Finite Group Databasebeta

← C3×#74361 #11808039

Subgroups — C3×#74361 #11808039

Order 1152.

1005 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#876C211yesmaximal, characteristic
2C32×#384C211yesmaximal, characteristic, complemented
3C3×#4990C213yesmaximal
4C3×#4989C213yesmaximal
5C3×#4978C213yesmaximal, complemented
6C3×#4976C213yesmaximal, complemented
7C3×#4937C211yesmaximal, characteristic, complemented
8C3×#2383—31nomaximal
9#74361C311yesmaximal, characteristic, direct product factor
10C22×C3×C4×D3C2211yescharacteristic
11C2×C32×C4⋊C4C2213yes—
12C2×C32×C4⋊C4C2213yes—
13C2×C32×C42C2211yescharacteristic
14C2×C3×(C2×D3)⋊C4C2213yes—
15C2×C3×(C2×D3)⋊C4C2213yes—
16C2×C3×Dic3⋊C4C2213yes—
17C2×C3×Dic3⋊C4C2213yes—
18C2×C3×C4×Dic3C2213yes—
19C3×#876C418yescomplemented
20C3×C3⋊#95C2213yes—
21C3×C3⋊#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—21no—
31C3×#384D311yescharacteristic, complemented
32C3×#384C2×C311yescharacteristic, complemented
33C3×#383—31no—
34#4990C2×C313yes—
35#4989C2×C313yes—
36#4978C2×C313yescomplemented
37#4976C2×C313yescomplemented
38#4937C2×C311yescharacteristic, complemented
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×C4⋊C4—43no—
48C32×C4⋊C4—43no—
49C32×C42C2×C414yescomplemented
50C3×(C2×D3)⋊C4—43no—
51C3×(C2×D3)⋊C4C2×C4112yes—
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—23no—
60C2×C3×C4⋊C4—23no—
61C2×C3×C4⋊C4—33no—
62C2×C3×C4⋊C4—33no—
63C2×C3×C4⋊C4C2×D313yes—
64C2×C3×C4⋊C4C2×D313yes—
65C2×C3×C4⋊C4C22×C313yes—
66C2×C3×C4⋊C4C22×C313yes—
67C2×C3×C22⋊C4—33no—
68C2×C3×C22⋊C4—33no—
69C2×C3×C42—21no—
70C2×C3×C42—33no—
71C2×C3×C42C2×D311yescharacteristic
72C2×C3×C42C22×C311yescharacteristic
73C2×(C2×D3)⋊C4C22×C313yes—
74C2×(C2×D3)⋊C4C22×C313yes—
75C2×Dic3⋊C4C22×C313yes—
76C2×Dic3⋊C4C22×C313yes—
77C2×C4×Dic3C22×C313yes—
78#876C3×C418yescomplemented
79C3×#95—33no—
80C3×#95—33no—
81C3×#95—33no—
82C3×#95—33no—
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—23no—
96C2×C32×C4—23no—
97C2×C32×C4C22×C416yes—
98C2×C3×Dic3—23no—
99C2×C3×Dic3—23no—
100C2×C3×Dic3—23no—
101C2×C3×Dic3—23no—
102C2×C3×Dic3—26no—
103C2×C3×Dic3C22×C416yes—
104C3×C4×D3—44no—
105C2×#126—31no—
106#389—33no—
107#388—33no—
108#387—33no—
109#385—33no—
110#384C3×D311yescharacteristic, complemented
111#383—31no—
112C24×C3—31no—
113C23×D3C23×C311yescharacteristic
114C22×C3×C4—23no—
115C22×C3×C4—21no—
116C22×C3×C4—23no—
117C22×C3×C4—33no—
118C22×C3×C4—33no—
119C22×C3×C4—31no—
120C22×C3×C4—123no—
121C22×C3×C4C22×D311yescharacteristic
122C22×C3×C4C22×D313yes—
123C22×C3×C4C22×D313yes—
124C22×C3×C4C23×C311yescharacteristic
125C22×C3×C4C23×C313yes—
126C22×C3×C4C23×C313yes—
127C22×Dic3C23×C313yes—
128C22×Dic3C23×C311yescharacteristic
129C22×Dic3C23×C313yes—
130C2×C4×D3—43no—
131C3×C4⋊C4—312no—
132C3×C4⋊C4—43no—
133C3×C4⋊C4—43no—
134C3×C4⋊C4—43no—
135C3×C4⋊C4—43no—
136C3×C4⋊C4—46no—
137C3×C4⋊C4—46no—
138C3×C4⋊C4—123no—
139C3×C22⋊C4—312no—
140C3×C22⋊C4—123no—
141C3×C42—24no—
142C3×C42—123no—
143C3×C42C4×D314yescomplemented
144C3×C42C2×C3×C414yescomplemented
145(C2×D3)⋊C4—43no—
146(C2×D3)⋊C4C2×C3×C4112yes—
147Dic3⋊C4—43no—
148Dic3⋊C4C2×C3×C4112yescomplemented
149C4×Dic3—43no—
150C22×C32C23×C411yescharacteristic
151C22×C32H(5,𝔽2)13yes—
152C22×C322−1+413yes—
153C2×C3×D3—26no—
154C2×C3×D3—41no—
155C2×C3×D3—43no—
156C32×C4—26no—
157C32×C4—41no—
158C32×C4—43no—
159C3×Dic3—26no—
160C3×Dic3—41no—
161C3×Dic3—43no—
162C23×C4—31no—
163#126—38no—
164C2×C4⋊C4—33no—
165C2×C4⋊C4—33no—
166C2×C4⋊C4C2×C3×D313yes—
167C2×C4⋊C4C2×C3×D313yes—
168C2×C22⋊C4—33no—
169C2×C22⋊C4—33no—
170C2×C42—33no—
171C2×C42C2×C3×D311yescharacteristic
172#95—33no—
173#95—33no—
174#95—33no—
175#95—33no—
176C23×C3—21no—
177C23×C3—32no—
178C23×C3—63no—
179C23×C3—63no—
180C23×C3C23×D311yescharacteristic
181C23×C3C24×C311yescharacteristic
182C22×D3—23no—
183C22×D3—23no—
184C22×D3C22×C3×C412yes—
185C2×C3×C4—26no—
186C2×C3×C4—26no—
187C2×C3×C4—23no—
188C2×C3×C4—23no—
189C2×C3×C4—23no—
190C2×C3×C4—23no—
191C2×C3×C4—23no—
192C2×C3×C4—23no—
193C2×C3×C4—23no—
194C2×C3×C4—23no—
195C2×C3×C4—23no—
196C2×C3×C4—23no—
197C2×C3×C4—23no—
198C2×C3×C4—23no—
199C2×C3×C4—26no—
200C2×C3×C4—36no—
201C2×C3×C4—43no—
202C2×C3×C4—43no—
203C2×C3×C4—43no—
204C2×C3×C4—43no—
205C2×C3×C4—63no—
206C2×C3×C4—63no—
207C2×C3×C4—63no—
208C2×C3×C4—63no—
209C2×C3×C4—66no—
210C2×C3×C4—124no—
211C2×C3×C4C2×C4×D316yes—
212C2×C3×C4C22×C3×C416yes—
213C2×Dic3—23no—
214C2×Dic3—23no—
215C2×Dic3—23no—
216C2×Dic3—23no—
217C2×Dic3—26no—
218C2×Dic3C22×C3×C416yes—
219C4×D3—44no—
220C2×C32#52013yes—
221C2×C32#56011yescharacteristic
222C2×C32#56313yes—
223C3×D3—42no—
224C24—31no—
225C22×C4—33no—
226C22×C4—33no—
227C22×C4—31no—
228C22×C4—123no—
229C22×C4C22×C3×D311yescharacteristic
230C22×C4C22×C3×D313yes—
231C22×C4C22×C3×D313yes—
232C4⋊C4—312no—
233C4⋊C4—43no—
234C4⋊C4—43no—
235C4⋊C4—123no—
236C22⋊C4—312no—
237C22⋊C4—123no—
238C42—123no—
239C42C3×C4×D314yescomplemented
240C22×C3—21no—
241C22×C3—23no—
242C22×C3—23no—
243C22×C3—66no—
244C22×C3—121no—
245C22×C3—123no—
246C22×C3C22×C4×D311yescharacteristic
247C22×C3#100413yes—
248C22×C3#100713yes—
249C22×C3C23×C3×C411yescharacteristic
250C22×C3C3×H(5,𝔽2)13yes—
251C22×C3C3×2−1+413yes—
252C2×D3—26no—
253C2×D3—41no—
254C2×D3—43no—
255C3×C4—212no—
256C3×C4—26no—
257C3×C4—26no—
258C3×C4—41no—
259C3×C4—43no—
260C3×C4—41no—
261C3×C4—43no—
262C3×C4—66no—
263C3×C4—81no—
264C3×C4—83no—
265C3×C4—121no—
266C3×C4—123no—
267Dic3—26no—
268Dic3—41no—
269Dic3—43no—
270C32#238311yescharacteristic, complemented, Sylow
271C23—32no—
272C23—63no—
273C23—63no—
274C23C23×C3×D311yescharacteristic
275C2×C4—23no—
276C2×C4—23no—
277C2×C4—23no—
278C2×C4—23no—
279C2×C4—23no—
280C2×C4—23no—
281C2×C4—36no—
282C2×C4—63no—
283C2×C4—63no—
284C2×C4—63no—
285C2×C4—63no—
286C2×C4—66no—
287C2×C4—124no—
288C2×C4C2×C3×C4×D316yes—
289C2×C3—23no—
290C2×C3—21no—
291C2×C3—23no—
292C2×C3—122no—
293C2×C3#550413yes—
294C2×C3#572011yescharacteristic
295C2×C3#573513yes—
296C2×C3C3×#52013yes—
297C2×C3C3×#56011yescharacteristic
298C2×C3C3×#56313yes—
299D3—42no—
300C22—66no—
301C22—121no—
302C22—123no—
303C22C22×C3×C4×D311yescharacteristic
304C22C3×#100413yes—
305C22C3×#100713yes—
306C4—26no—
307C4—41no—
308C4—43no—
309C4—66no—
310C4—121no—
311C4—123no—
312C3—21no—
313C3#7436111yescharacteristic, direct product factor
314C3C3×#238311yescharacteristic, complemented
315C2—122no—
316C2C3×#550413yes—
317C2C3×#572011yescharacteristic
318C2C3×#573513yes—
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#384C2
socleC23×C32C24
prime radicalC23×C3×D3C23
cosocleC23×C3C24×C3
hypercenterC3×#384D3
hypocenterC3C3×#2383
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#384

Complements

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

NH ≅ G/Ntype
2. C32×#384C2semidirect
5. C3×#4978C2semidirect
6. C3×#4976C2semidirect
7. C3×#4937C2semidirect
9. #74361C3direct (N × H)
19. C3×#876C4semidirect
31. C3×#384D3semidirect
32. C3×#384C2×C3semidirect
36. #4978C2×C3semidirect
37. #4976C2×C3semidirect
38. #4937C2×C3semidirect
49. C32×C42C2×C4semidirect
53. C3×Dic3⋊C4C2×C4semidirect
78. #876C3×C4semidirect
110. #384C3×D3semidirect
143. C3×C42C4×D3semidirect
144. C3×C42C2×C3×C4semidirect
148. Dic3⋊C4C2×C3×C4semidirect
239. C42C3×C4×D3semidirect
270. C32#2383semidirect
313. C3#74361direct (N × H)
314. 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×#3842
C3×#49902
C3×#49892
C3×#49782
C3×#49762
C3×#49372
C3×#23833
#743613