← #13250315
Subgroups — #13250315
Order 1792.
480 conjugacy classes of subgroups.
The subgroup lattice has 368 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C7×#3227 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #11740722 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #11729560 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #11729544 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×#89342 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11725551 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11725550 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C7×#532 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×C7×C4⋊Q8 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×#6511 | — | 2 | 1 | no | — |
| 11 | C7×#498 | — | 2 | 1 | no | — |
| 12 | C7×#486 | — | 2 | 1 | no | — |
| 13 | C7×#481 | C4 | 1 | 4 | yes | — |
| 14 | C7×#476 | — | 2 | 2 | no | — |
| 15 | C7×#431 | C22 | 1 | 1 | yes | characteristic |
| 16 | #90006 | — | 2 | 1 | no | — |
| 17 | #89784 | — | 2 | 1 | no | — |
| 18 | #89783 | — | 2 | 2 | no | — |
| 19 | D4×C7⋊C8 | — | 2 | 1 | no | — |
| 20 | #89696 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×C4⋊(C7⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×C4⋊(C7⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 23 | C4×#1136 | C22 | 1 | 1 | yes | characteristic |
| 24 | #89342 | — | 2 | 1 | no | — |
| 25 | #89342 | — | 2 | 1 | no | — |
| 26 | #89342 | — | 2 | 1 | no | — |
| 27 | #89339 | — | 2 | 1 | no | — |
| 28 | #89325 | — | 2 | 1 | no | — |
| 29 | #89325 | — | 2 | 1 | no | — |
| 30 | #9269 | — | 7 | 1 | no | maximal, Sylow |
| 31 | C2×C7×#41 | — | 2 | 1 | no | — |
| 32 | C22×C7×Q8 | — | 2 | 1 | no | — |
| 33 | C7×C4⋊Q8 | — | 2 | 1 | no | — |
| 34 | C7×C4⋊Q8 | — | 2 | 1 | no | — |
| 35 | C7×C4⋊Q8 | — | 2 | 1 | no | — |
| 36 | C7×C4⋊Q8 | — | 2 | 1 | no | — |
| 37 | C7×C4⋊Q8 | D4 | 1 | 1 | yes | characteristic |
| 38 | C7×#127 | D4 | 1 | 1 | yes | characteristic |
| 39 | C7×#124 | — | 2 | 1 | no | — |
| 40 | C7×#121 | — | 2 | 1 | no | — |
| 41 | C7×#121 | C2×C4 | 1 | 2 | yes | — |
| 42 | C4×C7×D4 | — | 2 | 1 | no | — |
| 43 | C4×C7×D4 | D4 | 1 | 2 | yes | — |
| 44 | C2×C7×C4⋊C4 | — | 2 | 1 | no | — |
| 45 | C2×C7×C4⋊C4 | C2×C4 | 1 | 2 | yes | — |
| 46 | C2×C42×C7 | C23 | 1 | 1 | yes | characteristic |
| 47 | #6511 | — | 4 | 2 | no | — |
| 48 | #6511 | — | 4 | 2 | no | — |
| 49 | C2×#1136 | — | 2 | 2 | no | — |
| 50 | C2×#1136 | — | 2 | 1 | no | — |
| 51 | C2×#1136 | D4 | 1 | 1 | yes | characteristic |
| 52 | C2×#1136 | D4 | 1 | 1 | yes | characteristic |
| 53 | C22×C7⋊C8 | — | 2 | 2 | no | — |
| 54 | C22×C7⋊C8 | — | 2 | 1 | no | — |
| 55 | C22×C7⋊C8 | — | 2 | 1 | no | — |
| 56 | C7×#106 | — | 2 | 4 | no | — |
| 57 | C7×C4⋊C8 | — | 2 | 1 | no | — |
| 58 | C7×#102 | — | 2 | 4 | no | — |
| 59 | C7×C22⋊C8 | C2×C4 | 1 | 2 | yes | — |
| 60 | C4×C7×C8 | — | 2 | 1 | no | — |
| 61 | C22⋊(C7⋊C8) | — | 2 | 2 | no | — |
| 62 | C22⋊(C7⋊C8) | — | 2 | 2 | no | — |
| 63 | C4⋊(C7⋊C8) | — | 2 | 1 | no | — |
| 64 | C4⋊(C7⋊C8) | — | 2 | 1 | no | — |
| 65 | C4⋊(C7⋊C8) | — | 2 | 1 | no | — |
| 66 | C4⋊(C7⋊C8) | — | 2 | 1 | no | — |
| 67 | C4⋊(C7⋊C8) | — | 2 | 1 | no | — |
| 68 | C4⋊(C7⋊C8) | D4 | 1 | 1 | yes | characteristic |
| 69 | C4⋊(C7⋊C8) | D4 | 1 | 1 | yes | characteristic |
| 70 | #6377 | — | 2 | 1 | no | — |
| 71 | C4×C7⋊C8 | — | 2 | 1 | no | — |
| 72 | #3227 | D7 | 1 | 1 | yes | characteristic |
| 73 | #2935 | — | 7 | 1 | no | — |
| 74 | #1997 | — | 7 | 1 | no | — |
| 75 | #1547 | — | 7 | 1 | no | — |
| 76 | C2×#332 | — | 7 | 1 | no | — |
| 77 | #1301 | — | 7 | 1 | no | — |
| 78 | #1283 | — | 7 | 1 | no | — |
| 79 | C7×#41 | — | 4 | 1 | no | — |
| 80 | C7×#41 | — | 4 | 1 | no | — |
| 81 | C7×#41 | — | 4 | 1 | no | — |
| 82 | C7×#41 | — | 4 | 1 | no | — |
| 83 | C2×C7×Q8 | — | 2 | 1 | no | — |
| 84 | C2×C7×Q8 | — | 4 | 1 | no | — |
| 85 | C2×C7×Q8 | — | 4 | 1 | no | — |
| 86 | C2×C7×Q8 | — | 8 | 1 | no | — |
| 87 | C2×C7×Q8 | — | 8 | 1 | no | — |
| 88 | C2×C7×D4 | — | 2 | 2 | no | — |
| 89 | C2×C7×D4 | — | 2 | 1 | no | — |
| 90 | C2×C7×D4 | — | 2 | 1 | no | — |
| 91 | C2×C7×D4 | C22⋊C4 | 1 | 2 | yes | — |
| 92 | C22×C4×C7 | — | 2 | 2 | no | — |
| 93 | C22×C4×C7 | — | 2 | 2 | no | — |
| 94 | C22×C4×C7 | C22×C4 | 1 | 1 | yes | characteristic |
| 95 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 96 | C22×C4×C7 | #41 | 1 | 1 | yes | characteristic |
| 97 | C2×C7×C8 | — | 2 | 2 | no | — |
| 98 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 99 | C7×C4⋊C4 | — | 2 | 2 | no | — |
| 100 | C7×C4⋊C4 | — | 2 | 2 | no | — |
| 101 | C7×C4⋊C4 | — | 4 | 1 | no | — |
| 102 | C7×C4⋊C4 | — | 4 | 1 | no | — |
| 103 | C7×C4⋊C4 | C22⋊C4 | 1 | 2 | yes | — |
| 104 | C7×C22⋊C4 | — | 2 | 2 | no | — |
| 105 | C7×C22⋊C4 | — | 2 | 2 | no | — |
| 106 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 107 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 108 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 109 | C42×C7 | #41 | 1 | 1 | yes | characteristic |
| 110 | #1136 | — | 2 | 1 | no | — |
| 111 | #1136 | — | 2 | 1 | no | — |
| 112 | #1136 | — | 2 | 1 | no | — |
| 113 | #1136 | — | 4 | 4 | no | — |
| 114 | #1136 | — | 4 | 1 | no | — |
| 115 | #1136 | — | 4 | 1 | no | — |
| 116 | #1136 | SD16 | 1 | 2 | yes | — |
| 117 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 118 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 119 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 120 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 121 | C2×C7⋊C8 | — | 4 | 4 | no | — |
| 122 | C2×C7⋊C8 | — | 4 | 1 | no | — |
| 123 | C2×C7⋊C8 | — | 4 | 1 | no | — |
| 124 | C2×C7⋊C8 | — | 4 | 1 | no | — |
| 125 | C2×C7⋊C8 | — | 4 | 1 | no | — |
| 126 | C2×C7⋊C8 | — | 8 | 1 | no | — |
| 127 | C2×#131 | — | 14 | 1 | no | — |
| 128 | #532 | C2×D7 | 1 | 1 | yes | characteristic |
| 129 | C2×C4⋊Q8 | C2×D7 | 1 | 1 | yes | characteristic |
| 130 | #498 | — | 2 | 1 | no | — |
| 131 | #486 | — | 2 | 1 | no | — |
| 132 | #481 | Dic7 | 1 | 4 | yes | — |
| 133 | #476 | — | 2 | 2 | no | — |
| 134 | #436 | — | 14 | 1 | no | — |
| 135 | #435 | — | 14 | 2 | no | — |
| 136 | C8×D4 | — | 14 | 1 | no | — |
| 137 | #431 | C2×D7 | 1 | 1 | yes | characteristic |
| 138 | #423 | — | 7 | 1 | no | — |
| 139 | C2×C4⋊C8 | — | 7 | 1 | no | — |
| 140 | C2×C4⋊C8 | — | 7 | 1 | no | — |
| 141 | #408 | — | 14 | 1 | no | — |
| 142 | C4×M16 | — | 7 | 1 | no | — |
| 143 | #343 | — | 14 | 1 | no | — |
| 144 | #343 | — | 14 | 1 | no | — |
| 145 | #332 | — | 14 | 1 | no | — |
| 146 | #332 | — | 14 | 1 | no | — |
| 147 | #332 | — | 14 | 1 | no | — |
| 148 | #331 | — | 14 | 1 | no | — |
| 149 | C23×C7 | — | 2 | 2 | no | — |
| 150 | C23×C7 | C4×D4 | 1 | 1 | yes | characteristic |
| 151 | C7×Q8 | — | 4 | 1 | no | — |
| 152 | C7×Q8 | — | 4 | 1 | no | — |
| 153 | C7×Q8 | — | 8 | 2 | no | — |
| 154 | C7×Q8 | — | 8 | 1 | no | — |
| 155 | C7×Q8 | — | 8 | 1 | no | — |
| 156 | C7×D4 | — | 4 | 2 | no | — |
| 157 | C7×D4 | — | 4 | 2 | no | — |
| 158 | C7×D4 | — | 4 | 2 | no | — |
| 159 | C7×D4 | — | 4 | 1 | no | — |
| 160 | C7×D4 | — | 4 | 1 | no | — |
| 161 | C7×D4 | — | 4 | 1 | no | — |
| 162 | C7×D4 | — | 4 | 1 | no | — |
| 163 | C2×C4×C7 | — | 2 | 1 | no | — |
| 164 | C2×C4×C7 | — | 2 | 1 | no | — |
| 165 | C2×C4×C7 | — | 2 | 2 | no | — |
| 166 | C2×C4×C7 | — | 4 | 1 | no | — |
| 167 | C2×C4×C7 | — | 4 | 2 | no | — |
| 168 | C2×C4×C7 | — | 4 | 2 | no | — |
| 169 | C2×C4×C7 | — | 4 | 2 | no | — |
| 170 | C2×C4×C7 | — | 8 | 2 | no | — |
| 171 | C2×C4×C7 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 172 | C2×C4×C7 | C4×D4 | 1 | 1 | yes | characteristic |
| 173 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 174 | C2×C4×C7 | #121 | 1 | 1 | yes | characteristic |
| 175 | C2×C4×C7 | #121 | 1 | 1 | yes | characteristic |
| 176 | C2×C4×C7 | #123 | 1 | 1 | yes | characteristic |
| 177 | C2×C4×C7 | C2×SD16 | 1 | 1 | yes | characteristic |
| 178 | C2×C4×C7 | #135 | 1 | 1 | yes | characteristic |
| 179 | C2×C4×C7 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 180 | C2×C4×C7 | #137 | 1 | 1 | yes | characteristic |
| 181 | C7×C8 | — | 4 | 2 | no | — |
| 182 | C7⋊C8 | — | 2 | 2 | no | — |
| 183 | C7⋊C8 | — | 4 | 1 | no | — |
| 184 | C7⋊C8 | — | 4 | 1 | no | — |
| 185 | C7⋊C8 | — | 4 | 1 | no | — |
| 186 | C7⋊C8 | — | 8 | 1 | no | — |
| 187 | C7⋊C8 | — | 8 | 1 | no | — |
| 188 | C2×#41 | — | 2 | 1 | no | — |
| 189 | C22×Q8 | — | 2 | 1 | no | — |
| 190 | #131 | — | 28 | 2 | no | — |
| 191 | #131 | — | 28 | 2 | no | — |
| 192 | C2×M16 | — | 7 | 1 | no | — |
| 193 | C2×M16 | — | 7 | 1 | no | — |
| 194 | C2×M16 | — | 14 | 2 | no | — |
| 195 | C2×M16 | — | 14 | 1 | no | — |
| 196 | C22×C8 | — | 14 | 2 | no | — |
| 197 | C22×C8 | — | 14 | 1 | no | — |
| 198 | C22×C8 | — | 14 | 1 | no | — |
| 199 | C4⋊Q8 | — | 2 | 1 | no | — |
| 200 | C4⋊Q8 | — | 2 | 1 | no | — |
| 201 | C4⋊Q8 | — | 2 | 1 | no | — |
| 202 | C4⋊Q8 | — | 2 | 1 | no | — |
| 203 | C4⋊Q8 | C22⋊D7 | 1 | 1 | yes | characteristic |
| 204 | #127 | C22⋊D7 | 1 | 1 | yes | characteristic |
| 205 | #124 | — | 2 | 1 | no | — |
| 206 | #121 | — | 2 | 1 | no | — |
| 207 | #121 | C2×Dic7 | 1 | 2 | yes | — |
| 208 | C4×D4 | — | 2 | 1 | no | — |
| 209 | C4×D4 | C22⋊D7 | 1 | 2 | yes | — |
| 210 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 211 | C2×C4⋊C4 | C2×Dic7 | 1 | 2 | yes | — |
| 212 | C2×C42 | C22×D7 | 1 | 1 | yes | characteristic |
| 213 | #106 | — | 2 | 4 | no | — |
| 214 | C4⋊C8 | — | 2 | 1 | no | — |
| 215 | C4⋊C8 | — | 7 | 1 | no | — |
| 216 | C4⋊C8 | — | 7 | 1 | no | — |
| 217 | C4⋊C8 | — | 14 | 1 | no | — |
| 218 | C4⋊C8 | — | 14 | 1 | no | — |
| 219 | C4⋊C8 | — | 14 | 1 | no | — |
| 220 | C4⋊C8 | — | 14 | 1 | no | — |
| 221 | C4⋊C8 | — | 14 | 1 | no | — |
| 222 | #102 | — | 2 | 4 | no | — |
| 223 | C22⋊C8 | — | 14 | 2 | no | — |
| 224 | C22⋊C8 | — | 14 | 2 | no | — |
| 225 | C22⋊C8 | C2×Dic7 | 1 | 2 | yes | — |
| 226 | #97 | — | 14 | 1 | no | — |
| 227 | C4×C8 | — | 2 | 1 | no | — |
| 228 | C4×C8 | — | 14 | 1 | no | — |
| 229 | C22×C7 | — | 2 | 1 | no | — |
| 230 | C22×C7 | — | 2 | 1 | no | — |
| 231 | C22×C7 | — | 4 | 2 | no | — |
| 232 | C22×C7 | — | 4 | 2 | no | — |
| 233 | C22×C7 | — | 4 | 2 | no | — |
| 234 | C22×C7 | #386 | 1 | 1 | yes | characteristic |
| 235 | C22×C7 | C4×SD16 | 1 | 1 | yes | characteristic |
| 236 | C22×C7 | #440 | 1 | 1 | yes | characteristic |
| 237 | C4×C7 | — | 2 | 1 | no | — |
| 238 | C4×C7 | — | 2 | 1 | no | — |
| 239 | C4×C7 | — | 2 | 1 | no | — |
| 240 | C4×C7 | — | 4 | 2 | no | — |
| 241 | C4×C7 | — | 8 | 2 | no | — |
| 242 | C4×C7 | #450 | 1 | 1 | yes | characteristic |
| 243 | C4×C7 | #452 | 1 | 1 | yes | characteristic |
| 244 | C4×C7 | #461 | 1 | 1 | yes | characteristic |
| 245 | C4×C7 | #463 | 1 | 1 | yes | characteristic |
| 246 | C4×C7 | #471 | 1 | 1 | yes | characteristic |
| 247 | C4×C7 | #472 | 1 | 1 | yes | characteristic |
| 248 | #41 | — | 4 | 1 | no | — |
| 249 | #41 | — | 4 | 1 | no | — |
| 250 | #41 | — | 4 | 1 | no | — |
| 251 | #41 | — | 4 | 1 | no | — |
| 252 | C2×Q8 | — | 2 | 1 | no | — |
| 253 | C2×Q8 | — | 4 | 1 | no | — |
| 254 | C2×Q8 | — | 4 | 1 | no | — |
| 255 | C2×Q8 | — | 8 | 1 | no | — |
| 256 | C2×Q8 | — | 8 | 1 | no | — |
| 257 | C2×D4 | — | 2 | 2 | no | — |
| 258 | C2×D4 | — | 2 | 1 | no | — |
| 259 | C2×D4 | — | 2 | 1 | no | — |
| 260 | C2×D4 | C22⋊Dic7 | 1 | 2 | yes | — |
| 261 | C22×C4 | — | 2 | 2 | no | — |
| 262 | C22×C4 | — | 2 | 2 | no | — |
| 263 | C22×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 264 | C22×C4 | #1159 | 1 | 1 | yes | characteristic |
| 265 | C22×C4 | C22×Dic7 | 1 | 1 | yes | characteristic |
| 266 | M16 | — | 7 | 2 | no | — |
| 267 | M16 | — | 14 | 1 | no | — |
| 268 | M16 | — | 14 | 1 | no | — |
| 269 | M16 | — | 14 | 1 | no | — |
| 270 | M16 | — | 28 | 4 | no | — |
| 271 | M16 | — | 28 | 1 | no | — |
| 272 | M16 | — | 28 | 1 | no | — |
| 273 | C2×C8 | — | 2 | 2 | no | — |
| 274 | C2×C8 | — | 14 | 1 | no | — |
| 275 | C2×C8 | — | 14 | 1 | no | — |
| 276 | C2×C8 | — | 14 | 1 | no | — |
| 277 | C2×C8 | — | 14 | 1 | no | — |
| 278 | C2×C8 | — | 28 | 4 | no | — |
| 279 | C2×C8 | — | 28 | 1 | no | — |
| 280 | C2×C8 | — | 28 | 1 | no | — |
| 281 | C2×C8 | — | 28 | 1 | no | — |
| 282 | C2×C8 | — | 28 | 1 | no | — |
| 283 | C2×C8 | — | 56 | 1 | no | — |
| 284 | C4⋊C4 | — | 2 | 1 | no | — |
| 285 | C4⋊C4 | — | 2 | 2 | no | — |
| 286 | C4⋊C4 | — | 2 | 2 | no | — |
| 287 | C4⋊C4 | — | 4 | 1 | no | — |
| 288 | C4⋊C4 | — | 4 | 1 | no | — |
| 289 | C4⋊C4 | C22⋊Dic7 | 1 | 2 | yes | — |
| 290 | C22⋊C4 | — | 2 | 2 | no | — |
| 291 | C22⋊C4 | — | 2 | 2 | no | — |
| 292 | C42 | D4×D7 | 1 | 1 | yes | characteristic |
| 293 | C42 | #1159 | 1 | 1 | yes | characteristic |
| 294 | C42 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 295 | C42 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 296 | C2×C7 | — | 2 | 1 | no | — |
| 297 | C2×C7 | — | 2 | 1 | no | — |
| 298 | C2×C7 | — | 8 | 2 | no | — |
| 299 | C2×C7 | #1877 | 1 | 1 | yes | characteristic |
| 300 | C2×C7 | #1907 | 1 | 1 | yes | characteristic |
| 301 | C2×C7 | #1915 | 1 | 1 | yes | characteristic |
| 302 | C23 | — | 2 | 2 | no | — |
| 303 | C23 | D4×Dic7 | 1 | 1 | yes | characteristic |
| 304 | Q8 | — | 4 | 1 | no | — |
| 305 | Q8 | — | 4 | 1 | no | — |
| 306 | Q8 | — | 8 | 2 | no | — |
| 307 | Q8 | — | 8 | 1 | no | — |
| 308 | Q8 | — | 8 | 1 | no | — |
| 309 | D4 | — | 4 | 2 | no | — |
| 310 | D4 | — | 4 | 2 | no | — |
| 311 | D4 | — | 4 | 2 | no | — |
| 312 | D4 | — | 4 | 1 | no | — |
| 313 | D4 | — | 4 | 1 | no | — |
| 314 | D4 | — | 4 | 1 | no | — |
| 315 | D4 | — | 4 | 1 | no | — |
| 316 | C2×C4 | — | 2 | 1 | no | — |
| 317 | C2×C4 | — | 2 | 1 | no | — |
| 318 | C2×C4 | — | 2 | 2 | no | — |
| 319 | C2×C4 | — | 4 | 1 | no | — |
| 320 | C2×C4 | — | 4 | 2 | no | — |
| 321 | C2×C4 | — | 4 | 2 | no | — |
| 322 | C2×C4 | — | 4 | 2 | no | — |
| 323 | C2×C4 | — | 8 | 2 | no | — |
| 324 | C2×C4 | D7×SD16 | 1 | 1 | yes | characteristic |
| 325 | C2×C4 | #6477 | 1 | 1 | yes | characteristic |
| 326 | C2×C4 | #6478 | 1 | 1 | yes | characteristic |
| 327 | C2×C4 | #6479 | 1 | 1 | yes | characteristic |
| 328 | C2×C4 | D4×Dic7 | 1 | 1 | yes | characteristic |
| 329 | C2×C4 | #6498 | 1 | 1 | yes | characteristic |
| 330 | C2×C4 | #6500 | 1 | 1 | yes | characteristic |
| 331 | C2×C4 | #6502 | 1 | 1 | yes | characteristic |
| 332 | C2×C4 | #6502 | 1 | 1 | yes | characteristic |
| 333 | C2×C4 | C2×C22⋊Dic7 | 1 | 1 | yes | characteristic |
| 334 | C8 | — | 4 | 2 | no | — |
| 335 | C8 | — | 14 | 2 | no | — |
| 336 | C8 | — | 28 | 1 | no | — |
| 337 | C8 | — | 28 | 1 | no | — |
| 338 | C8 | — | 28 | 1 | no | — |
| 339 | C8 | — | 56 | 1 | no | — |
| 340 | C8 | — | 56 | 1 | no | — |
| 341 | C7 | #9269 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 342 | C22 | — | 2 | 1 | no | — |
| 343 | C22 | — | 2 | 1 | no | — |
| 344 | C22 | — | 4 | 2 | no | — |
| 345 | C22 | — | 4 | 2 | no | — |
| 346 | C22 | — | 4 | 2 | no | — |
| 347 | C22 | SD16×Dic7 | 1 | 1 | yes | characteristic |
| 348 | C22 | #89936 | 1 | 1 | yes | characteristic |
| 349 | C22 | #89992 | 1 | 1 | yes | characteristic |
| 350 | C4 | — | 2 | 1 | no | — |
| 351 | C4 | — | 2 | 1 | no | — |
| 352 | C4 | — | 2 | 1 | no | — |
| 353 | C4 | — | 4 | 2 | no | — |
| 354 | C4 | — | 8 | 2 | no | — |
| 355 | C4 | #89934 | 1 | 1 | yes | characteristic |
| 356 | C4 | #89937 | 1 | 1 | yes | characteristic |
| 357 | C4 | #89941 | 1 | 1 | yes | characteristic |
| 358 | C4 | #89945 | 1 | 1 | yes | characteristic |
| 359 | C4 | #89971 | 1 | 1 | yes | characteristic |
| 360 | C4 | #89972 | 1 | 1 | yes | characteristic |
| 361 | C2 | — | 2 | 1 | no | — |
| 362 | C2 | — | 2 | 1 | no | — |
| 363 | C2 | — | 8 | 2 | no | — |
| 364 | C2 | #11729620 | 1 | 1 | yes | characteristic |
| 365 | C2 | #11729801 | 1 | 1 | yes | characteristic |
| 366 | C2 | #11729845 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta