← C61×#62946 #29566379
Subgroups — C61×#62946 #29566379
Order 15616.
6958 conjugacy classes of subgroups.
The subgroup lattice has 542 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C61×#3559 | C2 | 1 | 12 | yes | maximal, complemented |
| 2 | C61×#3554 | C2 | 1 | 12 | yes | maximal, complemented |
| 3 | C61×#3552 | C2 | 1 | 12 | yes | maximal, complemented |
| 4 | C61×#3522 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | C61×#3517 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | C61×#3503 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | C61×#3499 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | C61×#3497 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | C61×#3480 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | C2×C61×#557 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C61×#3461 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | C2×2−1+4×C61 | C22 | 1 | 6 | yes | — |
| 13 | C61×#563 | C22 | 1 | 24 | yes | — |
| 14 | C61×#562 | C22 | 1 | 24 | yes | — |
| 15 | C61×#559 | C22 | 1 | 6 | yes | — |
| 16 | C61×#559 | C22 | 1 | 12 | yes | — |
| 17 | Q82×C61 | C22 | 1 | 4 | yes | — |
| 18 | C61×#557 | C22 | 1 | 12 | yes | — |
| 19 | C61×#557 | C22 | 1 | 4 | yes | — |
| 20 | C61×#557 | C22 | 1 | 2 | yes | — |
| 21 | C61×#556 | C22 | 1 | 6 | yes | — |
| 22 | C61×#554 | C22 | 1 | 12 | yes | — |
| 23 | C61×#554 | C22 | 1 | 24 | yes | — |
| 24 | C61×#553 | C22 | 1 | 24 | yes | — |
| 25 | C61×#553 | C22 | 1 | 12 | yes | — |
| 26 | C61×#550 | C22 | 1 | 12 | yes | — |
| 27 | C61×#550 | C22 | 1 | 2 | yes | — |
| 28 | C61×#550 | C22 | 1 | 4 | yes | — |
| 29 | D4×Q8×C61 | C22 | 1 | 12 | yes | — |
| 30 | D4×Q8×C61 | C22 | 1 | 12 | yes | — |
| 31 | D4×Q8×C61 | C22 | 1 | 12 | yes | — |
| 32 | C61×#548 | C22 | 1 | 24 | yes | — |
| 33 | C61×#548 | C22 | 1 | 4 | yes | — |
| 34 | C61×#547 | C22 | 1 | 12 | yes | — |
| 35 | C61×#547 | C22 | 1 | 12 | yes | — |
| 36 | C61×#547 | C22 | 1 | 24 | yes | — |
| 37 | C61×#547 | C22 | 1 | 24 | yes | — |
| 38 | C61×#544 | C22 | 1 | 24 | yes | — |
| 39 | C61×#544 | C22 | 1 | 1 | yes | characteristic |
| 40 | C61×#542 | C22 | 1 | 24 | yes | — |
| 41 | C61×#542 | C22 | 1 | 12 | yes | — |
| 42 | C61×#541 | C22 | 1 | 12 | yes | — |
| 43 | C61×#540 | C22 | 1 | 24 | yes | — |
| 44 | C61×#539 | C22 | 1 | 48 | yes | — |
| 45 | C61×#539 | C22 | 1 | 12 | yes | — |
| 46 | C61×#537 | C22 | 1 | 12 | yes | — |
| 47 | C61×#537 | C22 | 1 | 3 | yes | — |
| 48 | C61×#536 | C22 | 1 | 24 | yes | — |
| 49 | C61×#536 | C22 | 1 | 6 | yes | — |
| 50 | C61×#533 | C22 | 1 | 12 | yes | — |
| 51 | C61×#532 | C22 | 1 | 12 | yes | — |
| 52 | C61×#532 | C22 | 1 | 12 | yes | — |
| 53 | C61×#532 | C22 | 1 | 6 | yes | — |
| 54 | C2×C4⋊Q8×C61 | C22 | 1 | 12 | yes | — |
| 55 | C2×C4⋊Q8×C61 | C22 | 1 | 3 | yes | — |
| 56 | C61×#529 | C22 | 1 | 12 | yes | — |
| 57 | C61×#529 | C22 | 1 | 12 | yes | — |
| 58 | C61×#529 | C22 | 1 | 12 | yes | — |
| 59 | C2×#125×C61 | C22 | 1 | 6 | yes | — |
| 60 | C61×#520 | C22 | 1 | 8 | yes | — |
| 61 | C4×#41×C61 | C22 | 1 | 6 | yes | — |
| 62 | C4×#41×C61 | C22 | 1 | 4 | yes | — |
| 63 | C2×C4×Q8×C61 | C22 | 1 | 3 | yes | — |
| 64 | C2×C4×Q8×C61 | C22 | 1 | 1 | yes | characteristic |
| 65 | C2×C4×Q8×C61 | C22 | 1 | 2 | yes | — |
| 66 | 2−1+4×C61 | — | 4 | 24 | no | — |
| 67 | C2×#41×C61 | C23 | 1 | 6 | yes | — |
| 68 | C2×#41×C61 | C23 | 1 | 4 | yes | — |
| 69 | C2×#41×C61 | C23 | 1 | 24 | yes | — |
| 70 | C2×#41×C61 | C23 | 1 | 24 | yes | — |
| 71 | C22×Q8×C61 | C23 | 1 | 3 | yes | — |
| 72 | C22×Q8×C61 | C23 | 1 | 1 | yes | characteristic |
| 73 | C22×Q8×C61 | C23 | 1 | 24 | yes | — |
| 74 | C4⋊Q8×C61 | C23 | 1 | 12 | yes | — |
| 75 | C4⋊Q8×C61 | C23 | 1 | 6 | yes | — |
| 76 | C4⋊Q8×C61 | C23 | 1 | 12 | yes | — |
| 77 | C4⋊Q8×C61 | C23 | 1 | 12 | yes | — |
| 78 | C4⋊Q8×C61 | C23 | 1 | 24 | yes | — |
| 79 | C4⋊Q8×C61 | C23 | 1 | 24 | yes | — |
| 80 | C4⋊Q8×C61 | C23 | 1 | 12 | yes | — |
| 81 | C4⋊Q8×C61 | C23 | 1 | 4 | yes | — |
| 82 | #127×C61 | C23 | 1 | 6 | yes | — |
| 83 | #127×C61 | C23 | 1 | 12 | yes | — |
| 84 | #126×C61 | C23 | 1 | 24 | yes | — |
| 85 | #126×C61 | C23 | 1 | 24 | yes | — |
| 86 | #126×C61 | C23 | 1 | 24 | yes | — |
| 87 | #125×C61 | C23 | 1 | 24 | yes | — |
| 88 | #125×C61 | C23 | 1 | 24 | yes | — |
| 89 | #125×C61 | C23 | 1 | 24 | yes | — |
| 90 | #125×C61 | C23 | 1 | 4 | yes | — |
| 91 | #125×C61 | C23 | 1 | 12 | yes | — |
| 92 | #125×C61 | C23 | 1 | 12 | yes | — |
| 93 | #124×C61 | C23 | 1 | 12 | yes | — |
| 94 | #124×C61 | C23 | 1 | 12 | yes | — |
| 95 | #124×C61 | C23 | 1 | 24 | yes | — |
| 96 | #124×C61 | C23 | 1 | 12 | yes | — |
| 97 | #124×C61 | C23 | 1 | 12 | yes | — |
| 98 | #123×C61 | C23 | 1 | 48 | yes | — |
| 99 | #123×C61 | C23 | 1 | 48 | yes | — |
| 100 | #123×C61 | C23 | 1 | 24 | yes | — |
| 101 | #123×C61 | C23 | 1 | 24 | yes | — |
| 102 | #123×C61 | C23 | 1 | 24 | yes | — |
| 103 | C22⋊Q8×C61 | C23 | 1 | 12 | yes | — |
| 104 | C22⋊Q8×C61 | C23 | 1 | 12 | yes | — |
| 105 | C22⋊Q8×C61 | C23 | 1 | 24 | yes | — |
| 106 | C22⋊Q8×C61 | C23 | 1 | 48 | yes | — |
| 107 | C22⋊Q8×C61 | C23 | 1 | 48 | yes | — |
| 108 | C22⋊Q8×C61 | C23 | 1 | 12 | yes | — |
| 109 | C22⋊Q8×C61 | C23 | 1 | 48 | yes | — |
| 110 | C22⋊Q8×C61 | C23 | 1 | 4 | yes | — |
| 111 | C22⋊Q8×C61 | C23 | 1 | 12 | yes | — |
| 112 | #121×C61 | C23 | 1 | 12 | yes | — |
| 113 | #121×C61 | C23 | 1 | 12 | yes | — |
| 114 | #121×C61 | C23 | 1 | 12 | yes | — |
| 115 | #121×C61 | C23 | 1 | 24 | yes | — |
| 116 | #121×C61 | C23 | 1 | 24 | yes | — |
| 117 | #121×C61 | C23 | 1 | 48 | yes | — |
| 118 | #121×C61 | C23 | 1 | 12 | yes | — |
| 119 | #121×C61 | C23 | 1 | 12 | yes | — |
| 120 | C4×Q8×C61 | C23 | 1 | 6 | yes | — |
| 121 | C4×Q8×C61 | C23 | 1 | 12 | yes | — |
| 122 | C4×Q8×C61 | C23 | 1 | 12 | yes | — |
| 123 | C4×Q8×C61 | C23 | 1 | 6 | yes | — |
| 124 | C4×Q8×C61 | C23 | 1 | 12 | yes | — |
| 125 | C4×Q8×C61 | C23 | 1 | 12 | yes | — |
| 126 | C4×Q8×C61 | C23 | 1 | 4 | yes | — |
| 127 | C4×Q8×C61 | C23 | 1 | 2 | yes | — |
| 128 | C4×Q8×C61 | C23 | 1 | 4 | yes | — |
| 129 | C4×Q8×C61 | C23 | 1 | 6 | yes | — |
| 130 | C4×D4×C61 | C23 | 1 | 24 | yes | — |
| 131 | C4×D4×C61 | C23 | 1 | 24 | yes | — |
| 132 | C4×D4×C61 | C23 | 1 | 24 | yes | — |
| 133 | C4×D4×C61 | C23 | 1 | 24 | yes | — |
| 134 | C4×D4×C61 | C23 | 1 | 12 | yes | — |
| 135 | C4×D4×C61 | C23 | 1 | 12 | yes | — |
| 136 | C4×D4×C61 | C23 | 1 | 12 | yes | — |
| 137 | C4×D4×C61 | C23 | 1 | 12 | yes | — |
| 138 | C4×D4×C61 | C23 | 1 | 6 | yes | — |
| 139 | C4×D4×C61 | C23 | 1 | 12 | yes | — |
| 140 | C4×D4×C61 | C23 | 1 | 6 | yes | — |
| 141 | C4×D4×C61 | C23 | 1 | 12 | yes | — |
| 142 | #117×C61 | C23 | 1 | 24 | yes | — |
| 143 | #117×C61 | C23 | 1 | 2 | yes | — |
| 144 | #117×C61 | C23 | 1 | 12 | yes | — |
| 145 | #117×C61 | C23 | 1 | 12 | yes | — |
| 146 | C2×C4⋊C4×C61 | C23 | 1 | 24 | yes | — |
| 147 | C2×C4⋊C4×C61 | C23 | 1 | 24 | yes | — |
| 148 | C2×C4⋊C4×C61 | C23 | 1 | 6 | yes | — |
| 149 | C2×C4⋊C4×C61 | C23 | 1 | 6 | yes | — |
| 150 | C2×C4⋊C4×C61 | C23 | 1 | 1 | yes | characteristic |
| 151 | C2×C4⋊C4×C61 | C23 | 1 | 6 | yes | — |
| 152 | C2×C4⋊C4×C61 | C23 | 1 | 3 | yes | — |
| 153 | C2×C42×C61 | C23 | 1 | 3 | yes | — |
| 154 | C2×C42×C61 | C23 | 1 | 12 | yes | — |
| 155 | C2×C42×C61 | C23 | 1 | 6 | yes | — |
| 156 | #41×C61 | — | 2 | 16 | no | — |
| 157 | #41×C61 | — | 2 | 24 | no | — |
| 158 | #41×C61 | — | 4 | 48 | no | — |
| 159 | #41×C61 | — | 4 | 48 | no | — |
| 160 | C2×Q8×C61 | — | 2 | 4 | no | — |
| 161 | C2×Q8×C61 | — | 2 | 12 | no | — |
| 162 | C2×Q8×C61 | — | 4 | 48 | no | — |
| 163 | C2×Q8×C61 | C24 | 1 | 3 | yes | — |
| 164 | C2×Q8×C61 | C24 | 1 | 6 | yes | — |
| 165 | C2×Q8×C61 | C24 | 1 | 12 | yes | — |
| 166 | C2×Q8×C61 | C24 | 1 | 4 | yes | — |
| 167 | C2×Q8×C61 | C24 | 1 | 24 | yes | — |
| 168 | C2×Q8×C61 | C24 | 1 | 1 | yes | characteristic |
| 169 | C2×D4×C61 | C24 | 1 | 12 | yes | — |
| 170 | C2×D4×C61 | C24 | 1 | 12 | yes | — |
| 171 | C2×D4×C61 | C24 | 1 | 6 | yes | — |
| 172 | C2×D4×C61 | C24 | 1 | 12 | yes | — |
| 173 | C2×D4×C61 | C24 | 1 | 12 | yes | — |
| 174 | C2×D4×C61 | C24 | 1 | 24 | yes | — |
| 175 | C22×C4×C61 | C24 | 1 | 3 | yes | — |
| 176 | C22×C4×C61 | C24 | 1 | 6 | yes | — |
| 177 | C22×C4×C61 | C24 | 1 | 12 | yes | — |
| 178 | C22×C4×C61 | C24 | 1 | 12 | yes | — |
| 179 | C22×C4×C61 | C24 | 1 | 2 | yes | — |
| 180 | C22×C4×C61 | C24 | 1 | 3 | yes | — |
| 181 | C22×C4×C61 | C24 | 1 | 12 | yes | — |
| 182 | C22×C4×C61 | C24 | 1 | 48 | yes | — |
| 183 | C22×C4×C61 | C24 | 1 | 1 | yes | characteristic |
| 184 | C4⋊C4×C61 | C24 | 1 | 12 | yes | — |
| 185 | C4⋊C4×C61 | C24 | 1 | 12 | yes | — |
| 186 | C4⋊C4×C61 | C24 | 1 | 24 | yes | — |
| 187 | C4⋊C4×C61 | C24 | 1 | 12 | yes | — |
| 188 | C4⋊C4×C61 | C24 | 1 | 24 | yes | — |
| 189 | C4⋊C4×C61 | C24 | 1 | 24 | yes | — |
| 190 | C4⋊C4×C61 | C24 | 1 | 6 | yes | — |
| 191 | C4⋊C4×C61 | C24 | 1 | 4 | yes | — |
| 192 | C4⋊C4×C61 | C24 | 1 | 24 | yes | — |
| 193 | C4⋊C4×C61 | C24 | 1 | 12 | yes | — |
| 194 | C4⋊C4×C61 | C24 | 1 | 6 | yes | — |
| 195 | C4⋊C4×C61 | C24 | 1 | 8 | yes | — |
| 196 | C4⋊C4×C61 | C24 | 1 | 2 | yes | — |
| 197 | C4⋊C4×C61 | C24 | 1 | 2 | yes | — |
| 198 | C4⋊C4×C61 | C24 | 1 | 12 | yes | — |
| 199 | C4⋊C4×C61 | C24 | 1 | 12 | yes | — |
| 200 | C4⋊C4×C61 | C24 | 1 | 4 | yes | — |
| 201 | C4⋊C4×C61 | C24 | 1 | 12 | yes | — |
| 202 | C22⋊C4×C61 | C24 | 1 | 4 | yes | — |
| 203 | C22⋊C4×C61 | C24 | 1 | 24 | yes | — |
| 204 | C22⋊C4×C61 | C24 | 1 | 24 | yes | — |
| 205 | C22⋊C4×C61 | C24 | 1 | 24 | yes | — |
| 206 | C22⋊C4×C61 | C24 | 1 | 12 | yes | — |
| 207 | C22⋊C4×C61 | C24 | 1 | 12 | yes | — |
| 208 | C22⋊C4×C61 | C24 | 1 | 24 | yes | — |
| 209 | C22⋊C4×C61 | C24 | 1 | 24 | yes | — |
| 210 | C42×C61 | C24 | 1 | 4 | yes | — |
| 211 | C42×C61 | C24 | 1 | 6 | yes | — |
| 212 | C42×C61 | C24 | 1 | 12 | yes | — |
| 213 | C42×C61 | C24 | 1 | 6 | yes | — |
| 214 | C42×C61 | C24 | 1 | 12 | yes | — |
| 215 | C42×C61 | C24 | 1 | 12 | yes | — |
| 216 | C42×C61 | C24 | 1 | 12 | yes | — |
| 217 | C23×C61 | C25 | 1 | 12 | yes | — |
| 218 | C23×C61 | C25 | 1 | 1 | yes | characteristic |
| 219 | Q8×C61 | — | 2 | 24 | no | — |
| 220 | Q8×C61 | — | 2 | 12 | no | — |
| 221 | Q8×C61 | — | 2 | 6 | no | — |
| 222 | Q8×C61 | — | 4 | 24 | no | — |
| 223 | Q8×C61 | — | 4 | 4 | no | — |
| 224 | Q8×C61 | 2−1+4 | 1 | 4 | yes | complemented |
| 225 | D4×C61 | — | 2 | 24 | no | — |
| 226 | D4×C61 | — | 2 | 12 | no | — |
| 227 | D4×C61 | — | 2 | 24 | no | — |
| 228 | D4×C61 | — | 4 | 12 | no | — |
| 229 | D4×C61 | — | 4 | 12 | no | — |
| 230 | D4×C61 | — | 4 | 24 | no | — |
| 231 | C2×C4×C61 | — | 2 | 12 | no | — |
| 232 | C2×C4×C61 | — | 2 | 24 | no | — |
| 233 | C2×C4×C61 | — | 2 | 6 | no | — |
| 234 | C2×C4×C61 | — | 2 | 24 | no | — |
| 235 | C2×C4×C61 | — | 4 | 3 | no | — |
| 236 | C2×C4×C61 | — | 4 | 12 | no | — |
| 237 | C2×C4×C61 | — | 4 | 2 | no | — |
| 238 | C2×C4×C61 | — | 4 | 48 | no | — |
| 239 | C2×C4×C61 | H(5,𝔽2) | 1 | 4 | yes | — |
| 240 | C2×C4×C61 | C25 | 1 | 3 | yes | — |
| 241 | C2×C4×C61 | C25 | 1 | 4 | yes | — |
| 242 | C2×C4×C61 | C25 | 1 | 4 | yes | — |
| 243 | C2×C4×C61 | C25 | 1 | 4 | yes | — |
| 244 | C2×C4×C61 | C25 | 1 | 6 | yes | — |
| 245 | C2×C4×C61 | C25 | 1 | 12 | yes | — |
| 246 | C2×C4×C61 | C25 | 1 | 12 | yes | — |
| 247 | C2×C4×C61 | C25 | 1 | 2 | yes | — |
| 248 | C2×C4×C61 | C25 | 1 | 3 | yes | — |
| 249 | #62946 | C61 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 250 | C22×C61 | — | 2 | 1 | no | — |
| 251 | C22×C61 | — | 2 | 1 | no | — |
| 252 | C22×C61 | — | 2 | 12 | no | — |
| 253 | C22×C61 | — | 2 | 12 | no | — |
| 254 | C22×C61 | — | 2 | 12 | no | — |
| 255 | C22×C61 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 256 | C22×C61 | C26 | 1 | 1 | yes | characteristic |
| 257 | C4×C61 | — | 2 | 12 | no | — |
| 258 | C4×C61 | — | 2 | 12 | no | — |
| 259 | C4×C61 | — | 2 | 4 | no | — |
| 260 | C4×C61 | — | 2 | 3 | no | — |
| 261 | C4×C61 | — | 2 | 6 | no | — |
| 262 | C4×C61 | — | 2 | 4 | no | — |
| 263 | C4×C61 | — | 2 | 4 | no | — |
| 264 | C4×C61 | C2×H(5,𝔽2) | 1 | 4 | yes | — |
| 265 | C4×C61 | C2×2−1+4 | 1 | 6 | yes | — |
| 266 | #3559 | C2×C61 | 1 | 12 | yes | complemented |
| 267 | #3554 | C2×C61 | 1 | 12 | yes | complemented |
| 268 | #3552 | C2×C61 | 1 | 12 | yes | complemented |
| 269 | #3522 | C2×C61 | 1 | 4 | yes | complemented |
| 270 | #3517 | C2×C61 | 1 | 4 | yes | complemented |
| 271 | #3503 | C2×C61 | 1 | 4 | yes | complemented |
| 272 | #3499 | C2×C61 | 1 | 6 | yes | complemented |
| 273 | #3497 | C2×C61 | 1 | 3 | yes | complemented |
| 274 | #3480 | C2×C61 | 1 | 2 | yes | complemented |
| 275 | C2×#557 | C2×C61 | 1 | 1 | yes | characteristic, complemented |
| 276 | #3461 | C2×C61 | 1 | 3 | yes | complemented |
| 277 | C2×C61 | — | 2 | 2 | no | — |
| 278 | C2×C61 | — | 4 | 12 | no | — |
| 279 | C2×C61 | C22×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 280 | C2×C61 | C22×2−1+4 | 1 | 1 | yes | characteristic |
| 281 | C2×C61 | 2−1+6 | 1 | 1 | yes | characteristic |
| 282 | C2×2−1+4 | C22×C61 | 1 | 6 | yes | — |
| 283 | #563 | C22×C61 | 1 | 24 | yes | — |
| 284 | #562 | C22×C61 | 1 | 24 | yes | — |
| 285 | #559 | C22×C61 | 1 | 6 | yes | — |
| 286 | #559 | C22×C61 | 1 | 12 | yes | — |
| 287 | Q82 | C22×C61 | 1 | 4 | yes | — |
| 288 | #557 | C22×C61 | 1 | 4 | yes | — |
| 289 | #557 | C22×C61 | 1 | 12 | yes | — |
| 290 | #557 | C22×C61 | 1 | 2 | yes | — |
| 291 | #556 | C22×C61 | 1 | 6 | yes | — |
| 292 | #554 | C22×C61 | 1 | 24 | yes | — |
| 293 | #554 | C22×C61 | 1 | 12 | yes | — |
| 294 | #553 | C22×C61 | 1 | 12 | yes | — |
| 295 | #553 | C22×C61 | 1 | 24 | yes | — |
| 296 | #550 | C22×C61 | 1 | 2 | yes | — |
| 297 | #550 | C22×C61 | 1 | 12 | yes | — |
| 298 | #550 | C22×C61 | 1 | 4 | yes | — |
| 299 | D4×Q8 | C22×C61 | 1 | 12 | yes | — |
| 300 | D4×Q8 | C22×C61 | 1 | 12 | yes | — |
| 301 | D4×Q8 | C22×C61 | 1 | 12 | yes | — |
| 302 | #548 | C22×C61 | 1 | 4 | yes | — |
| 303 | #548 | C22×C61 | 1 | 24 | yes | — |
| 304 | #547 | C22×C61 | 1 | 12 | yes | — |
| 305 | #547 | C22×C61 | 1 | 24 | yes | — |
| 306 | #547 | C22×C61 | 1 | 12 | yes | — |
| 307 | #547 | C22×C61 | 1 | 24 | yes | — |
| 308 | #544 | C22×C61 | 1 | 1 | yes | characteristic |
| 309 | #544 | C22×C61 | 1 | 24 | yes | — |
| 310 | #542 | C22×C61 | 1 | 12 | yes | — |
| 311 | #542 | C22×C61 | 1 | 24 | yes | — |
| 312 | #541 | C22×C61 | 1 | 12 | yes | — |
| 313 | #540 | C22×C61 | 1 | 24 | yes | — |
| 314 | #539 | C22×C61 | 1 | 12 | yes | — |
| 315 | #539 | C22×C61 | 1 | 48 | yes | — |
| 316 | #537 | C22×C61 | 1 | 3 | yes | — |
| 317 | #537 | C22×C61 | 1 | 12 | yes | — |
| 318 | #536 | C22×C61 | 1 | 6 | yes | — |
| 319 | #536 | C22×C61 | 1 | 24 | yes | — |
| 320 | #533 | C22×C61 | 1 | 12 | yes | — |
| 321 | #532 | C22×C61 | 1 | 6 | yes | — |
| 322 | #532 | C22×C61 | 1 | 12 | yes | — |
| 323 | #532 | C22×C61 | 1 | 12 | yes | — |
| 324 | C2×C4⋊Q8 | C22×C61 | 1 | 3 | yes | — |
| 325 | C2×C4⋊Q8 | C22×C61 | 1 | 12 | yes | — |
| 326 | #529 | C22×C61 | 1 | 12 | yes | — |
| 327 | #529 | C22×C61 | 1 | 12 | yes | — |
| 328 | #529 | C22×C61 | 1 | 12 | yes | — |
| 329 | C2×#125 | C22×C61 | 1 | 6 | yes | — |
| 330 | #520 | C22×C61 | 1 | 8 | yes | — |
| 331 | C4×#41 | C22×C61 | 1 | 6 | yes | — |
| 332 | C4×#41 | C22×C61 | 1 | 4 | yes | — |
| 333 | C2×C4×Q8 | C22×C61 | 1 | 3 | yes | — |
| 334 | C2×C4×Q8 | C22×C61 | 1 | 1 | yes | characteristic |
| 335 | C2×C4×Q8 | C22×C61 | 1 | 2 | yes | — |
| 336 | C61 | #62946 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 337 | 2−1+4 | — | 4 | 24 | no | — |
| 338 | C2×#41 | C23×C61 | 1 | 4 | yes | — |
| 339 | C2×#41 | C23×C61 | 1 | 6 | yes | — |
| 340 | C2×#41 | C23×C61 | 1 | 24 | yes | — |
| 341 | C2×#41 | C23×C61 | 1 | 24 | yes | — |
| 342 | C22×Q8 | C23×C61 | 1 | 1 | yes | characteristic |
| 343 | C22×Q8 | C23×C61 | 1 | 3 | yes | — |
| 344 | C22×Q8 | C23×C61 | 1 | 24 | yes | — |
| 345 | C4⋊Q8 | C23×C61 | 1 | 12 | yes | — |
| 346 | C4⋊Q8 | C23×C61 | 1 | 6 | yes | — |
| 347 | C4⋊Q8 | C23×C61 | 1 | 12 | yes | — |
| 348 | C4⋊Q8 | C23×C61 | 1 | 12 | yes | — |
| 349 | C4⋊Q8 | C23×C61 | 1 | 24 | yes | — |
| 350 | C4⋊Q8 | C23×C61 | 1 | 24 | yes | — |
| 351 | C4⋊Q8 | C23×C61 | 1 | 12 | yes | — |
| 352 | C4⋊Q8 | C23×C61 | 1 | 4 | yes | — |
| 353 | #127 | C23×C61 | 1 | 6 | yes | — |
| 354 | #127 | C23×C61 | 1 | 12 | yes | — |
| 355 | #126 | C23×C61 | 1 | 24 | yes | — |
| 356 | #126 | C23×C61 | 1 | 24 | yes | — |
| 357 | #126 | C23×C61 | 1 | 24 | yes | — |
| 358 | #125 | C23×C61 | 1 | 24 | yes | — |
| 359 | #125 | C23×C61 | 1 | 24 | yes | — |
| 360 | #125 | C23×C61 | 1 | 4 | yes | — |
| 361 | #125 | C23×C61 | 1 | 12 | yes | — |
| 362 | #125 | C23×C61 | 1 | 12 | yes | — |
| 363 | #125 | C23×C61 | 1 | 24 | yes | — |
| 364 | #124 | C23×C61 | 1 | 12 | yes | — |
| 365 | #124 | C23×C61 | 1 | 12 | yes | — |
| 366 | #124 | C23×C61 | 1 | 12 | yes | — |
| 367 | #124 | C23×C61 | 1 | 12 | yes | — |
| 368 | #124 | C23×C61 | 1 | 24 | yes | — |
| 369 | #123 | C23×C61 | 1 | 24 | yes | — |
| 370 | #123 | C23×C61 | 1 | 24 | yes | — |
| 371 | #123 | C23×C61 | 1 | 24 | yes | — |
| 372 | #123 | C23×C61 | 1 | 48 | yes | — |
| 373 | #123 | C23×C61 | 1 | 48 | yes | — |
| 374 | C22⋊Q8 | C23×C61 | 1 | 4 | yes | — |
| 375 | C22⋊Q8 | C23×C61 | 1 | 12 | yes | — |
| 376 | C22⋊Q8 | C23×C61 | 1 | 12 | yes | — |
| 377 | C22⋊Q8 | C23×C61 | 1 | 12 | yes | — |
| 378 | C22⋊Q8 | C23×C61 | 1 | 12 | yes | — |
| 379 | C22⋊Q8 | C23×C61 | 1 | 24 | yes | — |
| 380 | C22⋊Q8 | C23×C61 | 1 | 48 | yes | — |
| 381 | C22⋊Q8 | C23×C61 | 1 | 48 | yes | — |
| 382 | C22⋊Q8 | C23×C61 | 1 | 48 | yes | — |
| 383 | #121 | C23×C61 | 1 | 12 | yes | — |
| 384 | #121 | C23×C61 | 1 | 12 | yes | — |
| 385 | #121 | C23×C61 | 1 | 12 | yes | — |
| 386 | #121 | C23×C61 | 1 | 12 | yes | — |
| 387 | #121 | C23×C61 | 1 | 12 | yes | — |
| 388 | #121 | C23×C61 | 1 | 24 | yes | — |
| 389 | #121 | C23×C61 | 1 | 24 | yes | — |
| 390 | #121 | C23×C61 | 1 | 48 | yes | — |
| 391 | C4×Q8 | C23×C61 | 1 | 2 | yes | — |
| 392 | C4×Q8 | C23×C61 | 1 | 4 | yes | — |
| 393 | C4×Q8 | C23×C61 | 1 | 6 | yes | — |
| 394 | C4×Q8 | C23×C61 | 1 | 12 | yes | — |
| 395 | C4×Q8 | C23×C61 | 1 | 12 | yes | — |
| 396 | C4×Q8 | C23×C61 | 1 | 12 | yes | — |
| 397 | C4×Q8 | C23×C61 | 1 | 4 | yes | — |
| 398 | C4×Q8 | C23×C61 | 1 | 6 | yes | — |
| 399 | C4×Q8 | C23×C61 | 1 | 6 | yes | — |
| 400 | C4×Q8 | C23×C61 | 1 | 12 | yes | — |
| 401 | C4×D4 | C23×C61 | 1 | 12 | yes | — |
| 402 | C4×D4 | C23×C61 | 1 | 6 | yes | — |
| 403 | C4×D4 | C23×C61 | 1 | 12 | yes | — |
| 404 | C4×D4 | C23×C61 | 1 | 12 | yes | — |
| 405 | C4×D4 | C23×C61 | 1 | 12 | yes | — |
| 406 | C4×D4 | C23×C61 | 1 | 6 | yes | — |
| 407 | C4×D4 | C23×C61 | 1 | 24 | yes | — |
| 408 | C4×D4 | C23×C61 | 1 | 24 | yes | — |
| 409 | C4×D4 | C23×C61 | 1 | 12 | yes | — |
| 410 | C4×D4 | C23×C61 | 1 | 12 | yes | — |
| 411 | C4×D4 | C23×C61 | 1 | 24 | yes | — |
| 412 | C4×D4 | C23×C61 | 1 | 24 | yes | — |
| 413 | #117 | C23×C61 | 1 | 2 | yes | — |
| 414 | #117 | C23×C61 | 1 | 12 | yes | — |
| 415 | #117 | C23×C61 | 1 | 12 | yes | — |
| 416 | #117 | C23×C61 | 1 | 24 | yes | — |
| 417 | C2×C4⋊C4 | C23×C61 | 1 | 1 | yes | characteristic |
| 418 | C2×C4⋊C4 | C23×C61 | 1 | 6 | yes | — |
| 419 | C2×C4⋊C4 | C23×C61 | 1 | 3 | yes | — |
| 420 | C2×C4⋊C4 | C23×C61 | 1 | 6 | yes | — |
| 421 | C2×C4⋊C4 | C23×C61 | 1 | 24 | yes | — |
| 422 | C2×C4⋊C4 | C23×C61 | 1 | 6 | yes | — |
| 423 | C2×C4⋊C4 | C23×C61 | 1 | 24 | yes | — |
| 424 | C2×C42 | C23×C61 | 1 | 3 | yes | — |
| 425 | C2×C42 | C23×C61 | 1 | 6 | yes | — |
| 426 | C2×C42 | C23×C61 | 1 | 12 | yes | — |
| 427 | #41 | — | 2 | 16 | no | — |
| 428 | #41 | — | 2 | 24 | no | — |
| 429 | #41 | — | 4 | 48 | no | — |
| 430 | #41 | — | 4 | 48 | no | — |
| 431 | C2×Q8 | — | 2 | 4 | no | — |
| 432 | C2×Q8 | — | 2 | 12 | no | — |
| 433 | C2×Q8 | — | 4 | 48 | no | — |
| 434 | C2×Q8 | C24×C61 | 1 | 3 | yes | — |
| 435 | C2×Q8 | C24×C61 | 1 | 6 | yes | — |
| 436 | C2×Q8 | C24×C61 | 1 | 12 | yes | — |
| 437 | C2×Q8 | C24×C61 | 1 | 4 | yes | — |
| 438 | C2×Q8 | C24×C61 | 1 | 24 | yes | — |
| 439 | C2×Q8 | C24×C61 | 1 | 1 | yes | characteristic |
| 440 | C2×D4 | C24×C61 | 1 | 12 | yes | — |
| 441 | C2×D4 | C24×C61 | 1 | 12 | yes | — |
| 442 | C2×D4 | C24×C61 | 1 | 6 | yes | — |
| 443 | C2×D4 | C24×C61 | 1 | 12 | yes | — |
| 444 | C2×D4 | C24×C61 | 1 | 12 | yes | — |
| 445 | C2×D4 | C24×C61 | 1 | 24 | yes | — |
| 446 | C22×C4 | C24×C61 | 1 | 3 | yes | — |
| 447 | C22×C4 | C24×C61 | 1 | 6 | yes | — |
| 448 | C22×C4 | C24×C61 | 1 | 12 | yes | — |
| 449 | C22×C4 | C24×C61 | 1 | 12 | yes | — |
| 450 | C22×C4 | C24×C61 | 1 | 2 | yes | — |
| 451 | C22×C4 | C24×C61 | 1 | 3 | yes | — |
| 452 | C22×C4 | C24×C61 | 1 | 12 | yes | — |
| 453 | C22×C4 | C24×C61 | 1 | 48 | yes | — |
| 454 | C22×C4 | C24×C61 | 1 | 1 | yes | characteristic |
| 455 | C4⋊C4 | C24×C61 | 1 | 12 | yes | — |
| 456 | C4⋊C4 | C24×C61 | 1 | 12 | yes | — |
| 457 | C4⋊C4 | C24×C61 | 1 | 24 | yes | — |
| 458 | C4⋊C4 | C24×C61 | 1 | 12 | yes | — |
| 459 | C4⋊C4 | C24×C61 | 1 | 24 | yes | — |
| 460 | C4⋊C4 | C24×C61 | 1 | 24 | yes | — |
| 461 | C4⋊C4 | C24×C61 | 1 | 6 | yes | — |
| 462 | C4⋊C4 | C24×C61 | 1 | 4 | yes | — |
| 463 | C4⋊C4 | C24×C61 | 1 | 24 | yes | — |
| 464 | C4⋊C4 | C24×C61 | 1 | 12 | yes | — |
| 465 | C4⋊C4 | C24×C61 | 1 | 6 | yes | — |
| 466 | C4⋊C4 | C24×C61 | 1 | 8 | yes | — |
| 467 | C4⋊C4 | C24×C61 | 1 | 2 | yes | — |
| 468 | C4⋊C4 | C24×C61 | 1 | 2 | yes | — |
| 469 | C4⋊C4 | C24×C61 | 1 | 12 | yes | — |
| 470 | C4⋊C4 | C24×C61 | 1 | 12 | yes | — |
| 471 | C4⋊C4 | C24×C61 | 1 | 4 | yes | — |
| 472 | C4⋊C4 | C24×C61 | 1 | 12 | yes | — |
| 473 | C22⋊C4 | C24×C61 | 1 | 4 | yes | — |
| 474 | C22⋊C4 | C24×C61 | 1 | 24 | yes | — |
| 475 | C22⋊C4 | C24×C61 | 1 | 24 | yes | — |
| 476 | C22⋊C4 | C24×C61 | 1 | 24 | yes | — |
| 477 | C22⋊C4 | C24×C61 | 1 | 12 | yes | — |
| 478 | C22⋊C4 | C24×C61 | 1 | 12 | yes | — |
| 479 | C22⋊C4 | C24×C61 | 1 | 24 | yes | — |
| 480 | C22⋊C4 | C24×C61 | 1 | 24 | yes | — |
| 481 | C42 | C24×C61 | 1 | 4 | yes | — |
| 482 | C42 | C24×C61 | 1 | 6 | yes | — |
| 483 | C42 | C24×C61 | 1 | 12 | yes | — |
| 484 | C42 | C24×C61 | 1 | 6 | yes | — |
| 485 | C42 | C24×C61 | 1 | 12 | yes | — |
| 486 | C42 | C24×C61 | 1 | 12 | yes | — |
| 487 | C42 | C24×C61 | 1 | 12 | yes | — |
| 488 | C23 | C25×C61 | 1 | 12 | yes | — |
| 489 | C23 | C25×C61 | 1 | 1 | yes | characteristic |
| 490 | Q8 | — | 2 | 24 | no | — |
| 491 | Q8 | — | 2 | 12 | no | — |
| 492 | Q8 | — | 2 | 6 | no | — |
| 493 | Q8 | — | 4 | 24 | no | — |
| 494 | Q8 | — | 4 | 4 | no | — |
| 495 | Q8 | 2−1+4×C61 | 1 | 4 | yes | complemented |
| 496 | D4 | — | 2 | 24 | no | — |
| 497 | D4 | — | 2 | 12 | no | — |
| 498 | D4 | — | 2 | 24 | no | — |
| 499 | D4 | — | 4 | 12 | no | — |
| 500 | D4 | — | 4 | 12 | no | — |
| 501 | D4 | — | 4 | 24 | no | — |
| 502 | C2×C4 | — | 2 | 12 | no | — |
| 503 | C2×C4 | — | 2 | 24 | no | — |
| 504 | C2×C4 | — | 2 | 6 | no | — |
| 505 | C2×C4 | — | 2 | 24 | no | — |
| 506 | C2×C4 | — | 4 | 3 | no | — |
| 507 | C2×C4 | — | 4 | 12 | no | — |
| 508 | C2×C4 | — | 4 | 2 | no | — |
| 509 | C2×C4 | — | 4 | 48 | no | — |
| 510 | C2×C4 | H(5,𝔽2)×C61 | 1 | 4 | yes | — |
| 511 | C2×C4 | C25×C61 | 1 | 3 | yes | — |
| 512 | C2×C4 | C25×C61 | 1 | 4 | yes | — |
| 513 | C2×C4 | C25×C61 | 1 | 4 | yes | — |
| 514 | C2×C4 | C25×C61 | 1 | 4 | yes | — |
| 515 | C2×C4 | C25×C61 | 1 | 6 | yes | — |
| 516 | C2×C4 | C25×C61 | 1 | 12 | yes | — |
| 517 | C2×C4 | C25×C61 | 1 | 12 | yes | — |
| 518 | C2×C4 | C25×C61 | 1 | 2 | yes | — |
| 519 | C2×C4 | C25×C61 | 1 | 3 | yes | — |
| 520 | C22 | — | 2 | 1 | no | — |
| 521 | C22 | — | 2 | 1 | no | — |
| 522 | C22 | — | 2 | 12 | no | — |
| 523 | C22 | — | 2 | 12 | no | — |
| 524 | C22 | — | 2 | 12 | no | — |
| 525 | C22 | C2×H(5,𝔽2)×C61 | 1 | 2 | yes | — |
| 526 | C22 | C26×C61 | 1 | 1 | yes | characteristic |
| 527 | C4 | — | 2 | 12 | no | — |
| 528 | C4 | — | 2 | 12 | no | — |
| 529 | C4 | — | 2 | 4 | no | — |
| 530 | C4 | — | 2 | 3 | no | — |
| 531 | C4 | — | 2 | 6 | no | — |
| 532 | C4 | — | 2 | 4 | no | — |
| 533 | C4 | — | 2 | 4 | no | — |
| 534 | C4 | C2×H(5,𝔽2)×C61 | 1 | 4 | yes | — |
| 535 | C4 | C2×2−1+4×C61 | 1 | 6 | yes | — |
| 536 | C2 | — | 2 | 2 | no | — |
| 537 | C2 | — | 4 | 12 | no | — |
| 538 | C2 | C22×H(5,𝔽2)×C61 | 1 | 1 | yes | characteristic |
| 539 | C2 | C22×2−1+4×C61 | 1 | 1 | yes | characteristic |
| 540 | C2 | C61×2−1+6 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta