Finite Group Databasebeta

← C4×C3⋊#857 #11920937

Subgroups — C4×C3⋊#857 #11920937

Order 1152.

376 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 35 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⋊#857C211yesmaximal, characteristic
2C3×C4×C42⋊C3C211yesmaximal, characteristic, complemented
3C3⋊#4623C211yesmaximal, characteristic, complemented
4C4×#857—33nomaximal
5C4×#805—31nomaximal
6C4×C3⋊S4—41nomaximal
7C2×C3×C42⋊C3C2211yescharacteristic
8C3⋊#857C412yesdirect product factor
9C4×#235—31no—
10C2×#857—33no—
11C3×C43D311yescharacteristic, complemented
12C2×#805—31no—
13C2×#805—31no—
14C4×#208—31no—
15C4×C42⋊C3D313yescomplemented
16#4623—33no—
17#4523—31no—
18#4523—31no—
19C2×C3⋊S4—41no—
20C3×C4×A4—41no—
21C3⋊SL(2,ℤ/4)—41no—
22C3×C42⋊C3C2×C411yescharacteristic, complemented
23C4×#104—91noSylow
24C2×#235—31no—
25C4×S4—123no—
26C2×C3×C42—31no—
27C2×C3×C42—31no—
28C2×C3×C42C2×D311yescharacteristic
29C4×#67—61no—
30C4×#67—61no—
31#926—31no—
32C2×#208—31no—
33C2×#208—31no—
34C4×D12—31no—
35C4×D12—31no—
36#872—61no—
37C42×D3—61no—
38C4×Dic6—31no—
39C4×Dic6—31no—
40C2×C42⋊C3C2×D313yes—
41#857—36no—
42#805—32no—
43#805—34no—
44#805—32no—
45#803—61no—
46C4×C3⋊C8—61no—
47C2×C3×A4—41no—
48C3⋊S4—42no—
49C4×C3⋊D3—161no—
50C4×#41—91no—
51C2×#104—91no—
52C2×#104—91no—
53C4×M16—91no—
54C43C3⋊D311yescharacteristic, complemented
55#339—91no—
56#339—91no—
57C2×S4—123no—
58C22×C3×C4—31no—
59C22×C3×C4—31no—
60C22×C3×C4S411yescharacteristic
61C2×#67—61no—
62#235—32no—
63#235—32no—
64#235—61no—
65#235—61no—
66C2×D12—31no—
67C2×C4×D3—61no—
68C2×C4×D3—61no—
69C2×C4×D3—61no—
70C2×Dic6—31no—
71C4×A4—43no—
72SL(2,ℤ/4)—123no—
73C3×C42—31no—
74C3×C42—31no—
75C3×C42—31no—
76C3×C42—31no—
77C3×C42—31no—
78C3×C42—32no—
79C3×C42—61no—
80C3×C42C4×D311yescharacteristic, complemented
81#217—61no—
82(C2×D3)⋊C4—61no—
83(C2×D3)⋊C4—61no—
84C4⋊Dic3—31no—
85C4⋊Dic3—31no—
86Dic3⋊C4—61no—
87Dic3⋊C4—61no—
88C4×Dic3—61no—
89C4×Dic3—61no—
90C4×Dic3—61no—
91#208—32no—
92#208—32no—
93#208—61no—
94#208—61no—
95C2×C3⋊C8—61no—
96C2×C3⋊C8—61no—
97C42⋊C3C4×D313yescomplemented
98C2×C3⋊D3—161no—
99C3×A4—41no—
100C32×C4—161no—
101C3⋊Dic3—161no—
102C2×#41—91no—
103C2×M16—91no—
104C2×M16—91no—
105C4×Q8—91no—
106C4×Q8—91no—
107C4×D4—91no—
108C4×D4—91no—
109C4×D4—181no—
110C4×D4—181no—
111#117—91no—
112#117—181no—
113C2×C42—31no—
114C2×C42—31no—
115C2×C42—181no—
116C2×C42C2×C3⋊D311yescharacteristic
117#104—92no—
118#104—94no—
119#104—92no—
120#97—181no—
121C4×C8—181no—
122C23×C3C2×S411yescharacteristic
123C22×D3—61no—
124C2×A4—43no—
125S4—126no—
126C2×C3×C4—31no—
127C2×C3×C4—31no—
128C2×C3×C4—31no—
129C2×C3×C4—31no—
130C2×C3×C4—31no—
131C2×C3×C4—31no—
132C2×C3×C4—31no—
133C2×C3×C4—31no—
134C2×C3×C4—31no—
135C2×C3×C4—31no—
136C2×C3×C4—62no—
137#67—62no—
138#67—62no—
139C2×Dic3—61no—
140C2×Dic3—61no—
141C2×Dic3—61no—
142D12—32no—
143D12—61no—
144C4×D3—62no—
145C4×D3—62no—
146C4×D3—122no—
147C4×D3—121no—
148C4×D3—121no—
149C4×D3—483no—
150Dic6—32no—
151Dic6—61no—
152C3⋊C8—62no—
153C3⋊C8—62no—
154C2×C32—161no—
155C3⋊D3—162no—
156#41—92no—
157#41—92no—
158#41—181no—
159#41—181no—
160C2×Q8—91no—
161C2×D4—91no—
162C2×D4—181no—
163C22×C4—31no—
164C22×C4—31no—
165C22×C4—181no—
166C22×C4—181no—
167C22×C4—181no—
168C22×C4C3⋊S411yescharacteristic
169M16—92no—
170M16—92no—
171M16—181no—
172M16—181no—
173C2×C8—181no—
174C2×C8—181no—
175C4⋊C4—91no—
176C4⋊C4—91no—
177C4⋊C4—181no—
178C4⋊C4—181no—
179C22⋊C4—181no—
180C22⋊C4—181no—
181C22⋊C4—181no—
182C42—31no—
183C42—31no—
184C42—31no—
185C42—31no—
186C42—31no—
187C42—32no—
188C42—61no—
189C42—181no—
190C42—181no—
191C42—181no—
192C42C4×C3⋊D311yescharacteristic, complemented
193C22×C3—31no—
194C22×C3—31no—
195C22×C3C4×S411yescharacteristic
196C2×D3—62no—
197C2×D3—121no—
198C2×D3—121no—
199C2×D3—483no—
200A4—43no—
201C3×C4—31no—
202C3×C4—31no—
203C3×C4—31no—
204C3×C4—31no—
205C3×C4—32no—
206C3×C4—31no—
207C3×C4—61no—
208C3×C4—163no—
209C3×C4#85711yescharacteristic, complemented
210Dic3—62no—
211Dic3—121no—
212Dic3—121no—
213Dic3—483no—
214C32—161noSylow
215C23—181no—
216C23C2×C3⋊S411yescharacteristic
217Q8—92no—
218Q8—181no—
219D4—92no—
220D4—181no—
221D4—182no—
222D4—182no—
223C2×C4—31no—
224C2×C4—31no—
225C2×C4—31no—
226C2×C4—31no—
227C2×C4—31no—
228C2×C4—31no—
229C2×C4—31no—
230C2×C4—31no—
231C2×C4—31no—
232C2×C4—31no—
233C2×C4—62no—
234C2×C4—182no—
235C2×C4—182no—
236C2×C4—181no—
237C2×C4—181no—
238C2×C4—181no—
239C2×C4—362no—
240C2×C4—361no—
241C2×C4—361no—
242C8—182no—
243C8—182no—
244C2×C3—31no—
245C2×C3—31no—
246C2×C3—163no—
247C2×C3C2×#85711yescharacteristic
248D3—122no—
249D3—486no—
250C22—31no—
251C22—31no—
252C22—182no—
253C22—361no—
254C22—361no—
255C22C4×C3⋊S411yescharacteristic
256C4—31no—
257C4—31no—
258C4—31no—
259C4—31no—
260C4—32no—
261C4—31no—
262C4—61no—
263C4—182no—
264C4—361no—
265C4—361no—
266C4C3⋊#85711yescharacteristic, direct product factor
267C3—163no—
268C3C4×#85711yescharacteristic, complemented
269C2—31no—
270C2—31no—
271C2—362no—
272C2C2×C3⋊#85711yescharacteristic
subgroupG/H
center, hypercenterC4C3⋊#857
commutator, hypocenterC3×C42⋊C3C2×C4
FrattiniC23C2×C3⋊S4
FittingC3×C43D3
socleC23×C3C2×S4
prime radicalC2×C3⋊#857C2
cosocleC2×C3×C42⋊C3C22
LCSG ▷ C3×C42⋊C3
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
2. C3×C4×C42⋊C3C2semidirect
3. C3⋊#4623C2semidirect
8. C3⋊#857C4direct (N × H)
11. C3×C43D3semidirect
15. C4×C42⋊C3D3semidirect
22. C3×C42⋊C3C2×C4semidirect
54. C43C3⋊D3semidirect
80. C3×C42C4×D3semidirect
97. C42⋊C3C4×D3semidirect
192. C42C4×C3⋊D3semidirect
209. C3×C4#857semidirect
266. C4C3⋊#857direct (N × H)
268. C3C4×#857semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊#8572
C3×C4×C42⋊C32
C3⋊#46232
C4×#8573
C4×#8053
C4×C3⋊S44