Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1938 conjugacy classes of subgroups; only the 227 normal subgroups are shown.
This group has 1938 conjugacy classes of subgroups — too many to draw. Only its 227 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 | D7×#575 | C2 | 1 | 3 | yes | maximal, complemented |
| 2 | D7×#408 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | C7×#2017 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11729875 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #11727767 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #11726481 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | D7×#338 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×D7×#41 | C22 | 1 | 3 | yes | — |
| 9 | C7×#575 | C22 | 1 | 3 | yes | complemented |
| 10 | #90513 | C22 | 1 | 6 | yes | complemented |
| 11 | #90468 | — | 2 | 6 | no | — |
| 12 | D7×#137 | — | 2 | 6 | no | — |
| 13 | #90464 | — | 2 | 6 | no | — |
| 14 | D7×AGL(1,ℤ/8) | — | 2 | 6 | no | — |
| 15 | #90459 | — | 2 | 6 | no | — |
| 16 | D7×#135 | — | 2 | 6 | no | — |
| 17 | #90439 | C22 | 1 | 3 | yes | complemented |
| 18 | C2×D7×M16 | C22 | 1 | 3 | yes | — |
| 19 | C22×C8×D7 | C22 | 1 | 1 | yes | characteristic |
| 20 | C7×#408 | C22 | 1 | 3 | yes | complemented |
| 21 | #90006 | C22 | 1 | 3 | yes | complemented |
| 22 | #89901 | C22 | 1 | 3 | yes | complemented |
| 23 | #89882 | C22 | 1 | 3 | yes | complemented |
| 24 | #89499 | — | 2 | 6 | no | — |
| 25 | D7×C22⋊C8 | — | 2 | 6 | no | — |
| 26 | C7×#338 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | C7⋊#338 | C22 | 1 | 3 | yes | complemented |
| 28 | C2×#2017 | — | 7 | 1 | no | maximal, Sylow |
| 29 | C2×C7×#41 | C23 | 1 | 3 | yes | — |
| 30 | D7×#41 | — | 2 | 6 | no | — |
| 31 | D7×#41 | — | 2 | 6 | no | — |
| 32 | D7×#41 | — | 2 | 6 | no | — |
| 33 | D7×#41 | — | 2 | 6 | no | — |
| 34 | C2×#1161 | D4 | 1 | 3 | yes | — |
| 35 | C2×Q8×D7 | D4 | 1 | 3 | yes | — |
| 36 | C2×#1159 | — | 2 | 3 | no | — |
| 37 | C2×#1159 | D4 | 1 | 3 | yes | — |
| 38 | C2×D4×D7 | — | 2 | 3 | no | — |
| 39 | C2×D4×D7 | D4 | 1 | 3 | yes | — |
| 40 | C2×#1157 | — | 2 | 3 | no | — |
| 41 | C2×#1157 | C23 | 1 | 3 | yes | — |
| 42 | C22×C4×D7 | — | 2 | 3 | no | — |
| 43 | C22×C4×D7 | C23 | 1 | 1 | yes | characteristic |
| 44 | C7×#137 | — | 2 | 6 | no | — |
| 45 | C7×AGL(1,ℤ/8) | — | 2 | 6 | no | — |
| 46 | C7×#135 | — | 2 | 6 | no | — |
| 47 | C2×C7×M16 | C23 | 1 | 3 | yes | — |
| 48 | C22×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 49 | #6514 | — | 2 | 6 | no | — |
| 50 | #6513 | — | 2 | 12 | no | — |
| 51 | #6512 | — | 2 | 6 | no | — |
| 52 | #6505 | — | 2 | 6 | no | — |
| 53 | #6495 | — | 2 | 6 | no | — |
| 54 | C2×#1136 | C23 | 1 | 3 | yes | — |
| 55 | C22×C7⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 56 | #6482 | — | 2 | 6 | no | — |
| 57 | #6481 | — | 2 | 12 | no | — |
| 58 | D7×Q16 | — | 2 | 6 | no | — |
| 59 | #6479 | — | 2 | 12 | no | — |
| 60 | #6478 | — | 2 | 12 | no | — |
| 61 | #6477 | — | 2 | 12 | no | — |
| 62 | D7×SD16 | — | 2 | 12 | no | — |
| 63 | #6475 | — | 2 | 6 | no | — |
| 64 | #6474 | — | 2 | 12 | no | — |
| 65 | D7×D8 | — | 2 | 6 | no | — |
| 66 | #6472 | — | 2 | 6 | no | — |
| 67 | #6471 | — | 2 | 6 | no | — |
| 68 | D7×M16 | — | 2 | 6 | no | — |
| 69 | D7×M16 | — | 2 | 6 | no | — |
| 70 | #6467 | — | 2 | 6 | no | — |
| 71 | C2×#1131 | D4 | 1 | 6 | yes | — |
| 72 | C2×C8×D7 | — | 2 | 3 | no | — |
| 73 | C2×C8×D7 | — | 2 | 3 | no | — |
| 74 | C2×C8×D7 | D4 | 1 | 6 | yes | — |
| 75 | C7×C22⋊C8 | — | 2 | 6 | no | — |
| 76 | C22⋊(C7⋊C8) | — | 2 | 6 | no | — |
| 77 | (C2×D7)⋊C8 | — | 2 | 6 | no | — |
| 78 | (C2×D7)⋊C8 | — | 2 | 6 | no | — |
| 79 | C2×#575 | — | 7 | 3 | no | — |
| 80 | C2×#408 | — | 7 | 3 | no | — |
| 81 | #2017 | — | 7 | 3 | no | — |
| 82 | #2017 | — | 7 | 1 | no | — |
| 83 | #2017 | — | 7 | 3 | no | — |
| 84 | #2017 | D7 | 1 | 1 | yes | characteristic, direct product factor |
| 85 | C2×#338 | — | 7 | 1 | no | — |
| 86 | C23×D7 | — | 2 | 3 | no | — |
| 87 | C23×D7 | #41 | 1 | 1 | yes | characteristic |
| 88 | C7×#41 | — | 2 | 6 | no | — |
| 89 | C7×#41 | — | 2 | 6 | no | — |
| 90 | C2×C7×Q8 | C2×D4 | 1 | 3 | yes | — |
| 91 | C2×C7×D4 | — | 2 | 3 | no | — |
| 92 | C2×C7×D4 | C2×D4 | 1 | 3 | yes | — |
| 93 | C22×C4×C7 | — | 2 | 3 | no | — |
| 94 | C22×C4×C7 | C24 | 1 | 1 | yes | characteristic |
| 95 | C2×C22⋊D7 | — | 2 | 3 | no | — |
| 96 | C2×C22⋊D7 | — | 2 | 3 | no | — |
| 97 | C2×C22⋊D7 | — | 2 | 3 | no | — |
| 98 | C22×Dic7 | — | 2 | 3 | no | — |
| 99 | C22×Dic7 | #41 | 1 | 1 | yes | characteristic |
| 100 | #1161 | — | 2 | 6 | no | — |
| 101 | #1161 | — | 2 | 6 | no | — |
| 102 | Q8×D7 | — | 2 | 6 | no | — |
| 103 | Q8×D7 | — | 2 | 6 | no | — |
| 104 | #1159 | — | 2 | 6 | no | — |
| 105 | #1159 | — | 2 | 6 | no | — |
| 106 | #1159 | — | 4 | 6 | no | — |
| 107 | #1159 | — | 4 | 6 | no | — |
| 108 | D4×D7 | — | 2 | 6 | no | — |
| 109 | D4×D7 | — | 2 | 6 | no | — |
| 110 | D4×D7 | — | 4 | 6 | no | — |
| 111 | D4×D7 | — | 4 | 6 | no | — |
| 112 | #1157 | — | 2 | 6 | no | — |
| 113 | #1157 | — | 2 | 6 | no | — |
| 114 | #1157 | — | 4 | 6 | no | — |
| 115 | #1157 | — | 4 | 6 | no | — |
| 116 | C2×D28 | — | 2 | 3 | no | — |
| 117 | C2×D28 | C2×D4 | 1 | 3 | yes | — |
| 118 | C2×C4×D7 | — | 2 | 3 | no | — |
| 119 | C2×C4×D7 | — | 2 | 3 | no | — |
| 120 | C2×C4×D7 | — | 2 | 3 | no | — |
| 121 | C2×C4×D7 | — | 4 | 3 | no | — |
| 122 | C2×C4×D7 | — | 4 | 3 | no | — |
| 123 | C2×C4×D7 | — | 4 | 3 | no | — |
| 124 | C2×C4×D7 | — | 4 | 3 | no | — |
| 125 | C2×C4×D7 | C2×D4 | 1 | 3 | yes | — |
| 126 | C2×C4×D7 | C2×D4 | 1 | 3 | yes | — |
| 127 | C2×C4×D7 | C2×D4 | 1 | 3 | yes | — |
| 128 | C2×C4×D7 | C2×D4 | 1 | 3 | yes | — |
| 129 | C2×Dic14 | — | 2 | 3 | no | — |
| 130 | C2×Dic14 | C2×D4 | 1 | 3 | yes | — |
| 131 | C7×Q16 | — | 2 | 6 | no | — |
| 132 | C7×SD16 | — | 2 | 12 | no | — |
| 133 | C7×D8 | — | 2 | 6 | no | — |
| 134 | C7×M16 | — | 2 | 6 | no | — |
| 135 | C2×C7×C8 | — | 2 | 3 | no | — |
| 136 | C2×C7×C8 | C2×D4 | 1 | 6 | yes | — |
| 137 | #1144 | — | 2 | 12 | no | — |
| 138 | #1143 | — | 2 | 12 | no | — |
| 139 | #1142 | — | 2 | 12 | no | — |
| 140 | #1141 | — | 2 | 12 | no | — |
| 141 | #1136 | — | 2 | 6 | no | — |
| 142 | C2×C7⋊C8 | — | 2 | 3 | no | — |
| 143 | C2×C7⋊C8 | C2×D4 | 1 | 6 | yes | — |
| 144 | Dic28 | — | 2 | 6 | no | — |
| 145 | D56 | — | 2 | 6 | no | — |
| 146 | #1132 | — | 2 | 12 | no | — |
| 147 | #1131 | — | 2 | 12 | no | — |
| 148 | C8×D7 | — | 2 | 6 | no | — |
| 149 | C8×D7 | — | 2 | 6 | no | — |
| 150 | C8×D7 | — | 4 | 1 | no | — |
| 151 | C8×D7 | — | 4 | 3 | no | — |
| 152 | C22×#41 | — | 7 | 3 | no | — |
| 153 | #575 | — | 7 | 6 | no | — |
| 154 | #575 | — | 7 | 3 | no | — |
| 155 | #575 | — | 14 | 6 | no | — |
| 156 | #575 | — | 14 | 6 | no | — |
| 157 | #575 | — | 14 | 6 | no | — |
| 158 | #575 | C2×D7 | 1 | 3 | yes | complemented |
| 159 | C2×#137 | — | 14 | 6 | no | — |
| 160 | C2×AGL(1,ℤ/8) | — | 14 | 6 | no | — |
| 161 | C2×#135 | — | 14 | 6 | no | — |
| 162 | C22×M16 | — | 7 | 3 | no | — |
| 163 | C23×C8 | — | 7 | 1 | no | — |
| 164 | #408 | — | 7 | 3 | no | — |
| 165 | #408 | — | 7 | 3 | no | — |
| 166 | #408 | — | 7 | 3 | no | — |
| 167 | #408 | — | 14 | 6 | no | — |
| 168 | #408 | C2×D7 | 1 | 3 | yes | complemented |
| 169 | C2×C22⋊C8 | — | 14 | 6 | no | — |
| 170 | #338 | — | 7 | 3 | no | — |
| 171 | #338 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 172 | C23×C7 | — | 2 | 3 | no | — |
| 173 | C23×C7 | C2×#41 | 1 | 1 | yes | characteristic |
| 174 | C22×D7 | — | 2 | 3 | no | — |
| 175 | C22×D7 | — | 4 | 2 | no | — |
| 176 | C22×D7 | — | 4 | 12 | no | — |
| 177 | C22×D7 | — | 4 | 3 | no | — |
| 178 | C22×D7 | — | 4 | 3 | no | — |
| 179 | C22×D7 | #121 | 1 | 3 | yes | — |
| 180 | C22×D7 | #121 | 1 | 3 | yes | — |
| 181 | C7×Q8 | — | 2 | 6 | no | — |
| 182 | C7×D4 | — | 2 | 6 | no | — |
| 183 | C7×D4 | — | 4 | 6 | no | — |
| 184 | C2×C4×C7 | — | 2 | 3 | no | — |
| 185 | C2×C4×C7 | — | 4 | 3 | no | — |
| 186 | C2×C4×C7 | — | 4 | 3 | no | — |
| 187 | C2×C4×C7 | C22×D4 | 1 | 3 | yes | — |
| 188 | C2×C4×C7 | C22×D4 | 1 | 3 | yes | — |
| 189 | C22⋊D7 | — | 4 | 6 | no | — |
| 190 | C22⋊D7 | — | 4 | 6 | no | — |
| 191 | C22⋊D7 | — | 4 | 6 | no | — |
| 192 | C2×Dic7 | — | 2 | 3 | no | — |
| 193 | C2×Dic7 | — | 4 | 3 | no | — |
| 194 | C2×Dic7 | — | 4 | 3 | no | — |
| 195 | C2×Dic7 | #121 | 1 | 3 | yes | — |
| 196 | C2×Dic7 | #121 | 1 | 3 | yes | — |
| 197 | D28 | — | 2 | 6 | no | — |
| 198 | D28 | — | 4 | 6 | no | — |
| 199 | C4×D7 | — | 4 | 3 | no | — |
| 200 | C4×D7 | — | 4 | 3 | no | — |
| 201 | C4×D7 | — | 4 | 3 | no | — |
| 202 | C4×D7 | — | 4 | 3 | no | — |
| 203 | C4×D7 | — | 4 | 3 | no | — |
| 204 | C4×D7 | — | 4 | 3 | no | — |
| 205 | C4×D7 | #120 | 1 | 3 | yes | — |
| 206 | C4×D7 | #120 | 1 | 3 | yes | — |
| 207 | C4×D7 | #120 | 1 | 6 | yes | — |
| 208 | C4×D7 | #127 | 1 | 1 | yes | characteristic |
| 209 | C4×D7 | #127 | 1 | 3 | yes | — |
| 210 | Dic14 | — | 2 | 6 | no | — |
| 211 | Dic14 | — | 4 | 6 | no | — |
| 212 | C7×C8 | — | 2 | 6 | no | — |
| 213 | C7×C8 | — | 4 | 1 | no | — |
| 214 | C7⋊C8 | — | 2 | 6 | no | — |
| 215 | C7⋊C8 | — | 4 | 1 | no | — |
| 216 | C2×#41 | — | 7 | 3 | no | — |
| 217 | C2×#41 | — | 7 | 3 | no | — |
| 218 | C2×#41 | — | 7 | 3 | no | — |
| 219 | C2×#41 | — | 14 | 3 | no | — |
| 220 | C2×#41 | — | 14 | 3 | no | — |
| 221 | C2×#41 | — | 14 | 6 | no | — |
| 222 | C2×#41 | — | 14 | 6 | no | — |
| 223 | C2×#41 | — | 14 | 6 | no | — |
| 224 | C2×#41 | — | 14 | 6 | no | — |
| 225 | C2×#41 | C22×D7 | 1 | 3 | yes | — |
| 226 | C22×Q8 | — | 7 | 3 | no | — |
| 227 | C22×D4 | — | 7 | 3 | no | — |
| 228 | C22×D4 | — | 14 | 3 | no | — |
| 229 | C23×C4 | — | 7 | 1 | no | — |
| 230 | C23×C4 | — | 14 | 3 | no | — |
| 231 | #137 | — | 2 | 6 | no | — |
| 232 | #137 | — | 14 | 6 | no | — |
| 233 | #137 | — | 14 | 12 | no | — |
| 234 | #137 | — | 14 | 12 | no | — |
| 235 | #137 | — | 14 | 6 | no | — |
| 236 | #137 | — | 14 | 6 | no | — |
| 237 | AGL(1,ℤ/8) | — | 2 | 6 | no | — |
| 238 | AGL(1,ℤ/8) | — | 14 | 6 | no | — |
| 239 | AGL(1,ℤ/8) | — | 14 | 12 | no | — |
| 240 | AGL(1,ℤ/8) | — | 14 | 12 | no | — |
| 241 | AGL(1,ℤ/8) | — | 14 | 6 | no | — |
| 242 | AGL(1,ℤ/8) | — | 14 | 6 | no | — |
| 243 | #135 | — | 2 | 6 | no | — |
| 244 | #135 | — | 14 | 12 | no | — |
| 245 | #135 | — | 14 | 6 | no | — |
| 246 | #135 | — | 14 | 12 | no | — |
| 247 | #135 | — | 14 | 6 | no | — |
| 248 | #135 | — | 14 | 6 | no | — |
| 249 | C2×Q16 | — | 14 | 6 | no | — |
| 250 | C2×SD16 | — | 14 | 12 | no | — |
| 251 | C2×D8 | — | 14 | 6 | no | — |
| 252 | C2×M16 | — | 7 | 3 | no | — |
| 253 | C2×M16 | — | 7 | 6 | no | — |
| 254 | C2×M16 | — | 14 | 6 | no | — |
| 255 | C2×M16 | — | 14 | 6 | no | — |
| 256 | C2×M16 | C22×D7 | 1 | 3 | yes | — |
| 257 | C22×C8 | — | 7 | 6 | no | — |
| 258 | C22×C8 | — | 7 | 1 | no | — |
| 259 | C22×C8 | — | 14 | 3 | no | — |
| 260 | C22×C8 | — | 14 | 3 | no | — |
| 261 | C22×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 262 | C22⋊C8 | — | 2 | 6 | no | — |
| 263 | C22⋊C8 | — | 14 | 6 | no | — |
| 264 | C22⋊C8 | — | 14 | 6 | no | — |
| 265 | C22⋊C8 | — | 14 | 6 | no | — |
| 266 | C22×C7 | — | 4 | 1 | no | — |
| 267 | C22×C7 | — | 4 | 6 | no | — |
| 268 | C22×C7 | — | 4 | 3 | no | — |
| 269 | C22×C7 | C2×#121 | 1 | 3 | yes | — |
| 270 | C2×D7 | — | 2 | 6 | no | — |
| 271 | C2×D7 | — | 4 | 3 | no | — |
| 272 | C2×D7 | — | 4 | 6 | no | — |
| 273 | C2×D7 | — | 4 | 3 | no | — |
| 274 | C2×D7 | — | 8 | 6 | no | — |
| 275 | C2×D7 | — | 8 | 6 | no | — |
| 276 | C2×D7 | #392 | 1 | 3 | yes | — |
| 277 | C2×D7 | #392 | 1 | 1 | yes | characteristic |
| 278 | C4×C7 | — | 4 | 3 | no | — |
| 279 | C4×C7 | C2×#120 | 1 | 3 | yes | — |
| 280 | C4×C7 | C2×#127 | 1 | 1 | yes | characteristic |
| 281 | Dic7 | — | 4 | 3 | no | — |
| 282 | Dic7 | #392 | 1 | 3 | yes | — |
| 283 | Dic7 | #392 | 1 | 1 | yes | characteristic |
| 284 | C24 | — | 7 | 1 | no | — |
| 285 | C24 | — | 14 | 3 | no | — |
| 286 | #41 | — | 2 | 6 | no | — |
| 287 | #41 | — | 2 | 6 | no | — |
| 288 | #41 | — | 14 | 6 | no | — |
| 289 | #41 | — | 14 | 6 | no | — |
| 290 | #41 | — | 14 | 6 | no | — |
| 291 | #41 | — | 14 | 6 | no | — |
| 292 | #41 | — | 14 | 6 | no | — |
| 293 | #41 | — | 14 | 6 | no | — |
| 294 | #41 | — | 28 | 6 | no | — |
| 295 | #41 | — | 28 | 6 | no | — |
| 296 | #41 | — | 28 | 6 | no | — |
| 297 | #41 | — | 28 | 6 | no | — |
| 298 | C2×Q8 | — | 7 | 3 | no | — |
| 299 | C2×Q8 | — | 14 | 3 | no | — |
| 300 | C2×Q8 | — | 14 | 6 | no | — |
| 301 | C2×Q8 | — | 14 | 6 | no | — |
| 302 | C2×Q8 | D4×D7 | 1 | 3 | yes | — |
| 303 | C2×D4 | — | 2 | 3 | no | — |
| 304 | C2×D4 | — | 7 | 3 | no | — |
| 305 | C2×D4 | — | 14 | 3 | no | — |
| 306 | C2×D4 | — | 14 | 6 | no | — |
| 307 | C2×D4 | — | 14 | 6 | no | — |
| 308 | C2×D4 | — | 14 | 3 | no | — |
| 309 | C2×D4 | — | 14 | 3 | no | — |
| 310 | C2×D4 | — | 14 | 3 | no | — |
| 311 | C2×D4 | — | 28 | 6 | no | — |
| 312 | C2×D4 | — | 28 | 6 | no | — |
| 313 | C2×D4 | D4×D7 | 1 | 3 | yes | — |
| 314 | C22×C4 | — | 2 | 3 | no | — |
| 315 | C22×C4 | — | 7 | 1 | no | — |
| 316 | C22×C4 | — | 7 | 3 | no | — |
| 317 | C22×C4 | — | 7 | 3 | no | — |
| 318 | C22×C4 | — | 7 | 3 | no | — |
| 319 | C22×C4 | — | 7 | 3 | no | — |
| 320 | C22×C4 | — | 14 | 3 | no | — |
| 321 | C22×C4 | — | 14 | 3 | no | — |
| 322 | C22×C4 | — | 14 | 3 | no | — |
| 323 | C22×C4 | — | 14 | 3 | no | — |
| 324 | C22×C4 | — | 28 | 3 | no | — |
| 325 | C22×C4 | — | 28 | 3 | no | — |
| 326 | C22×C4 | — | 28 | 3 | no | — |
| 327 | C22×C4 | — | 28 | 3 | no | — |
| 328 | C22×C4 | C23×D7 | 1 | 1 | yes | characteristic |
| 329 | Q16 | — | 2 | 6 | no | — |
| 330 | Q16 | — | 14 | 6 | no | — |
| 331 | Q16 | — | 14 | 12 | no | — |
| 332 | SD16 | — | 2 | 12 | no | — |
| 333 | SD16 | — | 14 | 12 | no | — |
| 334 | SD16 | — | 14 | 12 | no | — |
| 335 | SD16 | — | 14 | 12 | no | — |
| 336 | D8 | — | 2 | 6 | no | — |
| 337 | D8 | — | 14 | 6 | no | — |
| 338 | D8 | — | 14 | 12 | no | — |
| 339 | M16 | — | 2 | 6 | no | — |
| 340 | M16 | — | 14 | 12 | no | — |
| 341 | M16 | — | 14 | 6 | no | — |
| 342 | C2×C8 | — | 2 | 3 | no | — |
| 343 | C2×C8 | — | 7 | 6 | no | — |
| 344 | C2×C8 | — | 14 | 6 | no | — |
| 345 | C2×C8 | — | 14 | 6 | no | — |
| 346 | C2×C8 | — | 14 | 3 | no | — |
| 347 | C2×C8 | — | 28 | 1 | no | — |
| 348 | C2×C8 | — | 28 | 3 | no | — |
| 349 | C2×C8 | D4×D7 | 1 | 6 | yes | — |
| 350 | C2×C7 | — | 2 | 3 | no | — |
| 351 | C2×C7 | — | 8 | 3 | no | — |
| 352 | C2×C7 | C2×#392 | 1 | 1 | yes | characteristic |
| 353 | D7 | — | 2 | 3 | no | — |
| 354 | D7 | — | 8 | 3 | no | — |
| 355 | D7 | #2017 | 1 | 2 | yes | direct product factor |
| 356 | C23 | — | 2 | 3 | no | — |
| 357 | C23 | — | 7 | 3 | no | — |
| 358 | C23 | — | 7 | 3 | no | — |
| 359 | C23 | — | 14 | 3 | no | — |
| 360 | C23 | — | 28 | 3 | no | — |
| 361 | C23 | — | 28 | 3 | no | — |
| 362 | C23 | — | 28 | 2 | no | — |
| 363 | C23 | — | 28 | 12 | no | — |
| 364 | C23 | D7×#41 | 1 | 1 | yes | characteristic |
| 365 | Q8 | — | 2 | 6 | no | — |
| 366 | Q8 | — | 14 | 6 | no | — |
| 367 | Q8 | — | 28 | 6 | no | — |
| 368 | D4 | — | 2 | 6 | no | — |
| 369 | D4 | — | 4 | 6 | no | — |
| 370 | D4 | — | 14 | 6 | no | — |
| 371 | D4 | — | 28 | 6 | no | — |
| 372 | D4 | — | 28 | 6 | no | — |
| 373 | D4 | — | 28 | 6 | no | — |
| 374 | D4 | — | 28 | 6 | no | — |
| 375 | C2×C4 | — | 2 | 3 | no | — |
| 376 | C2×C4 | — | 4 | 3 | no | — |
| 377 | C2×C4 | — | 4 | 3 | no | — |
| 378 | C2×C4 | — | 7 | 3 | no | — |
| 379 | C2×C4 | — | 7 | 3 | no | — |
| 380 | C2×C4 | — | 7 | 1 | no | — |
| 381 | C2×C4 | — | 7 | 3 | no | — |
| 382 | C2×C4 | — | 7 | 3 | no | — |
| 383 | C2×C4 | — | 7 | 3 | no | — |
| 384 | C2×C4 | — | 7 | 6 | no | — |
| 385 | C2×C4 | — | 14 | 3 | no | — |
| 386 | C2×C4 | — | 28 | 3 | no | — |
| 387 | C2×C4 | — | 28 | 3 | no | — |
| 388 | C2×C4 | — | 28 | 3 | no | — |
| 389 | C2×C4 | — | 28 | 3 | no | — |
| 390 | C2×C4 | — | 28 | 3 | no | — |
| 391 | C2×C4 | — | 28 | 3 | no | — |
| 392 | C2×C4 | — | 28 | 3 | no | — |
| 393 | C2×C4 | — | 28 | 3 | no | — |
| 394 | C2×C4 | C2×D4×D7 | 1 | 3 | yes | — |
| 395 | C2×C4 | C2×D4×D7 | 1 | 3 | yes | — |
| 396 | C8 | — | 2 | 6 | no | — |
| 397 | C8 | — | 4 | 1 | no | — |
| 398 | C8 | — | 14 | 6 | no | — |
| 399 | C8 | — | 28 | 1 | no | — |
| 400 | C7 | C2×#2017 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 401 | C22 | — | 4 | 1 | no | — |
| 402 | C22 | — | 4 | 6 | no | — |
| 403 | C22 | — | 4 | 3 | no | — |
| 404 | C22 | — | 7 | 1 | no | — |
| 405 | C22 | — | 7 | 3 | no | — |
| 406 | C22 | — | 14 | 6 | no | — |
| 407 | C22 | — | 28 | 3 | no | — |
| 408 | C22 | — | 28 | 6 | no | — |
| 409 | C22 | — | 28 | 3 | no | — |
| 410 | C22 | — | 56 | 6 | no | — |
| 411 | C22 | — | 56 | 6 | no | — |
| 412 | C22 | D7×#121 | 1 | 3 | yes | — |
| 413 | C4 | — | 4 | 3 | no | — |
| 414 | C4 | — | 7 | 1 | no | — |
| 415 | C4 | — | 7 | 3 | no | — |
| 416 | C4 | — | 28 | 3 | no | — |
| 417 | C4 | D7×#120 | 1 | 3 | yes | — |
| 418 | C4 | D7×#127 | 1 | 1 | yes | characteristic |
| 419 | C2 | — | 2 | 3 | no | — |
| 420 | C2 | — | 7 | 2 | no | — |
| 421 | C2 | — | 8 | 3 | no | — |
| 422 | C2 | — | 14 | 3 | no | — |
| 423 | C2 | — | 56 | 3 | no | — |
| 424 | C2 | D7×#392 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D7×#575 | C2 | semidirect |
| 2. D7×#408 | C2 | semidirect |
| 3. C7×#2017 | C2 | semidirect |
| 4. #11729875 | C2 | semidirect |
| 5. #11727767 | C2 | semidirect |
| 6. #11726481 | C2 | semidirect |
| 7. D7×#338 | C2 | semidirect |
| 9. C7×#575 | C22 | semidirect |
| 10. #90513 | C22 | semidirect |
| 17. #90439 | C22 | semidirect |
| 20. C7×#408 | C22 | semidirect |
| 21. #90006 | C22 | semidirect |
| 22. #89901 | C22 | semidirect |
| 23. #89882 | C22 | semidirect |
| 26. C7×#338 | C22 | semidirect |
| 27. C7⋊#338 | C22 | semidirect |
| 84. #2017 | D7 | direct (N × H) |
| 158. #575 | C2×D7 | semidirect |
| 168. #408 | C2×D7 | semidirect |
| 171. #338 | C2×D7 | semidirect |
| 355. D7 | #2017 | direct (N × H) |
| 400. C7 | C2×#2017 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D7×#575 | 2 |
| D7×#408 | 2 |
| C7×#2017 | 2 |
| #11729875 | 2 |
| #11727767 | 2 |
| #11726481 | 2 |
| D7×#338 | 2 |
| C2×#2017 | 7 |