Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1238 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 1238 conjugacy classes of subgroups — too many to draw. Only its 167 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 | #11724627 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11724620 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#64125 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #11723711 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #11723703 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #11723651 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11723646 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #10594757 | — | 3 | 3 | no | maximal |
| 9 | C3×#3832 | C22 | 1 | 3 | yes | — |
| 10 | C3×#3830 | C22 | 1 | 3 | yes | complemented |
| 11 | C2×#6296 | — | 2 | 1 | no | — |
| 12 | #89046 | — | 2 | 3 | no | — |
| 13 | C4⋊#1113 | — | 2 | 3 | no | — |
| 14 | C4⋊#1113 | C22 | 1 | 3 | yes | — |
| 15 | #89042 | — | 2 | 1 | no | — |
| 16 | #89042 | C22 | 1 | 1 | yes | characteristic |
| 17 | #89040 | C22 | 1 | 3 | yes | complemented |
| 18 | C33×SD16 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | C3×#3756 | C22 | 1 | 3 | yes | complemented |
| 20 | C3×#3753 | C22 | 1 | 3 | yes | complemented |
| 21 | C3×#3744 | C22 | 1 | 3 | yes | complemented |
| 22 | C3×C8×C3⋊D3 | C22 | 1 | 3 | yes | complemented |
| 23 | #88811 | C22 | 1 | 6 | yes | complemented |
| 24 | #88809 | C22 | 1 | 3 | yes | complemented |
| 25 | #64320 | — | 3 | 3 | no | — |
| 26 | #64309 | — | 3 | 3 | no | — |
| 27 | #64125 | D3 | 1 | 3 | yes | complemented |
| 28 | C3×#916 | — | 3 | 6 | no | — |
| 29 | C3×#916 | — | 6 | 3 | no | — |
| 30 | #63945 | — | 3 | 3 | no | — |
| 31 | #63943 | — | 3 | 6 | no | — |
| 32 | #63927 | — | 3 | 3 | no | — |
| 33 | #63925 | — | 3 | 6 | no | — |
| 34 | #63803 | — | 3 | 3 | no | — |
| 35 | #63796 | — | 3 | 3 | no | — |
| 36 | D3×#204 | — | 3 | 6 | no | — |
| 37 | C2×#1113 | — | 2 | 3 | no | — |
| 38 | C33×Q8 | C23 | 1 | 1 | yes | characteristic |
| 39 | C33×D4 | C23 | 1 | 1 | yes | characteristic |
| 40 | C3×#638 | — | 2 | 3 | no | — |
| 41 | C2×C3×C3⋊Dic3 | — | 2 | 3 | no | — |
| 42 | C3×C4⋊(C3⋊D3) | — | 2 | 3 | no | — |
| 43 | C3×C4⋊(C3⋊D3) | C23 | 1 | 3 | yes | — |
| 44 | C3×C4×C3⋊D3 | — | 2 | 3 | no | — |
| 45 | C3×C4×C3⋊D3 | C23 | 1 | 3 | yes | — |
| 46 | C3×#634 | C23 | 1 | 3 | yes | — |
| 47 | #6296 | — | 2 | 3 | no | — |
| 48 | #6296 | D4 | 1 | 1 | yes | characteristic |
| 49 | #6295 | — | 2 | 3 | no | — |
| 50 | #6295 | D4 | 1 | 3 | yes | — |
| 51 | #6294 | — | 2 | 3 | no | — |
| 52 | C33×C8 | C23 | 1 | 1 | yes | characteristic |
| 53 | C3×C3⋊(C3⋊C8) | C23 | 1 | 3 | yes | — |
| 54 | #5770 | — | 9 | 3 | no | — |
| 55 | #3832 | C2×D3 | 1 | 3 | yes | — |
| 56 | #3830 | C2×D3 | 1 | 3 | yes | complemented |
| 57 | C3×#239 | — | 3 | 6 | no | — |
| 58 | C3×#239 | — | 6 | 3 | no | — |
| 59 | C3×#237 | — | 3 | 6 | no | — |
| 60 | C3×#237 | — | 6 | 3 | no | — |
| 61 | C2×#627 | — | 6 | 3 | no | — |
| 62 | #3805 | — | 6 | 3 | no | — |
| 63 | #3804 | — | 6 | 6 | no | — |
| 64 | #3802 | — | 3 | 3 | no | — |
| 65 | #3802 | — | 6 | 3 | no | — |
| 66 | D3×D12 | — | 3 | 6 | no | — |
| 67 | D3×D12 | — | 6 | 6 | no | — |
| 68 | #3798 | — | 3 | 3 | no | — |
| 69 | #3798 | — | 6 | 3 | no | — |
| 70 | #3797 | — | 3 | 3 | no | — |
| 71 | D3×Dic6 | — | 3 | 6 | no | — |
| 72 | C32×SD16 | — | 2 | 3 | no | — |
| 73 | C32×SD16 | — | 4 | 1 | no | — |
| 74 | C32×SD16 | C2×D3 | 1 | 3 | yes | complemented |
| 75 | #3756 | C2×D3 | 1 | 3 | yes | complemented |
| 76 | #3753 | C2×D3 | 1 | 3 | yes | complemented |
| 77 | #3744 | C2×D3 | 1 | 3 | yes | complemented |
| 78 | C8×C3⋊D3 | C2×D3 | 1 | 3 | yes | complemented |
| 79 | C3×#216 | — | 3 | 6 | no | — |
| 80 | C3×#216 | — | 6 | 3 | no | — |
| 81 | C3×#213 | — | 3 | 6 | no | — |
| 82 | C3×#213 | — | 6 | 3 | no | — |
| 83 | C3×#204 | — | 3 | 6 | no | — |
| 84 | C3×#204 | — | 6 | 3 | no | — |
| 85 | C3×D3×C8 | — | 3 | 6 | no | — |
| 86 | C3×D3×C8 | — | 6 | 3 | no | — |
| 87 | #3717 | — | 3 | 6 | no | — |
| 88 | #3716 | — | 3 | 6 | no | — |
| 89 | #3715 | — | 3 | 6 | no | — |
| 90 | #3712 | — | 3 | 3 | no | — |
| 91 | #3711 | — | 3 | 6 | no | — |
| 92 | C22×C33 | — | 2 | 1 | no | — |
| 93 | C2×C3×C3⋊D3 | — | 2 | 3 | no | — |
| 94 | C2×C3×C3⋊D3 | C2×D4 | 1 | 3 | yes | — |
| 95 | #1113 | — | 8 | 3 | no | — |
| 96 | C33×C4 | — | 2 | 1 | no | — |
| 97 | C33×C4 | C24 | 1 | 1 | yes | characteristic |
| 98 | C3×C3⋊Dic3 | — | 2 | 3 | no | — |
| 99 | C3×C3⋊Dic3 | C2×D4 | 1 | 3 | yes | — |
| 100 | #1010 | — | 9 | 3 | no | — |
| 101 | #1009 | — | 9 | 3 | no | — |
| 102 | C3×#135 | — | 9 | 3 | no | — |
| 103 | #951 | — | 9 | 3 | no | — |
| 104 | #949 | — | 9 | 3 | no | — |
| 105 | #918 | — | 9 | 6 | no | — |
| 106 | #916 | — | 3 | 6 | no | — |
| 107 | #916 | — | 6 | 3 | no | — |
| 108 | D3×SD16 | — | 9 | 6 | no | — |
| 109 | #911 | — | 9 | 6 | no | — |
| 110 | C2×#204 | — | 9 | 3 | no | — |
| 111 | #901 | — | 9 | 3 | no | — |
| 112 | C2×D32 | — | 6 | 6 | no | — |
| 113 | C2×D32 | — | 6 | 3 | no | — |
| 114 | C32×Q8 | — | 2 | 3 | no | — |
| 115 | C32×Q8 | — | 4 | 1 | no | — |
| 116 | C32×Q8 | C22×D3 | 1 | 3 | yes | — |
| 117 | C32×D4 | — | 2 | 3 | no | — |
| 118 | C32×D4 | — | 4 | 1 | no | — |
| 119 | C32×D4 | C22×D3 | 1 | 3 | yes | — |
| 120 | #638 | — | 2 | 3 | no | — |
| 121 | C2×C3⋊Dic3 | — | 2 | 3 | no | — |
| 122 | C4⋊(C3⋊D3) | — | 2 | 3 | no | — |
| 123 | C4⋊(C3⋊D3) | C22×D3 | 1 | 3 | yes | — |
| 124 | C4×C3⋊D3 | — | 2 | 3 | no | — |
| 125 | C4×C3⋊D3 | C22×D3 | 1 | 3 | yes | — |
| 126 | #634 | C22×D3 | 1 | 3 | yes | — |
| 127 | C3×#67 | — | 6 | 6 | no | — |
| 128 | C3×#67 | — | 12 | 3 | no | — |
| 129 | C2×C3×Dic3 | — | 6 | 6 | no | — |
| 130 | C2×C3×Dic3 | — | 12 | 3 | no | — |
| 131 | C3×D12 | — | 3 | 6 | no | — |
| 132 | C3×D12 | — | 6 | 3 | no | — |
| 133 | C3×D12 | — | 6 | 6 | no | — |
| 134 | C3×D12 | — | 12 | 3 | no | — |
| 135 | C3×C4×D3 | — | 3 | 6 | no | — |
| 136 | C3×C4×D3 | — | 6 | 3 | no | — |
| 137 | C3×C4×D3 | — | 6 | 6 | no | — |
| 138 | C3×C4×D3 | — | 12 | 3 | no | — |
| 139 | C3×Dic6 | — | 3 | 6 | no | — |
| 140 | C3×Dic6 | — | 6 | 3 | no | — |
| 141 | #627 | — | 3 | 3 | no | — |
| 142 | #627 | — | 6 | 6 | no | — |
| 143 | #627 | — | 6 | 3 | no | — |
| 144 | #626 | — | 3 | 6 | no | — |
| 145 | #626 | — | 6 | 6 | no | — |
| 146 | #625 | — | 3 | 3 | no | — |
| 147 | #625 | — | 6 | 3 | no | — |
| 148 | #624 | — | 6 | 3 | no | — |
| 149 | D3×Dic3 | — | 6 | 6 | no | — |
| 150 | C32×C8 | — | 2 | 3 | no | — |
| 151 | C32×C8 | — | 4 | 1 | no | — |
| 152 | C32×C8 | C22×D3 | 1 | 3 | yes | — |
| 153 | C3⋊(C3⋊C8) | C22×D3 | 1 | 3 | yes | — |
| 154 | C3×C3⋊C8 | — | 3 | 6 | no | — |
| 155 | C3×C3⋊C8 | — | 6 | 3 | no | — |
| 156 | #577 | — | 27 | 1 | no | Sylow |
| 157 | C2×C33 | — | 4 | 1 | no | — |
| 158 | C2×C33 | C22×D4 | 1 | 1 | yes | characteristic |
| 159 | C3×C3⋊D3 | — | 2 | 3 | no | — |
| 160 | C3×C3⋊D3 | — | 4 | 3 | no | — |
| 161 | C3×#41 | — | 9 | 3 | no | — |
| 162 | C3×#41 | — | 9 | 3 | no | — |
| 163 | #239 | — | 3 | 6 | no | — |
| 164 | #239 | — | 6 | 3 | no | — |
| 165 | D3×Q8 | — | 9 | 6 | no | — |
| 166 | #237 | — | 3 | 6 | no | — |
| 167 | #237 | — | 6 | 3 | no | — |
| 168 | #237 | — | 18 | 6 | no | — |
| 169 | D3×D4 | — | 9 | 6 | no | — |
| 170 | D3×D4 | — | 18 | 6 | no | — |
| 171 | #235 | — | 9 | 3 | no | — |
| 172 | #235 | — | 18 | 3 | no | — |
| 173 | #235 | — | 18 | 3 | no | — |
| 174 | C2×D12 | — | 9 | 3 | no | — |
| 175 | C2×D12 | — | 18 | 3 | no | — |
| 176 | C2×Dic6 | — | 9 | 3 | no | — |
| 177 | C2×Dic6 | — | 18 | 3 | no | — |
| 178 | C3×Q16 | — | 9 | 3 | no | — |
| 179 | C3×SD16 | — | 2 | 3 | no | — |
| 180 | C3×SD16 | — | 4 | 1 | no | — |
| 181 | C3×SD16 | — | 9 | 3 | no | — |
| 182 | C3×SD16 | D32 | 1 | 3 | yes | complemented |
| 183 | C3×D8 | — | 9 | 3 | no | — |
| 184 | C2×C3×C8 | — | 9 | 3 | no | — |
| 185 | #216 | — | 3 | 6 | no | — |
| 186 | #216 | — | 6 | 3 | no | — |
| 187 | #215 | — | 9 | 6 | no | — |
| 188 | #214 | — | 9 | 6 | no | — |
| 189 | #213 | — | 3 | 6 | no | — |
| 190 | #213 | — | 6 | 3 | no | — |
| 191 | #208 | — | 9 | 3 | no | — |
| 192 | #204 | — | 3 | 6 | no | — |
| 193 | #204 | — | 6 | 3 | no | — |
| 194 | #204 | — | 9 | 6 | no | — |
| 195 | ΓL(1,𝔽25) | — | 9 | 6 | no | — |
| 196 | D3×C8 | — | 3 | 6 | no | — |
| 197 | D3×C8 | — | 6 | 3 | no | — |
| 198 | C22×C32 | — | 2 | 3 | no | — |
| 199 | C22×C32 | — | 4 | 3 | no | — |
| 200 | C22×C32 | — | 8 | 1 | no | — |
| 201 | C2×C3⋊D3 | — | 2 | 3 | no | — |
| 202 | C2×C3⋊D3 | D3×D4 | 1 | 3 | yes | — |
| 203 | C2×C3×D3 | — | 3 | 6 | no | — |
| 204 | C2×C3×D3 | — | 6 | 3 | no | — |
| 205 | C2×C3×D3 | — | 6 | 6 | no | — |
| 206 | C2×C3×D3 | — | 12 | 3 | no | — |
| 207 | D32 | — | 24 | 6 | no | — |
| 208 | D32 | — | 24 | 3 | no | — |
| 209 | C32×C4 | — | 2 | 3 | no | — |
| 210 | C32×C4 | — | 2 | 3 | no | — |
| 211 | C32×C4 | — | 4 | 1 | no | — |
| 212 | C32×C4 | — | 4 | 3 | no | — |
| 213 | C32×C4 | — | 8 | 1 | no | — |
| 214 | C32×C4 | C23×D3 | 1 | 3 | yes | — |
| 215 | C3⋊Dic3 | — | 2 | 3 | no | — |
| 216 | C3⋊Dic3 | D3×D4 | 1 | 3 | yes | — |
| 217 | C3×Dic3 | — | 3 | 6 | no | — |
| 218 | C3×Dic3 | — | 6 | 3 | no | — |
| 219 | C3×Dic3 | — | 6 | 6 | no | — |
| 220 | C3×Dic3 | — | 12 | 3 | no | — |
| 221 | 2−1+4 | — | 27 | 1 | no | — |
| 222 | H(5,𝔽2) | — | 27 | 1 | no | — |
| 223 | #137 | — | 27 | 3 | no | — |
| 224 | AGL(1,ℤ/8) | — | 27 | 3 | no | — |
| 225 | #135 | — | 9 | 3 | no | — |
| 226 | C2×SD16 | — | 27 | 3 | no | — |
| 227 | #131 | — | 27 | 1 | no | — |
| 228 | C33 | #577 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 229 | C22×D3 | — | 18 | 6 | no | — |
| 230 | C22×D3 | — | 18 | 3 | no | — |
| 231 | C3×Q8 | — | 2 | 3 | no | — |
| 232 | C3×Q8 | — | 4 | 1 | no | — |
| 233 | C3×Q8 | — | 9 | 3 | no | — |
| 234 | C3×Q8 | C2×D32 | 1 | 3 | yes | — |
| 235 | C3×D4 | — | 2 | 3 | no | — |
| 236 | C3×D4 | — | 4 | 1 | no | — |
| 237 | C3×D4 | — | 9 | 3 | no | — |
| 238 | C3×D4 | — | 18 | 3 | no | — |
| 239 | C3×D4 | — | 18 | 3 | no | — |
| 240 | C3×D4 | C2×D32 | 1 | 3 | yes | — |
| 241 | C2×C3×C4 | — | 9 | 3 | no | — |
| 242 | C2×C3×C4 | — | 18 | 3 | no | — |
| 243 | C2×C3×C4 | — | 18 | 3 | no | — |
| 244 | #67 | — | 6 | 6 | no | — |
| 245 | #67 | — | 9 | 6 | no | — |
| 246 | #67 | — | 12 | 3 | no | — |
| 247 | #67 | — | 18 | 6 | no | — |
| 248 | C2×Dic3 | — | 6 | 6 | no | — |
| 249 | C2×Dic3 | — | 12 | 3 | no | — |
| 250 | C2×Dic3 | — | 18 | 3 | no | — |
| 251 | D12 | — | 3 | 6 | no | — |
| 252 | D12 | — | 6 | 3 | no | — |
| 253 | D12 | — | 6 | 6 | no | — |
| 254 | D12 | — | 9 | 3 | no | — |
| 255 | D12 | — | 12 | 3 | no | — |
| 256 | D12 | — | 18 | 3 | no | — |
| 257 | C4×D3 | — | 3 | 6 | no | — |
| 258 | C4×D3 | — | 6 | 3 | no | — |
| 259 | C4×D3 | — | 6 | 6 | no | — |
| 260 | C4×D3 | — | 12 | 3 | no | — |
| 261 | C4×D3 | — | 18 | 6 | no | — |
| 262 | Dic6 | — | 3 | 6 | no | — |
| 263 | Dic6 | — | 6 | 3 | no | — |
| 264 | Dic6 | — | 9 | 3 | no | — |
| 265 | Dic6 | — | 18 | 6 | no | — |
| 266 | Dic6 | — | 18 | 3 | no | — |
| 267 | C3×C8 | — | 2 | 3 | no | — |
| 268 | C3×C8 | — | 4 | 1 | no | — |
| 269 | C3×C8 | — | 9 | 3 | no | — |
| 270 | C3×C8 | C2×D32 | 1 | 3 | yes | — |
| 271 | C3⋊C8 | — | 3 | 6 | no | — |
| 272 | C3⋊C8 | — | 6 | 3 | no | — |
| 273 | C2×C32 | — | 2 | 3 | no | — |
| 274 | C2×C32 | — | 4 | 1 | no | — |
| 275 | C2×C32 | — | 4 | 3 | no | — |
| 276 | C2×C32 | — | 8 | 3 | no | — |
| 277 | C2×C32 | — | 16 | 1 | no | — |
| 278 | C2×C32 | C2×D3×D4 | 1 | 3 | yes | — |
| 279 | C3⋊D3 | — | 2 | 3 | no | — |
| 280 | C3⋊D3 | — | 4 | 3 | no | — |
| 281 | C3×D3 | — | 6 | 6 | no | — |
| 282 | C3×D3 | — | 12 | 3 | no | — |
| 283 | C3×D3 | — | 12 | 6 | no | — |
| 284 | C3×D3 | — | 24 | 3 | no | — |
| 285 | #41 | — | 9 | 3 | no | — |
| 286 | #41 | — | 9 | 3 | no | — |
| 287 | #41 | — | 27 | 1 | no | — |
| 288 | #41 | — | 54 | 1 | no | — |
| 289 | #41 | — | 54 | 3 | no | — |
| 290 | C2×Q8 | — | 27 | 3 | no | — |
| 291 | C2×Q8 | — | 54 | 1 | no | — |
| 292 | C2×D4 | — | 27 | 3 | no | — |
| 293 | C2×D4 | — | 54 | 3 | no | — |
| 294 | Q16 | — | 9 | 3 | no | — |
| 295 | SD16 | — | 9 | 3 | no | — |
| 296 | SD16 | — | 27 | 6 | no | — |
| 297 | SD16 | #1113 | 1 | 1 | yes | characteristic, complemented |
| 298 | D8 | — | 9 | 3 | no | — |
| 299 | M16 | — | 27 | 3 | no | — |
| 300 | C2×C8 | — | 9 | 3 | no | — |
| 301 | C22×C3 | — | 2 | 3 | no | — |
| 302 | C22×C3 | — | 4 | 3 | no | — |
| 303 | C22×C3 | — | 8 | 1 | no | — |
| 304 | C22×C3 | — | 9 | 3 | no | — |
| 305 | C22×C3 | — | 18 | 3 | no | — |
| 306 | C2×D3 | — | 3 | 6 | no | — |
| 307 | C2×D3 | — | 6 | 3 | no | — |
| 308 | C2×D3 | — | 6 | 6 | no | — |
| 309 | C2×D3 | — | 12 | 3 | no | — |
| 310 | C2×D3 | — | 72 | 6 | no | — |
| 311 | C2×D3 | — | 72 | 3 | no | — |
| 312 | C3×C4 | — | 2 | 3 | no | — |
| 313 | C3×C4 | — | 2 | 3 | no | — |
| 314 | C3×C4 | — | 4 | 3 | no | — |
| 315 | C3×C4 | — | 4 | 1 | no | — |
| 316 | C3×C4 | — | 8 | 1 | no | — |
| 317 | C3×C4 | — | 9 | 3 | no | — |
| 318 | C3×C4 | — | 18 | 3 | no | — |
| 319 | C3×C4 | C22×D32 | 1 | 3 | yes | — |
| 320 | Dic3 | — | 3 | 6 | no | — |
| 321 | Dic3 | — | 6 | 3 | no | — |
| 322 | Dic3 | — | 6 | 6 | no | — |
| 323 | Dic3 | — | 12 | 3 | no | — |
| 324 | C32 | — | 2 | 3 | no | — |
| 325 | C32 | — | 4 | 1 | no | — |
| 326 | C32 | #5770 | 1 | 3 | yes | complemented |
| 327 | C23 | — | 54 | 3 | no | — |
| 328 | Q8 | — | 9 | 3 | no | — |
| 329 | Q8 | — | 27 | 1 | no | — |
| 330 | Q8 | — | 54 | 3 | no | — |
| 331 | Q8 | C2×#1113 | 1 | 1 | yes | characteristic |
| 332 | D4 | — | 9 | 3 | no | — |
| 333 | D4 | — | 18 | 3 | no | — |
| 334 | D4 | — | 18 | 3 | no | — |
| 335 | D4 | — | 27 | 3 | no | — |
| 336 | D4 | — | 54 | 3 | no | — |
| 337 | D4 | C2×#1113 | 1 | 1 | yes | characteristic |
| 338 | C2×C4 | — | 9 | 3 | no | — |
| 339 | C2×C4 | — | 18 | 3 | no | — |
| 340 | C2×C4 | — | 18 | 3 | no | — |
| 341 | C2×C4 | — | 54 | 3 | no | — |
| 342 | C8 | — | 9 | 3 | no | — |
| 343 | C8 | C2×#1113 | 1 | 1 | yes | characteristic |
| 344 | C2×C3 | — | 2 | 3 | no | — |
| 345 | C2×C3 | — | 4 | 3 | no | — |
| 346 | C2×C3 | — | 4 | 1 | no | — |
| 347 | C2×C3 | — | 8 | 3 | no | — |
| 348 | C2×C3 | — | 16 | 1 | no | — |
| 349 | C2×C3 | — | 18 | 3 | no | — |
| 350 | C2×C3 | — | 36 | 3 | no | — |
| 351 | C2×C3 | D32×D4 | 1 | 3 | yes | — |
| 352 | D3 | — | 6 | 6 | no | — |
| 353 | D3 | — | 12 | 3 | no | — |
| 354 | D3 | — | 12 | 6 | no | — |
| 355 | D3 | — | 24 | 3 | no | — |
| 356 | C22 | — | 2 | 1 | no | — |
| 357 | C22 | — | 9 | 3 | no | — |
| 358 | C22 | — | 18 | 3 | no | — |
| 359 | C22 | — | 216 | 3 | no | — |
| 360 | C4 | — | 2 | 1 | no | — |
| 361 | C4 | — | 9 | 3 | no | — |
| 362 | C4 | — | 18 | 3 | no | — |
| 363 | C4 | C22×#1113 | 1 | 1 | yes | characteristic |
| 364 | C3 | — | 2 | 3 | no | — |
| 365 | C3 | — | 4 | 1 | no | — |
| 366 | C3 | #10594757 | 1 | 3 | yes | complemented |
| 367 | C2 | — | 4 | 1 | no | — |
| 368 | C2 | — | 18 | 3 | no | — |
| 369 | C2 | — | 36 | 3 | no | — |
| 370 | 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×SD16 | C22 |
| socle | C2×C33 | C22×D4 |
| hypercenter | SD16 | #1113 |
| hypocenter | C33 | #577 |
| LCS | G ▷ C33×C4 ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ SD16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11724627 | C2 | semidirect |
| 2. #11724620 | C2 | semidirect |
| 3. C3×#64125 | C2 | semidirect |
| 4. #11723711 | C2 | semidirect |
| 5. #11723703 | C2 | semidirect |
| 6. #11723651 | C2 | semidirect |
| 7. #11723646 | C2 | semidirect |
| 10. C3×#3830 | C22 | semidirect |
| 17. #89040 | C22 | semidirect |
| 18. C33×SD16 | C22 | semidirect |
| 19. C3×#3756 | C22 | semidirect |
| 20. C3×#3753 | C22 | semidirect |
| 21. C3×#3744 | C22 | semidirect |
| 22. C3×C8×C3⋊D3 | C22 | semidirect |
| 23. #88811 | C22 | semidirect |
| 24. #88809 | C22 | semidirect |
| 27. #64125 | D3 | semidirect |
| 56. #3830 | C2×D3 | semidirect |
| 74. C32×SD16 | C2×D3 | semidirect |
| 75. #3756 | C2×D3 | semidirect |
| 76. #3753 | C2×D3 | semidirect |
| 77. #3744 | C2×D3 | semidirect |
| 78. C8×C3⋊D3 | C2×D3 | semidirect |
| 182. C3×SD16 | D32 | semidirect |
| 228. C33 | #577 | semidirect |
| 297. SD16 | #1113 | semidirect |
| 326. C32 | #5770 | semidirect |
| 366. C3 | #10594757 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724627 | 2 |
| #11724620 | 2 |
| C3×#64125 | 2 |
| #11723711 | 2 |
| #11723703 | 2 |
| #11723651 | 2 |
| #11723646 | 2 |
| #10594757 | 3 |