Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1306 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 1306 conjugacy classes of subgroups — too many to draw. Only its 212 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 | #22626926 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #22626652 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #22625943 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #22625903 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #22625776 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #22625689 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #22619324 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #17989666 | — | 2 | 3 | no | — |
| 9 | #17989665 | — | 2 | 3 | no | — |
| 10 | #17989665 | C22 | 1 | 3 | yes | — |
| 11 | D73⋊#131 | — | 2 | 3 | no | — |
| 12 | C2×#14556678 | — | 2 | 3 | no | — |
| 13 | C2×#14556678 | C22 | 1 | 3 | yes | — |
| 14 | C22×#11924038 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | #17989621 | — | 2 | 3 | no | — |
| 16 | #17989620 | — | 2 | 3 | no | — |
| 17 | #17989617 | — | 2 | 3 | no | — |
| 18 | #17989616 | — | 2 | 3 | no | — |
| 19 | #17989593 | C22 | 1 | 3 | yes | complemented |
| 20 | #17989574 | C22 | 1 | 3 | yes | — |
| 21 | #17989560 | C22 | 1 | 3 | yes | — |
| 22 | #17989559 | C22 | 1 | 3 | yes | complemented |
| 23 | #17989551 | C22 | 1 | 3 | yes | complemented |
| 24 | #17989468 | C22 | 1 | 6 | yes | complemented |
| 25 | #17989422 | C22 | 1 | 1 | yes | characteristic |
| 26 | #17989095 | C22 | 1 | 3 | yes | — |
| 27 | #17988776 | C4 | 1 | 3 | yes | — |
| 28 | #17988775 | C4 | 1 | 3 | yes | — |
| 29 | #17988774 | C4 | 1 | 1 | yes | characteristic |
| 30 | #17988559 | C22 | 1 | 3 | yes | — |
| 31 | #458×C73 | C4 | 1 | 1 | yes | characteristic |
| 32 | #14556679 | — | 2 | 1 | no | — |
| 33 | #14556679 | — | 2 | 3 | no | — |
| 34 | #14556678 | — | 2 | 3 | no | — |
| 35 | #14556678 | — | 2 | 6 | no | — |
| 36 | #14556678 | — | 2 | 3 | no | — |
| 37 | #14556678 | — | 2 | 6 | no | — |
| 38 | #14556678 | — | 2 | 6 | no | — |
| 39 | #14556678 | — | 2 | 6 | no | — |
| 40 | #14556678 | — | 2 | 6 | no | — |
| 41 | C2×#11924038 | — | 2 | 3 | no | — |
| 42 | C2×#11924038 | — | 2 | 3 | no | — |
| 43 | C2×#11924038 | — | 2 | 3 | no | — |
| 44 | C2×#11924038 | D4 | 1 | 3 | yes | complemented |
| 45 | D73⋊M16 | — | 2 | 6 | no | — |
| 46 | D73⋊M16 | — | 2 | 3 | no | — |
| 47 | C2×#11924037 | — | 2 | 3 | no | — |
| 48 | C2×#11924037 | — | 2 | 3 | no | — |
| 49 | C2×#11924037 | D4 | 1 | 3 | yes | complemented |
| 50 | C2×#11924037 | C23 | 1 | 3 | yes | — |
| 51 | C2×#11924037 | C23 | 1 | 3 | yes | — |
| 52 | C2×#11924036 | — | 2 | 3 | no | — |
| 53 | C2×#11924036 | D4 | 1 | 3 | yes | complemented |
| 54 | C22×#10596833 | — | 2 | 1 | no | — |
| 55 | C22×#10596833 | D4 | 1 | 3 | yes | complemented |
| 56 | C22×#10596833 | C23 | 1 | 1 | yes | characteristic |
| 57 | C22×#10596833 | C23 | 1 | 1 | yes | characteristic |
| 58 | #14556658 | — | 2 | 3 | no | — |
| 59 | C4⋊#10596833 | — | 2 | 3 | no | — |
| 60 | #14556652 | — | 2 | 3 | no | — |
| 61 | #14556651 | — | 2 | 3 | no | — |
| 62 | #14556648 | — | 2 | 3 | no | — |
| 63 | #14556648 | — | 2 | 3 | no | — |
| 64 | #14556648 | — | 2 | 3 | no | — |
| 65 | C22⋊#10596833 | — | 2 | 3 | no | — |
| 66 | #14556646 | — | 2 | 3 | no | — |
| 67 | C4×#10596833 | — | 2 | 3 | no | — |
| 68 | #14556638 | — | 2 | 3 | no | — |
| 69 | #14556636 | — | 2 | 3 | no | — |
| 70 | #14556636 | C2×C4 | 1 | 3 | yes | — |
| 71 | C2×#11924027 | — | 2 | 3 | no | — |
| 72 | C2×#11924027 | C23 | 1 | 3 | yes | — |
| 73 | #41×D73 | — | 2 | 3 | no | — |
| 74 | C22×C4×D73 | C23 | 1 | 1 | yes | characteristic |
| 75 | #14556574 | C2×C4 | 1 | 3 | yes | — |
| 76 | #14556569 | — | 2 | 3 | no | — |
| 77 | #14556564 | — | 2 | 3 | no | — |
| 78 | #14556561 | C2×C4 | 1 | 3 | yes | — |
| 79 | #14556559 | C2×C4 | 1 | 3 | yes | — |
| 80 | #14556553 | — | 2 | 3 | no | — |
| 81 | #14556551 | — | 2 | 3 | no | — |
| 82 | #14556547 | C23 | 1 | 3 | yes | — |
| 83 | #14556506 | C2×C4 | 1 | 3 | yes | — |
| 84 | #14556505 | C2×C4 | 1 | 6 | yes | — |
| 85 | H(5,𝔽2)×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 86 | #123×C73 | C2×C4 | 1 | 3 | yes | — |
| 87 | #99×C73 | C2×C4 | 1 | 3 | yes | — |
| 88 | #11924038 | — | 2 | 3 | no | — |
| 89 | #11924038 | — | 2 | 3 | no | — |
| 90 | #11924038 | — | 2 | 6 | no | — |
| 91 | #11924038 | — | 4 | 1 | no | — |
| 92 | #11924038 | — | 4 | 3 | no | — |
| 93 | #11924037 | — | 2 | 6 | no | — |
| 94 | #11924037 | — | 2 | 6 | no | — |
| 95 | #11924037 | — | 2 | 6 | no | — |
| 96 | #11924037 | — | 2 | 6 | no | — |
| 97 | #11924036 | — | 2 | 6 | no | — |
| 98 | #11924036 | — | 2 | 3 | no | — |
| 99 | #11924036 | — | 2 | 3 | no | — |
| 100 | C2×#10596833 | — | 2 | 3 | no | — |
| 101 | C2×#10596833 | — | 2 | 3 | no | — |
| 102 | C2×#10596833 | — | 2 | 3 | no | — |
| 103 | C2×#10596833 | — | 2 | 3 | no | — |
| 104 | C2×#10596833 | — | 2 | 3 | no | — |
| 105 | C2×#10596833 | — | 2 | 3 | no | — |
| 106 | C2×#10596833 | C2×D4 | 1 | 3 | yes | — |
| 107 | C2×#10596833 | C2×D4 | 1 | 3 | yes | — |
| 108 | C2×#10596833 | C2×D4 | 1 | 3 | yes | — |
| 109 | C2×#10596833 | C2×D4 | 1 | 3 | yes | — |
| 110 | C23×D73 | C22×C4 | 1 | 1 | yes | characteristic |
| 111 | #11924029 | — | 2 | 1 | no | — |
| 112 | #11924028 | — | 2 | 6 | no | — |
| 113 | #11924028 | — | 2 | 3 | no | — |
| 114 | #11924027 | — | 2 | 3 | no | — |
| 115 | #11924027 | — | 2 | 6 | no | — |
| 116 | #11924027 | — | 2 | 6 | no | — |
| 117 | #11924027 | — | 2 | 6 | no | — |
| 118 | #11924027 | — | 2 | 6 | no | — |
| 119 | C2×Dic146 | — | 2 | 3 | no | — |
| 120 | C2×Dic146 | #41 | 1 | 3 | yes | — |
| 121 | Q8×D73 | — | 2 | 3 | no | — |
| 122 | C2×D292 | — | 2 | 3 | no | — |
| 123 | C2×C22⋊D73 | — | 2 | 3 | no | — |
| 124 | C2×C22⋊D73 | — | 2 | 3 | no | — |
| 125 | C2×C22⋊D73 | — | 2 | 3 | no | — |
| 126 | C2×C22⋊D73 | C22×C4 | 1 | 3 | yes | — |
| 127 | C2×C22⋊D73 | #41 | 1 | 3 | yes | — |
| 128 | D4×D73 | — | 2 | 3 | no | — |
| 129 | D4×D73 | — | 2 | 6 | no | — |
| 130 | C22×Dic73 | — | 2 | 1 | no | — |
| 131 | C22×Dic73 | C2×D4 | 1 | 3 | yes | — |
| 132 | C22×Dic73 | C24 | 1 | 1 | yes | characteristic |
| 133 | C2×C4×D73 | — | 2 | 3 | no | — |
| 134 | C2×C4×D73 | — | 2 | 3 | no | — |
| 135 | C2×C4×D73 | — | 2 | 3 | no | — |
| 136 | C2×C4×D73 | C2×D4 | 1 | 3 | yes | — |
| 137 | #11924007 | — | 2 | 3 | no | — |
| 138 | #11924007 | — | 2 | 3 | no | — |
| 139 | C22⋊Dic73 | C22×C4 | 1 | 3 | yes | — |
| 140 | #11924005 | — | 2 | 3 | no | — |
| 141 | #11924005 | — | 2 | 3 | no | — |
| 142 | #11924005 | — | 2 | 3 | no | — |
| 143 | C4×Dic73 | — | 2 | 3 | no | — |
| 144 | #41×C73 | — | 2 | 3 | no | — |
| 145 | C2×D4×C73 | — | 2 | 3 | no | — |
| 146 | C2×D4×C73 | C22×C4 | 1 | 3 | yes | — |
| 147 | C22×C4×C73 | C22×C4 | 1 | 1 | yes | characteristic |
| 148 | C4⋊C4×C73 | — | 2 | 3 | no | — |
| 149 | C22⋊C4×C73 | — | 2 | 3 | no | — |
| 150 | C22⋊C4×C73 | C22×C4 | 1 | 3 | yes | — |
| 151 | C23×C73 | — | 2 | 1 | no | — |
| 152 | C23×C73 | C4×D4 | 1 | 3 | yes | — |
| 153 | C23×C73 | C23×C4 | 1 | 1 | yes | characteristic |
| 154 | C22×D73 | — | 2 | 3 | no | — |
| 155 | C22×D73 | — | 2 | 3 | no | — |
| 156 | C22×D73 | — | 8 | 1 | no | — |
| 157 | C22×D73 | C4×D4 | 1 | 3 | yes | — |
| 158 | Q8×C73 | — | 2 | 1 | no | — |
| 159 | D4×C73 | — | 2 | 3 | no | — |
| 160 | D4×C73 | — | 2 | 6 | no | — |
| 161 | C2×C4×C73 | — | 2 | 3 | no | — |
| 162 | C2×C4×C73 | — | 2 | 3 | no | — |
| 163 | C2×C4×C73 | — | 2 | 3 | no | — |
| 164 | C2×C4×C73 | C4×D4 | 1 | 3 | yes | — |
| 165 | C22⋊D73 | — | 2 | 6 | no | — |
| 166 | C22⋊D73 | — | 2 | 6 | no | — |
| 167 | C22⋊D73 | — | 2 | 6 | no | — |
| 168 | C22⋊D73 | — | 8 | 3 | no | — |
| 169 | C2×Dic73 | — | 2 | 3 | no | — |
| 170 | C2×Dic73 | — | 2 | 3 | no | — |
| 171 | C2×Dic73 | — | 2 | 3 | no | — |
| 172 | C2×Dic73 | — | 2 | 3 | no | — |
| 173 | C2×Dic73 | C4×D4 | 1 | 3 | yes | — |
| 174 | C2×Dic73 | C22×D4 | 1 | 3 | yes | — |
| 175 | C2×Dic73 | C2×#41 | 1 | 3 | yes | — |
| 176 | D292 | — | 2 | 3 | no | — |
| 177 | D292 | — | 8 | 3 | no | — |
| 178 | C4×D73 | — | 2 | 6 | no | — |
| 179 | C4×D73 | — | 2 | 3 | no | — |
| 180 | C4×D73 | — | 2 | 3 | no | — |
| 181 | C4×D73 | — | 4 | 1 | no | — |
| 182 | C4×D73 | — | 4 | 3 | no | — |
| 183 | Dic146 | — | 2 | 3 | no | — |
| 184 | Dic146 | — | 2 | 6 | no | — |
| 185 | #10596833 | — | 2 | 3 | no | — |
| 186 | #10596833 | — | 2 | 3 | no | — |
| 187 | #10596833 | — | 4 | 1 | no | — |
| 188 | #10596833 | — | 4 | 3 | no | — |
| 189 | #10596833 | #120 | 1 | 1 | yes | characteristic |
| 190 | #10596833 | #120 | 1 | 3 | yes | — |
| 191 | C22×C73 | — | 2 | 3 | no | — |
| 192 | C22×C73 | — | 4 | 1 | no | — |
| 193 | C22×C73 | — | 4 | 3 | no | — |
| 194 | C22×C73 | — | 8 | 1 | no | — |
| 195 | C22×C73 | C2×C4×D4 | 1 | 3 | yes | — |
| 196 | C2×D73 | — | 2 | 3 | no | — |
| 197 | C2×D73 | — | 4 | 3 | no | — |
| 198 | C2×D73 | — | 4 | 3 | no | — |
| 199 | C2×D73 | — | 4 | 3 | no | — |
| 200 | C2×D73 | — | 4 | 1 | no | — |
| 201 | C2×D73 | — | 8 | 3 | no | — |
| 202 | C4×C73 | — | 2 | 3 | no | — |
| 203 | C4×C73 | — | 4 | 3 | no | — |
| 204 | C4×C73 | — | 4 | 1 | no | — |
| 205 | Dic73 | — | 2 | 3 | no | — |
| 206 | Dic73 | — | 4 | 3 | no | — |
| 207 | Dic73 | C2×#120 | 1 | 1 | yes | characteristic |
| 208 | Dic73 | #525 | 1 | 3 | yes | — |
| 209 | #21484 | — | 73 | 1 | no | maximal, Sylow |
| 210 | C2×C73 | — | 2 | 3 | no | — |
| 211 | C2×C73 | — | 4 | 3 | no | — |
| 212 | C2×C73 | C4×#120 | 1 | 1 | yes | characteristic |
| 213 | D73 | — | 4 | 3 | no | — |
| 214 | D73 | — | 8 | 1 | no | — |
| 215 | #3573 | — | 73 | 1 | no | — |
| 216 | #3025 | — | 73 | 1 | no | — |
| 217 | #2930 | — | 73 | 3 | no | — |
| 218 | #1891 | — | 73 | 3 | no | — |
| 219 | #1868 | — | 73 | 3 | no | — |
| 220 | #1791 | — | 73 | 1 | no | — |
| 221 | #1757 | — | 73 | 3 | no | — |
| 222 | C73 | #21484 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 223 | #585 | — | 73 | 1 | no | — |
| 224 | #568 | — | 73 | 3 | no | — |
| 225 | #568 | — | 146 | 3 | no | — |
| 226 | #568 | — | 146 | 3 | no | — |
| 227 | C2×#131 | — | 73 | 3 | no | — |
| 228 | C2×#131 | — | 146 | 3 | no | — |
| 229 | C2×#131 | — | 146 | 3 | no | — |
| 230 | C22×M16 | — | 73 | 1 | no | — |
| 231 | #525 | — | 73 | 3 | no | — |
| 232 | #458 | — | 73 | 3 | no | — |
| 233 | #458 | #64408 | 1 | 1 | yes | characteristic |
| 234 | B(4,𝔽2) | — | 73 | 1 | no | — |
| 235 | B(4,𝔽2) | — | 73 | 3 | no | — |
| 236 | #436 | — | 146 | 3 | no | — |
| 237 | #436 | — | 146 | 3 | no | — |
| 238 | #435 | — | 146 | 3 | no | — |
| 239 | #435 | — | 146 | 3 | no | — |
| 240 | #424 | — | 73 | 3 | no | — |
| 241 | #413 | — | 73 | 3 | no | — |
| 242 | #410 | — | 73 | 3 | no | — |
| 243 | #408 | — | 73 | 3 | no | — |
| 244 | #407 | — | 73 | 3 | no | — |
| 245 | #405 | — | 73 | 3 | no | — |
| 246 | #344 | — | 73 | 6 | no | — |
| 247 | 2−1+4 | — | 146 | 3 | no | — |
| 248 | H(5,𝔽2) | — | 73 | 3 | no | — |
| 249 | H(5,𝔽2) | — | 146 | 3 | no | — |
| 250 | H(5,𝔽2) | C2×#64408 | 1 | 1 | yes | characteristic |
| 251 | C2×#41 | — | 73 | 3 | no | — |
| 252 | C2×#41 | — | 146 | 3 | no | — |
| 253 | C2×#41 | — | 146 | 3 | no | — |
| 254 | C23×C4 | — | 73 | 1 | no | — |
| 255 | #131 | — | 146 | 6 | no | — |
| 256 | #131 | — | 146 | 6 | no | — |
| 257 | #131 | — | 146 | 6 | no | — |
| 258 | #131 | — | 146 | 6 | no | — |
| 259 | #131 | — | 146 | 3 | no | — |
| 260 | #131 | — | 146 | 6 | no | — |
| 261 | #131 | — | 146 | 3 | no | — |
| 262 | #131 | — | 146 | 1 | no | — |
| 263 | #131 | — | 146 | 3 | no | — |
| 264 | C2×M16 | — | 73 | 3 | no | — |
| 265 | C2×M16 | — | 73 | 3 | no | — |
| 266 | C2×M16 | — | 73 | 3 | no | — |
| 267 | C2×M16 | — | 73 | 3 | no | — |
| 268 | C2×M16 | — | 146 | 3 | no | — |
| 269 | C2×M16 | — | 146 | 3 | no | — |
| 270 | C2×M16 | — | 146 | 3 | no | — |
| 271 | C2×M16 | — | 146 | 3 | no | — |
| 272 | C2×M16 | — | 146 | 3 | no | — |
| 273 | C2×M16 | — | 146 | 6 | no | — |
| 274 | C2×M16 | — | 146 | 3 | no | — |
| 275 | C22×C8 | — | 73 | 1 | no | — |
| 276 | C22×C8 | — | 73 | 3 | no | — |
| 277 | C22×C8 | — | 73 | 3 | no | — |
| 278 | C22×C8 | — | 73 | 1 | no | — |
| 279 | C22×C8 | — | 146 | 1 | no | — |
| 280 | C22×C8 | — | 146 | 3 | no | — |
| 281 | #123 | — | 73 | 3 | no | — |
| 282 | #123 | C2×#64408 | 1 | 3 | yes | — |
| 283 | C22⋊Q8 | — | 146 | 3 | no | — |
| 284 | #121 | — | 146 | 3 | no | — |
| 285 | #120 | — | 73 | 3 | no | — |
| 286 | #120 | — | 73 | 3 | no | — |
| 287 | C4×D4 | — | 146 | 3 | no | — |
| 288 | C4×D4 | — | 146 | 3 | no | — |
| 289 | #117 | — | 73 | 3 | no | — |
| 290 | C4⋊C8 | — | 146 | 3 | no | — |
| 291 | C4⋊C8 | — | 146 | 3 | no | — |
| 292 | #101 | — | 146 | 3 | no | — |
| 293 | #100 | — | 146 | 3 | no | — |
| 294 | #99 | — | 73 | 3 | no | — |
| 295 | #99 | — | 73 | 6 | no | — |
| 296 | #99 | C2×#64408 | 1 | 3 | yes | — |
| 297 | C22⋊C8 | — | 146 | 3 | no | — |
| 298 | C22⋊C8 | — | 146 | 3 | no | — |
| 299 | C22⋊C8 | — | 146 | 3 | no | — |
| 300 | C22⋊C8 | — | 146 | 3 | no | — |
| 301 | #97 | — | 146 | 3 | no | — |
| 302 | C4×C8 | — | 146 | 3 | no | — |
| 303 | C24 | — | 73 | 1 | no | — |
| 304 | #41 | — | 2 | 3 | no | — |
| 305 | #41 | — | 146 | 6 | no | — |
| 306 | #41 | — | 146 | 6 | no | — |
| 307 | #41 | — | 146 | 6 | no | — |
| 308 | #41 | — | 146 | 6 | no | — |
| 309 | #41 | — | 146 | 3 | no | — |
| 310 | #41 | — | 146 | 6 | no | — |
| 311 | #41 | — | 146 | 1 | no | — |
| 312 | #41 | — | 146 | 3 | no | — |
| 313 | C2×Q8 | — | 73 | 3 | no | — |
| 314 | C2×Q8 | — | 146 | 3 | no | — |
| 315 | C2×Q8 | — | 146 | 3 | no | — |
| 316 | C2×D4 | — | 2 | 3 | no | — |
| 317 | C2×D4 | — | 73 | 3 | no | — |
| 318 | C2×D4 | — | 73 | 3 | no | — |
| 319 | C2×D4 | — | 146 | 3 | no | — |
| 320 | C2×D4 | — | 146 | 6 | no | — |
| 321 | C2×D4 | — | 146 | 3 | no | — |
| 322 | C2×D4 | — | 146 | 3 | no | — |
| 323 | C2×D4 | — | 146 | 3 | no | — |
| 324 | C2×D4 | — | 146 | 3 | no | — |
| 325 | C2×D4 | C22×#64408 | 1 | 3 | yes | — |
| 326 | C22×C4 | — | 73 | 1 | no | — |
| 327 | C22×C4 | — | 73 | 3 | no | — |
| 328 | C22×C4 | — | 73 | 3 | no | — |
| 329 | C22×C4 | — | 146 | 3 | no | — |
| 330 | C22×C4 | — | 146 | 3 | no | — |
| 331 | C22×C4 | — | 146 | 3 | no | — |
| 332 | C22×C4 | — | 146 | 1 | no | — |
| 333 | C22×C4 | C22×#64408 | 1 | 1 | yes | characteristic |
| 334 | M16 | — | 292 | 1 | no | — |
| 335 | M16 | — | 292 | 3 | no | — |
| 336 | M16 | — | 146 | 6 | no | — |
| 337 | M16 | — | 146 | 6 | no | — |
| 338 | M16 | — | 146 | 6 | no | — |
| 339 | M16 | — | 146 | 6 | no | — |
| 340 | M16 | — | 146 | 6 | no | — |
| 341 | M16 | — | 146 | 3 | no | — |
| 342 | M16 | — | 146 | 3 | no | — |
| 343 | C2×C8 | — | 73 | 3 | no | — |
| 344 | C2×C8 | — | 73 | 3 | no | — |
| 345 | C2×C8 | — | 73 | 3 | no | — |
| 346 | C2×C8 | — | 73 | 3 | no | — |
| 347 | C2×C8 | — | 146 | 3 | no | — |
| 348 | C2×C8 | — | 146 | 3 | no | — |
| 349 | C2×C8 | — | 146 | 3 | no | — |
| 350 | C2×C8 | — | 146 | 3 | no | — |
| 351 | C2×C8 | — | 146 | 3 | no | — |
| 352 | C2×C8 | — | 146 | 3 | no | — |
| 353 | C2×C8 | — | 146 | 3 | no | — |
| 354 | C2×C8 | — | 146 | 3 | no | — |
| 355 | C2×C8 | — | 146 | 6 | no | — |
| 356 | C4⋊C4 | — | 2 | 3 | no | — |
| 357 | C4⋊C4 | — | 146 | 3 | no | — |
| 358 | C4⋊C4 | — | 146 | 3 | no | — |
| 359 | C22⋊C4 | — | 2 | 3 | no | — |
| 360 | C22⋊C4 | — | 73 | 3 | no | — |
| 361 | C22⋊C4 | — | 146 | 3 | no | — |
| 362 | C22⋊C4 | — | 146 | 3 | no | — |
| 363 | C22⋊C4 | — | 146 | 3 | no | — |
| 364 | C22⋊C4 | C22×#64408 | 1 | 3 | yes | — |
| 365 | C42 | — | 146 | 3 | no | — |
| 366 | C23 | — | 2 | 1 | no | — |
| 367 | C23 | — | 584 | 1 | no | — |
| 368 | C23 | — | 73 | 3 | no | — |
| 369 | C23 | — | 146 | 3 | no | — |
| 370 | C23 | — | 146 | 3 | no | — |
| 371 | C23 | D4×#64408 | 1 | 3 | yes | — |
| 372 | C23 | C23×#64408 | 1 | 1 | yes | characteristic |
| 373 | Q8 | — | 2 | 1 | no | — |
| 374 | Q8 | — | 146 | 6 | no | — |
| 375 | Q8 | — | 146 | 3 | no | — |
| 376 | D4 | — | 2 | 3 | no | — |
| 377 | D4 | — | 2 | 6 | no | — |
| 378 | D4 | — | 584 | 3 | no | — |
| 379 | D4 | — | 584 | 3 | no | — |
| 380 | D4 | — | 146 | 3 | no | — |
| 381 | D4 | — | 146 | 6 | no | — |
| 382 | D4 | — | 146 | 6 | no | — |
| 383 | D4 | — | 146 | 6 | no | — |
| 384 | C2×C4 | — | 2 | 3 | no | — |
| 385 | C2×C4 | — | 2 | 3 | no | — |
| 386 | C2×C4 | — | 2 | 3 | no | — |
| 387 | C2×C4 | — | 292 | 1 | no | — |
| 388 | C2×C4 | — | 292 | 3 | no | — |
| 389 | C2×C4 | — | 73 | 3 | no | — |
| 390 | C2×C4 | — | 73 | 3 | no | — |
| 391 | C2×C4 | — | 73 | 3 | no | — |
| 392 | C2×C4 | — | 146 | 3 | no | — |
| 393 | C2×C4 | — | 146 | 3 | no | — |
| 394 | C2×C4 | — | 146 | 6 | no | — |
| 395 | C2×C4 | — | 146 | 3 | no | — |
| 396 | C2×C4 | — | 146 | 3 | no | — |
| 397 | C2×C4 | — | 146 | 3 | no | — |
| 398 | C2×C4 | — | 146 | 3 | no | — |
| 399 | C2×C4 | D4×#64408 | 1 | 3 | yes | — |
| 400 | C8 | — | 292 | 1 | no | — |
| 401 | C8 | — | 292 | 3 | no | — |
| 402 | C8 | — | 73 | 1 | no | — |
| 403 | C8 | — | 73 | 3 | no | — |
| 404 | C8 | — | 146 | 3 | no | — |
| 405 | C8 | — | 146 | 3 | no | — |
| 406 | C22 | — | 2 | 3 | no | — |
| 407 | C22 | — | 4 | 1 | no | — |
| 408 | C22 | — | 4 | 3 | no | — |
| 409 | C22 | — | 8 | 1 | no | — |
| 410 | C22 | — | 292 | 3 | no | — |
| 411 | C22 | — | 292 | 3 | no | — |
| 412 | C22 | — | 292 | 3 | no | — |
| 413 | C22 | — | 292 | 1 | no | — |
| 414 | C22 | — | 584 | 3 | no | — |
| 415 | C22 | — | 146 | 3 | no | — |
| 416 | C22 | C2×D4×#64408 | 1 | 3 | yes | — |
| 417 | C4 | — | 2 | 3 | no | — |
| 418 | C4 | — | 4 | 3 | no | — |
| 419 | C4 | — | 4 | 1 | no | — |
| 420 | C4 | — | 292 | 3 | no | — |
| 421 | C4 | — | 73 | 1 | no | — |
| 422 | C4 | — | 73 | 3 | no | — |
| 423 | C4 | — | 146 | 3 | no | — |
| 424 | C2 | — | 2 | 3 | no | — |
| 425 | C2 | — | 4 | 3 | no | — |
| 426 | C2 | — | 292 | 3 | no | — |
| 427 | C2 | — | 584 | 1 | no | — |
| 428 | C2 | #120×#64408 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22626926 | C2 | semidirect |
| 2. #22626652 | C2 | semidirect |
| 3. #22625943 | C2 | semidirect |
| 4. #22625903 | C2 | semidirect |
| 5. #22625776 | C2 | semidirect |
| 6. #22625689 | C2 | semidirect |
| 14. C22×#11924038 | C22 | semidirect |
| 19. #17989593 | C22 | semidirect |
| 22. #17989559 | C22 | semidirect |
| 23. #17989551 | C22 | semidirect |
| 24. #17989468 | C22 | semidirect |
| 44. C2×#11924038 | D4 | semidirect |
| 49. C2×#11924037 | D4 | semidirect |
| 53. C2×#11924036 | D4 | semidirect |
| 55. C22×#10596833 | D4 | semidirect |
| 222. C73 | #21484 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626926 | 2 |
| #22626652 | 2 |
| #22625943 | 2 |
| #22625903 | 2 |
| #22625776 | 2 |
| #22625689 | 2 |
| #22619324 | 2 |
| #21484 | 73 |