Finite Group Databasebeta

← C4×C3⋊(#127⋊C3) #11921118

Subgroups — C4×C3⋊(#127⋊C3) #11921118

Order 1152.

397 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 397 conjugacy classes of subgroups — too many to draw. Only its 39 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⋊C3)C211yesmaximal, characteristic
2C3×C4×C42⋊C3C211yesmaximal, characteristic, complemented
3C3⋊(#384⋊C3)C211yesmaximal, characteristic, complemented
4C4×#874C311yesmaximal, characteristic, complemented
5C4×#127⋊C3—31nomaximal
6C4×D3×A4—41nomaximal
7C2×C3×C42⋊C3C2211yescharacteristic
8C3⋊(#127⋊C3)C412yesdirect product factor
9C2×#874C2×C311yescharacteristic
10C2×C4×D12—31no—
11C2×C4×D12—31no—
12C2×#127⋊C3—31no—
13C3×C43C2×C311yescharacteristic, complemented
14#4939—31no—
15#4939—31no—
16#4935C2×C311yescharacteristic, complemented
17#384⋊C3—31no—
18C4×C42⋊C3—21no—
19C4×C42⋊C3D311yescharacteristic, complemented
20C2×D3×A4—41no—
21C3×C4×A4—41no—
22Dic3×A4—41no—
23C3×C42⋊C3C2×C411yescharacteristic, complemented
24C4×#127—31noSylow
25C22×D12—31no—
26C22×D12—31no—
27C22×C4×D3—31no—
28C22×C4×D3A411yescharacteristic
29C2×C4×A4—121no—
30C2×C3×C42—31no—
31C2×C3×C42—31no—
32C2×C3×C42C22×C311yescharacteristic
33C2×(C2×D3)⋊C4—32no—
34C2×(C2×D3)⋊C4—31no—
35C2×(C2×D3)⋊C4—31no—
36C2×C4⋊Dic3—31no—
37C2×C4⋊Dic3—31no—
38#874—32no—
39#874C3×C412yescomplemented
40C4×D12—62no—
41C4×D12—62no—
42C4×D12—62no—
43C4×D12—62no—
44#127⋊C3—32no—
45C2×C42⋊C3—21no—
46C2×C42⋊C3C2×D311yescharacteristic
47C2×C3×A4—41no—
48D3×A4—42no—
49C3×C4×D3—161no—
50C2×#127—31no—
51C2×C4×D4—91no—
52C2×C4×D4—91no—
53#390—91no—
54#390—91no—
55#384—31no—
56C43C3×D311yescharacteristic, complemented
57C23×D3—31no—
58C23×D3C2×A411yescharacteristic
59C22×A4—121no—
60C22×C3×C4—31no—
61C22×C3×C4—31no—
62C22×C3×C4C2×A411yescharacteristic
63C22×Dic3—31no—
64C22×Dic3C2×A411yescharacteristic
65C2×D12—32no—
66C2×D12—32no—
67C2×D12—32no—
68C2×D12—32no—
69C2×D12—62no—
70C2×D12—62no—
71C2×D12—62no—
72C2×D12—62no—
73C2×C4×D3—61no—
74C2×C4×D3—62no—
75C2×C4×D3—61no—
76C2×C4×D3—61no—
77C2×C4×D3—62no—
78C2×C4×D3—61no—
79C4×A4—41no—
80C4×A4—81no—
81C4×A4—121no—
82C3×C42—31no—
83C3×C42—32no—
84C3×C42—32no—
85C3×C42—62no—
86C3×C42C2×C3×C411yescharacteristic, complemented
87(C2×D3)⋊C4—62no—
88(C2×D3)⋊C4—62no—
89(C2×D3)⋊C4—64no—
90C4⋊Dic3—62no—
91C4⋊Dic3—62no—
92C42⋊C3—21no—
93C42⋊C3C4×D311yescharacteristic, complemented
94C2×C3×D3—161no—
95C3×A4—41no—
96C32×C4—161no—
97C3×Dic3—161no—
98C22×D4—91no—
99C22×D4—91no—
100C23×C4—31no—
101C23×C4—91no—
102#127—32no—
103#127—92no—
104C4×D4—182no—
105C4×D4—182no—
106C4×D4—182no—
107C4×D4—182no—
108C2×C4⋊C4—91no—
109C2×C4⋊C4—91no—
110C2×C22⋊C4—91no—
111C2×C22⋊C4—91no—
112C2×C22⋊C4—92no—
113C2×C42—31no—
114C2×C42—31no—
115C2×C42C2×C3×D311yescharacteristic
116C23×C3C22×A411yescharacteristic
117C22×D3—32no—
118C22×D3—61no—
119C22×D3—61no—
120C22×D3—62no—
121C22×D3—62no—
122C22×D3—61no—
123C22×D3—61no—
124C22×D3C4×A412yes—
125C2×A4—41no—
126C2×A4—81no—
127C2×A4—122no—
128C2×C3×C4—32no—
129C2×C3×C4—32no—
130C2×C3×C4—31no—
131C2×C3×C4—31no—
132C2×C3×C4—31no—
133C2×C3×C4—31no—
134C2×C3×C4—32no—
135C2×C3×C4—62no—
136C2×C3×C4—481no—
137C2×Dic3—61no—
138C2×Dic3—61no—
139C2×Dic3—62no—
140D12—64no—
141D12—64no—
142D12—64no—
143D12—64no—
144C4×D3—41no—
145C4×D3—121no—
146C4×D3—121no—
147C4×D3—122no—
148C4×D3—121no—
149C2×C32—161no—
150C3×D3—162no—
151C24—31no—
152C24—91no—
153C2×D4—92no—
154C2×D4—92no—
155C2×D4—92no—
156C2×D4—92no—
157C2×D4—182no—
158C2×D4—182no—
159C2×D4—182no—
160C2×D4—182no—
161C22×C4—31no—
162C22×C4—31no—
163C22×C4—31no—
164C22×C4—91no—
165C22×C4—181no—
166C22×C4—181no—
167C22×C4—182no—
168C22×C4—182no—
169C22×C4—181no—
170C22×C4—181no—
171C22×C4D3×A411yescharacteristic
172C4⋊C4—182no—
173C4⋊C4—182no—
174C22⋊C4—182no—
175C22⋊C4—182no—
176C22⋊C4—184no—
177C42—31no—
178C42—32no—
179C42—32no—
180C42—62no—
181C42C3×C4×D311yescharacteristic, complemented
182C22×C3—31no—
183C22×C3—31no—
184C22×C3—481no—
185C22×C3C2×C4×A411yescharacteristic
186C2×D3—41no—
187C2×D3—62no—
188C2×D3—62no—
189C2×D3—64no—
190C2×D3—121no—
191C2×D3—121no—
192C2×D3—122no—
193C2×D3—121no—
194A4—41no—
195A4—81no—
196C3×C4—32no—
197C3×C4—32no—
198C3×C4—31no—
199C3×C4—62no—
200C3×C4—161no—
201C3×C4—321no—
202C3×C4—481no—
203C3×C4#127⋊C311yescharacteristic, complemented
204Dic3—41no—
205Dic3—121no—
206C32—161noSylow
207C23—32no—
208C23—92no—
209C23—181no—
210C23—181no—
211C23—181no—
212C23—182no—
213C23—181no—
214C23—182no—
215C23C2×D3×A411yescharacteristic
216D4—184no—
217D4—184no—
218D4—184no—
219D4—184no—
220C2×C4—32no—
221C2×C4—32no—
222C2×C4—31no—
223C2×C4—31no—
224C2×C4—31no—
225C2×C4—31no—
226C2×C4—32no—
227C2×C4—62no—
228C2×C4—121no—
229C2×C4—181no—
230C2×C4—181no—
231C2×C4—182no—
232C2×C4—361no—
233C2×C4—361no—
234C2×C4—362no—
235C2×C4—361no—
236C2×C3—31no—
237C2×C3—31no—
238C2×C3—161no—
239C2×C3—321no—
240C2×C3—482no—
241C2×C3C2×#127⋊C311yescharacteristic
242D3—42no—
243D3—122no—
244C22—31no—
245C22—31no—
246C22—121no—
247C22—182no—
248C22—182no—
249C22—184no—
250C22—361no—
251C22—361no—
252C22—362no—
253C22—361no—
254C22C4×D3×A411yescharacteristic
255C4—32no—
256C4—32no—
257C4—31no—
258C4—62no—
259C4—121no—
260C4—361no—
261C4C3⋊(#127⋊C3)11yescharacteristic, direct product factor
262C3—161no—
263C3—321no—
264C3C4×#127⋊C311yescharacteristic, complemented
265C2—31no—
266C2—31no—
267C2—122no—
268C2—362no—
269C2C2×C3⋊(#127⋊C3)11yescharacteristic
subgroupG/H
center, hypercenterC4C3⋊(#127⋊C3)
commutator, hypocenterC3×C42C2×C3×C4
FrattiniC23C2×D3×A4
FittingC3×C43C2×C3
socleC23×C3C22×A4
prime radicalC2×C3⋊(#127⋊C3)C2
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. C3⋊(#384⋊C3)C2semidirect
4. C4×#874C3semidirect
8. C3⋊(#127⋊C3)C4direct (N × H)
13. C3×C43C2×C3semidirect
16. #4935C2×C3semidirect
19. C4×C42⋊C3D3semidirect
23. C3×C42⋊C3C2×C4semidirect
39. #874C3×C4semidirect
56. C43C3×D3semidirect
86. C3×C42C2×C3×C4semidirect
93. C42⋊C3C4×D3semidirect
181. C42C3×C4×D3semidirect
203. C3×C4#127⋊C3semidirect
261. C4C3⋊(#127⋊C3)direct (N × H)
264. 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⋊C3)2
C3×C4×C42⋊C32
C3⋊(#384⋊C3)2
C4×#8743
C4×#127⋊C33
C4×D3×A44