Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1654 conjugacy classes of subgroups.
The subgroup lattice has 730 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#19152156 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #26029504 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #26023567 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #26019202 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #26019168 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #26018782 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #26018781 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #26018578 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C89×#3006 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C22×D4×D89 | — | 2 | 1 | no | — |
| 11 | C2×#15668037 | — | 2 | 1 | no | — |
| 12 | #19152156 | — | 2 | 2 | no | — |
| 13 | #19152156 | — | 2 | 2 | no | — |
| 14 | #19152156 | — | 2 | 2 | no | — |
| 15 | #19152156 | C22 | 1 | 4 | yes | — |
| 16 | C2×#15667997 | — | 2 | 1 | no | — |
| 17 | C2×#15667994 | — | 2 | 1 | no | — |
| 18 | C2×#15667986 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#15667984 | — | 2 | 1 | no | — |
| 20 | C2×#15667982 | — | 2 | 1 | no | — |
| 21 | C2×#15667980 | — | 2 | 1 | no | — |
| 22 | C2×#15667980 | — | 2 | 1 | no | — |
| 23 | C22×#13083551 | C22 | 1 | 1 | yes | characteristic |
| 24 | #19151743 | — | 2 | 2 | no | — |
| 25 | #19151737 | C22 | 1 | 2 | yes | complemented |
| 26 | #19151732 | C22 | 1 | 2 | yes | complemented |
| 27 | #19151599 | — | 2 | 1 | no | — |
| 28 | #19151562 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | #19151509 | C22 | 1 | 2 | yes | complemented |
| 30 | #19151506 | C22 | 1 | 2 | yes | complemented |
| 31 | #19151478 | — | 2 | 1 | no | — |
| 32 | #19151477 | — | 2 | 2 | no | — |
| 33 | #19151461 | C22 | 1 | 1 | yes | characteristic, complemented |
| 34 | #19151333 | C22 | 1 | 4 | yes | complemented |
| 35 | #19151332 | C22 | 1 | 4 | yes | complemented |
| 36 | #19151321 | C22 | 1 | 4 | yes | complemented |
| 37 | C22×#41×C89 | C22 | 1 | 1 | yes | characteristic, complemented |
| 38 | C2×AGL(1,ℤ/8)×C89 | — | 2 | 1 | no | — |
| 39 | C2×#121×C89 | C22 | 1 | 1 | yes | characteristic |
| 40 | #449×C89 | — | 2 | 2 | no | — |
| 41 | #448×C89 | C22 | 1 | 2 | yes | complemented |
| 42 | #447×C89 | C22 | 1 | 2 | yes | complemented |
| 43 | #417×C89 | — | 2 | 1 | no | — |
| 44 | #407×C89 | C22 | 1 | 1 | yes | characteristic, complemented |
| 45 | C24×D89 | — | 2 | 1 | no | — |
| 46 | C24×D89 | D4 | 1 | 1 | yes | characteristic |
| 47 | C22×D356 | — | 2 | 1 | no | — |
| 48 | C22×D356 | D4 | 1 | 1 | yes | characteristic, complemented |
| 49 | C22×C22⋊D89 | — | 2 | 1 | no | — |
| 50 | C22×C22⋊D89 | — | 2 | 1 | no | — |
| 51 | C22×C22⋊D89 | — | 2 | 2 | no | — |
| 52 | C22×C22⋊D89 | — | 2 | 1 | no | — |
| 53 | C2×D4×D89 | — | 2 | 4 | no | — |
| 54 | C2×D4×D89 | — | 2 | 4 | no | — |
| 55 | C2×D4×D89 | — | 4 | 8 | no | — |
| 56 | C23×Dic89 | D4 | 1 | 1 | yes | characteristic |
| 57 | C22×C4×D89 | — | 2 | 1 | no | — |
| 58 | #15668037 | — | 4 | 4 | no | — |
| 59 | C2×#13083561 | — | 2 | 2 | no | — |
| 60 | C2×#13083559 | — | 2 | 2 | no | — |
| 61 | C2×#13083558 | — | 2 | 1 | no | — |
| 62 | #15667997 | — | 2 | 4 | no | — |
| 63 | #15667997 | — | 2 | 4 | no | — |
| 64 | #15667994 | — | 2 | 4 | no | — |
| 65 | #15667994 | — | 2 | 4 | no | — |
| 66 | #15667986 | — | 2 | 1 | no | — |
| 67 | #15667986 | — | 2 | 1 | no | — |
| 68 | #15667986 | D4 | 1 | 2 | yes | complemented |
| 69 | #15667986 | C23 | 1 | 2 | yes | — |
| 70 | #15667984 | — | 2 | 4 | no | — |
| 71 | #15667984 | — | 2 | 4 | no | — |
| 72 | #15667982 | — | 2 | 4 | no | — |
| 73 | #15667982 | — | 2 | 4 | no | — |
| 74 | #15667980 | — | 2 | 4 | no | — |
| 75 | #15667980 | — | 2 | 4 | no | — |
| 76 | #15667980 | — | 4 | 4 | no | — |
| 77 | C2×C4⋊Dic89 | D4 | 1 | 1 | yes | characteristic, complemented |
| 78 | C2×#13083553 | — | 2 | 1 | no | — |
| 79 | C2×C22⋊Dic89 | — | 2 | 1 | no | — |
| 80 | C2×C22⋊Dic89 | — | 2 | 2 | no | — |
| 81 | C2×C22⋊Dic89 | — | 2 | 1 | no | — |
| 82 | C2×#13083551 | — | 2 | 1 | no | — |
| 83 | C2×#13083551 | — | 2 | 2 | no | — |
| 84 | C2×#13083551 | — | 2 | 1 | no | — |
| 85 | C2×#13083551 | — | 2 | 1 | no | — |
| 86 | C2×#13083551 | — | 2 | 1 | no | — |
| 87 | C2×#13083551 | — | 2 | 1 | no | — |
| 88 | C2×#13083551 | — | 2 | 1 | no | — |
| 89 | C2×#13083551 | D4 | 1 | 2 | yes | — |
| 90 | C2×#13083551 | C23 | 1 | 2 | yes | — |
| 91 | #15667936 | — | 2 | 2 | no | — |
| 92 | #15667933 | — | 2 | 2 | no | — |
| 93 | C22⋊#10623494 | — | 2 | 1 | no | — |
| 94 | C22⋊#10623494 | C23 | 1 | 2 | yes | complemented |
| 95 | #15667919 | — | 2 | 2 | no | — |
| 96 | #15667919 | — | 2 | 1 | no | — |
| 97 | #15667919 | C23 | 1 | 2 | yes | complemented |
| 98 | C2×#41×C89 | — | 2 | 1 | no | — |
| 99 | C2×#41×C89 | — | 2 | 1 | no | — |
| 100 | C2×#41×C89 | — | 2 | 1 | no | — |
| 101 | C2×#41×C89 | — | 2 | 1 | no | — |
| 102 | C2×#41×C89 | — | 4 | 4 | no | — |
| 103 | C22×Q8×C89 | C23 | 1 | 1 | yes | characteristic, complemented |
| 104 | C22×D4×C89 | — | 2 | 1 | no | — |
| 105 | C22×D4×C89 | — | 2 | 1 | no | — |
| 106 | C22×D4×C89 | D4 | 1 | 1 | yes | characteristic, complemented |
| 107 | C22×D4×C89 | C23 | 1 | 1 | yes | characteristic, complemented |
| 108 | C23×C4×C89 | — | 2 | 1 | no | — |
| 109 | C23×C4×C89 | C23 | 1 | 1 | yes | characteristic |
| 110 | AGL(1,ℤ/8)×C89 | — | 4 | 4 | no | — |
| 111 | C2×SD16×C89 | — | 2 | 2 | no | — |
| 112 | C2×D8×C89 | — | 2 | 2 | no | — |
| 113 | C2×M16×C89 | — | 2 | 1 | no | — |
| 114 | #121×C89 | — | 2 | 1 | no | — |
| 115 | #121×C89 | — | 2 | 1 | no | — |
| 116 | #121×C89 | D4 | 1 | 2 | yes | complemented |
| 117 | #121×C89 | C23 | 1 | 2 | yes | — |
| 118 | C2×C4⋊C4×C89 | D4 | 1 | 1 | yes | characteristic, complemented |
| 119 | C2×C22⋊C4×C89 | — | 2 | 1 | no | — |
| 120 | #103×C89 | — | 2 | 2 | no | — |
| 121 | #102×C89 | — | 2 | 2 | no | — |
| 122 | C22⋊C8×C89 | — | 2 | 1 | no | — |
| 123 | C22⋊C8×C89 | C23 | 1 | 2 | yes | complemented |
| 124 | C23×D89 | — | 2 | 1 | no | — |
| 125 | C23×D89 | — | 2 | 1 | no | — |
| 126 | C23×D89 | — | 2 | 4 | no | — |
| 127 | C23×D89 | — | 2 | 1 | no | — |
| 128 | C23×D89 | — | 2 | 4 | no | — |
| 129 | C23×D89 | — | 4 | 4 | no | — |
| 130 | C23×D89 | — | 4 | 2 | no | — |
| 131 | C23×D89 | — | 8 | 1 | no | — |
| 132 | C23×D89 | — | 8 | 2 | no | — |
| 133 | C23×D89 | — | 8 | 2 | no | — |
| 134 | C23×D89 | C2×D4 | 1 | 2 | yes | — |
| 135 | C2×D356 | — | 2 | 4 | no | — |
| 136 | C2×D356 | — | 2 | 1 | no | — |
| 137 | C2×D356 | — | 4 | 4 | no | — |
| 138 | C2×D356 | — | 4 | 2 | no | — |
| 139 | C2×D356 | C2×D4 | 1 | 2 | yes | — |
| 140 | C2×C22⋊D89 | — | 2 | 4 | no | — |
| 141 | C2×C22⋊D89 | — | 2 | 2 | no | — |
| 142 | C2×C22⋊D89 | — | 2 | 2 | no | — |
| 143 | C2×C22⋊D89 | — | 2 | 4 | no | — |
| 144 | C2×C22⋊D89 | — | 4 | 4 | no | — |
| 145 | C2×C22⋊D89 | — | 4 | 4 | no | — |
| 146 | C2×C22⋊D89 | — | 4 | 4 | no | — |
| 147 | C2×C22⋊D89 | — | 4 | 4 | no | — |
| 148 | C2×C22⋊D89 | — | 8 | 2 | no | — |
| 149 | C2×C22⋊D89 | — | 8 | 2 | no | — |
| 150 | D4×D89 | — | 4 | 16 | no | — |
| 151 | D4×D89 | — | 4 | 8 | no | — |
| 152 | D4×D89 | — | 4 | 8 | no | — |
| 153 | C22×Dic89 | — | 2 | 1 | no | — |
| 154 | C22×Dic89 | — | 2 | 1 | no | — |
| 155 | C22×Dic89 | — | 2 | 1 | no | — |
| 156 | C22×Dic89 | — | 2 | 2 | no | — |
| 157 | C22×Dic89 | — | 8 | 1 | no | — |
| 158 | C22×Dic89 | C2×D4 | 1 | 2 | yes | — |
| 159 | C2×C4×D89 | — | 2 | 4 | no | — |
| 160 | C2×C4×D89 | — | 4 | 4 | no | — |
| 161 | #13083561 | — | 4 | 4 | no | — |
| 162 | #13083559 | — | 4 | 4 | no | — |
| 163 | #13083558 | — | 4 | 2 | no | — |
| 164 | C2×#10623494 | — | 2 | 2 | no | — |
| 165 | C4⋊Dic89 | — | 2 | 1 | no | — |
| 166 | C4⋊Dic89 | C2×D4 | 1 | 2 | yes | — |
| 167 | #13083553 | — | 2 | 4 | no | — |
| 168 | C22⋊Dic89 | — | 2 | 4 | no | — |
| 169 | C22⋊Dic89 | — | 4 | 2 | no | — |
| 170 | C22⋊Dic89 | — | 8 | 2 | no | — |
| 171 | #13083551 | — | 2 | 4 | no | — |
| 172 | #13083551 | — | 2 | 2 | no | — |
| 173 | #13083551 | — | 2 | 2 | no | — |
| 174 | #13083551 | — | 2 | 2 | no | — |
| 175 | #13083551 | — | 2 | 2 | no | — |
| 176 | #13083551 | — | 2 | 2 | no | — |
| 177 | #13083551 | — | 2 | 2 | no | — |
| 178 | #13083551 | — | 4 | 4 | no | — |
| 179 | C24×C89 | — | 2 | 1 | no | — |
| 180 | C24×C89 | — | 2 | 1 | no | — |
| 181 | C24×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 182 | #41×C89 | — | 2 | 4 | no | — |
| 183 | #41×C89 | — | 2 | 4 | no | — |
| 184 | #41×C89 | — | 4 | 2 | no | — |
| 185 | #41×C89 | — | 4 | 2 | no | — |
| 186 | #41×C89 | — | 4 | 2 | no | — |
| 187 | #41×C89 | — | 4 | 2 | no | — |
| 188 | #41×C89 | — | 4 | 2 | no | — |
| 189 | #41×C89 | — | 4 | 2 | no | — |
| 190 | C2×Q8×C89 | — | 2 | 1 | no | — |
| 191 | C2×Q8×C89 | — | 2 | 1 | no | — |
| 192 | C2×Q8×C89 | — | 4 | 2 | no | — |
| 193 | C2×D4×C89 | — | 2 | 4 | no | — |
| 194 | C2×D4×C89 | — | 2 | 2 | no | — |
| 195 | C2×D4×C89 | — | 2 | 2 | no | — |
| 196 | C2×D4×C89 | — | 2 | 1 | no | — |
| 197 | C2×D4×C89 | — | 2 | 1 | no | — |
| 198 | C2×D4×C89 | — | 2 | 1 | no | — |
| 199 | C2×D4×C89 | — | 4 | 2 | no | — |
| 200 | C2×D4×C89 | — | 4 | 2 | no | — |
| 201 | C2×D4×C89 | — | 4 | 4 | no | — |
| 202 | C2×D4×C89 | — | 4 | 2 | no | — |
| 203 | C2×D4×C89 | — | 4 | 1 | no | — |
| 204 | C2×D4×C89 | — | 4 | 1 | no | — |
| 205 | C2×D4×C89 | C2×D4 | 1 | 2 | yes | — |
| 206 | C22×C4×C89 | — | 2 | 1 | no | — |
| 207 | C22×C4×C89 | — | 2 | 1 | no | — |
| 208 | C22×C4×C89 | — | 4 | 2 | no | — |
| 209 | C22×C4×C89 | — | 4 | 2 | no | — |
| 210 | C22×C4×C89 | — | 4 | 2 | no | — |
| 211 | C22×C4×C89 | — | 4 | 1 | no | — |
| 212 | C22×C4×C89 | — | 4 | 1 | no | — |
| 213 | C22×C4×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 214 | C22×C4×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 215 | C22×C4×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 216 | C22×C4×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 217 | C22×C4×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 218 | C22×C4×C89 | C24 | 1 | 1 | yes | characteristic |
| 219 | SD16×C89 | — | 4 | 4 | no | — |
| 220 | D8×C89 | — | 4 | 4 | no | — |
| 221 | M16×C89 | — | 4 | 2 | no | — |
| 222 | C2×C8×C89 | — | 2 | 2 | no | — |
| 223 | C4⋊C4×C89 | — | 2 | 1 | no | — |
| 224 | C4⋊C4×C89 | C2×D4 | 1 | 2 | yes | — |
| 225 | C22⋊C4×C89 | — | 2 | 2 | no | — |
| 226 | C22⋊C4×C89 | — | 2 | 2 | no | — |
| 227 | C23×C89 | — | 2 | 2 | no | — |
| 228 | C23×C89 | — | 2 | 2 | no | — |
| 229 | C23×C89 | — | 2 | 2 | no | — |
| 230 | C23×C89 | — | 2 | 2 | no | — |
| 231 | C23×C89 | — | 4 | 1 | no | — |
| 232 | C23×C89 | — | 4 | 1 | no | — |
| 233 | C23×C89 | — | 4 | 2 | no | — |
| 234 | C23×C89 | — | 4 | 2 | no | — |
| 235 | C23×C89 | — | 4 | 2 | no | — |
| 236 | C23×C89 | — | 4 | 1 | no | — |
| 237 | C23×C89 | — | 4 | 2 | no | — |
| 238 | C23×C89 | — | 4 | 2 | no | — |
| 239 | C23×C89 | #120 | 1 | 1 | yes | characteristic |
| 240 | C23×C89 | #120 | 1 | 1 | yes | characteristic |
| 241 | C23×C89 | C22×D4 | 1 | 1 | yes | characteristic |
| 242 | C22×D89 | — | 2 | 4 | no | — |
| 243 | C22×D89 | — | 2 | 2 | no | — |
| 244 | C22×D89 | — | 2 | 4 | no | — |
| 245 | C22×D89 | — | 2 | 2 | no | — |
| 246 | C22×D89 | — | 2 | 2 | no | — |
| 247 | C22×D89 | — | 4 | 8 | no | — |
| 248 | C22×D89 | — | 4 | 2 | no | — |
| 249 | C22×D89 | — | 4 | 2 | no | — |
| 250 | C22×D89 | — | 4 | 2 | no | — |
| 251 | C22×D89 | — | 4 | 2 | no | — |
| 252 | C22×D89 | — | 4 | 2 | no | — |
| 253 | C22×D89 | — | 4 | 2 | no | — |
| 254 | C22×D89 | — | 4 | 2 | no | — |
| 255 | C22×D89 | — | 8 | 8 | no | — |
| 256 | C22×D89 | — | 8 | 1 | no | — |
| 257 | C22×D89 | — | 8 | 1 | no | — |
| 258 | C22×D89 | — | 8 | 4 | no | — |
| 259 | C22×D89 | — | 8 | 4 | no | — |
| 260 | C22×D89 | — | 8 | 16 | no | — |
| 261 | C22×D89 | AGL(1,ℤ/8) | 1 | 4 | yes | complemented |
| 262 | Q8×C89 | — | 2 | 2 | no | — |
| 263 | Q8×C89 | — | 2 | 2 | no | — |
| 264 | Q8×C89 | — | 4 | 1 | no | — |
| 265 | Q8×C89 | — | 4 | 1 | no | — |
| 266 | D4×C89 | — | 2 | 2 | no | — |
| 267 | D4×C89 | — | 2 | 2 | no | — |
| 268 | D4×C89 | — | 4 | 2 | no | — |
| 269 | D4×C89 | — | 4 | 1 | no | — |
| 270 | D4×C89 | — | 4 | 1 | no | — |
| 271 | D4×C89 | — | 4 | 4 | no | — |
| 272 | D4×C89 | — | 4 | 4 | no | — |
| 273 | D4×C89 | — | 4 | 4 | no | — |
| 274 | D4×C89 | — | 4 | 4 | no | — |
| 275 | D4×C89 | — | 8 | 1 | no | — |
| 276 | C2×C4×C89 | — | 2 | 2 | no | — |
| 277 | C2×C4×C89 | — | 2 | 2 | no | — |
| 278 | C2×C4×C89 | — | 2 | 2 | no | — |
| 279 | C2×C4×C89 | — | 2 | 2 | no | — |
| 280 | C2×C4×C89 | — | 4 | 1 | no | — |
| 281 | C2×C4×C89 | — | 4 | 1 | no | — |
| 282 | C2×C4×C89 | — | 4 | 1 | no | — |
| 283 | C2×C4×C89 | — | 4 | 1 | no | — |
| 284 | C2×C4×C89 | — | 4 | 4 | no | — |
| 285 | C2×C4×C89 | — | 4 | 4 | no | — |
| 286 | C2×C4×C89 | — | 4 | 1 | no | — |
| 287 | C2×C4×C89 | — | 4 | 2 | no | — |
| 288 | C2×C4×C89 | — | 4 | 1 | no | — |
| 289 | C2×C4×C89 | #120 | 1 | 1 | yes | characteristic |
| 290 | C2×C4×C89 | #120 | 1 | 1 | yes | characteristic |
| 291 | C2×C4×C89 | C22×D4 | 1 | 1 | yes | characteristic |
| 292 | C2×C4×C89 | C22×D4 | 1 | 1 | yes | characteristic |
| 293 | C22⋊D89 | — | 4 | 8 | no | — |
| 294 | C22⋊D89 | — | 4 | 4 | no | — |
| 295 | C22⋊D89 | — | 4 | 4 | no | — |
| 296 | C22⋊D89 | — | 8 | 4 | no | — |
| 297 | C22⋊D89 | — | 8 | 8 | no | — |
| 298 | C2×Dic89 | — | 2 | 2 | no | — |
| 299 | C2×Dic89 | — | 2 | 2 | no | — |
| 300 | C2×Dic89 | — | 4 | 2 | no | — |
| 301 | C2×Dic89 | — | 4 | 2 | no | — |
| 302 | C2×Dic89 | — | 4 | 2 | no | — |
| 303 | C2×Dic89 | — | 4 | 2 | no | — |
| 304 | C2×Dic89 | — | 4 | 2 | no | — |
| 305 | C2×Dic89 | — | 4 | 2 | no | — |
| 306 | C2×Dic89 | — | 8 | 1 | no | — |
| 307 | D356 | — | 4 | 2 | no | — |
| 308 | D356 | — | 4 | 8 | no | — |
| 309 | D356 | — | 8 | 1 | no | — |
| 310 | C4×D89 | — | 4 | 8 | no | — |
| 311 | C8×C89 | — | 4 | 2 | no | — |
| 312 | #10623494 | — | 4 | 2 | no | — |
| 313 | C22×C89 | — | 2 | 1 | no | — |
| 314 | C22×C89 | — | 2 | 1 | no | — |
| 315 | C22×C89 | — | 2 | 1 | no | — |
| 316 | C22×C89 | — | 2 | 1 | no | — |
| 317 | C22×C89 | — | 2 | 1 | no | — |
| 318 | C22×C89 | — | 2 | 1 | no | — |
| 319 | C22×C89 | — | 2 | 1 | no | — |
| 320 | C22×C89 | — | 4 | 4 | no | — |
| 321 | C22×C89 | — | 4 | 4 | no | — |
| 322 | C22×C89 | — | 4 | 2 | no | — |
| 323 | C22×C89 | — | 4 | 2 | no | — |
| 324 | C22×C89 | — | 4 | 2 | no | — |
| 325 | C22×C89 | — | 4 | 2 | no | — |
| 326 | C22×C89 | — | 8 | 4 | no | — |
| 327 | C22×C89 | — | 8 | 2 | no | — |
| 328 | C22×C89 | — | 8 | 1 | no | — |
| 329 | C22×C89 | — | 8 | 1 | no | — |
| 330 | C22×C89 | B(4,𝔽2) | 1 | 2 | yes | — |
| 331 | C22×C89 | C2×#120 | 1 | 1 | yes | characteristic |
| 332 | C22×C89 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 333 | C2×D89 | — | 2 | 4 | no | — |
| 334 | C2×D89 | — | 4 | 8 | no | — |
| 335 | C2×D89 | — | 4 | 2 | no | — |
| 336 | C2×D89 | — | 4 | 2 | no | — |
| 337 | C2×D89 | — | 4 | 4 | no | — |
| 338 | C2×D89 | — | 4 | 2 | no | — |
| 339 | C2×D89 | — | 4 | 2 | no | — |
| 340 | C2×D89 | — | 4 | 2 | no | — |
| 341 | C2×D89 | — | 8 | 2 | no | — |
| 342 | C2×D89 | — | 8 | 4 | no | — |
| 343 | C2×D89 | — | 8 | 16 | no | — |
| 344 | C2×D89 | — | 8 | 4 | no | — |
| 345 | C4×C89 | — | 2 | 1 | no | — |
| 346 | C4×C89 | — | 2 | 1 | no | — |
| 347 | C4×C89 | — | 2 | 1 | no | — |
| 348 | C4×C89 | — | 2 | 1 | no | — |
| 349 | C4×C89 | — | 4 | 2 | no | — |
| 350 | C4×C89 | — | 4 | 2 | no | — |
| 351 | Dic89 | — | 4 | 2 | no | — |
| 352 | Dic89 | — | 4 | 2 | no | — |
| 353 | Dic89 | — | 8 | 2 | no | — |
| 354 | #18132 | — | 89 | 1 | no | maximal, Sylow |
| 355 | C2×C89 | — | 2 | 2 | no | — |
| 356 | C2×C89 | — | 2 | 2 | no | — |
| 357 | C2×C89 | — | 4 | 1 | no | — |
| 358 | C2×C89 | — | 8 | 2 | no | — |
| 359 | C2×C89 | — | 8 | 2 | no | — |
| 360 | C2×C89 | #3003 | 1 | 1 | yes | characteristic |
| 361 | C2×C89 | #3019 | 1 | 1 | yes | characteristic |
| 362 | C2×C89 | C2×B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 363 | D89 | — | 4 | 4 | no | — |
| 364 | D89 | — | 8 | 2 | no | — |
| 365 | C2×#534 | — | 89 | 1 | no | — |
| 366 | #3006 | — | 89 | 1 | no | — |
| 367 | #3006 | D89 | 1 | 1 | yes | characteristic, complemented |
| 368 | #2404 | — | 89 | 1 | no | — |
| 369 | #1601 | — | 89 | 4 | no | — |
| 370 | #1595 | — | 89 | 4 | no | — |
| 371 | #1510 | — | 89 | 1 | no | — |
| 372 | #1510 | — | 89 | 1 | no | — |
| 373 | #1462 | — | 89 | 1 | no | — |
| 374 | C89 | #18132 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 375 | C22×#41 | C2×D89 | 1 | 1 | yes | characteristic, complemented |
| 376 | C23×D4 | — | 178 | 1 | no | — |
| 377 | C2×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 378 | C2×AGL(1,ℤ/8) | — | 178 | 1 | no | — |
| 379 | #534 | — | 89 | 4 | no | — |
| 380 | #534 | — | 178 | 2 | no | — |
| 381 | #534 | — | 178 | 2 | no | — |
| 382 | #534 | — | 178 | 2 | no | — |
| 383 | C2×#123 | — | 178 | 1 | no | — |
| 384 | C2×#123 | — | 178 | 1 | no | — |
| 385 | C2×#121 | — | 89 | 1 | no | — |
| 386 | C2×#121 | — | 178 | 1 | no | — |
| 387 | C2×#121 | C2×D89 | 1 | 1 | yes | characteristic |
| 388 | C2×#120 | — | 178 | 1 | no | — |
| 389 | C2×#120 | — | 178 | 1 | no | — |
| 390 | C2×#120 | — | 178 | 1 | no | — |
| 391 | C22×C22⋊C4 | — | 89 | 1 | no | — |
| 392 | #449 | — | 2 | 2 | no | — |
| 393 | #449 | — | 178 | 2 | no | — |
| 394 | #448 | — | 89 | 2 | no | — |
| 395 | #448 | C2×D89 | 1 | 2 | yes | complemented |
| 396 | #447 | — | 89 | 2 | no | — |
| 397 | #447 | C2×D89 | 1 | 2 | yes | complemented |
| 398 | #417 | — | 2 | 1 | no | — |
| 399 | #417 | — | 178 | 1 | no | — |
| 400 | #407 | — | 89 | 1 | no | — |
| 401 | #407 | C2×D89 | 1 | 1 | yes | characteristic, complemented |
| 402 | #393 | — | 89 | 2 | no | — |
| 403 | #392 | — | 89 | 2 | no | — |
| 404 | #386 | — | 178 | 2 | no | — |
| 405 | #386 | — | 178 | 1 | no | — |
| 406 | #381 | — | 89 | 1 | no | — |
| 407 | #327 | — | 89 | 4 | no | — |
| 408 | #327 | — | 89 | 4 | no | — |
| 409 | #323 | — | 89 | 4 | no | — |
| 410 | C25 | — | 89 | 1 | no | — |
| 411 | C25 | — | 178 | 1 | no | — |
| 412 | C2×#41 | — | 2 | 1 | no | — |
| 413 | C2×#41 | — | 2 | 1 | no | — |
| 414 | C2×#41 | — | 2 | 1 | no | — |
| 415 | C2×#41 | — | 2 | 1 | no | — |
| 416 | C2×#41 | — | 4 | 4 | no | — |
| 417 | C22×Q8 | C22×D89 | 1 | 1 | yes | characteristic, complemented |
| 418 | C22×D4 | — | 2 | 1 | no | — |
| 419 | C22×D4 | — | 2 | 1 | no | — |
| 420 | C22×D4 | — | 89 | 1 | no | — |
| 421 | C22×D4 | — | 356 | 8 | no | — |
| 422 | C22×D4 | — | 178 | 1 | no | — |
| 423 | C22×D4 | — | 178 | 4 | no | — |
| 424 | C22×D4 | — | 178 | 4 | no | — |
| 425 | C22×D4 | — | 178 | 1 | no | — |
| 426 | C22×D4 | — | 178 | 1 | no | — |
| 427 | C22×D4 | — | 178 | 2 | no | — |
| 428 | C22×D4 | — | 178 | 1 | no | — |
| 429 | C22×D4 | C22⋊D89 | 1 | 1 | yes | characteristic, complemented |
| 430 | C22×D4 | C22×D89 | 1 | 1 | yes | characteristic, complemented |
| 431 | C23×C4 | — | 2 | 1 | no | — |
| 432 | C23×C4 | — | 89 | 1 | no | — |
| 433 | C23×C4 | — | 178 | 1 | no | — |
| 434 | C23×C4 | C22×D89 | 1 | 1 | yes | characteristic |
| 435 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 436 | AGL(1,ℤ/8) | — | 356 | 4 | no | — |
| 437 | C2×SD16 | — | 2 | 2 | no | — |
| 438 | C2×SD16 | — | 178 | 2 | no | — |
| 439 | C2×D8 | — | 2 | 2 | no | — |
| 440 | C2×D8 | — | 178 | 2 | no | — |
| 441 | C2×M16 | — | 2 | 1 | no | — |
| 442 | C2×M16 | — | 178 | 1 | no | — |
| 443 | #123 | — | 178 | 4 | no | — |
| 444 | #123 | — | 178 | 4 | no | — |
| 445 | #123 | — | 178 | 4 | no | — |
| 446 | #123 | — | 178 | 4 | no | — |
| 447 | #121 | — | 2 | 1 | no | — |
| 448 | #121 | — | 2 | 1 | no | — |
| 449 | #121 | — | 89 | 2 | no | — |
| 450 | #121 | — | 89 | 2 | no | — |
| 451 | #121 | — | 178 | 4 | no | — |
| 452 | #121 | — | 178 | 4 | no | — |
| 453 | #121 | — | 178 | 1 | no | — |
| 454 | #121 | — | 178 | 1 | no | — |
| 455 | #121 | C22⋊D89 | 1 | 2 | yes | complemented |
| 456 | #121 | C22×D89 | 1 | 2 | yes | — |
| 457 | #120 | — | 356 | 4 | no | — |
| 458 | #120 | — | 178 | 4 | no | — |
| 459 | #120 | — | 178 | 4 | no | — |
| 460 | #120 | — | 178 | 4 | no | — |
| 461 | #120 | — | 178 | 4 | no | — |
| 462 | C2×C4⋊C4 | — | 89 | 1 | no | — |
| 463 | C2×C4⋊C4 | — | 178 | 1 | no | — |
| 464 | C2×C4⋊C4 | C22⋊D89 | 1 | 1 | yes | characteristic, complemented |
| 465 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 466 | C2×C22⋊C4 | — | 89 | 2 | no | — |
| 467 | C2×C22⋊C4 | — | 89 | 2 | no | — |
| 468 | C2×C22⋊C4 | — | 178 | 2 | no | — |
| 469 | C2×C22⋊C4 | — | 178 | 1 | no | — |
| 470 | C2×C22⋊C4 | — | 178 | 1 | no | — |
| 471 | C2×C22⋊C4 | — | 178 | 1 | no | — |
| 472 | C2×C22⋊C4 | — | 178 | 1 | no | — |
| 473 | C2×C22⋊C4 | — | 178 | 1 | no | — |
| 474 | C2×C22⋊C4 | — | 178 | 1 | no | — |
| 475 | C2×C22⋊C4 | — | 178 | 1 | no | — |
| 476 | C2×C22⋊C4 | — | 178 | 1 | no | — |
| 477 | C2×C22⋊C4 | — | 178 | 2 | no | — |
| 478 | #103 | — | 2 | 2 | no | — |
| 479 | #103 | — | 178 | 2 | no | — |
| 480 | #102 | — | 2 | 2 | no | — |
| 481 | #102 | — | 178 | 2 | no | — |
| 482 | C22⋊C8 | — | 2 | 1 | no | — |
| 483 | C22⋊C8 | — | 89 | 2 | no | — |
| 484 | C22⋊C8 | — | 178 | 1 | no | — |
| 485 | C22⋊C8 | C22×D89 | 1 | 2 | yes | complemented |
| 486 | #95 | — | 89 | 2 | no | — |
| 487 | #95 | — | 178 | 2 | no | — |
| 488 | #95 | — | 178 | 1 | no | — |
| 489 | C24 | — | 2 | 1 | no | — |
| 490 | C24 | — | 2 | 1 | no | — |
| 491 | C24 | — | 89 | 2 | no | — |
| 492 | C24 | — | 356 | 2 | no | — |
| 493 | C24 | — | 356 | 4 | no | — |
| 494 | C24 | — | 178 | 4 | no | — |
| 495 | C24 | — | 178 | 4 | no | — |
| 496 | C24 | — | 178 | 1 | no | — |
| 497 | C24 | — | 178 | 1 | no | — |
| 498 | C24 | — | 178 | 1 | no | — |
| 499 | C24 | — | 712 | 1 | no | — |
| 500 | C24 | — | 712 | 2 | no | — |
| 501 | C24 | — | 712 | 2 | no | — |
| 502 | C24 | D4×D89 | 1 | 1 | yes | characteristic |
| 503 | #41 | — | 2 | 4 | no | — |
| 504 | #41 | — | 2 | 4 | no | — |
| 505 | #41 | — | 4 | 2 | no | — |
| 506 | #41 | — | 4 | 2 | no | — |
| 507 | #41 | — | 4 | 2 | no | — |
| 508 | #41 | — | 4 | 2 | no | — |
| 509 | #41 | — | 4 | 2 | no | — |
| 510 | #41 | — | 4 | 2 | no | — |
| 511 | C2×Q8 | — | 2 | 1 | no | — |
| 512 | C2×Q8 | — | 2 | 1 | no | — |
| 513 | C2×Q8 | — | 4 | 2 | no | — |
| 514 | C2×D4 | — | 2 | 4 | no | — |
| 515 | C2×D4 | — | 2 | 2 | no | — |
| 516 | C2×D4 | — | 2 | 2 | no | — |
| 517 | C2×D4 | — | 2 | 1 | no | — |
| 518 | C2×D4 | — | 2 | 1 | no | — |
| 519 | C2×D4 | — | 2 | 1 | no | — |
| 520 | C2×D4 | — | 4 | 2 | no | — |
| 521 | C2×D4 | — | 4 | 2 | no | — |
| 522 | C2×D4 | — | 4 | 4 | no | — |
| 523 | C2×D4 | — | 4 | 2 | no | — |
| 524 | C2×D4 | — | 4 | 1 | no | — |
| 525 | C2×D4 | — | 4 | 1 | no | — |
| 526 | C2×D4 | — | 89 | 2 | no | — |
| 527 | C2×D4 | — | 356 | 2 | no | — |
| 528 | C2×D4 | — | 356 | 4 | no | — |
| 529 | C2×D4 | — | 356 | 8 | no | — |
| 530 | C2×D4 | — | 356 | 16 | no | — |
| 531 | C2×D4 | — | 356 | 8 | no | — |
| 532 | C2×D4 | — | 356 | 4 | no | — |
| 533 | C2×D4 | — | 356 | 4 | no | — |
| 534 | C2×D4 | — | 356 | 4 | no | — |
| 535 | C2×D4 | — | 356 | 4 | no | — |
| 536 | C2×D4 | — | 178 | 4 | no | — |
| 537 | C2×D4 | — | 178 | 4 | no | — |
| 538 | C2×D4 | — | 178 | 2 | no | — |
| 539 | C2×D4 | — | 178 | 2 | no | — |
| 540 | C2×D4 | — | 178 | 4 | no | — |
| 541 | C2×D4 | — | 178 | 1 | no | — |
| 542 | C2×D4 | — | 712 | 2 | no | — |
| 543 | C2×D4 | — | 712 | 2 | no | — |
| 544 | C2×D4 | C2×C22⋊D89 | 1 | 2 | yes | — |
| 545 | C22×C4 | — | 2 | 1 | no | — |
| 546 | C22×C4 | — | 2 | 1 | no | — |
| 547 | C22×C4 | — | 4 | 2 | no | — |
| 548 | C22×C4 | — | 4 | 2 | no | — |
| 549 | C22×C4 | — | 4 | 2 | no | — |
| 550 | C22×C4 | — | 4 | 1 | no | — |
| 551 | C22×C4 | — | 4 | 1 | no | — |
| 552 | C22×C4 | — | 89 | 2 | no | — |
| 553 | C22×C4 | — | 356 | 4 | no | — |
| 554 | C22×C4 | — | 178 | 4 | no | — |
| 555 | C22×C4 | — | 178 | 2 | no | — |
| 556 | C22×C4 | — | 178 | 1 | no | — |
| 557 | C22×C4 | — | 178 | 1 | no | — |
| 558 | C22×C4 | — | 178 | 1 | no | — |
| 559 | C22×C4 | — | 712 | 1 | no | — |
| 560 | C22×C4 | D4×D89 | 1 | 1 | yes | characteristic |
| 561 | C22×C4 | D4×D89 | 1 | 1 | yes | characteristic |
| 562 | C22×C4 | D4×D89 | 1 | 1 | yes | characteristic |
| 563 | C22×C4 | C2×C22⋊D89 | 1 | 1 | yes | characteristic |
| 564 | C22×C4 | C2×C22⋊D89 | 1 | 1 | yes | characteristic |
| 565 | C22×C4 | C23×D89 | 1 | 1 | yes | characteristic |
| 566 | SD16 | — | 4 | 4 | no | — |
| 567 | SD16 | — | 356 | 4 | no | — |
| 568 | D8 | — | 4 | 4 | no | — |
| 569 | D8 | — | 356 | 4 | no | — |
| 570 | M16 | — | 4 | 2 | no | — |
| 571 | M16 | — | 356 | 2 | no | — |
| 572 | C2×C8 | — | 2 | 2 | no | — |
| 573 | C2×C8 | — | 178 | 2 | no | — |
| 574 | C4⋊C4 | — | 2 | 1 | no | — |
| 575 | C4⋊C4 | — | 89 | 2 | no | — |
| 576 | C4⋊C4 | — | 178 | 4 | no | — |
| 577 | C4⋊C4 | — | 178 | 1 | no | — |
| 578 | C4⋊C4 | C2×C22⋊D89 | 1 | 2 | yes | — |
| 579 | C22⋊C4 | — | 2 | 2 | no | — |
| 580 | C22⋊C4 | — | 2 | 2 | no | — |
| 581 | C22⋊C4 | — | 356 | 4 | no | — |
| 582 | C22⋊C4 | — | 356 | 2 | no | — |
| 583 | C22⋊C4 | — | 178 | 4 | no | — |
| 584 | C22⋊C4 | — | 178 | 4 | no | — |
| 585 | C22⋊C4 | — | 178 | 2 | no | — |
| 586 | C22⋊C4 | — | 178 | 2 | no | — |
| 587 | C22⋊C4 | — | 178 | 2 | no | — |
| 588 | C22⋊C4 | — | 178 | 2 | no | — |
| 589 | C22⋊C4 | — | 178 | 2 | no | — |
| 590 | C22⋊C4 | — | 178 | 2 | no | — |
| 591 | C22⋊C4 | — | 712 | 2 | no | — |
| 592 | C23 | — | 2 | 2 | no | — |
| 593 | C23 | — | 2 | 2 | no | — |
| 594 | C23 | — | 2 | 2 | no | — |
| 595 | C23 | — | 2 | 2 | no | — |
| 596 | C23 | — | 4 | 1 | no | — |
| 597 | C23 | — | 4 | 2 | no | — |
| 598 | C23 | — | 4 | 1 | no | — |
| 599 | C23 | — | 4 | 2 | no | — |
| 600 | C23 | — | 4 | 2 | no | — |
| 601 | C23 | — | 4 | 2 | no | — |
| 602 | C23 | — | 4 | 1 | no | — |
| 603 | C23 | — | 4 | 2 | no | — |
| 604 | C23 | — | 89 | 4 | no | — |
| 605 | C23 | — | 356 | 2 | no | — |
| 606 | C23 | — | 356 | 2 | no | — |
| 607 | C23 | — | 356 | 2 | no | — |
| 608 | C23 | — | 356 | 2 | no | — |
| 609 | C23 | — | 356 | 2 | no | — |
| 610 | C23 | — | 356 | 8 | no | — |
| 611 | C23 | — | 356 | 2 | no | — |
| 612 | C23 | — | 356 | 2 | no | — |
| 613 | C23 | — | 178 | 4 | no | — |
| 614 | C23 | — | 178 | 4 | no | — |
| 615 | C23 | — | 178 | 2 | no | — |
| 616 | C23 | — | 178 | 2 | no | — |
| 617 | C23 | — | 178 | 2 | no | — |
| 618 | C23 | — | 712 | 1 | no | — |
| 619 | C23 | — | 712 | 1 | no | — |
| 620 | C23 | — | 712 | 8 | no | — |
| 621 | C23 | — | 712 | 4 | no | — |
| 622 | C23 | — | 712 | 4 | no | — |
| 623 | C23 | — | 712 | 16 | no | — |
| 624 | C23 | #15667980 | 1 | 1 | yes | characteristic |
| 625 | C23 | #15667980 | 1 | 1 | yes | characteristic |
| 626 | C23 | C2×D4×D89 | 1 | 1 | yes | characteristic |
| 627 | Q8 | — | 2 | 2 | no | — |
| 628 | Q8 | — | 2 | 2 | no | — |
| 629 | Q8 | — | 4 | 1 | no | — |
| 630 | Q8 | — | 4 | 1 | no | — |
| 631 | D4 | — | 2 | 2 | no | — |
| 632 | D4 | — | 2 | 2 | no | — |
| 633 | D4 | — | 4 | 2 | no | — |
| 634 | D4 | — | 4 | 1 | no | — |
| 635 | D4 | — | 4 | 1 | no | — |
| 636 | D4 | — | 4 | 4 | no | — |
| 637 | D4 | — | 4 | 4 | no | — |
| 638 | D4 | — | 4 | 4 | no | — |
| 639 | D4 | — | 4 | 4 | no | — |
| 640 | D4 | — | 8 | 1 | no | — |
| 641 | D4 | — | 356 | 2 | no | — |
| 642 | D4 | — | 356 | 8 | no | — |
| 643 | D4 | — | 356 | 4 | no | — |
| 644 | D4 | — | 356 | 8 | no | — |
| 645 | D4 | — | 356 | 4 | no | — |
| 646 | D4 | — | 712 | 1 | no | — |
| 647 | D4 | — | 712 | 4 | no | — |
| 648 | D4 | — | 712 | 8 | no | — |
| 649 | C2×C4 | — | 2 | 2 | no | — |
| 650 | C2×C4 | — | 2 | 2 | no | — |
| 651 | C2×C4 | — | 2 | 2 | no | — |
| 652 | C2×C4 | — | 2 | 2 | no | — |
| 653 | C2×C4 | — | 4 | 1 | no | — |
| 654 | C2×C4 | — | 4 | 1 | no | — |
| 655 | C2×C4 | — | 4 | 1 | no | — |
| 656 | C2×C4 | — | 4 | 1 | no | — |
| 657 | C2×C4 | — | 4 | 4 | no | — |
| 658 | C2×C4 | — | 4 | 4 | no | — |
| 659 | C2×C4 | — | 4 | 1 | no | — |
| 660 | C2×C4 | — | 4 | 2 | no | — |
| 661 | C2×C4 | — | 4 | 1 | no | — |
| 662 | C2×C4 | — | 356 | 8 | no | — |
| 663 | C2×C4 | — | 356 | 2 | no | — |
| 664 | C2×C4 | — | 356 | 2 | no | — |
| 665 | C2×C4 | — | 356 | 2 | no | — |
| 666 | C2×C4 | — | 356 | 2 | no | — |
| 667 | C2×C4 | — | 356 | 2 | no | — |
| 668 | C2×C4 | — | 356 | 2 | no | — |
| 669 | C2×C4 | — | 178 | 2 | no | — |
| 670 | C2×C4 | — | 178 | 2 | no | — |
| 671 | C2×C4 | — | 712 | 1 | no | — |
| 672 | C2×C4 | #15667980 | 1 | 1 | yes | characteristic |
| 673 | C2×C4 | #15667980 | 1 | 1 | yes | characteristic |
| 674 | C2×C4 | C2×D4×D89 | 1 | 1 | yes | characteristic |
| 675 | C2×C4 | C22×C22⋊D89 | 1 | 1 | yes | characteristic |
| 676 | C8 | — | 4 | 2 | no | — |
| 677 | C8 | — | 356 | 2 | no | — |
| 678 | C22 | — | 2 | 1 | no | — |
| 679 | C22 | — | 2 | 1 | no | — |
| 680 | C22 | — | 2 | 1 | no | — |
| 681 | C22 | — | 2 | 1 | no | — |
| 682 | C22 | — | 2 | 1 | no | — |
| 683 | C22 | — | 2 | 1 | no | — |
| 684 | C22 | — | 2 | 1 | no | — |
| 685 | C22 | — | 4 | 4 | no | — |
| 686 | C22 | — | 4 | 4 | no | — |
| 687 | C22 | — | 4 | 2 | no | — |
| 688 | C22 | — | 4 | 2 | no | — |
| 689 | C22 | — | 4 | 2 | no | — |
| 690 | C22 | — | 4 | 2 | no | — |
| 691 | C22 | — | 8 | 4 | no | — |
| 692 | C22 | — | 8 | 2 | no | — |
| 693 | C22 | — | 8 | 1 | no | — |
| 694 | C22 | — | 8 | 1 | no | — |
| 695 | C22 | — | 356 | 4 | no | — |
| 696 | C22 | — | 356 | 8 | no | — |
| 697 | C22 | — | 356 | 2 | no | — |
| 698 | C22 | — | 356 | 2 | no | — |
| 699 | C22 | — | 356 | 2 | no | — |
| 700 | C22 | — | 356 | 2 | no | — |
| 701 | C22 | — | 356 | 2 | no | — |
| 702 | C22 | — | 178 | 4 | no | — |
| 703 | C22 | — | 712 | 2 | no | — |
| 704 | C22 | — | 712 | 4 | no | — |
| 705 | C22 | — | 712 | 4 | no | — |
| 706 | C22 | — | 712 | 16 | no | — |
| 707 | C22 | #19151784 | 1 | 2 | yes | — |
| 708 | C22 | C2×#15667980 | 1 | 1 | yes | characteristic |
| 709 | C22 | AGL(1,ℤ/8)×D89 | 1 | 2 | yes | — |
| 710 | C4 | — | 2 | 1 | no | — |
| 711 | C4 | — | 2 | 1 | no | — |
| 712 | C4 | — | 2 | 1 | no | — |
| 713 | C4 | — | 2 | 1 | no | — |
| 714 | C4 | — | 4 | 2 | no | — |
| 715 | C4 | — | 4 | 2 | no | — |
| 716 | C4 | — | 356 | 2 | no | — |
| 717 | C4 | — | 356 | 2 | no | — |
| 718 | C4 | — | 712 | 2 | no | — |
| 719 | C2 | — | 2 | 2 | no | — |
| 720 | C2 | — | 2 | 2 | no | — |
| 721 | C2 | — | 4 | 1 | no | — |
| 722 | C2 | — | 8 | 2 | no | — |
| 723 | C2 | — | 8 | 2 | no | — |
| 724 | C2 | — | 356 | 4 | no | — |
| 725 | C2 | — | 712 | 2 | no | — |
| 726 | C2 | #26029477 | 1 | 1 | yes | characteristic |
| 727 | C2 | #26029607 | 1 | 1 | yes | characteristic |
| 728 | C2 | C2×#19151784 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#19152156 | C2 | semidirect |
| 2. #26029504 | C2 | semidirect |
| 3. #26023567 | C2 | semidirect |
| 4. #26019202 | C2 | semidirect |
| 5. #26019168 | C2 | semidirect |
| 6. #26018782 | C2 | semidirect |
| 7. #26018781 | C2 | semidirect |
| 8. #26018578 | C2 | semidirect |
| 9. C89×#3006 | C2 | semidirect |
| 25. #19151737 | C22 | semidirect |
| 26. #19151732 | C22 | semidirect |
| 28. #19151562 | C22 | semidirect |
| 29. #19151509 | C22 | semidirect |
| 30. #19151506 | C22 | semidirect |
| 33. #19151461 | C22 | semidirect |
| 34. #19151333 | C22 | semidirect |
| 35. #19151332 | C22 | semidirect |
| 36. #19151321 | C22 | semidirect |
| 37. C22×#41×C89 | C22 | semidirect |
| 41. #448×C89 | C22 | semidirect |
| 42. #447×C89 | C22 | semidirect |
| 44. #407×C89 | C22 | semidirect |
| 48. C22×D356 | D4 | semidirect |
| 68. #15667986 | D4 | semidirect |
| 77. C2×C4⋊Dic89 | D4 | semidirect |
| 94. C22⋊#10623494 | C23 | semidirect |
| 97. #15667919 | C23 | semidirect |
| 103. C22×Q8×C89 | C23 | semidirect |
| 106. C22×D4×C89 | D4 | semidirect |
| 107. C22×D4×C89 | C23 | semidirect |
| 116. #121×C89 | D4 | semidirect |
| 118. C2×C4⋊C4×C89 | D4 | semidirect |
| 123. C22⋊C8×C89 | C23 | semidirect |
| 261. C22×D89 | AGL(1,ℤ/8) | semidirect |
| 367. #3006 | D89 | semidirect |
| 374. C89 | #18132 | semidirect |
| 375. C22×#41 | C2×D89 | semidirect |
| 395. #448 | C2×D89 | semidirect |
| 397. #447 | C2×D89 | semidirect |
| 401. #407 | C2×D89 | semidirect |
| 417. C22×Q8 | C22×D89 | semidirect |
| 429. C22×D4 | C22⋊D89 | semidirect |
| 430. C22×D4 | C22×D89 | semidirect |
| 455. #121 | C22⋊D89 | semidirect |
| 464. C2×C4⋊C4 | C22⋊D89 | semidirect |
| 485. C22⋊C8 | C22×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152156 | 2 |
| #26029504 | 2 |
| #26023567 | 2 |
| #26019202 | 2 |
| #26019168 | 2 |
| #26018782 | 2 |
| #26018781 | 2 |
| #26018578 | 2 |
| C89×#3006 | 2 |
| #18132 | 89 |