Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1248 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 1248 conjugacy classes of subgroups — too many to draw. Only its 137 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 | #22574611 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #22569609 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #22569554 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22562211 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #22562208 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #22562195 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #22562193 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #22562192 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #22561871 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #22561857 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | C67×#2196 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #16864231 | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | #16864192 | — | 2 | 1 | no | — |
| 14 | #16864139 | — | 2 | 1 | no | — |
| 15 | #16864139 | C22 | 1 | 2 | yes | complemented |
| 16 | #16864111 | — | 2 | 1 | no | — |
| 17 | #16864110 | — | 2 | 2 | no | — |
| 18 | #16864031 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | D4×C22⋊D67 | — | 2 | 2 | no | — |
| 20 | #16863963 | — | 2 | 2 | no | — |
| 21 | #16863962 | — | 2 | 2 | no | — |
| 22 | #16863961 | — | 2 | 1 | no | — |
| 23 | #16863961 | — | 2 | 2 | no | — |
| 24 | #16863961 | C22 | 1 | 2 | yes | — |
| 25 | #16863944 | C22 | 1 | 1 | yes | characteristic |
| 26 | #16863943 | — | 2 | 1 | no | — |
| 27 | #16863584 | — | 2 | 2 | no | — |
| 28 | #16863584 | C22 | 1 | 2 | yes | complemented |
| 29 | #16863583 | C22 | 1 | 2 | yes | complemented |
| 30 | #16863582 | — | 2 | 2 | no | — |
| 31 | #16863582 | C22 | 1 | 2 | yes | complemented |
| 32 | #16863580 | — | 2 | 1 | no | — |
| 33 | #16863576 | C22 | 1 | 1 | yes | characteristic, complemented |
| 34 | #16863574 | C22 | 1 | 1 | yes | characteristic, complemented |
| 35 | #16863567 | — | 2 | 1 | no | — |
| 36 | #16863563 | C22 | 1 | 1 | yes | characteristic |
| 37 | #104×D67 | — | 2 | 1 | no | — |
| 38 | #16863377 | C22 | 1 | 1 | yes | characteristic, complemented |
| 39 | #16863368 | — | 2 | 2 | no | — |
| 40 | #16863368 | C22 | 1 | 2 | yes | complemented |
| 41 | #16863190 | C22 | 1 | 2 | yes | complemented |
| 42 | #16863189 | C22 | 1 | 1 | yes | characteristic, complemented |
| 43 | #16863184 | C22 | 1 | 2 | yes | complemented |
| 44 | #16863183 | C22 | 1 | 2 | yes | complemented |
| 45 | #16863182 | C22 | 1 | 2 | yes | complemented |
| 46 | D42×C67 | C22 | 1 | 1 | yes | characteristic, complemented |
| 47 | B(4,𝔽2)×C67 | C22 | 1 | 2 | yes | complemented |
| 48 | #453×C67 | C22 | 1 | 1 | yes | characteristic |
| 49 | #353×C67 | C22 | 1 | 1 | yes | characteristic, complemented |
| 50 | AΣL(1,𝔽16)×C67 | C22 | 1 | 2 | yes | complemented |
| 51 | #14524090 | — | 2 | 1 | no | — |
| 52 | #14524090 | — | 4 | 1 | no | — |
| 53 | #14524088 | — | 2 | 2 | no | — |
| 54 | #14524088 | — | 4 | 1 | no | — |
| 55 | #14524088 | C23 | 1 | 1 | yes | characteristic |
| 56 | C2×#11761628 | — | 2 | 2 | no | — |
| 57 | C2×#11761627 | — | 2 | 2 | no | — |
| 58 | C2×#11761627 | — | 4 | 1 | no | — |
| 59 | C2×#11761627 | D4 | 1 | 1 | yes | characteristic, complemented |
| 60 | C2×#11761627 | C23 | 1 | 1 | yes | characteristic |
| 61 | #41×D67 | — | 2 | 1 | no | — |
| 62 | #41×D67 | — | 4 | 1 | no | — |
| 63 | C22×C22⋊D67 | — | 2 | 1 | no | — |
| 64 | C22×C22⋊D67 | D4 | 1 | 2 | yes | complemented |
| 65 | C2×D4×D67 | — | 2 | 2 | no | — |
| 66 | #14524076 | — | 2 | 1 | no | — |
| 67 | #14524073 | — | 2 | 1 | no | — |
| 68 | #14524072 | — | 4 | 1 | no | — |
| 69 | #14524069 | — | 2 | 1 | no | — |
| 70 | #14524067 | — | 4 | 1 | no | — |
| 71 | #14524064 | — | 4 | 1 | no | — |
| 72 | #14524062 | — | 4 | 1 | no | — |
| 73 | M16×D67 | — | 2 | 1 | no | — |
| 74 | #14524043 | D4 | 1 | 1 | yes | characteristic, complemented |
| 75 | #14524042 | — | 2 | 1 | no | — |
| 76 | #14524039 | — | 2 | 1 | no | — |
| 77 | #14524039 | — | 2 | 2 | no | — |
| 78 | #14524039 | — | 2 | 2 | no | — |
| 79 | #14524039 | — | 4 | 2 | no | — |
| 80 | #14524030 | — | 2 | 2 | no | — |
| 81 | #14524030 | — | 2 | 2 | no | — |
| 82 | #14524030 | D4 | 1 | 1 | yes | characteristic, complemented |
| 83 | #14524030 | C23 | 1 | 1 | yes | characteristic |
| 84 | #14524029 | — | 2 | 2 | no | — |
| 85 | #14524029 | — | 2 | 2 | no | — |
| 86 | #14524029 | — | 2 | 2 | no | — |
| 87 | #14524029 | — | 2 | 2 | no | — |
| 88 | #14524029 | — | 2 | 2 | no | — |
| 89 | #14524029 | — | 4 | 2 | no | — |
| 90 | #14524018 | — | 2 | 1 | no | — |
| 91 | #14524017 | — | 2 | 2 | no | — |
| 92 | #14524016 | — | 2 | 2 | no | — |
| 93 | #14524016 | — | 4 | 2 | no | — |
| 94 | #14524015 | — | 2 | 2 | no | — |
| 95 | #14524015 | — | 2 | 2 | no | — |
| 96 | #14524015 | — | 4 | 2 | no | — |
| 97 | #14524014 | — | 2 | 2 | no | — |
| 98 | #14524014 | — | 2 | 1 | no | — |
| 99 | #14524014 | — | 2 | 2 | no | — |
| 100 | #14524014 | — | 2 | 2 | no | — |
| 101 | #14524013 | — | 2 | 1 | no | — |
| 102 | #14524013 | — | 2 | 2 | no | — |
| 103 | #14524013 | D4 | 1 | 2 | yes | complemented |
| 104 | #14524012 | — | 2 | 2 | no | — |
| 105 | #14524012 | — | 2 | 1 | no | — |
| 106 | #14524012 | — | 2 | 2 | no | — |
| 107 | #14524012 | — | 2 | 2 | no | — |
| 108 | #14524012 | D4 | 1 | 2 | yes | complemented |
| 109 | #14524011 | — | 2 | 2 | no | — |
| 110 | #14524011 | — | 2 | 2 | no | — |
| 111 | #14524011 | — | 2 | 2 | no | — |
| 112 | #14524011 | — | 2 | 1 | no | — |
| 113 | #14524011 | C23 | 1 | 2 | yes | — |
| 114 | C4×D268 | — | 2 | 1 | no | — |
| 115 | D4×Dic67 | — | 2 | 2 | no | — |
| 116 | C4×C22⋊D67 | — | 2 | 2 | no | — |
| 117 | #14524002 | — | 2 | 2 | no | — |
| 118 | #14524001 | — | 2 | 2 | no | — |
| 119 | #14523999 | — | 2 | 1 | no | — |
| 120 | #14523999 | — | 2 | 2 | no | — |
| 121 | #14523999 | D4 | 1 | 2 | yes | complemented |
| 122 | C42×D67 | D4 | 1 | 1 | yes | characteristic, complemented |
| 123 | #14523971 | — | 2 | 1 | no | — |
| 124 | #14523970 | — | 2 | 1 | no | — |
| 125 | #14523969 | — | 2 | 1 | no | — |
| 126 | #14523961 | — | 2 | 1 | no | — |
| 127 | #14523960 | C23 | 1 | 1 | yes | characteristic |
| 128 | #14523958 | — | 2 | 2 | no | — |
| 129 | #14523958 | C23 | 1 | 2 | yes | — |
| 130 | #14523957 | — | 2 | 2 | no | — |
| 131 | #14523957 | — | 2 | 2 | no | — |
| 132 | #14523957 | — | 2 | 2 | no | — |
| 133 | H(5,𝔽2)×C67 | C23 | 1 | 1 | yes | characteristic |
| 134 | C22×D4×C67 | — | 2 | 2 | no | — |
| 135 | AGL(1,ℤ/8)×C67 | — | 2 | 1 | no | — |
| 136 | #127×C67 | C23 | 1 | 1 | yes | characteristic |
| 137 | #121×C67 | — | 2 | 2 | no | — |
| 138 | #120×C67 | — | 2 | 1 | no | — |
| 139 | #120×C67 | — | 2 | 2 | no | — |
| 140 | #120×C67 | C23 | 1 | 2 | yes | — |
| 141 | C4×D4×C67 | — | 2 | 1 | no | — |
| 142 | #104×C67 | — | 2 | 1 | no | — |
| 143 | #100×C67 | C23 | 1 | 1 | yes | characteristic |
| 144 | #99×C67 | — | 2 | 2 | no | — |
| 145 | #99×C67 | C23 | 1 | 2 | yes | — |
| 146 | C23×D67 | — | 2 | 1 | no | — |
| 147 | C23×D67 | C2×D4 | 1 | 2 | yes | — |
| 148 | #11761629 | — | 2 | 1 | no | — |
| 149 | #11761628 | — | 2 | 1 | no | — |
| 150 | #11761628 | — | 4 | 1 | no | — |
| 151 | #11761628 | — | 4 | 1 | no | — |
| 152 | #11761628 | — | 4 | 2 | no | — |
| 153 | #11761628 | — | 8 | 4 | no | — |
| 154 | #11761627 | — | 2 | 1 | no | — |
| 155 | #11761627 | — | 4 | 1 | no | — |
| 156 | #11761627 | — | 4 | 1 | no | — |
| 157 | #11761627 | — | 4 | 1 | no | — |
| 158 | #11761627 | — | 4 | 1 | no | — |
| 159 | #11761627 | — | 4 | 1 | no | — |
| 160 | #11761627 | — | 4 | 2 | no | — |
| 161 | #11761627 | — | 4 | 2 | no | — |
| 162 | #11761627 | — | 4 | 2 | no | — |
| 163 | #11761627 | — | 4 | 1 | no | — |
| 164 | #11761627 | — | 4 | 1 | no | — |
| 165 | #11761627 | — | 4 | 2 | no | — |
| 166 | C2×Dic134 | — | 2 | 2 | no | — |
| 167 | C2×Dic134 | — | 2 | 2 | no | — |
| 168 | C2×Dic134 | — | 4 | 1 | no | — |
| 169 | C2×Dic134 | C2×D4 | 1 | 1 | yes | characteristic |
| 170 | C2×Dic134 | C2×D4 | 1 | 1 | yes | characteristic |
| 171 | Q8×D67 | — | 2 | 1 | no | — |
| 172 | Q8×D67 | — | 4 | 1 | no | — |
| 173 | C2×D268 | — | 2 | 1 | no | — |
| 174 | C2×D268 | — | 2 | 2 | no | — |
| 175 | C2×D268 | — | 4 | 2 | no | — |
| 176 | C2×C22⋊D67 | — | 2 | 2 | no | — |
| 177 | C2×C22⋊D67 | — | 2 | 2 | no | — |
| 178 | C2×C22⋊D67 | — | 2 | 2 | no | — |
| 179 | C2×C22⋊D67 | — | 2 | 2 | no | — |
| 180 | C2×C22⋊D67 | — | 2 | 2 | no | — |
| 181 | C2×C22⋊D67 | — | 2 | 2 | no | — |
| 182 | C2×C22⋊D67 | — | 2 | 2 | no | — |
| 183 | C2×C22⋊D67 | — | 2 | 1 | no | — |
| 184 | C2×C22⋊D67 | — | 2 | 2 | no | — |
| 185 | C2×C22⋊D67 | — | 2 | 2 | no | — |
| 186 | C2×C22⋊D67 | — | 4 | 2 | no | — |
| 187 | C2×C22⋊D67 | — | 4 | 2 | no | — |
| 188 | C2×C22⋊D67 | — | 4 | 2 | no | — |
| 189 | C2×C22⋊D67 | — | 4 | 2 | no | — |
| 190 | C2×C22⋊D67 | — | 4 | 2 | no | — |
| 191 | C2×C22⋊D67 | — | 8 | 1 | no | — |
| 192 | C2×C22⋊D67 | — | 8 | 1 | no | — |
| 193 | C2×C22⋊D67 | C2×D4 | 1 | 2 | yes | — |
| 194 | D4×D67 | — | 2 | 1 | no | — |
| 195 | D4×D67 | — | 4 | 1 | no | — |
| 196 | D4×D67 | — | 4 | 2 | no | — |
| 197 | D4×D67 | — | 4 | 1 | no | — |
| 198 | D4×D67 | — | 8 | 4 | no | — |
| 199 | C22×Dic67 | — | 2 | 2 | no | — |
| 200 | C22×Dic67 | — | 2 | 1 | no | — |
| 201 | C22×Dic67 | C2×D4 | 1 | 2 | yes | — |
| 202 | C2×C4×D67 | — | 2 | 2 | no | — |
| 203 | C2×C4×D67 | — | 2 | 2 | no | — |
| 204 | C2×C4×D67 | — | 2 | 1 | no | — |
| 205 | C2×C4×D67 | — | 4 | 1 | no | — |
| 206 | C2×C4×D67 | C2×D4 | 1 | 1 | yes | characteristic |
| 207 | Dic268 | — | 4 | 1 | no | — |
| 208 | #11761618 | — | 4 | 1 | no | — |
| 209 | #11761617 | — | 4 | 1 | no | — |
| 210 | #11761616 | — | 4 | 1 | no | — |
| 211 | #11761616 | — | 4 | 1 | no | — |
| 212 | #11761613 | — | 4 | 1 | no | — |
| 213 | #11761612 | — | 2 | 1 | no | — |
| 214 | #11761611 | — | 4 | 1 | no | — |
| 215 | C8×D67 | — | 4 | 1 | no | — |
| 216 | C4⋊Dic67 | — | 2 | 1 | no | — |
| 217 | C4⋊Dic67 | — | 2 | 2 | no | — |
| 218 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 219 | Dic67⋊C4 | — | 4 | 2 | no | — |
| 220 | C22⋊Dic67 | — | 2 | 1 | no | — |
| 221 | C22⋊Dic67 | — | 2 | 2 | no | — |
| 222 | C22⋊Dic67 | — | 2 | 2 | no | — |
| 223 | C22⋊Dic67 | — | 2 | 2 | no | — |
| 224 | C22⋊Dic67 | — | 2 | 2 | no | — |
| 225 | C22⋊Dic67 | — | 2 | 2 | no | — |
| 226 | C22⋊Dic67 | — | 2 | 2 | no | — |
| 227 | C22⋊Dic67 | — | 4 | 2 | no | — |
| 228 | C22⋊Dic67 | C2×D4 | 1 | 2 | yes | — |
| 229 | (C2×D67)⋊C4 | — | 2 | 2 | no | — |
| 230 | (C2×D67)⋊C4 | — | 2 | 2 | no | — |
| 231 | (C2×D67)⋊C4 | — | 2 | 2 | no | — |
| 232 | (C2×D67)⋊C4 | — | 2 | 2 | no | — |
| 233 | (C2×D67)⋊C4 | — | 4 | 2 | no | — |
| 234 | (C2×D67)⋊C4 | — | 4 | 2 | no | — |
| 235 | C4×Dic67 | — | 2 | 2 | no | — |
| 236 | C4×Dic67 | — | 2 | 1 | no | — |
| 237 | C4×Dic67 | — | 2 | 2 | no | — |
| 238 | C4×Dic67 | — | 4 | 2 | no | — |
| 239 | C4×Dic67 | C2×D4 | 1 | 1 | yes | characteristic |
| 240 | C24×C67 | — | 2 | 1 | no | — |
| 241 | C24×C67 | C2×D4 | 1 | 2 | yes | — |
| 242 | #41×C67 | — | 2 | 1 | no | — |
| 243 | #41×C67 | — | 4 | 1 | no | — |
| 244 | C2×D4×C67 | — | 2 | 1 | no | — |
| 245 | C2×D4×C67 | — | 2 | 2 | no | — |
| 246 | C2×D4×C67 | — | 2 | 2 | no | — |
| 247 | C2×D4×C67 | — | 2 | 2 | no | — |
| 248 | C2×D4×C67 | — | 2 | 2 | no | — |
| 249 | C2×D4×C67 | — | 4 | 1 | no | — |
| 250 | C2×D4×C67 | — | 4 | 2 | no | — |
| 251 | C2×D4×C67 | — | 8 | 4 | no | — |
| 252 | C2×D4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 253 | C2×D4×C67 | C24 | 1 | 1 | yes | characteristic |
| 254 | C22×C4×C67 | — | 2 | 2 | no | — |
| 255 | SD16×C67 | — | 4 | 1 | no | — |
| 256 | D8×C67 | — | 4 | 1 | no | — |
| 257 | M16×C67 | — | 2 | 1 | no | — |
| 258 | C4⋊C4×C67 | — | 2 | 1 | no | — |
| 259 | C22⋊C4×C67 | — | 2 | 1 | no | — |
| 260 | C22⋊C4×C67 | — | 2 | 2 | no | — |
| 261 | C22⋊C4×C67 | — | 2 | 2 | no | — |
| 262 | C22⋊C4×C67 | — | 4 | 2 | no | — |
| 263 | C22⋊C4×C67 | C2×D4 | 1 | 2 | yes | — |
| 264 | C42×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 265 | C23×C67 | — | 2 | 2 | no | — |
| 266 | C23×C67 | — | 2 | 2 | no | — |
| 267 | C23×C67 | — | 2 | 1 | no | — |
| 268 | C23×C67 | — | 4 | 2 | no | — |
| 269 | C23×C67 | — | 8 | 2 | no | — |
| 270 | C23×C67 | — | 8 | 2 | no | — |
| 271 | C23×C67 | — | 8 | 1 | no | — |
| 272 | C23×C67 | C22×D4 | 1 | 2 | yes | — |
| 273 | C22×D67 | — | 2 | 2 | no | — |
| 274 | C22×D67 | — | 2 | 2 | no | — |
| 275 | C22×D67 | — | 4 | 1 | no | — |
| 276 | C22×D67 | — | 4 | 2 | no | — |
| 277 | C22×D67 | — | 8 | 2 | no | — |
| 278 | C22×D67 | — | 8 | 2 | no | — |
| 279 | C22×D67 | — | 8 | 1 | no | — |
| 280 | C22×D67 | #120 | 1 | 1 | yes | characteristic |
| 281 | Q8×C67 | — | 2 | 1 | no | — |
| 282 | D4×C67 | — | 2 | 1 | no | — |
| 283 | D4×C67 | — | 4 | 1 | no | — |
| 284 | D4×C67 | — | 4 | 1 | no | — |
| 285 | D4×C67 | — | 4 | 2 | no | — |
| 286 | D4×C67 | — | 4 | 4 | no | — |
| 287 | D4×C67 | — | 4 | 2 | no | — |
| 288 | D4×C67 | — | 4 | 1 | no | — |
| 289 | D4×C67 | — | 8 | 2 | no | — |
| 290 | D4×C67 | — | 8 | 2 | no | — |
| 291 | D4×C67 | — | 16 | 2 | no | — |
| 292 | C2×C4×C67 | — | 2 | 1 | no | — |
| 293 | C2×C4×C67 | — | 2 | 2 | no | — |
| 294 | C2×C4×C67 | — | 2 | 2 | no | — |
| 295 | C2×C4×C67 | — | 4 | 4 | no | — |
| 296 | C2×C4×C67 | — | 4 | 1 | no | — |
| 297 | C2×C4×C67 | — | 4 | 2 | no | — |
| 298 | C2×C4×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 299 | C22⋊D67 | — | 4 | 2 | no | — |
| 300 | C22⋊D67 | — | 4 | 2 | no | — |
| 301 | C22⋊D67 | — | 4 | 1 | no | — |
| 302 | C22⋊D67 | — | 4 | 2 | no | — |
| 303 | C22⋊D67 | — | 4 | 1 | no | — |
| 304 | C22⋊D67 | — | 4 | 1 | no | — |
| 305 | C22⋊D67 | — | 4 | 2 | no | — |
| 306 | C22⋊D67 | — | 4 | 2 | no | — |
| 307 | C22⋊D67 | — | 8 | 2 | no | — |
| 308 | C22⋊D67 | — | 8 | 1 | no | — |
| 309 | C22⋊D67 | — | 8 | 2 | no | — |
| 310 | C22⋊D67 | — | 8 | 2 | no | — |
| 311 | C22⋊D67 | — | 8 | 2 | no | — |
| 312 | C22⋊D67 | — | 8 | 2 | no | — |
| 313 | C22⋊D67 | — | 8 | 2 | no | — |
| 314 | C22⋊D67 | — | 16 | 2 | no | — |
| 315 | C22⋊D67 | — | 16 | 2 | no | — |
| 316 | C2×Dic67 | — | 2 | 2 | no | — |
| 317 | C2×Dic67 | — | 2 | 2 | no | — |
| 318 | C2×Dic67 | — | 2 | 2 | no | — |
| 319 | C2×Dic67 | — | 2 | 1 | no | — |
| 320 | C2×Dic67 | — | 2 | 2 | no | — |
| 321 | C2×Dic67 | — | 2 | 1 | no | — |
| 322 | C2×Dic67 | — | 4 | 2 | no | — |
| 323 | C2×Dic67 | — | 4 | 1 | no | — |
| 324 | C2×Dic67 | — | 4 | 1 | no | — |
| 325 | C2×Dic67 | — | 4 | 1 | no | — |
| 326 | C2×Dic67 | — | 4 | 2 | no | — |
| 327 | C2×Dic67 | #120 | 1 | 2 | yes | — |
| 328 | C2×Dic67 | #120 | 1 | 1 | yes | characteristic |
| 329 | D268 | — | 2 | 1 | no | — |
| 330 | D268 | — | 4 | 2 | no | — |
| 331 | D268 | — | 4 | 1 | no | — |
| 332 | D268 | — | 8 | 2 | no | — |
| 333 | D268 | — | 16 | 2 | no | — |
| 334 | C4×D67 | — | 2 | 1 | no | — |
| 335 | C4×D67 | — | 2 | 1 | no | — |
| 336 | C4×D67 | — | 4 | 2 | no | — |
| 337 | C4×D67 | — | 4 | 4 | no | — |
| 338 | C4×D67 | — | 4 | 2 | no | — |
| 339 | C4×D67 | — | 4 | 1 | no | — |
| 340 | C4×D67 | — | 4 | 1 | no | — |
| 341 | C4×D67 | — | 4 | 1 | no | — |
| 342 | Dic134 | — | 2 | 1 | no | — |
| 343 | Dic134 | — | 4 | 1 | no | — |
| 344 | Dic134 | — | 4 | 2 | no | — |
| 345 | Dic134 | — | 4 | 1 | no | — |
| 346 | Dic134 | — | 4 | 1 | no | — |
| 347 | Dic134 | — | 8 | 2 | no | — |
| 348 | C8×C67 | — | 4 | 1 | no | — |
| 349 | C67⋊C8 | — | 4 | 1 | no | — |
| 350 | C22×C67 | — | 2 | 2 | no | — |
| 351 | C22×C67 | — | 4 | 2 | no | — |
| 352 | C22×C67 | — | 4 | 2 | no | — |
| 353 | C22×C67 | — | 4 | 2 | no | — |
| 354 | C22×C67 | — | 4 | 2 | no | — |
| 355 | C22×C67 | — | 4 | 1 | no | — |
| 356 | C22×C67 | — | 4 | 1 | no | — |
| 357 | C22×C67 | — | 4 | 2 | no | — |
| 358 | C22×C67 | — | 8 | 2 | no | — |
| 359 | C22×C67 | — | 8 | 2 | no | — |
| 360 | C22×C67 | — | 8 | 2 | no | — |
| 361 | C22×C67 | — | 16 | 2 | no | — |
| 362 | C22×C67 | C2×#120 | 1 | 1 | yes | characteristic |
| 363 | C2×D67 | — | 2 | 1 | no | — |
| 364 | C2×D67 | — | 4 | 1 | no | — |
| 365 | C2×D67 | — | 4 | 2 | no | — |
| 366 | C2×D67 | — | 4 | 2 | no | — |
| 367 | C2×D67 | — | 4 | 1 | no | — |
| 368 | C2×D67 | — | 4 | 2 | no | — |
| 369 | C2×D67 | — | 8 | 2 | no | — |
| 370 | C2×D67 | — | 8 | 2 | no | — |
| 371 | C2×D67 | — | 8 | 2 | no | — |
| 372 | C2×D67 | — | 16 | 1 | no | — |
| 373 | C2×D67 | — | 16 | 2 | no | — |
| 374 | C4×C67 | — | 2 | 2 | no | — |
| 375 | C4×C67 | — | 2 | 1 | no | — |
| 376 | C4×C67 | — | 4 | 2 | no | — |
| 377 | C4×C67 | — | 4 | 1 | no | — |
| 378 | C4×C67 | — | 8 | 2 | no | — |
| 379 | Dic67 | — | 2 | 2 | no | — |
| 380 | Dic67 | — | 4 | 1 | no | — |
| 381 | Dic67 | — | 4 | 2 | no | — |
| 382 | Dic67 | — | 4 | 1 | no | — |
| 383 | Dic67 | — | 4 | 1 | no | — |
| 384 | Dic67 | — | 8 | 2 | no | — |
| 385 | Dic67 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 386 | Dic67 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 387 | #33559 | — | 67 | 1 | no | maximal, Sylow |
| 388 | C2×C67 | — | 2 | 1 | no | — |
| 389 | C2×C67 | — | 4 | 2 | no | — |
| 390 | C2×C67 | — | 8 | 1 | no | — |
| 391 | C2×C67 | — | 8 | 1 | no | — |
| 392 | C2×C67 | — | 8 | 2 | no | — |
| 393 | C2×C67 | C2×B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 394 | D67 | — | 4 | 1 | no | — |
| 395 | D67 | — | 8 | 2 | no | — |
| 396 | D67 | — | 8 | 1 | no | — |
| 397 | #3549 | — | 67 | 1 | no | — |
| 398 | #3027 | — | 67 | 2 | no | — |
| 399 | #3018 | — | 67 | 1 | no | — |
| 400 | #2199 | — | 67 | 2 | no | — |
| 401 | #2199 | — | 67 | 2 | no | — |
| 402 | #2196 | — | 67 | 1 | no | — |
| 403 | #2196 | — | 67 | 1 | no | — |
| 404 | #2196 | — | 67 | 1 | no | — |
| 405 | #2196 | D67 | 1 | 1 | yes | characteristic, complemented |
| 406 | #2126 | — | 67 | 1 | no | — |
| 407 | #2122 | — | 67 | 2 | no | — |
| 408 | C67 | #33559 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 409 | #585 | — | 67 | 1 | no | — |
| 410 | #575 | — | 134 | 1 | no | — |
| 411 | H(3,𝔽4) | — | 67 | 2 | no | — |
| 412 | H(3,𝔽4) | — | 134 | 1 | no | — |
| 413 | #555 | — | 134 | 2 | no | — |
| 414 | #555 | — | 134 | 1 | no | — |
| 415 | D42 | — | 67 | 1 | no | — |
| 416 | D42 | — | 134 | 2 | no | — |
| 417 | D42 | C2×D67 | 1 | 1 | yes | characteristic, complemented |
| 418 | #535 | — | 67 | 2 | no | — |
| 419 | #535 | — | 134 | 2 | no | — |
| 420 | #535 | — | 134 | 1 | no | — |
| 421 | #535 | — | 134 | 2 | no | — |
| 422 | #535 | — | 134 | 2 | no | — |
| 423 | #532 | — | 67 | 1 | no | — |
| 424 | #532 | — | 134 | 1 | no | — |
| 425 | B(4,𝔽2) | — | 67 | 2 | no | — |
| 426 | B(4,𝔽2) | — | 67 | 2 | no | — |
| 427 | B(4,𝔽2) | — | 67 | 2 | no | — |
| 428 | B(4,𝔽2) | — | 134 | 2 | no | — |
| 429 | B(4,𝔽2) | — | 134 | 2 | no | — |
| 430 | B(4,𝔽2) | C2×D67 | 1 | 2 | yes | complemented |
| 431 | #456 | — | 134 | 1 | no | — |
| 432 | #455 | — | 67 | 1 | no | — |
| 433 | #455 | — | 67 | 1 | no | — |
| 434 | #454 | — | 134 | 1 | no | — |
| 435 | #453 | — | 67 | 1 | no | — |
| 436 | #453 | C2×D67 | 1 | 1 | yes | characteristic |
| 437 | C2×#104 | — | 134 | 1 | no | — |
| 438 | #413 | — | 67 | 1 | no | — |
| 439 | #410 | — | 67 | 2 | no | — |
| 440 | #410 | — | 134 | 2 | no | — |
| 441 | #354 | — | 67 | 2 | no | — |
| 442 | #353 | — | 67 | 1 | no | — |
| 443 | #353 | C2×D67 | 1 | 1 | yes | characteristic, complemented |
| 444 | AΣL(1,𝔽16) | — | 67 | 2 | no | — |
| 445 | AΣL(1,𝔽16) | — | 67 | 2 | no | — |
| 446 | AΣL(1,𝔽16) | — | 67 | 2 | no | — |
| 447 | AΣL(1,𝔽16) | C2×D67 | 1 | 2 | yes | complemented |
| 448 | 2−1+4 | — | 268 | 1 | no | — |
| 449 | 2−1+4 | — | 134 | 1 | no | — |
| 450 | H(5,𝔽2) | — | 268 | 1 | no | — |
| 451 | H(5,𝔽2) | — | 67 | 1 | no | — |
| 452 | H(5,𝔽2) | — | 134 | 2 | no | — |
| 453 | H(5,𝔽2) | C22×D67 | 1 | 1 | yes | characteristic |
| 454 | C2×#41 | — | 268 | 1 | no | — |
| 455 | C2×#41 | — | 268 | 1 | no | — |
| 456 | C2×#41 | — | 67 | 1 | no | — |
| 457 | C2×#41 | — | 67 | 1 | no | — |
| 458 | C2×#41 | — | 134 | 2 | no | — |
| 459 | C2×#41 | — | 134 | 1 | no | — |
| 460 | C2×#41 | — | 134 | 2 | no | — |
| 461 | C22×D4 | — | 2 | 2 | no | — |
| 462 | C22×D4 | — | 67 | 2 | no | — |
| 463 | C22×D4 | — | 134 | 2 | no | — |
| 464 | C22×D4 | — | 134 | 1 | no | — |
| 465 | #137 | — | 268 | 1 | no | — |
| 466 | #137 | — | 134 | 1 | no | — |
| 467 | #137 | — | 134 | 1 | no | — |
| 468 | AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 469 | AGL(1,ℤ/8) | — | 268 | 1 | no | — |
| 470 | AGL(1,ℤ/8) | — | 134 | 1 | no | — |
| 471 | #135 | — | 268 | 1 | no | — |
| 472 | #135 | — | 268 | 1 | no | — |
| 473 | C2×M16 | — | 134 | 1 | no | — |
| 474 | C4⋊Q8 | — | 67 | 1 | no | — |
| 475 | C4⋊Q8 | — | 134 | 1 | no | — |
| 476 | #127 | — | 268 | 2 | no | — |
| 477 | #127 | — | 134 | 2 | no | — |
| 478 | #127 | — | 134 | 1 | no | — |
| 479 | #127 | — | 134 | 2 | no | — |
| 480 | #127 | C22×D67 | 1 | 1 | yes | characteristic |
| 481 | #124 | — | 268 | 2 | no | — |
| 482 | #124 | — | 67 | 1 | no | — |
| 483 | #124 | — | 67 | 1 | no | — |
| 484 | #124 | — | 134 | 2 | no | — |
| 485 | #124 | — | 134 | 2 | no | — |
| 486 | #124 | — | 134 | 2 | no | — |
| 487 | #124 | — | 134 | 2 | no | — |
| 488 | #124 | — | 134 | 2 | no | — |
| 489 | #124 | — | 134 | 2 | no | — |
| 490 | #124 | — | 134 | 2 | no | — |
| 491 | #121 | — | 2 | 2 | no | — |
| 492 | #121 | — | 268 | 2 | no | — |
| 493 | #121 | — | 268 | 2 | no | — |
| 494 | #121 | — | 134 | 2 | no | — |
| 495 | #121 | — | 134 | 2 | no | — |
| 496 | #121 | — | 134 | 1 | no | — |
| 497 | #121 | — | 134 | 2 | no | — |
| 498 | #121 | — | 134 | 2 | no | — |
| 499 | #121 | — | 134 | 2 | no | — |
| 500 | #121 | — | 134 | 1 | no | — |
| 501 | #121 | — | 134 | 2 | no | — |
| 502 | #121 | — | 134 | 2 | no | — |
| 503 | #120 | — | 2 | 1 | no | — |
| 504 | #120 | — | 2 | 2 | no | — |
| 505 | #120 | — | 67 | 2 | no | — |
| 506 | #120 | — | 67 | 2 | no | — |
| 507 | #120 | — | 67 | 2 | no | — |
| 508 | #120 | — | 134 | 2 | no | — |
| 509 | #120 | — | 134 | 1 | no | — |
| 510 | #120 | — | 134 | 2 | no | — |
| 511 | #120 | — | 134 | 2 | no | — |
| 512 | #120 | — | 134 | 2 | no | — |
| 513 | #120 | — | 134 | 2 | no | — |
| 514 | #120 | — | 134 | 1 | no | — |
| 515 | #120 | — | 134 | 2 | no | — |
| 516 | #120 | — | 134 | 2 | no | — |
| 517 | #120 | — | 134 | 1 | no | — |
| 518 | #120 | C22×D67 | 1 | 2 | yes | — |
| 519 | C4×D4 | — | 2 | 1 | no | — |
| 520 | C4×D4 | — | 134 | 2 | no | — |
| 521 | C4×D4 | — | 134 | 2 | no | — |
| 522 | C4×D4 | — | 134 | 1 | no | — |
| 523 | #117 | — | 67 | 2 | no | — |
| 524 | #117 | — | 134 | 2 | no | — |
| 525 | #117 | — | 134 | 1 | no | — |
| 526 | #117 | — | 134 | 2 | no | — |
| 527 | #117 | — | 134 | 2 | no | — |
| 528 | C2×C42 | — | 67 | 1 | no | — |
| 529 | #104 | — | 2 | 1 | no | — |
| 530 | #104 | — | 134 | 1 | no | — |
| 531 | #104 | — | 134 | 1 | no | — |
| 532 | #104 | — | 134 | 1 | no | — |
| 533 | #101 | — | 134 | 1 | no | — |
| 534 | #100 | — | 67 | 1 | no | — |
| 535 | #100 | C22×D67 | 1 | 1 | yes | characteristic |
| 536 | #99 | — | 2 | 2 | no | — |
| 537 | #99 | — | 67 | 2 | no | — |
| 538 | #99 | — | 134 | 2 | no | — |
| 539 | #99 | — | 134 | 2 | no | — |
| 540 | #99 | — | 134 | 2 | no | — |
| 541 | #99 | — | 134 | 2 | no | — |
| 542 | #99 | C22×D67 | 1 | 2 | yes | — |
| 543 | C24 | — | 2 | 1 | no | — |
| 544 | C24 | — | 67 | 2 | no | — |
| 545 | C24 | — | 134 | 1 | no | — |
| 546 | C24 | D4×D67 | 1 | 2 | yes | — |
| 547 | #41 | — | 2 | 1 | no | — |
| 548 | #41 | — | 4 | 1 | no | — |
| 549 | #41 | — | 268 | 2 | no | — |
| 550 | #41 | — | 268 | 1 | no | — |
| 551 | #41 | — | 268 | 1 | no | — |
| 552 | #41 | — | 268 | 1 | no | — |
| 553 | #41 | — | 268 | 1 | no | — |
| 554 | #41 | — | 268 | 2 | no | — |
| 555 | #41 | — | 268 | 2 | no | — |
| 556 | #41 | — | 268 | 2 | no | — |
| 557 | #41 | — | 268 | 2 | no | — |
| 558 | #41 | — | 268 | 1 | no | — |
| 559 | #41 | — | 268 | 1 | no | — |
| 560 | #41 | — | 268 | 1 | no | — |
| 561 | #41 | — | 268 | 1 | no | — |
| 562 | #41 | — | 268 | 1 | no | — |
| 563 | #41 | — | 536 | 4 | no | — |
| 564 | #41 | — | 134 | 1 | no | — |
| 565 | #41 | — | 134 | 1 | no | — |
| 566 | #41 | — | 134 | 1 | no | — |
| 567 | C2×Q8 | — | 268 | 1 | no | — |
| 568 | C2×Q8 | — | 268 | 1 | no | — |
| 569 | C2×Q8 | — | 67 | 1 | no | — |
| 570 | C2×Q8 | — | 67 | 1 | no | — |
| 571 | C2×Q8 | — | 134 | 2 | no | — |
| 572 | C2×Q8 | — | 134 | 2 | no | — |
| 573 | C2×Q8 | — | 134 | 1 | no | — |
| 574 | C2×D4 | — | 2 | 1 | no | — |
| 575 | C2×D4 | — | 2 | 2 | no | — |
| 576 | C2×D4 | — | 2 | 2 | no | — |
| 577 | C2×D4 | — | 2 | 2 | no | — |
| 578 | C2×D4 | — | 2 | 2 | no | — |
| 579 | C2×D4 | — | 4 | 1 | no | — |
| 580 | C2×D4 | — | 4 | 2 | no | — |
| 581 | C2×D4 | — | 8 | 4 | no | — |
| 582 | C2×D4 | — | 268 | 2 | no | — |
| 583 | C2×D4 | — | 268 | 1 | no | — |
| 584 | C2×D4 | — | 268 | 2 | no | — |
| 585 | C2×D4 | — | 268 | 1 | no | — |
| 586 | C2×D4 | — | 268 | 2 | no | — |
| 587 | C2×D4 | — | 268 | 2 | no | — |
| 588 | C2×D4 | — | 268 | 2 | no | — |
| 589 | C2×D4 | — | 268 | 2 | no | — |
| 590 | C2×D4 | — | 268 | 2 | no | — |
| 591 | C2×D4 | — | 536 | 4 | no | — |
| 592 | C2×D4 | — | 536 | 1 | no | — |
| 593 | C2×D4 | — | 536 | 1 | no | — |
| 594 | C2×D4 | — | 67 | 2 | no | — |
| 595 | C2×D4 | — | 134 | 1 | no | — |
| 596 | C2×D4 | — | 134 | 2 | no | — |
| 597 | C2×D4 | — | 134 | 2 | no | — |
| 598 | C2×D4 | — | 134 | 2 | no | — |
| 599 | C2×D4 | — | 134 | 1 | no | — |
| 600 | C2×D4 | — | 134 | 2 | no | — |
| 601 | C2×D4 | — | 134 | 2 | no | — |
| 602 | C2×D4 | — | 134 | 2 | no | — |
| 603 | C2×D4 | — | 134 | 1 | no | — |
| 604 | C2×D4 | — | 134 | 2 | no | — |
| 605 | C2×D4 | — | 134 | 2 | no | — |
| 606 | C2×D4 | — | 134 | 2 | no | — |
| 607 | C2×D4 | — | 134 | 2 | no | — |
| 608 | C2×D4 | D4×D67 | 1 | 1 | yes | characteristic |
| 609 | C2×D4 | C23×D67 | 1 | 1 | yes | characteristic |
| 610 | C22×C4 | — | 2 | 2 | no | — |
| 611 | C22×C4 | — | 268 | 1 | no | — |
| 612 | C22×C4 | — | 67 | 2 | no | — |
| 613 | C22×C4 | — | 67 | 1 | no | — |
| 614 | C22×C4 | — | 134 | 1 | no | — |
| 615 | C22×C4 | — | 134 | 2 | no | — |
| 616 | C22×C4 | — | 134 | 2 | no | — |
| 617 | C22×C4 | — | 134 | 1 | no | — |
| 618 | C22×C4 | — | 134 | 2 | no | — |
| 619 | Q16 | — | 268 | 1 | no | — |
| 620 | Q16 | — | 268 | 1 | no | — |
| 621 | SD16 | — | 4 | 1 | no | — |
| 622 | SD16 | — | 268 | 1 | no | — |
| 623 | SD16 | — | 268 | 1 | no | — |
| 624 | SD16 | — | 268 | 1 | no | — |
| 625 | D8 | — | 4 | 1 | no | — |
| 626 | D8 | — | 268 | 1 | no | — |
| 627 | M16 | — | 2 | 1 | no | — |
| 628 | M16 | — | 268 | 1 | no | — |
| 629 | M16 | — | 134 | 1 | no | — |
| 630 | C2×C8 | — | 268 | 1 | no | — |
| 631 | C4⋊C4 | — | 2 | 1 | no | — |
| 632 | C4⋊C4 | — | 268 | 2 | no | — |
| 633 | C4⋊C4 | — | 134 | 2 | no | — |
| 634 | C4⋊C4 | — | 134 | 2 | no | — |
| 635 | C4⋊C4 | — | 134 | 1 | no | — |
| 636 | C22⋊C4 | — | 2 | 1 | no | — |
| 637 | C22⋊C4 | — | 2 | 2 | no | — |
| 638 | C22⋊C4 | — | 2 | 2 | no | — |
| 639 | C22⋊C4 | — | 4 | 2 | no | — |
| 640 | C22⋊C4 | — | 268 | 2 | no | — |
| 641 | C22⋊C4 | — | 268 | 2 | no | — |
| 642 | C22⋊C4 | — | 268 | 2 | no | — |
| 643 | C22⋊C4 | — | 67 | 2 | no | — |
| 644 | C22⋊C4 | — | 134 | 2 | no | — |
| 645 | C22⋊C4 | — | 134 | 2 | no | — |
| 646 | C22⋊C4 | — | 134 | 2 | no | — |
| 647 | C22⋊C4 | — | 134 | 2 | no | — |
| 648 | C22⋊C4 | — | 134 | 2 | no | — |
| 649 | C22⋊C4 | — | 134 | 2 | no | — |
| 650 | C22⋊C4 | — | 134 | 1 | no | — |
| 651 | C22⋊C4 | — | 134 | 2 | no | — |
| 652 | C22⋊C4 | — | 134 | 2 | no | — |
| 653 | C22⋊C4 | — | 134 | 2 | no | — |
| 654 | C22⋊C4 | — | 134 | 2 | no | — |
| 655 | C22⋊C4 | D4×D67 | 1 | 2 | yes | — |
| 656 | C42 | — | 268 | 2 | no | — |
| 657 | C42 | — | 67 | 1 | no | — |
| 658 | C42 | — | 134 | 1 | no | — |
| 659 | C42 | — | 134 | 2 | no | — |
| 660 | C42 | — | 134 | 2 | no | — |
| 661 | C42 | D4×D67 | 1 | 1 | yes | characteristic |
| 662 | C23 | — | 2 | 2 | no | — |
| 663 | C23 | — | 2 | 2 | no | — |
| 664 | C23 | — | 2 | 1 | no | — |
| 665 | C23 | — | 4 | 2 | no | — |
| 666 | C23 | — | 8 | 2 | no | — |
| 667 | C23 | — | 8 | 2 | no | — |
| 668 | C23 | — | 8 | 1 | no | — |
| 669 | C23 | — | 268 | 2 | no | — |
| 670 | C23 | — | 268 | 1 | no | — |
| 671 | C23 | — | 536 | 2 | no | — |
| 672 | C23 | — | 536 | 2 | no | — |
| 673 | C23 | — | 536 | 1 | no | — |
| 674 | C23 | — | 67 | 1 | no | — |
| 675 | C23 | — | 134 | 2 | no | — |
| 676 | C23 | — | 134 | 2 | no | — |
| 677 | C23 | C2×D4×D67 | 1 | 2 | yes | — |
| 678 | Q8 | — | 2 | 1 | no | — |
| 679 | Q8 | — | 268 | 1 | no | — |
| 680 | Q8 | — | 268 | 1 | no | — |
| 681 | Q8 | — | 268 | 1 | no | — |
| 682 | Q8 | — | 268 | 2 | no | — |
| 683 | Q8 | — | 536 | 2 | no | — |
| 684 | Q8 | — | 134 | 1 | no | — |
| 685 | D4 | — | 2 | 1 | no | — |
| 686 | D4 | — | 4 | 1 | no | — |
| 687 | D4 | — | 4 | 1 | no | — |
| 688 | D4 | — | 4 | 2 | no | — |
| 689 | D4 | — | 4 | 4 | no | — |
| 690 | D4 | — | 4 | 2 | no | — |
| 691 | D4 | — | 4 | 1 | no | — |
| 692 | D4 | — | 8 | 2 | no | — |
| 693 | D4 | — | 8 | 2 | no | — |
| 694 | D4 | — | 268 | 2 | no | — |
| 695 | D4 | — | 268 | 1 | no | — |
| 696 | D4 | — | 268 | 2 | no | — |
| 697 | D4 | — | 268 | 1 | no | — |
| 698 | D4 | — | 268 | 1 | no | — |
| 699 | D4 | — | 268 | 2 | no | — |
| 700 | D4 | — | 268 | 2 | no | — |
| 701 | D4 | — | 268 | 1 | no | — |
| 702 | D4 | — | 268 | 2 | no | — |
| 703 | D4 | — | 268 | 2 | no | — |
| 704 | D4 | — | 16 | 2 | no | — |
| 705 | D4 | — | 536 | 2 | no | — |
| 706 | D4 | — | 536 | 2 | no | — |
| 707 | D4 | — | 536 | 2 | no | — |
| 708 | D4 | — | 536 | 2 | no | — |
| 709 | D4 | — | 536 | 2 | no | — |
| 710 | D4 | — | 536 | 2 | no | — |
| 711 | D4 | — | 536 | 1 | no | — |
| 712 | D4 | — | 536 | 2 | no | — |
| 713 | D4 | — | 1072 | 2 | no | — |
| 714 | D4 | — | 1072 | 2 | no | — |
| 715 | D4 | — | 1072 | 2 | no | — |
| 716 | D4 | — | 134 | 1 | no | — |
| 717 | C2×C4 | — | 2 | 1 | no | — |
| 718 | C2×C4 | — | 2 | 2 | no | — |
| 719 | C2×C4 | — | 2 | 2 | no | — |
| 720 | C2×C4 | — | 4 | 4 | no | — |
| 721 | C2×C4 | — | 4 | 1 | no | — |
| 722 | C2×C4 | — | 4 | 2 | no | — |
| 723 | C2×C4 | — | 268 | 1 | no | — |
| 724 | C2×C4 | — | 268 | 4 | no | — |
| 725 | C2×C4 | — | 268 | 2 | no | — |
| 726 | C2×C4 | — | 268 | 1 | no | — |
| 727 | C2×C4 | — | 268 | 1 | no | — |
| 728 | C2×C4 | — | 268 | 2 | no | — |
| 729 | C2×C4 | — | 268 | 1 | no | — |
| 730 | C2×C4 | — | 268 | 1 | no | — |
| 731 | C2×C4 | — | 268 | 1 | no | — |
| 732 | C2×C4 | — | 268 | 2 | no | — |
| 733 | C2×C4 | — | 268 | 2 | no | — |
| 734 | C2×C4 | — | 67 | 1 | no | — |
| 735 | C2×C4 | — | 67 | 2 | no | — |
| 736 | C2×C4 | — | 134 | 1 | no | — |
| 737 | C2×C4 | — | 134 | 1 | no | — |
| 738 | C2×C4 | — | 134 | 2 | no | — |
| 739 | C2×C4 | — | 134 | 1 | no | — |
| 740 | C2×C4 | — | 134 | 2 | no | — |
| 741 | C2×C4 | — | 134 | 1 | no | — |
| 742 | C2×C4 | — | 134 | 2 | no | — |
| 743 | C2×C4 | — | 134 | 2 | no | — |
| 744 | C2×C4 | C2×D4×D67 | 1 | 1 | yes | characteristic |
| 745 | C8 | — | 4 | 1 | no | — |
| 746 | C8 | — | 268 | 1 | no | — |
| 747 | C22 | — | 2 | 2 | no | — |
| 748 | C22 | — | 4 | 2 | no | — |
| 749 | C22 | — | 4 | 2 | no | — |
| 750 | C22 | — | 4 | 2 | no | — |
| 751 | C22 | — | 4 | 2 | no | — |
| 752 | C22 | — | 4 | 1 | no | — |
| 753 | C22 | — | 4 | 1 | no | — |
| 754 | C22 | — | 4 | 2 | no | — |
| 755 | C22 | — | 8 | 2 | no | — |
| 756 | C22 | — | 8 | 2 | no | — |
| 757 | C22 | — | 8 | 2 | no | — |
| 758 | C22 | — | 268 | 1 | no | — |
| 759 | C22 | — | 268 | 2 | no | — |
| 760 | C22 | — | 268 | 2 | no | — |
| 761 | C22 | — | 268 | 1 | no | — |
| 762 | C22 | — | 268 | 2 | no | — |
| 763 | C22 | — | 16 | 2 | no | — |
| 764 | C22 | — | 536 | 2 | no | — |
| 765 | C22 | — | 536 | 2 | no | — |
| 766 | C22 | — | 536 | 2 | no | — |
| 767 | C22 | — | 1072 | 1 | no | — |
| 768 | C22 | — | 1072 | 2 | no | — |
| 769 | C22 | — | 134 | 1 | no | — |
| 770 | C22 | #120×D67 | 1 | 1 | yes | characteristic |
| 771 | C4 | — | 2 | 2 | no | — |
| 772 | C4 | — | 2 | 1 | no | — |
| 773 | C4 | — | 4 | 2 | no | — |
| 774 | C4 | — | 4 | 1 | no | — |
| 775 | C4 | — | 8 | 2 | no | — |
| 776 | C4 | — | 268 | 2 | no | — |
| 777 | C4 | — | 268 | 1 | no | — |
| 778 | C4 | — | 268 | 1 | no | — |
| 779 | C4 | — | 268 | 1 | no | — |
| 780 | C4 | — | 536 | 2 | no | — |
| 781 | C4 | — | 67 | 1 | no | — |
| 782 | C4 | — | 67 | 1 | no | — |
| 783 | C4 | — | 134 | 2 | no | — |
| 784 | C2 | — | 2 | 1 | no | — |
| 785 | C2 | — | 4 | 2 | no | — |
| 786 | C2 | — | 8 | 2 | no | — |
| 787 | C2 | — | 8 | 1 | no | — |
| 788 | C2 | — | 8 | 1 | no | — |
| 789 | C2 | — | 268 | 1 | no | — |
| 790 | C2 | — | 536 | 2 | no | — |
| 791 | C2 | — | 536 | 1 | no | — |
| 792 | C2 | B(4,𝔽2)×D67 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22574611 | C2 | semidirect |
| 2. #22569609 | C2 | semidirect |
| 3. #22569554 | C2 | semidirect |
| 4. #22562211 | C2 | semidirect |
| 5. #22562208 | C2 | semidirect |
| 6. #22562195 | C2 | semidirect |
| 7. #22562193 | C2 | semidirect |
| 8. #22562192 | C2 | semidirect |
| 9. #22561871 | C2 | semidirect |
| 10. #22561857 | C2 | semidirect |
| 11. C67×#2196 | C2 | semidirect |
| 12. #16864231 | C22 | semidirect |
| 15. #16864139 | C22 | semidirect |
| 18. #16864031 | C22 | semidirect |
| 28. #16863584 | C22 | semidirect |
| 29. #16863583 | C22 | semidirect |
| 31. #16863582 | C22 | semidirect |
| 33. #16863576 | C22 | semidirect |
| 34. #16863574 | C22 | semidirect |
| 38. #16863377 | C22 | semidirect |
| 40. #16863368 | C22 | semidirect |
| 41. #16863190 | C22 | semidirect |
| 42. #16863189 | C22 | semidirect |
| 43. #16863184 | C22 | semidirect |
| 44. #16863183 | C22 | semidirect |
| 45. #16863182 | C22 | semidirect |
| 46. D42×C67 | C22 | semidirect |
| 47. B(4,𝔽2)×C67 | C22 | semidirect |
| 49. #353×C67 | C22 | semidirect |
| 50. AΣL(1,𝔽16)×C67 | C22 | semidirect |
| 59. C2×#11761627 | D4 | semidirect |
| 64. C22×C22⋊D67 | D4 | semidirect |
| 74. #14524043 | D4 | semidirect |
| 82. #14524030 | D4 | semidirect |
| 103. #14524013 | D4 | semidirect |
| 108. #14524012 | D4 | semidirect |
| 121. #14523999 | D4 | semidirect |
| 122. C42×D67 | D4 | semidirect |
| 405. #2196 | D67 | semidirect |
| 408. C67 | #33559 | semidirect |
| 417. D42 | C2×D67 | semidirect |
| 430. B(4,𝔽2) | C2×D67 | semidirect |
| 443. #353 | C2×D67 | semidirect |
| 447. AΣL(1,𝔽16) | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22574611 | 2 |
| #22569609 | 2 |
| #22569554 | 2 |
| #22562211 | 2 |
| #22562208 | 2 |
| #22562195 | 2 |
| #22562193 | 2 |
| #22562192 | 2 |
| #22561871 | 2 |
| #22561857 | 2 |
| C67×#2196 | 2 |
| #33559 | 67 |