Finite Group Databasebeta

← C4×D3×C42⋊C3 #11921117

Subgroups — C4×D3×C42⋊C3 #11921117

Order 1152.

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

normal subgroups only

This group has 513 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×D3×C42⋊C3C211yesmaximal, characteristic
2C3×C4×C42⋊C3C211yesmaximal, characteristic, complemented
3Dic3×C42⋊C3C211yesmaximal, characteristic, complemented
4C43×D3C311yesmaximal, characteristic, complemented
5C2×C4×C42⋊C3—31nomaximal
6C4×D3×A4—41nomaximal
7C2×C3×C42⋊C3C2211yescharacteristic
8D3×C42⋊C3C412yesdirect product factor
9C2×C42×D3—31no—
10C2×C42×D3—31no—
11C2×C42×D3C2×C311yescharacteristic
12C22×C42⋊C3—31no—
13C3×C43C2×C311yescharacteristic, complemented
14C42×Dic3—31no—
15C42×Dic3—31no—
16C42×Dic3C2×C311yescharacteristic, complemented
17C4×C42⋊C3—21no—
18C4×C42⋊C3—31no—
19C4×C42⋊C3D311yescharacteristic, direct product factor
20C2×D3×A4—41no—
21C3×C4×A4—41no—
22Dic3×A4—41no—
23C3×C42⋊C3C2×C411yescharacteristic, complemented
24C2×C43—31noSylow
25C22×C4×D3—31no—
26C22×C4×D3—31no—
27C22×C4×D3A411yescharacteristic
28C2×C4×A4—121no—
29C2×C3×C42—31no—
30C2×C3×C42—31no—
31C2×C3×C42C22×C311yescharacteristic
32C2×C4×Dic3—32no—
33C2×C4×Dic3—31no—
34C2×C4×Dic3—31no—
35C2×C4×Dic3—31no—
36C2×C4×Dic3—31no—
37C2×C4×Dic3—31no—
38C42×D3—32no—
39C42×D3—38no—
40C42×D3—32no—
41C42×D3—32no—
42C42×D3—32no—
43C42×D3—32no—
44C42×D3C3×C412yescomplemented
45C2×C42⋊C3—21no—
46C2×C42⋊C3—32no—
47C2×C42⋊C3C2×D311yescharacteristic
48C2×C3×A4—41no—
49D3×A4—42no—
50C3×C4×D3—161no—
51C22×C42—31no—
52C22×C42—91no—
53C22×C42—91no—
54C43—31no—
55C43—91no—
56C43—91no—
57C43C3×D311yescharacteristic, complemented
58C23×D3C2×A411yescharacteristic
59C22×A4—121no—
60C22×C3×C4—31no—
61C22×C3×C4—31no—
62C22×C3×C4C2×A411yescharacteristic
63C22×Dic3—31no—
64C22×Dic3—31no—
65C22×Dic3C2×A411yescharacteristic
66C2×C4×D3—32no—
67C2×C4×D3—32no—
68C2×C4×D3—32no—
69C2×C4×D3—38no—
70C2×C4×D3—34no—
71C2×C4×D3—32no—
72C2×C4×D3—32no—
73C2×C4×D3—32no—
74C2×C4×D3—31no—
75C2×C4×D3—31no—
76C2×C4×D3—31no—
77C2×C4×D3—31no—
78C4×A4—41no—
79C4×A4—81no—
80C4×A4—121no—
81C3×C42—31no—
82C3×C42—34no—
83C3×C42—32no—
84C3×C42—32no—
85C3×C42C2×C3×C411yescharacteristic, complemented
86C4×Dic3—38no—
87C4×Dic3—34no—
88C4×Dic3—32no—
89C4×Dic3—32no—
90C4×Dic3—32no—
91C4×Dic3—32no—
92C4×Dic3—32no—
93C4×Dic3—32no—
94C4×Dic3—32no—
95C4×Dic3—32no—
96C42⋊C3—21no—
97C42⋊C3C4×D311yescharacteristic, direct product factor
98C2×C3×D3—161no—
99C3×A4—41no—
100C32×C4—161no—
101C3×Dic3—161no—
102C23×C4—31no—
103C23×C4—91no—
104C23×C4—91no—
105C2×C42—31no—
106C2×C42—31no—
107C2×C42—32no—
108C2×C42—92no—
109C2×C42—92no—
110C2×C42—98no—
111C2×C42—92no—
112C2×C42—92no—
113C2×C42—92no—
114C2×C42—91no—
115C2×C42—91no—
116C2×C42—91no—
117C2×C42—91no—
118C2×C42—92no—
119C2×C42—91no—
120C2×C42C2×C3×D311yescharacteristic
121C23×C3C22×A411yescharacteristic
122C22×D3—31no—
123C22×D3—31no—
124C22×D3—32no—
125C22×D3C4×A412yes—
126C2×A4—41no—
127C2×A4—81no—
128C2×A4—122no—
129C2×C3×C4—32no—
130C2×C3×C4—34no—
131C2×C3×C4—32no—
132C2×C3×C4—32no—
133C2×C3×C4—31no—
134C2×C3×C4—31no—
135C2×C3×C4—31no—
136C2×C3×C4—31no—
137C2×C3×C4—481no—
138C2×Dic3—34no—
139C2×Dic3—32no—
140C2×Dic3—32no—
141C2×Dic3—32no—
142C2×Dic3—32no—
143C2×Dic3—31no—
144C2×Dic3—31no—
145C4×D3—38no—
146C4×D3—38no—
147C4×D3—34no—
148C4×D3—34no—
149C4×D3—34no—
150C4×D3—34no—
151C4×D3—32no—
152C4×D3—31no—
153C4×D3—31no—
154C4×D3—31no—
155C4×D3C42⋊C311yescharacteristic, direct product factor
156C2×C32—161no—
157C3×D3—162no—
158C24—31no—
159C22×C4—31no—
160C22×C4—31no—
161C22×C4—31no—
162C22×C4—91no—
163C22×C4—92no—
164C22×C4—92no—
165C22×C4—92no—
166C22×C4—92no—
167C22×C4—94no—
168C22×C4—92no—
169C22×C4—98no—
170C22×C4—92no—
171C22×C4—91no—
172C22×C4—91no—
173C22×C4—91no—
174C22×C4—91no—
175C22×C4—91no—
176C22×C4D3×A411yescharacteristic
177C42—31no—
178C42—34no—
179C42—32no—
180C42—32no—
181C42—92no—
182C42—92no—
183C42—92no—
184C42—94no—
185C42—98no—
186C42—92no—
187C42—92no—
188C42—92no—
189C42—92no—
190C42—92no—
191C42C3×C4×D311yescharacteristic, complemented
192C22×C3—31no—
193C22×C3—31no—
194C22×C3—481no—
195C22×C3C2×C4×A411yescharacteristic
196C2×D3—32no—
197C2×D3—31no—
198C2×D3—32no—
199C2×D3—32no—
200C2×D3—32no—
201C2×D3C2×C42⋊C311yescharacteristic
202A4—41no—
203A4—81no—
204C3×C4—34no—
205C3×C4—32no—
206C3×C4—32no—
207C3×C4—31no—
208C3×C4—161no—
209C3×C4—321no—
210C3×C4—481no—
211C3×C4C2×C42⋊C311yescharacteristic, complemented
212Dic3—34no—
213Dic3—34no—
214Dic3—31no—
215Dic3C2×C42⋊C311yescharacteristic, complemented
216C32—161noSylow
217C23—32no—
218C23—91no—
219C23—92no—
220C23—91no—
221C23C2×D3×A411yescharacteristic
222C2×C4—32no—
223C2×C4—34no—
224C2×C4—32no—
225C2×C4—32no—
226C2×C4—31no—
227C2×C4—31no—
228C2×C4—31no—
229C2×C4—31no—
230C2×C4—31no—
231C2×C4—91no—
232C2×C4—91no—
233C2×C4—91no—
234C2×C4—94no—
235C2×C4—94no—
236C2×C4—98no—
237C2×C4—94no—
238C2×C4—94no—
239C2×C4—98no—
240C2×C4—92no—
241C2×C4—92no—
242C2×C4—94no—
243C2×C4—92no—
244C2×C4—92no—
245C2×C4—92no—
246C2×C4—91no—
247C2×C4—91no—
248C2×C3—31no—
249C2×C3—31no—
250C2×C3—161no—
251C2×C3—321no—
252C2×C3—482no—
253C2×C3C22×C42⋊C311yescharacteristic
254D3—32no—
255D3C4×C42⋊C312yesdirect product factor
256C22—31no—
257C22—31no—
258C22—31no—
259C22—92no—
260C22—92no—
261C22—92no—
262C22—92no—
263C22—91no—
264C22C4×D3×A411yescharacteristic
265C4—32no—
266C4—32no—
267C4—34no—
268C4—31no—
269C4—31no—
270C4—94no—
271C4—94no—
272C4—91no—
273C4D3×C42⋊C311yescharacteristic, direct product factor
274C3—161no—
275C3—321no—
276C3C2×C4×C42⋊C311yescharacteristic, complemented
277C2—31no—
278C2—31no—
279C2—32no—
280C2—92no—
281C2C2×D3×C42⋊C311yescharacteristic
subgroupG/H
center, hypercenterC4D3×C42⋊C3
commutator, hypocenterC3×C42C2×C3×C4
FrattiniC23C2×D3×A4
FittingC3×C43C2×C3
socleC23×C3C22×A4
prime radicalC2×D3×C42⋊C3C2
cosocleC2×C3×C42C22×C3
LCSG ▷ C3×C42
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
2. C3×C4×C42⋊C3C2semidirect
3. Dic3×C42⋊C3C2semidirect
4. C43×D3C3semidirect
8. D3×C42⋊C3C4direct (N × H)
13. C3×C43C2×C3semidirect
16. C42×Dic3C2×C3semidirect
19. C4×C42⋊C3D3direct (N × H)
23. C3×C42⋊C3C2×C4semidirect
44. C42×D3C3×C4semidirect
57. C43C3×D3semidirect
85. C3×C42C2×C3×C4semidirect
97. C42⋊C3C4×D3direct (N × H)
155. C4×D3C42⋊C3direct (N × H)
191. C42C3×C4×D3semidirect
211. C3×C4C2×C42⋊C3semidirect
215. Dic3C2×C42⋊C3semidirect
255. D3C4×C42⋊C3direct (N × H)
273. C4D3×C42⋊C3direct (N × H)
276. C3C2×C4×C42⋊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×C4×C42⋊C32
Dic3×C42⋊C32
C43×D33
C2×C4×C42⋊C33
C4×D3×A44