Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1040 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 1040 conjugacy classes of subgroups — too many to draw. Only its 167 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 | #20288339 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #20285175 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #20284531 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #20273861 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #20273856 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #20273843 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #20273152 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | C53×#1560 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C2×#13133247 | — | 2 | 2 | no | — |
| 10 | #16811353 | C22 | 1 | 1 | yes | characteristic |
| 11 | #16811339 | C22 | 1 | 1 | yes | characteristic |
| 12 | #16811337 | — | 2 | 2 | no | — |
| 13 | #16811335 | — | 2 | 2 | no | — |
| 14 | #16811293 | C22 | 1 | 2 | yes | — |
| 15 | #16811291 | — | 2 | 2 | no | — |
| 16 | #16811170 | — | 2 | 2 | no | — |
| 17 | #16811169 | — | 2 | 2 | no | — |
| 18 | C2×#13133217 | C22 | 1 | 1 | yes | characteristic |
| 19 | C4×#11719945 | C22 | 1 | 2 | yes | — |
| 20 | C4×#11719947 | — | 2 | 2 | no | — |
| 21 | #16811018 | — | 2 | 2 | no | — |
| 22 | #16811002 | C22 | 1 | 2 | yes | — |
| 23 | #16810995 | C22 | 1 | 2 | yes | — |
| 24 | #16810919 | C22 | 1 | 4 | yes | — |
| 25 | #16810914 | C22 | 1 | 4 | yes | — |
| 26 | #16810909 | — | 2 | 2 | no | — |
| 27 | #16810904 | — | 2 | 2 | no | — |
| 28 | #16810665 | — | 2 | 2 | no | — |
| 29 | #16810625 | — | 2 | 2 | no | — |
| 30 | C4×#11719917 | C22 | 1 | 1 | yes | characteristic |
| 31 | #16810353 | C22 | 1 | 4 | yes | — |
| 32 | #16810350 | C22 | 1 | 4 | yes | — |
| 33 | C53×#532 | C22 | 1 | 1 | yes | characteristic |
| 34 | C53×#423 | C22 | 1 | 2 | yes | — |
| 35 | C53×#333 | C22 | 1 | 2 | yes | — |
| 36 | C53×#331 | C22 | 1 | 2 | yes | — |
| 37 | C2×#11719945 | — | 2 | 2 | no | — |
| 38 | C2×#11719945 | D4 | 1 | 2 | yes | — |
| 39 | C2×#11719947 | — | 2 | 2 | no | — |
| 40 | C22×Dic106 | — | 2 | 1 | no | — |
| 41 | #13133247 | — | 4 | 8 | no | — |
| 42 | C2×#11719925 | — | 2 | 4 | no | — |
| 43 | C2×#11719923 | — | 2 | 4 | no | — |
| 44 | C2×#11719917 | — | 2 | 1 | no | — |
| 45 | #13133217 | — | 2 | 1 | no | — |
| 46 | #13133217 | — | 2 | 2 | no | — |
| 47 | #13133217 | C23 | 1 | 2 | yes | — |
| 48 | #13133216 | — | 2 | 2 | no | — |
| 49 | #13133215 | — | 2 | 2 | no | — |
| 50 | #13133213 | — | 2 | 2 | no | — |
| 51 | #13133213 | — | 2 | 2 | no | — |
| 52 | #13133206 | — | 2 | 2 | no | — |
| 53 | #13133204 | — | 2 | 2 | no | — |
| 54 | #13133203 | — | 2 | 4 | no | — |
| 55 | #13133192 | — | 2 | 2 | no | — |
| 56 | #13133190 | — | 2 | 4 | no | — |
| 57 | #13133189 | — | 2 | 4 | no | — |
| 58 | #13133189 | — | 2 | 4 | no | — |
| 59 | #13133188 | — | 2 | 2 | no | — |
| 60 | C4×Dic106 | D4 | 1 | 2 | yes | — |
| 61 | C4×Dic106 | C23 | 1 | 2 | yes | — |
| 62 | #13133182 | — | 2 | 2 | no | — |
| 63 | C4×D212 | D4 | 1 | 2 | yes | — |
| 64 | C4×D212 | C23 | 1 | 2 | yes | — |
| 65 | D4×Dic53 | — | 2 | 2 | no | — |
| 66 | C4×C22⋊D53 | — | 2 | 4 | no | — |
| 67 | C4×C22⋊D53 | — | 2 | 2 | no | — |
| 68 | C4×C22⋊D53 | — | 2 | 2 | no | — |
| 69 | #13133177 | — | 2 | 4 | no | — |
| 70 | #13133176 | D4 | 1 | 2 | yes | — |
| 71 | #13133175 | — | 2 | 2 | no | — |
| 72 | #13133174 | — | 2 | 2 | no | — |
| 73 | #13133173 | — | 2 | 4 | no | — |
| 74 | C2×C4⋊Dic53 | — | 2 | 2 | no | — |
| 75 | C2×C4×Dic53 | — | 2 | 2 | no | — |
| 76 | C42×D53 | — | 2 | 2 | no | — |
| 77 | #13133151 | — | 2 | 4 | no | — |
| 78 | #13133149 | — | 2 | 4 | no | — |
| 79 | #13133142 | — | 2 | 4 | no | — |
| 80 | #13133139 | — | 2 | 4 | no | — |
| 81 | #13133128 | — | 2 | 1 | no | — |
| 82 | C4×#88322 | C23 | 1 | 2 | yes | — |
| 83 | C2×#41×C53 | D4 | 1 | 2 | yes | — |
| 84 | C2×M16×C53 | — | 2 | 2 | no | — |
| 85 | C4⋊Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 86 | #127×C53 | C23 | 1 | 1 | yes | characteristic |
| 87 | #124×C53 | D4 | 1 | 2 | yes | — |
| 88 | #121×C53 | — | 2 | 2 | no | — |
| 89 | C4×D4×C53 | — | 2 | 2 | no | — |
| 90 | C2×C42×C53 | C23 | 1 | 1 | yes | characteristic |
| 91 | C4⋊C8×C53 | — | 2 | 2 | no | — |
| 92 | C4⋊C8×C53 | C23 | 1 | 4 | yes | — |
| 93 | #41×C53 | — | 4 | 4 | no | — |
| 94 | C2×Q8×C53 | C2×D4 | 1 | 2 | yes | — |
| 95 | C2×D4×C53 | — | 2 | 2 | no | — |
| 96 | C2×D4×C53 | — | 2 | 2 | no | — |
| 97 | C2×D4×C53 | C2×D4 | 1 | 2 | yes | — |
| 98 | C22×C4×C53 | — | 2 | 2 | no | — |
| 99 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 100 | C22×C4×C53 | C2×D4 | 1 | 2 | yes | — |
| 101 | C2×C22⋊D53 | — | 2 | 4 | no | — |
| 102 | C2×C22⋊D53 | — | 2 | 2 | no | — |
| 103 | C2×C22⋊D53 | — | 2 | 4 | no | — |
| 104 | C22×Dic53 | — | 2 | 4 | no | — |
| 105 | C22×Dic53 | — | 4 | 1 | no | — |
| 106 | #11719947 | — | 4 | 4 | no | — |
| 107 | #11719947 | — | 4 | 4 | no | — |
| 108 | #11719945 | — | 2 | 4 | no | — |
| 109 | #11719945 | — | 4 | 2 | no | — |
| 110 | #11719945 | — | 8 | 4 | no | — |
| 111 | C2×D212 | — | 2 | 2 | no | — |
| 112 | C2×D212 | C2×D4 | 1 | 2 | yes | — |
| 113 | C2×C4×D53 | — | 2 | 2 | no | — |
| 114 | C2×C4×D53 | — | 2 | 2 | no | — |
| 115 | C2×C4×D53 | — | 2 | 2 | no | — |
| 116 | C2×Dic106 | — | 2 | 2 | no | — |
| 117 | C2×Dic106 | — | 2 | 2 | no | — |
| 118 | C2×Dic106 | — | 4 | 4 | no | — |
| 119 | C2×Dic106 | — | 4 | 1 | no | — |
| 120 | C2×Dic106 | C2×D4 | 1 | 2 | yes | — |
| 121 | M16×C53 | — | 4 | 4 | no | — |
| 122 | C2×C8×C53 | — | 2 | 4 | no | — |
| 123 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 124 | C22⋊C4×C53 | — | 2 | 4 | no | — |
| 125 | C42×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 126 | C42×C53 | C2×D4 | 1 | 2 | yes | — |
| 127 | C42×C53 | C24 | 1 | 1 | yes | characteristic |
| 128 | C22⋊Dic53 | — | 2 | 4 | no | — |
| 129 | C22⋊Dic53 | — | 2 | 2 | no | — |
| 130 | #11719925 | — | 4 | 8 | no | — |
| 131 | #11719923 | — | 4 | 8 | no | — |
| 132 | #11719921 | — | 2 | 4 | no | — |
| 133 | #11719921 | — | 2 | 2 | no | — |
| 134 | #11719921 | — | 2 | 2 | no | — |
| 135 | C4⋊Dic53 | — | 2 | 4 | no | — |
| 136 | C4⋊Dic53 | — | 4 | 2 | no | — |
| 137 | C4⋊Dic53 | C2×D4 | 1 | 2 | yes | — |
| 138 | C4⋊Dic53 | C2×D4 | 1 | 2 | yes | — |
| 139 | #11719919 | — | 2 | 4 | no | — |
| 140 | #11719919 | — | 2 | 2 | no | — |
| 141 | #11719919 | — | 2 | 2 | no | — |
| 142 | C4×Dic53 | — | 2 | 2 | no | — |
| 143 | C4×Dic53 | — | 2 | 2 | no | — |
| 144 | C4×Dic53 | — | 2 | 2 | no | — |
| 145 | C4×Dic53 | — | 2 | 2 | no | — |
| 146 | C4×Dic53 | — | 2 | 2 | no | — |
| 147 | #11719917 | — | 2 | 4 | no | — |
| 148 | C2×#88322 | — | 2 | 2 | no | — |
| 149 | C23×C53 | — | 2 | 2 | no | — |
| 150 | C23×C53 | #120 | 1 | 1 | yes | characteristic |
| 151 | C22×D53 | — | 2 | 2 | no | — |
| 152 | Q8×C53 | — | 4 | 2 | no | — |
| 153 | D4×C53 | — | 4 | 2 | no | — |
| 154 | D4×C53 | — | 4 | 2 | no | — |
| 155 | D4×C53 | — | 4 | 2 | no | — |
| 156 | D4×C53 | — | 8 | 2 | no | — |
| 157 | C2×C4×C53 | — | 2 | 2 | no | — |
| 158 | C2×C4×C53 | — | 2 | 2 | no | — |
| 159 | C2×C4×C53 | — | 2 | 2 | no | — |
| 160 | C2×C4×C53 | — | 2 | 2 | no | — |
| 161 | C2×C4×C53 | — | 4 | 4 | no | — |
| 162 | C2×C4×C53 | #120 | 1 | 2 | yes | — |
| 163 | C2×C4×C53 | #120 | 1 | 1 | yes | characteristic |
| 164 | C2×C4×C53 | C22×D4 | 1 | 2 | yes | — |
| 165 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 166 | C22⋊D53 | — | 4 | 4 | no | — |
| 167 | C22⋊D53 | — | 4 | 8 | no | — |
| 168 | C22⋊D53 | — | 8 | 4 | no | — |
| 169 | C2×Dic53 | — | 2 | 2 | no | — |
| 170 | C2×Dic53 | — | 2 | 2 | no | — |
| 171 | C2×Dic53 | — | 2 | 2 | no | — |
| 172 | C2×Dic53 | — | 4 | 8 | no | — |
| 173 | C2×Dic53 | — | 4 | 2 | no | — |
| 174 | C2×Dic53 | — | 8 | 2 | no | — |
| 175 | D212 | — | 2 | 2 | no | — |
| 176 | D212 | — | 2 | 2 | no | — |
| 177 | D212 | — | 8 | 2 | no | — |
| 178 | C4×D53 | — | 4 | 4 | no | — |
| 179 | C4×D53 | — | 4 | 2 | no | — |
| 180 | C4×D53 | — | 4 | 2 | no | — |
| 181 | C4×D53 | — | 4 | 4 | no | — |
| 182 | Dic106 | — | 2 | 2 | no | — |
| 183 | Dic106 | — | 4 | 4 | no | — |
| 184 | Dic106 | — | 8 | 2 | no | — |
| 185 | Dic106 | — | 8 | 2 | no | — |
| 186 | Dic106 | #137 | 1 | 4 | yes | complemented |
| 187 | C8×C53 | — | 4 | 4 | no | — |
| 188 | #88322 | — | 2 | 4 | no | — |
| 189 | #18549 | — | 53 | 1 | no | maximal, Sylow |
| 190 | C22×C53 | — | 2 | 2 | no | — |
| 191 | C22×C53 | — | 2 | 1 | no | — |
| 192 | C22×C53 | — | 4 | 4 | no | — |
| 193 | C22×C53 | — | 4 | 2 | no | — |
| 194 | C22×C53 | C2×#120 | 1 | 1 | yes | characteristic |
| 195 | C2×D53 | — | 4 | 2 | no | — |
| 196 | C2×D53 | — | 4 | 2 | no | — |
| 197 | C2×D53 | — | 4 | 2 | no | — |
| 198 | C4×C53 | — | 2 | 2 | no | — |
| 199 | C4×C53 | — | 2 | 1 | no | — |
| 200 | C4×C53 | — | 4 | 2 | no | — |
| 201 | C4×C53 | #453 | 1 | 2 | yes | — |
| 202 | C4×C53 | C2×#137 | 1 | 2 | yes | — |
| 203 | C4×C53 | #575 | 1 | 2 | yes | — |
| 204 | Dic53 | — | 2 | 4 | no | — |
| 205 | Dic53 | — | 4 | 2 | no | — |
| 206 | Dic53 | — | 4 | 2 | no | — |
| 207 | Dic53 | — | 8 | 2 | no | — |
| 208 | #3483 | — | 53 | 1 | no | — |
| 209 | #3152 | — | 53 | 1 | no | — |
| 210 | #3079 | — | 53 | 2 | no | — |
| 211 | #1634 | — | 53 | 2 | no | — |
| 212 | #1633 | — | 53 | 2 | no | — |
| 213 | #1631 | — | 53 | 4 | no | — |
| 214 | #1560 | D53 | 1 | 1 | yes | characteristic, complemented |
| 215 | #1489 | — | 53 | 2 | no | — |
| 216 | C2×C53 | — | 4 | 1 | no | — |
| 217 | C2×C53 | — | 8 | 2 | no | — |
| 218 | C2×C53 | #3007 | 1 | 2 | yes | — |
| 219 | C2×C53 | C2×#453 | 1 | 1 | yes | characteristic |
| 220 | D53 | — | 8 | 2 | no | — |
| 221 | C2×#137 | — | 106 | 2 | no | — |
| 222 | Q82 | — | 53 | 1 | no | — |
| 223 | #555 | — | 53 | 1 | no | — |
| 224 | #555 | — | 106 | 2 | no | — |
| 225 | #555 | — | 106 | 2 | no | — |
| 226 | #550 | — | 53 | 2 | no | — |
| 227 | #550 | — | 106 | 2 | no | — |
| 228 | #532 | — | 106 | 2 | no | — |
| 229 | #532 | — | 106 | 2 | no | — |
| 230 | #532 | C2×D53 | 1 | 1 | yes | characteristic |
| 231 | C2×C4⋊Q8 | — | 53 | 1 | no | — |
| 232 | C4×#41 | — | 53 | 2 | no | — |
| 233 | C4×#41 | — | 106 | 2 | no | — |
| 234 | #497 | — | 106 | 2 | no | — |
| 235 | #494 | — | 53 | 2 | no | — |
| 236 | #492 | — | 53 | 2 | no | — |
| 237 | #477 | — | 53 | 4 | no | — |
| 238 | #476 | — | 53 | 4 | no | — |
| 239 | #475 | — | 106 | 2 | no | — |
| 240 | #474 | — | 106 | 2 | no | — |
| 241 | #428 | — | 106 | 2 | no | — |
| 242 | #423 | C2×D53 | 1 | 2 | yes | — |
| 243 | #417 | — | 106 | 2 | no | — |
| 244 | C4×M16 | — | 53 | 1 | no | — |
| 245 | #333 | C2×D53 | 1 | 2 | yes | — |
| 246 | #331 | C2×D53 | 1 | 2 | yes | — |
| 247 | Q8⋊C8 | — | 53 | 4 | no | — |
| 248 | D4⋊C8 | — | 53 | 4 | no | — |
| 249 | C53 | #18549 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 250 | C2×#41 | — | 53 | 2 | no | — |
| 251 | C2×#41 | — | 106 | 2 | no | — |
| 252 | C2×#41 | — | 106 | 2 | no | — |
| 253 | C2×#41 | D212 | 1 | 2 | yes | — |
| 254 | C22×Q8 | — | 106 | 1 | no | — |
| 255 | #137 | — | 212 | 8 | no | — |
| 256 | C2×Q16 | — | 106 | 4 | no | — |
| 257 | C2×SD16 | — | 106 | 4 | no | — |
| 258 | C2×M16 | — | 2 | 2 | no | — |
| 259 | C2×M16 | — | 106 | 1 | no | — |
| 260 | C4⋊Q8 | — | 53 | 2 | no | — |
| 261 | C4⋊Q8 | — | 106 | 2 | no | — |
| 262 | C4⋊Q8 | — | 106 | 2 | no | — |
| 263 | C4⋊Q8 | — | 106 | 1 | no | — |
| 264 | C4⋊Q8 | — | 106 | 2 | no | — |
| 265 | C4⋊Q8 | C22×D53 | 1 | 1 | yes | characteristic |
| 266 | #127 | — | 106 | 2 | no | — |
| 267 | #127 | — | 106 | 2 | no | — |
| 268 | #127 | C22×D53 | 1 | 1 | yes | characteristic |
| 269 | #124 | — | 106 | 4 | no | — |
| 270 | #124 | — | 106 | 2 | no | — |
| 271 | #124 | — | 106 | 2 | no | — |
| 272 | #124 | D212 | 1 | 2 | yes | — |
| 273 | #121 | — | 2 | 2 | no | — |
| 274 | #121 | — | 106 | 4 | no | — |
| 275 | #121 | — | 106 | 2 | no | — |
| 276 | #121 | — | 106 | 2 | no | — |
| 277 | #121 | — | 106 | 4 | no | — |
| 278 | #121 | — | 106 | 4 | no | — |
| 279 | C4×Q8 | — | 53 | 2 | no | — |
| 280 | C4×Q8 | — | 53 | 2 | no | — |
| 281 | C4×Q8 | — | 106 | 2 | no | — |
| 282 | C4×D4 | — | 2 | 2 | no | — |
| 283 | C4×D4 | — | 53 | 2 | no | — |
| 284 | C4×D4 | — | 53 | 2 | no | — |
| 285 | C4×D4 | — | 106 | 4 | no | — |
| 286 | C4×D4 | — | 106 | 2 | no | — |
| 287 | C4×D4 | — | 106 | 4 | no | — |
| 288 | C4×D4 | — | 106 | 2 | no | — |
| 289 | C4×D4 | — | 106 | 2 | no | — |
| 290 | #117 | — | 53 | 2 | no | — |
| 291 | #117 | — | 106 | 4 | no | — |
| 292 | #117 | — | 106 | 2 | no | — |
| 293 | #117 | — | 106 | 2 | no | — |
| 294 | C2×C4⋊C4 | — | 106 | 2 | no | — |
| 295 | C2×C42 | — | 106 | 2 | no | — |
| 296 | C2×C42 | — | 106 | 2 | no | — |
| 297 | C2×C42 | C22×D53 | 1 | 1 | yes | characteristic |
| 298 | #107 | — | 106 | 4 | no | — |
| 299 | #106 | — | 106 | 4 | no | — |
| 300 | C4⋊C8 | — | 2 | 2 | no | — |
| 301 | C4⋊C8 | C22×D53 | 1 | 4 | yes | — |
| 302 | #103 | — | 106 | 4 | no | — |
| 303 | #102 | — | 106 | 4 | no | — |
| 304 | #97 | — | 106 | 1 | no | — |
| 305 | C4×C8 | — | 53 | 2 | no | — |
| 306 | #41 | — | 4 | 4 | no | — |
| 307 | #41 | — | 106 | 4 | no | — |
| 308 | #41 | — | 424 | 4 | no | — |
| 309 | #41 | — | 212 | 2 | no | — |
| 310 | #41 | — | 212 | 4 | no | — |
| 311 | #41 | — | 212 | 4 | no | — |
| 312 | C2×Q8 | — | 53 | 2 | no | — |
| 313 | C2×Q8 | — | 106 | 2 | no | — |
| 314 | C2×Q8 | — | 106 | 2 | no | — |
| 315 | C2×Q8 | — | 212 | 4 | no | — |
| 316 | C2×Q8 | — | 212 | 1 | no | — |
| 317 | C2×Q8 | C2×D212 | 1 | 2 | yes | — |
| 318 | C2×D4 | — | 2 | 2 | no | — |
| 319 | C2×D4 | — | 2 | 2 | no | — |
| 320 | C2×D4 | — | 53 | 2 | no | — |
| 321 | C2×D4 | — | 106 | 2 | no | — |
| 322 | C2×D4 | — | 106 | 4 | no | — |
| 323 | C2×D4 | — | 106 | 4 | no | — |
| 324 | C2×D4 | — | 106 | 2 | no | — |
| 325 | C2×D4 | C2×D212 | 1 | 2 | yes | — |
| 326 | C22×C4 | — | 2 | 2 | no | — |
| 327 | C22×C4 | — | 106 | 4 | no | — |
| 328 | C22×C4 | — | 106 | 2 | no | — |
| 329 | C22×C4 | — | 106 | 2 | no | — |
| 330 | C22×C4 | — | 106 | 2 | no | — |
| 331 | C22×C4 | — | 212 | 1 | no | — |
| 332 | C22×C4 | C2×D212 | 1 | 1 | yes | characteristic |
| 333 | C22×C4 | D4×D53 | 1 | 2 | yes | — |
| 334 | Q16 | — | 212 | 8 | no | — |
| 335 | SD16 | — | 212 | 8 | no | — |
| 336 | M16 | — | 4 | 4 | no | — |
| 337 | M16 | — | 106 | 4 | no | — |
| 338 | C2×C8 | — | 2 | 4 | no | — |
| 339 | C2×C8 | — | 106 | 2 | no | — |
| 340 | C4⋊C4 | — | 2 | 2 | no | — |
| 341 | C4⋊C4 | — | 53 | 2 | no | — |
| 342 | C4⋊C4 | — | 53 | 2 | no | — |
| 343 | C4⋊C4 | — | 106 | 4 | no | — |
| 344 | C4⋊C4 | — | 106 | 2 | no | — |
| 345 | C4⋊C4 | — | 106 | 2 | no | — |
| 346 | C4⋊C4 | — | 106 | 4 | no | — |
| 347 | C4⋊C4 | — | 212 | 2 | no | — |
| 348 | C22⋊C4 | — | 2 | 4 | no | — |
| 349 | C22⋊C4 | — | 106 | 4 | no | — |
| 350 | C22⋊C4 | — | 106 | 4 | no | — |
| 351 | C22⋊C4 | — | 106 | 2 | no | — |
| 352 | C22⋊C4 | — | 106 | 2 | no | — |
| 353 | C22⋊C4 | — | 106 | 2 | no | — |
| 354 | C42 | — | 106 | 2 | no | — |
| 355 | C42 | — | 106 | 2 | no | — |
| 356 | C42 | — | 106 | 2 | no | — |
| 357 | C42 | — | 106 | 2 | no | — |
| 358 | C42 | — | 106 | 2 | no | — |
| 359 | C42 | C2×D212 | 1 | 1 | yes | characteristic |
| 360 | C42 | D4×D53 | 1 | 2 | yes | — |
| 361 | C42 | C23×D53 | 1 | 1 | yes | characteristic |
| 362 | C23 | — | 2 | 2 | no | — |
| 363 | C23 | — | 106 | 2 | no | — |
| 364 | C23 | #13133187 | 1 | 1 | yes | characteristic |
| 365 | Q8 | — | 4 | 2 | no | — |
| 366 | Q8 | — | 53 | 4 | no | — |
| 367 | Q8 | — | 106 | 2 | no | — |
| 368 | Q8 | — | 424 | 2 | no | — |
| 369 | Q8 | — | 424 | 2 | no | — |
| 370 | Q8 | — | 212 | 4 | no | — |
| 371 | D4 | — | 4 | 2 | no | — |
| 372 | D4 | — | 4 | 2 | no | — |
| 373 | D4 | — | 4 | 2 | no | — |
| 374 | D4 | — | 8 | 2 | no | — |
| 375 | D4 | — | 106 | 2 | no | — |
| 376 | D4 | — | 106 | 2 | no | — |
| 377 | D4 | — | 424 | 2 | no | — |
| 378 | D4 | — | 424 | 4 | no | — |
| 379 | D4 | — | 212 | 4 | no | — |
| 380 | D4 | — | 212 | 8 | no | — |
| 381 | C2×C4 | — | 2 | 2 | no | — |
| 382 | C2×C4 | — | 2 | 2 | no | — |
| 383 | C2×C4 | — | 2 | 2 | no | — |
| 384 | C2×C4 | — | 2 | 2 | no | — |
| 385 | C2×C4 | — | 4 | 4 | no | — |
| 386 | C2×C4 | — | 106 | 2 | no | — |
| 387 | C2×C4 | — | 106 | 2 | no | — |
| 388 | C2×C4 | — | 106 | 2 | no | — |
| 389 | C2×C4 | — | 424 | 2 | no | — |
| 390 | C2×C4 | — | 212 | 4 | no | — |
| 391 | C2×C4 | — | 212 | 8 | no | — |
| 392 | C2×C4 | — | 212 | 2 | no | — |
| 393 | C2×C4 | — | 212 | 4 | no | — |
| 394 | C2×C4 | — | 212 | 2 | no | — |
| 395 | C2×C4 | — | 212 | 2 | no | — |
| 396 | C2×C4 | #13133187 | 1 | 2 | yes | — |
| 397 | C2×C4 | #13133187 | 1 | 1 | yes | characteristic |
| 398 | C2×C4 | C2×D4×D53 | 1 | 2 | yes | — |
| 399 | C2×C4 | C22×D212 | 1 | 1 | yes | characteristic |
| 400 | C8 | — | 4 | 4 | no | — |
| 401 | C8 | — | 106 | 4 | no | — |
| 402 | C22 | — | 2 | 2 | no | — |
| 403 | C22 | — | 2 | 1 | no | — |
| 404 | C22 | — | 4 | 4 | no | — |
| 405 | C22 | — | 4 | 2 | no | — |
| 406 | C22 | — | 212 | 2 | no | — |
| 407 | C22 | — | 212 | 2 | no | — |
| 408 | C22 | — | 212 | 2 | no | — |
| 409 | C22 | C2×#13133187 | 1 | 1 | yes | characteristic |
| 410 | C4 | — | 2 | 2 | no | — |
| 411 | C4 | — | 2 | 1 | no | — |
| 412 | C4 | — | 4 | 2 | no | — |
| 413 | C4 | — | 106 | 4 | no | — |
| 414 | C4 | — | 424 | 2 | no | — |
| 415 | C4 | — | 212 | 2 | no | — |
| 416 | C4 | — | 212 | 2 | no | — |
| 417 | C4 | #16810793 | 1 | 2 | yes | — |
| 418 | C4 | #137×D53 | 1 | 2 | yes | — |
| 419 | C4 | #16811419 | 1 | 2 | yes | — |
| 420 | C2 | — | 4 | 1 | no | — |
| 421 | C2 | — | 8 | 2 | no | — |
| 422 | C2 | — | 424 | 2 | no | — |
| 423 | C2 | #20283976 | 1 | 2 | yes | — |
| 424 | C2 | C2×#16810793 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #20285175 | C2 | semidirect |
| 3. #20284531 | C2 | semidirect |
| 4. #20273861 | C2 | semidirect |
| 5. #20273856 | C2 | semidirect |
| 6. #20273843 | C2 | semidirect |
| 7. #20273152 | C2 | semidirect |
| 8. C53×#1560 | C2 | semidirect |
| 186. Dic106 | #137 | semidirect |
| 214. #1560 | D53 | semidirect |
| 249. C53 | #18549 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20288339 | 2 |
| #20285175 | 2 |
| #20284531 | 2 |
| #20273861 | 2 |
| #20273856 | 2 |
| #20273843 | 2 |
| #20273152 | 2 |
| C53×#1560 | 2 |
| #18549 | 53 |