Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
604 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 87 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 | #11733706 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11727381 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11726428 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #11726383 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C7×#1271 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11725285 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11725283 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C22×D56 | — | 2 | 1 | no | — |
| 9 | C2×#6460 | — | 2 | 1 | no | — |
| 10 | C2×#6459 | — | 2 | 1 | no | — |
| 11 | C2×#6437 | C22 | 1 | 1 | yes | characteristic |
| 12 | C7×#389 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#6395 | — | 2 | 1 | no | — |
| 14 | C2×#6395 | — | 2 | 1 | no | — |
| 15 | C2×#6395 | — | 2 | 1 | no | — |
| 16 | #89766 | — | 2 | 1 | no | — |
| 17 | #89766 | — | 2 | 1 | no | — |
| 18 | C2×#6383 | — | 2 | 1 | no | — |
| 19 | C2×#6383 | — | 2 | 1 | no | — |
| 20 | #89711 | C22 | 1 | 1 | yes | characteristic |
| 21 | #89700 | C22 | 1 | 1 | yes | characteristic |
| 22 | #89437 | — | 2 | 1 | no | — |
| 23 | #89428 | — | 2 | 1 | no | — |
| 24 | C7×#336 | C22 | 1 | 1 | yes | characteristic |
| 25 | C7×#336 | C22 | 1 | 1 | yes | characteristic |
| 26 | #89319 | C22 | 1 | 1 | yes | characteristic |
| 27 | #7738 | — | 7 | 1 | no | maximal, Sylow |
| 28 | C22×D28 | — | 2 | 1 | no | — |
| 29 | C22×D28 | — | 2 | 1 | no | — |
| 30 | C22×D28 | — | 2 | 1 | no | — |
| 31 | C22×D28 | D4 | 1 | 1 | yes | characteristic |
| 32 | C22×C4×D7 | — | 2 | 1 | no | — |
| 33 | C22×Dic14 | — | 2 | 1 | no | — |
| 34 | C22×C7×C8 | — | 2 | 1 | no | — |
| 35 | C22×C7×C8 | — | 2 | 1 | no | — |
| 36 | C2×C7×C4⋊C4 | — | 2 | 1 | no | — |
| 37 | C2×C7×C4⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 38 | C2×C7×C4⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 39 | C2×C42×C7 | C23 | 1 | 1 | yes | characteristic |
| 40 | C2×(C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 41 | C2×(C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 42 | C2×(C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 43 | C2×(C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 44 | C2×(C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 45 | C2×C4⋊Dic7 | — | 2 | 1 | no | — |
| 46 | C2×C4⋊Dic7 | D4 | 1 | 1 | yes | characteristic |
| 47 | C2×C4⋊Dic7 | D4 | 1 | 1 | yes | characteristic |
| 48 | C2×C4⋊Dic7 | D4 | 1 | 1 | yes | characteristic |
| 49 | C2×Dic7⋊C4 | — | 2 | 1 | no | — |
| 50 | C2×Dic7⋊C4 | — | 2 | 1 | no | — |
| 51 | C22×C7⋊C8 | — | 2 | 1 | no | — |
| 52 | C2×D56 | — | 4 | 2 | no | — |
| 53 | C2×D56 | — | 4 | 2 | no | — |
| 54 | C2×D56 | — | 4 | 2 | no | — |
| 55 | #6460 | — | 4 | 2 | no | — |
| 56 | #6460 | — | 4 | 2 | no | — |
| 57 | #6459 | — | 4 | 2 | no | — |
| 58 | #6459 | — | 4 | 2 | no | — |
| 59 | #6437 | — | 4 | 2 | no | — |
| 60 | C7×#95 | — | 2 | 1 | no | — |
| 61 | C7⋊#95 | — | 2 | 1 | no | — |
| 62 | C7⋊#95 | — | 2 | 1 | no | — |
| 63 | #6395 | — | 4 | 2 | no | — |
| 64 | #6395 | — | 4 | 2 | no | — |
| 65 | #6395 | — | 4 | 2 | no | — |
| 66 | #6383 | — | 4 | 2 | no | — |
| 67 | #6383 | — | 4 | 2 | no | — |
| 68 | #2683 | — | 7 | 1 | no | — |
| 69 | #2041 | — | 7 | 1 | no | — |
| 70 | #2041 | — | 7 | 1 | no | — |
| 71 | #2011 | — | 7 | 1 | no | — |
| 72 | #1271 | — | 7 | 1 | no | — |
| 73 | #1271 | D7 | 1 | 1 | yes | characteristic, complemented |
| 74 | #1270 | — | 7 | 1 | no | — |
| 75 | C23×D7 | — | 2 | 1 | no | — |
| 76 | C23×D7 | — | 4 | 1 | no | — |
| 77 | C22×C4×C7 | — | 2 | 1 | no | — |
| 78 | C22×C4×C7 | — | 2 | 1 | no | — |
| 79 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 80 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 81 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 82 | C22×Dic7 | — | 2 | 1 | no | — |
| 83 | C22×Dic7 | — | 2 | 1 | no | — |
| 84 | C22×Dic7 | — | 2 | 1 | no | — |
| 85 | C2×D28 | — | 2 | 2 | no | — |
| 86 | C2×D28 | — | 2 | 2 | no | — |
| 87 | C2×D28 | — | 2 | 2 | no | — |
| 88 | C2×D28 | — | 2 | 1 | no | — |
| 89 | C2×D28 | — | 4 | 1 | no | — |
| 90 | C2×D28 | — | 4 | 1 | no | — |
| 91 | C2×D28 | — | 4 | 1 | no | — |
| 92 | C2×D28 | — | 4 | 1 | no | — |
| 93 | C2×D28 | — | 4 | 1 | no | — |
| 94 | C2×D28 | — | 4 | 1 | no | — |
| 95 | C2×D28 | — | 4 | 1 | no | — |
| 96 | C2×D28 | — | 4 | 1 | no | — |
| 97 | C2×D28 | — | 4 | 1 | no | — |
| 98 | C2×D28 | — | 4 | 1 | no | — |
| 99 | C2×D28 | — | 4 | 1 | no | — |
| 100 | C2×D28 | — | 4 | 1 | no | — |
| 101 | C2×D28 | — | 4 | 1 | no | — |
| 102 | C2×D28 | — | 4 | 1 | no | — |
| 103 | C2×D28 | — | 4 | 1 | no | — |
| 104 | C2×D28 | — | 4 | 1 | no | — |
| 105 | C2×D28 | — | 4 | 1 | no | — |
| 106 | C2×D28 | SD16 | 1 | 2 | yes | — |
| 107 | C2×C4×D7 | — | 4 | 2 | no | — |
| 108 | C2×C4×D7 | — | 4 | 2 | no | — |
| 109 | C2×C4×D7 | — | 8 | 1 | no | — |
| 110 | C2×Dic14 | — | 4 | 2 | no | — |
| 111 | C2×Dic14 | — | 4 | 2 | no | — |
| 112 | C2×Dic14 | — | 8 | 1 | no | — |
| 113 | C2×C7×C8 | — | 2 | 2 | no | — |
| 114 | C2×C7×C8 | — | 4 | 1 | no | — |
| 115 | C2×C7×C8 | — | 4 | 1 | no | — |
| 116 | C2×C7×C8 | — | 4 | 1 | no | — |
| 117 | C2×C7×C8 | — | 4 | 1 | no | — |
| 118 | C2×C7×C8 | — | 4 | 1 | no | — |
| 119 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 120 | C7×C4⋊C4 | — | 4 | 1 | no | — |
| 121 | C7×C4⋊C4 | — | 4 | 1 | no | — |
| 122 | C7×C4⋊C4 | — | 4 | 1 | no | — |
| 123 | C7×C4⋊C4 | D8 | 1 | 2 | yes | complemented |
| 124 | C42×C7 | — | 4 | 1 | no | — |
| 125 | (C2×D7)⋊C4 | — | 4 | 2 | no | — |
| 126 | (C2×D7)⋊C4 | — | 4 | 2 | no | — |
| 127 | (C2×D7)⋊C4 | — | 4 | 1 | no | — |
| 128 | (C2×D7)⋊C4 | — | 4 | 1 | no | — |
| 129 | (C2×D7)⋊C4 | — | 4 | 1 | no | — |
| 130 | (C2×D7)⋊C4 | — | 4 | 1 | no | — |
| 131 | (C2×D7)⋊C4 | — | 8 | 1 | no | — |
| 132 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 133 | C4⋊Dic7 | — | 4 | 2 | no | — |
| 134 | C4⋊Dic7 | — | 4 | 1 | no | — |
| 135 | C4⋊Dic7 | — | 4 | 1 | no | — |
| 136 | C4⋊Dic7 | D8 | 1 | 2 | yes | complemented |
| 137 | Dic7⋊C4 | — | 4 | 2 | no | — |
| 138 | Dic7⋊C4 | — | 4 | 1 | no | — |
| 139 | Dic7⋊C4 | — | 4 | 1 | no | — |
| 140 | C2×C7⋊C8 | — | 4 | 1 | no | — |
| 141 | C2×C7⋊C8 | — | 4 | 1 | no | — |
| 142 | C2×C7⋊C8 | — | 4 | 1 | no | — |
| 143 | D56 | — | 4 | 8 | no | — |
| 144 | C22×D8 | — | 14 | 1 | no | — |
| 145 | C2×#127 | — | 7 | 1 | no | — |
| 146 | C2×C22⋊Q8 | — | 14 | 1 | no | — |
| 147 | C2×C22⋊Q8 | — | 14 | 1 | no | — |
| 148 | C2×#102 | — | 14 | 1 | no | — |
| 149 | C2×#102 | — | 14 | 1 | no | — |
| 150 | C2×#102 | — | 14 | 1 | no | — |
| 151 | C2×#102 | — | 14 | 1 | no | — |
| 152 | C2×#102 | — | 14 | 1 | no | — |
| 153 | #396 | — | 14 | 1 | no | — |
| 154 | #396 | — | 14 | 1 | no | — |
| 155 | #395 | — | 14 | 1 | no | — |
| 156 | #390 | — | 7 | 1 | no | — |
| 157 | #389 | — | 7 | 1 | no | — |
| 158 | #389 | C2×D7 | 1 | 1 | yes | characteristic |
| 159 | #386 | — | 14 | 1 | no | — |
| 160 | #336 | — | 7 | 1 | no | — |
| 161 | #336 | C2×D7 | 1 | 1 | yes | characteristic |
| 162 | #336 | C2×D7 | 1 | 1 | yes | characteristic |
| 163 | C23×C7 | #120 | 1 | 1 | yes | characteristic |
| 164 | C22×D7 | — | 2 | 2 | no | — |
| 165 | C22×D7 | — | 4 | 1 | no | — |
| 166 | C22×D7 | — | 4 | 1 | no | — |
| 167 | C22×D7 | — | 4 | 1 | no | — |
| 168 | C22×D7 | — | 4 | 1 | no | — |
| 169 | C22×D7 | — | 4 | 1 | no | — |
| 170 | C22×D7 | — | 4 | 1 | no | — |
| 171 | C22×D7 | — | 4 | 2 | no | — |
| 172 | C22×D7 | — | 8 | 1 | no | — |
| 173 | C22×D7 | — | 8 | 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 | — | 2 | 2 | no | — |
| 185 | C2×C4×C7 | — | 4 | 1 | no | — |
| 186 | C2×C4×C7 | — | 4 | 1 | no | — |
| 187 | C2×C4×C7 | — | 4 | 1 | no | — |
| 188 | C2×C4×C7 | — | 4 | 1 | no | — |
| 189 | C2×C4×C7 | — | 4 | 1 | no | — |
| 190 | C2×C4×C7 | C2×D8 | 1 | 1 | yes | characteristic |
| 191 | C2×C4×C7 | C2×D8 | 1 | 1 | yes | characteristic |
| 192 | C2×C4×C7 | C2×SD16 | 1 | 1 | yes | characteristic |
| 193 | C2×C4×C7 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 194 | C2×C4×C7 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 195 | C2×C4×C7 | #137 | 1 | 1 | yes | characteristic |
| 196 | C2×Dic7 | — | 2 | 2 | no | — |
| 197 | C2×Dic7 | — | 4 | 1 | no | — |
| 198 | C2×Dic7 | — | 4 | 1 | no | — |
| 199 | C2×Dic7 | — | 4 | 1 | no | — |
| 200 | C2×Dic7 | — | 4 | 1 | no | — |
| 201 | C2×Dic7 | — | 4 | 1 | no | — |
| 202 | C2×Dic7 | — | 4 | 1 | no | — |
| 203 | C2×Dic7 | — | 4 | 1 | no | — |
| 204 | C2×Dic7 | — | 4 | 1 | no | — |
| 205 | D28 | — | 4 | 2 | no | — |
| 206 | D28 | — | 4 | 2 | no | — |
| 207 | D28 | — | 4 | 2 | no | — |
| 208 | D28 | — | 4 | 2 | no | — |
| 209 | D28 | — | 4 | 2 | no | — |
| 210 | D28 | — | 4 | 2 | no | — |
| 211 | D28 | — | 4 | 2 | no | — |
| 212 | D28 | — | 8 | 1 | no | — |
| 213 | D28 | — | 8 | 1 | no | — |
| 214 | D28 | — | 8 | 1 | no | — |
| 215 | D28 | — | 8 | 1 | no | — |
| 216 | D28 | — | 8 | 1 | no | — |
| 217 | D28 | — | 8 | 1 | no | — |
| 218 | D28 | — | 8 | 1 | no | — |
| 219 | C4×D7 | — | 8 | 4 | no | — |
| 220 | Dic14 | — | 8 | 4 | no | — |
| 221 | C7×C8 | — | 4 | 2 | no | — |
| 222 | C7×C8 | — | 8 | 1 | no | — |
| 223 | C7⋊C8 | — | 8 | 1 | no | — |
| 224 | C22×Q8 | — | 14 | 1 | no | — |
| 225 | C22×D4 | — | 7 | 1 | no | — |
| 226 | C22×D4 | — | 14 | 1 | no | — |
| 227 | C22×D4 | — | 14 | 1 | no | — |
| 228 | C22×D4 | — | 14 | 1 | no | — |
| 229 | C23×C4 | — | 14 | 1 | no | — |
| 230 | C2×D8 | — | 28 | 2 | no | — |
| 231 | C2×D8 | — | 28 | 2 | no | — |
| 232 | C2×D8 | — | 28 | 2 | no | — |
| 233 | C22×C8 | — | 2 | 1 | no | — |
| 234 | C22×C8 | — | 2 | 1 | no | — |
| 235 | C22×C8 | — | 14 | 1 | no | — |
| 236 | #127 | — | 28 | 2 | no | — |
| 237 | C22⋊Q8 | — | 28 | 2 | no | — |
| 238 | C22⋊Q8 | — | 28 | 2 | no | — |
| 239 | C22⋊Q8 | — | 28 | 2 | no | — |
| 240 | C22⋊Q8 | — | 28 | 2 | no | — |
| 241 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 242 | C2×C4⋊C4 | — | 7 | 1 | no | — |
| 243 | C2×C4⋊C4 | — | 7 | 1 | no | — |
| 244 | C2×C4⋊C4 | — | 7 | 1 | no | — |
| 245 | C2×C4⋊C4 | — | 14 | 1 | no | — |
| 246 | C2×C4⋊C4 | — | 14 | 1 | no | — |
| 247 | C2×C4⋊C4 | — | 14 | 1 | no | — |
| 248 | C2×C4⋊C4 | D28 | 1 | 1 | yes | characteristic |
| 249 | C2×C4⋊C4 | D28 | 1 | 1 | yes | characteristic |
| 250 | C2×C22⋊C4 | — | 14 | 1 | no | — |
| 251 | C2×C22⋊C4 | — | 14 | 1 | no | — |
| 252 | C2×C22⋊C4 | — | 14 | 1 | no | — |
| 253 | C2×C22⋊C4 | — | 14 | 1 | no | — |
| 254 | C2×C22⋊C4 | — | 14 | 1 | no | — |
| 255 | C2×C42 | C22×D7 | 1 | 1 | yes | characteristic |
| 256 | #102 | — | 28 | 2 | no | — |
| 257 | #102 | — | 28 | 2 | no | — |
| 258 | #102 | — | 28 | 2 | no | — |
| 259 | #102 | — | 28 | 2 | no | — |
| 260 | #102 | — | 28 | 2 | no | — |
| 261 | #95 | — | 2 | 1 | no | — |
| 262 | #95 | — | 14 | 1 | no | — |
| 263 | #95 | — | 14 | 1 | no | — |
| 264 | C22×C7 | #447 | 1 | 1 | yes | characteristic |
| 265 | C22×C7 | #447 | 1 | 1 | yes | characteristic |
| 266 | C22×C7 | #448 | 1 | 1 | yes | characteristic |
| 267 | C22×C7 | #453 | 1 | 1 | yes | characteristic |
| 268 | C22×C7 | #454 | 1 | 1 | yes | characteristic |
| 269 | C22×C7 | #454 | 1 | 1 | yes | characteristic |
| 270 | C22×C7 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 271 | C2×D7 | — | 4 | 2 | no | — |
| 272 | C2×D7 | — | 4 | 2 | no | — |
| 273 | C2×D7 | — | 4 | 2 | 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 | — | 8 | 2 | no | — |
| 279 | C2×D7 | — | 8 | 2 | no | — |
| 280 | C2×D7 | — | 8 | 2 | no | — |
| 281 | C2×D7 | — | 16 | 1 | no | — |
| 282 | C2×D7 | — | 16 | 1 | no | — |
| 283 | C2×D7 | — | 16 | 1 | no | — |
| 284 | C2×D7 | — | 16 | 1 | no | — |
| 285 | C4×C7 | — | 2 | 1 | no | — |
| 286 | C4×C7 | — | 2 | 1 | no | — |
| 287 | C4×C7 | — | 2 | 1 | no | — |
| 288 | C4×C7 | — | 2 | 1 | no | — |
| 289 | C4×C7 | — | 2 | 1 | no | — |
| 290 | C4×C7 | — | 2 | 1 | no | — |
| 291 | C4×C7 | — | 4 | 2 | no | — |
| 292 | C4×C7 | — | 8 | 1 | no | — |
| 293 | Dic7 | — | 4 | 2 | no | — |
| 294 | Dic7 | — | 8 | 1 | no | — |
| 295 | Dic7 | — | 8 | 1 | no | — |
| 296 | C24 | — | 14 | 1 | no | — |
| 297 | C24 | — | 28 | 1 | no | — |
| 298 | C2×Q8 | — | 28 | 2 | no | — |
| 299 | C2×Q8 | — | 28 | 2 | no | — |
| 300 | C2×Q8 | — | 56 | 1 | no | — |
| 301 | C2×D4 | — | 7 | 2 | no | — |
| 302 | C2×D4 | — | 14 | 2 | no | — |
| 303 | C2×D4 | — | 14 | 2 | no | — |
| 304 | C2×D4 | — | 14 | 2 | no | — |
| 305 | C2×D4 | — | 14 | 1 | no | — |
| 306 | C2×D4 | — | 28 | 1 | no | — |
| 307 | C2×D4 | — | 28 | 1 | no | — |
| 308 | C2×D4 | — | 28 | 1 | no | — |
| 309 | C2×D4 | — | 28 | 1 | no | — |
| 310 | C2×D4 | — | 28 | 1 | no | — |
| 311 | C2×D4 | — | 28 | 1 | no | — |
| 312 | C2×D4 | — | 28 | 1 | no | — |
| 313 | C2×D4 | — | 28 | 1 | no | — |
| 314 | C2×D4 | — | 28 | 1 | no | — |
| 315 | C2×D4 | — | 28 | 1 | no | — |
| 316 | C2×D4 | — | 28 | 1 | no | — |
| 317 | C2×D4 | — | 28 | 1 | no | — |
| 318 | C2×D4 | — | 28 | 1 | no | — |
| 319 | C2×D4 | — | 28 | 1 | no | — |
| 320 | C2×D4 | — | 28 | 1 | no | — |
| 321 | C2×D4 | — | 28 | 1 | no | — |
| 322 | C2×D4 | — | 28 | 1 | no | — |
| 323 | C22×C4 | — | 2 | 1 | no | — |
| 324 | C22×C4 | — | 2 | 1 | no | — |
| 325 | C22×C4 | — | 14 | 1 | no | — |
| 326 | C22×C4 | — | 14 | 1 | no | — |
| 327 | C22×C4 | — | 14 | 1 | no | — |
| 328 | C22×C4 | — | 28 | 2 | no | — |
| 329 | C22×C4 | — | 28 | 2 | no | — |
| 330 | C22×C4 | — | 56 | 1 | no | — |
| 331 | C22×C4 | C2×D28 | 1 | 1 | yes | characteristic |
| 332 | C22×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 333 | C22×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 334 | D8 | — | 28 | 8 | no | — |
| 335 | C2×C8 | — | 2 | 2 | no | — |
| 336 | C2×C8 | — | 4 | 1 | no | — |
| 337 | C2×C8 | — | 4 | 1 | no | — |
| 338 | C2×C8 | — | 4 | 1 | no | — |
| 339 | C2×C8 | — | 4 | 1 | no | — |
| 340 | C2×C8 | — | 4 | 1 | no | — |
| 341 | C2×C8 | — | 28 | 1 | no | — |
| 342 | C2×C8 | — | 28 | 1 | no | — |
| 343 | C2×C8 | — | 28 | 1 | no | — |
| 344 | C4⋊C4 | — | 2 | 1 | no | — |
| 345 | C4⋊C4 | — | 4 | 1 | no | — |
| 346 | C4⋊C4 | — | 4 | 1 | no | — |
| 347 | C4⋊C4 | — | 4 | 1 | no | — |
| 348 | C4⋊C4 | — | 7 | 2 | no | — |
| 349 | C4⋊C4 | — | 14 | 1 | no | — |
| 350 | C4⋊C4 | — | 28 | 1 | no | — |
| 351 | C4⋊C4 | — | 28 | 1 | no | — |
| 352 | C4⋊C4 | — | 28 | 2 | no | — |
| 353 | C4⋊C4 | — | 28 | 2 | no | — |
| 354 | C4⋊C4 | — | 28 | 1 | no | — |
| 355 | C4⋊C4 | — | 28 | 1 | no | — |
| 356 | C4⋊C4 | D56 | 1 | 2 | yes | complemented |
| 357 | C22⋊C4 | — | 28 | 2 | no | — |
| 358 | C22⋊C4 | — | 28 | 2 | no | — |
| 359 | C22⋊C4 | — | 28 | 1 | no | — |
| 360 | C22⋊C4 | — | 28 | 1 | no | — |
| 361 | C22⋊C4 | — | 28 | 1 | no | — |
| 362 | C22⋊C4 | — | 28 | 1 | no | — |
| 363 | C22⋊C4 | — | 56 | 1 | no | — |
| 364 | C42 | — | 4 | 1 | no | — |
| 365 | C2×C7 | #1596 | 1 | 1 | yes | characteristic |
| 366 | C2×C7 | #1598 | 1 | 1 | yes | characteristic |
| 367 | C2×C7 | #1598 | 1 | 1 | yes | characteristic |
| 368 | C2×C7 | #1619 | 1 | 1 | yes | characteristic |
| 369 | C2×C7 | #1627 | 1 | 1 | yes | characteristic |
| 370 | C2×C7 | #1627 | 1 | 1 | yes | characteristic |
| 371 | C2×C7 | #1657 | 1 | 1 | yes | characteristic |
| 372 | D7 | — | 8 | 2 | no | — |
| 373 | D7 | — | 16 | 2 | no | — |
| 374 | C23 | — | 14 | 2 | no | — |
| 375 | C23 | — | 28 | 1 | no | — |
| 376 | C23 | — | 28 | 1 | no | — |
| 377 | C23 | — | 28 | 1 | no | — |
| 378 | C23 | — | 28 | 1 | no | — |
| 379 | C23 | — | 28 | 1 | no | — |
| 380 | C23 | — | 28 | 1 | no | — |
| 381 | C23 | — | 28 | 2 | no | — |
| 382 | C23 | — | 56 | 1 | no | — |
| 383 | C23 | — | 56 | 1 | no | — |
| 384 | C23 | — | 56 | 1 | no | — |
| 385 | C23 | — | 56 | 1 | no | — |
| 386 | C23 | — | 56 | 1 | no | — |
| 387 | C23 | — | 56 | 1 | no | — |
| 388 | C23 | #6445 | 1 | 1 | yes | characteristic |
| 389 | Q8 | — | 56 | 4 | no | — |
| 390 | D4 | — | 28 | 2 | no | — |
| 391 | D4 | — | 28 | 2 | no | — |
| 392 | D4 | — | 28 | 2 | no | — |
| 393 | D4 | — | 28 | 2 | no | — |
| 394 | D4 | — | 28 | 2 | no | — |
| 395 | D4 | — | 28 | 2 | no | — |
| 396 | D4 | — | 28 | 2 | no | — |
| 397 | D4 | — | 56 | 1 | no | — |
| 398 | D4 | — | 56 | 1 | no | — |
| 399 | D4 | — | 56 | 1 | no | — |
| 400 | D4 | — | 56 | 1 | no | — |
| 401 | D4 | — | 56 | 1 | no | — |
| 402 | D4 | — | 56 | 1 | no | — |
| 403 | D4 | — | 56 | 1 | no | — |
| 404 | C2×C4 | — | 2 | 1 | no | — |
| 405 | C2×C4 | — | 2 | 1 | no | — |
| 406 | C2×C4 | — | 2 | 1 | no | — |
| 407 | C2×C4 | — | 2 | 1 | no | — |
| 408 | C2×C4 | — | 2 | 1 | no | — |
| 409 | C2×C4 | — | 2 | 1 | no | — |
| 410 | C2×C4 | — | 2 | 2 | no | — |
| 411 | C2×C4 | — | 4 | 1 | no | — |
| 412 | C2×C4 | — | 4 | 1 | no | — |
| 413 | C2×C4 | — | 4 | 1 | no | — |
| 414 | C2×C4 | — | 4 | 1 | no | — |
| 415 | C2×C4 | — | 4 | 1 | no | — |
| 416 | C2×C4 | — | 14 | 2 | no | — |
| 417 | C2×C4 | — | 28 | 1 | no | — |
| 418 | C2×C4 | — | 28 | 1 | no | — |
| 419 | C2×C4 | — | 28 | 1 | no | — |
| 420 | C2×C4 | — | 28 | 1 | no | — |
| 421 | C2×C4 | — | 28 | 1 | no | — |
| 422 | C2×C4 | — | 28 | 1 | no | — |
| 423 | C2×C4 | — | 28 | 1 | no | — |
| 424 | C2×C4 | — | 28 | 1 | no | — |
| 425 | C2×C4 | — | 56 | 4 | no | — |
| 426 | C2×C4 | C2×D56 | 1 | 1 | yes | characteristic |
| 427 | C2×C4 | #6471 | 1 | 1 | yes | characteristic |
| 428 | C2×C4 | D7×D8 | 1 | 1 | yes | characteristic |
| 429 | C2×C4 | D7×SD16 | 1 | 1 | yes | characteristic |
| 430 | C2×C4 | #6477 | 1 | 1 | yes | characteristic |
| 431 | C2×C4 | #6481 | 1 | 1 | yes | characteristic |
| 432 | C8 | — | 4 | 2 | no | — |
| 433 | C8 | — | 8 | 1 | no | — |
| 434 | C8 | — | 56 | 1 | no | — |
| 435 | C7 | #7738 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 436 | C22 | — | 28 | 2 | no | — |
| 437 | C22 | — | 28 | 2 | no | — |
| 438 | C22 | — | 28 | 2 | no | — |
| 439 | C22 | — | 56 | 1 | no | — |
| 440 | C22 | — | 56 | 1 | no | — |
| 441 | C22 | — | 56 | 1 | no | — |
| 442 | C22 | — | 56 | 1 | no | — |
| 443 | C22 | — | 56 | 2 | no | — |
| 444 | C22 | — | 56 | 2 | no | — |
| 445 | C22 | — | 56 | 2 | no | — |
| 446 | C22 | — | 112 | 1 | no | — |
| 447 | C22 | — | 112 | 1 | no | — |
| 448 | C22 | — | 112 | 1 | no | — |
| 449 | C22 | — | 112 | 1 | no | — |
| 450 | C22 | #89504 | 1 | 1 | yes | characteristic |
| 451 | C22 | #89513 | 1 | 1 | yes | characteristic |
| 452 | C22 | #89525 | 1 | 1 | yes | characteristic |
| 453 | C22 | #89545 | 1 | 1 | yes | characteristic |
| 454 | C22 | #89578 | 1 | 1 | yes | characteristic |
| 455 | C22 | #89594 | 1 | 1 | yes | characteristic |
| 456 | C22 | #89599 | 1 | 1 | yes | characteristic |
| 457 | C4 | — | 2 | 1 | no | — |
| 458 | C4 | — | 2 | 1 | no | — |
| 459 | C4 | — | 2 | 1 | no | — |
| 460 | C4 | — | 2 | 1 | no | — |
| 461 | C4 | — | 2 | 1 | no | — |
| 462 | C4 | — | 2 | 1 | no | — |
| 463 | C4 | — | 4 | 2 | no | — |
| 464 | C4 | — | 8 | 1 | no | — |
| 465 | C4 | — | 28 | 2 | no | — |
| 466 | C4 | — | 56 | 1 | no | — |
| 467 | C4 | — | 56 | 1 | no | — |
| 468 | C2 | — | 56 | 2 | no | — |
| 469 | C2 | — | 112 | 2 | no | — |
| 470 | C2 | #11725885 | 1 | 1 | yes | characteristic |
| 471 | C2 | #11725948 | 1 | 1 | yes | characteristic |
| 472 | C2 | #11726020 | 1 | 1 | yes | characteristic |
| 473 | C2 | #11726047 | 1 | 1 | yes | characteristic |
| 474 | C2 | #11726070 | 1 | 1 | yes | characteristic |
| 475 | C2 | #11726125 | 1 | 1 | yes | characteristic |
| 476 | C2 | #11726211 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11733706 | C2 | semidirect |
| 2. #11727381 | C2 | semidirect |
| 4. #11726383 | C2 | semidirect |
| 5. C7×#1271 | C2 | semidirect |
| 6. #11725285 | C2 | semidirect |
| 7. #11725283 | C2 | semidirect |
| 73. #1271 | D7 | semidirect |
| 123. C7×C4⋊C4 | D8 | semidirect |
| 136. C4⋊Dic7 | D8 | semidirect |
| 356. C4⋊C4 | D56 | semidirect |
| 435. C7 | #7738 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11733706 | 2 |
| #11727381 | 2 |
| #11726428 | 2 |
| #11726383 | 2 |
| C7×#1271 | 2 |
| #11725285 | 2 |
| #11725283 | 2 |
| #7738 | 7 |