Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
528 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 50 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 | Q8×(C22⋊C9)⋊C2 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | D4×(C22⋊C9)⋊C2 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | SD16×C22⋊C9 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10589519 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10589516 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10589503 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C8×(C22⋊C9)⋊C2 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | SD16×#67 | — | 3 | 1 | no | maximal |
| 9 | C22×(C22⋊C9)⋊C2 | — | 2 | 1 | no | — |
| 10 | Q8×C22⋊C9 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | D4×C22⋊C9 | C22 | 1 | 1 | yes | characteristic |
| 12 | #63694 | — | 2 | 1 | no | — |
| 13 | C4⋊((C22⋊C9)⋊C2) | C22 | 1 | 1 | yes | characteristic |
| 14 | C4×(C22⋊C9)⋊C2 | — | 2 | 1 | no | — |
| 15 | C4×(C22⋊C9)⋊C2 | C22 | 1 | 1 | yes | characteristic |
| 16 | (C22⋊C9)⋊Q8 | — | 2 | 1 | no | — |
| 17 | (C22⋊C9)⋊Q8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | SD16×D9 | — | 4 | 1 | no | maximal |
| 19 | C8×C22⋊C9 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | (C22⋊C9)⋊C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | C22×C3×SD16 | D3 | 1 | 1 | yes | characteristic |
| 22 | Q8×#67 | — | 3 | 1 | no | — |
| 23 | D4×#67 | — | 3 | 1 | no | — |
| 24 | C2×D3×SD16 | — | 3 | 1 | no | — |
| 25 | #5227 | — | 3 | 1 | no | — |
| 26 | #5218 | — | 3 | 1 | no | — |
| 27 | #5175 | — | 3 | 1 | no | — |
| 28 | #5171 | — | 3 | 1 | no | — |
| 29 | #5170 | — | 3 | 1 | no | — |
| 30 | #5169 | — | 3 | 1 | no | — |
| 31 | #5163 | — | 3 | 1 | no | — |
| 32 | #5162 | — | 3 | 1 | no | — |
| 33 | Dic3×SD16 | — | 3 | 1 | no | — |
| 34 | #5114 | — | 3 | 1 | no | — |
| 35 | C8×#67 | — | 3 | 1 | no | — |
| 36 | C22×C22⋊C9 | — | 2 | 1 | no | — |
| 37 | C2×(C22⋊C9)⋊C2 | — | 2 | 1 | no | — |
| 38 | C2×(C22⋊C9)⋊C2 | — | 4 | 2 | no | — |
| 39 | C2×(C22⋊C9)⋊C2 | D4 | 1 | 1 | yes | characteristic |
| 40 | Q8×D9 | — | 4 | 1 | no | — |
| 41 | D4×D9 | — | 4 | 1 | no | — |
| 42 | C4×C22⋊C9 | — | 2 | 1 | no | — |
| 43 | C4×C22⋊C9 | C23 | 1 | 1 | yes | characteristic |
| 44 | (C22⋊C9)⋊C4 | — | 2 | 1 | no | — |
| 45 | (C22⋊C9)⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 46 | C9×SD16 | — | 4 | 1 | no | — |
| 47 | #3675 | — | 4 | 1 | no | — |
| 48 | #3672 | — | 4 | 1 | no | — |
| 49 | #3664 | — | 4 | 1 | no | — |
| 50 | C8×D9 | — | 4 | 1 | no | — |
| 51 | D4×SD16 | — | 9 | 1 | no | Sylow |
| 52 | C22×C3×Q8 | C2×D3 | 1 | 1 | yes | characteristic |
| 53 | C22×C3×D4 | C2×D3 | 1 | 1 | yes | characteristic |
| 54 | C22×#67 | — | 6 | 1 | no | — |
| 55 | C2×D3×Q8 | — | 3 | 1 | no | — |
| 56 | C2×D3×D4 | — | 3 | 1 | no | — |
| 57 | C2×C3×SD16 | — | 3 | 1 | no | — |
| 58 | C2×C3×SD16 | — | 3 | 1 | no | — |
| 59 | C2×C3×SD16 | — | 3 | 1 | no | — |
| 60 | C2×C3×SD16 | — | 3 | 1 | no | — |
| 61 | C22×C3×C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 62 | #953 | — | 6 | 1 | no | — |
| 63 | #946 | — | 3 | 1 | no | — |
| 64 | #946 | — | 6 | 1 | no | — |
| 65 | Q8×Dic3 | — | 3 | 1 | no | — |
| 66 | #944 | — | 3 | 1 | no | — |
| 67 | #944 | — | 6 | 1 | no | — |
| 68 | C2×#215 | — | 3 | 1 | no | — |
| 69 | C2×#215 | — | 3 | 1 | no | — |
| 70 | #940 | — | 3 | 1 | no | — |
| 71 | #939 | — | 6 | 1 | no | — |
| 72 | #938 | — | 3 | 1 | no | — |
| 73 | #937 | — | 6 | 1 | no | — |
| 74 | D4×Dic3 | — | 3 | 1 | no | — |
| 75 | C2×#214 | — | 3 | 1 | no | — |
| 76 | C2×#214 | — | 3 | 1 | no | — |
| 77 | #930 | — | 3 | 1 | no | — |
| 78 | C4×#67 | — | 3 | 1 | no | — |
| 79 | C4×#67 | — | 6 | 1 | no | — |
| 80 | #924 | — | 3 | 1 | no | — |
| 81 | #924 | — | 6 | 1 | no | — |
| 82 | D3×SD16 | — | 6 | 1 | no | — |
| 83 | D3×SD16 | — | 6 | 1 | no | — |
| 84 | D3×SD16 | — | 6 | 1 | no | — |
| 85 | D3×SD16 | — | 6 | 1 | no | — |
| 86 | C2×#204 | — | 3 | 1 | no | — |
| 87 | C2×D3×C8 | — | 3 | 1 | no | — |
| 88 | #835 | — | 3 | 1 | no | — |
| 89 | #835 | — | 3 | 1 | no | — |
| 90 | #832 | — | 3 | 1 | no | — |
| 91 | #832 | — | 3 | 1 | no | — |
| 92 | #830 | — | 3 | 1 | no | — |
| 93 | #821 | — | 3 | 1 | no | — |
| 94 | (C2×D3)⋊C8 | — | 3 | 1 | no | — |
| 95 | #817 | — | 3 | 1 | no | — |
| 96 | #816 | — | 3 | 1 | no | — |
| 97 | Dic3⋊C8 | — | 3 | 1 | no | — |
| 98 | C8×Dic3 | — | 3 | 1 | no | — |
| 99 | C22×D9 | — | 8 | 1 | no | — |
| 100 | C2×C22⋊C9 | — | 4 | 1 | no | — |
| 101 | C2×C22⋊C9 | C2×D4 | 1 | 1 | yes | characteristic |
| 102 | (C22⋊C9)⋊C2 | — | 4 | 1 | no | — |
| 103 | (C22⋊C9)⋊C2 | SD16 | 1 | 2 | yes | direct product factor |
| 104 | Q8×C9 | — | 4 | 1 | no | — |
| 105 | D4×C9 | — | 4 | 1 | no | — |
| 106 | #611 | — | 8 | 1 | no | — |
| 107 | D36 | — | 4 | 1 | no | — |
| 108 | C4×D9 | — | 4 | 1 | no | — |
| 109 | C4×D9 | — | 8 | 1 | no | — |
| 110 | Dic18 | — | 4 | 1 | no | — |
| 111 | Dic18 | — | 8 | 1 | no | — |
| 112 | C8×C9 | — | 4 | 1 | no | — |
| 113 | C9⋊C8 | — | 4 | 1 | no | — |
| 114 | C22×SD16 | — | 9 | 1 | no | — |
| 115 | C22×SD16 | D9 | 1 | 1 | yes | characteristic, complemented |
| 116 | D4×Q8 | — | 9 | 1 | no | — |
| 117 | D42 | — | 9 | 1 | no | — |
| 118 | #492 | — | 9 | 1 | no | — |
| 119 | #465 | — | 9 | 1 | no | — |
| 120 | #465 | — | 9 | 1 | no | — |
| 121 | #461 | — | 9 | 1 | no | — |
| 122 | #460 | — | 9 | 1 | no | — |
| 123 | #450 | — | 9 | 1 | no | — |
| 124 | #450 | — | 9 | 1 | no | — |
| 125 | #448 | — | 9 | 1 | no | — |
| 126 | #448 | — | 9 | 1 | no | — |
| 127 | C4×SD16 | — | 9 | 1 | no | — |
| 128 | C8×D4 | — | 9 | 1 | no | — |
| 129 | C24×C3 | — | 2 | 1 | no | — |
| 130 | C23×D3 | — | 6 | 1 | no | — |
| 131 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 132 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 133 | C2×C3×Q8 | — | 6 | 1 | no | — |
| 134 | C2×C3×D4 | — | 3 | 1 | no | — |
| 135 | C2×C3×D4 | — | 3 | 1 | no | — |
| 136 | C2×C3×D4 | — | 6 | 1 | no | — |
| 137 | C22×C3×C4 | — | 2 | 1 | no | — |
| 138 | C22×C3×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 139 | C2×#67 | — | 3 | 1 | no | — |
| 140 | C2×#67 | — | 6 | 1 | no | — |
| 141 | C2×#67 | — | 6 | 1 | no | — |
| 142 | C2×#67 | — | 6 | 1 | no | — |
| 143 | C2×#67 | — | 6 | 1 | no | — |
| 144 | C2×#67 | — | 6 | 1 | no | — |
| 145 | C2×#67 | — | 12 | 2 | no | — |
| 146 | C2×#67 | — | 12 | 2 | no | — |
| 147 | C22×Dic3 | — | 6 | 1 | no | — |
| 148 | D3×Q8 | — | 6 | 1 | no | — |
| 149 | D3×Q8 | — | 6 | 1 | no | — |
| 150 | D3×Q8 | — | 12 | 1 | no | — |
| 151 | D3×D4 | — | 6 | 1 | no | — |
| 152 | D3×D4 | — | 6 | 1 | no | — |
| 153 | D3×D4 | — | 12 | 1 | no | — |
| 154 | C2×D12 | — | 3 | 1 | no | — |
| 155 | C2×C4×D3 | — | 3 | 1 | no | — |
| 156 | C2×C4×D3 | — | 6 | 1 | no | — |
| 157 | C2×Dic6 | — | 3 | 1 | no | — |
| 158 | C2×Dic6 | — | 6 | 1 | no | — |
| 159 | C3×SD16 | — | 3 | 1 | no | — |
| 160 | C3×SD16 | — | 3 | 1 | no | — |
| 161 | C3×SD16 | — | 3 | 1 | no | — |
| 162 | C3×SD16 | — | 6 | 1 | no | — |
| 163 | C3×SD16 | S4 | 1 | 1 | yes | characteristic |
| 164 | C2×C3×C8 | — | 3 | 1 | no | — |
| 165 | C2×C3×C8 | — | 3 | 1 | no | — |
| 166 | #217 | — | 3 | 1 | no | — |
| 167 | #217 | — | 6 | 1 | no | — |
| 168 | #217 | — | 6 | 1 | no | — |
| 169 | #217 | — | 6 | 1 | no | — |
| 170 | #215 | — | 6 | 1 | no | — |
| 171 | #215 | — | 6 | 1 | no | — |
| 172 | #215 | — | 12 | 1 | no | — |
| 173 | #214 | — | 6 | 1 | no | — |
| 174 | #214 | — | 6 | 1 | no | — |
| 175 | #214 | — | 12 | 1 | no | — |
| 176 | (C2×D3)⋊C4 | — | 3 | 1 | no | — |
| 177 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 178 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 179 | C4⋊Dic3 | — | 3 | 1 | no | — |
| 180 | C4⋊Dic3 | — | 3 | 1 | no | — |
| 181 | C4⋊Dic3 | — | 6 | 1 | no | — |
| 182 | Dic3⋊C4 | — | 3 | 1 | no | — |
| 183 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 184 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 185 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 186 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 187 | C4×Dic3 | — | 3 | 1 | no | — |
| 188 | C4×Dic3 | — | 6 | 1 | no | — |
| 189 | C2×C3⋊C8 | — | 3 | 1 | no | — |
| 190 | C2×C3⋊C8 | — | 3 | 1 | no | — |
| 191 | #204 | — | 6 | 1 | no | — |
| 192 | #204 | — | 6 | 1 | no | — |
| 193 | D3×C8 | — | 6 | 1 | no | — |
| 194 | D3×C8 | — | 6 | 1 | no | — |
| 195 | C22×C9 | — | 8 | 1 | no | — |
| 196 | C2×D9 | — | 4 | 1 | no | — |
| 197 | C2×D9 | — | 8 | 1 | no | — |
| 198 | C2×D9 | — | 16 | 2 | no | — |
| 199 | C22⋊C9 | C2×SD16 | 1 | 1 | yes | characteristic, complemented |
| 200 | C4×C9 | — | 4 | 1 | no | — |
| 201 | C4×C9 | — | 8 | 1 | no | — |
| 202 | Dic9 | — | 4 | 1 | no | — |
| 203 | Dic9 | — | 8 | 1 | no | — |
| 204 | C22×Q8 | — | 9 | 1 | no | — |
| 205 | C22×Q8 | C2×D9 | 1 | 1 | yes | characteristic, complemented |
| 206 | C22×D4 | — | 9 | 1 | no | — |
| 207 | C22×D4 | — | 18 | 1 | no | — |
| 208 | C22×D4 | C2×D9 | 1 | 1 | yes | characteristic |
| 209 | C2×SD16 | — | 3 | 1 | no | — |
| 210 | C2×SD16 | — | 3 | 1 | no | — |
| 211 | C2×SD16 | — | 3 | 1 | no | — |
| 212 | C2×SD16 | — | 3 | 1 | no | — |
| 213 | C2×SD16 | — | 9 | 1 | no | — |
| 214 | C2×SD16 | — | 9 | 1 | no | — |
| 215 | C2×SD16 | — | 9 | 1 | no | — |
| 216 | C2×SD16 | — | 9 | 1 | no | — |
| 217 | C2×SD16 | — | 9 | 1 | no | — |
| 218 | C2×SD16 | — | 18 | 1 | no | — |
| 219 | C2×SD16 | — | 18 | 1 | no | — |
| 220 | C2×SD16 | — | 18 | 1 | no | — |
| 221 | C2×SD16 | — | 18 | 1 | no | — |
| 222 | C22×C8 | — | 9 | 1 | no | — |
| 223 | C22×C8 | C2×D9 | 1 | 1 | yes | characteristic, complemented |
| 224 | C4⋊Q8 | — | 9 | 1 | no | — |
| 225 | C4⋊Q8 | — | 18 | 1 | no | — |
| 226 | #127 | — | 9 | 1 | no | — |
| 227 | C22⋊Q8 | — | 9 | 1 | no | — |
| 228 | C22⋊Q8 | — | 9 | 1 | no | — |
| 229 | C22⋊Q8 | — | 18 | 1 | no | — |
| 230 | C22⋊Q8 | — | 18 | 1 | no | — |
| 231 | #121 | — | 9 | 1 | no | — |
| 232 | #121 | — | 9 | 1 | no | — |
| 233 | #121 | — | 18 | 1 | no | — |
| 234 | #120 | — | 18 | 1 | no | — |
| 235 | #120 | — | 18 | 1 | no | — |
| 236 | C4×Q8 | — | 9 | 1 | no | — |
| 237 | C4×D4 | — | 9 | 1 | no | — |
| 238 | C4×D4 | — | 9 | 1 | no | — |
| 239 | C4×D4 | — | 18 | 1 | no | — |
| 240 | #106 | — | 9 | 1 | no | — |
| 241 | C4⋊C8 | — | 9 | 1 | no | — |
| 242 | #103 | — | 9 | 1 | no | — |
| 243 | #103 | — | 9 | 1 | no | — |
| 244 | #103 | — | 9 | 1 | no | — |
| 245 | #102 | — | 9 | 1 | no | — |
| 246 | #102 | — | 9 | 1 | no | — |
| 247 | #102 | — | 9 | 1 | no | — |
| 248 | C22⋊C8 | — | 9 | 1 | no | — |
| 249 | C22⋊C8 | — | 9 | 1 | no | — |
| 250 | C4×C8 | — | 9 | 1 | no | — |
| 251 | C23×C3 | — | 4 | 1 | no | — |
| 252 | C23×C3 | — | 6 | 1 | no | — |
| 253 | C23×C3 | — | 6 | 1 | no | — |
| 254 | C23×C3 | — | 12 | 1 | no | — |
| 255 | C23×C3 | D3×D4 | 1 | 1 | yes | characteristic |
| 256 | C22×D3 | — | 3 | 1 | no | — |
| 257 | C22×D3 | — | 6 | 1 | no | — |
| 258 | C22×D3 | — | 12 | 2 | no | — |
| 259 | C22×D3 | — | 12 | 1 | no | — |
| 260 | C22×D3 | — | 12 | 1 | no | — |
| 261 | C22×D3 | — | 24 | 1 | no | — |
| 262 | C3×Q8 | — | 3 | 1 | no | — |
| 263 | C3×Q8 | — | 6 | 1 | no | — |
| 264 | C3×Q8 | — | 6 | 1 | no | — |
| 265 | C3×Q8 | C2×S4 | 1 | 1 | yes | characteristic |
| 266 | C3×D4 | — | 3 | 1 | no | — |
| 267 | C3×D4 | — | 6 | 1 | no | — |
| 268 | C3×D4 | — | 6 | 1 | no | — |
| 269 | C3×D4 | C2×S4 | 1 | 1 | yes | characteristic |
| 270 | C2×C3×C4 | — | 3 | 1 | no | — |
| 271 | C2×C3×C4 | — | 3 | 1 | no | — |
| 272 | C2×C3×C4 | — | 6 | 1 | no | — |
| 273 | C2×C3×C4 | — | 6 | 1 | no | — |
| 274 | #67 | — | 3 | 2 | no | — |
| 275 | #67 | — | 3 | 2 | no | — |
| 276 | #67 | — | 12 | 2 | no | — |
| 277 | #67 | — | 12 | 1 | no | — |
| 278 | #67 | — | 12 | 1 | no | — |
| 279 | #67 | — | 12 | 2 | no | — |
| 280 | #67 | — | 12 | 1 | no | — |
| 281 | #67 | — | 12 | 1 | no | — |
| 282 | #67 | — | 24 | 1 | no | — |
| 283 | C2×Dic3 | — | 3 | 1 | no | — |
| 284 | C2×Dic3 | — | 3 | 1 | no | — |
| 285 | C2×Dic3 | — | 3 | 1 | no | — |
| 286 | C2×Dic3 | — | 6 | 1 | no | — |
| 287 | C2×Dic3 | — | 6 | 1 | no | — |
| 288 | C2×Dic3 | — | 6 | 1 | no | — |
| 289 | C2×Dic3 | — | 12 | 2 | no | — |
| 290 | D12 | — | 6 | 1 | no | — |
| 291 | D12 | — | 6 | 1 | no | — |
| 292 | C4×D3 | — | 6 | 1 | no | — |
| 293 | C4×D3 | — | 6 | 1 | no | — |
| 294 | C4×D3 | — | 12 | 1 | no | — |
| 295 | C4×D3 | — | 12 | 1 | no | — |
| 296 | Dic6 | — | 6 | 1 | no | — |
| 297 | Dic6 | — | 6 | 1 | no | — |
| 298 | Dic6 | — | 12 | 1 | no | — |
| 299 | Dic6 | — | 12 | 1 | no | — |
| 300 | C3×C8 | — | 3 | 1 | no | — |
| 301 | C3×C8 | C2×S4 | 1 | 1 | yes | characteristic |
| 302 | C3⋊C8 | — | 6 | 1 | no | — |
| 303 | C3⋊C8 | — | 6 | 1 | no | — |
| 304 | C2×C9 | — | 4 | 1 | no | — |
| 305 | C2×C9 | — | 16 | 1 | no | — |
| 306 | D9 | — | 4 | 2 | no | — |
| 307 | D9 | — | 16 | 1 | no | — |
| 308 | C24 | — | 2 | 1 | no | — |
| 309 | C24 | — | 18 | 1 | no | — |
| 310 | C2×Q8 | — | 3 | 1 | no | — |
| 311 | C2×Q8 | — | 3 | 1 | no | — |
| 312 | C2×Q8 | — | 6 | 1 | no | — |
| 313 | C2×Q8 | — | 9 | 1 | no | — |
| 314 | C2×Q8 | — | 18 | 1 | no | — |
| 315 | C2×Q8 | — | 18 | 1 | no | — |
| 316 | C2×Q8 | — | 18 | 1 | no | — |
| 317 | C2×Q8 | — | 36 | 1 | no | — |
| 318 | C2×D4 | — | 3 | 1 | no | — |
| 319 | C2×D4 | — | 3 | 1 | no | — |
| 320 | C2×D4 | — | 6 | 1 | no | — |
| 321 | C2×D4 | — | 9 | 1 | no | — |
| 322 | C2×D4 | — | 9 | 1 | no | — |
| 323 | C2×D4 | — | 18 | 1 | no | — |
| 324 | C2×D4 | — | 18 | 1 | no | — |
| 325 | C2×D4 | — | 18 | 1 | no | — |
| 326 | C2×D4 | — | 18 | 1 | no | — |
| 327 | C2×D4 | — | 18 | 1 | no | — |
| 328 | C2×D4 | — | 18 | 1 | no | — |
| 329 | C2×D4 | — | 18 | 1 | no | — |
| 330 | C2×D4 | — | 36 | 1 | no | — |
| 331 | C2×D4 | — | 36 | 2 | no | — |
| 332 | C2×D4 | — | 36 | 2 | no | — |
| 333 | C22×C4 | — | 2 | 1 | no | — |
| 334 | C22×C4 | — | 9 | 1 | no | — |
| 335 | C22×C4 | — | 18 | 1 | no | — |
| 336 | C22×C4 | — | 18 | 1 | no | — |
| 337 | C22×C4 | C22×D9 | 1 | 1 | yes | characteristic |
| 338 | SD16 | — | 3 | 1 | no | — |
| 339 | SD16 | — | 3 | 1 | no | — |
| 340 | SD16 | — | 3 | 1 | no | — |
| 341 | SD16 | — | 6 | 1 | no | — |
| 342 | SD16 | — | 18 | 1 | no | — |
| 343 | SD16 | — | 18 | 1 | no | — |
| 344 | SD16 | — | 18 | 1 | no | — |
| 345 | SD16 | — | 18 | 1 | no | — |
| 346 | SD16 | — | 18 | 1 | no | — |
| 347 | SD16 | — | 18 | 1 | no | — |
| 348 | SD16 | — | 36 | 1 | no | — |
| 349 | SD16 | — | 36 | 1 | no | — |
| 350 | SD16 | (C22⋊C9)⋊C2 | 1 | 1 | yes | characteristic, direct product factor |
| 351 | C2×C8 | — | 3 | 1 | no | — |
| 352 | C2×C8 | — | 3 | 1 | no | — |
| 353 | C2×C8 | — | 9 | 1 | no | — |
| 354 | C2×C8 | — | 9 | 1 | no | — |
| 355 | C2×C8 | — | 18 | 1 | no | — |
| 356 | C2×C8 | — | 18 | 1 | no | — |
| 357 | C4⋊C4 | — | 9 | 1 | no | — |
| 358 | C4⋊C4 | — | 9 | 1 | no | — |
| 359 | C4⋊C4 | — | 9 | 1 | no | — |
| 360 | C4⋊C4 | — | 18 | 1 | no | — |
| 361 | C4⋊C4 | — | 18 | 1 | no | — |
| 362 | C4⋊C4 | — | 18 | 1 | no | — |
| 363 | C4⋊C4 | — | 18 | 1 | no | — |
| 364 | C4⋊C4 | — | 18 | 1 | no | — |
| 365 | C22⋊C4 | — | 9 | 1 | no | — |
| 366 | C22⋊C4 | — | 9 | 1 | no | — |
| 367 | C22⋊C4 | — | 18 | 1 | no | — |
| 368 | C22⋊C4 | — | 18 | 1 | no | — |
| 369 | C22⋊C4 | — | 18 | 1 | no | — |
| 370 | C22⋊C4 | — | 18 | 1 | no | — |
| 371 | C22⋊C4 | — | 18 | 1 | no | — |
| 372 | C42 | — | 9 | 1 | no | — |
| 373 | C42 | — | 18 | 1 | no | — |
| 374 | C22×C3 | — | 2 | 1 | no | — |
| 375 | C22×C3 | — | 3 | 1 | no | — |
| 376 | C22×C3 | — | 3 | 1 | no | — |
| 377 | C22×C3 | — | 6 | 1 | no | — |
| 378 | C22×C3 | — | 12 | 1 | no | — |
| 379 | C22×C3 | — | 12 | 1 | no | — |
| 380 | C22×C3 | — | 12 | 1 | no | — |
| 381 | C22×C3 | — | 12 | 1 | no | — |
| 382 | C22×C3 | D3×SD16 | 1 | 1 | yes | characteristic |
| 383 | C2×D3 | — | 3 | 2 | no | — |
| 384 | C2×D3 | — | 6 | 1 | no | — |
| 385 | C2×D3 | — | 6 | 1 | no | — |
| 386 | C2×D3 | — | 12 | 1 | no | — |
| 387 | C2×D3 | — | 12 | 1 | no | — |
| 388 | C2×D3 | — | 12 | 1 | no | — |
| 389 | C2×D3 | — | 24 | 2 | no | — |
| 390 | C2×D3 | — | 24 | 2 | no | — |
| 391 | C3×C4 | — | 2 | 1 | no | — |
| 392 | C3×C4 | — | 3 | 1 | no | — |
| 393 | C3×C4 | — | 6 | 1 | no | — |
| 394 | C3×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 395 | Dic3 | — | 3 | 2 | no | — |
| 396 | Dic3 | — | 6 | 1 | no | — |
| 397 | Dic3 | — | 6 | 1 | no | — |
| 398 | Dic3 | — | 12 | 1 | no | — |
| 399 | Dic3 | — | 12 | 1 | no | — |
| 400 | Dic3 | — | 12 | 1 | no | — |
| 401 | C9 | — | 4 | 1 | no | Sylow |
| 402 | C23 | — | 4 | 1 | no | — |
| 403 | C23 | — | 6 | 1 | no | — |
| 404 | C23 | — | 6 | 1 | no | — |
| 405 | C23 | — | 9 | 1 | no | — |
| 406 | C23 | — | 12 | 1 | no | — |
| 407 | C23 | — | 18 | 1 | no | — |
| 408 | C23 | — | 36 | 1 | no | — |
| 409 | C23 | — | 36 | 1 | no | — |
| 410 | C23 | — | 36 | 2 | no | — |
| 411 | C23 | — | 72 | 1 | no | — |
| 412 | C23 | D4×D9 | 1 | 1 | yes | characteristic |
| 413 | Q8 | — | 3 | 1 | no | — |
| 414 | Q8 | — | 6 | 1 | no | — |
| 415 | Q8 | — | 6 | 1 | no | — |
| 416 | Q8 | — | 18 | 1 | no | — |
| 417 | Q8 | — | 18 | 1 | no | — |
| 418 | Q8 | — | 36 | 1 | no | — |
| 419 | Q8 | — | 36 | 1 | no | — |
| 420 | Q8 | C2×(C22⋊C9)⋊C2 | 1 | 1 | yes | characteristic, complemented |
| 421 | D4 | — | 3 | 1 | no | — |
| 422 | D4 | — | 6 | 1 | no | — |
| 423 | D4 | — | 6 | 1 | no | — |
| 424 | D4 | — | 9 | 2 | no | — |
| 425 | D4 | — | 9 | 2 | no | — |
| 426 | D4 | — | 18 | 1 | no | — |
| 427 | D4 | — | 18 | 1 | no | — |
| 428 | D4 | — | 36 | 2 | no | — |
| 429 | D4 | — | 36 | 1 | no | — |
| 430 | D4 | — | 36 | 1 | no | — |
| 431 | D4 | — | 36 | 1 | no | — |
| 432 | D4 | — | 36 | 2 | no | — |
| 433 | D4 | — | 36 | 1 | no | — |
| 434 | D4 | — | 72 | 1 | no | — |
| 435 | D4 | C2×(C22⋊C9)⋊C2 | 1 | 1 | yes | characteristic |
| 436 | C2×C4 | — | 3 | 1 | no | — |
| 437 | C2×C4 | — | 3 | 1 | no | — |
| 438 | C2×C4 | — | 6 | 1 | no | — |
| 439 | C2×C4 | — | 6 | 1 | no | — |
| 440 | C2×C4 | — | 9 | 1 | no | — |
| 441 | C2×C4 | — | 9 | 1 | no | — |
| 442 | C2×C4 | — | 9 | 1 | no | — |
| 443 | C2×C4 | — | 18 | 1 | no | — |
| 444 | C2×C4 | — | 18 | 1 | no | — |
| 445 | C2×C4 | — | 18 | 1 | no | — |
| 446 | C2×C4 | — | 18 | 1 | no | — |
| 447 | C2×C4 | — | 18 | 1 | no | — |
| 448 | C2×C4 | — | 36 | 1 | no | — |
| 449 | C2×C4 | — | 36 | 1 | no | — |
| 450 | C2×C4 | — | 36 | 2 | no | — |
| 451 | C8 | — | 3 | 1 | no | — |
| 452 | C8 | — | 18 | 1 | no | — |
| 453 | C8 | — | 18 | 1 | no | — |
| 454 | C8 | C2×(C22⋊C9)⋊C2 | 1 | 1 | yes | characteristic, complemented |
| 455 | C2×C3 | — | 3 | 1 | no | — |
| 456 | C2×C3 | — | 3 | 1 | no | — |
| 457 | C2×C3 | — | 4 | 1 | no | — |
| 458 | C2×C3 | — | 12 | 1 | no | — |
| 459 | C2×C3 | D4×S4 | 1 | 1 | yes | characteristic |
| 460 | D3 | — | 6 | 2 | no | — |
| 461 | D3 | — | 24 | 1 | no | — |
| 462 | C22 | — | 2 | 1 | no | — |
| 463 | C22 | — | 3 | 1 | no | — |
| 464 | C22 | — | 3 | 1 | no | — |
| 465 | C22 | — | 6 | 1 | no | — |
| 466 | C22 | — | 9 | 2 | no | — |
| 467 | C22 | — | 12 | 1 | no | — |
| 468 | C22 | — | 12 | 1 | no | — |
| 469 | C22 | — | 12 | 1 | no | — |
| 470 | C22 | — | 12 | 1 | no | — |
| 471 | C22 | — | 18 | 1 | no | — |
| 472 | C22 | — | 18 | 1 | no | — |
| 473 | C22 | — | 36 | 1 | no | — |
| 474 | C22 | — | 36 | 1 | no | — |
| 475 | C22 | — | 36 | 1 | no | — |
| 476 | C22 | — | 72 | 2 | no | — |
| 477 | C22 | — | 72 | 2 | no | — |
| 478 | C22 | SD16×D9 | 1 | 1 | yes | characteristic, complemented |
| 479 | C4 | — | 2 | 1 | no | — |
| 480 | C4 | — | 3 | 1 | no | — |
| 481 | C4 | — | 6 | 1 | no | — |
| 482 | C4 | — | 9 | 2 | no | — |
| 483 | C4 | — | 18 | 1 | no | — |
| 484 | C4 | — | 18 | 1 | no | — |
| 485 | C4 | — | 36 | 1 | no | — |
| 486 | C4 | — | 36 | 1 | no | — |
| 487 | C4 | — | 36 | 1 | no | — |
| 488 | C4 | C22×(C22⋊C9)⋊C2 | 1 | 1 | yes | characteristic |
| 489 | C3 | SD16×S4 | 1 | 1 | yes | characteristic |
| 490 | C2 | — | 3 | 1 | no | — |
| 491 | C2 | — | 3 | 1 | no | — |
| 492 | C2 | — | 4 | 1 | no | — |
| 493 | C2 | — | 12 | 1 | no | — |
| 494 | C2 | — | 18 | 2 | no | — |
| 495 | C2 | — | 72 | 1 | no | — |
| 496 | C2 | D4×(C22⋊C9)⋊C2 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Q8×(C22⋊C9)⋊C2 | C2 | semidirect |
| 3. SD16×C22⋊C9 | C2 | semidirect |
| 4. #10589519 | C2 | semidirect |
| 5. #10589516 | C2 | semidirect |
| 6. #10589503 | C2 | semidirect |
| 7. C8×(C22⋊C9)⋊C2 | C2 | semidirect |
| 10. Q8×C22⋊C9 | C22 | semidirect |
| 17. (C22⋊C9)⋊Q8 | C22 | semidirect |
| 19. C8×C22⋊C9 | C22 | semidirect |
| 20. (C22⋊C9)⋊C8 | C22 | semidirect |
| 103. (C22⋊C9)⋊C2 | SD16 | direct (N × H) |
| 115. C22×SD16 | D9 | semidirect |
| 199. C22⋊C9 | C2×SD16 | semidirect |
| 205. C22×Q8 | C2×D9 | semidirect |
| 223. C22×C8 | C2×D9 | semidirect |
| 350. SD16 | (C22⋊C9)⋊C2 | direct (N × H) |
| 420. Q8 | C2×(C22⋊C9)⋊C2 | semidirect |
| 454. C8 | C2×(C22⋊C9)⋊C2 | semidirect |
| 478. C22 | SD16×D9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×(C22⋊C9)⋊C2 | 2 |
| D4×(C22⋊C9)⋊C2 | 2 |
| SD16×C22⋊C9 | 2 |
| #10589519 | 2 |
| #10589516 | 2 |
| #10589503 | 2 |
| C8×(C22⋊C9)⋊C2 | 2 |
| SD16×#67 | 3 |
| SD16×D9 | 4 |