Finite Group Databasebeta

← C3×#71044 #11779705

Subgroups — C3×#71044 #11779705

Order 1152.

676 conjugacy classes of subgroups.

The subgroup lattice has 485 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D4×D12C211yesmaximal, characteristic
2C32×#461C211yesmaximal, characteristic, complemented
3C3×#5088C211yesmaximal, characteristic, complemented
4C3×#5087C211yesmaximal, characteristic, complemented
5C3×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6C3×#4485C211yesmaximal, characteristic, complemented
7C3×#4483C211yesmaximal, characteristic, complemented
8C3×#1639—31nomaximal
9#71044C311yesmaximal, characteristic, direct product factor
10C2×C3×D3×D4—21no—
11C22×C3×D12—21no—
12C2×C32×SD16—21no—
13C32×C4⋊Q8C2211yescharacteristic, complemented
14C32×C4×D4C2211yescharacteristic
15C3×#930—21no—
16C3×#895—21no—
17C3×#882—22no—
18C3×#874C2211yescharacteristic
19C3×C4×D12C2211yescharacteristic
20C32×C4⋊C8C2211yescharacteristic, complemented
21C32×#103—21no—
22C3×#809—21no—
23C3×#809—22no—
24C3×#807—21no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
26C3×C4×C3⋊C8C2211yescharacteristic, complemented
27C3×D42—31no—
28D4×D12C2×C311yescharacteristic
29C3×#486—31no—
30C3×#474—31no—
31C3×#461—21no—
32C3×#461D311yescharacteristic, complemented
33C3×#461C2×C311yescharacteristic, complemented
34#5088C2×C311yescharacteristic, complemented
35#5087C2×C311yescharacteristic, complemented
36C3×#331—31no—
37C3×D4⋊C8—31no—
38C3×D4⋊C8—31no—
39D4⋊(C3⋊C8)C2×C311yescharacteristic, complemented
40#4485C2×C311yescharacteristic, complemented
41#4483C2×C311yescharacteristic, complemented
42C23×C3×D3—22no—
43C2×C32×Q8—21no—
44C2×C32×D4D411yescharacteristic
45C22×C32×C4—21no—
46C2×C3×#67—22no—
47C3×D3×D4—42no—
48C3×D3×D4—42no—
49C2×C3×D12—22no—
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12—42no—
53C2×C3×D12—42no—
54C2×C3×D12D411yescharacteristic
55C2×C3×D12D412yes—
56C2×C3×C4×D3—21no—
57C32×SD16—42no—
58C2×C32×C8—21no—
59C32×C4⋊C4—21no—
60C32×C4⋊C4—21no—
61C32×C4⋊C4D411yescharacteristic
62C32×C22⋊C4—21no—
63C32×C42C2311yescharacteristic
64C3×(C2×D3)⋊C4—22no—
65C3×(C2×D3)⋊C4—21no—
66C3×C4⋊Dic3D411yescharacteristic
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8—21no—
69#1639—31noSylow
70C22×C3×D4—61no—
71C22×C3×D4—61no—
72C2×D3×D4—21no—
73C22×D12—21no—
74C2×C3×SD16—22no—
75C2×C3×SD16—21no—
76C2×C3×SD16—21no—
77C3×C4⋊Q8—21no—
78C3×C4⋊Q8C2×D311yescharacteristic, complemented
79C3×C4⋊Q8C22×C311yescharacteristic, complemented
80C3×#127—31no—
81C3×#121—61no—
82C3×#121—61no—
83C3×#120—62no—
84C3×C4×D4—21no—
85C3×C4×D4—31no—
86C3×C4×D4C2×D311yescharacteristic
87C3×C4×D4C22×C311yescharacteristic
88#930—21no—
89#895—21no—
90#882—22no—
91#874C22×C311yescharacteristic
92C4×D12C22×C311yescharacteristic
93C3×#107—61no—
94C3×C4⋊C8—21no—
95C3×C4⋊C8—31no—
96C3×C4⋊C8C2×D311yescharacteristic, complemented
97C3×C4⋊C8C22×C311yescharacteristic, complemented
98C3×#103—22no—
99C3×#103—21no—
100C3×#103—21no—
101C3×#102—61no—
102C3×#102—62no—
103C3×C4×C8—31no—
104#809—21no—
105#809—22no—
106#807—21no—
107C4⋊(C3⋊C8)C22×C311yescharacteristic, complemented
108C4×C3⋊C8C22×C311yescharacteristic, complemented
109C23×C32—21no—
110C22×C3×D3—21no—
111C22×C3×D3—22no—
112C22×C3×D3—44no—
113C22×C3×D3—44no—
114C22×C3×D3—82no—
115C32×Q8—41no—
116C32×Q8—41no—
117C32×D4—21no—
118C32×D4D812yes—
119C2×C32×C4—21no—
120C2×C32×C4—41no—
121C2×C32×C4—41no—
122C2×C32×C4—41no—
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C3×#67—44no—
127C2×C3×Dic3—21no—
128C3×D12—21no—
129C3×D12—42no—
130C3×D12—44no—
131C3×D12—41no—
132C3×D12—41no—
133C3×D12—41no—
134C3×D12—41no—
135C3×D12SD1612yescomplemented
136C3×C4×D3—41no—
137C3×C4×D3—41no—
138C32×C8—41no—
139C3×C3⋊C8—41no—
140C3×C3⋊C8—41no—
141D42—31no—
142#486—31no—
143#474—31no—
144#461C3×D311yescharacteristic, complemented
145#331—31no—
146D4⋊C8—31no—
147D4⋊C8—31no—
148C24×C3—62no—
149C23×D3—22no—
150C2×C3×Q8—22no—
151C2×C3×Q8—21no—
152C2×C3×Q8—21no—
153C2×C3×D4—21no—
154C2×C3×D4—31no—
155C2×C3×D4—32no—
156C2×C3×D4—62no—
157C2×C3×D4—62no—
158C2×C3×D4—61no—
159C2×C3×D4—61no—
160C2×C3×D4—122no—
161C2×C3×D4—122no—
162C2×C3×D4—122no—
163C2×C3×D4—122no—
164C2×C3×D4#6711yescharacteristic
165C2×C3×D4C3×D411yescharacteristic
166C22×C3×C4—21no—
167C22×C3×C4—21no—
168C22×C3×C4—41no—
169C22×C3×C4—61no—
170C2×#67—22no—
171D3×D4—42no—
172D3×D4—42no—
173C2×D12—22no—
174C2×D12—21no—
175C2×D12—21no—
176C2×D12—42no—
177C2×D12—42no—
178C2×D12C3×D411yescharacteristic
179C2×D12C3×D412yes—
180C2×C4×D3—21no—
181C3×SD16—44no—
182C3×SD16—42no—
183C3×SD16—42no—
184C2×C3×C8—22no—
185C2×C3×C8—21no—
186C2×C3×C8—21no—
187C2×C3×C8—61no—
188C2×C3×C8—61no—
189C3×C4⋊C4—21no—
190C3×C4⋊C4—21no—
191C3×C4⋊C4—21no—
192C3×C4⋊C4—21no—
193C3×C4⋊C4—21no—
194C3×C4⋊C4—31no—
195C3×C4⋊C4—41no—
196C3×C4⋊C4—41no—
197C3×C4⋊C4#6711yescharacteristic
198C3×C4⋊C4C3×D411yescharacteristic
199C3×C22⋊C4—21no—
200C3×C22⋊C4—21no—
201C3×C22⋊C4—41no—
202C3×C22⋊C4—62no—
203C3×C22⋊C4—61no—
204C3×C42—21no—
205C3×C42C22×D311yescharacteristic
206C3×C42C23×C311yescharacteristic
207(C2×D3)⋊C4—22no—
208(C2×D3)⋊C4—21no—
209C4⋊Dic3C3×D411yescharacteristic
210C2×C3⋊C8—21no—
211C2×C3⋊C8—21no—
212C22×C32—22no—
213C22×C32—41no—
214C22×C32—41no—
215C22×C32#12011yescharacteristic
216C2×C3×D3—22no—
217C2×C3×D3—41no—
218C2×C3×D3—41no—
219C2×C3×D3—42no—
220C2×C3×D3—42no—
221C2×C3×D3—42no—
222C2×C3×D3—88no—
223C32×C4—21no—
224C32×C4—41no—
225C32×C4—81no—
226C32×C4C2×D811yescharacteristic
227C32×C4C2×SD1611yescharacteristic
228C32×C4AGL(1,ℤ/8)11yescharacteristic
229C32×C4AGL(1,ℤ/8)11yescharacteristic
230C3×Dic3—41no—
231C22×D4—61no—
232C22×D4—61no—
233C2×SD16—21no—
234C4⋊Q8C2×C3×D311yescharacteristic, complemented
235#127—31no—
236#121—61no—
237#121—61no—
238#120—62no—
239C4×D4—31no—
240C4×D4C2×C3×D311yescharacteristic
241#107—61no—
242C4⋊C8—31no—
243C4⋊C8C2×C3×D311yescharacteristic, complemented
244#103—21no—
245#102—61no—
246#102—62no—
247C4×C8—31no—
248C23×C3—21no—
249C23×C3—21no—
250C23×C3—41no—
251C23×C3—61no—
252C23×C3—62no—
253C23×C3—124no—
254C23×C3—124no—
255C23×C3—242no—
256C22×D3—21no—
257C22×D3—22no—
258C22×D3—44no—
259C22×D3—44no—
260C22×D3—82no—
261C3×Q8—42no—
262C3×Q8—42no—
263C3×Q8—41no—
264C3×Q8—41no—
265C3×Q8—41no—
266C3×Q8—41no—
267C3×D4—21no—
268C3×D4—21no—
269C3×D4—22no—
270C3×D4—32no—
271C3×D4—41no—
272C3×D4—61no—
273C3×D4—122no—
274C3×D4—124no—
275C3×D4—124no—
276C3×D4—121no—
277C3×D4—121no—
278C3×D4—121no—
279C3×D4—121no—
280C3×D4#21312yes—
281C3×D4C3×D812yes—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—41no—
288C2×C3×C4—41no—
289C2×C3×C4—41no—
290C2×C3×C4—41no—
291C2×C3×C4—41no—
292C2×C3×C4—42no—
293C2×C3×C4—41no—
294C2×C3×C4—41no—
295C2×C3×C4—61no—
296C2×C3×C4—81no—
297C2×C3×C4—81no—
298C2×C3×C4—121no—
299C2×C3×C4—121no—
300C2×C3×C4D3×D411yescharacteristic
301C2×C3×C4D3×D411yescharacteristic
302C2×C3×C4C2×#6711yescharacteristic
303C2×C3×C4C2×C3×D411yescharacteristic
304C2×C3×C4C2×C3×D411yescharacteristic
305C2×C3×C4C2×C3×D411yescharacteristic
306#67—44no—
307C2×Dic3—21no—
308D12—21no—
309D12—42no—
310D12—44no—
311D12—41no—
312D12—41no—
313D12—41no—
314D12—41no—
315D12C3×SD1612yescomplemented
316C4×D3—41no—
317C4×D3—41no—
318C3×C8—42no—
319C3×C8—41no—
320C3×C8—41no—
321C3×C8—121no—
322C3×C8—121no—
323C3⋊C8—41no—
324C3⋊C8—41no—
325C2×C32—42no—
326C2×C32#44711yescharacteristic
327C2×C32#45011yescharacteristic
328C2×C32#45511yescharacteristic
329C3×D3—42no—
330C3×D3—82no—
331C24—62no—
332C2×Q8—21no—
333C2×D4—31no—
334C2×D4—32no—
335C2×D4—62no—
336C2×D4—62no—
337C2×D4—61no—
338C2×D4—61no—
339C2×D4—122no—
340C2×D4—122no—
341C2×D4—122no—
342C2×D4—122no—
343C2×D4C3×#6711yescharacteristic
344C22×C4—21no—
345C22×C4—61no—
346SD16—42no—
347C2×C8—21no—
348C2×C8—61no—
349C2×C8—61no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—31no—
353C4⋊C4C3×#6711yescharacteristic
354C22⋊C4—21no—
355C22⋊C4—62no—
356C22⋊C4—61no—
357C42C22×C3×D311yescharacteristic
358C22×C3—22no—
359C22×C3—22no—
360C22×C3—21no—
361C22×C3—42no—
362C22×C3—41no—
363C22×C3—41no—
364C22×C3—41no—
365C22×C3—41no—
366C22×C3—62no—
367C22×C3—81no—
368C22×C3—81no—
369C22×C3—121no—
370C22×C3—121no—
371C22×C3—122no—
372C22×C3—122no—
373C22×C3—122no—
374C22×C3—248no—
375C22×C3#93711yescharacteristic
376C22×C3C3×#12011yescharacteristic
377C2×D3—22no—
378C2×D3—41no—
379C2×D3—41no—
380C2×D3—42no—
381C2×D3—42no—
382C2×D3—42no—
383C2×D3—88no—
384C3×C4—21no—
385C3×C4—21no—
386C3×C4—21no—
387C3×C4—21no—
388C3×C4—21no—
389C3×C4—21no—
390C3×C4—41no—
391C3×C4—41no—
392C3×C4—41no—
393C3×C4—81no—
394C3×C4—82no—
395C3×C4—81no—
396C3×C4—81no—
397C3×C4—121no—
398C3×C4D3×SD1611yescharacteristic
399C3×C4#91411yescharacteristic
400C3×C4C2×#21311yescharacteristic
401C3×C4#94911yescharacteristic
402C3×C4C2×C3×D811yescharacteristic
403C3×C4C2×C3×SD1611yescharacteristic
404C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
405C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
406Dic3—41no—
407C32#163911yescharacteristic, complemented, Sylow
408C23—21no—
409C23—61no—
410C23—62no—
411C23—124no—
412C23—124no—
413C23—242no—
414Q8—41no—
415Q8—41no—
416D4—21no—
417D4—32no—
418D4—61no—
419D4—122no—
420D4—124no—
421D4—124no—
422D4—121no—
423D4—121no—
424D4—121no—
425D4—121no—
426D4C3×#21312yes—
427C2×C4—21no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—61no—
432C2×C4—121no—
433C2×C4—121no—
434C2×C4C3×D3×D411yescharacteristic
435C2×C4C3×D3×D411yescharacteristic
436C2×C4C2×C3×#6711yescharacteristic
437C8—41no—
438C8—121no—
439C8—121no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3—42no—
444C2×C3—42no—
445C2×C3—82no—
446C2×C3—122no—
447C2×C3—242no—
448C2×C3#503611yescharacteristic
449C2×C3#516911yescharacteristic
450C2×C3#520211yescharacteristic
451C2×C3C3×#44711yescharacteristic
452C2×C3C3×#45011yescharacteristic
453C2×C3C3×#45511yescharacteristic
454D3—42no—
455D3—82no—
456C22—22no—
457C22—41no—
458C22—41no—
459C22—62no—
460C22—121no—
461C22—121no—
462C22—122no—
463C22—122no—
464C22—122no—
465C22—248no—
466C22C3×#93711yescharacteristic
467C4—21no—
468C4—41no—
469C4—81no—
470C4—121no—
471C4C3×D3×SD1611yescharacteristic
472C4C3×#91411yescharacteristic
473C4C2×C3×#21311yescharacteristic
474C4C3×#94911yescharacteristic
475C3—21no—
476C3#7104411yescharacteristic, direct product factor
477C3C3×#163911yescharacteristic, complemented
478C2—42no—
479C2—122no—
480C2—242no—
481C2C3×#503611yescharacteristic
482C2C3×#516911yescharacteristic
483C2C3×#520211yescharacteristic
subgroupG/H
centerC22×C3#937
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#461C2
socleC22×C32#120
prime radicalC3×D4×D12C2
hypercenterC3×#461D3
hypocenterC3C3×#1639
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#461

Complements

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

NH ≅ G/Ntype
2. C32×#461C2semidirect
3. C3×#5088C2semidirect
4. C3×#5087C2semidirect
5. C3×D4⋊(C3⋊C8)C2semidirect
6. C3×#4485C2semidirect
7. C3×#4483C2semidirect
9. #71044C3direct (N × H)
13. C32×C4⋊Q8C22semidirect
20. C32×C4⋊C8C22semidirect
25. C3×C4⋊(C3⋊C8)C22semidirect
26. C3×C4×C3⋊C8C22semidirect
32. C3×#461D3semidirect
33. C3×#461C2×C3semidirect
34. #5088C2×C3semidirect
35. #5087C2×C3semidirect
39. D4⋊(C3⋊C8)C2×C3semidirect
40. #4485C2×C3semidirect
41. #4483C2×C3semidirect
78. C3×C4⋊Q8C2×D3semidirect
79. C3×C4⋊Q8C22×C3semidirect
96. C3×C4⋊C8C2×D3semidirect
97. C3×C4⋊C8C22×C3semidirect
107. C4⋊(C3⋊C8)C22×C3semidirect
108. C4×C3⋊C8C22×C3semidirect
135. C3×D12SD16semidirect
144. #461C3×D3semidirect
234. C4⋊Q8C2×C3×D3semidirect
243. C4⋊C8C2×C3×D3semidirect
315. D12C3×SD16semidirect
407. C32#1639semidirect
476. C3#71044direct (N × H)
477. C3C3×#1639semidirect

Maximal subgroups

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

subgroupindex
C3×D4×D122
C32×#4612
C3×#50882
C3×#50872
C3×D4⋊(C3⋊C8)2
C3×#44852
C3×#44832
C3×#16393
#710443