Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
2600 conjugacy classes of subgroups.
The subgroup lattice has 728 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #22574997 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #22574993 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #22572014 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #22572003 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #22571985 | C2 | 1 | 8 | yes | maximal, complemented |
| 6 | #22570668 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #22569947 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #22569946 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #22569560 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | C2×#16863580 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #22569120 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C67×#2956 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #16864232 | C22 | 1 | 2 | yes | complemented |
| 14 | C2×#14524090 | C22 | 1 | 2 | yes | — |
| 15 | #16864213 | — | 2 | 4 | no | — |
| 16 | #16864213 | C22 | 1 | 8 | yes | complemented |
| 17 | #16864212 | — | 2 | 4 | no | — |
| 18 | #16864210 | C22 | 1 | 8 | yes | complemented |
| 19 | #16864208 | — | 2 | 4 | no | — |
| 20 | #16864208 | C22 | 1 | 8 | yes | complemented |
| 21 | #16864206 | — | 2 | 4 | no | — |
| 22 | #16864203 | C22 | 1 | 8 | yes | complemented |
| 23 | #16864196 | — | 2 | 4 | no | — |
| 24 | #16864196 | C22 | 1 | 2 | yes | — |
| 25 | #16864196 | C22 | 1 | 1 | yes | characteristic |
| 26 | #16864194 | C22 | 1 | 2 | yes | — |
| 27 | #16864192 | — | 2 | 4 | no | — |
| 28 | C2×#14524076 | — | 2 | 4 | no | — |
| 29 | C2×#14524076 | C22 | 1 | 2 | yes | complemented |
| 30 | C2×#14524076 | C22 | 1 | 2 | yes | complemented |
| 31 | C2×#14524076 | C22 | 1 | 2 | yes | complemented |
| 32 | C2×#14524073 | C22 | 1 | 2 | yes | complemented |
| 33 | #137×D67 | — | 2 | 4 | no | — |
| 34 | #16864162 | C22 | 1 | 2 | yes | complemented |
| 35 | #16863946 | C22 | 1 | 1 | yes | characteristic |
| 36 | C2×#14524043 | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | #16863790 | C22 | 1 | 4 | yes | complemented |
| 38 | #16863776 | C22 | 1 | 2 | yes | complemented |
| 39 | #16863769 | C22 | 1 | 2 | yes | complemented |
| 40 | #16863672 | C22 | 1 | 8 | yes | complemented |
| 41 | #16863671 | C22 | 1 | 8 | yes | complemented |
| 42 | #16863660 | C22 | 1 | 8 | yes | complemented |
| 43 | #16863659 | C22 | 1 | 8 | yes | complemented |
| 44 | #16863580 | C22 | 1 | 8 | yes | complemented |
| 45 | #16863580 | C22 | 1 | 8 | yes | complemented |
| 46 | #16863580 | C22 | 1 | 4 | yes | complemented |
| 47 | #16863575 | C22 | 1 | 4 | yes | complemented |
| 48 | #16863570 | C22 | 1 | 4 | yes | complemented |
| 49 | #16863565 | C22 | 1 | 4 | yes | complemented |
| 50 | #16863519 | C22 | 1 | 4 | yes | complemented |
| 51 | #16863514 | C22 | 1 | 4 | yes | complemented |
| 52 | #16863445 | C22 | 1 | 1 | yes | characteristic, complemented |
| 53 | C2×#14523971 | C22 | 1 | 2 | yes | complemented |
| 54 | #16863378 | C22 | 1 | 2 | yes | complemented |
| 55 | C2×#14523961 | C22 | 1 | 2 | yes | complemented |
| 56 | #575×C67 | C22 | 1 | 1 | yes | characteristic |
| 57 | #568×C67 | C22 | 1 | 2 | yes | complemented |
| 58 | #444×C67 | C22 | 1 | 4 | yes | complemented |
| 59 | #443×C67 | C22 | 1 | 4 | yes | complemented |
| 60 | #430×C67 | C22 | 1 | 1 | yes | characteristic, complemented |
| 61 | C2×#104×C67 | C22 | 1 | 2 | yes | complemented |
| 62 | C4×M16×C67 | C22 | 1 | 1 | yes | characteristic, complemented |
| 63 | #14524091 | — | 2 | 2 | no | — |
| 64 | #14524090 | — | 2 | 4 | no | — |
| 65 | #14524090 | — | 2 | 2 | no | — |
| 66 | #14524090 | — | 2 | 4 | no | — |
| 67 | #14524090 | — | 4 | 2 | no | — |
| 68 | #14524090 | C23 | 1 | 4 | yes | — |
| 69 | #14524090 | C23 | 1 | 8 | yes | — |
| 70 | #14524089 | — | 2 | 2 | no | — |
| 71 | #14524089 | C23 | 1 | 4 | yes | — |
| 72 | #14524088 | — | 2 | 2 | no | — |
| 73 | #14524088 | — | 4 | 2 | no | — |
| 74 | C2×#11761628 | — | 2 | 4 | no | — |
| 75 | C2×#11761628 | — | 2 | 2 | no | — |
| 76 | C2×#11761628 | C23 | 1 | 2 | yes | — |
| 77 | C2×#11761628 | C23 | 1 | 2 | yes | — |
| 78 | C2×#11761627 | — | 2 | 2 | no | — |
| 79 | C2×#11761627 | — | 4 | 2 | no | — |
| 80 | #41×D67 | — | 2 | 4 | no | — |
| 81 | #41×D67 | — | 4 | 2 | no | — |
| 82 | C22×Dic134 | — | 2 | 2 | no | — |
| 83 | C22×Dic134 | C23 | 1 | 2 | yes | — |
| 84 | C2×Q8×D67 | — | 2 | 2 | no | — |
| 85 | #14524076 | — | 2 | 4 | no | — |
| 86 | #14524076 | — | 2 | 2 | no | — |
| 87 | #14524076 | — | 2 | 8 | no | — |
| 88 | #14524076 | — | 2 | 8 | no | — |
| 89 | #14524076 | — | 2 | 8 | no | — |
| 90 | #14524076 | — | 2 | 4 | no | — |
| 91 | #14524076 | — | 2 | 4 | no | — |
| 92 | #14524076 | — | 2 | 4 | no | — |
| 93 | #14524076 | — | 2 | 4 | no | — |
| 94 | #14524076 | D4 | 1 | 4 | yes | complemented |
| 95 | #14524076 | C23 | 1 | 4 | yes | — |
| 96 | #14524076 | C23 | 1 | 8 | yes | — |
| 97 | #14524075 | — | 2 | 8 | no | — |
| 98 | #14524074 | — | 2 | 2 | no | — |
| 99 | #14524073 | — | 2 | 4 | no | — |
| 100 | #14524073 | C23 | 1 | 4 | yes | — |
| 101 | #14524073 | C23 | 1 | 8 | yes | — |
| 102 | #14524072 | — | 2 | 8 | no | — |
| 103 | #14524072 | — | 2 | 8 | no | — |
| 104 | #14524071 | — | 2 | 2 | no | — |
| 105 | #14524071 | — | 2 | 8 | no | — |
| 106 | #14524071 | D4 | 1 | 4 | yes | complemented |
| 107 | #14524071 | C23 | 1 | 4 | yes | — |
| 108 | #14524069 | — | 2 | 2 | no | — |
| 109 | #14524068 | C23 | 1 | 4 | yes | — |
| 110 | #14524067 | — | 2 | 8 | no | — |
| 111 | #14524065 | — | 2 | 4 | no | — |
| 112 | #14524065 | — | 2 | 8 | no | — |
| 113 | #14524065 | — | 2 | 8 | no | — |
| 114 | #14524065 | C23 | 1 | 4 | yes | — |
| 115 | #14524064 | — | 2 | 8 | no | — |
| 116 | #14524063 | — | 2 | 4 | no | — |
| 117 | #14524062 | — | 2 | 8 | no | — |
| 118 | C2×Dic268 | — | 2 | 2 | no | — |
| 119 | C2×Dic268 | — | 2 | 8 | no | — |
| 120 | C2×Dic268 | C23 | 1 | 4 | yes | — |
| 121 | C2×Dic268 | C23 | 1 | 4 | yes | — |
| 122 | C2×#11761618 | — | 2 | 2 | no | — |
| 123 | Q16×D67 | — | 2 | 8 | no | — |
| 124 | C2×#11761617 | — | 2 | 2 | no | — |
| 125 | C2×#11761617 | — | 2 | 8 | no | — |
| 126 | C2×#11761617 | C23 | 1 | 4 | yes | — |
| 127 | C2×#11761617 | C23 | 1 | 4 | yes | — |
| 128 | C2×#11761616 | — | 2 | 2 | no | — |
| 129 | SD16×D67 | — | 2 | 8 | no | — |
| 130 | #14524051 | — | 2 | 4 | no | — |
| 131 | #14524049 | C23 | 1 | 8 | yes | — |
| 132 | C2×#11761612 | C23 | 1 | 2 | yes | — |
| 133 | M16×D67 | — | 2 | 4 | no | — |
| 134 | #14524043 | — | 4 | 1 | no | — |
| 135 | #14524043 | C23 | 1 | 2 | yes | — |
| 136 | #14524043 | C23 | 1 | 1 | yes | characteristic |
| 137 | #14524043 | C23 | 1 | 2 | yes | — |
| 138 | #14524040 | C23 | 1 | 1 | yes | characteristic |
| 139 | #14524031 | C23 | 1 | 2 | yes | — |
| 140 | #14524017 | — | 4 | 1 | no | — |
| 141 | C4×D268 | — | 4 | 1 | no | — |
| 142 | C2×C4⋊Dic67 | — | 4 | 1 | no | — |
| 143 | #14523979 | C23 | 1 | 4 | yes | — |
| 144 | #14523971 | C23 | 1 | 4 | yes | — |
| 145 | #14523971 | C23 | 1 | 4 | yes | — |
| 146 | #14523961 | C23 | 1 | 4 | yes | — |
| 147 | #14523961 | C23 | 1 | 8 | yes | — |
| 148 | #14523959 | C23 | 1 | 4 | yes | — |
| 149 | C2×#41×C67 | C23 | 1 | 2 | yes | — |
| 150 | #137×C67 | D4 | 1 | 4 | yes | complemented |
| 151 | AGL(1,ℤ/8)×C67 | D4 | 1 | 4 | yes | complemented |
| 152 | #135×C67 | C23 | 1 | 4 | yes | — |
| 153 | #131×C67 | — | 2 | 4 | no | — |
| 154 | #131×C67 | C23 | 1 | 8 | yes | — |
| 155 | C2×M16×C67 | — | 2 | 4 | no | — |
| 156 | C2×M16×C67 | C23 | 1 | 2 | yes | — |
| 157 | C2×M16×C67 | C23 | 1 | 1 | yes | characteristic |
| 158 | C2×M16×C67 | C23 | 1 | 1 | yes | characteristic |
| 159 | C2×C42×C67 | C23 | 1 | 1 | yes | characteristic |
| 160 | #108×C67 | C23 | 1 | 4 | yes | — |
| 161 | #104×C67 | C23 | 1 | 4 | yes | — |
| 162 | #104×C67 | C23 | 1 | 4 | yes | — |
| 163 | #97×C67 | C23 | 1 | 2 | yes | — |
| 164 | C4×C8×C67 | C23 | 1 | 2 | yes | — |
| 165 | #11761629 | — | 2 | 4 | no | — |
| 166 | #11761629 | — | 4 | 2 | no | — |
| 167 | #11761628 | — | 2 | 2 | no | — |
| 168 | #11761628 | — | 2 | 2 | no | — |
| 169 | #11761628 | — | 2 | 2 | no | — |
| 170 | #11761628 | — | 2 | 2 | no | — |
| 171 | #11761628 | — | 2 | 2 | no | — |
| 172 | #11761628 | — | 2 | 2 | no | — |
| 173 | #11761628 | — | 2 | 8 | no | — |
| 174 | #11761628 | — | 2 | 4 | no | — |
| 175 | #11761628 | — | 2 | 4 | no | — |
| 176 | #11761628 | — | 4 | 4 | no | — |
| 177 | #11761628 | — | 4 | 4 | no | — |
| 178 | #11761628 | — | 4 | 4 | no | — |
| 179 | #11761628 | C2×D4 | 1 | 4 | yes | — |
| 180 | #11761628 | C24 | 1 | 4 | yes | — |
| 181 | #11761627 | — | 2 | 4 | no | — |
| 182 | #11761627 | — | 2 | 8 | no | — |
| 183 | #11761627 | — | 4 | 2 | no | — |
| 184 | #11761627 | — | 4 | 4 | no | — |
| 185 | #11761627 | — | 4 | 4 | no | — |
| 186 | #11761627 | — | 4 | 8 | no | — |
| 187 | #11761627 | — | 4 | 4 | no | — |
| 188 | #11761627 | — | 4 | 8 | no | — |
| 189 | C2×Dic134 | — | 2 | 2 | no | — |
| 190 | C2×Dic134 | — | 2 | 2 | no | — |
| 191 | C2×Dic134 | — | 2 | 2 | no | — |
| 192 | C2×Dic134 | — | 2 | 2 | no | — |
| 193 | C2×Dic134 | — | 2 | 8 | no | — |
| 194 | C2×Dic134 | — | 2 | 4 | no | — |
| 195 | C2×Dic134 | — | 2 | 2 | no | — |
| 196 | C2×Dic134 | — | 4 | 4 | no | — |
| 197 | C2×Dic134 | — | 4 | 2 | no | — |
| 198 | C2×Dic134 | C2×D4 | 1 | 2 | yes | — |
| 199 | C2×Dic134 | C24 | 1 | 2 | yes | — |
| 200 | C2×Dic134 | C24 | 1 | 4 | yes | — |
| 201 | Q8×D67 | — | 2 | 8 | no | — |
| 202 | Q8×D67 | — | 2 | 4 | no | — |
| 203 | Q8×D67 | — | 4 | 2 | no | — |
| 204 | Q8×D67 | — | 4 | 4 | no | — |
| 205 | C2×D268 | — | 2 | 4 | no | — |
| 206 | C2×D268 | — | 4 | 1 | no | — |
| 207 | C2×D268 | C2×D4 | 1 | 2 | yes | — |
| 208 | C2×D268 | C24 | 1 | 2 | yes | — |
| 209 | C2×C22⋊D67 | — | 2 | 2 | no | — |
| 210 | C2×C22⋊D67 | — | 2 | 2 | no | — |
| 211 | C2×C22⋊D67 | — | 4 | 4 | no | — |
| 212 | C2×C22⋊D67 | — | 4 | 2 | no | — |
| 213 | D4×D67 | — | 2 | 4 | no | — |
| 214 | D4×D67 | — | 4 | 2 | no | — |
| 215 | D4×D67 | — | 4 | 4 | no | — |
| 216 | D4×D67 | — | 4 | 4 | no | — |
| 217 | C22×Dic67 | — | 2 | 2 | no | — |
| 218 | C22×Dic67 | — | 4 | 2 | no | — |
| 219 | C2×C4×D67 | — | 2 | 2 | no | — |
| 220 | C2×C4×D67 | — | 2 | 2 | no | — |
| 221 | C2×C4×D67 | — | 4 | 4 | no | — |
| 222 | C2×C4×D67 | — | 4 | 2 | no | — |
| 223 | Dic268 | — | 2 | 8 | no | — |
| 224 | Dic268 | — | 2 | 4 | no | — |
| 225 | Dic268 | — | 2 | 8 | no | — |
| 226 | Dic268 | — | 2 | 8 | no | — |
| 227 | Dic268 | C2×D4 | 1 | 4 | yes | — |
| 228 | #11761618 | — | 2 | 4 | no | — |
| 229 | #11761618 | — | 2 | 8 | no | — |
| 230 | #11761617 | — | 2 | 8 | no | — |
| 231 | #11761617 | — | 2 | 4 | no | — |
| 232 | #11761617 | — | 2 | 4 | no | — |
| 233 | #11761617 | — | 2 | 8 | no | — |
| 234 | #11761617 | — | 2 | 8 | no | — |
| 235 | #11761617 | C2×D4 | 1 | 8 | yes | — |
| 236 | #11761616 | — | 2 | 8 | no | — |
| 237 | #11761616 | — | 2 | 4 | no | — |
| 238 | #11761615 | — | 2 | 4 | no | — |
| 239 | D536 | — | 2 | 4 | no | — |
| 240 | D536 | C2×D4 | 1 | 4 | yes | — |
| 241 | #11761613 | — | 2 | 4 | no | — |
| 242 | #11761612 | — | 2 | 2 | no | — |
| 243 | #11761612 | C24 | 1 | 4 | yes | — |
| 244 | #11761611 | — | 2 | 8 | no | — |
| 245 | C2×C67⋊C8 | — | 2 | 2 | no | — |
| 246 | C8×D67 | — | 2 | 8 | no | — |
| 247 | C4⋊Dic67 | — | 4 | 2 | no | — |
| 248 | C4⋊Dic67 | — | 4 | 2 | no | — |
| 249 | C4⋊Dic67 | — | 4 | 1 | no | — |
| 250 | (C2×D67)⋊C4 | — | 4 | 2 | no | — |
| 251 | #41×C67 | — | 2 | 2 | no | — |
| 252 | #41×C67 | — | 2 | 2 | no | — |
| 253 | #41×C67 | C2×D4 | 1 | 4 | yes | — |
| 254 | #41×C67 | C24 | 1 | 4 | yes | — |
| 255 | C2×Q8×C67 | C2×D4 | 1 | 2 | yes | — |
| 256 | C2×D4×C67 | — | 2 | 2 | no | — |
| 257 | C2×D4×C67 | C2×D4 | 1 | 2 | yes | — |
| 258 | C22×C4×C67 | — | 2 | 2 | no | — |
| 259 | C22×C4×C67 | — | 2 | 1 | no | — |
| 260 | C22×C4×C67 | C24 | 1 | 1 | yes | characteristic |
| 261 | Q16×C67 | C2×D4 | 1 | 4 | yes | — |
| 262 | SD16×C67 | C2×D4 | 1 | 8 | yes | — |
| 263 | D8×C67 | C2×D4 | 1 | 4 | yes | — |
| 264 | M16×C67 | — | 2 | 2 | no | — |
| 265 | M16×C67 | — | 2 | 8 | no | — |
| 266 | M16×C67 | C2×D4 | 1 | 4 | yes | — |
| 267 | M16×C67 | C2×D4 | 1 | 4 | yes | — |
| 268 | M16×C67 | C24 | 1 | 4 | yes | — |
| 269 | C2×C8×C67 | — | 2 | 2 | no | — |
| 270 | C2×C8×C67 | — | 2 | 8 | no | — |
| 271 | C2×C8×C67 | C24 | 1 | 2 | yes | — |
| 272 | C2×C8×C67 | C24 | 1 | 2 | yes | — |
| 273 | C42×C67 | — | 2 | 1 | no | — |
| 274 | C42×C67 | C24 | 1 | 1 | yes | characteristic |
| 275 | C42×C67 | C24 | 1 | 1 | yes | characteristic |
| 276 | C23×C67 | — | 2 | 2 | no | — |
| 277 | C23×C67 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 278 | C22×D67 | — | 2 | 2 | no | — |
| 279 | C22×D67 | — | 2 | 2 | no | — |
| 280 | C22×D67 | — | 4 | 4 | no | — |
| 281 | Q8×C67 | — | 2 | 2 | no | — |
| 282 | Q8×C67 | C22×D4 | 1 | 4 | yes | — |
| 283 | D4×C67 | — | 2 | 4 | no | — |
| 284 | D4×C67 | — | 2 | 4 | no | — |
| 285 | D4×C67 | — | 2 | 2 | no | — |
| 286 | D4×C67 | C22×D4 | 1 | 4 | yes | — |
| 287 | C2×C4×C67 | — | 2 | 2 | no | — |
| 288 | C2×C4×C67 | — | 2 | 1 | no | — |
| 289 | C2×C4×C67 | — | 2 | 4 | no | — |
| 290 | C2×C4×C67 | — | 2 | 4 | no | — |
| 291 | C2×C4×C67 | — | 2 | 1 | no | — |
| 292 | C2×C4×C67 | — | 4 | 2 | no | — |
| 293 | C2×C4×C67 | C22×D4 | 1 | 2 | yes | — |
| 294 | C2×C4×C67 | C22×D4 | 1 | 2 | yes | — |
| 295 | C2×C4×C67 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 296 | C2×C4×C67 | C25 | 1 | 1 | yes | characteristic |
| 297 | C22⋊D67 | — | 2 | 4 | no | — |
| 298 | C22⋊D67 | — | 2 | 4 | no | — |
| 299 | C22⋊D67 | — | 4 | 4 | no | — |
| 300 | C22⋊D67 | — | 4 | 4 | no | — |
| 301 | C22⋊D67 | — | 4 | 8 | no | — |
| 302 | C22⋊D67 | — | 4 | 2 | no | — |
| 303 | C22⋊D67 | — | 4 | 2 | no | — |
| 304 | C2×Dic67 | — | 2 | 2 | no | — |
| 305 | C2×Dic67 | — | 2 | 2 | no | — |
| 306 | C2×Dic67 | — | 2 | 4 | no | — |
| 307 | C2×Dic67 | — | 4 | 4 | no | — |
| 308 | C2×Dic67 | — | 4 | 8 | no | — |
| 309 | C2×Dic67 | — | 4 | 2 | no | — |
| 310 | C2×Dic67 | — | 4 | 2 | no | — |
| 311 | D268 | — | 2 | 2 | no | — |
| 312 | D268 | — | 2 | 2 | no | — |
| 313 | D268 | — | 2 | 2 | no | — |
| 314 | D268 | — | 4 | 4 | no | — |
| 315 | D268 | — | 8 | 2 | no | — |
| 316 | D268 | C22×D4 | 1 | 4 | yes | — |
| 317 | C4×D67 | — | 2 | 4 | no | — |
| 318 | C4×D67 | — | 2 | 4 | no | — |
| 319 | C4×D67 | — | 4 | 4 | no | — |
| 320 | C4×D67 | — | 4 | 4 | no | — |
| 321 | C4×D67 | — | 4 | 8 | no | — |
| 322 | C4×D67 | — | 4 | 2 | no | — |
| 323 | C4×D67 | — | 4 | 2 | no | — |
| 324 | Dic134 | — | 2 | 2 | no | — |
| 325 | Dic134 | — | 2 | 4 | no | — |
| 326 | Dic134 | — | 2 | 2 | no | — |
| 327 | Dic134 | — | 2 | 4 | no | — |
| 328 | Dic134 | — | 2 | 2 | no | — |
| 329 | Dic134 | — | 4 | 8 | no | — |
| 330 | Dic134 | — | 4 | 4 | no | — |
| 331 | Dic134 | — | 4 | 2 | no | — |
| 332 | Dic134 | — | 4 | 2 | no | — |
| 333 | Dic134 | C22×D4 | 1 | 4 | yes | — |
| 334 | C8×C67 | — | 2 | 4 | no | — |
| 335 | C8×C67 | C22×D4 | 1 | 4 | yes | — |
| 336 | C8×C67 | C22×D4 | 1 | 4 | yes | — |
| 337 | C67⋊C8 | — | 2 | 4 | no | — |
| 338 | C22×C67 | — | 2 | 4 | no | — |
| 339 | C22×C67 | — | 4 | 1 | no | — |
| 340 | C22×C67 | — | 8 | 2 | no | — |
| 341 | C22×C67 | D42 | 1 | 2 | yes | — |
| 342 | C22×C67 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 343 | C2×D67 | — | 2 | 4 | no | — |
| 344 | C2×D67 | — | 4 | 2 | no | — |
| 345 | C2×D67 | — | 8 | 2 | no | — |
| 346 | C2×D67 | — | 8 | 2 | no | — |
| 347 | C2×D67 | — | 16 | 4 | no | — |
| 348 | C4×C67 | — | 2 | 2 | no | — |
| 349 | C4×C67 | — | 2 | 4 | no | — |
| 350 | C4×C67 | — | 4 | 1 | no | — |
| 351 | C4×C67 | D42 | 1 | 2 | yes | — |
| 352 | C4×C67 | C23×D4 | 1 | 1 | yes | characteristic |
| 353 | C4×C67 | C23×D4 | 1 | 1 | yes | characteristic |
| 354 | Dic67 | — | 2 | 4 | no | — |
| 355 | Dic67 | — | 4 | 4 | no | — |
| 356 | Dic67 | — | 4 | 2 | no | — |
| 357 | #61111 | — | 67 | 1 | no | maximal, Sylow |
| 358 | C2×C67 | — | 2 | 1 | no | — |
| 359 | C2×C67 | — | 2 | 2 | no | — |
| 360 | C2×C67 | — | 4 | 4 | no | — |
| 361 | C2×C67 | C2×D42 | 1 | 1 | yes | characteristic |
| 362 | D67 | — | 4 | 4 | no | — |
| 363 | D67 | — | 8 | 2 | no | — |
| 364 | #3586 | — | 67 | 2 | no | — |
| 365 | #3586 | — | 67 | 2 | no | — |
| 366 | #3293 | — | 67 | 4 | no | — |
| 367 | #3291 | — | 67 | 4 | no | — |
| 368 | #3289 | — | 67 | 8 | no | — |
| 369 | #3152 | — | 67 | 1 | no | — |
| 370 | #3069 | — | 67 | 2 | no | — |
| 371 | #3069 | — | 67 | 2 | no | — |
| 372 | #3018 | — | 67 | 2 | no | — |
| 373 | C2×#456 | — | 67 | 2 | no | — |
| 374 | #2956 | — | 67 | 1 | no | — |
| 375 | #2956 | D67 | 1 | 1 | yes | characteristic, complemented |
| 376 | C67 | #61111 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 377 | #585 | — | 67 | 2 | no | — |
| 378 | C2×2−1+4 | — | 67 | 2 | no | — |
| 379 | #578 | — | 67 | 8 | no | — |
| 380 | #578 | — | 67 | 8 | no | — |
| 381 | #578 | — | 134 | 4 | no | — |
| 382 | #578 | — | 134 | 4 | no | — |
| 383 | #577 | — | 67 | 8 | no | — |
| 384 | #577 | — | 67 | 8 | no | — |
| 385 | #577 | — | 134 | 4 | no | — |
| 386 | #577 | — | 134 | 4 | no | — |
| 387 | #575 | — | 67 | 2 | no | — |
| 388 | #575 | — | 67 | 1 | no | — |
| 389 | #575 | — | 67 | 2 | no | — |
| 390 | #575 | — | 134 | 4 | no | — |
| 391 | #575 | — | 134 | 4 | no | — |
| 392 | #575 | C2×D67 | 1 | 1 | yes | characteristic |
| 393 | C2×#137 | — | 67 | 2 | no | — |
| 394 | C2×#137 | — | 67 | 2 | no | — |
| 395 | C2×#137 | — | 67 | 2 | no | — |
| 396 | C2×#137 | — | 67 | 2 | no | — |
| 397 | C2×#137 | — | 134 | 4 | no | — |
| 398 | C2×#137 | — | 134 | 4 | no | — |
| 399 | #568 | — | 67 | 2 | no | — |
| 400 | #568 | C2×D67 | 1 | 2 | yes | complemented |
| 401 | #532 | — | 67 | 1 | no | — |
| 402 | C2×C4⋊Q8 | — | 67 | 1 | no | — |
| 403 | #497 | — | 67 | 4 | no | — |
| 404 | #494 | — | 67 | 2 | no | — |
| 405 | #492 | — | 67 | 2 | no | — |
| 406 | #473 | — | 67 | 8 | no | — |
| 407 | #473 | — | 67 | 8 | no | — |
| 408 | #471 | — | 67 | 8 | no | — |
| 409 | #471 | — | 67 | 8 | no | — |
| 410 | #456 | — | 67 | 8 | no | — |
| 411 | #456 | — | 67 | 8 | no | — |
| 412 | #456 | — | 67 | 4 | no | — |
| 413 | #455 | — | 67 | 4 | no | — |
| 414 | #454 | — | 67 | 4 | no | — |
| 415 | #453 | — | 67 | 4 | no | — |
| 416 | #444 | — | 67 | 4 | no | — |
| 417 | #444 | C2×D67 | 1 | 4 | yes | complemented |
| 418 | #443 | — | 67 | 4 | no | — |
| 419 | #443 | C2×D67 | 1 | 4 | yes | complemented |
| 420 | #430 | — | 67 | 1 | no | — |
| 421 | #430 | C2×D67 | 1 | 1 | yes | characteristic, complemented |
| 422 | C2×#104 | — | 67 | 2 | no | — |
| 423 | C2×#104 | C2×D67 | 1 | 2 | yes | complemented |
| 424 | #413 | — | 67 | 2 | no | — |
| 425 | C2×#101 | — | 67 | 2 | no | — |
| 426 | C4×M16 | C2×D67 | 1 | 1 | yes | characteristic, complemented |
| 427 | 2−1+4 | — | 268 | 2 | no | — |
| 428 | 2−1+4 | — | 67 | 8 | no | — |
| 429 | 2−1+4 | — | 67 | 4 | no | — |
| 430 | 2−1+4 | — | 134 | 2 | no | — |
| 431 | 2−1+4 | — | 134 | 4 | no | — |
| 432 | 2−1+4 | — | 134 | 4 | no | — |
| 433 | 2−1+4 | — | 134 | 2 | no | — |
| 434 | H(5,𝔽2) | — | 268 | 2 | no | — |
| 435 | H(5,𝔽2) | — | 67 | 4 | no | — |
| 436 | H(5,𝔽2) | — | 134 | 2 | no | — |
| 437 | H(5,𝔽2) | — | 134 | 2 | no | — |
| 438 | C2×#41 | — | 268 | 2 | no | — |
| 439 | C2×#41 | — | 268 | 2 | no | — |
| 440 | C2×#41 | — | 67 | 2 | no | — |
| 441 | C2×#41 | — | 67 | 2 | no | — |
| 442 | C2×#41 | — | 134 | 2 | no | — |
| 443 | C2×#41 | — | 134 | 4 | no | — |
| 444 | C2×#41 | — | 134 | 4 | no | — |
| 445 | C2×#41 | — | 134 | 2 | no | — |
| 446 | C2×#41 | C22×D67 | 1 | 2 | yes | — |
| 447 | C22×Q8 | — | 67 | 2 | no | — |
| 448 | C22×Q8 | — | 134 | 2 | no | — |
| 449 | C22×Q8 | — | 134 | 2 | no | — |
| 450 | #137 | — | 67 | 8 | no | — |
| 451 | #137 | — | 67 | 4 | no | — |
| 452 | #137 | — | 67 | 4 | no | — |
| 453 | #137 | — | 67 | 8 | no | — |
| 454 | #137 | — | 67 | 4 | no | — |
| 455 | #137 | — | 134 | 8 | no | — |
| 456 | #137 | — | 134 | 8 | no | — |
| 457 | #137 | — | 134 | 8 | no | — |
| 458 | #137 | — | 134 | 2 | no | — |
| 459 | #137 | — | 134 | 4 | no | — |
| 460 | #137 | — | 134 | 4 | no | — |
| 461 | #137 | — | 134 | 2 | no | — |
| 462 | #137 | — | 134 | 8 | no | — |
| 463 | #137 | — | 134 | 8 | no | — |
| 464 | #137 | — | 134 | 8 | no | — |
| 465 | #137 | — | 134 | 4 | no | — |
| 466 | #137 | — | 134 | 4 | no | — |
| 467 | #137 | — | 134 | 4 | no | — |
| 468 | #137 | — | 134 | 4 | no | — |
| 469 | #137 | D268 | 1 | 4 | yes | complemented |
| 470 | AGL(1,ℤ/8) | — | 67 | 4 | no | — |
| 471 | AGL(1,ℤ/8) | — | 67 | 4 | no | — |
| 472 | AGL(1,ℤ/8) | — | 67 | 4 | no | — |
| 473 | AGL(1,ℤ/8) | — | 134 | 8 | no | — |
| 474 | AGL(1,ℤ/8) | — | 134 | 2 | no | — |
| 475 | AGL(1,ℤ/8) | — | 134 | 2 | no | — |
| 476 | AGL(1,ℤ/8) | — | 134 | 8 | no | — |
| 477 | AGL(1,ℤ/8) | D268 | 1 | 4 | yes | complemented |
| 478 | #135 | — | 67 | 4 | no | — |
| 479 | #135 | — | 134 | 8 | no | — |
| 480 | #135 | — | 134 | 8 | no | — |
| 481 | #135 | — | 134 | 4 | no | — |
| 482 | #135 | — | 134 | 4 | no | — |
| 483 | #135 | — | 134 | 8 | no | — |
| 484 | #135 | — | 134 | 8 | no | — |
| 485 | #135 | C22×D67 | 1 | 4 | yes | — |
| 486 | C2×Q16 | — | 67 | 4 | no | — |
| 487 | C2×Q16 | — | 67 | 4 | no | — |
| 488 | C2×Q16 | — | 134 | 8 | no | — |
| 489 | C2×Q16 | — | 134 | 2 | no | — |
| 490 | C2×Q16 | — | 134 | 2 | no | — |
| 491 | C2×Q16 | — | 134 | 8 | no | — |
| 492 | C2×SD16 | — | 67 | 4 | no | — |
| 493 | C2×SD16 | — | 67 | 4 | no | — |
| 494 | C2×SD16 | — | 134 | 8 | no | — |
| 495 | C2×SD16 | — | 134 | 2 | no | — |
| 496 | C2×SD16 | — | 134 | 2 | no | — |
| 497 | C2×SD16 | — | 134 | 8 | no | — |
| 498 | #131 | — | 2 | 4 | no | — |
| 499 | #131 | — | 67 | 8 | no | — |
| 500 | #131 | — | 134 | 4 | no | — |
| 501 | #131 | C22×D67 | 1 | 8 | yes | — |
| 502 | C2×M16 | — | 2 | 4 | no | — |
| 503 | C2×M16 | — | 67 | 2 | no | — |
| 504 | C2×M16 | — | 134 | 4 | no | — |
| 505 | C2×M16 | C22×D67 | 1 | 2 | yes | — |
| 506 | C2×M16 | C22×D67 | 1 | 1 | yes | characteristic |
| 507 | C2×M16 | C22×D67 | 1 | 1 | yes | characteristic |
| 508 | C4⋊Q8 | — | 268 | 1 | no | — |
| 509 | C4⋊Q8 | — | 67 | 2 | no | — |
| 510 | C4⋊Q8 | — | 67 | 2 | no | — |
| 511 | C4⋊Q8 | — | 67 | 1 | no | — |
| 512 | #127 | — | 67 | 1 | no | — |
| 513 | #124 | — | 67 | 2 | no | — |
| 514 | #121 | — | 268 | 1 | no | — |
| 515 | C4×D4 | — | 268 | 1 | no | — |
| 516 | C2×C4⋊C4 | — | 268 | 1 | no | — |
| 517 | C2×C42 | C22×D67 | 1 | 1 | yes | characteristic |
| 518 | #108 | — | 67 | 4 | no | — |
| 519 | #108 | C22×D67 | 1 | 4 | yes | — |
| 520 | #104 | — | 67 | 4 | no | — |
| 521 | #104 | — | 67 | 4 | no | — |
| 522 | #104 | C22×D67 | 1 | 4 | yes | — |
| 523 | #104 | C22×D67 | 1 | 4 | yes | — |
| 524 | #101 | — | 67 | 8 | no | — |
| 525 | #101 | — | 67 | 4 | no | — |
| 526 | #100 | — | 67 | 4 | no | — |
| 527 | #97 | C22×D67 | 1 | 2 | yes | — |
| 528 | C4×C8 | C22×D67 | 1 | 2 | yes | — |
| 529 | #41 | — | 2 | 2 | no | — |
| 530 | #41 | — | 2 | 2 | no | — |
| 531 | #41 | — | 268 | 4 | no | — |
| 532 | #41 | — | 268 | 4 | no | — |
| 533 | #41 | — | 268 | 4 | no | — |
| 534 | #41 | — | 268 | 2 | no | — |
| 535 | #41 | — | 268 | 8 | no | — |
| 536 | #41 | — | 268 | 2 | no | — |
| 537 | #41 | — | 268 | 4 | no | — |
| 538 | #41 | — | 268 | 4 | no | — |
| 539 | #41 | — | 268 | 4 | no | — |
| 540 | #41 | — | 268 | 8 | no | — |
| 541 | #41 | — | 67 | 4 | no | — |
| 542 | #41 | — | 67 | 4 | no | — |
| 543 | #41 | — | 134 | 8 | no | — |
| 544 | #41 | — | 134 | 4 | no | — |
| 545 | #41 | — | 134 | 4 | no | — |
| 546 | #41 | — | 134 | 4 | no | — |
| 547 | #41 | — | 134 | 8 | no | — |
| 548 | #41 | — | 134 | 4 | no | — |
| 549 | #41 | — | 134 | 2 | no | — |
| 550 | #41 | — | 134 | 2 | no | — |
| 551 | #41 | — | 134 | 2 | no | — |
| 552 | #41 | — | 134 | 2 | no | — |
| 553 | #41 | — | 134 | 2 | no | — |
| 554 | #41 | — | 134 | 2 | no | — |
| 555 | #41 | C2×D268 | 1 | 4 | yes | — |
| 556 | #41 | C23×D67 | 1 | 4 | yes | — |
| 557 | C2×Q8 | — | 268 | 4 | no | — |
| 558 | C2×Q8 | — | 268 | 2 | no | — |
| 559 | C2×Q8 | — | 268 | 2 | no | — |
| 560 | C2×Q8 | — | 268 | 4 | no | — |
| 561 | C2×Q8 | — | 67 | 2 | no | — |
| 562 | C2×Q8 | — | 67 | 2 | no | — |
| 563 | C2×Q8 | — | 67 | 4 | no | — |
| 564 | C2×Q8 | — | 134 | 8 | no | — |
| 565 | C2×Q8 | — | 134 | 4 | no | — |
| 566 | C2×Q8 | — | 134 | 8 | no | — |
| 567 | C2×Q8 | — | 134 | 4 | no | — |
| 568 | C2×Q8 | — | 134 | 2 | no | — |
| 569 | C2×Q8 | — | 134 | 2 | no | — |
| 570 | C2×Q8 | — | 134 | 2 | no | — |
| 571 | C2×Q8 | — | 134 | 2 | no | — |
| 572 | C2×Q8 | — | 134 | 2 | no | — |
| 573 | C2×Q8 | C2×D268 | 1 | 2 | yes | — |
| 574 | C2×D4 | — | 2 | 2 | no | — |
| 575 | C2×D4 | — | 268 | 1 | no | — |
| 576 | C2×D4 | — | 268 | 4 | no | — |
| 577 | C2×D4 | — | 268 | 2 | no | — |
| 578 | C2×D4 | — | 268 | 4 | no | — |
| 579 | C2×D4 | — | 268 | 2 | no | — |
| 580 | C2×D4 | — | 268 | 4 | no | — |
| 581 | C2×D4 | — | 67 | 2 | no | — |
| 582 | C2×D4 | — | 67 | 2 | no | — |
| 583 | C2×D4 | — | 134 | 4 | no | — |
| 584 | C2×D4 | — | 134 | 2 | no | — |
| 585 | C2×D4 | — | 134 | 4 | no | — |
| 586 | C2×D4 | — | 134 | 2 | no | — |
| 587 | C2×D4 | C2×D268 | 1 | 2 | yes | — |
| 588 | C22×C4 | — | 2 | 2 | no | — |
| 589 | C22×C4 | — | 2 | 1 | no | — |
| 590 | C22×C4 | — | 268 | 2 | no | — |
| 591 | C22×C4 | — | 268 | 4 | no | — |
| 592 | C22×C4 | — | 268 | 2 | no | — |
| 593 | C22×C4 | — | 134 | 2 | no | — |
| 594 | C22×C4 | — | 134 | 2 | no | — |
| 595 | C22×C4 | — | 134 | 2 | no | — |
| 596 | C22×C4 | C23×D67 | 1 | 1 | yes | characteristic |
| 597 | Q16 | — | 67 | 4 | no | — |
| 598 | Q16 | — | 134 | 8 | no | — |
| 599 | Q16 | — | 134 | 4 | no | — |
| 600 | Q16 | — | 134 | 8 | no | — |
| 601 | Q16 | — | 134 | 4 | no | — |
| 602 | Q16 | — | 134 | 8 | no | — |
| 603 | Q16 | — | 134 | 8 | no | — |
| 604 | Q16 | C2×D268 | 1 | 4 | yes | — |
| 605 | SD16 | — | 67 | 8 | no | — |
| 606 | SD16 | — | 134 | 8 | no | — |
| 607 | SD16 | — | 134 | 4 | no | — |
| 608 | SD16 | — | 134 | 4 | no | — |
| 609 | SD16 | — | 134 | 4 | no | — |
| 610 | SD16 | — | 134 | 8 | no | — |
| 611 | SD16 | — | 134 | 4 | no | — |
| 612 | SD16 | — | 134 | 8 | no | — |
| 613 | SD16 | — | 134 | 8 | no | — |
| 614 | SD16 | C2×D268 | 1 | 8 | yes | — |
| 615 | D8 | — | 67 | 4 | no | — |
| 616 | D8 | — | 134 | 4 | no | — |
| 617 | D8 | — | 134 | 4 | no | — |
| 618 | D8 | C2×D268 | 1 | 4 | yes | — |
| 619 | M16 | — | 2 | 2 | no | — |
| 620 | M16 | — | 2 | 8 | no | — |
| 621 | M16 | — | 67 | 4 | no | — |
| 622 | M16 | — | 134 | 2 | no | — |
| 623 | M16 | — | 134 | 8 | no | — |
| 624 | M16 | D4×D67 | 1 | 4 | yes | — |
| 625 | M16 | C2×D268 | 1 | 4 | yes | — |
| 626 | M16 | C23×D67 | 1 | 4 | yes | — |
| 627 | C2×C8 | — | 2 | 2 | no | — |
| 628 | C2×C8 | — | 2 | 8 | no | — |
| 629 | C2×C8 | — | 134 | 2 | no | — |
| 630 | C2×C8 | — | 134 | 8 | no | — |
| 631 | C2×C8 | C23×D67 | 1 | 2 | yes | — |
| 632 | C2×C8 | C23×D67 | 1 | 2 | yes | — |
| 633 | C4⋊C4 | — | 268 | 2 | no | — |
| 634 | C4⋊C4 | — | 268 | 2 | no | — |
| 635 | C4⋊C4 | — | 268 | 1 | no | — |
| 636 | C22⋊C4 | — | 268 | 2 | no | — |
| 637 | C42 | — | 2 | 1 | no | — |
| 638 | C42 | C23×D67 | 1 | 1 | yes | characteristic |
| 639 | C42 | C23×D67 | 1 | 1 | yes | characteristic |
| 640 | C23 | — | 2 | 2 | no | — |
| 641 | C23 | — | 268 | 4 | no | — |
| 642 | C23 | — | 134 | 2 | no | — |
| 643 | C23 | — | 134 | 2 | no | — |
| 644 | C23 | #14524089 | 1 | 1 | yes | characteristic |
| 645 | Q8 | — | 2 | 2 | no | — |
| 646 | Q8 | — | 268 | 8 | no | — |
| 647 | Q8 | — | 268 | 4 | no | — |
| 648 | Q8 | — | 268 | 2 | no | — |
| 649 | Q8 | — | 268 | 2 | no | — |
| 650 | Q8 | — | 67 | 4 | no | — |
| 651 | Q8 | — | 134 | 4 | no | — |
| 652 | Q8 | — | 134 | 2 | no | — |
| 653 | Q8 | — | 134 | 4 | no | — |
| 654 | Q8 | — | 134 | 2 | no | — |
| 655 | Q8 | — | 134 | 2 | no | — |
| 656 | Q8 | C22×D268 | 1 | 4 | yes | — |
| 657 | D4 | — | 2 | 4 | no | — |
| 658 | D4 | — | 2 | 4 | no | — |
| 659 | D4 | — | 2 | 2 | no | — |
| 660 | D4 | — | 268 | 4 | no | — |
| 661 | D4 | — | 268 | 4 | no | — |
| 662 | D4 | — | 268 | 8 | no | — |
| 663 | D4 | — | 268 | 2 | no | — |
| 664 | D4 | — | 268 | 2 | no | — |
| 665 | D4 | — | 268 | 4 | no | — |
| 666 | D4 | — | 536 | 2 | no | — |
| 667 | D4 | — | 67 | 4 | no | — |
| 668 | D4 | — | 134 | 4 | no | — |
| 669 | D4 | — | 134 | 4 | no | — |
| 670 | D4 | — | 134 | 2 | no | — |
| 671 | D4 | — | 134 | 2 | no | — |
| 672 | D4 | — | 134 | 2 | no | — |
| 673 | D4 | C22×D268 | 1 | 4 | yes | — |
| 674 | C2×C4 | — | 2 | 2 | no | — |
| 675 | C2×C4 | — | 2 | 1 | no | — |
| 676 | C2×C4 | — | 2 | 4 | no | — |
| 677 | C2×C4 | — | 2 | 4 | no | — |
| 678 | C2×C4 | — | 2 | 1 | no | — |
| 679 | C2×C4 | — | 4 | 2 | no | — |
| 680 | C2×C4 | — | 268 | 4 | no | — |
| 681 | C2×C4 | — | 268 | 8 | no | — |
| 682 | C2×C4 | — | 268 | 4 | no | — |
| 683 | C2×C4 | — | 268 | 2 | no | — |
| 684 | C2×C4 | — | 268 | 2 | no | — |
| 685 | C2×C4 | — | 268 | 4 | no | — |
| 686 | C2×C4 | — | 268 | 8 | no | — |
| 687 | C2×C4 | — | 268 | 2 | no | — |
| 688 | C2×C4 | — | 268 | 2 | no | — |
| 689 | C2×C4 | — | 134 | 2 | no | — |
| 690 | C2×C4 | — | 134 | 4 | no | — |
| 691 | C2×C4 | — | 134 | 2 | no | — |
| 692 | C2×C4 | — | 134 | 4 | no | — |
| 693 | C2×C4 | — | 134 | 4 | no | — |
| 694 | C2×C4 | C2×D4×D67 | 1 | 2 | yes | — |
| 695 | C2×C4 | C22×D268 | 1 | 2 | yes | — |
| 696 | C2×C4 | #14524089 | 1 | 1 | yes | characteristic |
| 697 | C2×C4 | C24×D67 | 1 | 1 | yes | characteristic |
| 698 | C8 | — | 2 | 4 | no | — |
| 699 | C8 | — | 134 | 4 | no | — |
| 700 | C8 | C2×D4×D67 | 1 | 4 | yes | — |
| 701 | C8 | C22×D268 | 1 | 4 | yes | — |
| 702 | C22 | — | 2 | 4 | no | — |
| 703 | C22 | — | 4 | 1 | no | — |
| 704 | C22 | — | 8 | 2 | no | — |
| 705 | C22 | — | 268 | 2 | no | — |
| 706 | C22 | — | 536 | 2 | no | — |
| 707 | C22 | — | 536 | 2 | no | — |
| 708 | C22 | — | 1072 | 4 | no | — |
| 709 | C22 | — | 134 | 4 | no | — |
| 710 | C22 | D4×D268 | 1 | 2 | yes | — |
| 711 | C22 | C2×#14524089 | 1 | 1 | yes | characteristic |
| 712 | C4 | — | 2 | 2 | no | — |
| 713 | C4 | — | 2 | 4 | no | — |
| 714 | C4 | — | 4 | 1 | no | — |
| 715 | C4 | — | 268 | 2 | no | — |
| 716 | C4 | — | 268 | 4 | no | — |
| 717 | C4 | — | 134 | 4 | no | — |
| 718 | C4 | D4×D268 | 1 | 2 | yes | — |
| 719 | C4 | C22×D4×D67 | 1 | 1 | yes | characteristic |
| 720 | C4 | C23×D268 | 1 | 1 | yes | characteristic |
| 721 | C2 | — | 2 | 1 | no | — |
| 722 | C2 | — | 2 | 2 | no | — |
| 723 | C2 | — | 4 | 4 | no | — |
| 724 | C2 | — | 268 | 4 | no | — |
| 725 | C2 | — | 536 | 2 | no | — |
| 726 | C2 | C2×D4×D268 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22574997 | C2 | semidirect |
| 2. #22574993 | C2 | semidirect |
| 3. #22572014 | C2 | semidirect |
| 4. #22572003 | C2 | semidirect |
| 5. #22571985 | C2 | semidirect |
| 6. #22570668 | C2 | semidirect |
| 7. #22569947 | C2 | semidirect |
| 8. #22569946 | C2 | semidirect |
| 9. #22569560 | C2 | semidirect |
| 10. C2×#16863580 | C2 | semidirect |
| 11. #22569120 | C2 | semidirect |
| 12. C67×#2956 | C2 | semidirect |
| 13. #16864232 | C22 | semidirect |
| 16. #16864213 | C22 | semidirect |
| 18. #16864210 | C22 | semidirect |
| 20. #16864208 | C22 | semidirect |
| 22. #16864203 | C22 | semidirect |
| 29. C2×#14524076 | C22 | semidirect |
| 30. C2×#14524076 | C22 | semidirect |
| 31. C2×#14524076 | C22 | semidirect |
| 32. C2×#14524073 | C22 | semidirect |
| 34. #16864162 | C22 | semidirect |
| 36. C2×#14524043 | C22 | semidirect |
| 37. #16863790 | C22 | semidirect |
| 38. #16863776 | C22 | semidirect |
| 39. #16863769 | C22 | semidirect |
| 40. #16863672 | C22 | semidirect |
| 41. #16863671 | C22 | semidirect |
| 42. #16863660 | C22 | semidirect |
| 43. #16863659 | C22 | semidirect |
| 44. #16863580 | C22 | semidirect |
| 45. #16863580 | C22 | semidirect |
| 46. #16863580 | C22 | semidirect |
| 47. #16863575 | C22 | semidirect |
| 48. #16863570 | C22 | semidirect |
| 49. #16863565 | C22 | semidirect |
| 50. #16863519 | C22 | semidirect |
| 51. #16863514 | C22 | semidirect |
| 52. #16863445 | C22 | semidirect |
| 53. C2×#14523971 | C22 | semidirect |
| 54. #16863378 | C22 | semidirect |
| 55. C2×#14523961 | C22 | semidirect |
| 57. #568×C67 | C22 | semidirect |
| 58. #444×C67 | C22 | semidirect |
| 59. #443×C67 | C22 | semidirect |
| 60. #430×C67 | C22 | semidirect |
| 61. C2×#104×C67 | C22 | semidirect |
| 62. C4×M16×C67 | C22 | semidirect |
| 94. #14524076 | D4 | semidirect |
| 106. #14524071 | D4 | semidirect |
| 150. #137×C67 | D4 | semidirect |
| 151. AGL(1,ℤ/8)×C67 | D4 | semidirect |
| 375. #2956 | D67 | semidirect |
| 376. C67 | #61111 | semidirect |
| 400. #568 | C2×D67 | semidirect |
| 417. #444 | C2×D67 | semidirect |
| 419. #443 | C2×D67 | semidirect |
| 421. #430 | C2×D67 | semidirect |
| 423. C2×#104 | C2×D67 | semidirect |
| 426. C4×M16 | C2×D67 | semidirect |
| 469. #137 | D268 | semidirect |
| 477. AGL(1,ℤ/8) | D268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22574997 | 2 |
| #22574993 | 2 |
| #22572014 | 2 |
| #22572003 | 2 |
| #22571985 | 2 |
| #22570668 | 2 |
| #22569947 | 2 |
| #22569946 | 2 |
| #22569560 | 2 |
| C2×#16863580 | 2 |
| #22569120 | 2 |
| C67×#2956 | 2 |
| #61111 | 67 |