Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1308 conjugacy classes of subgroups.
The subgroup lattice has 410 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #21462737 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #21462467 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #21461330 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #21461327 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #21461316 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | D61⋊#331 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #21459596 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C2×#14519865 | — | 2 | 1 | no | — |
| 9 | Q8×#92420 | — | 2 | 1 | no | — |
| 10 | #16840790 | — | 2 | 3 | no | — |
| 11 | #16840780 | C22 | 1 | 3 | yes | complemented |
| 12 | #16840769 | — | 2 | 3 | no | — |
| 13 | #16840767 | C22 | 1 | 3 | yes | complemented |
| 14 | D61⋊(C4⋊C8) | C22 | 1 | 3 | yes | complemented |
| 15 | D61⋊(C4⋊C8) | C22 | 1 | 3 | yes | complemented |
| 16 | #16840621 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | #16840621 | C22 | 1 | 3 | yes | complemented |
| 18 | #16840620 | C22 | 1 | 3 | yes | complemented |
| 19 | #16840620 | C22 | 1 | 6 | yes | complemented |
| 20 | #16840620 | C22 | 1 | 3 | yes | complemented |
| 21 | C2×#14519823 | — | 2 | 1 | no | — |
| 22 | #16840434 | C4 | 1 | 1 | yes | characteristic |
| 23 | #16840431 | — | 2 | 1 | no | — |
| 24 | D4×D244 | C4 | 1 | 3 | yes | — |
| 25 | #16840397 | C4 | 1 | 3 | yes | — |
| 26 | #16840396 | — | 2 | 3 | no | — |
| 27 | #16840328 | — | 2 | 3 | no | — |
| 28 | #16840309 | C22 | 1 | 3 | yes | — |
| 29 | #127×D61 | C22 | 1 | 3 | yes | — |
| 30 | C4×#11758226 | C22 | 1 | 1 | yes | characteristic |
| 31 | C61×#550 | C4 | 1 | 1 | yes | characteristic |
| 32 | #14519865 | — | 4 | 4 | no | — |
| 33 | C2×#11758213 | — | 2 | 3 | no | — |
| 34 | C2×D61⋊C8 | — | 2 | 3 | no | — |
| 35 | C2×D61⋊C8 | — | 2 | 3 | no | — |
| 36 | #14519844 | — | 2 | 3 | no | — |
| 37 | #14519844 | C23 | 1 | 1 | yes | characteristic |
| 38 | #14519844 | C23 | 1 | 3 | yes | — |
| 39 | #14519844 | C23 | 1 | 3 | yes | — |
| 40 | #14519844 | C23 | 1 | 1 | yes | characteristic |
| 41 | C4⋊#92420 | — | 2 | 3 | no | — |
| 42 | C4⋊#92420 | — | 2 | 3 | no | — |
| 43 | #14519834 | — | 2 | 3 | no | — |
| 44 | C4×#92420 | — | 2 | 3 | no | — |
| 45 | #14519823 | — | 4 | 4 | no | — |
| 46 | #14519823 | — | 4 | 4 | no | — |
| 47 | C2×#11758226 | — | 2 | 1 | no | — |
| 48 | C2×#11758226 | D4 | 1 | 1 | yes | characteristic |
| 49 | C2×#11758222 | — | 2 | 3 | no | — |
| 50 | C22×D244 | — | 2 | 3 | no | — |
| 51 | C2×D4×D61 | — | 2 | 3 | no | — |
| 52 | C2×D4×D61 | — | 2 | 3 | no | — |
| 53 | C2×D4×D61 | — | 2 | 3 | no | — |
| 54 | C2×D4×D61 | C2×C4 | 1 | 6 | yes | — |
| 55 | #14519776 | C23 | 1 | 1 | yes | characteristic |
| 56 | #14519774 | C2×C4 | 1 | 3 | yes | — |
| 57 | #14519773 | — | 2 | 3 | no | — |
| 58 | #14519773 | — | 2 | 3 | no | — |
| 59 | #14519773 | C23 | 1 | 3 | yes | — |
| 60 | #14519763 | — | 2 | 3 | no | — |
| 61 | #14519752 | — | 2 | 3 | no | — |
| 62 | #14519752 | C2×C4 | 1 | 3 | yes | — |
| 63 | #14519751 | — | 2 | 3 | no | — |
| 64 | #14519750 | — | 2 | 3 | no | — |
| 65 | #14519748 | — | 2 | 3 | no | — |
| 66 | #14519748 | C2×C4 | 1 | 3 | yes | — |
| 67 | #14519747 | — | 2 | 6 | no | — |
| 68 | #14519745 | — | 2 | 6 | no | — |
| 69 | Q8×Dic61 | D4 | 1 | 1 | yes | characteristic |
| 70 | C4×D244 | C2×C4 | 1 | 3 | yes | — |
| 71 | C4×D244 | C2×C4 | 1 | 3 | yes | — |
| 72 | #14519739 | D4 | 1 | 3 | yes | — |
| 73 | C4×C22⋊D61 | — | 2 | 3 | no | — |
| 74 | #14519735 | D4 | 1 | 3 | yes | — |
| 75 | C42×D61 | C23 | 1 | 3 | yes | — |
| 76 | C2×#41×C61 | — | 2 | 1 | no | — |
| 77 | #127×C61 | C2×C4 | 1 | 3 | yes | — |
| 78 | #121×C61 | — | 2 | 3 | no | — |
| 79 | C4×Q8×C61 | C2×C4 | 1 | 1 | yes | characteristic |
| 80 | C4×D4×C61 | C2×C4 | 1 | 3 | yes | — |
| 81 | C23×D61 | — | 2 | 6 | no | — |
| 82 | #41×C61 | — | 4 | 4 | no | — |
| 83 | C2×Q8×C61 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 84 | C2×D4×C61 | — | 2 | 3 | no | — |
| 85 | C2×D4×C61 | — | 2 | 3 | no | — |
| 86 | C2×D4×C61 | C22×C4 | 1 | 3 | yes | — |
| 87 | C22×C4×C61 | — | 2 | 3 | no | — |
| 88 | C2×C22⋊D61 | — | 2 | 3 | no | — |
| 89 | C2×C22⋊D61 | — | 2 | 6 | no | — |
| 90 | C2×C22⋊D61 | — | 2 | 3 | no | — |
| 91 | C2×C22⋊D61 | — | 2 | 3 | no | — |
| 92 | #11758226 | — | 4 | 4 | no | — |
| 93 | #11758226 | D8 | 1 | 4 | yes | — |
| 94 | #11758226 | SD16 | 1 | 4 | yes | — |
| 95 | D4×D61 | — | 4 | 12 | no | — |
| 96 | D4×D61 | — | 4 | 6 | no | — |
| 97 | D4×D61 | — | 4 | 6 | no | — |
| 98 | D4×D61 | — | 8 | 3 | no | — |
| 99 | D4×D61 | — | 8 | 3 | no | — |
| 100 | D4×D61 | — | 8 | 6 | no | — |
| 101 | #11758222 | — | 4 | 6 | no | — |
| 102 | #11758222 | — | 4 | 6 | no | — |
| 103 | C2×D244 | — | 2 | 3 | no | — |
| 104 | C2×D244 | — | 2 | 3 | no | — |
| 105 | C2×D244 | — | 2 | 3 | no | — |
| 106 | C2×D244 | — | 4 | 12 | no | — |
| 107 | C2×D244 | C22⋊C4 | 1 | 3 | yes | — |
| 108 | C2×D244 | C22×C4 | 1 | 3 | yes | — |
| 109 | C2×C4×D61 | — | 2 | 3 | no | — |
| 110 | C2×C4×D61 | C22×C4 | 1 | 3 | yes | — |
| 111 | C2×C4×D61 | C2×D4 | 1 | 3 | yes | — |
| 112 | C2×C4×D61 | C2×D4 | 1 | 3 | yes | — |
| 113 | C2×Dic122 | — | 2 | 1 | no | — |
| 114 | C2×#92420 | — | 2 | 1 | no | — |
| 115 | C2×#92420 | — | 2 | 3 | no | — |
| 116 | C2×#92420 | — | 2 | 1 | no | — |
| 117 | C2×#92420 | — | 2 | 3 | no | — |
| 118 | #11758213 | — | 4 | 6 | no | — |
| 119 | D61⋊C8 | — | 4 | 6 | no | — |
| 120 | D61⋊C8 | — | 8 | 3 | no | — |
| 121 | C4⋊C4×C61 | C22⋊C4 | 1 | 3 | yes | — |
| 122 | C4⋊C4×C61 | C22×C4 | 1 | 1 | yes | characteristic |
| 123 | C22⋊C4×C61 | — | 2 | 3 | no | — |
| 124 | C42×C61 | C22×C4 | 1 | 3 | yes | — |
| 125 | C22⋊Dic61 | — | 2 | 3 | no | — |
| 126 | #11758198 | — | 2 | 3 | no | — |
| 127 | #11758198 | — | 2 | 3 | no | — |
| 128 | #11758198 | C22⋊C4 | 1 | 6 | yes | — |
| 129 | C4⋊Dic61 | C22⋊C4 | 1 | 3 | yes | — |
| 130 | C4⋊Dic61 | C22×C4 | 1 | 1 | yes | characteristic |
| 131 | #11758196 | — | 2 | 1 | no | — |
| 132 | C4×Dic61 | C2×D4 | 1 | 3 | yes | — |
| 133 | C4×Dic61 | C2×D4 | 1 | 3 | yes | — |
| 134 | C4×Dic61 | C24 | 1 | 1 | yes | characteristic |
| 135 | C23×C61 | — | 2 | 3 | no | — |
| 136 | C22×D61 | — | 2 | 3 | no | — |
| 137 | C22×D61 | — | 4 | 12 | no | — |
| 138 | C22×D61 | — | 8 | 6 | no | — |
| 139 | C22×D61 | — | 8 | 6 | no | — |
| 140 | C22×D61 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 141 | Q8×C61 | #102 | 1 | 4 | yes | — |
| 142 | D4×C61 | — | 4 | 3 | no | — |
| 143 | D4×C61 | — | 4 | 6 | no | — |
| 144 | D4×C61 | — | 8 | 3 | no | — |
| 145 | C2×C4×C61 | — | 2 | 1 | no | — |
| 146 | C2×C4×C61 | — | 4 | 6 | no | — |
| 147 | C2×C4×C61 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 148 | C2×C4×C61 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 149 | C2×C4×C61 | C23×C4 | 1 | 1 | yes | characteristic |
| 150 | C22⋊D61 | — | 4 | 6 | no | — |
| 151 | C22⋊D61 | — | 4 | 3 | no | — |
| 152 | C22⋊D61 | — | 4 | 3 | no | — |
| 153 | C22⋊D61 | — | 4 | 3 | no | — |
| 154 | C22⋊D61 | — | 4 | 3 | no | — |
| 155 | C22⋊D61 | — | 8 | 6 | no | — |
| 156 | C2×Dic61 | — | 2 | 1 | no | — |
| 157 | C2×Dic61 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 158 | C2×Dic61 | C22×D4 | 1 | 1 | yes | characteristic |
| 159 | C2×Dic61 | C22×D4 | 1 | 1 | yes | characteristic |
| 160 | D244 | — | 4 | 3 | no | — |
| 161 | D244 | — | 4 | 6 | no | — |
| 162 | D244 | — | 4 | 6 | no | — |
| 163 | D244 | — | 8 | 3 | no | — |
| 164 | D244 | #102 | 1 | 12 | yes | — |
| 165 | C4×D61 | — | 2 | 3 | no | — |
| 166 | C4×D61 | — | 2 | 3 | no | — |
| 167 | C4×D61 | — | 4 | 3 | no | — |
| 168 | C4×D61 | — | 4 | 6 | no | — |
| 169 | C4×D61 | C2×D8 | 1 | 6 | yes | — |
| 170 | C4×D61 | C2×SD16 | 1 | 6 | yes | — |
| 171 | Dic122 | — | 4 | 1 | no | — |
| 172 | Dic122 | — | 4 | 1 | no | — |
| 173 | #92420 | — | 4 | 1 | no | — |
| 174 | #92420 | — | 4 | 3 | no | — |
| 175 | #92420 | — | 4 | 3 | no | — |
| 176 | #92420 | — | 4 | 1 | no | — |
| 177 | #17720 | — | 61 | 1 | no | maximal, Sylow |
| 178 | C22×C61 | — | 4 | 3 | no | — |
| 179 | C22×C61 | — | 4 | 3 | no | — |
| 180 | C22×C61 | — | 4 | 3 | no | — |
| 181 | C22×C61 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 182 | C2×D61 | — | 2 | 3 | no | — |
| 183 | C2×D61 | — | 2 | 3 | no | — |
| 184 | C2×D61 | — | 4 | 3 | no | — |
| 185 | C2×D61 | — | 4 | 3 | no | — |
| 186 | C2×D61 | — | 4 | 3 | no | — |
| 187 | C2×D61 | — | 16 | 12 | no | — |
| 188 | C2×D61 | C2×#102 | 1 | 6 | yes | — |
| 189 | C4×C61 | — | 2 | 1 | no | — |
| 190 | C4×C61 | — | 2 | 3 | no | — |
| 191 | C4×C61 | — | 4 | 1 | no | — |
| 192 | C4×C61 | C2×#102 | 1 | 6 | yes | — |
| 193 | Dic61 | — | 2 | 3 | no | — |
| 194 | Dic61 | — | 4 | 1 | no | — |
| 195 | Dic61 | C22×D8 | 1 | 1 | yes | characteristic |
| 196 | Dic61 | C22×SD16 | 1 | 1 | yes | characteristic |
| 197 | Dic61 | #576 | 1 | 1 | yes | characteristic |
| 198 | Dic61 | #577 | 1 | 1 | yes | characteristic |
| 199 | #3498 | — | 61 | 1 | no | — |
| 200 | #2988 | — | 61 | 1 | no | — |
| 201 | #2906 | — | 61 | 1 | no | — |
| 202 | #1547 | — | 61 | 3 | no | — |
| 203 | #1545 | — | 61 | 3 | no | — |
| 204 | #1540 | — | 61 | 3 | no | — |
| 205 | C2×#331 | — | 61 | 3 | no | — |
| 206 | C2×C61 | — | 8 | 3 | no | — |
| 207 | C2×C61 | #2888 | 1 | 1 | yes | characteristic |
| 208 | C2×C61 | C22×#102 | 1 | 1 | yes | characteristic |
| 209 | C2×C61 | #2897 | 1 | 1 | yes | characteristic |
| 210 | D61 | — | 2 | 6 | no | — |
| 211 | D61 | — | 8 | 3 | no | — |
| 212 | C2×H(5,𝔽2) | — | 122 | 1 | no | — |
| 213 | C2×#131 | — | 122 | 1 | no | — |
| 214 | #550 | — | 61 | 1 | no | — |
| 215 | #550 | — | 122 | 1 | no | — |
| 216 | #550 | #6923 | 1 | 1 | yes | characteristic |
| 217 | D42 | — | 61 | 3 | no | — |
| 218 | D42 | — | 61 | 3 | no | — |
| 219 | D42 | — | 122 | 3 | no | — |
| 220 | #535 | — | 122 | 3 | no | — |
| 221 | #532 | — | 61 | 3 | no | — |
| 222 | C2×#127 | — | 61 | 3 | no | — |
| 223 | C4×#41 | — | 61 | 1 | no | — |
| 224 | C8×Q8 | — | 122 | 1 | no | — |
| 225 | C8×D4 | — | 122 | 3 | no | — |
| 226 | #431 | — | 61 | 3 | no | — |
| 227 | #424 | — | 122 | 3 | no | — |
| 228 | #423 | — | 61 | 3 | no | — |
| 229 | C2×C4⋊C8 | — | 61 | 3 | no | — |
| 230 | C2×C4⋊C8 | — | 61 | 3 | no | — |
| 231 | #332 | — | 61 | 1 | no | — |
| 232 | #332 | — | 61 | 3 | no | — |
| 233 | #331 | — | 61 | 3 | no | — |
| 234 | #331 | — | 61 | 6 | no | — |
| 235 | #331 | — | 61 | 3 | no | — |
| 236 | C61 | #17720 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 237 | H(5,𝔽2) | — | 244 | 4 | no | — |
| 238 | H(5,𝔽2) | — | 244 | 4 | no | — |
| 239 | C2×#41 | — | 2 | 1 | no | — |
| 240 | C2×#41 | — | 61 | 1 | no | — |
| 241 | C2×#41 | — | 122 | 3 | no | — |
| 242 | C2×#41 | — | 122 | 1 | no | — |
| 243 | C22×D4 | — | 61 | 6 | no | — |
| 244 | C22×D4 | — | 122 | 3 | no | — |
| 245 | C22×D4 | — | 122 | 3 | no | — |
| 246 | C22×D4 | — | 122 | 3 | no | — |
| 247 | C22×D4 | — | 122 | 3 | no | — |
| 248 | #131 | — | 244 | 4 | no | — |
| 249 | C2×M16 | — | 122 | 3 | no | — |
| 250 | C22×C8 | — | 122 | 3 | no | — |
| 251 | C22×C8 | — | 122 | 3 | no | — |
| 252 | C4⋊Q8 | — | 61 | 1 | no | — |
| 253 | #127 | — | 61 | 3 | no | — |
| 254 | #127 | — | 61 | 3 | no | — |
| 255 | #127 | — | 122 | 3 | no | — |
| 256 | #127 | — | 122 | 3 | no | — |
| 257 | #127 | C2×#6923 | 1 | 3 | yes | — |
| 258 | #124 | — | 122 | 3 | no | — |
| 259 | #121 | — | 2 | 3 | no | — |
| 260 | #121 | — | 61 | 3 | no | — |
| 261 | #121 | — | 61 | 3 | no | — |
| 262 | #121 | — | 122 | 3 | no | — |
| 263 | #121 | — | 122 | 3 | no | — |
| 264 | #121 | — | 122 | 3 | no | — |
| 265 | #121 | — | 122 | 3 | no | — |
| 266 | #120 | — | 122 | 6 | no | — |
| 267 | #120 | — | 122 | 6 | no | — |
| 268 | C4×Q8 | — | 61 | 1 | no | — |
| 269 | C4×Q8 | C2×#6923 | 1 | 1 | yes | characteristic |
| 270 | C4×D4 | — | 61 | 3 | no | — |
| 271 | C4×D4 | — | 61 | 3 | no | — |
| 272 | C4×D4 | — | 61 | 3 | no | — |
| 273 | C4×D4 | — | 122 | 3 | no | — |
| 274 | C4×D4 | C2×#6923 | 1 | 3 | yes | — |
| 275 | #117 | — | 61 | 3 | no | — |
| 276 | C2×C42 | — | 61 | 3 | no | — |
| 277 | C4⋊C8 | — | 61 | 1 | no | — |
| 278 | C4⋊C8 | — | 61 | 3 | no | — |
| 279 | C4⋊C8 | — | 61 | 3 | no | — |
| 280 | C4⋊C8 | — | 61 | 1 | no | — |
| 281 | C4⋊C8 | — | 122 | 3 | no | — |
| 282 | C4⋊C8 | — | 122 | 3 | no | — |
| 283 | C4⋊C8 | — | 122 | 3 | no | — |
| 284 | C22⋊C8 | — | 122 | 3 | no | — |
| 285 | C4×C8 | — | 122 | 3 | no | — |
| 286 | C24 | — | 122 | 6 | no | — |
| 287 | #41 | — | 4 | 4 | no | — |
| 288 | #41 | — | 61 | 4 | no | — |
| 289 | #41 | — | 61 | 4 | no | — |
| 290 | #41 | — | 244 | 6 | no | — |
| 291 | #41 | — | 244 | 6 | no | — |
| 292 | #41 | — | 244 | 4 | no | — |
| 293 | C2×Q8 | — | 122 | 1 | no | — |
| 294 | C2×Q8 | C22⋊#6923 | 1 | 1 | yes | characteristic |
| 295 | C2×D4 | — | 2 | 3 | no | — |
| 296 | C2×D4 | — | 2 | 3 | no | — |
| 297 | C2×D4 | — | 61 | 3 | no | — |
| 298 | C2×D4 | — | 61 | 3 | no | — |
| 299 | C2×D4 | — | 122 | 3 | no | — |
| 300 | C2×D4 | — | 122 | 6 | no | — |
| 301 | C2×D4 | — | 122 | 3 | no | — |
| 302 | C2×D4 | — | 122 | 3 | no | — |
| 303 | C2×D4 | — | 122 | 3 | no | — |
| 304 | C2×D4 | — | 122 | 3 | no | — |
| 305 | C2×D4 | — | 122 | 3 | no | — |
| 306 | C2×D4 | — | 488 | 3 | no | — |
| 307 | C2×D4 | — | 488 | 3 | no | — |
| 308 | C2×D4 | — | 488 | 6 | no | — |
| 309 | C2×D4 | — | 244 | 12 | no | — |
| 310 | C2×D4 | — | 244 | 6 | no | — |
| 311 | C2×D4 | — | 244 | 6 | no | — |
| 312 | C2×D4 | — | 244 | 12 | no | — |
| 313 | C2×D4 | C22×#6923 | 1 | 3 | yes | — |
| 314 | C22×C4 | — | 2 | 3 | no | — |
| 315 | C22×C4 | — | 61 | 3 | no | — |
| 316 | C22×C4 | — | 61 | 3 | no | — |
| 317 | C22×C4 | — | 61 | 3 | no | — |
| 318 | C22×C4 | — | 122 | 3 | no | — |
| 319 | M16 | — | 244 | 6 | no | — |
| 320 | C2×C8 | — | 122 | 1 | no | — |
| 321 | C2×C8 | — | 122 | 3 | no | — |
| 322 | C2×C8 | — | 122 | 1 | no | — |
| 323 | C2×C8 | — | 122 | 3 | no | — |
| 324 | C2×C8 | — | 488 | 3 | no | — |
| 325 | C2×C8 | — | 244 | 6 | no | — |
| 326 | C4⋊C4 | — | 61 | 3 | no | — |
| 327 | C4⋊C4 | — | 61 | 1 | no | — |
| 328 | C4⋊C4 | — | 122 | 1 | no | — |
| 329 | C4⋊C4 | C22⋊#6923 | 1 | 3 | yes | — |
| 330 | C4⋊C4 | C22×#6923 | 1 | 1 | yes | characteristic |
| 331 | C22⋊C4 | — | 2 | 3 | no | — |
| 332 | C22⋊C4 | — | 61 | 6 | no | — |
| 333 | C22⋊C4 | — | 122 | 3 | no | — |
| 334 | C22⋊C4 | — | 122 | 3 | no | — |
| 335 | C22⋊C4 | — | 122 | 3 | no | — |
| 336 | C42 | — | 61 | 3 | no | — |
| 337 | C42 | — | 61 | 3 | no | — |
| 338 | C42 | — | 61 | 1 | no | — |
| 339 | C42 | C22×#6923 | 1 | 3 | yes | — |
| 340 | C23 | — | 2 | 3 | no | — |
| 341 | C23 | — | 61 | 3 | no | — |
| 342 | C23 | — | 122 | 3 | no | — |
| 343 | C23 | — | 488 | 6 | no | — |
| 344 | C23 | — | 488 | 6 | no | — |
| 345 | C23 | — | 244 | 12 | no | — |
| 346 | Q8 | — | 244 | 1 | no | — |
| 347 | Q8 | — | 244 | 1 | no | — |
| 348 | Q8 | #14519839 | 1 | 4 | yes | — |
| 349 | D4 | — | 4 | 3 | no | — |
| 350 | D4 | — | 4 | 6 | no | — |
| 351 | D4 | — | 8 | 3 | no | — |
| 352 | D4 | — | 61 | 12 | no | — |
| 353 | D4 | — | 488 | 3 | no | — |
| 354 | D4 | — | 488 | 6 | no | — |
| 355 | D4 | — | 244 | 3 | no | — |
| 356 | D4 | — | 244 | 6 | no | — |
| 357 | D4 | — | 244 | 3 | no | — |
| 358 | D4 | — | 244 | 3 | no | — |
| 359 | D4 | — | 244 | 3 | no | — |
| 360 | D4 | — | 244 | 3 | no | — |
| 361 | D4 | — | 244 | 6 | no | — |
| 362 | D4 | — | 244 | 6 | no | — |
| 363 | C2×C4 | — | 2 | 1 | no | — |
| 364 | C2×C4 | — | 4 | 6 | no | — |
| 365 | C2×C4 | — | 61 | 1 | no | — |
| 366 | C2×C4 | — | 61 | 1 | no | — |
| 367 | C2×C4 | — | 61 | 6 | no | — |
| 368 | C2×C4 | — | 61 | 6 | no | — |
| 369 | C2×C4 | — | 61 | 3 | no | — |
| 370 | C2×C4 | — | 122 | 3 | no | — |
| 371 | C2×C4 | — | 122 | 3 | no | — |
| 372 | C2×C4 | — | 122 | 1 | no | — |
| 373 | C2×C4 | — | 244 | 3 | no | — |
| 374 | C2×C4 | — | 244 | 6 | no | — |
| 375 | C2×C4 | C2×C22⋊#6923 | 1 | 3 | yes | — |
| 376 | C2×C4 | C2×C22⋊#6923 | 1 | 3 | yes | — |
| 377 | C2×C4 | C23×#6923 | 1 | 1 | yes | characteristic |
| 378 | C8 | — | 244 | 1 | no | — |
| 379 | C8 | — | 244 | 3 | no | — |
| 380 | C8 | — | 244 | 1 | no | — |
| 381 | C8 | — | 244 | 3 | no | — |
| 382 | C22 | — | 4 | 3 | no | — |
| 383 | C22 | — | 4 | 3 | no | — |
| 384 | C22 | — | 4 | 3 | no | — |
| 385 | C22 | — | 61 | 6 | no | — |
| 386 | C22 | — | 122 | 3 | no | — |
| 387 | C22 | — | 122 | 3 | no | — |
| 388 | C22 | — | 976 | 12 | no | — |
| 389 | C22 | — | 244 | 3 | no | — |
| 390 | C22 | — | 244 | 3 | no | — |
| 391 | C22 | — | 244 | 3 | no | — |
| 392 | C22 | C22×C22⋊#6923 | 1 | 1 | yes | characteristic |
| 393 | C4 | — | 2 | 1 | no | — |
| 394 | C4 | — | 2 | 3 | no | — |
| 395 | C4 | — | 4 | 1 | no | — |
| 396 | C4 | — | 61 | 1 | no | — |
| 397 | C4 | — | 61 | 1 | no | — |
| 398 | C4 | — | 61 | 1 | no | — |
| 399 | C4 | — | 61 | 1 | no | — |
| 400 | C4 | — | 122 | 3 | no | — |
| 401 | C4 | — | 244 | 1 | no | — |
| 402 | C4 | C2×#14519839 | 1 | 6 | yes | — |
| 403 | C2 | — | 8 | 3 | no | — |
| 404 | C2 | — | 122 | 6 | no | — |
| 405 | C2 | — | 488 | 3 | no | — |
| 406 | C2 | #21462430 | 1 | 1 | yes | characteristic |
| 407 | C2 | C22×#14519839 | 1 | 1 | yes | characteristic |
| 408 | C2 | #21462440 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #21462737 | C2 | semidirect |
| 2. #21462467 | C2 | semidirect |
| 3. #21461330 | C2 | semidirect |
| 4. #21461327 | C2 | semidirect |
| 5. #21461316 | C2 | semidirect |
| 6. D61⋊#331 | C2 | semidirect |
| 11. #16840780 | C22 | semidirect |
| 13. #16840767 | C22 | semidirect |
| 14. D61⋊(C4⋊C8) | C22 | semidirect |
| 15. D61⋊(C4⋊C8) | C22 | semidirect |
| 16. #16840621 | C22 | semidirect |
| 17. #16840621 | C22 | semidirect |
| 18. #16840620 | C22 | semidirect |
| 19. #16840620 | C22 | semidirect |
| 20. #16840620 | C22 | semidirect |
| 236. C61 | #17720 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462737 | 2 |
| #21462467 | 2 |
| #21461330 | 2 |
| #21461327 | 2 |
| #21461316 | 2 |
| D61⋊#331 | 2 |
| #21459596 | 2 |
| #17720 | 61 |