Finite Group DatabasebetaFinite Group DatabasebetaOrder 5376.
3368 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 3368 conjugacy classes of subgroups — too many to draw. Only its 77 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 | #72228814 | C2 | 1 | 3 | yes | maximal, complemented |
| 2 | C7×#62817 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 3 | C22×C22⋊(C22⋊ΓL(1,𝔽8)) | — | 4 | 1 | no | maximal |
| 4 | C7⋊#5464 | C22 | 1 | 1 | yes | characteristic, complemented |
| 5 | #13060786 | — | 4 | 1 | no | maximal |
| 6 | #560⋊ΓL(1,𝔽8) | — | 4 | 3 | no | maximal |
| 7 | C7×#3532 | — | 3 | 1 | no | — |
| 8 | C7×#3532 | — | 3 | 3 | no | — |
| 9 | C7×#3532 | — | 3 | 3 | no | — |
| 10 | C7×#3532 | C2×C3 | 1 | 3 | yes | complemented |
| 11 | C7×#3490 | — | 3 | 3 | no | — |
| 12 | C7×#3490 | — | 3 | 3 | no | — |
| 13 | C7×#3484 | — | 3 | 3 | no | — |
| 14 | C7×#3484 | — | 3 | 3 | no | — |
| 15 | C22×C7×#120 | — | 3 | 1 | no | — |
| 16 | #11710731 | — | 7 | 1 | no | maximal, Hall |
| 17 | C2×C22⋊(C22⋊ΓL(1,𝔽8)) | — | 4 | 3 | no | — |
| 18 | #127⋊ΓL(1,𝔽8) | — | 4 | 3 | no | — |
| 19 | #10621175 | — | 4 | 3 | no | — |
| 20 | #10621174 | — | 4 | 3 | no | — |
| 21 | #120⋊ΓL(1,𝔽8) | — | 4 | 3 | no | — |
| 22 | C26×C7 | A4 | 1 | 1 | yes | characteristic, complemented |
| 23 | C2×C7×H(5,𝔽2) | — | 3 | 1 | no | — |
| 24 | C2×C7×H(5,𝔽2) | — | 3 | 1 | no | — |
| 25 | C23×C7×D4 | — | 3 | 3 | no | — |
| 26 | C7×H(3,𝔽4) | — | 3 | 1 | no | — |
| 27 | C7×H(3,𝔽4) | — | 3 | 1 | no | — |
| 28 | C7×H(3,𝔽4) | A4 | 1 | 1 | yes | characteristic, complemented |
| 29 | C7×H(3,𝔽4) | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 30 | C7×#560 | — | 3 | 1 | no | — |
| 31 | C7×#560 | — | 3 | 3 | no | — |
| 32 | C7×#560 | — | 3 | 3 | no | — |
| 33 | C7×#560 | A4 | 1 | 3 | yes | complemented |
| 34 | C7×#551 | — | 3 | 3 | no | — |
| 35 | C7×#551 | — | 3 | 3 | no | — |
| 36 | C7×#551 | — | 3 | 3 | no | — |
| 37 | C7×#551 | — | 3 | 3 | no | — |
| 38 | C7×#551 | — | 3 | 3 | no | — |
| 39 | C7×#551 | — | 3 | 3 | no | — |
| 40 | C7×#551 | — | 3 | 3 | no | — |
| 41 | C7×#551 | — | 3 | 3 | no | — |
| 42 | C7×#546 | — | 3 | 3 | no | — |
| 43 | C7×#546 | — | 3 | 3 | no | — |
| 44 | C7×#546 | — | 3 | 3 | no | — |
| 45 | C7×#546 | — | 3 | 3 | no | — |
| 46 | C7×#546 | — | 3 | 3 | no | — |
| 47 | C7×#546 | — | 3 | 3 | no | — |
| 48 | C7×#546 | — | 3 | 3 | no | — |
| 49 | C7×#546 | — | 3 | 3 | no | — |
| 50 | C7×#546 | — | 3 | 3 | no | — |
| 51 | C7×#546 | — | 3 | 3 | no | — |
| 52 | C7×#546 | — | 3 | 3 | no | — |
| 53 | C7×#546 | — | 3 | 3 | no | — |
| 54 | C7×#546 | — | 3 | 3 | no | — |
| 55 | C7×#546 | — | 3 | 3 | no | — |
| 56 | C7×#546 | — | 3 | 3 | no | — |
| 57 | C7×#546 | — | 3 | 3 | no | — |
| 58 | C7×D42 | — | 3 | 3 | no | — |
| 59 | C7×D42 | — | 3 | 3 | no | — |
| 60 | C7×D42 | — | 3 | 3 | no | — |
| 61 | C7×D42 | — | 3 | 3 | no | — |
| 62 | C7×D42 | — | 3 | 3 | no | — |
| 63 | C7×D42 | — | 3 | 3 | no | — |
| 64 | C7×D42 | — | 3 | 3 | no | — |
| 65 | C7×D42 | — | 3 | 3 | no | — |
| 66 | C7×#543 | — | 3 | 1 | no | — |
| 67 | C7×#543 | — | 3 | 1 | no | — |
| 68 | C7×#538 | — | 3 | 3 | no | — |
| 69 | C7×#538 | — | 3 | 3 | no | — |
| 70 | C7×#538 | — | 3 | 3 | no | — |
| 71 | C7×#538 | — | 3 | 3 | no | — |
| 72 | C7×#538 | — | 3 | 3 | no | — |
| 73 | C7×#538 | — | 3 | 3 | no | — |
| 74 | C7×#538 | — | 3 | 3 | no | — |
| 75 | C7×#538 | — | 3 | 3 | no | — |
| 76 | C7×#535 | — | 3 | 3 | no | — |
| 77 | C7×#535 | — | 3 | 3 | no | — |
| 78 | C7×#535 | — | 3 | 3 | no | — |
| 79 | C7×#535 | — | 3 | 3 | no | — |
| 80 | C7×#534 | — | 3 | 3 | no | — |
| 81 | C7×#534 | — | 3 | 3 | no | — |
| 82 | C7×#534 | — | 3 | 3 | no | — |
| 83 | C7×#534 | — | 3 | 3 | no | — |
| 84 | C7×#534 | — | 3 | 3 | no | — |
| 85 | C7×#534 | — | 3 | 3 | no | — |
| 86 | C7×#525 | — | 3 | 3 | no | — |
| 87 | C7×#525 | — | 3 | 3 | no | — |
| 88 | C7×#525 | — | 3 | 3 | no | — |
| 89 | C7×#525 | — | 3 | 3 | no | — |
| 90 | C2×C7×#120 | — | 3 | 3 | no | — |
| 91 | C2×C7×#120 | — | 3 | 3 | no | — |
| 92 | C2×C7×#120 | — | 3 | 3 | no | — |
| 93 | C2×C7×#120 | — | 3 | 3 | no | — |
| 94 | C2×C7×#120 | — | 3 | 3 | no | — |
| 95 | C2×C7×#120 | — | 3 | 3 | no | — |
| 96 | C2×C7×#120 | — | 3 | 3 | no | — |
| 97 | C2×C7×#120 | — | 3 | 1 | no | — |
| 98 | C2×C7×#120 | — | 3 | 3 | no | — |
| 99 | C2×C7×#120 | — | 3 | 3 | no | — |
| 100 | C7×#518 | — | 3 | 3 | no | — |
| 101 | C7×#518 | — | 3 | 3 | no | — |
| 102 | C22×C7×C22⋊C4 | — | 3 | 3 | no | — |
| 103 | #3532⋊C3 | — | 7 | 3 | no | — |
| 104 | C22⋊(C22⋊ΓL(1,𝔽8)) | — | 4 | 1 | no | — |
| 105 | C22⋊(C22⋊ΓL(1,𝔽8)) | — | 4 | 1 | no | — |
| 106 | C22×C22⋊ΓL(1,𝔽8) | — | 16 | 4 | no | — |
| 107 | C22×C22⋊ΓL(1,𝔽8) | — | 16 | 1 | no | — |
| 108 | C7⋊(C42⋊C3) | — | 4 | 3 | no | — |
| 109 | #62817 | ΓL(1,𝔽8) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 110 | C25×C7 | — | 3 | 1 | no | — |
| 111 | C25×C7 | — | 3 | 3 | no | — |
| 112 | C25×C7 | — | 3 | 1 | no | — |
| 113 | C25×C7 | — | 12 | 4 | no | — |
| 114 | C25×C7 | C2×A4 | 1 | 3 | yes | — |
| 115 | C7×H(5,𝔽2) | — | 12 | 4 | no | — |
| 116 | C7×H(5,𝔽2) | — | 12 | 4 | no | — |
| 117 | C2×C7×#41 | — | 3 | 3 | no | — |
| 118 | C2×C7×#41 | — | 3 | 3 | no | — |
| 119 | C2×C7×#41 | — | 3 | 3 | no | — |
| 120 | C2×C7×#41 | — | 3 | 3 | no | — |
| 121 | C22×C7×D4 | — | 3 | 3 | no | — |
| 122 | C22×C7×D4 | — | 3 | 3 | no | — |
| 123 | C22×C7×D4 | — | 3 | 3 | no | — |
| 124 | C22×C7×D4 | — | 3 | 3 | no | — |
| 125 | C22×C7×D4 | — | 3 | 3 | no | — |
| 126 | C22×C7×D4 | — | 3 | 3 | no | — |
| 127 | C22×C7×D4 | — | 3 | 3 | no | — |
| 128 | C22×C7×D4 | — | 3 | 3 | no | — |
| 129 | C22×C7×D4 | — | 3 | 3 | no | — |
| 130 | C22×C7×D4 | — | 3 | 3 | no | — |
| 131 | C22×C7×D4 | — | 3 | 3 | no | — |
| 132 | C22×C7×D4 | — | 3 | 3 | no | — |
| 133 | C22×C7×D4 | — | 3 | 3 | no | — |
| 134 | C22×C7×D4 | — | 3 | 3 | no | — |
| 135 | C22×C7×D4 | — | 3 | 3 | no | — |
| 136 | C22×C7×D4 | — | 3 | 3 | no | — |
| 137 | C22×C7×D4 | — | 12 | 12 | no | — |
| 138 | C23×C4×C7 | — | 3 | 3 | no | — |
| 139 | C7×#127 | — | 3 | 1 | no | — |
| 140 | C7×#127 | — | 3 | 3 | no | — |
| 141 | C7×#127 | — | 3 | 3 | no | — |
| 142 | C7×#127 | C2×A4 | 1 | 3 | yes | complemented |
| 143 | C7×#126 | — | 3 | 3 | no | — |
| 144 | C7×#126 | — | 3 | 3 | no | — |
| 145 | C7×#126 | — | 3 | 1 | no | — |
| 146 | C7×#126 | — | 3 | 1 | no | — |
| 147 | C7×#126 | — | 3 | 3 | no | — |
| 148 | C7×#126 | — | 3 | 3 | no | — |
| 149 | C7×#126 | C2×A4 | 1 | 3 | yes | complemented |
| 150 | C7×#126 | C2×A4 | 1 | 3 | yes | complemented |
| 151 | C7×#124 | — | 3 | 3 | no | — |
| 152 | C7×#124 | — | 3 | 3 | no | — |
| 153 | C7×#124 | — | 3 | 3 | no | — |
| 154 | C7×#124 | — | 3 | 3 | no | — |
| 155 | C7×#124 | — | 3 | 3 | no | — |
| 156 | C7×#124 | — | 3 | 3 | no | — |
| 157 | C7×#124 | — | 3 | 3 | no | — |
| 158 | C7×#124 | — | 3 | 3 | no | — |
| 159 | C7×#123 | — | 3 | 3 | no | — |
| 160 | C7×#123 | — | 3 | 3 | no | — |
| 161 | C7×#123 | — | 3 | 3 | no | — |
| 162 | C7×#123 | — | 3 | 3 | no | — |
| 163 | C7×#123 | — | 3 | 3 | no | — |
| 164 | C7×#123 | — | 3 | 3 | no | — |
| 165 | C7×#123 | — | 3 | 3 | no | — |
| 166 | C7×#123 | — | 3 | 3 | no | — |
| 167 | C7×#123 | — | 3 | 3 | no | — |
| 168 | C7×#123 | — | 3 | 3 | no | — |
| 169 | C7×#123 | — | 3 | 3 | no | — |
| 170 | C7×#123 | — | 3 | 3 | no | — |
| 171 | C7×#123 | — | 3 | 3 | no | — |
| 172 | C7×#123 | — | 3 | 3 | no | — |
| 173 | C7×#123 | — | 3 | 3 | no | — |
| 174 | C7×#123 | — | 3 | 3 | no | — |
| 175 | C7×C22⋊Q8 | — | 3 | 3 | no | — |
| 176 | C7×C22⋊Q8 | — | 3 | 3 | no | — |
| 177 | C7×C22⋊Q8 | — | 3 | 3 | no | — |
| 178 | C7×C22⋊Q8 | — | 3 | 3 | no | — |
| 179 | C7×C22⋊Q8 | — | 3 | 3 | no | — |
| 180 | C7×C22⋊Q8 | — | 3 | 3 | no | — |
| 181 | C7×C22⋊Q8 | — | 3 | 3 | no | — |
| 182 | C7×C22⋊Q8 | — | 3 | 3 | no | — |
| 183 | C7×#121 | — | 3 | 3 | no | — |
| 184 | C7×#121 | — | 3 | 3 | no | — |
| 185 | C7×#121 | — | 3 | 3 | no | — |
| 186 | C7×#121 | — | 3 | 3 | no | — |
| 187 | C7×#121 | — | 3 | 3 | no | — |
| 188 | C7×#121 | — | 3 | 3 | no | — |
| 189 | C7×#121 | — | 3 | 3 | no | — |
| 190 | C7×#121 | — | 3 | 3 | no | — |
| 191 | C7×#121 | — | 3 | 3 | no | — |
| 192 | C7×#121 | — | 3 | 3 | no | — |
| 193 | C7×#121 | — | 3 | 3 | no | — |
| 194 | C7×#121 | — | 3 | 3 | no | — |
| 195 | C7×#121 | — | 3 | 3 | no | — |
| 196 | C7×#121 | — | 3 | 3 | no | — |
| 197 | C7×#121 | — | 3 | 3 | no | — |
| 198 | C7×#121 | — | 3 | 3 | no | — |
| 199 | C7×#121 | — | 3 | 3 | no | — |
| 200 | C7×#121 | — | 3 | 3 | no | — |
| 201 | C7×#121 | — | 3 | 3 | no | — |
| 202 | C7×#121 | — | 3 | 3 | no | — |
| 203 | C7×#121 | — | 3 | 3 | no | — |
| 204 | C7×#121 | — | 3 | 3 | no | — |
| 205 | C7×#121 | — | 3 | 3 | no | — |
| 206 | C7×#121 | — | 3 | 3 | no | — |
| 207 | C7×#120 | — | 3 | 1 | no | — |
| 208 | C7×#120 | — | 3 | 1 | no | — |
| 209 | C7×#120 | — | 3 | 3 | no | — |
| 210 | C7×#120 | — | 3 | 3 | no | — |
| 211 | C7×#120 | — | 3 | 3 | no | — |
| 212 | C7×#120 | — | 3 | 3 | no | — |
| 213 | C7×#120 | — | 3 | 3 | no | — |
| 214 | C7×#120 | — | 3 | 3 | no | — |
| 215 | C7×#120 | — | 3 | 3 | no | — |
| 216 | C7×#120 | — | 3 | 3 | no | — |
| 217 | C7×#120 | — | 3 | 3 | no | — |
| 218 | C7×#120 | — | 3 | 3 | no | — |
| 219 | C7×#120 | — | 3 | 3 | no | — |
| 220 | C7×#120 | — | 3 | 3 | no | — |
| 221 | C7×#120 | — | 3 | 3 | no | — |
| 222 | C7×#120 | — | 3 | 3 | no | — |
| 223 | C7×#120 | — | 3 | 3 | no | — |
| 224 | C7×#120 | — | 3 | 3 | no | — |
| 225 | C7×#120 | — | 3 | 3 | no | — |
| 226 | C7×#120 | — | 3 | 3 | no | — |
| 227 | C7×#120 | — | 3 | 3 | no | — |
| 228 | C7×#120 | — | 3 | 3 | no | — |
| 229 | C7×#120 | — | 3 | 3 | no | — |
| 230 | C7×#120 | — | 3 | 3 | no | — |
| 231 | C7×#120 | — | 3 | 3 | no | — |
| 232 | C7×#120 | — | 3 | 3 | no | — |
| 233 | C7×#120 | — | 3 | 3 | no | — |
| 234 | C7×#120 | — | 3 | 3 | no | — |
| 235 | C7×#120 | — | 3 | 3 | no | — |
| 236 | C7×#120 | — | 3 | 3 | no | — |
| 237 | C7×#120 | — | 3 | 1 | no | — |
| 238 | C7×#120 | — | 3 | 3 | no | — |
| 239 | C7×#120 | — | 3 | 1 | no | — |
| 240 | C7×#120 | — | 3 | 1 | no | — |
| 241 | C7×#120 | — | 3 | 3 | no | — |
| 242 | C7×#120 | C2×A4 | 1 | 3 | yes | complemented |
| 243 | C4×C7×D4 | — | 3 | 3 | no | — |
| 244 | C4×C7×D4 | — | 3 | 3 | no | — |
| 245 | C4×C7×D4 | — | 3 | 3 | no | — |
| 246 | C4×C7×D4 | — | 3 | 3 | no | — |
| 247 | C4×C7×D4 | — | 3 | 3 | no | — |
| 248 | C4×C7×D4 | — | 3 | 3 | no | — |
| 249 | C4×C7×D4 | — | 3 | 3 | no | — |
| 250 | C4×C7×D4 | — | 3 | 3 | no | — |
| 251 | C4×C7×D4 | — | 3 | 3 | no | — |
| 252 | C4×C7×D4 | — | 3 | 3 | no | — |
| 253 | C4×C7×D4 | — | 3 | 3 | no | — |
| 254 | C4×C7×D4 | — | 3 | 3 | no | — |
| 255 | C4×C7×D4 | — | 3 | 3 | no | — |
| 256 | C4×C7×D4 | — | 3 | 3 | no | — |
| 257 | C4×C7×D4 | — | 3 | 3 | no | — |
| 258 | C4×C7×D4 | — | 3 | 3 | no | — |
| 259 | C7×#117 | — | 3 | 3 | no | — |
| 260 | C7×#117 | — | 3 | 3 | no | — |
| 261 | C7×#117 | — | 3 | 3 | no | — |
| 262 | C7×#117 | — | 3 | 3 | no | — |
| 263 | C2×C7×C22⋊C4 | — | 3 | 3 | no | — |
| 264 | C2×C7×C22⋊C4 | — | 3 | 3 | no | — |
| 265 | C2×C7×C22⋊C4 | — | 3 | 3 | no | — |
| 266 | C2×C7×C22⋊C4 | — | 3 | 3 | no | — |
| 267 | C2×C7×C22⋊C4 | — | 3 | 3 | no | — |
| 268 | C2×C7×C22⋊C4 | — | 3 | 3 | no | — |
| 269 | C2×C7×C22⋊C4 | — | 3 | 3 | no | — |
| 270 | C2×C7×C22⋊C4 | — | 3 | 3 | no | — |
| 271 | C2×C7×C22⋊C4 | — | 3 | 3 | no | — |
| 272 | C2×C7×C22⋊C4 | — | 3 | 3 | no | — |
| 273 | C2×C7×C22⋊C4 | — | 3 | 3 | no | — |
| 274 | C2×C7×C22⋊C4 | — | 3 | 3 | no | — |
| 275 | C2×C7×C22⋊C4 | — | 3 | 3 | no | — |
| 276 | C2×C7×C22⋊C4 | — | 3 | 3 | no | — |
| 277 | C2×C7×C22⋊C4 | — | 3 | 3 | no | — |
| 278 | C2×C7×C22⋊C4 | — | 3 | 3 | no | — |
| 279 | C22×C22⋊A4 | — | 28 | 1 | no | — |
| 280 | #5464 | — | 7 | 1 | no | — |
| 281 | #5450 | — | 28 | 1 | no | — |
| 282 | #560⋊C3 | — | 28 | 3 | no | — |
| 283 | C2×C22⋊ΓL(1,𝔽8) | — | 16 | 12 | no | — |
| 284 | C2×C22⋊ΓL(1,𝔽8) | — | 16 | 3 | no | — |
| 285 | #3532 | — | 3 | 1 | no | — |
| 286 | #3532 | — | 3 | 3 | no | — |
| 287 | #3532 | — | 3 | 3 | no | — |
| 288 | #3532 | C2×ΓL(1,𝔽8) | 1 | 3 | yes | complemented |
| 289 | #3490 | — | 3 | 3 | no | — |
| 290 | #3490 | — | 3 | 3 | no | — |
| 291 | #3484 | — | 3 | 3 | no | — |
| 292 | #3484 | — | 3 | 3 | no | — |
| 293 | C22×#120 | — | 3 | 1 | no | — |
| 294 | C24×C7 | — | 3 | 1 | no | — |
| 295 | C24×C7 | — | 3 | 1 | no | — |
| 296 | C24×C7 | — | 3 | 3 | no | — |
| 297 | C24×C7 | — | 3 | 3 | no | — |
| 298 | C24×C7 | — | 3 | 1 | no | — |
| 299 | C24×C7 | — | 3 | 3 | no | — |
| 300 | C24×C7 | — | 3 | 3 | no | — |
| 301 | C24×C7 | — | 3 | 3 | no | — |
| 302 | C24×C7 | — | 4 | 4 | no | — |
| 303 | C24×C7 | — | 6 | 12 | no | — |
| 304 | C24×C7 | — | 12 | 6 | no | — |
| 305 | C24×C7 | — | 12 | 12 | no | — |
| 306 | C24×C7 | — | 12 | 6 | no | — |
| 307 | C24×C7 | — | 12 | 6 | no | — |
| 308 | C24×C7 | — | 12 | 6 | no | — |
| 309 | C24×C7 | — | 12 | 6 | no | — |
| 310 | C24×C7 | — | 12 | 4 | no | — |
| 311 | C24×C7 | — | 12 | 4 | no | — |
| 312 | C24×C7 | C22×A4 | 1 | 1 | yes | characteristic |
| 313 | C24×C7 | C22×A4 | 1 | 1 | yes | characteristic, complemented |
| 314 | C24×C7 | C22⋊A4 | 1 | 1 | yes | characteristic |
| 315 | C7×#41 | — | 12 | 6 | no | — |
| 316 | C7×#41 | — | 12 | 6 | no | — |
| 317 | C7×#41 | — | 12 | 6 | no | — |
| 318 | C7×#41 | — | 12 | 6 | no | — |
| 319 | C2×C7×Q8 | — | 3 | 1 | no | — |
| 320 | C2×C7×Q8 | — | 3 | 1 | no | — |
| 321 | C2×C7×Q8 | — | 3 | 1 | no | — |
| 322 | C2×C7×Q8 | — | 3 | 1 | no | — |
| 323 | C2×C7×D4 | — | 3 | 3 | no | — |
| 324 | C2×C7×D4 | — | 3 | 3 | no | — |
| 325 | C2×C7×D4 | — | 3 | 3 | no | — |
| 326 | C2×C7×D4 | — | 3 | 3 | no | — |
| 327 | C2×C7×D4 | — | 3 | 3 | no | — |
| 328 | C2×C7×D4 | — | 3 | 3 | no | — |
| 329 | C2×C7×D4 | — | 3 | 3 | no | — |
| 330 | C2×C7×D4 | — | 3 | 3 | no | — |
| 331 | C2×C7×D4 | — | 3 | 3 | no | — |
| 332 | C2×C7×D4 | — | 3 | 3 | no | — |
| 333 | C2×C7×D4 | — | 3 | 3 | no | — |
| 334 | C2×C7×D4 | — | 3 | 3 | no | — |
| 335 | C2×C7×D4 | — | 3 | 3 | no | — |
| 336 | C2×C7×D4 | — | 3 | 3 | no | — |
| 337 | C2×C7×D4 | — | 3 | 3 | no | — |
| 338 | C2×C7×D4 | — | 3 | 3 | no | — |
| 339 | C2×C7×D4 | — | 3 | 3 | no | — |
| 340 | C2×C7×D4 | — | 3 | 3 | no | — |
| 341 | C2×C7×D4 | — | 3 | 3 | no | — |
| 342 | C2×C7×D4 | — | 3 | 3 | no | — |
| 343 | C2×C7×D4 | — | 6 | 12 | no | — |
| 344 | C2×C7×D4 | — | 6 | 12 | no | — |
| 345 | C2×C7×D4 | — | 12 | 6 | no | — |
| 346 | C2×C7×D4 | — | 12 | 6 | no | — |
| 347 | C2×C7×D4 | — | 12 | 6 | no | — |
| 348 | C2×C7×D4 | — | 12 | 6 | no | — |
| 349 | C2×C7×D4 | — | 12 | 6 | no | — |
| 350 | C2×C7×D4 | — | 12 | 6 | no | — |
| 351 | C2×C7×D4 | — | 12 | 6 | no | — |
| 352 | C2×C7×D4 | — | 12 | 6 | no | — |
| 353 | C2×C7×D4 | — | 12 | 6 | no | — |
| 354 | C2×C7×D4 | — | 12 | 6 | no | — |
| 355 | C2×C7×D4 | — | 12 | 6 | no | — |
| 356 | C2×C7×D4 | — | 12 | 6 | no | — |
| 357 | C2×C7×D4 | — | 12 | 6 | no | — |
| 358 | C2×C7×D4 | — | 12 | 6 | no | — |
| 359 | C22×C4×C7 | — | 3 | 3 | no | — |
| 360 | C22×C4×C7 | — | 3 | 3 | no | — |
| 361 | C22×C4×C7 | — | 3 | 3 | no | — |
| 362 | C22×C4×C7 | — | 3 | 3 | no | — |
| 363 | C22×C4×C7 | — | 3 | 3 | no | — |
| 364 | C22×C4×C7 | — | 3 | 3 | no | — |
| 365 | C22×C4×C7 | — | 3 | 3 | no | — |
| 366 | C22×C4×C7 | — | 3 | 3 | no | — |
| 367 | C22×C4×C7 | — | 3 | 3 | no | — |
| 368 | C22×C4×C7 | — | 3 | 3 | no | — |
| 369 | C22×C4×C7 | — | 12 | 6 | no | — |
| 370 | C7×C4⋊C4 | — | 3 | 3 | no | — |
| 371 | C7×C4⋊C4 | — | 3 | 3 | no | — |
| 372 | C7×C4⋊C4 | — | 3 | 3 | no | — |
| 373 | C7×C4⋊C4 | — | 3 | 3 | no | — |
| 374 | C7×C4⋊C4 | — | 3 | 3 | no | — |
| 375 | C7×C4⋊C4 | — | 3 | 3 | no | — |
| 376 | C7×C4⋊C4 | — | 3 | 3 | no | — |
| 377 | C7×C4⋊C4 | — | 3 | 3 | no | — |
| 378 | C7×C22⋊C4 | — | 3 | 3 | no | — |
| 379 | C7×C22⋊C4 | — | 3 | 3 | no | — |
| 380 | C7×C22⋊C4 | — | 3 | 3 | no | — |
| 381 | C7×C22⋊C4 | — | 3 | 3 | no | — |
| 382 | C7×C22⋊C4 | — | 3 | 3 | no | — |
| 383 | C7×C22⋊C4 | — | 3 | 3 | no | — |
| 384 | C7×C22⋊C4 | — | 3 | 3 | no | — |
| 385 | C7×C22⋊C4 | — | 3 | 3 | no | — |
| 386 | C7×C22⋊C4 | — | 3 | 3 | no | — |
| 387 | C7×C22⋊C4 | — | 3 | 3 | no | — |
| 388 | C7×C22⋊C4 | — | 3 | 3 | no | — |
| 389 | C7×C22⋊C4 | — | 3 | 3 | no | — |
| 390 | C7×C22⋊C4 | — | 3 | 3 | no | — |
| 391 | C7×C22⋊C4 | — | 3 | 3 | no | — |
| 392 | C7×C22⋊C4 | — | 3 | 3 | no | — |
| 393 | C7×C22⋊C4 | — | 3 | 3 | no | — |
| 394 | C7×C22⋊C4 | — | 3 | 3 | no | — |
| 395 | C7×C22⋊C4 | — | 3 | 3 | no | — |
| 396 | C7×C22⋊C4 | — | 3 | 3 | no | — |
| 397 | C7×C22⋊C4 | — | 3 | 3 | no | — |
| 398 | C7×C22⋊C4 | — | 3 | 3 | no | — |
| 399 | C7×C22⋊C4 | — | 3 | 3 | no | — |
| 400 | C7×C22⋊C4 | — | 3 | 3 | no | — |
| 401 | C7×C22⋊C4 | — | 3 | 3 | no | — |
| 402 | C42×C7 | — | 3 | 3 | no | — |
| 403 | C42×C7 | — | 3 | 3 | no | — |
| 404 | C42×C7 | — | 3 | 1 | no | — |
| 405 | C42×C7 | C22×A4 | 1 | 3 | yes | complemented |
| 406 | C2×C22⋊A4 | — | 28 | 3 | no | — |
| 407 | #127⋊C3 | — | 28 | 3 | no | — |
| 408 | #126⋊C3 | — | 28 | 3 | no | — |
| 409 | #126⋊C3 | — | 28 | 3 | no | — |
| 410 | #120⋊C3 | — | 28 | 3 | no | — |
| 411 | C22⋊ΓL(1,𝔽8) | — | 16 | 4 | no | — |
| 412 | C22⋊ΓL(1,𝔽8) | — | 16 | 1 | no | — |
| 413 | C22⋊ΓL(1,𝔽8) | — | 64 | 1 | no | — |
| 414 | C22×ΓL(1,𝔽8) | — | 64 | 1 | no | — |
| 415 | C26 | C22⋊ΓL(1,𝔽8) | 1 | 1 | yes | characteristic, complemented |
| 416 | C2×H(5,𝔽2) | — | 3 | 1 | no | — |
| 417 | C2×H(5,𝔽2) | — | 3 | 1 | no | — |
| 418 | C23×D4 | — | 3 | 3 | no | — |
| 419 | H(3,𝔽4) | — | 3 | 1 | no | — |
| 420 | H(3,𝔽4) | — | 3 | 1 | no | — |
| 421 | H(3,𝔽4) | C22×ΓL(1,𝔽8) | 1 | 1 | yes | characteristic, complemented |
| 422 | H(3,𝔽4) | C22⋊ΓL(1,𝔽8) | 1 | 1 | yes | characteristic, complemented |
| 423 | #560 | — | 3 | 1 | no | — |
| 424 | #560 | — | 3 | 3 | no | — |
| 425 | #560 | — | 3 | 3 | no | — |
| 426 | #560 | C22⋊ΓL(1,𝔽8) | 1 | 3 | yes | complemented |
| 427 | #551 | — | 3 | 3 | no | — |
| 428 | #551 | — | 3 | 3 | no | — |
| 429 | #551 | — | 3 | 3 | no | — |
| 430 | #551 | — | 3 | 3 | no | — |
| 431 | #551 | — | 3 | 3 | no | — |
| 432 | #551 | — | 3 | 3 | no | — |
| 433 | #551 | — | 3 | 3 | no | — |
| 434 | #551 | — | 3 | 3 | no | — |
| 435 | #546 | — | 3 | 3 | no | — |
| 436 | #546 | — | 3 | 3 | no | — |
| 437 | #546 | — | 3 | 3 | no | — |
| 438 | #546 | — | 3 | 3 | no | — |
| 439 | #546 | — | 3 | 3 | no | — |
| 440 | #546 | — | 3 | 3 | no | — |
| 441 | #546 | — | 3 | 3 | no | — |
| 442 | #546 | — | 3 | 3 | no | — |
| 443 | #546 | — | 3 | 3 | no | — |
| 444 | #546 | — | 3 | 3 | no | — |
| 445 | #546 | — | 3 | 3 | no | — |
| 446 | #546 | — | 3 | 3 | no | — |
| 447 | #546 | — | 3 | 3 | no | — |
| 448 | #546 | — | 3 | 3 | no | — |
| 449 | #546 | — | 3 | 3 | no | — |
| 450 | #546 | — | 3 | 3 | no | — |
| 451 | D42 | — | 3 | 3 | no | — |
| 452 | D42 | — | 3 | 3 | no | — |
| 453 | D42 | — | 3 | 3 | no | — |
| 454 | D42 | — | 3 | 3 | no | — |
| 455 | D42 | — | 3 | 3 | no | — |
| 456 | D42 | — | 3 | 3 | no | — |
| 457 | D42 | — | 3 | 3 | no | — |
| 458 | D42 | — | 3 | 3 | no | — |
| 459 | #543 | — | 3 | 1 | no | — |
| 460 | #543 | — | 3 | 1 | no | — |
| 461 | #538 | — | 3 | 3 | no | — |
| 462 | #538 | — | 3 | 3 | no | — |
| 463 | #538 | — | 3 | 3 | no | — |
| 464 | #538 | — | 3 | 3 | no | — |
| 465 | #538 | — | 3 | 3 | no | — |
| 466 | #538 | — | 3 | 3 | no | — |
| 467 | #538 | — | 3 | 3 | no | — |
| 468 | #538 | — | 3 | 3 | no | — |
| 469 | #535 | — | 3 | 3 | no | — |
| 470 | #535 | — | 3 | 3 | no | — |
| 471 | #535 | — | 3 | 3 | no | — |
| 472 | #535 | — | 3 | 3 | no | — |
| 473 | #534 | — | 3 | 3 | no | — |
| 474 | #534 | — | 3 | 3 | no | — |
| 475 | #534 | — | 3 | 3 | no | — |
| 476 | #534 | — | 3 | 3 | no | — |
| 477 | #534 | — | 3 | 3 | no | — |
| 478 | #534 | — | 3 | 3 | no | — |
| 479 | #525 | — | 3 | 3 | no | — |
| 480 | #525 | — | 3 | 3 | no | — |
| 481 | #525 | — | 3 | 3 | no | — |
| 482 | #525 | — | 3 | 3 | no | — |
| 483 | C2×#120 | — | 3 | 3 | no | — |
| 484 | C2×#120 | — | 3 | 3 | no | — |
| 485 | C2×#120 | — | 3 | 3 | no | — |
| 486 | C2×#120 | — | 3 | 3 | no | — |
| 487 | C2×#120 | — | 3 | 3 | no | — |
| 488 | C2×#120 | — | 3 | 3 | no | — |
| 489 | C2×#120 | — | 3 | 3 | no | — |
| 490 | C2×#120 | — | 3 | 1 | no | — |
| 491 | C2×#120 | — | 3 | 3 | no | — |
| 492 | C2×#120 | — | 3 | 3 | no | — |
| 493 | #518 | — | 3 | 3 | no | — |
| 494 | #518 | — | 3 | 3 | no | — |
| 495 | C22×C22⋊C4 | — | 3 | 3 | no | — |
| 496 | C23×C7 | — | 3 | 4 | no | — |
| 497 | C23×C7 | — | 3 | 3 | no | — |
| 498 | C23×C7 | — | 3 | 1 | no | — |
| 499 | C23×C7 | — | 3 | 1 | no | — |
| 500 | C23×C7 | — | 3 | 3 | no | — |
| 501 | C23×C7 | — | 4 | 12 | no | — |
| 502 | C23×C7 | — | 6 | 6 | no | — |
| 503 | C23×C7 | — | 6 | 6 | no | — |
| 504 | C23×C7 | — | 6 | 6 | no | — |
| 505 | C23×C7 | — | 6 | 6 | no | — |
| 506 | C23×C7 | — | 6 | 6 | no | — |
| 507 | C23×C7 | — | 6 | 6 | no | — |
| 508 | C23×C7 | — | 6 | 6 | no | — |
| 509 | C23×C7 | — | 6 | 6 | no | — |
| 510 | C23×C7 | — | 12 | 1 | no | — |
| 511 | C23×C7 | — | 12 | 1 | no | — |
| 512 | C23×C7 | — | 12 | 4 | no | — |
| 513 | C23×C7 | — | 12 | 12 | no | — |
| 514 | C23×C7 | — | 12 | 3 | no | — |
| 515 | C23×C7 | — | 12 | 3 | no | — |
| 516 | C23×C7 | — | 12 | 3 | no | — |
| 517 | C23×C7 | — | 12 | 1 | no | — |
| 518 | C23×C7 | — | 12 | 1 | no | — |
| 519 | C23×C7 | — | 12 | 3 | no | — |
| 520 | C23×C7 | — | 12 | 1 | no | — |
| 521 | C23×C7 | — | 12 | 3 | no | — |
| 522 | C23×C7 | — | 12 | 3 | no | — |
| 523 | C23×C7 | — | 12 | 3 | no | — |
| 524 | C23×C7 | — | 12 | 3 | no | — |
| 525 | C23×C7 | — | 12 | 1 | no | — |
| 526 | C23×C7 | — | 12 | 1 | no | — |
| 527 | C23×C7 | — | 12 | 1 | no | — |
| 528 | C23×C7 | — | 12 | 12 | no | — |
| 529 | C23×C7 | — | 12 | 12 | no | — |
| 530 | C23×C7 | — | 12 | 24 | no | — |
| 531 | C23×C7 | — | 12 | 12 | no | — |
| 532 | C23×C7 | — | 24 | 4 | no | — |
| 533 | C23×C7 | — | 24 | 4 | no | — |
| 534 | C23×C7 | C2×C22⋊A4 | 1 | 3 | yes | — |
| 535 | C7×Q8 | — | 12 | 1 | no | — |
| 536 | C7×Q8 | — | 12 | 1 | no | — |
| 537 | C7×Q8 | — | 12 | 1 | no | — |
| 538 | C7×Q8 | — | 12 | 1 | no | — |
| 539 | C7×D4 | — | 6 | 6 | no | — |
| 540 | C7×D4 | — | 6 | 6 | no | — |
| 541 | C7×D4 | — | 6 | 6 | no | — |
| 542 | C7×D4 | — | 6 | 6 | no | — |
| 543 | C7×D4 | — | 6 | 6 | no | — |
| 544 | C7×D4 | — | 6 | 6 | no | — |
| 545 | C7×D4 | — | 6 | 6 | no | — |
| 546 | C7×D4 | — | 6 | 6 | no | — |
| 547 | C7×D4 | — | 12 | 3 | no | — |
| 548 | C7×D4 | — | 12 | 3 | no | — |
| 549 | C7×D4 | — | 12 | 3 | no | — |
| 550 | C7×D4 | — | 12 | 3 | no | — |
| 551 | C7×D4 | — | 12 | 3 | no | — |
| 552 | C7×D4 | — | 12 | 3 | no | — |
| 553 | C7×D4 | — | 12 | 3 | no | — |
| 554 | C7×D4 | — | 12 | 3 | no | — |
| 555 | C7×D4 | — | 12 | 3 | no | — |
| 556 | C7×D4 | — | 12 | 3 | no | — |
| 557 | C7×D4 | — | 12 | 3 | no | — |
| 558 | C7×D4 | — | 12 | 3 | no | — |
| 559 | C2×C4×C7 | — | 3 | 3 | no | — |
| 560 | C2×C4×C7 | — | 3 | 3 | no | — |
| 561 | C2×C4×C7 | — | 3 | 3 | no | — |
| 562 | C2×C4×C7 | — | 3 | 3 | no | — |
| 563 | C2×C4×C7 | — | 6 | 6 | no | — |
| 564 | C2×C4×C7 | — | 6 | 6 | no | — |
| 565 | C2×C4×C7 | — | 12 | 3 | no | — |
| 566 | C2×C4×C7 | — | 12 | 3 | no | — |
| 567 | C2×C4×C7 | — | 12 | 3 | no | — |
| 568 | C2×C4×C7 | — | 12 | 3 | no | — |
| 569 | C2×C4×C7 | — | 12 | 3 | no | — |
| 570 | C2×C4×C7 | — | 12 | 3 | no | — |
| 571 | C2×C4×C7 | — | 12 | 3 | no | — |
| 572 | C2×C4×C7 | — | 12 | 3 | no | — |
| 573 | C22⋊A4 | — | 28 | 1 | no | — |
| 574 | C22⋊A4 | — | 28 | 1 | no | — |
| 575 | C22×A4 | — | 112 | 4 | no | — |
| 576 | C22×A4 | — | 112 | 1 | no | — |
| 577 | C42⋊C3 | — | 28 | 3 | no | — |
| 578 | C2×ΓL(1,𝔽8) | — | 64 | 3 | no | — |
| 579 | C25 | — | 3 | 1 | no | — |
| 580 | C25 | — | 3 | 3 | no | — |
| 581 | C25 | — | 3 | 1 | no | — |
| 582 | C25 | — | 12 | 4 | no | — |
| 583 | C25 | C2×C22⋊ΓL(1,𝔽8) | 1 | 3 | yes | — |
| 584 | H(5,𝔽2) | — | 12 | 4 | no | — |
| 585 | H(5,𝔽2) | — | 12 | 4 | no | — |
| 586 | C2×#41 | — | 3 | 3 | no | — |
| 587 | C2×#41 | — | 3 | 3 | no | — |
| 588 | C2×#41 | — | 3 | 3 | no | — |
| 589 | C2×#41 | — | 3 | 3 | no | — |
| 590 | C22×D4 | — | 3 | 3 | no | — |
| 591 | C22×D4 | — | 3 | 3 | no | — |
| 592 | C22×D4 | — | 3 | 3 | no | — |
| 593 | C22×D4 | — | 3 | 3 | no | — |
| 594 | C22×D4 | — | 3 | 3 | no | — |
| 595 | C22×D4 | — | 3 | 3 | no | — |
| 596 | C22×D4 | — | 3 | 3 | no | — |
| 597 | C22×D4 | — | 3 | 3 | no | — |
| 598 | C22×D4 | — | 3 | 3 | no | — |
| 599 | C22×D4 | — | 3 | 3 | no | — |
| 600 | C22×D4 | — | 3 | 3 | no | — |
| 601 | C22×D4 | — | 3 | 3 | no | — |
| 602 | C22×D4 | — | 3 | 3 | no | — |
| 603 | C22×D4 | — | 3 | 3 | no | — |
| 604 | C22×D4 | — | 3 | 3 | no | — |
| 605 | C22×D4 | — | 3 | 3 | no | — |
| 606 | C22×D4 | — | 12 | 12 | no | — |
| 607 | C23×C4 | — | 3 | 3 | no | — |
| 608 | #127 | — | 3 | 3 | no | — |
| 609 | #127 | — | 3 | 1 | no | — |
| 610 | #127 | — | 3 | 3 | no | — |
| 611 | #127 | C2×C22⋊ΓL(1,𝔽8) | 1 | 3 | yes | complemented |
| 612 | #126 | — | 3 | 3 | no | — |
| 613 | #126 | — | 3 | 3 | no | — |
| 614 | #126 | — | 3 | 1 | no | — |
| 615 | #126 | — | 3 | 1 | no | — |
| 616 | #126 | — | 3 | 3 | no | — |
| 617 | #126 | — | 3 | 3 | no | — |
| 618 | #126 | C2×C22⋊ΓL(1,𝔽8) | 1 | 3 | yes | complemented |
| 619 | #126 | C2×C22⋊ΓL(1,𝔽8) | 1 | 3 | yes | complemented |
| 620 | #124 | — | 3 | 3 | no | — |
| 621 | #124 | — | 3 | 3 | no | — |
| 622 | #124 | — | 3 | 3 | no | — |
| 623 | #124 | — | 3 | 3 | no | — |
| 624 | #124 | — | 3 | 3 | no | — |
| 625 | #124 | — | 3 | 3 | no | — |
| 626 | #124 | — | 3 | 3 | no | — |
| 627 | #124 | — | 3 | 3 | no | — |
| 628 | #123 | — | 3 | 3 | no | — |
| 629 | #123 | — | 3 | 3 | no | — |
| 630 | #123 | — | 3 | 3 | no | — |
| 631 | #123 | — | 3 | 3 | no | — |
| 632 | #123 | — | 3 | 3 | no | — |
| 633 | #123 | — | 3 | 3 | no | — |
| 634 | #123 | — | 3 | 3 | no | — |
| 635 | #123 | — | 3 | 3 | no | — |
| 636 | #123 | — | 3 | 3 | no | — |
| 637 | #123 | — | 3 | 3 | no | — |
| 638 | #123 | — | 3 | 3 | no | — |
| 639 | #123 | — | 3 | 3 | no | — |
| 640 | #123 | — | 3 | 3 | no | — |
| 641 | #123 | — | 3 | 3 | no | — |
| 642 | #123 | — | 3 | 3 | no | — |
| 643 | #123 | — | 3 | 3 | no | — |
| 644 | C22⋊Q8 | — | 3 | 3 | no | — |
| 645 | C22⋊Q8 | — | 3 | 3 | no | — |
| 646 | C22⋊Q8 | — | 3 | 3 | no | — |
| 647 | C22⋊Q8 | — | 3 | 3 | no | — |
| 648 | C22⋊Q8 | — | 3 | 3 | no | — |
| 649 | C22⋊Q8 | — | 3 | 3 | no | — |
| 650 | C22⋊Q8 | — | 3 | 3 | no | — |
| 651 | C22⋊Q8 | — | 3 | 3 | no | — |
| 652 | #121 | — | 3 | 3 | no | — |
| 653 | #121 | — | 3 | 3 | no | — |
| 654 | #121 | — | 3 | 3 | no | — |
| 655 | #121 | — | 3 | 3 | no | — |
| 656 | #121 | — | 3 | 3 | no | — |
| 657 | #121 | — | 3 | 3 | no | — |
| 658 | #121 | — | 3 | 3 | no | — |
| 659 | #121 | — | 3 | 3 | no | — |
| 660 | #121 | — | 3 | 3 | no | — |
| 661 | #121 | — | 3 | 3 | no | — |
| 662 | #121 | — | 3 | 3 | no | — |
| 663 | #121 | — | 3 | 3 | no | — |
| 664 | #121 | — | 3 | 3 | no | — |
| 665 | #121 | — | 3 | 3 | no | — |
| 666 | #121 | — | 3 | 3 | no | — |
| 667 | #121 | — | 3 | 3 | no | — |
| 668 | #121 | — | 3 | 3 | no | — |
| 669 | #121 | — | 3 | 3 | no | — |
| 670 | #121 | — | 3 | 3 | no | — |
| 671 | #121 | — | 3 | 3 | no | — |
| 672 | #121 | — | 3 | 3 | no | — |
| 673 | #121 | — | 3 | 3 | no | — |
| 674 | #121 | — | 3 | 3 | no | — |
| 675 | #121 | — | 3 | 3 | no | — |
| 676 | #120 | — | 3 | 1 | no | — |
| 677 | #120 | — | 3 | 1 | no | — |
| 678 | #120 | — | 3 | 3 | no | — |
| 679 | #120 | — | 3 | 3 | no | — |
| 680 | #120 | — | 3 | 3 | no | — |
| 681 | #120 | — | 3 | 3 | no | — |
| 682 | #120 | — | 3 | 3 | no | — |
| 683 | #120 | — | 3 | 3 | no | — |
| 684 | #120 | — | 3 | 3 | no | — |
| 685 | #120 | — | 3 | 3 | no | — |
| 686 | #120 | — | 3 | 3 | no | — |
| 687 | #120 | — | 3 | 3 | no | — |
| 688 | #120 | — | 3 | 3 | no | — |
| 689 | #120 | — | 3 | 3 | no | — |
| 690 | #120 | — | 3 | 3 | no | — |
| 691 | #120 | — | 3 | 3 | no | — |
| 692 | #120 | — | 3 | 3 | no | — |
| 693 | #120 | — | 3 | 3 | no | — |
| 694 | #120 | — | 3 | 3 | no | — |
| 695 | #120 | — | 3 | 3 | no | — |
| 696 | #120 | — | 3 | 3 | no | — |
| 697 | #120 | — | 3 | 3 | no | — |
| 698 | #120 | — | 3 | 3 | no | — |
| 699 | #120 | — | 3 | 3 | no | — |
| 700 | #120 | — | 3 | 3 | no | — |
| 701 | #120 | — | 3 | 3 | no | — |
| 702 | #120 | — | 3 | 3 | no | — |
| 703 | #120 | — | 3 | 3 | no | — |
| 704 | #120 | — | 3 | 3 | no | — |
| 705 | #120 | — | 3 | 3 | no | — |
| 706 | #120 | — | 3 | 1 | no | — |
| 707 | #120 | — | 3 | 3 | no | — |
| 708 | #120 | — | 3 | 1 | no | — |
| 709 | #120 | — | 3 | 1 | no | — |
| 710 | #120 | — | 3 | 3 | no | — |
| 711 | #120 | C2×C22⋊ΓL(1,𝔽8) | 1 | 3 | yes | complemented |
| 712 | C4×D4 | — | 3 | 3 | no | — |
| 713 | C4×D4 | — | 3 | 3 | no | — |
| 714 | C4×D4 | — | 3 | 3 | no | — |
| 715 | C4×D4 | — | 3 | 3 | no | — |
| 716 | C4×D4 | — | 3 | 3 | no | — |
| 717 | C4×D4 | — | 3 | 3 | no | — |
| 718 | C4×D4 | — | 3 | 3 | no | — |
| 719 | C4×D4 | — | 3 | 3 | no | — |
| 720 | C4×D4 | — | 3 | 3 | no | — |
| 721 | C4×D4 | — | 3 | 3 | no | — |
| 722 | C4×D4 | — | 3 | 3 | no | — |
| 723 | C4×D4 | — | 3 | 3 | no | — |
| 724 | C4×D4 | — | 3 | 3 | no | — |
| 725 | C4×D4 | — | 3 | 3 | no | — |
| 726 | C4×D4 | — | 3 | 3 | no | — |
| 727 | C4×D4 | — | 3 | 3 | no | — |
| 728 | #117 | — | 3 | 3 | no | — |
| 729 | #117 | — | 3 | 3 | no | — |
| 730 | #117 | — | 3 | 3 | no | — |
| 731 | #117 | — | 3 | 3 | no | — |
| 732 | C2×C22⋊C4 | — | 3 | 3 | no | — |
| 733 | C2×C22⋊C4 | — | 3 | 3 | no | — |
| 734 | C2×C22⋊C4 | — | 3 | 3 | no | — |
| 735 | C2×C22⋊C4 | — | 3 | 3 | no | — |
| 736 | C2×C22⋊C4 | — | 3 | 3 | no | — |
| 737 | C2×C22⋊C4 | — | 3 | 3 | no | — |
| 738 | C2×C22⋊C4 | — | 3 | 3 | no | — |
| 739 | C2×C22⋊C4 | — | 3 | 3 | no | — |
| 740 | C2×C22⋊C4 | — | 3 | 3 | no | — |
| 741 | C2×C22⋊C4 | — | 3 | 3 | no | — |
| 742 | C2×C22⋊C4 | — | 3 | 3 | no | — |
| 743 | C2×C22⋊C4 | — | 3 | 3 | no | — |
| 744 | C2×C22⋊C4 | — | 3 | 3 | no | — |
| 745 | C2×C22⋊C4 | — | 3 | 3 | no | — |
| 746 | C2×C22⋊C4 | — | 3 | 3 | no | — |
| 747 | C2×C22⋊C4 | — | 3 | 3 | no | — |
| 748 | C22×C7 | — | 3 | 6 | no | — |
| 749 | C22×C7 | — | 4 | 1 | no | — |
| 750 | C22×C7 | — | 4 | 4 | no | — |
| 751 | C22×C7 | — | 6 | 3 | no | — |
| 752 | C22×C7 | — | 6 | 3 | no | — |
| 753 | C22×C7 | — | 6 | 3 | no | — |
| 754 | C22×C7 | — | 6 | 3 | no | — |
| 755 | C22×C7 | — | 6 | 3 | no | — |
| 756 | C22×C7 | — | 6 | 3 | no | — |
| 757 | C22×C7 | — | 6 | 3 | no | — |
| 758 | C22×C7 | — | 6 | 3 | no | — |
| 759 | C22×C7 | — | 6 | 4 | no | — |
| 760 | C22×C7 | — | 6 | 4 | no | — |
| 761 | C22×C7 | — | 12 | 1 | no | — |
| 762 | C22×C7 | — | 12 | 12 | no | — |
| 763 | C22×C7 | — | 12 | 12 | no | — |
| 764 | C22×C7 | — | 12 | 4 | no | — |
| 765 | C22×C7 | — | 12 | 6 | no | — |
| 766 | C22×C7 | — | 12 | 6 | no | — |
| 767 | C22×C7 | — | 16 | 1 | no | — |
| 768 | C22×C7 | — | 24 | 6 | no | — |
| 769 | C22×C7 | — | 24 | 6 | no | — |
| 770 | C22×C7 | — | 48 | 1 | no | — |
| 771 | C22×C7 | C22×C22⋊A4 | 1 | 1 | yes | characteristic |
| 772 | C4×C7 | — | 6 | 3 | no | — |
| 773 | C4×C7 | — | 6 | 3 | no | — |
| 774 | C4×C7 | — | 6 | 3 | no | — |
| 775 | C4×C7 | — | 6 | 3 | no | — |
| 776 | C2×A4 | — | 112 | 12 | no | — |
| 777 | C2×A4 | — | 112 | 3 | no | — |
| 778 | ΓL(1,𝔽8) | — | 64 | 1 | no | Hall |
| 779 | C24 | — | 3 | 1 | no | — |
| 780 | C24 | — | 3 | 1 | no | — |
| 781 | C24 | — | 3 | 3 | no | — |
| 782 | C24 | — | 3 | 3 | no | — |
| 783 | C24 | — | 3 | 1 | no | — |
| 784 | C24 | — | 3 | 3 | no | — |
| 785 | C24 | — | 3 | 3 | no | — |
| 786 | C24 | — | 3 | 3 | no | — |
| 787 | C24 | — | 4 | 4 | no | — |
| 788 | C24 | — | 6 | 12 | no | — |
| 789 | C24 | — | 12 | 6 | no | — |
| 790 | C24 | — | 12 | 12 | no | — |
| 791 | C24 | — | 12 | 6 | no | — |
| 792 | C24 | — | 12 | 6 | no | — |
| 793 | C24 | — | 12 | 6 | no | — |
| 794 | C24 | — | 12 | 6 | no | — |
| 795 | C24 | — | 12 | 4 | no | — |
| 796 | C24 | — | 12 | 4 | no | — |
| 797 | C24 | C22×C22⋊ΓL(1,𝔽8) | 1 | 1 | yes | characteristic |
| 798 | C24 | C22×C22⋊ΓL(1,𝔽8) | 1 | 1 | yes | characteristic, complemented |
| 799 | C24 | C22⋊(C22⋊ΓL(1,𝔽8)) | 1 | 1 | yes | characteristic |
| 800 | #41 | — | 12 | 6 | no | — |
| 801 | #41 | — | 12 | 6 | no | — |
| 802 | #41 | — | 12 | 6 | no | — |
| 803 | #41 | — | 12 | 6 | no | — |
| 804 | C2×Q8 | — | 3 | 1 | no | — |
| 805 | C2×Q8 | — | 3 | 1 | no | — |
| 806 | C2×Q8 | — | 3 | 1 | no | — |
| 807 | C2×Q8 | — | 3 | 1 | no | — |
| 808 | C2×D4 | — | 3 | 3 | no | — |
| 809 | C2×D4 | — | 3 | 3 | no | — |
| 810 | C2×D4 | — | 3 | 3 | no | — |
| 811 | C2×D4 | — | 3 | 3 | no | — |
| 812 | C2×D4 | — | 3 | 3 | no | — |
| 813 | C2×D4 | — | 3 | 3 | no | — |
| 814 | C2×D4 | — | 3 | 3 | no | — |
| 815 | C2×D4 | — | 3 | 3 | no | — |
| 816 | C2×D4 | — | 3 | 3 | no | — |
| 817 | C2×D4 | — | 3 | 3 | no | — |
| 818 | C2×D4 | — | 3 | 3 | no | — |
| 819 | C2×D4 | — | 3 | 3 | no | — |
| 820 | C2×D4 | — | 3 | 3 | no | — |
| 821 | C2×D4 | — | 3 | 3 | no | — |
| 822 | C2×D4 | — | 3 | 3 | no | — |
| 823 | C2×D4 | — | 3 | 3 | no | — |
| 824 | C2×D4 | — | 3 | 3 | no | — |
| 825 | C2×D4 | — | 3 | 3 | no | — |
| 826 | C2×D4 | — | 3 | 3 | no | — |
| 827 | C2×D4 | — | 3 | 3 | no | — |
| 828 | C2×D4 | — | 6 | 12 | no | — |
| 829 | C2×D4 | — | 6 | 12 | no | — |
| 830 | C2×D4 | — | 12 | 6 | no | — |
| 831 | C2×D4 | — | 12 | 6 | no | — |
| 832 | C2×D4 | — | 12 | 6 | no | — |
| 833 | C2×D4 | — | 12 | 6 | no | — |
| 834 | C2×D4 | — | 12 | 6 | no | — |
| 835 | C2×D4 | — | 12 | 6 | no | — |
| 836 | C2×D4 | — | 12 | 6 | no | — |
| 837 | C2×D4 | — | 12 | 6 | no | — |
| 838 | C2×D4 | — | 12 | 6 | no | — |
| 839 | C2×D4 | — | 12 | 6 | no | — |
| 840 | C2×D4 | — | 12 | 6 | no | — |
| 841 | C2×D4 | — | 12 | 6 | no | — |
| 842 | C2×D4 | — | 12 | 6 | no | — |
| 843 | C2×D4 | — | 12 | 6 | no | — |
| 844 | C22×C4 | — | 3 | 3 | no | — |
| 845 | C22×C4 | — | 3 | 3 | no | — |
| 846 | C22×C4 | — | 3 | 3 | no | — |
| 847 | C22×C4 | — | 3 | 3 | no | — |
| 848 | C22×C4 | — | 3 | 3 | no | — |
| 849 | C22×C4 | — | 3 | 3 | no | — |
| 850 | C22×C4 | — | 3 | 3 | no | — |
| 851 | C22×C4 | — | 3 | 3 | no | — |
| 852 | C22×C4 | — | 3 | 3 | no | — |
| 853 | C22×C4 | — | 3 | 3 | no | — |
| 854 | C22×C4 | — | 12 | 6 | no | — |
| 855 | C4⋊C4 | — | 3 | 3 | no | — |
| 856 | C4⋊C4 | — | 3 | 3 | no | — |
| 857 | C4⋊C4 | — | 3 | 3 | no | — |
| 858 | C4⋊C4 | — | 3 | 3 | no | — |
| 859 | C4⋊C4 | — | 3 | 3 | no | — |
| 860 | C4⋊C4 | — | 3 | 3 | no | — |
| 861 | C4⋊C4 | — | 3 | 3 | no | — |
| 862 | C4⋊C4 | — | 3 | 3 | no | — |
| 863 | C22⋊C4 | — | 3 | 3 | no | — |
| 864 | C22⋊C4 | — | 3 | 3 | no | — |
| 865 | C22⋊C4 | — | 3 | 3 | no | — |
| 866 | C22⋊C4 | — | 3 | 3 | no | — |
| 867 | C22⋊C4 | — | 3 | 3 | no | — |
| 868 | C22⋊C4 | — | 3 | 3 | no | — |
| 869 | C22⋊C4 | — | 3 | 3 | no | — |
| 870 | C22⋊C4 | — | 3 | 3 | no | — |
| 871 | C22⋊C4 | — | 3 | 3 | no | — |
| 872 | C22⋊C4 | — | 3 | 3 | no | — |
| 873 | C22⋊C4 | — | 3 | 3 | no | — |
| 874 | C22⋊C4 | — | 3 | 3 | no | — |
| 875 | C22⋊C4 | — | 3 | 3 | no | — |
| 876 | C22⋊C4 | — | 3 | 3 | no | — |
| 877 | C22⋊C4 | — | 3 | 3 | no | — |
| 878 | C22⋊C4 | — | 3 | 3 | no | — |
| 879 | C22⋊C4 | — | 3 | 3 | no | — |
| 880 | C22⋊C4 | — | 3 | 3 | no | — |
| 881 | C22⋊C4 | — | 3 | 3 | no | — |
| 882 | C22⋊C4 | — | 3 | 3 | no | — |
| 883 | C22⋊C4 | — | 3 | 3 | no | — |
| 884 | C22⋊C4 | — | 3 | 3 | no | — |
| 885 | C22⋊C4 | — | 3 | 3 | no | — |
| 886 | C22⋊C4 | — | 3 | 3 | no | — |
| 887 | C42 | — | 3 | 3 | no | — |
| 888 | C42 | — | 3 | 3 | no | — |
| 889 | C42 | — | 3 | 1 | no | — |
| 890 | C42 | C22×C22⋊ΓL(1,𝔽8) | 1 | 3 | yes | complemented |
| 891 | C2×C7 | — | 3 | 1 | no | — |
| 892 | C2×C7 | — | 4 | 3 | no | — |
| 893 | C2×C7 | — | 6 | 6 | no | — |
| 894 | C2×C7 | — | 12 | 1 | no | — |
| 895 | C2×C7 | — | 12 | 1 | no | — |
| 896 | C2×C7 | — | 12 | 3 | no | — |
| 897 | C22×C3 | — | 448 | 1 | no | — |
| 898 | A4 | — | 112 | 4 | no | — |
| 899 | A4 | — | 112 | 1 | no | — |
| 900 | A4 | — | 448 | 1 | no | — |
| 901 | C23 | — | 3 | 4 | no | — |
| 902 | C23 | — | 3 | 3 | no | — |
| 903 | C23 | — | 3 | 1 | no | — |
| 904 | C23 | — | 3 | 1 | no | — |
| 905 | C23 | — | 3 | 3 | no | — |
| 906 | C23 | — | 4 | 12 | no | — |
| 907 | C23 | — | 6 | 6 | no | — |
| 908 | C23 | — | 6 | 6 | no | — |
| 909 | C23 | — | 6 | 6 | no | — |
| 910 | C23 | — | 6 | 6 | no | — |
| 911 | C23 | — | 6 | 6 | no | — |
| 912 | C23 | — | 6 | 6 | no | — |
| 913 | C23 | — | 6 | 6 | no | — |
| 914 | C23 | — | 6 | 6 | no | — |
| 915 | C23 | — | 12 | 1 | no | — |
| 916 | C23 | — | 12 | 1 | no | — |
| 917 | C23 | — | 12 | 4 | no | — |
| 918 | C23 | — | 12 | 12 | no | — |
| 919 | C23 | — | 12 | 3 | no | — |
| 920 | C23 | — | 12 | 3 | no | — |
| 921 | C23 | — | 12 | 3 | no | — |
| 922 | C23 | — | 12 | 1 | no | — |
| 923 | C23 | — | 12 | 1 | no | — |
| 924 | C23 | — | 12 | 3 | no | — |
| 925 | C23 | — | 12 | 1 | no | — |
| 926 | C23 | — | 12 | 3 | no | — |
| 927 | C23 | — | 12 | 3 | no | — |
| 928 | C23 | — | 12 | 3 | no | — |
| 929 | C23 | — | 12 | 3 | no | — |
| 930 | C23 | — | 12 | 1 | no | — |
| 931 | C23 | — | 12 | 1 | no | — |
| 932 | C23 | — | 12 | 1 | no | — |
| 933 | C23 | — | 12 | 12 | no | — |
| 934 | C23 | — | 12 | 12 | no | — |
| 935 | C23 | — | 12 | 24 | no | — |
| 936 | C23 | — | 12 | 12 | no | — |
| 937 | C23 | — | 24 | 4 | no | — |
| 938 | C23 | — | 24 | 4 | no | — |
| 939 | C23 | C2×C22⋊(C22⋊ΓL(1,𝔽8)) | 1 | 3 | yes | — |
| 940 | Q8 | — | 12 | 1 | no | — |
| 941 | Q8 | — | 12 | 1 | no | — |
| 942 | Q8 | — | 12 | 1 | no | — |
| 943 | Q8 | — | 12 | 1 | no | — |
| 944 | D4 | — | 6 | 6 | no | — |
| 945 | D4 | — | 6 | 6 | no | — |
| 946 | D4 | — | 6 | 6 | no | — |
| 947 | D4 | — | 6 | 6 | no | — |
| 948 | D4 | — | 6 | 6 | no | — |
| 949 | D4 | — | 6 | 6 | no | — |
| 950 | D4 | — | 6 | 6 | no | — |
| 951 | D4 | — | 6 | 6 | no | — |
| 952 | D4 | — | 12 | 3 | no | — |
| 953 | D4 | — | 12 | 3 | no | — |
| 954 | D4 | — | 12 | 3 | no | — |
| 955 | D4 | — | 12 | 3 | no | — |
| 956 | D4 | — | 12 | 3 | no | — |
| 957 | D4 | — | 12 | 3 | no | — |
| 958 | D4 | — | 12 | 3 | no | — |
| 959 | D4 | — | 12 | 3 | no | — |
| 960 | D4 | — | 12 | 3 | no | — |
| 961 | D4 | — | 12 | 3 | no | — |
| 962 | D4 | — | 12 | 3 | no | — |
| 963 | D4 | — | 12 | 3 | no | — |
| 964 | C2×C4 | — | 3 | 3 | no | — |
| 965 | C2×C4 | — | 3 | 3 | no | — |
| 966 | C2×C4 | — | 3 | 3 | no | — |
| 967 | C2×C4 | — | 3 | 3 | no | — |
| 968 | C2×C4 | — | 6 | 6 | no | — |
| 969 | C2×C4 | — | 6 | 6 | no | — |
| 970 | C2×C4 | — | 12 | 3 | no | — |
| 971 | C2×C4 | — | 12 | 3 | no | — |
| 972 | C2×C4 | — | 12 | 3 | no | — |
| 973 | C2×C4 | — | 12 | 3 | no | — |
| 974 | C2×C4 | — | 12 | 3 | no | — |
| 975 | C2×C4 | — | 12 | 3 | no | — |
| 976 | C2×C4 | — | 12 | 3 | no | — |
| 977 | C2×C4 | — | 12 | 3 | no | — |
| 978 | C7 | #11710731 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 979 | C2×C3 | — | 448 | 3 | no | — |
| 980 | C22 | — | 3 | 6 | no | — |
| 981 | C22 | — | 4 | 1 | no | — |
| 982 | C22 | — | 4 | 4 | no | — |
| 983 | C22 | — | 6 | 3 | no | — |
| 984 | C22 | — | 6 | 3 | no | — |
| 985 | C22 | — | 6 | 3 | no | — |
| 986 | C22 | — | 6 | 3 | no | — |
| 987 | C22 | — | 6 | 3 | no | — |
| 988 | C22 | — | 6 | 3 | no | — |
| 989 | C22 | — | 6 | 3 | no | — |
| 990 | C22 | — | 6 | 3 | no | — |
| 991 | C22 | — | 6 | 4 | no | — |
| 992 | C22 | — | 6 | 4 | no | — |
| 993 | C22 | — | 12 | 1 | no | — |
| 994 | C22 | — | 12 | 12 | no | — |
| 995 | C22 | — | 12 | 12 | no | — |
| 996 | C22 | — | 12 | 4 | no | — |
| 997 | C22 | — | 12 | 6 | no | — |
| 998 | C22 | — | 12 | 6 | no | — |
| 999 | C22 | — | 16 | 1 | no | — |
| 1000 | C22 | — | 24 | 6 | no | — |
| 1001 | C22 | — | 24 | 6 | no | — |
| 1002 | C22 | — | 48 | 1 | no | — |
| 1003 | C22 | C22×C22⋊(C22⋊ΓL(1,𝔽8)) | 1 | 1 | yes | characteristic |
| 1004 | C4 | — | 6 | 3 | no | — |
| 1005 | C4 | — | 6 | 3 | no | — |
| 1006 | C4 | — | 6 | 3 | no | — |
| 1007 | C4 | — | 6 | 3 | no | — |
| 1008 | C3 | — | 448 | 1 | no | Sylow |
| 1009 | C2 | — | 3 | 1 | no | — |
| 1010 | C2 | — | 4 | 3 | no | — |
| 1011 | C2 | — | 6 | 6 | no | — |
| 1012 | C2 | — | 12 | 1 | no | — |
| 1013 | C2 | — | 12 | 1 | no | — |
| 1014 | C2 | — | 12 | 3 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C7×H(3,𝔽4) | C22×C3 |
| Frattini | C22 | C22×C22⋊(C22⋊ΓL(1,𝔽8)) |
| Fitting | C7×#62817 | C3 |
| socle | C22×C7 | C22×C22⋊A4 |
| LCS | G ▷ C7×H(3,𝔽4) | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72228814 | C2 | semidirect |
| 2. C7×#62817 | C3 | semidirect |
| 4. C7⋊#5464 | C22 | semidirect |
| 10. C7×#3532 | C2×C3 | semidirect |
| 22. C26×C7 | A4 | semidirect |
| 28. C7×H(3,𝔽4) | A4 | semidirect |
| 29. C7×H(3,𝔽4) | C22×C3 | semidirect |
| 33. C7×#560 | A4 | semidirect |
| 109. #62817 | ΓL(1,𝔽8) | semidirect |
| 142. C7×#127 | C2×A4 | semidirect |
| 149. C7×#126 | C2×A4 | semidirect |
| 150. C7×#126 | C2×A4 | semidirect |
| 242. C7×#120 | C2×A4 | semidirect |
| 288. #3532 | C2×ΓL(1,𝔽8) | semidirect |
| 313. C24×C7 | C22×A4 | semidirect |
| 405. C42×C7 | C22×A4 | semidirect |
| 415. C26 | C22⋊ΓL(1,𝔽8) | semidirect |
| 421. H(3,𝔽4) | C22×ΓL(1,𝔽8) | semidirect |
| 422. H(3,𝔽4) | C22⋊ΓL(1,𝔽8) | semidirect |
| 426. #560 | C22⋊ΓL(1,𝔽8) | semidirect |
| 611. #127 | C2×C22⋊ΓL(1,𝔽8) | semidirect |
| 618. #126 | C2×C22⋊ΓL(1,𝔽8) | semidirect |
| 619. #126 | C2×C22⋊ΓL(1,𝔽8) | semidirect |
| 711. #120 | C2×C22⋊ΓL(1,𝔽8) | semidirect |
| 798. C24 | C22×C22⋊ΓL(1,𝔽8) | semidirect |
| 890. C42 | C22×C22⋊ΓL(1,𝔽8) | semidirect |
| 978. C7 | #11710731 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72228814 | 2 |
| C7×#62817 | 3 |
| C22×C22⋊(C22⋊ΓL(1,𝔽8)) | 4 |
| #13060786 | 4 |
| #560⋊ΓL(1,𝔽8) | 4 |
| #11710731 | 7 |