Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1110 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 1110 conjugacy classes of subgroups — too many to draw. Only its 151 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 | #20289072 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #20284079 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #20276739 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #20276735 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #20276731 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #20276402 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | C2×#16810420 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×C53×#454 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #16811421 | — | 2 | 2 | no | — |
| 10 | #16811373 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | #16811367 | — | 2 | 1 | no | — |
| 12 | #16811365 | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | #16811335 | C22 | 1 | 2 | yes | complemented |
| 14 | #16811303 | — | 2 | 1 | no | — |
| 15 | #16811299 | — | 2 | 2 | no | — |
| 16 | #16811263 | — | 2 | 2 | no | — |
| 17 | #16811237 | — | 2 | 2 | no | — |
| 18 | #16811207 | — | 2 | 2 | no | — |
| 19 | #16811197 | C22 | 1 | 2 | yes | — |
| 20 | #16811182 | — | 2 | 1 | no | — |
| 21 | #16811157 | — | 2 | 1 | no | — |
| 22 | #16810806 | — | 2 | 2 | no | — |
| 23 | #16810806 | C22 | 1 | 4 | yes | complemented |
| 24 | #16810796 | — | 2 | 2 | no | — |
| 25 | #16810796 | C22 | 1 | 4 | yes | complemented |
| 26 | #16810640 | — | 2 | 2 | no | — |
| 27 | C2×#13133136 | C22 | 1 | 2 | yes | complemented |
| 28 | #16810421 | C22 | 1 | 4 | yes | complemented |
| 29 | #16810420 | C22 | 1 | 2 | yes | complemented |
| 30 | #16810420 | C22 | 1 | 2 | yes | complemented |
| 31 | #16810419 | C22 | 1 | 4 | yes | complemented |
| 32 | C2×2−1+4×C53 | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | C2×AGL(1,ℤ/8)×C53 | — | 2 | 1 | no | — |
| 34 | C2×#124×C53 | C22 | 1 | 1 | yes | characteristic |
| 35 | C53×#454 | — | 2 | 1 | no | — |
| 36 | C53×#454 | — | 2 | 1 | no | — |
| 37 | C53×#454 | C22 | 1 | 2 | yes | — |
| 38 | C53×#454 | C22 | 1 | 2 | yes | complemented |
| 39 | C2×#104×C53 | — | 2 | 1 | no | — |
| 40 | C2×#101×C53 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | C2×#11719945 | D4 | 1 | 2 | yes | — |
| 42 | C22×C22⋊D53 | — | 2 | 1 | no | — |
| 43 | #13133248 | — | 4 | 2 | no | — |
| 44 | #13133247 | — | 2 | 4 | no | — |
| 45 | #13133243 | — | 4 | 2 | no | — |
| 46 | #13133242 | — | 2 | 4 | no | — |
| 47 | #13133237 | — | 4 | 4 | no | — |
| 48 | C2×#11719917 | — | 2 | 2 | no | — |
| 49 | #13133215 | D4 | 1 | 2 | yes | — |
| 50 | #13133215 | C23 | 1 | 2 | yes | — |
| 51 | #13133211 | — | 2 | 2 | no | — |
| 52 | #13133210 | — | 2 | 2 | no | — |
| 53 | #13133210 | — | 2 | 2 | no | — |
| 54 | #13133209 | — | 2 | 1 | no | — |
| 55 | #13133206 | D4 | 1 | 2 | yes | — |
| 56 | #13133206 | C23 | 1 | 2 | yes | — |
| 57 | #13133205 | — | 2 | 1 | no | — |
| 58 | #13133203 | — | 2 | 2 | no | — |
| 59 | #13133203 | — | 2 | 2 | no | — |
| 60 | #13133201 | — | 2 | 2 | no | — |
| 61 | #13133200 | — | 2 | 2 | no | — |
| 62 | #13133200 | — | 2 | 2 | no | — |
| 63 | #13133199 | — | 2 | 2 | no | — |
| 64 | #13133199 | — | 2 | 2 | no | — |
| 65 | #13133198 | — | 2 | 1 | no | — |
| 66 | #13133198 | — | 2 | 1 | no | — |
| 67 | #13133196 | — | 2 | 1 | no | — |
| 68 | #13133194 | — | 2 | 2 | no | — |
| 69 | #13133194 | — | 2 | 2 | no | — |
| 70 | #13133193 | — | 2 | 2 | no | — |
| 71 | #13133193 | — | 2 | 2 | no | — |
| 72 | #13133191 | — | 2 | 1 | no | — |
| 73 | #13133190 | — | 2 | 2 | no | — |
| 74 | #13133190 | — | 2 | 2 | no | — |
| 75 | #13133189 | — | 2 | 2 | no | — |
| 76 | #13133189 | — | 2 | 2 | no | — |
| 77 | #13133187 | — | 2 | 2 | no | — |
| 78 | #13133186 | — | 2 | 2 | no | — |
| 79 | #13133185 | — | 2 | 1 | no | — |
| 80 | #13133185 | — | 2 | 1 | no | — |
| 81 | C4×Dic106 | — | 2 | 1 | no | — |
| 82 | C4×D212 | — | 2 | 1 | no | — |
| 83 | C4×C22⋊D53 | — | 2 | 2 | no | — |
| 84 | #13133177 | — | 2 | 2 | no | — |
| 85 | #13133177 | — | 2 | 2 | no | — |
| 86 | #13133176 | D4 | 1 | 2 | yes | — |
| 87 | #13133174 | — | 2 | 2 | no | — |
| 88 | #13133173 | — | 2 | 2 | no | — |
| 89 | C2×C22⋊Dic53 | — | 2 | 1 | no | — |
| 90 | C22⋊C4×D53 | — | 2 | 2 | no | — |
| 91 | #13133144 | — | 2 | 4 | no | — |
| 92 | #13133144 | — | 2 | 4 | no | — |
| 93 | #13133136 | — | 2 | 2 | no | — |
| 94 | #13133136 | C23 | 1 | 4 | yes | — |
| 95 | 2−1+4×C53 | — | 2 | 2 | no | — |
| 96 | 2−1+4×C53 | — | 2 | 1 | no | — |
| 97 | 2−1+4×C53 | — | 4 | 2 | no | — |
| 98 | 2−1+4×C53 | C23 | 1 | 2 | yes | — |
| 99 | C2×#41×C53 | — | 2 | 1 | no | — |
| 100 | C2×#41×C53 | — | 2 | 2 | no | — |
| 101 | C2×#41×C53 | — | 4 | 1 | no | — |
| 102 | C22×Q8×C53 | — | 4 | 1 | no | — |
| 103 | C22×Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 104 | C22×D4×C53 | D4 | 1 | 1 | yes | characteristic |
| 105 | AGL(1,ℤ/8)×C53 | — | 2 | 2 | no | — |
| 106 | AGL(1,ℤ/8)×C53 | — | 2 | 2 | no | — |
| 107 | AGL(1,ℤ/8)×C53 | — | 4 | 2 | no | — |
| 108 | C2×SD16×C53 | — | 4 | 1 | no | — |
| 109 | C2×D8×C53 | — | 4 | 1 | no | — |
| 110 | C2×M16×C53 | — | 2 | 1 | no | — |
| 111 | #124×C53 | — | 2 | 2 | no | — |
| 112 | #124×C53 | D4 | 1 | 1 | yes | characteristic |
| 113 | #124×C53 | D4 | 1 | 1 | yes | characteristic |
| 114 | #124×C53 | C23 | 1 | 1 | yes | characteristic |
| 115 | #124×C53 | C23 | 1 | 1 | yes | characteristic |
| 116 | C2×C22⋊C4×C53 | — | 2 | 2 | no | — |
| 117 | C2×C42×C53 | D4 | 1 | 1 | yes | characteristic |
| 118 | #104×C53 | — | 2 | 2 | no | — |
| 119 | #104×C53 | — | 2 | 2 | no | — |
| 120 | #101×C53 | — | 2 | 1 | no | — |
| 121 | #101×C53 | C23 | 1 | 2 | yes | — |
| 122 | C24×C53 | — | 2 | 1 | no | — |
| 123 | C23×D53 | — | 2 | 1 | no | — |
| 124 | #41×C53 | — | 2 | 2 | no | — |
| 125 | #41×C53 | — | 2 | 4 | no | — |
| 126 | #41×C53 | — | 2 | 2 | no | — |
| 127 | #41×C53 | — | 2 | 4 | no | — |
| 128 | #41×C53 | — | 4 | 2 | no | — |
| 129 | #41×C53 | — | 4 | 1 | no | — |
| 130 | #41×C53 | — | 4 | 2 | no | — |
| 131 | #41×C53 | — | 4 | 4 | no | — |
| 132 | #41×C53 | — | 4 | 2 | no | — |
| 133 | #41×C53 | — | 4 | 2 | no | — |
| 134 | #41×C53 | — | 4 | 1 | no | — |
| 135 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 136 | C2×Q8×C53 | — | 2 | 2 | no | — |
| 137 | C2×Q8×C53 | — | 4 | 1 | no | — |
| 138 | C2×Q8×C53 | — | 4 | 1 | no | — |
| 139 | C2×Q8×C53 | — | 4 | 2 | no | — |
| 140 | C2×Q8×C53 | — | 4 | 4 | no | — |
| 141 | C2×Q8×C53 | — | 4 | 2 | no | — |
| 142 | C2×Q8×C53 | C2×D4 | 1 | 2 | yes | — |
| 143 | C2×Q8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 144 | C2×Q8×C53 | C24 | 1 | 1 | yes | characteristic |
| 145 | C2×D4×C53 | — | 2 | 1 | no | — |
| 146 | C2×D4×C53 | — | 2 | 2 | no | — |
| 147 | C2×D4×C53 | — | 2 | 1 | no | — |
| 148 | C2×D4×C53 | — | 4 | 1 | no | — |
| 149 | C2×D4×C53 | — | 4 | 1 | no | — |
| 150 | C2×D4×C53 | — | 4 | 1 | no | — |
| 151 | C2×D4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 152 | C2×D4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 153 | C22×C4×C53 | — | 2 | 1 | no | — |
| 154 | C22×C4×C53 | — | 4 | 2 | no | — |
| 155 | C22×C4×C53 | — | 4 | 1 | no | — |
| 156 | C22×C4×C53 | C2×D4 | 1 | 2 | yes | — |
| 157 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 158 | C2×C22⋊D53 | — | 2 | 2 | no | — |
| 159 | C2×C22⋊D53 | — | 2 | 2 | no | — |
| 160 | C2×C22⋊D53 | — | 2 | 2 | no | — |
| 161 | C2×C22⋊D53 | — | 2 | 2 | no | — |
| 162 | C2×C22⋊D53 | — | 8 | 1 | no | — |
| 163 | C2×C22⋊D53 | — | 8 | 1 | no | — |
| 164 | C22×Dic53 | — | 2 | 2 | no | — |
| 165 | C22×Dic53 | — | 2 | 1 | no | — |
| 166 | #11719945 | — | 4 | 2 | no | — |
| 167 | #11719945 | — | 4 | 2 | no | — |
| 168 | C2×D212 | — | 2 | 1 | no | — |
| 169 | C2×D212 | C2×D4 | 1 | 2 | yes | — |
| 170 | C2×C4×D53 | — | 2 | 2 | no | — |
| 171 | C2×C4×D53 | — | 2 | 2 | no | — |
| 172 | C2×Dic106 | — | 2 | 1 | no | — |
| 173 | C2×Dic106 | C2×D4 | 1 | 2 | yes | — |
| 174 | SD16×C53 | — | 4 | 2 | no | — |
| 175 | SD16×C53 | — | 4 | 2 | no | — |
| 176 | D8×C53 | — | 4 | 2 | no | — |
| 177 | D8×C53 | — | 4 | 2 | no | — |
| 178 | M16×C53 | — | 2 | 2 | no | — |
| 179 | M16×C53 | — | 4 | 1 | no | — |
| 180 | C2×C8×C53 | — | 4 | 1 | no | — |
| 181 | C22⋊C4×C53 | — | 2 | 2 | no | — |
| 182 | C22⋊C4×C53 | — | 2 | 2 | no | — |
| 183 | C22⋊C4×C53 | — | 2 | 2 | no | — |
| 184 | C22⋊C4×C53 | — | 2 | 2 | no | — |
| 185 | C42×C53 | — | 2 | 1 | no | — |
| 186 | C42×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 187 | C42×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 188 | C22⋊Dic53 | — | 2 | 2 | no | — |
| 189 | C22⋊Dic53 | — | 2 | 1 | no | — |
| 190 | C22⋊Dic53 | — | 2 | 1 | no | — |
| 191 | C22⋊Dic53 | — | 2 | 2 | no | — |
| 192 | C22⋊Dic53 | — | 2 | 2 | no | — |
| 193 | #11719925 | — | 4 | 4 | no | — |
| 194 | #11719924 | — | 4 | 4 | no | — |
| 195 | #11719923 | — | 4 | 4 | no | — |
| 196 | #11719922 | — | 4 | 4 | no | — |
| 197 | #11719921 | — | 2 | 2 | no | — |
| 198 | #11719921 | — | 2 | 2 | no | — |
| 199 | #11719921 | — | 2 | 2 | no | — |
| 200 | #11719921 | — | 2 | 2 | no | — |
| 201 | #11719921 | — | 2 | 2 | no | — |
| 202 | #11719921 | — | 2 | 2 | no | — |
| 203 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 204 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 205 | C4⋊Dic53 | — | 2 | 2 | no | — |
| 206 | #11719919 | — | 2 | 2 | no | — |
| 207 | #11719919 | — | 2 | 2 | no | — |
| 208 | #11719919 | — | 2 | 2 | no | — |
| 209 | #11719919 | — | 2 | 2 | no | — |
| 210 | #11719919 | — | 2 | 2 | no | — |
| 211 | #11719919 | — | 2 | 2 | no | — |
| 212 | C4×Dic53 | — | 2 | 2 | no | — |
| 213 | C4×Dic53 | C2×D4 | 1 | 2 | yes | — |
| 214 | C4×Dic53 | C2×D4 | 1 | 2 | yes | — |
| 215 | #11719917 | — | 2 | 4 | no | — |
| 216 | #11719917 | — | 4 | 2 | no | — |
| 217 | C2×#88322 | — | 4 | 2 | no | — |
| 218 | C23×C53 | — | 2 | 1 | no | — |
| 219 | C23×C53 | — | 2 | 1 | no | — |
| 220 | C23×C53 | — | 4 | 1 | no | — |
| 221 | C23×C53 | — | 4 | 1 | no | — |
| 222 | C23×C53 | — | 4 | 1 | no | — |
| 223 | C23×C53 | — | 8 | 2 | no | — |
| 224 | C23×C53 | #120 | 1 | 1 | yes | characteristic |
| 225 | C22×D53 | — | 2 | 2 | no | — |
| 226 | C22×D53 | — | 8 | 1 | no | — |
| 227 | C22×D53 | — | 8 | 2 | no | — |
| 228 | Q8×C53 | — | 2 | 4 | no | — |
| 229 | Q8×C53 | — | 2 | 2 | no | — |
| 230 | Q8×C53 | — | 4 | 2 | no | — |
| 231 | Q8×C53 | — | 4 | 1 | no | — |
| 232 | Q8×C53 | — | 4 | 1 | no | — |
| 233 | Q8×C53 | — | 4 | 2 | no | — |
| 234 | Q8×C53 | — | 4 | 1 | no | — |
| 235 | D4×C53 | — | 2 | 4 | no | — |
| 236 | D4×C53 | — | 2 | 2 | no | — |
| 237 | D4×C53 | — | 4 | 1 | no | — |
| 238 | D4×C53 | — | 4 | 1 | no | — |
| 239 | D4×C53 | — | 4 | 2 | no | — |
| 240 | D4×C53 | — | 4 | 1 | no | — |
| 241 | D4×C53 | — | 4 | 2 | no | — |
| 242 | D4×C53 | — | 4 | 2 | no | — |
| 243 | D4×C53 | — | 8 | 1 | no | — |
| 244 | C2×C4×C53 | — | 2 | 2 | no | — |
| 245 | C2×C4×C53 | — | 2 | 2 | no | — |
| 246 | C2×C4×C53 | — | 2 | 1 | no | — |
| 247 | C2×C4×C53 | — | 2 | 1 | no | — |
| 248 | C2×C4×C53 | — | 2 | 1 | no | — |
| 249 | C2×C4×C53 | — | 2 | 1 | no | — |
| 250 | C2×C4×C53 | — | 4 | 4 | no | — |
| 251 | C2×C4×C53 | — | 4 | 2 | no | — |
| 252 | C2×C4×C53 | — | 4 | 4 | no | — |
| 253 | C2×C4×C53 | — | 4 | 2 | no | — |
| 254 | C2×C4×C53 | — | 4 | 1 | no | — |
| 255 | C2×C4×C53 | — | 8 | 1 | no | — |
| 256 | C2×C4×C53 | #120 | 1 | 2 | yes | — |
| 257 | C2×C4×C53 | #120 | 1 | 1 | yes | characteristic |
| 258 | C2×C4×C53 | C22×D4 | 1 | 2 | yes | — |
| 259 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 260 | C22⋊D53 | — | 4 | 2 | no | — |
| 261 | C22⋊D53 | — | 4 | 2 | no | — |
| 262 | C22⋊D53 | — | 8 | 2 | no | — |
| 263 | C22⋊D53 | — | 8 | 2 | no | — |
| 264 | C22⋊D53 | — | 8 | 2 | no | — |
| 265 | C2×Dic53 | — | 2 | 2 | no | — |
| 266 | C2×Dic53 | — | 2 | 2 | no | — |
| 267 | C2×Dic53 | — | 2 | 2 | no | — |
| 268 | C2×Dic53 | — | 8 | 2 | no | — |
| 269 | C2×Dic53 | — | 8 | 1 | no | — |
| 270 | D212 | — | 4 | 2 | no | — |
| 271 | D212 | — | 8 | 1 | no | — |
| 272 | C4×D53 | — | 8 | 2 | no | — |
| 273 | C4×D53 | — | 8 | 2 | no | — |
| 274 | Dic106 | — | 4 | 2 | no | — |
| 275 | Dic106 | — | 8 | 1 | no | — |
| 276 | C8×C53 | — | 4 | 2 | no | — |
| 277 | #88322 | — | 4 | 4 | no | — |
| 278 | #33568 | — | 53 | 1 | no | maximal, Sylow |
| 279 | C22×C53 | — | 4 | 1 | no | — |
| 280 | C22×C53 | — | 4 | 2 | no | — |
| 281 | C22×C53 | — | 4 | 2 | no | — |
| 282 | C22×C53 | — | 4 | 1 | no | — |
| 283 | C22×C53 | — | 4 | 1 | no | — |
| 284 | C22×C53 | — | 4 | 2 | no | — |
| 285 | C22×C53 | — | 8 | 2 | no | — |
| 286 | C22×C53 | — | 16 | 1 | no | — |
| 287 | C22×C53 | — | 16 | 1 | no | — |
| 288 | C22×C53 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 289 | C22×C53 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 290 | C22×C53 | C2×#120 | 1 | 1 | yes | characteristic |
| 291 | C2×D53 | — | 4 | 2 | no | — |
| 292 | C2×D53 | — | 4 | 2 | no | — |
| 293 | C2×D53 | — | 4 | 2 | no | — |
| 294 | C2×D53 | — | 16 | 2 | no | — |
| 295 | C4×C53 | — | 2 | 2 | no | — |
| 296 | C4×C53 | — | 2 | 1 | no | — |
| 297 | C4×C53 | — | 2 | 2 | no | — |
| 298 | C4×C53 | — | 2 | 1 | no | — |
| 299 | C4×C53 | — | 4 | 1 | no | — |
| 300 | C4×C53 | — | 4 | 1 | no | — |
| 301 | C4×C53 | — | 4 | 2 | no | — |
| 302 | Dic53 | — | 4 | 2 | no | — |
| 303 | Dic53 | — | 4 | 2 | no | — |
| 304 | Dic53 | — | 4 | 2 | no | — |
| 305 | #3545 | — | 53 | 1 | no | — |
| 306 | #3020 | — | 53 | 2 | no | — |
| 307 | C2×#454 | D53 | 1 | 1 | yes | characteristic, complemented |
| 308 | #2204 | — | 53 | 4 | no | — |
| 309 | #2203 | — | 53 | 2 | no | — |
| 310 | #2202 | — | 53 | 2 | no | — |
| 311 | #2133 | — | 53 | 2 | no | — |
| 312 | C2×#355 | — | 53 | 1 | no | — |
| 313 | C2×C53 | — | 2 | 1 | no | — |
| 314 | C2×C53 | — | 2 | 1 | no | — |
| 315 | C2×C53 | — | 2 | 1 | no | — |
| 316 | C2×C53 | — | 8 | 1 | no | — |
| 317 | C2×C53 | — | 8 | 1 | no | — |
| 318 | C2×C53 | — | 8 | 2 | no | — |
| 319 | C2×C53 | C2×B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 320 | D53 | — | 8 | 2 | no | — |
| 321 | C2×2−1+4 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 322 | #575 | — | 106 | 2 | no | — |
| 323 | C2×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 324 | #563 | — | 53 | 1 | no | — |
| 325 | #562 | — | 106 | 1 | no | — |
| 326 | H(3,𝔽4) | — | 53 | 1 | no | — |
| 327 | #555 | — | 53 | 2 | no | — |
| 328 | #551 | — | 106 | 2 | no | — |
| 329 | #551 | — | 106 | 1 | no | — |
| 330 | #546 | — | 106 | 2 | no | — |
| 331 | #542 | — | 106 | 2 | no | — |
| 332 | #538 | — | 106 | 2 | no | — |
| 333 | #536 | — | 53 | 2 | no | — |
| 334 | #534 | — | 106 | 1 | no | — |
| 335 | #529 | — | 106 | 1 | no | — |
| 336 | C2×#124 | C2×D53 | 1 | 1 | yes | characteristic |
| 337 | #456 | — | 53 | 4 | no | — |
| 338 | #456 | — | 106 | 2 | no | — |
| 339 | #454 | — | 2 | 1 | no | — |
| 340 | #454 | — | 2 | 1 | no | — |
| 341 | #454 | — | 53 | 4 | no | — |
| 342 | #454 | — | 106 | 2 | no | — |
| 343 | #454 | C2×D53 | 1 | 2 | yes | — |
| 344 | #454 | C2×D53 | 1 | 2 | yes | complemented |
| 345 | #421 | — | 106 | 2 | no | — |
| 346 | C2×#104 | — | 2 | 1 | no | — |
| 347 | C2×#101 | — | 53 | 2 | no | — |
| 348 | C2×#101 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 349 | #356 | — | 53 | 4 | no | — |
| 350 | #355 | — | 53 | 2 | no | — |
| 351 | #355 | — | 53 | 2 | no | — |
| 352 | #355 | — | 53 | 4 | no | — |
| 353 | C53 | #33568 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 354 | 2−1+4 | — | 2 | 2 | no | — |
| 355 | 2−1+4 | — | 2 | 1 | no | — |
| 356 | 2−1+4 | — | 4 | 2 | no | — |
| 357 | 2−1+4 | C22×D53 | 1 | 2 | yes | — |
| 358 | C2×#41 | — | 2 | 2 | no | — |
| 359 | C2×#41 | — | 2 | 1 | no | — |
| 360 | C2×#41 | — | 4 | 1 | no | — |
| 361 | C2×#41 | — | 53 | 2 | no | — |
| 362 | C22×Q8 | — | 4 | 1 | no | — |
| 363 | C22×Q8 | C22×D53 | 1 | 1 | yes | characteristic |
| 364 | C22×D4 | — | 106 | 1 | no | — |
| 365 | C22×D4 | C22⋊D53 | 1 | 1 | yes | characteristic |
| 366 | #137 | — | 106 | 4 | no | — |
| 367 | #137 | — | 212 | 2 | no | — |
| 368 | AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 369 | AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 370 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 371 | AGL(1,ℤ/8) | — | 106 | 4 | no | — |
| 372 | AGL(1,ℤ/8) | — | 212 | 2 | no | — |
| 373 | #135 | — | 212 | 4 | no | — |
| 374 | C2×SD16 | — | 4 | 1 | no | — |
| 375 | C2×D8 | — | 4 | 1 | no | — |
| 376 | C2×M16 | — | 2 | 1 | no | — |
| 377 | C2×M16 | — | 106 | 2 | no | — |
| 378 | C4⋊Q8 | — | 53 | 2 | no | — |
| 379 | C4⋊Q8 | — | 53 | 2 | no | — |
| 380 | #126 | — | 106 | 2 | no | — |
| 381 | #126 | — | 106 | 2 | no | — |
| 382 | #126 | — | 106 | 2 | no | — |
| 383 | #125 | — | 106 | 1 | no | — |
| 384 | #124 | — | 2 | 2 | no | — |
| 385 | #124 | — | 53 | 2 | no | — |
| 386 | #124 | — | 53 | 2 | no | — |
| 387 | #124 | — | 106 | 2 | no | — |
| 388 | #124 | — | 106 | 2 | no | — |
| 389 | #124 | — | 106 | 1 | no | — |
| 390 | #124 | C22⋊D53 | 1 | 1 | yes | characteristic |
| 391 | #124 | C22⋊D53 | 1 | 1 | yes | characteristic |
| 392 | #124 | C22×D53 | 1 | 1 | yes | characteristic |
| 393 | #124 | C22×D53 | 1 | 1 | yes | characteristic |
| 394 | #123 | — | 106 | 2 | no | — |
| 395 | #123 | — | 106 | 2 | no | — |
| 396 | #123 | — | 106 | 2 | no | — |
| 397 | #123 | — | 106 | 1 | no | — |
| 398 | #123 | — | 106 | 1 | no | — |
| 399 | #123 | — | 106 | 2 | no | — |
| 400 | #123 | — | 106 | 2 | no | — |
| 401 | C22⋊Q8 | — | 106 | 2 | no | — |
| 402 | C22⋊Q8 | — | 106 | 2 | no | — |
| 403 | C22⋊Q8 | — | 106 | 1 | no | — |
| 404 | C22⋊Q8 | — | 106 | 2 | no | — |
| 405 | C22⋊Q8 | — | 106 | 2 | no | — |
| 406 | #121 | — | 106 | 2 | no | — |
| 407 | #121 | — | 106 | 2 | no | — |
| 408 | #121 | — | 106 | 1 | no | — |
| 409 | #121 | — | 106 | 2 | no | — |
| 410 | #121 | — | 106 | 2 | no | — |
| 411 | #120 | — | 106 | 2 | no | — |
| 412 | #120 | — | 106 | 1 | no | — |
| 413 | #120 | — | 106 | 2 | no | — |
| 414 | #120 | — | 106 | 1 | no | — |
| 415 | C4×Q8 | — | 106 | 1 | no | — |
| 416 | C4×D4 | — | 106 | 1 | no | — |
| 417 | C4×D4 | — | 106 | 2 | no | — |
| 418 | C4×D4 | — | 106 | 2 | no | — |
| 419 | C4×D4 | — | 106 | 2 | no | — |
| 420 | #117 | — | 53 | 2 | no | — |
| 421 | #117 | — | 106 | 2 | no | — |
| 422 | #117 | — | 106 | 2 | no | — |
| 423 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 424 | C2×C22⋊C4 | — | 106 | 2 | no | — |
| 425 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 426 | C2×C42 | C22⋊D53 | 1 | 1 | yes | characteristic |
| 427 | #104 | — | 2 | 2 | no | — |
| 428 | #104 | — | 2 | 2 | no | — |
| 429 | #104 | — | 106 | 4 | no | — |
| 430 | #104 | — | 106 | 4 | no | — |
| 431 | #101 | — | 2 | 1 | no | — |
| 432 | #101 | — | 53 | 4 | no | — |
| 433 | #101 | — | 106 | 2 | no | — |
| 434 | #101 | C22×D53 | 1 | 2 | yes | — |
| 435 | C24 | — | 2 | 1 | no | — |
| 436 | C24 | — | 106 | 1 | no | — |
| 437 | #41 | — | 2 | 4 | no | — |
| 438 | #41 | — | 2 | 2 | no | — |
| 439 | #41 | — | 2 | 4 | no | — |
| 440 | #41 | — | 2 | 2 | no | — |
| 441 | #41 | — | 4 | 2 | no | — |
| 442 | #41 | — | 4 | 1 | no | — |
| 443 | #41 | — | 4 | 2 | no | — |
| 444 | #41 | — | 4 | 2 | no | — |
| 445 | #41 | — | 4 | 4 | no | — |
| 446 | #41 | — | 4 | 1 | no | — |
| 447 | #41 | — | 4 | 2 | no | — |
| 448 | #41 | — | 212 | 2 | no | — |
| 449 | #41 | — | 212 | 2 | no | — |
| 450 | C2×Q8 | — | 2 | 1 | no | — |
| 451 | C2×Q8 | — | 2 | 2 | no | — |
| 452 | C2×Q8 | — | 4 | 1 | no | — |
| 453 | C2×Q8 | — | 4 | 1 | no | — |
| 454 | C2×Q8 | — | 4 | 2 | no | — |
| 455 | C2×Q8 | — | 4 | 2 | no | — |
| 456 | C2×Q8 | — | 4 | 4 | no | — |
| 457 | C2×Q8 | — | 53 | 2 | no | — |
| 458 | C2×Q8 | — | 106 | 1 | no | — |
| 459 | C2×Q8 | D4×D53 | 1 | 2 | yes | — |
| 460 | C2×Q8 | C2×C22⋊D53 | 1 | 1 | yes | characteristic |
| 461 | C2×Q8 | C23×D53 | 1 | 1 | yes | characteristic |
| 462 | C2×D4 | — | 2 | 1 | no | — |
| 463 | C2×D4 | — | 2 | 2 | no | — |
| 464 | C2×D4 | — | 2 | 1 | no | — |
| 465 | C2×D4 | — | 4 | 1 | no | — |
| 466 | C2×D4 | — | 4 | 1 | no | — |
| 467 | C2×D4 | — | 4 | 1 | no | — |
| 468 | C2×D4 | — | 53 | 2 | no | — |
| 469 | C2×D4 | — | 106 | 1 | no | — |
| 470 | C2×D4 | — | 106 | 2 | no | — |
| 471 | C2×D4 | — | 106 | 2 | no | — |
| 472 | C2×D4 | — | 106 | 2 | no | — |
| 473 | C2×D4 | — | 106 | 2 | no | — |
| 474 | C2×D4 | — | 424 | 1 | no | — |
| 475 | C2×D4 | — | 424 | 1 | no | — |
| 476 | C2×D4 | C2×C22⋊D53 | 1 | 1 | yes | characteristic |
| 477 | C2×D4 | C2×C22⋊D53 | 1 | 1 | yes | characteristic |
| 478 | C22×C4 | — | 2 | 1 | no | — |
| 479 | C22×C4 | — | 4 | 1 | no | — |
| 480 | C22×C4 | — | 4 | 2 | no | — |
| 481 | C22×C4 | — | 106 | 2 | no | — |
| 482 | C22×C4 | — | 106 | 2 | no | — |
| 483 | C22×C4 | — | 106 | 1 | no | — |
| 484 | C22×C4 | — | 106 | 2 | no | — |
| 485 | C22×C4 | D4×D53 | 1 | 2 | yes | — |
| 486 | C22×C4 | C2×C22⋊D53 | 1 | 1 | yes | characteristic |
| 487 | Q16 | — | 212 | 4 | no | — |
| 488 | SD16 | — | 4 | 2 | no | — |
| 489 | SD16 | — | 4 | 2 | no | — |
| 490 | SD16 | — | 212 | 4 | no | — |
| 491 | SD16 | — | 212 | 4 | no | — |
| 492 | D8 | — | 4 | 2 | no | — |
| 493 | D8 | — | 4 | 2 | no | — |
| 494 | D8 | — | 212 | 4 | no | — |
| 495 | M16 | — | 2 | 2 | no | — |
| 496 | M16 | — | 4 | 1 | no | — |
| 497 | M16 | — | 106 | 4 | no | — |
| 498 | M16 | — | 212 | 2 | no | — |
| 499 | C2×C8 | — | 4 | 1 | no | — |
| 500 | C2×C8 | — | 212 | 2 | no | — |
| 501 | C4⋊C4 | — | 106 | 2 | no | — |
| 502 | C4⋊C4 | — | 106 | 2 | no | — |
| 503 | C4⋊C4 | — | 106 | 1 | no | — |
| 504 | C4⋊C4 | — | 106 | 1 | no | — |
| 505 | C4⋊C4 | — | 106 | 2 | no | — |
| 506 | C4⋊C4 | — | 106 | 2 | no | — |
| 507 | C4⋊C4 | — | 106 | 2 | no | — |
| 508 | C4⋊C4 | — | 106 | 2 | no | — |
| 509 | C4⋊C4 | — | 106 | 2 | no | — |
| 510 | C22⋊C4 | — | 2 | 2 | no | — |
| 511 | C22⋊C4 | — | 2 | 2 | no | — |
| 512 | C22⋊C4 | — | 2 | 2 | no | — |
| 513 | C22⋊C4 | — | 2 | 2 | no | — |
| 514 | C22⋊C4 | — | 106 | 2 | no | — |
| 515 | C22⋊C4 | — | 106 | 2 | no | — |
| 516 | C22⋊C4 | — | 106 | 2 | no | — |
| 517 | C22⋊C4 | — | 106 | 1 | no | — |
| 518 | C22⋊C4 | — | 106 | 1 | no | — |
| 519 | C22⋊C4 | — | 106 | 2 | no | — |
| 520 | C22⋊C4 | — | 106 | 2 | no | — |
| 521 | C22⋊C4 | — | 106 | 2 | no | — |
| 522 | C22⋊C4 | — | 106 | 2 | no | — |
| 523 | C22⋊C4 | — | 106 | 2 | no | — |
| 524 | C22⋊C4 | — | 106 | 2 | no | — |
| 525 | C42 | — | 2 | 1 | no | — |
| 526 | C42 | — | 53 | 2 | no | — |
| 527 | C42 | — | 53 | 2 | no | — |
| 528 | C42 | — | 106 | 2 | no | — |
| 529 | C42 | C2×C22⋊D53 | 1 | 1 | yes | characteristic |
| 530 | C42 | C2×C22⋊D53 | 1 | 1 | yes | characteristic |
| 531 | C23 | — | 2 | 1 | no | — |
| 532 | C23 | — | 2 | 1 | no | — |
| 533 | C23 | — | 4 | 1 | no | — |
| 534 | C23 | — | 4 | 1 | no | — |
| 535 | C23 | — | 4 | 1 | no | — |
| 536 | C23 | — | 8 | 2 | no | — |
| 537 | C23 | — | 106 | 2 | no | — |
| 538 | C23 | — | 424 | 1 | no | — |
| 539 | C23 | — | 424 | 2 | no | — |
| 540 | C23 | #13133185 | 1 | 1 | yes | characteristic |
| 541 | Q8 | — | 2 | 2 | no | — |
| 542 | Q8 | — | 2 | 4 | no | — |
| 543 | Q8 | — | 4 | 2 | no | — |
| 544 | Q8 | — | 4 | 1 | no | — |
| 545 | Q8 | — | 4 | 1 | no | — |
| 546 | Q8 | — | 4 | 2 | no | — |
| 547 | Q8 | — | 4 | 1 | no | — |
| 548 | Q8 | — | 424 | 1 | no | — |
| 549 | Q8 | — | 212 | 2 | no | — |
| 550 | D4 | — | 2 | 2 | no | — |
| 551 | D4 | — | 2 | 4 | no | — |
| 552 | D4 | — | 4 | 1 | no | — |
| 553 | D4 | — | 4 | 1 | no | — |
| 554 | D4 | — | 4 | 2 | no | — |
| 555 | D4 | — | 4 | 1 | no | — |
| 556 | D4 | — | 4 | 2 | no | — |
| 557 | D4 | — | 4 | 2 | no | — |
| 558 | D4 | — | 8 | 1 | no | — |
| 559 | D4 | — | 424 | 1 | no | — |
| 560 | D4 | — | 424 | 2 | no | — |
| 561 | D4 | — | 424 | 2 | no | — |
| 562 | D4 | — | 424 | 2 | no | — |
| 563 | D4 | — | 212 | 2 | no | — |
| 564 | D4 | — | 212 | 2 | no | — |
| 565 | D4 | — | 212 | 2 | no | — |
| 566 | C2×C4 | — | 2 | 1 | no | — |
| 567 | C2×C4 | — | 2 | 2 | no | — |
| 568 | C2×C4 | — | 2 | 1 | no | — |
| 569 | C2×C4 | — | 2 | 2 | no | — |
| 570 | C2×C4 | — | 2 | 1 | no | — |
| 571 | C2×C4 | — | 2 | 1 | no | — |
| 572 | C2×C4 | — | 4 | 2 | no | — |
| 573 | C2×C4 | — | 4 | 4 | no | — |
| 574 | C2×C4 | — | 4 | 4 | no | — |
| 575 | C2×C4 | — | 4 | 2 | no | — |
| 576 | C2×C4 | — | 4 | 1 | no | — |
| 577 | C2×C4 | — | 8 | 1 | no | — |
| 578 | C2×C4 | — | 106 | 2 | no | — |
| 579 | C2×C4 | — | 106 | 2 | no | — |
| 580 | C2×C4 | — | 106 | 2 | no | — |
| 581 | C2×C4 | — | 424 | 2 | no | — |
| 582 | C2×C4 | — | 424 | 2 | no | — |
| 583 | C2×C4 | — | 424 | 2 | no | — |
| 584 | C2×C4 | — | 424 | 1 | no | — |
| 585 | C2×C4 | #13133185 | 1 | 1 | yes | characteristic |
| 586 | C2×C4 | #13133185 | 1 | 2 | yes | — |
| 587 | C2×C4 | C2×D4×D53 | 1 | 2 | yes | — |
| 588 | C2×C4 | C22×C22⋊D53 | 1 | 1 | yes | characteristic |
| 589 | C8 | — | 4 | 2 | no | — |
| 590 | C8 | — | 212 | 4 | no | — |
| 591 | C22 | — | 4 | 1 | no | — |
| 592 | C22 | — | 4 | 2 | no | — |
| 593 | C22 | — | 4 | 2 | no | — |
| 594 | C22 | — | 4 | 2 | no | — |
| 595 | C22 | — | 4 | 1 | no | — |
| 596 | C22 | — | 4 | 1 | no | — |
| 597 | C22 | — | 8 | 2 | no | — |
| 598 | C22 | — | 16 | 1 | no | — |
| 599 | C22 | — | 16 | 1 | no | — |
| 600 | C22 | — | 848 | 2 | no | — |
| 601 | C22 | — | 212 | 2 | no | — |
| 602 | C22 | — | 212 | 2 | no | — |
| 603 | C22 | — | 212 | 2 | no | — |
| 604 | C22 | #16810809 | 1 | 1 | yes | characteristic |
| 605 | C22 | #16810809 | 1 | 1 | yes | characteristic |
| 606 | C22 | C2×#13133185 | 1 | 1 | yes | characteristic |
| 607 | C4 | — | 2 | 1 | no | — |
| 608 | C4 | — | 2 | 2 | no | — |
| 609 | C4 | — | 2 | 2 | no | — |
| 610 | C4 | — | 2 | 1 | no | — |
| 611 | C4 | — | 4 | 1 | no | — |
| 612 | C4 | — | 4 | 1 | no | — |
| 613 | C4 | — | 4 | 2 | no | — |
| 614 | C4 | — | 212 | 2 | no | — |
| 615 | C4 | — | 212 | 2 | no | — |
| 616 | C4 | — | 212 | 2 | no | — |
| 617 | C2 | — | 2 | 1 | no | — |
| 618 | C2 | — | 2 | 1 | no | — |
| 619 | C2 | — | 2 | 1 | no | — |
| 620 | C2 | — | 8 | 1 | no | — |
| 621 | C2 | — | 8 | 1 | no | — |
| 622 | C2 | — | 8 | 2 | no | — |
| 623 | C2 | — | 424 | 2 | no | — |
| 624 | C2 | C2×#16810809 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20289072 | C2 | semidirect |
| 2. #20284079 | C2 | semidirect |
| 3. #20276739 | C2 | semidirect |
| 4. #20276735 | C2 | semidirect |
| 5. #20276731 | C2 | semidirect |
| 6. #20276402 | C2 | semidirect |
| 7. C2×#16810420 | C2 | semidirect |
| 8. C2×C53×#454 | C2 | semidirect |
| 10. #16811373 | C22 | semidirect |
| 12. #16811365 | C22 | semidirect |
| 13. #16811335 | C22 | semidirect |
| 23. #16810806 | C22 | semidirect |
| 25. #16810796 | C22 | semidirect |
| 27. C2×#13133136 | C22 | semidirect |
| 28. #16810421 | C22 | semidirect |
| 29. #16810420 | C22 | semidirect |
| 30. #16810420 | C22 | semidirect |
| 31. #16810419 | C22 | semidirect |
| 32. C2×2−1+4×C53 | C22 | semidirect |
| 38. C53×#454 | C22 | semidirect |
| 40. C2×#101×C53 | C22 | semidirect |
| 307. C2×#454 | D53 | semidirect |
| 321. C2×2−1+4 | C2×D53 | semidirect |
| 344. #454 | C2×D53 | semidirect |
| 348. C2×#101 | C2×D53 | semidirect |
| 353. C53 | #33568 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289072 | 2 |
| #20284079 | 2 |
| #20276739 | 2 |
| #20276735 | 2 |
| #20276731 | 2 |
| #20276402 | 2 |
| C2×#16810420 | 2 |
| C2×C53×#454 | 2 |
| #33568 | 53 |