Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1498 conjugacy classes of subgroups.
The subgroup lattice has 864 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #26034009 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #26029504 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #26023465 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #26019219 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #26019202 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #26019185 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #26019168 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #26018769 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #26018768 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #26018588 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C89×#3006 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#15668057 | — | 2 | 1 | no | — |
| 13 | C2×#15668037 | — | 2 | 1 | no | — |
| 14 | #19152249 | — | 2 | 1 | no | — |
| 15 | #19152248 | — | 2 | 1 | no | — |
| 16 | #19152238 | — | 2 | 2 | no | — |
| 17 | #19152237 | — | 2 | 2 | no | — |
| 18 | #19152232 | — | 2 | 1 | no | — |
| 19 | D4×C22⋊D89 | — | 2 | 1 | no | — |
| 20 | #19152175 | C22 | 1 | 2 | yes | — |
| 21 | #19152157 | — | 2 | 1 | no | — |
| 22 | #19152156 | C22 | 1 | 2 | yes | — |
| 23 | #19152143 | — | 2 | 1 | no | — |
| 24 | C2×#15667986 | C22 | 1 | 1 | yes | characteristic |
| 25 | #121×D89 | — | 2 | 1 | no | — |
| 26 | C2×C4×C22⋊D89 | — | 2 | 1 | no | — |
| 27 | C2×C4×C22⋊D89 | C22 | 1 | 1 | yes | characteristic |
| 28 | #19151743 | — | 2 | 2 | no | — |
| 29 | #19151737 | C22 | 1 | 2 | yes | complemented |
| 30 | #19151732 | C22 | 1 | 2 | yes | complemented |
| 31 | #19151599 | — | 2 | 1 | no | — |
| 32 | #19151562 | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | #19151517 | C22 | 1 | 1 | yes | characteristic, complemented |
| 34 | #19151512 | — | 2 | 1 | no | — |
| 35 | #19151512 | C22 | 1 | 1 | yes | characteristic, complemented |
| 36 | #19151509 | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | #19151506 | — | 2 | 1 | no | — |
| 38 | #19151506 | C22 | 1 | 1 | yes | characteristic, complemented |
| 39 | C4×C22⋊Dic89 | — | 2 | 1 | no | — |
| 40 | C4×C22⋊Dic89 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | #19151333 | C22 | 1 | 2 | yes | complemented |
| 42 | #19151333 | C22 | 1 | 2 | yes | complemented |
| 43 | #19151332 | C22 | 1 | 2 | yes | complemented |
| 44 | #19151332 | C22 | 1 | 2 | yes | complemented |
| 45 | #19151323 | C22 | 1 | 2 | yes | complemented |
| 46 | #19151321 | C22 | 1 | 2 | yes | complemented |
| 47 | C22×#41×C89 | C22 | 1 | 1 | yes | characteristic, complemented |
| 48 | C2×AGL(1,ℤ/8)×C89 | — | 2 | 1 | no | — |
| 49 | C2×#121×C89 | C22 | 1 | 1 | yes | characteristic |
| 50 | #449×C89 | — | 2 | 2 | no | — |
| 51 | #448×C89 | C22 | 1 | 2 | yes | complemented |
| 52 | #447×C89 | C22 | 1 | 2 | yes | complemented |
| 53 | #417×C89 | — | 2 | 1 | no | — |
| 54 | #407×C89 | C22 | 1 | 1 | yes | characteristic, complemented |
| 55 | #15668057 | — | 4 | 4 | no | — |
| 56 | #15668057 | — | 4 | 4 | no | — |
| 57 | C2×#13083574 | — | 2 | 2 | no | — |
| 58 | C2×#13083573 | — | 2 | 2 | no | — |
| 59 | C2×#13083573 | — | 2 | 2 | no | — |
| 60 | C22×D356 | D4 | 1 | 1 | yes | characteristic, complemented |
| 61 | C22×C22⋊D89 | — | 2 | 2 | no | — |
| 62 | C22×C22⋊D89 | — | 2 | 1 | no | — |
| 63 | C22×C22⋊D89 | — | 2 | 1 | no | — |
| 64 | C22×C22⋊D89 | D4 | 1 | 1 | yes | characteristic |
| 65 | C2×D4×D89 | — | 2 | 2 | no | — |
| 66 | C2×D4×D89 | — | 2 | 2 | no | — |
| 67 | C2×D4×D89 | — | 2 | 1 | no | — |
| 68 | C22×C4×D89 | D4 | 1 | 1 | yes | characteristic |
| 69 | #15668037 | — | 4 | 4 | no | — |
| 70 | C2×#13083561 | — | 2 | 2 | no | — |
| 71 | C2×#13083559 | — | 2 | 2 | no | — |
| 72 | C2×#13083558 | — | 2 | 1 | no | — |
| 73 | #15668011 | — | 2 | 1 | no | — |
| 74 | #15668008 | — | 2 | 1 | no | — |
| 75 | #15667998 | — | 2 | 2 | no | — |
| 76 | #15667997 | — | 2 | 2 | no | — |
| 77 | #15667995 | — | 2 | 2 | no | — |
| 78 | #15667994 | — | 2 | 2 | no | — |
| 79 | #15667993 | — | 2 | 2 | no | — |
| 80 | #15667990 | — | 2 | 2 | no | — |
| 81 | #15667989 | — | 2 | 2 | no | — |
| 82 | #15667987 | — | 2 | 1 | no | — |
| 83 | #15667986 | — | 2 | 1 | no | — |
| 84 | #15667986 | — | 2 | 1 | no | — |
| 85 | #15667986 | D4 | 1 | 2 | yes | complemented |
| 86 | #15667986 | C23 | 1 | 2 | yes | — |
| 87 | #15667985 | — | 2 | 2 | no | — |
| 88 | #15667985 | — | 2 | 2 | no | — |
| 89 | #15667984 | — | 2 | 2 | no | — |
| 90 | #15667984 | — | 2 | 2 | no | — |
| 91 | #15667984 | — | 2 | 2 | no | — |
| 92 | #15667983 | — | 2 | 1 | no | — |
| 93 | #15667982 | — | 2 | 2 | no | — |
| 94 | #15667981 | — | 2 | 2 | no | — |
| 95 | #15667980 | — | 2 | 2 | no | — |
| 96 | #15667980 | — | 2 | 2 | no | — |
| 97 | D4×Dic89 | — | 2 | 1 | no | — |
| 98 | #15667974 | — | 2 | 1 | no | — |
| 99 | C4×C22⋊D89 | — | 2 | 1 | no | — |
| 100 | C4×C22⋊D89 | — | 2 | 1 | no | — |
| 101 | C4×C22⋊D89 | — | 2 | 1 | no | — |
| 102 | C4×C22⋊D89 | — | 2 | 1 | no | — |
| 103 | C4×C22⋊D89 | — | 4 | 4 | no | — |
| 104 | #15667972 | — | 2 | 2 | no | — |
| 105 | C2×C4⋊Dic89 | D4 | 1 | 1 | yes | characteristic, complemented |
| 106 | C2×#13083553 | — | 2 | 1 | no | — |
| 107 | C2×#13083553 | C23 | 1 | 1 | yes | characteristic |
| 108 | C4⋊C4×D89 | — | 2 | 1 | no | — |
| 109 | C2×C22⋊Dic89 | — | 2 | 1 | no | — |
| 110 | C2×C22⋊Dic89 | — | 2 | 1 | no | — |
| 111 | C2×C22⋊Dic89 | — | 2 | 1 | no | — |
| 112 | C2×C22⋊Dic89 | — | 2 | 1 | no | — |
| 113 | C2×C22⋊Dic89 | D4 | 1 | 1 | yes | characteristic |
| 114 | C2×#13083551 | — | 2 | 1 | no | — |
| 115 | C2×#13083551 | — | 2 | 1 | no | — |
| 116 | C2×#13083551 | C23 | 1 | 1 | yes | characteristic |
| 117 | C22⋊C4×D89 | — | 2 | 2 | no | — |
| 118 | C2×C4×Dic89 | — | 2 | 1 | no | — |
| 119 | C2×C4×Dic89 | D4 | 1 | 1 | yes | characteristic |
| 120 | #15667936 | — | 2 | 2 | no | — |
| 121 | #15667933 | — | 2 | 2 | no | — |
| 122 | C22⋊#10623494 | — | 2 | 1 | no | — |
| 123 | C22⋊#10623494 | C23 | 1 | 2 | yes | — |
| 124 | #15667919 | — | 2 | 1 | no | — |
| 125 | #15667919 | — | 2 | 1 | no | — |
| 126 | #15667919 | C23 | 1 | 1 | yes | characteristic |
| 127 | #15667919 | C23 | 1 | 1 | yes | characteristic |
| 128 | C2×#41×C89 | — | 2 | 1 | no | — |
| 129 | C2×#41×C89 | — | 2 | 1 | no | — |
| 130 | C2×#41×C89 | — | 2 | 1 | no | — |
| 131 | C2×#41×C89 | — | 2 | 1 | no | — |
| 132 | C2×#41×C89 | — | 4 | 4 | no | — |
| 133 | C22×Q8×C89 | C23 | 1 | 1 | yes | characteristic |
| 134 | C22×D4×C89 | — | 2 | 1 | no | — |
| 135 | C22×D4×C89 | — | 2 | 1 | no | — |
| 136 | C22×D4×C89 | D4 | 1 | 1 | yes | characteristic, complemented |
| 137 | C22×D4×C89 | C23 | 1 | 1 | yes | characteristic |
| 138 | C23×C4×C89 | — | 2 | 1 | no | — |
| 139 | C23×C4×C89 | C23 | 1 | 1 | yes | characteristic |
| 140 | AGL(1,ℤ/8)×C89 | — | 4 | 4 | no | — |
| 141 | C2×SD16×C89 | — | 2 | 2 | no | — |
| 142 | C2×D8×C89 | — | 2 | 2 | no | — |
| 143 | C2×M16×C89 | — | 2 | 1 | no | — |
| 144 | #121×C89 | — | 2 | 1 | no | — |
| 145 | #121×C89 | — | 2 | 1 | no | — |
| 146 | #121×C89 | D4 | 1 | 2 | yes | complemented |
| 147 | #121×C89 | C23 | 1 | 2 | yes | — |
| 148 | C2×C4⋊C4×C89 | D4 | 1 | 1 | yes | characteristic, complemented |
| 149 | C2×C22⋊C4×C89 | — | 2 | 1 | no | — |
| 150 | #103×C89 | — | 2 | 2 | no | — |
| 151 | #102×C89 | — | 2 | 2 | no | — |
| 152 | C22⋊C8×C89 | — | 2 | 1 | no | — |
| 153 | C22⋊C8×C89 | C23 | 1 | 2 | yes | — |
| 154 | C23×D89 | — | 2 | 2 | no | — |
| 155 | C23×D89 | — | 2 | 1 | no | — |
| 156 | C23×D89 | C2×D4 | 1 | 1 | yes | characteristic |
| 157 | #13083574 | — | 4 | 8 | no | — |
| 158 | #13083573 | — | 4 | 4 | no | — |
| 159 | #13083573 | — | 4 | 8 | no | — |
| 160 | #13083573 | — | 4 | 4 | no | — |
| 161 | C2×Dic178 | — | 2 | 2 | no | — |
| 162 | C2×D356 | — | 2 | 2 | no | — |
| 163 | C2×D356 | — | 2 | 1 | no | — |
| 164 | C2×D356 | — | 4 | 2 | no | — |
| 165 | C2×D356 | C2×D4 | 1 | 2 | yes | — |
| 166 | C2×C22⋊D89 | — | 2 | 1 | no | — |
| 167 | C2×C22⋊D89 | — | 2 | 1 | no | — |
| 168 | C2×C22⋊D89 | — | 2 | 2 | no | — |
| 169 | C2×C22⋊D89 | — | 2 | 2 | no | — |
| 170 | C2×C22⋊D89 | — | 2 | 2 | no | — |
| 171 | C2×C22⋊D89 | — | 2 | 2 | no | — |
| 172 | C2×C22⋊D89 | — | 2 | 2 | no | — |
| 173 | C2×C22⋊D89 | — | 2 | 2 | no | — |
| 174 | C2×C22⋊D89 | — | 2 | 2 | no | — |
| 175 | C2×C22⋊D89 | — | 2 | 2 | no | — |
| 176 | C2×C22⋊D89 | — | 4 | 2 | no | — |
| 177 | C2×C22⋊D89 | — | 4 | 8 | no | — |
| 178 | C2×C22⋊D89 | — | 4 | 2 | no | — |
| 179 | C2×C22⋊D89 | — | 4 | 2 | no | — |
| 180 | C2×C22⋊D89 | — | 4 | 2 | no | — |
| 181 | C2×C22⋊D89 | — | 4 | 2 | no | — |
| 182 | D4×D89 | — | 4 | 8 | no | — |
| 183 | D4×D89 | — | 4 | 4 | no | — |
| 184 | D4×D89 | — | 4 | 4 | no | — |
| 185 | D4×D89 | — | 8 | 2 | no | — |
| 186 | C22×Dic89 | — | 2 | 2 | no | — |
| 187 | C22×Dic89 | — | 2 | 1 | no | — |
| 188 | C22×Dic89 | — | 2 | 1 | no | — |
| 189 | C22×Dic89 | — | 2 | 1 | no | — |
| 190 | C22×Dic89 | C2×D4 | 1 | 1 | yes | characteristic |
| 191 | C22×Dic89 | C2×D4 | 1 | 1 | yes | characteristic |
| 192 | C22×Dic89 | C2×D4 | 1 | 1 | yes | characteristic |
| 193 | C2×C4×D89 | — | 2 | 2 | no | — |
| 194 | C2×C4×D89 | — | 2 | 2 | no | — |
| 195 | C2×C4×D89 | — | 2 | 1 | no | — |
| 196 | C2×C4×D89 | — | 2 | 1 | no | — |
| 197 | C2×C4×D89 | — | 4 | 2 | no | — |
| 198 | #13083561 | — | 4 | 4 | no | — |
| 199 | #13083559 | — | 4 | 4 | no | — |
| 200 | #13083558 | — | 4 | 2 | no | — |
| 201 | C2×#10623494 | — | 2 | 2 | no | — |
| 202 | C4⋊Dic89 | — | 2 | 1 | no | — |
| 203 | C4⋊Dic89 | C2×D4 | 1 | 2 | yes | — |
| 204 | #13083553 | — | 2 | 2 | no | — |
| 205 | #13083553 | — | 2 | 2 | no | — |
| 206 | #13083553 | — | 2 | 1 | no | — |
| 207 | #13083553 | — | 2 | 1 | no | — |
| 208 | #13083553 | — | 4 | 2 | no | — |
| 209 | C22⋊Dic89 | — | 2 | 2 | no | — |
| 210 | C22⋊Dic89 | — | 2 | 2 | no | — |
| 211 | C22⋊Dic89 | — | 2 | 1 | no | — |
| 212 | C22⋊Dic89 | — | 2 | 1 | no | — |
| 213 | C22⋊Dic89 | — | 4 | 2 | no | — |
| 214 | C22⋊Dic89 | — | 4 | 2 | no | — |
| 215 | C22⋊Dic89 | — | 4 | 2 | no | — |
| 216 | C22⋊Dic89 | — | 4 | 2 | no | — |
| 217 | #13083551 | — | 2 | 2 | no | — |
| 218 | #13083551 | — | 2 | 2 | no | — |
| 219 | #13083551 | — | 2 | 2 | no | — |
| 220 | #13083551 | — | 2 | 1 | no | — |
| 221 | #13083551 | — | 2 | 1 | no | — |
| 222 | #13083551 | — | 2 | 2 | no | — |
| 223 | #13083551 | — | 4 | 2 | no | — |
| 224 | C4×Dic89 | — | 2 | 1 | no | — |
| 225 | C4×Dic89 | — | 2 | 1 | no | — |
| 226 | C4×Dic89 | — | 4 | 2 | no | — |
| 227 | C24×C89 | — | 2 | 1 | no | — |
| 228 | C24×C89 | — | 2 | 1 | no | — |
| 229 | C24×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 230 | #41×C89 | — | 2 | 4 | no | — |
| 231 | #41×C89 | — | 2 | 4 | no | — |
| 232 | #41×C89 | — | 4 | 2 | no | — |
| 233 | #41×C89 | — | 4 | 2 | no | — |
| 234 | #41×C89 | — | 4 | 2 | no | — |
| 235 | #41×C89 | — | 4 | 2 | no | — |
| 236 | #41×C89 | — | 4 | 2 | no | — |
| 237 | #41×C89 | — | 4 | 2 | no | — |
| 238 | C2×Q8×C89 | — | 2 | 1 | no | — |
| 239 | C2×Q8×C89 | — | 2 | 1 | no | — |
| 240 | C2×Q8×C89 | — | 4 | 2 | no | — |
| 241 | C2×D4×C89 | — | 2 | 2 | no | — |
| 242 | C2×D4×C89 | — | 2 | 2 | no | — |
| 243 | C2×D4×C89 | — | 2 | 1 | no | — |
| 244 | C2×D4×C89 | — | 2 | 1 | no | — |
| 245 | C2×D4×C89 | — | 2 | 1 | no | — |
| 246 | C2×D4×C89 | — | 4 | 2 | no | — |
| 247 | C2×D4×C89 | — | 4 | 2 | no | — |
| 248 | C2×D4×C89 | — | 4 | 2 | no | — |
| 249 | C2×D4×C89 | — | 4 | 2 | no | — |
| 250 | C2×D4×C89 | — | 4 | 2 | no | — |
| 251 | C2×D4×C89 | — | 4 | 2 | no | — |
| 252 | C2×D4×C89 | — | 4 | 1 | no | — |
| 253 | C2×D4×C89 | — | 4 | 1 | no | — |
| 254 | C2×D4×C89 | C2×D4 | 1 | 2 | yes | — |
| 255 | C22×C4×C89 | — | 2 | 4 | no | — |
| 256 | C22×C4×C89 | — | 2 | 1 | no | — |
| 257 | C22×C4×C89 | — | 2 | 1 | no | — |
| 258 | C22×C4×C89 | — | 4 | 2 | no | — |
| 259 | C22×C4×C89 | — | 4 | 2 | no | — |
| 260 | C22×C4×C89 | — | 4 | 1 | no | — |
| 261 | C22×C4×C89 | — | 4 | 1 | no | — |
| 262 | C22×C4×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 263 | C22×C4×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 264 | C22×C4×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 265 | C22×C4×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 266 | C22×C4×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 267 | C22×C4×C89 | C24 | 1 | 1 | yes | characteristic |
| 268 | SD16×C89 | — | 4 | 4 | no | — |
| 269 | D8×C89 | — | 4 | 4 | no | — |
| 270 | M16×C89 | — | 4 | 2 | no | — |
| 271 | C2×C8×C89 | — | 2 | 2 | no | — |
| 272 | C4⋊C4×C89 | — | 2 | 1 | no | — |
| 273 | C4⋊C4×C89 | C2×D4 | 1 | 2 | yes | — |
| 274 | C22⋊C4×C89 | — | 2 | 2 | no | — |
| 275 | C22⋊C4×C89 | — | 2 | 2 | no | — |
| 276 | C23×C89 | — | 2 | 1 | no | — |
| 277 | C23×C89 | — | 2 | 1 | no | — |
| 278 | C23×C89 | — | 2 | 2 | no | — |
| 279 | C23×C89 | — | 2 | 2 | no | — |
| 280 | C23×C89 | — | 4 | 1 | no | — |
| 281 | C23×C89 | — | 4 | 1 | no | — |
| 282 | C23×C89 | — | 4 | 1 | no | — |
| 283 | C23×C89 | — | 4 | 1 | no | — |
| 284 | C23×C89 | — | 4 | 1 | no | — |
| 285 | C23×C89 | — | 4 | 2 | no | — |
| 286 | C23×C89 | — | 4 | 1 | no | — |
| 287 | C23×C89 | — | 4 | 1 | no | — |
| 288 | C23×C89 | — | 4 | 1 | no | — |
| 289 | C23×C89 | — | 8 | 1 | no | — |
| 290 | C23×C89 | — | 8 | 1 | no | — |
| 291 | C23×C89 | #120 | 1 | 1 | yes | characteristic |
| 292 | C23×C89 | #120 | 1 | 1 | yes | characteristic |
| 293 | C23×C89 | C22×D4 | 1 | 1 | yes | characteristic |
| 294 | C22×D89 | — | 2 | 1 | no | — |
| 295 | C22×D89 | — | 2 | 1 | no | — |
| 296 | C22×D89 | — | 2 | 2 | no | — |
| 297 | C22×D89 | — | 4 | 4 | no | — |
| 298 | C22×D89 | — | 4 | 1 | no | — |
| 299 | C22×D89 | — | 4 | 1 | no | — |
| 300 | C22×D89 | — | 4 | 2 | no | — |
| 301 | C22×D89 | — | 8 | 1 | no | — |
| 302 | C22×D89 | — | 8 | 1 | no | — |
| 303 | C22×D89 | — | 8 | 2 | no | — |
| 304 | C22×D89 | — | 8 | 2 | no | — |
| 305 | C22×D89 | AGL(1,ℤ/8) | 1 | 2 | yes | complemented |
| 306 | Q8×C89 | — | 2 | 2 | no | — |
| 307 | Q8×C89 | — | 2 | 2 | no | — |
| 308 | Q8×C89 | — | 4 | 1 | no | — |
| 309 | Q8×C89 | — | 4 | 1 | no | — |
| 310 | D4×C89 | — | 2 | 2 | no | — |
| 311 | D4×C89 | — | 2 | 2 | no | — |
| 312 | D4×C89 | — | 4 | 2 | no | — |
| 313 | D4×C89 | — | 4 | 1 | no | — |
| 314 | D4×C89 | — | 4 | 1 | no | — |
| 315 | D4×C89 | — | 4 | 4 | no | — |
| 316 | D4×C89 | — | 4 | 4 | no | — |
| 317 | D4×C89 | — | 4 | 4 | no | — |
| 318 | D4×C89 | — | 4 | 2 | no | — |
| 319 | D4×C89 | — | 4 | 2 | no | — |
| 320 | D4×C89 | — | 4 | 2 | no | — |
| 321 | C2×C4×C89 | — | 2 | 2 | no | — |
| 322 | C2×C4×C89 | — | 2 | 2 | no | — |
| 323 | C2×C4×C89 | — | 2 | 2 | no | — |
| 324 | C2×C4×C89 | — | 2 | 2 | no | — |
| 325 | C2×C4×C89 | — | 2 | 2 | no | — |
| 326 | C2×C4×C89 | — | 4 | 1 | no | — |
| 327 | C2×C4×C89 | — | 4 | 1 | no | — |
| 328 | C2×C4×C89 | — | 4 | 1 | no | — |
| 329 | C2×C4×C89 | — | 4 | 4 | no | — |
| 330 | C2×C4×C89 | — | 4 | 1 | no | — |
| 331 | C2×C4×C89 | — | 4 | 2 | no | — |
| 332 | C2×C4×C89 | — | 4 | 1 | no | — |
| 333 | C2×C4×C89 | — | 4 | 4 | no | — |
| 334 | C2×C4×C89 | #120 | 1 | 1 | yes | characteristic |
| 335 | C2×C4×C89 | #120 | 1 | 1 | yes | characteristic |
| 336 | C2×C4×C89 | C22×D4 | 1 | 1 | yes | characteristic |
| 337 | C2×C4×C89 | C22×D4 | 1 | 1 | yes | characteristic |
| 338 | C22⋊D89 | — | 2 | 4 | no | — |
| 339 | C22⋊D89 | — | 2 | 4 | no | — |
| 340 | C22⋊D89 | — | 4 | 4 | no | — |
| 341 | C22⋊D89 | — | 4 | 4 | no | — |
| 342 | C22⋊D89 | — | 4 | 4 | no | — |
| 343 | C22⋊D89 | — | 4 | 8 | no | — |
| 344 | C22⋊D89 | — | 4 | 2 | no | — |
| 345 | C22⋊D89 | — | 4 | 2 | no | — |
| 346 | C22⋊D89 | — | 8 | 2 | no | — |
| 347 | C22⋊D89 | — | 8 | 2 | no | — |
| 348 | C2×Dic89 | — | 2 | 1 | no | — |
| 349 | C2×Dic89 | — | 2 | 1 | no | — |
| 350 | C2×Dic89 | — | 2 | 2 | no | — |
| 351 | C2×Dic89 | — | 2 | 1 | no | — |
| 352 | C2×Dic89 | — | 2 | 1 | no | — |
| 353 | C2×Dic89 | — | 2 | 2 | no | — |
| 354 | C2×Dic89 | — | 4 | 4 | no | — |
| 355 | C2×Dic89 | — | 4 | 1 | no | — |
| 356 | C2×Dic89 | — | 4 | 2 | no | — |
| 357 | C2×Dic89 | — | 4 | 1 | no | — |
| 358 | C2×Dic89 | — | 4 | 1 | no | — |
| 359 | C2×Dic89 | — | 4 | 1 | no | — |
| 360 | C2×Dic89 | — | 4 | 1 | no | — |
| 361 | C2×Dic89 | — | 4 | 1 | no | — |
| 362 | C2×Dic89 | — | 4 | 1 | no | — |
| 363 | C2×Dic89 | AGL(1,ℤ/8) | 1 | 2 | yes | complemented |
| 364 | D356 | — | 4 | 2 | no | — |
| 365 | D356 | — | 4 | 4 | no | — |
| 366 | D356 | — | 4 | 2 | no | — |
| 367 | C4×D89 | — | 4 | 4 | no | — |
| 368 | C4×D89 | — | 4 | 4 | no | — |
| 369 | C4×D89 | — | 4 | 2 | no | — |
| 370 | C4×D89 | — | 8 | 1 | no | — |
| 371 | Dic178 | — | 4 | 4 | no | — |
| 372 | C8×C89 | — | 4 | 2 | no | — |
| 373 | #10623494 | — | 4 | 2 | no | — |
| 374 | C22×C89 | — | 2 | 1 | no | — |
| 375 | C22×C89 | — | 2 | 1 | no | — |
| 376 | C22×C89 | — | 2 | 1 | no | — |
| 377 | C22×C89 | — | 2 | 1 | no | — |
| 378 | C22×C89 | — | 2 | 1 | no | — |
| 379 | C22×C89 | — | 2 | 1 | no | — |
| 380 | C22×C89 | — | 2 | 1 | no | — |
| 381 | C22×C89 | — | 2 | 1 | no | — |
| 382 | C22×C89 | — | 4 | 2 | no | — |
| 383 | C22×C89 | — | 4 | 2 | no | — |
| 384 | C22×C89 | — | 4 | 2 | no | — |
| 385 | C22×C89 | — | 4 | 2 | no | — |
| 386 | C22×C89 | — | 4 | 2 | no | — |
| 387 | C22×C89 | — | 4 | 2 | no | — |
| 388 | C22×C89 | — | 8 | 1 | no | — |
| 389 | C22×C89 | — | 8 | 1 | no | — |
| 390 | C22×C89 | — | 8 | 1 | no | — |
| 391 | C22×C89 | — | 8 | 1 | no | — |
| 392 | C22×C89 | — | 8 | 1 | no | — |
| 393 | C22×C89 | — | 8 | 1 | no | — |
| 394 | C22×C89 | — | 16 | 2 | no | — |
| 395 | C22×C89 | C2×#120 | 1 | 1 | yes | characteristic |
| 396 | C22×C89 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 397 | C22×C89 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 398 | C2×D89 | — | 2 | 2 | no | — |
| 399 | C2×D89 | — | 4 | 1 | no | — |
| 400 | C2×D89 | — | 4 | 1 | no | — |
| 401 | C2×D89 | — | 4 | 2 | no | — |
| 402 | C2×D89 | — | 4 | 2 | no | — |
| 403 | C2×D89 | — | 4 | 2 | no | — |
| 404 | C2×D89 | — | 4 | 2 | no | — |
| 405 | C2×D89 | — | 8 | 1 | no | — |
| 406 | C2×D89 | — | 16 | 4 | no | — |
| 407 | C2×D89 | — | 16 | 2 | no | — |
| 408 | C4×C89 | — | 2 | 1 | no | — |
| 409 | C4×C89 | — | 2 | 1 | no | — |
| 410 | C4×C89 | — | 2 | 1 | no | — |
| 411 | C4×C89 | — | 4 | 2 | no | — |
| 412 | C4×C89 | — | 4 | 2 | no | — |
| 413 | C4×C89 | B(4,𝔽2) | 1 | 2 | yes | — |
| 414 | Dic89 | — | 2 | 2 | no | — |
| 415 | Dic89 | — | 4 | 2 | no | — |
| 416 | Dic89 | — | 4 | 2 | no | — |
| 417 | Dic89 | — | 4 | 1 | no | — |
| 418 | Dic89 | — | 4 | 1 | no | — |
| 419 | Dic89 | — | 8 | 1 | no | — |
| 420 | #18166 | — | 89 | 1 | no | maximal, Sylow |
| 421 | C2×C89 | — | 2 | 1 | no | — |
| 422 | C2×C89 | — | 2 | 1 | no | — |
| 423 | C2×C89 | — | 4 | 1 | no | — |
| 424 | C2×C89 | — | 4 | 1 | no | — |
| 425 | C2×C89 | — | 8 | 2 | no | — |
| 426 | C2×C89 | — | 8 | 2 | no | — |
| 427 | C2×C89 | #3003 | 1 | 1 | yes | characteristic |
| 428 | C2×C89 | #3018 | 1 | 1 | yes | characteristic |
| 429 | C2×C89 | C2×B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 430 | D89 | — | 4 | 2 | no | — |
| 431 | D89 | — | 8 | 2 | no | — |
| 432 | #3496 | — | 89 | 1 | no | — |
| 433 | #3006 | — | 89 | 1 | no | — |
| 434 | #3006 | D89 | 1 | 1 | yes | characteristic, complemented |
| 435 | #2388 | — | 89 | 1 | no | — |
| 436 | #1604 | — | 89 | 2 | no | — |
| 437 | #1601 | — | 89 | 2 | no | — |
| 438 | #1598 | — | 89 | 2 | no | — |
| 439 | #1595 | — | 89 | 2 | no | — |
| 440 | #1507 | — | 89 | 1 | no | — |
| 441 | #1507 | — | 89 | 1 | no | — |
| 442 | #1465 | — | 89 | 1 | no | — |
| 443 | C89 | #18166 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 444 | C2×H(5,𝔽2) | — | 178 | 1 | no | — |
| 445 | C22×#41 | C2×D89 | 1 | 1 | yes | characteristic, complemented |
| 446 | C2×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 447 | C2×AGL(1,ℤ/8) | — | 178 | 1 | no | — |
| 448 | #547 | — | 178 | 1 | no | — |
| 449 | #547 | — | 178 | 1 | no | — |
| 450 | #546 | — | 178 | 2 | no | — |
| 451 | #546 | — | 178 | 2 | no | — |
| 452 | D42 | — | 178 | 1 | no | — |
| 453 | D42 | — | 178 | 1 | no | — |
| 454 | #537 | — | 89 | 2 | no | — |
| 455 | #534 | — | 89 | 2 | no | — |
| 456 | #534 | — | 178 | 1 | no | — |
| 457 | #532 | — | 178 | 1 | no | — |
| 458 | C2×#121 | — | 89 | 1 | no | — |
| 459 | C2×#121 | — | 178 | 1 | no | — |
| 460 | C2×#121 | C2×D89 | 1 | 1 | yes | characteristic |
| 461 | C2×C4×D4 | — | 89 | 1 | no | — |
| 462 | C2×C4×D4 | — | 178 | 1 | no | — |
| 463 | #449 | — | 2 | 2 | no | — |
| 464 | #449 | — | 178 | 2 | no | — |
| 465 | #448 | — | 89 | 2 | no | — |
| 466 | #448 | C2×D89 | 1 | 2 | yes | complemented |
| 467 | #447 | — | 89 | 2 | no | — |
| 468 | #447 | C2×D89 | 1 | 2 | yes | complemented |
| 469 | #417 | — | 2 | 1 | no | — |
| 470 | #417 | — | 178 | 1 | no | — |
| 471 | #407 | — | 89 | 1 | no | — |
| 472 | #407 | C2×D89 | 1 | 1 | yes | characteristic, complemented |
| 473 | #395 | — | 89 | 1 | no | — |
| 474 | #394 | — | 89 | 1 | no | — |
| 475 | #394 | — | 178 | 1 | no | — |
| 476 | #393 | — | 89 | 1 | no | — |
| 477 | #392 | — | 89 | 1 | no | — |
| 478 | #392 | — | 178 | 1 | no | — |
| 479 | C4×C22⋊C4 | — | 89 | 1 | no | — |
| 480 | C4×C22⋊C4 | — | 178 | 1 | no | — |
| 481 | #327 | — | 89 | 2 | no | — |
| 482 | #327 | — | 89 | 2 | no | — |
| 483 | #327 | — | 89 | 2 | no | — |
| 484 | #327 | — | 89 | 2 | no | — |
| 485 | #324 | — | 89 | 2 | no | — |
| 486 | #323 | — | 89 | 2 | no | — |
| 487 | H(5,𝔽2) | — | 356 | 4 | no | — |
| 488 | H(5,𝔽2) | — | 356 | 4 | no | — |
| 489 | C2×#41 | — | 2 | 1 | no | — |
| 490 | C2×#41 | — | 2 | 1 | no | — |
| 491 | C2×#41 | — | 2 | 1 | no | — |
| 492 | C2×#41 | — | 2 | 1 | no | — |
| 493 | C2×#41 | — | 4 | 4 | no | — |
| 494 | C2×#41 | — | 178 | 2 | no | — |
| 495 | C2×#41 | — | 178 | 2 | no | — |
| 496 | C2×#41 | — | 178 | 2 | no | — |
| 497 | C22×Q8 | C22×D89 | 1 | 1 | yes | characteristic |
| 498 | C22×D4 | — | 2 | 1 | no | — |
| 499 | C22×D4 | — | 2 | 1 | no | — |
| 500 | C22×D4 | — | 89 | 1 | no | — |
| 501 | C22×D4 | — | 89 | 1 | no | — |
| 502 | C22×D4 | — | 178 | 2 | no | — |
| 503 | C22×D4 | — | 178 | 2 | no | — |
| 504 | C22×D4 | — | 178 | 1 | no | — |
| 505 | C22×D4 | — | 178 | 1 | no | — |
| 506 | C22×D4 | — | 178 | 2 | no | — |
| 507 | C22×D4 | — | 178 | 1 | no | — |
| 508 | C22×D4 | C22⋊D89 | 1 | 1 | yes | characteristic, complemented |
| 509 | C22×D4 | C22×D89 | 1 | 1 | yes | characteristic |
| 510 | C23×C4 | — | 2 | 1 | no | — |
| 511 | C23×C4 | — | 89 | 1 | no | — |
| 512 | C23×C4 | C22×D89 | 1 | 1 | yes | characteristic |
| 513 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 514 | AGL(1,ℤ/8) | — | 356 | 4 | no | — |
| 515 | C2×SD16 | — | 2 | 2 | no | — |
| 516 | C2×SD16 | — | 178 | 2 | no | — |
| 517 | C2×D8 | — | 2 | 2 | no | — |
| 518 | C2×D8 | — | 178 | 2 | no | — |
| 519 | C2×M16 | — | 2 | 1 | no | — |
| 520 | C2×M16 | — | 178 | 1 | no | — |
| 521 | C4⋊Q8 | — | 178 | 1 | no | — |
| 522 | #127 | — | 178 | 1 | no | — |
| 523 | #124 | — | 178 | 2 | no | — |
| 524 | #123 | — | 178 | 2 | no | — |
| 525 | #123 | — | 178 | 2 | no | — |
| 526 | #123 | — | 178 | 2 | no | — |
| 527 | #123 | — | 178 | 2 | no | — |
| 528 | C22⋊Q8 | — | 178 | 2 | no | — |
| 529 | C22⋊Q8 | — | 178 | 2 | no | — |
| 530 | #121 | — | 2 | 1 | no | — |
| 531 | #121 | — | 2 | 1 | no | — |
| 532 | #121 | — | 89 | 2 | no | — |
| 533 | #121 | — | 89 | 2 | no | — |
| 534 | #121 | — | 178 | 2 | no | — |
| 535 | #121 | — | 178 | 2 | no | — |
| 536 | #121 | — | 178 | 1 | no | — |
| 537 | #121 | — | 178 | 2 | no | — |
| 538 | #121 | — | 178 | 2 | no | — |
| 539 | #121 | — | 178 | 1 | no | — |
| 540 | #121 | — | 178 | 2 | no | — |
| 541 | #121 | — | 178 | 1 | no | — |
| 542 | #121 | — | 178 | 1 | no | — |
| 543 | #121 | C22⋊D89 | 1 | 2 | yes | complemented |
| 544 | #121 | C22×D89 | 1 | 2 | yes | — |
| 545 | #120 | — | 178 | 2 | no | — |
| 546 | #120 | — | 178 | 2 | no | — |
| 547 | #120 | — | 178 | 2 | no | — |
| 548 | #120 | — | 178 | 2 | no | — |
| 549 | C4×D4 | — | 356 | 4 | no | — |
| 550 | C4×D4 | — | 178 | 2 | no | — |
| 551 | C4×D4 | — | 178 | 1 | no | — |
| 552 | C4×D4 | — | 178 | 1 | no | — |
| 553 | C4×D4 | — | 178 | 1 | no | — |
| 554 | C4×D4 | — | 178 | 1 | no | — |
| 555 | C4×D4 | — | 178 | 1 | no | — |
| 556 | C4×D4 | — | 178 | 1 | no | — |
| 557 | C2×C4⋊C4 | — | 89 | 1 | no | — |
| 558 | C2×C4⋊C4 | — | 89 | 1 | no | — |
| 559 | C2×C4⋊C4 | — | 178 | 1 | no | — |
| 560 | C2×C4⋊C4 | — | 178 | 1 | no | — |
| 561 | C2×C4⋊C4 | C22⋊D89 | 1 | 1 | yes | characteristic, complemented |
| 562 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 563 | C2×C22⋊C4 | — | 89 | 1 | no | — |
| 564 | C2×C22⋊C4 | — | 89 | 1 | no | — |
| 565 | C2×C22⋊C4 | — | 178 | 2 | no | — |
| 566 | C2×C22⋊C4 | — | 178 | 1 | no | — |
| 567 | C2×C22⋊C4 | — | 178 | 1 | no | — |
| 568 | C2×C22⋊C4 | — | 178 | 1 | no | — |
| 569 | C2×C22⋊C4 | — | 178 | 1 | no | — |
| 570 | C2×C22⋊C4 | — | 178 | 1 | no | — |
| 571 | C2×C22⋊C4 | — | 178 | 1 | no | — |
| 572 | C2×C42 | — | 89 | 1 | no | — |
| 573 | C2×C42 | — | 178 | 1 | no | — |
| 574 | #103 | — | 2 | 2 | no | — |
| 575 | #103 | — | 178 | 2 | no | — |
| 576 | #102 | — | 2 | 2 | no | — |
| 577 | #102 | — | 178 | 2 | no | — |
| 578 | C22⋊C8 | — | 2 | 1 | no | — |
| 579 | C22⋊C8 | — | 89 | 2 | no | — |
| 580 | C22⋊C8 | — | 178 | 1 | no | — |
| 581 | C22⋊C8 | C22×D89 | 1 | 2 | yes | — |
| 582 | #95 | — | 89 | 1 | no | — |
| 583 | #95 | — | 89 | 1 | no | — |
| 584 | #95 | — | 178 | 1 | no | — |
| 585 | #95 | — | 178 | 1 | no | — |
| 586 | C24 | — | 2 | 1 | no | — |
| 587 | C24 | — | 2 | 1 | no | — |
| 588 | C24 | — | 89 | 1 | no | — |
| 589 | C24 | — | 178 | 2 | no | — |
| 590 | C24 | — | 178 | 1 | no | — |
| 591 | C24 | D4×D89 | 1 | 1 | yes | characteristic |
| 592 | #41 | — | 2 | 4 | no | — |
| 593 | #41 | — | 2 | 4 | no | — |
| 594 | #41 | — | 4 | 2 | no | — |
| 595 | #41 | — | 4 | 2 | no | — |
| 596 | #41 | — | 4 | 2 | no | — |
| 597 | #41 | — | 4 | 2 | no | — |
| 598 | #41 | — | 4 | 2 | no | — |
| 599 | #41 | — | 4 | 2 | no | — |
| 600 | #41 | — | 356 | 8 | no | — |
| 601 | #41 | — | 356 | 4 | no | — |
| 602 | #41 | — | 356 | 8 | no | — |
| 603 | #41 | — | 356 | 4 | no | — |
| 604 | C2×Q8 | — | 2 | 1 | no | — |
| 605 | C2×Q8 | — | 2 | 1 | no | — |
| 606 | C2×Q8 | — | 4 | 2 | no | — |
| 607 | C2×Q8 | — | 178 | 2 | no | — |
| 608 | C2×D4 | — | 2 | 2 | no | — |
| 609 | C2×D4 | — | 2 | 2 | no | — |
| 610 | C2×D4 | — | 2 | 1 | no | — |
| 611 | C2×D4 | — | 2 | 1 | no | — |
| 612 | C2×D4 | — | 2 | 1 | no | — |
| 613 | C2×D4 | — | 4 | 2 | no | — |
| 614 | C2×D4 | — | 4 | 2 | no | — |
| 615 | C2×D4 | — | 4 | 2 | no | — |
| 616 | C2×D4 | — | 4 | 2 | no | — |
| 617 | C2×D4 | — | 4 | 2 | no | — |
| 618 | C2×D4 | — | 4 | 2 | no | — |
| 619 | C2×D4 | — | 4 | 1 | no | — |
| 620 | C2×D4 | — | 4 | 1 | no | — |
| 621 | C2×D4 | — | 89 | 2 | no | — |
| 622 | C2×D4 | — | 356 | 2 | no | — |
| 623 | C2×D4 | — | 356 | 4 | no | — |
| 624 | C2×D4 | — | 356 | 4 | no | — |
| 625 | C2×D4 | — | 356 | 8 | no | — |
| 626 | C2×D4 | — | 356 | 2 | no | — |
| 627 | C2×D4 | — | 356 | 2 | no | — |
| 628 | C2×D4 | — | 356 | 2 | no | — |
| 629 | C2×D4 | — | 356 | 2 | no | — |
| 630 | C2×D4 | — | 356 | 8 | no | — |
| 631 | C2×D4 | — | 356 | 2 | no | — |
| 632 | C2×D4 | — | 178 | 2 | no | — |
| 633 | C2×D4 | — | 178 | 2 | no | — |
| 634 | C2×D4 | — | 178 | 2 | no | — |
| 635 | C2×D4 | — | 178 | 2 | no | — |
| 636 | C2×D4 | — | 178 | 2 | no | — |
| 637 | C2×D4 | — | 178 | 2 | no | — |
| 638 | C2×D4 | — | 178 | 2 | no | — |
| 639 | C2×D4 | — | 178 | 1 | no | — |
| 640 | C2×D4 | — | 178 | 1 | no | — |
| 641 | C2×D4 | — | 178 | 2 | no | — |
| 642 | C2×D4 | — | 178 | 2 | no | — |
| 643 | C2×D4 | — | 178 | 1 | no | — |
| 644 | C2×D4 | — | 712 | 2 | no | — |
| 645 | C2×D4 | C2×C22⋊D89 | 1 | 2 | yes | — |
| 646 | C22×C4 | — | 2 | 4 | no | — |
| 647 | C22×C4 | — | 2 | 1 | no | — |
| 648 | C22×C4 | — | 2 | 1 | no | — |
| 649 | C22×C4 | — | 4 | 2 | no | — |
| 650 | C22×C4 | — | 4 | 2 | no | — |
| 651 | C22×C4 | — | 4 | 1 | no | — |
| 652 | C22×C4 | — | 4 | 1 | no | — |
| 653 | C22×C4 | — | 89 | 1 | no | — |
| 654 | C22×C4 | — | 89 | 1 | no | — |
| 655 | C22×C4 | — | 89 | 1 | no | — |
| 656 | C22×C4 | — | 356 | 2 | no | — |
| 657 | C22×C4 | — | 178 | 2 | no | — |
| 658 | C22×C4 | — | 178 | 2 | no | — |
| 659 | C22×C4 | — | 178 | 1 | no | — |
| 660 | C22×C4 | — | 178 | 2 | no | — |
| 661 | C22×C4 | — | 178 | 1 | no | — |
| 662 | C22×C4 | — | 178 | 1 | no | — |
| 663 | C22×C4 | — | 178 | 1 | no | — |
| 664 | C22×C4 | — | 178 | 1 | no | — |
| 665 | C22×C4 | D4×D89 | 1 | 1 | yes | characteristic |
| 666 | C22×C4 | D4×D89 | 1 | 1 | yes | characteristic |
| 667 | C22×C4 | D4×D89 | 1 | 1 | yes | characteristic |
| 668 | C22×C4 | C2×C22⋊D89 | 1 | 1 | yes | characteristic |
| 669 | C22×C4 | C2×C22⋊D89 | 1 | 1 | yes | characteristic |
| 670 | C22×C4 | C23×D89 | 1 | 1 | yes | characteristic |
| 671 | SD16 | — | 4 | 4 | no | — |
| 672 | SD16 | — | 356 | 4 | no | — |
| 673 | D8 | — | 4 | 4 | no | — |
| 674 | D8 | — | 356 | 4 | no | — |
| 675 | M16 | — | 4 | 2 | no | — |
| 676 | M16 | — | 356 | 2 | no | — |
| 677 | C2×C8 | — | 2 | 2 | no | — |
| 678 | C2×C8 | — | 178 | 2 | no | — |
| 679 | C4⋊C4 | — | 2 | 1 | no | — |
| 680 | C4⋊C4 | — | 89 | 2 | no | — |
| 681 | C4⋊C4 | — | 356 | 2 | no | — |
| 682 | C4⋊C4 | — | 178 | 2 | no | — |
| 683 | C4⋊C4 | — | 178 | 2 | no | — |
| 684 | C4⋊C4 | — | 178 | 1 | no | — |
| 685 | C4⋊C4 | — | 178 | 1 | no | — |
| 686 | C4⋊C4 | — | 178 | 1 | no | — |
| 687 | C4⋊C4 | C2×C22⋊D89 | 1 | 2 | yes | — |
| 688 | C22⋊C4 | — | 2 | 2 | no | — |
| 689 | C22⋊C4 | — | 2 | 2 | no | — |
| 690 | C22⋊C4 | — | 356 | 2 | no | — |
| 691 | C22⋊C4 | — | 356 | 2 | no | — |
| 692 | C22⋊C4 | — | 356 | 2 | no | — |
| 693 | C22⋊C4 | — | 356 | 2 | no | — |
| 694 | C22⋊C4 | — | 356 | 2 | no | — |
| 695 | C22⋊C4 | — | 178 | 2 | no | — |
| 696 | C22⋊C4 | — | 178 | 2 | no | — |
| 697 | C22⋊C4 | — | 178 | 2 | no | — |
| 698 | C22⋊C4 | — | 178 | 2 | no | — |
| 699 | C22⋊C4 | — | 178 | 1 | no | — |
| 700 | C22⋊C4 | — | 178 | 1 | no | — |
| 701 | C22⋊C4 | — | 178 | 2 | no | — |
| 702 | C22⋊C4 | — | 178 | 1 | no | — |
| 703 | C22⋊C4 | — | 178 | 1 | no | — |
| 704 | C22⋊C4 | — | 178 | 2 | no | — |
| 705 | C42 | — | 356 | 2 | no | — |
| 706 | C42 | — | 178 | 1 | no | — |
| 707 | C42 | — | 178 | 1 | no | — |
| 708 | C23 | — | 2 | 1 | no | — |
| 709 | C23 | — | 2 | 1 | no | — |
| 710 | C23 | — | 2 | 2 | no | — |
| 711 | C23 | — | 2 | 2 | no | — |
| 712 | C23 | — | 4 | 1 | no | — |
| 713 | C23 | — | 4 | 1 | no | — |
| 714 | C23 | — | 4 | 1 | no | — |
| 715 | C23 | — | 4 | 1 | no | — |
| 716 | C23 | — | 4 | 1 | no | — |
| 717 | C23 | — | 4 | 2 | no | — |
| 718 | C23 | — | 4 | 1 | no | — |
| 719 | C23 | — | 4 | 1 | no | — |
| 720 | C23 | — | 4 | 1 | no | — |
| 721 | C23 | — | 8 | 1 | no | — |
| 722 | C23 | — | 8 | 1 | no | — |
| 723 | C23 | — | 89 | 2 | no | — |
| 724 | C23 | — | 356 | 1 | no | — |
| 725 | C23 | — | 356 | 1 | no | — |
| 726 | C23 | — | 356 | 2 | no | — |
| 727 | C23 | — | 356 | 4 | no | — |
| 728 | C23 | — | 178 | 2 | no | — |
| 729 | C23 | — | 178 | 1 | no | — |
| 730 | C23 | — | 178 | 1 | no | — |
| 731 | C23 | — | 712 | 1 | no | — |
| 732 | C23 | — | 712 | 1 | no | — |
| 733 | C23 | — | 712 | 2 | no | — |
| 734 | C23 | — | 712 | 2 | no | — |
| 735 | C23 | #15667980 | 1 | 1 | yes | characteristic |
| 736 | C23 | #15667980 | 1 | 1 | yes | characteristic |
| 737 | C23 | C2×D4×D89 | 1 | 1 | yes | characteristic |
| 738 | Q8 | — | 2 | 2 | no | — |
| 739 | Q8 | — | 2 | 2 | no | — |
| 740 | Q8 | — | 4 | 1 | no | — |
| 741 | Q8 | — | 4 | 1 | no | — |
| 742 | Q8 | — | 356 | 4 | no | — |
| 743 | D4 | — | 2 | 2 | no | — |
| 744 | D4 | — | 2 | 2 | no | — |
| 745 | D4 | — | 4 | 2 | no | — |
| 746 | D4 | — | 4 | 1 | no | — |
| 747 | D4 | — | 4 | 1 | no | — |
| 748 | D4 | — | 4 | 4 | no | — |
| 749 | D4 | — | 4 | 4 | no | — |
| 750 | D4 | — | 4 | 4 | no | — |
| 751 | D4 | — | 4 | 2 | no | — |
| 752 | D4 | — | 4 | 2 | no | — |
| 753 | D4 | — | 4 | 2 | no | — |
| 754 | D4 | — | 356 | 2 | no | — |
| 755 | D4 | — | 356 | 4 | no | — |
| 756 | D4 | — | 356 | 4 | no | — |
| 757 | D4 | — | 356 | 8 | no | — |
| 758 | D4 | — | 356 | 4 | no | — |
| 759 | D4 | — | 356 | 2 | no | — |
| 760 | D4 | — | 356 | 2 | no | — |
| 761 | D4 | — | 356 | 4 | no | — |
| 762 | D4 | — | 356 | 2 | no | — |
| 763 | D4 | — | 178 | 4 | no | — |
| 764 | D4 | — | 178 | 4 | no | — |
| 765 | D4 | — | 712 | 2 | no | — |
| 766 | D4 | — | 712 | 2 | no | — |
| 767 | C2×C4 | — | 2 | 2 | no | — |
| 768 | C2×C4 | — | 2 | 2 | no | — |
| 769 | C2×C4 | — | 2 | 2 | no | — |
| 770 | C2×C4 | — | 2 | 2 | no | — |
| 771 | C2×C4 | — | 2 | 2 | no | — |
| 772 | C2×C4 | — | 4 | 1 | no | — |
| 773 | C2×C4 | — | 4 | 1 | no | — |
| 774 | C2×C4 | — | 4 | 1 | no | — |
| 775 | C2×C4 | — | 4 | 4 | no | — |
| 776 | C2×C4 | — | 4 | 1 | no | — |
| 777 | C2×C4 | — | 4 | 2 | no | — |
| 778 | C2×C4 | — | 4 | 1 | no | — |
| 779 | C2×C4 | — | 4 | 4 | no | — |
| 780 | C2×C4 | — | 89 | 2 | no | — |
| 781 | C2×C4 | — | 356 | 4 | no | — |
| 782 | C2×C4 | — | 356 | 4 | no | — |
| 783 | C2×C4 | — | 356 | 1 | no | — |
| 784 | C2×C4 | — | 356 | 2 | no | — |
| 785 | C2×C4 | — | 356 | 1 | no | — |
| 786 | C2×C4 | — | 356 | 4 | no | — |
| 787 | C2×C4 | — | 356 | 2 | no | — |
| 788 | C2×C4 | — | 356 | 1 | no | — |
| 789 | C2×C4 | — | 356 | 1 | no | — |
| 790 | C2×C4 | — | 356 | 1 | no | — |
| 791 | C2×C4 | — | 356 | 1 | no | — |
| 792 | C2×C4 | — | 356 | 1 | no | — |
| 793 | C2×C4 | — | 178 | 2 | no | — |
| 794 | C2×C4 | — | 178 | 1 | no | — |
| 795 | C2×C4 | — | 178 | 1 | no | — |
| 796 | C2×C4 | — | 178 | 2 | no | — |
| 797 | C2×C4 | — | 178 | 1 | no | — |
| 798 | C2×C4 | — | 178 | 1 | no | — |
| 799 | C2×C4 | — | 712 | 1 | no | — |
| 800 | C2×C4 | #15667980 | 1 | 1 | yes | characteristic |
| 801 | C2×C4 | #15667980 | 1 | 1 | yes | characteristic |
| 802 | C2×C4 | C2×D4×D89 | 1 | 1 | yes | characteristic |
| 803 | C2×C4 | C22×C22⋊D89 | 1 | 1 | yes | characteristic |
| 804 | C8 | — | 4 | 2 | no | — |
| 805 | C8 | — | 356 | 2 | no | — |
| 806 | C22 | — | 2 | 1 | no | — |
| 807 | C22 | — | 2 | 1 | no | — |
| 808 | C22 | — | 2 | 1 | no | — |
| 809 | C22 | — | 2 | 1 | no | — |
| 810 | C22 | — | 2 | 1 | no | — |
| 811 | C22 | — | 2 | 1 | no | — |
| 812 | C22 | — | 2 | 1 | no | — |
| 813 | C22 | — | 2 | 1 | no | — |
| 814 | C22 | — | 4 | 2 | no | — |
| 815 | C22 | — | 4 | 2 | no | — |
| 816 | C22 | — | 4 | 2 | no | — |
| 817 | C22 | — | 4 | 2 | no | — |
| 818 | C22 | — | 4 | 2 | no | — |
| 819 | C22 | — | 4 | 2 | no | — |
| 820 | C22 | — | 8 | 1 | no | — |
| 821 | C22 | — | 8 | 1 | no | — |
| 822 | C22 | — | 8 | 1 | no | — |
| 823 | C22 | — | 8 | 1 | no | — |
| 824 | C22 | — | 8 | 1 | no | — |
| 825 | C22 | — | 8 | 1 | no | — |
| 826 | C22 | — | 16 | 2 | no | — |
| 827 | C22 | — | 356 | 2 | no | — |
| 828 | C22 | — | 356 | 1 | no | — |
| 829 | C22 | — | 356 | 1 | no | — |
| 830 | C22 | — | 356 | 2 | no | — |
| 831 | C22 | — | 356 | 2 | no | — |
| 832 | C22 | — | 356 | 2 | no | — |
| 833 | C22 | — | 1424 | 2 | no | — |
| 834 | C22 | — | 1424 | 4 | no | — |
| 835 | C22 | — | 178 | 2 | no | — |
| 836 | C22 | — | 712 | 1 | no | — |
| 837 | C22 | C2×#15667980 | 1 | 1 | yes | characteristic |
| 838 | C22 | AGL(1,ℤ/8)×D89 | 1 | 1 | yes | characteristic |
| 839 | C22 | AGL(1,ℤ/8)×D89 | 1 | 1 | yes | characteristic |
| 840 | C4 | — | 2 | 1 | no | — |
| 841 | C4 | — | 2 | 1 | no | — |
| 842 | C4 | — | 2 | 1 | no | — |
| 843 | C4 | — | 4 | 2 | no | — |
| 844 | C4 | — | 4 | 2 | no | — |
| 845 | C4 | — | 356 | 2 | no | — |
| 846 | C4 | — | 356 | 1 | no | — |
| 847 | C4 | — | 356 | 1 | no | — |
| 848 | C4 | — | 356 | 2 | no | — |
| 849 | C4 | — | 178 | 2 | no | — |
| 850 | C4 | — | 712 | 1 | no | — |
| 851 | C4 | #19151784 | 1 | 2 | yes | — |
| 852 | C2 | — | 2 | 1 | no | — |
| 853 | C2 | — | 2 | 1 | no | — |
| 854 | C2 | — | 4 | 1 | no | — |
| 855 | C2 | — | 4 | 1 | no | — |
| 856 | C2 | — | 8 | 2 | no | — |
| 857 | C2 | — | 8 | 2 | no | — |
| 858 | C2 | — | 356 | 2 | no | — |
| 859 | C2 | — | 712 | 2 | no | — |
| 860 | C2 | #26029477 | 1 | 1 | yes | characteristic |
| 861 | C2 | #26029598 | 1 | 1 | yes | characteristic |
| 862 | C2 | C2×#19151784 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #26034009 | C2 | semidirect |
| 2. #26029504 | C2 | semidirect |
| 3. #26023465 | C2 | semidirect |
| 4. #26019219 | C2 | semidirect |
| 5. #26019202 | C2 | semidirect |
| 6. #26019185 | C2 | semidirect |
| 7. #26019168 | C2 | semidirect |
| 8. #26018769 | C2 | semidirect |
| 9. #26018768 | C2 | semidirect |
| 10. #26018588 | C2 | semidirect |
| 11. C89×#3006 | C2 | semidirect |
| 29. #19151737 | C22 | semidirect |
| 30. #19151732 | C22 | semidirect |
| 32. #19151562 | C22 | semidirect |
| 33. #19151517 | C22 | semidirect |
| 35. #19151512 | C22 | semidirect |
| 36. #19151509 | C22 | semidirect |
| 38. #19151506 | C22 | semidirect |
| 40. C4×C22⋊Dic89 | C22 | semidirect |
| 41. #19151333 | C22 | semidirect |
| 42. #19151333 | C22 | semidirect |
| 43. #19151332 | C22 | semidirect |
| 44. #19151332 | C22 | semidirect |
| 45. #19151323 | C22 | semidirect |
| 46. #19151321 | C22 | semidirect |
| 47. C22×#41×C89 | C22 | semidirect |
| 51. #448×C89 | C22 | semidirect |
| 52. #447×C89 | C22 | semidirect |
| 54. #407×C89 | C22 | semidirect |
| 60. C22×D356 | D4 | semidirect |
| 85. #15667986 | D4 | semidirect |
| 105. C2×C4⋊Dic89 | D4 | semidirect |
| 136. C22×D4×C89 | D4 | semidirect |
| 146. #121×C89 | D4 | semidirect |
| 148. C2×C4⋊C4×C89 | D4 | semidirect |
| 305. C22×D89 | AGL(1,ℤ/8) | semidirect |
| 363. C2×Dic89 | AGL(1,ℤ/8) | semidirect |
| 434. #3006 | D89 | semidirect |
| 443. C89 | #18166 | semidirect |
| 445. C22×#41 | C2×D89 | semidirect |
| 466. #448 | C2×D89 | semidirect |
| 468. #447 | C2×D89 | semidirect |
| 472. #407 | C2×D89 | semidirect |
| 508. C22×D4 | C22⋊D89 | semidirect |
| 543. #121 | C22⋊D89 | semidirect |
| 561. C2×C4⋊C4 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034009 | 2 |
| #26029504 | 2 |
| #26023465 | 2 |
| #26019219 | 2 |
| #26019202 | 2 |
| #26019185 | 2 |
| #26019168 | 2 |
| #26018769 | 2 |
| #26018768 | 2 |
| #26018588 | 2 |
| C89×#3006 | 2 |
| #18166 | 89 |