Finite Group Databasebeta

← C3⋊Dic3×C3⋊D9 #14518788

Subgroups — C3⋊Dic3×C3⋊D9 #14518788

Order 1944.

984 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 984 conjugacy classes of subgroups — too many to draw. Only its 150 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×C3⋊D9C211yesmaximal, characteristic
2C3⋊(C3⋊(C3⋊Dic9))C211yesmaximal, characteristic, complemented
3C3×C9×C3⋊Dic3C211yesmaximal, characteristic, complemented
4C3⋊D3×C3⋊Dic3—31nomaximal
5Dic3×C3⋊D9—34nomaximal
6D9×C3⋊Dic3—33nomaximal
7C2×C33×C9C2211yescharacteristic
8C32×C3⋊D9C412yescomplemented
9C2×C32×C3⋊D3—31no—
10C3⋊(C3⋊(C3⋊Dic3))—31no—
11C32×C3⋊Dic3D311yescharacteristic
12C2×C3×C3⋊D9D314yes—
13C2×C32×D9—33no—
14C3⋊(C3⋊Dic9)—33no—
15C3⋊(C3⋊Dic9)—34no—
16C3⋊(C3⋊Dic9)—612no—
17C3⋊(C3⋊Dic9)—64no—
18C9×C3⋊Dic3D313yescomplemented
19C3×C9×Dic3—34no—
20C33×C9C2×C411yescharacteristic, complemented, Sylow
21Dic3×C3⋊D3—94no—
22D3×C3⋊Dic3—93no—
23D3×C3⋊Dic3—91no—
24C4×C3⋊D9—91no—
25Dic3×D9—912no—
26C2×C34C2×D311yescharacteristic
27C32×C3⋊D3—32no—
28C2×C32×C9—24no—
29C2×C32×C9—212no—
30C2×C32×C9C2×D313yes—
31C2×C32×C9C2×D314yes—
32C3×C3⋊D9Dic318yescomplemented
33C32×D9—36no—
34C2×C3×C3⋊D3—34no—
35C2×C32×D3—93no—
36C2×C32×D3—91no—
37C3⋊(C3⋊Dic3)—93no—
38C3⋊(C3⋊Dic3)—94no—
39C3⋊(C3⋊Dic3)—91no—
40C3⋊(C3⋊Dic3)—184no—
41C3⋊(C3⋊Dic3)—1812no—
42C3×C3⋊Dic3D913yescomplemented
43C3×C3⋊Dic3C3⋊D311yescharacteristic
44C32×Dic3—34no—
45C2×C3⋊D9C3⋊D311yescharacteristic
46C2×C3×D9—312no—
47C3×C4×C9—91no—
48C3⋊Dic9—912no—
49C3⋊Dic9—91no—
50C3⋊Dic9—1812no—
51C3⋊Dic9—184no—
52C3⋊Dic9—1812no—
53C3⋊Dic9—1824no—
54C9×Dic3—312no—
55C34C4×D311yescharacteristic
56C32×C9—24no—
57C32×C9—212no—
58C32×C9C4×D313yescomplemented
59C32×C9C2×Dic314yescomplemented
60C2×C3⋊Dic3—271no—
61C4×C3⋊D3—271no—
62D3×Dic3—274no—
63D3×Dic3—2712no—
64C4×D9—273no—
65C2×C33—212no—
66C2×C33—24no—
67C2×C33C2×D913yes—
68C2×C33D3214yes—
69C2×C33C2×C3⋊D311yescharacteristic
70C3×C3⋊D3—38no—
71C32×D3—96no—
72C32×D3—92no—
73C2×C3×C9—224no—
74C2×C3×C9—212no—
75C2×C3×C9—24no—
76C2×C3×C9—212no—
77C2×C3×C9D32112yes—
78C2×C3×C9C2×C3⋊D311yescharacteristic
79C3⋊D9C3⋊Dic312yesdirect product factor
80C3×D9—324no—
81C22×C32—271no—
82C2×C3⋊D3—31no—
83C2×C3×D3—912no—
84C2×C3×D3—94no—
85C32×C4—91no—
86C3⋊Dic3—271no—
87C3⋊Dic3—271no—
88C3⋊Dic3—2712no—
89C3⋊Dic3—274no—
90C3⋊Dic3—544no—
91C3⋊Dic3—5412no—
92C3⋊Dic3—5412no—
93C3⋊Dic3—544no—
94C3⋊Dic3—5424no—
95C3⋊Dic3C3⋊D911yescharacteristic, direct product factor
96C3×Dic3—312no—
97C3×Dic3—34no—
98C2×D9—33no—
99C4×C9—93no—
100Dic9—273no—
101Dic9—5412no—
102C33—212no—
103C33—24no—
104C33C4×D913yescomplemented
105C33D3×Dic314yes—
106C33C4×C3⋊D311yescharacteristic
107C3×C9—224no—
108C3×C9—24no—
109C3×C9—212no—
110C3×C9—212no—
111C3×C9D3×Dic3112yescomplemented
112C3×C9C2×C3⋊Dic311yescharacteristic, complemented
113C2×Dic3—814no—
114C4×D3—811no—
115C4×D3—813no—
116C2×C32—224no—
117C2×C32—212no—
118C2×C32—212no—
119C2×C32—24no—
120C2×C32—24no—
121C2×C32—272no—
122C2×C32D3×D9112yes—
123C2×C32C2×C3⋊D911yescharacteristic
124C2×C32D3×C3⋊D314yes—
125C2×C32D3×C3⋊D311yescharacteristic
126C3⋊D3—32no—
127C3×D3—924no—
128C3×D3—98no—
129C2×C9—212no—
130C2×C9D3×C3⋊D313yes—
131D9—36no—
132C22×C3—274no—
133C2×D3—93no—
134C2×D3—91no—
135C3×C4—93no—
136C3×C4—91no—
137Dic3—34no—
138Dic3—813no—
139Dic3—814no—
140Dic3—811no—
141Dic3—16212no—
142Dic3—1624no—
143C32—224no—
144C32—212no—
145C32—212no—
146C32—24no—
147C32—24no—
148C32Dic3×D9112yescomplemented
149C32C4×C3⋊D911yescharacteristic, complemented
150C32D3×C3⋊Dic311yescharacteristic
151C32Dic3×C3⋊D314yes—
152C9—212no—
153C9D3×C3⋊Dic313yescomplemented
154C2×C4—2431noSylow
155C2×C3—212no—
156C2×C3—24no—
157C2×C3—278no—
158C2×C3D9×C3⋊D313yes—
159C2×C3D3×C3⋊D914yes—
160C2×C3C3⋊D3211yescharacteristic
161D3—96no—
162D3—92no—
163C22—271no—
164C4—91no—
165C4—2431no—
166C3—212no—
167C3—24no—
168C3D9×C3⋊Dic313yescomplemented
169C3Dic3×C3⋊D914yescomplemented
170C3C3⋊D3×C3⋊Dic311yescharacteristic
171C2—272no—
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⋊D9C2
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. C3×C9×C3⋊Dic3C2semidirect
8. C32×C3⋊D9C4semidirect
18. C9×C3⋊Dic3D3semidirect
20. C33×C9C2×C4semidirect
32. C3×C3⋊D9Dic3semidirect
42. C3×C3⋊Dic3D9semidirect
58. C32×C9C4×D3semidirect
59. C32×C9C2×Dic3semidirect
79. C3⋊D9C3⋊Dic3direct (N × H)
95. C3⋊Dic3C3⋊D9direct (N × H)
104. C33C4×D9semidirect
111. C3×C9D3×Dic3semidirect
112. C3×C9C2×C3⋊Dic3semidirect
148. C32Dic3×D9semidirect
149. C32C4×C3⋊D9semidirect
153. C9D3×C3⋊Dic3semidirect
168. C3D9×C3⋊Dic3semidirect
169. C3Dic3×C3⋊D9semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C3⋊D92
C3⋊(C3⋊(C3⋊Dic9))2
C3×C9×C3⋊Dic32
C3⋊D3×C3⋊Dic33
Dic3×C3⋊D93
D9×C3⋊Dic33