Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1616 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 1616 conjugacy classes of subgroups — too many to draw. Only its 199 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 | C4×#14556096 | C2 | 1 | 3 | yes | maximal, complemented |
| 2 | #22589692 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #22589588 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #22589503 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #22589464 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | C4×#14556043 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | C71×#3459 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C23×C4×D71 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×#14556096 | C22 | 1 | 3 | yes | — |
| 10 | C2×C4×C22⋊D71 | — | 2 | 3 | no | — |
| 11 | C2×#14556043 | C22 | 1 | 6 | yes | — |
| 12 | #17985879 | C22 | 1 | 3 | yes | — |
| 13 | #17985875 | — | 2 | 3 | no | — |
| 14 | #17985871 | C22 | 1 | 3 | yes | — |
| 15 | #17985870 | — | 2 | 3 | no | — |
| 16 | #17985854 | C22 | 1 | 3 | yes | — |
| 17 | C4×(C2×D71)⋊C4 | — | 2 | 3 | no | — |
| 18 | C4×C22⋊Dic71 | C22 | 1 | 3 | yes | — |
| 19 | #17985766 | C22 | 1 | 3 | yes | — |
| 20 | #17985766 | C22 | 1 | 3 | yes | — |
| 21 | #543×C71 | C22 | 1 | 1 | yes | characteristic |
| 22 | #539×C71 | — | 2 | 3 | no | — |
| 23 | #538×C71 | — | 2 | 3 | no | — |
| 24 | #534×C71 | C22 | 1 | 3 | yes | — |
| 25 | #529×C71 | — | 2 | 3 | no | — |
| 26 | #525×C71 | — | 2 | 3 | no | — |
| 27 | C2×C4×D4×C71 | C22 | 1 | 3 | yes | — |
| 28 | C24×D71 | C23 | 1 | 1 | yes | characteristic |
| 29 | C22×C22⋊D71 | — | 2 | 3 | no | — |
| 30 | C23×Dic71 | C23 | 1 | 1 | yes | characteristic |
| 31 | C22×C4×D71 | — | 2 | 3 | no | — |
| 32 | C22×C4×D71 | — | 2 | 3 | no | — |
| 33 | C22×C4×D71 | — | 4 | 4 | no | — |
| 34 | #14556096 | — | 2 | 6 | no | — |
| 35 | #14556096 | — | 2 | 6 | no | — |
| 36 | C4×C22⋊D71 | — | 4 | 12 | no | — |
| 37 | C2×Dic71⋊C4 | — | 2 | 3 | no | — |
| 38 | C2×C22⋊Dic71 | — | 2 | 3 | no | — |
| 39 | C2×C22⋊Dic71 | C23 | 1 | 3 | yes | — |
| 40 | C2×C22⋊Dic71 | C23 | 1 | 3 | yes | — |
| 41 | C2×(C2×D71)⋊C4 | — | 2 | 3 | no | — |
| 42 | C2×(C2×D71)⋊C4 | — | 2 | 3 | no | — |
| 43 | C2×(C2×D71)⋊C4 | — | 2 | 3 | no | — |
| 44 | C2×C4×Dic71 | — | 2 | 3 | no | — |
| 45 | #14556043 | — | 2 | 12 | no | — |
| 46 | C71⋊#95 | — | 2 | 3 | no | — |
| 47 | C71⋊#95 | — | 2 | 3 | no | — |
| 48 | C71⋊#95 | — | 2 | 3 | no | — |
| 49 | C2×#41×C71 | — | 2 | 1 | no | — |
| 50 | C22×D4×C71 | C23 | 1 | 3 | yes | — |
| 51 | C23×C4×C71 | D4 | 1 | 3 | yes | complemented |
| 52 | C23×C4×C71 | C23 | 1 | 1 | yes | characteristic |
| 53 | #126×C71 | — | 2 | 6 | no | — |
| 54 | #125×C71 | — | 2 | 3 | no | — |
| 55 | #124×C71 | — | 2 | 3 | no | — |
| 56 | #123×C71 | — | 2 | 6 | no | — |
| 57 | #123×C71 | — | 2 | 6 | no | — |
| 58 | C22⋊Q8×C71 | — | 2 | 3 | no | — |
| 59 | C22⋊Q8×C71 | — | 2 | 3 | no | — |
| 60 | C22⋊Q8×C71 | — | 2 | 3 | no | — |
| 61 | #121×C71 | — | 2 | 3 | no | — |
| 62 | #121×C71 | — | 2 | 3 | no | — |
| 63 | #121×C71 | — | 2 | 3 | no | — |
| 64 | #120×C71 | — | 2 | 6 | no | — |
| 65 | C4×Q8×C71 | — | 2 | 1 | no | — |
| 66 | C4×D4×C71 | — | 2 | 3 | no | — |
| 67 | C4×D4×C71 | — | 2 | 6 | no | — |
| 68 | C4×D4×C71 | — | 2 | 6 | no | — |
| 69 | #117×C71 | — | 2 | 3 | no | — |
| 70 | C2×C4⋊C4×C71 | D4 | 1 | 3 | yes | complemented |
| 71 | C2×C22⋊C4×C71 | D4 | 1 | 3 | yes | complemented |
| 72 | C2×C22⋊C4×C71 | C23 | 1 | 3 | yes | — |
| 73 | C2×C42×C71 | D4 | 1 | 3 | yes | complemented |
| 74 | C23×D71 | — | 2 | 3 | no | — |
| 75 | C23×D71 | — | 2 | 3 | no | — |
| 76 | C23×D71 | — | 4 | 2 | no | — |
| 77 | C23×D71 | — | 4 | 2 | no | — |
| 78 | C23×D71 | #41 | 1 | 2 | yes | complemented |
| 79 | C2×C22⋊D71 | — | 2 | 12 | no | — |
| 80 | C2×C22⋊D71 | — | 4 | 6 | no | — |
| 81 | C2×C22⋊D71 | — | 4 | 6 | no | — |
| 82 | C22×Dic71 | — | 2 | 3 | no | — |
| 83 | C22×Dic71 | — | 2 | 3 | no | — |
| 84 | C22×Dic71 | — | 2 | 3 | no | — |
| 85 | C22×Dic71 | — | 4 | 2 | no | — |
| 86 | C2×C4×D71 | — | 2 | 12 | no | — |
| 87 | C2×C4×D71 | — | 4 | 6 | no | — |
| 88 | C2×C4×D71 | — | 4 | 6 | no | — |
| 89 | C2×C4×D71 | — | 4 | 6 | no | — |
| 90 | C2×C4×D71 | — | 4 | 3 | no | — |
| 91 | C2×C4×D71 | — | 4 | 1 | no | — |
| 92 | Dic71⋊C4 | — | 4 | 6 | no | — |
| 93 | C22⋊Dic71 | — | 2 | 3 | no | — |
| 94 | C22⋊Dic71 | — | 2 | 6 | no | — |
| 95 | C22⋊Dic71 | — | 4 | 6 | no | — |
| 96 | C22⋊Dic71 | #41 | 1 | 6 | yes | complemented |
| 97 | (C2×D71)⋊C4 | — | 2 | 12 | no | — |
| 98 | (C2×D71)⋊C4 | — | 4 | 6 | no | — |
| 99 | (C2×D71)⋊C4 | — | 4 | 6 | no | — |
| 100 | C4×Dic71 | — | 4 | 6 | no | — |
| 101 | C24×C71 | C2×D4 | 1 | 3 | yes | — |
| 102 | C24×C71 | C24 | 1 | 1 | yes | characteristic |
| 103 | #41×C71 | — | 8 | 2 | no | — |
| 104 | C2×Q8×C71 | — | 2 | 1 | no | — |
| 105 | C2×Q8×C71 | — | 2 | 1 | no | — |
| 106 | C2×D4×C71 | — | 2 | 6 | no | — |
| 107 | C2×D4×C71 | — | 2 | 6 | no | — |
| 108 | C2×D4×C71 | — | 2 | 3 | no | — |
| 109 | C2×D4×C71 | — | 2 | 3 | no | — |
| 110 | C2×D4×C71 | — | 2 | 3 | no | — |
| 111 | C2×D4×C71 | — | 2 | 3 | no | — |
| 112 | C22×C4×C71 | — | 2 | 3 | no | — |
| 113 | C22×C4×C71 | — | 2 | 3 | no | — |
| 114 | C22×C4×C71 | — | 4 | 2 | no | — |
| 115 | C22×C4×C71 | — | 4 | 6 | no | — |
| 116 | C22×C4×C71 | C2×D4 | 1 | 3 | yes | — |
| 117 | C22×C4×C71 | C2×D4 | 1 | 3 | yes | — |
| 118 | C22×C4×C71 | C2×D4 | 1 | 3 | yes | — |
| 119 | C22×C4×C71 | C2×D4 | 1 | 3 | yes | — |
| 120 | C22×C4×C71 | C2×D4 | 1 | 3 | yes | — |
| 121 | C4⋊C4×C71 | — | 2 | 3 | no | — |
| 122 | C4⋊C4×C71 | — | 2 | 3 | no | — |
| 123 | C4⋊C4×C71 | — | 2 | 3 | no | — |
| 124 | C4⋊C4×C71 | — | 2 | 3 | no | — |
| 125 | C4⋊C4×C71 | — | 2 | 6 | no | — |
| 126 | C22⋊C4×C71 | — | 2 | 6 | no | — |
| 127 | C22⋊C4×C71 | — | 2 | 6 | no | — |
| 128 | C22⋊C4×C71 | — | 2 | 6 | no | — |
| 129 | C22⋊C4×C71 | — | 2 | 6 | no | — |
| 130 | C42×C71 | — | 2 | 3 | no | — |
| 131 | C42×C71 | — | 2 | 3 | no | — |
| 132 | C23×C71 | — | 2 | 3 | no | — |
| 133 | C23×C71 | — | 2 | 3 | no | — |
| 134 | C23×C71 | — | 2 | 3 | no | — |
| 135 | C23×C71 | — | 4 | 1 | no | — |
| 136 | C23×C71 | — | 4 | 1 | no | — |
| 137 | C23×C71 | — | 4 | 3 | no | — |
| 138 | C23×C71 | — | 4 | 3 | no | — |
| 139 | C23×C71 | C22×D4 | 1 | 3 | yes | — |
| 140 | C23×C71 | C2×#41 | 1 | 1 | yes | characteristic |
| 141 | C23×C71 | C2×#41 | 1 | 3 | yes | — |
| 142 | C22×D71 | — | 2 | 6 | no | — |
| 143 | C22×D71 | — | 2 | 6 | no | — |
| 144 | C22×D71 | — | 2 | 6 | no | — |
| 145 | C22×D71 | — | 4 | 4 | no | — |
| 146 | C22×D71 | — | 4 | 12 | no | — |
| 147 | C22×D71 | — | 4 | 3 | no | — |
| 148 | C22×D71 | — | 4 | 3 | no | — |
| 149 | C22×D71 | — | 4 | 1 | no | — |
| 150 | C22×D71 | — | 4 | 3 | no | — |
| 151 | Q8×C71 | — | 8 | 1 | no | — |
| 152 | Q8×C71 | — | 8 | 1 | no | — |
| 153 | D4×C71 | — | 4 | 6 | no | — |
| 154 | D4×C71 | — | 4 | 6 | no | — |
| 155 | D4×C71 | — | 8 | 3 | no | — |
| 156 | D4×C71 | — | 8 | 3 | no | — |
| 157 | C2×C4×C71 | — | 2 | 6 | no | — |
| 158 | C2×C4×C71 | — | 2 | 3 | no | — |
| 159 | C2×C4×C71 | — | 2 | 3 | no | — |
| 160 | C2×C4×C71 | — | 2 | 3 | no | — |
| 161 | C2×C4×C71 | — | 2 | 3 | no | — |
| 162 | C2×C4×C71 | — | 2 | 3 | no | — |
| 163 | C2×C4×C71 | — | 4 | 3 | no | — |
| 164 | C2×C4×C71 | — | 4 | 6 | no | — |
| 165 | C2×C4×C71 | — | 4 | 3 | no | — |
| 166 | C2×C4×C71 | — | 4 | 3 | no | — |
| 167 | C2×C4×C71 | — | 8 | 3 | no | — |
| 168 | C2×C4×C71 | #120 | 1 | 3 | yes | — |
| 169 | C2×C4×C71 | #120 | 1 | 1 | yes | characteristic |
| 170 | C22⋊D71 | — | 4 | 24 | no | — |
| 171 | C2×Dic71 | — | 2 | 6 | no | — |
| 172 | C2×Dic71 | — | 2 | 6 | no | — |
| 173 | C2×Dic71 | — | 4 | 3 | no | — |
| 174 | C2×Dic71 | — | 4 | 3 | no | — |
| 175 | C2×Dic71 | — | 4 | 3 | no | — |
| 176 | C2×Dic71 | — | 4 | 1 | no | — |
| 177 | C2×Dic71 | — | 4 | 3 | no | — |
| 178 | C2×Dic71 | — | 4 | 3 | no | — |
| 179 | C2×Dic71 | — | 4 | 3 | no | — |
| 180 | C4×D71 | — | 4 | 12 | no | — |
| 181 | C4×D71 | — | 4 | 4 | no | — |
| 182 | C22×C71 | — | 2 | 3 | no | — |
| 183 | C22×C71 | — | 2 | 3 | no | — |
| 184 | C22×C71 | — | 4 | 1 | no | — |
| 185 | C22×C71 | — | 4 | 3 | no | — |
| 186 | C22×C71 | — | 4 | 6 | no | — |
| 187 | C22×C71 | — | 4 | 3 | no | — |
| 188 | C22×C71 | — | 4 | 3 | no | — |
| 189 | C22×C71 | — | 4 | 3 | no | — |
| 190 | C22×C71 | — | 8 | 3 | no | — |
| 191 | C22×C71 | C2×#120 | 1 | 1 | yes | characteristic |
| 192 | C22×C71 | #525 | 1 | 3 | yes | — |
| 193 | C22×C71 | #532 | 1 | 3 | yes | — |
| 194 | C2×D71 | — | 2 | 12 | no | — |
| 195 | C2×D71 | — | 4 | 6 | no | — |
| 196 | C2×D71 | — | 4 | 6 | no | — |
| 197 | C2×D71 | — | 4 | 6 | no | — |
| 198 | C2×D71 | — | 4 | 2 | no | — |
| 199 | C2×D71 | — | 4 | 2 | no | — |
| 200 | C2×D71 | — | 4 | 2 | no | — |
| 201 | C4×C71 | — | 2 | 3 | no | — |
| 202 | C4×C71 | — | 4 | 3 | no | — |
| 203 | C4×C71 | — | 4 | 3 | no | — |
| 204 | C4×C71 | — | 4 | 3 | no | — |
| 205 | C4×C71 | B(4,𝔽2) | 1 | 2 | yes | — |
| 206 | Dic71 | — | 4 | 6 | no | — |
| 207 | Dic71 | — | 4 | 2 | no | — |
| 208 | Dic71 | — | 8 | 3 | no | — |
| 209 | #23595 | — | 71 | 1 | no | maximal, Sylow |
| 210 | C2×C71 | — | 2 | 3 | no | — |
| 211 | C2×C71 | — | 2 | 3 | no | — |
| 212 | C2×C71 | — | 8 | 3 | no | — |
| 213 | C2×C71 | #2388 | 1 | 1 | yes | characteristic |
| 214 | C2×C71 | C2×B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 215 | C2×C71 | #3025 | 1 | 1 | yes | characteristic |
| 216 | D71 | — | 4 | 4 | no | — |
| 217 | #3459 | D71 | 1 | 1 | yes | characteristic, complemented |
| 218 | C4×#120 | — | 71 | 3 | no | — |
| 219 | #2062 | — | 71 | 1 | no | — |
| 220 | #2044 | — | 71 | 3 | no | — |
| 221 | #2029 | — | 71 | 1 | no | — |
| 222 | #2021 | — | 71 | 3 | no | — |
| 223 | C4×#99 | — | 71 | 3 | no | — |
| 224 | C71 | #23595 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 225 | C24×C4 | — | 71 | 1 | no | — |
| 226 | #543 | C2×D71 | 1 | 1 | yes | characteristic |
| 227 | #539 | — | 2 | 3 | no | — |
| 228 | #538 | — | 2 | 3 | no | — |
| 229 | #534 | C2×D71 | 1 | 3 | yes | — |
| 230 | #529 | — | 2 | 3 | no | — |
| 231 | #525 | — | 2 | 3 | no | — |
| 232 | C2×#120 | — | 71 | 3 | no | — |
| 233 | C2×C4×D4 | — | 142 | 3 | no | — |
| 234 | C2×C4×D4 | C2×D71 | 1 | 3 | yes | — |
| 235 | C2×#99 | — | 71 | 6 | no | — |
| 236 | #386 | — | 71 | 3 | no | — |
| 237 | #386 | — | 142 | 3 | no | — |
| 238 | #385 | — | 71 | 3 | no | — |
| 239 | #385 | — | 142 | 3 | no | — |
| 240 | #379 | — | 71 | 3 | no | — |
| 241 | C4×C22⋊C4 | — | 71 | 3 | no | — |
| 242 | C4×C22⋊C4 | — | 142 | 3 | no | — |
| 243 | #342 | — | 71 | 3 | no | — |
| 244 | #342 | — | 71 | 3 | no | — |
| 245 | C25 | — | 71 | 1 | no | — |
| 246 | C2×#41 | — | 2 | 1 | no | — |
| 247 | C22×D4 | — | 142 | 3 | no | — |
| 248 | C22×D4 | C22×D71 | 1 | 3 | yes | — |
| 249 | C23×C4 | — | 284 | 4 | no | — |
| 250 | C23×C4 | — | 71 | 1 | no | — |
| 251 | C23×C4 | — | 142 | 3 | no | — |
| 252 | C23×C4 | — | 142 | 3 | no | — |
| 253 | C23×C4 | C22⋊D71 | 1 | 3 | yes | complemented |
| 254 | C23×C4 | C22×D71 | 1 | 1 | yes | characteristic |
| 255 | #126 | — | 2 | 6 | no | — |
| 256 | #125 | — | 2 | 3 | no | — |
| 257 | #124 | — | 2 | 3 | no | — |
| 258 | #123 | — | 2 | 6 | no | — |
| 259 | #123 | — | 2 | 6 | no | — |
| 260 | C22⋊Q8 | — | 2 | 3 | no | — |
| 261 | C22⋊Q8 | — | 2 | 3 | no | — |
| 262 | C22⋊Q8 | — | 2 | 3 | no | — |
| 263 | #121 | — | 2 | 3 | no | — |
| 264 | #121 | — | 2 | 3 | no | — |
| 265 | #121 | — | 2 | 3 | no | — |
| 266 | #120 | — | 2 | 6 | no | — |
| 267 | #120 | — | 142 | 6 | no | — |
| 268 | #120 | — | 142 | 6 | no | — |
| 269 | C4×Q8 | — | 2 | 1 | no | — |
| 270 | C4×D4 | — | 2 | 3 | no | — |
| 271 | C4×D4 | — | 2 | 6 | no | — |
| 272 | C4×D4 | — | 2 | 6 | no | — |
| 273 | C4×D4 | — | 284 | 12 | no | — |
| 274 | #117 | — | 2 | 3 | no | — |
| 275 | C2×C4⋊C4 | — | 142 | 3 | no | — |
| 276 | C2×C4⋊C4 | C22⋊D71 | 1 | 3 | yes | complemented |
| 277 | C2×C22⋊C4 | — | 71 | 3 | no | — |
| 278 | C2×C22⋊C4 | — | 71 | 3 | no | — |
| 279 | C2×C22⋊C4 | — | 142 | 3 | no | — |
| 280 | C2×C22⋊C4 | — | 142 | 3 | no | — |
| 281 | C2×C22⋊C4 | — | 142 | 3 | no | — |
| 282 | C2×C22⋊C4 | — | 142 | 3 | no | — |
| 283 | C2×C22⋊C4 | C22⋊D71 | 1 | 3 | yes | complemented |
| 284 | C2×C22⋊C4 | C22×D71 | 1 | 3 | yes | — |
| 285 | C2×C42 | — | 142 | 3 | no | — |
| 286 | C2×C42 | C22⋊D71 | 1 | 3 | yes | complemented |
| 287 | #99 | — | 142 | 12 | no | — |
| 288 | #95 | — | 142 | 3 | no | — |
| 289 | #95 | — | 142 | 3 | no | — |
| 290 | #95 | — | 142 | 3 | no | — |
| 291 | C24 | — | 284 | 2 | no | — |
| 292 | C24 | — | 284 | 2 | no | — |
| 293 | C24 | — | 71 | 2 | no | — |
| 294 | C24 | — | 142 | 3 | no | — |
| 295 | C24 | — | 142 | 3 | no | — |
| 296 | C24 | C2×C22⋊D71 | 1 | 3 | yes | — |
| 297 | C24 | C23×D71 | 1 | 1 | yes | characteristic |
| 298 | #41 | — | 8 | 2 | no | — |
| 299 | C2×Q8 | — | 2 | 1 | no | — |
| 300 | C2×Q8 | — | 2 | 1 | no | — |
| 301 | C2×D4 | — | 2 | 6 | no | — |
| 302 | C2×D4 | — | 2 | 6 | no | — |
| 303 | C2×D4 | — | 2 | 3 | no | — |
| 304 | C2×D4 | — | 2 | 3 | no | — |
| 305 | C2×D4 | — | 2 | 3 | no | — |
| 306 | C2×D4 | — | 2 | 3 | no | — |
| 307 | C2×D4 | — | 284 | 6 | no | — |
| 308 | C2×D4 | — | 284 | 6 | no | — |
| 309 | C2×D4 | — | 142 | 12 | no | — |
| 310 | C22×C4 | — | 2 | 3 | no | — |
| 311 | C22×C4 | — | 2 | 3 | no | — |
| 312 | C22×C4 | — | 4 | 2 | no | — |
| 313 | C22×C4 | — | 4 | 6 | no | — |
| 314 | C22×C4 | — | 284 | 6 | no | — |
| 315 | C22×C4 | — | 284 | 6 | no | — |
| 316 | C22×C4 | — | 284 | 6 | no | — |
| 317 | C22×C4 | — | 284 | 3 | no | — |
| 318 | C22×C4 | — | 284 | 1 | no | — |
| 319 | C22×C4 | — | 284 | 2 | no | — |
| 320 | C22×C4 | — | 142 | 12 | no | — |
| 321 | C22×C4 | — | 142 | 3 | no | — |
| 322 | C22×C4 | — | 142 | 3 | no | — |
| 323 | C22×C4 | — | 142 | 3 | no | — |
| 324 | C22×C4 | C2×C22⋊D71 | 1 | 3 | yes | — |
| 325 | C22×C4 | C2×C22⋊D71 | 1 | 3 | yes | — |
| 326 | C22×C4 | C2×C22⋊D71 | 1 | 3 | yes | — |
| 327 | C22×C4 | C2×C22⋊D71 | 1 | 3 | yes | — |
| 328 | C22×C4 | C2×C22⋊D71 | 1 | 3 | yes | — |
| 329 | C4⋊C4 | — | 2 | 3 | no | — |
| 330 | C4⋊C4 | — | 2 | 3 | no | — |
| 331 | C4⋊C4 | — | 2 | 3 | no | — |
| 332 | C4⋊C4 | — | 2 | 3 | no | — |
| 333 | C4⋊C4 | — | 2 | 6 | no | — |
| 334 | C4⋊C4 | — | 284 | 6 | no | — |
| 335 | C22⋊C4 | — | 2 | 6 | no | — |
| 336 | C22⋊C4 | — | 2 | 6 | no | — |
| 337 | C22⋊C4 | — | 2 | 6 | no | — |
| 338 | C22⋊C4 | — | 2 | 6 | no | — |
| 339 | C22⋊C4 | — | 284 | 6 | no | — |
| 340 | C22⋊C4 | — | 284 | 6 | no | — |
| 341 | C22⋊C4 | — | 284 | 6 | no | — |
| 342 | C22⋊C4 | — | 71 | 6 | no | — |
| 343 | C22⋊C4 | — | 142 | 12 | no | — |
| 344 | C22⋊C4 | — | 142 | 6 | no | — |
| 345 | C22⋊C4 | — | 142 | 3 | no | — |
| 346 | C42 | — | 2 | 3 | no | — |
| 347 | C42 | — | 2 | 3 | no | — |
| 348 | C42 | — | 284 | 6 | no | — |
| 349 | C23 | — | 2 | 3 | no | — |
| 350 | C23 | — | 2 | 3 | no | — |
| 351 | C23 | — | 2 | 3 | no | — |
| 352 | C23 | — | 4 | 1 | no | — |
| 353 | C23 | — | 4 | 1 | no | — |
| 354 | C23 | — | 4 | 3 | no | — |
| 355 | C23 | — | 4 | 3 | no | — |
| 356 | C23 | — | 284 | 3 | no | — |
| 357 | C23 | — | 284 | 3 | no | — |
| 358 | C23 | — | 284 | 12 | no | — |
| 359 | C23 | — | 284 | 4 | no | — |
| 360 | C23 | — | 284 | 1 | no | — |
| 361 | C23 | — | 284 | 3 | no | — |
| 362 | C23 | — | 142 | 6 | no | — |
| 363 | C23 | — | 142 | 6 | no | — |
| 364 | C23 | — | 142 | 6 | no | — |
| 365 | C23 | C22×C22⋊D71 | 1 | 3 | yes | — |
| 366 | C23 | #41×D71 | 1 | 1 | yes | characteristic |
| 367 | C23 | #41×D71 | 1 | 3 | yes | — |
| 368 | Q8 | — | 8 | 1 | no | — |
| 369 | Q8 | — | 8 | 1 | no | — |
| 370 | D4 | — | 4 | 6 | no | — |
| 371 | D4 | — | 4 | 6 | no | — |
| 372 | D4 | — | 8 | 3 | no | — |
| 373 | D4 | — | 8 | 3 | no | — |
| 374 | D4 | — | 284 | 24 | no | — |
| 375 | C2×C4 | — | 2 | 6 | no | — |
| 376 | C2×C4 | — | 2 | 3 | no | — |
| 377 | C2×C4 | — | 2 | 3 | no | — |
| 378 | C2×C4 | — | 2 | 3 | no | — |
| 379 | C2×C4 | — | 2 | 3 | no | — |
| 380 | C2×C4 | — | 2 | 3 | no | — |
| 381 | C2×C4 | — | 4 | 3 | no | — |
| 382 | C2×C4 | — | 4 | 6 | no | — |
| 383 | C2×C4 | — | 4 | 3 | no | — |
| 384 | C2×C4 | — | 4 | 3 | no | — |
| 385 | C2×C4 | — | 8 | 3 | no | — |
| 386 | C2×C4 | — | 284 | 12 | no | — |
| 387 | C2×C4 | — | 284 | 3 | no | — |
| 388 | C2×C4 | — | 284 | 3 | no | — |
| 389 | C2×C4 | — | 284 | 3 | no | — |
| 390 | C2×C4 | — | 284 | 1 | no | — |
| 391 | C2×C4 | — | 284 | 4 | no | — |
| 392 | C2×C4 | — | 284 | 3 | no | — |
| 393 | C2×C4 | — | 284 | 3 | no | — |
| 394 | C2×C4 | — | 284 | 3 | no | — |
| 395 | C2×C4 | — | 142 | 6 | no | — |
| 396 | C2×C4 | — | 142 | 6 | no | — |
| 397 | C2×C4 | #14556097 | 1 | 3 | yes | — |
| 398 | C2×C4 | #14556097 | 1 | 1 | yes | characteristic |
| 399 | C22 | — | 2 | 3 | no | — |
| 400 | C22 | — | 2 | 3 | no | — |
| 401 | C22 | — | 4 | 1 | no | — |
| 402 | C22 | — | 4 | 3 | no | — |
| 403 | C22 | — | 4 | 6 | no | — |
| 404 | C22 | — | 4 | 3 | no | — |
| 405 | C22 | — | 4 | 3 | no | — |
| 406 | C22 | — | 4 | 3 | no | — |
| 407 | C22 | — | 8 | 3 | no | — |
| 408 | C22 | — | 284 | 6 | no | — |
| 409 | C22 | — | 284 | 6 | no | — |
| 410 | C22 | — | 284 | 6 | no | — |
| 411 | C22 | — | 284 | 2 | no | — |
| 412 | C22 | — | 284 | 2 | no | — |
| 413 | C22 | — | 284 | 2 | no | — |
| 414 | C22 | — | 142 | 12 | no | — |
| 415 | C22 | C2×#14556097 | 1 | 1 | yes | characteristic |
| 416 | C22 | #17986506 | 1 | 3 | yes | — |
| 417 | C22 | #17986545 | 1 | 3 | yes | — |
| 418 | C4 | — | 2 | 3 | no | — |
| 419 | C4 | — | 4 | 3 | no | — |
| 420 | C4 | — | 4 | 3 | no | — |
| 421 | C4 | — | 4 | 3 | no | — |
| 422 | C4 | — | 284 | 6 | no | — |
| 423 | C4 | — | 284 | 2 | no | — |
| 424 | C4 | — | 568 | 3 | no | — |
| 425 | C4 | #17986186 | 1 | 2 | yes | — |
| 426 | C2 | — | 2 | 3 | no | — |
| 427 | C2 | — | 2 | 3 | no | — |
| 428 | C2 | — | 8 | 3 | no | — |
| 429 | C2 | — | 284 | 4 | no | — |
| 430 | C2 | #22591553 | 1 | 1 | yes | characteristic |
| 431 | C2 | C2×#17986186 | 1 | 1 | yes | characteristic |
| 432 | C2 | #22597732 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C4×#14556096 | C2 | semidirect |
| 2. #22589692 | C2 | semidirect |
| 3. #22589588 | C2 | semidirect |
| 4. #22589503 | C2 | semidirect |
| 5. #22589464 | C2 | semidirect |
| 6. C4×#14556043 | C2 | semidirect |
| 7. C71×#3459 | C2 | semidirect |
| 51. C23×C4×C71 | D4 | semidirect |
| 70. C2×C4⋊C4×C71 | D4 | semidirect |
| 71. C2×C22⋊C4×C71 | D4 | semidirect |
| 73. C2×C42×C71 | D4 | semidirect |
| 78. C23×D71 | #41 | semidirect |
| 96. C22⋊Dic71 | #41 | semidirect |
| 217. #3459 | D71 | semidirect |
| 224. C71 | #23595 | semidirect |
| 253. C23×C4 | C22⋊D71 | semidirect |
| 276. C2×C4⋊C4 | C22⋊D71 | semidirect |
| 283. C2×C22⋊C4 | C22⋊D71 | semidirect |
| 286. C2×C42 | C22⋊D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556096 | 2 |
| #22589692 | 2 |
| #22589588 | 2 |
| #22589503 | 2 |
| #22589464 | 2 |
| C4×#14556043 | 2 |
| C71×#3459 | 2 |
| #23595 | 71 |