← #29832867
Subgroups — #29832867
Order 15616.
1208 conjugacy classes of subgroups.
The subgroup lattice has 492 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #21459611 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #21454300 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #21447511 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #21447505 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #21447502 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #355×D61 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | C61×#2134 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#14519824 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×#14519822 | C4 | 1 | 1 | yes | characteristic |
| 10 | #16840528 | — | 2 | 2 | no | — |
| 11 | #16840418 | — | 2 | 2 | no | — |
| 12 | #16840409 | — | 2 | 2 | no | — |
| 13 | #16840399 | — | 2 | 4 | no | — |
| 14 | #16840338 | C4 | 1 | 1 | yes | characteristic |
| 15 | #16840332 | C22 | 1 | 2 | yes | — |
| 16 | #16840325 | C4 | 1 | 2 | yes | — |
| 17 | #16840310 | C4 | 1 | 2 | yes | — |
| 18 | #16840308 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#14519764 | C4 | 1 | 1 | yes | characteristic |
| 20 | #124×D61 | C22 | 1 | 2 | yes | — |
| 21 | #16840230 | C4 | 1 | 1 | yes | characteristic |
| 22 | #16839746 | C22 | 1 | 2 | yes | complemented |
| 23 | #16839743 | — | 2 | 4 | no | — |
| 24 | C2×#14519695 | — | 2 | 2 | no | — |
| 25 | #101×D61 | C22 | 1 | 8 | yes | complemented |
| 26 | #16839560 | C22 | 1 | 4 | yes | complemented |
| 27 | #16839559 | C22 | 1 | 4 | yes | complemented |
| 28 | #16839558 | C22 | 1 | 4 | yes | complemented |
| 29 | C61×#535 | C22 | 1 | 1 | yes | characteristic |
| 30 | C61×#413 | C22 | 1 | 2 | yes | complemented |
| 31 | C61×#355 | C22 | 1 | 4 | yes | complemented |
| 32 | #14519824 | — | 4 | 4 | no | — |
| 33 | #14519822 | — | 4 | 4 | no | — |
| 34 | C2×#11758222 | C2×C4 | 1 | 1 | yes | characteristic |
| 35 | C2×#11758222 | C2×C4 | 1 | 1 | yes | characteristic |
| 36 | C2×#11758222 | D4 | 1 | 2 | yes | — |
| 37 | C2×#11758224 | — | 2 | 1 | no | — |
| 38 | C2×#11758224 | C2×C4 | 1 | 2 | yes | — |
| 39 | C2×#11758224 | C2×C4 | 1 | 2 | yes | — |
| 40 | C2×#11758224 | D4 | 1 | 4 | yes | — |
| 41 | C22×Dic122 | C2×C4 | 1 | 1 | yes | characteristic |
| 42 | C22×Dic122 | D4 | 1 | 2 | yes | — |
| 43 | C2×Q8×D61 | C23 | 1 | 2 | yes | — |
| 44 | C22×C22⋊D61 | — | 2 | 2 | no | — |
| 45 | C2×D4×D61 | — | 2 | 1 | no | — |
| 46 | C2×D4×D61 | C2×C4 | 1 | 2 | yes | — |
| 47 | #14519785 | — | 4 | 4 | no | — |
| 48 | #14519783 | — | 4 | 4 | no | — |
| 49 | C2×#11758194 | — | 2 | 2 | no | — |
| 50 | M16×D61 | — | 2 | 8 | no | — |
| 51 | #14519777 | C2×C4 | 1 | 2 | yes | — |
| 52 | #14519775 | C23 | 1 | 1 | yes | characteristic |
| 53 | #14519773 | C2×C4 | 1 | 1 | yes | characteristic |
| 54 | #14519766 | C23 | 1 | 1 | yes | characteristic |
| 55 | #14519765 | C2×C4 | 1 | 2 | yes | — |
| 56 | #14519764 | — | 2 | 2 | no | — |
| 57 | #14519764 | C2×C4 | 1 | 2 | yes | — |
| 58 | #14519764 | C2×C4 | 1 | 2 | yes | — |
| 59 | #14519764 | C2×C4 | 1 | 1 | yes | characteristic |
| 60 | #14519763 | — | 2 | 4 | no | — |
| 61 | #14519761 | — | 2 | 2 | no | — |
| 62 | #14519759 | — | 2 | 4 | no | — |
| 63 | #14519757 | — | 2 | 2 | no | — |
| 64 | #14519754 | — | 2 | 4 | no | — |
| 65 | #14519749 | — | 2 | 2 | no | — |
| 66 | #14519749 | — | 2 | 4 | no | — |
| 67 | #14519748 | — | 2 | 4 | no | — |
| 68 | #14519745 | — | 2 | 4 | no | — |
| 69 | #14519742 | — | 2 | 1 | no | — |
| 70 | D4×Dic61 | — | 2 | 4 | no | — |
| 71 | #14519739 | — | 2 | 1 | no | — |
| 72 | C4×C22⋊D61 | — | 2 | 2 | no | — |
| 73 | #14519737 | — | 2 | 2 | no | — |
| 74 | #14519734 | C2×C4 | 1 | 2 | yes | — |
| 75 | C2×C22⋊Dic61 | — | 2 | 2 | no | — |
| 76 | C22⋊C4×D61 | — | 2 | 4 | no | — |
| 77 | C2×C4×Dic61 | C2×C4 | 1 | 1 | yes | characteristic |
| 78 | C42×D61 | C2×C4 | 1 | 2 | yes | — |
| 79 | #14519696 | C23 | 1 | 4 | yes | — |
| 80 | #14519695 | — | 2 | 8 | no | — |
| 81 | #14519694 | — | 2 | 2 | no | — |
| 82 | C2×#41×C61 | C23 | 1 | 1 | yes | characteristic |
| 83 | C22×D4×C61 | C2×C4 | 1 | 1 | yes | characteristic |
| 84 | C2×M16×C61 | — | 2 | 2 | no | — |
| 85 | #127×C61 | C2×C4 | 1 | 2 | yes | — |
| 86 | #124×C61 | C23 | 1 | 2 | yes | — |
| 87 | #121×C61 | — | 2 | 2 | no | — |
| 88 | #120×C61 | — | 2 | 2 | no | — |
| 89 | #117×C61 | C2×C4 | 1 | 1 | yes | characteristic |
| 90 | #101×C61 | C23 | 1 | 4 | yes | — |
| 91 | #100×C61 | — | 2 | 2 | no | — |
| 92 | C24×C61 | — | 2 | 1 | no | — |
| 93 | C23×D61 | — | 2 | 2 | no | — |
| 94 | #41×C61 | — | 4 | 2 | no | — |
| 95 | C2×Q8×C61 | C24 | 1 | 1 | yes | characteristic |
| 96 | C2×D4×C61 | — | 2 | 4 | no | — |
| 97 | C2×D4×C61 | — | 2 | 1 | no | — |
| 98 | C2×D4×C61 | — | 4 | 2 | no | — |
| 99 | C2×D4×C61 | C22×C4 | 1 | 2 | yes | — |
| 100 | C2×D4×C61 | C22×C4 | 1 | 1 | yes | characteristic |
| 101 | C2×D4×C61 | C2×D4 | 1 | 2 | yes | — |
| 102 | C22×C4×C61 | C22×C4 | 1 | 1 | yes | characteristic |
| 103 | C22×C4×C61 | C2×D4 | 1 | 2 | yes | — |
| 104 | C2×C22⋊D61 | — | 2 | 1 | no | — |
| 105 | C2×C22⋊D61 | — | 2 | 2 | no | — |
| 106 | C2×C22⋊D61 | — | 2 | 2 | no | — |
| 107 | C2×C22⋊D61 | — | 2 | 2 | no | — |
| 108 | C2×C22⋊D61 | — | 4 | 8 | no | — |
| 109 | C2×C22⋊D61 | C22⋊C4 | 1 | 2 | yes | — |
| 110 | C2×C22⋊D61 | C22⋊C4 | 1 | 4 | yes | — |
| 111 | C22×Dic61 | — | 2 | 1 | no | — |
| 112 | C22×Dic61 | — | 2 | 2 | no | — |
| 113 | C22×Dic61 | C22⋊C4 | 1 | 2 | yes | — |
| 114 | C22×Dic61 | C22⋊C4 | 1 | 4 | yes | — |
| 115 | Q8×D61 | — | 4 | 4 | no | — |
| 116 | #11758224 | — | 4 | 4 | no | — |
| 117 | #11758224 | — | 4 | 4 | no | — |
| 118 | #11758224 | — | 4 | 8 | no | — |
| 119 | #11758224 | — | 4 | 4 | no | — |
| 120 | D4×D61 | — | 4 | 4 | no | — |
| 121 | D4×D61 | — | 4 | 4 | no | — |
| 122 | #11758222 | — | 2 | 4 | no | — |
| 123 | #11758222 | — | 2 | 4 | no | — |
| 124 | #11758222 | — | 2 | 4 | no | — |
| 125 | #11758222 | — | 4 | 2 | no | — |
| 126 | C2×D244 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 127 | C2×D244 | C22×C4 | 1 | 1 | yes | characteristic |
| 128 | C2×C4×D61 | — | 2 | 1 | no | — |
| 129 | C2×C4×D61 | — | 2 | 2 | no | — |
| 130 | C2×C4×D61 | C22×C4 | 1 | 2 | yes | — |
| 131 | C2×C4×D61 | C2×D4 | 1 | 4 | yes | — |
| 132 | C2×Dic122 | — | 4 | 2 | no | — |
| 133 | C2×Dic122 | — | 4 | 2 | no | — |
| 134 | C2×Dic122 | — | 4 | 2 | no | — |
| 135 | C2×Dic122 | C22⋊C4 | 1 | 2 | yes | — |
| 136 | C2×Dic122 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 137 | C2×Dic122 | C22×C4 | 1 | 1 | yes | characteristic |
| 138 | C2×Dic122 | C22×C4 | 1 | 2 | yes | — |
| 139 | C2×Dic122 | C2×D4 | 1 | 4 | yes | — |
| 140 | M16×C61 | — | 2 | 4 | no | — |
| 141 | M16×C61 | — | 4 | 2 | no | — |
| 142 | C2×C8×C61 | — | 4 | 2 | no | — |
| 143 | C4⋊C4×C61 | — | 2 | 1 | no | — |
| 144 | C22⋊C4×C61 | — | 2 | 1 | no | — |
| 145 | C22⋊C4×C61 | — | 2 | 4 | no | — |
| 146 | C42×C61 | C22×C4 | 1 | 2 | yes | — |
| 147 | C22⋊Dic61 | — | 2 | 2 | no | — |
| 148 | C22⋊Dic61 | — | 2 | 4 | no | — |
| 149 | C22⋊Dic61 | — | 2 | 4 | no | — |
| 150 | #11758198 | — | 2 | 2 | no | — |
| 151 | #11758198 | — | 2 | 2 | no | — |
| 152 | #11758198 | — | 2 | 4 | no | — |
| 153 | C4⋊Dic61 | — | 2 | 4 | no | — |
| 154 | #11758196 | — | 2 | 2 | no | — |
| 155 | #11758196 | — | 2 | 2 | no | — |
| 156 | C4×Dic61 | — | 2 | 1 | no | — |
| 157 | C4×Dic61 | — | 2 | 2 | no | — |
| 158 | C4×Dic61 | C22×C4 | 1 | 1 | yes | characteristic |
| 159 | C4×Dic61 | C22×C4 | 1 | 1 | yes | characteristic |
| 160 | #11758194 | — | 2 | 4 | no | — |
| 161 | #11758194 | — | 4 | 2 | no | — |
| 162 | C2×#92418 | — | 4 | 2 | no | — |
| 163 | #11758189 | — | 4 | 8 | no | — |
| 164 | C8×D61 | — | 4 | 8 | no | — |
| 165 | C23×C61 | — | 2 | 2 | no | — |
| 166 | C23×C61 | — | 4 | 2 | no | — |
| 167 | C23×C61 | — | 8 | 2 | no | — |
| 168 | C23×C61 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 169 | C23×C61 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 170 | C22×D61 | — | 2 | 1 | no | — |
| 171 | C22×D61 | — | 4 | 4 | no | — |
| 172 | C22×D61 | — | 8 | 4 | no | — |
| 173 | C22×D61 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 174 | Q8×C61 | — | 4 | 1 | no | — |
| 175 | D4×C61 | — | 4 | 1 | no | — |
| 176 | D4×C61 | — | 4 | 2 | no | — |
| 177 | D4×C61 | — | 4 | 2 | no | — |
| 178 | D4×C61 | — | 4 | 2 | no | — |
| 179 | D4×C61 | — | 8 | 4 | no | — |
| 180 | C2×C4×C61 | — | 2 | 2 | no | — |
| 181 | C2×C4×C61 | — | 2 | 2 | no | — |
| 182 | C2×C4×C61 | — | 2 | 2 | no | — |
| 183 | C2×C4×C61 | — | 2 | 2 | no | — |
| 184 | C2×C4×C61 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 185 | C2×C4×C61 | C23×C4 | 1 | 1 | yes | characteristic |
| 186 | C2×C4×C61 | C22×D4 | 1 | 2 | yes | — |
| 187 | C22⋊D61 | — | 2 | 4 | no | — |
| 188 | C22⋊D61 | — | 2 | 8 | no | — |
| 189 | C22⋊D61 | — | 4 | 4 | no | — |
| 190 | C22⋊D61 | — | 4 | 2 | no | — |
| 191 | C22⋊D61 | — | 4 | 4 | no | — |
| 192 | C22⋊D61 | — | 8 | 2 | no | — |
| 193 | C2×Dic61 | — | 2 | 1 | no | — |
| 194 | C2×Dic61 | — | 2 | 1 | no | — |
| 195 | C2×Dic61 | — | 2 | 1 | no | — |
| 196 | C2×Dic61 | — | 4 | 4 | no | — |
| 197 | C2×Dic61 | — | 4 | 2 | no | — |
| 198 | C2×Dic61 | — | 4 | 4 | no | — |
| 199 | C2×Dic61 | — | 8 | 1 | no | — |
| 200 | C2×Dic61 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 201 | C2×Dic61 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 202 | D244 | — | 4 | 1 | no | — |
| 203 | D244 | #99 | 1 | 4 | yes | — |
| 204 | C4×D61 | — | 2 | 8 | no | — |
| 205 | C4×D61 | — | 2 | 4 | no | — |
| 206 | C4×D61 | — | 4 | 2 | no | — |
| 207 | C4×D61 | — | 8 | 2 | no | — |
| 208 | Dic122 | — | 2 | 2 | no | — |
| 209 | Dic122 | — | 2 | 2 | no | — |
| 210 | Dic122 | — | 2 | 2 | no | — |
| 211 | Dic122 | — | 4 | 2 | no | — |
| 212 | Dic122 | — | 4 | 4 | no | — |
| 213 | Dic122 | — | 4 | 1 | no | — |
| 214 | C8×C61 | — | 4 | 4 | no | — |
| 215 | #92418 | — | 4 | 4 | no | — |
| 216 | #33370 | — | 61 | 1 | no | maximal, Sylow |
| 217 | C22×C61 | — | 2 | 1 | no | — |
| 218 | C22×C61 | — | 2 | 2 | no | — |
| 219 | C22×C61 | — | 4 | 1 | no | — |
| 220 | C22×C61 | — | 4 | 2 | no | — |
| 221 | C22×C61 | — | 4 | 4 | no | — |
| 222 | C22×C61 | — | 4 | 2 | no | — |
| 223 | C22×C61 | — | 16 | 2 | no | — |
| 224 | C22×C61 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 225 | C2×D61 | — | 4 | 2 | no | — |
| 226 | C2×D61 | — | 4 | 2 | no | — |
| 227 | C2×D61 | — | 4 | 1 | no | — |
| 228 | C2×D61 | — | 16 | 4 | no | — |
| 229 | C2×D61 | C2×#99 | 1 | 4 | yes | — |
| 230 | C4×C61 | — | 2 | 2 | no | — |
| 231 | C4×C61 | — | 2 | 1 | no | — |
| 232 | C4×C61 | — | 4 | 2 | no | — |
| 233 | C4×C61 | C2×#99 | 1 | 2 | yes | — |
| 234 | Dic61 | — | 2 | 2 | no | — |
| 235 | Dic61 | — | 2 | 4 | no | — |
| 236 | Dic61 | — | 4 | 1 | no | — |
| 237 | Dic61 | — | 4 | 1 | no | — |
| 238 | Dic61 | — | 4 | 1 | no | — |
| 239 | #3500 | — | 61 | 1 | no | — |
| 240 | #2889 | — | 61 | 2 | no | — |
| 241 | #2134 | — | 61 | 1 | no | — |
| 242 | #2134 | D61 | 1 | 1 | yes | characteristic, complemented |
| 243 | #2133 | — | 61 | 4 | no | — |
| 244 | #2132 | — | 61 | 2 | no | — |
| 245 | C2×#355 | — | 61 | 4 | no | — |
| 246 | C2×C61 | — | 2 | 1 | no | — |
| 247 | C2×C61 | — | 4 | 2 | no | — |
| 248 | C2×C61 | — | 4 | 1 | no | — |
| 249 | C2×C61 | — | 8 | 2 | no | — |
| 250 | C2×C61 | C22×#99 | 1 | 1 | yes | characteristic |
| 251 | D61 | — | 2 | 4 | no | — |
| 252 | D61 | — | 8 | 1 | no | — |
| 253 | C2×2−1+4 | — | 61 | 1 | no | — |
| 254 | C2×H(5,𝔽2) | — | 61 | 1 | no | — |
| 255 | #568 | — | 122 | 2 | no | — |
| 256 | #548 | — | 122 | 2 | no | — |
| 257 | #546 | — | 122 | 4 | no | — |
| 258 | #546 | — | 122 | 2 | no | — |
| 259 | #536 | — | 61 | 2 | no | — |
| 260 | #536 | — | 61 | 1 | no | — |
| 261 | #535 | — | 61 | 2 | no | — |
| 262 | #535 | C2×D61 | 1 | 1 | yes | characteristic |
| 263 | #532 | — | 61 | 1 | no | — |
| 264 | #532 | — | 61 | 2 | no | — |
| 265 | C2×#124 | — | 61 | 1 | no | — |
| 266 | C2×#124 | — | 61 | 2 | no | — |
| 267 | C4×#41 | — | 61 | 1 | no | — |
| 268 | #413 | — | 61 | 2 | no | — |
| 269 | #413 | — | 122 | 4 | no | — |
| 270 | #413 | C2×D61 | 1 | 2 | yes | complemented |
| 271 | C2×#101 | — | 61 | 8 | no | — |
| 272 | C2×#101 | — | 122 | 2 | no | — |
| 273 | #356 | — | 61 | 4 | no | — |
| 274 | #355 | — | 61 | 4 | no | — |
| 275 | #355 | — | 61 | 4 | no | — |
| 276 | #355 | C2×D61 | 1 | 4 | yes | complemented |
| 277 | C61 | #33370 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 278 | 2−1+4 | — | 244 | 4 | no | — |
| 279 | H(5,𝔽2) | — | 244 | 4 | no | — |
| 280 | C2×#41 | — | 61 | 2 | no | — |
| 281 | C2×#41 | — | 61 | 4 | no | — |
| 282 | C2×#41 | — | 61 | 1 | no | — |
| 283 | C2×#41 | — | 61 | 2 | no | — |
| 284 | C2×#41 | — | 61 | 2 | no | — |
| 285 | C2×#41 | — | 61 | 1 | no | — |
| 286 | C2×#41 | — | 122 | 1 | no | — |
| 287 | C2×#41 | C22×D61 | 1 | 1 | yes | characteristic |
| 288 | C22×Q8 | — | 61 | 2 | no | — |
| 289 | C22×Q8 | — | 61 | 1 | no | — |
| 290 | C22×Q8 | — | 61 | 2 | no | — |
| 291 | C22×D4 | — | 61 | 2 | no | — |
| 292 | C22×D4 | — | 122 | 1 | no | — |
| 293 | C22×D4 | — | 122 | 2 | no | — |
| 294 | C22×D4 | C4×D61 | 1 | 1 | yes | characteristic |
| 295 | #131 | — | 244 | 4 | no | — |
| 296 | #131 | — | 244 | 4 | no | — |
| 297 | C2×M16 | — | 2 | 2 | no | — |
| 298 | C2×M16 | — | 122 | 8 | no | — |
| 299 | C2×M16 | — | 122 | 2 | no | — |
| 300 | C4⋊Q8 | — | 61 | 1 | no | — |
| 301 | C4⋊Q8 | — | 61 | 2 | no | — |
| 302 | #127 | — | 61 | 1 | no | — |
| 303 | #127 | C4×D61 | 1 | 2 | yes | — |
| 304 | #124 | — | 61 | 1 | no | — |
| 305 | #124 | — | 61 | 2 | no | — |
| 306 | #124 | — | 61 | 2 | no | — |
| 307 | #124 | — | 61 | 1 | no | — |
| 308 | #124 | — | 61 | 2 | no | — |
| 309 | #124 | — | 122 | 4 | no | — |
| 310 | #124 | — | 122 | 2 | no | — |
| 311 | #124 | C22×D61 | 1 | 2 | yes | — |
| 312 | #123 | — | 122 | 4 | no | — |
| 313 | #123 | — | 122 | 2 | no | — |
| 314 | C22⋊Q8 | — | 122 | 4 | no | — |
| 315 | C22⋊Q8 | — | 122 | 2 | no | — |
| 316 | #121 | — | 2 | 2 | no | — |
| 317 | #121 | — | 122 | 4 | no | — |
| 318 | #121 | — | 122 | 4 | no | — |
| 319 | #121 | — | 122 | 2 | no | — |
| 320 | #120 | — | 2 | 2 | no | — |
| 321 | #120 | — | 122 | 4 | no | — |
| 322 | C4×Q8 | — | 122 | 1 | no | — |
| 323 | C4×D4 | — | 122 | 2 | no | — |
| 324 | C4×D4 | — | 122 | 1 | no | — |
| 325 | C4×D4 | — | 122 | 4 | no | — |
| 326 | C4×D4 | — | 122 | 2 | no | — |
| 327 | #117 | — | 61 | 2 | no | — |
| 328 | #117 | C4×D61 | 1 | 1 | yes | characteristic |
| 329 | C2×C22⋊C4 | — | 122 | 4 | no | — |
| 330 | C2×C22⋊C4 | — | 122 | 2 | no | — |
| 331 | C2×C42 | — | 61 | 1 | no | — |
| 332 | C2×C42 | — | 61 | 2 | no | — |
| 333 | #101 | — | 61 | 4 | no | — |
| 334 | #101 | — | 122 | 8 | no | — |
| 335 | #101 | C22×D61 | 1 | 4 | yes | — |
| 336 | #100 | — | 2 | 2 | no | — |
| 337 | #100 | — | 122 | 2 | no | — |
| 338 | C24 | — | 2 | 1 | no | — |
| 339 | C24 | — | 122 | 2 | no | — |
| 340 | #41 | — | 4 | 2 | no | — |
| 341 | #41 | — | 122 | 4 | no | — |
| 342 | #41 | — | 122 | 4 | no | — |
| 343 | #41 | — | 122 | 4 | no | — |
| 344 | #41 | — | 244 | 2 | no | — |
| 345 | #41 | — | 244 | 8 | no | — |
| 346 | #41 | — | 244 | 4 | no | — |
| 347 | #41 | — | 244 | 4 | no | — |
| 348 | #41 | — | 244 | 4 | no | — |
| 349 | C2×Q8 | — | 61 | 2 | no | — |
| 350 | C2×Q8 | — | 61 | 4 | no | — |
| 351 | C2×Q8 | — | 61 | 1 | no | — |
| 352 | C2×Q8 | — | 61 | 2 | no | — |
| 353 | C2×Q8 | — | 61 | 1 | no | — |
| 354 | C2×Q8 | — | 244 | 2 | no | — |
| 355 | C2×Q8 | — | 244 | 2 | no | — |
| 356 | C2×Q8 | — | 244 | 2 | no | — |
| 357 | C2×Q8 | — | 244 | 4 | no | — |
| 358 | C2×Q8 | C23×D61 | 1 | 1 | yes | characteristic |
| 359 | C2×D4 | — | 2 | 4 | no | — |
| 360 | C2×D4 | — | 2 | 1 | no | — |
| 361 | C2×D4 | — | 4 | 2 | no | — |
| 362 | C2×D4 | — | 61 | 2 | no | — |
| 363 | C2×D4 | — | 61 | 4 | no | — |
| 364 | C2×D4 | — | 61 | 1 | no | — |
| 365 | C2×D4 | — | 61 | 1 | no | — |
| 366 | C2×D4 | — | 122 | 2 | no | — |
| 367 | C2×D4 | — | 122 | 2 | no | — |
| 368 | C2×D4 | — | 122 | 2 | no | — |
| 369 | C2×D4 | — | 122 | 1 | no | — |
| 370 | C2×D4 | — | 244 | 4 | no | — |
| 371 | C2×D4 | — | 244 | 4 | no | — |
| 372 | C2×D4 | — | 244 | 8 | no | — |
| 373 | C2×D4 | C2×C4×D61 | 1 | 2 | yes | — |
| 374 | C2×D4 | C2×C4×D61 | 1 | 1 | yes | characteristic |
| 375 | C2×D4 | D4×D61 | 1 | 2 | yes | — |
| 376 | C22×C4 | — | 61 | 2 | no | — |
| 377 | C22×C4 | — | 61 | 4 | no | — |
| 378 | C22×C4 | — | 61 | 2 | no | — |
| 379 | C22×C4 | — | 61 | 4 | no | — |
| 380 | C22×C4 | — | 122 | 2 | no | — |
| 381 | C22×C4 | — | 122 | 2 | no | — |
| 382 | C22×C4 | — | 122 | 1 | no | — |
| 383 | C22×C4 | — | 122 | 1 | no | — |
| 384 | C22×C4 | C2×C4×D61 | 1 | 1 | yes | characteristic |
| 385 | C22×C4 | D4×D61 | 1 | 2 | yes | — |
| 386 | M16 | — | 2 | 4 | no | — |
| 387 | M16 | — | 4 | 2 | no | — |
| 388 | M16 | — | 122 | 4 | no | — |
| 389 | M16 | — | 244 | 8 | no | — |
| 390 | M16 | — | 244 | 2 | no | — |
| 391 | C2×C8 | — | 4 | 2 | no | — |
| 392 | C2×C8 | — | 244 | 8 | no | — |
| 393 | C2×C8 | — | 244 | 2 | no | — |
| 394 | C4⋊C4 | — | 2 | 1 | no | — |
| 395 | C4⋊C4 | — | 122 | 2 | no | — |
| 396 | C4⋊C4 | — | 122 | 4 | no | — |
| 397 | C4⋊C4 | — | 122 | 2 | no | — |
| 398 | C22⋊C4 | — | 2 | 1 | no | — |
| 399 | C22⋊C4 | — | 2 | 4 | no | — |
| 400 | C22⋊C4 | — | 122 | 4 | no | — |
| 401 | C22⋊C4 | — | 122 | 2 | no | — |
| 402 | C22⋊C4 | — | 122 | 4 | no | — |
| 403 | C22⋊C4 | — | 122 | 4 | no | — |
| 404 | C22⋊C4 | — | 122 | 2 | no | — |
| 405 | C22⋊C4 | — | 122 | 2 | no | — |
| 406 | C42 | — | 61 | 1 | no | — |
| 407 | C42 | — | 61 | 1 | no | — |
| 408 | C42 | — | 122 | 2 | no | — |
| 409 | C42 | — | 122 | 1 | no | — |
| 410 | C42 | C2×C4×D61 | 1 | 2 | yes | — |
| 411 | C23 | — | 2 | 2 | no | — |
| 412 | C23 | — | 4 | 2 | no | — |
| 413 | C23 | — | 8 | 2 | no | — |
| 414 | C23 | — | 61 | 2 | no | — |
| 415 | C23 | — | 122 | 1 | no | — |
| 416 | C23 | — | 488 | 4 | no | — |
| 417 | C23 | — | 244 | 4 | no | — |
| 418 | C23 | C22⋊C4×D61 | 1 | 1 | yes | characteristic |
| 419 | C23 | C22⋊C4×D61 | 1 | 2 | yes | — |
| 420 | Q8 | — | 4 | 1 | no | — |
| 421 | Q8 | — | 122 | 2 | no | — |
| 422 | Q8 | — | 122 | 2 | no | — |
| 423 | Q8 | — | 122 | 2 | no | — |
| 424 | Q8 | — | 244 | 4 | no | — |
| 425 | Q8 | — | 244 | 2 | no | — |
| 426 | Q8 | — | 244 | 1 | no | — |
| 427 | D4 | — | 4 | 1 | no | — |
| 428 | D4 | — | 4 | 2 | no | — |
| 429 | D4 | — | 4 | 2 | no | — |
| 430 | D4 | — | 4 | 2 | no | — |
| 431 | D4 | — | 8 | 4 | no | — |
| 432 | D4 | — | 61 | 4 | no | — |
| 433 | D4 | — | 122 | 4 | no | — |
| 434 | D4 | — | 122 | 8 | no | — |
| 435 | D4 | — | 488 | 2 | no | — |
| 436 | D4 | — | 244 | 1 | no | — |
| 437 | D4 | — | 244 | 4 | no | — |
| 438 | D4 | — | 244 | 2 | no | — |
| 439 | D4 | — | 244 | 4 | no | — |
| 440 | C2×C4 | — | 2 | 2 | no | — |
| 441 | C2×C4 | — | 2 | 2 | no | — |
| 442 | C2×C4 | — | 2 | 2 | no | — |
| 443 | C2×C4 | — | 2 | 2 | no | — |
| 444 | C2×C4 | — | 61 | 2 | no | — |
| 445 | C2×C4 | — | 61 | 4 | no | — |
| 446 | C2×C4 | — | 122 | 8 | no | — |
| 447 | C2×C4 | — | 122 | 4 | no | — |
| 448 | C2×C4 | — | 122 | 1 | no | — |
| 449 | C2×C4 | — | 122 | 1 | no | — |
| 450 | C2×C4 | — | 122 | 1 | no | — |
| 451 | C2×C4 | — | 488 | 2 | no | — |
| 452 | C2×C4 | — | 488 | 1 | no | — |
| 453 | C2×C4 | — | 244 | 4 | no | — |
| 454 | C2×C4 | — | 244 | 2 | no | — |
| 455 | C2×C4 | — | 244 | 4 | no | — |
| 456 | C2×C4 | — | 244 | 2 | no | — |
| 457 | C2×C4 | C22⋊C4×D61 | 1 | 1 | yes | characteristic |
| 458 | C2×C4 | C22×C4×D61 | 1 | 1 | yes | characteristic |
| 459 | C2×C4 | C2×D4×D61 | 1 | 2 | yes | — |
| 460 | C8 | — | 4 | 4 | no | — |
| 461 | C8 | — | 244 | 4 | no | — |
| 462 | C22 | — | 2 | 1 | no | — |
| 463 | C22 | — | 2 | 2 | no | — |
| 464 | C22 | — | 4 | 1 | no | — |
| 465 | C22 | — | 4 | 2 | no | — |
| 466 | C22 | — | 4 | 4 | no | — |
| 467 | C22 | — | 4 | 2 | no | — |
| 468 | C22 | — | 16 | 2 | no | — |
| 469 | C22 | — | 61 | 4 | no | — |
| 470 | C22 | — | 976 | 4 | no | — |
| 471 | C22 | — | 244 | 2 | no | — |
| 472 | C22 | — | 244 | 2 | no | — |
| 473 | C22 | — | 244 | 1 | no | — |
| 474 | C22 | C2×C22⋊C4×D61 | 1 | 1 | yes | characteristic |
| 475 | C4 | — | 2 | 2 | no | — |
| 476 | C4 | — | 2 | 1 | no | — |
| 477 | C4 | — | 4 | 2 | no | — |
| 478 | C4 | — | 122 | 2 | no | — |
| 479 | C4 | — | 122 | 4 | no | — |
| 480 | C4 | — | 244 | 1 | no | — |
| 481 | C4 | — | 244 | 1 | no | — |
| 482 | C4 | — | 244 | 1 | no | — |
| 483 | C4 | #99×D61 | 1 | 2 | yes | — |
| 484 | C2 | — | 2 | 1 | no | — |
| 485 | C2 | — | 4 | 1 | no | — |
| 486 | C2 | — | 4 | 2 | no | — |
| 487 | C2 | — | 8 | 2 | no | — |
| 488 | C2 | — | 122 | 4 | no | — |
| 489 | C2 | — | 488 | 1 | no | — |
| 490 | C2 | C2×#99×D61 | 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