Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1266 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1266 conjugacy classes of subgroups — too many to draw. Only its 171 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 | #11724626 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C3×#64128 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C3×Q16×C3⋊D3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11723713 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #11723708 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #11723654 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #11723647 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C8×#1113 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #10594764 | — | 3 | 1 | no | maximal |
| 10 | D3×#919 | — | 3 | 2 | no | maximal |
| 11 | C3×#3832 | C22 | 1 | 4 | yes | complemented |
| 12 | C3×Q8×C3⋊D3 | C22 | 1 | 2 | yes | — |
| 13 | C4⋊#1113 | — | 2 | 2 | no | — |
| 14 | C4⋊#1113 | C22 | 1 | 2 | yes | — |
| 15 | C4×#1113 | — | 2 | 2 | no | — |
| 16 | C4×#1113 | C22 | 1 | 1 | yes | characteristic |
| 17 | #89041 | — | 2 | 4 | no | — |
| 18 | #89041 | C22 | 1 | 4 | yes | complemented |
| 19 | C33×Q16 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | C3×#3756 | C22 | 1 | 2 | yes | complemented |
| 21 | C3×#3755 | C22 | 1 | 4 | yes | complemented |
| 22 | C3×#3746 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | C3×#3745 | C22 | 1 | 2 | yes | complemented |
| 24 | C3×C8×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 25 | C3×C8×C3⋊D3 | C22 | 1 | 2 | yes | complemented |
| 26 | #88811 | C22 | 1 | 4 | yes | complemented |
| 27 | #88810 | C22 | 1 | 2 | yes | complemented |
| 28 | #88808 | C22 | 1 | 1 | yes | characteristic |
| 29 | #88808 | C22 | 1 | 2 | yes | complemented |
| 30 | #64319 | — | 3 | 2 | no | — |
| 31 | D3×#239 | — | 3 | 4 | no | — |
| 32 | #64128 | D3 | 1 | 2 | yes | complemented |
| 33 | Q16×C3⋊D3 | D3 | 1 | 1 | yes | characteristic, complemented |
| 34 | C3×#919 | — | 3 | 2 | no | — |
| 35 | C3×#919 | — | 3 | 2 | no | — |
| 36 | C3×#919 | — | 6 | 2 | no | — |
| 37 | C3×D3×Q16 | — | 3 | 2 | no | — |
| 38 | C3×D3×Q16 | — | 6 | 1 | no | — |
| 39 | #63950 | — | 3 | 4 | no | — |
| 40 | #63949 | — | 3 | 4 | no | — |
| 41 | #63947 | — | 3 | 4 | no | — |
| 42 | #63940 | — | 3 | 2 | no | — |
| 43 | D3×#215 | — | 3 | 4 | no | — |
| 44 | #63810 | — | 3 | 2 | no | — |
| 45 | #63808 | — | 3 | 2 | no | — |
| 46 | #63807 | — | 3 | 2 | no | — |
| 47 | #63797 | — | 3 | 1 | no | — |
| 48 | D3×D24 | — | 3 | 2 | no | — |
| 49 | D32×C8 | — | 3 | 1 | no | — |
| 50 | D32×C8 | — | 3 | 2 | no | — |
| 51 | C2×#1113 | — | 2 | 2 | no | — |
| 52 | C2×#1113 | D4 | 1 | 1 | yes | characteristic |
| 53 | C33×Q8 | C23 | 1 | 2 | yes | — |
| 54 | C3×C4⋊(C3⋊D3) | — | 2 | 4 | no | — |
| 55 | C3×C4⋊(C3⋊D3) | C23 | 1 | 4 | yes | — |
| 56 | C3×C4×C3⋊D3 | — | 2 | 2 | no | — |
| 57 | C3×C4×C3⋊D3 | — | 2 | 4 | no | — |
| 58 | C3×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 59 | C3×C4×C3⋊D3 | C23 | 1 | 2 | yes | — |
| 60 | C3×#634 | — | 2 | 2 | no | — |
| 61 | C3×#634 | C23 | 1 | 2 | yes | — |
| 62 | #6295 | — | 2 | 4 | no | — |
| 63 | #6295 | — | 2 | 2 | no | — |
| 64 | #6294 | — | 2 | 4 | no | — |
| 65 | #6294 | D4 | 1 | 2 | yes | — |
| 66 | #6294 | D4 | 1 | 1 | yes | characteristic |
| 67 | C33×C8 | C23 | 1 | 1 | yes | characteristic |
| 68 | C3×C3⋊(C3⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 69 | C3×C3⋊(C3⋊C8) | C23 | 1 | 2 | yes | — |
| 70 | D3×#135 | — | 9 | 2 | no | — |
| 71 | C2×#919 | — | 9 | 1 | no | — |
| 72 | #3832 | C2×D3 | 1 | 4 | yes | complemented |
| 73 | Q8×C3⋊D3 | C2×D3 | 1 | 2 | yes | — |
| 74 | C3×#239 | — | 3 | 4 | no | — |
| 75 | C3×#239 | — | 3 | 4 | no | — |
| 76 | C3×#239 | — | 6 | 4 | no | — |
| 77 | C3×D3×Q8 | — | 3 | 4 | no | — |
| 78 | C3×D3×Q8 | — | 6 | 2 | no | — |
| 79 | #3802 | — | 3 | 2 | no | — |
| 80 | #3802 | — | 6 | 2 | no | — |
| 81 | D3×D12 | — | 3 | 4 | no | — |
| 82 | D3×D12 | — | 6 | 4 | no | — |
| 83 | C4×D32 | — | 3 | 2 | no | — |
| 84 | C4×D32 | — | 3 | 1 | no | — |
| 85 | C4×D32 | — | 6 | 4 | no | — |
| 86 | C4×D32 | — | 6 | 2 | no | — |
| 87 | #3799 | — | 3 | 4 | no | — |
| 88 | #3799 | — | 6 | 4 | no | — |
| 89 | #3796 | — | 3 | 4 | no | — |
| 90 | #3796 | — | 6 | 4 | no | — |
| 91 | #3795 | — | 3 | 4 | no | — |
| 92 | #3795 | — | 6 | 4 | no | — |
| 93 | C32×Q16 | — | 2 | 1 | no | — |
| 94 | C32×Q16 | — | 2 | 2 | no | — |
| 95 | C32×Q16 | — | 4 | 1 | no | — |
| 96 | C32×Q16 | C2×D3 | 1 | 2 | yes | complemented |
| 97 | C32×Q16 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 98 | #3756 | C2×D3 | 1 | 2 | yes | complemented |
| 99 | #3755 | C2×D3 | 1 | 4 | yes | complemented |
| 100 | #3746 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 101 | #3745 | C2×D3 | 1 | 2 | yes | complemented |
| 102 | C8×C3⋊D3 | C2×D3 | 1 | 1 | yes | characteristic |
| 103 | C8×C3⋊D3 | C2×D3 | 1 | 2 | yes | complemented |
| 104 | C3×#216 | — | 3 | 4 | no | — |
| 105 | C3×#216 | — | 6 | 2 | no | — |
| 106 | C3×#215 | — | 3 | 4 | no | — |
| 107 | C3×#215 | — | 3 | 4 | no | — |
| 108 | C3×#215 | — | 6 | 4 | no | — |
| 109 | C3×Dic12 | — | 3 | 2 | no | — |
| 110 | C3×Dic12 | — | 6 | 1 | no | — |
| 111 | C3×D24 | — | 3 | 2 | no | — |
| 112 | C3×D24 | — | 3 | 2 | no | — |
| 113 | C3×D24 | — | 6 | 2 | no | — |
| 114 | C3×D3×C8 | — | 3 | 2 | no | — |
| 115 | C3×D3×C8 | — | 3 | 2 | no | — |
| 116 | C3×D3×C8 | — | 3 | 2 | no | — |
| 117 | C3×D3×C8 | — | 6 | 1 | no | — |
| 118 | C3×D3×C8 | — | 6 | 2 | no | — |
| 119 | #3717 | — | 3 | 4 | no | — |
| 120 | #3716 | — | 3 | 4 | no | — |
| 121 | #3715 | — | 3 | 4 | no | — |
| 122 | #3714 | — | 3 | 4 | no | — |
| 123 | #3713 | — | 3 | 2 | no | — |
| 124 | #3710 | — | 3 | 1 | no | — |
| 125 | #3710 | — | 3 | 2 | no | — |
| 126 | D3×C3⋊C8 | — | 3 | 2 | no | — |
| 127 | D3×C3⋊C8 | — | 3 | 2 | no | — |
| 128 | D3×C3⋊C8 | — | 3 | 2 | no | — |
| 129 | C2×C3×C3⋊D3 | — | 2 | 4 | no | — |
| 130 | C2×C3×C3⋊D3 | C2×D4 | 1 | 2 | yes | — |
| 131 | C2×C3×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 132 | #1113 | — | 2 | 2 | no | — |
| 133 | #1113 | — | 4 | 4 | no | — |
| 134 | C33×C4 | — | 2 | 2 | no | — |
| 135 | C33×C4 | C24 | 1 | 1 | yes | characteristic |
| 136 | C3×C3⋊Dic3 | — | 2 | 2 | no | — |
| 137 | C3×C3⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 138 | C3×C3⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 139 | D3×#41 | — | 9 | 4 | no | — |
| 140 | C2×#239 | — | 9 | 2 | no | — |
| 141 | C3×#135 | — | 9 | 2 | no | — |
| 142 | C2×C3×Q16 | — | 9 | 1 | no | — |
| 143 | #950 | — | 9 | 4 | no | — |
| 144 | C2×#215 | — | 9 | 2 | no | — |
| 145 | #919 | — | 3 | 2 | no | — |
| 146 | #919 | — | 3 | 2 | no | — |
| 147 | #919 | — | 6 | 2 | no | — |
| 148 | #919 | — | 9 | 2 | no | — |
| 149 | #919 | — | 9 | 4 | no | — |
| 150 | D3×Q16 | — | 3 | 2 | no | — |
| 151 | D3×Q16 | — | 6 | 1 | no | — |
| 152 | #916 | — | 9 | 4 | no | — |
| 153 | D3×SD16 | — | 9 | 4 | no | — |
| 154 | #912 | — | 9 | 2 | no | — |
| 155 | D3×D8 | — | 9 | 2 | no | — |
| 156 | #904 | — | 9 | 2 | no | — |
| 157 | C2×D24 | — | 9 | 1 | no | — |
| 158 | C2×D3×C8 | — | 9 | 1 | no | — |
| 159 | C2×D3×C8 | — | 9 | 2 | no | — |
| 160 | C2×D32 | — | 3 | 2 | no | — |
| 161 | C2×D32 | — | 3 | 1 | no | — |
| 162 | C2×D32 | — | 6 | 4 | no | — |
| 163 | C2×D32 | — | 6 | 2 | no | — |
| 164 | C32×Q8 | — | 2 | 4 | no | — |
| 165 | C32×Q8 | — | 2 | 2 | no | — |
| 166 | C32×Q8 | — | 4 | 2 | no | — |
| 167 | C32×Q8 | C22×D3 | 1 | 2 | yes | — |
| 168 | C32×Q8 | C22×D3 | 1 | 4 | yes | — |
| 169 | C4⋊(C3⋊D3) | — | 2 | 4 | no | — |
| 170 | C4⋊(C3⋊D3) | C22×D3 | 1 | 4 | yes | — |
| 171 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 172 | C4×C3⋊D3 | — | 2 | 4 | no | — |
| 173 | C4×C3⋊D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 174 | C4×C3⋊D3 | C22×D3 | 1 | 2 | yes | — |
| 175 | #634 | — | 2 | 2 | no | — |
| 176 | #634 | C22×D3 | 1 | 2 | yes | — |
| 177 | C3×D12 | — | 3 | 4 | no | — |
| 178 | C3×D12 | — | 3 | 4 | no | — |
| 179 | C3×D12 | — | 6 | 4 | no | — |
| 180 | C3×D12 | — | 6 | 4 | no | — |
| 181 | C3×D12 | — | 6 | 4 | no | — |
| 182 | C3×D12 | — | 12 | 4 | no | — |
| 183 | C3×C4×D3 | — | 3 | 2 | no | — |
| 184 | C3×C4×D3 | — | 3 | 2 | no | — |
| 185 | C3×C4×D3 | — | 3 | 2 | no | — |
| 186 | C3×C4×D3 | — | 6 | 1 | no | — |
| 187 | C3×C4×D3 | — | 6 | 2 | no | — |
| 188 | C3×C4×D3 | — | 6 | 4 | no | — |
| 189 | C3×C4×D3 | — | 6 | 4 | no | — |
| 190 | C3×C4×D3 | — | 6 | 4 | no | — |
| 191 | C3×C4×D3 | — | 12 | 4 | no | — |
| 192 | C3×C4×D3 | — | 12 | 2 | no | — |
| 193 | C3×Dic6 | — | 3 | 4 | no | — |
| 194 | C3×Dic6 | — | 6 | 2 | no | — |
| 195 | C3×Dic6 | — | 6 | 4 | no | — |
| 196 | C3×Dic6 | — | 12 | 2 | no | — |
| 197 | #626 | — | 6 | 4 | no | — |
| 198 | #626 | — | 6 | 4 | no | — |
| 199 | #626 | — | 6 | 4 | no | — |
| 200 | #625 | — | 6 | 4 | no | — |
| 201 | #625 | — | 6 | 2 | no | — |
| 202 | #624 | — | 3 | 2 | no | — |
| 203 | #624 | — | 3 | 1 | no | — |
| 204 | #624 | — | 6 | 4 | no | — |
| 205 | D3×Dic3 | — | 3 | 2 | no | — |
| 206 | D3×Dic3 | — | 3 | 2 | no | — |
| 207 | D3×Dic3 | — | 3 | 2 | no | — |
| 208 | D3×Dic3 | — | 6 | 4 | no | — |
| 209 | D3×Dic3 | — | 6 | 4 | no | — |
| 210 | C32×C8 | — | 2 | 2 | no | — |
| 211 | C32×C8 | — | 2 | 1 | no | — |
| 212 | C32×C8 | — | 4 | 1 | no | — |
| 213 | C32×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 214 | C32×C8 | C22×D3 | 1 | 2 | yes | — |
| 215 | C3⋊(C3⋊C8) | C22×D3 | 1 | 1 | yes | characteristic |
| 216 | C3⋊(C3⋊C8) | C22×D3 | 1 | 2 | yes | — |
| 217 | C3×C3⋊C8 | — | 3 | 2 | no | — |
| 218 | C3×C3⋊C8 | — | 3 | 2 | no | — |
| 219 | C3×C3⋊C8 | — | 3 | 2 | no | — |
| 220 | C3×C3⋊C8 | — | 6 | 2 | no | — |
| 221 | C3×C3⋊C8 | — | 6 | 1 | no | — |
| 222 | C2×#135 | — | 27 | 1 | no | Sylow |
| 223 | C2×C33 | C22×D4 | 1 | 1 | yes | characteristic |
| 224 | C3×C3⋊D3 | — | 2 | 2 | no | — |
| 225 | C3×C3⋊D3 | — | 4 | 4 | no | — |
| 226 | C3×C3⋊D3 | #135 | 1 | 2 | yes | complemented |
| 227 | C3×#41 | — | 9 | 4 | no | — |
| 228 | C2×C3×Q8 | — | 9 | 2 | no | — |
| 229 | #239 | — | 3 | 4 | no | — |
| 230 | #239 | — | 3 | 4 | no | — |
| 231 | #239 | — | 6 | 4 | no | — |
| 232 | #239 | — | 9 | 4 | no | — |
| 233 | #239 | — | 18 | 4 | no | — |
| 234 | D3×Q8 | — | 3 | 4 | no | — |
| 235 | D3×Q8 | — | 6 | 2 | no | — |
| 236 | #237 | — | 9 | 4 | no | — |
| 237 | #237 | — | 18 | 4 | no | — |
| 238 | D3×D4 | — | 9 | 4 | no | — |
| 239 | D3×D4 | — | 18 | 4 | no | — |
| 240 | #235 | — | 9 | 4 | no | — |
| 241 | #235 | — | 18 | 4 | no | — |
| 242 | C2×D12 | — | 9 | 2 | no | — |
| 243 | C2×D12 | — | 18 | 2 | no | — |
| 244 | C2×C4×D3 | — | 9 | 1 | no | — |
| 245 | C2×C4×D3 | — | 9 | 2 | no | — |
| 246 | C2×C4×D3 | — | 18 | 4 | no | — |
| 247 | C2×C4×D3 | — | 18 | 2 | no | — |
| 248 | C3×Q16 | — | 2 | 1 | no | — |
| 249 | C3×Q16 | — | 2 | 2 | no | — |
| 250 | C3×Q16 | — | 4 | 1 | no | — |
| 251 | C3×Q16 | — | 9 | 2 | no | — |
| 252 | C3×Q16 | — | 9 | 1 | no | — |
| 253 | C3×Q16 | D32 | 1 | 2 | yes | complemented |
| 254 | C3×Q16 | D32 | 1 | 1 | yes | characteristic, complemented |
| 255 | C3×SD16 | — | 9 | 4 | no | — |
| 256 | C3×D8 | — | 9 | 2 | no | — |
| 257 | C2×C3×C8 | — | 9 | 1 | no | — |
| 258 | C2×C3×C8 | — | 9 | 2 | no | — |
| 259 | #216 | — | 3 | 4 | no | — |
| 260 | #216 | — | 6 | 2 | no | — |
| 261 | #215 | — | 3 | 4 | no | — |
| 262 | #215 | — | 3 | 4 | no | — |
| 263 | #215 | — | 6 | 4 | no | — |
| 264 | #215 | — | 9 | 4 | no | — |
| 265 | #214 | — | 9 | 4 | no | — |
| 266 | #213 | — | 9 | 4 | no | — |
| 267 | C2×C3⋊C8 | — | 9 | 1 | no | — |
| 268 | C2×C3⋊C8 | — | 9 | 2 | no | — |
| 269 | Dic12 | — | 3 | 2 | no | — |
| 270 | Dic12 | — | 6 | 1 | no | — |
| 271 | D24 | — | 3 | 2 | no | — |
| 272 | D24 | — | 3 | 2 | no | — |
| 273 | D24 | — | 6 | 2 | no | — |
| 274 | D24 | — | 9 | 2 | no | — |
| 275 | #204 | — | 9 | 4 | no | — |
| 276 | D3×C8 | — | 3 | 2 | no | — |
| 277 | D3×C8 | — | 3 | 2 | no | — |
| 278 | D3×C8 | — | 3 | 2 | no | — |
| 279 | D3×C8 | — | 6 | 1 | no | — |
| 280 | D3×C8 | — | 6 | 2 | no | — |
| 281 | D3×C8 | — | 9 | 2 | no | — |
| 282 | D3×C8 | — | 9 | 2 | no | — |
| 283 | D3×C8 | — | 9 | 2 | no | — |
| 284 | C2×C3⋊D3 | — | 2 | 4 | no | — |
| 285 | C2×C3⋊D3 | D3×D4 | 1 | 2 | yes | — |
| 286 | C2×C3⋊D3 | D3×D4 | 1 | 1 | yes | characteristic |
| 287 | C2×C3×D3 | — | 3 | 2 | no | — |
| 288 | C2×C3×D3 | — | 3 | 2 | no | — |
| 289 | C2×C3×D3 | — | 3 | 2 | no | — |
| 290 | C2×C3×D3 | — | 6 | 1 | no | — |
| 291 | C2×C3×D3 | — | 6 | 2 | no | — |
| 292 | C2×C3×D3 | — | 6 | 4 | no | — |
| 293 | C2×C3×D3 | — | 6 | 4 | no | — |
| 294 | C2×C3×D3 | — | 12 | 4 | no | — |
| 295 | D32 | — | 6 | 4 | no | — |
| 296 | D32 | — | 6 | 2 | no | — |
| 297 | D32 | — | 12 | 8 | no | — |
| 298 | D32 | — | 12 | 4 | no | — |
| 299 | C32×C4 | — | 2 | 4 | no | — |
| 300 | C32×C4 | — | 2 | 2 | no | — |
| 301 | C32×C4 | — | 2 | 1 | no | — |
| 302 | C32×C4 | — | 2 | 2 | no | — |
| 303 | C32×C4 | — | 4 | 1 | no | — |
| 304 | C32×C4 | — | 4 | 2 | no | — |
| 305 | C32×C4 | — | 4 | 4 | no | — |
| 306 | C32×C4 | — | 8 | 2 | no | — |
| 307 | C32×C4 | C23×D3 | 1 | 2 | yes | — |
| 308 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 309 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 310 | C3⋊Dic3 | D3×D4 | 1 | 2 | yes | — |
| 311 | C3⋊Dic3 | D3×D4 | 1 | 1 | yes | characteristic |
| 312 | C3×Dic3 | — | 3 | 2 | no | — |
| 313 | C3×Dic3 | — | 3 | 2 | no | — |
| 314 | C3×Dic3 | — | 3 | 2 | no | — |
| 315 | C3×Dic3 | — | 6 | 1 | no | — |
| 316 | C3×Dic3 | — | 6 | 2 | no | — |
| 317 | C3×Dic3 | — | 6 | 4 | no | — |
| 318 | C3×Dic3 | — | 12 | 2 | no | — |
| 319 | C2×#41 | — | 27 | 2 | no | — |
| 320 | #135 | — | 9 | 2 | no | — |
| 321 | #135 | — | 27 | 2 | no | — |
| 322 | #135 | — | 27 | 4 | no | — |
| 323 | C2×Q16 | — | 9 | 1 | no | — |
| 324 | C2×SD16 | — | 27 | 2 | no | — |
| 325 | C2×D8 | — | 27 | 1 | no | — |
| 326 | C22×C8 | — | 27 | 1 | no | — |
| 327 | C33 | C2×#135 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 328 | C22×D3 | — | 9 | 1 | no | — |
| 329 | C22×D3 | — | 9 | 2 | no | — |
| 330 | C22×D3 | — | 18 | 4 | no | — |
| 331 | C22×D3 | — | 18 | 2 | no | — |
| 332 | C3×Q8 | — | 2 | 4 | no | — |
| 333 | C3×Q8 | — | 2 | 2 | no | — |
| 334 | C3×Q8 | — | 4 | 2 | no | — |
| 335 | C3×Q8 | — | 9 | 2 | no | — |
| 336 | C3×Q8 | — | 18 | 2 | no | — |
| 337 | C3×Q8 | C2×D32 | 1 | 2 | yes | — |
| 338 | C3×Q8 | C2×D32 | 1 | 4 | yes | — |
| 339 | C3×D4 | — | 9 | 4 | no | — |
| 340 | C3×D4 | — | 18 | 4 | no | — |
| 341 | C2×C3×C4 | — | 9 | 1 | no | — |
| 342 | C2×C3×C4 | — | 9 | 2 | no | — |
| 343 | C2×C3×C4 | — | 18 | 4 | no | — |
| 344 | C2×C3×C4 | — | 18 | 2 | no | — |
| 345 | #67 | — | 18 | 4 | no | — |
| 346 | #67 | — | 18 | 4 | no | — |
| 347 | #67 | — | 18 | 4 | no | — |
| 348 | C2×Dic3 | — | 9 | 1 | no | — |
| 349 | C2×Dic3 | — | 9 | 2 | no | — |
| 350 | C2×Dic3 | — | 18 | 4 | no | — |
| 351 | D12 | — | 3 | 4 | no | — |
| 352 | D12 | — | 3 | 4 | no | — |
| 353 | D12 | — | 6 | 4 | no | — |
| 354 | D12 | — | 6 | 4 | no | — |
| 355 | D12 | — | 6 | 4 | no | — |
| 356 | D12 | — | 12 | 4 | no | — |
| 357 | D12 | — | 18 | 2 | no | — |
| 358 | D12 | — | 18 | 4 | no | — |
| 359 | C4×D3 | — | 3 | 2 | no | — |
| 360 | C4×D3 | — | 3 | 2 | no | — |
| 361 | C4×D3 | — | 3 | 2 | no | — |
| 362 | C4×D3 | — | 6 | 1 | no | — |
| 363 | C4×D3 | — | 6 | 2 | no | — |
| 364 | C4×D3 | — | 6 | 4 | no | — |
| 365 | C4×D3 | — | 6 | 4 | no | — |
| 366 | C4×D3 | — | 6 | 4 | no | — |
| 367 | C4×D3 | — | 9 | 2 | no | — |
| 368 | C4×D3 | — | 9 | 2 | no | — |
| 369 | C4×D3 | — | 9 | 2 | no | — |
| 370 | C4×D3 | — | 12 | 4 | no | — |
| 371 | C4×D3 | — | 12 | 2 | no | — |
| 372 | C4×D3 | — | 18 | 4 | no | — |
| 373 | C4×D3 | — | 18 | 4 | no | — |
| 374 | Dic6 | — | 3 | 4 | no | — |
| 375 | Dic6 | — | 6 | 2 | no | — |
| 376 | Dic6 | — | 6 | 4 | no | — |
| 377 | Dic6 | — | 12 | 2 | no | — |
| 378 | C3×C8 | — | 2 | 2 | no | — |
| 379 | C3×C8 | — | 2 | 1 | no | — |
| 380 | C3×C8 | — | 4 | 1 | no | — |
| 381 | C3×C8 | — | 9 | 2 | no | — |
| 382 | C3×C8 | — | 9 | 1 | no | — |
| 383 | C3×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 384 | C3×C8 | C2×D32 | 1 | 2 | yes | — |
| 385 | C3⋊C8 | — | 3 | 2 | no | — |
| 386 | C3⋊C8 | — | 3 | 2 | no | — |
| 387 | C3⋊C8 | — | 3 | 2 | no | — |
| 388 | C3⋊C8 | — | 6 | 2 | no | — |
| 389 | C3⋊C8 | — | 6 | 1 | no | — |
| 390 | C2×C32 | — | 2 | 1 | no | — |
| 391 | C2×C32 | — | 2 | 2 | no | — |
| 392 | C2×C32 | — | 4 | 1 | no | — |
| 393 | C2×C32 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 394 | C2×C32 | C2×D3×D4 | 1 | 2 | yes | — |
| 395 | C3⋊D3 | — | 2 | 2 | no | — |
| 396 | C3⋊D3 | — | 4 | 4 | no | — |
| 397 | C3⋊D3 | #919 | 1 | 2 | yes | complemented |
| 398 | C3×D3 | — | 3 | 4 | no | — |
| 399 | C3×D3 | — | 6 | 2 | no | — |
| 400 | C3×D3 | — | 6 | 2 | no | — |
| 401 | C3×D3 | — | 6 | 2 | no | — |
| 402 | C3×D3 | — | 12 | 2 | no | — |
| 403 | C3×D3 | — | 12 | 4 | no | — |
| 404 | C3×D3 | — | 12 | 4 | no | — |
| 405 | C3×D3 | — | 24 | 4 | no | — |
| 406 | #41 | — | 9 | 4 | no | — |
| 407 | #41 | — | 27 | 4 | no | — |
| 408 | #41 | — | 54 | 4 | no | — |
| 409 | C2×Q8 | — | 9 | 2 | no | — |
| 410 | C2×D4 | — | 27 | 2 | no | — |
| 411 | C2×D4 | — | 54 | 2 | no | — |
| 412 | C22×C4 | — | 27 | 1 | no | — |
| 413 | C22×C4 | — | 54 | 2 | no | — |
| 414 | Q16 | — | 9 | 2 | no | — |
| 415 | Q16 | — | 9 | 1 | no | — |
| 416 | Q16 | #1113 | 1 | 1 | yes | characteristic, complemented |
| 417 | SD16 | — | 9 | 4 | no | — |
| 418 | SD16 | — | 27 | 4 | no | — |
| 419 | D8 | — | 9 | 2 | no | — |
| 420 | D8 | — | 27 | 2 | no | — |
| 421 | C2×C8 | — | 9 | 1 | no | — |
| 422 | C2×C8 | — | 9 | 2 | no | — |
| 423 | C2×C8 | — | 27 | 1 | no | — |
| 424 | C2×C8 | — | 27 | 2 | no | — |
| 425 | C22×C3 | — | 9 | 1 | no | — |
| 426 | C22×C3 | — | 9 | 2 | no | — |
| 427 | C22×C3 | — | 18 | 4 | no | — |
| 428 | C2×D3 | — | 3 | 2 | no | — |
| 429 | C2×D3 | — | 3 | 2 | no | — |
| 430 | C2×D3 | — | 3 | 2 | no | — |
| 431 | C2×D3 | — | 6 | 1 | no | — |
| 432 | C2×D3 | — | 6 | 2 | no | — |
| 433 | C2×D3 | — | 6 | 4 | no | — |
| 434 | C2×D3 | — | 6 | 4 | no | — |
| 435 | C2×D3 | — | 12 | 4 | no | — |
| 436 | C2×D3 | — | 18 | 4 | no | — |
| 437 | C2×D3 | — | 18 | 2 | no | — |
| 438 | C2×D3 | — | 36 | 8 | no | — |
| 439 | C2×D3 | — | 36 | 4 | no | — |
| 440 | C3×C4 | — | 2 | 4 | no | — |
| 441 | C3×C4 | — | 2 | 2 | no | — |
| 442 | C3×C4 | — | 2 | 1 | no | — |
| 443 | C3×C4 | — | 2 | 2 | no | — |
| 444 | C3×C4 | — | 4 | 2 | no | — |
| 445 | C3×C4 | — | 4 | 4 | no | — |
| 446 | C3×C4 | — | 4 | 1 | no | — |
| 447 | C3×C4 | — | 8 | 2 | no | — |
| 448 | C3×C4 | — | 9 | 2 | no | — |
| 449 | C3×C4 | — | 9 | 1 | no | — |
| 450 | C3×C4 | — | 18 | 2 | no | — |
| 451 | C3×C4 | C22×D32 | 1 | 2 | yes | — |
| 452 | C3×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 453 | Dic3 | — | 3 | 2 | no | — |
| 454 | Dic3 | — | 3 | 2 | no | — |
| 455 | Dic3 | — | 3 | 2 | no | — |
| 456 | Dic3 | — | 6 | 1 | no | — |
| 457 | Dic3 | — | 6 | 2 | no | — |
| 458 | Dic3 | — | 6 | 4 | no | — |
| 459 | Dic3 | — | 12 | 2 | no | — |
| 460 | C32 | — | 2 | 2 | no | — |
| 461 | C32 | — | 2 | 1 | no | — |
| 462 | C32 | — | 4 | 1 | no | — |
| 463 | C32 | C2×#919 | 1 | 1 | yes | characteristic, complemented |
| 464 | C32 | D3×#135 | 1 | 2 | yes | complemented |
| 465 | C23 | — | 27 | 1 | no | — |
| 466 | C23 | — | 54 | 2 | no | — |
| 467 | Q8 | — | 9 | 2 | no | — |
| 468 | Q8 | — | 18 | 2 | no | — |
| 469 | Q8 | C2×#1113 | 1 | 2 | yes | — |
| 470 | D4 | — | 9 | 4 | no | — |
| 471 | D4 | — | 18 | 4 | no | — |
| 472 | D4 | — | 54 | 2 | no | — |
| 473 | D4 | — | 54 | 4 | no | — |
| 474 | C2×C4 | — | 9 | 1 | no | — |
| 475 | C2×C4 | — | 9 | 2 | no | — |
| 476 | C2×C4 | — | 18 | 4 | no | — |
| 477 | C2×C4 | — | 18 | 2 | no | — |
| 478 | C2×C4 | — | 27 | 1 | no | — |
| 479 | C2×C4 | — | 27 | 2 | no | — |
| 480 | C2×C4 | — | 54 | 4 | no | — |
| 481 | C8 | — | 9 | 1 | no | — |
| 482 | C8 | — | 9 | 2 | no | — |
| 483 | C8 | C2×#1113 | 1 | 1 | yes | characteristic |
| 484 | C2×C3 | — | 2 | 1 | no | — |
| 485 | C2×C3 | — | 2 | 2 | no | — |
| 486 | C2×C3 | — | 4 | 1 | no | — |
| 487 | C2×C3 | — | 9 | 2 | no | — |
| 488 | C2×C3 | — | 18 | 2 | no | — |
| 489 | C2×C3 | — | 36 | 4 | no | — |
| 490 | C2×C3 | D32×D4 | 1 | 2 | yes | — |
| 491 | C2×C3 | D32×D4 | 1 | 1 | yes | characteristic |
| 492 | D3 | — | 3 | 4 | no | — |
| 493 | D3 | — | 6 | 2 | no | — |
| 494 | D3 | — | 6 | 2 | no | — |
| 495 | D3 | — | 6 | 2 | no | — |
| 496 | D3 | — | 12 | 2 | no | — |
| 497 | D3 | — | 12 | 4 | no | — |
| 498 | D3 | — | 12 | 4 | no | — |
| 499 | D3 | — | 24 | 4 | no | — |
| 500 | C22 | — | 9 | 1 | no | — |
| 501 | C22 | — | 9 | 2 | no | — |
| 502 | C22 | — | 18 | 4 | no | — |
| 503 | C22 | — | 54 | 2 | no | — |
| 504 | C22 | — | 108 | 4 | no | — |
| 505 | C4 | — | 2 | 2 | no | — |
| 506 | C4 | — | 9 | 2 | no | — |
| 507 | C4 | — | 9 | 1 | no | — |
| 508 | C4 | — | 18 | 2 | no | — |
| 509 | C4 | C22×#1113 | 1 | 1 | yes | characteristic |
| 510 | C3 | — | 2 | 1 | no | — |
| 511 | C3 | — | 2 | 2 | no | — |
| 512 | C3 | — | 4 | 1 | no | — |
| 513 | C3 | D3×#919 | 1 | 2 | yes | complemented |
| 514 | C3 | #10594764 | 1 | 1 | yes | characteristic, complemented |
| 515 | C2 | — | 9 | 2 | no | — |
| 516 | C2 | — | 18 | 2 | no | — |
| 517 | C2 | — | 36 | 4 | no | — |
| 518 | C2 | D4×#1113 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×#1113 |
| commutator, cosocle | C33×C4 | C24 |
| Frattini | C4 | C22×#1113 |
| Fitting | C33×Q16 | C22 |
| socle | C2×C33 | C22×D4 |
| hypercenter | Q16 | #1113 |
| hypocenter | C33 | C2×#135 |
| LCS | G ▷ C33×C4 ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ Q16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11724626 | C2 | semidirect |
| 2. C3×#64128 | C2 | semidirect |
| 3. C3×Q16×C3⋊D3 | C2 | semidirect |
| 4. #11723713 | C2 | semidirect |
| 5. #11723708 | C2 | semidirect |
| 6. #11723654 | C2 | semidirect |
| 7. #11723647 | C2 | semidirect |
| 8. C8×#1113 | C2 | semidirect |
| 11. C3×#3832 | C22 | semidirect |
| 18. #89041 | C22 | semidirect |
| 19. C33×Q16 | C22 | semidirect |
| 20. C3×#3756 | C22 | semidirect |
| 21. C3×#3755 | C22 | semidirect |
| 22. C3×#3746 | C22 | semidirect |
| 23. C3×#3745 | C22 | semidirect |
| 25. C3×C8×C3⋊D3 | C22 | semidirect |
| 26. #88811 | C22 | semidirect |
| 27. #88810 | C22 | semidirect |
| 29. #88808 | C22 | semidirect |
| 32. #64128 | D3 | semidirect |
| 33. Q16×C3⋊D3 | D3 | semidirect |
| 72. #3832 | C2×D3 | semidirect |
| 96. C32×Q16 | C2×D3 | semidirect |
| 97. C32×Q16 | C2×D3 | semidirect |
| 98. #3756 | C2×D3 | semidirect |
| 99. #3755 | C2×D3 | semidirect |
| 100. #3746 | C2×D3 | semidirect |
| 101. #3745 | C2×D3 | semidirect |
| 103. C8×C3⋊D3 | C2×D3 | semidirect |
| 226. C3×C3⋊D3 | #135 | semidirect |
| 253. C3×Q16 | D32 | semidirect |
| 254. C3×Q16 | D32 | semidirect |
| 327. C33 | C2×#135 | semidirect |
| 397. C3⋊D3 | #919 | semidirect |
| 416. Q16 | #1113 | semidirect |
| 463. C32 | C2×#919 | semidirect |
| 464. C32 | D3×#135 | semidirect |
| 513. C3 | D3×#919 | semidirect |
| 514. C3 | #10594764 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724626 | 2 |
| C3×#64128 | 2 |
| C3×Q16×C3⋊D3 | 2 |
| #11723713 | 2 |
| #11723708 | 2 |
| #11723654 | 2 |
| #11723647 | 2 |
| C8×#1113 | 2 |
| #10594764 | 3 |
| D3×#919 | 3 |