Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
594 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 99 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 | #11741349 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#89965 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#89680 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×C7×#360 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11728330 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×#89283 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11725618 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×C7×#135 | C22 | 1 | 1 | yes | characteristic |
| 9 | #90523 | — | 2 | 1 | no | — |
| 10 | C2×#6513 | — | 2 | 1 | no | — |
| 11 | C2×#6467 | C22 | 1 | 1 | yes | characteristic |
| 12 | C22×D56 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×C7×M32 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×C7×#106 | C22 | 1 | 1 | yes | characteristic |
| 15 | #89965 | — | 2 | 2 | no | — |
| 16 | #89965 | — | 2 | 2 | no | — |
| 17 | #89962 | — | 2 | 1 | no | — |
| 18 | C2×#6402 | — | 2 | 1 | no | — |
| 19 | #89948 | — | 2 | 1 | no | — |
| 20 | #89939 | — | 2 | 1 | no | — |
| 21 | #89926 | — | 2 | 1 | no | — |
| 22 | C2×#6400 | — | 2 | 1 | no | — |
| 23 | C2×#6389 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×#6386 | C22 | 1 | 1 | yes | characteristic |
| 25 | #89760 | — | 2 | 1 | no | — |
| 26 | C2×#6383 | — | 2 | 1 | no | — |
| 27 | #89680 | — | 2 | 2 | no | — |
| 28 | #89680 | — | 2 | 2 | no | — |
| 29 | C2×#6374 | — | 2 | 1 | no | — |
| 30 | C2×D112 | — | 2 | 1 | no | — |
| 31 | C7×#360 | — | 2 | 2 | no | — |
| 32 | #89283 | — | 2 | 2 | no | — |
| 33 | #13341 | — | 7 | 1 | no | maximal, Sylow |
| 34 | C2×C7×#41 | — | 2 | 1 | no | — |
| 35 | C2×#1157 | — | 2 | 1 | no | — |
| 36 | C22×D28 | — | 2 | 1 | no | — |
| 37 | C7×#135 | — | 2 | 1 | no | — |
| 38 | C7×#135 | — | 2 | 1 | no | — |
| 39 | C7×#135 | — | 2 | 1 | no | — |
| 40 | C7×#135 | — | 2 | 1 | no | — |
| 41 | C2×C7×Q16 | D4 | 1 | 1 | yes | characteristic |
| 42 | C2×C7×SD16 | — | 2 | 1 | no | — |
| 43 | C2×C7×D8 | D4 | 1 | 1 | yes | characteristic |
| 44 | C22×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 45 | C2×C7×C4⋊C4 | — | 2 | 1 | no | — |
| 46 | #6513 | — | 4 | 2 | no | — |
| 47 | #6513 | — | 4 | 2 | no | — |
| 48 | #6510 | — | 2 | 1 | no | — |
| 49 | #6507 | — | 2 | 1 | no | — |
| 50 | C2×#1144 | — | 2 | 1 | no | — |
| 51 | C2×#1143 | — | 2 | 1 | no | — |
| 52 | #6503 | — | 2 | 1 | no | — |
| 53 | #6502 | — | 4 | 2 | no | — |
| 54 | #6499 | — | 2 | 1 | no | — |
| 55 | C2×#1142 | — | 2 | 1 | no | — |
| 56 | C2×#1141 | — | 2 | 1 | no | — |
| 57 | C4×C22⋊D7 | — | 4 | 2 | no | — |
| 58 | C2×(C2×D7)⋊C4 | — | 4 | 2 | no | — |
| 59 | C2×C4×Dic7 | D4 | 1 | 1 | yes | characteristic |
| 60 | C22×C7⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 61 | C2×Dic28 | D4 | 1 | 1 | yes | characteristic |
| 62 | #6467 | — | 2 | 1 | no | — |
| 63 | #6467 | — | 2 | 1 | no | — |
| 64 | #6467 | — | 2 | 1 | no | — |
| 65 | #6467 | — | 2 | 1 | no | — |
| 66 | C2×D56 | — | 2 | 1 | no | — |
| 67 | C2×D56 | — | 2 | 1 | no | — |
| 68 | C2×D56 | — | 2 | 1 | no | — |
| 69 | C2×D56 | — | 2 | 1 | no | — |
| 70 | C2×D56 | — | 2 | 1 | no | — |
| 71 | C2×D56 | D4 | 1 | 1 | yes | characteristic |
| 72 | C2×D56 | D4 | 1 | 2 | yes | complemented |
| 73 | C2×#1132 | — | 2 | 1 | no | — |
| 74 | C7×M32 | — | 2 | 1 | no | — |
| 75 | C7×M32 | D4 | 1 | 2 | yes | complemented |
| 76 | C2×C7×C16 | — | 2 | 1 | no | — |
| 77 | C7×#106 | — | 2 | 1 | no | — |
| 78 | C7×#106 | — | 2 | 1 | no | — |
| 79 | #6402 | — | 2 | 4 | no | — |
| 80 | #6400 | — | 2 | 4 | no | — |
| 81 | #6389 | — | 2 | 1 | no | — |
| 82 | #6389 | — | 2 | 1 | no | — |
| 83 | #6386 | — | 2 | 1 | no | — |
| 84 | #6386 | D4 | 1 | 2 | yes | complemented |
| 85 | C2×C7⋊C16 | — | 2 | 1 | no | — |
| 86 | #6383 | — | 4 | 2 | no | — |
| 87 | #6374 | — | 2 | 4 | no | — |
| 88 | D112 | — | 2 | 4 | no | — |
| 89 | C2×#509 | — | 7 | 1 | no | — |
| 90 | C2×#509 | — | 7 | 1 | no | — |
| 91 | #3150 | — | 7 | 1 | no | — |
| 92 | C2×#360 | — | 7 | 1 | no | — |
| 93 | C2×#360 | D7 | 1 | 1 | yes | characteristic, complemented |
| 94 | #1972 | — | 7 | 1 | no | — |
| 95 | #1377 | — | 7 | 1 | no | — |
| 96 | C23×D7 | — | 4 | 1 | no | — |
| 97 | C7×#41 | — | 4 | 1 | no | — |
| 98 | C7×#41 | — | 4 | 1 | no | — |
| 99 | C7×#41 | — | 4 | 1 | no | — |
| 100 | C7×#41 | — | 4 | 1 | no | — |
| 101 | C2×C7×Q8 | — | 2 | 1 | no | — |
| 102 | C2×C7×D4 | — | 2 | 1 | no | — |
| 103 | C2×C7×D4 | — | 4 | 1 | no | — |
| 104 | C22×C4×C7 | — | 4 | 1 | no | — |
| 105 | C22×C4×C7 | — | 4 | 1 | no | — |
| 106 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 107 | C2×C22⋊D7 | — | 4 | 2 | no | — |
| 108 | C2×C22⋊D7 | — | 4 | 1 | no | — |
| 109 | C22×Dic7 | D8 | 1 | 2 | yes | — |
| 110 | #1157 | — | 4 | 1 | no | — |
| 111 | #1157 | — | 4 | 1 | no | — |
| 112 | #1157 | — | 4 | 1 | no | — |
| 113 | #1157 | — | 4 | 1 | no | — |
| 114 | C2×D28 | — | 2 | 1 | no | — |
| 115 | C2×D28 | — | 2 | 2 | no | — |
| 116 | C2×D28 | — | 4 | 1 | no | — |
| 117 | C2×D28 | — | 4 | 1 | no | — |
| 118 | C2×D28 | — | 4 | 1 | no | — |
| 119 | C2×D28 | — | 4 | 1 | no | — |
| 120 | C2×D28 | — | 4 | 1 | no | — |
| 121 | C2×C4×D7 | — | 4 | 1 | no | — |
| 122 | C2×Dic14 | — | 2 | 1 | no | — |
| 123 | C7×Q16 | — | 2 | 1 | no | — |
| 124 | C7×Q16 | — | 2 | 1 | no | — |
| 125 | C7×SD16 | — | 4 | 1 | no | — |
| 126 | C7×SD16 | — | 4 | 1 | no | — |
| 127 | C7×D8 | — | 2 | 1 | no | — |
| 128 | C7×D8 | — | 2 | 1 | no | — |
| 129 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 130 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 131 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 132 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 133 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 134 | C2×C7×C8 | #41 | 1 | 1 | yes | characteristic |
| 135 | C7×C4⋊C4 | — | 4 | 1 | no | — |
| 136 | C7×C4⋊C4 | — | 4 | 1 | no | — |
| 137 | C22⋊Dic7 | — | 4 | 2 | no | — |
| 138 | #1144 | — | 4 | 2 | no | — |
| 139 | #1143 | — | 4 | 2 | no | — |
| 140 | #1142 | — | 4 | 2 | no | — |
| 141 | #1141 | — | 4 | 2 | no | — |
| 142 | (C2×D7)⋊C4 | — | 4 | 2 | no | — |
| 143 | (C2×D7)⋊C4 | — | 8 | 4 | no | — |
| 144 | Dic7⋊C4 | — | 4 | 2 | no | — |
| 145 | C4×Dic7 | — | 2 | 1 | no | — |
| 146 | C4×Dic7 | — | 2 | 1 | no | — |
| 147 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 148 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 149 | C2×C7⋊C8 | D8 | 1 | 2 | yes | — |
| 150 | Dic28 | — | 2 | 1 | no | — |
| 151 | Dic28 | — | 2 | 1 | no | — |
| 152 | D56 | — | 2 | 2 | no | — |
| 153 | D56 | — | 2 | 2 | no | — |
| 154 | D56 | — | 2 | 1 | no | — |
| 155 | D56 | — | 2 | 1 | no | — |
| 156 | D56 | — | 4 | 1 | no | — |
| 157 | D56 | — | 4 | 1 | no | — |
| 158 | #1132 | — | 4 | 1 | no | — |
| 159 | #1132 | — | 4 | 1 | no | — |
| 160 | C7×C16 | — | 2 | 2 | no | — |
| 161 | C7⋊C16 | — | 2 | 2 | no | — |
| 162 | C2×#135 | — | 7 | 1 | no | — |
| 163 | C2×#135 | — | 14 | 1 | no | — |
| 164 | C2×#135 | C2×D7 | 1 | 1 | yes | characteristic |
| 165 | C22×D8 | — | 7 | 1 | no | — |
| 166 | #532 | — | 14 | 1 | no | — |
| 167 | #509 | — | 14 | 2 | no | — |
| 168 | #509 | — | 14 | 2 | no | — |
| 169 | #509 | — | 14 | 2 | no | — |
| 170 | #509 | — | 14 | 2 | no | — |
| 171 | C2×SD32 | — | 14 | 1 | no | — |
| 172 | C2×SD32 | — | 14 | 1 | no | — |
| 173 | C2×D16 | — | 14 | 1 | no | — |
| 174 | C2×D16 | — | 14 | 1 | no | — |
| 175 | C2×M32 | — | 7 | 1 | no | — |
| 176 | C2×M32 | C2×D7 | 1 | 1 | yes | characteristic |
| 177 | #497 | — | 14 | 1 | no | — |
| 178 | #497 | — | 14 | 1 | no | — |
| 179 | #496 | — | 14 | 1 | no | — |
| 180 | #496 | — | 14 | 1 | no | — |
| 181 | C2×#106 | C2×D7 | 1 | 1 | yes | characteristic |
| 182 | C2×#102 | — | 14 | 1 | no | — |
| 183 | C2×#97 | — | 7 | 1 | no | — |
| 184 | #390 | — | 14 | 1 | no | — |
| 185 | #360 | — | 2 | 2 | no | — |
| 186 | #360 | — | 14 | 2 | no | — |
| 187 | C23×C7 | — | 4 | 1 | no | — |
| 188 | C23×C7 | C2×D8 | 1 | 1 | yes | characteristic |
| 189 | C22×D7 | — | 4 | 1 | no | — |
| 190 | C22×D7 | — | 4 | 2 | no | — |
| 191 | C22×D7 | — | 8 | 2 | no | — |
| 192 | C22×D7 | — | 8 | 2 | no | — |
| 193 | C22×D7 | — | 8 | 1 | no | — |
| 194 | C22×D7 | — | 8 | 1 | no | — |
| 195 | C7×Q8 | — | 4 | 1 | no | — |
| 196 | C7×Q8 | — | 4 | 1 | no | — |
| 197 | C7×D4 | — | 4 | 1 | no | — |
| 198 | C7×D4 | — | 4 | 1 | no | — |
| 199 | C7×D4 | — | 8 | 1 | no | — |
| 200 | C7×D4 | — | 8 | 1 | no | — |
| 201 | C2×C4×C7 | — | 4 | 1 | no | — |
| 202 | C2×C4×C7 | — | 8 | 1 | no | — |
| 203 | C2×C4×C7 | — | 8 | 1 | no | — |
| 204 | C2×C4×C7 | — | 8 | 2 | no | — |
| 205 | C2×C4×C7 | — | 8 | 1 | no | — |
| 206 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 207 | C2×C4×C7 | #121 | 1 | 1 | yes | characteristic |
| 208 | C2×C4×C7 | #127 | 1 | 1 | yes | characteristic |
| 209 | C2×C4×C7 | C2×D8 | 1 | 1 | yes | characteristic |
| 210 | C2×C4×C7 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 211 | C2×C4×C7 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 212 | C22⋊D7 | — | 8 | 4 | no | — |
| 213 | C22⋊D7 | — | 8 | 1 | no | — |
| 214 | C22⋊D7 | — | 8 | 1 | no | — |
| 215 | C2×Dic7 | — | 2 | 2 | no | — |
| 216 | C2×Dic7 | — | 4 | 2 | no | — |
| 217 | C2×Dic7 | — | 4 | 1 | no | — |
| 218 | D28 | — | 4 | 1 | no | — |
| 219 | D28 | — | 4 | 2 | no | — |
| 220 | D28 | — | 4 | 1 | no | — |
| 221 | D28 | — | 4 | 2 | no | — |
| 222 | D28 | — | 8 | 1 | no | — |
| 223 | D28 | — | 8 | 1 | no | — |
| 224 | C4×D7 | — | 8 | 1 | no | — |
| 225 | C4×D7 | — | 8 | 1 | no | — |
| 226 | Dic14 | — | 4 | 1 | no | — |
| 227 | Dic14 | — | 4 | 1 | no | — |
| 228 | C7×C8 | #120 | 1 | 1 | yes | characteristic |
| 229 | C7×C8 | #120 | 1 | 1 | yes | characteristic |
| 230 | C7×C8 | #121 | 1 | 1 | yes | characteristic |
| 231 | C7×C8 | #121 | 1 | 1 | yes | characteristic |
| 232 | C7⋊C8 | — | 2 | 2 | no | — |
| 233 | C2×#41 | — | 2 | 1 | no | — |
| 234 | C2×#41 | — | 14 | 1 | no | — |
| 235 | C22×D4 | — | 14 | 1 | no | — |
| 236 | #135 | — | 2 | 1 | no | — |
| 237 | #135 | — | 2 | 1 | no | — |
| 238 | #135 | — | 2 | 1 | no | — |
| 239 | #135 | — | 2 | 1 | no | — |
| 240 | #135 | — | 14 | 1 | no | — |
| 241 | #135 | — | 14 | 1 | no | — |
| 242 | #135 | — | 14 | 1 | no | — |
| 243 | #135 | — | 14 | 1 | no | — |
| 244 | #135 | — | 28 | 2 | no | — |
| 245 | #135 | — | 28 | 2 | no | — |
| 246 | C2×Q16 | — | 7 | 1 | no | — |
| 247 | C2×Q16 | — | 14 | 1 | no | — |
| 248 | C2×Q16 | D28 | 1 | 1 | yes | characteristic |
| 249 | C2×SD16 | — | 2 | 1 | no | — |
| 250 | C2×SD16 | — | 14 | 1 | no | — |
| 251 | C2×SD16 | — | 14 | 1 | no | — |
| 252 | C2×SD16 | — | 14 | 1 | no | — |
| 253 | C2×D8 | — | 7 | 2 | no | — |
| 254 | C2×D8 | — | 7 | 1 | no | — |
| 255 | C2×D8 | — | 14 | 1 | no | — |
| 256 | C2×D8 | — | 14 | 1 | no | — |
| 257 | C2×D8 | — | 14 | 1 | no | — |
| 258 | C2×D8 | — | 14 | 1 | no | — |
| 259 | C2×D8 | — | 14 | 1 | no | — |
| 260 | C2×D8 | — | 14 | 1 | no | — |
| 261 | C2×D8 | D28 | 1 | 1 | yes | characteristic |
| 262 | C22×C8 | — | 7 | 1 | no | — |
| 263 | C22×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 264 | C4⋊Q8 | — | 14 | 1 | no | — |
| 265 | #127 | — | 14 | 1 | no | — |
| 266 | #124 | — | 14 | 1 | no | — |
| 267 | #124 | — | 14 | 1 | no | — |
| 268 | #121 | — | 28 | 2 | no | — |
| 269 | C4×D4 | — | 28 | 2 | no | — |
| 270 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 271 | C2×C22⋊C4 | — | 28 | 2 | no | — |
| 272 | C2×C42 | — | 7 | 1 | no | — |
| 273 | SD32 | — | 14 | 4 | no | — |
| 274 | SD32 | — | 14 | 4 | no | — |
| 275 | D16 | — | 14 | 4 | no | — |
| 276 | D16 | — | 14 | 4 | no | — |
| 277 | M32 | — | 2 | 1 | no | — |
| 278 | M32 | — | 7 | 2 | no | — |
| 279 | M32 | — | 14 | 1 | no | — |
| 280 | M32 | C22⋊D7 | 1 | 2 | yes | complemented |
| 281 | C2×C16 | — | 2 | 1 | no | — |
| 282 | C2×C16 | — | 14 | 1 | no | — |
| 283 | #106 | — | 2 | 1 | no | — |
| 284 | #106 | — | 2 | 1 | no | — |
| 285 | #102 | — | 28 | 2 | no | — |
| 286 | #97 | — | 14 | 1 | no | — |
| 287 | #97 | — | 14 | 1 | no | — |
| 288 | C22×C7 | — | 2 | 2 | no | — |
| 289 | C22×C7 | — | 8 | 2 | no | — |
| 290 | C22×C7 | — | 8 | 1 | no | — |
| 291 | C22×C7 | #447 | 1 | 1 | yes | characteristic |
| 292 | C22×C7 | #459 | 1 | 1 | yes | characteristic |
| 293 | C22×C7 | #493 | 1 | 1 | yes | characteristic |
| 294 | C2×D7 | — | 8 | 4 | no | — |
| 295 | C2×D7 | — | 8 | 2 | no | — |
| 296 | C2×D7 | — | 8 | 1 | no | — |
| 297 | C2×D7 | — | 8 | 2 | no | — |
| 298 | C2×D7 | — | 16 | 1 | no | — |
| 299 | C2×D7 | — | 16 | 1 | no | — |
| 300 | C2×D7 | — | 16 | 2 | no | — |
| 301 | C4×C7 | — | 8 | 1 | no | — |
| 302 | C4×C7 | — | 16 | 1 | no | — |
| 303 | C4×C7 | #392 | 1 | 1 | yes | characteristic |
| 304 | C4×C7 | #447 | 1 | 1 | yes | characteristic |
| 305 | C4×C7 | #459 | 1 | 1 | yes | characteristic |
| 306 | C4×C7 | #496 | 1 | 1 | yes | characteristic |
| 307 | Dic7 | — | 4 | 2 | no | — |
| 308 | Dic7 | — | 8 | 1 | no | — |
| 309 | C24 | — | 28 | 1 | no | — |
| 310 | #41 | — | 4 | 1 | no | — |
| 311 | #41 | — | 4 | 1 | no | — |
| 312 | #41 | — | 4 | 1 | no | — |
| 313 | #41 | — | 4 | 1 | no | — |
| 314 | #41 | — | 28 | 1 | no | — |
| 315 | #41 | — | 28 | 1 | no | — |
| 316 | #41 | — | 28 | 1 | no | — |
| 317 | #41 | — | 28 | 1 | no | — |
| 318 | C2×Q8 | — | 2 | 1 | no | — |
| 319 | C2×Q8 | — | 14 | 1 | no | — |
| 320 | C2×D4 | — | 2 | 1 | no | — |
| 321 | C2×D4 | — | 4 | 1 | no | — |
| 322 | C2×D4 | — | 14 | 1 | no | — |
| 323 | C2×D4 | — | 14 | 2 | no | — |
| 324 | C2×D4 | — | 28 | 2 | no | — |
| 325 | C2×D4 | — | 28 | 1 | no | — |
| 326 | C2×D4 | — | 28 | 1 | no | — |
| 327 | C2×D4 | — | 28 | 1 | no | — |
| 328 | C2×D4 | — | 28 | 1 | no | — |
| 329 | C2×D4 | — | 28 | 1 | no | — |
| 330 | C2×D4 | — | 28 | 1 | no | — |
| 331 | C22×C4 | — | 4 | 1 | no | — |
| 332 | C22×C4 | — | 4 | 1 | no | — |
| 333 | C22×C4 | — | 7 | 2 | no | — |
| 334 | C22×C4 | — | 28 | 1 | no | — |
| 335 | C22×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 336 | Q16 | — | 2 | 1 | no | — |
| 337 | Q16 | — | 2 | 1 | no | — |
| 338 | Q16 | — | 14 | 1 | no | — |
| 339 | Q16 | — | 14 | 1 | no | — |
| 340 | Q16 | — | 28 | 2 | no | — |
| 341 | SD16 | — | 4 | 1 | no | — |
| 342 | SD16 | — | 4 | 1 | no | — |
| 343 | SD16 | — | 28 | 2 | no | — |
| 344 | SD16 | — | 28 | 2 | no | — |
| 345 | SD16 | — | 28 | 1 | no | — |
| 346 | SD16 | — | 28 | 1 | no | — |
| 347 | D8 | — | 2 | 1 | no | — |
| 348 | D8 | — | 2 | 1 | no | — |
| 349 | D8 | — | 14 | 2 | no | — |
| 350 | D8 | — | 14 | 1 | no | — |
| 351 | D8 | — | 14 | 1 | no | — |
| 352 | D8 | — | 14 | 2 | no | — |
| 353 | D8 | — | 28 | 2 | no | — |
| 354 | D8 | — | 28 | 1 | no | — |
| 355 | D8 | — | 28 | 1 | no | — |
| 356 | C2×C8 | — | 7 | 2 | no | — |
| 357 | C2×C8 | — | 14 | 1 | no | — |
| 358 | C2×C8 | — | 14 | 1 | no | — |
| 359 | C2×C8 | C2×D28 | 1 | 1 | yes | characteristic |
| 360 | C2×C8 | #1157 | 1 | 1 | yes | characteristic |
| 361 | C2×C8 | D4×D7 | 1 | 1 | yes | characteristic |
| 362 | C2×C8 | D4×D7 | 1 | 1 | yes | characteristic |
| 363 | C2×C8 | D4×D7 | 1 | 1 | yes | characteristic |
| 364 | C2×C8 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 365 | C4⋊C4 | — | 4 | 1 | no | — |
| 366 | C4⋊C4 | — | 4 | 1 | no | — |
| 367 | C4⋊C4 | — | 28 | 2 | no | — |
| 368 | C22⋊C4 | — | 28 | 2 | no | — |
| 369 | C22⋊C4 | — | 28 | 2 | no | — |
| 370 | C22⋊C4 | — | 56 | 4 | no | — |
| 371 | C42 | — | 14 | 1 | no | — |
| 372 | C42 | — | 14 | 1 | no | — |
| 373 | C16 | — | 2 | 2 | no | — |
| 374 | C16 | — | 14 | 2 | no | — |
| 375 | C2×C7 | — | 2 | 1 | no | — |
| 376 | C2×C7 | — | 2 | 1 | no | — |
| 377 | C2×C7 | — | 16 | 1 | no | — |
| 378 | C2×C7 | #2011 | 1 | 1 | yes | characteristic |
| 379 | C2×C7 | #2190 | 1 | 2 | yes | — |
| 380 | D7 | — | 16 | 1 | no | — |
| 381 | D7 | — | 16 | 2 | no | — |
| 382 | C23 | — | 4 | 1 | no | — |
| 383 | C23 | — | 28 | 1 | no | — |
| 384 | C23 | — | 28 | 2 | no | — |
| 385 | C23 | — | 56 | 2 | no | — |
| 386 | C23 | — | 56 | 2 | no | — |
| 387 | C23 | — | 56 | 1 | no | — |
| 388 | C23 | — | 56 | 1 | no | — |
| 389 | C23 | D7×D8 | 1 | 1 | yes | characteristic |
| 390 | Q8 | — | 4 | 1 | no | — |
| 391 | Q8 | — | 4 | 1 | no | — |
| 392 | Q8 | — | 28 | 1 | no | — |
| 393 | Q8 | — | 28 | 1 | no | — |
| 394 | D4 | — | 4 | 1 | no | — |
| 395 | D4 | — | 4 | 1 | no | — |
| 396 | D4 | — | 8 | 1 | no | — |
| 397 | D4 | — | 8 | 1 | no | — |
| 398 | D4 | — | 28 | 2 | no | — |
| 399 | D4 | — | 28 | 1 | no | — |
| 400 | D4 | — | 28 | 1 | no | — |
| 401 | D4 | — | 28 | 2 | no | — |
| 402 | D4 | — | 56 | 4 | no | — |
| 403 | D4 | — | 56 | 1 | no | — |
| 404 | D4 | — | 56 | 1 | no | — |
| 405 | D4 | — | 56 | 1 | no | — |
| 406 | D4 | — | 56 | 1 | no | — |
| 407 | C2×C4 | — | 4 | 1 | no | — |
| 408 | C2×C4 | — | 8 | 1 | no | — |
| 409 | C2×C4 | — | 8 | 1 | no | — |
| 410 | C2×C4 | — | 8 | 2 | no | — |
| 411 | C2×C4 | — | 8 | 1 | no | — |
| 412 | C2×C4 | — | 14 | 2 | no | — |
| 413 | C2×C4 | — | 28 | 2 | no | — |
| 414 | C2×C4 | — | 28 | 1 | no | — |
| 415 | C2×C4 | — | 56 | 1 | no | — |
| 416 | C2×C4 | — | 56 | 1 | no | — |
| 417 | C2×C4 | #6445 | 1 | 1 | yes | characteristic |
| 418 | C2×C4 | #6447 | 1 | 1 | yes | characteristic |
| 419 | C2×C4 | D7×D8 | 1 | 1 | yes | characteristic |
| 420 | C2×C4 | #6477 | 1 | 1 | yes | characteristic |
| 421 | C2×C4 | #6477 | 1 | 1 | yes | characteristic |
| 422 | C2×C4 | #6503 | 1 | 1 | yes | characteristic |
| 423 | C8 | — | 14 | 2 | no | — |
| 424 | C8 | #6445 | 1 | 1 | yes | characteristic |
| 425 | C8 | #6447 | 1 | 1 | yes | characteristic |
| 426 | C8 | #6493 | 1 | 1 | yes | characteristic |
| 427 | C8 | #6500 | 1 | 1 | yes | characteristic |
| 428 | C7 | #13341 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 429 | C22 | — | 2 | 2 | no | — |
| 430 | C22 | — | 8 | 1 | no | — |
| 431 | C22 | — | 8 | 2 | no | — |
| 432 | C22 | — | 56 | 4 | no | — |
| 433 | C22 | — | 56 | 1 | no | — |
| 434 | C22 | — | 56 | 2 | no | — |
| 435 | C22 | — | 56 | 2 | no | — |
| 436 | C22 | — | 112 | 1 | no | — |
| 437 | C22 | — | 112 | 1 | no | — |
| 438 | C22 | — | 112 | 2 | no | — |
| 439 | C22 | #89545 | 1 | 1 | yes | characteristic |
| 440 | C22 | #89558 | 1 | 1 | yes | characteristic |
| 441 | C22 | #89923 | 1 | 1 | yes | characteristic |
| 442 | C4 | — | 8 | 1 | no | — |
| 443 | C4 | — | 16 | 1 | no | — |
| 444 | C4 | — | 28 | 2 | no | — |
| 445 | C4 | — | 56 | 1 | no | — |
| 446 | C4 | #89545 | 1 | 1 | yes | characteristic |
| 447 | C4 | #89558 | 1 | 1 | yes | characteristic |
| 448 | C4 | #89732 | 1 | 1 | yes | characteristic |
| 449 | C4 | #89948 | 1 | 1 | yes | characteristic |
| 450 | C2 | — | 2 | 1 | no | — |
| 451 | C2 | — | 2 | 1 | no | — |
| 452 | C2 | — | 16 | 1 | no | — |
| 453 | C2 | — | 112 | 2 | no | — |
| 454 | C2 | — | 112 | 1 | no | — |
| 455 | C2 | #11727006 | 1 | 2 | yes | — |
| 456 | C2 | #11727963 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11741349 | C2 | semidirect |
| 2. C2×#89965 | C2 | semidirect |
| 3. C2×#89680 | C2 | semidirect |
| 4. C2×C7×#360 | C2 | semidirect |
| 5. #11728330 | C2 | semidirect |
| 6. C2×#89283 | C2 | semidirect |
| 7. #11725618 | C2 | semidirect |
| 72. C2×D56 | D4 | semidirect |
| 75. C7×M32 | D4 | semidirect |
| 84. #6386 | D4 | semidirect |
| 93. C2×#360 | D7 | semidirect |
| 280. M32 | C22⋊D7 | semidirect |
| 428. C7 | #13341 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11741349 | 2 |
| C2×#89965 | 2 |
| C2×#89680 | 2 |
| C2×C7×#360 | 2 |
| #11728330 | 2 |
| C2×#89283 | 2 |
| #11725618 | 2 |
| #13341 | 7 |