Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1214 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1214 conjugacy classes of subgroups — too many to draw. Only its 191 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 | #11742886 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C7×#2568 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11740644 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C4×#6410 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11727446 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #11727317 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #11727246 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | C2×#6551 | C22 | 1 | 2 | yes | — |
| 9 | C2×C7×C4⋊Q8 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×C4×C7×Q8 | C22 | 1 | 1 | yes | characteristic |
| 11 | #90268 | — | 2 | 2 | no | — |
| 12 | #90267 | — | 2 | 4 | no | — |
| 13 | Q8×D28 | — | 2 | 2 | no | — |
| 14 | #90201 | — | 2 | 2 | no | — |
| 15 | #90201 | C22 | 1 | 2 | yes | — |
| 16 | #90168 | — | 2 | 2 | no | — |
| 17 | #90168 | C22 | 1 | 2 | yes | — |
| 18 | C7×#400 | — | 2 | 2 | no | — |
| 19 | C7×#391 | — | 2 | 2 | no | — |
| 20 | C7×#391 | C22 | 1 | 2 | yes | — |
| 21 | C7×#382 | C22 | 1 | 2 | yes | — |
| 22 | C4×C7×C4⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#6410 | C22 | 1 | 2 | yes | — |
| 24 | #89865 | — | 2 | 2 | no | — |
| 25 | #89861 | — | 2 | 4 | no | — |
| 26 | #89860 | — | 2 | 2 | no | — |
| 27 | #89738 | C22 | 1 | 8 | yes | — |
| 28 | C2×#6379 | C22 | 1 | 8 | yes | — |
| 29 | C4×#1136 | C22 | 1 | 2 | yes | — |
| 30 | #89325 | C22 | 1 | 2 | yes | — |
| 31 | #25872 | — | 7 | 1 | no | maximal, Sylow |
| 32 | C22×C7×Q8 | — | 2 | 1 | no | — |
| 33 | C22×C7×Q8 | C23 | 1 | 1 | yes | characteristic |
| 34 | #6551 | — | 2 | 8 | no | — |
| 35 | #6551 | — | 4 | 4 | no | — |
| 36 | C2×#1161 | — | 2 | 4 | no | — |
| 37 | C2×Q8×D7 | — | 2 | 4 | no | — |
| 38 | C2×#1157 | — | 2 | 4 | no | — |
| 39 | C2×#1157 | C23 | 1 | 4 | yes | — |
| 40 | C7×C4⋊Q8 | — | 2 | 2 | no | — |
| 41 | C7×C4⋊Q8 | — | 2 | 2 | no | — |
| 42 | C4×C7×Q8 | — | 2 | 2 | no | — |
| 43 | C4×C7×Q8 | — | 2 | 2 | no | — |
| 44 | C2×C7×C4⋊C4 | — | 2 | 1 | no | — |
| 45 | C2×C7×C4⋊C4 | — | 2 | 1 | no | — |
| 46 | C2×C7×C4⋊C4 | D4 | 1 | 2 | yes | — |
| 47 | C2×C7×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 48 | C2×C7×C4⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 49 | C2×C42×C7 | D4 | 1 | 2 | yes | — |
| 50 | C2×C42×C7 | C23 | 1 | 2 | yes | — |
| 51 | C2×C42×C7 | C23 | 1 | 1 | yes | characteristic |
| 52 | #6493 | — | 2 | 2 | no | — |
| 53 | #6493 | — | 2 | 4 | no | — |
| 54 | #6493 | — | 2 | 2 | no | — |
| 55 | C2×#1136 | C23 | 1 | 4 | yes | — |
| 56 | #6460 | — | 2 | 8 | no | — |
| 57 | #6460 | — | 2 | 4 | no | — |
| 58 | #6458 | — | 2 | 8 | no | — |
| 59 | #6458 | — | 2 | 4 | no | — |
| 60 | #6438 | — | 2 | 4 | no | — |
| 61 | #6438 | D4 | 1 | 4 | yes | — |
| 62 | #6437 | — | 2 | 2 | no | — |
| 63 | #6437 | D4 | 1 | 2 | yes | — |
| 64 | C4×D28 | — | 2 | 4 | no | — |
| 65 | C4×D28 | — | 2 | 4 | no | — |
| 66 | C4×D28 | — | 2 | 2 | no | — |
| 67 | C4×D28 | — | 2 | 2 | no | — |
| 68 | #6432 | — | 2 | 2 | no | — |
| 69 | #6432 | D4 | 1 | 2 | yes | — |
| 70 | C7×#95 | — | 2 | 1 | no | — |
| 71 | C7×#95 | — | 2 | 4 | no | — |
| 72 | C7×#95 | — | 2 | 4 | no | — |
| 73 | #6410 | — | 2 | 4 | no | — |
| 74 | #6384 | — | 2 | 8 | no | — |
| 75 | #6383 | — | 2 | 8 | no | — |
| 76 | #6379 | — | 4 | 8 | no | — |
| 77 | #6377 | — | 2 | 2 | no | — |
| 78 | C4×C7⋊C8 | — | 2 | 2 | no | — |
| 79 | #3497 | — | 7 | 1 | no | — |
| 80 | #3141 | — | 7 | 2 | no | — |
| 81 | #2568 | D7 | 1 | 1 | yes | characteristic, complemented |
| 82 | #2040 | — | 7 | 4 | no | — |
| 83 | #1980 | — | 7 | 2 | no | — |
| 84 | #1793 | — | 7 | 4 | no | — |
| 85 | C4×#101 | — | 7 | 1 | no | — |
| 86 | C2×C7×Q8 | — | 2 | 2 | no | — |
| 87 | C2×C7×Q8 | — | 2 | 2 | no | — |
| 88 | C2×C7×Q8 | — | 4 | 4 | no | — |
| 89 | C2×C7×Q8 | — | 4 | 1 | no | — |
| 90 | C2×C7×Q8 | — | 4 | 1 | no | — |
| 91 | C2×C7×Q8 | #41 | 1 | 4 | yes | — |
| 92 | C22×C4×C7 | — | 2 | 2 | no | — |
| 93 | C22×C4×C7 | — | 2 | 2 | no | — |
| 94 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 95 | C22×C4×C7 | C2×D4 | 1 | 2 | yes | — |
| 96 | C22×C4×C7 | C2×D4 | 1 | 2 | yes | — |
| 97 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 98 | C22×C4×C7 | C24 | 1 | 1 | yes | characteristic |
| 99 | C2×C22⋊D7 | — | 2 | 4 | no | — |
| 100 | #1161 | — | 4 | 16 | no | — |
| 101 | Q8×D7 | — | 4 | 16 | no | — |
| 102 | #1157 | — | 2 | 8 | no | — |
| 103 | #1157 | — | 2 | 8 | no | — |
| 104 | #1157 | — | 4 | 8 | no | — |
| 105 | #1157 | — | 4 | 8 | no | — |
| 106 | C2×D28 | — | 2 | 4 | no | — |
| 107 | C2×D28 | — | 2 | 2 | no | — |
| 108 | C2×D28 | — | 2 | 4 | no | — |
| 109 | C2×D28 | — | 2 | 2 | no | — |
| 110 | C2×D28 | C2×D4 | 1 | 4 | yes | — |
| 111 | C2×C4×D7 | — | 2 | 8 | no | — |
| 112 | C2×C4×D7 | — | 2 | 4 | no | — |
| 113 | C2×Dic14 | — | 2 | 4 | no | — |
| 114 | C2×Dic14 | C2×D4 | 1 | 4 | yes | — |
| 115 | C7×C4⋊C4 | — | 2 | 4 | no | — |
| 116 | C7×C4⋊C4 | — | 2 | 2 | no | — |
| 117 | C7×C4⋊C4 | — | 2 | 4 | no | — |
| 118 | C7×C4⋊C4 | — | 4 | 2 | no | — |
| 119 | C7×C4⋊C4 | — | 4 | 2 | no | — |
| 120 | C42×C7 | — | 2 | 2 | no | — |
| 121 | C42×C7 | — | 2 | 2 | no | — |
| 122 | C42×C7 | — | 2 | 4 | no | — |
| 123 | C42×C7 | C2×D4 | 1 | 2 | yes | — |
| 124 | C42×C7 | C2×D4 | 1 | 2 | yes | — |
| 125 | (C2×D7)⋊C4 | — | 2 | 8 | no | — |
| 126 | (C2×D7)⋊C4 | — | 2 | 4 | no | — |
| 127 | (C2×D7)⋊C4 | — | 2 | 4 | no | — |
| 128 | C4⋊Dic7 | — | 2 | 4 | no | — |
| 129 | C4⋊Dic7 | — | 2 | 2 | no | — |
| 130 | C4⋊Dic7 | — | 2 | 2 | no | — |
| 131 | #1136 | — | 2 | 4 | no | — |
| 132 | #1136 | — | 2 | 4 | no | — |
| 133 | C2×C7⋊C8 | — | 2 | 4 | no | — |
| 134 | C2×2−1+4 | — | 7 | 2 | no | — |
| 135 | #550 | — | 14 | 2 | no | — |
| 136 | D4×Q8 | — | 14 | 2 | no | — |
| 137 | #548 | — | 14 | 4 | no | — |
| 138 | #537 | — | 7 | 2 | no | — |
| 139 | #537 | — | 14 | 2 | no | — |
| 140 | #532 | — | 7 | 2 | no | — |
| 141 | #532 | — | 14 | 2 | no | — |
| 142 | C2×C4⋊Q8 | C2×D7 | 1 | 1 | yes | characteristic |
| 143 | C2×C4×Q8 | C2×D7 | 1 | 1 | yes | characteristic |
| 144 | #489 | — | 14 | 4 | no | — |
| 145 | #487 | — | 14 | 2 | no | — |
| 146 | #486 | — | 14 | 2 | no | — |
| 147 | C2×#104 | — | 7 | 8 | no | — |
| 148 | #417 | — | 7 | 8 | no | — |
| 149 | C2×#101 | — | 7 | 2 | no | — |
| 150 | C4×M16 | — | 7 | 2 | no | — |
| 151 | #400 | — | 2 | 2 | no | — |
| 152 | #391 | — | 2 | 2 | no | — |
| 153 | #391 | C2×D7 | 1 | 2 | yes | — |
| 154 | #382 | C2×D7 | 1 | 2 | yes | — |
| 155 | C4×C4⋊C4 | C2×D7 | 1 | 1 | yes | characteristic |
| 156 | #343 | — | 7 | 2 | no | — |
| 157 | C23×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 158 | C22×D7 | — | 2 | 4 | no | — |
| 159 | C7×Q8 | — | 2 | 8 | no | — |
| 160 | C7×Q8 | — | 8 | 2 | no | — |
| 161 | C7×Q8 | — | 8 | 2 | no | — |
| 162 | C2×C4×C7 | — | 2 | 2 | no | — |
| 163 | C2×C4×C7 | — | 2 | 2 | no | — |
| 164 | C2×C4×C7 | — | 2 | 2 | no | — |
| 165 | C2×C4×C7 | — | 2 | 2 | no | — |
| 166 | C2×C4×C7 | — | 4 | 1 | no | — |
| 167 | C2×C4×C7 | — | 4 | 2 | no | — |
| 168 | C2×C4×C7 | — | 4 | 2 | no | — |
| 169 | C2×C4×C7 | — | 4 | 2 | no | — |
| 170 | C2×C4×C7 | — | 4 | 4 | no | — |
| 171 | C2×C4×C7 | — | 4 | 2 | no | — |
| 172 | C2×C4×C7 | — | 4 | 2 | no | — |
| 173 | C2×C4×C7 | #120 | 1 | 2 | yes | — |
| 174 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 175 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 176 | C2×C4×C7 | #124 | 1 | 4 | yes | — |
| 177 | C2×C4×C7 | C22×D4 | 1 | 2 | yes | — |
| 178 | C2×C4×C7 | C2×#41 | 1 | 2 | yes | — |
| 179 | C2×C4×C7 | H(5,𝔽2) | 1 | 2 | yes | — |
| 180 | C22⋊D7 | — | 4 | 4 | no | — |
| 181 | C22⋊D7 | — | 4 | 4 | no | — |
| 182 | C2×Dic7 | — | 2 | 4 | no | — |
| 183 | D28 | — | 2 | 8 | no | — |
| 184 | D28 | — | 4 | 8 | no | — |
| 185 | D28 | — | 4 | 4 | no | — |
| 186 | D28 | — | 8 | 2 | no | — |
| 187 | D28 | — | 8 | 4 | no | — |
| 188 | C4×D7 | — | 4 | 16 | no | — |
| 189 | C4×D7 | — | 4 | 8 | no | — |
| 190 | Dic14 | — | 2 | 8 | no | — |
| 191 | Dic14 | — | 4 | 8 | no | — |
| 192 | C7⋊C8 | — | 4 | 4 | no | — |
| 193 | 2−1+4 | — | 14 | 8 | no | — |
| 194 | 2−1+4 | — | 28 | 4 | no | — |
| 195 | C2×#41 | — | 7 | 4 | no | — |
| 196 | C2×#41 | — | 14 | 4 | no | — |
| 197 | C2×#41 | — | 14 | 4 | no | — |
| 198 | C22×Q8 | — | 2 | 1 | no | — |
| 199 | C22×Q8 | — | 14 | 4 | no | — |
| 200 | C22×Q8 | C22×D7 | 1 | 1 | yes | characteristic |
| 201 | C2×M16 | — | 7 | 4 | no | — |
| 202 | C4⋊Q8 | — | 2 | 2 | no | — |
| 203 | C4⋊Q8 | — | 2 | 2 | no | — |
| 204 | C4⋊Q8 | — | 7 | 2 | no | — |
| 205 | C4⋊Q8 | — | 14 | 2 | no | — |
| 206 | #127 | — | 7 | 2 | no | — |
| 207 | #127 | — | 14 | 2 | no | — |
| 208 | #124 | — | 7 | 4 | no | — |
| 209 | #124 | — | 14 | 4 | no | — |
| 210 | C22⋊Q8 | — | 14 | 4 | no | — |
| 211 | C22⋊Q8 | — | 14 | 8 | no | — |
| 212 | #121 | — | 14 | 4 | no | — |
| 213 | #121 | — | 14 | 8 | no | — |
| 214 | #121 | — | 14 | 2 | no | — |
| 215 | #121 | — | 14 | 2 | no | — |
| 216 | #121 | — | 14 | 4 | no | — |
| 217 | C4×Q8 | — | 2 | 2 | no | — |
| 218 | C4×Q8 | — | 2 | 2 | no | — |
| 219 | C4×D4 | — | 14 | 4 | no | — |
| 220 | C4×D4 | — | 14 | 4 | no | — |
| 221 | C4×D4 | — | 14 | 2 | no | — |
| 222 | C4×D4 | — | 14 | 2 | no | — |
| 223 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 224 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 225 | C2×C4⋊C4 | C22⋊D7 | 1 | 2 | yes | — |
| 226 | C2×C4⋊C4 | C22×D7 | 1 | 2 | yes | — |
| 227 | C2×C4⋊C4 | C22×D7 | 1 | 1 | yes | characteristic |
| 228 | C2×C42 | C22⋊D7 | 1 | 2 | yes | — |
| 229 | C2×C42 | C22×D7 | 1 | 2 | yes | — |
| 230 | C2×C42 | C22×D7 | 1 | 1 | yes | characteristic |
| 231 | #104 | — | 28 | 8 | no | — |
| 232 | #103 | — | 14 | 8 | no | — |
| 233 | #102 | — | 14 | 8 | no | — |
| 234 | #101 | — | 14 | 4 | no | — |
| 235 | #97 | — | 14 | 2 | no | — |
| 236 | C4×C8 | — | 14 | 2 | no | — |
| 237 | #95 | — | 2 | 1 | no | — |
| 238 | #95 | — | 2 | 4 | no | — |
| 239 | #95 | — | 2 | 4 | no | — |
| 240 | C22×C7 | — | 2 | 1 | no | — |
| 241 | C22×C7 | — | 2 | 1 | no | — |
| 242 | C22×C7 | C2×#120 | 1 | 1 | yes | characteristic |
| 243 | C22×C7 | C2×#124 | 1 | 1 | yes | characteristic |
| 244 | C22×C7 | #535 | 1 | 1 | yes | characteristic |
| 245 | C2×D7 | — | 4 | 4 | no | — |
| 246 | C2×D7 | — | 4 | 4 | no | — |
| 247 | C2×D7 | — | 4 | 4 | no | — |
| 248 | C4×C7 | — | 2 | 4 | no | — |
| 249 | C4×C7 | — | 2 | 1 | no | — |
| 250 | C4×C7 | — | 2 | 2 | no | — |
| 251 | C4×C7 | — | 4 | 2 | no | — |
| 252 | C4×C7 | — | 8 | 2 | no | — |
| 253 | C4×C7 | — | 8 | 2 | no | — |
| 254 | C4×C7 | #454 | 1 | 2 | yes | — |
| 255 | C4×C7 | #546 | 1 | 4 | yes | — |
| 256 | Dic7 | — | 4 | 4 | no | — |
| 257 | #41 | — | 14 | 8 | no | — |
| 258 | #41 | — | 14 | 8 | no | — |
| 259 | #41 | — | 28 | 8 | no | — |
| 260 | #41 | — | 28 | 16 | no | — |
| 261 | #41 | — | 28 | 8 | no | — |
| 262 | C2×Q8 | — | 2 | 2 | no | — |
| 263 | C2×Q8 | — | 2 | 2 | no | — |
| 264 | C2×Q8 | — | 4 | 4 | no | — |
| 265 | C2×Q8 | — | 4 | 1 | no | — |
| 266 | C2×Q8 | — | 4 | 1 | no | — |
| 267 | C2×Q8 | — | 7 | 4 | no | — |
| 268 | C2×Q8 | — | 14 | 4 | no | — |
| 269 | C2×Q8 | — | 28 | 16 | no | — |
| 270 | C2×Q8 | #1161 | 1 | 4 | yes | — |
| 271 | C2×D4 | — | 7 | 4 | no | — |
| 272 | C2×D4 | — | 14 | 4 | no | — |
| 273 | C2×D4 | — | 14 | 4 | no | — |
| 274 | C2×D4 | — | 14 | 4 | no | — |
| 275 | C2×D4 | — | 14 | 2 | no | — |
| 276 | C2×D4 | — | 14 | 2 | no | — |
| 277 | C22×C4 | — | 2 | 2 | no | — |
| 278 | C22×C4 | — | 2 | 2 | no | — |
| 279 | C22×C4 | — | 14 | 8 | no | — |
| 280 | C22×C4 | — | 14 | 4 | no | — |
| 281 | C22×C4 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 282 | C22×C4 | C2×C22⋊D7 | 1 | 2 | yes | — |
| 283 | C22×C4 | C2×C22⋊D7 | 1 | 2 | yes | — |
| 284 | C22×C4 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 285 | C22×C4 | C23×D7 | 1 | 1 | yes | characteristic |
| 286 | M16 | — | 14 | 4 | no | — |
| 287 | M16 | — | 14 | 4 | no | — |
| 288 | C2×C8 | — | 14 | 4 | no | — |
| 289 | C4⋊C4 | — | 2 | 4 | no | — |
| 290 | C4⋊C4 | — | 2 | 2 | no | — |
| 291 | C4⋊C4 | — | 2 | 4 | no | — |
| 292 | C4⋊C4 | — | 4 | 2 | no | — |
| 293 | C4⋊C4 | — | 4 | 2 | no | — |
| 294 | C4⋊C4 | — | 14 | 4 | no | — |
| 295 | C4⋊C4 | — | 14 | 2 | no | — |
| 296 | C4⋊C4 | — | 14 | 2 | no | — |
| 297 | C22⋊C4 | — | 14 | 8 | no | — |
| 298 | C22⋊C4 | — | 14 | 4 | no | — |
| 299 | C22⋊C4 | — | 14 | 4 | no | — |
| 300 | C42 | — | 2 | 2 | no | — |
| 301 | C42 | — | 2 | 2 | no | — |
| 302 | C42 | — | 2 | 4 | no | — |
| 303 | C42 | D4×D7 | 1 | 2 | yes | — |
| 304 | C42 | D4×D7 | 1 | 2 | yes | — |
| 305 | C2×C7 | — | 2 | 1 | no | — |
| 306 | C2×C7 | — | 2 | 1 | no | — |
| 307 | C2×C7 | #2435 | 1 | 1 | yes | characteristic |
| 308 | C2×C7 | C2×#454 | 1 | 1 | yes | characteristic |
| 309 | C2×C7 | #3022 | 1 | 1 | yes | characteristic |
| 310 | D7 | — | 8 | 4 | no | — |
| 311 | C23 | — | 14 | 4 | no | — |
| 312 | C23 | C22×C22⋊D7 | 1 | 1 | yes | characteristic |
| 313 | Q8 | — | 2 | 8 | no | — |
| 314 | Q8 | — | 8 | 2 | no | — |
| 315 | Q8 | — | 8 | 2 | no | — |
| 316 | Q8 | — | 14 | 8 | no | — |
| 317 | Q8 | — | 28 | 8 | no | — |
| 318 | D4 | — | 14 | 8 | no | — |
| 319 | D4 | — | 28 | 8 | no | — |
| 320 | D4 | — | 28 | 4 | no | — |
| 321 | D4 | — | 28 | 4 | no | — |
| 322 | D4 | — | 28 | 4 | no | — |
| 323 | D4 | — | 56 | 2 | no | — |
| 324 | D4 | — | 56 | 4 | no | — |
| 325 | C2×C4 | — | 2 | 2 | no | — |
| 326 | C2×C4 | — | 2 | 2 | no | — |
| 327 | C2×C4 | — | 2 | 2 | no | — |
| 328 | C2×C4 | — | 2 | 2 | no | — |
| 329 | C2×C4 | — | 4 | 1 | no | — |
| 330 | C2×C4 | — | 4 | 2 | no | — |
| 331 | C2×C4 | — | 4 | 2 | no | — |
| 332 | C2×C4 | — | 4 | 2 | no | — |
| 333 | C2×C4 | — | 4 | 4 | no | — |
| 334 | C2×C4 | — | 4 | 2 | no | — |
| 335 | C2×C4 | — | 4 | 2 | no | — |
| 336 | C2×C4 | — | 14 | 4 | no | — |
| 337 | C2×C4 | — | 28 | 16 | no | — |
| 338 | C2×C4 | — | 28 | 8 | no | — |
| 339 | C2×C4 | #6500 | 1 | 1 | yes | characteristic |
| 340 | C2×C4 | #6500 | 1 | 2 | yes | — |
| 341 | C2×C4 | #6500 | 1 | 1 | yes | characteristic |
| 342 | C2×C4 | #6510 | 1 | 4 | yes | — |
| 343 | C2×C4 | C2×D4×D7 | 1 | 2 | yes | — |
| 344 | C2×C4 | C2×#1161 | 1 | 2 | yes | — |
| 345 | C2×C4 | #6553 | 1 | 2 | yes | — |
| 346 | C8 | — | 28 | 4 | no | — |
| 347 | C7 | #25872 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 348 | C22 | — | 2 | 1 | no | — |
| 349 | C22 | — | 2 | 1 | no | — |
| 350 | C22 | — | 28 | 4 | no | — |
| 351 | C22 | — | 28 | 4 | no | — |
| 352 | C22 | — | 28 | 4 | no | — |
| 353 | C22 | C2×#6500 | 1 | 1 | yes | characteristic |
| 354 | C22 | C2×#6510 | 1 | 1 | yes | characteristic |
| 355 | C22 | #90521 | 1 | 1 | yes | characteristic |
| 356 | C4 | — | 2 | 4 | no | — |
| 357 | C4 | — | 2 | 2 | no | — |
| 358 | C4 | — | 2 | 1 | no | — |
| 359 | C4 | — | 4 | 2 | no | — |
| 360 | C4 | — | 8 | 2 | no | — |
| 361 | C4 | — | 8 | 2 | no | — |
| 362 | C4 | — | 28 | 4 | no | — |
| 363 | C4 | #89834 | 1 | 2 | yes | — |
| 364 | C4 | #90321 | 1 | 4 | yes | — |
| 365 | C2 | — | 2 | 1 | no | — |
| 366 | C2 | — | 2 | 1 | no | — |
| 367 | C2 | — | 56 | 4 | no | — |
| 368 | C2 | #11740206 | 1 | 1 | yes | characteristic |
| 369 | C2 | C2×#89834 | 1 | 1 | yes | characteristic |
| 370 | C2 | #11740861 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C7×#2568 | C2 | semidirect |
| 3. #11740644 | C2 | semidirect |
| 4. C4×#6410 | C2 | semidirect |
| 5. #11727446 | C2 | semidirect |
| 6. #11727317 | C2 | semidirect |
| 7. #11727246 | C2 | semidirect |
| 81. #2568 | D7 | semidirect |
| 347. C7 | #25872 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11742886 | 2 |
| C7×#2568 | 2 |
| #11740644 | 2 |
| C4×#6410 | 2 |
| #11727446 | 2 |
| #11727317 | 2 |
| #11727246 | 2 |
| #25872 | 7 |