Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
1364 conjugacy classes of subgroups.
The subgroup lattice has 809 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #72322771 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #72322768 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #72322766 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #72322764 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #72322761 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #72322760 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #72321329 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #72321140 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #72320480 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #72286491 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #72232017 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | #7623249 | — | 2 | 1 | no | — |
| 13 | #513308 | C22 | 1 | 1 | yes | characteristic |
| 14 | #513308 | C22 | 1 | 1 | yes | characteristic |
| 15 | #513084 | C4 | 1 | 2 | yes | complemented |
| 16 | #513082 | C4 | 1 | 2 | yes | complemented |
| 17 | #513080 | — | 2 | 2 | no | — |
| 18 | #513078 | — | 2 | 2 | no | — |
| 19 | #513076 | C4 | 1 | 2 | yes | complemented |
| 20 | #513074 | C4 | 1 | 2 | yes | complemented |
| 21 | #513064 | C22 | 1 | 1 | yes | characteristic |
| 22 | #513054 | C22 | 1 | 1 | yes | characteristic |
| 23 | #513036 | — | 2 | 1 | no | — |
| 24 | #512946 | — | 2 | 1 | no | — |
| 25 | #512945 | C22 | 1 | 1 | yes | characteristic |
| 26 | #512941 | C22 | 1 | 1 | yes | characteristic |
| 27 | C4×#2263 | — | 2 | 1 | no | — |
| 28 | #512761 | C22 | 1 | 1 | yes | characteristic |
| 29 | C2×#13654 | C22 | 1 | 1 | yes | characteristic |
| 30 | #512545 | C22 | 1 | 1 | yes | characteristic |
| 31 | #494211 | — | 2 | 1 | no | — |
| 32 | C2×#7541 | C22 | 1 | 2 | yes | — |
| 33 | #153562 | C22 | 1 | 2 | yes | — |
| 34 | #153560 | C22 | 1 | 2 | yes | — |
| 35 | #153557 | C22 | 1 | 2 | yes | — |
| 36 | #153425 | — | 2 | 2 | no | — |
| 37 | #153425 | C22 | 1 | 2 | yes | — |
| 38 | C2×#7511 | — | 2 | 2 | no | — |
| 39 | C2×#7511 | C22 | 1 | 2 | yes | — |
| 40 | #152409 | C22 | 1 | 2 | yes | — |
| 41 | #152391 | — | 2 | 1 | no | — |
| 42 | #152300 | — | 2 | 1 | no | — |
| 43 | #152295 | C22 | 1 | 1 | yes | characteristic |
| 44 | #152294 | C22 | 1 | 1 | yes | characteristic |
| 45 | #151998 | — | 2 | 1 | no | — |
| 46 | #151996 | C22 | 1 | 2 | yes | — |
| 47 | #94770 | C22 | 1 | 2 | yes | — |
| 48 | #94767 | C22 | 1 | 2 | yes | — |
| 49 | #94765 | C22 | 1 | 2 | yes | — |
| 50 | #94764 | C22 | 1 | 2 | yes | — |
| 51 | #60695 | — | 4 | 1 | no | — |
| 52 | C2×#2263 | — | 2 | 1 | no | — |
| 53 | C2×#2262 | C23 | 1 | 1 | yes | characteristic |
| 54 | C22×D32 | C23 | 1 | 1 | yes | characteristic |
| 55 | C2×#2258 | D4 | 1 | 1 | yes | characteristic |
| 56 | C2×#2258 | C23 | 1 | 1 | yes | characteristic |
| 57 | #33744 | — | 4 | 2 | no | — |
| 58 | #33740 | — | 2 | 2 | no | — |
| 59 | #33739 | — | 2 | 2 | no | — |
| 60 | #33737 | — | 4 | 2 | no | — |
| 61 | #33735 | — | 2 | 2 | no | — |
| 62 | #33733 | — | 2 | 2 | no | — |
| 63 | #33729 | — | 2 | 1 | no | — |
| 64 | #33720 | — | 2 | 1 | no | — |
| 65 | #33702 | — | 4 | 1 | no | — |
| 66 | #33612 | — | 4 | 1 | no | — |
| 67 | #33610 | — | 2 | 1 | no | — |
| 68 | #33607 | — | 2 | 1 | no | — |
| 69 | C4×#509 | — | 4 | 1 | no | — |
| 70 | C4×#508 | — | 2 | 1 | no | — |
| 71 | C2×C4×D16 | — | 2 | 1 | no | — |
| 72 | C4×#504 | D4 | 1 | 1 | yes | characteristic |
| 73 | #20787 | — | 4 | 1 | no | — |
| 74 | #13737 | — | 2 | 4 | no | — |
| 75 | #13737 | — | 2 | 4 | no | — |
| 76 | C2×M128 | — | 2 | 2 | no | — |
| 77 | C2×M128 | — | 2 | 2 | no | — |
| 78 | C2×M128 | C23 | 1 | 2 | yes | — |
| 79 | C2×M128 | C23 | 1 | 2 | yes | — |
| 80 | #13734 | — | 2 | 2 | no | — |
| 81 | #13733 | C2×C4 | 1 | 2 | yes | — |
| 82 | #13732 | C2×C4 | 1 | 2 | yes | — |
| 83 | #13729 | — | 2 | 2 | no | — |
| 84 | #13728 | C2×C4 | 1 | 2 | yes | — |
| 85 | #13725 | C2×C4 | 1 | 2 | yes | — |
| 86 | #13723 | — | 2 | 2 | no | — |
| 87 | #13722 | — | 2 | 2 | no | — |
| 88 | #13721 | — | 2 | 2 | no | — |
| 89 | #13719 | — | 2 | 2 | no | — |
| 90 | #13699 | — | 2 | 2 | no | — |
| 91 | #13698 | C2×C4 | 1 | 2 | yes | — |
| 92 | #13697 | — | 2 | 2 | no | — |
| 93 | #13697 | C2×C4 | 1 | 2 | yes | — |
| 94 | #13697 | C2×C4 | 1 | 2 | yes | — |
| 95 | #13697 | C2×C4 | 1 | 2 | yes | — |
| 96 | #13696 | — | 2 | 2 | no | — |
| 97 | #13696 | — | 2 | 2 | no | — |
| 98 | #13694 | — | 2 | 2 | no | — |
| 99 | #13694 | — | 2 | 2 | no | — |
| 100 | #13654 | — | 2 | 2 | no | — |
| 101 | #13654 | — | 2 | 1 | no | — |
| 102 | #13654 | — | 2 | 1 | no | — |
| 103 | #13654 | C2×C4 | 1 | 1 | yes | characteristic |
| 104 | #13654 | C2×C4 | 1 | 2 | yes | — |
| 105 | #13654 | C2×C4 | 1 | 1 | yes | characteristic |
| 106 | #13654 | C2×C4 | 1 | 2 | yes | — |
| 107 | #13653 | C2×C4 | 1 | 1 | yes | characteristic |
| 108 | #13653 | C2×C4 | 1 | 1 | yes | characteristic |
| 109 | #13652 | — | 2 | 2 | no | — |
| 110 | #13652 | — | 2 | 1 | no | — |
| 111 | #13652 | — | 2 | 1 | no | — |
| 112 | C4×SD64 | — | 2 | 2 | no | — |
| 113 | C4×D32 | — | 2 | 2 | no | — |
| 114 | #13638 | — | 2 | 2 | no | — |
| 115 | C2×#1425 | C23 | 1 | 2 | yes | — |
| 116 | #13634 | — | 2 | 1 | no | — |
| 117 | #13633 | C23 | 1 | 2 | yes | — |
| 118 | #13633 | C23 | 1 | 1 | yes | characteristic |
| 119 | C2×#1424 | C23 | 1 | 1 | yes | characteristic |
| 120 | #13617 | — | 2 | 1 | no | — |
| 121 | #13616 | — | 2 | 1 | no | — |
| 122 | #13615 | — | 2 | 1 | no | — |
| 123 | C2×#1415 | — | 2 | 1 | no | — |
| 124 | #13549 | C2×C4 | 1 | 2 | yes | — |
| 125 | #13549 | D4 | 1 | 2 | yes | — |
| 126 | #13549 | D4 | 1 | 1 | yes | characteristic |
| 127 | #13549 | C23 | 1 | 1 | yes | characteristic |
| 128 | C4×M64 | C2×C4 | 1 | 2 | yes | — |
| 129 | C4×M64 | D4 | 1 | 1 | yes | characteristic |
| 130 | C2×#1397 | D4 | 1 | 2 | yes | — |
| 131 | C2×#1397 | C23 | 1 | 1 | yes | characteristic |
| 132 | #12911 | — | 2 | 2 | no | — |
| 133 | #12893 | — | 4 | 1 | no | — |
| 134 | #12840 | — | 2 | 1 | no | — |
| 135 | #12839 | — | 2 | 1 | no | — |
| 136 | #12832 | — | 4 | 1 | no | — |
| 137 | #12670 | — | 2 | 2 | no | — |
| 138 | #12668 | — | 4 | 1 | no | — |
| 139 | #7541 | — | 2 | 4 | no | — |
| 140 | #7540 | — | 2 | 4 | no | — |
| 141 | #7539 | — | 2 | 4 | no | — |
| 142 | #7537 | — | 2 | 4 | no | — |
| 143 | #7511 | — | 2 | 2 | no | — |
| 144 | #7511 | — | 2 | 4 | no | — |
| 145 | #7511 | — | 2 | 2 | no | — |
| 146 | #7476 | — | 2 | 1 | no | — |
| 147 | #7475 | — | 2 | 1 | no | — |
| 148 | #7473 | — | 2 | 2 | no | — |
| 149 | #3460 | — | 8 | 1 | no | — |
| 150 | C2×#509 | — | 4 | 1 | no | — |
| 151 | C2×#508 | — | 2 | 1 | no | — |
| 152 | C22×D16 | — | 2 | 1 | no | — |
| 153 | C2×#504 | D8 | 1 | 1 | yes | characteristic |
| 154 | C2×#504 | C2×D4 | 1 | 1 | yes | characteristic |
| 155 | #3179 | — | 8 | 2 | no | — |
| 156 | #3176 | — | 4 | 2 | no | — |
| 157 | #3175 | — | 4 | 2 | no | — |
| 158 | #3171 | — | 8 | 2 | no | — |
| 159 | #3169 | — | 4 | 2 | no | — |
| 160 | #3168 | — | 4 | 2 | no | — |
| 161 | #3164 | — | 4 | 1 | no | — |
| 162 | #3155 | — | 4 | 1 | no | — |
| 163 | #3136 | — | 8 | 1 | no | — |
| 164 | #3062 | — | 8 | 1 | no | — |
| 165 | #3061 | — | 4 | 1 | no | — |
| 166 | #3058 | — | 4 | 1 | no | — |
| 167 | C4×AGL(1,ℤ/8) | — | 8 | 1 | no | — |
| 168 | C4×#135 | — | 4 | 1 | no | — |
| 169 | C2×C4×D8 | — | 4 | 1 | no | — |
| 170 | C4×#131 | D8 | 1 | 1 | yes | characteristic |
| 171 | #2263 | — | 4 | 4 | no | — |
| 172 | #2262 | — | 2 | 2 | no | — |
| 173 | #2262 | — | 2 | 2 | no | — |
| 174 | C2×Q64 | C22×C4 | 1 | 1 | yes | characteristic |
| 175 | C2×SD64 | — | 2 | 2 | no | — |
| 176 | C2×SD64 | — | 2 | 1 | no | — |
| 177 | C2×D32 | — | 2 | 2 | no | — |
| 178 | C2×D32 | — | 2 | 1 | no | — |
| 179 | C2×D32 | — | 2 | 2 | no | — |
| 180 | C2×D32 | — | 2 | 2 | no | — |
| 181 | C2×D32 | C22×C4 | 1 | 1 | yes | characteristic |
| 182 | C2×D32 | C22×C4 | 1 | 2 | yes | — |
| 183 | #2258 | — | 2 | 4 | no | — |
| 184 | #2258 | — | 2 | 2 | no | — |
| 185 | #2258 | — | 2 | 2 | no | — |
| 186 | C2×M64 | C22⋊C4 | 1 | 2 | yes | — |
| 187 | C2×M64 | C22×C4 | 1 | 2 | yes | — |
| 188 | C2×M64 | C2×D4 | 1 | 1 | yes | characteristic |
| 189 | C2×M64 | C2×D4 | 1 | 1 | yes | characteristic |
| 190 | C22×C32 | C22⋊C4 | 1 | 2 | yes | — |
| 191 | C22×C32 | C2×D4 | 1 | 1 | yes | characteristic |
| 192 | C22×C32 | C2×D4 | 1 | 2 | yes | — |
| 193 | C22×C32 | C24 | 1 | 1 | yes | characteristic |
| 194 | #2255 | — | 4 | 2 | no | — |
| 195 | #2253 | — | 2 | 2 | no | — |
| 196 | #2252 | — | 2 | 2 | no | — |
| 197 | #2250 | — | 4 | 2 | no | — |
| 198 | #2249 | — | 2 | 2 | no | — |
| 199 | #2246 | — | 2 | 2 | no | — |
| 200 | #2244 | — | 4 | 2 | no | — |
| 201 | #2243 | — | 4 | 2 | no | — |
| 202 | #2242 | — | 4 | 2 | no | — |
| 203 | #2240 | — | 4 | 2 | no | — |
| 204 | #2220 | — | 4 | 2 | no | — |
| 205 | #2220 | — | 4 | 2 | no | — |
| 206 | #2218 | — | 4 | 2 | no | — |
| 207 | #2218 | — | 4 | 2 | no | — |
| 208 | #2217 | — | 4 | 2 | no | — |
| 209 | #2216 | — | 2 | 2 | no | — |
| 210 | #2215 | — | 2 | 2 | no | — |
| 211 | #2215 | — | 2 | 2 | no | — |
| 212 | #2215 | — | 2 | 2 | no | — |
| 213 | #2215 | — | 4 | 2 | no | — |
| 214 | #2177 | — | 4 | 2 | no | — |
| 215 | #2175 | — | 4 | 2 | no | — |
| 216 | C4×Q32 | — | 2 | 1 | no | — |
| 217 | C4×Q32 | — | 2 | 1 | no | — |
| 218 | C4×SD32 | — | 4 | 2 | no | — |
| 219 | C4×SD32 | — | 4 | 1 | no | — |
| 220 | C4×SD32 | — | 4 | 1 | no | — |
| 221 | C4×D16 | — | 2 | 1 | no | — |
| 222 | C4×D16 | — | 2 | 2 | no | — |
| 223 | C4×D16 | — | 2 | 2 | no | — |
| 224 | C4×D16 | — | 2 | 1 | no | — |
| 225 | C4×D16 | — | 4 | 2 | no | — |
| 226 | C4×D16 | — | 4 | 1 | no | — |
| 227 | C4×D16 | — | 4 | 1 | no | — |
| 228 | C2×#368 | — | 2 | 2 | no | — |
| 229 | #2159 | — | 4 | 1 | no | — |
| 230 | #2158 | — | 2 | 1 | no | — |
| 231 | #2158 | — | 2 | 2 | no | — |
| 232 | C2×#366 | — | 2 | 1 | no | — |
| 233 | #2155 | — | 4 | 2 | no | — |
| 234 | #2140 | — | 4 | 1 | no | — |
| 235 | #2139 | — | 4 | 1 | no | — |
| 236 | #2138 | — | 4 | 1 | no | — |
| 237 | C2×#357 | — | 4 | 1 | no | — |
| 238 | #2108 | C22⋊C4 | 1 | 2 | yes | — |
| 239 | #2108 | D8 | 1 | 1 | yes | characteristic |
| 240 | #2108 | SD16 | 1 | 2 | yes | — |
| 241 | #2108 | C2×D4 | 1 | 1 | yes | characteristic |
| 242 | C4×M32 | D8 | 1 | 1 | yes | characteristic |
| 243 | C4×M32 | SD16 | 1 | 2 | yes | — |
| 244 | C2×C4×C16 | C22⋊C4 | 1 | 2 | yes | — |
| 245 | C2×C4×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 246 | #1841 | — | 8 | 1 | no | — |
| 247 | #1833 | — | 4 | 2 | no | — |
| 248 | #1827 | — | 8 | 1 | no | — |
| 249 | #1813 | — | 4 | 1 | no | — |
| 250 | #1812 | — | 4 | 1 | no | — |
| 251 | #1772 | — | 4 | 2 | no | — |
| 252 | #1757 | — | 8 | 1 | no | — |
| 253 | #1747 | — | 8 | 1 | no | — |
| 254 | M128 | — | 2 | 4 | no | — |
| 255 | M128 | — | 2 | 4 | no | — |
| 256 | M128 | — | 2 | 2 | no | — |
| 257 | M128 | — | 2 | 2 | no | — |
| 258 | M128 | — | 2 | 2 | no | — |
| 259 | M128 | #41 | 1 | 4 | yes | complemented |
| 260 | C2×C64 | — | 2 | 4 | no | — |
| 261 | C2×C64 | — | 2 | 4 | no | — |
| 262 | C2×C64 | — | 2 | 2 | no | — |
| 263 | C2×C64 | #41 | 1 | 4 | yes | complemented |
| 264 | #1426 | — | 4 | 4 | no | — |
| 265 | #1425 | — | 2 | 2 | no | — |
| 266 | #1425 | — | 2 | 2 | no | — |
| 267 | #1424 | — | 2 | 2 | no | — |
| 268 | #1424 | — | 2 | 1 | no | — |
| 269 | #1424 | — | 2 | 2 | no | — |
| 270 | #1424 | C22×C4 | 1 | 2 | yes | — |
| 271 | #1424 | C22×C4 | 1 | 1 | yes | characteristic |
| 272 | #1424 | C22×C4 | 1 | 1 | yes | characteristic |
| 273 | #1423 | — | 2 | 2 | no | — |
| 274 | #1423 | — | 2 | 1 | no | — |
| 275 | #1423 | — | 2 | 2 | no | — |
| 276 | #1416 | — | 2 | 1 | no | — |
| 277 | #1416 | — | 2 | 1 | no | — |
| 278 | #1416 | — | 2 | 2 | no | — |
| 279 | #1415 | — | 2 | 2 | no | — |
| 280 | #1415 | — | 2 | 2 | no | — |
| 281 | #1415 | — | 2 | 1 | no | — |
| 282 | #1415 | — | 2 | 1 | no | — |
| 283 | #1415 | — | 2 | 2 | no | — |
| 284 | #1415 | — | 2 | 2 | no | — |
| 285 | #1415 | — | 2 | 2 | no | — |
| 286 | #1397 | C22⋊C4 | 1 | 2 | yes | — |
| 287 | #1397 | C22⋊C4 | 1 | 2 | yes | — |
| 288 | #1397 | C22×C4 | 1 | 1 | yes | characteristic |
| 289 | #1397 | C22×C4 | 1 | 1 | yes | characteristic |
| 290 | #1397 | C2×D4 | 1 | 1 | yes | characteristic |
| 291 | #1397 | C2×D4 | 1 | 1 | yes | characteristic |
| 292 | #1397 | C2×D4 | 1 | 2 | yes | — |
| 293 | C4×C32 | C22⋊C4 | 1 | 2 | yes | — |
| 294 | C4×C32 | C22⋊C4 | 1 | 2 | yes | — |
| 295 | C4×C32 | C22×C4 | 1 | 2 | yes | — |
| 296 | #1385 | — | 4 | 1 | no | — |
| 297 | #1384 | — | 4 | 1 | no | — |
| 298 | #1382 | — | 4 | 2 | no | — |
| 299 | C2×AGL(1,ℤ/8) | — | 8 | 1 | no | — |
| 300 | C2×#135 | — | 4 | 1 | no | — |
| 301 | C22×D8 | — | 4 | 1 | no | — |
| 302 | C2×#131 | D16 | 1 | 1 | yes | characteristic |
| 303 | C2×#131 | C2×D8 | 1 | 1 | yes | characteristic |
| 304 | #544 | — | 8 | 1 | no | — |
| 305 | #542 | — | 8 | 2 | no | — |
| 306 | #542 | — | 16 | 1 | no | — |
| 307 | #540 | — | 8 | 2 | no | — |
| 308 | #540 | — | 16 | 1 | no | — |
| 309 | #538 | — | 16 | 2 | no | — |
| 310 | #537 | — | 8 | 1 | no | — |
| 311 | #535 | — | 8 | 1 | no | — |
| 312 | #535 | — | 8 | 1 | no | — |
| 313 | #532 | — | 8 | 2 | no | — |
| 314 | #532 | — | 16 | 1 | no | — |
| 315 | #529 | — | 8 | 2 | no | — |
| 316 | #529 | — | 16 | 1 | no | — |
| 317 | #525 | — | 16 | 2 | no | — |
| 318 | C4×#41 | — | 8 | 1 | no | — |
| 319 | C4×#41 | D16 | 1 | 1 | yes | characteristic |
| 320 | C2×C4×D4 | — | 8 | 1 | no | — |
| 321 | #509 | — | 8 | 4 | no | — |
| 322 | #508 | — | 4 | 2 | no | — |
| 323 | #508 | — | 4 | 2 | no | — |
| 324 | C2×Q32 | — | 2 | 1 | no | — |
| 325 | C2×SD32 | — | 4 | 1 | no | — |
| 326 | C2×SD32 | — | 4 | 2 | no | — |
| 327 | C2×D16 | — | 2 | 2 | no | — |
| 328 | C2×D16 | — | 2 | 1 | no | — |
| 329 | C2×D16 | — | 4 | 2 | no | — |
| 330 | C2×D16 | — | 4 | 1 | no | — |
| 331 | C2×D16 | — | 4 | 2 | no | — |
| 332 | C2×D16 | — | 4 | 2 | no | — |
| 333 | #504 | — | 2 | 4 | no | — |
| 334 | #504 | — | 2 | 2 | no | — |
| 335 | #504 | — | 2 | 2 | no | — |
| 336 | C2×M32 | #102 | 1 | 2 | yes | — |
| 337 | C2×M32 | C2×D8 | 1 | 1 | yes | characteristic |
| 338 | C2×M32 | C2×D8 | 1 | 1 | yes | characteristic |
| 339 | C2×M32 | C2×SD16 | 1 | 2 | yes | — |
| 340 | C22×C16 | #102 | 1 | 2 | yes | — |
| 341 | C22×C16 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 342 | C22×C16 | C2×D8 | 1 | 1 | yes | characteristic |
| 343 | C22×C16 | C22×D4 | 1 | 1 | yes | characteristic |
| 344 | #501 | — | 8 | 2 | no | — |
| 345 | #500 | — | 4 | 2 | no | — |
| 346 | #499 | — | 4 | 2 | no | — |
| 347 | #496 | — | 8 | 2 | no | — |
| 348 | #495 | — | 4 | 2 | no | — |
| 349 | #493 | — | 4 | 2 | no | — |
| 350 | #490 | — | 8 | 2 | no | — |
| 351 | #489 | — | 8 | 2 | no | — |
| 352 | #488 | — | 8 | 2 | no | — |
| 353 | #486 | — | 8 | 2 | no | — |
| 354 | #469 | — | 8 | 2 | no | — |
| 355 | #469 | — | 8 | 2 | no | — |
| 356 | #468 | — | 8 | 2 | no | — |
| 357 | #468 | — | 8 | 2 | no | — |
| 358 | #467 | — | 4 | 2 | no | — |
| 359 | #466 | — | 4 | 2 | no | — |
| 360 | #466 | — | 4 | 2 | no | — |
| 361 | #466 | — | 4 | 2 | no | — |
| 362 | #466 | — | 8 | 2 | no | — |
| 363 | #465 | — | 8 | 2 | no | — |
| 364 | #442 | — | 8 | 2 | no | — |
| 365 | #440 | — | 8 | 2 | no | — |
| 366 | C4×Q16 | — | 4 | 1 | no | — |
| 367 | C4×Q16 | — | 4 | 1 | no | — |
| 368 | C4×SD16 | — | 8 | 2 | no | — |
| 369 | C4×SD16 | — | 8 | 1 | no | — |
| 370 | C4×SD16 | — | 8 | 1 | no | — |
| 371 | C4×D8 | — | 4 | 2 | no | — |
| 372 | C4×D8 | — | 4 | 1 | no | — |
| 373 | C4×D8 | — | 4 | 2 | no | — |
| 374 | C4×D8 | — | 4 | 1 | no | — |
| 375 | C4×D8 | — | 8 | 2 | no | — |
| 376 | C4×D8 | — | 8 | 1 | no | — |
| 377 | C4×D8 | — | 8 | 1 | no | — |
| 378 | C2×#108 | — | 4 | 2 | no | — |
| 379 | #428 | — | 8 | 1 | no | — |
| 380 | #427 | — | 4 | 1 | no | — |
| 381 | #427 | — | 4 | 2 | no | — |
| 382 | C2×#107 | — | 4 | 1 | no | — |
| 383 | #418 | — | 8 | 1 | no | — |
| 384 | #417 | — | 8 | 1 | no | — |
| 385 | #416 | — | 8 | 1 | no | — |
| 386 | C2×#102 | — | 8 | 1 | no | — |
| 387 | #413 | — | 8 | 1 | no | — |
| 388 | #410 | — | 8 | 1 | no | — |
| 389 | #405 | — | 8 | 2 | no | — |
| 390 | #405 | #102 | 1 | 2 | yes | — |
| 391 | #405 | D16 | 1 | 1 | yes | characteristic |
| 392 | #405 | SD32 | 1 | 2 | yes | — |
| 393 | #405 | C2×D8 | 1 | 1 | yes | characteristic |
| 394 | C4×M16 | D16 | 1 | 1 | yes | characteristic |
| 395 | C4×M16 | SD32 | 1 | 2 | yes | — |
| 396 | C2×C4×C8 | #102 | 1 | 2 | yes | — |
| 397 | C2×C4×C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 398 | Q64 | — | 2 | 2 | no | — |
| 399 | SD64 | — | 4 | 1 | no | — |
| 400 | SD64 | — | 4 | 1 | no | — |
| 401 | SD64 | — | 4 | 4 | no | — |
| 402 | D32 | — | 2 | 4 | no | — |
| 403 | D32 | — | 2 | 2 | no | — |
| 404 | D32 | — | 4 | 1 | no | — |
| 405 | D32 | — | 4 | 1 | no | — |
| 406 | D32 | — | 4 | 4 | no | — |
| 407 | M64 | — | 2 | 2 | no | — |
| 408 | M64 | — | 2 | 4 | no | — |
| 409 | M64 | — | 2 | 4 | no | — |
| 410 | M64 | #135 | 1 | 4 | yes | — |
| 411 | C2×C32 | — | 2 | 2 | no | — |
| 412 | C2×C32 | — | 2 | 2 | no | — |
| 413 | C2×C32 | — | 2 | 2 | no | — |
| 414 | C2×C32 | — | 2 | 4 | no | — |
| 415 | C2×C32 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 416 | C2×C32 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 417 | C2×C32 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 418 | C2×C32 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 419 | C2×C32 | C23×C4 | 1 | 1 | yes | characteristic |
| 420 | C2×C32 | C22×D4 | 1 | 1 | yes | characteristic |
| 421 | C2×C32 | C2×#41 | 1 | 2 | yes | — |
| 422 | C2×C32 | C2×#41 | 1 | 2 | yes | — |
| 423 | #368 | — | 4 | 2 | no | — |
| 424 | #368 | — | 4 | 2 | no | — |
| 425 | #367 | — | 4 | 1 | no | — |
| 426 | #367 | — | 4 | 2 | no | — |
| 427 | #367 | — | 4 | 2 | no | — |
| 428 | #366 | — | 2 | 2 | no | — |
| 429 | #366 | — | 2 | 1 | no | — |
| 430 | #366 | — | 2 | 1 | no | — |
| 431 | #366 | — | 4 | 1 | no | — |
| 432 | #366 | — | 4 | 2 | no | — |
| 433 | #366 | — | 4 | 2 | no | — |
| 434 | #365 | — | 8 | 4 | no | — |
| 435 | #358 | — | 4 | 1 | no | — |
| 436 | #358 | — | 4 | 1 | no | — |
| 437 | #358 | — | 4 | 2 | no | — |
| 438 | #357 | — | 4 | 2 | no | — |
| 439 | #357 | — | 4 | 2 | no | — |
| 440 | #357 | — | 4 | 1 | no | — |
| 441 | #357 | — | 4 | 1 | no | — |
| 442 | #357 | — | 4 | 2 | no | — |
| 443 | #357 | — | 4 | 2 | no | — |
| 444 | #357 | — | 4 | 2 | no | — |
| 445 | #346 | #102 | 1 | 2 | yes | — |
| 446 | #346 | #102 | 1 | 2 | yes | — |
| 447 | #346 | C2×SD16 | 1 | 2 | yes | — |
| 448 | C4×C16 | #102 | 1 | 2 | yes | — |
| 449 | C4×C16 | #102 | 1 | 2 | yes | — |
| 450 | C4×C16 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 451 | C4×C16 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 452 | C4×C16 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 453 | C4×C16 | C2×SD16 | 1 | 1 | yes | characteristic |
| 454 | C4×C16 | C2×SD16 | 1 | 1 | yes | characteristic |
| 455 | #344 | — | 8 | 2 | no | — |
| 456 | #339 | — | 8 | 2 | no | — |
| 457 | #338 | — | 8 | 1 | no | — |
| 458 | H(3,ℤ/4) | — | 8 | 1 | no | — |
| 459 | H(3,ℤ/4) | — | 8 | 2 | no | — |
| 460 | C64 | — | 2 | 4 | no | — |
| 461 | C64 | — | 2 | 4 | no | — |
| 462 | C2×#41 | — | 8 | 1 | no | — |
| 463 | C2×#41 | — | 16 | 2 | no | — |
| 464 | C2×#41 | C2×D16 | 1 | 1 | yes | characteristic |
| 465 | C22×D4 | — | 8 | 1 | no | — |
| 466 | C23×C4 | — | 16 | 1 | no | — |
| 467 | AGL(1,ℤ/8) | — | 16 | 4 | no | — |
| 468 | #135 | — | 8 | 2 | no | — |
| 469 | #135 | — | 8 | 2 | no | — |
| 470 | C2×Q16 | — | 4 | 1 | no | — |
| 471 | C2×SD16 | — | 8 | 1 | no | — |
| 472 | C2×SD16 | — | 8 | 2 | no | — |
| 473 | C2×D8 | — | 4 | 2 | no | — |
| 474 | C2×D8 | — | 4 | 1 | no | — |
| 475 | C2×D8 | — | 8 | 1 | no | — |
| 476 | C2×D8 | — | 8 | 2 | no | — |
| 477 | C2×D8 | — | 8 | 2 | no | — |
| 478 | C2×D8 | — | 8 | 2 | no | — |
| 479 | #131 | — | 2 | 2 | no | — |
| 480 | #131 | — | 2 | 2 | no | — |
| 481 | #131 | — | 4 | 2 | no | — |
| 482 | C2×M16 | — | 8 | 2 | no | — |
| 483 | C2×M16 | #357 | 1 | 2 | yes | — |
| 484 | C2×M16 | C2×D16 | 1 | 1 | yes | characteristic |
| 485 | C2×M16 | C2×D16 | 1 | 1 | yes | characteristic |
| 486 | C2×M16 | C2×SD32 | 1 | 2 | yes | — |
| 487 | C22×C8 | #357 | 1 | 2 | yes | — |
| 488 | C22×C8 | C2×#102 | 1 | 2 | yes | — |
| 489 | C22×C8 | C2×D16 | 1 | 1 | yes | characteristic |
| 490 | C22×C8 | C22×D8 | 1 | 1 | yes | characteristic |
| 491 | C4⋊Q8 | — | 8 | 2 | no | — |
| 492 | C4⋊Q8 | — | 16 | 1 | no | — |
| 493 | #127 | — | 8 | 2 | no | — |
| 494 | #127 | — | 16 | 1 | no | — |
| 495 | #126 | — | 16 | 2 | no | — |
| 496 | #126 | — | 16 | 2 | no | — |
| 497 | #125 | — | 8 | 2 | no | — |
| 498 | #125 | — | 16 | 1 | no | — |
| 499 | #124 | — | 8 | 2 | no | — |
| 500 | #124 | — | 16 | 2 | no | — |
| 501 | #124 | — | 16 | 2 | no | — |
| 502 | #124 | — | 16 | 1 | no | — |
| 503 | #123 | — | 16 | 2 | no | — |
| 504 | #123 | — | 16 | 2 | no | — |
| 505 | #123 | — | 16 | 2 | no | — |
| 506 | #123 | — | 16 | 2 | no | — |
| 507 | C22⋊Q8 | — | 8 | 2 | no | — |
| 508 | C22⋊Q8 | — | 16 | 2 | no | — |
| 509 | C22⋊Q8 | — | 16 | 2 | no | — |
| 510 | C22⋊Q8 | — | 16 | 1 | no | — |
| 511 | #121 | — | 8 | 2 | no | — |
| 512 | #121 | — | 8 | 2 | no | — |
| 513 | #121 | — | 8 | 2 | no | — |
| 514 | #121 | — | 16 | 2 | no | — |
| 515 | #121 | — | 16 | 2 | no | — |
| 516 | #121 | — | 16 | 1 | no | — |
| 517 | #121 | — | 16 | 1 | no | — |
| 518 | #121 | — | 16 | 2 | no | — |
| 519 | #121 | — | 16 | 2 | no | — |
| 520 | #121 | — | 16 | 1 | no | — |
| 521 | #120 | — | 16 | 2 | no | — |
| 522 | #120 | — | 16 | 2 | no | — |
| 523 | C4×Q8 | — | 2 | 1 | no | — |
| 524 | C4×Q8 | — | 8 | 1 | no | — |
| 525 | C4×Q8 | — | 8 | 1 | no | — |
| 526 | C4×D4 | — | 2 | 2 | no | — |
| 527 | C4×D4 | — | 2 | 1 | no | — |
| 528 | C4×D4 | — | 8 | 2 | no | — |
| 529 | C4×D4 | — | 8 | 2 | no | — |
| 530 | C4×D4 | — | 8 | 1 | no | — |
| 531 | C4×D4 | — | 8 | 1 | no | — |
| 532 | C4×D4 | — | 16 | 1 | no | — |
| 533 | C4×D4 | — | 16 | 1 | no | — |
| 534 | C4×D4 | — | 16 | 2 | no | — |
| 535 | C4×D4 | — | 16 | 1 | no | — |
| 536 | C4×D4 | — | 16 | 1 | no | — |
| 537 | C4×D4 | — | 16 | 2 | no | — |
| 538 | #117 | — | 8 | 1 | no | — |
| 539 | #117 | — | 8 | 2 | no | — |
| 540 | #117 | — | 16 | 1 | no | — |
| 541 | #117 | — | 16 | 2 | no | — |
| 542 | #117 | #357 | 1 | 2 | yes | — |
| 543 | #117 | C2×D16 | 1 | 1 | yes | characteristic |
| 544 | C2×C4⋊C4 | — | 8 | 1 | no | — |
| 545 | C2×C22⋊C4 | — | 16 | 1 | no | — |
| 546 | C2×C42 | — | 16 | 1 | no | — |
| 547 | C2×C42 | #357 | 1 | 2 | yes | — |
| 548 | C2×C42 | C2×D16 | 1 | 1 | yes | characteristic |
| 549 | Q32 | — | 4 | 1 | no | — |
| 550 | Q32 | — | 4 | 1 | no | — |
| 551 | SD32 | — | 8 | 4 | no | — |
| 552 | SD32 | — | 8 | 2 | no | — |
| 553 | D16 | — | 4 | 1 | no | — |
| 554 | D16 | — | 4 | 2 | no | — |
| 555 | D16 | — | 4 | 2 | no | — |
| 556 | D16 | — | 4 | 1 | no | — |
| 557 | D16 | — | 8 | 4 | no | — |
| 558 | D16 | — | 8 | 2 | no | — |
| 559 | M32 | — | 2 | 2 | no | — |
| 560 | M32 | — | 2 | 4 | no | — |
| 561 | M32 | — | 2 | 4 | no | — |
| 562 | M32 | #508 | 1 | 4 | yes | — |
| 563 | C2×C16 | — | 2 | 2 | no | — |
| 564 | C2×C16 | — | 2 | 2 | no | — |
| 565 | C2×C16 | — | 2 | 4 | no | — |
| 566 | C2×C16 | — | 2 | 2 | no | — |
| 567 | C2×C16 | C2×#102 | 1 | 1 | yes | characteristic |
| 568 | C2×C16 | C2×#102 | 1 | 2 | yes | — |
| 569 | C2×C16 | C2×#102 | 1 | 1 | yes | characteristic |
| 570 | C2×C16 | C2×#102 | 1 | 2 | yes | — |
| 571 | C2×C16 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 572 | C2×C16 | #532 | 1 | 2 | yes | — |
| 573 | C2×C16 | C22×SD16 | 1 | 1 | yes | characteristic |
| 574 | C2×C16 | C2×#135 | 1 | 2 | yes | — |
| 575 | #108 | — | 8 | 2 | no | — |
| 576 | #108 | — | 8 | 2 | no | — |
| 577 | #107 | — | 4 | 2 | no | — |
| 578 | #107 | — | 4 | 1 | no | — |
| 579 | #107 | — | 4 | 1 | no | — |
| 580 | #107 | — | 8 | 1 | no | — |
| 581 | #107 | — | 8 | 2 | no | — |
| 582 | #107 | — | 8 | 2 | no | — |
| 583 | #106 | — | 8 | 1 | no | — |
| 584 | #106 | — | 8 | 2 | no | — |
| 585 | #106 | — | 8 | 2 | no | — |
| 586 | #103 | — | 8 | 1 | no | — |
| 587 | #103 | — | 8 | 1 | no | — |
| 588 | #103 | — | 8 | 2 | no | — |
| 589 | #102 | — | 8 | 2 | no | — |
| 590 | #102 | — | 8 | 2 | no | — |
| 591 | #102 | — | 8 | 1 | no | — |
| 592 | #102 | — | 8 | 1 | no | — |
| 593 | #102 | — | 8 | 2 | no | — |
| 594 | #102 | — | 8 | 2 | no | — |
| 595 | #102 | — | 8 | 2 | no | — |
| 596 | #101 | — | 16 | 1 | no | — |
| 597 | #100 | — | 16 | 1 | no | — |
| 598 | #99 | — | 16 | 2 | no | — |
| 599 | #97 | — | 16 | 2 | no | — |
| 600 | #97 | #357 | 1 | 2 | yes | — |
| 601 | #97 | #357 | 1 | 2 | yes | — |
| 602 | #97 | C2×SD32 | 1 | 2 | yes | — |
| 603 | C4×C8 | — | 16 | 2 | no | — |
| 604 | C4×C8 | #357 | 1 | 2 | yes | — |
| 605 | C4×C8 | #357 | 1 | 2 | yes | — |
| 606 | C4×C8 | C2×#102 | 1 | 1 | yes | characteristic |
| 607 | C4×C8 | C2×#102 | 1 | 2 | yes | — |
| 608 | C4×C8 | C2×#102 | 1 | 1 | yes | characteristic |
| 609 | C4×C8 | C2×SD32 | 1 | 1 | yes | characteristic |
| 610 | C4×C8 | C2×SD32 | 1 | 1 | yes | characteristic |
| 611 | C32 | — | 2 | 1 | no | — |
| 612 | C32 | — | 2 | 1 | no | — |
| 613 | C32 | — | 2 | 2 | no | — |
| 614 | C32 | #416 | 1 | 4 | yes | — |
| 615 | C32 | C4×#41 | 1 | 2 | yes | — |
| 616 | C32 | #525 | 1 | 1 | yes | characteristic |
| 617 | C32 | #525 | 1 | 1 | yes | characteristic |
| 618 | C24 | — | 16 | 1 | no | — |
| 619 | #41 | — | 2 | 2 | no | — |
| 620 | #41 | — | 2 | 2 | no | — |
| 621 | #41 | — | 16 | 2 | no | — |
| 622 | #41 | — | 16 | 2 | no | — |
| 623 | #41 | — | 64 | 4 | no | — |
| 624 | C2×Q8 | — | 8 | 1 | no | — |
| 625 | C2×Q8 | — | 16 | 2 | no | — |
| 626 | C2×Q8 | #2263 | 1 | 1 | yes | characteristic |
| 627 | C2×D4 | — | 8 | 2 | no | — |
| 628 | C2×D4 | — | 8 | 1 | no | — |
| 629 | C2×D4 | — | 16 | 2 | no | — |
| 630 | C2×D4 | — | 16 | 2 | no | — |
| 631 | C2×D4 | — | 16 | 1 | no | — |
| 632 | C2×D4 | — | 16 | 2 | no | — |
| 633 | C2×D4 | — | 16 | 2 | no | — |
| 634 | C2×D4 | — | 16 | 2 | no | — |
| 635 | C2×D4 | — | 16 | 1 | no | — |
| 636 | C2×D4 | — | 16 | 2 | no | — |
| 637 | C2×D4 | — | 16 | 2 | no | — |
| 638 | C2×D4 | #2263 | 1 | 2 | yes | — |
| 639 | C2×D4 | #2263 | 1 | 1 | yes | characteristic |
| 640 | C22×C4 | — | 2 | 2 | no | — |
| 641 | C22×C4 | — | 2 | 1 | no | — |
| 642 | C22×C4 | — | 16 | 1 | no | — |
| 643 | C22×C4 | — | 16 | 2 | no | — |
| 644 | C22×C4 | — | 16 | 1 | no | — |
| 645 | C22×C4 | — | 16 | 2 | no | — |
| 646 | C22×C4 | — | 16 | 1 | no | — |
| 647 | C22×C4 | — | 16 | 1 | no | — |
| 648 | C22×C4 | — | 64 | 2 | no | — |
| 649 | C22×C4 | C2×#357 | 1 | 2 | yes | — |
| 650 | C22×C4 | C22×D16 | 1 | 1 | yes | characteristic |
| 651 | Q16 | — | 8 | 1 | no | — |
| 652 | Q16 | — | 8 | 1 | no | — |
| 653 | SD16 | — | 16 | 4 | no | — |
| 654 | SD16 | — | 16 | 2 | no | — |
| 655 | D8 | — | 8 | 1 | no | — |
| 656 | D8 | — | 8 | 2 | no | — |
| 657 | D8 | — | 8 | 2 | no | — |
| 658 | D8 | — | 8 | 1 | no | — |
| 659 | D8 | — | 16 | 4 | no | — |
| 660 | D8 | — | 16 | 2 | no | — |
| 661 | M16 | — | 2 | 2 | no | — |
| 662 | M16 | — | 2 | 2 | no | — |
| 663 | M16 | — | 2 | 4 | no | — |
| 664 | M16 | — | 4 | 2 | no | — |
| 665 | M16 | — | 16 | 2 | no | — |
| 666 | M16 | — | 16 | 2 | no | — |
| 667 | C2×C8 | — | 2 | 2 | no | — |
| 668 | C2×C8 | — | 2 | 2 | no | — |
| 669 | C2×C8 | — | 2 | 2 | no | — |
| 670 | C2×C8 | — | 4 | 2 | no | — |
| 671 | C2×C8 | — | 16 | 2 | no | — |
| 672 | C2×C8 | C2×#357 | 1 | 1 | yes | characteristic |
| 673 | C2×C8 | C2×#357 | 1 | 2 | yes | — |
| 674 | C2×C8 | C2×#357 | 1 | 2 | yes | — |
| 675 | C2×C8 | C2×#357 | 1 | 1 | yes | characteristic |
| 676 | C2×C8 | C22×#102 | 1 | 1 | yes | characteristic |
| 677 | C2×C8 | #3169 | 1 | 2 | yes | — |
| 678 | C2×C8 | C22×SD32 | 1 | 1 | yes | characteristic |
| 679 | C2×C8 | C2×#508 | 1 | 2 | yes | — |
| 680 | C4⋊C4 | — | 2 | 2 | no | — |
| 681 | C4⋊C4 | — | 2 | 1 | no | — |
| 682 | C4⋊C4 | — | 8 | 1 | no | — |
| 683 | C4⋊C4 | — | 8 | 2 | no | — |
| 684 | C4⋊C4 | — | 8 | 1 | no | — |
| 685 | C4⋊C4 | — | 16 | 1 | no | — |
| 686 | C4⋊C4 | — | 16 | 1 | no | — |
| 687 | C4⋊C4 | — | 16 | 2 | no | — |
| 688 | C4⋊C4 | — | 16 | 2 | no | — |
| 689 | C4⋊C4 | — | 16 | 2 | no | — |
| 690 | C4⋊C4 | — | 16 | 2 | no | — |
| 691 | C4⋊C4 | — | 16 | 1 | no | — |
| 692 | C4⋊C4 | — | 16 | 2 | no | — |
| 693 | C22⋊C4 | — | 2 | 2 | no | — |
| 694 | C22⋊C4 | — | 2 | 1 | no | — |
| 695 | C22⋊C4 | — | 16 | 2 | no | — |
| 696 | C22⋊C4 | — | 16 | 2 | no | — |
| 697 | C22⋊C4 | — | 16 | 1 | no | — |
| 698 | C22⋊C4 | — | 16 | 1 | no | — |
| 699 | C22⋊C4 | — | 16 | 2 | no | — |
| 700 | C22⋊C4 | — | 16 | 2 | no | — |
| 701 | C22⋊C4 | — | 16 | 2 | no | — |
| 702 | C22⋊C4 | — | 16 | 1 | no | — |
| 703 | C22⋊C4 | — | 16 | 2 | no | — |
| 704 | C22⋊C4 | — | 16 | 2 | no | — |
| 705 | C22⋊C4 | — | 16 | 2 | no | — |
| 706 | C22⋊C4 | — | 16 | 2 | no | — |
| 707 | C42 | — | 2 | 2 | no | — |
| 708 | C42 | — | 2 | 1 | no | — |
| 709 | C42 | — | 16 | 1 | no | — |
| 710 | C42 | — | 16 | 1 | no | — |
| 711 | C42 | — | 16 | 1 | no | — |
| 712 | C42 | — | 16 | 2 | no | — |
| 713 | C42 | C2×#357 | 1 | 1 | yes | characteristic |
| 714 | C42 | C2×#357 | 1 | 2 | yes | — |
| 715 | C42 | C2×#357 | 1 | 1 | yes | characteristic |
| 716 | C16 | — | 2 | 1 | no | — |
| 717 | C16 | — | 2 | 1 | no | — |
| 718 | C16 | — | 2 | 2 | no | — |
| 719 | C16 | #2138 | 1 | 4 | yes | — |
| 720 | C16 | #2297 | 1 | 1 | yes | characteristic |
| 721 | C16 | C2×#416 | 1 | 1 | yes | characteristic |
| 722 | C16 | #3167 | 1 | 2 | yes | — |
| 723 | C23 | — | 16 | 2 | no | — |
| 724 | C23 | — | 16 | 1 | no | — |
| 725 | C23 | — | 32 | 2 | no | — |
| 726 | C23 | — | 64 | 1 | no | — |
| 727 | C23 | — | 64 | 1 | no | — |
| 728 | C23 | #13617 | 1 | 2 | yes | — |
| 729 | C23 | C2×#2263 | 1 | 1 | yes | characteristic |
| 730 | Q8 | — | 2 | 2 | no | — |
| 731 | Q8 | — | 16 | 1 | no | — |
| 732 | Q8 | — | 16 | 1 | no | — |
| 733 | Q8 | — | 64 | 2 | no | — |
| 734 | D4 | — | 2 | 4 | no | — |
| 735 | D4 | — | 2 | 2 | no | — |
| 736 | D4 | — | 16 | 1 | no | — |
| 737 | D4 | — | 16 | 2 | no | — |
| 738 | D4 | — | 16 | 2 | no | — |
| 739 | D4 | — | 16 | 1 | no | — |
| 740 | D4 | — | 32 | 2 | no | — |
| 741 | D4 | — | 32 | 2 | no | — |
| 742 | D4 | — | 64 | 2 | no | — |
| 743 | D4 | — | 64 | 2 | no | — |
| 744 | D4 | — | 64 | 2 | no | — |
| 745 | D4 | — | 64 | 2 | no | — |
| 746 | D4 | — | 64 | 2 | no | — |
| 747 | C2×C4 | — | 2 | 2 | no | — |
| 748 | C2×C4 | — | 2 | 2 | no | — |
| 749 | C2×C4 | — | 2 | 1 | no | — |
| 750 | C2×C4 | — | 2 | 1 | no | — |
| 751 | C2×C4 | — | 2 | 2 | no | — |
| 752 | C2×C4 | — | 8 | 1 | no | — |
| 753 | C2×C4 | — | 8 | 2 | no | — |
| 754 | C2×C4 | — | 16 | 1 | no | — |
| 755 | C2×C4 | — | 16 | 1 | no | — |
| 756 | C2×C4 | — | 16 | 1 | no | — |
| 757 | C2×C4 | — | 16 | 2 | no | — |
| 758 | C2×C4 | — | 32 | 4 | no | — |
| 759 | C2×C4 | — | 32 | 2 | no | — |
| 760 | C2×C4 | — | 32 | 2 | no | — |
| 761 | C2×C4 | — | 32 | 2 | no | — |
| 762 | C2×C4 | — | 64 | 1 | no | — |
| 763 | C2×C4 | — | 64 | 2 | no | — |
| 764 | C2×C4 | — | 64 | 1 | no | — |
| 765 | C2×C4 | #13617 | 1 | 2 | yes | — |
| 766 | C2×C4 | C22×#357 | 1 | 1 | yes | characteristic |
| 767 | C2×C4 | #33733 | 1 | 2 | yes | — |
| 768 | C2×C4 | C2×#2263 | 1 | 1 | yes | characteristic |
| 769 | C2×C4 | #33981 | 1 | 2 | yes | — |
| 770 | C8 | — | 2 | 1 | no | — |
| 771 | C8 | — | 2 | 1 | no | — |
| 772 | C8 | — | 2 | 2 | no | — |
| 773 | C8 | — | 2 | 2 | no | — |
| 774 | C8 | — | 32 | 2 | no | — |
| 775 | C8 | #21401 | 1 | 1 | yes | characteristic |
| 776 | C8 | C2×#2138 | 1 | 1 | yes | characteristic |
| 777 | C8 | #33736 | 1 | 2 | yes | — |
| 778 | C22 | — | 2 | 2 | no | — |
| 779 | C22 | — | 4 | 1 | no | — |
| 780 | C22 | — | 4 | 2 | no | — |
| 781 | C22 | — | 32 | 2 | no | — |
| 782 | C22 | — | 32 | 1 | no | — |
| 783 | C22 | — | 32 | 1 | no | — |
| 784 | C22 | — | 32 | 2 | no | — |
| 785 | C22 | — | 32 | 1 | no | — |
| 786 | C22 | — | 32 | 2 | no | — |
| 787 | C22 | — | 64 | 4 | no | — |
| 788 | C22 | C2×#13617 | 1 | 1 | yes | characteristic |
| 789 | C22 | #513080 | 1 | 2 | yes | — |
| 790 | C4 | — | 2 | 2 | no | — |
| 791 | C4 | — | 4 | 1 | no | — |
| 792 | C4 | — | 4 | 1 | no | — |
| 793 | C4 | — | 4 | 2 | no | — |
| 794 | C4 | — | 32 | 2 | no | — |
| 795 | C4 | — | 32 | 1 | no | — |
| 796 | C4 | — | 32 | 1 | no | — |
| 797 | C4 | — | 32 | 1 | no | — |
| 798 | C4 | — | 64 | 2 | no | — |
| 799 | C4 | #495544 | 1 | 1 | yes | characteristic |
| 800 | C4 | #512690 | 1 | 1 | yes | characteristic |
| 801 | C4 | #513080 | 1 | 2 | yes | — |
| 802 | C2 | — | 2 | 1 | no | — |
| 803 | C2 | — | 2 | 2 | no | — |
| 804 | C2 | — | 4 | 2 | no | — |
| 805 | C2 | — | 64 | 1 | no | — |
| 806 | C2 | — | 64 | 2 | no | — |
| 807 | C2 | #72322759 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #72322759 |
| commutator | C2×C32 | C23×C4 |
| Frattini, cosocle | C22×C32 | C24 |
| prime radical | #72232017 | C2 |
| LCS | G ▷ C2×C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ C4×#131 ◁ C4×#504 ◁ #512545 ◁ G | |
| LECS | G ▷ C22×C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72322771 | C2 | semidirect |
| 2. #72322768 | C2 | semidirect |
| 3. #72322766 | C2 | semidirect |
| 4. #72322764 | C2 | semidirect |
| 5. #72322761 | C2 | semidirect |
| 6. #72322760 | C2 | semidirect |
| 7. #72321329 | C2 | semidirect |
| 8. #72321140 | C2 | semidirect |
| 9. #72320480 | C2 | semidirect |
| 10. #72286491 | C2 | semidirect |
| 15. #513084 | C4 | semidirect |
| 16. #513082 | C4 | semidirect |
| 19. #513076 | C4 | semidirect |
| 20. #513074 | C4 | semidirect |
| 259. M128 | #41 | semidirect |
| 263. C2×C64 | #41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72322771 | 2 |
| #72322768 | 2 |
| #72322766 | 2 |
| #72322764 | 2 |
| #72322761 | 2 |
| #72322760 | 2 |
| #72321329 | 2 |
| #72321140 | 2 |
| #72320480 | 2 |
| #72286491 | 2 |
| #72232017 | 2 |