Finite Group Databasebeta

← C3⋊D3×C3⋊Dic9 #14518791

Subgroups — C3⋊D3×C3⋊Dic9 #14518791

Order 1944.

984 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 984 conjugacy classes of subgroups — too many to draw. Only its 158 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×C9×C3⋊D3C211yesmaximal, characteristic
2C3⋊(C3⋊(C3⋊Dic9))C211yesmaximal, characteristic, complemented
3C32×C3⋊Dic9C211yesmaximal, characteristic, complemented
4C3⋊D3×C3⋊Dic3—31nomaximal
5D3×C3⋊Dic9—34nomaximal
6C3⋊D3×Dic9—33nomaximal
7C2×C33×C9C2211yescharacteristic
8C3×C9×C3⋊D3C412yescomplemented
9C2×C32×C3⋊D3D311yescharacteristic
10C3⋊(C3⋊(C3⋊Dic3))—31no—
11C32×C3⋊Dic3—31no—
12C2×C9×C3⋊D3D313yes—
13C2×C3×D3×C9—34no—
14C3⋊(C3⋊Dic9)—33no—
15C3⋊(C3⋊Dic9)—34no—
16C3⋊(C3⋊Dic9)—612no—
17C3⋊(C3⋊Dic9)—64no—
18C3×C3⋊Dic9D314yescomplemented
19C32×Dic9—33no—
20C33×C9C2×C411yescharacteristic, complemented, Sylow
21Dic3×C3⋊D3—93no—
22Dic3×C3⋊D3—91no—
23D3×C3⋊Dic3—94no—
24C2×C3⋊Dic9—91no—
25D3×Dic9—912no—
26C2×C34C2×D311yescharacteristic
27C32×C3⋊D3Dic312yes—
28C2×C32×C9—24no—
29C2×C32×C9—212no—
30C2×C32×C9C2×D313yes—
31C2×C32×C9C2×D314yes—
32C9×C3⋊D3Dic316yescomplemented
33C3×D3×C9—38no—
34C2×C3×C3⋊D3D913yes—
35C2×C3×C3⋊D3C3⋊D311yescharacteristic
36C2×C32×D3—34no—
37C3⋊(C3⋊Dic3)—93no—
38C3⋊(C3⋊Dic3)—94no—
39C3⋊(C3⋊Dic3)—91no—
40C3⋊(C3⋊Dic3)—184no—
41C3⋊(C3⋊Dic3)—1812no—
42C3×C3⋊Dic3—34no—
43C32×Dic3—93no—
44C32×Dic3—91no—
45C22×C3×C9—91no—
46C2×D3×C9—312no—
47C3⋊Dic9—912no—
48C3⋊Dic9—91no—
49C3⋊Dic9—1812no—
50C3⋊Dic9—184no—
51C3⋊Dic9—1812no—
52C3⋊Dic9—1824no—
53C3⋊Dic9C3⋊D311yescharacteristic, direct product factor
54C3×Dic9—312no—
55C34C2×Dic311yescharacteristic
56C32×C9—24no—
57C32×C9—212no—
58C32×C9C4×D314yescomplemented
59C32×C9C2×Dic313yescomplemented
60C2×C3⋊Dic3—271no—
61C4×C3⋊D3—271no—
62D3×Dic3—274no—
63D3×Dic3—2712no—
64C2×Dic9—273no—
65C2×C33—212no—
66C2×C33—24no—
67C2×C33C2×D913yes—
68C2×C33D3214yes—
69C2×C33C2×C3⋊D311yescharacteristic
70C3×C3⋊D3Dic916yescomplemented
71C3×C3⋊D3C3⋊Dic312yes—
72C32×D3—38no—
73C2×C3×C9—224no—
74C2×C3×C9—212no—
75C2×C3×C9—24no—
76C2×C3×C9—212no—
77C2×C3×C9—92no—
78C2×C3×C9D32112yes—
79C2×C3×C9C2×C3⋊D311yescharacteristic
80D3×C9—324no—
81C22×C32—91no—
82C2×C3⋊D3C3⋊D911yescharacteristic
83C2×C3×D3—312no—
84C2×C3×D3—34no—
85C32×C4—271no—
86C3⋊Dic3—31no—
87C3⋊Dic3—271no—
88C3⋊Dic3—271no—
89C3⋊Dic3—2712no—
90C3⋊Dic3—274no—
91C3⋊Dic3—544no—
92C3⋊Dic3—5412no—
93C3⋊Dic3—5412no—
94C3⋊Dic3—544no—
95C3⋊Dic3—5424no—
96C3×Dic3—912no—
97C3×Dic3—94no—
98C22×C9—93no—
99Dic9—33no—
100Dic9—273no—
101Dic9—5412no—
102C33—212no—
103C33—24no—
104C33C2×Dic913yescomplemented
105C33D3×Dic314yes—
106C33C2×C3⋊Dic311yescharacteristic
107C3×C9—224no—
108C3×C9—212no—
109C3×C9—24no—
110C3×C9—212no—
111C3×C9D3×Dic3112yescomplemented
112C3×C9C4×C3⋊D311yescharacteristic, complemented
113C2×Dic3—811no—
114C2×Dic3—813no—
115C4×D3—814no—
116C2×C32—224no—
117C2×C32—212no—
118C2×C32—212no—
119C2×C32—24no—
120C2×C32—24no—
121C2×C32—92no—
122C2×C32D3×D9112yes—
123C2×C32C2×C3⋊D911yescharacteristic
124C2×C32D3×C3⋊D314yes—
125C2×C32D3×C3⋊D311yescharacteristic
126C3⋊D3C3⋊Dic912yesdirect product factor
127C3×D3—324no—
128C3×D3—38no—
129C2×C9—212no—
130C2×C9—96no—
131C2×C9D3×C3⋊D313yes—
132C22×C3—93no—
133C22×C3—91no—
134C2×D3—34no—
135C3×C4—274no—
136Dic3—93no—
137Dic3—91no—
138Dic3—813no—
139Dic3—814no—
140Dic3—811no—
141Dic3—16212no—
142Dic3—1624no—
143C32—224no—
144C32—212no—
145C32—212no—
146C32—24no—
147C32—24no—
148C32D3×Dic9112yescomplemented
149C32C2×C3⋊Dic911yescharacteristic, complemented
150C32D3×C3⋊Dic314yes—
151C32Dic3×C3⋊D311yescharacteristic
152C9—212no—
153C9Dic3×C3⋊D313yescomplemented
154C2×C4—2431noSylow
155C2×C3—212no—
156C2×C3—24no—
157C2×C3—96no—
158C2×C3—92no—
159C2×C3D9×C3⋊D313yes—
160C2×C3D3×C3⋊D914yes—
161C2×C3C3⋊D3211yescharacteristic
162D3—38no—
163C22—91no—
164C4—271no—
165C4—2431no—
166C3—212no—
167C3—24no—
168C3C3⋊D3×Dic913yescomplemented
169C3D3×C3⋊Dic914yescomplemented
170C3C3⋊D3×C3⋊Dic311yescharacteristic
171C2—92no—
172C2C3⋊D3×C3⋊D911yescharacteristic
subgroupG/H
center, hypercenterC2C3⋊D3×C3⋊D9
commutator, hypocenterC33×C9C2×C4
FrattiniC2×C3C3⋊D32
Fitting, cosocleC2×C33×C9C22
socleC2×C34C2×D3
prime radicalC2×C32×C3⋊D3D3
LCSG ▷ C33×C9
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C3⋊(C3⋊(C3⋊Dic9))C2semidirect
3. C32×C3⋊Dic9C2semidirect
8. C3×C9×C3⋊D3C4semidirect
18. C3×C3⋊Dic9D3semidirect
20. C33×C9C2×C4semidirect
32. C9×C3⋊D3Dic3semidirect
53. C3⋊Dic9C3⋊D3direct (N × H)
58. C32×C9C4×D3semidirect
59. C32×C9C2×Dic3semidirect
70. C3×C3⋊D3Dic9semidirect
104. C33C2×Dic9semidirect
111. C3×C9D3×Dic3semidirect
112. C3×C9C4×C3⋊D3semidirect
126. C3⋊D3C3⋊Dic9direct (N × H)
148. C32D3×Dic9semidirect
149. C32C2×C3⋊Dic9semidirect
153. C9Dic3×C3⋊D3semidirect
168. C3C3⋊D3×Dic9semidirect
169. C3D3×C3⋊Dic9semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C9×C3⋊D32
C3⋊(C3⋊(C3⋊Dic9))2
C32×C3⋊Dic92
C3⋊D3×C3⋊Dic33
D3×C3⋊Dic93
C3⋊D3×Dic93