Finite Group Databasebeta

← C3×#76667 #11808737

Subgroups — C3×#76667 #11808737

Order 1152.

1841 conjugacy classes of subgroups.

The subgroup lattice has 383 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×Dic3C213yesmaximal, complemented
2C2×C3×#67⋊C4C213yesmaximal, complemented
3C32×#392C211yesmaximal, characteristic, complemented
4C3×#5223C213yesmaximal, complemented
5C3×#4949C213yesmaximal, complemented
6C3×#4677C211yesmaximal, characteristic, complemented
7C3×#4648C211yesmaximal, characteristic, complemented
8C3×#2397—31nomaximal
9#76667C311yesmaximal, characteristic, direct product factor
10C22×C32×D4C2213yes—
11C22×C3×#67C2213yes—
12C23×C3×Dic3C2213yes—
13C22×C3×C4×D3C2211yescharacteristic
14C2×C32×C22⋊C4C2213yes—
15C2×C3×#217C2216yes—
16C3×D4×Dic3—212no—
17C2×C3×(C2×D3)⋊C4C2213yes—
18C2×C3×C4⋊Dic3C2213yes—
19C2×C3×Dic3⋊C4C2213yes—
20C2×C3×C4×Dic3C2213yes—
21C3×#67⋊C4—212no—
22C32×#95C2211yescharacteristic
23C3×C3⋊#95C2213yes—
24C2×C3×C4×D4—33no—
25C2×C3×C4×D4—33no—
26C2×D4×Dic3C2×C313yescomplemented
27C2×#67⋊C4C2×C313yescomplemented
28C3×#399—33no—
29C3×#399—31no—
30C3×#392—21no—
31C3×#392—33no—
32C3×#392D311yescharacteristic, complemented
33C3×#392C2×C311yescharacteristic, complemented
34C3×#376—31no—
35#5223C2×C313yescomplemented
36#4949C2×C313yescomplemented
37#4677C2×C311yescharacteristic, complemented
38#4648C2×C311yescharacteristic, complemented
39C24×C32C2313yes—
40C23×C3×D3C2311yescharacteristic
41C2×C32×D4—212no—
42C2×C32×D4—26no—
43C22×C32×C4C2311yescharacteristic
44C22×C32×C4C2313yes—
45C2×C3×#67—26no—
46C2×C3×#67—26no—
47C2×C3×#67—26no—
48C22×C3×Dic3—26no—
49C22×C3×Dic3—212no—
50C22×C3×Dic3C2313yes—
51C22×C3×Dic3C2313yes—
52C22×C3×Dic3C2311yescharacteristic
53C2×C3×C4×D3—26no—
54C32×C22⋊C4—26no—
55C3×#217—212no—
56C3×(C2×D3)⋊C4—26no—
57C3×C4⋊Dic3—26no—
58C3×Dic3⋊C4—26no—
59C3×C4×Dic3D4112yescomplemented
60#2397—31noSylow
61C22×C3×D4—23no—
62C22×C3×D4—33no—
63C22×C3×D4C2×D313yes—
64C22×C3×D4C22×C313yes—
65C23×C3×C4—33no—
66C23×C3×C4—31no—
67C22×#67C22×C313yes—
68C23×Dic3C22×C313yes—
69C22×C4×D3C22×C311yescharacteristic
70C3×C4×D4—612no—
71C3×C4×D4—612no—
72C2×C3×C4⋊C4—33no—
73C2×C3×C4⋊C4—33no—
74C2×C3×C22⋊C4—23no—
75C2×C3×C22⋊C4—36no—
76C2×C3×C22⋊C4—33no—
77C2×C3×C22⋊C4C2×D313yes—
78C2×C3×C22⋊C4C22×C313yes—
79C2×C3×C42—33no—
80C2×#217C22×C316yes—
81D4×Dic3—212no—
82C2×(C2×D3)⋊C4C22×C313yes—
83C2×C4⋊Dic3C22×C313yes—
84C2×Dic3⋊C4C22×C313yes—
85C2×C4×Dic3C22×C313yes—
86#67⋊C4—212no—
87C3×#95—21no—
88C3×#95—33no—
89C3×#95C2×D311yescharacteristic
90C3×#95C22×C311yescharacteristic
91C3⋊#95C22×C313yes—
92C23×C32—26no—
93C23×C32—23no—
94C23×C32—23no—
95C23×C32—26no—
96C23×C32#4116yes—
97C23×C32C2411yescharacteristic
98C22×C3×D3—23no—
99C22×C3×D3—23no—
100C22×C3×D3#4112yes—
101C32×D4—224no—
102C2×C32×C4—26no—
103C2×C32×C4—23no—
104C2×C32×C4C2×D416yes—
105C3×#67—224no—
106C2×C3×Dic3—23no—
107C2×C3×Dic3—23no—
108C2×C3×Dic3—23no—
109C2×C3×Dic3—26no—
110C2×C3×Dic3—412no—
111C2×C3×Dic3C2×D416yes—
112C2×C3×Dic3C2×D416yes—
113C3×C4×D3—44no—
114C2×C4×D4—33no—
115C2×C4×D4—33no—
116#399—33no—
117#399—31no—
118#392—33no—
119#392C3×D311yescharacteristic, complemented
120#376—31no—
121C24×C3—23no—
122C24×C3—31no—
123C24×C3C22×D313yes—
124C24×C3C23×C313yes—
125C23×D3C23×C311yescharacteristic
126C2×C3×D4—212no—
127C2×C3×D4—212no—
128C2×C3×D4—26no—
129C2×C3×D4—26no—
130C2×C3×D4—46no—
131C2×C3×D4—412no—
132C2×C3×D4—66no—
133C2×C3×D4—66no—
134C2×C3×D4—66no—
135C22×C3×C4—23no—
136C22×C3×C4—21no—
137C22×C3×C4—31no—
138C22×C3×C4—33no—
139C22×C3×C4—33no—
140C22×C3×C4—66no—
141C22×C3×C4—66no—
142C22×C3×C4—612no—
143C22×C3×C4C22×D311yescharacteristic
144C22×C3×C4C22×D313yes—
145C22×C3×C4C23×C311yescharacteristic
146C22×C3×C4C23×C313yes—
147C2×#67—26no—
148C2×#67—26no—
149C2×#67—26no—
150C22×Dic3—26no—
151C22×Dic3—212no—
152C22×Dic3C23×C313yes—
153C22×Dic3C23×C313yes—
154C22×Dic3C23×C311yescharacteristic
155C2×C4×D3—26no—
156C3×C4⋊C4—66no—
157C3×C4⋊C4—66no—
158C3×C22⋊C4—26no—
159C3×C22⋊C4—26no—
160C3×C22⋊C4—46no—
161C3×C22⋊C4—612no—
162C3×C22⋊C4—66no—
163C3×C42—312no—
164#217—212no—
165(C2×D3)⋊C4—26no—
166C4⋊Dic3—26no—
167Dic3⋊C4—26no—
168C4×Dic3C3×D4112yescomplemented
169C22×C32—26no—
170C22×C32—212no—
171C22×C32—43no—
172C22×C32—46no—
173C22×C32—43no—
174C22×C32C22×D413yes—
175C22×C32C2×#4113yes—
176C22×C32C2×#4111yescharacteristic
177C2×C3×D3—26no—
178C2×C3×D3—43no—
179C2×C3×D3—41no—
180C32×C4—26no—
181C32×C4—41no—
182C3×Dic3—26no—
183C3×Dic3—43no—
184C3×Dic3#12714yes—
185C22×D4—33no—
186C22×D4C2×C3×D313yes—
187C23×C4—33no—
188C23×C4—31no—
189C4×D4—612no—
190C4×D4—612no—
191C2×C4⋊C4—33no—
192C2×C4⋊C4—33no—
193C2×C22⋊C4—36no—
194C2×C22⋊C4—33no—
195C2×C22⋊C4C2×C3×D313yes—
196C2×C42—33no—
197#95—33no—
198#95C2×C3×D311yescharacteristic
199C23×C3—23no—
200C23×C3—26no—
201C23×C3—26no—
202C23×C3—23no—
203C23×C3—26no—
204C23×C3—23no—
205C23×C3—23no—
206C23×C3—26no—
207C23×C3—21no—
208C23×C3—26no—
209C23×C3—32no—
210C23×C3—43no—
211C23×C3—46no—
212C23×C3—46no—
213C23×C3—43no—
214C23×C3—63no—
215C23×C3—63no—
216C23×C3#23716yes—
217C23×C3C3×#4116yes—
218C23×C3C23×D311yescharacteristic
219C23×C3C24×C311yescharacteristic
220C22×D3—23no—
221C22×D3—23no—
222C22×D3C3×#4112yes—
223C3×D4—224no—
224C3×D4—224no—
225C3×D4—424no—
226C3×D4—624no—
227C2×C3×C4—26no—
228C2×C3×C4—26no—
229C2×C3×C4—23no—
230C2×C3×C4—23no—
231C2×C3×C4—26no—
232C2×C3×C4—36no—
233C2×C3×C4—36no—
234C2×C3×C4—46no—
235C2×C3×C4—43no—
236C2×C3×C4—63no—
237C2×C3×C4—63no—
238C2×C3×C4—63no—
239C2×C3×C4—66no—
240C2×C3×C4—124no—
241C2×C3×C4—1212no—
242C2×C3×C4D3×D416yes—
243C2×C3×C4C2×C3×D416yes—
244#67—224no—
245C2×Dic3—23no—
246C2×Dic3—23no—
247C2×Dic3—23no—
248C2×Dic3—26no—
249C2×Dic3—412no—
250C2×Dic3C2×C3×D416yes—
251C2×Dic3C2×C3×D416yes—
252C4×D3—44no—
253C2×C32—46no—
254C2×C32#52513yes—
255C2×C32#52513yes—
256C2×C32C2×#12711yescharacteristic
257C3×D3—42no—
258C24—31no—
259C24C22×C3×D313yes—
260C2×D4—212no—
261C2×D4—26no—
262C2×D4—66no—
263C2×D4—66no—
264C2×D4—66no—
265C22×C4—31no—
266C22×C4—33no—
267C22×C4—33no—
268C22×C4—66no—
269C22×C4—66no—
270C22×C4—612no—
271C22×C4C22×C3×D311yescharacteristic
272C22×C4C22×C3×D313yes—
273C4⋊C4—66no—
274C4⋊C4—66no—
275C22⋊C4—26no—
276C22⋊C4—612no—
277C22⋊C4—66no—
278C42—312no—
279C22×C3—212no—
280C22×C3—26no—
281C22×C3—212no—
282C22×C3—26no—
283C22×C3—23no—
284C22×C3—23no—
285C22×C3—21no—
286C22×C3—412no—
287C22×C3—46no—
288C22×C3—43no—
289C22×C3—43no—
290C22×C3—43no—
291C22×C3—46no—
292C22×C3—43no—
293C22×C3—46no—
294C22×C3—66no—
295C22×C3—83no—
296C22×C3—86no—
297C22×C3—83no—
298C22×C3—121no—
299C22×C3—123no—
300C22×C3C2×D3×D413yes—
301C22×C3C2×#23713yes—
302C22×C3D3×#4111yescharacteristic
303C22×C3C22×C3×D413yes—
304C22×C3C2×C3×#4113yes—
305C22×C3C2×C3×#4111yescharacteristic
306C2×D3—26no—
307C2×D3—43no—
308C2×D3—41no—
309C3×C4—26no—
310C3×C4—26no—
311C3×C4—34no—
312C3×C4—46no—
313C3×C4—41no—
314C3×C4—41no—
315C3×C4—66no—
316C3×C4—81no—
317C3×C4—123no—
318Dic3—26no—
319Dic3—43no—
320Dic3C3×#12714yes—
321C32#239711yescharacteristic, complemented, Sylow
322C23—23no—
323C23—26no—
324C23—26no—
325C23—23no—
326C23—32no—
327C23—63no—
328C23—63no—
329C23C3×#23716yes—
330C23C23×C3×D311yescharacteristic
331D4—224no—
332D4—624no—
333C2×C4—26no—
334C2×C4—23no—
335C2×C4—36no—
336C2×C4—36no—
337C2×C4—63no—
338C2×C4—63no—
339C2×C4—66no—
340C2×C4—63no—
341C2×C4—124no—
342C2×C4—1212no—
343C2×C4C3×D3×D416yes—
344C2×C3—23no—
345C2×C3—23no—
346C2×C3—21no—
347C2×C3—46no—
348C2×C3—46no—
349C2×C3—86no—
350C2×C3—122no—
351C2×C3#558613yes—
352C2×C3#560613yes—
353C2×C3D3×#12711yescharacteristic
354C2×C3C3×#52513yes—
355C2×C3C3×#52513yes—
356C2×C3C2×C3×#12711yescharacteristic
357D3—42no—
358C22—212no—
359C22—26no—
360C22—43no—
361C22—46no—
362C22—43no—
363C22—66no—
364C22—123no—
365C22—121no—
366C22C2×C3×D3×D413yes—
367C22C2×C3×#23713yes—
368C22C3×D3×#4111yescharacteristic
369C4—26no—
370C4—34no—
371C4—41no—
372C4—66no—
373C4—123no—
374C3—21no—
375C3#7666711yescharacteristic, direct product factor
376C3C3×#239711yescharacteristic, complemented
377C2—46no—
378C2—122no—
379C2C3×#558613yes—
380C2C3×#560613yes—
381C2C3×D3×#12711yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#392C2
socleC23×C32C24
hypercenterC3×#392D3
hypocenterC3C3×#2397
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#392

Complements

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

NH ≅ G/Ntype
1. C2×C3×D4×Dic3C2semidirect
2. C2×C3×#67⋊C4C2semidirect
3. C32×#392C2semidirect
4. C3×#5223C2semidirect
5. C3×#4949C2semidirect
6. C3×#4677C2semidirect
7. C3×#4648C2semidirect
9. #76667C3direct (N × H)
26. C2×D4×Dic3C2×C3semidirect
27. C2×#67⋊C4C2×C3semidirect
32. C3×#392D3semidirect
33. C3×#392C2×C3semidirect
35. #5223C2×C3semidirect
36. #4949C2×C3semidirect
37. #4677C2×C3semidirect
38. #4648C2×C3semidirect
59. C3×C4×Dic3D4semidirect
119. #392C3×D3semidirect
168. C4×Dic3C3×D4semidirect
321. C32#2397semidirect
375. C3#76667direct (N × H)
376. C3C3×#2397semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×Dic32
C2×C3×#67⋊C42
C32×#3922
C3×#52232
C3×#49492
C3×#46772
C3×#46482
C3×#23973
#766673