← #13257622
Subgroups — #13257622
Order 1792.
506 conjugacy classes of subgroups.
The subgroup lattice has 420 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#89791 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C7×#1954 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #11729358 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C2×#89281 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11727531 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×#89252 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11725508 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×C4×C7×D4 | C22 | 1 | 1 | yes | characteristic |
| 9 | C22×#1142 | — | 2 | 1 | no | — |
| 10 | C2×#6432 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×C7×C4⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×C7×C22⋊C8 | — | 2 | 1 | no | — |
| 13 | C2×C7×C22⋊C8 | — | 2 | 1 | no | — |
| 14 | C2×C4×C7×C8 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×#6406 | — | 2 | 1 | no | — |
| 16 | #89791 | — | 2 | 2 | no | — |
| 17 | #89791 | — | 2 | 2 | no | — |
| 18 | C2×#6384 | — | 2 | 1 | no | — |
| 19 | #89707 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×C4⋊(C7⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×C4⋊(C7⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 22 | #89346 | — | 2 | 1 | no | — |
| 23 | #89346 | — | 2 | 1 | no | — |
| 24 | #89324 | — | 2 | 1 | no | — |
| 25 | #89281 | — | 2 | 2 | no | — |
| 26 | #89252 | — | 2 | 2 | no | — |
| 27 | #10477 | — | 7 | 1 | no | maximal, Sylow |
| 28 | C22×C7×D4 | D4 | 1 | 1 | yes | characteristic |
| 29 | C23×C4×C7 | — | 2 | 1 | no | — |
| 30 | C22×Dic14 | — | 2 | 1 | no | — |
| 31 | C22×C7×C8 | — | 2 | 1 | no | — |
| 32 | C22×C7×C8 | D4 | 1 | 1 | yes | characteristic |
| 33 | C22×C7×C8 | D4 | 1 | 1 | yes | characteristic |
| 34 | C4×C7×D4 | — | 2 | 1 | no | — |
| 35 | C4×C7×D4 | — | 2 | 1 | no | — |
| 36 | C4×C7×D4 | — | 2 | 1 | no | — |
| 37 | C4×C7×D4 | — | 2 | 1 | no | — |
| 38 | C2×C7×C4⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 39 | C2×C7×C22⋊C4 | — | 2 | 1 | no | — |
| 40 | C2×C42×C7 | C23 | 1 | 1 | yes | characteristic |
| 41 | C2×#1142 | — | 2 | 4 | no | — |
| 42 | C2×#1142 | — | 4 | 2 | no | — |
| 43 | C2×#1142 | — | 4 | 2 | no | — |
| 44 | C2×C4⋊Dic7 | — | 2 | 1 | no | — |
| 45 | C2×C4⋊Dic7 | — | 2 | 1 | no | — |
| 46 | C2×C4⋊Dic7 | — | 2 | 1 | no | — |
| 47 | C2×C4⋊Dic7 | — | 2 | 1 | no | — |
| 48 | C2×C4⋊Dic7 | — | 2 | 1 | no | — |
| 49 | C22×C7⋊C8 | — | 2 | 1 | no | — |
| 50 | C22×C7⋊C8 | — | 2 | 1 | no | — |
| 51 | #6432 | — | 2 | 1 | no | — |
| 52 | #6432 | — | 2 | 1 | no | — |
| 53 | #6432 | — | 2 | 1 | no | — |
| 54 | #6432 | D4 | 1 | 2 | yes | — |
| 55 | C7×C4⋊C8 | — | 2 | 1 | no | — |
| 56 | C7×C4⋊C8 | — | 2 | 1 | no | — |
| 57 | C7×C22⋊C8 | — | 4 | 2 | no | — |
| 58 | C7×C22⋊C8 | — | 4 | 2 | no | — |
| 59 | C4×C7×C8 | — | 2 | 1 | no | — |
| 60 | C4×C7×C8 | — | 2 | 1 | no | — |
| 61 | #6406 | — | 4 | 2 | no | — |
| 62 | #6384 | — | 2 | 4 | 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) | D4 | 1 | 2 | yes | — |
| 67 | C2×#461 | — | 7 | 1 | no | — |
| 68 | #1990 | — | 7 | 1 | no | — |
| 69 | #1954 | D7 | 1 | 1 | yes | characteristic |
| 70 | #1802 | — | 7 | 1 | no | — |
| 71 | C2×#334 | — | 7 | 1 | no | — |
| 72 | C2×#332 | — | 7 | 1 | no | — |
| 73 | #1296 | — | 7 | 1 | no | — |
| 74 | C24×C7 | — | 2 | 1 | no | — |
| 75 | C2×C7×D4 | — | 2 | 1 | no | — |
| 76 | C2×C7×D4 | — | 2 | 1 | no | — |
| 77 | C2×C7×D4 | — | 2 | 1 | no | — |
| 78 | C2×C7×D4 | — | 2 | 1 | no | — |
| 79 | C2×C7×D4 | — | 2 | 1 | no | — |
| 80 | C2×C7×D4 | SD16 | 1 | 2 | yes | — |
| 81 | C22×C4×C7 | — | 2 | 1 | no | — |
| 82 | C22×C4×C7 | — | 4 | 1 | no | — |
| 83 | C22×C4×C7 | — | 4 | 1 | no | — |
| 84 | C22×C4×C7 | — | 4 | 1 | no | — |
| 85 | C22×C4×C7 | — | 4 | 1 | no | — |
| 86 | C22×C4×C7 | — | 4 | 1 | no | — |
| 87 | C22×C4×C7 | — | 4 | 1 | no | — |
| 88 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 89 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 90 | C22×C4×C7 | #41 | 1 | 1 | yes | characteristic |
| 91 | C22×Dic7 | — | 4 | 1 | no | — |
| 92 | C22×Dic7 | — | 4 | 1 | no | — |
| 93 | C2×Dic14 | — | 2 | 2 | no | — |
| 94 | C2×Dic14 | — | 4 | 1 | no | — |
| 95 | C2×Dic14 | — | 4 | 1 | no | — |
| 96 | C2×Dic14 | — | 4 | 1 | no | — |
| 97 | C2×Dic14 | — | 4 | 1 | no | — |
| 98 | C2×Dic14 | — | 4 | 1 | no | — |
| 99 | C2×C7×C8 | — | 2 | 1 | no | — |
| 100 | C2×C7×C8 | — | 2 | 1 | no | — |
| 101 | C2×C7×C8 | — | 2 | 1 | no | — |
| 102 | C2×C7×C8 | — | 2 | 1 | no | — |
| 103 | C2×C7×C8 | — | 2 | 1 | no | — |
| 104 | C2×C7×C8 | — | 4 | 1 | no | — |
| 105 | C2×C7×C8 | — | 4 | 1 | no | — |
| 106 | C2×C7×C8 | — | 4 | 1 | no | — |
| 107 | C2×C7×C8 | SD16 | 1 | 2 | yes | complemented |
| 108 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 109 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 110 | C7×C22⋊C4 | — | 4 | 1 | no | — |
| 111 | C7×C22⋊C4 | — | 4 | 1 | no | — |
| 112 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 113 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 114 | C42×C7 | #41 | 1 | 1 | yes | characteristic |
| 115 | C42×C7 | #41 | 1 | 1 | yes | characteristic |
| 116 | #1142 | — | 4 | 8 | no | — |
| 117 | C4⋊Dic7 | — | 2 | 2 | no | — |
| 118 | C4⋊Dic7 | — | 2 | 2 | no | — |
| 119 | C4⋊Dic7 | — | 4 | 1 | no | — |
| 120 | C4⋊Dic7 | — | 4 | 1 | no | — |
| 121 | C4⋊Dic7 | — | 4 | 1 | no | — |
| 122 | C4⋊Dic7 | — | 4 | 1 | no | — |
| 123 | C4⋊Dic7 | — | 4 | 1 | no | — |
| 124 | C4⋊Dic7 | — | 4 | 1 | no | — |
| 125 | C4⋊Dic7 | — | 8 | 1 | no | — |
| 126 | C2×C7⋊C8 | — | 2 | 2 | no | — |
| 127 | C2×C7⋊C8 | — | 4 | 1 | no | — |
| 128 | C2×C7⋊C8 | — | 4 | 1 | no | — |
| 129 | C2×C7⋊C8 | — | 4 | 1 | no | — |
| 130 | C2×C7⋊C8 | — | 4 | 1 | no | — |
| 131 | C2×C7⋊C8 | — | 4 | 1 | no | — |
| 132 | C22×SD16 | — | 14 | 1 | no | — |
| 133 | C2×C4⋊Q8 | — | 7 | 1 | no | — |
| 134 | C2×C4×D4 | C2×D7 | 1 | 1 | yes | characteristic |
| 135 | #461 | — | 14 | 2 | no | — |
| 136 | #461 | — | 14 | 2 | no | — |
| 137 | C2×C4⋊C8 | — | 7 | 1 | no | — |
| 138 | C2×C4⋊C8 | — | 7 | 1 | no | — |
| 139 | C2×C4⋊C8 | C2×D7 | 1 | 1 | yes | characteristic |
| 140 | C2×#103 | — | 14 | 1 | no | — |
| 141 | C2×#102 | — | 14 | 1 | no | — |
| 142 | C2×C22⋊C8 | — | 2 | 1 | no | — |
| 143 | C2×C22⋊C8 | — | 2 | 1 | no | — |
| 144 | C2×C4×C8 | C2×D7 | 1 | 1 | yes | characteristic |
| 145 | #384 | — | 7 | 1 | no | — |
| 146 | #340 | — | 14 | 1 | no | — |
| 147 | #340 | — | 14 | 1 | no | — |
| 148 | #340 | — | 14 | 1 | no | — |
| 149 | #334 | — | 14 | 2 | no | — |
| 150 | #332 | — | 14 | 2 | no | — |
| 151 | C23×C7 | — | 2 | 2 | no | — |
| 152 | C23×C7 | — | 4 | 1 | no | — |
| 153 | C23×C7 | — | 4 | 1 | no | — |
| 154 | C23×C7 | — | 4 | 1 | no | — |
| 155 | C23×C7 | — | 4 | 1 | no | — |
| 156 | C23×C7 | — | 4 | 1 | no | — |
| 157 | C23×C7 | — | 4 | 1 | no | — |
| 158 | C23×C7 | #121 | 1 | 1 | yes | characteristic |
| 159 | C7×D4 | — | 2 | 2 | no | — |
| 160 | C7×D4 | — | 2 | 2 | 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 | — | 4 | 1 | no | — |
| 166 | C2×C4×C7 | — | 4 | 1 | no | — |
| 167 | C2×C4×C7 | — | 4 | 1 | no | — |
| 168 | C2×C4×C7 | — | 8 | 1 | no | — |
| 169 | C2×C4×C7 | — | 8 | 1 | no | — |
| 170 | C2×C4×C7 | — | 8 | 1 | no | — |
| 171 | C2×C4×C7 | — | 8 | 1 | no | — |
| 172 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 173 | C2×C4×C7 | #121 | 1 | 1 | yes | characteristic |
| 174 | C2×C4×C7 | #121 | 1 | 1 | yes | characteristic |
| 175 | C2×C4×C7 | #123 | 1 | 1 | yes | characteristic |
| 176 | C2×C4×C7 | #123 | 1 | 1 | yes | characteristic |
| 177 | C2×C4×C7 | #124 | 1 | 1 | yes | characteristic |
| 178 | C2×C4×C7 | C2×SD16 | 1 | 1 | yes | characteristic |
| 179 | C2×C4×C7 | C2×SD16 | 1 | 1 | yes | characteristic |
| 180 | C2×C4×C7 | #135 | 1 | 1 | yes | characteristic |
| 181 | C2×C4×C7 | #135 | 1 | 1 | yes | characteristic |
| 182 | C2×C4×C7 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 183 | C2×C4×C7 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 184 | C2×C4×C7 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 185 | C2×C4×C7 | #137 | 1 | 1 | yes | characteristic |
| 186 | C2×Dic7 | — | 4 | 2 | no | — |
| 187 | C2×Dic7 | — | 8 | 1 | no | — |
| 188 | C2×Dic7 | — | 8 | 1 | no | — |
| 189 | C2×Dic7 | — | 8 | 1 | no | — |
| 190 | C2×Dic7 | — | 8 | 1 | no | — |
| 191 | C2×Dic7 | — | 8 | 1 | no | — |
| 192 | Dic14 | — | 4 | 2 | no | — |
| 193 | Dic14 | — | 4 | 2 | no | — |
| 194 | Dic14 | — | 8 | 1 | no | — |
| 195 | Dic14 | — | 8 | 1 | no | — |
| 196 | C7×C8 | — | 2 | 2 | no | — |
| 197 | C7×C8 | — | 4 | 1 | no | — |
| 198 | C7×C8 | — | 8 | 1 | no | — |
| 199 | C7⋊C8 | — | 4 | 2 | no | — |
| 200 | C7⋊C8 | — | 8 | 1 | no | — |
| 201 | C22×Q8 | — | 14 | 1 | no | — |
| 202 | C22×D4 | D28 | 1 | 1 | yes | characteristic |
| 203 | C23×C4 | — | 2 | 1 | no | — |
| 204 | C2×SD16 | — | 14 | 4 | no | — |
| 205 | C2×SD16 | — | 28 | 2 | no | — |
| 206 | C2×SD16 | — | 28 | 2 | no | — |
| 207 | C22×C8 | — | 2 | 1 | no | — |
| 208 | C22×C8 | — | 14 | 1 | no | — |
| 209 | C22×C8 | — | 14 | 1 | no | — |
| 210 | C22×C8 | C22⋊D7 | 1 | 1 | yes | characteristic |
| 211 | C22×C8 | C22⋊D7 | 1 | 1 | yes | characteristic |
| 212 | C4⋊Q8 | — | 7 | 2 | no | — |
| 213 | C4⋊Q8 | — | 14 | 1 | no | — |
| 214 | C4⋊Q8 | — | 14 | 1 | no | — |
| 215 | C4⋊Q8 | — | 14 | 1 | no | — |
| 216 | C4×D4 | — | 2 | 1 | no | — |
| 217 | C4×D4 | — | 2 | 1 | no | — |
| 218 | C4×D4 | — | 2 | 1 | no | — |
| 219 | C4×D4 | — | 2 | 1 | no | — |
| 220 | C2×C4⋊C4 | — | 14 | 1 | no | — |
| 221 | C2×C4⋊C4 | — | 14 | 1 | no | — |
| 222 | C2×C4⋊C4 | — | 14 | 1 | no | — |
| 223 | C2×C4⋊C4 | — | 14 | 1 | no | — |
| 224 | C2×C4⋊C4 | — | 14 | 1 | no | — |
| 225 | C2×C4⋊C4 | D28 | 1 | 1 | yes | characteristic |
| 226 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 227 | C2×C42 | C22×D7 | 1 | 1 | yes | characteristic |
| 228 | C4⋊C8 | — | 2 | 1 | no | — |
| 229 | C4⋊C8 | — | 2 | 1 | no | — |
| 230 | C4⋊C8 | — | 7 | 2 | no | — |
| 231 | C4⋊C8 | — | 14 | 1 | no | — |
| 232 | C4⋊C8 | — | 14 | 1 | no | — |
| 233 | C4⋊C8 | — | 14 | 1 | no | — |
| 234 | #103 | — | 14 | 4 | no | — |
| 235 | #102 | — | 28 | 2 | no | — |
| 236 | C22⋊C8 | — | 4 | 2 | no | — |
| 237 | C22⋊C8 | — | 4 | 2 | no | — |
| 238 | C4×C8 | — | 2 | 1 | no | — |
| 239 | C4×C8 | — | 2 | 1 | no | — |
| 240 | C22×C7 | — | 4 | 2 | no | — |
| 241 | C22×C7 | — | 4 | 2 | no | — |
| 242 | C22×C7 | — | 4 | 2 | no | — |
| 243 | C22×C7 | — | 8 | 1 | no | — |
| 244 | C22×C7 | — | 8 | 1 | no | — |
| 245 | C22×C7 | — | 8 | 1 | no | — |
| 246 | C22×C7 | — | 8 | 1 | no | — |
| 247 | C22×C7 | #394 | 1 | 1 | yes | characteristic |
| 248 | C22×C7 | #461 | 1 | 1 | yes | characteristic |
| 249 | C22×C7 | #463 | 1 | 1 | yes | characteristic |
| 250 | C22×C7 | #465 | 1 | 1 | yes | characteristic |
| 251 | C22×C7 | #469 | 1 | 1 | yes | characteristic |
| 252 | C22×C7 | #471 | 1 | 1 | yes | characteristic |
| 253 | C22×C7 | #473 | 1 | 1 | yes | characteristic |
| 254 | C4×C7 | — | 2 | 1 | no | — |
| 255 | C4×C7 | — | 2 | 1 | no | — |
| 256 | C4×C7 | — | 8 | 1 | no | — |
| 257 | C4×C7 | #449 | 1 | 1 | yes | characteristic |
| 258 | C4×C7 | #450 | 1 | 1 | yes | characteristic |
| 259 | C4×C7 | #460 | 1 | 1 | yes | characteristic |
| 260 | C4×C7 | #464 | 1 | 1 | yes | characteristic |
| 261 | C4×C7 | #465 | 1 | 1 | yes | characteristic |
| 262 | C4×C7 | #468 | 1 | 1 | yes | characteristic |
| 263 | C4×C7 | #481 | 1 | 1 | yes | characteristic |
| 264 | C4×C7 | #482 | 1 | 1 | yes | characteristic |
| 265 | Dic7 | — | 8 | 2 | no | — |
| 266 | Dic7 | — | 16 | 1 | no | — |
| 267 | C24 | — | 2 | 1 | no | — |
| 268 | C2×Q8 | — | 14 | 2 | no | — |
| 269 | C2×Q8 | — | 28 | 1 | no | — |
| 270 | C2×Q8 | — | 28 | 1 | no | — |
| 271 | C2×Q8 | — | 28 | 1 | no | — |
| 272 | C2×Q8 | — | 28 | 1 | no | — |
| 273 | C2×Q8 | — | 28 | 1 | no | — |
| 274 | C2×D4 | — | 2 | 1 | no | — |
| 275 | C2×D4 | — | 2 | 1 | no | — |
| 276 | C2×D4 | — | 2 | 1 | no | — |
| 277 | C2×D4 | — | 2 | 1 | no | — |
| 278 | C2×D4 | — | 2 | 1 | no | — |
| 279 | C2×D4 | #1132 | 1 | 2 | yes | — |
| 280 | C22×C4 | — | 2 | 1 | no | — |
| 281 | C22×C4 | — | 4 | 1 | no | — |
| 282 | C22×C4 | — | 4 | 1 | no | — |
| 283 | C22×C4 | — | 4 | 1 | no | — |
| 284 | C22×C4 | — | 4 | 1 | no | — |
| 285 | C22×C4 | — | 4 | 1 | no | — |
| 286 | C22×C4 | — | 4 | 1 | no | — |
| 287 | C22×C4 | — | 28 | 1 | no | — |
| 288 | C22×C4 | — | 28 | 1 | no | — |
| 289 | C22×C4 | C2×D28 | 1 | 1 | yes | characteristic |
| 290 | C22×C4 | #1157 | 1 | 1 | yes | characteristic |
| 291 | C22×C4 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 292 | SD16 | — | 28 | 8 | no | — |
| 293 | C2×C8 | — | 2 | 1 | no | — |
| 294 | C2×C8 | — | 2 | 1 | no | — |
| 295 | C2×C8 | — | 2 | 1 | no | — |
| 296 | C2×C8 | — | 2 | 1 | no | — |
| 297 | C2×C8 | — | 2 | 1 | no | — |
| 298 | C2×C8 | — | 4 | 1 | no | — |
| 299 | C2×C8 | — | 4 | 1 | no | — |
| 300 | C2×C8 | — | 4 | 1 | no | — |
| 301 | C2×C8 | — | 14 | 2 | no | — |
| 302 | C2×C8 | — | 28 | 1 | no | — |
| 303 | C2×C8 | — | 28 | 1 | no | — |
| 304 | C2×C8 | — | 28 | 1 | no | — |
| 305 | C2×C8 | — | 28 | 1 | no | — |
| 306 | C2×C8 | — | 28 | 1 | no | — |
| 307 | C2×C8 | #1142 | 1 | 2 | yes | complemented |
| 308 | C4⋊C4 | — | 2 | 1 | no | — |
| 309 | C4⋊C4 | — | 2 | 1 | no | — |
| 310 | C4⋊C4 | — | 14 | 2 | no | — |
| 311 | C4⋊C4 | — | 14 | 2 | no | — |
| 312 | C4⋊C4 | — | 28 | 1 | no | — |
| 313 | C4⋊C4 | — | 28 | 1 | no | — |
| 314 | C4⋊C4 | — | 28 | 1 | no | — |
| 315 | C4⋊C4 | — | 28 | 1 | no | — |
| 316 | C4⋊C4 | — | 28 | 1 | no | — |
| 317 | C4⋊C4 | — | 28 | 1 | no | — |
| 318 | C4⋊C4 | — | 56 | 1 | no | — |
| 319 | C22⋊C4 | — | 4 | 1 | no | — |
| 320 | C22⋊C4 | — | 4 | 1 | no | — |
| 321 | C42 | D4×D7 | 1 | 1 | yes | characteristic |
| 322 | C42 | D4×D7 | 1 | 1 | yes | characteristic |
| 323 | C42 | #1159 | 1 | 1 | yes | characteristic |
| 324 | C42 | #1159 | 1 | 1 | yes | characteristic |
| 325 | C2×C7 | — | 8 | 2 | no | — |
| 326 | C2×C7 | #1671 | 1 | 1 | yes | characteristic |
| 327 | C2×C7 | #1679 | 1 | 1 | yes | characteristic |
| 328 | C2×C7 | #1693 | 1 | 1 | yes | characteristic |
| 329 | C2×C7 | #1701 | 1 | 1 | yes | characteristic |
| 330 | C2×C7 | #2034 | 1 | 1 | yes | characteristic |
| 331 | C2×C7 | #2052 | 1 | 1 | yes | characteristic |
| 332 | C2×C7 | #2055 | 1 | 1 | yes | characteristic |
| 333 | C23 | — | 2 | 2 | no | — |
| 334 | C23 | — | 4 | 1 | no | — |
| 335 | C23 | — | 4 | 1 | no | — |
| 336 | C23 | — | 4 | 1 | no | — |
| 337 | C23 | — | 4 | 1 | no | — |
| 338 | C23 | — | 4 | 1 | no | — |
| 339 | C23 | — | 4 | 1 | no | — |
| 340 | C23 | #6493 | 1 | 1 | yes | characteristic |
| 341 | Q8 | — | 28 | 2 | no | — |
| 342 | Q8 | — | 28 | 2 | no | — |
| 343 | Q8 | — | 56 | 1 | no | — |
| 344 | Q8 | — | 56 | 1 | no | — |
| 345 | D4 | — | 2 | 2 | no | — |
| 346 | D4 | — | 2 | 2 | no | — |
| 347 | D4 | — | 4 | 1 | no | — |
| 348 | D4 | — | 4 | 1 | no | — |
| 349 | C2×C4 | — | 2 | 1 | no | — |
| 350 | C2×C4 | — | 2 | 1 | no | — |
| 351 | C2×C4 | — | 4 | 1 | no | — |
| 352 | C2×C4 | — | 4 | 1 | no | — |
| 353 | C2×C4 | — | 4 | 1 | no | — |
| 354 | C2×C4 | — | 8 | 1 | no | — |
| 355 | C2×C4 | — | 8 | 1 | no | — |
| 356 | C2×C4 | — | 8 | 1 | no | — |
| 357 | C2×C4 | — | 8 | 1 | no | — |
| 358 | C2×C4 | — | 28 | 2 | no | — |
| 359 | C2×C4 | — | 56 | 1 | no | — |
| 360 | C2×C4 | — | 56 | 1 | no | — |
| 361 | C2×C4 | — | 56 | 1 | no | — |
| 362 | C2×C4 | — | 56 | 1 | no | — |
| 363 | C2×C4 | — | 56 | 1 | no | — |
| 364 | C2×C4 | #6445 | 1 | 1 | yes | characteristic |
| 365 | C2×C4 | #6446 | 1 | 1 | yes | characteristic |
| 366 | C2×C4 | #6448 | 1 | 1 | yes | characteristic |
| 367 | C2×C4 | #6449 | 1 | 1 | yes | characteristic |
| 368 | C2×C4 | C2×#1132 | 1 | 1 | yes | characteristic |
| 369 | C2×C4 | #6467 | 1 | 1 | yes | characteristic |
| 370 | C2×C4 | #6471 | 1 | 1 | yes | characteristic |
| 371 | C2×C4 | #6471 | 1 | 1 | yes | characteristic |
| 372 | C2×C4 | #6495 | 1 | 1 | yes | characteristic |
| 373 | C2×C4 | C2×#1142 | 1 | 1 | yes | characteristic |
| 374 | C2×C4 | #6501 | 1 | 1 | yes | characteristic |
| 375 | C2×C4 | #6502 | 1 | 1 | yes | characteristic |
| 376 | C2×C4 | #6513 | 1 | 1 | yes | characteristic |
| 377 | C2×C4 | #6514 | 1 | 1 | yes | characteristic |
| 378 | C8 | — | 2 | 2 | no | — |
| 379 | C8 | — | 4 | 1 | no | — |
| 380 | C8 | — | 8 | 1 | no | — |
| 381 | C8 | — | 28 | 2 | no | — |
| 382 | C8 | — | 56 | 1 | no | — |
| 383 | C7 | #10477 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 384 | C22 | — | 4 | 2 | no | — |
| 385 | C22 | — | 4 | 2 | no | — |
| 386 | C22 | — | 4 | 2 | no | — |
| 387 | C22 | — | 8 | 1 | no | — |
| 388 | C22 | — | 8 | 1 | no | — |
| 389 | C22 | — | 8 | 1 | no | — |
| 390 | C22 | — | 8 | 1 | no | — |
| 391 | C22 | #89733 | 1 | 1 | yes | characteristic |
| 392 | C22 | #89788 | 1 | 1 | yes | characteristic |
| 393 | C22 | #89791 | 1 | 1 | yes | characteristic |
| 394 | C22 | #89886 | 1 | 1 | yes | characteristic |
| 395 | C22 | #89907 | 1 | 1 | yes | characteristic |
| 396 | C22 | #89913 | 1 | 1 | yes | characteristic |
| 397 | C22 | #89915 | 1 | 1 | yes | characteristic |
| 398 | C4 | — | 2 | 1 | no | — |
| 399 | C4 | — | 2 | 1 | no | — |
| 400 | C4 | — | 8 | 1 | no | — |
| 401 | C4 | — | 56 | 2 | no | — |
| 402 | C4 | — | 112 | 1 | no | — |
| 403 | C4 | #89503 | 1 | 1 | yes | characteristic |
| 404 | C4 | #89506 | 1 | 1 | yes | characteristic |
| 405 | C4 | #89507 | 1 | 1 | yes | characteristic |
| 406 | C4 | #89509 | 1 | 1 | yes | characteristic |
| 407 | C4 | #89813 | 1 | 1 | yes | characteristic |
| 408 | C4 | #89814 | 1 | 1 | yes | characteristic |
| 409 | C4 | #89826 | 1 | 1 | yes | characteristic |
| 410 | C4 | #89847 | 1 | 1 | yes | characteristic |
| 411 | C2 | — | 8 | 2 | no | — |
| 412 | C2 | #11727405 | 1 | 1 | yes | characteristic |
| 413 | C2 | #11727689 | 1 | 1 | yes | characteristic |
| 414 | C2 | #11727758 | 1 | 1 | yes | characteristic |
| 415 | C2 | #11728605 | 1 | 1 | yes | characteristic |
| 416 | C2 | #11728608 | 1 | 1 | yes | characteristic |
| 417 | C2 | #11728624 | 1 | 1 | yes | characteristic |
| 418 | C2 | #11728627 | 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