Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1012 conjugacy classes of subgroups.
The subgroup lattice has 606 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #26034817 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #26031272 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#19151987 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #26030628 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #26019552 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #26019547 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #26018851 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #26018838 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C89×#1531 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C22×#13083563 | — | 2 | 1 | no | — |
| 11 | C22×D712 | — | 2 | 1 | no | — |
| 12 | #19152352 | C22 | 1 | 2 | yes | complemented |
| 13 | #19152346 | C22 | 1 | 2 | yes | complemented |
| 14 | #19152320 | — | 2 | 1 | no | — |
| 15 | #19152272 | — | 2 | 2 | no | — |
| 16 | #19152261 | — | 2 | 1 | no | — |
| 17 | #19152260 | — | 2 | 1 | no | — |
| 18 | #19152239 | — | 2 | 1 | no | — |
| 19 | #19152223 | — | 2 | 1 | no | — |
| 20 | #19152222 | — | 2 | 1 | no | — |
| 21 | #19152220 | — | 2 | 2 | no | — |
| 22 | #19152188 | — | 2 | 1 | no | — |
| 23 | #19152173 | — | 2 | 1 | no | — |
| 24 | C2×#15668009 | C22 | 1 | 1 | yes | characteristic |
| 25 | #19152132 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×#15668000 | C22 | 1 | 1 | yes | characteristic |
| 27 | #19151987 | — | 2 | 2 | no | — |
| 28 | #19151987 | C22 | 1 | 4 | yes | — |
| 29 | #19151987 | C22 | 1 | 2 | yes | complemented |
| 30 | #19151964 | C22 | 1 | 4 | yes | complemented |
| 31 | #19151963 | C22 | 1 | 2 | yes | complemented |
| 32 | #19151946 | — | 2 | 1 | no | — |
| 33 | #19151946 | — | 2 | 1 | no | — |
| 34 | #19151799 | — | 2 | 1 | no | — |
| 35 | #19151794 | — | 2 | 1 | no | — |
| 36 | #19151751 | — | 2 | 1 | no | — |
| 37 | #19151734 | — | 2 | 1 | no | — |
| 38 | #19151602 | — | 2 | 2 | no | — |
| 39 | C4×#13083558 | C22 | 1 | 1 | yes | characteristic |
| 40 | #19151339 | C22 | 1 | 2 | yes | complemented |
| 41 | #19151337 | C22 | 1 | 2 | yes | complemented |
| 42 | #19151337 | C22 | 1 | 4 | yes | complemented |
| 43 | #533×C89 | C22 | 1 | 1 | yes | characteristic |
| 44 | #432×C89 | C22 | 1 | 1 | yes | characteristic |
| 45 | C2×#97×C89 | C22 | 1 | 1 | yes | characteristic |
| 46 | #330×C89 | C22 | 1 | 4 | yes | complemented |
| 47 | C2×#13083575 | — | 2 | 1 | no | — |
| 48 | C22×Dic178 | D4 | 1 | 1 | yes | characteristic |
| 49 | C2×Q8×D89 | — | 2 | 1 | no | — |
| 50 | C22×D356 | — | 2 | 1 | no | — |
| 51 | C22×D356 | — | 2 | 1 | no | — |
| 52 | C22×D356 | — | 2 | 1 | no | — |
| 53 | C22×D356 | D4 | 1 | 1 | yes | characteristic |
| 54 | C2×#13083563 | — | 2 | 4 | no | — |
| 55 | C2×#13083563 | — | 2 | 2 | no | — |
| 56 | C2×#13083563 | — | 4 | 4 | no | — |
| 57 | C2×D712 | — | 2 | 4 | no | — |
| 58 | C2×D712 | — | 2 | 2 | no | — |
| 59 | C2×D712 | — | 4 | 4 | no | — |
| 60 | C2×#13083558 | — | 2 | 1 | no | — |
| 61 | #15668011 | — | 2 | 2 | no | — |
| 62 | #15668010 | — | 2 | 1 | no | — |
| 63 | #15668009 | — | 2 | 1 | no | — |
| 64 | #15668009 | — | 2 | 1 | no | — |
| 65 | #15668009 | — | 2 | 1 | no | — |
| 66 | #15668009 | C23 | 1 | 2 | yes | — |
| 67 | #15668007 | — | 2 | 2 | no | — |
| 68 | #15668007 | — | 2 | 2 | no | — |
| 69 | #15668006 | — | 2 | 2 | no | — |
| 70 | #15668006 | — | 2 | 1 | no | — |
| 71 | #15668004 | C23 | 1 | 1 | yes | characteristic |
| 72 | #15668001 | — | 2 | 1 | no | — |
| 73 | #15668001 | — | 2 | 2 | no | — |
| 74 | #15668000 | — | 2 | 2 | no | — |
| 75 | #15668000 | — | 2 | 1 | no | — |
| 76 | #15668000 | — | 2 | 1 | no | — |
| 77 | #15668000 | D4 | 1 | 2 | yes | — |
| 78 | #15668000 | C23 | 1 | 1 | yes | characteristic |
| 79 | #15668000 | C23 | 1 | 2 | yes | — |
| 80 | #15667997 | — | 2 | 2 | no | — |
| 81 | #15667997 | — | 2 | 2 | no | — |
| 82 | #15667997 | — | 2 | 2 | no | — |
| 83 | #15667997 | — | 2 | 2 | no | — |
| 84 | #15667995 | — | 2 | 1 | no | — |
| 85 | #15667992 | — | 2 | 1 | no | — |
| 86 | #15667992 | — | 2 | 2 | no | — |
| 87 | #15667991 | D4 | 1 | 1 | yes | characteristic |
| 88 | #15667990 | — | 2 | 2 | no | — |
| 89 | #15667990 | — | 2 | 2 | no | — |
| 90 | #15667990 | — | 2 | 2 | no | — |
| 91 | #15667990 | — | 2 | 2 | no | — |
| 92 | #15667989 | — | 2 | 2 | no | — |
| 93 | #15667988 | — | 2 | 2 | no | — |
| 94 | #15667987 | — | 2 | 1 | no | — |
| 95 | #15667987 | — | 2 | 2 | no | — |
| 96 | #15667987 | — | 2 | 2 | no | — |
| 97 | #15667986 | D4 | 1 | 1 | yes | characteristic |
| 98 | #15667982 | — | 2 | 2 | no | — |
| 99 | C4×Dic178 | D4 | 1 | 1 | yes | characteristic |
| 100 | #15667977 | — | 2 | 1 | no | — |
| 101 | C4×D356 | — | 2 | 2 | no | — |
| 102 | C4×D356 | D4 | 1 | 1 | yes | characteristic |
| 103 | #15667974 | — | 2 | 1 | no | — |
| 104 | C4×C22⋊D89 | — | 2 | 1 | no | — |
| 105 | #15667972 | — | 2 | 2 | no | — |
| 106 | #15667969 | — | 2 | 2 | no | — |
| 107 | #15667969 | — | 2 | 1 | no | — |
| 108 | C2×#13083551 | — | 2 | 1 | no | — |
| 109 | C2×#13083551 | — | 2 | 1 | no | — |
| 110 | C22⋊C4×D89 | — | 2 | 2 | no | — |
| 111 | #15667934 | — | 2 | 2 | no | — |
| 112 | #15667934 | — | 2 | 2 | no | — |
| 113 | #15667932 | — | 2 | 4 | no | — |
| 114 | #15667932 | — | 2 | 4 | no | — |
| 115 | #15667923 | C23 | 1 | 2 | yes | — |
| 116 | C4×#10623494 | — | 2 | 1 | no | — |
| 117 | C22×C8×C89 | — | 2 | 1 | no | — |
| 118 | C4⋊Q8×C89 | D4 | 1 | 1 | yes | characteristic |
| 119 | C4⋊Q8×C89 | D4 | 1 | 1 | yes | characteristic |
| 120 | #125×C89 | C23 | 1 | 2 | yes | — |
| 121 | C22⋊Q8×C89 | — | 2 | 1 | no | — |
| 122 | C22⋊Q8×C89 | — | 2 | 1 | no | — |
| 123 | C4×Q8×C89 | — | 2 | 1 | no | — |
| 124 | C4×Q8×C89 | — | 2 | 1 | no | — |
| 125 | #117×C89 | D4 | 1 | 2 | yes | — |
| 126 | C2×C42×C89 | C23 | 1 | 1 | yes | characteristic |
| 127 | C4⋊C8×C89 | — | 2 | 1 | no | — |
| 128 | C22⋊C8×C89 | — | 2 | 1 | no | — |
| 129 | #97×C89 | — | 2 | 1 | no | — |
| 130 | #97×C89 | C23 | 1 | 2 | yes | — |
| 131 | #97×C89 | C23 | 1 | 2 | yes | — |
| 132 | C23×D89 | — | 2 | 1 | no | — |
| 133 | C23×D89 | — | 4 | 1 | no | — |
| 134 | #13083575 | — | 8 | 2 | no | — |
| 135 | C2×Dic178 | — | 2 | 1 | no | — |
| 136 | C2×Dic178 | — | 2 | 2 | no | — |
| 137 | C2×Dic178 | — | 4 | 2 | no | — |
| 138 | C2×Dic178 | C2×D4 | 1 | 1 | yes | characteristic |
| 139 | C2×Dic178 | C2×D4 | 1 | 2 | yes | — |
| 140 | Q8×D89 | — | 8 | 2 | no | — |
| 141 | C2×D356 | — | 2 | 1 | no | — |
| 142 | C2×D356 | — | 2 | 2 | no | — |
| 143 | C2×D356 | — | 2 | 2 | no | — |
| 144 | C2×D356 | — | 2 | 2 | no | — |
| 145 | C2×D356 | — | 2 | 2 | no | — |
| 146 | C2×D356 | — | 2 | 2 | no | — |
| 147 | C2×D356 | — | 4 | 2 | no | — |
| 148 | C2×D356 | — | 4 | 2 | no | — |
| 149 | C2×D356 | — | 4 | 2 | no | — |
| 150 | C2×D356 | — | 4 | 4 | no | — |
| 151 | C2×D356 | — | 4 | 1 | no | — |
| 152 | C2×D356 | — | 4 | 1 | no | — |
| 153 | C2×D356 | — | 4 | 1 | no | — |
| 154 | C2×D356 | — | 8 | 2 | no | — |
| 155 | C2×D356 | C2×D4 | 1 | 1 | yes | characteristic |
| 156 | C2×D356 | C2×D4 | 1 | 2 | yes | — |
| 157 | C2×C22⋊D89 | — | 2 | 1 | no | — |
| 158 | C22×Dic89 | — | 2 | 1 | no | — |
| 159 | C2×C4×D89 | — | 2 | 1 | no | — |
| 160 | C2×C4×D89 | — | 2 | 2 | no | — |
| 161 | C2×C4×D89 | — | 2 | 2 | no | — |
| 162 | C2×C4×D89 | — | 2 | 2 | no | — |
| 163 | #13083563 | — | 4 | 8 | no | — |
| 164 | #13083563 | — | 8 | 2 | no | — |
| 165 | D712 | — | 4 | 8 | no | — |
| 166 | D712 | — | 8 | 2 | no | — |
| 167 | #13083558 | — | 4 | 2 | no | — |
| 168 | C2×#10623494 | — | 2 | 2 | no | — |
| 169 | C4⋊Dic89 | — | 2 | 2 | no | — |
| 170 | C4⋊Dic89 | C2×D4 | 1 | 1 | yes | characteristic |
| 171 | C4⋊Dic89 | C2×D4 | 1 | 1 | yes | characteristic |
| 172 | #13083553 | — | 2 | 2 | no | — |
| 173 | #13083553 | — | 2 | 2 | no | — |
| 174 | #13083553 | — | 2 | 2 | no | — |
| 175 | #13083553 | — | 2 | 1 | no | — |
| 176 | #13083553 | — | 2 | 1 | no | — |
| 177 | #13083553 | — | 2 | 1 | no | — |
| 178 | #13083553 | — | 2 | 1 | no | — |
| 179 | C22⋊Dic89 | — | 2 | 1 | no | — |
| 180 | #13083551 | — | 2 | 2 | no | — |
| 181 | #13083551 | — | 2 | 2 | no | — |
| 182 | #13083551 | — | 2 | 2 | no | — |
| 183 | #13083551 | — | 2 | 2 | no | — |
| 184 | #13083551 | — | 2 | 2 | no | — |
| 185 | #13083551 | — | 2 | 2 | no | — |
| 186 | #13083551 | — | 2 | 1 | no | — |
| 187 | #13083551 | — | 2 | 1 | no | — |
| 188 | #13083551 | — | 2 | 2 | no | — |
| 189 | #13083551 | — | 2 | 1 | no | — |
| 190 | #13083551 | — | 2 | 1 | no | — |
| 191 | #13083551 | — | 2 | 2 | no | — |
| 192 | #13083551 | — | 2 | 2 | no | — |
| 193 | C4×Dic89 | — | 2 | 2 | no | — |
| 194 | C4×Dic89 | — | 2 | 1 | no | — |
| 195 | C2×Q8×C89 | — | 2 | 1 | no | — |
| 196 | C2×Q8×C89 | — | 2 | 1 | no | — |
| 197 | C22×C4×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 198 | C22×C4×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 199 | C22×C4×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 200 | C2×C8×C89 | — | 2 | 4 | no | — |
| 201 | C2×C8×C89 | — | 2 | 2 | no | — |
| 202 | C2×C8×C89 | — | 2 | 2 | no | — |
| 203 | C4⋊C4×C89 | — | 2 | 1 | no | — |
| 204 | C4⋊C4×C89 | — | 2 | 1 | no | — |
| 205 | C4⋊C4×C89 | — | 2 | 2 | no | — |
| 206 | C4⋊C4×C89 | — | 2 | 2 | no | — |
| 207 | C4⋊C4×C89 | C2×D4 | 1 | 2 | yes | — |
| 208 | C4⋊C4×C89 | C2×D4 | 1 | 2 | yes | — |
| 209 | C22⋊C4×C89 | — | 2 | 2 | no | — |
| 210 | C42×C89 | — | 2 | 2 | no | — |
| 211 | C42×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 212 | C42×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 213 | C42×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 214 | C42×C89 | C24 | 1 | 1 | yes | characteristic |
| 215 | C23×C89 | #120 | 1 | 1 | yes | characteristic |
| 216 | C22×D89 | — | 2 | 2 | no | — |
| 217 | C22×D89 | — | 2 | 1 | no | — |
| 218 | C22×D89 | — | 4 | 2 | no | — |
| 219 | C22×D89 | — | 4 | 2 | no | — |
| 220 | C22×D89 | — | 8 | 1 | no | — |
| 221 | C22×D89 | — | 8 | 1 | no | — |
| 222 | C22×D89 | — | 8 | 2 | no | — |
| 223 | C22×D89 | — | 8 | 2 | no | — |
| 224 | C22×D89 | — | 8 | 2 | no | — |
| 225 | Q8×C89 | — | 4 | 2 | no | — |
| 226 | Q8×C89 | — | 8 | 1 | no | — |
| 227 | C2×C4×C89 | — | 2 | 2 | no | — |
| 228 | C2×C4×C89 | — | 2 | 2 | no | — |
| 229 | C2×C4×C89 | — | 2 | 2 | no | — |
| 230 | C2×C4×C89 | — | 2 | 2 | no | — |
| 231 | C2×C4×C89 | — | 4 | 1 | no | — |
| 232 | C2×C4×C89 | #120 | 1 | 1 | yes | characteristic |
| 233 | C2×C4×C89 | #120 | 1 | 1 | yes | characteristic |
| 234 | C2×C4×C89 | #120 | 1 | 1 | yes | characteristic |
| 235 | C2×C4×C89 | C22×D4 | 1 | 1 | yes | characteristic |
| 236 | C2×C4×C89 | C22×D4 | 1 | 1 | yes | characteristic |
| 237 | C2×C4×C89 | C22×D4 | 1 | 1 | yes | characteristic |
| 238 | C22⋊D89 | — | 4 | 2 | no | — |
| 239 | C2×Dic89 | — | 2 | 1 | no | — |
| 240 | C2×Dic89 | — | 2 | 2 | no | — |
| 241 | C2×Dic89 | — | 2 | 1 | no | — |
| 242 | C2×Dic89 | — | 2 | 1 | no | — |
| 243 | C2×Dic89 | — | 8 | 1 | no | — |
| 244 | D356 | — | 4 | 2 | no | — |
| 245 | D356 | — | 4 | 1 | no | — |
| 246 | D356 | — | 4 | 2 | no | — |
| 247 | D356 | — | 4 | 2 | no | — |
| 248 | D356 | — | 4 | 2 | no | — |
| 249 | D356 | — | 4 | 2 | no | — |
| 250 | D356 | — | 4 | 4 | no | — |
| 251 | D356 | — | 4 | 2 | no | — |
| 252 | D356 | — | 8 | 2 | no | — |
| 253 | D356 | — | 8 | 2 | no | — |
| 254 | D356 | — | 8 | 2 | no | — |
| 255 | D356 | — | 8 | 2 | no | — |
| 256 | D356 | — | 8 | 2 | no | — |
| 257 | C4×D89 | — | 4 | 2 | no | — |
| 258 | C4×D89 | — | 8 | 2 | no | — |
| 259 | C4×D89 | — | 8 | 2 | no | — |
| 260 | C4×D89 | — | 8 | 2 | no | — |
| 261 | Dic178 | — | 4 | 2 | no | — |
| 262 | Dic178 | — | 4 | 2 | no | — |
| 263 | Dic178 | — | 4 | 1 | no | — |
| 264 | Dic178 | — | 8 | 2 | no | — |
| 265 | C8×C89 | — | 2 | 4 | no | — |
| 266 | C8×C89 | — | 4 | 2 | no | — |
| 267 | #10623494 | — | 4 | 2 | no | — |
| 268 | C22×C89 | — | 2 | 1 | no | — |
| 269 | C22×C89 | — | 2 | 1 | no | — |
| 270 | C22×C89 | #454 | 1 | 2 | yes | — |
| 271 | C22×C89 | C2×#120 | 1 | 1 | yes | characteristic |
| 272 | C2×D89 | — | 4 | 1 | no | — |
| 273 | C2×D89 | — | 4 | 2 | no | — |
| 274 | C2×D89 | — | 4 | 1 | no | — |
| 275 | C2×D89 | — | 4 | 2 | no | — |
| 276 | C2×D89 | — | 4 | 2 | no | — |
| 277 | C2×D89 | — | 4 | 1 | no | — |
| 278 | C2×D89 | — | 8 | 2 | no | — |
| 279 | C2×D89 | — | 8 | 2 | no | — |
| 280 | C2×D89 | — | 8 | 2 | no | — |
| 281 | C2×D89 | — | 16 | 2 | no | — |
| 282 | C2×D89 | — | 16 | 4 | no | — |
| 283 | C4×C89 | — | 2 | 1 | no | — |
| 284 | C4×C89 | — | 2 | 1 | no | — |
| 285 | C4×C89 | — | 2 | 1 | no | — |
| 286 | C4×C89 | — | 2 | 1 | no | — |
| 287 | C4×C89 | — | 2 | 1 | no | — |
| 288 | C4×C89 | — | 4 | 2 | no | — |
| 289 | C4×C89 | — | 4 | 2 | no | — |
| 290 | C4×C89 | #453 | 1 | 2 | yes | — |
| 291 | Dic89 | — | 4 | 2 | no | — |
| 292 | Dic89 | — | 4 | 1 | no | — |
| 293 | Dic89 | — | 4 | 1 | no | — |
| 294 | Dic89 | — | 4 | 1 | no | — |
| 295 | #19026 | — | 89 | 1 | no | maximal, Sylow |
| 296 | C2×C89 | — | 2 | 2 | no | — |
| 297 | C2×C89 | C2×#453 | 1 | 1 | yes | characteristic |
| 298 | C2×C89 | C2×#454 | 1 | 1 | yes | characteristic |
| 299 | C2×C89 | #3021 | 1 | 1 | yes | characteristic |
| 300 | D89 | — | 8 | 1 | no | — |
| 301 | D89 | — | 8 | 2 | no | — |
| 302 | D89 | — | 16 | 2 | no | — |
| 303 | #3561 | — | 89 | 1 | no | — |
| 304 | #3217 | — | 89 | 1 | no | — |
| 305 | C2×#496 | — | 89 | 1 | no | — |
| 306 | #3138 | — | 89 | 1 | no | — |
| 307 | #1657 | — | 89 | 4 | no | — |
| 308 | #1656 | — | 89 | 4 | no | — |
| 309 | #1531 | D89 | 1 | 1 | yes | characteristic, complemented |
| 310 | #1527 | — | 89 | 1 | no | — |
| 311 | #1524 | — | 89 | 1 | no | — |
| 312 | C89 | #19026 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 313 | C22×SD16 | — | 178 | 1 | no | — |
| 314 | C22×D8 | — | 178 | 1 | no | — |
| 315 | #563 | — | 89 | 2 | no | — |
| 316 | #562 | — | 89 | 2 | no | — |
| 317 | #556 | — | 178 | 1 | no | — |
| 318 | #551 | — | 178 | 2 | no | — |
| 319 | D4×Q8 | — | 178 | 1 | no | — |
| 320 | #548 | — | 178 | 1 | no | — |
| 321 | #546 | — | 178 | 1 | no | — |
| 322 | #543 | — | 178 | 1 | no | — |
| 323 | #542 | — | 178 | 2 | no | — |
| 324 | #542 | — | 178 | 1 | no | — |
| 325 | #538 | — | 178 | 1 | no | — |
| 326 | #536 | — | 178 | 1 | no | — |
| 327 | #533 | C2×D89 | 1 | 1 | yes | characteristic |
| 328 | C2×#127 | — | 89 | 1 | no | — |
| 329 | #529 | — | 89 | 1 | no | — |
| 330 | C2×#124 | — | 89 | 1 | no | — |
| 331 | #496 | — | 89 | 4 | no | — |
| 332 | #496 | — | 89 | 2 | no | — |
| 333 | #496 | — | 178 | 2 | no | — |
| 334 | #490 | — | 89 | 4 | no | — |
| 335 | #490 | — | 89 | 2 | no | — |
| 336 | #486 | — | 178 | 1 | no | — |
| 337 | #486 | — | 178 | 1 | no | — |
| 338 | #460 | — | 178 | 1 | no | — |
| 339 | #459 | — | 178 | 1 | no | — |
| 340 | #450 | — | 178 | 1 | no | — |
| 341 | #447 | — | 178 | 1 | no | — |
| 342 | #432 | C2×D89 | 1 | 1 | yes | characteristic |
| 343 | #418 | — | 178 | 2 | no | — |
| 344 | C4×M16 | — | 89 | 1 | no | — |
| 345 | C2×#97 | C2×D89 | 1 | 1 | yes | characteristic |
| 346 | #330 | — | 89 | 2 | no | — |
| 347 | #330 | C2×D89 | 1 | 4 | yes | complemented |
| 348 | #329 | — | 89 | 2 | no | — |
| 349 | #329 | — | 89 | 4 | no | — |
| 350 | C2×#41 | — | 178 | 1 | no | — |
| 351 | C22×Q8 | — | 89 | 1 | no | — |
| 352 | C22×Q8 | — | 178 | 1 | no | — |
| 353 | C22×D4 | — | 89 | 1 | no | — |
| 354 | C22×D4 | — | 178 | 1 | no | — |
| 355 | C22×D4 | — | 178 | 1 | no | — |
| 356 | C22×D4 | — | 178 | 1 | no | — |
| 357 | C2×SD16 | — | 356 | 4 | no | — |
| 358 | C2×SD16 | — | 178 | 4 | no | — |
| 359 | C2×SD16 | — | 178 | 2 | no | — |
| 360 | C2×D8 | — | 356 | 4 | no | — |
| 361 | C2×D8 | — | 178 | 4 | no | — |
| 362 | C2×D8 | — | 178 | 2 | no | — |
| 363 | C2×M16 | — | 178 | 1 | no | — |
| 364 | C22×C8 | — | 2 | 1 | no | — |
| 365 | C4⋊Q8 | — | 178 | 2 | no | — |
| 366 | C4⋊Q8 | — | 178 | 1 | no | — |
| 367 | C4⋊Q8 | D356 | 1 | 1 | yes | characteristic |
| 368 | C4⋊Q8 | D356 | 1 | 1 | yes | characteristic |
| 369 | #127 | — | 89 | 2 | no | — |
| 370 | #127 | — | 178 | 1 | no | — |
| 371 | #127 | — | 178 | 1 | no | — |
| 372 | #127 | — | 178 | 1 | no | — |
| 373 | #126 | — | 178 | 2 | no | — |
| 374 | #126 | — | 178 | 2 | no | — |
| 375 | #126 | — | 178 | 2 | no | — |
| 376 | #126 | — | 178 | 1 | no | — |
| 377 | #125 | — | 89 | 1 | no | — |
| 378 | #125 | C22×D89 | 1 | 2 | yes | — |
| 379 | #124 | — | 89 | 2 | no | — |
| 380 | #124 | — | 89 | 2 | no | — |
| 381 | #124 | — | 89 | 1 | no | — |
| 382 | #124 | — | 178 | 2 | no | — |
| 383 | #124 | — | 178 | 1 | no | — |
| 384 | #124 | — | 178 | 2 | no | — |
| 385 | #124 | — | 178 | 1 | no | — |
| 386 | #124 | — | 178 | 1 | no | — |
| 387 | #123 | — | 178 | 2 | no | — |
| 388 | #123 | — | 178 | 2 | no | — |
| 389 | #123 | — | 178 | 1 | no | — |
| 390 | #123 | — | 178 | 2 | no | — |
| 391 | #123 | — | 178 | 2 | no | — |
| 392 | C22⋊Q8 | — | 2 | 1 | no | — |
| 393 | C22⋊Q8 | — | 2 | 1 | no | — |
| 394 | C22⋊Q8 | — | 89 | 1 | no | — |
| 395 | C22⋊Q8 | — | 178 | 2 | no | — |
| 396 | C22⋊Q8 | — | 178 | 2 | no | — |
| 397 | C22⋊Q8 | — | 178 | 2 | no | — |
| 398 | C22⋊Q8 | — | 178 | 2 | no | — |
| 399 | C22⋊Q8 | — | 178 | 2 | no | — |
| 400 | C22⋊Q8 | — | 178 | 1 | no | — |
| 401 | C22⋊Q8 | — | 178 | 2 | no | — |
| 402 | C22⋊Q8 | — | 178 | 2 | no | — |
| 403 | #121 | — | 89 | 1 | no | — |
| 404 | #121 | — | 178 | 2 | no | — |
| 405 | #121 | — | 178 | 2 | no | — |
| 406 | #121 | — | 178 | 1 | no | — |
| 407 | #120 | — | 178 | 2 | no | — |
| 408 | C4×Q8 | — | 2 | 1 | no | — |
| 409 | C4×Q8 | — | 2 | 1 | no | — |
| 410 | C4×Q8 | — | 89 | 1 | no | — |
| 411 | C4×Q8 | — | 178 | 1 | no | — |
| 412 | C4×D4 | — | 89 | 1 | no | — |
| 413 | C4×D4 | — | 178 | 2 | no | — |
| 414 | C4×D4 | — | 178 | 2 | no | — |
| 415 | C4×D4 | — | 178 | 1 | no | — |
| 416 | C4×D4 | — | 178 | 1 | no | — |
| 417 | #117 | — | 178 | 2 | no | — |
| 418 | #117 | — | 178 | 1 | no | — |
| 419 | #117 | D356 | 1 | 2 | yes | — |
| 420 | C2×C22⋊C4 | — | 178 | 2 | no | — |
| 421 | C2×C22⋊C4 | — | 178 | 1 | no | — |
| 422 | C2×C22⋊C4 | — | 178 | 1 | no | — |
| 423 | C2×C42 | C22×D89 | 1 | 1 | yes | characteristic |
| 424 | C4⋊C8 | — | 2 | 1 | no | — |
| 425 | #102 | — | 178 | 2 | no | — |
| 426 | #102 | — | 178 | 2 | no | — |
| 427 | #102 | — | 178 | 4 | no | — |
| 428 | #102 | — | 178 | 4 | no | — |
| 429 | C22⋊C8 | — | 2 | 1 | no | — |
| 430 | #97 | — | 2 | 1 | no | — |
| 431 | #97 | — | 89 | 2 | no | — |
| 432 | #97 | C22×D89 | 1 | 2 | yes | — |
| 433 | #97 | C22×D89 | 1 | 2 | yes | — |
| 434 | C4×C8 | — | 178 | 1 | no | — |
| 435 | C24 | — | 356 | 1 | no | — |
| 436 | C24 | — | 178 | 1 | no | — |
| 437 | #41 | — | 712 | 2 | no | — |
| 438 | C2×Q8 | — | 2 | 1 | no | — |
| 439 | C2×Q8 | — | 2 | 1 | no | — |
| 440 | C2×Q8 | — | 89 | 1 | no | — |
| 441 | C2×Q8 | — | 89 | 2 | no | — |
| 442 | C2×Q8 | — | 356 | 2 | no | — |
| 443 | C2×Q8 | — | 178 | 2 | no | — |
| 444 | C2×Q8 | — | 178 | 1 | no | — |
| 445 | C2×Q8 | — | 712 | 2 | no | — |
| 446 | C2×D4 | — | 89 | 1 | no | — |
| 447 | C2×D4 | — | 89 | 2 | no | — |
| 448 | C2×D4 | — | 356 | 2 | no | — |
| 449 | C2×D4 | — | 356 | 2 | no | — |
| 450 | C2×D4 | — | 356 | 2 | no | — |
| 451 | C2×D4 | — | 356 | 4 | no | — |
| 452 | C2×D4 | — | 356 | 1 | no | — |
| 453 | C2×D4 | — | 356 | 1 | no | — |
| 454 | C2×D4 | — | 356 | 1 | no | — |
| 455 | C2×D4 | — | 178 | 2 | no | — |
| 456 | C2×D4 | — | 178 | 2 | no | — |
| 457 | C2×D4 | — | 178 | 1 | no | — |
| 458 | C2×D4 | — | 178 | 1 | no | — |
| 459 | C2×D4 | — | 178 | 2 | no | — |
| 460 | C2×D4 | — | 178 | 2 | no | — |
| 461 | C2×D4 | — | 178 | 2 | no | — |
| 462 | C2×D4 | — | 712 | 2 | no | — |
| 463 | C22×C4 | — | 178 | 2 | no | — |
| 464 | C22×C4 | — | 178 | 2 | no | — |
| 465 | C22×C4 | — | 178 | 2 | no | — |
| 466 | C22×C4 | — | 178 | 1 | no | — |
| 467 | C22×C4 | — | 178 | 1 | no | — |
| 468 | C22×C4 | D4×D89 | 1 | 1 | yes | characteristic |
| 469 | C22×C4 | D4×D89 | 1 | 1 | yes | characteristic |
| 470 | C22×C4 | C2×D356 | 1 | 1 | yes | characteristic |
| 471 | SD16 | — | 356 | 8 | no | — |
| 472 | SD16 | — | 712 | 2 | no | — |
| 473 | D8 | — | 356 | 8 | no | — |
| 474 | D8 | — | 712 | 2 | no | — |
| 475 | M16 | — | 356 | 2 | no | — |
| 476 | C2×C8 | — | 2 | 4 | no | — |
| 477 | C2×C8 | — | 2 | 2 | no | — |
| 478 | C2×C8 | — | 2 | 2 | no | — |
| 479 | C2×C8 | — | 178 | 2 | no | — |
| 480 | C4⋊C4 | — | 2 | 1 | no | — |
| 481 | C4⋊C4 | — | 2 | 1 | no | — |
| 482 | C4⋊C4 | — | 2 | 2 | no | — |
| 483 | C4⋊C4 | — | 2 | 2 | no | — |
| 484 | C4⋊C4 | — | 89 | 1 | no | — |
| 485 | C4⋊C4 | — | 89 | 1 | no | — |
| 486 | C4⋊C4 | — | 178 | 2 | no | — |
| 487 | C4⋊C4 | — | 178 | 2 | no | — |
| 488 | C4⋊C4 | — | 178 | 2 | no | — |
| 489 | C4⋊C4 | — | 178 | 2 | no | — |
| 490 | C4⋊C4 | — | 178 | 1 | no | — |
| 491 | C4⋊C4 | — | 178 | 1 | no | — |
| 492 | C4⋊C4 | — | 178 | 1 | no | — |
| 493 | C4⋊C4 | — | 178 | 1 | no | — |
| 494 | C4⋊C4 | C2×D356 | 1 | 2 | yes | — |
| 495 | C4⋊C4 | C2×D356 | 1 | 2 | yes | — |
| 496 | C22⋊C4 | — | 2 | 2 | no | — |
| 497 | C22⋊C4 | — | 178 | 2 | no | — |
| 498 | C22⋊C4 | — | 178 | 2 | no | — |
| 499 | C22⋊C4 | — | 178 | 2 | no | — |
| 500 | C22⋊C4 | — | 178 | 2 | no | — |
| 501 | C22⋊C4 | — | 178 | 2 | no | — |
| 502 | C22⋊C4 | — | 178 | 1 | no | — |
| 503 | C22⋊C4 | — | 178 | 2 | no | — |
| 504 | C22⋊C4 | — | 178 | 2 | no | — |
| 505 | C22⋊C4 | — | 178 | 1 | no | — |
| 506 | C22⋊C4 | — | 178 | 1 | no | — |
| 507 | C22⋊C4 | — | 178 | 2 | no | — |
| 508 | C22⋊C4 | — | 178 | 1 | no | — |
| 509 | C22⋊C4 | — | 178 | 2 | no | — |
| 510 | C22⋊C4 | — | 178 | 1 | no | — |
| 511 | C42 | — | 2 | 2 | no | — |
| 512 | C42 | — | 178 | 2 | no | — |
| 513 | C42 | — | 178 | 1 | no | — |
| 514 | C42 | D4×D89 | 1 | 1 | yes | characteristic |
| 515 | C42 | D4×D89 | 1 | 1 | yes | characteristic |
| 516 | C42 | C2×D356 | 1 | 1 | yes | characteristic |
| 517 | C42 | C23×D89 | 1 | 1 | yes | characteristic |
| 518 | C23 | — | 356 | 2 | no | — |
| 519 | C23 | — | 356 | 2 | no | — |
| 520 | C23 | — | 178 | 2 | no | — |
| 521 | C23 | — | 178 | 1 | no | — |
| 522 | C23 | — | 712 | 1 | no | — |
| 523 | C23 | — | 712 | 1 | no | — |
| 524 | C23 | — | 712 | 2 | no | — |
| 525 | C23 | — | 712 | 2 | no | — |
| 526 | C23 | — | 712 | 2 | no | — |
| 527 | C23 | #15667982 | 1 | 1 | yes | characteristic |
| 528 | Q8 | — | 4 | 2 | no | — |
| 529 | Q8 | — | 8 | 1 | no | — |
| 530 | Q8 | — | 356 | 2 | no | — |
| 531 | Q8 | — | 356 | 1 | no | — |
| 532 | Q8 | — | 356 | 2 | no | — |
| 533 | Q8 | — | 712 | 2 | no | — |
| 534 | D4 | — | 356 | 2 | no | — |
| 535 | D4 | — | 356 | 1 | no | — |
| 536 | D4 | — | 356 | 2 | no | — |
| 537 | D4 | — | 356 | 2 | no | — |
| 538 | D4 | — | 356 | 2 | no | — |
| 539 | D4 | — | 356 | 2 | no | — |
| 540 | D4 | — | 356 | 4 | no | — |
| 541 | D4 | — | 356 | 2 | no | — |
| 542 | D4 | — | 356 | 2 | no | — |
| 543 | D4 | — | 712 | 2 | no | — |
| 544 | D4 | — | 712 | 2 | no | — |
| 545 | D4 | — | 712 | 2 | no | — |
| 546 | D4 | — | 712 | 2 | no | — |
| 547 | D4 | — | 712 | 2 | no | — |
| 548 | C2×C4 | — | 2 | 2 | no | — |
| 549 | C2×C4 | — | 2 | 2 | no | — |
| 550 | C2×C4 | — | 2 | 2 | no | — |
| 551 | C2×C4 | — | 2 | 2 | no | — |
| 552 | C2×C4 | — | 4 | 1 | no | — |
| 553 | C2×C4 | — | 356 | 2 | no | — |
| 554 | C2×C4 | — | 178 | 1 | no | — |
| 555 | C2×C4 | — | 178 | 1 | no | — |
| 556 | C2×C4 | — | 178 | 2 | no | — |
| 557 | C2×C4 | — | 178 | 1 | no | — |
| 558 | C2×C4 | — | 712 | 2 | no | — |
| 559 | C2×C4 | — | 712 | 2 | no | — |
| 560 | C2×C4 | — | 712 | 2 | no | — |
| 561 | C2×C4 | — | 712 | 1 | no | — |
| 562 | C2×C4 | #15667982 | 1 | 1 | yes | characteristic |
| 563 | C2×C4 | #15667982 | 1 | 1 | yes | characteristic |
| 564 | C2×C4 | #15667982 | 1 | 1 | yes | characteristic |
| 565 | C2×C4 | C2×D4×D89 | 1 | 1 | yes | characteristic |
| 566 | C2×C4 | C2×D4×D89 | 1 | 1 | yes | characteristic |
| 567 | C2×C4 | C22×D356 | 1 | 1 | yes | characteristic |
| 568 | C8 | — | 2 | 4 | no | — |
| 569 | C8 | — | 4 | 2 | no | — |
| 570 | C8 | — | 356 | 2 | no | — |
| 571 | C22 | — | 2 | 1 | no | — |
| 572 | C22 | — | 2 | 1 | no | — |
| 573 | C22 | — | 356 | 1 | no | — |
| 574 | C22 | — | 356 | 2 | no | — |
| 575 | C22 | — | 356 | 1 | no | — |
| 576 | C22 | — | 356 | 2 | no | — |
| 577 | C22 | — | 356 | 2 | no | — |
| 578 | C22 | — | 356 | 1 | no | — |
| 579 | C22 | — | 1424 | 4 | no | — |
| 580 | C22 | — | 1424 | 2 | no | — |
| 581 | C22 | — | 712 | 2 | no | — |
| 582 | C22 | — | 712 | 2 | no | — |
| 583 | C22 | — | 712 | 2 | no | — |
| 584 | C22 | #19151773 | 1 | 2 | yes | — |
| 585 | C22 | C2×#15667982 | 1 | 1 | yes | characteristic |
| 586 | C4 | — | 2 | 1 | no | — |
| 587 | C4 | — | 2 | 1 | no | — |
| 588 | C4 | — | 2 | 1 | no | — |
| 589 | C4 | — | 2 | 1 | no | — |
| 590 | C4 | — | 2 | 1 | no | — |
| 591 | C4 | — | 4 | 2 | no | — |
| 592 | C4 | — | 4 | 2 | no | — |
| 593 | C4 | — | 356 | 1 | no | — |
| 594 | C4 | — | 356 | 2 | no | — |
| 595 | C4 | — | 356 | 1 | no | — |
| 596 | C4 | — | 356 | 1 | no | — |
| 597 | C4 | #19151767 | 1 | 2 | yes | — |
| 598 | C2 | — | 2 | 2 | no | — |
| 599 | C2 | — | 1424 | 2 | no | — |
| 600 | C2 | — | 712 | 1 | no | — |
| 601 | C2 | — | 712 | 2 | no | — |
| 602 | C2 | C2×#19151767 | 1 | 1 | yes | characteristic |
| 603 | C2 | C2×#19151773 | 1 | 1 | yes | characteristic |
| 604 | C2 | #26029625 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #26034817 | C2 | semidirect |
| 2. #26031272 | C2 | semidirect |
| 3. C2×#19151987 | C2 | semidirect |
| 4. #26030628 | C2 | semidirect |
| 5. #26019552 | C2 | semidirect |
| 6. #26019547 | C2 | semidirect |
| 7. #26018851 | C2 | semidirect |
| 8. #26018838 | C2 | semidirect |
| 9. C89×#1531 | C2 | semidirect |
| 12. #19152352 | C22 | semidirect |
| 13. #19152346 | C22 | semidirect |
| 29. #19151987 | C22 | semidirect |
| 30. #19151964 | C22 | semidirect |
| 31. #19151963 | C22 | semidirect |
| 40. #19151339 | C22 | semidirect |
| 41. #19151337 | C22 | semidirect |
| 42. #19151337 | C22 | semidirect |
| 46. #330×C89 | C22 | semidirect |
| 309. #1531 | D89 | semidirect |
| 312. C89 | #19026 | semidirect |
| 347. #330 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034817 | 2 |
| #26031272 | 2 |
| C2×#19151987 | 2 |
| #26030628 | 2 |
| #26019552 | 2 |
| #26019547 | 2 |
| #26018851 | 2 |
| #26018838 | 2 |
| C89×#1531 | 2 |
| #19026 | 89 |