Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1222 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 1222 conjugacy classes of subgroups — too many to draw. Only its 187 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 | #20288486 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #20284716 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #20279620 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #20273720 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #20273652 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #20273276 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | C53×#1461 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#13133265 | — | 2 | 1 | no | — |
| 9 | #16811295 | — | 2 | 2 | no | — |
| 10 | Q8×D212 | — | 2 | 2 | no | — |
| 11 | #16811285 | — | 2 | 4 | no | — |
| 12 | #16811204 | — | 2 | 1 | no | — |
| 13 | #16811204 | C22 | 1 | 4 | yes | — |
| 14 | #16811173 | — | 2 | 2 | no | — |
| 15 | #16811173 | C22 | 1 | 2 | yes | — |
| 16 | C2×#13133193 | — | 2 | 1 | no | — |
| 17 | C2×C4×D212 | C22 | 1 | 1 | yes | characteristic |
| 18 | #16810937 | C22 | 1 | 4 | yes | — |
| 19 | #16810904 | — | 2 | 2 | no | — |
| 20 | #16810819 | — | 2 | 2 | no | — |
| 21 | #16810759 | C22 | 1 | 4 | yes | — |
| 22 | C4×D424 | — | 2 | 4 | no | — |
| 23 | #16810553 | C22 | 1 | 2 | yes | — |
| 24 | #16810540 | C22 | 1 | 2 | yes | — |
| 25 | #16810514 | — | 2 | 2 | no | — |
| 26 | #16810489 | C22 | 1 | 1 | yes | characteristic |
| 27 | #16810480 | — | 2 | 1 | no | — |
| 28 | #16810358 | C22 | 1 | 8 | yes | — |
| 29 | C2×C4×Q8×C53 | C22 | 1 | 1 | yes | characteristic |
| 30 | C53×#431 | C22 | 1 | 2 | yes | — |
| 31 | C53×#324 | C22 | 1 | 4 | yes | — |
| 32 | #13133265 | — | 4 | 4 | no | — |
| 33 | #13133265 | — | 4 | 4 | no | — |
| 34 | C2×#11719949 | — | 2 | 4 | no | — |
| 35 | C2×#11719945 | — | 2 | 4 | no | — |
| 36 | C2×#11719945 | — | 2 | 2 | no | — |
| 37 | C2×Q8×D53 | — | 2 | 4 | no | — |
| 38 | C22×D212 | C23 | 1 | 1 | yes | characteristic |
| 39 | C22×C4×D53 | — | 2 | 1 | no | — |
| 40 | C2×D424 | — | 2 | 4 | no | — |
| 41 | #13133217 | — | 2 | 2 | no | — |
| 42 | #13133217 | D4 | 1 | 2 | yes | — |
| 43 | #13133214 | — | 2 | 2 | no | — |
| 44 | #13133214 | D4 | 1 | 2 | yes | — |
| 45 | #13133205 | — | 2 | 4 | no | — |
| 46 | #13133205 | — | 2 | 2 | no | — |
| 47 | #13133197 | — | 2 | 4 | no | — |
| 48 | #13133197 | — | 2 | 8 | no | — |
| 49 | #13133193 | — | 4 | 4 | no | — |
| 50 | #13133192 | — | 2 | 4 | no | — |
| 51 | #13133192 | — | 2 | 8 | no | — |
| 52 | #13133191 | — | 2 | 2 | no | — |
| 53 | #13133191 | — | 2 | 4 | no | — |
| 54 | #13133191 | C23 | 1 | 4 | yes | — |
| 55 | C4×D212 | — | 2 | 4 | no | — |
| 56 | C4×D212 | — | 2 | 4 | no | — |
| 57 | C4×D212 | — | 2 | 2 | no | — |
| 58 | C4×D212 | — | 2 | 2 | no | — |
| 59 | C4×D212 | — | 2 | 2 | no | — |
| 60 | C4×D212 | D4 | 1 | 4 | yes | — |
| 61 | C2×C4⋊Dic53 | — | 2 | 1 | no | — |
| 62 | C2×C4⋊Dic53 | C23 | 1 | 1 | yes | characteristic |
| 63 | C2×#11719919 | — | 2 | 2 | no | — |
| 64 | C2×#11719921 | — | 2 | 1 | no | — |
| 65 | C2×#11719921 | — | 2 | 2 | no | — |
| 66 | C2×#11719921 | — | 2 | 2 | no | — |
| 67 | #13133151 | — | 2 | 4 | no | — |
| 68 | #13133139 | — | 2 | 4 | no | — |
| 69 | #13133139 | — | 2 | 4 | no | — |
| 70 | #13133124 | — | 2 | 1 | no | — |
| 71 | #13133124 | — | 2 | 2 | no | — |
| 72 | #13133124 | C23 | 1 | 2 | yes | — |
| 73 | C22×Q8×C53 | D4 | 1 | 1 | yes | characteristic |
| 74 | C4×Q8×C53 | — | 2 | 2 | no | — |
| 75 | C4×Q8×C53 | — | 2 | 2 | no | — |
| 76 | C2×C4⋊C4×C53 | D4 | 1 | 1 | yes | characteristic |
| 77 | C2×C4⋊C4×C53 | C23 | 1 | 2 | yes | — |
| 78 | C2×C42×C53 | D4 | 1 | 2 | yes | — |
| 79 | C2×C42×C53 | C23 | 1 | 1 | yes | characteristic |
| 80 | C4⋊C8×C53 | — | 2 | 2 | no | — |
| 81 | C22⋊C8×C53 | C23 | 1 | 4 | yes | — |
| 82 | C4×C8×C53 | — | 2 | 2 | no | — |
| 83 | C23×D53 | — | 2 | 1 | no | — |
| 84 | C2×Q8×C53 | — | 2 | 2 | no | — |
| 85 | C2×Q8×C53 | — | 2 | 2 | no | — |
| 86 | C2×Q8×C53 | D8 | 1 | 4 | yes | complemented |
| 87 | C22×C4×C53 | C2×D4 | 1 | 2 | yes | — |
| 88 | C22×C4×C53 | C2×D4 | 1 | 2 | yes | — |
| 89 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 90 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 91 | C22×C4×C53 | C24 | 1 | 1 | yes | characteristic |
| 92 | C2×C22⋊D53 | — | 2 | 4 | no | — |
| 93 | C22×Dic53 | — | 2 | 2 | no | — |
| 94 | C22×Dic53 | — | 2 | 1 | no | — |
| 95 | #11719949 | — | 4 | 16 | no | — |
| 96 | Q8×D53 | — | 4 | 16 | no | — |
| 97 | #11719945 | — | 4 | 8 | no | — |
| 98 | #11719945 | — | 4 | 8 | no | — |
| 99 | #11719945 | — | 4 | 4 | no | — |
| 100 | #11719945 | — | 4 | 4 | no | — |
| 101 | C2×D212 | — | 2 | 2 | no | — |
| 102 | C2×D212 | — | 2 | 4 | no | — |
| 103 | C2×D212 | — | 2 | 2 | no | — |
| 104 | C2×D212 | — | 2 | 2 | no | — |
| 105 | C2×D212 | — | 2 | 4 | no | — |
| 106 | C2×D212 | — | 4 | 2 | no | — |
| 107 | C2×D212 | C2×D4 | 1 | 4 | yes | — |
| 108 | C2×C4×D53 | — | 2 | 8 | no | — |
| 109 | C2×C4×D53 | — | 2 | 4 | no | — |
| 110 | C2×C4×D53 | — | 4 | 2 | no | — |
| 111 | C2×C4×D53 | — | 4 | 2 | no | — |
| 112 | C2×C4×D53 | — | 4 | 2 | no | — |
| 113 | C2×Dic106 | — | 2 | 4 | no | — |
| 114 | C2×Dic106 | — | 2 | 2 | no | — |
| 115 | C2×C8×C53 | — | 2 | 4 | no | — |
| 116 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 117 | C4⋊C4×C53 | — | 2 | 4 | no | — |
| 118 | C42×C53 | — | 2 | 2 | no | — |
| 119 | C42×C53 | — | 2 | 2 | no | — |
| 120 | C42×C53 | C2×D4 | 1 | 2 | yes | — |
| 121 | C42×C53 | C2×D4 | 1 | 2 | yes | — |
| 122 | #11719921 | — | 2 | 8 | no | — |
| 123 | #11719921 | — | 2 | 4 | no | — |
| 124 | #11719921 | — | 2 | 4 | no | — |
| 125 | #11719921 | — | 4 | 4 | no | — |
| 126 | #11719921 | — | 4 | 1 | no | — |
| 127 | #11719921 | — | 4 | 1 | no | — |
| 128 | #11719921 | — | 4 | 4 | no | — |
| 129 | C4⋊Dic53 | — | 2 | 4 | no | — |
| 130 | C4⋊Dic53 | — | 2 | 2 | no | — |
| 131 | C4⋊Dic53 | — | 2 | 2 | no | — |
| 132 | C4⋊Dic53 | — | 4 | 2 | no | — |
| 133 | C4⋊Dic53 | C2×D4 | 1 | 4 | yes | — |
| 134 | #11719919 | — | 4 | 4 | no | — |
| 135 | D424 | — | 4 | 8 | no | — |
| 136 | C23×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 137 | C22×D53 | — | 2 | 2 | no | — |
| 138 | C22×D53 | — | 2 | 4 | no | — |
| 139 | C22×D53 | — | 4 | 1 | no | — |
| 140 | C22×D53 | — | 4 | 1 | no | — |
| 141 | C22×D53 | — | 4 | 1 | no | — |
| 142 | C22×D53 | — | 4 | 1 | no | — |
| 143 | C22×D53 | — | 4 | 1 | no | — |
| 144 | C22×D53 | — | 4 | 1 | no | — |
| 145 | Q8×C53 | — | 2 | 8 | no | — |
| 146 | C2×C4×C53 | — | 2 | 2 | no | — |
| 147 | C2×C4×C53 | — | 2 | 2 | no | — |
| 148 | C2×C4×C53 | — | 2 | 2 | no | — |
| 149 | C2×C4×C53 | — | 4 | 1 | no | — |
| 150 | C2×C4×C53 | — | 4 | 1 | no | — |
| 151 | C2×C4×C53 | — | 4 | 2 | no | — |
| 152 | C2×C4×C53 | #120 | 1 | 1 | yes | characteristic |
| 153 | C2×C4×C53 | #120 | 1 | 1 | yes | characteristic |
| 154 | C2×C4×C53 | #120 | 1 | 2 | yes | — |
| 155 | C2×C4×C53 | C2×D8 | 1 | 4 | yes | — |
| 156 | C2×C4×C53 | C2×D8 | 1 | 2 | yes | — |
| 157 | C2×C4×C53 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 158 | C2×C4×C53 | C22×D4 | 1 | 2 | yes | — |
| 159 | C22⋊D53 | — | 4 | 4 | no | — |
| 160 | C22⋊D53 | — | 4 | 4 | no | — |
| 161 | C2×Dic53 | — | 2 | 4 | no | — |
| 162 | C2×Dic53 | — | 4 | 2 | no | — |
| 163 | C2×Dic53 | — | 4 | 2 | no | — |
| 164 | C2×Dic53 | — | 4 | 1 | no | — |
| 165 | C2×Dic53 | — | 4 | 1 | no | — |
| 166 | C2×Dic53 | — | 4 | 2 | no | — |
| 167 | C2×Dic53 | — | 4 | 1 | no | — |
| 168 | D212 | — | 2 | 4 | no | — |
| 169 | D212 | — | 4 | 4 | no | — |
| 170 | D212 | — | 4 | 4 | no | — |
| 171 | D212 | — | 4 | 2 | no | — |
| 172 | D212 | — | 4 | 8 | no | — |
| 173 | D212 | — | 4 | 4 | no | — |
| 174 | D212 | — | 8 | 4 | no | — |
| 175 | C4×D53 | — | 4 | 16 | no | — |
| 176 | C4×D53 | — | 4 | 8 | no | — |
| 177 | C4×D53 | — | 8 | 4 | no | — |
| 178 | Dic106 | — | 4 | 8 | no | — |
| 179 | Dic106 | — | 4 | 4 | no | — |
| 180 | C8×C53 | — | 4 | 4 | no | — |
| 181 | #18218 | — | 53 | 1 | no | maximal, Sylow |
| 182 | C22×C53 | — | 2 | 1 | no | — |
| 183 | C22×C53 | — | 2 | 1 | no | — |
| 184 | C22×C53 | C2×#120 | 1 | 1 | yes | characteristic |
| 185 | C22×C53 | C22×D8 | 1 | 1 | yes | characteristic |
| 186 | C22×C53 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 187 | C2×D53 | — | 4 | 2 | no | — |
| 188 | C2×D53 | — | 4 | 2 | no | — |
| 189 | C2×D53 | — | 4 | 4 | no | — |
| 190 | C2×D53 | — | 4 | 4 | no | — |
| 191 | C2×D53 | — | 4 | 2 | no | — |
| 192 | C2×D53 | — | 4 | 4 | no | — |
| 193 | C2×D53 | — | 8 | 1 | no | — |
| 194 | C2×D53 | — | 8 | 1 | no | — |
| 195 | C2×D53 | — | 8 | 1 | no | — |
| 196 | C2×D53 | — | 8 | 1 | no | — |
| 197 | C4×C53 | — | 2 | 4 | no | — |
| 198 | C4×C53 | — | 2 | 1 | no | — |
| 199 | C4×C53 | — | 2 | 1 | no | — |
| 200 | C4×C53 | — | 2 | 2 | no | — |
| 201 | C4×C53 | — | 4 | 2 | no | — |
| 202 | C4×C53 | #447 | 1 | 4 | yes | — |
| 203 | Dic53 | — | 4 | 4 | no | — |
| 204 | Dic53 | — | 8 | 2 | no | — |
| 205 | Dic53 | — | 8 | 1 | no | — |
| 206 | #3497 | — | 53 | 1 | no | — |
| 207 | #3100 | — | 53 | 2 | no | — |
| 208 | #2536 | — | 53 | 1 | no | — |
| 209 | #1610 | — | 53 | 4 | no | — |
| 210 | #1598 | — | 53 | 4 | no | — |
| 211 | #1517 | — | 53 | 2 | no | — |
| 212 | #1461 | D53 | 1 | 1 | yes | characteristic, complemented |
| 213 | C2×C53 | — | 2 | 1 | no | — |
| 214 | C2×C53 | — | 2 | 1 | no | — |
| 215 | C2×C53 | C2×#447 | 1 | 1 | yes | characteristic |
| 216 | C2×C53 | #3020 | 1 | 1 | yes | characteristic |
| 217 | C2×C53 | #3025 | 1 | 1 | yes | characteristic |
| 218 | D53 | — | 8 | 4 | no | — |
| 219 | D53 | — | 8 | 2 | no | — |
| 220 | C2×2−1+4 | — | 106 | 1 | no | — |
| 221 | #550 | — | 106 | 2 | no | — |
| 222 | D4×Q8 | — | 106 | 2 | no | — |
| 223 | #548 | — | 106 | 4 | no | — |
| 224 | #537 | — | 53 | 4 | no | — |
| 225 | #537 | — | 106 | 1 | no | — |
| 226 | #532 | — | 53 | 2 | no | — |
| 227 | #532 | — | 106 | 2 | no | — |
| 228 | C2×C22⋊Q8 | — | 106 | 1 | no | — |
| 229 | C2×C4×Q8 | C2×D53 | 1 | 1 | yes | characteristic |
| 230 | C2×C4×D4 | — | 53 | 1 | no | — |
| 231 | #480 | — | 53 | 4 | no | — |
| 232 | #474 | — | 106 | 2 | no | — |
| 233 | #459 | — | 106 | 2 | no | — |
| 234 | #447 | — | 53 | 4 | no | — |
| 235 | C4×D8 | — | 106 | 4 | no | — |
| 236 | #431 | C2×D53 | 1 | 2 | yes | — |
| 237 | #398 | — | 53 | 2 | no | — |
| 238 | #394 | — | 53 | 2 | no | — |
| 239 | #388 | — | 106 | 2 | no | — |
| 240 | #382 | — | 53 | 1 | no | — |
| 241 | #380 | — | 106 | 1 | no | — |
| 242 | #327 | — | 53 | 8 | no | — |
| 243 | #324 | C2×D53 | 1 | 4 | yes | — |
| 244 | C53 | #18218 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 245 | 2−1+4 | — | 212 | 4 | no | — |
| 246 | 2−1+4 | — | 212 | 4 | no | — |
| 247 | C2×#41 | — | 106 | 4 | no | — |
| 248 | C2×#41 | — | 106 | 2 | no | — |
| 249 | C2×#41 | — | 106 | 4 | no | — |
| 250 | C22×Q8 | — | 106 | 4 | no | — |
| 251 | C22×Q8 | D212 | 1 | 1 | yes | characteristic |
| 252 | C22×D4 | — | 53 | 1 | no | — |
| 253 | C23×C4 | — | 106 | 1 | no | — |
| 254 | C2×D8 | — | 106 | 4 | no | — |
| 255 | C4⋊Q8 | — | 53 | 2 | no | — |
| 256 | C4⋊Q8 | — | 106 | 2 | no | — |
| 257 | #127 | — | 53 | 2 | no | — |
| 258 | #127 | — | 106 | 2 | no | — |
| 259 | #124 | — | 106 | 4 | no | — |
| 260 | #124 | — | 106 | 2 | no | — |
| 261 | C22⋊Q8 | — | 106 | 8 | no | — |
| 262 | C22⋊Q8 | — | 106 | 4 | no | — |
| 263 | C22⋊Q8 | — | 212 | 4 | no | — |
| 264 | #121 | — | 53 | 4 | no | — |
| 265 | #121 | — | 106 | 8 | no | — |
| 266 | #121 | — | 106 | 4 | no | — |
| 267 | #121 | — | 106 | 2 | no | — |
| 268 | #121 | — | 106 | 4 | no | — |
| 269 | C4×Q8 | — | 2 | 2 | no | — |
| 270 | C4×Q8 | — | 2 | 2 | no | — |
| 271 | C4×D4 | — | 53 | 4 | no | — |
| 272 | C4×D4 | — | 106 | 4 | no | — |
| 273 | C4×D4 | — | 106 | 4 | no | — |
| 274 | C4×D4 | — | 106 | 2 | no | — |
| 275 | C4×D4 | — | 106 | 2 | no | — |
| 276 | C4×D4 | — | 106 | 2 | no | — |
| 277 | C2×C4⋊C4 | — | 53 | 1 | no | — |
| 278 | C2×C4⋊C4 | — | 106 | 2 | no | — |
| 279 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 280 | C2×C4⋊C4 | D212 | 1 | 1 | yes | characteristic |
| 281 | C2×C4⋊C4 | C22×D53 | 1 | 2 | yes | — |
| 282 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 283 | C2×C22⋊C4 | — | 106 | 2 | no | — |
| 284 | C2×C22⋊C4 | — | 106 | 2 | no | — |
| 285 | C2×C42 | D212 | 1 | 2 | yes | — |
| 286 | C2×C42 | C22×D53 | 1 | 1 | yes | characteristic |
| 287 | #107 | — | 106 | 4 | no | — |
| 288 | C4⋊C8 | — | 2 | 2 | no | — |
| 289 | #102 | — | 106 | 4 | no | — |
| 290 | #102 | — | 106 | 4 | no | — |
| 291 | C22⋊C8 | C22×D53 | 1 | 4 | yes | — |
| 292 | C4×C8 | — | 2 | 2 | no | — |
| 293 | #95 | — | 53 | 2 | no | — |
| 294 | #95 | — | 106 | 2 | no | — |
| 295 | #95 | — | 106 | 1 | no | — |
| 296 | C24 | — | 106 | 1 | no | — |
| 297 | #41 | — | 212 | 8 | no | — |
| 298 | #41 | — | 212 | 16 | no | — |
| 299 | #41 | — | 212 | 8 | no | — |
| 300 | #41 | — | 212 | 4 | no | — |
| 301 | #41 | — | 212 | 4 | no | — |
| 302 | C2×Q8 | — | 2 | 2 | no | — |
| 303 | C2×Q8 | — | 2 | 2 | no | — |
| 304 | C2×Q8 | — | 106 | 4 | no | — |
| 305 | C2×Q8 | — | 106 | 2 | no | — |
| 306 | C2×Q8 | — | 212 | 16 | no | — |
| 307 | C2×Q8 | D424 | 1 | 4 | yes | complemented |
| 308 | C2×D4 | — | 53 | 4 | no | — |
| 309 | C2×D4 | — | 106 | 4 | no | — |
| 310 | C2×D4 | — | 106 | 4 | no | — |
| 311 | C2×D4 | — | 106 | 4 | no | — |
| 312 | C2×D4 | — | 106 | 2 | no | — |
| 313 | C2×D4 | — | 106 | 2 | no | — |
| 314 | C2×D4 | — | 106 | 2 | no | — |
| 315 | C2×D4 | — | 212 | 2 | no | — |
| 316 | C22×C4 | — | 106 | 8 | no | — |
| 317 | C22×C4 | — | 106 | 4 | no | — |
| 318 | C22×C4 | — | 106 | 2 | no | — |
| 319 | C22×C4 | — | 106 | 1 | no | — |
| 320 | C22×C4 | — | 212 | 2 | no | — |
| 321 | C22×C4 | — | 212 | 2 | no | — |
| 322 | C22×C4 | — | 212 | 2 | no | — |
| 323 | C22×C4 | C2×D212 | 1 | 2 | yes | — |
| 324 | C22×C4 | C2×D212 | 1 | 2 | yes | — |
| 325 | C22×C4 | C2×D212 | 1 | 1 | yes | characteristic |
| 326 | C22×C4 | C2×D212 | 1 | 1 | yes | characteristic |
| 327 | C22×C4 | C23×D53 | 1 | 1 | yes | characteristic |
| 328 | D8 | — | 212 | 8 | no | — |
| 329 | C2×C8 | — | 2 | 4 | no | — |
| 330 | C4⋊C4 | — | 2 | 2 | no | — |
| 331 | C4⋊C4 | — | 2 | 4 | no | — |
| 332 | C4⋊C4 | — | 53 | 4 | no | — |
| 333 | C4⋊C4 | — | 106 | 4 | no | — |
| 334 | C4⋊C4 | — | 106 | 2 | no | — |
| 335 | C4⋊C4 | — | 106 | 2 | no | — |
| 336 | C4⋊C4 | — | 212 | 4 | no | — |
| 337 | C4⋊C4 | — | 212 | 2 | no | — |
| 338 | C22⋊C4 | — | 106 | 8 | no | — |
| 339 | C22⋊C4 | — | 106 | 4 | no | — |
| 340 | C22⋊C4 | — | 106 | 4 | no | — |
| 341 | C22⋊C4 | — | 212 | 4 | no | — |
| 342 | C22⋊C4 | — | 212 | 1 | no | — |
| 343 | C22⋊C4 | — | 212 | 1 | no | — |
| 344 | C22⋊C4 | — | 212 | 4 | no | — |
| 345 | C42 | — | 2 | 2 | no | — |
| 346 | C42 | — | 2 | 2 | no | — |
| 347 | C42 | D4×D53 | 1 | 2 | yes | — |
| 348 | C42 | D4×D53 | 1 | 2 | yes | — |
| 349 | C23 | — | 106 | 2 | no | — |
| 350 | C23 | — | 106 | 4 | no | — |
| 351 | C23 | — | 212 | 1 | no | — |
| 352 | C23 | — | 212 | 1 | no | — |
| 353 | C23 | — | 212 | 1 | no | — |
| 354 | C23 | — | 212 | 1 | no | — |
| 355 | C23 | — | 212 | 1 | no | — |
| 356 | C23 | — | 212 | 1 | no | — |
| 357 | C23 | C22×D212 | 1 | 1 | yes | characteristic |
| 358 | Q8 | — | 2 | 8 | no | — |
| 359 | Q8 | — | 212 | 8 | no | — |
| 360 | Q8 | — | 212 | 4 | no | — |
| 361 | D4 | — | 106 | 4 | no | — |
| 362 | D4 | — | 424 | 4 | no | — |
| 363 | D4 | — | 212 | 4 | no | — |
| 364 | D4 | — | 212 | 4 | no | — |
| 365 | D4 | — | 212 | 2 | no | — |
| 366 | D4 | — | 212 | 8 | no | — |
| 367 | D4 | — | 212 | 4 | no | — |
| 368 | D4 | — | 212 | 4 | no | — |
| 369 | D4 | — | 212 | 4 | no | — |
| 370 | C2×C4 | — | 2 | 2 | no | — |
| 371 | C2×C4 | — | 2 | 2 | no | — |
| 372 | C2×C4 | — | 2 | 2 | no | — |
| 373 | C2×C4 | — | 4 | 1 | no | — |
| 374 | C2×C4 | — | 4 | 1 | no | — |
| 375 | C2×C4 | — | 4 | 2 | no | — |
| 376 | C2×C4 | — | 106 | 4 | no | — |
| 377 | C2×C4 | — | 424 | 4 | no | — |
| 378 | C2×C4 | — | 212 | 16 | no | — |
| 379 | C2×C4 | — | 212 | 2 | no | — |
| 380 | C2×C4 | — | 212 | 2 | no | — |
| 381 | C2×C4 | — | 212 | 1 | no | — |
| 382 | C2×C4 | — | 212 | 2 | no | — |
| 383 | C2×C4 | — | 212 | 1 | no | — |
| 384 | C2×C4 | — | 212 | 1 | no | — |
| 385 | C2×C4 | — | 212 | 8 | no | — |
| 386 | C2×C4 | #13133187 | 1 | 1 | yes | characteristic |
| 387 | C2×C4 | #13133187 | 1 | 1 | yes | characteristic |
| 388 | C2×C4 | #13133187 | 1 | 2 | yes | — |
| 389 | C2×C4 | C2×D424 | 1 | 4 | yes | — |
| 390 | C2×C4 | C2×D424 | 1 | 2 | yes | — |
| 391 | C2×C4 | #13133245 | 1 | 2 | yes | — |
| 392 | C2×C4 | C2×D4×D53 | 1 | 2 | yes | — |
| 393 | C8 | — | 4 | 4 | no | — |
| 394 | C22 | — | 2 | 1 | no | — |
| 395 | C22 | — | 2 | 1 | no | — |
| 396 | C22 | — | 424 | 1 | no | — |
| 397 | C22 | — | 424 | 1 | no | — |
| 398 | C22 | — | 424 | 1 | no | — |
| 399 | C22 | — | 424 | 1 | no | — |
| 400 | C22 | — | 212 | 2 | no | — |
| 401 | C22 | — | 212 | 2 | no | — |
| 402 | C22 | — | 212 | 4 | no | — |
| 403 | C22 | — | 212 | 2 | no | — |
| 404 | C22 | — | 212 | 4 | no | — |
| 405 | C22 | — | 212 | 4 | no | — |
| 406 | C22 | C2×#13133187 | 1 | 1 | yes | characteristic |
| 407 | C22 | C22×D424 | 1 | 1 | yes | characteristic |
| 408 | C22 | C2×#13133245 | 1 | 1 | yes | characteristic |
| 409 | C4 | — | 2 | 1 | no | — |
| 410 | C4 | — | 2 | 1 | no | — |
| 411 | C4 | — | 2 | 2 | no | — |
| 412 | C4 | — | 2 | 4 | no | — |
| 413 | C4 | — | 4 | 2 | no | — |
| 414 | C4 | — | 424 | 2 | no | — |
| 415 | C4 | — | 424 | 1 | no | — |
| 416 | C4 | — | 212 | 4 | no | — |
| 417 | C4 | #16810759 | 1 | 4 | yes | — |
| 418 | C2 | — | 2 | 1 | no | — |
| 419 | C2 | — | 2 | 1 | no | — |
| 420 | C2 | — | 424 | 2 | no | — |
| 421 | C2 | — | 424 | 4 | no | — |
| 422 | C2 | C2×#16810759 | 1 | 1 | yes | characteristic |
| 423 | C2 | #20284082 | 1 | 1 | yes | characteristic |
| 424 | C2 | #20284109 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20288486 | C2 | semidirect |
| 2. #20284716 | C2 | semidirect |
| 3. #20279620 | C2 | semidirect |
| 4. #20273720 | C2 | semidirect |
| 5. #20273652 | C2 | semidirect |
| 6. #20273276 | C2 | semidirect |
| 7. C53×#1461 | C2 | semidirect |
| 86. C2×Q8×C53 | D8 | semidirect |
| 212. #1461 | D53 | semidirect |
| 244. C53 | #18218 | semidirect |
| 307. C2×Q8 | D424 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20288486 | 2 |
| #20284716 | 2 |
| #20279620 | 2 |
| #20273720 | 2 |
| #20273652 | 2 |
| #20273276 | 2 |
| C53×#1461 | 2 |
| #18218 | 53 |