← C23×#2955 #15670574
Subgroups — C23×#2955 #15670574
Order 2944.
456 conjugacy classes of subgroups.
The subgroup lattice has 180 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C23×#575 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×C23×#131 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C23×#444 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | C23×#443 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | C23×#430 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C23×#421 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | C23×#405 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#41×C23 | C22 | 1 | 2 | yes | — |
| 9 | C23×#137 | C4 | 1 | 4 | yes | complemented |
| 10 | C23×AGL(1,ℤ/8) | C4 | 1 | 4 | yes | complemented |
| 11 | C23×#135 | C22 | 1 | 4 | yes | — |
| 12 | C23×#131 | — | 2 | 2 | no | — |
| 13 | C23×#131 | — | 2 | 2 | no | — |
| 14 | C23×#131 | C22 | 1 | 4 | yes | complemented |
| 15 | C23×#131 | C22 | 1 | 4 | yes | complemented |
| 16 | C2×M16×C23 | — | 2 | 2 | no | — |
| 17 | C2×M16×C23 | C22 | 1 | 2 | yes | — |
| 18 | C2×M16×C23 | C22 | 1 | 1 | yes | characteristic |
| 19 | C22×C8×C23 | — | 2 | 2 | no | — |
| 20 | C22×C8×C23 | C22 | 1 | 1 | yes | characteristic |
| 21 | C23×#117 | C22 | 1 | 1 | yes | characteristic |
| 22 | C23×#108 | C22 | 1 | 4 | yes | complemented |
| 23 | C23×#104 | C22 | 1 | 8 | yes | complemented |
| 24 | C23×#97 | C22 | 1 | 2 | yes | complemented |
| 25 | C4×C8×C23 | C22 | 1 | 2 | yes | complemented |
| 26 | #41×C23 | — | 2 | 2 | no | — |
| 27 | #41×C23 | — | 2 | 2 | no | — |
| 28 | #41×C23 | C2×C4 | 1 | 4 | yes | — |
| 29 | #41×C23 | C23 | 1 | 4 | yes | — |
| 30 | C2×Q8×C23 | C2×C4 | 1 | 2 | yes | — |
| 31 | C2×D4×C23 | — | 2 | 2 | no | — |
| 32 | C2×D4×C23 | C2×C4 | 1 | 2 | yes | — |
| 33 | C22×C4×C23 | — | 2 | 2 | no | — |
| 34 | C22×C4×C23 | C23 | 1 | 1 | yes | characteristic |
| 35 | Q16×C23 | C2×C4 | 1 | 4 | yes | — |
| 36 | SD16×C23 | C2×C4 | 1 | 8 | yes | — |
| 37 | D8×C23 | C2×C4 | 1 | 4 | yes | — |
| 38 | M16×C23 | — | 2 | 2 | no | — |
| 39 | M16×C23 | — | 2 | 4 | no | — |
| 40 | M16×C23 | — | 2 | 4 | no | — |
| 41 | M16×C23 | C2×C4 | 1 | 4 | yes | — |
| 42 | M16×C23 | C23 | 1 | 4 | yes | — |
| 43 | C2×C8×C23 | — | 2 | 2 | no | — |
| 44 | C2×C8×C23 | — | 2 | 4 | no | — |
| 45 | C2×C8×C23 | — | 2 | 4 | no | — |
| 46 | C2×C8×C23 | D4 | 1 | 2 | yes | — |
| 47 | C2×C8×C23 | D4 | 1 | 2 | yes | — |
| 48 | C2×C8×C23 | C23 | 1 | 2 | yes | — |
| 49 | C2×C8×C23 | C23 | 1 | 1 | yes | characteristic |
| 50 | C2×C8×C23 | C23 | 1 | 1 | yes | characteristic |
| 51 | C4⋊C4×C23 | — | 2 | 1 | no | — |
| 52 | C22⋊C4×C23 | — | 2 | 1 | no | — |
| 53 | C42×C23 | C23 | 1 | 2 | yes | — |
| 54 | C23×C23 | — | 2 | 2 | no | — |
| 55 | C23×C23 | #41 | 1 | 1 | yes | characteristic |
| 56 | Q8×C23 | — | 2 | 2 | no | — |
| 57 | Q8×C23 | C22×C4 | 1 | 4 | yes | — |
| 58 | D4×C23 | — | 2 | 4 | no | — |
| 59 | D4×C23 | — | 2 | 4 | no | — |
| 60 | D4×C23 | — | 2 | 2 | no | — |
| 61 | D4×C23 | C22×C4 | 1 | 4 | yes | — |
| 62 | C2×C4×C23 | — | 2 | 2 | no | — |
| 63 | C2×C4×C23 | — | 2 | 4 | no | — |
| 64 | C2×C4×C23 | — | 2 | 4 | no | — |
| 65 | C2×C4×C23 | — | 2 | 2 | no | — |
| 66 | C2×C4×C23 | C22×C4 | 1 | 2 | yes | — |
| 67 | C2×C4×C23 | C2×D4 | 1 | 2 | yes | — |
| 68 | C2×C4×C23 | #41 | 1 | 1 | yes | characteristic |
| 69 | C2×C4×C23 | C24 | 1 | 1 | yes | characteristic |
| 70 | C8×C23 | — | 2 | 4 | no | — |
| 71 | C8×C23 | C22×C4 | 1 | 4 | yes | — |
| 72 | C8×C23 | C2×D4 | 1 | 2 | yes | — |
| 73 | C8×C23 | C2×D4 | 1 | 1 | yes | characteristic |
| 74 | C8×C23 | C2×D4 | 1 | 1 | yes | characteristic |
| 75 | #2955 | C23 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 76 | C22×C23 | — | 2 | 4 | no | — |
| 77 | C22×C23 | — | 4 | 1 | no | — |
| 78 | C22×C23 | — | 4 | 4 | no | — |
| 79 | C22×C23 | C4×D4 | 1 | 2 | yes | — |
| 80 | C22×C23 | C2×#41 | 1 | 1 | yes | characteristic |
| 81 | C4×C23 | — | 2 | 4 | no | — |
| 82 | C4×C23 | — | 4 | 2 | no | — |
| 83 | C4×C23 | C4×D4 | 1 | 2 | yes | — |
| 84 | C4×C23 | C23×C4 | 1 | 1 | yes | characteristic |
| 85 | C4×C23 | C22×D4 | 1 | 1 | yes | characteristic |
| 86 | #575 | C2×C23 | 1 | 1 | yes | characteristic |
| 87 | C2×#131 | C2×C23 | 1 | 2 | yes | complemented |
| 88 | #444 | C2×C23 | 1 | 4 | yes | complemented |
| 89 | #443 | C2×C23 | 1 | 4 | yes | complemented |
| 90 | #430 | C2×C23 | 1 | 1 | yes | characteristic, complemented |
| 91 | #421 | C2×C23 | 1 | 2 | yes | complemented |
| 92 | #405 | C2×C23 | 1 | 1 | yes | characteristic, complemented |
| 93 | C2×C23 | — | 2 | 1 | no | — |
| 94 | C2×C23 | — | 2 | 2 | no | — |
| 95 | C2×C23 | — | 4 | 4 | no | — |
| 96 | C2×C23 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 97 | C2×#41 | C22×C23 | 1 | 2 | yes | — |
| 98 | #137 | C4×C23 | 1 | 4 | yes | complemented |
| 99 | AGL(1,ℤ/8) | C4×C23 | 1 | 4 | yes | complemented |
| 100 | #135 | C22×C23 | 1 | 4 | yes | — |
| 101 | #131 | — | 2 | 2 | no | — |
| 102 | #131 | — | 2 | 2 | no | — |
| 103 | #131 | C22×C23 | 1 | 4 | yes | complemented |
| 104 | #131 | C22×C23 | 1 | 4 | yes | complemented |
| 105 | C2×M16 | — | 2 | 2 | no | — |
| 106 | C2×M16 | C22×C23 | 1 | 2 | yes | — |
| 107 | C2×M16 | C22×C23 | 1 | 1 | yes | characteristic |
| 108 | C22×C8 | — | 2 | 2 | no | — |
| 109 | C22×C8 | C22×C23 | 1 | 1 | yes | characteristic |
| 110 | #117 | C22×C23 | 1 | 1 | yes | characteristic |
| 111 | #108 | C22×C23 | 1 | 4 | yes | complemented |
| 112 | #104 | C22×C23 | 1 | 8 | yes | complemented |
| 113 | #97 | C22×C23 | 1 | 2 | yes | complemented |
| 114 | C4×C8 | C22×C23 | 1 | 2 | yes | complemented |
| 115 | C23 | #2955 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 116 | #41 | — | 2 | 2 | no | — |
| 117 | #41 | — | 2 | 2 | no | — |
| 118 | #41 | C2×C4×C23 | 1 | 4 | yes | — |
| 119 | #41 | C23×C23 | 1 | 4 | yes | — |
| 120 | C2×Q8 | C2×C4×C23 | 1 | 2 | yes | — |
| 121 | C2×D4 | — | 2 | 2 | no | — |
| 122 | C2×D4 | C2×C4×C23 | 1 | 2 | yes | — |
| 123 | C22×C4 | — | 2 | 2 | no | — |
| 124 | C22×C4 | C23×C23 | 1 | 1 | yes | characteristic |
| 125 | Q16 | C2×C4×C23 | 1 | 4 | yes | — |
| 126 | SD16 | C2×C4×C23 | 1 | 8 | yes | — |
| 127 | D8 | C2×C4×C23 | 1 | 4 | yes | — |
| 128 | M16 | — | 2 | 2 | no | — |
| 129 | M16 | — | 2 | 4 | no | — |
| 130 | M16 | — | 2 | 4 | no | — |
| 131 | M16 | C2×C4×C23 | 1 | 4 | yes | — |
| 132 | M16 | C23×C23 | 1 | 4 | yes | — |
| 133 | C2×C8 | — | 2 | 2 | no | — |
| 134 | C2×C8 | — | 2 | 4 | no | — |
| 135 | C2×C8 | — | 2 | 4 | no | — |
| 136 | C2×C8 | D4×C23 | 1 | 2 | yes | — |
| 137 | C2×C8 | D4×C23 | 1 | 2 | yes | — |
| 138 | C2×C8 | C23×C23 | 1 | 2 | yes | — |
| 139 | C2×C8 | C23×C23 | 1 | 1 | yes | characteristic |
| 140 | C2×C8 | C23×C23 | 1 | 1 | yes | characteristic |
| 141 | C4⋊C4 | — | 2 | 1 | no | — |
| 142 | C22⋊C4 | — | 2 | 1 | no | — |
| 143 | C42 | C23×C23 | 1 | 2 | yes | — |
| 144 | C23 | — | 2 | 2 | no | — |
| 145 | C23 | #41×C23 | 1 | 1 | yes | characteristic |
| 146 | Q8 | — | 2 | 2 | no | — |
| 147 | Q8 | C22×C4×C23 | 1 | 4 | yes | — |
| 148 | D4 | — | 2 | 4 | no | — |
| 149 | D4 | — | 2 | 4 | no | — |
| 150 | D4 | — | 2 | 2 | no | — |
| 151 | D4 | C22×C4×C23 | 1 | 4 | yes | — |
| 152 | C2×C4 | — | 2 | 2 | no | — |
| 153 | C2×C4 | — | 2 | 4 | no | — |
| 154 | C2×C4 | — | 2 | 4 | no | — |
| 155 | C2×C4 | — | 2 | 2 | no | — |
| 156 | C2×C4 | C22×C4×C23 | 1 | 2 | yes | — |
| 157 | C2×C4 | C2×D4×C23 | 1 | 2 | yes | — |
| 158 | C2×C4 | #41×C23 | 1 | 1 | yes | characteristic |
| 159 | C2×C4 | C24×C23 | 1 | 1 | yes | characteristic |
| 160 | C8 | — | 2 | 4 | no | — |
| 161 | C8 | C22×C4×C23 | 1 | 4 | yes | — |
| 162 | C8 | C2×D4×C23 | 1 | 1 | yes | characteristic |
| 163 | C8 | C2×D4×C23 | 1 | 2 | yes | — |
| 164 | C8 | C2×D4×C23 | 1 | 1 | yes | characteristic |
| 165 | C22 | — | 2 | 4 | no | — |
| 166 | C22 | — | 4 | 1 | no | — |
| 167 | C22 | — | 4 | 4 | no | — |
| 168 | C22 | C4×D4×C23 | 1 | 2 | yes | — |
| 169 | C22 | C2×#41×C23 | 1 | 1 | yes | characteristic |
| 170 | C4 | — | 2 | 4 | no | — |
| 171 | C4 | — | 4 | 2 | no | — |
| 172 | C4 | C4×D4×C23 | 1 | 2 | yes | — |
| 173 | C4 | C23×C4×C23 | 1 | 1 | yes | characteristic |
| 174 | C4 | C22×D4×C23 | 1 | 1 | yes | characteristic |
| 175 | C2 | — | 2 | 1 | no | — |
| 176 | C2 | — | 2 | 2 | no | — |
| 177 | C2 | — | 4 | 4 | no | — |
| 178 | C2 | C2×C4×D4×C23 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta