Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1144 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 1144 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #22602481 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #22597733 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #22597690 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22590353 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #22590348 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #22590344 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #22590343 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #22590340 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #22590004 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #22589980 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | C71×#2201 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #17986834 | C22 | 1 | 1 | yes | characteristic |
| 13 | #17986798 | — | 2 | 1 | no | — |
| 14 | #17986748 | — | 2 | 1 | no | — |
| 15 | #17986747 | — | 2 | 1 | no | — |
| 16 | #17986745 | — | 2 | 2 | no | — |
| 17 | #17986741 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | #17986740 | — | 2 | 2 | no | — |
| 19 | #17986739 | C22 | 1 | 2 | yes | complemented |
| 20 | #17986550 | — | 2 | 1 | no | — |
| 21 | #17986548 | C22 | 1 | 1 | yes | characteristic |
| 22 | #17986534 | — | 2 | 1 | no | — |
| 23 | #17986532 | — | 2 | 2 | no | — |
| 24 | #17986512 | — | 2 | 2 | no | — |
| 25 | #17986507 | — | 2 | 2 | no | — |
| 26 | #17986507 | C22 | 1 | 2 | yes | — |
| 27 | #17986188 | — | 2 | 2 | no | — |
| 28 | #17986188 | C22 | 1 | 2 | yes | — |
| 29 | #17986187 | — | 2 | 2 | no | — |
| 30 | #17986187 | C22 | 1 | 2 | yes | — |
| 31 | #17986186 | C22 | 1 | 2 | yes | — |
| 32 | #17986180 | — | 2 | 1 | no | — |
| 33 | #17986176 | C22 | 1 | 1 | yes | characteristic |
| 34 | #17986173 | — | 2 | 1 | no | — |
| 35 | #17986169 | C22 | 1 | 1 | yes | characteristic |
| 36 | #17986167 | C22 | 1 | 1 | yes | characteristic |
| 37 | #104×D71 | — | 2 | 1 | no | — |
| 38 | #17985980 | C22 | 1 | 1 | yes | characteristic |
| 39 | #17985971 | — | 2 | 2 | no | — |
| 40 | #17985971 | C22 | 1 | 2 | yes | — |
| 41 | #17985794 | C22 | 1 | 1 | yes | characteristic, complemented |
| 42 | #17985791 | C22 | 1 | 2 | yes | complemented |
| 43 | #17985789 | C22 | 1 | 2 | yes | complemented |
| 44 | #17985787 | C22 | 1 | 2 | yes | complemented |
| 45 | #17985785 | C22 | 1 | 2 | yes | complemented |
| 46 | #563×C71 | C22 | 1 | 1 | yes | characteristic, complemented |
| 47 | #458×C71 | C22 | 1 | 2 | yes | — |
| 48 | #455×C71 | C22 | 1 | 1 | yes | characteristic |
| 49 | #354×C71 | C22 | 1 | 1 | yes | characteristic, complemented |
| 50 | #352×C71 | C22 | 1 | 2 | yes | complemented |
| 51 | #14556175 | — | 2 | 1 | no | — |
| 52 | #14556175 | — | 4 | 1 | no | — |
| 53 | #14556173 | — | 2 | 2 | no | — |
| 54 | #14556173 | — | 4 | 1 | no | — |
| 55 | #14556173 | C23 | 1 | 1 | yes | characteristic |
| 56 | C2×#11765866 | — | 2 | 1 | no | — |
| 57 | C2×#11765866 | D4 | 1 | 1 | yes | characteristic, complemented |
| 58 | C2×#11765864 | — | 2 | 2 | no | — |
| 59 | C2×#11765864 | — | 4 | 1 | no | — |
| 60 | C2×#11765864 | C23 | 1 | 1 | yes | characteristic |
| 61 | #41×D71 | — | 2 | 1 | no | — |
| 62 | #41×D71 | — | 4 | 1 | no | — |
| 63 | C22×C4×D71 | D4 | 1 | 2 | yes | complemented |
| 64 | #14556160 | — | 4 | 1 | no | — |
| 65 | #14556159 | — | 2 | 1 | no | — |
| 66 | #14556156 | — | 2 | 1 | no | — |
| 67 | #14556155 | — | 4 | 1 | no | — |
| 68 | #14556153 | — | 2 | 1 | no | — |
| 69 | #14556151 | — | 4 | 1 | no | — |
| 70 | #14556149 | — | 4 | 1 | no | — |
| 71 | M16×D71 | — | 2 | 1 | no | — |
| 72 | #14556126 | D4 | 1 | 1 | yes | characteristic, complemented |
| 73 | #14556125 | — | 2 | 1 | no | — |
| 74 | #14556124 | C23 | 1 | 1 | yes | characteristic |
| 75 | #14556123 | — | 2 | 2 | no | — |
| 76 | #14556122 | — | 2 | 2 | no | — |
| 77 | #14556118 | — | 2 | 2 | no | — |
| 78 | #14556117 | — | 2 | 1 | no | — |
| 79 | #14556117 | — | 2 | 1 | no | — |
| 80 | #14556116 | — | 2 | 1 | no | — |
| 81 | #14556116 | D4 | 1 | 1 | yes | characteristic, complemented |
| 82 | #14556114 | — | 2 | 2 | no | — |
| 83 | #14556113 | — | 2 | 2 | no | — |
| 84 | #14556113 | — | 2 | 2 | no | — |
| 85 | #14556113 | — | 2 | 2 | no | — |
| 86 | #14556113 | — | 2 | 2 | no | — |
| 87 | #14556111 | — | 2 | 2 | no | — |
| 88 | #14556111 | D4 | 1 | 2 | yes | complemented |
| 89 | #14556110 | — | 2 | 2 | no | — |
| 90 | #14556108 | — | 2 | 1 | no | — |
| 91 | #14556106 | — | 2 | 2 | no | — |
| 92 | #14556106 | — | 2 | 2 | no | — |
| 93 | #14556106 | — | 4 | 2 | no | — |
| 94 | #14556104 | — | 2 | 2 | no | — |
| 95 | #14556103 | — | 2 | 1 | no | — |
| 96 | #14556103 | — | 2 | 2 | no | — |
| 97 | #14556103 | — | 2 | 2 | no | — |
| 98 | #14556103 | — | 2 | 2 | no | — |
| 99 | #14556102 | — | 2 | 2 | no | — |
| 100 | #14556101 | — | 2 | 2 | no | — |
| 101 | #14556101 | — | 2 | 2 | no | — |
| 102 | #14556101 | — | 2 | 2 | no | — |
| 103 | #14556101 | — | 4 | 2 | no | — |
| 104 | #14556098 | — | 2 | 2 | no | — |
| 105 | #14556098 | — | 2 | 2 | no | — |
| 106 | #14556098 | — | 2 | 2 | no | — |
| 107 | #14556098 | D4 | 1 | 2 | yes | complemented |
| 108 | #14556096 | — | 2 | 2 | no | — |
| 109 | #14556096 | C23 | 1 | 2 | yes | — |
| 110 | #14556093 | — | 2 | 1 | no | — |
| 111 | #14556090 | — | 2 | 1 | no | — |
| 112 | #14556090 | — | 2 | 2 | no | — |
| 113 | #14556090 | — | 2 | 2 | no | — |
| 114 | #14556090 | — | 4 | 2 | no | — |
| 115 | (C22⋊D71)⋊C4 | — | 2 | 2 | no | — |
| 116 | (C22⋊D71)⋊C4 | — | 2 | 2 | no | — |
| 117 | (C22⋊D71)⋊C4 | — | 4 | 2 | no | — |
| 118 | #14556086 | — | 2 | 2 | no | — |
| 119 | #14556084 | — | 2 | 2 | no | — |
| 120 | #14556084 | D4 | 1 | 2 | yes | complemented |
| 121 | C42×D71 | — | 2 | 1 | no | — |
| 122 | C42×D71 | D4 | 1 | 1 | yes | characteristic, complemented |
| 123 | #14556056 | — | 2 | 1 | no | — |
| 124 | #14556055 | — | 2 | 1 | no | — |
| 125 | #14556054 | — | 2 | 1 | no | — |
| 126 | #14556046 | — | 2 | 1 | no | — |
| 127 | #14556045 | C23 | 1 | 1 | yes | characteristic |
| 128 | #14556043 | — | 2 | 2 | no | — |
| 129 | #14556043 | C23 | 1 | 2 | yes | — |
| 130 | #14556042 | — | 2 | 2 | no | — |
| 131 | #14556042 | — | 2 | 2 | no | — |
| 132 | #14556042 | — | 2 | 2 | no | — |
| 133 | H(5,𝔽2)×C71 | C23 | 1 | 1 | yes | characteristic |
| 134 | #137×C71 | — | 2 | 1 | no | — |
| 135 | C4⋊Q8×C71 | — | 2 | 1 | no | — |
| 136 | #126×C71 | — | 2 | 2 | no | — |
| 137 | #125×C71 | — | 2 | 1 | no | — |
| 138 | #124×C71 | C23 | 1 | 1 | yes | characteristic |
| 139 | #123×C71 | — | 2 | 2 | no | — |
| 140 | #123×C71 | C23 | 1 | 2 | yes | — |
| 141 | C22⋊Q8×C71 | — | 2 | 2 | no | — |
| 142 | #104×C71 | — | 2 | 1 | no | — |
| 143 | #100×C71 | C23 | 1 | 1 | yes | characteristic |
| 144 | #99×C71 | — | 2 | 2 | no | — |
| 145 | #99×C71 | C23 | 1 | 2 | yes | — |
| 146 | C23×D71 | C2×D4 | 1 | 2 | yes | — |
| 147 | #11765866 | — | 2 | 1 | no | — |
| 148 | #11765866 | — | 4 | 1 | no | — |
| 149 | #11765866 | — | 4 | 1 | no | — |
| 150 | #11765866 | — | 8 | 1 | no | — |
| 151 | #11765866 | — | 8 | 1 | no | — |
| 152 | #11765865 | — | 2 | 1 | no | — |
| 153 | #11765865 | — | 4 | 1 | no | — |
| 154 | #11765865 | — | 4 | 1 | no | — |
| 155 | #11765865 | — | 4 | 2 | no | — |
| 156 | #11765864 | — | 2 | 1 | no | — |
| 157 | #11765864 | — | 4 | 1 | no | — |
| 158 | #11765864 | — | 4 | 1 | no | — |
| 159 | #11765864 | — | 4 | 1 | no | — |
| 160 | #11765864 | — | 4 | 2 | no | — |
| 161 | #11765864 | — | 4 | 2 | no | — |
| 162 | #11765864 | — | 4 | 2 | no | — |
| 163 | #11765864 | — | 4 | 1 | no | — |
| 164 | #11765864 | — | 4 | 1 | no | — |
| 165 | #11765864 | — | 4 | 2 | no | — |
| 166 | C2×Dic142 | — | 2 | 2 | no | — |
| 167 | C2×Dic142 | — | 2 | 1 | no | — |
| 168 | C2×Dic142 | — | 4 | 1 | no | — |
| 169 | C2×Dic142 | C2×D4 | 1 | 1 | yes | characteristic |
| 170 | Q8×D71 | — | 2 | 1 | no | — |
| 171 | Q8×D71 | — | 4 | 1 | no | — |
| 172 | C2×D284 | — | 2 | 1 | no | — |
| 173 | C2×D284 | — | 2 | 2 | no | — |
| 174 | C2×D284 | — | 2 | 1 | no | — |
| 175 | C2×D284 | — | 2 | 2 | no | — |
| 176 | C2×D284 | — | 2 | 1 | no | — |
| 177 | C2×D284 | — | 2 | 2 | no | — |
| 178 | C2×D284 | — | 4 | 2 | no | — |
| 179 | C2×D284 | C2×D4 | 1 | 1 | yes | characteristic |
| 180 | C2×C22⋊D71 | — | 2 | 2 | no | — |
| 181 | C2×C22⋊D71 | — | 2 | 2 | no | — |
| 182 | C2×C22⋊D71 | — | 2 | 2 | no | — |
| 183 | C2×C22⋊D71 | — | 2 | 2 | no | — |
| 184 | C2×C22⋊D71 | — | 4 | 2 | no | — |
| 185 | C2×C22⋊D71 | — | 4 | 2 | no | — |
| 186 | C2×C22⋊D71 | C2×D4 | 1 | 2 | yes | — |
| 187 | D4×D71 | — | 2 | 1 | no | — |
| 188 | D4×D71 | — | 4 | 1 | no | — |
| 189 | D4×D71 | — | 4 | 2 | no | — |
| 190 | D4×D71 | — | 4 | 1 | no | — |
| 191 | C22×Dic71 | — | 2 | 2 | no | — |
| 192 | C22×Dic71 | C2×D4 | 1 | 2 | yes | — |
| 193 | C2×C4×D71 | — | 2 | 2 | no | — |
| 194 | C2×C4×D71 | — | 2 | 2 | no | — |
| 195 | C2×C4×D71 | — | 2 | 1 | no | — |
| 196 | C2×C4×D71 | — | 2 | 2 | no | — |
| 197 | C2×C4×D71 | — | 2 | 1 | no | — |
| 198 | C2×C4×D71 | — | 2 | 2 | no | — |
| 199 | C2×C4×D71 | — | 4 | 1 | no | — |
| 200 | C2×C4×D71 | — | 4 | 2 | no | — |
| 201 | C2×C4×D71 | — | 4 | 2 | no | — |
| 202 | C2×C4×D71 | C2×D4 | 1 | 1 | yes | characteristic |
| 203 | #11765855 | — | 4 | 1 | no | — |
| 204 | #11765854 | — | 4 | 1 | no | — |
| 205 | #11765852 | — | 4 | 1 | no | — |
| 206 | #11765852 | — | 4 | 1 | no | — |
| 207 | D568 | — | 4 | 1 | no | — |
| 208 | #11765850 | — | 4 | 1 | no | — |
| 209 | #11765849 | — | 2 | 1 | no | — |
| 210 | #11765848 | — | 4 | 1 | no | — |
| 211 | C8×D71 | — | 4 | 1 | no | — |
| 212 | C4⋊Dic71 | — | 2 | 2 | no | — |
| 213 | Dic71⋊C4 | — | 2 | 2 | no | — |
| 214 | Dic71⋊C4 | — | 2 | 2 | no | — |
| 215 | Dic71⋊C4 | — | 2 | 2 | no | — |
| 216 | Dic71⋊C4 | — | 2 | 2 | no | — |
| 217 | Dic71⋊C4 | — | 4 | 2 | no | — |
| 218 | Dic71⋊C4 | — | 4 | 2 | no | — |
| 219 | C22⋊Dic71 | — | 2 | 2 | no | — |
| 220 | C22⋊Dic71 | C2×D4 | 1 | 2 | yes | — |
| 221 | (C2×D71)⋊C4 | — | 2 | 2 | no | — |
| 222 | (C2×D71)⋊C4 | — | 2 | 2 | no | — |
| 223 | (C2×D71)⋊C4 | — | 2 | 2 | no | — |
| 224 | (C2×D71)⋊C4 | — | 2 | 2 | no | — |
| 225 | (C2×D71)⋊C4 | — | 2 | 2 | no | — |
| 226 | (C2×D71)⋊C4 | — | 2 | 2 | no | — |
| 227 | (C2×D71)⋊C4 | — | 2 | 2 | no | — |
| 228 | (C2×D71)⋊C4 | — | 2 | 2 | no | — |
| 229 | (C2×D71)⋊C4 | — | 2 | 2 | no | — |
| 230 | (C2×D71)⋊C4 | — | 4 | 2 | no | — |
| 231 | (C2×D71)⋊C4 | — | 4 | 2 | no | — |
| 232 | (C2×D71)⋊C4 | — | 4 | 2 | no | — |
| 233 | C4×Dic71 | — | 2 | 1 | no | — |
| 234 | C4×Dic71 | — | 2 | 2 | no | — |
| 235 | C4×Dic71 | — | 2 | 1 | no | — |
| 236 | C4×Dic71 | — | 4 | 2 | no | — |
| 237 | C4×Dic71 | C2×D4 | 1 | 1 | yes | characteristic |
| 238 | #41×C71 | — | 2 | 1 | no | — |
| 239 | #41×C71 | — | 4 | 1 | no | — |
| 240 | C2×Q8×C71 | — | 2 | 1 | no | — |
| 241 | C2×Q8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 242 | C2×D4×C71 | — | 2 | 2 | no | — |
| 243 | C2×D4×C71 | — | 4 | 1 | no | — |
| 244 | C2×D4×C71 | C24 | 1 | 1 | yes | characteristic |
| 245 | C22×C4×C71 | C2×D4 | 1 | 2 | yes | — |
| 246 | Q16×C71 | — | 4 | 1 | no | — |
| 247 | SD16×C71 | — | 4 | 1 | no | — |
| 248 | M16×C71 | — | 2 | 1 | no | — |
| 249 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 250 | C4⋊C4×C71 | — | 2 | 2 | no | — |
| 251 | C4⋊C4×C71 | — | 2 | 2 | no | — |
| 252 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 253 | C4⋊C4×C71 | — | 2 | 2 | no | — |
| 254 | C4⋊C4×C71 | — | 4 | 2 | no | — |
| 255 | C22⋊C4×C71 | — | 2 | 2 | no | — |
| 256 | C22⋊C4×C71 | — | 2 | 2 | no | — |
| 257 | C22⋊C4×C71 | — | 2 | 2 | no | — |
| 258 | C22⋊C4×C71 | — | 4 | 2 | no | — |
| 259 | C22⋊C4×C71 | C2×D4 | 1 | 2 | yes | — |
| 260 | C42×C71 | — | 2 | 1 | no | — |
| 261 | C42×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 262 | C23×C71 | — | 2 | 2 | no | — |
| 263 | C23×C71 | C22×D4 | 1 | 2 | yes | — |
| 264 | C22×D71 | — | 2 | 2 | no | — |
| 265 | C22×D71 | — | 2 | 1 | no | — |
| 266 | C22×D71 | — | 2 | 2 | no | — |
| 267 | C22×D71 | — | 4 | 1 | no | — |
| 268 | C22×D71 | — | 4 | 2 | no | — |
| 269 | C22×D71 | — | 8 | 2 | no | — |
| 270 | C22×D71 | #120 | 1 | 1 | yes | characteristic |
| 271 | Q8×C71 | — | 2 | 1 | no | — |
| 272 | Q8×C71 | — | 4 | 1 | no | — |
| 273 | Q8×C71 | — | 8 | 1 | no | — |
| 274 | D4×C71 | — | 2 | 1 | no | — |
| 275 | D4×C71 | — | 4 | 1 | no | — |
| 276 | D4×C71 | — | 4 | 2 | no | — |
| 277 | D4×C71 | — | 4 | 1 | no | — |
| 278 | C2×C4×C71 | — | 2 | 2 | no | — |
| 279 | C2×C4×C71 | — | 2 | 1 | no | — |
| 280 | C2×C4×C71 | — | 2 | 2 | no | — |
| 281 | C2×C4×C71 | — | 2 | 1 | no | — |
| 282 | C2×C4×C71 | — | 2 | 2 | no | — |
| 283 | C2×C4×C71 | — | 4 | 1 | no | — |
| 284 | C2×C4×C71 | — | 4 | 2 | no | — |
| 285 | C2×C4×C71 | — | 4 | 2 | no | — |
| 286 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 287 | C22⋊D71 | — | 4 | 2 | no | — |
| 288 | C22⋊D71 | — | 4 | 2 | no | — |
| 289 | C22⋊D71 | — | 4 | 1 | no | — |
| 290 | C22⋊D71 | — | 4 | 2 | no | — |
| 291 | C22⋊D71 | — | 4 | 1 | no | — |
| 292 | C22⋊D71 | — | 4 | 1 | no | — |
| 293 | C22⋊D71 | — | 8 | 2 | no | — |
| 294 | C22⋊D71 | — | 8 | 2 | no | — |
| 295 | C22⋊D71 | — | 8 | 4 | no | — |
| 296 | C2×Dic71 | — | 2 | 2 | no | — |
| 297 | C2×Dic71 | — | 2 | 2 | no | — |
| 298 | C2×Dic71 | — | 2 | 2 | no | — |
| 299 | C2×Dic71 | — | 2 | 2 | no | — |
| 300 | C2×Dic71 | — | 2 | 1 | no | — |
| 301 | C2×Dic71 | — | 4 | 2 | no | — |
| 302 | C2×Dic71 | — | 4 | 1 | no | — |
| 303 | C2×Dic71 | — | 4 | 2 | no | — |
| 304 | C2×Dic71 | #120 | 1 | 2 | yes | — |
| 305 | C2×Dic71 | #120 | 1 | 1 | yes | characteristic |
| 306 | D284 | — | 2 | 1 | no | — |
| 307 | D284 | — | 4 | 1 | no | — |
| 308 | D284 | — | 4 | 1 | no | — |
| 309 | D284 | — | 8 | 1 | no | — |
| 310 | D284 | — | 8 | 1 | no | — |
| 311 | D284 | — | 8 | 2 | no | — |
| 312 | D284 | — | 8 | 2 | no | — |
| 313 | D284 | — | 8 | 2 | no | — |
| 314 | D284 | — | 8 | 1 | no | — |
| 315 | D284 | — | 8 | 4 | no | — |
| 316 | C4×D71 | — | 2 | 1 | no | — |
| 317 | C4×D71 | — | 2 | 1 | no | — |
| 318 | C4×D71 | — | 4 | 2 | no | — |
| 319 | C4×D71 | — | 4 | 1 | no | — |
| 320 | C4×D71 | — | 4 | 1 | no | — |
| 321 | C4×D71 | — | 4 | 1 | no | — |
| 322 | C4×D71 | — | 4 | 2 | no | — |
| 323 | C4×D71 | — | 4 | 2 | no | — |
| 324 | C4×D71 | — | 4 | 1 | no | — |
| 325 | C4×D71 | — | 4 | 1 | no | — |
| 326 | C4×D71 | — | 8 | 2 | no | — |
| 327 | C4×D71 | — | 8 | 2 | no | — |
| 328 | C4×D71 | — | 8 | 1 | no | — |
| 329 | Dic142 | — | 2 | 1 | no | — |
| 330 | Dic142 | — | 4 | 1 | no | — |
| 331 | Dic142 | — | 4 | 2 | no | — |
| 332 | Dic142 | — | 4 | 1 | no | — |
| 333 | Dic142 | — | 8 | 1 | no | — |
| 334 | C8×C71 | — | 4 | 1 | no | — |
| 335 | C71⋊C8 | — | 4 | 1 | no | — |
| 336 | C22×C71 | — | 2 | 2 | no | — |
| 337 | C22×C71 | — | 4 | 2 | no | — |
| 338 | C22×C71 | — | 4 | 1 | no | — |
| 339 | C22×C71 | — | 8 | 2 | no | — |
| 340 | C22×C71 | C2×#120 | 1 | 1 | yes | characteristic |
| 341 | C2×D71 | — | 2 | 1 | no | — |
| 342 | C2×D71 | — | 4 | 1 | no | — |
| 343 | C2×D71 | — | 4 | 2 | no | — |
| 344 | C2×D71 | — | 4 | 2 | no | — |
| 345 | C2×D71 | — | 4 | 2 | no | — |
| 346 | C2×D71 | — | 4 | 4 | no | — |
| 347 | C2×D71 | — | 4 | 1 | no | — |
| 348 | C2×D71 | — | 4 | 2 | no | — |
| 349 | C2×D71 | — | 4 | 1 | no | — |
| 350 | C2×D71 | — | 8 | 2 | no | — |
| 351 | C2×D71 | — | 8 | 2 | no | — |
| 352 | C2×D71 | — | 16 | 1 | no | — |
| 353 | C4×C71 | — | 2 | 1 | no | — |
| 354 | C4×C71 | — | 4 | 1 | no | — |
| 355 | C4×C71 | — | 4 | 2 | no | — |
| 356 | C4×C71 | — | 4 | 1 | no | — |
| 357 | C4×C71 | — | 4 | 2 | no | — |
| 358 | C4×C71 | — | 4 | 1 | no | — |
| 359 | C4×C71 | — | 8 | 2 | no | — |
| 360 | Dic71 | — | 2 | 2 | no | — |
| 361 | Dic71 | — | 4 | 2 | no | — |
| 362 | Dic71 | — | 4 | 1 | no | — |
| 363 | Dic71 | — | 4 | 1 | no | — |
| 364 | Dic71 | — | 8 | 2 | no | — |
| 365 | Dic71 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 366 | Dic71 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 367 | #33550 | — | 71 | 1 | no | maximal, Sylow |
| 368 | C2×C71 | — | 2 | 1 | no | — |
| 369 | C2×C71 | — | 4 | 2 | no | — |
| 370 | C2×C71 | — | 8 | 1 | no | — |
| 371 | C2×C71 | C2×B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 372 | D71 | — | 4 | 1 | no | — |
| 373 | D71 | — | 8 | 1 | no | — |
| 374 | D71 | — | 8 | 2 | no | — |
| 375 | D71 | — | 8 | 1 | no | — |
| 376 | #3529 | — | 71 | 1 | no | — |
| 377 | #3025 | — | 71 | 2 | no | — |
| 378 | #3018 | — | 71 | 1 | no | — |
| 379 | #2201 | — | 71 | 1 | no | — |
| 380 | #2201 | D71 | 1 | 1 | yes | characteristic, complemented |
| 381 | #2200 | — | 71 | 2 | no | — |
| 382 | #2200 | — | 71 | 2 | no | — |
| 383 | #2199 | — | 71 | 1 | no | — |
| 384 | #2199 | — | 71 | 1 | no | — |
| 385 | #2126 | — | 71 | 1 | no | — |
| 386 | #2120 | — | 71 | 2 | no | — |
| 387 | C71 | #33550 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 388 | #585 | — | 71 | 1 | no | — |
| 389 | #575 | — | 142 | 1 | no | — |
| 390 | #563 | — | 142 | 1 | no | — |
| 391 | #563 | C2×D71 | 1 | 1 | yes | characteristic, complemented |
| 392 | #562 | — | 142 | 2 | no | — |
| 393 | #562 | — | 142 | 1 | no | — |
| 394 | H(3,𝔽4) | — | 71 | 1 | no | — |
| 395 | #560 | — | 71 | 2 | no | — |
| 396 | #560 | — | 142 | 2 | no | — |
| 397 | #532 | — | 71 | 1 | no | — |
| 398 | #532 | — | 142 | 1 | no | — |
| 399 | #529 | — | 142 | 1 | no | — |
| 400 | #529 | — | 142 | 2 | no | — |
| 401 | #525 | — | 71 | 2 | no | — |
| 402 | #525 | — | 142 | 2 | no | — |
| 403 | #525 | — | 142 | 2 | no | — |
| 404 | #458 | — | 71 | 2 | no | — |
| 405 | #458 | — | 142 | 2 | no | — |
| 406 | #458 | C2×D71 | 1 | 2 | yes | — |
| 407 | B(4,𝔽2) | — | 71 | 2 | no | — |
| 408 | B(4,𝔽2) | — | 71 | 2 | no | — |
| 409 | B(4,𝔽2) | — | 142 | 2 | no | — |
| 410 | #456 | — | 142 | 1 | no | — |
| 411 | #455 | — | 71 | 1 | no | — |
| 412 | #455 | C2×D71 | 1 | 1 | yes | characteristic |
| 413 | #454 | — | 142 | 1 | no | — |
| 414 | #453 | — | 71 | 1 | no | — |
| 415 | #453 | — | 71 | 1 | no | — |
| 416 | C2×#104 | — | 142 | 1 | no | — |
| 417 | #413 | — | 71 | 1 | no | — |
| 418 | #410 | — | 71 | 2 | no | — |
| 419 | #410 | — | 142 | 2 | no | — |
| 420 | #354 | — | 71 | 1 | no | — |
| 421 | #354 | C2×D71 | 1 | 1 | yes | characteristic, complemented |
| 422 | #353 | — | 71 | 2 | no | — |
| 423 | #352 | — | 71 | 2 | no | — |
| 424 | #352 | C2×D71 | 1 | 2 | yes | complemented |
| 425 | AΣL(1,𝔽16) | — | 71 | 2 | no | — |
| 426 | AΣL(1,𝔽16) | — | 71 | 2 | no | — |
| 427 | 2−1+4 | — | 284 | 1 | no | — |
| 428 | 2−1+4 | — | 142 | 1 | no | — |
| 429 | H(5,𝔽2) | — | 284 | 1 | no | — |
| 430 | H(5,𝔽2) | — | 71 | 1 | no | — |
| 431 | H(5,𝔽2) | — | 142 | 2 | no | — |
| 432 | H(5,𝔽2) | C22×D71 | 1 | 1 | yes | characteristic |
| 433 | C2×#41 | — | 284 | 1 | no | — |
| 434 | C2×#41 | — | 284 | 1 | no | — |
| 435 | C2×#41 | — | 71 | 1 | no | — |
| 436 | C2×#41 | — | 71 | 1 | no | — |
| 437 | C2×#41 | — | 142 | 1 | no | — |
| 438 | C2×#41 | — | 142 | 2 | no | — |
| 439 | C2×#41 | — | 142 | 1 | no | — |
| 440 | C23×C4 | — | 71 | 2 | no | — |
| 441 | #137 | — | 2 | 1 | no | — |
| 442 | #137 | — | 284 | 1 | no | — |
| 443 | #137 | — | 142 | 1 | no | — |
| 444 | AGL(1,ℤ/8) | — | 284 | 1 | no | — |
| 445 | AGL(1,ℤ/8) | — | 142 | 1 | no | — |
| 446 | AGL(1,ℤ/8) | — | 142 | 1 | no | — |
| 447 | #135 | — | 284 | 1 | no | — |
| 448 | #135 | — | 284 | 1 | no | — |
| 449 | C2×M16 | — | 142 | 1 | no | — |
| 450 | C4⋊Q8 | — | 2 | 1 | no | — |
| 451 | C4⋊Q8 | — | 71 | 1 | no | — |
| 452 | #127 | — | 71 | 1 | no | — |
| 453 | #127 | — | 142 | 1 | no | — |
| 454 | #126 | — | 2 | 2 | no | — |
| 455 | #126 | — | 142 | 2 | no | — |
| 456 | #126 | — | 142 | 2 | no | — |
| 457 | #125 | — | 2 | 1 | no | — |
| 458 | #125 | — | 142 | 2 | no | — |
| 459 | #124 | — | 71 | 1 | no | — |
| 460 | #124 | — | 142 | 2 | no | — |
| 461 | #124 | — | 142 | 1 | no | — |
| 462 | #124 | — | 142 | 1 | no | — |
| 463 | #124 | — | 142 | 1 | no | — |
| 464 | #124 | C22×D71 | 1 | 1 | yes | characteristic |
| 465 | #123 | — | 2 | 2 | no | — |
| 466 | #123 | — | 71 | 2 | no | — |
| 467 | #123 | — | 142 | 2 | no | — |
| 468 | #123 | — | 142 | 2 | no | — |
| 469 | #123 | — | 142 | 2 | no | — |
| 470 | #123 | — | 142 | 2 | no | — |
| 471 | #123 | — | 142 | 2 | no | — |
| 472 | #123 | — | 142 | 2 | no | — |
| 473 | #123 | C22×D71 | 1 | 2 | yes | — |
| 474 | C22⋊Q8 | — | 2 | 2 | no | — |
| 475 | C22⋊Q8 | — | 284 | 2 | no | — |
| 476 | C22⋊Q8 | — | 142 | 2 | no | — |
| 477 | C22⋊Q8 | — | 142 | 2 | no | — |
| 478 | C22⋊Q8 | — | 142 | 1 | no | — |
| 479 | C22⋊Q8 | — | 142 | 2 | no | — |
| 480 | #121 | — | 284 | 2 | no | — |
| 481 | #121 | — | 142 | 2 | no | — |
| 482 | #121 | — | 142 | 2 | no | — |
| 483 | #121 | — | 142 | 2 | no | — |
| 484 | #121 | — | 142 | 2 | no | — |
| 485 | #121 | — | 142 | 1 | no | — |
| 486 | #121 | — | 142 | 2 | no | — |
| 487 | #121 | — | 142 | 2 | no | — |
| 488 | #121 | — | 142 | 2 | no | — |
| 489 | #120 | — | 71 | 2 | no | — |
| 490 | #120 | — | 71 | 2 | no | — |
| 491 | #120 | — | 142 | 2 | no | — |
| 492 | #120 | — | 142 | 2 | no | — |
| 493 | #120 | — | 142 | 2 | no | — |
| 494 | #120 | — | 142 | 2 | no | — |
| 495 | C4×Q8 | — | 142 | 1 | no | — |
| 496 | C4×D4 | — | 284 | 2 | no | — |
| 497 | C4×D4 | — | 284 | 2 | no | — |
| 498 | C4×D4 | — | 142 | 2 | no | — |
| 499 | C4×D4 | — | 142 | 2 | no | — |
| 500 | C4×D4 | — | 142 | 2 | no | — |
| 501 | C4×D4 | — | 142 | 1 | no | — |
| 502 | C4×D4 | — | 142 | 2 | no | — |
| 503 | #117 | — | 71 | 2 | no | — |
| 504 | #117 | — | 142 | 2 | no | — |
| 505 | #117 | — | 142 | 2 | no | — |
| 506 | C2×C42 | — | 71 | 1 | no | — |
| 507 | C2×C42 | — | 142 | 1 | no | — |
| 508 | #104 | — | 2 | 1 | no | — |
| 509 | #104 | — | 142 | 1 | no | — |
| 510 | #104 | — | 142 | 1 | no | — |
| 511 | #104 | — | 142 | 1 | no | — |
| 512 | #101 | — | 142 | 1 | no | — |
| 513 | #100 | — | 71 | 1 | no | — |
| 514 | #100 | C22×D71 | 1 | 1 | yes | characteristic |
| 515 | #99 | — | 2 | 2 | no | — |
| 516 | #99 | — | 71 | 2 | no | — |
| 517 | #99 | — | 142 | 2 | no | — |
| 518 | #99 | — | 142 | 2 | no | — |
| 519 | #99 | — | 142 | 2 | no | — |
| 520 | #99 | — | 142 | 2 | no | — |
| 521 | #99 | C22×D71 | 1 | 2 | yes | — |
| 522 | C24 | — | 71 | 2 | no | — |
| 523 | #41 | — | 2 | 1 | no | — |
| 524 | #41 | — | 4 | 1 | no | — |
| 525 | #41 | — | 284 | 2 | no | — |
| 526 | #41 | — | 284 | 1 | no | — |
| 527 | #41 | — | 284 | 1 | no | — |
| 528 | #41 | — | 284 | 1 | no | — |
| 529 | #41 | — | 284 | 1 | no | — |
| 530 | #41 | — | 284 | 2 | no | — |
| 531 | #41 | — | 284 | 2 | no | — |
| 532 | #41 | — | 284 | 2 | no | — |
| 533 | #41 | — | 284 | 2 | no | — |
| 534 | #41 | — | 284 | 1 | no | — |
| 535 | #41 | — | 284 | 1 | no | — |
| 536 | #41 | — | 284 | 1 | no | — |
| 537 | #41 | — | 284 | 1 | no | — |
| 538 | #41 | — | 284 | 1 | no | — |
| 539 | #41 | — | 568 | 1 | no | — |
| 540 | #41 | — | 568 | 1 | no | — |
| 541 | #41 | — | 142 | 1 | no | — |
| 542 | #41 | — | 142 | 1 | no | — |
| 543 | #41 | — | 142 | 1 | no | — |
| 544 | C2×Q8 | — | 2 | 1 | no | — |
| 545 | C2×Q8 | — | 284 | 1 | no | — |
| 546 | C2×Q8 | — | 284 | 1 | no | — |
| 547 | C2×Q8 | — | 71 | 1 | no | — |
| 548 | C2×Q8 | — | 142 | 2 | no | — |
| 549 | C2×Q8 | — | 142 | 1 | no | — |
| 550 | C2×Q8 | — | 142 | 1 | no | — |
| 551 | C2×Q8 | D4×D71 | 1 | 1 | yes | characteristic |
| 552 | C2×D4 | — | 2 | 2 | no | — |
| 553 | C2×D4 | — | 4 | 1 | no | — |
| 554 | C2×D4 | — | 284 | 2 | no | — |
| 555 | C2×D4 | — | 284 | 1 | no | — |
| 556 | C2×D4 | — | 284 | 2 | no | — |
| 557 | C2×D4 | — | 284 | 1 | no | — |
| 558 | C2×D4 | — | 284 | 2 | no | — |
| 559 | C2×D4 | — | 284 | 2 | no | — |
| 560 | C2×D4 | — | 71 | 2 | no | — |
| 561 | C2×D4 | — | 71 | 1 | no | — |
| 562 | C2×D4 | — | 142 | 2 | no | — |
| 563 | C2×D4 | — | 142 | 1 | no | — |
| 564 | C2×D4 | — | 142 | 1 | no | — |
| 565 | C2×D4 | — | 142 | 2 | no | — |
| 566 | C2×D4 | — | 142 | 1 | no | — |
| 567 | C2×D4 | — | 142 | 2 | no | — |
| 568 | C2×D4 | — | 142 | 1 | no | — |
| 569 | C2×D4 | — | 142 | 2 | no | — |
| 570 | C2×D4 | — | 142 | 2 | no | — |
| 571 | C2×D4 | — | 142 | 2 | no | — |
| 572 | C2×D4 | — | 142 | 2 | no | — |
| 573 | C2×D4 | C23×D71 | 1 | 1 | yes | characteristic |
| 574 | C22×C4 | — | 284 | 1 | no | — |
| 575 | C22×C4 | — | 284 | 2 | no | — |
| 576 | C22×C4 | — | 284 | 2 | no | — |
| 577 | C22×C4 | — | 71 | 2 | no | — |
| 578 | C22×C4 | — | 71 | 1 | no | — |
| 579 | C22×C4 | — | 142 | 1 | no | — |
| 580 | C22×C4 | — | 142 | 2 | no | — |
| 581 | C22×C4 | — | 142 | 2 | no | — |
| 582 | C22×C4 | — | 142 | 2 | no | — |
| 583 | C22×C4 | — | 142 | 1 | no | — |
| 584 | C22×C4 | — | 142 | 2 | no | — |
| 585 | C22×C4 | — | 142 | 2 | no | — |
| 586 | C22×C4 | D4×D71 | 1 | 2 | yes | — |
| 587 | Q16 | — | 4 | 1 | no | — |
| 588 | Q16 | — | 284 | 1 | no | — |
| 589 | SD16 | — | 4 | 1 | no | — |
| 590 | SD16 | — | 284 | 1 | no | — |
| 591 | SD16 | — | 284 | 1 | no | — |
| 592 | SD16 | — | 284 | 1 | no | — |
| 593 | D8 | — | 284 | 1 | no | — |
| 594 | D8 | — | 284 | 1 | no | — |
| 595 | M16 | — | 2 | 1 | no | — |
| 596 | M16 | — | 284 | 1 | no | — |
| 597 | M16 | — | 142 | 1 | no | — |
| 598 | C2×C8 | — | 284 | 1 | no | — |
| 599 | C4⋊C4 | — | 2 | 2 | no | — |
| 600 | C4⋊C4 | — | 2 | 2 | no | — |
| 601 | C4⋊C4 | — | 2 | 1 | no | — |
| 602 | C4⋊C4 | — | 2 | 1 | no | — |
| 603 | C4⋊C4 | — | 2 | 2 | no | — |
| 604 | C4⋊C4 | — | 4 | 2 | no | — |
| 605 | C4⋊C4 | — | 284 | 2 | no | — |
| 606 | C4⋊C4 | — | 284 | 2 | no | — |
| 607 | C4⋊C4 | — | 142 | 2 | no | — |
| 608 | C4⋊C4 | — | 142 | 2 | no | — |
| 609 | C4⋊C4 | — | 142 | 2 | no | — |
| 610 | C4⋊C4 | — | 142 | 2 | no | — |
| 611 | C4⋊C4 | — | 142 | 2 | no | — |
| 612 | C22⋊C4 | — | 2 | 2 | no | — |
| 613 | C22⋊C4 | — | 2 | 2 | no | — |
| 614 | C22⋊C4 | — | 2 | 2 | no | — |
| 615 | C22⋊C4 | — | 4 | 2 | no | — |
| 616 | C22⋊C4 | — | 284 | 2 | no | — |
| 617 | C22⋊C4 | — | 284 | 2 | no | — |
| 618 | C22⋊C4 | — | 284 | 2 | no | — |
| 619 | C22⋊C4 | — | 71 | 2 | no | — |
| 620 | C22⋊C4 | — | 142 | 2 | no | — |
| 621 | C22⋊C4 | — | 142 | 2 | no | — |
| 622 | C22⋊C4 | — | 142 | 2 | no | — |
| 623 | C22⋊C4 | — | 142 | 2 | no | — |
| 624 | C22⋊C4 | — | 142 | 2 | no | — |
| 625 | C22⋊C4 | — | 142 | 2 | no | — |
| 626 | C22⋊C4 | — | 142 | 2 | no | — |
| 627 | C22⋊C4 | — | 142 | 2 | no | — |
| 628 | C22⋊C4 | — | 142 | 2 | no | — |
| 629 | C22⋊C4 | — | 142 | 2 | no | — |
| 630 | C22⋊C4 | D4×D71 | 1 | 2 | yes | — |
| 631 | C42 | — | 2 | 1 | no | — |
| 632 | C42 | — | 284 | 2 | no | — |
| 633 | C42 | — | 71 | 1 | no | — |
| 634 | C42 | — | 142 | 1 | no | — |
| 635 | C42 | — | 142 | 2 | no | — |
| 636 | C42 | — | 142 | 1 | no | — |
| 637 | C42 | D4×D71 | 1 | 1 | yes | characteristic |
| 638 | C23 | — | 2 | 2 | no | — |
| 639 | C23 | — | 284 | 2 | no | — |
| 640 | C23 | — | 284 | 1 | no | — |
| 641 | C23 | — | 568 | 2 | no | — |
| 642 | C23 | — | 71 | 1 | no | — |
| 643 | C23 | — | 142 | 2 | no | — |
| 644 | C23 | — | 142 | 2 | no | — |
| 645 | C23 | — | 142 | 1 | no | — |
| 646 | C23 | C2×D4×D71 | 1 | 2 | yes | — |
| 647 | Q8 | — | 2 | 1 | no | — |
| 648 | Q8 | — | 4 | 1 | no | — |
| 649 | Q8 | — | 8 | 1 | no | — |
| 650 | Q8 | — | 284 | 1 | no | — |
| 651 | Q8 | — | 284 | 1 | no | — |
| 652 | Q8 | — | 284 | 2 | no | — |
| 653 | Q8 | — | 568 | 1 | no | — |
| 654 | Q8 | — | 142 | 1 | no | — |
| 655 | D4 | — | 2 | 1 | no | — |
| 656 | D4 | — | 4 | 1 | no | — |
| 657 | D4 | — | 4 | 2 | no | — |
| 658 | D4 | — | 4 | 1 | no | — |
| 659 | D4 | — | 284 | 1 | no | — |
| 660 | D4 | — | 284 | 1 | no | — |
| 661 | D4 | — | 284 | 2 | no | — |
| 662 | D4 | — | 284 | 1 | no | — |
| 663 | D4 | — | 284 | 1 | no | — |
| 664 | D4 | — | 284 | 1 | no | — |
| 665 | D4 | — | 284 | 2 | no | — |
| 666 | D4 | — | 284 | 2 | no | — |
| 667 | D4 | — | 568 | 2 | no | — |
| 668 | D4 | — | 568 | 1 | no | — |
| 669 | D4 | — | 568 | 2 | no | — |
| 670 | D4 | — | 568 | 2 | no | — |
| 671 | D4 | — | 568 | 1 | no | — |
| 672 | D4 | — | 568 | 1 | no | — |
| 673 | D4 | — | 568 | 4 | no | — |
| 674 | D4 | — | 568 | 2 | no | — |
| 675 | D4 | — | 568 | 2 | no | — |
| 676 | D4 | — | 568 | 4 | no | — |
| 677 | D4 | — | 142 | 1 | no | — |
| 678 | C2×C4 | — | 2 | 2 | no | — |
| 679 | C2×C4 | — | 2 | 1 | no | — |
| 680 | C2×C4 | — | 2 | 2 | no | — |
| 681 | C2×C4 | — | 2 | 1 | no | — |
| 682 | C2×C4 | — | 2 | 2 | no | — |
| 683 | C2×C4 | — | 4 | 1 | no | — |
| 684 | C2×C4 | — | 4 | 2 | no | — |
| 685 | C2×C4 | — | 4 | 2 | no | — |
| 686 | C2×C4 | — | 284 | 1 | no | — |
| 687 | C2×C4 | — | 284 | 1 | no | — |
| 688 | C2×C4 | — | 284 | 1 | no | — |
| 689 | C2×C4 | — | 284 | 2 | no | — |
| 690 | C2×C4 | — | 284 | 2 | no | — |
| 691 | C2×C4 | — | 284 | 1 | no | — |
| 692 | C2×C4 | — | 284 | 1 | no | — |
| 693 | C2×C4 | — | 284 | 2 | no | — |
| 694 | C2×C4 | — | 284 | 1 | no | — |
| 695 | C2×C4 | — | 284 | 2 | no | — |
| 696 | C2×C4 | — | 284 | 2 | no | — |
| 697 | C2×C4 | — | 568 | 2 | no | — |
| 698 | C2×C4 | — | 568 | 1 | no | — |
| 699 | C2×C4 | — | 568 | 2 | no | — |
| 700 | C2×C4 | — | 71 | 1 | no | — |
| 701 | C2×C4 | — | 71 | 2 | no | — |
| 702 | C2×C4 | — | 142 | 1 | no | — |
| 703 | C2×C4 | — | 142 | 1 | no | — |
| 704 | C2×C4 | — | 142 | 2 | no | — |
| 705 | C2×C4 | — | 142 | 1 | no | — |
| 706 | C2×C4 | — | 142 | 2 | no | — |
| 707 | C2×C4 | — | 142 | 2 | no | — |
| 708 | C2×C4 | — | 142 | 2 | no | — |
| 709 | C2×C4 | C2×D4×D71 | 1 | 1 | yes | characteristic |
| 710 | C8 | — | 4 | 1 | no | — |
| 711 | C8 | — | 284 | 1 | no | — |
| 712 | C22 | — | 2 | 2 | no | — |
| 713 | C22 | — | 4 | 2 | no | — |
| 714 | C22 | — | 4 | 1 | no | — |
| 715 | C22 | — | 8 | 2 | no | — |
| 716 | C22 | — | 284 | 1 | no | — |
| 717 | C22 | — | 284 | 2 | no | — |
| 718 | C22 | — | 284 | 2 | no | — |
| 719 | C22 | — | 284 | 2 | no | — |
| 720 | C22 | — | 284 | 4 | no | — |
| 721 | C22 | — | 284 | 1 | no | — |
| 722 | C22 | — | 284 | 2 | no | — |
| 723 | C22 | — | 284 | 1 | no | — |
| 724 | C22 | — | 568 | 2 | no | — |
| 725 | C22 | — | 568 | 2 | no | — |
| 726 | C22 | — | 1136 | 1 | no | — |
| 727 | C22 | — | 142 | 1 | no | — |
| 728 | C22 | #120×D71 | 1 | 1 | yes | characteristic |
| 729 | C4 | — | 2 | 1 | no | — |
| 730 | C4 | — | 4 | 2 | no | — |
| 731 | C4 | — | 4 | 1 | no | — |
| 732 | C4 | — | 4 | 1 | no | — |
| 733 | C4 | — | 4 | 2 | no | — |
| 734 | C4 | — | 4 | 1 | no | — |
| 735 | C4 | — | 8 | 2 | no | — |
| 736 | C4 | — | 284 | 1 | no | — |
| 737 | C4 | — | 284 | 2 | no | — |
| 738 | C4 | — | 284 | 1 | no | — |
| 739 | C4 | — | 568 | 2 | no | — |
| 740 | C4 | — | 71 | 1 | no | — |
| 741 | C4 | — | 71 | 1 | no | — |
| 742 | C4 | — | 142 | 2 | no | — |
| 743 | C2 | — | 2 | 1 | no | — |
| 744 | C2 | — | 4 | 2 | no | — |
| 745 | C2 | — | 8 | 1 | no | — |
| 746 | C2 | — | 284 | 1 | no | — |
| 747 | C2 | — | 568 | 2 | no | — |
| 748 | C2 | — | 568 | 1 | no | — |
| 749 | C2 | — | 568 | 1 | no | — |
| 750 | C2 | B(4,𝔽2)×D71 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22602481 | C2 | semidirect |
| 2. #22597733 | C2 | semidirect |
| 3. #22597690 | C2 | semidirect |
| 4. #22590353 | C2 | semidirect |
| 5. #22590348 | C2 | semidirect |
| 6. #22590344 | C2 | semidirect |
| 7. #22590343 | C2 | semidirect |
| 8. #22590340 | C2 | semidirect |
| 9. #22590004 | C2 | semidirect |
| 10. #22589980 | C2 | semidirect |
| 11. C71×#2201 | C2 | semidirect |
| 17. #17986741 | C22 | semidirect |
| 19. #17986739 | C22 | semidirect |
| 41. #17985794 | C22 | semidirect |
| 42. #17985791 | C22 | semidirect |
| 43. #17985789 | C22 | semidirect |
| 44. #17985787 | C22 | semidirect |
| 45. #17985785 | C22 | semidirect |
| 46. #563×C71 | C22 | semidirect |
| 49. #354×C71 | C22 | semidirect |
| 50. #352×C71 | C22 | semidirect |
| 57. C2×#11765866 | D4 | semidirect |
| 63. C22×C4×D71 | D4 | semidirect |
| 72. #14556126 | D4 | semidirect |
| 81. #14556116 | D4 | semidirect |
| 88. #14556111 | D4 | semidirect |
| 107. #14556098 | D4 | semidirect |
| 120. #14556084 | D4 | semidirect |
| 122. C42×D71 | D4 | semidirect |
| 380. #2201 | D71 | semidirect |
| 387. C71 | #33550 | semidirect |
| 391. #563 | C2×D71 | semidirect |
| 421. #354 | C2×D71 | semidirect |
| 424. #352 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22602481 | 2 |
| #22597733 | 2 |
| #22597690 | 2 |
| #22590353 | 2 |
| #22590348 | 2 |
| #22590344 | 2 |
| #22590343 | 2 |
| #22590340 | 2 |
| #22590004 | 2 |
| #22589980 | 2 |
| C71×#2201 | 2 |
| #33550 | 71 |