← M16×#6107 #15834377
Subgroups — M16×#6107 #15834377
Order 3328.
638 conjugacy classes of subgroups.
The subgroup lattice has 488 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | M16×Dic26 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×C4×#6107 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #13113731 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #13113686 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #13113684 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | C8×#6107 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #13113594 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #13113265 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #13113264 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | M16×#1055 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | Q8×C13×M16 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | C2×C4×Q8×C13 | C22 | 1 | 1 | yes | characteristic |
| 13 | C22×#6107 | C4 | 1 | 1 | yes | characteristic |
| 14 | C2×C4×Dic26 | C22 | 1 | 1 | yes | characteristic |
| 15 | C13×#446 | — | 2 | 2 | no | — |
| 16 | C13×#446 | C22 | 1 | 2 | yes | — |
| 17 | C8×Q8×C13 | C22 | 1 | 2 | yes | — |
| 18 | C13×#423 | — | 2 | 1 | no | — |
| 19 | C13×#423 | C22 | 1 | 1 | yes | characteristic |
| 20 | C4×C13×M16 | — | 2 | 1 | no | — |
| 21 | C4×C13×M16 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#88075 | C4 | 1 | 1 | yes | characteristic |
| 23 | #11718779 | — | 2 | 1 | no | — |
| 24 | M16×Dic13 | — | 2 | 1 | no | — |
| 25 | C4×#6107 | C4 | 1 | 1 | yes | characteristic |
| 26 | C4×#6107 | C4 | 1 | 1 | yes | characteristic |
| 27 | C4×#6107 | C4 | 1 | 1 | yes | characteristic |
| 28 | C4×#6107 | C4 | 1 | 1 | yes | characteristic |
| 29 | C4×#6107 | C22 | 1 | 1 | yes | characteristic |
| 30 | C4×#6107 | C22 | 1 | 1 | yes | characteristic |
| 31 | C4×#6107 | C22 | 1 | 1 | yes | characteristic |
| 32 | C4×#6107 | C22 | 1 | 1 | yes | characteristic |
| 33 | C2×#88050 | C4 | 1 | 1 | yes | characteristic |
| 34 | C2×#88047 | C4 | 1 | 1 | yes | characteristic |
| 35 | #11718586 | C22 | 1 | 1 | yes | characteristic |
| 36 | #11718585 | C22 | 1 | 1 | yes | characteristic |
| 37 | C2×C4×#1055 | C22 | 1 | 1 | yes | characteristic |
| 38 | #11718362 | — | 2 | 2 | no | — |
| 39 | #11718340 | C22 | 1 | 2 | yes | — |
| 40 | C8×Dic26 | C22 | 1 | 2 | yes | — |
| 41 | Q8⋊#1055 | C22 | 1 | 2 | yes | — |
| 42 | Q8⋊#1055 | C22 | 1 | 2 | yes | — |
| 43 | #11718076 | C22 | 1 | 2 | yes | — |
| 44 | #11718076 | C22 | 1 | 2 | yes | — |
| 45 | #11718071 | C22 | 1 | 2 | yes | — |
| 46 | #11718071 | C22 | 1 | 2 | yes | — |
| 47 | #11718047 | C22 | 1 | 2 | yes | — |
| 48 | C8×#1055 | C22 | 1 | 2 | yes | — |
| 49 | C22×Q8×C13 | C2×C4 | 1 | 1 | yes | characteristic |
| 50 | C22×Dic26 | C2×C4 | 1 | 1 | yes | characteristic |
| 51 | C2×C13×M16 | — | 2 | 1 | no | — |
| 52 | C2×C13×M16 | D4 | 1 | 1 | yes | characteristic |
| 53 | C2×C13×M16 | D4 | 1 | 1 | yes | characteristic |
| 54 | C4×Q8×C13 | — | 2 | 1 | no | — |
| 55 | C4×Q8×C13 | — | 2 | 1 | no | — |
| 56 | C4×Q8×C13 | C2×C4 | 1 | 1 | yes | characteristic |
| 57 | C4×Q8×C13 | C2×C4 | 1 | 1 | yes | characteristic |
| 58 | C4×Q8×C13 | C23 | 1 | 1 | yes | characteristic |
| 59 | C4×Q8×C13 | C23 | 1 | 1 | yes | characteristic |
| 60 | C2×C13×C4⋊C4 | — | 2 | 1 | no | — |
| 61 | C2×C13×C4⋊C4 | C2×C4 | 1 | 1 | yes | characteristic |
| 62 | C2×C42×C13 | — | 2 | 1 | no | — |
| 63 | C2×C42×C13 | C23 | 1 | 1 | yes | characteristic |
| 64 | C2×#6107 | — | 2 | 4 | no | — |
| 65 | C2×#6107 | C2×C4 | 1 | 1 | yes | characteristic |
| 66 | C2×#6107 | C2×C4 | 1 | 1 | yes | characteristic |
| 67 | C2×#6107 | C2×C4 | 1 | 1 | yes | characteristic |
| 68 | C2×#6107 | C2×C4 | 1 | 1 | yes | characteristic |
| 69 | C2×C4⋊Dic13 | C2×C4 | 1 | 1 | yes | characteristic |
| 70 | C2×#6101 | — | 2 | 1 | no | — |
| 71 | C2×C4×Dic13 | — | 2 | 1 | no | — |
| 72 | C2×#6099 | — | 2 | 1 | no | — |
| 73 | C22×#1055 | C2×C4 | 1 | 1 | yes | characteristic |
| 74 | C22×#1055 | C2×C4 | 1 | 1 | yes | characteristic |
| 75 | C4×Dic26 | — | 2 | 1 | no | — |
| 76 | C4×Dic26 | — | 2 | 1 | no | — |
| 77 | C4×Dic26 | C2×C4 | 1 | 1 | yes | characteristic |
| 78 | C4×Dic26 | C2×C4 | 1 | 1 | yes | characteristic |
| 79 | C4×Dic26 | C23 | 1 | 1 | yes | characteristic |
| 80 | C4×Dic26 | C23 | 1 | 1 | yes | characteristic |
| 81 | C13×C4⋊C8 | — | 2 | 2 | no | — |
| 82 | C13×C4⋊C8 | — | 2 | 2 | no | — |
| 83 | C13×C4⋊C8 | — | 2 | 1 | no | — |
| 84 | C13×C4⋊C8 | C23 | 1 | 2 | yes | — |
| 85 | C13×#97 | — | 2 | 2 | no | — |
| 86 | C13×#97 | D4 | 1 | 2 | yes | — |
| 87 | C4×C8×C13 | — | 2 | 2 | no | — |
| 88 | C4×C8×C13 | C23 | 1 | 2 | yes | — |
| 89 | #88075 | C2×C4 | 1 | 1 | yes | characteristic |
| 90 | #88075 | C2×C4 | 1 | 1 | yes | characteristic |
| 91 | #88075 | C2×C4 | 1 | 1 | yes | characteristic |
| 92 | #88075 | C2×C4 | 1 | 1 | yes | characteristic |
| 93 | C22⋊#1055 | — | 2 | 1 | no | — |
| 94 | #88055 | — | 2 | 2 | no | — |
| 95 | #88054 | — | 2 | 2 | no | — |
| 96 | #88054 | — | 2 | 2 | no | — |
| 97 | C8×Dic13 | — | 2 | 2 | no | — |
| 98 | #88050 | C2×C4 | 1 | 1 | yes | characteristic |
| 99 | #88050 | C2×C4 | 1 | 1 | yes | characteristic |
| 100 | #88050 | C2×C4 | 1 | 1 | yes | characteristic |
| 101 | #88050 | C2×C4 | 1 | 1 | yes | characteristic |
| 102 | #88047 | C2×C4 | 1 | 1 | yes | characteristic |
| 103 | #88047 | C2×C4 | 1 | 1 | yes | characteristic |
| 104 | #88047 | C2×C4 | 1 | 1 | yes | characteristic |
| 105 | #88047 | C2×C4 | 1 | 1 | yes | characteristic |
| 106 | C4⋊#1055 | — | 2 | 1 | no | — |
| 107 | C4⋊#1055 | — | 2 | 1 | no | — |
| 108 | C4⋊#1055 | C23 | 1 | 2 | yes | — |
| 109 | C4×#1055 | C2×C4 | 1 | 1 | yes | characteristic |
| 110 | C4×#1055 | C2×C4 | 1 | 1 | yes | characteristic |
| 111 | C4×#1055 | C23 | 1 | 2 | yes | — |
| 112 | C4×#1055 | C23 | 1 | 1 | yes | characteristic |
| 113 | C4×#1055 | C23 | 1 | 1 | yes | characteristic |
| 114 | M16×Q16 | — | 13 | 1 | no | maximal, Sylow |
| 115 | C2×Q8×C13 | — | 2 | 1 | no | — |
| 116 | C2×Q8×C13 | — | 2 | 2 | no | — |
| 117 | C2×Q8×C13 | — | 4 | 1 | no | — |
| 118 | C2×Q8×C13 | C22×C4 | 1 | 1 | yes | characteristic |
| 119 | C2×Q8×C13 | C22×C4 | 1 | 1 | yes | characteristic |
| 120 | C22×C4×C13 | — | 2 | 1 | no | — |
| 121 | C22×C4×C13 | — | 2 | 1 | no | — |
| 122 | C22×C4×C13 | C22×C4 | 1 | 1 | yes | characteristic |
| 123 | C22×C4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 124 | C22×C4×C13 | #41 | 1 | 1 | yes | characteristic |
| 125 | C22×Dic13 | — | 2 | 1 | no | — |
| 126 | C22×Dic13 | — | 2 | 1 | no | — |
| 127 | C2×Dic26 | — | 2 | 2 | no | — |
| 128 | C2×Dic26 | — | 2 | 1 | no | — |
| 129 | C2×Dic26 | — | 4 | 1 | no | — |
| 130 | C2×Dic26 | C22×C4 | 1 | 1 | yes | characteristic |
| 131 | C2×Dic26 | C22×C4 | 1 | 1 | yes | characteristic |
| 132 | C13×M16 | — | 2 | 2 | no | — |
| 133 | C13×M16 | — | 4 | 2 | no | — |
| 134 | C13×M16 | Q16 | 1 | 4 | yes | complemented |
| 135 | C2×C8×C13 | — | 2 | 2 | no | — |
| 136 | C2×C8×C13 | C2×D4 | 1 | 2 | yes | — |
| 137 | C2×C8×C13 | C2×D4 | 1 | 2 | yes | — |
| 138 | C13×C4⋊C4 | — | 2 | 1 | no | — |
| 139 | C13×C4⋊C4 | — | 2 | 1 | no | — |
| 140 | C13×C4⋊C4 | — | 2 | 1 | no | — |
| 141 | C13×C4⋊C4 | — | 2 | 1 | no | — |
| 142 | C13×C4⋊C4 | — | 2 | 1 | no | — |
| 143 | C13×C4⋊C4 | C22×C4 | 1 | 1 | yes | characteristic |
| 144 | C13×C4⋊C4 | C22×C4 | 1 | 1 | yes | characteristic |
| 145 | C42×C13 | — | 2 | 1 | no | — |
| 146 | C42×C13 | — | 2 | 1 | no | — |
| 147 | C42×C13 | — | 2 | 1 | no | — |
| 148 | C42×C13 | — | 2 | 1 | no | — |
| 149 | C42×C13 | C22×C4 | 1 | 1 | yes | characteristic |
| 150 | C42×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 151 | C42×C13 | #41 | 1 | 1 | yes | characteristic |
| 152 | C42×C13 | C24 | 1 | 1 | yes | characteristic |
| 153 | #6107 | — | 2 | 2 | no | — |
| 154 | #6107 | — | 2 | 2 | no | — |
| 155 | #6107 | — | 2 | 2 | no | — |
| 156 | #6107 | M16 | 1 | 4 | yes | direct product factor |
| 157 | C4⋊Dic13 | — | 2 | 1 | no | — |
| 158 | C4⋊Dic13 | C22×C4 | 1 | 1 | yes | characteristic |
| 159 | C4⋊Dic13 | C22×C4 | 1 | 1 | yes | characteristic |
| 160 | #6101 | — | 2 | 1 | no | — |
| 161 | #6101 | — | 2 | 1 | no | — |
| 162 | #6101 | — | 2 | 1 | no | — |
| 163 | #6101 | — | 2 | 1 | no | — |
| 164 | C4×Dic13 | — | 2 | 1 | no | — |
| 165 | C4×Dic13 | — | 2 | 1 | no | — |
| 166 | C4×Dic13 | — | 2 | 1 | no | — |
| 167 | C4×Dic13 | — | 2 | 1 | no | — |
| 168 | #6099 | — | 4 | 2 | no | — |
| 169 | C2×#1055 | — | 2 | 2 | no | — |
| 170 | C2×#1055 | — | 2 | 2 | no | — |
| 171 | C2×#1055 | — | 2 | 2 | no | — |
| 172 | C2×#1055 | — | 4 | 1 | no | — |
| 173 | C2×#1055 | C22×C4 | 1 | 1 | yes | characteristic |
| 174 | C2×#1055 | C22×C4 | 1 | 1 | yes | characteristic |
| 175 | C2×#1055 | C22×C4 | 1 | 1 | yes | characteristic |
| 176 | C2×#1055 | C22×C4 | 1 | 1 | yes | characteristic |
| 177 | Q8×M16 | — | 13 | 1 | no | — |
| 178 | Q8×M16 | D13 | 1 | 1 | yes | characteristic |
| 179 | C2×C4×Q16 | — | 13 | 1 | no | — |
| 180 | #1591 | — | 13 | 2 | no | — |
| 181 | #1584 | — | 13 | 2 | no | — |
| 182 | #1584 | — | 13 | 2 | no | — |
| 183 | C8×Q16 | — | 13 | 2 | no | — |
| 184 | #1567 | — | 13 | 1 | no | — |
| 185 | #1487 | — | 13 | 1 | no | — |
| 186 | #1487 | — | 13 | 1 | no | — |
| 187 | C8×M16 | — | 13 | 1 | no | — |
| 188 | C23×C13 | C4×D4 | 1 | 1 | yes | characteristic |
| 189 | Q8×C13 | — | 2 | 1 | no | — |
| 190 | Q8×C13 | — | 2 | 1 | no | — |
| 191 | Q8×C13 | — | 2 | 1 | no | — |
| 192 | Q8×C13 | — | 4 | 2 | no | — |
| 193 | Q8×C13 | C2×M16 | 1 | 2 | yes | — |
| 194 | C2×C4×C13 | — | 2 | 1 | no | — |
| 195 | C2×C4×C13 | — | 2 | 1 | no | — |
| 196 | C2×C4×C13 | — | 2 | 1 | no | — |
| 197 | C2×C4×C13 | — | 2 | 1 | no | — |
| 198 | C2×C4×C13 | — | 2 | 1 | no | — |
| 199 | C2×C4×C13 | — | 2 | 1 | no | — |
| 200 | C2×C4×C13 | — | 4 | 1 | no | — |
| 201 | C2×C4×C13 | — | 4 | 2 | no | — |
| 202 | C2×C4×C13 | — | 8 | 1 | no | — |
| 203 | C2×C4×C13 | C4×D4 | 1 | 1 | yes | characteristic |
| 204 | C2×C4×C13 | C4×D4 | 1 | 1 | yes | characteristic |
| 205 | C2×C4×C13 | C4×D4 | 1 | 1 | yes | characteristic |
| 206 | C2×C4×C13 | C2×Q16 | 1 | 2 | yes | — |
| 207 | C2×C4×C13 | #135 | 1 | 2 | yes | — |
| 208 | C2×C4×C13 | C23×C4 | 1 | 1 | yes | characteristic |
| 209 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 210 | C2×C4×C13 | C2×#41 | 1 | 1 | yes | characteristic |
| 211 | C2×Dic13 | — | 2 | 1 | no | — |
| 212 | C2×Dic13 | — | 2 | 1 | no | — |
| 213 | C2×Dic13 | — | 2 | 1 | no | — |
| 214 | C2×Dic13 | — | 2 | 1 | no | — |
| 215 | C2×Dic13 | — | 4 | 2 | no | — |
| 216 | C2×Dic13 | — | 8 | 1 | no | — |
| 217 | Dic26 | — | 2 | 1 | no | — |
| 218 | Dic26 | — | 2 | 1 | no | — |
| 219 | Dic26 | — | 2 | 1 | no | — |
| 220 | Dic26 | — | 4 | 2 | no | — |
| 221 | Dic26 | C2×M16 | 1 | 2 | yes | — |
| 222 | C8×C13 | — | 2 | 2 | no | — |
| 223 | C8×C13 | — | 4 | 2 | no | — |
| 224 | C8×C13 | C2×Q16 | 1 | 4 | yes | complemented |
| 225 | #1055 | — | 2 | 1 | no | — |
| 226 | #1055 | — | 2 | 1 | no | — |
| 227 | #1055 | — | 2 | 1 | no | — |
| 228 | #1055 | — | 4 | 2 | no | — |
| 229 | #1055 | — | 4 | 2 | no | — |
| 230 | #1055 | C2×M16 | 1 | 2 | yes | — |
| 231 | C22×Q16 | — | 13 | 1 | no | — |
| 232 | C2×C4×Q8 | — | 13 | 1 | no | — |
| 233 | C2×C4×Q8 | C2×D13 | 1 | 1 | yes | characteristic |
| 234 | #446 | — | 2 | 2 | no | — |
| 235 | #446 | — | 13 | 2 | no | — |
| 236 | #446 | — | 26 | 2 | no | — |
| 237 | #446 | C2×D13 | 1 | 2 | yes | — |
| 238 | C8×Q8 | — | 13 | 2 | no | — |
| 239 | C8×Q8 | C2×D13 | 1 | 2 | yes | — |
| 240 | C4×Q16 | — | 13 | 1 | no | — |
| 241 | C4×Q16 | — | 13 | 1 | no | — |
| 242 | C4×Q16 | — | 13 | 1 | no | — |
| 243 | C4×Q16 | — | 13 | 1 | no | — |
| 244 | C4×Q16 | — | 13 | 1 | no | — |
| 245 | C4×Q16 | — | 13 | 1 | no | — |
| 246 | C4×Q16 | — | 13 | 1 | no | — |
| 247 | C4×Q16 | — | 13 | 1 | no | — |
| 248 | #431 | — | 13 | 1 | no | — |
| 249 | C2×#107 | — | 13 | 1 | no | — |
| 250 | #423 | — | 2 | 1 | no | — |
| 251 | #423 | — | 13 | 1 | no | — |
| 252 | #423 | — | 26 | 1 | no | — |
| 253 | #423 | C2×D13 | 1 | 1 | yes | characteristic |
| 254 | C2×#103 | — | 13 | 1 | no | — |
| 255 | C2×#103 | — | 13 | 1 | no | — |
| 256 | C4×M16 | — | 2 | 1 | no | — |
| 257 | C4×M16 | — | 26 | 1 | no | — |
| 258 | C4×M16 | C2×D13 | 1 | 1 | yes | characteristic |
| 259 | C2×C4×C8 | — | 13 | 1 | no | — |
| 260 | #335 | — | 13 | 2 | no | — |
| 261 | #335 | — | 13 | 2 | no | — |
| 262 | Q8⋊C8 | — | 13 | 2 | no | — |
| 263 | Q8⋊C8 | — | 13 | 2 | no | — |
| 264 | Q8⋊C8 | — | 13 | 2 | no | — |
| 265 | Q8⋊C8 | — | 13 | 2 | no | — |
| 266 | #322 | — | 13 | 2 | no | — |
| 267 | C82 | — | 13 | 2 | no | — |
| 268 | C22×C13 | — | 2 | 1 | no | — |
| 269 | C22×C13 | — | 2 | 1 | no | — |
| 270 | C22×C13 | C4×Q16 | 1 | 2 | yes | — |
| 271 | C22×C13 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 272 | C4×C13 | — | 2 | 1 | no | — |
| 273 | C4×C13 | — | 2 | 2 | no | — |
| 274 | C4×C13 | — | 2 | 1 | no | — |
| 275 | C4×C13 | — | 2 | 1 | no | — |
| 276 | C4×C13 | — | 4 | 1 | no | — |
| 277 | C4×C13 | — | 4 | 1 | no | — |
| 278 | C4×C13 | — | 4 | 1 | no | — |
| 279 | C4×C13 | C4×Q16 | 1 | 2 | yes | — |
| 280 | C4×C13 | C22×M16 | 1 | 1 | yes | characteristic |
| 281 | C4×C13 | #568 | 1 | 1 | yes | characteristic |
| 282 | C4×C13 | C22×Q16 | 1 | 1 | yes | characteristic |
| 283 | C4×C13 | C2×#135 | 1 | 1 | yes | characteristic |
| 284 | Dic13 | — | 2 | 2 | no | — |
| 285 | Dic13 | — | 4 | 1 | no | — |
| 286 | Dic13 | — | 4 | 1 | no | — |
| 287 | Dic13 | — | 4 | 1 | no | — |
| 288 | C22×Q8 | — | 13 | 1 | no | — |
| 289 | C22×Q8 | C4×D13 | 1 | 1 | yes | characteristic |
| 290 | C2×Q16 | — | 13 | 1 | no | — |
| 291 | C2×Q16 | — | 13 | 1 | no | — |
| 292 | C2×Q16 | — | 13 | 1 | no | — |
| 293 | C2×Q16 | — | 13 | 1 | no | — |
| 294 | C2×Q16 | — | 26 | 4 | no | — |
| 295 | C2×M16 | — | 2 | 1 | no | — |
| 296 | C2×M16 | — | 26 | 1 | no | — |
| 297 | C2×M16 | C22⋊D13 | 1 | 1 | yes | characteristic |
| 298 | C2×M16 | C22⋊D13 | 1 | 1 | yes | characteristic |
| 299 | C22×C8 | — | 13 | 1 | no | — |
| 300 | C22×C8 | — | 13 | 1 | no | — |
| 301 | C4×Q8 | — | 2 | 1 | no | — |
| 302 | C4×Q8 | — | 2 | 1 | no | — |
| 303 | C4×Q8 | — | 13 | 1 | no | — |
| 304 | C4×Q8 | — | 13 | 1 | no | — |
| 305 | C4×Q8 | — | 13 | 1 | no | — |
| 306 | C4×Q8 | — | 13 | 1 | no | — |
| 307 | C4×Q8 | — | 26 | 1 | no | — |
| 308 | C4×Q8 | — | 26 | 1 | no | — |
| 309 | C4×Q8 | C4×D13 | 1 | 1 | yes | characteristic |
| 310 | C4×Q8 | C4×D13 | 1 | 1 | yes | characteristic |
| 311 | C4×Q8 | C22×D13 | 1 | 1 | yes | characteristic |
| 312 | C4×Q8 | C22×D13 | 1 | 1 | yes | characteristic |
| 313 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 314 | C2×C4⋊C4 | — | 13 | 1 | no | — |
| 315 | C2×C4⋊C4 | — | 26 | 1 | no | — |
| 316 | C2×C4⋊C4 | C4×D13 | 1 | 1 | yes | characteristic |
| 317 | C2×C42 | — | 2 | 1 | no | — |
| 318 | C2×C42 | — | 26 | 1 | no | — |
| 319 | C2×C42 | C22×D13 | 1 | 1 | yes | characteristic |
| 320 | #107 | — | 13 | 1 | no | — |
| 321 | #107 | — | 13 | 1 | no | — |
| 322 | #107 | — | 13 | 1 | no | — |
| 323 | #107 | — | 13 | 1 | no | — |
| 324 | C4⋊C8 | — | 2 | 2 | no | — |
| 325 | C4⋊C8 | — | 2 | 2 | no | — |
| 326 | C4⋊C8 | — | 2 | 1 | no | — |
| 327 | C4⋊C8 | — | 13 | 2 | no | — |
| 328 | C4⋊C8 | — | 26 | 2 | no | — |
| 329 | C4⋊C8 | — | 26 | 2 | no | — |
| 330 | C4⋊C8 | — | 26 | 1 | no | — |
| 331 | C4⋊C8 | — | 26 | 1 | no | — |
| 332 | C4⋊C8 | C22×D13 | 1 | 2 | yes | — |
| 333 | #103 | — | 13 | 1 | no | — |
| 334 | #103 | — | 13 | 1 | no | — |
| 335 | #103 | — | 13 | 1 | no | — |
| 336 | #103 | — | 13 | 1 | no | — |
| 337 | #103 | — | 13 | 1 | no | — |
| 338 | #103 | — | 13 | 1 | no | — |
| 339 | #103 | — | 13 | 1 | no | — |
| 340 | #103 | — | 13 | 1 | no | — |
| 341 | C22⋊C8 | — | 26 | 1 | no | — |
| 342 | #97 | — | 2 | 2 | no | — |
| 343 | #97 | — | 26 | 2 | no | — |
| 344 | #97 | C22⋊D13 | 1 | 2 | yes | — |
| 345 | C4×C8 | — | 2 | 2 | no | — |
| 346 | C4×C8 | — | 13 | 1 | no | — |
| 347 | C4×C8 | — | 13 | 1 | no | — |
| 348 | C4×C8 | — | 13 | 1 | no | — |
| 349 | C4×C8 | — | 13 | 1 | no | — |
| 350 | C4×C8 | — | 13 | 2 | no | — |
| 351 | C4×C8 | — | 26 | 2 | no | — |
| 352 | C4×C8 | C22×D13 | 1 | 2 | yes | — |
| 353 | C2×C13 | — | 2 | 2 | no | — |
| 354 | C2×C13 | D4×M16 | 1 | 1 | yes | characteristic |
| 355 | C2×C13 | C2×C4×Q16 | 1 | 1 | yes | characteristic |
| 356 | C2×C13 | #2957 | 1 | 1 | yes | characteristic |
| 357 | C2×Q8 | — | 2 | 1 | no | — |
| 358 | C2×Q8 | — | 2 | 2 | no | — |
| 359 | C2×Q8 | — | 4 | 1 | no | — |
| 360 | C2×Q8 | — | 13 | 1 | no | — |
| 361 | C2×Q8 | — | 13 | 1 | no | — |
| 362 | C2×Q8 | — | 26 | 2 | no | — |
| 363 | C2×Q8 | — | 26 | 1 | no | — |
| 364 | C2×Q8 | — | 52 | 1 | no | — |
| 365 | C2×Q8 | C2×C4×D13 | 1 | 1 | yes | characteristic |
| 366 | C2×Q8 | C2×C4×D13 | 1 | 1 | yes | characteristic |
| 367 | C22×C4 | — | 2 | 1 | no | — |
| 368 | C22×C4 | — | 2 | 1 | no | — |
| 369 | C22×C4 | — | 26 | 1 | no | — |
| 370 | C22×C4 | — | 26 | 1 | no | — |
| 371 | C22×C4 | C2×C4×D13 | 1 | 1 | yes | characteristic |
| 372 | C22×C4 | #6127 | 1 | 1 | yes | characteristic |
| 373 | C22×C4 | C2×C22⋊D13 | 1 | 1 | yes | characteristic |
| 374 | Q16 | — | 13 | 4 | no | — |
| 375 | Q16 | — | 26 | 2 | no | — |
| 376 | Q16 | — | 26 | 2 | no | — |
| 377 | Q16 | — | 26 | 2 | no | — |
| 378 | M16 | — | 2 | 2 | no | — |
| 379 | M16 | — | 4 | 2 | no | — |
| 380 | M16 | — | 52 | 2 | no | — |
| 381 | M16 | #6107 | 1 | 4 | yes | direct product factor |
| 382 | C2×C8 | — | 2 | 2 | no | — |
| 383 | C2×C8 | — | 13 | 1 | no | — |
| 384 | C2×C8 | — | 13 | 1 | no | — |
| 385 | C2×C8 | — | 13 | 1 | no | — |
| 386 | C2×C8 | — | 13 | 1 | no | — |
| 387 | C2×C8 | — | 26 | 2 | no | — |
| 388 | C2×C8 | — | 26 | 2 | no | — |
| 389 | C2×C8 | — | 26 | 2 | no | — |
| 390 | C2×C8 | — | 52 | 1 | no | — |
| 391 | C2×C8 | C2×C22⋊D13 | 1 | 2 | yes | — |
| 392 | C2×C8 | C2×C22⋊D13 | 1 | 2 | yes | — |
| 393 | C4⋊C4 | — | 2 | 1 | no | — |
| 394 | C4⋊C4 | — | 2 | 1 | no | — |
| 395 | C4⋊C4 | — | 2 | 1 | no | — |
| 396 | C4⋊C4 | — | 2 | 1 | no | — |
| 397 | C4⋊C4 | — | 2 | 1 | no | — |
| 398 | C4⋊C4 | — | 13 | 1 | no | — |
| 399 | C4⋊C4 | — | 13 | 1 | no | — |
| 400 | C4⋊C4 | — | 26 | 1 | no | — |
| 401 | C4⋊C4 | — | 26 | 1 | no | — |
| 402 | C4⋊C4 | — | 26 | 1 | no | — |
| 403 | C4⋊C4 | — | 26 | 1 | no | — |
| 404 | C4⋊C4 | — | 26 | 1 | no | — |
| 405 | C4⋊C4 | C2×C4×D13 | 1 | 1 | yes | characteristic |
| 406 | C4⋊C4 | C2×C4×D13 | 1 | 1 | yes | characteristic |
| 407 | C42 | — | 2 | 1 | no | — |
| 408 | C42 | — | 2 | 1 | no | — |
| 409 | C42 | — | 2 | 1 | no | — |
| 410 | C42 | — | 2 | 1 | no | — |
| 411 | C42 | — | 26 | 1 | no | — |
| 412 | C42 | — | 26 | 1 | no | — |
| 413 | C42 | — | 26 | 1 | no | — |
| 414 | C42 | — | 26 | 1 | no | — |
| 415 | C42 | C2×C4×D13 | 1 | 1 | yes | characteristic |
| 416 | C42 | #6127 | 1 | 1 | yes | characteristic |
| 417 | C42 | C2×C22⋊D13 | 1 | 1 | yes | characteristic |
| 418 | C42 | C23×D13 | 1 | 1 | yes | characteristic |
| 419 | C13 | M16×Q16 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 420 | C23 | C4×C22⋊D13 | 1 | 1 | yes | characteristic |
| 421 | Q8 | — | 2 | 1 | no | — |
| 422 | Q8 | — | 2 | 1 | no | — |
| 423 | Q8 | — | 2 | 1 | no | — |
| 424 | Q8 | — | 4 | 2 | no | — |
| 425 | Q8 | — | 13 | 2 | no | — |
| 426 | Q8 | — | 26 | 1 | no | — |
| 427 | Q8 | — | 26 | 1 | no | — |
| 428 | Q8 | — | 26 | 1 | no | — |
| 429 | Q8 | — | 52 | 2 | no | — |
| 430 | Q8 | M16×D13 | 1 | 2 | yes | — |
| 431 | C2×C4 | — | 2 | 1 | no | — |
| 432 | C2×C4 | — | 2 | 1 | no | — |
| 433 | C2×C4 | — | 2 | 1 | no | — |
| 434 | C2×C4 | — | 2 | 1 | no | — |
| 435 | C2×C4 | — | 2 | 1 | no | — |
| 436 | C2×C4 | — | 2 | 1 | no | — |
| 437 | C2×C4 | — | 4 | 1 | no | — |
| 438 | C2×C4 | — | 4 | 2 | no | — |
| 439 | C2×C4 | — | 8 | 1 | no | — |
| 440 | C2×C4 | — | 26 | 1 | no | — |
| 441 | C2×C4 | — | 26 | 1 | no | — |
| 442 | C2×C4 | — | 26 | 1 | no | — |
| 443 | C2×C4 | — | 26 | 1 | no | — |
| 444 | C2×C4 | — | 52 | 2 | no | — |
| 445 | C2×C4 | — | 104 | 1 | no | — |
| 446 | C2×C4 | C4×C22⋊D13 | 1 | 1 | yes | characteristic |
| 447 | C2×C4 | C4×C22⋊D13 | 1 | 1 | yes | characteristic |
| 448 | C2×C4 | C4×C22⋊D13 | 1 | 1 | yes | characteristic |
| 449 | C2×C4 | C2×#6107 | 1 | 2 | yes | — |
| 450 | C2×C4 | #88204 | 1 | 2 | yes | — |
| 451 | C2×C4 | C22×C4×D13 | 1 | 1 | yes | characteristic |
| 452 | C2×C4 | C2×#6127 | 1 | 1 | yes | characteristic |
| 453 | C2×C4 | C22×C22⋊D13 | 1 | 1 | yes | characteristic |
| 454 | C8 | — | 2 | 2 | no | — |
| 455 | C8 | — | 4 | 2 | no | — |
| 456 | C8 | — | 13 | 2 | no | — |
| 457 | C8 | — | 26 | 1 | no | — |
| 458 | C8 | — | 26 | 1 | no | — |
| 459 | C8 | — | 26 | 1 | no | — |
| 460 | C8 | — | 52 | 2 | no | — |
| 461 | C8 | — | 52 | 2 | no | — |
| 462 | C8 | C2×#6107 | 1 | 4 | yes | complemented |
| 463 | C22 | — | 2 | 1 | no | — |
| 464 | C22 | — | 2 | 1 | no | — |
| 465 | C22 | C4×#6107 | 1 | 2 | yes | — |
| 466 | C22 | C2×C4×C22⋊D13 | 1 | 1 | yes | characteristic |
| 467 | C4 | — | 2 | 1 | no | — |
| 468 | C4 | — | 2 | 1 | no | — |
| 469 | C4 | — | 2 | 1 | no | — |
| 470 | C4 | — | 2 | 2 | no | — |
| 471 | C4 | — | 4 | 1 | no | — |
| 472 | C4 | — | 4 | 1 | no | — |
| 473 | C4 | — | 4 | 1 | no | — |
| 474 | C4 | — | 26 | 2 | no | — |
| 475 | C4 | — | 52 | 1 | no | — |
| 476 | C4 | — | 52 | 1 | no | — |
| 477 | C4 | — | 52 | 1 | no | — |
| 478 | C4 | C4×#6107 | 1 | 2 | yes | — |
| 479 | C4 | C2×M16×D13 | 1 | 1 | yes | characteristic |
| 480 | C4 | #11719450 | 1 | 1 | yes | characteristic |
| 481 | C4 | C22×#6107 | 1 | 1 | yes | characteristic |
| 482 | C4 | C2×#88204 | 1 | 1 | yes | characteristic |
| 483 | C2 | — | 2 | 2 | no | — |
| 484 | C2 | M16×C22⋊D13 | 1 | 1 | yes | characteristic |
| 485 | C2 | C2×C4×#6107 | 1 | 1 | yes | characteristic |
| 486 | C2 | #13123751 | 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