Finite Group Databasebeta

← C3×D3×#396 #11808255

Subgroups — C3×D3×#396 #11808255

Order 1152.

1909 conjugacy classes of subgroups.

The subgroup lattice has 424 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×#396C211yesmaximal, characteristic, complemented
4C3×#4994C213yesmaximal, complemented
5C3×#4948C213yesmaximal, complemented
6C3×#4676C211yesmaximal, characteristic, complemented
7C3×D3×#95C211yesmaximal, characteristic, complemented
8C2×C3×#396—31nomaximal
9D3×#396C311yesmaximal, 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⋊C4C2213yescomplemented
20C2×C3×Dic3⋊C4C2213yescomplemented
21C3×D3×C4⋊C4—212no—
22C3×D3×C22⋊C4—212no—
23C32×#95C2211yescharacteristic, complemented
24C3×C3⋊#95C2213yescomplemented
25C22×C3×C4⋊C4—33no—
26C22×C3×C22⋊C4—33no—
27C2×D3×C4⋊C4C2×C313yescomplemented
28C2×D3×C22⋊C4C2×C313yes—
29C3×#396—21no—
30C3×#396—33no—
31C3×#396—33no—
32C3×#396—31no—
33C3×#396D311yescharacteristic, direct product factor
34C3×#396C2×C311yescharacteristic, complemented
35C2×C3×#95—31no—
36#4994C2×C313yescomplemented
37#4948C2×C313yescomplemented
38#4676C2×C311yescharacteristic, complemented
39D3×#95C2×C311yescharacteristic, complemented
40C24×C32C2311yescharacteristic
41C23×C3×D3—26no—
42C23×C3×D3—26no—
43C23×C3×D3Q814yes—
44C23×C3×D3C2311yescharacteristic
45C23×C3×D3C2311yescharacteristic
46C22×C32×C4C2313yes—
47C22×C32×C4C2313yes—
48C22×C3×Dic3C2313yes—
49C22×C3×Dic3C2313yes—
50C2×C3×C4×D3—26no—
51C2×C3×C4×D3—26no—
52C2×C3×C4×D3—26no—
53C2×C3×C4×D3—26no—
54C2×C3×C4×D3—26no—
55C2×C3×C4×D3D4112yes—
56C32×C4⋊C4—26no—
57C32×C22⋊C4—26no—
58C3×#217—26no—
59C3×(C2×D3)⋊C4—26no—
60C3×(C2×D3)⋊C4—26no—
61C3×C4⋊Dic3—26no—
62C3×Dic3⋊C4—26no—
63C3×Dic3⋊C4—26no—
64C2×#396—31noSylow
65C25×C3—31no—
66C24×D3C22×C311yescharacteristic
67C23×C3×C4—33no—
68C23×C3×C4—33no—
69C22×C4×D3C22×C313yes—
70C22×C4×D3C22×C313yes—
71C2×C3×C4⋊C4—23no—
72C2×C3×C4⋊C4—33no—
73C2×C3×C4⋊C4—33no—
74C2×C3×C4⋊C4—33no—
75C2×C3×C4⋊C4—612no—
76C2×C3×C4⋊C4C2×D313yescomplemented
77C2×C3×C4⋊C4C22×C313yescomplemented
78C2×C3×C22⋊C4—23no—
79C2×C3×C22⋊C4—33no—
80C2×C3×C22⋊C4—33no—
81C2×C3×C22⋊C4—33no—
82C2×C3×C22⋊C4—612no—
83C2×C3×C22⋊C4C2×D313yes—
84C2×C3×C22⋊C4C22×C313yes—
85C2×#217C22×C313yes—
86C2×(C2×D3)⋊C4C22×C313yes—
87C2×(C2×D3)⋊C4C22×C313yes—
88C2×C4⋊Dic3C22×C313yescomplemented
89C2×Dic3⋊C4C22×C313yescomplemented
90C2×Dic3⋊C4C22×C313yescomplemented
91D3×C4⋊C4—212no—
92D3×C22⋊C4—212no—
93C3×#95—21no—
94C3×#95—33no—
95C3×#95C2×D311yescharacteristic, complemented
96C3×#95C22×C311yescharacteristic, complemented
97C3⋊#95C22×C313yescomplemented
98C23×C32—23no—
99C23×C32—23no—
100C23×C32C2×Q812yes—
101C23×C32C2411yescharacteristic
102C22×C3×D3—23no—
103C22×C3×D3—23no—
104C22×C3×D3—224no—
105C22×C3×D3—412no—
106C22×C3×D3—44no—
107C22×C3×D3C2×D416yes—
108C22×C3×D3C2×Q812yes—
109C22×C3×D3C2×Q812yes—
110C22×C3×D3#4116yes—
111C2×C32×C4—23no—
112C2×C32×C4—23no—
113C2×C32×C4—23no—
114C2×C32×C4—23no—
115C2×C32×C4—23no—
116C2×C32×C4C2×D416yes—
117C2×C3×Dic3—23no—
118C2×C3×Dic3—23no—
119C2×C3×Dic3—23no—
120C2×C3×Dic3—23no—
121C2×C3×Dic3—23no—
122C2×C3×Dic3C2×D416yes—
123C3×C4×D3—224no—
124C3×C4×D3—412no—
125C22×C4⋊C4—33no—
126C22×C22⋊C4—33no—
127#396—33no—
128#396—33no—
129#396—31no—
130#396C3×D311yescharacteristic, direct product factor
131C2×#95—31no—
132C24×C3—21no—
133C24×C3—31no—
134C24×C3—34no—
135C24×C3—31no—
136C24×C3—66no—
137C24×C3—66no—
138C24×C3C22×D311yescharacteristic
139C24×C3C23×C311yescharacteristic
140C23×D3—26no—
141C23×D3—26no—
142C23×D3C3×Q814yes—
143C23×D3C23×C311yescharacteristic
144C23×D3C23×C311yescharacteristic
145C22×C3×C4—23no—
146C22×C3×C4—23no—
147C22×C3×C4—33no—
148C22×C3×C4—312no—
149C22×C3×C4—33no—
150C22×C3×C4—66no—
151C22×C3×C4—66no—
152C22×C3×C4—66no—
153C22×C3×C4—66no—
154C22×C3×C4—66no—
155C22×C3×C4C22×D313yes—
156C22×C3×C4C22×D313yes—
157C22×C3×C4C23×C313yes—
158C22×C3×C4C23×C313yes—
159C22×Dic3C23×C313yes—
160C22×Dic3C23×C313yes—
161C2×C4×D3—26no—
162C2×C4×D3—26no—
163C2×C4×D3—26no—
164C2×C4×D3—26no—
165C2×C4×D3—26no—
166C2×C4×D3C3×D4112yes—
167C3×C4⋊C4—26no—
168C3×C4⋊C4—26no—
169C3×C4⋊C4—46no—
170C3×C4⋊C4—66no—
171C3×C4⋊C4—66no—
172C3×C4⋊C4—66no—
173C3×C22⋊C4—26no—
174C3×C22⋊C4—26no—
175C3×C22⋊C4—46no—
176C3×C22⋊C4—66no—
177C3×C22⋊C4—66no—
178C3×C22⋊C4—66no—
179#217—26no—
180(C2×D3)⋊C4—26no—
181(C2×D3)⋊C4—26no—
182C4⋊Dic3—26no—
183Dic3⋊C4—26no—
184Dic3⋊C4—26no—
185C22×C32—26no—
186C22×C32—43no—
187C22×C32—41no—
188C22×C32C22×D413yes—
189C22×C32C22×Q811yescharacteristic
190C22×C32C2×#4113yes—
191C2×C3×D3—26no—
192C2×C3×D3—43no—
193C2×C3×D3—41no—
194C2×C3×D3—416no—
195C2×C3×D3#121112yes—
196C2×C3×D3C22⋊Q8112yes—
197C2×C3×D3#12614yes—
198C32×C4—26no—
199C32×C4—43no—
200C3×Dic3—26no—
201C3×Dic3—43no—
202C25—31no—
203C23×C4—33no—
204C23×C4—33no—
205C2×C4⋊C4—33no—
206C2×C4⋊C4—33no—
207C2×C4⋊C4—33no—
208C2×C4⋊C4—612no—
209C2×C4⋊C4C2×C3×D313yescomplemented
210C2×C22⋊C4—33no—
211C2×C22⋊C4—33no—
212C2×C22⋊C4—33no—
213C2×C22⋊C4—612no—
214C2×C22⋊C4C2×C3×D313yes—
215#95—33no—
216#95C2×C3×D311yescharacteristic, complemented
217C23×C3—23no—
218C23×C3—23no—
219C23×C3—23no—
220C23×C3—23no—
221C23×C3—21no—
222C23×C3—22no—
223C23×C3—36no—
224C23×C3—32no—
225C23×C3—36no—
226C23×C3—32no—
227C23×C3—43no—
228C23×C3—43no—
229C23×C3—624no—
230C23×C3—63no—
231C23×C3—63no—
232C23×C3—124no—
233C23×C3—1212no—
234C23×C3D3×Q812yes—
235C23×C3C2×C3×Q812yes—
236C23×C3C23×D311yescharacteristic
237C23×C3C24×C311yescharacteristic
238C22×D3—23no—
239C22×D3—23no—
240C22×D3—224no—
241C22×D3—412no—
242C22×D3—44no—
243C22×D3C2×C3×D416yes—
244C22×D3C2×C3×Q812yes—
245C22×D3C2×C3×Q812yes—
246C22×D3C3×#4116yes—
247C2×C3×C4—23no—
248C2×C3×C4—23no—
249C2×C3×C4—23no—
250C2×C3×C4—23no—
251C2×C3×C4—23no—
252C2×C3×C4—23no—
253C2×C3×C4—23no—
254C2×C3×C4—23no—
255C2×C3×C4—23no—
256C2×C3×C4—23no—
257C2×C3×C4—26no—
258C2×C3×C4—36no—
259C2×C3×C4—43no—
260C2×C3×C4—43no—
261C2×C3×C4—43no—
262C2×C3×C4—43no—
263C2×C3×C4—43no—
264C2×C3×C4—624no—
265C2×C3×C4—63no—
266C2×C3×C4—63no—
267C2×C3×C4—63no—
268C2×C3×C4—63no—
269C2×C3×C4—63no—
270C2×C3×C4—1212no—
271C2×C3×C4D3×D416yes—
272C2×C3×C4C2×C3×D416yes—
273C2×Dic3—23no—
274C2×Dic3—23no—
275C2×Dic3—23no—
276C2×Dic3—23no—
277C2×Dic3—23no—
278C2×Dic3C2×C3×D416yes—
279C4×D3—224no—
280C4×D3—412no—
281C2×C32—42no—
282C2×C32C2×#12113yes—
283C2×C32C2×C22⋊Q813yes—
284C2×C32C2×#12611yescharacteristic
285C3×D3—42no—
286C3×D3#39618yesdirect product factor
287C24—31no—
288C24—31no—
289C24—34no—
290C24—66no—
291C24—66no—
292C24C22×C3×D311yescharacteristic
293C22×C4—33no—
294C22×C4—312no—
295C22×C4—33no—
296C22×C4—66no—
297C22×C4—66no—
298C22×C4—66no—
299C22×C4—66no—
300C22×C4—66no—
301C22×C4C22×C3×D313yes—
302C22×C4C22×C3×D313yes—
303C4⋊C4—26no—
304C4⋊C4—66no—
305C4⋊C4—66no—
306C4⋊C4—66no—
307C22⋊C4—26no—
308C22⋊C4—66no—
309C22⋊C4—66no—
310C22⋊C4—66no—
311C22×C3—26no—
312C22×C3—26no—
313C22×C3—23no—
314C22×C3—21no—
315C22×C3—23no—
316C22×C3—34no—
317C22×C3—312no—
318C22×C3—312no—
319C22×C3—46no—
320C22×C3—41no—
321C22×C3—43no—
322C22×C3—41no—
323C22×C3—43no—
324C22×C3—66no—
325C22×C3—83no—
326C22×C3—81no—
327C22×C3—1216no—
328C22×C3—121no—
329C22×C3—123no—
330C22×C3C2×D3×D413yes—
331C22×C3C2×D3×Q811yescharacteristic
332C22×C3D3×#4113yes—
333C22×C3C22×C3×D413yes—
334C22×C3C22×C3×Q811yescharacteristic
335C22×C3C2×C3×#4113yes—
336C2×D3—26no—
337C2×D3—43no—
338C2×D3—41no—
339C2×D3—416no—
340C2×D3C3×#121112yes—
341C2×D3C3×C22⋊Q8112yes—
342C2×D3C3×#12614yes—
343C3×C4—26no—
344C3×C4—26no—
345C3×C4—46no—
346C3×C4—43no—
347C3×C4—43no—
348C3×C4—66no—
349C3×C4—83no—
350C3×C4—123no—
351Dic3—26no—
352Dic3—43no—
353C32C2×#39611yescharacteristic, complemented, Sylow
354C23—23no—
355C23—23no—
356C23—36no—
357C23—32no—
358C23—36no—
359C23—32no—
360C23—624no—
361C23—63no—
362C23—63no—
363C23—1212no—
364C23—124no—
365C23C3×D3×Q812yes—
366C23C23×C3×D311yescharacteristic
367C2×C4—23no—
368C2×C4—23no—
369C2×C4—23no—
370C2×C4—23no—
371C2×C4—23no—
372C2×C4—36no—
373C2×C4—624no—
374C2×C4—63no—
375C2×C4—63no—
376C2×C4—63no—
377C2×C4—63no—
378C2×C4—63no—
379C2×C4—1212no—
380C2×C4C3×D3×D416yes—
381C2×C3—23no—
382C2×C3—23no—
383C2×C3—21no—
384C2×C3—38no—
385C2×C3—42no—
386C2×C3—42no—
387C2×C3—82no—
388C2×C3—122no—
389C2×C3D3×#12113yes—
390C2×C3D3×C22⋊Q813yes—
391C2×C3D3×#12611yescharacteristic
392C2×C3C2×C3×#12113yes—
393C2×C3C2×C3×C22⋊Q813yes—
394C2×C3C2×C3×#12611yescharacteristic
395D3—42no—
396D3C3×#39618yesdirect product factor
397C22—26no—
398C22—312no—
399C22—312no—
400C22—34no—
401C22—43no—
402C22—41no—
403C22—66no—
404C22—1216no—
405C22—123no—
406C22—121no—
407C22C2×C3×D3×D413yes—
408C22C2×C3×D3×Q811yescharacteristic
409C22C3×D3×#4113yes—
410C4—26no—
411C4—43no—
412C4—66no—
413C4—123no—
414C3—21no—
415C3D3×#39611yescharacteristic, direct product factor
416C3C2×C3×#39611yescharacteristic, complemented
417C2—38no—
418C2—42no—
419C2—122no—
420C2C3×D3×#12113yes—
421C2C3×D3×C22⋊Q813yes—
422C2C3×D3×#12611yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#396C2
socleC23×C32C24
prime radicalC24×C3×D3C22
hypercenterC3×#396D3
hypocenterC3C2×C3×#396
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#396

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×C4⋊C4C2semidirect
3. C32×#396C2semidirect
4. C3×#4994C2semidirect
5. C3×#4948C2semidirect
6. C3×#4676C2semidirect
7. C3×D3×#95C2semidirect
9. D3×#396C3direct (N × H)
13. C2×C32×C4⋊C4C22semidirect
18. C2×C3×C4⋊Dic3C22semidirect
19. C2×C3×Dic3⋊C4C22semidirect
20. C2×C3×Dic3⋊C4C22semidirect
23. C32×#95C22semidirect
24. C3×C3⋊#95C22semidirect
27. C2×D3×C4⋊C4C2×C3semidirect
33. C3×#396D3direct (N × H)
34. C3×#396C2×C3semidirect
36. #4994C2×C3semidirect
37. #4948C2×C3semidirect
38. #4676C2×C3semidirect
39. D3×#95C2×C3semidirect
76. C2×C3×C4⋊C4C2×D3semidirect
77. C2×C3×C4⋊C4C22×C3semidirect
88. C2×C4⋊Dic3C22×C3semidirect
89. C2×Dic3⋊C4C22×C3semidirect
90. C2×Dic3⋊C4C22×C3semidirect
95. C3×#95C2×D3semidirect
96. C3×#95C22×C3semidirect
97. C3⋊#95C22×C3semidirect
130. #396C3×D3direct (N × H)
209. C2×C4⋊C4C2×C3×D3semidirect
216. #95C2×C3×D3semidirect
286. C3×D3#396direct (N × H)
353. C32C2×#396semidirect
396. D3C3×#396direct (N × H)
415. C3D3×#396direct (N × H)
416. C3C2×C3×#396semidirect

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×#3962
C3×#49942
C3×#49482
C3×#46762
C3×D3×#952
C2×C3×#3963
D3×#3963