Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
836 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 836 conjugacy classes of subgroups — too many to draw. Only its 102 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 | #22626098 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #22625805 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #22625448 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22625439 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #22625313 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #22625227 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #22623801 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #17989605 | C22 | 1 | 1 | yes | characteristic |
| 9 | #17989592 | C22 | 1 | 1 | yes | characteristic |
| 10 | #17989588 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×#14556655 | — | 2 | 1 | no | — |
| 12 | C2×#14556653 | — | 2 | 2 | no | — |
| 13 | C4×C4⋊#64408 | C22 | 1 | 1 | yes | characteristic |
| 14 | #17989457 | — | 2 | 1 | no | — |
| 15 | #17989447 | — | 2 | 1 | no | — |
| 16 | #17989446 | — | 2 | 1 | no | — |
| 17 | #17989445 | — | 2 | 2 | no | — |
| 18 | #17989441 | — | 2 | 1 | no | — |
| 19 | #17989440 | — | 2 | 1 | no | — |
| 20 | #17989437 | — | 2 | 1 | no | — |
| 21 | D4⋊#10596833 | — | 2 | 1 | no | — |
| 22 | #17989323 | C4 | 1 | 1 | yes | characteristic, complemented |
| 23 | #17989322 | C4 | 1 | 1 | yes | characteristic, complemented |
| 24 | #17989320 | — | 2 | 1 | no | — |
| 25 | #17989258 | C4 | 1 | 1 | yes | characteristic, complemented |
| 26 | #17989257 | — | 2 | 1 | no | — |
| 27 | #17989234 | — | 2 | 1 | no | — |
| 28 | #17989226 | — | 2 | 2 | no | — |
| 29 | #17989225 | — | 2 | 1 | no | — |
| 30 | #17989187 | — | 2 | 2 | no | — |
| 31 | #17989150 | — | 2 | 1 | no | — |
| 32 | #17989141 | C22 | 1 | 1 | yes | characteristic |
| 33 | #17989133 | — | 2 | 1 | no | — |
| 34 | #17989132 | — | 2 | 1 | no | — |
| 35 | #127×D73 | C22 | 1 | 1 | yes | characteristic |
| 36 | #17989059 | — | 2 | 1 | no | — |
| 37 | C4×#11924027 | C22 | 1 | 1 | yes | characteristic |
| 38 | #550×C73 | C4 | 1 | 1 | yes | characteristic, complemented |
| 39 | C2×#11924038 | — | 2 | 1 | no | — |
| 40 | C2×#11924036 | — | 2 | 1 | no | — |
| 41 | C2×C4⋊#64408 | — | 2 | 1 | no | — |
| 42 | C2×C4×#64408 | — | 2 | 1 | no | — |
| 43 | #14556658 | — | 2 | 1 | no | — |
| 44 | #14556658 | — | 2 | 1 | no | — |
| 45 | #14556658 | — | 2 | 1 | no | — |
| 46 | #14556658 | — | 2 | 1 | no | — |
| 47 | C4⋊#10596833 | — | 2 | 1 | no | — |
| 48 | #14556655 | — | 4 | 2 | no | — |
| 49 | #14556653 | — | 4 | 4 | no | — |
| 50 | #14556648 | — | 2 | 1 | no | — |
| 51 | C4×#10596833 | — | 2 | 1 | no | — |
| 52 | (C2×#64408)⋊C4 | — | 2 | 1 | no | — |
| 53 | C2×#11924028 | — | 2 | 1 | no | — |
| 54 | C2×#11924027 | — | 2 | 2 | no | — |
| 55 | C2×#11924027 | D4 | 1 | 1 | yes | characteristic |
| 56 | C2×D4×D73 | — | 2 | 1 | no | — |
| 57 | C2×D4×D73 | — | 2 | 1 | no | — |
| 58 | C2×D4×D73 | D4 | 1 | 2 | yes | — |
| 59 | #14556590 | D4 | 1 | 1 | yes | characteristic |
| 60 | #14556589 | D4 | 1 | 1 | yes | characteristic |
| 61 | #14556588 | C2×C4 | 1 | 1 | yes | characteristic |
| 62 | #14556587 | — | 2 | 1 | no | — |
| 63 | #14556587 | — | 2 | 1 | no | — |
| 64 | #14556587 | — | 2 | 1 | no | — |
| 65 | #14556587 | D4 | 1 | 2 | yes | — |
| 66 | #14556581 | — | 2 | 1 | no | — |
| 67 | #14556580 | — | 2 | 1 | no | — |
| 68 | #14556579 | — | 2 | 1 | no | — |
| 69 | #14556578 | — | 2 | 1 | no | — |
| 70 | #14556578 | — | 2 | 1 | no | — |
| 71 | #14556577 | — | 2 | 2 | no | — |
| 72 | #14556576 | — | 2 | 2 | no | — |
| 73 | #14556574 | — | 2 | 2 | no | — |
| 74 | #14556573 | — | 2 | 2 | no | — |
| 75 | #14556572 | — | 2 | 2 | no | — |
| 76 | #14556571 | D4 | 1 | 1 | yes | characteristic |
| 77 | #14556569 | — | 2 | 1 | no | — |
| 78 | #14556567 | D4 | 1 | 1 | yes | characteristic |
| 79 | #14556565 | — | 2 | 1 | no | — |
| 80 | #14556564 | — | 2 | 2 | no | — |
| 81 | #14556563 | — | 2 | 2 | no | — |
| 82 | #14556563 | — | 2 | 2 | no | — |
| 83 | #14556563 | — | 2 | 2 | no | — |
| 84 | #14556563 | — | 2 | 2 | no | — |
| 85 | #14556562 | — | 2 | 2 | no | — |
| 86 | #14556559 | — | 2 | 2 | no | — |
| 87 | #14556559 | — | 2 | 2 | no | — |
| 88 | C4×Dic146 | — | 2 | 1 | no | — |
| 89 | C4×Dic146 | C2×C4 | 1 | 1 | yes | characteristic |
| 90 | C4×Dic146 | C2×C4 | 1 | 1 | yes | characteristic |
| 91 | #14556556 | D4 | 1 | 1 | yes | characteristic |
| 92 | C4×D292 | — | 2 | 1 | no | — |
| 93 | D4×Dic73 | — | 2 | 1 | no | — |
| 94 | D4×Dic73 | — | 2 | 1 | no | — |
| 95 | D4×Dic73 | D4 | 1 | 1 | yes | characteristic |
| 96 | #14556553 | — | 2 | 1 | no | — |
| 97 | #14556553 | — | 2 | 1 | no | — |
| 98 | C4×C22⋊D73 | — | 2 | 2 | no | — |
| 99 | C4×C22⋊D73 | — | 2 | 2 | no | — |
| 100 | C4×C22⋊D73 | — | 2 | 1 | no | — |
| 101 | #14556551 | — | 2 | 2 | no | — |
| 102 | #14556551 | — | 2 | 1 | no | — |
| 103 | #14556549 | D4 | 1 | 1 | yes | characteristic |
| 104 | #14556548 | — | 2 | 1 | no | — |
| 105 | #14556547 | — | 2 | 1 | no | — |
| 106 | C2×#11924005 | — | 2 | 2 | no | — |
| 107 | C22⋊C4×D73 | — | 2 | 2 | no | — |
| 108 | C2×C4×Dic73 | — | 2 | 1 | no | — |
| 109 | C42×D73 | C23 | 1 | 1 | yes | characteristic |
| 110 | C2×#41×C73 | — | 2 | 1 | no | — |
| 111 | #127×C73 | — | 2 | 1 | no | — |
| 112 | #127×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 113 | #121×C73 | — | 2 | 2 | no | — |
| 114 | #121×C73 | — | 2 | 1 | no | — |
| 115 | C4×Q8×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 116 | C4×D4×C73 | — | 2 | 1 | no | — |
| 117 | C4×D4×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 118 | C22×#64408 | — | 4 | 1 | no | — |
| 119 | #11924038 | — | 4 | 1 | no | — |
| 120 | #11924038 | — | 4 | 1 | no | — |
| 121 | #11924036 | — | 4 | 2 | no | — |
| 122 | C2×#10596833 | — | 4 | 1 | no | — |
| 123 | C2×#10596833 | — | 4 | 1 | no | — |
| 124 | C2×#10596833 | — | 4 | 1 | no | — |
| 125 | C4⋊#64408 | — | 2 | 2 | no | — |
| 126 | C4⋊#64408 | — | 4 | 1 | no | — |
| 127 | C4×#64408 | — | 4 | 1 | no | — |
| 128 | C4×#64408 | — | 4 | 1 | no | — |
| 129 | C23×D73 | — | 2 | 2 | no | — |
| 130 | #11924028 | — | 8 | 2 | no | — |
| 131 | #11924027 | — | 2 | 1 | no | — |
| 132 | #11924027 | — | 2 | 1 | no | — |
| 133 | #11924027 | — | 2 | 1 | no | — |
| 134 | #11924027 | — | 2 | 1 | no | — |
| 135 | #11924027 | — | 8 | 2 | no | — |
| 136 | #11924027 | — | 8 | 2 | no | — |
| 137 | C2×Dic146 | — | 2 | 1 | no | — |
| 138 | C2×Dic146 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 139 | C2×Dic146 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 140 | C2×D292 | — | 2 | 1 | no | — |
| 141 | C2×D292 | — | 2 | 1 | no | — |
| 142 | C2×D292 | C22⋊C4 | 1 | 2 | yes | — |
| 143 | C2×C22⋊D73 | — | 2 | 1 | no | — |
| 144 | C2×C22⋊D73 | — | 2 | 2 | no | — |
| 145 | C2×C22⋊D73 | — | 2 | 2 | no | — |
| 146 | C2×C22⋊D73 | — | 2 | 2 | no | — |
| 147 | C2×C22⋊D73 | — | 2 | 2 | no | — |
| 148 | C2×C22⋊D73 | — | 2 | 2 | no | — |
| 149 | D4×D73 | — | 4 | 2 | no | — |
| 150 | D4×D73 | — | 4 | 2 | no | — |
| 151 | D4×D73 | — | 4 | 1 | no | — |
| 152 | D4×D73 | — | 4 | 1 | no | — |
| 153 | D4×D73 | — | 4 | 1 | no | — |
| 154 | D4×D73 | — | 4 | 1 | no | — |
| 155 | D4×D73 | — | 8 | 2 | no | — |
| 156 | C22×Dic73 | — | 2 | 2 | no | — |
| 157 | C22×Dic73 | — | 2 | 1 | no | — |
| 158 | C22×Dic73 | — | 2 | 1 | no | — |
| 159 | C2×C4×D73 | — | 2 | 2 | no | — |
| 160 | C2×C4×D73 | — | 2 | 2 | no | — |
| 161 | C2×C4×D73 | C2×D4 | 1 | 1 | yes | characteristic |
| 162 | C2×C4×D73 | C2×D4 | 1 | 1 | yes | characteristic |
| 163 | C2×C4×D73 | C2×D4 | 1 | 1 | yes | characteristic |
| 164 | C4⋊Dic73 | — | 2 | 1 | no | — |
| 165 | C4⋊Dic73 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 166 | C4⋊Dic73 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 167 | #11924007 | — | 2 | 1 | no | — |
| 168 | #11924007 | — | 2 | 1 | no | — |
| 169 | #11924007 | — | 2 | 1 | no | — |
| 170 | #11924007 | — | 2 | 1 | no | — |
| 171 | #11924007 | — | 2 | 1 | no | — |
| 172 | #11924007 | — | 2 | 1 | no | — |
| 173 | #11924007 | — | 2 | 1 | no | — |
| 174 | C22⋊Dic73 | — | 2 | 2 | no | — |
| 175 | C22⋊Dic73 | — | 2 | 2 | no | — |
| 176 | C22⋊Dic73 | — | 2 | 2 | no | — |
| 177 | C22⋊Dic73 | — | 2 | 1 | no | — |
| 178 | #11924005 | — | 2 | 2 | no | — |
| 179 | #11924005 | — | 2 | 2 | no | — |
| 180 | #11924005 | — | 2 | 2 | no | — |
| 181 | #11924005 | — | 2 | 2 | no | — |
| 182 | #11924005 | — | 2 | 1 | no | — |
| 183 | #11924005 | — | 2 | 1 | no | — |
| 184 | #11924005 | — | 2 | 1 | no | — |
| 185 | C4×Dic73 | — | 2 | 1 | no | — |
| 186 | C4×Dic73 | — | 2 | 1 | no | — |
| 187 | C4×Dic73 | — | 2 | 1 | no | — |
| 188 | C4×Dic73 | — | 2 | 1 | no | — |
| 189 | C4×Dic73 | C2×D4 | 1 | 1 | yes | characteristic |
| 190 | C4×Dic73 | C2×D4 | 1 | 1 | yes | characteristic |
| 191 | C4×Dic73 | C2×D4 | 1 | 1 | yes | characteristic |
| 192 | #41×C73 | — | 8 | 2 | no | — |
| 193 | C2×Q8×C73 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 194 | C2×D4×C73 | — | 2 | 2 | no | — |
| 195 | C2×D4×C73 | — | 2 | 2 | no | — |
| 196 | C2×D4×C73 | — | 2 | 1 | no | — |
| 197 | C2×D4×C73 | — | 2 | 1 | no | — |
| 198 | C2×D4×C73 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 199 | C2×D4×C73 | C22⋊C4 | 1 | 2 | yes | — |
| 200 | C22×C4×C73 | — | 2 | 2 | no | — |
| 201 | C22×C4×C73 | — | 2 | 1 | no | — |
| 202 | C4⋊C4×C73 | — | 2 | 1 | no | — |
| 203 | C4⋊C4×C73 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 204 | C4⋊C4×C73 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 205 | C22⋊C4×C73 | — | 2 | 2 | no | — |
| 206 | C22⋊C4×C73 | — | 2 | 1 | no | — |
| 207 | C42×C73 | — | 2 | 1 | no | — |
| 208 | C42×C73 | C22×C4 | 1 | 1 | yes | characteristic |
| 209 | C23×C73 | — | 2 | 2 | no | — |
| 210 | C23×C73 | — | 2 | 1 | no | — |
| 211 | C22×D73 | — | 2 | 2 | no | — |
| 212 | C22×D73 | — | 4 | 2 | no | — |
| 213 | C22×D73 | — | 4 | 2 | no | — |
| 214 | C22×D73 | — | 8 | 2 | no | — |
| 215 | C22×D73 | — | 8 | 2 | no | — |
| 216 | C22×D73 | #120 | 1 | 1 | yes | characteristic |
| 217 | C2×#64408 | — | 4 | 2 | no | — |
| 218 | C2×#64408 | — | 8 | 1 | no | — |
| 219 | C2×#64408 | — | 8 | 1 | no | — |
| 220 | Q8×C73 | — | 4 | 1 | no | — |
| 221 | D4×C73 | — | 2 | 1 | no | — |
| 222 | D4×C73 | — | 2 | 1 | no | — |
| 223 | D4×C73 | — | 4 | 2 | no | — |
| 224 | D4×C73 | — | 4 | 2 | no | — |
| 225 | D4×C73 | — | 4 | 1 | no | — |
| 226 | D4×C73 | — | 4 | 1 | no | — |
| 227 | D4×C73 | — | 8 | 2 | no | — |
| 228 | D4×C73 | — | 8 | 2 | no | — |
| 229 | C2×C4×C73 | — | 2 | 1 | no | — |
| 230 | C2×C4×C73 | — | 2 | 1 | no | — |
| 231 | C2×C4×C73 | — | 2 | 1 | no | — |
| 232 | C2×C4×C73 | — | 4 | 2 | no | — |
| 233 | C2×C4×C73 | — | 8 | 2 | no | — |
| 234 | C2×C4×C73 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 235 | C2×C4×C73 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 236 | C2×C4×C73 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 237 | C22⋊D73 | — | 4 | 1 | no | — |
| 238 | C22⋊D73 | — | 4 | 1 | no | — |
| 239 | C22⋊D73 | — | 4 | 2 | no | — |
| 240 | C22⋊D73 | — | 4 | 2 | no | — |
| 241 | C22⋊D73 | — | 4 | 2 | no | — |
| 242 | C22⋊D73 | — | 4 | 2 | no | — |
| 243 | C22⋊D73 | — | 8 | 2 | no | — |
| 244 | C22⋊D73 | — | 8 | 2 | no | — |
| 245 | C22⋊D73 | — | 8 | 2 | no | — |
| 246 | C2×Dic73 | — | 2 | 1 | no | — |
| 247 | C2×Dic73 | — | 2 | 1 | no | — |
| 248 | C2×Dic73 | — | 2 | 1 | no | — |
| 249 | C2×Dic73 | — | 2 | 1 | no | — |
| 250 | C2×Dic73 | — | 4 | 1 | no | — |
| 251 | C2×Dic73 | — | 4 | 1 | no | — |
| 252 | C2×Dic73 | — | 4 | 1 | no | — |
| 253 | C2×Dic73 | — | 4 | 1 | no | — |
| 254 | C2×Dic73 | — | 8 | 2 | no | — |
| 255 | C2×Dic73 | #120 | 1 | 1 | yes | characteristic |
| 256 | C2×Dic73 | #120 | 1 | 1 | yes | characteristic |
| 257 | C2×Dic73 | #120 | 1 | 1 | yes | characteristic |
| 258 | D292 | — | 4 | 2 | no | — |
| 259 | D292 | — | 4 | 2 | no | — |
| 260 | D292 | — | 4 | 1 | no | — |
| 261 | D292 | — | 4 | 1 | no | — |
| 262 | C4×D73 | — | 2 | 1 | no | — |
| 263 | C4×D73 | — | 2 | 1 | no | — |
| 264 | C4×D73 | — | 4 | 1 | no | — |
| 265 | C4×D73 | — | 8 | 2 | no | — |
| 266 | C4×D73 | — | 8 | 2 | no | — |
| 267 | C4×D73 | #135 | 1 | 1 | yes | characteristic |
| 268 | C4×D73 | #135 | 1 | 1 | yes | characteristic |
| 269 | C4×D73 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 270 | C4×D73 | #137 | 1 | 1 | yes | characteristic |
| 271 | Dic146 | — | 2 | 1 | no | — |
| 272 | Dic146 | — | 2 | 1 | no | — |
| 273 | Dic146 | — | 4 | 1 | no | — |
| 274 | Dic146 | — | 4 | 1 | no | — |
| 275 | Dic146 | — | 4 | 1 | no | — |
| 276 | #10596833 | — | 8 | 1 | no | — |
| 277 | #10596833 | — | 8 | 1 | no | — |
| 278 | #10596833 | — | 8 | 1 | no | — |
| 279 | C22×C73 | — | 4 | 1 | no | — |
| 280 | C22×C73 | — | 4 | 2 | no | — |
| 281 | C22×C73 | — | 4 | 1 | no | — |
| 282 | C22×C73 | — | 4 | 2 | no | — |
| 283 | C22×C73 | — | 4 | 1 | no | — |
| 284 | C22×C73 | — | 4 | 2 | no | — |
| 285 | C22×C73 | #379 | 1 | 1 | yes | characteristic |
| 286 | C2×D73 | — | 2 | 1 | no | — |
| 287 | C2×D73 | — | 2 | 1 | no | — |
| 288 | C2×D73 | — | 4 | 2 | no | — |
| 289 | C2×D73 | — | 4 | 2 | no | — |
| 290 | C2×D73 | — | 4 | 2 | no | — |
| 291 | C2×D73 | — | 16 | 2 | no | — |
| 292 | C2×D73 | — | 16 | 2 | no | — |
| 293 | C2×D73 | #449 | 1 | 1 | yes | characteristic |
| 294 | C2×D73 | #452 | 1 | 1 | yes | characteristic |
| 295 | #64408 | — | 8 | 2 | no | — |
| 296 | C4×C73 | — | 2 | 1 | no | — |
| 297 | C4×C73 | — | 2 | 1 | no | — |
| 298 | C4×C73 | — | 4 | 1 | no | — |
| 299 | C4×C73 | — | 4 | 1 | no | — |
| 300 | C4×C73 | — | 4 | 1 | no | — |
| 301 | C4×C73 | #416 | 1 | 1 | yes | characteristic |
| 302 | C4×C73 | #417 | 1 | 1 | yes | characteristic |
| 303 | Dic73 | — | 2 | 1 | no | — |
| 304 | Dic73 | — | 4 | 1 | no | — |
| 305 | Dic73 | — | 4 | 1 | no | — |
| 306 | Dic73 | — | 4 | 1 | no | — |
| 307 | Dic73 | — | 4 | 1 | no | — |
| 308 | Dic73 | #449 | 1 | 1 | yes | characteristic |
| 309 | Dic73 | #452 | 1 | 1 | yes | characteristic |
| 310 | Dic73 | #453 | 1 | 1 | yes | characteristic |
| 311 | Dic73 | #455 | 1 | 1 | yes | characteristic |
| 312 | #8426 | — | 73 | 1 | no | maximal, Sylow |
| 313 | C2×C73 | — | 8 | 2 | no | — |
| 314 | C2×C73 | — | 8 | 1 | no | — |
| 315 | C2×C73 | #1788 | 1 | 1 | yes | characteristic |
| 316 | C2×C73 | #1792 | 1 | 1 | yes | characteristic |
| 317 | C2×C73 | #1795 | 1 | 1 | yes | characteristic |
| 318 | D73 | — | 2 | 1 | no | — |
| 319 | D73 | — | 2 | 1 | no | — |
| 320 | D73 | — | 8 | 2 | no | — |
| 321 | #3508 | — | 73 | 1 | no | — |
| 322 | #1982 | — | 73 | 1 | no | — |
| 323 | #1806 | — | 73 | 1 | no | — |
| 324 | #1550 | — | 73 | 1 | no | — |
| 325 | #1545 | — | 73 | 1 | no | — |
| 326 | #1503 | — | 73 | 1 | no | — |
| 327 | #1477 | — | 73 | 1 | no | — |
| 328 | C73 | #8426 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 329 | #559 | — | 73 | 1 | no | — |
| 330 | #559 | — | 73 | 1 | no | — |
| 331 | #559 | — | 146 | 1 | no | — |
| 332 | #550 | — | 73 | 1 | no | — |
| 333 | #550 | — | 146 | 1 | no | — |
| 334 | #550 | #64408 | 1 | 1 | yes | characteristic, complemented |
| 335 | #546 | — | 146 | 1 | no | — |
| 336 | #546 | — | 146 | 2 | no | — |
| 337 | #546 | — | 146 | 1 | no | — |
| 338 | #540 | — | 146 | 2 | no | — |
| 339 | #535 | — | 146 | 1 | no | — |
| 340 | #533 | — | 73 | 1 | no | — |
| 341 | #532 | — | 146 | 1 | no | — |
| 342 | #532 | — | 146 | 1 | no | — |
| 343 | C2×#127 | — | 73 | 1 | no | — |
| 344 | #518 | — | 146 | 1 | no | — |
| 345 | C4×#41 | — | 73 | 1 | no | — |
| 346 | #431 | — | 73 | 1 | no | — |
| 347 | #423 | — | 73 | 1 | no | — |
| 348 | C2×C4⋊C8 | — | 73 | 1 | no | — |
| 349 | C2×#104 | — | 146 | 1 | no | — |
| 350 | C2×#102 | — | 146 | 2 | no | — |
| 351 | C4×C4⋊C4 | — | 73 | 1 | no | — |
| 352 | #339 | — | 146 | 1 | no | — |
| 353 | #333 | — | 146 | 1 | no | — |
| 354 | #332 | — | 146 | 1 | no | — |
| 355 | #331 | — | 146 | 2 | no | — |
| 356 | #328 | — | 146 | 1 | no | — |
| 357 | #328 | — | 146 | 1 | no | — |
| 358 | Q8⋊C8 | — | 146 | 1 | no | — |
| 359 | D4⋊C8 | — | 146 | 1 | no | — |
| 360 | C2×#41 | — | 2 | 1 | no | — |
| 361 | C2×#41 | — | 73 | 1 | no | — |
| 362 | C2×#41 | — | 146 | 1 | no | — |
| 363 | C2×#41 | — | 146 | 2 | no | — |
| 364 | C22×D4 | — | 73 | 2 | no | — |
| 365 | C22×D4 | — | 146 | 1 | no | — |
| 366 | C22×D4 | — | 146 | 1 | no | — |
| 367 | C2×M16 | — | 146 | 1 | no | — |
| 368 | C22×C8 | — | 146 | 1 | no | — |
| 369 | C4⋊Q8 | — | 73 | 1 | no | — |
| 370 | C4⋊Q8 | — | 73 | 1 | no | — |
| 371 | #127 | — | 2 | 1 | no | — |
| 372 | #127 | — | 73 | 2 | no | — |
| 373 | #127 | — | 73 | 1 | no | — |
| 374 | #127 | — | 146 | 1 | no | — |
| 375 | #127 | — | 146 | 1 | no | — |
| 376 | #127 | — | 146 | 1 | no | — |
| 377 | #127 | C2×#64408 | 1 | 1 | yes | characteristic |
| 378 | #125 | — | 146 | 1 | no | — |
| 379 | #124 | — | 146 | 1 | no | — |
| 380 | #124 | — | 146 | 2 | no | — |
| 381 | #124 | — | 146 | 1 | no | — |
| 382 | #124 | — | 146 | 1 | no | — |
| 383 | #124 | — | 146 | 1 | no | — |
| 384 | #123 | — | 146 | 2 | no | — |
| 385 | #123 | — | 146 | 2 | no | — |
| 386 | #123 | — | 146 | 2 | no | — |
| 387 | #123 | — | 146 | 2 | no | — |
| 388 | C22⋊Q8 | — | 73 | 1 | no | — |
| 389 | C22⋊Q8 | — | 73 | 1 | no | — |
| 390 | C22⋊Q8 | — | 146 | 1 | no | — |
| 391 | #121 | — | 2 | 2 | no | — |
| 392 | #121 | — | 2 | 1 | no | — |
| 393 | #121 | — | 146 | 2 | no | — |
| 394 | #121 | — | 146 | 1 | no | — |
| 395 | #121 | — | 146 | 2 | no | — |
| 396 | #121 | — | 146 | 2 | no | — |
| 397 | #121 | — | 146 | 2 | no | — |
| 398 | #121 | — | 146 | 2 | no | — |
| 399 | #121 | — | 146 | 2 | no | — |
| 400 | #120 | — | 146 | 2 | no | — |
| 401 | #120 | — | 146 | 2 | no | — |
| 402 | C4×Q8 | — | 73 | 1 | no | — |
| 403 | C4×Q8 | — | 73 | 1 | no | — |
| 404 | C4×Q8 | — | 73 | 1 | no | — |
| 405 | C4×Q8 | — | 146 | 1 | no | — |
| 406 | C4×Q8 | C2×#64408 | 1 | 1 | yes | characteristic |
| 407 | C4×D4 | — | 2 | 1 | no | — |
| 408 | C4×D4 | — | 73 | 1 | no | — |
| 409 | C4×D4 | — | 146 | 1 | no | — |
| 410 | C4×D4 | — | 146 | 1 | no | — |
| 411 | C4×D4 | — | 146 | 2 | no | — |
| 412 | C4×D4 | — | 146 | 1 | no | — |
| 413 | C4×D4 | — | 146 | 1 | no | — |
| 414 | C4×D4 | — | 146 | 1 | no | — |
| 415 | C4×D4 | — | 146 | 2 | no | — |
| 416 | C4×D4 | — | 146 | 2 | no | — |
| 417 | C4×D4 | — | 146 | 1 | no | — |
| 418 | C4×D4 | — | 146 | 1 | no | — |
| 419 | C4×D4 | C2×#64408 | 1 | 1 | yes | characteristic |
| 420 | #117 | — | 73 | 1 | no | — |
| 421 | #117 | — | 146 | 1 | no | — |
| 422 | #117 | — | 146 | 1 | no | — |
| 423 | C2×C4⋊C4 | — | 146 | 1 | no | — |
| 424 | C2×C22⋊C4 | — | 146 | 2 | no | — |
| 425 | C2×C22⋊C4 | — | 146 | 2 | no | — |
| 426 | C2×C42 | — | 73 | 1 | no | — |
| 427 | C2×C42 | — | 146 | 1 | no | — |
| 428 | C2×C42 | — | 146 | 1 | no | — |
| 429 | C4⋊C8 | — | 146 | 1 | no | — |
| 430 | C4⋊C8 | — | 146 | 1 | no | — |
| 431 | C4⋊C8 | — | 146 | 1 | no | — |
| 432 | C4⋊C8 | — | 146 | 1 | no | — |
| 433 | C4⋊C8 | — | 146 | 1 | no | — |
| 434 | #104 | — | 292 | 2 | no | — |
| 435 | #102 | — | 292 | 4 | no | — |
| 436 | C22⋊C8 | — | 146 | 1 | no | — |
| 437 | C4×C8 | — | 146 | 1 | no | — |
| 438 | #95 | — | 146 | 1 | no | — |
| 439 | C24 | — | 146 | 2 | no | — |
| 440 | #41 | — | 8 | 2 | no | — |
| 441 | #41 | — | 584 | 2 | no | — |
| 442 | #41 | — | 584 | 2 | no | — |
| 443 | #41 | — | 584 | 2 | no | — |
| 444 | #41 | — | 146 | 1 | no | — |
| 445 | #41 | — | 146 | 1 | no | — |
| 446 | #41 | — | 146 | 1 | no | — |
| 447 | #41 | — | 146 | 1 | no | — |
| 448 | C2×Q8 | — | 73 | 1 | no | — |
| 449 | C2×Q8 | — | 73 | 1 | no | — |
| 450 | C2×Q8 | — | 146 | 1 | no | — |
| 451 | C2×Q8 | C22⋊#64408 | 1 | 1 | yes | characteristic |
| 452 | C2×D4 | — | 2 | 2 | no | — |
| 453 | C2×D4 | — | 2 | 2 | no | — |
| 454 | C2×D4 | — | 2 | 1 | no | — |
| 455 | C2×D4 | — | 2 | 1 | no | — |
| 456 | C2×D4 | — | 292 | 1 | no | — |
| 457 | C2×D4 | — | 292 | 1 | no | — |
| 458 | C2×D4 | — | 292 | 1 | no | — |
| 459 | C2×D4 | — | 292 | 1 | no | — |
| 460 | C2×D4 | — | 292 | 2 | no | — |
| 461 | C2×D4 | — | 292 | 2 | no | — |
| 462 | C2×D4 | — | 584 | 2 | no | — |
| 463 | C2×D4 | — | 73 | 2 | no | — |
| 464 | C2×D4 | — | 146 | 2 | no | — |
| 465 | C2×D4 | — | 146 | 2 | no | — |
| 466 | C2×D4 | — | 146 | 2 | no | — |
| 467 | C2×D4 | — | 146 | 1 | no | — |
| 468 | C2×D4 | — | 146 | 2 | no | — |
| 469 | C2×D4 | — | 146 | 2 | no | — |
| 470 | C2×D4 | — | 146 | 1 | no | — |
| 471 | C2×D4 | — | 146 | 1 | no | — |
| 472 | C2×D4 | C22⋊#64408 | 1 | 1 | yes | characteristic |
| 473 | C2×D4 | C22⋊#64408 | 1 | 2 | yes | — |
| 474 | C22×C4 | — | 2 | 2 | no | — |
| 475 | C22×C4 | — | 2 | 1 | no | — |
| 476 | C22×C4 | — | 292 | 1 | no | — |
| 477 | C22×C4 | — | 73 | 1 | no | — |
| 478 | C22×C4 | — | 73 | 1 | no | — |
| 479 | C22×C4 | — | 73 | 1 | no | — |
| 480 | C22×C4 | — | 146 | 2 | no | — |
| 481 | C22×C4 | — | 146 | 2 | no | — |
| 482 | C22×C4 | — | 146 | 1 | no | — |
| 483 | C22×C4 | — | 146 | 1 | no | — |
| 484 | C22×C4 | — | 146 | 2 | no | — |
| 485 | M16 | — | 292 | 1 | no | — |
| 486 | M16 | — | 292 | 1 | no | — |
| 487 | C2×C8 | — | 292 | 1 | no | — |
| 488 | C2×C8 | — | 292 | 1 | no | — |
| 489 | C2×C8 | — | 292 | 1 | no | — |
| 490 | C2×C8 | — | 292 | 2 | no | — |
| 491 | C4⋊C4 | — | 2 | 1 | no | — |
| 492 | C4⋊C4 | — | 292 | 1 | no | — |
| 493 | C4⋊C4 | — | 73 | 1 | no | — |
| 494 | C4⋊C4 | — | 73 | 1 | no | — |
| 495 | C4⋊C4 | — | 146 | 1 | no | — |
| 496 | C4⋊C4 | — | 146 | 1 | no | — |
| 497 | C4⋊C4 | — | 146 | 1 | no | — |
| 498 | C4⋊C4 | — | 146 | 1 | no | — |
| 499 | C4⋊C4 | — | 146 | 1 | no | — |
| 500 | C4⋊C4 | — | 146 | 1 | no | — |
| 501 | C4⋊C4 | — | 146 | 2 | no | — |
| 502 | C4⋊C4 | — | 146 | 1 | no | — |
| 503 | C4⋊C4 | — | 146 | 1 | no | — |
| 504 | C4⋊C4 | C22⋊#64408 | 1 | 1 | yes | characteristic |
| 505 | C4⋊C4 | C22⋊#64408 | 1 | 1 | yes | characteristic |
| 506 | C22⋊C4 | — | 2 | 2 | no | — |
| 507 | C22⋊C4 | — | 2 | 1 | no | — |
| 508 | C22⋊C4 | — | 146 | 1 | no | — |
| 509 | C22⋊C4 | — | 146 | 1 | no | — |
| 510 | C22⋊C4 | — | 146 | 1 | no | — |
| 511 | C22⋊C4 | — | 146 | 2 | no | — |
| 512 | C22⋊C4 | — | 146 | 2 | no | — |
| 513 | C22⋊C4 | — | 146 | 2 | no | — |
| 514 | C22⋊C4 | — | 146 | 2 | no | — |
| 515 | C22⋊C4 | — | 146 | 1 | no | — |
| 516 | C22⋊C4 | — | 146 | 2 | no | — |
| 517 | C22⋊C4 | — | 146 | 2 | no | — |
| 518 | C22⋊C4 | — | 146 | 2 | no | — |
| 519 | C42 | — | 2 | 1 | no | — |
| 520 | C42 | — | 292 | 1 | no | — |
| 521 | C42 | — | 292 | 1 | no | — |
| 522 | C42 | — | 73 | 1 | no | — |
| 523 | C42 | — | 73 | 1 | no | — |
| 524 | C42 | — | 73 | 1 | no | — |
| 525 | C42 | — | 146 | 1 | no | — |
| 526 | C42 | — | 146 | 1 | no | — |
| 527 | C42 | — | 146 | 1 | no | — |
| 528 | C42 | — | 146 | 1 | no | — |
| 529 | C42 | C22×#64408 | 1 | 1 | yes | characteristic |
| 530 | C23 | — | 2 | 2 | no | — |
| 531 | C23 | — | 2 | 1 | no | — |
| 532 | C23 | — | 292 | 2 | no | — |
| 533 | C23 | — | 292 | 2 | no | — |
| 534 | C23 | — | 584 | 2 | no | — |
| 535 | C23 | — | 584 | 2 | no | — |
| 536 | C23 | — | 73 | 1 | no | — |
| 537 | C23 | — | 146 | 2 | no | — |
| 538 | Q8 | — | 4 | 1 | no | — |
| 539 | Q8 | — | 292 | 1 | no | — |
| 540 | Q8 | — | 292 | 1 | no | — |
| 541 | Q8 | — | 292 | 1 | no | — |
| 542 | Q8 | — | 146 | 1 | no | — |
| 543 | Q8 | — | 146 | 1 | no | — |
| 544 | D4 | — | 2 | 1 | no | — |
| 545 | D4 | — | 2 | 1 | no | — |
| 546 | D4 | — | 4 | 2 | no | — |
| 547 | D4 | — | 4 | 2 | no | — |
| 548 | D4 | — | 4 | 1 | no | — |
| 549 | D4 | — | 4 | 1 | no | — |
| 550 | D4 | — | 8 | 2 | no | — |
| 551 | D4 | — | 8 | 2 | no | — |
| 552 | D4 | — | 292 | 2 | no | — |
| 553 | D4 | — | 292 | 2 | no | — |
| 554 | D4 | — | 292 | 1 | no | — |
| 555 | D4 | — | 292 | 1 | no | — |
| 556 | D4 | — | 292 | 2 | no | — |
| 557 | D4 | — | 292 | 2 | no | — |
| 558 | D4 | — | 292 | 2 | no | — |
| 559 | D4 | — | 292 | 2 | no | — |
| 560 | D4 | — | 292 | 1 | no | — |
| 561 | D4 | — | 292 | 1 | no | — |
| 562 | D4 | — | 584 | 2 | no | — |
| 563 | D4 | — | 584 | 2 | no | — |
| 564 | D4 | — | 584 | 2 | no | — |
| 565 | C2×C4 | — | 2 | 1 | no | — |
| 566 | C2×C4 | — | 2 | 1 | no | — |
| 567 | C2×C4 | — | 2 | 1 | no | — |
| 568 | C2×C4 | — | 4 | 2 | no | — |
| 569 | C2×C4 | — | 8 | 2 | no | — |
| 570 | C2×C4 | — | 292 | 1 | no | — |
| 571 | C2×C4 | — | 292 | 1 | no | — |
| 572 | C2×C4 | — | 292 | 1 | no | — |
| 573 | C2×C4 | — | 292 | 1 | no | — |
| 574 | C2×C4 | — | 292 | 1 | no | — |
| 575 | C2×C4 | — | 292 | 2 | no | — |
| 576 | C2×C4 | — | 584 | 2 | no | — |
| 577 | C2×C4 | — | 584 | 2 | no | — |
| 578 | C2×C4 | — | 584 | 2 | no | — |
| 579 | C2×C4 | — | 584 | 1 | no | — |
| 580 | C2×C4 | — | 584 | 1 | no | — |
| 581 | C2×C4 | — | 73 | 1 | no | — |
| 582 | C2×C4 | — | 73 | 1 | no | — |
| 583 | C2×C4 | — | 73 | 1 | no | — |
| 584 | C2×C4 | — | 73 | 1 | no | — |
| 585 | C2×C4 | — | 73 | 1 | no | — |
| 586 | C2×C4 | — | 73 | 1 | no | — |
| 587 | C2×C4 | — | 73 | 1 | no | — |
| 588 | C2×C4 | — | 146 | 1 | no | — |
| 589 | C2×C4 | — | 146 | 1 | no | — |
| 590 | C2×C4 | — | 146 | 1 | no | — |
| 591 | C2×C4 | — | 146 | 1 | no | — |
| 592 | C2×C4 | — | 146 | 1 | no | — |
| 593 | C2×C4 | — | 146 | 1 | no | — |
| 594 | C2×C4 | C2×C22⋊#64408 | 1 | 1 | yes | characteristic |
| 595 | C2×C4 | C2×C22⋊#64408 | 1 | 1 | yes | characteristic |
| 596 | C2×C4 | C2×C22⋊#64408 | 1 | 1 | yes | characteristic |
| 597 | C8 | — | 584 | 1 | no | — |
| 598 | C8 | — | 584 | 1 | no | — |
| 599 | C8 | — | 584 | 1 | no | — |
| 600 | C22 | — | 4 | 1 | no | — |
| 601 | C22 | — | 4 | 2 | no | — |
| 602 | C22 | — | 4 | 1 | no | — |
| 603 | C22 | — | 4 | 2 | no | — |
| 604 | C22 | — | 4 | 1 | no | — |
| 605 | C22 | — | 4 | 2 | no | — |
| 606 | C22 | — | 292 | 2 | no | — |
| 607 | C22 | — | 292 | 2 | no | — |
| 608 | C22 | — | 292 | 2 | no | — |
| 609 | C22 | — | 73 | 1 | no | — |
| 610 | C22 | — | 73 | 1 | no | — |
| 611 | C22 | — | 1168 | 2 | no | — |
| 612 | C22 | — | 1168 | 2 | no | — |
| 613 | C22 | — | 146 | 1 | no | — |
| 614 | C22 | — | 146 | 1 | no | — |
| 615 | C22 | #17989528 | 1 | 1 | yes | characteristic |
| 616 | C4 | — | 2 | 1 | no | — |
| 617 | C4 | — | 2 | 1 | no | — |
| 618 | C4 | — | 4 | 1 | no | — |
| 619 | C4 | — | 4 | 1 | no | — |
| 620 | C4 | — | 4 | 1 | no | — |
| 621 | C4 | — | 292 | 1 | no | — |
| 622 | C4 | — | 292 | 1 | no | — |
| 623 | C4 | — | 292 | 1 | no | — |
| 624 | C4 | — | 292 | 1 | no | — |
| 625 | C4 | — | 584 | 2 | no | — |
| 626 | C4 | — | 73 | 1 | no | — |
| 627 | C4 | — | 73 | 1 | no | — |
| 628 | C4 | — | 73 | 1 | no | — |
| 629 | C4 | — | 73 | 1 | no | — |
| 630 | C4 | — | 146 | 1 | no | — |
| 631 | C4 | #17989577 | 1 | 1 | yes | characteristic |
| 632 | C4 | #17989578 | 1 | 1 | yes | characteristic |
| 633 | C2 | — | 8 | 2 | no | — |
| 634 | C2 | — | 8 | 1 | no | — |
| 635 | C2 | — | 584 | 2 | no | — |
| 636 | C2 | — | 146 | 1 | no | — |
| 637 | C2 | — | 146 | 1 | no | — |
| 638 | C2 | #22625771 | 1 | 1 | yes | characteristic |
| 639 | C2 | #22625777 | 1 | 1 | yes | characteristic |
| 640 | C2 | #22625781 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22626098 | C2 | semidirect |
| 2. #22625805 | C2 | semidirect |
| 3. #22625448 | C2 | semidirect |
| 4. #22625439 | C2 | semidirect |
| 5. #22625313 | C2 | semidirect |
| 6. #22625227 | C2 | semidirect |
| 22. #17989323 | C4 | semidirect |
| 23. #17989322 | C4 | semidirect |
| 25. #17989258 | C4 | semidirect |
| 38. #550×C73 | C4 | semidirect |
| 328. C73 | #8426 | semidirect |
| 334. #550 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626098 | 2 |
| #22625805 | 2 |
| #22625448 | 2 |
| #22625439 | 2 |
| #22625313 | 2 |
| #22625227 | 2 |
| #22623801 | 2 |
| #8426 | 73 |