Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1078 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1078 conjugacy classes of subgroups — too many to draw. Only its 171 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 | C7×#3549 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11740752 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #11740731 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11729703 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #11729702 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #11729553 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11729552 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | C7×H(3,𝔽4) | C22 | 1 | 4 | yes | — |
| 9 | C7×#555 | — | 2 | 1 | no | — |
| 10 | C7×#555 | — | 2 | 2 | no | — |
| 11 | C7×D42 | — | 2 | 2 | no | — |
| 12 | C7×D42 | — | 2 | 1 | no | — |
| 13 | C7×#535 | — | 2 | 2 | no | — |
| 14 | C7×#535 | — | 2 | 4 | no | — |
| 15 | C7×#532 | C22 | 1 | 1 | yes | characteristic |
| 16 | C7×#532 | C22 | 1 | 2 | yes | — |
| 17 | C2×#6513 | — | 2 | 2 | no | — |
| 18 | #90168 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | #90010 | — | 2 | 4 | no | — |
| 20 | #89858 | — | 2 | 1 | no | — |
| 21 | #89855 | — | 2 | 2 | no | — |
| 22 | #89846 | — | 2 | 1 | no | — |
| 23 | #89844 | — | 2 | 2 | no | — |
| 24 | #89832 | C22 | 1 | 2 | yes | complemented |
| 25 | #89830 | C22 | 1 | 2 | yes | complemented |
| 26 | #89830 | C22 | 1 | 4 | yes | complemented |
| 27 | #89827 | C22 | 1 | 4 | yes | complemented |
| 28 | #89698 | C22 | 1 | 2 | yes | complemented |
| 29 | C2×#6377 | C22 | 1 | 1 | yes | characteristic, complemented |
| 30 | #89335 | C22 | 1 | 8 | yes | complemented |
| 31 | #89335 | C22 | 1 | 4 | yes | complemented |
| 32 | #19052 | — | 7 | 1 | no | maximal, Sylow |
| 33 | C2×C7×#41 | D4 | 1 | 2 | yes | — |
| 34 | C2×C7×#41 | D4 | 1 | 4 | yes | — |
| 35 | C22×C7×D4 | — | 2 | 4 | no | — |
| 36 | C22×C7×D4 | — | 2 | 2 | no | — |
| 37 | C2×#1157 | — | 2 | 1 | no | — |
| 38 | C7×C4⋊Q8 | D4 | 1 | 1 | yes | characteristic |
| 39 | C7×C4⋊Q8 | D4 | 1 | 2 | yes | — |
| 40 | C7×#127 | — | 2 | 4 | no | — |
| 41 | C7×#127 | D4 | 1 | 2 | yes | — |
| 42 | C7×#127 | D4 | 1 | 1 | yes | characteristic |
| 43 | C7×#124 | — | 2 | 8 | no | — |
| 44 | C7×#124 | — | 2 | 4 | no | — |
| 45 | C7×#124 | C23 | 1 | 4 | yes | — |
| 46 | C7×#124 | C23 | 1 | 2 | yes | — |
| 47 | C7×#121 | — | 2 | 4 | no | — |
| 48 | C7×#121 | — | 2 | 4 | no | — |
| 49 | C7×#121 | — | 2 | 4 | no | — |
| 50 | C7×#121 | — | 2 | 2 | no | — |
| 51 | C7×#121 | — | 2 | 2 | no | — |
| 52 | C7×#121 | — | 2 | 2 | no | — |
| 53 | C7×#120 | — | 2 | 4 | no | — |
| 54 | C7×#120 | — | 2 | 8 | no | — |
| 55 | C7×#120 | — | 2 | 4 | no | — |
| 56 | C4×C7×D4 | — | 2 | 2 | no | — |
| 57 | C4×C7×D4 | — | 2 | 2 | no | — |
| 58 | C4×C7×D4 | — | 2 | 2 | no | — |
| 59 | C7×#117 | — | 2 | 4 | no | — |
| 60 | C7×#117 | — | 2 | 2 | no | — |
| 61 | C2×C42×C7 | C23 | 1 | 1 | yes | characteristic |
| 62 | #6513 | — | 4 | 8 | no | — |
| 63 | C2×#1144 | — | 2 | 2 | no | — |
| 64 | C2×#1143 | — | 2 | 2 | no | — |
| 65 | C2×#1143 | — | 2 | 4 | no | — |
| 66 | C2×#1142 | — | 2 | 2 | no | — |
| 67 | C2×#1141 | — | 2 | 2 | no | — |
| 68 | C2×#1141 | — | 2 | 4 | no | — |
| 69 | #6493 | — | 2 | 2 | no | — |
| 70 | C22×C7⋊C8 | — | 2 | 1 | no | — |
| 71 | #6438 | — | 2 | 1 | no | — |
| 72 | #6437 | C23 | 1 | 1 | yes | characteristic |
| 73 | C4×D28 | — | 2 | 2 | no | — |
| 74 | #6432 | C23 | 1 | 1 | yes | characteristic |
| 75 | #6409 | — | 2 | 4 | no | — |
| 76 | #6406 | — | 2 | 4 | no | — |
| 77 | C22⋊(C7⋊C8) | — | 2 | 2 | no | — |
| 78 | C4⋊(C7⋊C8) | — | 2 | 2 | no | — |
| 79 | #6377 | — | 2 | 1 | no | — |
| 80 | #6377 | C23 | 1 | 2 | yes | — |
| 81 | #6377 | C23 | 1 | 4 | yes | — |
| 82 | #3549 | D7 | 1 | 1 | yes | characteristic, complemented |
| 83 | #3214 | — | 7 | 2 | no | — |
| 84 | #3150 | — | 7 | 1 | no | — |
| 85 | #1659 | — | 7 | 4 | no | — |
| 86 | #1655 | — | 7 | 4 | no | — |
| 87 | #1536 | — | 7 | 1 | no | — |
| 88 | #1530 | — | 7 | 2 | no | — |
| 89 | C24×C7 | — | 2 | 4 | no | — |
| 90 | C7×#41 | — | 4 | 4 | no | — |
| 91 | C7×#41 | — | 8 | 4 | no | — |
| 92 | C2×C7×Q8 | C2×D4 | 1 | 4 | yes | — |
| 93 | C2×C7×Q8 | C2×D4 | 1 | 2 | yes | — |
| 94 | C2×C7×D4 | — | 2 | 4 | no | — |
| 95 | C2×C7×D4 | — | 2 | 8 | no | — |
| 96 | C2×C7×D4 | — | 2 | 2 | no | — |
| 97 | C2×C7×D4 | — | 2 | 4 | no | — |
| 98 | C2×C7×D4 | — | 2 | 2 | no | — |
| 99 | C2×C7×D4 | — | 2 | 2 | no | — |
| 100 | C2×C7×D4 | — | 2 | 2 | no | — |
| 101 | C2×C7×D4 | — | 8 | 8 | no | — |
| 102 | C2×C7×D4 | — | 8 | 4 | no | — |
| 103 | C2×C7×D4 | C2×D4 | 1 | 4 | yes | — |
| 104 | C2×C7×D4 | C2×D4 | 1 | 2 | yes | — |
| 105 | C22×C4×C7 | — | 2 | 4 | no | — |
| 106 | C22×C4×C7 | — | 2 | 2 | no | — |
| 107 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 108 | C22×C4×C7 | C2×D4 | 1 | 2 | yes | — |
| 109 | C2×C22⋊D7 | — | 4 | 1 | no | — |
| 110 | #1157 | — | 4 | 4 | no | — |
| 111 | C2×D28 | — | 2 | 2 | no | — |
| 112 | C2×D28 | — | 2 | 1 | no | — |
| 113 | C2×C4×D7 | — | 4 | 1 | no | — |
| 114 | C2×Dic14 | — | 2 | 1 | no | — |
| 115 | C7×C4⋊C4 | — | 2 | 2 | no | — |
| 116 | C7×C4⋊C4 | — | 2 | 2 | no | — |
| 117 | C7×C4⋊C4 | — | 2 | 2 | no | — |
| 118 | C7×C22⋊C4 | — | 2 | 8 | no | — |
| 119 | C7×C22⋊C4 | — | 2 | 4 | no | — |
| 120 | C7×C22⋊C4 | — | 2 | 4 | no | — |
| 121 | C7×C22⋊C4 | — | 2 | 4 | no | — |
| 122 | C7×C22⋊C4 | — | 2 | 4 | no | — |
| 123 | C42×C7 | — | 2 | 4 | no | — |
| 124 | C42×C7 | C2×D4 | 1 | 2 | yes | — |
| 125 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 126 | C42×C7 | C24 | 1 | 1 | yes | characteristic |
| 127 | #1144 | — | 4 | 4 | no | — |
| 128 | #1143 | — | 4 | 4 | no | — |
| 129 | #1143 | — | 8 | 4 | no | — |
| 130 | #1142 | — | 4 | 4 | no | — |
| 131 | #1141 | — | 4 | 4 | no | — |
| 132 | #1141 | — | 8 | 4 | no | — |
| 133 | (C2×D7)⋊C4 | — | 4 | 2 | no | — |
| 134 | C4⋊Dic7 | — | 2 | 2 | no | — |
| 135 | C2×C7⋊C8 | — | 2 | 4 | no | — |
| 136 | C2×C7⋊C8 | — | 2 | 2 | no | — |
| 137 | C2×C7⋊C8 | — | 2 | 4 | no | — |
| 138 | C2×#135 | — | 14 | 2 | no | — |
| 139 | H(3,𝔽4) | C2×D7 | 1 | 4 | yes | — |
| 140 | #555 | — | 2 | 2 | no | — |
| 141 | #555 | — | 2 | 1 | no | — |
| 142 | D42 | — | 2 | 2 | no | — |
| 143 | D42 | — | 2 | 1 | no | — |
| 144 | #535 | — | 2 | 2 | no | — |
| 145 | #535 | — | 2 | 4 | no | — |
| 146 | #532 | — | 7 | 1 | no | — |
| 147 | #532 | C2×D7 | 1 | 1 | yes | characteristic |
| 148 | #532 | C2×D7 | 1 | 2 | yes | — |
| 149 | #497 | — | 7 | 2 | no | — |
| 150 | #497 | — | 14 | 1 | no | — |
| 151 | #496 | — | 7 | 2 | no | — |
| 152 | #496 | — | 7 | 4 | no | — |
| 153 | #496 | — | 14 | 1 | no | — |
| 154 | #489 | — | 7 | 4 | no | — |
| 155 | #461 | — | 14 | 2 | no | — |
| 156 | #459 | — | 14 | 2 | no | — |
| 157 | #449 | — | 14 | 4 | no | — |
| 158 | #432 | — | 7 | 2 | no | — |
| 159 | C2×#97 | — | 7 | 1 | no | — |
| 160 | #329 | — | 7 | 4 | no | — |
| 161 | #329 | — | 7 | 8 | no | — |
| 162 | C23×C7 | — | 2 | 2 | no | — |
| 163 | C23×C7 | — | 2 | 4 | no | — |
| 164 | C23×C7 | — | 8 | 4 | no | — |
| 165 | C23×C7 | — | 8 | 8 | no | — |
| 166 | C23×C7 | #120 | 1 | 1 | yes | characteristic |
| 167 | C22×D7 | — | 4 | 1 | no | — |
| 168 | C7×Q8 | — | 4 | 2 | no | — |
| 169 | C7×Q8 | — | 4 | 4 | no | — |
| 170 | C7×D4 | — | 4 | 2 | no | — |
| 171 | C7×D4 | — | 4 | 4 | no | — |
| 172 | C7×D4 | — | 4 | 4 | no | — |
| 173 | C7×D4 | — | 4 | 4 | no | — |
| 174 | C7×D4 | — | 4 | 4 | no | — |
| 175 | C7×D4 | — | 8 | 2 | no | — |
| 176 | C7×D4 | — | 8 | 4 | no | — |
| 177 | C7×D4 | — | 8 | 4 | no | — |
| 178 | C7×D4 | — | 8 | 8 | no | — |
| 179 | C2×C4×C7 | — | 2 | 2 | no | — |
| 180 | C2×C4×C7 | — | 2 | 2 | no | — |
| 181 | C2×C4×C7 | — | 2 | 4 | no | — |
| 182 | C2×C4×C7 | — | 4 | 2 | no | — |
| 183 | C2×C4×C7 | — | 4 | 8 | no | — |
| 184 | C2×C4×C7 | — | 4 | 4 | no | — |
| 185 | C2×C4×C7 | #120 | 1 | 2 | yes | — |
| 186 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 187 | C2×C4×C7 | C22×D4 | 1 | 2 | yes | — |
| 188 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 189 | C22⋊D7 | — | 8 | 2 | no | — |
| 190 | C2×Dic7 | — | 4 | 1 | no | — |
| 191 | D28 | — | 4 | 2 | no | — |
| 192 | D28 | — | 4 | 2 | no | — |
| 193 | D28 | — | 4 | 2 | no | — |
| 194 | C4×D7 | — | 8 | 2 | no | — |
| 195 | Dic14 | — | 4 | 2 | no | — |
| 196 | C7⋊C8 | — | 2 | 4 | no | — |
| 197 | C7⋊C8 | — | 4 | 4 | no | — |
| 198 | C2×#41 | — | 14 | 1 | no | — |
| 199 | C2×#41 | C22⋊D7 | 1 | 2 | yes | — |
| 200 | C2×#41 | C22⋊D7 | 1 | 4 | yes | — |
| 201 | C22×D4 | — | 2 | 4 | no | — |
| 202 | C22×D4 | — | 2 | 2 | no | — |
| 203 | #135 | — | 28 | 8 | no | — |
| 204 | C2×Q16 | — | 14 | 2 | no | — |
| 205 | C2×SD16 | — | 14 | 2 | no | — |
| 206 | C2×SD16 | — | 14 | 2 | no | — |
| 207 | C2×SD16 | — | 14 | 4 | no | — |
| 208 | C2×D8 | — | 14 | 2 | no | — |
| 209 | C2×D8 | — | 14 | 4 | no | — |
| 210 | C22×C8 | — | 14 | 1 | no | — |
| 211 | C4⋊Q8 | — | 7 | 1 | no | — |
| 212 | C4⋊Q8 | C22⋊D7 | 1 | 2 | yes | — |
| 213 | C4⋊Q8 | C22⋊D7 | 1 | 1 | yes | characteristic |
| 214 | #127 | — | 2 | 4 | no | — |
| 215 | #127 | — | 7 | 1 | no | — |
| 216 | #127 | C22⋊D7 | 1 | 2 | yes | — |
| 217 | #127 | C22⋊D7 | 1 | 1 | yes | characteristic |
| 218 | #124 | — | 2 | 8 | no | — |
| 219 | #124 | — | 2 | 4 | no | — |
| 220 | #124 | — | 14 | 1 | no | — |
| 221 | #124 | C22×D7 | 1 | 4 | yes | — |
| 222 | #124 | C22×D7 | 1 | 2 | yes | — |
| 223 | #121 | — | 2 | 4 | no | — |
| 224 | #121 | — | 2 | 4 | no | — |
| 225 | #121 | — | 2 | 4 | no | — |
| 226 | #121 | — | 2 | 2 | no | — |
| 227 | #121 | — | 2 | 2 | no | — |
| 228 | #121 | — | 2 | 2 | no | — |
| 229 | #121 | — | 14 | 2 | no | — |
| 230 | #120 | — | 2 | 4 | no | — |
| 231 | #120 | — | 2 | 8 | no | — |
| 232 | #120 | — | 2 | 4 | no | — |
| 233 | C4×D4 | — | 2 | 2 | no | — |
| 234 | C4×D4 | — | 2 | 2 | no | — |
| 235 | C4×D4 | — | 2 | 2 | no | — |
| 236 | C4×D4 | — | 14 | 2 | no | — |
| 237 | #117 | — | 2 | 4 | no | — |
| 238 | #117 | — | 2 | 2 | no | — |
| 239 | C2×C42 | C22×D7 | 1 | 1 | yes | characteristic |
| 240 | C4⋊C8 | — | 14 | 2 | no | — |
| 241 | #103 | — | 14 | 4 | no | — |
| 242 | #102 | — | 14 | 4 | no | — |
| 243 | C22⋊C8 | — | 14 | 2 | no | — |
| 244 | #97 | — | 7 | 2 | no | — |
| 245 | #97 | — | 7 | 4 | no | — |
| 246 | #97 | — | 14 | 1 | no | — |
| 247 | C22×C7 | — | 2 | 1 | no | — |
| 248 | C22×C7 | — | 2 | 2 | no | — |
| 249 | C22×C7 | — | 4 | 2 | no | — |
| 250 | C22×C7 | — | 4 | 4 | no | — |
| 251 | C22×C7 | — | 4 | 4 | no | — |
| 252 | C22×C7 | — | 4 | 4 | no | — |
| 253 | C22×C7 | — | 4 | 4 | no | — |
| 254 | C22×C7 | — | 16 | 8 | no | — |
| 255 | C22×C7 | C2×#120 | 1 | 1 | yes | characteristic |
| 256 | C2×D7 | — | 8 | 1 | no | — |
| 257 | C2×D7 | — | 8 | 2 | no | — |
| 258 | C4×C7 | — | 2 | 1 | no | — |
| 259 | C4×C7 | — | 2 | 2 | no | — |
| 260 | C4×C7 | — | 2 | 2 | no | — |
| 261 | C4×C7 | — | 4 | 2 | no | — |
| 262 | C4×C7 | — | 4 | 4 | no | — |
| 263 | C4×C7 | #453 | 1 | 2 | yes | — |
| 264 | Dic7 | — | 8 | 1 | no | — |
| 265 | C24 | — | 2 | 4 | no | — |
| 266 | #41 | — | 4 | 4 | no | — |
| 267 | #41 | — | 8 | 4 | no | — |
| 268 | #41 | — | 28 | 4 | no | — |
| 269 | C2×Q8 | — | 14 | 1 | no | — |
| 270 | C2×Q8 | C2×C22⋊D7 | 1 | 4 | yes | — |
| 271 | C2×Q8 | C2×C22⋊D7 | 1 | 2 | yes | — |
| 272 | C2×D4 | — | 2 | 4 | no | — |
| 273 | C2×D4 | — | 2 | 8 | no | — |
| 274 | C2×D4 | — | 2 | 2 | no | — |
| 275 | C2×D4 | — | 2 | 4 | no | — |
| 276 | C2×D4 | — | 2 | 2 | no | — |
| 277 | C2×D4 | — | 2 | 2 | no | — |
| 278 | C2×D4 | — | 2 | 2 | no | — |
| 279 | C2×D4 | — | 8 | 8 | no | — |
| 280 | C2×D4 | — | 8 | 4 | no | — |
| 281 | C2×D4 | — | 14 | 2 | no | — |
| 282 | C2×D4 | — | 14 | 1 | no | — |
| 283 | C2×D4 | — | 28 | 1 | no | — |
| 284 | C2×D4 | C2×C22⋊D7 | 1 | 4 | yes | — |
| 285 | C2×D4 | C2×C22⋊D7 | 1 | 2 | yes | — |
| 286 | C22×C4 | — | 2 | 4 | no | — |
| 287 | C22×C4 | — | 2 | 2 | no | — |
| 288 | C22×C4 | — | 28 | 1 | no | — |
| 289 | C22×C4 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 290 | C22×C4 | C2×C22⋊D7 | 1 | 2 | yes | — |
| 291 | Q16 | — | 28 | 4 | no | — |
| 292 | SD16 | — | 28 | 4 | no | — |
| 293 | SD16 | — | 28 | 4 | no | — |
| 294 | SD16 | — | 56 | 4 | no | — |
| 295 | D8 | — | 28 | 4 | no | — |
| 296 | D8 | — | 56 | 4 | no | — |
| 297 | C2×C8 | — | 14 | 4 | no | — |
| 298 | C2×C8 | — | 14 | 2 | no | — |
| 299 | C2×C8 | — | 14 | 4 | no | — |
| 300 | C4⋊C4 | — | 2 | 2 | no | — |
| 301 | C4⋊C4 | — | 2 | 2 | no | — |
| 302 | C4⋊C4 | — | 2 | 2 | no | — |
| 303 | C4⋊C4 | — | 14 | 2 | no | — |
| 304 | C22⋊C4 | — | 2 | 8 | no | — |
| 305 | C22⋊C4 | — | 2 | 4 | no | — |
| 306 | C22⋊C4 | — | 2 | 4 | no | — |
| 307 | C22⋊C4 | — | 2 | 4 | no | — |
| 308 | C22⋊C4 | — | 2 | 4 | no | — |
| 309 | C22⋊C4 | — | 28 | 2 | no | — |
| 310 | C42 | — | 2 | 4 | no | — |
| 311 | C42 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 312 | C42 | C2×C22⋊D7 | 1 | 2 | yes | — |
| 313 | C42 | C23×D7 | 1 | 1 | yes | characteristic |
| 314 | C2×C7 | — | 4 | 1 | no | — |
| 315 | C2×C7 | — | 8 | 2 | no | — |
| 316 | C2×C7 | — | 8 | 4 | no | — |
| 317 | C2×C7 | C2×#453 | 1 | 1 | yes | characteristic |
| 318 | C2×C7 | #3019 | 1 | 2 | yes | — |
| 319 | D7 | — | 16 | 1 | no | — |
| 320 | C23 | — | 2 | 2 | no | — |
| 321 | C23 | — | 2 | 4 | no | — |
| 322 | C23 | — | 8 | 4 | no | — |
| 323 | C23 | — | 8 | 8 | no | — |
| 324 | C23 | — | 28 | 1 | no | — |
| 325 | C23 | #6516 | 1 | 1 | yes | characteristic |
| 326 | Q8 | — | 4 | 2 | no | — |
| 327 | Q8 | — | 4 | 4 | no | — |
| 328 | Q8 | — | 28 | 2 | no | — |
| 329 | D4 | — | 4 | 2 | no | — |
| 330 | D4 | — | 4 | 4 | no | — |
| 331 | D4 | — | 4 | 4 | no | — |
| 332 | D4 | — | 4 | 4 | no | — |
| 333 | D4 | — | 4 | 4 | no | — |
| 334 | D4 | — | 8 | 2 | no | — |
| 335 | D4 | — | 8 | 4 | no | — |
| 336 | D4 | — | 8 | 4 | no | — |
| 337 | D4 | — | 8 | 8 | no | — |
| 338 | D4 | — | 28 | 2 | no | — |
| 339 | D4 | — | 28 | 2 | no | — |
| 340 | D4 | — | 28 | 2 | no | — |
| 341 | D4 | — | 56 | 2 | no | — |
| 342 | C2×C4 | — | 2 | 2 | no | — |
| 343 | C2×C4 | — | 2 | 2 | no | — |
| 344 | C2×C4 | — | 2 | 4 | no | — |
| 345 | C2×C4 | — | 4 | 2 | no | — |
| 346 | C2×C4 | — | 4 | 8 | no | — |
| 347 | C2×C4 | — | 4 | 4 | no | — |
| 348 | C2×C4 | — | 28 | 1 | no | — |
| 349 | C2×C4 | — | 56 | 2 | no | — |
| 350 | C2×C4 | #6516 | 1 | 2 | yes | — |
| 351 | C2×C4 | #6516 | 1 | 1 | yes | characteristic |
| 352 | C2×C4 | C22×C22⋊D7 | 1 | 2 | yes | — |
| 353 | C2×C4 | C22×C22⋊D7 | 1 | 1 | yes | characteristic |
| 354 | C8 | — | 14 | 4 | no | — |
| 355 | C8 | — | 28 | 4 | no | — |
| 356 | C7 | #19052 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 357 | C22 | — | 2 | 1 | no | — |
| 358 | C22 | — | 2 | 2 | no | — |
| 359 | C22 | — | 4 | 2 | no | — |
| 360 | C22 | — | 4 | 4 | no | — |
| 361 | C22 | — | 4 | 4 | no | — |
| 362 | C22 | — | 4 | 4 | no | — |
| 363 | C22 | — | 4 | 4 | no | — |
| 364 | C22 | — | 16 | 8 | no | — |
| 365 | C22 | — | 56 | 1 | no | — |
| 366 | C22 | — | 56 | 2 | no | — |
| 367 | C22 | C2×#6516 | 1 | 1 | yes | characteristic |
| 368 | C4 | — | 2 | 1 | no | — |
| 369 | C4 | — | 2 | 2 | no | — |
| 370 | C4 | — | 2 | 2 | no | — |
| 371 | C4 | — | 4 | 2 | no | — |
| 372 | C4 | — | 4 | 4 | no | — |
| 373 | C4 | — | 56 | 1 | no | — |
| 374 | C4 | #90013 | 1 | 2 | yes | — |
| 375 | C2 | — | 4 | 1 | no | — |
| 376 | C2 | — | 8 | 2 | no | — |
| 377 | C2 | — | 8 | 4 | no | — |
| 378 | C2 | — | 112 | 1 | no | — |
| 379 | C2 | C2×#90013 | 1 | 1 | yes | characteristic |
| 380 | C2 | #11741549 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×#6516 |
| commutator, cosocle | C42×C7 | C24 |
| Frattini | C42 | C23×D7 |
| Fitting | C7×#3549 | C2 |
| socle | C22×C7 | C2×#120 |
| hypercenter | #3549 | D7 |
| hypocenter | C7 | #19052 |
| LCS | G ▷ C42×C7 ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #3549 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C7×#3549 | C2 | semidirect |
| 2. #11740752 | C2 | semidirect |
| 3. #11740731 | C2 | semidirect |
| 4. #11729703 | C2 | semidirect |
| 5. #11729702 | C2 | semidirect |
| 6. #11729553 | C2 | semidirect |
| 7. #11729552 | C2 | semidirect |
| 18. #90168 | C22 | semidirect |
| 24. #89832 | C22 | semidirect |
| 25. #89830 | C22 | semidirect |
| 26. #89830 | C22 | semidirect |
| 27. #89827 | C22 | semidirect |
| 28. #89698 | C22 | semidirect |
| 29. C2×#6377 | C22 | semidirect |
| 30. #89335 | C22 | semidirect |
| 31. #89335 | C22 | semidirect |
| 82. #3549 | D7 | semidirect |
| 356. C7 | #19052 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3549 | 2 |
| #11740752 | 2 |
| #11740731 | 2 |
| #11729703 | 2 |
| #11729702 | 2 |
| #11729553 | 2 |
| #11729552 | 2 |
| #19052 | 7 |