Finite Group Databasebeta

← C3×#74299 #11808027

Subgroups — C3×#74299 #11808027

Order 1152.

981 conjugacy classes of subgroups.

The subgroup lattice has 317 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#876C211yesmaximal, characteristic
2C32×#383C211yesmaximal, characteristic, complemented
3C3×#4935C211yesmaximal, characteristic, complemented
4C3×#4670C213yesmaximal
5C3×#4668C213yesmaximal
6C3×#4655C213yesmaximal, complemented
7C3×#4647C213yesmaximal, complemented
8C3×#2383—31nomaximal
9#74299C311yesmaximal, characteristic, direct product factor
10C22×C3×C4×D3C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12C2×C3×(C2×D3)⋊C4C2213yes—
13C2×C3×(C2×D3)⋊C4C2213yes—
14C2×C3×C4⋊Dic3C2213yes—
15C2×C3×C4⋊Dic3C2213yes—
16C2×C3×Dic3⋊C4C2213yes—
17C2×C3×Dic3⋊C4C2213yes—
18C2×C3×C4×Dic3C2213yes—
19C3×#876C418yescomplemented
20C32×#95C2213yes—
21C32×#95C2213yes—
22C3×C3⋊#95C2213yes—
23C3×C3⋊#95C2213yes—
24C2×C3×#126—31no—
25C2×#876C2×C311yescharacteristic
26C3×#389—33no—
27C3×#388—33no—
28C3×#387—33no—
29C3×#385—33no—
30C3×#384—31no—
31C3×#383—21no—
32C3×#383D311yescharacteristic, complemented
33C3×#383C2×C311yescharacteristic, complemented
34#4935C2×C311yescharacteristic, complemented
35#4670C2×C313yes—
36#4668C2×C313yes—
37#4655C2×C313yescomplemented
38#4647C2×C313yescomplemented
39C23×C3×D3C2311yescharacteristic
40C22×C32×C4C2313yes—
41C22×C32×C4C2311yescharacteristic
42C22×C32×C4C2313yes—
43C22×C3×Dic3C2313yes—
44C22×C3×Dic3C2311yescharacteristic
45C22×C3×Dic3C2313yes—
46C2×C3×C4×D3—43no—
47C32×C42C2×C414yescomplemented
48C3×(C2×D3)⋊C4—43no—
49C3×(C2×D3)⋊C4C2×C4112yes—
50C3×C4⋊Dic3—43no—
51C3×C4⋊Dic3—43no—
52C3×Dic3⋊C4—43no—
53C3×Dic3⋊C4C2×C4112yescomplemented
54C3×C4×Dic3—43no—
55#2383—31noSylow
56C23×C3×C4—31no—
57C22×C4×D3C22×C311yescharacteristic
58C3×#126—38no—
59C2×C3×C4⋊C4—33no—
60C2×C3×C4⋊C4—33no—
61C2×C3×C4⋊C4—33no—
62C2×C3×C4⋊C4—33no—
63C2×C3×C22⋊C4—33no—
64C2×C3×C22⋊C4—33no—
65C2×C3×C42—21no—
66C2×C3×C42—33no—
67C2×C3×C42C2×D311yescharacteristic
68C2×C3×C42C22×C311yescharacteristic
69C2×(C2×D3)⋊C4C22×C313yes—
70C2×(C2×D3)⋊C4C22×C313yes—
71C2×C4⋊Dic3C22×C313yes—
72C2×C4⋊Dic3C22×C313yes—
73C2×Dic3⋊C4C22×C313yes—
74C2×Dic3⋊C4C22×C313yes—
75C2×C4×Dic3C22×C313yes—
76#876C3×C418yescomplemented
77C3×#95—23no—
78C3×#95—23no—
79C3×#95—33no—
80C3×#95—33no—
81C3×#95C2×D313yes—
82C3×#95C2×D313yes—
83C3×#95C22×C313yes—
84C3×#95C22×C313yes—
85C3⋊#95C22×C313yes—
86C3⋊#95C22×C313yes—
87C23×C32C2411yescharacteristic
88C22×C3×D3—23no—
89C22×C3×D3—23no—
90C22×C3×D3C22×C412yes—
91C2×C32×C4—23no—
92C2×C32×C4—23no—
93C2×C32×C4—23no—
94C2×C32×C4—23no—
95C2×C32×C4—26no—
96C2×C32×C4C22×C416yes—
97C2×C3×Dic3—23no—
98C2×C3×Dic3—23no—
99C2×C3×Dic3—23no—
100C2×C3×Dic3—23no—
101C2×C3×Dic3—23no—
102C2×C3×Dic3—23no—
103C2×C3×Dic3C22×C416yes—
104C3×C4×D3—44no—
105C2×#126—31no—
106#389—33no—
107#388—33no—
108#387—33no—
109#385—33no—
110#384—31no—
111#383C3×D311yescharacteristic, complemented
112C24×C3—31no—
113C23×D3C23×C311yescharacteristic
114C22×C3×C4—23no—
115C22×C3×C4—23no—
116C22×C3×C4—21no—
117C22×C3×C4—33no—
118C22×C3×C4—31no—
119C22×C3×C4—33no—
120C22×C3×C4—123no—
121C22×C3×C4C22×D313yes—
122C22×C3×C4C22×D311yescharacteristic
123C22×C3×C4C22×D313yes—
124C22×C3×C4C23×C313yes—
125C22×C3×C4C23×C311yescharacteristic
126C22×C3×C4C23×C313yes—
127C22×Dic3C23×C311yescharacteristic
128C22×Dic3C23×C313yes—
129C22×Dic3C23×C313yes—
130C2×C4×D3—43no—
131C3×C4⋊C4—312no—
132C3×C4⋊C4—123no—
133C3×C4⋊C4—123no—
134C3×C4⋊C4—123no—
135C3×C22⋊C4—312no—
136C3×C22⋊C4—123no—
137C3×C42—24no—
138C3×C42—123no—
139C3×C42C4×D314yescomplemented
140C3×C42C2×C3×C414yescomplemented
141(C2×D3)⋊C4—43no—
142(C2×D3)⋊C4C2×C3×C4112yes—
143C4⋊Dic3—43no—
144C4⋊Dic3—43no—
145Dic3⋊C4—43no—
146Dic3⋊C4C2×C3×C4112yescomplemented
147C4×Dic3—43no—
148C22×C32C23×C411yescharacteristic
149C22×C32H(5,𝔽2)13yes—
150C22×C322−1+413yes—
151C2×C3×D3—26no—
152C2×C3×D3—41no—
153C2×C3×D3—43no—
154C32×C4—26no—
155C32×C4—41no—
156C32×C4—43no—
157C3×Dic3—26no—
158C3×Dic3—41no—
159C3×Dic3—43no—
160C23×C4—31no—
161#126—38no—
162C2×C4⋊C4—33no—
163C2×C4⋊C4—33no—
164C2×C4⋊C4—33no—
165C2×C4⋊C4—33no—
166C2×C22⋊C4—33no—
167C2×C22⋊C4—33no—
168C2×C42—33no—
169C2×C42C2×C3×D311yescharacteristic
170#95—33no—
171#95—33no—
172#95C2×C3×D313yes—
173#95C2×C3×D313yes—
174C23×C3—21no—
175C23×C3—32no—
176C23×C3—63no—
177C23×C3—63no—
178C23×C3C23×D311yescharacteristic
179C23×C3C24×C311yescharacteristic
180C22×D3—23no—
181C22×D3—23no—
182C22×D3C22×C3×C412yes—
183C2×C3×C4—23no—
184C2×C3×C4—23no—
185C2×C3×C4—23no—
186C2×C3×C4—23no—
187C2×C3×C4—23no—
188C2×C3×C4—23no—
189C2×C3×C4—26no—
190C2×C3×C4—23no—
191C2×C3×C4—23no—
192C2×C3×C4—26no—
193C2×C3×C4—26no—
194C2×C3×C4—36no—
195C2×C3×C4—43no—
196C2×C3×C4—43no—
197C2×C3×C4—43no—
198C2×C3×C4—43no—
199C2×C3×C4—46no—
200C2×C3×C4—63no—
201C2×C3×C4—63no—
202C2×C3×C4—63no—
203C2×C3×C4—63no—
204C2×C3×C4—63no—
205C2×C3×C4—63no—
206C2×C3×C4—124no—
207C2×C3×C4C2×C4×D316yes—
208C2×C3×C4C22×C3×C416yes—
209C2×Dic3—23no—
210C2×Dic3—23no—
211C2×Dic3—23no—
212C2×Dic3—23no—
213C2×Dic3—23no—
214C2×Dic3—23no—
215C2×Dic3C22×C3×C416yes—
216C4×D3—44no—
217C2×C32#52013yes—
218C2×C32#56011yescharacteristic
219C2×C32#56313yes—
220C3×D3—42no—
221C24—31no—
222C22×C4—33no—
223C22×C4—31no—
224C22×C4—33no—
225C22×C4—123no—
226C22×C4C22×C3×D313yes—
227C22×C4C22×C3×D311yescharacteristic
228C22×C4C22×C3×D313yes—
229C4⋊C4—312no—
230C4⋊C4—123no—
231C4⋊C4—123no—
232C4⋊C4—123no—
233C22⋊C4—312no—
234C22⋊C4—123no—
235C42—123no—
236C42C3×C4×D314yescomplemented
237C22×C3—21no—
238C22×C3—23no—
239C22×C3—23no—
240C22×C3—66no—
241C22×C3—121no—
242C22×C3—123no—
243C22×C3C22×C4×D311yescharacteristic
244C22×C3#100913yes—
245C22×C3#101013yes—
246C22×C3C23×C3×C411yescharacteristic
247C22×C3C3×H(5,𝔽2)13yes—
248C22×C3C3×2−1+413yes—
249C2×D3—26no—
250C2×D3—41no—
251C2×D3—43no—
252C3×C4—26no—
253C3×C4—26no—
254C3×C4—46no—
255C3×C4—41no—
256C3×C4—43no—
257C3×C4—41no—
258C3×C4—43no—
259C3×C4—66no—
260C3×C4—81no—
261C3×C4—83no—
262C3×C4—121no—
263C3×C4—123no—
264Dic3—26no—
265Dic3—41no—
266Dic3—43no—
267C32#238311yescharacteristic, complemented, Sylow
268C23—32no—
269C23—63no—
270C23—63no—
271C23C23×C3×D311yescharacteristic
272C2×C4—23no—
273C2×C4—23no—
274C2×C4—23no—
275C2×C4—23no—
276C2×C4—26no—
277C2×C4—36no—
278C2×C4—63no—
279C2×C4—63no—
280C2×C4—63no—
281C2×C4—63no—
282C2×C4—63no—
283C2×C4—63no—
284C2×C4—124no—
285C2×C4C2×C3×C4×D316yes—
286C2×C3—23no—
287C2×C3—21no—
288C2×C3—23no—
289C2×C3—122no—
290C2×C3#552313yes—
291C2×C3#571111yescharacteristic
292C2×C3#571213yes—
293C2×C3C3×#52013yes—
294C2×C3C3×#56011yescharacteristic
295C2×C3C3×#56313yes—
296D3—42no—
297C22—66no—
298C22—121no—
299C22—123no—
300C22C22×C3×C4×D311yescharacteristic
301C22C3×#100913yes—
302C22C3×#101013yes—
303C4—26no—
304C4—41no—
305C4—43no—
306C4—66no—
307C4—121no—
308C4—123no—
309C3—21no—
310C3#7429911yescharacteristic, direct product factor
311C3C3×#238311yescharacteristic, complemented
312C2—122no—
313C2C3×#552313yes—
314C2C3×#571111yescharacteristic
315C2C3×#571213yes—
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#383C2
socleC23×C32C24
prime radicalC23×C3×D3C23
cosocleC23×C3C24×C3
hypercenterC3×#383D3
hypocenterC3C3×#2383
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#383

Complements

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

NH ≅ G/Ntype
2. C32×#383C2semidirect
3. C3×#4935C2semidirect
6. C3×#4655C2semidirect
7. C3×#4647C2semidirect
9. #74299C3direct (N × H)
19. C3×#876C4semidirect
32. C3×#383D3semidirect
33. C3×#383C2×C3semidirect
34. #4935C2×C3semidirect
37. #4655C2×C3semidirect
38. #4647C2×C3semidirect
47. C32×C42C2×C4semidirect
53. C3×Dic3⋊C4C2×C4semidirect
76. #876C3×C4semidirect
111. #383C3×D3semidirect
139. C3×C42C4×D3semidirect
140. C3×C42C2×C3×C4semidirect
146. Dic3⋊C4C2×C3×C4semidirect
236. C42C3×C4×D3semidirect
267. C32#2383semidirect
310. C3#74299direct (N × H)
311. C3C3×#2383semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8762
C32×#3832
C3×#49352
C3×#46702
C3×#46682
C3×#46552
C3×#46472
C3×#23833
#742993