Finite Group Databasebeta

← C32×C4×AGL(1,ℤ/9) #14518886

Subgroups — C32×C4×AGL(1,ℤ/9) #14518886

Order 1944.

978 conjugacy classes of subgroups; only the 326 normal subgroups are shown.

normal subgroups only

This group has 978 conjugacy classes of subgroups — too many to draw. Only its 326 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×C32×AGL(1,ℤ/9)C211yesmaximal, characteristic
2C32×C4×3−1+2C211yesmaximal, characteristic, complemented
3C32×3−1+2⋊C4C211yesmaximal, characteristic, complemented
4C33×C4×D3—31nomaximal
5C3×C4×AGL(1,ℤ/9)C3112yesmaximal, direct product factor
6C32×C4×D9C311yesmaximal, characteristic, complemented
7C2×C32×3−1+2C2211yescharacteristic
8C32×AGL(1,ℤ/9)C412yesdirect product factor
9C2×C33×D3—31no—
10C34×C4D311yescharacteristic
11C33×Dic3—31no—
12C2×C3×AGL(1,ℤ/9)C2×C3112yes—
13C2×C32×D9C2×C311yescharacteristic
14C3×C4×3−1+2—212no—
15C3×C4×3−1+2C2×C3112yescomplemented
16C32×C4×C9—21no—
17C32×C4×C9C2×C311yescharacteristic, complemented
18C3×3−1+2⋊C4C2×C3112yescomplemented
19C32×Dic9C2×C311yescharacteristic, complemented
20C32×3−1+2C2×C411yescharacteristic, complemented, Sylow
21C2×C33×C4—91no—
22C32×C4×D3—31no—
23C32×C4×D3—312no—
24C4×AGL(1,ℤ/9)C3219yesdirect product factor
25C3×C4×D9C3214yescomplemented
26C2×C34C2×D311yescharacteristic
27C33×D3—32no—
28C2×C3×3−1+2—212no—
29C2×C3×3−1+2C22×C3112yes—
30C2×C32×C9—21no—
31C2×C32×C9C22×C311yescharacteristic
32C3×AGL(1,ℤ/9)C3×C4124yesdirect product factor
33C32×D9C3×C412yescomplemented
34C22×C33—91no—
35C2×C32×D3—31no—
36C2×C32×D3—312no—
37C33×C4—31no—
38C33×C4—64no—
39C33×C4—91no—
40C33×C4C3×D311yescharacteristic
41C33×C4C3×D3112yes—
42C32×Dic3—31no—
43C32×Dic3—312no—
44C2×AGL(1,ℤ/9)C2×C3219yes—
45C2×C3×D9C2×C3214yes—
46C4×3−1+2—236no—
47C4×3−1+2C2×C3219yescomplemented
48C3×C4×C9—212no—
49C3×C4×C9—24no—
50C3×C4×C9C2×C3214yescomplemented
513−1+2⋊C4C2×C3219yescomplemented
52C3×Dic9C2×C3214yescomplemented
53C34C4×D311yescharacteristic
54C3×3−1+2—212no—
55C3×3−1+2C2×C3×C4112yescomplemented
56C32×C9—21no—
57C32×C9C2×C3×C411yescharacteristic, complemented
58C2×C32×C4—912no—
59C2×C32×C4—91no—
60C3×C4×D3—34no—
61C3×C4×D3—39no—
62C4×D9C3311yescharacteristic, complemented
63C2×C33—31no—
64C2×C33—64no—
65C2×C33—92no—
66C2×C33C2×C3×D311yescharacteristic
67C2×C33C2×C3×D3112yes—
68C32×D3—32no—
69C32×D3—324no—
70C2×3−1+2—236no—
71C2×3−1+2C22×C3219yes—
72C2×C3×C9—212no—
73C2×C3×C9—24no—
74C2×C3×C9C22×C3214yes—
75AGL(1,ℤ/9)C32×C4118yesdirect product factor
76C3×D9C32×C418yescomplemented
77C22×C32—912no—
78C22×C32—91no—
79C2×C3×D3—34no—
80C2×C3×D3—39no—
81C32×C4—24no—
82C32×C4—312no—
83C32×C4—612no—
84C32×C4—912no—
85C32×C4—91no—
86C32×C4AGL(1,ℤ/9)11yescharacteristic, direct product factor
87C32×C4C32×D314yes—
88C32×C4C32×D319yes—
89C3×Dic3—34no—
90C3×Dic3—39no—
91C2×D9C2×C3311yescharacteristic
92C4×C9—29no—
93C4×C9—24no—
94C4×C9C2×C3311yescharacteristic, complemented
95Dic9C2×C3311yescharacteristic, complemented
96C33—31no—
97C33—64no—
98C33C3×C4×D311yescharacteristic
99C33C3×C4×D3112yes—
1003−1+2—236no—
1013−1+2C2×C32×C419yescomplemented
102C3×C9—212no—
103C3×C9—24no—
104C3×C9C2×C32×C414yescomplemented
105C2×C3×C4—99no—
106C2×C3×C4—94no—
107C4×D3—31no—
108C2×C32—24no—
109C2×C32—312no—
110C2×C32—612no—
111C2×C32—924no—
112C2×C32—92no—
113C2×C32C2×AGL(1,ℤ/9)11yescharacteristic
114C2×C32C2×C32×D314yes—
115C2×C32C2×C32×D319yes—
116C3×D3—38no—
117C3×D3—318no—
118C2×C9—29no—
119C2×C9—24no—
120C2×C9C22×C3311yescharacteristic
121D9C33×C412yescomplemented
122C22×C3—99no—
123C22×C3—94no—
124C2×D3—31no—
125C3×C4—24no—
126C3×C4—39no—
127C3×C4—99no—
128C3×C4—94no—
129C3×C4C3×AGL(1,ℤ/9)14yesdirect product factor
130C3×C4C33×D311yescharacteristic
131Dic3—31no—
132C32—24no—
133C32—312no—
134C32—612no—
135C32C4×AGL(1,ℤ/9)11yescharacteristic, direct product factor
136C32C32×C4×D314yes—
137C32C32×C4×D319yes—
138C9—29no—
139C9—24no—
140C9C2×C33×C411yescharacteristic, complemented
141C2×C4—91noSylow
142C2×C3—24no—
143C2×C3—39no—
144C2×C3—918no—
145C2×C3—98no—
146C2×C3C2×C3×AGL(1,ℤ/9)14yes—
147C2×C3C2×C33×D311yescharacteristic
148D3—32no—
149C22—91no—
150C4—91no—
151C4C32×AGL(1,ℤ/9)11yescharacteristic, direct product factor
152C3—24no—
153C3—39no—
154C3C3×C4×AGL(1,ℤ/9)14yesdirect product factor
155C3C33×C4×D311yescharacteristic
156C2—92no—
157C2C2×C32×AGL(1,ℤ/9)11yescharacteristic
subgroupG/H
center, hypercenterC32×C4AGL(1,ℤ/9)
commutator, hypocenterC9C2×C33×C4
FrattiniC2×C3C2×C33×D3
FittingC32×C4×3−1+2C2
socleC2×C33C2×C3×D3
prime radicalC2×C32×AGL(1,ℤ/9)C2
cosocleC2×C9C22×C33
LCSG ▷ C9
UCSC1 ◁ C32×C4

Complements

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

NH ≅ G/Ntype
2. C32×C4×3−1+2C2semidirect
3. C32×3−1+2⋊C4C2semidirect
5. C3×C4×AGL(1,ℤ/9)C3direct (N × H)
6. C32×C4×D9C3semidirect
8. C32×AGL(1,ℤ/9)C4direct (N × H)
15. C3×C4×3−1+2C2×C3semidirect
17. C32×C4×C9C2×C3semidirect
18. C3×3−1+2⋊C4C2×C3semidirect
19. C32×Dic9C2×C3semidirect
20. C32×3−1+2C2×C4semidirect
24. C4×AGL(1,ℤ/9)C32direct (N × H)
25. C3×C4×D9C32semidirect
32. C3×AGL(1,ℤ/9)C3×C4direct (N × H)
33. C32×D9C3×C4semidirect
47. C4×3−1+2C2×C32semidirect
50. C3×C4×C9C2×C32semidirect
51. 3−1+2⋊C4C2×C32semidirect
52. C3×Dic9C2×C32semidirect
55. C3×3−1+2C2×C3×C4semidirect
57. C32×C9C2×C3×C4semidirect
62. C4×D9C33semidirect
75. AGL(1,ℤ/9)C32×C4direct (N × H)
76. C3×D9C32×C4semidirect
86. C32×C4AGL(1,ℤ/9)direct (N × H)
94. C4×C9C2×C33semidirect
95. Dic9C2×C33semidirect
101. 3−1+2C2×C32×C4semidirect
104. C3×C9C2×C32×C4semidirect
121. D9C33×C4semidirect
129. C3×C4C3×AGL(1,ℤ/9)direct (N × H)
135. C32C4×AGL(1,ℤ/9)direct (N × H)
140. C9C2×C33×C4semidirect
151. C4C32×AGL(1,ℤ/9)direct (N × H)
154. C3C3×C4×AGL(1,ℤ/9)direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×AGL(1,ℤ/9)2
C32×C4×3−1+22
C32×3−1+2⋊C42
C33×C4×D33
C3×C4×AGL(1,ℤ/9)3
C32×C4×D93