Finite Group Databasebeta

← Dic3×#127⋊C3 #11921294

Subgroups — Dic3×#127⋊C3 #11921294

Order 1152.

403 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 403 conjugacy classes of subgroups — too many to draw. Only its 44 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×#127⋊C3C211yesmaximal, characteristic
2Dic3×C42⋊C3C211yesmaximal, characteristic, complemented
3C3⋊(#384⋊C3)C211yesmaximal, characteristic, complemented
4Dic3×#127C311yesmaximal, characteristic, complemented
5C4×#127⋊C3—31nomaximal
6C2×Dic3×A4—41nomaximal
7C3×#127⋊C3C412yescomplemented
8C2×C3×C42⋊C3C2211yescharacteristic
9C2×C3×#127C2×C311yescharacteristic
10C2×D4×Dic3—31no—
11C2×D4×Dic3—31no—
12C2×#127⋊C3—21no—
13C2×#127⋊C3D311yescharacteristic
14#5221—31no—
15#5221—31no—
16#4935C2×C311yescharacteristic, complemented
17C42×Dic3C2×C311yescharacteristic, complemented
18#384⋊C3—31no—
19C4×C42⋊C3—31no—
20C22×C3×A4—41no—
21Dic3×A4—41no—
22Dic3×A4—41no—
23C3×C42⋊C3C2×C411yescharacteristic, complemented
24C4×#127—31noSylow
25C22×C3×D4—31no—
26C22×C3×D4—31no—
27C23×Dic3—31no—
28C23×Dic3A411yescharacteristic
29C2×C4×A4—121no—
30C3×#127—32no—
31C3×#127C3×C412yescomplemented
32C2×C3×C42C22×C311yescharacteristic
33C2×#217—32no—
34C2×#217—31no—
35C2×#217—31no—
36D4×Dic3—62no—
37D4×Dic3—62no—
38D4×Dic3—62no—
39D4×Dic3—62no—
40C2×C4⋊Dic3—31no—
41C2×C4⋊Dic3—31no—
42C2×C4×Dic3—31no—
43C2×C4×Dic3—31no—
44#127⋊C3—22no—
45#127⋊C3Dic312yesdirect product factor
46C2×C42⋊C3—21no—
47C2×C42⋊C3C2×D311yescharacteristic
48C2×C3×A4—42no—
49C2×C3×A4—41no—
50C2×C3×Dic3—161no—
51C2×#127C3×D311yescharacteristic
52C2×C4×D4—91no—
53C2×C4×D4—91no—
54#390—91no—
55#390—91no—
56#384—31no—
57C43—31no—
58C24×C3—31no—
59C24×C3C2×A411yescharacteristic
60C22×A4—41no—
61C22×A4—81no—
62C2×C3×D4—32no—
63C2×C3×D4—32no—
64C2×C3×D4—32no—
65C2×C3×D4—32no—
66C2×C3×D4—62no—
67C2×C3×D4—62no—
68C2×C3×D4—62no—
69C2×C3×D4—62no—
70C22×C3×C4—31no—
71C22×Dic3—31no—
72C22×Dic3—31no—
73C22×Dic3—61no—
74C22×Dic3—61no—
75C22×Dic3—62no—
76C22×Dic3—62no—
77C22×Dic3—61no—
78C22×Dic3—61no—
79C22×Dic3C2×A411yescharacteristic
80C22×Dic3C2×A411yescharacteristic
81C4×A4—121no—
82C4×A4—121no—
83C3×C42—31no—
84C3×C42C2×C3×C411yescharacteristic, complemented
85#217—62no—
86#217—62no—
87#217—64no—
88C4⋊Dic3—62no—
89C4⋊Dic3—62no—
90C4×Dic3—32no—
91C4×Dic3—32no—
92C4×Dic3—62no—
93C42⋊C3—21no—
94C42⋊C3C2×Dic311yescharacteristic, complemented
95C22×C32—161no—
96C3×A4—41no—
97C3×Dic3—161no—
98C3×Dic3—161no—
99C22×D4—31no—
100C22×D4—31no—
101C23×C4—31no—
102C23×C4—91no—
103#127—32no—
104#127C3×Dic312yescomplemented
105C4×D4—182no—
106C4×D4—182no—
107C4×D4—182no—
108C4×D4—182no—
109C2×C4⋊C4—91no—
110C2×C4⋊C4—91no—
111C2×C22⋊C4—91no—
112C2×C22⋊C4—92no—
113C2×C22⋊C4—91no—
114C2×C42—91no—
115C2×C42—91no—
116C2×C42C2×C3×D311yescharacteristic
117C23×C3—32no—
118C23×C3—61no—
119C23×C3—61no—
120C23×C3—61no—
121C23×C3—62no—
122C23×C3—61no—
123C23×C3—62no—
124C23×C3C4×A412yes—
125C23×C3C22×A411yescharacteristic
126C2×A4—41no—
127C2×A4—42no—
128C2×A4—81no—
129C2×A4—82no—
130C3×D4—64no—
131C3×D4—64no—
132C3×D4—64no—
133C3×D4—64no—
134C2×C3×C4—32no—
135C2×C3×C4—32no—
136C2×C3×C4—31no—
137C2×C3×C4—31no—
138C2×C3×C4—481no—
139C2×Dic3—31no—
140C2×Dic3—31no—
141C2×Dic3—32no—
142C2×Dic3—41no—
143C2×Dic3—61no—
144C2×Dic3—62no—
145C2×Dic3—61no—
146C2×Dic3—62no—
147C2×Dic3—121no—
148C2×Dic3—121no—
149C2×Dic3—122no—
150C2×Dic3—121no—
151C2×C32—162no—
152C2×C32—161no—
153C24—31no—
154C24D3×A411yescharacteristic
155C2×D4—32no—
156C2×D4—32no—
157C2×D4—32no—
158C2×D4—32no—
159C2×D4—62no—
160C2×D4—62no—
161C2×D4—62no—
162C2×D4—62no—
163C22×C4—31no—
164C22×C4—31no—
165C22×C4—31no—
166C22×C4—91no—
167C22×C4—91no—
168C22×C4—181no—
169C22×C4—181no—
170C22×C4—182no—
171C22×C4—182no—
172C22×C4—181no—
173C22×C4—181no—
174C4⋊C4—182no—
175C4⋊C4—182no—
176C22⋊C4—182no—
177C22⋊C4—182no—
178C22⋊C4—184no—
179C42—31no—
180C42—92no—
181C42—92no—
182C42—182no—
183C42C2×C3×Dic311yescharacteristic, complemented
184C22×C3—31no—
185C22×C3—31no—
186C22×C3—41no—
187C22×C3—62no—
188C22×C3—62no—
189C22×C3—64no—
190C22×C3—121no—
191C22×C3—121no—
192C22×C3—122no—
193C22×C3—121no—
194C22×C3—161no—
195C22×C3—321no—
196C22×C3C2×C4×A411yescharacteristic
197A4—41no—
198A4—81no—
199C3×C4—32no—
200C3×C4—32no—
201C3×C4—481no—
202C3×C4—481no—
203Dic3—31no—
204Dic3—41no—
205Dic3—62no—
206Dic3—121no—
207Dic3#127⋊C311yescharacteristic, direct product factor
208C32—161noSylow
209C23—32no—
210C23—61no—
211C23—61no—
212C23—61no—
213C23—62no—
214C23—61no—
215C23—62no—
216C23Dic3×A412yes—
217C23C2×D3×A411yescharacteristic
218D4—64no—
219D4—64no—
220D4—64no—
221D4—64no—
222C2×C4—32no—
223C2×C4—32no—
224C2×C4—31no—
225C2×C4—31no—
226C2×C4—91no—
227C2×C4—91no—
228C2×C4—92no—
229C2×C4—121no—
230C2×C4—181no—
231C2×C4—182no—
232C2×C4—181no—
233C2×C4—182no—
234C2×C4—361no—
235C2×C4—361no—
236C2×C4—361no—
237C2×C4—362no—
238C2×C3—31no—
239C2×C3—31no—
240C2×C3—42no—
241C2×C3—122no—
242C2×C3—162no—
243C2×C3—161no—
244C2×C3—322no—
245C2×C3—321no—
246C2×C3C2×#127⋊C311yescharacteristic
247C22—31no—
248C22—31no—
249C22—41no—
250C22—62no—
251C22—62no—
252C22—64no—
253C22—121no—
254C22—121no—
255C22—122no—
256C22—121no—
257C22C2×Dic3×A411yescharacteristic
258C4—32no—
259C4—32no—
260C4—31no—
261C4—91no—
262C4—121no—
263C4—182no—
264C4—361no—
265C3—161no—
266C3—321no—
267C3C4×#127⋊C311yescharacteristic, complemented
268C2—31no—
269C2—31no—
270C2—42no—
271C2—122no—
272C2D3×#127⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2D3×#127⋊C3
commutator, hypocenterC3×C42C2×C3×C4
FrattiniC23C2×D3×A4
FittingC2×C3×#127C2×C3
socleC23×C3C22×A4
prime radicalC2×C3×#127⋊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. Dic3×C42⋊C3C2semidirect
3. C3⋊(#384⋊C3)C2semidirect
4. Dic3×#127C3semidirect
7. C3×#127⋊C3C4semidirect
16. #4935C2×C3semidirect
17. C42×Dic3C2×C3semidirect
23. C3×C42⋊C3C2×C4semidirect
31. C3×#127C3×C4semidirect
45. #127⋊C3Dic3direct (N × H)
84. C3×C42C2×C3×C4semidirect
94. C42⋊C3C2×Dic3semidirect
104. #127C3×Dic3semidirect
183. C42C2×C3×Dic3semidirect
207. Dic3#127⋊C3direct (N × H)
267. C3C4×#127⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#127⋊C32
Dic3×C42⋊C32
C3⋊(#384⋊C3)2
Dic3×#1273
C4×#127⋊C33
C2×Dic3×A44