p-groups

Groups of order 2

dρLabelID
C2Cyclic group21+C22,1

Groups of order 3

dρLabelID
C3Cyclic group; = A3 = triangle rotations31C33,1

Groups of order 4

dρLabelID
C4Cyclic group; = square rotations41C44,1
C22Klein 4-group V4 = elementary abelian group of type [2,2]; = rectangle symmetries4C2^24,2

Groups of order 5

dρLabelID
C5Cyclic group; = pentagon rotations51C55,1

Groups of order 7

dρLabelID
C7Cyclic group71C77,1

Groups of order 8

dρLabelID
C8Cyclic group81C88,1
D4Dihedral group; = He2 = AΣL1(𝔽4) = 2+ 1+2 = square symmetries42+D48,3
Q8Quaternion group; = C4.C2 = Dic2 = 2- 1+282-Q88,4
C23Elementary abelian group of type [2,2,2]8C2^38,5
C2×C4Abelian group of type [2,4]8C2xC48,2

Groups of order 9

dρLabelID
C9Cyclic group91C99,1
C32Elementary abelian group of type [3,3]9C3^29,2

Groups of order 11

dρLabelID
C11Cyclic group111C1111,1

Groups of order 13

dρLabelID
C13Cyclic group131C1313,1

Groups of order 16

dρLabelID
C16Cyclic group161C1616,1
D8Dihedral group82+D816,7
Q16Generalised quaternion group; = C8.C2 = Dic4162-Q1616,9
SD16Semidihedral group; = Q8C2 = QD1682SD1616,8
M4(2)Modular maximal-cyclic group; = C83C282M4(2)16,6
C4○D4Pauli group = central product of C4 and D482C4oD416,13
C22⋊C4The semidirect product of C22 and C4 acting via C4/C2=C28C2^2:C416,3
C4⋊C4The semidirect product of C4 and C4 acting via C4/C2=C216C4:C416,4
C42Abelian group of type [4,4]16C4^216,2
C24Elementary abelian group of type [2,2,2,2]16C2^416,14
C2×C8Abelian group of type [2,8]16C2xC816,5
C22×C4Abelian group of type [2,2,4]16C2^2xC416,10
C2×D4Direct product of C2 and D48C2xD416,11
C2×Q8Direct product of C2 and Q816C2xQ816,12

Groups of order 17

dρLabelID
C17Cyclic group171C1717,1

Groups of order 19

dρLabelID
C19Cyclic group191C1919,1

Groups of order 23

dρLabelID
C23Cyclic group231C2323,1

Groups of order 25

dρLabelID
C25Cyclic group251C2525,1
C52Elementary abelian group of type [5,5]25C5^225,2

Groups of order 27

dρLabelID
C27Cyclic group271C2727,1
He3Heisenberg group; = C32C3 = 3+ 1+293He327,3
3- 1+2Extraspecial group93ES-(3,1)27,4
C33Elementary abelian group of type [3,3,3]27C3^327,5
C3×C9Abelian group of type [3,9]27C3xC927,2

Groups of order 29

dρLabelID
C29Cyclic group291C2929,1

Groups of order 31

dρLabelID
C31Cyclic group311C3131,1

Groups of order 32

dρLabelID
C32Cyclic group321C3232,1
D16Dihedral group162+D1632,18
Q32Generalised quaternion group; = C16.C2 = Dic8322-Q3232,20
2+ 1+4Extraspecial group; = D4D484+ES+(2,2)32,49
SD32Semidihedral group; = C162C2 = QD32162SD3232,19
2- 1+4Gamma matrices = Extraspecial group; = D4Q8164-ES-(2,2)32,50
M5(2)Modular maximal-cyclic group; = C163C2162M5(2)32,17
C4≀C2Wreath product of C4 by C282C4wrC232,11
C22≀C2Wreath product of C22 by C28C2^2wrC232,27
C8○D4Central product of C8 and D4162C8oD432,38
C4○D8Central product of C4 and D8162C4oD832,42
C23⋊C4The semidirect product of C23 and C4 acting faithfully84+C2^3:C432,6
C8⋊C22The semidirect product of C8 and C22 acting faithfully; = Aut(D8) = Hol(C8)84+C8:C2^232,43
C4⋊D4The semidirect product of C4 and D4 acting via D4/C22=C216C4:D432,28
C41D4The semidirect product of C4 and D4 acting via D4/C4=C216C4:1D432,34
C22⋊C8The semidirect product of C22 and C8 acting via C8/C4=C216C2^2:C832,5
C22⋊Q8The semidirect product of C22 and Q8 acting via Q8/C4=C216C2^2:Q832,29
D4⋊C41st semidirect product of D4 and C4 acting via C4/C2=C216D4:C432,9
C42⋊C21st semidirect product of C42 and C2 acting faithfully16C4^2:C232,24
C422C22nd semidirect product of C42 and C2 acting faithfully16C4^2:2C232,33
C4⋊C8The semidirect product of C4 and C8 acting via C8/C4=C232C4:C832,12
C4⋊Q8The semidirect product of C4 and Q8 acting via Q8/C4=C232C4:Q832,35
C8⋊C43rd semidirect product of C8 and C4 acting via C4/C2=C232C8:C432,4
Q8⋊C41st semidirect product of Q8 and C4 acting via C4/C2=C232Q8:C432,10
C4.D41st non-split extension by C4 of D4 acting via D4/C22=C284+C4.D432,7
C8.C41st non-split extension by C8 of C4 acting via C4/C2=C2162C8.C432,15
C4.4D44th non-split extension by C4 of D4 acting via D4/C4=C216C4.4D432,31
C8.C22The non-split extension by C8 of C22 acting faithfully164-C8.C2^232,44
C4.10D42nd non-split extension by C4 of D4 acting via D4/C22=C2164-C4.10D432,8
C22.D43rd non-split extension by C22 of D4 acting via D4/C22=C216C2^2.D432,30
C2.D82nd central extension by C2 of D832C2.D832,14
C4.Q81st non-split extension by C4 of Q8 acting via Q8/C4=C232C4.Q832,13
C2.C421st central stem extension by C2 of C4232C2.C4^232,2
C42.C24th non-split extension by C42 of C2 acting faithfully32C4^2.C232,32
C25Elementary abelian group of type [2,2,2,2,2]32C2^532,51
C4×C8Abelian group of type [4,8]32C4xC832,3
C2×C16Abelian group of type [2,16]32C2xC1632,16
C2×C42Abelian group of type [2,4,4]32C2xC4^232,21
C22×C8Abelian group of type [2,2,8]32C2^2xC832,36
C23×C4Abelian group of type [2,2,2,4]32C2^3xC432,45
C4×D4Direct product of C4 and D416C4xD432,25
C2×D8Direct product of C2 and D816C2xD832,39
C2×SD16Direct product of C2 and SD1616C2xSD1632,40
C22×D4Direct product of C22 and D416C2^2xD432,46
C2×M4(2)Direct product of C2 and M4(2)16C2xM4(2)32,37
C4×Q8Direct product of C4 and Q832C4xQ832,26
C2×Q16Direct product of C2 and Q1632C2xQ1632,41
C22×Q8Direct product of C22 and Q832C2^2xQ832,47
C2×C4○D4Direct product of C2 and C4○D416C2xC4oD432,48
C2×C22⋊C4Direct product of C2 and C22⋊C416C2xC2^2:C432,22
C2×C4⋊C4Direct product of C2 and C4⋊C432C2xC4:C432,23

Groups of order 37

dρLabelID
C37Cyclic group371C3737,1

Groups of order 41

dρLabelID
C41Cyclic group411C4141,1

Groups of order 43

dρLabelID
C43Cyclic group431C4343,1

Groups of order 47

dρLabelID
C47Cyclic group471C4747,1

Groups of order 49

dρLabelID
C49Cyclic group491C4949,1
C72Elementary abelian group of type [7,7]49C7^249,2

Groups of order 53

dρLabelID
C53Cyclic group531C5353,1

Groups of order 59

dρLabelID
C59Cyclic group591C5959,1

Groups of order 61

dρLabelID
C61Cyclic group611C6161,1

Groups of order 64

dρLabelID
C64Cyclic group641C6464,1
D32Dihedral group322+D3264,52
Q64Generalised quaternion group; = C32.C2 = Dic16642-Q6464,54
SD64Semidihedral group; = C322C2 = QD64322SD6464,53
M6(2)Modular maximal-cyclic group; = C323C2322M6(2)64,51
C2≀C4Wreath product of C2 by C4; = AΣL1(𝔽16)84+C2wrC464,32
C2≀C22Wreath product of C2 by C22; = Hol(C2×C4)84+C2wrC2^264,138
C8○D8Central product of C8 and D8162C8oD864,124
D4○D8Central product of D4 and D8164+D4oD864,257
Q8○SD16Central product of Q8 and SD16164Q8oSD1664,258
D4○M4(2)Central product of D4 and M4(2)164D4oM4(2)64,249
Q8○D8Central product of Q8 and D8324-Q8oD864,259
D4○C16Central product of D4 and C16322D4oC1664,185
C4○D16Central product of C4 and D16322C4oD1664,189
C82M4(2)Central product of C8 and M4(2)32C8o2M4(2)64,86
D44D43rd semidirect product of D4 and D4 acting via D4/C22=C2; = Hol(D4)84+D4:4D464,134
C42⋊C42nd semidirect product of C42 and C4 acting faithfully84+C4^2:C464,34
C23⋊C8The semidirect product of C23 and C8 acting via C8/C2=C416C2^3:C864,4
C16⋊C42nd semidirect product of C16 and C4 acting faithfully164C16:C464,28
D82C42nd semidirect product of D8 and C4 acting via C4/C2=C2164D8:2C464,41
D45D41st semidirect product of D4 and D4 acting through Inn(D4)16D4:5D464,227
C16⋊C22The semidirect product of C16 and C22 acting faithfully164+C16:C2^264,190
C426C43rd semidirect product of C42 and C4 acting via C4/C2=C216C4^2:6C464,20
C423C43rd semidirect product of C42 and C4 acting faithfully164C4^2:3C464,35
C243C41st semidirect product of C24 and C4 acting via C4/C2=C216C2^4:3C464,60
C22⋊D8The semidirect product of C22 and D8 acting via D8/D4=C216C2^2:D864,128
C233D42nd semidirect product of C23 and D4 acting via D4/C2=C2216C2^3:3D464,215
C232Q82nd semidirect product of C23 and Q8 acting via Q8/C2=C2216C2^3:2Q864,224
D8⋊C224th semidirect product of D8 and C22 acting via C22/C2=C2164D8:C2^264,256
M4(2)⋊4C44th semidirect product of M4(2) and C4 acting via C4/C2=C2164M4(2):4C464,25
M5(2)⋊C26th semidirect product of M5(2) and C2 acting faithfully164+M5(2):C264,42
C42⋊C221st semidirect product of C42 and C22 acting faithfully164C4^2:C2^264,102
C24⋊C224th semidirect product of C24 and C22 acting faithfully16C2^4:C2^264,242
C22⋊SD16The semidirect product of C22 and SD16 acting via SD16/D4=C216C2^2:SD1664,131
D4⋊C8The semidirect product of D4 and C8 acting via C8/C4=C232D4:C864,6
C89D43rd semidirect product of C8 and D4 acting via D4/C22=C232C8:9D464,116
C86D43rd semidirect product of C8 and D4 acting via D4/C4=C232C8:6D464,117
C4⋊D8The semidirect product of C4 and D8 acting via D8/D4=C232C4:D864,140
C88D42nd semidirect product of C8 and D4 acting via D4/C22=C232C8:8D464,146
C87D41st semidirect product of C8 and D4 acting via D4/C22=C232C8:7D464,147
C8⋊D41st semidirect product of C8 and D4 acting via D4/C2=C2232C8:D464,149
C82D42nd semidirect product of C8 and D4 acting via D4/C2=C2232C8:2D464,150
C85D42nd semidirect product of C8 and D4 acting via D4/C4=C232C8:5D464,173
C84D41st semidirect product of C8 and D4 acting via D4/C4=C232C8:4D464,174
C83D43rd semidirect product of C8 and D4 acting via D4/C2=C2232C8:3D464,177
D8⋊C43rd semidirect product of D8 and C4 acting via C4/C2=C2; = Aut(SD32)32D8:C464,123
D4⋊D42nd semidirect product of D4 and D4 acting via D4/C22=C232D4:D464,130
D46D42nd semidirect product of D4 and D4 acting through Inn(D4)32D4:6D464,228
C22⋊C16The semidirect product of C22 and C16 acting via C16/C8=C232C2^2:C1664,29
Q8⋊D41st semidirect product of Q8 and D4 acting via D4/C22=C232Q8:D464,129
D4⋊Q81st semidirect product of D4 and Q8 acting via Q8/C4=C232D4:Q864,155
D42Q82nd semidirect product of D4 and Q8 acting via Q8/C4=C232D4:2Q864,157
Q85D41st semidirect product of Q8 and D4 acting through Inn(Q8)32Q8:5D464,229
Q86D42nd semidirect product of Q8 and D4 acting through Inn(Q8)32Q8:6D464,231
D43Q8The semidirect product of D4 and Q8 acting through Inn(D4)32D4:3Q864,235
Q32⋊C22nd semidirect product of Q32 and C2 acting faithfully324-Q32:C264,191
C4⋊SD16The semidirect product of C4 and SD16 acting via SD16/Q8=C232C4:SD1664,141
C232D41st semidirect product of C23 and D4 acting via D4/C2=C2232C2^3:2D464,73
C23⋊Q81st semidirect product of C23 and Q8 acting via Q8/C2=C2232C2^3:Q864,74
SD16⋊C41st semidirect product of SD16 and C4 acting via C4/C2=C232SD16:C464,121
C4⋊M4(2)The semidirect product of C4 and M4(2) acting via M4(2)/C2×C4=C232C4:M4(2)64,104
C22⋊Q16The semidirect product of C22 and Q16 acting via Q16/Q8=C232C2^2:Q1664,132
M4(2)⋊C41st semidirect product of M4(2) and C4 acting via C4/C2=C232M4(2):C464,109
C8⋊Q8The semidirect product of C8 and Q8 acting via Q8/C2=C2264C8:Q864,182
C4⋊C16The semidirect product of C4 and C16 acting via C16/C8=C264C4:C1664,44
Q8⋊C8The semidirect product of Q8 and C8 acting via C8/C4=C264Q8:C864,7
C8⋊C83rd semidirect product of C8 and C8 acting via C8/C4=C264C8:C864,3
C82C82nd semidirect product of C8 and C8 acting via C8/C4=C264C8:2C864,15
C81C81st semidirect product of C8 and C8 acting via C8/C4=C264C8:1C864,16
C84Q83rd semidirect product of C8 and Q8 acting via Q8/C4=C264C8:4Q864,127
C83Q82nd semidirect product of C8 and Q8 acting via Q8/C4=C264C8:3Q864,179
C82Q81st semidirect product of C8 and Q8 acting via Q8/C4=C264C8:2Q864,181
C165C43rd semidirect product of C16 and C4 acting via C4/C2=C264C16:5C464,27
C163C41st semidirect product of C16 and C4 acting via C4/C2=C264C16:3C464,47
C164C42nd semidirect product of C16 and C4 acting via C4/C2=C264C16:4C464,48
Q8⋊Q81st semidirect product of Q8 and Q8 acting via Q8/C4=C264Q8:Q864,156
Q83Q8The semidirect product of Q8 and Q8 acting through Inn(Q8)64Q8:3Q864,238
C42Q16The semidirect product of C4 and Q16 acting via Q16/Q8=C264C4:2Q1664,143
C4⋊Q16The semidirect product of C4 and Q16 acting via Q16/C8=C264C4:Q1664,175
C424C41st semidirect product of C42 and C4 acting via C4/C2=C264C4^2:4C464,57
C428C45th semidirect product of C42 and C4 acting via C4/C2=C264C4^2:8C464,63
C425C42nd semidirect product of C42 and C4 acting via C4/C2=C264C4^2:5C464,64
C429C46th semidirect product of C42 and C4 acting via C4/C2=C264C4^2:9C464,65
Q16⋊C43rd semidirect product of Q16 and C4 acting via C4/C2=C264Q16:C464,122
(C22×C8)⋊C22nd semidirect product of C22×C8 and C2 acting faithfully32(C2^2xC8):C264,89
C8.Q8The non-split extension by C8 of Q8 acting via Q8/C2=C22164C8.Q864,46
C8.C81st non-split extension by C8 of C8 acting via C8/C4=C2162C8.C864,45
C23.C8The non-split extension by C23 of C8 acting via C8/C2=C4164C2^3.C864,30
D4.8D43rd non-split extension by D4 of D4 acting via D4/C22=C2164D4.8D464,135
D4.9D44th non-split extension by D4 of D4 acting via D4/C22=C2164D4.9D464,136
D4.3D43rd non-split extension by D4 of D4 acting via D4/C4=C2164D4.3D464,152
D4.4D44th non-split extension by D4 of D4 acting via D4/C4=C2164+D4.4D464,153
C8.26D413rd non-split extension by C8 of D4 acting via D4/C22=C2164C8.26D464,125
D4.10D45th non-split extension by D4 of D4 acting via D4/C22=C2164-D4.10D464,137
C4.9C421st central stem extension by C4 of C42164C4.9C4^264,18
C42.C42nd non-split extension by C42 of C4 acting faithfully164C4^2.C464,36
C42.3C43rd non-split extension by C42 of C4 acting faithfully164-C4^2.3C464,37
C24.4C42nd non-split extension by C24 of C4 acting via C4/C2=C216C2^4.4C464,88
C2.C256th central stem extension by C2 of C25164C2.C2^564,266
C23.9D42nd non-split extension by C23 of D4 acting via D4/C2=C2216C2^3.9D464,23
C23.D42nd non-split extension by C23 of D4 acting faithfully164C2^3.D464,33
C23.7D47th non-split extension by C23 of D4 acting faithfully164C2^3.7D464,139
C4.10C422nd central stem extension by C4 of C42164C4.10C4^264,19
C23.31D42nd non-split extension by C23 of D4 acting via D4/C22=C216C2^3.31D464,9
C23.37D48th non-split extension by C23 of D4 acting via D4/C22=C216C2^3.37D464,99
M4(2).C41st non-split extension by M4(2) of C4 acting via C4/C2=C2164M4(2).C464,111
C23.C232nd non-split extension by C23 of C23 acting via C23/C2=C22164C2^3.C2^364,91
C22.SD161st non-split extension by C22 of SD16 acting via SD16/Q8=C216C2^2.SD1664,8
C22.11C247th central extension by C22 of C2416C2^2.11C2^464,199
C22.19C245th central stem extension by C22 of C2416C2^2.19C2^464,206
C22.29C2415th central stem extension by C22 of C2416C2^2.29C2^464,216
C22.32C2418th central stem extension by C22 of C2416C2^2.32C2^464,219
C22.45C2431st central stem extension by C22 of C2416C2^2.45C2^464,232
C22.54C2440th central stem extension by C22 of C2416C2^2.54C2^464,241
M4(2).8C223rd non-split extension by M4(2) of C22 acting via C22/C2=C2164M4(2).8C2^264,94
D4.C8The non-split extension by D4 of C8 acting via C8/C4=C2322D4.C864,31
D4.Q8The non-split extension by D4 of Q8 acting via Q8/C4=C232D4.Q864,159
C4.D81st non-split extension by C4 of D8 acting via D8/D4=C232C4.D864,12
C8.D41st non-split extension by C8 of D4 acting via D4/C2=C2232C8.D464,151
C4.4D84th non-split extension by C4 of D8 acting via D8/C8=C232C4.4D864,167
C8.2D42nd non-split extension by C8 of D4 acting via D4/C2=C2232C8.2D464,178
C8.4Q83rd non-split extension by C8 of Q8 acting via Q8/C4=C2322C8.4Q864,49
D8.C41st non-split extension by D8 of C4 acting via C4/C2=C2322D8.C464,40
D4.7D42nd non-split extension by D4 of D4 acting via D4/C22=C232D4.7D464,133
D4.D41st non-split extension by D4 of D4 acting via D4/C4=C232D4.D464,142
D4.2D42nd non-split extension by D4 of D4 acting via D4/C4=C232D4.2D464,144
D4.5D45th non-split extension by D4 of D4 acting via D4/C4=C2324-D4.5D464,154
C2.D161st central extension by C2 of D1632C2.D1664,38
C8.17D44th non-split extension by C8 of D4 acting via D4/C22=C2324-C8.17D464,43
C8.18D45th non-split extension by C8 of D4 acting via D4/C22=C232C8.18D464,148
C8.12D48th non-split extension by C8 of D4 acting via D4/C4=C232C8.12D464,176
Q8.D42nd non-split extension by Q8 of D4 acting via D4/C4=C232Q8.D464,145
C4.C423rd non-split extension by C4 of C42 acting via C42/C2×C4=C232C4.C4^264,22
C42.6C43rd non-split extension by C42 of C4 acting via C4/C2=C232C4^2.6C464,113
C22.D83rd non-split extension by C22 of D8 acting via D8/D4=C232C2^2.D864,161
C23.7Q82nd non-split extension by C23 of Q8 acting via Q8/C4=C232C2^3.7Q864,61
C23.8Q83rd non-split extension by C23 of Q8 acting via Q8/C4=C232C2^3.8Q864,66
C23.Q83rd non-split extension by C23 of Q8 acting via Q8/C2=C2232C2^3.Q864,77
C23.4Q84th non-split extension by C23 of Q8 acting via Q8/C2=C2232C2^3.4Q864,80
C42.12C49th non-split extension by C42 of C4 acting via C4/C2=C232C4^2.12C464,112
C23.34D45th non-split extension by C23 of D4 acting via D4/C22=C232C2^3.34D464,62
C23.23D42nd non-split extension by C23 of D4 acting via D4/C4=C232C2^3.23D464,67
C23.10D43rd non-split extension by C23 of D4 acting via D4/C2=C2232C2^3.10D464,75
C23.11D44th non-split extension by C23 of D4 acting via D4/C2=C2232C2^3.11D464,78
C23.24D43rd non-split extension by C23 of D4 acting via D4/C4=C232C2^3.24D464,97
C23.36D47th non-split extension by C23 of D4 acting via D4/C22=C232C2^3.36D464,98
C23.38D49th non-split extension by C23 of D4 acting via D4/C22=C232C2^3.38D464,100
C23.25D44th non-split extension by C23 of D4 acting via D4/C4=C232C2^3.25D464,108
C23.46D417th non-split extension by C23 of D4 acting via D4/C22=C232C2^3.46D464,162
C23.19D412nd non-split extension by C23 of D4 acting via D4/C2=C2232C2^3.19D464,163
C23.47D418th non-split extension by C23 of D4 acting via D4/C22=C232C2^3.47D464,164
C23.48D419th non-split extension by C23 of D4 acting via D4/C22=C232C2^3.48D464,165
C23.20D413rd non-split extension by C23 of D4 acting via D4/C2=C2232C2^3.20D464,166
C42.C221st non-split extension by C42 of C22 acting faithfully32C4^2.C2^264,10
C22.C422nd non-split extension by C22 of C42 acting via C42/C2×C4=C232C2^2.C4^264,24
C24.C222nd non-split extension by C24 of C22 acting faithfully32C2^4.C2^264,69
C24.3C223rd non-split extension by C24 of C22 acting faithfully32C2^4.3C2^264,71
C42.6C226th non-split extension by C42 of C22 acting faithfully32C4^2.6C2^264,105
C42.7C227th non-split extension by C42 of C22 acting faithfully32C4^2.7C2^264,114
C42.78C2221st non-split extension by C42 of C22 acting via C22/C2=C232C4^2.78C2^264,169
C42.28C2228th non-split extension by C42 of C22 acting faithfully32C4^2.28C2^264,170
C42.29C2229th non-split extension by C42 of C22 acting faithfully32C4^2.29C2^264,171
C23.32C235th non-split extension by C23 of C23 acting via C23/C22=C232C2^3.32C2^364,200
C22.13C249th central extension by C22 of C2432C2^2.13C2^464,201
C22.23C249th central stem extension by C22 of C2432C2^2.23C2^464,210
C22.26C2412nd central stem extension by C22 of C2432C2^2.26C2^464,213
C22.27C2413rd central stem extension by C22 of C2432C2^2.27C2^464,214
C22.30C2416th central stem extension by C22 of C2432C2^2.30C2^464,217
C22.31C2417th central stem extension by C22 of C2432C2^2.31C2^464,218
C23.39C2312nd non-split extension by C23 of C23 acting via C23/C22=C232C2^3.39C2^364,220
C22.34C2420th central stem extension by C22 of C2432C2^2.34C2^464,221
C22.35C2421st central stem extension by C22 of C2432C2^2.35C2^464,222
C22.36C2422nd central stem extension by C22 of C2432C2^2.36C2^464,223
C22.38C2424th central stem extension by C22 of C2432C2^2.38C2^464,225
C23.47C2320th non-split extension by C23 of C23 acting via C23/C22=C232C2^3.47C2^364,233
C22.47C2433rd central stem extension by C22 of C2432C2^2.47C2^464,234
C22.49C2435th central stem extension by C22 of C2432C2^2.49C2^464,236
C22.50C2436th central stem extension by C22 of C2432C2^2.50C2^464,237
C22.53C2439th central stem extension by C22 of C2432C2^2.53C2^464,240
C22.56C2442nd central stem extension by C22 of C2432C2^2.56C2^464,243
C22.57C2443rd central stem extension by C22 of C2432C2^2.57C2^464,244
C22.M4(2)2nd non-split extension by C22 of M4(2) acting via M4(2)/C2×C4=C232C2^2.M4(2)64,5
Q8.Q8The non-split extension by Q8 of Q8 acting via Q8/C4=C264Q8.Q864,160
C8.5Q84th non-split extension by C8 of Q8 acting via Q8/C4=C264C8.5Q864,180
C4.10D82nd non-split extension by C4 of D8 acting via D8/D4=C264C4.10D864,13
C4.6Q162nd non-split extension by C4 of Q16 acting via Q16/Q8=C264C4.6Q1664,14
C2.Q321st central extension by C2 of Q3264C2.Q3264,39
C4.Q163rd non-split extension by C4 of Q16 acting via Q16/Q8=C264C4.Q1664,158
C4.SD164th non-split extension by C4 of SD16 acting via SD16/C8=C264C4.SD1664,168
C22.4Q161st central extension by C22 of Q1664C2^2.4Q1664,21
C42.2C222nd non-split extension by C42 of C22 acting faithfully64C4^2.2C2^264,11
C22.7C422nd central extension by C22 of C4264C2^2.7C4^264,17
C23.63C2313rd central extension by C23 of C2364C2^3.63C2^364,68
C23.65C2315th central extension by C23 of C2364C2^3.65C2^364,70
C23.67C2317th central extension by C23 of C2364C2^3.67C2^364,72
C23.78C234th central stem extension by C23 of C2364C2^3.78C2^364,76
C23.81C237th central stem extension by C23 of C2364C2^3.81C2^364,79
C23.83C239th central stem extension by C23 of C2364C2^3.83C2^364,81
C23.84C2310th central stem extension by C23 of C2364C2^3.84C2^364,82
C42.30C2230th non-split extension by C42 of C22 acting faithfully64C4^2.30C2^264,172
C22.58C2444th central stem extension by C22 of C2464C2^2.58C2^464,245
C82Abelian group of type [8,8]64C8^264,2
C43Abelian group of type [4,4,4]64C4^364,55
C26Elementary abelian group of type [2,2,2,2,2,2]64C2^664,267
C4×C16Abelian group of type [4,16]64C4xC1664,26
C2×C32Abelian group of type [2,32]64C2xC3264,50
C23×C8Abelian group of type [2,2,2,8]64C2^3xC864,246
C24×C4Abelian group of type [2,2,2,2,4]64C2^4xC464,260
C22×C16Abelian group of type [2,2,16]64C2^2xC1664,183
C22×C42Abelian group of type [2,2,4,4]64C2^2xC4^264,192
C2×C4×C8Abelian group of type [2,4,8]64C2xC4xC864,83
D42Direct product of D4 and D416D4^264,226
C2×2+ 1+4Direct product of C2 and 2+ 1+416C2xES+(2,2)64,264
C8×D4Direct product of C8 and D432C8xD464,115
C4×D8Direct product of C4 and D832C4xD864,118
D4×Q8Direct product of D4 and Q832D4xQ864,230
C2×D16Direct product of C2 and D1632C2xD1664,186
C4×SD16Direct product of C4 and SD1632C4xSD1664,119
C2×SD32Direct product of C2 and SD3232C2xSD3264,187
C22×D8Direct product of C22 and D832C2^2xD864,250
D4×C23Direct product of C23 and D432D4xC2^364,261
C4×M4(2)Direct product of C4 and M4(2)32C4xM4(2)64,85
C2×M5(2)Direct product of C2 and M5(2)32C2xM5(2)64,184
C22×SD16Direct product of C22 and SD1632C2^2xSD1664,251
C22×M4(2)Direct product of C22 and M4(2)32C2^2xM4(2)64,247
C2×2- 1+4Direct product of C2 and 2- 1+432C2xES-(2,2)64,265
Q82Direct product of Q8 and Q864Q8^264,239
C8×Q8Direct product of C8 and Q864C8xQ864,126
C4×Q16Direct product of C4 and Q1664C4xQ1664,120
C2×Q32Direct product of C2 and Q3264C2xQ3264,188
Q8×C23Direct product of C23 and Q864Q8xC2^364,262
C22×Q16Direct product of C22 and Q1664C2^2xQ1664,252
C2×C4≀C2Direct product of C2 and C4≀C216C2xC4wrC264,101
C2×C23⋊C4Direct product of C2 and C23⋊C416C2xC2^3:C464,90
C2×C8⋊C22Direct product of C2 and C8⋊C2216C2xC8:C2^264,254
C2×C4.D4Direct product of C2 and C4.D416C2xC4.D464,92
C2×C22≀C2Direct product of C2 and C22≀C216C2xC2^2wrC264,202
C2×C4×D4Direct product of C2×C4 and D432C2xC4xD464,196
C4×C4○D4Direct product of C4 and C4○D432C4xC4oD464,198
C2×C8○D4Direct product of C2 and C8○D432C2xC8oD464,248
C2×C4○D8Direct product of C2 and C4○D832C2xC4oD864,253
C2×C4⋊D4Direct product of C2 and C4⋊D432C2xC4:D464,203
C2×D4⋊C4Direct product of C2 and D4⋊C432C2xD4:C464,95
C2×C8.C4Direct product of C2 and C8.C432C2xC8.C464,110
C2×C41D4Direct product of C2 and C41D432C2xC4:1D464,211
C4×C22⋊C4Direct product of C4 and C22⋊C432C4xC2^2:C464,58
C2×C22⋊C8Direct product of C2 and C22⋊C832C2xC2^2:C864,87
C2×C22⋊Q8Direct product of C2 and C22⋊Q832C2xC2^2:Q864,204
C2×C42⋊C2Direct product of C2 and C42⋊C232C2xC4^2:C264,195
C2×C4.4D4Direct product of C2 and C4.4D432C2xC4.4D464,207
C22×C4○D4Direct product of C22 and C4○D432C2^2xC4oD464,263
C2×C8.C22Direct product of C2 and C8.C2232C2xC8.C2^264,255
C2×C422C2Direct product of C2 and C422C232C2xC4^2:2C264,209
C2×C4.10D4Direct product of C2 and C4.10D432C2xC4.10D464,93
C22×C22⋊C4Direct product of C22 and C22⋊C432C2^2xC2^2:C464,193
C2×C22.D4Direct product of C2 and C22.D432C2xC2^2.D464,205
C4×C4⋊C4Direct product of C4 and C4⋊C464C4xC4:C464,59
C2×C4⋊C8Direct product of C2 and C4⋊C864C2xC4:C864,103
C2×C4×Q8Direct product of C2×C4 and Q864C2xC4xQ864,197
C2×C4⋊Q8Direct product of C2 and C4⋊Q864C2xC4:Q864,212
C2×C8⋊C4Direct product of C2 and C8⋊C464C2xC8:C464,84
C22×C4⋊C4Direct product of C22 and C4⋊C464C2^2xC4:C464,194
C2×Q8⋊C4Direct product of C2 and Q8⋊C464C2xQ8:C464,96
C2×C2.D8Direct product of C2 and C2.D864C2xC2.D864,107
C2×C4.Q8Direct product of C2 and C4.Q864C2xC4.Q864,106
C2×C2.C42Direct product of C2 and C2.C4264C2xC2.C4^264,56
C2×C42.C2Direct product of C2 and C42.C264C2xC4^2.C264,208

Groups of order 67

dρLabelID
C67Cyclic group671C6767,1

Groups of order 71

dρLabelID
C71Cyclic group711C7171,1

Groups of order 73

dρLabelID
C73Cyclic group731C7373,1

Groups of order 79

dρLabelID
C79Cyclic group791C7979,1

Groups of order 81

dρLabelID
C81Cyclic group811C8181,1
C3≀C3Wreath product of C3 by C3; = AΣL1(𝔽27)93C3wrC381,7
C9○He3Central product of C9 and He3273C9oHe381,14
C27⋊C3The semidirect product of C27 and C3 acting faithfully273C27:C381,6
C32⋊C9The semidirect product of C32 and C9 acting via C9/C3=C327C3^2:C981,3
He3⋊C32nd semidirect product of He3 and C3 acting faithfully273He3:C381,9
C9⋊C9The semidirect product of C9 and C9 acting via C9/C3=C381C9:C981,4
He3.C3The non-split extension by He3 of C3 acting faithfully273He3.C381,8
C3.He34th central stem extension by C3 of He3273C3.He381,10
C92Abelian group of type [9,9]81C9^281,2
C34Elementary abelian group of type [3,3,3,3]81C3^481,15
C3×C27Abelian group of type [3,27]81C3xC2781,5
C32×C9Abelian group of type [3,3,9]81C3^2xC981,11
C3×He3Direct product of C3 and He327C3xHe381,12
C3×3- 1+2Direct product of C3 and 3- 1+227C3xES-(3,1)81,13

Groups of order 83

dρLabelID
C83Cyclic group831C8383,1

Groups of order 89

dρLabelID
C89Cyclic group891C8989,1

Groups of order 97

dρLabelID
C97Cyclic group971C9797,1

Groups of order 101

dρLabelID
C101Cyclic group1011C101101,1

Groups of order 103

dρLabelID
C103Cyclic group1031C103103,1

Groups of order 107

dρLabelID
C107Cyclic group1071C107107,1

Groups of order 109

dρLabelID
C109Cyclic group1091C109109,1

Groups of order 113

dρLabelID
C113Cyclic group1131C113113,1
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