Finite Group Databasebeta

← C3×#70760 #11774426

Subgroups — C3×#70760 #11774426

Order 1152.

483 conjugacy classes of subgroups.

The subgroup lattice has 399 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5479C211yesmaximal, characteristic
2C32×#431C211yesmaximal, characteristic, complemented
3C3×#4925C211yesmaximal, characteristic, complemented
4C3×#4459C212yesmaximal, complemented
5C3×#4456C212yesmaximal, complemented
6C3×#1482—31nomaximal
7#70760C311yesmaximal, characteristic, direct product factor
8C2×C32×C42C2211yescharacteristic
9C3×#930C411yescharacteristic
10C3×#929—21no—
11C3×C4×#67—21no—
12C3×#924C411yescharacteristic
13C3×#876—21no—
14C3×#875C411yescharacteristic
15C3×C4×D12C2211yescharacteristic
16C3×#872—21no—
17C3×#870C411yescharacteristic
18C3×C4×Dic6C2211yescharacteristic
19C32×C4⋊C8—21no—
20C32×C22⋊C8—21no—
21C32×C4×C8C2212yes—
22C3×#830—21no—
23C3×C4⋊(C3⋊C8)C2212yes—
24C3×C4×C3⋊C8—21no—
25C3×#529—31no—
26#5479C2×C311yescharacteristic
27C3×#431—21no—
28C3×#431—31no—
29C3×#431D311yescharacteristic, complemented
30C3×#431C2×C311yescharacteristic, complemented
31#4925C2×C311yescharacteristic, complemented
32C3×Q8⋊C8—32no—
33C3×D4⋊C8—32no—
34#4459C2×C312yescomplemented
35#4456C2×C312yescomplemented
36C22×C32×C4C2×C411yescharacteristic
37C22×C32×C4D411yescharacteristic
38C22×C32×C4D411yescharacteristic
39C2×C3×#67—21no—
40C2×C3×D12C2×C411yescharacteristic
41C2×C3×C4×D3—21no—
42C2×C3×Dic6C2×C411yescharacteristic
43C2×C32×C8—22no—
44C32×C42C2×C411yescharacteristic
45C32×C42D411yescharacteristic
46C32×C42D411yescharacteristic
47C32×C42C2311yescharacteristic
48C3×#217—21no—
49C3×(C2×D3)⋊C4—21no—
50C3×(C2×D3)⋊C4—21no—
51C3×(C2×D3)⋊C4—21no—
52C3×(C2×D3)⋊C4—21no—
53C3×C4⋊Dic3C2×C411yescharacteristic
54C3×C4⋊Dic3C2×C411yescharacteristic
55C3×Dic3⋊C4—21no—
56C3×Dic3⋊C4—21no—
57C3×Dic3⋊C4—21no—
58C3×Dic3⋊C4—21no—
59C3×C4×Dic3—21no—
60C2×C3×C3⋊C8—22no—
61#1482—31noSylow
62C3×#126—61no—
63C3×#125—31no—
64C3×#124—31no—
65C3×#123—61no—
66C3×C22⋊Q8—31no—
67C3×#121—31no—
68C3×C4×Q8—31no—
69C3×C4×D4—31no—
70C3×C4×D4—61no—
71C3×#117—61no—
72C2×C3×C42—21no—
73C2×C3×C42C2×D311yescharacteristic
74C2×C3×C42C22×C311yescharacteristic
75#930C3×C411yescharacteristic
76#929—21no—
77C4×#67—21no—
78#924C3×C411yescharacteristic
79#876—21no—
80#875C3×C411yescharacteristic
81C4×D12C22×C311yescharacteristic
82#872—21no—
83#870C3×C411yescharacteristic
84C4×Dic6C22×C311yescharacteristic
85C3×C4⋊C8—22no—
86C3×C4⋊C8—21no—
87C3×C4⋊C8—21no—
88C3×C4⋊C8—32no—
89C3×C22⋊C8—22no—
90C3×C22⋊C8—21no—
91C3×C22⋊C8—21no—
92C3×C22⋊C8—61no—
93C3×C4×C8—22no—
94C3×C4×C8—61no—
95C3×C4×C8C2×D312yes—
96C3×C4×C8C22×C312yes—
97#830—21no—
98C4⋊(C3⋊C8)C22×C312yes—
99C4×C3⋊C8—21no—
100C23×C32C22⋊C411yescharacteristic
101C22×C3×D3—21no—
102C2×C32×C4—22no—
103C2×C32×C4—22no—
104C2×C32×C4—41no—
105C2×C32×C4C22⋊C411yescharacteristic
106C2×C32×C4C22⋊C411yescharacteristic
107C2×C32×C4C22⋊C411yescharacteristic
108C2×C32×C4C22×C411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C3×#67—42no—
112C2×C3×Dic3—21no—
113C2×C3×Dic3—21no—
114C2×C3×Dic3—21no—
115C3×D12—22no—
116C3×C4×D3—42no—
117C3×Dic6—22no—
118C32×C8—42no—
119C3×C3⋊C8—42no—
120#529—31no—
121#431—31no—
122#431C3×D311yescharacteristic, complemented
123Q8⋊C8—32no—
124D4⋊C8—32no—
125C2×C3×Q8—31no—
126C2×C3×D4—31no—
127C2×C3×D4—61no—
128C22×C3×C4—21no—
129C22×C3×C4—21no—
130C22×C3×C4—21no—
131C22×C3×C4—61no—
132C22×C3×C4C4×D311yescharacteristic
133C22×C3×C4D1211yescharacteristic
134C22×C3×C4#6711yescharacteristic
135C22×C3×C4C2×C3×C411yescharacteristic
136C22×C3×C4C3×D411yescharacteristic
137C22×C3×C4C3×D411yescharacteristic
138C2×#67—21no—
139C2×D12C2×C3×C411yescharacteristic
140C2×C4×D3—21no—
141C2×Dic6C2×C3×C411yescharacteristic
142C2×C3×C8—24no—
143C2×C3×C8—22no—
144C2×C3×C8—22no—
145C2×C3×C8—62no—
146C3×C4⋊C4—31no—
147C3×C4⋊C4—31no—
148C3×C4⋊C4—61no—
149C3×C4⋊C4—61no—
150C3×C4⋊C4—61no—
151C3×C4⋊C4—61no—
152C3×C22⋊C4—61no—
153C3×C22⋊C4—61no—
154C3×C22⋊C4—61no—
155C3×C22⋊C4—61no—
156C3×C22⋊C4—61no—
157C3×C42—21no—
158C3×C42—21no—
159C3×C42—21no—
160C3×C42—21no—
161C3×C42—61no—
162C3×C42C4×D311yescharacteristic
163C3×C42D1211yescharacteristic
164C3×C42#6711yescharacteristic
165C3×C42C2×C3×C411yescharacteristic
166C3×C42C3×D411yescharacteristic
167C3×C42C3×D411yescharacteristic
168C3×C42C22×D311yescharacteristic
169C3×C42C23×C311yescharacteristic
170#217—21no—
171(C2×D3)⋊C4—21no—
172(C2×D3)⋊C4—21no—
173(C2×D3)⋊C4—21no—
174(C2×D3)⋊C4—21no—
175C4⋊Dic3C2×C3×C411yescharacteristic
176C4⋊Dic3C2×C3×C411yescharacteristic
177Dic3⋊C4—21no—
178Dic3⋊C4—21no—
179Dic3⋊C4—21no—
180Dic3⋊C4—21no—
181C4×Dic3—21no—
182C2×C3⋊C8—22no—
183C22×C32—21no—
184C22×C32—21no—
185C22×C32—21no—
186C22×C32C2×C22⋊C411yescharacteristic
187C2×C3×D3—41no—
188C2×C3×D3—41no—
189C2×C3×D3—41no—
190C32×C4—21no—
191C32×C4—21no—
192C32×C4—21no—
193C32×C4—21no—
194C32×C4#13112yes—
195C32×C4#13512yes—
196C3×Dic3—41no—
197C3×Dic3—41no—
198C3×Dic3—41no—
199#126—61no—
200#125—31no—
201#124—31no—
202#123—61no—
203C22⋊Q8—31no—
204#121—31no—
205C4×Q8—31no—
206C4×D4—31no—
207C4×D4—61no—
208#117—61no—
209C2×C42C2×C3×D311yescharacteristic
210C4⋊C8—21no—
211C4⋊C8—32no—
212C22⋊C8—21no—
213C22⋊C8—61no—
214C4×C8—61no—
215C4×C8C2×C3×D312yes—
216C23×C3—21no—
217C23×C3—61no—
218C23×C3(C2×D3)⋊C411yescharacteristic
219C23×C3C3×C22⋊C411yescharacteristic
220C22×D3—21no—
221C3×Q8—62no—
222C3×D4—62no—
223C3×D4—122no—
224C2×C3×C4—24no—
225C2×C3×C4—22no—
226C2×C3×C4—22no—
227C2×C3×C4—22no—
228C2×C3×C4—22no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—42no—
236C2×C3×C4—41no—
237C2×C3×C4—41no—
238C2×C3×C4—42no—
239C2×C3×C4—61no—
240C2×C3×C4—61no—
241C2×C3×C4—61no—
242C2×C3×C4—122no—
243C2×C3×C4(C2×D3)⋊C411yescharacteristic
244C2×C3×C4(C2×D3)⋊C411yescharacteristic
245C2×C3×C4(C2×D3)⋊C411yescharacteristic
246C2×C3×C4C3×C22⋊C411yescharacteristic
247C2×C3×C4C3×C22⋊C411yescharacteristic
248C2×C3×C4C3×C22⋊C411yescharacteristic
249C2×C3×C4C2×C4×D311yescharacteristic
250C2×C3×C4C2×D1211yescharacteristic
251C2×C3×C4C2×#6711yescharacteristic
252C2×C3×C4C22×C3×C411yescharacteristic
253C2×C3×C4C2×C3×D411yescharacteristic
254C2×C3×C4C2×C3×D411yescharacteristic
255#67—42no—
256C2×Dic3—21no—
257C2×Dic3—21no—
258C2×Dic3—21no—
259D12—22no—
260C4×D3—42no—
261Dic6—22no—
262C3×C8—44no—
263C3×C8—42no—
264C3×C8—42no—
265C3×C8—122no—
266C3⋊C8—42no—
267C2×C32—41no—
268C2×C32#40811yescharacteristic
269C2×C32#41611yescharacteristic
270C2×C32#42111yescharacteristic
271C3×D3—81no—
272C2×Q8—31no—
273C2×D4—31no—
274C2×D4—61no—
275C22×C4—61no—
276C22×C4C3×C4×D311yescharacteristic
277C22×C4C3×D1211yescharacteristic
278C22×C4C3×#6711yescharacteristic
279C2×C8—22no—
280C2×C8—62no—
281C4⋊C4—31no—
282C4⋊C4—31no—
283C4⋊C4—61no—
284C4⋊C4—61no—
285C4⋊C4—61no—
286C4⋊C4—61no—
287C22⋊C4—61no—
288C22⋊C4—61no—
289C22⋊C4—61no—
290C22⋊C4—61no—
291C22⋊C4—61no—
292C42—61no—
293C42C3×C4×D311yescharacteristic
294C42C3×D1211yescharacteristic
295C42C3×#6711yescharacteristic
296C42C22×C3×D311yescharacteristic
297C22×C3—22no—
298C22×C3—21no—
299C22×C3—21no—
300C22×C3—21no—
301C22×C3—21no—
302C22×C3—21no—
303C22×C3—21no—
304C22×C3—21no—
305C22×C3—41no—
306C22×C3—41no—
307C22×C3—121no—
308C22×C3—121no—
309C22×C3—121no—
310C22×C3C2×(C2×D3)⋊C411yescharacteristic
311C22×C3C2×C3×C22⋊C411yescharacteristic
312C2×D3—41no—
313C2×D3—41no—
314C2×D3—41no—
315C3×C4—22no—
316C3×C4—22no—
317C3×C4—21no—
318C3×C4—21no—
319C3×C4—21no—
320C3×C4—21no—
321C3×C4—21no—
322C3×C4—21no—
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—22no—
326C3×C4—22no—
327C3×C4—41no—
328C3×C4—41no—
329C3×C4—121no—
330C3×C4—121no—
331C3×C4—121no—
332C3×C4#90412yes—
333C3×C4#90712yes—
334C3×C4C3×#13112yes—
335C3×C4C3×#13512yes—
336Dic3—41no—
337Dic3—41no—
338Dic3—41no—
339C32#148211yescharacteristic, complemented, Sylow
340C23—61no—
341C23C3×(C2×D3)⋊C411yescharacteristic
342Q8—62no—
343D4—62no—
344D4—122no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—41no—
348C2×C4—61no—
349C2×C4—61no—
350C2×C4—61no—
351C2×C4—122no—
352C2×C4C3×(C2×D3)⋊C411yescharacteristic
353C2×C4C3×(C2×D3)⋊C411yescharacteristic
354C2×C4C3×(C2×D3)⋊C411yescharacteristic
355C2×C4C2×C3×C4×D311yescharacteristic
356C2×C4C2×C3×D1211yescharacteristic
357C2×C4C2×C3×#6711yescharacteristic
358C8—42no—
359C8—122no—
360C2×C3—21no—
361C2×C3—21no—
362C2×C3—21no—
363C2×C3—42no—
364C2×C3—41no—
365C2×C3—41no—
366C2×C3—241no—
367C2×C3#500511yescharacteristic
368C2×C3#511311yescharacteristic
369C2×C3#512911yescharacteristic
370C2×C3C3×#40811yescharacteristic
371C2×C3C3×#41611yescharacteristic
372C2×C3C3×#42111yescharacteristic
373D3—81no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—121no—
378C22—121no—
379C22—121no—
380C22C2×C3×(C2×D3)⋊C411yescharacteristic
381C4—21no—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—121no—
386C4—121no—
387C4—121no—
388C4C3×#90412yes—
389C4C3×#90712yes—
390C3—21no—
391C3#7076011yescharacteristic, direct product factor
392C3C3×#148211yescharacteristic, complemented
393C2—41no—
394C2—241no—
395C2C3×#500511yescharacteristic
396C2C3×#511311yescharacteristic
397C2C3×#512911yescharacteristic
subgroupG/H
centerC2×C3×C4C2×D12
commutatorC2×C3×C4C22×C3×C4
FrattiniC42C22×C3×D3
FittingC32×#431C2
socleC22×C32C2×C22⋊C4
prime radicalC3×#930C4
cosocleC3×C42C23×C3
hypercenterC3×#431D3
hypocenterC3C3×#1482
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C3×#431

Complements

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

NH ≅ G/Ntype
2. C32×#431C2semidirect
3. C3×#4925C2semidirect
4. C3×#4459C2semidirect
5. C3×#4456C2semidirect
7. #70760C3direct (N × H)
29. C3×#431D3semidirect
30. C3×#431C2×C3semidirect
31. #4925C2×C3semidirect
34. #4459C2×C3semidirect
35. #4456C2×C3semidirect
122. #431C3×D3semidirect
339. C32#1482semidirect
391. C3#70760direct (N × H)
392. C3C3×#1482semidirect

Maximal subgroups

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

subgroupindex
C3×#54792
C32×#4312
C3×#49252
C3×#44592
C3×#44562
C3×#14823
#707603