Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1152 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 1152 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | H(3,𝔽4)×D53 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #20285703 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #20285178 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #20274020 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #20274019 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #20274005 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #20274005 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #20274004 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #20273337 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #20273311 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | C53×#1659 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#13133249 | — | 2 | 1 | no | — |
| 13 | C2×#13133244 | — | 2 | 1 | no | — |
| 14 | #16811366 | — | 2 | 2 | no | — |
| 15 | #16811366 | — | 2 | 1 | no | — |
| 16 | #16811365 | — | 2 | 1 | no | — |
| 17 | #16811365 | — | 2 | 2 | no | — |
| 18 | #16811365 | C22 | 1 | 1 | yes | characteristic |
| 19 | #16811365 | C22 | 1 | 2 | yes | — |
| 20 | #16811174 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | #124×D53 | — | 2 | 1 | no | — |
| 22 | #124×D53 | — | 2 | 2 | no | — |
| 23 | #124×D53 | C22 | 1 | 2 | yes | — |
| 24 | #124×D53 | C22 | 1 | 1 | yes | characteristic |
| 25 | #120×D53 | — | 2 | 1 | no | — |
| 26 | #120×D53 | — | 2 | 2 | no | — |
| 27 | #16811015 | C22 | 1 | 1 | yes | characteristic, complemented |
| 28 | #16811013 | C22 | 1 | 2 | yes | complemented |
| 29 | #16811013 | C22 | 1 | 1 | yes | characteristic, complemented |
| 30 | #16811012 | C22 | 1 | 2 | yes | complemented |
| 31 | #16811012 | C22 | 1 | 1 | yes | characteristic, complemented |
| 32 | #16811008 | — | 2 | 1 | no | — |
| 33 | #16811004 | — | 2 | 1 | no | — |
| 34 | #16810985 | C22 | 1 | 2 | yes | complemented |
| 35 | #16810841 | — | 2 | 2 | no | — |
| 36 | #16810837 | — | 2 | 2 | no | — |
| 37 | #16810763 | — | 2 | 2 | no | — |
| 38 | #16810758 | — | 2 | 2 | no | — |
| 39 | #16810678 | C22 | 1 | 2 | yes | complemented |
| 40 | #16810575 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | #16810363 | C22 | 1 | 1 | yes | characteristic, complemented |
| 42 | #16810363 | C22 | 1 | 2 | yes | complemented |
| 43 | #16810362 | C22 | 1 | 2 | yes | complemented |
| 44 | #16810362 | C22 | 1 | 2 | yes | complemented |
| 45 | #16810362 | C22 | 1 | 2 | yes | complemented |
| 46 | C53×H(3,𝔽4) | C22 | 1 | 1 | yes | characteristic |
| 47 | C53×#497 | C22 | 1 | 1 | yes | characteristic, complemented |
| 48 | C53×#489 | C22 | 1 | 2 | yes | complemented |
| 49 | C53×#329 | C22 | 1 | 2 | yes | complemented |
| 50 | C53×#329 | C22 | 1 | 1 | yes | characteristic, complemented |
| 51 | C24×D53 | — | 2 | 1 | no | — |
| 52 | C2×#11719949 | — | 2 | 1 | no | — |
| 53 | C2×Q8×D53 | D4 | 1 | 1 | yes | characteristic |
| 54 | C2×Q8×D53 | D4 | 1 | 2 | yes | — |
| 55 | C2×D4×D53 | — | 2 | 2 | no | — |
| 56 | C2×D4×D53 | — | 2 | 1 | no | — |
| 57 | C2×D4×D53 | D4 | 1 | 1 | yes | characteristic |
| 58 | C2×D4×D53 | D4 | 1 | 2 | yes | — |
| 59 | #13133249 | — | 4 | 4 | no | — |
| 60 | #13133244 | — | 4 | 4 | no | — |
| 61 | C2×#11719925 | — | 2 | 1 | no | — |
| 62 | C2×#11719913 | — | 2 | 1 | no | — |
| 63 | C2×#11719913 | — | 2 | 2 | no | — |
| 64 | C2×#11719924 | — | 2 | 1 | no | — |
| 65 | C2×#11719924 | — | 2 | 2 | no | — |
| 66 | C2×#11719924 | — | 2 | 1 | no | — |
| 67 | C2×D424 | — | 2 | 1 | no | — |
| 68 | C2×D424 | — | 2 | 2 | no | — |
| 69 | C2×#11719922 | — | 2 | 1 | no | — |
| 70 | C2×#11719922 | — | 2 | 2 | no | — |
| 71 | C2×#11719912 | — | 2 | 1 | no | — |
| 72 | #13133214 | C23 | 1 | 1 | yes | characteristic, complemented |
| 73 | #13133206 | — | 2 | 1 | no | — |
| 74 | #13133206 | — | 2 | 2 | no | — |
| 75 | #13133206 | — | 2 | 1 | no | — |
| 76 | #13133206 | D4 | 1 | 1 | yes | characteristic |
| 77 | #13133206 | D4 | 1 | 2 | yes | — |
| 78 | #13133205 | — | 2 | 1 | no | — |
| 79 | #13133205 | — | 2 | 2 | no | — |
| 80 | #13133205 | C23 | 1 | 1 | yes | characteristic |
| 81 | #13133205 | C23 | 1 | 2 | yes | — |
| 82 | #13133204 | — | 2 | 1 | no | — |
| 83 | #13133204 | — | 2 | 2 | no | — |
| 84 | #13133204 | D4 | 1 | 2 | yes | — |
| 85 | #13133204 | D4 | 1 | 1 | yes | characteristic |
| 86 | #13133203 | — | 2 | 2 | no | — |
| 87 | #13133203 | — | 2 | 2 | no | — |
| 88 | #13133203 | — | 2 | 2 | no | — |
| 89 | #13133203 | — | 2 | 2 | no | — |
| 90 | #13133203 | — | 2 | 2 | no | — |
| 91 | #13133203 | — | 2 | 2 | no | — |
| 92 | #13133203 | — | 2 | 2 | no | — |
| 93 | #13133203 | — | 2 | 2 | no | — |
| 94 | #13133203 | — | 2 | 2 | no | — |
| 95 | #13133192 | — | 2 | 2 | no | — |
| 96 | #13133187 | — | 2 | 1 | no | — |
| 97 | #13133187 | — | 2 | 2 | no | — |
| 98 | #13133187 | — | 2 | 2 | no | — |
| 99 | #13133187 | — | 2 | 2 | no | — |
| 100 | #13133187 | — | 2 | 2 | no | — |
| 101 | #13133186 | — | 2 | 1 | no | — |
| 102 | #13133186 | — | 2 | 2 | no | — |
| 103 | #13133185 | — | 2 | 2 | no | — |
| 104 | #13133185 | — | 2 | 2 | no | — |
| 105 | #13133185 | — | 2 | 2 | no | — |
| 106 | #13133185 | — | 2 | 2 | no | — |
| 107 | #13133185 | — | 2 | 1 | no | — |
| 108 | #13133179 | — | 2 | 2 | no | — |
| 109 | C22⋊C4×D53 | — | 2 | 1 | no | — |
| 110 | C22⋊C4×D53 | — | 2 | 2 | no | — |
| 111 | C22⋊C4×D53 | — | 2 | 2 | no | — |
| 112 | C22⋊C4×D53 | — | 2 | 2 | no | — |
| 113 | C22⋊C4×D53 | — | 2 | 2 | no | — |
| 114 | C42×D53 | — | 2 | 1 | no | — |
| 115 | C42×D53 | C23 | 1 | 1 | yes | characteristic |
| 116 | #13133146 | — | 2 | 2 | no | — |
| 117 | #13133140 | — | 2 | 2 | no | — |
| 118 | #13133137 | — | 2 | 2 | no | — |
| 119 | #13133129 | — | 2 | 2 | no | — |
| 120 | #13133128 | C23 | 1 | 1 | yes | characteristic, complemented |
| 121 | #13133128 | C23 | 1 | 2 | yes | complemented |
| 122 | C8×Dic53 | — | 2 | 1 | no | — |
| 123 | C2×Q16×C53 | — | 2 | 1 | no | — |
| 124 | C2×SD16×C53 | — | 2 | 1 | no | — |
| 125 | C4⋊Q8×C53 | C23 | 1 | 1 | yes | characteristic, complemented |
| 126 | #124×C53 | — | 2 | 2 | no | — |
| 127 | #124×C53 | — | 2 | 1 | no | — |
| 128 | #124×C53 | C23 | 1 | 2 | yes | — |
| 129 | #124×C53 | C23 | 1 | 1 | yes | characteristic |
| 130 | #120×C53 | — | 2 | 2 | no | — |
| 131 | #120×C53 | — | 2 | 1 | no | — |
| 132 | #103×C53 | — | 2 | 2 | no | — |
| 133 | #102×C53 | — | 2 | 2 | no | — |
| 134 | #97×C53 | C23 | 1 | 2 | yes | complemented |
| 135 | #97×C53 | C23 | 1 | 1 | yes | characteristic, complemented |
| 136 | C24×C53 | — | 2 | 1 | no | — |
| 137 | C23×D53 | — | 2 | 2 | no | — |
| 138 | C23×D53 | — | 2 | 1 | no | — |
| 139 | C23×D53 | — | 2 | 1 | no | — |
| 140 | C23×D53 | — | 2 | 2 | no | — |
| 141 | C23×D53 | — | 8 | 4 | no | — |
| 142 | C23×D53 | — | 8 | 2 | no | — |
| 143 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 144 | C2×Q8×C53 | C2×D4 | 1 | 2 | yes | — |
| 145 | C2×Q8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 146 | C2×D4×C53 | — | 2 | 1 | no | — |
| 147 | C2×D4×C53 | — | 2 | 2 | no | — |
| 148 | C2×D4×C53 | C2×D4 | 1 | 2 | yes | — |
| 149 | C2×D4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 150 | C2×C22⋊D53 | — | 2 | 2 | no | — |
| 151 | C2×C22⋊D53 | — | 2 | 2 | no | — |
| 152 | C2×C22⋊D53 | — | 2 | 2 | no | — |
| 153 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 154 | C2×C22⋊D53 | — | 2 | 2 | no | — |
| 155 | #11719949 | — | 4 | 2 | no | — |
| 156 | #11719949 | — | 4 | 2 | no | — |
| 157 | Q8×D53 | — | 4 | 2 | no | — |
| 158 | Q8×D53 | — | 8 | 2 | no | — |
| 159 | D4×D53 | — | 4 | 2 | no | — |
| 160 | D4×D53 | — | 8 | 2 | no | — |
| 161 | D4×D53 | — | 8 | 4 | no | — |
| 162 | D4×D53 | — | 8 | 2 | no | — |
| 163 | C2×D212 | — | 2 | 2 | no | — |
| 164 | C2×D212 | — | 2 | 1 | no | — |
| 165 | C2×D212 | — | 2 | 1 | no | — |
| 166 | C2×D212 | — | 2 | 2 | no | — |
| 167 | C2×D212 | — | 4 | 1 | no | — |
| 168 | C2×D212 | C2×D4 | 1 | 2 | yes | — |
| 169 | C2×D212 | C2×D4 | 1 | 1 | yes | characteristic |
| 170 | C2×C4×D53 | — | 2 | 2 | no | — |
| 171 | C2×C4×D53 | — | 2 | 1 | no | — |
| 172 | C2×C4×D53 | — | 4 | 1 | no | — |
| 173 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 174 | C2×C4×D53 | C2×D4 | 1 | 2 | yes | — |
| 175 | C2×Dic106 | — | 2 | 1 | no | — |
| 176 | C2×Dic106 | — | 2 | 2 | no | — |
| 177 | C2×Dic106 | C2×D4 | 1 | 2 | yes | — |
| 178 | C2×Dic106 | C2×D4 | 1 | 1 | yes | characteristic |
| 179 | Q16×C53 | — | 4 | 2 | no | — |
| 180 | SD16×C53 | — | 4 | 2 | no | — |
| 181 | C2×C8×C53 | — | 2 | 1 | no | — |
| 182 | C2×C8×C53 | — | 2 | 2 | no | — |
| 183 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 184 | C22⋊C4×C53 | — | 2 | 2 | no | — |
| 185 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 186 | C22⋊C4×C53 | — | 2 | 2 | no | — |
| 187 | C22⋊C4×C53 | — | 2 | 2 | no | — |
| 188 | C22⋊C4×C53 | — | 2 | 2 | no | — |
| 189 | C42×C53 | — | 2 | 1 | no | — |
| 190 | C42×C53 | C24 | 1 | 1 | yes | characteristic |
| 191 | C22⋊Dic53 | — | 2 | 2 | no | — |
| 192 | C22⋊Dic53 | — | 2 | 1 | no | — |
| 193 | C22⋊Dic53 | — | 2 | 2 | no | — |
| 194 | C22⋊Dic53 | — | 2 | 2 | no | — |
| 195 | C22⋊Dic53 | — | 2 | 2 | no | — |
| 196 | #11719925 | — | 4 | 2 | no | — |
| 197 | #11719924 | — | 4 | 2 | no | — |
| 198 | #11719924 | — | 4 | 2 | no | — |
| 199 | #11719924 | — | 8 | 2 | no | — |
| 200 | #11719922 | — | 4 | 2 | no | — |
| 201 | #11719922 | — | 8 | 2 | no | — |
| 202 | #11719921 | — | 2 | 2 | no | — |
| 203 | #11719921 | — | 2 | 2 | no | — |
| 204 | #11719921 | — | 2 | 2 | no | — |
| 205 | #11719921 | — | 2 | 2 | no | — |
| 206 | #11719921 | — | 2 | 2 | no | — |
| 207 | #11719921 | — | 2 | 2 | no | — |
| 208 | #11719921 | — | 2 | 2 | no | — |
| 209 | #11719921 | — | 2 | 2 | no | — |
| 210 | #11719921 | — | 2 | 2 | no | — |
| 211 | #11719921 | — | 4 | 2 | no | — |
| 212 | C4×Dic53 | — | 2 | 2 | no | — |
| 213 | C4×Dic53 | — | 2 | 1 | no | — |
| 214 | C4×Dic53 | C2×D4 | 1 | 1 | yes | characteristic |
| 215 | C4×Dic53 | C2×D4 | 1 | 2 | yes | — |
| 216 | C2×#88322 | — | 2 | 1 | no | — |
| 217 | C2×#88322 | — | 2 | 2 | no | — |
| 218 | D424 | — | 4 | 2 | no | — |
| 219 | D424 | — | 8 | 2 | no | — |
| 220 | #11719913 | — | 4 | 2 | no | — |
| 221 | #11719913 | — | 8 | 2 | no | — |
| 222 | #11719912 | — | 2 | 4 | no | — |
| 223 | C23×C53 | — | 2 | 1 | no | — |
| 224 | C23×C53 | — | 2 | 2 | no | — |
| 225 | C23×C53 | — | 8 | 1 | no | — |
| 226 | C23×C53 | — | 8 | 2 | no | — |
| 227 | C22×D53 | — | 2 | 1 | no | — |
| 228 | C22×D53 | — | 2 | 2 | no | — |
| 229 | C22×D53 | — | 4 | 4 | no | — |
| 230 | C22×D53 | — | 4 | 4 | no | — |
| 231 | C22×D53 | — | 4 | 4 | no | — |
| 232 | C22×D53 | — | 4 | 2 | no | — |
| 233 | C22×D53 | — | 4 | 4 | no | — |
| 234 | C22×D53 | — | 4 | 1 | no | — |
| 235 | C22×D53 | — | 8 | 2 | no | — |
| 236 | C22×D53 | — | 8 | 1 | no | — |
| 237 | C22×D53 | — | 8 | 2 | no | — |
| 238 | C22×D53 | — | 8 | 2 | no | — |
| 239 | C22×D53 | — | 8 | 2 | no | — |
| 240 | C22×D53 | — | 8 | 16 | no | — |
| 241 | C22×D53 | #120 | 1 | 1 | yes | characteristic |
| 242 | Q8×C53 | — | 4 | 1 | no | — |
| 243 | Q8×C53 | — | 4 | 2 | no | — |
| 244 | Q8×C53 | — | 4 | 1 | no | — |
| 245 | Q8×C53 | — | 4 | 1 | no | — |
| 246 | D4×C53 | — | 4 | 1 | no | — |
| 247 | D4×C53 | — | 4 | 2 | no | — |
| 248 | D4×C53 | — | 8 | 1 | no | — |
| 249 | D4×C53 | — | 8 | 2 | no | — |
| 250 | C2×C4×C53 | — | 2 | 1 | no | — |
| 251 | C2×C4×C53 | — | 2 | 2 | no | — |
| 252 | C2×C4×C53 | — | 4 | 1 | no | — |
| 253 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 254 | C2×C4×C53 | C22×D4 | 1 | 2 | yes | — |
| 255 | C22⋊D53 | — | 8 | 1 | no | — |
| 256 | C22⋊D53 | — | 8 | 2 | no | — |
| 257 | C22⋊D53 | — | 8 | 2 | no | — |
| 258 | C22⋊D53 | — | 8 | 2 | no | — |
| 259 | C22⋊D53 | — | 8 | 2 | no | — |
| 260 | C2×Dic53 | — | 2 | 1 | no | — |
| 261 | C2×Dic53 | — | 2 | 2 | no | — |
| 262 | C2×Dic53 | #120 | 1 | 1 | yes | characteristic |
| 263 | C2×Dic53 | #120 | 1 | 2 | yes | — |
| 264 | D212 | — | 4 | 1 | no | — |
| 265 | D212 | — | 4 | 2 | no | — |
| 266 | D212 | — | 4 | 1 | no | — |
| 267 | D212 | — | 4 | 1 | no | — |
| 268 | D212 | — | 4 | 2 | no | — |
| 269 | D212 | — | 4 | 2 | no | — |
| 270 | D212 | — | 8 | 1 | no | — |
| 271 | D212 | — | 8 | 2 | no | — |
| 272 | D212 | — | 8 | 2 | no | — |
| 273 | C4×D53 | — | 2 | 2 | no | — |
| 274 | C4×D53 | — | 4 | 2 | no | — |
| 275 | C4×D53 | — | 4 | 4 | no | — |
| 276 | C4×D53 | — | 4 | 2 | no | — |
| 277 | C4×D53 | — | 8 | 2 | no | — |
| 278 | Dic106 | — | 4 | 1 | no | — |
| 279 | Dic106 | — | 4 | 2 | no | — |
| 280 | Dic106 | — | 8 | 1 | no | — |
| 281 | Dic106 | — | 8 | 2 | no | — |
| 282 | C8×C53 | — | 2 | 2 | no | — |
| 283 | C8×C53 | — | 4 | 2 | no | — |
| 284 | #88322 | — | 2 | 2 | no | — |
| 285 | #88322 | — | 4 | 2 | no | — |
| 286 | #18992 | — | 53 | 1 | no | maximal, Sylow |
| 287 | C22×C53 | — | 4 | 1 | no | — |
| 288 | C22×C53 | — | 4 | 2 | no | — |
| 289 | C22×C53 | — | 4 | 2 | no | — |
| 290 | C22×C53 | — | 4 | 2 | no | — |
| 291 | C22×C53 | — | 4 | 2 | no | — |
| 292 | C22×C53 | — | 8 | 4 | no | — |
| 293 | C22×C53 | C2×#120 | 1 | 1 | yes | characteristic |
| 294 | C2×D53 | — | 2 | 2 | no | — |
| 295 | C2×D53 | — | 4 | 1 | no | — |
| 296 | C2×D53 | — | 4 | 2 | no | — |
| 297 | C2×D53 | — | 4 | 2 | no | — |
| 298 | C2×D53 | — | 4 | 2 | no | — |
| 299 | C2×D53 | — | 4 | 2 | no | — |
| 300 | C2×D53 | — | 8 | 4 | no | — |
| 301 | C2×D53 | — | 8 | 8 | no | — |
| 302 | C2×D53 | — | 8 | 8 | no | — |
| 303 | C2×D53 | — | 8 | 4 | no | — |
| 304 | C2×D53 | — | 8 | 1 | no | — |
| 305 | C2×D53 | — | 8 | 2 | no | — |
| 306 | C2×D53 | #453 | 1 | 2 | yes | — |
| 307 | C4×C53 | — | 2 | 1 | no | — |
| 308 | C4×C53 | — | 2 | 2 | no | — |
| 309 | C4×C53 | — | 4 | 1 | no | — |
| 310 | C4×C53 | — | 4 | 2 | no | — |
| 311 | C4×C53 | — | 8 | 1 | no | — |
| 312 | Dic53 | — | 2 | 1 | no | — |
| 313 | Dic53 | — | 2 | 2 | no | — |
| 314 | Dic53 | — | 4 | 1 | no | — |
| 315 | Dic53 | — | 4 | 2 | no | — |
| 316 | C2×H(3,𝔽4) | — | 53 | 1 | no | — |
| 317 | #3213 | — | 53 | 2 | no | — |
| 318 | #3153 | — | 53 | 1 | no | — |
| 319 | #1659 | — | 53 | 1 | no | — |
| 320 | #1659 | — | 53 | 2 | no | — |
| 321 | #1659 | D53 | 1 | 1 | yes | characteristic, complemented |
| 322 | #1655 | — | 53 | 1 | no | — |
| 323 | #1655 | — | 53 | 2 | no | — |
| 324 | #1655 | — | 53 | 1 | no | — |
| 325 | #1533 | — | 53 | 1 | no | — |
| 326 | #1527 | — | 53 | 2 | no | — |
| 327 | C2×C53 | — | 8 | 1 | no | — |
| 328 | C2×C53 | — | 8 | 2 | no | — |
| 329 | C2×C53 | C2×#453 | 1 | 1 | yes | characteristic |
| 330 | C2×C53 | #3019 | 1 | 2 | yes | — |
| 331 | D53 | — | 2 | 2 | no | — |
| 332 | D53 | — | 8 | 1 | no | — |
| 333 | D53 | — | 8 | 2 | no | — |
| 334 | D53 | — | 16 | 1 | no | — |
| 335 | C2×#137 | — | 106 | 1 | no | — |
| 336 | C2×AGL(1,ℤ/8) | — | 106 | 1 | no | — |
| 337 | H(3,𝔽4) | — | 53 | 1 | no | — |
| 338 | H(3,𝔽4) | — | 53 | 2 | no | — |
| 339 | H(3,𝔽4) | — | 106 | 2 | no | — |
| 340 | H(3,𝔽4) | — | 106 | 1 | no | — |
| 341 | H(3,𝔽4) | — | 106 | 2 | no | — |
| 342 | H(3,𝔽4) | — | 106 | 1 | no | — |
| 343 | H(3,𝔽4) | C2×D53 | 1 | 1 | yes | characteristic |
| 344 | #532 | — | 53 | 1 | no | — |
| 345 | C2×#124 | — | 53 | 1 | no | — |
| 346 | C2×#124 | — | 53 | 2 | no | — |
| 347 | C2×#124 | — | 106 | 2 | no | — |
| 348 | C2×#124 | — | 106 | 1 | no | — |
| 349 | C2×#120 | — | 106 | 2 | no | — |
| 350 | C2×#120 | — | 106 | 1 | no | — |
| 351 | #497 | — | 53 | 1 | no | — |
| 352 | #497 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 353 | #496 | — | 53 | 1 | no | — |
| 354 | #496 | — | 53 | 2 | no | — |
| 355 | #496 | — | 53 | 1 | no | — |
| 356 | #496 | — | 53 | 2 | no | — |
| 357 | #495 | — | 106 | 1 | no | — |
| 358 | #495 | — | 106 | 1 | no | — |
| 359 | #489 | — | 53 | 2 | no | — |
| 360 | #489 | C2×D53 | 1 | 2 | yes | complemented |
| 361 | #463 | — | 106 | 2 | no | — |
| 362 | #463 | — | 106 | 2 | no | — |
| 363 | #448 | — | 106 | 2 | no | — |
| 364 | #447 | — | 106 | 2 | no | — |
| 365 | #432 | — | 53 | 2 | no | — |
| 366 | C4×M16 | — | 53 | 1 | no | — |
| 367 | #329 | — | 53 | 2 | no | — |
| 368 | #329 | — | 53 | 1 | no | — |
| 369 | #329 | — | 53 | 2 | no | — |
| 370 | #329 | — | 53 | 2 | no | — |
| 371 | #329 | — | 53 | 2 | no | — |
| 372 | #329 | C2×D53 | 1 | 2 | yes | complemented |
| 373 | #329 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 374 | C53 | #18992 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 375 | C25 | — | 106 | 1 | no | — |
| 376 | C2×#41 | — | 106 | 1 | no | — |
| 377 | C22×Q8 | — | 53 | 2 | no | — |
| 378 | C22×Q8 | — | 53 | 1 | no | — |
| 379 | C22×D4 | — | 53 | 2 | no | — |
| 380 | C22×D4 | — | 53 | 1 | no | — |
| 381 | C22×D4 | — | 106 | 1 | no | — |
| 382 | C22×D4 | — | 106 | 2 | no | — |
| 383 | #137 | — | 212 | 4 | no | — |
| 384 | AGL(1,ℤ/8) | — | 212 | 4 | no | — |
| 385 | C2×Q16 | — | 2 | 1 | no | — |
| 386 | C2×Q16 | — | 106 | 1 | no | — |
| 387 | C2×SD16 | — | 2 | 1 | no | — |
| 388 | C2×SD16 | — | 106 | 2 | no | — |
| 389 | C2×SD16 | — | 106 | 1 | no | — |
| 390 | C2×SD16 | — | 106 | 2 | no | — |
| 391 | C2×SD16 | — | 106 | 1 | no | — |
| 392 | C2×SD16 | — | 106 | 1 | no | — |
| 393 | C2×D8 | — | 106 | 2 | no | — |
| 394 | C2×D8 | — | 106 | 1 | no | — |
| 395 | C2×D8 | — | 106 | 2 | no | — |
| 396 | C2×D8 | — | 106 | 1 | no | — |
| 397 | C2×M16 | — | 106 | 1 | no | — |
| 398 | C4⋊Q8 | C22×D53 | 1 | 1 | yes | characteristic, complemented |
| 399 | #127 | — | 53 | 1 | no | — |
| 400 | #124 | — | 2 | 2 | no | — |
| 401 | #124 | — | 2 | 1 | no | — |
| 402 | #124 | — | 53 | 2 | no | — |
| 403 | #124 | — | 53 | 1 | no | — |
| 404 | #124 | — | 53 | 2 | no | — |
| 405 | #124 | — | 53 | 1 | no | — |
| 406 | #124 | — | 53 | 2 | no | — |
| 407 | #124 | — | 53 | 1 | no | — |
| 408 | #124 | — | 106 | 2 | no | — |
| 409 | #124 | — | 106 | 1 | no | — |
| 410 | #124 | — | 106 | 2 | no | — |
| 411 | #124 | — | 106 | 2 | no | — |
| 412 | #124 | — | 106 | 2 | no | — |
| 413 | #124 | — | 106 | 1 | no | — |
| 414 | #124 | — | 106 | 2 | no | — |
| 415 | #124 | — | 106 | 2 | no | — |
| 416 | #124 | — | 106 | 2 | no | — |
| 417 | #124 | — | 106 | 2 | no | — |
| 418 | #124 | — | 106 | 2 | no | — |
| 419 | #124 | — | 106 | 2 | no | — |
| 420 | #124 | — | 106 | 2 | no | — |
| 421 | #124 | — | 106 | 1 | no | — |
| 422 | #124 | — | 106 | 2 | no | — |
| 423 | #124 | — | 106 | 1 | no | — |
| 424 | #124 | C22×D53 | 1 | 2 | yes | — |
| 425 | #124 | C22×D53 | 1 | 1 | yes | characteristic |
| 426 | #121 | — | 106 | 2 | no | — |
| 427 | #120 | — | 2 | 2 | no | — |
| 428 | #120 | — | 2 | 1 | no | — |
| 429 | #120 | — | 106 | 2 | no | — |
| 430 | #120 | — | 106 | 2 | no | — |
| 431 | #120 | — | 106 | 2 | no | — |
| 432 | #120 | — | 106 | 2 | no | — |
| 433 | #120 | — | 106 | 1 | no | — |
| 434 | #120 | — | 106 | 2 | no | — |
| 435 | #120 | — | 106 | 2 | no | — |
| 436 | #120 | — | 106 | 2 | no | — |
| 437 | #120 | — | 106 | 2 | no | — |
| 438 | #120 | — | 106 | 1 | no | — |
| 439 | #120 | — | 106 | 2 | no | — |
| 440 | #120 | — | 106 | 1 | no | — |
| 441 | C4×D4 | — | 106 | 2 | no | — |
| 442 | C2×C22⋊C4 | — | 106 | 2 | no | — |
| 443 | C2×C22⋊C4 | — | 106 | 2 | no | — |
| 444 | C2×C22⋊C4 | — | 106 | 2 | no | — |
| 445 | C2×C22⋊C4 | — | 106 | 2 | no | — |
| 446 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 447 | C2×C42 | — | 53 | 1 | no | — |
| 448 | C2×C42 | — | 106 | 1 | no | — |
| 449 | C4⋊C8 | — | 106 | 2 | no | — |
| 450 | #103 | — | 2 | 2 | no | — |
| 451 | #103 | — | 106 | 2 | no | — |
| 452 | #102 | — | 2 | 2 | no | — |
| 453 | #102 | — | 106 | 2 | no | — |
| 454 | C22⋊C8 | — | 106 | 2 | no | — |
| 455 | #97 | — | 53 | 1 | no | — |
| 456 | #97 | — | 53 | 2 | no | — |
| 457 | #97 | C22×D53 | 1 | 1 | yes | characteristic, complemented |
| 458 | #97 | C22×D53 | 1 | 2 | yes | complemented |
| 459 | C4×C8 | — | 106 | 1 | no | — |
| 460 | C24 | — | 2 | 1 | no | — |
| 461 | C24 | — | 106 | 2 | no | — |
| 462 | C24 | — | 106 | 1 | no | — |
| 463 | C24 | — | 106 | 1 | no | — |
| 464 | C24 | — | 106 | 2 | no | — |
| 465 | C24 | — | 424 | 2 | no | — |
| 466 | C24 | — | 424 | 4 | no | — |
| 467 | #41 | — | 212 | 2 | no | — |
| 468 | #41 | — | 212 | 2 | no | — |
| 469 | C2×Q8 | — | 2 | 1 | no | — |
| 470 | C2×Q8 | — | 53 | 2 | no | — |
| 471 | C2×Q8 | — | 53 | 1 | no | — |
| 472 | C2×Q8 | — | 106 | 2 | no | — |
| 473 | C2×Q8 | — | 106 | 1 | no | — |
| 474 | C2×Q8 | — | 424 | 2 | no | — |
| 475 | C2×Q8 | — | 212 | 2 | no | — |
| 476 | C2×Q8 | D4×D53 | 1 | 2 | yes | — |
| 477 | C2×Q8 | D4×D53 | 1 | 1 | yes | characteristic |
| 478 | C2×D4 | — | 2 | 1 | no | — |
| 479 | C2×D4 | — | 2 | 2 | no | — |
| 480 | C2×D4 | — | 53 | 2 | no | — |
| 481 | C2×D4 | — | 53 | 1 | no | — |
| 482 | C2×D4 | — | 106 | 1 | no | — |
| 483 | C2×D4 | — | 106 | 2 | no | — |
| 484 | C2×D4 | — | 106 | 2 | no | — |
| 485 | C2×D4 | — | 106 | 1 | no | — |
| 486 | C2×D4 | — | 106 | 2 | no | — |
| 487 | C2×D4 | — | 106 | 2 | no | — |
| 488 | C2×D4 | — | 106 | 2 | no | — |
| 489 | C2×D4 | — | 106 | 2 | no | — |
| 490 | C2×D4 | — | 106 | 1 | no | — |
| 491 | C2×D4 | — | 424 | 2 | no | — |
| 492 | C2×D4 | — | 424 | 2 | no | — |
| 493 | C2×D4 | — | 424 | 4 | no | — |
| 494 | C2×D4 | — | 212 | 1 | no | — |
| 495 | C2×D4 | — | 212 | 2 | no | — |
| 496 | C2×D4 | D4×D53 | 1 | 2 | yes | — |
| 497 | C2×D4 | D4×D53 | 1 | 1 | yes | characteristic |
| 498 | C22×C4 | — | 53 | 1 | no | — |
| 499 | C22×C4 | — | 53 | 2 | no | — |
| 500 | C22×C4 | — | 106 | 1 | no | — |
| 501 | C22×C4 | — | 106 | 2 | no | — |
| 502 | C22×C4 | — | 212 | 1 | no | — |
| 503 | Q16 | — | 4 | 2 | no | — |
| 504 | Q16 | — | 212 | 2 | no | — |
| 505 | SD16 | — | 4 | 2 | no | — |
| 506 | SD16 | — | 424 | 2 | no | — |
| 507 | SD16 | — | 424 | 2 | no | — |
| 508 | SD16 | — | 212 | 2 | no | — |
| 509 | SD16 | — | 212 | 2 | no | — |
| 510 | SD16 | — | 212 | 2 | no | — |
| 511 | D8 | — | 424 | 2 | no | — |
| 512 | D8 | — | 424 | 2 | no | — |
| 513 | D8 | — | 212 | 2 | no | — |
| 514 | D8 | — | 212 | 2 | no | — |
| 515 | M16 | — | 106 | 4 | no | — |
| 516 | C2×C8 | — | 2 | 1 | no | — |
| 517 | C2×C8 | — | 2 | 2 | no | — |
| 518 | C2×C8 | — | 106 | 1 | no | — |
| 519 | C2×C8 | — | 106 | 2 | no | — |
| 520 | C4⋊C4 | — | 2 | 2 | no | — |
| 521 | C22⋊C4 | — | 2 | 2 | no | — |
| 522 | C22⋊C4 | — | 2 | 1 | no | — |
| 523 | C22⋊C4 | — | 2 | 2 | no | — |
| 524 | C22⋊C4 | — | 2 | 2 | no | — |
| 525 | C22⋊C4 | — | 2 | 2 | no | — |
| 526 | C22⋊C4 | — | 106 | 2 | no | — |
| 527 | C22⋊C4 | — | 106 | 2 | no | — |
| 528 | C22⋊C4 | — | 106 | 2 | no | — |
| 529 | C22⋊C4 | — | 106 | 2 | no | — |
| 530 | C22⋊C4 | — | 106 | 2 | no | — |
| 531 | C22⋊C4 | — | 106 | 2 | no | — |
| 532 | C22⋊C4 | — | 106 | 2 | no | — |
| 533 | C22⋊C4 | — | 106 | 2 | no | — |
| 534 | C22⋊C4 | — | 106 | 2 | no | — |
| 535 | C22⋊C4 | — | 106 | 2 | no | — |
| 536 | C22⋊C4 | — | 106 | 1 | no | — |
| 537 | C22⋊C4 | — | 106 | 2 | no | — |
| 538 | C22⋊C4 | — | 106 | 2 | no | — |
| 539 | C22⋊C4 | — | 106 | 2 | no | — |
| 540 | C22⋊C4 | — | 212 | 2 | no | — |
| 541 | C42 | — | 2 | 1 | no | — |
| 542 | C42 | — | 53 | 1 | no | — |
| 543 | C42 | — | 53 | 2 | no | — |
| 544 | C42 | — | 106 | 1 | no | — |
| 545 | C42 | — | 106 | 2 | no | — |
| 546 | C42 | C23×D53 | 1 | 1 | yes | characteristic |
| 547 | C23 | — | 2 | 1 | no | — |
| 548 | C23 | — | 2 | 2 | no | — |
| 549 | C23 | — | 8 | 1 | no | — |
| 550 | C23 | — | 8 | 2 | no | — |
| 551 | C23 | — | 53 | 1 | no | — |
| 552 | C23 | — | 106 | 2 | no | — |
| 553 | C23 | — | 106 | 1 | no | — |
| 554 | C23 | — | 424 | 1 | no | — |
| 555 | C23 | — | 424 | 2 | no | — |
| 556 | C23 | — | 424 | 2 | no | — |
| 557 | C23 | — | 424 | 2 | no | — |
| 558 | C23 | — | 424 | 2 | no | — |
| 559 | C23 | — | 424 | 16 | no | — |
| 560 | C23 | — | 212 | 4 | no | — |
| 561 | C23 | — | 212 | 2 | no | — |
| 562 | C23 | — | 212 | 4 | no | — |
| 563 | C23 | — | 212 | 4 | no | — |
| 564 | C23 | — | 212 | 4 | no | — |
| 565 | C23 | — | 212 | 1 | no | — |
| 566 | Q8 | — | 4 | 2 | no | — |
| 567 | Q8 | — | 4 | 1 | no | — |
| 568 | Q8 | — | 4 | 1 | no | — |
| 569 | Q8 | — | 4 | 1 | no | — |
| 570 | Q8 | — | 424 | 2 | no | — |
| 571 | Q8 | — | 424 | 1 | no | — |
| 572 | Q8 | — | 212 | 2 | no | — |
| 573 | Q8 | — | 212 | 1 | no | — |
| 574 | D4 | — | 4 | 2 | no | — |
| 575 | D4 | — | 4 | 1 | no | — |
| 576 | D4 | — | 8 | 1 | no | — |
| 577 | D4 | — | 8 | 2 | no | — |
| 578 | D4 | — | 424 | 1 | no | — |
| 579 | D4 | — | 424 | 2 | no | — |
| 580 | D4 | — | 424 | 2 | no | — |
| 581 | D4 | — | 424 | 2 | no | — |
| 582 | D4 | — | 424 | 1 | no | — |
| 583 | D4 | — | 424 | 2 | no | — |
| 584 | D4 | — | 424 | 2 | no | — |
| 585 | D4 | — | 424 | 2 | no | — |
| 586 | D4 | — | 212 | 2 | no | — |
| 587 | D4 | — | 212 | 2 | no | — |
| 588 | D4 | — | 212 | 1 | no | — |
| 589 | D4 | — | 212 | 1 | no | — |
| 590 | D4 | — | 212 | 2 | no | — |
| 591 | D4 | — | 212 | 1 | no | — |
| 592 | C2×C4 | — | 2 | 1 | no | — |
| 593 | C2×C4 | — | 2 | 2 | no | — |
| 594 | C2×C4 | — | 4 | 1 | no | — |
| 595 | C2×C4 | — | 53 | 2 | no | — |
| 596 | C2×C4 | — | 53 | 1 | no | — |
| 597 | C2×C4 | — | 106 | 2 | no | — |
| 598 | C2×C4 | — | 106 | 1 | no | — |
| 599 | C2×C4 | — | 106 | 2 | no | — |
| 600 | C2×C4 | — | 424 | 2 | no | — |
| 601 | C2×C4 | — | 212 | 2 | no | — |
| 602 | C2×C4 | — | 212 | 2 | no | — |
| 603 | C2×C4 | — | 212 | 4 | no | — |
| 604 | C2×C4 | C2×D4×D53 | 1 | 2 | yes | — |
| 605 | C2×C4 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 606 | C8 | — | 2 | 2 | no | — |
| 607 | C8 | — | 4 | 2 | no | — |
| 608 | C8 | — | 106 | 2 | no | — |
| 609 | C8 | — | 212 | 2 | no | — |
| 610 | C22 | — | 4 | 1 | no | — |
| 611 | C22 | — | 4 | 2 | no | — |
| 612 | C22 | — | 4 | 2 | no | — |
| 613 | C22 | — | 4 | 2 | no | — |
| 614 | C22 | — | 4 | 2 | no | — |
| 615 | C22 | — | 8 | 4 | no | — |
| 616 | C22 | — | 53 | 2 | no | — |
| 617 | C22 | — | 106 | 2 | no | — |
| 618 | C22 | — | 424 | 8 | no | — |
| 619 | C22 | — | 424 | 4 | no | — |
| 620 | C22 | — | 424 | 4 | no | — |
| 621 | C22 | — | 424 | 8 | no | — |
| 622 | C22 | — | 424 | 1 | no | — |
| 623 | C22 | — | 424 | 2 | no | — |
| 624 | C22 | — | 212 | 2 | no | — |
| 625 | C22 | — | 212 | 1 | no | — |
| 626 | C22 | — | 212 | 2 | no | — |
| 627 | C22 | — | 212 | 2 | no | — |
| 628 | C22 | — | 212 | 2 | no | — |
| 629 | C22 | #120×D53 | 1 | 1 | yes | characteristic |
| 630 | C4 | — | 2 | 1 | no | — |
| 631 | C4 | — | 2 | 2 | no | — |
| 632 | C4 | — | 4 | 1 | no | — |
| 633 | C4 | — | 4 | 2 | no | — |
| 634 | C4 | — | 8 | 1 | no | — |
| 635 | C4 | — | 106 | 1 | no | — |
| 636 | C4 | — | 106 | 2 | no | — |
| 637 | C4 | — | 212 | 1 | no | — |
| 638 | C4 | — | 212 | 2 | no | — |
| 639 | C2 | — | 8 | 1 | no | — |
| 640 | C2 | — | 8 | 2 | no | — |
| 641 | C2 | — | 848 | 1 | no | — |
| 642 | C2 | — | 106 | 2 | no | — |
| 643 | C2 | — | 424 | 2 | no | — |
| 644 | C2 | — | 424 | 1 | no | — |
| 645 | C2 | #453×D53 | 1 | 1 | yes | characteristic |
| 646 | C2 | #20284073 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. H(3,𝔽4)×D53 | C2 | semidirect |
| 2. #20285703 | C2 | semidirect |
| 3. #20285178 | C2 | semidirect |
| 4. #20274020 | C2 | semidirect |
| 5. #20274019 | C2 | semidirect |
| 6. #20274005 | C2 | semidirect |
| 7. #20274005 | C2 | semidirect |
| 8. #20274004 | C2 | semidirect |
| 9. #20273337 | C2 | semidirect |
| 10. #20273311 | C2 | semidirect |
| 11. C53×#1659 | C2 | semidirect |
| 20. #16811174 | C22 | semidirect |
| 27. #16811015 | C22 | semidirect |
| 28. #16811013 | C22 | semidirect |
| 29. #16811013 | C22 | semidirect |
| 30. #16811012 | C22 | semidirect |
| 31. #16811012 | C22 | semidirect |
| 34. #16810985 | C22 | semidirect |
| 39. #16810678 | C22 | semidirect |
| 40. #16810575 | C22 | semidirect |
| 41. #16810363 | C22 | semidirect |
| 42. #16810363 | C22 | semidirect |
| 43. #16810362 | C22 | semidirect |
| 44. #16810362 | C22 | semidirect |
| 45. #16810362 | C22 | semidirect |
| 47. C53×#497 | C22 | semidirect |
| 48. C53×#489 | C22 | semidirect |
| 49. C53×#329 | C22 | semidirect |
| 50. C53×#329 | C22 | semidirect |
| 72. #13133214 | C23 | semidirect |
| 120. #13133128 | C23 | semidirect |
| 121. #13133128 | C23 | semidirect |
| 125. C4⋊Q8×C53 | C23 | semidirect |
| 134. #97×C53 | C23 | semidirect |
| 135. #97×C53 | C23 | semidirect |
| 321. #1659 | D53 | semidirect |
| 352. #497 | C2×D53 | semidirect |
| 360. #489 | C2×D53 | semidirect |
| 372. #329 | C2×D53 | semidirect |
| 373. #329 | C2×D53 | semidirect |
| 374. C53 | #18992 | semidirect |
| 398. C4⋊Q8 | C22×D53 | semidirect |
| 457. #97 | C22×D53 | semidirect |
| 458. #97 | C22×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(3,𝔽4)×D53 | 2 |
| #20285703 | 2 |
| #20285178 | 2 |
| #20274020 | 2 |
| #20274019 | 2 |
| #20274005 | 2 |
| #20274004 | 2 |
| #20273337 | 2 |
| #20273311 | 2 |
| C53×#1659 | 2 |
| #18992 | 53 |