Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1908 conjugacy classes of subgroups.
The subgroup lattice has 420 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C7×#2823 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11740563 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | Dic7×#126 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #11735457 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #11735183 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #11734900 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #11734726 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | #11734612 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #11734334 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #11731799 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #11731764 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C22×#1159 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×C7×#126 | C22 | 1 | 2 | yes | — |
| 14 | C2×#6456 | C22 | 1 | 3 | yes | — |
| 15 | C2×#6456 | C22 | 1 | 3 | yes | — |
| 16 | C2×#6455 | C22 | 1 | 3 | yes | — |
| 17 | C2×(C22⋊D7)⋊C4 | C22 | 1 | 6 | yes | — |
| 18 | C2×#6437 | C22 | 1 | 1 | yes | characteristic |
| 19 | C7×#398 | C22 | 1 | 3 | yes | — |
| 20 | C7×#396 | C22 | 1 | 6 | yes | — |
| 21 | C7×#394 | C22 | 1 | 3 | yes | — |
| 22 | C7×#384 | C22 | 1 | 1 | yes | characteristic |
| 23 | #89995 | C22 | 1 | 3 | yes | — |
| 24 | #89766 | C22 | 1 | 6 | yes | — |
| 25 | #89765 | C22 | 1 | 3 | yes | — |
| 26 | #89763 | C22 | 1 | 6 | yes | — |
| 27 | #89763 | C22 | 1 | 6 | yes | — |
| 28 | #89760 | C22 | 1 | 3 | yes | — |
| 29 | #89760 | C22 | 1 | 3 | yes | — |
| 30 | #89758 | C22 | 1 | 3 | yes | — |
| 31 | #89756 | C22 | 1 | 6 | yes | — |
| 32 | #89753 | C22 | 1 | 6 | yes | — |
| 33 | #89751 | C22 | 1 | 3 | yes | — |
| 34 | C4⋊C4×Dic7 | C22 | 1 | 6 | yes | — |
| 35 | #89733 | C22 | 1 | 6 | yes | — |
| 36 | #89733 | C22 | 1 | 6 | yes | — |
| 37 | #89732 | C22 | 1 | 6 | yes | — |
| 38 | #89732 | C22 | 1 | 6 | yes | — |
| 39 | #89731 | C22 | 1 | 6 | yes | — |
| 40 | #89723 | C22 | 1 | 6 | yes | — |
| 41 | C22⋊C4×Dic7 | C22 | 1 | 6 | yes | — |
| 42 | #89709 | C22 | 1 | 2 | yes | — |
| 43 | C42×Dic7 | C22 | 1 | 1 | yes | characteristic |
| 44 | #89449 | C22 | 1 | 3 | yes | — |
| 45 | #89447 | C22 | 1 | 6 | yes | — |
| 46 | #89446 | C22 | 1 | 6 | yes | — |
| 47 | #89445 | C22 | 1 | 3 | yes | — |
| 48 | #89438 | C22 | 1 | 3 | yes | — |
| 49 | #89438 | C22 | 1 | 3 | yes | — |
| 50 | #36696 | — | 7 | 1 | no | maximal, Sylow |
| 51 | C22×C7×D4 | C23 | 1 | 1 | yes | characteristic |
| 52 | C22×C22⋊D7 | C23 | 1 | 6 | yes | — |
| 53 | C22×C22⋊D7 | C23 | 1 | 2 | yes | — |
| 54 | C23×Dic7 | C23 | 1 | 2 | yes | — |
| 55 | C2×#1159 | — | 4 | 6 | no | — |
| 56 | C22×D28 | C23 | 1 | 3 | yes | — |
| 57 | C22×D28 | C23 | 1 | 3 | yes | — |
| 58 | C22×C4×D7 | C23 | 1 | 3 | yes | — |
| 59 | C22×C4×D7 | C23 | 1 | 1 | yes | characteristic |
| 60 | C22×Dic14 | C23 | 1 | 1 | yes | characteristic |
| 61 | C7×#126 | — | 2 | 8 | no | — |
| 62 | C2×C7×C4⋊C4 | C23 | 1 | 6 | yes | — |
| 63 | C2×C7×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 64 | C2×C7×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 65 | C2×C7×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 66 | C2×C7×C22⋊C4 | C23 | 1 | 6 | yes | — |
| 67 | C2×C7×C22⋊C4 | C23 | 1 | 6 | yes | — |
| 68 | C2×C42×C7 | C23 | 1 | 1 | yes | characteristic |
| 69 | C2×C22⋊Dic7 | C23 | 1 | 6 | yes | — |
| 70 | C2×(C2×D7)⋊C4 | C23 | 1 | 6 | yes | — |
| 71 | C2×(C2×D7)⋊C4 | C23 | 1 | 6 | yes | — |
| 72 | C2×(C2×D7)⋊C4 | C23 | 1 | 3 | yes | — |
| 73 | C2×(C2×D7)⋊C4 | C23 | 1 | 6 | yes | — |
| 74 | C2×(C2×D7)⋊C4 | C23 | 1 | 3 | yes | — |
| 75 | C2×(C2×D7)⋊C4 | C23 | 1 | 6 | yes | — |
| 76 | C2×(C2×D7)⋊C4 | C23 | 1 | 6 | yes | — |
| 77 | C2×C4⋊Dic7 | C23 | 1 | 3 | yes | — |
| 78 | C2×C4⋊Dic7 | C23 | 1 | 6 | yes | — |
| 79 | C2×Dic7⋊C4 | C23 | 1 | 6 | yes | — |
| 80 | C2×C4×Dic7 | C23 | 1 | 6 | yes | — |
| 81 | C2×C4×Dic7 | C23 | 1 | 3 | yes | — |
| 82 | C2×C4×Dic7 | C23 | 1 | 3 | yes | — |
| 83 | #6456 | — | 4 | 6 | no | — |
| 84 | #6456 | — | 4 | 6 | no | — |
| 85 | #6455 | — | 4 | 6 | no | — |
| 86 | (C22⋊D7)⋊C4 | — | 4 | 12 | no | — |
| 87 | #6437 | — | 2 | 4 | no | — |
| 88 | C7×#95 | C23 | 1 | 3 | yes | — |
| 89 | C7×#95 | C23 | 1 | 3 | yes | — |
| 90 | C7⋊#95 | C23 | 1 | 3 | yes | — |
| 91 | C7⋊#95 | C23 | 1 | 3 | yes | — |
| 92 | C7⋊#95 | C23 | 1 | 6 | yes | — |
| 93 | C7⋊#95 | C23 | 1 | 6 | yes | — |
| 94 | C7⋊#95 | C23 | 1 | 6 | yes | — |
| 95 | C7⋊#95 | C23 | 1 | 6 | yes | — |
| 96 | #2843 | — | 7 | 1 | no | — |
| 97 | #2830 | — | 7 | 3 | no | — |
| 98 | #2829 | — | 7 | 6 | no | — |
| 99 | #2828 | — | 7 | 3 | no | — |
| 100 | #2823 | D7 | 1 | 1 | yes | characteristic, complemented |
| 101 | #2818 | — | 7 | 2 | no | — |
| 102 | #2395 | — | 7 | 3 | no | — |
| 103 | #2392 | — | 7 | 6 | no | — |
| 104 | #2388 | — | 7 | 3 | no | — |
| 105 | C4×#127 | — | 7 | 1 | no | — |
| 106 | C4×#126 | — | 7 | 2 | no | — |
| 107 | C24×C7 | C24 | 1 | 2 | yes | — |
| 108 | C23×D7 | C24 | 1 | 3 | yes | — |
| 109 | C23×D7 | C24 | 1 | 1 | yes | characteristic |
| 110 | C2×C7×D4 | — | 4 | 3 | no | — |
| 111 | C22×C4×C7 | C24 | 1 | 1 | yes | characteristic |
| 112 | C22×C4×C7 | C24 | 1 | 6 | yes | — |
| 113 | C22×C4×C7 | C24 | 1 | 3 | yes | — |
| 114 | C22×C4×C7 | C24 | 1 | 3 | yes | — |
| 115 | C2×C22⋊D7 | — | 4 | 6 | no | — |
| 116 | C2×C22⋊D7 | — | 4 | 6 | no | — |
| 117 | C2×C22⋊D7 | — | 4 | 6 | no | — |
| 118 | C2×C22⋊D7 | — | 4 | 6 | no | — |
| 119 | C22×Dic7 | — | 2 | 12 | no | — |
| 120 | C22×Dic7 | C24 | 1 | 6 | yes | — |
| 121 | C22×Dic7 | C24 | 1 | 2 | yes | — |
| 122 | C22×Dic7 | C24 | 1 | 3 | yes | — |
| 123 | C22×Dic7 | C24 | 1 | 1 | yes | characteristic |
| 124 | #1159 | — | 4 | 16 | no | — |
| 125 | C2×D28 | — | 2 | 6 | no | — |
| 126 | C2×D28 | — | 2 | 6 | no | — |
| 127 | C2×D28 | — | 4 | 3 | no | — |
| 128 | C2×D28 | — | 4 | 3 | no | — |
| 129 | C2×D28 | — | 4 | 3 | no | — |
| 130 | C2×D28 | — | 4 | 3 | no | — |
| 131 | C2×C4×D7 | — | 2 | 12 | no | — |
| 132 | C2×C4×D7 | — | 2 | 6 | no | — |
| 133 | C2×C4×D7 | — | 2 | 6 | no | — |
| 134 | C2×Dic14 | — | 4 | 3 | no | — |
| 135 | C7×C4⋊C4 | — | 2 | 12 | no | — |
| 136 | C7×C4⋊C4 | — | 4 | 3 | no | — |
| 137 | C7×C4⋊C4 | — | 4 | 3 | no | — |
| 138 | C7×C4⋊C4 | — | 4 | 3 | no | — |
| 139 | C7×C22⋊C4 | — | 2 | 12 | no | — |
| 140 | C7×C22⋊C4 | — | 4 | 6 | no | — |
| 141 | C42×C7 | #41 | 1 | 4 | yes | complemented |
| 142 | C22⋊Dic7 | — | 4 | 6 | no | — |
| 143 | (C2×D7)⋊C4 | — | 4 | 6 | no | — |
| 144 | (C2×D7)⋊C4 | — | 4 | 6 | no | — |
| 145 | (C2×D7)⋊C4 | — | 4 | 6 | no | — |
| 146 | (C2×D7)⋊C4 | — | 4 | 3 | no | — |
| 147 | (C2×D7)⋊C4 | — | 4 | 3 | no | — |
| 148 | (C2×D7)⋊C4 | — | 4 | 6 | no | — |
| 149 | (C2×D7)⋊C4 | — | 4 | 6 | no | — |
| 150 | C4⋊Dic7 | — | 4 | 3 | no | — |
| 151 | C4⋊Dic7 | — | 4 | 6 | no | — |
| 152 | Dic7⋊C4 | — | 4 | 6 | no | — |
| 153 | C4×Dic7 | — | 2 | 12 | no | — |
| 154 | C4×Dic7 | — | 2 | 6 | no | — |
| 155 | C4×Dic7 | — | 4 | 3 | no | — |
| 156 | C22×#41 | — | 7 | 1 | no | — |
| 157 | C2×#127 | — | 7 | 1 | no | — |
| 158 | C2×#126 | C2×D7 | 1 | 2 | yes | — |
| 159 | C2×C4×D4 | — | 7 | 3 | no | — |
| 160 | C2×C4×D4 | — | 7 | 3 | no | — |
| 161 | C2×C4×D4 | — | 7 | 6 | no | — |
| 162 | C2×#117 | — | 7 | 3 | no | — |
| 163 | #400 | — | 7 | 3 | no | — |
| 164 | #399 | — | 7 | 3 | no | — |
| 165 | #398 | — | 7 | 6 | no | — |
| 166 | #398 | C2×D7 | 1 | 3 | yes | — |
| 167 | #397 | — | 7 | 3 | no | — |
| 168 | #397 | — | 7 | 6 | no | — |
| 169 | #397 | — | 7 | 6 | no | — |
| 170 | #396 | — | 7 | 6 | no | — |
| 171 | #396 | C2×D7 | 1 | 6 | yes | — |
| 172 | #395 | — | 7 | 3 | no | — |
| 173 | #394 | — | 7 | 6 | no | — |
| 174 | #394 | — | 7 | 6 | no | — |
| 175 | #394 | — | 7 | 6 | no | — |
| 176 | #394 | — | 7 | 6 | no | — |
| 177 | #394 | — | 7 | 6 | no | — |
| 178 | #394 | C2×D7 | 1 | 3 | yes | — |
| 179 | #393 | — | 7 | 3 | no | — |
| 180 | #392 | — | 7 | 3 | no | — |
| 181 | #392 | — | 7 | 6 | no | — |
| 182 | #392 | — | 7 | 6 | no | — |
| 183 | #390 | — | 7 | 3 | no | — |
| 184 | #390 | — | 7 | 3 | no | — |
| 185 | #388 | — | 7 | 6 | no | — |
| 186 | #387 | — | 7 | 6 | no | — |
| 187 | #384 | C2×D7 | 1 | 1 | yes | characteristic |
| 188 | #383 | — | 7 | 2 | no | — |
| 189 | C4×C4⋊C4 | — | 7 | 6 | no | — |
| 190 | C4×C22⋊C4 | — | 7 | 6 | no | — |
| 191 | C4×C22⋊C4 | — | 7 | 3 | no | — |
| 192 | C4×C22⋊C4 | — | 7 | 3 | no | — |
| 193 | C43 | — | 7 | 1 | no | — |
| 194 | C23×C7 | — | 2 | 2 | no | — |
| 195 | C23×C7 | — | 2 | 6 | no | — |
| 196 | C23×C7 | — | 2 | 6 | no | — |
| 197 | C23×C7 | C25 | 1 | 1 | yes | characteristic |
| 198 | C22×D7 | — | 2 | 3 | no | — |
| 199 | C22×D7 | — | 2 | 1 | no | — |
| 200 | C22×D7 | — | 2 | 3 | no | — |
| 201 | C22×D7 | — | 2 | 6 | no | — |
| 202 | C22×D7 | — | 2 | 3 | no | — |
| 203 | C22×D7 | — | 2 | 3 | no | — |
| 204 | C22×D7 | — | 2 | 6 | no | — |
| 205 | C22×D7 | — | 2 | 3 | no | — |
| 206 | C7×D4 | — | 4 | 4 | no | — |
| 207 | C2×C4×C7 | — | 2 | 3 | no | — |
| 208 | C2×C4×C7 | — | 2 | 3 | no | — |
| 209 | C2×C4×C7 | — | 2 | 6 | no | — |
| 210 | C2×C4×C7 | — | 2 | 6 | no | — |
| 211 | C2×C4×C7 | — | 2 | 6 | no | — |
| 212 | C2×C4×C7 | — | 2 | 3 | no | — |
| 213 | C2×C4×C7 | — | 2 | 3 | no | — |
| 214 | C2×C4×C7 | — | 2 | 6 | no | — |
| 215 | C2×C4×C7 | C2×#41 | 1 | 6 | yes | — |
| 216 | C22⋊D7 | — | 4 | 8 | no | — |
| 217 | C22⋊D7 | — | 4 | 24 | no | — |
| 218 | C2×Dic7 | — | 2 | 6 | no | — |
| 219 | C2×Dic7 | — | 2 | 3 | no | — |
| 220 | C2×Dic7 | — | 2 | 6 | no | — |
| 221 | C2×Dic7 | — | 2 | 6 | no | — |
| 222 | C2×Dic7 | — | 2 | 6 | no | — |
| 223 | C2×Dic7 | — | 2 | 6 | no | — |
| 224 | C2×Dic7 | — | 4 | 8 | no | — |
| 225 | C2×Dic7 | H(5,𝔽2) | 1 | 6 | yes | — |
| 226 | D28 | — | 4 | 12 | no | — |
| 227 | D28 | — | 4 | 12 | no | — |
| 228 | C4×D7 | — | 4 | 12 | no | — |
| 229 | C4×D7 | — | 4 | 4 | no | — |
| 230 | Dic14 | — | 4 | 4 | no | — |
| 231 | C2×#41 | — | 28 | 6 | no | — |
| 232 | C22×Q8 | — | 7 | 1 | no | — |
| 233 | C22×D4 | — | 7 | 6 | no | — |
| 234 | C22×D4 | — | 7 | 2 | no | — |
| 235 | C22×D4 | — | 7 | 3 | no | — |
| 236 | C22×D4 | — | 7 | 3 | no | — |
| 237 | C22×D4 | C22×D7 | 1 | 1 | yes | characteristic |
| 238 | C23×C4 | — | 7 | 2 | no | — |
| 239 | C23×C4 | — | 7 | 3 | no | — |
| 240 | C23×C4 | — | 7 | 1 | no | — |
| 241 | #127 | — | 14 | 4 | no | — |
| 242 | #126 | — | 2 | 8 | no | — |
| 243 | C4×D4 | — | 28 | 12 | no | — |
| 244 | C4×D4 | — | 28 | 6 | no | — |
| 245 | C4×D4 | — | 28 | 6 | no | — |
| 246 | #117 | — | 28 | 6 | no | — |
| 247 | C2×C4⋊C4 | — | 7 | 3 | no | — |
| 248 | C2×C4⋊C4 | — | 7 | 6 | no | — |
| 249 | C2×C4⋊C4 | — | 7 | 6 | no | — |
| 250 | C2×C4⋊C4 | C22×D7 | 1 | 6 | yes | — |
| 251 | C2×C4⋊C4 | C22×D7 | 1 | 3 | yes | — |
| 252 | C2×C4⋊C4 | C22×D7 | 1 | 3 | yes | — |
| 253 | C2×C4⋊C4 | C22×D7 | 1 | 3 | yes | — |
| 254 | C2×C22⋊C4 | — | 7 | 6 | no | — |
| 255 | C2×C22⋊C4 | — | 7 | 6 | no | — |
| 256 | C2×C22⋊C4 | — | 7 | 3 | no | — |
| 257 | C2×C22⋊C4 | — | 7 | 6 | no | — |
| 258 | C2×C22⋊C4 | — | 7 | 3 | no | — |
| 259 | C2×C22⋊C4 | — | 7 | 6 | no | — |
| 260 | C2×C22⋊C4 | — | 7 | 6 | no | — |
| 261 | C2×C22⋊C4 | — | 7 | 6 | no | — |
| 262 | C2×C22⋊C4 | C22×D7 | 1 | 6 | yes | — |
| 263 | C2×C22⋊C4 | C22×D7 | 1 | 6 | yes | — |
| 264 | C2×C42 | — | 7 | 6 | no | — |
| 265 | C2×C42 | — | 7 | 3 | no | — |
| 266 | C2×C42 | — | 7 | 3 | no | — |
| 267 | C2×C42 | C22×D7 | 1 | 1 | yes | characteristic |
| 268 | #95 | — | 7 | 6 | no | — |
| 269 | #95 | — | 7 | 6 | no | — |
| 270 | #95 | — | 7 | 3 | no | — |
| 271 | #95 | — | 7 | 3 | no | — |
| 272 | #95 | — | 7 | 6 | no | — |
| 273 | #95 | — | 7 | 6 | no | — |
| 274 | #95 | C22×D7 | 1 | 3 | yes | — |
| 275 | #95 | C22×D7 | 1 | 3 | yes | — |
| 276 | C22×C7 | — | 4 | 6 | no | — |
| 277 | C22×C7 | — | 4 | 2 | no | — |
| 278 | C22×C7 | — | 4 | 6 | no | — |
| 279 | C22×C7 | C22×#41 | 1 | 1 | yes | characteristic |
| 280 | C22×C7 | C2×H(5,𝔽2) | 1 | 3 | yes | — |
| 281 | C22×C7 | #585 | 1 | 3 | yes | — |
| 282 | C2×D7 | — | 4 | 3 | no | — |
| 283 | C2×D7 | — | 4 | 6 | no | — |
| 284 | C2×D7 | — | 4 | 3 | no | — |
| 285 | C2×D7 | — | 4 | 1 | no | — |
| 286 | C2×D7 | — | 4 | 3 | no | — |
| 287 | C2×D7 | — | 4 | 6 | no | — |
| 288 | C2×D7 | — | 4 | 3 | no | — |
| 289 | C2×D7 | — | 4 | 3 | no | — |
| 290 | C4×C7 | — | 2 | 6 | no | — |
| 291 | C4×C7 | — | 4 | 6 | no | — |
| 292 | C4×C7 | — | 4 | 1 | no | — |
| 293 | C4×C7 | — | 4 | 3 | no | — |
| 294 | Dic7 | — | 4 | 2 | no | — |
| 295 | Dic7 | — | 4 | 3 | no | — |
| 296 | Dic7 | — | 4 | 6 | no | — |
| 297 | Dic7 | #560 | 1 | 4 | yes | — |
| 298 | C24 | — | 7 | 3 | no | — |
| 299 | C24 | — | 7 | 1 | no | — |
| 300 | C24 | C23×D7 | 1 | 2 | yes | — |
| 301 | #41 | — | 28 | 16 | no | — |
| 302 | C2×Q8 | — | 28 | 3 | no | — |
| 303 | C2×D4 | — | 4 | 3 | no | — |
| 304 | C2×D4 | — | 14 | 6 | no | — |
| 305 | C2×D4 | — | 14 | 6 | no | — |
| 306 | C2×D4 | — | 28 | 3 | no | — |
| 307 | C2×D4 | — | 28 | 3 | no | — |
| 308 | C2×D4 | — | 28 | 3 | no | — |
| 309 | C2×D4 | — | 28 | 3 | no | — |
| 310 | C2×D4 | — | 28 | 6 | no | — |
| 311 | C2×D4 | — | 28 | 6 | no | — |
| 312 | C2×D4 | — | 28 | 6 | no | — |
| 313 | C2×D4 | — | 28 | 6 | no | — |
| 314 | C22×C4 | — | 7 | 1 | no | — |
| 315 | C22×C4 | — | 7 | 6 | no | — |
| 316 | C22×C4 | — | 7 | 2 | no | — |
| 317 | C22×C4 | — | 7 | 3 | no | — |
| 318 | C22×C4 | — | 14 | 6 | no | — |
| 319 | C22×C4 | — | 14 | 12 | no | — |
| 320 | C22×C4 | — | 14 | 6 | no | — |
| 321 | C22×C4 | — | 14 | 12 | no | — |
| 322 | C22×C4 | C23×D7 | 1 | 1 | yes | characteristic |
| 323 | C22×C4 | C23×D7 | 1 | 6 | yes | — |
| 324 | C22×C4 | C23×D7 | 1 | 3 | yes | — |
| 325 | C22×C4 | C23×D7 | 1 | 3 | yes | — |
| 326 | C4⋊C4 | — | 2 | 12 | no | — |
| 327 | C4⋊C4 | — | 4 | 3 | no | — |
| 328 | C4⋊C4 | — | 4 | 3 | no | — |
| 329 | C4⋊C4 | — | 4 | 3 | no | — |
| 330 | C4⋊C4 | — | 28 | 6 | no | — |
| 331 | C4⋊C4 | — | 28 | 6 | no | — |
| 332 | C4⋊C4 | — | 28 | 3 | no | — |
| 333 | C22⋊C4 | — | 2 | 12 | no | — |
| 334 | C22⋊C4 | — | 4 | 6 | no | — |
| 335 | C22⋊C4 | — | 28 | 6 | no | — |
| 336 | C22⋊C4 | — | 28 | 6 | no | — |
| 337 | C22⋊C4 | — | 28 | 6 | no | — |
| 338 | C22⋊C4 | — | 28 | 6 | no | — |
| 339 | C22⋊C4 | — | 28 | 6 | no | — |
| 340 | C22⋊C4 | — | 28 | 3 | no | — |
| 341 | C22⋊C4 | — | 28 | 3 | no | — |
| 342 | C22⋊C4 | — | 28 | 6 | no | — |
| 343 | C42 | — | 14 | 12 | no | — |
| 344 | C42 | — | 14 | 6 | no | — |
| 345 | C42 | — | 28 | 3 | no | — |
| 346 | C42 | #1159 | 1 | 4 | yes | complemented |
| 347 | C2×C7 | — | 8 | 2 | no | — |
| 348 | C2×C7 | #3460 | 1 | 3 | yes | — |
| 349 | C2×C7 | C2×#560 | 1 | 1 | yes | characteristic |
| 350 | C2×C7 | #3529 | 1 | 3 | yes | — |
| 351 | D7 | — | 8 | 1 | no | — |
| 352 | D7 | — | 8 | 3 | no | — |
| 353 | C23 | — | 2 | 2 | no | — |
| 354 | C23 | — | 2 | 6 | no | — |
| 355 | C23 | — | 2 | 6 | no | — |
| 356 | C23 | — | 14 | 3 | no | — |
| 357 | C23 | — | 14 | 1 | no | — |
| 358 | C23 | — | 14 | 3 | no | — |
| 359 | C23 | — | 14 | 6 | no | — |
| 360 | C23 | — | 14 | 3 | no | — |
| 361 | C23 | — | 14 | 3 | no | — |
| 362 | C23 | — | 14 | 6 | no | — |
| 363 | C23 | — | 14 | 3 | no | — |
| 364 | C23 | C24×D7 | 1 | 1 | yes | characteristic |
| 365 | Q8 | — | 28 | 4 | no | — |
| 366 | D4 | — | 4 | 4 | no | — |
| 367 | D4 | — | 28 | 12 | no | — |
| 368 | D4 | — | 28 | 12 | no | — |
| 369 | D4 | — | 28 | 24 | no | — |
| 370 | D4 | — | 28 | 8 | no | — |
| 371 | C2×C4 | — | 2 | 3 | no | — |
| 372 | C2×C4 | — | 2 | 3 | no | — |
| 373 | C2×C4 | — | 2 | 6 | no | — |
| 374 | C2×C4 | — | 2 | 6 | no | — |
| 375 | C2×C4 | — | 2 | 6 | no | — |
| 376 | C2×C4 | — | 2 | 3 | no | — |
| 377 | C2×C4 | — | 2 | 3 | no | — |
| 378 | C2×C4 | — | 2 | 6 | no | — |
| 379 | C2×C4 | — | 7 | 6 | no | — |
| 380 | C2×C4 | — | 14 | 3 | no | — |
| 381 | C2×C4 | — | 14 | 6 | no | — |
| 382 | C2×C4 | — | 14 | 6 | no | — |
| 383 | C2×C4 | — | 14 | 6 | no | — |
| 384 | C2×C4 | — | 14 | 6 | no | — |
| 385 | C2×C4 | — | 14 | 6 | no | — |
| 386 | C2×C4 | — | 28 | 12 | no | — |
| 387 | C2×C4 | — | 28 | 4 | no | — |
| 388 | C2×C4 | — | 28 | 8 | no | — |
| 389 | C2×C4 | C2×#1159 | 1 | 6 | yes | — |
| 390 | C7 | #36696 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 391 | C22 | — | 4 | 2 | no | — |
| 392 | C22 | — | 4 | 6 | no | — |
| 393 | C22 | — | 4 | 6 | no | — |
| 394 | C22 | — | 28 | 1 | no | — |
| 395 | C22 | — | 28 | 3 | no | — |
| 396 | C22 | — | 28 | 6 | no | — |
| 397 | C22 | — | 28 | 3 | no | — |
| 398 | C22 | — | 28 | 3 | no | — |
| 399 | C22 | — | 28 | 3 | no | — |
| 400 | C22 | — | 28 | 6 | no | — |
| 401 | C22 | — | 28 | 3 | no | — |
| 402 | C22 | C22×#1159 | 1 | 1 | yes | characteristic |
| 403 | C22 | D7×H(5,𝔽2) | 1 | 3 | yes | — |
| 404 | C22 | #90620 | 1 | 3 | yes | — |
| 405 | C4 | — | 2 | 6 | no | — |
| 406 | C4 | — | 4 | 1 | no | — |
| 407 | C4 | — | 4 | 3 | no | — |
| 408 | C4 | — | 4 | 6 | no | — |
| 409 | C4 | — | 7 | 4 | no | — |
| 410 | C4 | — | 28 | 2 | no | — |
| 411 | C4 | — | 28 | 6 | no | — |
| 412 | C4 | — | 28 | 3 | no | — |
| 413 | C2 | — | 8 | 2 | no | — |
| 414 | C2 | — | 56 | 1 | no | — |
| 415 | C2 | — | 56 | 3 | no | — |
| 416 | C2 | #11743432 | 1 | 3 | yes | — |
| 417 | C2 | D7×#560 | 1 | 1 | yes | characteristic |
| 418 | C2 | #11744183 | 1 | 3 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D7 |
| commutator, socle, cosocle | C23×C7 | C25 |
| Fitting | C7×#2823 | C2 |
| hypercenter | #2823 | D7 |
| hypocenter | C7 | #36696 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ #2823 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C7×#2823 | C2 | semidirect |
| 2. #11740563 | C2 | semidirect |
| 3. Dic7×#126 | C2 | semidirect |
| 4. #11735457 | C2 | semidirect |
| 5. #11735183 | C2 | semidirect |
| 6. #11734900 | C2 | semidirect |
| 7. #11734726 | C2 | semidirect |
| 8. #11734612 | C2 | semidirect |
| 9. #11734334 | C2 | semidirect |
| 10. #11731799 | C2 | semidirect |
| 11. #11731764 | C2 | semidirect |
| 100. #2823 | D7 | semidirect |
| 141. C42×C7 | #41 | semidirect |
| 346. C42 | #1159 | semidirect |
| 390. C7 | #36696 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2823 | 2 |
| #11740563 | 2 |
| Dic7×#126 | 2 |
| #11735457 | 2 |
| #11735183 | 2 |
| #11734900 | 2 |
| #11734726 | 2 |
| #11734612 | 2 |
| #11734334 | 2 |
| #11731799 | 2 |
| #11731764 | 2 |
| #36696 | 7 |