Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
490 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 77 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 | #11736086 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #11727739 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11727738 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11727724 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11727271 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11727263 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C7×#1305 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#6493 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×#6493 | C22 | 1 | 1 | yes | characteristic |
| 10 | C22×#1136 | C22 | 1 | 1 | yes | characteristic |
| 11 | C7×#407 | C22 | 1 | 1 | yes | characteristic |
| 12 | C7×#407 | C22 | 1 | 1 | yes | characteristic |
| 13 | C7×#380 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×C22⋊(C7⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 15 | #89907 | — | 2 | 1 | no | — |
| 16 | #89907 | — | 2 | 1 | no | — |
| 17 | C2×#6397 | — | 2 | 1 | no | — |
| 18 | C2×#6396 | — | 2 | 1 | no | — |
| 19 | C2×#6383 | — | 2 | 1 | no | — |
| 20 | #89507 | — | 2 | 1 | no | — |
| 21 | #89507 | — | 2 | 1 | no | — |
| 22 | #89504 | — | 2 | 1 | no | — |
| 23 | #89504 | — | 2 | 1 | no | — |
| 24 | #89353 | — | 2 | 1 | no | — |
| 25 | #89349 | — | 2 | 1 | no | — |
| 26 | #89324 | — | 2 | 1 | no | — |
| 27 | #89263 | — | 2 | 2 | no | — |
| 28 | #89246 | — | 2 | 2 | no | — |
| 29 | #10560 | — | 7 | 1 | no | maximal, Sylow |
| 30 | C23×C4×C7 | C23 | 1 | 1 | yes | characteristic |
| 31 | C22×C22⋊D7 | — | 2 | 1 | no | — |
| 32 | C22×C22⋊D7 | — | 2 | 1 | no | — |
| 33 | C22×D28 | D4 | 1 | 1 | yes | characteristic |
| 34 | C22×D28 | D4 | 1 | 1 | yes | characteristic |
| 35 | C2×C7×M16 | — | 2 | 1 | no | — |
| 36 | C2×C7×M16 | D4 | 1 | 1 | yes | characteristic |
| 37 | C2×C7×M16 | D4 | 1 | 1 | yes | characteristic |
| 38 | C2×C7×C4⋊C4 | — | 2 | 1 | no | — |
| 39 | C2×C7×C22⋊C4 | — | 2 | 1 | no | — |
| 40 | #6493 | — | 2 | 1 | no | — |
| 41 | #6493 | — | 2 | 1 | no | — |
| 42 | #6493 | — | 2 | 1 | no | — |
| 43 | #6493 | — | 2 | 1 | no | — |
| 44 | #6493 | — | 2 | 1 | no | — |
| 45 | #6493 | — | 2 | 1 | no | — |
| 46 | #6493 | — | 2 | 1 | no | — |
| 47 | #6493 | — | 2 | 1 | no | — |
| 48 | C2×(C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 49 | C2×(C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 50 | C2×C4⋊Dic7 | D4 | 1 | 1 | yes | characteristic |
| 51 | C2×C4⋊Dic7 | D4 | 1 | 1 | yes | characteristic |
| 52 | C2×#1136 | — | 2 | 1 | no | — |
| 53 | C2×#1136 | — | 2 | 1 | no | — |
| 54 | C2×#1136 | — | 4 | 2 | no | — |
| 55 | C22×C7⋊C8 | — | 2 | 1 | no | — |
| 56 | C22×C7⋊C8 | — | 2 | 1 | no | — |
| 57 | C2×D56 | — | 2 | 1 | no | — |
| 58 | C2×D56 | — | 2 | 1 | no | — |
| 59 | C7×C22⋊C8 | — | 2 | 1 | no | — |
| 60 | C7×C22⋊C8 | — | 2 | 1 | no | — |
| 61 | C7×C22⋊C8 | — | 2 | 1 | no | — |
| 62 | C7×C22⋊C8 | — | 2 | 1 | no | — |
| 63 | C7×#95 | — | 2 | 1 | no | — |
| 64 | C22⋊(C7⋊C8) | — | 2 | 1 | no | — |
| 65 | C22⋊(C7⋊C8) | D4 | 1 | 2 | yes | — |
| 66 | #6397 | — | 4 | 2 | no | — |
| 67 | #6396 | — | 4 | 2 | no | — |
| 68 | #6395 | — | 2 | 1 | no | — |
| 69 | #6395 | — | 2 | 1 | no | — |
| 70 | #6395 | — | 2 | 1 | no | — |
| 71 | #6395 | — | 2 | 1 | no | — |
| 72 | #6391 | — | 2 | 1 | no | — |
| 73 | #6391 | — | 2 | 1 | no | — |
| 74 | #6383 | — | 4 | 2 | no | — |
| 75 | #3192 | — | 7 | 1 | no | — |
| 76 | #1900 | — | 7 | 1 | no | — |
| 77 | #1895 | — | 7 | 1 | no | — |
| 78 | #1855 | — | 7 | 1 | no | — |
| 79 | #1519 | — | 7 | 1 | no | — |
| 80 | #1471 | — | 7 | 1 | no | — |
| 81 | #1305 | D7 | 1 | 1 | yes | characteristic, complemented |
| 82 | C24×C7 | #41 | 1 | 1 | yes | characteristic |
| 83 | C23×D7 | — | 2 | 1 | no | — |
| 84 | C23×D7 | — | 2 | 1 | no | — |
| 85 | C22×C4×C7 | — | 4 | 1 | no | — |
| 86 | C22×C4×C7 | — | 4 | 1 | no | — |
| 87 | C22×C4×C7 | — | 4 | 1 | no | — |
| 88 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 89 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 90 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 91 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 92 | C22×C4×C7 | #41 | 1 | 1 | yes | characteristic |
| 93 | C22×C4×C7 | #41 | 1 | 1 | yes | characteristic |
| 94 | C2×C22⋊D7 | — | 4 | 1 | no | — |
| 95 | C2×C22⋊D7 | — | 4 | 1 | no | — |
| 96 | C2×C22⋊D7 | — | 4 | 1 | no | — |
| 97 | C2×C22⋊D7 | — | 4 | 1 | no | — |
| 98 | C2×C22⋊D7 | — | 8 | 1 | no | — |
| 99 | C2×C22⋊D7 | — | 8 | 1 | no | — |
| 100 | C2×C22⋊D7 | — | 8 | 2 | no | — |
| 101 | C22×Dic7 | — | 2 | 1 | no | — |
| 102 | C22×Dic7 | — | 2 | 1 | no | — |
| 103 | C2×D28 | — | 2 | 1 | no | — |
| 104 | C2×D28 | — | 2 | 1 | no | — |
| 105 | C2×D28 | — | 2 | 1 | no | — |
| 106 | C2×D28 | — | 2 | 1 | no | — |
| 107 | C2×D28 | — | 4 | 1 | no | — |
| 108 | C2×D28 | — | 4 | 1 | no | — |
| 109 | C2×D28 | — | 4 | 1 | no | — |
| 110 | C2×D28 | — | 4 | 1 | no | — |
| 111 | C7×M16 | — | 4 | 1 | no | — |
| 112 | C7×M16 | — | 4 | 1 | no | — |
| 113 | C7×M16 | — | 4 | 1 | no | — |
| 114 | C7×M16 | — | 4 | 1 | no | — |
| 115 | C2×C7×C8 | — | 2 | 1 | no | — |
| 116 | C2×C7×C8 | — | 2 | 1 | no | — |
| 117 | C2×C7×C8 | — | 4 | 1 | no | — |
| 118 | C7×C4⋊C4 | — | 4 | 1 | no | — |
| 119 | C7×C4⋊C4 | — | 4 | 1 | no | — |
| 120 | C7×C22⋊C4 | — | 8 | 1 | no | — |
| 121 | (C2×D7)⋊C4 | — | 4 | 1 | no | — |
| 122 | (C2×D7)⋊C4 | — | 4 | 1 | no | — |
| 123 | (C2×D7)⋊C4 | — | 4 | 1 | no | — |
| 124 | (C2×D7)⋊C4 | — | 4 | 1 | no | — |
| 125 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 126 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 127 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 128 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 129 | #1136 | — | 2 | 2 | no | — |
| 130 | #1136 | — | 2 | 2 | no | — |
| 131 | #1136 | — | 4 | 1 | no | — |
| 132 | #1136 | — | 4 | 1 | no | — |
| 133 | C2×C7⋊C8 | — | 2 | 2 | no | — |
| 134 | C2×C7⋊C8 | — | 2 | 2 | no | — |
| 135 | C2×C7⋊C8 | — | 4 | 1 | no | — |
| 136 | C2×C7⋊C8 | — | 4 | 1 | no | — |
| 137 | C2×C7⋊C8 | — | 4 | 1 | no | — |
| 138 | C2×C7⋊C8 | — | 4 | 1 | no | — |
| 139 | D56 | — | 8 | 1 | no | — |
| 140 | D56 | — | 8 | 1 | no | — |
| 141 | C22×M16 | — | 7 | 1 | no | — |
| 142 | C2×#121 | — | 7 | 1 | no | — |
| 143 | C2×#121 | — | 7 | 1 | no | — |
| 144 | #481 | — | 14 | 1 | no | — |
| 145 | #481 | — | 14 | 1 | no | — |
| 146 | #469 | — | 14 | 1 | no | — |
| 147 | #469 | — | 14 | 1 | no | — |
| 148 | #447 | — | 14 | 1 | no | — |
| 149 | #447 | — | 14 | 1 | no | — |
| 150 | C2×#108 | — | 14 | 1 | no | — |
| 151 | C2×#102 | — | 14 | 1 | no | — |
| 152 | C2×#100 | — | 14 | 1 | no | — |
| 153 | #407 | C2×D7 | 1 | 1 | yes | characteristic |
| 154 | #407 | C2×D7 | 1 | 1 | yes | characteristic |
| 155 | C2×C22⋊C8 | — | 7 | 1 | no | — |
| 156 | #380 | C2×D7 | 1 | 1 | yes | characteristic |
| 157 | #343 | — | 14 | 1 | no | — |
| 158 | #341 | — | 14 | 1 | no | — |
| 159 | #340 | — | 14 | 1 | no | — |
| 160 | #327 | — | 14 | 2 | no | — |
| 161 | #323 | — | 14 | 2 | no | — |
| 162 | C23×C7 | — | 2 | 1 | no | — |
| 163 | C23×C7 | — | 2 | 1 | no | — |
| 164 | C23×C7 | — | 4 | 1 | no | — |
| 165 | C23×C7 | — | 4 | 1 | no | — |
| 166 | C23×C7 | #121 | 1 | 1 | yes | characteristic |
| 167 | C23×C7 | #123 | 1 | 1 | yes | characteristic |
| 168 | C23×C7 | #124 | 1 | 1 | yes | characteristic |
| 169 | C22×D7 | — | 4 | 1 | no | — |
| 170 | C22×D7 | — | 4 | 1 | no | — |
| 171 | C22×D7 | — | 4 | 2 | no | — |
| 172 | C22×D7 | — | 4 | 1 | no | — |
| 173 | C22×D7 | — | 4 | 1 | no | — |
| 174 | C22×D7 | — | 8 | 1 | no | — |
| 175 | C22×D7 | — | 8 | 1 | no | — |
| 176 | C22×D7 | — | 8 | 1 | no | — |
| 177 | C22×D7 | — | 8 | 1 | no | — |
| 178 | C2×C4×C7 | — | 2 | 1 | no | — |
| 179 | C2×C4×C7 | — | 2 | 1 | no | — |
| 180 | C2×C4×C7 | — | 2 | 1 | no | — |
| 181 | C2×C4×C7 | — | 2 | 1 | no | — |
| 182 | C2×C4×C7 | — | 2 | 1 | no | — |
| 183 | C2×C4×C7 | — | 2 | 1 | no | — |
| 184 | C2×C4×C7 | — | 4 | 1 | no | — |
| 185 | C2×C4×C7 | — | 4 | 1 | no | — |
| 186 | C2×C4×C7 | — | 4 | 1 | no | — |
| 187 | C2×C4×C7 | — | 8 | 1 | no | — |
| 188 | C2×C4×C7 | — | 8 | 1 | no | — |
| 189 | C2×C4×C7 | — | 8 | 1 | no | — |
| 190 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 191 | C2×C4×C7 | #121 | 1 | 1 | yes | characteristic |
| 192 | C2×C4×C7 | #121 | 1 | 1 | yes | characteristic |
| 193 | C2×C4×C7 | #123 | 1 | 1 | yes | characteristic |
| 194 | C22⋊D7 | — | 8 | 2 | no | — |
| 195 | C22⋊D7 | — | 8 | 2 | no | — |
| 196 | C22⋊D7 | — | 8 | 2 | no | — |
| 197 | C22⋊D7 | — | 8 | 1 | no | — |
| 198 | C22⋊D7 | — | 8 | 1 | no | — |
| 199 | C2×Dic7 | — | 4 | 1 | no | — |
| 200 | C2×Dic7 | — | 4 | 1 | no | — |
| 201 | C2×Dic7 | — | 8 | 1 | no | — |
| 202 | C2×Dic7 | — | 8 | 1 | no | — |
| 203 | D28 | — | 4 | 2 | no | — |
| 204 | D28 | — | 4 | 1 | no | — |
| 205 | D28 | — | 4 | 1 | no | — |
| 206 | D28 | — | 4 | 1 | no | — |
| 207 | D28 | — | 4 | 1 | no | — |
| 208 | D28 | — | 8 | 1 | no | — |
| 209 | C7×C8 | — | 4 | 1 | no | — |
| 210 | C7×C8 | — | 4 | 1 | no | — |
| 211 | C7×C8 | — | 8 | 1 | no | — |
| 212 | C7⋊C8 | — | 4 | 2 | no | — |
| 213 | C7⋊C8 | — | 4 | 2 | no | — |
| 214 | C22×D4 | — | 7 | 1 | no | — |
| 215 | C22×D4 | — | 7 | 1 | no | — |
| 216 | C22×D4 | — | 14 | 1 | no | — |
| 217 | C22×D4 | — | 14 | 1 | no | — |
| 218 | C23×C4 | C22×D7 | 1 | 1 | yes | characteristic |
| 219 | C2×D8 | — | 14 | 1 | no | — |
| 220 | C2×D8 | — | 14 | 1 | no | — |
| 221 | C2×M16 | — | 2 | 1 | no | — |
| 222 | C2×M16 | — | 14 | 1 | no | — |
| 223 | C2×M16 | — | 14 | 1 | no | — |
| 224 | C2×M16 | — | 28 | 2 | no | — |
| 225 | C2×M16 | D28 | 1 | 1 | yes | characteristic |
| 226 | C2×M16 | D28 | 1 | 1 | yes | characteristic |
| 227 | C22×C8 | — | 14 | 1 | no | — |
| 228 | C22×C8 | — | 14 | 1 | no | — |
| 229 | #121 | — | 14 | 1 | no | — |
| 230 | #121 | — | 14 | 1 | no | — |
| 231 | #121 | — | 14 | 1 | no | — |
| 232 | #121 | — | 14 | 1 | no | — |
| 233 | #121 | — | 14 | 1 | no | — |
| 234 | #121 | — | 14 | 1 | no | — |
| 235 | #121 | — | 14 | 1 | no | — |
| 236 | #121 | — | 14 | 1 | no | — |
| 237 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 238 | C2×C4⋊C4 | — | 7 | 1 | no | — |
| 239 | C2×C4⋊C4 | — | 7 | 1 | no | — |
| 240 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 241 | C2×C22⋊C4 | — | 14 | 1 | no | — |
| 242 | C2×C22⋊C4 | — | 14 | 1 | no | — |
| 243 | #108 | — | 28 | 2 | no | — |
| 244 | #106 | — | 14 | 1 | no | — |
| 245 | #106 | — | 14 | 1 | no | — |
| 246 | #102 | — | 14 | 1 | no | — |
| 247 | #102 | — | 14 | 1 | no | — |
| 248 | #102 | — | 14 | 1 | no | — |
| 249 | #102 | — | 14 | 1 | no | — |
| 250 | #102 | — | 28 | 2 | no | — |
| 251 | #100 | — | 28 | 2 | no | — |
| 252 | C22⋊C8 | — | 2 | 1 | no | — |
| 253 | C22⋊C8 | — | 2 | 1 | no | — |
| 254 | C22⋊C8 | — | 2 | 1 | no | — |
| 255 | C22⋊C8 | — | 2 | 1 | no | — |
| 256 | C22⋊C8 | — | 7 | 2 | no | — |
| 257 | C22⋊C8 | — | 14 | 1 | no | — |
| 258 | #95 | — | 2 | 1 | no | — |
| 259 | C22×C7 | — | 2 | 1 | no | — |
| 260 | C22×C7 | — | 2 | 1 | no | — |
| 261 | C22×C7 | — | 2 | 1 | no | — |
| 262 | C22×C7 | — | 2 | 1 | no | — |
| 263 | C22×C7 | — | 2 | 1 | no | — |
| 264 | C22×C7 | — | 2 | 1 | no | — |
| 265 | C22×C7 | — | 2 | 1 | no | — |
| 266 | C22×C7 | — | 2 | 1 | no | — |
| 267 | C22×C7 | — | 8 | 1 | no | — |
| 268 | C22×C7 | — | 8 | 1 | no | — |
| 269 | C22×C7 | #394 | 1 | 1 | yes | characteristic |
| 270 | C22×C7 | #471 | 1 | 1 | yes | characteristic |
| 271 | C22×C7 | #472 | 1 | 1 | yes | characteristic |
| 272 | C2×D7 | — | 8 | 1 | no | — |
| 273 | C2×D7 | — | 8 | 1 | no | — |
| 274 | C2×D7 | — | 8 | 1 | no | — |
| 275 | C2×D7 | — | 8 | 1 | no | — |
| 276 | C2×D7 | — | 8 | 1 | no | — |
| 277 | C2×D7 | — | 8 | 1 | no | — |
| 278 | C2×D7 | — | 16 | 1 | no | — |
| 279 | C2×D7 | — | 16 | 1 | no | — |
| 280 | C2×D7 | — | 16 | 2 | no | — |
| 281 | C4×C7 | — | 2 | 1 | no | — |
| 282 | C4×C7 | — | 2 | 1 | no | — |
| 283 | C4×C7 | — | 2 | 1 | no | — |
| 284 | C4×C7 | — | 16 | 1 | no | — |
| 285 | C4×C7 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 286 | C4×C7 | #458 | 1 | 1 | yes | characteristic |
| 287 | Dic7 | — | 8 | 1 | no | — |
| 288 | Dic7 | — | 8 | 1 | no | — |
| 289 | C24 | — | 14 | 1 | no | — |
| 290 | C24 | — | 14 | 1 | no | — |
| 291 | C24 | #1157 | 1 | 1 | yes | characteristic |
| 292 | C2×D4 | — | 14 | 1 | no | — |
| 293 | C2×D4 | — | 14 | 1 | no | — |
| 294 | C2×D4 | — | 14 | 1 | no | — |
| 295 | C2×D4 | — | 14 | 1 | no | — |
| 296 | C2×D4 | — | 28 | 1 | no | — |
| 297 | C2×D4 | — | 28 | 1 | no | — |
| 298 | C2×D4 | — | 28 | 1 | no | — |
| 299 | C2×D4 | — | 28 | 1 | no | — |
| 300 | C2×D4 | — | 28 | 1 | no | — |
| 301 | C2×D4 | — | 28 | 1 | no | — |
| 302 | C2×D4 | — | 28 | 1 | no | — |
| 303 | C2×D4 | — | 28 | 1 | no | — |
| 304 | C2×D4 | — | 56 | 1 | no | — |
| 305 | C2×D4 | — | 56 | 1 | no | — |
| 306 | C2×D4 | — | 56 | 2 | no | — |
| 307 | C22×C4 | — | 4 | 1 | no | — |
| 308 | C22×C4 | — | 4 | 1 | no | — |
| 309 | C22×C4 | — | 4 | 1 | no | — |
| 310 | C22×C4 | — | 14 | 1 | no | — |
| 311 | C22×C4 | — | 14 | 1 | no | — |
| 312 | C22×C4 | C2×D28 | 1 | 1 | yes | characteristic |
| 313 | C22×C4 | #1157 | 1 | 1 | yes | characteristic |
| 314 | C22×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 315 | C22×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 316 | C22×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 317 | C22×C4 | #1161 | 1 | 1 | yes | characteristic |
| 318 | D8 | — | 56 | 1 | no | — |
| 319 | D8 | — | 56 | 1 | no | — |
| 320 | M16 | — | 4 | 1 | no | — |
| 321 | M16 | — | 4 | 1 | no | — |
| 322 | M16 | — | 4 | 1 | no | — |
| 323 | M16 | — | 4 | 1 | no | — |
| 324 | M16 | — | 14 | 2 | no | — |
| 325 | M16 | — | 14 | 2 | no | — |
| 326 | M16 | — | 28 | 1 | no | — |
| 327 | M16 | — | 28 | 1 | no | — |
| 328 | C2×C8 | — | 2 | 1 | no | — |
| 329 | C2×C8 | — | 2 | 1 | no | — |
| 330 | C2×C8 | — | 4 | 1 | no | — |
| 331 | C2×C8 | — | 14 | 2 | no | — |
| 332 | C2×C8 | — | 14 | 2 | no | — |
| 333 | C2×C8 | — | 28 | 1 | no | — |
| 334 | C2×C8 | — | 28 | 1 | no | — |
| 335 | C2×C8 | — | 28 | 1 | no | — |
| 336 | C2×C8 | — | 28 | 1 | no | — |
| 337 | C4⋊C4 | — | 4 | 1 | no | — |
| 338 | C4⋊C4 | — | 4 | 1 | no | — |
| 339 | C4⋊C4 | — | 14 | 1 | no | — |
| 340 | C4⋊C4 | — | 14 | 1 | no | — |
| 341 | C4⋊C4 | — | 14 | 1 | no | — |
| 342 | C4⋊C4 | — | 14 | 1 | no | — |
| 343 | C22⋊C4 | — | 8 | 1 | no | — |
| 344 | C22⋊C4 | — | 28 | 1 | no | — |
| 345 | C22⋊C4 | — | 28 | 1 | no | — |
| 346 | C22⋊C4 | — | 28 | 1 | no | — |
| 347 | C22⋊C4 | — | 28 | 1 | no | — |
| 348 | C2×C7 | — | 2 | 1 | no | — |
| 349 | C2×C7 | — | 2 | 1 | no | — |
| 350 | C2×C7 | — | 4 | 1 | no | — |
| 351 | C2×C7 | — | 4 | 1 | no | — |
| 352 | C2×C7 | #2044 | 1 | 1 | yes | characteristic |
| 353 | C2×C7 | #2048 | 1 | 1 | yes | characteristic |
| 354 | C2×C7 | #2051 | 1 | 1 | yes | characteristic |
| 355 | D7 | — | 16 | 1 | no | — |
| 356 | D7 | — | 16 | 1 | no | — |
| 357 | C23 | — | 2 | 1 | no | — |
| 358 | C23 | — | 2 | 1 | no | — |
| 359 | C23 | — | 4 | 1 | no | — |
| 360 | C23 | — | 4 | 1 | no | — |
| 361 | C23 | — | 28 | 2 | no | — |
| 362 | C23 | — | 28 | 1 | no | — |
| 363 | C23 | — | 28 | 1 | no | — |
| 364 | C23 | — | 28 | 1 | no | — |
| 365 | C23 | — | 28 | 1 | no | — |
| 366 | C23 | — | 56 | 1 | no | — |
| 367 | C23 | — | 56 | 1 | no | — |
| 368 | C23 | — | 56 | 1 | no | — |
| 369 | C23 | — | 56 | 1 | no | — |
| 370 | C23 | #6438 | 1 | 1 | yes | characteristic |
| 371 | C23 | #6447 | 1 | 1 | yes | characteristic |
| 372 | C23 | #6457 | 1 | 1 | yes | characteristic |
| 373 | D4 | — | 28 | 2 | no | — |
| 374 | D4 | — | 28 | 1 | no | — |
| 375 | D4 | — | 28 | 1 | no | — |
| 376 | D4 | — | 28 | 1 | no | — |
| 377 | D4 | — | 28 | 1 | no | — |
| 378 | D4 | — | 56 | 1 | no | — |
| 379 | D4 | — | 56 | 2 | no | — |
| 380 | D4 | — | 56 | 2 | no | — |
| 381 | D4 | — | 56 | 2 | no | — |
| 382 | D4 | — | 56 | 1 | no | — |
| 383 | D4 | — | 56 | 1 | no | — |
| 384 | C2×C4 | — | 2 | 1 | no | — |
| 385 | C2×C4 | — | 2 | 1 | no | — |
| 386 | C2×C4 | — | 2 | 1 | no | — |
| 387 | C2×C4 | — | 2 | 1 | no | — |
| 388 | C2×C4 | — | 2 | 1 | no | — |
| 389 | C2×C4 | — | 2 | 1 | no | — |
| 390 | C2×C4 | — | 4 | 1 | no | — |
| 391 | C2×C4 | — | 4 | 1 | no | — |
| 392 | C2×C4 | — | 4 | 1 | no | — |
| 393 | C2×C4 | — | 8 | 1 | no | — |
| 394 | C2×C4 | — | 8 | 1 | no | — |
| 395 | C2×C4 | — | 8 | 1 | no | — |
| 396 | C2×C4 | — | 28 | 1 | no | — |
| 397 | C2×C4 | — | 28 | 1 | no | — |
| 398 | C2×C4 | — | 56 | 1 | no | — |
| 399 | C2×C4 | — | 56 | 1 | no | — |
| 400 | C2×C4 | #6445 | 1 | 1 | yes | characteristic |
| 401 | C2×C4 | #6447 | 1 | 1 | yes | characteristic |
| 402 | C2×C4 | #6457 | 1 | 1 | yes | characteristic |
| 403 | C2×C4 | #6458 | 1 | 1 | yes | characteristic |
| 404 | C8 | — | 4 | 1 | no | — |
| 405 | C8 | — | 4 | 1 | no | — |
| 406 | C8 | — | 8 | 1 | no | — |
| 407 | C8 | — | 28 | 2 | no | — |
| 408 | C8 | — | 28 | 2 | no | — |
| 409 | C7 | #10560 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 410 | C22 | — | 2 | 1 | no | — |
| 411 | C22 | — | 2 | 1 | no | — |
| 412 | C22 | — | 2 | 1 | no | — |
| 413 | C22 | — | 2 | 1 | no | — |
| 414 | C22 | — | 2 | 1 | no | — |
| 415 | C22 | — | 2 | 1 | no | — |
| 416 | C22 | — | 2 | 1 | no | — |
| 417 | C22 | — | 2 | 1 | no | — |
| 418 | C22 | — | 8 | 1 | no | — |
| 419 | C22 | — | 8 | 1 | no | — |
| 420 | C22 | — | 56 | 1 | no | — |
| 421 | C22 | — | 56 | 1 | no | — |
| 422 | C22 | — | 56 | 1 | no | — |
| 423 | C22 | — | 56 | 1 | no | — |
| 424 | C22 | — | 56 | 1 | no | — |
| 425 | C22 | — | 56 | 1 | no | — |
| 426 | C22 | — | 112 | 1 | no | — |
| 427 | C22 | — | 112 | 1 | no | — |
| 428 | C22 | — | 112 | 2 | no | — |
| 429 | C22 | #89444 | 1 | 1 | yes | characteristic |
| 430 | C22 | #89521 | 1 | 1 | yes | characteristic |
| 431 | C22 | #89526 | 1 | 1 | yes | characteristic |
| 432 | C4 | — | 2 | 1 | no | — |
| 433 | C4 | — | 2 | 1 | no | — |
| 434 | C4 | — | 2 | 1 | no | — |
| 435 | C4 | — | 16 | 1 | no | — |
| 436 | C4 | — | 56 | 1 | no | — |
| 437 | C4 | — | 56 | 1 | no | — |
| 438 | C4 | #89513 | 1 | 1 | yes | characteristic |
| 439 | C4 | #89514 | 1 | 1 | yes | characteristic |
| 440 | C2 | — | 2 | 1 | no | — |
| 441 | C2 | — | 2 | 1 | no | — |
| 442 | C2 | — | 4 | 1 | no | — |
| 443 | C2 | — | 4 | 1 | no | — |
| 444 | C2 | — | 112 | 1 | no | — |
| 445 | C2 | — | 112 | 1 | no | — |
| 446 | C2 | #11726711 | 1 | 1 | yes | characteristic |
| 447 | C2 | #11726740 | 1 | 1 | yes | characteristic |
| 448 | C2 | #11726772 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11727739 | C2 | semidirect |
| 3. #11727738 | C2 | semidirect |
| 4. #11727724 | C2 | semidirect |
| 5. #11727271 | C2 | semidirect |
| 6. #11727263 | C2 | semidirect |
| 7. C7×#1305 | C2 | semidirect |
| 81. #1305 | D7 | semidirect |
| 409. C7 | #10560 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736086 | 2 |
| #11727739 | 2 |
| #11727738 | 2 |
| #11727724 | 2 |
| #11727271 | 2 |
| #11727263 | 2 |
| C7×#1305 | 2 |
| #10560 | 7 |