Finite Group Databasebeta

← C3×D3×#399 #11808469

Subgroups — C3×D3×#399 #11808469

Order 1152.

1909 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×C4⋊C4C213yesmaximal, complemented
2C2×C3×D3×C22⋊C4C213yesmaximal
3C32×#399C211yesmaximal, characteristic, complemented
4C3×#4993C213yesmaximal, complemented
5C3×#4949C213yesmaximal, complemented
6C3×#4677C211yesmaximal, characteristic, complemented
7C3×D3×#95C211yesmaximal, characteristic, complemented
8C2×C3×#399—31nomaximal
9D3×#399C311yesmaximal, characteristic, direct product factor
10C24×C3×D3C2211yescharacteristic
11C22×C3×C4×D3C2213yes—
12C22×C3×C4×D3C2213yes—
13C2×C32×C4⋊C4C2213yescomplemented
14C2×C32×C22⋊C4C2213yes—
15C2×C3×#217C2213yes—
16C2×C3×(C2×D3)⋊C4C2213yes—
17C2×C3×(C2×D3)⋊C4C2213yes—
18C2×C3×C4⋊Dic3C2213yescomplemented
19C2×C3×Dic3⋊C4C2216yescomplemented
20C3×D3×C4⋊C4—212no—
21C3×D3×C22⋊C4—212no—
22C32×#95C2211yescharacteristic, complemented
23C3×C3⋊#95C2213yescomplemented
24C22×C3×C4⋊C4—33no—
25C22×C3×C22⋊C4—33no—
26C2×D3×C4⋊C4C2×C313yescomplemented
27C2×D3×C22⋊C4C2×C313yes—
28C3×#399—21no—
29C3×#399—33no—
30C3×#399—33no—
31C3×#399—31no—
32C3×#399D311yescharacteristic, direct product factor
33C3×#399C2×C311yescharacteristic, complemented
34C2×C3×#95—31no—
35#4993C2×C313yescomplemented
36#4949C2×C313yescomplemented
37#4677C2×C311yescharacteristic, complemented
38D3×#95C2×C311yescharacteristic, complemented
39C24×C32C2311yescharacteristic
40C23×C3×D3—26no—
41C23×C3×D3—26no—
42C23×C3×D3Q814yes—
43C23×C3×D3C2311yescharacteristic
44C23×C3×D3C2311yescharacteristic
45C22×C32×C4C2313yes—
46C22×C32×C4C2313yes—
47C22×C3×Dic3C2313yes—
48C22×C3×Dic3C2313yes—
49C2×C3×C4×D3—212no—
50C2×C3×C4×D3—26no—
51C2×C3×C4×D3—212no—
52C2×C3×C4×D3D4112yes—
53C32×C4⋊C4—26no—
54C32×C22⋊C4—26no—
55C3×#217—26no—
56C3×(C2×D3)⋊C4—26no—
57C3×(C2×D3)⋊C4—26no—
58C3×C4⋊Dic3—26no—
59C3×Dic3⋊C4—212no—
60C2×#399—31noSylow
61C25×C3—31no—
62C24×D3C22×C311yescharacteristic
63C23×C3×C4—33no—
64C23×C3×C4—33no—
65C22×C4×D3C22×C313yes—
66C22×C4×D3C22×C313yes—
67C2×C3×C4⋊C4—23no—
68C2×C3×C4⋊C4—36no—
69C2×C3×C4⋊C4—33no—
70C2×C3×C4⋊C4—612no—
71C2×C3×C4⋊C4C2×D313yescomplemented
72C2×C3×C4⋊C4C22×C313yescomplemented
73C2×C3×C22⋊C4—23no—
74C2×C3×C22⋊C4—33no—
75C2×C3×C22⋊C4—33no—
76C2×C3×C22⋊C4—33no—
77C2×C3×C22⋊C4—612no—
78C2×C3×C22⋊C4C2×D313yes—
79C2×C3×C22⋊C4C22×C313yes—
80C2×#217C22×C313yes—
81C2×(C2×D3)⋊C4C22×C313yes—
82C2×(C2×D3)⋊C4C22×C313yes—
83C2×C4⋊Dic3C22×C313yescomplemented
84C2×Dic3⋊C4C22×C316yescomplemented
85D3×C4⋊C4—212no—
86D3×C22⋊C4—212no—
87C3×#95—21no—
88C3×#95—33no—
89C3×#95C2×D311yescharacteristic, complemented
90C3×#95C22×C311yescharacteristic, complemented
91C3⋊#95C22×C313yescomplemented
92C23×C32—23no—
93C23×C32—23no—
94C23×C32C2×Q812yes—
95C23×C32C2411yescharacteristic
96C22×C3×D3—23no—
97C22×C3×D3—23no—
98C22×C3×D3—224no—
99C22×C3×D3—412no—
100C22×C3×D3—44no—
101C22×C3×D3C2×D416yes—
102C22×C3×D3C2×Q812yes—
103C22×C3×D3C2×Q812yes—
104C22×C3×D3#4116yes—
105C2×C32×C4—26no—
106C2×C32×C4—26no—
107C2×C32×C4—23no—
108C2×C32×C4C2×D416yes—
109C2×C3×Dic3—26no—
110C2×C3×Dic3—26no—
111C2×C3×Dic3—23no—
112C2×C3×Dic3C2×D416yes—
113C3×C4×D3—224no—
114C3×C4×D3—412no—
115C22×C4⋊C4—33no—
116C22×C22⋊C4—33no—
117#399—33no—
118#399—33no—
119#399—31no—
120#399C3×D311yescharacteristic, direct product factor
121C2×#95—31no—
122C24×C3—21no—
123C24×C3—31no—
124C24×C3—34no—
125C24×C3—31no—
126C24×C3—66no—
127C24×C3—66no—
128C24×C3C22×D311yescharacteristic
129C24×C3C23×C311yescharacteristic
130C23×D3—26no—
131C23×D3—26no—
132C23×D3C3×Q814yes—
133C23×D3C23×C311yescharacteristic
134C23×D3C23×C311yescharacteristic
135C22×C3×C4—23no—
136C22×C3×C4—23no—
137C22×C3×C4—33no—
138C22×C3×C4—312no—
139C22×C3×C4—33no—
140C22×C3×C4—612no—
141C22×C3×C4—66no—
142C22×C3×C4—612no—
143C22×C3×C4C22×D313yes—
144C22×C3×C4C22×D313yes—
145C22×C3×C4C23×C313yes—
146C22×C3×C4C23×C313yes—
147C22×Dic3C23×C313yes—
148C22×Dic3C23×C313yes—
149C2×C4×D3—212no—
150C2×C4×D3—26no—
151C2×C4×D3—212no—
152C2×C4×D3C3×D4112yes—
153C3×C4⋊C4—26no—
154C3×C4⋊C4—26no—
155C3×C4⋊C4—46no—
156C3×C4⋊C4—612no—
157C3×C4⋊C4—66no—
158C3×C22⋊C4—26no—
159C3×C22⋊C4—26no—
160C3×C22⋊C4—46no—
161C3×C22⋊C4—66no—
162C3×C22⋊C4—66no—
163C3×C22⋊C4—66no—
164#217—26no—
165(C2×D3)⋊C4—26no—
166(C2×D3)⋊C4—26no—
167C4⋊Dic3—26no—
168Dic3⋊C4—212no—
169C22×C32—26no—
170C22×C32—43no—
171C22×C32—41no—
172C22×C32C22×D413yes—
173C22×C32C22×Q811yescharacteristic
174C22×C32C2×#4113yes—
175C2×C3×D3—26no—
176C2×C3×D3—43no—
177C2×C3×D3—41no—
178C2×C3×D3—416no—
179C2×C3×D3C22⋊Q8112yes—
180C2×C3×D3#123112yes—
181C2×C3×D3#12714yes—
182C32×C4—26no—
183C32×C4—43no—
184C3×Dic3—26no—
185C3×Dic3—43no—
186C25—31no—
187C23×C4—33no—
188C23×C4—33no—
189C2×C4⋊C4—36no—
190C2×C4⋊C4—33no—
191C2×C4⋊C4—612no—
192C2×C4⋊C4C2×C3×D313yescomplemented
193C2×C22⋊C4—33no—
194C2×C22⋊C4—33no—
195C2×C22⋊C4—33no—
196C2×C22⋊C4—612no—
197C2×C22⋊C4C2×C3×D313yes—
198#95—33no—
199#95C2×C3×D311yescharacteristic, complemented
200C23×C3—23no—
201C23×C3—23no—
202C23×C3—23no—
203C23×C3—23no—
204C23×C3—21no—
205C23×C3—22no—
206C23×C3—36no—
207C23×C3—32no—
208C23×C3—36no—
209C23×C3—32no—
210C23×C3—43no—
211C23×C3—43no—
212C23×C3—624no—
213C23×C3—63no—
214C23×C3—63no—
215C23×C3—1212no—
216C23×C3—124no—
217C23×C3D3×Q812yes—
218C23×C3C2×C3×Q812yes—
219C23×C3C23×D311yescharacteristic
220C23×C3C24×C311yescharacteristic
221C22×D3—23no—
222C22×D3—23no—
223C22×D3—224no—
224C22×D3—412no—
225C22×D3—44no—
226C22×D3C2×C3×D416yes—
227C22×D3C2×C3×Q812yes—
228C22×D3C2×C3×Q812yes—
229C22×D3C3×#4116yes—
230C2×C3×C4—26no—
231C2×C3×C4—26no—
232C2×C3×C4—23no—
233C2×C3×C4—26no—
234C2×C3×C4—26no—
235C2×C3×C4—23no—
236C2×C3×C4—26no—
237C2×C3×C4—36no—
238C2×C3×C4—46no—
239C2×C3×C4—43no—
240C2×C3×C4—46no—
241C2×C3×C4—624no—
242C2×C3×C4—66no—
243C2×C3×C4—63no—
244C2×C3×C4—66no—
245C2×C3×C4—1212no—
246C2×C3×C4D3×D416yes—
247C2×C3×C4C2×C3×D416yes—
248C2×Dic3—26no—
249C2×Dic3—26no—
250C2×Dic3—23no—
251C2×Dic3C2×C3×D416yes—
252C4×D3—224no—
253C4×D3—412no—
254C2×C32—42no—
255C2×C32C2×C22⋊Q813yes—
256C2×C32C2×#12313yes—
257C2×C32C2×#12711yescharacteristic
258C3×D3—42no—
259C3×D3#39918yesdirect product factor
260C24—31no—
261C24—31no—
262C24—34no—
263C24—66no—
264C24—66no—
265C24C22×C3×D311yescharacteristic
266C22×C4—33no—
267C22×C4—312no—
268C22×C4—33no—
269C22×C4—612no—
270C22×C4—66no—
271C22×C4—612no—
272C22×C4C22×C3×D313yes—
273C22×C4C22×C3×D313yes—
274C4⋊C4—26no—
275C4⋊C4—612no—
276C4⋊C4—66no—
277C22⋊C4—26no—
278C22⋊C4—66no—
279C22⋊C4—66no—
280C22⋊C4—66no—
281C22×C3—26no—
282C22×C3—26no—
283C22×C3—23no—
284C22×C3—21no—
285C22×C3—23no—
286C22×C3—312no—
287C22×C3—34no—
288C22×C3—312no—
289C22×C3—46no—
290C22×C3—43no—
291C22×C3—41no—
292C22×C3—43no—
293C22×C3—41no—
294C22×C3—66no—
295C22×C3—83no—
296C22×C3—81no—
297C22×C3—1216no—
298C22×C3—123no—
299C22×C3—121no—
300C22×C3C2×D3×D413yes—
301C22×C3C2×D3×Q811yescharacteristic
302C22×C3D3×#4113yes—
303C22×C3C22×C3×D413yes—
304C22×C3C22×C3×Q811yescharacteristic
305C22×C3C2×C3×#4113yes—
306C2×D3—26no—
307C2×D3—43no—
308C2×D3—41no—
309C2×D3—416no—
310C2×D3C3×C22⋊Q8112yes—
311C2×D3C3×#123112yes—
312C2×D3C3×#12714yes—
313C3×C4—26no—
314C3×C4—26no—
315C3×C4—46no—
316C3×C4—43no—
317C3×C4—43no—
318C3×C4—66no—
319C3×C4—83no—
320C3×C4—123no—
321Dic3—26no—
322Dic3—43no—
323C32C2×#39911yescharacteristic, complemented, Sylow
324C23—23no—
325C23—23no—
326C23—36no—
327C23—32no—
328C23—36no—
329C23—32no—
330C23—624no—
331C23—63no—
332C23—63no—
333C23—1212no—
334C23—124no—
335C23C3×D3×Q812yes—
336C23C23×C3×D311yescharacteristic
337C2×C4—26no—
338C2×C4—23no—
339C2×C4—26no—
340C2×C4—36no—
341C2×C4—624no—
342C2×C4—66no—
343C2×C4—63no—
344C2×C4—66no—
345C2×C4—1212no—
346C2×C4C3×D3×D416yes—
347C2×C3—23no—
348C2×C3—23no—
349C2×C3—21no—
350C2×C3—38no—
351C2×C3—42no—
352C2×C3—42no—
353C2×C3—82no—
354C2×C3—122no—
355C2×C3D3×C22⋊Q813yes—
356C2×C3D3×#12313yes—
357C2×C3D3×#12711yescharacteristic
358C2×C3C2×C3×C22⋊Q813yes—
359C2×C3C2×C3×#12313yes—
360C2×C3C2×C3×#12711yescharacteristic
361D3—42no—
362D3C3×#39918yesdirect product factor
363C22—26no—
364C22—312no—
365C22—312no—
366C22—34no—
367C22—43no—
368C22—41no—
369C22—66no—
370C22—1216no—
371C22—123no—
372C22—121no—
373C22C2×C3×D3×D413yes—
374C22C2×C3×D3×Q811yescharacteristic
375C22C3×D3×#4113yes—
376C4—26no—
377C4—43no—
378C4—66no—
379C4—123no—
380C3—21no—
381C3D3×#39911yescharacteristic, direct product factor
382C3C2×C3×#39911yescharacteristic, complemented
383C2—38no—
384C2—42no—
385C2—122no—
386C2C3×D3×C22⋊Q813yes—
387C2C3×D3×#12313yes—
388C2C3×D3×#12711yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#399C2
socleC23×C32C24
prime radicalC24×C3×D3C22
hypercenterC3×#399D3
hypocenterC3C2×C3×#399
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#399

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×C4⋊C4C2semidirect
3. C32×#399C2semidirect
4. C3×#4993C2semidirect
5. C3×#4949C2semidirect
6. C3×#4677C2semidirect
7. C3×D3×#95C2semidirect
9. D3×#399C3direct (N × H)
13. C2×C32×C4⋊C4C22semidirect
18. C2×C3×C4⋊Dic3C22semidirect
19. C2×C3×Dic3⋊C4C22semidirect
22. C32×#95C22semidirect
23. C3×C3⋊#95C22semidirect
26. C2×D3×C4⋊C4C2×C3semidirect
32. C3×#399D3direct (N × H)
33. C3×#399C2×C3semidirect
35. #4993C2×C3semidirect
36. #4949C2×C3semidirect
37. #4677C2×C3semidirect
38. D3×#95C2×C3semidirect
71. C2×C3×C4⋊C4C2×D3semidirect
72. C2×C3×C4⋊C4C22×C3semidirect
83. C2×C4⋊Dic3C22×C3semidirect
84. C2×Dic3⋊C4C22×C3semidirect
89. C3×#95C2×D3semidirect
90. C3×#95C22×C3semidirect
91. C3⋊#95C22×C3semidirect
120. #399C3×D3direct (N × H)
192. C2×C4⋊C4C2×C3×D3semidirect
199. #95C2×C3×D3semidirect
259. C3×D3#399direct (N × H)
323. C32C2×#399semidirect
362. D3C3×#399direct (N × H)
381. C3D3×#399direct (N × H)
382. C3C2×C3×#399semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×C4⋊C42
C2×C3×D3×C22⋊C42
C32×#3992
C3×#49932
C3×#49492
C3×#46772
C3×D3×#952
C2×C3×#3993
D3×#3993