Finite Group Databasebeta

← D3×A4×C4⋊C4 #11923165

Subgroups — D3×A4×C4⋊C4 #11923165

Order 1152.

1162 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 1162 conjugacy classes of subgroups — too many to draw. Only its 147 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×C4×D3×A4C212yesmaximal
2C2×C4×D3×A4C211yesmaximal, characteristic
3C3×A4×C4⋊C4C211yesmaximal, characteristic, complemented
4A4×C4⋊Dic3C211yesmaximal, characteristic, complemented
5A4×Dic3⋊C4C212yesmaximal, complemented
6C22×D3×C4⋊C4C311yesmaximal, characteristic, complemented
7C2×A4×C4⋊C4—31nomaximal
8C22×D3×A4C2211yescharacteristic
9C2×C3×C4×A4C2212yes—
10C2×C3×C4×A4C2211yescharacteristic
11C2×Dic3×A4C2212yes—
12C2×Dic3×A4C2211yescharacteristic
13C4×D3×A4—24no—
14C4×D3×A4C414yescomplemented
15C3×D3×C4⋊C4—41nomaximal
16C23×C4×D3C2×C312yes—
17C23×C4×D3C2×C311yescharacteristic
18C22×C4×A4—31no—
19C22×C4×A4—32no—
20C22×C3×C4⋊C4C2×C311yescharacteristic, complemented
21C22×C4⋊Dic3C2×C311yescharacteristic, complemented
22C22×Dic3⋊C4C2×C312yescomplemented
23C2×D3×C4⋊C4—31no—
24C2×D3×C4⋊C4—31no—
25C2×D3×C4⋊C4—32no—
26C2×D3×C4⋊C4—31no—
27C2×D3×C4⋊C4—31no—
28C2×D3×C4⋊C4—32no—
29A4×C4⋊C4—21no—
30A4×C4⋊C4—32no—
31A4×C4⋊C4—31no—
32A4×C4⋊C4D311yescharacteristic, direct product factor
33C22×C3×A4C2311yescharacteristic
34C2×D3×A4C2×C412yes—
35C2×D3×A4D412yes—
36C2×D3×A4Q812yes—
37C2×C3×C4×D3—41no—
38C2×C3×C4×D3—42no—
39C3×C4×A4—22no—
40C3×C4×A4C2×C412yescomplemented
41Dic3×A4—22no—
42Dic3×A4C2×C412yescomplemented
43C32×C4⋊C4—41no—
44C3×C4⋊Dic3—41no—
45C3×Dic3⋊C4—42no—
46C23×C4⋊C4—31noSylow
47C24×D3C22×C311yescharacteristic
48C23×A4—31no—
49C23×C3×C4C22×C312yes—
50C23×C3×C4C22×C311yescharacteristic
51C23×Dic3C22×C312yes—
52C23×Dic3C22×C311yescharacteristic
53C22×C4×D3—24no—
54C22×C4×D3—31no—
55C22×C4×D3—34no—
56C22×C4×D3—31no—
57C22×C4×D3—31no—
58C22×C4×D3—31no—
59C22×C4×D3—32no—
60C22×C4×D3—32no—
61C22×C4×D3—32no—
62C22×C4×D3—32no—
63C22×C4×D3—64no—
64C22×C4×D3C3×C414yescomplemented
65C2×C4×A4—21no—
66C2×C4×A4—22no—
67C2×C4×A4—31no—
68C2×C4×A4—34no—
69C2×C4×A4—32no—
70C2×C4×A4—64no—
71C2×C4×A4C2×D312yes—
72C2×C4×A4C2×D311yescharacteristic
73C2×C3×C4⋊C4—31no—
74C2×C3×C4⋊C4—31no—
75C2×C3×C4⋊C4—32no—
76C2×C3×C4⋊C4—121no—
77C2×C4⋊Dic3—31no—
78C2×C4⋊Dic3—31no—
79C2×C4⋊Dic3—32no—
80C2×Dic3⋊C4—32no—
81C2×Dic3⋊C4—32no—
82C2×Dic3⋊C4—32no—
83C2×Dic3⋊C4—32no—
84D3×C4⋊C4—32no—
85D3×C4⋊C4—32no—
86D3×C4⋊C4—34no—
87D3×C4⋊C4—34no—
88D3×C4⋊C4—32no—
89D3×C4⋊C4—32no—
90D3×C4⋊C4—31no—
91D3×C4⋊C4—31no—
92D3×C4⋊C4—31no—
93D3×C4⋊C4—32no—
94D3×C4⋊C4A411yescharacteristic, direct product factor
95C22×C3×D3—41no—
96C2×C3×A4C22×C411yescharacteristic
97C2×C3×A4C2×D411yescharacteristic
98C2×C3×A4C2×Q811yescharacteristic
99D3×A4C4⋊C414yesdirect product factor
100C2×C32×C4—41no—
101C2×C32×C4—42no—
102C2×C3×Dic3—41no—
103C2×C3×Dic3—42no—
104C3×C4×D3—44no—
105C3×C4×D3—84no—
106C24×C4—31no—
107C24×C4—32no—
108C22×C4⋊C4—32no—
109C22×C4⋊C4—31no—
110C22×C4⋊C4—91no—
111C22×C4⋊C4—91no—
112C22×C4⋊C4—92no—
113C22×C4⋊C4—91no—
114C22×C4⋊C4—91no—
115C22×C4⋊C4—92no—
116C22×C4⋊C4C3×D311yescharacteristic, complemented
117C24×C3C23×C311yescharacteristic
118C23×D3—31no—
119C23×D3—31no—
120C23×D3—32no—
121C23×D3—32no—
122C23×D3—32no—
123C23×D3C2×C3×C412yes—
124C23×D3C3×D412yes—
125C23×D3C3×Q812yes—
126C22×A4—21no—
127C22×A4—32no—
128C22×A4—32no—
129C22×A4—32no—
130C22×A4C22×D311yescharacteristic
131C22×C3×C4—22no—
132C22×C3×C4—31no—
133C22×C3×C4—31no—
134C22×C3×C4—32no—
135C22×C3×C4—32no—
136C22×C3×C4—32no—
137C22×C3×C4—62no—
138C22×C3×C4—121no—
139C22×C3×C4—122no—
140C22×C3×C4C2×C3×C412yescomplemented
141C22×Dic3—22no—
142C22×Dic3—31no—
143C22×Dic3—31no—
144C22×Dic3—32no—
145C22×Dic3—32no—
146C22×Dic3—32no—
147C22×Dic3—62no—
148C22×Dic3C2×C3×C412yescomplemented
149C2×C4×D3—32no—
150C2×C4×D3—34no—
151C2×C4×D3—34no—
152C2×C4×D3—34no—
153C2×C4×D3—31no—
154C2×C4×D3—31no—
155C2×C4×D3—31no—
156C2×C4×D3—34no—
157C2×C4×D3—34no—
158C2×C4×D3—34no—
159C2×C4×D3—34no—
160C2×C4×D3—34no—
161C2×C4×D3—34no—
162C2×C4×D3—32no—
163C2×C4×D3—32no—
164C2×C4×D3—32no—
165C2×C4×D3—64no—
166C2×C4×D3—64no—
167C2×C4×D3—64no—
168C2×C4×D3—64no—
169C2×C4×D3—64no—
170C2×C4×D3—64no—
171C2×C4×D3—64no—
172C2×C4×D3—64no—
173C2×C4×D3C2×A412yes—
174C2×C4×D3C2×A411yescharacteristic
175C4×A4—22no—
176C4×A4—22no—
177C4×A4—32no—
178C4×A4—42no—
179C4×A4—62no—
180C4×A4C4×D312yescomplemented
181C3×C4⋊C4—32no—
182C3×C4⋊C4—32no—
183C3×C4⋊C4—31no—
184C3×C4⋊C4—41no—
185C3×C4⋊C4—81no—
186C3×C4⋊C4—122no—
187C3×C4⋊C4—121no—
188C3×C4⋊C4C2×A411yescharacteristic, complemented
189C4⋊Dic3—32no—
190C4⋊Dic3—31no—
191C4⋊Dic3—32no—
192C4⋊Dic3C2×A411yescharacteristic, complemented
193Dic3⋊C4—34no—
194Dic3⋊C4—32no—
195Dic3⋊C4—32no—
196Dic3⋊C4—32no—
197Dic3⋊C4C2×A412yescomplemented
198C22×C32—41no—
199C2×C3×D3—42no—
200C2×C3×D3—42no—
201C2×C3×D3—42no—
202C3×A4C2×C4⋊C411yescharacteristic, complemented
203C32×C4—42no—
204C32×C4—82no—
205C3×Dic3—42no—
206C3×Dic3—82no—
207C25—31no—
208C23×C4—31no—
209C23×C4—34no—
210C23×C4—32no—
211C23×C4—64no—
212C23×C4—91no—
213C23×C4—92no—
214C23×C4—91no—
215C23×C4—91no—
216C23×C4—91no—
217C23×C4—94no—
218C23×C4—92no—
219C23×C4—92no—
220C23×C4—92no—
221C23×C4—184no—
222C23×C4C2×C3×D312yes—
223C23×C4C2×C3×D311yescharacteristic
224C2×C4⋊C4—31no—
225C2×C4⋊C4—31no—
226C2×C4⋊C4—31no—
227C2×C4⋊C4—32no—
228C2×C4⋊C4—92no—
229C2×C4⋊C4—91no—
230C2×C4⋊C4—92no—
231C2×C4⋊C4—91no—
232C2×C4⋊C4—91no—
233C2×C4⋊C4—92no—
234C2×C4⋊C4—92no—
235C2×C4⋊C4—94no—
236C2×C4⋊C4—92no—
237C2×C4⋊C4—92no—
238C2×C4⋊C4—94no—
239C2×C4⋊C4—91no—
240C2×C4⋊C4—92no—
241C2×C4⋊C4—92no—
242C2×C4⋊C4—92no—
243C2×C4⋊C4—92no—
244C2×C4⋊C4—91no—
245C23×C3—31no—
246C23×C3—31no—
247C23×C3—31no—
248C23×C3—31no—
249C23×C3—121no—
250C23×C3C22×C3×C411yescharacteristic
251C23×C3C2×C3×D411yescharacteristic
252C23×C3C2×C3×Q811yescharacteristic
253C22×D3—32no—
254C22×D3—32no—
255C22×D3—32no—
256C22×D3—38no—
257C22×D3—31no—
258C22×D3—32no—
259C22×D3—32no—
260C22×D3—32no—
261C22×D3—32no—
262C22×D3—32no—
263C22×D3—32no—
264C22×D3—32no—
265C22×D3—32no—
266C22×D3—34no—
267C22×D3—34no—
268C22×D3—32no—
269C22×D3—34no—
270C22×D3C3×C4⋊C414yescomplemented
271C22×D3C22×A411yescharacteristic
272C2×A4—21no—
273C2×A4—21no—
274C2×A4—21no—
275C2×A4—34no—
276C2×A4C2×C4×D311yescharacteristic
277C2×A4D3×D411yescharacteristic
278C2×A4D3×Q811yescharacteristic
279C2×C3×C4—32no—
280C2×C3×C4—31no—
281C2×C3×C4—32no—
282C2×C3×C4—32no—
283C2×C3×C4—32no—
284C2×C3×C4—32no—
285C2×C3×C4—41no—
286C2×C3×C4—42no—
287C2×C3×C4—62no—
288C2×C3×C4—62no—
289C2×C3×C4—62no—
290C2×C3×C4—62no—
291C2×C3×C4—81no—
292C2×C3×C4—82no—
293C2×C3×C4—124no—
294C2×C3×C4—121no—
295C2×C3×C4—122no—
296C2×C3×C4—244no—
297C2×C3×C4C22×A412yes—
298C2×C3×C4C22×A411yescharacteristic
299C2×Dic3—32no—
300C2×Dic3—31no—
301C2×Dic3—32no—
302C2×Dic3—32no—
303C2×Dic3—32no—
304C2×Dic3—32no—
305C2×Dic3—62no—
306C2×Dic3—62no—
307C2×Dic3—62no—
308C2×Dic3—62no—
309C2×Dic3C22×A412yes—
310C2×Dic3C22×A411yescharacteristic
311C4×D3—24no—
312C4×D3—38no—
313C4×D3—34no—
314C4×D3—34no—
315C4×D3—34no—
316C4×D3—64no—
317C4×D3—64no—
318C4×D3—68no—
319C4×D3—64no—
320C4×D3C4×A414yescomplemented
321C2×C32—41no—
322C2×C32—41no—
323C2×C32—41no—
324C3×D3—44no—
325C24—32no—
326C24—32no—
327C24—32no—
328C24—91no—
329C24—91no—
330C24—92no—
331C24—92no—
332C24—92no—
333C24C22×C3×D311yescharacteristic
334C22×C4—22no—
335C22×C4—31no—
336C22×C4—31no—
337C22×C4—31no—
338C22×C4—32no—
339C22×C4—32no—
340C22×C4—32no—
341C22×C4—32no—
342C22×C4—32no—
343C22×C4—62no—
344C22×C4—62no—
345C22×C4—91no—
346C22×C4—94no—
347C22×C4—94no—
348C22×C4—92no—
349C22×C4—91no—
350C22×C4—91no—
351C22×C4—92no—
352C22×C4—94no—
353C22×C4—94no—
354C22×C4—94no—
355C22×C4—94no—
356C22×C4—94no—
357C22×C4—94no—
358C22×C4—92no—
359C22×C4—92no—
360C22×C4—94no—
361C22×C4—91no—
362C22×C4—91no—
363C22×C4—92no—
364C22×C4—92no—
365C22×C4—92no—
366C22×C4—184no—
367C22×C4—184no—
368C22×C4—184no—
369C22×C4—184no—
370C22×C4—184no—
371C22×C4—184no—
372C22×C4—184no—
373C22×C4—184no—
374C22×C4—182no—
375C22×C4C3×C4×D312yescomplemented
376C4⋊C4—32no—
377C4⋊C4—32no—
378C4⋊C4—31no—
379C4⋊C4—32no—
380C4⋊C4—31no—
381C4⋊C4—92no—
382C4⋊C4—92no—
383C4⋊C4—92no—
384C4⋊C4—94no—
385C4⋊C4—92no—
386C4⋊C4—92no—
387C4⋊C4—91no—
388C4⋊C4D3×A411yescharacteristic, direct product factor
389C22×C3—31no—
390C22×C3—31no—
391C22×C3—31no—
392C22×C3—32no—
393C22×C3—31no—
394C22×C3—31no—
395C22×C3—31no—
396C22×C3—31no—
397C22×C3—31no—
398C22×C3—31no—
399C22×C3—41no—
400C22×C3—81no—
401C22×C3—122no—
402C22×C3—122no—
403C22×C3—122no—
404C22×C3C2×C3×C4⋊C411yescharacteristic, complemented
405C22×C3C23×A411yescharacteristic
406C2×D3—34no—
407C2×D3—34no—
408C2×D3—34no—
409C2×D3—32no—
410C2×D3—32no—
411C2×D3—32no—
412C2×D3—34no—
413C2×D3—34no—
414C2×D3—34no—
415C2×D3—34no—
416C2×D3—34no—
417C2×D3C2×C4×A412yes—
418C2×D3D4×A412yes—
419C2×D3Q8×A412yes—
420A4—21no—
421A4D3×C4⋊C411yescharacteristic, direct product factor
422C3×C4—22no—
423C3×C4—32no—
424C3×C4—42no—
425C3×C4—62no—
426C3×C4—82no—
427C3×C4—82no—
428C3×C4—122no—
429C3×C4—162no—
430C3×C4—242no—
431C3×C4C2×C4×A412yescomplemented
432Dic3—22no—
433Dic3—32no—
434Dic3—62no—
435Dic3C2×C4×A412yescomplemented
436C32—41noSylow
437C23—31no—
438C23—31no—
439C23—31no—
440C23—31no—
441C23—31no—
442C23—34no—
443C23—92no—
444C23—92no—
445C23—92no—
446C23—92no—
447C23—92no—
448C23—92no—
449C23—92no—
450C23—92no—
451C23—94no—
452C23—94no—
453C23—94no—
454C23—92no—
455C23—92no—
456C23—92no—
457C23—98no—
458C23—92no—
459C23—91no—
460C23C2×C3×C4×D311yescharacteristic
461C23C3×D3×D411yescharacteristic
462C23C3×D3×Q811yescharacteristic
463C2×C4—32no—
464C2×C4—31no—
465C2×C4—31no—
466C2×C4—32no—
467C2×C4—32no—
468C2×C4—34no—
469C2×C4—32no—
470C2×C4—32no—
471C2×C4—32no—
472C2×C4—62no—
473C2×C4—62no—
474C2×C4—64no—
475C2×C4—62no—
476C2×C4—62no—
477C2×C4—94no—
478C2×C4—92no—
479C2×C4—94no—
480C2×C4—92no—
481C2×C4—98no—
482C2×C4—92no—
483C2×C4—91no—
484C2×C4—94no—
485C2×C4—92no—
486C2×C4—92no—
487C2×C4—184no—
488C2×C4—184no—
489C2×C4—182no—
490C2×C4—182no—
491C2×C4—184no—
492C2×C4—188no—
493C2×C4—182no—
494C2×C4—182no—
495C2×C4C2×D3×A412yes—
496C2×C4C2×D3×A411yescharacteristic
497C2×C3—31no—
498C2×C3—31no—
499C2×C3—31no—
500C2×C3—31no—
501C2×C3—41no—
502C2×C3—41no—
503C2×C3—41no—
504C2×C3—81no—
505C2×C3—81no—
506C2×C3—81no—
507C2×C3—124no—
508C2×C3C22×C4×A411yescharacteristic
509C2×C3C2×D4×A411yescharacteristic
510C2×C3C2×Q8×A411yescharacteristic
511D3—34no—
512D3A4×C4⋊C414yesdirect product factor
513C22—31no—
514C22—31no—
515C22—31no—
516C22—32no—
517C22—31no—
518C22—31no—
519C22—32no—
520C22—31no—
521C22—31no—
522C22—32no—
523C22—31no—
524C22—31no—
525C22—32no—
526C22—94no—
527C22—94no—
528C22—94no—
529C22—94no—
530C22—94no—
531C22—94no—
532C22—94no—
533C22—94no—
534C22—92no—
535C22—92no—
536C22—92no—
537C22C3×D3×C4⋊C411yescharacteristic, complemented
538C22C22×D3×A411yescharacteristic
539C4—22no—
540C4—32no—
541C4—32no—
542C4—62no—
543C4—62no—
544C4—92no—
545C4—182no—
546C4C4×D3×A412yescomplemented
547C3—41no—
548C3—81no—
549C3C2×A4×C4⋊C411yescharacteristic, complemented
550C2—31no—
551C2—31no—
552C2—31no—
553C2—31no—
554C2—34no—
555C2—94no—
556C2C2×C4×D3×A411yescharacteristic
557C2D3×D4×A411yescharacteristic
558C2D3×Q8×A411yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×A4
commutatorC23×C3C22×C3×C4
FittingC22×C3×C4⋊C4C2×C3
socle, cosocleC24×C3C23×C3
prime radicalC22×D3×A4C22
hypercenterC4⋊C4D3×A4
hypocenterC22×C3C2×C3×C4⋊C4
LCSG ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C3×A4×C4⋊C4C2semidirect
4. A4×C4⋊Dic3C2semidirect
5. A4×Dic3⋊C4C2semidirect
6. C22×D3×C4⋊C4C3semidirect
14. C4×D3×A4C4semidirect
20. C22×C3×C4⋊C4C2×C3semidirect
21. C22×C4⋊Dic3C2×C3semidirect
22. C22×Dic3⋊C4C2×C3semidirect
32. A4×C4⋊C4D3direct (N × H)
40. C3×C4×A4C2×C4semidirect
42. Dic3×A4C2×C4semidirect
64. C22×C4×D3C3×C4semidirect
94. D3×C4⋊C4A4direct (N × H)
99. D3×A4C4⋊C4direct (N × H)
116. C22×C4⋊C4C3×D3semidirect
140. C22×C3×C4C2×C3×C4semidirect
148. C22×Dic3C2×C3×C4semidirect
180. C4×A4C4×D3semidirect
188. C3×C4⋊C4C2×A4semidirect
192. C4⋊Dic3C2×A4semidirect
197. Dic3⋊C4C2×A4semidirect
202. C3×A4C2×C4⋊C4semidirect
270. C22×D3C3×C4⋊C4semidirect
320. C4×D3C4×A4semidirect
375. C22×C4C3×C4×D3semidirect
388. C4⋊C4D3×A4direct (N × H)
404. C22×C3C2×C3×C4⋊C4semidirect
421. A4D3×C4⋊C4direct (N × H)
431. C3×C4C2×C4×A4semidirect
435. Dic3C2×C4×A4semidirect
512. D3A4×C4⋊C4direct (N × H)
537. C22C3×D3×C4⋊C4semidirect
546. C4C4×D3×A4semidirect
549. C3C2×A4×C4⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D3×A42
C3×A4×C4⋊C42
A4×C4⋊Dic32
A4×Dic3⋊C42
C22×D3×C4⋊C43
C2×A4×C4⋊C43
C3×D3×C4⋊C44