Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
822 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 822 conjugacy classes of subgroups — too many to draw. Only its 155 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 | #26034708 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #26031473 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #26019583 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #26019578 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #26019573 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #26018879 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #26018870 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | C2×#491×C89 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C89⋊#564 | C22 | 1 | 1 | yes | characteristic |
| 10 | #19152352 | C22 | 1 | 2 | yes | — |
| 11 | #19152346 | C22 | 1 | 1 | yes | characteristic |
| 12 | #19152303 | — | 2 | 2 | no | — |
| 13 | #19152296 | — | 2 | 2 | no | — |
| 14 | #19152280 | — | 2 | 2 | no | — |
| 15 | #19152207 | — | 2 | 2 | no | — |
| 16 | #19152196 | — | 2 | 2 | no | — |
| 17 | #19152195 | — | 2 | 2 | no | — |
| 18 | #19152132 | C22 | 1 | 2 | yes | — |
| 19 | #19152004 | C22 | 1 | 4 | yes | — |
| 20 | #19151960 | C22 | 1 | 4 | yes | — |
| 21 | #19151928 | — | 2 | 2 | no | — |
| 22 | #19151911 | — | 2 | 2 | no | — |
| 23 | #19151890 | — | 2 | 2 | no | — |
| 24 | #19151885 | — | 2 | 2 | no | — |
| 25 | #19151655 | C22 | 1 | 2 | yes | — |
| 26 | #19151340 | C22 | 1 | 2 | yes | — |
| 27 | #19151340 | C22 | 1 | 2 | yes | — |
| 28 | #19151339 | C22 | 1 | 4 | yes | — |
| 29 | #19151337 | C22 | 1 | 4 | yes | — |
| 30 | C2×C4⋊Q8×C89 | C22 | 1 | 1 | yes | characteristic |
| 31 | C2×#125×C89 | C22 | 1 | 1 | yes | characteristic |
| 32 | #491×C89 | — | 2 | 2 | no | — |
| 33 | #491×C89 | C22 | 1 | 2 | yes | — |
| 34 | #491×C89 | C22 | 1 | 2 | yes | — |
| 35 | C2×#103×C89 | — | 2 | 2 | no | — |
| 36 | C2×#97×C89 | C22 | 1 | 1 | yes | characteristic |
| 37 | #15668011 | — | 2 | 2 | no | — |
| 38 | #15668007 | — | 2 | 2 | no | — |
| 39 | #15668007 | — | 2 | 2 | no | — |
| 40 | #15668007 | — | 2 | 2 | no | — |
| 41 | #15668007 | — | 2 | 2 | no | — |
| 42 | #15668006 | — | 2 | 2 | no | — |
| 43 | #15668004 | C23 | 1 | 2 | yes | — |
| 44 | #15668003 | — | 2 | 2 | no | — |
| 45 | #15668002 | — | 2 | 2 | no | — |
| 46 | #15668002 | — | 2 | 2 | no | — |
| 47 | #15668002 | — | 2 | 2 | no | — |
| 48 | #15668002 | — | 2 | 2 | no | — |
| 49 | #15668000 | C23 | 1 | 2 | yes | — |
| 50 | #15667997 | — | 2 | 2 | no | — |
| 51 | #15667997 | — | 2 | 2 | no | — |
| 52 | #15667997 | — | 2 | 2 | no | — |
| 53 | #15667997 | — | 2 | 2 | no | — |
| 54 | #15667995 | — | 2 | 2 | no | — |
| 55 | #15667992 | — | 2 | 2 | no | — |
| 56 | #15667991 | — | 2 | 2 | no | — |
| 57 | #15667991 | D4 | 1 | 2 | yes | — |
| 58 | #15667990 | — | 2 | 2 | no | — |
| 59 | #15667990 | — | 2 | 2 | no | — |
| 60 | #15667990 | — | 2 | 2 | no | — |
| 61 | #15667990 | — | 2 | 2 | no | — |
| 62 | #15667987 | — | 2 | 2 | no | — |
| 63 | #15667986 | — | 2 | 2 | no | — |
| 64 | #15667986 | D4 | 1 | 2 | yes | — |
| 65 | C4×Dic178 | D4 | 1 | 2 | yes | — |
| 66 | #15667977 | — | 2 | 2 | no | — |
| 67 | C4×D356 | D4 | 1 | 2 | yes | — |
| 68 | #15667974 | — | 2 | 2 | no | — |
| 69 | C4×C22⋊D89 | — | 2 | 2 | no | — |
| 70 | C4×C22⋊D89 | — | 2 | 2 | no | — |
| 71 | C4×C22⋊D89 | — | 2 | 2 | no | — |
| 72 | #15667970 | — | 2 | 2 | no | — |
| 73 | #15667969 | — | 2 | 2 | no | — |
| 74 | C4⋊C4×D89 | — | 2 | 2 | no | — |
| 75 | #15667945 | — | 2 | 4 | no | — |
| 76 | #15667943 | — | 2 | 4 | no | — |
| 77 | C4⋊#10623494 | — | 2 | 2 | no | — |
| 78 | #15667935 | — | 2 | 4 | no | — |
| 79 | #15667932 | — | 2 | 4 | no | — |
| 80 | C22⋊#10623494 | — | 2 | 2 | no | — |
| 81 | #15667923 | C23 | 1 | 4 | yes | — |
| 82 | C22×Q8×C89 | — | 2 | 1 | no | — |
| 83 | C22×C8×C89 | — | 2 | 1 | no | — |
| 84 | C4⋊Q8×C89 | — | 2 | 2 | no | — |
| 85 | C4⋊Q8×C89 | — | 2 | 1 | no | — |
| 86 | C4⋊Q8×C89 | C23 | 1 | 2 | yes | — |
| 87 | #125×C89 | — | 2 | 2 | no | — |
| 88 | #125×C89 | D4 | 1 | 2 | yes | — |
| 89 | #125×C89 | C23 | 1 | 1 | yes | characteristic |
| 90 | #125×C89 | C23 | 1 | 1 | yes | characteristic |
| 91 | C2×C4⋊C4×C89 | — | 2 | 2 | no | — |
| 92 | C2×C4⋊C4×C89 | — | 2 | 2 | no | — |
| 93 | C2×C4⋊C4×C89 | D4 | 1 | 2 | yes | — |
| 94 | C2×C42×C89 | C23 | 1 | 1 | yes | characteristic |
| 95 | #103×C89 | — | 2 | 4 | no | — |
| 96 | #103×C89 | — | 2 | 4 | no | — |
| 97 | #97×C89 | — | 2 | 1 | no | — |
| 98 | #97×C89 | C23 | 1 | 2 | yes | — |
| 99 | C2×Dic178 | — | 2 | 2 | no | — |
| 100 | C2×Dic178 | C2×D4 | 1 | 2 | yes | — |
| 101 | C2×D356 | — | 2 | 2 | no | — |
| 102 | C2×D356 | C2×D4 | 1 | 2 | yes | — |
| 103 | C2×C22⋊D89 | — | 2 | 2 | no | — |
| 104 | C2×C4×D89 | — | 2 | 2 | no | — |
| 105 | C2×C4×D89 | — | 2 | 2 | no | — |
| 106 | C2×C4×D89 | — | 2 | 2 | no | — |
| 107 | C2×#10623494 | — | 2 | 4 | no | — |
| 108 | C4⋊Dic89 | — | 2 | 2 | no | — |
| 109 | C4⋊Dic89 | — | 2 | 2 | no | — |
| 110 | C4⋊Dic89 | C2×D4 | 1 | 2 | yes | — |
| 111 | C4⋊Dic89 | C2×D4 | 1 | 2 | yes | — |
| 112 | #13083553 | — | 2 | 2 | no | — |
| 113 | #13083553 | — | 2 | 2 | no | — |
| 114 | #13083553 | — | 2 | 2 | no | — |
| 115 | #13083553 | — | 2 | 2 | no | — |
| 116 | #13083553 | — | 2 | 2 | no | — |
| 117 | #13083553 | — | 2 | 2 | no | — |
| 118 | #13083553 | — | 2 | 2 | no | — |
| 119 | #13083553 | — | 2 | 2 | no | — |
| 120 | C22⋊Dic89 | — | 2 | 2 | no | — |
| 121 | #13083551 | — | 2 | 2 | no | — |
| 122 | #13083551 | — | 2 | 2 | no | — |
| 123 | #13083551 | — | 2 | 2 | no | — |
| 124 | #13083551 | — | 2 | 2 | no | — |
| 125 | #13083551 | — | 2 | 2 | no | — |
| 126 | #13083551 | — | 2 | 2 | no | — |
| 127 | #13083551 | — | 2 | 2 | no | — |
| 128 | #13083551 | — | 2 | 2 | no | — |
| 129 | C4×Dic89 | — | 2 | 2 | no | — |
| 130 | C4×Dic89 | — | 2 | 2 | no | — |
| 131 | C4×Dic89 | — | 2 | 2 | no | — |
| 132 | C2×Q8×C89 | — | 2 | 2 | no | — |
| 133 | C2×Q8×C89 | — | 4 | 4 | no | — |
| 134 | C2×Q8×C89 | — | 4 | 1 | no | — |
| 135 | C22×C4×C89 | — | 2 | 2 | no | — |
| 136 | C22×C4×C89 | — | 4 | 1 | no | — |
| 137 | C22×C4×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 138 | C22×C4×C89 | C2×D4 | 1 | 2 | yes | — |
| 139 | C2×C8×C89 | — | 2 | 2 | no | — |
| 140 | C2×C8×C89 | — | 4 | 2 | no | — |
| 141 | C4⋊C4×C89 | — | 2 | 2 | no | — |
| 142 | C4⋊C4×C89 | — | 2 | 2 | no | — |
| 143 | C4⋊C4×C89 | — | 2 | 2 | no | — |
| 144 | C4⋊C4×C89 | — | 2 | 2 | no | — |
| 145 | C4⋊C4×C89 | — | 2 | 2 | no | — |
| 146 | C4⋊C4×C89 | — | 2 | 4 | no | — |
| 147 | C4⋊C4×C89 | — | 4 | 2 | no | — |
| 148 | C4⋊C4×C89 | C2×D4 | 1 | 2 | yes | — |
| 149 | C4⋊C4×C89 | C2×D4 | 1 | 2 | yes | — |
| 150 | C42×C89 | C2×D4 | 1 | 2 | yes | — |
| 151 | C42×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 152 | C42×C89 | C24 | 1 | 1 | yes | characteristic |
| 153 | C23×C89 | #120 | 1 | 1 | yes | characteristic |
| 154 | C22×D89 | — | 2 | 2 | no | — |
| 155 | Q8×C89 | — | 4 | 4 | no | — |
| 156 | Q8×C89 | — | 8 | 2 | no | — |
| 157 | C2×C4×C89 | — | 2 | 2 | no | — |
| 158 | C2×C4×C89 | — | 2 | 2 | no | — |
| 159 | C2×C4×C89 | — | 2 | 2 | no | — |
| 160 | C2×C4×C89 | — | 4 | 2 | no | — |
| 161 | C2×C4×C89 | — | 4 | 2 | no | — |
| 162 | C2×C4×C89 | — | 8 | 2 | no | — |
| 163 | C2×C4×C89 | — | 8 | 2 | no | — |
| 164 | C2×C4×C89 | #120 | 1 | 2 | yes | — |
| 165 | C2×C4×C89 | #120 | 1 | 1 | yes | characteristic |
| 166 | C2×C4×C89 | C22×D4 | 1 | 2 | yes | — |
| 167 | C2×C4×C89 | C22×D4 | 1 | 1 | yes | characteristic |
| 168 | C22⋊D89 | — | 4 | 4 | no | — |
| 169 | C2×Dic89 | — | 2 | 2 | no | — |
| 170 | C2×Dic89 | — | 2 | 2 | no | — |
| 171 | C2×Dic89 | — | 2 | 2 | no | — |
| 172 | D356 | — | 4 | 2 | no | — |
| 173 | D356 | — | 8 | 2 | no | — |
| 174 | C4×D89 | — | 8 | 2 | no | — |
| 175 | C4×D89 | — | 8 | 2 | no | — |
| 176 | C4×D89 | — | 8 | 2 | no | — |
| 177 | Dic178 | — | 4 | 2 | no | — |
| 178 | Dic178 | — | 8 | 2 | no | — |
| 179 | C8×C89 | — | 4 | 2 | no | — |
| 180 | #10623494 | — | 4 | 4 | no | — |
| 181 | C22×C89 | — | 2 | 2 | no | — |
| 182 | C22×C89 | #454 | 1 | 2 | yes | — |
| 183 | C22×C89 | C2×#120 | 1 | 1 | yes | characteristic |
| 184 | C2×D89 | — | 4 | 2 | no | — |
| 185 | C2×D89 | — | 4 | 2 | no | — |
| 186 | C2×D89 | — | 4 | 2 | no | — |
| 187 | C4×C89 | — | 2 | 1 | no | — |
| 188 | C4×C89 | — | 2 | 1 | no | — |
| 189 | C4×C89 | — | 2 | 2 | no | — |
| 190 | C4×C89 | — | 2 | 2 | no | — |
| 191 | C4×C89 | — | 4 | 2 | no | — |
| 192 | C4×C89 | — | 4 | 2 | no | — |
| 193 | C4×C89 | — | 8 | 2 | no | — |
| 194 | Dic89 | — | 4 | 2 | no | — |
| 195 | Dic89 | — | 4 | 2 | no | — |
| 196 | Dic89 | — | 4 | 2 | no | — |
| 197 | #19060 | — | 89 | 1 | no | maximal, Sylow |
| 198 | C2×C89 | — | 2 | 2 | no | — |
| 199 | C2×C89 | C2×#454 | 1 | 1 | yes | characteristic |
| 200 | C2×C89 | #3022 | 1 | 2 | yes | — |
| 201 | D89 | — | 8 | 2 | no | — |
| 202 | #3553 | — | 89 | 1 | no | — |
| 203 | #3238 | — | 89 | 2 | no | — |
| 204 | C2×#491 | D89 | 1 | 1 | yes | characteristic, complemented |
| 205 | #1664 | — | 89 | 4 | no | — |
| 206 | #1663 | — | 89 | 2 | no | — |
| 207 | #1662 | — | 89 | 2 | no | — |
| 208 | #1534 | — | 89 | 1 | no | — |
| 209 | #1532 | — | 89 | 2 | no | — |
| 210 | C89 | #19060 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 211 | #564 | — | 89 | 1 | no | — |
| 212 | #563 | — | 89 | 2 | no | — |
| 213 | #562 | — | 89 | 1 | no | — |
| 214 | #554 | — | 178 | 2 | no | — |
| 215 | #553 | — | 178 | 2 | no | — |
| 216 | #552 | — | 178 | 2 | no | — |
| 217 | #541 | — | 178 | 2 | no | — |
| 218 | #539 | — | 178 | 2 | no | — |
| 219 | #539 | — | 178 | 2 | no | — |
| 220 | C2×C4⋊Q8 | C2×D89 | 1 | 1 | yes | characteristic |
| 221 | #529 | — | 89 | 2 | no | — |
| 222 | C2×#125 | C2×D89 | 1 | 1 | yes | characteristic |
| 223 | #501 | — | 89 | 4 | no | — |
| 224 | #491 | — | 2 | 2 | no | — |
| 225 | #491 | C2×D89 | 1 | 2 | yes | — |
| 226 | #491 | C2×D89 | 1 | 2 | yes | — |
| 227 | #489 | — | 89 | 4 | no | — |
| 228 | #483 | — | 178 | 2 | no | — |
| 229 | #480 | — | 178 | 2 | no | — |
| 230 | #477 | — | 178 | 2 | no | — |
| 231 | #476 | — | 178 | 2 | no | — |
| 232 | #432 | — | 89 | 2 | no | — |
| 233 | C2×#103 | — | 2 | 2 | no | — |
| 234 | C2×#97 | C2×D89 | 1 | 1 | yes | characteristic |
| 235 | #330 | — | 89 | 2 | no | — |
| 236 | #330 | — | 89 | 2 | no | — |
| 237 | #330 | — | 89 | 4 | no | — |
| 238 | #329 | — | 89 | 4 | no | — |
| 239 | C22×Q8 | — | 2 | 1 | no | — |
| 240 | C22×C8 | — | 2 | 1 | no | — |
| 241 | C4⋊Q8 | — | 2 | 2 | no | — |
| 242 | C4⋊Q8 | — | 2 | 1 | no | — |
| 243 | C4⋊Q8 | — | 178 | 2 | no | — |
| 244 | C4⋊Q8 | C22×D89 | 1 | 2 | yes | — |
| 245 | #126 | — | 178 | 2 | no | — |
| 246 | #126 | — | 178 | 2 | no | — |
| 247 | #126 | — | 178 | 2 | no | — |
| 248 | #126 | — | 178 | 2 | no | — |
| 249 | #126 | — | 178 | 2 | no | — |
| 250 | #125 | — | 2 | 2 | no | — |
| 251 | #125 | — | 89 | 2 | no | — |
| 252 | #125 | — | 178 | 2 | no | — |
| 253 | #125 | — | 178 | 2 | no | — |
| 254 | #125 | — | 178 | 2 | no | — |
| 255 | #125 | — | 178 | 2 | no | — |
| 256 | #125 | — | 178 | 2 | no | — |
| 257 | #125 | C22⋊D89 | 1 | 2 | yes | — |
| 258 | #125 | C22×D89 | 1 | 1 | yes | characteristic |
| 259 | #125 | C22×D89 | 1 | 1 | yes | characteristic |
| 260 | #124 | — | 89 | 2 | no | — |
| 261 | #123 | — | 178 | 2 | no | — |
| 262 | #123 | — | 178 | 2 | no | — |
| 263 | #123 | — | 178 | 2 | no | — |
| 264 | #123 | — | 178 | 2 | no | — |
| 265 | #123 | — | 178 | 2 | no | — |
| 266 | C22⋊Q8 | — | 89 | 2 | no | — |
| 267 | C22⋊Q8 | — | 178 | 2 | no | — |
| 268 | C22⋊Q8 | — | 178 | 2 | no | — |
| 269 | C22⋊Q8 | — | 178 | 2 | no | — |
| 270 | C22⋊Q8 | — | 178 | 2 | no | — |
| 271 | C22⋊Q8 | — | 178 | 2 | no | — |
| 272 | C22⋊Q8 | — | 178 | 2 | no | — |
| 273 | #121 | — | 89 | 2 | no | — |
| 274 | #121 | — | 178 | 2 | no | — |
| 275 | #121 | — | 178 | 2 | no | — |
| 276 | C4×Q8 | — | 89 | 2 | no | — |
| 277 | C4×Q8 | — | 178 | 2 | no | — |
| 278 | C4×D4 | — | 89 | 2 | no | — |
| 279 | C4×D4 | — | 178 | 2 | no | — |
| 280 | C4×D4 | — | 178 | 2 | no | — |
| 281 | C4×D4 | — | 178 | 2 | no | — |
| 282 | C4×D4 | — | 178 | 2 | no | — |
| 283 | #117 | — | 178 | 2 | no | — |
| 284 | #117 | — | 178 | 2 | no | — |
| 285 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 286 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 287 | C2×C4⋊C4 | — | 178 | 2 | no | — |
| 288 | C2×C4⋊C4 | C22⋊D89 | 1 | 2 | yes | — |
| 289 | C2×C42 | C22×D89 | 1 | 1 | yes | characteristic |
| 290 | #107 | — | 178 | 4 | no | — |
| 291 | #106 | — | 178 | 4 | no | — |
| 292 | C4⋊C8 | — | 178 | 2 | no | — |
| 293 | #103 | — | 2 | 4 | no | — |
| 294 | #103 | — | 2 | 4 | no | — |
| 295 | #103 | — | 178 | 4 | no | — |
| 296 | #102 | — | 178 | 4 | no | — |
| 297 | C22⋊C8 | — | 178 | 2 | no | — |
| 298 | #97 | — | 2 | 1 | no | — |
| 299 | #97 | — | 89 | 4 | no | — |
| 300 | #97 | C22×D89 | 1 | 2 | yes | — |
| 301 | C2×Q8 | — | 2 | 2 | no | — |
| 302 | C2×Q8 | — | 4 | 4 | no | — |
| 303 | C2×Q8 | — | 4 | 1 | no | — |
| 304 | C2×Q8 | — | 89 | 2 | no | — |
| 305 | C2×Q8 | — | 178 | 2 | no | — |
| 306 | C2×D4 | — | 89 | 2 | no | — |
| 307 | C2×D4 | — | 178 | 2 | no | — |
| 308 | C2×D4 | — | 178 | 2 | no | — |
| 309 | C22×C4 | — | 2 | 2 | no | — |
| 310 | C22×C4 | — | 4 | 1 | no | — |
| 311 | C22×C4 | — | 178 | 2 | no | — |
| 312 | C22×C4 | — | 178 | 2 | no | — |
| 313 | C22×C4 | — | 178 | 2 | no | — |
| 314 | C22×C4 | D4×D89 | 1 | 2 | yes | — |
| 315 | C22×C4 | C2×C22⋊D89 | 1 | 1 | yes | characteristic |
| 316 | C2×C8 | — | 2 | 2 | no | — |
| 317 | C2×C8 | — | 4 | 2 | no | — |
| 318 | C2×C8 | — | 178 | 4 | no | — |
| 319 | C4⋊C4 | — | 2 | 2 | no | — |
| 320 | C4⋊C4 | — | 2 | 2 | no | — |
| 321 | C4⋊C4 | — | 2 | 2 | no | — |
| 322 | C4⋊C4 | — | 2 | 2 | no | — |
| 323 | C4⋊C4 | — | 2 | 2 | no | — |
| 324 | C4⋊C4 | — | 2 | 4 | no | — |
| 325 | C4⋊C4 | — | 4 | 2 | no | — |
| 326 | C4⋊C4 | — | 89 | 2 | no | — |
| 327 | C4⋊C4 | — | 89 | 2 | no | — |
| 328 | C4⋊C4 | — | 178 | 2 | no | — |
| 329 | C4⋊C4 | — | 178 | 2 | no | — |
| 330 | C4⋊C4 | — | 178 | 2 | no | — |
| 331 | C4⋊C4 | — | 178 | 2 | no | — |
| 332 | C4⋊C4 | — | 178 | 2 | no | — |
| 333 | C4⋊C4 | — | 178 | 2 | no | — |
| 334 | C4⋊C4 | — | 178 | 2 | no | — |
| 335 | C4⋊C4 | — | 178 | 2 | no | — |
| 336 | C4⋊C4 | — | 178 | 2 | no | — |
| 337 | C4⋊C4 | — | 178 | 2 | no | — |
| 338 | C4⋊C4 | C2×C22⋊D89 | 1 | 2 | yes | — |
| 339 | C4⋊C4 | C2×C22⋊D89 | 1 | 2 | yes | — |
| 340 | C22⋊C4 | — | 178 | 2 | no | — |
| 341 | C22⋊C4 | — | 178 | 2 | no | — |
| 342 | C22⋊C4 | — | 178 | 2 | no | — |
| 343 | C22⋊C4 | — | 178 | 2 | no | — |
| 344 | C22⋊C4 | — | 178 | 2 | no | — |
| 345 | C22⋊C4 | — | 178 | 2 | no | — |
| 346 | C22⋊C4 | — | 178 | 2 | no | — |
| 347 | C22⋊C4 | — | 178 | 2 | no | — |
| 348 | C22⋊C4 | — | 178 | 2 | no | — |
| 349 | C42 | — | 178 | 2 | no | — |
| 350 | C42 | — | 178 | 2 | no | — |
| 351 | C42 | — | 178 | 2 | no | — |
| 352 | C42 | D4×D89 | 1 | 2 | yes | — |
| 353 | C42 | C2×C22⋊D89 | 1 | 1 | yes | characteristic |
| 354 | C42 | C23×D89 | 1 | 1 | yes | characteristic |
| 355 | C23 | — | 178 | 2 | no | — |
| 356 | C23 | #15667980 | 1 | 1 | yes | characteristic |
| 357 | Q8 | — | 4 | 4 | no | — |
| 358 | Q8 | — | 8 | 2 | no | — |
| 359 | Q8 | — | 356 | 2 | no | — |
| 360 | Q8 | — | 712 | 2 | no | — |
| 361 | D4 | — | 356 | 2 | no | — |
| 362 | D4 | — | 356 | 4 | no | — |
| 363 | D4 | — | 712 | 2 | no | — |
| 364 | C2×C4 | — | 2 | 2 | no | — |
| 365 | C2×C4 | — | 2 | 2 | no | — |
| 366 | C2×C4 | — | 2 | 2 | no | — |
| 367 | C2×C4 | — | 4 | 2 | no | — |
| 368 | C2×C4 | — | 4 | 2 | no | — |
| 369 | C2×C4 | — | 8 | 2 | no | — |
| 370 | C2×C4 | — | 8 | 2 | no | — |
| 371 | C2×C4 | — | 178 | 2 | no | — |
| 372 | C2×C4 | — | 178 | 2 | no | — |
| 373 | C2×C4 | — | 178 | 2 | no | — |
| 374 | C2×C4 | — | 712 | 2 | no | — |
| 375 | C2×C4 | — | 712 | 2 | no | — |
| 376 | C2×C4 | — | 712 | 2 | no | — |
| 377 | C2×C4 | #15667980 | 1 | 2 | yes | — |
| 378 | C2×C4 | #15667980 | 1 | 1 | yes | characteristic |
| 379 | C2×C4 | C2×D4×D89 | 1 | 2 | yes | — |
| 380 | C2×C4 | C22×C22⋊D89 | 1 | 1 | yes | characteristic |
| 381 | C8 | — | 4 | 2 | no | — |
| 382 | C8 | — | 356 | 4 | no | — |
| 383 | C22 | — | 2 | 2 | no | — |
| 384 | C22 | — | 356 | 2 | no | — |
| 385 | C22 | — | 356 | 2 | no | — |
| 386 | C22 | — | 356 | 2 | no | — |
| 387 | C22 | #19151770 | 1 | 2 | yes | — |
| 388 | C22 | C2×#15667980 | 1 | 1 | yes | characteristic |
| 389 | C4 | — | 2 | 1 | no | — |
| 390 | C4 | — | 2 | 1 | no | — |
| 391 | C4 | — | 2 | 2 | no | — |
| 392 | C4 | — | 2 | 2 | no | — |
| 393 | C4 | — | 4 | 2 | no | — |
| 394 | C4 | — | 4 | 2 | no | — |
| 395 | C4 | — | 8 | 2 | no | — |
| 396 | C4 | — | 356 | 2 | no | — |
| 397 | C4 | — | 356 | 2 | no | — |
| 398 | C4 | — | 356 | 2 | no | — |
| 399 | C2 | — | 2 | 2 | no | — |
| 400 | C2 | — | 712 | 2 | no | — |
| 401 | C2 | C2×#19151770 | 1 | 1 | yes | characteristic |
| 402 | C2 | #26029628 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #26031473 | C2 | semidirect |
| 3. #26019583 | C2 | semidirect |
| 4. #26019578 | C2 | semidirect |
| 5. #26019573 | C2 | semidirect |
| 6. #26018879 | C2 | semidirect |
| 7. #26018870 | C2 | semidirect |
| 8. C2×#491×C89 | C2 | semidirect |
| 204. C2×#491 | D89 | semidirect |
| 210. C89 | #19060 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034708 | 2 |
| #26031473 | 2 |
| #26019583 | 2 |
| #26019578 | 2 |
| #26019573 | 2 |
| #26018879 | 2 |
| #26018870 | 2 |
| C2×#491×C89 | 2 |
| #19060 | 89 |