← #30622673
Subgroups — #30622673
Order 15616.
638 conjugacy classes of subgroups.
The subgroup lattice has 378 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #21462617 | C2 | 1 | 2 | yes | maximal |
| 2 | #21461996 | C2 | 1 | 2 | yes | maximal |
| 3 | #21461926 | C2 | 1 | 2 | yes | maximal |
| 4 | #21461887 | C2 | 1 | 2 | yes | maximal |
| 5 | #21461884 | C2 | 1 | 2 | yes | maximal |
| 6 | C4×#14519847 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #21461622 | C2 | 1 | 2 | yes | maximal |
| 8 | C8×C4⋊#6923 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #21456332 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #16840814 | — | 2 | 2 | no | — |
| 11 | #16840814 | — | 2 | 2 | no | — |
| 12 | #16840812 | — | 2 | 2 | no | — |
| 13 | #16840811 | — | 2 | 2 | no | — |
| 14 | C2×#14519847 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×#14519847 | C22 | 1 | 1 | yes | characteristic |
| 16 | #16840769 | C22 | 1 | 2 | yes | — |
| 17 | #16840769 | C22 | 1 | 2 | yes | — |
| 18 | D61⋊(C4⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 19 | #16840727 | C22 | 1 | 2 | yes | — |
| 20 | #16840727 | C22 | 1 | 2 | yes | — |
| 21 | C4×#11758213 | C22 | 1 | 2 | yes | — |
| 22 | C2×C8×#6923 | C22 | 1 | 2 | yes | — |
| 23 | C4×C4⋊#6923 | C22 | 1 | 1 | yes | characteristic |
| 24 | #16840638 | C22 | 1 | 2 | yes | — |
| 25 | #16840632 | C22 | 1 | 2 | yes | — |
| 26 | #16840632 | C22 | 1 | 2 | yes | — |
| 27 | #16840632 | C22 | 1 | 2 | yes | — |
| 28 | #16840632 | C22 | 1 | 2 | yes | — |
| 29 | (C2×#6923)⋊C8 | C22 | 1 | 2 | yes | — |
| 30 | #16840318 | C22 | 1 | 2 | yes | — |
| 31 | #16840166 | C4 | 1 | 1 | yes | characteristic, complemented |
| 32 | #16840166 | C4 | 1 | 1 | yes | characteristic, complemented |
| 33 | #16840164 | C4 | 1 | 1 | yes | characteristic, complemented |
| 34 | #16840161 | C4 | 1 | 2 | yes | complemented |
| 35 | #16840159 | C4 | 1 | 2 | yes | complemented |
| 36 | #16839799 | C22 | 1 | 1 | yes | characteristic |
| 37 | #16839799 | C22 | 1 | 1 | yes | characteristic |
| 38 | #16839797 | C22 | 1 | 2 | yes | — |
| 39 | C4×C8×D61 | C22 | 1 | 1 | yes | characteristic |
| 40 | C61×#499 | C4 | 1 | 1 | yes | characteristic, complemented |
| 41 | C2×#11758213 | C23 | 1 | 2 | yes | — |
| 42 | C2×#11758213 | C23 | 1 | 2 | yes | — |
| 43 | C2×D61⋊C8 | C23 | 1 | 2 | yes | — |
| 44 | C2×C4⋊#6923 | — | 2 | 1 | no | — |
| 45 | C2×C4×#6923 | C23 | 1 | 2 | yes | — |
| 46 | #14519847 | — | 2 | 2 | no | — |
| 47 | #14519847 | Q8 | 1 | 4 | yes | complemented |
| 48 | #14519844 | — | 2 | 2 | no | — |
| 49 | #14519844 | — | 2 | 2 | no | — |
| 50 | #14519844 | D4 | 1 | 1 | yes | characteristic |
| 51 | #14519844 | D4 | 1 | 1 | yes | characteristic |
| 52 | C4⋊#92420 | — | 2 | 2 | no | — |
| 53 | C4⋊#92420 | — | 2 | 2 | no | — |
| 54 | C4⋊#92420 | D4 | 1 | 2 | yes | — |
| 55 | #14519832 | — | 2 | 2 | no | — |
| 56 | #14519832 | — | 2 | 2 | no | — |
| 57 | #14519832 | — | 2 | 2 | no | — |
| 58 | C4×#92420 | — | 2 | 2 | no | — |
| 59 | C4×#92420 | — | 2 | 2 | no | — |
| 60 | C4×#92420 | — | 2 | 2 | no | — |
| 61 | C8×#6923 | — | 2 | 4 | no | — |
| 62 | (C2×#6923)⋊C4 | — | 2 | 1 | no | — |
| 63 | C2×C8×D61 | C23 | 1 | 1 | yes | characteristic |
| 64 | C2×C8×D61 | C23 | 1 | 1 | yes | characteristic |
| 65 | #14519776 | C2×C4 | 1 | 2 | yes | — |
| 66 | #14519776 | C2×C4 | 1 | 2 | yes | — |
| 67 | #14519769 | C2×C4 | 1 | 2 | yes | — |
| 68 | #14519755 | — | 2 | 2 | no | — |
| 69 | #14519755 | — | 2 | 2 | no | — |
| 70 | #14519742 | — | 2 | 2 | no | — |
| 71 | #14519742 | — | 2 | 2 | no | — |
| 72 | #14519735 | C23 | 1 | 2 | yes | — |
| 73 | #14519735 | C23 | 1 | 2 | yes | — |
| 74 | C42×D61 | C23 | 1 | 1 | yes | characteristic |
| 75 | #14519711 | C2×C4 | 1 | 1 | yes | characteristic |
| 76 | #14519711 | C2×C4 | 1 | 1 | yes | characteristic |
| 77 | #14519710 | C2×C4 | 1 | 2 | yes | — |
| 78 | #14519710 | C2×C4 | 1 | 2 | yes | — |
| 79 | #14519709 | C2×C4 | 1 | 2 | yes | — |
| 80 | #14519708 | C2×C4 | 1 | 2 | yes | — |
| 81 | #14519708 | C2×C4 | 1 | 2 | yes | — |
| 82 | C4×#92418 | C2×C4 | 1 | 1 | yes | characteristic |
| 83 | C8×Dic61 | C2×C4 | 1 | 1 | yes | characteristic |
| 84 | C8×Dic61 | C2×C4 | 1 | 1 | yes | characteristic |
| 85 | #125×C61 | C2×C4 | 1 | 2 | yes | — |
| 86 | #107×C61 | C2×C4 | 1 | 1 | yes | characteristic |
| 87 | #107×C61 | C2×C4 | 1 | 1 | yes | characteristic |
| 88 | #106×C61 | C2×C4 | 1 | 2 | yes | — |
| 89 | C4×C8×C61 | C2×C4 | 1 | 1 | yes | characteristic |
| 90 | C22×#6923 | — | 2 | 2 | no | — |
| 91 | C2×C4×D61 | #41 | 1 | 1 | yes | characteristic |
| 92 | C2×C4×D61 | #41 | 1 | 1 | yes | characteristic |
| 93 | C2×C4×D61 | C24 | 1 | 1 | yes | characteristic |
| 94 | C2×Dic122 | — | 2 | 2 | no | — |
| 95 | C2×Dic122 | — | 2 | 2 | no | — |
| 96 | C2×#92420 | — | 2 | 2 | no | — |
| 97 | C2×#92420 | — | 2 | 2 | no | — |
| 98 | C2×#92420 | C2×D4 | 1 | 2 | yes | — |
| 99 | C2×#92420 | C2×D4 | 1 | 2 | yes | — |
| 100 | C4⋊#6923 | — | 2 | 4 | no | — |
| 101 | C4×#6923 | — | 2 | 2 | no | — |
| 102 | C4×#6923 | — | 2 | 2 | no | — |
| 103 | #11758213 | — | 2 | 2 | no | — |
| 104 | #11758213 | — | 2 | 2 | no | — |
| 105 | #11758213 | — | 2 | 2 | no | — |
| 106 | #11758213 | C2×Q8 | 1 | 4 | yes | — |
| 107 | D61⋊C8 | — | 2 | 2 | no | — |
| 108 | D61⋊C8 | — | 2 | 2 | no | — |
| 109 | C2×C8×C61 | C22×C4 | 1 | 1 | yes | characteristic |
| 110 | C2×C8×C61 | C22×C4 | 1 | 1 | yes | characteristic |
| 111 | C4⋊C4×C61 | — | 2 | 2 | no | — |
| 112 | C4⋊C4×C61 | — | 2 | 2 | no | — |
| 113 | C4⋊C4×C61 | C22×C4 | 1 | 2 | yes | — |
| 114 | C4⋊C4×C61 | C22×C4 | 1 | 2 | yes | — |
| 115 | C42×C61 | C22×C4 | 1 | 1 | yes | characteristic |
| 116 | #11758198 | — | 2 | 2 | no | — |
| 117 | #11758198 | — | 2 | 2 | no | — |
| 118 | C4⋊Dic61 | C22×C4 | 1 | 2 | yes | — |
| 119 | C4⋊Dic61 | C22×C4 | 1 | 2 | yes | — |
| 120 | #11758196 | — | 2 | 2 | no | — |
| 121 | #11758196 | — | 2 | 2 | no | — |
| 122 | #11758196 | — | 2 | 2 | no | — |
| 123 | #11758196 | — | 2 | 2 | no | — |
| 124 | C4×Dic61 | — | 2 | 2 | no | — |
| 125 | C4×Dic61 | — | 2 | 2 | no | — |
| 126 | C4×Dic61 | C22×C4 | 1 | 1 | yes | characteristic |
| 127 | C4×Dic61 | C2×D4 | 1 | 1 | yes | characteristic |
| 128 | C4×Dic61 | C2×D4 | 1 | 1 | yes | characteristic |
| 129 | C2×#92418 | C22×C4 | 1 | 1 | yes | characteristic |
| 130 | C2×#92418 | C22×C4 | 1 | 1 | yes | characteristic |
| 131 | C8×D61 | — | 2 | 1 | no | — |
| 132 | C8×D61 | — | 2 | 1 | no | — |
| 133 | C8×D61 | C2×Q8 | 1 | 2 | yes | — |
| 134 | C8×D61 | #41 | 1 | 2 | yes | — |
| 135 | C22×D61 | C2×#41 | 1 | 1 | yes | characteristic |
| 136 | C2×#6923 | — | 2 | 4 | no | — |
| 137 | C2×#6923 | — | 4 | 2 | no | — |
| 138 | C2×#6923 | — | 4 | 2 | no | — |
| 139 | C2×C4×C61 | — | 2 | 2 | no | — |
| 140 | C2×C4×C61 | — | 2 | 2 | no | — |
| 141 | C2×C4×C61 | C4×D4 | 1 | 1 | yes | characteristic |
| 142 | C2×C4×C61 | C4×D4 | 1 | 1 | yes | characteristic |
| 143 | C2×C4×C61 | C23×C4 | 1 | 1 | yes | characteristic |
| 144 | C2×Dic61 | — | 2 | 2 | no | — |
| 145 | C2×Dic61 | — | 2 | 2 | no | — |
| 146 | C2×Dic61 | C4×D4 | 1 | 1 | yes | characteristic |
| 147 | C2×Dic61 | C4×D4 | 1 | 1 | yes | characteristic |
| 148 | C2×Dic61 | C22×D4 | 1 | 1 | yes | characteristic |
| 149 | C4×D61 | — | 2 | 2 | no | — |
| 150 | C4×D61 | — | 4 | 1 | no | — |
| 151 | C4×D61 | C22×Q8 | 1 | 1 | yes | characteristic |
| 152 | C4×D61 | C2×#41 | 1 | 1 | yes | characteristic |
| 153 | C4×D61 | 2−1+4 | 1 | 1 | yes | characteristic |
| 154 | C4×D61 | 2−1+4 | 1 | 1 | yes | characteristic |
| 155 | Dic122 | — | 4 | 4 | no | — |
| 156 | Dic122 | — | 8 | 2 | no | — |
| 157 | #92420 | — | 2 | 2 | no | — |
| 158 | #92420 | — | 2 | 2 | no | — |
| 159 | #92420 | — | 2 | 4 | no | — |
| 160 | #92420 | — | 4 | 2 | no | — |
| 161 | C8×C61 | — | 2 | 1 | no | — |
| 162 | C8×C61 | C4×Q8 | 1 | 2 | yes | — |
| 163 | #92418 | — | 2 | 1 | no | — |
| 164 | #92418 | C4×Q8 | 1 | 2 | yes | — |
| 165 | #23170 | — | 61 | 1 | no | maximal, Sylow |
| 166 | C22×C61 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 167 | C2×D61 | — | 2 | 1 | no | — |
| 168 | C2×D61 | — | 2 | 1 | no | — |
| 169 | C2×D61 | #556 | 1 | 1 | yes | characteristic |
| 170 | C2×D61 | #557 | 1 | 1 | yes | characteristic |
| 171 | #6923 | — | 4 | 4 | no | — |
| 172 | C4×C61 | — | 2 | 1 | no | — |
| 173 | C4×C61 | — | 2 | 1 | no | — |
| 174 | C4×C61 | — | 4 | 2 | no | — |
| 175 | C4×C61 | — | 4 | 2 | no | — |
| 176 | C4×C61 | C2×C4×Q8 | 1 | 1 | yes | characteristic |
| 177 | C4×C61 | #519 | 1 | 1 | yes | characteristic |
| 178 | Dic61 | — | 2 | 1 | no | — |
| 179 | Dic61 | — | 4 | 2 | no | — |
| 180 | Dic61 | — | 4 | 2 | no | — |
| 181 | Dic61 | #443 | 1 | 2 | yes | — |
| 182 | Dic61 | #547 | 1 | 1 | yes | characteristic |
| 183 | Dic61 | D4×Q8 | 1 | 1 | yes | characteristic |
| 184 | #3160 | — | 61 | 1 | no | — |
| 185 | #2962 | — | 61 | 2 | no | — |
| 186 | #1986 | — | 61 | 2 | no | — |
| 187 | #1945 | — | 61 | 2 | no | — |
| 188 | #1922 | — | 61 | 2 | no | — |
| 189 | #1922 | — | 61 | 2 | no | — |
| 190 | C4×#108 | — | 61 | 1 | no | — |
| 191 | #1772 | — | 61 | 2 | no | — |
| 192 | C8×C4⋊C4 | — | 61 | 1 | no | — |
| 193 | C2×C61 | #2365 | 1 | 1 | yes | characteristic |
| 194 | C2×C61 | C2×#443 | 1 | 1 | yes | characteristic |
| 195 | C2×C61 | #2957 | 1 | 1 | yes | characteristic |
| 196 | D61 | — | 2 | 1 | no | — |
| 197 | D61 | — | 2 | 1 | no | — |
| 198 | #533 | — | 61 | 2 | no | — |
| 199 | #500 | — | 61 | 1 | no | — |
| 200 | #500 | — | 61 | 1 | no | — |
| 201 | #499 | — | 61 | 2 | no | — |
| 202 | #499 | — | 61 | 1 | no | — |
| 203 | #499 | #6923 | 1 | 1 | yes | characteristic, complemented |
| 204 | #498 | — | 61 | 2 | no | — |
| 205 | #446 | — | 122 | 2 | no | — |
| 206 | #446 | — | 122 | 2 | no | — |
| 207 | #446 | — | 122 | 2 | no | — |
| 208 | C8×Q8 | — | 122 | 2 | no | — |
| 209 | C2×#108 | — | 61 | 1 | no | — |
| 210 | C2×#108 | — | 61 | 1 | no | — |
| 211 | #427 | — | 61 | 1 | no | — |
| 212 | #427 | — | 61 | 1 | no | — |
| 213 | #427 | — | 61 | 2 | no | — |
| 214 | #424 | — | 61 | 2 | no | — |
| 215 | #424 | — | 61 | 2 | no | — |
| 216 | C2×C4⋊C8 | — | 61 | 1 | no | — |
| 217 | #405 | — | 61 | 2 | no | — |
| 218 | #405 | — | 61 | 2 | no | — |
| 219 | C4×M16 | — | 61 | 2 | no | — |
| 220 | C2×C4×C8 | — | 61 | 1 | no | — |
| 221 | C2×C4×C8 | — | 61 | 2 | no | — |
| 222 | C4×C4⋊C4 | — | 61 | 1 | no | — |
| 223 | #341 | — | 61 | 2 | no | — |
| 224 | #339 | — | 61 | 2 | no | — |
| 225 | #339 | — | 61 | 2 | no | — |
| 226 | #339 | — | 61 | 2 | no | — |
| 227 | #339 | — | 61 | 2 | no | — |
| 228 | #336 | — | 61 | 2 | no | — |
| 229 | C61 | #23170 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 230 | C2×M16 | — | 61 | 2 | no | — |
| 231 | C2×M16 | — | 61 | 2 | no | — |
| 232 | C22×C8 | — | 61 | 1 | no | — |
| 233 | C22×C8 | — | 61 | 2 | no | — |
| 234 | C22×C8 | — | 61 | 1 | no | — |
| 235 | C4⋊Q8 | — | 61 | 2 | no | — |
| 236 | C4⋊Q8 | — | 61 | 2 | no | — |
| 237 | #125 | — | 61 | 2 | no | — |
| 238 | #125 | C2×#6923 | 1 | 2 | yes | — |
| 239 | C22⋊Q8 | — | 122 | 2 | no | — |
| 240 | C22⋊Q8 | — | 122 | 2 | no | — |
| 241 | C4×Q8 | — | 122 | 2 | no | — |
| 242 | C4×Q8 | — | 122 | 2 | no | — |
| 243 | #117 | — | 61 | 2 | no | — |
| 244 | #117 | — | 61 | 2 | no | — |
| 245 | C2×C4⋊C4 | — | 122 | 1 | no | — |
| 246 | C2×C42 | — | 61 | 1 | no | — |
| 247 | C2×C42 | — | 61 | 2 | no | — |
| 248 | #108 | — | 61 | 4 | no | — |
| 249 | #108 | — | 122 | 2 | no | — |
| 250 | #107 | — | 61 | 1 | no | — |
| 251 | #107 | — | 61 | 1 | no | — |
| 252 | #107 | — | 61 | 2 | no | — |
| 253 | #107 | — | 61 | 2 | no | — |
| 254 | #107 | C2×#6923 | 1 | 1 | yes | characteristic |
| 255 | #107 | C2×#6923 | 1 | 1 | yes | characteristic |
| 256 | #106 | — | 61 | 2 | no | — |
| 257 | #106 | — | 61 | 2 | no | — |
| 258 | #106 | — | 61 | 2 | no | — |
| 259 | #106 | C2×#6923 | 1 | 2 | yes | — |
| 260 | C4⋊C8 | — | 61 | 2 | no | — |
| 261 | C4⋊C8 | — | 61 | 1 | no | — |
| 262 | C4⋊C8 | — | 61 | 1 | no | — |
| 263 | C4⋊C8 | — | 122 | 2 | no | — |
| 264 | C4⋊C8 | — | 122 | 2 | no | — |
| 265 | C4⋊C8 | — | 122 | 2 | no | — |
| 266 | C4⋊C8 | — | 122 | 2 | no | — |
| 267 | #97 | — | 122 | 2 | no | — |
| 268 | #97 | — | 122 | 2 | no | — |
| 269 | #97 | — | 122 | 2 | no | — |
| 270 | C4×C8 | — | 61 | 1 | no | — |
| 271 | C4×C8 | — | 61 | 1 | no | — |
| 272 | C4×C8 | — | 61 | 1 | no | — |
| 273 | C4×C8 | — | 122 | 2 | no | — |
| 274 | C4×C8 | — | 122 | 4 | no | — |
| 275 | C4×C8 | — | 122 | 2 | no | — |
| 276 | C4×C8 | — | 122 | 2 | no | — |
| 277 | C4×C8 | C2×#6923 | 1 | 1 | yes | characteristic |
| 278 | #95 | — | 122 | 1 | no | — |
| 279 | C2×Q8 | — | 122 | 2 | no | — |
| 280 | C2×Q8 | — | 122 | 2 | no | — |
| 281 | C22×C4 | — | 61 | 1 | no | — |
| 282 | C22×C4 | — | 61 | 1 | no | — |
| 283 | C22×C4 | — | 61 | 1 | no | — |
| 284 | C22×C4 | — | 122 | 2 | no | — |
| 285 | M16 | — | 61 | 4 | no | — |
| 286 | M16 | — | 122 | 2 | no | — |
| 287 | M16 | — | 122 | 2 | no | — |
| 288 | M16 | — | 122 | 2 | no | — |
| 289 | C2×C8 | — | 61 | 1 | no | — |
| 290 | C2×C8 | — | 61 | 2 | no | — |
| 291 | C2×C8 | — | 61 | 2 | no | — |
| 292 | C2×C8 | — | 61 | 2 | no | — |
| 293 | C2×C8 | — | 61 | 2 | no | — |
| 294 | C2×C8 | — | 61 | 1 | no | — |
| 295 | C2×C8 | — | 122 | 1 | no | — |
| 296 | C2×C8 | — | 122 | 1 | no | — |
| 297 | C2×C8 | — | 122 | 2 | no | — |
| 298 | C2×C8 | — | 122 | 2 | no | — |
| 299 | C2×C8 | — | 122 | 2 | no | — |
| 300 | C2×C8 | — | 122 | 2 | no | — |
| 301 | C2×C8 | C22×#6923 | 1 | 1 | yes | characteristic |
| 302 | C2×C8 | C22×#6923 | 1 | 1 | yes | characteristic |
| 303 | C4⋊C4 | — | 2 | 2 | no | — |
| 304 | C4⋊C4 | — | 2 | 2 | no | — |
| 305 | C4⋊C4 | — | 61 | 2 | no | — |
| 306 | C4⋊C4 | — | 61 | 2 | no | — |
| 307 | C4⋊C4 | — | 122 | 2 | no | — |
| 308 | C4⋊C4 | — | 122 | 2 | no | — |
| 309 | C4⋊C4 | — | 122 | 4 | no | — |
| 310 | C4⋊C4 | — | 122 | 2 | no | — |
| 311 | C4⋊C4 | — | 122 | 2 | no | — |
| 312 | C4⋊C4 | C22×#6923 | 1 | 2 | yes | — |
| 313 | C4⋊C4 | C22×#6923 | 1 | 2 | yes | — |
| 314 | C22⋊C4 | — | 122 | 2 | no | — |
| 315 | C22⋊C4 | — | 122 | 2 | no | — |
| 316 | C42 | — | 61 | 1 | no | — |
| 317 | C42 | — | 61 | 1 | no | — |
| 318 | C42 | — | 61 | 1 | no | — |
| 319 | C42 | — | 122 | 2 | no | — |
| 320 | C42 | — | 122 | 2 | no | — |
| 321 | C42 | — | 122 | 2 | no | — |
| 322 | C42 | — | 122 | 2 | no | — |
| 323 | C42 | C22×#6923 | 1 | 1 | yes | characteristic |
| 324 | C23 | — | 61 | 1 | no | — |
| 325 | Q8 | — | 488 | 2 | no | — |
| 326 | Q8 | — | 244 | 4 | no | — |
| 327 | C2×C4 | — | 2 | 2 | no | — |
| 328 | C2×C4 | — | 2 | 2 | no | — |
| 329 | C2×C4 | — | 61 | 1 | no | — |
| 330 | C2×C4 | — | 61 | 1 | no | — |
| 331 | C2×C4 | — | 61 | 1 | no | — |
| 332 | C2×C4 | — | 61 | 1 | no | — |
| 333 | C2×C4 | — | 61 | 1 | no | — |
| 334 | C2×C4 | — | 61 | 1 | no | — |
| 335 | C2×C4 | — | 61 | 1 | no | — |
| 336 | C2×C4 | — | 122 | 2 | no | — |
| 337 | C2×C4 | — | 122 | 4 | no | — |
| 338 | C2×C4 | — | 122 | 2 | no | — |
| 339 | C2×C4 | — | 122 | 2 | no | — |
| 340 | C2×C4 | — | 244 | 1 | no | — |
| 341 | C2×C4 | — | 244 | 2 | no | — |
| 342 | C2×C4 | — | 244 | 2 | no | — |
| 343 | C2×C4 | D4×#6923 | 1 | 1 | yes | characteristic |
| 344 | C2×C4 | D4×#6923 | 1 | 1 | yes | characteristic |
| 345 | C2×C4 | C23×#6923 | 1 | 1 | yes | characteristic |
| 346 | C8 | — | 2 | 1 | no | — |
| 347 | C8 | — | 61 | 2 | no | — |
| 348 | C8 | — | 122 | 2 | no | — |
| 349 | C8 | — | 122 | 2 | no | — |
| 350 | C8 | — | 122 | 4 | no | — |
| 351 | C8 | — | 122 | 1 | no | — |
| 352 | C8 | — | 244 | 2 | no | — |
| 353 | C8 | Q8×#6923 | 1 | 2 | yes | — |
| 354 | C22 | — | 61 | 1 | no | — |
| 355 | C22 | — | 61 | 1 | no | — |
| 356 | C22 | — | 122 | 1 | no | — |
| 357 | C22 | — | 122 | 1 | no | — |
| 358 | C22 | C2×D4×#6923 | 1 | 1 | yes | characteristic |
| 359 | C4 | — | 2 | 1 | no | — |
| 360 | C4 | — | 2 | 1 | no | — |
| 361 | C4 | — | 4 | 2 | no | — |
| 362 | C4 | — | 4 | 2 | no | — |
| 363 | C4 | — | 61 | 2 | no | — |
| 364 | C4 | — | 61 | 1 | no | — |
| 365 | C4 | — | 61 | 1 | no | — |
| 366 | C4 | — | 122 | 1 | no | — |
| 367 | C4 | — | 244 | 4 | no | — |
| 368 | C4 | — | 244 | 2 | no | — |
| 369 | C4 | — | 244 | 2 | no | — |
| 370 | C4 | C2×Q8×#6923 | 1 | 1 | yes | characteristic |
| 371 | C4 | #16840830 | 1 | 1 | yes | characteristic |
| 372 | C2 | — | 122 | 1 | no | — |
| 373 | C2 | — | 122 | 1 | no | — |
| 374 | C2 | #21462348 | 1 | 1 | yes | characteristic |
| 375 | C2 | D61⋊#443 | 1 | 1 | yes | characteristic |
| 376 | C2 | #21462598 | 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