← C7×#19172 #13196388
Subgroups — C7×#19172 #13196388
Order 1792.
628 conjugacy classes of subgroups.
The subgroup lattice has 462 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C7×#3165 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C7×#3104 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C2×C7×#462 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C7×Q8×M16 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | C7×#1694 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | C7×#1692 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | C7×#1674 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | C7×#1672 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | C7×#1565 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | C7×#1550 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | C7×#1549 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | C22×C7×Q16 | — | 2 | 1 | no | — |
| 13 | C7×#533 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×C7×C4⋊Q8 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×C4×C7×Q8 | C22 | 1 | 1 | yes | characteristic |
| 16 | C7×#501 | — | 2 | 2 | no | — |
| 17 | C7×#500 | C22 | 1 | 2 | yes | — |
| 18 | C7×#498 | C22 | 1 | 2 | yes | — |
| 19 | C7×#484 | — | 2 | 1 | no | — |
| 20 | C7×#477 | C22 | 1 | 1 | yes | characteristic |
| 21 | C7×#477 | C22 | 1 | 1 | yes | characteristic |
| 22 | C7×#462 | — | 2 | 1 | no | — |
| 23 | C7×#462 | — | 2 | 1 | no | — |
| 24 | C7×#462 | C22 | 1 | 2 | yes | — |
| 25 | C7×#462 | C22 | 1 | 2 | yes | — |
| 26 | C7×#462 | C22 | 1 | 1 | yes | characteristic |
| 27 | C7×#462 | C22 | 1 | 1 | yes | characteristic |
| 28 | C7×#451 | — | 2 | 1 | no | — |
| 29 | C7×#446 | — | 2 | 2 | no | — |
| 30 | C7×#446 | C22 | 1 | 2 | yes | — |
| 31 | C7×C8×Q8 | C22 | 1 | 2 | yes | — |
| 32 | C4×C7×Q16 | — | 2 | 1 | no | — |
| 33 | C4×C7×Q16 | — | 2 | 1 | no | — |
| 34 | C7×#431 | C22 | 1 | 1 | yes | characteristic |
| 35 | C7×#428 | — | 2 | 1 | no | — |
| 36 | C7×#428 | — | 2 | 1 | no | — |
| 37 | C7×#423 | — | 2 | 1 | no | — |
| 38 | C7×#423 | C22 | 1 | 1 | yes | characteristic |
| 39 | C2×C7×C4⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 40 | C2×C7×#103 | — | 2 | 1 | no | — |
| 41 | C4×C7×M16 | — | 2 | 1 | no | — |
| 42 | C4×C7×M16 | C22 | 1 | 1 | yes | characteristic |
| 43 | C7×#335 | C22 | 1 | 2 | yes | — |
| 44 | C7×#334 | C22 | 1 | 2 | yes | — |
| 45 | C7×#333 | C22 | 1 | 2 | yes | — |
| 46 | C7×#332 | C22 | 1 | 2 | yes | — |
| 47 | C7×#332 | C22 | 1 | 2 | yes | — |
| 48 | C7×#332 | C22 | 1 | 2 | yes | — |
| 49 | #19172 | C7 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 50 | C22×C7×Q8 | — | 2 | 1 | no | — |
| 51 | C22×C7×Q8 | D4 | 1 | 1 | yes | characteristic |
| 52 | C2×C7×Q16 | — | 2 | 2 | no | — |
| 53 | C2×C7×Q16 | — | 2 | 2 | no | — |
| 54 | C2×C7×Q16 | — | 2 | 1 | no | — |
| 55 | C2×C7×Q16 | — | 2 | 1 | no | — |
| 56 | C2×C7×Q16 | — | 4 | 4 | no | — |
| 57 | C2×C7×M16 | — | 2 | 1 | no | — |
| 58 | C2×C7×M16 | D4 | 1 | 1 | yes | characteristic |
| 59 | C2×C7×M16 | D4 | 1 | 1 | yes | characteristic |
| 60 | C22×C7×C8 | — | 2 | 1 | no | — |
| 61 | C7×C4⋊Q8 | — | 2 | 1 | no | — |
| 62 | C7×C4⋊Q8 | — | 2 | 1 | no | — |
| 63 | C7×C4⋊Q8 | — | 2 | 1 | no | — |
| 64 | C7×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 65 | C7×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 66 | C7×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 67 | C7×#125 | — | 2 | 1 | no | — |
| 68 | C7×C22⋊Q8 | — | 2 | 1 | no | — |
| 69 | C7×C22⋊Q8 | — | 2 | 1 | no | — |
| 70 | C4×C7×Q8 | — | 2 | 1 | no | — |
| 71 | C4×C7×Q8 | — | 2 | 1 | no | — |
| 72 | C4×C7×Q8 | — | 2 | 1 | no | — |
| 73 | C4×C7×Q8 | — | 2 | 1 | no | — |
| 74 | C4×C7×Q8 | D4 | 1 | 1 | yes | characteristic |
| 75 | C4×C7×Q8 | D4 | 1 | 1 | yes | characteristic |
| 76 | C4×C7×Q8 | C23 | 1 | 1 | yes | characteristic |
| 77 | C4×C7×Q8 | C23 | 1 | 1 | yes | characteristic |
| 78 | C7×#117 | — | 2 | 1 | no | — |
| 79 | C2×C7×C4⋊C4 | — | 2 | 1 | no | — |
| 80 | C2×C7×C4⋊C4 | — | 2 | 1 | no | — |
| 81 | C2×C7×C4⋊C4 | — | 2 | 1 | no | — |
| 82 | C2×C7×C4⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 83 | C2×C42×C7 | — | 2 | 1 | no | — |
| 84 | C2×C42×C7 | C23 | 1 | 1 | yes | characteristic |
| 85 | C7×#107 | — | 2 | 2 | no | — |
| 86 | C7×#107 | — | 2 | 2 | no | — |
| 87 | C7×#107 | — | 2 | 1 | no | — |
| 88 | C7×#107 | — | 2 | 1 | no | — |
| 89 | C7×#106 | — | 2 | 2 | no | — |
| 90 | C7×#106 | — | 2 | 2 | no | — |
| 91 | C7×C4⋊C8 | — | 2 | 2 | no | — |
| 92 | C7×C4⋊C8 | — | 2 | 2 | no | — |
| 93 | C7×C4⋊C8 | — | 2 | 1 | no | — |
| 94 | C7×C4⋊C8 | — | 2 | 1 | no | — |
| 95 | C7×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 96 | C7×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 97 | C7×C4⋊C8 | C23 | 1 | 2 | yes | — |
| 98 | C7×C4⋊C8 | C23 | 1 | 2 | yes | — |
| 99 | C7×#103 | — | 2 | 1 | no | — |
| 100 | C7×#103 | — | 2 | 1 | no | — |
| 101 | C7×#103 | — | 2 | 1 | no | — |
| 102 | C7×#103 | — | 2 | 1 | no | — |
| 103 | C7×#103 | — | 2 | 2 | no | — |
| 104 | C7×#103 | — | 2 | 2 | no | — |
| 105 | C7×C22⋊C8 | — | 2 | 1 | no | — |
| 106 | C7×#97 | — | 2 | 2 | no | — |
| 107 | C7×#97 | D4 | 1 | 2 | yes | — |
| 108 | C4×C7×C8 | — | 2 | 2 | no | — |
| 109 | C4×C7×C8 | — | 2 | 1 | no | — |
| 110 | C4×C7×C8 | C23 | 1 | 2 | yes | — |
| 111 | #3165 | C2×C7 | 1 | 1 | yes | characteristic |
| 112 | #3104 | C2×C7 | 1 | 1 | yes | characteristic |
| 113 | C2×#462 | C2×C7 | 1 | 1 | yes | characteristic |
| 114 | Q8×M16 | C2×C7 | 1 | 1 | yes | characteristic |
| 115 | #1694 | C2×C7 | 1 | 2 | yes | complemented |
| 116 | #1692 | C2×C7 | 1 | 2 | yes | complemented |
| 117 | #1674 | C2×C7 | 1 | 2 | yes | complemented |
| 118 | #1672 | C2×C7 | 1 | 2 | yes | complemented |
| 119 | #1565 | C2×C7 | 1 | 1 | yes | characteristic |
| 120 | #1550 | C2×C7 | 1 | 1 | yes | characteristic |
| 121 | #1549 | C2×C7 | 1 | 1 | yes | characteristic |
| 122 | C2×C7×Q8 | — | 2 | 1 | no | — |
| 123 | C2×C7×Q8 | — | 2 | 2 | no | — |
| 124 | C2×C7×Q8 | — | 2 | 1 | no | — |
| 125 | C2×C7×Q8 | — | 2 | 2 | no | — |
| 126 | C2×C7×Q8 | — | 2 | 1 | no | — |
| 127 | C2×C7×Q8 | — | 4 | 1 | no | — |
| 128 | C2×C7×Q8 | — | 4 | 2 | no | — |
| 129 | C2×C7×Q8 | — | 4 | 2 | no | — |
| 130 | C2×C7×Q8 | — | 4 | 1 | no | — |
| 131 | C2×C7×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 132 | C2×C7×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 133 | C22×C4×C7 | — | 2 | 1 | no | — |
| 134 | C22×C4×C7 | — | 2 | 1 | no | — |
| 135 | C22×C4×C7 | — | 4 | 1 | no | — |
| 136 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 137 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 138 | C22×C4×C7 | #41 | 1 | 1 | yes | characteristic |
| 139 | C7×Q16 | — | 4 | 2 | no | — |
| 140 | C7×Q16 | — | 4 | 4 | no | — |
| 141 | C7×Q16 | — | 4 | 2 | no | — |
| 142 | C7×Q16 | — | 4 | 4 | no | — |
| 143 | C7×M16 | — | 2 | 2 | no | — |
| 144 | C7×M16 | — | 4 | 2 | no | — |
| 145 | C7×M16 | Q16 | 1 | 4 | yes | complemented |
| 146 | C2×C7×C8 | — | 2 | 2 | no | — |
| 147 | C2×C7×C8 | — | 2 | 1 | no | — |
| 148 | C2×C7×C8 | — | 2 | 1 | no | — |
| 149 | C2×C7×C8 | — | 2 | 2 | no | — |
| 150 | C2×C7×C8 | — | 4 | 2 | no | — |
| 151 | C2×C7×C8 | C2×D4 | 1 | 2 | yes | — |
| 152 | C2×C7×C8 | C2×D4 | 1 | 2 | yes | — |
| 153 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 154 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 155 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 156 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 157 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 158 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 159 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 160 | C7×C4⋊C4 | — | 2 | 2 | no | — |
| 161 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 162 | C7×C4⋊C4 | — | 2 | 2 | no | — |
| 163 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 164 | C7×C4⋊C4 | — | 4 | 1 | no | — |
| 165 | C7×C4⋊C4 | — | 4 | 1 | no | — |
| 166 | C7×C4⋊C4 | — | 4 | 1 | no | — |
| 167 | C7×C4⋊C4 | — | 4 | 1 | no | — |
| 168 | C7×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 169 | C7×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 170 | C7×C22⋊C4 | — | 4 | 1 | no | — |
| 171 | C42×C7 | — | 2 | 1 | no | — |
| 172 | C42×C7 | — | 2 | 1 | no | — |
| 173 | C42×C7 | — | 2 | 1 | no | — |
| 174 | C42×C7 | — | 2 | 1 | no | — |
| 175 | C42×C7 | — | 4 | 1 | no | — |
| 176 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 177 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 178 | C42×C7 | #41 | 1 | 1 | yes | characteristic |
| 179 | C42×C7 | C24 | 1 | 1 | yes | characteristic |
| 180 | C22×Q16 | — | 2 | 1 | no | — |
| 181 | #533 | C22×C7 | 1 | 1 | yes | characteristic |
| 182 | C2×C4⋊Q8 | C22×C7 | 1 | 1 | yes | characteristic |
| 183 | C2×C4×Q8 | C22×C7 | 1 | 1 | yes | characteristic |
| 184 | #501 | — | 2 | 2 | no | — |
| 185 | #500 | C22×C7 | 1 | 2 | yes | — |
| 186 | #498 | C22×C7 | 1 | 2 | yes | — |
| 187 | #484 | — | 2 | 1 | no | — |
| 188 | #477 | C22×C7 | 1 | 1 | yes | characteristic |
| 189 | #477 | C22×C7 | 1 | 1 | yes | characteristic |
| 190 | #462 | — | 2 | 1 | no | — |
| 191 | #462 | — | 2 | 1 | no | — |
| 192 | #462 | C22×C7 | 1 | 1 | yes | characteristic |
| 193 | #462 | C22×C7 | 1 | 1 | yes | characteristic |
| 194 | #462 | C22×C7 | 1 | 2 | yes | — |
| 195 | #462 | C22×C7 | 1 | 2 | yes | — |
| 196 | #451 | — | 2 | 1 | no | — |
| 197 | #446 | — | 2 | 2 | no | — |
| 198 | #446 | C22×C7 | 1 | 2 | yes | — |
| 199 | C8×Q8 | C22×C7 | 1 | 2 | yes | — |
| 200 | C4×Q16 | — | 2 | 1 | no | — |
| 201 | C4×Q16 | — | 2 | 1 | no | — |
| 202 | #431 | C22×C7 | 1 | 1 | yes | characteristic |
| 203 | #428 | — | 2 | 1 | no | — |
| 204 | #428 | — | 2 | 1 | no | — |
| 205 | #423 | — | 2 | 1 | no | — |
| 206 | #423 | C22×C7 | 1 | 1 | yes | characteristic |
| 207 | C2×C4⋊C8 | C22×C7 | 1 | 1 | yes | characteristic |
| 208 | C2×#103 | — | 2 | 1 | no | — |
| 209 | C4×M16 | — | 2 | 1 | no | — |
| 210 | C4×M16 | C22×C7 | 1 | 1 | yes | characteristic |
| 211 | #335 | C22×C7 | 1 | 2 | yes | — |
| 212 | #334 | C22×C7 | 1 | 2 | yes | — |
| 213 | #333 | C22×C7 | 1 | 2 | yes | — |
| 214 | #332 | C22×C7 | 1 | 2 | yes | — |
| 215 | #332 | C22×C7 | 1 | 2 | yes | — |
| 216 | #332 | C22×C7 | 1 | 2 | yes | — |
| 217 | C23×C7 | #121 | 1 | 1 | yes | characteristic |
| 218 | C7×Q8 | — | 2 | 1 | no | — |
| 219 | C7×Q8 | — | 2 | 1 | no | — |
| 220 | C7×Q8 | — | 2 | 1 | no | — |
| 221 | C7×Q8 | — | 4 | 2 | no | — |
| 222 | C7×Q8 | — | 4 | 2 | no | — |
| 223 | C7×Q8 | — | 4 | 1 | no | — |
| 224 | C7×Q8 | — | 4 | 1 | no | — |
| 225 | C7×Q8 | — | 4 | 2 | no | — |
| 226 | C7×Q8 | — | 8 | 1 | no | — |
| 227 | C7×Q8 | — | 8 | 2 | no | — |
| 228 | C7×Q8 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 229 | C2×C4×C7 | — | 2 | 1 | no | — |
| 230 | C2×C4×C7 | — | 2 | 1 | no | — |
| 231 | C2×C4×C7 | — | 2 | 1 | no | — |
| 232 | C2×C4×C7 | — | 2 | 1 | no | — |
| 233 | C2×C4×C7 | — | 2 | 1 | no | — |
| 234 | C2×C4×C7 | — | 2 | 1 | no | — |
| 235 | C2×C4×C7 | — | 4 | 1 | no | — |
| 236 | C2×C4×C7 | — | 4 | 2 | no | — |
| 237 | C2×C4×C7 | — | 4 | 1 | no | — |
| 238 | C2×C4×C7 | — | 4 | 1 | no | — |
| 239 | C2×C4×C7 | — | 4 | 2 | no | — |
| 240 | C2×C4×C7 | — | 8 | 1 | no | — |
| 241 | C2×C4×C7 | — | 8 | 2 | no | — |
| 242 | C2×C4×C7 | #121 | 1 | 1 | yes | characteristic |
| 243 | C2×C4×C7 | #121 | 1 | 1 | yes | characteristic |
| 244 | C2×C4×C7 | #121 | 1 | 1 | yes | characteristic |
| 245 | C2×C4×C7 | C2×Q16 | 1 | 2 | yes | — |
| 246 | C2×C4×C7 | #137 | 1 | 2 | yes | — |
| 247 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 248 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 249 | C2×C4×C7 | C2×#41 | 1 | 1 | yes | characteristic |
| 250 | C7×C8 | — | 2 | 2 | no | — |
| 251 | C7×C8 | — | 4 | 2 | no | — |
| 252 | C7×C8 | — | 4 | 1 | no | — |
| 253 | C7×C8 | — | 4 | 2 | no | — |
| 254 | C7×C8 | — | 4 | 1 | no | — |
| 255 | C7×C8 | C2×Q16 | 1 | 4 | yes | complemented |
| 256 | C22×Q8 | — | 2 | 1 | no | — |
| 257 | C22×Q8 | C7×D4 | 1 | 1 | yes | characteristic |
| 258 | C2×Q16 | — | 2 | 2 | no | — |
| 259 | C2×Q16 | — | 2 | 2 | no | — |
| 260 | C2×Q16 | — | 2 | 1 | no | — |
| 261 | C2×Q16 | — | 2 | 1 | no | — |
| 262 | C2×Q16 | — | 4 | 4 | no | — |
| 263 | C2×M16 | — | 2 | 1 | no | — |
| 264 | C2×M16 | C7×D4 | 1 | 1 | yes | characteristic |
| 265 | C2×M16 | C7×D4 | 1 | 1 | yes | characteristic |
| 266 | C22×C8 | — | 2 | 1 | no | — |
| 267 | C4⋊Q8 | — | 2 | 1 | no | — |
| 268 | C4⋊Q8 | — | 2 | 1 | no | — |
| 269 | C4⋊Q8 | — | 2 | 1 | no | — |
| 270 | C4⋊Q8 | C23×C7 | 1 | 2 | yes | — |
| 271 | C4⋊Q8 | C23×C7 | 1 | 1 | yes | characteristic |
| 272 | C4⋊Q8 | C23×C7 | 1 | 1 | yes | characteristic |
| 273 | #125 | — | 2 | 1 | no | — |
| 274 | C22⋊Q8 | — | 2 | 1 | no | — |
| 275 | C22⋊Q8 | — | 2 | 1 | no | — |
| 276 | C4×Q8 | — | 2 | 1 | no | — |
| 277 | C4×Q8 | — | 2 | 1 | no | — |
| 278 | C4×Q8 | — | 2 | 1 | no | — |
| 279 | C4×Q8 | — | 2 | 1 | no | — |
| 280 | C4×Q8 | C7×D4 | 1 | 1 | yes | characteristic |
| 281 | C4×Q8 | C7×D4 | 1 | 1 | yes | characteristic |
| 282 | C4×Q8 | C23×C7 | 1 | 1 | yes | characteristic |
| 283 | C4×Q8 | C23×C7 | 1 | 1 | yes | characteristic |
| 284 | #117 | — | 2 | 1 | no | — |
| 285 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 286 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 287 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 288 | C2×C4⋊C4 | C7×D4 | 1 | 1 | yes | characteristic |
| 289 | C2×C42 | — | 2 | 1 | no | — |
| 290 | C2×C42 | C23×C7 | 1 | 1 | yes | characteristic |
| 291 | #107 | — | 2 | 2 | no | — |
| 292 | #107 | — | 2 | 2 | no | — |
| 293 | #107 | — | 2 | 1 | no | — |
| 294 | #107 | — | 2 | 1 | no | — |
| 295 | #106 | — | 2 | 2 | no | — |
| 296 | #106 | — | 2 | 2 | no | — |
| 297 | C4⋊C8 | — | 2 | 2 | no | — |
| 298 | C4⋊C8 | — | 2 | 2 | no | — |
| 299 | C4⋊C8 | — | 2 | 1 | no | — |
| 300 | C4⋊C8 | — | 2 | 1 | no | — |
| 301 | C4⋊C8 | C23×C7 | 1 | 2 | yes | — |
| 302 | C4⋊C8 | C23×C7 | 1 | 1 | yes | characteristic |
| 303 | C4⋊C8 | C23×C7 | 1 | 1 | yes | characteristic |
| 304 | C4⋊C8 | C23×C7 | 1 | 2 | yes | — |
| 305 | #103 | — | 2 | 1 | no | — |
| 306 | #103 | — | 2 | 1 | no | — |
| 307 | #103 | — | 2 | 2 | no | — |
| 308 | #103 | — | 2 | 2 | no | — |
| 309 | #103 | — | 2 | 1 | no | — |
| 310 | #103 | — | 2 | 1 | no | — |
| 311 | C22⋊C8 | — | 2 | 1 | no | — |
| 312 | #97 | — | 2 | 2 | no | — |
| 313 | #97 | C7×D4 | 1 | 2 | yes | — |
| 314 | C4×C8 | — | 2 | 2 | no | — |
| 315 | C4×C8 | — | 2 | 1 | no | — |
| 316 | C4×C8 | C23×C7 | 1 | 2 | yes | — |
| 317 | C22×C7 | — | 2 | 1 | no | — |
| 318 | C22×C7 | — | 2 | 1 | no | — |
| 319 | C22×C7 | #462 | 1 | 2 | yes | — |
| 320 | C22×C7 | C2×#121 | 1 | 1 | yes | characteristic |
| 321 | C4×C7 | — | 2 | 1 | no | — |
| 322 | C4×C7 | — | 2 | 2 | no | — |
| 323 | C4×C7 | — | 2 | 1 | no | — |
| 324 | C4×C7 | — | 2 | 1 | no | — |
| 325 | C4×C7 | — | 4 | 1 | no | — |
| 326 | C4×C7 | — | 4 | 1 | no | — |
| 327 | C4×C7 | — | 4 | 1 | no | — |
| 328 | C4×C7 | — | 8 | 2 | no | — |
| 329 | C4×C7 | — | 8 | 1 | no | — |
| 330 | C4×C7 | — | 8 | 1 | no | — |
| 331 | C4×C7 | #462 | 1 | 2 | yes | — |
| 332 | C4×C7 | C22×Q16 | 1 | 1 | yes | characteristic |
| 333 | C4×C7 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 334 | C4×C7 | C2×#137 | 1 | 1 | yes | characteristic |
| 335 | C4×C7 | #575 | 1 | 1 | yes | characteristic |
| 336 | C2×Q8 | — | 2 | 1 | no | — |
| 337 | C2×Q8 | — | 2 | 2 | no | — |
| 338 | C2×Q8 | — | 2 | 1 | no | — |
| 339 | C2×Q8 | — | 2 | 2 | no | — |
| 340 | C2×Q8 | — | 2 | 1 | no | — |
| 341 | C2×Q8 | — | 4 | 1 | no | — |
| 342 | C2×Q8 | — | 4 | 2 | no | — |
| 343 | C2×Q8 | — | 4 | 2 | no | — |
| 344 | C2×Q8 | — | 4 | 1 | no | — |
| 345 | C2×Q8 | C2×C7×D4 | 1 | 1 | yes | characteristic |
| 346 | C2×Q8 | C2×C7×D4 | 1 | 1 | yes | characteristic |
| 347 | C22×C4 | — | 2 | 1 | no | — |
| 348 | C22×C4 | — | 2 | 1 | no | — |
| 349 | C22×C4 | — | 4 | 1 | no | — |
| 350 | C22×C4 | C2×C7×D4 | 1 | 1 | yes | characteristic |
| 351 | C22×C4 | C2×C7×D4 | 1 | 1 | yes | characteristic |
| 352 | C22×C4 | C7×#41 | 1 | 1 | yes | characteristic |
| 353 | Q16 | — | 4 | 2 | no | — |
| 354 | Q16 | — | 4 | 4 | no | — |
| 355 | Q16 | — | 4 | 2 | no | — |
| 356 | Q16 | — | 4 | 4 | no | — |
| 357 | M16 | — | 2 | 2 | no | — |
| 358 | M16 | — | 4 | 2 | no | — |
| 359 | M16 | C7×Q16 | 1 | 4 | yes | complemented |
| 360 | C2×C8 | — | 2 | 2 | no | — |
| 361 | C2×C8 | — | 2 | 1 | no | — |
| 362 | C2×C8 | — | 2 | 1 | no | — |
| 363 | C2×C8 | — | 2 | 2 | no | — |
| 364 | C2×C8 | — | 4 | 2 | no | — |
| 365 | C2×C8 | C2×C7×D4 | 1 | 2 | yes | — |
| 366 | C2×C8 | C2×C7×D4 | 1 | 2 | yes | — |
| 367 | C4⋊C4 | — | 2 | 1 | no | — |
| 368 | C4⋊C4 | — | 2 | 1 | no | — |
| 369 | C4⋊C4 | — | 2 | 1 | no | — |
| 370 | C4⋊C4 | — | 2 | 1 | no | — |
| 371 | C4⋊C4 | — | 2 | 1 | no | — |
| 372 | C4⋊C4 | — | 2 | 1 | no | — |
| 373 | C4⋊C4 | — | 2 | 1 | no | — |
| 374 | C4⋊C4 | — | 2 | 2 | no | — |
| 375 | C4⋊C4 | — | 2 | 1 | no | — |
| 376 | C4⋊C4 | — | 2 | 2 | no | — |
| 377 | C4⋊C4 | — | 2 | 1 | no | — |
| 378 | C4⋊C4 | — | 4 | 1 | no | — |
| 379 | C4⋊C4 | — | 4 | 1 | no | — |
| 380 | C4⋊C4 | — | 4 | 1 | no | — |
| 381 | C4⋊C4 | — | 4 | 1 | no | — |
| 382 | C4⋊C4 | C2×C7×D4 | 1 | 1 | yes | characteristic |
| 383 | C4⋊C4 | C2×C7×D4 | 1 | 1 | yes | characteristic |
| 384 | C22⋊C4 | — | 4 | 1 | no | — |
| 385 | C42 | — | 2 | 1 | no | — |
| 386 | C42 | — | 2 | 1 | no | — |
| 387 | C42 | — | 2 | 1 | no | — |
| 388 | C42 | — | 2 | 1 | no | — |
| 389 | C42 | — | 4 | 1 | no | — |
| 390 | C42 | C2×C7×D4 | 1 | 1 | yes | characteristic |
| 391 | C42 | C2×C7×D4 | 1 | 1 | yes | characteristic |
| 392 | C42 | C7×#41 | 1 | 1 | yes | characteristic |
| 393 | C42 | C24×C7 | 1 | 1 | yes | characteristic |
| 394 | C2×C7 | — | 2 | 2 | no | — |
| 395 | C2×C7 | C2×#462 | 1 | 1 | yes | characteristic |
| 396 | C2×C7 | #3055 | 1 | 1 | yes | characteristic |
| 397 | C2×C7 | #3069 | 1 | 1 | yes | characteristic |
| 398 | C23 | C7×#121 | 1 | 1 | yes | characteristic |
| 399 | Q8 | — | 2 | 1 | no | — |
| 400 | Q8 | — | 2 | 1 | no | — |
| 401 | Q8 | — | 2 | 1 | no | — |
| 402 | Q8 | — | 4 | 2 | no | — |
| 403 | Q8 | — | 4 | 2 | no | — |
| 404 | Q8 | — | 4 | 1 | no | — |
| 405 | Q8 | — | 4 | 1 | no | — |
| 406 | Q8 | — | 4 | 2 | no | — |
| 407 | Q8 | — | 8 | 1 | no | — |
| 408 | Q8 | — | 8 | 2 | no | — |
| 409 | Q8 | C7×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 410 | C2×C4 | — | 2 | 1 | no | — |
| 411 | C2×C4 | — | 2 | 1 | no | — |
| 412 | C2×C4 | — | 2 | 1 | no | — |
| 413 | C2×C4 | — | 2 | 1 | no | — |
| 414 | C2×C4 | — | 2 | 1 | no | — |
| 415 | C2×C4 | — | 2 | 1 | no | — |
| 416 | C2×C4 | — | 4 | 1 | no | — |
| 417 | C2×C4 | — | 4 | 2 | no | — |
| 418 | C2×C4 | — | 4 | 1 | no | — |
| 419 | C2×C4 | — | 4 | 1 | no | — |
| 420 | C2×C4 | — | 4 | 2 | no | — |
| 421 | C2×C4 | — | 8 | 1 | no | — |
| 422 | C2×C4 | — | 8 | 2 | no | — |
| 423 | C2×C4 | C7×#121 | 1 | 1 | yes | characteristic |
| 424 | C2×C4 | C7×#121 | 1 | 1 | yes | characteristic |
| 425 | C2×C4 | C7×#121 | 1 | 1 | yes | characteristic |
| 426 | C2×C4 | C2×C7×Q16 | 1 | 2 | yes | — |
| 427 | C2×C4 | C7×#137 | 1 | 2 | yes | — |
| 428 | C2×C4 | C22×C7×D4 | 1 | 1 | yes | characteristic |
| 429 | C2×C4 | C22×C7×D4 | 1 | 1 | yes | characteristic |
| 430 | C2×C4 | C2×C7×#41 | 1 | 1 | yes | characteristic |
| 431 | C8 | — | 2 | 2 | no | — |
| 432 | C8 | — | 4 | 2 | no | — |
| 433 | C8 | — | 4 | 1 | no | — |
| 434 | C8 | — | 4 | 2 | no | — |
| 435 | C8 | — | 4 | 1 | no | — |
| 436 | C8 | C2×C7×Q16 | 1 | 4 | yes | complemented |
| 437 | C7 | #19172 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 438 | C22 | — | 2 | 1 | no | — |
| 439 | C22 | — | 2 | 1 | no | — |
| 440 | C22 | C7×#462 | 1 | 2 | yes | — |
| 441 | C22 | C2×C7×#121 | 1 | 1 | yes | characteristic |
| 442 | C4 | — | 2 | 1 | no | — |
| 443 | C4 | — | 2 | 2 | no | — |
| 444 | C4 | — | 2 | 1 | no | — |
| 445 | C4 | — | 2 | 1 | no | — |
| 446 | C4 | — | 4 | 1 | no | — |
| 447 | C4 | — | 4 | 1 | no | — |
| 448 | C4 | — | 4 | 1 | no | — |
| 449 | C4 | — | 8 | 2 | no | — |
| 450 | C4 | — | 8 | 1 | no | — |
| 451 | C4 | — | 8 | 1 | no | — |
| 452 | C4 | C7×#462 | 1 | 2 | yes | — |
| 453 | C4 | C22×C7×Q16 | 1 | 1 | yes | characteristic |
| 454 | C4 | C2×C7×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 455 | C4 | C2×C7×#137 | 1 | 1 | yes | characteristic |
| 456 | C4 | C7×#575 | 1 | 1 | yes | characteristic |
| 457 | C2 | — | 2 | 2 | no | — |
| 458 | C2 | C2×C7×#462 | 1 | 1 | yes | characteristic |
| 459 | C2 | C7×#3055 | 1 | 1 | yes | characteristic |
| 460 | C2 | C7×#3069 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta