Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1084 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 1084 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 | #20289129 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #20284096 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #20284063 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #20276746 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #20276738 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #20276409 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | C53×#2132 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #16811459 | C22 | 1 | 1 | yes | characteristic |
| 9 | #16811421 | — | 2 | 1 | no | — |
| 10 | C2×#13133250 | — | 2 | 2 | no | — |
| 11 | #16811373 | — | 2 | 1 | no | — |
| 12 | #16811373 | C22 | 1 | 2 | yes | complemented |
| 13 | #16811359 | — | 2 | 1 | no | — |
| 14 | #16811353 | C22 | 1 | 2 | yes | complemented |
| 15 | #16811343 | — | 2 | 2 | no | — |
| 16 | D4×Dic106 | — | 2 | 2 | no | — |
| 17 | #16811240 | — | 2 | 4 | no | — |
| 18 | #16811194 | — | 2 | 1 | no | — |
| 19 | #16811194 | C22 | 1 | 2 | yes | — |
| 20 | #16811180 | — | 2 | 1 | no | — |
| 21 | #16810808 | C22 | 1 | 8 | yes | — |
| 22 | #16810805 | C22 | 1 | 2 | yes | — |
| 23 | #16810803 | — | 2 | 4 | no | — |
| 24 | #16810800 | — | 2 | 1 | no | — |
| 25 | #16810795 | C22 | 1 | 2 | yes | — |
| 26 | #16810790 | — | 2 | 1 | no | — |
| 27 | #16810639 | — | 2 | 2 | no | — |
| 28 | C2×#13133145 | — | 2 | 1 | no | — |
| 29 | #16810607 | C22 | 1 | 1 | yes | characteristic |
| 30 | #16810421 | C22 | 1 | 8 | yes | complemented |
| 31 | C53×#532 | C22 | 1 | 1 | yes | characteristic |
| 32 | C53×#413 | C22 | 1 | 2 | yes | — |
| 33 | C53×#356 | C22 | 1 | 2 | yes | complemented |
| 34 | C53×#355 | C22 | 1 | 2 | yes | complemented |
| 35 | #13133265 | C23 | 1 | 2 | yes | — |
| 36 | #13133264 | — | 4 | 1 | no | — |
| 37 | #13133263 | — | 4 | 1 | no | — |
| 38 | #13133262 | — | 2 | 1 | no | — |
| 39 | #13133262 | — | 2 | 2 | no | — |
| 40 | C2×#11719945 | — | 2 | 1 | no | — |
| 41 | C2×#11719945 | — | 2 | 2 | no | — |
| 42 | #41×D53 | — | 4 | 2 | no | — |
| 43 | C22×Dic106 | — | 2 | 1 | no | — |
| 44 | C22×Dic106 | D4 | 1 | 2 | yes | — |
| 45 | #13133250 | — | 2 | 8 | no | — |
| 46 | #13133250 | — | 4 | 4 | no | — |
| 47 | #13133248 | — | 2 | 2 | no | — |
| 48 | #13133247 | — | 4 | 1 | no | — |
| 49 | #13133243 | — | 2 | 2 | no | — |
| 50 | #13133242 | — | 4 | 1 | no | — |
| 51 | #13133237 | — | 4 | 2 | no | — |
| 52 | C2×Dic212 | — | 4 | 2 | no | — |
| 53 | C2×#11719913 | — | 4 | 2 | no | — |
| 54 | C2×#11719917 | — | 2 | 1 | no | — |
| 55 | #13133217 | — | 2 | 1 | no | — |
| 56 | #13133217 | — | 2 | 1 | no | — |
| 57 | #13133216 | — | 2 | 4 | no | — |
| 58 | #13133215 | — | 2 | 2 | no | — |
| 59 | #13133215 | C23 | 1 | 4 | yes | — |
| 60 | #13133210 | — | 2 | 4 | no | — |
| 61 | #13133210 | — | 2 | 4 | no | — |
| 62 | #13133209 | — | 2 | 2 | no | — |
| 63 | #13133204 | — | 2 | 4 | no | — |
| 64 | #13133204 | — | 2 | 2 | no | — |
| 65 | #13133204 | D4 | 1 | 4 | yes | — |
| 66 | #13133198 | — | 2 | 2 | no | — |
| 67 | #13133198 | — | 2 | 2 | no | — |
| 68 | #13133198 | — | 2 | 2 | no | — |
| 69 | #13133198 | — | 2 | 2 | no | — |
| 70 | #13133196 | — | 2 | 2 | no | — |
| 71 | #13133196 | — | 2 | 2 | no | — |
| 72 | #13133196 | — | 2 | 2 | no | — |
| 73 | #13133196 | — | 2 | 2 | no | — |
| 74 | #13133194 | — | 2 | 4 | no | — |
| 75 | #13133194 | — | 2 | 4 | no | — |
| 76 | C4×Dic106 | — | 2 | 2 | no | — |
| 77 | C4×Dic106 | — | 2 | 2 | no | — |
| 78 | #13133182 | — | 2 | 4 | no | — |
| 79 | D4×Dic53 | — | 2 | 4 | no | — |
| 80 | #13133176 | — | 2 | 1 | no | — |
| 81 | #13133176 | — | 2 | 2 | no | — |
| 82 | #13133176 | D4 | 1 | 2 | yes | — |
| 83 | #13133145 | — | 2 | 2 | no | — |
| 84 | #13133145 | — | 2 | 2 | no | — |
| 85 | #13133143 | — | 2 | 8 | no | — |
| 86 | #13133136 | C23 | 1 | 2 | yes | — |
| 87 | #13133134 | — | 2 | 1 | no | — |
| 88 | C2×#41×C53 | D4 | 1 | 1 | yes | characteristic |
| 89 | C2×#41×C53 | C23 | 1 | 1 | yes | characteristic |
| 90 | C2×M16×C53 | — | 2 | 2 | no | — |
| 91 | C4⋊Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 92 | #127×C53 | D4 | 1 | 1 | yes | characteristic |
| 93 | #124×C53 | D4 | 1 | 1 | yes | characteristic |
| 94 | #124×C53 | C23 | 1 | 1 | yes | characteristic |
| 95 | #121×C53 | — | 2 | 2 | no | — |
| 96 | C4×D4×C53 | — | 2 | 2 | no | — |
| 97 | C2×C42×C53 | D4 | 1 | 1 | yes | characteristic |
| 98 | #101×C53 | C23 | 1 | 4 | yes | — |
| 99 | #100×C53 | — | 2 | 2 | no | — |
| 100 | #41×C53 | — | 4 | 1 | no | — |
| 101 | #41×C53 | — | 4 | 1 | no | — |
| 102 | #41×C53 | — | 4 | 1 | no | — |
| 103 | #41×C53 | — | 4 | 1 | no | — |
| 104 | C2×Q8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 105 | C2×Q8×C53 | C24 | 1 | 1 | yes | characteristic |
| 106 | C2×D4×C53 | — | 2 | 2 | no | — |
| 107 | C2×D4×C53 | — | 2 | 1 | no | — |
| 108 | C2×D4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 109 | C2×D4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 110 | C2×D4×C53 | C2×D4 | 1 | 2 | yes | — |
| 111 | C22×C4×C53 | — | 2 | 1 | no | — |
| 112 | C22×C4×C53 | — | 2 | 1 | no | — |
| 113 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 114 | C22×C4×C53 | C2×D4 | 1 | 2 | yes | — |
| 115 | C2×C22⋊D53 | — | 4 | 2 | no | — |
| 116 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 117 | C22×Dic53 | — | 2 | 2 | no | — |
| 118 | C22×Dic53 | — | 2 | 2 | no | — |
| 119 | #11719949 | — | 4 | 2 | no | — |
| 120 | Q8×D53 | — | 4 | 2 | no | — |
| 121 | #11719947 | — | 4 | 4 | no | — |
| 122 | #11719947 | — | 4 | 2 | no | — |
| 123 | D4×D53 | — | 4 | 4 | no | — |
| 124 | D4×D53 | — | 4 | 2 | no | — |
| 125 | #11719945 | — | 2 | 2 | no | — |
| 126 | #11719945 | — | 2 | 4 | no | — |
| 127 | #11719945 | — | 2 | 4 | no | — |
| 128 | #11719945 | — | 2 | 2 | no | — |
| 129 | #11719945 | — | 4 | 2 | no | — |
| 130 | #11719945 | — | 4 | 1 | no | — |
| 131 | #11719945 | — | 4 | 1 | no | — |
| 132 | C2×D212 | — | 2 | 2 | no | — |
| 133 | C2×D212 | — | 2 | 1 | no | — |
| 134 | C2×C4×D53 | — | 4 | 2 | no | — |
| 135 | C2×C4×D53 | — | 4 | 1 | no | — |
| 136 | C2×Dic106 | — | 2 | 2 | no | — |
| 137 | C2×Dic106 | — | 2 | 1 | no | — |
| 138 | C2×Dic106 | — | 2 | 2 | no | — |
| 139 | C2×Dic106 | — | 2 | 2 | no | — |
| 140 | C2×Dic106 | — | 2 | 2 | no | — |
| 141 | C2×Dic106 | — | 4 | 2 | no | — |
| 142 | C2×Dic106 | — | 4 | 2 | no | — |
| 143 | C2×Dic106 | — | 8 | 1 | no | — |
| 144 | C2×Dic106 | — | 8 | 1 | no | — |
| 145 | C2×Dic106 | C2×D4 | 1 | 4 | yes | — |
| 146 | M16×C53 | — | 2 | 4 | no | — |
| 147 | M16×C53 | — | 4 | 2 | no | — |
| 148 | C2×C8×C53 | — | 4 | 2 | no | — |
| 149 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 150 | C22⋊C4×C53 | — | 2 | 2 | no | — |
| 151 | C22⋊C4×C53 | — | 2 | 2 | no | — |
| 152 | C42×C53 | — | 2 | 1 | no | — |
| 153 | C42×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 154 | C42×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 155 | C22⋊Dic53 | — | 2 | 2 | no | — |
| 156 | C22⋊Dic53 | — | 2 | 4 | no | — |
| 157 | C22⋊Dic53 | — | 2 | 4 | no | — |
| 158 | C22⋊Dic53 | — | 2 | 2 | no | — |
| 159 | C22⋊Dic53 | — | 2 | 4 | no | — |
| 160 | #11719925 | — | 4 | 2 | no | — |
| 161 | #11719924 | — | 4 | 2 | no | — |
| 162 | #11719923 | — | 4 | 2 | no | — |
| 163 | #11719922 | — | 4 | 2 | no | — |
| 164 | C4⋊Dic53 | — | 2 | 2 | no | — |
| 165 | C4⋊Dic53 | — | 2 | 2 | no | — |
| 166 | C4⋊Dic53 | — | 2 | 2 | no | — |
| 167 | C4⋊Dic53 | — | 2 | 2 | no | — |
| 168 | #11719919 | — | 2 | 4 | no | — |
| 169 | #11719919 | — | 2 | 4 | no | — |
| 170 | #11719919 | — | 2 | 4 | no | — |
| 171 | #11719919 | — | 2 | 4 | no | — |
| 172 | C4×Dic53 | — | 2 | 4 | no | — |
| 173 | C4×Dic53 | — | 2 | 2 | no | — |
| 174 | C4×Dic53 | C2×D4 | 1 | 4 | yes | — |
| 175 | #11719917 | — | 2 | 2 | no | — |
| 176 | #11719917 | — | 4 | 1 | no | — |
| 177 | C2×#88322 | — | 4 | 1 | no | — |
| 178 | Dic212 | — | 4 | 8 | no | — |
| 179 | #11719913 | — | 4 | 8 | no | — |
| 180 | C23×C53 | — | 2 | 1 | no | — |
| 181 | C23×C53 | #120 | 1 | 2 | yes | — |
| 182 | C23×C53 | #120 | 1 | 1 | yes | characteristic |
| 183 | C22×D53 | — | 4 | 2 | no | — |
| 184 | C22×D53 | — | 4 | 1 | no | — |
| 185 | Q8×C53 | — | 4 | 1 | no | — |
| 186 | Q8×C53 | — | 4 | 1 | no | — |
| 187 | D4×C53 | — | 4 | 1 | no | — |
| 188 | D4×C53 | — | 4 | 2 | no | — |
| 189 | D4×C53 | — | 4 | 1 | no | — |
| 190 | D4×C53 | — | 4 | 4 | no | — |
| 191 | D4×C53 | — | 8 | 1 | no | — |
| 192 | C2×C4×C53 | — | 2 | 1 | no | — |
| 193 | C2×C4×C53 | — | 2 | 2 | no | — |
| 194 | C2×C4×C53 | — | 2 | 1 | no | — |
| 195 | C2×C4×C53 | — | 2 | 2 | no | — |
| 196 | C2×C4×C53 | — | 2 | 1 | no | — |
| 197 | C2×C4×C53 | — | 2 | 1 | no | — |
| 198 | C2×C4×C53 | — | 2 | 1 | no | — |
| 199 | C2×C4×C53 | — | 4 | 2 | no | — |
| 200 | C2×C4×C53 | — | 4 | 1 | no | — |
| 201 | C2×C4×C53 | — | 4 | 1 | no | — |
| 202 | C2×C4×C53 | #120 | 1 | 1 | yes | characteristic |
| 203 | C2×C4×C53 | C22×D4 | 1 | 2 | yes | — |
| 204 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 205 | C22⋊D53 | — | 4 | 4 | no | — |
| 206 | C22⋊D53 | — | 4 | 2 | no | — |
| 207 | C22⋊D53 | — | 4 | 2 | no | — |
| 208 | C2×Dic53 | — | 2 | 4 | no | — |
| 209 | C2×Dic53 | — | 2 | 4 | no | — |
| 210 | C2×Dic53 | — | 4 | 2 | no | — |
| 211 | C2×Dic53 | — | 4 | 1 | no | — |
| 212 | C2×Dic53 | — | 8 | 2 | no | — |
| 213 | C2×Dic53 | — | 8 | 2 | no | — |
| 214 | D212 | — | 2 | 4 | no | — |
| 215 | D212 | — | 2 | 2 | no | — |
| 216 | D212 | — | 4 | 1 | no | — |
| 217 | C4×D53 | — | 4 | 2 | no | — |
| 218 | C4×D53 | — | 4 | 4 | no | — |
| 219 | C4×D53 | — | 4 | 2 | no | — |
| 220 | Dic106 | — | 2 | 4 | no | — |
| 221 | Dic106 | — | 2 | 2 | no | — |
| 222 | Dic106 | — | 4 | 4 | no | — |
| 223 | Dic106 | — | 4 | 1 | no | — |
| 224 | Dic106 | — | 4 | 2 | no | — |
| 225 | Dic106 | — | 4 | 2 | no | — |
| 226 | Dic106 | — | 4 | 4 | no | — |
| 227 | Dic106 | — | 8 | 2 | no | — |
| 228 | C8×C53 | — | 4 | 4 | no | — |
| 229 | #88322 | — | 4 | 2 | no | — |
| 230 | #33571 | — | 53 | 1 | no | maximal, Sylow |
| 231 | C22×C53 | — | 2 | 2 | no | — |
| 232 | C22×C53 | — | 2 | 1 | no | — |
| 233 | C22×C53 | — | 4 | 1 | no | — |
| 234 | C22×C53 | — | 4 | 2 | no | — |
| 235 | C22×C53 | — | 4 | 2 | no | — |
| 236 | C22×C53 | — | 4 | 1 | no | — |
| 237 | C22×C53 | C2×#120 | 1 | 1 | yes | characteristic |
| 238 | C2×D53 | — | 4 | 2 | no | — |
| 239 | C2×D53 | — | 16 | 2 | no | — |
| 240 | C2×D53 | — | 16 | 1 | no | — |
| 241 | C4×C53 | — | 2 | 2 | no | — |
| 242 | C4×C53 | — | 2 | 1 | no | — |
| 243 | C4×C53 | — | 2 | 2 | no | — |
| 244 | C4×C53 | — | 4 | 1 | no | — |
| 245 | C4×C53 | — | 4 | 1 | no | — |
| 246 | C4×C53 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 247 | C4×C53 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 248 | Dic53 | — | 4 | 4 | no | — |
| 249 | Dic53 | — | 4 | 2 | no | — |
| 250 | Dic53 | — | 4 | 4 | no | — |
| 251 | #3550 | — | 53 | 1 | no | — |
| 252 | #3022 | — | 53 | 2 | no | — |
| 253 | #3018 | — | 53 | 1 | no | — |
| 254 | #2205 | — | 53 | 4 | no | — |
| 255 | #2203 | — | 53 | 4 | no | — |
| 256 | #2135 | — | 53 | 2 | no | — |
| 257 | #2132 | D53 | 1 | 1 | yes | characteristic, complemented |
| 258 | C2×C53 | — | 2 | 1 | no | — |
| 259 | C2×C53 | — | 4 | 2 | no | — |
| 260 | C2×C53 | — | 4 | 1 | no | — |
| 261 | C2×C53 | — | 8 | 1 | no | — |
| 262 | C2×C53 | C2×B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 263 | D53 | — | 8 | 2 | no | — |
| 264 | #585 | — | 53 | 1 | no | — |
| 265 | #575 | — | 106 | 1 | no | — |
| 266 | C2×#137 | — | 106 | 2 | no | — |
| 267 | #563 | — | 53 | 2 | no | — |
| 268 | #563 | — | 106 | 1 | no | — |
| 269 | #559 | — | 106 | 1 | no | — |
| 270 | Q82 | — | 53 | 2 | no | — |
| 271 | #556 | — | 106 | 2 | no | — |
| 272 | D4×Q8 | — | 106 | 2 | no | — |
| 273 | #542 | — | 106 | 4 | no | — |
| 274 | #536 | — | 53 | 2 | no | — |
| 275 | #536 | — | 106 | 1 | no | — |
| 276 | #533 | — | 106 | 1 | no | — |
| 277 | #532 | C2×D53 | 1 | 1 | yes | characteristic |
| 278 | #456 | — | 53 | 2 | no | — |
| 279 | #456 | — | 53 | 8 | no | — |
| 280 | #455 | — | 106 | 4 | no | — |
| 281 | #455 | — | 106 | 1 | no | — |
| 282 | #454 | — | 53 | 2 | no | — |
| 283 | #453 | — | 106 | 1 | no | — |
| 284 | #421 | — | 106 | 2 | no | — |
| 285 | C2×#104 | — | 106 | 1 | no | — |
| 286 | #413 | — | 53 | 1 | no | — |
| 287 | #413 | C2×D53 | 1 | 2 | yes | — |
| 288 | #356 | — | 53 | 8 | no | — |
| 289 | #356 | C2×D53 | 1 | 2 | yes | complemented |
| 290 | #355 | C2×D53 | 1 | 2 | yes | complemented |
| 291 | C53 | #33571 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 292 | 2−1+4 | — | 53 | 2 | no | — |
| 293 | 2−1+4 | — | 212 | 1 | no | — |
| 294 | H(5,𝔽2) | — | 106 | 1 | no | — |
| 295 | H(5,𝔽2) | — | 106 | 2 | no | — |
| 296 | H(5,𝔽2) | — | 212 | 1 | no | — |
| 297 | C2×#41 | — | 106 | 1 | no | — |
| 298 | C2×#41 | — | 106 | 2 | no | — |
| 299 | C2×#41 | — | 212 | 2 | no | — |
| 300 | C2×#41 | D212 | 1 | 1 | yes | characteristic |
| 301 | C2×#41 | C22×D53 | 1 | 1 | yes | characteristic |
| 302 | C22×Q8 | — | 53 | 2 | no | — |
| 303 | C22×Q8 | — | 106 | 1 | no | — |
| 304 | #137 | — | 106 | 8 | no | — |
| 305 | #137 | — | 106 | 2 | no | — |
| 306 | #137 | — | 212 | 4 | no | — |
| 307 | #137 | — | 212 | 1 | no | — |
| 308 | AGL(1,ℤ/8) | — | 106 | 2 | no | — |
| 309 | AGL(1,ℤ/8) | — | 212 | 1 | no | — |
| 310 | #135 | — | 212 | 2 | no | — |
| 311 | C2×Q16 | — | 212 | 2 | no | — |
| 312 | C2×SD16 | — | 212 | 2 | no | — |
| 313 | C2×M16 | — | 2 | 2 | no | — |
| 314 | C2×M16 | — | 106 | 1 | no | — |
| 315 | C4⋊Q8 | — | 53 | 4 | no | — |
| 316 | C4⋊Q8 | — | 106 | 1 | no | — |
| 317 | C4⋊Q8 | — | 106 | 1 | no | — |
| 318 | C4⋊Q8 | — | 106 | 4 | no | — |
| 319 | C4⋊Q8 | — | 106 | 2 | no | — |
| 320 | C4⋊Q8 | C22×D53 | 1 | 1 | yes | characteristic |
| 321 | #127 | D212 | 1 | 1 | yes | characteristic |
| 322 | #126 | — | 106 | 4 | no | — |
| 323 | #126 | — | 106 | 4 | no | — |
| 324 | #125 | — | 106 | 2 | no | — |
| 325 | #124 | — | 53 | 4 | no | — |
| 326 | #124 | — | 106 | 2 | no | — |
| 327 | #124 | — | 106 | 4 | no | — |
| 328 | #124 | D212 | 1 | 1 | yes | characteristic |
| 329 | #124 | C22×D53 | 1 | 1 | yes | characteristic |
| 330 | #123 | — | 106 | 2 | no | — |
| 331 | #123 | — | 106 | 2 | no | — |
| 332 | #123 | — | 106 | 2 | no | — |
| 333 | #123 | — | 106 | 2 | no | — |
| 334 | C22⋊Q8 | — | 106 | 4 | no | — |
| 335 | C22⋊Q8 | — | 106 | 4 | no | — |
| 336 | C22⋊Q8 | — | 106 | 2 | no | — |
| 337 | C22⋊Q8 | — | 106 | 2 | no | — |
| 338 | C22⋊Q8 | — | 106 | 2 | no | — |
| 339 | C22⋊Q8 | — | 106 | 2 | no | — |
| 340 | #121 | — | 2 | 2 | no | — |
| 341 | C4×Q8 | — | 106 | 2 | no | — |
| 342 | C4×Q8 | — | 106 | 4 | no | — |
| 343 | C4×Q8 | — | 106 | 2 | no | — |
| 344 | C4×D4 | — | 2 | 2 | no | — |
| 345 | C4×D4 | — | 106 | 4 | no | — |
| 346 | #117 | — | 53 | 2 | no | — |
| 347 | #117 | — | 106 | 2 | no | — |
| 348 | #117 | — | 106 | 1 | no | — |
| 349 | C2×C42 | D212 | 1 | 1 | yes | characteristic |
| 350 | #104 | — | 106 | 8 | no | — |
| 351 | #104 | — | 106 | 2 | no | — |
| 352 | #104 | — | 106 | 2 | no | — |
| 353 | #101 | — | 53 | 2 | no | — |
| 354 | #101 | C22×D53 | 1 | 4 | yes | — |
| 355 | #100 | — | 2 | 2 | no | — |
| 356 | #100 | — | 106 | 1 | no | — |
| 357 | #41 | — | 4 | 1 | no | — |
| 358 | #41 | — | 4 | 1 | no | — |
| 359 | #41 | — | 4 | 1 | no | — |
| 360 | #41 | — | 4 | 1 | no | — |
| 361 | #41 | — | 106 | 2 | no | — |
| 362 | #41 | — | 106 | 4 | no | — |
| 363 | #41 | — | 106 | 4 | no | — |
| 364 | #41 | — | 106 | 2 | no | — |
| 365 | #41 | — | 212 | 2 | no | — |
| 366 | #41 | — | 212 | 1 | no | — |
| 367 | #41 | — | 212 | 2 | no | — |
| 368 | #41 | — | 212 | 4 | no | — |
| 369 | #41 | — | 212 | 2 | no | — |
| 370 | #41 | — | 212 | 1 | no | — |
| 371 | C2×Q8 | — | 53 | 4 | no | — |
| 372 | C2×Q8 | — | 106 | 2 | no | — |
| 373 | C2×Q8 | — | 106 | 2 | no | — |
| 374 | C2×Q8 | — | 106 | 2 | no | — |
| 375 | C2×Q8 | — | 106 | 1 | no | — |
| 376 | C2×Q8 | — | 106 | 2 | no | — |
| 377 | C2×Q8 | — | 424 | 1 | no | — |
| 378 | C2×Q8 | — | 424 | 1 | no | — |
| 379 | C2×Q8 | — | 212 | 2 | no | — |
| 380 | C2×Q8 | — | 212 | 2 | no | — |
| 381 | C2×Q8 | — | 212 | 2 | no | — |
| 382 | C2×Q8 | C2×D212 | 1 | 1 | yes | characteristic |
| 383 | C2×Q8 | C23×D53 | 1 | 1 | yes | characteristic |
| 384 | C2×D4 | — | 2 | 2 | no | — |
| 385 | C2×D4 | — | 2 | 1 | no | — |
| 386 | C2×D4 | — | 106 | 2 | no | — |
| 387 | C2×D4 | — | 106 | 1 | no | — |
| 388 | C2×D4 | — | 212 | 2 | no | — |
| 389 | C2×D4 | — | 212 | 4 | no | — |
| 390 | C2×D4 | — | 212 | 2 | no | — |
| 391 | C2×D4 | — | 212 | 1 | no | — |
| 392 | C2×D4 | C2×D212 | 1 | 1 | yes | characteristic |
| 393 | C2×D4 | C2×D212 | 1 | 1 | yes | characteristic |
| 394 | C2×D4 | D4×D53 | 1 | 2 | yes | — |
| 395 | C22×C4 | — | 2 | 1 | no | — |
| 396 | C22×C4 | — | 2 | 1 | no | — |
| 397 | C22×C4 | — | 106 | 2 | no | — |
| 398 | C22×C4 | — | 106 | 2 | no | — |
| 399 | C22×C4 | — | 212 | 1 | no | — |
| 400 | C22×C4 | — | 212 | 2 | no | — |
| 401 | C22×C4 | C2×D212 | 1 | 1 | yes | characteristic |
| 402 | C22×C4 | D4×D53 | 1 | 2 | yes | — |
| 403 | Q16 | — | 212 | 8 | no | — |
| 404 | Q16 | — | 212 | 2 | no | — |
| 405 | SD16 | — | 212 | 8 | no | — |
| 406 | SD16 | — | 212 | 2 | no | — |
| 407 | SD16 | — | 212 | 2 | no | — |
| 408 | D8 | — | 212 | 2 | no | — |
| 409 | M16 | — | 2 | 4 | no | — |
| 410 | M16 | — | 4 | 2 | no | — |
| 411 | M16 | — | 106 | 2 | no | — |
| 412 | M16 | — | 212 | 1 | no | — |
| 413 | C2×C8 | — | 4 | 2 | no | — |
| 414 | C2×C8 | — | 212 | 1 | no | — |
| 415 | C4⋊C4 | — | 2 | 2 | no | — |
| 416 | C4⋊C4 | — | 106 | 2 | no | — |
| 417 | C4⋊C4 | — | 106 | 2 | no | — |
| 418 | C4⋊C4 | — | 106 | 2 | no | — |
| 419 | C4⋊C4 | — | 106 | 4 | no | — |
| 420 | C4⋊C4 | — | 106 | 4 | no | — |
| 421 | C4⋊C4 | — | 106 | 2 | no | — |
| 422 | C4⋊C4 | — | 106 | 4 | no | — |
| 423 | C4⋊C4 | — | 106 | 4 | no | — |
| 424 | C22⋊C4 | — | 2 | 2 | no | — |
| 425 | C22⋊C4 | — | 2 | 2 | no | — |
| 426 | C22⋊C4 | — | 106 | 2 | no | — |
| 427 | C22⋊C4 | — | 106 | 4 | no | — |
| 428 | C22⋊C4 | — | 106 | 2 | no | — |
| 429 | C22⋊C4 | — | 106 | 4 | no | — |
| 430 | C22⋊C4 | — | 106 | 4 | no | — |
| 431 | C42 | — | 2 | 1 | no | — |
| 432 | C42 | — | 53 | 4 | no | — |
| 433 | C42 | — | 106 | 4 | no | — |
| 434 | C42 | — | 106 | 2 | no | — |
| 435 | C42 | C2×D212 | 1 | 1 | yes | characteristic |
| 436 | C42 | C2×D212 | 1 | 1 | yes | characteristic |
| 437 | C23 | — | 2 | 1 | no | — |
| 438 | C23 | — | 212 | 2 | no | — |
| 439 | C23 | — | 212 | 1 | no | — |
| 440 | C23 | #13133187 | 1 | 2 | yes | — |
| 441 | C23 | #13133187 | 1 | 1 | yes | characteristic |
| 442 | Q8 | — | 4 | 1 | no | — |
| 443 | Q8 | — | 4 | 1 | no | — |
| 444 | Q8 | — | 106 | 2 | no | — |
| 445 | Q8 | — | 106 | 4 | no | — |
| 446 | Q8 | — | 424 | 2 | no | — |
| 447 | Q8 | — | 212 | 4 | no | — |
| 448 | Q8 | — | 212 | 4 | no | — |
| 449 | Q8 | — | 212 | 1 | no | — |
| 450 | Q8 | — | 212 | 2 | no | — |
| 451 | Q8 | — | 212 | 2 | no | — |
| 452 | D4 | — | 4 | 1 | no | — |
| 453 | D4 | — | 4 | 2 | no | — |
| 454 | D4 | — | 4 | 1 | no | — |
| 455 | D4 | — | 4 | 4 | no | — |
| 456 | D4 | — | 8 | 1 | no | — |
| 457 | D4 | — | 106 | 2 | no | — |
| 458 | D4 | — | 106 | 4 | no | — |
| 459 | D4 | — | 212 | 4 | no | — |
| 460 | D4 | — | 212 | 2 | no | — |
| 461 | D4 | — | 212 | 2 | no | — |
| 462 | D4 | — | 212 | 1 | no | — |
| 463 | C2×C4 | — | 2 | 1 | no | — |
| 464 | C2×C4 | — | 2 | 2 | no | — |
| 465 | C2×C4 | — | 2 | 1 | no | — |
| 466 | C2×C4 | — | 2 | 2 | no | — |
| 467 | C2×C4 | — | 2 | 1 | no | — |
| 468 | C2×C4 | — | 2 | 1 | no | — |
| 469 | C2×C4 | — | 2 | 1 | no | — |
| 470 | C2×C4 | — | 4 | 2 | no | — |
| 471 | C2×C4 | — | 4 | 1 | no | — |
| 472 | C2×C4 | — | 4 | 1 | no | — |
| 473 | C2×C4 | — | 106 | 4 | no | — |
| 474 | C2×C4 | — | 106 | 4 | no | — |
| 475 | C2×C4 | — | 424 | 2 | no | — |
| 476 | C2×C4 | — | 424 | 2 | no | — |
| 477 | C2×C4 | — | 212 | 4 | no | — |
| 478 | C2×C4 | — | 212 | 2 | no | — |
| 479 | C2×C4 | — | 212 | 2 | no | — |
| 480 | C2×C4 | — | 212 | 1 | no | — |
| 481 | C2×C4 | — | 212 | 2 | no | — |
| 482 | C2×C4 | #13133187 | 1 | 1 | yes | characteristic |
| 483 | C2×C4 | C2×D4×D53 | 1 | 2 | yes | — |
| 484 | C2×C4 | C22×D212 | 1 | 1 | yes | characteristic |
| 485 | C8 | — | 4 | 4 | no | — |
| 486 | C8 | — | 212 | 2 | no | — |
| 487 | C22 | — | 2 | 2 | no | — |
| 488 | C22 | — | 2 | 1 | no | — |
| 489 | C22 | — | 4 | 1 | no | — |
| 490 | C22 | — | 4 | 2 | no | — |
| 491 | C22 | — | 4 | 2 | no | — |
| 492 | C22 | — | 4 | 1 | no | — |
| 493 | C22 | — | 848 | 2 | no | — |
| 494 | C22 | — | 848 | 1 | no | — |
| 495 | C22 | — | 212 | 2 | no | — |
| 496 | C22 | C2×#13133187 | 1 | 1 | yes | characteristic |
| 497 | C4 | — | 2 | 2 | no | — |
| 498 | C4 | — | 2 | 2 | no | — |
| 499 | C4 | — | 2 | 1 | no | — |
| 500 | C4 | — | 4 | 1 | no | — |
| 501 | C4 | — | 4 | 1 | no | — |
| 502 | C4 | — | 212 | 4 | no | — |
| 503 | C4 | — | 212 | 4 | no | — |
| 504 | C4 | — | 212 | 2 | no | — |
| 505 | C4 | #16810811 | 1 | 1 | yes | characteristic |
| 506 | C4 | #16810811 | 1 | 1 | yes | characteristic |
| 507 | C2 | — | 2 | 1 | no | — |
| 508 | C2 | — | 4 | 2 | no | — |
| 509 | C2 | — | 4 | 1 | no | — |
| 510 | C2 | — | 8 | 1 | no | — |
| 511 | C2 | — | 424 | 2 | no | — |
| 512 | C2 | C2×#16810811 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20289129 | C2 | semidirect |
| 2. #20284096 | C2 | semidirect |
| 4. #20276746 | C2 | semidirect |
| 5. #20276738 | C2 | semidirect |
| 6. #20276409 | C2 | semidirect |
| 7. C53×#2132 | C2 | semidirect |
| 12. #16811373 | C22 | semidirect |
| 14. #16811353 | C22 | semidirect |
| 30. #16810421 | C22 | semidirect |
| 33. C53×#356 | C22 | semidirect |
| 34. C53×#355 | C22 | semidirect |
| 257. #2132 | D53 | semidirect |
| 289. #356 | C2×D53 | semidirect |
| 290. #355 | C2×D53 | semidirect |
| 291. C53 | #33571 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289129 | 2 |
| #20284096 | 2 |
| #20284063 | 2 |
| #20276746 | 2 |
| #20276738 | 2 |
| #20276409 | 2 |
| C53×#2132 | 2 |
| #33571 | 53 |