Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
670 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 64 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 | #10596065 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3×#5032 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10591531 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10591513 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#4536 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10589181 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10589174 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #70997 | — | 3 | 1 | no | maximal |
| 9 | #69131 | — | 3 | 1 | no | maximal |
| 10 | C3×#1004 | C22 | 1 | 1 | yes | characteristic |
| 11 | C32×#120 | C22 | 1 | 1 | yes | characteristic |
| 12 | #64162 | — | 2 | 1 | no | — |
| 13 | #64146 | — | 2 | 1 | no | — |
| 14 | #64146 | C22 | 1 | 1 | yes | characteristic |
| 15 | #64145 | — | 2 | 1 | no | — |
| 16 | #64145 | C22 | 1 | 1 | yes | characteristic |
| 17 | #64094 | — | 2 | 1 | no | — |
| 18 | #64094 | — | 2 | 1 | no | — |
| 19 | #64094 | — | 2 | 1 | no | — |
| 20 | C3×#953 | — | 2 | 1 | no | — |
| 21 | #63981 | — | 2 | 1 | no | — |
| 22 | #63831 | — | 2 | 1 | no | — |
| 23 | C3×#834 | C22 | 1 | 1 | yes | characteristic |
| 24 | C3×#834 | C22 | 1 | 1 | yes | characteristic |
| 25 | C3×#833 | C22 | 1 | 1 | yes | characteristic |
| 26 | C3×#806 | — | 2 | 1 | no | — |
| 27 | #63580 | — | 2 | 1 | no | — |
| 28 | #63568 | — | 2 | 1 | no | — |
| 29 | #5594 | — | 3 | 1 | no | — |
| 30 | #5594 | — | 3 | 1 | no | — |
| 31 | #5594 | — | 6 | 1 | no | — |
| 32 | C3×B(4,𝔽2) | — | 3 | 1 | no | — |
| 33 | #5244 | — | 3 | 1 | no | — |
| 34 | #5242 | — | 3 | 1 | no | — |
| 35 | #5032 | D3 | 1 | 1 | yes | characteristic, complemented |
| 36 | #4746 | — | 3 | 1 | no | — |
| 37 | #4741 | — | 3 | 1 | no | — |
| 38 | C3×AΣL(1,𝔽16) | — | 3 | 1 | no | — |
| 39 | #4536 | D3 | 1 | 1 | yes | characteristic, complemented |
| 40 | #4475 | — | 3 | 1 | no | — |
| 41 | #4473 | — | 3 | 1 | no | — |
| 42 | #4473 | — | 3 | 1 | no | — |
| 43 | #4471 | — | 3 | 1 | no | — |
| 44 | C24×C32 | D4 | 1 | 1 | yes | characteristic, complemented |
| 45 | C23×C3⋊D3 | D4 | 1 | 1 | yes | characteristic, complemented |
| 46 | C2×C32×D4 | — | 2 | 1 | no | — |
| 47 | C2×C32×D4 | C23 | 1 | 1 | yes | characteristic |
| 48 | C2×#638 | — | 2 | 1 | no | — |
| 49 | C2×#638 | — | 2 | 1 | no | — |
| 50 | C2×#638 | — | 2 | 1 | no | — |
| 51 | C2×#634 | — | 2 | 1 | no | — |
| 52 | C2×#634 | D4 | 1 | 1 | yes | characteristic, complemented |
| 53 | C2×C3×#67 | — | 2 | 1 | no | — |
| 54 | C2×C3×#67 | — | 2 | 1 | no | — |
| 55 | C2×C3×#67 | — | 4 | 1 | no | — |
| 56 | C3×#237 | — | 4 | 1 | no | — |
| 57 | C3×D3×D4 | — | 4 | 1 | no | — |
| 58 | C3×#235 | — | 2 | 1 | no | — |
| 59 | C2×#626 | — | 4 | 1 | no | — |
| 60 | C32×C22⋊C4 | — | 2 | 1 | no | — |
| 61 | C32×C22⋊C4 | D4 | 1 | 1 | yes | characteristic, complemented |
| 62 | #3757 | — | 2 | 1 | no | — |
| 63 | #3757 | — | 2 | 1 | no | — |
| 64 | #3757 | — | 2 | 1 | no | — |
| 65 | #3757 | — | 2 | 1 | no | — |
| 66 | #3757 | D4 | 1 | 1 | yes | characteristic, complemented |
| 67 | #3752 | — | 2 | 1 | no | — |
| 68 | #3752 | — | 2 | 1 | no | — |
| 69 | #3752 | — | 2 | 1 | no | — |
| 70 | C4×C3⋊Dic3 | — | 2 | 1 | no | — |
| 71 | C4×C3⋊Dic3 | D4 | 1 | 1 | yes | characteristic, complemented |
| 72 | C3×#217 | — | 2 | 1 | no | — |
| 73 | C3×#217 | — | 2 | 1 | no | — |
| 74 | C3×#217 | — | 4 | 1 | no | — |
| 75 | C3×#208 | — | 2 | 1 | no | — |
| 76 | #3722 | — | 4 | 1 | no | — |
| 77 | #3719 | — | 4 | 1 | no | — |
| 78 | #3716 | — | 4 | 1 | no | — |
| 79 | #2199 | — | 9 | 1 | no | Sylow |
| 80 | C3×H(5,𝔽2) | — | 3 | 1 | no | — |
| 81 | #1004 | C2×D3 | 1 | 1 | yes | characteristic |
| 82 | C3×#120 | — | 2 | 1 | no | — |
| 83 | C3×#120 | — | 6 | 1 | no | — |
| 84 | C3×#120 | C2×D3 | 1 | 1 | yes | characteristic |
| 85 | C3×#120 | C2×D3 | 1 | 1 | yes | characteristic |
| 86 | #953 | — | 2 | 1 | no | — |
| 87 | #953 | — | 6 | 2 | no | — |
| 88 | #953 | — | 6 | 1 | no | — |
| 89 | #953 | — | 6 | 1 | no | — |
| 90 | #951 | — | 6 | 1 | no | — |
| 91 | #937 | — | 3 | 1 | no | — |
| 92 | #937 | — | 3 | 1 | no | — |
| 93 | #937 | — | 6 | 1 | no | — |
| 94 | #937 | — | 6 | 1 | no | — |
| 95 | #937 | — | 6 | 1 | no | — |
| 96 | #937 | — | 6 | 2 | no | — |
| 97 | #937 | — | 6 | 1 | no | — |
| 98 | #936 | — | 3 | 1 | no | — |
| 99 | #936 | — | 3 | 1 | no | — |
| 100 | #936 | — | 6 | 1 | no | — |
| 101 | #936 | — | 6 | 1 | no | — |
| 102 | #936 | — | 6 | 1 | no | — |
| 103 | #936 | — | 6 | 2 | no | — |
| 104 | #909 | — | 6 | 1 | no | — |
| 105 | #885 | — | 6 | 1 | no | — |
| 106 | #885 | — | 6 | 1 | no | — |
| 107 | #885 | — | 6 | 1 | no | — |
| 108 | #885 | — | 6 | 1 | no | — |
| 109 | #885 | — | 6 | 2 | no | — |
| 110 | #885 | — | 6 | 2 | no | — |
| 111 | #885 | — | 6 | 2 | no | — |
| 112 | #885 | — | 6 | 1 | no | — |
| 113 | #885 | — | 6 | 1 | no | — |
| 114 | #882 | — | 6 | 1 | no | — |
| 115 | C3×#100 | — | 3 | 1 | no | — |
| 116 | C3×#99 | — | 3 | 1 | no | — |
| 117 | C3×#99 | — | 3 | 1 | no | — |
| 118 | C3×#99 | — | 6 | 1 | no | — |
| 119 | #837 | — | 6 | 1 | no | — |
| 120 | #834 | — | 6 | 1 | no | — |
| 121 | #834 | C2×D3 | 1 | 1 | yes | characteristic |
| 122 | #834 | C2×D3 | 1 | 1 | yes | characteristic |
| 123 | #833 | C2×D3 | 1 | 1 | yes | characteristic |
| 124 | #825 | — | 6 | 1 | no | — |
| 125 | #806 | — | 2 | 1 | no | — |
| 126 | #806 | — | 6 | 1 | no | — |
| 127 | C23×C32 | — | 2 | 1 | no | — |
| 128 | C23×C32 | — | 4 | 1 | no | — |
| 129 | C23×C32 | — | 8 | 1 | no | — |
| 130 | C23×C32 | C2×D4 | 1 | 1 | yes | characteristic |
| 131 | C23×C32 | C2×D4 | 1 | 1 | yes | characteristic |
| 132 | C22×C3⋊D3 | — | 2 | 1 | no | — |
| 133 | C22×C3⋊D3 | — | 4 | 1 | no | — |
| 134 | C22×C3⋊D3 | — | 8 | 1 | no | — |
| 135 | C22×C3×D3 | — | 2 | 1 | no | — |
| 136 | C22×C3×D3 | — | 2 | 1 | no | — |
| 137 | C32×D4 | — | 4 | 1 | no | — |
| 138 | C32×D4 | — | 8 | 1 | no | — |
| 139 | C2×C32×C4 | — | 2 | 1 | no | — |
| 140 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 141 | #638 | — | 8 | 1 | no | — |
| 142 | #638 | — | 8 | 1 | no | — |
| 143 | #638 | — | 8 | 1 | no | — |
| 144 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 145 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 146 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 147 | #634 | — | 4 | 1 | no | — |
| 148 | #634 | — | 8 | 1 | no | — |
| 149 | C3×#67 | — | 4 | 1 | no | — |
| 150 | C3×#67 | — | 4 | 1 | no | — |
| 151 | C3×#67 | — | 4 | 1 | no | — |
| 152 | C3×#67 | — | 8 | 2 | no | — |
| 153 | C2×C3×Dic3 | — | 2 | 1 | no | — |
| 154 | C2×C3×Dic3 | — | 2 | 1 | no | — |
| 155 | C2×C3×Dic3 | — | 4 | 1 | no | — |
| 156 | C2×C3×Dic3 | — | 4 | 1 | no | — |
| 157 | C3×D12 | — | 2 | 1 | no | — |
| 158 | C3×C4×D3 | — | 4 | 1 | no | — |
| 159 | C3×Dic6 | — | 2 | 1 | no | — |
| 160 | #626 | — | 8 | 2 | no | — |
| 161 | C3×C3⋊C8 | — | 4 | 1 | no | — |
| 162 | H(3,𝔽4) | — | 9 | 1 | no | — |
| 163 | B(4,𝔽2) | — | 3 | 1 | no | — |
| 164 | B(4,𝔽2) | — | 9 | 1 | no | — |
| 165 | #455 | — | 9 | 1 | no | — |
| 166 | #354 | — | 9 | 1 | no | — |
| 167 | AΣL(1,𝔽16) | — | 3 | 1 | no | — |
| 168 | AΣL(1,𝔽16) | — | 9 | 1 | no | — |
| 169 | C24×C3 | — | 2 | 1 | no | — |
| 170 | C24×C3 | D12 | 1 | 1 | yes | characteristic, complemented |
| 171 | C24×C3 | #67 | 1 | 1 | yes | characteristic, complemented |
| 172 | C23×D3 | — | 3 | 1 | no | — |
| 173 | C23×D3 | — | 3 | 1 | no | — |
| 174 | C23×D3 | — | 6 | 1 | no | — |
| 175 | C3×#41 | — | 6 | 1 | no | — |
| 176 | C3×#41 | — | 12 | 1 | no | — |
| 177 | C2×C3×D4 | — | 2 | 2 | no | — |
| 178 | C2×C3×D4 | — | 2 | 1 | no | — |
| 179 | C2×C3×D4 | — | 2 | 1 | no | — |
| 180 | C2×C3×D4 | — | 2 | 1 | no | — |
| 181 | C2×C3×D4 | — | 6 | 1 | no | — |
| 182 | C2×C3×D4 | — | 6 | 1 | no | — |
| 183 | C2×C3×D4 | — | 12 | 1 | no | — |
| 184 | C2×C3×D4 | — | 12 | 1 | no | — |
| 185 | C2×C3×D4 | C22×D3 | 1 | 1 | yes | characteristic |
| 186 | C2×C3×D4 | C22×D3 | 1 | 1 | yes | characteristic |
| 187 | C2×#67 | — | 2 | 1 | no | — |
| 188 | C2×#67 | — | 2 | 1 | no | — |
| 189 | C2×#67 | — | 4 | 1 | no | — |
| 190 | C2×#67 | — | 6 | 2 | no | — |
| 191 | C2×#67 | — | 6 | 2 | no | — |
| 192 | C2×#67 | — | 6 | 1 | no | — |
| 193 | C2×#67 | — | 6 | 1 | no | — |
| 194 | C2×#67 | — | 6 | 1 | no | — |
| 195 | C2×#67 | — | 6 | 1 | no | — |
| 196 | C2×#67 | — | 6 | 2 | no | — |
| 197 | C2×#67 | — | 6 | 1 | no | — |
| 198 | C2×#67 | — | 6 | 1 | no | — |
| 199 | C2×#67 | — | 12 | 1 | no | — |
| 200 | #237 | — | 4 | 1 | no | — |
| 201 | D3×D4 | — | 4 | 1 | no | — |
| 202 | #235 | — | 2 | 1 | no | — |
| 203 | C2×D12 | — | 12 | 1 | no | — |
| 204 | C2×Dic6 | — | 3 | 1 | no | — |
| 205 | C2×Dic6 | — | 3 | 1 | no | — |
| 206 | C2×Dic6 | — | 6 | 1 | no | — |
| 207 | C2×Dic6 | — | 6 | 2 | no | — |
| 208 | C2×Dic6 | — | 6 | 1 | no | — |
| 209 | C2×Dic6 | — | 6 | 1 | no | — |
| 210 | C3×M16 | — | 6 | 1 | no | — |
| 211 | C3×C22⋊C4 | — | 2 | 2 | no | — |
| 212 | C3×C22⋊C4 | — | 2 | 1 | no | — |
| 213 | C3×C22⋊C4 | — | 2 | 1 | no | — |
| 214 | C3×C22⋊C4 | — | 2 | 1 | no | — |
| 215 | C3×C22⋊C4 | — | 6 | 1 | no | — |
| 216 | C3×C22⋊C4 | — | 6 | 1 | no | — |
| 217 | C3×C22⋊C4 | — | 12 | 1 | no | — |
| 218 | C3×C22⋊C4 | D12 | 1 | 1 | yes | characteristic, complemented |
| 219 | C3×C22⋊C4 | #67 | 1 | 1 | yes | characteristic, complemented |
| 220 | #217 | — | 2 | 1 | no | — |
| 221 | #217 | — | 2 | 1 | no | — |
| 222 | #217 | — | 3 | 1 | no | — |
| 223 | #217 | — | 3 | 1 | no | — |
| 224 | #217 | — | 4 | 1 | no | — |
| 225 | #217 | — | 6 | 1 | no | — |
| 226 | #217 | — | 6 | 2 | no | — |
| 227 | #217 | — | 6 | 2 | no | — |
| 228 | #217 | — | 6 | 1 | no | — |
| 229 | #217 | — | 6 | 1 | no | — |
| 230 | #217 | — | 6 | 1 | no | — |
| 231 | #217 | — | 6 | 1 | no | — |
| 232 | #217 | — | 6 | 2 | no | — |
| 233 | #217 | — | 6 | 2 | no | — |
| 234 | #217 | — | 6 | 1 | no | — |
| 235 | #217 | — | 6 | 1 | no | — |
| 236 | #217 | — | 6 | 1 | no | — |
| 237 | #217 | — | 6 | 1 | no | — |
| 238 | #216 | — | 12 | 1 | no | — |
| 239 | #214 | — | 12 | 1 | no | — |
| 240 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 241 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 242 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 243 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 244 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 245 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 246 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 247 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 248 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 249 | (C2×D3)⋊C4 | — | 12 | 1 | no | — |
| 250 | (C2×D3)⋊C4 | — | 12 | 1 | no | — |
| 251 | C4×Dic3 | — | 3 | 1 | no | — |
| 252 | C4×Dic3 | — | 3 | 1 | no | — |
| 253 | C4×Dic3 | — | 6 | 1 | no | — |
| 254 | C4×Dic3 | — | 6 | 2 | no | — |
| 255 | C4×Dic3 | — | 6 | 1 | no | — |
| 256 | C4×Dic3 | — | 6 | 1 | no | — |
| 257 | #208 | — | 2 | 1 | no | — |
| 258 | Dic12 | — | 12 | 1 | no | — |
| 259 | #204 | — | 12 | 1 | no | — |
| 260 | C22×C32 | — | 2 | 1 | no | — |
| 261 | C22×C32 | — | 2 | 1 | no | — |
| 262 | C22×C32 | — | 4 | 1 | no | — |
| 263 | C22×C32 | — | 4 | 1 | no | — |
| 264 | C22×C32 | — | 4 | 1 | no | — |
| 265 | C22×C32 | — | 4 | 1 | no | — |
| 266 | C22×C32 | — | 4 | 1 | no | — |
| 267 | C22×C32 | — | 4 | 2 | no | — |
| 268 | C22×C32 | — | 8 | 1 | no | — |
| 269 | C22×C32 | #120 | 1 | 1 | yes | characteristic |
| 270 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 271 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 272 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 273 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 274 | C2×C3⋊D3 | — | 8 | 1 | no | — |
| 275 | C2×C3×D3 | — | 4 | 1 | no | — |
| 276 | C2×C3×D3 | — | 8 | 1 | no | — |
| 277 | C2×C3×D3 | — | 8 | 1 | no | — |
| 278 | C32×C4 | — | 2 | 1 | no | — |
| 279 | C32×C4 | — | 4 | 1 | no | — |
| 280 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 281 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 282 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 283 | C3×Dic3 | — | 4 | 1 | no | — |
| 284 | C3×Dic3 | — | 8 | 1 | no | — |
| 285 | C3×Dic3 | — | 8 | 1 | no | — |
| 286 | H(5,𝔽2) | — | 3 | 1 | no | — |
| 287 | #137 | — | 18 | 1 | no | — |
| 288 | #124 | — | 9 | 1 | no | — |
| 289 | #124 | — | 18 | 1 | no | — |
| 290 | #124 | — | 18 | 1 | no | — |
| 291 | #124 | — | 18 | 1 | no | — |
| 292 | #124 | — | 18 | 1 | no | — |
| 293 | #120 | — | 6 | 1 | no | — |
| 294 | #120 | — | 9 | 1 | no | — |
| 295 | #120 | — | 18 | 1 | no | — |
| 296 | #120 | — | 18 | 1 | no | — |
| 297 | #120 | — | 18 | 1 | no | — |
| 298 | #120 | D32 | 1 | 1 | yes | characteristic |
| 299 | #104 | — | 18 | 1 | no | — |
| 300 | #100 | — | 3 | 1 | no | — |
| 301 | #99 | — | 3 | 1 | no | — |
| 302 | #99 | — | 3 | 1 | no | — |
| 303 | #99 | — | 6 | 1 | no | — |
| 304 | #99 | — | 18 | 1 | no | — |
| 305 | C23×C3 | — | 2 | 2 | no | — |
| 306 | C23×C3 | — | 2 | 1 | no | — |
| 307 | C23×C3 | — | 2 | 1 | no | — |
| 308 | C23×C3 | — | 2 | 1 | no | — |
| 309 | C23×C3 | — | 2 | 1 | no | — |
| 310 | C23×C3 | — | 4 | 1 | no | — |
| 311 | C23×C3 | — | 4 | 1 | no | — |
| 312 | C23×C3 | — | 6 | 1 | no | — |
| 313 | C23×C3 | — | 6 | 1 | no | — |
| 314 | C23×C3 | — | 8 | 1 | no | — |
| 315 | C23×C3 | — | 8 | 1 | no | — |
| 316 | C23×C3 | — | 8 | 1 | no | — |
| 317 | C23×C3 | — | 8 | 2 | no | — |
| 318 | C23×C3 | C2×D12 | 1 | 1 | yes | characteristic |
| 319 | C23×C3 | D3×D4 | 1 | 1 | yes | characteristic |
| 320 | C23×C3 | D3×D4 | 1 | 1 | yes | characteristic |
| 321 | C23×C3 | C2×#67 | 1 | 1 | yes | characteristic |
| 322 | C22×D3 | — | 2 | 1 | no | — |
| 323 | C22×D3 | — | 2 | 1 | no | — |
| 324 | C22×D3 | — | 6 | 2 | no | — |
| 325 | C22×D3 | — | 6 | 1 | no | — |
| 326 | C22×D3 | — | 6 | 1 | no | — |
| 327 | C22×D3 | — | 12 | 1 | no | — |
| 328 | C22×D3 | — | 12 | 1 | no | — |
| 329 | C22×D3 | — | 24 | 1 | no | — |
| 330 | C22×D3 | — | 24 | 1 | no | — |
| 331 | C22×D3 | — | 24 | 1 | no | — |
| 332 | C22×D3 | — | 24 | 2 | no | — |
| 333 | C3×Q8 | — | 6 | 1 | no | — |
| 334 | C3×D4 | — | 4 | 1 | no | — |
| 335 | C3×D4 | — | 4 | 1 | no | — |
| 336 | C3×D4 | — | 6 | 1 | no | — |
| 337 | C3×D4 | — | 8 | 1 | no | — |
| 338 | C3×D4 | — | 8 | 1 | no | — |
| 339 | C3×D4 | — | 8 | 1 | no | — |
| 340 | C3×D4 | — | 8 | 2 | no | — |
| 341 | C3×D4 | — | 12 | 1 | no | — |
| 342 | C3×D4 | — | 12 | 1 | no | — |
| 343 | C3×D4 | — | 12 | 1 | no | — |
| 344 | C3×D4 | — | 24 | 2 | no | — |
| 345 | C2×C3×C4 | — | 2 | 2 | no | — |
| 346 | C2×C3×C4 | — | 2 | 1 | no | — |
| 347 | C2×C3×C4 | — | 2 | 1 | no | — |
| 348 | C2×C3×C4 | — | 2 | 1 | no | — |
| 349 | C2×C3×C4 | — | 6 | 1 | no | — |
| 350 | C2×C3×C4 | — | 6 | 1 | no | — |
| 351 | C2×C3×C4 | — | 12 | 1 | no | — |
| 352 | C2×C3×C4 | — | 12 | 1 | no | — |
| 353 | C2×C3×C4 | — | 12 | 1 | no | — |
| 354 | C2×C3×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 355 | C2×C3×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 356 | #67 | — | 4 | 1 | no | — |
| 357 | #67 | — | 4 | 1 | no | — |
| 358 | #67 | — | 4 | 1 | no | — |
| 359 | #67 | — | 8 | 2 | no | — |
| 360 | #67 | — | 24 | 2 | no | — |
| 361 | #67 | — | 24 | 1 | no | — |
| 362 | #67 | — | 24 | 1 | no | — |
| 363 | #67 | — | 24 | 2 | no | — |
| 364 | #67 | — | 24 | 2 | no | — |
| 365 | #67 | — | 24 | 1 | no | — |
| 366 | #67 | — | 24 | 1 | no | — |
| 367 | #67 | — | 24 | 2 | no | — |
| 368 | #67 | — | 24 | 1 | no | — |
| 369 | #67 | — | 24 | 1 | no | — |
| 370 | C2×Dic3 | — | 2 | 1 | no | — |
| 371 | C2×Dic3 | — | 2 | 1 | no | — |
| 372 | C2×Dic3 | — | 4 | 1 | no | — |
| 373 | C2×Dic3 | — | 4 | 1 | no | — |
| 374 | C2×Dic3 | — | 6 | 2 | no | — |
| 375 | C2×Dic3 | — | 6 | 2 | no | — |
| 376 | C2×Dic3 | — | 6 | 2 | no | — |
| 377 | C2×Dic3 | — | 6 | 1 | no | — |
| 378 | C2×Dic3 | — | 6 | 1 | no | — |
| 379 | C2×Dic3 | — | 6 | 1 | no | — |
| 380 | C2×Dic3 | — | 6 | 1 | no | — |
| 381 | C2×Dic3 | — | 6 | 1 | no | — |
| 382 | C2×Dic3 | — | 6 | 1 | no | — |
| 383 | D12 | — | 2 | 1 | no | — |
| 384 | D12 | — | 24 | 2 | no | — |
| 385 | C4×D3 | — | 4 | 1 | no | — |
| 386 | Dic6 | — | 2 | 1 | no | — |
| 387 | Dic6 | — | 12 | 1 | no | — |
| 388 | Dic6 | — | 12 | 1 | no | — |
| 389 | Dic6 | — | 24 | 1 | no | — |
| 390 | Dic6 | — | 24 | 2 | no | — |
| 391 | Dic6 | — | 24 | 1 | no | — |
| 392 | Dic6 | — | 24 | 1 | no | — |
| 393 | C3×C8 | — | 12 | 1 | no | — |
| 394 | C3⋊C8 | — | 4 | 1 | no | — |
| 395 | C2×C32 | — | 2 | 1 | no | — |
| 396 | C2×C32 | — | 4 | 1 | no | — |
| 397 | C2×C32 | — | 4 | 1 | no | — |
| 398 | C2×C32 | — | 8 | 1 | no | — |
| 399 | C2×C32 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 400 | C3⋊D3 | — | 8 | 1 | no | — |
| 401 | C3×D3 | — | 8 | 1 | no | — |
| 402 | C24 | — | 9 | 1 | no | — |
| 403 | C24 | #626 | 1 | 1 | yes | characteristic, complemented |
| 404 | #41 | — | 6 | 1 | no | — |
| 405 | #41 | — | 12 | 1 | no | — |
| 406 | C2×Q8 | — | 9 | 1 | no | — |
| 407 | C2×Q8 | — | 18 | 1 | no | — |
| 408 | C2×D4 | — | 2 | 1 | no | — |
| 409 | C2×D4 | — | 6 | 1 | no | — |
| 410 | C2×D4 | — | 6 | 1 | no | — |
| 411 | C2×D4 | — | 12 | 1 | no | — |
| 412 | C2×D4 | — | 12 | 1 | no | — |
| 413 | C2×D4 | — | 18 | 1 | no | — |
| 414 | C2×D4 | — | 18 | 1 | no | — |
| 415 | C2×D4 | — | 18 | 1 | no | — |
| 416 | C2×D4 | — | 36 | 1 | no | — |
| 417 | C2×D4 | C2×D32 | 1 | 1 | yes | characteristic |
| 418 | Q16 | — | 36 | 1 | no | — |
| 419 | SD16 | — | 36 | 1 | no | — |
| 420 | M16 | — | 6 | 1 | no | — |
| 421 | C22⋊C4 | — | 2 | 1 | no | — |
| 422 | C22⋊C4 | — | 6 | 1 | no | — |
| 423 | C22⋊C4 | — | 6 | 1 | no | — |
| 424 | C22⋊C4 | — | 9 | 1 | no | — |
| 425 | C22⋊C4 | — | 12 | 1 | no | — |
| 426 | C22⋊C4 | — | 18 | 1 | no | — |
| 427 | C22⋊C4 | — | 18 | 1 | no | — |
| 428 | C22⋊C4 | — | 18 | 1 | no | — |
| 429 | C22⋊C4 | — | 18 | 1 | no | — |
| 430 | C22⋊C4 | — | 18 | 1 | no | — |
| 431 | C22⋊C4 | — | 18 | 1 | no | — |
| 432 | C22⋊C4 | — | 18 | 1 | no | — |
| 433 | C22⋊C4 | — | 36 | 1 | no | — |
| 434 | C22⋊C4 | #626 | 1 | 1 | yes | characteristic, complemented |
| 435 | C42 | — | 9 | 1 | no | — |
| 436 | C42 | — | 18 | 1 | no | — |
| 437 | C22×C3 | — | 2 | 1 | no | — |
| 438 | C22×C3 | — | 2 | 1 | no | — |
| 439 | C22×C3 | — | 2 | 1 | no | — |
| 440 | C22×C3 | — | 2 | 1 | no | — |
| 441 | C22×C3 | — | 2 | 1 | no | — |
| 442 | C22×C3 | — | 4 | 1 | no | — |
| 443 | C22×C3 | — | 4 | 1 | no | — |
| 444 | C22×C3 | — | 4 | 1 | no | — |
| 445 | C22×C3 | — | 4 | 1 | no | — |
| 446 | C22×C3 | — | 4 | 1 | no | — |
| 447 | C22×C3 | — | 4 | 1 | no | — |
| 448 | C22×C3 | — | 4 | 2 | no | — |
| 449 | C22×C3 | — | 4 | 2 | no | — |
| 450 | C22×C3 | — | 4 | 1 | no | — |
| 451 | C22×C3 | — | 4 | 1 | no | — |
| 452 | C22×C3 | — | 4 | 2 | no | — |
| 453 | C22×C3 | — | 4 | 2 | no | — |
| 454 | C22×C3 | — | 4 | 2 | no | — |
| 455 | C22×C3 | — | 4 | 1 | no | — |
| 456 | C22×C3 | — | 4 | 1 | no | — |
| 457 | C22×C3 | — | 4 | 2 | no | — |
| 458 | C22×C3 | — | 4 | 2 | no | — |
| 459 | C22×C3 | — | 4 | 1 | no | — |
| 460 | C22×C3 | — | 4 | 1 | no | — |
| 461 | C22×C3 | — | 8 | 2 | no | — |
| 462 | C22×C3 | — | 8 | 1 | no | — |
| 463 | C22×C3 | — | 8 | 1 | no | — |
| 464 | C22×C3 | — | 8 | 2 | no | — |
| 465 | C22×C3 | — | 12 | 1 | no | — |
| 466 | C22×C3 | — | 24 | 1 | no | — |
| 467 | C22×C3 | — | 24 | 1 | no | — |
| 468 | C22×C3 | #882 | 1 | 1 | yes | characteristic |
| 469 | C22×C3 | #937 | 1 | 1 | yes | characteristic |
| 470 | C2×D3 | — | 4 | 1 | no | — |
| 471 | C2×D3 | — | 8 | 1 | no | — |
| 472 | C2×D3 | — | 8 | 1 | no | — |
| 473 | C2×D3 | — | 12 | 2 | no | — |
| 474 | C2×D3 | — | 12 | 2 | no | — |
| 475 | C2×D3 | — | 12 | 1 | no | — |
| 476 | C2×D3 | — | 12 | 1 | no | — |
| 477 | C2×D3 | — | 12 | 1 | no | — |
| 478 | C2×D3 | — | 12 | 1 | no | — |
| 479 | C2×D3 | — | 12 | 2 | no | — |
| 480 | C2×D3 | — | 12 | 2 | no | — |
| 481 | C2×D3 | — | 12 | 2 | no | — |
| 482 | C2×D3 | — | 12 | 1 | no | — |
| 483 | C2×D3 | — | 12 | 1 | no | — |
| 484 | C2×D3 | — | 24 | 2 | no | — |
| 485 | C2×D3 | — | 24 | 2 | no | — |
| 486 | C2×D3 | — | 24 | 1 | no | — |
| 487 | C2×D3 | — | 24 | 1 | no | — |
| 488 | C3×C4 | — | 2 | 1 | no | — |
| 489 | C3×C4 | — | 2 | 1 | no | — |
| 490 | C3×C4 | — | 4 | 1 | no | — |
| 491 | C3×C4 | — | 4 | 2 | no | — |
| 492 | C3×C4 | — | 4 | 1 | no | — |
| 493 | C3×C4 | — | 4 | 1 | no | — |
| 494 | C3×C4 | — | 12 | 1 | no | — |
| 495 | C3×C4 | — | 24 | 1 | no | — |
| 496 | C3×C4 | — | 24 | 1 | no | — |
| 497 | Dic3 | — | 4 | 1 | no | — |
| 498 | Dic3 | — | 8 | 1 | no | — |
| 499 | Dic3 | — | 8 | 1 | no | — |
| 500 | Dic3 | — | 12 | 2 | no | — |
| 501 | Dic3 | — | 12 | 2 | no | — |
| 502 | Dic3 | — | 12 | 1 | no | — |
| 503 | Dic3 | — | 12 | 1 | no | — |
| 504 | Dic3 | — | 12 | 1 | no | — |
| 505 | Dic3 | — | 12 | 1 | no | — |
| 506 | Dic3 | — | 12 | 2 | no | — |
| 507 | Dic3 | — | 12 | 1 | no | — |
| 508 | Dic3 | — | 12 | 1 | no | — |
| 509 | C32 | #2199 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 510 | C23 | — | 2 | 1 | no | — |
| 511 | C23 | — | 4 | 1 | no | — |
| 512 | C23 | — | 6 | 1 | no | — |
| 513 | C23 | — | 6 | 1 | no | — |
| 514 | C23 | — | 8 | 1 | no | — |
| 515 | C23 | — | 18 | 1 | no | — |
| 516 | C23 | — | 36 | 1 | no | — |
| 517 | C23 | — | 72 | 1 | no | — |
| 518 | C23 | C2×#626 | 1 | 1 | yes | characteristic |
| 519 | C23 | #3811 | 1 | 1 | yes | characteristic |
| 520 | Q8 | — | 6 | 1 | no | — |
| 521 | Q8 | — | 36 | 1 | no | — |
| 522 | Q8 | — | 72 | 1 | no | — |
| 523 | D4 | — | 4 | 1 | no | — |
| 524 | D4 | — | 6 | 1 | no | — |
| 525 | D4 | — | 8 | 1 | no | — |
| 526 | D4 | — | 12 | 1 | no | — |
| 527 | D4 | — | 12 | 1 | no | — |
| 528 | D4 | — | 12 | 1 | no | — |
| 529 | D4 | — | 24 | 2 | no | — |
| 530 | D4 | — | 72 | 2 | no | — |
| 531 | D4 | — | 72 | 1 | no | — |
| 532 | D4 | — | 72 | 1 | no | — |
| 533 | D4 | — | 72 | 1 | no | — |
| 534 | C2×C4 | — | 2 | 1 | no | — |
| 535 | C2×C4 | — | 6 | 1 | no | — |
| 536 | C2×C4 | — | 6 | 1 | no | — |
| 537 | C2×C4 | — | 12 | 1 | no | — |
| 538 | C2×C4 | — | 12 | 1 | no | — |
| 539 | C2×C4 | — | 12 | 1 | no | — |
| 540 | C2×C4 | — | 18 | 1 | no | — |
| 541 | C2×C4 | — | 18 | 1 | no | — |
| 542 | C2×C4 | — | 18 | 1 | no | — |
| 543 | C2×C4 | #3811 | 1 | 1 | yes | characteristic |
| 544 | C8 | — | 12 | 1 | no | — |
| 545 | C2×C3 | — | 2 | 2 | no | — |
| 546 | C2×C3 | — | 2 | 1 | no | — |
| 547 | C2×C3 | — | 2 | 1 | no | — |
| 548 | C2×C3 | — | 2 | 1 | no | — |
| 549 | C2×C3 | — | 4 | 1 | no | — |
| 550 | C2×C3 | — | 4 | 1 | no | — |
| 551 | C2×C3 | — | 4 | 1 | no | — |
| 552 | C2×C3 | — | 4 | 1 | no | — |
| 553 | C2×C3 | — | 8 | 1 | no | — |
| 554 | C2×C3 | — | 8 | 1 | no | — |
| 555 | C2×C3 | — | 8 | 2 | no | — |
| 556 | C2×C3 | — | 8 | 1 | no | — |
| 557 | C2×C3 | — | 8 | 1 | no | — |
| 558 | C2×C3 | — | 24 | 1 | no | — |
| 559 | C2×C3 | #4741 | 1 | 1 | yes | characteristic |
| 560 | C2×C3 | #5032 | 1 | 1 | yes | characteristic |
| 561 | D3 | — | 8 | 1 | no | — |
| 562 | D3 | — | 24 | 2 | no | — |
| 563 | D3 | — | 24 | 1 | no | — |
| 564 | D3 | — | 24 | 1 | no | — |
| 565 | C22 | — | 2 | 1 | no | — |
| 566 | C22 | — | 2 | 1 | no | — |
| 567 | C22 | — | 4 | 1 | no | — |
| 568 | C22 | — | 4 | 1 | no | — |
| 569 | C22 | — | 4 | 1 | no | — |
| 570 | C22 | — | 4 | 1 | no | — |
| 571 | C22 | — | 4 | 2 | no | — |
| 572 | C22 | — | 4 | 1 | no | — |
| 573 | C22 | — | 8 | 1 | no | — |
| 574 | C22 | — | 12 | 1 | no | — |
| 575 | C22 | — | 24 | 1 | no | — |
| 576 | C22 | — | 24 | 1 | no | — |
| 577 | C22 | — | 36 | 1 | no | — |
| 578 | C22 | — | 36 | 1 | no | — |
| 579 | C22 | — | 36 | 2 | no | — |
| 580 | C22 | — | 36 | 1 | no | — |
| 581 | C22 | — | 72 | 1 | no | — |
| 582 | C22 | #63981 | 1 | 1 | yes | characteristic |
| 583 | C4 | — | 2 | 1 | no | — |
| 584 | C4 | — | 4 | 1 | no | — |
| 585 | C4 | — | 12 | 1 | no | — |
| 586 | C4 | — | 24 | 1 | no | — |
| 587 | C4 | — | 24 | 1 | no | — |
| 588 | C4 | — | 36 | 1 | no | — |
| 589 | C4 | — | 36 | 1 | no | — |
| 590 | C4 | — | 36 | 1 | no | — |
| 591 | C3 | — | 2 | 1 | no | — |
| 592 | C3 | #69131 | 1 | 1 | yes | characteristic, complemented |
| 593 | C3 | #70997 | 1 | 1 | yes | characteristic, complemented |
| 594 | C2 | — | 2 | 1 | no | — |
| 595 | C2 | — | 4 | 1 | no | — |
| 596 | C2 | — | 4 | 1 | no | — |
| 597 | C2 | — | 8 | 1 | no | — |
| 598 | C2 | — | 24 | 1 | no | — |
| 599 | C2 | — | 72 | 1 | no | — |
| 600 | C2 | #10591532 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10596065 | C2 | semidirect |
| 2. C3×#5032 | C2 | semidirect |
| 3. #10591531 | C2 | semidirect |
| 4. #10591513 | C2 | semidirect |
| 5. C3×#4536 | C2 | semidirect |
| 6. #10589181 | C2 | semidirect |
| 7. #10589174 | C2 | semidirect |
| 35. #5032 | D3 | semidirect |
| 39. #4536 | D3 | semidirect |
| 44. C24×C32 | D4 | semidirect |
| 45. C23×C3⋊D3 | D4 | semidirect |
| 52. C2×#634 | D4 | semidirect |
| 61. C32×C22⋊C4 | D4 | semidirect |
| 66. #3757 | D4 | semidirect |
| 71. C4×C3⋊Dic3 | D4 | semidirect |
| 170. C24×C3 | D12 | semidirect |
| 171. C24×C3 | #67 | semidirect |
| 218. C3×C22⋊C4 | D12 | semidirect |
| 219. C3×C22⋊C4 | #67 | semidirect |
| 403. C24 | #626 | semidirect |
| 434. C22⋊C4 | #626 | semidirect |
| 509. C32 | #2199 | semidirect |
| 592. C3 | #69131 | semidirect |
| 593. C3 | #70997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596065 | 2 |
| C3×#5032 | 2 |
| #10591531 | 2 |
| #10591513 | 2 |
| C3×#4536 | 2 |
| #10589181 | 2 |
| #10589174 | 2 |
| #70997 | 3 |
| #69131 | 3 |