Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
4732 conjugacy classes of subgroups; only the 727 normal subgroups are shown.
This group has 4732 conjugacy classes of subgroups — too many to draw. Only its 727 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 | #11744563 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11744362 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11742949 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C7×#2884 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11740001 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #11736137 | C2 | 1 | 12 | yes | maximal, complemented |
| 7 | #11736135 | C2 | 1 | 12 | yes | maximal, complemented |
| 8 | C2×C7×2−1+4 | C22 | 1 | 1 | yes | characteristic |
| 9 | #90620 | — | 2 | 8 | no | — |
| 10 | D7×2−1+4 | — | 2 | 8 | no | — |
| 11 | #90616 | — | 2 | 4 | no | — |
| 12 | #90616 | C22 | 1 | 12 | yes | — |
| 13 | C2×#6551 | — | 2 | 4 | no | — |
| 14 | C2×#6551 | C22 | 1 | 2 | yes | — |
| 15 | C22×Q8×D7 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | C7×#519 | C22 | 1 | 2 | yes | complemented |
| 17 | #90522 | — | 2 | 4 | no | — |
| 18 | #90519 | C22 | 1 | 6 | yes | complemented |
| 19 | #90516 | C22 | 1 | 6 | yes | complemented |
| 20 | Q8×C22⋊D7 | — | 2 | 4 | no | — |
| 21 | #90503 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | #90267 | — | 2 | 8 | no | — |
| 23 | Q8×D28 | — | 2 | 8 | no | — |
| 24 | #90217 | C22 | 1 | 12 | yes | complemented |
| 25 | #90215 | C22 | 1 | 12 | yes | complemented |
| 26 | C7×#410 | C22 | 1 | 12 | yes | complemented |
| 27 | #89778 | C22 | 1 | 24 | yes | complemented |
| 28 | #89514 | C22 | 1 | 48 | yes | complemented |
| 29 | #89513 | C22 | 1 | 16 | yes | complemented |
| 30 | #60400 | — | 7 | 1 | no | maximal, Sylow |
| 31 | C7×2−1+4 | — | 2 | 8 | no | — |
| 32 | C2×C7×#41 | D4 | 1 | 4 | yes | complemented |
| 33 | C2×C7×#41 | C23 | 1 | 6 | yes | — |
| 34 | C22×C7×Q8 | D4 | 1 | 4 | yes | complemented |
| 35 | C22×C7×Q8 | C23 | 1 | 1 | yes | characteristic |
| 36 | #6554 | — | 2 | 16 | no | — |
| 37 | #6554 | — | 2 | 24 | no | — |
| 38 | #6553 | — | 2 | 16 | no | — |
| 39 | #6553 | — | 2 | 24 | no | — |
| 40 | D7×#41 | — | 2 | 32 | no | — |
| 41 | D7×#41 | — | 2 | 48 | no | — |
| 42 | #6551 | — | 2 | 32 | no | — |
| 43 | #6551 | — | 2 | 12 | no | — |
| 44 | #6551 | — | 2 | 8 | no | — |
| 45 | #6551 | — | 2 | 8 | no | — |
| 46 | C2×#1161 | — | 2 | 16 | no | — |
| 47 | C2×#1161 | D4 | 1 | 8 | yes | complemented |
| 48 | C2×Q8×D7 | — | 2 | 16 | no | — |
| 49 | C2×Q8×D7 | — | 2 | 4 | no | — |
| 50 | C2×Q8×D7 | — | 2 | 8 | no | — |
| 51 | C2×Q8×D7 | D4 | 1 | 8 | yes | complemented |
| 52 | #6548 | — | 2 | 12 | no | — |
| 53 | #6548 | C23 | 1 | 16 | yes | — |
| 54 | C2×#1157 | — | 2 | 24 | no | — |
| 55 | C2×#1157 | C23 | 1 | 12 | yes | — |
| 56 | C22×C4×D7 | C23 | 1 | 3 | yes | — |
| 57 | C22×Dic14 | C23 | 1 | 3 | yes | — |
| 58 | C4×C7×Q8 | — | 2 | 8 | no | — |
| 59 | C7×#117 | C23 | 1 | 12 | yes | — |
| 60 | #6509 | — | 2 | 6 | no | — |
| 61 | Q8×Dic7 | — | 2 | 4 | no | — |
| 62 | #6507 | — | 2 | 6 | no | — |
| 63 | #6501 | — | 2 | 6 | no | — |
| 64 | #6500 | C23 | 1 | 4 | yes | — |
| 65 | #6499 | — | 2 | 6 | no | — |
| 66 | #6498 | C23 | 1 | 12 | yes | — |
| 67 | C4×C22⋊D7 | — | 2 | 12 | no | — |
| 68 | #6489 | C23 | 1 | 6 | yes | — |
| 69 | #6487 | — | 2 | 12 | no | — |
| 70 | #6460 | — | 2 | 24 | no | — |
| 71 | #6460 | — | 2 | 12 | no | — |
| 72 | #6458 | — | 2 | 12 | no | — |
| 73 | #6449 | C23 | 1 | 24 | yes | — |
| 74 | #6445 | C23 | 1 | 8 | yes | — |
| 75 | #6438 | — | 2 | 12 | no | — |
| 76 | C4×D28 | — | 2 | 24 | no | — |
| 77 | #6432 | — | 2 | 12 | no | — |
| 78 | C7×#99 | C23 | 1 | 16 | yes | — |
| 79 | #6380 | C23 | 1 | 32 | yes | — |
| 80 | 2−1+6 | — | 7 | 1 | no | — |
| 81 | #3486 | — | 7 | 1 | no | — |
| 82 | #3486 | — | 7 | 2 | no | — |
| 83 | #3028 | — | 7 | 12 | no | — |
| 84 | #3025 | — | 7 | 12 | no | — |
| 85 | #2884 | — | 7 | 2 | no | — |
| 86 | #2884 | D7 | 1 | 1 | yes | characteristic, complemented |
| 87 | C23×D7 | C24 | 1 | 1 | yes | characteristic |
| 88 | C7×#41 | — | 2 | 16 | no | — |
| 89 | C7×#41 | — | 2 | 24 | no | — |
| 90 | C2×C7×Q8 | — | 2 | 16 | no | — |
| 91 | C2×C7×Q8 | C2×D4 | 1 | 6 | yes | — |
| 92 | C2×C7×Q8 | C2×D4 | 1 | 4 | yes | — |
| 93 | C2×C7×Q8 | C2×D4 | 1 | 8 | yes | — |
| 94 | C2×C7×D4 | C2×D4 | 1 | 6 | yes | — |
| 95 | C2×C7×D4 | C24 | 1 | 4 | yes | — |
| 96 | C22×C4×C7 | C2×D4 | 1 | 12 | yes | — |
| 97 | C22×C4×C7 | C24 | 1 | 3 | yes | — |
| 98 | C2×C22⋊D7 | — | 2 | 16 | no | — |
| 99 | C2×C22⋊D7 | — | 2 | 4 | no | — |
| 100 | C2×C22⋊D7 | C24 | 1 | 8 | yes | — |
| 101 | C22×Dic7 | C24 | 1 | 3 | yes | — |
| 102 | #1161 | — | 2 | 48 | no | — |
| 103 | #1161 | — | 2 | 32 | no | — |
| 104 | Q8×D7 | — | 2 | 48 | no | — |
| 105 | Q8×D7 | — | 2 | 32 | no | — |
| 106 | Q8×D7 | — | 4 | 16 | no | — |
| 107 | #1159 | — | 2 | 48 | no | — |
| 108 | #1159 | — | 2 | 32 | no | — |
| 109 | D4×D7 | — | 2 | 48 | no | — |
| 110 | D4×D7 | — | 2 | 32 | no | — |
| 111 | #1157 | — | 2 | 48 | no | — |
| 112 | #1157 | — | 2 | 48 | no | — |
| 113 | #1157 | — | 2 | 16 | no | — |
| 114 | #1157 | — | 2 | 24 | no | — |
| 115 | #1157 | — | 2 | 24 | no | — |
| 116 | C2×D28 | — | 2 | 24 | no | — |
| 117 | C2×D28 | — | 2 | 8 | no | — |
| 118 | C2×D28 | C2×D4 | 1 | 12 | yes | — |
| 119 | C2×C4×D7 | — | 2 | 48 | no | — |
| 120 | C2×C4×D7 | — | 2 | 12 | no | — |
| 121 | C2×C4×D7 | — | 2 | 6 | no | — |
| 122 | C2×C4×D7 | C2×D4 | 1 | 24 | yes | — |
| 123 | C2×Dic14 | — | 2 | 24 | no | — |
| 124 | C2×Dic14 | — | 2 | 12 | no | — |
| 125 | C2×Dic14 | — | 2 | 6 | no | — |
| 126 | C2×Dic14 | C2×D4 | 1 | 12 | yes | — |
| 127 | C7×C4⋊C4 | — | 2 | 12 | no | — |
| 128 | C7×C22⋊C4 | C24 | 1 | 8 | yes | — |
| 129 | C42×C7 | — | 2 | 12 | no | — |
| 130 | C22⋊Dic7 | — | 2 | 12 | no | — |
| 131 | C22⋊Dic7 | C24 | 1 | 4 | yes | — |
| 132 | (C2×D7)⋊C4 | — | 2 | 24 | no | — |
| 133 | (C2×D7)⋊C4 | — | 2 | 4 | no | — |
| 134 | (C2×D7)⋊C4 | — | 2 | 8 | no | — |
| 135 | C4⋊Dic7 | — | 2 | 6 | no | — |
| 136 | C4⋊Dic7 | — | 2 | 24 | no | — |
| 137 | Dic7⋊C4 | — | 2 | 12 | no | — |
| 138 | C4×Dic7 | — | 2 | 6 | no | — |
| 139 | #585 | — | 7 | 12 | no | — |
| 140 | #585 | — | 14 | 8 | no | — |
| 141 | #585 | — | 14 | 4 | no | — |
| 142 | C2×2−1+4 | — | 7 | 2 | no | — |
| 143 | C2×2−1+4 | — | 14 | 8 | no | — |
| 144 | C2×2−1+4 | — | 14 | 4 | no | — |
| 145 | C2×2−1+4 | C2×D7 | 1 | 1 | yes | characteristic |
| 146 | C23×Q8 | — | 7 | 1 | no | — |
| 147 | D4×Q8 | — | 14 | 8 | no | — |
| 148 | D4×Q8 | — | 14 | 4 | no | — |
| 149 | #548 | — | 14 | 8 | no | — |
| 150 | #548 | — | 14 | 4 | no | — |
| 151 | #536 | — | 7 | 6 | no | — |
| 152 | #536 | — | 7 | 12 | no | — |
| 153 | #525 | — | 7 | 6 | no | — |
| 154 | #525 | — | 7 | 12 | no | — |
| 155 | #519 | — | 7 | 1 | no | — |
| 156 | #519 | C2×D7 | 1 | 2 | yes | complemented |
| 157 | #458 | — | 7 | 48 | no | — |
| 158 | B(4,𝔽2) | — | 7 | 16 | no | — |
| 159 | #410 | — | 7 | 24 | no | — |
| 160 | #410 | C2×D7 | 1 | 12 | yes | complemented |
| 161 | C23×C7 | C22×D4 | 1 | 4 | yes | — |
| 162 | C23×C7 | C25 | 1 | 1 | yes | characteristic |
| 163 | C22×D7 | — | 2 | 2 | no | — |
| 164 | C22×D7 | — | 2 | 1 | no | — |
| 165 | C22×D7 | — | 2 | 16 | no | — |
| 166 | C22×D7 | — | 4 | 2 | no | — |
| 167 | C22×D7 | C22×D4 | 1 | 8 | yes | — |
| 168 | C7×Q8 | — | 2 | 12 | no | — |
| 169 | C7×Q8 | #120 | 1 | 16 | yes | — |
| 170 | C7×D4 | — | 2 | 8 | no | — |
| 171 | C7×D4 | — | 2 | 12 | no | — |
| 172 | C2×C4×C7 | — | 2 | 24 | no | — |
| 173 | C2×C4×C7 | — | 2 | 8 | no | — |
| 174 | C2×C4×C7 | C22×D4 | 1 | 4 | yes | — |
| 175 | C2×C4×C7 | C22×D4 | 1 | 6 | yes | — |
| 176 | C2×C4×C7 | C22×D4 | 1 | 12 | yes | — |
| 177 | C22⋊D7 | — | 2 | 32 | no | — |
| 178 | C22⋊D7 | — | 2 | 8 | no | — |
| 179 | C22⋊D7 | — | 2 | 8 | no | — |
| 180 | C22⋊D7 | — | 4 | 8 | no | — |
| 181 | C2×Dic7 | — | 2 | 16 | no | — |
| 182 | C2×Dic7 | — | 2 | 4 | no | — |
| 183 | C2×Dic7 | — | 2 | 3 | no | — |
| 184 | C2×Dic7 | — | 2 | 6 | no | — |
| 185 | C2×Dic7 | C22×D4 | 1 | 8 | yes | — |
| 186 | D28 | — | 2 | 16 | no | — |
| 187 | D28 | — | 2 | 24 | no | — |
| 188 | D28 | — | 4 | 16 | no | — |
| 189 | C4×D7 | — | 2 | 32 | no | — |
| 190 | C4×D7 | — | 2 | 48 | no | — |
| 191 | C4×D7 | — | 4 | 12 | no | — |
| 192 | Dic14 | — | 2 | 16 | no | — |
| 193 | Dic14 | — | 2 | 24 | no | — |
| 194 | Dic14 | — | 4 | 12 | no | — |
| 195 | 2−1+4 | — | 2 | 8 | no | — |
| 196 | 2−1+4 | — | 14 | 32 | no | — |
| 197 | 2−1+4 | — | 14 | 24 | no | — |
| 198 | 2−1+4 | — | 14 | 16 | no | — |
| 199 | 2−1+4 | — | 14 | 8 | no | — |
| 200 | 2−1+4 | — | 14 | 12 | no | — |
| 201 | 2−1+4 | — | 14 | 8 | no | — |
| 202 | H(5,𝔽2) | — | 7 | 16 | no | — |
| 203 | H(5,𝔽2) | — | 14 | 24 | no | — |
| 204 | H(5,𝔽2) | — | 14 | 16 | no | — |
| 205 | H(5,𝔽2) | — | 14 | 12 | no | — |
| 206 | C2×#41 | — | 7 | 8 | no | — |
| 207 | C2×#41 | — | 7 | 12 | no | — |
| 208 | C2×#41 | — | 14 | 48 | no | — |
| 209 | C2×#41 | — | 14 | 16 | no | — |
| 210 | C2×#41 | — | 14 | 32 | no | — |
| 211 | C2×#41 | — | 14 | 24 | no | — |
| 212 | C2×#41 | D28 | 1 | 4 | yes | complemented |
| 213 | C2×#41 | C22×D7 | 1 | 6 | yes | — |
| 214 | C22×Q8 | — | 7 | 8 | no | — |
| 215 | C22×Q8 | — | 7 | 3 | no | — |
| 216 | C22×Q8 | — | 14 | 16 | no | — |
| 217 | C22×Q8 | — | 14 | 4 | no | — |
| 218 | C22×Q8 | — | 14 | 8 | no | — |
| 219 | C22×Q8 | D28 | 1 | 4 | yes | complemented |
| 220 | C22×Q8 | C22×D7 | 1 | 1 | yes | characteristic |
| 221 | C23×C4 | — | 7 | 3 | no | — |
| 222 | C4⋊Q8 | — | 14 | 12 | no | — |
| 223 | C4⋊Q8 | — | 14 | 6 | no | — |
| 224 | #124 | — | 14 | 12 | no | — |
| 225 | #124 | — | 14 | 6 | no | — |
| 226 | #123 | — | 7 | 12 | no | — |
| 227 | #123 | — | 7 | 24 | no | — |
| 228 | C22⋊Q8 | — | 14 | 24 | no | — |
| 229 | C22⋊Q8 | — | 14 | 12 | no | — |
| 230 | C22⋊Q8 | — | 14 | 6 | no | — |
| 231 | C22⋊Q8 | — | 14 | 12 | no | — |
| 232 | #121 | — | 14 | 12 | no | — |
| 233 | #121 | — | 14 | 6 | no | — |
| 234 | #120 | — | 7 | 4 | no | — |
| 235 | #120 | — | 7 | 8 | no | — |
| 236 | C4×Q8 | — | 2 | 8 | no | — |
| 237 | C4×Q8 | — | 14 | 4 | no | — |
| 238 | C4×D4 | — | 14 | 24 | no | — |
| 239 | C4×D4 | — | 14 | 12 | no | — |
| 240 | #117 | — | 7 | 6 | no | — |
| 241 | #117 | C22×D7 | 1 | 12 | yes | — |
| 242 | #99 | — | 7 | 32 | no | — |
| 243 | #99 | C22×D7 | 1 | 16 | yes | — |
| 244 | C22×C7 | — | 2 | 4 | no | — |
| 245 | C22×C7 | — | 4 | 1 | no | — |
| 246 | C22×C7 | — | 4 | 4 | no | — |
| 247 | C22×C7 | C23×D4 | 1 | 1 | yes | characteristic |
| 248 | C22×C7 | C23×D4 | 1 | 2 | yes | — |
| 249 | C2×D7 | — | 2 | 4 | no | — |
| 250 | C2×D7 | — | 2 | 2 | no | — |
| 251 | C2×D7 | — | 2 | 8 | no | — |
| 252 | C2×D7 | — | 4 | 1 | no | — |
| 253 | C2×D7 | — | 4 | 2 | no | — |
| 254 | C2×D7 | — | 4 | 1 | no | — |
| 255 | C2×D7 | — | 4 | 8 | no | — |
| 256 | C2×D7 | — | 8 | 16 | no | — |
| 257 | C4×C7 | — | 2 | 4 | no | — |
| 258 | C4×C7 | — | 4 | 8 | no | — |
| 259 | C4×C7 | C2×#120 | 1 | 12 | yes | — |
| 260 | Dic7 | — | 2 | 8 | no | — |
| 261 | Dic7 | — | 4 | 4 | no | — |
| 262 | Dic7 | — | 4 | 3 | no | — |
| 263 | C24 | — | 7 | 1 | no | — |
| 264 | #41 | — | 2 | 16 | no | — |
| 265 | #41 | — | 2 | 24 | no | — |
| 266 | #41 | — | 14 | 48 | no | — |
| 267 | #41 | — | 14 | 48 | no | — |
| 268 | #41 | — | 14 | 32 | no | — |
| 269 | #41 | — | 14 | 48 | no | — |
| 270 | #41 | — | 14 | 48 | no | — |
| 271 | #41 | — | 14 | 32 | no | — |
| 272 | #41 | — | 14 | 24 | no | — |
| 273 | #41 | — | 14 | 16 | no | — |
| 274 | #41 | — | 14 | 24 | no | — |
| 275 | C2×Q8 | — | 2 | 16 | no | — |
| 276 | C2×Q8 | — | 7 | 12 | no | — |
| 277 | C2×Q8 | — | 14 | 24 | no | — |
| 278 | C2×Q8 | — | 14 | 48 | no | — |
| 279 | C2×Q8 | — | 14 | 32 | no | — |
| 280 | C2×Q8 | — | 14 | 6 | no | — |
| 281 | C2×Q8 | — | 14 | 12 | no | — |
| 282 | C2×Q8 | — | 28 | 16 | no | — |
| 283 | C2×Q8 | C2×D28 | 1 | 6 | yes | — |
| 284 | C2×Q8 | C2×D28 | 1 | 4 | yes | — |
| 285 | C2×Q8 | D4×D7 | 1 | 8 | yes | — |
| 286 | C2×D4 | — | 7 | 8 | no | — |
| 287 | C2×D4 | — | 7 | 12 | no | — |
| 288 | C2×D4 | — | 14 | 24 | no | — |
| 289 | C2×D4 | — | 14 | 8 | no | — |
| 290 | C2×D4 | — | 14 | 32 | no | — |
| 291 | C2×D4 | — | 14 | 48 | no | — |
| 292 | C2×D4 | — | 14 | 16 | no | — |
| 293 | C2×D4 | — | 14 | 4 | no | — |
| 294 | C2×D4 | C2×D28 | 1 | 6 | yes | — |
| 295 | C2×D4 | C23×D7 | 1 | 4 | yes | — |
| 296 | C22×C4 | — | 7 | 24 | no | — |
| 297 | C22×C4 | — | 7 | 3 | no | — |
| 298 | C22×C4 | — | 14 | 48 | no | — |
| 299 | C22×C4 | — | 14 | 6 | no | — |
| 300 | C22×C4 | — | 14 | 12 | no | — |
| 301 | C22×C4 | C2×D28 | 1 | 12 | yes | — |
| 302 | C22×C4 | C23×D7 | 1 | 3 | yes | — |
| 303 | C4⋊C4 | — | 2 | 12 | no | — |
| 304 | C4⋊C4 | — | 14 | 24 | no | — |
| 305 | C4⋊C4 | — | 14 | 12 | no | — |
| 306 | C4⋊C4 | — | 14 | 6 | no | — |
| 307 | C22⋊C4 | — | 7 | 4 | no | — |
| 308 | C22⋊C4 | — | 14 | 8 | no | — |
| 309 | C22⋊C4 | — | 14 | 24 | no | — |
| 310 | C22⋊C4 | — | 14 | 12 | no | — |
| 311 | C22⋊C4 | — | 14 | 4 | no | — |
| 312 | C22⋊C4 | C23×D7 | 1 | 8 | yes | — |
| 313 | C42 | — | 2 | 12 | no | — |
| 314 | C42 | — | 14 | 6 | no | — |
| 315 | C2×C7 | — | 2 | 1 | no | — |
| 316 | C2×C7 | — | 2 | 2 | no | — |
| 317 | C2×C7 | — | 4 | 4 | no | — |
| 318 | C2×C7 | C22×#120 | 1 | 1 | yes | characteristic |
| 319 | D7 | — | 4 | 2 | no | — |
| 320 | D7 | — | 4 | 8 | no | — |
| 321 | C23 | — | 7 | 8 | no | — |
| 322 | C23 | — | 14 | 16 | no | — |
| 323 | C23 | — | 14 | 1 | no | — |
| 324 | C23 | — | 14 | 2 | no | — |
| 325 | C23 | — | 28 | 2 | no | — |
| 326 | C23 | C22×D28 | 1 | 4 | yes | — |
| 327 | C23 | C24×D7 | 1 | 1 | yes | characteristic |
| 328 | Q8 | — | 2 | 12 | no | — |
| 329 | Q8 | — | 14 | 16 | no | — |
| 330 | Q8 | — | 14 | 24 | no | — |
| 331 | Q8 | — | 28 | 12 | no | — |
| 332 | Q8 | #6445 | 1 | 16 | yes | — |
| 333 | D4 | — | 2 | 8 | no | — |
| 334 | D4 | — | 2 | 12 | no | — |
| 335 | D4 | — | 14 | 16 | no | — |
| 336 | D4 | — | 14 | 32 | no | — |
| 337 | D4 | — | 14 | 8 | no | — |
| 338 | D4 | — | 14 | 8 | no | — |
| 339 | D4 | — | 14 | 24 | no | — |
| 340 | D4 | — | 28 | 16 | no | — |
| 341 | D4 | — | 28 | 8 | no | — |
| 342 | C2×C4 | — | 2 | 24 | no | — |
| 343 | C2×C4 | — | 2 | 8 | no | — |
| 344 | C2×C4 | — | 7 | 8 | no | — |
| 345 | C2×C4 | — | 14 | 32 | no | — |
| 346 | C2×C4 | — | 14 | 16 | no | — |
| 347 | C2×C4 | — | 14 | 48 | no | — |
| 348 | C2×C4 | — | 14 | 4 | no | — |
| 349 | C2×C4 | — | 14 | 3 | no | — |
| 350 | C2×C4 | — | 14 | 6 | no | — |
| 351 | C2×C4 | — | 28 | 12 | no | — |
| 352 | C2×C4 | C22×D28 | 1 | 4 | yes | — |
| 353 | C2×C4 | C22×D28 | 1 | 6 | yes | — |
| 354 | C2×C4 | C2×D4×D7 | 1 | 12 | yes | — |
| 355 | C7 | #60400 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 356 | C22 | — | 2 | 4 | no | — |
| 357 | C22 | — | 4 | 1 | no | — |
| 358 | C22 | — | 4 | 4 | no | — |
| 359 | C22 | — | 14 | 4 | no | — |
| 360 | C22 | — | 14 | 2 | no | — |
| 361 | C22 | — | 14 | 8 | no | — |
| 362 | C22 | — | 28 | 8 | no | — |
| 363 | C22 | — | 28 | 2 | no | — |
| 364 | C22 | — | 28 | 1 | no | — |
| 365 | C22 | — | 28 | 1 | no | — |
| 366 | C22 | — | 56 | 16 | no | — |
| 367 | C22 | C23×D28 | 1 | 1 | yes | characteristic |
| 368 | C22 | C22×D4×D7 | 1 | 2 | yes | — |
| 369 | C4 | — | 2 | 4 | no | — |
| 370 | C4 | — | 4 | 8 | no | — |
| 371 | C4 | — | 14 | 8 | no | — |
| 372 | C4 | — | 28 | 4 | no | — |
| 373 | C4 | — | 28 | 3 | no | — |
| 374 | C4 | C2×#6445 | 1 | 12 | yes | — |
| 375 | C2 | — | 2 | 2 | no | — |
| 376 | C2 | — | 2 | 1 | no | — |
| 377 | C2 | — | 4 | 4 | no | — |
| 378 | C2 | — | 28 | 2 | no | — |
| 379 | C2 | — | 28 | 8 | no | — |
| 380 | C2 | C22×#6445 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×#6445 |
| commutator, cosocle | C23×C7 | C25 |
| Frattini | C23 | C24×D7 |
| Fitting | C7×#2884 | C2 |
| socle | C2×C7 | C22×#120 |
| hypercenter | #2884 | D7 |
| hypocenter | C7 | #60400 |
| LCS | G ▷ C23×C7 ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C2 ◁ C22×Q8 ◁ #2884 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11744563 | C2 | semidirect |
| 2. #11744362 | C2 | semidirect |
| 3. #11742949 | C2 | semidirect |
| 4. C7×#2884 | C2 | semidirect |
| 5. #11740001 | C2 | semidirect |
| 6. #11736137 | C2 | semidirect |
| 7. #11736135 | C2 | semidirect |
| 15. C22×Q8×D7 | C22 | semidirect |
| 16. C7×#519 | C22 | semidirect |
| 18. #90519 | C22 | semidirect |
| 19. #90516 | C22 | semidirect |
| 21. #90503 | C22 | semidirect |
| 24. #90217 | C22 | semidirect |
| 25. #90215 | C22 | semidirect |
| 26. C7×#410 | C22 | semidirect |
| 27. #89778 | C22 | semidirect |
| 28. #89514 | C22 | semidirect |
| 29. #89513 | C22 | semidirect |
| 32. C2×C7×#41 | D4 | semidirect |
| 34. C22×C7×Q8 | D4 | semidirect |
| 47. C2×#1161 | D4 | semidirect |
| 51. C2×Q8×D7 | D4 | semidirect |
| 86. #2884 | D7 | semidirect |
| 156. #519 | C2×D7 | semidirect |
| 160. #410 | C2×D7 | semidirect |
| 212. C2×#41 | D28 | semidirect |
| 219. C22×Q8 | D28 | semidirect |
| 355. C7 | #60400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11744563 | 2 |
| #11744362 | 2 |
| #11742949 | 2 |
| C7×#2884 | 2 |
| #11740001 | 2 |
| #11736137 | 2 |
| #11736135 | 2 |
| #60400 | 7 |