Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
990 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 990 conjugacy classes of subgroups — too many to draw. Only its 170 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 | C2×#16811622 | C2 | 1 | 2 | yes | maximal |
| 2 | #20291281 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #20290415 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#16811494 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #20277204 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | C2×D53⋊M16 | C22 | 1 | 2 | yes | — |
| 7 | C2×#13133296 | C22 | 1 | 2 | yes | — |
| 8 | #16811622 | — | 2 | 4 | no | — |
| 9 | #16811622 | C4 | 1 | 8 | yes | complemented |
| 10 | C2×#13133282 | — | 2 | 4 | no | — |
| 11 | #16811588 | — | 2 | 4 | no | — |
| 12 | C4×#11719940 | — | 2 | 2 | no | — |
| 13 | #16811501 | — | 2 | 2 | no | — |
| 14 | #16811494 | — | 2 | 4 | no | — |
| 15 | C22×#11719949 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×#13133175 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×C42×D53 | C22 | 1 | 1 | yes | characteristic |
| 18 | #16810530 | C4 | 1 | 1 | yes | characteristic, complemented |
| 19 | #16810525 | C4 | 1 | 1 | yes | characteristic, complemented |
| 20 | #16810524 | C4 | 1 | 1 | yes | characteristic, complemented |
| 21 | #16810501 | — | 2 | 2 | no | — |
| 22 | #16810470 | — | 2 | 2 | no | — |
| 23 | C53×#391 | C4 | 1 | 1 | yes | characteristic, complemented |
| 24 | C2×#11719936 | D4 | 1 | 4 | yes | — |
| 25 | D53⋊M16 | — | 2 | 2 | no | — |
| 26 | D53⋊M16 | — | 2 | 2 | no | — |
| 27 | D53⋊M16 | C2×C4 | 1 | 4 | yes | — |
| 28 | D53⋊M16 | D4 | 1 | 4 | yes | — |
| 29 | C2×#11719940 | — | 2 | 2 | no | — |
| 30 | C2×D53⋊C8 | — | 2 | 2 | no | — |
| 31 | #13133296 | — | 2 | 2 | no | — |
| 32 | #13133296 | — | 2 | 2 | no | — |
| 33 | #13133296 | — | 2 | 2 | no | — |
| 34 | #13133296 | C2×C4 | 1 | 4 | yes | — |
| 35 | C2×C4⋊#6157 | — | 2 | 2 | no | — |
| 36 | C2×C22⋊#6157 | — | 2 | 2 | no | — |
| 37 | C2×C4×#6157 | — | 2 | 2 | no | — |
| 38 | #13133282 | — | 2 | 16 | no | — |
| 39 | #13133272 | — | 2 | 4 | no | — |
| 40 | C4×#88324 | — | 2 | 4 | no | — |
| 41 | C2×#11719949 | — | 2 | 2 | no | — |
| 42 | C2×#11719949 | — | 2 | 2 | no | — |
| 43 | C2×#11719949 | — | 2 | 2 | no | — |
| 44 | C2×#11719949 | — | 2 | 2 | no | — |
| 45 | C2×#11719949 | — | 2 | 2 | no | — |
| 46 | C2×#11719949 | C2×C4 | 1 | 4 | yes | — |
| 47 | C22×D212 | — | 2 | 1 | no | — |
| 48 | C22×D212 | C2×C4 | 1 | 1 | yes | characteristic |
| 49 | C22×C4×D53 | — | 2 | 1 | no | — |
| 50 | C22×C4×D53 | — | 2 | 1 | no | — |
| 51 | C22×C4×D53 | C23 | 1 | 1 | yes | characteristic |
| 52 | #13133175 | — | 2 | 2 | no | — |
| 53 | #13133175 | — | 2 | 2 | no | — |
| 54 | C2×C4⋊Dic53 | C2×C4 | 1 | 1 | yes | characteristic |
| 55 | C2×#11719921 | — | 2 | 2 | no | — |
| 56 | C2×#11719921 | — | 2 | 2 | no | — |
| 57 | C2×#11719921 | D4 | 1 | 2 | yes | — |
| 58 | C2×C4×Dic53 | — | 2 | 1 | no | — |
| 59 | C2×C4×Dic53 | C2×C4 | 1 | 1 | yes | characteristic |
| 60 | C2×C4×Dic53 | D4 | 1 | 2 | yes | — |
| 61 | C42×D53 | — | 2 | 2 | no | — |
| 62 | C42×D53 | — | 2 | 2 | no | — |
| 63 | #13133124 | — | 2 | 2 | no | — |
| 64 | C22×Q8×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 65 | C2×C4⋊C4×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 66 | C2×C42×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 67 | #95×C53 | — | 2 | 2 | no | — |
| 68 | C23×D53 | — | 2 | 1 | no | — |
| 69 | C23×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 70 | C22×#6157 | — | 4 | 2 | no | — |
| 71 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 72 | C2×Q8×C53 | — | 2 | 2 | no | — |
| 73 | C2×Q8×C53 | — | 2 | 2 | no | — |
| 74 | C2×Q8×C53 | C42 | 1 | 2 | yes | — |
| 75 | C22×C4×C53 | — | 2 | 1 | no | — |
| 76 | C22×C4×C53 | — | 2 | 1 | no | — |
| 77 | C22×C4×C53 | C22⋊C4 | 1 | 2 | yes | — |
| 78 | C22×C4×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 79 | C22×Dic53 | — | 2 | 1 | no | — |
| 80 | C22×Dic53 | C22⋊C4 | 1 | 2 | yes | — |
| 81 | C22×Dic53 | C2×D4 | 1 | 1 | yes | characteristic |
| 82 | #11719949 | — | 2 | 4 | no | — |
| 83 | #11719949 | — | 2 | 4 | no | — |
| 84 | #11719949 | — | 2 | 4 | no | — |
| 85 | #11719949 | — | 2 | 4 | no | — |
| 86 | #11719949 | — | 4 | 2 | no | — |
| 87 | #11719949 | — | 4 | 2 | no | — |
| 88 | #11719949 | — | 4 | 2 | no | — |
| 89 | #11719949 | — | 4 | 2 | no | — |
| 90 | C2×D212 | — | 2 | 2 | no | — |
| 91 | C2×D212 | — | 2 | 2 | no | — |
| 92 | C2×D212 | — | 2 | 4 | no | — |
| 93 | C2×D212 | — | 2 | 1 | no | — |
| 94 | C2×D212 | — | 4 | 2 | no | — |
| 95 | C2×D212 | — | 4 | 1 | no | — |
| 96 | C2×D212 | — | 4 | 1 | no | — |
| 97 | C2×D212 | C42 | 1 | 2 | yes | — |
| 98 | C2×C4×D53 | — | 2 | 4 | no | — |
| 99 | C2×C4×D53 | — | 4 | 2 | no | — |
| 100 | C2×C4×D53 | — | 4 | 2 | no | — |
| 101 | C2×C4×D53 | — | 4 | 1 | no | — |
| 102 | C2×C4×D53 | — | 4 | 1 | no | — |
| 103 | C2×C4×D53 | — | 4 | 1 | no | — |
| 104 | C2×C4×D53 | — | 4 | 2 | no | — |
| 105 | C2×C4×D53 | — | 4 | 1 | no | — |
| 106 | C2×C4×D53 | C22×C4 | 1 | 2 | yes | — |
| 107 | C2×C4×D53 | C2×D4 | 1 | 2 | yes | — |
| 108 | C2×C4×D53 | C2×D4 | 1 | 2 | yes | — |
| 109 | C2×C4×D53 | #41 | 1 | 2 | yes | — |
| 110 | C2×C4×D53 | #41 | 1 | 2 | yes | — |
| 111 | C2×C4×D53 | #41 | 1 | 2 | yes | — |
| 112 | C22⋊#6157 | — | 2 | 4 | no | — |
| 113 | C22⋊#6157 | — | 4 | 2 | no | — |
| 114 | #11719940 | — | 2 | 4 | no | — |
| 115 | #11719940 | — | 2 | 4 | no | — |
| 116 | C2×#88324 | — | 2 | 4 | no | — |
| 117 | C4⋊#6157 | — | 2 | 4 | no | — |
| 118 | C4⋊#6157 | — | 4 | 2 | no | — |
| 119 | C4×#6157 | — | 2 | 4 | no | — |
| 120 | C4×#6157 | — | 4 | 2 | no | — |
| 121 | #11719936 | — | 2 | 4 | no | — |
| 122 | #11719936 | C22⋊C4 | 1 | 8 | yes | complemented |
| 123 | D53⋊C8 | — | 2 | 4 | no | — |
| 124 | D53⋊C8 | — | 2 | 4 | no | — |
| 125 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 126 | C42×C53 | — | 2 | 2 | no | — |
| 127 | #11719921 | — | 2 | 4 | no | — |
| 128 | #11719921 | — | 4 | 4 | no | — |
| 129 | #11719921 | — | 4 | 4 | no | — |
| 130 | C4⋊Dic53 | — | 2 | 2 | no | — |
| 131 | C4×Dic53 | — | 2 | 2 | no | — |
| 132 | C4×Dic53 | — | 2 | 2 | no | — |
| 133 | C4×Dic53 | — | 2 | 2 | no | — |
| 134 | C4×Dic53 | — | 4 | 2 | no | — |
| 135 | C23×C53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 136 | C22×D53 | — | 2 | 2 | no | — |
| 137 | C22×D53 | — | 4 | 1 | no | — |
| 138 | C22×D53 | — | 4 | 1 | no | — |
| 139 | C22×D53 | — | 4 | 2 | no | — |
| 140 | C22×D53 | — | 4 | 2 | no | — |
| 141 | C22×D53 | — | 4 | 1 | no | — |
| 142 | C22×D53 | — | 4 | 1 | no | — |
| 143 | C22×D53 | C4×D4 | 1 | 2 | yes | — |
| 144 | C22×D53 | #121 | 1 | 2 | yes | — |
| 145 | C22×D53 | #124 | 1 | 1 | yes | characteristic |
| 146 | C22×D53 | #127 | 1 | 1 | yes | characteristic |
| 147 | C2×#6157 | — | 4 | 4 | no | — |
| 148 | C2×#6157 | — | 8 | 2 | no | — |
| 149 | C2×#6157 | — | 8 | 2 | no | — |
| 150 | Q8×C53 | — | 2 | 4 | no | — |
| 151 | Q8×C53 | — | 4 | 2 | no | — |
| 152 | C2×C4×C53 | — | 2 | 2 | no | — |
| 153 | C2×C4×C53 | — | 2 | 2 | no | — |
| 154 | C2×C4×C53 | — | 2 | 2 | no | — |
| 155 | C2×C4×C53 | — | 4 | 1 | no | — |
| 156 | C2×C4×C53 | — | 4 | 1 | no | — |
| 157 | C2×C4×C53 | — | 4 | 1 | no | — |
| 158 | C2×C4×C53 | — | 4 | 1 | no | — |
| 159 | C2×C4×C53 | — | 4 | 2 | no | — |
| 160 | C2×C4×C53 | C2×C42 | 1 | 1 | yes | characteristic |
| 161 | C2×C4×C53 | #117 | 1 | 1 | yes | characteristic |
| 162 | C2×C4×C53 | C4×D4 | 1 | 2 | yes | — |
| 163 | C2×C4×C53 | C4×D4 | 1 | 2 | yes | — |
| 164 | C2×Dic53 | — | 2 | 2 | no | — |
| 165 | C2×Dic53 | — | 2 | 2 | no | — |
| 166 | C2×Dic53 | — | 4 | 1 | no | — |
| 167 | C2×Dic53 | — | 4 | 1 | no | — |
| 168 | C2×Dic53 | — | 4 | 2 | no | — |
| 169 | C2×Dic53 | C4×D4 | 1 | 2 | yes | — |
| 170 | C2×Dic53 | #120 | 1 | 1 | yes | characteristic |
| 171 | C2×Dic53 | #121 | 1 | 2 | yes | — |
| 172 | C2×Dic53 | #123 | 1 | 1 | yes | characteristic |
| 173 | D212 | — | 2 | 4 | no | — |
| 174 | D212 | — | 4 | 4 | no | — |
| 175 | D212 | — | 4 | 4 | no | — |
| 176 | D212 | — | 4 | 2 | no | — |
| 177 | C4×D53 | — | 4 | 4 | no | — |
| 178 | C4×D53 | — | 4 | 4 | no | — |
| 179 | C4×D53 | — | 4 | 4 | no | — |
| 180 | C4×D53 | — | 4 | 4 | no | — |
| 181 | C4×D53 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 182 | C4×D53 | #117 | 1 | 2 | yes | — |
| 183 | C4×D53 | C4×D4 | 1 | 2 | yes | — |
| 184 | C4×D53 | C4×D4 | 1 | 2 | yes | — |
| 185 | C4×D53 | #121 | 1 | 2 | yes | — |
| 186 | C4×D53 | #123 | 1 | 2 | yes | — |
| 187 | C4×D53 | #124 | 1 | 2 | yes | — |
| 188 | C4×D53 | #126 | 1 | 2 | yes | — |
| 189 | #88324 | — | 2 | 8 | no | — |
| 190 | #10959 | — | 53 | 1 | no | maximal, Sylow |
| 191 | C22×C53 | — | 2 | 1 | no | — |
| 192 | C22×C53 | — | 2 | 1 | no | — |
| 193 | C22×C53 | C4×C22⋊C4 | 1 | 1 | yes | characteristic |
| 194 | C22×C53 | #386 | 1 | 1 | yes | characteristic |
| 195 | C22×C53 | #390 | 1 | 1 | yes | characteristic |
| 196 | C2×D53 | — | 2 | 2 | no | — |
| 197 | C2×D53 | — | 2 | 2 | no | — |
| 198 | C2×D53 | — | 4 | 1 | no | — |
| 199 | C2×D53 | — | 4 | 1 | no | — |
| 200 | C2×D53 | — | 4 | 2 | no | — |
| 201 | C2×D53 | — | 4 | 4 | no | — |
| 202 | C2×D53 | — | 4 | 2 | no | — |
| 203 | C2×D53 | — | 8 | 2 | no | — |
| 204 | C2×D53 | — | 8 | 1 | no | — |
| 205 | C2×D53 | — | 8 | 1 | no | — |
| 206 | C2×D53 | #388 | 1 | 2 | yes | — |
| 207 | C2×D53 | #390 | 1 | 2 | yes | — |
| 208 | #6157 | — | 8 | 4 | no | — |
| 209 | C4×C53 | — | 4 | 2 | no | — |
| 210 | C4×C53 | — | 4 | 2 | no | — |
| 211 | C4×C53 | — | 4 | 2 | no | — |
| 212 | C4×C53 | C4×C22⋊C4 | 1 | 2 | yes | — |
| 213 | C4×C53 | #388 | 1 | 2 | yes | — |
| 214 | Dic53 | — | 4 | 2 | no | — |
| 215 | Dic53 | — | 4 | 2 | no | — |
| 216 | Dic53 | #386 | 1 | 2 | yes | — |
| 217 | Dic53 | #388 | 1 | 2 | yes | — |
| 218 | C2×#421 | — | 53 | 2 | no | — |
| 219 | #2873 | — | 53 | 1 | no | — |
| 220 | #2297 | — | 53 | 1 | no | — |
| 221 | #1740 | — | 53 | 1 | no | — |
| 222 | C2×#339 | — | 53 | 2 | no | — |
| 223 | C2×C53 | — | 2 | 1 | no | — |
| 224 | C2×C53 | — | 2 | 1 | no | — |
| 225 | C2×C53 | #1437 | 1 | 1 | yes | characteristic |
| 226 | C2×C53 | #1884 | 1 | 1 | yes | characteristic |
| 227 | C2×C53 | #1884 | 1 | 1 | yes | characteristic |
| 228 | D53 | — | 2 | 2 | no | — |
| 229 | D53 | — | 2 | 2 | no | — |
| 230 | D53 | — | 8 | 2 | no | — |
| 231 | C22×#41 | — | 53 | 1 | no | — |
| 232 | C22×M16 | — | 53 | 2 | no | — |
| 233 | C2×#117 | — | 53 | 1 | no | — |
| 234 | C2×#117 | — | 53 | 2 | no | — |
| 235 | C22×C42 | — | 53 | 1 | no | — |
| 236 | #421 | — | 53 | 8 | no | — |
| 237 | #421 | — | 106 | 4 | no | — |
| 238 | C2×#104 | — | 106 | 4 | no | — |
| 239 | #405 | — | 106 | 4 | no | — |
| 240 | C4×M16 | — | 106 | 2 | no | — |
| 241 | #391 | — | 53 | 1 | no | — |
| 242 | #391 | #6157 | 1 | 1 | yes | characteristic, complemented |
| 243 | #390 | — | 53 | 1 | no | — |
| 244 | #390 | — | 53 | 1 | no | — |
| 245 | #386 | — | 106 | 2 | no | — |
| 246 | C4×C22⋊C4 | — | 106 | 2 | no | — |
| 247 | #342 | — | 106 | 2 | no | — |
| 248 | #339 | — | 106 | 4 | no | — |
| 249 | C53 | #10959 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 250 | C2×#41 | — | 53 | 4 | no | — |
| 251 | C2×#41 | — | 106 | 2 | no | — |
| 252 | C2×#41 | — | 106 | 2 | no | — |
| 253 | C2×#41 | — | 106 | 2 | no | — |
| 254 | C2×#41 | — | 106 | 2 | no | — |
| 255 | C2×#41 | — | 106 | 2 | no | — |
| 256 | C22×Q8 | C2×#6157 | 1 | 1 | yes | characteristic |
| 257 | C22×D4 | — | 53 | 1 | no | — |
| 258 | C22×D4 | — | 106 | 1 | no | — |
| 259 | C23×C4 | — | 53 | 1 | no | — |
| 260 | C23×C4 | — | 106 | 1 | no | — |
| 261 | C23×C4 | — | 106 | 1 | no | — |
| 262 | C2×M16 | — | 53 | 4 | no | — |
| 263 | C2×M16 | — | 53 | 4 | no | — |
| 264 | C2×M16 | — | 53 | 4 | no | — |
| 265 | C2×M16 | — | 106 | 2 | no | — |
| 266 | C2×M16 | — | 106 | 2 | no | — |
| 267 | C2×M16 | — | 106 | 2 | no | — |
| 268 | C22×C8 | — | 106 | 2 | no | — |
| 269 | #117 | — | 53 | 4 | no | — |
| 270 | #117 | — | 106 | 2 | no | — |
| 271 | #117 | — | 106 | 2 | no | — |
| 272 | #117 | — | 106 | 2 | no | — |
| 273 | #117 | — | 106 | 2 | no | — |
| 274 | #117 | — | 106 | 2 | no | — |
| 275 | C2×C4⋊C4 | — | 53 | 1 | no | — |
| 276 | C2×C4⋊C4 | — | 106 | 2 | no | — |
| 277 | C2×C4⋊C4 | C2×#6157 | 1 | 1 | yes | characteristic |
| 278 | C2×C22⋊C4 | — | 53 | 2 | no | — |
| 279 | C2×C22⋊C4 | — | 106 | 2 | no | — |
| 280 | C2×C22⋊C4 | — | 106 | 2 | no | — |
| 281 | C2×C22⋊C4 | — | 106 | 2 | no | — |
| 282 | C2×C42 | — | 53 | 2 | no | — |
| 283 | C2×C42 | — | 53 | 1 | no | — |
| 284 | C2×C42 | — | 106 | 2 | no | — |
| 285 | C2×C42 | — | 106 | 2 | no | — |
| 286 | C2×C42 | — | 106 | 2 | no | — |
| 287 | C2×C42 | — | 106 | 1 | no | — |
| 288 | C2×C42 | C2×#6157 | 1 | 1 | yes | characteristic |
| 289 | #104 | — | 106 | 16 | no | — |
| 290 | #97 | — | 106 | 4 | no | — |
| 291 | C4×C8 | — | 106 | 4 | no | — |
| 292 | #95 | — | 2 | 2 | no | — |
| 293 | #95 | — | 106 | 2 | no | — |
| 294 | C24 | — | 53 | 1 | no | — |
| 295 | C24 | — | 106 | 1 | no | — |
| 296 | #41 | — | 106 | 4 | no | — |
| 297 | #41 | — | 106 | 4 | no | — |
| 298 | #41 | — | 106 | 4 | no | — |
| 299 | #41 | — | 106 | 4 | no | — |
| 300 | #41 | — | 212 | 2 | no | — |
| 301 | #41 | — | 212 | 2 | no | — |
| 302 | #41 | — | 212 | 2 | no | — |
| 303 | #41 | — | 212 | 2 | no | — |
| 304 | C2×Q8 | — | 2 | 1 | no | — |
| 305 | C2×Q8 | — | 2 | 2 | no | — |
| 306 | C2×Q8 | — | 2 | 2 | no | — |
| 307 | C2×Q8 | C4×#6157 | 1 | 2 | yes | — |
| 308 | C2×D4 | — | 53 | 2 | no | — |
| 309 | C2×D4 | — | 106 | 4 | no | — |
| 310 | C2×D4 | — | 106 | 1 | no | — |
| 311 | C2×D4 | — | 106 | 2 | no | — |
| 312 | C2×D4 | — | 106 | 2 | no | — |
| 313 | C2×D4 | — | 212 | 2 | no | — |
| 314 | C2×D4 | — | 212 | 1 | no | — |
| 315 | C2×D4 | — | 212 | 1 | no | — |
| 316 | C22×C4 | — | 2 | 1 | no | — |
| 317 | C22×C4 | — | 2 | 1 | no | — |
| 318 | C22×C4 | — | 53 | 1 | no | — |
| 319 | C22×C4 | — | 53 | 2 | no | — |
| 320 | C22×C4 | — | 53 | 2 | no | — |
| 321 | C22×C4 | — | 53 | 2 | no | — |
| 322 | C22×C4 | — | 53 | 2 | no | — |
| 323 | C22×C4 | — | 53 | 2 | no | — |
| 324 | C22×C4 | — | 53 | 2 | no | — |
| 325 | C22×C4 | — | 53 | 2 | no | — |
| 326 | C22×C4 | — | 106 | 4 | no | — |
| 327 | C22×C4 | — | 106 | 1 | no | — |
| 328 | C22×C4 | — | 212 | 2 | no | — |
| 329 | C22×C4 | — | 212 | 1 | no | — |
| 330 | C22×C4 | — | 212 | 1 | no | — |
| 331 | C22×C4 | — | 212 | 2 | no | — |
| 332 | C22×C4 | — | 212 | 2 | no | — |
| 333 | C22×C4 | — | 212 | 1 | no | — |
| 334 | C22×C4 | — | 212 | 1 | no | — |
| 335 | C22×C4 | — | 212 | 2 | no | — |
| 336 | C22×C4 | C22⋊#6157 | 1 | 2 | yes | — |
| 337 | C22×C4 | C22×#6157 | 1 | 1 | yes | characteristic |
| 338 | M16 | — | 53 | 8 | no | — |
| 339 | M16 | — | 106 | 4 | no | — |
| 340 | M16 | — | 106 | 4 | no | — |
| 341 | M16 | — | 106 | 4 | no | — |
| 342 | C2×C8 | — | 106 | 4 | no | — |
| 343 | C2×C8 | — | 106 | 4 | no | — |
| 344 | C2×C8 | — | 106 | 4 | no | — |
| 345 | C4⋊C4 | — | 2 | 2 | no | — |
| 346 | C4⋊C4 | — | 106 | 4 | no | — |
| 347 | C4⋊C4 | — | 106 | 2 | no | — |
| 348 | C4⋊C4 | — | 212 | 2 | no | — |
| 349 | C22⋊C4 | — | 106 | 4 | no | — |
| 350 | C22⋊C4 | — | 106 | 4 | no | — |
| 351 | C22⋊C4 | — | 212 | 4 | no | — |
| 352 | C22⋊C4 | — | 212 | 4 | no | — |
| 353 | C22⋊C4 | — | 212 | 2 | no | — |
| 354 | C42 | — | 2 | 2 | no | — |
| 355 | C42 | — | 106 | 2 | no | — |
| 356 | C42 | — | 106 | 2 | no | — |
| 357 | C42 | — | 106 | 4 | no | — |
| 358 | C42 | — | 106 | 2 | no | — |
| 359 | C42 | — | 212 | 2 | no | — |
| 360 | C42 | — | 212 | 2 | no | — |
| 361 | C23 | — | 53 | 2 | no | — |
| 362 | C23 | — | 53 | 2 | no | — |
| 363 | C23 | — | 53 | 1 | no | — |
| 364 | C23 | — | 53 | 1 | no | — |
| 365 | C23 | — | 106 | 2 | no | — |
| 366 | C23 | — | 212 | 1 | no | — |
| 367 | C23 | — | 212 | 1 | no | — |
| 368 | C23 | — | 212 | 2 | no | — |
| 369 | C23 | — | 212 | 2 | no | — |
| 370 | C23 | — | 212 | 1 | no | — |
| 371 | C23 | — | 212 | 1 | no | — |
| 372 | C23 | C2×C22⋊#6157 | 1 | 1 | yes | characteristic |
| 373 | Q8 | — | 2 | 4 | no | — |
| 374 | Q8 | — | 4 | 2 | no | — |
| 375 | D4 | — | 106 | 4 | no | — |
| 376 | D4 | — | 212 | 4 | no | — |
| 377 | D4 | — | 212 | 4 | no | — |
| 378 | D4 | — | 212 | 2 | no | — |
| 379 | C2×C4 | — | 2 | 2 | no | — |
| 380 | C2×C4 | — | 2 | 2 | no | — |
| 381 | C2×C4 | — | 2 | 2 | no | — |
| 382 | C2×C4 | — | 4 | 1 | no | — |
| 383 | C2×C4 | — | 4 | 1 | no | — |
| 384 | C2×C4 | — | 4 | 1 | no | — |
| 385 | C2×C4 | — | 4 | 1 | no | — |
| 386 | C2×C4 | — | 4 | 2 | no | — |
| 387 | C2×C4 | — | 53 | 2 | no | — |
| 388 | C2×C4 | — | 53 | 1 | no | — |
| 389 | C2×C4 | — | 53 | 1 | no | — |
| 390 | C2×C4 | — | 53 | 2 | no | — |
| 391 | C2×C4 | — | 53 | 2 | no | — |
| 392 | C2×C4 | — | 53 | 2 | no | — |
| 393 | C2×C4 | — | 53 | 2 | no | — |
| 394 | C2×C4 | — | 53 | 2 | no | — |
| 395 | C2×C4 | — | 53 | 2 | no | — |
| 396 | C2×C4 | — | 53 | 2 | no | — |
| 397 | C2×C4 | — | 53 | 2 | no | — |
| 398 | C2×C4 | — | 53 | 2 | no | — |
| 399 | C2×C4 | — | 106 | 2 | no | — |
| 400 | C2×C4 | — | 106 | 2 | no | — |
| 401 | C2×C4 | — | 424 | 2 | no | — |
| 402 | C2×C4 | — | 424 | 2 | no | — |
| 403 | C2×C4 | — | 212 | 4 | no | — |
| 404 | C2×C4 | — | 212 | 4 | no | — |
| 405 | C2×C4 | — | 212 | 4 | no | — |
| 406 | C2×C4 | — | 212 | 4 | no | — |
| 407 | C2×C4 | — | 212 | 4 | no | — |
| 408 | C2×C4 | — | 212 | 1 | no | — |
| 409 | C2×C4 | — | 212 | 1 | no | — |
| 410 | C2×C4 | — | 212 | 2 | no | — |
| 411 | C2×C4 | C2×C4×#6157 | 1 | 1 | yes | characteristic |
| 412 | C2×C4 | #13133296 | 1 | 1 | yes | characteristic |
| 413 | C2×C4 | D4×#6157 | 1 | 2 | yes | — |
| 414 | C2×C4 | D4×#6157 | 1 | 2 | yes | — |
| 415 | C8 | — | 106 | 8 | no | — |
| 416 | C22 | — | 2 | 1 | no | — |
| 417 | C22 | — | 2 | 1 | no | — |
| 418 | C22 | — | 53 | 2 | no | — |
| 419 | C22 | — | 53 | 2 | no | — |
| 420 | C22 | — | 106 | 2 | no | — |
| 421 | C22 | — | 106 | 2 | no | — |
| 422 | C22 | — | 424 | 2 | no | — |
| 423 | C22 | — | 424 | 1 | no | — |
| 424 | C22 | — | 424 | 1 | no | — |
| 425 | C22 | — | 212 | 1 | no | — |
| 426 | C22 | — | 212 | 1 | no | — |
| 427 | C22 | — | 212 | 2 | no | — |
| 428 | C22 | — | 212 | 4 | no | — |
| 429 | C22 | — | 212 | 2 | no | — |
| 430 | C22 | C4×C22⋊#6157 | 1 | 1 | yes | characteristic |
| 431 | C22 | #16811571 | 1 | 1 | yes | characteristic |
| 432 | C22 | #16811575 | 1 | 1 | yes | characteristic |
| 433 | C4 | — | 4 | 2 | no | — |
| 434 | C4 | — | 4 | 2 | no | — |
| 435 | C4 | — | 4 | 2 | no | — |
| 436 | C4 | — | 53 | 2 | no | — |
| 437 | C4 | — | 53 | 2 | no | — |
| 438 | C4 | — | 424 | 4 | no | — |
| 439 | C4 | — | 212 | 2 | no | — |
| 440 | C4 | — | 212 | 2 | no | — |
| 441 | C4 | C22⋊C4×#6157 | 1 | 2 | yes | — |
| 442 | C4 | #16811573 | 1 | 2 | yes | — |
| 443 | C2 | — | 2 | 1 | no | — |
| 444 | C2 | — | 2 | 1 | no | — |
| 445 | C2 | — | 106 | 2 | no | — |
| 446 | C2 | — | 106 | 2 | no | — |
| 447 | C2 | — | 424 | 2 | no | — |
| 448 | C2 | #20289896 | 1 | 1 | yes | characteristic |
| 449 | C2 | #20290716 | 1 | 1 | yes | characteristic |
| 450 | C2 | #20290717 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #20291281 | C2 | semidirect |
| 3. #20290415 | C2 | semidirect |
| 4. C2×#16811494 | C2 | semidirect |
| 9. #16811622 | C4 | semidirect |
| 18. #16810530 | C4 | semidirect |
| 19. #16810525 | C4 | semidirect |
| 20. #16810524 | C4 | semidirect |
| 23. C53×#391 | C4 | semidirect |
| 122. #11719936 | C22⋊C4 | semidirect |
| 242. #391 | #6157 | semidirect |
| 249. C53 | #10959 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811622 | 2 |
| #20291281 | 2 |
| #20290415 | 2 |
| C2×#16811494 | 2 |
| #20277204 | 2 |
| #10959 | 53 |