Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
532 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 93 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 | #11741361 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11741339 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11736701 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C7×#2143 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×#89313 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11729192 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11725536 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×C7×#135 | C22 | 1 | 1 | yes | characteristic |
| 9 | #90524 | — | 2 | 1 | no | — |
| 10 | #90439 | — | 2 | 1 | no | — |
| 11 | C2×#6467 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×#6464 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×C7×M32 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×C7×#108 | C22 | 1 | 1 | yes | characteristic |
| 15 | #90004 | — | 2 | 1 | no | — |
| 16 | #89967 | — | 2 | 1 | no | — |
| 17 | #89966 | — | 2 | 2 | no | — |
| 18 | #89965 | — | 2 | 1 | no | — |
| 19 | #89961 | — | 2 | 1 | no | — |
| 20 | #89951 | — | 2 | 1 | no | — |
| 21 | #89943 | — | 2 | 2 | no | — |
| 22 | #89931 | — | 2 | 1 | no | — |
| 23 | #89919 | — | 2 | 1 | no | — |
| 24 | #89904 | — | 2 | 1 | no | — |
| 25 | C2×#6391 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×#6386 | C22 | 1 | 1 | yes | characteristic |
| 27 | #89670 | — | 2 | 2 | no | — |
| 28 | #89669 | — | 2 | 1 | no | — |
| 29 | #89668 | — | 2 | 1 | no | — |
| 30 | C7×#359 | — | 2 | 2 | no | — |
| 31 | #89313 | — | 2 | 2 | no | — |
| 32 | #89310 | — | 2 | 2 | no | — |
| 33 | #13318 | — | 7 | 1 | no | maximal, Sylow |
| 34 | C2×C7×#41 | — | 2 | 1 | no | — |
| 35 | C2×#1157 | — | 2 | 1 | no | — |
| 36 | C2×#1157 | D4 | 1 | 1 | yes | characteristic |
| 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 | C2×C7×M16 | — | 2 | 1 | no | — |
| 45 | C22×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 46 | #6509 | — | 2 | 2 | no | — |
| 47 | #6502 | — | 4 | 2 | no | — |
| 48 | #6501 | — | 2 | 2 | no | — |
| 49 | #6493 | — | 4 | 1 | no | — |
| 50 | C2×C4⋊Dic7 | — | 2 | 1 | no | — |
| 51 | #6487 | — | 4 | 1 | no | — |
| 52 | C2×#1136 | D4 | 1 | 1 | yes | characteristic |
| 53 | #6472 | — | 2 | 2 | no | — |
| 54 | #6472 | — | 4 | 1 | no | — |
| 55 | #6471 | — | 2 | 2 | no | — |
| 56 | #6471 | — | 4 | 1 | no | — |
| 57 | C2×Dic28 | D4 | 1 | 1 | yes | characteristic, complemented |
| 58 | #6467 | — | 2 | 1 | no | — |
| 59 | #6467 | — | 2 | 1 | no | — |
| 60 | #6467 | — | 2 | 1 | no | — |
| 61 | #6467 | — | 2 | 1 | no | — |
| 62 | #6467 | — | 4 | 2 | no | — |
| 63 | C2×D56 | D4 | 1 | 1 | yes | characteristic, complemented |
| 64 | C2×#1132 | — | 2 | 1 | no | — |
| 65 | #6464 | — | 2 | 1 | no | — |
| 66 | #6464 | — | 2 | 1 | no | — |
| 67 | #6464 | — | 2 | 1 | no | — |
| 68 | #6464 | — | 2 | 1 | no | — |
| 69 | C2×#1131 | — | 2 | 1 | no | — |
| 70 | C2×C8×D7 | — | 2 | 1 | no | — |
| 71 | C7×M32 | — | 2 | 1 | no | — |
| 72 | C7×M32 | — | 2 | 1 | no | — |
| 73 | C2×C7×C16 | — | 2 | 1 | no | — |
| 74 | C7×#108 | — | 2 | 1 | no | — |
| 75 | C7×#108 | D4 | 1 | 2 | yes | complemented |
| 76 | #6409 | — | 2 | 2 | no | — |
| 77 | #6406 | — | 2 | 2 | no | — |
| 78 | #6403 | — | 2 | 2 | no | — |
| 79 | #6402 | — | 2 | 2 | no | — |
| 80 | #6401 | — | 2 | 2 | no | — |
| 81 | #6400 | — | 2 | 2 | no | — |
| 82 | #6398 | — | 2 | 2 | no | — |
| 83 | #6397 | — | 2 | 2 | no | — |
| 84 | #6391 | — | 2 | 1 | no | — |
| 85 | #6391 | D4 | 1 | 2 | yes | — |
| 86 | #6386 | — | 2 | 1 | no | — |
| 87 | #6386 | — | 2 | 1 | no | — |
| 88 | C2×C7⋊C16 | D4 | 1 | 2 | yes | complemented |
| 89 | #3414 | — | 7 | 1 | no | — |
| 90 | #3067 | — | 7 | 1 | no | — |
| 91 | #3060 | — | 7 | 1 | no | — |
| 92 | C2×#360 | — | 7 | 1 | no | — |
| 93 | #2143 | D7 | 1 | 1 | yes | characteristic, complemented |
| 94 | #2117 | — | 7 | 1 | no | — |
| 95 | #1383 | — | 7 | 1 | no | — |
| 96 | C7×#41 | — | 4 | 1 | no | — |
| 97 | C7×#41 | — | 4 | 1 | no | — |
| 98 | C7×#41 | — | 4 | 1 | no | — |
| 99 | C7×#41 | — | 4 | 1 | no | — |
| 100 | C2×C7×Q8 | — | 2 | 1 | no | — |
| 101 | C2×C7×D4 | — | 2 | 1 | no | — |
| 102 | C2×C7×D4 | — | 4 | 1 | no | — |
| 103 | C22×C4×C7 | — | 4 | 1 | no | — |
| 104 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 105 | C2×C22⋊D7 | — | 2 | 1 | no | — |
| 106 | C2×C22⋊D7 | — | 4 | 1 | no | — |
| 107 | C2×C22⋊D7 | — | 4 | 2 | no | — |
| 108 | C22×Dic7 | — | 4 | 1 | no | — |
| 109 | #1157 | — | 2 | 1 | no | — |
| 110 | #1157 | — | 2 | 1 | no | — |
| 111 | #1157 | — | 2 | 1 | no | — |
| 112 | #1157 | — | 2 | 1 | no | — |
| 113 | #1157 | — | 4 | 1 | no | — |
| 114 | #1157 | — | 4 | 1 | no | — |
| 115 | #1157 | — | 4 | 1 | no | — |
| 116 | #1157 | — | 4 | 1 | no | — |
| 117 | C2×D28 | — | 2 | 1 | no | — |
| 118 | C2×D28 | D8 | 1 | 1 | yes | characteristic |
| 119 | C2×C4×D7 | — | 2 | 1 | no | — |
| 120 | C2×C4×D7 | — | 4 | 1 | no | — |
| 121 | C2×Dic14 | — | 2 | 1 | no | — |
| 122 | C2×Dic14 | D8 | 1 | 1 | yes | characteristic |
| 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 | C7×M16 | — | 2 | 2 | no | — |
| 130 | C7×M16 | — | 4 | 1 | no | — |
| 131 | C2×C7×C8 | — | 4 | 1 | no | — |
| 132 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 133 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 134 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 135 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 136 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 137 | C2×C7×C8 | #41 | 1 | 1 | yes | characteristic |
| 138 | C22⋊Dic7 | — | 4 | 2 | no | — |
| 139 | (C2×D7)⋊C4 | — | 4 | 2 | no | — |
| 140 | C4⋊Dic7 | — | 2 | 2 | no | — |
| 141 | C4⋊Dic7 | — | 4 | 1 | no | — |
| 142 | Dic7⋊C4 | — | 4 | 2 | no | — |
| 143 | #1136 | — | 2 | 1 | no | — |
| 144 | #1136 | — | 2 | 1 | no | — |
| 145 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 146 | Dic28 | — | 2 | 1 | no | — |
| 147 | Dic28 | — | 2 | 1 | no | — |
| 148 | Dic28 | — | 4 | 2 | no | — |
| 149 | D56 | — | 2 | 1 | no | — |
| 150 | D56 | — | 2 | 1 | no | — |
| 151 | D56 | — | 4 | 2 | no | — |
| 152 | #1132 | — | 4 | 2 | no | — |
| 153 | #1132 | — | 4 | 2 | no | — |
| 154 | #1132 | — | 4 | 1 | no | — |
| 155 | #1132 | — | 4 | 1 | no | — |
| 156 | #1131 | — | 4 | 1 | no | — |
| 157 | #1131 | — | 4 | 1 | no | — |
| 158 | C8×D7 | — | 4 | 1 | no | — |
| 159 | C8×D7 | — | 4 | 1 | no | — |
| 160 | C7×C16 | — | 4 | 1 | no | — |
| 161 | C7⋊C16 | — | 2 | 2 | no | — |
| 162 | #575 | — | 14 | 1 | no | — |
| 163 | C2×#135 | — | 7 | 1 | no | — |
| 164 | C2×#135 | C2×D7 | 1 | 1 | yes | characteristic |
| 165 | C2×#131 | — | 7 | 1 | no | — |
| 166 | #537 | — | 14 | 1 | no | — |
| 167 | #510 | — | 14 | 1 | no | — |
| 168 | #510 | — | 14 | 1 | no | — |
| 169 | #509 | — | 14 | 1 | no | — |
| 170 | #509 | — | 14 | 1 | no | — |
| 171 | #508 | — | 14 | 2 | no | — |
| 172 | C2×M32 | — | 7 | 1 | no | — |
| 173 | C2×M32 | C2×D7 | 1 | 1 | yes | characteristic |
| 174 | #473 | — | 14 | 1 | no | — |
| 175 | #472 | — | 14 | 1 | no | — |
| 176 | #471 | — | 14 | 2 | no | — |
| 177 | #470 | — | 14 | 1 | no | — |
| 178 | #469 | — | 14 | 1 | no | — |
| 179 | #465 | — | 14 | 2 | no | — |
| 180 | C2×#108 | C2×D7 | 1 | 1 | yes | characteristic |
| 181 | C2×#106 | — | 7 | 1 | no | — |
| 182 | #417 | — | 14 | 1 | no | — |
| 183 | #413 | — | 14 | 1 | no | — |
| 184 | #360 | — | 14 | 2 | no | — |
| 185 | #359 | — | 2 | 2 | no | — |
| 186 | #350 | — | 14 | 2 | no | — |
| 187 | C23×C7 | — | 4 | 1 | no | — |
| 188 | C23×C7 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 189 | C22×D7 | — | 2 | 1 | no | — |
| 190 | C22×D7 | — | 4 | 1 | no | — |
| 191 | C7×Q8 | — | 4 | 1 | no | — |
| 192 | C7×Q8 | — | 4 | 1 | no | — |
| 193 | C7×D4 | — | 4 | 1 | no | — |
| 194 | C7×D4 | — | 4 | 1 | no | — |
| 195 | C7×D4 | — | 8 | 1 | no | — |
| 196 | C7×D4 | — | 8 | 1 | no | — |
| 197 | C2×C4×C7 | — | 4 | 1 | no | — |
| 198 | C2×C4×C7 | — | 8 | 1 | no | — |
| 199 | C2×C4×C7 | — | 8 | 1 | no | — |
| 200 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 201 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 202 | C2×C4×C7 | #121 | 1 | 1 | yes | characteristic |
| 203 | C2×C4×C7 | C2×D8 | 1 | 1 | yes | characteristic |
| 204 | C2×C4×C7 | #135 | 1 | 1 | yes | characteristic |
| 205 | C2×C4×C7 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 206 | C22⋊D7 | — | 4 | 1 | no | — |
| 207 | C22⋊D7 | — | 4 | 1 | no | — |
| 208 | C22⋊D7 | — | 8 | 1 | no | — |
| 209 | C22⋊D7 | — | 8 | 1 | no | — |
| 210 | C22⋊D7 | — | 16 | 2 | no | — |
| 211 | C2×Dic7 | — | 2 | 1 | no | — |
| 212 | C2×Dic7 | — | 4 | 2 | no | — |
| 213 | C2×Dic7 | — | 4 | 1 | no | — |
| 214 | C2×Dic7 | — | 16 | 1 | no | — |
| 215 | D28 | — | 2 | 1 | no | — |
| 216 | D28 | — | 2 | 1 | no | — |
| 217 | D28 | — | 4 | 1 | no | — |
| 218 | D28 | — | 4 | 1 | no | — |
| 219 | C4×D7 | — | 4 | 1 | no | — |
| 220 | C4×D7 | — | 4 | 1 | no | — |
| 221 | C4×D7 | — | 8 | 1 | no | — |
| 222 | C4×D7 | — | 8 | 1 | no | — |
| 223 | Dic14 | — | 2 | 1 | no | — |
| 224 | Dic14 | — | 2 | 1 | no | — |
| 225 | Dic14 | — | 4 | 1 | no | — |
| 226 | Dic14 | — | 4 | 1 | no | — |
| 227 | C7×C8 | — | 4 | 2 | no | — |
| 228 | C7×C8 | #120 | 1 | 1 | yes | characteristic |
| 229 | C7×C8 | #121 | 1 | 1 | yes | characteristic |
| 230 | C7×C8 | #121 | 1 | 1 | yes | characteristic |
| 231 | C7×C8 | #127 | 1 | 1 | yes | characteristic |
| 232 | C7⋊C8 | — | 4 | 1 | no | — |
| 233 | C2×#41 | — | 2 | 1 | no | — |
| 234 | C2×#41 | — | 7 | 1 | no | — |
| 235 | C2×#41 | — | 14 | 1 | no | — |
| 236 | #137 | — | 14 | 2 | no | — |
| 237 | #137 | — | 28 | 1 | no | — |
| 238 | AGL(1,ℤ/8) | — | 14 | 2 | no | — |
| 239 | AGL(1,ℤ/8) | — | 28 | 1 | no | — |
| 240 | #135 | — | 2 | 1 | no | — |
| 241 | #135 | — | 2 | 1 | no | — |
| 242 | #135 | — | 2 | 1 | no | — |
| 243 | #135 | — | 2 | 1 | no | — |
| 244 | #135 | — | 14 | 1 | no | — |
| 245 | #135 | — | 14 | 1 | no | — |
| 246 | #135 | — | 14 | 1 | no | — |
| 247 | #135 | — | 14 | 1 | no | — |
| 248 | #135 | — | 28 | 2 | no | — |
| 249 | C2×Q16 | — | 7 | 1 | no | — |
| 250 | C2×Q16 | D28 | 1 | 1 | yes | characteristic |
| 251 | C2×SD16 | — | 2 | 1 | no | — |
| 252 | C2×SD16 | — | 14 | 1 | no | — |
| 253 | C2×D8 | — | 7 | 1 | no | — |
| 254 | C2×D8 | D28 | 1 | 1 | yes | characteristic |
| 255 | #131 | — | 14 | 1 | no | — |
| 256 | #131 | — | 14 | 1 | no | — |
| 257 | #131 | — | 14 | 1 | no | — |
| 258 | #131 | — | 14 | 1 | no | — |
| 259 | C2×M16 | — | 2 | 1 | no | — |
| 260 | C2×M16 | — | 7 | 1 | no | — |
| 261 | C2×M16 | — | 14 | 1 | no | — |
| 262 | C22×C8 | — | 14 | 1 | no | — |
| 263 | C22×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 264 | C22⋊Q8 | — | 14 | 2 | no | — |
| 265 | C22⋊Q8 | — | 28 | 1 | no | — |
| 266 | #121 | — | 14 | 2 | no | — |
| 267 | #121 | — | 28 | 1 | no | — |
| 268 | #121 | — | 28 | 2 | no | — |
| 269 | C2×C4⋊C4 | — | 14 | 1 | no | — |
| 270 | Q32 | — | 14 | 2 | no | — |
| 271 | SD32 | — | 14 | 2 | no | — |
| 272 | SD32 | — | 14 | 2 | no | — |
| 273 | D16 | — | 14 | 2 | no | — |
| 274 | M32 | — | 2 | 1 | no | — |
| 275 | M32 | — | 2 | 1 | no | — |
| 276 | M32 | — | 14 | 1 | no | — |
| 277 | M32 | — | 14 | 1 | no | — |
| 278 | C2×C16 | — | 2 | 1 | no | — |
| 279 | C2×C16 | — | 7 | 2 | no | — |
| 280 | #108 | — | 2 | 1 | no | — |
| 281 | #108 | C22⋊D7 | 1 | 2 | yes | complemented |
| 282 | #106 | — | 7 | 2 | no | — |
| 283 | #106 | — | 14 | 1 | no | — |
| 284 | #103 | — | 14 | 2 | no | — |
| 285 | #102 | — | 14 | 2 | no | — |
| 286 | #101 | — | 14 | 2 | no | — |
| 287 | #100 | — | 14 | 2 | no | — |
| 288 | C22×C7 | — | 4 | 1 | no | — |
| 289 | C22×C7 | — | 8 | 1 | no | — |
| 290 | C22×C7 | — | 8 | 1 | no | — |
| 291 | C22×C7 | — | 8 | 1 | no | — |
| 292 | C22×C7 | #447 | 1 | 1 | yes | characteristic |
| 293 | C22×C7 | #449 | 1 | 1 | yes | characteristic |
| 294 | C22×C7 | #469 | 1 | 1 | yes | characteristic |
| 295 | C2×D7 | — | 4 | 2 | no | — |
| 296 | C2×D7 | — | 4 | 1 | no | — |
| 297 | C2×D7 | — | 8 | 1 | no | — |
| 298 | C2×D7 | — | 16 | 1 | no | — |
| 299 | C4×C7 | — | 8 | 1 | no | — |
| 300 | C4×C7 | #392 | 1 | 1 | yes | characteristic |
| 301 | C4×C7 | #447 | 1 | 1 | yes | characteristic |
| 302 | C4×C7 | #449 | 1 | 1 | yes | characteristic |
| 303 | C4×C7 | #466 | 1 | 1 | yes | characteristic |
| 304 | Dic7 | — | 4 | 1 | no | — |
| 305 | Dic7 | — | 8 | 2 | no | — |
| 306 | Dic7 | — | 8 | 1 | no | — |
| 307 | #41 | — | 4 | 1 | no | — |
| 308 | #41 | — | 4 | 1 | no | — |
| 309 | #41 | — | 4 | 1 | no | — |
| 310 | #41 | — | 4 | 1 | no | — |
| 311 | #41 | — | 14 | 1 | no | — |
| 312 | #41 | — | 14 | 1 | no | — |
| 313 | #41 | — | 14 | 1 | no | — |
| 314 | #41 | — | 14 | 1 | no | — |
| 315 | #41 | — | 28 | 1 | no | — |
| 316 | #41 | — | 28 | 1 | no | — |
| 317 | #41 | — | 28 | 1 | no | — |
| 318 | #41 | — | 28 | 1 | no | — |
| 319 | C2×Q8 | — | 2 | 1 | no | — |
| 320 | C2×Q8 | — | 7 | 1 | no | — |
| 321 | C2×Q8 | — | 14 | 1 | no | — |
| 322 | C2×D4 | — | 2 | 1 | no | — |
| 323 | C2×D4 | — | 4 | 1 | no | — |
| 324 | C2×D4 | — | 7 | 1 | no | — |
| 325 | C2×D4 | — | 14 | 1 | no | — |
| 326 | C2×D4 | — | 14 | 1 | no | — |
| 327 | C2×D4 | — | 28 | 1 | no | — |
| 328 | C2×D4 | — | 28 | 2 | no | — |
| 329 | C22×C4 | — | 4 | 1 | no | — |
| 330 | C22×C4 | — | 14 | 1 | no | — |
| 331 | C22×C4 | — | 28 | 1 | no | — |
| 332 | C22×C4 | — | 28 | 1 | no | — |
| 333 | C22×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 334 | Q16 | — | 2 | 1 | no | — |
| 335 | Q16 | — | 2 | 1 | no | — |
| 336 | Q16 | — | 14 | 1 | no | — |
| 337 | Q16 | — | 14 | 1 | no | — |
| 338 | Q16 | — | 28 | 2 | no | — |
| 339 | SD16 | — | 4 | 1 | no | — |
| 340 | SD16 | — | 4 | 1 | no | — |
| 341 | SD16 | — | 28 | 2 | no | — |
| 342 | SD16 | — | 28 | 2 | no | — |
| 343 | SD16 | — | 28 | 1 | no | — |
| 344 | SD16 | — | 28 | 1 | no | — |
| 345 | D8 | — | 2 | 1 | no | — |
| 346 | D8 | — | 2 | 1 | no | — |
| 347 | D8 | — | 14 | 1 | no | — |
| 348 | D8 | — | 14 | 1 | no | — |
| 349 | D8 | — | 28 | 2 | no | — |
| 350 | M16 | — | 2 | 2 | no | — |
| 351 | M16 | — | 4 | 1 | no | — |
| 352 | M16 | — | 14 | 1 | no | — |
| 353 | M16 | — | 14 | 1 | no | — |
| 354 | M16 | — | 28 | 1 | no | — |
| 355 | M16 | — | 28 | 1 | no | — |
| 356 | C2×C8 | — | 4 | 1 | no | — |
| 357 | C2×C8 | — | 14 | 1 | no | — |
| 358 | C2×C8 | — | 28 | 1 | no | — |
| 359 | C2×C8 | — | 28 | 1 | no | — |
| 360 | C2×C8 | C2×D28 | 1 | 1 | yes | characteristic |
| 361 | C2×C8 | #1157 | 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 | D4×D7 | 1 | 1 | yes | characteristic |
| 365 | C2×C8 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 366 | C4⋊C4 | — | 14 | 2 | no | — |
| 367 | C4⋊C4 | — | 28 | 2 | no | — |
| 368 | C4⋊C4 | — | 28 | 1 | no | — |
| 369 | C22⋊C4 | — | 28 | 2 | no | — |
| 370 | C22⋊C4 | — | 28 | 2 | no | — |
| 371 | C16 | — | 4 | 1 | no | — |
| 372 | C16 | — | 14 | 2 | no | — |
| 373 | C2×C7 | — | 2 | 1 | no | — |
| 374 | C2×C7 | — | 2 | 1 | no | — |
| 375 | C2×C7 | — | 2 | 1 | no | — |
| 376 | C2×C7 | — | 16 | 1 | no | — |
| 377 | C2×C7 | #1999 | 1 | 1 | yes | characteristic |
| 378 | D7 | — | 8 | 1 | no | — |
| 379 | D7 | — | 16 | 1 | no | — |
| 380 | C23 | — | 4 | 1 | no | — |
| 381 | C23 | — | 14 | 1 | no | — |
| 382 | C23 | — | 28 | 1 | no | — |
| 383 | C23 | #6477 | 1 | 1 | yes | characteristic |
| 384 | Q8 | — | 4 | 1 | no | — |
| 385 | Q8 | — | 4 | 1 | no | — |
| 386 | Q8 | — | 14 | 1 | no | — |
| 387 | Q8 | — | 14 | 1 | no | — |
| 388 | Q8 | — | 28 | 1 | no | — |
| 389 | Q8 | — | 28 | 1 | no | — |
| 390 | D4 | — | 4 | 1 | no | — |
| 391 | D4 | — | 4 | 1 | no | — |
| 392 | D4 | — | 8 | 1 | no | — |
| 393 | D4 | — | 8 | 1 | no | — |
| 394 | D4 | — | 14 | 1 | no | — |
| 395 | D4 | — | 14 | 1 | no | — |
| 396 | D4 | — | 28 | 1 | no | — |
| 397 | D4 | — | 28 | 1 | no | — |
| 398 | D4 | — | 28 | 1 | no | — |
| 399 | D4 | — | 28 | 1 | no | — |
| 400 | D4 | — | 56 | 1 | no | — |
| 401 | D4 | — | 56 | 1 | no | — |
| 402 | D4 | — | 112 | 2 | no | — |
| 403 | C2×C4 | — | 4 | 1 | no | — |
| 404 | C2×C4 | — | 8 | 1 | no | — |
| 405 | C2×C4 | — | 8 | 1 | no | — |
| 406 | C2×C4 | — | 14 | 1 | no | — |
| 407 | C2×C4 | — | 28 | 1 | no | — |
| 408 | C2×C4 | — | 28 | 1 | no | — |
| 409 | C2×C4 | — | 28 | 1 | no | — |
| 410 | C2×C4 | — | 28 | 2 | no | — |
| 411 | C2×C4 | — | 56 | 1 | no | — |
| 412 | C2×C4 | — | 56 | 1 | no | — |
| 413 | C2×C4 | — | 112 | 1 | no | — |
| 414 | C2×C4 | #6445 | 1 | 1 | yes | characteristic |
| 415 | C2×C4 | #6447 | 1 | 1 | yes | characteristic |
| 416 | C2×C4 | D7×D8 | 1 | 1 | yes | characteristic |
| 417 | C2×C4 | #6474 | 1 | 1 | yes | characteristic |
| 418 | C2×C4 | #6479 | 1 | 1 | yes | characteristic |
| 419 | C2×C4 | #6500 | 1 | 1 | yes | characteristic |
| 420 | C8 | — | 4 | 2 | no | — |
| 421 | C8 | — | 28 | 1 | no | — |
| 422 | C8 | #6445 | 1 | 1 | yes | characteristic |
| 423 | C8 | #6447 | 1 | 1 | yes | characteristic |
| 424 | C8 | #6493 | 1 | 1 | yes | characteristic |
| 425 | C8 | #6503 | 1 | 1 | yes | characteristic |
| 426 | C7 | #13318 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 427 | C22 | — | 4 | 1 | no | — |
| 428 | C22 | — | 8 | 1 | no | — |
| 429 | C22 | — | 8 | 1 | no | — |
| 430 | C22 | — | 8 | 1 | no | — |
| 431 | C22 | — | 28 | 2 | no | — |
| 432 | C22 | — | 28 | 1 | no | — |
| 433 | C22 | — | 56 | 1 | no | — |
| 434 | C22 | — | 112 | 1 | no | — |
| 435 | C22 | #89545 | 1 | 1 | yes | characteristic |
| 436 | C22 | #89554 | 1 | 1 | yes | characteristic |
| 437 | C22 | #89944 | 1 | 1 | yes | characteristic |
| 438 | C4 | — | 8 | 1 | no | — |
| 439 | C4 | — | 28 | 1 | no | — |
| 440 | C4 | — | 56 | 2 | no | — |
| 441 | C4 | — | 56 | 1 | no | — |
| 442 | C4 | #89547 | 1 | 1 | yes | characteristic |
| 443 | C4 | #89553 | 1 | 1 | yes | characteristic |
| 444 | C4 | #89732 | 1 | 1 | yes | characteristic |
| 445 | C4 | #89928 | 1 | 1 | yes | characteristic |
| 446 | C2 | — | 2 | 1 | no | — |
| 447 | C2 | — | 2 | 1 | no | — |
| 448 | C2 | — | 2 | 1 | no | — |
| 449 | C2 | — | 16 | 1 | no | — |
| 450 | C2 | — | 56 | 1 | no | — |
| 451 | C2 | — | 112 | 1 | no | — |
| 452 | C2 | #11727958 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11741361 | C2 | semidirect |
| 2. #11741339 | C2 | semidirect |
| 3. #11736701 | C2 | semidirect |
| 4. C7×#2143 | C2 | semidirect |
| 5. C2×#89313 | C2 | semidirect |
| 6. #11729192 | C2 | semidirect |
| 7. #11725536 | C2 | semidirect |
| 57. C2×Dic28 | D4 | semidirect |
| 63. C2×D56 | D4 | semidirect |
| 75. C7×#108 | D4 | semidirect |
| 88. C2×C7⋊C16 | D4 | semidirect |
| 93. #2143 | D7 | semidirect |
| 281. #108 | C22⋊D7 | semidirect |
| 426. C7 | #13318 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11741361 | 2 |
| #11741339 | 2 |
| #11736701 | 2 |
| C7×#2143 | 2 |
| C2×#89313 | 2 |
| #11729192 | 2 |
| #11725536 | 2 |
| #13318 | 7 |