Finite Group Databasebeta

← C3×C4×D4×A4 #11919672

Subgroups — C3×C4×D4×A4 #11919672

Order 1152.

1344 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×A4C211yesmaximal, characteristic
2C22×C3×C4×A4C212yesmaximal, complemented
3C3×A4×C4⋊C4C211yesmaximal, characteristic, complemented
4C3×A4×C22⋊C4C212yesmaximal, complemented
5C3×C42×A4C211yesmaximal, characteristic, complemented
6C22×C3×C4×D4C311yesmaximal, characteristic, complemented
7C4×D4×A4C313yesmaximal, direct product factor
8C23×C3×A4C2212yes—
9C3×D4×A4C414yesdirect product factor
10C2×C3×C4×A4—24no—
11C2×C3×C4×A4C2212yes—
12C2×C3×C4×A4C2211yescharacteristic
13C2×C3×C4×A4C2211yescharacteristic
14C2×C3×C4×A4C2211yescharacteristic
15C32×C4×D4—41nomaximal
16C23×C3×D4C2×C311yescharacteristic
17C24×C3×C4C2×C312yescomplemented
18C2×D4×A4C2×C313yes—
19C22×C4×A4C2×C316yescomplemented
20C2×C3×C4×D4—31no—
21C2×C3×C4×D4—31no—
22C2×C3×C4×D4—32no—
23C2×C3×C4×D4—31no—
24C2×C3×C4×D4—31no—
25C2×C3×C4×D4—32no—
26C22×C3×C4⋊C4C2×C311yescharacteristic, complemented
27C22×C3×C22⋊C4C2×C312yescomplemented
28C22×C3×C42C2×C311yescharacteristic, complemented
29A4×C4⋊C4C2×C313yescomplemented
30A4×C22⋊C4C2×C316yescomplemented
31C42×A4C2×C313yescomplemented
32C22×C3×A4—22no—
33C22×C3×A4—22no—
34C22×C3×A4C2×C414yescomplemented
35C22×C3×A4C2311yescharacteristic
36C2×C32×D4—41no—
37C22×C32×C4—42no—
38C3×C4×A4—22no—
39C3×C4×A4—21no—
40C3×C4×A4C2×C412yescomplemented
41C3×C4×A4D412yesdirect product factor
42C32×C4⋊C4—41no—
43C32×C22⋊C4—42no—
44C32×C42—41no—
45C22×C4×D4C3211yescharacteristic, complemented, Sylow
46C25×C3C22×C312yes—
47C23×A4C22×C316yes—
48C22×C3×D4—31no—
49C22×C3×D4—34no—
50C22×C3×D4—31no—
51C22×C3×D4—32no—
52C22×C3×D4C3×C414yescomplemented
53C23×C3×C4—24no—
54C23×C3×C4—32no—
55C23×C3×C4—32no—
56C23×C3×C4—32no—
57C23×C3×C4—32no—
58C23×C3×C4—64no—
59C23×C3×C4C22×C312yes—
60C23×C3×C4C22×C311yescharacteristic
61C23×C3×C4C22×C311yescharacteristic
62C23×C3×C4C22×C311yescharacteristic
63D4×A4C3×C4112yesdirect product factor
64C2×C4×A4—212no—
65C2×C4×A4C22×C316yes—
66C2×C4×A4C22×C313yes—
67C2×C4×A4C22×C313yes—
68C2×C4×A4C22×C313yes—
69C3×C4×D4—34no—
70C3×C4×D4—34no—
71C3×C4×D4—32no—
72C3×C4×D4—32no—
73C3×C4×D4—32no—
74C3×C4×D4—31no—
75C3×C4×D4—32no—
76C3×C4×D4—31no—
77C3×C4×D4—32no—
78C3×C4×D4—31no—
79C3×C4×D4—43no—
80C3×C4×D4A411yescharacteristic, direct product factor
81C2×C3×C4⋊C4—31no—
82C2×C3×C4⋊C4—31no—
83C2×C3×C4⋊C4—32no—
84C2×C3×C22⋊C4—32no—
85C2×C3×C22⋊C4—32no—
86C2×C3×C22⋊C4—32no—
87C2×C3×C22⋊C4—32no—
88C2×C3×C42—31no—
89C2×C3×C42—31no—
90C2×C3×C42—31no—
91C2×C3×C42—31no—
92C23×C32—42no—
93C2×C3×A4—24no—
94C2×C3×A4C22×C411yescharacteristic
95C2×C3×A4C2×D411yescharacteristic
96C2×C3×A4#4111yescharacteristic
97C32×D4—44no—
98C2×C32×C4—41no—
99C2×C32×C4—41no—
100C2×C32×C4—42no—
101C2×C32×C4—41no—
102C2×C32×C4—84no—
103C23×D4C2×C3211yescharacteristic
104C24×C4C2×C3212yescomplemented
105C2×C4×D4—31no—
106C2×C4×D4—31no—
107C2×C4×D4—32no—
108C2×C4×D4—31no—
109C2×C4×D4—31no—
110C2×C4×D4—32no—
111C22×C4⋊C4C2×C3211yescharacteristic, complemented
112C22×C22⋊C4C2×C3212yescomplemented
113C22×C42C2×C3211yescharacteristic, complemented
114C24×C3—22no—
115C24×C3—22no—
116C24×C3—32no—
117C24×C3—34no—
118C24×C3—32no—
119C24×C3—62no—
120C24×C3—62no—
121C24×C3C2×C3×C414yescomplemented
122C24×C3C23×C311yescharacteristic
123C22×A4—26no—
124C22×A4—26no—
125C22×A4C2×C3×C4112yescomplemented
126C22×A4C23×C313yes—
127C2×C3×D4—32no—
128C2×C3×D4—38no—
129C2×C3×D4—34no—
130C2×C3×D4—32no—
131C2×C3×D4—34no—
132C2×C3×D4—34no—
133C2×C3×D4—34no—
134C2×C3×D4—38no—
135C2×C3×D4—31no—
136C2×C3×D4—43no—
137C2×C3×D4C2×A411yescharacteristic
138C22×C3×C4—22no—
139C22×C3×C4—21no—
140C22×C3×C4—31no—
141C22×C3×C4—31no—
142C22×C3×C4—31no—
143C22×C3×C4—31no—
144C22×C3×C4—32no—
145C22×C3×C4—32no—
146C22×C3×C4—34no—
147C22×C3×C4—32no—
148C22×C3×C4—31no—
149C22×C3×C4—32no—
150C22×C3×C4—32no—
151C22×C3×C4—32no—
152C22×C3×C4—31no—
153C22×C3×C4—32no—
154C22×C3×C4—46no—
155C22×C3×C4—64no—
156C22×C3×C4—64no—
157C22×C3×C4—64no—
158C22×C3×C4—64no—
159C22×C3×C4—64no—
160C22×C3×C4—64no—
161C22×C3×C4—64no—
162C22×C3×C4—64no—
163C22×C3×C4—62no—
164C22×C3×C4—61no—
165C22×C3×C4C2×C3×C412yescomplemented
166C22×C3×C4C3×D412yescomplemented
167C22×C3×C4C2×A412yescomplemented
168C4×A4—26no—
169C4×A4—23no—
170C4×A4C2×C3×C416yescomplemented
171C4×A4C3×D416yesdirect product factor
172C3×C4⋊C4—32no—
173C3×C4⋊C4—32no—
174C3×C4⋊C4—31no—
175C3×C4⋊C4—43no—
176C3×C4⋊C4C2×A411yescharacteristic, complemented
177C3×C22⋊C4—34no—
178C3×C22⋊C4—32no—
179C3×C22⋊C4—32no—
180C3×C22⋊C4—32no—
181C3×C22⋊C4—46no—
182C3×C22⋊C4C2×A412yescomplemented
183C3×C42—32no—
184C3×C42—31no—
185C3×C42—31no—
186C3×C42—31no—
187C3×C42—43no—
188C3×C42C2×A411yescharacteristic, complemented
189C22×C32—44no—
190C22×C32—41no—
191C22×C32—82no—
192C22×C32—82no—
193C3×A4C4×D411yescharacteristic, direct product factor
194C32×C4—42no—
195C32×C4—42no—
196C32×C4—82no—
197C32×C4—81no—
198C25C22×C3212yes—
199C22×D4—31no—
200C22×D4—31no—
201C22×D4—32no—
202C22×D4—34no—
203C22×D4C32×C414yescomplemented
204C23×C4—24no—
205C23×C4—32no—
206C23×C4—32no—
207C23×C4—32no—
208C23×C4—32no—
209C23×C4—64no—
210C23×C4C22×C3211yescharacteristic
211C23×C4C22×C3212yes—
212C23×C4C22×C3211yescharacteristic
213C23×C4C22×C3211yescharacteristic
214C4×D4—34no—
215C4×D4—34no—
216C4×D4—32no—
217C4×D4—32no—
218C4×D4—32no—
219C4×D4—31no—
220C4×D4—32no—
221C4×D4—31no—
222C4×D4—32no—
223C4×D4—31no—
224C4×D4C3×A411yescharacteristic, direct product factor
225C2×C4⋊C4—31no—
226C2×C4⋊C4—31no—
227C2×C4⋊C4—32no—
228C2×C22⋊C4—32no—
229C2×C22⋊C4—32no—
230C2×C22⋊C4—32no—
231C2×C22⋊C4—32no—
232C2×C42—31no—
233C2×C42—31no—
234C2×C42—31no—
235C2×C42—31no—
236C23×C3—24no—
237C23×C3—31no—
238C23×C3—31no—
239C23×C3—31no—
240C23×C3—31no—
241C23×C3—34no—
242C23×C3—34no—
243C23×C3—34no—
244C23×C3—34no—
245C23×C3—32no—
246C23×C3—46no—
247C23×C3—62no—
248C23×C3—62no—
249C23×C3—62no—
250C23×C3—62no—
251C23×C3—64no—
252C23×C3—62no—
253C23×C3—62no—
254C23×C3—64no—
255C23×C3—64no—
256C23×C3—62no—
257C23×C3—62no—
258C23×C3—68no—
259C23×C3C22×C3×C411yescharacteristic
260C23×C3C2×C3×D411yescharacteristic
261C23×C3C3×#4111yescharacteristic
262C23×C3C22×A412yes—
263C2×A4—212no—
264C2×A4C22×C3×C413yes—
265C2×A4C2×C3×D413yes—
266C2×A4C3×#4113yes—
267C3×D4—38no—
268C3×D4—38no—
269C3×D4—34no—
270C3×D4—412no—
271C3×D4C4×A414yesdirect product factor
272C2×C3×C4—24no—
273C2×C3×C4—32no—
274C2×C3×C4—32no—
275C2×C3×C4—31no—
276C2×C3×C4—31no—
277C2×C3×C4—32no—
278C2×C3×C4—32no—
279C2×C3×C4—32no—
280C2×C3×C4—32no—
281C2×C3×C4—32no—
282C2×C3×C4—32no—
283C2×C3×C4—31no—
284C2×C3×C4—32no—
285C2×C3×C4—43no—
286C2×C3×C4—43no—
287C2×C3×C4—43no—
288C2×C3×C4—46no—
289C2×C3×C4—64no—
290C2×C3×C4—61no—
291C2×C3×C4—62no—
292C2×C3×C4—61no—
293C2×C3×C4—62no—
294C2×C3×C4—64no—
295C2×C3×C4—68no—
296C2×C3×C4—64no—
297C2×C3×C4—61no—
298C2×C3×C4—62no—
299C2×C3×C4—61no—
300C2×C3×C4—62no—
301C2×C3×C4—812no—
302C2×C3×C4C22×A411yescharacteristic
303C2×C3×C4C22×A412yes—
304C2×C3×C4C22×A411yescharacteristic
305C2×C3×C4C22×A411yescharacteristic
306C2×C32—41no—
307C2×C32—41no—
308C2×C32—41no—
309C2×C32—84no—
310C24—22no—
311C24—22no—
312C24—32no—
313C24—34no—
314C24—32no—
315C24—62no—
316C24—62no—
317C24C2×C32×C414yescomplemented
318C24C23×C3211yescharacteristic
319C2×D4—32no—
320C2×D4—38no—
321C2×D4—34no—
322C2×D4—32no—
323C2×D4—34no—
324C2×D4—34no—
325C2×D4—34no—
326C2×D4—38no—
327C2×D4—31no—
328C2×D4C2×C3×A411yescharacteristic
329C22×C4—22no—
330C22×C4—21no—
331C22×C4—31no—
332C22×C4—31no—
333C22×C4—31no—
334C22×C4—31no—
335C22×C4—32no—
336C22×C4—32no—
337C22×C4—34no—
338C22×C4—32no—
339C22×C4—31no—
340C22×C4—32no—
341C22×C4—32no—
342C22×C4—32no—
343C22×C4—31no—
344C22×C4—32no—
345C22×C4—64no—
346C22×C4—64no—
347C22×C4—64no—
348C22×C4—64no—
349C22×C4—64no—
350C22×C4—64no—
351C22×C4—64no—
352C22×C4—64no—
353C22×C4—62no—
354C22×C4—61no—
355C22×C4C2×C32×C412yescomplemented
356C22×C4C32×D412yescomplemented
357C22×C4C2×C3×A412yescomplemented
358C4⋊C4—32no—
359C4⋊C4—32no—
360C4⋊C4—31no—
361C4⋊C4C2×C3×A411yescharacteristic, complemented
362C22⋊C4—34no—
363C22⋊C4—32no—
364C22⋊C4—32no—
365C22⋊C4—32no—
366C22⋊C4C2×C3×A412yescomplemented
367C42—32no—
368C42—31no—
369C42—31no—
370C42—31no—
371C42C2×C3×A411yescharacteristic, complemented
372C22×C3—22no—
373C22×C3—22no—
374C22×C3—31no—
375C22×C3—31no—
376C22×C3—31no—
377C22×C3—32no—
378C22×C3—31no—
379C22×C3—31no—
380C22×C3—31no—
381C22×C3—31no—
382C22×C3—31no—
383C22×C3—31no—
384C22×C3—34no—
385C22×C3—412no—
386C22×C3—43no—
387C22×C3—64no—
388C22×C3—64no—
389C22×C3—64no—
390C22×C3—64no—
391C22×C3—64no—
392C22×C3—64no—
393C22×C3—64no—
394C22×C3—64no—
395C22×C3—62no—
396C22×C3—62no—
397C22×C3—86no—
398C22×C3—86no—
399C22×C3C3×C4×D411yescharacteristic, complemented
400C22×C3C2×C4×A414yescomplemented
401C22×C3C23×A411yescharacteristic
402A4C3×C4×D413yesdirect product factor
403C3×C4—22no—
404C3×C4—21no—
405C3×C4—32no—
406C3×C4—32no—
407C3×C4—46no—
408C3×C4—46no—
409C3×C4—62no—
410C3×C4—61no—
411C3×C4—86no—
412C3×C4—83no—
413C3×C4C2×C4×A412yescomplemented
414C3×C4D4×A412yesdirect product factor
415C32—41noSylow
416C23—24no—
417C23—31no—
418C23—31no—
419C23—31no—
420C23—31no—
421C23—34no—
422C23—34no—
423C23—34no—
424C23—34no—
425C23—32no—
426C23—62no—
427C23—62no—
428C23—62no—
429C23—62no—
430C23—64no—
431C23—62no—
432C23—62no—
433C23—64no—
434C23—64no—
435C23—62no—
436C23—62no—
437C23—68no—
438C23C22×C32×C411yescharacteristic
439C23C2×C32×D411yescharacteristic
440C23C32×#4111yescharacteristic
441C23C22×C3×A412yes—
442D4—38no—
443D4—38no—
444D4—34no—
445D4C3×C4×A414yesdirect product factor
446C2×C4—24no—
447C2×C4—32no—
448C2×C4—32no—
449C2×C4—31no—
450C2×C4—31no—
451C2×C4—32no—
452C2×C4—32no—
453C2×C4—32no—
454C2×C4—32no—
455C2×C4—32no—
456C2×C4—32no—
457C2×C4—31no—
458C2×C4—32no—
459C2×C4—64no—
460C2×C4—62no—
461C2×C4—61no—
462C2×C4—62no—
463C2×C4—61no—
464C2×C4—64no—
465C2×C4—68no—
466C2×C4—64no—
467C2×C4—62no—
468C2×C4—61no—
469C2×C4—62no—
470C2×C4—61no—
471C2×C4C22×C3×A411yescharacteristic
472C2×C4C22×C3×A412yes—
473C2×C4C22×C3×A411yescharacteristic
474C2×C4C22×C3×A411yescharacteristic
475C2×C3—24no—
476C2×C3—31no—
477C2×C3—31no—
478C2×C3—31no—
479C2×C3—31no—
480C2×C3—43no—
481C2×C3—43no—
482C2×C3—43no—
483C2×C3—64no—
484C2×C3—812no—
485C2×C3C22×C4×A411yescharacteristic
486C2×C3C2×D4×A411yescharacteristic
487C2×C3A4×#4111yescharacteristic
488C22—22no—
489C22—22no—
490C22—31no—
491C22—31no—
492C22—31no—
493C22—32no—
494C22—31no—
495C22—31no—
496C22—31no—
497C22—31no—
498C22—31no—
499C22—31no—
500C22—34no—
501C22—64no—
502C22—64no—
503C22—64no—
504C22—64no—
505C22—64no—
506C22—64no—
507C22—64no—
508C22—64no—
509C22—62no—
510C22—62no—
511C22C32×C4×D411yescharacteristic, complemented
512C22C2×C3×C4×A414yescomplemented
513C22C23×C3×A411yescharacteristic
514C4—22no—
515C4—21no—
516C4—32no—
517C4—32no—
518C4—62no—
519C4—61no—
520C4C2×C3×C4×A412yescomplemented
521C4C3×D4×A412yesdirect product factor
522C3—43no—
523C3C4×D4×A411yescharacteristic, direct product factor
524C2—24no—
525C2—31no—
526C2—31no—
527C2—31no—
528C2—31no—
529C2—64no—
530C2C22×C3×C4×A411yescharacteristic
531C2C2×C3×D4×A411yescharacteristic
532C2C3×A4×#4111yescharacteristic
subgroupG/H
centerC2×C3×C4C22×A4
commutatorC23C22×C32×C4
FrattiniC22C23×C3×A4
FittingC22×C3×C4×D4C3
socleC24×C3C23×C3
prime radicalC2×C3×D4×A4C2
cosocleC24C23×C32
hypercenterC3×C4×D4A4
hypocenterC22C32×C4×D4
LCSG ▷ C23 ▷ C22
UCSC1 ◁ C2×C3×C4 ◁ C3×C4×D4

Complements

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

NH ≅ G/Ntype
2. C22×C3×C4×A4C2semidirect
3. C3×A4×C4⋊C4C2semidirect
4. C3×A4×C22⋊C4C2semidirect
5. C3×C42×A4C2semidirect
6. C22×C3×C4×D4C3semidirect
7. C4×D4×A4C3direct (N × H)
9. C3×D4×A4C4direct (N × H)
17. C24×C3×C4C2×C3semidirect
19. C22×C4×A4C2×C3semidirect
26. C22×C3×C4⋊C4C2×C3semidirect
27. C22×C3×C22⋊C4C2×C3semidirect
28. C22×C3×C42C2×C3semidirect
29. A4×C4⋊C4C2×C3semidirect
30. A4×C22⋊C4C2×C3semidirect
31. C42×A4C2×C3semidirect
34. C22×C3×A4C2×C4semidirect
40. C3×C4×A4C2×C4semidirect
41. C3×C4×A4D4direct (N × H)
45. C22×C4×D4C32semidirect
52. C22×C3×D4C3×C4semidirect
63. D4×A4C3×C4direct (N × H)
80. C3×C4×D4A4direct (N × H)
104. C24×C4C2×C32semidirect
111. C22×C4⋊C4C2×C32semidirect
112. C22×C22⋊C4C2×C32semidirect
113. C22×C42C2×C32semidirect
121. C24×C3C2×C3×C4semidirect
125. C22×A4C2×C3×C4semidirect
165. C22×C3×C4C2×C3×C4semidirect
166. C22×C3×C4C3×D4semidirect
167. C22×C3×C4C2×A4semidirect
170. C4×A4C2×C3×C4semidirect
171. C4×A4C3×D4direct (N × H)
176. C3×C4⋊C4C2×A4semidirect
182. C3×C22⋊C4C2×A4semidirect
188. C3×C42C2×A4semidirect
193. C3×A4C4×D4direct (N × H)
203. C22×D4C32×C4semidirect
224. C4×D4C3×A4direct (N × H)
271. C3×D4C4×A4direct (N × H)
317. C24C2×C32×C4semidirect
355. C22×C4C2×C32×C4semidirect
356. C22×C4C32×D4semidirect
357. C22×C4C2×C3×A4semidirect
361. C4⋊C4C2×C3×A4semidirect
366. C22⋊C4C2×C3×A4semidirect
371. C42C2×C3×A4semidirect
399. C22×C3C3×C4×D4semidirect
400. C22×C3C2×C4×A4semidirect
402. A4C3×C4×D4direct (N × H)
413. C3×C4C2×C4×A4semidirect
414. C3×C4D4×A4direct (N × H)
445. D4C3×C4×A4direct (N × H)
511. C22C32×C4×D4semidirect
512. C22C2×C3×C4×A4semidirect
520. C4C2×C3×C4×A4semidirect
521. C4C3×D4×A4direct (N × H)
523. C3C4×D4×A4direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D4×A42
C22×C3×C4×A42
C3×A4×C4⋊C42
C3×A4×C22⋊C42
C3×C42×A42
C22×C3×C4×D43
C4×D4×A43
C32×C4×D44