | #102 | — | 8 | 1 | no | — |
| 556 | #102 | — | 8 | 1 | no | — |
| 557 | #102 | — | 8 | 2 | no | — |
| 558 | #102 | — | 8 | 2 | no | — |
| 559 | #102 | — | 8 | 2 | no | — |
| 560 | #102 | — | 8 | 2 | no | — |
| 561 | #97 | #357 | 1 | 2 | yes | — |
| 562 | #97 | C2×D16 | 1 | 2 | yes | — |
| 563 | #97 | C2×SD32 | 1 | 2 | yes | — |
| 564 | C4×C8 | #357 | 1 | 2 | yes | — |
| 565 | C4×C8 | #357 | 1 | 2 | yes | — |
| 566 | C4×C8 | C2×#102 | 1 | 1 | yes | characteristic |
| 567 | C4×C8 | C2×#102 | 1 | 2 | yes | — |
| 568 | C4×C8 | C2×D16 | 1 | 1 | yes | characteristic |
| 569 | C4×C8 | C2×SD32 | 1 | 1 | yes | characteristic |
| 570 | C4×C8 | C22×D8 | 1 | 1 | yes | characteristic |
| 571 | C32 | — | 2 | 2 | no | — |
| 572 | C32 | — | 2 | 1 | no | — |
| 573 | C32 | — | 2 | 1 | no | — |
| 574 | C32 | — | 2 | 2 | no | — |
| 575 | C32 | #407 | 1 | 2 | yes | — |
| 576 | C32 | C22×M16 | 1 | 1 | yes | characteristic |
| 577 | C32 | C22×M16 | 1 | 1 | yes | characteristic |
| 578 | C24 | — | 16 | 2 | no | — |
| 579 | C24 | — | 16 | 1 | no | — |
| 580 | #41 | — | 2 | 2 | no | — |
| 581 | #41 | — | 2 | 2 | no | — |
| 582 | #41 | — | 8 | 8 | no | — |
| 583 | #41 | — | 8 | 4 | no | — |
| 584 | #41 | — | 16 | 4 | no | — |
| 585 | #41 | — | 16 | 8 | no | — |
| 586 | #41 | — | 16 | 2 | no | — |
| 587 | C2×Q8 | — | 8 | 1 | no | — |
| 588 | C2×Q8 | #1419 | 1 | 1 | yes | characteristic |
| 589 | C2×D4 | — | 8 | 8 | no | — |
| 590 | C2×D4 | — | 8 | 2 | no | — |
| 591 | C2×D4 | — | 8 | 1 | no | — |
| 592 | C2×D4 | — | 8 | 4 | no | — |
| 593 | C2×D4 | — | 16 | 4 | no | — |
| 594 | C2×D4 | — | 16 | 16 | no | — |
| 595 | C2×D4 | — | 16 | 8 | no | — |
| 596 | C2×D4 | — | 16 | 2 | no | — |
| 597 | C2×D4 | — | 16 | 1 | no | — |
| 598 | C2×D4 | — | 16 | 2 | no | — |
| 599 | C2×D4 | — | 16 | 2 | no | — |
| 600 | C2×D4 | — | 16 | 1 | no | — |
| 601 | C2×D4 | #1419 | 1 | 2 | yes | — |
| 602 | C2×D4 | #1419 | 1 | 1 | yes | characteristic |
| 603 | C22×C4 | — | 2 | 2 | no | — |
| 604 | C22×C4 | — | 2 | 1 | no | — |
| 605 | C22×C4 | — | 16 | 2 | no | — |
| 606 | C22×C4 | — | 16 | 1 | no | — |
| 607 | C22×C4 | — | 16 | 1 | no | — |
| 608 | C22×C4 | — | 16 | 2 | no | — |
| 609 | C22×C4 | — | 16 | 2 | no | — |
| 610 | C22×C4 | — | 16 | 2 | no | — |
| 611 | C22×C4 | — | 16 | 2 | no | — |
| 612 | C22×C4 | — | 16 | 2 | no | — |
| 613 | C22×C4 | — | 16 | 1 | no | — |
| 614 | C22×C4 | — | 16 | 2 | no | — |
| 615 | C22×C4 | — | 16 | 1 | no | — |
| 616 | C22×C4 | — | 64 | 2 | no | — |
| 617 | C22×C4 | — | 64 | 4 | no | — |
| 618 | C22×C4 | C2×#357 | 1 | 2 | yes | — |
| 619 | C22×C4 | C2×#357 | 1 | 1 | yes | characteristic |
| 620 | Q16 | — | 4 | 2 | no | — |
| 621 | Q16 | — | 8 | 1 | no | — |
| 622 | SD16 | — | 8 | 8 | no | — |
| 623 | SD16 | — | 8 | 4 | no | — |
| 624 | D8 | — | 4 | 2 | no | — |
| 625 | D8 | — | 4 | 4 | no | — |
| 626 | D8 | — | 8 | 8 | no | — |
| 627 | D8 | — | 8 | 1 | no | — |
| 628 | D8 | — | 8 | 2 | no | — |
| 629 | D8 | — | 8 | 4 | no | — |
| 630 | M16 | — | 2 | 2 | no | — |
| 631 | M16 | — | 2 | 2 | no | — |
| 632 | M16 | — | 2 | 4 | no | — |
| 633 | M16 | — | 4 | 2 | no | — |
| 634 | C2×C8 | — | 2 | 2 | no | — |
| 635 | C2×C8 | — | 2 | 2 | no | — |
| 636 | C2×C8 | — | 2 | 2 | no | — |
| 637 | C2×C8 | — | 4 | 2 | no | — |
| 638 | C2×C8 | #1486 | 1 | 2 | yes | — |
| 639 | C2×C8 | C2×#357 | 1 | 1 | yes | characteristic |
| 640 | C2×C8 | C2×#357 | 1 | 2 | yes | — |
| 641 | C2×C8 | C2×#357 | 1 | 2 | yes | — |
| 642 | C2×C8 | C2×#357 | 1 | 1 | yes | characteristic |
| 643 | C2×C8 | #2143 | 1 | 2 | yes | — |
| 644 | C2×C8 | C22×#102 | 1 | 1 | yes | characteristic |
| 645 | C2×C8 | C22×D16 | 1 | 1 | yes | characteristic |
| 646 | C4⋊C4 | — | 2 | 1 | no | — |
| 647 | C4⋊C4 | — | 2 | 2 | no | — |
| 648 | C4⋊C4 | — | 8 | 1 | no | — |
| 649 | C4⋊C4 | — | 8 | 2 | no | — |
| 650 | C4⋊C4 | — | 8 | 1 | no | — |
| 651 | C4⋊C4 | — | 16 | 1 | no | — |
| 652 | C4⋊C4 | — | 16 | 2 | no | — |
| 653 | C4⋊C4 | — | 16 | 1 | no | — |
| 654 | C4⋊C4 | — | 16 | 2 | no | — |
| 655 | C4⋊C4 | — | 16 | 1 | no | — |
| 656 | C22⋊C4 | — | 2 | 1 | no | — |
| 657 | C22⋊C4 | — | 2 | 2 | no | — |
| 658 | C22⋊C4 | — | 16 | 1 | no | — |
| 659 | C22⋊C4 | — | 16 | 2 | no | — |
| 660 | C22⋊C4 | — | 16 | 1 | no | — |
| 661 | C22⋊C4 | — | 16 | 2 | no | — |
| 662 | C22⋊C4 | — | 16 | 2 | no | — |
| 663 | C22⋊C4 | — | 16 | 2 | no | — |
| 664 | C22⋊C4 | — | 16 | 2 | no | — |
| 665 | C22⋊C4 | — | 16 | 2 | no | — |
| 666 | C22⋊C4 | — | 16 | 1 | no | — |
| 667 | C42 | — | 2 | 2 | no | — |
| 668 | C42 | — | 2 | 1 | no | — |
| 669 | C42 | — | 16 | 1 | no | — |
| 670 | C42 | — | 16 | 1 | no | — |
| 671 | C42 | — | 16 | 2 | no | — |
| 672 | C42 | — | 16 | 2 | no | — |
| 673 | C42 | — | 16 | 1 | no | — |
| 674 | C42 | C2×#357 | 1 | 1 | yes | characteristic |
| 675 | C42 | C2×#357 | 1 | 2 | yes | — |
| 676 | C42 | C22×SD32 | 1 | 1 | yes | characteristic |
| 677 | C16 | — | 2 | 2 | no | — |
| 678 | C16 | — | 2 | 1 | no | — |
| 679 | C16 | — | 2 | 1 | no | — |
| 680 | C16 | — | 2 | 2 | no | — |
| 681 | C16 | — | 16 | 4 | no | — |
| 682 | C16 | #1486 | 1 | 2 | yes | — |
| 683 | C16 | C2×#407 | 1 | 1 | yes | characteristic |
| 684 | C16 | C2×#421 | 1 | 1 | yes | characteristic |
| 685 | C23 | — | 16 | 8 | no | — |
| 686 | C23 | — | 16 | 2 | no | — |
| 687 | C23 | — | 16 | 1 | no | — |
| 688 | C23 | — | 16 | 4 | no | — |
| 689 | C23 | — | 64 | 1 | no | — |
| 690 | C23 | — | 64 | 2 | no | — |
| 691 | C23 | — | 64 | 1 | no | — |
| 692 | C23 | — | 64 | 2 | no | — |
| 693 | C23 | C2×#1419 | 1 | 2 | yes | — |
| 694 | C23 | C2×#1419 | 1 | 1 | yes | characteristic |
| 695 | Q8 | — | 2 | 2 | no | — |
| 696 | Q8 | — | 8 | 2 | no | — |
| 697 | Q8 | — | 16 | 1 | no | — |
| 698 | D4 | — | 2 | 4 | no | — |
| 699 | D4 | — | 2 | 2 | no | — |
| 700 | D4 | — | 8 | 2 | no | — |
| 701 | D4 | — | 8 | 4 | no | — |
| 702 | D4 | — | 16 | 8 | no | — |
| 703 | D4 | — | 16 | 8 | no | — |
| 704 | D4 | — | 16 | 4 | no | — |
| 705 | D4 | — | 16 | 4 | no | — |
| 706 | D4 | — | 16 | 1 | no | — |
| 707 | D4 | — | 16 | 2 | no | — |
| 708 | C2×C4 | — | 2 | 2 | no | — |
| 709 | C2×C4 | — | 2 | 2 | no | — |
| 710 | C2×C4 | — | 2 | 1 | no | — |
| 711 | C2×C4 | — | 2 | 1 | no | — |
| 712 | C2×C4 | — | 2 | 2 | no | — |
| 713 | C2×C4 | — | 8 | 1 | no | — |
| 714 | C2×C4 | — | 8 | 2 | no | — |
| 715 | C2×C4 | — | 16 | 8 | no | — |
| 716 | C2×C4 | — | 16 | 1 | no | — |
| 717 | C2×C4 | — | 16 | 4 | no | — |
| 718 | C2×C4 | — | 16 | 1 | no | — |
| 719 | C2×C4 | — | 16 | 1 | no | — |
| 720 | C2×C4 | — | 16 | 2 | no | — |
| 721 | C2×C4 | — | 32 | 4 | no | — |
| 722 | C2×C4 | — | 32 | 2 | no | — |
| 723 | C2×C4 | — | 64 | 1 | no | — |
| 724 | C2×C4 | — | 64 | 2 | no | — |
| 725 | C2×C4 | — | 64 | 2 | no | — |
| 726 | C2×C4 | — | 64 | 2 | no | — |
| 727 | C2×C4 | — | 64 | 2 | no | — |
| 728 | C2×C4 | — | 64 | 1 | no | — |
| 729 | C2×C4 | — | 64 | 2 | no | — |
| 730 | C2×C4 | #11657 | 1 | 2 | yes | — |
| 731 | C2×C4 | #13622 | 1 | 2 | yes | — |
| 732 | C2×C4 | C2×#1419 | 1 | 2 | yes | — |
| 733 | C2×C4 | C2×#1419 | 1 | 1 | yes | characteristic |
| 734 | C2×C4 | C22×#357 | 1 | 1 | yes | characteristic |
| 735 | C8 | — | 2 | 1 | no | — |
| 736 | C8 | — | 2 | 1 | no | — |
| 737 | C8 | — | 2 | 2 | no | — |
| 738 | C8 | — | 2 | 2 | no | — |
| 739 | C8 | #11657 | 1 | 2 | yes | — |
| 740 | C8 | C2×#1486 | 1 | 1 | yes | characteristic |
| 741 | C8 | C2×#2143 | 1 | 1 | yes | characteristic |
| 742 | C22 | — | 2 | 2 | no | — |
| 743 | C22 | — | 4 | 1 | no | — |
| 744 | C22 | — | 4 | 2 | no | — |
| 745 | C22 | — | 16 | 4 | no | — |
| 746 | C22 | — | 16 | 2 | no | — |
| 747 | C22 | — | 32 | 2 | no | — |
| 748 | C22 | — | 32 | 1 | no | — |
| 749 | C22 | — | 32 | 2 | no | — |
| 750 | C22 | — | 32 | 1 | no | — |
| 751 | C22 | — | 64 | 4 | no | — |
| 752 | C22 | — | 64 | 8 | no | — |
| 753 | C22 | #150142 | 1 | 2 | yes | — |
| 754 | C22 | C22×#1419 | 1 | 1 | yes | characteristic |
| 755 | C4 | — | 2 | 2 | no | — |
| 756 | C4 | — | 4 | 1 | no | — |
| 757 | C4 | — | 4 | 1 | no | — |
| 758 | C4 | — | 4 | 2 | no | — |
| 759 | C4 | — | 16 | 2 | no | — |
| 760 | C4 | — | 32 | 2 | no | — |
| 761 | C4 | — | 32 | 1 | no | — |
| 762 | C4 | — | 32 | 1 | no | — |
| 763 | C4 | #150142 | 1 | 2 | yes | — |
| 764 | C4 | C2×#11657 | 1 | 1 | yes | characteristic |
| 765 | C4 | C2×#13622 | 1 | 1 | yes | characteristic |
| 766 | C2 | — | 2 | 1 | no | — |
| 767 | C2 | — | 2 | 2 | no | — |
| 768 | C2 | — | 4 | 2 | no | — |
| 769 | C2 | — | 32 | 4 | no | — |
| 770 | C2 | — | 32 | 2 | no | — |
| 771 | C2 | C2×#150142 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | C2×#150142 |
| commutator | C2×C32 | C23×C4 |
| Frattini, cosocle | #1397 | C24 |
| prime radical | C2×#33982 | C4 |
| LCS | G ▷ C2×C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ C4×#131 ◁ C4×#504 ◁ #512545 ◁ G | |
| LECS | G ▷ #1397 ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72322647 | C2 | semidirect |
| 2. #72322645 | C2 | semidirect |
| 3. #72321739 | C2 | semidirect |
| 4. #72321119 | C2 | semidirect |
| 5. #72320649 | C2 | semidirect |
| 6. C2×#94614 | C2 | semidirect |
| 26. #153583 | C22 | semidirect |
| 30. C2×#7511 | C22 | semidirect |
| 31. #151058 | C22 | semidirect |
| 33. C2×#7464 | C22 | semidirect |
| 35. #94615 | C22 | semidirect |
| 36. #94614 | C22 | semidirect |
| 37. #94614 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72322647 | 2 |
| #72322645 | 2 |
| #72321739 | 2 |
| #72321119 | 2 |
| #72320649 | 2 |
| C2×#94614 | 2 |
| #72232007 | 2 |