Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1716 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1716 conjugacy classes of subgroups — too many to draw. Only its 171 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 | C2×#90408 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11740608 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11736788 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C7×#1555 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11728553 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #11726145 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #11726144 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | C22×D4×D7 | — | 2 | 2 | no | — |
| 9 | C2×C7×#127 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×#6501 | — | 2 | 2 | no | — |
| 11 | C2×#6500 | — | 2 | 2 | no | — |
| 12 | C2×#6495 | — | 2 | 2 | no | — |
| 13 | #90408 | — | 2 | 2 | no | — |
| 14 | #90408 | — | 2 | 4 | no | — |
| 15 | #90408 | C22 | 1 | 4 | yes | — |
| 16 | #90168 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | C2×C4×D28 | C22 | 1 | 2 | yes | — |
| 18 | C7×#432 | C22 | 1 | 2 | yes | complemented |
| 19 | #89848 | C22 | 1 | 2 | yes | complemented |
| 20 | #89846 | — | 2 | 2 | no | — |
| 21 | #89845 | C22 | 1 | 2 | yes | complemented |
| 22 | C4×#1136 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | #89615 | C22 | 1 | 4 | yes | complemented |
| 24 | #89614 | C22 | 1 | 4 | yes | complemented |
| 25 | #89507 | — | 2 | 2 | no | — |
| 26 | #89504 | — | 2 | 2 | no | — |
| 27 | #89483 | — | 2 | 4 | no | — |
| 28 | C7×#331 | C22 | 1 | 4 | yes | complemented |
| 29 | #89278 | C22 | 1 | 8 | yes | complemented |
| 30 | #18524 | — | 7 | 1 | no | maximal, Sylow |
| 31 | C24×D7 | — | 2 | 2 | no | — |
| 32 | C22×C7×D4 | — | 2 | 2 | no | — |
| 33 | C22×C7×D4 | D4 | 1 | 2 | yes | — |
| 34 | C22×C22⋊D7 | — | 2 | 4 | no | — |
| 35 | C2×D4×D7 | — | 2 | 8 | no | — |
| 36 | C2×D4×D7 | — | 2 | 8 | no | — |
| 37 | C2×D4×D7 | — | 4 | 16 | no | — |
| 38 | C2×#1157 | — | 2 | 1 | no | — |
| 39 | C22×D28 | D4 | 1 | 2 | yes | — |
| 40 | C22×C4×D7 | — | 2 | 2 | no | — |
| 41 | C7×#127 | — | 2 | 2 | no | — |
| 42 | C7×#127 | D4 | 1 | 2 | yes | — |
| 43 | C7×#127 | C23 | 1 | 2 | yes | — |
| 44 | C2×C42×C7 | C23 | 1 | 1 | yes | characteristic |
| 45 | C2×C22⋊Dic7 | — | 2 | 2 | no | — |
| 46 | #6501 | — | 2 | 8 | no | — |
| 47 | #6501 | — | 2 | 8 | no | — |
| 48 | #6500 | — | 2 | 8 | no | — |
| 49 | #6500 | — | 2 | 8 | no | — |
| 50 | C2×#1142 | — | 2 | 4 | no | — |
| 51 | #6495 | — | 4 | 8 | no | — |
| 52 | C2×#1141 | — | 2 | 4 | no | — |
| 53 | #6493 | — | 2 | 2 | no | — |
| 54 | C2×(C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 55 | C2×C4⋊Dic7 | D4 | 1 | 2 | yes | — |
| 56 | C2×#1136 | — | 2 | 1 | no | — |
| 57 | C2×D56 | — | 2 | 4 | no | — |
| 58 | #6438 | — | 2 | 1 | no | — |
| 59 | #6437 | C23 | 1 | 1 | yes | characteristic, complemented |
| 60 | C4×D28 | — | 2 | 2 | no | — |
| 61 | C4×D28 | — | 2 | 2 | no | — |
| 62 | C4×D28 | — | 2 | 2 | no | — |
| 63 | C4×D28 | D4 | 1 | 4 | yes | — |
| 64 | C4×D28 | C23 | 1 | 4 | yes | — |
| 65 | #6432 | C23 | 1 | 1 | yes | characteristic, complemented |
| 66 | C7×C4⋊C8 | C23 | 1 | 4 | yes | complemented |
| 67 | C7×C22⋊C8 | — | 2 | 2 | no | — |
| 68 | C7×#97 | — | 2 | 2 | no | — |
| 69 | #6395 | — | 2 | 4 | no | — |
| 70 | #6395 | — | 2 | 4 | no | — |
| 71 | #6391 | — | 2 | 4 | no | — |
| 72 | #6377 | — | 2 | 1 | no | — |
| 73 | C4×C7⋊C8 | C23 | 1 | 2 | yes | complemented |
| 74 | C2×D42 | — | 7 | 1 | no | — |
| 75 | #3151 | — | 7 | 1 | no | — |
| 76 | #3109 | — | 7 | 2 | no | — |
| 77 | #1629 | — | 7 | 4 | no | — |
| 78 | #1619 | — | 7 | 4 | no | — |
| 79 | #1555 | D7 | 1 | 1 | yes | characteristic, complemented |
| 80 | #1490 | — | 7 | 2 | no | — |
| 81 | C24×C7 | — | 2 | 2 | no | — |
| 82 | C23×D7 | — | 2 | 2 | no | — |
| 83 | C23×D7 | — | 2 | 8 | no | — |
| 84 | C23×D7 | — | 4 | 16 | no | — |
| 85 | C23×D7 | — | 8 | 4 | no | — |
| 86 | C2×C7×D4 | — | 2 | 4 | no | — |
| 87 | C2×C7×D4 | — | 2 | 2 | no | — |
| 88 | C2×C7×D4 | — | 2 | 4 | no | — |
| 89 | C2×C7×D4 | — | 4 | 8 | no | — |
| 90 | C2×C7×D4 | — | 4 | 4 | no | — |
| 91 | C2×C7×D4 | C2×D4 | 1 | 4 | yes | — |
| 92 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 93 | C22×C4×C7 | C2×D4 | 1 | 2 | yes | — |
| 94 | C2×C22⋊D7 | — | 2 | 16 | no | — |
| 95 | C2×C22⋊D7 | — | 4 | 16 | no | — |
| 96 | C2×C22⋊D7 | — | 4 | 1 | no | — |
| 97 | C22×Dic7 | — | 2 | 2 | no | — |
| 98 | D4×D7 | — | 4 | 32 | no | — |
| 99 | D4×D7 | — | 4 | 16 | no | — |
| 100 | D4×D7 | — | 4 | 16 | no | — |
| 101 | #1157 | — | 4 | 4 | no | — |
| 102 | C2×D28 | — | 2 | 2 | no | — |
| 103 | C2×D28 | — | 2 | 8 | no | — |
| 104 | C2×D28 | — | 2 | 2 | no | — |
| 105 | C2×D28 | — | 2 | 1 | no | — |
| 106 | C2×D28 | C2×D4 | 1 | 4 | yes | — |
| 107 | C2×C4×D7 | — | 2 | 4 | no | — |
| 108 | C2×C4×D7 | — | 2 | 4 | no | — |
| 109 | C2×C4×D7 | — | 4 | 8 | no | — |
| 110 | C2×C4×D7 | — | 4 | 1 | no | — |
| 111 | C2×Dic14 | — | 2 | 1 | no | — |
| 112 | C2×C7×C8 | — | 2 | 4 | no | — |
| 113 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 114 | C42×C7 | C2×D4 | 1 | 2 | yes | — |
| 115 | C42×C7 | C24 | 1 | 1 | yes | characteristic |
| 116 | C22⋊Dic7 | — | 2 | 8 | no | — |
| 117 | #1142 | — | 4 | 8 | no | — |
| 118 | #1141 | — | 4 | 8 | no | — |
| 119 | (C2×D7)⋊C4 | — | 2 | 4 | no | — |
| 120 | (C2×D7)⋊C4 | — | 2 | 4 | no | — |
| 121 | (C2×D7)⋊C4 | — | 4 | 2 | no | — |
| 122 | C4⋊Dic7 | — | 2 | 2 | no | — |
| 123 | C4⋊Dic7 | — | 2 | 2 | no | — |
| 124 | C4⋊Dic7 | C2×D4 | 1 | 4 | yes | — |
| 125 | #1136 | — | 2 | 4 | no | — |
| 126 | C2×C7⋊C8 | — | 2 | 2 | no | — |
| 127 | D56 | — | 4 | 8 | no | — |
| 128 | C23×D4 | — | 14 | 2 | no | — |
| 129 | C2×AGL(1,ℤ/8) | — | 14 | 2 | no | — |
| 130 | D42 | — | 7 | 4 | no | — |
| 131 | D42 | — | 14 | 4 | no | — |
| 132 | D42 | — | 14 | 2 | no | — |
| 133 | #532 | — | 7 | 1 | no | — |
| 134 | C2×#127 | C2×D7 | 1 | 1 | yes | characteristic |
| 135 | C2×#121 | — | 14 | 2 | no | — |
| 136 | C2×#120 | — | 14 | 2 | no | — |
| 137 | C2×C4×D4 | — | 7 | 2 | no | — |
| 138 | #496 | — | 14 | 2 | no | — |
| 139 | #493 | — | 7 | 2 | no | — |
| 140 | #492 | — | 7 | 2 | no | — |
| 141 | #481 | — | 14 | 2 | no | — |
| 142 | #476 | — | 7 | 4 | no | — |
| 143 | #459 | — | 7 | 4 | no | — |
| 144 | #447 | — | 14 | 2 | no | — |
| 145 | #442 | — | 14 | 4 | no | — |
| 146 | #432 | C2×D7 | 1 | 2 | yes | complemented |
| 147 | C4×M16 | — | 7 | 1 | no | — |
| 148 | #331 | C2×D7 | 1 | 4 | yes | complemented |
| 149 | D4⋊C8 | — | 7 | 8 | no | — |
| 150 | C23×C7 | — | 2 | 4 | no | — |
| 151 | C23×C7 | — | 4 | 8 | no | — |
| 152 | C23×C7 | — | 4 | 4 | no | — |
| 153 | C23×C7 | #120 | 1 | 1 | yes | characteristic |
| 154 | C22×D7 | — | 2 | 8 | no | — |
| 155 | C22×D7 | — | 2 | 4 | no | — |
| 156 | C22×D7 | — | 4 | 32 | no | — |
| 157 | C22×D7 | — | 4 | 4 | no | — |
| 158 | C22×D7 | — | 4 | 4 | no | — |
| 159 | C22×D7 | — | 4 | 1 | no | — |
| 160 | C22×D7 | — | 8 | 8 | no | — |
| 161 | C22×D7 | — | 8 | 32 | no | — |
| 162 | C7×D4 | — | 4 | 4 | no | — |
| 163 | C7×D4 | — | 4 | 8 | no | — |
| 164 | C7×D4 | — | 4 | 8 | no | — |
| 165 | C7×D4 | — | 8 | 2 | no | — |
| 166 | C2×C4×C7 | — | 2 | 2 | no | — |
| 167 | C2×C4×C7 | — | 2 | 4 | no | — |
| 168 | C2×C4×C7 | #120 | 1 | 2 | yes | — |
| 169 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 170 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 171 | C2×C4×C7 | C22×D4 | 1 | 2 | yes | — |
| 172 | C22⋊D7 | — | 4 | 32 | no | — |
| 173 | C22⋊D7 | — | 8 | 2 | no | — |
| 174 | C2×Dic7 | — | 2 | 4 | no | — |
| 175 | C2×Dic7 | — | 4 | 4 | no | — |
| 176 | C2×Dic7 | — | 4 | 1 | no | — |
| 177 | D28 | — | 2 | 8 | no | — |
| 178 | D28 | — | 2 | 4 | no | — |
| 179 | D28 | — | 4 | 2 | no | — |
| 180 | D28 | — | 4 | 4 | no | — |
| 181 | D28 | AGL(1,ℤ/8) | 1 | 8 | yes | complemented |
| 182 | C4×D7 | — | 4 | 8 | no | — |
| 183 | C4×D7 | — | 4 | 8 | no | — |
| 184 | C4×D7 | — | 8 | 2 | no | — |
| 185 | Dic14 | — | 4 | 2 | no | — |
| 186 | C7×C8 | — | 4 | 4 | no | — |
| 187 | C7⋊C8 | — | 2 | 4 | no | — |
| 188 | C25 | — | 14 | 2 | no | — |
| 189 | C2×#41 | — | 14 | 1 | no | — |
| 190 | C22×D4 | — | 2 | 2 | no | — |
| 191 | C22×D4 | — | 7 | 2 | no | — |
| 192 | C22×D4 | — | 14 | 8 | no | — |
| 193 | C22×D4 | — | 14 | 8 | no | — |
| 194 | C22×D4 | — | 14 | 4 | no | — |
| 195 | C22×D4 | — | 28 | 16 | no | — |
| 196 | C22×D4 | D28 | 1 | 2 | yes | — |
| 197 | C23×C4 | — | 14 | 2 | no | — |
| 198 | AGL(1,ℤ/8) | — | 28 | 8 | no | — |
| 199 | C2×SD16 | — | 14 | 4 | no | — |
| 200 | C2×D8 | — | 14 | 4 | no | — |
| 201 | C2×D8 | — | 14 | 4 | no | — |
| 202 | C2×M16 | — | 14 | 1 | no | — |
| 203 | C4⋊Q8 | — | 7 | 1 | no | — |
| 204 | #127 | — | 2 | 2 | no | — |
| 205 | #127 | — | 7 | 1 | no | — |
| 206 | #127 | D28 | 1 | 2 | yes | — |
| 207 | #127 | C22×D7 | 1 | 2 | yes | — |
| 208 | #124 | — | 14 | 1 | no | — |
| 209 | #121 | — | 14 | 8 | no | — |
| 210 | #121 | — | 14 | 8 | no | — |
| 211 | #121 | — | 14 | 2 | no | — |
| 212 | #120 | — | 14 | 8 | no | — |
| 213 | #120 | — | 14 | 8 | no | — |
| 214 | C4×D4 | — | 7 | 4 | no | — |
| 215 | C4×D4 | — | 7 | 4 | no | — |
| 216 | C4×D4 | — | 14 | 2 | no | — |
| 217 | C4×D4 | — | 14 | 2 | no | — |
| 218 | C4×D4 | — | 14 | 2 | no | — |
| 219 | C2×C4⋊C4 | — | 7 | 2 | no | — |
| 220 | C2×C22⋊C4 | — | 14 | 2 | no | — |
| 221 | C2×C22⋊C4 | — | 14 | 2 | no | — |
| 222 | C2×C42 | C22×D7 | 1 | 1 | yes | characteristic |
| 223 | #106 | — | 14 | 4 | no | — |
| 224 | C4⋊C8 | C22×D7 | 1 | 4 | yes | complemented |
| 225 | #102 | — | 14 | 4 | no | — |
| 226 | #102 | — | 14 | 4 | no | — |
| 227 | C22⋊C8 | — | 2 | 2 | no | — |
| 228 | #97 | — | 2 | 2 | no | — |
| 229 | #97 | — | 14 | 1 | no | — |
| 230 | C4×C8 | — | 7 | 2 | no | — |
| 231 | C22×C7 | — | 2 | 2 | no | — |
| 232 | C22×C7 | — | 4 | 8 | no | — |
| 233 | C22×C7 | — | 4 | 4 | no | — |
| 234 | C22×C7 | — | 8 | 8 | no | — |
| 235 | C22×C7 | #453 | 1 | 2 | yes | — |
| 236 | C22×C7 | C2×#120 | 1 | 1 | yes | characteristic |
| 237 | C2×D7 | — | 2 | 8 | no | — |
| 238 | C2×D7 | — | 4 | 16 | no | — |
| 239 | C2×D7 | — | 4 | 4 | no | — |
| 240 | C2×D7 | — | 4 | 4 | no | — |
| 241 | C2×D7 | — | 8 | 32 | no | — |
| 242 | C2×D7 | — | 8 | 2 | no | — |
| 243 | C2×D7 | — | 8 | 1 | no | — |
| 244 | C4×C7 | — | 2 | 2 | no | — |
| 245 | C4×C7 | — | 2 | 1 | no | — |
| 246 | C4×C7 | — | 2 | 1 | no | — |
| 247 | C4×C7 | C2×AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 248 | Dic7 | — | 4 | 4 | no | — |
| 249 | Dic7 | — | 8 | 1 | no | — |
| 250 | C24 | — | 2 | 2 | no | — |
| 251 | C24 | — | 14 | 8 | no | — |
| 252 | C24 | — | 14 | 2 | no | — |
| 253 | C24 | — | 28 | 16 | no | — |
| 254 | C24 | — | 56 | 4 | no | — |
| 255 | #41 | — | 28 | 4 | no | — |
| 256 | C2×Q8 | — | 14 | 1 | no | — |
| 257 | C2×D4 | — | 2 | 4 | no | — |
| 258 | C2×D4 | — | 2 | 2 | no | — |
| 259 | C2×D4 | — | 2 | 4 | no | — |
| 260 | C2×D4 | — | 4 | 8 | no | — |
| 261 | C2×D4 | — | 4 | 4 | no | — |
| 262 | C2×D4 | — | 7 | 4 | no | — |
| 263 | C2×D4 | — | 14 | 8 | no | — |
| 264 | C2×D4 | — | 14 | 16 | no | — |
| 265 | C2×D4 | — | 14 | 2 | no | — |
| 266 | C2×D4 | — | 14 | 1 | no | — |
| 267 | C2×D4 | — | 14 | 2 | no | — |
| 268 | C2×D4 | — | 28 | 16 | no | — |
| 269 | C2×D4 | — | 28 | 32 | no | — |
| 270 | C2×D4 | — | 28 | 16 | no | — |
| 271 | C2×D4 | — | 28 | 16 | no | — |
| 272 | C2×D4 | — | 28 | 1 | no | — |
| 273 | C2×D4 | C2×D28 | 1 | 4 | yes | — |
| 274 | C22×C4 | — | 14 | 2 | no | — |
| 275 | C22×C4 | — | 14 | 4 | no | — |
| 276 | C22×C4 | — | 14 | 4 | no | — |
| 277 | C22×C4 | — | 28 | 8 | no | — |
| 278 | C22×C4 | — | 28 | 1 | no | — |
| 279 | C22×C4 | C2×D28 | 1 | 1 | yes | characteristic |
| 280 | C22×C4 | D4×D7 | 1 | 2 | yes | — |
| 281 | SD16 | — | 28 | 8 | no | — |
| 282 | D8 | — | 28 | 8 | no | — |
| 283 | D8 | — | 28 | 8 | no | — |
| 284 | M16 | — | 14 | 4 | no | — |
| 285 | C2×C8 | — | 2 | 4 | no | — |
| 286 | C2×C8 | — | 14 | 2 | no | — |
| 287 | C4⋊C4 | — | 7 | 4 | no | — |
| 288 | C4⋊C4 | — | 14 | 2 | no | — |
| 289 | C4⋊C4 | — | 14 | 2 | no | — |
| 290 | C22⋊C4 | — | 14 | 8 | no | — |
| 291 | C22⋊C4 | — | 14 | 4 | no | — |
| 292 | C22⋊C4 | — | 14 | 4 | no | — |
| 293 | C22⋊C4 | — | 28 | 2 | no | — |
| 294 | C42 | C2×D28 | 1 | 1 | yes | characteristic |
| 295 | C42 | D4×D7 | 1 | 2 | yes | — |
| 296 | C42 | C23×D7 | 1 | 1 | yes | characteristic |
| 297 | C2×C7 | — | 2 | 2 | no | — |
| 298 | C2×C7 | — | 8 | 4 | no | — |
| 299 | C2×C7 | #3003 | 1 | 2 | yes | — |
| 300 | C2×C7 | C2×#453 | 1 | 1 | yes | characteristic |
| 301 | D7 | — | 4 | 8 | no | — |
| 302 | D7 | — | 16 | 1 | no | — |
| 303 | C23 | — | 2 | 4 | no | — |
| 304 | C23 | — | 4 | 8 | no | — |
| 305 | C23 | — | 4 | 4 | no | — |
| 306 | C23 | — | 14 | 8 | no | — |
| 307 | C23 | — | 14 | 4 | no | — |
| 308 | C23 | — | 28 | 4 | no | — |
| 309 | C23 | — | 28 | 32 | no | — |
| 310 | C23 | — | 28 | 4 | no | — |
| 311 | C23 | — | 28 | 1 | no | — |
| 312 | C23 | — | 56 | 8 | no | — |
| 313 | C23 | — | 56 | 32 | no | — |
| 314 | C23 | #6445 | 1 | 1 | yes | characteristic |
| 315 | Q8 | — | 28 | 2 | no | — |
| 316 | D4 | — | 4 | 4 | no | — |
| 317 | D4 | — | 4 | 8 | no | — |
| 318 | D4 | — | 4 | 8 | no | — |
| 319 | D4 | — | 7 | 8 | no | — |
| 320 | D4 | — | 8 | 2 | no | — |
| 321 | D4 | — | 14 | 8 | no | — |
| 322 | D4 | — | 14 | 4 | no | — |
| 323 | D4 | — | 28 | 2 | no | — |
| 324 | D4 | — | 28 | 32 | no | — |
| 325 | D4 | — | 28 | 4 | no | — |
| 326 | D4 | — | 56 | 2 | no | — |
| 327 | C2×C4 | — | 2 | 2 | no | — |
| 328 | C2×C4 | — | 2 | 4 | no | — |
| 329 | C2×C4 | — | 14 | 4 | no | — |
| 330 | C2×C4 | — | 28 | 8 | no | — |
| 331 | C2×C4 | — | 28 | 4 | no | — |
| 332 | C2×C4 | — | 28 | 8 | no | — |
| 333 | C2×C4 | — | 28 | 1 | no | — |
| 334 | C2×C4 | — | 56 | 2 | no | — |
| 335 | C2×C4 | #6445 | 1 | 2 | yes | — |
| 336 | C2×C4 | #6445 | 1 | 1 | yes | characteristic |
| 337 | C2×C4 | C22×D28 | 1 | 1 | yes | characteristic |
| 338 | C2×C4 | C2×D4×D7 | 1 | 2 | yes | — |
| 339 | C8 | — | 4 | 4 | no | — |
| 340 | C8 | — | 14 | 4 | no | — |
| 341 | C7 | #18524 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 342 | C22 | — | 2 | 2 | no | — |
| 343 | C22 | — | 4 | 8 | no | — |
| 344 | C22 | — | 4 | 4 | no | — |
| 345 | C22 | — | 8 | 8 | no | — |
| 346 | C22 | — | 14 | 8 | no | — |
| 347 | C22 | — | 28 | 16 | no | — |
| 348 | C22 | — | 28 | 4 | no | — |
| 349 | C22 | — | 28 | 4 | no | — |
| 350 | C22 | — | 56 | 32 | no | — |
| 351 | C22 | — | 56 | 2 | no | — |
| 352 | C22 | — | 56 | 1 | no | — |
| 353 | C22 | #89519 | 1 | 2 | yes | — |
| 354 | C22 | C2×#6445 | 1 | 1 | yes | characteristic |
| 355 | C4 | — | 2 | 2 | no | — |
| 356 | C4 | — | 2 | 1 | no | — |
| 357 | C4 | — | 2 | 1 | no | — |
| 358 | C4 | — | 28 | 4 | no | — |
| 359 | C4 | — | 56 | 1 | no | — |
| 360 | C4 | D7×AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 361 | C2 | — | 2 | 2 | no | — |
| 362 | C2 | — | 8 | 4 | no | — |
| 363 | C2 | — | 28 | 8 | no | — |
| 364 | C2 | — | 112 | 1 | no | — |
| 365 | C2 | C2×#89519 | 1 | 1 | yes | characteristic |
| 366 | C2 | #11736371 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×#6445 |
| commutator, cosocle | C42×C7 | C24 |
| Frattini | C42 | C23×D7 |
| Fitting | C7×#1555 | C2 |
| socle | C22×C7 | C2×#120 |
| hypercenter | #1555 | D7 |
| hypocenter | C7 | #18524 |
| LCS | G ▷ C42×C7 ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #1555 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#90408 | C2 | semidirect |
| 2. #11740608 | C2 | semidirect |
| 3. #11736788 | C2 | semidirect |
| 4. C7×#1555 | C2 | semidirect |
| 5. #11728553 | C2 | semidirect |
| 6. #11726145 | C2 | semidirect |
| 7. #11726144 | C2 | semidirect |
| 16. #90168 | C22 | semidirect |
| 18. C7×#432 | C22 | semidirect |
| 19. #89848 | C22 | semidirect |
| 21. #89845 | C22 | semidirect |
| 22. C4×#1136 | C22 | semidirect |
| 23. #89615 | C22 | semidirect |
| 24. #89614 | C22 | semidirect |
| 28. C7×#331 | C22 | semidirect |
| 29. #89278 | C22 | semidirect |
| 59. #6437 | C23 | semidirect |
| 65. #6432 | C23 | semidirect |
| 66. C7×C4⋊C8 | C23 | semidirect |
| 73. C4×C7⋊C8 | C23 | semidirect |
| 79. #1555 | D7 | semidirect |
| 146. #432 | C2×D7 | semidirect |
| 148. #331 | C2×D7 | semidirect |
| 181. D28 | AGL(1,ℤ/8) | semidirect |
| 224. C4⋊C8 | C22×D7 | semidirect |
| 341. C7 | #18524 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#90408 | 2 |
| #11740608 | 2 |
| #11736788 | 2 |
| C7×#1555 | 2 |
| #11728553 | 2 |
| #11726145 | 2 |
| #11726144 | 2 |
| #18524 | 7 |