Finite Group Databasebeta

← C22×C32×D3×C9 #14519353

Subgroups — C22×C32×D3×C9 #14519353

Order 1944.

2340 conjugacy classes of subgroups; only the 1050 normal subgroups are shown.

normal subgroups only

This group has 2340 conjugacy classes of subgroups — too many to draw. Only its 1050 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
1C22×C33×C9C211yesmaximal, characteristic, complemented
2C2×C32×D3×C9C216yesmaximal, direct product factor
3C22×C33×D3C311yesmaximal, characteristic
4C23×C32×C9—31nomaximal
5C22×C3×D3×C9C3112yesmaximal, direct product factor
6C2×C33×C9C2213yescomplemented
7C32×D3×C9C2214yesdirect product factor
8C22×C34C2×C311yescharacteristic
9C2×C33×D3C2×C316yes—
10C22×C32×C9—21no—
11C22×C32×C9—212no—
12C22×C32×C9—36no—
13C22×C32×C9D311yescharacteristic, direct product factor
14C22×C32×C9C2×C3112yescomplemented
15C2×C3×D3×C9C2×C3172yesdirect product factor
16C33×C9C2311yescharacteristic, complemented, Sylow
17C23×C33—31no—
18C22×C32×D3C919yesdirect product factor
19C22×C32×D3C3214yes—
20C23×C3×C9—312no—
21C22×D3×C9C3219yesdirect product factor
22C2×C34C22×C313yes—
23C33×D3C22×C314yes—
24C2×C32×C9—23no—
25C2×C32×C9—236no—
26C2×C32×C9—34no—
27C2×C32×C9C2×D313yesdirect product factor
28C2×C32×C9C22×C3136yescomplemented
29C3×D3×C9C22×C3148yesdirect product factor
30C22×C33—29no—
31C22×C33—24no—
32C22×C33—36no—
33C22×C33C2×C919yescomplemented
34C22×C33C3×D311yescharacteristic
35C22×C33C2×C3214yes—
36C2×C32×D3C2×C9154yesdirect product factor
37C2×C32×D3C2×C32124yes—
38C22×C3×C9—212no—
39C22×C3×C9—236no—
40C22×C3×C9—372no—
41C22×C3×C9C3×D3112yesdirect product factor
42C22×C3×C9C2×C3219yescomplemented
43C2×D3×C9C2×C32154yesdirect product factor
44C34C23×C311yescharacteristic
45C32×C9—21no—
46C32×C9—212no—
47C32×C9C22×D311yescharacteristic, direct product factor
48C32×C9C23×C3112yescomplemented
49C23×C32—39no—
50C23×C32—34no—
51C22×C3×D3C3×C9112yesdirect product factor
52C22×C3×D3C3311yescharacteristic
53C23×C9—39no—
54C2×C33—227no—
55C2×C33—212no—
56C2×C33—34no—
57C2×C33C22×C9127yescomplemented
58C2×C33C2×C3×D313yes—
59C2×C33C22×C32112yes—
60C32×D3C22×C9136yesdirect product factor
61C32×D3C22×C32116yes—
62C2×C3×C9—236no—
63C2×C3×C9—2108no—
64C2×C3×C9—348no—
65C2×C3×C9C2×C3×D3136yesdirect product factor
66C2×C3×C9C22×C32127yescomplemented
67D3×C9C22×C32136yesdirect product factor
68C22×C32—236no—
69C22×C32—212no—
70C22×C32—24no—
71C22×C32—354no—
72C22×C32—324no—
73C22×C32D3×C919yesdirect product factor
74C22×C32C2×C3×C9112yescomplemented
75C22×C32C32×D314yes—
76C22×C32C2×C3311yescharacteristic
77C2×C3×D3C2×C3×C9172yesdirect product factor
78C2×C3×D3C2×C3316yes—
79C22×C9—29no—
80C22×C9—354no—
81C22×C9C32×D319yesdirect product factor
82C33—29no—
83C33—24no—
84C33C23×C919yescomplemented
85C33C22×C3×D311yescharacteristic
86C33C23×C3214yes—
87C3×C9—212no—
88C3×C9—236no—
89C3×C9C22×C3×D3112yesdirect product factor
90C3×C9C23×C3219yescomplemented
91C23×C3—312no—
92C23×C3—31no—
93C22×D3C32×C911yescharacteristic, direct product factor
94C2×C32—2108no—
95C2×C32—236no—
96C2×C32—212no—
97C2×C32—336no—
98C2×C32—316no—
99C2×C32C2×D3×C9127yesdirect product factor
100C2×C32C22×C3×C9136yescomplemented
101C2×C32C2×C32×D3112yes—
102C2×C32C22×C3313yes—
103C3×D3C22×C3×C9148yesdirect product factor
104C3×D3C22×C3314yes—
105C2×C9—227no—
106C2×C9—336no—
107C2×C9C2×C32×D3127yesdirect product factor
108C22×C3—212no—
109C22×C3—21no—
110C22×C3—372no—
111C22×C3—36no—
112C22×C3C3×D3×C9112yesdirect product factor
113C22×C3C2×C32×C911yescharacteristic, complemented
114C22×C3C33×D311yescharacteristic
115C2×D3C2×C32×C916yesdirect product factor
116C32—24no—
117C32—236no—
118C32—212no—
119C32C22×D3×C919yesdirect product factor
120C32C23×C3×C9112yescomplemented
121C32C22×C32×D314yes—
122C32C23×C3311yescharacteristic
123C9—29no—
124C9C22×C32×D319yesdirect product factor
125C23—31noSylow
126C2×C3—236no—
127C2×C3—23no—
128C2×C3—34no—
129C2×C3—348no—
130C2×C3C2×C3×D3×C9136yesdirect product factor
131C2×C3C22×C32×C913yescomplemented
132C2×C3C2×C33×D313yes—
133D3C22×C32×C914yesdirect product factor
134C22—36no—
135C22C32×D3×C911yescharacteristic, direct product factor
136C3—212no—
137C3—21no—
138C3C22×C3×D3×C9112yesdirect product factor
139C3C23×C32×C911yescharacteristic, complemented
140C3C22×C33×D311yescharacteristic
141C2—34no—
142C2C2×C32×D3×C913yesdirect product factor
subgroupG/H
center, hypercenterC22×C32×C9D3
commutator, hypocenterC3C23×C32×C9
FrattiniC3C22×C33×D3
FittingC22×C33×C9C2
socleC22×C34C2×C3
prime radicalC22×C33×D3C3
cosocleC32C23×C33
LCSG ▷ C3
UCSC1 ◁ C22×C32×C9

Complements

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

NH ≅ G/Ntype
1. C22×C33×C9C2semidirect
2. C2×C32×D3×C9C2direct (N × H)
5. C22×C3×D3×C9C3direct (N × H)
6. C2×C33×C9C22semidirect
7. C32×D3×C9C22direct (N × H)
13. C22×C32×C9D3direct (N × H)
14. C22×C32×C9C2×C3semidirect
15. C2×C3×D3×C9C2×C3direct (N × H)
16. C33×C9C23semidirect
18. C22×C32×D3C9direct (N × H)
21. C22×D3×C9C32direct (N × H)
27. C2×C32×C9C2×D3direct (N × H)
28. C2×C32×C9C22×C3semidirect
29. C3×D3×C9C22×C3direct (N × H)
33. C22×C33C2×C9semidirect
36. C2×C32×D3C2×C9direct (N × H)
41. C22×C3×C9C3×D3direct (N × H)
42. C22×C3×C9C2×C32semidirect
43. C2×D3×C9C2×C32direct (N × H)
47. C32×C9C22×D3direct (N × H)
48. C32×C9C23×C3semidirect
51. C22×C3×D3C3×C9direct (N × H)
57. C2×C33C22×C9semidirect
60. C32×D3C22×C9direct (N × H)
65. C2×C3×C9C2×C3×D3direct (N × H)
66. C2×C3×C9C22×C32semidirect
67. D3×C9C22×C32direct (N × H)
73. C22×C32D3×C9direct (N × H)
74. C22×C32C2×C3×C9semidirect
77. C2×C3×D3C2×C3×C9direct (N × H)
81. C22×C9C32×D3direct (N × H)
84. C33C23×C9semidirect
89. C3×C9C22×C3×D3direct (N × H)
90. C3×C9C23×C32semidirect
93. C22×D3C32×C9direct (N × H)
99. C2×C32C2×D3×C9direct (N × H)
100. C2×C32C22×C3×C9semidirect
103. C3×D3C22×C3×C9direct (N × H)
107. C2×C9C2×C32×D3direct (N × H)
112. C22×C3C3×D3×C9direct (N × H)
113. C22×C3C2×C32×C9semidirect
115. C2×D3C2×C32×C9direct (N × H)
119. C32C22×D3×C9direct (N × H)
120. C32C23×C3×C9semidirect
124. C9C22×C32×D3direct (N × H)
130. C2×C3C2×C3×D3×C9direct (N × H)
131. C2×C3C22×C32×C9semidirect
133. D3C22×C32×C9direct (N × H)
135. C22C32×D3×C9direct (N × H)
138. C3C22×C3×D3×C9direct (N × H)
139. C3C23×C32×C9semidirect
142. C2C2×C32×D3×C9direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C33×C92
C2×C32×D3×C92
C22×C33×D33
C23×C32×C93
C22×C3×D3×C93