Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1972 conjugacy classes of subgroups.
The subgroup lattice has 582 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C7×#2819 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11740452 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | Dic7×#124 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #11734612 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #11734545 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #11734338 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #11734334 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11734302 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #11734224 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #11734194 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | #11734110 | C2 | 1 | 4 | yes | maximal, complemented |
| 12 | #11731663 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #11731594 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | C22×#1159 | C22 | 1 | 2 | yes | — |
| 15 | C2×C7×#124 | C22 | 1 | 2 | yes | — |
| 16 | C2×Q8×Dic7 | C22 | 1 | 2 | yes | — |
| 17 | C2×D4×Dic7 | C22 | 1 | 2 | yes | — |
| 18 | C2×D4×Dic7 | C22 | 1 | 2 | yes | — |
| 19 | C2×#6456 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#6450 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×(C22⋊D7)⋊C4 | C22 | 1 | 4 | yes | — |
| 22 | C2×#6438 | C22 | 1 | 1 | yes | characteristic |
| 23 | C7×#394 | C22 | 1 | 2 | yes | — |
| 24 | C7×#394 | C22 | 1 | 2 | yes | — |
| 25 | C7×#393 | C22 | 1 | 4 | yes | — |
| 26 | C7×#392 | C22 | 1 | 4 | yes | — |
| 27 | C7×#382 | C22 | 1 | 1 | yes | characteristic |
| 28 | #90003 | C22 | 1 | 4 | yes | — |
| 29 | #90002 | C22 | 1 | 2 | yes | — |
| 30 | #89995 | C22 | 1 | 4 | yes | — |
| 31 | #89995 | C22 | 1 | 2 | yes | — |
| 32 | #89995 | C22 | 1 | 4 | yes | — |
| 33 | #89994 | C22 | 1 | 4 | yes | — |
| 34 | #89994 | C22 | 1 | 2 | yes | — |
| 35 | #89993 | C22 | 1 | 2 | yes | — |
| 36 | #89760 | C22 | 1 | 1 | yes | characteristic |
| 37 | #89758 | C22 | 1 | 2 | yes | — |
| 38 | #89751 | C22 | 1 | 2 | yes | — |
| 39 | #89746 | C22 | 1 | 1 | yes | characteristic |
| 40 | #89733 | C22 | 1 | 4 | yes | — |
| 41 | #89733 | C22 | 1 | 4 | yes | — |
| 42 | #89733 | C22 | 1 | 4 | yes | — |
| 43 | #89733 | C22 | 1 | 4 | yes | — |
| 44 | #89732 | C22 | 1 | 4 | yes | — |
| 45 | #89731 | C22 | 1 | 4 | yes | — |
| 46 | #89725 | C22 | 1 | 4 | yes | — |
| 47 | #89724 | C22 | 1 | 4 | yes | — |
| 48 | #89723 | C22 | 1 | 4 | yes | — |
| 49 | #89723 | C22 | 1 | 4 | yes | — |
| 50 | #89719 | C22 | 1 | 4 | yes | — |
| 51 | #89719 | C22 | 1 | 4 | yes | — |
| 52 | C22⋊C4×Dic7 | C22 | 1 | 4 | yes | — |
| 53 | C22⋊C4×Dic7 | C22 | 1 | 4 | yes | — |
| 54 | C22⋊C4×Dic7 | C22 | 1 | 4 | yes | — |
| 55 | #89708 | C22 | 1 | 2 | yes | — |
| 56 | C42×Dic7 | C22 | 1 | 1 | yes | characteristic |
| 57 | #89446 | C22 | 1 | 4 | yes | — |
| 58 | #89445 | C22 | 1 | 2 | yes | — |
| 59 | #89441 | C22 | 1 | 4 | yes | — |
| 60 | #89438 | C22 | 1 | 2 | yes | — |
| 61 | #89438 | C22 | 1 | 4 | yes | — |
| 62 | #89432 | C22 | 1 | 4 | yes | — |
| 63 | #89432 | C22 | 1 | 4 | yes | — |
| 64 | #89431 | C22 | 1 | 2 | yes | — |
| 65 | #89428 | C22 | 1 | 4 | yes | — |
| 66 | #89420 | C22 | 1 | 2 | yes | — |
| 67 | #36694 | — | 7 | 1 | no | maximal, Sylow |
| 68 | C22×C7×Q8 | C23 | 1 | 2 | yes | — |
| 69 | C22×C7×D4 | C23 | 1 | 2 | yes | — |
| 70 | C22×C7×D4 | C23 | 1 | 2 | yes | — |
| 71 | C22×C7×D4 | C23 | 1 | 2 | yes | — |
| 72 | C22×C22⋊D7 | C23 | 1 | 4 | yes | — |
| 73 | C22×C22⋊D7 | C23 | 1 | 4 | yes | — |
| 74 | C23×Dic7 | C23 | 1 | 4 | yes | — |
| 75 | C2×#1159 | — | 4 | 8 | no | — |
| 76 | C2×#1159 | — | 4 | 4 | no | — |
| 77 | C22×D28 | C23 | 1 | 1 | yes | characteristic |
| 78 | C22×C4×D7 | C23 | 1 | 2 | yes | — |
| 79 | C22×Dic14 | C23 | 1 | 1 | yes | characteristic |
| 80 | C22×Dic14 | C23 | 1 | 2 | yes | — |
| 81 | C7×#124 | — | 2 | 8 | no | — |
| 82 | C2×C7×C4⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 83 | C2×C7×C4⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 84 | C2×C7×C22⋊C4 | C23 | 1 | 4 | yes | — |
| 85 | C2×C7×C22⋊C4 | C23 | 1 | 4 | yes | — |
| 86 | C2×C7×C22⋊C4 | C23 | 1 | 4 | yes | — |
| 87 | C2×C7×C22⋊C4 | C23 | 1 | 4 | yes | — |
| 88 | C2×C42×C7 | C23 | 1 | 1 | yes | characteristic |
| 89 | C2×C22⋊Dic7 | C23 | 1 | 4 | yes | — |
| 90 | C2×C22⋊Dic7 | C23 | 1 | 4 | yes | — |
| 91 | C2×C22⋊Dic7 | C23 | 1 | 4 | yes | — |
| 92 | C2×C22⋊Dic7 | C23 | 1 | 4 | yes | — |
| 93 | C2×C22⋊Dic7 | C23 | 1 | 4 | yes | — |
| 94 | Q8×Dic7 | — | 4 | 4 | no | — |
| 95 | D4×Dic7 | — | 4 | 4 | no | — |
| 96 | D4×Dic7 | — | 4 | 4 | no | — |
| 97 | C2×(C2×D7)⋊C4 | C23 | 1 | 4 | yes | — |
| 98 | C2×(C2×D7)⋊C4 | C23 | 1 | 4 | yes | — |
| 99 | C2×(C2×D7)⋊C4 | C23 | 1 | 2 | yes | — |
| 100 | C2×(C2×D7)⋊C4 | C23 | 1 | 4 | yes | — |
| 101 | C2×(C2×D7)⋊C4 | C23 | 1 | 4 | yes | — |
| 102 | C2×C4⋊Dic7 | C23 | 1 | 2 | yes | — |
| 103 | C2×C4⋊Dic7 | C23 | 1 | 2 | yes | — |
| 104 | C2×C4⋊Dic7 | C23 | 1 | 2 | yes | — |
| 105 | C2×C4⋊Dic7 | C23 | 1 | 4 | yes | — |
| 106 | C2×Dic7⋊C4 | C23 | 1 | 4 | yes | — |
| 107 | C2×Dic7⋊C4 | C23 | 1 | 2 | yes | — |
| 108 | C2×C4×Dic7 | C23 | 1 | 4 | yes | — |
| 109 | C2×C4×Dic7 | C23 | 1 | 2 | yes | — |
| 110 | C2×C4×Dic7 | C23 | 1 | 1 | yes | characteristic |
| 111 | C2×C4×Dic7 | C23 | 1 | 2 | yes | — |
| 112 | C2×C4×Dic7 | C23 | 1 | 2 | yes | — |
| 113 | C2×C4×Dic7 | C23 | 1 | 1 | yes | characteristic |
| 114 | #6456 | — | 4 | 2 | no | — |
| 115 | #6450 | — | 4 | 2 | no | — |
| 116 | (C22⋊D7)⋊C4 | — | 4 | 8 | no | — |
| 117 | #6438 | — | 2 | 4 | no | — |
| 118 | C7×#95 | C23 | 1 | 2 | yes | — |
| 119 | C7×#95 | C23 | 1 | 4 | yes | — |
| 120 | C7×#95 | C23 | 1 | 2 | yes | — |
| 121 | C7⋊#95 | C23 | 1 | 2 | yes | — |
| 122 | C7⋊#95 | C23 | 1 | 4 | yes | — |
| 123 | C7⋊#95 | C23 | 1 | 4 | yes | — |
| 124 | C7⋊#95 | C23 | 1 | 4 | yes | — |
| 125 | C7⋊#95 | C23 | 1 | 4 | yes | — |
| 126 | C7⋊#95 | C23 | 1 | 4 | yes | — |
| 127 | C7⋊#95 | C23 | 1 | 2 | yes | — |
| 128 | C7⋊#95 | C23 | 1 | 4 | yes | — |
| 129 | C7⋊#95 | C23 | 1 | 4 | yes | — |
| 130 | C7⋊#95 | C23 | 1 | 4 | yes | — |
| 131 | #2844 | — | 7 | 1 | no | — |
| 132 | #2832 | — | 7 | 2 | no | — |
| 133 | #2832 | — | 7 | 4 | no | — |
| 134 | #2828 | — | 7 | 2 | no | — |
| 135 | #2828 | — | 7 | 4 | no | — |
| 136 | #2819 | — | 7 | 2 | no | — |
| 137 | #2819 | D7 | 1 | 1 | yes | characteristic, complemented |
| 138 | #2398 | — | 7 | 2 | no | — |
| 139 | #2398 | — | 7 | 4 | no | — |
| 140 | #2388 | — | 7 | 2 | no | — |
| 141 | #2388 | — | 7 | 4 | no | — |
| 142 | C4×#124 | — | 7 | 1 | no | — |
| 143 | C4×#124 | — | 7 | 2 | no | — |
| 144 | C24×C7 | C24 | 1 | 4 | yes | — |
| 145 | C23×D7 | C24 | 1 | 2 | yes | — |
| 146 | C2×C7×Q8 | — | 2 | 4 | no | — |
| 147 | C2×C7×Q8 | — | 4 | 2 | no | — |
| 148 | C2×C7×Q8 | — | 4 | 2 | no | — |
| 149 | C2×C7×D4 | — | 2 | 4 | no | — |
| 150 | C2×C7×D4 | — | 4 | 2 | no | — |
| 151 | C2×C7×D4 | — | 4 | 2 | no | — |
| 152 | C2×C7×D4 | — | 4 | 4 | no | — |
| 153 | C2×C7×D4 | — | 4 | 2 | no | — |
| 154 | C2×C7×D4 | — | 4 | 2 | no | — |
| 155 | C2×C7×D4 | — | 4 | 4 | no | — |
| 156 | C22×C4×C7 | C24 | 1 | 4 | yes | — |
| 157 | C22×C4×C7 | C24 | 1 | 2 | yes | — |
| 158 | C22×C4×C7 | C24 | 1 | 2 | yes | — |
| 159 | C22×C4×C7 | C24 | 1 | 1 | yes | characteristic |
| 160 | C22×C4×C7 | C24 | 1 | 2 | yes | — |
| 161 | C2×C22⋊D7 | — | 4 | 4 | no | — |
| 162 | C2×C22⋊D7 | — | 4 | 4 | no | — |
| 163 | C2×C22⋊D7 | — | 4 | 4 | no | — |
| 164 | C2×C22⋊D7 | — | 4 | 4 | no | — |
| 165 | C2×C22⋊D7 | — | 4 | 4 | no | — |
| 166 | C2×C22⋊D7 | — | 4 | 4 | no | — |
| 167 | C22×Dic7 | — | 2 | 8 | no | — |
| 168 | C22×Dic7 | — | 2 | 8 | no | — |
| 169 | C22×Dic7 | — | 2 | 8 | no | — |
| 170 | C22×Dic7 | C24 | 1 | 4 | yes | — |
| 171 | C22×Dic7 | C24 | 1 | 2 | yes | — |
| 172 | C22×Dic7 | C24 | 1 | 4 | yes | — |
| 173 | C22×Dic7 | C24 | 1 | 1 | yes | characteristic |
| 174 | C22×Dic7 | C24 | 1 | 2 | yes | — |
| 175 | C22×Dic7 | C24 | 1 | 1 | yes | characteristic |
| 176 | #1159 | — | 4 | 32 | no | — |
| 177 | C2×D28 | — | 2 | 2 | no | — |
| 178 | C2×D28 | — | 4 | 1 | no | — |
| 179 | C2×D28 | — | 4 | 1 | no | — |
| 180 | C2×C4×D7 | — | 2 | 8 | no | — |
| 181 | C2×C4×D7 | — | 2 | 4 | no | — |
| 182 | C2×Dic14 | — | 2 | 2 | no | — |
| 183 | C2×Dic14 | — | 4 | 1 | no | — |
| 184 | C2×Dic14 | — | 4 | 1 | no | — |
| 185 | C2×Dic14 | — | 4 | 4 | no | — |
| 186 | C2×Dic14 | — | 4 | 2 | no | — |
| 187 | C7×C4⋊C4 | — | 4 | 1 | no | — |
| 188 | C7×C4⋊C4 | — | 4 | 1 | no | — |
| 189 | C7×C22⋊C4 | — | 2 | 8 | no | — |
| 190 | C7×C22⋊C4 | — | 2 | 8 | no | — |
| 191 | C7×C22⋊C4 | — | 4 | 4 | no | — |
| 192 | C7×C22⋊C4 | — | 4 | 4 | no | — |
| 193 | C42×C7 | #41 | 1 | 4 | yes | complemented |
| 194 | C22⋊Dic7 | — | 4 | 4 | no | — |
| 195 | C22⋊Dic7 | — | 4 | 4 | no | — |
| 196 | C22⋊Dic7 | — | 4 | 4 | no | — |
| 197 | C22⋊Dic7 | — | 4 | 4 | no | — |
| 198 | C22⋊Dic7 | — | 4 | 4 | no | — |
| 199 | (C2×D7)⋊C4 | — | 2 | 8 | no | — |
| 200 | (C2×D7)⋊C4 | — | 4 | 4 | no | — |
| 201 | (C2×D7)⋊C4 | — | 4 | 2 | no | — |
| 202 | (C2×D7)⋊C4 | — | 4 | 4 | no | — |
| 203 | (C2×D7)⋊C4 | — | 4 | 4 | no | — |
| 204 | C4⋊Dic7 | — | 4 | 2 | no | — |
| 205 | C4⋊Dic7 | — | 4 | 2 | no | — |
| 206 | C4⋊Dic7 | — | 4 | 2 | no | — |
| 207 | C4⋊Dic7 | — | 4 | 4 | no | — |
| 208 | Dic7⋊C4 | — | 4 | 4 | no | — |
| 209 | Dic7⋊C4 | — | 4 | 2 | no | — |
| 210 | C4×Dic7 | — | 2 | 8 | no | — |
| 211 | C4×Dic7 | — | 2 | 2 | no | — |
| 212 | C4×Dic7 | — | 2 | 4 | no | — |
| 213 | C4×Dic7 | — | 2 | 4 | no | — |
| 214 | C4×Dic7 | — | 4 | 2 | no | — |
| 215 | C4×Dic7 | — | 4 | 1 | no | — |
| 216 | C22×#41 | — | 7 | 2 | no | — |
| 217 | C2×#124 | — | 7 | 1 | no | — |
| 218 | C2×#124 | C2×D7 | 1 | 2 | yes | — |
| 219 | C2×C4×Q8 | — | 7 | 2 | no | — |
| 220 | C2×C4×Q8 | — | 7 | 1 | no | — |
| 221 | C2×C4×D4 | — | 7 | 2 | no | — |
| 222 | C2×C4×D4 | — | 7 | 2 | no | — |
| 223 | C2×C4×D4 | — | 7 | 1 | no | — |
| 224 | C2×C4×D4 | — | 7 | 4 | no | — |
| 225 | #400 | — | 7 | 2 | no | — |
| 226 | #400 | — | 7 | 4 | no | — |
| 227 | #400 | — | 7 | 2 | no | — |
| 228 | #400 | — | 7 | 4 | no | — |
| 229 | #397 | — | 7 | 4 | no | — |
| 230 | #397 | — | 7 | 4 | no | — |
| 231 | #397 | — | 7 | 4 | no | — |
| 232 | #395 | — | 7 | 2 | no | — |
| 233 | #395 | — | 7 | 4 | no | — |
| 234 | #394 | — | 7 | 2 | no | — |
| 235 | #394 | — | 7 | 4 | no | — |
| 236 | #394 | — | 7 | 4 | no | — |
| 237 | #394 | — | 7 | 4 | no | — |
| 238 | #394 | — | 7 | 4 | no | — |
| 239 | #394 | — | 7 | 4 | no | — |
| 240 | #394 | — | 7 | 4 | no | — |
| 241 | #394 | C2×D7 | 1 | 2 | yes | — |
| 242 | #394 | C2×D7 | 1 | 2 | yes | — |
| 243 | #393 | — | 7 | 4 | no | — |
| 244 | #393 | — | 7 | 4 | no | — |
| 245 | #393 | — | 7 | 4 | no | — |
| 246 | #393 | — | 7 | 2 | no | — |
| 247 | #393 | C2×D7 | 1 | 4 | yes | — |
| 248 | #392 | — | 7 | 4 | no | — |
| 249 | #392 | — | 7 | 4 | no | — |
| 250 | #392 | — | 7 | 2 | no | — |
| 251 | #392 | — | 7 | 4 | no | — |
| 252 | #392 | C2×D7 | 1 | 4 | yes | — |
| 253 | #391 | — | 7 | 2 | no | — |
| 254 | #391 | — | 7 | 1 | no | — |
| 255 | #390 | — | 7 | 2 | no | — |
| 256 | #390 | — | 7 | 1 | no | — |
| 257 | #388 | — | 7 | 4 | no | — |
| 258 | #388 | — | 7 | 4 | no | — |
| 259 | #388 | — | 7 | 4 | no | — |
| 260 | #382 | — | 7 | 2 | no | — |
| 261 | #382 | C2×D7 | 1 | 1 | yes | characteristic |
| 262 | C4×C22⋊C4 | — | 7 | 4 | no | — |
| 263 | C4×C22⋊C4 | — | 7 | 4 | no | — |
| 264 | C4×C22⋊C4 | — | 7 | 4 | no | — |
| 265 | C4×C22⋊C4 | — | 7 | 2 | no | — |
| 266 | C4×C22⋊C4 | — | 7 | 4 | no | — |
| 267 | #376 | — | 7 | 2 | no | — |
| 268 | C43 | — | 7 | 1 | no | — |
| 269 | C23×C7 | — | 2 | 4 | no | — |
| 270 | C23×C7 | — | 2 | 4 | no | — |
| 271 | C23×C7 | — | 2 | 4 | no | — |
| 272 | C23×C7 | — | 2 | 4 | no | — |
| 273 | C23×C7 | — | 2 | 4 | no | — |
| 274 | C23×C7 | — | 2 | 4 | no | — |
| 275 | C23×C7 | — | 2 | 4 | no | — |
| 276 | C23×C7 | C25 | 1 | 1 | yes | characteristic |
| 277 | C22×D7 | — | 2 | 2 | no | — |
| 278 | C22×D7 | — | 2 | 2 | no | — |
| 279 | C22×D7 | — | 2 | 4 | no | — |
| 280 | C22×D7 | — | 2 | 4 | no | — |
| 281 | C22×D7 | — | 2 | 2 | no | — |
| 282 | C7×Q8 | — | 4 | 8 | no | — |
| 283 | C7×D4 | — | 4 | 8 | no | — |
| 284 | C7×D4 | — | 4 | 8 | no | — |
| 285 | C7×D4 | — | 4 | 8 | no | — |
| 286 | C2×C4×C7 | — | 2 | 2 | no | — |
| 287 | C2×C4×C7 | — | 2 | 1 | no | — |
| 288 | C2×C4×C7 | — | 2 | 1 | no | — |
| 289 | C2×C4×C7 | — | 2 | 2 | no | — |
| 290 | C2×C4×C7 | — | 2 | 4 | no | — |
| 291 | C2×C4×C7 | — | 2 | 2 | no | — |
| 292 | C2×C4×C7 | — | 2 | 4 | no | — |
| 293 | C2×C4×C7 | — | 2 | 4 | no | — |
| 294 | C2×C4×C7 | — | 2 | 2 | no | — |
| 295 | C2×C4×C7 | — | 2 | 4 | no | — |
| 296 | C2×C4×C7 | — | 2 | 4 | no | — |
| 297 | C2×C4×C7 | C2×#41 | 1 | 4 | yes | — |
| 298 | C2×C4×C7 | C2×#41 | 1 | 2 | yes | — |
| 299 | C22⋊D7 | — | 4 | 16 | no | — |
| 300 | C22⋊D7 | — | 4 | 16 | no | — |
| 301 | C2×Dic7 | — | 2 | 2 | no | — |
| 302 | C2×Dic7 | — | 2 | 1 | no | — |
| 303 | C2×Dic7 | — | 2 | 4 | no | — |
| 304 | C2×Dic7 | — | 2 | 2 | no | — |
| 305 | C2×Dic7 | — | 2 | 2 | no | — |
| 306 | C2×Dic7 | — | 2 | 4 | no | — |
| 307 | C2×Dic7 | — | 2 | 4 | no | — |
| 308 | C2×Dic7 | — | 2 | 4 | no | — |
| 309 | C2×Dic7 | — | 2 | 2 | no | — |
| 310 | C2×Dic7 | — | 2 | 2 | no | — |
| 311 | C2×Dic7 | — | 2 | 2 | no | — |
| 312 | C2×Dic7 | — | 2 | 4 | no | — |
| 313 | C2×Dic7 | — | 2 | 2 | no | — |
| 314 | C2×Dic7 | — | 2 | 4 | no | — |
| 315 | C2×Dic7 | — | 4 | 16 | no | — |
| 316 | C2×Dic7 | H(5,𝔽2) | 1 | 4 | yes | — |
| 317 | C2×Dic7 | H(5,𝔽2) | 1 | 2 | yes | — |
| 318 | D28 | — | 4 | 4 | no | — |
| 319 | C4×D7 | — | 4 | 8 | no | — |
| 320 | Dic14 | — | 4 | 4 | no | — |
| 321 | Dic14 | — | 4 | 8 | no | — |
| 322 | C2×#41 | — | 28 | 8 | no | — |
| 323 | C2×#41 | — | 28 | 4 | no | — |
| 324 | C22×Q8 | — | 7 | 1 | no | — |
| 325 | C22×Q8 | — | 7 | 2 | no | — |
| 326 | C22×Q8 | C22×D7 | 1 | 2 | yes | — |
| 327 | C22×D4 | — | 7 | 4 | no | — |
| 328 | C22×D4 | — | 7 | 4 | no | — |
| 329 | C22×D4 | — | 7 | 1 | no | — |
| 330 | C22×D4 | C22×D7 | 1 | 2 | yes | — |
| 331 | C22×D4 | C22×D7 | 1 | 2 | yes | — |
| 332 | C22×D4 | C22×D7 | 1 | 2 | yes | — |
| 333 | C23×C4 | — | 7 | 4 | no | — |
| 334 | C23×C4 | — | 7 | 2 | no | — |
| 335 | #124 | — | 2 | 8 | no | — |
| 336 | #124 | — | 14 | 4 | no | — |
| 337 | C4×Q8 | — | 28 | 2 | no | — |
| 338 | C4×Q8 | — | 28 | 4 | no | — |
| 339 | C4×D4 | — | 28 | 8 | no | — |
| 340 | C4×D4 | — | 28 | 2 | no | — |
| 341 | C4×D4 | — | 28 | 4 | no | — |
| 342 | C4×D4 | — | 28 | 4 | no | — |
| 343 | C2×C4⋊C4 | — | 7 | 4 | no | — |
| 344 | C2×C4⋊C4 | — | 7 | 2 | no | — |
| 345 | C2×C4⋊C4 | — | 7 | 2 | no | — |
| 346 | C2×C4⋊C4 | — | 7 | 2 | no | — |
| 347 | C2×C4⋊C4 | — | 7 | 2 | no | — |
| 348 | C2×C4⋊C4 | — | 7 | 4 | no | — |
| 349 | C2×C4⋊C4 | C22×D7 | 1 | 1 | yes | characteristic |
| 350 | C2×C4⋊C4 | C22×D7 | 1 | 1 | yes | characteristic |
| 351 | C2×C22⋊C4 | — | 7 | 4 | no | — |
| 352 | C2×C22⋊C4 | — | 7 | 4 | no | — |
| 353 | C2×C22⋊C4 | — | 7 | 4 | no | — |
| 354 | C2×C22⋊C4 | — | 7 | 4 | no | — |
| 355 | C2×C22⋊C4 | — | 7 | 4 | no | — |
| 356 | C2×C22⋊C4 | — | 7 | 4 | no | — |
| 357 | C2×C22⋊C4 | — | 7 | 2 | no | — |
| 358 | C2×C22⋊C4 | — | 7 | 4 | no | — |
| 359 | C2×C22⋊C4 | — | 7 | 4 | no | — |
| 360 | C2×C22⋊C4 | — | 7 | 4 | no | — |
| 361 | C2×C22⋊C4 | C22×D7 | 1 | 4 | yes | — |
| 362 | C2×C22⋊C4 | C22×D7 | 1 | 4 | yes | — |
| 363 | C2×C22⋊C4 | C22×D7 | 1 | 4 | yes | — |
| 364 | C2×C22⋊C4 | C22×D7 | 1 | 4 | yes | — |
| 365 | C2×C42 | — | 7 | 1 | no | — |
| 366 | C2×C42 | — | 7 | 2 | no | — |
| 367 | C2×C42 | — | 7 | 2 | no | — |
| 368 | C2×C42 | — | 7 | 4 | no | — |
| 369 | C2×C42 | — | 7 | 1 | no | — |
| 370 | C2×C42 | — | 7 | 2 | no | — |
| 371 | C2×C42 | C22×D7 | 1 | 1 | yes | characteristic |
| 372 | #95 | — | 7 | 4 | no | — |
| 373 | #95 | — | 7 | 2 | no | — |
| 374 | #95 | — | 7 | 4 | no | — |
| 375 | #95 | — | 7 | 4 | no | — |
| 376 | #95 | — | 7 | 4 | no | — |
| 377 | #95 | — | 7 | 4 | no | — |
| 378 | #95 | — | 7 | 4 | no | — |
| 379 | #95 | — | 7 | 2 | no | — |
| 380 | #95 | — | 7 | 4 | no | — |
| 381 | #95 | — | 7 | 4 | no | — |
| 382 | #95 | C22×D7 | 1 | 2 | yes | — |
| 383 | #95 | C22×D7 | 1 | 4 | yes | — |
| 384 | #95 | C22×D7 | 1 | 2 | yes | — |
| 385 | C22×C7 | — | 4 | 4 | no | — |
| 386 | C22×C7 | — | 4 | 4 | no | — |
| 387 | C22×C7 | — | 4 | 4 | no | — |
| 388 | C22×C7 | — | 4 | 4 | no | — |
| 389 | C22×C7 | — | 4 | 4 | no | — |
| 390 | C22×C7 | — | 4 | 4 | no | — |
| 391 | C22×C7 | — | 4 | 4 | no | — |
| 392 | C22×C7 | C22×#41 | 1 | 1 | yes | characteristic |
| 393 | C22×C7 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 394 | C22×C7 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 395 | C22×C7 | #585 | 1 | 2 | yes | — |
| 396 | C22×C7 | #585 | 1 | 1 | yes | characteristic |
| 397 | C2×D7 | — | 4 | 2 | no | — |
| 398 | C2×D7 | — | 4 | 4 | no | — |
| 399 | C2×D7 | — | 4 | 2 | no | — |
| 400 | C2×D7 | — | 4 | 4 | no | — |
| 401 | C2×D7 | — | 4 | 2 | no | — |
| 402 | C4×C7 | — | 2 | 2 | no | — |
| 403 | C4×C7 | — | 2 | 4 | no | — |
| 404 | C4×C7 | — | 4 | 4 | no | — |
| 405 | C4×C7 | — | 4 | 2 | no | — |
| 406 | C4×C7 | — | 4 | 2 | no | — |
| 407 | Dic7 | — | 4 | 2 | no | — |
| 408 | Dic7 | — | 4 | 4 | no | — |
| 409 | Dic7 | — | 4 | 1 | no | — |
| 410 | Dic7 | — | 4 | 2 | no | — |
| 411 | Dic7 | — | 4 | 4 | no | — |
| 412 | Dic7 | H(3,𝔽4) | 1 | 4 | yes | — |
| 413 | C24 | — | 7 | 2 | no | — |
| 414 | C24 | C23×D7 | 1 | 4 | yes | — |
| 415 | #41 | — | 28 | 32 | no | — |
| 416 | C2×Q8 | — | 2 | 4 | no | — |
| 417 | C2×Q8 | — | 4 | 2 | no | — |
| 418 | C2×Q8 | — | 4 | 2 | no | — |
| 419 | C2×Q8 | — | 14 | 2 | no | — |
| 420 | C2×Q8 | — | 28 | 1 | no | — |
| 421 | C2×Q8 | — | 28 | 1 | no | — |
| 422 | C2×Q8 | — | 28 | 4 | no | — |
| 423 | C2×Q8 | — | 28 | 2 | no | — |
| 424 | C2×D4 | — | 2 | 4 | no | — |
| 425 | C2×D4 | — | 4 | 2 | no | — |
| 426 | C2×D4 | — | 4 | 2 | no | — |
| 427 | C2×D4 | — | 4 | 4 | no | — |
| 428 | C2×D4 | — | 4 | 2 | no | — |
| 429 | C2×D4 | — | 4 | 2 | no | — |
| 430 | C2×D4 | — | 4 | 4 | no | — |
| 431 | C2×D4 | — | 14 | 2 | no | — |
| 432 | C2×D4 | — | 28 | 1 | no | — |
| 433 | C2×D4 | — | 28 | 1 | no | — |
| 434 | C2×D4 | — | 28 | 4 | no | — |
| 435 | C2×D4 | — | 28 | 4 | no | — |
| 436 | C2×D4 | — | 28 | 4 | no | — |
| 437 | C2×D4 | — | 28 | 4 | no | — |
| 438 | C2×D4 | — | 28 | 4 | no | — |
| 439 | C2×D4 | — | 28 | 4 | no | — |
| 440 | C22×C4 | — | 7 | 1 | no | — |
| 441 | C22×C4 | — | 7 | 2 | no | — |
| 442 | C22×C4 | — | 7 | 4 | no | — |
| 443 | C22×C4 | — | 7 | 4 | no | — |
| 444 | C22×C4 | — | 7 | 1 | no | — |
| 445 | C22×C4 | — | 7 | 2 | no | — |
| 446 | C22×C4 | — | 14 | 8 | no | — |
| 447 | C22×C4 | — | 14 | 4 | no | — |
| 448 | C22×C4 | — | 14 | 8 | no | — |
| 449 | C22×C4 | — | 14 | 8 | no | — |
| 450 | C22×C4 | — | 14 | 8 | no | — |
| 451 | C22×C4 | C23×D7 | 1 | 4 | yes | — |
| 452 | C22×C4 | C23×D7 | 1 | 2 | yes | — |
| 453 | C22×C4 | C23×D7 | 1 | 2 | yes | — |
| 454 | C22×C4 | C23×D7 | 1 | 1 | yes | characteristic |
| 455 | C22×C4 | C23×D7 | 1 | 2 | yes | — |
| 456 | C4⋊C4 | — | 4 | 1 | no | — |
| 457 | C4⋊C4 | — | 4 | 1 | no | — |
| 458 | C4⋊C4 | — | 28 | 4 | no | — |
| 459 | C4⋊C4 | — | 28 | 2 | no | — |
| 460 | C4⋊C4 | — | 28 | 2 | no | — |
| 461 | C4⋊C4 | — | 28 | 2 | no | — |
| 462 | C4⋊C4 | — | 28 | 2 | no | — |
| 463 | C4⋊C4 | — | 28 | 4 | no | — |
| 464 | C22⋊C4 | — | 2 | 8 | no | — |
| 465 | C22⋊C4 | — | 2 | 8 | no | — |
| 466 | C22⋊C4 | — | 4 | 4 | no | — |
| 467 | C22⋊C4 | — | 4 | 4 | no | — |
| 468 | C22⋊C4 | — | 14 | 8 | no | — |
| 469 | C22⋊C4 | — | 28 | 4 | no | — |
| 470 | C22⋊C4 | — | 28 | 4 | no | — |
| 471 | C22⋊C4 | — | 28 | 4 | no | — |
| 472 | C22⋊C4 | — | 28 | 2 | no | — |
| 473 | C22⋊C4 | — | 28 | 4 | no | — |
| 474 | C22⋊C4 | — | 28 | 4 | no | — |
| 475 | C22⋊C4 | — | 28 | 4 | no | — |
| 476 | C22⋊C4 | — | 28 | 4 | no | — |
| 477 | C22⋊C4 | — | 28 | 4 | no | — |
| 478 | C42 | — | 14 | 2 | no | — |
| 479 | C42 | — | 14 | 4 | no | — |
| 480 | C42 | — | 14 | 8 | no | — |
| 481 | C42 | — | 14 | 4 | no | — |
| 482 | C42 | — | 28 | 2 | no | — |
| 483 | C42 | — | 28 | 1 | no | — |
| 484 | C42 | #1159 | 1 | 4 | yes | complemented |
| 485 | C2×C7 | — | 8 | 4 | no | — |
| 486 | C2×C7 | #3460 | 1 | 2 | yes | — |
| 487 | C2×C7 | #3460 | 1 | 1 | yes | characteristic |
| 488 | C2×C7 | C2×H(3,𝔽4) | 1 | 1 | yes | characteristic |
| 489 | C2×C7 | #3529 | 1 | 1 | yes | characteristic |
| 490 | C2×C7 | #3529 | 1 | 2 | yes | — |
| 491 | D7 | — | 8 | 2 | no | — |
| 492 | C23 | — | 2 | 4 | no | — |
| 493 | C23 | — | 2 | 4 | no | — |
| 494 | C23 | — | 2 | 4 | no | — |
| 495 | C23 | — | 2 | 4 | no | — |
| 496 | C23 | — | 2 | 4 | no | — |
| 497 | C23 | — | 2 | 4 | no | — |
| 498 | C23 | — | 2 | 4 | no | — |
| 499 | C23 | — | 14 | 2 | no | — |
| 500 | C23 | — | 14 | 4 | no | — |
| 501 | C23 | — | 14 | 2 | no | — |
| 502 | C23 | — | 14 | 4 | no | — |
| 503 | C23 | — | 14 | 2 | no | — |
| 504 | C23 | C24×D7 | 1 | 1 | yes | characteristic |
| 505 | Q8 | — | 4 | 8 | no | — |
| 506 | Q8 | — | 28 | 4 | no | — |
| 507 | Q8 | — | 28 | 8 | no | — |
| 508 | D4 | — | 4 | 8 | no | — |
| 509 | D4 | — | 4 | 8 | no | — |
| 510 | D4 | — | 4 | 8 | no | — |
| 511 | D4 | — | 28 | 4 | no | — |
| 512 | D4 | — | 28 | 16 | no | — |
| 513 | D4 | — | 28 | 16 | no | — |
| 514 | C2×C4 | — | 2 | 1 | no | — |
| 515 | C2×C4 | — | 2 | 2 | no | — |
| 516 | C2×C4 | — | 2 | 2 | no | — |
| 517 | C2×C4 | — | 2 | 1 | no | — |
| 518 | C2×C4 | — | 2 | 4 | no | — |
| 519 | C2×C4 | — | 2 | 4 | no | — |
| 520 | C2×C4 | — | 2 | 2 | no | — |
| 521 | C2×C4 | — | 2 | 4 | no | — |
| 522 | C2×C4 | — | 2 | 2 | no | — |
| 523 | C2×C4 | — | 2 | 4 | no | — |
| 524 | C2×C4 | — | 2 | 4 | no | — |
| 525 | C2×C4 | — | 7 | 4 | no | — |
| 526 | C2×C4 | — | 7 | 2 | no | — |
| 527 | C2×C4 | — | 14 | 2 | no | — |
| 528 | C2×C4 | — | 14 | 1 | no | — |
| 529 | C2×C4 | — | 14 | 2 | no | — |
| 530 | C2×C4 | — | 14 | 2 | no | — |
| 531 | C2×C4 | — | 14 | 4 | no | — |
| 532 | C2×C4 | — | 14 | 4 | no | — |
| 533 | C2×C4 | — | 14 | 4 | no | — |
| 534 | C2×C4 | — | 14 | 4 | no | — |
| 535 | C2×C4 | — | 14 | 2 | no | — |
| 536 | C2×C4 | — | 14 | 2 | no | — |
| 537 | C2×C4 | — | 14 | 4 | no | — |
| 538 | C2×C4 | — | 14 | 2 | no | — |
| 539 | C2×C4 | — | 14 | 4 | no | — |
| 540 | C2×C4 | — | 14 | 2 | no | — |
| 541 | C2×C4 | — | 28 | 8 | no | — |
| 542 | C2×C4 | — | 28 | 16 | no | — |
| 543 | C2×C4 | C2×#1159 | 1 | 2 | yes | — |
| 544 | C2×C4 | C2×#1159 | 1 | 4 | yes | — |
| 545 | C7 | #36694 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 546 | C22 | — | 4 | 4 | no | — |
| 547 | C22 | — | 4 | 4 | no | — |
| 548 | C22 | — | 4 | 4 | no | — |
| 549 | C22 | — | 4 | 4 | no | — |
| 550 | C22 | — | 4 | 4 | no | — |
| 551 | C22 | — | 4 | 4 | no | — |
| 552 | C22 | — | 4 | 4 | no | — |
| 553 | C22 | — | 28 | 4 | no | — |
| 554 | C22 | — | 28 | 2 | no | — |
| 555 | C22 | — | 28 | 2 | no | — |
| 556 | C22 | — | 28 | 4 | no | — |
| 557 | C22 | — | 28 | 2 | no | — |
| 558 | C22 | C22×#1159 | 1 | 1 | yes | characteristic |
| 559 | C22 | D7×H(5,𝔽2) | 1 | 2 | yes | — |
| 560 | C22 | D7×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 561 | C22 | #90618 | 1 | 2 | yes | — |
| 562 | C22 | #90620 | 1 | 1 | yes | characteristic |
| 563 | C4 | — | 2 | 4 | no | — |
| 564 | C4 | — | 2 | 2 | no | — |
| 565 | C4 | — | 4 | 4 | no | — |
| 566 | C4 | — | 4 | 2 | no | — |
| 567 | C4 | — | 4 | 2 | no | — |
| 568 | C4 | — | 7 | 4 | no | — |
| 569 | C4 | — | 28 | 1 | no | — |
| 570 | C4 | — | 28 | 4 | no | — |
| 571 | C4 | — | 28 | 4 | no | — |
| 572 | C4 | — | 28 | 2 | no | — |
| 573 | C4 | — | 28 | 2 | no | — |
| 574 | C2 | — | 8 | 4 | no | — |
| 575 | C2 | — | 56 | 2 | no | — |
| 576 | C2 | #11743382 | 1 | 2 | yes | — |
| 577 | C2 | #11743432 | 1 | 1 | yes | characteristic |
| 578 | C2 | #11744153 | 1 | 1 | yes | characteristic |
| 579 | C2 | D7×H(3,𝔽4) | 1 | 1 | yes | characteristic |
| 580 | C2 | #11744161 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D7 |
| commutator, socle, cosocle | C23×C7 | C25 |
| Fitting | C7×#2819 | C2 |
| hypercenter | #2819 | D7 |
| hypocenter | C7 | #36694 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ #2819 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C7×#2819 | C2 | semidirect |
| 2. #11740452 | C2 | semidirect |
| 3. Dic7×#124 | C2 | semidirect |
| 4. #11734612 | C2 | semidirect |
| 5. #11734545 | C2 | semidirect |
| 6. #11734338 | C2 | semidirect |
| 7. #11734334 | C2 | semidirect |
| 8. #11734302 | C2 | semidirect |
| 9. #11734224 | C2 | semidirect |
| 10. #11734194 | C2 | semidirect |
| 11. #11734110 | C2 | semidirect |
| 12. #11731663 | C2 | semidirect |
| 13. #11731594 | C2 | semidirect |
| 137. #2819 | D7 | semidirect |
| 193. C42×C7 | #41 | semidirect |
| 484. C42 | #1159 | semidirect |
| 545. C7 | #36694 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2819 | 2 |
| #11740452 | 2 |
| Dic7×#124 | 2 |
| #11734612 | 2 |
| #11734545 | 2 |
| #11734338 | 2 |
| #11734334 | 2 |
| #11734302 | 2 |
| #11734224 | 2 |
| #11734194 | 2 |
| #11734110 | 2 |
| #11731663 | 2 |
| #11731594 | 2 |
| #36694 | 7 |