Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
2620 conjugacy classes of subgroups.
The subgroup lattice has 598 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #22574979 | C2 | 1 | 4 | yes | maximal, complemented |
| 2 | #22572013 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #22572009 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #22571999 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #22571998 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #22571995 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #22570638 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #22569931 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #22569561 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #443×D67 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | C67×#3293 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #16864233 | C22 | 1 | 4 | yes | complemented |
| 13 | #16864209 | — | 2 | 4 | no | — |
| 14 | #16864209 | C22 | 1 | 4 | yes | complemented |
| 15 | #16864205 | — | 2 | 8 | no | — |
| 16 | #16864205 | C22 | 1 | 8 | yes | complemented |
| 17 | #16864204 | C22 | 1 | 8 | yes | complemented |
| 18 | #16864201 | C22 | 1 | 4 | yes | complemented |
| 19 | #16864198 | — | 2 | 4 | no | — |
| 20 | #16864198 | C22 | 1 | 4 | yes | complemented |
| 21 | #16864195 | — | 2 | 8 | no | — |
| 22 | #16864195 | C22 | 1 | 8 | yes | complemented |
| 23 | C2×#14524066 | — | 2 | 4 | no | — |
| 24 | C2×#14524066 | C22 | 1 | 4 | yes | complemented |
| 25 | #135×D67 | — | 2 | 4 | no | — |
| 26 | #135×D67 | C22 | 1 | 2 | yes | — |
| 27 | #131×D67 | C22 | 1 | 4 | yes | complemented |
| 28 | #16863947 | C22 | 1 | 2 | yes | complemented |
| 29 | #16863781 | C22 | 1 | 4 | yes | complemented |
| 30 | #16863773 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | #16863770 | C22 | 1 | 2 | yes | complemented |
| 32 | #16863668 | C22 | 1 | 4 | yes | complemented |
| 33 | #16863667 | C22 | 1 | 4 | yes | complemented |
| 34 | #16863666 | C22 | 1 | 4 | yes | complemented |
| 35 | #16863662 | C22 | 1 | 8 | yes | complemented |
| 36 | #16863661 | C22 | 1 | 8 | yes | complemented |
| 37 | #16863578 | C22 | 1 | 4 | yes | complemented |
| 38 | #16863572 | C22 | 1 | 8 | yes | complemented |
| 39 | #16863571 | C22 | 1 | 4 | yes | complemented |
| 40 | #16863569 | C22 | 1 | 4 | yes | complemented |
| 41 | #16863565 | C22 | 1 | 8 | yes | complemented |
| 42 | #16863514 | C22 | 1 | 2 | yes | complemented |
| 43 | #16863513 | C22 | 1 | 2 | yes | complemented |
| 44 | #16863512 | C22 | 1 | 2 | yes | complemented |
| 45 | #16863511 | C22 | 1 | 4 | yes | complemented |
| 46 | #16863510 | C22 | 1 | 4 | yes | complemented |
| 47 | #108×D67 | C22 | 1 | 2 | yes | complemented |
| 48 | #104×D67 | C22 | 1 | 4 | yes | complemented |
| 49 | #16863379 | C22 | 1 | 4 | yes | complemented |
| 50 | C4×C8×D67 | C22 | 1 | 1 | yes | characteristic, complemented |
| 51 | #578×C67 | C22 | 1 | 4 | yes | complemented |
| 52 | #494×C67 | C22 | 1 | 1 | yes | characteristic, complemented |
| 53 | #473×C67 | C22 | 1 | 4 | yes | complemented |
| 54 | #456×C67 | C22 | 1 | 4 | yes | complemented |
| 55 | #443×C67 | C22 | 1 | 2 | yes | complemented |
| 56 | #14524091 | — | 2 | 8 | no | — |
| 57 | #14524091 | C23 | 1 | 4 | yes | — |
| 58 | #14524089 | — | 2 | 8 | no | — |
| 59 | #14524089 | — | 4 | 4 | no | — |
| 60 | #14524089 | C23 | 1 | 8 | yes | — |
| 61 | C2×#11761629 | — | 2 | 8 | no | — |
| 62 | C2×#11761629 | C23 | 1 | 4 | yes | — |
| 63 | #41×D67 | — | 2 | 8 | no | — |
| 64 | #41×D67 | — | 4 | 4 | no | — |
| 65 | #41×D67 | C23 | 1 | 4 | yes | — |
| 66 | #14524075 | — | 2 | 8 | no | — |
| 67 | #14524075 | — | 2 | 8 | no | — |
| 68 | #14524075 | — | 2 | 8 | no | — |
| 69 | #14524074 | — | 2 | 8 | no | — |
| 70 | #14524074 | C23 | 1 | 8 | yes | — |
| 71 | #14524071 | — | 2 | 8 | no | — |
| 72 | #14524071 | C23 | 1 | 8 | yes | — |
| 73 | #14524070 | — | 2 | 8 | no | — |
| 74 | #14524070 | — | 2 | 8 | no | — |
| 75 | #14524070 | — | 2 | 8 | no | — |
| 76 | #14524068 | — | 2 | 8 | no | — |
| 77 | #14524068 | C23 | 1 | 8 | yes | — |
| 78 | #14524066 | — | 2 | 8 | no | — |
| 79 | #14524066 | — | 2 | 8 | no | — |
| 80 | #14524066 | — | 2 | 4 | no | — |
| 81 | #14524066 | — | 2 | 4 | no | — |
| 82 | #14524066 | — | 2 | 4 | no | — |
| 83 | #14524066 | — | 2 | 4 | no | — |
| 84 | #14524066 | — | 2 | 4 | no | — |
| 85 | #14524066 | — | 2 | 4 | no | — |
| 86 | #14524066 | D4 | 1 | 2 | yes | complemented |
| 87 | #14524065 | — | 2 | 4 | no | — |
| 88 | #14524065 | C23 | 1 | 2 | yes | — |
| 89 | #14524064 | — | 2 | 8 | no | — |
| 90 | #14524064 | D4 | 1 | 4 | yes | complemented |
| 91 | #14524063 | — | 2 | 8 | no | — |
| 92 | #14524063 | C23 | 1 | 4 | yes | — |
| 93 | #14524062 | D4 | 1 | 2 | yes | complemented |
| 94 | Q16×D67 | — | 2 | 4 | no | — |
| 95 | Q16×D67 | D4 | 1 | 2 | yes | complemented |
| 96 | C2×#11761615 | — | 2 | 8 | no | — |
| 97 | C2×#11761615 | C23 | 1 | 8 | yes | — |
| 98 | SD16×D67 | — | 2 | 8 | no | — |
| 99 | SD16×D67 | D4 | 1 | 4 | yes | complemented |
| 100 | C2×D536 | — | 2 | 4 | no | — |
| 101 | C2×D536 | C23 | 1 | 4 | yes | — |
| 102 | D8×D67 | — | 2 | 4 | no | — |
| 103 | D8×D67 | D4 | 1 | 2 | yes | complemented |
| 104 | #14524051 | — | 2 | 4 | no | — |
| 105 | #14524051 | C23 | 1 | 4 | yes | — |
| 106 | #14524050 | C23 | 1 | 4 | yes | — |
| 107 | #14524049 | — | 2 | 4 | no | — |
| 108 | #14524049 | C23 | 1 | 4 | yes | — |
| 109 | M16×D67 | — | 2 | 4 | no | — |
| 110 | M16×D67 | C23 | 1 | 4 | yes | — |
| 111 | C2×C8×D67 | — | 2 | 4 | no | — |
| 112 | C2×C8×D67 | C23 | 1 | 2 | yes | — |
| 113 | #14524040 | C23 | 1 | 2 | yes | — |
| 114 | #14524032 | C23 | 1 | 4 | yes | — |
| 115 | #14524018 | — | 4 | 2 | no | — |
| 116 | #14524005 | — | 4 | 2 | no | — |
| 117 | C42×D67 | C23 | 1 | 1 | yes | characteristic |
| 118 | #14523979 | C23 | 1 | 2 | yes | — |
| 119 | #14523978 | C23 | 1 | 4 | yes | — |
| 120 | #14523971 | C23 | 1 | 4 | yes | — |
| 121 | #14523970 | C23 | 1 | 4 | yes | — |
| 122 | #14523969 | C23 | 1 | 4 | yes | — |
| 123 | #14523962 | C23 | 1 | 4 | yes | — |
| 124 | #14523959 | C23 | 1 | 8 | yes | — |
| 125 | C4×C67⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 126 | C8×Dic67 | C23 | 1 | 2 | yes | — |
| 127 | 2−1+4×C67 | C23 | 1 | 4 | yes | — |
| 128 | #137×C67 | — | 2 | 8 | no | — |
| 129 | #137×C67 | C23 | 1 | 8 | yes | — |
| 130 | #135×C67 | — | 2 | 4 | no | — |
| 131 | #135×C67 | C23 | 1 | 2 | yes | — |
| 132 | C2×Q16×C67 | — | 2 | 4 | no | — |
| 133 | C2×Q16×C67 | C23 | 1 | 4 | yes | — |
| 134 | #131×C67 | C23 | 1 | 4 | yes | — |
| 135 | C4⋊Q8×C67 | C23 | 1 | 2 | yes | — |
| 136 | #108×C67 | C23 | 1 | 2 | yes | — |
| 137 | #104×C67 | C23 | 1 | 4 | yes | — |
| 138 | #101×C67 | C23 | 1 | 4 | yes | — |
| 139 | C4×C8×C67 | C23 | 1 | 1 | yes | characteristic |
| 140 | #11761629 | — | 2 | 8 | no | — |
| 141 | #11761629 | — | 2 | 8 | no | — |
| 142 | #11761629 | — | 2 | 8 | no | — |
| 143 | #11761629 | — | 2 | 8 | no | — |
| 144 | #11761629 | — | 4 | 4 | no | — |
| 145 | #11761629 | — | 4 | 8 | no | — |
| 146 | #11761629 | C2×D4 | 1 | 4 | yes | — |
| 147 | #11761628 | — | 2 | 4 | no | — |
| 148 | #11761628 | — | 2 | 8 | no | — |
| 149 | #11761628 | — | 4 | 8 | no | — |
| 150 | #11761628 | — | 4 | 8 | no | — |
| 151 | #11761628 | — | 4 | 4 | no | — |
| 152 | #11761628 | C24 | 1 | 4 | yes | — |
| 153 | #11761627 | — | 2 | 4 | no | — |
| 154 | #11761627 | — | 4 | 4 | no | — |
| 155 | #11761627 | C2×D4 | 1 | 4 | yes | — |
| 156 | Q8×D67 | — | 2 | 8 | no | — |
| 157 | Q8×D67 | — | 4 | 4 | no | — |
| 158 | Q8×D67 | C2×D4 | 1 | 4 | yes | — |
| 159 | C2×D268 | — | 2 | 8 | no | — |
| 160 | C2×D268 | — | 2 | 4 | no | — |
| 161 | C2×D268 | — | 4 | 8 | no | — |
| 162 | C2×D268 | — | 4 | 2 | no | — |
| 163 | C2×D268 | C24 | 1 | 4 | yes | — |
| 164 | D4×D67 | — | 2 | 4 | no | — |
| 165 | D4×D67 | — | 2 | 8 | no | — |
| 166 | D4×D67 | — | 4 | 4 | no | — |
| 167 | D4×D67 | — | 4 | 8 | no | — |
| 168 | D4×D67 | — | 4 | 8 | no | — |
| 169 | D4×D67 | C2×D4 | 1 | 4 | yes | — |
| 170 | C2×C4×D67 | — | 2 | 4 | no | — |
| 171 | C2×C4×D67 | — | 2 | 1 | no | — |
| 172 | C2×C4×D67 | — | 2 | 4 | no | — |
| 173 | C2×C4×D67 | — | 4 | 8 | no | — |
| 174 | C2×C4×D67 | C24 | 1 | 1 | yes | characteristic |
| 175 | Dic268 | C2×D4 | 1 | 2 | yes | — |
| 176 | #11761618 | — | 2 | 8 | no | — |
| 177 | #11761618 | C2×D4 | 1 | 4 | yes | — |
| 178 | #11761617 | — | 2 | 8 | no | — |
| 179 | #11761617 | C2×D4 | 1 | 4 | yes | — |
| 180 | #11761616 | C2×D4 | 1 | 4 | yes | — |
| 181 | #11761615 | — | 2 | 8 | no | — |
| 182 | #11761615 | — | 2 | 8 | no | — |
| 183 | #11761615 | — | 2 | 8 | no | — |
| 184 | #11761615 | — | 2 | 8 | no | — |
| 185 | #11761615 | C2×D4 | 1 | 4 | yes | — |
| 186 | D536 | — | 2 | 8 | no | — |
| 187 | D536 | — | 2 | 4 | no | — |
| 188 | D536 | — | 2 | 4 | no | — |
| 189 | D536 | C2×D4 | 1 | 2 | yes | — |
| 190 | #11761613 | — | 2 | 8 | no | — |
| 191 | #11761613 | C2×D4 | 1 | 4 | yes | — |
| 192 | #11761612 | — | 2 | 4 | no | — |
| 193 | #11761612 | C24 | 1 | 4 | yes | — |
| 194 | #11761611 | — | 2 | 4 | no | — |
| 195 | #11761611 | — | 2 | 4 | no | — |
| 196 | #11761611 | — | 2 | 4 | no | — |
| 197 | C2×C67⋊C8 | — | 2 | 4 | no | — |
| 198 | C2×C67⋊C8 | C24 | 1 | 2 | yes | — |
| 199 | C8×D67 | — | 2 | 4 | no | — |
| 200 | C8×D67 | — | 2 | 4 | no | — |
| 201 | C8×D67 | — | 2 | 4 | no | — |
| 202 | C8×D67 | C2×D4 | 1 | 2 | yes | — |
| 203 | C8×D67 | C2×D4 | 1 | 2 | yes | — |
| 204 | C8×D67 | C2×D4 | 1 | 2 | yes | — |
| 205 | C8×D67 | C2×D4 | 1 | 2 | yes | — |
| 206 | (C2×D67)⋊C4 | — | 4 | 4 | no | — |
| 207 | C4×Dic67 | — | 2 | 1 | no | — |
| 208 | C4×Dic67 | C24 | 1 | 1 | yes | characteristic |
| 209 | #41×C67 | — | 2 | 8 | no | — |
| 210 | #41×C67 | — | 4 | 4 | no | — |
| 211 | #41×C67 | C24 | 1 | 4 | yes | — |
| 212 | C2×Q8×C67 | — | 2 | 8 | no | — |
| 213 | C2×Q8×C67 | C24 | 1 | 4 | yes | — |
| 214 | Q16×C67 | — | 2 | 8 | no | — |
| 215 | Q16×C67 | — | 2 | 4 | no | — |
| 216 | Q16×C67 | — | 2 | 4 | no | — |
| 217 | Q16×C67 | C2×D4 | 1 | 2 | yes | — |
| 218 | SD16×C67 | — | 2 | 8 | no | — |
| 219 | SD16×C67 | C2×D4 | 1 | 4 | yes | — |
| 220 | D8×C67 | C2×D4 | 1 | 2 | yes | — |
| 221 | M16×C67 | — | 2 | 4 | no | — |
| 222 | M16×C67 | C24 | 1 | 4 | yes | — |
| 223 | C2×C8×C67 | — | 2 | 4 | no | — |
| 224 | C2×C8×C67 | C24 | 1 | 2 | yes | — |
| 225 | C4⋊C4×C67 | — | 4 | 2 | no | — |
| 226 | C42×C67 | C24 | 1 | 1 | yes | characteristic |
| 227 | C22×D67 | — | 2 | 4 | no | — |
| 228 | C22×D67 | — | 2 | 4 | no | — |
| 229 | C22×D67 | — | 4 | 8 | no | — |
| 230 | C22×D67 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 231 | Q8×C67 | — | 2 | 8 | no | — |
| 232 | Q8×C67 | — | 4 | 4 | no | — |
| 233 | Q8×C67 | C22×D4 | 1 | 4 | yes | — |
| 234 | D4×C67 | — | 2 | 4 | no | — |
| 235 | D4×C67 | — | 4 | 4 | no | — |
| 236 | D4×C67 | C22×D4 | 1 | 4 | yes | — |
| 237 | C2×C4×C67 | — | 2 | 1 | no | — |
| 238 | C2×C4×C67 | — | 2 | 4 | no | — |
| 239 | C2×C4×C67 | — | 2 | 4 | no | — |
| 240 | C2×C4×C67 | — | 4 | 8 | no | — |
| 241 | C2×C4×C67 | C25 | 1 | 1 | yes | characteristic |
| 242 | C22⋊D67 | — | 2 | 4 | no | — |
| 243 | C22⋊D67 | — | 2 | 4 | no | — |
| 244 | C22⋊D67 | — | 2 | 4 | no | — |
| 245 | C22⋊D67 | — | 4 | 8 | no | — |
| 246 | C2×Dic67 | — | 2 | 4 | no | — |
| 247 | C2×Dic67 | — | 2 | 1 | no | — |
| 248 | C2×Dic67 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 249 | D268 | — | 2 | 4 | no | — |
| 250 | D268 | — | 2 | 8 | no | — |
| 251 | D268 | — | 4 | 8 | no | — |
| 252 | D268 | — | 4 | 4 | no | — |
| 253 | D268 | — | 4 | 8 | no | — |
| 254 | D268 | — | 8 | 4 | no | — |
| 255 | D268 | C22×D4 | 1 | 4 | yes | — |
| 256 | C4×D67 | — | 2 | 4 | no | — |
| 257 | C4×D67 | — | 2 | 4 | no | — |
| 258 | C4×D67 | — | 2 | 4 | no | — |
| 259 | C4×D67 | — | 4 | 8 | no | — |
| 260 | C4×D67 | — | 4 | 8 | no | — |
| 261 | C4×D67 | — | 4 | 2 | no | — |
| 262 | C4×D67 | — | 4 | 4 | no | — |
| 263 | C4×D67 | — | 4 | 4 | no | — |
| 264 | C4×D67 | C22×D4 | 1 | 2 | yes | — |
| 265 | C4×D67 | C22×D4 | 1 | 2 | yes | — |
| 266 | Dic134 | — | 2 | 4 | no | — |
| 267 | Dic134 | — | 4 | 4 | no | — |
| 268 | Dic134 | C22×D4 | 1 | 4 | yes | — |
| 269 | C8×C67 | — | 2 | 4 | no | — |
| 270 | C8×C67 | C22×D4 | 1 | 2 | yes | — |
| 271 | C8×C67 | C22×D4 | 1 | 2 | yes | — |
| 272 | C67⋊C8 | — | 2 | 4 | no | — |
| 273 | C67⋊C8 | C22×D4 | 1 | 2 | yes | — |
| 274 | C67⋊C8 | C22×D4 | 1 | 2 | yes | — |
| 275 | C22×C67 | — | 2 | 4 | no | — |
| 276 | C22×C67 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 277 | C2×D67 | — | 2 | 4 | no | — |
| 278 | C2×D67 | — | 4 | 1 | no | — |
| 279 | C2×D67 | — | 4 | 4 | no | — |
| 280 | C2×D67 | — | 8 | 4 | no | — |
| 281 | C2×D67 | — | 8 | 4 | no | — |
| 282 | C2×D67 | — | 16 | 8 | no | — |
| 283 | C2×D67 | D42 | 1 | 2 | yes | — |
| 284 | C4×C67 | — | 2 | 2 | no | — |
| 285 | C4×C67 | — | 2 | 4 | no | — |
| 286 | C4×C67 | — | 4 | 4 | no | — |
| 287 | C4×C67 | C23×D4 | 1 | 2 | yes | — |
| 288 | Dic67 | — | 2 | 4 | no | — |
| 289 | Dic67 | — | 4 | 1 | no | — |
| 290 | Dic67 | D42 | 1 | 1 | yes | characteristic |
| 291 | Dic67 | D42 | 1 | 1 | yes | characteristic |
| 292 | #61105 | — | 67 | 1 | no | maximal, Sylow |
| 293 | C2×C67 | — | 2 | 1 | no | — |
| 294 | C2×C67 | — | 4 | 4 | no | — |
| 295 | C2×C67 | C2×D42 | 1 | 1 | yes | characteristic |
| 296 | D67 | — | 2 | 2 | no | — |
| 297 | D67 | — | 4 | 4 | no | — |
| 298 | D67 | — | 8 | 4 | no | — |
| 299 | #3584 | — | 67 | 4 | no | — |
| 300 | #3293 | — | 67 | 1 | no | — |
| 301 | #3293 | D67 | 1 | 1 | yes | characteristic, complemented |
| 302 | #3292 | — | 67 | 2 | no | — |
| 303 | #3291 | — | 67 | 4 | no | — |
| 304 | #3290 | — | 67 | 4 | no | — |
| 305 | #3290 | — | 67 | 4 | no | — |
| 306 | #3147 | — | 67 | 1 | no | — |
| 307 | #3067 | — | 67 | 4 | no | — |
| 308 | #3018 | — | 67 | 4 | no | — |
| 309 | C2×#443 | — | 67 | 2 | no | — |
| 310 | C67 | #61105 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 311 | #585 | — | 67 | 4 | no | — |
| 312 | #578 | — | 67 | 4 | no | — |
| 313 | #578 | — | 134 | 4 | no | — |
| 314 | #578 | C2×D67 | 1 | 4 | yes | complemented |
| 315 | #577 | — | 67 | 8 | no | — |
| 316 | #577 | — | 67 | 8 | no | — |
| 317 | #577 | — | 134 | 8 | no | — |
| 318 | #576 | — | 67 | 4 | no | — |
| 319 | #576 | — | 67 | 4 | no | — |
| 320 | #576 | — | 134 | 4 | no | — |
| 321 | #575 | — | 67 | 8 | no | — |
| 322 | #575 | — | 134 | 8 | no | — |
| 323 | C2×#135 | — | 67 | 2 | no | — |
| 324 | C2×#135 | — | 67 | 4 | no | — |
| 325 | C2×#135 | — | 134 | 4 | no | — |
| 326 | C2×#135 | — | 134 | 4 | no | — |
| 327 | C2×#131 | — | 67 | 4 | no | — |
| 328 | #532 | — | 67 | 2 | no | — |
| 329 | #495 | — | 67 | 4 | no | — |
| 330 | #494 | C2×D67 | 1 | 1 | yes | characteristic, complemented |
| 331 | #493 | — | 67 | 1 | no | — |
| 332 | #492 | — | 67 | 2 | no | — |
| 333 | #473 | — | 67 | 4 | no | — |
| 334 | #473 | C2×D67 | 1 | 4 | yes | complemented |
| 335 | #472 | — | 67 | 4 | no | — |
| 336 | #472 | — | 67 | 4 | no | — |
| 337 | #471 | — | 67 | 8 | no | — |
| 338 | #471 | — | 67 | 8 | no | — |
| 339 | #456 | — | 67 | 4 | no | — |
| 340 | #456 | C2×D67 | 1 | 4 | yes | complemented |
| 341 | #455 | — | 67 | 8 | no | — |
| 342 | #454 | — | 67 | 4 | no | — |
| 343 | #454 | — | 67 | 4 | no | — |
| 344 | #453 | — | 67 | 8 | no | — |
| 345 | #443 | — | 67 | 2 | no | — |
| 346 | #443 | — | 67 | 4 | no | — |
| 347 | #443 | — | 67 | 2 | no | — |
| 348 | #443 | — | 67 | 4 | no | — |
| 349 | #443 | — | 67 | 2 | no | — |
| 350 | #443 | C2×D67 | 1 | 2 | yes | complemented |
| 351 | C2×#108 | — | 67 | 2 | no | — |
| 352 | C2×#104 | — | 67 | 4 | no | — |
| 353 | #413 | — | 67 | 4 | no | — |
| 354 | C2×C4×C8 | — | 67 | 1 | no | — |
| 355 | 2−1+4 | — | 67 | 4 | no | — |
| 356 | 2−1+4 | — | 134 | 8 | no | — |
| 357 | 2−1+4 | C22×D67 | 1 | 4 | yes | — |
| 358 | H(5,𝔽2) | — | 268 | 4 | no | — |
| 359 | H(5,𝔽2) | — | 67 | 8 | no | — |
| 360 | H(5,𝔽2) | — | 134 | 8 | no | — |
| 361 | C2×#41 | — | 268 | 4 | no | — |
| 362 | C2×#41 | — | 67 | 4 | no | — |
| 363 | C2×#41 | — | 67 | 4 | no | — |
| 364 | C2×#41 | — | 134 | 8 | no | — |
| 365 | C2×#41 | — | 134 | 8 | no | — |
| 366 | #137 | — | 2 | 8 | no | — |
| 367 | #137 | — | 67 | 8 | no | — |
| 368 | #137 | — | 134 | 8 | no | — |
| 369 | #137 | — | 134 | 8 | no | — |
| 370 | #137 | — | 134 | 8 | no | — |
| 371 | #137 | — | 134 | 8 | no | — |
| 372 | #137 | C22×D67 | 1 | 8 | yes | — |
| 373 | AGL(1,ℤ/8) | — | 67 | 8 | no | — |
| 374 | AGL(1,ℤ/8) | — | 67 | 8 | no | — |
| 375 | AGL(1,ℤ/8) | — | 134 | 8 | no | — |
| 376 | AGL(1,ℤ/8) | — | 134 | 8 | no | — |
| 377 | AGL(1,ℤ/8) | — | 134 | 8 | no | — |
| 378 | AGL(1,ℤ/8) | — | 134 | 8 | no | — |
| 379 | AGL(1,ℤ/8) | — | 134 | 8 | no | — |
| 380 | #135 | — | 2 | 4 | no | — |
| 381 | #135 | — | 67 | 4 | no | — |
| 382 | #135 | — | 67 | 2 | no | — |
| 383 | #135 | — | 67 | 4 | no | — |
| 384 | #135 | — | 67 | 2 | no | — |
| 385 | #135 | — | 67 | 2 | no | — |
| 386 | #135 | — | 134 | 4 | no | — |
| 387 | #135 | — | 134 | 4 | no | — |
| 388 | #135 | — | 134 | 4 | no | — |
| 389 | #135 | — | 134 | 4 | no | — |
| 390 | #135 | — | 134 | 4 | no | — |
| 391 | #135 | — | 134 | 4 | no | — |
| 392 | #135 | — | 134 | 8 | no | — |
| 393 | #135 | — | 134 | 8 | no | — |
| 394 | #135 | — | 134 | 8 | no | — |
| 395 | #135 | — | 134 | 8 | no | — |
| 396 | #135 | — | 134 | 4 | no | — |
| 397 | #135 | C22×D67 | 1 | 2 | yes | — |
| 398 | C2×Q16 | — | 2 | 4 | no | — |
| 399 | C2×Q16 | — | 67 | 2 | no | — |
| 400 | C2×Q16 | — | 134 | 4 | no | — |
| 401 | C2×Q16 | C22×D67 | 1 | 4 | yes | — |
| 402 | C2×SD16 | — | 67 | 4 | no | — |
| 403 | C2×SD16 | — | 67 | 8 | no | — |
| 404 | C2×SD16 | — | 134 | 8 | no | — |
| 405 | C2×SD16 | — | 134 | 8 | no | — |
| 406 | C2×D8 | — | 67 | 2 | no | — |
| 407 | C2×D8 | — | 67 | 4 | no | — |
| 408 | C2×D8 | — | 134 | 4 | no | — |
| 409 | C2×D8 | — | 134 | 4 | no | — |
| 410 | #131 | — | 67 | 4 | no | — |
| 411 | #131 | — | 67 | 4 | no | — |
| 412 | #131 | — | 67 | 4 | no | — |
| 413 | #131 | — | 134 | 4 | no | — |
| 414 | #131 | — | 134 | 4 | no | — |
| 415 | #131 | C22×D67 | 1 | 4 | yes | — |
| 416 | C2×M16 | — | 67 | 4 | no | — |
| 417 | C2×M16 | — | 134 | 4 | no | — |
| 418 | C22×C8 | — | 67 | 2 | no | — |
| 419 | C22×C8 | — | 134 | 4 | no | — |
| 420 | C4⋊Q8 | C22×D67 | 1 | 2 | yes | — |
| 421 | #127 | — | 67 | 2 | no | — |
| 422 | #124 | — | 67 | 4 | no | — |
| 423 | #121 | — | 268 | 2 | no | — |
| 424 | C4×D4 | — | 268 | 2 | no | — |
| 425 | C2×C42 | — | 67 | 1 | no | — |
| 426 | #108 | — | 67 | 4 | no | — |
| 427 | #108 | — | 67 | 2 | no | — |
| 428 | #108 | C22×D67 | 1 | 2 | yes | — |
| 429 | #104 | — | 67 | 4 | no | — |
| 430 | #104 | — | 67 | 4 | no | — |
| 431 | #104 | — | 67 | 4 | no | — |
| 432 | #104 | C22×D67 | 1 | 4 | yes | — |
| 433 | #101 | — | 67 | 4 | no | — |
| 434 | #101 | C22×D67 | 1 | 4 | yes | — |
| 435 | #100 | — | 67 | 8 | no | — |
| 436 | C4×C8 | — | 67 | 2 | no | — |
| 437 | C4×C8 | — | 67 | 1 | no | — |
| 438 | C4×C8 | C22×D67 | 1 | 1 | yes | characteristic |
| 439 | #41 | — | 2 | 8 | no | — |
| 440 | #41 | — | 4 | 4 | no | — |
| 441 | #41 | — | 268 | 4 | no | — |
| 442 | #41 | — | 268 | 8 | no | — |
| 443 | #41 | — | 268 | 8 | no | — |
| 444 | #41 | — | 268 | 8 | no | — |
| 445 | #41 | — | 268 | 4 | no | — |
| 446 | #41 | — | 268 | 4 | no | — |
| 447 | #41 | — | 67 | 4 | no | — |
| 448 | #41 | — | 67 | 4 | no | — |
| 449 | #41 | — | 67 | 4 | no | — |
| 450 | #41 | — | 134 | 8 | no | — |
| 451 | #41 | — | 134 | 4 | no | — |
| 452 | #41 | — | 134 | 8 | no | — |
| 453 | #41 | — | 134 | 8 | no | — |
| 454 | #41 | — | 134 | 8 | no | — |
| 455 | #41 | — | 134 | 8 | no | — |
| 456 | #41 | — | 134 | 4 | no | — |
| 457 | #41 | C23×D67 | 1 | 4 | yes | — |
| 458 | C2×Q8 | — | 2 | 8 | no | — |
| 459 | C2×Q8 | — | 268 | 4 | no | — |
| 460 | C2×Q8 | — | 67 | 4 | no | — |
| 461 | C2×Q8 | — | 134 | 8 | no | — |
| 462 | C2×Q8 | C23×D67 | 1 | 4 | yes | — |
| 463 | C2×D4 | — | 268 | 2 | no | — |
| 464 | C2×D4 | — | 268 | 8 | no | — |
| 465 | C2×D4 | — | 268 | 8 | no | — |
| 466 | C2×D4 | — | 268 | 8 | no | — |
| 467 | C2×D4 | — | 268 | 4 | no | — |
| 468 | C2×D4 | — | 67 | 4 | no | — |
| 469 | C2×D4 | — | 67 | 4 | no | — |
| 470 | C2×D4 | — | 134 | 4 | no | — |
| 471 | C2×D4 | — | 134 | 8 | no | — |
| 472 | C2×D4 | — | 134 | 4 | no | — |
| 473 | C2×D4 | — | 134 | 8 | no | — |
| 474 | C22×C4 | — | 268 | 8 | no | — |
| 475 | C22×C4 | — | 67 | 1 | no | — |
| 476 | C22×C4 | — | 134 | 4 | no | — |
| 477 | C22×C4 | — | 134 | 1 | no | — |
| 478 | C22×C4 | — | 134 | 4 | no | — |
| 479 | Q16 | — | 2 | 8 | no | — |
| 480 | Q16 | — | 2 | 4 | no | — |
| 481 | Q16 | — | 2 | 4 | no | — |
| 482 | Q16 | — | 67 | 4 | no | — |
| 483 | Q16 | — | 67 | 2 | no | — |
| 484 | Q16 | — | 134 | 8 | no | — |
| 485 | Q16 | D4×D67 | 1 | 2 | yes | — |
| 486 | SD16 | — | 2 | 8 | no | — |
| 487 | SD16 | — | 67 | 4 | no | — |
| 488 | SD16 | — | 67 | 4 | no | — |
| 489 | SD16 | — | 67 | 4 | no | — |
| 490 | SD16 | — | 134 | 8 | no | — |
| 491 | SD16 | — | 134 | 8 | no | — |
| 492 | SD16 | — | 134 | 8 | no | — |
| 493 | SD16 | — | 134 | 8 | no | — |
| 494 | SD16 | — | 134 | 8 | no | — |
| 495 | SD16 | D4×D67 | 1 | 4 | yes | — |
| 496 | D8 | — | 67 | 4 | no | — |
| 497 | D8 | — | 67 | 2 | no | — |
| 498 | D8 | — | 134 | 8 | no | — |
| 499 | D8 | — | 134 | 8 | no | — |
| 500 | D8 | — | 134 | 4 | no | — |
| 501 | D8 | — | 134 | 4 | no | — |
| 502 | D8 | D4×D67 | 1 | 2 | yes | — |
| 503 | M16 | — | 2 | 4 | no | — |
| 504 | M16 | — | 67 | 4 | no | — |
| 505 | M16 | — | 134 | 4 | no | — |
| 506 | M16 | — | 134 | 4 | no | — |
| 507 | M16 | — | 134 | 4 | no | — |
| 508 | M16 | — | 134 | 4 | no | — |
| 509 | M16 | C23×D67 | 1 | 4 | yes | — |
| 510 | C2×C8 | — | 2 | 4 | no | — |
| 511 | C2×C8 | — | 67 | 2 | no | — |
| 512 | C2×C8 | — | 67 | 2 | no | — |
| 513 | C2×C8 | — | 67 | 2 | no | — |
| 514 | C2×C8 | — | 67 | 2 | no | — |
| 515 | C2×C8 | — | 67 | 2 | no | — |
| 516 | C2×C8 | — | 134 | 4 | no | — |
| 517 | C2×C8 | — | 134 | 4 | no | — |
| 518 | C2×C8 | — | 134 | 4 | no | — |
| 519 | C2×C8 | — | 134 | 4 | no | — |
| 520 | C2×C8 | C23×D67 | 1 | 2 | yes | — |
| 521 | C4⋊C4 | — | 4 | 2 | no | — |
| 522 | C22⋊C4 | — | 268 | 4 | no | — |
| 523 | C42 | — | 67 | 1 | no | — |
| 524 | C42 | — | 134 | 1 | no | — |
| 525 | C42 | C23×D67 | 1 | 1 | yes | characteristic |
| 526 | C23 | — | 268 | 8 | no | — |
| 527 | C23 | — | 67 | 1 | no | — |
| 528 | C23 | — | 134 | 4 | no | — |
| 529 | C23 | — | 134 | 4 | no | — |
| 530 | Q8 | — | 2 | 8 | no | — |
| 531 | Q8 | — | 4 | 4 | no | — |
| 532 | Q8 | — | 268 | 4 | no | — |
| 533 | Q8 | — | 67 | 4 | no | — |
| 534 | Q8 | — | 134 | 4 | no | — |
| 535 | Q8 | C2×D4×D67 | 1 | 4 | yes | — |
| 536 | D4 | — | 2 | 4 | no | — |
| 537 | D4 | — | 4 | 4 | no | — |
| 538 | D4 | — | 268 | 8 | no | — |
| 539 | D4 | — | 268 | 8 | no | — |
| 540 | D4 | — | 268 | 4 | no | — |
| 541 | D4 | — | 268 | 8 | no | — |
| 542 | D4 | — | 536 | 4 | no | — |
| 543 | D4 | — | 67 | 4 | no | — |
| 544 | D4 | — | 134 | 4 | no | — |
| 545 | D4 | — | 134 | 4 | no | — |
| 546 | D4 | — | 134 | 4 | no | — |
| 547 | D4 | — | 134 | 4 | no | — |
| 548 | D4 | — | 134 | 8 | no | — |
| 549 | D4 | C2×D4×D67 | 1 | 4 | yes | — |
| 550 | C2×C4 | — | 2 | 1 | no | — |
| 551 | C2×C4 | — | 2 | 4 | no | — |
| 552 | C2×C4 | — | 2 | 4 | no | — |
| 553 | C2×C4 | — | 4 | 8 | no | — |
| 554 | C2×C4 | — | 268 | 2 | no | — |
| 555 | C2×C4 | — | 268 | 8 | no | — |
| 556 | C2×C4 | — | 268 | 4 | no | — |
| 557 | C2×C4 | — | 268 | 4 | no | — |
| 558 | C2×C4 | — | 268 | 8 | no | — |
| 559 | C2×C4 | — | 67 | 1 | no | — |
| 560 | C2×C4 | — | 67 | 2 | no | — |
| 561 | C2×C4 | — | 67 | 2 | no | — |
| 562 | C2×C4 | — | 134 | 4 | no | — |
| 563 | C2×C4 | — | 134 | 4 | no | — |
| 564 | C2×C4 | — | 134 | 1 | no | — |
| 565 | C2×C4 | — | 134 | 4 | no | — |
| 566 | C2×C4 | — | 134 | 4 | no | — |
| 567 | C2×C4 | C24×D67 | 1 | 1 | yes | characteristic |
| 568 | C8 | — | 2 | 4 | no | — |
| 569 | C8 | — | 67 | 2 | no | — |
| 570 | C8 | — | 67 | 2 | no | — |
| 571 | C8 | — | 134 | 4 | no | — |
| 572 | C8 | C2×D4×D67 | 1 | 2 | yes | — |
| 573 | C8 | C2×D4×D67 | 1 | 2 | yes | — |
| 574 | C22 | — | 2 | 4 | no | — |
| 575 | C22 | — | 268 | 1 | no | — |
| 576 | C22 | — | 268 | 4 | no | — |
| 577 | C22 | — | 536 | 4 | no | — |
| 578 | C22 | — | 536 | 4 | no | — |
| 579 | C22 | — | 1072 | 8 | no | — |
| 580 | C22 | — | 67 | 2 | no | — |
| 581 | C22 | — | 134 | 4 | no | — |
| 582 | C22 | H(5,𝔽2)×D67 | 1 | 1 | yes | characteristic |
| 583 | C4 | — | 2 | 2 | no | — |
| 584 | C4 | — | 2 | 4 | no | — |
| 585 | C4 | — | 4 | 4 | no | — |
| 586 | C4 | — | 268 | 1 | no | — |
| 587 | C4 | — | 67 | 1 | no | — |
| 588 | C4 | — | 67 | 1 | no | — |
| 589 | C4 | — | 134 | 4 | no | — |
| 590 | C4 | C22×D4×D67 | 1 | 2 | yes | — |
| 591 | C2 | — | 2 | 1 | no | — |
| 592 | C2 | — | 4 | 4 | no | — |
| 593 | C2 | — | 268 | 4 | no | — |
| 594 | C2 | — | 536 | 4 | no | — |
| 595 | C2 | — | 134 | 2 | no | — |
| 596 | C2 | D42×D67 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22574979 | C2 | semidirect |
| 2. #22572013 | C2 | semidirect |
| 3. #22572009 | C2 | semidirect |
| 4. #22571999 | C2 | semidirect |
| 5. #22571998 | C2 | semidirect |
| 6. #22571995 | C2 | semidirect |
| 7. #22570638 | C2 | semidirect |
| 8. #22569931 | C2 | semidirect |
| 9. #22569561 | C2 | semidirect |
| 10. #443×D67 | C2 | semidirect |
| 11. C67×#3293 | C2 | semidirect |
| 12. #16864233 | C22 | semidirect |
| 14. #16864209 | C22 | semidirect |
| 16. #16864205 | C22 | semidirect |
| 17. #16864204 | C22 | semidirect |
| 18. #16864201 | C22 | semidirect |
| 20. #16864198 | C22 | semidirect |
| 22. #16864195 | C22 | semidirect |
| 24. C2×#14524066 | C22 | semidirect |
| 27. #131×D67 | C22 | semidirect |
| 28. #16863947 | C22 | semidirect |
| 29. #16863781 | C22 | semidirect |
| 30. #16863773 | C22 | semidirect |
| 31. #16863770 | C22 | semidirect |
| 32. #16863668 | C22 | semidirect |
| 33. #16863667 | C22 | semidirect |
| 34. #16863666 | C22 | semidirect |
| 35. #16863662 | C22 | semidirect |
| 36. #16863661 | C22 | semidirect |
| 37. #16863578 | C22 | semidirect |
| 38. #16863572 | C22 | semidirect |
| 39. #16863571 | C22 | semidirect |
| 40. #16863569 | C22 | semidirect |
| 41. #16863565 | C22 | semidirect |
| 42. #16863514 | C22 | semidirect |
| 43. #16863513 | C22 | semidirect |
| 44. #16863512 | C22 | semidirect |
| 45. #16863511 | C22 | semidirect |
| 46. #16863510 | C22 | semidirect |
| 47. #108×D67 | C22 | semidirect |
| 48. #104×D67 | C22 | semidirect |
| 49. #16863379 | C22 | semidirect |
| 50. C4×C8×D67 | C22 | semidirect |
| 51. #578×C67 | C22 | semidirect |
| 52. #494×C67 | C22 | semidirect |
| 53. #473×C67 | C22 | semidirect |
| 54. #456×C67 | C22 | semidirect |
| 55. #443×C67 | C22 | semidirect |
| 86. #14524066 | D4 | semidirect |
| 90. #14524064 | D4 | semidirect |
| 93. #14524062 | D4 | semidirect |
| 95. Q16×D67 | D4 | semidirect |
| 99. SD16×D67 | D4 | semidirect |
| 103. D8×D67 | D4 | semidirect |
| 301. #3293 | D67 | semidirect |
| 310. C67 | #61105 | semidirect |
| 314. #578 | C2×D67 | semidirect |
| 330. #494 | C2×D67 | semidirect |
| 334. #473 | C2×D67 | semidirect |
| 340. #456 | C2×D67 | semidirect |
| 350. #443 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22574979 | 2 |
| #22572013 | 2 |
| #22572009 | 2 |
| #22571999 | 2 |
| #22571998 | 2 |
| #22571995 | 2 |
| #22570638 | 2 |
| #22569931 | 2 |
| #22569561 | 2 |
| #443×D67 | 2 |
| C67×#3293 | 2 |
| #61105 | 67 |