Finite Group Databasebeta

← C32×C4×(C3⋊D3)⋊C3 #14518880

Subgroups — C32×C4×(C3⋊D3)⋊C3 #14518880

Order 1944.

1260 conjugacy classes of subgroups; only the 326 normal subgroups are shown.

normal subgroups only

This group has 1260 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×(C3⋊D3)⋊C3C211yesmaximal, characteristic
2C32×C4×H(3,𝔽3)C211yesmaximal, characteristic, complemented
3C32×(C3⋊Dic3)⋊C3C211yesmaximal, characteristic, complemented
4C32×C4×C3⋊D3C311yesmaximal, characteristic, complemented
5C33×C4×D3—31nomaximal
6C3×C4×(C3⋊D3)⋊C3C3112yesmaximal, direct product factor
7C2×C32×H(3,𝔽3)C2211yescharacteristic
8C32×(C3⋊D3)⋊C3C412yesdirect product factor
9C2×C32×C3⋊D3C2×C311yescharacteristic
10C2×C33×D3—31no—
11C34×C4—21no—
12C34×C4D311yescharacteristic, complemented
13C34×C4C2×C311yescharacteristic, complemented
14C32×C3⋊Dic3C2×C311yescharacteristic, complemented
15C33×Dic3—31no—
16C2×C3×(C3⋊D3)⋊C3C2×C3112yes—
17C3×C4×H(3,𝔽3)—212no—
18C3×C4×H(3,𝔽3)C2×C3112yescomplemented
19C3×(C3⋊Dic3)⋊C3C2×C3112yescomplemented
20C32×H(3,𝔽3)C2×C411yescharacteristic, complemented, Sylow
21C2×C33×C4—91no—
22C3×C4×C3⋊D3C3214yescomplemented
23C32×C4×D3—31no—
24C32×C4×D3—312no—
25C32×C4×D3—91no—
26C4×(C3⋊D3)⋊C3C3219yesdirect product factor
27C2×C34—21no—
28C2×C34C2×D311yescharacteristic
29C2×C34C22×C311yescharacteristic
30C32×C3⋊D3C3×C412yescomplemented
31C33×D3—32no—
32C2×C3×H(3,𝔽3)—212no—
33C2×C3×H(3,𝔽3)C22×C3112yes—
34C3×(C3⋊D3)⋊C3C3×C4124yesdirect product factor
35C22×C33—91no—
36C2×C3×C3⋊D3C2×C3214yes—
37C2×C32×D3—312no—
38C2×C32×D3—31no—
39C2×C32×D3—91no—
40C33×C4—24no—
41C33×C4—212no—
42C33×C4—31no—
43C33×C4—31no—
44C33×C4—64no—
45C33×C4—64no—
46C33×C4—68no—
47C33×C4—61no—
48C33×C4—91no—
49C33×C4C3×D311yescharacteristic
50C33×C4C3×D3112yescomplemented
51C33×C4C2×C3214yescomplemented
52C3×C3⋊Dic3C2×C3214yescomplemented
53C32×Dic3—312no—
54C32×Dic3—31no—
55C32×Dic3—91no—
56C2×(C3⋊D3)⋊C3C2×C3219yes—
57C4×H(3,𝔽3)—236no—
58C4×H(3,𝔽3)C2×C3219yescomplemented
59(C3⋊Dic3)⋊C3C2×C3219yescomplemented
60C34—21no—
61C34C4×D311yescharacteristic, complemented
62C34C2×C3×C411yescharacteristic, complemented
63C3×H(3,𝔽3)—212no—
64C3×H(3,𝔽3)C2×C3×C4112yescomplemented
65C2×C32×C4—912no—
66C2×C32×C4—91no—
67C4×C3⋊D3C3311yescharacteristic, complemented
68C3×C4×D3—34no—
69C3×C4×D3—39no—
70C3×C4×D3—94no—
71C2×C33—24no—
72C2×C33—212no—
73C2×C33—31no—
74C2×C33—31no—
75C2×C33—64no—
76C2×C33—64no—
77C2×C33—68no—
78C2×C33—61no—
79C2×C33—92no—
80C2×C33C2×C3×D311yescharacteristic
81C2×C33C2×C3×D3112yes—
82C2×C33C22×C3214yes—
83C3×C3⋊D3C32×C418yescomplemented
84C32×D3—32no—
85C32×D3—324no—
86C32×D3—92no—
87C2×H(3,𝔽3)—236no—
88C2×H(3,𝔽3)C22×C3219yes—
89(C3⋊D3)⋊C3C32×C4118yesdirect product factor
90C22×C32—912no—
91C22×C32—91no—
92C2×C3⋊D3C2×C3311yescharacteristic
93C2×C3×D3—39no—
94C2×C3×D3—34no—
95C2×C3×D3—94no—
96C32×C4—24no—
97C32×C4—24no—
98C32×C4—29no—
99C32×C4—312no—
100C32×C4—34no—
101C32×C4—612no—
102C32×C4—64no—
103C32×C4—68no—
104C32×C4—624no—
105C32×C4—64no—
106C32×C4—612no—
107C32×C4—912no—
108C32×C4—91no—
109C32×C4(C3⋊D3)⋊C311yescharacteristic, direct product factor
110C32×C4C32×D314yes—
111C32×C4C32×D319yescomplemented
112C32×C4C2×C3311yescharacteristic, complemented
113C3⋊Dic3C2×C3311yescharacteristic, complemented
114C3×Dic3—39no—
115C3×Dic3—34no—
116C3×Dic3—94no—
117C33—24no—
118C33—212no—
119C33—31no—
120C33—31no—
121C33—64no—
122C33—64no—
123C33—68no—
124C33—61no—
125C33C3×C4×D311yescharacteristic
126C33C3×C4×D3112yescomplemented
127C33C2×C32×C414yescomplemented
128H(3,𝔽3)—236no—
129H(3,𝔽3)C2×C32×C419yescomplemented
130C2×C3×C4—99no—
131C2×C3×C4—94no—
132C4×D3—31no—
133C4×D3—91no—
134C2×C32—24no—
135C2×C32—24no—
136C2×C32—29no—
137C2×C32—312no—
138C2×C32—34no—
139C2×C32—612no—
140C2×C32—64no—
141C2×C32—68no—
142C2×C32—624no—
143C2×C32—64no—
144C2×C32—612no—
145C2×C32—924no—
146C2×C32—92no—
147C2×C32C2×(C3⋊D3)⋊C311yescharacteristic
148C2×C32C2×C32×D314yes—
149C2×C32C2×C32×D319yes—
150C2×C32C22×C3311yescharacteristic
151C3⋊D3C33×C412yescomplemented
152C3×D3—38no—
153C3×D3—318no—
154C3×D3—98no—
155C22×C3—99no—
156C22×C3—94no—
157C2×D3—31no—
158C2×D3—91no—
159C3×C4—24no—
160C3×C4—31no—
161C3×C4—39no—
162C3×C4—64no—
163C3×C4—69no—
164C3×C4—99no—
165C3×C4—94no—
166C3×C4C3×(C3⋊D3)⋊C314yesdirect product factor
167C3×C4C33×D311yescharacteristic
168Dic3—31no—
169Dic3—91no—
170C32—24no—
171C32—24no—
172C32—29no—
173C32—312no—
174C32—34no—
175C32—612no—
176C32—64no—
177C32—68no—
178C32—624no—
179C32—64no—
180C32—612no—
181C32C4×(C3⋊D3)⋊C311yescharacteristic, direct product factor
182C32C32×C4×D314yes—
183C32C32×C4×D319yescomplemented
184C32C2×C33×C411yescharacteristic, complemented
185C2×C4—91noSylow
186C2×C3—24no—
187C2×C3—31no—
188C2×C3—39no—
189C2×C3—64no—
190C2×C3—69no—
191C2×C3—918no—
192C2×C3—98no—
193C2×C3C2×C3×(C3⋊D3)⋊C314yes—
194C2×C3C2×C33×D311yescharacteristic
195D3—32no—
196D3—92no—
197C22—91no—
198C4—91no—
199C4C32×(C3⋊D3)⋊C311yescharacteristic, direct product factor
200C3—24no—
201C3—31no—
202C3—39no—
203C3—64no—
204C3—69no—
205C3C3×C4×(C3⋊D3)⋊C314yesdirect product factor
206C3C33×C4×D311yescharacteristic
207C2—92no—
208C2C2×C32×(C3⋊D3)⋊C311yescharacteristic
subgroupG/H
center, hypercenterC32×C4(C3⋊D3)⋊C3
commutator, hypocenterC32C2×C33×C4
FrattiniC2×C3C2×C33×D3
FittingC32×C4×H(3,𝔽3)C2
socleC2×C33C2×C3×D3
prime radicalC2×C32×(C3⋊D3)⋊C3C2
cosocleC2×C32C22×C33
LCSG ▷ C32
UCSC1 ◁ C32×C4

Complements

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

NH ≅ G/Ntype
2. C32×C4×H(3,𝔽3)C2semidirect
3. C32×(C3⋊Dic3)⋊C3C2semidirect
4. C32×C4×C3⋊D3C3semidirect
6. C3×C4×(C3⋊D3)⋊C3C3direct (N × H)
8. C32×(C3⋊D3)⋊C3C4direct (N × H)
12. C34×C4D3semidirect
13. C34×C4C2×C3semidirect
14. C32×C3⋊Dic3C2×C3semidirect
18. C3×C4×H(3,𝔽3)C2×C3semidirect
19. C3×(C3⋊Dic3)⋊C3C2×C3semidirect
20. C32×H(3,𝔽3)C2×C4semidirect
22. C3×C4×C3⋊D3C32semidirect
26. C4×(C3⋊D3)⋊C3C32direct (N × H)
30. C32×C3⋊D3C3×C4semidirect
34. C3×(C3⋊D3)⋊C3C3×C4direct (N × H)
50. C33×C4C3×D3semidirect
51. C33×C4C2×C32semidirect
52. C3×C3⋊Dic3C2×C32semidirect
58. C4×H(3,𝔽3)C2×C32semidirect
59. (C3⋊Dic3)⋊C3C2×C32semidirect
61. C34C4×D3semidirect
62. C34C2×C3×C4semidirect
64. C3×H(3,𝔽3)C2×C3×C4semidirect
67. C4×C3⋊D3C33semidirect
83. C3×C3⋊D3C32×C4semidirect
89. (C3⋊D3)⋊C3C32×C4direct (N × H)
109. C32×C4(C3⋊D3)⋊C3direct (N × H)
111. C32×C4C32×D3semidirect
112. C32×C4C2×C33semidirect
113. C3⋊Dic3C2×C33semidirect
126. C33C3×C4×D3semidirect
127. C33C2×C32×C4semidirect
129. H(3,𝔽3)C2×C32×C4semidirect
151. C3⋊D3C33×C4semidirect
166. C3×C4C3×(C3⋊D3)⋊C3direct (N × H)
181. C32C4×(C3⋊D3)⋊C3direct (N × H)
183. C32C32×C4×D3semidirect
184. C32C2×C33×C4semidirect
199. C4C32×(C3⋊D3)⋊C3direct (N × H)
205. C3C3×C4×(C3⋊D3)⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×(C3⋊D3)⋊C32
C32×C4×H(3,𝔽3)2
C32×(C3⋊Dic3)⋊C32
C32×C4×C3⋊D33
C33×C4×D33
C3×C4×(C3⋊D3)⋊C33