← #29458065
Subgroups — #29458065
Order 15104.
2066 conjugacy classes of subgroups.
The subgroup lattice has 512 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #21437889 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #21434492 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #21434485 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #21434466 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | #21434455 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #21434444 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | C2×#16837764 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #21432626 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #21432619 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #21432524 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C59×#3503 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#14273774 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#14273773 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×#14273734 | C22 | 1 | 2 | yes | — |
| 15 | #16838064 | — | 2 | 1 | no | — |
| 16 | #16838064 | — | 2 | 1 | no | — |
| 17 | #16838047 | — | 2 | 3 | no | — |
| 18 | #16838047 | — | 2 | 3 | no | — |
| 19 | #16837978 | C22 | 1 | 3 | yes | — |
| 20 | #16837971 | C22 | 1 | 3 | yes | — |
| 21 | #16837952 | C22 | 1 | 3 | yes | — |
| 22 | C2×#14273715 | C22 | 1 | 3 | yes | — |
| 23 | #16837772 | C22 | 1 | 6 | yes | complemented |
| 24 | #16837768 | C22 | 1 | 6 | yes | complemented |
| 25 | #16837764 | C22 | 1 | 3 | yes | complemented |
| 26 | #16837764 | C22 | 1 | 12 | yes | complemented |
| 27 | #16837764 | C22 | 1 | 6 | yes | complemented |
| 28 | #16837764 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | #16837764 | C22 | 1 | 3 | yes | complemented |
| 30 | #16837764 | C22 | 1 | 3 | yes | complemented |
| 31 | #16837759 | C22 | 1 | 12 | yes | complemented |
| 32 | #16837754 | C22 | 1 | 6 | yes | complemented |
| 33 | #16837750 | C22 | 1 | 6 | yes | complemented |
| 34 | #16837410 | C22 | 1 | 6 | yes | complemented |
| 35 | #16837406 | C22 | 1 | 6 | yes | — |
| 36 | #16837401 | C22 | 1 | 6 | yes | — |
| 37 | #16837401 | C22 | 1 | 6 | yes | complemented |
| 38 | #16837396 | C22 | 1 | 6 | yes | — |
| 39 | #16837396 | C22 | 1 | 6 | yes | complemented |
| 40 | C2×#14273650 | C22 | 1 | 6 | yes | complemented |
| 41 | C2×#14273647 | C22 | 1 | 6 | yes | — |
| 42 | #16837358 | C22 | 1 | 6 | yes | complemented |
| 43 | C4×#11745664 | C22 | 1 | 3 | yes | complemented |
| 44 | C2×#14273638 | C22 | 1 | 3 | yes | complemented |
| 45 | Q82×C59 | — | 2 | 1 | no | — |
| 46 | C59×#557 | — | 2 | 1 | no | — |
| 47 | C59×#554 | — | 2 | 3 | no | — |
| 48 | D4×Q8×C59 | — | 2 | 3 | no | — |
| 49 | C59×#544 | C22 | 1 | 6 | yes | complemented |
| 50 | C59×#533 | C22 | 1 | 3 | yes | complemented |
| 51 | C2×C4⋊Q8×C59 | C22 | 1 | 3 | yes | complemented |
| 52 | C59×#520 | C22 | 1 | 2 | yes | — |
| 53 | C4×#41×C59 | C22 | 1 | 1 | yes | characteristic |
| 54 | #14273774 | — | 2 | 8 | no | — |
| 55 | #14273773 | — | 2 | 8 | no | — |
| 56 | C2×#11745689 | — | 2 | 1 | no | — |
| 57 | C2×#11745685 | C23 | 1 | 3 | yes | — |
| 58 | C2×#11745685 | C23 | 1 | 3 | yes | — |
| 59 | C2×#11745687 | — | 2 | 3 | no | — |
| 60 | C22×Dic118 | C23 | 1 | 3 | yes | — |
| 61 | C2×Q8×D59 | — | 2 | 1 | no | — |
| 62 | C22×D236 | C23 | 1 | 3 | yes | — |
| 63 | C2×D4×D59 | — | 2 | 3 | no | — |
| 64 | #14273734 | — | 2 | 8 | no | — |
| 65 | C2×#11745664 | C23 | 1 | 6 | yes | — |
| 66 | C22×C59⋊C8 | C23 | 1 | 6 | yes | — |
| 67 | #14273727 | C23 | 1 | 3 | yes | — |
| 68 | #14273724 | C23 | 1 | 3 | yes | — |
| 69 | #14273715 | — | 2 | 3 | no | — |
| 70 | #14273715 | — | 2 | 3 | no | — |
| 71 | #14273715 | C23 | 1 | 3 | yes | — |
| 72 | #14273715 | C23 | 1 | 6 | yes | — |
| 73 | #14273715 | C23 | 1 | 1 | yes | characteristic |
| 74 | #14273711 | — | 2 | 6 | no | — |
| 75 | #14273707 | — | 2 | 3 | no | — |
| 76 | #14273707 | — | 2 | 3 | no | — |
| 77 | #14273702 | — | 2 | 3 | no | — |
| 78 | #14273702 | — | 2 | 3 | no | — |
| 79 | #14273701 | — | 2 | 3 | no | — |
| 80 | #14273701 | — | 2 | 3 | no | — |
| 81 | #14273697 | — | 2 | 6 | no | — |
| 82 | C4×D236 | — | 2 | 3 | no | — |
| 83 | C4×D236 | — | 2 | 3 | no | — |
| 84 | C2×(C2×D59)⋊C4 | — | 2 | 3 | no | — |
| 85 | C2×(C2×D59)⋊C4 | — | 2 | 3 | no | — |
| 86 | #14273650 | C23 | 1 | 6 | yes | — |
| 87 | #14273650 | C23 | 1 | 12 | yes | — |
| 88 | #14273650 | C23 | 1 | 2 | yes | — |
| 89 | #14273650 | C23 | 1 | 6 | yes | — |
| 90 | #14273650 | C23 | 1 | 6 | yes | — |
| 91 | #14273647 | C23 | 1 | 6 | yes | — |
| 92 | #14273647 | C23 | 1 | 12 | yes | — |
| 93 | #14273647 | C23 | 1 | 6 | yes | — |
| 94 | #14273647 | C23 | 1 | 2 | yes | — |
| 95 | #14273647 | C23 | 1 | 6 | yes | — |
| 96 | #14273638 | C23 | 1 | 1 | yes | characteristic |
| 97 | #14273638 | C23 | 1 | 3 | yes | — |
| 98 | #14273638 | C23 | 1 | 6 | yes | — |
| 99 | C4×C59⋊C8 | C23 | 1 | 6 | yes | — |
| 100 | C2×#41×C59 | C23 | 1 | 1 | yes | characteristic |
| 101 | C22×Q8×C59 | — | 2 | 3 | no | — |
| 102 | C4⋊Q8×C59 | — | 2 | 6 | no | — |
| 103 | C4⋊Q8×C59 | — | 2 | 3 | no | — |
| 104 | C4⋊Q8×C59 | — | 2 | 3 | no | — |
| 105 | C4⋊Q8×C59 | C23 | 1 | 6 | yes | — |
| 106 | C4⋊Q8×C59 | C23 | 1 | 3 | yes | — |
| 107 | C4⋊Q8×C59 | C23 | 1 | 1 | yes | characteristic |
| 108 | #125×C59 | — | 2 | 6 | no | — |
| 109 | #125×C59 | C23 | 1 | 6 | yes | — |
| 110 | C22⋊Q8×C59 | — | 2 | 3 | no | — |
| 111 | C22⋊Q8×C59 | — | 2 | 3 | no | — |
| 112 | C22⋊Q8×C59 | — | 2 | 12 | no | — |
| 113 | C4×Q8×C59 | — | 2 | 2 | no | — |
| 114 | C4×Q8×C59 | — | 2 | 3 | no | — |
| 115 | C4×Q8×C59 | — | 2 | 3 | no | — |
| 116 | C4×Q8×C59 | D4 | 1 | 1 | yes | characteristic |
| 117 | C4×Q8×C59 | D4 | 1 | 1 | yes | characteristic |
| 118 | C4×D4×C59 | — | 2 | 6 | no | — |
| 119 | C4×D4×C59 | D4 | 1 | 3 | yes | — |
| 120 | C4×D4×C59 | D4 | 1 | 3 | yes | — |
| 121 | #117×C59 | C23 | 1 | 6 | yes | — |
| 122 | #117×C59 | C23 | 1 | 3 | yes | — |
| 123 | C2×C4⋊C4×C59 | — | 2 | 3 | no | — |
| 124 | C2×C4⋊C4×C59 | C23 | 1 | 6 | yes | — |
| 125 | C2×C42×C59 | C23 | 1 | 3 | yes | — |
| 126 | C23×D59 | — | 2 | 3 | no | — |
| 127 | #41×C59 | #41 | 1 | 8 | yes | — |
| 128 | C2×Q8×C59 | — | 2 | 1 | no | — |
| 129 | C2×Q8×C59 | — | 2 | 3 | no | — |
| 130 | C2×Q8×C59 | — | 2 | 6 | no | — |
| 131 | C2×Q8×C59 | — | 8 | 6 | no | — |
| 132 | C2×Q8×C59 | C2×D4 | 1 | 1 | yes | characteristic |
| 133 | C2×D4×C59 | C2×D4 | 1 | 3 | yes | — |
| 134 | C22×C4×C59 | — | 2 | 6 | no | — |
| 135 | C22×C4×C59 | C2×D4 | 1 | 3 | yes | — |
| 136 | C22×C4×C59 | C2×D4 | 1 | 3 | yes | — |
| 137 | C22×C4×C59 | C24 | 1 | 3 | yes | — |
| 138 | C2×C22⋊D59 | — | 2 | 3 | no | — |
| 139 | C2×C22⋊D59 | — | 2 | 3 | no | — |
| 140 | C22×Dic59 | — | 2 | 3 | no | — |
| 141 | #11745689 | — | 4 | 4 | no | — |
| 142 | Q8×D59 | — | 4 | 4 | no | — |
| 143 | #11745687 | — | 4 | 12 | no | — |
| 144 | D4×D59 | — | 4 | 12 | no | — |
| 145 | #11745685 | — | 2 | 12 | no | — |
| 146 | #11745685 | — | 2 | 12 | no | — |
| 147 | C2×D236 | — | 2 | 12 | no | — |
| 148 | C2×D236 | — | 2 | 3 | no | — |
| 149 | C2×D236 | — | 2 | 3 | no | — |
| 150 | C2×D236 | — | 2 | 3 | no | — |
| 151 | C2×D236 | C24 | 1 | 3 | yes | — |
| 152 | C2×D236 | C24 | 1 | 1 | yes | characteristic |
| 153 | C2×C4×D59 | — | 2 | 3 | no | — |
| 154 | C2×C4×D59 | — | 2 | 3 | no | — |
| 155 | C2×Dic118 | — | 2 | 12 | no | — |
| 156 | C2×Dic118 | — | 2 | 3 | no | — |
| 157 | C2×Dic118 | C24 | 1 | 3 | yes | — |
| 158 | C2×Dic118 | C24 | 1 | 1 | yes | characteristic |
| 159 | C4⋊C4×C59 | — | 2 | 3 | no | — |
| 160 | C4⋊C4×C59 | — | 2 | 6 | no | — |
| 161 | C4⋊C4×C59 | — | 2 | 6 | no | — |
| 162 | C4⋊C4×C59 | — | 2 | 1 | no | — |
| 163 | C4⋊C4×C59 | — | 2 | 6 | no | — |
| 164 | C4⋊C4×C59 | — | 2 | 6 | no | — |
| 165 | C4⋊C4×C59 | C2×D4 | 1 | 3 | yes | — |
| 166 | C4⋊C4×C59 | C2×D4 | 1 | 3 | yes | — |
| 167 | C4⋊C4×C59 | C24 | 1 | 6 | yes | — |
| 168 | C4⋊C4×C59 | C24 | 1 | 2 | yes | — |
| 169 | C22⋊C4×C59 | — | 2 | 6 | no | — |
| 170 | C22⋊C4×C59 | C2×D4 | 1 | 6 | yes | — |
| 171 | C42×C59 | — | 2 | 6 | no | — |
| 172 | C42×C59 | C2×D4 | 1 | 3 | yes | — |
| 173 | C42×C59 | C2×D4 | 1 | 3 | yes | — |
| 174 | C42×C59 | C24 | 1 | 1 | yes | characteristic |
| 175 | C42×C59 | C24 | 1 | 3 | yes | — |
| 176 | (C2×D59)⋊C4 | — | 2 | 3 | no | — |
| 177 | (C2×D59)⋊C4 | — | 2 | 3 | no | — |
| 178 | (C2×D59)⋊C4 | — | 2 | 6 | no | — |
| 179 | (C2×D59)⋊C4 | — | 2 | 6 | no | — |
| 180 | (C2×D59)⋊C4 | — | 2 | 1 | no | — |
| 181 | (C2×D59)⋊C4 | — | 2 | 1 | no | — |
| 182 | C4⋊Dic59 | — | 2 | 3 | no | — |
| 183 | C4⋊Dic59 | — | 2 | 3 | no | — |
| 184 | #11745664 | — | 2 | 12 | no | — |
| 185 | C2×C59⋊C8 | — | 2 | 12 | no | — |
| 186 | C2×C59⋊C8 | C24 | 1 | 6 | yes | — |
| 187 | C2×C59⋊C8 | C24 | 1 | 2 | yes | — |
| 188 | C23×C59 | C22×D4 | 1 | 3 | yes | — |
| 189 | C22×D59 | — | 2 | 3 | no | — |
| 190 | C22×D59 | — | 2 | 1 | no | — |
| 191 | C22×D59 | — | 4 | 6 | no | — |
| 192 | C22×D59 | — | 8 | 3 | no | — |
| 193 | C22×D59 | — | 8 | 3 | no | — |
| 194 | Q8×C59 | — | 4 | 2 | no | — |
| 195 | Q8×C59 | — | 4 | 6 | no | — |
| 196 | Q8×C59 | — | 8 | 6 | no | — |
| 197 | Q8×C59 | #124 | 1 | 4 | yes | — |
| 198 | D4×C59 | #124 | 1 | 12 | yes | — |
| 199 | C2×C4×C59 | — | 2 | 2 | no | — |
| 200 | C2×C4×C59 | — | 2 | 6 | no | — |
| 201 | C2×C4×C59 | — | 4 | 3 | no | — |
| 202 | C2×C4×C59 | — | 4 | 3 | no | — |
| 203 | C2×C4×C59 | — | 8 | 6 | no | — |
| 204 | C2×C4×C59 | C22×D4 | 1 | 3 | yes | — |
| 205 | C2×C4×C59 | C22×D4 | 1 | 3 | yes | — |
| 206 | C2×C4×C59 | C22×D4 | 1 | 1 | yes | characteristic |
| 207 | C2×C4×C59 | C22×D4 | 1 | 1 | yes | characteristic |
| 208 | C2×C4×C59 | C22×D4 | 1 | 3 | yes | — |
| 209 | C2×C4×C59 | C2×#41 | 1 | 12 | yes | — |
| 210 | C2×C4×C59 | C25 | 1 | 1 | yes | characteristic |
| 211 | C22⋊D59 | — | 4 | 6 | no | — |
| 212 | C22⋊D59 | — | 4 | 6 | no | — |
| 213 | C2×Dic59 | — | 2 | 1 | no | — |
| 214 | C2×Dic59 | — | 2 | 3 | no | — |
| 215 | C2×Dic59 | — | 4 | 6 | no | — |
| 216 | D236 | — | 2 | 6 | no | — |
| 217 | D236 | — | 2 | 2 | no | — |
| 218 | D236 | — | 4 | 6 | no | — |
| 219 | D236 | — | 8 | 3 | no | — |
| 220 | D236 | — | 8 | 3 | no | — |
| 221 | C4×D59 | — | 4 | 6 | no | — |
| 222 | C4×D59 | — | 4 | 6 | no | — |
| 223 | Dic118 | — | 2 | 6 | no | — |
| 224 | Dic118 | — | 2 | 2 | no | — |
| 225 | Dic118 | — | 4 | 6 | no | — |
| 226 | C59⋊C8 | — | 2 | 2 | no | — |
| 227 | C59⋊C8 | — | 2 | 6 | no | — |
| 228 | #60625 | — | 59 | 1 | no | maximal, Sylow |
| 229 | C22×C59 | — | 2 | 3 | no | — |
| 230 | C22×C59 | — | 2 | 3 | no | — |
| 231 | C22×C59 | C2×#124 | 1 | 6 | yes | — |
| 232 | C22×C59 | C23×D4 | 1 | 1 | yes | characteristic |
| 233 | C2×D59 | — | 4 | 1 | no | — |
| 234 | C2×D59 | — | 4 | 3 | no | — |
| 235 | C2×D59 | — | 4 | 1 | no | — |
| 236 | C2×D59 | — | 4 | 3 | no | — |
| 237 | C2×D59 | — | 4 | 1 | no | — |
| 238 | C2×D59 | — | 4 | 3 | no | — |
| 239 | C2×D59 | — | 16 | 6 | no | — |
| 240 | C4×C59 | — | 2 | 3 | no | — |
| 241 | C4×C59 | — | 2 | 1 | no | — |
| 242 | C4×C59 | — | 2 | 3 | no | — |
| 243 | C4×C59 | — | 2 | 1 | no | — |
| 244 | C4×C59 | — | 4 | 6 | no | — |
| 245 | C4×C59 | — | 4 | 2 | no | — |
| 246 | C4×C59 | C2×#124 | 1 | 6 | yes | — |
| 247 | C4×C59 | C22×#41 | 1 | 2 | yes | — |
| 248 | Dic59 | — | 4 | 3 | no | — |
| 249 | Dic59 | — | 4 | 1 | no | — |
| 250 | #3503 | D59 | 1 | 1 | yes | characteristic, complemented |
| 251 | #3500 | — | 59 | 1 | no | — |
| 252 | #3141 | — | 59 | 3 | no | — |
| 253 | #3140 | — | 59 | 3 | no | — |
| 254 | #3137 | — | 59 | 6 | no | — |
| 255 | #3136 | — | 59 | 6 | no | — |
| 256 | #3135 | — | 59 | 3 | no | — |
| 257 | C2×#489 | — | 59 | 3 | no | — |
| 258 | #2898 | — | 59 | 2 | no | — |
| 259 | #2897 | — | 59 | 2 | no | — |
| 260 | #2875 | — | 59 | 1 | no | — |
| 261 | C2×C59 | — | 2 | 6 | no | — |
| 262 | C2×C59 | C22×#124 | 1 | 1 | yes | characteristic |
| 263 | C2×C59 | #3585 | 1 | 1 | yes | characteristic |
| 264 | C2×C59 | #3586 | 1 | 1 | yes | characteristic |
| 265 | D59 | — | 8 | 1 | no | — |
| 266 | D59 | — | 8 | 3 | no | — |
| 267 | C2×2−1+4 | — | 59 | 1 | no | — |
| 268 | C2×H(5,𝔽2) | — | 59 | 1 | no | — |
| 269 | C2×#131 | — | 59 | 2 | no | — |
| 270 | Q82 | — | 2 | 1 | no | — |
| 271 | #557 | — | 2 | 1 | no | — |
| 272 | #554 | — | 2 | 3 | no | — |
| 273 | D4×Q8 | — | 2 | 3 | no | — |
| 274 | #548 | — | 118 | 1 | no | — |
| 275 | #548 | — | 118 | 1 | no | — |
| 276 | #546 | — | 118 | 3 | no | — |
| 277 | #546 | — | 118 | 3 | no | — |
| 278 | #544 | C2×D59 | 1 | 6 | yes | complemented |
| 279 | #536 | — | 59 | 3 | no | — |
| 280 | #535 | — | 59 | 3 | no | — |
| 281 | #533 | C2×D59 | 1 | 3 | yes | complemented |
| 282 | #532 | — | 59 | 3 | no | — |
| 283 | C2×C4⋊Q8 | C2×D59 | 1 | 3 | yes | complemented |
| 284 | C2×#124 | — | 59 | 3 | no | — |
| 285 | #520 | C2×D59 | 1 | 2 | yes | — |
| 286 | C4×#41 | C2×D59 | 1 | 1 | yes | characteristic |
| 287 | #491 | — | 59 | 6 | no | — |
| 288 | #490 | — | 59 | 6 | no | — |
| 289 | #489 | — | 59 | 3 | no | — |
| 290 | #489 | — | 59 | 12 | no | — |
| 291 | #489 | — | 59 | 6 | no | — |
| 292 | #489 | — | 59 | 1 | no | — |
| 293 | #489 | — | 59 | 3 | no | — |
| 294 | #489 | — | 59 | 3 | no | — |
| 295 | #488 | — | 59 | 12 | no | — |
| 296 | #487 | — | 59 | 6 | no | — |
| 297 | #486 | — | 59 | 6 | no | — |
| 298 | #419 | — | 59 | 6 | no | — |
| 299 | #418 | — | 59 | 6 | no | — |
| 300 | #417 | — | 59 | 6 | no | — |
| 301 | #417 | — | 59 | 6 | no | — |
| 302 | #416 | — | 59 | 6 | no | — |
| 303 | #416 | — | 59 | 6 | no | — |
| 304 | C2×#103 | — | 59 | 6 | no | — |
| 305 | C2×#102 | — | 59 | 6 | no | — |
| 306 | #405 | — | 59 | 6 | no | — |
| 307 | C4×M16 | — | 59 | 3 | no | — |
| 308 | C2×#97 | — | 59 | 3 | no | — |
| 309 | C59 | #60625 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 310 | 2−1+4 | — | 118 | 8 | no | — |
| 311 | H(5,𝔽2) | — | 118 | 8 | no | — |
| 312 | C2×#41 | — | 59 | 3 | no | — |
| 313 | C2×#41 | — | 59 | 3 | no | — |
| 314 | C2×#41 | — | 118 | 1 | no | — |
| 315 | C2×#41 | — | 118 | 3 | no | — |
| 316 | C2×#41 | C22×D59 | 1 | 1 | yes | characteristic |
| 317 | C22×Q8 | — | 2 | 3 | no | — |
| 318 | C22×Q8 | — | 59 | 3 | no | — |
| 319 | C22×Q8 | — | 118 | 1 | no | — |
| 320 | C22×D4 | — | 59 | 3 | no | — |
| 321 | C22×D4 | — | 118 | 3 | no | — |
| 322 | #131 | — | 118 | 8 | no | — |
| 323 | C2×M16 | — | 59 | 6 | no | — |
| 324 | C22×C8 | — | 59 | 6 | no | — |
| 325 | C4⋊Q8 | — | 2 | 6 | no | — |
| 326 | C4⋊Q8 | — | 2 | 3 | no | — |
| 327 | C4⋊Q8 | — | 2 | 3 | no | — |
| 328 | C4⋊Q8 | — | 59 | 3 | no | — |
| 329 | C4⋊Q8 | C22×D59 | 1 | 3 | yes | — |
| 330 | C4⋊Q8 | C22×D59 | 1 | 6 | yes | — |
| 331 | C4⋊Q8 | C22×D59 | 1 | 1 | yes | characteristic |
| 332 | #127 | — | 59 | 3 | no | — |
| 333 | #125 | — | 2 | 6 | no | — |
| 334 | #125 | C22×D59 | 1 | 6 | yes | — |
| 335 | #124 | — | 59 | 3 | no | — |
| 336 | #124 | — | 59 | 6 | no | — |
| 337 | #124 | — | 59 | 1 | no | — |
| 338 | #124 | — | 118 | 3 | no | — |
| 339 | #124 | — | 118 | 3 | no | — |
| 340 | #123 | — | 118 | 6 | no | — |
| 341 | C22⋊Q8 | — | 2 | 3 | no | — |
| 342 | C22⋊Q8 | — | 2 | 3 | no | — |
| 343 | C22⋊Q8 | — | 2 | 12 | no | — |
| 344 | C22⋊Q8 | — | 118 | 3 | no | — |
| 345 | C22⋊Q8 | — | 118 | 3 | no | — |
| 346 | #121 | — | 118 | 3 | no | — |
| 347 | #121 | — | 118 | 3 | no | — |
| 348 | #121 | — | 118 | 3 | no | — |
| 349 | #121 | — | 118 | 3 | no | — |
| 350 | #120 | — | 118 | 6 | no | — |
| 351 | C4×Q8 | — | 2 | 2 | no | — |
| 352 | C4×Q8 | — | 2 | 3 | no | — |
| 353 | C4×Q8 | — | 2 | 3 | no | — |
| 354 | C4×Q8 | C22⋊D59 | 1 | 1 | yes | characteristic |
| 355 | C4×Q8 | C22⋊D59 | 1 | 1 | yes | characteristic |
| 356 | C4×D4 | — | 2 | 6 | no | — |
| 357 | C4×D4 | — | 118 | 3 | no | — |
| 358 | C4×D4 | — | 118 | 3 | no | — |
| 359 | C4×D4 | C22⋊D59 | 1 | 3 | yes | — |
| 360 | C4×D4 | C22⋊D59 | 1 | 3 | yes | — |
| 361 | #117 | C22×D59 | 1 | 6 | yes | — |
| 362 | #117 | C22×D59 | 1 | 3 | yes | — |
| 363 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 364 | C2×C4⋊C4 | C22×D59 | 1 | 6 | yes | — |
| 365 | C2×C22⋊C4 | — | 118 | 3 | no | — |
| 366 | C2×C22⋊C4 | — | 118 | 3 | no | — |
| 367 | C2×C42 | C22×D59 | 1 | 3 | yes | — |
| 368 | #103 | — | 59 | 6 | no | — |
| 369 | #103 | — | 59 | 12 | no | — |
| 370 | #103 | — | 59 | 2 | no | — |
| 371 | #103 | — | 59 | 6 | no | — |
| 372 | #103 | — | 59 | 6 | no | — |
| 373 | #102 | — | 59 | 6 | no | — |
| 374 | #102 | — | 59 | 12 | no | — |
| 375 | #102 | — | 59 | 2 | no | — |
| 376 | #102 | — | 59 | 6 | no | — |
| 377 | #102 | — | 59 | 6 | no | — |
| 378 | #97 | — | 59 | 1 | no | — |
| 379 | #97 | — | 59 | 3 | no | — |
| 380 | #97 | — | 59 | 6 | no | — |
| 381 | C4×C8 | — | 59 | 6 | no | — |
| 382 | C24 | — | 118 | 3 | no | — |
| 383 | #41 | — | 118 | 12 | no | — |
| 384 | #41 | — | 118 | 12 | no | — |
| 385 | #41 | — | 236 | 4 | no | — |
| 386 | #41 | — | 236 | 12 | no | — |
| 387 | #41 | #11745689 | 1 | 8 | yes | — |
| 388 | C2×Q8 | — | 2 | 1 | no | — |
| 389 | C2×Q8 | — | 2 | 3 | no | — |
| 390 | C2×Q8 | — | 2 | 6 | no | — |
| 391 | C2×Q8 | — | 8 | 6 | no | — |
| 392 | C2×Q8 | — | 59 | 3 | no | — |
| 393 | C2×Q8 | — | 59 | 1 | no | — |
| 394 | C2×Q8 | — | 118 | 3 | no | — |
| 395 | C2×Q8 | — | 118 | 12 | no | — |
| 396 | C2×Q8 | — | 236 | 4 | no | — |
| 397 | C2×Q8 | C2×C22⋊D59 | 1 | 1 | yes | characteristic |
| 398 | C2×D4 | — | 59 | 3 | no | — |
| 399 | C2×D4 | — | 59 | 1 | no | — |
| 400 | C2×D4 | — | 118 | 3 | no | — |
| 401 | C2×D4 | — | 118 | 3 | no | — |
| 402 | C2×D4 | — | 118 | 3 | no | — |
| 403 | C2×D4 | — | 118 | 3 | no | — |
| 404 | C2×D4 | — | 118 | 3 | no | — |
| 405 | C2×D4 | — | 118 | 12 | no | — |
| 406 | C2×D4 | — | 236 | 12 | no | — |
| 407 | C2×D4 | C2×C22⋊D59 | 1 | 3 | yes | — |
| 408 | C22×C4 | — | 2 | 6 | no | — |
| 409 | C22×C4 | — | 118 | 3 | no | — |
| 410 | C22×C4 | — | 118 | 3 | no | — |
| 411 | C22×C4 | — | 118 | 3 | no | — |
| 412 | C22×C4 | C2×C22⋊D59 | 1 | 3 | yes | — |
| 413 | C22×C4 | C2×C22⋊D59 | 1 | 3 | yes | — |
| 414 | C22×C4 | C23×D59 | 1 | 3 | yes | — |
| 415 | M16 | — | 118 | 12 | no | — |
| 416 | C2×C8 | — | 59 | 6 | no | — |
| 417 | C2×C8 | — | 59 | 2 | no | — |
| 418 | C2×C8 | — | 118 | 12 | no | — |
| 419 | C4⋊C4 | — | 2 | 3 | no | — |
| 420 | C4⋊C4 | — | 2 | 6 | no | — |
| 421 | C4⋊C4 | — | 2 | 6 | no | — |
| 422 | C4⋊C4 | — | 2 | 1 | no | — |
| 423 | C4⋊C4 | — | 2 | 6 | no | — |
| 424 | C4⋊C4 | — | 2 | 6 | no | — |
| 425 | C4⋊C4 | — | 118 | 3 | no | — |
| 426 | C4⋊C4 | — | 118 | 3 | no | — |
| 427 | C4⋊C4 | C2×C22⋊D59 | 1 | 3 | yes | — |
| 428 | C4⋊C4 | C2×C22⋊D59 | 1 | 3 | yes | — |
| 429 | C4⋊C4 | C23×D59 | 1 | 6 | yes | — |
| 430 | C4⋊C4 | C23×D59 | 1 | 2 | yes | — |
| 431 | C22⋊C4 | — | 2 | 6 | no | — |
| 432 | C22⋊C4 | — | 118 | 3 | no | — |
| 433 | C22⋊C4 | — | 118 | 3 | no | — |
| 434 | C22⋊C4 | — | 118 | 6 | no | — |
| 435 | C22⋊C4 | — | 118 | 6 | no | — |
| 436 | C22⋊C4 | — | 118 | 1 | no | — |
| 437 | C22⋊C4 | — | 118 | 1 | no | — |
| 438 | C22⋊C4 | C2×C22⋊D59 | 1 | 6 | yes | — |
| 439 | C42 | — | 2 | 6 | no | — |
| 440 | C42 | C2×C22⋊D59 | 1 | 3 | yes | — |
| 441 | C42 | C2×C22⋊D59 | 1 | 3 | yes | — |
| 442 | C42 | C23×D59 | 1 | 3 | yes | — |
| 443 | C42 | C23×D59 | 1 | 1 | yes | characteristic |
| 444 | C23 | — | 118 | 3 | no | — |
| 445 | C23 | — | 118 | 1 | no | — |
| 446 | C23 | — | 472 | 3 | no | — |
| 447 | C23 | — | 472 | 3 | no | — |
| 448 | C23 | — | 236 | 6 | no | — |
| 449 | C23 | C22×C22⋊D59 | 1 | 3 | yes | — |
| 450 | Q8 | — | 4 | 2 | no | — |
| 451 | Q8 | — | 4 | 6 | no | — |
| 452 | Q8 | — | 8 | 6 | no | — |
| 453 | Q8 | — | 118 | 6 | no | — |
| 454 | Q8 | — | 118 | 2 | no | — |
| 455 | Q8 | — | 236 | 6 | no | — |
| 456 | Q8 | #14273716 | 1 | 4 | yes | — |
| 457 | D4 | — | 118 | 6 | no | — |
| 458 | D4 | — | 118 | 2 | no | — |
| 459 | D4 | — | 472 | 3 | no | — |
| 460 | D4 | — | 472 | 3 | no | — |
| 461 | D4 | — | 236 | 6 | no | — |
| 462 | D4 | — | 236 | 6 | no | — |
| 463 | D4 | — | 236 | 6 | no | — |
| 464 | D4 | #14273716 | 1 | 12 | yes | — |
| 465 | C2×C4 | — | 2 | 2 | no | — |
| 466 | C2×C4 | — | 2 | 6 | no | — |
| 467 | C2×C4 | — | 4 | 3 | no | — |
| 468 | C2×C4 | — | 4 | 3 | no | — |
| 469 | C2×C4 | — | 8 | 6 | no | — |
| 470 | C2×C4 | — | 118 | 3 | no | — |
| 471 | C2×C4 | — | 118 | 1 | no | — |
| 472 | C2×C4 | — | 236 | 6 | no | — |
| 473 | C2×C4 | — | 236 | 6 | no | — |
| 474 | C2×C4 | — | 236 | 6 | no | — |
| 475 | C2×C4 | C22×C22⋊D59 | 1 | 1 | yes | characteristic |
| 476 | C2×C4 | C22×C22⋊D59 | 1 | 1 | yes | characteristic |
| 477 | C2×C4 | C22×C22⋊D59 | 1 | 3 | yes | — |
| 478 | C2×C4 | C22×C22⋊D59 | 1 | 3 | yes | — |
| 479 | C2×C4 | C22×C22⋊D59 | 1 | 3 | yes | — |
| 480 | C2×C4 | C2×#11745689 | 1 | 12 | yes | — |
| 481 | C2×C4 | C24×D59 | 1 | 1 | yes | characteristic |
| 482 | C8 | — | 118 | 2 | no | — |
| 483 | C8 | — | 118 | 6 | no | — |
| 484 | C22 | — | 2 | 3 | no | — |
| 485 | C22 | — | 2 | 3 | no | — |
| 486 | C22 | — | 944 | 6 | no | — |
| 487 | C22 | — | 236 | 1 | no | — |
| 488 | C22 | — | 236 | 3 | no | — |
| 489 | C22 | — | 236 | 1 | no | — |
| 490 | C22 | — | 236 | 3 | no | — |
| 491 | C22 | — | 236 | 1 | no | — |
| 492 | C22 | — | 236 | 3 | no | — |
| 493 | C22 | C2×#14273716 | 1 | 6 | yes | — |
| 494 | C22 | C23×C22⋊D59 | 1 | 1 | yes | characteristic |
| 495 | C4 | — | 2 | 1 | no | — |
| 496 | C4 | — | 2 | 3 | no | — |
| 497 | C4 | — | 2 | 1 | no | — |
| 498 | C4 | — | 2 | 3 | no | — |
| 499 | C4 | — | 4 | 6 | no | — |
| 500 | C4 | — | 4 | 2 | no | — |
| 501 | C4 | — | 236 | 1 | no | — |
| 502 | C4 | — | 236 | 3 | no | — |
| 503 | C4 | C2×#14273716 | 1 | 6 | yes | — |
| 504 | C4 | C22×#11745689 | 1 | 2 | yes | — |
| 505 | C2 | — | 2 | 6 | no | — |
| 506 | C2 | — | 472 | 3 | no | — |
| 507 | C2 | — | 472 | 1 | no | — |
| 508 | C2 | C22×#14273716 | 1 | 1 | yes | characteristic |
| 509 | C2 | #21438876 | 1 | 1 | yes | characteristic |
| 510 | C2 | #21438883 | 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