Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
758 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 758 conjugacy classes of subgroups — too many to draw. Only its 144 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 | C2×#3415 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #33981 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#2263 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #33617 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #13671 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #13669 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | C2×#1419 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #13620 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #13558 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C2×#576 | — | 2 | 1 | no | — |
| 11 | #3415 | — | 2 | 2 | no | — |
| 12 | #3415 | — | 2 | 2 | no | — |
| 13 | #3415 | — | 2 | 2 | no | — |
| 14 | #3415 | C22 | 1 | 4 | yes | — |
| 15 | C2×#509 | — | 2 | 2 | no | — |
| 16 | C2×#509 | — | 2 | 1 | no | — |
| 17 | C2×#508 | — | 2 | 1 | no | — |
| 18 | C2×#508 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#508 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | C22×D16 | — | 2 | 1 | no | — |
| 21 | C22×D16 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#504 | C22 | 1 | 1 | yes | characteristic |
| 23 | #3067 | — | 2 | 1 | no | — |
| 24 | #2264 | — | 2 | 1 | no | — |
| 25 | #2264 | C22 | 1 | 2 | yes | complemented |
| 26 | #2263 | — | 2 | 2 | no | — |
| 27 | #2263 | — | 2 | 2 | no | — |
| 28 | #2263 | — | 2 | 1 | no | — |
| 29 | #2263 | C22 | 1 | 2 | yes | complemented |
| 30 | #2262 | — | 2 | 2 | no | — |
| 31 | C2×SD64 | C22 | 1 | 2 | yes | complemented |
| 32 | C2×D32 | C22 | 1 | 2 | yes | complemented |
| 33 | C2×M64 | C22 | 1 | 1 | yes | characteristic, complemented |
| 34 | C2×M64 | C22 | 1 | 1 | yes | characteristic, complemented |
| 35 | #2223 | — | 2 | 2 | no | — |
| 36 | #2222 | C22 | 1 | 2 | yes | complemented |
| 37 | #2221 | C22 | 1 | 2 | yes | complemented |
| 38 | C2×#368 | C22 | 1 | 1 | yes | characteristic, complemented |
| 39 | #2148 | — | 2 | 1 | no | — |
| 40 | #1419 | C22 | 1 | 4 | yes | complemented |
| 41 | #1417 | C22 | 1 | 4 | yes | complemented |
| 42 | #1401 | C22 | 1 | 4 | yes | complemented |
| 43 | C2×H(5,𝔽2) | — | 4 | 1 | no | — |
| 44 | #576 | — | 2 | 4 | no | — |
| 45 | #576 | — | 2 | 4 | no | — |
| 46 | #576 | — | 4 | 2 | no | — |
| 47 | #576 | — | 4 | 2 | no | — |
| 48 | #575 | — | 4 | 1 | no | — |
| 49 | C2×AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 50 | C2×AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 51 | C2×#135 | — | 2 | 2 | no | — |
| 52 | C2×#135 | — | 2 | 1 | no | — |
| 53 | C2×#135 | — | 2 | 1 | no | — |
| 54 | C22×D8 | — | 2 | 2 | no | — |
| 55 | C22×D8 | — | 2 | 1 | no | — |
| 56 | C2×#131 | D4 | 1 | 1 | yes | characteristic |
| 57 | #509 | — | 2 | 4 | no | — |
| 58 | #509 | — | 2 | 8 | no | — |
| 59 | #509 | — | 2 | 8 | no | — |
| 60 | #509 | — | 2 | 4 | no | — |
| 61 | #508 | — | 2 | 4 | no | — |
| 62 | #508 | — | 2 | 4 | no | — |
| 63 | #508 | — | 2 | 1 | no | — |
| 64 | #508 | — | 2 | 1 | no | — |
| 65 | #508 | — | 2 | 1 | no | — |
| 66 | #508 | — | 2 | 1 | no | — |
| 67 | #508 | — | 2 | 1 | no | — |
| 68 | #508 | — | 2 | 1 | no | — |
| 69 | #508 | D4 | 1 | 2 | yes | — |
| 70 | #508 | C23 | 1 | 2 | yes | — |
| 71 | C2×Q32 | D4 | 1 | 1 | yes | characteristic |
| 72 | C2×Q32 | C23 | 1 | 1 | yes | characteristic, complemented |
| 73 | C2×SD32 | — | 2 | 2 | no | — |
| 74 | C2×SD32 | — | 2 | 1 | no | — |
| 75 | C2×SD32 | — | 2 | 1 | no | — |
| 76 | C2×D16 | — | 2 | 2 | no | — |
| 77 | C2×D16 | — | 2 | 4 | no | — |
| 78 | C2×D16 | — | 2 | 4 | no | — |
| 79 | C2×D16 | — | 2 | 1 | no | — |
| 80 | C2×D16 | — | 2 | 1 | no | — |
| 81 | C2×D16 | — | 2 | 1 | no | — |
| 82 | C2×D16 | D4 | 1 | 1 | yes | characteristic |
| 83 | C2×D16 | D4 | 1 | 2 | yes | — |
| 84 | C2×D16 | D4 | 1 | 2 | yes | — |
| 85 | C2×D16 | C23 | 1 | 2 | yes | — |
| 86 | C2×D16 | C23 | 1 | 1 | yes | characteristic, complemented |
| 87 | #504 | — | 2 | 1 | no | — |
| 88 | #504 | — | 2 | 1 | no | — |
| 89 | #504 | D4 | 1 | 2 | yes | — |
| 90 | #504 | C23 | 1 | 2 | yes | — |
| 91 | C2×M32 | — | 2 | 1 | no | — |
| 92 | C2×M32 | D4 | 1 | 1 | yes | characteristic |
| 93 | C22×C16 | — | 2 | 1 | no | — |
| 94 | C22×C16 | C23 | 1 | 1 | yes | characteristic |
| 95 | #473 | — | 2 | 2 | no | — |
| 96 | #472 | — | 2 | 2 | no | — |
| 97 | #471 | — | 4 | 2 | no | — |
| 98 | C2×#108 | — | 2 | 1 | no | — |
| 99 | #413 | — | 4 | 1 | no | — |
| 100 | Q64 | — | 2 | 2 | no | — |
| 101 | SD64 | — | 2 | 2 | no | — |
| 102 | SD64 | — | 2 | 4 | no | — |
| 103 | SD64 | — | 2 | 2 | no | — |
| 104 | D32 | — | 2 | 4 | no | — |
| 105 | D32 | — | 2 | 2 | no | — |
| 106 | M64 | — | 2 | 1 | no | — |
| 107 | M64 | — | 2 | 1 | no | — |
| 108 | M64 | — | 2 | 1 | no | — |
| 109 | M64 | C23 | 1 | 2 | yes | complemented |
| 110 | C2×C32 | — | 2 | 1 | no | — |
| 111 | C2×C32 | C23 | 1 | 2 | yes | complemented |
| 112 | #368 | — | 2 | 1 | no | — |
| 113 | #368 | C23 | 1 | 2 | yes | complemented |
| 114 | #362 | — | 2 | 2 | no | — |
| 115 | #361 | — | 2 | 2 | no | — |
| 116 | H(5,𝔽2) | — | 4 | 4 | no | — |
| 117 | H(5,𝔽2) | — | 4 | 4 | no | — |
| 118 | H(5,𝔽2) | — | 8 | 2 | no | — |
| 119 | H(5,𝔽2) | — | 8 | 2 | no | — |
| 120 | C2×#41 | — | 4 | 2 | no | — |
| 121 | C2×#41 | — | 4 | 1 | no | — |
| 122 | C2×#41 | — | 4 | 1 | no | — |
| 123 | C2×#41 | — | 8 | 1 | no | — |
| 124 | C2×#41 | D8 | 1 | 1 | yes | characteristic |
| 125 | C22×D4 | — | 4 | 2 | no | — |
| 126 | C22×D4 | — | 4 | 1 | no | — |
| 127 | C22×D4 | — | 8 | 2 | no | — |
| 128 | C22×D4 | — | 8 | 1 | no | — |
| 129 | #137 | — | 4 | 2 | no | — |
| 130 | #137 | — | 8 | 1 | no | — |
| 131 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 132 | AGL(1,ℤ/8) | — | 4 | 8 | no | — |
| 133 | AGL(1,ℤ/8) | — | 4 | 8 | no | — |
| 134 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 135 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 136 | AGL(1,ℤ/8) | — | 8 | 1 | no | — |
| 137 | #135 | — | 2 | 8 | no | — |
| 138 | #135 | — | 2 | 2 | no | — |
| 139 | #135 | — | 2 | 2 | no | — |
| 140 | #135 | — | 4 | 4 | no | — |
| 141 | #135 | — | 4 | 1 | no | — |
| 142 | #135 | — | 4 | 1 | no | — |
| 143 | #135 | — | 4 | 1 | no | — |
| 144 | #135 | — | 4 | 1 | no | — |
| 145 | #135 | — | 4 | 1 | no | — |
| 146 | #135 | — | 4 | 1 | no | — |
| 147 | #135 | — | 8 | 2 | no | — |
| 148 | C2×Q16 | — | 2 | 1 | no | — |
| 149 | C2×Q16 | — | 2 | 1 | no | — |
| 150 | C2×SD16 | — | 4 | 2 | no | — |
| 151 | C2×SD16 | — | 4 | 1 | no | — |
| 152 | C2×SD16 | — | 4 | 1 | no | — |
| 153 | C2×D8 | — | 2 | 8 | no | — |
| 154 | C2×D8 | — | 2 | 1 | no | — |
| 155 | C2×D8 | — | 2 | 2 | no | — |
| 156 | C2×D8 | — | 2 | 2 | no | — |
| 157 | C2×D8 | — | 2 | 2 | no | — |
| 158 | C2×D8 | — | 2 | 1 | no | — |
| 159 | C2×D8 | — | 4 | 2 | no | — |
| 160 | C2×D8 | — | 4 | 4 | no | — |
| 161 | C2×D8 | — | 4 | 1 | no | — |
| 162 | C2×D8 | — | 4 | 1 | no | — |
| 163 | C2×D8 | — | 4 | 1 | no | — |
| 164 | #131 | — | 2 | 1 | no | — |
| 165 | #131 | — | 2 | 1 | no | — |
| 166 | #131 | D8 | 1 | 2 | yes | — |
| 167 | #131 | C2×D4 | 1 | 2 | yes | — |
| 168 | C2×M16 | — | 2 | 1 | no | — |
| 169 | C2×M16 | — | 4 | 1 | no | — |
| 170 | C2×M16 | D8 | 1 | 1 | yes | characteristic |
| 171 | C22×C8 | — | 2 | 1 | no | — |
| 172 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 173 | Q32 | — | 2 | 1 | no | — |
| 174 | Q32 | — | 2 | 1 | no | — |
| 175 | Q32 | — | 2 | 1 | no | — |
| 176 | Q32 | C2×D4 | 1 | 2 | yes | — |
| 177 | SD32 | — | 2 | 8 | no | — |
| 178 | SD32 | — | 2 | 2 | no | — |
| 179 | SD32 | — | 2 | 2 | no | — |
| 180 | SD32 | — | 4 | 1 | no | — |
| 181 | SD32 | — | 4 | 1 | no | — |
| 182 | D16 | — | 2 | 8 | no | — |
| 183 | D16 | — | 2 | 1 | no | — |
| 184 | D16 | — | 2 | 2 | no | — |
| 185 | D16 | — | 2 | 2 | no | — |
| 186 | D16 | — | 2 | 2 | no | — |
| 187 | D16 | — | 2 | 1 | no | — |
| 188 | D16 | — | 2 | 1 | no | — |
| 189 | D16 | C2×D4 | 1 | 2 | yes | — |
| 190 | D16 | C2×D4 | 1 | 4 | yes | — |
| 191 | M32 | — | 2 | 1 | no | — |
| 192 | M32 | — | 2 | 2 | no | — |
| 193 | M32 | — | 2 | 2 | no | — |
| 194 | M32 | C2×D4 | 1 | 2 | yes | — |
| 195 | C2×C16 | — | 2 | 1 | no | — |
| 196 | C2×C16 | — | 2 | 2 | no | — |
| 197 | C2×C16 | — | 2 | 2 | no | — |
| 198 | C2×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 199 | C2×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 200 | C2×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 201 | C2×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 202 | C2×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 203 | C2×C16 | C24 | 1 | 1 | yes | characteristic |
| 204 | #108 | — | 2 | 2 | no | — |
| 205 | #108 | — | 4 | 1 | no | — |
| 206 | #101 | — | 4 | 2 | no | — |
| 207 | #100 | — | 4 | 2 | no | — |
| 208 | C32 | — | 2 | 2 | no | — |
| 209 | C32 | — | 2 | 2 | no | — |
| 210 | C24 | — | 8 | 2 | no | — |
| 211 | C24 | — | 8 | 1 | no | — |
| 212 | #41 | — | 2 | 1 | no | — |
| 213 | #41 | — | 2 | 1 | no | — |
| 214 | #41 | — | 4 | 8 | no | — |
| 215 | #41 | — | 4 | 2 | no | — |
| 216 | #41 | — | 4 | 2 | no | — |
| 217 | #41 | — | 8 | 4 | no | — |
| 218 | #41 | — | 8 | 4 | no | — |
| 219 | #41 | — | 8 | 4 | no | — |
| 220 | #41 | — | 8 | 1 | no | — |
| 221 | #41 | — | 8 | 1 | no | — |
| 222 | #41 | — | 8 | 1 | no | — |
| 223 | #41 | — | 8 | 1 | no | — |
| 224 | #41 | — | 8 | 1 | no | — |
| 225 | #41 | — | 8 | 1 | no | — |
| 226 | #41 | D16 | 1 | 2 | yes | — |
| 227 | #41 | C2×D8 | 1 | 2 | yes | — |
| 228 | C2×Q8 | — | 4 | 1 | no | — |
| 229 | C2×Q8 | — | 4 | 1 | no | — |
| 230 | C2×Q8 | D16 | 1 | 1 | yes | characteristic |
| 231 | C2×D4 | — | 2 | 1 | no | — |
| 232 | C2×D4 | — | 4 | 8 | no | — |
| 233 | C2×D4 | — | 4 | 2 | no | — |
| 234 | C2×D4 | — | 4 | 1 | no | — |
| 235 | C2×D4 | — | 4 | 1 | no | — |
| 236 | C2×D4 | — | 4 | 2 | no | — |
| 237 | C2×D4 | — | 4 | 2 | no | — |
| 238 | C2×D4 | — | 8 | 2 | no | — |
| 239 | C2×D4 | — | 8 | 4 | no | — |
| 240 | C2×D4 | — | 8 | 8 | no | — |
| 241 | C2×D4 | — | 8 | 8 | no | — |
| 242 | C2×D4 | — | 8 | 4 | no | — |
| 243 | C2×D4 | — | 8 | 2 | no | — |
| 244 | C2×D4 | — | 8 | 1 | no | — |
| 245 | C2×D4 | — | 8 | 4 | no | — |
| 246 | C2×D4 | — | 8 | 1 | no | — |
| 247 | C2×D4 | — | 8 | 1 | no | — |
| 248 | C2×D4 | — | 8 | 1 | no | — |
| 249 | C2×D4 | — | 8 | 1 | no | — |
| 250 | C2×D4 | D16 | 1 | 1 | yes | characteristic |
| 251 | C22×C4 | — | 2 | 1 | no | — |
| 252 | C22×C4 | — | 8 | 2 | no | — |
| 253 | C22×C4 | — | 8 | 1 | no | — |
| 254 | C22×C4 | — | 8 | 1 | no | — |
| 255 | C22×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 256 | Q16 | — | 2 | 2 | no | — |
| 257 | Q16 | — | 4 | 1 | no | — |
| 258 | Q16 | — | 4 | 1 | no | — |
| 259 | Q16 | — | 4 | 1 | no | — |
| 260 | Q16 | — | 8 | 2 | no | — |
| 261 | SD16 | — | 4 | 8 | no | — |
| 262 | SD16 | — | 4 | 2 | no | — |
| 263 | SD16 | — | 4 | 2 | no | — |
| 264 | SD16 | — | 8 | 2 | no | — |
| 265 | SD16 | — | 8 | 2 | no | — |
| 266 | SD16 | — | 8 | 1 | no | — |
| 267 | SD16 | — | 8 | 1 | no | — |
| 268 | D8 | — | 2 | 2 | no | — |
| 269 | D8 | — | 2 | 4 | no | — |
| 270 | D8 | — | 4 | 8 | no | — |
| 271 | D8 | — | 4 | 1 | no | — |
| 272 | D8 | — | 4 | 2 | no | — |
| 273 | D8 | — | 4 | 1 | no | — |
| 274 | D8 | — | 4 | 1 | no | — |
| 275 | D8 | — | 4 | 2 | no | — |
| 276 | D8 | — | 4 | 2 | no | — |
| 277 | D8 | — | 8 | 2 | no | — |
| 278 | M16 | — | 2 | 1 | no | — |
| 279 | M16 | — | 2 | 2 | no | — |
| 280 | M16 | — | 2 | 2 | no | — |
| 281 | M16 | — | 4 | 2 | no | — |
| 282 | M16 | — | 8 | 1 | no | — |
| 283 | M16 | C2×D8 | 1 | 2 | yes | — |
| 284 | C2×C8 | — | 2 | 1 | no | — |
| 285 | C2×C8 | — | 2 | 2 | no | — |
| 286 | C2×C8 | — | 2 | 2 | no | — |
| 287 | C2×C8 | — | 8 | 1 | no | — |
| 288 | C2×C8 | #120 | 1 | 1 | yes | characteristic |
| 289 | C2×C8 | #120 | 1 | 1 | yes | characteristic |
| 290 | C2×C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 291 | C2×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 292 | C2×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 293 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 294 | C16 | — | 2 | 2 | no | — |
| 295 | C16 | #120 | 1 | 1 | yes | characteristic |
| 296 | C16 | #120 | 1 | 1 | yes | characteristic |
| 297 | C16 | C22×D4 | 1 | 1 | yes | characteristic |
| 298 | C16 | C22×D4 | 1 | 1 | yes | characteristic |
| 299 | C23 | — | 2 | 1 | no | — |
| 300 | C23 | — | 8 | 8 | no | — |
| 301 | C23 | — | 8 | 2 | no | — |
| 302 | C23 | — | 8 | 1 | no | — |
| 303 | C23 | — | 8 | 2 | no | — |
| 304 | C23 | — | 8 | 2 | no | — |
| 305 | C23 | — | 8 | 1 | no | — |
| 306 | C23 | — | 32 | 2 | no | — |
| 307 | C23 | — | 32 | 4 | no | — |
| 308 | C23 | #509 | 1 | 1 | yes | characteristic |
| 309 | Q8 | — | 2 | 1 | no | — |
| 310 | Q8 | — | 4 | 2 | no | — |
| 311 | Q8 | — | 8 | 1 | no | — |
| 312 | Q8 | — | 8 | 1 | no | — |
| 313 | Q8 | — | 8 | 1 | no | — |
| 314 | Q8 | C2×D16 | 1 | 2 | yes | — |
| 315 | D4 | — | 2 | 2 | no | — |
| 316 | D4 | — | 2 | 2 | no | — |
| 317 | D4 | — | 2 | 1 | no | — |
| 318 | D4 | — | 4 | 2 | no | — |
| 319 | D4 | — | 4 | 4 | no | — |
| 320 | D4 | — | 8 | 8 | no | — |
| 321 | D4 | — | 8 | 8 | no | — |
| 322 | D4 | — | 8 | 2 | no | — |
| 323 | D4 | — | 8 | 2 | no | — |
| 324 | D4 | — | 8 | 2 | no | — |
| 325 | D4 | — | 8 | 1 | no | — |
| 326 | D4 | — | 8 | 1 | no | — |
| 327 | D4 | — | 8 | 2 | no | — |
| 328 | D4 | — | 8 | 2 | no | — |
| 329 | D4 | — | 8 | 1 | no | — |
| 330 | D4 | — | 16 | 1 | no | — |
| 331 | D4 | — | 16 | 1 | no | — |
| 332 | D4 | C2×D16 | 1 | 2 | yes | — |
| 333 | C2×C4 | — | 2 | 1 | no | — |
| 334 | C2×C4 | — | 2 | 2 | no | — |
| 335 | C2×C4 | — | 2 | 2 | no | — |
| 336 | C2×C4 | — | 8 | 8 | no | — |
| 337 | C2×C4 | — | 8 | 1 | no | — |
| 338 | C2×C4 | — | 8 | 2 | no | — |
| 339 | C2×C4 | — | 8 | 2 | no | — |
| 340 | C2×C4 | — | 8 | 1 | no | — |
| 341 | C2×C4 | — | 16 | 1 | no | — |
| 342 | C2×C4 | — | 16 | 1 | no | — |
| 343 | C2×C4 | #447 | 1 | 1 | yes | characteristic |
| 344 | C2×C4 | #447 | 1 | 1 | yes | characteristic |
| 345 | C2×C4 | C2×D16 | 1 | 1 | yes | characteristic |
| 346 | C2×C4 | C2×D16 | 1 | 1 | yes | characteristic |
| 347 | C2×C4 | #509 | 1 | 1 | yes | characteristic |
| 348 | C2×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 349 | C8 | — | 2 | 2 | no | — |
| 350 | C8 | — | 8 | 2 | no | — |
| 351 | C8 | #447 | 1 | 1 | yes | characteristic |
| 352 | C8 | #447 | 1 | 1 | yes | characteristic |
| 353 | C8 | C2×#120 | 1 | 1 | yes | characteristic |
| 354 | C8 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 355 | C22 | — | 2 | 2 | no | — |
| 356 | C22 | — | 4 | 1 | no | — |
| 357 | C22 | — | 4 | 2 | no | — |
| 358 | C22 | — | 8 | 4 | no | — |
| 359 | C22 | — | 8 | 2 | no | — |
| 360 | C22 | — | 16 | 4 | no | — |
| 361 | C22 | — | 16 | 2 | no | — |
| 362 | C22 | — | 16 | 1 | no | — |
| 363 | C22 | — | 32 | 2 | no | — |
| 364 | C22 | — | 32 | 2 | no | — |
| 365 | C22 | — | 32 | 1 | no | — |
| 366 | C22 | — | 32 | 8 | no | — |
| 367 | C22 | #2184 | 1 | 1 | yes | characteristic |
| 368 | C22 | #2184 | 1 | 1 | yes | characteristic |
| 369 | C22 | C2×#509 | 1 | 1 | yes | characteristic |
| 370 | C4 | — | 2 | 2 | no | — |
| 371 | C4 | — | 8 | 2 | no | — |
| 372 | C4 | — | 16 | 1 | no | — |
| 373 | C4 | #2184 | 1 | 1 | yes | characteristic |
| 374 | C4 | #2184 | 1 | 1 | yes | characteristic |
| 375 | C4 | C2×#447 | 1 | 1 | yes | characteristic |
| 376 | C4 | C22×D16 | 1 | 1 | yes | characteristic |
| 377 | C2 | — | 2 | 1 | no | — |
| 378 | C2 | — | 2 | 1 | no | — |
| 379 | C2 | — | 2 | 1 | no | — |
| 380 | C2 | — | 4 | 2 | no | — |
| 381 | C2 | — | 16 | 4 | no | — |
| 382 | C2 | — | 16 | 2 | no | — |
| 383 | C2 | — | 32 | 1 | no | — |
| 384 | C2 | C2×#2184 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | C2×#2184 |
| commutator, Frattini, cosocle | C2×C16 | C24 |
| LCS | G ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ C2×#131 ◁ C2×#504 ◁ G | |
| LECS | G ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#3415 | C2 | semidirect |
| 2. #33981 | C2 | semidirect |
| 3. C2×#2263 | C2 | semidirect |
| 4. #33617 | C2 | semidirect |
| 5. #13671 | C2 | semidirect |
| 6. #13669 | C2 | semidirect |
| 7. C2×#1419 | C2 | semidirect |
| 8. #13620 | C2 | semidirect |
| 9. #13558 | C2 | semidirect |
| 19. C2×#508 | C22 | semidirect |
| 25. #2264 | C22 | semidirect |
| 29. #2263 | C22 | semidirect |
| 31. C2×SD64 | C22 | semidirect |
| 32. C2×D32 | C22 | semidirect |
| 33. C2×M64 | C22 | semidirect |
| 34. C2×M64 | C22 | semidirect |
| 36. #2222 | C22 | semidirect |
| 37. #2221 | C22 | semidirect |
| 38. C2×#368 | C22 | semidirect |
| 40. #1419 | C22 | semidirect |
| 41. #1417 | C22 | semidirect |
| 42. #1401 | C22 | semidirect |
| 72. C2×Q32 | C23 | semidirect |
| 86. C2×D16 | C23 | semidirect |
| 109. M64 | C23 | semidirect |
| 111. C2×C32 | C23 | semidirect |
| 113. #368 | C23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3415 | 2 |
| #33981 | 2 |
| C2×#2263 | 2 |
| #33617 | 2 |
| #13671 | 2 |
| #13669 | 2 |
| C2×#1419 | 2 |
| #13620 | 2 |
| #13558 | 2 |