Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
808 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 808 conjugacy classes of subgroups — too many to draw. Only its 141 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 | #564×D89 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #26031443 | C2 | 1 | 2 | yes | maximal |
| 3 | #26030654 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #26019579 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #26019578 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #26019555 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #26019555 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #26019554 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #26018877 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #26018852 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | C89×#1663 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C89⋊#564 | — | 2 | 2 | no | — |
| 13 | C89⋊#564 | — | 2 | 2 | no | — |
| 14 | C89⋊#564 | — | 2 | 2 | no | — |
| 15 | C89⋊#564 | C22 | 1 | 1 | yes | characteristic |
| 16 | C89⋊#564 | C22 | 1 | 2 | yes | — |
| 17 | #19152149 | C22 | 1 | 1 | yes | characteristic |
| 18 | #125×D89 | — | 2 | 2 | no | — |
| 19 | #125×D89 | — | 2 | 2 | no | — |
| 20 | #125×D89 | — | 2 | 2 | no | — |
| 21 | #125×D89 | C22 | 1 | 2 | yes | — |
| 22 | #125×D89 | C22 | 1 | 1 | yes | characteristic |
| 23 | #19152004 | C22 | 1 | 2 | yes | — |
| 24 | #19151966 | C22 | 1 | 1 | yes | characteristic |
| 25 | #19151964 | C22 | 1 | 1 | yes | characteristic |
| 26 | #19151964 | C22 | 1 | 2 | yes | — |
| 27 | #19151963 | C22 | 1 | 1 | yes | characteristic |
| 28 | #19151963 | C22 | 1 | 2 | yes | — |
| 29 | #19151954 | — | 2 | 2 | no | — |
| 30 | #19151918 | — | 2 | 2 | no | — |
| 31 | #19151913 | — | 2 | 2 | no | — |
| 32 | #19151901 | — | 2 | 2 | no | — |
| 33 | #19151897 | — | 2 | 2 | no | — |
| 34 | #19151653 | C22 | 1 | 2 | yes | — |
| 35 | #19151598 | — | 2 | 2 | no | — |
| 36 | #19151550 | C22 | 1 | 1 | yes | characteristic |
| 37 | #19151340 | C22 | 1 | 2 | yes | — |
| 38 | #19151340 | C22 | 1 | 1 | yes | characteristic |
| 39 | #19151339 | C22 | 1 | 2 | yes | — |
| 40 | #19151339 | C22 | 1 | 2 | yes | — |
| 41 | #19151339 | C22 | 1 | 2 | yes | — |
| 42 | #564×C89 | C22 | 1 | 1 | yes | characteristic |
| 43 | #501×C89 | C22 | 1 | 2 | yes | — |
| 44 | #491×C89 | C22 | 1 | 1 | yes | characteristic |
| 45 | #330×C89 | C22 | 1 | 2 | yes | — |
| 46 | #330×C89 | C22 | 1 | 1 | yes | characteristic |
| 47 | C2×#13083575 | — | 2 | 1 | no | — |
| 48 | C2×#13083557 | — | 2 | 1 | no | — |
| 49 | #15668009 | C23 | 1 | 1 | yes | characteristic |
| 50 | #15668004 | — | 2 | 2 | no | — |
| 51 | #15668004 | — | 2 | 2 | no | — |
| 52 | #15668004 | — | 2 | 2 | no | — |
| 53 | #15668004 | C23 | 1 | 1 | yes | characteristic |
| 54 | #15668004 | C23 | 1 | 2 | yes | — |
| 55 | #15668003 | — | 2 | 2 | no | — |
| 56 | #15668003 | — | 2 | 2 | no | — |
| 57 | #15668003 | — | 2 | 2 | no | — |
| 58 | #15668003 | — | 2 | 2 | no | — |
| 59 | #15668003 | — | 2 | 2 | no | — |
| 60 | #15668003 | — | 2 | 2 | no | — |
| 61 | #15668003 | D4 | 1 | 2 | yes | — |
| 62 | #15668003 | D4 | 1 | 2 | yes | — |
| 63 | #15668003 | D4 | 1 | 2 | yes | — |
| 64 | #15668002 | — | 2 | 2 | no | — |
| 65 | #15668002 | — | 2 | 2 | no | — |
| 66 | #15668002 | — | 2 | 2 | no | — |
| 67 | #15668002 | — | 2 | 2 | no | — |
| 68 | #15668002 | — | 2 | 2 | no | — |
| 69 | #15668002 | — | 2 | 2 | no | — |
| 70 | #15668002 | — | 2 | 2 | no | — |
| 71 | #15668002 | — | 2 | 2 | no | — |
| 72 | #15668002 | — | 2 | 2 | no | — |
| 73 | #15668002 | — | 2 | 2 | no | — |
| 74 | #15668002 | — | 2 | 2 | no | — |
| 75 | #15668002 | — | 2 | 2 | no | — |
| 76 | #15668002 | — | 2 | 2 | no | — |
| 77 | #15668002 | — | 2 | 2 | no | — |
| 78 | #15668002 | — | 2 | 2 | no | — |
| 79 | #15668001 | — | 2 | 1 | no | — |
| 80 | #15667987 | — | 2 | 2 | no | — |
| 81 | #15667974 | — | 2 | 2 | no | — |
| 82 | C4⋊C4×D89 | — | 2 | 2 | no | — |
| 83 | C4⋊C4×D89 | — | 2 | 2 | no | — |
| 84 | C4⋊C4×D89 | — | 2 | 2 | no | — |
| 85 | C4⋊C4×D89 | — | 2 | 2 | no | — |
| 86 | C4⋊C4×D89 | — | 2 | 2 | no | — |
| 87 | C4⋊C4×D89 | — | 2 | 2 | no | — |
| 88 | C4⋊C4×D89 | D4 | 1 | 2 | yes | — |
| 89 | C4⋊C4×D89 | D4 | 1 | 2 | yes | — |
| 90 | C4⋊C4×D89 | D4 | 1 | 2 | yes | — |
| 91 | C42×D89 | — | 2 | 2 | no | — |
| 92 | C42×D89 | C23 | 1 | 1 | yes | characteristic |
| 93 | #15667945 | — | 2 | 2 | no | — |
| 94 | #15667943 | — | 2 | 2 | no | — |
| 95 | #15667941 | — | 2 | 2 | no | — |
| 96 | #15667936 | — | 2 | 2 | no | — |
| 97 | #15667934 | — | 2 | 2 | no | — |
| 98 | #15667934 | — | 2 | 2 | no | — |
| 99 | #15667934 | — | 2 | 2 | no | — |
| 100 | #15667932 | — | 2 | 2 | no | — |
| 101 | #15667932 | — | 2 | 2 | no | — |
| 102 | #15667932 | — | 2 | 2 | no | — |
| 103 | #15667924 | — | 2 | 2 | no | — |
| 104 | #15667923 | C23 | 1 | 2 | yes | — |
| 105 | #15667923 | C23 | 1 | 1 | yes | characteristic |
| 106 | C8×Dic89 | — | 2 | 1 | no | — |
| 107 | C4⋊Q8×C89 | C23 | 1 | 1 | yes | characteristic |
| 108 | #125×C89 | — | 2 | 2 | no | — |
| 109 | #125×C89 | — | 2 | 2 | no | — |
| 110 | #125×C89 | — | 2 | 2 | no | — |
| 111 | #125×C89 | C23 | 1 | 1 | yes | characteristic |
| 112 | #125×C89 | C23 | 1 | 2 | yes | — |
| 113 | #107×C89 | — | 2 | 2 | no | — |
| 114 | #106×C89 | — | 2 | 2 | no | — |
| 115 | #103×C89 | — | 2 | 2 | no | — |
| 116 | #97×C89 | C23 | 1 | 2 | yes | — |
| 117 | #97×C89 | C23 | 1 | 1 | yes | characteristic |
| 118 | #13083575 | — | 4 | 4 | no | — |
| 119 | C2×D356 | — | 2 | 2 | no | — |
| 120 | C2×D356 | — | 2 | 1 | no | — |
| 121 | C2×D356 | — | 4 | 1 | no | — |
| 122 | C2×C4×D89 | — | 2 | 2 | no | — |
| 123 | C2×C4×D89 | — | 2 | 2 | no | — |
| 124 | C2×C4×D89 | — | 2 | 2 | no | — |
| 125 | C2×C4×D89 | — | 4 | 1 | no | — |
| 126 | C2×C4×D89 | C2×D4 | 1 | 1 | yes | characteristic |
| 127 | C2×C4×D89 | C2×D4 | 1 | 2 | yes | — |
| 128 | #13083557 | — | 4 | 2 | no | — |
| 129 | C2×#10623494 | — | 2 | 1 | no | — |
| 130 | C2×#10623494 | — | 2 | 2 | no | — |
| 131 | C4⋊Dic89 | — | 2 | 2 | no | — |
| 132 | C4⋊Dic89 | — | 2 | 2 | no | — |
| 133 | C4⋊Dic89 | — | 2 | 2 | no | — |
| 134 | C4⋊Dic89 | — | 2 | 2 | no | — |
| 135 | C4⋊Dic89 | — | 2 | 2 | no | — |
| 136 | C4⋊Dic89 | — | 2 | 2 | no | — |
| 137 | C4⋊Dic89 | C2×D4 | 1 | 2 | yes | — |
| 138 | C4⋊Dic89 | C2×D4 | 1 | 2 | yes | — |
| 139 | C4⋊Dic89 | C2×D4 | 1 | 2 | yes | — |
| 140 | #13083553 | — | 2 | 2 | no | — |
| 141 | #13083553 | — | 2 | 2 | no | — |
| 142 | #13083553 | — | 2 | 2 | no | — |
| 143 | #13083553 | — | 2 | 2 | no | — |
| 144 | #13083553 | — | 2 | 2 | no | — |
| 145 | #13083553 | — | 2 | 2 | no | — |
| 146 | #13083553 | — | 2 | 2 | no | — |
| 147 | #13083553 | — | 2 | 2 | no | — |
| 148 | #13083553 | — | 2 | 2 | no | — |
| 149 | #13083553 | — | 2 | 2 | no | — |
| 150 | #13083553 | — | 2 | 2 | no | — |
| 151 | #13083553 | — | 2 | 2 | no | — |
| 152 | #13083553 | — | 2 | 2 | no | — |
| 153 | #13083553 | — | 2 | 2 | no | — |
| 154 | #13083553 | — | 2 | 2 | no | — |
| 155 | #13083551 | — | 4 | 2 | no | — |
| 156 | C4×Dic89 | — | 2 | 2 | no | — |
| 157 | C4×Dic89 | — | 2 | 2 | no | — |
| 158 | C4×Dic89 | — | 2 | 2 | no | — |
| 159 | C4×Dic89 | C2×D4 | 1 | 2 | yes | — |
| 160 | C4×Dic89 | C2×D4 | 1 | 1 | yes | characteristic |
| 161 | C2×Q8×C89 | — | 2 | 1 | no | — |
| 162 | C2×C8×C89 | — | 2 | 1 | no | — |
| 163 | C2×C8×C89 | — | 2 | 2 | no | — |
| 164 | C4⋊C4×C89 | — | 2 | 2 | no | — |
| 165 | C4⋊C4×C89 | — | 2 | 2 | no | — |
| 166 | C4⋊C4×C89 | — | 2 | 2 | no | — |
| 167 | C4⋊C4×C89 | — | 2 | 2 | no | — |
| 168 | C4⋊C4×C89 | — | 2 | 2 | no | — |
| 169 | C4⋊C4×C89 | — | 2 | 2 | no | — |
| 170 | C4⋊C4×C89 | — | 2 | 2 | no | — |
| 171 | C4⋊C4×C89 | C2×D4 | 1 | 2 | yes | — |
| 172 | C4⋊C4×C89 | C2×D4 | 1 | 2 | yes | — |
| 173 | C4⋊C4×C89 | C2×D4 | 1 | 2 | yes | — |
| 174 | C42×C89 | — | 2 | 2 | no | — |
| 175 | C42×C89 | C24 | 1 | 1 | yes | characteristic |
| 176 | C22×D89 | — | 4 | 1 | no | — |
| 177 | C22×D89 | #120 | 1 | 1 | yes | characteristic |
| 178 | Q8×C89 | — | 4 | 2 | no | — |
| 179 | C2×C4×C89 | — | 2 | 2 | no | — |
| 180 | C2×C4×C89 | — | 2 | 2 | no | — |
| 181 | C2×C4×C89 | — | 2 | 2 | no | — |
| 182 | C2×C4×C89 | — | 4 | 1 | no | — |
| 183 | C2×C4×C89 | C22×D4 | 1 | 2 | yes | — |
| 184 | C2×C4×C89 | C22×D4 | 1 | 1 | yes | characteristic |
| 185 | C2×Dic89 | — | 2 | 2 | no | — |
| 186 | C2×Dic89 | — | 2 | 2 | no | — |
| 187 | C2×Dic89 | — | 2 | 2 | no | — |
| 188 | C2×Dic89 | #120 | 1 | 2 | yes | — |
| 189 | C2×Dic89 | #120 | 1 | 1 | yes | characteristic |
| 190 | D356 | — | 4 | 4 | no | — |
| 191 | D356 | — | 4 | 2 | no | — |
| 192 | D356 | — | 8 | 2 | no | — |
| 193 | C4×D89 | — | 2 | 2 | no | — |
| 194 | C4×D89 | — | 4 | 2 | no | — |
| 195 | C4×D89 | — | 4 | 4 | no | — |
| 196 | C4×D89 | — | 4 | 4 | no | — |
| 197 | C4×D89 | — | 4 | 4 | no | — |
| 198 | C4×D89 | — | 8 | 2 | no | — |
| 199 | C8×C89 | — | 4 | 2 | no | — |
| 200 | C8×C89 | — | 4 | 1 | no | — |
| 201 | #10623494 | — | 4 | 2 | no | — |
| 202 | #10623494 | — | 4 | 1 | no | — |
| 203 | C22×C89 | C2×#120 | 1 | 1 | yes | characteristic |
| 204 | C2×D89 | — | 2 | 2 | no | — |
| 205 | C2×D89 | — | 8 | 1 | no | — |
| 206 | C2×D89 | — | 8 | 2 | no | — |
| 207 | C2×D89 | #454 | 1 | 2 | yes | — |
| 208 | C4×C89 | — | 2 | 1 | no | — |
| 209 | C4×C89 | — | 2 | 2 | no | — |
| 210 | C4×C89 | — | 4 | 2 | no | — |
| 211 | C4×C89 | — | 4 | 2 | no | — |
| 212 | C4×C89 | — | 4 | 2 | no | — |
| 213 | C4×C89 | — | 8 | 1 | no | — |
| 214 | Dic89 | — | 2 | 1 | no | — |
| 215 | Dic89 | — | 2 | 2 | no | — |
| 216 | Dic89 | — | 4 | 2 | no | — |
| 217 | Dic89 | — | 4 | 2 | no | — |
| 218 | Dic89 | — | 4 | 2 | no | — |
| 219 | #19003 | — | 89 | 1 | no | maximal, Sylow |
| 220 | C2×C89 | C2×#454 | 1 | 1 | yes | characteristic |
| 221 | C2×C89 | #3020 | 1 | 2 | yes | — |
| 222 | D89 | — | 2 | 2 | no | — |
| 223 | D89 | — | 16 | 1 | no | — |
| 224 | C2×#564 | — | 89 | 1 | no | — |
| 225 | #3234 | — | 89 | 2 | no | — |
| 226 | #3142 | — | 89 | 1 | no | — |
| 227 | #1663 | — | 89 | 2 | no | — |
| 228 | #1663 | — | 89 | 1 | no | — |
| 229 | #1663 | D89 | 1 | 1 | yes | characteristic, complemented |
| 230 | #1658 | — | 89 | 1 | no | — |
| 231 | #1658 | — | 89 | 2 | no | — |
| 232 | #1658 | — | 89 | 1 | no | — |
| 233 | #1534 | — | 89 | 1 | no | — |
| 234 | #1528 | — | 89 | 2 | no | — |
| 235 | C89 | #19003 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 236 | #564 | — | 89 | 2 | no | — |
| 237 | #564 | — | 89 | 1 | no | — |
| 238 | #564 | — | 178 | 2 | no | — |
| 239 | #564 | — | 178 | 2 | no | — |
| 240 | #564 | — | 178 | 2 | no | — |
| 241 | #564 | C2×D89 | 1 | 1 | yes | characteristic |
| 242 | #532 | — | 89 | 1 | no | — |
| 243 | C2×#125 | — | 89 | 1 | no | — |
| 244 | C2×#125 | — | 89 | 2 | no | — |
| 245 | C2×#125 | — | 178 | 2 | no | — |
| 246 | C2×#125 | — | 178 | 2 | no | — |
| 247 | C2×#125 | — | 178 | 2 | no | — |
| 248 | #501 | — | 89 | 2 | no | — |
| 249 | #501 | C2×D89 | 1 | 2 | yes | — |
| 250 | #491 | — | 89 | 1 | no | — |
| 251 | #491 | C2×D89 | 1 | 1 | yes | characteristic |
| 252 | #490 | — | 89 | 1 | no | — |
| 253 | #490 | — | 89 | 2 | no | — |
| 254 | #490 | — | 89 | 1 | no | — |
| 255 | #490 | — | 89 | 2 | no | — |
| 256 | #488 | — | 178 | 2 | no | — |
| 257 | #481 | — | 178 | 2 | no | — |
| 258 | #480 | — | 178 | 2 | no | — |
| 259 | #478 | — | 178 | 2 | no | — |
| 260 | #478 | — | 178 | 2 | no | — |
| 261 | #432 | — | 89 | 2 | no | — |
| 262 | #417 | — | 178 | 2 | no | — |
| 263 | C4×M16 | — | 89 | 1 | no | — |
| 264 | #330 | — | 89 | 2 | no | — |
| 265 | #330 | — | 89 | 1 | no | — |
| 266 | #330 | — | 89 | 2 | no | — |
| 267 | #330 | — | 89 | 2 | no | — |
| 268 | #330 | — | 89 | 2 | no | — |
| 269 | #330 | C2×D89 | 1 | 2 | yes | — |
| 270 | #330 | C2×D89 | 1 | 1 | yes | characteristic |
| 271 | C2×#41 | — | 178 | 1 | no | — |
| 272 | C2×M16 | — | 178 | 1 | no | — |
| 273 | C4⋊Q8 | C22×D89 | 1 | 1 | yes | characteristic |
| 274 | #127 | — | 89 | 1 | no | — |
| 275 | #125 | — | 2 | 2 | no | — |
| 276 | #125 | — | 2 | 2 | no | — |
| 277 | #125 | — | 2 | 2 | no | — |
| 278 | #125 | — | 89 | 2 | no | — |
| 279 | #125 | — | 89 | 2 | no | — |
| 280 | #125 | — | 89 | 2 | no | — |
| 281 | #125 | — | 89 | 1 | no | — |
| 282 | #125 | — | 89 | 2 | no | — |
| 283 | #125 | — | 178 | 2 | no | — |
| 284 | #125 | — | 178 | 2 | no | — |
| 285 | #125 | — | 178 | 2 | no | — |
| 286 | #125 | — | 178 | 2 | no | — |
| 287 | #125 | — | 178 | 2 | no | — |
| 288 | #125 | — | 178 | 2 | no | — |
| 289 | #125 | — | 178 | 2 | no | — |
| 290 | #125 | — | 178 | 2 | no | — |
| 291 | #125 | — | 178 | 2 | no | — |
| 292 | #125 | — | 178 | 2 | no | — |
| 293 | #125 | — | 178 | 2 | no | — |
| 294 | #125 | — | 178 | 2 | no | — |
| 295 | #125 | — | 178 | 2 | no | — |
| 296 | #125 | — | 178 | 2 | no | — |
| 297 | #125 | — | 178 | 2 | no | — |
| 298 | #125 | — | 178 | 2 | no | — |
| 299 | #125 | — | 178 | 2 | no | — |
| 300 | #125 | — | 178 | 2 | no | — |
| 301 | #125 | — | 178 | 2 | no | — |
| 302 | #125 | — | 178 | 2 | no | — |
| 303 | #125 | — | 178 | 2 | no | — |
| 304 | #125 | — | 178 | 2 | no | — |
| 305 | #125 | — | 178 | 2 | no | — |
| 306 | #125 | — | 178 | 2 | no | — |
| 307 | #125 | C22×D89 | 1 | 1 | yes | characteristic |
| 308 | #125 | C22×D89 | 1 | 2 | yes | — |
| 309 | #124 | — | 178 | 1 | no | — |
| 310 | #121 | — | 178 | 2 | no | — |
| 311 | C4×D4 | — | 178 | 2 | no | — |
| 312 | C2×C4⋊C4 | — | 89 | 2 | no | — |
| 313 | C2×C4⋊C4 | — | 89 | 2 | no | — |
| 314 | C2×C4⋊C4 | — | 89 | 2 | no | — |
| 315 | C2×C4⋊C4 | — | 178 | 2 | no | — |
| 316 | C2×C4⋊C4 | — | 178 | 2 | no | — |
| 317 | C2×C4⋊C4 | — | 178 | 2 | no | — |
| 318 | C2×C4⋊C4 | — | 178 | 2 | no | — |
| 319 | C2×C4⋊C4 | — | 178 | 2 | no | — |
| 320 | C2×C4⋊C4 | — | 178 | 2 | no | — |
| 321 | C2×C42 | — | 89 | 1 | no | — |
| 322 | C2×C42 | — | 178 | 2 | no | — |
| 323 | #107 | — | 2 | 2 | no | — |
| 324 | #107 | — | 178 | 2 | no | — |
| 325 | #106 | — | 2 | 2 | no | — |
| 326 | #106 | — | 178 | 2 | no | — |
| 327 | C4⋊C8 | — | 178 | 2 | no | — |
| 328 | #103 | — | 2 | 2 | no | — |
| 329 | #103 | — | 178 | 2 | no | — |
| 330 | #102 | — | 178 | 2 | no | — |
| 331 | #102 | — | 178 | 2 | no | — |
| 332 | #102 | — | 178 | 2 | no | — |
| 333 | #102 | — | 178 | 2 | no | — |
| 334 | #102 | — | 178 | 2 | no | — |
| 335 | #102 | — | 178 | 2 | no | — |
| 336 | C22⋊C8 | — | 178 | 2 | no | — |
| 337 | #97 | — | 89 | 1 | no | — |
| 338 | #97 | — | 89 | 2 | no | — |
| 339 | #97 | C22×D89 | 1 | 1 | yes | characteristic |
| 340 | #97 | C22×D89 | 1 | 2 | yes | — |
| 341 | C4×C8 | — | 178 | 1 | no | — |
| 342 | #41 | — | 356 | 4 | no | — |
| 343 | C2×Q8 | — | 2 | 1 | no | — |
| 344 | C2×D4 | — | 356 | 1 | no | — |
| 345 | C2×D4 | — | 178 | 2 | no | — |
| 346 | C2×D4 | — | 178 | 1 | no | — |
| 347 | C22×C4 | — | 89 | 2 | no | — |
| 348 | C22×C4 | — | 89 | 1 | no | — |
| 349 | C22×C4 | — | 356 | 1 | no | — |
| 350 | C22×C4 | — | 178 | 2 | no | — |
| 351 | C22×C4 | — | 178 | 2 | no | — |
| 352 | C22×C4 | — | 178 | 2 | no | — |
| 353 | M16 | — | 356 | 2 | no | — |
| 354 | C2×C8 | — | 2 | 1 | no | — |
| 355 | C2×C8 | — | 2 | 2 | no | — |
| 356 | C2×C8 | — | 178 | 1 | no | — |
| 357 | C2×C8 | — | 178 | 2 | no | — |
| 358 | C4⋊C4 | — | 2 | 2 | no | — |
| 359 | C4⋊C4 | — | 2 | 2 | no | — |
| 360 | C4⋊C4 | — | 2 | 2 | no | — |
| 361 | C4⋊C4 | — | 2 | 2 | no | — |
| 362 | C4⋊C4 | — | 2 | 2 | no | — |
| 363 | C4⋊C4 | — | 2 | 2 | no | — |
| 364 | C4⋊C4 | — | 2 | 2 | no | — |
| 365 | C4⋊C4 | — | 89 | 2 | no | — |
| 366 | C4⋊C4 | — | 89 | 2 | no | — |
| 367 | C4⋊C4 | — | 89 | 2 | no | — |
| 368 | C4⋊C4 | — | 178 | 2 | no | — |
| 369 | C4⋊C4 | — | 178 | 2 | no | — |
| 370 | C4⋊C4 | — | 178 | 2 | no | — |
| 371 | C4⋊C4 | — | 178 | 2 | no | — |
| 372 | C4⋊C4 | — | 178 | 2 | no | — |
| 373 | C4⋊C4 | — | 178 | 2 | no | — |
| 374 | C4⋊C4 | — | 178 | 2 | no | — |
| 375 | C4⋊C4 | — | 178 | 2 | no | — |
| 376 | C4⋊C4 | — | 178 | 2 | no | — |
| 377 | C4⋊C4 | — | 178 | 2 | no | — |
| 378 | C4⋊C4 | — | 178 | 2 | no | — |
| 379 | C4⋊C4 | — | 178 | 2 | no | — |
| 380 | C4⋊C4 | — | 178 | 2 | no | — |
| 381 | C4⋊C4 | — | 178 | 2 | no | — |
| 382 | C4⋊C4 | — | 178 | 2 | no | — |
| 383 | C4⋊C4 | — | 178 | 2 | no | — |
| 384 | C4⋊C4 | — | 178 | 2 | no | — |
| 385 | C4⋊C4 | — | 178 | 2 | no | — |
| 386 | C4⋊C4 | — | 178 | 2 | no | — |
| 387 | C4⋊C4 | — | 178 | 2 | no | — |
| 388 | C4⋊C4 | — | 178 | 2 | no | — |
| 389 | C4⋊C4 | D4×D89 | 1 | 2 | yes | — |
| 390 | C4⋊C4 | D4×D89 | 1 | 2 | yes | — |
| 391 | C4⋊C4 | D4×D89 | 1 | 2 | yes | — |
| 392 | C22⋊C4 | — | 356 | 2 | no | — |
| 393 | C42 | — | 2 | 2 | no | — |
| 394 | C42 | — | 89 | 1 | no | — |
| 395 | C42 | — | 89 | 2 | no | — |
| 396 | C42 | — | 178 | 2 | no | — |
| 397 | C42 | — | 178 | 2 | no | — |
| 398 | C42 | — | 178 | 2 | no | — |
| 399 | C42 | C23×D89 | 1 | 1 | yes | characteristic |
| 400 | C23 | — | 89 | 1 | no | — |
| 401 | C23 | — | 356 | 1 | no | — |
| 402 | Q8 | — | 4 | 2 | no | — |
| 403 | D4 | — | 356 | 4 | no | — |
| 404 | D4 | — | 356 | 2 | no | — |
| 405 | D4 | — | 712 | 2 | no | — |
| 406 | C2×C4 | — | 2 | 2 | no | — |
| 407 | C2×C4 | — | 2 | 2 | no | — |
| 408 | C2×C4 | — | 2 | 2 | no | — |
| 409 | C2×C4 | — | 4 | 1 | no | — |
| 410 | C2×C4 | — | 89 | 2 | no | — |
| 411 | C2×C4 | — | 89 | 1 | no | — |
| 412 | C2×C4 | — | 356 | 2 | no | — |
| 413 | C2×C4 | — | 356 | 4 | no | — |
| 414 | C2×C4 | — | 356 | 4 | no | — |
| 415 | C2×C4 | — | 356 | 4 | no | — |
| 416 | C2×C4 | — | 178 | 2 | no | — |
| 417 | C2×C4 | — | 178 | 2 | no | — |
| 418 | C2×C4 | — | 178 | 2 | no | — |
| 419 | C2×C4 | — | 178 | 2 | no | — |
| 420 | C2×C4 | — | 712 | 2 | no | — |
| 421 | C2×C4 | C2×D4×D89 | 1 | 2 | yes | — |
| 422 | C2×C4 | C2×D4×D89 | 1 | 1 | yes | characteristic |
| 423 | C8 | — | 4 | 2 | no | — |
| 424 | C8 | — | 4 | 1 | no | — |
| 425 | C8 | — | 356 | 2 | no | — |
| 426 | C8 | — | 356 | 1 | no | — |
| 427 | C22 | — | 89 | 2 | no | — |
| 428 | C22 | — | 178 | 2 | no | — |
| 429 | C22 | — | 712 | 1 | no | — |
| 430 | C22 | — | 712 | 2 | no | — |
| 431 | C22 | #120×D89 | 1 | 1 | yes | characteristic |
| 432 | C4 | — | 2 | 1 | no | — |
| 433 | C4 | — | 2 | 2 | no | — |
| 434 | C4 | — | 4 | 2 | no | — |
| 435 | C4 | — | 4 | 2 | no | — |
| 436 | C4 | — | 4 | 2 | no | — |
| 437 | C4 | — | 8 | 1 | no | — |
| 438 | C4 | — | 356 | 2 | no | — |
| 439 | C4 | — | 356 | 2 | no | — |
| 440 | C4 | — | 356 | 2 | no | — |
| 441 | C4 | — | 178 | 1 | no | — |
| 442 | C4 | — | 178 | 2 | no | — |
| 443 | C2 | — | 1424 | 1 | no | — |
| 444 | C2 | — | 178 | 2 | no | — |
| 445 | C2 | #454×D89 | 1 | 1 | yes | characteristic |
| 446 | C2 | #26029617 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #564×D89 | C2 | semidirect |
| 4. #26019579 | C2 | semidirect |
| 5. #26019578 | C2 | semidirect |
| 6. #26019555 | C2 | semidirect |
| 7. #26019555 | C2 | semidirect |
| 8. #26019554 | C2 | semidirect |
| 9. #26018877 | C2 | semidirect |
| 10. #26018852 | C2 | semidirect |
| 11. C89×#1663 | C2 | semidirect |
| 229. #1663 | D89 | semidirect |
| 235. C89 | #19003 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #564×D89 | 2 |
| #26031443 | 2 |
| #26030654 | 2 |
| #26019579 | 2 |
| #26019578 | 2 |
| #26019555 | 2 |
| #26019554 | 2 |
| #26018877 | 2 |
| #26018852 | 2 |
| C89×#1663 | 2 |
| #19003 | 89 |