Finite Group Databasebeta

← C3×#70763 #11774612

Subgroups — C3×#70763 #11774612

Order 1152.

551 conjugacy classes of subgroups.

The subgroup lattice has 433 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#235C211yesmaximal, characteristic
2C32×#431C211yesmaximal, characteristic, complemented
3C3×#4926C211yesmaximal, characteristic, complemented
4C3×#4459C212yesmaximal, complemented
5C3×#4456C212yesmaximal, complemented
6C3×#1488—31nomaximal
7#70763C311yesmaximal, characteristic, direct product factor
8C2×C3×#235C411yescharacteristic
9C2×C32×C42C2211yescharacteristic
10C3×C4×#67—21no—
11C3×C4×#67—21no—
12C3×#926C411yescharacteristic
13C3×C4×D12C411yescharacteristic
14C3×C4×D12C2211yescharacteristic
15C3×#872—21no—
16C3×C42×D3—21no—
17C3×C4×Dic6C411yescharacteristic
18C3×C4×Dic6C2211yescharacteristic
19C32×C4⋊C8—21no—
20C32×C22⋊C8—21no—
21C32×C4×C8C2212yes—
22C3×#830—21no—
23C3×C4⋊(C3⋊C8)C2212yes—
24C3×#803—21no—
25C3×C4×#41—31no—
26C4×#235C2×C311yescharacteristic
27C3×#432—31no—
28C3×#431—21no—
29C3×#431D311yescharacteristic, complemented
30C3×#431C2×C311yescharacteristic, complemented
31#4926C2×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—
40C3×#235—22no—
41C3×#235—22no—
42C2×C3×D12C2×C411yescharacteristic
43C2×C3×C4×D3—21no—
44C2×C3×C4×D3—21no—
45C2×C3×C4×D3—21no—
46C2×C3×Dic6C2×C411yescharacteristic
47C2×C32×C8—22no—
48C32×C42C2×C411yescharacteristic
49C32×C42D411yescharacteristic
50C32×C42D411yescharacteristic
51C32×C42C2311yescharacteristic
52C3×#217—21no—
53C3×(C2×D3)⋊C4—21no—
54C3×(C2×D3)⋊C4—21no—
55C3×C4⋊Dic3C2×C411yescharacteristic
56C3×C4⋊Dic3C2×C411yescharacteristic
57C3×Dic3⋊C4—21no—
58C3×Dic3⋊C4—21no—
59C3×C4×Dic3—21no—
60C3×C4×Dic3—21no—
61C3×C4×Dic3—21no—
62C2×C3×C3⋊C8—22no—
63#1488—31noSylow
64C2×C3×#41—31no—
65C2×#235C3×C411yescharacteristic
66C3×C4×Q8—31no—
67C3×C4×Q8—31no—
68C3×C4×D4—31no—
69C3×C4×D4—31no—
70C3×C4×D4—61no—
71C3×C4×D4—61no—
72C3×#117—31no—
73C3×#117—61no—
74C2×C3×C42—21no—
75C2×C3×C42—61no—
76C2×C3×C42C2×D311yescharacteristic
77C2×C3×C42C22×C311yescharacteristic
78C4×#67—21no—
79C4×#67—21no—
80#926C3×C411yescharacteristic
81C4×D12C3×C411yescharacteristic
82C4×D12C22×C311yescharacteristic
83#872—21no—
84C42×D3—21no—
85C4×Dic6C3×C411yescharacteristic
86C4×Dic6C22×C311yescharacteristic
87C3×C4⋊C8—22no—
88C3×C4⋊C8—21no—
89C3×C4⋊C8—21no—
90C3×C4⋊C8—32no—
91C3×C22⋊C8—22no—
92C3×C22⋊C8—21no—
93C3×C22⋊C8—21no—
94C3×C22⋊C8—61no—
95C3×#97—61no—
96C3×C4×C8—22no—
97C3×C4×C8C2×D312yes—
98C3×C4×C8C22×C312yes—
99#830—21no—
100C4⋊(C3⋊C8)C22×C312yes—
101#803—21no—
102C23×C32C22⋊C411yescharacteristic
103C22×C3×D3—21no—
104C2×C32×C4—22no—
105C2×C32×C4—21no—
106C2×C32×C4—21no—
107C2×C32×C4—41no—
108C2×C32×C4C22⋊C411yescharacteristic
109C2×C32×C4C22⋊C411yescharacteristic
110C2×C32×C4C22⋊C411yescharacteristic
111C2×C32×C4C22×C411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C3×#67—24no—
115C2×C3×Dic3—21no—
116C2×C3×Dic3—21no—
117C2×C3×Dic3—21no—
118C3×D12—21no—
119C3×D12M1612yes—
120C3×C4×D3—24no—
121C3×C4×D3—42no—
122C3×C4×D3—42no—
123C3×Dic6—21no—
124C3×Dic6M1612yes—
125C32×C8—42no—
126C3×C3⋊C8—42no—
127C4×#41—31no—
128#432—31no—
129#431C3×D311yescharacteristic, complemented
130Q8⋊C8—32no—
131D4⋊C8—32no—
132C3×#41—62no—
133C3×#41—62no—
134C2×C3×Q8—31no—
135C2×C3×D4—31no—
136C2×C3×D4—61no—
137C22×C3×C4—21no—
138C22×C3×C4—21no—
139C22×C3×C4—21no—
140C22×C3×C4—61no—
141C22×C3×C4—61no—
142C22×C3×C4—61no—
143C22×C3×C4C4×D311yescharacteristic
144C22×C3×C4D1211yescharacteristic
145C22×C3×C4#6711yescharacteristic
146C22×C3×C4C2×C3×C411yescharacteristic
147C22×C3×C4C3×D411yescharacteristic
148C22×C3×C4C3×D411yescharacteristic
149C2×#67—21no—
150#235—22no—
151#235—22no—
152C2×D12C2×C3×C411yescharacteristic
153C2×C4×D3—21no—
154C2×C4×D3—21no—
155C2×C4×D3—21no—
156C2×Dic6C2×C3×C411yescharacteristic
157C2×C3×C8—24no—
158C2×C3×C8—22no—
159C2×C3×C8—22no—
160C2×C3×C8—62no—
161C3×C4⋊C4—31no—
162C3×C4⋊C4—31no—
163C3×C4⋊C4—61no—
164C3×C4⋊C4—61no—
165C3×C22⋊C4—61no—
166C3×C22⋊C4—61no—
167C3×C22⋊C4—61no—
168C3×C42—21no—
169C3×C42—21no—
170C3×C42—21no—
171C3×C42—21no—
172C3×C42—61no—
173C3×C42—61no—
174C3×C42—61no—
175C3×C42C4×D311yescharacteristic
176C3×C42D1211yescharacteristic
177C3×C42#6711yescharacteristic
178C3×C42C2×C3×C411yescharacteristic
179C3×C42C3×D411yescharacteristic
180C3×C42C3×D411yescharacteristic
181C3×C42C22×D311yescharacteristic
182C3×C42C23×C311yescharacteristic
183#217—21no—
184(C2×D3)⋊C4—21no—
185(C2×D3)⋊C4—21no—
186C4⋊Dic3C2×C3×C411yescharacteristic
187C4⋊Dic3C2×C3×C411yescharacteristic
188Dic3⋊C4—21no—
189Dic3⋊C4—21no—
190C4×Dic3—21no—
191C4×Dic3—21no—
192C4×Dic3—21no—
193C2×C3⋊C8—22no—
194C22×C32—21no—
195C22×C32—21no—
196C22×C32—21no—
197C22×C32C2×C22⋊C411yescharacteristic
198C2×C3×D3—22no—
199C2×C3×D3—41no—
200C2×C3×D3—41no—
201C32×C4—21no—
202C32×C4—21no—
203C32×C4—21no—
204C32×C4—21no—
205C32×C4C2×M1611yescharacteristic
206C32×C4C2×M1611yescharacteristic
207C32×C4#13512yes—
208C3×Dic3—22no—
209C3×Dic3—41no—
210C3×Dic3—41no—
211C2×#41—31no—
212C4×Q8—31no—
213C4×Q8—31no—
214C4×D4—31no—
215C4×D4—31no—
216C4×D4—61no—
217C4×D4—61no—
218#117—31no—
219#117—61no—
220C2×C42—61no—
221C2×C42C2×C3×D311yescharacteristic
222C4⋊C8—21no—
223C4⋊C8—32no—
224C22⋊C8—21no—
225C22⋊C8—61no—
226#97—61no—
227C4×C8C2×C3×D312yes—
228C23×C3—21no—
229C23×C3—61no—
230C23×C3(C2×D3)⋊C411yescharacteristic
231C23×C3C3×C22⋊C411yescharacteristic
232C22×D3—21no—
233C3×Q8—32no—
234C3×Q8—61no—
235C3×D4—32no—
236C3×D4—64no—
237C3×D4—61no—
238C2×C3×C4—24no—
239C2×C3×C4—22no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—22no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—41no—
252C2×C3×C4—41no—
253C2×C3×C4—41no—
254C2×C3×C4—41no—
255C2×C3×C4—42no—
256C2×C3×C4—64no—
257C2×C3×C4—61no—
258C2×C3×C4—61no—
259C2×C3×C4—61no—
260C2×C3×C4—122no—
261C2×C3×C4—122no—
262C2×C3×C4(C2×D3)⋊C411yescharacteristic
263C2×C3×C4(C2×D3)⋊C411yescharacteristic
264C2×C3×C4(C2×D3)⋊C411yescharacteristic
265C2×C3×C4C3×C22⋊C411yescharacteristic
266C2×C3×C4C3×C22⋊C411yescharacteristic
267C2×C3×C4C3×C22⋊C411yescharacteristic
268C2×C3×C4C2×C4×D311yescharacteristic
269C2×C3×C4C2×D1211yescharacteristic
270C2×C3×C4C2×#6711yescharacteristic
271C2×C3×C4C22×C3×C411yescharacteristic
272C2×C3×C4C2×C3×D411yescharacteristic
273C2×C3×C4C2×C3×D411yescharacteristic
274#67—24no—
275C2×Dic3—21no—
276C2×Dic3—21no—
277C2×Dic3—21no—
278D12—21no—
279D12C3×M1612yes—
280C4×D3—24no—
281C4×D3—42no—
282C4×D3—42no—
283Dic6—21no—
284Dic6C3×M1612yes—
285C3×C8—44no—
286C3×C8—42no—
287C3×C8—42no—
288C3×C8—122no—
289C3⋊C8—42no—
290C2×C32—41no—
291C2×C32#40711yescharacteristic
292C2×C32#41611yescharacteristic
293C2×C32#42111yescharacteristic
294C3×D3—42no—
295#41—62no—
296#41—62no—
297C2×Q8—31no—
298C2×D4—31no—
299C2×D4—61no—
300C22×C4—61no—
301C22×C4—61no—
302C22×C4—61no—
303C22×C4C3×C4×D311yescharacteristic
304C22×C4C3×D1211yescharacteristic
305C22×C4C3×#6711yescharacteristic
306C2×C8—22no—
307C2×C8—62no—
308C4⋊C4—31no—
309C4⋊C4—31no—
310C4⋊C4—61no—
311C4⋊C4—61no—
312C22⋊C4—61no—
313C22⋊C4—61no—
314C22⋊C4—61no—
315C42—61no—
316C42—61no—
317C42—61no—
318C42C3×C4×D311yescharacteristic
319C42C3×D1211yescharacteristic
320C42C3×#6711yescharacteristic
321C42C22×C3×D311yescharacteristic
322C22×C3—22no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3—41no—
331C22×C3—41no—
332C22×C3—62no—
333C22×C3—121no—
334C22×C3—121no—
335C22×C3C2×(C2×D3)⋊C411yescharacteristic
336C22×C3C2×C3×C22⋊C411yescharacteristic
337C2×D3—22no—
338C2×D3—41no—
339C2×D3—41no—
340C3×C4—22no—
341C3×C4—22no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—22no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—41no—
354C3×C4—41no—
355C3×C4—62no—
356C3×C4—121no—
357C3×C4—121no—
358C3×C4#90412yes—
359C3×C4D3×M1611yescharacteristic
360C3×C4D3×M1611yescharacteristic
361C3×C4C2×C3×M1611yescharacteristic
362C3×C4C2×C3×M1611yescharacteristic
363C3×C4C3×#13512yes—
364Dic3—22no—
365Dic3—41no—
366Dic3—41no—
367C32#148811yescharacteristic, complemented, Sylow
368C23—61no—
369C23C3×(C2×D3)⋊C411yescharacteristic
370Q8—32no—
371Q8—61no—
372D4—32no—
373D4—64no—
374D4—61no—
375C2×C4—22no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—41no—
379C2×C4—64no—
380C2×C4—61no—
381C2×C4—61no—
382C2×C4—61no—
383C2×C4—122no—
384C2×C4—122no—
385C2×C4C3×(C2×D3)⋊C411yescharacteristic
386C2×C4C3×(C2×D3)⋊C411yescharacteristic
387C2×C4C3×(C2×D3)⋊C411yescharacteristic
388C2×C4C2×C3×C4×D311yescharacteristic
389C2×C4C2×C3×D1211yescharacteristic
390C2×C4C2×C3×#6711yescharacteristic
391C8—42no—
392C8—122no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—42no—
397C2×C3—41no—
398C2×C3—41no—
399C2×C3—122no—
400C2×C3#500511yescharacteristic
401C2×C3#511311yescharacteristic
402C2×C3#512611yescharacteristic
403C2×C3C3×#40711yescharacteristic
404C2×C3C3×#41611yescharacteristic
405C2×C3C3×#42111yescharacteristic
406D3—42no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—62no—
411C22—121no—
412C22—121no—
413C22C2×C3×(C2×D3)⋊C411yescharacteristic
414C4—21no—
415C4—21no—
416C4—21no—
417C4—21no—
418C4—62no—
419C4—121no—
420C4—121no—
421C4C3×#90412yes—
422C4C3×D3×M1611yescharacteristic
423C4C3×D3×M1611yescharacteristic
424C3—21no—
425C3#7076311yescharacteristic, direct product factor
426C3C3×#148811yescharacteristic, complemented
427C2—41no—
428C2—122no—
429C2C3×#500511yescharacteristic
430C2C3×#511311yescharacteristic
431C2C3×#512611yescharacteristic
subgroupG/H
centerC2×C3×C4C2×D12
commutatorC2×C3×C4C22×C3×C4
FrattiniC42C22×C3×D3
FittingC32×#431C2
socleC22×C32C2×C22⋊C4
prime radicalC2×C3×#235C4
cosocleC3×C42C23×C3
hypercenterC3×#431D3
hypocenterC3C3×#1488
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×#4926C2semidirect
4. C3×#4459C2semidirect
5. C3×#4456C2semidirect
7. #70763C3direct (N × H)
29. C3×#431D3semidirect
30. C3×#431C2×C3semidirect
31. #4926C2×C3semidirect
34. #4459C2×C3semidirect
35. #4456C2×C3semidirect
129. #431C3×D3semidirect
367. C32#1488semidirect
425. C3#70763direct (N × H)
426. C3C3×#1488semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#2352
C32×#4312
C3×#49262
C3×#44592
C3×#44562
C3×#14883
#707633