Finite Group Databasebeta

← D3×#384⋊C3 #11921158

Subgroups — D3×#384⋊C3 #11921158

Order 1152.

385 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 385 conjugacy classes of subgroups — too many to draw. Only its 40 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×D3×C42⋊C3C211yesmaximal, characteristic
2C3×#384⋊C3C211yesmaximal, characteristic, complemented
3C3⋊(#384⋊C3)C211yesmaximal, characteristic, complemented
4D3×#384C311yesmaximal, characteristic, complemented
5C2×#384⋊C3—31nomaximal
6C4×D3×A4—41nomaximal
7C2×C3×C42⋊C3C2211yescharacteristic
8D3×C42⋊C3C412yescomplemented
9C2×D3×C4⋊C4—31no—
10C2×D3×C4⋊C4—31no—
11C2×C42×D3C2×C311yescharacteristic
12C22×C42⋊C3—31no—
13C3×#384C2×C311yescharacteristic, complemented
14#4975—31no—
15#4975—31no—
16#4935C2×C311yescharacteristic, complemented
17#384⋊C3—21no—
18#384⋊C3—31no—
19#384⋊C3D311yescharacteristic, direct product factor
20C2×D3×A4—41no—
21C3×C4×A4—41no—
22Dic3×A4—41no—
23C3×C42⋊C3C2×C411yescharacteristic, complemented
24C2×#384—31noSylow
25C22×C4×D3—31no—
26C22×C4×D3—31no—
27C22×C4×D3A411yescharacteristic
28C2×C4×A4—121no—
29C2×C3×C4⋊C4—31no—
30C2×C3×C4⋊C4—31no—
31C2×C3×C42C22×C311yescharacteristic
32C2×C4⋊Dic3—31no—
33C2×C4⋊Dic3—31no—
34C2×Dic3⋊C4—32no—
35C2×Dic3⋊C4—31no—
36C2×Dic3⋊C4—31no—
37C2×C4×Dic3—31no—
38D3×C4⋊C4—62no—
39D3×C4⋊C4—62no—
40D3×C4⋊C4—62no—
41D3×C4⋊C4—62no—
42C42×D3—32no—
43C42×D3C3×C412yescomplemented
44C2×C42⋊C3—21no—
45C2×C42⋊C3—32no—
46C2×C42⋊C3C2×D311yescharacteristic
47C2×C3×A4—41no—
48D3×A4—42no—
49C3×C4×D3—161no—
50C22×C4⋊C4—91no—
51C22×C4⋊C4—91no—
52C22×C42—31no—
53#384—31no—
54#384—91no—
55#384—91no—
56#384C3×D311yescharacteristic, complemented
57C23×D3C2×A411yescharacteristic
58C22×A4—121no—
59C22×C3×C4—31no—
60C22×C3×C4—31no—
61C22×C3×C4C2×A411yescharacteristic
62C22×Dic3—31no—
63C22×Dic3—31no—
64C22×Dic3C2×A411yescharacteristic
65C2×C4×D3—32no—
66C2×C4×D3—32no—
67C2×C4×D3—34no—
68C2×C4×D3—32no—
69C2×C4×D3—32no—
70C2×C4×D3—61no—
71C2×C4×D3—62no—
72C2×C4×D3—61no—
73C2×C4×D3—61no—
74C2×C4×D3—62no—
75C2×C4×D3—61no—
76C4×A4—41no—
77C4×A4—81no—
78C4×A4—121no—
79C3×C4⋊C4—62no—
80C3×C4⋊C4—62no—
81C3×C42—31no—
82C3×C42C2×C3×C411yescharacteristic, complemented
83C4⋊Dic3—62no—
84C4⋊Dic3—62no—
85Dic3⋊C4—62no—
86Dic3⋊C4—62no—
87Dic3⋊C4—64no—
88C4×Dic3—32no—
89C4×Dic3—32no—
90C42⋊C3—21no—
91C42⋊C3C4×D311yescharacteristic, complemented
92C2×C3×D3—161no—
93C3×A4—41no—
94C32×C4—161no—
95C3×Dic3—161no—
96C23×C4—31no—
97C23×C4—91no—
98C23×C4—91no—
99C2×C4⋊C4—31no—
100C2×C4⋊C4—31no—
101C2×C4⋊C4—91no—
102C2×C4⋊C4—91no—
103C2×C4⋊C4—91no—
104C2×C4⋊C4—92no—
105C2×C4⋊C4—91no—
106C2×C4⋊C4—182no—
107C2×C4⋊C4—182no—
108C2×C4⋊C4—182no—
109C2×C4⋊C4—182no—
110C2×C42—32no—
111C2×C42—92no—
112C2×C42—91no—
113C2×C42C2×C3×D311yescharacteristic
114C23×C3C22×A411yescharacteristic
115C22×D3—31no—
116C22×D3—31no—
117C22×D3—32no—
118C22×D3C4×A412yes—
119C2×A4—41no—
120C2×A4—81no—
121C2×A4—122no—
122C2×C3×C4—32no—
123C2×C3×C4—32no—
124C2×C3×C4—31no—
125C2×C3×C4—31no—
126C2×C3×C4—61no—
127C2×C3×C4—61no—
128C2×C3×C4—62no—
129C2×C3×C4—481no—
130C2×Dic3—32no—
131C2×Dic3—32no—
132C2×Dic3—32no—
133C2×Dic3—61no—
134C2×Dic3—61no—
135C2×Dic3—62no—
136C4×D3—34no—
137C4×D3—34no—
138C4×D3—34no—
139C4×D3—34no—
140C4×D3—41no—
141C4×D3—121no—
142C4×D3—121no—
143C4×D3—122no—
144C4×D3—121no—
145C2×C32—161no—
146C3×D3—162no—
147C24—31no—
148C22×C4—31no—
149C22×C4—31no—
150C22×C4—31no—
151C22×C4—92no—
152C22×C4—92no—
153C22×C4—92no—
154C22×C4—92no—
155C22×C4—94no—
156C22×C4—91no—
157C22×C4—91no—
158C22×C4—181no—
159C22×C4—181no—
160C22×C4—182no—
161C22×C4—182no—
162C22×C4—181no—
163C22×C4—181no—
164C22×C4D3×A411yescharacteristic
165C4⋊C4—62no—
166C4⋊C4—62no—
167C4⋊C4—182no—
168C4⋊C4—182no—
169C4⋊C4—182no—
170C4⋊C4—182no—
171C4⋊C4—184no—
172C42—31no—
173C42—92no—
174C42—92no—
175C42C3×C4×D311yescharacteristic, complemented
176C22×C3—31no—
177C22×C3—31no—
178C22×C3—481no—
179C22×C3C2×C4×A411yescharacteristic
180C2×D3—32no—
181C2×D3—31no—
182C2×D3—32no—
183C2×D3—32no—
184C2×D3—32no—
185C2×D3#127⋊C311yescharacteristic
186A4—41no—
187A4—81no—
188C3×C4—32no—
189C3×C4—32no—
190C3×C4—41no—
191C3×C4—121no—
192C3×C4—161no—
193C3×C4—321no—
194C3×C4—481no—
195Dic3—34no—
196Dic3—41no—
197Dic3—121no—
198C32—161noSylow
199C23—32no—
200C23—91no—
201C23—91no—
202C23—92no—
203C23C2×D3×A411yescharacteristic
204C2×C4—32no—
205C2×C4—32no—
206C2×C4—31no—
207C2×C4—31no—
208C2×C4—61no—
209C2×C4—61no—
210C2×C4—62no—
211C2×C4—94no—
212C2×C4—94no—
213C2×C4—94no—
214C2×C4—94no—
215C2×C4—92no—
216C2×C4—92no—
217C2×C4—92no—
218C2×C4—121no—
219C2×C4—181no—
220C2×C4—181no—
221C2×C4—182no—
222C2×C4—361no—
223C2×C4—361no—
224C2×C4—361no—
225C2×C4—362no—
226C2×C3—31no—
227C2×C3—31no—
228C2×C3—161no—
229C2×C3—321no—
230C2×C3—482no—
231C2×C3C2×#127⋊C311yescharacteristic
232D3—32no—
233D3#384⋊C312yesdirect product factor
234C22—31no—
235C22—31no—
236C22—31no—
237C22—92no—
238C22—92no—
239C22—92no—
240C22—92no—
241C22—91no—
242C22C4×D3×A411yescharacteristic
243C4—32no—
244C4—32no—
245C4—41no—
246C4—94no—
247C4—121no—
248C4—121no—
249C4—361no—
250C3—161no—
251C3—321no—
252C3C2×#384⋊C311yescharacteristic, complemented
253C2—31no—
254C2—31no—
255C2—32no—
256C2—92no—
257C2D3×#127⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2D3×#127⋊C3
commutator, hypocenterC3×C42C2×C3×C4
FrattiniC23C2×D3×A4
FittingC3×#384C2×C3
socleC23×C3C22×A4
prime radicalC2×D3×C42⋊C3C2
cosocleC2×C3×C42C22×C3
LCSG ▷ C3×C42
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C3×#384⋊C3C2semidirect
3. C3⋊(#384⋊C3)C2semidirect
4. D3×#384C3semidirect
8. D3×C42⋊C3C4semidirect
13. C3×#384C2×C3semidirect
16. #4935C2×C3semidirect
19. #384⋊C3D3direct (N × H)
23. C3×C42⋊C3C2×C4semidirect
43. C42×D3C3×C4semidirect
56. #384C3×D3semidirect
82. C3×C42C2×C3×C4semidirect
91. C42⋊C3C4×D3semidirect
175. C42C3×C4×D3semidirect
233. D3#384⋊C3direct (N × H)
252. C3C2×#384⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C42⋊C32
C3×#384⋊C32
C3⋊(#384⋊C3)2
D3×#3843
C2×#384⋊C33
C4×D3×A44