Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
3540 conjugacy classes of subgroups; only the 247 normal subgroups are shown.
This group has 3540 conjugacy classes of subgroups — too many to draw. Only its 247 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 | #22575022 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #22569611 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #22569583 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #22569497 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #22560185 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #22560172 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | C67×#1791 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #16864232 | — | 2 | 6 | no | — |
| 9 | #16864232 | C22 | 1 | 3 | yes | — |
| 10 | #16864231 | — | 2 | 6 | no | — |
| 11 | #16864231 | — | 2 | 4 | no | — |
| 12 | C2×#14524090 | — | 2 | 6 | no | — |
| 13 | C2×#14524090 | C22 | 1 | 3 | yes | — |
| 14 | 2−1+4×D67 | — | 2 | 6 | no | — |
| 15 | C2×#14524071 | C22 | 1 | 3 | yes | complemented |
| 16 | C22×#11761617 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | #16863960 | C22 | 1 | 3 | yes | complemented |
| 18 | #16863583 | — | 2 | 4 | no | — |
| 19 | #16863571 | — | 2 | 6 | no | — |
| 20 | #16863566 | — | 2 | 6 | no | — |
| 21 | #16863543 | — | 2 | 6 | no | — |
| 22 | #16863537 | — | 2 | 6 | no | — |
| 23 | #16863412 | C22 | 1 | 6 | yes | complemented |
| 24 | #16863406 | C22 | 1 | 3 | yes | complemented |
| 25 | #16863393 | C22 | 1 | 3 | yes | complemented |
| 26 | #16863370 | C22 | 1 | 3 | yes | complemented |
| 27 | #585×C67 | C22 | 1 | 1 | yes | characteristic |
| 28 | #413×C67 | C22 | 1 | 3 | yes | complemented |
| 29 | #408×C67 | C22 | 1 | 3 | yes | complemented |
| 30 | #14524091 | — | 2 | 12 | no | — |
| 31 | #14524091 | D4 | 1 | 6 | yes | complemented |
| 32 | #14524090 | — | 2 | 24 | no | — |
| 33 | #14524090 | — | 2 | 24 | no | — |
| 34 | #14524090 | — | 2 | 12 | no | — |
| 35 | #14524090 | — | 2 | 12 | no | — |
| 36 | #14524090 | — | 2 | 6 | no | — |
| 37 | #14524090 | — | 2 | 12 | no | — |
| 38 | #14524089 | — | 2 | 4 | no | — |
| 39 | #14524089 | — | 2 | 6 | no | — |
| 40 | #14524088 | — | 2 | 12 | no | — |
| 41 | #14524088 | — | 2 | 24 | no | — |
| 42 | #14524088 | — | 2 | 6 | no | — |
| 43 | #14524088 | D4 | 1 | 6 | yes | complemented |
| 44 | C2×#11761628 | — | 2 | 12 | no | — |
| 45 | C2×#11761628 | — | 2 | 6 | no | — |
| 46 | C2×#11761628 | D4 | 1 | 6 | yes | complemented |
| 47 | C2×#11761628 | C23 | 1 | 3 | yes | — |
| 48 | C2×#11761627 | — | 2 | 12 | no | — |
| 49 | C2×#11761627 | — | 2 | 24 | no | — |
| 50 | C2×#11761627 | — | 2 | 3 | no | — |
| 51 | C2×#11761627 | — | 2 | 6 | no | — |
| 52 | #41×D67 | — | 2 | 24 | no | — |
| 53 | #41×D67 | — | 2 | 24 | no | — |
| 54 | #41×D67 | — | 2 | 12 | no | — |
| 55 | C22×Dic134 | — | 2 | 4 | no | — |
| 56 | C22×Dic134 | D4 | 1 | 6 | yes | complemented |
| 57 | C22×Dic134 | C23 | 1 | 1 | yes | characteristic |
| 58 | C2×Q8×D67 | — | 2 | 12 | no | — |
| 59 | C2×Q8×D67 | — | 2 | 3 | no | — |
| 60 | C22×D268 | C23 | 1 | 1 | yes | characteristic |
| 61 | #14524071 | — | 2 | 12 | no | — |
| 62 | C2×#11761617 | — | 2 | 3 | no | — |
| 63 | C2×#11761617 | — | 2 | 6 | no | — |
| 64 | C2×D536 | — | 2 | 3 | no | — |
| 65 | #14524039 | — | 2 | 3 | no | — |
| 66 | #14524032 | — | 2 | 3 | no | — |
| 67 | #14524017 | — | 2 | 6 | no | — |
| 68 | #14524011 | — | 2 | 6 | no | — |
| 69 | #14524002 | C23 | 1 | 3 | yes | — |
| 70 | #14523969 | — | 2 | 12 | no | — |
| 71 | #14523968 | — | 2 | 3 | no | — |
| 72 | #14523968 | — | 2 | 6 | no | — |
| 73 | #14523965 | — | 2 | 3 | no | — |
| 74 | #14523958 | — | 2 | 6 | no | — |
| 75 | 2−1+4×C67 | — | 2 | 3 | no | — |
| 76 | H(5,𝔽2)×C67 | — | 2 | 3 | no | — |
| 77 | H(5,𝔽2)×C67 | D4 | 1 | 4 | yes | — |
| 78 | C2×#41×C67 | — | 2 | 6 | no | — |
| 79 | C2×#41×C67 | C23 | 1 | 3 | yes | — |
| 80 | C2×M16×C67 | C23 | 1 | 3 | yes | — |
| 81 | C22×C8×C67 | C23 | 1 | 1 | yes | characteristic |
| 82 | #101×C67 | — | 2 | 3 | no | — |
| 83 | #100×C67 | — | 2 | 3 | no | — |
| 84 | C22⋊C8×C67 | — | 2 | 6 | no | — |
| 85 | C23×D67 | — | 2 | 1 | no | — |
| 86 | #11761629 | — | 2 | 8 | no | — |
| 87 | #11761629 | — | 2 | 12 | no | — |
| 88 | #11761628 | — | 2 | 48 | no | — |
| 89 | #11761628 | — | 2 | 12 | no | — |
| 90 | #11761628 | — | 2 | 12 | no | — |
| 91 | #11761628 | — | 2 | 12 | no | — |
| 92 | #11761628 | — | 2 | 6 | no | — |
| 93 | #11761628 | — | 2 | 12 | no | — |
| 94 | #11761628 | — | 2 | 12 | no | — |
| 95 | #11761628 | C2×D4 | 1 | 12 | yes | — |
| 96 | #11761627 | — | 2 | 48 | no | — |
| 97 | #11761627 | — | 2 | 24 | no | — |
| 98 | #11761627 | — | 2 | 48 | no | — |
| 99 | #11761627 | — | 2 | 24 | no | — |
| 100 | #11761627 | — | 2 | 24 | no | — |
| 101 | #11761627 | — | 2 | 12 | no | — |
| 102 | C2×Dic134 | — | 2 | 24 | no | — |
| 103 | C2×Dic134 | — | 2 | 6 | no | — |
| 104 | C2×Dic134 | — | 2 | 6 | no | — |
| 105 | C2×Dic134 | — | 2 | 3 | no | — |
| 106 | C2×Dic134 | — | 2 | 12 | no | — |
| 107 | C2×Dic134 | — | 2 | 12 | no | — |
| 108 | C2×Dic134 | C2×D4 | 1 | 3 | yes | — |
| 109 | C2×Dic134 | C2×D4 | 1 | 6 | yes | — |
| 110 | Q8×D67 | — | 2 | 24 | no | — |
| 111 | Q8×D67 | — | 2 | 24 | no | — |
| 112 | Q8×D67 | — | 2 | 12 | no | — |
| 113 | C2×D268 | — | 2 | 6 | no | — |
| 114 | C2×D268 | — | 2 | 3 | no | — |
| 115 | C2×D268 | — | 2 | 3 | no | — |
| 116 | C2×D268 | C2×D4 | 1 | 3 | yes | — |
| 117 | C2×C22⋊D67 | — | 2 | 24 | no | — |
| 118 | C2×C22⋊D67 | — | 2 | 12 | no | — |
| 119 | C2×C22⋊D67 | — | 2 | 6 | no | — |
| 120 | C2×C22⋊D67 | — | 2 | 3 | no | — |
| 121 | C2×C22⋊D67 | — | 4 | 6 | no | — |
| 122 | D4×D67 | — | 2 | 24 | no | — |
| 123 | D4×D67 | — | 2 | 24 | no | — |
| 124 | D4×D67 | — | 2 | 12 | no | — |
| 125 | C22×Dic67 | — | 2 | 8 | no | — |
| 126 | C22×Dic67 | — | 2 | 6 | no | — |
| 127 | C22×Dic67 | — | 2 | 1 | no | — |
| 128 | C2×C4×D67 | — | 2 | 24 | no | — |
| 129 | C2×C4×D67 | — | 2 | 12 | no | — |
| 130 | C2×C4×D67 | — | 2 | 6 | no | — |
| 131 | C2×C4×D67 | — | 2 | 3 | no | — |
| 132 | #11761617 | — | 4 | 4 | no | — |
| 133 | #11761617 | — | 4 | 6 | no | — |
| 134 | D536 | — | 4 | 6 | no | — |
| 135 | C4⋊Dic67 | — | 2 | 3 | no | — |
| 136 | C22⋊Dic67 | — | 2 | 3 | no | — |
| 137 | (C2×D67)⋊C4 | — | 4 | 6 | no | — |
| 138 | C4×Dic67 | — | 2 | 3 | no | — |
| 139 | #41×C67 | — | 2 | 4 | no | — |
| 140 | #41×C67 | — | 2 | 12 | no | — |
| 141 | #41×C67 | — | 2 | 12 | no | — |
| 142 | #41×C67 | — | 2 | 6 | no | — |
| 143 | #41×C67 | — | 2 | 6 | no | — |
| 144 | C2×Q8×C67 | — | 2 | 6 | no | — |
| 145 | C2×Q8×C67 | C2×D4 | 1 | 3 | yes | — |
| 146 | C2×D4×C67 | — | 2 | 6 | no | — |
| 147 | C2×D4×C67 | — | 2 | 12 | no | — |
| 148 | C2×D4×C67 | C2×D4 | 1 | 3 | yes | — |
| 149 | C2×D4×C67 | C2×D4 | 1 | 6 | yes | — |
| 150 | C22×C4×C67 | — | 2 | 4 | no | — |
| 151 | C22×C4×C67 | C2×D4 | 1 | 6 | yes | — |
| 152 | C22×C4×C67 | C24 | 1 | 1 | yes | characteristic |
| 153 | M16×C67 | — | 2 | 6 | no | — |
| 154 | C2×C8×C67 | — | 2 | 3 | no | — |
| 155 | C2×C8×C67 | — | 2 | 3 | no | — |
| 156 | C23×C67 | — | 2 | 4 | no | — |
| 157 | C23×C67 | #120 | 1 | 6 | yes | — |
| 158 | C23×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 159 | C22×D67 | — | 2 | 12 | no | — |
| 160 | C22×D67 | — | 2 | 3 | no | — |
| 161 | C22×D67 | — | 4 | 3 | no | — |
| 162 | C22×D67 | — | 16 | 1 | no | — |
| 163 | Q8×C67 | — | 2 | 4 | no | — |
| 164 | Q8×C67 | — | 2 | 6 | no | — |
| 165 | D4×C67 | — | 2 | 12 | no | — |
| 166 | D4×C67 | — | 2 | 12 | no | — |
| 167 | D4×C67 | — | 2 | 6 | no | — |
| 168 | C2×C4×C67 | — | 2 | 12 | no | — |
| 169 | C2×C4×C67 | — | 2 | 6 | no | — |
| 170 | C2×C4×C67 | — | 2 | 6 | no | — |
| 171 | C2×C4×C67 | #120 | 1 | 6 | yes | — |
| 172 | C2×C4×C67 | C22×D4 | 1 | 3 | yes | — |
| 173 | C2×C4×C67 | C22×D4 | 1 | 3 | yes | — |
| 174 | C22⋊D67 | — | 2 | 24 | no | — |
| 175 | C22⋊D67 | — | 2 | 24 | no | — |
| 176 | C22⋊D67 | — | 2 | 12 | no | — |
| 177 | C22⋊D67 | — | 16 | 6 | no | — |
| 178 | C2×Dic67 | — | 2 | 12 | no | — |
| 179 | C2×Dic67 | — | 2 | 24 | no | — |
| 180 | C2×Dic67 | — | 2 | 6 | no | — |
| 181 | C2×Dic67 | — | 2 | 3 | no | — |
| 182 | C2×Dic67 | — | 4 | 3 | no | — |
| 183 | D268 | — | 2 | 12 | no | — |
| 184 | D268 | — | 2 | 3 | no | — |
| 185 | D268 | — | 4 | 3 | no | — |
| 186 | D268 | — | 4 | 1 | no | — |
| 187 | D268 | #120 | 1 | 6 | yes | — |
| 188 | C4×D67 | — | 2 | 24 | no | — |
| 189 | C4×D67 | — | 2 | 24 | no | — |
| 190 | C4×D67 | — | 2 | 12 | no | — |
| 191 | Dic134 | — | 2 | 24 | no | — |
| 192 | Dic134 | — | 2 | 12 | no | — |
| 193 | Dic134 | — | 2 | 6 | no | — |
| 194 | Dic134 | — | 2 | 3 | no | — |
| 195 | Dic134 | #120 | 1 | 6 | yes | — |
| 196 | Dic134 | #120 | 1 | 4 | yes | — |
| 197 | C8×C67 | — | 4 | 1 | no | — |
| 198 | C8×C67 | — | 4 | 3 | no | — |
| 199 | C22×C67 | — | 2 | 6 | no | — |
| 200 | C22×C67 | — | 4 | 1 | no | — |
| 201 | C22×C67 | — | 4 | 6 | no | — |
| 202 | C22×C67 | — | 8 | 4 | no | — |
| 203 | C22×C67 | C2×#120 | 1 | 3 | yes | — |
| 204 | C2×D67 | — | 2 | 6 | no | — |
| 205 | C2×D67 | — | 8 | 3 | no | — |
| 206 | C2×D67 | — | 8 | 12 | no | — |
| 207 | C2×D67 | — | 8 | 6 | no | — |
| 208 | C2×D67 | — | 8 | 1 | no | — |
| 209 | C4×C67 | — | 2 | 6 | no | — |
| 210 | C4×C67 | C2×#120 | 1 | 1 | yes | characteristic |
| 211 | C4×C67 | C2×#120 | 1 | 3 | yes | — |
| 212 | Dic67 | — | 2 | 6 | no | — |
| 213 | Dic67 | — | 2 | 4 | no | — |
| 214 | Dic67 | — | 8 | 3 | no | — |
| 215 | #32895 | — | 67 | 1 | no | maximal, Sylow |
| 216 | C2×C67 | — | 2 | 3 | no | — |
| 217 | C2×C67 | — | 4 | 6 | no | — |
| 218 | C2×C67 | #2846 | 1 | 1 | yes | characteristic |
| 219 | D67 | — | 4 | 6 | no | — |
| 220 | D67 | — | 16 | 1 | no | — |
| 221 | 2−1+6 | — | 67 | 1 | no | — |
| 222 | #3027 | — | 67 | 1 | no | — |
| 223 | #3021 | — | 67 | 3 | no | — |
| 224 | #3010 | — | 67 | 3 | no | — |
| 225 | #1796 | — | 67 | 3 | no | — |
| 226 | #1794 | — | 67 | 3 | no | — |
| 227 | #1791 | D67 | 1 | 1 | yes | characteristic, complemented |
| 228 | C67 | #32895 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 229 | #585 | — | 67 | 3 | no | — |
| 230 | #585 | — | 134 | 6 | no | — |
| 231 | #585 | — | 134 | 6 | no | — |
| 232 | #585 | — | 134 | 4 | no | — |
| 233 | #585 | C2×D67 | 1 | 1 | yes | characteristic |
| 234 | C2×2−1+4 | — | 67 | 3 | no | — |
| 235 | C2×2−1+4 | — | 134 | 6 | no | — |
| 236 | C2×2−1+4 | — | 134 | 6 | no | — |
| 237 | C2×AGL(1,ℤ/8) | — | 67 | 3 | no | — |
| 238 | C22×SD16 | — | 67 | 1 | no | — |
| 239 | #535 | — | 67 | 3 | no | — |
| 240 | B(4,𝔽2) | — | 134 | 4 | no | — |
| 241 | #454 | — | 134 | 6 | no | — |
| 242 | #453 | — | 134 | 6 | no | — |
| 243 | #449 | — | 134 | 6 | no | — |
| 244 | #448 | — | 134 | 6 | no | — |
| 245 | #421 | — | 67 | 6 | no | — |
| 246 | #419 | — | 67 | 3 | no | — |
| 247 | #416 | — | 67 | 3 | no | — |
| 248 | #413 | C2×D67 | 1 | 3 | yes | complemented |
| 249 | #410 | — | 67 | 3 | no | — |
| 250 | #408 | C2×D67 | 1 | 3 | yes | complemented |
| 251 | 2−1+4 | — | 2 | 3 | no | — |
| 252 | 2−1+4 | — | 67 | 6 | no | — |
| 253 | 2−1+4 | — | 134 | 12 | no | — |
| 254 | 2−1+4 | — | 134 | 12 | no | — |
| 255 | 2−1+4 | — | 134 | 6 | no | — |
| 256 | 2−1+4 | — | 134 | 12 | no | — |
| 257 | 2−1+4 | — | 134 | 12 | no | — |
| 258 | 2−1+4 | — | 134 | 24 | no | — |
| 259 | 2−1+4 | — | 134 | 24 | no | — |
| 260 | H(5,𝔽2) | — | 2 | 3 | no | — |
| 261 | H(5,𝔽2) | — | 67 | 6 | no | — |
| 262 | H(5,𝔽2) | — | 134 | 12 | no | — |
| 263 | H(5,𝔽2) | — | 134 | 24 | no | — |
| 264 | H(5,𝔽2) | — | 134 | 6 | no | — |
| 265 | H(5,𝔽2) | — | 134 | 4 | no | — |
| 266 | H(5,𝔽2) | — | 134 | 6 | no | — |
| 267 | H(5,𝔽2) | D268 | 1 | 4 | yes | — |
| 268 | C2×#41 | — | 2 | 6 | no | — |
| 269 | C2×#41 | — | 67 | 6 | no | — |
| 270 | C2×#41 | — | 67 | 3 | no | — |
| 271 | C2×#41 | — | 134 | 12 | no | — |
| 272 | C2×#41 | — | 134 | 12 | no | — |
| 273 | C2×#41 | — | 134 | 24 | no | — |
| 274 | C2×#41 | — | 134 | 12 | no | — |
| 275 | C2×#41 | — | 134 | 24 | no | — |
| 276 | C2×#41 | — | 134 | 24 | no | — |
| 277 | C2×#41 | — | 134 | 3 | no | — |
| 278 | C2×#41 | — | 134 | 6 | no | — |
| 279 | C2×#41 | — | 134 | 6 | no | — |
| 280 | C2×#41 | C22×D67 | 1 | 3 | yes | — |
| 281 | C22×Q8 | — | 67 | 6 | no | — |
| 282 | C22×Q8 | — | 67 | 1 | no | — |
| 283 | C22×Q8 | — | 134 | 4 | no | — |
| 284 | C22×Q8 | — | 134 | 12 | no | — |
| 285 | C22×Q8 | — | 134 | 3 | no | — |
| 286 | C22×D4 | — | 67 | 1 | no | — |
| 287 | AGL(1,ℤ/8) | — | 134 | 12 | no | — |
| 288 | C2×SD16 | — | 134 | 6 | no | — |
| 289 | C2×SD16 | — | 134 | 3 | no | — |
| 290 | C2×D8 | — | 134 | 3 | no | — |
| 291 | C2×M16 | C22×D67 | 1 | 3 | yes | — |
| 292 | C22×C8 | C22×D67 | 1 | 1 | yes | characteristic |
| 293 | #127 | — | 134 | 3 | no | — |
| 294 | #124 | — | 134 | 3 | no | — |
| 295 | #121 | — | 134 | 6 | no | — |
| 296 | #120 | — | 134 | 6 | no | — |
| 297 | #117 | — | 67 | 3 | no | — |
| 298 | #104 | — | 134 | 12 | no | — |
| 299 | #103 | — | 134 | 3 | no | — |
| 300 | #103 | — | 134 | 6 | no | — |
| 301 | #102 | — | 134 | 3 | no | — |
| 302 | #101 | — | 2 | 3 | no | — |
| 303 | #100 | — | 2 | 3 | no | — |
| 304 | #99 | — | 134 | 6 | no | — |
| 305 | C22⋊C8 | — | 2 | 6 | no | — |
| 306 | C24 | — | 134 | 1 | no | — |
| 307 | #41 | — | 2 | 4 | no | — |
| 308 | #41 | — | 2 | 12 | no | — |
| 309 | #41 | — | 2 | 12 | no | — |
| 310 | #41 | — | 2 | 6 | no | — |
| 311 | #41 | — | 2 | 6 | no | — |
| 312 | #41 | — | 67 | 12 | no | — |
| 313 | #41 | — | 134 | 12 | no | — |
| 314 | #41 | — | 134 | 12 | no | — |
| 315 | #41 | — | 134 | 48 | no | — |
| 316 | #41 | — | 134 | 12 | no | — |
| 317 | #41 | — | 134 | 12 | no | — |
| 318 | #41 | — | 134 | 12 | no | — |
| 319 | #41 | — | 134 | 48 | no | — |
| 320 | #41 | — | 134 | 24 | no | — |
| 321 | #41 | — | 134 | 24 | no | — |
| 322 | #41 | — | 134 | 48 | no | — |
| 323 | #41 | — | 134 | 24 | no | — |
| 324 | #41 | — | 134 | 12 | no | — |
| 325 | #41 | — | 134 | 8 | no | — |
| 326 | #41 | — | 134 | 12 | no | — |
| 327 | #41 | — | 134 | 6 | no | — |
| 328 | C2×Q8 | — | 2 | 6 | no | — |
| 329 | C2×Q8 | — | 67 | 6 | no | — |
| 330 | C2×Q8 | — | 67 | 3 | no | — |
| 331 | C2×Q8 | — | 134 | 12 | no | — |
| 332 | C2×Q8 | — | 134 | 12 | no | — |
| 333 | C2×Q8 | — | 134 | 24 | no | — |
| 334 | C2×Q8 | — | 134 | 6 | no | — |
| 335 | C2×Q8 | — | 134 | 12 | no | — |
| 336 | C2×Q8 | — | 134 | 24 | no | — |
| 337 | C2×Q8 | — | 134 | 24 | no | — |
| 338 | C2×Q8 | — | 134 | 6 | no | — |
| 339 | C2×Q8 | — | 134 | 3 | no | — |
| 340 | C2×Q8 | D4×D67 | 1 | 3 | yes | — |
| 341 | C2×D4 | — | 2 | 6 | no | — |
| 342 | C2×D4 | — | 2 | 12 | no | — |
| 343 | C2×D4 | — | 268 | 6 | no | — |
| 344 | C2×D4 | — | 67 | 3 | no | — |
| 345 | C2×D4 | — | 134 | 6 | no | — |
| 346 | C2×D4 | — | 134 | 12 | no | — |
| 347 | C2×D4 | — | 134 | 24 | no | — |
| 348 | C2×D4 | — | 134 | 24 | no | — |
| 349 | C2×D4 | — | 134 | 24 | no | — |
| 350 | C2×D4 | — | 134 | 6 | no | — |
| 351 | C2×D4 | — | 134 | 12 | no | — |
| 352 | C2×D4 | — | 134 | 3 | no | — |
| 353 | C2×D4 | — | 134 | 3 | no | — |
| 354 | C2×D4 | — | 134 | 3 | no | — |
| 355 | C2×D4 | D4×D67 | 1 | 3 | yes | — |
| 356 | C2×D4 | C2×D268 | 1 | 6 | yes | — |
| 357 | C22×C4 | — | 2 | 4 | no | — |
| 358 | C22×C4 | — | 134 | 24 | no | — |
| 359 | C22×C4 | — | 134 | 12 | no | — |
| 360 | C22×C4 | — | 134 | 8 | no | — |
| 361 | C22×C4 | — | 134 | 6 | no | — |
| 362 | C22×C4 | — | 134 | 1 | no | — |
| 363 | C22×C4 | — | 134 | 6 | no | — |
| 364 | C22×C4 | — | 134 | 3 | no | — |
| 365 | C22×C4 | D4×D67 | 1 | 6 | yes | — |
| 366 | C22×C4 | C23×D67 | 1 | 1 | yes | characteristic |
| 367 | SD16 | — | 268 | 4 | no | — |
| 368 | SD16 | — | 268 | 6 | no | — |
| 369 | D8 | — | 268 | 6 | no | — |
| 370 | M16 | — | 2 | 6 | no | — |
| 371 | C2×C8 | — | 2 | 3 | no | — |
| 372 | C2×C8 | — | 2 | 3 | no | — |
| 373 | C4⋊C4 | — | 134 | 3 | no | — |
| 374 | C22⋊C4 | — | 268 | 6 | no | — |
| 375 | C22⋊C4 | — | 134 | 3 | no | — |
| 376 | C42 | — | 134 | 3 | no | — |
| 377 | C23 | — | 2 | 4 | no | — |
| 378 | C23 | — | 268 | 3 | no | — |
| 379 | C23 | — | 1072 | 1 | no | — |
| 380 | C23 | — | 134 | 12 | no | — |
| 381 | C23 | — | 134 | 3 | no | — |
| 382 | C23 | #14524013 | 1 | 6 | yes | — |
| 383 | C23 | C22×D268 | 1 | 1 | yes | characteristic |
| 384 | Q8 | — | 2 | 4 | no | — |
| 385 | Q8 | — | 2 | 6 | no | — |
| 386 | Q8 | — | 67 | 4 | no | — |
| 387 | Q8 | — | 67 | 6 | no | — |
| 388 | Q8 | — | 134 | 24 | no | — |
| 389 | Q8 | — | 134 | 12 | no | — |
| 390 | Q8 | — | 134 | 3 | no | — |
| 391 | Q8 | — | 134 | 6 | no | — |
| 392 | D4 | — | 2 | 12 | no | — |
| 393 | D4 | — | 2 | 12 | no | — |
| 394 | D4 | — | 2 | 6 | no | — |
| 395 | D4 | — | 268 | 3 | no | — |
| 396 | D4 | — | 268 | 1 | no | — |
| 397 | D4 | — | 1072 | 6 | no | — |
| 398 | D4 | — | 67 | 6 | no | — |
| 399 | D4 | — | 134 | 12 | no | — |
| 400 | D4 | — | 134 | 24 | no | — |
| 401 | D4 | — | 134 | 24 | no | — |
| 402 | D4 | — | 134 | 12 | no | — |
| 403 | D4 | — | 134 | 3 | no | — |
| 404 | C2×C4 | — | 2 | 12 | no | — |
| 405 | C2×C4 | — | 2 | 6 | no | — |
| 406 | C2×C4 | — | 2 | 6 | no | — |
| 407 | C2×C4 | — | 268 | 3 | no | — |
| 408 | C2×C4 | — | 134 | 24 | no | — |
| 409 | C2×C4 | — | 134 | 24 | no | — |
| 410 | C2×C4 | — | 134 | 12 | no | — |
| 411 | C2×C4 | — | 134 | 24 | no | — |
| 412 | C2×C4 | — | 134 | 3 | no | — |
| 413 | C2×C4 | — | 134 | 6 | no | — |
| 414 | C2×C4 | — | 134 | 12 | no | — |
| 415 | C2×C4 | #14524013 | 1 | 6 | yes | — |
| 416 | C2×C4 | C2×D4×D67 | 1 | 3 | yes | — |
| 417 | C2×C4 | C2×D4×D67 | 1 | 3 | yes | — |
| 418 | C8 | — | 4 | 1 | no | — |
| 419 | C8 | — | 4 | 3 | no | — |
| 420 | C22 | — | 2 | 6 | no | — |
| 421 | C22 | — | 4 | 1 | no | — |
| 422 | C22 | — | 4 | 6 | no | — |
| 423 | C22 | — | 8 | 4 | no | — |
| 424 | C22 | — | 536 | 3 | no | — |
| 425 | C22 | — | 536 | 6 | no | — |
| 426 | C22 | — | 536 | 12 | no | — |
| 427 | C22 | — | 536 | 1 | no | — |
| 428 | C22 | — | 134 | 6 | no | — |
| 429 | C22 | C2×#14524013 | 1 | 3 | yes | — |
| 430 | C4 | — | 2 | 6 | no | — |
| 431 | C4 | — | 536 | 3 | no | — |
| 432 | C4 | — | 134 | 4 | no | — |
| 433 | C4 | — | 134 | 6 | no | — |
| 434 | C4 | #120×D67 | 1 | 1 | yes | characteristic |
| 435 | C4 | #120×D67 | 1 | 3 | yes | — |
| 436 | C2 | — | 2 | 3 | no | — |
| 437 | C2 | — | 4 | 6 | no | — |
| 438 | C2 | — | 268 | 6 | no | — |
| 439 | C2 | — | 1072 | 1 | no | — |
| 440 | C2 | #22568487 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22575022 | C2 | semidirect |
| 2. #22569611 | C2 | semidirect |
| 3. #22569583 | C2 | semidirect |
| 4. #22569497 | C2 | semidirect |
| 5. #22560185 | C2 | semidirect |
| 6. #22560172 | C2 | semidirect |
| 7. C67×#1791 | C2 | semidirect |
| 15. C2×#14524071 | C22 | semidirect |
| 16. C22×#11761617 | C22 | semidirect |
| 17. #16863960 | C22 | semidirect |
| 23. #16863412 | C22 | semidirect |
| 24. #16863406 | C22 | semidirect |
| 25. #16863393 | C22 | semidirect |
| 26. #16863370 | C22 | semidirect |
| 28. #413×C67 | C22 | semidirect |
| 29. #408×C67 | C22 | semidirect |
| 31. #14524091 | D4 | semidirect |
| 43. #14524088 | D4 | semidirect |
| 46. C2×#11761628 | D4 | semidirect |
| 56. C22×Dic134 | D4 | semidirect |
| 227. #1791 | D67 | semidirect |
| 228. C67 | #32895 | semidirect |
| 248. #413 | C2×D67 | semidirect |
| 250. #408 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22575022 | 2 |
| #22569611 | 2 |
| #22569583 | 2 |
| #22569497 | 2 |
| #22560185 | 2 |
| #22560172 | 2 |
| C67×#1791 | 2 |
| #32895 | 67 |