← C89×#63090 #36440938
Subgroups — C89×#63090 #36440938
Order 22784.
10836 conjugacy classes of subgroups.
The subgroup lattice has 366 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#585×C89 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C89×#3586 | C2 | 1 | 16 | yes | maximal, complemented |
| 3 | C89×#3585 | C2 | 1 | 16 | yes | maximal, complemented |
| 4 | C89×#3584 | C2 | 1 | 16 | yes | maximal, complemented |
| 5 | C2×#575×C89 | C2 | 1 | 12 | yes | maximal, complemented |
| 6 | C2×#568×C89 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #585×C89 | — | 2 | 8 | no | — |
| 8 | #585×C89 | — | 2 | 8 | no | — |
| 9 | #585×C89 | C22 | 1 | 16 | yes | complemented |
| 10 | #585×C89 | C22 | 1 | 16 | yes | complemented |
| 11 | C2×2−1+4×C89 | — | 2 | 2 | no | — |
| 12 | C2×2−1+4×C89 | C22 | 1 | 8 | yes | complemented |
| 13 | C2×H(5,𝔽2)×C89 | — | 2 | 6 | no | — |
| 14 | C2×H(5,𝔽2)×C89 | C22 | 1 | 8 | yes | complemented |
| 15 | C22×#41×C89 | — | 2 | 8 | no | — |
| 16 | C22×#41×C89 | C22 | 1 | 1 | yes | characteristic |
| 17 | C22×#41×C89 | C22 | 1 | 12 | yes | complemented |
| 18 | #578×C89 | C22 | 1 | 64 | yes | complemented |
| 19 | #577×C89 | C22 | 1 | 128 | yes | complemented |
| 20 | #576×C89 | C22 | 1 | 64 | yes | complemented |
| 21 | #575×C89 | C22 | 1 | 16 | yes | complemented |
| 22 | #575×C89 | C22 | 1 | 96 | yes | complemented |
| 23 | #575×C89 | C22 | 1 | 48 | yes | complemented |
| 24 | C2×#137×C89 | C22 | 1 | 48 | yes | complemented |
| 25 | C2×AGL(1,ℤ/8)×C89 | C22 | 1 | 48 | yes | complemented |
| 26 | C2×#135×C89 | C22 | 1 | 48 | yes | complemented |
| 27 | #568×C89 | C22 | 1 | 16 | yes | complemented |
| 28 | C2×#131×C89 | C22 | 1 | 8 | yes | complemented |
| 29 | C22×M16×C89 | C22 | 1 | 6 | yes | complemented |
| 30 | 2−1+4×C89 | — | 2 | 32 | no | — |
| 31 | 2−1+4×C89 | — | 2 | 16 | no | — |
| 32 | 2−1+4×C89 | — | 2 | 16 | no | — |
| 33 | 2−1+4×C89 | C23 | 1 | 64 | yes | complemented |
| 34 | H(5,𝔽2)×C89 | — | 2 | 32 | no | — |
| 35 | H(5,𝔽2)×C89 | — | 2 | 48 | no | — |
| 36 | H(5,𝔽2)×C89 | — | 2 | 48 | no | — |
| 37 | H(5,𝔽2)×C89 | C23 | 1 | 64 | yes | complemented |
| 38 | C2×#41×C89 | — | 2 | 64 | no | — |
| 39 | C2×#41×C89 | — | 2 | 64 | no | — |
| 40 | C2×#41×C89 | — | 2 | 8 | no | — |
| 41 | C2×#41×C89 | — | 2 | 24 | no | — |
| 42 | C2×#41×C89 | — | 2 | 12 | no | — |
| 43 | C2×#41×C89 | — | 2 | 12 | no | — |
| 44 | C2×#41×C89 | — | 2 | 24 | no | — |
| 45 | C2×#41×C89 | — | 2 | 24 | no | — |
| 46 | C2×#41×C89 | D4 | 1 | 8 | yes | — |
| 47 | C2×#41×C89 | D4 | 1 | 4 | yes | — |
| 48 | C2×#41×C89 | C23 | 1 | 48 | yes | — |
| 49 | C2×#41×C89 | C23 | 1 | 8 | yes | — |
| 50 | C2×#41×C89 | C23 | 1 | 4 | yes | — |
| 51 | C2×#41×C89 | C23 | 1 | 8 | yes | — |
| 52 | C2×#41×C89 | C23 | 1 | 48 | yes | complemented |
| 53 | C2×#41×C89 | C23 | 1 | 24 | yes | complemented |
| 54 | C22×Q8×C89 | — | 2 | 8 | no | — |
| 55 | C22×Q8×C89 | D4 | 1 | 1 | yes | characteristic |
| 56 | C22×Q8×C89 | C23 | 1 | 12 | yes | complemented |
| 57 | C22×D4×C89 | — | 2 | 12 | no | — |
| 58 | C22×D4×C89 | — | 2 | 24 | no | — |
| 59 | C22×D4×C89 | D4 | 1 | 3 | yes | — |
| 60 | C22×D4×C89 | C23 | 1 | 12 | yes | complemented |
| 61 | C23×C4×C89 | — | 2 | 12 | no | — |
| 62 | C23×C4×C89 | C23 | 1 | 3 | yes | — |
| 63 | #137×C89 | C23 | 1 | 64 | yes | complemented |
| 64 | #137×C89 | C23 | 1 | 192 | yes | complemented |
| 65 | AGL(1,ℤ/8)×C89 | C23 | 1 | 64 | yes | complemented |
| 66 | AGL(1,ℤ/8)×C89 | C23 | 1 | 192 | yes | complemented |
| 67 | #135×C89 | C23 | 1 | 64 | yes | complemented |
| 68 | #135×C89 | C23 | 1 | 192 | yes | complemented |
| 69 | C2×Q16×C89 | C23 | 1 | 48 | yes | complemented |
| 70 | C2×SD16×C89 | C23 | 1 | 96 | yes | complemented |
| 71 | C2×D8×C89 | C23 | 1 | 48 | yes | complemented |
| 72 | #131×C89 | C23 | 1 | 64 | yes | complemented |
| 73 | C2×M16×C89 | C23 | 1 | 4 | yes | — |
| 74 | C2×M16×C89 | C23 | 1 | 12 | yes | complemented |
| 75 | C2×M16×C89 | C23 | 1 | 48 | yes | complemented |
| 76 | C22×C8×C89 | C23 | 1 | 12 | yes | complemented |
| 77 | C24×C89 | — | 2 | 12 | no | — |
| 78 | C24×C89 | C2×D4 | 1 | 3 | yes | — |
| 79 | #41×C89 | — | 2 | 64 | no | — |
| 80 | #41×C89 | — | 2 | 192 | no | — |
| 81 | #41×C89 | — | 2 | 48 | no | — |
| 82 | #41×C89 | — | 2 | 8 | no | — |
| 83 | #41×C89 | — | 2 | 8 | no | — |
| 84 | #41×C89 | — | 2 | 48 | no | — |
| 85 | #41×C89 | — | 2 | 48 | no | — |
| 86 | #41×C89 | — | 2 | 48 | no | — |
| 87 | #41×C89 | — | 2 | 48 | no | — |
| 88 | #41×C89 | C2×D4 | 1 | 16 | yes | — |
| 89 | #41×C89 | C2×D4 | 1 | 32 | yes | — |
| 90 | #41×C89 | C24 | 1 | 16 | yes | — |
| 91 | #41×C89 | C24 | 1 | 96 | yes | — |
| 92 | #41×C89 | C24 | 1 | 16 | yes | — |
| 93 | #41×C89 | C24 | 1 | 16 | yes | — |
| 94 | C2×Q8×C89 | — | 2 | 64 | no | — |
| 95 | C2×Q8×C89 | — | 2 | 12 | no | — |
| 96 | C2×Q8×C89 | — | 2 | 24 | no | — |
| 97 | C2×Q8×C89 | C2×D4 | 1 | 8 | yes | — |
| 98 | C2×Q8×C89 | C2×D4 | 1 | 4 | yes | — |
| 99 | C2×Q8×C89 | C24 | 1 | 48 | yes | — |
| 100 | C2×Q8×C89 | C24 | 1 | 8 | yes | — |
| 101 | C2×D4×C89 | — | 2 | 8 | no | — |
| 102 | C2×D4×C89 | — | 2 | 24 | no | — |
| 103 | C2×D4×C89 | — | 2 | 48 | no | — |
| 104 | C2×D4×C89 | — | 2 | 48 | no | — |
| 105 | C2×D4×C89 | — | 2 | 192 | no | — |
| 106 | C2×D4×C89 | — | 2 | 12 | no | — |
| 107 | C2×D4×C89 | — | 2 | 24 | no | — |
| 108 | C2×D4×C89 | C2×D4 | 1 | 24 | yes | — |
| 109 | C2×D4×C89 | C2×D4 | 1 | 12 | yes | — |
| 110 | C2×D4×C89 | C24 | 1 | 48 | yes | — |
| 111 | C2×D4×C89 | C24 | 1 | 8 | yes | — |
| 112 | C22×C4×C89 | — | 2 | 12 | no | — |
| 113 | C22×C4×C89 | — | 2 | 8 | no | — |
| 114 | C22×C4×C89 | — | 2 | 24 | no | — |
| 115 | C22×C4×C89 | — | 2 | 48 | no | — |
| 116 | C22×C4×C89 | — | 2 | 48 | no | — |
| 117 | C22×C4×C89 | C2×D4 | 1 | 12 | yes | — |
| 118 | C22×C4×C89 | C2×D4 | 1 | 3 | yes | — |
| 119 | C22×C4×C89 | C2×D4 | 1 | 6 | yes | — |
| 120 | C22×C4×C89 | C24 | 1 | 6 | yes | — |
| 121 | C22×C4×C89 | C24 | 1 | 1 | yes | characteristic |
| 122 | C22×C4×C89 | C24 | 1 | 12 | yes | — |
| 123 | Q16×C89 | C24 | 1 | 64 | yes | — |
| 124 | SD16×C89 | C24 | 1 | 128 | yes | — |
| 125 | D8×C89 | C24 | 1 | 64 | yes | — |
| 126 | M16×C89 | C24 | 1 | 16 | yes | — |
| 127 | M16×C89 | C24 | 1 | 48 | yes | — |
| 128 | C2×C8×C89 | C24 | 1 | 8 | yes | — |
| 129 | C2×C8×C89 | C24 | 1 | 48 | yes | — |
| 130 | C23×C89 | — | 2 | 8 | no | — |
| 131 | C23×C89 | — | 2 | 48 | no | — |
| 132 | C23×C89 | — | 8 | 3 | no | — |
| 133 | C23×C89 | — | 8 | 24 | no | — |
| 134 | C23×C89 | C22×D4 | 1 | 12 | yes | — |
| 135 | C23×C89 | C22×D4 | 1 | 1 | yes | characteristic |
| 136 | C23×C89 | C22×D4 | 1 | 6 | yes | — |
| 137 | Q8×C89 | — | 2 | 8 | no | — |
| 138 | Q8×C89 | — | 2 | 48 | no | — |
| 139 | Q8×C89 | C22×D4 | 1 | 16 | yes | — |
| 140 | Q8×C89 | C25 | 1 | 16 | yes | — |
| 141 | D4×C89 | — | 2 | 16 | no | — |
| 142 | D4×C89 | — | 2 | 96 | no | — |
| 143 | D4×C89 | — | 2 | 16 | no | — |
| 144 | D4×C89 | — | 2 | 8 | no | — |
| 145 | D4×C89 | — | 2 | 48 | no | — |
| 146 | D4×C89 | C22×D4 | 1 | 48 | yes | — |
| 147 | D4×C89 | C25 | 1 | 16 | yes | — |
| 148 | C2×C4×C89 | — | 2 | 8 | no | — |
| 149 | C2×C4×C89 | — | 2 | 48 | no | — |
| 150 | C2×C4×C89 | — | 2 | 16 | no | — |
| 151 | C2×C4×C89 | — | 2 | 96 | no | — |
| 152 | C2×C4×C89 | — | 2 | 16 | no | — |
| 153 | C2×C4×C89 | C22×D4 | 1 | 12 | yes | — |
| 154 | C2×C4×C89 | C22×D4 | 1 | 24 | yes | — |
| 155 | C2×C4×C89 | C22×D4 | 1 | 1 | yes | characteristic |
| 156 | C2×C4×C89 | C22×D4 | 1 | 6 | yes | — |
| 157 | C2×C4×C89 | C22×D4 | 1 | 2 | yes | — |
| 158 | C2×C4×C89 | C22×D4 | 1 | 12 | yes | — |
| 159 | C2×C4×C89 | C25 | 1 | 12 | yes | — |
| 160 | C2×C4×C89 | C25 | 1 | 2 | yes | — |
| 161 | C2×C4×C89 | C25 | 1 | 1 | yes | characteristic |
| 162 | C8×C89 | C25 | 1 | 16 | yes | — |
| 163 | C22×C89 | — | 2 | 16 | no | — |
| 164 | C22×C89 | — | 4 | 1 | no | — |
| 165 | C22×C89 | — | 4 | 12 | no | — |
| 166 | C22×C89 | — | 4 | 6 | no | — |
| 167 | C22×C89 | — | 4 | 16 | no | — |
| 168 | C22×C89 | — | 8 | 48 | no | — |
| 169 | C22×C89 | C23×D4 | 1 | 2 | yes | — |
| 170 | C22×C89 | C23×D4 | 1 | 12 | yes | — |
| 171 | C22×C89 | C23×D4 | 1 | 1 | yes | characteristic |
| 172 | C4×C89 | — | 2 | 16 | no | — |
| 173 | C4×C89 | C23×D4 | 1 | 2 | yes | — |
| 174 | C4×C89 | C23×D4 | 1 | 12 | yes | — |
| 175 | C4×C89 | C23×D4 | 1 | 1 | yes | characteristic |
| 176 | C4×C89 | C26 | 1 | 1 | yes | characteristic |
| 177 | #63090 | C89 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 178 | C2×C89 | — | 2 | 2 | no | — |
| 179 | C2×C89 | — | 2 | 1 | no | — |
| 180 | C2×C89 | — | 2 | 12 | no | — |
| 181 | C2×C89 | — | 4 | 16 | no | — |
| 182 | C2×C89 | C24×D4 | 1 | 1 | yes | characteristic |
| 183 | C2×#585 | C2×C89 | 1 | 2 | yes | complemented |
| 184 | #3586 | C2×C89 | 1 | 16 | yes | complemented |
| 185 | #3585 | C2×C89 | 1 | 16 | yes | complemented |
| 186 | #3584 | C2×C89 | 1 | 16 | yes | complemented |
| 187 | C2×#575 | C2×C89 | 1 | 12 | yes | complemented |
| 188 | C2×#568 | C2×C89 | 1 | 1 | yes | characteristic, complemented |
| 189 | C89 | #63090 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 190 | #585 | — | 2 | 8 | no | — |
| 191 | #585 | — | 2 | 8 | no | — |
| 192 | #585 | C22×C89 | 1 | 16 | yes | complemented |
| 193 | #585 | C22×C89 | 1 | 16 | yes | complemented |
| 194 | C2×2−1+4 | — | 2 | 2 | no | — |
| 195 | C2×2−1+4 | C22×C89 | 1 | 8 | yes | complemented |
| 196 | C2×H(5,𝔽2) | — | 2 | 6 | no | — |
| 197 | C2×H(5,𝔽2) | C22×C89 | 1 | 8 | yes | complemented |
| 198 | C22×#41 | — | 2 | 8 | no | — |
| 199 | C22×#41 | C22×C89 | 1 | 1 | yes | characteristic |
| 200 | C22×#41 | C22×C89 | 1 | 12 | yes | complemented |
| 201 | #578 | C22×C89 | 1 | 64 | yes | complemented |
| 202 | #577 | C22×C89 | 1 | 128 | yes | complemented |
| 203 | #576 | C22×C89 | 1 | 64 | yes | complemented |
| 204 | #575 | C22×C89 | 1 | 16 | yes | complemented |
| 205 | #575 | C22×C89 | 1 | 96 | yes | complemented |
| 206 | #575 | C22×C89 | 1 | 48 | yes | complemented |
| 207 | C2×#137 | C22×C89 | 1 | 48 | yes | complemented |
| 208 | C2×AGL(1,ℤ/8) | C22×C89 | 1 | 48 | yes | complemented |
| 209 | C2×#135 | C22×C89 | 1 | 48 | yes | complemented |
| 210 | #568 | C22×C89 | 1 | 16 | yes | complemented |
| 211 | C2×#131 | C22×C89 | 1 | 8 | yes | complemented |
| 212 | C22×M16 | C22×C89 | 1 | 6 | yes | complemented |
| 213 | 2−1+4 | — | 2 | 32 | no | — |
| 214 | 2−1+4 | — | 2 | 16 | no | — |
| 215 | 2−1+4 | — | 2 | 16 | no | — |
| 216 | 2−1+4 | C23×C89 | 1 | 64 | yes | complemented |
| 217 | H(5,𝔽2) | — | 2 | 32 | no | — |
| 218 | H(5,𝔽2) | — | 2 | 48 | no | — |
| 219 | H(5,𝔽2) | — | 2 | 48 | no | — |
| 220 | H(5,𝔽2) | C23×C89 | 1 | 64 | yes | complemented |
| 221 | C2×#41 | — | 2 | 64 | no | — |
| 222 | C2×#41 | — | 2 | 64 | no | — |
| 223 | C2×#41 | — | 2 | 8 | no | — |
| 224 | C2×#41 | — | 2 | 24 | no | — |
| 225 | C2×#41 | — | 2 | 12 | no | — |
| 226 | C2×#41 | — | 2 | 12 | no | — |
| 227 | C2×#41 | — | 2 | 24 | no | — |
| 228 | C2×#41 | — | 2 | 24 | no | — |
| 229 | C2×#41 | D4×C89 | 1 | 8 | yes | — |
| 230 | C2×#41 | D4×C89 | 1 | 4 | yes | — |
| 231 | C2×#41 | C23×C89 | 1 | 48 | yes | — |
| 232 | C2×#41 | C23×C89 | 1 | 8 | yes | — |
| 233 | C2×#41 | C23×C89 | 1 | 4 | yes | — |
| 234 | C2×#41 | C23×C89 | 1 | 8 | yes | — |
| 235 | C2×#41 | C23×C89 | 1 | 48 | yes | complemented |
| 236 | C2×#41 | C23×C89 | 1 | 24 | yes | complemented |
| 237 | C22×Q8 | — | 2 | 8 | no | — |
| 238 | C22×Q8 | D4×C89 | 1 | 1 | yes | characteristic |
| 239 | C22×Q8 | C23×C89 | 1 | 12 | yes | complemented |
| 240 | C22×D4 | — | 2 | 12 | no | — |
| 241 | C22×D4 | — | 2 | 24 | no | — |
| 242 | C22×D4 | D4×C89 | 1 | 3 | yes | — |
| 243 | C22×D4 | C23×C89 | 1 | 12 | yes | complemented |
| 244 | C23×C4 | — | 2 | 12 | no | — |
| 245 | C23×C4 | C23×C89 | 1 | 3 | yes | — |
| 246 | #137 | C23×C89 | 1 | 64 | yes | complemented |
| 247 | #137 | C23×C89 | 1 | 192 | yes | complemented |
| 248 | AGL(1,ℤ/8) | C23×C89 | 1 | 64 | yes | complemented |
| 249 | AGL(1,ℤ/8) | C23×C89 | 1 | 192 | yes | complemented |
| 250 | #135 | C23×C89 | 1 | 64 | yes | complemented |
| 251 | #135 | C23×C89 | 1 | 192 | yes | complemented |
| 252 | C2×Q16 | C23×C89 | 1 | 48 | yes | complemented |
| 253 | C2×SD16 | C23×C89 | 1 | 96 | yes | complemented |
| 254 | C2×D8 | C23×C89 | 1 | 48 | yes | complemented |
| 255 | #131 | C23×C89 | 1 | 64 | yes | complemented |
| 256 | C2×M16 | C23×C89 | 1 | 4 | yes | — |
| 257 | C2×M16 | C23×C89 | 1 | 12 | yes | complemented |
| 258 | C2×M16 | C23×C89 | 1 | 48 | yes | complemented |
| 259 | C22×C8 | C23×C89 | 1 | 12 | yes | complemented |
| 260 | C24 | — | 2 | 12 | no | — |
| 261 | C24 | C2×D4×C89 | 1 | 3 | yes | — |
| 262 | #41 | — | 2 | 64 | no | — |
| 263 | #41 | — | 2 | 192 | no | — |
| 264 | #41 | — | 2 | 8 | no | — |
| 265 | #41 | — | 2 | 48 | no | — |
| 266 | #41 | — | 2 | 8 | no | — |
| 267 | #41 | — | 2 | 48 | no | — |
| 268 | #41 | — | 2 | 48 | no | — |
| 269 | #41 | — | 2 | 48 | no | — |
| 270 | #41 | — | 2 | 48 | no | — |
| 271 | #41 | C2×D4×C89 | 1 | 16 | yes | — |
| 272 | #41 | C2×D4×C89 | 1 | 32 | yes | — |
| 273 | #41 | C24×C89 | 1 | 16 | yes | — |
| 274 | #41 | C24×C89 | 1 | 96 | yes | — |
| 275 | #41 | C24×C89 | 1 | 16 | yes | — |
| 276 | #41 | C24×C89 | 1 | 16 | yes | — |
| 277 | C2×Q8 | — | 2 | 64 | no | — |
| 278 | C2×Q8 | — | 2 | 12 | no | — |
| 279 | C2×Q8 | — | 2 | 24 | no | — |
| 280 | C2×Q8 | C2×D4×C89 | 1 | 8 | yes | — |
| 281 | C2×Q8 | C2×D4×C89 | 1 | 4 | yes | — |
| 282 | C2×Q8 | C24×C89 | 1 | 48 | yes | — |
| 283 | C2×Q8 | C24×C89 | 1 | 8 | yes | — |
| 284 | C2×D4 | — | 2 | 8 | no | — |
| 285 | C2×D4 | — | 2 | 24 | no | — |
| 286 | C2×D4 | — | 2 | 48 | no | — |
| 287 | C2×D4 | — | 2 | 48 | no | — |
| 288 | C2×D4 | — | 2 | 192 | no | — |
| 289 | C2×D4 | — | 2 | 12 | no | — |
| 290 | C2×D4 | — | 2 | 24 | no | — |
| 291 | C2×D4 | C2×D4×C89 | 1 | 24 | yes | — |
| 292 | C2×D4 | C2×D4×C89 | 1 | 12 | yes | — |
| 293 | C2×D4 | C24×C89 | 1 | 48 | yes | — |
| 294 | C2×D4 | C24×C89 | 1 | 8 | yes | — |
| 295 | C22×C4 | — | 2 | 12 | no | — |
| 296 | C22×C4 | — | 2 | 8 | no | — |
| 297 | C22×C4 | — | 2 | 24 | no | — |
| 298 | C22×C4 | — | 2 | 48 | no | — |
| 299 | C22×C4 | — | 2 | 48 | no | — |
| 300 | C22×C4 | C2×D4×C89 | 1 | 12 | yes | — |
| 301 | C22×C4 | C2×D4×C89 | 1 | 3 | yes | — |
| 302 | C22×C4 | C2×D4×C89 | 1 | 6 | yes | — |
| 303 | C22×C4 | C24×C89 | 1 | 6 | yes | — |
| 304 | C22×C4 | C24×C89 | 1 | 1 | yes | characteristic |
| 305 | C22×C4 | C24×C89 | 1 | 12 | yes | — |
| 306 | Q16 | C24×C89 | 1 | 64 | yes | — |
| 307 | SD16 | C24×C89 | 1 | 128 | yes | — |
| 308 | D8 | C24×C89 | 1 | 64 | yes | — |
| 309 | M16 | C24×C89 | 1 | 16 | yes | — |
| 310 | M16 | C24×C89 | 1 | 48 | yes | — |
| 311 | C2×C8 | C24×C89 | 1 | 8 | yes | — |
| 312 | C2×C8 | C24×C89 | 1 | 48 | yes | — |
| 313 | C23 | — | 2 | 8 | no | — |
| 314 | C23 | — | 2 | 48 | no | — |
| 315 | C23 | — | 8 | 3 | no | — |
| 316 | C23 | — | 8 | 24 | no | — |
| 317 | C23 | C22×D4×C89 | 1 | 12 | yes | — |
| 318 | C23 | C22×D4×C89 | 1 | 1 | yes | characteristic |
| 319 | C23 | C22×D4×C89 | 1 | 6 | yes | — |
| 320 | Q8 | — | 2 | 8 | no | — |
| 321 | Q8 | — | 2 | 48 | no | — |
| 322 | Q8 | C22×D4×C89 | 1 | 16 | yes | — |
| 323 | Q8 | C25×C89 | 1 | 16 | yes | — |
| 324 | D4 | — | 2 | 16 | no | — |
| 325 | D4 | — | 2 | 96 | no | — |
| 326 | D4 | — | 2 | 16 | no | — |
| 327 | D4 | — | 2 | 8 | no | — |
| 328 | D4 | — | 2 | 48 | no | — |
| 329 | D4 | C22×D4×C89 | 1 | 48 | yes | — |
| 330 | D4 | C25×C89 | 1 | 16 | yes | — |
| 331 | C2×C4 | — | 2 | 8 | no | — |
| 332 | C2×C4 | — | 2 | 48 | no | — |
| 333 | C2×C4 | — | 2 | 16 | no | — |
| 334 | C2×C4 | — | 2 | 16 | no | — |
| 335 | C2×C4 | — | 2 | 96 | no | — |
| 336 | C2×C4 | C22×D4×C89 | 1 | 2 | yes | — |
| 337 | C2×C4 | C22×D4×C89 | 1 | 12 | yes | — |
| 338 | C2×C4 | C22×D4×C89 | 1 | 12 | yes | — |
| 339 | C2×C4 | C22×D4×C89 | 1 | 24 | yes | — |
| 340 | C2×C4 | C22×D4×C89 | 1 | 1 | yes | characteristic |
| 341 | C2×C4 | C22×D4×C89 | 1 | 6 | yes | — |
| 342 | C2×C4 | C25×C89 | 1 | 1 | yes | characteristic |
| 343 | C2×C4 | C25×C89 | 1 | 12 | yes | — |
| 344 | C2×C4 | C25×C89 | 1 | 2 | yes | — |
| 345 | C8 | C25×C89 | 1 | 16 | yes | — |
| 346 | C22 | — | 2 | 16 | no | — |
| 347 | C22 | — | 4 | 1 | no | — |
| 348 | C22 | — | 4 | 12 | no | — |
| 349 | C22 | — | 4 | 6 | no | — |
| 350 | C22 | — | 4 | 16 | no | — |
| 351 | C22 | — | 8 | 48 | no | — |
| 352 | C22 | C23×D4×C89 | 1 | 2 | yes | — |
| 353 | C22 | C23×D4×C89 | 1 | 12 | yes | — |
| 354 | C22 | C23×D4×C89 | 1 | 1 | yes | characteristic |
| 355 | C4 | — | 2 | 16 | no | — |
| 356 | C4 | C23×D4×C89 | 1 | 1 | yes | characteristic |
| 357 | C4 | C23×D4×C89 | 1 | 2 | yes | — |
| 358 | C4 | C23×D4×C89 | 1 | 12 | yes | — |
| 359 | C4 | C26×C89 | 1 | 1 | yes | characteristic |
| 360 | C2 | — | 2 | 2 | no | — |
| 361 | C2 | — | 2 | 1 | no | — |
| 362 | C2 | — | 2 | 12 | no | — |
| 363 | C2 | — | 4 | 16 | no | — |
| 364 | C2 | C24×D4×C89 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|
| 1. C2×#585×C89 | C2 | semidirect |
| 2. C89×#3586 | C2 | semidirect |
| 3. C89×#3585 | C2 | semidirect |
| 4. C89×#3584 | C2 | semidirect |
| 5. C2×#575×C89 | C2 | semidirect |
| 6. C2×#568×C89 | C2 | semidirect |
| 9. #585×C89 | C22 | semidirect |
| 10. #585×C89 | C22 | semidirect |
| 12. C2×2−1+4×C89 | C22 | semidirect |
| 14. C2×H(5,𝔽2)×C89 | C22 | semidirect |
| 17. C22×#41×C89 | C22 | semidirect |
| 18. #578×C89 | C22 | semidirect |
| 19. #577×C89 | C22 | semidirect |
| 20. #576×C89 | C22 | semidirect |
| 21. #575×C89 | C22 | semidirect |
| 22. #575×C89 | C22 | semidirect |
| 23. #575×C89 | C22 | semidirect |
| 24. C2×#137×C89 | C22 | semidirect |
| 25. C2×AGL(1,ℤ/8)×C89 | C22 | semidirect |
| 26. C2×#135×C89 | C22 | semidirect |
| 27. #568×C89 | C22 | semidirect |
| 28. C2×#131×C89 | C22 | semidirect |
| 29. C22×M16×C89 | C22 | semidirect |
| 33. 2−1+4×C89 | C23 | semidirect |
| 37. H(5,𝔽2)×C89 | C23 | semidirect |
| 52. C2×#41×C89 | C23 | semidirect |
| 53. C2×#41×C89 | C23 | semidirect |
| 56. C22×Q8×C89 | C23 | semidirect |
| 60. C22×D4×C89 | C23 | semidirect |
| 63. #137×C89 | C23 | semidirect |
| 64. #137×C89 | C23 | semidirect |
| 65. AGL(1,ℤ/8)×C89 | C23 | semidirect |
| 66. AGL(1,ℤ/8)×C89 | C23 | semidirect |
| 67. #135×C89 | C23 | semidirect |
| 68. #135×C89 | C23 | semidirect |
| 69. C2×Q16×C89 | C23 | semidirect |
| 70. C2×SD16×C89 | C23 | semidirect |
| 71. C2×D8×C89 | C23 | semidirect |
| 72. #131×C89 | C23 | semidirect |
| 74. C2×M16×C89 | C23 | semidirect |
| 75. C2×M16×C89 | C23 | semidirect |
| 76. C22×C8×C89 | C23 | semidirect |
| 177. #63090 | C89 | direct (N × H) |
| 183. C2×#585 | C2×C89 | semidirect |
| 184. #3586 | C2×C89 | semidirect |
| 185. #3585 | C2×C89 | semidirect |
| 186. #3584 | C2×C89 | semidirect |
| 187. C2×#575 | C2×C89 | semidirect |
| 188. C2×#568 | C2×C89 | semidirect |
| 189. C89 | #63090 | direct (N × H) |
| 192. #585 | C22×C89 | semidirect |
| 193. #585 | C22×C89 | semidirect |
| 195. C2×2−1+4 | C22×C89 | semidirect |
| 197. C2×H(5,𝔽2) | C22×C89 | semidirect |
| 200. C22×#41 | C22×C89 | semidirect |
| 201. #578 | C22×C89 | semidirect |
| 202. #577 | C22×C89 | semidirect |
| 203. #576 | C22×C89 | semidirect |
| 204. #575 | C22×C89 | semidirect |
| 205. #575 | C22×C89 | semidirect |
| 206. #575 | C22×C89 | semidirect |
| 207. C2×#137 | C22×C89 | semidirect |
| 208. C2×AGL(1,ℤ/8) | C22×C89 | semidirect |
| 209. C2×#135 | C22×C89 | semidirect |
| 210. #568 | C22×C89 | semidirect |
| 211. C2×#131 | C22×C89 | semidirect |
| 212. C22×M16 | C22×C89 | semidirect |
| 216. 2−1+4 | C23×C89 | semidirect |
| 220. H(5,𝔽2) | C23×C89 | semidirect |
| 235. C2×#41 | C23×C89 | semidirect |
| 236. C2×#41 | C23×C89 | semidirect |
| 239. C22×Q8 | C23×C89 | semidirect |
| 243. C22×D4 | C23×C89 | semidirect |
| 246. #137 | C23×C89 | semidirect |
| 247. #137 | C23×C89 | semidirect |
| 248. AGL(1,ℤ/8) | C23×C89 | semidirect |
| 249. AGL(1,ℤ/8) | C23×C89 | semidirect |
| 250. #135 | C23×C89 | semidirect |
| 251. #135 | C23×C89 | semidirect |
| 252. C2×Q16 | C23×C89 | semidirect |
| 253. C2×SD16 | C23×C89 | semidirect |
| 254. C2×D8 | C23×C89 | semidirect |
| 255. #131 | C23×C89 | semidirect |
| 257. C2×M16 | C23×C89 | semidirect |
| 258. C2×M16 | C23×C89 | semidirect |
| 259. C22×C8 | C23×C89 | semidirect |
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta