Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1623 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 1623 conjugacy classes of subgroups — too many to draw. Only its 172 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 | #10596679 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10595239 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10594192 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #10592439 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#4741 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #10591530 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #10590407 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #10590406 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #80305 | — | 3 | 2 | no | maximal |
| 10 | C2×#3830 | C22 | 1 | 1 | yes | characteristic |
| 11 | C3×#1004 | C22 | 1 | 2 | yes | — |
| 12 | #64330 | — | 2 | 1 | no | — |
| 13 | #64330 | C22 | 1 | 2 | yes | — |
| 14 | C22×#625 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | C2×#3805 | — | 2 | 1 | no | — |
| 16 | C2×#3805 | C22 | 1 | 2 | yes | — |
| 17 | #64313 | — | 2 | 2 | no | — |
| 18 | D3×#237 | — | 2 | 4 | no | — |
| 19 | #64309 | — | 2 | 2 | no | — |
| 20 | #64306 | — | 2 | 1 | no | — |
| 21 | #64298 | — | 2 | 1 | no | — |
| 22 | #64086 | C22 | 1 | 2 | yes | complemented |
| 23 | C3×#937 | C22 | 1 | 2 | yes | complemented |
| 24 | C3×#882 | C22 | 1 | 4 | yes | complemented |
| 25 | #63980 | — | 2 | 1 | no | — |
| 26 | #63979 | — | 2 | 1 | no | — |
| 27 | #63977 | C22 | 1 | 2 | yes | complemented |
| 28 | #63976 | C22 | 1 | 4 | yes | complemented |
| 29 | #63957 | C22 | 1 | 1 | yes | characteristic, complemented |
| 30 | #63915 | — | 2 | 2 | no | — |
| 31 | #63914 | — | 2 | 2 | no | — |
| 32 | #63913 | — | 2 | 1 | no | — |
| 33 | #63912 | — | 2 | 1 | no | — |
| 34 | #63885 | — | 2 | 4 | no | — |
| 35 | C32×#99 | C22 | 1 | 1 | yes | characteristic, complemented |
| 36 | #63661 | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | #63633 | C22 | 1 | 2 | yes | complemented |
| 38 | C3×#806 | C22 | 1 | 4 | yes | complemented |
| 39 | #63580 | C22 | 1 | 4 | yes | complemented |
| 40 | #5966 | — | 3 | 2 | no | — |
| 41 | #5592 | — | 3 | 2 | no | — |
| 42 | #5592 | — | 3 | 4 | no | — |
| 43 | C3×B(4,𝔽2) | — | 3 | 2 | no | — |
| 44 | #5244 | — | 3 | 2 | no | — |
| 45 | #5032 | — | 3 | 2 | no | — |
| 46 | #5032 | — | 3 | 4 | no | — |
| 47 | #4741 | — | 3 | 4 | no | — |
| 48 | #4741 | D3 | 1 | 2 | yes | complemented |
| 49 | #4740 | — | 3 | 2 | no | — |
| 50 | #4740 | — | 3 | 4 | no | — |
| 51 | #4740 | — | 6 | 1 | no | — |
| 52 | C23×C3×D3 | C23 | 1 | 2 | yes | — |
| 53 | C2×C32×D4 | C23 | 1 | 1 | yes | characteristic |
| 54 | C2×#638 | D4 | 1 | 1 | yes | characteristic, complemented |
| 55 | C2×#638 | C23 | 1 | 1 | yes | characteristic |
| 56 | C22×C3⋊Dic3 | D4 | 1 | 1 | yes | characteristic, complemented |
| 57 | C22×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 58 | #3830 | — | 2 | 2 | no | — |
| 59 | #3830 | — | 2 | 2 | no | — |
| 60 | C2×C4×C3⋊D3 | D4 | 1 | 1 | yes | characteristic, complemented |
| 61 | C2×#634 | D4 | 1 | 1 | yes | characteristic, complemented |
| 62 | C2×C3×#67 | — | 2 | 2 | no | — |
| 63 | C2×C3×#67 | — | 2 | 2 | no | — |
| 64 | C2×C3×#67 | C23 | 1 | 4 | yes | — |
| 65 | C3×#237 | — | 2 | 4 | no | — |
| 66 | C3×D3×D4 | — | 2 | 4 | no | — |
| 67 | C3×#235 | — | 2 | 2 | no | — |
| 68 | C2×C3×D12 | — | 2 | 4 | no | — |
| 69 | #3811 | — | 2 | 2 | no | — |
| 70 | D3×#67 | — | 2 | 4 | no | — |
| 71 | D3×#67 | — | 2 | 4 | no | — |
| 72 | C2×#627 | — | 2 | 1 | no | — |
| 73 | C2×#627 | D4 | 1 | 2 | yes | complemented |
| 74 | C2×#626 | — | 2 | 2 | no | — |
| 75 | C2×#625 | — | 2 | 1 | no | — |
| 76 | C2×#625 | — | 2 | 2 | no | — |
| 77 | C2×#625 | — | 2 | 1 | no | — |
| 78 | C2×#625 | — | 2 | 1 | no | — |
| 79 | C2×#625 | — | 2 | 2 | no | — |
| 80 | C2×#625 | — | 2 | 4 | no | — |
| 81 | C2×#625 | D4 | 1 | 2 | yes | complemented |
| 82 | #3805 | — | 2 | 2 | no | — |
| 83 | #3805 | — | 2 | 2 | no | — |
| 84 | #3805 | — | 2 | 2 | no | — |
| 85 | #3805 | — | 2 | 2 | no | — |
| 86 | #3805 | — | 2 | 2 | no | — |
| 87 | #3805 | — | 2 | 2 | no | — |
| 88 | #3805 | — | 2 | 2 | no | — |
| 89 | #3804 | — | 2 | 4 | no | — |
| 90 | #3804 | — | 2 | 4 | no | — |
| 91 | C2×D3×Dic3 | — | 2 | 2 | no | — |
| 92 | C2×D3×Dic3 | D4 | 1 | 4 | yes | complemented |
| 93 | #3802 | — | 2 | 1 | no | — |
| 94 | C4×D32 | — | 2 | 2 | no | — |
| 95 | #3798 | — | 2 | 2 | no | — |
| 96 | #3797 | — | 2 | 1 | no | — |
| 97 | #3796 | — | 2 | 2 | no | — |
| 98 | #3795 | — | 2 | 4 | no | — |
| 99 | D3×Dic6 | — | 2 | 4 | no | — |
| 100 | C32×C22⋊C4 | C23 | 1 | 2 | yes | — |
| 101 | #3757 | C23 | 1 | 2 | yes | — |
| 102 | #3750 | — | 2 | 2 | no | — |
| 103 | C4×C3⋊Dic3 | — | 2 | 2 | no | — |
| 104 | C3×#217 | C23 | 1 | 2 | yes | — |
| 105 | C3×(C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 106 | C3×(C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 107 | #3724 | — | 2 | 1 | no | — |
| 108 | (C2×D3)⋊Dic3 | — | 2 | 2 | no | — |
| 109 | (C2×D3)⋊Dic3 | — | 2 | 4 | no | — |
| 110 | Dic32 | — | 2 | 1 | no | — |
| 111 | #3027 | — | 9 | 1 | no | Sylow |
| 112 | C3×H(5,𝔽2) | — | 3 | 2 | no | — |
| 113 | C22×#67 | — | 3 | 2 | no | — |
| 114 | #1010 | — | 6 | 2 | no | — |
| 115 | #1010 | — | 6 | 4 | no | — |
| 116 | D3×#41 | — | 6 | 2 | no | — |
| 117 | D3×#41 | — | 6 | 4 | no | — |
| 118 | #1004 | — | 3 | 4 | no | — |
| 119 | #1004 | — | 6 | 4 | no | — |
| 120 | #1004 | — | 6 | 2 | no | — |
| 121 | #1004 | C2×D3 | 1 | 2 | yes | — |
| 122 | C2×#237 | — | 3 | 2 | no | — |
| 123 | C2×#237 | — | 3 | 4 | no | — |
| 124 | C2×#237 | — | 6 | 1 | no | — |
| 125 | C2×#237 | — | 6 | 4 | no | — |
| 126 | C2×#237 | — | 6 | 2 | no | — |
| 127 | C3×#120 | — | 3 | 2 | no | — |
| 128 | C3×#120 | — | 3 | 4 | no | — |
| 129 | #953 | — | 3 | 4 | no | — |
| 130 | #953 | — | 3 | 2 | no | — |
| 131 | #940 | — | 6 | 4 | no | — |
| 132 | #940 | — | 6 | 2 | no | — |
| 133 | #939 | — | 6 | 4 | no | — |
| 134 | #939 | — | 6 | 2 | no | — |
| 135 | #937 | — | 3 | 4 | no | — |
| 136 | #937 | C2×D3 | 1 | 2 | yes | complemented |
| 137 | #885 | — | 6 | 2 | no | — |
| 138 | #885 | — | 6 | 4 | no | — |
| 139 | #884 | — | 6 | 2 | no | — |
| 140 | #884 | — | 6 | 4 | no | — |
| 141 | #882 | — | 3 | 2 | no | — |
| 142 | #882 | C2×D3 | 1 | 4 | yes | complemented |
| 143 | #877 | — | 3 | 4 | no | — |
| 144 | #877 | — | 3 | 2 | no | — |
| 145 | #877 | — | 6 | 2 | no | — |
| 146 | C3×#99 | — | 2 | 1 | no | — |
| 147 | C3×#99 | — | 3 | 4 | no | — |
| 148 | C3×#99 | C2×D3 | 1 | 2 | yes | complemented |
| 149 | #834 | — | 3 | 2 | no | — |
| 150 | #834 | — | 3 | 4 | no | — |
| 151 | #834 | — | 6 | 1 | no | — |
| 152 | #806 | — | 3 | 4 | no | — |
| 153 | #806 | — | 3 | 4 | no | — |
| 154 | #806 | — | 6 | 2 | no | — |
| 155 | #806 | C2×D3 | 1 | 4 | yes | complemented |
| 156 | C23×C32 | C2×D4 | 1 | 1 | yes | characteristic |
| 157 | C23×C32 | C24 | 1 | 1 | yes | characteristic |
| 158 | C22×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 159 | C22×C3×D3 | — | 2 | 2 | no | — |
| 160 | C22×C3×D3 | — | 2 | 4 | no | — |
| 161 | C22×C3×D3 | — | 2 | 2 | no | — |
| 162 | C22×C3×D3 | — | 8 | 2 | no | — |
| 163 | C22×C3×D3 | C2×D4 | 1 | 4 | yes | — |
| 164 | C2×D32 | — | 2 | 2 | no | — |
| 165 | C32×D4 | — | 2 | 2 | no | — |
| 166 | C2×C32×C4 | — | 2 | 2 | no | — |
| 167 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 168 | #638 | — | 2 | 2 | no | — |
| 169 | #638 | — | 2 | 2 | no | — |
| 170 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 171 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 172 | C2×C3⋊Dic3 | — | 2 | 2 | no | — |
| 173 | C2×C3⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 174 | C2×C3⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 175 | C2×C3⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 176 | C2×C3⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 177 | C2×C3⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 178 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 179 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 180 | #634 | — | 2 | 2 | no | — |
| 181 | C3×#67 | — | 2 | 4 | no | — |
| 182 | C3×#67 | — | 2 | 4 | no | — |
| 183 | C3×#67 | — | 2 | 4 | no | — |
| 184 | C3×#67 | — | 8 | 2 | no | — |
| 185 | C2×C3×Dic3 | — | 2 | 2 | no | — |
| 186 | C2×C3×Dic3 | — | 2 | 2 | no | — |
| 187 | C2×C3×Dic3 | C2×D4 | 1 | 4 | yes | — |
| 188 | C3×D12 | — | 2 | 2 | no | — |
| 189 | C3×D12 | — | 8 | 4 | no | — |
| 190 | C3×C4×D3 | — | 2 | 4 | no | — |
| 191 | C3×Dic6 | — | 2 | 2 | no | — |
| 192 | #627 | — | 2 | 2 | no | — |
| 193 | #627 | — | 2 | 2 | no | — |
| 194 | #627 | — | 2 | 2 | no | — |
| 195 | #626 | — | 2 | 4 | no | — |
| 196 | #626 | — | 8 | 2 | no | — |
| 197 | #625 | — | 2 | 2 | no | — |
| 198 | #625 | — | 2 | 2 | no | — |
| 199 | #625 | — | 2 | 2 | no | — |
| 200 | #625 | — | 4 | 1 | no | — |
| 201 | #625 | — | 4 | 2 | no | — |
| 202 | #625 | — | 4 | 1 | no | — |
| 203 | #625 | — | 8 | 4 | no | — |
| 204 | #624 | — | 2 | 2 | no | — |
| 205 | D3×Dic3 | — | 2 | 4 | no | — |
| 206 | D3×Dic3 | — | 2 | 4 | no | — |
| 207 | D3×Dic3 | — | 2 | 4 | no | — |
| 208 | #585 | — | 9 | 1 | no | — |
| 209 | #535 | — | 9 | 1 | no | — |
| 210 | #535 | — | 9 | 2 | no | — |
| 211 | B(4,𝔽2) | — | 3 | 2 | no | — |
| 212 | B(4,𝔽2) | — | 9 | 4 | no | — |
| 213 | B(4,𝔽2) | — | 9 | 2 | no | — |
| 214 | #410 | — | 9 | 2 | no | — |
| 215 | #410 | — | 9 | 1 | no | — |
| 216 | C24×C3 | — | 3 | 2 | no | — |
| 217 | C23×D3 | C22×D3 | 1 | 2 | yes | — |
| 218 | C3×#41 | — | 6 | 4 | no | — |
| 219 | C3×#41 | — | 6 | 2 | no | — |
| 220 | C2×C3×D4 | — | 2 | 1 | no | — |
| 221 | C2×C3×D4 | — | 3 | 4 | no | — |
| 222 | C2×C3×D4 | — | 6 | 4 | no | — |
| 223 | C2×C3×D4 | — | 6 | 4 | no | — |
| 224 | C2×C3×D4 | — | 6 | 2 | no | — |
| 225 | C2×C3×D4 | — | 6 | 2 | no | — |
| 226 | C2×C3×D4 | C22×D3 | 1 | 2 | yes | — |
| 227 | C2×#67 | — | 2 | 2 | no | — |
| 228 | C2×#67 | — | 2 | 2 | no | — |
| 229 | C2×#67 | — | 3 | 2 | no | — |
| 230 | C2×#67 | — | 3 | 2 | no | — |
| 231 | C2×#67 | — | 3 | 4 | no | — |
| 232 | C2×#67 | — | 6 | 1 | no | — |
| 233 | C2×#67 | — | 6 | 1 | no | — |
| 234 | C2×#67 | — | 6 | 2 | no | — |
| 235 | C2×#67 | — | 6 | 4 | no | — |
| 236 | C2×#67 | — | 6 | 2 | no | — |
| 237 | C2×#67 | — | 6 | 4 | no | — |
| 238 | C2×#67 | — | 6 | 2 | no | — |
| 239 | C2×#67 | — | 6 | 4 | no | — |
| 240 | C2×#67 | — | 6 | 4 | no | — |
| 241 | C2×#67 | — | 6 | 2 | no | — |
| 242 | C2×#67 | — | 6 | 4 | no | — |
| 243 | C2×#67 | — | 6 | 4 | no | — |
| 244 | C2×#67 | C22×D3 | 1 | 4 | yes | — |
| 245 | C22×Dic3 | — | 3 | 2 | no | — |
| 246 | C22×Dic3 | — | 3 | 2 | no | — |
| 247 | C22×Dic3 | — | 3 | 4 | no | — |
| 248 | C22×Dic3 | — | 6 | 1 | no | — |
| 249 | C22×Dic3 | — | 6 | 1 | no | — |
| 250 | C22×Dic3 | — | 6 | 2 | no | — |
| 251 | #239 | — | 6 | 2 | no | — |
| 252 | D3×Q8 | — | 6 | 2 | no | — |
| 253 | D3×Q8 | — | 6 | 4 | no | — |
| 254 | #237 | — | 2 | 4 | no | — |
| 255 | #237 | — | 6 | 2 | no | — |
| 256 | #237 | — | 6 | 4 | no | — |
| 257 | #237 | — | 6 | 4 | no | — |
| 258 | #237 | — | 6 | 4 | no | — |
| 259 | #237 | — | 6 | 4 | no | — |
| 260 | #237 | — | 6 | 4 | no | — |
| 261 | #237 | — | 6 | 4 | no | — |
| 262 | #237 | — | 6 | 4 | no | — |
| 263 | #237 | — | 6 | 4 | no | — |
| 264 | #237 | — | 6 | 4 | no | — |
| 265 | #237 | — | 6 | 4 | no | — |
| 266 | #237 | — | 6 | 4 | no | — |
| 267 | #237 | — | 6 | 4 | no | — |
| 268 | #237 | — | 12 | 2 | no | — |
| 269 | #237 | — | 12 | 2 | no | — |
| 270 | D3×D4 | — | 2 | 4 | no | — |
| 271 | D3×D4 | — | 6 | 2 | no | — |
| 272 | D3×D4 | — | 6 | 4 | no | — |
| 273 | D3×D4 | — | 6 | 4 | no | — |
| 274 | D3×D4 | — | 6 | 4 | no | — |
| 275 | #235 | — | 2 | 2 | no | — |
| 276 | #235 | — | 6 | 4 | no | — |
| 277 | #235 | — | 6 | 4 | no | — |
| 278 | #235 | — | 6 | 4 | no | — |
| 279 | #235 | — | 6 | 4 | no | — |
| 280 | C2×D12 | — | 2 | 4 | no | — |
| 281 | C2×D12 | — | 6 | 2 | no | — |
| 282 | C2×C4×D3 | — | 3 | 4 | no | — |
| 283 | C2×C4×D3 | — | 3 | 2 | no | — |
| 284 | C2×C4×D3 | — | 6 | 1 | no | — |
| 285 | C2×C4×D3 | — | 6 | 4 | no | — |
| 286 | C2×C4×D3 | — | 6 | 2 | no | — |
| 287 | C2×Dic6 | — | 3 | 2 | no | — |
| 288 | C2×Dic6 | — | 3 | 4 | no | — |
| 289 | C2×Dic6 | — | 6 | 1 | no | — |
| 290 | C2×Dic6 | — | 6 | 4 | no | — |
| 291 | C2×Dic6 | — | 6 | 2 | no | — |
| 292 | C3×C22⋊C4 | — | 2 | 2 | no | — |
| 293 | C3×C22⋊C4 | — | 3 | 2 | no | — |
| 294 | C3×C22⋊C4 | — | 6 | 4 | no | — |
| 295 | C3×C22⋊C4 | — | 6 | 2 | no | — |
| 296 | C3×C22⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 297 | #217 | — | 3 | 4 | no | — |
| 298 | #217 | — | 6 | 2 | no | — |
| 299 | #217 | — | 6 | 2 | no | — |
| 300 | #217 | — | 6 | 4 | no | — |
| 301 | #217 | C22×D3 | 1 | 2 | yes | — |
| 302 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 303 | (C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 304 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 305 | (C2×D3)⋊C4 | — | 6 | 4 | no | — |
| 306 | Dic3⋊C4 | — | 6 | 2 | no | — |
| 307 | Dic3⋊C4 | — | 6 | 4 | no | — |
| 308 | Dic3⋊C4 | — | 12 | 2 | no | — |
| 309 | C4×Dic3 | — | 6 | 2 | no | — |
| 310 | C4×Dic3 | — | 6 | 4 | no | — |
| 311 | C4×Dic3 | — | 12 | 2 | no | — |
| 312 | C22×C32 | — | 2 | 1 | no | — |
| 313 | C22×C32 | — | 4 | 1 | no | — |
| 314 | C22×C32 | — | 4 | 1 | no | — |
| 315 | C22×C32 | C22×D4 | 1 | 1 | yes | characteristic |
| 316 | C22×C32 | C22×D4 | 1 | 2 | yes | — |
| 317 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 318 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 319 | C2×C3×D3 | — | 2 | 4 | no | — |
| 320 | C2×C3×D3 | — | 4 | 4 | no | — |
| 321 | C2×C3×D3 | — | 4 | 4 | no | — |
| 322 | C2×C3×D3 | — | 4 | 2 | no | — |
| 323 | C2×C3×D3 | — | 4 | 4 | no | — |
| 324 | C2×C3×D3 | — | 4 | 2 | no | — |
| 325 | C2×C3×D3 | — | 4 | 2 | no | — |
| 326 | C2×C3×D3 | — | 8 | 2 | no | — |
| 327 | D32 | — | 8 | 2 | no | — |
| 328 | C32×C4 | — | 2 | 1 | no | — |
| 329 | C32×C4 | — | 4 | 2 | no | — |
| 330 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 331 | C3⋊Dic3 | — | 4 | 2 | no | — |
| 332 | C3⋊Dic3 | #120 | 1 | 1 | yes | characteristic |
| 333 | C3⋊Dic3 | #120 | 1 | 2 | yes | — |
| 334 | C3⋊Dic3 | #120 | 1 | 1 | yes | characteristic |
| 335 | C3×Dic3 | — | 2 | 4 | no | — |
| 336 | C3×Dic3 | — | 4 | 2 | no | — |
| 337 | 2−1+4 | — | 18 | 2 | no | — |
| 338 | 2−1+4 | — | 18 | 1 | no | — |
| 339 | H(5,𝔽2) | — | 3 | 2 | no | — |
| 340 | H(5,𝔽2) | — | 9 | 2 | no | — |
| 341 | H(5,𝔽2) | — | 18 | 2 | no | — |
| 342 | H(5,𝔽2) | — | 18 | 1 | no | — |
| 343 | C2×#41 | — | 9 | 2 | no | — |
| 344 | C2×#41 | — | 9 | 1 | no | — |
| 345 | C2×#41 | — | 18 | 1 | no | — |
| 346 | C2×#41 | — | 18 | 4 | no | — |
| 347 | C2×#41 | — | 18 | 1 | no | — |
| 348 | C22×D4 | — | 9 | 1 | no | — |
| 349 | #127 | — | 18 | 2 | no | — |
| 350 | #127 | — | 18 | 1 | no | — |
| 351 | #124 | — | 18 | 2 | no | — |
| 352 | #124 | — | 18 | 1 | no | — |
| 353 | #121 | — | 18 | 1 | no | — |
| 354 | #121 | — | 18 | 4 | no | — |
| 355 | #121 | — | 18 | 1 | no | — |
| 356 | #120 | — | 3 | 2 | no | — |
| 357 | #120 | — | 3 | 4 | no | — |
| 358 | #120 | — | 9 | 2 | no | — |
| 359 | #120 | — | 9 | 4 | no | — |
| 360 | #117 | — | 9 | 1 | no | — |
| 361 | #117 | — | 9 | 2 | no | — |
| 362 | #99 | — | 3 | 4 | no | — |
| 363 | #99 | — | 9 | 4 | no | — |
| 364 | #99 | — | 9 | 1 | no | — |
| 365 | #99 | — | 9 | 2 | no | — |
| 366 | #99 | D32 | 1 | 1 | yes | characteristic, complemented |
| 367 | C23×C3 | — | 2 | 1 | no | — |
| 368 | C23×C3 | — | 2 | 1 | no | — |
| 369 | C23×C3 | — | 3 | 4 | no | — |
| 370 | C23×C3 | — | 6 | 2 | no | — |
| 371 | C23×C3 | — | 6 | 2 | no | — |
| 372 | C23×C3 | — | 6 | 4 | no | — |
| 373 | C23×C3 | — | 24 | 2 | no | — |
| 374 | C23×C3 | D3×D4 | 1 | 2 | yes | — |
| 375 | C23×C3 | C23×D3 | 1 | 2 | yes | — |
| 376 | C22×D3 | — | 2 | 2 | no | — |
| 377 | C22×D3 | — | 2 | 4 | no | — |
| 378 | C22×D3 | — | 2 | 2 | no | — |
| 379 | C22×D3 | — | 3 | 2 | no | — |
| 380 | C22×D3 | — | 6 | 1 | no | — |
| 381 | C22×D3 | — | 6 | 4 | no | — |
| 382 | C22×D3 | — | 8 | 2 | no | — |
| 383 | C22×D3 | D3×D4 | 1 | 4 | yes | — |
| 384 | C3×Q8 | — | 6 | 2 | no | — |
| 385 | C3×D4 | — | 2 | 4 | no | — |
| 386 | C3×D4 | — | 4 | 2 | no | — |
| 387 | C3×D4 | — | 6 | 2 | no | — |
| 388 | C3×D4 | — | 6 | 4 | no | — |
| 389 | C3×D4 | — | 6 | 4 | no | — |
| 390 | C3×D4 | — | 6 | 4 | no | — |
| 391 | C3×D4 | — | 24 | 4 | no | — |
| 392 | C3×D4 | — | 24 | 2 | no | — |
| 393 | C2×C3×C4 | — | 2 | 4 | no | — |
| 394 | C2×C3×C4 | — | 2 | 1 | no | — |
| 395 | C2×C3×C4 | — | 3 | 4 | no | — |
| 396 | C2×C3×C4 | — | 4 | 2 | no | — |
| 397 | C2×C3×C4 | — | 6 | 4 | no | — |
| 398 | C2×C3×C4 | — | 6 | 2 | no | — |
| 399 | C2×C3×C4 | — | 6 | 2 | no | — |
| 400 | C2×C3×C4 | D3×D4 | 1 | 2 | yes | — |
| 401 | #67 | — | 2 | 4 | no | — |
| 402 | #67 | — | 2 | 4 | no | — |
| 403 | #67 | — | 2 | 4 | no | — |
| 404 | #67 | — | 6 | 4 | no | — |
| 405 | #67 | — | 6 | 4 | no | — |
| 406 | #67 | — | 6 | 4 | no | — |
| 407 | #67 | — | 6 | 4 | no | — |
| 408 | #67 | — | 6 | 4 | no | — |
| 409 | #67 | — | 6 | 4 | no | — |
| 410 | #67 | — | 8 | 2 | no | — |
| 411 | #67 | — | 12 | 2 | no | — |
| 412 | #67 | — | 12 | 2 | no | — |
| 413 | #67 | — | 12 | 2 | no | — |
| 414 | #67 | — | 12 | 4 | no | — |
| 415 | #67 | — | 12 | 2 | no | — |
| 416 | #67 | — | 24 | 2 | no | — |
| 417 | #67 | — | 24 | 4 | no | — |
| 418 | #67 | — | 24 | 4 | no | — |
| 419 | C2×Dic3 | — | 2 | 2 | no | — |
| 420 | C2×Dic3 | — | 2 | 2 | no | — |
| 421 | C2×Dic3 | — | 3 | 2 | no | — |
| 422 | C2×Dic3 | — | 3 | 4 | no | — |
| 423 | C2×Dic3 | — | 3 | 2 | no | — |
| 424 | C2×Dic3 | — | 3 | 4 | no | — |
| 425 | C2×Dic3 | — | 3 | 2 | no | — |
| 426 | C2×Dic3 | — | 6 | 2 | no | — |
| 427 | C2×Dic3 | — | 6 | 2 | no | — |
| 428 | C2×Dic3 | — | 6 | 1 | no | — |
| 429 | C2×Dic3 | — | 6 | 1 | no | — |
| 430 | C2×Dic3 | — | 6 | 1 | no | — |
| 431 | C2×Dic3 | — | 6 | 4 | no | — |
| 432 | C2×Dic3 | — | 6 | 4 | no | — |
| 433 | C2×Dic3 | — | 6 | 4 | no | — |
| 434 | C2×Dic3 | — | 6 | 2 | no | — |
| 435 | C2×Dic3 | — | 6 | 2 | no | — |
| 436 | C2×Dic3 | — | 6 | 4 | no | — |
| 437 | C2×Dic3 | — | 12 | 1 | no | — |
| 438 | C2×Dic3 | — | 12 | 1 | no | — |
| 439 | C2×Dic3 | — | 12 | 2 | no | — |
| 440 | C2×Dic3 | D3×D4 | 1 | 4 | yes | — |
| 441 | D12 | — | 2 | 2 | no | — |
| 442 | D12 | — | 6 | 4 | no | — |
| 443 | D12 | — | 8 | 4 | no | — |
| 444 | D12 | — | 24 | 2 | no | — |
| 445 | C4×D3 | — | 2 | 4 | no | — |
| 446 | C4×D3 | — | 6 | 4 | no | — |
| 447 | C4×D3 | — | 6 | 2 | no | — |
| 448 | C4×D3 | — | 6 | 2 | no | — |
| 449 | C4×D3 | — | 6 | 4 | no | — |
| 450 | C4×D3 | — | 6 | 4 | no | — |
| 451 | C4×D3 | — | 6 | 4 | no | — |
| 452 | C4×D3 | — | 12 | 1 | no | — |
| 453 | C4×D3 | — | 12 | 1 | no | — |
| 454 | Dic6 | — | 2 | 2 | no | — |
| 455 | Dic6 | — | 6 | 4 | no | — |
| 456 | Dic6 | — | 6 | 4 | no | — |
| 457 | Dic6 | — | 6 | 4 | no | — |
| 458 | Dic6 | — | 6 | 4 | no | — |
| 459 | Dic6 | — | 12 | 2 | no | — |
| 460 | C2×C32 | — | 2 | 1 | no | — |
| 461 | C2×C32 | — | 2 | 2 | no | — |
| 462 | C2×C32 | — | 4 | 1 | no | — |
| 463 | C2×C32 | C2×#120 | 1 | 1 | yes | characteristic |
| 464 | C3⋊D3 | — | 4 | 1 | no | — |
| 465 | C3×D3 | — | 4 | 4 | no | — |
| 466 | C3×D3 | — | 8 | 2 | no | — |
| 467 | C24 | — | 3 | 2 | no | — |
| 468 | #41 | — | 6 | 4 | no | — |
| 469 | #41 | — | 6 | 2 | no | — |
| 470 | #41 | — | 18 | 4 | no | — |
| 471 | #41 | — | 18 | 2 | no | — |
| 472 | #41 | — | 18 | 4 | no | — |
| 473 | #41 | — | 18 | 4 | no | — |
| 474 | #41 | — | 18 | 2 | no | — |
| 475 | #41 | — | 18 | 2 | no | — |
| 476 | #41 | — | 18 | 2 | no | — |
| 477 | #41 | — | 18 | 2 | no | — |
| 478 | #41 | — | 18 | 2 | no | — |
| 479 | #41 | — | 18 | 2 | no | — |
| 480 | #41 | — | 18 | 2 | no | — |
| 481 | #41 | — | 18 | 2 | no | — |
| 482 | #41 | — | 18 | 2 | no | — |
| 483 | #41 | — | 18 | 2 | no | — |
| 484 | C2×Q8 | — | 9 | 2 | no | — |
| 485 | C2×Q8 | — | 9 | 1 | no | — |
| 486 | C2×Q8 | — | 18 | 1 | no | — |
| 487 | C2×Q8 | — | 18 | 4 | no | — |
| 488 | C2×Q8 | — | 18 | 1 | no | — |
| 489 | C2×D4 | — | 3 | 4 | no | — |
| 490 | C2×D4 | — | 6 | 4 | no | — |
| 491 | C2×D4 | — | 6 | 4 | no | — |
| 492 | C2×D4 | — | 6 | 2 | no | — |
| 493 | C2×D4 | — | 6 | 2 | no | — |
| 494 | C2×D4 | — | 9 | 2 | no | — |
| 495 | C2×D4 | — | 9 | 1 | no | — |
| 496 | C2×D4 | — | 9 | 1 | no | — |
| 497 | C2×D4 | — | 18 | 2 | no | — |
| 498 | C2×D4 | — | 18 | 1 | no | — |
| 499 | C2×D4 | — | 18 | 2 | no | — |
| 500 | C2×D4 | — | 18 | 1 | no | — |
| 501 | C2×D4 | — | 18 | 2 | no | — |
| 502 | C2×D4 | — | 18 | 2 | no | — |
| 503 | C2×D4 | — | 18 | 1 | no | — |
| 504 | C2×D4 | — | 18 | 4 | no | — |
| 505 | C2×D4 | — | 18 | 4 | no | — |
| 506 | C2×D4 | — | 18 | 1 | no | — |
| 507 | C2×D4 | — | 18 | 4 | no | — |
| 508 | C2×D4 | C2×D32 | 1 | 1 | yes | characteristic |
| 509 | C22×C4 | — | 9 | 4 | no | — |
| 510 | C22×C4 | — | 9 | 1 | no | — |
| 511 | C22×C4 | — | 9 | 1 | no | — |
| 512 | C22×C4 | — | 9 | 1 | no | — |
| 513 | C22×C4 | — | 18 | 2 | no | — |
| 514 | C22×C4 | — | 18 | 2 | no | — |
| 515 | C4⋊C4 | — | 18 | 2 | no | — |
| 516 | C4⋊C4 | — | 18 | 1 | no | — |
| 517 | C22⋊C4 | — | 3 | 2 | no | — |
| 518 | C22⋊C4 | — | 6 | 4 | no | — |
| 519 | C22⋊C4 | — | 6 | 2 | no | — |
| 520 | C22⋊C4 | — | 9 | 2 | no | — |
| 521 | C22⋊C4 | — | 18 | 4 | no | — |
| 522 | C22⋊C4 | — | 18 | 2 | no | — |
| 523 | C22⋊C4 | C2×D32 | 1 | 2 | yes | — |
| 524 | C42 | — | 18 | 2 | no | — |
| 525 | C42 | — | 18 | 1 | no | — |
| 526 | C22×C3 | — | 2 | 2 | no | — |
| 527 | C22×C3 | — | 2 | 1 | no | — |
| 528 | C22×C3 | — | 2 | 2 | no | — |
| 529 | C22×C3 | — | 4 | 1 | no | — |
| 530 | C22×C3 | — | 4 | 2 | no | — |
| 531 | C22×C3 | — | 4 | 2 | no | — |
| 532 | C22×C3 | — | 6 | 4 | no | — |
| 533 | C22×C3 | — | 8 | 1 | no | — |
| 534 | C22×C3 | — | 8 | 1 | no | — |
| 535 | C22×C3 | — | 12 | 4 | no | — |
| 536 | C22×C3 | — | 12 | 2 | no | — |
| 537 | C22×C3 | — | 12 | 4 | no | — |
| 538 | C22×C3 | — | 12 | 2 | no | — |
| 539 | C22×C3 | — | 12 | 4 | no | — |
| 540 | C22×C3 | — | 12 | 2 | no | — |
| 541 | C22×C3 | — | 24 | 2 | no | — |
| 542 | C22×C3 | C2×D3×D4 | 1 | 2 | yes | — |
| 543 | C22×C3 | C2×D3×D4 | 1 | 4 | yes | — |
| 544 | C2×D3 | — | 2 | 4 | no | — |
| 545 | C2×D3 | — | 4 | 4 | no | — |
| 546 | C2×D3 | — | 4 | 4 | no | — |
| 547 | C2×D3 | — | 4 | 2 | no | — |
| 548 | C2×D3 | — | 4 | 2 | no | — |
| 549 | C2×D3 | — | 4 | 4 | no | — |
| 550 | C2×D3 | — | 4 | 2 | no | — |
| 551 | C2×D3 | — | 6 | 2 | no | — |
| 552 | C2×D3 | — | 8 | 2 | no | — |
| 553 | C2×D3 | — | 12 | 1 | no | — |
| 554 | C2×D3 | — | 12 | 2 | no | — |
| 555 | C2×D3 | — | 24 | 1 | no | — |
| 556 | C2×D3 | — | 24 | 4 | no | — |
| 557 | C3×C4 | — | 2 | 2 | no | — |
| 558 | C3×C4 | — | 4 | 1 | no | — |
| 559 | C3×C4 | — | 4 | 4 | no | — |
| 560 | C3×C4 | — | 6 | 4 | no | — |
| 561 | C3×C4 | — | 8 | 2 | no | — |
| 562 | C3×C4 | — | 12 | 2 | no | — |
| 563 | Dic3 | — | 2 | 4 | no | — |
| 564 | Dic3 | — | 3 | 2 | no | — |
| 565 | Dic3 | — | 3 | 4 | no | — |
| 566 | Dic3 | — | 3 | 2 | no | — |
| 567 | Dic3 | — | 4 | 2 | no | — |
| 568 | Dic3 | — | 6 | 2 | no | — |
| 569 | Dic3 | — | 6 | 1 | no | — |
| 570 | Dic3 | — | 6 | 1 | no | — |
| 571 | Dic3 | — | 6 | 2 | no | — |
| 572 | Dic3 | — | 12 | 1 | no | — |
| 573 | Dic3 | — | 12 | 4 | no | — |
| 574 | Dic3 | — | 24 | 2 | no | — |
| 575 | C32 | #3027 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 576 | C23 | — | 3 | 4 | no | — |
| 577 | C23 | — | 6 | 2 | no | — |
| 578 | C23 | — | 6 | 2 | no | — |
| 579 | C23 | — | 6 | 4 | no | — |
| 580 | C23 | — | 9 | 1 | no | — |
| 581 | C23 | — | 18 | 2 | no | — |
| 582 | C23 | — | 24 | 2 | no | — |
| 583 | C23 | #3802 | 1 | 1 | yes | characteristic |
| 584 | C23 | C22×D32 | 1 | 1 | yes | characteristic |
| 585 | Q8 | — | 6 | 2 | no | — |
| 586 | Q8 | — | 18 | 2 | no | — |
| 587 | Q8 | — | 18 | 2 | no | — |
| 588 | Q8 | — | 18 | 2 | no | — |
| 589 | Q8 | — | 18 | 2 | no | — |
| 590 | D4 | — | 2 | 2 | no | — |
| 591 | D4 | — | 6 | 2 | no | — |
| 592 | D4 | — | 6 | 4 | no | — |
| 593 | D4 | — | 6 | 4 | no | — |
| 594 | D4 | — | 6 | 4 | no | — |
| 595 | D4 | — | 18 | 4 | no | — |
| 596 | D4 | — | 18 | 2 | no | — |
| 597 | D4 | — | 18 | 2 | no | — |
| 598 | D4 | — | 18 | 2 | no | — |
| 599 | D4 | — | 18 | 2 | no | — |
| 600 | D4 | — | 18 | 2 | no | — |
| 601 | D4 | — | 24 | 4 | no | — |
| 602 | D4 | — | 24 | 2 | no | — |
| 603 | D4 | — | 36 | 1 | no | — |
| 604 | D4 | — | 36 | 2 | no | — |
| 605 | D4 | — | 36 | 1 | no | — |
| 606 | D4 | — | 72 | 2 | no | — |
| 607 | D4 | — | 72 | 4 | no | — |
| 608 | C2×C4 | — | 2 | 2 | no | — |
| 609 | C2×C4 | — | 3 | 4 | no | — |
| 610 | C2×C4 | — | 6 | 4 | no | — |
| 611 | C2×C4 | — | 6 | 2 | no | — |
| 612 | C2×C4 | — | 6 | 2 | no | — |
| 613 | C2×C4 | — | 9 | 1 | no | — |
| 614 | C2×C4 | — | 9 | 1 | no | — |
| 615 | C2×C4 | — | 9 | 2 | no | — |
| 616 | C2×C4 | — | 9 | 2 | no | — |
| 617 | C2×C4 | — | 9 | 1 | no | — |
| 618 | C2×C4 | — | 18 | 1 | no | — |
| 619 | C2×C4 | — | 18 | 1 | no | — |
| 620 | C2×C4 | — | 18 | 2 | no | — |
| 621 | C2×C4 | — | 18 | 4 | no | — |
| 622 | C2×C4 | — | 18 | 4 | no | — |
| 623 | C2×C4 | — | 18 | 4 | no | — |
| 624 | C2×C4 | — | 18 | 1 | no | — |
| 625 | C2×C4 | — | 18 | 1 | no | — |
| 626 | C2×C4 | — | 18 | 2 | no | — |
| 627 | C2×C4 | #3802 | 1 | 1 | yes | characteristic |
| 628 | C2×C3 | — | 2 | 2 | no | — |
| 629 | C2×C3 | — | 2 | 4 | no | — |
| 630 | C2×C3 | — | 2 | 1 | no | — |
| 631 | C2×C3 | — | 4 | 2 | no | — |
| 632 | C2×C3 | — | 4 | 1 | no | — |
| 633 | C2×C3 | — | 4 | 2 | no | — |
| 634 | C2×C3 | — | 8 | 1 | no | — |
| 635 | C2×C3 | — | 12 | 4 | no | — |
| 636 | C2×C3 | — | 24 | 2 | no | — |
| 637 | C2×C3 | D3×#120 | 1 | 2 | yes | — |
| 638 | D3 | — | 4 | 4 | no | — |
| 639 | D3 | — | 8 | 2 | no | — |
| 640 | D3 | — | 12 | 2 | no | — |
| 641 | D3 | — | 24 | 1 | no | — |
| 642 | C22 | — | 2 | 1 | no | — |
| 643 | C22 | — | 4 | 1 | no | — |
| 644 | C22 | — | 4 | 1 | no | — |
| 645 | C22 | — | 6 | 4 | no | — |
| 646 | C22 | — | 12 | 4 | no | — |
| 647 | C22 | — | 12 | 4 | no | — |
| 648 | C22 | — | 12 | 2 | no | — |
| 649 | C22 | — | 12 | 4 | no | — |
| 650 | C22 | — | 12 | 2 | no | — |
| 651 | C22 | — | 12 | 2 | no | — |
| 652 | C22 | — | 18 | 1 | no | — |
| 653 | C22 | — | 24 | 2 | no | — |
| 654 | C22 | — | 36 | 1 | no | — |
| 655 | C22 | — | 72 | 2 | no | — |
| 656 | C22 | C2×#3802 | 1 | 1 | yes | characteristic |
| 657 | C22 | D32×D4 | 1 | 2 | yes | — |
| 658 | C4 | — | 2 | 1 | no | — |
| 659 | C4 | — | 4 | 2 | no | — |
| 660 | C4 | — | 6 | 4 | no | — |
| 661 | C4 | — | 9 | 1 | no | — |
| 662 | C4 | — | 9 | 2 | no | — |
| 663 | C4 | — | 9 | 1 | no | — |
| 664 | C4 | — | 12 | 2 | no | — |
| 665 | C4 | — | 18 | 1 | no | — |
| 666 | C4 | — | 36 | 2 | no | — |
| 667 | C3 | — | 2 | 1 | no | — |
| 668 | C3 | #80305 | 1 | 2 | yes | complemented |
| 669 | C2 | — | 2 | 2 | no | — |
| 670 | C2 | — | 2 | 1 | no | — |
| 671 | C2 | — | 4 | 1 | no | — |
| 672 | C2 | — | 12 | 4 | no | — |
| 673 | C2 | — | 24 | 2 | no | — |
| 674 | C2 | — | 36 | 1 | no | — |
| 675 | C2 | #10594258 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #10594258 |
| commutator, cosocle | C23×C32 | C24 |
| Frattini | C23 | C22×D32 |
| Fitting | C32×#99 | C22 |
| socle | C2×C32 | C2×#120 |
| hypercenter | #99 | D32 |
| hypocenter | C32 | #3027 |
| LCS | G ▷ C23×C32 ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C2 ◁ C23 ◁ #99 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10596679 | C2 | semidirect |
| 2. #10595239 | C2 | semidirect |
| 3. #10594192 | C2 | semidirect |
| 4. #10592439 | C2 | semidirect |
| 5. C3×#4741 | C2 | semidirect |
| 6. #10591530 | C2 | semidirect |
| 7. #10590407 | C2 | semidirect |
| 8. #10590406 | C2 | semidirect |
| 14. C22×#625 | C22 | semidirect |
| 22. #64086 | C22 | semidirect |
| 23. C3×#937 | C22 | semidirect |
| 24. C3×#882 | C22 | semidirect |
| 27. #63977 | C22 | semidirect |
| 28. #63976 | C22 | semidirect |
| 29. #63957 | C22 | semidirect |
| 35. C32×#99 | C22 | semidirect |
| 36. #63661 | C22 | semidirect |
| 37. #63633 | C22 | semidirect |
| 38. C3×#806 | C22 | semidirect |
| 39. #63580 | C22 | semidirect |
| 48. #4741 | D3 | semidirect |
| 54. C2×#638 | D4 | semidirect |
| 56. C22×C3⋊Dic3 | D4 | semidirect |
| 60. C2×C4×C3⋊D3 | D4 | semidirect |
| 61. C2×#634 | D4 | semidirect |
| 73. C2×#627 | D4 | semidirect |
| 81. C2×#625 | D4 | semidirect |
| 92. C2×D3×Dic3 | D4 | semidirect |
| 136. #937 | C2×D3 | semidirect |
| 142. #882 | C2×D3 | semidirect |
| 148. C3×#99 | C2×D3 | semidirect |
| 155. #806 | C2×D3 | semidirect |
| 366. #99 | D32 | semidirect |
| 575. C32 | #3027 | semidirect |
| 668. C3 | #80305 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596679 | 2 |
| #10595239 | 2 |
| #10594192 | 2 |
| #10592439 | 2 |
| C3×#4741 | 2 |
| #10591530 | 2 |
| #10590407 | 2 |
| #10590406 | 2 |
| #80305 | 3 |