Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1154 conjugacy classes of subgroups.
The subgroup lattice has 424 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #22626899 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #22626592 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #22626259 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #22626258 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | D73⋊#361 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | C2×#17989505 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #576×D73 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #17989666 | — | 2 | 1 | no | — |
| 9 | #17989646 | — | 2 | 3 | no | — |
| 10 | #17989645 | — | 2 | 1 | no | — |
| 11 | C2×#14556666 | C22 | 1 | 3 | yes | complemented |
| 12 | #17989643 | C22 | 1 | 3 | yes | complemented |
| 13 | #17989602 | — | 2 | 3 | no | — |
| 14 | D73⋊#108 | C22 | 1 | 3 | yes | complemented |
| 15 | C2×#14556661 | C22 | 1 | 3 | yes | complemented |
| 16 | #17989506 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | #17989506 | C22 | 1 | 3 | yes | complemented |
| 18 | #17989505 | C22 | 1 | 3 | yes | complemented |
| 19 | #17989505 | C22 | 1 | 6 | yes | complemented |
| 20 | #17989505 | C22 | 1 | 3 | yes | complemented |
| 21 | H(5,𝔽2)×D73 | — | 2 | 1 | no | — |
| 22 | #17989392 | C4 | 1 | 1 | yes | characteristic |
| 23 | #17989391 | — | 2 | 3 | no | — |
| 24 | #17989390 | — | 2 | 1 | no | — |
| 25 | #17989389 | C4 | 1 | 3 | yes | — |
| 26 | #17989388 | C4 | 1 | 3 | yes | — |
| 27 | AGL(1,ℤ/8)×D73 | — | 2 | 3 | no | — |
| 28 | #135×D73 | C22 | 1 | 3 | yes | — |
| 29 | C2×D8×D73 | C22 | 1 | 3 | yes | — |
| 30 | #131×D73 | C22 | 1 | 1 | yes | characteristic |
| 31 | #576×C73 | C4 | 1 | 1 | yes | characteristic |
| 32 | #14556679 | — | 4 | 1 | no | — |
| 33 | #14556678 | — | 4 | 3 | no | — |
| 34 | C2×#11924038 | — | 2 | 3 | no | — |
| 35 | D73⋊M16 | — | 2 | 3 | no | — |
| 36 | #14556666 | — | 2 | 3 | no | — |
| 37 | #14556666 | C23 | 1 | 3 | yes | — |
| 38 | #14556666 | C23 | 1 | 1 | yes | characteristic |
| 39 | #14556665 | — | 2 | 3 | no | — |
| 40 | #14556664 | — | 2 | 3 | no | — |
| 41 | C2×#11924031 | — | 2 | 3 | no | — |
| 42 | #14556662 | — | 2 | 3 | no | — |
| 43 | #14556661 | — | 2 | 3 | no | — |
| 44 | #14556661 | C23 | 1 | 3 | yes | — |
| 45 | #14556661 | C23 | 1 | 1 | yes | characteristic |
| 46 | #14556637 | — | 2 | 3 | no | — |
| 47 | #14556637 | — | 2 | 1 | no | — |
| 48 | #14556637 | — | 4 | 1 | no | — |
| 49 | #14556636 | — | 2 | 3 | no | — |
| 50 | #14556636 | — | 4 | 3 | no | — |
| 51 | #41×D73 | — | 2 | 3 | no | — |
| 52 | #41×D73 | — | 4 | 1 | no | — |
| 53 | #41×D73 | D4 | 1 | 1 | yes | characteristic |
| 54 | C2×D4×D73 | — | 2 | 3 | no | — |
| 55 | C2×D4×D73 | — | 4 | 3 | no | — |
| 56 | #14556619 | — | 2 | 3 | no | — |
| 57 | #14556618 | — | 2 | 6 | no | — |
| 58 | #14556617 | — | 2 | 3 | no | — |
| 59 | #14556616 | — | 2 | 3 | no | — |
| 60 | #14556615 | — | 2 | 6 | no | — |
| 61 | #14556614 | C2×C4 | 1 | 3 | yes | — |
| 62 | #14556613 | C2×C4 | 1 | 3 | yes | — |
| 63 | #14556612 | — | 2 | 3 | no | — |
| 64 | #14556611 | — | 2 | 3 | no | — |
| 65 | #14556610 | C2×C4 | 1 | 3 | yes | — |
| 66 | Q16×D73 | C23 | 1 | 1 | yes | characteristic |
| 67 | SD16×D73 | — | 2 | 3 | no | — |
| 68 | C2×D584 | C2×C4 | 1 | 3 | yes | — |
| 69 | C2×#11924013 | — | 2 | 3 | no | — |
| 70 | D8×D73 | — | 2 | 3 | no | — |
| 71 | D8×D73 | — | 2 | 3 | no | — |
| 72 | D8×D73 | C2×C4 | 1 | 6 | yes | — |
| 73 | D8×D73 | C23 | 1 | 3 | yes | — |
| 74 | #14556599 | D4 | 1 | 3 | yes | — |
| 75 | #14556598 | D4 | 1 | 1 | yes | characteristic |
| 76 | #14556597 | C2×C4 | 1 | 3 | yes | — |
| 77 | M16×D73 | D4 | 1 | 3 | yes | — |
| 78 | C2×C8×D73 | C23 | 1 | 3 | yes | — |
| 79 | H(5,𝔽2)×C73 | — | 2 | 1 | no | — |
| 80 | AGL(1,ℤ/8)×C73 | — | 2 | 3 | no | — |
| 81 | #135×C73 | C2×C4 | 1 | 3 | yes | — |
| 82 | C2×D8×C73 | C2×C4 | 1 | 3 | yes | — |
| 83 | #131×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 84 | #11924038 | — | 2 | 1 | no | — |
| 85 | #11924038 | — | 2 | 3 | no | — |
| 86 | #11924038 | — | 4 | 3 | no | — |
| 87 | #11924037 | — | 4 | 3 | no | — |
| 88 | #11924036 | — | 4 | 3 | no | — |
| 89 | C2×#10596833 | — | 4 | 3 | no | — |
| 90 | #11924031 | — | 2 | 1 | no | — |
| 91 | #11924031 | — | 2 | 3 | no | — |
| 92 | C23×D73 | — | 4 | 3 | no | — |
| 93 | #11924029 | — | 2 | 3 | no | — |
| 94 | #11924029 | — | 4 | 1 | no | — |
| 95 | #11924029 | D8 | 1 | 1 | yes | characteristic |
| 96 | #11924028 | — | 2 | 3 | no | — |
| 97 | #11924028 | — | 4 | 3 | no | — |
| 98 | #11924028 | — | 4 | 3 | no | — |
| 99 | #11924028 | C22⋊C4 | 1 | 3 | yes | — |
| 100 | #11924027 | — | 2 | 3 | no | — |
| 101 | #11924027 | — | 4 | 3 | no | — |
| 102 | #11924027 | — | 4 | 3 | no | — |
| 103 | #11924027 | D8 | 1 | 3 | yes | — |
| 104 | Q8×D73 | — | 2 | 1 | no | — |
| 105 | Q8×D73 | SD16 | 1 | 1 | yes | characteristic |
| 106 | C2×D292 | — | 2 | 3 | no | — |
| 107 | C2×D292 | — | 4 | 3 | no | — |
| 108 | C2×C22⋊D73 | — | 4 | 6 | no | — |
| 109 | C2×C22⋊D73 | — | 4 | 3 | no | — |
| 110 | D4×D73 | — | 2 | 6 | no | — |
| 111 | D4×D73 | — | 2 | 3 | no | — |
| 112 | D4×D73 | — | 4 | 3 | no | — |
| 113 | D4×D73 | — | 4 | 3 | no | — |
| 114 | D4×D73 | — | 4 | 6 | no | — |
| 115 | D4×D73 | — | 4 | 3 | no | — |
| 116 | D4×D73 | — | 4 | 3 | no | — |
| 117 | D4×D73 | — | 4 | 3 | no | — |
| 118 | D4×D73 | SD16 | 1 | 3 | yes | — |
| 119 | C2×C4×D73 | — | 4 | 3 | no | — |
| 120 | C2×C4×D73 | C2×D4 | 1 | 3 | yes | — |
| 121 | Dic292 | C22×C4 | 1 | 1 | yes | characteristic |
| 122 | #11924018 | — | 2 | 1 | no | — |
| 123 | #11924017 | — | 2 | 3 | no | — |
| 124 | #11924016 | — | 2 | 3 | no | — |
| 125 | #11924015 | — | 2 | 3 | no | — |
| 126 | D584 | — | 2 | 3 | no | — |
| 127 | D584 | C22×C4 | 1 | 3 | yes | — |
| 128 | #11924013 | — | 2 | 6 | no | — |
| 129 | #11924013 | — | 2 | 3 | no | — |
| 130 | #11924012 | C22⋊C4 | 1 | 3 | yes | — |
| 131 | #11924011 | C22⋊C4 | 1 | 6 | yes | — |
| 132 | C2×#10596831 | C2×D4 | 1 | 3 | yes | — |
| 133 | C8×D73 | C22×C4 | 1 | 3 | yes | — |
| 134 | C8×D73 | C2×D4 | 1 | 3 | yes | — |
| 135 | C8×D73 | C2×D4 | 1 | 3 | yes | — |
| 136 | C8×D73 | C24 | 1 | 1 | yes | characteristic |
| 137 | #41×C73 | — | 2 | 3 | no | — |
| 138 | #41×C73 | — | 4 | 1 | no | — |
| 139 | #41×C73 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 140 | C2×D4×C73 | — | 2 | 3 | no | — |
| 141 | C2×D4×C73 | — | 4 | 3 | no | — |
| 142 | Q16×C73 | C22×C4 | 1 | 1 | yes | characteristic |
| 143 | SD16×C73 | — | 2 | 3 | no | — |
| 144 | D8×C73 | — | 2 | 3 | no | — |
| 145 | D8×C73 | C22×C4 | 1 | 3 | yes | — |
| 146 | M16×C73 | C22⋊C4 | 1 | 3 | yes | — |
| 147 | C2×C8×C73 | C22×C4 | 1 | 3 | yes | — |
| 148 | C23×C73 | — | 4 | 3 | no | — |
| 149 | C22×D73 | — | 4 | 3 | no | — |
| 150 | C22×D73 | — | 4 | 3 | no | — |
| 151 | C22×D73 | — | 4 | 6 | no | — |
| 152 | C22×D73 | — | 16 | 6 | no | — |
| 153 | C22×D73 | C2×SD16 | 1 | 3 | yes | — |
| 154 | Q8×C73 | — | 2 | 1 | no | — |
| 155 | Q8×C73 | #102 | 1 | 1 | yes | characteristic |
| 156 | D4×C73 | — | 2 | 3 | no | — |
| 157 | D4×C73 | — | 4 | 3 | no | — |
| 158 | D4×C73 | — | 4 | 3 | no | — |
| 159 | D4×C73 | #102 | 1 | 3 | yes | — |
| 160 | C2×C4×C73 | — | 4 | 3 | no | — |
| 161 | C2×C4×C73 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 162 | C22⋊D73 | — | 4 | 3 | no | — |
| 163 | C22⋊D73 | — | 4 | 3 | no | — |
| 164 | C22⋊D73 | — | 4 | 3 | no | — |
| 165 | C22⋊D73 | — | 4 | 6 | no | — |
| 166 | C22⋊D73 | #102 | 1 | 6 | yes | — |
| 167 | C2×Dic73 | — | 4 | 3 | no | — |
| 168 | C2×Dic73 | C2×D8 | 1 | 3 | yes | — |
| 169 | D292 | — | 2 | 3 | no | — |
| 170 | D292 | — | 4 | 3 | no | — |
| 171 | D292 | — | 4 | 3 | no | — |
| 172 | D292 | #102 | 1 | 3 | yes | — |
| 173 | C4×D73 | — | 4 | 1 | no | — |
| 174 | C4×D73 | — | 4 | 3 | no | — |
| 175 | C4×D73 | — | 4 | 3 | no | — |
| 176 | C4×D73 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 177 | C4×D73 | C2×D8 | 1 | 3 | yes | — |
| 178 | C4×D73 | C2×SD16 | 1 | 3 | yes | — |
| 179 | C4×D73 | C22×D4 | 1 | 1 | yes | characteristic |
| 180 | Dic146 | — | 2 | 1 | no | — |
| 181 | Dic146 | — | 4 | 1 | no | — |
| 182 | Dic146 | #102 | 1 | 3 | yes | — |
| 183 | #10596833 | — | 4 | 3 | no | — |
| 184 | #10596833 | — | 4 | 1 | no | — |
| 185 | C8×C73 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 186 | C8×C73 | C23×C4 | 1 | 1 | yes | characteristic |
| 187 | #10596831 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 188 | #10596831 | C22×D4 | 1 | 1 | yes | characteristic |
| 189 | C22×C73 | — | 4 | 3 | no | — |
| 190 | C22×C73 | — | 16 | 3 | no | — |
| 191 | C22×C73 | C2×#102 | 1 | 3 | yes | — |
| 192 | C2×D73 | — | 4 | 3 | no | — |
| 193 | C2×D73 | — | 4 | 3 | no | — |
| 194 | C2×D73 | — | 8 | 6 | no | — |
| 195 | C2×D73 | — | 16 | 6 | no | — |
| 196 | C2×D73 | — | 16 | 3 | no | — |
| 197 | C2×D73 | C2×#102 | 1 | 3 | yes | — |
| 198 | C2×D73 | C22×SD16 | 1 | 1 | yes | characteristic |
| 199 | C4×C73 | — | 4 | 1 | no | — |
| 200 | C4×C73 | C2×#102 | 1 | 3 | yes | — |
| 201 | C4×C73 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 202 | Dic73 | — | 4 | 1 | no | — |
| 203 | Dic73 | C2×#102 | 1 | 3 | yes | — |
| 204 | Dic73 | C22×D8 | 1 | 1 | yes | characteristic |
| 205 | #33392 | — | 73 | 1 | no | maximal, Sylow |
| 206 | C2×C73 | — | 2 | 3 | no | — |
| 207 | C2×C73 | — | 8 | 3 | no | — |
| 208 | C2×C73 | C22×#102 | 1 | 1 | yes | characteristic |
| 209 | D73 | — | 2 | 1 | no | — |
| 210 | D73 | — | 2 | 3 | no | — |
| 211 | D73 | — | 8 | 3 | no | — |
| 212 | C2×#576 | — | 73 | 1 | no | — |
| 213 | #3407 | — | 73 | 1 | no | — |
| 214 | #2916 | — | 73 | 1 | no | — |
| 215 | #2148 | — | 73 | 3 | no | — |
| 216 | #2148 | — | 73 | 3 | no | — |
| 217 | C2×#361 | — | 73 | 3 | no | — |
| 218 | C2×#361 | — | 73 | 3 | no | — |
| 219 | C73 | #33392 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 220 | C2×H(5,𝔽2) | — | 146 | 1 | no | — |
| 221 | #576 | — | 73 | 3 | no | — |
| 222 | #576 | — | 73 | 3 | no | — |
| 223 | #576 | — | 73 | 1 | no | — |
| 224 | #576 | — | 146 | 3 | no | — |
| 225 | #576 | — | 146 | 1 | no | — |
| 226 | #576 | #64408 | 1 | 1 | yes | characteristic |
| 227 | C2×AGL(1,ℤ/8) | — | 146 | 3 | no | — |
| 228 | C2×#135 | — | 73 | 3 | no | — |
| 229 | C22×D8 | — | 73 | 3 | no | — |
| 230 | #568 | — | 146 | 1 | no | — |
| 231 | C2×#131 | — | 73 | 1 | no | — |
| 232 | #504 | — | 146 | 1 | no | — |
| 233 | #504 | — | 146 | 3 | no | — |
| 234 | C2×M32 | — | 73 | 3 | no | — |
| 235 | C2×M32 | — | 73 | 3 | no | — |
| 236 | #430 | — | 146 | 3 | no | — |
| 237 | C2×#108 | — | 73 | 3 | no | — |
| 238 | C2×#108 | — | 73 | 3 | no | — |
| 239 | #362 | — | 73 | 1 | no | — |
| 240 | #362 | — | 73 | 3 | no | — |
| 241 | #361 | — | 73 | 3 | no | — |
| 242 | #361 | — | 73 | 6 | no | — |
| 243 | #361 | — | 73 | 3 | no | — |
| 244 | H(5,𝔽2) | — | 2 | 1 | no | — |
| 245 | H(5,𝔽2) | — | 292 | 3 | no | — |
| 246 | H(5,𝔽2) | — | 292 | 1 | no | — |
| 247 | H(5,𝔽2) | — | 146 | 3 | no | — |
| 248 | H(5,𝔽2) | — | 146 | 3 | no | — |
| 249 | H(5,𝔽2) | — | 146 | 1 | no | — |
| 250 | C2×#41 | — | 292 | 1 | no | — |
| 251 | C2×#41 | — | 73 | 1 | no | — |
| 252 | C2×#41 | — | 146 | 3 | no | — |
| 253 | C22×D4 | — | 292 | 3 | no | — |
| 254 | C22×D4 | — | 146 | 3 | no | — |
| 255 | AGL(1,ℤ/8) | — | 2 | 3 | no | — |
| 256 | AGL(1,ℤ/8) | — | 146 | 6 | no | — |
| 257 | AGL(1,ℤ/8) | — | 146 | 6 | no | — |
| 258 | AGL(1,ℤ/8) | — | 146 | 3 | no | — |
| 259 | AGL(1,ℤ/8) | — | 146 | 3 | no | — |
| 260 | AGL(1,ℤ/8) | — | 146 | 3 | no | — |
| 261 | #135 | — | 73 | 3 | no | — |
| 262 | #135 | — | 73 | 3 | no | — |
| 263 | #135 | — | 73 | 3 | no | — |
| 264 | #135 | — | 146 | 3 | no | — |
| 265 | #135 | — | 146 | 3 | no | — |
| 266 | #135 | C2×#64408 | 1 | 3 | yes | — |
| 267 | C2×Q16 | — | 73 | 1 | no | — |
| 268 | C2×SD16 | — | 146 | 3 | no | — |
| 269 | C2×D8 | — | 73 | 3 | no | — |
| 270 | C2×D8 | — | 73 | 6 | no | — |
| 271 | C2×D8 | — | 73 | 3 | no | — |
| 272 | C2×D8 | — | 146 | 3 | no | — |
| 273 | C2×D8 | — | 146 | 3 | no | — |
| 274 | C2×D8 | — | 146 | 3 | no | — |
| 275 | C2×D8 | C2×#64408 | 1 | 3 | yes | — |
| 276 | #131 | — | 292 | 3 | no | — |
| 277 | #131 | — | 292 | 1 | no | — |
| 278 | #131 | — | 73 | 1 | no | — |
| 279 | #131 | — | 73 | 3 | no | — |
| 280 | #131 | — | 73 | 3 | no | — |
| 281 | #131 | C2×#64408 | 1 | 1 | yes | characteristic |
| 282 | C2×M16 | — | 73 | 3 | no | — |
| 283 | C2×M16 | — | 146 | 3 | no | — |
| 284 | C2×M16 | — | 146 | 3 | no | — |
| 285 | C22×C8 | — | 73 | 3 | no | — |
| 286 | M32 | — | 73 | 3 | no | — |
| 287 | M32 | — | 73 | 1 | no | — |
| 288 | M32 | — | 146 | 3 | no | — |
| 289 | M32 | — | 146 | 3 | no | — |
| 290 | C2×C16 | — | 146 | 3 | no | — |
| 291 | C2×C16 | — | 146 | 3 | no | — |
| 292 | #108 | — | 73 | 3 | no | — |
| 293 | #108 | — | 73 | 1 | no | — |
| 294 | #108 | — | 146 | 3 | no | — |
| 295 | #108 | — | 146 | 3 | no | — |
| 296 | C24 | — | 292 | 3 | no | — |
| 297 | #41 | — | 2 | 3 | no | — |
| 298 | #41 | — | 4 | 1 | no | — |
| 299 | #41 | — | 292 | 3 | no | — |
| 300 | #41 | — | 292 | 3 | no | — |
| 301 | #41 | — | 292 | 3 | no | — |
| 302 | #41 | — | 292 | 1 | no | — |
| 303 | #41 | — | 292 | 3 | no | — |
| 304 | #41 | — | 73 | 1 | no | — |
| 305 | #41 | — | 73 | 3 | no | — |
| 306 | #41 | — | 73 | 3 | no | — |
| 307 | #41 | — | 146 | 3 | no | — |
| 308 | #41 | — | 146 | 3 | no | — |
| 309 | #41 | — | 146 | 3 | no | — |
| 310 | #41 | C22⋊#64408 | 1 | 1 | yes | characteristic |
| 311 | C2×Q8 | — | 73 | 1 | no | — |
| 312 | C2×Q8 | — | 146 | 1 | no | — |
| 313 | C2×D4 | — | 2 | 3 | no | — |
| 314 | C2×D4 | — | 4 | 3 | no | — |
| 315 | C2×D4 | — | 292 | 3 | no | — |
| 316 | C2×D4 | — | 292 | 3 | no | — |
| 317 | C2×D4 | — | 292 | 6 | no | — |
| 318 | C2×D4 | — | 292 | 3 | no | — |
| 319 | C2×D4 | — | 292 | 6 | no | — |
| 320 | C2×D4 | — | 292 | 3 | no | — |
| 321 | C2×D4 | — | 292 | 3 | no | — |
| 322 | C2×D4 | — | 292 | 3 | no | — |
| 323 | C2×D4 | — | 292 | 3 | no | — |
| 324 | C2×D4 | — | 73 | 3 | no | — |
| 325 | C2×D4 | — | 146 | 3 | no | — |
| 326 | C2×D4 | — | 146 | 6 | no | — |
| 327 | C2×D4 | — | 146 | 3 | no | — |
| 328 | C22×C4 | — | 292 | 3 | no | — |
| 329 | C22×C4 | — | 73 | 3 | no | — |
| 330 | Q16 | — | 73 | 1 | no | — |
| 331 | Q16 | — | 146 | 1 | no | — |
| 332 | Q16 | C22×#64408 | 1 | 1 | yes | characteristic |
| 333 | SD16 | — | 2 | 3 | no | — |
| 334 | SD16 | — | 146 | 3 | no | — |
| 335 | SD16 | — | 146 | 3 | no | — |
| 336 | SD16 | — | 146 | 3 | no | — |
| 337 | D8 | — | 2 | 3 | no | — |
| 338 | D8 | — | 73 | 3 | no | — |
| 339 | D8 | — | 146 | 3 | no | — |
| 340 | D8 | — | 146 | 6 | no | — |
| 341 | D8 | — | 146 | 3 | no | — |
| 342 | D8 | C22×#64408 | 1 | 3 | yes | — |
| 343 | M16 | — | 292 | 3 | no | — |
| 344 | M16 | — | 292 | 3 | no | — |
| 345 | M16 | — | 73 | 3 | no | — |
| 346 | M16 | — | 73 | 6 | no | — |
| 347 | M16 | — | 146 | 1 | no | — |
| 348 | M16 | — | 146 | 3 | no | — |
| 349 | M16 | C22⋊#64408 | 1 | 3 | yes | — |
| 350 | C2×C8 | — | 292 | 3 | no | — |
| 351 | C2×C8 | — | 292 | 3 | no | — |
| 352 | C2×C8 | — | 73 | 3 | no | — |
| 353 | C2×C8 | — | 73 | 3 | no | — |
| 354 | C2×C8 | — | 73 | 1 | no | — |
| 355 | C2×C8 | — | 73 | 3 | no | — |
| 356 | C2×C8 | — | 73 | 3 | no | — |
| 357 | C2×C8 | C22×#64408 | 1 | 3 | yes | — |
| 358 | C16 | — | 146 | 1 | no | — |
| 359 | C16 | — | 146 | 3 | no | — |
| 360 | C23 | — | 4 | 3 | no | — |
| 361 | C23 | — | 292 | 3 | no | — |
| 362 | C23 | — | 292 | 6 | no | — |
| 363 | C23 | — | 292 | 3 | no | — |
| 364 | C23 | — | 73 | 3 | no | — |
| 365 | C23 | — | 1168 | 6 | no | — |
| 366 | Q8 | — | 2 | 1 | no | — |
| 367 | Q8 | — | 292 | 1 | no | — |
| 368 | Q8 | — | 73 | 3 | no | — |
| 369 | Q8 | — | 146 | 1 | no | — |
| 370 | Q8 | #14556653 | 1 | 1 | yes | characteristic |
| 371 | D4 | — | 2 | 3 | no | — |
| 372 | D4 | — | 4 | 3 | no | — |
| 373 | D4 | — | 4 | 3 | no | — |
| 374 | D4 | — | 292 | 3 | no | — |
| 375 | D4 | — | 292 | 3 | no | — |
| 376 | D4 | — | 292 | 3 | no | — |
| 377 | D4 | — | 292 | 3 | no | — |
| 378 | D4 | — | 292 | 6 | no | — |
| 379 | D4 | — | 292 | 3 | no | — |
| 380 | D4 | — | 73 | 6 | no | — |
| 381 | D4 | — | 73 | 3 | no | — |
| 382 | D4 | — | 146 | 3 | no | — |
| 383 | D4 | #14556653 | 1 | 3 | yes | — |
| 384 | C2×C4 | — | 4 | 3 | no | — |
| 385 | C2×C4 | — | 292 | 1 | no | — |
| 386 | C2×C4 | — | 292 | 3 | no | — |
| 387 | C2×C4 | — | 292 | 3 | no | — |
| 388 | C2×C4 | — | 292 | 3 | no | — |
| 389 | C2×C4 | — | 73 | 3 | no | — |
| 390 | C2×C4 | — | 73 | 1 | no | — |
| 391 | C2×C4 | — | 73 | 3 | no | — |
| 392 | C2×C4 | — | 73 | 3 | no | — |
| 393 | C2×C4 | — | 73 | 3 | no | — |
| 394 | C2×C4 | C2×C22⋊#64408 | 1 | 3 | yes | — |
| 395 | C8 | — | 292 | 3 | no | — |
| 396 | C8 | — | 292 | 1 | no | — |
| 397 | C8 | — | 73 | 1 | no | — |
| 398 | C8 | — | 73 | 3 | no | — |
| 399 | C8 | C2×C22⋊#64408 | 1 | 3 | yes | — |
| 400 | C8 | C23×#64408 | 1 | 1 | yes | characteristic |
| 401 | C22 | — | 4 | 3 | no | — |
| 402 | C22 | — | 16 | 3 | no | — |
| 403 | C22 | — | 292 | 3 | no | — |
| 404 | C22 | — | 292 | 3 | no | — |
| 405 | C22 | — | 584 | 6 | no | — |
| 406 | C22 | — | 73 | 1 | no | — |
| 407 | C22 | — | 73 | 3 | no | — |
| 408 | C22 | — | 1168 | 3 | no | — |
| 409 | C22 | — | 1168 | 6 | no | — |
| 410 | C22 | C2×#14556653 | 1 | 3 | yes | — |
| 411 | C4 | — | 4 | 1 | no | — |
| 412 | C4 | — | 292 | 1 | no | — |
| 413 | C4 | — | 73 | 1 | no | — |
| 414 | C4 | — | 73 | 3 | no | — |
| 415 | C4 | C2×#14556653 | 1 | 3 | yes | — |
| 416 | C4 | C22×C22⋊#64408 | 1 | 1 | yes | characteristic |
| 417 | C2 | — | 2 | 3 | no | — |
| 418 | C2 | — | 8 | 3 | no | — |
| 419 | C2 | — | 584 | 3 | no | — |
| 420 | C2 | — | 146 | 1 | no | — |
| 421 | C2 | — | 146 | 3 | no | — |
| 422 | C2 | C22×#14556653 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22626899 | C2 | semidirect |
| 2. #22626592 | C2 | semidirect |
| 3. #22626259 | C2 | semidirect |
| 4. #22626258 | C2 | semidirect |
| 5. D73⋊#361 | C2 | semidirect |
| 6. C2×#17989505 | C2 | semidirect |
| 11. C2×#14556666 | C22 | semidirect |
| 12. #17989643 | C22 | semidirect |
| 14. D73⋊#108 | C22 | semidirect |
| 15. C2×#14556661 | C22 | semidirect |
| 16. #17989506 | C22 | semidirect |
| 17. #17989506 | C22 | semidirect |
| 18. #17989505 | C22 | semidirect |
| 19. #17989505 | C22 | semidirect |
| 20. #17989505 | C22 | semidirect |
| 219. C73 | #33392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626899 | 2 |
| #22626592 | 2 |
| #22626259 | 2 |
| #22626258 | 2 |
| D73⋊#361 | 2 |
| C2×#17989505 | 2 |
| #576×D73 | 2 |
| #33392 | 73 |