Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1284 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 1284 conjugacy classes of subgroups — too many to draw. Only its 139 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 | D7×H(3,𝔽4) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | D7×#454 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | C7×#2202 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11729705 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11728741 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | D7×#355 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #11726914 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | D7×2−1+4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 9 | C7×H(3,𝔽4) | C22 | 1 | 1 | yes | characteristic, complemented |
| 10 | D7×AGL(1,ℤ/8) | — | 2 | 3 | no | — |
| 11 | #90374 | — | 2 | 3 | no | — |
| 12 | #90374 | C22 | 1 | 3 | yes | complemented |
| 13 | D7×#124 | — | 2 | 3 | no | — |
| 14 | D7×#124 | C22 | 1 | 3 | yes | — |
| 15 | #90285 | — | 2 | 3 | no | — |
| 16 | D7×#120 | — | 2 | 3 | no | — |
| 17 | C7×#454 | C22 | 1 | 3 | yes | complemented |
| 18 | #90017 | C22 | 1 | 3 | yes | complemented |
| 19 | #89973 | — | 2 | 3 | no | — |
| 20 | #89834 | C22 | 1 | 3 | yes | complemented |
| 21 | #89599 | — | 2 | 3 | no | — |
| 22 | D7×#104 | — | 2 | 3 | no | — |
| 23 | #89525 | C22 | 1 | 3 | yes | complemented |
| 24 | D7×#101 | C22 | 1 | 3 | yes | complemented |
| 25 | C7×#355 | C22 | 1 | 3 | yes | complemented |
| 26 | #89337 | C22 | 1 | 3 | yes | complemented |
| 27 | #89272 | C22 | 1 | 6 | yes | complemented |
| 28 | C2×#2202 | — | 7 | 1 | no | maximal, Sylow |
| 29 | C24×D7 | — | 2 | 1 | no | — |
| 30 | C7×2−1+4 | C23 | 1 | 1 | yes | characteristic, complemented |
| 31 | #6554 | — | 2 | 3 | no | — |
| 32 | #6554 | — | 4 | 1 | no | — |
| 33 | D7×#41 | — | 2 | 3 | no | — |
| 34 | D7×#41 | — | 4 | 1 | no | — |
| 35 | #6551 | — | 4 | 1 | no | — |
| 36 | #6551 | C23 | 1 | 1 | yes | characteristic, complemented |
| 37 | C2×Q8×D7 | — | 2 | 1 | no | — |
| 38 | C2×Q8×D7 | — | 4 | 1 | no | — |
| 39 | C2×Q8×D7 | C23 | 1 | 1 | yes | characteristic |
| 40 | C2×D4×D7 | — | 2 | 3 | no | — |
| 41 | C2×D4×D7 | D4 | 1 | 3 | yes | — |
| 42 | C7×AGL(1,ℤ/8) | — | 2 | 3 | no | — |
| 43 | C7×#124 | — | 2 | 3 | no | — |
| 44 | C7×#124 | C23 | 1 | 3 | yes | — |
| 45 | C7×#120 | — | 2 | 3 | no | — |
| 46 | #6516 | — | 2 | 3 | no | — |
| 47 | #6512 | — | 2 | 3 | no | — |
| 48 | #6510 | — | 2 | 3 | no | — |
| 49 | #6510 | C23 | 1 | 3 | yes | — |
| 50 | #6500 | — | 2 | 6 | no | — |
| 51 | #6500 | — | 2 | 3 | no | — |
| 52 | #6499 | — | 2 | 3 | no | — |
| 53 | #6499 | D4 | 1 | 3 | yes | — |
| 54 | #6495 | — | 2 | 3 | no | — |
| 55 | #6477 | — | 4 | 3 | no | — |
| 56 | D7×SD16 | — | 4 | 3 | no | — |
| 57 | #6474 | — | 4 | 3 | no | — |
| 58 | D7×D8 | — | 4 | 3 | no | — |
| 59 | #6471 | — | 2 | 3 | no | — |
| 60 | D7×M16 | — | 2 | 3 | no | — |
| 61 | #6448 | — | 2 | 6 | no | — |
| 62 | #6448 | — | 2 | 6 | no | — |
| 63 | #6448 | — | 2 | 6 | no | — |
| 64 | #6445 | — | 2 | 3 | no | — |
| 65 | #6445 | — | 2 | 6 | no | — |
| 66 | D7×C22⋊C4 | — | 2 | 3 | no | — |
| 67 | D7×C22⋊C4 | — | 2 | 6 | no | — |
| 68 | #6438 | — | 2 | 3 | no | — |
| 69 | #6438 | D4 | 1 | 3 | yes | — |
| 70 | C42×D7 | D4 | 1 | 3 | yes | — |
| 71 | C7×#104 | — | 2 | 3 | no | — |
| 72 | C7×#101 | C23 | 1 | 3 | yes | complemented |
| 73 | #6411 | — | 2 | 3 | no | — |
| 74 | #6410 | C23 | 1 | 3 | yes | complemented |
| 75 | #6399 | — | 2 | 3 | no | — |
| 76 | #6398 | — | 2 | 3 | no | — |
| 77 | #6379 | — | 2 | 3 | no | — |
| 78 | C2×H(3,𝔽4) | — | 7 | 1 | no | — |
| 79 | C2×#454 | — | 7 | 3 | no | — |
| 80 | #2202 | — | 7 | 3 | no | — |
| 81 | #2202 | — | 7 | 3 | no | — |
| 82 | #2202 | — | 7 | 1 | no | — |
| 83 | #2202 | D7 | 1 | 1 | yes | characteristic, direct product factor |
| 84 | C2×#355 | — | 7 | 3 | no | — |
| 85 | C24×C7 | — | 2 | 1 | no | — |
| 86 | C23×D7 | — | 2 | 3 | no | — |
| 87 | C23×D7 | — | 2 | 3 | no | — |
| 88 | C23×D7 | — | 8 | 4 | no | — |
| 89 | C23×D7 | — | 8 | 1 | no | — |
| 90 | C23×D7 | — | 8 | 1 | no | — |
| 91 | C7×#41 | — | 2 | 3 | no | — |
| 92 | C7×#41 | — | 4 | 1 | no | — |
| 93 | C2×C7×Q8 | — | 2 | 1 | no | — |
| 94 | C2×C7×Q8 | — | 4 | 1 | no | — |
| 95 | C2×C7×Q8 | C24 | 1 | 1 | yes | characteristic |
| 96 | C2×C7×D4 | — | 2 | 3 | no | — |
| 97 | C2×C7×D4 | C2×D4 | 1 | 3 | yes | — |
| 98 | C2×C22⋊D7 | — | 2 | 6 | no | — |
| 99 | C2×C22⋊D7 | — | 2 | 3 | no | — |
| 100 | #1161 | — | 2 | 3 | no | — |
| 101 | #1161 | — | 4 | 1 | no | — |
| 102 | Q8×D7 | — | 2 | 3 | no | — |
| 103 | Q8×D7 | — | 4 | 1 | no | — |
| 104 | Q8×D7 | — | 4 | 1 | no | — |
| 105 | Q8×D7 | — | 4 | 1 | no | — |
| 106 | Q8×D7 | — | 4 | 3 | no | — |
| 107 | Q8×D7 | — | 8 | 2 | no | — |
| 108 | #1159 | — | 2 | 3 | no | — |
| 109 | #1159 | — | 4 | 3 | no | — |
| 110 | #1159 | — | 4 | 3 | no | — |
| 111 | D4×D7 | — | 2 | 3 | no | — |
| 112 | D4×D7 | — | 4 | 3 | no | — |
| 113 | D4×D7 | — | 4 | 3 | no | — |
| 114 | D4×D7 | — | 4 | 1 | no | — |
| 115 | D4×D7 | — | 8 | 6 | no | — |
| 116 | #1157 | — | 2 | 3 | no | — |
| 117 | #1157 | — | 4 | 3 | no | — |
| 118 | #1157 | — | 4 | 3 | no | — |
| 119 | C2×D28 | — | 2 | 3 | no | — |
| 120 | C2×D28 | C2×D4 | 1 | 3 | yes | — |
| 121 | C2×C4×D7 | — | 2 | 3 | no | — |
| 122 | C2×C4×D7 | — | 4 | 3 | no | — |
| 123 | C2×C4×D7 | C2×D4 | 1 | 3 | yes | — |
| 124 | C2×Dic14 | — | 2 | 3 | no | — |
| 125 | C2×Dic14 | — | 4 | 3 | no | — |
| 126 | C2×Dic14 | C2×D4 | 1 | 3 | yes | — |
| 127 | C7×SD16 | — | 4 | 3 | no | — |
| 128 | C7×D8 | — | 4 | 3 | no | — |
| 129 | C7×M16 | — | 2 | 3 | no | — |
| 130 | C7×C22⋊C4 | — | 2 | 3 | no | — |
| 131 | C7×C22⋊C4 | — | 2 | 6 | no | — |
| 132 | C42×C7 | C2×D4 | 1 | 3 | yes | — |
| 133 | C22⋊Dic7 | — | 2 | 3 | no | — |
| 134 | C22⋊Dic7 | — | 2 | 6 | no | — |
| 135 | #1143 | — | 4 | 3 | no | — |
| 136 | #1142 | — | 4 | 3 | no | — |
| 137 | #1141 | — | 4 | 3 | no | — |
| 138 | #1141 | — | 4 | 3 | no | — |
| 139 | (C2×D7)⋊C4 | — | 2 | 6 | no | — |
| 140 | (C2×D7)⋊C4 | — | 2 | 6 | no | — |
| 141 | (C2×D7)⋊C4 | — | 2 | 6 | no | — |
| 142 | C4×Dic7 | — | 2 | 3 | no | — |
| 143 | C4×Dic7 | C2×D4 | 1 | 3 | yes | — |
| 144 | #1136 | — | 2 | 3 | no | — |
| 145 | D56 | — | 4 | 3 | no | — |
| 146 | #1132 | — | 4 | 3 | no | — |
| 147 | #1131 | — | 4 | 3 | no | — |
| 148 | C8×D7 | — | 4 | 3 | no | — |
| 149 | C2×2−1+4 | — | 7 | 1 | no | — |
| 150 | C2×AGL(1,ℤ/8) | — | 14 | 3 | no | — |
| 151 | H(3,𝔽4) | — | 7 | 3 | no | — |
| 152 | H(3,𝔽4) | — | 14 | 3 | no | — |
| 153 | H(3,𝔽4) | — | 14 | 3 | no | — |
| 154 | H(3,𝔽4) | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 155 | C2×#124 | — | 7 | 3 | no | — |
| 156 | C2×#124 | — | 14 | 3 | no | — |
| 157 | C2×#120 | — | 14 | 3 | no | — |
| 158 | #454 | — | 7 | 3 | no | — |
| 159 | #454 | — | 7 | 3 | no | — |
| 160 | #454 | — | 7 | 3 | no | — |
| 161 | #454 | — | 14 | 3 | no | — |
| 162 | #454 | — | 14 | 3 | no | — |
| 163 | #454 | C2×D7 | 1 | 3 | yes | complemented |
| 164 | C2×#104 | — | 14 | 3 | no | — |
| 165 | C2×#101 | — | 7 | 3 | no | — |
| 166 | #355 | — | 7 | 3 | no | — |
| 167 | #355 | — | 7 | 6 | no | — |
| 168 | #355 | C2×D7 | 1 | 3 | yes | complemented |
| 169 | C23×C7 | — | 2 | 3 | no | — |
| 170 | C23×C7 | — | 8 | 2 | no | — |
| 171 | C23×C7 | — | 8 | 1 | no | — |
| 172 | C22×D7 | — | 2 | 3 | no | — |
| 173 | C22×D7 | — | 4 | 12 | no | — |
| 174 | C22×D7 | — | 4 | 1 | no | — |
| 175 | C22×D7 | — | 4 | 3 | no | — |
| 176 | C22×D7 | — | 4 | 3 | no | — |
| 177 | C22×D7 | — | 8 | 6 | no | — |
| 178 | C22×D7 | — | 8 | 3 | no | — |
| 179 | C22×D7 | — | 8 | 8 | no | — |
| 180 | C22×D7 | — | 8 | 8 | no | — |
| 181 | C22×D7 | #120 | 1 | 1 | yes | characteristic |
| 182 | C7×Q8 | — | 2 | 3 | no | — |
| 183 | C7×Q8 | — | 4 | 1 | no | — |
| 184 | C7×Q8 | — | 8 | 1 | no | — |
| 185 | C7×D4 | — | 2 | 3 | no | — |
| 186 | C7×D4 | — | 4 | 3 | no | — |
| 187 | C7×D4 | — | 4 | 1 | no | — |
| 188 | C7×D4 | — | 8 | 3 | no | — |
| 189 | C2×C4×C7 | — | 2 | 3 | no | — |
| 190 | C2×C4×C7 | — | 4 | 3 | no | — |
| 191 | C2×C4×C7 | C22×D4 | 1 | 3 | yes | — |
| 192 | C22⋊D7 | — | 4 | 3 | no | — |
| 193 | C22⋊D7 | — | 4 | 1 | no | — |
| 194 | C22⋊D7 | — | 4 | 1 | no | — |
| 195 | C22⋊D7 | — | 8 | 3 | no | — |
| 196 | C22⋊D7 | — | 8 | 6 | no | — |
| 197 | C2×Dic7 | — | 2 | 3 | no | — |
| 198 | C2×Dic7 | — | 4 | 3 | no | — |
| 199 | C2×Dic7 | #120 | 1 | 3 | yes | — |
| 200 | D28 | — | 2 | 3 | no | — |
| 201 | D28 | — | 4 | 3 | no | — |
| 202 | D28 | — | 4 | 1 | no | — |
| 203 | D28 | — | 8 | 3 | no | — |
| 204 | C4×D7 | — | 2 | 3 | no | — |
| 205 | C4×D7 | — | 2 | 3 | no | — |
| 206 | C4×D7 | — | 4 | 3 | no | — |
| 207 | C4×D7 | — | 4 | 3 | no | — |
| 208 | C4×D7 | — | 4 | 6 | no | — |
| 209 | C4×D7 | — | 4 | 1 | no | — |
| 210 | Dic14 | — | 2 | 3 | no | — |
| 211 | Dic14 | — | 4 | 3 | no | — |
| 212 | Dic14 | — | 4 | 3 | no | — |
| 213 | Dic14 | — | 8 | 3 | no | — |
| 214 | C7×C8 | — | 4 | 3 | no | — |
| 215 | C7⋊C8 | — | 4 | 3 | no | — |
| 216 | C25 | — | 14 | 1 | no | — |
| 217 | 2−1+4 | — | 7 | 1 | no | — |
| 218 | 2−1+4 | — | 14 | 3 | no | — |
| 219 | 2−1+4 | — | 28 | 1 | no | — |
| 220 | 2−1+4 | — | 28 | 1 | no | — |
| 221 | 2−1+4 | C22×D7 | 1 | 1 | yes | characteristic, complemented |
| 222 | C2×#41 | — | 14 | 3 | no | — |
| 223 | C2×#41 | — | 28 | 1 | no | — |
| 224 | C22×Q8 | — | 7 | 1 | no | — |
| 225 | C22×Q8 | — | 14 | 1 | no | — |
| 226 | C22×Q8 | — | 28 | 1 | no | — |
| 227 | C22×D4 | — | 7 | 3 | no | — |
| 228 | C22×D4 | — | 14 | 3 | no | — |
| 229 | AGL(1,ℤ/8) | — | 2 | 3 | no | — |
| 230 | AGL(1,ℤ/8) | — | 14 | 3 | no | — |
| 231 | AGL(1,ℤ/8) | — | 14 | 3 | no | — |
| 232 | AGL(1,ℤ/8) | — | 14 | 3 | no | — |
| 233 | AGL(1,ℤ/8) | — | 28 | 3 | no | — |
| 234 | AGL(1,ℤ/8) | — | 28 | 3 | no | — |
| 235 | C2×SD16 | — | 28 | 3 | no | — |
| 236 | C2×D8 | — | 28 | 3 | no | — |
| 237 | C2×M16 | — | 14 | 3 | no | — |
| 238 | #124 | — | 2 | 3 | no | — |
| 239 | #124 | — | 7 | 3 | no | — |
| 240 | #124 | — | 7 | 3 | no | — |
| 241 | #124 | — | 7 | 3 | no | — |
| 242 | #124 | — | 14 | 6 | no | — |
| 243 | #124 | — | 14 | 6 | no | — |
| 244 | #124 | — | 14 | 6 | no | — |
| 245 | #124 | — | 14 | 3 | no | — |
| 246 | #124 | — | 14 | 3 | no | — |
| 247 | #124 | — | 14 | 3 | no | — |
| 248 | #124 | C22×D7 | 1 | 3 | yes | — |
| 249 | #120 | — | 2 | 3 | no | — |
| 250 | #120 | — | 14 | 6 | no | — |
| 251 | #120 | — | 14 | 3 | no | — |
| 252 | #120 | — | 14 | 6 | no | — |
| 253 | #120 | — | 14 | 3 | no | — |
| 254 | #120 | — | 14 | 3 | no | — |
| 255 | C2×C22⋊C4 | — | 14 | 6 | no | — |
| 256 | C2×C22⋊C4 | — | 14 | 3 | no | — |
| 257 | C2×C42 | — | 7 | 3 | no | — |
| 258 | #104 | — | 2 | 3 | no | — |
| 259 | #104 | — | 14 | 3 | no | — |
| 260 | #104 | — | 14 | 3 | no | — |
| 261 | #104 | — | 14 | 3 | no | — |
| 262 | #101 | — | 7 | 3 | no | — |
| 263 | #101 | — | 14 | 3 | no | — |
| 264 | #101 | C22×D7 | 1 | 3 | yes | complemented |
| 265 | C22×C7 | — | 4 | 6 | no | — |
| 266 | C22×C7 | — | 4 | 1 | no | — |
| 267 | C22×C7 | — | 4 | 3 | no | — |
| 268 | C22×C7 | — | 8 | 4 | no | — |
| 269 | C22×C7 | C2×#120 | 1 | 1 | yes | characteristic |
| 270 | C2×D7 | — | 2 | 2 | no | — |
| 271 | C2×D7 | — | 4 | 6 | no | — |
| 272 | C2×D7 | — | 4 | 1 | no | — |
| 273 | C2×D7 | — | 4 | 3 | no | — |
| 274 | C2×D7 | — | 8 | 6 | no | — |
| 275 | C2×D7 | — | 8 | 12 | no | — |
| 276 | C2×D7 | — | 8 | 2 | no | — |
| 277 | C2×D7 | — | 8 | 6 | no | — |
| 278 | C2×D7 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 279 | C2×D7 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 280 | C4×C7 | — | 2 | 3 | no | — |
| 281 | C4×C7 | — | 4 | 3 | no | — |
| 282 | C4×C7 | — | 4 | 1 | no | — |
| 283 | Dic7 | — | 2 | 3 | no | — |
| 284 | Dic7 | — | 4 | 3 | no | — |
| 285 | Dic7 | — | 4 | 1 | no | — |
| 286 | C24 | — | 2 | 1 | no | — |
| 287 | C24 | — | 14 | 3 | no | — |
| 288 | C24 | — | 14 | 3 | no | — |
| 289 | C24 | — | 56 | 1 | no | — |
| 290 | C24 | — | 56 | 1 | no | — |
| 291 | C24 | — | 56 | 4 | no | — |
| 292 | #41 | — | 2 | 3 | no | — |
| 293 | #41 | — | 4 | 1 | no | — |
| 294 | #41 | — | 14 | 3 | no | — |
| 295 | #41 | — | 14 | 3 | no | — |
| 296 | #41 | — | 14 | 3 | no | — |
| 297 | #41 | — | 28 | 3 | no | — |
| 298 | #41 | — | 28 | 3 | no | — |
| 299 | #41 | — | 28 | 3 | no | — |
| 300 | #41 | — | 28 | 3 | no | — |
| 301 | #41 | — | 28 | 1 | no | — |
| 302 | C2×Q8 | — | 2 | 1 | no | — |
| 303 | C2×Q8 | — | 4 | 1 | no | — |
| 304 | C2×Q8 | — | 7 | 3 | no | — |
| 305 | C2×Q8 | — | 14 | 3 | no | — |
| 306 | C2×Q8 | — | 14 | 3 | no | — |
| 307 | C2×Q8 | — | 28 | 3 | no | — |
| 308 | C2×Q8 | — | 28 | 1 | no | — |
| 309 | C2×Q8 | — | 28 | 1 | no | — |
| 310 | C2×Q8 | — | 28 | 3 | no | — |
| 311 | C2×Q8 | — | 28 | 1 | no | — |
| 312 | C2×Q8 | — | 56 | 2 | no | — |
| 313 | C2×Q8 | C23×D7 | 1 | 1 | yes | characteristic |
| 314 | C2×D4 | — | 2 | 3 | no | — |
| 315 | C2×D4 | — | 7 | 3 | no | — |
| 316 | C2×D4 | — | 14 | 3 | no | — |
| 317 | C2×D4 | — | 14 | 3 | no | — |
| 318 | C2×D4 | — | 14 | 3 | no | — |
| 319 | C2×D4 | — | 14 | 6 | no | — |
| 320 | C2×D4 | — | 28 | 3 | no | — |
| 321 | C2×D4 | — | 28 | 3 | no | — |
| 322 | C2×D4 | — | 28 | 1 | no | — |
| 323 | C2×D4 | — | 56 | 6 | no | — |
| 324 | C2×D4 | D4×D7 | 1 | 3 | yes | — |
| 325 | C22×C4 | — | 7 | 3 | no | — |
| 326 | C22×C4 | — | 14 | 3 | no | — |
| 327 | C22×C4 | — | 28 | 3 | no | — |
| 328 | SD16 | — | 4 | 3 | no | — |
| 329 | SD16 | — | 28 | 3 | no | — |
| 330 | SD16 | — | 28 | 3 | no | — |
| 331 | SD16 | — | 28 | 3 | no | — |
| 332 | D8 | — | 4 | 3 | no | — |
| 333 | D8 | — | 28 | 3 | no | — |
| 334 | D8 | — | 28 | 3 | no | — |
| 335 | D8 | — | 28 | 3 | no | — |
| 336 | M16 | — | 2 | 3 | no | — |
| 337 | M16 | — | 14 | 3 | no | — |
| 338 | M16 | — | 28 | 3 | no | — |
| 339 | C2×C8 | — | 28 | 3 | no | — |
| 340 | C22⋊C4 | — | 2 | 3 | no | — |
| 341 | C22⋊C4 | — | 2 | 6 | no | — |
| 342 | C22⋊C4 | — | 14 | 6 | no | — |
| 343 | C22⋊C4 | — | 14 | 6 | no | — |
| 344 | C22⋊C4 | — | 14 | 6 | no | — |
| 345 | C22⋊C4 | — | 14 | 3 | no | — |
| 346 | C22⋊C4 | — | 14 | 6 | no | — |
| 347 | C42 | — | 7 | 3 | no | — |
| 348 | C42 | — | 14 | 3 | no | — |
| 349 | C42 | D4×D7 | 1 | 3 | yes | — |
| 350 | C2×C7 | — | 2 | 1 | no | — |
| 351 | C2×C7 | — | 8 | 3 | no | — |
| 352 | C2×C7 | — | 8 | 1 | no | — |
| 353 | C2×C7 | C2×B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 354 | D7 | — | 2 | 1 | no | — |
| 355 | D7 | — | 8 | 3 | no | — |
| 356 | D7 | — | 8 | 1 | no | — |
| 357 | D7 | #2202 | 1 | 2 | yes | direct product factor |
| 358 | C23 | — | 2 | 3 | no | — |
| 359 | C23 | — | 7 | 1 | no | — |
| 360 | C23 | — | 8 | 2 | no | — |
| 361 | C23 | — | 8 | 1 | no | — |
| 362 | C23 | — | 14 | 3 | no | — |
| 363 | C23 | — | 28 | 1 | no | — |
| 364 | C23 | — | 28 | 3 | no | — |
| 365 | C23 | — | 28 | 3 | no | — |
| 366 | C23 | — | 28 | 12 | no | — |
| 367 | C23 | — | 56 | 6 | no | — |
| 368 | C23 | — | 56 | 3 | no | — |
| 369 | C23 | — | 56 | 8 | no | — |
| 370 | C23 | — | 56 | 8 | no | — |
| 371 | Q8 | — | 2 | 3 | no | — |
| 372 | Q8 | — | 4 | 1 | no | — |
| 373 | Q8 | — | 8 | 1 | no | — |
| 374 | Q8 | — | 14 | 3 | no | — |
| 375 | Q8 | — | 28 | 3 | no | — |
| 376 | Q8 | — | 28 | 3 | no | — |
| 377 | Q8 | — | 56 | 3 | no | — |
| 378 | D4 | — | 2 | 3 | no | — |
| 379 | D4 | — | 4 | 3 | no | — |
| 380 | D4 | — | 4 | 1 | no | — |
| 381 | D4 | — | 8 | 3 | no | — |
| 382 | D4 | — | 14 | 3 | no | — |
| 383 | D4 | — | 28 | 3 | no | — |
| 384 | D4 | — | 28 | 1 | no | — |
| 385 | D4 | — | 28 | 3 | no | — |
| 386 | D4 | — | 28 | 1 | no | — |
| 387 | D4 | — | 28 | 1 | no | — |
| 388 | D4 | — | 56 | 3 | no | — |
| 389 | D4 | — | 56 | 3 | no | — |
| 390 | D4 | — | 56 | 6 | no | — |
| 391 | C2×C4 | — | 2 | 3 | no | — |
| 392 | C2×C4 | — | 4 | 3 | no | — |
| 393 | C2×C4 | — | 7 | 3 | no | — |
| 394 | C2×C4 | — | 14 | 3 | no | — |
| 395 | C2×C4 | — | 14 | 3 | no | — |
| 396 | C2×C4 | — | 14 | 3 | no | — |
| 397 | C2×C4 | — | 28 | 3 | no | — |
| 398 | C2×C4 | — | 28 | 3 | no | — |
| 399 | C2×C4 | — | 28 | 1 | no | — |
| 400 | C2×C4 | — | 28 | 6 | no | — |
| 401 | C2×C4 | — | 28 | 3 | no | — |
| 402 | C2×C4 | C2×D4×D7 | 1 | 3 | yes | — |
| 403 | C8 | — | 4 | 3 | no | — |
| 404 | C8 | — | 28 | 3 | no | — |
| 405 | C7 | C2×#2202 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 406 | C22 | — | 4 | 6 | no | — |
| 407 | C22 | — | 4 | 1 | no | — |
| 408 | C22 | — | 4 | 3 | no | — |
| 409 | C22 | — | 7 | 1 | no | — |
| 410 | C22 | — | 7 | 1 | no | — |
| 411 | C22 | — | 8 | 4 | no | — |
| 412 | C22 | — | 14 | 2 | no | — |
| 413 | C22 | — | 28 | 6 | no | — |
| 414 | C22 | — | 28 | 1 | no | — |
| 415 | C22 | — | 28 | 3 | no | — |
| 416 | C22 | — | 56 | 6 | no | — |
| 417 | C22 | — | 56 | 2 | no | — |
| 418 | C22 | — | 56 | 6 | no | — |
| 419 | C22 | — | 56 | 12 | no | — |
| 420 | C22 | D7×#120 | 1 | 1 | yes | characteristic |
| 421 | C4 | — | 2 | 3 | no | — |
| 422 | C4 | — | 4 | 3 | no | — |
| 423 | C4 | — | 4 | 1 | no | — |
| 424 | C4 | — | 14 | 3 | no | — |
| 425 | C4 | — | 28 | 3 | no | — |
| 426 | C4 | — | 28 | 1 | no | — |
| 427 | C2 | — | 2 | 1 | no | — |
| 428 | C2 | — | 7 | 2 | no | — |
| 429 | C2 | — | 8 | 3 | no | — |
| 430 | C2 | — | 8 | 1 | no | — |
| 431 | C2 | — | 14 | 1 | no | — |
| 432 | C2 | — | 56 | 3 | no | — |
| 433 | C2 | — | 56 | 1 | no | — |
| 434 | C2 | D7×B(4,𝔽2) | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D7×H(3,𝔽4) | C2 | semidirect |
| 2. D7×#454 | C2 | semidirect |
| 3. C7×#2202 | C2 | semidirect |
| 4. #11729705 | C2 | semidirect |
| 5. #11728741 | C2 | semidirect |
| 6. D7×#355 | C2 | semidirect |
| 7. #11726914 | C2 | semidirect |
| 8. D7×2−1+4 | C22 | semidirect |
| 9. C7×H(3,𝔽4) | C22 | semidirect |
| 12. #90374 | C22 | semidirect |
| 17. C7×#454 | C22 | semidirect |
| 18. #90017 | C22 | semidirect |
| 20. #89834 | C22 | semidirect |
| 23. #89525 | C22 | semidirect |
| 24. D7×#101 | C22 | semidirect |
| 25. C7×#355 | C22 | semidirect |
| 26. #89337 | C22 | semidirect |
| 27. #89272 | C22 | semidirect |
| 30. C7×2−1+4 | C23 | semidirect |
| 36. #6551 | C23 | semidirect |
| 72. C7×#101 | C23 | semidirect |
| 74. #6410 | C23 | semidirect |
| 83. #2202 | D7 | direct (N × H) |
| 154. H(3,𝔽4) | C2×D7 | semidirect |
| 163. #454 | C2×D7 | semidirect |
| 168. #355 | C2×D7 | semidirect |
| 221. 2−1+4 | C22×D7 | semidirect |
| 264. #101 | C22×D7 | semidirect |
| 357. D7 | #2202 | direct (N × H) |
| 405. C7 | C2×#2202 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D7×H(3,𝔽4) | 2 |
| D7×#454 | 2 |
| C7×#2202 | 2 |
| #11729705 | 2 |
| #11728741 | 2 |
| D7×#355 | 2 |
| #11726914 | 2 |
| C2×#2202 | 7 |