Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
646 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 646 conjugacy classes of subgroups — too many to draw. Only its 78 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 | #20291317 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #20290994 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #20290974 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #20290568 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #20289816 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #20289804 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #20284000 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #16811691 | — | 2 | 1 | no | — |
| 9 | #16811621 | — | 2 | 1 | no | — |
| 10 | #16811616 | — | 2 | 1 | no | — |
| 11 | #16811609 | C22 | 1 | 1 | yes | characteristic |
| 12 | #16811603 | — | 2 | 2 | no | — |
| 13 | #16811603 | — | 2 | 1 | no | — |
| 14 | #16811602 | — | 2 | 2 | no | — |
| 15 | #16811602 | C22 | 1 | 1 | yes | characteristic |
| 16 | #16811602 | C22 | 1 | 1 | yes | characteristic |
| 17 | #16811602 | C22 | 1 | 1 | yes | characteristic |
| 18 | #16811527 | — | 2 | 2 | no | — |
| 19 | #16811523 | — | 2 | 2 | no | — |
| 20 | C2×#13133264 | C22 | 1 | 1 | yes | characteristic |
| 21 | C22×#11719923 | C4 | 1 | 1 | yes | characteristic, complemented |
| 22 | #16811190 | C22 | 1 | 1 | yes | characteristic |
| 23 | #16810765 | — | 2 | 1 | no | — |
| 24 | #16810765 | — | 2 | 1 | no | — |
| 25 | #16810760 | — | 2 | 1 | no | — |
| 26 | #16810760 | — | 2 | 1 | no | — |
| 27 | #16810633 | C4 | 1 | 1 | yes | characteristic, complemented |
| 28 | #16810619 | C4 | 1 | 1 | yes | characteristic, complemented |
| 29 | #16810591 | C22 | 1 | 1 | yes | characteristic |
| 30 | C2×AGL(1,ℤ/8)×C53 | C4 | 1 | 1 | yes | characteristic, complemented |
| 31 | D53⋊M16 | — | 2 | 1 | no | — |
| 32 | Q8×#6157 | — | 4 | 2 | no | — |
| 33 | Q8×#6157 | — | 4 | 2 | no | — |
| 34 | #13133296 | — | 2 | 4 | no | — |
| 35 | #13133296 | — | 2 | 1 | no | — |
| 36 | #13133296 | — | 2 | 1 | no | — |
| 37 | #13133296 | — | 2 | 1 | no | — |
| 38 | #13133281 | — | 4 | 2 | no | — |
| 39 | #13133280 | — | 4 | 2 | no | — |
| 40 | #13133278 | — | 2 | 1 | no | — |
| 41 | #13133277 | — | 2 | 1 | no | — |
| 42 | #13133276 | — | 2 | 1 | no | — |
| 43 | #13133276 | — | 2 | 1 | no | — |
| 44 | #13133276 | D4 | 1 | 2 | yes | — |
| 45 | #13133275 | — | 2 | 4 | no | — |
| 46 | #13133275 | — | 2 | 1 | no | — |
| 47 | #13133275 | — | 2 | 1 | no | — |
| 48 | #13133275 | D4 | 1 | 2 | yes | — |
| 49 | #13133264 | — | 4 | 2 | no | — |
| 50 | #13133264 | — | 4 | 2 | no | — |
| 51 | C2×#11719945 | — | 2 | 1 | no | — |
| 52 | C2×#11719945 | C23 | 1 | 1 | yes | characteristic |
| 53 | C2×#11719947 | — | 2 | 1 | no | — |
| 54 | C2×#11719947 | — | 2 | 1 | no | — |
| 55 | C2×#11719947 | D4 | 1 | 1 | yes | characteristic |
| 56 | C2×#11719947 | D4 | 1 | 1 | yes | characteristic |
| 57 | C22×Dic106 | — | 2 | 1 | no | — |
| 58 | C22×Dic106 | C2×C4 | 1 | 1 | yes | characteristic |
| 59 | C2×Q8×D53 | D4 | 1 | 1 | yes | characteristic |
| 60 | C2×Q8×D53 | D4 | 1 | 1 | yes | characteristic |
| 61 | C2×#11719923 | — | 2 | 1 | no | — |
| 62 | C2×#11719923 | — | 2 | 1 | no | — |
| 63 | C2×#11719923 | — | 4 | 2 | no | — |
| 64 | C22×#88322 | C2×C4 | 1 | 1 | yes | characteristic |
| 65 | #13133213 | — | 2 | 1 | no | — |
| 66 | #13133204 | — | 2 | 1 | no | — |
| 67 | #13133188 | — | 2 | 1 | no | — |
| 68 | #13133188 | — | 2 | 1 | no | — |
| 69 | #13133186 | — | 2 | 1 | no | — |
| 70 | #13133186 | — | 2 | 1 | no | — |
| 71 | #13133176 | C2×C4 | 1 | 1 | yes | characteristic |
| 72 | #13133142 | — | 2 | 1 | no | — |
| 73 | #13133142 | — | 2 | 1 | no | — |
| 74 | #13133141 | — | 2 | 1 | no | — |
| 75 | #13133138 | — | 2 | 1 | no | — |
| 76 | #13133129 | — | 2 | 1 | no | — |
| 77 | #13133129 | — | 2 | 1 | no | — |
| 78 | C2×#41×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 79 | C22×D4×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 80 | AGL(1,ℤ/8)×C53 | — | 4 | 2 | no | — |
| 81 | C2×SD16×C53 | — | 2 | 1 | no | — |
| 82 | C2×D8×C53 | — | 2 | 1 | no | — |
| 83 | C2×M16×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 84 | C24×C53 | — | 2 | 1 | no | — |
| 85 | #41×C53 | — | 2 | 2 | no | — |
| 86 | #41×C53 | — | 4 | 1 | no | — |
| 87 | C2×Q8×C53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 88 | C2×D4×C53 | — | 2 | 1 | no | — |
| 89 | C2×D4×C53 | — | 2 | 1 | no | — |
| 90 | C2×D4×C53 | — | 2 | 1 | no | — |
| 91 | C2×D4×C53 | — | 4 | 1 | no | — |
| 92 | C2×D4×C53 | — | 4 | 1 | no | — |
| 93 | C2×D4×C53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 94 | C22×C4×C53 | — | 2 | 1 | no | — |
| 95 | C22×C4×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 96 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 97 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 98 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 99 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 100 | C2×C22⋊D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 101 | C2×C22⋊D53 | #41 | 1 | 1 | yes | characteristic |
| 102 | C22×Dic53 | — | 2 | 1 | no | — |
| 103 | C22×Dic53 | — | 2 | 1 | no | — |
| 104 | C22×Dic53 | — | 2 | 1 | no | — |
| 105 | Q8×D53 | — | 2 | 2 | no | — |
| 106 | Q8×D53 | — | 2 | 2 | no | — |
| 107 | Q8×D53 | — | 2 | 2 | no | — |
| 108 | Q8×D53 | — | 4 | 1 | no | — |
| 109 | #11719947 | — | 2 | 2 | no | — |
| 110 | #11719947 | — | 4 | 1 | no | — |
| 111 | #11719947 | — | 4 | 1 | no | — |
| 112 | #11719947 | — | 4 | 1 | no | — |
| 113 | #11719947 | — | 4 | 4 | no | — |
| 114 | #11719947 | — | 4 | 4 | no | — |
| 115 | #11719945 | — | 4 | 1 | no | — |
| 116 | #11719945 | — | 4 | 1 | no | — |
| 117 | #11719945 | — | 4 | 4 | no | — |
| 118 | C2×D212 | C2×D4 | 1 | 1 | yes | characteristic |
| 119 | C2×C4×D53 | — | 2 | 1 | no | — |
| 120 | C2×C4×D53 | — | 2 | 1 | no | — |
| 121 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 122 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 123 | C2×Dic106 | — | 2 | 1 | no | — |
| 124 | C2×Dic106 | — | 2 | 2 | no | — |
| 125 | C2×Dic106 | — | 2 | 1 | no | — |
| 126 | C2×Dic106 | — | 2 | 1 | no | — |
| 127 | C2×Dic106 | — | 4 | 1 | no | — |
| 128 | C2×Dic106 | — | 4 | 4 | no | — |
| 129 | C2×Dic106 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 130 | C2×Dic106 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 131 | C2×Dic106 | #41 | 1 | 1 | yes | characteristic |
| 132 | C22⋊#6157 | — | 2 | 2 | no | — |
| 133 | C22⋊#6157 | — | 2 | 2 | no | — |
| 134 | C22⋊#6157 | — | 4 | 1 | no | — |
| 135 | #11719940 | — | 4 | 1 | no | — |
| 136 | C4⋊#6157 | — | 4 | 4 | no | — |
| 137 | C4⋊#6157 | — | 4 | 1 | no | — |
| 138 | C4⋊#6157 | — | 4 | 1 | no | — |
| 139 | C4⋊#6157 | — | 4 | 1 | no | — |
| 140 | C4×#6157 | — | 4 | 4 | no | — |
| 141 | C4×#6157 | — | 4 | 1 | no | — |
| 142 | C4×#6157 | — | 4 | 1 | no | — |
| 143 | C4×#6157 | — | 4 | 1 | no | — |
| 144 | #11719936 | — | 4 | 1 | no | — |
| 145 | D53⋊C8 | — | 4 | 1 | no | — |
| 146 | SD16×C53 | — | 4 | 2 | no | — |
| 147 | D8×C53 | — | 4 | 2 | no | — |
| 148 | M16×C53 | — | 4 | 1 | no | — |
| 149 | C2×C8×C53 | — | 2 | 1 | no | — |
| 150 | C22⋊Dic53 | — | 2 | 1 | no | — |
| 151 | C22⋊Dic53 | — | 4 | 1 | no | — |
| 152 | C22⋊Dic53 | — | 4 | 1 | no | — |
| 153 | #11719923 | — | 4 | 2 | no | — |
| 154 | #11719923 | — | 4 | 2 | no | — |
| 155 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 156 | C4×Dic53 | — | 2 | 1 | no | — |
| 157 | C2×#88322 | — | 2 | 1 | no | — |
| 158 | C2×#88322 | — | 4 | 1 | no | — |
| 159 | C23×C53 | — | 2 | 1 | no | — |
| 160 | C23×C53 | — | 4 | 1 | no | — |
| 161 | C23×C53 | — | 8 | 1 | no | — |
| 162 | C23×C53 | — | 16 | 1 | no | — |
| 163 | C23×C53 | C4×D4 | 1 | 1 | yes | characteristic |
| 164 | C22×D53 | #120 | 1 | 1 | yes | characteristic |
| 165 | C22×D53 | #121 | 1 | 1 | yes | characteristic |
| 166 | C2×#6157 | — | 4 | 2 | no | — |
| 167 | C2×#6157 | — | 4 | 2 | no | — |
| 168 | C2×#6157 | — | 8 | 1 | no | — |
| 169 | Q8×C53 | — | 2 | 1 | no | — |
| 170 | Q8×C53 | #99 | 1 | 2 | yes | — |
| 171 | D4×C53 | — | 2 | 1 | no | — |
| 172 | D4×C53 | — | 2 | 1 | no | — |
| 173 | D4×C53 | — | 4 | 2 | no | — |
| 174 | D4×C53 | — | 4 | 1 | no | — |
| 175 | D4×C53 | — | 4 | 1 | no | — |
| 176 | D4×C53 | — | 8 | 1 | no | — |
| 177 | C2×C4×C53 | — | 2 | 1 | no | — |
| 178 | C2×C4×C53 | — | 2 | 1 | no | — |
| 179 | C2×C4×C53 | — | 2 | 1 | no | — |
| 180 | C2×C4×C53 | — | 4 | 2 | no | — |
| 181 | C2×C4×C53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 182 | C2×C4×C53 | C4×D4 | 1 | 1 | yes | characteristic |
| 183 | C22⋊D53 | — | 4 | 1 | no | — |
| 184 | C22⋊D53 | — | 4 | 1 | no | — |
| 185 | C22⋊D53 | — | 4 | 2 | no | — |
| 186 | C22⋊D53 | — | 4 | 2 | no | — |
| 187 | C22⋊D53 | — | 16 | 1 | no | — |
| 188 | C22⋊D53 | — | 16 | 1 | no | — |
| 189 | C2×Dic53 | — | 2 | 1 | no | — |
| 190 | C2×Dic53 | — | 2 | 1 | no | — |
| 191 | C2×Dic53 | — | 4 | 2 | no | — |
| 192 | C2×Dic53 | — | 4 | 2 | no | — |
| 193 | C2×Dic53 | — | 4 | 2 | no | — |
| 194 | C2×Dic53 | — | 4 | 1 | no | — |
| 195 | C2×Dic53 | #121 | 1 | 1 | yes | characteristic |
| 196 | C2×Dic53 | #123 | 1 | 1 | yes | characteristic |
| 197 | D212 | — | 4 | 1 | no | — |
| 198 | C4×D53 | — | 2 | 4 | no | — |
| 199 | C4×D53 | — | 2 | 1 | no | — |
| 200 | C4×D53 | — | 2 | 1 | no | — |
| 201 | C4×D53 | — | 2 | 1 | no | — |
| 202 | C4×D53 | — | 2 | 1 | no | — |
| 203 | C4×D53 | — | 4 | 2 | no | — |
| 204 | Dic106 | — | 2 | 4 | no | — |
| 205 | Dic106 | — | 2 | 1 | no | — |
| 206 | Dic106 | — | 2 | 1 | no | — |
| 207 | Dic106 | — | 2 | 1 | no | — |
| 208 | Dic106 | — | 4 | 1 | no | — |
| 209 | Dic106 | — | 4 | 2 | no | — |
| 210 | Dic106 | — | 4 | 2 | no | — |
| 211 | Dic106 | #99 | 1 | 2 | yes | — |
| 212 | #88324 | — | 8 | 1 | no | — |
| 213 | C8×C53 | — | 4 | 1 | no | — |
| 214 | #88322 | — | 4 | 1 | no | — |
| 215 | #13103 | — | 53 | 1 | no | maximal, Sylow |
| 216 | C22×C53 | — | 2 | 1 | no | — |
| 217 | C22×C53 | — | 4 | 1 | no | — |
| 218 | C22×C53 | — | 4 | 1 | no | — |
| 219 | C22×C53 | — | 8 | 1 | no | — |
| 220 | C22×C53 | — | 8 | 1 | no | — |
| 221 | C22×C53 | — | 8 | 1 | no | — |
| 222 | C22×C53 | — | 8 | 1 | no | — |
| 223 | C22×C53 | — | 16 | 2 | no | — |
| 224 | C22×C53 | #386 | 1 | 1 | yes | characteristic |
| 225 | C2×D53 | — | 2 | 1 | no | — |
| 226 | C2×D53 | — | 2 | 1 | no | — |
| 227 | C2×D53 | — | 4 | 1 | no | — |
| 228 | C2×D53 | — | 4 | 1 | no | — |
| 229 | #6157 | — | 8 | 2 | no | — |
| 230 | #6157 | — | 8 | 2 | no | — |
| 231 | #6157 | — | 16 | 1 | no | — |
| 232 | C4×C53 | — | 2 | 2 | no | — |
| 233 | C4×C53 | — | 2 | 1 | no | — |
| 234 | C4×C53 | C2×#99 | 1 | 1 | yes | characteristic |
| 235 | C4×C53 | C2×#99 | 1 | 1 | yes | characteristic |
| 236 | Dic53 | — | 2 | 1 | no | — |
| 237 | Dic53 | — | 2 | 1 | no | — |
| 238 | Dic53 | — | 2 | 2 | no | — |
| 239 | Dic53 | — | 4 | 1 | no | — |
| 240 | Dic53 | — | 8 | 1 | no | — |
| 241 | #3010 | — | 53 | 1 | no | — |
| 242 | #2884 | — | 53 | 1 | no | — |
| 243 | #2128 | — | 53 | 1 | no | — |
| 244 | #2122 | — | 53 | 1 | no | — |
| 245 | #1796 | — | 53 | 1 | no | — |
| 246 | #1395 | — | 53 | 1 | no | — |
| 247 | #1391 | — | 53 | 1 | no | — |
| 248 | C2×C53 | — | 2 | 1 | no | — |
| 249 | C2×C53 | — | 4 | 1 | no | — |
| 250 | C2×C53 | — | 8 | 1 | no | — |
| 251 | C2×C53 | — | 16 | 1 | no | — |
| 252 | C2×C53 | #1898 | 1 | 1 | yes | characteristic |
| 253 | D53 | — | 4 | 1 | no | — |
| 254 | D53 | — | 4 | 1 | no | — |
| 255 | C2×2−1+4 | — | 53 | 1 | no | — |
| 256 | C2×AGL(1,ℤ/8) | #6157 | 1 | 1 | yes | characteristic, complemented |
| 257 | C22×SD16 | — | 53 | 1 | no | — |
| 258 | #535 | — | 53 | 1 | no | — |
| 259 | #519 | — | 106 | 1 | no | — |
| 260 | #449 | — | 106 | 1 | no | — |
| 261 | #449 | — | 106 | 1 | no | — |
| 262 | #448 | — | 106 | 1 | no | — |
| 263 | #448 | — | 106 | 1 | no | — |
| 264 | #421 | — | 106 | 1 | no | — |
| 265 | #419 | — | 53 | 1 | no | — |
| 266 | #419 | — | 106 | 1 | no | — |
| 267 | #416 | — | 53 | 1 | no | — |
| 268 | #413 | — | 53 | 1 | no | — |
| 269 | #410 | — | 53 | 1 | no | — |
| 270 | #410 | — | 53 | 1 | no | — |
| 271 | #410 | — | 53 | 1 | no | — |
| 272 | #410 | — | 106 | 2 | no | — |
| 273 | #410 | — | 106 | 2 | no | — |
| 274 | #410 | — | 106 | 1 | no | — |
| 275 | #408 | — | 53 | 1 | no | — |
| 276 | #353 | — | 106 | 2 | no | — |
| 277 | AΣL(1,𝔽16) | — | 106 | 2 | no | — |
| 278 | C53 | #13103 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 279 | 2−1+4 | — | 212 | 2 | no | — |
| 280 | 2−1+4 | — | 212 | 2 | no | — |
| 281 | C2×#41 | — | 53 | 1 | no | — |
| 282 | C2×#41 | — | 53 | 1 | no | — |
| 283 | C2×#41 | — | 53 | 1 | no | — |
| 284 | C2×#41 | — | 106 | 1 | no | — |
| 285 | C2×#41 | — | 106 | 1 | no | — |
| 286 | C2×#41 | — | 106 | 1 | no | — |
| 287 | C2×#41 | C2×#6157 | 1 | 1 | yes | characteristic |
| 288 | C22×Q8 | — | 53 | 1 | no | — |
| 289 | C22×Q8 | — | 53 | 1 | no | — |
| 290 | C22×Q8 | — | 53 | 1 | no | — |
| 291 | C22×Q8 | — | 106 | 1 | no | — |
| 292 | C22×D4 | C2×#6157 | 1 | 1 | yes | characteristic |
| 293 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 294 | C2×SD16 | — | 2 | 1 | no | — |
| 295 | C2×SD16 | — | 106 | 1 | no | — |
| 296 | C2×SD16 | — | 106 | 1 | no | — |
| 297 | C2×SD16 | — | 212 | 2 | no | — |
| 298 | C2×D8 | — | 2 | 1 | no | — |
| 299 | C2×M16 | — | 106 | 1 | no | — |
| 300 | C2×M16 | C2×#6157 | 1 | 1 | yes | characteristic |
| 301 | C22×C8 | — | 53 | 1 | no | — |
| 302 | #127 | — | 106 | 1 | no | — |
| 303 | #124 | — | 106 | 1 | no | — |
| 304 | #121 | — | 106 | 1 | no | — |
| 305 | #121 | — | 106 | 1 | no | — |
| 306 | #120 | — | 106 | 1 | no | — |
| 307 | #120 | — | 106 | 1 | no | — |
| 308 | C4×Q8 | — | 212 | 2 | no | — |
| 309 | C4×Q8 | — | 212 | 2 | no | — |
| 310 | #117 | — | 53 | 1 | no | — |
| 311 | #117 | — | 106 | 1 | no | — |
| 312 | #117 | — | 106 | 1 | no | — |
| 313 | #117 | — | 106 | 4 | no | — |
| 314 | #117 | — | 106 | 1 | no | — |
| 315 | #104 | — | 212 | 2 | no | — |
| 316 | #103 | — | 106 | 1 | no | — |
| 317 | #103 | — | 106 | 1 | no | — |
| 318 | #103 | — | 106 | 1 | no | — |
| 319 | #103 | — | 212 | 2 | no | — |
| 320 | #102 | — | 106 | 1 | no | — |
| 321 | #101 | — | 106 | 1 | no | — |
| 322 | #100 | — | 106 | 1 | no | — |
| 323 | #99 | — | 53 | 2 | no | — |
| 324 | #99 | — | 53 | 2 | no | — |
| 325 | #99 | — | 106 | 1 | no | — |
| 326 | #99 | — | 106 | 1 | no | — |
| 327 | #99 | — | 106 | 4 | no | — |
| 328 | #99 | — | 106 | 1 | no | — |
| 329 | #99 | — | 106 | 1 | no | — |
| 330 | C22⋊C8 | — | 106 | 1 | no | — |
| 331 | C22⋊C8 | — | 106 | 1 | no | — |
| 332 | C24 | — | 2 | 1 | no | — |
| 333 | #41 | — | 2 | 2 | no | — |
| 334 | #41 | — | 4 | 1 | no | — |
| 335 | #41 | — | 106 | 2 | no | — |
| 336 | #41 | — | 212 | 1 | no | — |
| 337 | #41 | — | 212 | 1 | no | — |
| 338 | #41 | — | 212 | 4 | no | — |
| 339 | #41 | — | 212 | 1 | no | — |
| 340 | #41 | — | 212 | 1 | no | — |
| 341 | #41 | — | 212 | 1 | no | — |
| 342 | #41 | — | 212 | 4 | no | — |
| 343 | #41 | — | 212 | 4 | no | — |
| 344 | C2×Q8 | — | 53 | 1 | no | — |
| 345 | C2×Q8 | — | 53 | 1 | no | — |
| 346 | C2×Q8 | — | 53 | 1 | no | — |
| 347 | C2×Q8 | — | 106 | 1 | no | — |
| 348 | C2×Q8 | — | 106 | 1 | no | — |
| 349 | C2×Q8 | — | 106 | 2 | no | — |
| 350 | C2×Q8 | — | 106 | 2 | no | — |
| 351 | C2×Q8 | — | 106 | 2 | no | — |
| 352 | C2×Q8 | — | 106 | 1 | no | — |
| 353 | C2×Q8 | — | 106 | 2 | no | — |
| 354 | C2×Q8 | — | 212 | 1 | no | — |
| 355 | C2×Q8 | — | 212 | 4 | no | — |
| 356 | C2×Q8 | — | 212 | 1 | no | — |
| 357 | C2×Q8 | C22⋊#6157 | 1 | 1 | yes | characteristic |
| 358 | C2×D4 | — | 2 | 1 | no | — |
| 359 | C2×D4 | — | 2 | 1 | no | — |
| 360 | C2×D4 | — | 2 | 1 | no | — |
| 361 | C2×D4 | — | 4 | 1 | no | — |
| 362 | C2×D4 | — | 4 | 1 | no | — |
| 363 | C2×D4 | — | 53 | 1 | no | — |
| 364 | C2×D4 | — | 53 | 1 | no | — |
| 365 | C2×D4 | — | 53 | 1 | no | — |
| 366 | C2×D4 | — | 106 | 1 | no | — |
| 367 | C2×D4 | — | 106 | 1 | no | — |
| 368 | C2×D4 | — | 212 | 1 | no | — |
| 369 | C2×D4 | — | 212 | 1 | no | — |
| 370 | C2×D4 | C22⋊#6157 | 1 | 1 | yes | characteristic |
| 371 | C22×C4 | — | 2 | 1 | no | — |
| 372 | C22×C4 | — | 53 | 1 | no | — |
| 373 | C22×C4 | — | 53 | 1 | no | — |
| 374 | C22×C4 | — | 106 | 1 | no | — |
| 375 | C22×C4 | — | 106 | 1 | no | — |
| 376 | C22×C4 | — | 106 | 1 | no | — |
| 377 | C22×C4 | — | 106 | 1 | no | — |
| 378 | C22×C4 | — | 106 | 1 | no | — |
| 379 | C22×C4 | C22×#6157 | 1 | 1 | yes | characteristic |
| 380 | SD16 | — | 4 | 2 | no | — |
| 381 | SD16 | — | 212 | 2 | no | — |
| 382 | SD16 | — | 212 | 2 | no | — |
| 383 | D8 | — | 4 | 2 | no | — |
| 384 | M16 | — | 4 | 1 | no | — |
| 385 | M16 | — | 212 | 1 | no | — |
| 386 | M16 | — | 212 | 1 | no | — |
| 387 | C2×C8 | — | 2 | 1 | no | — |
| 388 | C2×C8 | — | 106 | 1 | no | — |
| 389 | C2×C8 | — | 212 | 1 | no | — |
| 390 | C2×C8 | — | 212 | 1 | no | — |
| 391 | C4⋊C4 | — | 106 | 1 | no | — |
| 392 | C4⋊C4 | — | 212 | 1 | no | — |
| 393 | C4⋊C4 | — | 212 | 4 | no | — |
| 394 | C4⋊C4 | — | 212 | 1 | no | — |
| 395 | C4⋊C4 | — | 212 | 1 | no | — |
| 396 | C22⋊C4 | — | 106 | 2 | no | — |
| 397 | C22⋊C4 | — | 106 | 2 | no | — |
| 398 | C22⋊C4 | — | 106 | 1 | no | — |
| 399 | C22⋊C4 | — | 212 | 1 | no | — |
| 400 | C22⋊C4 | — | 212 | 1 | no | — |
| 401 | C22⋊C4 | — | 212 | 1 | no | — |
| 402 | C42 | — | 106 | 1 | no | — |
| 403 | C42 | — | 212 | 1 | no | — |
| 404 | C42 | — | 212 | 4 | no | — |
| 405 | C42 | — | 212 | 1 | no | — |
| 406 | C42 | — | 212 | 1 | no | — |
| 407 | C23 | — | 2 | 1 | no | — |
| 408 | C23 | — | 4 | 1 | no | — |
| 409 | C23 | — | 8 | 1 | no | — |
| 410 | C23 | — | 16 | 1 | no | — |
| 411 | C23 | — | 53 | 1 | no | — |
| 412 | C23 | — | 53 | 1 | no | — |
| 413 | C23 | D4×#6157 | 1 | 1 | yes | characteristic |
| 414 | Q8 | — | 2 | 1 | no | — |
| 415 | Q8 | — | 53 | 2 | no | — |
| 416 | Q8 | — | 106 | 4 | no | — |
| 417 | Q8 | — | 106 | 1 | no | — |
| 418 | Q8 | — | 106 | 1 | no | — |
| 419 | Q8 | — | 106 | 1 | no | — |
| 420 | Q8 | — | 212 | 1 | no | — |
| 421 | Q8 | — | 212 | 2 | no | — |
| 422 | Q8 | — | 212 | 2 | no | — |
| 423 | Q8 | #13133275 | 1 | 2 | yes | — |
| 424 | D4 | — | 2 | 1 | no | — |
| 425 | D4 | — | 2 | 1 | no | — |
| 426 | D4 | — | 4 | 2 | no | — |
| 427 | D4 | — | 4 | 1 | no | — |
| 428 | D4 | — | 4 | 1 | no | — |
| 429 | D4 | — | 8 | 1 | no | — |
| 430 | D4 | — | 848 | 1 | no | — |
| 431 | D4 | — | 848 | 1 | no | — |
| 432 | D4 | — | 212 | 1 | no | — |
| 433 | D4 | — | 212 | 1 | no | — |
| 434 | D4 | — | 212 | 1 | no | — |
| 435 | D4 | — | 212 | 2 | no | — |
| 436 | D4 | — | 212 | 2 | no | — |
| 437 | C2×C4 | — | 2 | 1 | no | — |
| 438 | C2×C4 | — | 2 | 1 | no | — |
| 439 | C2×C4 | — | 2 | 1 | no | — |
| 440 | C2×C4 | — | 4 | 2 | no | — |
| 441 | C2×C4 | — | 53 | 1 | no | — |
| 442 | C2×C4 | — | 53 | 1 | no | — |
| 443 | C2×C4 | — | 106 | 4 | no | — |
| 444 | C2×C4 | — | 106 | 1 | no | — |
| 445 | C2×C4 | — | 106 | 1 | no | — |
| 446 | C2×C4 | — | 106 | 1 | no | — |
| 447 | C2×C4 | — | 106 | 1 | no | — |
| 448 | C2×C4 | — | 106 | 1 | no | — |
| 449 | C2×C4 | — | 106 | 1 | no | — |
| 450 | C2×C4 | — | 424 | 1 | no | — |
| 451 | C2×C4 | — | 212 | 2 | no | — |
| 452 | C2×C4 | — | 212 | 2 | no | — |
| 453 | C2×C4 | — | 212 | 2 | no | — |
| 454 | C2×C4 | — | 212 | 2 | no | — |
| 455 | C2×C4 | — | 212 | 2 | no | — |
| 456 | C2×C4 | — | 212 | 2 | no | — |
| 457 | C2×C4 | — | 212 | 1 | no | — |
| 458 | C2×C4 | C2×C22⋊#6157 | 1 | 1 | yes | characteristic |
| 459 | C2×C4 | D4×#6157 | 1 | 1 | yes | characteristic |
| 460 | C8 | — | 4 | 1 | no | — |
| 461 | C8 | — | 424 | 1 | no | — |
| 462 | C8 | — | 212 | 1 | no | — |
| 463 | C22 | — | 2 | 1 | no | — |
| 464 | C22 | — | 4 | 1 | no | — |
| 465 | C22 | — | 4 | 1 | no | — |
| 466 | C22 | — | 8 | 1 | no | — |
| 467 | C22 | — | 8 | 1 | no | — |
| 468 | C22 | — | 8 | 1 | no | — |
| 469 | C22 | — | 8 | 1 | no | — |
| 470 | C22 | — | 16 | 2 | no | — |
| 471 | C22 | — | 106 | 1 | no | — |
| 472 | C22 | — | 106 | 1 | no | — |
| 473 | C22 | — | 212 | 1 | no | — |
| 474 | C22 | — | 212 | 1 | no | — |
| 475 | C22 | #16811571 | 1 | 1 | yes | characteristic |
| 476 | C4 | — | 2 | 1 | no | — |
| 477 | C4 | — | 2 | 2 | no | — |
| 478 | C4 | — | 848 | 1 | no | — |
| 479 | C4 | — | 106 | 1 | no | — |
| 480 | C4 | — | 106 | 1 | no | — |
| 481 | C4 | — | 106 | 2 | no | — |
| 482 | C4 | — | 424 | 1 | no | — |
| 483 | C4 | — | 424 | 2 | no | — |
| 484 | C4 | — | 424 | 2 | no | — |
| 485 | C4 | — | 212 | 1 | no | — |
| 486 | C4 | C2×#13133275 | 1 | 1 | yes | characteristic |
| 487 | C4 | D53⋊#99 | 1 | 1 | yes | characteristic |
| 488 | C2 | — | 2 | 1 | no | — |
| 489 | C2 | — | 4 | 1 | no | — |
| 490 | C2 | — | 8 | 1 | no | — |
| 491 | C2 | — | 16 | 1 | no | — |
| 492 | C2 | — | 212 | 1 | no | — |
| 493 | C2 | — | 212 | 1 | no | — |
| 494 | C2 | #20290736 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20291317 | C2 | semidirect |
| 2. #20290994 | C2 | semidirect |
| 3. #20290974 | C2 | semidirect |
| 4. #20290568 | C2 | semidirect |
| 5. #20289816 | C2 | semidirect |
| 6. #20289804 | C2 | semidirect |
| 21. C22×#11719923 | C4 | semidirect |
| 27. #16810633 | C4 | semidirect |
| 28. #16810619 | C4 | semidirect |
| 30. C2×AGL(1,ℤ/8)×C53 | C4 | semidirect |
| 256. C2×AGL(1,ℤ/8) | #6157 | semidirect |
| 278. C53 | #13103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291317 | 2 |
| #20290994 | 2 |
| #20290974 | 2 |
| #20290568 | 2 |
| #20289816 | 2 |
| #20289804 | 2 |
| #20284000 | 2 |
| #13103 | 53 |