Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1328 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 1328 conjugacy classes of subgroups — too many to draw. Only its 212 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 | #20291710 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #20291432 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #20290727 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #20290687 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #20290560 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #20290473 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #20284108 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #16811702 | — | 2 | 3 | no | — |
| 9 | #16811701 | — | 2 | 3 | no | — |
| 10 | #16811701 | C22 | 1 | 3 | yes | — |
| 11 | D53⋊#131 | — | 2 | 3 | no | — |
| 12 | C2×#13133304 | — | 2 | 3 | no | — |
| 13 | C2×#13133304 | C22 | 1 | 3 | yes | — |
| 14 | C22×D53⋊C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | #16811655 | — | 2 | 3 | no | — |
| 16 | #16811653 | — | 2 | 3 | no | — |
| 17 | #16811651 | — | 2 | 3 | no | — |
| 18 | #16811650 | — | 2 | 3 | no | — |
| 19 | #16811629 | C22 | 1 | 3 | yes | complemented |
| 20 | #16811610 | C22 | 1 | 3 | yes | — |
| 21 | #16811596 | C22 | 1 | 3 | yes | — |
| 22 | #16811595 | C22 | 1 | 3 | yes | complemented |
| 23 | #16811587 | C22 | 1 | 3 | yes | complemented |
| 24 | #16811504 | C22 | 1 | 6 | yes | complemented |
| 25 | #16811458 | C22 | 1 | 1 | yes | characteristic |
| 26 | #16811131 | C22 | 1 | 3 | yes | — |
| 27 | #16810812 | C4 | 1 | 3 | yes | — |
| 28 | #16810811 | C4 | 1 | 3 | yes | — |
| 29 | #16810810 | C4 | 1 | 1 | yes | characteristic |
| 30 | #16810595 | C22 | 1 | 3 | yes | — |
| 31 | C53×#458 | C4 | 1 | 1 | yes | characteristic |
| 32 | #13133305 | — | 2 | 1 | no | — |
| 33 | #13133305 | — | 2 | 3 | no | — |
| 34 | #13133304 | — | 2 | 3 | no | — |
| 35 | #13133304 | — | 2 | 6 | no | — |
| 36 | #13133304 | — | 2 | 3 | no | — |
| 37 | #13133304 | — | 2 | 6 | no | — |
| 38 | #13133304 | — | 2 | 6 | no | — |
| 39 | #13133304 | — | 2 | 6 | no | — |
| 40 | #13133304 | — | 2 | 6 | no | — |
| 41 | C2×#11719936 | — | 2 | 3 | no | — |
| 42 | C2×#11719936 | D4 | 1 | 3 | yes | complemented |
| 43 | D53⋊M16 | — | 2 | 6 | no | — |
| 44 | D53⋊M16 | — | 2 | 3 | no | — |
| 45 | C2×#11719940 | — | 2 | 3 | no | — |
| 46 | C2×#11719940 | — | 2 | 3 | no | — |
| 47 | C2×#11719940 | D4 | 1 | 3 | yes | complemented |
| 48 | C2×#11719940 | C23 | 1 | 3 | yes | — |
| 49 | C2×#11719940 | C23 | 1 | 3 | yes | — |
| 50 | C2×D53⋊C8 | — | 2 | 3 | no | — |
| 51 | C2×D53⋊C8 | — | 2 | 3 | no | — |
| 52 | C2×D53⋊C8 | — | 2 | 3 | no | — |
| 53 | C2×D53⋊C8 | D4 | 1 | 3 | yes | complemented |
| 54 | C22×#88324 | — | 2 | 1 | no | — |
| 55 | C22×#88324 | D4 | 1 | 3 | yes | complemented |
| 56 | C22×#88324 | C23 | 1 | 1 | yes | characteristic |
| 57 | C22×#88324 | C23 | 1 | 1 | yes | characteristic |
| 58 | #13133284 | — | 2 | 3 | no | — |
| 59 | C4⋊#88324 | — | 2 | 3 | no | — |
| 60 | #13133278 | — | 2 | 3 | no | — |
| 61 | #13133277 | — | 2 | 3 | no | — |
| 62 | #13133274 | — | 2 | 3 | no | — |
| 63 | #13133274 | — | 2 | 3 | no | — |
| 64 | #13133274 | — | 2 | 3 | no | — |
| 65 | C22⋊#88324 | — | 2 | 3 | no | — |
| 66 | #13133272 | — | 2 | 3 | no | — |
| 67 | C4×#88324 | — | 2 | 3 | no | — |
| 68 | #13133264 | — | 2 | 3 | no | — |
| 69 | #13133262 | — | 2 | 3 | no | — |
| 70 | #13133262 | C2×C4 | 1 | 3 | yes | — |
| 71 | C2×#11719947 | — | 2 | 3 | no | — |
| 72 | C2×#11719947 | C23 | 1 | 3 | yes | — |
| 73 | #41×D53 | — | 2 | 3 | no | — |
| 74 | C22×C4×D53 | C23 | 1 | 1 | yes | characteristic |
| 75 | #13133200 | C2×C4 | 1 | 3 | yes | — |
| 76 | #13133195 | — | 2 | 3 | no | — |
| 77 | #13133190 | — | 2 | 3 | no | — |
| 78 | #13133187 | C2×C4 | 1 | 3 | yes | — |
| 79 | #13133185 | C2×C4 | 1 | 3 | yes | — |
| 80 | #13133179 | — | 2 | 3 | no | — |
| 81 | #13133177 | — | 2 | 3 | no | — |
| 82 | #13133173 | C23 | 1 | 3 | yes | — |
| 83 | #13133132 | C2×C4 | 1 | 3 | yes | — |
| 84 | #13133131 | C2×C4 | 1 | 6 | yes | — |
| 85 | H(5,𝔽2)×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 86 | #123×C53 | C2×C4 | 1 | 3 | yes | — |
| 87 | #99×C53 | C2×C4 | 1 | 3 | yes | — |
| 88 | C23×D53 | C22×C4 | 1 | 1 | yes | characteristic |
| 89 | #41×C53 | — | 2 | 3 | no | — |
| 90 | C2×D4×C53 | — | 2 | 3 | no | — |
| 91 | C2×D4×C53 | C22×C4 | 1 | 3 | yes | — |
| 92 | C22×C4×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 93 | C2×C22⋊D53 | — | 2 | 3 | no | — |
| 94 | C2×C22⋊D53 | — | 2 | 3 | no | — |
| 95 | C2×C22⋊D53 | — | 2 | 3 | no | — |
| 96 | C2×C22⋊D53 | C22×C4 | 1 | 3 | yes | — |
| 97 | C2×C22⋊D53 | #41 | 1 | 3 | yes | — |
| 98 | C22×Dic53 | — | 2 | 1 | no | — |
| 99 | C22×Dic53 | C2×D4 | 1 | 3 | yes | — |
| 100 | C22×Dic53 | C24 | 1 | 1 | yes | characteristic |
| 101 | #11719949 | — | 2 | 1 | no | — |
| 102 | Q8×D53 | — | 2 | 3 | no | — |
| 103 | #11719947 | — | 2 | 3 | no | — |
| 104 | #11719947 | — | 2 | 6 | no | — |
| 105 | #11719947 | — | 2 | 6 | no | — |
| 106 | #11719947 | — | 2 | 6 | no | — |
| 107 | #11719947 | — | 2 | 6 | no | — |
| 108 | D4×D53 | — | 2 | 3 | no | — |
| 109 | D4×D53 | — | 2 | 6 | no | — |
| 110 | #11719945 | — | 2 | 6 | no | — |
| 111 | #11719945 | — | 2 | 3 | no | — |
| 112 | C2×D212 | — | 2 | 3 | no | — |
| 113 | C2×C4×D53 | — | 2 | 3 | no | — |
| 114 | C2×C4×D53 | — | 2 | 3 | no | — |
| 115 | C2×C4×D53 | — | 2 | 3 | no | — |
| 116 | C2×C4×D53 | C2×D4 | 1 | 3 | yes | — |
| 117 | C2×Dic106 | — | 2 | 3 | no | — |
| 118 | C2×Dic106 | #41 | 1 | 3 | yes | — |
| 119 | #11719940 | — | 2 | 6 | no | — |
| 120 | #11719940 | — | 2 | 6 | no | — |
| 121 | #11719940 | — | 2 | 6 | no | — |
| 122 | #11719940 | — | 2 | 6 | no | — |
| 123 | C2×#88324 | — | 2 | 3 | no | — |
| 124 | C2×#88324 | — | 2 | 3 | no | — |
| 125 | C2×#88324 | — | 2 | 3 | no | — |
| 126 | C2×#88324 | — | 2 | 3 | no | — |
| 127 | C2×#88324 | — | 2 | 3 | no | — |
| 128 | C2×#88324 | — | 2 | 3 | no | — |
| 129 | C2×#88324 | C2×D4 | 1 | 3 | yes | — |
| 130 | C2×#88324 | C2×D4 | 1 | 3 | yes | — |
| 131 | C2×#88324 | C2×D4 | 1 | 3 | yes | — |
| 132 | C2×#88324 | C2×D4 | 1 | 3 | yes | — |
| 133 | #11719936 | — | 2 | 3 | no | — |
| 134 | #11719936 | — | 2 | 3 | no | — |
| 135 | #11719936 | — | 2 | 6 | no | — |
| 136 | D53⋊C8 | — | 2 | 6 | no | — |
| 137 | D53⋊C8 | — | 2 | 3 | no | — |
| 138 | D53⋊C8 | — | 2 | 3 | no | — |
| 139 | D53⋊C8 | — | 4 | 3 | no | — |
| 140 | D53⋊C8 | — | 4 | 1 | no | — |
| 141 | C4⋊C4×C53 | — | 2 | 3 | no | — |
| 142 | C22⋊C4×C53 | — | 2 | 3 | no | — |
| 143 | C22⋊C4×C53 | C22×C4 | 1 | 3 | yes | — |
| 144 | C22⋊Dic53 | C22×C4 | 1 | 3 | yes | — |
| 145 | #11719921 | — | 2 | 3 | no | — |
| 146 | #11719921 | — | 2 | 3 | no | — |
| 147 | #11719921 | — | 2 | 3 | no | — |
| 148 | #11719919 | — | 2 | 3 | no | — |
| 149 | #11719919 | — | 2 | 3 | no | — |
| 150 | C4×Dic53 | — | 2 | 3 | no | — |
| 151 | C23×C53 | — | 2 | 1 | no | — |
| 152 | C23×C53 | C4×D4 | 1 | 3 | yes | — |
| 153 | C23×C53 | C23×C4 | 1 | 1 | yes | characteristic |
| 154 | C22×D53 | — | 2 | 3 | no | — |
| 155 | C22×D53 | — | 2 | 3 | no | — |
| 156 | C22×D53 | — | 4 | 2 | no | — |
| 157 | C22×D53 | C4×D4 | 1 | 3 | yes | — |
| 158 | Q8×C53 | — | 2 | 1 | no | — |
| 159 | D4×C53 | — | 2 | 3 | no | — |
| 160 | D4×C53 | — | 2 | 6 | no | — |
| 161 | C2×C4×C53 | — | 2 | 3 | no | — |
| 162 | C2×C4×C53 | — | 2 | 3 | no | — |
| 163 | C2×C4×C53 | — | 2 | 3 | no | — |
| 164 | C2×C4×C53 | C4×D4 | 1 | 3 | yes | — |
| 165 | C22⋊D53 | — | 2 | 6 | no | — |
| 166 | C22⋊D53 | — | 2 | 6 | no | — |
| 167 | C22⋊D53 | — | 2 | 6 | no | — |
| 168 | C22⋊D53 | — | 4 | 6 | no | — |
| 169 | C2×Dic53 | — | 2 | 3 | no | — |
| 170 | C2×Dic53 | — | 2 | 3 | no | — |
| 171 | C2×Dic53 | — | 2 | 3 | no | — |
| 172 | C2×Dic53 | — | 2 | 3 | no | — |
| 173 | C2×Dic53 | C4×D4 | 1 | 3 | yes | — |
| 174 | C2×Dic53 | C22×D4 | 1 | 3 | yes | — |
| 175 | C2×Dic53 | C2×#41 | 1 | 3 | yes | — |
| 176 | D212 | — | 2 | 3 | no | — |
| 177 | D212 | — | 4 | 6 | no | — |
| 178 | C4×D53 | — | 2 | 6 | no | — |
| 179 | C4×D53 | — | 2 | 3 | no | — |
| 180 | C4×D53 | — | 2 | 3 | no | — |
| 181 | C4×D53 | — | 4 | 1 | no | — |
| 182 | C4×D53 | — | 4 | 3 | no | — |
| 183 | Dic106 | — | 2 | 3 | no | — |
| 184 | Dic106 | — | 2 | 6 | no | — |
| 185 | #88324 | — | 2 | 3 | no | — |
| 186 | #88324 | — | 2 | 3 | no | — |
| 187 | #88324 | — | 4 | 1 | no | — |
| 188 | #88324 | — | 4 | 3 | no | — |
| 189 | #88324 | #120 | 1 | 3 | yes | — |
| 190 | #88324 | #120 | 1 | 1 | yes | characteristic |
| 191 | #21483 | — | 53 | 1 | no | maximal, Sylow |
| 192 | C22×C53 | — | 2 | 3 | no | — |
| 193 | C22×C53 | — | 4 | 1 | no | — |
| 194 | C22×C53 | — | 4 | 3 | no | — |
| 195 | C22×C53 | — | 8 | 1 | no | — |
| 196 | C22×C53 | C2×C4×D4 | 1 | 3 | yes | — |
| 197 | C2×D53 | — | 2 | 6 | no | — |
| 198 | C2×D53 | — | 2 | 3 | no | — |
| 199 | C2×D53 | — | 4 | 3 | no | — |
| 200 | C2×D53 | — | 4 | 1 | no | — |
| 201 | C2×D53 | — | 4 | 3 | no | — |
| 202 | C2×D53 | — | 8 | 3 | no | — |
| 203 | C4×C53 | — | 2 | 3 | no | — |
| 204 | C4×C53 | — | 4 | 3 | no | — |
| 205 | C4×C53 | — | 4 | 1 | no | — |
| 206 | Dic53 | — | 2 | 3 | no | — |
| 207 | Dic53 | — | 4 | 3 | no | — |
| 208 | Dic53 | C2×#120 | 1 | 1 | yes | characteristic |
| 209 | Dic53 | #525 | 1 | 3 | yes | — |
| 210 | #3573 | — | 53 | 1 | no | — |
| 211 | #3025 | — | 53 | 1 | no | — |
| 212 | #2929 | — | 53 | 3 | no | — |
| 213 | #1891 | — | 53 | 3 | no | — |
| 214 | #1868 | — | 53 | 3 | no | — |
| 215 | #1791 | — | 53 | 1 | no | — |
| 216 | #1757 | — | 53 | 3 | no | — |
| 217 | C2×C53 | — | 2 | 3 | no | — |
| 218 | C2×C53 | — | 4 | 3 | no | — |
| 219 | C2×C53 | C4×#120 | 1 | 1 | yes | characteristic |
| 220 | D53 | — | 4 | 2 | no | — |
| 221 | D53 | — | 4 | 3 | no | — |
| 222 | #585 | — | 53 | 1 | no | — |
| 223 | #568 | — | 53 | 3 | no | — |
| 224 | #568 | — | 106 | 3 | no | — |
| 225 | #568 | — | 106 | 3 | no | — |
| 226 | C2×#131 | — | 53 | 3 | no | — |
| 227 | C2×#131 | — | 106 | 3 | no | — |
| 228 | C2×#131 | — | 106 | 3 | no | — |
| 229 | C23×C8 | — | 53 | 1 | no | — |
| 230 | #525 | — | 53 | 3 | no | — |
| 231 | #458 | — | 53 | 3 | no | — |
| 232 | #458 | #6157 | 1 | 1 | yes | characteristic |
| 233 | B(4,𝔽2) | — | 53 | 1 | no | — |
| 234 | B(4,𝔽2) | — | 53 | 3 | no | — |
| 235 | #435 | — | 106 | 3 | no | — |
| 236 | #435 | — | 106 | 3 | no | — |
| 237 | C8×D4 | — | 106 | 3 | no | — |
| 238 | C8×D4 | — | 106 | 3 | no | — |
| 239 | #424 | — | 53 | 3 | no | — |
| 240 | #413 | — | 53 | 3 | no | — |
| 241 | #410 | — | 53 | 3 | no | — |
| 242 | #408 | — | 53 | 3 | no | — |
| 243 | #407 | — | 53 | 3 | no | — |
| 244 | #405 | — | 53 | 3 | no | — |
| 245 | #344 | — | 53 | 6 | no | — |
| 246 | C53 | #21483 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 247 | 2−1+4 | — | 106 | 3 | no | — |
| 248 | H(5,𝔽2) | — | 53 | 3 | no | — |
| 249 | H(5,𝔽2) | — | 106 | 3 | no | — |
| 250 | H(5,𝔽2) | C2×#6157 | 1 | 1 | yes | characteristic |
| 251 | C2×#41 | — | 53 | 3 | no | — |
| 252 | C2×#41 | — | 106 | 3 | no | — |
| 253 | C2×#41 | — | 106 | 3 | no | — |
| 254 | C23×C4 | — | 53 | 1 | no | — |
| 255 | #131 | — | 106 | 6 | no | — |
| 256 | #131 | — | 106 | 6 | no | — |
| 257 | #131 | — | 106 | 6 | no | — |
| 258 | #131 | — | 106 | 6 | no | — |
| 259 | #131 | — | 106 | 3 | no | — |
| 260 | #131 | — | 106 | 1 | no | — |
| 261 | #131 | — | 106 | 6 | no | — |
| 262 | #131 | — | 106 | 3 | no | — |
| 263 | #131 | — | 106 | 3 | no | — |
| 264 | C2×M16 | — | 53 | 3 | no | — |
| 265 | C2×M16 | — | 53 | 3 | no | — |
| 266 | C2×M16 | — | 53 | 3 | no | — |
| 267 | C2×M16 | — | 53 | 3 | no | — |
| 268 | C2×M16 | — | 106 | 3 | no | — |
| 269 | C2×M16 | — | 106 | 3 | no | — |
| 270 | C2×M16 | — | 106 | 3 | no | — |
| 271 | C2×M16 | — | 106 | 6 | no | — |
| 272 | C2×M16 | — | 106 | 3 | no | — |
| 273 | C22×C8 | — | 53 | 1 | no | — |
| 274 | C22×C8 | — | 53 | 3 | no | — |
| 275 | C22×C8 | — | 53 | 3 | no | — |
| 276 | C22×C8 | — | 53 | 1 | no | — |
| 277 | C22×C8 | — | 106 | 3 | no | — |
| 278 | C22×C8 | — | 106 | 3 | no | — |
| 279 | C22×C8 | — | 106 | 1 | no | — |
| 280 | C22×C8 | — | 106 | 3 | no | — |
| 281 | #123 | — | 53 | 3 | no | — |
| 282 | #123 | C2×#6157 | 1 | 3 | yes | — |
| 283 | C22⋊Q8 | — | 106 | 3 | no | — |
| 284 | #121 | — | 106 | 3 | no | — |
| 285 | #120 | — | 53 | 3 | no | — |
| 286 | #120 | — | 53 | 3 | no | — |
| 287 | C4×D4 | — | 106 | 3 | no | — |
| 288 | C4×D4 | — | 106 | 3 | no | — |
| 289 | #117 | — | 53 | 3 | no | — |
| 290 | C4⋊C8 | — | 106 | 3 | no | — |
| 291 | C4⋊C8 | — | 106 | 3 | no | — |
| 292 | #101 | — | 106 | 3 | no | — |
| 293 | #100 | — | 106 | 3 | no | — |
| 294 | #99 | — | 53 | 3 | no | — |
| 295 | #99 | — | 53 | 6 | no | — |
| 296 | #99 | C2×#6157 | 1 | 3 | yes | — |
| 297 | C22⋊C8 | — | 106 | 3 | no | — |
| 298 | C22⋊C8 | — | 106 | 3 | no | — |
| 299 | C22⋊C8 | — | 106 | 3 | no | — |
| 300 | C22⋊C8 | — | 106 | 3 | no | — |
| 301 | #97 | — | 106 | 3 | no | — |
| 302 | C4×C8 | — | 106 | 3 | no | — |
| 303 | C24 | — | 53 | 1 | no | — |
| 304 | #41 | — | 2 | 3 | no | — |
| 305 | #41 | — | 106 | 6 | no | — |
| 306 | #41 | — | 106 | 6 | no | — |
| 307 | #41 | — | 106 | 6 | no | — |
| 308 | #41 | — | 106 | 6 | no | — |
| 309 | #41 | — | 106 | 3 | no | — |
| 310 | #41 | — | 106 | 6 | no | — |
| 311 | #41 | — | 106 | 1 | no | — |
| 312 | #41 | — | 106 | 3 | no | — |
| 313 | C2×Q8 | — | 53 | 3 | no | — |
| 314 | C2×Q8 | — | 106 | 3 | no | — |
| 315 | C2×Q8 | — | 106 | 3 | no | — |
| 316 | C2×D4 | — | 2 | 3 | no | — |
| 317 | C2×D4 | — | 53 | 3 | no | — |
| 318 | C2×D4 | — | 53 | 3 | no | — |
| 319 | C2×D4 | — | 106 | 3 | no | — |
| 320 | C2×D4 | — | 106 | 6 | no | — |
| 321 | C2×D4 | — | 106 | 3 | no | — |
| 322 | C2×D4 | — | 106 | 3 | no | — |
| 323 | C2×D4 | — | 106 | 3 | no | — |
| 324 | C2×D4 | — | 106 | 3 | no | — |
| 325 | C2×D4 | C22×#6157 | 1 | 3 | yes | — |
| 326 | C22×C4 | — | 53 | 1 | no | — |
| 327 | C22×C4 | — | 53 | 3 | no | — |
| 328 | C22×C4 | — | 53 | 3 | no | — |
| 329 | C22×C4 | — | 106 | 3 | no | — |
| 330 | C22×C4 | — | 106 | 3 | no | — |
| 331 | C22×C4 | — | 106 | 3 | no | — |
| 332 | C22×C4 | — | 106 | 1 | no | — |
| 333 | C22×C4 | C22×#6157 | 1 | 1 | yes | characteristic |
| 334 | M16 | — | 106 | 6 | no | — |
| 335 | M16 | — | 106 | 6 | no | — |
| 336 | M16 | — | 106 | 6 | no | — |
| 337 | M16 | — | 106 | 3 | no | — |
| 338 | M16 | — | 106 | 3 | no | — |
| 339 | M16 | — | 106 | 6 | no | — |
| 340 | M16 | — | 106 | 6 | no | — |
| 341 | C2×C8 | — | 53 | 3 | no | — |
| 342 | C2×C8 | — | 53 | 3 | no | — |
| 343 | C2×C8 | — | 53 | 3 | no | — |
| 344 | C2×C8 | — | 53 | 3 | no | — |
| 345 | C2×C8 | — | 106 | 3 | no | — |
| 346 | C2×C8 | — | 106 | 3 | no | — |
| 347 | C2×C8 | — | 106 | 3 | no | — |
| 348 | C2×C8 | — | 106 | 3 | no | — |
| 349 | C2×C8 | — | 106 | 3 | no | — |
| 350 | C2×C8 | — | 106 | 3 | no | — |
| 351 | C2×C8 | — | 106 | 6 | no | — |
| 352 | C2×C8 | — | 106 | 3 | no | — |
| 353 | C2×C8 | — | 106 | 3 | no | — |
| 354 | C2×C8 | — | 212 | 1 | no | — |
| 355 | C2×C8 | — | 212 | 3 | no | — |
| 356 | C4⋊C4 | — | 2 | 3 | no | — |
| 357 | C4⋊C4 | — | 106 | 3 | no | — |
| 358 | C4⋊C4 | — | 106 | 3 | no | — |
| 359 | C22⋊C4 | — | 2 | 3 | no | — |
| 360 | C22⋊C4 | — | 53 | 3 | no | — |
| 361 | C22⋊C4 | — | 106 | 3 | no | — |
| 362 | C22⋊C4 | — | 106 | 3 | no | — |
| 363 | C22⋊C4 | — | 106 | 3 | no | — |
| 364 | C22⋊C4 | C22×#6157 | 1 | 3 | yes | — |
| 365 | C42 | — | 106 | 3 | no | — |
| 366 | C23 | — | 2 | 1 | no | — |
| 367 | C23 | — | 53 | 3 | no | — |
| 368 | C23 | — | 106 | 3 | no | — |
| 369 | C23 | — | 106 | 3 | no | — |
| 370 | C23 | — | 212 | 2 | no | — |
| 371 | C23 | D4×#6157 | 1 | 3 | yes | — |
| 372 | C23 | C23×#6157 | 1 | 1 | yes | characteristic |
| 373 | Q8 | — | 2 | 1 | no | — |
| 374 | Q8 | — | 106 | 6 | no | — |
| 375 | Q8 | — | 106 | 3 | no | — |
| 376 | D4 | — | 2 | 3 | no | — |
| 377 | D4 | — | 2 | 6 | no | — |
| 378 | D4 | — | 106 | 3 | no | — |
| 379 | D4 | — | 106 | 6 | no | — |
| 380 | D4 | — | 106 | 6 | no | — |
| 381 | D4 | — | 106 | 6 | no | — |
| 382 | D4 | — | 212 | 6 | no | — |
| 383 | D4 | — | 212 | 6 | no | — |
| 384 | C2×C4 | — | 2 | 3 | no | — |
| 385 | C2×C4 | — | 2 | 3 | no | — |
| 386 | C2×C4 | — | 2 | 3 | no | — |
| 387 | C2×C4 | — | 53 | 3 | no | — |
| 388 | C2×C4 | — | 53 | 3 | no | — |
| 389 | C2×C4 | — | 53 | 3 | no | — |
| 390 | C2×C4 | — | 106 | 3 | no | — |
| 391 | C2×C4 | — | 106 | 3 | no | — |
| 392 | C2×C4 | — | 106 | 6 | no | — |
| 393 | C2×C4 | — | 106 | 3 | no | — |
| 394 | C2×C4 | — | 106 | 3 | no | — |
| 395 | C2×C4 | — | 106 | 3 | no | — |
| 396 | C2×C4 | — | 106 | 3 | no | — |
| 397 | C2×C4 | — | 212 | 1 | no | — |
| 398 | C2×C4 | — | 212 | 3 | no | — |
| 399 | C2×C4 | D4×#6157 | 1 | 3 | yes | — |
| 400 | C8 | — | 53 | 1 | no | — |
| 401 | C8 | — | 53 | 3 | no | — |
| 402 | C8 | — | 106 | 3 | no | — |
| 403 | C8 | — | 106 | 3 | no | — |
| 404 | C8 | — | 212 | 1 | no | — |
| 405 | C8 | — | 212 | 3 | no | — |
| 406 | C22 | — | 2 | 3 | no | — |
| 407 | C22 | — | 4 | 1 | no | — |
| 408 | C22 | — | 4 | 3 | no | — |
| 409 | C22 | — | 8 | 1 | no | — |
| 410 | C22 | — | 106 | 6 | no | — |
| 411 | C22 | — | 106 | 3 | no | — |
| 412 | C22 | — | 424 | 3 | no | — |
| 413 | C22 | — | 212 | 3 | no | — |
| 414 | C22 | — | 212 | 3 | no | — |
| 415 | C22 | — | 212 | 1 | no | — |
| 416 | C22 | C2×D4×#6157 | 1 | 3 | yes | — |
| 417 | C4 | — | 2 | 3 | no | — |
| 418 | C4 | — | 4 | 3 | no | — |
| 419 | C4 | — | 4 | 1 | no | — |
| 420 | C4 | — | 53 | 1 | no | — |
| 421 | C4 | — | 53 | 3 | no | — |
| 422 | C4 | — | 106 | 3 | no | — |
| 423 | C4 | — | 212 | 3 | no | — |
| 424 | C2 | — | 2 | 3 | no | — |
| 425 | C2 | — | 4 | 3 | no | — |
| 426 | C2 | — | 212 | 2 | no | — |
| 427 | C2 | — | 212 | 3 | no | — |
| 428 | C2 | #120×#6157 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20291710 | C2 | semidirect |
| 2. #20291432 | C2 | semidirect |
| 3. #20290727 | C2 | semidirect |
| 4. #20290687 | C2 | semidirect |
| 5. #20290560 | C2 | semidirect |
| 6. #20290473 | C2 | semidirect |
| 14. C22×D53⋊C8 | C22 | semidirect |
| 19. #16811629 | C22 | semidirect |
| 22. #16811595 | C22 | semidirect |
| 23. #16811587 | C22 | semidirect |
| 24. #16811504 | C22 | semidirect |
| 42. C2×#11719936 | D4 | semidirect |
| 47. C2×#11719940 | D4 | semidirect |
| 53. C2×D53⋊C8 | D4 | semidirect |
| 55. C22×#88324 | D4 | semidirect |
| 246. C53 | #21483 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291710 | 2 |
| #20291432 | 2 |
| #20290727 | 2 |
| #20290687 | 2 |
| #20290560 | 2 |
| #20290473 | 2 |
| #20284108 | 2 |
| #21483 | 53 |