Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1716 conjugacy classes of subgroups.
The subgroup lattice has 454 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C7×#2402 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11735851 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #11735771 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #11735456 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #11735380 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #11731222 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #11731221 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11731221 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #11731062 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #11730863 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #11730830 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×C4×D28 | C22 | 1 | 2 | yes | — |
| 13 | C2×C4×D28 | C22 | 1 | 4 | yes | — |
| 14 | C2×C4×D28 | C22 | 1 | 4 | yes | — |
| 15 | C2×#6435 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×#6435 | C22 | 1 | 4 | yes | — |
| 17 | C7×#400 | C22 | 1 | 4 | yes | — |
| 18 | C7×#398 | C22 | 1 | 4 | yes | — |
| 19 | C4×C7×C4⋊C4 | C22 | 1 | 4 | yes | — |
| 20 | C4×C7×C4⋊C4 | C22 | 1 | 2 | yes | — |
| 21 | C7×#376 | C22 | 1 | 1 | yes | characteristic |
| 22 | #89766 | C22 | 1 | 4 | yes | — |
| 23 | #89766 | C22 | 1 | 4 | yes | — |
| 24 | #89766 | C22 | 1 | 4 | yes | — |
| 25 | #89765 | C22 | 1 | 4 | yes | — |
| 26 | #89764 | C22 | 1 | 4 | yes | — |
| 27 | #89763 | C22 | 1 | 4 | yes | — |
| 28 | #89763 | C22 | 1 | 4 | yes | — |
| 29 | #89763 | C22 | 1 | 4 | yes | — |
| 30 | #89763 | C22 | 1 | 4 | yes | — |
| 31 | #89760 | C22 | 1 | 4 | yes | — |
| 32 | #89756 | C22 | 1 | 4 | yes | — |
| 33 | #89745 | C22 | 1 | 4 | yes | — |
| 34 | C4×(C2×D7)⋊C4 | C22 | 1 | 2 | yes | — |
| 35 | C4×(C2×D7)⋊C4 | C22 | 1 | 4 | yes | — |
| 36 | C4×(C2×D7)⋊C4 | C22 | 1 | 4 | yes | — |
| 37 | C4×Dic7⋊C4 | C22 | 1 | 2 | yes | — |
| 38 | C42×Dic7 | C22 | 1 | 1 | yes | characteristic |
| 39 | #89449 | C22 | 1 | 4 | yes | — |
| 40 | #89447 | C22 | 1 | 4 | yes | — |
| 41 | #89447 | C22 | 1 | 4 | yes | — |
| 42 | #89446 | C22 | 1 | 2 | yes | — |
| 43 | #89446 | C22 | 1 | 4 | yes | — |
| 44 | #89444 | C22 | 1 | 4 | yes | — |
| 45 | #89444 | C22 | 1 | 2 | yes | — |
| 46 | #89444 | C22 | 1 | 4 | yes | — |
| 47 | #89443 | C22 | 1 | 2 | yes | — |
| 48 | #89443 | C22 | 1 | 4 | yes | — |
| 49 | #89443 | C22 | 1 | 4 | yes | — |
| 50 | #89441 | C22 | 1 | 4 | yes | — |
| 51 | #89441 | C22 | 1 | 4 | yes | — |
| 52 | #89441 | C22 | 1 | 4 | yes | — |
| 53 | #89433 | C22 | 1 | 4 | yes | — |
| 54 | #89433 | C22 | 1 | 2 | yes | — |
| 55 | #89432 | C22 | 1 | 4 | yes | — |
| 56 | #89424 | C22 | 1 | 4 | yes | — |
| 57 | #36692 | — | 7 | 1 | no | maximal, Sylow |
| 58 | C22×D28 | C23 | 1 | 2 | yes | — |
| 59 | C22×D28 | C23 | 1 | 4 | yes | — |
| 60 | C22×D28 | C23 | 1 | 4 | yes | — |
| 61 | C22×C4×D7 | C23 | 1 | 1 | yes | characteristic |
| 62 | C22×C4×D7 | C23 | 1 | 4 | yes | — |
| 63 | C2×C7×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 64 | C2×C7×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 65 | C2×C7×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 66 | C2×C42×C7 | C23 | 1 | 4 | yes | — |
| 67 | C2×C42×C7 | C23 | 1 | 2 | yes | — |
| 68 | C2×C42×C7 | C23 | 1 | 1 | yes | characteristic |
| 69 | C2×(C2×D7)⋊C4 | C23 | 1 | 2 | yes | — |
| 70 | C2×(C2×D7)⋊C4 | C23 | 1 | 4 | yes | — |
| 71 | C2×(C2×D7)⋊C4 | C23 | 1 | 4 | yes | — |
| 72 | C2×(C2×D7)⋊C4 | C23 | 1 | 4 | yes | — |
| 73 | C2×(C2×D7)⋊C4 | C23 | 1 | 4 | yes | — |
| 74 | C2×(C2×D7)⋊C4 | C23 | 1 | 4 | yes | — |
| 75 | C2×(C2×D7)⋊C4 | C23 | 1 | 4 | yes | — |
| 76 | C2×(C2×D7)⋊C4 | C23 | 1 | 4 | yes | — |
| 77 | C2×(C2×D7)⋊C4 | C23 | 1 | 4 | yes | — |
| 78 | C2×(C2×D7)⋊C4 | C23 | 1 | 4 | yes | — |
| 79 | C2×(C2×D7)⋊C4 | C23 | 1 | 4 | yes | — |
| 80 | C2×(C2×D7)⋊C4 | C23 | 1 | 4 | yes | — |
| 81 | C2×(C2×D7)⋊C4 | C23 | 1 | 4 | yes | — |
| 82 | C2×C4⋊Dic7 | C23 | 1 | 2 | yes | — |
| 83 | C2×C4⋊Dic7 | C23 | 1 | 4 | yes | — |
| 84 | C2×C4⋊Dic7 | C23 | 1 | 4 | yes | — |
| 85 | C2×Dic7⋊C4 | C23 | 1 | 2 | yes | — |
| 86 | C2×Dic7⋊C4 | C23 | 1 | 4 | yes | — |
| 87 | C2×Dic7⋊C4 | C23 | 1 | 4 | yes | — |
| 88 | C2×Dic7⋊C4 | C23 | 1 | 4 | yes | — |
| 89 | C2×C4×Dic7 | C23 | 1 | 2 | yes | — |
| 90 | C2×C4×Dic7 | C23 | 1 | 1 | yes | characteristic |
| 91 | C2×C4×Dic7 | C23 | 1 | 4 | yes | — |
| 92 | C4×D28 | — | 2 | 8 | no | — |
| 93 | C4×D28 | — | 4 | 8 | no | — |
| 94 | C4×D28 | — | 4 | 8 | no | — |
| 95 | #6435 | — | 2 | 4 | no | — |
| 96 | #6435 | — | 4 | 8 | no | — |
| 97 | C7×#95 | C23 | 1 | 4 | yes | — |
| 98 | C7×#95 | C23 | 1 | 4 | yes | — |
| 99 | C7×#95 | C23 | 1 | 2 | yes | — |
| 100 | C7×#95 | C23 | 1 | 4 | yes | — |
| 101 | C7×#95 | C23 | 1 | 2 | yes | — |
| 102 | C7⋊#95 | C23 | 1 | 4 | yes | — |
| 103 | C7⋊#95 | C23 | 1 | 4 | yes | — |
| 104 | C7⋊#95 | C23 | 1 | 4 | yes | — |
| 105 | C7⋊#95 | C23 | 1 | 4 | yes | — |
| 106 | C7⋊#95 | C23 | 1 | 4 | yes | — |
| 107 | C7⋊#95 | C23 | 1 | 4 | yes | — |
| 108 | #2837 | — | 7 | 4 | no | — |
| 109 | #2836 | — | 7 | 4 | no | — |
| 110 | #2829 | — | 7 | 4 | no | — |
| 111 | #2828 | — | 7 | 4 | no | — |
| 112 | #2402 | D7 | 1 | 1 | yes | characteristic, complemented |
| 113 | #2397 | — | 7 | 1 | no | — |
| 114 | #2395 | — | 7 | 4 | no | — |
| 115 | #2392 | — | 7 | 2 | no | — |
| 116 | #2392 | — | 7 | 4 | no | — |
| 117 | #2298 | — | 7 | 1 | no | — |
| 118 | #2293 | — | 7 | 2 | no | — |
| 119 | C23×D7 | C24 | 1 | 1 | yes | characteristic |
| 120 | C23×D7 | C24 | 1 | 4 | yes | — |
| 121 | C22×C4×C7 | C24 | 1 | 4 | yes | — |
| 122 | C22×C4×C7 | C24 | 1 | 4 | yes | — |
| 123 | C22×C4×C7 | C24 | 1 | 4 | yes | — |
| 124 | C22×C4×C7 | C24 | 1 | 2 | yes | — |
| 125 | C22×C4×C7 | C24 | 1 | 1 | yes | characteristic |
| 126 | C22×Dic7 | C24 | 1 | 2 | yes | — |
| 127 | C22×Dic7 | C24 | 1 | 4 | yes | — |
| 128 | C22×Dic7 | C24 | 1 | 1 | yes | characteristic |
| 129 | C22×Dic7 | C24 | 1 | 4 | yes | — |
| 130 | C2×D28 | — | 2 | 4 | no | — |
| 131 | C2×D28 | — | 4 | 4 | no | — |
| 132 | C2×D28 | — | 4 | 4 | no | — |
| 133 | C2×D28 | — | 4 | 4 | no | — |
| 134 | C2×D28 | — | 4 | 4 | no | — |
| 135 | C2×D28 | — | 4 | 4 | no | — |
| 136 | C2×D28 | — | 4 | 4 | no | — |
| 137 | C2×D28 | — | 4 | 4 | no | — |
| 138 | C2×C4×D7 | — | 2 | 2 | no | — |
| 139 | C2×C4×D7 | — | 2 | 8 | no | — |
| 140 | C2×C4×D7 | — | 2 | 8 | no | — |
| 141 | C2×C4×D7 | — | 2 | 4 | no | — |
| 142 | C2×C4×D7 | — | 2 | 8 | no | — |
| 143 | C7×C4⋊C4 | — | 4 | 4 | no | — |
| 144 | C7×C4⋊C4 | — | 4 | 4 | no | — |
| 145 | C7×C4⋊C4 | — | 4 | 4 | no | — |
| 146 | C42×C7 | — | 2 | 8 | no | — |
| 147 | C42×C7 | — | 2 | 4 | no | — |
| 148 | C42×C7 | #41 | 1 | 4 | yes | — |
| 149 | (C2×D7)⋊C4 | — | 2 | 4 | no | — |
| 150 | (C2×D7)⋊C4 | — | 2 | 8 | no | — |
| 151 | (C2×D7)⋊C4 | — | 4 | 4 | no | — |
| 152 | (C2×D7)⋊C4 | — | 4 | 4 | no | — |
| 153 | (C2×D7)⋊C4 | — | 4 | 4 | no | — |
| 154 | (C2×D7)⋊C4 | — | 4 | 4 | no | — |
| 155 | (C2×D7)⋊C4 | — | 4 | 4 | no | — |
| 156 | (C2×D7)⋊C4 | — | 4 | 4 | no | — |
| 157 | (C2×D7)⋊C4 | — | 4 | 4 | no | — |
| 158 | (C2×D7)⋊C4 | — | 4 | 4 | no | — |
| 159 | (C2×D7)⋊C4 | — | 4 | 4 | no | — |
| 160 | (C2×D7)⋊C4 | — | 4 | 4 | no | — |
| 161 | (C2×D7)⋊C4 | — | 4 | 4 | no | — |
| 162 | C4⋊Dic7 | — | 2 | 4 | no | — |
| 163 | C4⋊Dic7 | — | 4 | 4 | no | — |
| 164 | C4⋊Dic7 | — | 4 | 4 | no | — |
| 165 | Dic7⋊C4 | — | 2 | 4 | no | — |
| 166 | Dic7⋊C4 | — | 4 | 4 | no | — |
| 167 | Dic7⋊C4 | — | 4 | 4 | no | — |
| 168 | Dic7⋊C4 | — | 4 | 4 | no | — |
| 169 | C4×Dic7 | — | 2 | 2 | no | — |
| 170 | C4×Dic7 | — | 2 | 4 | no | — |
| 171 | C4×Dic7 | — | 4 | 4 | no | — |
| 172 | C2×C4×D4 | — | 7 | 2 | no | — |
| 173 | C2×C4×D4 | — | 7 | 4 | no | — |
| 174 | C2×C4×D4 | — | 7 | 4 | no | — |
| 175 | C2×#117 | — | 7 | 1 | no | — |
| 176 | C2×#117 | — | 7 | 4 | no | — |
| 177 | #400 | — | 7 | 4 | no | — |
| 178 | #400 | C2×D7 | 1 | 4 | yes | — |
| 179 | #399 | — | 7 | 4 | no | — |
| 180 | #399 | — | 7 | 4 | no | — |
| 181 | #398 | — | 7 | 4 | no | — |
| 182 | #398 | — | 7 | 4 | no | — |
| 183 | #398 | — | 7 | 2 | no | — |
| 184 | #398 | C2×D7 | 1 | 4 | yes | — |
| 185 | #397 | — | 7 | 4 | no | — |
| 186 | #397 | — | 7 | 4 | no | — |
| 187 | #397 | — | 7 | 4 | no | — |
| 188 | #397 | — | 7 | 4 | no | — |
| 189 | #397 | — | 7 | 2 | no | — |
| 190 | #396 | — | 7 | 4 | no | — |
| 191 | #396 | — | 7 | 4 | no | — |
| 192 | #396 | — | 7 | 4 | no | — |
| 193 | #394 | — | 7 | 4 | no | — |
| 194 | #394 | — | 7 | 4 | no | — |
| 195 | #394 | — | 7 | 4 | no | — |
| 196 | #394 | — | 7 | 4 | no | — |
| 197 | #394 | — | 7 | 4 | no | — |
| 198 | #394 | — | 7 | 4 | no | — |
| 199 | #394 | — | 7 | 2 | no | — |
| 200 | #392 | — | 7 | 2 | no | — |
| 201 | #392 | — | 7 | 4 | no | — |
| 202 | #392 | — | 7 | 4 | no | — |
| 203 | #390 | — | 7 | 4 | no | — |
| 204 | #389 | — | 7 | 4 | no | — |
| 205 | #388 | — | 7 | 4 | no | — |
| 206 | #388 | — | 7 | 4 | no | — |
| 207 | #388 | — | 7 | 4 | no | — |
| 208 | #387 | — | 7 | 4 | no | — |
| 209 | C4×C4⋊C4 | — | 7 | 2 | no | — |
| 210 | C4×C4⋊C4 | C2×D7 | 1 | 4 | yes | — |
| 211 | C4×C4⋊C4 | C2×D7 | 1 | 2 | yes | — |
| 212 | C4×C22⋊C4 | — | 7 | 2 | no | — |
| 213 | C4×C22⋊C4 | — | 7 | 4 | no | — |
| 214 | C4×C22⋊C4 | — | 7 | 4 | no | — |
| 215 | #376 | C2×D7 | 1 | 1 | yes | characteristic |
| 216 | C43 | — | 7 | 1 | no | — |
| 217 | C23×C7 | C25 | 1 | 1 | yes | characteristic |
| 218 | C22×D7 | — | 2 | 1 | no | — |
| 219 | C22×D7 | — | 2 | 4 | no | — |
| 220 | C22×D7 | — | 2 | 4 | no | — |
| 221 | C22×D7 | — | 2 | 2 | no | — |
| 222 | C22×D7 | — | 2 | 4 | no | — |
| 223 | C22×D7 | — | 2 | 4 | no | — |
| 224 | C22×D7 | — | 2 | 4 | no | — |
| 225 | C22×D7 | — | 2 | 4 | no | — |
| 226 | C22×D7 | — | 2 | 4 | no | — |
| 227 | C22×D7 | — | 2 | 4 | no | — |
| 228 | C2×C4×C7 | — | 2 | 4 | no | — |
| 229 | C2×C4×C7 | — | 2 | 4 | no | — |
| 230 | C2×C4×C7 | — | 2 | 4 | no | — |
| 231 | C2×C4×C7 | — | 2 | 4 | no | — |
| 232 | C2×C4×C7 | — | 2 | 4 | no | — |
| 233 | C2×C4×C7 | — | 2 | 4 | no | — |
| 234 | C2×C4×C7 | — | 2 | 4 | no | — |
| 235 | C2×C4×C7 | — | 2 | 4 | no | — |
| 236 | C2×C4×C7 | — | 2 | 4 | no | — |
| 237 | C2×C4×C7 | — | 2 | 4 | no | — |
| 238 | C2×C4×C7 | C2×#41 | 1 | 4 | yes | — |
| 239 | C2×C4×C7 | C2×#41 | 1 | 2 | yes | — |
| 240 | C2×C4×C7 | H(5,𝔽2) | 1 | 4 | yes | — |
| 241 | C2×Dic7 | — | 2 | 2 | no | — |
| 242 | C2×Dic7 | — | 2 | 1 | no | — |
| 243 | C2×Dic7 | — | 2 | 4 | no | — |
| 244 | C2×Dic7 | — | 2 | 4 | no | — |
| 245 | C2×Dic7 | — | 2 | 4 | no | — |
| 246 | C2×Dic7 | — | 2 | 2 | no | — |
| 247 | C2×Dic7 | — | 2 | 4 | no | — |
| 248 | C2×Dic7 | — | 2 | 4 | no | — |
| 249 | C2×Dic7 | — | 2 | 4 | no | — |
| 250 | C2×Dic7 | — | 2 | 4 | no | — |
| 251 | D28 | — | 4 | 8 | no | — |
| 252 | D28 | — | 4 | 16 | no | — |
| 253 | D28 | — | 4 | 16 | no | — |
| 254 | C4×D7 | — | 4 | 4 | no | — |
| 255 | C4×D7 | — | 4 | 16 | no | — |
| 256 | C22×D4 | — | 7 | 2 | no | — |
| 257 | C22×D4 | — | 7 | 4 | no | — |
| 258 | C22×D4 | — | 7 | 4 | no | — |
| 259 | C23×C4 | — | 7 | 1 | no | — |
| 260 | C23×C4 | — | 7 | 4 | no | — |
| 261 | C4×D4 | — | 14 | 8 | no | — |
| 262 | C4×D4 | — | 28 | 8 | no | — |
| 263 | C4×D4 | — | 28 | 8 | no | — |
| 264 | #117 | — | 14 | 4 | no | — |
| 265 | #117 | — | 28 | 8 | no | — |
| 266 | C2×C4⋊C4 | — | 7 | 2 | no | — |
| 267 | C2×C4⋊C4 | — | 7 | 2 | no | — |
| 268 | C2×C4⋊C4 | — | 7 | 4 | no | — |
| 269 | C2×C4⋊C4 | — | 7 | 4 | no | — |
| 270 | C2×C4⋊C4 | — | 7 | 4 | no | — |
| 271 | C2×C4⋊C4 | — | 7 | 4 | no | — |
| 272 | C2×C4⋊C4 | — | 7 | 4 | no | — |
| 273 | C2×C4⋊C4 | C22×D7 | 1 | 4 | yes | — |
| 274 | C2×C4⋊C4 | C22×D7 | 1 | 4 | yes | — |
| 275 | C2×C4⋊C4 | C22×D7 | 1 | 4 | yes | — |
| 276 | C2×C22⋊C4 | — | 7 | 2 | no | — |
| 277 | C2×C22⋊C4 | — | 7 | 4 | no | — |
| 278 | C2×C22⋊C4 | — | 7 | 4 | no | — |
| 279 | C2×C22⋊C4 | — | 7 | 4 | no | — |
| 280 | C2×C22⋊C4 | — | 7 | 4 | no | — |
| 281 | C2×C22⋊C4 | — | 7 | 4 | no | — |
| 282 | C2×C22⋊C4 | — | 7 | 4 | no | — |
| 283 | C2×C22⋊C4 | — | 7 | 4 | no | — |
| 284 | C2×C22⋊C4 | — | 7 | 4 | no | — |
| 285 | C2×C22⋊C4 | — | 7 | 4 | no | — |
| 286 | C2×C22⋊C4 | — | 7 | 4 | no | — |
| 287 | C2×C22⋊C4 | — | 7 | 4 | no | — |
| 288 | C2×C22⋊C4 | — | 7 | 4 | no | — |
| 289 | C2×C42 | — | 7 | 2 | no | — |
| 290 | C2×C42 | — | 7 | 1 | no | — |
| 291 | C2×C42 | — | 7 | 4 | no | — |
| 292 | C2×C42 | C22×D7 | 1 | 4 | yes | — |
| 293 | C2×C42 | C22×D7 | 1 | 2 | yes | — |
| 294 | C2×C42 | C22×D7 | 1 | 1 | yes | characteristic |
| 295 | #95 | — | 7 | 4 | no | — |
| 296 | #95 | — | 7 | 4 | no | — |
| 297 | #95 | — | 7 | 4 | no | — |
| 298 | #95 | — | 7 | 4 | no | — |
| 299 | #95 | — | 7 | 4 | no | — |
| 300 | #95 | — | 7 | 4 | no | — |
| 301 | #95 | C22×D7 | 1 | 4 | yes | — |
| 302 | #95 | C22×D7 | 1 | 2 | yes | — |
| 303 | #95 | C22×D7 | 1 | 2 | yes | — |
| 304 | #95 | C22×D7 | 1 | 4 | yes | — |
| 305 | #95 | C22×D7 | 1 | 4 | yes | — |
| 306 | C22×C7 | C22×#41 | 1 | 1 | yes | characteristic |
| 307 | C22×C7 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 308 | C22×C7 | #585 | 1 | 4 | yes | — |
| 309 | C2×D7 | — | 4 | 1 | no | — |
| 310 | C2×D7 | — | 4 | 4 | no | — |
| 311 | C2×D7 | — | 4 | 4 | no | — |
| 312 | C2×D7 | — | 4 | 2 | no | — |
| 313 | C2×D7 | — | 4 | 4 | no | — |
| 314 | C2×D7 | — | 4 | 4 | no | — |
| 315 | C2×D7 | — | 4 | 4 | no | — |
| 316 | C2×D7 | — | 4 | 4 | no | — |
| 317 | C2×D7 | — | 4 | 4 | no | — |
| 318 | C2×D7 | — | 4 | 4 | no | — |
| 319 | C4×C7 | — | 2 | 4 | no | — |
| 320 | C4×C7 | — | 4 | 4 | no | — |
| 321 | C4×C7 | — | 4 | 4 | no | — |
| 322 | C4×C7 | — | 4 | 4 | no | — |
| 323 | C4×C7 | #540 | 1 | 4 | yes | — |
| 324 | Dic7 | — | 4 | 1 | no | — |
| 325 | Dic7 | — | 4 | 4 | no | — |
| 326 | Dic7 | — | 4 | 2 | no | — |
| 327 | Dic7 | — | 4 | 4 | no | — |
| 328 | C24 | — | 7 | 1 | no | — |
| 329 | C24 | — | 7 | 4 | no | — |
| 330 | C2×D4 | — | 14 | 4 | no | — |
| 331 | C2×D4 | — | 28 | 4 | no | — |
| 332 | C2×D4 | — | 28 | 4 | no | — |
| 333 | C2×D4 | — | 28 | 4 | no | — |
| 334 | C2×D4 | — | 28 | 4 | no | — |
| 335 | C2×D4 | — | 28 | 4 | no | — |
| 336 | C2×D4 | — | 28 | 4 | no | — |
| 337 | C2×D4 | — | 28 | 4 | no | — |
| 338 | C22×C4 | — | 7 | 2 | no | — |
| 339 | C22×C4 | — | 7 | 4 | no | — |
| 340 | C22×C4 | — | 7 | 4 | no | — |
| 341 | C22×C4 | — | 7 | 1 | no | — |
| 342 | C22×C4 | — | 14 | 2 | no | — |
| 343 | C22×C4 | — | 14 | 8 | no | — |
| 344 | C22×C4 | — | 14 | 8 | no | — |
| 345 | C22×C4 | — | 14 | 4 | no | — |
| 346 | C22×C4 | — | 14 | 8 | no | — |
| 347 | C22×C4 | C23×D7 | 1 | 4 | yes | — |
| 348 | C22×C4 | C23×D7 | 1 | 4 | yes | — |
| 349 | C22×C4 | C23×D7 | 1 | 4 | yes | — |
| 350 | C22×C4 | C23×D7 | 1 | 2 | yes | — |
| 351 | C22×C4 | C23×D7 | 1 | 1 | yes | characteristic |
| 352 | C4⋊C4 | — | 4 | 4 | no | — |
| 353 | C4⋊C4 | — | 4 | 4 | no | — |
| 354 | C4⋊C4 | — | 4 | 4 | no | — |
| 355 | C4⋊C4 | — | 14 | 4 | no | — |
| 356 | C4⋊C4 | — | 14 | 4 | no | — |
| 357 | C4⋊C4 | — | 28 | 4 | no | — |
| 358 | C4⋊C4 | — | 28 | 4 | no | — |
| 359 | C4⋊C4 | — | 28 | 4 | no | — |
| 360 | C4⋊C4 | — | 28 | 4 | no | — |
| 361 | C4⋊C4 | — | 28 | 4 | no | — |
| 362 | C22⋊C4 | — | 14 | 4 | no | — |
| 363 | C22⋊C4 | — | 14 | 8 | no | — |
| 364 | C22⋊C4 | — | 28 | 4 | no | — |
| 365 | C22⋊C4 | — | 28 | 4 | no | — |
| 366 | C22⋊C4 | — | 28 | 4 | no | — |
| 367 | C22⋊C4 | — | 28 | 4 | no | — |
| 368 | C22⋊C4 | — | 28 | 4 | no | — |
| 369 | C22⋊C4 | — | 28 | 4 | no | — |
| 370 | C22⋊C4 | — | 28 | 4 | no | — |
| 371 | C22⋊C4 | — | 28 | 4 | no | — |
| 372 | C22⋊C4 | — | 28 | 4 | no | — |
| 373 | C22⋊C4 | — | 28 | 4 | no | — |
| 374 | C22⋊C4 | — | 28 | 4 | no | — |
| 375 | C42 | — | 2 | 8 | no | — |
| 376 | C42 | — | 2 | 4 | no | — |
| 377 | C42 | — | 14 | 2 | no | — |
| 378 | C42 | — | 14 | 4 | no | — |
| 379 | C42 | — | 28 | 4 | no | — |
| 380 | C42 | #1161 | 1 | 4 | yes | — |
| 381 | C2×C7 | C2×#540 | 1 | 1 | yes | characteristic |
| 382 | C2×C7 | #3455 | 1 | 2 | yes | — |
| 383 | C2×C7 | #3529 | 1 | 4 | yes | — |
| 384 | D7 | — | 8 | 4 | no | — |
| 385 | D7 | — | 8 | 1 | no | — |
| 386 | C23 | — | 14 | 1 | no | — |
| 387 | C23 | — | 14 | 4 | no | — |
| 388 | C23 | — | 14 | 4 | no | — |
| 389 | C23 | — | 14 | 4 | no | — |
| 390 | C23 | — | 14 | 2 | no | — |
| 391 | C23 | — | 14 | 4 | no | — |
| 392 | C23 | — | 14 | 4 | no | — |
| 393 | C23 | — | 14 | 4 | no | — |
| 394 | C23 | — | 14 | 4 | no | — |
| 395 | C23 | — | 14 | 4 | no | — |
| 396 | C23 | C24×D7 | 1 | 1 | yes | characteristic |
| 397 | D4 | — | 28 | 8 | no | — |
| 398 | D4 | — | 28 | 16 | no | — |
| 399 | D4 | — | 28 | 16 | no | — |
| 400 | C2×C4 | — | 2 | 4 | no | — |
| 401 | C2×C4 | — | 2 | 4 | no | — |
| 402 | C2×C4 | — | 2 | 4 | no | — |
| 403 | C2×C4 | — | 2 | 4 | no | — |
| 404 | C2×C4 | — | 2 | 4 | no | — |
| 405 | C2×C4 | — | 2 | 4 | no | — |
| 406 | C2×C4 | — | 2 | 4 | no | — |
| 407 | C2×C4 | — | 2 | 4 | no | — |
| 408 | C2×C4 | — | 2 | 4 | no | — |
| 409 | C2×C4 | — | 2 | 4 | no | — |
| 410 | C2×C4 | — | 14 | 2 | no | — |
| 411 | C2×C4 | — | 14 | 4 | no | — |
| 412 | C2×C4 | — | 14 | 1 | no | — |
| 413 | C2×C4 | — | 14 | 4 | no | — |
| 414 | C2×C4 | — | 14 | 4 | no | — |
| 415 | C2×C4 | — | 14 | 2 | no | — |
| 416 | C2×C4 | — | 14 | 4 | no | — |
| 417 | C2×C4 | — | 14 | 4 | no | — |
| 418 | C2×C4 | — | 14 | 4 | no | — |
| 419 | C2×C4 | — | 14 | 4 | no | — |
| 420 | C2×C4 | — | 28 | 4 | no | — |
| 421 | C2×C4 | — | 28 | 16 | no | — |
| 422 | C2×C4 | C2×#1161 | 1 | 4 | yes | — |
| 423 | C2×C4 | C2×#1161 | 1 | 2 | yes | — |
| 424 | C2×C4 | #6553 | 1 | 4 | yes | — |
| 425 | C7 | #36692 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 426 | C22 | — | 28 | 4 | no | — |
| 427 | C22 | — | 28 | 4 | no | — |
| 428 | C22 | — | 28 | 4 | no | — |
| 429 | C22 | — | 28 | 4 | no | — |
| 430 | C22 | — | 28 | 4 | no | — |
| 431 | C22 | — | 28 | 4 | no | — |
| 432 | C22 | — | 28 | 2 | no | — |
| 433 | C22 | — | 28 | 4 | no | — |
| 434 | C22 | — | 28 | 1 | no | — |
| 435 | C22 | — | 28 | 4 | no | — |
| 436 | C22 | C22×#1161 | 1 | 1 | yes | characteristic |
| 437 | C22 | C2×#6553 | 1 | 2 | yes | — |
| 438 | C22 | #90616 | 1 | 4 | yes | — |
| 439 | C4 | — | 2 | 4 | no | — |
| 440 | C4 | — | 4 | 4 | no | — |
| 441 | C4 | — | 4 | 4 | no | — |
| 442 | C4 | — | 4 | 4 | no | — |
| 443 | C4 | — | 28 | 4 | no | — |
| 444 | C4 | — | 28 | 2 | no | — |
| 445 | C4 | — | 28 | 4 | no | — |
| 446 | C4 | — | 28 | 1 | no | — |
| 447 | C4 | #90389 | 1 | 4 | yes | — |
| 448 | C2 | — | 56 | 1 | no | — |
| 449 | C2 | — | 56 | 4 | no | — |
| 450 | C2 | C2×#90389 | 1 | 1 | yes | characteristic |
| 451 | C2 | #11743239 | 1 | 4 | yes | — |
| 452 | C2 | #11743341 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C23×D7 |
| commutator, socle, cosocle | C23×C7 | C25 |
| Frattini | C23 | C24×D7 |
| Fitting | C7×#2402 | C2 |
| hypercenter | #2402 | D7 |
| hypocenter | C7 | #36692 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C22×C4 ◁ #2402 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C7×#2402 | C2 | semidirect |
| 2. #11735851 | C2 | semidirect |
| 3. #11735771 | C2 | semidirect |
| 4. #11735456 | C2 | semidirect |
| 5. #11735380 | C2 | semidirect |
| 6. #11731222 | C2 | semidirect |
| 7. #11731221 | C2 | semidirect |
| 8. #11731221 | C2 | semidirect |
| 9. #11731062 | C2 | semidirect |
| 10. #11730863 | C2 | semidirect |
| 11. #11730830 | C2 | semidirect |
| 112. #2402 | D7 | semidirect |
| 425. C7 | #36692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2402 | 2 |
| #11735851 | 2 |
| #11735771 | 2 |
| #11735456 | 2 |
| #11735380 | 2 |
| #11731222 | 2 |
| #11731221 | 2 |
| #11731062 | 2 |
| #11730863 | 2 |
| #11730830 | 2 |
| #36692 | 7 |