Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1256 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 1256 conjugacy classes of subgroups — too many to draw. Only its 234 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 | #11724398 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #11723651 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3⋊D3×ΓL(1,𝔽25) | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | C3×#63805 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #11722827 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11722821 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | D3×#3712 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #10594708 | — | 3 | 3 | no | maximal |
| 9 | #89042 | C22 | 1 | 1 | yes | characteristic |
| 10 | C4×D3×C3⋊D3 | C22 | 1 | 3 | yes | — |
| 11 | C3×#3798 | C22 | 1 | 3 | yes | — |
| 12 | #88964 | C4 | 1 | 3 | yes | — |
| 13 | #88963 | C4 | 1 | 1 | yes | characteristic |
| 14 | #88958 | C4 | 1 | 1 | yes | characteristic |
| 15 | #88954 | C4 | 1 | 3 | yes | — |
| 16 | #88850 | C22 | 1 | 1 | yes | characteristic |
| 17 | C3×C8×C3⋊D3 | C22 | 1 | 3 | yes | complemented |
| 18 | C32×ΓL(1,𝔽25) | C22 | 1 | 3 | yes | complemented |
| 19 | #88809 | C22 | 1 | 3 | yes | complemented |
| 20 | #88788 | C22 | 1 | 3 | yes | — |
| 21 | #88786 | C22 | 1 | 3 | yes | complemented |
| 22 | C3⋊D3×C3⋊C8 | C22 | 1 | 3 | yes | complemented |
| 23 | C3×#3712 | C22 | 1 | 3 | yes | complemented |
| 24 | C3×D3×C3⋊C8 | C22 | 1 | 6 | yes | complemented |
| 25 | #64306 | — | 3 | 3 | no | — |
| 26 | M16×C3⋊D3 | — | 3 | 3 | no | — |
| 27 | C3×#907 | — | 3 | 6 | no | — |
| 28 | C2×#3712 | — | 3 | 3 | no | — |
| 29 | #63814 | — | 3 | 6 | no | — |
| 30 | #63805 | — | 3 | 3 | no | — |
| 31 | #63805 | D3 | 1 | 3 | yes | complemented |
| 32 | #63803 | — | 3 | 3 | no | — |
| 33 | #63803 | — | 3 | 3 | no | — |
| 34 | D3×ΓL(1,𝔽25) | — | 3 | 6 | no | — |
| 35 | D3×ΓL(1,𝔽25) | — | 3 | 6 | no | — |
| 36 | D3×ΓL(1,𝔽25) | — | 6 | 3 | no | — |
| 37 | C2×D3×C3⋊D3 | C2×C4 | 1 | 3 | yes | — |
| 38 | C4×C3⋊(C3⋊D3) | C23 | 1 | 1 | yes | characteristic |
| 39 | C3×C4×C3⋊D3 | C23 | 1 | 3 | yes | — |
| 40 | C32×C4×D3 | C23 | 1 | 3 | yes | — |
| 41 | #6296 | C2×C4 | 1 | 1 | yes | characteristic |
| 42 | #6295 | C2×C4 | 1 | 3 | yes | — |
| 43 | #6289 | C2×C4 | 1 | 3 | yes | — |
| 44 | Dic3×C3⋊D3 | C2×C4 | 1 | 3 | yes | — |
| 45 | D3×C3⋊Dic3 | C2×C4 | 1 | 3 | yes | — |
| 46 | C3×#627 | C2×C4 | 1 | 3 | yes | — |
| 47 | C3×#626 | C2×C4 | 1 | 6 | yes | — |
| 48 | C3×#625 | C2×C4 | 1 | 3 | yes | — |
| 49 | C33×C8 | C23 | 1 | 1 | yes | characteristic |
| 50 | C3⋊(C3⋊(C3⋊C8)) | C23 | 1 | 1 | yes | characteristic |
| 51 | C3×C3⋊(C3⋊C8) | C23 | 1 | 3 | yes | — |
| 52 | C32×C3⋊C8 | C23 | 1 | 3 | yes | — |
| 53 | #5750 | — | 9 | 3 | no | — |
| 54 | C2×C4×C3⋊D3 | — | 3 | 3 | no | — |
| 55 | C3×#235 | — | 3 | 6 | no | — |
| 56 | #3811 | — | 3 | 6 | no | — |
| 57 | #3805 | — | 3 | 3 | no | — |
| 58 | #3805 | — | 3 | 3 | no | — |
| 59 | #3802 | — | 3 | 3 | no | — |
| 60 | C4×D32 | — | 3 | 6 | no | — |
| 61 | C4×D32 | — | 6 | 3 | no | — |
| 62 | #3798 | — | 3 | 3 | no | — |
| 63 | #3798 | C2×D3 | 1 | 3 | yes | — |
| 64 | #3797 | — | 3 | 3 | no | — |
| 65 | #3796 | — | 3 | 6 | no | — |
| 66 | C32×M16 | — | 3 | 3 | no | — |
| 67 | #3748 | — | 3 | 3 | no | — |
| 68 | #3743 | — | 3 | 3 | no | — |
| 69 | #3743 | — | 3 | 3 | no | — |
| 70 | #3743 | — | 6 | 3 | no | — |
| 71 | #3743 | — | 12 | 1 | no | — |
| 72 | C8×C3⋊D3 | — | 3 | 3 | no | — |
| 73 | C8×C3⋊D3 | C2×D3 | 1 | 3 | yes | complemented |
| 74 | C2×C3×C3⋊C8 | — | 3 | 6 | no | — |
| 75 | C3×ΓL(1,𝔽25) | — | 2 | 3 | no | — |
| 76 | C3×ΓL(1,𝔽25) | — | 3 | 6 | no | — |
| 77 | C3×ΓL(1,𝔽25) | C2×D3 | 1 | 6 | yes | complemented |
| 78 | C3×D3×C8 | — | 3 | 6 | no | — |
| 79 | C3×D3×C8 | — | 3 | 6 | no | — |
| 80 | C3×D3×C8 | — | 6 | 3 | no | — |
| 81 | #3712 | — | 3 | 3 | no | — |
| 82 | #3712 | — | 3 | 6 | no | — |
| 83 | #3712 | — | 6 | 3 | no | — |
| 84 | #3712 | C2×D3 | 1 | 3 | yes | complemented |
| 85 | #3711 | — | 3 | 6 | no | — |
| 86 | #3711 | — | 3 | 6 | no | — |
| 87 | #3711 | — | 6 | 3 | no | — |
| 88 | D3×C3⋊C8 | — | 3 | 6 | no | — |
| 89 | D3×C3⋊C8 | — | 6 | 3 | no | — |
| 90 | D3×C3⋊C8 | C2×D3 | 1 | 6 | yes | complemented |
| 91 | C2×C3⋊(C3⋊D3) | C22×C4 | 1 | 1 | yes | characteristic |
| 92 | C2×C3×C3⋊D3 | C22×C4 | 1 | 3 | yes | — |
| 93 | C2×C32×D3 | C22×C4 | 1 | 3 | yes | — |
| 94 | D3×C3⋊D3 | — | 4 | 3 | no | — |
| 95 | C33×C4 | C24 | 1 | 1 | yes | characteristic |
| 96 | C3⋊(C3⋊Dic3) | C22×C4 | 1 | 1 | yes | characteristic |
| 97 | C3×C3⋊Dic3 | C22×C4 | 1 | 3 | yes | — |
| 98 | C32×Dic3 | C22×C4 | 1 | 3 | yes | — |
| 99 | D3×#41 | — | 9 | 3 | no | — |
| 100 | C3×#131 | — | 9 | 3 | no | — |
| 101 | #948 | — | 9 | 3 | no | — |
| 102 | #907 | — | 3 | 6 | no | — |
| 103 | #907 | — | 9 | 3 | no | — |
| 104 | D3×M16 | — | 9 | 3 | no | — |
| 105 | D3×M16 | — | 9 | 6 | no | — |
| 106 | D3×M16 | — | 18 | 3 | no | — |
| 107 | #901 | — | 9 | 3 | no | — |
| 108 | #901 | — | 9 | 6 | no | — |
| 109 | C2×ΓL(1,𝔽25) | — | 9 | 6 | no | — |
| 110 | C2×ΓL(1,𝔽25) | — | 9 | 3 | no | — |
| 111 | C22×C3⋊D3 | — | 3 | 3 | no | — |
| 112 | C2×D32 | — | 3 | 6 | no | — |
| 113 | C2×D32 | — | 6 | 3 | no | — |
| 114 | C2×C32×C4 | — | 3 | 3 | no | — |
| 115 | C2×C3⋊Dic3 | — | 3 | 3 | no | — |
| 116 | C4×C3⋊D3 | — | 3 | 3 | no | — |
| 117 | C4×C3⋊D3 | — | 3 | 3 | no | — |
| 118 | C4×C3⋊D3 | — | 3 | 3 | no | — |
| 119 | C4×C3⋊D3 | — | 6 | 3 | no | — |
| 120 | C4×C3⋊D3 | — | 12 | 1 | no | — |
| 121 | C4×C3⋊D3 | C22×D3 | 1 | 3 | yes | — |
| 122 | C3×#67 | — | 3 | 6 | no | — |
| 123 | C3×#67 | — | 3 | 6 | no | — |
| 124 | C3×D12 | — | 3 | 6 | no | — |
| 125 | C3×C4×D3 | — | 2 | 3 | no | — |
| 126 | C3×C4×D3 | — | 3 | 6 | no | — |
| 127 | C3×C4×D3 | — | 6 | 3 | no | — |
| 128 | C3×C4×D3 | C22×D3 | 1 | 6 | yes | — |
| 129 | C3×Dic6 | — | 3 | 6 | no | — |
| 130 | #627 | — | 3 | 3 | no | — |
| 131 | #627 | C4×D3 | 1 | 3 | yes | — |
| 132 | #626 | — | 3 | 6 | no | — |
| 133 | #626 | C4×D3 | 1 | 6 | yes | — |
| 134 | #625 | — | 3 | 3 | no | — |
| 135 | #625 | C4×D3 | 1 | 3 | yes | — |
| 136 | #624 | — | 3 | 6 | no | — |
| 137 | #624 | — | 6 | 3 | no | — |
| 138 | D3×Dic3 | — | 3 | 6 | no | — |
| 139 | D3×Dic3 | — | 3 | 6 | no | — |
| 140 | D3×Dic3 | — | 6 | 3 | no | — |
| 141 | D3×Dic3 | — | 6 | 3 | no | — |
| 142 | C32×C8 | — | 2 | 3 | no | — |
| 143 | C32×C8 | — | 3 | 3 | no | — |
| 144 | C32×C8 | — | 4 | 1 | no | — |
| 145 | C32×C8 | C22×D3 | 1 | 3 | yes | — |
| 146 | C3⋊(C3⋊C8) | — | 3 | 3 | no | — |
| 147 | C3⋊(C3⋊C8) | — | 6 | 3 | no | — |
| 148 | C3⋊(C3⋊C8) | — | 12 | 1 | no | — |
| 149 | C3⋊(C3⋊C8) | C22×D3 | 1 | 3 | yes | — |
| 150 | C3×C3⋊C8 | — | 2 | 3 | no | — |
| 151 | C3×C3⋊C8 | — | 3 | 6 | no | — |
| 152 | C3×C3⋊C8 | — | 6 | 3 | no | — |
| 153 | C3×C3⋊C8 | C22×D3 | 1 | 6 | yes | — |
| 154 | #568 | — | 27 | 1 | no | Sylow |
| 155 | C2×C33 | C23×C4 | 1 | 1 | yes | characteristic |
| 156 | C3⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 157 | C3×C3⋊D3 | — | 2 | 3 | no | — |
| 158 | C32×D3 | — | 2 | 3 | no | — |
| 159 | C3×#41 | — | 9 | 3 | no | — |
| 160 | #239 | — | 9 | 3 | no | — |
| 161 | D3×Q8 | — | 9 | 3 | no | — |
| 162 | #237 | — | 9 | 6 | no | — |
| 163 | #237 | — | 9 | 3 | no | — |
| 164 | D3×D4 | — | 9 | 6 | no | — |
| 165 | D3×D4 | — | 9 | 3 | no | — |
| 166 | #235 | — | 3 | 6 | no | — |
| 167 | #235 | — | 9 | 3 | no | — |
| 168 | C2×C4×D3 | — | 9 | 6 | no | — |
| 169 | C2×C4×D3 | — | 9 | 3 | no | — |
| 170 | C2×C4×D3 | — | 18 | 3 | no | — |
| 171 | C3×M16 | — | 3 | 6 | no | — |
| 172 | C3×M16 | — | 6 | 3 | no | — |
| 173 | C3×M16 | — | 9 | 3 | no | — |
| 174 | C2×C3×C8 | — | 9 | 6 | no | — |
| 175 | C2×C3×C8 | — | 9 | 3 | no | — |
| 176 | #208 | — | 9 | 3 | no | — |
| 177 | #208 | — | 9 | 6 | no | — |
| 178 | #208 | — | 18 | 3 | no | — |
| 179 | C2×C3⋊C8 | — | 3 | 6 | no | — |
| 180 | C2×C3⋊C8 | — | 9 | 3 | no | — |
| 181 | ΓL(1,𝔽25) | — | 3 | 6 | no | — |
| 182 | ΓL(1,𝔽25) | — | 9 | 6 | no | — |
| 183 | ΓL(1,𝔽25) | — | 9 | 6 | no | — |
| 184 | ΓL(1,𝔽25) | — | 9 | 3 | no | — |
| 185 | ΓL(1,𝔽25) | — | 9 | 3 | no | — |
| 186 | ΓL(1,𝔽25) | — | 9 | 3 | no | — |
| 187 | ΓL(1,𝔽25) | — | 18 | 3 | no | — |
| 188 | ΓL(1,𝔽25) | — | 18 | 3 | no | — |
| 189 | ΓL(1,𝔽25) | — | 36 | 1 | no | — |
| 190 | ΓL(1,𝔽25) | D32 | 1 | 3 | yes | complemented |
| 191 | D3×C8 | — | 3 | 6 | no | — |
| 192 | D3×C8 | — | 3 | 6 | no | — |
| 193 | D3×C8 | — | 6 | 3 | no | — |
| 194 | D3×C8 | — | 9 | 6 | no | — |
| 195 | D3×C8 | — | 18 | 3 | no | — |
| 196 | C22×C32 | — | 3 | 3 | no | — |
| 197 | C2×C3⋊D3 | — | 3 | 3 | no | — |
| 198 | C2×C3⋊D3 | — | 6 | 3 | no | — |
| 199 | C2×C3⋊D3 | — | 12 | 1 | no | — |
| 200 | C2×C3⋊D3 | — | 12 | 3 | no | — |
| 201 | C2×C3⋊D3 | C2×C4×D3 | 1 | 3 | yes | — |
| 202 | C2×C3×D3 | — | 2 | 3 | no | — |
| 203 | C2×C3×D3 | — | 3 | 6 | no | — |
| 204 | C2×C3×D3 | — | 6 | 3 | no | — |
| 205 | C2×C3×D3 | C2×C4×D3 | 1 | 6 | yes | — |
| 206 | D32 | — | 12 | 6 | no | — |
| 207 | D32 | — | 12 | 6 | no | — |
| 208 | C32×C4 | — | 2 | 3 | no | — |
| 209 | C32×C4 | — | 3 | 3 | no | — |
| 210 | C32×C4 | — | 4 | 1 | no | — |
| 211 | C32×C4 | C23×D3 | 1 | 3 | yes | — |
| 212 | C3⋊Dic3 | — | 3 | 3 | no | — |
| 213 | C3⋊Dic3 | — | 6 | 3 | no | — |
| 214 | C3⋊Dic3 | — | 12 | 1 | no | — |
| 215 | C3⋊Dic3 | C2×C4×D3 | 1 | 3 | yes | — |
| 216 | C3×Dic3 | — | 2 | 3 | no | — |
| 217 | C3×Dic3 | — | 3 | 6 | no | — |
| 218 | C3×Dic3 | — | 6 | 3 | no | — |
| 219 | C3×Dic3 | C2×C4×D3 | 1 | 6 | yes | — |
| 220 | C2×#41 | — | 27 | 1 | no | — |
| 221 | #131 | — | 9 | 3 | no | — |
| 222 | #131 | — | 27 | 1 | no | — |
| 223 | #131 | — | 27 | 3 | no | — |
| 224 | #131 | — | 27 | 1 | no | — |
| 225 | C2×M16 | — | 27 | 3 | no | — |
| 226 | C2×M16 | — | 27 | 3 | no | — |
| 227 | C33 | #568 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 228 | C22×D3 | — | 9 | 6 | no | — |
| 229 | C22×D3 | — | 9 | 3 | no | — |
| 230 | C22×D3 | — | 18 | 3 | no | — |
| 231 | C3×Q8 | — | 9 | 3 | no | — |
| 232 | C3×D4 | — | 9 | 6 | no | — |
| 233 | C3×D4 | — | 9 | 3 | no | — |
| 234 | C2×C3×C4 | — | 3 | 6 | no | — |
| 235 | C2×C3×C4 | — | 6 | 3 | no | — |
| 236 | C2×C3×C4 | — | 9 | 3 | no | — |
| 237 | #67 | — | 3 | 6 | no | — |
| 238 | #67 | — | 3 | 6 | no | — |
| 239 | #67 | — | 9 | 6 | no | — |
| 240 | C2×Dic3 | — | 9 | 6 | no | — |
| 241 | C2×Dic3 | — | 9 | 3 | no | — |
| 242 | C2×Dic3 | — | 18 | 3 | no | — |
| 243 | D12 | — | 3 | 6 | no | — |
| 244 | D12 | — | 9 | 3 | no | — |
| 245 | C4×D3 | — | 3 | 6 | no | — |
| 246 | C4×D3 | — | 6 | 3 | no | — |
| 247 | C4×D3 | — | 9 | 6 | no | — |
| 248 | C4×D3 | — | 9 | 6 | no | — |
| 249 | C4×D3 | — | 9 | 3 | no | — |
| 250 | C4×D3 | — | 9 | 3 | no | — |
| 251 | C4×D3 | — | 9 | 3 | no | — |
| 252 | C4×D3 | — | 18 | 3 | no | — |
| 253 | C4×D3 | — | 18 | 3 | no | — |
| 254 | C4×D3 | — | 18 | 3 | no | — |
| 255 | C4×D3 | — | 36 | 1 | no | — |
| 256 | C4×D3 | C2×D32 | 1 | 3 | yes | — |
| 257 | Dic6 | — | 3 | 6 | no | — |
| 258 | Dic6 | — | 9 | 3 | no | — |
| 259 | C3×C8 | — | 2 | 3 | no | — |
| 260 | C3×C8 | — | 3 | 6 | no | — |
| 261 | C3×C8 | — | 4 | 1 | no | — |
| 262 | C3×C8 | — | 6 | 3 | no | — |
| 263 | C3×C8 | — | 9 | 3 | no | — |
| 264 | C3×C8 | C2×D32 | 1 | 3 | yes | — |
| 265 | C3⋊C8 | — | 3 | 6 | no | — |
| 266 | C3⋊C8 | — | 6 | 3 | no | — |
| 267 | C3⋊C8 | — | 9 | 3 | no | — |
| 268 | C3⋊C8 | — | 18 | 3 | no | — |
| 269 | C3⋊C8 | — | 36 | 1 | no | — |
| 270 | C3⋊C8 | C2×D32 | 1 | 3 | yes | — |
| 271 | C2×C32 | — | 2 | 3 | no | — |
| 272 | C2×C32 | — | 4 | 1 | no | — |
| 273 | C2×C32 | — | 6 | 3 | no | — |
| 274 | C2×C32 | C22×C4×D3 | 1 | 3 | yes | — |
| 275 | C3⋊D3 | — | 2 | 3 | no | — |
| 276 | C3⋊D3 | — | 6 | 3 | no | — |
| 277 | C3⋊D3 | — | 12 | 3 | no | — |
| 278 | C3⋊D3 | — | 24 | 1 | no | — |
| 279 | C3×D3 | — | 2 | 6 | no | — |
| 280 | C3×D3 | — | 4 | 3 | no | — |
| 281 | C3×D3 | — | 6 | 6 | no | — |
| 282 | C3×D3 | — | 6 | 6 | no | — |
| 283 | #41 | — | 9 | 3 | no | — |
| 284 | #41 | — | 27 | 1 | no | — |
| 285 | #41 | — | 27 | 1 | no | — |
| 286 | #41 | — | 27 | 3 | no | — |
| 287 | C2×Q8 | — | 27 | 1 | no | — |
| 288 | C2×D4 | — | 27 | 3 | no | — |
| 289 | C22×C4 | — | 27 | 3 | no | — |
| 290 | M16 | — | 3 | 3 | no | — |
| 291 | M16 | — | 9 | 3 | no | — |
| 292 | M16 | — | 27 | 3 | no | — |
| 293 | M16 | — | 27 | 3 | no | — |
| 294 | M16 | — | 27 | 3 | no | — |
| 295 | M16 | — | 27 | 1 | no | — |
| 296 | C2×C8 | — | 9 | 6 | no | — |
| 297 | C2×C8 | — | 9 | 3 | no | — |
| 298 | C2×C8 | — | 27 | 3 | no | — |
| 299 | C22×C3 | — | 3 | 6 | no | — |
| 300 | C22×C3 | — | 6 | 3 | no | — |
| 301 | C22×C3 | — | 9 | 3 | no | — |
| 302 | C2×D3 | — | 3 | 6 | no | — |
| 303 | C2×D3 | — | 6 | 3 | no | — |
| 304 | C2×D3 | — | 9 | 3 | no | — |
| 305 | C2×D3 | — | 18 | 3 | no | — |
| 306 | C2×D3 | — | 36 | 1 | no | — |
| 307 | C2×D3 | — | 36 | 3 | no | — |
| 308 | C2×D3 | — | 36 | 6 | no | — |
| 309 | C2×D3 | — | 36 | 6 | no | — |
| 310 | C2×D3 | C4×D32 | 1 | 3 | yes | — |
| 311 | C3×C4 | — | 2 | 3 | no | — |
| 312 | C3×C4 | — | 3 | 6 | no | — |
| 313 | C3×C4 | — | 4 | 1 | no | — |
| 314 | C3×C4 | — | 6 | 3 | no | — |
| 315 | C3×C4 | — | 9 | 3 | no | — |
| 316 | C3×C4 | C22×D32 | 1 | 3 | yes | — |
| 317 | Dic3 | — | 3 | 6 | no | — |
| 318 | Dic3 | — | 6 | 3 | no | — |
| 319 | Dic3 | — | 9 | 3 | no | — |
| 320 | Dic3 | — | 18 | 3 | no | — |
| 321 | Dic3 | — | 36 | 1 | no | — |
| 322 | Dic3 | C4×D32 | 1 | 3 | yes | — |
| 323 | C32 | — | 2 | 3 | no | — |
| 324 | C32 | — | 4 | 1 | no | — |
| 325 | C32 | #5750 | 1 | 3 | yes | complemented |
| 326 | C23 | — | 27 | 3 | no | — |
| 327 | Q8 | — | 9 | 3 | no | — |
| 328 | Q8 | — | 27 | 1 | no | — |
| 329 | D4 | — | 9 | 6 | no | — |
| 330 | D4 | — | 9 | 3 | no | — |
| 331 | D4 | — | 27 | 3 | no | — |
| 332 | C2×C4 | — | 3 | 3 | no | — |
| 333 | C2×C4 | — | 9 | 3 | no | — |
| 334 | C2×C4 | — | 27 | 3 | no | — |
| 335 | C2×C4 | — | 27 | 3 | no | — |
| 336 | C2×C4 | — | 27 | 3 | no | — |
| 337 | C2×C4 | — | 27 | 1 | no | — |
| 338 | C8 | — | 3 | 3 | no | — |
| 339 | C8 | — | 9 | 3 | no | — |
| 340 | C8 | — | 27 | 1 | no | — |
| 341 | C8 | D33 | 1 | 1 | yes | characteristic |
| 342 | C2×C3 | — | 2 | 3 | no | — |
| 343 | C2×C3 | — | 4 | 1 | no | — |
| 344 | C2×C3 | — | 6 | 6 | no | — |
| 345 | C2×C3 | — | 12 | 3 | no | — |
| 346 | C2×C3 | — | 18 | 3 | no | — |
| 347 | C2×C3 | C2×C4×D32 | 1 | 3 | yes | — |
| 348 | D3 | — | 2 | 3 | no | — |
| 349 | D3 | — | 6 | 6 | no | — |
| 350 | D3 | — | 6 | 6 | no | — |
| 351 | D3 | — | 18 | 3 | no | — |
| 352 | D3 | — | 36 | 3 | no | — |
| 353 | D3 | — | 72 | 1 | no | — |
| 354 | C22 | — | 3 | 3 | no | — |
| 355 | C22 | — | 9 | 3 | no | — |
| 356 | C22 | — | 27 | 1 | no | — |
| 357 | C22 | — | 108 | 3 | no | — |
| 358 | C4 | — | 3 | 3 | no | — |
| 359 | C4 | — | 9 | 3 | no | — |
| 360 | C4 | — | 27 | 1 | no | — |
| 361 | C4 | C2×D33 | 1 | 1 | yes | characteristic |
| 362 | C3 | — | 2 | 3 | no | — |
| 363 | C3 | — | 4 | 1 | no | — |
| 364 | C3 | #10594708 | 1 | 3 | yes | complemented |
| 365 | C2 | — | 6 | 3 | no | — |
| 366 | C2 | — | 18 | 3 | no | — |
| 367 | C2 | — | 54 | 1 | no | — |
| 368 | C2 | C4×D33 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×D33 |
| commutator, socle | C2×C33 | C23×C4 |
| Fitting | C33×C8 | C23 |
| prime radical | #11724398 | C2 |
| cosocle | C33×C4 | C24 |
| hypercenter | C8 | D33 |
| hypocenter | C33 | #568 |
| LCS | G ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C4 ◁ C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11723651 | C2 | semidirect |
| 3. C3⋊D3×ΓL(1,𝔽25) | C2 | semidirect |
| 4. C3×#63805 | C2 | semidirect |
| 5. #11722827 | C2 | semidirect |
| 6. #11722821 | C2 | semidirect |
| 7. D3×#3712 | C2 | semidirect |
| 17. C3×C8×C3⋊D3 | C22 | semidirect |
| 18. C32×ΓL(1,𝔽25) | C22 | semidirect |
| 19. #88809 | C22 | semidirect |
| 21. #88786 | C22 | semidirect |
| 22. C3⋊D3×C3⋊C8 | C22 | semidirect |
| 23. C3×#3712 | C22 | semidirect |
| 24. C3×D3×C3⋊C8 | C22 | semidirect |
| 31. #63805 | D3 | semidirect |
| 73. C8×C3⋊D3 | C2×D3 | semidirect |
| 77. C3×ΓL(1,𝔽25) | C2×D3 | semidirect |
| 84. #3712 | C2×D3 | semidirect |
| 90. D3×C3⋊C8 | C2×D3 | semidirect |
| 190. ΓL(1,𝔽25) | D32 | semidirect |
| 227. C33 | #568 | semidirect |
| 325. C32 | #5750 | semidirect |
| 364. C3 | #10594708 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724398 | 2 |
| #11723651 | 2 |
| C3⋊D3×ΓL(1,𝔽25) | 2 |
| C3×#63805 | 2 |
| #11722827 | 2 |
| #11722821 | 2 |
| D3×#3712 | 2 |
| #10594708 | 3 |