Finite Group Databasebeta

← C4×C3⋊D3×3−1+2 #14518926

Subgroups — C4×C3⋊D3×3−1+2 #14518926

Order 1944.

744 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 744 conjugacy classes of subgroups — too many to draw. Only its 161 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×C3⋊D3×3−1+2C211yesmaximal, characteristic
2C32×C4×3−1+2C211yesmaximal, characteristic, complemented
33−1+2×C3⋊Dic3C211yesmaximal, characteristic, complemented
4C32×C4×C3⋊D3C311yesmaximal, characteristic
5C4×C9×C3⋊D3C313yesmaximal, complemented
6C4×D3×3−1+2—34nomaximal
7C2×C32×3−1+2C2211yescharacteristic
8C3⋊D3×3−1+2C412yesdirect product factor
9C2×C32×C3⋊D3C2×C311yescharacteristic
10C34×C4C2×C311yescharacteristic
11C32×C3⋊Dic3C2×C311yescharacteristic
12C2×C9×C3⋊D3C2×C313yes—
13C2×D3×3−1+2—34no—
14C3×C4×3−1+2—24no—
15C3×C4×3−1+2—212no—
16C3×C4×3−1+2D314yescomplemented
17C32×C4×C9C2×C313yescomplemented
18C9×C3⋊Dic3C2×C313yescomplemented
19Dic3×3−1+2—34no—
20C32×3−1+2C2×C411yescharacteristic, complemented, Sylow
21C3×C4×C3⋊D3—31no—
22C3×C4×C3⋊D3C3211yescharacteristic
23C32×C4×D3—34no—
24C2×C4×3−1+2—91no—
25C4×D3×C9—312no—
26C2×C34C22×C311yescharacteristic
27C32×C3⋊D3C3×C412yes—
28C2×C3×3−1+2—24no—
29C2×C3×3−1+2—212no—
30C2×C3×3−1+2C2×D314yes—
31C2×C32×C9C22×C313yes—
32C9×C3⋊D3C3×C416yescomplemented
33D3×3−1+2—38no—
34C2×C3×C3⋊D3—31no—
35C2×C3×C3⋊D3C2×C3211yescharacteristic
36C2×C32×D3—34no—
37C33×C4—24no—
38C33×C4—31no—
39C33×C4—64no—
40C33×C4C3×D314yes—
41C33×C4C2×C3211yescharacteristic
42C3×C3⋊Dic3—31no—
43C3×C3⋊Dic3C2×C3211yescharacteristic
44C32×Dic3—34no—
45C22×3−1+2—91no—
46C2×D3×C9—312no—
47C4×3−1+2—224no—
48C4×3−1+2—24no—
49C4×3−1+2—212no—
50C4×3−1+2—91no—
51C4×3−1+2C3⋊D311yescharacteristic, direct product factor
52C3×C4×C9—212no—
53C3×C4×C9C3×D3112yescomplemented
54C9×Dic3—312no—
55C34C2×C3×C411yescharacteristic
56C3×3−1+2—24no—
57C3×3−1+2—212no—
58C3×3−1+2C4×D314yescomplemented
59C32×C9C2×C3×C413yescomplemented
60C2×C32×C4—91no—
61C4×C3⋊D33−1+211yescharacteristic, direct product factor
62C3×C4×D3—34no—
63C3×C4×D3—94no—
64C2×C4×C9—93no—
65C2×C33—24no—
66C2×C33—31no—
67C2×C33—64no—
68C2×C33C2×C3×D314yes—
69C2×C33C22×C3211yescharacteristic
70C3×C3⋊D3—32no—
71C3×C3⋊D3C32×C412yes—
72C32×D3—38no—
73C2×3−1+2—224no—
74C2×3−1+2—24no—
75C2×3−1+2—212no—
76C2×3−1+2—92no—
77C2×3−1+2C2×C3⋊D311yescharacteristic
78C2×C3×C9—212no—
79C2×C3×C9C2×C3×D3112yes—
80D3×C9—324no—
81C22×C32—91no—
82C2×C3⋊D3C2×3−1+211yescharacteristic
83C2×C3×D3—34no—
84C2×C3×D3—94no—
85C32×C4—24no—
86C32×C4—24no—
87C32×C4—34no—
88C32×C4—64no—
89C32×C4—68no—
90C32×C4—64no—
91C32×C4—91no—
92C32×C4C2×3−1+211yescharacteristic, complemented
93C32×C4C32×D314yes—
94C32×C4C3×C3⋊D311yescharacteristic
95C3⋊Dic3C2×3−1+211yescharacteristic, complemented
96C3×Dic3—34no—
97C3×Dic3—94no—
98C22×C9—93no—
99C4×C9—212no—
100C4×C9—93no—
101C4×C9C3×C3⋊D313yescomplemented
102C33—24no—
103C33—31no—
104C33—64no—
105C33C3×C4×D314yes—
106C33C2×C32×C411yescharacteristic
1073−1+2—224no—
1083−1+2—24no—
1093−1+2—212no—
1103−1+2C4×C3⋊D311yescharacteristic, direct product factor
111C3×C9—212no—
112C3×C9C3×C4×D3112yescomplemented
113C2×C3×C4—91no—
114C2×C3×C4—271no—
115C4×D3—34no—
116C2×C32—24no—
117C2×C32—24no—
118C2×C32—34no—
119C2×C32—64no—
120C2×C32—68no—
121C2×C32—64no—
122C2×C32—92no—
123C2×C32C22×3−1+211yescharacteristic
124C2×C32C2×C32×D314yes—
125C2×C32C2×C3×C3⋊D311yescharacteristic
126C3⋊D3C4×3−1+212yesdirect product factor
127C3×D3—38no—
128C3×D3—98no—
129C2×C9—212no—
130C2×C9—96no—
131C2×C9C2×C3×C3⋊D313yes—
132C22×C3—91no—
133C22×C3—271no—
134C2×D3—34no—
135C3×C4—24no—
136C3×C4—31no—
137C3×C4—64no—
138C3×C4—91no—
139C3×C4—271no—
140C3×C4D3×3−1+214yescomplemented
141C3×C4C32×C3⋊D311yescharacteristic
142Dic3—34no—
143C32—24no—
144C32—24no—
145C32—34no—
146C32—64no—
147C32—68no—
148C32—64no—
149C32C2×C4×3−1+211yescharacteristic, complemented
150C32C32×C4×D314yes—
151C32C3×C4×C3⋊D311yescharacteristic
152C9—212no—
153C9C3×C4×C3⋊D313yescomplemented
154C2×C4—91noSylow
155C2×C3—24no—
156C2×C3—31no—
157C2×C3—64no—
158C2×C3—92no—
159C2×C3—272no—
160C2×C3C2×D3×3−1+214yes—
161C2×C3C2×C32×C3⋊D311yescharacteristic
162D3—38no—
163C22—91no—
164C4—91no—
165C4C3⋊D3×3−1+211yescharacteristic, direct product factor
166C3—24no—
167C3—31no—
168C3—64no—
169C3C4×D3×3−1+214yescomplemented
170C3C32×C4×C3⋊D311yescharacteristic
171C2—92no—
172C2C2×C3⋊D3×3−1+211yescharacteristic
subgroupG/H
centerC3×C4C32×C3⋊D3
commutatorC33C2×C32×C4
FrattiniC2×C3C2×C32×C3⋊D3
FittingC32×C4×3−1+2C2
socle, cosocleC2×C33C22×C32
prime radicalC2×C32×C3⋊D3C2×C3
hypercenterC4×3−1+2C3⋊D3
hypocenterC32C2×C4×3−1+2
LCSG ▷ C33 ▷ C32
UCSC1 ◁ C3×C4 ◁ C4×3−1+2

Complements

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

NH ≅ G/Ntype
2. C32×C4×3−1+2C2semidirect
3. 3−1+2×C3⋊Dic3C2semidirect
5. C4×C9×C3⋊D3C3semidirect
8. C3⋊D3×3−1+2C4direct (N × H)
16. C3×C4×3−1+2D3semidirect
17. C32×C4×C9C2×C3semidirect
18. C9×C3⋊Dic3C2×C3semidirect
20. C32×3−1+2C2×C4semidirect
32. C9×C3⋊D3C3×C4semidirect
51. C4×3−1+2C3⋊D3direct (N × H)
53. C3×C4×C9C3×D3semidirect
58. C3×3−1+2C4×D3semidirect
59. C32×C9C2×C3×C4semidirect
61. C4×C3⋊D33−1+2direct (N × H)
92. C32×C4C2×3−1+2semidirect
95. C3⋊Dic3C2×3−1+2semidirect
101. C4×C9C3×C3⋊D3semidirect
110. 3−1+2C4×C3⋊D3direct (N × H)
112. C3×C9C3×C4×D3semidirect
126. C3⋊D3C4×3−1+2direct (N × H)
140. C3×C4D3×3−1+2semidirect
149. C32C2×C4×3−1+2semidirect
153. C9C3×C4×C3⋊D3semidirect
165. C4C3⋊D3×3−1+2direct (N × H)
169. C3C4×D3×3−1+2semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊D3×3−1+22
C32×C4×3−1+22
3−1+2×C3⋊Dic32
C32×C4×C3⋊D33
C4×C9×C3⋊D33
C4×D3×3−1+23