Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1302 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 1302 conjugacy classes of subgroups — too many to draw. Only its 187 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 | #22573867 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #22570142 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #22562700 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22561420 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #22560650 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #22560426 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #22560170 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | C67×#1785 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C2×#14524091 | C22 | 1 | 1 | yes | characteristic |
| 10 | #16864065 | — | 2 | 4 | no | — |
| 11 | #16864053 | — | 2 | 4 | no | — |
| 12 | #16863963 | — | 2 | 2 | no | — |
| 13 | #16863963 | C22 | 1 | 2 | yes | — |
| 14 | #16863907 | — | 2 | 2 | no | — |
| 15 | #16863907 | C22 | 1 | 2 | yes | — |
| 16 | #16863874 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×#14524002 | C22 | 1 | 1 | yes | characteristic |
| 18 | C22×C4×Dic67 | C22 | 1 | 1 | yes | characteristic |
| 19 | #16863738 | — | 2 | 4 | no | — |
| 20 | #16863721 | — | 2 | 4 | no | — |
| 21 | #16863438 | C22 | 1 | 4 | yes | — |
| 22 | C2×#14523969 | C22 | 1 | 4 | yes | — |
| 23 | #16863398 | C22 | 1 | 4 | yes | — |
| 24 | #16863303 | C22 | 1 | 2 | yes | — |
| 25 | #16863299 | C22 | 1 | 2 | yes | — |
| 26 | #16863276 | — | 2 | 2 | no | — |
| 27 | C4×C22⋊Dic67 | — | 2 | 2 | no | — |
| 28 | #16863157 | C22 | 1 | 4 | yes | — |
| 29 | C22×#41×C67 | C22 | 1 | 1 | yes | characteristic |
| 30 | C2×#101×C67 | C22 | 1 | 2 | yes | — |
| 31 | C2×#100×C67 | C22 | 1 | 2 | yes | — |
| 32 | #407×C67 | C22 | 1 | 2 | yes | — |
| 33 | #14524091 | — | 2 | 4 | no | — |
| 34 | #14524091 | — | 4 | 2 | no | — |
| 35 | C2×#11761629 | — | 2 | 2 | no | — |
| 36 | C2×#11761628 | — | 2 | 2 | no | — |
| 37 | C2×#11761628 | C23 | 1 | 2 | yes | — |
| 38 | C2×Q8×D67 | — | 2 | 2 | no | — |
| 39 | C23×Dic67 | — | 2 | 1 | no | — |
| 40 | #14524039 | — | 2 | 4 | no | — |
| 41 | #14524039 | — | 2 | 2 | no | — |
| 42 | #14524030 | — | 2 | 4 | no | — |
| 43 | #14524030 | — | 2 | 2 | no | — |
| 44 | #14524026 | — | 2 | 2 | no | — |
| 45 | #14524022 | — | 2 | 4 | no | — |
| 46 | #14524022 | D4 | 1 | 4 | yes | — |
| 47 | #14524017 | — | 2 | 4 | no | — |
| 48 | #14524017 | D4 | 1 | 4 | yes | — |
| 49 | #14524014 | — | 2 | 8 | no | — |
| 50 | #14524014 | — | 2 | 4 | no | — |
| 51 | #14524012 | — | 2 | 4 | no | — |
| 52 | #14524012 | — | 2 | 2 | no | — |
| 53 | Q8×Dic67 | — | 2 | 4 | no | — |
| 54 | C4×C22⋊D67 | — | 2 | 8 | no | — |
| 55 | C4×C22⋊D67 | — | 2 | 4 | no | — |
| 56 | #14524002 | — | 2 | 2 | no | — |
| 57 | #14524002 | — | 2 | 4 | no | — |
| 58 | #14524002 | C23 | 1 | 2 | yes | — |
| 59 | C2×C4⋊Dic67 | C23 | 1 | 2 | yes | — |
| 60 | C2×C22⋊Dic67 | — | 2 | 4 | no | — |
| 61 | C2×C22⋊Dic67 | — | 2 | 1 | no | — |
| 62 | C2×C4×Dic67 | — | 2 | 1 | no | — |
| 63 | C2×C4×Dic67 | — | 2 | 1 | no | — |
| 64 | C2×C4×Dic67 | — | 4 | 2 | no | — |
| 65 | C2×C4×Dic67 | C23 | 1 | 2 | yes | — |
| 66 | #14523977 | — | 2 | 4 | no | — |
| 67 | #14523975 | — | 2 | 4 | no | — |
| 68 | #14523969 | — | 4 | 4 | no | — |
| 69 | #14523968 | — | 2 | 4 | no | — |
| 70 | #14523965 | — | 2 | 4 | no | — |
| 71 | C67⋊#95 | — | 2 | 4 | no | — |
| 72 | C2×#41×C67 | — | 2 | 4 | no | — |
| 73 | C2×#41×C67 | — | 2 | 4 | no | — |
| 74 | C2×#41×C67 | — | 4 | 2 | no | — |
| 75 | C22×Q8×C67 | C23 | 1 | 1 | yes | characteristic |
| 76 | C22×D4×C67 | D4 | 1 | 2 | yes | — |
| 77 | C22×D4×C67 | C23 | 1 | 1 | yes | characteristic |
| 78 | C23×C4×C67 | D4 | 1 | 2 | yes | — |
| 79 | C23×C4×C67 | C23 | 1 | 1 | yes | characteristic |
| 80 | C2×M16×C67 | C23 | 1 | 4 | yes | — |
| 81 | #101×C67 | — | 2 | 4 | no | — |
| 82 | #100×C67 | — | 4 | 2 | no | — |
| 83 | C22⋊C8×C67 | — | 2 | 4 | no | — |
| 84 | #11761629 | — | 4 | 8 | no | — |
| 85 | #11761628 | — | 2 | 4 | no | — |
| 86 | #11761628 | — | 2 | 4 | no | — |
| 87 | #11761628 | — | 4 | 4 | no | — |
| 88 | #11761628 | — | 4 | 4 | no | — |
| 89 | C2×Dic134 | — | 2 | 2 | no | — |
| 90 | C2×Dic134 | C2×D4 | 1 | 2 | yes | — |
| 91 | Q8×D67 | — | 4 | 8 | no | — |
| 92 | C2×D268 | — | 2 | 2 | no | — |
| 93 | C2×D268 | C2×D4 | 1 | 2 | yes | — |
| 94 | C2×C22⋊D67 | — | 2 | 2 | no | — |
| 95 | C2×C22⋊D67 | — | 2 | 8 | no | — |
| 96 | C2×C22⋊D67 | — | 2 | 4 | no | — |
| 97 | C22×Dic67 | — | 2 | 2 | no | — |
| 98 | C22×Dic67 | — | 2 | 2 | no | — |
| 99 | C22×Dic67 | — | 4 | 4 | no | — |
| 100 | C22×Dic67 | — | 4 | 2 | no | — |
| 101 | C2×C4×D67 | — | 2 | 4 | no | — |
| 102 | C2×C4×D67 | — | 2 | 2 | no | — |
| 103 | C4⋊Dic67 | — | 2 | 4 | no | — |
| 104 | C4⋊Dic67 | — | 2 | 4 | no | — |
| 105 | C4⋊Dic67 | C2×D4 | 1 | 4 | yes | — |
| 106 | Dic67⋊C4 | — | 2 | 4 | no | — |
| 107 | C22⋊Dic67 | — | 2 | 8 | no | — |
| 108 | C22⋊Dic67 | — | 2 | 4 | no | — |
| 109 | C22⋊Dic67 | — | 2 | 2 | no | — |
| 110 | C22⋊Dic67 | — | 4 | 8 | no | — |
| 111 | C22⋊Dic67 | — | 4 | 2 | no | — |
| 112 | (C2×D67)⋊C4 | — | 2 | 4 | no | — |
| 113 | C4×Dic67 | — | 2 | 4 | no | — |
| 114 | C4×Dic67 | — | 2 | 2 | no | — |
| 115 | C4×Dic67 | — | 2 | 4 | no | — |
| 116 | C4×Dic67 | — | 4 | 2 | no | — |
| 117 | C4×Dic67 | — | 4 | 2 | no | — |
| 118 | C24×C67 | C2×D4 | 1 | 2 | yes | — |
| 119 | C24×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 120 | #41×C67 | — | 4 | 16 | no | — |
| 121 | C2×Q8×C67 | — | 2 | 2 | no | — |
| 122 | C2×Q8×C67 | — | 2 | 2 | no | — |
| 123 | C2×Q8×C67 | #41 | 1 | 4 | yes | — |
| 124 | C2×D4×C67 | — | 2 | 4 | no | — |
| 125 | C2×D4×C67 | — | 2 | 4 | no | — |
| 126 | C2×D4×C67 | — | 2 | 2 | no | — |
| 127 | C2×D4×C67 | — | 2 | 2 | no | — |
| 128 | C2×D4×C67 | — | 2 | 2 | no | — |
| 129 | C2×D4×C67 | — | 4 | 2 | no | — |
| 130 | C22×C4×C67 | — | 2 | 2 | no | — |
| 131 | C22×C4×C67 | — | 2 | 2 | no | — |
| 132 | C22×C4×C67 | — | 2 | 4 | no | — |
| 133 | C22×C4×C67 | — | 2 | 4 | no | — |
| 134 | C22×C4×C67 | — | 4 | 2 | no | — |
| 135 | C22×C4×C67 | C2×D4 | 1 | 4 | yes | — |
| 136 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 137 | C22×C4×C67 | C2×D4 | 1 | 2 | yes | — |
| 138 | C22×C4×C67 | C24 | 1 | 1 | yes | characteristic |
| 139 | M16×C67 | — | 2 | 4 | no | — |
| 140 | M16×C67 | — | 2 | 4 | no | — |
| 141 | C2×C8×C67 | — | 2 | 4 | no | — |
| 142 | C23×C67 | — | 2 | 1 | no | — |
| 143 | C23×C67 | — | 2 | 1 | no | — |
| 144 | C23×C67 | — | 2 | 2 | no | — |
| 145 | C23×C67 | — | 2 | 2 | no | — |
| 146 | C23×C67 | — | 2 | 2 | no | — |
| 147 | C23×C67 | — | 4 | 2 | no | — |
| 148 | C23×C67 | — | 4 | 4 | no | — |
| 149 | C23×C67 | #120 | 1 | 2 | yes | — |
| 150 | C23×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 151 | C22×D67 | — | 2 | 2 | no | — |
| 152 | Q8×C67 | — | 2 | 8 | no | — |
| 153 | D4×C67 | — | 4 | 8 | no | — |
| 154 | D4×C67 | — | 4 | 4 | no | — |
| 155 | C2×C4×C67 | — | 2 | 2 | no | — |
| 156 | C2×C4×C67 | — | 2 | 1 | no | — |
| 157 | C2×C4×C67 | — | 2 | 1 | no | — |
| 158 | C2×C4×C67 | — | 2 | 2 | no | — |
| 159 | C2×C4×C67 | — | 2 | 8 | no | — |
| 160 | C2×C4×C67 | — | 4 | 8 | no | — |
| 161 | C2×C4×C67 | #120 | 1 | 2 | yes | — |
| 162 | C2×C4×C67 | #123 | 1 | 4 | yes | — |
| 163 | C2×C4×C67 | C22×D4 | 1 | 2 | yes | — |
| 164 | C2×C4×C67 | C2×#41 | 1 | 2 | yes | — |
| 165 | C2×C4×C67 | H(5,𝔽2) | 1 | 2 | yes | — |
| 166 | C22⋊D67 | — | 4 | 2 | no | — |
| 167 | C22⋊D67 | — | 4 | 2 | no | — |
| 168 | C22⋊D67 | — | 8 | 4 | no | — |
| 169 | C22⋊D67 | — | 8 | 8 | no | — |
| 170 | C2×Dic67 | — | 2 | 4 | no | — |
| 171 | C2×Dic67 | — | 2 | 4 | no | — |
| 172 | C2×Dic67 | — | 2 | 2 | no | — |
| 173 | C2×Dic67 | — | 4 | 2 | no | — |
| 174 | C2×Dic67 | — | 4 | 8 | no | — |
| 175 | C2×Dic67 | — | 4 | 2 | no | — |
| 176 | C2×Dic67 | — | 4 | 4 | no | — |
| 177 | C2×Dic67 | — | 4 | 2 | no | — |
| 178 | D268 | — | 2 | 4 | no | — |
| 179 | D268 | — | 4 | 4 | no | — |
| 180 | C4×D67 | — | 4 | 8 | no | — |
| 181 | C4×D67 | — | 4 | 4 | no | — |
| 182 | Dic134 | — | 2 | 4 | no | — |
| 183 | Dic134 | — | 4 | 4 | no | — |
| 184 | C8×C67 | — | 4 | 4 | no | — |
| 185 | C22×C67 | — | 2 | 2 | no | — |
| 186 | C22×C67 | — | 2 | 2 | no | — |
| 187 | C22×C67 | — | 2 | 4 | no | — |
| 188 | C22×C67 | — | 4 | 2 | no | — |
| 189 | C22×C67 | — | 4 | 2 | no | — |
| 190 | C22×C67 | — | 4 | 4 | no | — |
| 191 | C22×C67 | — | 4 | 2 | no | — |
| 192 | C22×C67 | — | 4 | 4 | no | — |
| 193 | C22×C67 | — | 8 | 2 | no | — |
| 194 | C22×C67 | C2×#120 | 1 | 1 | yes | characteristic |
| 195 | C22×C67 | C2×#123 | 1 | 1 | yes | characteristic |
| 196 | C22×C67 | #534 | 1 | 1 | yes | characteristic |
| 197 | C2×D67 | — | 4 | 2 | no | — |
| 198 | C2×D67 | — | 4 | 4 | no | — |
| 199 | C4×C67 | — | 2 | 4 | no | — |
| 200 | C4×C67 | — | 2 | 2 | no | — |
| 201 | C4×C67 | #546 | 1 | 4 | yes | — |
| 202 | Dic67 | — | 4 | 4 | no | — |
| 203 | Dic67 | — | 4 | 2 | no | — |
| 204 | Dic67 | — | 4 | 4 | no | — |
| 205 | Dic67 | — | 8 | 2 | no | — |
| 206 | #24020 | — | 67 | 1 | no | maximal, Sylow |
| 207 | C2×C67 | — | 2 | 1 | no | — |
| 208 | C2×C67 | — | 2 | 1 | no | — |
| 209 | C2×C67 | — | 4 | 2 | no | — |
| 210 | C2×C67 | — | 8 | 2 | no | — |
| 211 | C2×C67 | #2405 | 1 | 1 | yes | characteristic |
| 212 | C2×C67 | #3018 | 1 | 2 | yes | — |
| 213 | D67 | — | 8 | 2 | no | — |
| 214 | #3487 | — | 67 | 1 | no | — |
| 215 | #3093 | — | 67 | 2 | no | — |
| 216 | #2297 | — | 67 | 1 | no | — |
| 217 | #2037 | — | 67 | 4 | no | — |
| 218 | #1896 | — | 67 | 2 | no | — |
| 219 | #1857 | — | 67 | 2 | no | — |
| 220 | #1793 | — | 67 | 2 | no | — |
| 221 | #1785 | D67 | 1 | 1 | yes | characteristic, complemented |
| 222 | C67 | #24020 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 223 | C2×2−1+4 | — | 67 | 1 | no | — |
| 224 | C22×#41 | C2×D67 | 1 | 1 | yes | characteristic |
| 225 | #550 | — | 134 | 4 | no | — |
| 226 | #548 | — | 134 | 4 | no | — |
| 227 | #535 | — | 67 | 2 | no | — |
| 228 | #535 | — | 134 | 2 | no | — |
| 229 | #525 | — | 67 | 2 | no | — |
| 230 | #525 | — | 134 | 2 | no | — |
| 231 | #519 | — | 67 | 1 | no | — |
| 232 | C2×#117 | — | 67 | 1 | no | — |
| 233 | C22×C42 | — | 67 | 1 | no | — |
| 234 | #485 | — | 134 | 4 | no | — |
| 235 | #482 | — | 134 | 4 | no | — |
| 236 | #428 | — | 67 | 4 | no | — |
| 237 | C2×#104 | — | 67 | 4 | no | — |
| 238 | #417 | — | 67 | 4 | no | — |
| 239 | C2×#101 | C2×D67 | 1 | 2 | yes | — |
| 240 | C2×#100 | C2×D67 | 1 | 2 | yes | — |
| 241 | #407 | C2×D67 | 1 | 2 | yes | — |
| 242 | #391 | — | 67 | 2 | no | — |
| 243 | #390 | — | 67 | 2 | no | — |
| 244 | #386 | — | 134 | 2 | no | — |
| 245 | C4×C22⋊C4 | — | 134 | 2 | no | — |
| 246 | #339 | — | 67 | 4 | no | — |
| 247 | 2−1+4 | — | 268 | 2 | no | — |
| 248 | 2−1+4 | — | 134 | 4 | no | — |
| 249 | C2×#41 | — | 2 | 4 | no | — |
| 250 | C2×#41 | — | 2 | 4 | no | — |
| 251 | C2×#41 | — | 4 | 2 | no | — |
| 252 | C2×#41 | — | 67 | 2 | no | — |
| 253 | C2×#41 | — | 134 | 2 | no | — |
| 254 | C2×#41 | — | 134 | 2 | no | — |
| 255 | C22×Q8 | — | 134 | 2 | no | — |
| 256 | C22×Q8 | C22×D67 | 1 | 1 | yes | characteristic |
| 257 | C22×D4 | D268 | 1 | 2 | yes | — |
| 258 | C22×D4 | C22×D67 | 1 | 1 | yes | characteristic |
| 259 | C23×C4 | — | 134 | 1 | no | — |
| 260 | C23×C4 | D268 | 1 | 2 | yes | — |
| 261 | C23×C4 | C22×D67 | 1 | 1 | yes | characteristic |
| 262 | C2×M16 | C22×D67 | 1 | 4 | yes | — |
| 263 | #127 | — | 134 | 2 | no | — |
| 264 | #127 | — | 134 | 4 | no | — |
| 265 | #124 | — | 134 | 2 | no | — |
| 266 | #124 | — | 134 | 4 | no | — |
| 267 | #123 | — | 134 | 2 | no | — |
| 268 | C22⋊Q8 | — | 67 | 4 | no | — |
| 269 | C22⋊Q8 | — | 134 | 4 | no | — |
| 270 | #121 | — | 67 | 4 | no | — |
| 271 | #121 | — | 134 | 4 | no | — |
| 272 | #121 | — | 134 | 4 | no | — |
| 273 | #121 | — | 134 | 8 | no | — |
| 274 | #120 | — | 134 | 2 | no | — |
| 275 | #120 | — | 134 | 4 | no | — |
| 276 | C4×Q8 | — | 134 | 4 | no | — |
| 277 | C4×D4 | — | 134 | 8 | no | — |
| 278 | C4×D4 | — | 134 | 4 | no | — |
| 279 | #117 | — | 67 | 2 | no | — |
| 280 | #117 | — | 134 | 4 | no | — |
| 281 | #117 | — | 134 | 2 | no | — |
| 282 | C2×C4⋊C4 | — | 67 | 2 | no | — |
| 283 | C2×C22⋊C4 | — | 134 | 1 | no | — |
| 284 | C2×C22⋊C4 | — | 134 | 4 | no | — |
| 285 | C2×C42 | — | 268 | 2 | no | — |
| 286 | C2×C42 | — | 67 | 2 | no | — |
| 287 | C2×C42 | — | 134 | 1 | no | — |
| 288 | C2×C42 | — | 134 | 1 | no | — |
| 289 | #107 | — | 134 | 4 | no | — |
| 290 | #106 | — | 134 | 4 | no | — |
| 291 | #104 | — | 268 | 4 | no | — |
| 292 | #103 | — | 134 | 4 | no | — |
| 293 | #102 | — | 134 | 4 | no | — |
| 294 | #101 | — | 2 | 4 | no | — |
| 295 | #100 | — | 4 | 2 | no | — |
| 296 | C22⋊C8 | — | 2 | 4 | no | — |
| 297 | #95 | — | 134 | 4 | no | — |
| 298 | C24 | C2×D268 | 1 | 2 | yes | — |
| 299 | C24 | C2×D268 | 1 | 1 | yes | characteristic |
| 300 | #41 | — | 4 | 16 | no | — |
| 301 | #41 | — | 268 | 4 | no | — |
| 302 | #41 | — | 268 | 8 | no | — |
| 303 | #41 | — | 268 | 4 | no | — |
| 304 | #41 | — | 134 | 4 | no | — |
| 305 | #41 | — | 134 | 4 | no | — |
| 306 | C2×Q8 | — | 2 | 2 | no | — |
| 307 | C2×Q8 | — | 2 | 2 | no | — |
| 308 | C2×Q8 | — | 268 | 8 | no | — |
| 309 | C2×Q8 | — | 67 | 2 | no | — |
| 310 | C2×Q8 | — | 134 | 2 | no | — |
| 311 | C2×Q8 | #11761627 | 1 | 4 | yes | — |
| 312 | C2×D4 | — | 2 | 4 | no | — |
| 313 | C2×D4 | — | 2 | 4 | no | — |
| 314 | C2×D4 | — | 2 | 2 | no | — |
| 315 | C2×D4 | — | 2 | 2 | no | — |
| 316 | C2×D4 | — | 2 | 2 | no | — |
| 317 | C2×D4 | — | 4 | 2 | no | — |
| 318 | C2×D4 | — | 67 | 2 | no | — |
| 319 | C2×D4 | — | 134 | 2 | no | — |
| 320 | C2×D4 | — | 134 | 2 | no | — |
| 321 | C2×D4 | — | 134 | 8 | no | — |
| 322 | C2×D4 | — | 134 | 4 | no | — |
| 323 | C22×C4 | — | 2 | 2 | no | — |
| 324 | C22×C4 | — | 2 | 2 | no | — |
| 325 | C22×C4 | — | 2 | 4 | no | — |
| 326 | C22×C4 | — | 2 | 4 | no | — |
| 327 | C22×C4 | — | 4 | 2 | no | — |
| 328 | C22×C4 | — | 268 | 2 | no | — |
| 329 | C22×C4 | — | 268 | 4 | no | — |
| 330 | C22×C4 | — | 134 | 4 | no | — |
| 331 | C22×C4 | — | 134 | 2 | no | — |
| 332 | C22×C4 | — | 134 | 2 | no | — |
| 333 | C22×C4 | — | 134 | 2 | no | — |
| 334 | C22×C4 | D4×D67 | 1 | 4 | yes | — |
| 335 | C22×C4 | C2×D268 | 1 | 1 | yes | characteristic |
| 336 | C22×C4 | C2×D268 | 1 | 2 | yes | — |
| 337 | C22×C4 | C23×D67 | 1 | 1 | yes | characteristic |
| 338 | M16 | — | 2 | 4 | no | — |
| 339 | M16 | — | 2 | 4 | no | — |
| 340 | C2×C8 | — | 2 | 4 | no | — |
| 341 | C4⋊C4 | — | 67 | 4 | no | — |
| 342 | C4⋊C4 | — | 134 | 4 | no | — |
| 343 | C4⋊C4 | — | 134 | 4 | no | — |
| 344 | C4⋊C4 | — | 134 | 4 | no | — |
| 345 | C22⋊C4 | — | 268 | 2 | no | — |
| 346 | C22⋊C4 | — | 268 | 8 | no | — |
| 347 | C22⋊C4 | — | 134 | 8 | no | — |
| 348 | C22⋊C4 | — | 134 | 4 | no | — |
| 349 | C22⋊C4 | — | 134 | 2 | no | — |
| 350 | C22⋊C4 | — | 134 | 4 | no | — |
| 351 | C42 | — | 268 | 2 | no | — |
| 352 | C42 | — | 268 | 2 | no | — |
| 353 | C42 | — | 134 | 4 | no | — |
| 354 | C42 | — | 134 | 4 | no | — |
| 355 | C42 | — | 134 | 2 | no | — |
| 356 | C23 | — | 2 | 1 | no | — |
| 357 | C23 | — | 2 | 1 | no | — |
| 358 | C23 | — | 2 | 2 | no | — |
| 359 | C23 | — | 2 | 2 | no | — |
| 360 | C23 | — | 2 | 2 | no | — |
| 361 | C23 | — | 4 | 2 | no | — |
| 362 | C23 | — | 4 | 4 | no | — |
| 363 | C23 | — | 134 | 2 | no | — |
| 364 | C23 | #14524013 | 1 | 2 | yes | — |
| 365 | C23 | C22×D268 | 1 | 1 | yes | characteristic |
| 366 | Q8 | — | 2 | 8 | no | — |
| 367 | Q8 | — | 268 | 4 | no | — |
| 368 | Q8 | — | 134 | 4 | no | — |
| 369 | D4 | — | 4 | 8 | no | — |
| 370 | D4 | — | 4 | 4 | no | — |
| 371 | D4 | — | 268 | 4 | no | — |
| 372 | D4 | — | 268 | 2 | no | — |
| 373 | D4 | — | 268 | 2 | no | — |
| 374 | D4 | — | 536 | 4 | no | — |
| 375 | D4 | — | 536 | 8 | no | — |
| 376 | D4 | — | 134 | 4 | no | — |
| 377 | C2×C4 | — | 2 | 2 | no | — |
| 378 | C2×C4 | — | 2 | 1 | no | — |
| 379 | C2×C4 | — | 2 | 1 | no | — |
| 380 | C2×C4 | — | 2 | 2 | no | — |
| 381 | C2×C4 | — | 2 | 8 | no | — |
| 382 | C2×C4 | — | 4 | 8 | no | — |
| 383 | C2×C4 | — | 268 | 8 | no | — |
| 384 | C2×C4 | — | 268 | 2 | no | — |
| 385 | C2×C4 | — | 268 | 8 | no | — |
| 386 | C2×C4 | — | 268 | 2 | no | — |
| 387 | C2×C4 | — | 268 | 4 | no | — |
| 388 | C2×C4 | — | 268 | 4 | no | — |
| 389 | C2×C4 | — | 268 | 2 | no | — |
| 390 | C2×C4 | — | 134 | 4 | no | — |
| 391 | C2×C4 | — | 134 | 4 | no | — |
| 392 | C2×C4 | — | 134 | 2 | no | — |
| 393 | C2×C4 | #14524013 | 1 | 2 | yes | — |
| 394 | C2×C4 | #14524027 | 1 | 4 | yes | — |
| 395 | C2×C4 | C2×D4×D67 | 1 | 2 | yes | — |
| 396 | C2×C4 | C2×#11761627 | 1 | 2 | yes | — |
| 397 | C2×C4 | #14524088 | 1 | 2 | yes | — |
| 398 | C8 | — | 4 | 4 | no | — |
| 399 | C22 | — | 2 | 2 | no | — |
| 400 | C22 | — | 2 | 4 | no | — |
| 401 | C22 | — | 2 | 2 | no | — |
| 402 | C22 | — | 4 | 2 | no | — |
| 403 | C22 | — | 4 | 2 | no | — |
| 404 | C22 | — | 4 | 4 | no | — |
| 405 | C22 | — | 4 | 4 | no | — |
| 406 | C22 | — | 4 | 2 | no | — |
| 407 | C22 | — | 8 | 2 | no | — |
| 408 | C22 | — | 268 | 4 | no | — |
| 409 | C22 | — | 268 | 2 | no | — |
| 410 | C22 | C2×#14524013 | 1 | 1 | yes | characteristic |
| 411 | C22 | C2×#14524027 | 1 | 1 | yes | characteristic |
| 412 | C22 | #16863958 | 1 | 1 | yes | characteristic |
| 413 | C4 | — | 2 | 2 | no | — |
| 414 | C4 | — | 2 | 4 | no | — |
| 415 | C4 | — | 268 | 4 | no | — |
| 416 | C4 | — | 268 | 4 | no | — |
| 417 | C4 | — | 268 | 2 | no | — |
| 418 | C4 | — | 536 | 2 | no | — |
| 419 | C4 | #16864033 | 1 | 4 | yes | — |
| 420 | C2 | — | 2 | 1 | no | — |
| 421 | C2 | — | 2 | 1 | no | — |
| 422 | C2 | — | 4 | 2 | no | — |
| 423 | C2 | — | 8 | 2 | no | — |
| 424 | C2 | — | 536 | 2 | no | — |
| 425 | C2 | #22563537 | 1 | 1 | yes | characteristic |
| 426 | C2 | #22569562 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #22570142 | C2 | semidirect |
| 3. #22562700 | C2 | semidirect |
| 4. #22561420 | C2 | semidirect |
| 5. #22560650 | C2 | semidirect |
| 6. #22560426 | C2 | semidirect |
| 7. #22560170 | C2 | semidirect |
| 8. C67×#1785 | C2 | semidirect |
| 221. #1785 | D67 | semidirect |
| 222. C67 | #24020 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22573867 | 2 |
| #22570142 | 2 |
| #22562700 | 2 |
| #22561420 | 2 |
| #22560650 | 2 |
| #22560426 | 2 |
| #22560170 | 2 |
| C67×#1785 | 2 |
| #24020 | 67 |