Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
678 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 678 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
| 2 | #11736713 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11730758 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11728532 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11728528 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11727149 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C7×#1276 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #90168 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×#6438 | — | 2 | 2 | no | — |
| 10 | C2×#6437 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×#6432 | C22 | 1 | 1 | yes | characteristic |
| 12 | C7×#431 | C22 | 1 | 1 | yes | characteristic |
| 13 | C7×#431 | C22 | 1 | 1 | yes | characteristic |
| 14 | C43×C7 | C22 | 1 | 1 | yes | characteristic |
| 15 | #89711 | — | 2 | 2 | no | — |
| 16 | #89711 | — | 2 | 2 | no | — |
| 17 | C2×#6379 | — | 2 | 2 | no | — |
| 18 | #89696 | C22 | 1 | 1 | yes | characteristic |
| 19 | #89618 | — | 2 | 2 | no | — |
| 20 | #89615 | — | 2 | 2 | no | — |
| 21 | #89508 | — | 2 | 2 | no | — |
| 22 | #89504 | — | 2 | 2 | no | — |
| 23 | #89467 | — | 2 | 1 | no | — |
| 24 | #89466 | — | 2 | 1 | no | — |
| 25 | #89466 | — | 2 | 1 | no | — |
| 26 | #89454 | — | 2 | 1 | no | — |
| 27 | #89281 | — | 2 | 2 | no | — |
| 28 | #89280 | — | 2 | 2 | no | — |
| 29 | #10284 | — | 7 | 1 | no | maximal, Sylow |
| 30 | C2×#1157 | — | 2 | 1 | no | — |
| 31 | C22×D28 | — | 2 | 1 | no | — |
| 32 | C22×D28 | — | 2 | 1 | no | — |
| 33 | C22×D28 | D4 | 1 | 2 | yes | — |
| 34 | C22×Dic14 | — | 2 | 1 | no | — |
| 35 | C2×C42×C7 | — | 2 | 1 | no | — |
| 36 | C2×C42×C7 | — | 2 | 1 | no | — |
| 37 | C2×C42×C7 | D4 | 1 | 2 | yes | — |
| 38 | C2×C42×C7 | C23 | 1 | 1 | yes | characteristic |
| 39 | #6493 | — | 2 | 1 | no | — |
| 40 | #6493 | — | 2 | 1 | no | — |
| 41 | C2×(C2×D7)⋊C4 | — | 2 | 8 | no | — |
| 42 | C2×C4⋊Dic7 | — | 2 | 1 | no | — |
| 43 | C2×C4⋊Dic7 | D4 | 1 | 2 | yes | — |
| 44 | C2×#1136 | — | 2 | 1 | no | — |
| 45 | C2×D56 | — | 2 | 4 | no | — |
| 46 | #6438 | — | 2 | 1 | no | — |
| 47 | #6438 | — | 4 | 4 | no | — |
| 48 | #6438 | — | 4 | 4 | no | — |
| 49 | #6437 | — | 2 | 1 | no | — |
| 50 | #6437 | — | 2 | 1 | no | — |
| 51 | #6437 | — | 2 | 1 | no | — |
| 52 | #6437 | — | 2 | 1 | no | — |
| 53 | #6437 | D4 | 1 | 1 | yes | characteristic |
| 54 | C4×D28 | — | 2 | 1 | no | — |
| 55 | C4×D28 | — | 2 | 1 | no | — |
| 56 | #6432 | — | 2 | 1 | no | — |
| 57 | #6432 | — | 2 | 1 | no | — |
| 58 | #6432 | — | 2 | 1 | no | — |
| 59 | #6432 | — | 2 | 1 | no | — |
| 60 | #6432 | D4 | 1 | 1 | yes | characteristic |
| 61 | C7×C4⋊C8 | D4 | 1 | 2 | yes | — |
| 62 | C7×C4⋊C8 | D4 | 1 | 2 | yes | — |
| 63 | C7×C22⋊C8 | — | 2 | 1 | no | — |
| 64 | C7×C22⋊C8 | — | 2 | 1 | no | — |
| 65 | C4×C7×C8 | — | 2 | 1 | no | — |
| 66 | C4×C7×C8 | — | 2 | 1 | no | — |
| 67 | #6395 | — | 2 | 4 | no | — |
| 68 | #6395 | — | 2 | 4 | no | — |
| 69 | #6392 | — | 2 | 4 | no | — |
| 70 | #6379 | — | 4 | 4 | no | — |
| 71 | C4⋊(C7⋊C8) | — | 2 | 1 | no | — |
| 72 | C4⋊(C7⋊C8) | — | 2 | 1 | no | — |
| 73 | #3226 | — | 7 | 1 | no | — |
| 74 | #3205 | — | 7 | 1 | no | — |
| 75 | #2858 | — | 7 | 1 | no | — |
| 76 | #1962 | — | 7 | 1 | no | — |
| 77 | #1546 | — | 7 | 1 | no | — |
| 78 | #1545 | — | 7 | 1 | no | — |
| 79 | #1276 | D7 | 1 | 1 | yes | characteristic, complemented |
| 80 | C23×D7 | — | 2 | 2 | no | — |
| 81 | C22×C4×C7 | — | 2 | 2 | no | — |
| 82 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 83 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 84 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 85 | C2×C22⋊D7 | — | 4 | 1 | no | — |
| 86 | C22×Dic7 | — | 2 | 2 | no | — |
| 87 | #1157 | — | 4 | 2 | no | — |
| 88 | #1157 | — | 4 | 2 | no | — |
| 89 | C2×D28 | — | 2 | 1 | no | — |
| 90 | C2×D28 | — | 2 | 1 | no | — |
| 91 | C2×D28 | — | 2 | 2 | no | — |
| 92 | C2×D28 | — | 2 | 1 | no | — |
| 93 | C2×D28 | — | 2 | 2 | no | — |
| 94 | C2×D28 | — | 4 | 4 | no | — |
| 95 | C2×D28 | — | 4 | 4 | no | — |
| 96 | C2×D28 | — | 4 | 1 | no | — |
| 97 | C2×D28 | — | 4 | 1 | no | — |
| 98 | C2×D28 | — | 4 | 1 | no | — |
| 99 | C2×D28 | — | 4 | 1 | no | — |
| 100 | C2×D28 | — | 4 | 2 | no | — |
| 101 | C2×D28 | — | 4 | 2 | no | — |
| 102 | C2×C4×D7 | — | 4 | 1 | no | — |
| 103 | C2×Dic14 | — | 2 | 1 | no | — |
| 104 | C2×Dic14 | — | 4 | 1 | no | — |
| 105 | C2×Dic14 | — | 4 | 1 | no | — |
| 106 | C2×Dic14 | — | 4 | 2 | no | — |
| 107 | C2×Dic14 | — | 4 | 2 | no | — |
| 108 | C2×C7×C8 | — | 2 | 2 | no | — |
| 109 | C2×C7×C8 | — | 2 | 2 | no | — |
| 110 | C42×C7 | — | 2 | 2 | no | — |
| 111 | C42×C7 | — | 4 | 2 | no | — |
| 112 | C42×C7 | — | 4 | 2 | no | — |
| 113 | C42×C7 | D8 | 1 | 4 | yes | complemented |
| 114 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 115 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 116 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 117 | C42×C7 | #41 | 1 | 1 | yes | characteristic |
| 118 | (C2×D7)⋊C4 | — | 4 | 16 | no | — |
| 119 | (C2×D7)⋊C4 | — | 4 | 1 | no | — |
| 120 | (C2×D7)⋊C4 | — | 4 | 1 | no | — |
| 121 | C4⋊Dic7 | — | 2 | 2 | no | — |
| 122 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 123 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 124 | C4⋊Dic7 | — | 2 | 2 | no | — |
| 125 | C4⋊Dic7 | — | 4 | 1 | no | — |
| 126 | C4⋊Dic7 | — | 4 | 1 | no | — |
| 127 | #1136 | — | 4 | 2 | no | — |
| 128 | C2×C7⋊C8 | — | 4 | 1 | no | — |
| 129 | D56 | — | 8 | 4 | no | — |
| 130 | #532 | — | 7 | 1 | no | — |
| 131 | C2×C4⋊Q8 | — | 7 | 1 | no | — |
| 132 | C2×#127 | — | 7 | 1 | no | — |
| 133 | C2×#124 | — | 14 | 2 | no | — |
| 134 | #500 | — | 14 | 1 | no | — |
| 135 | #493 | — | 14 | 1 | no | — |
| 136 | #486 | — | 14 | 1 | no | — |
| 137 | #486 | — | 14 | 1 | no | — |
| 138 | #480 | — | 14 | 2 | no | — |
| 139 | #474 | — | 14 | 2 | no | — |
| 140 | #459 | — | 14 | 2 | no | — |
| 141 | #447 | — | 14 | 2 | no | — |
| 142 | #431 | C2×D7 | 1 | 1 | yes | characteristic |
| 143 | #431 | C2×D7 | 1 | 1 | yes | characteristic |
| 144 | #423 | — | 7 | 1 | no | — |
| 145 | C2×#104 | — | 14 | 2 | no | — |
| 146 | #390 | — | 14 | 2 | no | — |
| 147 | #390 | — | 14 | 2 | no | — |
| 148 | C43 | C2×D7 | 1 | 1 | yes | characteristic |
| 149 | #332 | — | 14 | 2 | no | — |
| 150 | #331 | — | 14 | 2 | no | — |
| 151 | C23×C7 | #120 | 1 | 1 | yes | characteristic |
| 152 | C22×D7 | — | 4 | 4 | no | — |
| 153 | C22×D7 | — | 4 | 4 | no | — |
| 154 | C22×D7 | — | 4 | 1 | no | — |
| 155 | C22×D7 | — | 4 | 2 | no | — |
| 156 | C22×D7 | — | 4 | 4 | no | — |
| 157 | C2×C4×C7 | — | 2 | 2 | no | — |
| 158 | C2×C4×C7 | — | 2 | 2 | no | — |
| 159 | C2×C4×C7 | — | 2 | 4 | no | — |
| 160 | C2×C4×C7 | — | 4 | 2 | no | — |
| 161 | C2×C4×C7 | — | 4 | 2 | no | — |
| 162 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 163 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 164 | C2×C4×C7 | #121 | 1 | 1 | yes | characteristic |
| 165 | C2×C4×C7 | #121 | 1 | 1 | yes | characteristic |
| 166 | C2×C4×C7 | #121 | 1 | 1 | yes | characteristic |
| 167 | C2×C4×C7 | #127 | 1 | 1 | yes | characteristic |
| 168 | C2×C4×C7 | C2×D8 | 1 | 2 | yes | — |
| 169 | C2×C4×C7 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 170 | C22⋊D7 | — | 8 | 2 | no | — |
| 171 | C2×Dic7 | — | 4 | 2 | no | — |
| 172 | C2×Dic7 | — | 4 | 1 | no | — |
| 173 | C2×Dic7 | — | 4 | 4 | no | — |
| 174 | D28 | — | 4 | 2 | no | — |
| 175 | D28 | — | 4 | 2 | no | — |
| 176 | D28 | — | 4 | 4 | no | — |
| 177 | D28 | — | 4 | 2 | no | — |
| 178 | D28 | — | 8 | 2 | no | — |
| 179 | D28 | — | 8 | 2 | no | — |
| 180 | D28 | — | 8 | 2 | no | — |
| 181 | D28 | — | 8 | 2 | no | — |
| 182 | D28 | — | 8 | 1 | no | — |
| 183 | D28 | — | 8 | 1 | no | — |
| 184 | C4×D7 | — | 8 | 1 | no | — |
| 185 | C4×D7 | — | 8 | 1 | no | — |
| 186 | Dic14 | — | 4 | 2 | no | — |
| 187 | Dic14 | — | 8 | 2 | no | — |
| 188 | Dic14 | — | 8 | 1 | no | — |
| 189 | Dic14 | — | 8 | 1 | no | — |
| 190 | C7×C8 | — | 4 | 2 | no | — |
| 191 | C7×C8 | — | 4 | 2 | no | — |
| 192 | C7⋊C8 | — | 8 | 1 | no | — |
| 193 | C2×#41 | — | 14 | 1 | no | — |
| 194 | C22×Q8 | — | 14 | 1 | no | — |
| 195 | C22×D4 | — | 7 | 2 | no | — |
| 196 | C22×D4 | — | 14 | 1 | no | — |
| 197 | C22×D4 | — | 14 | 1 | no | — |
| 198 | C2×D8 | — | 14 | 4 | no | — |
| 199 | C2×M16 | — | 14 | 1 | no | — |
| 200 | C4⋊Q8 | — | 7 | 1 | no | — |
| 201 | C4⋊Q8 | — | 14 | 1 | no | — |
| 202 | C4⋊Q8 | — | 14 | 1 | no | — |
| 203 | C4⋊Q8 | — | 14 | 1 | no | — |
| 204 | C4⋊Q8 | — | 14 | 1 | no | — |
| 205 | #127 | — | 7 | 1 | no | — |
| 206 | #127 | — | 14 | 1 | no | — |
| 207 | #127 | — | 14 | 1 | no | — |
| 208 | #127 | — | 14 | 1 | no | — |
| 209 | #127 | — | 14 | 1 | no | — |
| 210 | #124 | — | 14 | 1 | no | — |
| 211 | #124 | — | 28 | 4 | no | — |
| 212 | #124 | — | 28 | 4 | no | — |
| 213 | #121 | — | 14 | 1 | no | — |
| 214 | #121 | — | 14 | 1 | no | — |
| 215 | C4×D4 | — | 14 | 1 | no | — |
| 216 | C4×D4 | — | 14 | 1 | no | — |
| 217 | C2×C4⋊C4 | — | 7 | 2 | no | — |
| 218 | C2×C4⋊C4 | — | 14 | 1 | no | — |
| 219 | C2×C22⋊C4 | — | 14 | 8 | no | — |
| 220 | C2×C42 | — | 2 | 1 | no | — |
| 221 | C2×C42 | — | 2 | 1 | no | — |
| 222 | C2×C42 | D28 | 1 | 2 | yes | — |
| 223 | C2×C42 | C22×D7 | 1 | 1 | yes | characteristic |
| 224 | #107 | — | 14 | 4 | no | — |
| 225 | C4⋊C8 | — | 14 | 1 | no | — |
| 226 | C4⋊C8 | — | 14 | 1 | no | — |
| 227 | C4⋊C8 | D28 | 1 | 2 | yes | — |
| 228 | C4⋊C8 | D28 | 1 | 2 | yes | — |
| 229 | #104 | — | 28 | 4 | no | — |
| 230 | #102 | — | 14 | 4 | no | — |
| 231 | #102 | — | 14 | 4 | no | — |
| 232 | C22⋊C8 | — | 2 | 1 | no | — |
| 233 | C22⋊C8 | — | 2 | 1 | no | — |
| 234 | C4×C8 | — | 2 | 1 | no | — |
| 235 | C4×C8 | — | 2 | 1 | no | — |
| 236 | C22×C7 | — | 2 | 1 | no | — |
| 237 | C22×C7 | — | 2 | 1 | no | — |
| 238 | C22×C7 | #392 | 1 | 1 | yes | characteristic |
| 239 | C22×C7 | #447 | 1 | 2 | yes | — |
| 240 | C2×D7 | — | 8 | 8 | no | — |
| 241 | C2×D7 | — | 8 | 1 | no | — |
| 242 | C2×D7 | — | 8 | 2 | no | — |
| 243 | C2×D7 | — | 8 | 2 | no | — |
| 244 | C2×D7 | — | 8 | 1 | no | — |
| 245 | C2×D7 | — | 8 | 1 | no | — |
| 246 | C2×D7 | — | 8 | 2 | no | — |
| 247 | C4×C7 | — | 2 | 1 | no | — |
| 248 | C4×C7 | — | 2 | 1 | no | — |
| 249 | C4×C7 | — | 4 | 4 | no | — |
| 250 | C4×C7 | #454 | 1 | 2 | yes | — |
| 251 | C4×C7 | #455 | 1 | 2 | yes | — |
| 252 | C4×C7 | #459 | 1 | 2 | yes | — |
| 253 | C4×C7 | #493 | 1 | 1 | yes | characteristic |
| 254 | C4×C7 | #496 | 1 | 1 | yes | characteristic |
| 255 | Dic7 | — | 8 | 1 | no | — |
| 256 | Dic7 | — | 8 | 2 | no | — |
| 257 | C24 | — | 14 | 2 | no | — |
| 258 | #41 | — | 28 | 2 | no | — |
| 259 | #41 | — | 28 | 2 | no | — |
| 260 | C2×Q8 | — | 14 | 1 | no | — |
| 261 | C2×Q8 | — | 28 | 1 | no | — |
| 262 | C2×Q8 | — | 28 | 1 | no | — |
| 263 | C2×Q8 | — | 28 | 2 | no | — |
| 264 | C2×Q8 | — | 28 | 2 | no | — |
| 265 | C2×D4 | — | 14 | 1 | no | — |
| 266 | C2×D4 | — | 14 | 2 | no | — |
| 267 | C2×D4 | — | 14 | 1 | no | — |
| 268 | C2×D4 | — | 14 | 1 | no | — |
| 269 | C2×D4 | — | 14 | 2 | no | — |
| 270 | C2×D4 | — | 28 | 4 | no | — |
| 271 | C2×D4 | — | 28 | 4 | no | — |
| 272 | C2×D4 | — | 28 | 1 | no | — |
| 273 | C2×D4 | — | 28 | 1 | no | — |
| 274 | C2×D4 | — | 28 | 1 | no | — |
| 275 | C2×D4 | — | 28 | 1 | no | — |
| 276 | C2×D4 | — | 28 | 1 | no | — |
| 277 | C2×D4 | — | 28 | 2 | no | — |
| 278 | C2×D4 | — | 28 | 2 | no | — |
| 279 | C22×C4 | — | 2 | 2 | no | — |
| 280 | C22×C4 | — | 14 | 2 | no | — |
| 281 | C22×C4 | — | 28 | 1 | no | — |
| 282 | C22×C4 | C2×D28 | 1 | 1 | yes | characteristic |
| 283 | C22×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 284 | C22×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 285 | D8 | — | 56 | 4 | no | — |
| 286 | M16 | — | 28 | 2 | no | — |
| 287 | C2×C8 | — | 2 | 2 | no | — |
| 288 | C2×C8 | — | 2 | 2 | no | — |
| 289 | C2×C8 | — | 28 | 1 | no | — |
| 290 | C4⋊C4 | — | 14 | 1 | no | — |
| 291 | C4⋊C4 | — | 14 | 2 | no | — |
| 292 | C4⋊C4 | — | 14 | 1 | no | — |
| 293 | C4⋊C4 | — | 14 | 2 | no | — |
| 294 | C4⋊C4 | — | 28 | 1 | no | — |
| 295 | C4⋊C4 | — | 28 | 1 | no | — |
| 296 | C22⋊C4 | — | 28 | 16 | no | — |
| 297 | C22⋊C4 | — | 28 | 1 | no | — |
| 298 | C22⋊C4 | — | 28 | 1 | no | — |
| 299 | C42 | — | 2 | 2 | no | — |
| 300 | C42 | — | 4 | 2 | no | — |
| 301 | C42 | — | 4 | 2 | no | — |
| 302 | C42 | D56 | 1 | 4 | yes | complemented |
| 303 | C42 | C2×D28 | 1 | 1 | yes | characteristic |
| 304 | C42 | C2×D28 | 1 | 1 | yes | characteristic |
| 305 | C42 | D4×D7 | 1 | 1 | yes | characteristic |
| 306 | C42 | #1161 | 1 | 1 | yes | characteristic |
| 307 | C2×C7 | — | 2 | 2 | no | — |
| 308 | C2×C7 | #2003 | 1 | 1 | yes | characteristic |
| 309 | C2×C7 | #2004 | 1 | 1 | yes | characteristic |
| 310 | C2×C7 | #2011 | 1 | 1 | yes | characteristic |
| 311 | D7 | — | 16 | 1 | no | — |
| 312 | D7 | — | 16 | 2 | no | — |
| 313 | C23 | — | 28 | 4 | no | — |
| 314 | C23 | — | 28 | 4 | no | — |
| 315 | C23 | — | 28 | 1 | no | — |
| 316 | C23 | — | 28 | 2 | no | — |
| 317 | C23 | — | 28 | 4 | no | — |
| 318 | C23 | #6445 | 1 | 1 | yes | characteristic |
| 319 | Q8 | — | 28 | 2 | no | — |
| 320 | Q8 | — | 56 | 2 | no | — |
| 321 | Q8 | — | 56 | 1 | no | — |
| 322 | Q8 | — | 56 | 1 | no | — |
| 323 | D4 | — | 28 | 2 | no | — |
| 324 | D4 | — | 28 | 2 | no | — |
| 325 | D4 | — | 28 | 4 | no | — |
| 326 | D4 | — | 28 | 2 | no | — |
| 327 | D4 | — | 56 | 2 | no | — |
| 328 | D4 | — | 56 | 2 | no | — |
| 329 | D4 | — | 56 | 2 | no | — |
| 330 | D4 | — | 56 | 2 | no | — |
| 331 | D4 | — | 56 | 1 | no | — |
| 332 | D4 | — | 56 | 1 | no | — |
| 333 | D4 | — | 56 | 2 | no | — |
| 334 | C2×C4 | — | 2 | 2 | no | — |
| 335 | C2×C4 | — | 2 | 2 | no | — |
| 336 | C2×C4 | — | 2 | 4 | no | — |
| 337 | C2×C4 | — | 4 | 2 | no | — |
| 338 | C2×C4 | — | 4 | 2 | no | — |
| 339 | C2×C4 | — | 28 | 1 | no | — |
| 340 | C2×C4 | — | 28 | 2 | no | — |
| 341 | C2×C4 | — | 28 | 4 | no | — |
| 342 | C2×C4 | — | 56 | 1 | no | — |
| 343 | C2×C4 | — | 56 | 1 | no | — |
| 344 | C2×C4 | #6437 | 1 | 1 | yes | characteristic |
| 345 | C2×C4 | #6445 | 1 | 1 | yes | characteristic |
| 346 | C2×C4 | #6445 | 1 | 1 | yes | characteristic |
| 347 | C2×C4 | #6458 | 1 | 1 | yes | characteristic |
| 348 | C2×C4 | #6458 | 1 | 1 | yes | characteristic |
| 349 | C2×C4 | #6458 | 1 | 1 | yes | characteristic |
| 350 | C2×C4 | C2×D56 | 1 | 2 | yes | — |
| 351 | C2×C4 | #6471 | 1 | 2 | yes | — |
| 352 | C8 | — | 4 | 2 | no | — |
| 353 | C8 | — | 4 | 2 | no | — |
| 354 | C8 | — | 56 | 1 | no | — |
| 355 | C7 | #10284 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 356 | C22 | — | 2 | 1 | no | — |
| 357 | C22 | — | 2 | 1 | no | — |
| 358 | C22 | — | 56 | 8 | no | — |
| 359 | C22 | — | 56 | 1 | no | — |
| 360 | C22 | — | 56 | 2 | no | — |
| 361 | C22 | — | 56 | 2 | no | — |
| 362 | C22 | — | 56 | 1 | no | — |
| 363 | C22 | — | 56 | 1 | no | — |
| 364 | C22 | — | 56 | 2 | no | — |
| 365 | C22 | #89443 | 1 | 1 | yes | characteristic |
| 366 | C22 | #89504 | 1 | 2 | yes | — |
| 367 | C4 | — | 2 | 1 | no | — |
| 368 | C4 | — | 2 | 1 | no | — |
| 369 | C4 | — | 4 | 4 | no | — |
| 370 | C4 | — | 56 | 2 | no | — |
| 371 | C4 | — | 56 | 1 | no | — |
| 372 | C4 | #89467 | 1 | 1 | yes | characteristic |
| 373 | C4 | #89484 | 1 | 1 | yes | characteristic |
| 374 | C4 | #89597 | 1 | 2 | yes | — |
| 375 | C4 | #89599 | 1 | 2 | yes | — |
| 376 | C4 | #89615 | 1 | 2 | yes | — |
| 377 | C2 | — | 2 | 2 | no | — |
| 378 | C2 | — | 112 | 2 | no | — |
| 379 | C2 | — | 112 | 1 | no | — |
| 380 | C2 | #11726428 | 1 | 1 | yes | characteristic |
| 381 | C2 | #11726516 | 1 | 1 | yes | characteristic |
| 382 | C2 | #11726521 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11736713 | C2 | semidirect |
| 3. #11730758 | C2 | semidirect |
| 4. #11728532 | C2 | semidirect |
| 5. #11728528 | C2 | semidirect |
| 6. #11727149 | C2 | semidirect |
| 7. C7×#1276 | C2 | semidirect |
| 79. #1276 | D7 | semidirect |
| 113. C42×C7 | D8 | semidirect |
| 302. C42 | D56 | semidirect |
| 355. C7 | #10284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736748 | 2 |
| #11736713 | 2 |
| #11730758 | 2 |
| #11728532 | 2 |
| #11728528 | 2 |
| #11727149 | 2 |
| C7×#1276 | 2 |
| #10284 | 7 |