Finite Group Databasebeta

← C3×#83076 #11808036

Subgroups — C3×#83076 #11808036

Order 1152.

1035 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#126C211yesmaximal, characteristic
2C3×#4984C213yesmaximal, complemented
3C3×#4980C213yesmaximal, complemented
4C3×#4951C213yesmaximal
5C3×#4950C213yesmaximal
6C3×#4937C211yesmaximal, characteristic, complemented
7C3×#4935C211yesmaximal, characteristic, complemented
8C3×#2383—31nomaximal
9#83076C311yesmaximal, characteristic, direct product factor
10C23×C3×Dic3C2211yescharacteristic
11C32×#126C418yescomplemented
12C2×C32×C4⋊C4C2213yes—
13C2×C32×C22⋊C4C2213yes—
14C2×C32×C42C2211yescharacteristic
15C2×C3×#217C2213yes—
16C2×C3×C4⋊Dic3C2213yes—
17C2×C3×C4⋊Dic3C2213yes—
18C2×C3×C4⋊Dic3C2213yes—
19C2×C3×C4×Dic3C2213yes—
20C3×C3⋊#95C2213yes—
21C3×C3⋊#95C2213yes—
22C3×C3⋊#95C2213yes—
23C3×C3⋊#95C2213yes—
24C2×C3×#126—21no—
25C2×C3×#126D311yescharacteristic
26C2×C3×#126C2×C311yescharacteristic
27C3×#389—33no—
28C3×#388—33no—
29C3×#387—33no—
30C3×#385—33no—
31C3×#384—31no—
32C3×#383—31no—
33#4984C2×C313yescomplemented
34#4980C2×C313yescomplemented
35#4951C2×C313yes—
36#4950C2×C313yes—
37#4937C2×C311yescharacteristic, complemented
38#4935C2×C311yescharacteristic, complemented
39C24×C32C2311yescharacteristic
40C22×C32×C4C2313yes—
41C22×C32×C4C2313yes—
42C22×C3×Dic3—43no—
43C22×C3×Dic3C2313yes—
44C22×C3×Dic3C2313yes—
45C22×C3×Dic3C2311yescharacteristic
46C22×C3×Dic3C2311yescharacteristic
47C32×C4⋊C4C2×C4112yescomplemented
48C32×C22⋊C4C2×C4112yes—
49C32×C42C2×C414yescomplemented
50C3×#217—43no—
51C3×C4⋊Dic3—43no—
52C3×C4⋊Dic3—43no—
53C3×C4⋊Dic3—43no—
54C3×C4×Dic3—43no—
55#2383—31noSylow
56C23×C3×C4—31no—
57C23×Dic3C22×C311yescharacteristic
58C3×#126—28no—
59C3×#126Dic318yescomplemented
60C3×#126C3×C418yescomplemented
61C2×C3×C4⋊C4—23no—
62C2×C3×C4⋊C4—33no—
63C2×C3×C4⋊C4—33no—
64C2×C3×C4⋊C4—33no—
65C2×C3×C4⋊C4C2×D313yes—
66C2×C3×C4⋊C4C22×C313yes—
67C2×C3×C22⋊C4—23no—
68C2×C3×C22⋊C4—33no—
69C2×C3×C22⋊C4C2×D313yes—
70C2×C3×C22⋊C4C22×C313yes—
71C2×C3×C42—21no—
72C2×C3×C42—33no—
73C2×C3×C42C2×D311yescharacteristic
74C2×C3×C42C22×C311yescharacteristic
75C2×#217C22×C313yes—
76C2×C4⋊Dic3C22×C313yes—
77C2×C4⋊Dic3C22×C313yes—
78C2×C4⋊Dic3C22×C313yes—
79C2×C4×Dic3C22×C313yes—
80C3×#95—33no—
81C3×#95—33no—
82C3×#95—33no—
83C3×#95—33no—
84C3⋊#95C22×C313yes—
85C3⋊#95C22×C313yes—
86C3⋊#95C22×C313yes—
87C3⋊#95C22×C313yes—
88C23×C32—23no—
89C23×C32—23no—
90C23×C32C22×C412yes—
91C23×C32C2411yescharacteristic
92C2×C32×C4—23no—
93C2×C32×C4—23no—
94C2×C32×C4—23no—
95C2×C32×C4—23no—
96C2×C32×C4C22×C416yes—
97C2×C32×C4C22×C416yes—
98C2×C3×Dic3—23no—
99C2×C3×Dic3—23no—
100C2×C3×Dic3—23no—
101C2×C3×Dic3—23no—
102C2×C3×Dic3—23no—
103C2×C3×Dic3—23no—
104C2×C3×Dic3—26no—
105C2×C3×Dic3—44no—
106C2×#126C3×D311yescharacteristic
107#389—33no—
108#388—33no—
109#387—33no—
110#385—33no—
111#384—31no—
112#383—31no—
113C24×C3—21no—
114C24×C3C22×D311yescharacteristic
115C24×C3C23×C311yescharacteristic
116C22×C3×C4—23no—
117C22×C3×C4—23no—
118C22×C3×C4—33no—
119C22×C3×C4—31no—
120C22×C3×C4—31no—
121C22×C3×C4—33no—
122C22×C3×C4—123no—
123C22×C3×C4C22×D313yes—
124C22×C3×C4C22×D313yes—
125C22×C3×C4C23×C313yes—
126C22×C3×C4C23×C313yes—
127C22×Dic3—43no—
128C22×Dic3C23×C313yes—
129C22×Dic3C23×C311yescharacteristic
130C22×Dic3C23×C311yescharacteristic
131C22×Dic3C23×C313yes—
132C3×C4⋊C4—212no—
133C3×C4⋊C4—123no—
134C3×C4⋊C4—123no—
135C3×C4⋊C4—123no—
136C3×C4⋊C4C2×Dic3112yescomplemented
137C3×C4⋊C4C2×C3×C4112yescomplemented
138C3×C22⋊C4—212no—
139C3×C22⋊C4—123no—
140C3×C22⋊C4C2×Dic3112yes—
141C3×C22⋊C4C2×C3×C4112yes—
142C3×C42—24no—
143C3×C42—123no—
144C3×C42C2×Dic314yescomplemented
145C3×C42C2×C3×C414yescomplemented
146#217—43no—
147C4⋊Dic3—43no—
148C4⋊Dic3—43no—
149C4⋊Dic3—43no—
150C4×Dic3—43no—
151C22×C32—26no—
152C22×C32—41no—
153C22×C32—43no—
154C22×C32C23×C411yescharacteristic
155C22×C32H(5,𝔽2)13yes—
156C22×C322−1+413yes—
157C32×C4—26no—
158C32×C4—26no—
159C3×Dic3—43no—
160C3×Dic3—41no—
161C3×Dic3—41no—
162C3×Dic3—43no—
163C23×C4—31no—
164#126C3×Dic318yescomplemented
165C2×C4⋊C4—33no—
166C2×C4⋊C4—33no—
167C2×C4⋊C4—33no—
168C2×C4⋊C4C2×C3×D313yes—
169C2×C22⋊C4—33no—
170C2×C22⋊C4C2×C3×D313yes—
171C2×C42—33no—
172C2×C42C2×C3×D311yescharacteristic
173#95—33no—
174#95—33no—
175#95—33no—
176#95—33no—
177C23×C3—23no—
178C23×C3—23no—
179C23×C3—23no—
180C23×C3—23no—
181C23×C3—21no—
182C23×C3—22no—
183C23×C3—43no—
184C23×C3—43no—
185C23×C3C22×Dic312yes—
186C23×C3C22×C3×C412yes—
187C23×C3C23×D311yescharacteristic
188C23×C3C24×C311yescharacteristic
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—26no—
198C2×C3×C4—26no—
199C2×C3×C4—43no—
200C2×C3×C4—43no—
201C2×C3×C4—43no—
202C2×C3×C4—43no—
203C2×C3×C4—63no—
204C2×C3×C4—63no—
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×C4C22×Dic316yes—
212C2×C3×C4C22×Dic316yes—
213C2×C3×C4C22×C3×C416yes—
214C2×C3×C4C22×C3×C416yes—
215C2×Dic3—23no—
216C2×Dic3—23no—
217C2×Dic3—23no—
218C2×Dic3—23no—
219C2×Dic3—23no—
220C2×Dic3—23no—
221C2×Dic3—26no—
222C2×Dic3—44no—
223C2×C32—42no—
224C2×C32#52013yes—
225C2×C32#56011yescharacteristic
226C2×C32#56313yes—
227C24C22×C3×D311yescharacteristic
228C22×C4—33no—
229C22×C4—31no—
230C22×C4—31no—
231C22×C4—33no—
232C22×C4—123no—
233C22×C4C22×C3×D313yes—
234C22×C4C22×C3×D313yes—
235C4⋊C4—123no—
236C4⋊C4—123no—
237C4⋊C4—123no—
238C4⋊C4C2×C3×Dic3112yescomplemented
239C22⋊C4—123no—
240C22⋊C4C2×C3×Dic3112yes—
241C42—123no—
242C42C2×C3×Dic314yescomplemented
243C22×C3—26no—
244C22×C3—26no—
245C22×C3—23no—
246C22×C3—23no—
247C22×C3—21no—
248C22×C3—46no—
249C22×C3—41no—
250C22×C3—43no—
251C22×C3—41no—
252C22×C3—43no—
253C22×C3—81no—
254C22×C3—83no—
255C22×C3#100913yes—
256C22×C3#101013yes—
257C22×C3C23×Dic311yescharacteristic
258C22×C3C23×C3×C411yescharacteristic
259C22×C3C3×H(5,𝔽2)13yes—
260C22×C3C3×2−1+413yes—
261C3×C4—26no—
262C3×C4—26no—
263C3×C4—26no—
264C3×C4—26no—
265C3×C4—46no—
266C3×C4—46no—
267C3×C4—121no—
268C3×C4—121no—
269C3×C4—123no—
270C3×C4—123no—
271Dic3—41no—
272Dic3—41no—
273Dic3—43no—
274Dic3—43no—
275C32#238311yescharacteristic, complemented, Sylow
276C23—23no—
277C23—23no—
278C23C22×C3×Dic312yes—
279C23C23×C3×D311yescharacteristic
280C2×C4—23no—
281C2×C4—23no—
282C2×C4—23no—
283C2×C4—23no—
284C2×C4—63no—
285C2×C4—63no—
286C2×C4—63no—
287C2×C4—63no—
288C2×C4—63no—
289C2×C4—63no—
290C2×C4—66no—
291C2×C4—124no—
292C2×C4C22×C3×Dic316yes—
293C2×C4C22×C3×Dic316yes—
294C2×C3—23no—
295C2×C3—21no—
296C2×C3—23no—
297C2×C3—42no—
298C2×C3—42no—
299C2×C3—82no—
300C2×C3#571111yescharacteristic
301C2×C3#571213yes—
302C2×C3#582713yes—
303C2×C3C3×#52013yes—
304C2×C3C3×#56011yescharacteristic
305C2×C3C3×#56313yes—
306C22—26no—
307C22—41no—
308C22—43no—
309C22C3×#100913yes—
310C22C3×#101013yes—
311C22C23×C3×Dic311yescharacteristic
312C4—26no—
313C4—26no—
314C4—121no—
315C4—121no—
316C4—123no—
317C4—123no—
318C3—21no—
319C3#8307611yescharacteristic, direct product factor
320C3C3×#238311yescharacteristic, complemented
321C2—42no—
322C2C3×#571111yescharacteristic
323C2C3×#571213yes—
324C2C3×#582713yes—
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC2×C32×#126C2
socleC23×C32C24
prime radicalC24×C32C23
cosocleC23×C3C24×C3
hypercenterC2×C3×#126D3
hypocenterC3C3×#2383
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#126

Complements

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

NH ≅ G/Ntype
2. C3×#4984C2semidirect
3. C3×#4980C2semidirect
6. C3×#4937C2semidirect
7. C3×#4935C2semidirect
9. #83076C3direct (N × H)
11. C32×#126C4semidirect
33. #4984C2×C3semidirect
34. #4980C2×C3semidirect
37. #4937C2×C3semidirect
38. #4935C2×C3semidirect
47. C32×C4⋊C4C2×C4semidirect
49. C32×C42C2×C4semidirect
59. C3×#126Dic3semidirect
60. C3×#126C3×C4semidirect
136. C3×C4⋊C4C2×Dic3semidirect
137. C3×C4⋊C4C2×C3×C4semidirect
144. C3×C42C2×Dic3semidirect
145. C3×C42C2×C3×C4semidirect
164. #126C3×Dic3semidirect
238. C4⋊C4C2×C3×Dic3semidirect
242. C42C2×C3×Dic3semidirect
275. C32#2383semidirect
319. C3#83076direct (N × H)
320. C3C3×#2383semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1262
C3×#49842
C3×#49802
C3×#49512
C3×#49502
C3×#49372
C3×#49352
C3×#23833
#830763