Finite Group Databasebeta

← C3×C42×C3⋊Dic3 #13162966

Subgroups — C3×C42×C3⋊Dic3 #13162966

Order 1728.

1980 conjugacy classes of subgroups; only the 798 normal subgroups are shown.

normal subgroups only

This group has 1980 conjugacy classes of subgroups — too many to draw. Only its 798 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
1C2×C33×C42C211yesmaximal, characteristic
2C2×C3×C4×C3⋊Dic3C216yesmaximal
3C42×C3⋊Dic3C311yesmaximal, characteristic, direct product factor
4C3×C42×Dic3—34nomaximal
5C22×C33×C4C2213yes—
6C22×C3×C3⋊Dic3C2214yes—
7C33×C42C414yescomplemented
8C3×C4×C3⋊Dic3C4124yesdirect product factor
9C2×C32×C42—24no—
10C2×C32×C42D314yes—
11C2×C32×C42C2×C311yescharacteristic
12C2×C4×C3⋊Dic3C2×C316yes—
13C2×C3×C4×Dic3—324no—
14C23×C33C2311yescharacteristic
15C2×C33×C4C2×C4112yes—
16C2×C33×C4C2×C416yes—
17C2×C3×C3⋊Dic3C2×C4124yes—
18C3×C43—91no—
19C42×Dic3—34no—
20C22×C32×C4—212no—
21C22×C32×C4C2×D3112yes—
22C22×C32×C4C22×C313yes—
23C22×C3⋊Dic3C22×C314yes—
24C22×C3×Dic3—316no—
25C32×C42—216no—
26C32×C42Dic3116yescomplemented
27C32×C42C3×C414yescomplemented
28C4×C3⋊Dic3C3×C4124yesdirect product factor
29C3×C4×Dic3—396no—
30C22×C33C22×C416yes—
31C22×C33C22×C411yescharacteristic
32C33×C4C42112yescomplemented
33C3×C3⋊Dic3C42116yesdirect product factor
34C2×C3×C42—24no—
35C2×C3×C42—96no—
36C2×C3×C42C3×D314yes—
37C2×C3×C42C3⋊D311yescharacteristic
38C2×C4×Dic3—324no—
39C23×C32—24no—
40C23×C32C22×D314yes—
41C23×C32C23×C311yescharacteristic
42C2×C32×C4—248no—
43C2×C32×C4—224no—
44C2×C32×C4C4×D3148yes—
45C2×C32×C4C2×Dic3124yes—
46C2×C32×C4C2×C3×C4112yes—
47C2×C32×C4C2×C3×C416yes—
48C2×C3⋊Dic3C2×C3×C4124yes—
49C2×C3×Dic3—396no—
50C43—91noSylow
51C2×C33C2×C4214yes—
52C2×C33C2×C4213yes—
53C22×C3×C4—212no—
54C22×C3×C4—94no—
55C22×C3×C4C2×C3×D3112yes—
56C22×C3×C4C2×C3⋊D313yes—
57C22×Dic3—316no—
58C3×C42—216no—
59C3×C42—924no—
60C3×C42C3×Dic3116yescomplemented
61C3×C42C3⋊Dic314yesdirect product factor
62C4×Dic3—396no—
63C22×C32—224no—
64C22×C32—24no—
65C22×C32C2×C4×D3124yes—
66C22×C32C22×Dic314yes—
67C22×C32C22×C3×C416yes—
68C22×C32C22×C3×C411yescharacteristic
69C32×C4—248no—
70C32×C4C4×Dic3148yescomplemented
71C32×C4C3×C42112yescomplemented
72C3⋊Dic3C3×C42116yesdirect product factor
73C3×Dic3—364no—
74C2×C42—96no—
75C2×C42C3×C3⋊D311yescharacteristic
76C33C4311yescharacteristic, complemented, Sylow
77C23×C3—24no—
78C23×C3C22×C3×D314yes—
79C23×C3C22×C3⋊D311yescharacteristic
80C2×C3×C4—248no—
81C2×C3×C4—224no—
82C2×C3×C4—924no—
83C2×C3×C4C3×C4×D3148yes—
84C2×C3×C4C2×C3×Dic3124yes—
85C2×C3×C4C4×C3⋊D3112yes—
86C2×C3×C4C2×C3⋊Dic316yes—
87C2×Dic3—396no—
88C2×C32—212no—
89C2×C32—216no—
90C2×C32C42×D3116yes—
91C2×C32C2×C4×Dic3112yes—
92C2×C32C2×C3×C4213yes—
93C2×C32C2×C3×C4214yes—
94C22×C4—94no—
95C22×C4C2×C3×C3⋊D313yes—
96C42—924no—
97C42C3×C3⋊Dic314yesdirect product factor
98C22×C3—224no—
99C22×C3—24no—
100C22×C3C2×C3×C4×D3124yes—
101C22×C3C22×C3×Dic314yes—
102C22×C3C2×C4×C3⋊D316yes—
103C22×C3C22×C3⋊Dic311yescharacteristic
104C3×C4—248no—
105C3×C4—916no—
106C3×C4C3×C4×Dic3148yescomplemented
107C3×C4C4×C3⋊Dic3112yesdirect product factor
108Dic3—364no—
109C32—24no—
110C32C42×Dic314yescomplemented
111C32C3×C4311yescharacteristic, complemented
112C23C22×C3×C3⋊D311yescharacteristic
113C2×C4—924no—
114C2×C4C3×C4×C3⋊D3112yes—
115C2×C4C2×C3×C3⋊Dic316yes—
116C2×C3—216no—
117C2×C3—212no—
118C2×C3C3×C42×D3116yes—
119C2×C3C2×C3×C4×Dic3112yes—
120C2×C3C42×C3⋊D314yes—
121C2×C3C2×C4×C3⋊Dic313yes—
122C22C2×C3×C4×C3⋊D316yes—
123C22C22×C3×C3⋊Dic311yescharacteristic
124C4—916no—
125C4C3×C4×C3⋊Dic3112yesdirect product factor
126C3—24no—
127C3C3×C42×Dic314yescomplemented
128C3C42×C3⋊Dic311yescharacteristic, direct product factor
129C2C3×C42×C3⋊D314yes—
130C2C2×C3×C4×C3⋊Dic313yes—
subgroupG/H
center, hypercenterC2×C3×C42C3⋊D3
commutator, hypocenterC32C3×C43
FrattiniC23C22×C3×C3⋊D3
FittingC2×C33×C42C2
socle, prime radicalC23×C33C23
cosocleC23×C32C23×C3
LCSG ▷ C32
UCSC1 ◁ C2×C3×C42

Complements

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

NH ≅ G/Ntype
3. C42×C3⋊Dic3C3direct (N × H)
7. C33×C42C4semidirect
8. C3×C4×C3⋊Dic3C4direct (N × H)
26. C32×C42Dic3semidirect
27. C32×C42C3×C4semidirect
28. C4×C3⋊Dic3C3×C4direct (N × H)
32. C33×C4C42semidirect
33. C3×C3⋊Dic3C42direct (N × H)
60. C3×C42C3×Dic3semidirect
61. C3×C42C3⋊Dic3direct (N × H)
70. C32×C4C4×Dic3semidirect
71. C32×C4C3×C42semidirect
72. C3⋊Dic3C3×C42direct (N × H)
76. C33C43semidirect
97. C42C3×C3⋊Dic3direct (N × H)
106. C3×C4C3×C4×Dic3semidirect
107. C3×C4C4×C3⋊Dic3direct (N × H)
110. C32C42×Dic3semidirect
111. C32C3×C43semidirect
125. C4C3×C4×C3⋊Dic3direct (N × H)
127. C3C3×C42×Dic3semidirect
128. C3C42×C3⋊Dic3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C33×C422
C2×C3×C4×C3⋊Dic32
C42×C3⋊Dic33
C3×C42×Dic33