Finite Group Databasebeta

← D4×Dic3×A4 #11923351

Subgroups — D4×Dic3×A4 #11923351

Order 1152.

1210 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 1210 conjugacy classes of subgroups — too many to draw. Only its 153 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×A4C211yesmaximal, characteristic
2C22×Dic3×A4C212yesmaximal, complemented
3A4×#217C212yesmaximal, complemented
4A4×C4⋊Dic3C211yesmaximal, characteristic, complemented
5C4×Dic3×A4C211yesmaximal, characteristic, complemented
6C22×D4×Dic3C311yesmaximal, characteristic, complemented
7C4×D4×A4—31nomaximal
8C23×C3×A4C2212yes—
9C3×D4×A4C414yescomplemented
10C2×C3×C4×A4C2211yescharacteristic
11C2×Dic3×A4—24no—
12C2×Dic3×A4C2212yes—
13C2×Dic3×A4C2211yescharacteristic
14C2×Dic3×A4C2211yescharacteristic
15C3×D4×Dic3—41nomaximal
16C23×C3×D4C2×C311yescharacteristic
17C24×Dic3C2×C312yescomplemented
18C2×D4×A4—21no—
19C2×D4×A4D311yescharacteristic
20C22×C4×A4—32no—
21C22×#217C2×C312yescomplemented
22C2×D4×Dic3—31no—
23C2×D4×Dic3—31no—
24C2×D4×Dic3—31no—
25C2×D4×Dic3—31no—
26C2×D4×Dic3—32no—
27C2×D4×Dic3—32no—
28C22×C4⋊Dic3C2×C311yescharacteristic, complemented
29C22×C4×Dic3C2×C311yescharacteristic, complemented
30A4×C4⋊C4—31no—
31A4×C22⋊C4—32no—
32C42×A4—31no—
33C22×C3×A4—22no—
34C22×C3×A4—22no—
35C22×C3×A4C2×C414yescomplemented
36C22×C3×A4C2311yescharacteristic
37C2×C32×D4—41no—
38C22×C3×Dic3—42no—
39C3×C4×A4C2×C412yescomplemented
40Dic3×A4—22no—
41Dic3×A4—21no—
42Dic3×A4D412yesdirect product factor
43C3×#217—42no—
44C3×C4⋊Dic3—41no—
45C3×C4×Dic3—41no—
46C22×C4×D4—31noSylow
47C25×C3C22×C312yes—
48C23×A4—22no—
49C23×A4C2×D312yes—
50C22×C3×D4—31no—
51C22×C3×D4—34no—
52C22×C3×D4—31no—
53C22×C3×D4—32no—
54C22×C3×D4C3×C414yescomplemented
55C23×C3×C4C22×C311yescharacteristic
56C23×Dic3—24no—
57C23×Dic3—32no—
58C23×Dic3—32no—
59C23×Dic3—32no—
60C23×Dic3—32no—
61C23×Dic3—64no—
62C23×Dic3C22×C312yes—
63C23×Dic3C22×C311yescharacteristic
64C23×Dic3C22×C311yescharacteristic
65D4×A4—24no—
66D4×A4Dic314yesdirect product factor
67C2×C4×A4—21no—
68C2×C4×A4—31no—
69C2×C4×A4—32no—
70C2×C4×A4—31no—
71C2×C4×A4—64no—
72C2×C4×A4C2×D311yescharacteristic
73C3×C4×D4—121no—
74C2×#217—32no—
75C2×#217—32no—
76C2×#217—32no—
77C2×#217—32no—
78D4×Dic3—34no—
79D4×Dic3—34no—
80D4×Dic3—32no—
81D4×Dic3—32no—
82D4×Dic3—32no—
83D4×Dic3—31no—
84D4×Dic3—32no—
85D4×Dic3—32no—
86D4×Dic3—31no—
87D4×Dic3—31no—
88D4×Dic3A411yescharacteristic, direct product factor
89C2×C4⋊Dic3—31no—
90C2×C4⋊Dic3—31no—
91C2×C4⋊Dic3—32no—
92C2×C4×Dic3—31no—
93C2×C4×Dic3—31no—
94C2×C4×Dic3—31no—
95C2×C4×Dic3—31no—
96C23×C32—42no—
97C2×C3×A4—24no—
98C2×C3×A4C22×C411yescharacteristic
99C2×C3×A4C2×D411yescharacteristic
100C2×C3×A4#4111yescharacteristic
101C32×D4—44no—
102C2×C32×C4—41no—
103C2×C3×Dic3—41no—
104C2×C3×Dic3—41no—
105C2×C3×Dic3—42no—
106C2×C3×Dic3—84no—
107C23×D4C3×D311yescharacteristic
108C24×C4—32no—
109C2×C4×D4—91no—
110C2×C4×D4—91no—
111C2×C4×D4—92no—
112C2×C4×D4—91no—
113C2×C4×D4—92no—
114C2×C4×D4—91no—
115C22×C4⋊C4—31no—
116C22×C22⋊C4—32no—
117C22×C42—31no—
118C24×C3—22no—
119C24×C3—22no—
120C24×C3—32no—
121C24×C3—34no—
122C24×C3—32no—
123C24×C3—62no—
124C24×C3—62no—
125C24×C3C2×C3×C414yescomplemented
126C24×C3C23×C311yescharacteristic
127C22×A4—22no—
128C22×A4—22no—
129C22×A4—24no—
130C22×A4—21no—
131C22×A4—42no—
132C22×A4—42no—
133C22×A4C2×Dic314yescomplemented
134C22×A4C22×D311yescharacteristic
135C2×C3×D4—32no—
136C2×C3×D4—38no—
137C2×C3×D4—34no—
138C2×C3×D4—32no—
139C2×C3×D4—34no—
140C2×C3×D4—34no—
141C2×C3×D4—34no—
142C2×C3×D4—38no—
143C2×C3×D4—31no—
144C2×C3×D4—41no—
145C2×C3×D4—81no—
146C2×C3×D4C2×A411yescharacteristic
147C22×C3×C4—31no—
148C22×C3×C4—31no—
149C22×C3×C4—32no—
150C22×C3×C4—122no—
151C22×C3×C4C2×C3×C412yescomplemented
152C22×Dic3—22no—
153C22×Dic3—21no—
154C22×Dic3—31no—
155C22×Dic3—31no—
156C22×Dic3—32no—
157C22×Dic3—34no—
158C22×Dic3—32no—
159C22×Dic3—31no—
160C22×Dic3—32no—
161C22×Dic3—32no—
162C22×Dic3—32no—
163C22×Dic3—31no—
164C22×Dic3—32no—
165C22×Dic3—64no—
166C22×Dic3—64no—
167C22×Dic3—64no—
168C22×Dic3—64no—
169C22×Dic3—64no—
170C22×Dic3—64no—
171C22×Dic3—64no—
172C22×Dic3—64no—
173C22×Dic3—62no—
174C22×Dic3—61no—
175C22×Dic3C3×D412yescomplemented
176C22×Dic3C2×A412yescomplemented
177C4×A4—22no—
178C4×A4—32no—
179C4×A4—62no—
180C4×A4—61no—
181C4×A4C2×Dic312yescomplemented
182C3×C4⋊C4—121no—
183C3×C22⋊C4—122no—
184C3×C42—121no—
185#217—34no—
186#217—32no—
187#217—32no—
188#217—32no—
189#217C2×A412yescomplemented
190C4⋊Dic3—32no—
191C4⋊Dic3—31no—
192C4⋊Dic3—32no—
193C4⋊Dic3C2×A411yescharacteristic, complemented
194C4×Dic3—32no—
195C4×Dic3—31no—
196C4×Dic3—31no—
197C4×Dic3—31no—
198C4×Dic3C2×A411yescharacteristic, complemented
199C22×C32—44no—
200C22×C32—41no—
201C22×C32—82no—
202C22×C32—82no—
203C3×A4C4×D411yescharacteristic, complemented
204C32×C4—42no—
205C3×Dic3—42no—
206C3×Dic3—82no—
207C3×Dic3—81no—
208C25C2×C3×D312yes—
209C22×D4—31no—
210C22×D4—31no—
211C22×D4—32no—
212C22×D4—34no—
213C22×D4C3×Dic314yescomplemented
214C23×C4—31no—
215C23×C4—31no—
216C23×C4—32no—
217C23×C4—64no—
218C23×C4—92no—
219C23×C4—92no—
220C23×C4—92no—
221C23×C4—92no—
222C23×C4—184no—
223C23×C4C2×C3×D311yescharacteristic
224C4×D4—31no—
225C4×D4—91no—
226C4×D4—92no—
227C4×D4—91no—
228C4×D4—92no—
229C4×D4—92no—
230C4×D4—92no—
231C4×D4—94no—
232C4×D4—94no—
233C4×D4—92no—
234C4×D4—91no—
235C2×C4⋊C4—91no—
236C2×C4⋊C4—92no—
237C2×C4⋊C4—91no—
238C2×C22⋊C4—92no—
239C2×C22⋊C4—92no—
240C2×C22⋊C4—92no—
241C2×C22⋊C4—92no—
242C2×C42—91no—
243C2×C42—91no—
244C2×C42—91no—
245C2×C42—91no—
246C23×C3—24no—
247C23×C3—31no—
248C23×C3—31no—
249C23×C3—31no—
250C23×C3—31no—
251C23×C3—34no—
252C23×C3—34no—
253C23×C3—34no—
254C23×C3—34no—
255C23×C3—32no—
256C23×C3—42no—
257C23×C3—62no—
258C23×C3—62no—
259C23×C3—62no—
260C23×C3—62no—
261C23×C3—64no—
262C23×C3—62no—
263C23×C3—62no—
264C23×C3—64no—
265C23×C3—64no—
266C23×C3—62no—
267C23×C3—62no—
268C23×C3—68no—
269C23×C3—82no—
270C23×C3C22×C3×C411yescharacteristic
271C23×C3C2×C3×D411yescharacteristic
272C23×C3C3×#4111yescharacteristic
273C23×C3C22×A412yes—
274C2×A4—24no—
275C2×A4—21no—
276C2×A4—21no—
277C2×A4—21no—
278C2×A4—44no—
279C2×A4D3×D411yescharacteristic
280C2×A4#23711yescharacteristic
281C2×A4C22×Dic311yescharacteristic
282C3×D4—38no—
283C3×D4—38no—
284C3×D4—34no—
285C3×D4—44no—
286C3×D4—84no—
287C3×D4C4×A414yescomplemented
288C2×C3×C4—32no—
289C2×C3×C4—31no—
290C2×C3×C4—32no—
291C2×C3×C4—32no—
292C2×C3×C4—32no—
293C2×C3×C4—41no—
294C2×C3×C4—81no—
295C2×C3×C4—121no—
296C2×C3×C4—121no—
297C2×C3×C4—122no—
298C2×C3×C4—244no—
299C2×C3×C4C22×A411yescharacteristic
300C2×Dic3—24no—
301C2×Dic3—32no—
302C2×Dic3—31no—
303C2×Dic3—32no—
304C2×Dic3—32no—
305C2×Dic3—32no—
306C2×Dic3—31no—
307C2×Dic3—32no—
308C2×Dic3—64no—
309C2×Dic3—61no—
310C2×Dic3—62no—
311C2×Dic3—61no—
312C2×Dic3—62no—
313C2×Dic3—64no—
314C2×Dic3—68no—
315C2×Dic3—64no—
316C2×Dic3—61no—
317C2×Dic3—62no—
318C2×Dic3—61no—
319C2×Dic3—62no—
320C2×Dic3C22×A411yescharacteristic
321C2×Dic3C22×A412yes—
322C2×Dic3C22×A411yescharacteristic
323C2×C32—41no—
324C2×C32—41no—
325C2×C32—41no—
326C2×C32—84no—
327C24—22no—
328C24—22no—
329C24—32no—
330C24—34no—
331C24—32no—
332C24—62no—
333C24—62no—
334C24C2×C3×Dic314yescomplemented
335C24C22×C3×D311yescharacteristic
336C2×D4—32no—
337C2×D4—38no—
338C2×D4—34no—
339C2×D4—32no—
340C2×D4—34no—
341C2×D4—34no—
342C2×D4—34no—
343C2×D4—38no—
344C2×D4—31no—
345C2×D4D3×A411yescharacteristic
346C22×C4—31no—
347C22×C4—31no—
348C22×C4—32no—
349C22×C4—32no—
350C22×C4—32no—
351C22×C4—62no—
352C22×C4—61no—
353C22×C4—91no—
354C22×C4—91no—
355C22×C4—92no—
356C22×C4—92no—
357C22×C4—92no—
358C22×C4—91no—
359C22×C4—92no—
360C22×C4—94no—
361C22×C4—92no—
362C22×C4—91no—
363C22×C4—92no—
364C22×C4—184no—
365C22×C4—184no—
366C22×C4—184no—
367C22×C4—184no—
368C22×C4—184no—
369C22×C4—184no—
370C22×C4—184no—
371C22×C4—184no—
372C22×C4—182no—
373C22×C4—181no—
374C22×C4C2×C3×Dic312yescomplemented
375C4⋊C4—31no—
376C4⋊C4—92no—
377C4⋊C4—92no—
378C4⋊C4—91no—
379C22⋊C4—32no—
380C22⋊C4—92no—
381C22⋊C4—92no—
382C22⋊C4—94no—
383C22⋊C4—92no—
384C42—31no—
385C42—91no—
386C42—91no—
387C42—92no—
388C42—91no—
389C22×C3—22no—
390C22×C3—22no—
391C22×C3—31no—
392C22×C3—31no—
393C22×C3—31no—
394C22×C3—32no—
395C22×C3—31no—
396C22×C3—31no—
397C22×C3—31no—
398C22×C3—31no—
399C22×C3—31no—
400C22×C3—31no—
401C22×C3—34no—
402C22×C3—44no—
403C22×C3—41no—
404C22×C3—64no—
405C22×C3—64no—
406C22×C3—64no—
407C22×C3—64no—
408C22×C3—64no—
409C22×C3—64no—
410C22×C3—64no—
411C22×C3—64no—
412C22×C3—62no—
413C22×C3—62no—
414C22×C3—82no—
415C22×C3—82no—
416C22×C3—84no—
417C22×C3—81no—
418C22×C3—162no—
419C22×C3—162no—
420C22×C3C3×C4×D411yescharacteristic, complemented
421C22×C3C2×C4×A414yescomplemented
422C22×C3C23×A411yescharacteristic
423A4—21no—
424A4D4×Dic311yescharacteristic, direct product factor
425C3×C4—32no—
426C3×C4—42no—
427C3×C4—82no—
428C3×C4—122no—
429C3×C4—242no—
430C3×C4—241no—
431C3×C4C2×C4×A412yescomplemented
432Dic3—22no—
433Dic3—21no—
434Dic3—32no—
435Dic3—62no—
436Dic3—61no—
437Dic3D4×A412yesdirect product factor
438C32—41noSylow
439C23—24no—
440C23—31no—
441C23—31no—
442C23—31no—
443C23—31no—
444C23—34no—
445C23—34no—
446C23—34no—
447C23—34no—
448C23—32no—
449C23—62no—
450C23—62no—
451C23—62no—
452C23—62no—
453C23—64no—
454C23—62no—
455C23—62no—
456C23—64no—
457C23—64no—
458C23—62no—
459C23—62no—
460C23—68no—
461C23C3×D3×D411yescharacteristic
462C23C3×#23711yescharacteristic
463C23C22×C3×Dic311yescharacteristic
464C23C2×D3×A412yes—
465D4—38no—
466D4—38no—
467D4—34no—
468D4Dic3×A414yesdirect product factor
469C2×C4—32no—
470C2×C4—31no—
471C2×C4—31no—
472C2×C4—32no—
473C2×C4—32no—
474C2×C4—32no—
475C2×C4—31no—
476C2×C4—32no—
477C2×C4—64no—
478C2×C4—92no—
479C2×C4—92no—
480C2×C4—92no—
481C2×C4—91no—
482C2×C4—92no—
483C2×C4—91no—
484C2×C4—92no—
485C2×C4—184no—
486C2×C4—184no—
487C2×C4—182no—
488C2×C4—181no—
489C2×C4—182no—
490C2×C4—181no—
491C2×C4—184no—
492C2×C4—188no—
493C2×C4—182no—
494C2×C4—181no—
495C2×C4—182no—
496C2×C4—181no—
497C2×C4C2×D3×A411yescharacteristic
498C2×C3—24no—
499C2×C3—31no—
500C2×C3—31no—
501C2×C3—31no—
502C2×C3—31no—
503C2×C3—41no—
504C2×C3—41no—
505C2×C3—41no—
506C2×C3—64no—
507C2×C3—84no—
508C2×C3—81no—
509C2×C3—81no—
510C2×C3—81no—
511C2×C3—164no—
512C2×C3C22×C4×A411yescharacteristic
513C2×C3C2×D4×A411yescharacteristic
514C2×C3A4×#4111yescharacteristic
515C22—22no—
516C22—22no—
517C22—31no—
518C22—31no—
519C22—31no—
520C22—32no—
521C22—31no—
522C22—31no—
523C22—31no—
524C22—31no—
525C22—31no—
526C22—31no—
527C22—34no—
528C22—64no—
529C22—64no—
530C22—64no—
531C22—64no—
532C22—64no—
533C22—64no—
534C22—64no—
535C22—64no—
536C22—62no—
537C22—62no—
538C22C3×D4×Dic311yescharacteristic, complemented
539C22C2×Dic3×A414yescomplemented
540C22C22×D3×A411yescharacteristic
541C4—32no—
542C4—32no—
543C4—62no—
544C4—61no—
545C4—92no—
546C4—182no—
547C4—181no—
548C4C2×Dic3×A412yescomplemented
549C3—41no—
550C3—81no—
551C3C4×D4×A411yescharacteristic, complemented
552C2—24no—
553C2—31no—
554C2—31no—
555C2—31no—
556C2—31no—
557C2—64no—
558C2D3×D4×A411yescharacteristic
559C2A4×#23711yescharacteristic
560C2C22×Dic3×A411yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×A4
commutatorC23×C3C22×C3×C4
FittingC23×C3×D4C2×C3
socle, cosocleC24×C3C23×C3
prime radicalC2×C3×D4×A4C2
hypercenterC2×D4D3×A4
hypocenterC22×C3C3×C4×D4
LCSG ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. C22×Dic3×A4C2semidirect
3. A4×#217C2semidirect
4. A4×C4⋊Dic3C2semidirect
5. C4×Dic3×A4C2semidirect
6. C22×D4×Dic3C3semidirect
9. C3×D4×A4C4semidirect
17. C24×Dic3C2×C3semidirect
21. C22×#217C2×C3semidirect
28. C22×C4⋊Dic3C2×C3semidirect
29. C22×C4×Dic3C2×C3semidirect
35. C22×C3×A4C2×C4semidirect
39. C3×C4×A4C2×C4semidirect
42. Dic3×A4D4direct (N × H)
54. C22×C3×D4C3×C4semidirect
66. D4×A4Dic3direct (N × H)
88. D4×Dic3A4direct (N × H)
125. C24×C3C2×C3×C4semidirect
133. C22×A4C2×Dic3semidirect
151. C22×C3×C4C2×C3×C4semidirect
175. C22×Dic3C3×D4semidirect
176. C22×Dic3C2×A4semidirect
181. C4×A4C2×Dic3semidirect
189. #217C2×A4semidirect
193. C4⋊Dic3C2×A4semidirect
198. C4×Dic3C2×A4semidirect
203. C3×A4C4×D4semidirect
213. C22×D4C3×Dic3semidirect
287. C3×D4C4×A4semidirect
334. C24C2×C3×Dic3semidirect
374. C22×C4C2×C3×Dic3semidirect
420. C22×C3C3×C4×D4semidirect
421. C22×C3C2×C4×A4semidirect
424. A4D4×Dic3direct (N × H)
431. C3×C4C2×C4×A4semidirect
437. Dic3D4×A4direct (N × H)
468. D4Dic3×A4direct (N × H)
538. C22C3×D4×Dic3semidirect
539. C22C2×Dic3×A4semidirect
548. C4C2×Dic3×A4semidirect
551. C3C4×D4×A4semidirect

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×Dic3×A42
A4×#2172
A4×C4⋊Dic32
C4×Dic3×A42
C22×D4×Dic33
C4×D4×A43
C3×D4×Dic34