Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
416 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 49 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 | #11724343 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #11724333 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11723646 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11723645 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#63769 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11722784 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11722783 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10593286 | — | 3 | 1 | no | maximal |
| 9 | C2×#157⋊D3 | — | 2 | 1 | no | — |
| 10 | C4⋊#1113 | C22 | 1 | 1 | yes | characteristic |
| 11 | C4×#1113 | C22 | 1 | 1 | yes | characteristic |
| 12 | #89040 | C22 | 1 | 1 | yes | characteristic |
| 13 | C3×C4⋊#157 | C22 | 1 | 1 | yes | characteristic |
| 14 | C3×C4⋊#157 | C22 | 1 | 1 | yes | characteristic |
| 15 | #88940 | — | 2 | 1 | no | — |
| 16 | #88939 | — | 2 | 1 | no | — |
| 17 | #88939 | — | 2 | 1 | no | — |
| 18 | C3×#3744 | — | 2 | 1 | no | — |
| 19 | C3×#3743 | — | 2 | 1 | no | — |
| 20 | C3×C8×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 21 | #88811 | — | 2 | 1 | no | — |
| 22 | #88809 | — | 2 | 1 | no | — |
| 23 | #88808 | C22 | 1 | 1 | yes | characteristic |
| 24 | #64230 | — | 3 | 1 | no | — |
| 25 | D32⋊Q8 | — | 3 | 1 | no | — |
| 26 | #63796 | — | 3 | 1 | no | — |
| 27 | D3×#204 | — | 6 | 1 | no | — |
| 28 | #63791 | — | 3 | 1 | no | — |
| 29 | D3×ΓL(1,𝔽25) | — | 6 | 1 | no | — |
| 30 | #63769 | D3 | 1 | 1 | yes | characteristic, complemented |
| 31 | #63730 | — | 3 | 1 | no | — |
| 32 | #63729 | — | 3 | 1 | no | — |
| 33 | C2×#1113 | — | 2 | 1 | no | — |
| 34 | C2×#1113 | D4 | 1 | 1 | yes | characteristic |
| 35 | C2×C3×#157 | — | 2 | 1 | no | — |
| 36 | C2×C3×#157 | — | 2 | 1 | no | — |
| 37 | #157⋊D3 | — | 4 | 2 | no | — |
| 38 | C3×C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 39 | C3×C4×C3⋊D3 | — | 2 | 1 | no | — |
| 40 | C3×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 41 | C3×#634 | — | 2 | 1 | no | — |
| 42 | #6296 | — | 2 | 1 | no | — |
| 43 | #6295 | — | 2 | 1 | no | — |
| 44 | #6294 | — | 2 | 1 | no | — |
| 45 | #6294 | — | 2 | 1 | no | — |
| 46 | #6294 | D4 | 1 | 1 | yes | characteristic |
| 47 | C33×C8 | D4 | 1 | 1 | yes | characteristic, complemented |
| 48 | C3×C3⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 49 | C3×C3⋊(C3⋊C8) | D4 | 1 | 1 | yes | characteristic, complemented |
| 50 | #4886 | — | 9 | 1 | no | maximal |
| 51 | C2×GO+(4,𝔽2) | — | 6 | 1 | no | — |
| 52 | #3802 | — | 3 | 1 | no | — |
| 53 | D3×D12 | — | 6 | 1 | no | — |
| 54 | C4×D32 | — | 3 | 1 | no | — |
| 55 | C4×D32 | — | 6 | 1 | no | — |
| 56 | #3797 | — | 3 | 1 | no | — |
| 57 | D3×Dic6 | — | 6 | 1 | no | — |
| 58 | C4⋊#157 | C2×D3 | 1 | 1 | yes | characteristic |
| 59 | C4⋊#157 | C2×D3 | 1 | 1 | yes | characteristic |
| 60 | #3773 | — | 6 | 1 | no | — |
| 61 | D32⋊C4 | — | 6 | 1 | no | — |
| 62 | D32⋊C4 | — | 6 | 1 | no | — |
| 63 | #3744 | — | 2 | 1 | no | — |
| 64 | #3743 | — | 2 | 1 | no | — |
| 65 | C8×C3⋊D3 | C2×D3 | 1 | 1 | yes | characteristic |
| 66 | C3×#204 | — | 6 | 1 | no | — |
| 67 | C3×#204 | — | 6 | 1 | no | — |
| 68 | C3×#204 | — | 12 | 1 | no | — |
| 69 | C3×ΓL(1,𝔽25) | — | 6 | 1 | no | — |
| 70 | C3×ΓL(1,𝔽25) | — | 6 | 1 | no | — |
| 71 | C3×ΓL(1,𝔽25) | — | 12 | 1 | no | — |
| 72 | C3×D3×C8 | — | 6 | 1 | no | — |
| 73 | C3×D3×C8 | — | 6 | 1 | no | — |
| 74 | #3717 | — | 6 | 1 | no | — |
| 75 | #3716 | — | 6 | 1 | no | — |
| 76 | #3715 | — | 6 | 1 | no | — |
| 77 | #3712 | — | 6 | 1 | no | — |
| 78 | #3711 | — | 6 | 1 | no | — |
| 79 | #3711 | — | 6 | 1 | no | — |
| 80 | #3710 | — | 3 | 1 | no | — |
| 81 | D3×C3⋊C8 | — | 6 | 1 | no | — |
| 82 | C2×C3×C3⋊D3 | — | 2 | 1 | no | — |
| 83 | C2×C3×C3⋊D3 | — | 4 | 1 | no | — |
| 84 | C2×C3×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 85 | #1113 | — | 2 | 1 | no | — |
| 86 | #1113 | — | 2 | 1 | no | — |
| 87 | #1113 | — | 4 | 1 | no | — |
| 88 | #1113 | — | 4 | 1 | no | — |
| 89 | C3×#157 | — | 4 | 1 | no | — |
| 90 | C3×#157 | — | 4 | 1 | no | — |
| 91 | C33×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 92 | C3×C3⋊Dic3 | — | 2 | 1 | no | — |
| 93 | C3×C3⋊Dic3 | — | 4 | 1 | no | — |
| 94 | C3×C3⋊Dic3 | #41 | 1 | 1 | yes | characteristic |
| 95 | D3×SD16 | — | 18 | 1 | no | — |
| 96 | D3×M16 | — | 18 | 1 | no | — |
| 97 | C2×#204 | — | 9 | 1 | no | — |
| 98 | C2×ΓL(1,𝔽25) | — | 9 | 1 | no | — |
| 99 | #897 | — | 9 | 1 | no | — |
| 100 | #895 | — | 9 | 1 | no | — |
| 101 | C3×#107 | — | 9 | 1 | no | — |
| 102 | #810 | — | 9 | 1 | no | — |
| 103 | #809 | — | 9 | 1 | no | — |
| 104 | C2×D32 | — | 3 | 1 | no | — |
| 105 | C2×D32 | — | 6 | 1 | no | — |
| 106 | C2×D32 | — | 6 | 1 | no | — |
| 107 | C2×D32 | — | 12 | 1 | no | — |
| 108 | C2×#157 | — | 2 | 1 | no | — |
| 109 | C2×#157 | — | 2 | 1 | no | — |
| 110 | GO+(4,𝔽2) | — | 12 | 2 | no | — |
| 111 | C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 112 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 113 | C4×C3⋊D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 114 | #634 | — | 2 | 1 | no | — |
| 115 | C3×D12 | — | 6 | 1 | no | — |
| 116 | C3×D12 | — | 6 | 1 | no | — |
| 117 | C3×D12 | — | 12 | 1 | no | — |
| 118 | C3×C4×D3 | — | 6 | 1 | no | — |
| 119 | C3×C4×D3 | — | 6 | 1 | no | — |
| 120 | C3×C4×D3 | — | 6 | 1 | no | — |
| 121 | C3×C4×D3 | — | 6 | 1 | no | — |
| 122 | C3×C4×D3 | — | 12 | 1 | no | — |
| 123 | C3×Dic6 | — | 6 | 1 | no | — |
| 124 | C3×Dic6 | — | 6 | 1 | no | — |
| 125 | C3×Dic6 | — | 12 | 1 | no | — |
| 126 | #627 | — | 6 | 1 | no | — |
| 127 | #627 | — | 12 | 1 | no | — |
| 128 | #626 | — | 12 | 1 | no | — |
| 129 | #625 | — | 6 | 1 | no | — |
| 130 | #624 | — | 3 | 1 | no | — |
| 131 | #624 | — | 6 | 1 | no | — |
| 132 | #624 | — | 6 | 1 | no | — |
| 133 | D3×Dic3 | — | 6 | 1 | no | — |
| 134 | D3×Dic3 | — | 6 | 1 | no | — |
| 135 | D3×Dic3 | — | 6 | 1 | no | — |
| 136 | D3×Dic3 | — | 12 | 1 | no | — |
| 137 | C32×C8 | — | 2 | 1 | no | — |
| 138 | C32×C8 | — | 2 | 1 | no | — |
| 139 | C32×C8 | — | 4 | 1 | no | — |
| 140 | C32×C8 | — | 4 | 1 | no | — |
| 141 | C32×C8 | D12 | 1 | 1 | yes | characteristic, complemented |
| 142 | C3⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 143 | C3⋊(C3⋊C8) | D12 | 1 | 1 | yes | characteristic, complemented |
| 144 | C3×C3⋊C8 | — | 6 | 1 | no | — |
| 145 | C3×C3⋊C8 | — | 6 | 1 | no | — |
| 146 | C3×C3⋊C8 | — | 6 | 1 | no | — |
| 147 | C3×C3⋊C8 | — | 6 | 1 | no | — |
| 148 | C3×C3⋊C8 | — | 12 | 1 | no | — |
| 149 | #468 | — | 27 | 1 | no | Sylow |
| 150 | C2×C33 | #121 | 1 | 1 | yes | characteristic |
| 151 | C3×C3⋊D3 | — | 4 | 1 | no | — |
| 152 | C3×C3⋊D3 | — | 8 | 1 | no | — |
| 153 | C3×C3⋊D3 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 154 | C3×C3⋊D3 | #137 | 1 | 1 | yes | characteristic |
| 155 | D3×Q8 | — | 18 | 1 | no | — |
| 156 | D3×D4 | — | 18 | 1 | no | — |
| 157 | C2×D12 | — | 9 | 1 | no | — |
| 158 | C2×D12 | — | 18 | 1 | no | — |
| 159 | C2×C4×D3 | — | 9 | 1 | no | — |
| 160 | C2×C4×D3 | — | 18 | 1 | no | — |
| 161 | C2×Dic6 | — | 9 | 1 | no | — |
| 162 | C3×SD16 | — | 18 | 1 | no | — |
| 163 | C3×M16 | — | 18 | 1 | no | — |
| 164 | C2×C3×C8 | — | 9 | 1 | no | — |
| 165 | C3×C4⋊C4 | — | 9 | 1 | no | — |
| 166 | C3×C4⋊C4 | — | 9 | 1 | no | — |
| 167 | #215 | — | 18 | 1 | no | — |
| 168 | #214 | — | 18 | 1 | no | — |
| 169 | (C2×D3)⋊C4 | — | 18 | 1 | no | — |
| 170 | (C2×D3)⋊C4 | — | 18 | 1 | no | — |
| 171 | C4⋊Dic3 | — | 18 | 1 | no | — |
| 172 | #208 | — | 18 | 1 | no | — |
| 173 | C2×C3⋊C8 | — | 9 | 1 | no | — |
| 174 | #204 | — | 6 | 1 | no | — |
| 175 | #204 | — | 6 | 1 | no | — |
| 176 | #204 | — | 12 | 1 | no | — |
| 177 | #204 | — | 18 | 1 | no | — |
| 178 | ΓL(1,𝔽25) | — | 6 | 1 | no | — |
| 179 | ΓL(1,𝔽25) | — | 6 | 1 | no | — |
| 180 | ΓL(1,𝔽25) | — | 12 | 1 | no | — |
| 181 | ΓL(1,𝔽25) | — | 18 | 1 | no | — |
| 182 | ΓL(1,𝔽25) | — | 18 | 1 | no | — |
| 183 | D3×C8 | — | 6 | 1 | no | — |
| 184 | D3×C8 | — | 6 | 1 | no | — |
| 185 | D3×C8 | — | 18 | 1 | no | — |
| 186 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 187 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 188 | C2×C3⋊D3 | D3×D4 | 1 | 1 | yes | characteristic |
| 189 | C2×C3×D3 | — | 6 | 1 | no | — |
| 190 | C2×C3×D3 | — | 6 | 1 | no | — |
| 191 | C2×C3×D3 | — | 6 | 1 | no | — |
| 192 | C2×C3×D3 | — | 6 | 1 | no | — |
| 193 | C2×C3×D3 | — | 12 | 1 | no | — |
| 194 | C2×C3×D3 | — | 12 | 1 | no | — |
| 195 | C2×C3×D3 | — | 12 | 1 | no | — |
| 196 | C2×C3×D3 | — | 24 | 1 | no | — |
| 197 | D32 | — | 6 | 1 | no | — |
| 198 | D32 | — | 6 | 1 | no | — |
| 199 | D32 | — | 12 | 1 | no | — |
| 200 | D32 | — | 12 | 1 | no | — |
| 201 | D32 | — | 12 | 1 | no | — |
| 202 | D32 | — | 12 | 1 | no | — |
| 203 | D32 | — | 24 | 1 | no | — |
| 204 | D32 | — | 24 | 1 | no | — |
| 205 | #157 | — | 4 | 1 | no | — |
| 206 | #157 | — | 4 | 1 | no | — |
| 207 | C32×C4 | — | 2 | 1 | no | — |
| 208 | C32×C4 | — | 2 | 1 | no | — |
| 209 | C32×C4 | — | 4 | 1 | no | — |
| 210 | C32×C4 | — | 4 | 1 | no | — |
| 211 | C32×C4 | C2×D12 | 1 | 1 | yes | characteristic |
| 212 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 213 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 214 | C3⋊Dic3 | #239 | 1 | 1 | yes | characteristic |
| 215 | C3×Dic3 | — | 6 | 1 | no | — |
| 216 | C3×Dic3 | — | 6 | 1 | no | — |
| 217 | C3×Dic3 | — | 6 | 1 | no | — |
| 218 | C3×Dic3 | — | 6 | 1 | no | — |
| 219 | C3×Dic3 | — | 12 | 1 | no | — |
| 220 | C3×Dic3 | — | 12 | 1 | no | — |
| 221 | C3×Dic3 | — | 12 | 1 | no | — |
| 222 | C3×Dic3 | — | 24 | 1 | no | — |
| 223 | C2×SD16 | — | 27 | 1 | no | — |
| 224 | C2×M16 | — | 27 | 1 | no | — |
| 225 | C22⋊Q8 | — | 27 | 1 | no | — |
| 226 | #121 | — | 27 | 1 | no | — |
| 227 | #107 | — | 9 | 1 | no | — |
| 228 | #103 | — | 27 | 1 | no | — |
| 229 | #102 | — | 27 | 1 | no | — |
| 230 | C33 | #468 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 231 | C22×D3 | — | 9 | 1 | no | — |
| 232 | C22×D3 | — | 18 | 1 | no | — |
| 233 | C22×D3 | — | 18 | 1 | no | — |
| 234 | C22×D3 | — | 36 | 1 | no | — |
| 235 | C3×Q8 | — | 18 | 1 | no | — |
| 236 | C3×D4 | — | 18 | 1 | no | — |
| 237 | C2×C3×C4 | — | 9 | 1 | no | — |
| 238 | C2×C3×C4 | — | 18 | 1 | no | — |
| 239 | C2×C3×C4 | — | 18 | 1 | no | — |
| 240 | C2×C3×C4 | — | 18 | 1 | no | — |
| 241 | #67 | — | 36 | 1 | no | — |
| 242 | C2×Dic3 | — | 9 | 1 | no | — |
| 243 | C2×Dic3 | — | 18 | 1 | no | — |
| 244 | C2×Dic3 | — | 18 | 1 | no | — |
| 245 | D12 | — | 6 | 1 | no | — |
| 246 | D12 | — | 6 | 1 | no | — |
| 247 | D12 | — | 12 | 1 | no | — |
| 248 | D12 | — | 18 | 1 | no | — |
| 249 | D12 | — | 36 | 2 | no | — |
| 250 | C4×D3 | — | 6 | 1 | no | — |
| 251 | C4×D3 | — | 6 | 1 | no | — |
| 252 | C4×D3 | — | 6 | 1 | no | — |
| 253 | C4×D3 | — | 6 | 1 | no | — |
| 254 | C4×D3 | — | 12 | 1 | no | — |
| 255 | C4×D3 | — | 18 | 1 | no | — |
| 256 | C4×D3 | — | 18 | 1 | no | — |
| 257 | C4×D3 | — | 18 | 1 | no | — |
| 258 | C4×D3 | — | 36 | 1 | no | — |
| 259 | Dic6 | — | 6 | 1 | no | — |
| 260 | Dic6 | — | 6 | 1 | no | — |
| 261 | Dic6 | — | 12 | 1 | no | — |
| 262 | Dic6 | — | 18 | 1 | no | — |
| 263 | Dic6 | — | 36 | 1 | no | — |
| 264 | C3×C8 | — | 2 | 1 | no | — |
| 265 | C3×C8 | — | 2 | 1 | no | — |
| 266 | C3×C8 | — | 4 | 1 | no | — |
| 267 | C3×C8 | — | 4 | 1 | no | — |
| 268 | C3×C8 | — | 9 | 1 | no | — |
| 269 | C3×C8 | — | 18 | 1 | no | — |
| 270 | C3×C8 | GO+(4,𝔽2) | 1 | 1 | yes | characteristic, complemented |
| 271 | C3⋊C8 | — | 6 | 1 | no | — |
| 272 | C3⋊C8 | — | 6 | 1 | no | — |
| 273 | C3⋊C8 | — | 6 | 1 | no | — |
| 274 | C3⋊C8 | — | 6 | 1 | no | — |
| 275 | C3⋊C8 | — | 12 | 1 | no | — |
| 276 | C2×C32 | — | 2 | 1 | no | — |
| 277 | C2×C32 | — | 2 | 1 | no | — |
| 278 | C2×C32 | — | 4 | 1 | no | — |
| 279 | C2×C32 | — | 4 | 1 | no | — |
| 280 | C2×C32 | #895 | 1 | 1 | yes | characteristic |
| 281 | C3⋊D3 | — | 4 | 1 | no | — |
| 282 | C3⋊D3 | — | 8 | 1 | no | — |
| 283 | C3⋊D3 | #911 | 1 | 1 | yes | characteristic |
| 284 | C3⋊D3 | #918 | 1 | 1 | yes | characteristic |
| 285 | C3×D3 | — | 6 | 1 | no | — |
| 286 | C3×D3 | — | 6 | 1 | no | — |
| 287 | C3×D3 | — | 6 | 1 | no | — |
| 288 | C3×D3 | — | 6 | 1 | no | — |
| 289 | C3×D3 | — | 12 | 1 | no | — |
| 290 | C3×D3 | — | 12 | 1 | no | — |
| 291 | C3×D3 | — | 24 | 1 | no | — |
| 292 | C3×D3 | — | 24 | 1 | no | — |
| 293 | C3×D3 | — | 24 | 1 | no | — |
| 294 | C3×D3 | — | 48 | 1 | no | — |
| 295 | C2×Q8 | — | 27 | 1 | no | — |
| 296 | C2×D4 | — | 27 | 1 | no | — |
| 297 | C2×D4 | — | 54 | 1 | no | — |
| 298 | C22×C4 | — | 27 | 1 | no | — |
| 299 | SD16 | — | 18 | 1 | no | — |
| 300 | SD16 | — | 54 | 1 | no | — |
| 301 | M16 | — | 18 | 1 | no | — |
| 302 | M16 | — | 54 | 1 | no | — |
| 303 | C2×C8 | — | 9 | 1 | no | — |
| 304 | C2×C8 | — | 27 | 1 | no | — |
| 305 | C4⋊C4 | — | 9 | 1 | no | — |
| 306 | C4⋊C4 | — | 9 | 1 | no | — |
| 307 | C4⋊C4 | — | 54 | 1 | no | — |
| 308 | C22⋊C4 | — | 54 | 1 | no | — |
| 309 | C22⋊C4 | — | 54 | 1 | no | — |
| 310 | C22×C3 | — | 9 | 1 | no | — |
| 311 | C22×C3 | — | 18 | 1 | no | — |
| 312 | C22×C3 | — | 36 | 1 | no | — |
| 313 | C2×D3 | — | 6 | 1 | no | — |
| 314 | C2×D3 | — | 6 | 1 | no | — |
| 315 | C2×D3 | — | 6 | 1 | no | — |
| 316 | C2×D3 | — | 6 | 1 | no | — |
| 317 | C2×D3 | — | 12 | 1 | no | — |
| 318 | C2×D3 | — | 12 | 1 | no | — |
| 319 | C2×D3 | — | 12 | 1 | no | — |
| 320 | C2×D3 | — | 18 | 1 | no | — |
| 321 | C2×D3 | — | 18 | 1 | no | — |
| 322 | C2×D3 | — | 24 | 1 | no | — |
| 323 | C2×D3 | — | 36 | 1 | no | — |
| 324 | C2×D3 | — | 36 | 1 | no | — |
| 325 | C2×D3 | — | 36 | 1 | no | — |
| 326 | C2×D3 | — | 36 | 1 | no | — |
| 327 | C2×D3 | — | 72 | 1 | no | — |
| 328 | C2×D3 | — | 72 | 1 | no | — |
| 329 | C3×C4 | — | 2 | 1 | no | — |
| 330 | C3×C4 | — | 2 | 1 | no | — |
| 331 | C3×C4 | — | 4 | 1 | no | — |
| 332 | C3×C4 | — | 4 | 1 | no | — |
| 333 | C3×C4 | — | 9 | 1 | no | — |
| 334 | C3×C4 | — | 18 | 1 | no | — |
| 335 | C3×C4 | — | 36 | 1 | no | — |
| 336 | C3×C4 | — | 36 | 1 | no | — |
| 337 | C3×C4 | — | 36 | 1 | no | — |
| 338 | C3×C4 | C2×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 339 | Dic3 | — | 6 | 1 | no | — |
| 340 | Dic3 | — | 6 | 1 | no | — |
| 341 | Dic3 | — | 6 | 1 | no | — |
| 342 | Dic3 | — | 6 | 1 | no | — |
| 343 | Dic3 | — | 12 | 1 | no | — |
| 344 | Dic3 | — | 12 | 1 | no | — |
| 345 | Dic3 | — | 12 | 1 | no | — |
| 346 | Dic3 | — | 24 | 1 | no | — |
| 347 | C32 | — | 2 | 1 | no | — |
| 348 | C32 | — | 2 | 1 | no | — |
| 349 | C32 | — | 4 | 1 | no | — |
| 350 | C32 | — | 4 | 1 | no | — |
| 351 | C32 | #4886 | 1 | 1 | yes | characteristic, complemented |
| 352 | C23 | — | 27 | 1 | no | — |
| 353 | C23 | — | 54 | 1 | no | — |
| 354 | Q8 | — | 18 | 1 | no | — |
| 355 | Q8 | — | 54 | 1 | no | — |
| 356 | D4 | — | 18 | 1 | no | — |
| 357 | D4 | — | 54 | 1 | no | — |
| 358 | D4 | — | 108 | 2 | no | — |
| 359 | C2×C4 | — | 9 | 1 | no | — |
| 360 | C2×C4 | — | 18 | 1 | no | — |
| 361 | C2×C4 | — | 18 | 1 | no | — |
| 362 | C2×C4 | — | 18 | 1 | no | — |
| 363 | C2×C4 | — | 27 | 1 | no | — |
| 364 | C2×C4 | — | 54 | 1 | no | — |
| 365 | C2×C4 | — | 54 | 1 | no | — |
| 366 | C8 | — | 9 | 1 | no | — |
| 367 | C8 | — | 18 | 1 | no | — |
| 368 | C8 | #157⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 369 | C2×C3 | — | 2 | 1 | no | — |
| 370 | C2×C3 | — | 2 | 1 | no | — |
| 371 | C2×C3 | — | 4 | 1 | no | — |
| 372 | C2×C3 | — | 4 | 1 | no | — |
| 373 | C2×C3 | — | 9 | 1 | no | — |
| 374 | C2×C3 | — | 9 | 1 | no | — |
| 375 | C2×C3 | — | 36 | 1 | no | — |
| 376 | C2×C3 | — | 72 | 1 | no | — |
| 377 | C2×C3 | #64230 | 1 | 1 | yes | characteristic |
| 378 | D3 | — | 6 | 1 | no | — |
| 379 | D3 | — | 6 | 1 | no | — |
| 380 | D3 | — | 6 | 1 | no | — |
| 381 | D3 | — | 6 | 1 | no | — |
| 382 | D3 | — | 12 | 1 | no | — |
| 383 | D3 | — | 12 | 1 | no | — |
| 384 | D3 | — | 24 | 1 | no | — |
| 385 | D3 | — | 24 | 1 | no | — |
| 386 | D3 | — | 24 | 1 | no | — |
| 387 | D3 | — | 48 | 1 | no | — |
| 388 | C22 | — | 9 | 1 | no | — |
| 389 | C22 | — | 18 | 1 | no | — |
| 390 | C22 | — | 36 | 1 | no | — |
| 391 | C22 | — | 54 | 1 | no | — |
| 392 | C22 | — | 54 | 1 | no | — |
| 393 | C22 | — | 108 | 1 | no | — |
| 394 | C22 | — | 108 | 1 | no | — |
| 395 | C4 | — | 9 | 1 | no | — |
| 396 | C4 | — | 18 | 1 | no | — |
| 397 | C4 | — | 36 | 1 | no | — |
| 398 | C4 | — | 36 | 1 | no | — |
| 399 | C4 | — | 36 | 1 | no | — |
| 400 | C4 | C2×#157⋊D3 | 1 | 1 | yes | characteristic |
| 401 | C3 | — | 2 | 1 | no | — |
| 402 | C3 | — | 2 | 1 | no | — |
| 403 | C3 | — | 4 | 1 | no | — |
| 404 | C3 | — | 4 | 1 | no | — |
| 405 | C3 | #10593286 | 1 | 1 | yes | characteristic, complemented |
| 406 | C2 | — | 9 | 1 | no | — |
| 407 | C2 | — | 9 | 1 | no | — |
| 408 | C2 | — | 36 | 1 | no | — |
| 409 | C2 | — | 72 | 1 | no | — |
| 410 | C2 | #11724343 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11724333 | C2 | semidirect |
| 3. #11723646 | C2 | semidirect |
| 4. #11723645 | C2 | semidirect |
| 5. C3×#63769 | C2 | semidirect |
| 6. #11722784 | C2 | semidirect |
| 7. #11722783 | C2 | semidirect |
| 30. #63769 | D3 | semidirect |
| 47. C33×C8 | D4 | semidirect |
| 49. C3×C3⋊(C3⋊C8) | D4 | semidirect |
| 141. C32×C8 | D12 | semidirect |
| 143. C3⋊(C3⋊C8) | D12 | semidirect |
| 230. C33 | #468 | semidirect |
| 270. C3×C8 | GO+(4,𝔽2) | semidirect |
| 351. C32 | #4886 | semidirect |
| 368. C8 | #157⋊D3 | semidirect |
| 405. C3 | #10593286 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724343 | 2 |
| #11724333 | 2 |
| #11723646 | 2 |
| #11723645 | 2 |
| C3×#63769 | 2 |
| #11722784 | 2 |
| #11722783 | 2 |
| #10593286 | 3 |
| #4886 | 9 |