← #13508465
Subgroups — #13508465
Order 1792.
574 conjugacy classes of subgroups.
The subgroup lattice has 398 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | Dic7×#135 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#89646 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C7×#2139 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #11729832 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #11729182 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11729174 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11728350 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11726965 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #11726964 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #11726933 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #11726932 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | C2×C7×#135 | C22 | 1 | 1 | yes | characteristic |
| 13 | #41×Dic7 | — | 2 | 1 | no | — |
| 14 | C2×#6451 | — | 2 | 1 | no | — |
| 15 | C2×C7×M32 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×C7×#107 | C22 | 1 | 1 | yes | characteristic |
| 17 | #90005 | — | 2 | 1 | no | — |
| 18 | Q16×Dic7 | C22 | 1 | 1 | yes | characteristic |
| 19 | Q16×Dic7 | C22 | 1 | 1 | yes | characteristic |
| 20 | SD16×Dic7 | — | 2 | 1 | no | — |
| 21 | SD16×Dic7 | — | 2 | 1 | no | — |
| 22 | D8×Dic7 | C22 | 1 | 1 | yes | characteristic |
| 23 | D8×Dic7 | C22 | 1 | 1 | yes | characteristic |
| 24 | #89878 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×#6392 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×C8×Dic7 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×#6386 | C22 | 1 | 1 | yes | characteristic |
| 28 | C2×#6381 | — | 2 | 1 | no | — |
| 29 | #89646 | — | 2 | 1 | no | — |
| 30 | #89646 | — | 2 | 1 | no | — |
| 31 | #89646 | C22 | 1 | 2 | yes | — |
| 32 | #89646 | C22 | 1 | 2 | yes | — |
| 33 | C7×#358 | C22 | 1 | 2 | yes | — |
| 34 | C7×#357 | C22 | 1 | 2 | yes | — |
| 35 | #89359 | C22 | 1 | 2 | yes | — |
| 36 | #89357 | C22 | 1 | 2 | yes | — |
| 37 | #89300 | C22 | 1 | 2 | yes | — |
| 38 | #89299 | C22 | 1 | 2 | yes | — |
| 39 | Dic7⋊C16 | C22 | 1 | 2 | yes | — |
| 40 | Dic7⋊C16 | C22 | 1 | 2 | yes | — |
| 41 | #89285 | C22 | 1 | 2 | yes | — |
| 42 | #89284 | C22 | 1 | 2 | yes | — |
| 43 | #33629 | — | 7 | 1 | no | maximal, Sylow |
| 44 | C2×C7×#41 | — | 2 | 1 | no | — |
| 45 | C22×Dic14 | — | 4 | 1 | no | — |
| 46 | C7×#135 | — | 2 | 2 | no | — |
| 47 | C7×#135 | Q8 | 1 | 4 | yes | complemented |
| 48 | C2×C7×Q16 | C23 | 1 | 1 | yes | characteristic |
| 49 | C2×C7×SD16 | — | 2 | 1 | no | — |
| 50 | C2×C7×D8 | C23 | 1 | 1 | yes | characteristic |
| 51 | C22×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 52 | C2×C7×C4⋊C4 | — | 2 | 1 | no | — |
| 53 | Q8×Dic7 | — | 2 | 1 | no | — |
| 54 | Q8×Dic7 | — | 2 | 1 | no | — |
| 55 | D4×Dic7 | — | 2 | 1 | no | — |
| 56 | D4×Dic7 | — | 2 | 1 | no | — |
| 57 | D4×Dic7 | — | 4 | 1 | no | — |
| 58 | D4×Dic7 | — | 4 | 1 | no | — |
| 59 | #6489 | — | 2 | 1 | no | — |
| 60 | #6489 | — | 4 | 1 | no | — |
| 61 | C2×C4⋊Dic7 | — | 2 | 1 | no | — |
| 62 | C2×Dic7⋊C4 | — | 4 | 1 | no | — |
| 63 | C2×C4×Dic7 | — | 4 | 1 | no | — |
| 64 | C2×C4×Dic7 | D4 | 1 | 1 | yes | characteristic |
| 65 | C22×C7⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 66 | #6451 | — | 2 | 2 | no | — |
| 67 | #6451 | — | 2 | 2 | no | — |
| 68 | #6451 | — | 4 | 1 | no | — |
| 69 | #6451 | — | 4 | 1 | no | — |
| 70 | C7×M32 | — | 2 | 2 | no | — |
| 71 | C2×C7×C16 | C23 | 1 | 2 | yes | — |
| 72 | C7×#107 | — | 2 | 1 | no | — |
| 73 | C7×#107 | C23 | 1 | 2 | yes | — |
| 74 | #6409 | — | 2 | 1 | no | — |
| 75 | #6409 | — | 2 | 1 | no | — |
| 76 | #6406 | — | 2 | 1 | no | — |
| 77 | #6406 | — | 2 | 1 | no | — |
| 78 | #6392 | — | 2 | 1 | no | — |
| 79 | #6392 | C23 | 1 | 2 | yes | — |
| 80 | #6392 | C23 | 1 | 1 | yes | characteristic |
| 81 | #6392 | C23 | 1 | 1 | yes | characteristic |
| 82 | #6391 | — | 2 | 1 | no | — |
| 83 | C8×Dic7 | D4 | 1 | 1 | yes | characteristic |
| 84 | C8×Dic7 | D4 | 1 | 1 | yes | characteristic |
| 85 | C8×Dic7 | C23 | 1 | 1 | yes | characteristic |
| 86 | C8×Dic7 | C23 | 1 | 1 | yes | characteristic |
| 87 | #6386 | — | 2 | 2 | no | — |
| 88 | C2×C7⋊C16 | C23 | 1 | 2 | yes | — |
| 89 | #6381 | — | 2 | 2 | no | — |
| 90 | #6381 | — | 2 | 2 | no | — |
| 91 | C2×#500 | — | 7 | 1 | no | — |
| 92 | C4×#135 | — | 7 | 1 | no | — |
| 93 | #2227 | — | 7 | 2 | no | — |
| 94 | #2226 | — | 7 | 2 | no | — |
| 95 | #2225 | — | 7 | 2 | no | — |
| 96 | #2224 | — | 7 | 2 | no | — |
| 97 | #2159 | — | 7 | 1 | no | — |
| 98 | #2159 | — | 7 | 1 | no | — |
| 99 | #2150 | — | 7 | 1 | no | — |
| 100 | #2139 | — | 7 | 1 | no | — |
| 101 | #2139 | D7 | 1 | 1 | yes | characteristic |
| 102 | C7×#41 | — | 2 | 4 | no | — |
| 103 | C7×#41 | — | 4 | 2 | no | — |
| 104 | C2×C7×Q8 | — | 2 | 1 | no | — |
| 105 | C2×C7×D4 | — | 2 | 1 | no | — |
| 106 | C2×C7×D4 | — | 4 | 1 | no | — |
| 107 | C22×C4×C7 | — | 4 | 1 | no | — |
| 108 | C22×C4×C7 | — | 4 | 1 | no | — |
| 109 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 110 | C22×Dic7 | — | 4 | 1 | no | — |
| 111 | C22×Dic7 | — | 4 | 1 | no | — |
| 112 | C22×Dic7 | — | 4 | 1 | no | — |
| 113 | C22×Dic7 | D8 | 1 | 1 | yes | characteristic |
| 114 | C22×Dic7 | D8 | 1 | 1 | yes | characteristic |
| 115 | C2×Dic14 | — | 4 | 2 | no | — |
| 116 | C2×Dic14 | — | 4 | 2 | no | — |
| 117 | C2×Dic14 | — | 8 | 4 | no | — |
| 118 | C7×Q16 | — | 2 | 1 | no | — |
| 119 | C7×Q16 | C2×Q8 | 1 | 2 | yes | complemented |
| 120 | C7×SD16 | — | 2 | 4 | no | — |
| 121 | C7×D8 | — | 2 | 1 | no | — |
| 122 | C7×D8 | C2×Q8 | 1 | 2 | yes | complemented |
| 123 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 124 | C2×C7×C8 | C2×Q8 | 1 | 2 | yes | — |
| 125 | C2×C7×C8 | #41 | 1 | 2 | yes | — |
| 126 | C2×C7×C8 | C24 | 1 | 1 | yes | characteristic |
| 127 | C7×C4⋊C4 | — | 2 | 2 | no | — |
| 128 | C7×C4⋊C4 | — | 4 | 1 | no | — |
| 129 | C22⋊Dic7 | — | 4 | 1 | no | — |
| 130 | C22⋊Dic7 | — | 4 | 1 | no | — |
| 131 | C22⋊Dic7 | — | 4 | 1 | no | — |
| 132 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 133 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 134 | C4⋊Dic7 | — | 2 | 2 | no | — |
| 135 | C4⋊Dic7 | — | 4 | 1 | no | — |
| 136 | C4⋊Dic7 | — | 4 | 1 | no | — |
| 137 | C4⋊Dic7 | — | 4 | 1 | no | — |
| 138 | Dic7⋊C4 | — | 4 | 2 | no | — |
| 139 | Dic7⋊C4 | — | 4 | 2 | no | — |
| 140 | C4×Dic7 | — | 4 | 1 | no | — |
| 141 | C4×Dic7 | — | 4 | 1 | no | — |
| 142 | C4×Dic7 | — | 4 | 1 | no | — |
| 143 | C4×Dic7 | D8 | 1 | 1 | yes | characteristic |
| 144 | C4×Dic7 | D8 | 1 | 1 | yes | characteristic |
| 145 | C4×Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 146 | C4×Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 147 | C2×C7⋊C8 | — | 2 | 2 | no | — |
| 148 | C2×C7⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 149 | C2×C7⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 150 | C7×C16 | — | 2 | 2 | no | — |
| 151 | C7⋊C16 | — | 2 | 2 | no | — |
| 152 | C2×#135 | C2×D7 | 1 | 1 | yes | characteristic |
| 153 | C2×C4⋊Q8 | — | 14 | 1 | no | — |
| 154 | C4×#41 | — | 14 | 1 | no | — |
| 155 | C2×M32 | — | 7 | 1 | no | — |
| 156 | C2×M32 | C2×D7 | 1 | 1 | yes | characteristic |
| 157 | #500 | — | 7 | 2 | no | — |
| 158 | #500 | — | 7 | 2 | no | — |
| 159 | #500 | — | 14 | 1 | no | — |
| 160 | #500 | — | 14 | 1 | no | — |
| 161 | C4×Q16 | — | 7 | 1 | no | — |
| 162 | C4×Q16 | — | 7 | 1 | no | — |
| 163 | C4×SD16 | — | 14 | 1 | no | — |
| 164 | C4×SD16 | — | 14 | 1 | no | — |
| 165 | C4×D8 | — | 7 | 1 | no | — |
| 166 | C4×D8 | — | 7 | 1 | no | — |
| 167 | #427 | — | 7 | 1 | no | — |
| 168 | C2×#107 | — | 7 | 1 | no | — |
| 169 | C2×#107 | — | 14 | 1 | no | — |
| 170 | C2×#107 | C2×D7 | 1 | 1 | yes | characteristic |
| 171 | #416 | — | 14 | 1 | no | — |
| 172 | C2×C4×C8 | — | 7 | 1 | no | — |
| 173 | #367 | — | 7 | 2 | no | — |
| 174 | #367 | — | 7 | 2 | no | — |
| 175 | #366 | — | 7 | 2 | no | — |
| 176 | #366 | — | 7 | 2 | no | — |
| 177 | C4⋊C16 | — | 7 | 2 | no | — |
| 178 | C4⋊C16 | — | 7 | 2 | no | — |
| 179 | #358 | — | 7 | 2 | no | — |
| 180 | #358 | C2×D7 | 1 | 2 | yes | — |
| 181 | #357 | — | 7 | 2 | no | — |
| 182 | #357 | C2×D7 | 1 | 2 | yes | — |
| 183 | C23×C7 | — | 4 | 1 | no | — |
| 184 | C23×C7 | C2×D8 | 1 | 1 | yes | characteristic |
| 185 | C7×Q8 | — | 2 | 2 | no | — |
| 186 | C7×Q8 | — | 4 | 1 | no | — |
| 187 | C7×D4 | — | 2 | 2 | no | — |
| 188 | C7×D4 | — | 4 | 4 | no | — |
| 189 | C7×D4 | — | 4 | 1 | no | — |
| 190 | C2×C4×C7 | — | 4 | 1 | no | — |
| 191 | C2×C4×C7 | — | 4 | 4 | no | — |
| 192 | C2×C4×C7 | — | 4 | 2 | no | — |
| 193 | C2×C4×C7 | — | 8 | 2 | no | — |
| 194 | C2×C4×C7 | C22⋊Q8 | 1 | 2 | yes | — |
| 195 | C2×C4×C7 | C2×D8 | 1 | 1 | yes | characteristic |
| 196 | C2×C4×C7 | #137 | 1 | 2 | yes | — |
| 197 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 198 | C2×Dic7 | — | 2 | 2 | no | — |
| 199 | C2×Dic7 | — | 2 | 2 | no | — |
| 200 | C2×Dic7 | — | 4 | 1 | no | — |
| 201 | C2×Dic7 | — | 4 | 1 | no | — |
| 202 | C2×Dic7 | — | 4 | 2 | no | — |
| 203 | C2×Dic7 | — | 8 | 2 | no | — |
| 204 | C2×Dic7 | — | 8 | 2 | no | — |
| 205 | C2×Dic7 | — | 8 | 2 | no | — |
| 206 | C2×Dic7 | C2×D8 | 1 | 1 | yes | characteristic |
| 207 | C2×Dic7 | C2×D8 | 1 | 1 | yes | characteristic |
| 208 | C2×Dic7 | C2×D8 | 1 | 1 | yes | characteristic |
| 209 | C2×Dic7 | C2×D8 | 1 | 1 | yes | characteristic |
| 210 | Dic14 | — | 8 | 4 | no | — |
| 211 | Dic14 | — | 8 | 4 | no | — |
| 212 | C7×C8 | C22⋊Q8 | 1 | 2 | yes | — |
| 213 | C7×C8 | C22×Q8 | 1 | 1 | yes | characteristic |
| 214 | C7×C8 | C2×#41 | 1 | 1 | yes | characteristic |
| 215 | C7⋊C8 | — | 2 | 1 | no | — |
| 216 | C7⋊C8 | — | 2 | 1 | no | — |
| 217 | C2×#41 | — | 2 | 1 | no | — |
| 218 | C22×Q8 | — | 28 | 1 | no | — |
| 219 | #135 | — | 2 | 2 | no | — |
| 220 | #135 | Dic14 | 1 | 4 | yes | complemented |
| 221 | C2×Q16 | C22×D7 | 1 | 1 | yes | characteristic |
| 222 | C2×SD16 | — | 2 | 1 | no | — |
| 223 | C2×D8 | C22×D7 | 1 | 1 | yes | characteristic |
| 224 | C22×C8 | — | 7 | 1 | no | — |
| 225 | C22×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 226 | C4⋊Q8 | — | 14 | 2 | no | — |
| 227 | C4⋊Q8 | — | 14 | 2 | no | — |
| 228 | C4⋊Q8 | — | 28 | 1 | no | — |
| 229 | C4⋊Q8 | — | 28 | 1 | no | — |
| 230 | C4×Q8 | — | 14 | 1 | no | — |
| 231 | C4×Q8 | — | 14 | 1 | no | — |
| 232 | C4×D4 | — | 14 | 1 | no | — |
| 233 | C4×D4 | — | 14 | 1 | no | — |
| 234 | C4×D4 | — | 28 | 1 | no | — |
| 235 | C4×D4 | — | 28 | 1 | no | — |
| 236 | #117 | — | 14 | 1 | no | — |
| 237 | #117 | — | 28 | 1 | no | — |
| 238 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 239 | C2×C4⋊C4 | — | 14 | 1 | no | — |
| 240 | C2×C4⋊C4 | — | 28 | 1 | no | — |
| 241 | C2×C42 | — | 7 | 1 | no | — |
| 242 | C2×C42 | — | 28 | 1 | no | — |
| 243 | M32 | — | 2 | 2 | no | — |
| 244 | M32 | — | 14 | 2 | no | — |
| 245 | C2×C16 | — | 7 | 2 | no | — |
| 246 | C2×C16 | C22×D7 | 1 | 2 | yes | — |
| 247 | #107 | — | 2 | 1 | no | — |
| 248 | #107 | — | 7 | 2 | no | — |
| 249 | #107 | — | 7 | 1 | no | — |
| 250 | #107 | — | 7 | 1 | no | — |
| 251 | #107 | — | 14 | 2 | no | — |
| 252 | #107 | — | 14 | 2 | no | — |
| 253 | #107 | — | 14 | 1 | no | — |
| 254 | #107 | C22×D7 | 1 | 2 | yes | — |
| 255 | #106 | — | 14 | 1 | no | — |
| 256 | #103 | — | 14 | 1 | no | — |
| 257 | #103 | — | 14 | 1 | no | — |
| 258 | #102 | — | 14 | 1 | no | — |
| 259 | #102 | — | 14 | 1 | no | — |
| 260 | C4×C8 | — | 7 | 1 | no | — |
| 261 | C4×C8 | — | 7 | 1 | no | — |
| 262 | C4×C8 | — | 7 | 1 | no | — |
| 263 | C4×C8 | — | 7 | 1 | no | — |
| 264 | C22×C7 | — | 2 | 1 | no | — |
| 265 | C22×C7 | — | 2 | 1 | no | — |
| 266 | C22×C7 | — | 4 | 2 | no | — |
| 267 | C22×C7 | — | 8 | 1 | no | — |
| 268 | C22×C7 | — | 8 | 1 | no | — |
| 269 | C22×C7 | #474 | 1 | 2 | yes | — |
| 270 | C22×C7 | C22×D8 | 1 | 1 | yes | characteristic |
| 271 | C4×C7 | — | 4 | 2 | no | — |
| 272 | C4×C7 | — | 8 | 2 | no | — |
| 273 | C4×C7 | #474 | 1 | 2 | yes | — |
| 274 | C4×C7 | C2×C22⋊Q8 | 1 | 1 | yes | characteristic |
| 275 | C4×C7 | C2×#137 | 1 | 1 | yes | characteristic |
| 276 | Dic7 | — | 2 | 1 | no | — |
| 277 | Dic7 | — | 2 | 1 | no | — |
| 278 | Dic7 | — | 8 | 2 | no | — |
| 279 | Dic7 | — | 8 | 1 | no | — |
| 280 | Dic7 | — | 8 | 1 | no | — |
| 281 | Dic7 | #509 | 1 | 2 | yes | — |
| 282 | Dic7 | #510 | 1 | 2 | yes | — |
| 283 | #41 | — | 2 | 4 | no | — |
| 284 | #41 | — | 4 | 2 | no | — |
| 285 | C2×Q8 | — | 2 | 1 | no | — |
| 286 | C2×Q8 | — | 28 | 2 | no | — |
| 287 | C2×Q8 | — | 28 | 2 | no | — |
| 288 | C2×Q8 | — | 56 | 4 | no | — |
| 289 | C2×D4 | — | 2 | 1 | no | — |
| 290 | C2×D4 | — | 4 | 1 | no | — |
| 291 | C22×C4 | — | 4 | 1 | no | — |
| 292 | C22×C4 | — | 4 | 1 | no | — |
| 293 | C22×C4 | — | 7 | 1 | no | — |
| 294 | C22×C4 | — | 7 | 1 | no | — |
| 295 | C22×C4 | — | 28 | 1 | no | — |
| 296 | C22×C4 | — | 28 | 1 | no | — |
| 297 | C22×C4 | — | 28 | 1 | no | — |
| 298 | C22×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 299 | Q16 | — | 2 | 1 | no | — |
| 300 | Q16 | C2×Dic14 | 1 | 2 | yes | complemented |
| 301 | SD16 | — | 2 | 4 | no | — |
| 302 | D8 | — | 2 | 1 | no | — |
| 303 | D8 | C2×Dic14 | 1 | 2 | yes | complemented |
| 304 | C2×C8 | — | 7 | 1 | no | — |
| 305 | C2×C8 | — | 7 | 1 | no | — |
| 306 | C2×C8 | — | 14 | 2 | no | — |
| 307 | C2×C8 | C2×Dic14 | 1 | 2 | yes | — |
| 308 | C2×C8 | D4×D7 | 1 | 1 | yes | characteristic |
| 309 | C2×C8 | #1159 | 1 | 2 | yes | — |
| 310 | C2×C8 | C23×D7 | 1 | 1 | yes | characteristic |
| 311 | C4⋊C4 | — | 2 | 2 | no | — |
| 312 | C4⋊C4 | — | 4 | 1 | no | — |
| 313 | C4⋊C4 | — | 14 | 1 | no | — |
| 314 | C4⋊C4 | — | 14 | 1 | no | — |
| 315 | C4⋊C4 | — | 14 | 2 | no | — |
| 316 | C4⋊C4 | — | 28 | 2 | no | — |
| 317 | C4⋊C4 | — | 28 | 2 | no | — |
| 318 | C4⋊C4 | — | 28 | 1 | no | — |
| 319 | C4⋊C4 | — | 28 | 1 | no | — |
| 320 | C4⋊C4 | — | 28 | 1 | no | — |
| 321 | C22⋊C4 | — | 28 | 1 | no | — |
| 322 | C22⋊C4 | — | 28 | 1 | no | — |
| 323 | C22⋊C4 | — | 28 | 1 | no | — |
| 324 | C42 | — | 7 | 1 | no | — |
| 325 | C42 | — | 7 | 1 | no | — |
| 326 | C42 | — | 7 | 1 | no | — |
| 327 | C42 | — | 7 | 1 | no | — |
| 328 | C42 | — | 28 | 1 | no | — |
| 329 | C42 | — | 28 | 1 | no | — |
| 330 | C42 | — | 28 | 1 | no | — |
| 331 | C16 | — | 2 | 2 | no | — |
| 332 | C16 | — | 14 | 2 | no | — |
| 333 | C2×C7 | — | 2 | 2 | no | — |
| 334 | C2×C7 | — | 8 | 2 | no | — |
| 335 | C2×C7 | C2×#474 | 1 | 1 | yes | characteristic |
| 336 | C2×C7 | C2×#509 | 1 | 1 | yes | characteristic |
| 337 | C2×C7 | C2×#510 | 1 | 1 | yes | characteristic |
| 338 | C23 | — | 4 | 1 | no | — |
| 339 | C23 | D7×D8 | 1 | 1 | yes | characteristic |
| 340 | Q8 | — | 2 | 2 | no | — |
| 341 | Q8 | — | 4 | 1 | no | — |
| 342 | Q8 | — | 56 | 4 | no | — |
| 343 | Q8 | — | 56 | 4 | no | — |
| 344 | D4 | — | 2 | 2 | no | — |
| 345 | D4 | — | 4 | 4 | no | — |
| 346 | D4 | — | 4 | 1 | no | — |
| 347 | C2×C4 | — | 4 | 1 | no | — |
| 348 | C2×C4 | — | 4 | 4 | no | — |
| 349 | C2×C4 | — | 4 | 2 | no | — |
| 350 | C2×C4 | — | 7 | 1 | no | — |
| 351 | C2×C4 | — | 7 | 1 | no | — |
| 352 | C2×C4 | — | 7 | 1 | no | — |
| 353 | C2×C4 | — | 7 | 1 | no | — |
| 354 | C2×C4 | — | 8 | 2 | no | — |
| 355 | C2×C4 | — | 14 | 2 | no | — |
| 356 | C2×C4 | — | 14 | 2 | no | — |
| 357 | C2×C4 | — | 28 | 1 | no | — |
| 358 | C2×C4 | — | 28 | 1 | no | — |
| 359 | C2×C4 | — | 28 | 2 | no | — |
| 360 | C2×C4 | — | 56 | 2 | no | — |
| 361 | C2×C4 | — | 56 | 2 | no | — |
| 362 | C2×C4 | — | 56 | 2 | no | — |
| 363 | C2×C4 | #6441 | 1 | 2 | yes | — |
| 364 | C2×C4 | D7×D8 | 1 | 1 | yes | characteristic |
| 365 | C2×C4 | #6478 | 1 | 2 | yes | — |
| 366 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 367 | C8 | — | 14 | 1 | no | — |
| 368 | C8 | — | 14 | 1 | no | — |
| 369 | C8 | #6441 | 1 | 2 | yes | — |
| 370 | C8 | C22×Dic14 | 1 | 1 | yes | characteristic |
| 371 | C8 | C2×#1159 | 1 | 1 | yes | characteristic |
| 372 | C7 | #33629 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 373 | C22 | — | 2 | 1 | no | — |
| 374 | C22 | — | 2 | 1 | no | — |
| 375 | C22 | — | 4 | 2 | no | — |
| 376 | C22 | — | 8 | 1 | no | — |
| 377 | C22 | — | 8 | 1 | no | — |
| 378 | C22 | #89531 | 1 | 2 | yes | — |
| 379 | C22 | C2×D7×D8 | 1 | 1 | yes | characteristic |
| 380 | C4 | — | 4 | 2 | no | — |
| 381 | C4 | — | 7 | 2 | no | — |
| 382 | C4 | — | 7 | 2 | no | — |
| 383 | C4 | — | 8 | 2 | no | — |
| 384 | C4 | — | 14 | 1 | no | — |
| 385 | C4 | — | 14 | 1 | no | — |
| 386 | C4 | — | 56 | 2 | no | — |
| 387 | C4 | — | 56 | 1 | no | — |
| 388 | C4 | — | 56 | 1 | no | — |
| 389 | C4 | #89531 | 1 | 2 | yes | — |
| 390 | C4 | C2×#6441 | 1 | 1 | yes | characteristic |
| 391 | C4 | C2×#6478 | 1 | 1 | yes | characteristic |
| 392 | C2 | — | 2 | 2 | no | — |
| 393 | C2 | — | 8 | 2 | no | — |
| 394 | C2 | C2×#89531 | 1 | 1 | yes | characteristic |
| 395 | C2 | D7×#509 | 1 | 1 | yes | characteristic |
| 396 | C2 | D7×#510 | 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