Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1058 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 1058 conjugacy classes of subgroups — too many to draw. Only its 163 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 | #26034585 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #26031475 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C2×#19151970 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #26019380 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #26019374 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #26019369 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #26018710 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | C89×#1555 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C22×#13083562 | — | 2 | 2 | no | — |
| 10 | #19152335 | — | 2 | 2 | no | — |
| 11 | #19152334 | C22 | 1 | 1 | yes | characteristic |
| 12 | #19152268 | C22 | 1 | 2 | yes | — |
| 13 | #19152242 | — | 2 | 2 | no | — |
| 14 | #19152233 | C22 | 1 | 1 | yes | characteristic |
| 15 | D4×C22⋊D89 | — | 2 | 2 | no | — |
| 16 | #19152202 | — | 2 | 2 | no | — |
| 17 | #19152161 | — | 2 | 2 | no | — |
| 18 | #19152157 | — | 2 | 2 | no | — |
| 19 | C2×#15668012 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | #19152132 | C22 | 1 | 2 | yes | — |
| 21 | #19152007 | — | 2 | 2 | no | — |
| 22 | #19151970 | — | 2 | 2 | no | — |
| 23 | #19151970 | C22 | 1 | 2 | yes | — |
| 24 | #19151970 | C22 | 1 | 2 | yes | complemented |
| 25 | #19151958 | — | 2 | 2 | no | — |
| 26 | #19151929 | — | 2 | 2 | no | — |
| 27 | #19151912 | — | 2 | 2 | no | — |
| 28 | #19151894 | C22 | 1 | 4 | yes | complemented |
| 29 | #19151889 | C22 | 1 | 4 | yes | complemented |
| 30 | C2×C4×#10623494 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | #19151328 | C22 | 1 | 4 | yes | complemented |
| 32 | #19151325 | C22 | 1 | 4 | yes | complemented |
| 33 | C2×#127×C89 | C22 | 1 | 1 | yes | characteristic |
| 34 | #432×C89 | C22 | 1 | 2 | yes | complemented |
| 35 | #331×C89 | C22 | 1 | 2 | yes | — |
| 36 | #331×C89 | C22 | 1 | 2 | yes | complemented |
| 37 | C2×#13083573 | — | 2 | 2 | no | — |
| 38 | C22×Dic178 | — | 2 | 1 | no | — |
| 39 | C22×C22⋊D89 | — | 2 | 2 | no | — |
| 40 | C2×D4×D89 | — | 2 | 2 | no | — |
| 41 | C2×#13083562 | — | 2 | 4 | no | — |
| 42 | C2×#13083562 | — | 2 | 4 | no | — |
| 43 | C2×#13083562 | — | 4 | 8 | no | — |
| 44 | C22×#10623494 | — | 2 | 1 | no | — |
| 45 | #15668012 | — | 2 | 2 | no | — |
| 46 | #15668012 | — | 2 | 1 | no | — |
| 47 | #15668012 | C23 | 1 | 2 | yes | — |
| 48 | #15668008 | — | 2 | 2 | no | — |
| 49 | #15668006 | — | 2 | 2 | no | — |
| 50 | #15668004 | D4 | 1 | 2 | yes | — |
| 51 | #15668000 | D4 | 1 | 2 | yes | — |
| 52 | #15667999 | — | 2 | 2 | no | — |
| 53 | #15667995 | — | 2 | 2 | no | — |
| 54 | #15667993 | — | 2 | 2 | no | — |
| 55 | #15667993 | — | 2 | 4 | no | — |
| 56 | #15667993 | — | 2 | 2 | no | — |
| 57 | #15667991 | D4 | 1 | 2 | yes | — |
| 58 | #15667986 | D4 | 1 | 2 | yes | — |
| 59 | #15667984 | — | 2 | 4 | no | — |
| 60 | #15667984 | — | 2 | 4 | no | — |
| 61 | #15667984 | — | 2 | 4 | no | — |
| 62 | #15667984 | — | 2 | 4 | no | — |
| 63 | #15667983 | — | 2 | 2 | no | — |
| 64 | #15667983 | — | 2 | 2 | no | — |
| 65 | #15667981 | — | 2 | 4 | no | — |
| 66 | #15667980 | — | 2 | 2 | no | — |
| 67 | #15667980 | — | 2 | 4 | no | — |
| 68 | #15667980 | — | 2 | 2 | no | — |
| 69 | C4×Dic178 | C23 | 1 | 2 | yes | — |
| 70 | C4×D356 | C23 | 1 | 2 | yes | — |
| 71 | D4×Dic89 | — | 2 | 2 | no | — |
| 72 | D4×Dic89 | — | 2 | 2 | no | — |
| 73 | C4×C22⋊D89 | — | 2 | 2 | no | — |
| 74 | #15667969 | — | 2 | 2 | no | — |
| 75 | C2×C4⋊Dic89 | — | 2 | 2 | no | — |
| 76 | C2×C22⋊Dic89 | — | 2 | 2 | no | — |
| 77 | #15667946 | — | 2 | 4 | no | — |
| 78 | #15667944 | — | 2 | 4 | no | — |
| 79 | #15667937 | — | 2 | 4 | no | — |
| 80 | #15667934 | — | 2 | 4 | no | — |
| 81 | C4×#10623494 | — | 2 | 1 | no | — |
| 82 | C4×#10623494 | C23 | 1 | 2 | yes | — |
| 83 | C22×D4×C89 | — | 2 | 2 | no | — |
| 84 | C22×D4×C89 | D4 | 1 | 2 | yes | — |
| 85 | #127×C89 | — | 2 | 2 | no | — |
| 86 | #127×C89 | D4 | 1 | 2 | yes | — |
| 87 | #127×C89 | C23 | 1 | 1 | yes | characteristic |
| 88 | #127×C89 | C23 | 1 | 1 | yes | characteristic |
| 89 | C2×C42×C89 | C23 | 1 | 1 | yes | characteristic |
| 90 | C4⋊C8×C89 | C23 | 1 | 4 | yes | — |
| 91 | C22⋊C8×C89 | — | 2 | 2 | no | — |
| 92 | #97×C89 | — | 2 | 2 | no | — |
| 93 | C23×D89 | — | 2 | 2 | no | — |
| 94 | #13083573 | — | 8 | 4 | no | — |
| 95 | C2×Dic178 | — | 2 | 2 | no | — |
| 96 | C2×Dic178 | — | 4 | 4 | no | — |
| 97 | C2×Dic178 | — | 4 | 1 | no | — |
| 98 | C2×Dic178 | C2×D4 | 1 | 2 | yes | — |
| 99 | C2×D356 | C2×D4 | 1 | 2 | yes | — |
| 100 | C2×C22⋊D89 | — | 2 | 2 | no | — |
| 101 | C2×C22⋊D89 | — | 2 | 4 | no | — |
| 102 | C2×C22⋊D89 | — | 2 | 4 | no | — |
| 103 | C2×C22⋊D89 | — | 2 | 4 | no | — |
| 104 | C2×C22⋊D89 | — | 8 | 4 | no | — |
| 105 | D4×D89 | — | 8 | 4 | no | — |
| 106 | C22×Dic89 | — | 2 | 2 | no | — |
| 107 | C22×Dic89 | — | 2 | 4 | no | — |
| 108 | C22×Dic89 | — | 4 | 1 | no | — |
| 109 | C2×C4×D89 | — | 2 | 2 | no | — |
| 110 | #13083562 | — | 4 | 8 | no | — |
| 111 | #13083562 | — | 4 | 8 | no | — |
| 112 | C2×#10623494 | — | 2 | 4 | no | — |
| 113 | C2×#10623494 | — | 2 | 2 | no | — |
| 114 | C4⋊Dic89 | — | 2 | 4 | no | — |
| 115 | C4⋊Dic89 | — | 4 | 2 | no | — |
| 116 | C4⋊Dic89 | C2×D4 | 1 | 2 | yes | — |
| 117 | C4⋊Dic89 | C2×D4 | 1 | 2 | yes | — |
| 118 | #13083553 | — | 2 | 2 | no | — |
| 119 | #13083553 | — | 2 | 2 | no | — |
| 120 | #13083553 | — | 2 | 2 | no | — |
| 121 | #13083553 | — | 2 | 2 | no | — |
| 122 | C22⋊Dic89 | — | 2 | 4 | no | — |
| 123 | C22⋊Dic89 | — | 2 | 4 | no | — |
| 124 | C22⋊Dic89 | — | 2 | 2 | no | — |
| 125 | C22⋊Dic89 | — | 2 | 2 | no | — |
| 126 | C22⋊Dic89 | — | 2 | 2 | no | — |
| 127 | #13083551 | — | 2 | 2 | no | — |
| 128 | #13083551 | — | 2 | 2 | no | — |
| 129 | #13083551 | — | 2 | 2 | no | — |
| 130 | #13083551 | — | 2 | 2 | no | — |
| 131 | C4×Dic89 | — | 2 | 2 | no | — |
| 132 | C24×C89 | — | 2 | 2 | no | — |
| 133 | C2×D4×C89 | — | 2 | 2 | no | — |
| 134 | C2×D4×C89 | — | 2 | 4 | no | — |
| 135 | C2×D4×C89 | — | 2 | 2 | no | — |
| 136 | C2×D4×C89 | — | 2 | 2 | no | — |
| 137 | C2×D4×C89 | — | 4 | 4 | no | — |
| 138 | C2×D4×C89 | — | 8 | 4 | no | — |
| 139 | C2×D4×C89 | C2×D4 | 1 | 2 | yes | — |
| 140 | C2×D4×C89 | C2×D4 | 1 | 2 | yes | — |
| 141 | C22×C4×C89 | C2×D4 | 1 | 2 | yes | — |
| 142 | C22×C4×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 143 | C2×C8×C89 | — | 2 | 4 | no | — |
| 144 | C42×C89 | C2×D4 | 1 | 2 | yes | — |
| 145 | C42×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 146 | C42×C89 | C24 | 1 | 1 | yes | characteristic |
| 147 | C23×C89 | — | 2 | 2 | no | — |
| 148 | C23×C89 | — | 2 | 2 | no | — |
| 149 | C23×C89 | — | 4 | 4 | no | — |
| 150 | C23×C89 | — | 8 | 4 | no | — |
| 151 | C23×C89 | #120 | 1 | 1 | yes | characteristic |
| 152 | C22×D89 | — | 2 | 2 | no | — |
| 153 | C22×D89 | — | 8 | 4 | no | — |
| 154 | C22×D89 | — | 8 | 2 | no | — |
| 155 | D4×C89 | — | 4 | 2 | no | — |
| 156 | D4×C89 | — | 4 | 2 | no | — |
| 157 | D4×C89 | — | 4 | 4 | no | — |
| 158 | D4×C89 | — | 4 | 4 | no | — |
| 159 | D4×C89 | — | 8 | 2 | no | — |
| 160 | D4×C89 | — | 8 | 4 | no | — |
| 161 | C2×C4×C89 | — | 2 | 2 | no | — |
| 162 | C2×C4×C89 | — | 2 | 4 | no | — |
| 163 | C2×C4×C89 | #120 | 1 | 2 | yes | — |
| 164 | C2×C4×C89 | #120 | 1 | 1 | yes | characteristic |
| 165 | C2×C4×C89 | C22×D4 | 1 | 2 | yes | — |
| 166 | C2×C4×C89 | C22×D4 | 1 | 1 | yes | characteristic |
| 167 | C22⋊D89 | — | 4 | 4 | no | — |
| 168 | C22⋊D89 | — | 8 | 4 | no | — |
| 169 | C22⋊D89 | — | 8 | 4 | no | — |
| 170 | C22⋊D89 | — | 8 | 4 | no | — |
| 171 | C2×Dic89 | — | 2 | 2 | no | — |
| 172 | C2×Dic89 | — | 2 | 2 | no | — |
| 173 | C2×Dic89 | — | 2 | 2 | no | — |
| 174 | C2×Dic89 | — | 4 | 2 | no | — |
| 175 | C2×Dic89 | — | 8 | 2 | no | — |
| 176 | C2×Dic89 | — | 8 | 4 | no | — |
| 177 | C2×Dic89 | — | 8 | 2 | no | — |
| 178 | D356 | — | 2 | 4 | no | — |
| 179 | C4×D89 | — | 4 | 4 | no | — |
| 180 | Dic178 | — | 2 | 4 | no | — |
| 181 | Dic178 | — | 4 | 4 | no | — |
| 182 | Dic178 | — | 8 | 2 | no | — |
| 183 | C8×C89 | — | 4 | 4 | no | — |
| 184 | #10623494 | — | 2 | 4 | no | — |
| 185 | C22×C89 | — | 2 | 2 | no | — |
| 186 | C22×C89 | — | 4 | 4 | no | — |
| 187 | C22×C89 | — | 4 | 4 | no | — |
| 188 | C22×C89 | — | 4 | 2 | no | — |
| 189 | C22×C89 | — | 4 | 2 | no | — |
| 190 | C22×C89 | — | 16 | 4 | no | — |
| 191 | C22×C89 | #453 | 1 | 2 | yes | — |
| 192 | C22×C89 | C2×#120 | 1 | 1 | yes | characteristic |
| 193 | C2×D89 | — | 4 | 2 | no | — |
| 194 | C2×D89 | — | 4 | 2 | no | — |
| 195 | C2×D89 | — | 4 | 2 | no | — |
| 196 | C2×D89 | — | 16 | 4 | no | — |
| 197 | C4×C89 | — | 2 | 2 | no | — |
| 198 | C4×C89 | — | 2 | 1 | no | — |
| 199 | C4×C89 | — | 2 | 1 | no | — |
| 200 | C4×C89 | #577 | 1 | 4 | yes | — |
| 201 | Dic89 | — | 4 | 2 | no | — |
| 202 | Dic89 | — | 4 | 2 | no | — |
| 203 | Dic89 | — | 4 | 2 | no | — |
| 204 | Dic89 | — | 8 | 2 | no | — |
| 205 | #18683 | — | 89 | 1 | no | maximal, Sylow |
| 206 | C2×C89 | — | 2 | 2 | no | — |
| 207 | C2×C89 | — | 8 | 2 | no | — |
| 208 | C2×C89 | — | 8 | 2 | no | — |
| 209 | C2×C89 | #3009 | 1 | 2 | yes | — |
| 210 | C2×C89 | C2×#453 | 1 | 1 | yes | characteristic |
| 211 | D89 | — | 8 | 2 | no | — |
| 212 | #3543 | — | 89 | 1 | no | — |
| 213 | #3238 | — | 89 | 2 | no | — |
| 214 | C2×#492 | — | 89 | 1 | no | — |
| 215 | #1631 | — | 89 | 4 | no | — |
| 216 | #1630 | — | 89 | 2 | no | — |
| 217 | #1629 | — | 89 | 2 | no | — |
| 218 | #1555 | D89 | 1 | 1 | yes | characteristic, complemented |
| 219 | #1494 | — | 89 | 2 | no | — |
| 220 | C89 | #18683 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 221 | C22×SD16 | — | 178 | 2 | no | — |
| 222 | #560 | — | 178 | 2 | no | — |
| 223 | #559 | — | 89 | 1 | no | — |
| 224 | #550 | — | 89 | 2 | no | — |
| 225 | #546 | — | 178 | 2 | no | — |
| 226 | D42 | — | 89 | 1 | no | — |
| 227 | D42 | — | 178 | 2 | no | — |
| 228 | #540 | — | 178 | 2 | no | — |
| 229 | #535 | — | 178 | 2 | no | — |
| 230 | #534 | — | 178 | 2 | no | — |
| 231 | C2×C4⋊Q8 | — | 89 | 1 | no | — |
| 232 | C2×#127 | C2×D89 | 1 | 1 | yes | characteristic |
| 233 | #529 | — | 89 | 2 | no | — |
| 234 | #501 | — | 178 | 2 | no | — |
| 235 | #492 | — | 89 | 2 | no | — |
| 236 | #492 | — | 89 | 2 | no | — |
| 237 | #492 | — | 178 | 2 | no | — |
| 238 | #489 | — | 178 | 2 | no | — |
| 239 | #483 | — | 178 | 2 | no | — |
| 240 | #480 | — | 178 | 2 | no | — |
| 241 | #477 | — | 89 | 4 | no | — |
| 242 | #476 | — | 89 | 4 | no | — |
| 243 | #432 | C2×D89 | 1 | 2 | yes | complemented |
| 244 | C2×C4×C8 | — | 89 | 1 | no | — |
| 245 | #331 | C2×D89 | 1 | 2 | yes | — |
| 246 | #331 | C2×D89 | 1 | 2 | yes | complemented |
| 247 | Q8⋊C8 | — | 89 | 4 | no | — |
| 248 | D4⋊C8 | — | 89 | 4 | no | — |
| 249 | C2×#41 | — | 178 | 2 | no | — |
| 250 | C22×Q8 | — | 178 | 1 | no | — |
| 251 | C22×D4 | — | 2 | 2 | no | — |
| 252 | C22×D4 | — | 178 | 2 | no | — |
| 253 | C22×D4 | — | 178 | 2 | no | — |
| 254 | C22×D4 | D356 | 1 | 2 | yes | — |
| 255 | C2×SD16 | — | 356 | 8 | no | — |
| 256 | C2×SD16 | — | 178 | 4 | no | — |
| 257 | C2×SD16 | — | 178 | 4 | no | — |
| 258 | C22×C8 | — | 178 | 1 | no | — |
| 259 | C4⋊Q8 | — | 89 | 2 | no | — |
| 260 | C4⋊Q8 | — | 178 | 2 | no | — |
| 261 | C4⋊Q8 | — | 178 | 1 | no | — |
| 262 | #127 | — | 2 | 2 | no | — |
| 263 | #127 | — | 178 | 2 | no | — |
| 264 | #127 | D356 | 1 | 2 | yes | — |
| 265 | #127 | C22×D89 | 1 | 1 | yes | characteristic |
| 266 | #127 | C22×D89 | 1 | 1 | yes | characteristic |
| 267 | #126 | — | 178 | 2 | no | — |
| 268 | #125 | — | 89 | 2 | no | — |
| 269 | #124 | — | 89 | 2 | no | — |
| 270 | #124 | — | 178 | 2 | no | — |
| 271 | #123 | — | 178 | 2 | no | — |
| 272 | #123 | — | 178 | 4 | no | — |
| 273 | #123 | — | 178 | 2 | no | — |
| 274 | #123 | — | 178 | 2 | no | — |
| 275 | C22⋊Q8 | — | 89 | 2 | no | — |
| 276 | #121 | — | 89 | 2 | no | — |
| 277 | #121 | — | 178 | 2 | no | — |
| 278 | #121 | — | 178 | 2 | no | — |
| 279 | #121 | — | 178 | 4 | no | — |
| 280 | #121 | — | 178 | 4 | no | — |
| 281 | #121 | — | 178 | 4 | no | — |
| 282 | #121 | — | 178 | 4 | no | — |
| 283 | #120 | — | 178 | 2 | no | — |
| 284 | #120 | — | 178 | 4 | no | — |
| 285 | #120 | — | 178 | 4 | no | — |
| 286 | #120 | — | 178 | 2 | no | — |
| 287 | C4×Q8 | — | 89 | 2 | no | — |
| 288 | C4×D4 | — | 89 | 2 | no | — |
| 289 | C4×D4 | — | 178 | 2 | no | — |
| 290 | C4×D4 | — | 178 | 2 | no | — |
| 291 | C4×D4 | — | 178 | 2 | no | — |
| 292 | #117 | — | 178 | 2 | no | — |
| 293 | C2×C4⋊C4 | — | 178 | 2 | no | — |
| 294 | C2×C22⋊C4 | — | 178 | 2 | no | — |
| 295 | C2×C42 | C22×D89 | 1 | 1 | yes | characteristic |
| 296 | #107 | — | 178 | 4 | no | — |
| 297 | #106 | — | 178 | 4 | no | — |
| 298 | C4⋊C8 | C22×D89 | 1 | 4 | yes | — |
| 299 | #103 | — | 178 | 4 | no | — |
| 300 | #102 | — | 178 | 4 | no | — |
| 301 | C22⋊C8 | — | 2 | 2 | no | — |
| 302 | #97 | — | 2 | 2 | no | — |
| 303 | C4×C8 | — | 89 | 2 | no | — |
| 304 | C4×C8 | — | 178 | 1 | no | — |
| 305 | C24 | — | 2 | 2 | no | — |
| 306 | C24 | — | 178 | 2 | no | — |
| 307 | #41 | — | 712 | 4 | no | — |
| 308 | C2×Q8 | — | 89 | 2 | no | — |
| 309 | C2×Q8 | — | 356 | 4 | no | — |
| 310 | C2×Q8 | — | 356 | 1 | no | — |
| 311 | C2×Q8 | — | 178 | 2 | no | — |
| 312 | C2×D4 | — | 2 | 2 | no | — |
| 313 | C2×D4 | — | 2 | 4 | no | — |
| 314 | C2×D4 | — | 2 | 2 | no | — |
| 315 | C2×D4 | — | 2 | 2 | no | — |
| 316 | C2×D4 | — | 4 | 4 | no | — |
| 317 | C2×D4 | — | 8 | 4 | no | — |
| 318 | C2×D4 | — | 89 | 2 | no | — |
| 319 | C2×D4 | — | 178 | 2 | no | — |
| 320 | C2×D4 | — | 178 | 4 | no | — |
| 321 | C2×D4 | — | 178 | 4 | no | — |
| 322 | C2×D4 | — | 178 | 4 | no | — |
| 323 | C2×D4 | — | 712 | 4 | no | — |
| 324 | C2×D4 | — | 712 | 4 | no | — |
| 325 | C2×D4 | C2×D356 | 1 | 2 | yes | — |
| 326 | C2×D4 | C2×D356 | 1 | 2 | yes | — |
| 327 | C22×C4 | — | 356 | 1 | no | — |
| 328 | C22×C4 | — | 178 | 2 | no | — |
| 329 | C22×C4 | — | 178 | 4 | no | — |
| 330 | C22×C4 | — | 178 | 2 | no | — |
| 331 | C22×C4 | D4×D89 | 1 | 2 | yes | — |
| 332 | C22×C4 | C2×D356 | 1 | 1 | yes | characteristic |
| 333 | SD16 | — | 356 | 8 | no | — |
| 334 | SD16 | — | 356 | 8 | no | — |
| 335 | C2×C8 | — | 2 | 4 | no | — |
| 336 | C2×C8 | — | 178 | 4 | no | — |
| 337 | C2×C8 | — | 178 | 2 | no | — |
| 338 | C4⋊C4 | — | 89 | 2 | no | — |
| 339 | C4⋊C4 | — | 89 | 2 | no | — |
| 340 | C4⋊C4 | — | 356 | 2 | no | — |
| 341 | C4⋊C4 | — | 178 | 4 | no | — |
| 342 | C4⋊C4 | — | 178 | 2 | no | — |
| 343 | C4⋊C4 | — | 178 | 2 | no | — |
| 344 | C4⋊C4 | — | 178 | 2 | no | — |
| 345 | C4⋊C4 | — | 178 | 2 | no | — |
| 346 | C22⋊C4 | — | 178 | 2 | no | — |
| 347 | C22⋊C4 | — | 178 | 2 | no | — |
| 348 | C22⋊C4 | — | 178 | 4 | no | — |
| 349 | C22⋊C4 | — | 178 | 4 | no | — |
| 350 | C22⋊C4 | — | 178 | 2 | no | — |
| 351 | C22⋊C4 | — | 178 | 2 | no | — |
| 352 | C22⋊C4 | — | 178 | 2 | no | — |
| 353 | C22⋊C4 | — | 178 | 2 | no | — |
| 354 | C22⋊C4 | — | 178 | 2 | no | — |
| 355 | C42 | — | 178 | 2 | no | — |
| 356 | C42 | D4×D89 | 1 | 2 | yes | — |
| 357 | C42 | C2×D356 | 1 | 1 | yes | characteristic |
| 358 | C42 | C23×D89 | 1 | 1 | yes | characteristic |
| 359 | C23 | — | 2 | 2 | no | — |
| 360 | C23 | — | 2 | 2 | no | — |
| 361 | C23 | — | 4 | 4 | no | — |
| 362 | C23 | — | 8 | 4 | no | — |
| 363 | C23 | — | 178 | 2 | no | — |
| 364 | C23 | — | 712 | 2 | no | — |
| 365 | C23 | — | 712 | 4 | no | — |
| 366 | C23 | #15667982 | 1 | 1 | yes | characteristic |
| 367 | Q8 | — | 356 | 4 | no | — |
| 368 | Q8 | — | 178 | 4 | no | — |
| 369 | Q8 | — | 712 | 2 | no | — |
| 370 | D4 | — | 4 | 2 | no | — |
| 371 | D4 | — | 4 | 2 | no | — |
| 372 | D4 | — | 4 | 4 | no | — |
| 373 | D4 | — | 4 | 4 | no | — |
| 374 | D4 | — | 8 | 2 | no | — |
| 375 | D4 | — | 8 | 4 | no | — |
| 376 | D4 | — | 356 | 4 | no | — |
| 377 | D4 | — | 178 | 4 | no | — |
| 378 | D4 | — | 712 | 4 | no | — |
| 379 | D4 | — | 712 | 4 | no | — |
| 380 | D4 | — | 712 | 4 | no | — |
| 381 | C2×C4 | — | 2 | 2 | no | — |
| 382 | C2×C4 | — | 2 | 4 | no | — |
| 383 | C2×C4 | — | 356 | 4 | no | — |
| 384 | C2×C4 | — | 356 | 2 | no | — |
| 385 | C2×C4 | — | 178 | 2 | no | — |
| 386 | C2×C4 | — | 178 | 2 | no | — |
| 387 | C2×C4 | — | 178 | 2 | no | — |
| 388 | C2×C4 | — | 712 | 2 | no | — |
| 389 | C2×C4 | — | 712 | 4 | no | — |
| 390 | C2×C4 | — | 712 | 2 | no | — |
| 391 | C2×C4 | #15667982 | 1 | 1 | yes | characteristic |
| 392 | C2×C4 | #15667982 | 1 | 2 | yes | — |
| 393 | C2×C4 | C2×D4×D89 | 1 | 2 | yes | — |
| 394 | C2×C4 | C22×D356 | 1 | 1 | yes | characteristic |
| 395 | C8 | — | 4 | 4 | no | — |
| 396 | C8 | — | 178 | 4 | no | — |
| 397 | C22 | — | 2 | 2 | no | — |
| 398 | C22 | — | 4 | 2 | no | — |
| 399 | C22 | — | 4 | 2 | no | — |
| 400 | C22 | — | 4 | 4 | no | — |
| 401 | C22 | — | 4 | 4 | no | — |
| 402 | C22 | — | 16 | 4 | no | — |
| 403 | C22 | — | 356 | 2 | no | — |
| 404 | C22 | — | 356 | 2 | no | — |
| 405 | C22 | — | 356 | 2 | no | — |
| 406 | C22 | — | 1424 | 4 | no | — |
| 407 | C22 | #19151768 | 1 | 2 | yes | — |
| 408 | C22 | C2×#15667982 | 1 | 1 | yes | characteristic |
| 409 | C4 | — | 2 | 1 | no | — |
| 410 | C4 | — | 2 | 1 | no | — |
| 411 | C4 | — | 2 | 2 | no | — |
| 412 | C4 | — | 356 | 2 | no | — |
| 413 | C4 | — | 356 | 2 | no | — |
| 414 | C4 | — | 356 | 2 | no | — |
| 415 | C4 | — | 712 | 2 | no | — |
| 416 | C4 | #19152408 | 1 | 4 | yes | — |
| 417 | C2 | — | 2 | 2 | no | — |
| 418 | C2 | — | 8 | 2 | no | — |
| 419 | C2 | — | 8 | 2 | no | — |
| 420 | C2 | — | 712 | 2 | no | — |
| 421 | C2 | #26029530 | 1 | 2 | yes | — |
| 422 | C2 | C2×#19151768 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #26031475 | C2 | semidirect |
| 3. C2×#19151970 | C2 | semidirect |
| 4. #26019380 | C2 | semidirect |
| 5. #26019374 | C2 | semidirect |
| 6. #26019369 | C2 | semidirect |
| 7. #26018710 | C2 | semidirect |
| 8. C89×#1555 | C2 | semidirect |
| 19. C2×#15668012 | C22 | semidirect |
| 24. #19151970 | C22 | semidirect |
| 28. #19151894 | C22 | semidirect |
| 29. #19151889 | C22 | semidirect |
| 30. C2×C4×#10623494 | C22 | semidirect |
| 31. #19151328 | C22 | semidirect |
| 32. #19151325 | C22 | semidirect |
| 34. #432×C89 | C22 | semidirect |
| 36. #331×C89 | C22 | semidirect |
| 218. #1555 | D89 | semidirect |
| 220. C89 | #18683 | semidirect |
| 243. #432 | C2×D89 | semidirect |
| 246. #331 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034585 | 2 |
| #26031475 | 2 |
| C2×#19151970 | 2 |
| #26019380 | 2 |
| #26019374 | 2 |
| #26019369 | 2 |
| #26018710 | 2 |
| C89×#1555 | 2 |
| #18683 | 89 |