Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
542 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 47 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 | C22×A4×D7 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×D7×S4 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10621506 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C7×GL(2,ℤ/4) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10621483 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10621482 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | D7×SL(2,ℤ/4) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | D7×#120 | — | 3 | 1 | no | maximal, Hall |
| 9 | C22×C7×A4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 10 | C2×A4×D7 | — | 2 | 2 | no | — |
| 11 | C2×A4×D7 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×A4×D7 | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | C2×C7⋊S4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | C2×C7×S4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | D7×S4 | — | 2 | 2 | no | — |
| 16 | D7×#67 | — | 4 | 1 | no | maximal |
| 17 | C7⋊SL(2,ℤ/4) | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | C7×SL(2,ℤ/4) | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | C24×D7 | D3 | 1 | 1 | yes | characteristic, complemented |
| 20 | C2×D4×D7 | — | 3 | 1 | no | — |
| 21 | C2×D4×D7 | — | 3 | 1 | no | — |
| 22 | C2×D4×D7 | — | 3 | 1 | no | — |
| 23 | C7×#120 | — | 3 | 1 | no | — |
| 24 | #6516 | — | 3 | 1 | no | — |
| 25 | #6500 | — | 3 | 1 | no | — |
| 26 | #6500 | — | 3 | 1 | no | — |
| 27 | #6500 | — | 3 | 1 | no | — |
| 28 | #6445 | — | 3 | 1 | no | — |
| 29 | #6445 | — | 3 | 1 | no | — |
| 30 | #6445 | — | 3 | 1 | no | — |
| 31 | D7×C22⋊C4 | — | 3 | 1 | no | — |
| 32 | D7×C22⋊C4 | — | 3 | 1 | no | — |
| 33 | D7×C22⋊C4 | — | 3 | 1 | no | — |
| 34 | C2×GL(2,ℤ/4) | — | 7 | 1 | no | maximal, Hall |
| 35 | C22×C3×D7 | — | 4 | 1 | no | — |
| 36 | C2×C7×A4 | — | 2 | 1 | no | — |
| 37 | C2×C7×A4 | C23 | 1 | 1 | yes | characteristic |
| 38 | C2×D3×D7 | — | 4 | 1 | no | — |
| 39 | A4×D7 | — | 2 | 1 | no | — |
| 40 | A4×D7 | D4 | 1 | 2 | yes | complemented |
| 41 | C7⋊S4 | — | 2 | 1 | no | — |
| 42 | C7×S4 | — | 2 | 1 | no | — |
| 43 | #4268 | — | 4 | 1 | no | — |
| 44 | C7×#67 | — | 4 | 1 | no | — |
| 45 | #4246 | — | 4 | 1 | no | — |
| 46 | #4245 | — | 4 | 1 | no | — |
| 47 | Dic3×D7 | — | 4 | 1 | no | — |
| 48 | C24×C7 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 49 | C23×D7 | — | 2 | 2 | no | — |
| 50 | C23×D7 | — | 3 | 1 | no | — |
| 51 | C23×D7 | — | 3 | 1 | no | — |
| 52 | C23×D7 | — | 3 | 1 | no | — |
| 53 | C23×D7 | — | 3 | 1 | no | — |
| 54 | C23×D7 | — | 3 | 1 | no | — |
| 55 | C23×D7 | — | 6 | 2 | no | — |
| 56 | C23×D7 | C2×D3 | 1 | 1 | yes | characteristic |
| 57 | C23×D7 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 58 | C2×C7×D4 | — | 3 | 1 | no | — |
| 59 | C2×C7×D4 | — | 3 | 1 | no | — |
| 60 | C2×C7×D4 | — | 3 | 1 | no | — |
| 61 | C2×C22⋊D7 | — | 3 | 1 | no | — |
| 62 | C2×C22⋊D7 | — | 3 | 1 | no | — |
| 63 | C2×C22⋊D7 | — | 3 | 1 | no | — |
| 64 | C2×C22⋊D7 | — | 3 | 1 | no | — |
| 65 | C2×C22⋊D7 | — | 3 | 1 | no | — |
| 66 | C2×C22⋊D7 | — | 3 | 1 | no | — |
| 67 | D4×D7 | — | 6 | 2 | no | — |
| 68 | D4×D7 | — | 6 | 4 | no | — |
| 69 | D4×D7 | — | 6 | 1 | no | — |
| 70 | D4×D7 | — | 6 | 1 | no | — |
| 71 | D4×D7 | — | 6 | 1 | no | — |
| 72 | D4×D7 | — | 6 | 2 | no | — |
| 73 | D4×D7 | — | 6 | 1 | no | — |
| 74 | C2×D28 | — | 3 | 1 | no | — |
| 75 | C2×D28 | — | 3 | 1 | no | — |
| 76 | C2×D28 | — | 3 | 1 | no | — |
| 77 | C2×C4×D7 | — | 3 | 1 | no | — |
| 78 | C2×C4×D7 | — | 3 | 1 | no | — |
| 79 | C2×C4×D7 | — | 3 | 1 | no | — |
| 80 | C7×C22⋊C4 | — | 3 | 1 | no | — |
| 81 | C7×C22⋊C4 | — | 3 | 1 | no | — |
| 82 | C7×C22⋊C4 | — | 3 | 1 | no | — |
| 83 | C22⋊Dic7 | — | 3 | 1 | no | — |
| 84 | C22⋊Dic7 | — | 3 | 1 | no | — |
| 85 | C22⋊Dic7 | — | 3 | 1 | no | — |
| 86 | (C2×D7)⋊C4 | — | 3 | 1 | no | — |
| 87 | (C2×D7)⋊C4 | — | 3 | 1 | no | — |
| 88 | (C2×D7)⋊C4 | — | 3 | 1 | no | — |
| 89 | (C2×D7)⋊C4 | — | 3 | 1 | no | — |
| 90 | (C2×D7)⋊C4 | — | 3 | 1 | no | — |
| 91 | (C2×D7)⋊C4 | — | 3 | 1 | no | — |
| 92 | C23×A4 | — | 7 | 1 | no | — |
| 93 | C22×S4 | — | 7 | 1 | no | — |
| 94 | GL(2,ℤ/4) | — | 7 | 1 | no | — |
| 95 | GL(2,ℤ/4) | — | 7 | 1 | no | — |
| 96 | GL(2,ℤ/4) | — | 7 | 1 | no | — |
| 97 | GL(2,ℤ/4) | D7 | 1 | 1 | yes | characteristic, direct product factor |
| 98 | C2×SL(2,ℤ/4) | — | 7 | 1 | no | — |
| 99 | C22×C3×C7 | — | 4 | 1 | no | — |
| 100 | C2×D21 | — | 4 | 1 | no | — |
| 101 | C2×D3×C7 | — | 4 | 1 | no | — |
| 102 | C2×C3×D7 | — | 4 | 1 | no | — |
| 103 | C2×C3×D7 | — | 4 | 1 | no | — |
| 104 | C2×C3×D7 | — | 8 | 2 | no | — |
| 105 | C7×A4 | C2×D4 | 1 | 1 | yes | characteristic, complemented |
| 106 | D3×D7 | — | 8 | 2 | no | — |
| 107 | Dic21 | — | 4 | 1 | no | — |
| 108 | C7×Dic3 | — | 4 | 1 | no | — |
| 109 | C2×#120 | — | 21 | 1 | no | Sylow |
| 110 | C23×C7 | — | 2 | 1 | no | — |
| 111 | C23×C7 | — | 3 | 1 | no | — |
| 112 | C23×C7 | — | 3 | 1 | no | — |
| 113 | C23×C7 | — | 3 | 1 | no | — |
| 114 | C23×C7 | — | 6 | 1 | no | — |
| 115 | C23×C7 | C22×D3 | 1 | 1 | yes | characteristic |
| 116 | C22×D7 | — | 2 | 1 | no | — |
| 117 | C22×D7 | — | 3 | 1 | no | — |
| 118 | C22×D7 | — | 3 | 1 | no | — |
| 119 | C22×D7 | — | 3 | 1 | no | — |
| 120 | C22×D7 | — | 3 | 2 | no | — |
| 121 | C22×D7 | — | 3 | 4 | no | — |
| 122 | C22×D7 | — | 3 | 1 | no | — |
| 123 | C22×D7 | — | 3 | 1 | no | — |
| 124 | C22×D7 | — | 3 | 1 | no | — |
| 125 | C22×D7 | — | 3 | 1 | no | — |
| 126 | C22×D7 | — | 3 | 1 | no | — |
| 127 | C22×D7 | — | 6 | 2 | no | — |
| 128 | C22×D7 | — | 6 | 2 | no | — |
| 129 | C22×D7 | — | 6 | 1 | no | — |
| 130 | C22×D7 | — | 6 | 1 | no | — |
| 131 | C22×D7 | — | 6 | 2 | no | — |
| 132 | C22×D7 | — | 6 | 2 | no | — |
| 133 | C22×D7 | — | 6 | 2 | no | — |
| 134 | C22×D7 | — | 6 | 2 | no | — |
| 135 | C22×D7 | — | 6 | 1 | no | — |
| 136 | C22×D7 | — | 6 | 2 | no | — |
| 137 | C22×D7 | — | 6 | 2 | no | — |
| 138 | C22×D7 | — | 6 | 2 | no | — |
| 139 | C22×D7 | — | 6 | 1 | no | — |
| 140 | C22×D7 | #67 | 1 | 2 | yes | complemented |
| 141 | C22×D7 | S4 | 1 | 1 | yes | characteristic, complemented |
| 142 | C7×D4 | — | 6 | 1 | no | — |
| 143 | C7×D4 | — | 6 | 2 | no | — |
| 144 | C7×D4 | — | 6 | 1 | no | — |
| 145 | C7×D4 | — | 6 | 1 | no | — |
| 146 | C7×D4 | — | 6 | 1 | no | — |
| 147 | C2×C4×C7 | — | 3 | 1 | no | — |
| 148 | C2×C4×C7 | — | 3 | 1 | no | — |
| 149 | C2×C4×C7 | — | 3 | 1 | no | — |
| 150 | C22⋊D7 | — | 6 | 2 | no | — |
| 151 | C22⋊D7 | — | 6 | 2 | no | — |
| 152 | C22⋊D7 | — | 6 | 1 | no | — |
| 153 | C22⋊D7 | — | 6 | 1 | no | — |
| 154 | C22⋊D7 | — | 6 | 2 | no | — |
| 155 | C22⋊D7 | — | 6 | 1 | no | — |
| 156 | C22⋊D7 | — | 6 | 1 | no | — |
| 157 | C22⋊D7 | — | 6 | 1 | no | — |
| 158 | C22⋊D7 | — | 6 | 1 | no | — |
| 159 | C2×Dic7 | — | 3 | 1 | no | — |
| 160 | C2×Dic7 | — | 3 | 1 | no | — |
| 161 | C2×Dic7 | — | 3 | 1 | no | — |
| 162 | D28 | — | 6 | 2 | no | — |
| 163 | D28 | — | 6 | 2 | no | — |
| 164 | D28 | — | 6 | 1 | no | — |
| 165 | D28 | — | 6 | 1 | no | — |
| 166 | C4×D7 | — | 6 | 2 | no | — |
| 167 | C4×D7 | — | 6 | 2 | no | — |
| 168 | C4×D7 | — | 6 | 1 | no | — |
| 169 | C4×D7 | — | 6 | 1 | no | — |
| 170 | C22×A4 | — | 7 | 1 | no | — |
| 171 | C22×A4 | — | 7 | 1 | no | — |
| 172 | C22×A4 | — | 14 | 2 | no | — |
| 173 | C22×A4 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 174 | C2×S4 | — | 7 | 1 | no | — |
| 175 | C2×S4 | — | 14 | 2 | no | — |
| 176 | C2×S4 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 177 | C2×#67 | — | 28 | 1 | no | — |
| 178 | SL(2,ℤ/4) | — | 7 | 1 | no | — |
| 179 | SL(2,ℤ/4) | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 180 | C2×C3×C7 | — | 4 | 1 | no | — |
| 181 | C2×C3×C7 | — | 8 | 1 | no | — |
| 182 | D21 | — | 8 | 1 | no | — |
| 183 | C3×D7 | — | 4 | 2 | no | — |
| 184 | C3×D7 | — | 8 | 1 | no | — |
| 185 | D3×C7 | — | 8 | 1 | no | — |
| 186 | C25 | — | 7 | 1 | no | — |
| 187 | C22×D4 | — | 21 | 1 | no | — |
| 188 | C22×D4 | — | 21 | 1 | no | — |
| 189 | C22×D4 | — | 21 | 1 | no | — |
| 190 | #120 | — | 3 | 1 | no | — |
| 191 | #120 | — | 21 | 1 | no | — |
| 192 | #120 | — | 21 | 1 | no | — |
| 193 | #120 | — | 21 | 1 | no | — |
| 194 | #120 | — | 21 | 1 | no | — |
| 195 | #120 | — | 21 | 1 | no | — |
| 196 | #120 | — | 21 | 1 | no | — |
| 197 | #120 | — | 21 | 1 | no | — |
| 198 | C2×C22⋊C4 | — | 21 | 1 | no | — |
| 199 | C2×C22⋊C4 | — | 21 | 1 | no | — |
| 200 | C2×C22⋊C4 | — | 21 | 1 | no | — |
| 201 | C22×C7 | — | 3 | 1 | no | — |
| 202 | C22×C7 | — | 3 | 1 | no | — |
| 203 | C22×C7 | — | 3 | 2 | no | — |
| 204 | C22×C7 | — | 3 | 1 | no | — |
| 205 | C22×C7 | — | 6 | 1 | no | — |
| 206 | C22×C7 | — | 6 | 1 | no | — |
| 207 | C22×C7 | — | 6 | 1 | no | — |
| 208 | C22×C7 | — | 6 | 1 | no | — |
| 209 | C22×C7 | — | 6 | 1 | no | — |
| 210 | C22×C7 | — | 6 | 1 | no | — |
| 211 | C22×C7 | C2×#67 | 1 | 1 | yes | characteristic, complemented |
| 212 | C22×C7 | C2×S4 | 1 | 1 | yes | characteristic, complemented |
| 213 | C2×D7 | — | 2 | 2 | no | — |
| 214 | C2×D7 | — | 3 | 1 | no | — |
| 215 | C2×D7 | — | 3 | 2 | no | — |
| 216 | C2×D7 | — | 3 | 2 | no | — |
| 217 | C2×D7 | — | 3 | 2 | no | — |
| 218 | C2×D7 | — | 3 | 2 | no | — |
| 219 | C2×D7 | — | 3 | 1 | no | — |
| 220 | C2×D7 | — | 6 | 2 | no | — |
| 221 | C2×D7 | — | 6 | 1 | no | — |
| 222 | C2×D7 | — | 6 | 1 | no | — |
| 223 | C2×D7 | — | 6 | 1 | no | — |
| 224 | C2×D7 | — | 6 | 2 | no | — |
| 225 | C2×D7 | — | 6 | 4 | no | — |
| 226 | C2×D7 | — | 6 | 2 | no | — |
| 227 | C2×D7 | — | 6 | 1 | no | — |
| 228 | C2×D7 | — | 6 | 1 | no | — |
| 229 | C2×D7 | — | 6 | 1 | no | — |
| 230 | C2×D7 | — | 6 | 1 | no | — |
| 231 | C2×D7 | — | 12 | 2 | no | — |
| 232 | C2×D7 | — | 12 | 2 | no | — |
| 233 | C2×D7 | C2×S4 | 1 | 1 | yes | characteristic |
| 234 | C2×D7 | C2×S4 | 1 | 1 | yes | characteristic, complemented |
| 235 | C4×C7 | — | 6 | 1 | no | — |
| 236 | C4×C7 | — | 6 | 1 | no | — |
| 237 | C4×C7 | — | 6 | 1 | no | — |
| 238 | Dic7 | — | 6 | 1 | no | — |
| 239 | Dic7 | — | 6 | 1 | no | — |
| 240 | Dic7 | — | 6 | 1 | no | — |
| 241 | C23×C3 | — | 28 | 1 | no | — |
| 242 | C22×D3 | — | 28 | 1 | no | — |
| 243 | C2×A4 | — | 2 | 1 | no | — |
| 244 | C2×A4 | — | 7 | 2 | no | — |
| 245 | C2×A4 | — | 14 | 1 | no | — |
| 246 | C2×A4 | C22×D7 | 1 | 1 | yes | characteristic |
| 247 | S4 | — | 2 | 1 | no | — |
| 248 | S4 | — | 14 | 1 | no | — |
| 249 | #67 | — | 4 | 1 | no | — |
| 250 | #67 | — | 28 | 1 | no | — |
| 251 | #67 | — | 28 | 1 | no | — |
| 252 | #67 | — | 28 | 1 | no | — |
| 253 | C2×Dic3 | — | 28 | 1 | no | — |
| 254 | C3×C7 | — | 4 | 1 | no | Hall |
| 255 | C24 | — | 7 | 1 | no | — |
| 256 | C24 | — | 7 | 1 | no | — |
| 257 | C24 | — | 14 | 2 | no | — |
| 258 | C24 | — | 21 | 1 | no | — |
| 259 | C24 | — | 21 | 1 | no | — |
| 260 | C24 | — | 21 | 1 | no | — |
| 261 | C24 | — | 21 | 1 | no | — |
| 262 | C24 | — | 21 | 1 | no | — |
| 263 | C24 | — | 42 | 2 | no | — |
| 264 | C24 | D3×D7 | 1 | 1 | yes | characteristic, complemented |
| 265 | C2×D4 | — | 3 | 1 | no | — |
| 266 | C2×D4 | — | 3 | 1 | no | — |
| 267 | C2×D4 | — | 3 | 1 | no | — |
| 268 | C2×D4 | — | 21 | 1 | no | — |
| 269 | C2×D4 | — | 21 | 1 | no | — |
| 270 | C2×D4 | — | 21 | 1 | no | — |
| 271 | C2×D4 | — | 21 | 1 | no | — |
| 272 | C2×D4 | — | 21 | 1 | no | — |
| 273 | C2×D4 | — | 21 | 1 | no | — |
| 274 | C2×D4 | — | 21 | 1 | no | — |
| 275 | C2×D4 | — | 21 | 1 | no | — |
| 276 | C2×D4 | — | 21 | 1 | no | — |
| 277 | C2×D4 | — | 42 | 1 | no | — |
| 278 | C2×D4 | — | 42 | 2 | no | — |
| 279 | C2×D4 | — | 42 | 1 | no | — |
| 280 | C2×D4 | — | 42 | 1 | no | — |
| 281 | C2×D4 | — | 42 | 2 | no | — |
| 282 | C2×D4 | — | 42 | 4 | no | — |
| 283 | C2×D4 | — | 42 | 1 | no | — |
| 284 | C22×C4 | — | 21 | 1 | no | — |
| 285 | C22×C4 | — | 21 | 1 | no | — |
| 286 | C22×C4 | — | 21 | 1 | no | — |
| 287 | C22⋊C4 | — | 3 | 1 | no | — |
| 288 | C22⋊C4 | — | 3 | 1 | no | — |
| 289 | C22⋊C4 | — | 3 | 1 | no | — |
| 290 | C22⋊C4 | — | 21 | 1 | no | — |
| 291 | C22⋊C4 | — | 21 | 1 | no | — |
| 292 | C22⋊C4 | — | 21 | 1 | no | — |
| 293 | C22⋊C4 | — | 21 | 1 | no | — |
| 294 | C22⋊C4 | — | 21 | 1 | no | — |
| 295 | C22⋊C4 | — | 21 | 1 | no | — |
| 296 | C22⋊C4 | — | 21 | 1 | no | — |
| 297 | C22⋊C4 | — | 21 | 1 | no | — |
| 298 | C22⋊C4 | — | 21 | 1 | no | — |
| 299 | C2×C7 | — | 2 | 1 | no | — |
| 300 | C2×C7 | — | 3 | 1 | no | — |
| 301 | C2×C7 | — | 3 | 1 | no | — |
| 302 | C2×C7 | — | 6 | 1 | no | — |
| 303 | C2×C7 | — | 12 | 1 | no | — |
| 304 | C2×C7 | C22×S4 | 1 | 1 | yes | characteristic |
| 305 | D7 | — | 2 | 1 | no | — |
| 306 | D7 | — | 3 | 2 | no | — |
| 307 | D7 | — | 6 | 1 | no | — |
| 308 | D7 | — | 12 | 1 | no | — |
| 309 | D7 | GL(2,ℤ/4) | 1 | 2 | yes | direct product factor |
| 310 | C22×C3 | — | 4 | 1 | no | — |
| 311 | C22×C3 | — | 28 | 1 | no | — |
| 312 | C22×C3 | — | 28 | 1 | no | — |
| 313 | C22×C3 | — | 56 | 2 | no | — |
| 314 | C2×D3 | — | 4 | 1 | no | — |
| 315 | C2×D3 | — | 28 | 1 | no | — |
| 316 | C2×D3 | — | 56 | 2 | no | — |
| 317 | A4 | D4×D7 | 1 | 1 | yes | characteristic, complemented |
| 318 | Dic3 | — | 4 | 1 | no | — |
| 319 | Dic3 | — | 28 | 1 | no | — |
| 320 | C23 | — | 2 | 1 | no | — |
| 321 | C23 | — | 3 | 1 | no | — |
| 322 | C23 | — | 3 | 1 | no | — |
| 323 | C23 | — | 3 | 1 | no | — |
| 324 | C23 | — | 6 | 1 | no | — |
| 325 | C23 | — | 7 | 1 | no | — |
| 326 | C23 | — | 7 | 2 | no | — |
| 327 | C23 | — | 14 | 1 | no | — |
| 328 | C23 | — | 21 | 1 | no | — |
| 329 | C23 | — | 21 | 1 | no | — |
| 330 | C23 | — | 21 | 1 | no | — |
| 331 | C23 | — | 21 | 1 | no | — |
| 332 | C23 | — | 21 | 1 | no | — |
| 333 | C23 | — | 21 | 1 | no | — |
| 334 | C23 | — | 21 | 2 | no | — |
| 335 | C23 | — | 21 | 4 | no | — |
| 336 | C23 | — | 21 | 1 | no | — |
| 337 | C23 | — | 21 | 1 | no | — |
| 338 | C23 | — | 42 | 1 | no | — |
| 339 | C23 | — | 42 | 1 | no | — |
| 340 | C23 | — | 42 | 2 | no | — |
| 341 | C23 | — | 42 | 1 | no | — |
| 342 | C23 | — | 42 | 2 | no | — |
| 343 | C23 | — | 42 | 2 | no | — |
| 344 | C23 | — | 42 | 2 | no | — |
| 345 | C23 | — | 42 | 2 | no | — |
| 346 | C23 | — | 42 | 2 | no | — |
| 347 | C23 | — | 42 | 2 | no | — |
| 348 | C23 | — | 42 | 2 | no | — |
| 349 | C23 | — | 42 | 2 | no | — |
| 350 | C23 | — | 42 | 1 | no | — |
| 351 | C23 | C2×D3×D7 | 1 | 1 | yes | characteristic |
| 352 | D4 | — | 6 | 1 | no | — |
| 353 | D4 | — | 6 | 2 | no | — |
| 354 | D4 | — | 6 | 1 | no | — |
| 355 | D4 | — | 6 | 1 | no | — |
| 356 | D4 | — | 6 | 1 | no | — |
| 357 | D4 | — | 42 | 1 | no | — |
| 358 | D4 | — | 42 | 2 | no | — |
| 359 | D4 | — | 42 | 2 | no | — |
| 360 | D4 | — | 42 | 1 | no | — |
| 361 | D4 | — | 42 | 1 | no | — |
| 362 | D4 | — | 42 | 2 | no | — |
| 363 | D4 | — | 42 | 1 | no | — |
| 364 | D4 | — | 42 | 1 | no | — |
| 365 | D4 | — | 42 | 2 | no | — |
| 366 | D4 | — | 42 | 2 | no | — |
| 367 | D4 | — | 42 | 1 | no | — |
| 368 | D4 | — | 42 | 1 | no | — |
| 369 | D4 | — | 42 | 1 | no | — |
| 370 | C2×C4 | — | 3 | 1 | no | — |
| 371 | C2×C4 | — | 3 | 1 | no | — |
| 372 | C2×C4 | — | 3 | 1 | no | — |
| 373 | C2×C4 | — | 21 | 1 | no | — |
| 374 | C2×C4 | — | 21 | 1 | no | — |
| 375 | C2×C4 | — | 21 | 1 | no | — |
| 376 | C2×C4 | — | 42 | 1 | no | — |
| 377 | C2×C4 | — | 42 | 2 | no | — |
| 378 | C2×C4 | — | 42 | 2 | no | — |
| 379 | C2×C4 | — | 42 | 1 | no | — |
| 380 | C7 | C2×GL(2,ℤ/4) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 381 | C2×C3 | — | 4 | 1 | no | — |
| 382 | C2×C3 | — | 8 | 1 | no | — |
| 383 | C2×C3 | — | 28 | 2 | no | — |
| 384 | C2×C3 | — | 56 | 1 | no | — |
| 385 | D3 | — | 8 | 1 | no | — |
| 386 | D3 | — | 56 | 1 | no | — |
| 387 | C22 | — | 3 | 1 | no | — |
| 388 | C22 | — | 3 | 1 | no | — |
| 389 | C22 | — | 3 | 2 | no | — |
| 390 | C22 | — | 3 | 1 | no | — |
| 391 | C22 | — | 6 | 1 | no | — |
| 392 | C22 | — | 6 | 1 | no | — |
| 393 | C22 | — | 6 | 1 | no | — |
| 394 | C22 | — | 6 | 1 | no | — |
| 395 | C22 | — | 6 | 1 | no | — |
| 396 | C22 | — | 6 | 1 | no | — |
| 397 | C22 | — | 7 | 1 | no | — |
| 398 | C22 | — | 7 | 1 | no | — |
| 399 | C22 | — | 14 | 2 | no | — |
| 400 | C22 | — | 21 | 2 | no | — |
| 401 | C22 | — | 21 | 2 | no | — |
| 402 | C22 | — | 21 | 2 | no | — |
| 403 | C22 | — | 21 | 2 | no | — |
| 404 | C22 | — | 21 | 1 | no | — |
| 405 | C22 | — | 21 | 1 | no | — |
| 406 | C22 | — | 42 | 2 | no | — |
| 407 | C22 | — | 42 | 1 | no | — |
| 408 | C22 | — | 42 | 1 | no | — |
| 409 | C22 | — | 42 | 1 | no | — |
| 410 | C22 | — | 42 | 1 | no | — |
| 411 | C22 | — | 42 | 1 | no | — |
| 412 | C22 | — | 42 | 1 | no | — |
| 413 | C22 | — | 42 | 2 | no | — |
| 414 | C22 | — | 42 | 2 | no | — |
| 415 | C22 | — | 42 | 4 | no | — |
| 416 | C22 | — | 42 | 1 | no | — |
| 417 | C22 | — | 84 | 2 | no | — |
| 418 | C22 | — | 84 | 2 | no | — |
| 419 | C22 | D7×#67 | 1 | 1 | yes | characteristic, complemented |
| 420 | C22 | D7×S4 | 1 | 1 | yes | characteristic, complemented |
| 421 | C4 | — | 6 | 1 | no | — |
| 422 | C4 | — | 6 | 1 | no | — |
| 423 | C4 | — | 6 | 1 | no | — |
| 424 | C4 | — | 42 | 1 | no | — |
| 425 | C4 | — | 42 | 1 | no | — |
| 426 | C4 | — | 42 | 1 | no | — |
| 427 | C3 | — | 4 | 1 | no | Sylow |
| 428 | C2 | — | 2 | 1 | no | — |
| 429 | C2 | — | 3 | 1 | no | — |
| 430 | C2 | — | 3 | 1 | no | — |
| 431 | C2 | — | 6 | 1 | no | — |
| 432 | C2 | — | 7 | 2 | no | — |
| 433 | C2 | — | 12 | 1 | no | — |
| 434 | C2 | — | 14 | 1 | no | — |
| 435 | C2 | — | 21 | 2 | no | — |
| 436 | C2 | — | 42 | 1 | no | — |
| 437 | C2 | — | 84 | 1 | no | — |
| 438 | C2 | C2×D7×S4 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D7×S4 |
| commutator, cosocle | C2×C7×A4 | C23 |
| Fitting | C24×C7 | C2×D3 |
| socle | C23×C7 | C22×D3 |
| hypercenter | C22 | D7×S4 |
| hypocenter | C7×A4 | C2×D4 |
| LCS | G ▷ C2×C7×A4 ▷ C7×A4 | |
| UCS | C1 ◁ C2 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×A4×D7 | C2 | semidirect |
| 2. C2×D7×S4 | C2 | semidirect |
| 3. #10621506 | C2 | semidirect |
| 4. C7×GL(2,ℤ/4) | C2 | semidirect |
| 5. #10621483 | C2 | semidirect |
| 6. #10621482 | C2 | semidirect |
| 7. D7×SL(2,ℤ/4) | C2 | semidirect |
| 9. C22×C7×A4 | C22 | semidirect |
| 12. C2×A4×D7 | C22 | semidirect |
| 13. C2×C7⋊S4 | C22 | semidirect |
| 14. C2×C7×S4 | C22 | semidirect |
| 17. C7⋊SL(2,ℤ/4) | C22 | semidirect |
| 18. C7×SL(2,ℤ/4) | C22 | semidirect |
| 19. C24×D7 | D3 | semidirect |
| 40. A4×D7 | D4 | semidirect |
| 48. C24×C7 | C2×D3 | semidirect |
| 57. C23×D7 | C2×D3 | semidirect |
| 97. GL(2,ℤ/4) | D7 | direct (N × H) |
| 105. C7×A4 | C2×D4 | semidirect |
| 140. C22×D7 | #67 | semidirect |
| 141. C22×D7 | S4 | semidirect |
| 173. C22×A4 | C2×D7 | semidirect |
| 176. C2×S4 | C2×D7 | semidirect |
| 179. SL(2,ℤ/4) | C2×D7 | semidirect |
| 211. C22×C7 | C2×#67 | semidirect |
| 212. C22×C7 | C2×S4 | semidirect |
| 234. C2×D7 | C2×S4 | semidirect |
| 264. C24 | D3×D7 | semidirect |
| 309. D7 | GL(2,ℤ/4) | direct (N × H) |
| 317. A4 | D4×D7 | semidirect |
| 380. C7 | C2×GL(2,ℤ/4) | semidirect |
| 419. C22 | D7×#67 | semidirect |
| 420. C22 | D7×S4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×A4×D7 | 2 |
| C2×D7×S4 | 2 |
| #10621506 | 2 |
| C7×GL(2,ℤ/4) | 2 |
| #10621483 | 2 |
| #10621482 | 2 |
| D7×SL(2,ℤ/4) | 2 |
| D7×#120 | 3 |
| D7×#67 | 4 |
| C2×GL(2,ℤ/4) | 7 |