Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
480 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #21462776 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #21461961 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #21461346 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #21461287 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #21460724 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #21460687 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #21456840 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #16840813 | — | 2 | 1 | no | — |
| 9 | #16840795 | — | 2 | 1 | no | — |
| 10 | #16840794 | — | 2 | 1 | no | — |
| 11 | #16840792 | — | 2 | 1 | no | — |
| 12 | #16840787 | — | 2 | 1 | no | — |
| 13 | #16840782 | C22 | 1 | 1 | yes | characteristic |
| 14 | #16840782 | C22 | 1 | 1 | yes | characteristic |
| 15 | #16840769 | — | 2 | 1 | no | — |
| 16 | #16840765 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×#14519837 | — | 2 | 1 | no | — |
| 18 | C2×#14519837 | — | 2 | 1 | no | — |
| 19 | C4×#11758217 | C22 | 1 | 1 | yes | characteristic |
| 20 | #16840620 | — | 2 | 1 | no | — |
| 21 | #16840620 | — | 2 | 1 | no | — |
| 22 | #16840619 | — | 2 | 1 | no | — |
| 23 | #16840618 | — | 2 | 1 | no | — |
| 24 | C2×#14519773 | C22 | 1 | 1 | yes | characteristic |
| 25 | #16840298 | C22 | 1 | 1 | yes | characteristic |
| 26 | #16840148 | — | 2 | 1 | no | — |
| 27 | #16840125 | — | 2 | 1 | no | — |
| 28 | #16839960 | — | 2 | 1 | no | — |
| 29 | #16839956 | — | 2 | 1 | no | — |
| 30 | #16839912 | C4 | 1 | 1 | yes | characteristic |
| 31 | #16839898 | C4 | 1 | 1 | yes | characteristic |
| 32 | #16839896 | C4 | 1 | 1 | yes | characteristic |
| 33 | #16839816 | C22 | 1 | 1 | yes | characteristic |
| 34 | C61×#450 | C4 | 1 | 1 | yes | characteristic |
| 35 | C2×#11758213 | — | 2 | 1 | no | — |
| 36 | C2×#11758217 | — | 2 | 1 | no | — |
| 37 | C2×#11758217 | D4 | 1 | 1 | yes | characteristic |
| 38 | C2×#11758217 | D4 | 1 | 1 | yes | characteristic |
| 39 | C2×D61⋊C8 | — | 2 | 1 | no | — |
| 40 | #14519844 | — | 2 | 1 | no | — |
| 41 | #14519844 | — | 2 | 1 | no | — |
| 42 | #14519844 | — | 2 | 1 | no | — |
| 43 | #14519844 | D4 | 1 | 1 | yes | characteristic |
| 44 | #14519844 | D4 | 1 | 1 | yes | characteristic |
| 45 | C4⋊#92420 | — | 2 | 1 | no | — |
| 46 | C4⋊#92420 | — | 2 | 1 | no | — |
| 47 | #14519837 | — | 4 | 2 | no | — |
| 48 | #14519837 | — | 4 | 2 | no | — |
| 49 | #14519834 | — | 2 | 1 | no | — |
| 50 | #14519834 | — | 2 | 1 | no | — |
| 51 | C22⋊#92420 | — | 2 | 1 | no | — |
| 52 | C22⋊#92420 | — | 2 | 1 | no | — |
| 53 | #14519832 | — | 2 | 1 | no | — |
| 54 | #14519832 | — | 2 | 1 | no | — |
| 55 | #14519832 | — | 2 | 1 | no | — |
| 56 | #14519832 | — | 2 | 1 | no | — |
| 57 | C4×#92420 | — | 2 | 1 | no | — |
| 58 | C4×#92420 | — | 2 | 1 | no | — |
| 59 | C22×D244 | C2×C4 | 1 | 1 | yes | characteristic |
| 60 | C22×C22⋊D61 | — | 2 | 1 | no | — |
| 61 | C22×C22⋊D61 | — | 2 | 1 | no | — |
| 62 | C2×#11758201 | — | 2 | 1 | no | — |
| 63 | C2×D488 | — | 2 | 1 | no | — |
| 64 | C2×#11758199 | — | 2 | 1 | no | — |
| 65 | #14519773 | — | 2 | 1 | no | — |
| 66 | #14519773 | — | 2 | 1 | no | — |
| 67 | #14519773 | — | 2 | 1 | no | — |
| 68 | #14519773 | — | 2 | 1 | no | — |
| 69 | #14519772 | — | 2 | 1 | no | — |
| 70 | #14519768 | D4 | 1 | 1 | yes | characteristic |
| 71 | #14519766 | D4 | 1 | 1 | yes | characteristic |
| 72 | #14519761 | — | 2 | 1 | no | — |
| 73 | #14519751 | C2×C4 | 1 | 1 | yes | characteristic |
| 74 | Q8×Dic61 | D4 | 1 | 1 | yes | characteristic |
| 75 | #14519739 | D4 | 1 | 1 | yes | characteristic |
| 76 | #14519737 | — | 2 | 1 | no | — |
| 77 | #14519735 | — | 2 | 1 | no | — |
| 78 | C2×C4×Dic61 | C23 | 1 | 1 | yes | characteristic |
| 79 | #14519706 | — | 2 | 1 | no | — |
| 80 | #14519699 | — | 2 | 1 | no | — |
| 81 | #14519698 | — | 2 | 1 | no | — |
| 82 | #14519697 | — | 2 | 1 | no | — |
| 83 | C22⋊#92418 | C2×C4 | 1 | 1 | yes | characteristic |
| 84 | #14519687 | — | 2 | 1 | no | — |
| 85 | C22×D4×C61 | C2×C4 | 1 | 1 | yes | characteristic |
| 86 | C2×SD16×C61 | — | 2 | 1 | no | — |
| 87 | C22⋊Q8×C61 | C2×C4 | 1 | 1 | yes | characteristic |
| 88 | #102×C61 | — | 2 | 1 | no | — |
| 89 | C22⋊C8×C61 | C2×C4 | 1 | 1 | yes | characteristic |
| 90 | C24×C61 | — | 2 | 1 | no | — |
| 91 | C23×D61 | — | 2 | 1 | no | — |
| 92 | C2×Q8×C61 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 93 | C2×D4×C61 | — | 2 | 1 | no | — |
| 94 | C2×D4×C61 | — | 2 | 1 | no | — |
| 95 | C2×D4×C61 | — | 8 | 1 | no | — |
| 96 | C22×C4×C61 | C22×C4 | 1 | 1 | yes | characteristic |
| 97 | C2×C22⋊D61 | — | 2 | 1 | no | — |
| 98 | C2×C22⋊D61 | — | 4 | 1 | no | — |
| 99 | C2×C22⋊D61 | — | 4 | 1 | no | — |
| 100 | C2×C22⋊D61 | — | 4 | 1 | no | — |
| 101 | C2×C22⋊D61 | — | 4 | 1 | no | — |
| 102 | C2×C22⋊D61 | — | 4 | 1 | no | — |
| 103 | C2×C22⋊D61 | — | 4 | 1 | no | — |
| 104 | C2×C22⋊D61 | — | 4 | 1 | no | — |
| 105 | C2×C22⋊D61 | — | 4 | 1 | no | — |
| 106 | C2×C22⋊D61 | — | 8 | 2 | no | — |
| 107 | C22×Dic61 | C2×D4 | 1 | 1 | yes | characteristic |
| 108 | C22×Dic61 | #41 | 1 | 1 | yes | characteristic |
| 109 | C2×D244 | — | 2 | 1 | no | — |
| 110 | C2×D244 | — | 2 | 1 | no | — |
| 111 | C2×D244 | — | 8 | 1 | no | — |
| 112 | C2×D244 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 113 | C2×C4×D61 | — | 2 | 1 | no | — |
| 114 | #11758217 | — | 2 | 2 | no | — |
| 115 | #11758217 | — | 4 | 1 | no | — |
| 116 | #11758217 | — | 4 | 1 | no | — |
| 117 | #11758217 | — | 4 | 1 | no | — |
| 118 | C2×#92420 | — | 2 | 1 | no | — |
| 119 | C2×#92420 | — | 2 | 1 | no | — |
| 120 | C2×#92420 | — | 2 | 1 | no | — |
| 121 | C2×#92420 | — | 2 | 1 | no | — |
| 122 | C2×#92420 | — | 4 | 1 | no | — |
| 123 | C2×#92420 | — | 4 | 1 | no | — |
| 124 | #11758213 | — | 8 | 1 | no | — |
| 125 | D61⋊C8 | — | 8 | 1 | no | — |
| 126 | SD16×C61 | — | 8 | 1 | no | — |
| 127 | C2×C8×C61 | — | 2 | 1 | no | — |
| 128 | C4⋊C4×C61 | — | 2 | 1 | no | — |
| 129 | C4⋊C4×C61 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 130 | C22⋊C4×C61 | — | 2 | 1 | no | — |
| 131 | #11758201 | — | 8 | 1 | no | — |
| 132 | #11758199 | — | 8 | 1 | no | — |
| 133 | #11758198 | — | 2 | 1 | no | — |
| 134 | #11758198 | — | 2 | 1 | no | — |
| 135 | #11758198 | — | 2 | 1 | no | — |
| 136 | #11758198 | — | 2 | 1 | no | — |
| 137 | C4⋊Dic61 | — | 2 | 1 | no | — |
| 138 | C4⋊Dic61 | — | 2 | 1 | no | — |
| 139 | C4⋊Dic61 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 140 | #11758196 | — | 2 | 1 | no | — |
| 141 | C4×Dic61 | — | 2 | 1 | no | — |
| 142 | C4×Dic61 | C2×D4 | 1 | 1 | yes | characteristic |
| 143 | C4×Dic61 | C2×D4 | 1 | 1 | yes | characteristic |
| 144 | C4×Dic61 | C2×D4 | 1 | 1 | yes | characteristic |
| 145 | C4×Dic61 | #41 | 1 | 1 | yes | characteristic |
| 146 | C2×#92418 | — | 2 | 1 | no | — |
| 147 | D488 | — | 8 | 1 | no | — |
| 148 | C23×C61 | — | 4 | 1 | no | — |
| 149 | C23×C61 | — | 4 | 1 | no | — |
| 150 | C23×C61 | — | 4 | 1 | no | — |
| 151 | C23×C61 | — | 8 | 1 | no | — |
| 152 | C23×C61 | — | 8 | 1 | no | — |
| 153 | C23×C61 | C4×D4 | 1 | 1 | yes | characteristic |
| 154 | C22×D61 | — | 2 | 1 | no | — |
| 155 | C22×D61 | — | 4 | 1 | no | — |
| 156 | C22×D61 | — | 4 | 1 | no | — |
| 157 | C22×D61 | — | 4 | 1 | no | — |
| 158 | C22×D61 | — | 8 | 1 | no | — |
| 159 | C22×D61 | — | 8 | 1 | no | — |
| 160 | Q8×C61 | — | 4 | 1 | no | — |
| 161 | D4×C61 | — | 4 | 1 | no | — |
| 162 | D4×C61 | — | 4 | 1 | no | — |
| 163 | D4×C61 | — | 8 | 1 | no | — |
| 164 | C2×C4×C61 | — | 2 | 1 | no | — |
| 165 | C2×C4×C61 | — | 2 | 1 | no | — |
| 166 | C2×C4×C61 | — | 4 | 1 | no | — |
| 167 | C2×C4×C61 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 168 | C2×C4×C61 | C4×D4 | 1 | 1 | yes | characteristic |
| 169 | C22⋊D61 | — | 8 | 1 | no | — |
| 170 | C22⋊D61 | — | 8 | 1 | no | — |
| 171 | C22⋊D61 | — | 8 | 2 | no | — |
| 172 | C22⋊D61 | — | 8 | 2 | no | — |
| 173 | C22⋊D61 | — | 8 | 1 | no | — |
| 174 | C22⋊D61 | — | 8 | 1 | no | — |
| 175 | C22⋊D61 | — | 8 | 1 | no | — |
| 176 | C2×Dic61 | — | 2 | 1 | no | — |
| 177 | C2×Dic61 | — | 2 | 1 | no | — |
| 178 | C2×Dic61 | — | 2 | 1 | no | — |
| 179 | C2×Dic61 | — | 4 | 1 | no | — |
| 180 | C2×Dic61 | #120 | 1 | 1 | yes | characteristic |
| 181 | C2×Dic61 | #121 | 1 | 1 | yes | characteristic |
| 182 | C2×Dic61 | #121 | 1 | 1 | yes | characteristic |
| 183 | C2×Dic61 | #123 | 1 | 1 | yes | characteristic |
| 184 | D244 | — | 4 | 1 | no | — |
| 185 | D244 | — | 4 | 1 | no | — |
| 186 | D244 | — | 4 | 1 | no | — |
| 187 | D244 | — | 8 | 1 | no | — |
| 188 | C4×D61 | — | 4 | 1 | no | — |
| 189 | C4×D61 | — | 4 | 1 | no | — |
| 190 | #92420 | — | 4 | 2 | no | — |
| 191 | #92420 | — | 4 | 1 | no | — |
| 192 | #92420 | — | 4 | 1 | no | — |
| 193 | #92420 | — | 4 | 1 | no | — |
| 194 | #92420 | — | 4 | 1 | no | — |
| 195 | #92420 | — | 8 | 1 | no | — |
| 196 | C8×C61 | — | 4 | 1 | no | — |
| 197 | #92418 | — | 4 | 1 | no | — |
| 198 | #9340 | — | 61 | 1 | no | maximal, Sylow |
| 199 | C22×C61 | — | 2 | 1 | no | — |
| 200 | C22×C61 | — | 2 | 1 | no | — |
| 201 | C22×C61 | — | 2 | 1 | no | — |
| 202 | C22×C61 | — | 8 | 1 | no | — |
| 203 | C22×C61 | — | 8 | 1 | no | — |
| 204 | C22×C61 | — | 8 | 1 | no | — |
| 205 | C22×C61 | — | 16 | 1 | no | — |
| 206 | C22×C61 | — | 16 | 1 | no | — |
| 207 | C22×C61 | #386 | 1 | 1 | yes | characteristic |
| 208 | C2×D61 | — | 4 | 1 | no | — |
| 209 | C2×D61 | — | 4 | 1 | no | — |
| 210 | C2×D61 | — | 4 | 1 | no | — |
| 211 | C2×D61 | — | 8 | 1 | no | — |
| 212 | C2×D61 | — | 8 | 1 | no | — |
| 213 | C2×D61 | — | 8 | 1 | no | — |
| 214 | C2×D61 | — | 16 | 1 | no | — |
| 215 | C2×D61 | — | 16 | 1 | no | — |
| 216 | C4×C61 | — | 2 | 1 | no | — |
| 217 | C4×C61 | — | 2 | 1 | no | — |
| 218 | C4×C61 | — | 4 | 1 | no | — |
| 219 | C4×C61 | — | 4 | 1 | no | — |
| 220 | Dic61 | — | 2 | 1 | no | — |
| 221 | Dic61 | — | 2 | 1 | no | — |
| 222 | Dic61 | — | 2 | 1 | no | — |
| 223 | Dic61 | — | 4 | 1 | no | — |
| 224 | Dic61 | #453 | 1 | 1 | yes | characteristic |
| 225 | Dic61 | #454 | 1 | 1 | yes | characteristic |
| 226 | #3217 | — | 61 | 1 | no | — |
| 227 | #2995 | — | 61 | 1 | no | — |
| 228 | #1965 | — | 61 | 1 | no | — |
| 229 | #1555 | — | 61 | 1 | no | — |
| 230 | #1529 | — | 61 | 1 | no | — |
| 231 | #1307 | — | 61 | 1 | no | — |
| 232 | #1291 | — | 61 | 1 | no | — |
| 233 | C2×C61 | — | 4 | 1 | no | — |
| 234 | C2×C61 | — | 16 | 1 | no | — |
| 235 | C2×C61 | #1883 | 1 | 1 | yes | characteristic |
| 236 | C2×C61 | #1903 | 1 | 1 | yes | characteristic |
| 237 | C2×C61 | #1914 | 1 | 1 | yes | characteristic |
| 238 | D61 | — | 8 | 1 | no | — |
| 239 | D61 | — | 16 | 1 | no | — |
| 240 | C2×#127 | — | 61 | 1 | no | — |
| 241 | #529 | — | 61 | 1 | no | — |
| 242 | #496 | — | 122 | 1 | no | — |
| 243 | #490 | — | 122 | 1 | no | — |
| 244 | #460 | — | 122 | 1 | no | — |
| 245 | #459 | — | 122 | 1 | no | — |
| 246 | #450 | — | 61 | 1 | no | — |
| 247 | #450 | #6923 | 1 | 1 | yes | characteristic |
| 248 | #447 | — | 61 | 1 | no | — |
| 249 | #447 | — | 61 | 1 | no | — |
| 250 | #446 | — | 122 | 1 | no | — |
| 251 | #436 | — | 122 | 1 | no | — |
| 252 | #435 | — | 122 | 1 | no | — |
| 253 | #435 | — | 122 | 1 | no | — |
| 254 | #433 | — | 122 | 1 | no | — |
| 255 | #432 | — | 61 | 1 | no | — |
| 256 | #432 | — | 61 | 1 | no | — |
| 257 | #432 | — | 61 | 1 | no | — |
| 258 | #424 | — | 122 | 1 | no | — |
| 259 | #423 | — | 61 | 1 | no | — |
| 260 | C2×#100 | — | 122 | 1 | no | — |
| 261 | C2×#100 | — | 122 | 1 | no | — |
| 262 | C4×M16 | — | 61 | 1 | no | — |
| 263 | #331 | — | 122 | 1 | no | — |
| 264 | #331 | — | 122 | 1 | no | — |
| 265 | #330 | — | 122 | 1 | no | — |
| 266 | #329 | — | 122 | 1 | no | — |
| 267 | C61 | #9340 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 268 | C22×D4 | — | 61 | 1 | no | — |
| 269 | C22×D4 | — | 122 | 1 | no | — |
| 270 | C22×D4 | — | 122 | 1 | no | — |
| 271 | C22×D4 | C2×#6923 | 1 | 1 | yes | characteristic |
| 272 | C2×SD16 | — | 2 | 1 | no | — |
| 273 | C2×SD16 | — | 122 | 1 | no | — |
| 274 | C2×D8 | — | 122 | 1 | no | — |
| 275 | C2×D8 | — | 122 | 1 | no | — |
| 276 | C2×M16 | — | 61 | 1 | no | — |
| 277 | C2×M16 | — | 61 | 1 | no | — |
| 278 | C2×M16 | — | 122 | 1 | no | — |
| 279 | C2×M16 | — | 122 | 1 | no | — |
| 280 | C22×C8 | — | 122 | 1 | no | — |
| 281 | #127 | — | 122 | 1 | no | — |
| 282 | #127 | — | 122 | 1 | no | — |
| 283 | #127 | — | 122 | 1 | no | — |
| 284 | #127 | — | 122 | 1 | no | — |
| 285 | #126 | — | 122 | 1 | no | — |
| 286 | #125 | — | 61 | 1 | no | — |
| 287 | #124 | — | 61 | 1 | no | — |
| 288 | #123 | — | 122 | 1 | no | — |
| 289 | C22⋊Q8 | C2×#6923 | 1 | 1 | yes | characteristic |
| 290 | #121 | — | 61 | 1 | no | — |
| 291 | C4×Q8 | — | 61 | 1 | no | — |
| 292 | C4×D4 | — | 61 | 1 | no | — |
| 293 | C4×D4 | — | 122 | 1 | no | — |
| 294 | #117 | — | 122 | 1 | no | — |
| 295 | C2×C42 | — | 61 | 1 | no | — |
| 296 | C4⋊C8 | — | 61 | 1 | no | — |
| 297 | C4⋊C8 | — | 61 | 1 | no | — |
| 298 | C4⋊C8 | — | 122 | 1 | no | — |
| 299 | C4⋊C8 | — | 122 | 1 | no | — |
| 300 | C4⋊C8 | — | 122 | 1 | no | — |
| 301 | C4⋊C8 | — | 122 | 1 | no | — |
| 302 | C4⋊C8 | — | 122 | 1 | no | — |
| 303 | C4⋊C8 | — | 122 | 1 | no | — |
| 304 | #102 | — | 2 | 1 | no | — |
| 305 | #102 | — | 122 | 1 | no | — |
| 306 | #102 | — | 122 | 1 | no | — |
| 307 | #102 | — | 122 | 1 | no | — |
| 308 | #100 | — | 244 | 2 | no | — |
| 309 | #100 | — | 244 | 2 | no | — |
| 310 | C22⋊C8 | — | 61 | 1 | no | — |
| 311 | C22⋊C8 | — | 122 | 1 | no | — |
| 312 | C22⋊C8 | — | 122 | 1 | no | — |
| 313 | C22⋊C8 | — | 122 | 1 | no | — |
| 314 | C22⋊C8 | — | 122 | 1 | no | — |
| 315 | C22⋊C8 | C2×#6923 | 1 | 1 | yes | characteristic |
| 316 | #97 | — | 122 | 1 | no | — |
| 317 | #97 | — | 122 | 1 | no | — |
| 318 | #97 | — | 122 | 1 | no | — |
| 319 | #97 | — | 122 | 1 | no | — |
| 320 | #97 | — | 122 | 1 | no | — |
| 321 | C4×C8 | — | 122 | 1 | no | — |
| 322 | C4×C8 | — | 122 | 1 | no | — |
| 323 | C24 | — | 2 | 1 | no | — |
| 324 | C24 | — | 122 | 1 | no | — |
| 325 | C2×Q8 | C22⋊#6923 | 1 | 1 | yes | characteristic |
| 326 | C2×D4 | — | 2 | 1 | no | — |
| 327 | C2×D4 | — | 2 | 1 | no | — |
| 328 | C2×D4 | — | 8 | 1 | no | — |
| 329 | C2×D4 | — | 61 | 1 | no | — |
| 330 | C2×D4 | — | 122 | 1 | no | — |
| 331 | C2×D4 | — | 122 | 1 | no | — |
| 332 | C2×D4 | — | 122 | 1 | no | — |
| 333 | C2×D4 | — | 488 | 1 | no | — |
| 334 | C2×D4 | — | 488 | 2 | no | — |
| 335 | C2×D4 | — | 244 | 1 | no | — |
| 336 | C2×D4 | — | 244 | 1 | no | — |
| 337 | C2×D4 | — | 244 | 1 | no | — |
| 338 | C2×D4 | — | 244 | 1 | no | — |
| 339 | C2×D4 | — | 244 | 1 | no | — |
| 340 | C2×D4 | — | 244 | 1 | no | — |
| 341 | C2×D4 | — | 244 | 1 | no | — |
| 342 | C2×D4 | — | 244 | 1 | no | — |
| 343 | C22×C4 | — | 61 | 1 | no | — |
| 344 | C22×C4 | — | 61 | 1 | no | — |
| 345 | C22×C4 | — | 122 | 1 | no | — |
| 346 | C22×C4 | C22×#6923 | 1 | 1 | yes | characteristic |
| 347 | SD16 | — | 8 | 1 | no | — |
| 348 | SD16 | — | 488 | 1 | no | — |
| 349 | D8 | — | 488 | 1 | no | — |
| 350 | D8 | — | 488 | 1 | no | — |
| 351 | M16 | — | 122 | 2 | no | — |
| 352 | M16 | — | 488 | 1 | no | — |
| 353 | M16 | — | 244 | 1 | no | — |
| 354 | M16 | — | 244 | 1 | no | — |
| 355 | M16 | — | 244 | 1 | no | — |
| 356 | C2×C8 | — | 2 | 1 | no | — |
| 357 | C2×C8 | — | 122 | 1 | no | — |
| 358 | C2×C8 | — | 122 | 1 | no | — |
| 359 | C2×C8 | — | 122 | 1 | no | — |
| 360 | C2×C8 | — | 122 | 1 | no | — |
| 361 | C2×C8 | — | 122 | 1 | no | — |
| 362 | C2×C8 | — | 488 | 1 | no | — |
| 363 | C2×C8 | — | 244 | 1 | no | — |
| 364 | C2×C8 | — | 244 | 1 | no | — |
| 365 | C4⋊C4 | — | 2 | 1 | no | — |
| 366 | C4⋊C4 | — | 61 | 1 | no | — |
| 367 | C4⋊C4 | — | 122 | 1 | no | — |
| 368 | C4⋊C4 | — | 122 | 1 | no | — |
| 369 | C4⋊C4 | — | 122 | 1 | no | — |
| 370 | C4⋊C4 | C22⋊#6923 | 1 | 1 | yes | characteristic |
| 371 | C22⋊C4 | — | 2 | 1 | no | — |
| 372 | C22⋊C4 | — | 122 | 1 | no | — |
| 373 | C22⋊C4 | — | 122 | 1 | no | — |
| 374 | C22⋊C4 | — | 122 | 1 | no | — |
| 375 | C22⋊C4 | — | 122 | 1 | no | — |
| 376 | C42 | — | 61 | 1 | no | — |
| 377 | C42 | — | 61 | 1 | no | — |
| 378 | C42 | — | 61 | 1 | no | — |
| 379 | C42 | — | 61 | 1 | no | — |
| 380 | C42 | — | 122 | 1 | no | — |
| 381 | C23 | — | 4 | 1 | no | — |
| 382 | C23 | — | 4 | 1 | no | — |
| 383 | C23 | — | 4 | 1 | no | — |
| 384 | C23 | — | 8 | 1 | no | — |
| 385 | C23 | — | 8 | 1 | no | — |
| 386 | C23 | — | 122 | 1 | no | — |
| 387 | C23 | — | 488 | 1 | no | — |
| 388 | C23 | — | 488 | 1 | no | — |
| 389 | C23 | — | 244 | 1 | no | — |
| 390 | C23 | — | 244 | 1 | no | — |
| 391 | C23 | — | 244 | 1 | no | — |
| 392 | C23 | D4×#6923 | 1 | 1 | yes | characteristic |
| 393 | Q8 | — | 4 | 1 | no | — |
| 394 | D4 | — | 4 | 1 | no | — |
| 395 | D4 | — | 4 | 1 | no | — |
| 396 | D4 | — | 8 | 1 | no | — |
| 397 | D4 | — | 488 | 1 | no | — |
| 398 | D4 | — | 488 | 1 | no | — |
| 399 | D4 | — | 488 | 1 | no | — |
| 400 | D4 | — | 488 | 2 | no | — |
| 401 | D4 | — | 488 | 2 | no | — |
| 402 | D4 | — | 488 | 1 | no | — |
| 403 | D4 | — | 488 | 1 | no | — |
| 404 | D4 | — | 488 | 1 | no | — |
| 405 | D4 | — | 244 | 1 | no | — |
| 406 | D4 | — | 244 | 1 | no | — |
| 407 | D4 | — | 244 | 1 | no | — |
| 408 | C2×C4 | — | 2 | 1 | no | — |
| 409 | C2×C4 | — | 2 | 1 | no | — |
| 410 | C2×C4 | — | 4 | 1 | no | — |
| 411 | C2×C4 | — | 61 | 1 | no | — |
| 412 | C2×C4 | — | 61 | 1 | no | — |
| 413 | C2×C4 | — | 61 | 1 | no | — |
| 414 | C2×C4 | — | 61 | 1 | no | — |
| 415 | C2×C4 | — | 122 | 1 | no | — |
| 416 | C2×C4 | — | 122 | 1 | no | — |
| 417 | C2×C4 | — | 122 | 1 | no | — |
| 418 | C2×C4 | — | 244 | 1 | no | — |
| 419 | C2×C4 | — | 244 | 1 | no | — |
| 420 | C2×C4 | — | 244 | 1 | no | — |
| 421 | C2×C4 | C2×C22⋊#6923 | 1 | 1 | yes | characteristic |
| 422 | C2×C4 | D4×#6923 | 1 | 1 | yes | characteristic |
| 423 | C8 | — | 4 | 1 | no | — |
| 424 | C8 | — | 488 | 1 | no | — |
| 425 | C8 | — | 244 | 1 | no | — |
| 426 | C8 | — | 244 | 1 | no | — |
| 427 | C8 | — | 244 | 1 | no | — |
| 428 | C8 | — | 244 | 1 | no | — |
| 429 | C8 | — | 244 | 1 | no | — |
| 430 | C8 | — | 244 | 2 | no | — |
| 431 | C22 | — | 2 | 1 | no | — |
| 432 | C22 | — | 2 | 1 | no | — |
| 433 | C22 | — | 2 | 1 | no | — |
| 434 | C22 | — | 8 | 1 | no | — |
| 435 | C22 | — | 8 | 1 | no | — |
| 436 | C22 | — | 8 | 1 | no | — |
| 437 | C22 | — | 16 | 1 | no | — |
| 438 | C22 | — | 16 | 1 | no | — |
| 439 | C22 | — | 976 | 1 | no | — |
| 440 | C22 | — | 976 | 1 | no | — |
| 441 | C22 | — | 488 | 1 | no | — |
| 442 | C22 | — | 488 | 1 | no | — |
| 443 | C22 | — | 488 | 1 | no | — |
| 444 | C22 | — | 244 | 1 | no | — |
| 445 | C22 | — | 244 | 1 | no | — |
| 446 | C22 | — | 244 | 1 | no | — |
| 447 | C22 | #16840710 | 1 | 1 | yes | characteristic |
| 448 | C4 | — | 2 | 1 | no | — |
| 449 | C4 | — | 2 | 1 | no | — |
| 450 | C4 | — | 4 | 1 | no | — |
| 451 | C4 | — | 4 | 1 | no | — |
| 452 | C4 | — | 61 | 1 | no | — |
| 453 | C4 | — | 61 | 1 | no | — |
| 454 | C4 | — | 122 | 1 | no | — |
| 455 | C4 | — | 122 | 1 | no | — |
| 456 | C4 | — | 122 | 1 | no | — |
| 457 | C4 | — | 244 | 1 | no | — |
| 458 | C2 | — | 4 | 1 | no | — |
| 459 | C2 | — | 16 | 1 | no | — |
| 460 | C2 | — | 976 | 1 | no | — |
| 461 | C2 | — | 488 | 1 | no | — |
| 462 | C2 | #21461819 | 1 | 1 | yes | characteristic |
| 463 | C2 | #21461851 | 1 | 1 | yes | characteristic |
| 464 | C2 | #21461870 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #21462776 | C2 | semidirect |
| 2. #21461961 | C2 | semidirect |
| 3. #21461346 | C2 | semidirect |
| 4. #21461287 | C2 | semidirect |
| 5. #21460724 | C2 | semidirect |
| 6. #21460687 | C2 | semidirect |
| 267. C61 | #9340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462776 | 2 |
| #21461961 | 2 |
| #21461346 | 2 |
| #21461287 | 2 |
| #21460724 | 2 |
| #21460687 | 2 |
| #21456840 | 2 |
| #9340 | 61 |