Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1102 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 183 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 | #22574983 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #22573345 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #22569871 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22562162 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #22562157 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | C2×#16863207 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | C67×#2115 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #16864232 | — | 2 | 1 | no | — |
| 9 | #16864213 | — | 2 | 2 | no | — |
| 10 | #16864208 | — | 2 | 4 | no | — |
| 11 | #16864201 | — | 2 | 2 | no | — |
| 12 | #16864196 | — | 2 | 1 | no | — |
| 13 | #16864196 | C22 | 1 | 4 | yes | — |
| 14 | C2×#14524065 | — | 2 | 2 | no | — |
| 15 | C2×#14524065 | C22 | 1 | 2 | yes | — |
| 16 | C2×#14524065 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | #16863974 | — | 2 | 1 | no | — |
| 18 | #16863839 | — | 2 | 2 | no | — |
| 19 | #16863839 | C22 | 1 | 4 | yes | complemented |
| 20 | #16863834 | — | 2 | 2 | no | — |
| 21 | #16863834 | C22 | 1 | 4 | yes | complemented |
| 22 | #16863828 | — | 2 | 4 | no | — |
| 23 | #16863654 | C22 | 1 | 2 | yes | complemented |
| 24 | #16863649 | C22 | 1 | 2 | yes | complemented |
| 25 | #16863625 | — | 2 | 2 | no | — |
| 26 | C2×#14523975 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | #16863398 | — | 2 | 1 | no | — |
| 28 | #16863207 | C22 | 1 | 8 | yes | complemented |
| 29 | C2×#131×C67 | C22 | 1 | 1 | yes | characteristic |
| 30 | C2×M32×C67 | C22 | 1 | 2 | yes | complemented |
| 31 | #349×C67 | C22 | 1 | 4 | yes | complemented |
| 32 | #14524091 | — | 4 | 1 | no | — |
| 33 | #14524090 | — | 2 | 4 | no | — |
| 34 | #14524089 | — | 2 | 4 | no | — |
| 35 | #14524088 | — | 4 | 1 | no | — |
| 36 | #14524088 | — | 4 | 2 | no | — |
| 37 | C2×#11761628 | — | 2 | 4 | no | — |
| 38 | C2×#11761628 | — | 2 | 2 | no | — |
| 39 | C2×#11761628 | — | 2 | 1 | no | — |
| 40 | #41×D67 | — | 4 | 4 | no | — |
| 41 | #14524076 | — | 2 | 4 | no | — |
| 42 | #14524076 | — | 2 | 8 | no | — |
| 43 | #14524071 | — | 2 | 4 | no | — |
| 44 | #14524071 | — | 2 | 8 | no | — |
| 45 | #14524065 | — | 2 | 4 | no | — |
| 46 | #14524065 | — | 2 | 4 | no | — |
| 47 | #14524065 | — | 2 | 2 | no | — |
| 48 | #14524065 | — | 2 | 4 | no | — |
| 49 | #14524065 | — | 2 | 2 | no | — |
| 50 | #14524065 | — | 2 | 2 | no | — |
| 51 | #14524065 | — | 2 | 2 | no | — |
| 52 | #14524065 | D4 | 1 | 4 | yes | complemented |
| 53 | #14524065 | C23 | 1 | 4 | yes | — |
| 54 | C2×Dic268 | — | 2 | 2 | no | — |
| 55 | C2×Dic268 | D4 | 1 | 2 | yes | complemented |
| 56 | C2×Dic268 | C23 | 1 | 1 | yes | characteristic |
| 57 | C2×#11761617 | — | 2 | 4 | no | — |
| 58 | C2×#11761617 | — | 2 | 2 | no | — |
| 59 | C2×#11761617 | — | 2 | 1 | no | — |
| 60 | C2×D536 | — | 2 | 2 | no | — |
| 61 | C2×D536 | D4 | 1 | 2 | yes | complemented |
| 62 | C2×D536 | C23 | 1 | 1 | yes | characteristic |
| 63 | #14524022 | — | 2 | 2 | no | — |
| 64 | #14524019 | — | 4 | 1 | no | — |
| 65 | #14524017 | — | 2 | 2 | no | — |
| 66 | #14524015 | — | 4 | 2 | no | — |
| 67 | #14524014 | — | 4 | 1 | no | — |
| 68 | C2×C4⋊Dic67 | — | 2 | 1 | no | — |
| 69 | Dic536 | — | 2 | 4 | no | — |
| 70 | #14523988 | — | 2 | 4 | no | — |
| 71 | #14523988 | — | 2 | 4 | no | — |
| 72 | D1072 | — | 2 | 4 | no | — |
| 73 | #14523975 | — | 2 | 1 | no | — |
| 74 | #14523975 | C23 | 1 | 2 | yes | — |
| 75 | #14523968 | — | 2 | 2 | no | — |
| 76 | #14523965 | — | 2 | 2 | no | — |
| 77 | C2×#41×C67 | D4 | 1 | 1 | yes | characteristic |
| 78 | #131×C67 | — | 2 | 2 | no | — |
| 79 | #131×C67 | — | 2 | 2 | no | — |
| 80 | C2×M16×C67 | D4 | 1 | 1 | yes | characteristic |
| 81 | C2×M16×C67 | C23 | 1 | 2 | yes | — |
| 82 | C22×C8×C67 | D4 | 1 | 2 | yes | — |
| 83 | C22×C8×C67 | C23 | 1 | 1 | yes | characteristic |
| 84 | M32×C67 | — | 2 | 2 | no | — |
| 85 | M32×C67 | C23 | 1 | 4 | yes | — |
| 86 | C2×C16×C67 | — | 2 | 2 | no | — |
| 87 | #11761629 | — | 4 | 4 | no | — |
| 88 | #11761628 | — | 2 | 8 | no | — |
| 89 | #11761628 | — | 2 | 4 | no | — |
| 90 | #11761628 | — | 2 | 4 | no | — |
| 91 | #11761628 | — | 4 | 4 | no | — |
| 92 | #11761628 | — | 4 | 4 | no | — |
| 93 | #11761628 | — | 4 | 2 | no | — |
| 94 | #11761628 | — | 4 | 2 | no | — |
| 95 | #11761628 | — | 4 | 2 | no | — |
| 96 | #11761628 | — | 4 | 2 | no | — |
| 97 | #11761627 | — | 4 | 8 | no | — |
| 98 | #11761627 | — | 4 | 4 | no | — |
| 99 | C2×Dic134 | — | 2 | 4 | no | — |
| 100 | C2×Dic134 | — | 2 | 2 | no | — |
| 101 | C2×Dic134 | — | 2 | 1 | no | — |
| 102 | Q8×D67 | — | 4 | 4 | no | — |
| 103 | C2×D268 | — | 2 | 4 | no | — |
| 104 | C2×D268 | — | 2 | 2 | no | — |
| 105 | C2×D268 | — | 2 | 1 | no | — |
| 106 | C2×C22⋊D67 | — | 4 | 4 | no | — |
| 107 | C2×C22⋊D67 | — | 4 | 2 | no | — |
| 108 | C2×C22⋊D67 | — | 4 | 1 | no | — |
| 109 | C2×C22⋊D67 | — | 4 | 2 | no | — |
| 110 | D4×D67 | — | 4 | 8 | no | — |
| 111 | D4×D67 | — | 4 | 4 | no | — |
| 112 | C22×Dic67 | — | 4 | 1 | no | — |
| 113 | C2×C4×D67 | — | 4 | 4 | no | — |
| 114 | C2×C4×D67 | — | 4 | 2 | no | — |
| 115 | C2×C4×D67 | — | 4 | 1 | no | — |
| 116 | Dic268 | — | 2 | 4 | no | — |
| 117 | Dic268 | — | 2 | 2 | no | — |
| 118 | Dic268 | — | 2 | 2 | no | — |
| 119 | Dic268 | C2×D4 | 1 | 4 | yes | — |
| 120 | #11761617 | — | 2 | 8 | no | — |
| 121 | #11761617 | — | 2 | 4 | no | — |
| 122 | #11761617 | — | 2 | 4 | no | — |
| 123 | #11761617 | — | 4 | 1 | no | — |
| 124 | #11761617 | — | 4 | 1 | no | — |
| 125 | D536 | — | 2 | 4 | no | — |
| 126 | D536 | — | 2 | 2 | no | — |
| 127 | D536 | — | 2 | 2 | no | — |
| 128 | D536 | C2×D4 | 1 | 4 | yes | — |
| 129 | C4⋊Dic67 | — | 2 | 2 | no | — |
| 130 | C4⋊Dic67 | — | 4 | 1 | no | — |
| 131 | Dic67⋊C4 | — | 4 | 2 | no | — |
| 132 | C22⋊Dic67 | — | 4 | 2 | no | — |
| 133 | (C2×D67)⋊C4 | — | 4 | 2 | no | — |
| 134 | #41×C67 | — | 2 | 2 | no | — |
| 135 | #41×C67 | — | 2 | 2 | no | — |
| 136 | C2×Q8×C67 | D8 | 1 | 1 | yes | characteristic |
| 137 | C2×D4×C67 | D8 | 1 | 1 | yes | characteristic |
| 138 | C2×D4×C67 | D8 | 1 | 2 | yes | — |
| 139 | C22×C4×C67 | C2×D4 | 1 | 2 | yes | — |
| 140 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 141 | M16×C67 | — | 2 | 2 | no | — |
| 142 | M16×C67 | — | 2 | 4 | no | — |
| 143 | C2×C8×C67 | — | 2 | 2 | no | — |
| 144 | C2×C8×C67 | — | 2 | 2 | no | — |
| 145 | C2×C8×C67 | C2×D4 | 1 | 2 | yes | — |
| 146 | C2×C8×C67 | C2×D4 | 1 | 2 | yes | — |
| 147 | C2×C8×C67 | C2×D4 | 1 | 2 | yes | — |
| 148 | C2×C8×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 149 | C2×C8×C67 | C24 | 1 | 1 | yes | characteristic |
| 150 | C16×C67 | — | 2 | 4 | no | — |
| 151 | C23×C67 | C2×D8 | 1 | 2 | yes | — |
| 152 | C23×C67 | C2×D8 | 1 | 1 | yes | characteristic |
| 153 | C22×D67 | — | 4 | 4 | no | — |
| 154 | C22×D67 | — | 4 | 2 | no | — |
| 155 | C22×D67 | — | 4 | 1 | no | — |
| 156 | Q8×C67 | — | 2 | 2 | no | — |
| 157 | D4×C67 | — | 2 | 4 | no | — |
| 158 | D4×C67 | — | 2 | 2 | no | — |
| 159 | C2×C4×C67 | — | 2 | 2 | no | — |
| 160 | C2×C4×C67 | — | 2 | 2 | no | — |
| 161 | C2×C4×C67 | #120 | 1 | 2 | yes | — |
| 162 | C2×C4×C67 | C2×D8 | 1 | 2 | yes | — |
| 163 | C2×C4×C67 | C2×D8 | 1 | 1 | yes | characteristic |
| 164 | C2×C4×C67 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 165 | C2×C4×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 166 | C22⋊D67 | — | 4 | 8 | no | — |
| 167 | C22⋊D67 | — | 4 | 4 | no | — |
| 168 | C22⋊D67 | — | 4 | 4 | no | — |
| 169 | C22⋊D67 | — | 8 | 2 | no | — |
| 170 | C22⋊D67 | — | 16 | 2 | no | — |
| 171 | C2×Dic67 | — | 4 | 4 | no | — |
| 172 | C2×Dic67 | — | 4 | 2 | no | — |
| 173 | C2×Dic67 | — | 4 | 2 | no | — |
| 174 | C2×Dic67 | — | 4 | 1 | no | — |
| 175 | C2×Dic67 | — | 16 | 1 | no | — |
| 176 | D268 | — | 2 | 4 | no | — |
| 177 | D268 | — | 4 | 4 | no | — |
| 178 | D268 | — | 4 | 1 | no | — |
| 179 | D268 | — | 4 | 1 | no | — |
| 180 | D268 | — | 4 | 2 | no | — |
| 181 | C4×D67 | — | 4 | 8 | no | — |
| 182 | C4×D67 | — | 4 | 4 | no | — |
| 183 | C4×D67 | — | 4 | 4 | no | — |
| 184 | C4×D67 | — | 8 | 2 | no | — |
| 185 | Dic134 | — | 2 | 4 | no | — |
| 186 | Dic134 | — | 4 | 4 | no | — |
| 187 | Dic134 | — | 4 | 2 | no | — |
| 188 | Dic134 | — | 4 | 1 | no | — |
| 189 | Dic134 | — | 4 | 1 | no | — |
| 190 | C8×C67 | — | 2 | 2 | no | — |
| 191 | C8×C67 | #120 | 1 | 1 | yes | characteristic |
| 192 | C8×C67 | #120 | 1 | 1 | yes | characteristic |
| 193 | C8×C67 | C22×D4 | 1 | 2 | yes | — |
| 194 | C22×C67 | — | 2 | 2 | no | — |
| 195 | C22×C67 | — | 4 | 1 | no | — |
| 196 | C22×C67 | — | 4 | 2 | no | — |
| 197 | C22×C67 | #447 | 1 | 2 | yes | — |
| 198 | C22×C67 | C22×D8 | 1 | 1 | yes | characteristic |
| 199 | C2×D67 | — | 4 | 4 | no | — |
| 200 | C2×D67 | — | 8 | 1 | no | — |
| 201 | C2×D67 | — | 8 | 1 | no | — |
| 202 | C2×D67 | — | 8 | 1 | no | — |
| 203 | C2×D67 | — | 16 | 2 | no | — |
| 204 | C2×D67 | — | 16 | 4 | no | — |
| 205 | C4×C67 | — | 2 | 2 | no | — |
| 206 | C4×C67 | #447 | 1 | 2 | yes | — |
| 207 | C4×C67 | C2×#120 | 1 | 1 | yes | characteristic |
| 208 | C4×C67 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 209 | Dic67 | — | 4 | 4 | no | — |
| 210 | Dic67 | — | 8 | 2 | no | — |
| 211 | Dic67 | — | 8 | 1 | no | — |
| 212 | #33533 | — | 67 | 1 | no | maximal, Sylow |
| 213 | C2×C67 | — | 2 | 1 | no | — |
| 214 | C2×C67 | — | 2 | 2 | no | — |
| 215 | C2×C67 | — | 4 | 2 | no | — |
| 216 | C2×C67 | C2×#447 | 1 | 1 | yes | characteristic |
| 217 | D67 | — | 8 | 4 | no | — |
| 218 | D67 | — | 16 | 1 | no | — |
| 219 | #3584 | — | 67 | 1 | no | — |
| 220 | #3414 | — | 67 | 2 | no | — |
| 221 | #3060 | — | 67 | 1 | no | — |
| 222 | #2191 | — | 67 | 4 | no | — |
| 223 | #2190 | — | 67 | 4 | no | — |
| 224 | C2×#360 | — | 67 | 2 | no | — |
| 225 | #2115 | D67 | 1 | 1 | yes | characteristic, complemented |
| 226 | C67 | #33533 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 227 | #585 | — | 134 | 1 | no | — |
| 228 | #578 | — | 134 | 2 | no | — |
| 229 | #577 | — | 134 | 4 | no | — |
| 230 | #576 | — | 134 | 2 | no | — |
| 231 | #575 | — | 67 | 4 | no | — |
| 232 | #575 | — | 134 | 1 | no | — |
| 233 | C2×#135 | — | 67 | 2 | no | — |
| 234 | C2×#135 | — | 67 | 1 | no | — |
| 235 | C2×#135 | — | 134 | 2 | no | — |
| 236 | C2×#131 | C2×D67 | 1 | 1 | yes | characteristic |
| 237 | #537 | — | 134 | 1 | no | — |
| 238 | #510 | — | 67 | 4 | no | — |
| 239 | #510 | — | 134 | 2 | no | — |
| 240 | #509 | — | 67 | 4 | no | — |
| 241 | #509 | — | 134 | 2 | no | — |
| 242 | #508 | — | 134 | 4 | no | — |
| 243 | C2×M32 | C2×D67 | 1 | 2 | yes | complemented |
| 244 | #470 | — | 67 | 2 | no | — |
| 245 | #469 | — | 67 | 2 | no | — |
| 246 | #465 | — | 134 | 2 | no | — |
| 247 | C2×#106 | — | 67 | 1 | no | — |
| 248 | #417 | — | 134 | 1 | no | — |
| 249 | #360 | — | 67 | 8 | no | — |
| 250 | #349 | C2×D67 | 1 | 4 | yes | complemented |
| 251 | 2−1+4 | — | 268 | 1 | no | — |
| 252 | 2−1+4 | — | 134 | 4 | no | — |
| 253 | H(5,𝔽2) | — | 268 | 2 | no | — |
| 254 | H(5,𝔽2) | — | 268 | 1 | no | — |
| 255 | H(5,𝔽2) | — | 134 | 4 | no | — |
| 256 | C2×#41 | — | 268 | 4 | no | — |
| 257 | C2×#41 | — | 134 | 4 | no | — |
| 258 | C2×#41 | — | 134 | 1 | no | — |
| 259 | C2×#41 | — | 134 | 2 | no | — |
| 260 | C2×#41 | D268 | 1 | 1 | yes | characteristic |
| 261 | #137 | — | 134 | 8 | no | — |
| 262 | #137 | — | 134 | 4 | no | — |
| 263 | AGL(1,ℤ/8) | — | 134 | 8 | no | — |
| 264 | AGL(1,ℤ/8) | — | 134 | 4 | no | — |
| 265 | #135 | — | 67 | 4 | no | — |
| 266 | #135 | — | 67 | 4 | no | — |
| 267 | #135 | — | 134 | 4 | no | — |
| 268 | #135 | — | 134 | 4 | no | — |
| 269 | #135 | — | 134 | 2 | no | — |
| 270 | #135 | — | 134 | 2 | no | — |
| 271 | #135 | — | 134 | 2 | no | — |
| 272 | #135 | — | 134 | 2 | no | — |
| 273 | #135 | — | 134 | 4 | no | — |
| 274 | C2×Q16 | — | 67 | 2 | no | — |
| 275 | C2×Q16 | — | 67 | 1 | no | — |
| 276 | C2×Q16 | — | 134 | 2 | no | — |
| 277 | C2×SD16 | — | 134 | 4 | no | — |
| 278 | C2×SD16 | — | 134 | 2 | no | — |
| 279 | C2×SD16 | — | 134 | 1 | no | — |
| 280 | C2×D8 | — | 67 | 2 | no | — |
| 281 | C2×D8 | — | 67 | 1 | no | — |
| 282 | C2×D8 | — | 134 | 2 | no | — |
| 283 | #131 | — | 2 | 2 | no | — |
| 284 | #131 | — | 2 | 2 | no | — |
| 285 | C2×M16 | D268 | 1 | 1 | yes | characteristic |
| 286 | C2×M16 | C22×D67 | 1 | 2 | yes | — |
| 287 | C22×C8 | D268 | 1 | 2 | yes | — |
| 288 | C22×C8 | C22×D67 | 1 | 1 | yes | characteristic |
| 289 | C22⋊Q8 | — | 268 | 1 | no | — |
| 290 | C22⋊Q8 | — | 134 | 2 | no | — |
| 291 | #121 | — | 268 | 1 | no | — |
| 292 | #121 | — | 268 | 2 | no | — |
| 293 | #121 | — | 134 | 2 | no | — |
| 294 | C2×C4⋊C4 | — | 134 | 1 | no | — |
| 295 | Q32 | — | 134 | 4 | no | — |
| 296 | SD32 | — | 134 | 4 | no | — |
| 297 | SD32 | — | 134 | 4 | no | — |
| 298 | D16 | — | 134 | 4 | no | — |
| 299 | M32 | — | 2 | 2 | no | — |
| 300 | M32 | C22×D67 | 1 | 4 | yes | — |
| 301 | C2×C16 | — | 2 | 2 | no | — |
| 302 | #106 | — | 67 | 2 | no | — |
| 303 | #106 | — | 134 | 1 | no | — |
| 304 | #103 | — | 134 | 2 | no | — |
| 305 | #102 | — | 134 | 2 | no | — |
| 306 | #41 | — | 2 | 2 | no | — |
| 307 | #41 | — | 2 | 2 | no | — |
| 308 | #41 | — | 268 | 4 | no | — |
| 309 | #41 | — | 268 | 8 | no | — |
| 310 | #41 | — | 268 | 4 | no | — |
| 311 | #41 | — | 268 | 4 | no | — |
| 312 | #41 | — | 268 | 4 | no | — |
| 313 | #41 | — | 268 | 2 | no | — |
| 314 | #41 | — | 268 | 2 | no | — |
| 315 | #41 | — | 268 | 2 | no | — |
| 316 | #41 | — | 268 | 2 | no | — |
| 317 | #41 | — | 134 | 8 | no | — |
| 318 | #41 | — | 134 | 4 | no | — |
| 319 | #41 | — | 134 | 4 | no | — |
| 320 | C2×Q8 | — | 268 | 4 | no | — |
| 321 | C2×Q8 | — | 134 | 4 | no | — |
| 322 | C2×Q8 | — | 134 | 2 | no | — |
| 323 | C2×Q8 | — | 134 | 1 | no | — |
| 324 | C2×Q8 | D536 | 1 | 1 | yes | characteristic |
| 325 | C2×D4 | — | 268 | 8 | no | — |
| 326 | C2×D4 | — | 268 | 4 | no | — |
| 327 | C2×D4 | — | 268 | 4 | no | — |
| 328 | C2×D4 | — | 268 | 2 | no | — |
| 329 | C2×D4 | — | 268 | 1 | no | — |
| 330 | C2×D4 | — | 268 | 2 | no | — |
| 331 | C2×D4 | — | 134 | 4 | no | — |
| 332 | C2×D4 | — | 134 | 2 | no | — |
| 333 | C2×D4 | — | 134 | 1 | no | — |
| 334 | C2×D4 | D536 | 1 | 2 | yes | — |
| 335 | C2×D4 | D536 | 1 | 1 | yes | characteristic |
| 336 | C22×C4 | — | 268 | 4 | no | — |
| 337 | C22×C4 | — | 268 | 2 | no | — |
| 338 | C22×C4 | — | 268 | 1 | no | — |
| 339 | C22×C4 | — | 268 | 1 | no | — |
| 340 | C22×C4 | C2×D268 | 1 | 2 | yes | — |
| 341 | C22×C4 | C2×D268 | 1 | 1 | yes | characteristic |
| 342 | Q16 | — | 67 | 4 | no | — |
| 343 | Q16 | — | 134 | 4 | no | — |
| 344 | Q16 | — | 134 | 2 | no | — |
| 345 | Q16 | — | 134 | 2 | no | — |
| 346 | SD16 | — | 268 | 1 | no | — |
| 347 | SD16 | — | 268 | 1 | no | — |
| 348 | SD16 | — | 134 | 8 | no | — |
| 349 | SD16 | — | 134 | 4 | no | — |
| 350 | SD16 | — | 134 | 4 | no | — |
| 351 | D8 | — | 67 | 4 | no | — |
| 352 | D8 | — | 134 | 4 | no | — |
| 353 | D8 | — | 134 | 2 | no | — |
| 354 | D8 | — | 134 | 2 | no | — |
| 355 | M16 | — | 2 | 2 | no | — |
| 356 | M16 | — | 2 | 4 | no | — |
| 357 | C2×C8 | — | 2 | 2 | no | — |
| 358 | C2×C8 | — | 2 | 2 | no | — |
| 359 | C2×C8 | D4×D67 | 1 | 2 | yes | — |
| 360 | C2×C8 | D4×D67 | 1 | 2 | yes | — |
| 361 | C2×C8 | C2×D268 | 1 | 2 | yes | — |
| 362 | C2×C8 | C2×D268 | 1 | 1 | yes | characteristic |
| 363 | C2×C8 | C23×D67 | 1 | 1 | yes | characteristic |
| 364 | C4⋊C4 | — | 268 | 1 | no | — |
| 365 | C4⋊C4 | — | 268 | 2 | no | — |
| 366 | C4⋊C4 | — | 134 | 2 | no | — |
| 367 | C22⋊C4 | — | 268 | 2 | no | — |
| 368 | C22⋊C4 | — | 268 | 2 | no | — |
| 369 | C16 | — | 2 | 4 | no | — |
| 370 | C23 | — | 268 | 4 | no | — |
| 371 | C23 | — | 268 | 2 | no | — |
| 372 | C23 | — | 268 | 1 | no | — |
| 373 | C23 | C2×D536 | 1 | 2 | yes | — |
| 374 | C23 | C2×D536 | 1 | 1 | yes | characteristic |
| 375 | Q8 | — | 2 | 2 | no | — |
| 376 | Q8 | — | 268 | 4 | no | — |
| 377 | Q8 | — | 268 | 2 | no | — |
| 378 | Q8 | — | 268 | 1 | no | — |
| 379 | Q8 | — | 268 | 1 | no | — |
| 380 | Q8 | — | 134 | 4 | no | — |
| 381 | D4 | — | 2 | 4 | no | — |
| 382 | D4 | — | 2 | 2 | no | — |
| 383 | D4 | — | 268 | 4 | no | — |
| 384 | D4 | — | 268 | 8 | no | — |
| 385 | D4 | — | 268 | 4 | no | — |
| 386 | D4 | — | 268 | 4 | no | — |
| 387 | D4 | — | 268 | 2 | no | — |
| 388 | D4 | — | 268 | 1 | no | — |
| 389 | D4 | — | 268 | 1 | no | — |
| 390 | D4 | — | 536 | 2 | no | — |
| 391 | D4 | — | 1072 | 2 | no | — |
| 392 | D4 | — | 134 | 4 | no | — |
| 393 | C2×C4 | — | 2 | 2 | no | — |
| 394 | C2×C4 | — | 2 | 2 | no | — |
| 395 | C2×C4 | — | 268 | 8 | no | — |
| 396 | C2×C4 | — | 268 | 4 | no | — |
| 397 | C2×C4 | — | 268 | 2 | no | — |
| 398 | C2×C4 | — | 268 | 4 | no | — |
| 399 | C2×C4 | — | 268 | 4 | no | — |
| 400 | C2×C4 | — | 268 | 2 | no | — |
| 401 | C2×C4 | — | 268 | 1 | no | — |
| 402 | C2×C4 | — | 536 | 2 | no | — |
| 403 | C2×C4 | — | 1072 | 1 | no | — |
| 404 | C2×C4 | #14524013 | 1 | 2 | yes | — |
| 405 | C2×C4 | C2×D536 | 1 | 2 | yes | — |
| 406 | C2×C4 | C2×D536 | 1 | 1 | yes | characteristic |
| 407 | C2×C4 | #14524071 | 1 | 2 | yes | — |
| 408 | C2×C4 | C22×D268 | 1 | 1 | yes | characteristic |
| 409 | C8 | — | 2 | 2 | no | — |
| 410 | C8 | #14524013 | 1 | 1 | yes | characteristic |
| 411 | C8 | #14524013 | 1 | 1 | yes | characteristic |
| 412 | C8 | C2×D4×D67 | 1 | 2 | yes | — |
| 413 | C22 | — | 2 | 2 | no | — |
| 414 | C22 | — | 4 | 1 | no | — |
| 415 | C22 | — | 4 | 2 | no | — |
| 416 | C22 | — | 268 | 4 | no | — |
| 417 | C22 | — | 536 | 1 | no | — |
| 418 | C22 | — | 536 | 1 | no | — |
| 419 | C22 | — | 536 | 1 | no | — |
| 420 | C22 | — | 1072 | 2 | no | — |
| 421 | C22 | — | 1072 | 4 | no | — |
| 422 | C22 | #16863532 | 1 | 2 | yes | — |
| 423 | C22 | C22×D536 | 1 | 1 | yes | characteristic |
| 424 | C4 | — | 2 | 2 | no | — |
| 425 | C4 | — | 268 | 4 | no | — |
| 426 | C4 | — | 536 | 2 | no | — |
| 427 | C4 | — | 536 | 1 | no | — |
| 428 | C4 | #16863532 | 1 | 2 | yes | — |
| 429 | C4 | C2×#14524013 | 1 | 1 | yes | characteristic |
| 430 | C4 | C2×#14524071 | 1 | 1 | yes | characteristic |
| 431 | C2 | — | 2 | 1 | no | — |
| 432 | C2 | — | 2 | 2 | no | — |
| 433 | C2 | — | 4 | 2 | no | — |
| 434 | C2 | — | 536 | 4 | no | — |
| 435 | C2 | — | 1072 | 1 | no | — |
| 436 | C2 | C2×#16863532 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22574983 | C2 | semidirect |
| 2. #22573345 | C2 | semidirect |
| 3. #22569871 | C2 | semidirect |
| 4. #22562162 | C2 | semidirect |
| 5. #22562157 | C2 | semidirect |
| 6. C2×#16863207 | C2 | semidirect |
| 7. C67×#2115 | C2 | semidirect |
| 16. C2×#14524065 | C22 | semidirect |
| 19. #16863839 | C22 | semidirect |
| 21. #16863834 | C22 | semidirect |
| 23. #16863654 | C22 | semidirect |
| 24. #16863649 | C22 | semidirect |
| 26. C2×#14523975 | C22 | semidirect |
| 28. #16863207 | C22 | semidirect |
| 30. C2×M32×C67 | C22 | semidirect |
| 31. #349×C67 | C22 | semidirect |
| 52. #14524065 | D4 | semidirect |
| 55. C2×Dic268 | D4 | semidirect |
| 61. C2×D536 | D4 | semidirect |
| 225. #2115 | D67 | semidirect |
| 226. C67 | #33533 | semidirect |
| 243. C2×M32 | C2×D67 | semidirect |
| 250. #349 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22574983 | 2 |
| #22573345 | 2 |
| #22569871 | 2 |
| #22562162 | 2 |
| #22562157 | 2 |
| C2×#16863207 | 2 |
| C67×#2115 | 2 |
| #33533 | 67 |