Finite Group Databasebeta

← C3⋊D3×(C3⋊Dic3)⋊C3 #14518678

Subgroups — C3⋊D3×(C3⋊Dic3)⋊C3 #14518678

Order 1944.

748 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 748 conjugacy classes of subgroups — too many to draw. Only its 91 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×H(3,𝔽3)C211yesmaximal, characteristic
2C3⋊(C3⋊((C3⋊Dic3)⋊C3))C211yesmaximal, characteristic, complemented
3C32×(C3⋊Dic3)⋊C3C211yesmaximal, characteristic, complemented
4C3⋊D3×C3⋊Dic3C311yesmaximal, characteristic, complemented
5C3×Dic3×C3⋊D3—31nomaximal
6D3×(C3⋊Dic3)⋊C3—34nomaximal
7C2×C32×H(3,𝔽3)C2211yescharacteristic
8C3⋊D3×H(3,𝔽3)C412yescomplemented
9C2×C32×C3⋊D3—21no—
10C2×C32×C3⋊D3D311yescharacteristic
11C2×C32×C3⋊D3C2×C311yescharacteristic
12C3⋊(C3⋊(C3⋊Dic3))C2×C311yescharacteristic, complemented
13C3×C3⋊(C3⋊Dic3)—31no—
14C32×C3⋊Dic3C2×C311yescharacteristic, complemented
15C33×Dic3—31no—
16C2×D3×H(3,𝔽3)—34no—
17C3⋊((C3⋊Dic3)⋊C3)—34no—
18C3⋊((C3⋊Dic3)⋊C3)—64no—
19C3×(C3⋊Dic3)⋊C3—24no—
20C3×(C3⋊Dic3)⋊C3D314yescomplemented
21C32×H(3,𝔽3)C2×C411yescharacteristic, complemented, Sylow
22C3×C4×C3⋊D3—91no—
23Dic3×C3⋊D3—31no—
24Dic3×C3⋊D3—91no—
25D3×C3⋊Dic3—34no—
26C3×D3×Dic3—94no—
27C2×(C3⋊Dic3)⋊C3—91no—
28C2×C34—21no—
29C2×C34C2×D311yescharacteristic
30C2×C34C22×C311yescharacteristic
31C32×C3⋊D3—22no—
32C32×C3⋊D3Dic312yescomplemented
33C32×C3⋊D3C3×C412yescomplemented
34C2×C3×H(3,𝔽3)—24no—
35C2×C3×H(3,𝔽3)—24no—
36C2×C3×H(3,𝔽3)—44no—
37C2×C3×H(3,𝔽3)C2×D314yes—
38D3×H(3,𝔽3)—38no—
39C2×C3×C3⋊D3—31no—
40C2×C3×C3⋊D3—31no—
41C2×C3×C3⋊D3—61no—
42C2×C3×C3⋊D3C3×D311yescharacteristic
43C2×C32×D3—34no—
44C2×C32×D3—34no—
45C2×C32×D3—64no—
46C33×C4—91no—
47C3⋊(C3⋊Dic3)—31no—
48C3⋊(C3⋊Dic3)—34no—
49C3⋊(C3⋊Dic3)—64no—
50C3⋊(C3⋊Dic3)—91no—
51C3⋊(C3⋊Dic3)—184no—
52C3×C3⋊Dic3—91no—
53C3×C3⋊Dic3—94no—
54C3×C3⋊Dic3—184no—
55C3×C3⋊Dic3C3×D314yescomplemented
56C32×Dic3—34no—
57C32×Dic3—31no—
58C32×Dic3—64no—
59C32×Dic3—91no—
60C22×H(3,𝔽3)—91no—
61(C3⋊Dic3)⋊C3—24no—
62(C3⋊Dic3)⋊C3—91no—
63(C3⋊Dic3)⋊C3—184no—
64(C3⋊Dic3)⋊C3C3⋊D311yescharacteristic, direct product factor
65C34—21no—
66C34C2×Dic311yescharacteristic, complemented
67C34C2×C3×C411yescharacteristic, complemented
68C3×H(3,𝔽3)—24no—
69C3×H(3,𝔽3)—24no—
70C3×H(3,𝔽3)—44no—
71C3×H(3,𝔽3)C4×D314yescomplemented
72C2×C3⋊Dic3—91no—
73C4×C3⋊D3—91no—
74C2×C3×Dic3—271no—
75C3×C4×D3—274no—
76D3×Dic3—94no—
77D3×Dic3—274no—
78C2×C33—24no—
79C2×C33—24no—
80C2×C33—24no—
81C2×C33—31no—
82C2×C33—31no—
83C2×C33—44no—
84C2×C33—64no—
85C2×C33—64no—
86C2×C33—61no—
87C2×C33—124no—
88C2×C33D3214yes—
89C2×C33C2×C3×D311yescharacteristic
90C2×C33C2×C3×D314yes—
91C3×C3⋊D3—32no—
92C3×C3⋊D3—32no—
93C3×C3⋊D3—62no—
94C3×C3⋊D3C3×Dic312yes—
95C32×D3—38no—
96C32×D3—38no—
97C32×D3—68no—
98C2×H(3,𝔽3)—24no—
99C2×H(3,𝔽3)—24no—
100C2×H(3,𝔽3)—44no—
101C2×H(3,𝔽3)—412no—
102C2×H(3,𝔽3)—92no—
103C2×H(3,𝔽3)C2×C3⋊D311yescharacteristic
104C22×C32—91no—
105C22×C32—91no—
106C22×C32—181no—
107C2×C3⋊D3(C3⋊D3)⋊C311yescharacteristic
108C2×C3×D3—34no—
109C2×C3×D3—94no—
110C2×C3×D3—94no—
111C2×C3×D3—184no—
112C32×C4—91no—
113C32×C4—94no—
114C32×C4—184no—
115C3⋊Dic3—91no—
116C3⋊Dic3—94no—
117C3⋊Dic3—91no—
118C3⋊Dic3—184no—
119C3⋊Dic3—184no—
120C3⋊Dic3—274no—
121C3⋊Dic3—544no—
122C3⋊Dic3—544no—
123C3⋊Dic3—548no—
124C3⋊Dic3C3×C3⋊D311yescharacteristic, complemented
125C3×Dic3—34no—
126C3×Dic3—31no—
127C3×Dic3—64no—
128C3×Dic3—94no—
129C3×Dic3—274no—
130C3×Dic3—271no—
131C3×Dic3—544no—
132C33—24no—
133C33—24no—
134C33—24no—
135C33—31no—
136C33—31no—
137C33—44no—
138C33—64no—
139C33—64no—
140C33—61no—
141C33—124no—
142C33D3×Dic314yescomplemented
143C33C3×C4×D314yescomplemented
144C33C2×C3×Dic311yescharacteristic
145H(3,𝔽3)—24no—
146H(3,𝔽3)—24no—
147H(3,𝔽3)—44no—
148H(3,𝔽3)—412no—
149H(3,𝔽3)C4×C3⋊D311yescharacteristic, complemented
150C2×C3×C4—811no—
151C2×Dic3—271no—
152C2×Dic3—811no—
153C4×D3—274no—
154C2×C32—24no—
155C2×C32—24no—
156C2×C32—24no—
157C2×C32—21no—
158C2×C32—34no—
159C2×C32—34no—
160C2×C32—44no—
161C2×C32—64no—
162C2×C32—64no—
163C2×C32—68no—
164C2×C32—64no—
165C2×C32—64no—
166C2×C32—64no—
167C2×C32—92no—
168C2×C32—92no—
169C2×C32—124no—
170C2×C32—124no—
171C2×C32—128no—
172C2×C32—124no—
173C2×C32—182no—
174C2×C32C2×(C3⋊D3)⋊C311yescharacteristic
175C2×C32C3×D3214yes—
176C2×C32D3×C3⋊D311yescharacteristic
177C2×C32C2×C3×C3⋊D311yescharacteristic
178C3⋊D3(C3⋊Dic3)⋊C312yesdirect product factor
179C3×D3—38no—
180C3×D3—98no—
181C3×D3—98no—
182C3×D3—188no—
183C22×C3—91no—
184C22×C3—271no—
185C22×C3—271no—
186C22×C3—541no—
187C2×D3—34no—
188C3×C4—91no—
189C3×C4—94no—
190C3×C4—184no—
191C3×C4—811no—
192Dic3—31no—
193Dic3—91no—
194Dic3—274no—
195Dic3—271no—
196Dic3—544no—
197Dic3—811no—
198Dic3—1624no—
199C32—24no—
200C32—21no—
201C32—24no—
202C32—24no—
203C32—34no—
204C32—34no—
205C32—44no—
206C32—64no—
207C32—64no—
208C32—68no—
209C32—64no—
210C32—64no—
211C32—64no—
212C32—124no—
213C32—124no—
214C32—128no—
215C32—124no—
216C32C2×(C3⋊Dic3)⋊C311yescharacteristic, complemented
217C32C3×D3×Dic314yes—
218C32Dic3×C3⋊D311yescharacteristic, complemented
219C32C3×C4×C3⋊D311yescharacteristic, complemented
220C2×C4—811noSylow
221C2×C3—24no—
222C2×C3—31no—
223C2×C3—31no—
224C2×C3—64no—
225C2×C3—64no—
226C2×C3—61no—
227C2×C3—92no—
228C2×C3—124no—
229C2×C3—272no—
230C2×C3—272no—
231C2×C3—542no—
232C2×C3D3×(C3⋊D3)⋊C314yes—
233C2×C3C3×D3×C3⋊D311yescharacteristic
234D3—38no—
235C22—91no—
236C4—91no—
237C4—811no—
238C3—24no—
239C3—31no—
240C3—31no—
241C3—61no—
242C3—64no—
243C3—64no—
244C3—124no—
245C3D3×(C3⋊Dic3)⋊C314yescomplemented
246C3C3×Dic3×C3⋊D311yescharacteristic
247C2—92no—
248C2C3⋊D3×(C3⋊D3)⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2C3⋊D3×(C3⋊D3)⋊C3
commutator, hypocenterC34C2×C3×C4
FrattiniC2×C3C3×D3×C3⋊D3
FittingC2×C32×H(3,𝔽3)C22
socleC2×C33C2×C3×D3
prime radicalC2×C3⋊D3×H(3,𝔽3)C2
cosocleC2×C34C22×C3
LCSG ▷ C34
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C3⋊(C3⋊((C3⋊Dic3)⋊C3))C2semidirect
3. C32×(C3⋊Dic3)⋊C3C2semidirect
4. C3⋊D3×C3⋊Dic3C3semidirect
8. C3⋊D3×H(3,𝔽3)C4semidirect
12. C3⋊(C3⋊(C3⋊Dic3))C2×C3semidirect
14. C32×C3⋊Dic3C2×C3semidirect
20. C3×(C3⋊Dic3)⋊C3D3semidirect
21. C32×H(3,𝔽3)C2×C4semidirect
32. C32×C3⋊D3Dic3semidirect
33. C32×C3⋊D3C3×C4semidirect
55. C3×C3⋊Dic3C3×D3semidirect
64. (C3⋊Dic3)⋊C3C3⋊D3direct (N × H)
66. C34C2×Dic3semidirect
67. C34C2×C3×C4semidirect
71. C3×H(3,𝔽3)C4×D3semidirect
124. C3⋊Dic3C3×C3⋊D3semidirect
142. C33D3×Dic3semidirect
143. C33C3×C4×D3semidirect
149. H(3,𝔽3)C4×C3⋊D3semidirect
178. C3⋊D3(C3⋊Dic3)⋊C3direct (N × H)
216. C32C2×(C3⋊Dic3)⋊C3semidirect
218. C32Dic3×C3⋊D3semidirect
219. C32C3×C4×C3⋊D3semidirect
245. C3D3×(C3⋊Dic3)⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊D3×H(3,𝔽3)2
C3⋊(C3⋊((C3⋊Dic3)⋊C3))2
C32×(C3⋊Dic3)⋊C32
C3⋊D3×C3⋊Dic33
C3×Dic3×C3⋊D33
D3×(C3⋊Dic3)⋊C33