← #13339221
Subgroups — #13339221
Order 1792.
620 conjugacy classes of subgroups.
The subgroup lattice has 466 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C7×#2988 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #11739953 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #11739952 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #11736758 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11728701 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #11728696 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #11728609 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11728604 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #11728504 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #11728192 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C2×#89277 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C4×C7×#41 | C22 | 1 | 1 | yes | characteristic |
| 13 | #90161 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×#6432 | C22 | 1 | 1 | yes | characteristic |
| 15 | C7×C8×Q8 | C22 | 1 | 2 | yes | — |
| 16 | C7×C8×D4 | — | 2 | 2 | no | — |
| 17 | C7×C8×D4 | C22 | 1 | 2 | yes | — |
| 18 | C7×#431 | — | 2 | 1 | no | — |
| 19 | C7×#431 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×C7×C4⋊C8 | — | 2 | 1 | no | — |
| 21 | C2×C7×C4⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 22 | #90005 | — | 2 | 1 | no | — |
| 23 | #90004 | — | 2 | 1 | no | — |
| 24 | #89794 | — | 2 | 1 | no | — |
| 25 | #89793 | — | 2 | 1 | no | — |
| 26 | #89793 | C22 | 1 | 1 | yes | characteristic |
| 27 | #89792 | C22 | 1 | 1 | yes | characteristic |
| 28 | #89792 | C22 | 1 | 2 | yes | — |
| 29 | #89781 | — | 2 | 1 | no | — |
| 30 | #89780 | — | 2 | 1 | no | — |
| 31 | #89780 | C22 | 1 | 1 | yes | characteristic |
| 32 | #89779 | C22 | 1 | 1 | yes | characteristic |
| 33 | #89779 | C22 | 1 | 2 | yes | — |
| 34 | #89770 | — | 2 | 1 | no | — |
| 35 | #89767 | — | 2 | 1 | no | — |
| 36 | #89696 | C22 | 1 | 1 | yes | characteristic |
| 37 | C2×C4⋊(C7⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 38 | #89621 | — | 2 | 1 | no | — |
| 39 | #89621 | — | 2 | 1 | no | — |
| 40 | #89511 | — | 2 | 2 | no | — |
| 41 | #89471 | C22 | 1 | 2 | yes | — |
| 42 | #89453 | C22 | 1 | 2 | yes | — |
| 43 | #89277 | C22 | 1 | 2 | yes | — |
| 44 | #89277 | C22 | 1 | 2 | yes | — |
| 45 | #89277 | C22 | 1 | 2 | yes | — |
| 46 | #89276 | C22 | 1 | 2 | yes | — |
| 47 | #89253 | C22 | 1 | 2 | yes | — |
| 48 | #89253 | C22 | 1 | 2 | yes | — |
| 49 | #19411 | — | 7 | 1 | no | maximal, Sylow |
| 50 | C2×C7×#41 | D4 | 1 | 1 | yes | characteristic |
| 51 | C22×Dic14 | — | 2 | 1 | no | — |
| 52 | C22×C7×C8 | — | 2 | 1 | no | — |
| 53 | C22×C7×C8 | — | 2 | 2 | no | — |
| 54 | C4×C7×Q8 | D4 | 1 | 1 | yes | characteristic |
| 55 | C4×C7×Q8 | C23 | 1 | 1 | yes | characteristic |
| 56 | C4×C7×D4 | — | 2 | 1 | no | — |
| 57 | C4×C7×D4 | — | 2 | 1 | no | — |
| 58 | C4×C7×D4 | D4 | 1 | 1 | yes | characteristic |
| 59 | C4×C7×D4 | C23 | 1 | 1 | yes | characteristic |
| 60 | C7×#117 | — | 2 | 1 | no | — |
| 61 | C7×#117 | D4 | 1 | 1 | yes | characteristic |
| 62 | C2×C42×C7 | — | 2 | 1 | no | — |
| 63 | C2×C42×C7 | C23 | 1 | 1 | yes | characteristic |
| 64 | #6489 | — | 2 | 1 | no | — |
| 65 | C2×C4⋊Dic7 | — | 2 | 1 | no | — |
| 66 | C2×C4⋊Dic7 | — | 2 | 1 | no | — |
| 67 | #6487 | — | 2 | 1 | no | — |
| 68 | #6487 | — | 2 | 1 | no | — |
| 69 | C2×#1136 | — | 2 | 1 | no | — |
| 70 | C22×C7⋊C8 | — | 2 | 1 | no | — |
| 71 | C2×Dic28 | — | 2 | 2 | no | — |
| 72 | C2×Dic28 | — | 2 | 2 | no | — |
| 73 | #6433 | — | 2 | 1 | no | — |
| 74 | #6432 | — | 2 | 1 | no | — |
| 75 | #6432 | — | 2 | 1 | no | — |
| 76 | #6432 | — | 2 | 1 | no | — |
| 77 | #6432 | C23 | 1 | 2 | yes | — |
| 78 | #6432 | C23 | 1 | 1 | yes | characteristic |
| 79 | #6432 | C23 | 1 | 1 | yes | characteristic |
| 80 | C4×Dic14 | — | 2 | 1 | no | — |
| 81 | C4×Dic14 | — | 2 | 1 | no | — |
| 82 | C7×C4⋊C8 | — | 2 | 2 | no | — |
| 83 | C7×C4⋊C8 | — | 2 | 1 | no | — |
| 84 | C7×C4⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 85 | C7×C4⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 86 | C7×C4⋊C8 | C23 | 1 | 2 | yes | — |
| 87 | C7×C22⋊C8 | — | 2 | 2 | no | — |
| 88 | C7×C22⋊C8 | D4 | 1 | 2 | yes | — |
| 89 | C4×C7×C8 | — | 2 | 2 | no | — |
| 90 | C4×C7×C8 | C23 | 1 | 2 | yes | — |
| 91 | #6409 | — | 2 | 2 | no | — |
| 92 | #6409 | — | 2 | 1 | no | — |
| 93 | #6409 | — | 2 | 1 | no | — |
| 94 | #6406 | — | 2 | 2 | no | — |
| 95 | #6406 | — | 2 | 1 | no | — |
| 96 | #6406 | — | 2 | 1 | no | — |
| 97 | #6390 | — | 2 | 2 | no | — |
| 98 | #6390 | — | 2 | 2 | no | — |
| 99 | #6382 | — | 2 | 2 | no | — |
| 100 | #6382 | — | 2 | 1 | no | — |
| 101 | #6382 | — | 2 | 1 | no | — |
| 102 | #6381 | — | 2 | 2 | no | — |
| 103 | #6381 | — | 2 | 1 | no | — |
| 104 | #6381 | — | 2 | 1 | no | — |
| 105 | C4⋊(C7⋊C8) | — | 2 | 1 | no | — |
| 106 | C4⋊(C7⋊C8) | — | 2 | 1 | no | — |
| 107 | C4⋊(C7⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 108 | C4⋊(C7⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 109 | C4⋊(C7⋊C8) | C23 | 1 | 2 | yes | — |
| 110 | #3209 | — | 7 | 1 | no | — |
| 111 | #3079 | — | 7 | 1 | no | — |
| 112 | #3076 | — | 7 | 1 | no | — |
| 113 | #2988 | D7 | 1 | 1 | yes | characteristic |
| 114 | #1684 | — | 7 | 2 | no | — |
| 115 | #1683 | — | 7 | 2 | no | — |
| 116 | #1670 | — | 7 | 2 | no | — |
| 117 | #1669 | — | 7 | 2 | no | — |
| 118 | #1571 | — | 7 | 1 | no | — |
| 119 | #1550 | — | 7 | 1 | no | — |
| 120 | C2×#332 | — | 7 | 1 | no | — |
| 121 | C7×#41 | — | 2 | 2 | no | — |
| 122 | C7×#41 | Q16 | 1 | 4 | yes | complemented |
| 123 | C2×C7×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 124 | C2×C7×D4 | — | 2 | 1 | no | — |
| 125 | C2×C7×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 126 | C22×C4×C7 | — | 2 | 1 | no | — |
| 127 | C22×C4×C7 | — | 2 | 1 | no | — |
| 128 | C22×C4×C7 | — | 2 | 1 | no | — |
| 129 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 130 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 131 | C22×C4×C7 | #41 | 1 | 1 | yes | characteristic |
| 132 | C22×Dic7 | — | 4 | 1 | no | — |
| 133 | C2×Dic14 | — | 2 | 1 | no | — |
| 134 | C2×Dic14 | — | 2 | 2 | no | — |
| 135 | C2×Dic14 | — | 2 | 1 | no | — |
| 136 | C2×Dic14 | — | 4 | 1 | no | — |
| 137 | C2×Dic14 | — | 8 | 1 | no | — |
| 138 | C2×Dic14 | — | 8 | 1 | no | — |
| 139 | C2×C7×C8 | — | 2 | 2 | no | — |
| 140 | C2×C7×C8 | — | 8 | 2 | no | — |
| 141 | C2×C7×C8 | — | 8 | 1 | no | — |
| 142 | C2×C7×C8 | C2×D4 | 1 | 2 | yes | — |
| 143 | C2×C7×C8 | C2×D4 | 1 | 2 | yes | — |
| 144 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 145 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 146 | C7×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 147 | C7×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 148 | C7×C22⋊C4 | — | 2 | 1 | no | — |
| 149 | C7×C22⋊C4 | — | 2 | 1 | no | — |
| 150 | C7×C22⋊C4 | — | 2 | 1 | no | — |
| 151 | C42×C7 | — | 2 | 1 | no | — |
| 152 | C42×C7 | — | 2 | 1 | no | — |
| 153 | C42×C7 | — | 2 | 1 | no | — |
| 154 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 155 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 156 | C42×C7 | #41 | 1 | 1 | yes | characteristic |
| 157 | C42×C7 | C24 | 1 | 1 | yes | characteristic |
| 158 | C22⋊Dic7 | — | 4 | 1 | no | — |
| 159 | C4⋊Dic7 | — | 2 | 2 | no | — |
| 160 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 161 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 162 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 163 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 164 | C4⋊Dic7 | — | 2 | 2 | no | — |
| 165 | C4⋊Dic7 | — | 4 | 1 | no | — |
| 166 | C4⋊Dic7 | — | 4 | 1 | no | — |
| 167 | Dic7⋊C4 | — | 4 | 1 | no | — |
| 168 | Dic7⋊C4 | — | 4 | 1 | no | — |
| 169 | C4×Dic7 | — | 4 | 1 | no | — |
| 170 | #1136 | — | 4 | 2 | no | — |
| 171 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 172 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 173 | C2×C7⋊C8 | — | 2 | 2 | no | — |
| 174 | C2×C7⋊C8 | — | 4 | 2 | no | — |
| 175 | Dic28 | — | 8 | 2 | no | — |
| 176 | Dic28 | — | 8 | 2 | no | — |
| 177 | #533 | — | 7 | 1 | no | — |
| 178 | C2×C4⋊Q8 | — | 7 | 1 | no | — |
| 179 | C4×#41 | C2×D7 | 1 | 1 | yes | characteristic |
| 180 | #494 | — | 7 | 2 | no | — |
| 181 | #487 | — | 7 | 2 | no | — |
| 182 | #479 | — | 14 | 1 | no | — |
| 183 | #478 | — | 14 | 1 | no | — |
| 184 | #477 | — | 7 | 1 | no | — |
| 185 | #477 | — | 14 | 1 | no | — |
| 186 | #476 | — | 7 | 1 | no | — |
| 187 | #476 | — | 14 | 1 | no | — |
| 188 | #475 | — | 7 | 1 | no | — |
| 189 | #475 | — | 7 | 2 | no | — |
| 190 | #474 | — | 7 | 1 | no | — |
| 191 | #474 | — | 7 | 2 | no | — |
| 192 | #462 | — | 14 | 1 | no | — |
| 193 | #462 | — | 14 | 1 | no | — |
| 194 | #451 | — | 14 | 2 | no | — |
| 195 | C8×Q8 | C2×D7 | 1 | 2 | yes | — |
| 196 | C8×D4 | — | 2 | 2 | no | — |
| 197 | C8×D4 | C2×D7 | 1 | 2 | yes | — |
| 198 | #431 | — | 2 | 1 | no | — |
| 199 | #431 | C2×D7 | 1 | 1 | yes | characteristic |
| 200 | #428 | — | 14 | 1 | no | — |
| 201 | #427 | — | 14 | 1 | no | — |
| 202 | #423 | — | 7 | 1 | no | — |
| 203 | C2×C4⋊C8 | — | 2 | 1 | no | — |
| 204 | C2×C4⋊C8 | — | 7 | 1 | no | — |
| 205 | C2×C4⋊C8 | C2×D7 | 1 | 1 | yes | characteristic |
| 206 | #417 | — | 14 | 1 | no | — |
| 207 | #416 | — | 14 | 1 | no | — |
| 208 | #335 | — | 7 | 2 | no | — |
| 209 | #335 | — | 7 | 2 | no | — |
| 210 | #333 | — | 7 | 2 | no | — |
| 211 | #332 | — | 7 | 2 | no | — |
| 212 | #332 | — | 7 | 2 | no | — |
| 213 | #332 | — | 7 | 2 | no | — |
| 214 | C23×C7 | — | 2 | 1 | no | — |
| 215 | C23×C7 | #121 | 1 | 1 | yes | characteristic |
| 216 | C7×Q8 | — | 2 | 1 | no | — |
| 217 | C7×Q8 | C2×Q16 | 1 | 2 | yes | — |
| 218 | C7×D4 | — | 2 | 4 | no | — |
| 219 | C7×D4 | — | 2 | 1 | no | — |
| 220 | C7×D4 | C2×Q16 | 1 | 2 | yes | — |
| 221 | C2×C4×C7 | — | 2 | 1 | no | — |
| 222 | C2×C4×C7 | — | 2 | 1 | no | — |
| 223 | C2×C4×C7 | — | 2 | 1 | no | — |
| 224 | C2×C4×C7 | — | 2 | 4 | no | — |
| 225 | C2×C4×C7 | — | 2 | 1 | no | — |
| 226 | C2×C4×C7 | — | 2 | 1 | no | — |
| 227 | C2×C4×C7 | — | 4 | 1 | no | — |
| 228 | C2×C4×C7 | — | 4 | 1 | no | — |
| 229 | C2×C4×C7 | — | 4 | 1 | no | — |
| 230 | C2×C4×C7 | — | 8 | 1 | no | — |
| 231 | C2×C4×C7 | #121 | 1 | 1 | yes | characteristic |
| 232 | C2×C4×C7 | #121 | 1 | 1 | yes | characteristic |
| 233 | C2×C4×C7 | #121 | 1 | 1 | yes | characteristic |
| 234 | C2×C4×C7 | C2×Q16 | 1 | 2 | yes | — |
| 235 | C2×C4×C7 | #135 | 1 | 2 | yes | — |
| 236 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 237 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 238 | C2×C4×C7 | C2×#41 | 1 | 1 | yes | characteristic |
| 239 | C2×Dic7 | — | 4 | 1 | no | — |
| 240 | C2×Dic7 | — | 4 | 1 | no | — |
| 241 | C2×Dic7 | — | 4 | 2 | no | — |
| 242 | C2×Dic7 | — | 8 | 2 | no | — |
| 243 | Dic14 | — | 4 | 1 | no | — |
| 244 | Dic14 | — | 4 | 2 | no | — |
| 245 | Dic14 | — | 4 | 1 | no | — |
| 246 | Dic14 | — | 4 | 2 | no | — |
| 247 | Dic14 | — | 8 | 2 | no | — |
| 248 | Dic14 | — | 8 | 1 | no | — |
| 249 | C7×C8 | — | 2 | 2 | no | — |
| 250 | C7×C8 | — | 2 | 2 | no | — |
| 251 | C7×C8 | — | 4 | 2 | no | — |
| 252 | C7⋊C8 | — | 4 | 1 | no | — |
| 253 | C7⋊C8 | — | 4 | 1 | no | — |
| 254 | C7⋊C8 | — | 4 | 2 | no | — |
| 255 | C2×#41 | D28 | 1 | 1 | yes | characteristic |
| 256 | C22×Q8 | — | 14 | 1 | no | — |
| 257 | C2×Q16 | — | 14 | 2 | no | — |
| 258 | C2×Q16 | — | 14 | 2 | no | — |
| 259 | C2×M16 | — | 14 | 1 | no | — |
| 260 | C22×C8 | — | 2 | 1 | no | — |
| 261 | C22×C8 | — | 2 | 2 | no | — |
| 262 | C22×C8 | — | 14 | 1 | no | — |
| 263 | C4⋊Q8 | — | 7 | 2 | no | — |
| 264 | C4⋊Q8 | — | 7 | 1 | no | — |
| 265 | C4⋊Q8 | — | 7 | 1 | no | — |
| 266 | C4⋊Q8 | — | 14 | 1 | no | — |
| 267 | C4⋊Q8 | — | 14 | 1 | no | — |
| 268 | C4⋊Q8 | — | 14 | 1 | no | — |
| 269 | #125 | — | 14 | 1 | no | — |
| 270 | C22⋊Q8 | — | 14 | 1 | no | — |
| 271 | C22⋊Q8 | — | 14 | 1 | no | — |
| 272 | C4×Q8 | — | 14 | 1 | no | — |
| 273 | C4×Q8 | — | 14 | 1 | no | — |
| 274 | C4×Q8 | D28 | 1 | 1 | yes | characteristic |
| 275 | C4×Q8 | C22×D7 | 1 | 1 | yes | characteristic |
| 276 | C4×D4 | — | 2 | 1 | no | — |
| 277 | C4×D4 | — | 2 | 1 | no | — |
| 278 | C4×D4 | D28 | 1 | 1 | yes | characteristic |
| 279 | C4×D4 | C22×D7 | 1 | 1 | yes | characteristic |
| 280 | #117 | — | 2 | 1 | no | — |
| 281 | #117 | — | 14 | 1 | no | — |
| 282 | #117 | D28 | 1 | 1 | yes | characteristic |
| 283 | C2×C4⋊C4 | — | 14 | 1 | no | — |
| 284 | C2×C4⋊C4 | — | 14 | 1 | no | — |
| 285 | C2×C42 | — | 2 | 1 | no | — |
| 286 | C2×C42 | C22×D7 | 1 | 1 | yes | characteristic |
| 287 | #107 | — | 14 | 1 | no | — |
| 288 | #107 | — | 14 | 1 | no | — |
| 289 | #107 | — | 14 | 2 | no | — |
| 290 | #106 | — | 14 | 1 | no | — |
| 291 | #106 | — | 14 | 1 | no | — |
| 292 | #106 | — | 14 | 2 | no | — |
| 293 | C4⋊C8 | — | 2 | 2 | no | — |
| 294 | C4⋊C8 | — | 2 | 1 | no | — |
| 295 | C4⋊C8 | — | 7 | 1 | no | — |
| 296 | C4⋊C8 | — | 7 | 1 | no | — |
| 297 | C4⋊C8 | — | 7 | 2 | no | — |
| 298 | C4⋊C8 | — | 14 | 1 | no | — |
| 299 | C4⋊C8 | — | 14 | 1 | no | — |
| 300 | C4⋊C8 | C22⋊D7 | 1 | 1 | yes | characteristic |
| 301 | C4⋊C8 | C22⋊D7 | 1 | 1 | yes | characteristic |
| 302 | C4⋊C8 | C22×D7 | 1 | 2 | yes | — |
| 303 | #103 | — | 14 | 1 | no | — |
| 304 | #103 | — | 14 | 1 | no | — |
| 305 | #103 | — | 14 | 2 | no | — |
| 306 | #103 | — | 14 | 2 | no | — |
| 307 | #103 | — | 14 | 2 | no | — |
| 308 | #102 | — | 14 | 1 | no | — |
| 309 | #102 | — | 14 | 1 | no | — |
| 310 | #102 | — | 14 | 2 | no | — |
| 311 | C22⋊C8 | — | 2 | 2 | no | — |
| 312 | C22⋊C8 | C22⋊D7 | 1 | 2 | yes | — |
| 313 | C4×C8 | — | 2 | 2 | no | — |
| 314 | C4×C8 | C22×D7 | 1 | 2 | yes | — |
| 315 | C22×C7 | — | 2 | 1 | no | — |
| 316 | C22×C7 | — | 2 | 1 | no | — |
| 317 | C22×C7 | — | 2 | 2 | no | — |
| 318 | C22×C7 | — | 4 | 1 | no | — |
| 319 | C22×C7 | — | 4 | 1 | no | — |
| 320 | C22×C7 | #467 | 1 | 2 | yes | — |
| 321 | C22×C7 | C2×#121 | 1 | 1 | yes | characteristic |
| 322 | C4×C7 | — | 2 | 1 | no | — |
| 323 | C4×C7 | — | 2 | 2 | no | — |
| 324 | C4×C7 | — | 2 | 1 | no | — |
| 325 | C4×C7 | — | 2 | 1 | no | — |
| 326 | C4×C7 | — | 4 | 1 | no | — |
| 327 | C4×C7 | — | 4 | 1 | no | — |
| 328 | C4×C7 | #467 | 1 | 2 | yes | — |
| 329 | C4×C7 | C22×Q16 | 1 | 1 | yes | characteristic |
| 330 | C4×C7 | C2×#135 | 1 | 1 | yes | characteristic |
| 331 | C4×C7 | #576 | 1 | 1 | yes | characteristic |
| 332 | C4×C7 | #577 | 1 | 1 | yes | characteristic |
| 333 | Dic7 | — | 8 | 2 | no | — |
| 334 | Dic7 | — | 8 | 1 | no | — |
| 335 | Dic7 | — | 8 | 1 | no | — |
| 336 | #41 | — | 2 | 2 | no | — |
| 337 | #41 | Dic28 | 1 | 4 | yes | complemented |
| 338 | C2×Q8 | — | 14 | 1 | no | — |
| 339 | C2×Q8 | — | 14 | 2 | no | — |
| 340 | C2×Q8 | — | 14 | 1 | no | — |
| 341 | C2×Q8 | — | 28 | 1 | no | — |
| 342 | C2×Q8 | — | 56 | 1 | no | — |
| 343 | C2×Q8 | — | 56 | 1 | no | — |
| 344 | C2×Q8 | C2×D28 | 1 | 1 | yes | characteristic |
| 345 | C2×D4 | — | 2 | 1 | no | — |
| 346 | C2×D4 | C2×D28 | 1 | 1 | yes | characteristic |
| 347 | C22×C4 | — | 2 | 1 | no | — |
| 348 | C22×C4 | — | 2 | 1 | no | — |
| 349 | C22×C4 | — | 2 | 1 | no | — |
| 350 | C22×C4 | — | 28 | 1 | no | — |
| 351 | C22×C4 | C2×D28 | 1 | 1 | yes | characteristic |
| 352 | C22×C4 | #1157 | 1 | 1 | yes | characteristic |
| 353 | C22×C4 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 354 | Q16 | — | 56 | 2 | no | — |
| 355 | Q16 | — | 56 | 2 | no | — |
| 356 | M16 | — | 28 | 2 | no | — |
| 357 | C2×C8 | — | 2 | 2 | no | — |
| 358 | C2×C8 | — | 8 | 2 | no | — |
| 359 | C2×C8 | — | 8 | 1 | no | — |
| 360 | C2×C8 | — | 14 | 1 | no | — |
| 361 | C2×C8 | — | 14 | 2 | no | — |
| 362 | C2×C8 | — | 14 | 1 | no | — |
| 363 | C2×C8 | — | 28 | 2 | no | — |
| 364 | C2×C8 | C2×C22⋊D7 | 1 | 2 | yes | — |
| 365 | C2×C8 | C2×C22⋊D7 | 1 | 2 | yes | — |
| 366 | C4⋊C4 | — | 2 | 1 | no | — |
| 367 | C4⋊C4 | — | 2 | 1 | no | — |
| 368 | C4⋊C4 | — | 14 | 2 | no | — |
| 369 | C4⋊C4 | — | 14 | 1 | no | — |
| 370 | C4⋊C4 | — | 14 | 1 | no | — |
| 371 | C4⋊C4 | — | 14 | 2 | no | — |
| 372 | C4⋊C4 | — | 14 | 1 | no | — |
| 373 | C4⋊C4 | — | 14 | 1 | no | — |
| 374 | C4⋊C4 | — | 28 | 1 | no | — |
| 375 | C4⋊C4 | — | 28 | 1 | no | — |
| 376 | C4⋊C4 | — | 28 | 1 | no | — |
| 377 | C4⋊C4 | — | 28 | 1 | no | — |
| 378 | C4⋊C4 | C2×D28 | 1 | 1 | yes | characteristic |
| 379 | C4⋊C4 | C2×D28 | 1 | 1 | yes | characteristic |
| 380 | C22⋊C4 | — | 2 | 1 | no | — |
| 381 | C22⋊C4 | — | 2 | 1 | no | — |
| 382 | C22⋊C4 | — | 2 | 1 | no | — |
| 383 | C22⋊C4 | — | 28 | 1 | no | — |
| 384 | C42 | — | 2 | 1 | no | — |
| 385 | C42 | — | 2 | 1 | no | — |
| 386 | C42 | — | 2 | 1 | no | — |
| 387 | C42 | — | 28 | 1 | no | — |
| 388 | C42 | C2×D28 | 1 | 1 | yes | characteristic |
| 389 | C42 | #1157 | 1 | 1 | yes | characteristic |
| 390 | C42 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 391 | C42 | C23×D7 | 1 | 1 | yes | characteristic |
| 392 | C2×C7 | — | 2 | 2 | no | — |
| 393 | C2×C7 | — | 4 | 2 | no | — |
| 394 | C2×C7 | #3045 | 1 | 1 | yes | characteristic |
| 395 | C2×C7 | C2×#467 | 1 | 1 | yes | characteristic |
| 396 | C2×C7 | #3069 | 1 | 1 | yes | characteristic |
| 397 | C23 | — | 2 | 1 | no | — |
| 398 | C23 | #6493 | 1 | 1 | yes | characteristic |
| 399 | Q8 | — | 2 | 1 | no | — |
| 400 | Q8 | — | 28 | 1 | no | — |
| 401 | Q8 | — | 28 | 2 | no | — |
| 402 | Q8 | — | 28 | 1 | no | — |
| 403 | Q8 | — | 28 | 2 | no | — |
| 404 | Q8 | — | 56 | 1 | no | — |
| 405 | Q8 | — | 56 | 2 | no | — |
| 406 | Q8 | C2×Dic28 | 1 | 2 | yes | — |
| 407 | D4 | — | 2 | 4 | no | — |
| 408 | D4 | — | 2 | 1 | no | — |
| 409 | D4 | C2×Dic28 | 1 | 2 | yes | — |
| 410 | C2×C4 | — | 2 | 1 | no | — |
| 411 | C2×C4 | — | 2 | 4 | no | — |
| 412 | C2×C4 | — | 2 | 1 | no | — |
| 413 | C2×C4 | — | 2 | 1 | no | — |
| 414 | C2×C4 | — | 2 | 1 | no | — |
| 415 | C2×C4 | — | 2 | 1 | no | — |
| 416 | C2×C4 | — | 4 | 1 | no | — |
| 417 | C2×C4 | — | 4 | 1 | no | — |
| 418 | C2×C4 | — | 4 | 1 | no | — |
| 419 | C2×C4 | — | 8 | 1 | no | — |
| 420 | C2×C4 | — | 28 | 1 | no | — |
| 421 | C2×C4 | — | 28 | 1 | no | — |
| 422 | C2×C4 | — | 28 | 2 | no | — |
| 423 | C2×C4 | — | 56 | 2 | no | — |
| 424 | C2×C4 | #6467 | 1 | 2 | yes | — |
| 425 | C2×C4 | C2×Dic28 | 1 | 2 | yes | — |
| 426 | C2×C4 | #6493 | 1 | 1 | yes | characteristic |
| 427 | C2×C4 | #6493 | 1 | 1 | yes | characteristic |
| 428 | C2×C4 | #6493 | 1 | 1 | yes | characteristic |
| 429 | C2×C4 | C22×D28 | 1 | 1 | yes | characteristic |
| 430 | C2×C4 | C2×#1157 | 1 | 1 | yes | characteristic |
| 431 | C2×C4 | C22×C22⋊D7 | 1 | 1 | yes | characteristic |
| 432 | C8 | — | 2 | 2 | no | — |
| 433 | C8 | — | 2 | 2 | no | — |
| 434 | C8 | — | 4 | 2 | no | — |
| 435 | C8 | — | 28 | 1 | no | — |
| 436 | C8 | — | 28 | 1 | no | — |
| 437 | C8 | — | 28 | 2 | no | — |
| 438 | C7 | #19411 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 439 | C22 | — | 2 | 1 | no | — |
| 440 | C22 | — | 2 | 1 | no | — |
| 441 | C22 | — | 2 | 2 | no | — |
| 442 | C22 | — | 4 | 1 | no | — |
| 443 | C22 | — | 4 | 1 | no | — |
| 444 | C22 | #89888 | 1 | 2 | yes | — |
| 445 | C22 | C2×#6493 | 1 | 1 | yes | characteristic |
| 446 | C4 | — | 2 | 2 | no | — |
| 447 | C4 | — | 2 | 1 | no | — |
| 448 | C4 | — | 2 | 1 | no | — |
| 449 | C4 | — | 2 | 1 | no | — |
| 450 | C4 | — | 4 | 1 | no | — |
| 451 | C4 | — | 4 | 1 | no | — |
| 452 | C4 | — | 56 | 1 | no | — |
| 453 | C4 | — | 56 | 2 | no | — |
| 454 | C4 | — | 56 | 1 | no | — |
| 455 | C4 | #89888 | 1 | 2 | yes | — |
| 456 | C4 | C2×#6467 | 1 | 1 | yes | characteristic |
| 457 | C4 | C22×Dic28 | 1 | 1 | yes | characteristic |
| 458 | C4 | #90526 | 1 | 1 | yes | characteristic |
| 459 | C4 | #90528 | 1 | 1 | yes | characteristic |
| 460 | C2 | — | 2 | 2 | no | — |
| 461 | C2 | — | 4 | 2 | no | — |
| 462 | C2 | #11740010 | 1 | 1 | yes | characteristic |
| 463 | C2 | C2×#89888 | 1 | 1 | yes | characteristic |
| 464 | C2 | #11741261 | 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