Finite Group Databasebeta

← D3×C3⋊SL(2,ℤ/4) #11724203

Subgroups — D3×C3⋊SL(2,ℤ/4) #11724203

Order 864.

371 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 371 conjugacy classes of subgroups — too many to draw. Only its 60 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×A4C211yesmaximal, characteristic
2C3⋊(C3⋊SL(2,ℤ/4))C211yesmaximal, characteristic, complemented
3C3×C3⋊SL(2,ℤ/4)C211yesmaximal, characteristic, complemented
4C2×C3⋊SL(2,ℤ/4)—31nomaximal
5D3×SL(2,ℤ/4)—33nomaximal
6D3×#217—31nomaximal
7C2×C32×A4C2211yescharacteristic
8C3×D3×A4C412yescomplemented
9D3×C3⋊Dic3—41nomaximal
10C23×C3×D3D311yescharacteristic
11C22×C3×A4—31no—
12C2×D3×A4D313yes—
13C2×D3×Dic3—31no—
14C2×D3×Dic3—31no—
15C3⋊SL(2,ℤ/4)—31no—
16C3⋊SL(2,ℤ/4)—33no—
17C3⋊SL(2,ℤ/4)—61no—
18C3⋊SL(2,ℤ/4)—63no—
19C3⋊SL(2,ℤ/4)D311yescharacteristic, direct product factor
20C3×SL(2,ℤ/4)—33no—
21#3757—31no—
22C3×#217—31no—
23(C2×D3)⋊Dic3—31no—
24(C2×D3)⋊Dic3—31no—
25C2×C32×D3—41no—
26C32×A4C2×C411yescharacteristic, complemented
27C3⋊(C3⋊Dic3)—41no—
28C3×C3⋊Dic3—41no—
29C2×SL(2,ℤ/4)—93no—
30C2×#217—91no—
31D3×C22⋊C4—91no—
32C23×C32C2×D311yescharacteristic
33C22×C3×D3—31no—
34C22×C3×D3—32no—
35C22×C3×D3—31no—
36C22×C3×D3Dic312yescomplemented
37C2×C3×A4—21no—
38C2×C3×A4—23no—
39C2×C3×A4—32no—
40C2×C3×A4C2×D313yes—
41C2×C3×A4C2×D311yescharacteristic
42D3×A4Dic316yescomplemented
43C2×C3⋊Dic3—31no—
44C2×C3⋊Dic3—31no—
45C2×C3⋊Dic3—121no—
46C2×C3×Dic3—31no—
47C2×C3×Dic3—31no—
48D3×Dic3—62no—
49D3×Dic3—61no—
50D3×Dic3—61no—
51D3×Dic3—123no—
52C2×C33—41no—
53C32×D3—42no—
54C24×C3—31no—
55C23×D3C3⋊D311yescharacteristic
56C22×A4—33no—
57C22×Dic3—91no—
58C22×Dic3—91no—
59C2×C4×D3—91no—
60C2×C4×D3—91no—
61SL(2,ℤ/4)—33no—
62SL(2,ℤ/4)—93no—
63SL(2,ℤ/4)—183no—
64C3×C22⋊C4—91no—
65#217—31no—
66#217—91no—
67#217—91no—
68#217—91no—
69#217—91no—
70#217—181no—
71(C2×D3)⋊C4—91no—
72(C2×D3)⋊C4—91no—
73C22×C32—31no—
74C22×C32—31no—
75C22×C32—121no—
76C22×C32C2×Dic311yescharacteristic, complemented
77C2×C3×D3—31no—
78C2×C3×D3—32no—
79C2×C3×D3—32no—
80C2×C3×D3—32no—
81C2×C3×D3—43no—
82C2×C3×D3—61no—
83C2×C3×D3S411yescharacteristic
84C3×A4—21no—
85C3×A4—23no—
86C3×A4C4×D311yescharacteristic, complemented
87C3×A4C2×Dic313yescomplemented
88C3⋊Dic3—41no—
89C3⋊Dic3—61no—
90C3⋊Dic3—61no—
91C3⋊Dic3—121no—
92C3⋊Dic3—123no—
93C3⋊Dic3—241no—
94C3⋊Dic3—243no—
95C3×Dic3—61no—
96C3×Dic3—61no—
97C3×Dic3—123no—
98C2×C22⋊C4—271noSylow
99C33—41noSylow
100C23×C3—21no—
101C23×C3—32no—
102C23×C3—91no—
103C23×C3—91no—
104C23×C3—92no—
105C23×C3D3211yescharacteristic
106C23×C3C2×C3⋊D311yescharacteristic
107C22×D3—31no—
108C22×D3—31no—
109C22×D3—32no—
110C22×D3C3⋊Dic312yescomplemented
111C2×A4—23no—
112C2×A4—36no—
113C2×A4D3213yes—
114C2×C3×C4—91no—
115C2×C3×C4—91no—
116C2×Dic3—31no—
117C2×Dic3—31no—
118C2×Dic3—91no—
119C2×Dic3—91no—
120C2×Dic3—91no—
121C2×Dic3—91no—
122C2×Dic3—181no—
123C2×Dic3—181no—
124C2×Dic3—181no—
125C2×Dic3—182no—
126C2×Dic3—181no—
127C2×Dic3—363no—
128C4×D3—182no—
129C4×D3—181no—
130C4×D3—181no—
131C2×C32—31no—
132C2×C32—31no—
133C2×C32—41no—
134C2×C32—43no—
135C2×C32—83no—
136C2×C32—81no—
137C2×C32—122no—
138C2×C32C2×S411yescharacteristic
139C3×D3—32no—
140C3×D3—46no—
141C3×D3SL(2,ℤ/4)12yescomplemented
142C24—31no—
143C22×C4—271no—
144C22×C4—271no—
145C22⋊C4—91no—
146C22⋊C4—271no—
147C22⋊C4—271no—
148C22⋊C4—271no—
149C22×C3—21no—
150C22×C3—31no—
151C22×C3—31no—
152C22×C3—31no—
153C22×C3—31no—
154C22×C3—31no—
155C22×C3—61no—
156C22×C3—61no—
157C22×C3—92no—
158C22×C3—92no—
159C22×C3—92no—
160C22×C3—91no—
161C22×C3—123no—
162C22×C3—181no—
163C22×C3D3×Dic311yescharacteristic, complemented
164C22×C3C2×C3⋊Dic311yescharacteristic, complemented
165C2×D3—31no—
166C2×D3—32no—
167C2×D3—32no—
168C2×D3—32no—
169C2×D3—61no—
170C2×D3C3⋊S411yescharacteristic
171A4—23no—
172A4D3×Dic313yescomplemented
173C3×C4—181no—
174C3×C4—181no—
175Dic3—61no—
176Dic3—61no—
177Dic3—123no—
178Dic3—181no—
179Dic3—181no—
180Dic3—181no—
181Dic3—181no—
182Dic3—361no—
183Dic3—363no—
184Dic3—361no—
185Dic3—723no—
186C32—41no—
187C32—43no—
188C32—83no—
189C32—81no—
190C32C2×SL(2,ℤ/4)11yescharacteristic, complemented
191C23—32no—
192C23—91no—
193C23—91no—
194C23—92no—
195C23D3×C3⋊D311yescharacteristic
196C2×C4—91no—
197C2×C4—91no—
198C2×C4—271no—
199C2×C4—271no—
200C2×C4—541no—
201C2×C4—542no—
202C2×C4—541no—
203C2×C3—21no—
204C2×C3—31no—
205C2×C3—31no—
206C2×C3—31no—
207C2×C3—31no—
208C2×C3—32no—
209C2×C3—43no—
210C2×C3—61no—
211C2×C3—61no—
212C2×C3—83no—
213C2×C3—92no—
214C2×C3—126no—
215C2×C3D3×S411yescharacteristic
216C2×C3C2×C3⋊S411yescharacteristic
217D3—32no—
218D3C3⋊SL(2,ℤ/4)12yesdirect product factor
219C22—31no—
220C22—31no—
221C22—31no—
222C22—92no—
223C22—92no—
224C22—92no—
225C22—91no—
226C22—181no—
227C22D3×C3⋊Dic311yescharacteristic, complemented
228C4—181no—
229C4—181no—
230C4—541no—
231C4—541no—
232C3—21no—
233C3—43no—
234C3—83no—
235C3D3×SL(2,ℤ/4)11yescharacteristic, complemented
236C3C2×C3⋊SL(2,ℤ/4)11yescharacteristic, complemented
237C2—31no—
238C2—31no—
239C2—32no—
240C2—92no—
241C2D3×C3⋊S411yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2D3×C3⋊S4
commutator, hypocenterC32×A4C2×C4
Fitting, socleC23×C32C2×D3
prime radicalC2×C3×D3×A4C2
cosocleC2×C32×A4C22
LCSG ▷ C32×A4
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C3⋊(C3⋊SL(2,ℤ/4))C2semidirect
3. C3×C3⋊SL(2,ℤ/4)C2semidirect
8. C3×D3×A4C4semidirect
19. C3⋊SL(2,ℤ/4)D3direct (N × H)
26. C32×A4C2×C4semidirect
36. C22×C3×D3Dic3semidirect
42. D3×A4Dic3semidirect
76. C22×C32C2×Dic3semidirect
86. C3×A4C4×D3semidirect
87. C3×A4C2×Dic3semidirect
110. C22×D3C3⋊Dic3semidirect
141. C3×D3SL(2,ℤ/4)semidirect
163. C22×C3D3×Dic3semidirect
164. C22×C3C2×C3⋊Dic3semidirect
172. A4D3×Dic3semidirect
190. C32C2×SL(2,ℤ/4)semidirect
218. D3C3⋊SL(2,ℤ/4)direct (N × H)
227. C22D3×C3⋊Dic3semidirect
235. C3D3×SL(2,ℤ/4)semidirect
236. C3C2×C3⋊SL(2,ℤ/4)semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×A42
C3⋊(C3⋊SL(2,ℤ/4))2
C3×C3⋊SL(2,ℤ/4)2
C2×C3⋊SL(2,ℤ/4)3
D3×SL(2,ℤ/4)3
D3×#2173
D3×C3⋊Dic34