Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1402 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 1402 conjugacy classes of subgroups — too many to draw. Only its 117 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 | #10596675 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10596512 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10596501 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#63926 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10593814 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10593458 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #10593457 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #10593317 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #10593308 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C2×D4×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 11 | C3×#1004 | — | 2 | 1 | no | — |
| 12 | #64330 | — | 2 | 2 | no | — |
| 13 | C2×#3811 | — | 2 | 2 | no | — |
| 14 | #64314 | — | 2 | 2 | no | — |
| 15 | #64314 | — | 2 | 2 | no | — |
| 16 | #64312 | — | 2 | 1 | no | — |
| 17 | #64312 | C22 | 1 | 2 | yes | complemented |
| 18 | D32×D4 | — | 2 | 1 | no | — |
| 19 | D32×D4 | C22 | 1 | 2 | yes | complemented |
| 20 | #64308 | — | 2 | 1 | no | — |
| 21 | #64306 | C22 | 1 | 1 | yes | characteristic |
| 22 | #64306 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#3802 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | #64286 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | #64283 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | #64241 | — | 2 | 2 | no | — |
| 27 | #64236 | — | 2 | 2 | no | — |
| 28 | #64231 | — | 2 | 1 | no | — |
| 29 | #64230 | C22 | 1 | 4 | yes | complemented |
| 30 | #64227 | C22 | 1 | 2 | yes | complemented |
| 31 | #64225 | C22 | 1 | 2 | yes | complemented |
| 32 | #64224 | — | 2 | 2 | no | — |
| 33 | #64221 | — | 2 | 1 | no | — |
| 34 | C2×C3×#213 | — | 2 | 1 | no | — |
| 35 | #63926 | — | 2 | 2 | no | — |
| 36 | #63926 | C22 | 1 | 4 | yes | complemented |
| 37 | C2×#3714 | — | 2 | 1 | no | — |
| 38 | C2×#3710 | C22 | 1 | 1 | yes | characteristic, complemented |
| 39 | #63782 | C22 | 1 | 4 | yes | complemented |
| 40 | #63730 | C22 | 1 | 2 | yes | complemented |
| 41 | #63729 | C22 | 1 | 2 | yes | complemented |
| 42 | D32⋊C8 | C22 | 1 | 4 | yes | complemented |
| 43 | D3×H(5,𝔽2) | — | 6 | 1 | no | — |
| 44 | C2×D3×D8 | — | 6 | 1 | no | — |
| 45 | C23×C3⋊D3 | — | 2 | 1 | no | — |
| 46 | C22×D32 | — | 2 | 2 | no | — |
| 47 | C22×D32 | — | 2 | 1 | no | — |
| 48 | C2×GO+(4,𝔽2) | — | 2 | 4 | no | — |
| 49 | C2×C32×D4 | D4 | 1 | 1 | yes | characteristic, complemented |
| 50 | C2×#638 | — | 2 | 1 | no | — |
| 51 | D4×C3⋊D3 | — | 2 | 1 | no | — |
| 52 | D4×C3⋊D3 | — | 2 | 1 | no | — |
| 53 | D4×C3⋊D3 | D4 | 1 | 2 | yes | complemented |
| 54 | D4×C3⋊D3 | C23 | 1 | 2 | yes | — |
| 55 | C2×C4⋊(C3⋊D3) | D4 | 1 | 1 | yes | characteristic, complemented |
| 56 | C2×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 57 | C2×C3×#67 | — | 2 | 4 | no | — |
| 58 | C3×#237 | — | 2 | 2 | no | — |
| 59 | C3×#237 | — | 2 | 2 | no | — |
| 60 | C3×D3×D4 | — | 2 | 2 | no | — |
| 61 | C3×D3×D4 | — | 2 | 2 | no | — |
| 62 | C3×#235 | — | 2 | 1 | no | — |
| 63 | C3×#235 | — | 2 | 1 | no | — |
| 64 | C2×C3×D12 | — | 2 | 1 | no | — |
| 65 | #3811 | — | 2 | 4 | no | — |
| 66 | #3811 | — | 2 | 4 | no | — |
| 67 | #3811 | — | 2 | 1 | no | — |
| 68 | #3811 | — | 2 | 2 | no | — |
| 69 | #3811 | — | 2 | 2 | no | — |
| 70 | #3811 | D4 | 1 | 2 | yes | — |
| 71 | D3×#67 | — | 2 | 4 | no | — |
| 72 | D3×#67 | — | 2 | 4 | no | — |
| 73 | C2×#626 | — | 2 | 4 | no | — |
| 74 | C2×#625 | — | 2 | 1 | no | — |
| 75 | C2×#624 | — | 2 | 2 | no | — |
| 76 | #3805 | — | 2 | 1 | no | — |
| 77 | #3805 | D4 | 1 | 2 | yes | complemented |
| 78 | #3804 | — | 2 | 4 | no | — |
| 79 | #3804 | — | 2 | 4 | no | — |
| 80 | #3802 | — | 2 | 1 | no | — |
| 81 | #3802 | — | 2 | 1 | no | — |
| 82 | #3802 | — | 2 | 1 | no | — |
| 83 | #3802 | D4 | 1 | 1 | yes | characteristic |
| 84 | #3802 | C23 | 1 | 2 | yes | — |
| 85 | #3802 | C23 | 1 | 1 | yes | characteristic |
| 86 | D3×D12 | — | 2 | 2 | no | — |
| 87 | D3×D12 | — | 2 | 2 | no | — |
| 88 | C4×D32 | — | 2 | 1 | no | — |
| 89 | C4×D32 | C23 | 1 | 2 | yes | — |
| 90 | #3799 | — | 2 | 2 | no | — |
| 91 | #3799 | — | 2 | 2 | no | — |
| 92 | #3798 | — | 2 | 1 | no | — |
| 93 | #3798 | D4 | 1 | 2 | yes | complemented |
| 94 | #3797 | D4 | 1 | 1 | yes | characteristic |
| 95 | #3797 | C23 | 1 | 1 | yes | characteristic |
| 96 | #3796 | — | 2 | 1 | no | — |
| 97 | #3796 | — | 2 | 1 | no | — |
| 98 | C22⋊#157 | — | 2 | 1 | no | — |
| 99 | #3792 | — | 2 | 1 | no | — |
| 100 | C4⋊#157 | C23 | 1 | 2 | yes | — |
| 101 | C4×#157 | — | 2 | 1 | no | — |
| 102 | #3788 | — | 2 | 1 | no | — |
| 103 | #3787 | C23 | 1 | 2 | yes | — |
| 104 | #3775 | — | 2 | 4 | no | — |
| 105 | #3774 | — | 2 | 4 | no | — |
| 106 | D32⋊C4 | — | 2 | 4 | no | — |
| 107 | C3×#213 | — | 2 | 4 | no | — |
| 108 | C2×C3×C3⋊C8 | — | 2 | 1 | no | — |
| 109 | #3714 | — | 2 | 4 | no | — |
| 110 | #3710 | — | 2 | 1 | no | — |
| 111 | #3710 | C23 | 1 | 2 | yes | — |
| 112 | #3008 | — | 9 | 1 | no | maximal, Sylow |
| 113 | C3×H(5,𝔽2) | — | 6 | 1 | no | — |
| 114 | #1009 | — | 6 | 1 | no | — |
| 115 | #1009 | — | 6 | 1 | no | — |
| 116 | #1009 | — | 6 | 2 | no | — |
| 117 | #1009 | — | 6 | 2 | no | — |
| 118 | D3×#41 | — | 6 | 1 | no | — |
| 119 | D3×#41 | — | 6 | 1 | no | — |
| 120 | D3×#41 | — | 6 | 2 | no | — |
| 121 | D3×#41 | — | 6 | 2 | no | — |
| 122 | #1004 | — | 2 | 1 | no | — |
| 123 | #1004 | — | 6 | 2 | no | — |
| 124 | #1004 | — | 6 | 2 | no | — |
| 125 | #1004 | — | 6 | 4 | no | — |
| 126 | C2×D3×D4 | — | 6 | 1 | no | — |
| 127 | C2×D3×D4 | — | 6 | 2 | no | — |
| 128 | C2×D3×D4 | — | 6 | 1 | no | — |
| 129 | C2×D3×D4 | — | 6 | 1 | no | — |
| 130 | C2×D3×D4 | — | 6 | 2 | no | — |
| 131 | C2×D3×D4 | — | 6 | 4 | no | — |
| 132 | C2×C3×D8 | — | 6 | 1 | no | — |
| 133 | C2×#213 | — | 2 | 1 | no | — |
| 134 | C2×#213 | — | 6 | 1 | no | — |
| 135 | D3×D8 | — | 6 | 4 | no | — |
| 136 | D3×D8 | — | 6 | 4 | no | — |
| 137 | C2×D24 | — | 6 | 1 | no | — |
| 138 | C2×D3×C8 | — | 6 | 1 | no | — |
| 139 | C23×C32 | — | 2 | 1 | no | — |
| 140 | C22×C3⋊D3 | — | 2 | 1 | no | — |
| 141 | C22×C3⋊D3 | — | 2 | 2 | no | — |
| 142 | C22×C3⋊D3 | — | 2 | 2 | no | — |
| 143 | C22×C3⋊D3 | — | 8 | 2 | no | — |
| 144 | C22×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 145 | C22×C3×D3 | — | 2 | 4 | no | — |
| 146 | C22×C3×D3 | — | 4 | 1 | no | — |
| 147 | C2×D32 | — | 2 | 1 | no | — |
| 148 | C2×D32 | — | 2 | 4 | no | — |
| 149 | C2×D32 | — | 2 | 2 | no | — |
| 150 | C2×D32 | — | 4 | 1 | no | — |
| 151 | C2×D32 | — | 8 | 4 | no | — |
| 152 | C2×D32 | — | 8 | 2 | no | — |
| 153 | C2×D32 | C2×D4 | 1 | 2 | yes | — |
| 154 | C2×#157 | — | 2 | 2 | no | — |
| 155 | GO+(4,𝔽2) | — | 8 | 4 | no | — |
| 156 | C32×D4 | — | 2 | 1 | no | — |
| 157 | C32×D4 | C2×D4 | 1 | 2 | yes | — |
| 158 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 159 | #638 | — | 2 | 2 | no | — |
| 160 | #638 | — | 2 | 2 | no | — |
| 161 | C2×C3⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 162 | C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 163 | C4⋊(C3⋊D3) | C2×D4 | 1 | 2 | yes | — |
| 164 | C4×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 165 | C4×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 166 | C4×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 167 | C4×C3⋊D3 | C24 | 1 | 1 | yes | characteristic |
| 168 | C3×#67 | — | 2 | 4 | no | — |
| 169 | C3×#67 | — | 2 | 4 | no | — |
| 170 | C3×#67 | — | 2 | 2 | no | — |
| 171 | C3×#67 | — | 2 | 2 | no | — |
| 172 | C2×C3×Dic3 | — | 2 | 4 | no | — |
| 173 | C3×D12 | — | 2 | 1 | no | — |
| 174 | C3×D12 | — | 2 | 1 | no | — |
| 175 | C3×D12 | — | 2 | 2 | no | — |
| 176 | C3×D12 | — | 4 | 1 | no | — |
| 177 | C3×C4×D3 | — | 2 | 2 | no | — |
| 178 | C3×C4×D3 | — | 2 | 2 | no | — |
| 179 | C3×Dic6 | — | 2 | 1 | no | — |
| 180 | C3×Dic6 | — | 2 | 1 | no | — |
| 181 | #627 | — | 2 | 1 | no | — |
| 182 | #627 | C2×D4 | 1 | 2 | yes | — |
| 183 | #626 | — | 2 | 4 | no | — |
| 184 | #626 | — | 2 | 4 | no | — |
| 185 | #626 | — | 2 | 2 | no | — |
| 186 | #626 | — | 2 | 2 | no | — |
| 187 | #625 | — | 2 | 1 | no | — |
| 188 | #625 | — | 2 | 2 | no | — |
| 189 | #625 | — | 4 | 1 | no | — |
| 190 | #625 | C2×D4 | 1 | 2 | yes | — |
| 191 | #624 | — | 2 | 4 | no | — |
| 192 | #624 | — | 2 | 1 | no | — |
| 193 | #624 | C2×D4 | 1 | 2 | yes | — |
| 194 | D3×Dic3 | — | 2 | 2 | no | — |
| 195 | D3×Dic3 | — | 2 | 2 | no | — |
| 196 | #622 | — | 2 | 2 | no | — |
| 197 | C3×C3⋊C8 | — | 2 | 2 | no | — |
| 198 | C2×H(5,𝔽2) | — | 9 | 1 | no | — |
| 199 | C2×AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 200 | C22×D8 | — | 9 | 1 | no | — |
| 201 | #535 | — | 9 | 1 | no | — |
| 202 | #449 | — | 9 | 4 | no | — |
| 203 | #447 | — | 9 | 4 | no | — |
| 204 | #418 | — | 9 | 1 | no | — |
| 205 | #416 | — | 9 | 1 | no | — |
| 206 | #408 | — | 9 | 1 | no | — |
| 207 | C23×D3 | — | 6 | 4 | no | — |
| 208 | C23×D3 | — | 6 | 2 | no | — |
| 209 | C23×D3 | — | 12 | 1 | no | — |
| 210 | C23×D3 | — | 12 | 1 | no | — |
| 211 | C3×#41 | — | 6 | 1 | no | — |
| 212 | C3×#41 | — | 6 | 1 | no | — |
| 213 | C3×#41 | — | 6 | 2 | no | — |
| 214 | C3×#41 | — | 6 | 2 | no | — |
| 215 | C2×C3×D4 | — | 2 | 1 | no | — |
| 216 | C2×C3×D4 | — | 2 | 1 | no | — |
| 217 | C2×C3×D4 | — | 6 | 1 | no | — |
| 218 | C2×C3×D4 | — | 6 | 2 | no | — |
| 219 | C2×C3×D4 | — | 6 | 2 | no | — |
| 220 | C2×C3×D4 | — | 6 | 4 | no | — |
| 221 | C2×#67 | — | 2 | 4 | no | — |
| 222 | C2×#67 | — | 6 | 4 | no | — |
| 223 | C2×#67 | — | 6 | 4 | no | — |
| 224 | C2×#67 | — | 6 | 4 | no | — |
| 225 | C2×#67 | — | 6 | 2 | no | — |
| 226 | C2×#67 | — | 12 | 1 | no | — |
| 227 | C2×#67 | — | 12 | 1 | no | — |
| 228 | #239 | — | 6 | 2 | no | — |
| 229 | #239 | — | 6 | 2 | no | — |
| 230 | #239 | — | 6 | 1 | no | — |
| 231 | #239 | — | 6 | 1 | no | — |
| 232 | D3×Q8 | — | 6 | 1 | no | — |
| 233 | D3×Q8 | — | 6 | 1 | no | — |
| 234 | #237 | — | 2 | 2 | no | — |
| 235 | #237 | — | 2 | 2 | no | — |
| 236 | #237 | — | 6 | 2 | no | — |
| 237 | #237 | — | 6 | 1 | no | — |
| 238 | #237 | — | 6 | 1 | no | — |
| 239 | #237 | — | 6 | 4 | no | — |
| 240 | #237 | — | 6 | 4 | no | — |
| 241 | #237 | — | 6 | 2 | no | — |
| 242 | D3×D4 | — | 2 | 2 | no | — |
| 243 | D3×D4 | — | 2 | 2 | no | — |
| 244 | D3×D4 | — | 6 | 1 | no | — |
| 245 | D3×D4 | — | 6 | 1 | no | — |
| 246 | D3×D4 | — | 6 | 2 | no | — |
| 247 | D3×D4 | — | 6 | 2 | no | — |
| 248 | D3×D4 | — | 6 | 2 | no | — |
| 249 | D3×D4 | — | 6 | 2 | no | — |
| 250 | D3×D4 | — | 6 | 2 | no | — |
| 251 | D3×D4 | — | 6 | 2 | no | — |
| 252 | D3×D4 | — | 6 | 2 | no | — |
| 253 | D3×D4 | — | 6 | 2 | no | — |
| 254 | D3×D4 | — | 6 | 2 | no | — |
| 255 | D3×D4 | — | 6 | 4 | no | — |
| 256 | D3×D4 | — | 6 | 2 | no | — |
| 257 | D3×D4 | — | 6 | 4 | no | — |
| 258 | D3×D4 | — | 6 | 4 | no | — |
| 259 | D3×D4 | — | 6 | 4 | no | — |
| 260 | D3×D4 | — | 6 | 4 | no | — |
| 261 | D3×D4 | — | 6 | 4 | no | — |
| 262 | D3×D4 | — | 6 | 2 | no | — |
| 263 | D3×D4 | — | 6 | 2 | no | — |
| 264 | D3×D4 | — | 6 | 4 | no | — |
| 265 | D3×D4 | — | 6 | 4 | no | — |
| 266 | D3×D4 | — | 12 | 1 | no | — |
| 267 | D3×D4 | — | 12 | 1 | no | — |
| 268 | D3×D4 | — | 12 | 1 | no | — |
| 269 | D3×D4 | — | 12 | 1 | no | — |
| 270 | #235 | — | 2 | 1 | no | — |
| 271 | #235 | — | 2 | 1 | no | — |
| 272 | #235 | — | 6 | 2 | no | — |
| 273 | #235 | — | 6 | 2 | no | — |
| 274 | #235 | — | 6 | 2 | no | — |
| 275 | #235 | — | 6 | 2 | no | — |
| 276 | #235 | — | 6 | 4 | no | — |
| 277 | #235 | — | 6 | 4 | no | — |
| 278 | C2×D12 | — | 2 | 1 | no | — |
| 279 | C2×D12 | — | 6 | 1 | no | — |
| 280 | C2×D12 | — | 6 | 1 | no | — |
| 281 | C2×D12 | — | 6 | 2 | no | — |
| 282 | C2×D12 | — | 6 | 2 | no | — |
| 283 | C2×D12 | — | 6 | 4 | no | — |
| 284 | C2×C4×D3 | — | 6 | 2 | no | — |
| 285 | C2×C4×D3 | — | 6 | 1 | no | — |
| 286 | C2×C4×D3 | — | 6 | 1 | no | — |
| 287 | C2×C4×D3 | — | 6 | 2 | no | — |
| 288 | C2×C4×D3 | — | 6 | 4 | no | — |
| 289 | C3×D8 | — | 6 | 4 | no | — |
| 290 | C2×C3×C8 | — | 6 | 1 | no | — |
| 291 | #213 | — | 2 | 4 | no | — |
| 292 | #213 | — | 6 | 4 | no | — |
| 293 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 294 | D24 | — | 6 | 4 | no | — |
| 295 | D3×C8 | — | 6 | 2 | no | — |
| 296 | D3×C8 | — | 6 | 2 | no | — |
| 297 | C22×C32 | — | 2 | 2 | no | — |
| 298 | C22×C32 | — | 8 | 1 | no | — |
| 299 | C22×C32 | #120 | 1 | 1 | yes | characteristic |
| 300 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 301 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 302 | C2×C3⋊D3 | — | 4 | 4 | no | — |
| 303 | C2×C3⋊D3 | — | 8 | 2 | no | — |
| 304 | C2×C3⋊D3 | — | 8 | 1 | no | — |
| 305 | C2×C3⋊D3 | #120 | 1 | 1 | yes | characteristic |
| 306 | C2×C3⋊D3 | C22×D4 | 1 | 1 | yes | characteristic |
| 307 | C2×C3×D3 | — | 2 | 2 | no | — |
| 308 | C2×C3×D3 | — | 2 | 2 | no | — |
| 309 | C2×C3×D3 | — | 4 | 2 | no | — |
| 310 | C2×C3×D3 | — | 8 | 4 | no | — |
| 311 | C2×C3×D3 | — | 8 | 2 | no | — |
| 312 | D32 | — | 2 | 4 | no | — |
| 313 | D32 | — | 4 | 2 | no | — |
| 314 | D32 | — | 4 | 4 | no | — |
| 315 | D32 | — | 8 | 4 | no | — |
| 316 | D32 | — | 8 | 2 | no | — |
| 317 | #157 | — | 4 | 2 | no | — |
| 318 | C32×C4 | #120 | 1 | 1 | yes | characteristic |
| 319 | C32×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 320 | C3⋊Dic3 | #120 | 1 | 1 | yes | characteristic |
| 321 | C3⋊Dic3 | C22×D4 | 1 | 1 | yes | characteristic |
| 322 | C3×Dic3 | — | 2 | 2 | no | — |
| 323 | C3×Dic3 | — | 2 | 2 | no | — |
| 324 | H(5,𝔽2) | — | 6 | 1 | no | — |
| 325 | H(5,𝔽2) | — | 18 | 2 | no | — |
| 326 | H(5,𝔽2) | — | 18 | 2 | no | — |
| 327 | H(5,𝔽2) | — | 18 | 2 | no | — |
| 328 | H(5,𝔽2) | — | 18 | 1 | no | — |
| 329 | C2×#41 | — | 9 | 1 | no | — |
| 330 | C2×#41 | — | 9 | 1 | no | — |
| 331 | C2×#41 | — | 9 | 2 | no | — |
| 332 | C2×#41 | — | 18 | 1 | no | — |
| 333 | C22×D4 | — | 9 | 1 | no | — |
| 334 | C22×D4 | — | 9 | 2 | no | — |
| 335 | C22×D4 | — | 9 | 1 | no | — |
| 336 | C22×D4 | — | 18 | 1 | no | — |
| 337 | C22×D4 | — | 18 | 2 | no | — |
| 338 | AGL(1,ℤ/8) | — | 18 | 2 | no | — |
| 339 | AGL(1,ℤ/8) | — | 18 | 2 | no | — |
| 340 | C2×SD16 | — | 9 | 2 | no | — |
| 341 | C2×D8 | — | 6 | 1 | no | — |
| 342 | C2×D8 | — | 9 | 4 | no | — |
| 343 | C2×D8 | — | 9 | 2 | no | — |
| 344 | C2×D8 | — | 18 | 1 | no | — |
| 345 | C2×D8 | — | 18 | 2 | no | — |
| 346 | C2×M16 | — | 9 | 1 | no | — |
| 347 | C22×C8 | — | 9 | 1 | no | — |
| 348 | #127 | — | 18 | 1 | no | — |
| 349 | #124 | — | 18 | 1 | no | — |
| 350 | #121 | — | 9 | 4 | no | — |
| 351 | #120 | — | 18 | 2 | no | — |
| 352 | #117 | — | 9 | 1 | no | — |
| 353 | #103 | — | 9 | 2 | no | — |
| 354 | #102 | — | 9 | 4 | no | — |
| 355 | #102 | — | 9 | 2 | no | — |
| 356 | C22⋊C8 | — | 9 | 4 | no | — |
| 357 | C23×C3 | — | 2 | 2 | no | — |
| 358 | C23×C3 | — | 4 | 1 | no | — |
| 359 | C23×C3 | — | 6 | 4 | no | — |
| 360 | C23×C3 | — | 12 | 1 | no | — |
| 361 | C22×D3 | — | 2 | 4 | no | — |
| 362 | C22×D3 | — | 4 | 1 | no | — |
| 363 | C22×D3 | — | 6 | 2 | no | — |
| 364 | C22×D3 | — | 6 | 1 | no | — |
| 365 | C22×D3 | — | 6 | 1 | no | — |
| 366 | C22×D3 | — | 6 | 2 | no | — |
| 367 | C22×D3 | — | 6 | 4 | no | — |
| 368 | C22×D3 | — | 6 | 4 | no | — |
| 369 | C22×D3 | — | 6 | 4 | no | — |
| 370 | C22×D3 | — | 6 | 4 | no | — |
| 371 | C22×D3 | — | 6 | 2 | no | — |
| 372 | C22×D3 | — | 12 | 2 | no | — |
| 373 | C22×D3 | — | 12 | 2 | no | — |
| 374 | C22×D3 | — | 12 | 2 | no | — |
| 375 | C22×D3 | — | 12 | 1 | no | — |
| 376 | C22×D3 | — | 12 | 2 | no | — |
| 377 | C22×D3 | — | 24 | 4 | no | — |
| 378 | C22×D3 | — | 24 | 4 | no | — |
| 379 | C22×D3 | — | 24 | 8 | no | — |
| 380 | C22×D3 | — | 24 | 4 | no | — |
| 381 | C3×Q8 | — | 6 | 1 | no | — |
| 382 | C3×Q8 | — | 6 | 1 | no | — |
| 383 | C3×D4 | — | 2 | 2 | no | — |
| 384 | C3×D4 | — | 2 | 2 | no | — |
| 385 | C3×D4 | — | 2 | 2 | no | — |
| 386 | C3×D4 | — | 4 | 1 | no | — |
| 387 | C3×D4 | — | 6 | 1 | no | — |
| 388 | C3×D4 | — | 6 | 1 | no | — |
| 389 | C3×D4 | — | 6 | 2 | no | — |
| 390 | C3×D4 | — | 6 | 4 | no | — |
| 391 | C3×D4 | — | 6 | 4 | no | — |
| 392 | C3×D4 | — | 6 | 2 | no | — |
| 393 | C3×D4 | — | 6 | 2 | no | — |
| 394 | C3×D4 | — | 12 | 1 | no | — |
| 395 | C2×C3×C4 | — | 2 | 1 | no | — |
| 396 | C2×C3×C4 | — | 2 | 1 | no | — |
| 397 | C2×C3×C4 | — | 6 | 2 | no | — |
| 398 | C2×C3×C4 | — | 6 | 2 | no | — |
| 399 | C2×C3×C4 | — | 6 | 4 | no | — |
| 400 | #67 | — | 2 | 2 | no | — |
| 401 | #67 | — | 2 | 2 | no | — |
| 402 | #67 | — | 2 | 4 | no | — |
| 403 | #67 | — | 2 | 4 | no | — |
| 404 | #67 | — | 6 | 2 | no | — |
| 405 | #67 | — | 6 | 2 | no | — |
| 406 | #67 | — | 6 | 2 | no | — |
| 407 | #67 | — | 6 | 4 | no | — |
| 408 | #67 | — | 6 | 4 | no | — |
| 409 | #67 | — | 6 | 2 | no | — |
| 410 | #67 | — | 6 | 4 | no | — |
| 411 | #67 | — | 6 | 4 | no | — |
| 412 | #67 | — | 12 | 2 | no | — |
| 413 | #67 | — | 12 | 2 | no | — |
| 414 | #67 | — | 12 | 2 | no | — |
| 415 | #67 | — | 12 | 2 | no | — |
| 416 | C2×Dic3 | — | 2 | 4 | no | — |
| 417 | C2×Dic3 | — | 6 | 1 | no | — |
| 418 | C2×Dic3 | — | 6 | 1 | no | — |
| 419 | C2×Dic3 | — | 6 | 2 | no | — |
| 420 | C2×Dic3 | — | 6 | 2 | no | — |
| 421 | D12 | — | 2 | 1 | no | — |
| 422 | D12 | — | 2 | 1 | no | — |
| 423 | D12 | — | 2 | 2 | no | — |
| 424 | D12 | — | 4 | 1 | no | — |
| 425 | D12 | — | 6 | 2 | no | — |
| 426 | D12 | — | 6 | 2 | no | — |
| 427 | D12 | — | 6 | 2 | no | — |
| 428 | D12 | — | 6 | 2 | no | — |
| 429 | D12 | — | 6 | 2 | no | — |
| 430 | D12 | — | 6 | 4 | no | — |
| 431 | D12 | — | 6 | 4 | no | — |
| 432 | D12 | — | 12 | 1 | no | — |
| 433 | C4×D3 | — | 2 | 2 | no | — |
| 434 | C4×D3 | — | 2 | 2 | no | — |
| 435 | C4×D3 | — | 6 | 2 | no | — |
| 436 | C4×D3 | — | 6 | 1 | no | — |
| 437 | C4×D3 | — | 6 | 1 | no | — |
| 438 | C4×D3 | — | 6 | 1 | no | — |
| 439 | C4×D3 | — | 6 | 1 | no | — |
| 440 | C4×D3 | — | 6 | 1 | no | — |
| 441 | C4×D3 | — | 6 | 1 | no | — |
| 442 | C4×D3 | — | 6 | 1 | no | — |
| 443 | C4×D3 | — | 6 | 1 | no | — |
| 444 | C4×D3 | — | 6 | 2 | no | — |
| 445 | C4×D3 | — | 6 | 4 | no | — |
| 446 | C4×D3 | — | 6 | 4 | no | — |
| 447 | C4×D3 | — | 6 | 2 | no | — |
| 448 | C4×D3 | — | 6 | 2 | no | — |
| 449 | Dic6 | — | 2 | 1 | no | — |
| 450 | Dic6 | — | 2 | 1 | no | — |
| 451 | Dic6 | — | 6 | 2 | no | — |
| 452 | Dic6 | — | 6 | 2 | no | — |
| 453 | C3×C8 | — | 6 | 2 | no | — |
| 454 | C3⋊C8 | — | 2 | 2 | no | — |
| 455 | C2×C32 | — | 2 | 1 | no | — |
| 456 | C2×C32 | — | 4 | 2 | no | — |
| 457 | C2×C32 | C2×#120 | 1 | 1 | yes | characteristic |
| 458 | C3⋊D3 | — | 2 | 1 | no | — |
| 459 | C3⋊D3 | — | 4 | 2 | no | — |
| 460 | C3⋊D3 | #576 | 1 | 2 | yes | — |
| 461 | C3×D3 | — | 4 | 2 | no | — |
| 462 | C3×D3 | — | 4 | 2 | no | — |
| 463 | C3×D3 | — | 8 | 2 | no | — |
| 464 | C24 | — | 18 | 1 | no | — |
| 465 | C24 | — | 18 | 2 | no | — |
| 466 | C24 | — | 18 | 1 | no | — |
| 467 | #41 | — | 6 | 2 | no | — |
| 468 | #41 | — | 6 | 2 | no | — |
| 469 | #41 | — | 6 | 1 | no | — |
| 470 | #41 | — | 6 | 1 | no | — |
| 471 | #41 | — | 9 | 2 | no | — |
| 472 | #41 | — | 9 | 2 | no | — |
| 473 | #41 | — | 18 | 1 | no | — |
| 474 | #41 | — | 18 | 4 | no | — |
| 475 | #41 | — | 18 | 4 | no | — |
| 476 | #41 | — | 18 | 2 | no | — |
| 477 | #41 | — | 18 | 2 | no | — |
| 478 | #41 | — | 18 | 1 | no | — |
| 479 | #41 | — | 18 | 1 | no | — |
| 480 | #41 | — | 18 | 1 | no | — |
| 481 | C2×Q8 | — | 9 | 1 | no | — |
| 482 | C2×Q8 | — | 9 | 1 | no | — |
| 483 | C2×D4 | — | 6 | 2 | no | — |
| 484 | C2×D4 | — | 6 | 4 | no | — |
| 485 | C2×D4 | — | 6 | 2 | no | — |
| 486 | C2×D4 | — | 6 | 1 | no | — |
| 487 | C2×D4 | — | 9 | 1 | no | — |
| 488 | C2×D4 | — | 9 | 2 | no | — |
| 489 | C2×D4 | — | 9 | 1 | no | — |
| 490 | C2×D4 | — | 9 | 2 | no | — |
| 491 | C2×D4 | — | 9 | 2 | no | — |
| 492 | C2×D4 | — | 9 | 2 | no | — |
| 493 | C2×D4 | — | 9 | 1 | no | — |
| 494 | C2×D4 | — | 18 | 2 | no | — |
| 495 | C2×D4 | — | 18 | 2 | no | — |
| 496 | C2×D4 | — | 18 | 4 | no | — |
| 497 | C2×D4 | — | 18 | 1 | no | — |
| 498 | C2×D4 | — | 18 | 1 | no | — |
| 499 | C2×D4 | — | 18 | 2 | no | — |
| 500 | C2×D4 | — | 18 | 1 | no | — |
| 501 | C2×D4 | — | 18 | 1 | no | — |
| 502 | C2×D4 | — | 18 | 1 | no | — |
| 503 | C2×D4 | — | 18 | 1 | no | — |
| 504 | C2×D4 | — | 18 | 1 | no | — |
| 505 | C2×D4 | — | 18 | 2 | no | — |
| 506 | C2×D4 | — | 18 | 1 | no | — |
| 507 | C2×D4 | — | 18 | 4 | no | — |
| 508 | C2×D4 | — | 18 | 4 | no | — |
| 509 | C2×D4 | — | 18 | 4 | no | — |
| 510 | C2×D4 | — | 18 | 4 | no | — |
| 511 | C2×D4 | — | 18 | 4 | no | — |
| 512 | C2×D4 | GO+(4,𝔽2) | 1 | 1 | yes | characteristic, complemented |
| 513 | C22×C4 | — | 9 | 2 | no | — |
| 514 | C22×C4 | — | 9 | 1 | no | — |
| 515 | C22×C4 | — | 18 | 2 | no | — |
| 516 | C22×C4 | — | 18 | 1 | no | — |
| 517 | SD16 | — | 18 | 4 | no | — |
| 518 | D8 | — | 6 | 4 | no | — |
| 519 | D8 | — | 18 | 4 | no | — |
| 520 | D8 | — | 18 | 4 | no | — |
| 521 | M16 | — | 18 | 1 | no | — |
| 522 | M16 | — | 18 | 1 | no | — |
| 523 | C2×C8 | — | 6 | 1 | no | — |
| 524 | C2×C8 | — | 9 | 2 | no | — |
| 525 | C2×C8 | — | 9 | 2 | no | — |
| 526 | C2×C8 | — | 18 | 1 | no | — |
| 527 | C4⋊C4 | — | 9 | 2 | no | — |
| 528 | C22⋊C4 | — | 18 | 4 | no | — |
| 529 | C22⋊C4 | — | 18 | 1 | no | — |
| 530 | C42 | — | 18 | 1 | no | — |
| 531 | C22×C3 | — | 2 | 4 | no | — |
| 532 | C22×C3 | — | 2 | 1 | no | — |
| 533 | C22×C3 | — | 2 | 1 | no | — |
| 534 | C22×C3 | — | 4 | 2 | no | — |
| 535 | C22×C3 | — | 6 | 2 | no | — |
| 536 | C22×C3 | — | 6 | 2 | no | — |
| 537 | C22×C3 | — | 8 | 2 | no | — |
| 538 | C22×C3 | — | 8 | 2 | no | — |
| 539 | C22×C3 | — | 12 | 2 | no | — |
| 540 | C22×C3 | — | 24 | 2 | no | — |
| 541 | C22×C3 | — | 24 | 4 | no | — |
| 542 | C2×D3 | — | 2 | 2 | no | — |
| 543 | C2×D3 | — | 2 | 2 | no | — |
| 544 | C2×D3 | — | 4 | 2 | no | — |
| 545 | C2×D3 | — | 6 | 1 | no | — |
| 546 | C2×D3 | — | 6 | 1 | no | — |
| 547 | C2×D3 | — | 6 | 1 | no | — |
| 548 | C2×D3 | — | 6 | 1 | no | — |
| 549 | C2×D3 | — | 6 | 4 | no | — |
| 550 | C2×D3 | — | 6 | 4 | no | — |
| 551 | C2×D3 | — | 8 | 4 | no | — |
| 552 | C2×D3 | — | 8 | 2 | no | — |
| 553 | C2×D3 | — | 12 | 4 | no | — |
| 554 | C2×D3 | — | 12 | 2 | no | — |
| 555 | C2×D3 | — | 12 | 2 | no | — |
| 556 | C2×D3 | — | 12 | 4 | no | — |
| 557 | C2×D3 | — | 12 | 8 | no | — |
| 558 | C2×D3 | — | 24 | 4 | no | — |
| 559 | C2×D3 | — | 24 | 4 | no | — |
| 560 | C2×D3 | — | 24 | 4 | no | — |
| 561 | C2×D3 | — | 24 | 4 | no | — |
| 562 | C2×D3 | — | 24 | 4 | no | — |
| 563 | C2×D3 | — | 24 | 4 | no | — |
| 564 | C2×D3 | — | 24 | 2 | no | — |
| 565 | C2×D3 | — | 24 | 4 | no | — |
| 566 | C2×D3 | — | 24 | 2 | no | — |
| 567 | C3×C4 | — | 2 | 1 | no | — |
| 568 | C3×C4 | — | 2 | 1 | no | — |
| 569 | C3×C4 | — | 2 | 1 | no | — |
| 570 | C3×C4 | — | 2 | 1 | no | — |
| 571 | C3×C4 | — | 6 | 2 | no | — |
| 572 | C3×C4 | — | 6 | 2 | no | — |
| 573 | Dic3 | — | 2 | 2 | no | — |
| 574 | Dic3 | — | 2 | 2 | no | — |
| 575 | Dic3 | — | 6 | 1 | no | — |
| 576 | Dic3 | — | 6 | 1 | no | — |
| 577 | Dic3 | — | 6 | 1 | no | — |
| 578 | Dic3 | — | 6 | 1 | no | — |
| 579 | C32 | #3008 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 580 | C23 | — | 2 | 1 | no | — |
| 581 | C23 | — | 6 | 4 | no | — |
| 582 | C23 | — | 9 | 2 | no | — |
| 583 | C23 | — | 9 | 1 | no | — |
| 584 | C23 | — | 12 | 1 | no | — |
| 585 | C23 | — | 18 | 2 | no | — |
| 586 | C23 | — | 18 | 2 | no | — |
| 587 | C23 | — | 18 | 1 | no | — |
| 588 | C23 | — | 18 | 4 | no | — |
| 589 | C23 | — | 18 | 2 | no | — |
| 590 | C23 | — | 18 | 1 | no | — |
| 591 | C23 | — | 36 | 1 | no | — |
| 592 | C23 | — | 72 | 2 | no | — |
| 593 | C23 | — | 72 | 2 | no | — |
| 594 | C23 | — | 72 | 4 | no | — |
| 595 | Q8 | — | 6 | 1 | no | — |
| 596 | Q8 | — | 6 | 1 | no | — |
| 597 | Q8 | — | 9 | 2 | no | — |
| 598 | Q8 | — | 18 | 1 | no | — |
| 599 | D4 | — | 2 | 1 | no | — |
| 600 | D4 | — | 6 | 4 | no | — |
| 601 | D4 | — | 6 | 4 | no | — |
| 602 | D4 | — | 6 | 2 | no | — |
| 603 | D4 | — | 6 | 2 | no | — |
| 604 | D4 | — | 6 | 1 | no | — |
| 605 | D4 | — | 6 | 2 | no | — |
| 606 | D4 | — | 6 | 1 | no | — |
| 607 | D4 | — | 9 | 2 | no | — |
| 608 | D4 | — | 9 | 2 | no | — |
| 609 | D4 | — | 12 | 1 | no | — |
| 610 | D4 | — | 18 | 2 | no | — |
| 611 | D4 | — | 18 | 2 | no | — |
| 612 | D4 | — | 18 | 4 | no | — |
| 613 | D4 | — | 18 | 4 | no | — |
| 614 | D4 | — | 18 | 2 | no | — |
| 615 | D4 | — | 18 | 2 | no | — |
| 616 | D4 | — | 18 | 1 | no | — |
| 617 | D4 | — | 18 | 2 | no | — |
| 618 | D4 | — | 18 | 1 | no | — |
| 619 | D4 | — | 36 | 1 | no | — |
| 620 | D4 | — | 72 | 4 | no | — |
| 621 | D4 | C2×GO+(4,𝔽2) | 1 | 2 | yes | — |
| 622 | C2×C4 | — | 6 | 4 | no | — |
| 623 | C2×C4 | — | 6 | 2 | no | — |
| 624 | C2×C4 | — | 6 | 2 | no | — |
| 625 | C2×C4 | — | 9 | 2 | no | — |
| 626 | C2×C4 | — | 9 | 1 | no | — |
| 627 | C2×C4 | — | 9 | 1 | no | — |
| 628 | C2×C4 | — | 9 | 1 | no | — |
| 629 | C2×C4 | — | 9 | 1 | no | — |
| 630 | C2×C4 | — | 9 | 1 | no | — |
| 631 | C2×C4 | — | 18 | 1 | no | — |
| 632 | C2×C4 | — | 18 | 4 | no | — |
| 633 | C2×C4 | — | 18 | 2 | no | — |
| 634 | C2×C4 | — | 18 | 2 | no | — |
| 635 | C2×C4 | — | 18 | 2 | no | — |
| 636 | C2×C4 | C2×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 637 | C8 | — | 6 | 2 | no | — |
| 638 | C8 | — | 18 | 2 | no | — |
| 639 | C2×C3 | — | 2 | 2 | no | — |
| 640 | C2×C3 | — | 2 | 1 | no | — |
| 641 | C2×C3 | — | 2 | 1 | no | — |
| 642 | C2×C3 | — | 4 | 1 | no | — |
| 643 | C2×C3 | — | 4 | 4 | no | — |
| 644 | C2×C3 | — | 8 | 2 | no | — |
| 645 | C2×C3 | — | 12 | 2 | no | — |
| 646 | C2×C3 | — | 12 | 2 | no | — |
| 647 | C2×C3 | — | 24 | 2 | no | — |
| 648 | D3 | — | 4 | 2 | no | — |
| 649 | D3 | — | 4 | 2 | no | — |
| 650 | D3 | — | 6 | 2 | no | — |
| 651 | D3 | — | 6 | 2 | no | — |
| 652 | D3 | — | 6 | 2 | no | — |
| 653 | D3 | — | 8 | 2 | no | — |
| 654 | D3 | — | 12 | 1 | no | — |
| 655 | D3 | — | 12 | 4 | no | — |
| 656 | D3 | — | 24 | 2 | no | — |
| 657 | C22 | — | 2 | 2 | no | — |
| 658 | C22 | — | 6 | 2 | no | — |
| 659 | C22 | — | 6 | 2 | no | — |
| 660 | C22 | — | 8 | 1 | no | — |
| 661 | C22 | — | 9 | 1 | no | — |
| 662 | C22 | — | 9 | 1 | no | — |
| 663 | C22 | — | 12 | 2 | no | — |
| 664 | C22 | — | 18 | 2 | no | — |
| 665 | C22 | — | 18 | 4 | no | — |
| 666 | C22 | — | 18 | 2 | no | — |
| 667 | C22 | — | 24 | 2 | no | — |
| 668 | C22 | — | 24 | 4 | no | — |
| 669 | C22 | — | 36 | 4 | no | — |
| 670 | C22 | — | 36 | 2 | no | — |
| 671 | C22 | — | 36 | 4 | no | — |
| 672 | C22 | — | 72 | 1 | no | — |
| 673 | C22 | — | 72 | 2 | no | — |
| 674 | C22 | — | 72 | 4 | no | — |
| 675 | C22 | — | 72 | 2 | no | — |
| 676 | C22 | #64241 | 1 | 1 | yes | characteristic |
| 677 | C4 | — | 6 | 2 | no | — |
| 678 | C4 | — | 6 | 2 | no | — |
| 679 | C4 | — | 9 | 1 | no | — |
| 680 | C4 | — | 9 | 1 | no | — |
| 681 | C4 | — | 36 | 2 | no | — |
| 682 | C4 | #64241 | 1 | 1 | yes | characteristic |
| 683 | C4 | C22×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 684 | C3 | — | 2 | 1 | no | — |
| 685 | C3 | — | 2 | 1 | no | — |
| 686 | C2 | — | 2 | 1 | no | — |
| 687 | C2 | — | 4 | 2 | no | — |
| 688 | C2 | — | 9 | 2 | no | — |
| 689 | C2 | — | 12 | 2 | no | — |
| 690 | C2 | — | 12 | 2 | no | — |
| 691 | C2 | — | 18 | 1 | no | — |
| 692 | C2 | — | 24 | 2 | no | — |
| 693 | C2 | — | 36 | 2 | no | — |
| 694 | C2 | C2×#64241 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10596675 | C2 | semidirect |
| 2. #10596512 | C2 | semidirect |
| 3. #10596501 | C2 | semidirect |
| 4. C2×#63926 | C2 | semidirect |
| 5. #10593814 | C2 | semidirect |
| 6. #10593458 | C2 | semidirect |
| 7. #10593457 | C2 | semidirect |
| 8. #10593317 | C2 | semidirect |
| 9. #10593308 | C2 | semidirect |
| 17. #64312 | C22 | semidirect |
| 19. D32×D4 | C22 | semidirect |
| 23. C2×#3802 | C22 | semidirect |
| 24. #64286 | C22 | semidirect |
| 25. #64283 | C22 | semidirect |
| 29. #64230 | C22 | semidirect |
| 30. #64227 | C22 | semidirect |
| 31. #64225 | C22 | semidirect |
| 36. #63926 | C22 | semidirect |
| 38. C2×#3710 | C22 | semidirect |
| 39. #63782 | C22 | semidirect |
| 40. #63730 | C22 | semidirect |
| 41. #63729 | C22 | semidirect |
| 42. D32⋊C8 | C22 | semidirect |
| 49. C2×C32×D4 | D4 | semidirect |
| 53. D4×C3⋊D3 | D4 | semidirect |
| 55. C2×C4⋊(C3⋊D3) | D4 | semidirect |
| 77. #3805 | D4 | semidirect |
| 93. #3798 | D4 | semidirect |
| 512. C2×D4 | GO+(4,𝔽2) | semidirect |
| 579. C32 | #3008 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596675 | 2 |
| #10596512 | 2 |
| #10596501 | 2 |
| C2×#63926 | 2 |
| #10593814 | 2 |
| #10593458 | 2 |
| #10593457 | 2 |
| #10593317 | 2 |
| #10593308 | 2 |
| #3008 | 9 |