Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
794 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 103 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 | #11736748 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11736500 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11731244 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11728510 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11728256 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11727223 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C7×#1303 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#6471 | — | 2 | 1 | no | — |
| 9 | C2×#6458 | — | 2 | 2 | no | — |
| 10 | #90168 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×#6437 | — | 2 | 1 | no | — |
| 12 | C2×#6437 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×C4×D28 | C22 | 1 | 1 | yes | characteristic |
| 14 | C7×#431 | C22 | 1 | 1 | yes | characteristic |
| 15 | C7×#423 | C22 | 1 | 1 | yes | characteristic |
| 16 | C4×C7×C4⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 17 | #89905 | — | 2 | 1 | no | — |
| 18 | #89711 | — | 2 | 1 | no | — |
| 19 | #89697 | C22 | 1 | 1 | yes | characteristic |
| 20 | #89616 | — | 2 | 2 | no | — |
| 21 | #89615 | — | 2 | 1 | no | — |
| 22 | #89615 | — | 2 | 2 | no | — |
| 23 | #89613 | — | 2 | 1 | no | — |
| 24 | #89504 | — | 2 | 2 | no | — |
| 25 | #89467 | — | 2 | 1 | no | — |
| 26 | #89466 | — | 2 | 1 | no | — |
| 27 | #89443 | — | 2 | 2 | no | — |
| 28 | #89280 | — | 2 | 2 | no | — |
| 29 | #89278 | — | 2 | 2 | no | — |
| 30 | #89246 | — | 2 | 2 | no | — |
| 31 | #10238 | — | 7 | 1 | no | maximal, Sylow |
| 32 | C2×#1157 | — | 2 | 1 | no | — |
| 33 | C22×D28 | — | 2 | 1 | no | — |
| 34 | C22×D28 | — | 2 | 4 | no | — |
| 35 | C22×D28 | — | 2 | 1 | no | — |
| 36 | C22×D28 | D4 | 1 | 1 | yes | characteristic |
| 37 | C22×D28 | D4 | 1 | 2 | yes | — |
| 38 | C22×C4×D7 | — | 2 | 1 | no | — |
| 39 | C2×C7×M16 | — | 2 | 1 | no | — |
| 40 | C2×C7×C4⋊C4 | — | 2 | 1 | no | — |
| 41 | C2×C42×C7 | — | 2 | 1 | no | — |
| 42 | C2×C42×C7 | C23 | 1 | 1 | yes | characteristic |
| 43 | #6493 | — | 2 | 1 | no | — |
| 44 | #6493 | — | 2 | 1 | no | — |
| 45 | C2×(C2×D7)⋊C4 | — | 2 | 4 | no | — |
| 46 | C2×(C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 47 | C2×C4⋊Dic7 | D4 | 1 | 1 | yes | characteristic |
| 48 | #6471 | — | 4 | 2 | no | — |
| 49 | #6471 | — | 4 | 2 | no | — |
| 50 | C2×D56 | — | 2 | 2 | no | — |
| 51 | C2×D56 | — | 2 | 4 | no | — |
| 52 | C2×#1132 | — | 2 | 2 | no | — |
| 53 | #6458 | — | 4 | 8 | no | — |
| 54 | #6438 | — | 2 | 1 | no | — |
| 55 | #6437 | — | 2 | 1 | no | — |
| 56 | #6437 | — | 2 | 1 | no | — |
| 57 | #6437 | — | 2 | 1 | no | — |
| 58 | #6437 | — | 2 | 1 | no | — |
| 59 | #6437 | — | 4 | 2 | no | — |
| 60 | #6437 | — | 4 | 2 | no | — |
| 61 | #6437 | D4 | 1 | 1 | yes | characteristic, complemented |
| 62 | C4×D28 | — | 2 | 1 | no | — |
| 63 | C4×D28 | — | 2 | 1 | no | — |
| 64 | C4×D28 | — | 2 | 1 | no | — |
| 65 | C4×D28 | — | 2 | 1 | no | — |
| 66 | C4×D28 | — | 2 | 1 | no | — |
| 67 | C4×D28 | — | 2 | 1 | no | — |
| 68 | #6432 | D4 | 1 | 1 | yes | characteristic, complemented |
| 69 | C7×C4⋊C8 | — | 2 | 1 | no | — |
| 70 | C7×C4⋊C8 | D4 | 1 | 2 | yes | complemented |
| 71 | C7×C4⋊C8 | D4 | 1 | 2 | yes | complemented |
| 72 | C7×C22⋊C8 | — | 2 | 1 | no | — |
| 73 | C4×C7×C8 | — | 2 | 1 | no | — |
| 74 | C7×#95 | D4 | 1 | 2 | yes | — |
| 75 | C22⋊(C7⋊C8) | — | 2 | 1 | no | — |
| 76 | #6395 | — | 2 | 2 | no | — |
| 77 | #6395 | — | 2 | 4 | no | — |
| 78 | #6390 | — | 2 | 2 | no | — |
| 79 | C4⋊(C7⋊C8) | — | 2 | 1 | no | — |
| 80 | C4×C7⋊C8 | — | 2 | 1 | no | — |
| 81 | #3205 | — | 7 | 1 | no | — |
| 82 | #3036 | — | 7 | 1 | no | — |
| 83 | #2541 | — | 7 | 1 | no | — |
| 84 | #1545 | — | 7 | 1 | no | — |
| 85 | #1502 | — | 7 | 1 | no | — |
| 86 | #1478 | — | 7 | 1 | no | — |
| 87 | #1303 | D7 | 1 | 1 | yes | characteristic, complemented |
| 88 | C23×D7 | — | 2 | 1 | no | — |
| 89 | C23×D7 | — | 2 | 2 | no | — |
| 90 | C22×C4×C7 | — | 2 | 2 | no | — |
| 91 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 92 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 93 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 94 | C2×C22⋊D7 | — | 4 | 1 | no | — |
| 95 | C22×Dic7 | — | 2 | 1 | no | — |
| 96 | #1157 | — | 4 | 1 | no | — |
| 97 | #1157 | — | 4 | 1 | no | — |
| 98 | #1157 | — | 4 | 1 | no | — |
| 99 | #1157 | — | 4 | 1 | no | — |
| 100 | C2×D28 | — | 2 | 1 | no | — |
| 101 | C2×D28 | — | 2 | 1 | no | — |
| 102 | C2×D28 | — | 2 | 1 | no | — |
| 103 | C2×D28 | — | 2 | 1 | no | — |
| 104 | C2×D28 | — | 2 | 1 | no | — |
| 105 | C2×D28 | — | 2 | 2 | no | — |
| 106 | C2×D28 | — | 2 | 1 | no | — |
| 107 | C2×D28 | — | 2 | 1 | no | — |
| 108 | C2×D28 | — | 2 | 1 | no | — |
| 109 | C2×D28 | — | 2 | 2 | no | — |
| 110 | C2×D28 | — | 4 | 4 | no | — |
| 111 | C2×D28 | — | 4 | 8 | no | — |
| 112 | C2×D28 | — | 4 | 8 | no | — |
| 113 | C2×D28 | — | 4 | 1 | no | — |
| 114 | C2×D28 | — | 4 | 1 | no | — |
| 115 | C2×D28 | — | 4 | 1 | no | — |
| 116 | C2×D28 | — | 4 | 1 | no | — |
| 117 | C2×D28 | — | 4 | 1 | no | — |
| 118 | C2×D28 | — | 4 | 1 | no | — |
| 119 | C2×D28 | — | 4 | 1 | no | — |
| 120 | C2×D28 | — | 4 | 1 | no | — |
| 121 | C2×D28 | — | 8 | 2 | no | — |
| 122 | C2×D28 | — | 8 | 4 | no | — |
| 123 | C2×D28 | D8 | 1 | 2 | yes | complemented |
| 124 | C2×C4×D7 | — | 4 | 4 | no | — |
| 125 | C2×C4×D7 | — | 4 | 1 | no | — |
| 126 | C2×C4×D7 | — | 4 | 1 | no | — |
| 127 | C2×C4×D7 | — | 4 | 1 | no | — |
| 128 | C2×Dic14 | — | 2 | 1 | no | — |
| 129 | C7×M16 | — | 4 | 1 | no | — |
| 130 | C7×M16 | — | 4 | 1 | no | — |
| 131 | C2×C7×C8 | — | 2 | 2 | no | — |
| 132 | C2×C7×C8 | — | 2 | 2 | no | — |
| 133 | C7×C4⋊C4 | — | 2 | 4 | no | — |
| 134 | C42×C7 | — | 4 | 1 | no | — |
| 135 | C42×C7 | — | 4 | 1 | no | — |
| 136 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 137 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 138 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 139 | C42×C7 | #41 | 1 | 1 | yes | characteristic |
| 140 | (C2×D7)⋊C4 | — | 4 | 8 | no | — |
| 141 | (C2×D7)⋊C4 | — | 4 | 1 | no | — |
| 142 | (C2×D7)⋊C4 | — | 4 | 1 | no | — |
| 143 | (C2×D7)⋊C4 | — | 4 | 1 | no | — |
| 144 | (C2×D7)⋊C4 | — | 4 | 1 | no | — |
| 145 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 146 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 147 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 148 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 149 | C2×C7⋊C8 | — | 4 | 1 | no | — |
| 150 | D56 | — | 4 | 4 | no | — |
| 151 | D56 | — | 8 | 4 | no | — |
| 152 | #1132 | — | 4 | 4 | no | — |
| 153 | C2×AGL(1,ℤ/8) | — | 14 | 1 | no | — |
| 154 | #532 | — | 7 | 1 | no | — |
| 155 | C2×#127 | — | 7 | 1 | no | — |
| 156 | C2×#127 | — | 14 | 1 | no | — |
| 157 | C2×#121 | — | 14 | 2 | no | — |
| 158 | C2×C4×D4 | — | 7 | 1 | no | — |
| 159 | #493 | — | 14 | 1 | no | — |
| 160 | #486 | — | 14 | 1 | no | — |
| 161 | #463 | — | 14 | 2 | no | — |
| 162 | #461 | — | 14 | 1 | no | — |
| 163 | #459 | — | 14 | 1 | no | — |
| 164 | #459 | — | 14 | 2 | no | — |
| 165 | #447 | — | 14 | 2 | no | — |
| 166 | #431 | — | 7 | 1 | no | — |
| 167 | #431 | C2×D7 | 1 | 1 | yes | characteristic |
| 168 | #423 | C2×D7 | 1 | 1 | yes | characteristic |
| 169 | #417 | — | 14 | 1 | no | — |
| 170 | #392 | — | 14 | 2 | no | — |
| 171 | #390 | — | 14 | 1 | no | — |
| 172 | C4×C4⋊C4 | C2×D7 | 1 | 1 | yes | characteristic |
| 173 | #331 | — | 14 | 2 | no | — |
| 174 | #327 | — | 14 | 2 | no | — |
| 175 | D4⋊C8 | — | 14 | 2 | no | — |
| 176 | C23×C7 | #120 | 1 | 1 | yes | characteristic |
| 177 | C22×D7 | — | 2 | 2 | no | — |
| 178 | C22×D7 | — | 4 | 2 | no | — |
| 179 | C22×D7 | — | 4 | 2 | no | — |
| 180 | C22×D7 | — | 4 | 1 | no | — |
| 181 | C22×D7 | — | 4 | 1 | no | — |
| 182 | C22×D7 | — | 4 | 4 | no | — |
| 183 | C22×D7 | — | 4 | 4 | no | — |
| 184 | C22×D7 | — | 4 | 1 | no | — |
| 185 | C22×D7 | — | 4 | 2 | no | — |
| 186 | C22×D7 | — | 4 | 2 | no | — |
| 187 | C22×D7 | — | 4 | 2 | no | — |
| 188 | C2×C4×C7 | — | 2 | 2 | no | — |
| 189 | C2×C4×C7 | — | 2 | 4 | no | — |
| 190 | C2×C4×C7 | — | 4 | 1 | no | — |
| 191 | C2×C4×C7 | — | 4 | 2 | no | — |
| 192 | C2×C4×C7 | — | 4 | 2 | no | — |
| 193 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 194 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 195 | C2×C4×C7 | #121 | 1 | 1 | yes | characteristic |
| 196 | C2×C4×C7 | #121 | 1 | 1 | yes | characteristic |
| 197 | C2×C4×C7 | #121 | 1 | 1 | yes | characteristic |
| 198 | C2×C4×C7 | #127 | 1 | 1 | yes | characteristic |
| 199 | C2×C4×C7 | C2×D8 | 1 | 1 | yes | characteristic |
| 200 | C2×C4×C7 | #135 | 1 | 1 | yes | characteristic |
| 201 | C2×C4×C7 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 202 | C2×C4×C7 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 203 | C22⋊D7 | — | 8 | 1 | no | — |
| 204 | C22⋊D7 | — | 8 | 1 | no | — |
| 205 | C2×Dic7 | — | 4 | 2 | no | — |
| 206 | C2×Dic7 | — | 4 | 1 | no | — |
| 207 | C2×Dic7 | — | 4 | 1 | no | — |
| 208 | D28 | — | 2 | 2 | no | — |
| 209 | D28 | — | 2 | 2 | no | — |
| 210 | D28 | — | 4 | 1 | no | — |
| 211 | D28 | — | 4 | 1 | no | — |
| 212 | D28 | — | 4 | 1 | no | — |
| 213 | D28 | — | 4 | 2 | no | — |
| 214 | D28 | — | 4 | 4 | no | — |
| 215 | D28 | — | 4 | 1 | no | — |
| 216 | D28 | — | 8 | 1 | no | — |
| 217 | D28 | — | 8 | 2 | no | — |
| 218 | D28 | — | 8 | 2 | no | — |
| 219 | D28 | — | 8 | 2 | no | — |
| 220 | D28 | — | 8 | 16 | no | — |
| 221 | D28 | — | 8 | 1 | no | — |
| 222 | D28 | — | 8 | 1 | no | — |
| 223 | D28 | — | 8 | 1 | no | — |
| 224 | D28 | — | 8 | 1 | no | — |
| 225 | C4×D7 | — | 8 | 2 | no | — |
| 226 | C4×D7 | — | 8 | 2 | no | — |
| 227 | C4×D7 | — | 8 | 1 | no | — |
| 228 | C4×D7 | — | 8 | 1 | no | — |
| 229 | Dic14 | — | 4 | 1 | no | — |
| 230 | Dic14 | — | 4 | 1 | no | — |
| 231 | C7×C8 | — | 4 | 2 | no | — |
| 232 | C7×C8 | — | 4 | 2 | no | — |
| 233 | C7⋊C8 | — | 8 | 1 | no | — |
| 234 | C2×#41 | — | 14 | 1 | no | — |
| 235 | C22×D4 | — | 7 | 1 | no | — |
| 236 | C22×D4 | — | 7 | 2 | no | — |
| 237 | C22×D4 | — | 14 | 4 | no | — |
| 238 | C22×D4 | — | 14 | 1 | no | — |
| 239 | C22×D4 | — | 14 | 1 | no | — |
| 240 | C23×C4 | — | 14 | 1 | no | — |
| 241 | AGL(1,ℤ/8) | — | 28 | 2 | no | — |
| 242 | AGL(1,ℤ/8) | — | 28 | 2 | no | — |
| 243 | C2×SD16 | — | 14 | 2 | no | — |
| 244 | C2×D8 | — | 14 | 2 | no | — |
| 245 | C2×D8 | — | 14 | 4 | no | — |
| 246 | C2×M16 | — | 2 | 1 | no | — |
| 247 | C4⋊Q8 | — | 7 | 1 | no | — |
| 248 | #127 | — | 7 | 1 | no | — |
| 249 | #127 | — | 14 | 1 | no | — |
| 250 | #127 | — | 14 | 1 | no | — |
| 251 | #127 | — | 14 | 1 | no | — |
| 252 | #127 | — | 14 | 1 | no | — |
| 253 | #127 | — | 28 | 2 | no | — |
| 254 | #127 | — | 28 | 2 | no | — |
| 255 | #124 | — | 14 | 1 | no | — |
| 256 | #121 | — | 14 | 1 | no | — |
| 257 | #121 | — | 14 | 1 | no | — |
| 258 | #121 | — | 28 | 8 | no | — |
| 259 | C4×D4 | — | 14 | 1 | no | — |
| 260 | C4×D4 | — | 14 | 1 | no | — |
| 261 | C4×D4 | — | 14 | 1 | no | — |
| 262 | C4×D4 | — | 14 | 1 | no | — |
| 263 | C4×D4 | — | 14 | 1 | no | — |
| 264 | C4×D4 | — | 14 | 1 | no | — |
| 265 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 266 | C2×C4⋊C4 | — | 7 | 1 | no | — |
| 267 | C2×C22⋊C4 | — | 14 | 4 | no | — |
| 268 | C2×C22⋊C4 | — | 14 | 1 | no | — |
| 269 | C2×C42 | — | 2 | 1 | no | — |
| 270 | C2×C42 | C22×D7 | 1 | 1 | yes | characteristic |
| 271 | C4⋊C8 | — | 2 | 1 | no | — |
| 272 | C4⋊C8 | — | 14 | 1 | no | — |
| 273 | C4⋊C8 | D28 | 1 | 2 | yes | complemented |
| 274 | C4⋊C8 | D28 | 1 | 2 | yes | complemented |
| 275 | #103 | — | 14 | 2 | no | — |
| 276 | #102 | — | 14 | 2 | no | — |
| 277 | #102 | — | 14 | 4 | no | — |
| 278 | C22⋊C8 | — | 2 | 1 | no | — |
| 279 | C22⋊C8 | — | 14 | 1 | no | — |
| 280 | C4×C8 | — | 2 | 1 | no | — |
| 281 | C4×C8 | — | 14 | 1 | no | — |
| 282 | #95 | D28 | 1 | 2 | yes | — |
| 283 | C22×C7 | — | 2 | 1 | no | — |
| 284 | C22×C7 | — | 2 | 1 | no | — |
| 285 | C22×C7 | #392 | 1 | 1 | yes | characteristic |
| 286 | C22×C7 | #447 | 1 | 1 | yes | characteristic |
| 287 | C22×C7 | #449 | 1 | 1 | yes | characteristic |
| 288 | C2×D7 | — | 4 | 4 | no | — |
| 289 | C2×D7 | — | 4 | 2 | no | — |
| 290 | C2×D7 | — | 8 | 2 | no | — |
| 291 | C2×D7 | — | 8 | 1 | no | — |
| 292 | C2×D7 | — | 8 | 1 | no | — |
| 293 | C2×D7 | — | 8 | 4 | no | — |
| 294 | C2×D7 | — | 8 | 4 | no | — |
| 295 | C2×D7 | — | 8 | 1 | no | — |
| 296 | C2×D7 | — | 8 | 2 | no | — |
| 297 | C2×D7 | — | 8 | 2 | no | — |
| 298 | C2×D7 | — | 8 | 1 | no | — |
| 299 | C2×D7 | — | 8 | 2 | no | — |
| 300 | C2×D7 | — | 8 | 1 | no | — |
| 301 | C4×C7 | — | 2 | 1 | no | — |
| 302 | C4×C7 | — | 2 | 1 | no | — |
| 303 | C4×C7 | — | 2 | 1 | no | — |
| 304 | C4×C7 | — | 4 | 4 | no | — |
| 305 | C4×C7 | #447 | 1 | 1 | yes | characteristic |
| 306 | C4×C7 | #449 | 1 | 1 | yes | characteristic |
| 307 | C4×C7 | #453 | 1 | 2 | yes | — |
| 308 | C4×C7 | #466 | 1 | 1 | yes | characteristic |
| 309 | C4×C7 | #469 | 1 | 1 | yes | characteristic |
| 310 | Dic7 | — | 8 | 1 | no | — |
| 311 | Dic7 | — | 8 | 1 | no | — |
| 312 | C24 | — | 14 | 1 | no | — |
| 313 | C24 | — | 14 | 2 | no | — |
| 314 | #41 | — | 28 | 1 | no | — |
| 315 | #41 | — | 28 | 1 | no | — |
| 316 | #41 | — | 28 | 1 | no | — |
| 317 | #41 | — | 28 | 1 | no | — |
| 318 | C2×Q8 | — | 14 | 1 | no | — |
| 319 | C2×D4 | — | 7 | 2 | no | — |
| 320 | C2×D4 | — | 14 | 1 | no | — |
| 321 | C2×D4 | — | 14 | 1 | no | — |
| 322 | C2×D4 | — | 14 | 2 | no | — |
| 323 | C2×D4 | — | 14 | 1 | no | — |
| 324 | C2×D4 | — | 14 | 1 | no | — |
| 325 | C2×D4 | — | 14 | 1 | no | — |
| 326 | C2×D4 | — | 14 | 2 | no | — |
| 327 | C2×D4 | — | 14 | 1 | no | — |
| 328 | C2×D4 | — | 14 | 1 | no | — |
| 329 | C2×D4 | — | 14 | 1 | no | — |
| 330 | C2×D4 | — | 28 | 4 | no | — |
| 331 | C2×D4 | — | 28 | 8 | no | — |
| 332 | C2×D4 | — | 28 | 8 | no | — |
| 333 | C2×D4 | — | 28 | 1 | no | — |
| 334 | C2×D4 | — | 28 | 1 | no | — |
| 335 | C2×D4 | — | 28 | 1 | no | — |
| 336 | C2×D4 | — | 28 | 1 | no | — |
| 337 | C2×D4 | — | 28 | 1 | no | — |
| 338 | C2×D4 | — | 28 | 1 | no | — |
| 339 | C2×D4 | — | 28 | 1 | no | — |
| 340 | C2×D4 | — | 28 | 1 | no | — |
| 341 | C2×D4 | — | 28 | 1 | no | — |
| 342 | C2×D4 | — | 56 | 2 | no | — |
| 343 | C2×D4 | — | 56 | 4 | no | — |
| 344 | C22×C4 | — | 2 | 2 | no | — |
| 345 | C22×C4 | — | 14 | 1 | no | — |
| 346 | C22×C4 | — | 28 | 4 | no | — |
| 347 | C22×C4 | — | 28 | 1 | no | — |
| 348 | C22×C4 | — | 28 | 1 | no | — |
| 349 | C22×C4 | — | 28 | 1 | no | — |
| 350 | C22×C4 | C2×D28 | 1 | 1 | yes | characteristic |
| 351 | C22×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 352 | C22×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 353 | SD16 | — | 28 | 4 | no | — |
| 354 | D8 | — | 28 | 4 | no | — |
| 355 | D8 | — | 56 | 4 | no | — |
| 356 | M16 | — | 4 | 1 | no | — |
| 357 | M16 | — | 4 | 1 | no | — |
| 358 | C2×C8 | — | 2 | 2 | no | — |
| 359 | C2×C8 | — | 2 | 2 | no | — |
| 360 | C2×C8 | — | 28 | 1 | no | — |
| 361 | C4⋊C4 | — | 2 | 4 | no | — |
| 362 | C4⋊C4 | — | 14 | 1 | no | — |
| 363 | C4⋊C4 | — | 14 | 1 | no | — |
| 364 | C4⋊C4 | — | 14 | 1 | no | — |
| 365 | C4⋊C4 | — | 14 | 1 | no | — |
| 366 | C22⋊C4 | — | 28 | 8 | no | — |
| 367 | C22⋊C4 | — | 28 | 1 | no | — |
| 368 | C22⋊C4 | — | 28 | 1 | no | — |
| 369 | C22⋊C4 | — | 28 | 1 | no | — |
| 370 | C22⋊C4 | — | 28 | 1 | no | — |
| 371 | C42 | — | 4 | 1 | no | — |
| 372 | C42 | — | 4 | 1 | no | — |
| 373 | C42 | C2×D28 | 1 | 1 | yes | characteristic |
| 374 | C42 | C2×D28 | 1 | 1 | yes | characteristic |
| 375 | C42 | D4×D7 | 1 | 1 | yes | characteristic |
| 376 | C42 | #1161 | 1 | 1 | yes | characteristic |
| 377 | C2×C7 | — | 2 | 1 | no | — |
| 378 | C2×C7 | — | 2 | 1 | no | — |
| 379 | C2×C7 | #1999 | 1 | 1 | yes | characteristic |
| 380 | C2×C7 | #2002 | 1 | 1 | yes | characteristic |
| 381 | C2×C7 | #2008 | 1 | 1 | yes | characteristic |
| 382 | D7 | — | 8 | 2 | no | — |
| 383 | D7 | — | 16 | 1 | no | — |
| 384 | D7 | — | 16 | 2 | no | — |
| 385 | C23 | — | 14 | 2 | no | — |
| 386 | C23 | — | 28 | 2 | no | — |
| 387 | C23 | — | 28 | 2 | no | — |
| 388 | C23 | — | 28 | 4 | no | — |
| 389 | C23 | — | 28 | 4 | no | — |
| 390 | C23 | — | 28 | 1 | no | — |
| 391 | C23 | — | 28 | 1 | no | — |
| 392 | C23 | — | 28 | 1 | no | — |
| 393 | C23 | — | 28 | 2 | no | — |
| 394 | C23 | — | 28 | 2 | no | — |
| 395 | C23 | — | 28 | 2 | no | — |
| 396 | C23 | #6445 | 1 | 1 | yes | characteristic |
| 397 | Q8 | — | 28 | 1 | no | — |
| 398 | Q8 | — | 28 | 1 | no | — |
| 399 | D4 | — | 14 | 2 | no | — |
| 400 | D4 | — | 14 | 2 | no | — |
| 401 | D4 | — | 28 | 1 | no | — |
| 402 | D4 | — | 28 | 1 | no | — |
| 403 | D4 | — | 28 | 1 | no | — |
| 404 | D4 | — | 28 | 1 | no | — |
| 405 | D4 | — | 28 | 2 | no | — |
| 406 | D4 | — | 28 | 4 | no | — |
| 407 | D4 | — | 56 | 1 | no | — |
| 408 | D4 | — | 56 | 2 | no | — |
| 409 | D4 | — | 56 | 2 | no | — |
| 410 | D4 | — | 56 | 2 | no | — |
| 411 | D4 | — | 56 | 16 | no | — |
| 412 | D4 | — | 56 | 1 | no | — |
| 413 | D4 | — | 56 | 1 | no | — |
| 414 | D4 | — | 56 | 1 | no | — |
| 415 | D4 | — | 56 | 1 | no | — |
| 416 | D4 | — | 56 | 1 | no | — |
| 417 | D4 | — | 56 | 1 | no | — |
| 418 | C2×C4 | — | 2 | 2 | no | — |
| 419 | C2×C4 | — | 2 | 4 | no | — |
| 420 | C2×C4 | — | 4 | 1 | no | — |
| 421 | C2×C4 | — | 4 | 2 | no | — |
| 422 | C2×C4 | — | 4 | 2 | no | — |
| 423 | C2×C4 | — | 28 | 2 | no | — |
| 424 | C2×C4 | — | 28 | 1 | no | — |
| 425 | C2×C4 | — | 28 | 1 | no | — |
| 426 | C2×C4 | — | 56 | 2 | no | — |
| 427 | C2×C4 | — | 56 | 1 | no | — |
| 428 | C2×C4 | — | 56 | 1 | no | — |
| 429 | C2×C4 | — | 56 | 2 | no | — |
| 430 | C2×C4 | #6437 | 1 | 1 | yes | characteristic |
| 431 | C2×C4 | #6445 | 1 | 1 | yes | characteristic |
| 432 | C2×C4 | #6445 | 1 | 1 | yes | characteristic |
| 433 | C2×C4 | #6458 | 1 | 1 | yes | characteristic |
| 434 | C2×C4 | #6458 | 1 | 1 | yes | characteristic |
| 435 | C2×C4 | #6458 | 1 | 1 | yes | characteristic |
| 436 | C2×C4 | D7×D8 | 1 | 1 | yes | characteristic |
| 437 | C2×C4 | #6477 | 1 | 1 | yes | characteristic |
| 438 | C2×C4 | #6477 | 1 | 1 | yes | characteristic |
| 439 | C2×C4 | #6482 | 1 | 1 | yes | characteristic |
| 440 | C8 | — | 4 | 2 | no | — |
| 441 | C8 | — | 4 | 2 | no | — |
| 442 | C8 | — | 56 | 1 | no | — |
| 443 | C7 | #10238 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 444 | C22 | — | 2 | 1 | no | — |
| 445 | C22 | — | 2 | 1 | no | — |
| 446 | C22 | — | 28 | 4 | no | — |
| 447 | C22 | — | 28 | 2 | no | — |
| 448 | C22 | — | 56 | 2 | no | — |
| 449 | C22 | — | 56 | 4 | no | — |
| 450 | C22 | — | 56 | 4 | no | — |
| 451 | C22 | — | 56 | 1 | no | — |
| 452 | C22 | — | 56 | 1 | no | — |
| 453 | C22 | — | 56 | 1 | no | — |
| 454 | C22 | — | 56 | 2 | no | — |
| 455 | C22 | — | 56 | 2 | no | — |
| 456 | C22 | — | 56 | 1 | no | — |
| 457 | C22 | — | 56 | 2 | no | — |
| 458 | C22 | — | 56 | 1 | no | — |
| 459 | C22 | #89443 | 1 | 1 | yes | characteristic |
| 460 | C22 | #89545 | 1 | 1 | yes | characteristic |
| 461 | C22 | #89583 | 1 | 1 | yes | characteristic |
| 462 | C4 | — | 2 | 1 | no | — |
| 463 | C4 | — | 2 | 1 | no | — |
| 464 | C4 | — | 2 | 1 | no | — |
| 465 | C4 | — | 4 | 4 | no | — |
| 466 | C4 | — | 56 | 1 | no | — |
| 467 | C4 | — | 56 | 1 | no | — |
| 468 | C4 | #89545 | 1 | 1 | yes | characteristic |
| 469 | C4 | #89583 | 1 | 1 | yes | characteristic |
| 470 | C4 | #89594 | 1 | 2 | yes | — |
| 471 | C4 | #89637 | 1 | 1 | yes | characteristic |
| 472 | C4 | #89655 | 1 | 1 | yes | characteristic |
| 473 | C2 | — | 2 | 1 | no | — |
| 474 | C2 | — | 2 | 1 | no | — |
| 475 | C2 | — | 56 | 2 | no | — |
| 476 | C2 | — | 112 | 2 | no | — |
| 477 | C2 | — | 112 | 1 | no | — |
| 478 | C2 | #11726515 | 1 | 1 | yes | characteristic |
| 479 | C2 | #11726640 | 1 | 1 | yes | characteristic |
| 480 | C2 | #11726782 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11736748 | C2 | semidirect |
| 2. #11736500 | C2 | semidirect |
| 3. #11731244 | C2 | semidirect |
| 4. #11728510 | C2 | semidirect |
| 5. #11728256 | C2 | semidirect |
| 6. #11727223 | C2 | semidirect |
| 7. C7×#1303 | C2 | semidirect |
| 61. #6437 | D4 | semidirect |
| 68. #6432 | D4 | semidirect |
| 70. C7×C4⋊C8 | D4 | semidirect |
| 71. C7×C4⋊C8 | D4 | semidirect |
| 87. #1303 | D7 | semidirect |
| 123. C2×D28 | D8 | semidirect |
| 273. C4⋊C8 | D28 | semidirect |
| 274. C4⋊C8 | D28 | semidirect |
| 443. C7 | #10238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736748 | 2 |
| #11736500 | 2 |
| #11731244 | 2 |
| #11728510 | 2 |
| #11728256 | 2 |
| #11727223 | 2 |
| C7×#1303 | 2 |
| #10238 | 7 |