Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
896 conjugacy classes of subgroups.
The subgroup lattice has 512 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#89914 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11741240 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#89665 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#89637 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11736333 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | C7×#1815 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11728463 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11728326 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #11728061 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #11726750 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #11726746 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | C2×C7×#131 | C22 | 1 | 1 | yes | characteristic |
| 13 | #90519 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×#6512 | C22 | 1 | 2 | yes | — |
| 15 | C2×D7×M16 | C22 | 1 | 2 | yes | — |
| 16 | C22×D56 | C22 | 1 | 1 | yes | characteristic |
| 17 | C22×#1131 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#6458 | C22 | 1 | 2 | yes | — |
| 19 | C2×C7×#108 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×C7×#106 | C22 | 1 | 1 | yes | characteristic |
| 21 | C7×#417 | C22 | 1 | 2 | yes | — |
| 22 | #90006 | C22 | 1 | 1 | yes | characteristic |
| 23 | #89914 | — | 2 | 4 | no | — |
| 24 | #89903 | C22 | 1 | 2 | yes | — |
| 25 | C2×#6397 | C22 | 1 | 2 | yes | — |
| 26 | C2×#6397 | C22 | 1 | 2 | yes | — |
| 27 | #89900 | — | 2 | 2 | no | — |
| 28 | #89898 | C22 | 1 | 1 | yes | characteristic |
| 29 | C2×#6396 | C22 | 1 | 2 | yes | — |
| 30 | #89891 | C22 | 1 | 1 | yes | characteristic |
| 31 | #89883 | — | 2 | 2 | no | — |
| 32 | C2×#6393 | C22 | 1 | 1 | yes | characteristic |
| 33 | #89873 | C22 | 1 | 1 | yes | characteristic |
| 34 | C2×#6383 | C22 | 1 | 2 | yes | — |
| 35 | #89736 | C22 | 1 | 2 | yes | — |
| 36 | #89665 | — | 2 | 4 | no | — |
| 37 | #89637 | — | 2 | 2 | no | — |
| 38 | #89637 | — | 2 | 2 | no | — |
| 39 | #89584 | — | 2 | 2 | no | — |
| 40 | #89579 | — | 2 | 2 | no | — |
| 41 | #89554 | — | 2 | 2 | no | — |
| 42 | #89547 | — | 2 | 2 | no | — |
| 43 | C7×#343 | C22 | 1 | 2 | yes | — |
| 44 | #89325 | C22 | 1 | 2 | yes | — |
| 45 | #24806 | — | 7 | 1 | no | maximal, Sylow |
| 46 | C2×C7×#41 | C23 | 1 | 1 | yes | characteristic |
| 47 | C22×D28 | — | 2 | 2 | no | — |
| 48 | C22×D28 | C23 | 1 | 2 | yes | — |
| 49 | C22×C4×D7 | C23 | 1 | 1 | yes | characteristic |
| 50 | C7×#131 | — | 2 | 2 | no | — |
| 51 | C7×#131 | — | 2 | 2 | no | — |
| 52 | C2×C7×M16 | — | 2 | 1 | no | — |
| 53 | C2×C7×M16 | C23 | 1 | 1 | yes | characteristic |
| 54 | C2×C7×M16 | C23 | 1 | 2 | yes | — |
| 55 | C22×C7×C8 | — | 2 | 1 | no | — |
| 56 | C22×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 57 | C2×C7×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 58 | #6512 | — | 2 | 4 | no | — |
| 59 | #6512 | — | 4 | 2 | no | — |
| 60 | #6509 | D4 | 1 | 2 | yes | — |
| 61 | C2×#1143 | — | 2 | 2 | no | — |
| 62 | #6501 | D4 | 1 | 2 | yes | — |
| 63 | #6500 | — | 2 | 1 | no | — |
| 64 | #6498 | — | 2 | 1 | no | — |
| 65 | C2×#1141 | — | 2 | 2 | no | — |
| 66 | C4×C22⋊D7 | — | 2 | 2 | no | — |
| 67 | C2×(C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 68 | #6489 | C23 | 1 | 1 | yes | characteristic |
| 69 | C2×#1136 | C23 | 1 | 1 | yes | characteristic |
| 70 | C2×#1136 | C23 | 1 | 2 | yes | — |
| 71 | C22×C7⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 72 | D7×M16 | — | 2 | 4 | no | — |
| 73 | D7×M16 | — | 4 | 2 | no | — |
| 74 | C2×D56 | — | 2 | 1 | no | — |
| 75 | C2×D56 | — | 2 | 1 | no | — |
| 76 | C2×D56 | — | 2 | 2 | no | — |
| 77 | C2×D56 | — | 2 | 2 | no | — |
| 78 | C2×#1131 | — | 2 | 2 | no | — |
| 79 | C2×#1131 | — | 2 | 2 | no | — |
| 80 | C2×#1131 | — | 2 | 2 | no | — |
| 81 | C2×#1131 | D4 | 1 | 2 | yes | — |
| 82 | C2×#1131 | D4 | 1 | 2 | yes | — |
| 83 | C2×C8×D7 | — | 2 | 2 | no | — |
| 84 | #6458 | — | 2 | 2 | no | — |
| 85 | #6458 | — | 2 | 2 | no | — |
| 86 | #6458 | — | 2 | 2 | no | — |
| 87 | #6458 | — | 2 | 2 | no | — |
| 88 | C7×#108 | — | 2 | 2 | no | — |
| 89 | C7×#106 | — | 2 | 1 | no | — |
| 90 | C7×#106 | — | 2 | 1 | no | — |
| 91 | C7×#103 | — | 2 | 2 | no | — |
| 92 | C7×#102 | — | 2 | 2 | no | — |
| 93 | C22⋊(C7⋊C8) | — | 2 | 2 | no | — |
| 94 | #6397 | — | 2 | 4 | no | — |
| 95 | #6397 | — | 4 | 2 | no | — |
| 96 | #6396 | — | 2 | 4 | no | — |
| 97 | #6395 | — | 2 | 2 | no | — |
| 98 | #6395 | — | 2 | 2 | no | — |
| 99 | (C2×D7)⋊C8 | — | 2 | 2 | no | — |
| 100 | #6393 | D4 | 1 | 4 | yes | complemented |
| 101 | #6389 | — | 2 | 1 | no | — |
| 102 | Dic7⋊C8 | — | 2 | 2 | no | — |
| 103 | C8×Dic7 | — | 2 | 1 | no | — |
| 104 | #6383 | — | 2 | 4 | no | — |
| 105 | #6382 | — | 2 | 2 | no | — |
| 106 | #6381 | — | 2 | 2 | no | — |
| 107 | C2×#472 | — | 7 | 1 | no | — |
| 108 | #3055 | — | 7 | 2 | no | — |
| 109 | C2×#469 | — | 7 | 1 | no | — |
| 110 | #2930 | — | 7 | 1 | no | — |
| 111 | C2×#430 | — | 7 | 1 | no | — |
| 112 | #2063 | — | 7 | 2 | no | — |
| 113 | #2051 | — | 7 | 2 | no | — |
| 114 | #1978 | — | 7 | 1 | no | — |
| 115 | #1951 | — | 7 | 1 | no | — |
| 116 | #1900 | — | 7 | 2 | no | — |
| 117 | #1815 | D7 | 1 | 1 | yes | characteristic, complemented |
| 118 | C23×D7 | — | 2 | 2 | no | — |
| 119 | C23×D7 | #41 | 1 | 1 | yes | characteristic |
| 120 | C7×#41 | — | 2 | 1 | no | — |
| 121 | C7×#41 | — | 2 | 1 | no | — |
| 122 | C7×#41 | — | 2 | 1 | no | — |
| 123 | C7×#41 | — | 2 | 1 | no | — |
| 124 | C2×C7×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 125 | C2×C7×D4 | — | 2 | 1 | no | — |
| 126 | C2×C7×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 127 | C22×C4×C7 | — | 2 | 1 | no | — |
| 128 | C22×C4×C7 | — | 2 | 2 | no | — |
| 129 | C22×C4×C7 | C24 | 1 | 1 | yes | characteristic |
| 130 | C2×C22⋊D7 | — | 2 | 2 | no | — |
| 131 | C22×Dic7 | #41 | 1 | 1 | yes | characteristic |
| 132 | C2×D28 | — | 2 | 2 | no | — |
| 133 | C2×D28 | — | 2 | 2 | no | — |
| 134 | C2×D28 | — | 2 | 2 | no | — |
| 135 | C2×D28 | — | 2 | 2 | no | — |
| 136 | C2×D28 | — | 2 | 2 | no | — |
| 137 | C2×D28 | — | 2 | 2 | no | — |
| 138 | C2×D28 | — | 4 | 2 | no | — |
| 139 | C2×D28 | — | 4 | 2 | no | — |
| 140 | C2×D28 | — | 8 | 4 | no | — |
| 141 | C2×C4×D7 | — | 2 | 1 | no | — |
| 142 | C2×C4×D7 | — | 2 | 1 | no | — |
| 143 | C2×C4×D7 | — | 2 | 1 | no | — |
| 144 | C2×C4×D7 | — | 2 | 1 | no | — |
| 145 | C2×C4×D7 | C2×D4 | 1 | 2 | yes | — |
| 146 | C2×C4×D7 | C2×D4 | 1 | 2 | yes | — |
| 147 | C7×M16 | — | 2 | 2 | no | — |
| 148 | C7×M16 | — | 2 | 1 | no | — |
| 149 | C7×M16 | — | 2 | 1 | no | — |
| 150 | C7×M16 | — | 2 | 2 | no | — |
| 151 | C7×M16 | — | 4 | 2 | no | — |
| 152 | C2×C7×C8 | — | 2 | 2 | no | — |
| 153 | C2×C7×C8 | — | 2 | 1 | no | — |
| 154 | C2×C7×C8 | — | 4 | 2 | no | — |
| 155 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 156 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 157 | C2×C7×C8 | C2×D4 | 1 | 2 | yes | — |
| 158 | C2×C7×C8 | #41 | 1 | 2 | yes | — |
| 159 | C7×C4⋊C4 | — | 2 | 2 | no | — |
| 160 | C7×C4⋊C4 | — | 2 | 2 | no | — |
| 161 | C22⋊Dic7 | — | 2 | 1 | no | — |
| 162 | C22⋊Dic7 | — | 2 | 2 | no | — |
| 163 | #1143 | — | 4 | 4 | no | — |
| 164 | #1141 | — | 4 | 4 | no | — |
| 165 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 166 | (C2×D7)⋊C4 | — | 4 | 2 | no | — |
| 167 | (C2×D7)⋊C4 | — | 4 | 2 | no | — |
| 168 | C4⋊Dic7 | C2×D4 | 1 | 2 | yes | — |
| 169 | Dic7⋊C4 | — | 2 | 2 | no | — |
| 170 | C4×Dic7 | — | 2 | 1 | no | — |
| 171 | #1136 | — | 2 | 2 | no | — |
| 172 | #1136 | — | 2 | 1 | no | — |
| 173 | #1136 | — | 2 | 1 | no | — |
| 174 | #1136 | C2×D4 | 1 | 4 | yes | — |
| 175 | C2×C7⋊C8 | — | 2 | 2 | no | — |
| 176 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 177 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 178 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 179 | C2×C7⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 180 | D56 | — | 4 | 2 | no | — |
| 181 | D56 | — | 4 | 2 | no | — |
| 182 | #1131 | — | 2 | 4 | no | — |
| 183 | #1131 | — | 2 | 4 | no | — |
| 184 | #1131 | — | 4 | 4 | no | — |
| 185 | C8×D7 | — | 4 | 4 | no | — |
| 186 | C2×AGL(1,ℤ/8) | — | 7 | 2 | no | — |
| 187 | C22×D8 | — | 7 | 1 | no | — |
| 188 | C2×#131 | C2×D7 | 1 | 1 | yes | characteristic |
| 189 | C22×M16 | — | 7 | 1 | no | — |
| 190 | C22×M16 | — | 7 | 2 | no | — |
| 191 | #525 | — | 7 | 1 | no | — |
| 192 | C2×#121 | — | 7 | 2 | no | — |
| 193 | #472 | — | 14 | 4 | no | — |
| 194 | #469 | — | 14 | 2 | no | — |
| 195 | #469 | — | 14 | 2 | no | — |
| 196 | #469 | — | 14 | 2 | no | — |
| 197 | #468 | — | 14 | 2 | no | — |
| 198 | #466 | — | 14 | 2 | no | — |
| 199 | #465 | — | 14 | 2 | no | — |
| 200 | #436 | — | 14 | 2 | no | — |
| 201 | #435 | — | 14 | 2 | no | — |
| 202 | #430 | — | 14 | 4 | no | — |
| 203 | C2×#108 | — | 7 | 1 | no | — |
| 204 | C2×#108 | — | 7 | 2 | no | — |
| 205 | C2×#108 | C2×D7 | 1 | 1 | yes | characteristic |
| 206 | #428 | — | 7 | 2 | no | — |
| 207 | C2×#106 | C2×D7 | 1 | 1 | yes | characteristic |
| 208 | #424 | — | 7 | 1 | no | — |
| 209 | #418 | — | 7 | 2 | no | — |
| 210 | #417 | C2×D7 | 1 | 2 | yes | — |
| 211 | C2×#102 | — | 7 | 2 | no | — |
| 212 | C2×#100 | — | 7 | 2 | no | — |
| 213 | C2×#100 | — | 7 | 2 | no | — |
| 214 | #408 | — | 7 | 1 | no | — |
| 215 | #407 | — | 7 | 1 | no | — |
| 216 | #405 | — | 7 | 1 | no | — |
| 217 | #343 | — | 7 | 2 | no | — |
| 218 | #343 | C2×D7 | 1 | 2 | yes | — |
| 219 | C23×C7 | — | 2 | 1 | no | — |
| 220 | C23×C7 | C2×#41 | 1 | 1 | yes | characteristic |
| 221 | C22×D7 | — | 2 | 1 | no | — |
| 222 | C22×D7 | — | 2 | 1 | no | — |
| 223 | C22×D7 | — | 4 | 2 | no | — |
| 224 | C22×D7 | — | 4 | 2 | no | — |
| 225 | C22×D7 | — | 4 | 2 | no | — |
| 226 | C22×D7 | — | 4 | 2 | no | — |
| 227 | C22×D7 | — | 8 | 2 | no | — |
| 228 | C22×D7 | — | 8 | 2 | no | — |
| 229 | C22×D7 | #121 | 1 | 2 | yes | — |
| 230 | C7×Q8 | — | 2 | 1 | no | — |
| 231 | C7×Q8 | — | 2 | 1 | no | — |
| 232 | C7×D4 | — | 2 | 1 | no | — |
| 233 | C7×D4 | — | 2 | 1 | no | — |
| 234 | C7×D4 | — | 4 | 1 | no | — |
| 235 | C7×D4 | — | 4 | 1 | no | — |
| 236 | C2×C4×C7 | — | 2 | 1 | no | — |
| 237 | C2×C4×C7 | — | 4 | 1 | no | — |
| 238 | C2×C4×C7 | — | 4 | 1 | no | — |
| 239 | C2×C4×C7 | — | 4 | 2 | no | — |
| 240 | C2×C4×C7 | — | 8 | 2 | no | — |
| 241 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 242 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 243 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 244 | C2×C4×C7 | C2×#41 | 1 | 1 | yes | characteristic |
| 245 | C2×C4×C7 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 246 | C2×C4×C7 | 2−1+4 | 1 | 1 | yes | characteristic |
| 247 | C22⋊D7 | — | 8 | 2 | no | — |
| 248 | C2×Dic7 | — | 2 | 1 | no | — |
| 249 | C2×Dic7 | — | 2 | 1 | no | — |
| 250 | C2×Dic7 | — | 2 | 2 | no | — |
| 251 | C2×Dic7 | #121 | 1 | 2 | yes | — |
| 252 | D28 | — | 4 | 2 | no | — |
| 253 | D28 | — | 4 | 2 | no | — |
| 254 | D28 | — | 4 | 2 | no | — |
| 255 | D28 | — | 4 | 2 | no | — |
| 256 | D28 | — | 8 | 4 | no | — |
| 257 | D28 | — | 8 | 4 | no | — |
| 258 | C4×D7 | — | 2 | 2 | no | — |
| 259 | C4×D7 | — | 2 | 2 | no | — |
| 260 | C4×D7 | — | 2 | 2 | no | — |
| 261 | C4×D7 | — | 2 | 2 | no | — |
| 262 | C7×C8 | — | 4 | 1 | no | — |
| 263 | C7×C8 | — | 4 | 2 | no | — |
| 264 | C7×C8 | #121 | 1 | 2 | yes | — |
| 265 | C7×C8 | #121 | 1 | 2 | yes | — |
| 266 | C7⋊C8 | — | 2 | 2 | no | — |
| 267 | C7⋊C8 | — | 2 | 4 | no | — |
| 268 | C7⋊C8 | — | 4 | 1 | no | — |
| 269 | C2×#41 | C22×D7 | 1 | 1 | yes | characteristic |
| 270 | C22×D4 | — | 7 | 2 | no | — |
| 271 | C22×D4 | — | 14 | 2 | no | — |
| 272 | C23×C4 | — | 7 | 1 | no | — |
| 273 | AGL(1,ℤ/8) | — | 14 | 4 | no | — |
| 274 | AGL(1,ℤ/8) | — | 28 | 2 | no | — |
| 275 | C2×SD16 | — | 14 | 2 | no | — |
| 276 | C2×D8 | — | 14 | 2 | no | — |
| 277 | C2×D8 | — | 14 | 2 | no | — |
| 278 | C2×D8 | — | 14 | 1 | no | — |
| 279 | C2×D8 | — | 14 | 1 | no | — |
| 280 | C2×D8 | — | 14 | 2 | no | — |
| 281 | #131 | — | 2 | 2 | no | — |
| 282 | #131 | — | 2 | 2 | no | — |
| 283 | C2×M16 | — | 2 | 1 | no | — |
| 284 | C2×M16 | — | 7 | 2 | no | — |
| 285 | C2×M16 | — | 7 | 2 | no | — |
| 286 | C2×M16 | — | 7 | 2 | no | — |
| 287 | C2×M16 | — | 7 | 1 | no | — |
| 288 | C2×M16 | — | 14 | 2 | no | — |
| 289 | C2×M16 | — | 14 | 2 | no | — |
| 290 | C2×M16 | — | 14 | 2 | no | — |
| 291 | C2×M16 | — | 14 | 4 | no | — |
| 292 | C2×M16 | — | 28 | 2 | no | — |
| 293 | C2×M16 | C22×D7 | 1 | 2 | yes | — |
| 294 | C2×M16 | C22×D7 | 1 | 1 | yes | characteristic |
| 295 | C22×C8 | — | 2 | 1 | no | — |
| 296 | C22×C8 | — | 7 | 1 | no | — |
| 297 | C22×C8 | — | 14 | 2 | no | — |
| 298 | C22×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 299 | #123 | — | 14 | 1 | no | — |
| 300 | C22⋊Q8 | — | 7 | 2 | no | — |
| 301 | #121 | — | 7 | 2 | no | — |
| 302 | #121 | — | 14 | 2 | no | — |
| 303 | #121 | — | 14 | 2 | no | — |
| 304 | #121 | — | 14 | 2 | no | — |
| 305 | #121 | — | 14 | 2 | no | — |
| 306 | #120 | — | 14 | 1 | no | — |
| 307 | C4×D4 | — | 14 | 2 | no | — |
| 308 | #117 | — | 7 | 1 | no | — |
| 309 | C2×C4⋊C4 | C22×D7 | 1 | 2 | yes | — |
| 310 | C2×C22⋊C4 | — | 14 | 2 | no | — |
| 311 | #108 | — | 2 | 2 | no | — |
| 312 | #108 | — | 7 | 4 | no | — |
| 313 | #108 | — | 14 | 4 | no | — |
| 314 | #107 | — | 14 | 2 | no | — |
| 315 | #106 | — | 2 | 1 | no | — |
| 316 | #106 | — | 2 | 1 | no | — |
| 317 | #106 | — | 14 | 2 | no | — |
| 318 | C4⋊C8 | — | 14 | 2 | no | — |
| 319 | #103 | — | 2 | 2 | no | — |
| 320 | #102 | — | 2 | 2 | no | — |
| 321 | #102 | — | 14 | 4 | no | — |
| 322 | #102 | — | 14 | 2 | no | — |
| 323 | #102 | — | 14 | 2 | no | — |
| 324 | #100 | — | 14 | 4 | no | — |
| 325 | #100 | — | 28 | 2 | no | — |
| 326 | C22⋊C8 | — | 14 | 2 | no | — |
| 327 | C22⋊C8 | — | 14 | 2 | no | — |
| 328 | #97 | — | 14 | 1 | no | — |
| 329 | C4×C8 | — | 14 | 1 | no | — |
| 330 | C22×C7 | — | 2 | 2 | no | — |
| 331 | C22×C7 | — | 4 | 1 | no | — |
| 332 | C22×C7 | — | 4 | 2 | no | — |
| 333 | C22×C7 | C2×#121 | 1 | 1 | yes | characteristic |
| 334 | C22×C7 | #548 | 1 | 1 | yes | characteristic |
| 335 | C22×C7 | #553 | 1 | 1 | yes | characteristic |
| 336 | C2×D7 | — | 2 | 2 | no | — |
| 337 | C2×D7 | — | 2 | 2 | no | — |
| 338 | C2×D7 | — | 2 | 2 | no | — |
| 339 | C2×D7 | — | 8 | 1 | no | — |
| 340 | C2×D7 | — | 8 | 1 | no | — |
| 341 | C2×D7 | — | 8 | 2 | no | — |
| 342 | C2×D7 | — | 8 | 2 | no | — |
| 343 | C2×D7 | — | 8 | 2 | no | — |
| 344 | C2×D7 | — | 16 | 2 | no | — |
| 345 | C2×D7 | — | 16 | 2 | no | — |
| 346 | C4×C7 | — | 4 | 1 | no | — |
| 347 | C4×C7 | — | 8 | 2 | no | — |
| 348 | C4×C7 | C2×#121 | 1 | 1 | yes | characteristic |
| 349 | C4×C7 | #537 | 1 | 1 | yes | characteristic |
| 350 | C4×C7 | D42 | 1 | 1 | yes | characteristic |
| 351 | C4×C7 | #547 | 1 | 1 | yes | characteristic |
| 352 | Dic7 | — | 2 | 2 | no | — |
| 353 | Dic7 | — | 4 | 2 | no | — |
| 354 | C24 | — | 7 | 1 | no | — |
| 355 | C24 | — | 14 | 2 | no | — |
| 356 | #41 | — | 2 | 1 | no | — |
| 357 | #41 | — | 2 | 1 | no | — |
| 358 | #41 | — | 2 | 1 | no | — |
| 359 | #41 | — | 2 | 1 | no | — |
| 360 | C2×Q8 | D4×D7 | 1 | 1 | yes | characteristic |
| 361 | C2×D4 | — | 2 | 1 | no | — |
| 362 | C2×D4 | — | 14 | 2 | no | — |
| 363 | C2×D4 | — | 14 | 2 | no | — |
| 364 | C2×D4 | — | 14 | 2 | no | — |
| 365 | C2×D4 | — | 14 | 2 | no | — |
| 366 | C2×D4 | — | 14 | 2 | no | — |
| 367 | C2×D4 | — | 14 | 2 | no | — |
| 368 | C2×D4 | — | 14 | 2 | no | — |
| 369 | C2×D4 | — | 28 | 2 | no | — |
| 370 | C2×D4 | — | 28 | 2 | no | — |
| 371 | C2×D4 | — | 56 | 4 | no | — |
| 372 | C2×D4 | D4×D7 | 1 | 1 | yes | characteristic |
| 373 | C22×C4 | — | 2 | 1 | no | — |
| 374 | C22×C4 | — | 2 | 2 | no | — |
| 375 | C22×C4 | — | 7 | 1 | no | — |
| 376 | C22×C4 | — | 7 | 2 | no | — |
| 377 | C22×C4 | — | 7 | 2 | no | — |
| 378 | C22×C4 | — | 14 | 1 | no | — |
| 379 | C22×C4 | — | 14 | 1 | no | — |
| 380 | C22×C4 | — | 14 | 1 | no | — |
| 381 | C22×C4 | — | 14 | 1 | no | — |
| 382 | C22×C4 | C23×D7 | 1 | 1 | yes | characteristic |
| 383 | SD16 | — | 28 | 4 | no | — |
| 384 | D8 | — | 28 | 4 | no | — |
| 385 | D8 | — | 28 | 2 | no | — |
| 386 | D8 | — | 28 | 2 | no | — |
| 387 | M16 | — | 2 | 1 | no | — |
| 388 | M16 | — | 2 | 1 | no | — |
| 389 | M16 | — | 2 | 2 | no | — |
| 390 | M16 | — | 2 | 2 | no | — |
| 391 | M16 | — | 4 | 2 | no | — |
| 392 | M16 | — | 7 | 4 | no | — |
| 393 | M16 | — | 14 | 2 | no | — |
| 394 | M16 | — | 14 | 4 | no | — |
| 395 | M16 | — | 14 | 4 | no | — |
| 396 | M16 | — | 14 | 1 | no | — |
| 397 | M16 | — | 14 | 1 | no | — |
| 398 | M16 | — | 28 | 4 | no | — |
| 399 | C2×C8 | — | 2 | 1 | no | — |
| 400 | C2×C8 | — | 2 | 2 | no | — |
| 401 | C2×C8 | — | 4 | 2 | no | — |
| 402 | C2×C8 | — | 7 | 2 | no | — |
| 403 | C2×C8 | — | 14 | 1 | no | — |
| 404 | C2×C8 | — | 14 | 2 | no | — |
| 405 | C2×C8 | — | 14 | 1 | no | — |
| 406 | C2×C8 | — | 14 | 1 | no | — |
| 407 | C2×C8 | — | 28 | 4 | no | — |
| 408 | C2×C8 | #1157 | 1 | 2 | yes | — |
| 409 | C2×C8 | D4×D7 | 1 | 1 | yes | characteristic |
| 410 | C2×C8 | D4×D7 | 1 | 1 | yes | characteristic |
| 411 | C2×C8 | D4×D7 | 1 | 2 | yes | — |
| 412 | C4⋊C4 | — | 2 | 2 | no | — |
| 413 | C4⋊C4 | — | 2 | 2 | no | — |
| 414 | C4⋊C4 | — | 7 | 2 | no | — |
| 415 | C4⋊C4 | — | 14 | 2 | no | — |
| 416 | C22⋊C4 | — | 14 | 2 | no | — |
| 417 | C22⋊C4 | — | 14 | 2 | no | — |
| 418 | C22⋊C4 | — | 14 | 1 | no | — |
| 419 | C22⋊C4 | — | 28 | 2 | no | — |
| 420 | C22⋊C4 | — | 28 | 2 | no | — |
| 421 | C42 | — | 14 | 1 | no | — |
| 422 | C2×C7 | — | 2 | 1 | no | — |
| 423 | C2×C7 | — | 2 | 1 | no | — |
| 424 | C2×C7 | — | 8 | 1 | no | — |
| 425 | C2×C7 | #2416 | 1 | 1 | yes | characteristic |
| 426 | C2×C7 | #3068 | 1 | 2 | yes | — |
| 427 | D7 | — | 4 | 2 | no | — |
| 428 | D7 | — | 16 | 2 | no | — |
| 429 | C23 | — | 2 | 1 | no | — |
| 430 | C23 | — | 7 | 2 | no | — |
| 431 | C23 | — | 14 | 1 | no | — |
| 432 | C23 | — | 14 | 1 | no | — |
| 433 | C23 | — | 28 | 2 | no | — |
| 434 | C23 | — | 28 | 2 | no | — |
| 435 | C23 | — | 28 | 2 | no | — |
| 436 | C23 | — | 28 | 2 | no | — |
| 437 | C23 | — | 56 | 2 | no | — |
| 438 | C23 | — | 56 | 2 | no | — |
| 439 | C23 | D7×#41 | 1 | 1 | yes | characteristic |
| 440 | Q8 | — | 2 | 1 | no | — |
| 441 | Q8 | — | 2 | 1 | no | — |
| 442 | D4 | — | 2 | 1 | no | — |
| 443 | D4 | — | 2 | 1 | no | — |
| 444 | D4 | — | 4 | 1 | no | — |
| 445 | D4 | — | 4 | 1 | no | — |
| 446 | D4 | — | 28 | 2 | no | — |
| 447 | D4 | — | 28 | 2 | no | — |
| 448 | D4 | — | 28 | 2 | no | — |
| 449 | D4 | — | 28 | 2 | no | — |
| 450 | D4 | — | 56 | 4 | no | — |
| 451 | D4 | — | 56 | 4 | no | — |
| 452 | D4 | — | 56 | 2 | no | — |
| 453 | C2×C4 | — | 2 | 1 | no | — |
| 454 | C2×C4 | — | 4 | 1 | no | — |
| 455 | C2×C4 | — | 4 | 1 | no | — |
| 456 | C2×C4 | — | 4 | 2 | no | — |
| 457 | C2×C4 | — | 7 | 2 | no | — |
| 458 | C2×C4 | — | 8 | 2 | no | — |
| 459 | C2×C4 | — | 14 | 1 | no | — |
| 460 | C2×C4 | — | 14 | 1 | no | — |
| 461 | C2×C4 | — | 14 | 2 | no | — |
| 462 | C2×C4 | — | 14 | 2 | no | — |
| 463 | C2×C4 | — | 14 | 2 | no | — |
| 464 | C2×C4 | — | 14 | 2 | no | — |
| 465 | C2×C4 | — | 14 | 2 | no | — |
| 466 | C2×C4 | C2×#1157 | 1 | 1 | yes | characteristic |
| 467 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 468 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 469 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 470 | C2×C4 | #6551 | 1 | 1 | yes | characteristic |
| 471 | C2×C4 | #6553 | 1 | 1 | yes | characteristic |
| 472 | C8 | — | 4 | 1 | no | — |
| 473 | C8 | — | 4 | 2 | no | — |
| 474 | C8 | — | 14 | 2 | no | — |
| 475 | C8 | — | 14 | 4 | no | — |
| 476 | C8 | — | 28 | 1 | no | — |
| 477 | C8 | #6447 | 1 | 2 | yes | — |
| 478 | C8 | #6447 | 1 | 2 | yes | — |
| 479 | C7 | #24806 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 480 | C22 | — | 2 | 2 | no | — |
| 481 | C22 | — | 4 | 2 | no | — |
| 482 | C22 | — | 4 | 1 | no | — |
| 483 | C22 | — | 14 | 2 | no | — |
| 484 | C22 | — | 14 | 2 | no | — |
| 485 | C22 | — | 14 | 2 | no | — |
| 486 | C22 | — | 56 | 1 | no | — |
| 487 | C22 | — | 56 | 1 | no | — |
| 488 | C22 | — | 56 | 2 | no | — |
| 489 | C22 | — | 56 | 2 | no | — |
| 490 | C22 | — | 56 | 2 | no | — |
| 491 | C22 | — | 112 | 2 | no | — |
| 492 | C22 | — | 112 | 2 | no | — |
| 493 | C22 | #90221 | 1 | 1 | yes | characteristic |
| 494 | C22 | D7×#121 | 1 | 1 | yes | characteristic |
| 495 | C22 | #90324 | 1 | 1 | yes | characteristic |
| 496 | C4 | — | 4 | 1 | no | — |
| 497 | C4 | — | 8 | 2 | no | — |
| 498 | C4 | — | 14 | 2 | no | — |
| 499 | C4 | — | 28 | 2 | no | — |
| 500 | C4 | C2×#6447 | 1 | 1 | yes | characteristic |
| 501 | C4 | #90198 | 1 | 1 | yes | characteristic |
| 502 | C4 | #90300 | 1 | 1 | yes | characteristic |
| 503 | C4 | #90320 | 1 | 1 | yes | characteristic |
| 504 | C2 | — | 2 | 1 | no | — |
| 505 | C2 | — | 2 | 1 | no | — |
| 506 | C2 | — | 8 | 1 | no | — |
| 507 | C2 | — | 28 | 2 | no | — |
| 508 | C2 | — | 112 | 2 | no | — |
| 509 | C2 | #11731332 | 1 | 1 | yes | characteristic |
| 510 | C2 | #11738375 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#89914 | C2 | semidirect |
| 2. #11741240 | C2 | semidirect |
| 3. C2×#89665 | C2 | semidirect |
| 4. C2×#89637 | C2 | semidirect |
| 5. #11736333 | C2 | semidirect |
| 6. C7×#1815 | C2 | semidirect |
| 7. #11728463 | C2 | semidirect |
| 8. #11728326 | C2 | semidirect |
| 9. #11728061 | C2 | semidirect |
| 10. #11726750 | C2 | semidirect |
| 11. #11726746 | C2 | semidirect |
| 100. #6393 | D4 | semidirect |
| 117. #1815 | D7 | semidirect |
| 479. C7 | #24806 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89914 | 2 |
| #11741240 | 2 |
| C2×#89665 | 2 |
| C2×#89637 | 2 |
| #11736333 | 2 |
| C7×#1815 | 2 |
| #11728463 | 2 |
| #11728326 | 2 |
| #11728061 | 2 |
| #11726750 | 2 |
| #11726746 | 2 |
| #24806 | 7 |