Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
1395 conjugacy classes of subgroups.
The subgroup lattice has 1075 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #72322057 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #72322055 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #72322053 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #72322052 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #72322050 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #72322047 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #72322045 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #72322042 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #72321570 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #72321140 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #72321113 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #72320566 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #72286491 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | C2×#153598 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #72232017 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #7623249 | — | 2 | 1 | no | — |
| 17 | #513315 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#13742 | C22 | 1 | 1 | yes | characteristic |
| 19 | #513084 | — | 2 | 1 | no | — |
| 20 | #513082 | — | 2 | 1 | no | — |
| 21 | #513080 | — | 2 | 2 | no | — |
| 22 | #513078 | — | 2 | 2 | no | — |
| 23 | #513076 | — | 2 | 1 | no | — |
| 24 | #513074 | — | 2 | 1 | no | — |
| 25 | #513064 | C22 | 1 | 1 | yes | characteristic |
| 26 | #513054 | C22 | 1 | 1 | yes | characteristic |
| 27 | #513036 | — | 2 | 1 | no | — |
| 28 | #512951 | C22 | 1 | 1 | yes | characteristic |
| 29 | #512946 | — | 2 | 1 | no | — |
| 30 | #512945 | C22 | 1 | 1 | yes | characteristic |
| 31 | #512941 | C22 | 1 | 1 | yes | characteristic |
| 32 | C2×#13656 | C22 | 1 | 1 | yes | characteristic |
| 33 | C4×#2263 | — | 2 | 1 | no | — |
| 34 | #512761 | C22 | 1 | 1 | yes | characteristic |
| 35 | C2×#13654 | C22 | 1 | 1 | yes | characteristic |
| 36 | #512545 | C22 | 1 | 1 | yes | characteristic |
| 37 | #495893 | — | 2 | 1 | no | — |
| 38 | #153598 | — | 2 | 2 | no | — |
| 39 | #153598 | — | 2 | 2 | no | — |
| 40 | #153598 | — | 2 | 1 | no | — |
| 41 | #153598 | — | 2 | 1 | no | — |
| 42 | #153597 | — | 2 | 1 | no | — |
| 43 | #153597 | — | 2 | 1 | no | — |
| 44 | #153578 | C22 | 1 | 1 | yes | characteristic |
| 45 | C2×#7548 | C22 | 1 | 1 | yes | characteristic |
| 46 | #153565 | C22 | 1 | 1 | yes | characteristic |
| 47 | C2×#7541 | C22 | 1 | 1 | yes | characteristic |
| 48 | C2×#7541 | C22 | 1 | 1 | yes | characteristic |
| 49 | #153562 | C22 | 1 | 1 | yes | characteristic |
| 50 | #153562 | C22 | 1 | 1 | yes | characteristic |
| 51 | C2×#7540 | C22 | 1 | 1 | yes | characteristic |
| 52 | #153560 | C22 | 1 | 1 | yes | characteristic |
| 53 | #153557 | C22 | 1 | 1 | yes | characteristic |
| 54 | #153432 | C22 | 1 | 1 | yes | characteristic |
| 55 | #153432 | C22 | 1 | 1 | yes | characteristic |
| 56 | C2×#7511 | C22 | 1 | 1 | yes | characteristic |
| 57 | C2×#7511 | C22 | 1 | 1 | yes | characteristic |
| 58 | #152977 | C22 | 1 | 1 | yes | characteristic |
| 59 | #152859 | C22 | 1 | 1 | yes | characteristic |
| 60 | #152838 | — | 2 | 1 | no | — |
| 61 | #152641 | — | 2 | 1 | no | — |
| 62 | #152296 | C22 | 1 | 1 | yes | characteristic |
| 63 | #151996 | C22 | 1 | 1 | yes | characteristic |
| 64 | #151968 | — | 2 | 1 | no | — |
| 65 | #94770 | C22 | 1 | 1 | yes | characteristic |
| 66 | #94767 | C22 | 1 | 1 | yes | characteristic |
| 67 | #94765 | C22 | 1 | 1 | yes | characteristic |
| 68 | #94764 | C22 | 1 | 1 | yes | characteristic |
| 69 | #94759 | C22 | 1 | 1 | yes | characteristic |
| 70 | #94759 | C22 | 1 | 1 | yes | characteristic |
| 71 | #60695 | — | 4 | 1 | no | — |
| 72 | C2×#2263 | — | 2 | 1 | no | — |
| 73 | C2×#2262 | C23 | 1 | 1 | yes | characteristic |
| 74 | C2×#2262 | C23 | 1 | 1 | yes | characteristic |
| 75 | C22×D32 | C23 | 1 | 1 | yes | characteristic |
| 76 | C2×#2258 | D4 | 1 | 1 | yes | characteristic |
| 77 | C2×#2258 | C23 | 1 | 1 | yes | characteristic |
| 78 | #33744 | — | 4 | 2 | no | — |
| 79 | #33740 | — | 2 | 2 | no | — |
| 80 | #33739 | — | 2 | 2 | no | — |
| 81 | #33737 | — | 4 | 2 | no | — |
| 82 | #33735 | — | 2 | 2 | no | — |
| 83 | #33733 | — | 2 | 2 | no | — |
| 84 | #33729 | — | 2 | 1 | no | — |
| 85 | #33720 | — | 2 | 1 | no | — |
| 86 | #33702 | — | 4 | 1 | no | — |
| 87 | #33617 | — | 2 | 1 | no | — |
| 88 | #33612 | — | 4 | 1 | no | — |
| 89 | #33610 | — | 2 | 1 | no | — |
| 90 | #33607 | — | 2 | 1 | no | — |
| 91 | C2×#2178 | — | 2 | 1 | no | — |
| 92 | C4×#509 | — | 4 | 1 | no | — |
| 93 | C4×#508 | — | 2 | 1 | no | — |
| 94 | C2×C4×D16 | — | 2 | 1 | no | — |
| 95 | C4×#504 | D4 | 1 | 1 | yes | characteristic |
| 96 | #21558 | — | 4 | 1 | no | — |
| 97 | #13743 | — | 2 | 1 | no | — |
| 98 | #13743 | — | 2 | 1 | no | — |
| 99 | #13742 | — | 2 | 2 | no | — |
| 100 | #13742 | — | 2 | 1 | no | — |
| 101 | #13742 | — | 2 | 1 | no | — |
| 102 | #13742 | — | 2 | 2 | no | — |
| 103 | #13741 | — | 2 | 2 | no | — |
| 104 | C2×SD128 | — | 2 | 1 | no | — |
| 105 | C2×D64 | — | 2 | 1 | no | — |
| 106 | C2×M128 | C23 | 1 | 1 | yes | characteristic |
| 107 | C2×M128 | C23 | 1 | 1 | yes | characteristic |
| 108 | C2×M128 | C23 | 1 | 1 | yes | characteristic |
| 109 | C2×M128 | C23 | 1 | 1 | yes | characteristic |
| 110 | #13734 | — | 2 | 2 | no | — |
| 111 | #13733 | — | 2 | 1 | no | — |
| 112 | #13732 | — | 2 | 1 | no | — |
| 113 | #13729 | — | 2 | 2 | no | — |
| 114 | #13728 | — | 2 | 1 | no | — |
| 115 | #13725 | — | 2 | 1 | no | — |
| 116 | #13723 | — | 2 | 2 | no | — |
| 117 | #13722 | — | 2 | 2 | no | — |
| 118 | #13721 | — | 2 | 2 | no | — |
| 119 | #13719 | — | 2 | 2 | no | — |
| 120 | #13702 | — | 2 | 2 | no | — |
| 121 | #13701 | — | 2 | 1 | no | — |
| 122 | #13700 | — | 2 | 1 | no | — |
| 123 | #13699 | — | 2 | 2 | no | — |
| 124 | #13698 | — | 2 | 1 | no | — |
| 125 | #13697 | — | 2 | 2 | no | — |
| 126 | #13697 | — | 2 | 1 | no | — |
| 127 | #13697 | — | 2 | 1 | no | — |
| 128 | #13697 | — | 2 | 1 | no | — |
| 129 | #13696 | — | 2 | 2 | no | — |
| 130 | #13696 | — | 2 | 2 | no | — |
| 131 | #13694 | — | 2 | 2 | no | — |
| 132 | #13694 | — | 2 | 2 | no | — |
| 133 | #13656 | — | 2 | 1 | no | — |
| 134 | #13656 | — | 2 | 1 | no | — |
| 135 | #13656 | — | 2 | 1 | no | — |
| 136 | #13656 | — | 2 | 1 | no | — |
| 137 | #13654 | — | 2 | 2 | no | — |
| 138 | #13654 | — | 2 | 1 | no | — |
| 139 | #13654 | — | 2 | 1 | no | — |
| 140 | #13654 | D4 | 1 | 1 | yes | characteristic |
| 141 | #13654 | D4 | 1 | 2 | yes | — |
| 142 | #13654 | D4 | 1 | 2 | yes | — |
| 143 | #13654 | D4 | 1 | 1 | yes | characteristic |
| 144 | #13653 | D4 | 1 | 1 | yes | characteristic |
| 145 | #13653 | D4 | 1 | 1 | yes | characteristic |
| 146 | #13652 | — | 2 | 2 | no | — |
| 147 | #13652 | — | 2 | 1 | no | — |
| 148 | #13652 | — | 2 | 1 | no | — |
| 149 | C4×SD64 | — | 2 | 2 | no | — |
| 150 | C4×D32 | — | 2 | 2 | no | — |
| 151 | C2×#1425 | C23 | 1 | 1 | yes | characteristic |
| 152 | C2×#1425 | C23 | 1 | 1 | yes | characteristic |
| 153 | #13634 | — | 2 | 1 | no | — |
| 154 | #13633 | C23 | 1 | 1 | yes | characteristic |
| 155 | #13633 | C23 | 1 | 1 | yes | characteristic |
| 156 | C2×#1424 | C23 | 1 | 1 | yes | characteristic |
| 157 | #13625 | — | 2 | 1 | no | — |
| 158 | #13622 | — | 2 | 1 | no | — |
| 159 | C2×#1417 | — | 2 | 1 | no | — |
| 160 | #13617 | — | 2 | 1 | no | — |
| 161 | #13616 | — | 2 | 1 | no | — |
| 162 | #13615 | — | 2 | 1 | no | — |
| 163 | C2×#1415 | — | 2 | 1 | no | — |
| 164 | #13549 | — | 2 | 1 | no | — |
| 165 | #13549 | — | 2 | 1 | no | — |
| 166 | #13549 | D4 | 1 | 1 | yes | characteristic |
| 167 | #13549 | C23 | 1 | 1 | yes | characteristic |
| 168 | C4×M64 | — | 2 | 1 | no | — |
| 169 | C4×M64 | D4 | 1 | 1 | yes | characteristic |
| 170 | C2×#1397 | — | 2 | 1 | no | — |
| 171 | C2×#1397 | C23 | 1 | 1 | yes | characteristic |
| 172 | #13243 | — | 2 | 1 | no | — |
| 173 | #13173 | — | 2 | 1 | no | — |
| 174 | #13146 | — | 4 | 1 | no | — |
| 175 | #13071 | — | 4 | 1 | no | — |
| 176 | #12841 | — | 2 | 1 | no | — |
| 177 | #12670 | — | 2 | 1 | no | — |
| 178 | #12646 | — | 4 | 1 | no | — |
| 179 | #7548 | — | 2 | 2 | no | — |
| 180 | #7548 | — | 2 | 1 | no | — |
| 181 | #7548 | — | 2 | 1 | no | — |
| 182 | #7542 | — | 2 | 1 | no | — |
| 183 | #7541 | — | 2 | 2 | no | — |
| 184 | #7541 | — | 2 | 1 | no | — |
| 185 | #7541 | — | 2 | 2 | no | — |
| 186 | #7540 | — | 2 | 2 | no | — |
| 187 | #7540 | — | 2 | 2 | no | — |
| 188 | #7540 | — | 2 | 1 | no | — |
| 189 | #7540 | — | 2 | 1 | no | — |
| 190 | #7539 | — | 2 | 2 | no | — |
| 191 | #7537 | — | 2 | 2 | no | — |
| 192 | #7514 | — | 2 | 2 | no | — |
| 193 | #7514 | — | 2 | 2 | no | — |
| 194 | #7511 | — | 2 | 1 | no | — |
| 195 | #7511 | — | 2 | 1 | no | — |
| 196 | #7511 | — | 2 | 1 | no | — |
| 197 | #7511 | — | 2 | 1 | no | — |
| 198 | #7480 | — | 2 | 1 | no | — |
| 199 | #7479 | — | 2 | 1 | no | — |
| 200 | #7473 | — | 2 | 1 | no | — |
| 201 | #3460 | — | 8 | 1 | no | — |
| 202 | C2×#509 | — | 4 | 1 | no | — |
| 203 | C2×#508 | — | 2 | 1 | no | — |
| 204 | C2×#508 | — | 2 | 1 | no | — |
| 205 | C22×D16 | — | 2 | 1 | no | — |
| 206 | C2×#504 | D8 | 1 | 1 | yes | characteristic |
| 207 | C2×#504 | C2×D4 | 1 | 1 | yes | characteristic |
| 208 | #3179 | — | 8 | 2 | no | — |
| 209 | #3176 | — | 4 | 2 | no | — |
| 210 | #3175 | — | 4 | 2 | no | — |
| 211 | #3171 | — | 8 | 2 | no | — |
| 212 | #3169 | — | 4 | 2 | no | — |
| 213 | #3168 | — | 4 | 2 | no | — |
| 214 | #3164 | — | 4 | 1 | no | — |
| 215 | #3155 | — | 4 | 1 | no | — |
| 216 | #3136 | — | 8 | 1 | no | — |
| 217 | #3067 | — | 4 | 1 | no | — |
| 218 | #3062 | — | 8 | 1 | no | — |
| 219 | #3061 | — | 4 | 1 | no | — |
| 220 | #3058 | — | 4 | 1 | no | — |
| 221 | #2955 | — | 8 | 1 | no | — |
| 222 | C2×#443 | — | 4 | 1 | no | — |
| 223 | C4×AGL(1,ℤ/8) | — | 8 | 1 | no | — |
| 224 | C4×#135 | — | 4 | 1 | no | — |
| 225 | C2×C4×D8 | — | 4 | 1 | no | — |
| 226 | C4×#131 | D8 | 1 | 1 | yes | characteristic |
| 227 | #2263 | — | 4 | 2 | no | — |
| 228 | #2263 | — | 4 | 2 | no | — |
| 229 | #2262 | — | 2 | 1 | no | — |
| 230 | #2262 | — | 2 | 1 | no | — |
| 231 | #2262 | — | 2 | 1 | no | — |
| 232 | #2262 | — | 2 | 1 | no | — |
| 233 | #2262 | — | 2 | 1 | no | — |
| 234 | #2262 | — | 2 | 1 | no | — |
| 235 | #2262 | — | 2 | 1 | no | — |
| 236 | #2262 | — | 2 | 1 | no | — |
| 237 | C2×Q64 | C2×D4 | 1 | 1 | yes | characteristic |
| 238 | C2×Q64 | #41 | 1 | 1 | yes | characteristic, complemented |
| 239 | C2×SD64 | — | 2 | 2 | no | — |
| 240 | C2×SD64 | — | 2 | 1 | no | — |
| 241 | C2×SD64 | — | 2 | 1 | no | — |
| 242 | C2×D32 | — | 2 | 2 | no | — |
| 243 | C2×D32 | — | 2 | 1 | no | — |
| 244 | C2×D32 | — | 2 | 1 | no | — |
| 245 | C2×D32 | — | 2 | 1 | no | — |
| 246 | C2×D32 | — | 2 | 1 | no | — |
| 247 | C2×D32 | — | 2 | 1 | no | — |
| 248 | C2×D32 | C2×D4 | 1 | 2 | yes | — |
| 249 | C2×D32 | C2×D4 | 1 | 1 | yes | characteristic |
| 250 | C2×D32 | #41 | 1 | 1 | yes | characteristic, complemented |
| 251 | #2258 | — | 2 | 2 | no | — |
| 252 | #2258 | — | 2 | 1 | no | — |
| 253 | #2258 | — | 2 | 1 | no | — |
| 254 | #2258 | — | 2 | 1 | no | — |
| 255 | #2258 | — | 2 | 1 | no | — |
| 256 | #2258 | — | 4 | 1 | no | — |
| 257 | C2×M64 | — | 2 | 1 | no | — |
| 258 | C2×M64 | — | 2 | 1 | no | — |
| 259 | C2×M64 | C2×D4 | 1 | 1 | yes | characteristic |
| 260 | C2×M64 | C2×D4 | 1 | 1 | yes | characteristic |
| 261 | C22×C32 | — | 2 | 1 | no | — |
| 262 | C22×C32 | — | 2 | 1 | no | — |
| 263 | C22×C32 | C2×D4 | 1 | 1 | yes | characteristic |
| 264 | C22×C32 | C24 | 1 | 1 | yes | characteristic |
| 265 | #2255 | — | 4 | 2 | no | — |
| 266 | #2253 | — | 2 | 2 | no | — |
| 267 | #2252 | — | 2 | 2 | no | — |
| 268 | #2250 | — | 4 | 2 | no | — |
| 269 | #2249 | — | 2 | 2 | no | — |
| 270 | #2246 | — | 2 | 2 | no | — |
| 271 | #2244 | — | 4 | 2 | no | — |
| 272 | #2243 | — | 4 | 2 | no | — |
| 273 | #2242 | — | 4 | 2 | no | — |
| 274 | #2240 | — | 4 | 2 | no | — |
| 275 | #2223 | — | 4 | 2 | no | — |
| 276 | #2222 | — | 2 | 2 | no | — |
| 277 | #2221 | — | 2 | 2 | no | — |
| 278 | #2220 | — | 4 | 2 | no | — |
| 279 | #2220 | — | 4 | 2 | no | — |
| 280 | #2218 | — | 4 | 2 | no | — |
| 281 | #2218 | — | 4 | 2 | no | — |
| 282 | #2217 | — | 4 | 2 | no | — |
| 283 | #2216 | — | 2 | 2 | no | — |
| 284 | #2215 | — | 2 | 2 | no | — |
| 285 | #2215 | — | 2 | 2 | no | — |
| 286 | #2215 | — | 2 | 2 | no | — |
| 287 | #2215 | — | 4 | 2 | no | — |
| 288 | #2178 | — | 4 | 1 | no | — |
| 289 | #2178 | — | 4 | 1 | no | — |
| 290 | #2178 | — | 4 | 1 | no | — |
| 291 | #2178 | — | 4 | 1 | no | — |
| 292 | #2177 | — | 4 | 2 | no | — |
| 293 | #2175 | — | 4 | 2 | no | — |
| 294 | C4×Q32 | — | 2 | 1 | no | — |
| 295 | C4×Q32 | — | 2 | 1 | no | — |
| 296 | C4×SD32 | — | 4 | 2 | no | — |
| 297 | C4×SD32 | — | 4 | 1 | no | — |
| 298 | C4×SD32 | — | 4 | 1 | no | — |
| 299 | C4×D16 | — | 2 | 1 | no | — |
| 300 | C4×D16 | — | 2 | 2 | no | — |
| 301 | C4×D16 | — | 2 | 2 | no | — |
| 302 | C4×D16 | — | 2 | 1 | no | — |
| 303 | C4×D16 | — | 4 | 2 | no | — |
| 304 | C4×D16 | — | 4 | 1 | no | — |
| 305 | C4×D16 | — | 4 | 1 | no | — |
| 306 | C2×#368 | — | 2 | 1 | no | — |
| 307 | C2×#368 | — | 2 | 1 | no | — |
| 308 | #2159 | — | 4 | 1 | no | — |
| 309 | #2158 | — | 2 | 1 | no | — |
| 310 | #2158 | — | 2 | 1 | no | — |
| 311 | C2×#366 | — | 2 | 1 | no | — |
| 312 | #2148 | — | 4 | 1 | no | — |
| 313 | #2145 | — | 4 | 1 | no | — |
| 314 | C2×#359 | — | 4 | 1 | no | — |
| 315 | #2140 | — | 4 | 1 | no | — |
| 316 | #2139 | — | 4 | 1 | no | — |
| 317 | #2138 | — | 4 | 1 | no | — |
| 318 | C2×#357 | — | 4 | 1 | no | — |
| 319 | #2108 | — | 2 | 1 | no | — |
| 320 | #2108 | — | 2 | 1 | no | — |
| 321 | #2108 | D8 | 1 | 1 | yes | characteristic |
| 322 | #2108 | C2×D4 | 1 | 1 | yes | characteristic |
| 323 | C4×M32 | — | 2 | 1 | no | — |
| 324 | C4×M32 | D8 | 1 | 1 | yes | characteristic |
| 325 | C2×C4×C16 | — | 2 | 1 | no | — |
| 326 | C2×C4×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 327 | #1976 | — | 4 | 1 | no | — |
| 328 | #1953 | — | 4 | 1 | no | — |
| 329 | #1932 | — | 8 | 1 | no | — |
| 330 | #1906 | — | 8 | 1 | no | — |
| 331 | #1814 | — | 4 | 1 | no | — |
| 332 | #1772 | — | 4 | 1 | no | — |
| 333 | #1757 | — | 8 | 1 | no | — |
| 334 | Q128 | — | 2 | 2 | no | — |
| 335 | SD128 | — | 2 | 4 | no | — |
| 336 | SD128 | — | 2 | 2 | no | — |
| 337 | SD128 | — | 2 | 2 | no | — |
| 338 | D64 | — | 2 | 4 | no | — |
| 339 | D64 | — | 2 | 2 | no | — |
| 340 | M128 | — | 2 | 1 | no | — |
| 341 | M128 | — | 2 | 1 | no | — |
| 342 | M128 | — | 2 | 1 | no | — |
| 343 | M128 | — | 2 | 1 | no | — |
| 344 | M128 | — | 2 | 1 | no | — |
| 345 | M128 | — | 2 | 1 | no | — |
| 346 | M128 | — | 2 | 1 | no | — |
| 347 | M128 | #41 | 1 | 2 | yes | complemented |
| 348 | C2×C64 | — | 2 | 1 | no | — |
| 349 | C2×C64 | — | 2 | 1 | no | — |
| 350 | C2×C64 | — | 2 | 1 | no | — |
| 351 | C2×C64 | #41 | 1 | 2 | yes | complemented |
| 352 | #1425 | — | 2 | 1 | no | — |
| 353 | #1425 | — | 2 | 1 | no | — |
| 354 | #1425 | — | 2 | 1 | no | — |
| 355 | #1425 | #41 | 1 | 2 | yes | complemented |
| 356 | #1424 | — | 2 | 2 | no | — |
| 357 | #1424 | — | 2 | 1 | no | — |
| 358 | #1424 | — | 2 | 1 | no | — |
| 359 | #1424 | C2×D4 | 1 | 2 | yes | — |
| 360 | #1424 | C2×D4 | 1 | 1 | yes | characteristic |
| 361 | #1424 | C2×D4 | 1 | 1 | yes | characteristic |
| 362 | #1423 | — | 2 | 2 | no | — |
| 363 | #1423 | — | 2 | 1 | no | — |
| 364 | #1423 | — | 2 | 1 | no | — |
| 365 | #1420 | — | 2 | 2 | no | — |
| 366 | #1419 | — | 2 | 2 | no | — |
| 367 | #1418 | — | 4 | 2 | no | — |
| 368 | #1417 | — | 4 | 1 | no | — |
| 369 | #1417 | — | 4 | 1 | no | — |
| 370 | #1416 | — | 2 | 2 | no | — |
| 371 | #1416 | — | 2 | 1 | no | — |
| 372 | #1416 | — | 2 | 1 | no | — |
| 373 | #1415 | — | 2 | 2 | no | — |
| 374 | #1415 | — | 2 | 2 | no | — |
| 375 | #1415 | — | 2 | 2 | no | — |
| 376 | #1415 | — | 2 | 2 | no | — |
| 377 | #1415 | — | 2 | 2 | no | — |
| 378 | #1415 | — | 2 | 1 | no | — |
| 379 | #1415 | — | 2 | 1 | no | — |
| 380 | #1397 | — | 2 | 1 | no | — |
| 381 | #1397 | — | 2 | 1 | no | — |
| 382 | #1397 | — | 2 | 1 | no | — |
| 383 | #1397 | C2×D4 | 1 | 1 | yes | characteristic |
| 384 | #1397 | C2×D4 | 1 | 1 | yes | characteristic |
| 385 | #1397 | C2×D4 | 1 | 1 | yes | characteristic |
| 386 | #1397 | C2×D4 | 1 | 1 | yes | characteristic |
| 387 | C4×C32 | — | 2 | 1 | no | — |
| 388 | C4×C32 | — | 2 | 1 | no | — |
| 389 | C4×C32 | — | 2 | 1 | no | — |
| 390 | #1389 | — | 4 | 1 | no | — |
| 391 | #1388 | — | 4 | 1 | no | — |
| 392 | #1382 | — | 4 | 1 | no | — |
| 393 | #575 | — | 8 | 1 | no | — |
| 394 | C2×AGL(1,ℤ/8) | — | 8 | 1 | no | — |
| 395 | C2×#135 | — | 4 | 1 | no | — |
| 396 | C2×#135 | — | 4 | 1 | no | — |
| 397 | C22×D8 | — | 4 | 1 | no | — |
| 398 | C2×#131 | — | 8 | 1 | no | — |
| 399 | C2×#131 | D16 | 1 | 1 | yes | characteristic |
| 400 | C2×#131 | C2×D8 | 1 | 1 | yes | characteristic |
| 401 | #544 | — | 8 | 1 | no | — |
| 402 | #542 | — | 8 | 2 | no | — |
| 403 | #542 | — | 16 | 1 | no | — |
| 404 | #540 | — | 8 | 2 | no | — |
| 405 | #540 | — | 16 | 1 | no | — |
| 406 | #538 | — | 16 | 2 | no | — |
| 407 | #537 | — | 8 | 1 | no | — |
| 408 | #535 | — | 8 | 1 | no | — |
| 409 | #535 | — | 8 | 1 | no | — |
| 410 | #532 | — | 8 | 2 | no | — |
| 411 | #532 | — | 16 | 1 | no | — |
| 412 | #529 | — | 8 | 2 | no | — |
| 413 | #529 | — | 16 | 1 | no | — |
| 414 | #525 | — | 16 | 2 | no | — |
| 415 | C4×#41 | — | 8 | 1 | no | — |
| 416 | C4×#41 | D16 | 1 | 1 | yes | characteristic |
| 417 | C2×C4×D4 | — | 8 | 1 | no | — |
| 418 | #509 | — | 8 | 2 | no | — |
| 419 | #509 | — | 8 | 2 | no | — |
| 420 | #508 | — | 4 | 1 | no | — |
| 421 | #508 | — | 4 | 1 | no | — |
| 422 | #508 | — | 4 | 1 | no | — |
| 423 | #508 | — | 4 | 1 | no | — |
| 424 | #508 | — | 4 | 1 | no | — |
| 425 | #508 | — | 4 | 1 | no | — |
| 426 | #508 | — | 4 | 1 | no | — |
| 427 | #508 | — | 4 | 1 | no | — |
| 428 | C2×Q32 | — | 2 | 1 | no | — |
| 429 | C2×Q32 | — | 2 | 1 | no | — |
| 430 | C2×SD32 | — | 4 | 2 | no | — |
| 431 | C2×SD32 | — | 4 | 1 | no | — |
| 432 | C2×SD32 | — | 4 | 1 | no | — |
| 433 | C2×D16 | — | 2 | 2 | no | — |
| 434 | C2×D16 | — | 2 | 1 | no | — |
| 435 | C2×D16 | — | 2 | 1 | no | — |
| 436 | C2×D16 | — | 4 | 2 | no | — |
| 437 | C2×D16 | — | 4 | 1 | no | — |
| 438 | C2×D16 | — | 4 | 1 | no | — |
| 439 | C2×D16 | — | 4 | 1 | no | — |
| 440 | C2×D16 | — | 4 | 1 | no | — |
| 441 | C2×D16 | — | 4 | 1 | no | — |
| 442 | #504 | — | 2 | 2 | no | — |
| 443 | #504 | — | 2 | 1 | no | — |
| 444 | #504 | — | 2 | 1 | no | — |
| 445 | #504 | — | 2 | 1 | no | — |
| 446 | #504 | — | 2 | 1 | no | — |
| 447 | #504 | — | 4 | 1 | no | — |
| 448 | C2×M32 | — | 2 | 1 | no | — |
| 449 | C2×M32 | — | 2 | 1 | no | — |
| 450 | C2×M32 | C2×D8 | 1 | 1 | yes | characteristic |
| 451 | C2×M32 | C2×D8 | 1 | 1 | yes | characteristic |
| 452 | C22×C16 | — | 2 | 1 | no | — |
| 453 | C22×C16 | — | 2 | 1 | no | — |
| 454 | C22×C16 | C2×D8 | 1 | 1 | yes | characteristic |
| 455 | C22×C16 | C22×D4 | 1 | 1 | yes | characteristic |
| 456 | #501 | — | 8 | 2 | no | — |
| 457 | #500 | — | 4 | 2 | no | — |
| 458 | #499 | — | 4 | 2 | no | — |
| 459 | #496 | — | 8 | 2 | no | — |
| 460 | #495 | — | 4 | 2 | no | — |
| 461 | #493 | — | 4 | 2 | no | — |
| 462 | #490 | — | 8 | 2 | no | — |
| 463 | #489 | — | 8 | 2 | no | — |
| 464 | #488 | — | 8 | 2 | no | — |
| 465 | #486 | — | 8 | 2 | no | — |
| 466 | #473 | — | 4 | 2 | no | — |
| 467 | #472 | — | 4 | 2 | no | — |
| 468 | #471 | — | 8 | 2 | no | — |
| 469 | #469 | — | 8 | 2 | no | — |
| 470 | #469 | — | 8 | 2 | no | — |
| 471 | #468 | — | 8 | 2 | no | — |
| 472 | #468 | — | 8 | 2 | no | — |
| 473 | #467 | — | 4 | 2 | no | — |
| 474 | #466 | — | 4 | 2 | no | — |
| 475 | #466 | — | 4 | 2 | no | — |
| 476 | #466 | — | 4 | 2 | no | — |
| 477 | #466 | — | 8 | 2 | no | — |
| 478 | #465 | — | 8 | 2 | no | — |
| 479 | #444 | — | 16 | 2 | no | — |
| 480 | #443 | — | 8 | 1 | no | — |
| 481 | #443 | — | 8 | 1 | no | — |
| 482 | #443 | — | 8 | 1 | no | — |
| 483 | #443 | — | 8 | 1 | no | — |
| 484 | #443 | — | 16 | 2 | no | — |
| 485 | #442 | — | 8 | 2 | no | — |
| 486 | #440 | — | 8 | 2 | no | — |
| 487 | C4×Q16 | — | 4 | 1 | no | — |
| 488 | C4×Q16 | — | 4 | 1 | no | — |
| 489 | C4×SD16 | — | 8 | 2 | no | — |
| 490 | C4×SD16 | — | 8 | 1 | no | — |
| 491 | C4×SD16 | — | 8 | 1 | no | — |
| 492 | C4×D8 | — | 4 | 2 | no | — |
| 493 | C4×D8 | — | 4 | 1 | no | — |
| 494 | C4×D8 | — | 4 | 2 | no | — |
| 495 | C4×D8 | — | 4 | 1 | no | — |
| 496 | C4×D8 | — | 8 | 2 | no | — |
| 497 | C4×D8 | — | 8 | 1 | no | — |
| 498 | C4×D8 | — | 8 | 1 | no | — |
| 499 | #430 | — | 8 | 1 | no | — |
| 500 | C2×#108 | — | 4 | 1 | no | — |
| 501 | C2×#108 | — | 4 | 1 | no | — |
| 502 | #428 | — | 8 | 1 | no | — |
| 503 | #427 | — | 4 | 1 | no | — |
| 504 | #427 | — | 4 | 1 | no | — |
| 505 | C2×#107 | — | 4 | 1 | no | — |
| 506 | #421 | — | 8 | 1 | no | — |
| 507 | #421 | — | 8 | 1 | no | — |
| 508 | C2×#104 | — | 8 | 1 | no | — |
| 509 | #418 | — | 8 | 1 | no | — |
| 510 | #417 | — | 8 | 1 | no | — |
| 511 | #416 | — | 8 | 1 | no | — |
| 512 | C2×#102 | — | 8 | 1 | no | — |
| 513 | #413 | — | 8 | 1 | no | — |
| 514 | #410 | — | 8 | 1 | no | — |
| 515 | #405 | — | 2 | 1 | no | — |
| 516 | #405 | — | 2 | 1 | no | — |
| 517 | #405 | — | 8 | 1 | no | — |
| 518 | #405 | D16 | 1 | 1 | yes | characteristic |
| 519 | #405 | C2×D8 | 1 | 1 | yes | characteristic |
| 520 | C4×M16 | — | 2 | 1 | no | — |
| 521 | C4×M16 | D16 | 1 | 1 | yes | characteristic |
| 522 | C2×C4×C8 | — | 2 | 1 | no | — |
| 523 | C2×C4×C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 524 | Q64 | — | 2 | 1 | no | — |
| 525 | Q64 | — | 2 | 1 | no | — |
| 526 | Q64 | — | 2 | 1 | no | — |
| 527 | Q64 | — | 2 | 1 | no | — |
| 528 | SD64 | — | 4 | 4 | no | — |
| 529 | SD64 | — | 4 | 1 | no | — |
| 530 | SD64 | — | 4 | 1 | no | — |
| 531 | SD64 | — | 4 | 1 | no | — |
| 532 | SD64 | — | 4 | 1 | no | — |
| 533 | D32 | — | 2 | 1 | no | — |
| 534 | D32 | — | 2 | 2 | no | — |
| 535 | D32 | — | 2 | 1 | no | — |
| 536 | D32 | — | 2 | 1 | no | — |
| 537 | D32 | — | 2 | 2 | no | — |
| 538 | D32 | — | 2 | 1 | no | — |
| 539 | D32 | — | 4 | 4 | no | — |
| 540 | D32 | — | 4 | 1 | no | — |
| 541 | D32 | — | 4 | 1 | no | — |
| 542 | M64 | — | 2 | 1 | no | — |
| 543 | M64 | — | 2 | 1 | no | — |
| 544 | M64 | — | 2 | 1 | no | — |
| 545 | M64 | — | 4 | 2 | no | — |
| 546 | M64 | — | 4 | 1 | no | — |
| 547 | M64 | — | 4 | 1 | no | — |
| 548 | M64 | #135 | 1 | 2 | yes | — |
| 549 | C2×C32 | — | 2 | 1 | no | — |
| 550 | C2×C32 | — | 2 | 1 | no | — |
| 551 | C2×C32 | — | 2 | 1 | no | — |
| 552 | C2×C32 | — | 2 | 1 | no | — |
| 553 | C2×C32 | — | 4 | 2 | no | — |
| 554 | C2×C32 | — | 4 | 1 | no | — |
| 555 | C2×C32 | — | 4 | 1 | no | — |
| 556 | C2×C32 | #120 | 1 | 1 | yes | characteristic |
| 557 | C2×C32 | #120 | 1 | 1 | yes | characteristic |
| 558 | C2×C32 | C22×D4 | 1 | 1 | yes | characteristic |
| 559 | C2×C32 | C22×D4 | 1 | 1 | yes | characteristic |
| 560 | C2×C32 | C2×#41 | 1 | 1 | yes | characteristic |
| 561 | C2×C32 | C2×#41 | 1 | 1 | yes | characteristic |
| 562 | C2×C32 | C2×#41 | 1 | 1 | yes | characteristic |
| 563 | C2×C32 | C2×#41 | 1 | 1 | yes | characteristic |
| 564 | #368 | — | 2 | 2 | no | — |
| 565 | #368 | — | 4 | 1 | no | — |
| 566 | #368 | — | 4 | 1 | no | — |
| 567 | #368 | — | 4 | 1 | no | — |
| 568 | #367 | — | 4 | 2 | no | — |
| 569 | #367 | — | 4 | 1 | no | — |
| 570 | #367 | — | 4 | 1 | no | — |
| 571 | #366 | — | 2 | 2 | no | — |
| 572 | #366 | — | 2 | 1 | no | — |
| 573 | #366 | — | 2 | 1 | no | — |
| 574 | #366 | — | 4 | 2 | no | — |
| 575 | #366 | — | 4 | 1 | no | — |
| 576 | #366 | — | 4 | 1 | no | — |
| 577 | #362 | — | 4 | 2 | no | — |
| 578 | #361 | — | 4 | 2 | no | — |
| 579 | #360 | — | 8 | 2 | no | — |
| 580 | #359 | — | 8 | 1 | no | — |
| 581 | #359 | — | 8 | 1 | no | — |
| 582 | #358 | — | 4 | 2 | no | — |
| 583 | #358 | — | 4 | 1 | no | — |
| 584 | #358 | — | 4 | 1 | no | — |
| 585 | #357 | — | 4 | 2 | no | — |
| 586 | #357 | — | 4 | 2 | no | — |
| 587 | #357 | — | 4 | 2 | no | — |
| 588 | #357 | — | 4 | 2 | no | — |
| 589 | #357 | — | 4 | 2 | no | — |
| 590 | #357 | — | 4 | 1 | no | — |
| 591 | #357 | — | 4 | 1 | no | — |
| 592 | #346 | — | 2 | 1 | no | — |
| 593 | #346 | — | 2 | 1 | no | — |
| 594 | #346 | — | 2 | 1 | no | — |
| 595 | C4×C16 | — | 2 | 1 | no | — |
| 596 | C4×C16 | — | 2 | 1 | no | — |
| 597 | C4×C16 | — | 2 | 1 | no | — |
| 598 | C4×C16 | #120 | 1 | 1 | yes | characteristic |
| 599 | C4×C16 | #120 | 1 | 1 | yes | characteristic |
| 600 | C4×C16 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 601 | C4×C16 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 602 | #344 | — | 8 | 1 | no | — |
| 603 | #344 | — | 8 | 1 | no | — |
| 604 | #339 | — | 8 | 1 | no | — |
| 605 | C64 | — | 2 | 2 | no | — |
| 606 | C64 | — | 2 | 2 | no | — |
| 607 | C64 | — | 4 | 1 | no | — |
| 608 | C64 | — | 4 | 1 | no | — |
| 609 | C2×#41 | — | 8 | 1 | no | — |
| 610 | C2×#41 | — | 8 | 1 | no | — |
| 611 | C2×#41 | — | 16 | 2 | no | — |
| 612 | C2×#41 | C2×D16 | 1 | 1 | yes | characteristic |
| 613 | C22×D4 | — | 8 | 1 | no | — |
| 614 | C23×C4 | — | 16 | 1 | no | — |
| 615 | #137 | — | 8 | 2 | no | — |
| 616 | #137 | — | 16 | 1 | no | — |
| 617 | AGL(1,ℤ/8) | — | 8 | 2 | no | — |
| 618 | AGL(1,ℤ/8) | — | 16 | 2 | no | — |
| 619 | AGL(1,ℤ/8) | — | 16 | 1 | no | — |
| 620 | AGL(1,ℤ/8) | — | 16 | 2 | no | — |
| 621 | #135 | — | 8 | 1 | no | — |
| 622 | #135 | — | 8 | 1 | no | — |
| 623 | #135 | — | 8 | 1 | no | — |
| 624 | #135 | — | 8 | 1 | no | — |
| 625 | #135 | — | 8 | 1 | no | — |
| 626 | #135 | — | 8 | 1 | no | — |
| 627 | #135 | — | 8 | 1 | no | — |
| 628 | #135 | — | 8 | 1 | no | — |
| 629 | #135 | — | 16 | 2 | no | — |
| 630 | C2×Q16 | — | 4 | 1 | no | — |
| 631 | C2×Q16 | — | 4 | 1 | no | — |
| 632 | C2×SD16 | — | 8 | 2 | no | — |
| 633 | C2×SD16 | — | 8 | 1 | no | — |
| 634 | C2×SD16 | — | 8 | 1 | no | — |
| 635 | C2×D8 | — | 4 | 1 | no | — |
| 636 | C2×D8 | — | 4 | 2 | no | — |
| 637 | C2×D8 | — | 4 | 1 | no | — |
| 638 | C2×D8 | — | 8 | 2 | no | — |
| 639 | C2×D8 | — | 8 | 1 | no | — |
| 640 | C2×D8 | — | 8 | 1 | no | — |
| 641 | C2×D8 | — | 8 | 1 | no | — |
| 642 | C2×D8 | — | 8 | 1 | no | — |
| 643 | C2×D8 | — | 8 | 1 | no | — |
| 644 | #131 | — | 2 | 2 | no | — |
| 645 | #131 | — | 2 | 1 | no | — |
| 646 | #131 | — | 2 | 1 | no | — |
| 647 | #131 | — | 2 | 1 | no | — |
| 648 | #131 | — | 2 | 1 | no | — |
| 649 | #131 | — | 4 | 1 | no | — |
| 650 | #131 | — | 16 | 1 | no | — |
| 651 | #131 | — | 16 | 1 | no | — |
| 652 | #131 | — | 16 | 1 | no | — |
| 653 | #131 | — | 16 | 1 | no | — |
| 654 | C2×M16 | — | 2 | 1 | no | — |
| 655 | C2×M16 | — | 2 | 1 | no | — |
| 656 | C2×M16 | — | 8 | 1 | no | — |
| 657 | C2×M16 | — | 8 | 1 | no | — |
| 658 | C2×M16 | — | 16 | 1 | no | — |
| 659 | C2×M16 | C2×D16 | 1 | 1 | yes | characteristic |
| 660 | C2×M16 | C2×D16 | 1 | 1 | yes | characteristic |
| 661 | C22×C8 | — | 2 | 1 | no | — |
| 662 | C22×C8 | — | 2 | 1 | no | — |
| 663 | C22×C8 | — | 16 | 1 | no | — |
| 664 | C22×C8 | C2×D16 | 1 | 1 | yes | characteristic |
| 665 | C22×C8 | C22×D8 | 1 | 1 | yes | characteristic |
| 666 | C4⋊Q8 | — | 8 | 2 | no | — |
| 667 | C4⋊Q8 | — | 16 | 1 | no | — |
| 668 | #127 | — | 8 | 2 | no | — |
| 669 | #127 | — | 16 | 1 | no | — |
| 670 | #126 | — | 16 | 2 | no | — |
| 671 | #126 | — | 16 | 2 | no | — |
| 672 | #125 | — | 8 | 2 | no | — |
| 673 | #125 | — | 16 | 1 | no | — |
| 674 | #124 | — | 8 | 2 | no | — |
| 675 | #124 | — | 16 | 2 | no | — |
| 676 | #124 | — | 16 | 2 | no | — |
| 677 | #124 | — | 16 | 1 | no | — |
| 678 | #123 | — | 16 | 2 | no | — |
| 679 | #123 | — | 16 | 2 | no | — |
| 680 | #123 | — | 16 | 2 | no | — |
| 681 | #123 | — | 16 | 2 | no | — |
| 682 | C22⋊Q8 | — | 8 | 2 | no | — |
| 683 | C22⋊Q8 | — | 16 | 2 | no | — |
| 684 | C22⋊Q8 | — | 16 | 1 | no | — |
| 685 | C22⋊Q8 | — | 16 | 2 | no | — |
| 686 | #121 | — | 8 | 2 | no | — |
| 687 | #121 | — | 8 | 2 | no | — |
| 688 | #121 | — | 8 | 2 | no | — |
| 689 | #121 | — | 16 | 2 | no | — |
| 690 | #121 | — | 16 | 2 | no | — |
| 691 | #121 | — | 16 | 1 | no | — |
| 692 | #121 | — | 16 | 1 | no | — |
| 693 | #121 | — | 16 | 2 | no | — |
| 694 | #121 | — | 16 | 2 | no | — |
| 695 | #121 | — | 16 | 1 | no | — |
| 696 | #120 | — | 16 | 2 | no | — |
| 697 | #120 | — | 16 | 2 | no | — |
| 698 | C4×Q8 | — | 2 | 1 | no | — |
| 699 | C4×Q8 | — | 8 | 1 | no | — |
| 700 | C4×Q8 | — | 8 | 1 | no | — |
| 701 | C4×D4 | — | 2 | 1 | no | — |
| 702 | C4×D4 | — | 2 | 2 | no | — |
| 703 | C4×D4 | — | 8 | 2 | no | — |
| 704 | C4×D4 | — | 8 | 2 | no | — |
| 705 | C4×D4 | — | 8 | 1 | no | — |
| 706 | C4×D4 | — | 8 | 1 | no | — |
| 707 | C4×D4 | — | 16 | 1 | no | — |
| 708 | C4×D4 | — | 16 | 1 | no | — |
| 709 | C4×D4 | — | 16 | 2 | no | — |
| 710 | C4×D4 | — | 16 | 1 | no | — |
| 711 | C4×D4 | — | 16 | 1 | no | — |
| 712 | C4×D4 | — | 16 | 2 | no | — |
| 713 | #117 | — | 2 | 1 | no | — |
| 714 | #117 | — | 8 | 1 | no | — |
| 715 | #117 | — | 8 | 1 | no | — |
| 716 | #117 | — | 16 | 1 | no | — |
| 717 | #117 | — | 16 | 2 | no | — |
| 718 | #117 | C2×D16 | 1 | 1 | yes | characteristic |
| 719 | C2×C4⋊C4 | — | 8 | 1 | no | — |
| 720 | C2×C22⋊C4 | — | 16 | 1 | no | — |
| 721 | C2×C42 | — | 2 | 1 | no | — |
| 722 | C2×C42 | — | 16 | 1 | no | — |
| 723 | C2×C42 | C2×D16 | 1 | 1 | yes | characteristic |
| 724 | Q32 | — | 4 | 1 | no | — |
| 725 | Q32 | — | 4 | 1 | no | — |
| 726 | Q32 | — | 4 | 1 | no | — |
| 727 | Q32 | — | 4 | 1 | no | — |
| 728 | SD32 | — | 8 | 4 | no | — |
| 729 | SD32 | — | 8 | 1 | no | — |
| 730 | SD32 | — | 8 | 1 | no | — |
| 731 | SD32 | — | 8 | 1 | no | — |
| 732 | SD32 | — | 8 | 1 | no | — |
| 733 | D16 | — | 4 | 1 | no | — |
| 734 | D16 | — | 4 | 2 | no | — |
| 735 | D16 | — | 4 | 1 | no | — |
| 736 | D16 | — | 4 | 1 | no | — |
| 737 | D16 | — | 4 | 1 | no | — |
| 738 | D16 | — | 4 | 2 | no | — |
| 739 | D16 | — | 8 | 4 | no | — |
| 740 | D16 | — | 8 | 1 | no | — |
| 741 | D16 | — | 8 | 1 | no | — |
| 742 | M32 | — | 2 | 1 | no | — |
| 743 | M32 | — | 2 | 1 | no | — |
| 744 | M32 | — | 2 | 1 | no | — |
| 745 | M32 | — | 4 | 2 | no | — |
| 746 | M32 | — | 4 | 1 | no | — |
| 747 | M32 | — | 4 | 1 | no | — |
| 748 | M32 | #508 | 1 | 2 | yes | — |
| 749 | C2×C16 | — | 2 | 1 | no | — |
| 750 | C2×C16 | — | 2 | 1 | no | — |
| 751 | C2×C16 | — | 2 | 1 | no | — |
| 752 | C2×C16 | — | 2 | 1 | no | — |
| 753 | C2×C16 | — | 4 | 2 | no | — |
| 754 | C2×C16 | — | 4 | 1 | no | — |
| 755 | C2×C16 | — | 4 | 1 | no | — |
| 756 | C2×C16 | #447 | 1 | 1 | yes | characteristic |
| 757 | C2×C16 | #447 | 1 | 1 | yes | characteristic |
| 758 | C2×C16 | C2×#120 | 1 | 1 | yes | characteristic |
| 759 | C2×C16 | #525 | 1 | 1 | yes | characteristic |
| 760 | C2×C16 | #532 | 1 | 1 | yes | characteristic |
| 761 | C2×C16 | C2×#135 | 1 | 1 | yes | characteristic |
| 762 | C2×C16 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 763 | C2×C16 | #575 | 1 | 1 | yes | characteristic |
| 764 | #108 | — | 4 | 2 | no | — |
| 765 | #108 | — | 8 | 1 | no | — |
| 766 | #108 | — | 8 | 1 | no | — |
| 767 | #108 | — | 8 | 1 | no | — |
| 768 | #108 | — | 16 | 2 | no | — |
| 769 | #107 | — | 4 | 2 | no | — |
| 770 | #107 | — | 4 | 1 | no | — |
| 771 | #107 | — | 4 | 1 | no | — |
| 772 | #107 | — | 8 | 2 | no | — |
| 773 | #107 | — | 8 | 1 | no | — |
| 774 | #107 | — | 8 | 1 | no | — |
| 775 | #106 | — | 8 | 2 | no | — |
| 776 | #106 | — | 8 | 1 | no | — |
| 777 | #106 | — | 8 | 1 | no | — |
| 778 | #104 | — | 16 | 2 | no | — |
| 779 | #104 | — | 16 | 2 | no | — |
| 780 | #104 | — | 16 | 1 | no | — |
| 781 | #104 | — | 16 | 1 | no | — |
| 782 | #103 | — | 8 | 2 | no | — |
| 783 | #103 | — | 8 | 1 | no | — |
| 784 | #103 | — | 8 | 1 | no | — |
| 785 | #102 | — | 8 | 2 | no | — |
| 786 | #102 | — | 8 | 2 | no | — |
| 787 | #102 | — | 8 | 2 | no | — |
| 788 | #102 | — | 8 | 2 | no | — |
| 789 | #102 | — | 8 | 2 | no | — |
| 790 | #102 | — | 8 | 1 | no | — |
| 791 | #102 | — | 8 | 1 | no | — |
| 792 | #101 | — | 8 | 2 | no | — |
| 793 | #100 | — | 8 | 2 | no | — |
| 794 | #99 | — | 16 | 2 | no | — |
| 795 | #97 | — | 2 | 1 | no | — |
| 796 | #97 | — | 2 | 1 | no | — |
| 797 | #97 | — | 2 | 1 | no | — |
| 798 | #97 | — | 16 | 1 | no | — |
| 799 | C4×C8 | — | 2 | 1 | no | — |
| 800 | C4×C8 | — | 2 | 1 | no | — |
| 801 | C4×C8 | — | 2 | 1 | no | — |
| 802 | C4×C8 | — | 16 | 1 | no | — |
| 803 | C4×C8 | #447 | 1 | 1 | yes | characteristic |
| 804 | C4×C8 | #447 | 1 | 1 | yes | characteristic |
| 805 | C4×C8 | #509 | 1 | 1 | yes | characteristic |
| 806 | C4×C8 | #509 | 1 | 1 | yes | characteristic |
| 807 | C32 | — | 2 | 1 | no | — |
| 808 | C32 | — | 2 | 1 | no | — |
| 809 | C32 | — | 2 | 2 | no | — |
| 810 | C32 | — | 4 | 1 | no | — |
| 811 | C32 | #525 | 1 | 1 | yes | characteristic |
| 812 | C32 | #525 | 1 | 1 | yes | characteristic |
| 813 | C32 | #532 | 1 | 1 | yes | characteristic |
| 814 | C32 | #532 | 1 | 1 | yes | characteristic |
| 815 | C24 | — | 16 | 1 | no | — |
| 816 | #41 | — | 2 | 1 | no | — |
| 817 | #41 | — | 2 | 1 | no | — |
| 818 | #41 | — | 2 | 1 | no | — |
| 819 | #41 | — | 2 | 1 | no | — |
| 820 | #41 | — | 16 | 1 | no | — |
| 821 | #41 | — | 16 | 1 | no | — |
| 822 | #41 | — | 16 | 1 | no | — |
| 823 | #41 | — | 16 | 1 | no | — |
| 824 | #41 | — | 16 | 1 | no | — |
| 825 | #41 | — | 16 | 1 | no | — |
| 826 | #41 | — | 16 | 1 | no | — |
| 827 | #41 | — | 16 | 1 | no | — |
| 828 | #41 | — | 64 | 4 | no | — |
| 829 | C2×Q8 | — | 8 | 1 | no | — |
| 830 | C2×Q8 | — | 8 | 1 | no | — |
| 831 | C2×Q8 | — | 16 | 2 | no | — |
| 832 | C2×Q8 | #2263 | 1 | 1 | yes | characteristic |
| 833 | C2×D4 | — | 2 | 1 | no | — |
| 834 | C2×D4 | — | 8 | 1 | no | — |
| 835 | C2×D4 | — | 8 | 2 | no | — |
| 836 | C2×D4 | — | 8 | 1 | no | — |
| 837 | C2×D4 | — | 16 | 2 | no | — |
| 838 | C2×D4 | — | 16 | 2 | no | — |
| 839 | C2×D4 | — | 16 | 1 | no | — |
| 840 | C2×D4 | — | 16 | 1 | no | — |
| 841 | C2×D4 | — | 16 | 2 | no | — |
| 842 | C2×D4 | — | 16 | 2 | no | — |
| 843 | C2×D4 | — | 16 | 2 | no | — |
| 844 | C2×D4 | — | 16 | 1 | no | — |
| 845 | C2×D4 | — | 16 | 1 | no | — |
| 846 | C2×D4 | — | 16 | 1 | no | — |
| 847 | C2×D4 | — | 16 | 1 | no | — |
| 848 | C2×D4 | — | 16 | 1 | no | — |
| 849 | C2×D4 | #2263 | 1 | 1 | yes | characteristic |
| 850 | C22×C4 | — | 2 | 2 | no | — |
| 851 | C22×C4 | — | 2 | 1 | no | — |
| 852 | C22×C4 | — | 2 | 1 | no | — |
| 853 | C22×C4 | — | 16 | 1 | no | — |
| 854 | C22×C4 | — | 16 | 2 | no | — |
| 855 | C22×C4 | — | 16 | 1 | no | — |
| 856 | C22×C4 | — | 16 | 2 | no | — |
| 857 | C22×C4 | — | 16 | 1 | no | — |
| 858 | C22×C4 | — | 16 | 1 | no | — |
| 859 | C22×C4 | — | 16 | 1 | no | — |
| 860 | C22×C4 | — | 64 | 2 | no | — |
| 861 | C22×C4 | C22×D16 | 1 | 1 | yes | characteristic |
| 862 | Q16 | — | 8 | 1 | no | — |
| 863 | Q16 | — | 8 | 1 | no | — |
| 864 | Q16 | — | 8 | 1 | no | — |
| 865 | Q16 | — | 8 | 1 | no | — |
| 866 | Q16 | — | 16 | 2 | no | — |
| 867 | SD16 | — | 16 | 4 | no | — |
| 868 | SD16 | — | 16 | 2 | no | — |
| 869 | SD16 | — | 16 | 2 | no | — |
| 870 | SD16 | — | 16 | 1 | no | — |
| 871 | SD16 | — | 16 | 1 | no | — |
| 872 | SD16 | — | 16 | 1 | no | — |
| 873 | SD16 | — | 16 | 1 | no | — |
| 874 | D8 | — | 8 | 2 | no | — |
| 875 | D8 | — | 8 | 1 | no | — |
| 876 | D8 | — | 8 | 1 | no | — |
| 877 | D8 | — | 8 | 1 | no | — |
| 878 | D8 | — | 8 | 1 | no | — |
| 879 | D8 | — | 8 | 2 | no | — |
| 880 | D8 | — | 16 | 4 | no | — |
| 881 | D8 | — | 16 | 2 | no | — |
| 882 | D8 | — | 16 | 1 | no | — |
| 883 | D8 | — | 16 | 1 | no | — |
| 884 | M16 | — | 2 | 1 | no | — |
| 885 | M16 | — | 2 | 1 | no | — |
| 886 | M16 | — | 2 | 1 | no | — |
| 887 | M16 | — | 4 | 2 | no | — |
| 888 | M16 | — | 4 | 1 | no | — |
| 889 | M16 | — | 4 | 1 | no | — |
| 890 | M16 | — | 8 | 2 | no | — |
| 891 | M16 | — | 16 | 1 | no | — |
| 892 | M16 | — | 16 | 1 | no | — |
| 893 | M16 | — | 16 | 1 | no | — |
| 894 | M16 | — | 32 | 1 | no | — |
| 895 | M16 | — | 32 | 1 | no | — |
| 896 | M16 | #2263 | 1 | 2 | yes | — |
| 897 | C2×C8 | — | 2 | 1 | no | — |
| 898 | C2×C8 | — | 2 | 1 | no | — |
| 899 | C2×C8 | — | 2 | 1 | no | — |
| 900 | C2×C8 | — | 2 | 1 | no | — |
| 901 | C2×C8 | — | 4 | 2 | no | — |
| 902 | C2×C8 | — | 4 | 1 | no | — |
| 903 | C2×C8 | — | 4 | 1 | no | — |
| 904 | C2×C8 | — | 16 | 1 | no | — |
| 905 | C2×C8 | — | 16 | 1 | no | — |
| 906 | C2×C8 | — | 32 | 1 | no | — |
| 907 | C2×C8 | — | 32 | 1 | no | — |
| 908 | C2×C8 | #2184 | 1 | 1 | yes | characteristic |
| 909 | C2×C8 | #2184 | 1 | 1 | yes | characteristic |
| 910 | C2×C8 | C2×#447 | 1 | 1 | yes | characteristic |
| 911 | C2×C8 | #3100 | 1 | 1 | yes | characteristic |
| 912 | C2×C8 | #3169 | 1 | 1 | yes | characteristic |
| 913 | C2×C8 | C2×#508 | 1 | 1 | yes | characteristic |
| 914 | C2×C8 | C2×#509 | 1 | 1 | yes | characteristic |
| 915 | C2×C8 | #3414 | 1 | 1 | yes | characteristic |
| 916 | C4⋊C4 | — | 2 | 2 | no | — |
| 917 | C4⋊C4 | — | 2 | 1 | no | — |
| 918 | C4⋊C4 | — | 8 | 1 | no | — |
| 919 | C4⋊C4 | — | 8 | 2 | no | — |
| 920 | C4⋊C4 | — | 8 | 1 | no | — |
| 921 | C4⋊C4 | — | 16 | 1 | no | — |
| 922 | C4⋊C4 | — | 16 | 1 | no | — |
| 923 | C4⋊C4 | — | 16 | 2 | no | — |
| 924 | C4⋊C4 | — | 16 | 2 | no | — |
| 925 | C4⋊C4 | — | 16 | 2 | no | — |
| 926 | C4⋊C4 | — | 16 | 2 | no | — |
| 927 | C4⋊C4 | — | 16 | 1 | no | — |
| 928 | C4⋊C4 | — | 16 | 1 | no | — |
| 929 | C22⋊C4 | — | 2 | 2 | no | — |
| 930 | C22⋊C4 | — | 16 | 2 | no | — |
| 931 | C22⋊C4 | — | 16 | 2 | no | — |
| 932 | C22⋊C4 | — | 16 | 1 | no | — |
| 933 | C22⋊C4 | — | 16 | 1 | no | — |
| 934 | C22⋊C4 | — | 16 | 2 | no | — |
| 935 | C22⋊C4 | — | 16 | 2 | no | — |
| 936 | C22⋊C4 | — | 16 | 2 | no | — |
| 937 | C22⋊C4 | — | 16 | 2 | no | — |
| 938 | C22⋊C4 | — | 16 | 2 | no | — |
| 939 | C22⋊C4 | — | 16 | 2 | no | — |
| 940 | C22⋊C4 | — | 16 | 1 | no | — |
| 941 | C22⋊C4 | — | 16 | 1 | no | — |
| 942 | C22⋊C4 | #2263 | 1 | 2 | yes | — |
| 943 | C42 | — | 2 | 2 | no | — |
| 944 | C42 | — | 2 | 1 | no | — |
| 945 | C42 | — | 2 | 1 | no | — |
| 946 | C42 | — | 16 | 1 | no | — |
| 947 | C42 | — | 16 | 1 | no | — |
| 948 | C42 | — | 16 | 1 | no | — |
| 949 | C42 | — | 16 | 1 | no | — |
| 950 | C42 | #2184 | 1 | 1 | yes | characteristic |
| 951 | C42 | #2184 | 1 | 1 | yes | characteristic |
| 952 | C16 | — | 2 | 1 | no | — |
| 953 | C16 | — | 2 | 1 | no | — |
| 954 | C16 | — | 2 | 2 | no | — |
| 955 | C16 | — | 4 | 1 | no | — |
| 956 | C16 | #2388 | 1 | 1 | yes | characteristic |
| 957 | C16 | #3002 | 1 | 1 | yes | characteristic |
| 958 | C16 | #3106 | 1 | 1 | yes | characteristic |
| 959 | C16 | #3171 | 1 | 1 | yes | characteristic |
| 960 | C23 | — | 2 | 1 | no | — |
| 961 | C23 | — | 16 | 2 | no | — |
| 962 | C23 | — | 16 | 1 | no | — |
| 963 | C23 | — | 16 | 1 | no | — |
| 964 | C23 | — | 32 | 1 | no | — |
| 965 | C23 | — | 32 | 1 | no | — |
| 966 | C23 | — | 64 | 1 | no | — |
| 967 | C23 | — | 64 | 1 | no | — |
| 968 | C23 | C2×#2263 | 1 | 1 | yes | characteristic |
| 969 | Q8 | — | 2 | 1 | no | — |
| 970 | Q8 | — | 2 | 1 | no | — |
| 971 | Q8 | — | 16 | 1 | no | — |
| 972 | Q8 | — | 16 | 1 | no | — |
| 973 | Q8 | — | 16 | 1 | no | — |
| 974 | Q8 | — | 16 | 1 | no | — |
| 975 | Q8 | — | 64 | 2 | no | — |
| 976 | D4 | — | 2 | 1 | no | — |
| 977 | D4 | — | 2 | 1 | no | — |
| 978 | D4 | — | 4 | 1 | no | — |
| 979 | D4 | — | 4 | 1 | no | — |
| 980 | D4 | — | 16 | 2 | no | — |
| 981 | D4 | — | 16 | 1 | no | — |
| 982 | D4 | — | 16 | 1 | no | — |
| 983 | D4 | — | 16 | 1 | no | — |
| 984 | D4 | — | 16 | 2 | no | — |
| 985 | D4 | — | 16 | 1 | no | — |
| 986 | D4 | — | 32 | 1 | no | — |
| 987 | D4 | — | 32 | 1 | no | — |
| 988 | D4 | — | 32 | 1 | no | — |
| 989 | D4 | — | 32 | 1 | no | — |
| 990 | D4 | — | 32 | 1 | no | — |
| 991 | D4 | — | 32 | 1 | no | — |
| 992 | D4 | — | 64 | 2 | no | — |
| 993 | D4 | — | 64 | 2 | no | — |
| 994 | D4 | — | 64 | 2 | no | — |
| 995 | D4 | — | 64 | 2 | no | — |
| 996 | D4 | — | 64 | 2 | no | — |
| 997 | C2×C4 | — | 2 | 1 | no | — |
| 998 | C2×C4 | — | 2 | 2 | no | — |
| 999 | C2×C4 | — | 2 | 1 | no | — |
| 1000 | C2×C4 | — | 2 | 1 | no | — |
| 1001 | C2×C4 | — | 4 | 1 | no | — |
| 1002 | C2×C4 | — | 4 | 1 | no | — |
| 1003 | C2×C4 | — | 8 | 1 | no | — |
| 1004 | C2×C4 | — | 8 | 2 | no | — |
| 1005 | C2×C4 | — | 16 | 1 | no | — |
| 1006 | C2×C4 | — | 16 | 1 | no | — |
| 1007 | C2×C4 | — | 16 | 1 | no | — |
| 1008 | C2×C4 | — | 16 | 2 | no | — |
| 1009 | C2×C4 | — | 16 | 1 | no | — |
| 1010 | C2×C4 | — | 32 | 4 | no | — |
| 1011 | C2×C4 | — | 32 | 2 | no | — |
| 1012 | C2×C4 | — | 32 | 1 | no | — |
| 1013 | C2×C4 | — | 32 | 1 | no | — |
| 1014 | C2×C4 | — | 32 | 1 | no | — |
| 1015 | C2×C4 | — | 32 | 1 | no | — |
| 1016 | C2×C4 | — | 32 | 1 | no | — |
| 1017 | C2×C4 | — | 64 | 1 | no | — |
| 1018 | C2×C4 | — | 64 | 2 | no | — |
| 1019 | C2×C4 | — | 64 | 1 | no | — |
| 1020 | C2×C4 | C2×#2184 | 1 | 1 | yes | characteristic |
| 1021 | C2×C4 | #33660 | 1 | 1 | yes | characteristic |
| 1022 | C2×C4 | #33733 | 1 | 1 | yes | characteristic |
| 1023 | C2×C4 | C2×#2263 | 1 | 1 | yes | characteristic |
| 1024 | C2×C4 | C2×#2263 | 1 | 1 | yes | characteristic |
| 1025 | C2×C4 | #33981 | 1 | 1 | yes | characteristic |
| 1026 | C8 | — | 2 | 1 | no | — |
| 1027 | C8 | — | 2 | 1 | no | — |
| 1028 | C8 | — | 2 | 2 | no | — |
| 1029 | C8 | — | 4 | 1 | no | — |
| 1030 | C8 | — | 16 | 2 | no | — |
| 1031 | C8 | — | 32 | 1 | no | — |
| 1032 | C8 | #23567 | 1 | 1 | yes | characteristic |
| 1033 | C8 | #33516 | 1 | 1 | yes | characteristic |
| 1034 | C8 | #33666 | 1 | 1 | yes | characteristic |
| 1035 | C8 | #33737 | 1 | 1 | yes | characteristic |
| 1036 | C22 | — | 4 | 1 | no | — |
| 1037 | C22 | — | 4 | 2 | no | — |
| 1038 | C22 | — | 4 | 1 | no | — |
| 1039 | C22 | — | 32 | 2 | no | — |
| 1040 | C22 | — | 32 | 1 | no | — |
| 1041 | C22 | — | 32 | 1 | no | — |
| 1042 | C22 | — | 32 | 2 | no | — |
| 1043 | C22 | — | 32 | 1 | no | — |
| 1044 | C22 | — | 32 | 1 | no | — |
| 1045 | C22 | — | 32 | 2 | no | — |
| 1046 | C22 | — | 64 | 1 | no | — |
| 1047 | C22 | — | 64 | 2 | no | — |
| 1048 | C22 | — | 64 | 2 | no | — |
| 1049 | C22 | #512827 | 1 | 1 | yes | characteristic |
| 1050 | C22 | #513009 | 1 | 1 | yes | characteristic |
| 1051 | C22 | #513082 | 1 | 1 | yes | characteristic |
| 1052 | C4 | — | 4 | 1 | no | — |
| 1053 | C4 | — | 4 | 1 | no | — |
| 1054 | C4 | — | 4 | 2 | no | — |
| 1055 | C4 | — | 4 | 1 | no | — |
| 1056 | C4 | — | 32 | 2 | no | — |
| 1057 | C4 | — | 32 | 1 | no | — |
| 1058 | C4 | — | 32 | 1 | no | — |
| 1059 | C4 | — | 32 | 1 | no | — |
| 1060 | C4 | — | 32 | 1 | no | — |
| 1061 | C4 | — | 64 | 1 | no | — |
| 1062 | C4 | #499229 | 1 | 1 | yes | characteristic |
| 1063 | C4 | #512830 | 1 | 1 | yes | characteristic |
| 1064 | C4 | #513003 | 1 | 1 | yes | characteristic |
| 1065 | C4 | #513080 | 1 | 1 | yes | characteristic |
| 1066 | C2 | — | 2 | 1 | no | — |
| 1067 | C2 | — | 2 | 1 | no | — |
| 1068 | C2 | — | 2 | 1 | no | — |
| 1069 | C2 | — | 8 | 1 | no | — |
| 1070 | C2 | — | 64 | 1 | no | — |
| 1071 | C2 | — | 64 | 2 | no | — |
| 1072 | C2 | — | 64 | 1 | no | — |
| 1073 | C2 | #72321065 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #72321065 |
| commutator, Frattini, cosocle | C22×C32 | C24 |
| LCS | G ▷ C22×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. #72322057 | C2 | semidirect |
| 2. #72322055 | C2 | semidirect |
| 3. #72322053 | C2 | semidirect |
| 4. #72322052 | C2 | semidirect |
| 5. #72322050 | C2 | semidirect |
| 6. #72322047 | C2 | semidirect |
| 7. #72322045 | C2 | semidirect |
| 8. #72322042 | C2 | semidirect |
| 9. #72321570 | C2 | semidirect |
| 10. #72321140 | C2 | semidirect |
| 11. #72321113 | C2 | semidirect |
| 12. #72320566 | C2 | semidirect |
| 13. #72286491 | C2 | semidirect |
| 14. C2×#153598 | C2 | semidirect |
| 15. #72232017 | C2 | semidirect |
| 238. C2×Q64 | #41 | semidirect |
| 250. C2×D32 | #41 | semidirect |
| 347. M128 | #41 | semidirect |
| 351. C2×C64 | #41 | semidirect |
| 355. #1425 | #41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72322057 | 2 |
| #72322055 | 2 |
| #72322053 | 2 |
| #72322052 | 2 |
| #72322050 | 2 |
| #72322047 | 2 |
| #72322045 | 2 |
| #72322042 | 2 |
| #72321570 | 2 |
| #72321140 | 2 |
| #72321113 | 2 |
| #72320566 | 2 |
| #72286491 | 2 |
| C2×#153598 | 2 |
| #72232017 | 2 |