← #14218082
Subgroups — #14218082
Order 1792.
2818 conjugacy classes of subgroups.
The subgroup lattice has 432 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#90443 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C4×#6553 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C7×#2875 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11741242 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #11741229 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11736019 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #11736006 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #11736005 | C2 | 1 | 6 | yes | maximal, complemented |
| 9 | C4×#6471 | C2 | 1 | 6 | yes | maximal, complemented |
| 10 | #11735939 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | C2×#89483 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | C2×#6553 | C22 | 1 | 2 | yes | — |
| 13 | C2×C7×#131 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×C7×#131 | C22 | 1 | 1 | yes | characteristic |
| 15 | C4×C7×#41 | C22 | 1 | 1 | yes | characteristic |
| 16 | #90518 | C22 | 1 | 2 | yes | — |
| 17 | #90443 | C4 | 1 | 16 | yes | complemented |
| 18 | C2×#6471 | C22 | 1 | 6 | yes | — |
| 19 | C2×#6467 | C22 | 1 | 3 | yes | — |
| 20 | C22×D56 | C22 | 1 | 3 | yes | — |
| 21 | #90265 | — | 2 | 2 | no | — |
| 22 | C4×#1161 | — | 2 | 2 | no | — |
| 23 | #90236 | — | 2 | 6 | no | — |
| 24 | C4×D4×D7 | — | 2 | 6 | no | — |
| 25 | #90214 | C22 | 1 | 6 | yes | complemented |
| 26 | #90212 | C22 | 1 | 6 | yes | complemented |
| 27 | C4×#1157 | C22 | 1 | 6 | yes | complemented |
| 28 | C2×C4×D28 | C22 | 1 | 6 | yes | complemented |
| 29 | C7×#405 | C22 | 1 | 3 | yes | complemented |
| 30 | C7×#405 | C22 | 1 | 3 | yes | complemented |
| 31 | C4×C7×M16 | C22 | 1 | 3 | yes | complemented |
| 32 | C2×C7×#97 | C22 | 1 | 3 | yes | complemented |
| 33 | #89905 | C22 | 1 | 6 | yes | complemented |
| 34 | #89903 | C22 | 1 | 6 | yes | complemented |
| 35 | #89893 | C22 | 1 | 6 | yes | complemented |
| 36 | #89885 | C22 | 1 | 6 | yes | complemented |
| 37 | C2×#6395 | C22 | 1 | 6 | yes | complemented |
| 38 | #89878 | C22 | 1 | 3 | yes | complemented |
| 39 | C2×#6391 | C22 | 1 | 3 | yes | complemented |
| 40 | #89488 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | #89488 | C22 | 1 | 3 | yes | complemented |
| 42 | #89483 | C22 | 1 | 3 | yes | complemented |
| 43 | #89483 | C22 | 1 | 6 | yes | complemented |
| 44 | #89483 | C22 | 1 | 6 | yes | complemented |
| 45 | #89483 | C22 | 1 | 6 | yes | complemented |
| 46 | #89483 | C22 | 1 | 3 | yes | complemented |
| 47 | #89482 | C22 | 1 | 6 | yes | complemented |
| 48 | #89482 | C22 | 1 | 6 | yes | complemented |
| 49 | C4×D56 | C22 | 1 | 12 | yes | complemented |
| 50 | C4×#1132 | C22 | 1 | 12 | yes | complemented |
| 51 | #60176 | — | 7 | 1 | no | maximal, Sylow |
| 52 | C2×C7×#41 | C23 | 1 | 1 | yes | characteristic |
| 53 | #6553 | — | 2 | 8 | no | — |
| 54 | #6553 | C2×C4 | 1 | 16 | yes | complemented |
| 55 | C2×#1161 | — | 2 | 2 | no | — |
| 56 | C2×D4×D7 | — | 2 | 6 | no | — |
| 57 | C2×#1157 | C23 | 1 | 6 | yes | — |
| 58 | C22×D28 | C23 | 1 | 6 | yes | — |
| 59 | C22×C4×D7 | — | 2 | 6 | no | — |
| 60 | C7×#131 | — | 2 | 4 | no | — |
| 61 | C7×#131 | C2×C4 | 1 | 8 | yes | complemented |
| 62 | C2×C7×M16 | C23 | 1 | 3 | yes | — |
| 63 | C2×C7×M16 | C23 | 1 | 3 | yes | — |
| 64 | C22×C7×C8 | C23 | 1 | 3 | yes | — |
| 65 | C22×C7×C8 | C23 | 1 | 3 | yes | — |
| 66 | C4×C7×Q8 | D4 | 1 | 2 | yes | — |
| 67 | C4×C7×D4 | D4 | 1 | 6 | yes | — |
| 68 | C7×#117 | C23 | 1 | 3 | yes | — |
| 69 | C2×C42×C7 | C23 | 1 | 3 | yes | — |
| 70 | Q8×Dic7 | — | 2 | 2 | no | — |
| 71 | D4×Dic7 | — | 2 | 6 | no | — |
| 72 | C4×C22⋊D7 | — | 2 | 6 | no | — |
| 73 | C4×C22⋊D7 | — | 2 | 6 | no | — |
| 74 | C2×(C2×D7)⋊C4 | — | 2 | 6 | no | — |
| 75 | #6489 | C23 | 1 | 6 | yes | — |
| 76 | C2×C4⋊Dic7 | C23 | 1 | 6 | yes | — |
| 77 | #6471 | C2×C4 | 1 | 48 | yes | complemented |
| 78 | C2×Dic28 | C23 | 1 | 1 | yes | characteristic |
| 79 | #6467 | C2×C4 | 1 | 24 | yes | complemented |
| 80 | C2×D56 | C2×C4 | 1 | 24 | yes | complemented |
| 81 | C2×D56 | C23 | 1 | 3 | yes | — |
| 82 | C2×D56 | C23 | 1 | 6 | yes | — |
| 83 | C2×#1132 | C23 | 1 | 6 | yes | — |
| 84 | #6456 | — | 2 | 6 | no | — |
| 85 | #6456 | — | 2 | 6 | no | — |
| 86 | #6455 | — | 2 | 6 | no | — |
| 87 | D7×C4⋊C4 | — | 2 | 6 | no | — |
| 88 | (C22⋊D7)⋊C4 | — | 2 | 12 | no | — |
| 89 | D7×C22⋊C4 | — | 2 | 12 | no | — |
| 90 | C4×D28 | — | 2 | 6 | no | — |
| 91 | C4×D28 | — | 2 | 6 | no | — |
| 92 | C4×D28 | C23 | 1 | 6 | yes | — |
| 93 | C4×D28 | C23 | 1 | 12 | yes | — |
| 94 | C4×D28 | C23 | 1 | 6 | yes | — |
| 95 | #6435 | — | 2 | 6 | no | — |
| 96 | C42×D7 | — | 2 | 6 | no | — |
| 97 | C4×Dic14 | C23 | 1 | 2 | yes | — |
| 98 | C4×Dic14 | C23 | 1 | 6 | yes | — |
| 99 | C7×#97 | C23 | 1 | 3 | yes | — |
| 100 | C7×#97 | C23 | 1 | 3 | yes | — |
| 101 | C7×#97 | C23 | 1 | 1 | yes | characteristic |
| 102 | C7×#97 | C23 | 1 | 3 | yes | — |
| 103 | C4×C7×C8 | C23 | 1 | 6 | yes | — |
| 104 | #6395 | C23 | 1 | 6 | yes | — |
| 105 | #6395 | C23 | 1 | 12 | yes | — |
| 106 | #6395 | C23 | 1 | 6 | yes | — |
| 107 | #6392 | C23 | 1 | 6 | yes | — |
| 108 | #6391 | C23 | 1 | 3 | yes | — |
| 109 | #6391 | C23 | 1 | 6 | yes | — |
| 110 | #6391 | C23 | 1 | 1 | yes | characteristic |
| 111 | #6390 | C23 | 1 | 2 | yes | — |
| 112 | #6390 | C23 | 1 | 6 | yes | — |
| 113 | C2×#576 | — | 7 | 1 | no | — |
| 114 | C4×H(5,𝔽2) | — | 7 | 2 | no | — |
| 115 | #2952 | — | 7 | 3 | no | — |
| 116 | #2948 | — | 7 | 3 | no | — |
| 117 | #2946 | — | 7 | 6 | no | — |
| 118 | C4×AGL(1,ℤ/8) | — | 7 | 6 | no | — |
| 119 | #2943 | — | 7 | 3 | no | — |
| 120 | C2×#442 | — | 7 | 3 | no | — |
| 121 | #2912 | — | 7 | 1 | no | — |
| 122 | #2897 | — | 7 | 2 | no | — |
| 123 | #2875 | D7 | 1 | 1 | yes | characteristic, complemented |
| 124 | C23×D7 | — | 2 | 6 | no | — |
| 125 | C7×#41 | C22×C4 | 1 | 4 | yes | — |
| 126 | C7×#41 | #41 | 1 | 4 | yes | — |
| 127 | C2×C7×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 128 | C2×C7×D4 | C2×D4 | 1 | 3 | yes | — |
| 129 | C22×C4×C7 | C2×D4 | 1 | 6 | yes | — |
| 130 | C22×C4×C7 | C24 | 1 | 3 | yes | — |
| 131 | C2×C22⋊D7 | — | 2 | 6 | no | — |
| 132 | C22×Dic7 | — | 2 | 6 | no | — |
| 133 | #1161 | — | 2 | 16 | no | — |
| 134 | D4×D7 | — | 2 | 48 | no | — |
| 135 | #1157 | — | 2 | 12 | no | — |
| 136 | #1157 | C22×C4 | 1 | 24 | yes | complemented |
| 137 | C2×D28 | — | 2 | 6 | no | — |
| 138 | C2×D28 | — | 2 | 12 | no | — |
| 139 | C2×D28 | C22×C4 | 1 | 24 | yes | complemented |
| 140 | C2×D28 | C24 | 1 | 6 | yes | — |
| 141 | C2×C4×D7 | — | 2 | 6 | no | — |
| 142 | C2×C4×D7 | — | 2 | 6 | no | — |
| 143 | C2×C4×D7 | — | 2 | 6 | no | — |
| 144 | C2×C4×D7 | — | 2 | 12 | no | — |
| 145 | C2×C4×D7 | — | 8 | 12 | no | — |
| 146 | C2×Dic14 | C24 | 1 | 2 | yes | — |
| 147 | C7×M16 | — | 2 | 6 | no | — |
| 148 | C7×M16 | C22×C4 | 1 | 12 | yes | complemented |
| 149 | C2×C7×C8 | — | 2 | 6 | no | — |
| 150 | C2×C7×C8 | C22×C4 | 1 | 12 | yes | complemented |
| 151 | C2×C7×C8 | C24 | 1 | 3 | yes | — |
| 152 | C2×C7×C8 | C24 | 1 | 1 | yes | characteristic |
| 153 | C2×C7×C8 | C24 | 1 | 3 | yes | — |
| 154 | C2×C7×C8 | C24 | 1 | 1 | yes | characteristic |
| 155 | C7×C4⋊C4 | C2×D4 | 1 | 6 | yes | — |
| 156 | C7×C22⋊C4 | C2×D4 | 1 | 6 | yes | — |
| 157 | C42×C7 | C2×D4 | 1 | 6 | yes | — |
| 158 | C42×C7 | C24 | 1 | 3 | yes | — |
| 159 | C42×C7 | C24 | 1 | 1 | yes | characteristic |
| 160 | C22⋊Dic7 | — | 2 | 6 | no | — |
| 161 | (C2×D7)⋊C4 | — | 2 | 6 | no | — |
| 162 | (C2×D7)⋊C4 | — | 2 | 6 | no | — |
| 163 | (C2×D7)⋊C4 | — | 2 | 12 | no | — |
| 164 | C4⋊Dic7 | — | 2 | 6 | no | — |
| 165 | C4⋊Dic7 | C24 | 1 | 6 | yes | — |
| 166 | C4⋊Dic7 | C24 | 1 | 2 | yes | — |
| 167 | Dic7⋊C4 | — | 2 | 2 | no | — |
| 168 | Dic7⋊C4 | — | 2 | 6 | no | — |
| 169 | C4×Dic7 | — | 2 | 2 | no | — |
| 170 | C4×Dic7 | — | 2 | 6 | no | — |
| 171 | C4×Dic7 | — | 2 | 6 | no | — |
| 172 | Dic28 | C22×C4 | 1 | 4 | yes | complemented |
| 173 | D56 | C22×C4 | 1 | 12 | yes | complemented |
| 174 | D56 | C22×C4 | 1 | 24 | yes | complemented |
| 175 | #1132 | C22×C4 | 1 | 24 | yes | complemented |
| 176 | C2×H(5,𝔽2) | — | 7 | 2 | no | — |
| 177 | #576 | — | 7 | 16 | no | — |
| 178 | C2×AGL(1,ℤ/8) | — | 7 | 6 | no | — |
| 179 | C2×#135 | — | 7 | 3 | no | — |
| 180 | C22×D8 | — | 7 | 3 | no | — |
| 181 | C2×#131 | C2×D7 | 1 | 1 | yes | characteristic |
| 182 | C2×#131 | C2×D7 | 1 | 1 | yes | characteristic |
| 183 | #520 | — | 7 | 2 | no | — |
| 184 | #520 | — | 7 | 6 | no | — |
| 185 | #520 | — | 14 | 2 | no | — |
| 186 | #518 | — | 7 | 6 | no | — |
| 187 | #518 | — | 14 | 6 | no | — |
| 188 | C4×#41 | — | 7 | 6 | no | — |
| 189 | C4×#41 | — | 14 | 2 | no | — |
| 190 | C4×#41 | C2×D7 | 1 | 1 | yes | characteristic |
| 191 | C2×C4×D4 | — | 7 | 6 | no | — |
| 192 | C2×C4×D4 | — | 14 | 6 | no | — |
| 193 | #442 | — | 7 | 3 | no | — |
| 194 | #442 | — | 7 | 6 | no | — |
| 195 | #442 | — | 7 | 6 | no | — |
| 196 | #442 | — | 7 | 6 | no | — |
| 197 | #442 | — | 7 | 3 | no | — |
| 198 | #441 | — | 7 | 1 | no | — |
| 199 | #441 | — | 7 | 3 | no | — |
| 200 | #440 | — | 7 | 6 | no | — |
| 201 | #440 | — | 7 | 6 | no | — |
| 202 | C4×SD16 | — | 7 | 12 | no | — |
| 203 | C4×D8 | — | 7 | 12 | no | — |
| 204 | #428 | — | 7 | 6 | no | — |
| 205 | #427 | — | 7 | 3 | no | — |
| 206 | C2×#106 | — | 7 | 3 | no | — |
| 207 | #418 | — | 7 | 6 | no | — |
| 208 | #417 | — | 7 | 6 | no | — |
| 209 | #416 | — | 7 | 6 | no | — |
| 210 | C2×#102 | — | 7 | 6 | no | — |
| 211 | #405 | C2×D7 | 1 | 3 | yes | complemented |
| 212 | #405 | C2×D7 | 1 | 3 | yes | complemented |
| 213 | C4×M16 | C2×D7 | 1 | 3 | yes | complemented |
| 214 | C2×#97 | C2×D7 | 1 | 3 | yes | complemented |
| 215 | C23×C7 | C22×D4 | 1 | 3 | yes | — |
| 216 | C22×D7 | — | 2 | 6 | no | — |
| 217 | C22×D7 | — | 2 | 24 | no | — |
| 218 | C22×D7 | — | 8 | 6 | no | — |
| 219 | C22×D7 | — | 8 | 6 | no | — |
| 220 | C7×Q8 | C4×D4 | 1 | 4 | yes | — |
| 221 | C7×D4 | C4×D4 | 1 | 12 | yes | — |
| 222 | C2×C4×C7 | — | 4 | 6 | no | — |
| 223 | C2×C4×C7 | C23×C4 | 1 | 6 | yes | — |
| 224 | C2×C4×C7 | C22×D4 | 1 | 2 | yes | — |
| 225 | C2×C4×C7 | C22×D4 | 1 | 6 | yes | — |
| 226 | C2×C4×C7 | C22×D4 | 1 | 3 | yes | — |
| 227 | C2×C4×C7 | C2×#41 | 1 | 6 | yes | — |
| 228 | C2×C4×C7 | C25 | 1 | 1 | yes | characteristic |
| 229 | C22⋊D7 | — | 2 | 24 | no | — |
| 230 | C2×Dic7 | — | 2 | 2 | no | — |
| 231 | C2×Dic7 | — | 2 | 2 | no | — |
| 232 | C2×Dic7 | — | 2 | 6 | no | — |
| 233 | C2×Dic7 | — | 8 | 6 | no | — |
| 234 | D28 | — | 2 | 24 | no | — |
| 235 | D28 | — | 2 | 6 | no | — |
| 236 | D28 | C23×C4 | 1 | 12 | yes | — |
| 237 | C4×D7 | — | 2 | 24 | no | — |
| 238 | C4×D7 | — | 4 | 12 | no | — |
| 239 | C4×D7 | — | 8 | 6 | no | — |
| 240 | C4×D7 | — | 8 | 12 | no | — |
| 241 | Dic14 | — | 2 | 2 | no | — |
| 242 | Dic14 | C23×C4 | 1 | 4 | yes | — |
| 243 | C7×C8 | — | 2 | 1 | no | — |
| 244 | C7×C8 | — | 2 | 3 | no | — |
| 245 | C7×C8 | C23×C4 | 1 | 6 | yes | — |
| 246 | C7×C8 | C23×C4 | 1 | 2 | yes | — |
| 247 | H(5,𝔽2) | — | 7 | 16 | no | — |
| 248 | H(5,𝔽2) | — | 14 | 8 | no | — |
| 249 | C2×#41 | — | 7 | 6 | no | — |
| 250 | C2×#41 | — | 14 | 2 | no | — |
| 251 | C2×#41 | C22×D7 | 1 | 1 | yes | characteristic |
| 252 | C22×D4 | — | 7 | 6 | no | — |
| 253 | C22×D4 | — | 14 | 6 | no | — |
| 254 | C23×C4 | — | 14 | 6 | no | — |
| 255 | AGL(1,ℤ/8) | — | 7 | 48 | no | — |
| 256 | #135 | — | 7 | 24 | no | — |
| 257 | C2×Q16 | — | 7 | 1 | no | — |
| 258 | C2×SD16 | — | 7 | 6 | no | — |
| 259 | C2×D8 | — | 7 | 24 | no | — |
| 260 | C2×D8 | — | 7 | 3 | no | — |
| 261 | C2×D8 | — | 7 | 6 | no | — |
| 262 | #131 | — | 2 | 4 | no | — |
| 263 | #131 | C4×D7 | 1 | 8 | yes | complemented |
| 264 | C2×M16 | C22×D7 | 1 | 3 | yes | — |
| 265 | C2×M16 | C22×D7 | 1 | 3 | yes | — |
| 266 | C22×C8 | C22×D7 | 1 | 3 | yes | — |
| 267 | C22×C8 | C22×D7 | 1 | 3 | yes | — |
| 268 | C4×Q8 | — | 7 | 2 | no | — |
| 269 | C4×Q8 | — | 7 | 6 | no | — |
| 270 | C4×Q8 | — | 14 | 2 | no | — |
| 271 | C4×Q8 | D28 | 1 | 2 | yes | — |
| 272 | C4×D4 | — | 7 | 6 | no | — |
| 273 | C4×D4 | — | 7 | 12 | no | — |
| 274 | C4×D4 | — | 7 | 6 | no | — |
| 275 | C4×D4 | — | 14 | 6 | no | — |
| 276 | C4×D4 | — | 14 | 6 | no | — |
| 277 | C4×D4 | — | 14 | 6 | no | — |
| 278 | C4×D4 | — | 14 | 6 | no | — |
| 279 | C4×D4 | — | 14 | 6 | no | — |
| 280 | C4×D4 | — | 14 | 12 | no | — |
| 281 | C4×D4 | — | 14 | 6 | no | — |
| 282 | C4×D4 | — | 14 | 6 | no | — |
| 283 | C4×D4 | D28 | 1 | 6 | yes | — |
| 284 | #117 | — | 7 | 6 | no | — |
| 285 | #117 | — | 14 | 6 | no | — |
| 286 | #117 | — | 14 | 6 | no | — |
| 287 | #117 | C22×D7 | 1 | 3 | yes | — |
| 288 | C2×C4⋊C4 | — | 7 | 6 | no | — |
| 289 | C2×C4⋊C4 | — | 14 | 6 | no | — |
| 290 | C2×C22⋊C4 | — | 14 | 6 | no | — |
| 291 | C2×C22⋊C4 | — | 14 | 12 | no | — |
| 292 | C2×C42 | — | 14 | 6 | no | — |
| 293 | C2×C42 | C22×D7 | 1 | 3 | yes | — |
| 294 | #107 | — | 7 | 6 | no | — |
| 295 | #106 | — | 7 | 3 | no | — |
| 296 | #106 | — | 7 | 6 | no | — |
| 297 | #106 | — | 7 | 1 | no | — |
| 298 | #103 | — | 7 | 2 | no | — |
| 299 | #103 | — | 7 | 6 | no | — |
| 300 | #102 | — | 7 | 6 | no | — |
| 301 | #102 | — | 7 | 12 | no | — |
| 302 | #102 | — | 7 | 6 | no | — |
| 303 | #97 | C22×D7 | 1 | 1 | yes | characteristic |
| 304 | #97 | C22×D7 | 1 | 3 | yes | — |
| 305 | #97 | C22×D7 | 1 | 3 | yes | — |
| 306 | #97 | C22×D7 | 1 | 3 | yes | — |
| 307 | C4×C8 | C22×D7 | 1 | 6 | yes | — |
| 308 | C22×C7 | — | 2 | 6 | no | — |
| 309 | C22×C7 | C2×C4×D4 | 1 | 6 | yes | — |
| 310 | C22×C7 | C23×D4 | 1 | 1 | yes | characteristic |
| 311 | C2×D7 | — | 2 | 12 | no | — |
| 312 | C2×D7 | — | 4 | 6 | no | — |
| 313 | C2×D7 | — | 4 | 6 | no | — |
| 314 | C2×D7 | — | 8 | 24 | no | — |
| 315 | C4×C7 | — | 2 | 2 | no | — |
| 316 | C4×C7 | — | 2 | 6 | no | — |
| 317 | C4×C7 | C2×C4×D4 | 1 | 6 | yes | — |
| 318 | C4×C7 | C24×C4 | 1 | 1 | yes | characteristic |
| 319 | C4×C7 | C22×#41 | 1 | 1 | yes | characteristic |
| 320 | Dic7 | — | 2 | 4 | no | — |
| 321 | Dic7 | — | 4 | 6 | no | — |
| 322 | Dic7 | — | 4 | 2 | no | — |
| 323 | C24 | — | 14 | 6 | no | — |
| 324 | #41 | — | 7 | 24 | no | — |
| 325 | #41 | — | 14 | 16 | no | — |
| 326 | #41 | — | 14 | 12 | no | — |
| 327 | #41 | C2×C4×D7 | 1 | 4 | yes | — |
| 328 | #41 | #1157 | 1 | 4 | yes | — |
| 329 | C2×Q8 | — | 7 | 2 | no | — |
| 330 | C2×Q8 | C2×D28 | 1 | 1 | yes | characteristic |
| 331 | C2×D4 | — | 7 | 24 | no | — |
| 332 | C2×D4 | — | 7 | 6 | no | — |
| 333 | C2×D4 | — | 14 | 6 | no | — |
| 334 | C2×D4 | — | 14 | 48 | no | — |
| 335 | C2×D4 | — | 14 | 6 | no | — |
| 336 | C2×D4 | — | 14 | 12 | no | — |
| 337 | C2×D4 | C2×D28 | 1 | 3 | yes | — |
| 338 | C22×C4 | — | 14 | 6 | no | — |
| 339 | C22×C4 | — | 14 | 6 | no | — |
| 340 | C22×C4 | — | 14 | 6 | no | — |
| 341 | C22×C4 | — | 14 | 6 | no | — |
| 342 | C22×C4 | — | 14 | 12 | no | — |
| 343 | C22×C4 | — | 56 | 12 | no | — |
| 344 | C22×C4 | C2×D28 | 1 | 6 | yes | — |
| 345 | C22×C4 | C23×D7 | 1 | 3 | yes | — |
| 346 | Q16 | — | 7 | 4 | no | — |
| 347 | SD16 | — | 7 | 24 | no | — |
| 348 | D8 | — | 7 | 12 | no | — |
| 349 | D8 | — | 7 | 24 | no | — |
| 350 | M16 | — | 2 | 6 | no | — |
| 351 | M16 | C2×C4×D7 | 1 | 12 | yes | complemented |
| 352 | C2×C8 | — | 2 | 6 | no | — |
| 353 | C2×C8 | C2×C4×D7 | 1 | 12 | yes | complemented |
| 354 | C2×C8 | C23×D7 | 1 | 3 | yes | — |
| 355 | C2×C8 | C23×D7 | 1 | 1 | yes | characteristic |
| 356 | C2×C8 | C23×D7 | 1 | 3 | yes | — |
| 357 | C2×C8 | C23×D7 | 1 | 1 | yes | characteristic |
| 358 | C4⋊C4 | — | 7 | 6 | no | — |
| 359 | C4⋊C4 | — | 7 | 2 | no | — |
| 360 | C4⋊C4 | — | 14 | 6 | no | — |
| 361 | C4⋊C4 | — | 14 | 2 | no | — |
| 362 | C4⋊C4 | — | 14 | 6 | no | — |
| 363 | C4⋊C4 | C2×D28 | 1 | 6 | yes | — |
| 364 | C22⋊C4 | — | 14 | 6 | no | — |
| 365 | C22⋊C4 | — | 14 | 6 | no | — |
| 366 | C22⋊C4 | — | 14 | 6 | no | — |
| 367 | C22⋊C4 | — | 14 | 12 | no | — |
| 368 | C22⋊C4 | C2×D28 | 1 | 6 | yes | — |
| 369 | C42 | — | 14 | 2 | no | — |
| 370 | C42 | — | 14 | 6 | no | — |
| 371 | C42 | — | 14 | 6 | no | — |
| 372 | C42 | C2×D28 | 1 | 6 | yes | — |
| 373 | C42 | C23×D7 | 1 | 3 | yes | — |
| 374 | C42 | C23×D7 | 1 | 1 | yes | characteristic |
| 375 | C2×C7 | — | 2 | 6 | no | — |
| 376 | C2×C7 | C22×C4×D4 | 1 | 1 | yes | characteristic |
| 377 | C2×C7 | #3585 | 1 | 2 | yes | — |
| 378 | D7 | — | 4 | 12 | no | — |
| 379 | C23 | — | 14 | 6 | no | — |
| 380 | C23 | — | 14 | 24 | no | — |
| 381 | C23 | — | 56 | 6 | no | — |
| 382 | C23 | — | 56 | 6 | no | — |
| 383 | C23 | C22×D28 | 1 | 3 | yes | — |
| 384 | Q8 | — | 7 | 4 | no | — |
| 385 | Q8 | — | 14 | 2 | no | — |
| 386 | Q8 | C4×D28 | 1 | 4 | yes | — |
| 387 | D4 | — | 7 | 12 | no | — |
| 388 | D4 | — | 14 | 24 | no | — |
| 389 | D4 | — | 14 | 24 | no | — |
| 390 | D4 | — | 14 | 6 | no | — |
| 391 | D4 | C4×D28 | 1 | 12 | yes | — |
| 392 | C2×C4 | — | 4 | 6 | no | — |
| 393 | C2×C4 | — | 14 | 2 | no | — |
| 394 | C2×C4 | — | 14 | 24 | no | — |
| 395 | C2×C4 | — | 14 | 2 | no | — |
| 396 | C2×C4 | — | 14 | 6 | no | — |
| 397 | C2×C4 | — | 28 | 12 | no | — |
| 398 | C2×C4 | — | 56 | 6 | no | — |
| 399 | C2×C4 | — | 56 | 12 | no | — |
| 400 | C2×C4 | — | 56 | 6 | no | — |
| 401 | C2×C4 | C22×C4×D7 | 1 | 6 | yes | — |
| 402 | C2×C4 | C22×D28 | 1 | 2 | yes | — |
| 403 | C2×C4 | C22×D28 | 1 | 6 | yes | — |
| 404 | C2×C4 | C22×D28 | 1 | 3 | yes | — |
| 405 | C2×C4 | C2×#1157 | 1 | 6 | yes | — |
| 406 | C2×C4 | C24×D7 | 1 | 1 | yes | characteristic |
| 407 | C8 | — | 2 | 1 | no | — |
| 408 | C8 | — | 2 | 3 | no | — |
| 409 | C8 | C22×C4×D7 | 1 | 2 | yes | — |
| 410 | C8 | C22×C4×D7 | 1 | 6 | yes | — |
| 411 | C7 | #60176 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 412 | C22 | — | 2 | 6 | no | — |
| 413 | C22 | — | 14 | 12 | no | — |
| 414 | C22 | — | 28 | 6 | no | — |
| 415 | C22 | — | 28 | 6 | no | — |
| 416 | C22 | — | 56 | 24 | no | — |
| 417 | C22 | C2×C4×D28 | 1 | 6 | yes | — |
| 418 | C22 | C23×D28 | 1 | 1 | yes | characteristic |
| 419 | C4 | — | 2 | 2 | no | — |
| 420 | C4 | — | 2 | 6 | no | — |
| 421 | C4 | — | 14 | 4 | no | — |
| 422 | C4 | — | 28 | 6 | no | — |
| 423 | C4 | — | 28 | 2 | no | — |
| 424 | C4 | C2×C4×D28 | 1 | 6 | yes | — |
| 425 | C4 | C23×C4×D7 | 1 | 1 | yes | characteristic |
| 426 | C4 | C22×#1157 | 1 | 1 | yes | characteristic |
| 427 | C2 | — | 2 | 6 | no | — |
| 428 | C2 | — | 28 | 12 | no | — |
| 429 | C2 | C22×C4×D28 | 1 | 1 | yes | characteristic |
| 430 | C2 | #11744235 | 1 | 2 | yes | — |
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