← #27402983
Subgroups — #27402983
Order 13568.
658 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 | M16×Dic106 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #20283666 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C2×#16810747 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #20275491 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #20275489 | C2 | 1 | 2 | yes | maximal |
| 6 | #20275487 | C2 | 1 | 2 | yes | maximal |
| 7 | #20274886 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #20274885 | C2 | 1 | 2 | yes | maximal |
| 9 | C4×#13133152 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #20274616 | C2 | 1 | 2 | yes | maximal |
| 11 | C53×#1950 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | C2×C4×Dic106 | C22 | 1 | 1 | yes | characteristic |
| 13 | #16810753 | — | 2 | 1 | no | — |
| 14 | #16810752 | — | 2 | 2 | no | — |
| 15 | #16810751 | — | 2 | 2 | no | — |
| 16 | #16810750 | — | 2 | 1 | no | — |
| 17 | C8×Dic106 | — | 2 | 1 | no | — |
| 18 | #16810747 | — | 2 | 1 | no | — |
| 19 | #16810747 | C4 | 1 | 4 | yes | — |
| 20 | #16810747 | C4 | 1 | 2 | yes | — |
| 21 | #16810747 | C4 | 1 | 2 | yes | — |
| 22 | C2×#13133153 | C22 | 1 | 2 | yes | — |
| 23 | C2×#13133152 | C22 | 1 | 2 | yes | — |
| 24 | C2×#13133152 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×#13133152 | C22 | 1 | 2 | yes | — |
| 26 | C2×#13133152 | C22 | 1 | 1 | yes | characteristic |
| 27 | #16810647 | C22 | 1 | 1 | yes | characteristic |
| 28 | #16810646 | C22 | 1 | 2 | yes | — |
| 29 | #16810646 | C22 | 1 | 2 | yes | — |
| 30 | C2×#13133146 | C22 | 1 | 2 | yes | — |
| 31 | C4×#11719917 | C22 | 1 | 1 | yes | characteristic |
| 32 | M16×Dic53 | C22 | 1 | 2 | yes | — |
| 33 | M16×Dic53 | C22 | 1 | 2 | yes | — |
| 34 | C2×C4×#88322 | C22 | 1 | 1 | yes | characteristic |
| 35 | C2×C8×Dic53 | C22 | 1 | 2 | yes | — |
| 36 | #16810388 | C22 | 1 | 2 | yes | — |
| 37 | #16810387 | C22 | 1 | 1 | yes | characteristic |
| 38 | #16810387 | C22 | 1 | 1 | yes | characteristic |
| 39 | C2×#108×C53 | C22 | 1 | 2 | yes | — |
| 40 | C53×#423 | C22 | 1 | 1 | yes | characteristic |
| 41 | C2×C4⋊C8×C53 | C22 | 1 | 1 | yes | characteristic |
| 42 | C4×M16×C53 | C22 | 1 | 1 | yes | characteristic |
| 43 | C53×#341 | C22 | 1 | 2 | yes | — |
| 44 | C22×Dic106 | Q8 | 1 | 1 | yes | characteristic |
| 45 | C2×#11719917 | C23 | 1 | 2 | yes | — |
| 46 | C2×#11719917 | C23 | 1 | 1 | yes | characteristic |
| 47 | C2×#11719917 | C23 | 1 | 1 | yes | characteristic |
| 48 | C22×#88322 | C23 | 1 | 1 | yes | characteristic |
| 49 | C22×#88322 | C23 | 1 | 1 | yes | characteristic |
| 50 | C4×Dic106 | C2×C4 | 1 | 1 | yes | characteristic |
| 51 | C4×Dic106 | C2×C4 | 1 | 2 | yes | — |
| 52 | C4×Dic106 | C2×C4 | 1 | 1 | yes | characteristic |
| 53 | C4×Dic106 | D4 | 1 | 2 | yes | — |
| 54 | C4×Dic106 | D4 | 1 | 1 | yes | characteristic |
| 55 | C4×Dic106 | D4 | 1 | 1 | yes | characteristic |
| 56 | C2×C4⋊Dic53 | Q8 | 1 | 1 | yes | characteristic |
| 57 | C2×#11719919 | Q8 | 1 | 2 | yes | — |
| 58 | C2×C4×Dic53 | C23 | 1 | 2 | yes | — |
| 59 | #13133153 | — | 4 | 2 | no | — |
| 60 | #13133152 | — | 2 | 4 | no | — |
| 61 | #13133152 | — | 2 | 2 | no | — |
| 62 | #13133152 | — | 4 | 2 | no | — |
| 63 | #13133152 | Q8 | 1 | 4 | yes | complemented |
| 64 | C4⋊#88322 | — | 2 | 1 | no | — |
| 65 | C4⋊#88322 | — | 2 | 1 | no | — |
| 66 | #13133146 | — | 2 | 2 | no | — |
| 67 | #13133146 | — | 2 | 2 | no | — |
| 68 | #13133146 | — | 2 | 2 | no | — |
| 69 | #13133146 | — | 2 | 2 | no | — |
| 70 | #13133146 | C2×C4 | 1 | 4 | yes | — |
| 71 | #13133146 | C2×C4 | 1 | 4 | yes | — |
| 72 | #13133128 | — | 2 | 1 | no | — |
| 73 | #13133127 | — | 2 | 2 | no | — |
| 74 | #13133127 | — | 2 | 2 | no | — |
| 75 | C4×#88322 | — | 2 | 1 | no | — |
| 76 | C4×#88322 | C2×C4 | 1 | 2 | yes | — |
| 77 | C4×#88322 | C2×C4 | 1 | 2 | yes | — |
| 78 | C8×Dic53 | — | 2 | 2 | no | — |
| 79 | C8×Dic53 | — | 2 | 2 | no | — |
| 80 | C8×Dic53 | C2×C4 | 1 | 4 | yes | — |
| 81 | C8×Dic53 | C2×C4 | 1 | 4 | yes | — |
| 82 | C2×M16×C53 | C23 | 1 | 2 | yes | — |
| 83 | C2×M16×C53 | C23 | 1 | 1 | yes | characteristic |
| 84 | C2×M16×C53 | C23 | 1 | 1 | yes | characteristic |
| 85 | C22×C8×C53 | C23 | 1 | 2 | yes | — |
| 86 | C2×C42×C53 | C23 | 1 | 1 | yes | characteristic |
| 87 | #108×C53 | — | 4 | 2 | no | — |
| 88 | C4⋊C8×C53 | — | 2 | 1 | no | — |
| 89 | C4⋊C8×C53 | — | 2 | 1 | no | — |
| 90 | C4⋊C8×C53 | C2×C4 | 1 | 2 | yes | — |
| 91 | C4⋊C8×C53 | C2×C4 | 1 | 2 | yes | — |
| 92 | #97×C53 | — | 2 | 1 | no | — |
| 93 | C4×C8×C53 | — | 2 | 1 | no | — |
| 94 | C22×C4×C53 | C2×Q8 | 1 | 1 | yes | characteristic |
| 95 | C22×C4×C53 | C2×Q8 | 1 | 1 | yes | characteristic |
| 96 | C22×C4×C53 | C24 | 1 | 1 | yes | characteristic |
| 97 | C22×Dic53 | C2×Q8 | 1 | 2 | yes | — |
| 98 | C22×Dic53 | C2×Q8 | 1 | 2 | yes | — |
| 99 | C2×Dic106 | — | 2 | 4 | no | — |
| 100 | C2×Dic106 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 101 | C2×Dic106 | C4⋊C4 | 1 | 2 | yes | — |
| 102 | C2×Dic106 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 103 | M16×C53 | — | 2 | 1 | no | — |
| 104 | M16×C53 | — | 2 | 2 | no | — |
| 105 | M16×C53 | — | 2 | 1 | no | — |
| 106 | M16×C53 | — | 2 | 1 | no | — |
| 107 | M16×C53 | — | 2 | 2 | no | — |
| 108 | M16×C53 | C2×Q8 | 1 | 2 | yes | — |
| 109 | C2×C8×C53 | — | 2 | 1 | no | — |
| 110 | C2×C8×C53 | — | 2 | 2 | no | — |
| 111 | C2×C8×C53 | — | 2 | 2 | no | — |
| 112 | C2×C8×C53 | — | 2 | 1 | no | — |
| 113 | C2×C8×C53 | — | 2 | 2 | no | — |
| 114 | C2×C8×C53 | C22×C4 | 1 | 4 | yes | — |
| 115 | C42×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 116 | C42×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 117 | C42×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 118 | C42×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 119 | C4⋊Dic53 | C4⋊C4 | 1 | 2 | yes | — |
| 120 | C4⋊Dic53 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 121 | C4⋊Dic53 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 122 | #11719919 | C4⋊C4 | 1 | 2 | yes | — |
| 123 | #11719919 | C4⋊C4 | 1 | 2 | yes | — |
| 124 | #11719919 | C4⋊C4 | 1 | 2 | yes | — |
| 125 | #11719919 | C4⋊C4 | 1 | 2 | yes | — |
| 126 | C4×Dic53 | C22×C4 | 1 | 2 | yes | — |
| 127 | C4×Dic53 | C22×C4 | 1 | 2 | yes | — |
| 128 | C4×Dic53 | C2×D4 | 1 | 2 | yes | — |
| 129 | C4×Dic53 | C2×D4 | 1 | 2 | yes | — |
| 130 | #11719917 | — | 2 | 1 | no | — |
| 131 | #11719917 | — | 2 | 2 | no | — |
| 132 | #11719917 | — | 2 | 1 | no | — |
| 133 | #11719917 | — | 2 | 2 | no | — |
| 134 | #11719917 | — | 2 | 1 | no | — |
| 135 | #11719917 | C2×Q8 | 1 | 2 | yes | — |
| 136 | C2×#88322 | — | 2 | 1 | no | — |
| 137 | C2×#88322 | — | 2 | 1 | no | — |
| 138 | C2×#88322 | — | 2 | 1 | no | — |
| 139 | C2×#88322 | — | 2 | 2 | no | — |
| 140 | C2×#88322 | — | 2 | 1 | no | — |
| 141 | C2×#88322 | C22×C4 | 1 | 2 | yes | — |
| 142 | C2×#88322 | C22×C4 | 1 | 2 | yes | — |
| 143 | C2×#88322 | C2×Q8 | 1 | 2 | yes | — |
| 144 | C2×#88322 | #41 | 1 | 2 | yes | — |
| 145 | C23×C53 | C22×Q8 | 1 | 1 | yes | characteristic |
| 146 | C2×C4×C53 | — | 2 | 2 | no | — |
| 147 | C2×C4×C53 | — | 4 | 1 | no | — |
| 148 | C2×C4×C53 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 149 | C2×C4×C53 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 150 | C2×C4×C53 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 151 | C2×C4×C53 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 152 | C2×C4×C53 | C23×C4 | 1 | 1 | yes | characteristic |
| 153 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 154 | C2×C4×C53 | C22×Q8 | 1 | 1 | yes | characteristic |
| 155 | C2×C4×C53 | C2×#41 | 1 | 1 | yes | characteristic |
| 156 | C2×C4×C53 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 157 | C2×C4×C53 | 2−1+4 | 1 | 1 | yes | characteristic |
| 158 | C2×Dic53 | — | 2 | 4 | no | — |
| 159 | C2×Dic53 | — | 4 | 2 | no | — |
| 160 | C2×Dic53 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 161 | C2×Dic53 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 162 | C2×Dic53 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 163 | C2×Dic53 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 164 | Dic106 | — | 2 | 2 | no | — |
| 165 | Dic106 | — | 2 | 4 | no | — |
| 166 | Dic106 | #108 | 1 | 4 | yes | complemented |
| 167 | C8×C53 | — | 2 | 4 | no | — |
| 168 | C8×C53 | — | 2 | 2 | no | — |
| 169 | C8×C53 | — | 4 | 1 | no | — |
| 170 | C8×C53 | — | 4 | 2 | no | — |
| 171 | #88322 | — | 2 | 2 | no | — |
| 172 | #88322 | — | 2 | 2 | no | — |
| 173 | #88322 | — | 4 | 2 | no | — |
| 174 | #88322 | — | 4 | 1 | no | — |
| 175 | #88322 | C4×Q8 | 1 | 4 | yes | — |
| 176 | Q8×#108 | — | 53 | 1 | no | maximal, Sylow |
| 177 | C22×C53 | — | 2 | 1 | no | — |
| 178 | C22×C53 | — | 2 | 1 | no | — |
| 179 | C22×C53 | C22×C4⋊C4 | 1 | 1 | yes | characteristic |
| 180 | C22×C53 | #557 | 1 | 1 | yes | characteristic |
| 181 | C22×C53 | Q82 | 1 | 1 | yes | characteristic |
| 182 | C4×C53 | — | 2 | 1 | no | — |
| 183 | C4×C53 | — | 2 | 1 | no | — |
| 184 | C4×C53 | — | 2 | 1 | no | — |
| 185 | C4×C53 | C2×#108 | 1 | 2 | yes | — |
| 186 | C4×C53 | C2×C4×Q8 | 1 | 1 | yes | characteristic |
| 187 | C4×C53 | #520 | 1 | 1 | yes | characteristic |
| 188 | C4×C53 | D4×Q8 | 1 | 1 | yes | characteristic |
| 189 | C4×C53 | #550 | 1 | 1 | yes | characteristic |
| 190 | Dic53 | — | 2 | 2 | no | — |
| 191 | Dic53 | — | 2 | 2 | no | — |
| 192 | Dic53 | — | 2 | 2 | no | — |
| 193 | Dic53 | C2×#108 | 1 | 4 | yes | — |
| 194 | Q8×M16 | — | 53 | 1 | no | — |
| 195 | Q8×M16 | — | 53 | 1 | no | — |
| 196 | C2×C8×Q8 | — | 53 | 1 | no | — |
| 197 | #1950 | — | 53 | 2 | no | — |
| 198 | #1950 | — | 53 | 1 | no | — |
| 199 | #1950 | — | 53 | 2 | no | — |
| 200 | #1950 | D53 | 1 | 1 | yes | characteristic |
| 201 | #1848 | — | 53 | 2 | no | — |
| 202 | #1848 | — | 53 | 1 | no | — |
| 203 | C4×#108 | — | 53 | 1 | no | — |
| 204 | C4×#108 | — | 53 | 2 | no | — |
| 205 | C2×C53 | — | 2 | 1 | no | — |
| 206 | C2×C53 | — | 2 | 1 | no | — |
| 207 | C2×C53 | Q8×C4⋊C4 | 1 | 1 | yes | characteristic |
| 208 | C2×C53 | C22×#108 | 1 | 1 | yes | characteristic |
| 209 | C2×C53 | #2916 | 1 | 1 | yes | characteristic |
| 210 | C2×C4×Q8 | — | 53 | 1 | no | — |
| 211 | #446 | — | 106 | 1 | no | — |
| 212 | #446 | — | 106 | 2 | no | — |
| 213 | #446 | — | 106 | 2 | no | — |
| 214 | #446 | — | 106 | 1 | no | — |
| 215 | C8×Q8 | — | 53 | 2 | no | — |
| 216 | C8×Q8 | — | 53 | 4 | no | — |
| 217 | C8×Q8 | — | 53 | 2 | no | — |
| 218 | C8×Q8 | — | 106 | 1 | no | — |
| 219 | C8×Q8 | — | 106 | 1 | no | — |
| 220 | C2×#108 | — | 53 | 1 | no | — |
| 221 | C2×#108 | — | 53 | 1 | no | — |
| 222 | C2×#108 | — | 53 | 2 | no | — |
| 223 | C2×#108 | — | 53 | 2 | no | — |
| 224 | C2×#108 | — | 53 | 2 | no | — |
| 225 | C2×#108 | C2×D53 | 1 | 2 | yes | — |
| 226 | #423 | — | 53 | 2 | no | — |
| 227 | #423 | — | 53 | 2 | no | — |
| 228 | #423 | — | 53 | 1 | no | — |
| 229 | #423 | C2×D53 | 1 | 1 | yes | characteristic |
| 230 | C2×C4⋊C8 | — | 53 | 2 | no | — |
| 231 | C2×C4⋊C8 | C2×D53 | 1 | 1 | yes | characteristic |
| 232 | C4×M16 | — | 53 | 2 | no | — |
| 233 | C4×M16 | — | 53 | 2 | no | — |
| 234 | C4×M16 | — | 53 | 1 | no | — |
| 235 | C4×M16 | C2×D53 | 1 | 1 | yes | characteristic |
| 236 | C2×C4×C8 | — | 53 | 2 | no | — |
| 237 | C2×C4×C8 | — | 53 | 1 | no | — |
| 238 | #341 | — | 53 | 1 | no | — |
| 239 | #341 | — | 53 | 1 | no | — |
| 240 | #341 | — | 53 | 2 | no | — |
| 241 | #341 | C2×D53 | 1 | 2 | yes | — |
| 242 | C53 | Q8×#108 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 243 | C22×Q8 | — | 53 | 1 | no | — |
| 244 | C2×M16 | — | 53 | 1 | no | — |
| 245 | C2×M16 | — | 53 | 1 | no | — |
| 246 | C2×M16 | — | 53 | 2 | no | — |
| 247 | C2×M16 | C22×D53 | 1 | 1 | yes | characteristic |
| 248 | C2×M16 | C22×D53 | 1 | 2 | yes | — |
| 249 | C2×M16 | C22×D53 | 1 | 1 | yes | characteristic |
| 250 | C22×C8 | — | 53 | 1 | no | — |
| 251 | C22×C8 | — | 53 | 1 | no | — |
| 252 | C22×C8 | C22×D53 | 1 | 2 | yes | — |
| 253 | C4×Q8 | — | 53 | 1 | no | — |
| 254 | C4×Q8 | — | 53 | 2 | no | — |
| 255 | C4×Q8 | — | 53 | 1 | no | — |
| 256 | C4×Q8 | — | 53 | 1 | no | — |
| 257 | C4×Q8 | — | 53 | 2 | no | — |
| 258 | C4×Q8 | — | 53 | 1 | no | — |
| 259 | C2×C4⋊C4 | — | 53 | 2 | no | — |
| 260 | C2×C4⋊C4 | — | 53 | 1 | no | — |
| 261 | C2×C42 | — | 53 | 2 | no | — |
| 262 | C2×C42 | C22×D53 | 1 | 1 | yes | characteristic |
| 263 | #108 | — | 4 | 2 | no | — |
| 264 | #108 | — | 53 | 4 | no | — |
| 265 | #108 | — | 106 | 2 | no | — |
| 266 | #108 | — | 106 | 4 | no | — |
| 267 | #108 | — | 212 | 2 | no | — |
| 268 | #108 | — | 212 | 2 | no | — |
| 269 | C4⋊C8 | — | 2 | 1 | no | — |
| 270 | C4⋊C8 | — | 2 | 1 | no | — |
| 271 | C4⋊C8 | — | 53 | 4 | no | — |
| 272 | C4⋊C8 | — | 53 | 4 | no | — |
| 273 | C4⋊C8 | — | 106 | 2 | no | — |
| 274 | C4⋊C8 | — | 106 | 2 | no | — |
| 275 | C4⋊C8 | — | 106 | 2 | no | — |
| 276 | C4⋊C8 | — | 106 | 2 | no | — |
| 277 | C4⋊C8 | — | 106 | 1 | no | — |
| 278 | C4⋊C8 | — | 106 | 1 | no | — |
| 279 | C4⋊C8 | C4×D53 | 1 | 2 | yes | — |
| 280 | C4⋊C8 | C4×D53 | 1 | 2 | yes | — |
| 281 | #97 | — | 2 | 1 | no | — |
| 282 | #97 | — | 106 | 2 | no | — |
| 283 | #97 | — | 106 | 2 | no | — |
| 284 | #97 | — | 106 | 1 | no | — |
| 285 | C4×C8 | — | 2 | 1 | no | — |
| 286 | C4×C8 | — | 53 | 4 | no | — |
| 287 | C4×C8 | — | 53 | 4 | no | — |
| 288 | C4×C8 | — | 53 | 2 | no | — |
| 289 | C4×C8 | — | 53 | 2 | no | — |
| 290 | C4×C8 | — | 106 | 2 | no | — |
| 291 | C4×C8 | — | 106 | 2 | no | — |
| 292 | C4×C8 | — | 106 | 1 | no | — |
| 293 | C2×Q8 | — | 53 | 1 | no | — |
| 294 | C2×Q8 | — | 53 | 2 | no | — |
| 295 | C2×Q8 | — | 53 | 1 | no | — |
| 296 | C2×Q8 | — | 106 | 4 | no | — |
| 297 | C22×C4 | — | 53 | 2 | no | — |
| 298 | C22×C4 | — | 53 | 2 | no | — |
| 299 | C22×C4 | Q8×D53 | 1 | 1 | yes | characteristic |
| 300 | C22×C4 | Q8×D53 | 1 | 1 | yes | characteristic |
| 301 | C22×C4 | C23×D53 | 1 | 1 | yes | characteristic |
| 302 | M16 | — | 2 | 1 | no | — |
| 303 | M16 | — | 2 | 1 | no | — |
| 304 | M16 | — | 2 | 2 | no | — |
| 305 | M16 | — | 2 | 1 | no | — |
| 306 | M16 | — | 2 | 2 | no | — |
| 307 | M16 | — | 53 | 2 | no | — |
| 308 | M16 | — | 106 | 1 | no | — |
| 309 | M16 | — | 106 | 1 | no | — |
| 310 | M16 | — | 106 | 2 | no | — |
| 311 | M16 | — | 106 | 1 | no | — |
| 312 | M16 | — | 106 | 2 | no | — |
| 313 | M16 | Q8×D53 | 1 | 2 | yes | — |
| 314 | C2×C8 | — | 2 | 1 | no | — |
| 315 | C2×C8 | — | 2 | 2 | no | — |
| 316 | C2×C8 | — | 2 | 2 | no | — |
| 317 | C2×C8 | — | 2 | 1 | no | — |
| 318 | C2×C8 | — | 2 | 2 | no | — |
| 319 | C2×C8 | — | 53 | 2 | no | — |
| 320 | C2×C8 | — | 53 | 2 | no | — |
| 321 | C2×C8 | — | 53 | 2 | no | — |
| 322 | C2×C8 | — | 53 | 2 | no | — |
| 323 | C2×C8 | — | 106 | 1 | no | — |
| 324 | C2×C8 | — | 106 | 1 | no | — |
| 325 | C2×C8 | — | 106 | 1 | no | — |
| 326 | C2×C8 | — | 106 | 2 | no | — |
| 327 | C2×C8 | — | 106 | 1 | no | — |
| 328 | C2×C8 | C2×C4×D53 | 1 | 4 | yes | — |
| 329 | C4⋊C4 | — | 53 | 2 | no | — |
| 330 | C4⋊C4 | — | 53 | 2 | no | — |
| 331 | C4⋊C4 | — | 53 | 2 | no | — |
| 332 | C4⋊C4 | — | 53 | 2 | no | — |
| 333 | C4⋊C4 | — | 53 | 2 | no | — |
| 334 | C4⋊C4 | — | 53 | 1 | no | — |
| 335 | C4⋊C4 | — | 53 | 1 | no | — |
| 336 | C42 | — | 53 | 2 | no | — |
| 337 | C42 | — | 53 | 2 | no | — |
| 338 | C42 | — | 53 | 2 | no | — |
| 339 | C42 | — | 53 | 2 | no | — |
| 340 | C42 | C2×C4×D53 | 1 | 1 | yes | characteristic |
| 341 | C42 | C2×C4×D53 | 1 | 1 | yes | characteristic |
| 342 | C42 | D4×D53 | 1 | 1 | yes | characteristic |
| 343 | C42 | D4×D53 | 1 | 1 | yes | characteristic |
| 344 | C23 | C2×Q8×D53 | 1 | 1 | yes | characteristic |
| 345 | Q8 | — | 53 | 4 | no | — |
| 346 | Q8 | — | 106 | 4 | no | — |
| 347 | Q8 | — | 106 | 2 | no | — |
| 348 | C2×C4 | — | 2 | 2 | no | — |
| 349 | C2×C4 | — | 4 | 1 | no | — |
| 350 | C2×C4 | — | 53 | 2 | no | — |
| 351 | C2×C4 | — | 53 | 2 | no | — |
| 352 | C2×C4 | — | 53 | 2 | no | — |
| 353 | C2×C4 | — | 53 | 2 | no | — |
| 354 | C2×C4 | — | 106 | 4 | no | — |
| 355 | C2×C4 | — | 212 | 2 | no | — |
| 356 | C2×C4 | C4⋊C4×D53 | 1 | 1 | yes | characteristic |
| 357 | C2×C4 | C4⋊C4×D53 | 1 | 1 | yes | characteristic |
| 358 | C2×C4 | C4⋊C4×D53 | 1 | 1 | yes | characteristic |
| 359 | C2×C4 | C4⋊C4×D53 | 1 | 1 | yes | characteristic |
| 360 | C2×C4 | C22×C4×D53 | 1 | 1 | yes | characteristic |
| 361 | C2×C4 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 362 | C2×C4 | C2×Q8×D53 | 1 | 1 | yes | characteristic |
| 363 | C2×C4 | #41×D53 | 1 | 1 | yes | characteristic |
| 364 | C2×C4 | #13133262 | 1 | 1 | yes | characteristic |
| 365 | C2×C4 | #13133264 | 1 | 1 | yes | characteristic |
| 366 | C8 | — | 2 | 2 | no | — |
| 367 | C8 | — | 2 | 4 | no | — |
| 368 | C8 | — | 4 | 1 | no | — |
| 369 | C8 | — | 4 | 2 | no | — |
| 370 | C8 | — | 53 | 4 | no | — |
| 371 | C8 | — | 106 | 2 | no | — |
| 372 | C8 | — | 106 | 2 | no | — |
| 373 | C8 | — | 212 | 2 | no | — |
| 374 | C8 | — | 212 | 1 | no | — |
| 375 | C22 | — | 2 | 1 | no | — |
| 376 | C22 | — | 2 | 1 | no | — |
| 377 | C22 | C2×C4⋊C4×D53 | 1 | 1 | yes | characteristic |
| 378 | C22 | #16811350 | 1 | 1 | yes | characteristic |
| 379 | C22 | #16811353 | 1 | 1 | yes | characteristic |
| 380 | C4 | — | 2 | 1 | no | — |
| 381 | C4 | — | 2 | 1 | no | — |
| 382 | C4 | — | 2 | 1 | no | — |
| 383 | C4 | — | 53 | 4 | no | — |
| 384 | C4 | — | 106 | 2 | no | — |
| 385 | C4 | — | 106 | 2 | no | — |
| 386 | C4 | — | 106 | 2 | no | — |
| 387 | C4 | #108×D53 | 1 | 2 | yes | — |
| 388 | C4 | C4×Q8×D53 | 1 | 1 | yes | characteristic |
| 389 | C4 | #16811102 | 1 | 1 | yes | characteristic |
| 390 | C4 | #16811286 | 1 | 1 | yes | characteristic |
| 391 | C4 | #16811291 | 1 | 1 | yes | characteristic |
| 392 | C2 | — | 2 | 1 | no | — |
| 393 | C2 | — | 2 | 1 | no | — |
| 394 | C2 | #20277629 | 1 | 1 | yes | characteristic |
| 395 | C2 | C2×#108×D53 | 1 | 1 | yes | characteristic |
| 396 | C2 | #20283325 | 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