Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1764 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 1764 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 | #22601984 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #22597739 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #22589471 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #22588880 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | C71×#1782 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×#14556173 | C22 | 1 | 2 | yes | complemented |
| 7 | #17986648 | — | 2 | 8 | no | — |
| 8 | #17986637 | — | 2 | 8 | no | — |
| 9 | #17986573 | — | 2 | 2 | no | — |
| 10 | #17986561 | C22 | 1 | 4 | yes | — |
| 11 | #17986558 | — | 2 | 2 | no | — |
| 12 | #17986558 | C22 | 1 | 4 | yes | — |
| 13 | #17986510 | — | 2 | 2 | no | — |
| 14 | C2×#14556111 | — | 2 | 2 | no | — |
| 15 | C2×#14556111 | C22 | 1 | 4 | yes | complemented |
| 16 | #17986474 | C22 | 1 | 2 | yes | complemented |
| 17 | #17986190 | — | 2 | 8 | no | — |
| 18 | #17986187 | — | 2 | 8 | no | — |
| 19 | C2×#14556042 | C22 | 1 | 8 | yes | complemented |
| 20 | #17985766 | C22 | 1 | 4 | yes | complemented |
| 21 | C22×#41×C71 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#99×C71 | C22 | 1 | 4 | yes | complemented |
| 23 | #381×C71 | C22 | 1 | 2 | yes | complemented |
| 24 | #14556173 | — | 2 | 8 | no | — |
| 25 | #14556173 | — | 4 | 4 | no | — |
| 26 | C2×#11765865 | — | 2 | 2 | no | — |
| 27 | C2×#11765864 | — | 2 | 4 | no | — |
| 28 | C22×C22⋊D71 | — | 2 | 2 | no | — |
| 29 | C22×C22⋊D71 | C23 | 1 | 4 | yes | — |
| 30 | C2×D4×D71 | — | 2 | 4 | no | — |
| 31 | #14556126 | — | 2 | 4 | no | — |
| 32 | #14556117 | — | 2 | 4 | no | — |
| 33 | #14556112 | — | 2 | 8 | no | — |
| 34 | #14556111 | — | 2 | 8 | no | — |
| 35 | #14556111 | — | 2 | 8 | no | — |
| 36 | #14556111 | — | 2 | 4 | no | — |
| 37 | #14556111 | — | 2 | 4 | no | — |
| 38 | #14556111 | — | 2 | 4 | no | — |
| 39 | #14556109 | — | 2 | 4 | no | — |
| 40 | #14556109 | D4 | 1 | 8 | yes | complemented |
| 41 | #14556107 | — | 2 | 4 | no | — |
| 42 | #14556104 | — | 2 | 8 | no | — |
| 43 | #14556102 | — | 2 | 4 | no | — |
| 44 | #14556102 | — | 4 | 4 | no | — |
| 45 | #14556100 | — | 2 | 8 | no | — |
| 46 | #14556100 | — | 2 | 8 | no | — |
| 47 | #14556098 | — | 2 | 8 | no | — |
| 48 | #14556097 | — | 2 | 4 | no | — |
| 49 | #14556096 | — | 2 | 4 | no | — |
| 50 | #14556096 | D4 | 1 | 8 | yes | complemented |
| 51 | D4×Dic71 | — | 2 | 8 | no | — |
| 52 | C4×C22⋊D71 | — | 2 | 8 | no | — |
| 53 | #14556087 | — | 2 | 2 | no | — |
| 54 | C2×Dic71⋊C4 | — | 2 | 4 | no | — |
| 55 | C2×Dic71⋊C4 | — | 2 | 4 | no | — |
| 56 | C2×C22⋊Dic71 | — | 2 | 2 | no | — |
| 57 | C2×C22⋊Dic71 | C23 | 1 | 4 | yes | — |
| 58 | C2×(C2×D71)⋊C4 | — | 2 | 4 | no | — |
| 59 | C2×(C2×D71)⋊C4 | — | 2 | 4 | no | — |
| 60 | #14556042 | — | 2 | 16 | no | — |
| 61 | C2×#41×C71 | — | 2 | 8 | no | — |
| 62 | C2×#41×C71 | — | 4 | 2 | no | — |
| 63 | C22×Q8×C71 | D4 | 1 | 1 | yes | characteristic, complemented |
| 64 | C22×D4×C71 | D4 | 1 | 1 | yes | characteristic, complemented |
| 65 | C22×D4×C71 | C23 | 1 | 2 | yes | — |
| 66 | C23×C4×C71 | D4 | 1 | 2 | yes | complemented |
| 67 | C23×C4×C71 | C23 | 1 | 1 | yes | characteristic |
| 68 | C2×C22⋊C4×C71 | C23 | 1 | 4 | yes | — |
| 69 | #99×C71 | — | 2 | 8 | no | — |
| 70 | #95×C71 | — | 4 | 2 | no | — |
| 71 | C23×D71 | — | 2 | 2 | no | — |
| 72 | C23×D71 | C2×D4 | 1 | 4 | yes | — |
| 73 | #11765865 | — | 4 | 4 | no | — |
| 74 | #11765865 | — | 4 | 4 | no | — |
| 75 | #11765864 | — | 4 | 16 | no | — |
| 76 | C2×Dic142 | — | 2 | 2 | no | — |
| 77 | C2×D284 | — | 2 | 2 | no | — |
| 78 | C2×D284 | — | 4 | 4 | no | — |
| 79 | C2×C22⋊D71 | — | 2 | 4 | no | — |
| 80 | C2×C22⋊D71 | — | 2 | 4 | no | — |
| 81 | C2×C22⋊D71 | — | 2 | 4 | no | — |
| 82 | C2×C22⋊D71 | — | 2 | 8 | no | — |
| 83 | C2×C22⋊D71 | — | 2 | 8 | no | — |
| 84 | C2×C22⋊D71 | — | 2 | 8 | no | — |
| 85 | C2×C22⋊D71 | — | 4 | 4 | no | — |
| 86 | C2×C22⋊D71 | — | 4 | 4 | no | — |
| 87 | D4×D71 | — | 4 | 16 | no | — |
| 88 | C22×Dic71 | — | 2 | 2 | no | — |
| 89 | C22×Dic71 | — | 2 | 4 | no | — |
| 90 | C22×Dic71 | — | 2 | 4 | no | — |
| 91 | C22×Dic71 | C2×D4 | 1 | 4 | yes | — |
| 92 | C2×C4×D71 | — | 2 | 4 | no | — |
| 93 | C4⋊Dic71 | — | 2 | 4 | no | — |
| 94 | C4⋊Dic71 | — | 4 | 4 | no | — |
| 95 | Dic71⋊C4 | — | 2 | 8 | no | — |
| 96 | Dic71⋊C4 | — | 2 | 8 | no | — |
| 97 | Dic71⋊C4 | — | 2 | 8 | no | — |
| 98 | C22⋊Dic71 | — | 2 | 4 | no | — |
| 99 | C22⋊Dic71 | — | 2 | 8 | no | — |
| 100 | C22⋊Dic71 | — | 2 | 4 | no | — |
| 101 | C22⋊Dic71 | C2×D4 | 1 | 8 | yes | — |
| 102 | (C2×D71)⋊C4 | — | 2 | 8 | no | — |
| 103 | (C2×D71)⋊C4 | — | 2 | 8 | no | — |
| 104 | (C2×D71)⋊C4 | — | 2 | 8 | no | — |
| 105 | (C2×D71)⋊C4 | — | 4 | 8 | no | — |
| 106 | C4×Dic71 | — | 2 | 4 | no | — |
| 107 | C24×C71 | C2×D4 | 1 | 2 | yes | — |
| 108 | C24×C71 | C24 | 1 | 1 | yes | characteristic |
| 109 | #41×C71 | — | 4 | 16 | no | — |
| 110 | C2×Q8×C71 | — | 2 | 4 | no | — |
| 111 | C2×Q8×C71 | — | 4 | 1 | no | — |
| 112 | C2×D4×C71 | — | 2 | 4 | no | — |
| 113 | C2×D4×C71 | — | 2 | 4 | no | — |
| 114 | C2×D4×C71 | — | 2 | 4 | no | — |
| 115 | C2×D4×C71 | — | 4 | 1 | no | — |
| 116 | C2×D4×C71 | C2×D4 | 1 | 8 | yes | — |
| 117 | C22×C4×C71 | — | 2 | 4 | no | — |
| 118 | C22×C4×C71 | — | 2 | 4 | no | — |
| 119 | C22×C4×C71 | — | 2 | 2 | no | — |
| 120 | C22×C4×C71 | — | 2 | 4 | no | — |
| 121 | C22×C4×C71 | — | 2 | 4 | no | — |
| 122 | C22×C4×C71 | — | 4 | 2 | no | — |
| 123 | C22×C4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 124 | C22×C4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 125 | C22×C4×C71 | C2×D4 | 1 | 2 | yes | — |
| 126 | C22⋊C4×C71 | — | 2 | 8 | no | — |
| 127 | C23×C71 | — | 2 | 2 | no | — |
| 128 | C23×C71 | — | 2 | 2 | no | — |
| 129 | C23×C71 | — | 8 | 1 | no | — |
| 130 | C23×C71 | — | 8 | 2 | no | — |
| 131 | C23×C71 | #120 | 1 | 4 | yes | — |
| 132 | C23×C71 | C22×D4 | 1 | 4 | yes | — |
| 133 | C23×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 134 | C23×C71 | H(5,𝔽2) | 1 | 2 | yes | — |
| 135 | C22×D71 | — | 2 | 4 | no | — |
| 136 | C22×D71 | — | 2 | 8 | no | — |
| 137 | C22×D71 | — | 4 | 4 | no | — |
| 138 | C22×D71 | — | 8 | 4 | no | — |
| 139 | C22×D71 | — | 8 | 4 | no | — |
| 140 | Q8×C71 | — | 4 | 4 | no | — |
| 141 | D4×C71 | — | 2 | 16 | no | — |
| 142 | D4×C71 | — | 4 | 4 | no | — |
| 143 | C2×C4×C71 | — | 2 | 2 | no | — |
| 144 | C2×C4×C71 | — | 2 | 2 | no | — |
| 145 | C2×C4×C71 | — | 2 | 2 | no | — |
| 146 | C2×C4×C71 | — | 2 | 2 | no | — |
| 147 | C2×C4×C71 | — | 2 | 1 | no | — |
| 148 | C2×C4×C71 | — | 2 | 1 | no | — |
| 149 | C2×C4×C71 | — | 4 | 8 | no | — |
| 150 | C2×C4×C71 | — | 4 | 4 | no | — |
| 151 | C2×C4×C71 | — | 4 | 4 | no | — |
| 152 | C2×C4×C71 | — | 8 | 4 | no | — |
| 153 | C2×C4×C71 | #120 | 1 | 4 | yes | — |
| 154 | C22⋊D71 | — | 4 | 8 | no | — |
| 155 | C22⋊D71 | — | 4 | 4 | no | — |
| 156 | C22⋊D71 | — | 4 | 4 | no | — |
| 157 | C22⋊D71 | — | 4 | 8 | no | — |
| 158 | C22⋊D71 | — | 8 | 8 | no | — |
| 159 | C2×Dic71 | — | 2 | 8 | no | — |
| 160 | C2×Dic71 | — | 2 | 4 | no | — |
| 161 | C2×Dic71 | — | 2 | 8 | no | — |
| 162 | C2×Dic71 | — | 4 | 4 | no | — |
| 163 | C2×Dic71 | — | 8 | 4 | no | — |
| 164 | C2×Dic71 | — | 8 | 4 | no | — |
| 165 | D284 | — | 4 | 4 | no | — |
| 166 | D284 | — | 16 | 4 | no | — |
| 167 | C4×D71 | — | 4 | 8 | no | — |
| 168 | Dic142 | — | 4 | 4 | no | — |
| 169 | C22×C71 | — | 2 | 4 | no | — |
| 170 | C22×C71 | — | 4 | 4 | no | — |
| 171 | C22×C71 | — | 4 | 2 | no | — |
| 172 | C22×C71 | — | 4 | 1 | no | — |
| 173 | C22×C71 | — | 4 | 4 | no | — |
| 174 | C22×C71 | — | 4 | 4 | no | — |
| 175 | C22×C71 | — | 8 | 2 | no | — |
| 176 | C22×C71 | C2×#120 | 1 | 2 | yes | — |
| 177 | C22×C71 | #534 | 1 | 1 | yes | characteristic |
| 178 | C22×C71 | D42 | 1 | 4 | yes | — |
| 179 | C2×D71 | — | 4 | 8 | no | — |
| 180 | C2×D71 | — | 4 | 4 | no | — |
| 181 | C2×D71 | — | 8 | 8 | no | — |
| 182 | C2×D71 | — | 16 | 4 | no | — |
| 183 | C4×C71 | — | 2 | 4 | no | — |
| 184 | C4×C71 | — | 4 | 1 | no | — |
| 185 | C4×C71 | — | 4 | 1 | no | — |
| 186 | C4×C71 | — | 8 | 4 | no | — |
| 187 | Dic71 | — | 4 | 8 | no | — |
| 188 | Dic71 | — | 4 | 4 | no | — |
| 189 | #23896 | — | 71 | 1 | no | maximal, Sylow |
| 190 | C2×C71 | — | 2 | 2 | no | — |
| 191 | C2×C71 | — | 2 | 4 | no | — |
| 192 | C2×C71 | — | 2 | 1 | no | — |
| 193 | C2×C71 | — | 4 | 4 | no | — |
| 194 | C2×C71 | #2403 | 1 | 1 | yes | characteristic |
| 195 | D71 | — | 8 | 4 | no | — |
| 196 | #3485 | — | 71 | 2 | no | — |
| 197 | #3026 | — | 71 | 4 | no | — |
| 198 | #2022 | — | 71 | 4 | no | — |
| 199 | #1913 | — | 71 | 4 | no | — |
| 200 | #1782 | D71 | 1 | 1 | yes | characteristic, complemented |
| 201 | C71 | #23896 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 202 | C2×H(5,𝔽2) | — | 71 | 2 | no | — |
| 203 | C22×#41 | C2×D71 | 1 | 1 | yes | characteristic |
| 204 | #547 | — | 142 | 8 | no | — |
| 205 | #546 | — | 142 | 8 | no | — |
| 206 | #536 | — | 142 | 2 | no | — |
| 207 | #534 | — | 71 | 4 | no | — |
| 208 | #534 | — | 71 | 4 | no | — |
| 209 | #534 | — | 142 | 2 | no | — |
| 210 | #525 | — | 142 | 2 | no | — |
| 211 | C2×#123 | — | 71 | 4 | no | — |
| 212 | C2×#123 | — | 142 | 2 | no | — |
| 213 | #518 | — | 71 | 2 | no | — |
| 214 | #458 | — | 142 | 8 | no | — |
| 215 | B(4,𝔽2) | — | 142 | 8 | no | — |
| 216 | C2×#99 | — | 71 | 8 | no | — |
| 217 | C2×#99 | C2×D71 | 1 | 4 | yes | complemented |
| 218 | #381 | C2×D71 | 1 | 2 | yes | complemented |
| 219 | #342 | — | 71 | 4 | no | — |
| 220 | H(5,𝔽2) | — | 284 | 4 | no | — |
| 221 | H(5,𝔽2) | — | 142 | 8 | no | — |
| 222 | C2×#41 | — | 2 | 8 | no | — |
| 223 | C2×#41 | — | 4 | 2 | no | — |
| 224 | C2×#41 | — | 142 | 4 | no | — |
| 225 | C2×#41 | — | 142 | 2 | no | — |
| 226 | C22×Q8 | D284 | 1 | 1 | yes | characteristic, complemented |
| 227 | C22×D4 | — | 71 | 4 | no | — |
| 228 | C22×D4 | — | 142 | 4 | no | — |
| 229 | C22×D4 | — | 142 | 2 | no | — |
| 230 | C22×D4 | D284 | 1 | 1 | yes | characteristic, complemented |
| 231 | C22×D4 | C22×D71 | 1 | 2 | yes | — |
| 232 | C23×C4 | D284 | 1 | 2 | yes | complemented |
| 233 | C23×C4 | C22×D71 | 1 | 1 | yes | characteristic |
| 234 | C4⋊Q8 | — | 142 | 4 | no | — |
| 235 | #124 | — | 142 | 4 | no | — |
| 236 | #123 | — | 71 | 8 | no | — |
| 237 | #123 | — | 142 | 8 | no | — |
| 238 | #123 | — | 142 | 8 | no | — |
| 239 | #123 | — | 142 | 8 | no | — |
| 240 | #123 | — | 142 | 4 | no | — |
| 241 | #123 | — | 142 | 4 | no | — |
| 242 | #123 | — | 142 | 4 | no | — |
| 243 | #123 | — | 142 | 4 | no | — |
| 244 | C22⋊Q8 | — | 142 | 4 | no | — |
| 245 | C22⋊Q8 | — | 142 | 8 | no | — |
| 246 | #121 | — | 284 | 4 | no | — |
| 247 | #121 | — | 142 | 4 | no | — |
| 248 | #121 | — | 142 | 8 | no | — |
| 249 | #121 | — | 142 | 8 | no | — |
| 250 | #120 | — | 71 | 8 | no | — |
| 251 | #120 | — | 142 | 8 | no | — |
| 252 | #120 | — | 142 | 4 | no | — |
| 253 | #120 | — | 142 | 4 | no | — |
| 254 | C4×D4 | — | 142 | 8 | no | — |
| 255 | C4×D4 | — | 142 | 8 | no | — |
| 256 | #117 | — | 142 | 2 | no | — |
| 257 | C2×C4⋊C4 | — | 142 | 4 | no | — |
| 258 | C2×C4⋊C4 | — | 142 | 4 | no | — |
| 259 | C2×C22⋊C4 | — | 71 | 4 | no | — |
| 260 | C2×C22⋊C4 | — | 142 | 4 | no | — |
| 261 | C2×C22⋊C4 | — | 142 | 4 | no | — |
| 262 | C2×C22⋊C4 | — | 142 | 2 | no | — |
| 263 | C2×C22⋊C4 | C22×D71 | 1 | 4 | yes | — |
| 264 | #99 | — | 2 | 8 | no | — |
| 265 | #99 | — | 142 | 16 | no | — |
| 266 | #95 | — | 4 | 2 | no | — |
| 267 | C24 | — | 71 | 4 | no | — |
| 268 | C24 | — | 142 | 2 | no | — |
| 269 | C24 | C2×D284 | 1 | 2 | yes | — |
| 270 | C24 | C23×D71 | 1 | 1 | yes | characteristic |
| 271 | #41 | — | 4 | 16 | no | — |
| 272 | #41 | — | 284 | 4 | no | — |
| 273 | #41 | — | 284 | 16 | no | — |
| 274 | #41 | — | 284 | 4 | no | — |
| 275 | C2×Q8 | — | 2 | 4 | no | — |
| 276 | C2×Q8 | — | 4 | 1 | no | — |
| 277 | C2×Q8 | — | 142 | 2 | no | — |
| 278 | C2×D4 | — | 2 | 4 | no | — |
| 279 | C2×D4 | — | 2 | 4 | no | — |
| 280 | C2×D4 | — | 2 | 4 | no | — |
| 281 | C2×D4 | — | 4 | 1 | no | — |
| 282 | C2×D4 | — | 284 | 4 | no | — |
| 283 | C2×D4 | — | 284 | 16 | no | — |
| 284 | C2×D4 | — | 284 | 4 | no | — |
| 285 | C2×D4 | — | 284 | 4 | no | — |
| 286 | C2×D4 | — | 142 | 2 | no | — |
| 287 | C2×D4 | — | 142 | 4 | no | — |
| 288 | C2×D4 | — | 142 | 8 | no | — |
| 289 | C2×D4 | — | 142 | 4 | no | — |
| 290 | C2×D4 | — | 142 | 4 | no | — |
| 291 | C2×D4 | — | 142 | 8 | no | — |
| 292 | C2×D4 | — | 142 | 8 | no | — |
| 293 | C2×D4 | D4×D71 | 1 | 8 | yes | — |
| 294 | C22×C4 | — | 2 | 4 | no | — |
| 295 | C22×C4 | — | 2 | 2 | no | — |
| 296 | C22×C4 | — | 2 | 4 | no | — |
| 297 | C22×C4 | — | 2 | 4 | no | — |
| 298 | C22×C4 | — | 2 | 4 | no | — |
| 299 | C22×C4 | — | 4 | 2 | no | — |
| 300 | C22×C4 | — | 71 | 4 | no | — |
| 301 | C22×C4 | — | 142 | 4 | no | — |
| 302 | C22×C4 | — | 142 | 2 | no | — |
| 303 | C22×C4 | — | 142 | 4 | no | — |
| 304 | C22×C4 | — | 142 | 4 | no | — |
| 305 | C22×C4 | C2×D284 | 1 | 1 | yes | characteristic |
| 306 | C22×C4 | C2×D284 | 1 | 1 | yes | characteristic |
| 307 | C22×C4 | C2×D284 | 1 | 2 | yes | — |
| 308 | C4⋊C4 | — | 284 | 4 | no | — |
| 309 | C4⋊C4 | — | 142 | 8 | no | — |
| 310 | C4⋊C4 | — | 142 | 8 | no | — |
| 311 | C4⋊C4 | — | 142 | 4 | no | — |
| 312 | C4⋊C4 | — | 142 | 8 | no | — |
| 313 | C22⋊C4 | — | 2 | 8 | no | — |
| 314 | C22⋊C4 | — | 284 | 8 | no | — |
| 315 | C22⋊C4 | — | 71 | 8 | no | — |
| 316 | C22⋊C4 | — | 142 | 8 | no | — |
| 317 | C22⋊C4 | — | 142 | 8 | no | — |
| 318 | C22⋊C4 | — | 142 | 4 | no | — |
| 319 | C22⋊C4 | — | 142 | 4 | no | — |
| 320 | C22⋊C4 | — | 142 | 8 | no | — |
| 321 | C22⋊C4 | — | 142 | 8 | no | — |
| 322 | C42 | — | 142 | 4 | no | — |
| 323 | C23 | — | 2 | 2 | no | — |
| 324 | C23 | — | 2 | 2 | no | — |
| 325 | C23 | — | 8 | 1 | no | — |
| 326 | C23 | — | 8 | 2 | no | — |
| 327 | C23 | — | 284 | 4 | no | — |
| 328 | C23 | — | 568 | 4 | no | — |
| 329 | C23 | — | 568 | 4 | no | — |
| 330 | C23 | — | 142 | 4 | no | — |
| 331 | C23 | — | 142 | 8 | no | — |
| 332 | C23 | #14556098 | 1 | 4 | yes | — |
| 333 | C23 | C2×D4×D71 | 1 | 4 | yes | — |
| 334 | C23 | C22×D284 | 1 | 1 | yes | characteristic |
| 335 | C23 | #14556173 | 1 | 2 | yes | — |
| 336 | Q8 | — | 4 | 4 | no | — |
| 337 | Q8 | — | 284 | 4 | no | — |
| 338 | D4 | — | 2 | 16 | no | — |
| 339 | D4 | — | 4 | 4 | no | — |
| 340 | D4 | — | 284 | 4 | no | — |
| 341 | D4 | — | 284 | 8 | no | — |
| 342 | D4 | — | 284 | 4 | no | — |
| 343 | D4 | — | 284 | 8 | no | — |
| 344 | D4 | — | 284 | 4 | no | — |
| 345 | D4 | — | 568 | 8 | no | — |
| 346 | D4 | — | 1136 | 4 | no | — |
| 347 | C2×C4 | — | 2 | 2 | no | — |
| 348 | C2×C4 | — | 2 | 2 | no | — |
| 349 | C2×C4 | — | 2 | 1 | no | — |
| 350 | C2×C4 | — | 2 | 1 | no | — |
| 351 | C2×C4 | — | 2 | 2 | no | — |
| 352 | C2×C4 | — | 2 | 2 | no | — |
| 353 | C2×C4 | — | 4 | 8 | no | — |
| 354 | C2×C4 | — | 4 | 4 | no | — |
| 355 | C2×C4 | — | 4 | 4 | no | — |
| 356 | C2×C4 | — | 8 | 4 | no | — |
| 357 | C2×C4 | — | 284 | 8 | no | — |
| 358 | C2×C4 | — | 284 | 4 | no | — |
| 359 | C2×C4 | — | 568 | 4 | no | — |
| 360 | C2×C4 | — | 568 | 4 | no | — |
| 361 | C2×C4 | — | 142 | 8 | no | — |
| 362 | C2×C4 | — | 142 | 8 | no | — |
| 363 | C2×C4 | — | 142 | 4 | no | — |
| 364 | C2×C4 | #14556098 | 1 | 4 | yes | — |
| 365 | C22 | — | 2 | 4 | no | — |
| 366 | C22 | — | 4 | 2 | no | — |
| 367 | C22 | — | 4 | 4 | no | — |
| 368 | C22 | — | 4 | 1 | no | — |
| 369 | C22 | — | 4 | 4 | no | — |
| 370 | C22 | — | 4 | 4 | no | — |
| 371 | C22 | — | 8 | 2 | no | — |
| 372 | C22 | — | 284 | 8 | no | — |
| 373 | C22 | — | 284 | 4 | no | — |
| 374 | C22 | — | 568 | 8 | no | — |
| 375 | C22 | — | 1136 | 4 | no | — |
| 376 | C22 | C2×#14556098 | 1 | 2 | yes | — |
| 377 | C22 | #17986561 | 1 | 1 | yes | characteristic |
| 378 | C22 | #17986631 | 1 | 4 | yes | — |
| 379 | C4 | — | 2 | 4 | no | — |
| 380 | C4 | — | 4 | 1 | no | — |
| 381 | C4 | — | 4 | 1 | no | — |
| 382 | C4 | — | 8 | 4 | no | — |
| 383 | C4 | — | 284 | 8 | no | — |
| 384 | C4 | — | 284 | 4 | no | — |
| 385 | C2 | — | 2 | 4 | no | — |
| 386 | C2 | — | 2 | 2 | no | — |
| 387 | C2 | — | 2 | 1 | no | — |
| 388 | C2 | — | 4 | 4 | no | — |
| 389 | C2 | — | 568 | 4 | no | — |
| 390 | C2 | #22591653 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22601984 | C2 | semidirect |
| 2. #22597739 | C2 | semidirect |
| 3. #22589471 | C2 | semidirect |
| 4. #22588880 | C2 | semidirect |
| 5. C71×#1782 | C2 | semidirect |
| 6. C2×#14556173 | C22 | semidirect |
| 15. C2×#14556111 | C22 | semidirect |
| 16. #17986474 | C22 | semidirect |
| 19. C2×#14556042 | C22 | semidirect |
| 20. #17985766 | C22 | semidirect |
| 22. C2×#99×C71 | C22 | semidirect |
| 23. #381×C71 | C22 | semidirect |
| 40. #14556109 | D4 | semidirect |
| 50. #14556096 | D4 | semidirect |
| 63. C22×Q8×C71 | D4 | semidirect |
| 64. C22×D4×C71 | D4 | semidirect |
| 66. C23×C4×C71 | D4 | semidirect |
| 200. #1782 | D71 | semidirect |
| 201. C71 | #23896 | semidirect |
| 217. C2×#99 | C2×D71 | semidirect |
| 218. #381 | C2×D71 | semidirect |
| 226. C22×Q8 | D284 | semidirect |
| 230. C22×D4 | D284 | semidirect |
| 232. C23×C4 | D284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601984 | 2 |
| #22597739 | 2 |
| #22589471 | 2 |
| #22588880 | 2 |
| C71×#1782 | 2 |
| #23896 | 71 |