Finite Group Databasebeta

← D3×A4×M16 #11923305

Subgroups — D3×A4×M16 #11923305

Order 1152.

820 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 820 conjugacy classes of subgroups — too many to draw. Only its 117 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×A4C211yesmaximal, characteristic
2C3×A4×M16C211yesmaximal, characteristic, complemented
3A4×#208C211yesmaximal, characteristic, complemented
4A4×ΓL(1,𝔽25)C212yesmaximal, complemented
5D3×C8×A4C212yesmaximal, complemented
6C22×D3×M16C311yesmaximal, characteristic, complemented
7C2×A4×M16—31nomaximal
8C22×D3×A4C411yescharacteristic
9C2×C3×C4×A4C2211yescharacteristic
10C2×Dic3×A4C411yescharacteristic
11C4×D3×A4C411yescharacteristic
12C4×D3×A4C411yescharacteristic
13C4×D3×A4C2211yescharacteristic
14C4×D3×A4C2211yescharacteristic
15C3×D3×M16—41nomaximal
16C3×C8×A4C2212yescomplemented
17A4×C3⋊C8C2212yescomplemented
18C23×C4×D3C2×C311yescharacteristic
19C22×C4×A4—31no—
20C22×C3×M16C2×C311yescharacteristic, complemented
21C22×#208C2×C311yescharacteristic, complemented
22C2×D3×M16—31no—
23C2×D3×M16—32no—
24C2×D3×M16—32no—
25C2×D3×M16—31no—
26C2×D3×M16—31no—
27C2×D3×M16—31no—
28C22×ΓL(1,𝔽25)C2×C312yescomplemented
29C22×D3×C8C2×C312yescomplemented
30A4×M16—21no—
31A4×M16—31no—
32A4×M16—32no—
33A4×M16D311yescharacteristic, direct product factor
34C2×C8×A4—32no—
35C22×C3×A4C2×C411yescharacteristic
36C2×D3×A4—22no—
37C2×D3×A4C2×C411yescharacteristic
38C2×D3×A4C2×C411yescharacteristic
39C2×C3×C4×D3—41no—
40C3×C4×A4C2×C411yescharacteristic
41C3×C4×A4C2311yescharacteristic
42Dic3×A4C2×C411yescharacteristic
43Dic3×A4C2×C411yescharacteristic
44C32×M16—41no—
45C3×#208—41no—
46C3×ΓL(1,𝔽25)—42no—
47C3×D3×C8—42no—
48C23×M16—31noSylow
49C24×D3C3×C411yescharacteristic
50C23×A4—31no—
51C23×C3×C4C22×C311yescharacteristic
52C23×Dic3C3×C411yescharacteristic
53C22×C4×D3—31no—
54C22×C4×D3—31no—
55C22×C4×D3—31no—
56C22×C4×D3—31no—
57C22×C4×D3—31no—
58C22×C4×D3—31no—
59C22×C4×D3—31no—
60C22×C4×D3—31no—
61C22×C4×D3C3×C411yescharacteristic
62C22×C4×D3C3×C411yescharacteristic
63C22×C4×D3C22×C311yescharacteristic
64C22×C4×D3C22×C311yescharacteristic
65C2×C4×A4—21no—
66C2×C4×A4—31no—
67C2×C4×A4—31no—
68C2×C4×A4—31no—
69C2×C4×A4—31no—
70C2×C4×A4—31no—
71C2×C4×A4C2×D311yescharacteristic
72C2×C3×M16—31no—
73C2×C3×M16—32no—
74C2×C3×M16—31no—
75C2×C3×M16—121no—
76C22×C3×C8C22×C312yescomplemented
77C2×#208—31no—
78C2×#208—32no—
79C2×#208—31no—
80C22×C3⋊C8C22×C312yescomplemented
81D3×M16—32no—
82D3×M16—32no—
83D3×M16—34no—
84D3×M16—34no—
85D3×M16—32no—
86D3×M16—31no—
87D3×M16—31no—
88D3×M16—31no—
89D3×M16—32no—
90D3×M16—32no—
91D3×M16A411yescharacteristic, direct product factor
92C2×ΓL(1,𝔽25)—32no—
93C2×ΓL(1,𝔽25)—32no—
94C2×ΓL(1,𝔽25)—32no—
95C2×ΓL(1,𝔽25)—32no—
96C2×D3×C8—32no—
97C2×D3×C8—32no—
98C2×D3×C8—32no—
99C2×D3×C8—32no—
100C8×A4—22no—
101C8×A4—32no—
102C8×A4C2×D312yescomplemented
103C22×C3×D3—41no—
104C2×C3×A4—21no—
105C2×C3×A4C22×C411yescharacteristic
106D3×A4—21no—
107D3×A4M1612yesdirect product factor
108C2×C32×C4—41no—
109C2×C3×Dic3—41no—
110C3×C4×D3—41no—
111C3×C4×D3—41no—
112C3×C4×D3—41no—
113C3×C4×D3—41no—
114C32×C8—42no—
115C3×C3⋊C8—42no—
116C24×C4—31no—
117C22×M16—31no—
118C22×M16—32no—
119C22×M16—91no—
120C22×M16—92no—
121C22×M16—91no—
122C22×M16—92no—
123C22×M16—91no—
124C22×M16—91no—
125C22×M16C3×D311yescharacteristic, complemented
126C23×C8—32no—
127C24×C3C2×C3×C411yescharacteristic
128C23×D3—22no—
129C23×D3—31no—
130C23×D3—31no—
131C23×D3—31no—
132C23×D3—31no—
133C23×D3—62no—
134C23×D3C2×C3×C411yescharacteristic
135C23×D3C2×C3×C411yescharacteristic
136C22×A4—21no—
137C22×A4—31no—
138C22×A4—31no—
139C22×A4—62no—
140C22×A4C4×D311yescharacteristic
141C22×C3×C4—31no—
142C22×C3×C4—31no—
143C22×C3×C4—31no—
144C22×C3×C4—31no—
145C22×C3×C4—121no—
146C22×C3×C4C2×C3×C411yescharacteristic
147C22×C3×C4C23×C311yescharacteristic
148C22×Dic3—31no—
149C22×Dic3—31no—
150C22×Dic3—31no—
151C22×Dic3—31no—
152C22×Dic3C2×C3×C411yescharacteristic
153C22×Dic3C2×C3×C411yescharacteristic
154C2×C4×D3—32no—
155C2×C4×D3—32no—
156C2×C4×D3—32no—
157C2×C4×D3—32no—
158C2×C4×D3—32no—
159C2×C4×D3—32no—
160C2×C4×D3—32no—
161C2×C4×D3—31no—
162C2×C4×D3—31no—
163C2×C4×D3—31no—
164C2×C4×D3—31no—
165C2×C4×D3—31no—
166C2×C4×D3—31no—
167C2×C4×D3—31no—
168C2×C4×D3—31no—
169C2×C4×D3—31no—
170C2×C4×D3—31no—
171C2×C4×D3—31no—
172C2×C4×D3—31no—
173C2×C4×D3—31no—
174C2×C4×D3—31no—
175C2×C4×D3—31no—
176C2×C4×D3—31no—
177C2×C4×D3—31no—
178C2×C4×D3—31no—
179C2×C4×D3—31no—
180C2×C4×D3—31no—
181C2×C4×D3—31no—
182C2×C4×D3—31no—
183C2×C4×D3—31no—
184C2×C4×D3C2×A411yescharacteristic
185C4×A4—21no—
186C4×A4—21no—
187C4×A4—31no—
188C4×A4—31no—
189C4×A4C4×D311yescharacteristic
190C4×A4C22×D311yescharacteristic
191C3×M16—32no—
192C3×M16—31no—
193C3×M16—32no—
194C3×M16—41no—
195C3×M16—81no—
196C3×M16—122no—
197C3×M16—121no—
198C3×M16C2×A411yescharacteristic, complemented
199C2×C3×C8—32no—
200C2×C3×C8—32no—
201C2×C3×C8—122no—
202#208—32no—
203#208—31no—
204#208—32no—
205#208C2×A411yescharacteristic, complemented
206C2×C3⋊C8—32no—
207C2×C3⋊C8—32no—
208ΓL(1,𝔽25)—34no—
209ΓL(1,𝔽25)—32no—
210ΓL(1,𝔽25)—32no—
211ΓL(1,𝔽25)—32no—
212ΓL(1,𝔽25)C2×A412yescomplemented
213D3×C8—34no—
214D3×C8—32no—
215D3×C8—32no—
216D3×C8—32no—
217D3×C8C2×A412yescomplemented
218C22×C32—41no—
219C2×C3×D3—41no—
220C2×C3×D3—41no—
221C2×C3×D3—82no—
222C3×A4C2×M1611yescharacteristic, complemented
223C32×C4—41no—
224C32×C4—41no—
225C3×Dic3—41no—
226C3×Dic3—41no—
227C25—31no—
228C23×C4—31no—
229C23×C4—31no—
230C23×C4—31no—
231C23×C4—31no—
232C23×C4—31no—
233C23×C4—91no—
234C23×C4—91no—
235C23×C4—91no—
236C23×C4—91no—
237C23×C4—91no—
238C23×C4—91no—
239C23×C4—91no—
240C23×C4—91no—
241C23×C4C2×C3×D311yescharacteristic
242C2×M16—31no—
243C2×M16—31no—
244C2×M16—32no—
245C2×M16—31no—
246C2×M16—92no—
247C2×M16—92no—
248C2×M16—92no—
249C2×M16—92no—
250C2×M16—92no—
251C2×M16—91no—
252C2×M16—92no—
253C2×M16—91no—
254C2×M16—91no—
255C2×M16—94no—
256C2×M16—92no—
257C2×M16—92no—
258C2×M16—92no—
259C2×M16—94no—
260C2×M16—91no—
261C2×M16—92no—
262C2×M16—91no—
263C22×C8—32no—
264C22×C8—92no—
265C22×C8—92no—
266C22×C8—92no—
267C22×C8—92no—
268C22×C8C2×C3×D312yescomplemented
269C23×C3—21no—
270C23×C3—31no—
271C23×C3—31no—
272C23×C3—61no—
273C23×C3—121no—
274C23×C3C22×C3×C411yescharacteristic
275C22×D3—21no—
276C22×D3—31no—
277C22×D3—31no—
278C22×D3—32no—
279C22×D3—32no—
280C22×D3—31no—
281C22×D3—31no—
282C22×D3—31no—
283C22×D3—31no—
284C22×D3—31no—
285C22×D3—62no—
286C22×D3—62no—
287C22×D3—62no—
288C22×D3—62no—
289C22×D3—62no—
290C22×D3—62no—
291C22×D3—62no—
292C22×D3—62no—
293C22×D3—61no—
294C22×D3C3×M1612yescomplemented
295C22×D3C4×A411yescharacteristic
296C2×A4—21no—
297C2×A4—21no—
298C2×A4—32no—
299C2×A4—41no—
300C2×A4—61no—
301C2×A4C2×C4×D311yescharacteristic
302C2×C3×C4—32no—
303C2×C3×C4—31no—
304C2×C3×C4—31no—
305C2×C3×C4—31no—
306C2×C3×C4—31no—
307C2×C3×C4—31no—
308C2×C3×C4—31no—
309C2×C3×C4—31no—
310C2×C3×C4—41no—
311C2×C3×C4—81no—
312C2×C3×C4—121no—
313C2×C3×C4—121no—
314C2×C3×C4—121no—
315C2×C3×C4—121no—
316C2×C3×C4—121no—
317C2×C3×C4C22×A411yescharacteristic
318C2×Dic3—32no—
319C2×Dic3—31no—
320C2×Dic3—31no—
321C2×Dic3—31no—
322C2×Dic3—31no—
323C2×Dic3—31no—
324C2×Dic3—31no—
325C2×Dic3—31no—
326C2×Dic3C4×A411yescharacteristic
327C4×D3—32no—
328C4×D3—32no—
329C4×D3—32no—
330C4×D3—32no—
331C4×D3—31no—
332C4×D3—31no—
333C4×D3—31no—
334C4×D3—31no—
335C4×D3—31no—
336C4×D3—31no—
337C4×D3—31no—
338C4×D3—31no—
339C4×D3—31no—
340C4×D3—31no—
341C4×D3—31no—
342C4×D3—31no—
343C4×D3C4×A411yescharacteristic
344C4×D3C4×A411yescharacteristic
345C4×D3C22×A411yescharacteristic
346C4×D3C22×A411yescharacteristic
347C3×C8—32no—
348C3×C8—42no—
349C3×C8—82no—
350C3×C8—122no—
351C3×C8C22×A412yescomplemented
352C3⋊C8—32no—
353C3⋊C8C22×A412yescomplemented
354C2×C32—41no—
355C2×C32—81no—
356C3×D3—42no—
357C3×D3—81no—
358C24—31no—
359C24—31no—
360C24—62no—
361C24—91no—
362C24—91no—
363C24—91no—
364C24—91no—
365C24—182no—
366C24C3×C4×D311yescharacteristic
367C22×C4—31no—
368C22×C4—31no—
369C22×C4—31no—
370C22×C4—31no—
371C22×C4—31no—
372C22×C4—31no—
373C22×C4—31no—
374C22×C4—91no—
375C22×C4—91no—
376C22×C4—91no—
377C22×C4—91no—
378C22×C4—91no—
379C22×C4—91no—
380C22×C4—91no—
381C22×C4—91no—
382C22×C4—91no—
383C22×C4—91no—
384C22×C4—91no—
385C22×C4—92no—
386C22×C4—92no—
387C22×C4—92no—
388C22×C4—92no—
389C22×C4—92no—
390C22×C4—92no—
391C22×C4—92no—
392C22×C4—91no—
393C22×C4—91no—
394C22×C4—91no—
395C22×C4—91no—
396C22×C4—91no—
397C22×C4—91no—
398C22×C4—91no—
399C22×C4—91no—
400C22×C4—91no—
401C22×C4—91no—
402C22×C4—91no—
403C22×C4—91no—
404C22×C4—91no—
405C22×C4—91no—
406C22×C4—91no—
407C22×C4—91no—
408C22×C4C3×C4×D311yescharacteristic
409C22×C4C22×C3×D311yescharacteristic
410M16—32no—
411M16—31no—
412M16—31no—
413M16—32no—
414M16—32no—
415M16—92no—
416M16—92no—
417M16—92no—
418M16—94no—
419M16—92no—
420M16—91no—
421M16—92no—
422M16D3×A411yescharacteristic, direct product factor
423C2×C8—32no—
424C2×C8—32no—
425C2×C8—32no—
426C2×C8—92no—
427C2×C8—92no—
428C2×C8—92no—
429C2×C8—94no—
430C2×C8—92no—
431C2×C8—92no—
432C22×C3—31no—
433C22×C3—31no—
434C22×C3—31no—
435C22×C3—41no—
436C22×C3—61no—
437C22×C3—61no—
438C22×C3—61no—
439C22×C3—61no—
440C22×C3—81no—
441C22×C3—121no—
442C22×C3—121no—
443C22×C3—242no—
444C22×C3C2×C3×M1611yescharacteristic, complemented
445C22×C3C2×C4×A411yescharacteristic
446C2×D3—22no—
447C2×D3—32no—
448C2×D3—31no—
449C2×D3—32no—
450C2×D3—32no—
451C2×D3—32no—
452C2×D3—31no—
453C2×D3—62no—
454C2×D3—61no—
455C2×D3—61no—
456C2×D3—62no—
457C2×D3—64no—
458C2×D3—62no—
459C2×D3—61no—
460C2×D3—61no—
461C2×D3C2×C4×A411yescharacteristic
462C2×D3C2×C4×A411yescharacteristic
463A4—21no—
464A4D3×M1611yescharacteristic, direct product factor
465C3×C4—31no—
466C3×C4—31no—
467C3×C4—41no—
468C3×C4—41no—
469C3×C4—81no—
470C3×C4—81no—
471C3×C4—121no—
472C3×C4—121no—
473C3×C4C2×C4×A411yescharacteristic
474C3×C4C23×A411yescharacteristic
475Dic3—31no—
476Dic3—31no—
477Dic3C2×C4×A411yescharacteristic
478Dic3C2×C4×A411yescharacteristic
479C32—41noSylow
480C23—21no—
481C23—31no—
482C23—31no—
483C23—31no—
484C23—32no—
485C23—61no—
486C23—61no—
487C23—91no—
488C23—91no—
489C23—91no—
490C23—91no—
491C23—91no—
492C23—92no—
493C23—92no—
494C23—91no—
495C23—91no—
496C23—181no—
497C23—182no—
498C23—182no—
499C23—182no—
500C23—182no—
501C23—182no—
502C23—182no—
503C23—182no—
504C23—182no—
505C23C2×C3×C4×D311yescharacteristic
506C2×C4—32no—
507C2×C4—31no—
508C2×C4—31no—
509C2×C4—31no—
510C2×C4—31no—
511C2×C4—31no—
512C2×C4—31no—
513C2×C4—31no—
514C2×C4—31no—
515C2×C4—31no—
516C2×C4—31no—
517C2×C4—31no—
518C2×C4—31no—
519C2×C4—91no—
520C2×C4—91no—
521C2×C4—91no—
522C2×C4—91no—
523C2×C4—91no—
524C2×C4—91no—
525C2×C4—91no—
526C2×C4—91no—
527C2×C4—91no—
528C2×C4—91no—
529C2×C4—91no—
530C2×C4—91no—
531C2×C4—92no—
532C2×C4—92no—
533C2×C4—92no—
534C2×C4—92no—
535C2×C4—92no—
536C2×C4—91no—
537C2×C4—91no—
538C2×C4—91no—
539C2×C4—91no—
540C2×C4—91no—
541C2×C4—91no—
542C2×C4—91no—
543C2×C4C2×D3×A411yescharacteristic
544C8—32no—
545C8—32no—
546C8—92no—
547C8C2×D3×A412yescomplemented
548C2×C3—21no—
549C2×C3—31no—
550C2×C3—31no—
551C2×C3—41no—
552C2×C3—61no—
553C2×C3—81no—
554C2×C3—81no—
555C2×C3—122no—
556C2×C3—161no—
557C2×C3—241no—
558C2×C3C22×C4×A411yescharacteristic
559D3—21no—
560D3—32no—
561D3—61no—
562D3A4×M1612yesdirect product factor
563C22—31no—
564C22—31no—
565C22—31no—
566C22—31no—
567C22—31no—
568C22—61no—
569C22—61no—
570C22—62no—
571C22—61no—
572C22—61no—
573C22—92no—
574C22—92no—
575C22—92no—
576C22—92no—
577C22—91no—
578C22—91no—
579C22—182no—
580C22—181no—
581C22—181no—
582C22—182no—
583C22—181no—
584C22—181no—
585C22—182no—
586C22—184no—
587C22C3×D3×M1611yescharacteristic, complemented
588C22C4×D3×A411yescharacteristic
589C4—31no—
590C4—31no—
591C4—31no—
592C4—31no—
593C4—91no—
594C4—91no—
595C4C4×D3×A411yescharacteristic
596C4C22×D3×A411yescharacteristic
597C3—41no—
598C3—81no—
599C3C2×A4×M1611yescharacteristic, complemented
600C2—21no—
601C2—31no—
602C2—31no—
603C2—32no—
604C2—61no—
605C2—61no—
606C2—92no—
607C2—181no—
608C2C2×C4×D3×A411yescharacteristic
subgroupG/H
center, FrattiniC4C22×D3×A4
commutator, socleC23×C3C22×C3×C4
FittingC22×C3×M16C2×C3
prime radicalC22×D3×A4C4
cosocleC22×C3×C4C23×C3
hypercenterM16D3×A4
hypocenterC22×C3C2×C3×M16
LCSG ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C4 ◁ M16

Complements

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

NH ≅ G/Ntype
2. C3×A4×M16C2semidirect
3. A4×#208C2semidirect
4. A4×ΓL(1,𝔽25)C2semidirect
5. D3×C8×A4C2semidirect
6. C22×D3×M16C3semidirect
16. C3×C8×A4C22semidirect
17. A4×C3⋊C8C22semidirect
20. C22×C3×M16C2×C3semidirect
21. C22×#208C2×C3semidirect
28. C22×ΓL(1,𝔽25)C2×C3semidirect
29. C22×D3×C8C2×C3semidirect
33. A4×M16D3direct (N × H)
76. C22×C3×C8C22×C3semidirect
80. C22×C3⋊C8C22×C3semidirect
91. D3×M16A4direct (N × H)
102. C8×A4C2×D3semidirect
107. D3×A4M16direct (N × H)
125. C22×M16C3×D3semidirect
198. C3×M16C2×A4semidirect
205. #208C2×A4semidirect
212. ΓL(1,𝔽25)C2×A4semidirect
217. D3×C8C2×A4semidirect
222. C3×A4C2×M16semidirect
268. C22×C8C2×C3×D3semidirect
294. C22×D3C3×M16semidirect
351. C3×C8C22×A4semidirect
353. C3⋊C8C22×A4semidirect
422. M16D3×A4direct (N × H)
444. C22×C3C2×C3×M16semidirect
464. A4D3×M16direct (N × H)
547. C8C2×D3×A4semidirect
562. D3A4×M16direct (N × H)
587. C22C3×D3×M16semidirect
599. C3C2×A4×M16semidirect

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×M162
A4×#2082
A4×ΓL(1,𝔽25)2
D3×C8×A42
C22×D3×M163
C2×A4×M163
C3×D3×M164