Finite Group Databasebeta

← C22×C4×C7×Dic3 #13061498

Subgroups — C22×C4×C7×Dic3 #13061498

Order 1344.

996 conjugacy classes of subgroups; only the 734 normal subgroups are shown.

normal subgroups only

This group has 996 conjugacy classes of subgroups — too many to draw. Only its 734 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C4×C7C211yesmaximal, characteristic
2C23×C7×Dic3C212yesmaximal
3C2×C4×C7×Dic3C2112yesmaximal, direct product factor
4C22×C42×C7—31nomaximal, Hall
5C24×C3×C7C2211yescharacteristic
6C22×C3×C4×C7C418yescomplemented
7C22×C3×C4×C7C2216yes—
8C22×C7×Dic3C4116yesdirect product factor
9C22×C7×Dic3C22112yes—
10C4×C7×Dic3C22116yesdirect product factor
11C23×C4×C7—32no—
12C23×C4×C7D311yescharacteristic
13C2×C42×C7—312no—
14C22×C4×Dic3C711yesmaximal, characteristic, direct product factor, Hall
15C23×C3×C7C2×C418yes—
16C23×C3×C7C2×C414yes—
17C23×C3×C7C2313yes—
18C2×C3×C4×C7C2×C4124yescomplemented
19C2×C3×C4×C7C2314yes—
20C2×C7×Dic3C2×C4148yesdirect product factor
21C2×C7×Dic3C2318yes—
22C24×C7C2×D311yescharacteristic
23C22×C4×C7—316no—
24C22×C4×C7—312no—
25C22×C4×C7Dic318yesdirect product factor
26C22×C4×C7C2×D316yes—
27C42×C7—316no—
28C23×C3×C4C2×C711yescharacteristic
29C23×Dic3C2×C712yes—
30C2×C4×Dic3C2×C7112yesdirect product factor
31C22×C3×C7C42116yescomplemented
32C22×C3×C7C22×C4112yes—
33C22×C3×C7C22×C416yes—
34C22×C3×C7C2411yescharacteristic
35C3×C4×C7C22×C418yescomplemented
36C7×Dic3C22×C4116yesdirect product factor
37C22×C42—31noSylow
38C23×C7C4×D318yes—
39C23×C7C2×Dic314yes—
40C23×C7C22×D313yes—
41C2×C4×C7—348no—
42C2×C4×C7—38no—
43C2×C4×C7C2×Dic3124yesdirect product factor
44C2×C4×C7C22×D314yes—
45C24×C3C22×C711yescharacteristic
46C22×C3×C4C4×C718yescomplemented
47C22×C3×C4C22×C716yes—
48C22×Dic3C4×C7116yesdirect product factor
49C22×Dic3C22×C7112yes—
50C4×Dic3C22×C7116yesdirect product factor
51C2×C3×C7C2×C42112yescomplemented
52C2×C3×C7C23×C412yes—
53C2×C3×C7C23×C411yescharacteristic
54C23×C4—32no—
55C23×C4D3×C711yescharacteristic
56C2×C42—312no—
57C22×C7C4×Dic3116yesdirect product factor
58C22×C7C2×C4×D3112yes—
59C22×C7C22×Dic316yes—
60C22×C7C23×D311yescharacteristic
61C4×C7—316no—
62C4×C7C22×Dic318yesdirect product factor
63C23×C3C2×C4×C718yes—
64C23×C3C2×C4×C714yes—
65C23×C3C23×C713yes—
66C2×C3×C4C2×C4×C7124yescomplemented
67C2×C3×C4C23×C714yes—
68C2×Dic3C2×C4×C7148yesdirect product factor
69C2×Dic3C23×C718yes—
70C3×C7C22×C4211yescharacteristic, complemented, Hall
71C24C2×D3×C711yescharacteristic
72C22×C4—316no—
73C22×C4—312no—
74C22×C4C7×Dic318yesdirect product factor
75C22×C4C2×D3×C716yes—
76C42—316no—
77C2×C7C2×C4×Dic3112yesdirect product factor
78C2×C7C22×C4×D312yes—
79C2×C7C23×Dic311yescharacteristic
80C22×C3C42×C7116yescomplemented
81C22×C3C22×C4×C7112yes—
82C22×C3C22×C4×C716yes—
83C22×C3C24×C711yescharacteristic
84C3×C4C22×C4×C718yescomplemented
85Dic3C22×C4×C7116yesdirect product factor
86C23C4×D3×C718yes—
87C23C2×C7×Dic314yes—
88C23C22×D3×C713yes—
89C2×C4—348no—
90C2×C4—38no—
91C2×C4C2×C7×Dic3124yesdirect product factor
92C2×C4C22×D3×C714yes—
93C7C22×C4×Dic311yescharacteristic, direct product factor, Sylow
94C2×C3C2×C42×C7112yescomplemented
95C2×C3C23×C4×C712yes—
96C2×C3C23×C4×C711yescharacteristic
97C22C4×C7×Dic3116yesdirect product factor
98C22C2×C4×D3×C7112yes—
99C22C22×C7×Dic316yes—
100C22C23×D3×C711yescharacteristic
101C4—316no—
102C4C22×C7×Dic318yesdirect product factor
103C3C22×C42×C711yescharacteristic, complemented, Sylow
104C2C2×C4×C7×Dic3112yesdirect product factor
105C2C22×C4×D3×C712yes—
106C2C23×C7×Dic311yescharacteristic
subgroupG/H
center, hypercenterC23×C4×C7D3
commutator, hypocenterC3C22×C42×C7
FrattiniC22C23×D3×C7
FittingC23×C3×C4×C7C2
socle, prime radicalC24×C3×C7C22
cosocleC22×C3C24×C7
LCSG ▷ C3
UCSC1 ◁ C23×C4×C7

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C2×C4×C7×Dic3C2direct (N × H)
6. C22×C3×C4×C7C4semidirect
8. C22×C7×Dic3C4direct (N × H)
10. C4×C7×Dic3C22direct (N × H)
14. C22×C4×Dic3C7direct (N × H)
18. C2×C3×C4×C7C2×C4semidirect
20. C2×C7×Dic3C2×C4direct (N × H)
25. C22×C4×C7Dic3direct (N × H)
30. C2×C4×Dic3C2×C7direct (N × H)
31. C22×C3×C7C42semidirect
35. C3×C4×C7C22×C4semidirect
36. C7×Dic3C22×C4direct (N × H)
43. C2×C4×C7C2×Dic3direct (N × H)
46. C22×C3×C4C4×C7semidirect
48. C22×Dic3C4×C7direct (N × H)
50. C4×Dic3C22×C7direct (N × H)
51. C2×C3×C7C2×C42semidirect
57. C22×C7C4×Dic3direct (N × H)
62. C4×C7C22×Dic3direct (N × H)
66. C2×C3×C4C2×C4×C7semidirect
68. C2×Dic3C2×C4×C7direct (N × H)
70. C3×C7C22×C42semidirect
74. C22×C4C7×Dic3direct (N × H)
77. C2×C7C2×C4×Dic3direct (N × H)
80. C22×C3C42×C7semidirect
84. C3×C4C22×C4×C7semidirect
85. Dic3C22×C4×C7direct (N × H)
91. C2×C4C2×C7×Dic3direct (N × H)
93. C7C22×C4×Dic3direct (N × H)
94. C2×C3C2×C42×C7semidirect
97. C22C4×C7×Dic3direct (N × H)
102. C4C22×C7×Dic3direct (N × H)
103. C3C22×C42×C7semidirect
104. C2C2×C4×C7×Dic3direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C23×C3×C4×C72
C23×C7×Dic32
C2×C4×C7×Dic32
C22×C42×C73
C22×C4×Dic37