Finite Group Databasebeta

← C3×#71108 #11779708

Subgroups — C3×#71108 #11779708

Order 1152.

670 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D4×D12C211yesmaximal, characteristic
2C32×#474C211yesmaximal, characteristic, complemented
3C3×#5088C211yesmaximal, characteristic, complemented
4C3×#5083C211yesmaximal, characteristic, complemented
5C3×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6C3×#4485C211yesmaximal, characteristic, complemented
7C3×#4483C211yesmaximal, characteristic, complemented
8C3×#1639—31nomaximal
9#71108C311yesmaximal, characteristic, direct product factor
10C2×C3×D3×D4—21no—
11C22×C3×D12—21no—
12C32×C4⋊Q8C2211yescharacteristic, complemented
13C32×C4×D4C2211yescharacteristic
14C2×C3×#215—21no—
15C3×#930—21no—
16C3×#895—21no—
17C3×#882—22no—
18C3×#874C2211yescharacteristic
19C3×C4×D12C2211yescharacteristic
20C32×#107—21no—
21C32×C4⋊C8C2211yescharacteristic, complemented
22C32×#102—21no—
23C3×#835—21no—
24C3×#809—22no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
26C3×C4×C3⋊C8C2211yescharacteristic, complemented
27C3×D42—31no—
28D4×D12C2×C311yescharacteristic
29C3×#486—31no—
30C3×#474—21no—
31C3×#474D311yescharacteristic, complemented
32C3×#474C2×C311yescharacteristic, complemented
33C3×#461—31no—
34#5088C2×C311yescharacteristic, complemented
35#5083C2×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—
57C2×C32×C8—21no—
58C32×C4⋊C4—21no—
59C32×C4⋊C4—21no—
60C32×C4⋊C4D411yescharacteristic
61C32×C22⋊C4—21no—
62C32×C42C2311yescharacteristic
63C3×#215—42no—
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—61no—
75C3×C4⋊Q8—21no—
76C3×C4⋊Q8C2×D311yescharacteristic, complemented
77C3×C4⋊Q8C22×C311yescharacteristic, complemented
78C3×#127—31no—
79C3×#121—61no—
80C3×#121—61no—
81C3×#120—62no—
82C3×C4×D4—21no—
83C3×C4×D4—31no—
84C3×C4×D4C2×D311yescharacteristic
85C3×C4×D4C22×C311yescharacteristic
86C2×#215—21no—
87#930—21no—
88#895—21no—
89#882—22no—
90#874C22×C311yescharacteristic
91C4×D12C22×C311yescharacteristic
92C3×#107—22no—
93C3×#107—21no—
94C3×#107—21no—
95C3×C4⋊C8—21no—
96C3×C4⋊C8—31no—
97C3×C4⋊C8C2×D311yescharacteristic, complemented
98C3×C4⋊C8C22×C311yescharacteristic, complemented
99C3×#103—61no—
100C3×#102—22no—
101C3×#102—21no—
102C3×#102—21no—
103C3×#102—62no—
104C3×C4×C8—31no—
105#835—21no—
106#809—22no—
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×D4SD1612yescomplemented
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×D12D812yes—
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#474C3×D311yescharacteristic, complemented
144#461—31no—
145#331—31no—
146D4⋊C8—31no—
147D4⋊C8—31no—
148C24×C3—62no—
149C23×D3—22no—
150C2×C3×Q8—21no—
151C2×C3×Q8—21no—
152C2×C3×Q8—41no—
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—122no—
182C2×C3×C8—22no—
183C2×C3×C8—21no—
184C2×C3×C8—21no—
185C2×C3×C8—61no—
186C2×C3×C8—61no—
187C3×C4⋊C4—22no—
188C3×C4⋊C4—21no—
189C3×C4⋊C4—21no—
190C3×C4⋊C4—21no—
191C3×C4⋊C4—21no—
192C3×C4⋊C4—21no—
193C3×C4⋊C4—31no—
194C3×C4⋊C4—41no—
195C3×C4⋊C4#6711yescharacteristic
196C3×C4⋊C4C3×D411yescharacteristic
197C3×C22⋊C4—21no—
198C3×C22⋊C4—21no—
199C3×C22⋊C4—41no—
200C3×C22⋊C4—62no—
201C3×C22⋊C4—61no—
202C3×C42—21no—
203C3×C42C22×D311yescharacteristic
204C3×C42C23×C311yescharacteristic
205#215—42no—
206(C2×D3)⋊C4—22no—
207(C2×D3)⋊C4—21no—
208C4⋊Dic3C3×D411yescharacteristic
209C2×C3⋊C8—21no—
210C2×C3⋊C8—21no—
211C22×C32—22no—
212C22×C32—41no—
213C22×C32—41no—
214C22×C32#12011yescharacteristic
215C2×C3×D3—22no—
216C2×C3×D3—41no—
217C2×C3×D3—41no—
218C2×C3×D3—42no—
219C2×C3×D3—42no—
220C2×C3×D3—42no—
221C2×C3×D3—88no—
222C32×C4—21no—
223C32×C4—41no—
224C32×C4—81no—
225C32×C4C2×D811yescharacteristic
226C32×C4C2×SD1611yescharacteristic
227C32×C4AGL(1,ℤ/8)11yescharacteristic
228C32×C4AGL(1,ℤ/8)11yescharacteristic
229C3×Dic3—41no—
230C22×D4—61no—
231C22×D4—61no—
232C2×SD16—61no—
233C4⋊Q8C2×C3×D311yescharacteristic, complemented
234#127—31no—
235#121—61no—
236#121—61no—
237#120—62no—
238C4×D4—31no—
239C4×D4C2×C3×D311yescharacteristic
240#107—21no—
241C4⋊C8—31no—
242C4⋊C8C2×C3×D311yescharacteristic, complemented
243#103—61no—
244#102—21no—
245#102—62no—
246C4×C8—31no—
247C23×C3—21no—
248C23×C3—21no—
249C23×C3—41no—
250C23×C3—61no—
251C23×C3—62no—
252C23×C3—124no—
253C23×C3—124no—
254C23×C3—242no—
255C22×D3—21no—
256C22×D3—22no—
257C22×D3—44no—
258C22×D3—44no—
259C22×D3—82no—
260C3×Q8—41no—
261C3×Q8—41no—
262C3×Q8—41no—
263C3×Q8—41no—
264C3×Q8—81no—
265C3×Q8—81no—
266C3×D4—21no—
267C3×D4—21no—
268C3×D4—22no—
269C3×D4—32no—
270C3×D4—41no—
271C3×D4—61no—
272C3×D4—122no—
273C3×D4—124no—
274C3×D4—124no—
275C3×D4—121no—
276C3×D4—121no—
277C3×D4—121no—
278C3×D4—121no—
279C3×D4#21512yescomplemented
280C3×D4C3×SD1612yescomplemented
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—41no—
289C2×C3×C4—41no—
290C2×C3×C4—41no—
291C2×C3×C4—42no—
292C2×C3×C4—41no—
293C2×C3×C4—41no—
294C2×C3×C4—61no—
295C2×C3×C4—81no—
296C2×C3×C4—81no—
297C2×C3×C4—121no—
298C2×C3×C4—121no—
299C2×C3×C4D3×D411yescharacteristic
300C2×C3×C4D3×D411yescharacteristic
301C2×C3×C4C2×#6711yescharacteristic
302C2×C3×C4C2×C3×D411yescharacteristic
303C2×C3×C4C2×C3×D411yescharacteristic
304C2×C3×C4C2×C3×D411yescharacteristic
305#67—44no—
306C2×Dic3—21no—
307D12—21no—
308D12—42no—
309D12—44no—
310D12—41no—
311D12—41no—
312D12—41no—
313D12—41no—
314D12C3×D812yes—
315C4×D3—41no—
316C4×D3—41no—
317C3×C8—42no—
318C3×C8—41no—
319C3×C8—41no—
320C3×C8—121no—
321C3×C8—121no—
322C3⋊C8—41no—
323C3⋊C8—41no—
324C2×C32—42no—
325C2×C32#44711yescharacteristic
326C2×C32#45011yescharacteristic
327C2×C32#45511yescharacteristic
328C3×D3—42no—
329C3×D3—82no—
330C24—62no—
331C2×Q8—21no—
332C2×D4—31no—
333C2×D4—32no—
334C2×D4—62no—
335C2×D4—62no—
336C2×D4—61no—
337C2×D4—61no—
338C2×D4—122no—
339C2×D4—122no—
340C2×D4—122no—
341C2×D4—122no—
342C2×D4C3×#6711yescharacteristic
343C22×C4—21no—
344C22×C4—61no—
345SD16—122no—
346C2×C8—21no—
347C2×C8—61no—
348C2×C8—61no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—31no—
352C4⋊C4C3×#6711yescharacteristic
353C22⋊C4—21no—
354C22⋊C4—62no—
355C22⋊C4—61no—
356C42C22×C3×D311yescharacteristic
357C22×C3—22no—
358C22×C3—22no—
359C22×C3—21no—
360C22×C3—42no—
361C22×C3—41no—
362C22×C3—41no—
363C22×C3—41no—
364C22×C3—41no—
365C22×C3—62no—
366C22×C3—81no—
367C22×C3—81no—
368C22×C3—121no—
369C22×C3—121no—
370C22×C3—122no—
371C22×C3—122no—
372C22×C3—122no—
373C22×C3—248no—
374C22×C3#93711yescharacteristic
375C22×C3C3×#12011yescharacteristic
376C2×D3—22no—
377C2×D3—41no—
378C2×D3—41no—
379C2×D3—42no—
380C2×D3—42no—
381C2×D3—42no—
382C2×D3—88no—
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—21no—
386C3×C4—21no—
387C3×C4—21no—
388C3×C4—21no—
389C3×C4—41no—
390C3×C4—41no—
391C3×C4—41no—
392C3×C4—81no—
393C3×C4—82no—
394C3×C4—81no—
395C3×C4—81no—
396C3×C4—121no—
397C3×C4D3×D811yescharacteristic
398C3×C4#91111yescharacteristic
399C3×C4C2×#21511yescharacteristic
400C3×C4#94911yescharacteristic
401C3×C4C2×C3×D811yescharacteristic
402C3×C4C2×C3×SD1611yescharacteristic
403C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
404C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
405Dic3—41no—
406C32#163911yescharacteristic, complemented, Sylow
407C23—21no—
408C23—61no—
409C23—62no—
410C23—124no—
411C23—124no—
412C23—242no—
413Q8—41no—
414Q8—41no—
415D4—21no—
416D4—32no—
417D4—61no—
418D4—122no—
419D4—124no—
420D4—124no—
421D4—121no—
422D4—121no—
423D4—121no—
424D4—121no—
425D4C3×#21512yescomplemented
426C2×C4—21no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—61no—
431C2×C4—121no—
432C2×C4—121no—
433C2×C4C3×D3×D411yescharacteristic
434C2×C4C3×D3×D411yescharacteristic
435C2×C4C2×C3×#6711yescharacteristic
436C8—41no—
437C8—121no—
438C8—121no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—42no—
443C2×C3—42no—
444C2×C3—82no—
445C2×C3—122no—
446C2×C3—242no—
447C2×C3#504611yescharacteristic
448C2×C3#515611yescharacteristic
449C2×C3#520211yescharacteristic
450C2×C3C3×#44711yescharacteristic
451C2×C3C3×#45011yescharacteristic
452C2×C3C3×#45511yescharacteristic
453D3—42no—
454D3—82no—
455C22—22no—
456C22—41no—
457C22—41no—
458C22—62no—
459C22—121no—
460C22—121no—
461C22—122no—
462C22—122no—
463C22—122no—
464C22—248no—
465C22C3×#93711yescharacteristic
466C4—21no—
467C4—41no—
468C4—81no—
469C4—121no—
470C4C3×D3×D811yescharacteristic
471C4C3×#91111yescharacteristic
472C4C2×C3×#21511yescharacteristic
473C4C3×#94911yescharacteristic
474C3—21no—
475C3#7110811yescharacteristic, direct product factor
476C3C3×#163911yescharacteristic, complemented
477C2—42no—
478C2—122no—
479C2—242no—
480C2C3×#504611yescharacteristic
481C2C3×#515611yescharacteristic
482C2C3×#520211yescharacteristic
subgroupG/H
centerC22×C3#937
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#474C2
socleC22×C32#120
prime radicalC3×D4×D12C2
hypercenterC3×#474D3
hypocenterC3C3×#1639
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#474

Complements

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

NH ≅ G/Ntype
2. C32×#474C2semidirect
3. C3×#5088C2semidirect
4. C3×#5083C2semidirect
5. C3×D4⋊(C3⋊C8)C2semidirect
6. C3×#4485C2semidirect
7. C3×#4483C2semidirect
9. #71108C3direct (N × H)
12. C32×C4⋊Q8C22semidirect
21. C32×C4⋊C8C22semidirect
25. C3×C4⋊(C3⋊C8)C22semidirect
26. C3×C4×C3⋊C8C22semidirect
31. C3×#474D3semidirect
32. C3×#474C2×C3semidirect
34. #5088C2×C3semidirect
35. #5083C2×C3semidirect
39. D4⋊(C3⋊C8)C2×C3semidirect
40. #4485C2×C3semidirect
41. #4483C2×C3semidirect
76. C3×C4⋊Q8C2×D3semidirect
77. C3×C4⋊Q8C22×C3semidirect
97. C3×C4⋊C8C2×D3semidirect
98. C3×C4⋊C8C22×C3semidirect
107. C4⋊(C3⋊C8)C22×C3semidirect
108. C4×C3⋊C8C22×C3semidirect
118. C32×D4SD16semidirect
143. #474C3×D3semidirect
233. C4⋊Q8C2×C3×D3semidirect
242. C4⋊C8C2×C3×D3semidirect
279. C3×D4#215semidirect
280. C3×D4C3×SD16semidirect
406. C32#1639semidirect
425. D4C3×#215semidirect
475. C3#71108direct (N × H)
476. 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×#4742
C3×#50882
C3×#50832
C3×D4⋊(C3⋊C8)2
C3×#44852
C3×#44832
C3×#16393
#711083