Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2646 conjugacy classes of subgroups; only the 449 normal subgroups are shown.
This group has 2646 conjugacy classes of subgroups — too many to draw. Only its 449 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 | #10596692 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #41×#157 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10596525 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | D4×GO+(4,𝔽2) | C2 | 1 | 12 | yes | maximal, complemented |
| 5 | #10596512 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #10596511 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | C2×#64231 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | C22×GO+(4,𝔽2) | C22 | 1 | 12 | yes | complemented |
| 9 | #41×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 10 | C3×#1009 | — | 2 | 2 | no | — |
| 11 | #64320 | — | 2 | 2 | no | — |
| 12 | #64319 | C22 | 1 | 4 | yes | complemented |
| 13 | #64313 | — | 2 | 6 | no | — |
| 14 | D32×D4 | C22 | 1 | 12 | yes | complemented |
| 15 | #64307 | — | 2 | 6 | no | — |
| 16 | #64306 | C22 | 1 | 6 | yes | complemented |
| 17 | C2×#3802 | C22 | 1 | 6 | yes | complemented |
| 18 | Q8×#157 | C22 | 1 | 2 | yes | complemented |
| 19 | D4×#157 | C22 | 1 | 6 | yes | complemented |
| 20 | #64286 | C22 | 1 | 3 | yes | complemented |
| 21 | C2×C4×#157 | C22 | 1 | 3 | yes | complemented |
| 22 | #64242 | C22 | 1 | 12 | yes | complemented |
| 23 | #64241 | C22 | 1 | 24 | yes | complemented |
| 24 | #64231 | C22 | 1 | 3 | yes | complemented |
| 25 | #64231 | C22 | 1 | 6 | yes | complemented |
| 26 | #64231 | C22 | 1 | 12 | yes | complemented |
| 27 | #64230 | C22 | 1 | 24 | yes | complemented |
| 28 | C4×GO+(4,𝔽2) | C22 | 1 | 12 | yes | complemented |
| 29 | #64222 | C22 | 1 | 1 | yes | characteristic, complemented |
| 30 | #64221 | C22 | 1 | 6 | yes | complemented |
| 31 | D3×H(5,𝔽2) | — | 6 | 2 | no | — |
| 32 | C22×D32 | C23 | 1 | 12 | yes | — |
| 33 | C22×#157 | C23 | 1 | 6 | yes | — |
| 34 | C2×GO+(4,𝔽2) | — | 4 | 24 | no | — |
| 35 | C2×GO+(4,𝔽2) | C23 | 1 | 12 | yes | — |
| 36 | C2×GO+(4,𝔽2) | C23 | 1 | 24 | yes | — |
| 37 | C32×#41 | D4 | 1 | 1 | yes | characteristic, complemented |
| 38 | #3832 | D4 | 1 | 1 | yes | characteristic, complemented |
| 39 | Q8×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 40 | #3830 | D4 | 1 | 3 | yes | complemented |
| 41 | D4×C3⋊D3 | C23 | 1 | 3 | yes | — |
| 42 | #3828 | D4 | 1 | 3 | yes | complemented |
| 43 | C2×C4×C3⋊D3 | C23 | 1 | 3 | yes | — |
| 44 | C3×#239 | — | 2 | 4 | no | — |
| 45 | C3×D3×D4 | — | 2 | 12 | no | — |
| 46 | C3×#235 | — | 2 | 6 | no | — |
| 47 | C2×C3×D12 | — | 2 | 6 | no | — |
| 48 | #3811 | C23 | 1 | 12 | yes | — |
| 49 | D3×#67 | — | 2 | 24 | no | — |
| 50 | C2×#625 | — | 2 | 6 | no | — |
| 51 | #3805 | — | 2 | 6 | no | — |
| 52 | #3802 | — | 2 | 6 | no | — |
| 53 | #3802 | — | 2 | 6 | no | — |
| 54 | #3802 | C23 | 1 | 6 | yes | — |
| 55 | #3802 | C23 | 1 | 12 | yes | — |
| 56 | D3×D12 | — | 2 | 12 | no | — |
| 57 | C4×D32 | C23 | 1 | 12 | yes | — |
| 58 | #3798 | — | 2 | 6 | no | — |
| 59 | #3797 | C23 | 1 | 2 | yes | — |
| 60 | #3796 | — | 2 | 6 | no | — |
| 61 | #3795 | — | 2 | 12 | no | — |
| 62 | C22⋊#157 | C23 | 1 | 6 | yes | — |
| 63 | C4⋊#157 | C23 | 1 | 6 | yes | — |
| 64 | C4×#157 | C23 | 1 | 1 | yes | characteristic |
| 65 | C4×#157 | C23 | 1 | 3 | yes | — |
| 66 | C4×#157 | C23 | 1 | 6 | yes | — |
| 67 | #3773 | C23 | 1 | 4 | yes | — |
| 68 | D32⋊C4 | C23 | 1 | 24 | yes | — |
| 69 | #3498 | — | 9 | 1 | no | maximal, Sylow |
| 70 | C3×H(5,𝔽2) | — | 6 | 2 | no | — |
| 71 | #1009 | — | 2 | 2 | no | — |
| 72 | #1009 | — | 6 | 6 | no | — |
| 73 | #1009 | — | 6 | 4 | no | — |
| 74 | D3×#41 | — | 6 | 6 | no | — |
| 75 | D3×#41 | — | 6 | 4 | no | — |
| 76 | D3×#41 | — | 6 | 2 | no | — |
| 77 | #1004 | — | 6 | 6 | no | — |
| 78 | #1004 | — | 6 | 12 | no | — |
| 79 | C2×D3×D4 | — | 6 | 6 | no | — |
| 80 | C2×D3×D4 | — | 6 | 12 | no | — |
| 81 | C22×C3⋊D3 | C24 | 1 | 3 | yes | — |
| 82 | C22×C3×D3 | — | 2 | 12 | no | — |
| 83 | C2×D32 | — | 2 | 12 | no | — |
| 84 | C2×D32 | — | 4 | 24 | no | — |
| 85 | C2×D32 | C24 | 1 | 12 | yes | — |
| 86 | C2×#157 | — | 2 | 12 | no | — |
| 87 | C2×#157 | C24 | 1 | 6 | yes | — |
| 88 | C2×#157 | C24 | 1 | 2 | yes | — |
| 89 | GO+(4,𝔽2) | — | 2 | 24 | no | — |
| 90 | GO+(4,𝔽2) | — | 4 | 24 | no | — |
| 91 | C32×Q8 | C2×D4 | 1 | 1 | yes | characteristic, complemented |
| 92 | C32×D4 | C2×D4 | 1 | 3 | yes | complemented |
| 93 | C2×C32×C4 | C2×D4 | 1 | 3 | yes | complemented |
| 94 | #638 | C2×D4 | 1 | 6 | yes | complemented |
| 95 | C2×C3⋊Dic3 | C2×D4 | 1 | 3 | yes | complemented |
| 96 | C4⋊(C3⋊D3) | C2×D4 | 1 | 3 | yes | complemented |
| 97 | C4×C3⋊D3 | C2×D4 | 1 | 3 | yes | complemented |
| 98 | C4×C3⋊D3 | C2×D4 | 1 | 3 | yes | complemented |
| 99 | C4×C3⋊D3 | C24 | 1 | 1 | yes | characteristic |
| 100 | C4×C3⋊D3 | C24 | 1 | 3 | yes | — |
| 101 | #634 | C2×D4 | 1 | 3 | yes | complemented |
| 102 | C3×#67 | — | 2 | 12 | no | — |
| 103 | C3×D12 | — | 2 | 12 | no | — |
| 104 | C3×D12 | — | 2 | 6 | no | — |
| 105 | C3×C4×D3 | — | 2 | 12 | no | — |
| 106 | C3×Dic6 | — | 2 | 2 | no | — |
| 107 | #627 | — | 2 | 2 | no | — |
| 108 | #626 | — | 2 | 12 | no | — |
| 109 | #625 | — | 2 | 12 | no | — |
| 110 | #625 | — | 2 | 6 | no | — |
| 111 | #624 | C24 | 1 | 4 | yes | — |
| 112 | D3×Dic3 | — | 2 | 12 | no | — |
| 113 | C2×H(5,𝔽2) | — | 9 | 2 | no | — |
| 114 | #550 | — | 9 | 4 | no | — |
| 115 | D42 | — | 9 | 12 | no | — |
| 116 | #535 | — | 9 | 6 | no | — |
| 117 | #532 | — | 9 | 3 | no | — |
| 118 | C2×#127 | — | 9 | 3 | no | — |
| 119 | C4×#41 | — | 9 | 1 | no | — |
| 120 | C23×D3 | — | 6 | 12 | no | — |
| 121 | C3×#41 | — | 2 | 2 | no | — |
| 122 | C3×#41 | — | 6 | 6 | no | — |
| 123 | C3×#41 | — | 6 | 4 | no | — |
| 124 | C2×C3×D4 | — | 6 | 6 | no | — |
| 125 | C2×C3×D4 | — | 6 | 12 | no | — |
| 126 | C2×#67 | — | 6 | 24 | no | — |
| 127 | C2×#67 | — | 6 | 12 | no | — |
| 128 | #239 | — | 2 | 4 | no | — |
| 129 | #239 | — | 6 | 2 | no | — |
| 130 | #239 | — | 6 | 6 | no | — |
| 131 | D3×Q8 | — | 6 | 2 | no | — |
| 132 | D3×Q8 | — | 6 | 2 | no | — |
| 133 | #237 | — | 6 | 6 | no | — |
| 134 | #237 | — | 6 | 6 | no | — |
| 135 | #237 | — | 6 | 12 | no | — |
| 136 | #237 | — | 6 | 12 | no | — |
| 137 | D3×D4 | — | 2 | 12 | no | — |
| 138 | D3×D4 | — | 6 | 12 | no | — |
| 139 | D3×D4 | — | 6 | 6 | no | — |
| 140 | D3×D4 | — | 6 | 12 | no | — |
| 141 | D3×D4 | — | 6 | 6 | no | — |
| 142 | D3×D4 | — | 6 | 12 | no | — |
| 143 | D3×D4 | — | 6 | 12 | no | — |
| 144 | D3×D4 | — | 6 | 12 | no | — |
| 145 | D3×D4 | — | 6 | 24 | no | — |
| 146 | #235 | — | 2 | 6 | no | — |
| 147 | #235 | — | 6 | 6 | no | — |
| 148 | #235 | — | 6 | 12 | no | — |
| 149 | #235 | — | 6 | 12 | no | — |
| 150 | C2×D12 | — | 2 | 6 | no | — |
| 151 | C2×D12 | — | 6 | 12 | no | — |
| 152 | C2×C4×D3 | — | 6 | 12 | no | — |
| 153 | C2×C4×D3 | — | 6 | 6 | no | — |
| 154 | C22×C32 | C22×D4 | 1 | 3 | yes | — |
| 155 | C2×C3⋊D3 | — | 2 | 6 | no | — |
| 156 | C2×C3⋊D3 | C22×D4 | 1 | 3 | yes | — |
| 157 | C2×C3⋊D3 | C25 | 1 | 1 | yes | characteristic |
| 158 | C2×C3×D3 | — | 2 | 12 | no | — |
| 159 | C2×C3×D3 | — | 8 | 12 | no | — |
| 160 | D32 | — | 2 | 24 | no | — |
| 161 | D32 | — | 8 | 12 | no | — |
| 162 | #157 | — | 2 | 6 | no | — |
| 163 | #157 | H(5,𝔽2) | 1 | 4 | yes | complemented |
| 164 | C32×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 165 | C32×C4 | C22×D4 | 1 | 3 | yes | — |
| 166 | C3⋊Dic3 | C22×D4 | 1 | 3 | yes | — |
| 167 | C3⋊Dic3 | C22×D4 | 1 | 1 | yes | characteristic |
| 168 | C3×Dic3 | — | 2 | 4 | no | — |
| 169 | H(5,𝔽2) | — | 6 | 2 | no | — |
| 170 | H(5,𝔽2) | — | 18 | 6 | no | — |
| 171 | H(5,𝔽2) | — | 18 | 6 | no | — |
| 172 | H(5,𝔽2) | — | 18 | 2 | no | — |
| 173 | C2×#41 | — | 9 | 6 | no | — |
| 174 | C2×#41 | — | 9 | 4 | no | — |
| 175 | C2×#41 | — | 9 | 1 | no | — |
| 176 | C22×D4 | — | 9 | 6 | no | — |
| 177 | C22×D4 | — | 9 | 12 | no | — |
| 178 | C22×D4 | — | 9 | 12 | no | — |
| 179 | C4⋊Q8 | — | 9 | 1 | no | — |
| 180 | #127 | — | 9 | 3 | no | — |
| 181 | #127 | — | 9 | 6 | no | — |
| 182 | #127 | — | 9 | 12 | no | — |
| 183 | #124 | — | 9 | 6 | no | — |
| 184 | #121 | — | 9 | 12 | no | — |
| 185 | #121 | — | 9 | 24 | no | — |
| 186 | #120 | — | 9 | 24 | no | — |
| 187 | C4×Q8 | — | 9 | 2 | no | — |
| 188 | C4×D4 | — | 9 | 6 | no | — |
| 189 | C4×D4 | — | 9 | 12 | no | — |
| 190 | #117 | — | 9 | 3 | no | — |
| 191 | C2×C42 | — | 9 | 3 | no | — |
| 192 | C23×C3 | — | 6 | 12 | no | — |
| 193 | C22×D3 | — | 2 | 12 | no | — |
| 194 | C22×D3 | — | 6 | 12 | no | — |
| 195 | C22×D3 | — | 6 | 6 | no | — |
| 196 | C22×D3 | — | 6 | 24 | no | — |
| 197 | C22×D3 | — | 24 | 24 | no | — |
| 198 | C3×Q8 | — | 2 | 2 | no | — |
| 199 | C3×Q8 | — | 6 | 2 | no | — |
| 200 | C3×D4 | — | 2 | 6 | no | — |
| 201 | C3×D4 | — | 6 | 6 | no | — |
| 202 | C3×D4 | — | 6 | 12 | no | — |
| 203 | C3×D4 | — | 6 | 12 | no | — |
| 204 | C2×C3×C4 | — | 2 | 6 | no | — |
| 205 | C2×C3×C4 | — | 6 | 12 | no | — |
| 206 | #67 | — | 2 | 12 | no | — |
| 207 | #67 | — | 6 | 12 | no | — |
| 208 | #67 | — | 6 | 12 | no | — |
| 209 | #67 | — | 6 | 24 | no | — |
| 210 | #67 | — | 6 | 12 | no | — |
| 211 | C2×Dic3 | — | 6 | 6 | no | — |
| 212 | C2×Dic3 | — | 6 | 12 | no | — |
| 213 | D12 | — | 2 | 6 | no | — |
| 214 | D12 | — | 2 | 12 | no | — |
| 215 | D12 | — | 6 | 6 | no | — |
| 216 | D12 | — | 6 | 12 | no | — |
| 217 | C4×D3 | — | 2 | 12 | no | — |
| 218 | C4×D3 | — | 6 | 4 | no | — |
| 219 | C4×D3 | — | 6 | 6 | no | — |
| 220 | C4×D3 | — | 6 | 6 | no | — |
| 221 | C4×D3 | — | 6 | 2 | no | — |
| 222 | C4×D3 | — | 6 | 6 | no | — |
| 223 | C4×D3 | — | 6 | 12 | no | — |
| 224 | Dic6 | — | 2 | 2 | no | — |
| 225 | Dic6 | — | 6 | 6 | no | — |
| 226 | Dic6 | — | 6 | 4 | no | — |
| 227 | C2×C32 | — | 2 | 3 | no | — |
| 228 | C2×C32 | C23×D4 | 1 | 1 | yes | characteristic |
| 229 | C3⋊D3 | — | 2 | 3 | no | — |
| 230 | C3⋊D3 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 231 | C3×D3 | — | 4 | 12 | no | — |
| 232 | C24 | — | 9 | 12 | no | — |
| 233 | #41 | — | 6 | 4 | no | — |
| 234 | #41 | — | 6 | 6 | no | — |
| 235 | #41 | — | 9 | 1 | no | — |
| 236 | #41 | — | 9 | 3 | no | — |
| 237 | #41 | — | 9 | 3 | no | — |
| 238 | #41 | — | 18 | 6 | no | — |
| 239 | #41 | — | 18 | 12 | no | — |
| 240 | #41 | — | 18 | 6 | no | — |
| 241 | #41 | — | 18 | 6 | no | — |
| 242 | #41 | GO+(4,𝔽2) | 1 | 1 | yes | characteristic, complemented |
| 243 | C2×Q8 | — | 9 | 2 | no | — |
| 244 | C2×Q8 | — | 9 | 1 | no | — |
| 245 | C2×D4 | — | 6 | 12 | no | — |
| 246 | C2×D4 | — | 6 | 6 | no | — |
| 247 | C2×D4 | — | 9 | 12 | no | — |
| 248 | C2×D4 | — | 9 | 12 | no | — |
| 249 | C2×D4 | — | 9 | 6 | no | — |
| 250 | C2×D4 | — | 9 | 3 | no | — |
| 251 | C2×D4 | — | 9 | 12 | no | — |
| 252 | C2×D4 | — | 9 | 24 | no | — |
| 253 | C2×D4 | — | 18 | 12 | no | — |
| 254 | C2×D4 | — | 18 | 6 | no | — |
| 255 | C2×D4 | — | 18 | 6 | no | — |
| 256 | C2×D4 | — | 18 | 6 | no | — |
| 257 | C2×D4 | — | 18 | 24 | no | — |
| 258 | C2×D4 | — | 36 | 24 | no | — |
| 259 | C22×C4 | — | 9 | 12 | no | — |
| 260 | C22×C4 | — | 9 | 3 | no | — |
| 261 | C22×C4 | — | 9 | 6 | no | — |
| 262 | C4⋊C4 | — | 9 | 6 | no | — |
| 263 | C4⋊C4 | — | 9 | 4 | no | — |
| 264 | C22⋊C4 | — | 9 | 6 | no | — |
| 265 | C22⋊C4 | — | 9 | 24 | no | — |
| 266 | C42 | — | 9 | 1 | no | — |
| 267 | C42 | — | 9 | 3 | no | — |
| 268 | C42 | — | 9 | 6 | no | — |
| 269 | C22×C3 | — | 2 | 6 | no | — |
| 270 | C22×C3 | — | 6 | 12 | no | — |
| 271 | C22×C3 | — | 24 | 12 | no | — |
| 272 | C2×D3 | — | 2 | 12 | no | — |
| 273 | C2×D3 | — | 6 | 2 | no | — |
| 274 | C2×D3 | — | 6 | 6 | no | — |
| 275 | C2×D3 | — | 8 | 12 | no | — |
| 276 | C2×D3 | — | 12 | 24 | no | — |
| 277 | C2×D3 | — | 12 | 12 | no | — |
| 278 | C2×D3 | — | 24 | 24 | no | — |
| 279 | C3×C4 | — | 2 | 2 | no | — |
| 280 | C3×C4 | — | 2 | 6 | no | — |
| 281 | C3×C4 | — | 6 | 4 | no | — |
| 282 | Dic3 | — | 2 | 4 | no | — |
| 283 | Dic3 | — | 6 | 2 | no | — |
| 284 | Dic3 | — | 6 | 6 | no | — |
| 285 | C32 | #3498 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 286 | C23 | — | 6 | 12 | no | — |
| 287 | C23 | — | 9 | 12 | no | — |
| 288 | C23 | — | 9 | 3 | no | — |
| 289 | C23 | — | 18 | 12 | no | — |
| 290 | C23 | — | 36 | 24 | no | — |
| 291 | Q8 | — | 6 | 2 | no | — |
| 292 | Q8 | — | 9 | 3 | no | — |
| 293 | Q8 | — | 18 | 2 | no | — |
| 294 | Q8 | C2×GO+(4,𝔽2) | 1 | 1 | yes | characteristic, complemented |
| 295 | D4 | — | 6 | 12 | no | — |
| 296 | D4 | — | 6 | 12 | no | — |
| 297 | D4 | — | 6 | 6 | no | — |
| 298 | D4 | — | 9 | 6 | no | — |
| 299 | D4 | — | 9 | 3 | no | — |
| 300 | D4 | — | 18 | 12 | no | — |
| 301 | D4 | — | 18 | 6 | no | — |
| 302 | D4 | — | 18 | 12 | no | — |
| 303 | D4 | — | 18 | 24 | no | — |
| 304 | D4 | — | 36 | 24 | no | — |
| 305 | D4 | C2×GO+(4,𝔽2) | 1 | 3 | yes | complemented |
| 306 | C2×C4 | — | 6 | 12 | no | — |
| 307 | C2×C4 | — | 9 | 4 | no | — |
| 308 | C2×C4 | — | 9 | 2 | no | — |
| 309 | C2×C4 | — | 9 | 3 | no | — |
| 310 | C2×C4 | — | 9 | 1 | no | — |
| 311 | C2×C4 | — | 9 | 3 | no | — |
| 312 | C2×C4 | — | 9 | 3 | no | — |
| 313 | C2×C4 | — | 9 | 3 | no | — |
| 314 | C2×C4 | — | 9 | 6 | no | — |
| 315 | C2×C4 | — | 18 | 12 | no | — |
| 316 | C2×C4 | — | 18 | 12 | no | — |
| 317 | C2×C4 | C2×GO+(4,𝔽2) | 1 | 3 | yes | complemented |
| 318 | C2×C3 | — | 2 | 2 | no | — |
| 319 | C2×C3 | — | 4 | 6 | no | — |
| 320 | C2×C3 | — | 12 | 12 | no | — |
| 321 | D3 | — | 4 | 12 | no | — |
| 322 | D3 | — | 6 | 4 | no | — |
| 323 | D3 | — | 12 | 6 | no | — |
| 324 | C22 | — | 6 | 12 | no | — |
| 325 | C22 | — | 9 | 1 | no | — |
| 326 | C22 | — | 9 | 3 | no | — |
| 327 | C22 | — | 18 | 6 | no | — |
| 328 | C22 | — | 18 | 24 | no | — |
| 329 | C22 | — | 24 | 12 | no | — |
| 330 | C22 | — | 72 | 12 | no | — |
| 331 | C22 | C22×GO+(4,𝔽2) | 1 | 3 | yes | — |
| 332 | C4 | — | 6 | 4 | no | — |
| 333 | C4 | — | 9 | 4 | no | — |
| 334 | C4 | — | 9 | 1 | no | — |
| 335 | C4 | — | 9 | 3 | no | — |
| 336 | C4 | — | 18 | 6 | no | — |
| 337 | C4 | C22×GO+(4,𝔽2) | 1 | 3 | yes | — |
| 338 | C4 | C22×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 339 | C3 | — | 2 | 2 | no | — |
| 340 | C2 | — | 2 | 3 | no | — |
| 341 | C2 | — | 9 | 2 | no | — |
| 342 | C2 | — | 12 | 12 | no | — |
| 343 | C2 | — | 18 | 3 | no | — |
| 344 | C2 | C23×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×GO+(4,𝔽2) |
| commutator, cosocle | C2×C3⋊D3 | C25 |
| Fitting | C32×#41 | D4 |
| socle | C2×C32 | C23×D4 |
| hypercenter | #41 | GO+(4,𝔽2) |
| hypocenter | C32 | #3498 |
| LCS | G ▷ C2×C3⋊D3 ▷ C32 | |
| UCS | C1 ◁ C2 ◁ #41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10596692 | C2 | semidirect |
| 2. #41×#157 | C2 | semidirect |
| 3. #10596525 | C2 | semidirect |
| 4. D4×GO+(4,𝔽2) | C2 | semidirect |
| 5. #10596512 | C2 | semidirect |
| 6. #10596511 | C2 | semidirect |
| 7. C2×#64231 | C2 | semidirect |
| 8. C22×GO+(4,𝔽2) | C22 | semidirect |
| 12. #64319 | C22 | semidirect |
| 14. D32×D4 | C22 | semidirect |
| 16. #64306 | C22 | semidirect |
| 17. C2×#3802 | C22 | semidirect |
| 18. Q8×#157 | C22 | semidirect |
| 19. D4×#157 | C22 | semidirect |
| 20. #64286 | C22 | semidirect |
| 21. C2×C4×#157 | C22 | semidirect |
| 22. #64242 | C22 | semidirect |
| 23. #64241 | C22 | semidirect |
| 24. #64231 | C22 | semidirect |
| 25. #64231 | C22 | semidirect |
| 26. #64231 | C22 | semidirect |
| 27. #64230 | C22 | semidirect |
| 28. C4×GO+(4,𝔽2) | C22 | semidirect |
| 29. #64222 | C22 | semidirect |
| 30. #64221 | C22 | semidirect |
| 37. C32×#41 | D4 | semidirect |
| 38. #3832 | D4 | semidirect |
| 40. #3830 | D4 | semidirect |
| 42. #3828 | D4 | semidirect |
| 91. C32×Q8 | C2×D4 | semidirect |
| 92. C32×D4 | C2×D4 | semidirect |
| 93. C2×C32×C4 | C2×D4 | semidirect |
| 94. #638 | C2×D4 | semidirect |
| 95. C2×C3⋊Dic3 | C2×D4 | semidirect |
| 96. C4⋊(C3⋊D3) | C2×D4 | semidirect |
| 97. C4×C3⋊D3 | C2×D4 | semidirect |
| 98. C4×C3⋊D3 | C2×D4 | semidirect |
| 101. #634 | C2×D4 | semidirect |
| 163. #157 | H(5,𝔽2) | semidirect |
| 242. #41 | GO+(4,𝔽2) | semidirect |
| 285. C32 | #3498 | semidirect |
| 294. Q8 | C2×GO+(4,𝔽2) | semidirect |
| 305. D4 | C2×GO+(4,𝔽2) | semidirect |
| 317. C2×C4 | C2×GO+(4,𝔽2) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596692 | 2 |
| #41×#157 | 2 |
| #10596525 | 2 |
| D4×GO+(4,𝔽2) | 2 |
| #10596512 | 2 |
| #10596511 | 2 |
| C2×#64231 | 2 |
| #3498 | 9 |