Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
932 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 932 conjugacy classes of subgroups — too many to draw. Only its 157 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×#6503 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#6500 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#6493 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C2×#6445 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C7×#386 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #89733 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #89732 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #89443 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #89442 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | C24×D7 | C22 | 1 | 1 | yes | characteristic |
| 11 | C22×C7×D4 | C22 | 1 | 1 | yes | characteristic |
| 12 | C23×C4×C7 | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | C22×C22⋊D7 | C22 | 1 | 2 | yes | — |
| 14 | C22×C22⋊D7 | C22 | 1 | 2 | yes | — |
| 15 | C22×C22⋊D7 | C22 | 1 | 2 | yes | complemented |
| 16 | C22×D28 | C22 | 1 | 2 | yes | — |
| 17 | C22×D28 | C22 | 1 | 2 | yes | — |
| 18 | C22×D28 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | C2×C7×C22⋊C4 | C22 | 1 | 2 | yes | — |
| 20 | C2×C7×C22⋊C4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | C2×C22⋊Dic7 | C22 | 1 | 1 | yes | characteristic |
| 22 | #6503 | — | 2 | 4 | no | — |
| 23 | #6500 | — | 2 | 4 | no | — |
| 24 | #6493 | — | 2 | 8 | no | — |
| 25 | C2×(C2×D7)⋊C4 | C22 | 1 | 2 | yes | — |
| 26 | C2×(C2×D7)⋊C4 | C22 | 1 | 2 | yes | — |
| 27 | C2×(C2×D7)⋊C4 | C22 | 1 | 2 | yes | — |
| 28 | C2×(C2×D7)⋊C4 | C22 | 1 | 2 | yes | complemented |
| 29 | C2×(C2×D7)⋊C4 | C22 | 1 | 2 | yes | complemented |
| 30 | C2×C4⋊Dic7 | C22 | 1 | 2 | yes | complemented |
| 31 | C2×C4×Dic7 | C22 | 1 | 1 | yes | characteristic, complemented |
| 32 | #6445 | — | 2 | 8 | no | — |
| 33 | C7×#95 | C22 | 1 | 2 | yes | complemented |
| 34 | C7⋊#95 | C22 | 1 | 2 | yes | complemented |
| 35 | #2669 | — | 7 | 1 | no | maximal, Sylow |
| 36 | C24×C7 | C23 | 1 | 1 | yes | characteristic |
| 37 | C24×C7 | C23 | 1 | 1 | yes | characteristic |
| 38 | C23×D7 | — | 2 | 2 | no | — |
| 39 | C23×D7 | — | 2 | 4 | no | — |
| 40 | C23×D7 | — | 4 | 1 | no | — |
| 41 | C23×D7 | — | 4 | 1 | no | — |
| 42 | C23×D7 | — | 4 | 2 | no | — |
| 43 | C23×D7 | C23 | 1 | 2 | yes | — |
| 44 | C23×D7 | C23 | 1 | 2 | yes | — |
| 45 | C2×C7×D4 | — | 4 | 1 | no | — |
| 46 | C2×C7×D4 | — | 4 | 1 | no | — |
| 47 | C2×C7×D4 | D4 | 1 | 4 | yes | complemented |
| 48 | C22×C4×C7 | — | 2 | 4 | no | — |
| 49 | C22×C4×C7 | — | 4 | 1 | no | — |
| 50 | C22×C4×C7 | C23 | 1 | 2 | yes | — |
| 51 | C22×C4×C7 | C23 | 1 | 1 | yes | characteristic |
| 52 | C22×C4×C7 | C23 | 1 | 2 | yes | — |
| 53 | C2×C22⋊D7 | — | 2 | 4 | no | — |
| 54 | C2×C22⋊D7 | — | 2 | 4 | no | — |
| 55 | C2×C22⋊D7 | — | 2 | 4 | no | — |
| 56 | C2×C22⋊D7 | — | 2 | 4 | no | — |
| 57 | C2×C22⋊D7 | — | 2 | 4 | no | — |
| 58 | C2×C22⋊D7 | — | 2 | 4 | no | — |
| 59 | C2×C22⋊D7 | — | 4 | 2 | no | — |
| 60 | C2×C22⋊D7 | — | 4 | 2 | no | — |
| 61 | C2×C22⋊D7 | — | 4 | 2 | no | — |
| 62 | C22×Dic7 | C23 | 1 | 2 | yes | — |
| 63 | C22×Dic7 | C23 | 1 | 2 | yes | — |
| 64 | C2×D28 | — | 2 | 4 | no | — |
| 65 | C2×D28 | — | 2 | 4 | no | — |
| 66 | C2×D28 | — | 2 | 4 | no | — |
| 67 | C2×D28 | — | 2 | 2 | no | — |
| 68 | C2×D28 | — | 4 | 2 | no | — |
| 69 | C2×D28 | — | 4 | 2 | no | — |
| 70 | C2×D28 | — | 4 | 2 | no | — |
| 71 | C2×D28 | — | 4 | 1 | no | — |
| 72 | C2×D28 | — | 4 | 1 | no | — |
| 73 | C7×C22⋊C4 | — | 2 | 4 | no | — |
| 74 | C7×C22⋊C4 | — | 4 | 1 | no | — |
| 75 | C22⋊Dic7 | — | 2 | 2 | no | — |
| 76 | (C2×D7)⋊C4 | — | 2 | 4 | no | — |
| 77 | (C2×D7)⋊C4 | — | 2 | 4 | no | — |
| 78 | (C2×D7)⋊C4 | — | 2 | 4 | no | — |
| 79 | (C2×D7)⋊C4 | — | 4 | 2 | no | — |
| 80 | (C2×D7)⋊C4 | D4 | 1 | 8 | yes | complemented |
| 81 | C4⋊Dic7 | — | 2 | 4 | no | — |
| 82 | C4×Dic7 | — | 2 | 2 | no | — |
| 83 | C2×#127 | — | 7 | 1 | no | — |
| 84 | C2×#121 | — | 7 | 2 | no | — |
| 85 | C2×#120 | — | 7 | 1 | no | — |
| 86 | C2×#120 | — | 7 | 2 | no | — |
| 87 | #394 | — | 7 | 2 | no | — |
| 88 | #392 | — | 7 | 2 | no | — |
| 89 | #392 | — | 7 | 2 | no | — |
| 90 | #388 | — | 7 | 2 | no | — |
| 91 | #386 | D7 | 1 | 1 | yes | characteristic, complemented |
| 92 | C23×C7 | — | 2 | 2 | no | — |
| 93 | C23×C7 | — | 2 | 2 | no | — |
| 94 | C23×C7 | — | 2 | 1 | no | — |
| 95 | C23×C7 | — | 2 | 2 | no | — |
| 96 | C23×C7 | — | 2 | 2 | no | — |
| 97 | C23×C7 | — | 2 | 1 | no | — |
| 98 | C23×C7 | — | 2 | 1 | no | — |
| 99 | C23×C7 | — | 2 | 1 | no | — |
| 100 | C23×C7 | C2×D4 | 1 | 2 | yes | — |
| 101 | C23×C7 | C2×D4 | 1 | 2 | yes | — |
| 102 | C23×C7 | C24 | 1 | 1 | yes | characteristic |
| 103 | C22×D7 | — | 2 | 2 | no | — |
| 104 | C22×D7 | — | 2 | 2 | no | — |
| 105 | C22×D7 | — | 2 | 2 | no | — |
| 106 | C22×D7 | — | 2 | 2 | no | — |
| 107 | C22×D7 | — | 2 | 2 | no | — |
| 108 | C22×D7 | — | 2 | 2 | no | — |
| 109 | C22×D7 | — | 2 | 2 | no | — |
| 110 | C22×D7 | — | 2 | 2 | no | — |
| 111 | C22×D7 | — | 2 | 2 | no | — |
| 112 | C22×D7 | — | 2 | 2 | no | — |
| 113 | C22×D7 | — | 2 | 2 | no | — |
| 114 | C22×D7 | — | 2 | 2 | no | — |
| 115 | C22×D7 | — | 2 | 2 | no | — |
| 116 | C22×D7 | — | 4 | 4 | no | — |
| 117 | C22×D7 | — | 4 | 8 | no | — |
| 118 | C22×D7 | — | 4 | 8 | no | — |
| 119 | C22×D7 | — | 4 | 4 | no | — |
| 120 | C22×D7 | — | 4 | 4 | no | — |
| 121 | C22×D7 | C2×D4 | 1 | 4 | yes | — |
| 122 | C7×D4 | — | 4 | 4 | no | — |
| 123 | C2×C4×C7 | — | 2 | 2 | no | — |
| 124 | C2×C4×C7 | — | 2 | 2 | no | — |
| 125 | C2×C4×C7 | — | 2 | 1 | no | — |
| 126 | C2×C4×C7 | — | 2 | 1 | no | — |
| 127 | C2×C4×C7 | — | 2 | 2 | no | — |
| 128 | C2×C4×C7 | — | 2 | 2 | no | — |
| 129 | C2×C4×C7 | — | 2 | 2 | no | — |
| 130 | C2×C4×C7 | — | 4 | 4 | no | — |
| 131 | C2×C4×C7 | C2×D4 | 1 | 2 | yes | — |
| 132 | C2×C4×C7 | C2×D4 | 1 | 4 | yes | — |
| 133 | C22⋊D7 | — | 4 | 8 | no | — |
| 134 | C22⋊D7 | — | 4 | 8 | no | — |
| 135 | C22⋊D7 | — | 4 | 8 | no | — |
| 136 | C2×Dic7 | — | 2 | 2 | no | — |
| 137 | C2×Dic7 | — | 2 | 2 | no | — |
| 138 | C2×Dic7 | — | 2 | 2 | no | — |
| 139 | C2×Dic7 | — | 2 | 2 | no | — |
| 140 | C2×Dic7 | — | 2 | 2 | no | — |
| 141 | C2×Dic7 | C2×D4 | 1 | 4 | yes | — |
| 142 | D28 | — | 4 | 8 | no | — |
| 143 | D28 | — | 4 | 4 | no | — |
| 144 | D28 | — | 4 | 8 | no | — |
| 145 | C25 | — | 7 | 1 | no | — |
| 146 | C22×D4 | — | 7 | 2 | no | — |
| 147 | C22×D4 | — | 7 | 2 | no | — |
| 148 | C22×D4 | — | 7 | 2 | no | — |
| 149 | C22×D4 | — | 7 | 2 | no | — |
| 150 | C22×D4 | — | 7 | 2 | no | — |
| 151 | C22×D4 | — | 7 | 1 | no | — |
| 152 | C22×D4 | C2×D7 | 1 | 1 | yes | characteristic |
| 153 | C23×C4 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 154 | #127 | — | 14 | 4 | no | — |
| 155 | #121 | — | 14 | 8 | no | — |
| 156 | #120 | — | 14 | 8 | no | — |
| 157 | #120 | — | 14 | 4 | no | — |
| 158 | C2×C4⋊C4 | — | 7 | 2 | no | — |
| 159 | C2×C22⋊C4 | — | 7 | 2 | no | — |
| 160 | C2×C22⋊C4 | — | 7 | 1 | no | — |
| 161 | C2×C22⋊C4 | — | 7 | 2 | no | — |
| 162 | C2×C22⋊C4 | — | 7 | 2 | no | — |
| 163 | C2×C22⋊C4 | — | 7 | 2 | no | — |
| 164 | C2×C22⋊C4 | — | 7 | 2 | no | — |
| 165 | C2×C22⋊C4 | C2×D7 | 1 | 2 | yes | — |
| 166 | C2×C22⋊C4 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 167 | C2×C42 | — | 7 | 1 | no | — |
| 168 | #95 | — | 7 | 2 | no | — |
| 169 | #95 | C2×D7 | 1 | 2 | yes | complemented |
| 170 | C22×C7 | — | 2 | 2 | no | — |
| 171 | C22×C7 | — | 2 | 2 | no | — |
| 172 | C22×C7 | — | 2 | 4 | no | — |
| 173 | C22×C7 | — | 2 | 4 | no | — |
| 174 | C22×C7 | — | 4 | 2 | no | — |
| 175 | C22×C7 | — | 4 | 2 | no | — |
| 176 | C22×C7 | — | 4 | 1 | no | — |
| 177 | C22×C7 | — | 4 | 1 | no | — |
| 178 | C22×C7 | — | 4 | 1 | no | — |
| 179 | C22×C7 | — | 4 | 1 | no | — |
| 180 | C22×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 181 | C22×C7 | C22×D4 | 1 | 2 | yes | — |
| 182 | C22×C7 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 183 | C22×C7 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 184 | C22×C7 | H(5,𝔽2) | 1 | 2 | yes | — |
| 185 | C2×D7 | — | 2 | 4 | no | — |
| 186 | C2×D7 | — | 2 | 4 | no | — |
| 187 | C2×D7 | — | 2 | 4 | no | — |
| 188 | C2×D7 | — | 4 | 16 | no | — |
| 189 | C2×D7 | — | 4 | 2 | no | — |
| 190 | C2×D7 | — | 4 | 2 | no | — |
| 191 | C2×D7 | — | 4 | 2 | no | — |
| 192 | C2×D7 | — | 4 | 2 | no | — |
| 193 | C2×D7 | — | 4 | 2 | no | — |
| 194 | C2×D7 | — | 4 | 2 | no | — |
| 195 | C2×D7 | — | 4 | 2 | no | — |
| 196 | C2×D7 | — | 4 | 2 | no | — |
| 197 | C2×D7 | — | 4 | 2 | no | — |
| 198 | C2×D7 | — | 4 | 2 | no | — |
| 199 | C2×D7 | — | 4 | 2 | no | — |
| 200 | C4×C7 | — | 2 | 2 | no | — |
| 201 | C4×C7 | — | 2 | 4 | no | — |
| 202 | C4×C7 | — | 4 | 2 | no | — |
| 203 | Dic7 | — | 2 | 4 | no | — |
| 204 | Dic7 | — | 4 | 2 | no | — |
| 205 | C24 | — | 7 | 2 | no | — |
| 206 | C24 | — | 7 | 2 | no | — |
| 207 | C24 | — | 14 | 4 | no | — |
| 208 | C24 | — | 14 | 2 | no | — |
| 209 | C24 | — | 28 | 1 | no | — |
| 210 | C24 | — | 28 | 1 | no | — |
| 211 | C24 | — | 28 | 2 | no | — |
| 212 | C24 | C22×D7 | 1 | 1 | yes | characteristic |
| 213 | C24 | C22×D7 | 1 | 1 | yes | characteristic |
| 214 | C2×D4 | — | 4 | 1 | no | — |
| 215 | C2×D4 | — | 4 | 1 | no | — |
| 216 | C2×D4 | — | 14 | 4 | no | — |
| 217 | C2×D4 | — | 14 | 4 | no | — |
| 218 | C2×D4 | — | 14 | 4 | no | — |
| 219 | C2×D4 | — | 14 | 4 | no | — |
| 220 | C2×D4 | — | 14 | 4 | no | — |
| 221 | C2×D4 | — | 14 | 4 | no | — |
| 222 | C2×D4 | — | 14 | 4 | no | — |
| 223 | C2×D4 | — | 14 | 4 | no | — |
| 224 | C2×D4 | — | 14 | 2 | no | — |
| 225 | C2×D4 | — | 14 | 4 | no | — |
| 226 | C2×D4 | — | 28 | 2 | no | — |
| 227 | C2×D4 | — | 28 | 1 | no | — |
| 228 | C2×D4 | — | 28 | 1 | no | — |
| 229 | C2×D4 | — | 28 | 2 | no | — |
| 230 | C2×D4 | — | 28 | 2 | no | — |
| 231 | C2×D4 | — | 28 | 2 | no | — |
| 232 | C2×D4 | — | 28 | 2 | no | — |
| 233 | C2×D4 | — | 28 | 2 | no | — |
| 234 | C2×D4 | D28 | 1 | 4 | yes | complemented |
| 235 | C22×C4 | — | 2 | 4 | no | — |
| 236 | C22×C4 | — | 4 | 1 | no | — |
| 237 | C22×C4 | — | 7 | 2 | no | — |
| 238 | C22×C4 | — | 7 | 2 | no | — |
| 239 | C22×C4 | C22×D7 | 1 | 2 | yes | — |
| 240 | C22×C4 | C22×D7 | 1 | 1 | yes | characteristic |
| 241 | C22×C4 | C22×D7 | 1 | 2 | yes | — |
| 242 | C4⋊C4 | — | 14 | 4 | no | — |
| 243 | C22⋊C4 | — | 2 | 4 | no | — |
| 244 | C22⋊C4 | — | 4 | 1 | no | — |
| 245 | C22⋊C4 | — | 7 | 8 | no | — |
| 246 | C22⋊C4 | — | 14 | 4 | no | — |
| 247 | C22⋊C4 | — | 14 | 2 | no | — |
| 248 | C22⋊C4 | — | 14 | 4 | no | — |
| 249 | C22⋊C4 | — | 14 | 4 | no | — |
| 250 | C22⋊C4 | — | 28 | 2 | no | — |
| 251 | C42 | — | 14 | 2 | no | — |
| 252 | C2×C7 | — | 4 | 2 | no | — |
| 253 | C2×C7 | — | 4 | 2 | no | — |
| 254 | C2×C7 | #534 | 1 | 1 | yes | characteristic |
| 255 | C2×C7 | #535 | 1 | 2 | yes | — |
| 256 | C2×C7 | D42 | 1 | 2 | yes | — |
| 257 | C2×C7 | D42 | 1 | 1 | yes | characteristic |
| 258 | C2×C7 | #560 | 1 | 1 | yes | characteristic |
| 259 | D7 | — | 4 | 4 | no | — |
| 260 | D7 | — | 8 | 2 | no | — |
| 261 | C23 | — | 2 | 2 | no | — |
| 262 | C23 | — | 2 | 2 | no | — |
| 263 | C23 | — | 2 | 1 | no | — |
| 264 | C23 | — | 2 | 1 | no | — |
| 265 | C23 | — | 2 | 1 | no | — |
| 266 | C23 | — | 2 | 1 | no | — |
| 267 | C23 | — | 2 | 2 | no | — |
| 268 | C23 | — | 2 | 2 | no | — |
| 269 | C23 | — | 7 | 4 | no | — |
| 270 | C23 | — | 14 | 2 | no | — |
| 271 | C23 | — | 14 | 2 | no | — |
| 272 | C23 | — | 14 | 2 | no | — |
| 273 | C23 | — | 14 | 2 | no | — |
| 274 | C23 | — | 14 | 2 | no | — |
| 275 | C23 | — | 14 | 2 | no | — |
| 276 | C23 | — | 14 | 2 | no | — |
| 277 | C23 | — | 14 | 2 | no | — |
| 278 | C23 | — | 14 | 2 | no | — |
| 279 | C23 | — | 14 | 2 | no | — |
| 280 | C23 | — | 14 | 2 | no | — |
| 281 | C23 | — | 14 | 2 | no | — |
| 282 | C23 | — | 14 | 2 | no | — |
| 283 | C23 | — | 28 | 8 | no | — |
| 284 | C23 | — | 28 | 4 | no | — |
| 285 | C23 | — | 28 | 4 | no | — |
| 286 | C23 | — | 28 | 8 | no | — |
| 287 | C23 | — | 28 | 4 | no | — |
| 288 | C23 | C2×D28 | 1 | 2 | yes | — |
| 289 | C23 | C2×D28 | 1 | 2 | yes | — |
| 290 | C23 | C23×D7 | 1 | 1 | yes | characteristic |
| 291 | D4 | — | 4 | 4 | no | — |
| 292 | D4 | — | 28 | 8 | no | — |
| 293 | D4 | — | 28 | 4 | no | — |
| 294 | D4 | — | 28 | 8 | no | — |
| 295 | D4 | — | 28 | 8 | no | — |
| 296 | D4 | — | 28 | 8 | no | — |
| 297 | D4 | — | 28 | 8 | no | — |
| 298 | C2×C4 | — | 2 | 2 | no | — |
| 299 | C2×C4 | — | 2 | 2 | no | — |
| 300 | C2×C4 | — | 2 | 1 | no | — |
| 301 | C2×C4 | — | 2 | 1 | no | — |
| 302 | C2×C4 | — | 2 | 2 | no | — |
| 303 | C2×C4 | — | 2 | 2 | no | — |
| 304 | C2×C4 | — | 2 | 2 | no | — |
| 305 | C2×C4 | — | 4 | 4 | no | — |
| 306 | C2×C4 | — | 7 | 4 | no | — |
| 307 | C2×C4 | — | 14 | 2 | no | — |
| 308 | C2×C4 | — | 14 | 2 | no | — |
| 309 | C2×C4 | — | 14 | 2 | no | — |
| 310 | C2×C4 | — | 14 | 2 | no | — |
| 311 | C2×C4 | — | 14 | 2 | no | — |
| 312 | C2×C4 | C2×D28 | 1 | 2 | yes | — |
| 313 | C2×C4 | D4×D7 | 1 | 4 | yes | — |
| 314 | C7 | #2669 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 315 | C22 | — | 2 | 2 | no | — |
| 316 | C22 | — | 2 | 2 | no | — |
| 317 | C22 | — | 2 | 4 | no | — |
| 318 | C22 | — | 2 | 4 | no | — |
| 319 | C22 | — | 4 | 1 | no | — |
| 320 | C22 | — | 4 | 1 | no | — |
| 321 | C22 | — | 4 | 2 | no | — |
| 322 | C22 | — | 4 | 2 | no | — |
| 323 | C22 | — | 4 | 1 | no | — |
| 324 | C22 | — | 4 | 1 | no | — |
| 325 | C22 | — | 14 | 4 | no | — |
| 326 | C22 | — | 14 | 4 | no | — |
| 327 | C22 | — | 14 | 4 | no | — |
| 328 | C22 | — | 28 | 16 | no | — |
| 329 | C22 | — | 28 | 2 | no | — |
| 330 | C22 | — | 28 | 2 | no | — |
| 331 | C22 | — | 28 | 2 | no | — |
| 332 | C22 | — | 28 | 2 | no | — |
| 333 | C22 | — | 28 | 2 | no | — |
| 334 | C22 | — | 28 | 2 | no | — |
| 335 | C22 | — | 28 | 2 | no | — |
| 336 | C22 | — | 28 | 2 | no | — |
| 337 | C22 | — | 28 | 2 | no | — |
| 338 | C22 | — | 28 | 2 | no | — |
| 339 | C22 | — | 28 | 2 | no | — |
| 340 | C22 | C22×D28 | 1 | 1 | yes | characteristic |
| 341 | C22 | C2×D4×D7 | 1 | 2 | yes | — |
| 342 | C22 | #6548 | 1 | 1 | yes | characteristic |
| 343 | C22 | #6548 | 1 | 1 | yes | characteristic |
| 344 | C22 | #6553 | 1 | 2 | yes | — |
| 345 | C4 | — | 2 | 2 | no | — |
| 346 | C4 | — | 2 | 4 | no | — |
| 347 | C4 | — | 4 | 2 | no | — |
| 348 | C4 | — | 14 | 4 | no | — |
| 349 | C4 | — | 28 | 2 | no | — |
| 350 | C2 | — | 4 | 2 | no | — |
| 351 | C2 | — | 4 | 2 | no | — |
| 352 | C2 | — | 28 | 4 | no | — |
| 353 | C2 | — | 56 | 2 | no | — |
| 354 | C2 | #90184 | 1 | 1 | yes | characteristic |
| 355 | C2 | D4×D28 | 1 | 2 | yes | — |
| 356 | C2 | #90281 | 1 | 1 | yes | characteristic |
| 357 | C2 | #90298 | 1 | 2 | yes | — |
| 358 | C2 | #90357 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D7 |
| commutator, socle, cosocle | C23×C7 | C24 |
| Fitting | C7×#386 | C2 |
| hypercenter | #386 | D7 |
| hypocenter | C7 | #2669 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ #386 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#6503 | C2 | semidirect |
| 2. C2×#6500 | C2 | semidirect |
| 3. C2×#6493 | C2 | semidirect |
| 4. C2×#6445 | C2 | semidirect |
| 5. C7×#386 | C2 | semidirect |
| 6. #89733 | C2 | semidirect |
| 7. #89732 | C2 | semidirect |
| 8. #89443 | C2 | semidirect |
| 9. #89442 | C2 | semidirect |
| 12. C23×C4×C7 | C22 | semidirect |
| 15. C22×C22⋊D7 | C22 | semidirect |
| 18. C22×D28 | C22 | semidirect |
| 20. C2×C7×C22⋊C4 | C22 | semidirect |
| 28. C2×(C2×D7)⋊C4 | C22 | semidirect |
| 29. C2×(C2×D7)⋊C4 | C22 | semidirect |
| 30. C2×C4⋊Dic7 | C22 | semidirect |
| 31. C2×C4×Dic7 | C22 | semidirect |
| 33. C7×#95 | C22 | semidirect |
| 34. C7⋊#95 | C22 | semidirect |
| 47. C2×C7×D4 | D4 | semidirect |
| 80. (C2×D7)⋊C4 | D4 | semidirect |
| 91. #386 | D7 | semidirect |
| 153. C23×C4 | C2×D7 | semidirect |
| 166. C2×C22⋊C4 | C2×D7 | semidirect |
| 169. #95 | C2×D7 | semidirect |
| 234. C2×D4 | D28 | semidirect |
| 314. C7 | #2669 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6503 | 2 |
| C2×#6500 | 2 |
| C2×#6493 | 2 |
| C2×#6445 | 2 |
| C7×#386 | 2 |
| #89733 | 2 |
| #89732 | 2 |
| #89443 | 2 |
| #89442 | 2 |
| #2669 | 7 |