Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
640 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 109 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 | #11736750 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11736472 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11735975 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #11728543 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11728211 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11727622 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C7×#1283 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#6471 | — | 2 | 2 | no | — |
| 9 | #90168 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×#6437 | C22 | 1 | 1 | yes | characteristic |
| 11 | #90161 | C22 | 1 | 1 | yes | characteristic |
| 12 | C7×#431 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×C7×C4⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 14 | C4×C7×M16 | C22 | 1 | 1 | yes | characteristic |
| 15 | #89886 | — | 2 | 2 | no | — |
| 16 | C2×#6395 | — | 2 | 2 | no | — |
| 17 | C4×C4⋊Dic7 | C22 | 1 | 1 | yes | characteristic |
| 18 | #89623 | — | 2 | 1 | no | — |
| 19 | #89620 | — | 2 | 1 | no | — |
| 20 | #89620 | — | 2 | 2 | no | — |
| 21 | #89614 | — | 2 | 1 | no | — |
| 22 | #89613 | — | 2 | 1 | no | — |
| 23 | #89503 | — | 2 | 2 | no | — |
| 24 | #89484 | — | 2 | 2 | no | — |
| 25 | #89467 | — | 2 | 1 | no | — |
| 26 | #89466 | — | 2 | 1 | no | — |
| 27 | #89465 | — | 2 | 1 | no | — |
| 28 | #89465 | — | 2 | 1 | no | — |
| 29 | #89350 | — | 2 | 2 | no | — |
| 30 | #89265 | — | 2 | 2 | no | — |
| 31 | #10194 | — | 7 | 1 | no | maximal, Sylow |
| 32 | C2×#1157 | — | 2 | 1 | no | — |
| 33 | C22×D28 | — | 2 | 1 | no | — |
| 34 | C22×D28 | — | 2 | 1 | no | — |
| 35 | C22×D28 | — | 2 | 1 | no | — |
| 36 | C2×C7×M16 | D4 | 1 | 2 | yes | — |
| 37 | C22×C7×C8 | D4 | 1 | 2 | yes | — |
| 38 | C2×C42×C7 | C23 | 1 | 1 | yes | characteristic |
| 39 | #6493 | — | 2 | 1 | no | — |
| 40 | #6493 | — | 2 | 1 | no | — |
| 41 | #6489 | — | 2 | 1 | no | — |
| 42 | C2×C4⋊Dic7 | — | 2 | 1 | no | — |
| 43 | #6487 | — | 2 | 1 | no | — |
| 44 | #6487 | — | 2 | 1 | no | — |
| 45 | C2×C4×Dic7 | — | 2 | 1 | no | — |
| 46 | #6471 | — | 4 | 4 | no | — |
| 47 | #6471 | — | 4 | 4 | no | — |
| 48 | C2×D56 | — | 2 | 4 | no | — |
| 49 | C2×#1132 | — | 2 | 4 | no | — |
| 50 | C2×#1132 | — | 2 | 2 | no | — |
| 51 | C2×#1132 | — | 2 | 4 | no | — |
| 52 | #6438 | — | 2 | 1 | no | — |
| 53 | #6437 | — | 2 | 1 | no | — |
| 54 | #6437 | — | 2 | 1 | no | — |
| 55 | #6437 | — | 2 | 1 | no | — |
| 56 | #6437 | D4 | 1 | 2 | yes | — |
| 57 | #6437 | D4 | 1 | 1 | yes | characteristic |
| 58 | C4×D28 | — | 2 | 1 | no | — |
| 59 | C4×D28 | — | 2 | 1 | no | — |
| 60 | #6433 | — | 2 | 1 | no | — |
| 61 | #6432 | D4 | 1 | 1 | yes | characteristic |
| 62 | #6432 | D4 | 1 | 1 | yes | characteristic |
| 63 | #6432 | D4 | 1 | 1 | yes | characteristic |
| 64 | C4×Dic14 | — | 2 | 1 | no | — |
| 65 | C4×Dic14 | — | 2 | 1 | no | — |
| 66 | C7×C4⋊C8 | — | 2 | 1 | no | — |
| 67 | C7×C4⋊C8 | — | 2 | 1 | no | — |
| 68 | C7×C4⋊C8 | — | 2 | 1 | no | — |
| 69 | C7×C22⋊C8 | D4 | 1 | 2 | yes | — |
| 70 | C7×#97 | — | 2 | 1 | no | — |
| 71 | C4×C7×C8 | — | 2 | 1 | no | — |
| 72 | C4×C7×C8 | — | 2 | 1 | no | — |
| 73 | C7⋊#95 | — | 2 | 1 | no | — |
| 74 | #6395 | — | 2 | 2 | no | — |
| 75 | #6395 | — | 2 | 4 | no | — |
| 76 | #6395 | — | 4 | 4 | no | — |
| 77 | #6391 | — | 2 | 2 | no | — |
| 78 | #6390 | — | 2 | 2 | no | — |
| 79 | #3246 | — | 7 | 1 | no | — |
| 80 | #3208 | — | 7 | 1 | no | — |
| 81 | #3151 | — | 7 | 1 | no | — |
| 82 | #1986 | — | 7 | 1 | no | — |
| 83 | #1982 | — | 7 | 1 | no | — |
| 84 | #1502 | — | 7 | 1 | no | — |
| 85 | #1283 | D7 | 1 | 1 | yes | characteristic, complemented |
| 86 | C23×D7 | — | 4 | 1 | no | — |
| 87 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 88 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 89 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 90 | C2×C22⋊D7 | — | 4 | 1 | no | — |
| 91 | C22×Dic7 | — | 4 | 1 | no | — |
| 92 | #1157 | — | 4 | 2 | no | — |
| 93 | #1157 | — | 4 | 2 | no | — |
| 94 | C2×D28 | — | 2 | 1 | no | — |
| 95 | C2×D28 | — | 2 | 2 | no | — |
| 96 | C2×D28 | — | 2 | 2 | no | — |
| 97 | C2×D28 | — | 2 | 1 | no | — |
| 98 | C2×D28 | — | 2 | 2 | no | — |
| 99 | C2×D28 | — | 2 | 1 | no | — |
| 100 | C2×D28 | — | 4 | 2 | no | — |
| 101 | C2×D28 | — | 4 | 2 | no | — |
| 102 | C2×D28 | — | 4 | 2 | no | — |
| 103 | C2×D28 | — | 4 | 2 | no | — |
| 104 | C2×D28 | — | 4 | 1 | no | — |
| 105 | C2×D28 | — | 4 | 1 | no | — |
| 106 | C2×D28 | — | 4 | 1 | no | — |
| 107 | C2×D28 | — | 8 | 2 | no | — |
| 108 | C2×C4×D7 | — | 4 | 1 | no | — |
| 109 | C2×Dic14 | — | 2 | 1 | no | — |
| 110 | C2×Dic14 | — | 2 | 1 | no | — |
| 111 | C2×Dic14 | — | 2 | 1 | no | — |
| 112 | C7×M16 | — | 2 | 2 | no | — |
| 113 | C7×M16 | SD16 | 1 | 4 | yes | complemented |
| 114 | C2×C7×C8 | — | 2 | 2 | no | — |
| 115 | C2×C7×C8 | — | 2 | 2 | no | — |
| 116 | C2×C7×C8 | — | 2 | 2 | no | — |
| 117 | C2×C7×C8 | — | 4 | 2 | no | — |
| 118 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 119 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 120 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 121 | C42×C7 | #41 | 1 | 1 | yes | characteristic |
| 122 | C22⋊Dic7 | — | 4 | 1 | no | — |
| 123 | (C2×D7)⋊C4 | — | 4 | 1 | no | — |
| 124 | (C2×D7)⋊C4 | — | 4 | 1 | no | — |
| 125 | C4⋊Dic7 | — | 2 | 2 | no | — |
| 126 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 127 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 128 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 129 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 130 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 131 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 132 | C4⋊Dic7 | — | 4 | 1 | no | — |
| 133 | Dic7⋊C4 | — | 4 | 1 | no | — |
| 134 | Dic7⋊C4 | — | 4 | 1 | no | — |
| 135 | C4×Dic7 | — | 4 | 1 | no | — |
| 136 | C4×Dic7 | — | 4 | 2 | no | — |
| 137 | D56 | — | 4 | 8 | no | — |
| 138 | #1132 | — | 4 | 8 | no | — |
| 139 | #1132 | — | 8 | 4 | no | — |
| 140 | #1132 | — | 8 | 2 | no | — |
| 141 | C2×AGL(1,ℤ/8) | — | 14 | 2 | no | — |
| 142 | #533 | — | 7 | 1 | no | — |
| 143 | #532 | — | 7 | 1 | no | — |
| 144 | C2×#127 | — | 7 | 1 | no | — |
| 145 | #496 | — | 14 | 2 | no | — |
| 146 | #493 | — | 14 | 1 | no | — |
| 147 | #492 | — | 14 | 1 | no | — |
| 148 | #492 | — | 14 | 1 | no | — |
| 149 | #486 | — | 14 | 1 | no | — |
| 150 | #476 | — | 14 | 1 | no | — |
| 151 | #475 | — | 14 | 1 | no | — |
| 152 | #465 | — | 14 | 2 | no | — |
| 153 | #461 | — | 14 | 1 | no | — |
| 154 | #460 | — | 14 | 2 | no | — |
| 155 | #460 | — | 14 | 1 | no | — |
| 156 | #450 | — | 14 | 2 | no | — |
| 157 | #431 | C2×D7 | 1 | 1 | yes | characteristic |
| 158 | C2×C4⋊C8 | C2×D7 | 1 | 1 | yes | characteristic |
| 159 | C2×#102 | — | 14 | 2 | no | — |
| 160 | C4×M16 | C2×D7 | 1 | 1 | yes | characteristic |
| 161 | C4×C4⋊C4 | — | 7 | 1 | no | — |
| 162 | #339 | — | 14 | 2 | no | — |
| 163 | #327 | — | 14 | 2 | no | — |
| 164 | C23×C7 | #127 | 1 | 1 | yes | characteristic |
| 165 | C22×D7 | — | 4 | 1 | no | — |
| 166 | C22×D7 | — | 4 | 2 | no | — |
| 167 | C22×D7 | — | 8 | 2 | no | — |
| 168 | C22×D7 | — | 8 | 2 | no | — |
| 169 | C22×D7 | — | 8 | 1 | no | — |
| 170 | C22×D7 | — | 8 | 1 | no | — |
| 171 | C2×C4×C7 | — | 2 | 1 | no | — |
| 172 | C2×C4×C7 | — | 2 | 1 | no | — |
| 173 | C2×C4×C7 | — | 4 | 1 | no | — |
| 174 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 175 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 176 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 177 | C2×C4×C7 | #121 | 1 | 1 | yes | characteristic |
| 178 | C2×C4×C7 | #121 | 1 | 1 | yes | characteristic |
| 179 | C2×C4×C7 | #121 | 1 | 1 | yes | characteristic |
| 180 | C2×C4×C7 | C2×SD16 | 1 | 2 | yes | — |
| 181 | C2×C4×C7 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 182 | C22⋊D7 | — | 8 | 1 | no | — |
| 183 | C22⋊D7 | — | 8 | 1 | no | — |
| 184 | C2×Dic7 | — | 4 | 2 | no | — |
| 185 | C2×Dic7 | — | 4 | 1 | no | — |
| 186 | C2×Dic7 | — | 4 | 1 | no | — |
| 187 | C2×Dic7 | — | 4 | 1 | no | — |
| 188 | C2×Dic7 | — | 8 | 1 | no | — |
| 189 | C2×Dic7 | — | 8 | 1 | no | — |
| 190 | D28 | — | 4 | 4 | no | — |
| 191 | D28 | — | 4 | 4 | no | — |
| 192 | D28 | — | 4 | 4 | no | — |
| 193 | D28 | — | 4 | 2 | no | — |
| 194 | D28 | — | 4 | 1 | no | — |
| 195 | D28 | — | 4 | 1 | no | — |
| 196 | D28 | — | 8 | 1 | no | — |
| 197 | D28 | — | 8 | 2 | no | — |
| 198 | D28 | — | 8 | 1 | no | — |
| 199 | D28 | — | 8 | 1 | no | — |
| 200 | D28 | — | 8 | 2 | no | — |
| 201 | C4×D7 | — | 8 | 2 | no | — |
| 202 | Dic14 | — | 4 | 2 | no | — |
| 203 | Dic14 | — | 4 | 2 | no | — |
| 204 | Dic14 | — | 4 | 1 | no | — |
| 205 | Dic14 | — | 4 | 1 | no | — |
| 206 | C7×C8 | — | 2 | 4 | no | — |
| 207 | C7×C8 | — | 4 | 2 | no | — |
| 208 | C7×C8 | — | 4 | 2 | no | — |
| 209 | C2×#41 | — | 14 | 1 | no | — |
| 210 | C22×D4 | — | 14 | 1 | no | — |
| 211 | C22×D4 | — | 14 | 1 | no | — |
| 212 | C22×D4 | — | 14 | 1 | no | — |
| 213 | AGL(1,ℤ/8) | — | 28 | 4 | no | — |
| 214 | AGL(1,ℤ/8) | — | 28 | 4 | no | — |
| 215 | C2×SD16 | — | 14 | 4 | no | — |
| 216 | C2×SD16 | — | 14 | 4 | no | — |
| 217 | C2×SD16 | — | 14 | 2 | no | — |
| 218 | C2×D8 | — | 14 | 4 | no | — |
| 219 | C2×M16 | D28 | 1 | 2 | yes | — |
| 220 | C22×C8 | D28 | 1 | 2 | yes | — |
| 221 | C4⋊Q8 | — | 7 | 1 | no | — |
| 222 | C4⋊Q8 | — | 7 | 1 | no | — |
| 223 | C4⋊Q8 | — | 7 | 1 | no | — |
| 224 | #127 | — | 7 | 2 | no | — |
| 225 | #127 | — | 7 | 1 | no | — |
| 226 | #127 | — | 14 | 1 | no | — |
| 227 | #127 | — | 14 | 1 | no | — |
| 228 | #127 | — | 14 | 1 | no | — |
| 229 | #125 | — | 14 | 1 | no | — |
| 230 | #124 | — | 14 | 1 | no | — |
| 231 | C22⋊Q8 | — | 14 | 1 | no | — |
| 232 | C22⋊Q8 | — | 14 | 1 | no | — |
| 233 | #121 | — | 14 | 1 | no | — |
| 234 | #121 | — | 14 | 1 | no | — |
| 235 | C4×Q8 | — | 14 | 1 | no | — |
| 236 | C4×Q8 | — | 14 | 1 | no | — |
| 237 | C4×D4 | — | 14 | 1 | no | — |
| 238 | C4×D4 | — | 14 | 1 | no | — |
| 239 | #117 | — | 14 | 1 | no | — |
| 240 | C2×C4⋊C4 | — | 14 | 1 | no | — |
| 241 | C2×C42 | — | 14 | 1 | no | — |
| 242 | C2×C42 | C22×D7 | 1 | 1 | yes | characteristic |
| 243 | #106 | — | 14 | 2 | no | — |
| 244 | C4⋊C8 | — | 2 | 1 | no | — |
| 245 | C4⋊C8 | — | 2 | 1 | no | — |
| 246 | C4⋊C8 | — | 2 | 1 | no | — |
| 247 | #103 | — | 14 | 2 | no | — |
| 248 | #102 | — | 14 | 4 | no | — |
| 249 | #102 | — | 14 | 2 | no | — |
| 250 | #102 | — | 28 | 4 | no | — |
| 251 | C22⋊C8 | D28 | 1 | 2 | yes | — |
| 252 | #97 | — | 2 | 1 | no | — |
| 253 | C4×C8 | — | 2 | 1 | no | — |
| 254 | C4×C8 | — | 2 | 1 | no | — |
| 255 | #95 | — | 14 | 1 | no | — |
| 256 | C22×C7 | — | 2 | 1 | no | — |
| 257 | C22×C7 | — | 2 | 1 | no | — |
| 258 | C22×C7 | #392 | 1 | 1 | yes | characteristic |
| 259 | C22×C7 | #492 | 1 | 1 | yes | characteristic |
| 260 | C22×C7 | #496 | 1 | 1 | yes | characteristic |
| 261 | C2×D7 | — | 8 | 2 | no | — |
| 262 | C2×D7 | — | 8 | 1 | no | — |
| 263 | C2×D7 | — | 8 | 2 | no | — |
| 264 | C2×D7 | — | 8 | 1 | no | — |
| 265 | C2×D7 | — | 8 | 1 | no | — |
| 266 | C2×D7 | — | 8 | 2 | no | — |
| 267 | C2×D7 | — | 16 | 2 | no | — |
| 268 | C2×D7 | — | 16 | 2 | no | — |
| 269 | C4×C7 | — | 2 | 1 | no | — |
| 270 | C4×C7 | — | 2 | 1 | no | — |
| 271 | C4×C7 | — | 2 | 1 | no | — |
| 272 | C4×C7 | #450 | 1 | 2 | yes | — |
| 273 | C4×C7 | #453 | 1 | 1 | yes | characteristic |
| 274 | C4×C7 | #454 | 1 | 1 | yes | characteristic |
| 275 | C4×C7 | #460 | 1 | 2 | yes | — |
| 276 | Dic7 | — | 8 | 2 | no | — |
| 277 | Dic7 | — | 8 | 1 | no | — |
| 278 | Dic7 | — | 8 | 1 | no | — |
| 279 | Dic7 | — | 8 | 1 | no | — |
| 280 | C24 | — | 28 | 1 | no | — |
| 281 | #41 | — | 28 | 2 | no | — |
| 282 | #41 | — | 28 | 2 | no | — |
| 283 | C2×Q8 | — | 14 | 1 | no | — |
| 284 | C2×Q8 | — | 14 | 1 | no | — |
| 285 | C2×Q8 | — | 14 | 1 | no | — |
| 286 | C2×D4 | — | 14 | 1 | no | — |
| 287 | C2×D4 | — | 14 | 2 | no | — |
| 288 | C2×D4 | — | 14 | 1 | no | — |
| 289 | C2×D4 | — | 14 | 2 | no | — |
| 290 | C2×D4 | — | 14 | 2 | no | — |
| 291 | C2×D4 | — | 14 | 1 | no | — |
| 292 | C2×D4 | — | 28 | 2 | no | — |
| 293 | C2×D4 | — | 28 | 2 | no | — |
| 294 | C2×D4 | — | 28 | 1 | no | — |
| 295 | C2×D4 | — | 28 | 1 | no | — |
| 296 | C2×D4 | — | 28 | 1 | no | — |
| 297 | C2×D4 | — | 28 | 1 | no | — |
| 298 | C2×D4 | — | 28 | 2 | no | — |
| 299 | C2×D4 | — | 28 | 2 | no | — |
| 300 | C2×D4 | — | 56 | 2 | no | — |
| 301 | C22×C4 | — | 28 | 1 | no | — |
| 302 | C22×C4 | — | 28 | 1 | no | — |
| 303 | C22×C4 | C2×D28 | 1 | 1 | yes | characteristic |
| 304 | C22×C4 | C2×D28 | 1 | 1 | yes | characteristic |
| 305 | C22×C4 | C2×D28 | 1 | 1 | yes | characteristic |
| 306 | SD16 | — | 28 | 8 | no | — |
| 307 | SD16 | — | 56 | 4 | no | — |
| 308 | SD16 | — | 56 | 2 | no | — |
| 309 | D8 | — | 28 | 8 | no | — |
| 310 | M16 | — | 2 | 2 | no | — |
| 311 | M16 | #1132 | 1 | 4 | yes | complemented |
| 312 | C2×C8 | — | 2 | 2 | no | — |
| 313 | C2×C8 | — | 2 | 2 | no | — |
| 314 | C2×C8 | — | 2 | 2 | no | — |
| 315 | C2×C8 | — | 4 | 2 | no | — |
| 316 | C4⋊C4 | — | 14 | 2 | no | — |
| 317 | C4⋊C4 | — | 14 | 1 | no | — |
| 318 | C4⋊C4 | — | 14 | 1 | no | — |
| 319 | C4⋊C4 | — | 14 | 1 | no | — |
| 320 | C4⋊C4 | — | 14 | 1 | no | — |
| 321 | C4⋊C4 | — | 14 | 1 | no | — |
| 322 | C4⋊C4 | — | 14 | 1 | no | — |
| 323 | C4⋊C4 | — | 28 | 1 | no | — |
| 324 | C4⋊C4 | — | 28 | 1 | no | — |
| 325 | C4⋊C4 | — | 28 | 1 | no | — |
| 326 | C22⋊C4 | — | 28 | 1 | no | — |
| 327 | C22⋊C4 | — | 28 | 1 | no | — |
| 328 | C22⋊C4 | — | 28 | 1 | no | — |
| 329 | C42 | — | 28 | 1 | no | — |
| 330 | C42 | — | 28 | 2 | no | — |
| 331 | C42 | D4×D7 | 1 | 1 | yes | characteristic |
| 332 | C42 | D4×D7 | 1 | 1 | yes | characteristic |
| 333 | C42 | D4×D7 | 1 | 1 | yes | characteristic |
| 334 | C42 | #1161 | 1 | 1 | yes | characteristic |
| 335 | C2×C7 | — | 2 | 1 | no | — |
| 336 | C2×C7 | — | 2 | 1 | no | — |
| 337 | C2×C7 | #2006 | 1 | 1 | yes | characteristic |
| 338 | C2×C7 | #2008 | 1 | 1 | yes | characteristic |
| 339 | C2×C7 | #2014 | 1 | 1 | yes | characteristic |
| 340 | D7 | — | 16 | 1 | no | — |
| 341 | D7 | — | 16 | 2 | no | — |
| 342 | C23 | — | 28 | 1 | no | — |
| 343 | C23 | — | 28 | 2 | no | — |
| 344 | C23 | — | 56 | 2 | no | — |
| 345 | C23 | — | 56 | 2 | no | — |
| 346 | C23 | — | 56 | 1 | no | — |
| 347 | C23 | — | 56 | 1 | no | — |
| 348 | C23 | #6437 | 1 | 1 | yes | characteristic |
| 349 | Q8 | — | 28 | 2 | no | — |
| 350 | Q8 | — | 28 | 2 | no | — |
| 351 | Q8 | — | 28 | 1 | no | — |
| 352 | Q8 | — | 28 | 1 | no | — |
| 353 | D4 | — | 28 | 4 | no | — |
| 354 | D4 | — | 28 | 4 | no | — |
| 355 | D4 | — | 28 | 2 | no | — |
| 356 | D4 | — | 28 | 4 | no | — |
| 357 | D4 | — | 28 | 1 | no | — |
| 358 | D4 | — | 28 | 1 | no | — |
| 359 | D4 | — | 56 | 1 | no | — |
| 360 | D4 | — | 56 | 2 | no | — |
| 361 | D4 | — | 56 | 1 | no | — |
| 362 | D4 | — | 56 | 1 | no | — |
| 363 | D4 | — | 56 | 2 | no | — |
| 364 | D4 | — | 56 | 1 | no | — |
| 365 | D4 | — | 56 | 1 | no | — |
| 366 | C2×C4 | — | 2 | 1 | no | — |
| 367 | C2×C4 | — | 2 | 1 | no | — |
| 368 | C2×C4 | — | 4 | 1 | no | — |
| 369 | C2×C4 | — | 28 | 2 | no | — |
| 370 | C2×C4 | — | 28 | 1 | no | — |
| 371 | C2×C4 | — | 28 | 1 | no | — |
| 372 | C2×C4 | — | 28 | 1 | no | — |
| 373 | C2×C4 | — | 56 | 1 | no | — |
| 374 | C2×C4 | — | 56 | 1 | no | — |
| 375 | C2×C4 | — | 56 | 2 | no | — |
| 376 | C2×C4 | #6445 | 1 | 1 | yes | characteristic |
| 377 | C2×C4 | #6445 | 1 | 1 | yes | characteristic |
| 378 | C2×C4 | #6445 | 1 | 1 | yes | characteristic |
| 379 | C2×C4 | #6458 | 1 | 1 | yes | characteristic |
| 380 | C2×C4 | #6458 | 1 | 1 | yes | characteristic |
| 381 | C2×C4 | #6458 | 1 | 1 | yes | characteristic |
| 382 | C2×C4 | C2×#1132 | 1 | 2 | yes | — |
| 383 | C2×C4 | #6471 | 1 | 2 | yes | — |
| 384 | C8 | — | 2 | 4 | no | — |
| 385 | C8 | — | 4 | 2 | no | — |
| 386 | C8 | — | 4 | 2 | no | — |
| 387 | C7 | #10194 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 388 | C22 | — | 2 | 1 | no | — |
| 389 | C22 | — | 2 | 1 | no | — |
| 390 | C22 | — | 56 | 1 | no | — |
| 391 | C22 | — | 56 | 2 | no | — |
| 392 | C22 | — | 56 | 2 | no | — |
| 393 | C22 | — | 56 | 1 | no | — |
| 394 | C22 | — | 56 | 2 | no | — |
| 395 | C22 | — | 56 | 1 | no | — |
| 396 | C22 | — | 112 | 2 | no | — |
| 397 | C22 | — | 112 | 2 | no | — |
| 398 | C22 | #89443 | 1 | 1 | yes | characteristic |
| 399 | C22 | #89465 | 1 | 1 | yes | characteristic |
| 400 | C22 | #89484 | 1 | 1 | yes | characteristic |
| 401 | C4 | — | 2 | 1 | no | — |
| 402 | C4 | — | 2 | 1 | no | — |
| 403 | C4 | — | 2 | 1 | no | — |
| 404 | C4 | — | 56 | 2 | no | — |
| 405 | C4 | — | 56 | 1 | no | — |
| 406 | C4 | — | 56 | 1 | no | — |
| 407 | C4 | — | 56 | 1 | no | — |
| 408 | C4 | #89503 | 1 | 2 | yes | — |
| 409 | C4 | #89519 | 1 | 1 | yes | characteristic |
| 410 | C4 | #89525 | 1 | 1 | yes | characteristic |
| 411 | C4 | #89620 | 1 | 2 | yes | — |
| 412 | C2 | — | 2 | 1 | no | — |
| 413 | C2 | — | 2 | 1 | no | — |
| 414 | C2 | — | 112 | 2 | no | — |
| 415 | C2 | — | 112 | 1 | no | — |
| 416 | C2 | #11726430 | 1 | 1 | yes | characteristic |
| 417 | C2 | #11726762 | 1 | 1 | yes | characteristic |
| 418 | C2 | #11726782 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11736750 | C2 | semidirect |
| 2. #11736472 | C2 | semidirect |
| 4. #11728543 | C2 | semidirect |
| 5. #11728211 | C2 | semidirect |
| 6. #11727622 | C2 | semidirect |
| 7. C7×#1283 | C2 | semidirect |
| 85. #1283 | D7 | semidirect |
| 113. C7×M16 | SD16 | semidirect |
| 311. M16 | #1132 | semidirect |
| 387. C7 | #10194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736750 | 2 |
| #11736472 | 2 |
| #11735975 | 2 |
| #11728543 | 2 |
| #11728211 | 2 |
| #11727622 | 2 |
| C7×#1283 | 2 |
| #10194 | 7 |