Finite Group Databasebeta

← D3×#5409 #11921877

Subgroups — D3×#5409 #11921877

Order 1152.

746 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 746 conjugacy classes of subgroups — too many to draw. Only its 89 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
2#10593643C211yesmaximal, characteristic, complemented
3C3×#5409C211yesmaximal, characteristic, complemented
4#10593182C212yesmaximal, complemented
5D3×A4⋊C8C212yesmaximal, complemented
6C2×#5409—31nomaximal
7D3×#407—31nomaximal
8C22×D3×A4C411yescharacteristic
9C2×C3×C4×A4C2211yescharacteristic
10C2×Dic3×A4C411yescharacteristic
11C4×D3×A4C411yescharacteristic
12C4×D3×A4C411yescharacteristic
13C4×D3×A4C2211yescharacteristic
14C4×D3×A4C2211yescharacteristic
15D3×#208—41nomaximal
16C3⋊(A4⋊C8)C2212yescomplemented
17C3×A4⋊C8C2212yescomplemented
18C23×C4×D3D311yescharacteristic
19C22×C4×A4—31no—
20C2×D3×M16—31no—
21C2×D3×M16—31no—
22#5409—31no—
23#5409—32no—
24#5409—61no—
25#5409D311yescharacteristic, direct product factor
26C2×A4⋊C8—32no—
27C3×#407—31no—
28#5207—31no—
29#5126—31no—
30#5126—31no—
31#4726—32no—
32#4726—32no—
33D3×C22⋊C8—32no—
34D3×C22⋊C8—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
44#3748—41no—
45C3×#208—41no—
46#3711—42no—
47D3×C3⋊C8—42no—
48C2×#407—91noSylow
49C24×D3Dic311yescharacteristic
50C23×A4—31no—
51C23×C3×C4C2×D311yescharacteristic
52C23×Dic3Dic311yescharacteristic
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×D3Dic311yescharacteristic
62C22×C4×D3Dic311yescharacteristic
63C22×C4×D3C2×D311yescharacteristic
64C22×C4×D3C2×D311yescharacteristic
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—31no—
74C2×#208—31no—
75C2×#208—31no—
76C2×#208—121no—
77D3×M16—61no—
78D3×M16—61no—
79D3×M16—61no—
80D3×M16—61no—
81D3×M16—61no—
82D3×M16—61no—
83D3×M16—61no—
84D3×M16—61no—
85C2×ΓL(1,𝔽25)—32no—
86C2×ΓL(1,𝔽25)—32no—
87C2×D3×C8—32no—
88C2×D3×C8—32no—
89A4⋊C8—32no—
90A4⋊C8—62no—
91A4⋊C8C2×D312yescomplemented
92C3×C22⋊C8—32no—
93C3×C22⋊C8—32no—
94#830—32no—
95#830—32no—
96(C2×D3)⋊C8—32no—
97(C2×D3)⋊C8—32no—
98(C2×D3)⋊C8—32no—
99(C2×D3)⋊C8—32no—
100C22×C3×D3—41no—
101C2×C3×A4—21no—
102C2×C3×A4C22×C411yescharacteristic
103D3×A4—21no—
104D3×A4M1612yescomplemented
105C2×C32×C4—41no—
106C2×C3×Dic3—41no—
107C3×C4×D3—41no—
108C3×C4×D3—41no—
109C3×C4×D3—41no—
110C3×C4×D3—41no—
111C3⋊(C3⋊C8)—42no—
112C3×C3⋊C8—42no—
113C24×C4—31no—
114C22×M16—91no—
115C22×M16—91no—
116#407—31no—
117#407—92no—
118#407—92no—
119#407—91no—
120#407—91no—
121#407—91no—
122C2×C22⋊C8—92no—
123C2×C22⋊C8—92no—
124C24×C3C2×Dic311yescharacteristic
125C23×D3—22no—
126C23×D3—31no—
127C23×D3—31no—
128C23×D3—31no—
129C23×D3—31no—
130C23×D3—62no—
131C23×D3C2×Dic311yescharacteristic
132C23×D3C2×Dic311yescharacteristic
133C22×A4—21no—
134C22×A4—31no—
135C22×A4—31no—
136C22×A4—62no—
137C22×A4C4×D311yescharacteristic
138C22×C3×C4—31no—
139C22×C3×C4—31no—
140C22×C3×C4—31no—
141C22×C3×C4—31no—
142C22×C3×C4—121no—
143C22×C3×C4C2×Dic311yescharacteristic
144C22×C3×C4C22×D311yescharacteristic
145C22×Dic3—31no—
146C22×Dic3—31no—
147C22×Dic3—31no—
148C22×Dic3—31no—
149C22×Dic3C2×Dic311yescharacteristic
150C22×Dic3C2×Dic311yescharacteristic
151C2×C4×D3—31no—
152C2×C4×D3—31no—
153C2×C4×D3—31no—
154C2×C4×D3—31no—
155C2×C4×D3—31no—
156C2×C4×D3—31no—
157C2×C4×D3—31no—
158C2×C4×D3—31no—
159C2×C4×D3—31no—
160C2×C4×D3—31no—
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—61no—
175C2×C4×D3—61no—
176C2×C4×D3—61no—
177C2×C4×D3—61no—
178C2×C4×D3—61no—
179C2×C4×D3—61no—
180C2×C4×D3—61no—
181C2×C4×D3S411yescharacteristic
182C4×A4—21no—
183C4×A4—21no—
184C4×A4—31no—
185C4×A4—31no—
186C4×A4C4×D311yescharacteristic
187C4×A4C22×D311yescharacteristic
188C3×M16—61no—
189C3×M16—61no—
190C3×M16—61no—
191C3×M16—61no—
192C2×C3×C8—32no—
193C2×C3×C8—32no—
194#208—41no—
195#208—61no—
196#208—61no—
197#208—61no—
198#208—61no—
199#208—122no—
200#208—121no—
201#208—241no—
202C2×C3⋊C8—32no—
203C2×C3⋊C8—32no—
204C2×C3⋊C8—122no—
205ΓL(1,𝔽25)—62no—
206ΓL(1,𝔽25)—62no—
207ΓL(1,𝔽25)—62no—
208ΓL(1,𝔽25)—62no—
209D3×C8—62no—
210D3×C8—62no—
211D3×C8—62no—
212D3×C8—62no—
213C22×C32—41no—
214C2×C3×D3—41no—
215C2×C3×D3—41no—
216C2×C3×D3—82no—
217C3×A4C2×M1611yescharacteristic, complemented
218C32×C4—41no—
219C32×C4—41no—
220C3×Dic3—41no—
221C3×Dic3—41no—
222C25—31no—
223C23×C4—31no—
224C23×C4—31no—
225C23×C4—31no—
226C23×C4—31no—
227C23×C4—31no—
228C23×C4—91no—
229C23×C4—91no—
230C23×C4—91no—
231C23×C4—91no—
232C23×C4—91no—
233C23×C4—91no—
234C23×C4—91no—
235C23×C4—91no—
236C23×C4D3211yescharacteristic
237C2×M16—31no—
238C2×M16—31no—
239C2×M16—92no—
240C2×M16—92no—
241C2×M16—91no—
242C2×M16—91no—
243C2×M16—181no—
244C2×M16—181no—
245C2×M16—181no—
246C2×M16—181no—
247C2×M16—181no—
248C2×M16—181no—
249C2×M16—181no—
250C2×M16—181no—
251C22×C8—92no—
252C22×C8—92no—
253C22⋊C8—32no—
254C22⋊C8—32no—
255C22⋊C8—92no—
256C22⋊C8—92no—
257C22⋊C8—92no—
258C22⋊C8—92no—
259C22⋊C8—92no—
260C22⋊C8—92no—
261C23×C3—21no—
262C23×C3—31no—
263C23×C3—31no—
264C23×C3—61no—
265C23×C3—121no—
266C23×C3C22×Dic311yescharacteristic
267C22×D3—21no—
268C22×D3—31no—
269C22×D3—31no—
270C22×D3—31no—
271C22×D3—32no—
272C22×D3—34no—
273C22×D3—31no—
274C22×D3—31no—
275C22×D3—31no—
276C22×D3—31no—
277C22×D3—62no—
278C22×D3—62no—
279C22×D3—61no—
280C22×D3—61no—
281C22×D3—62no—
282C22×D3—62no—
283C22×D3—62no—
284C22×D3—62no—
285C22×D3—62no—
286C22×D3#20812yescomplemented
287C22×D3SL(2,ℤ/4)11yescharacteristic
288C2×A4—21no—
289C2×A4—21no—
290C2×A4—32no—
291C2×A4—41no—
292C2×A4—61no—
293C2×A4C2×C4×D311yescharacteristic
294C2×C3×C4—31no—
295C2×C3×C4—31no—
296C2×C3×C4—31no—
297C2×C3×C4—31no—
298C2×C3×C4—31no—
299C2×C3×C4—31no—
300C2×C3×C4—31no—
301C2×C3×C4—41no—
302C2×C3×C4—61no—
303C2×C3×C4—81no—
304C2×C3×C4—121no—
305C2×C3×C4—121no—
306C2×C3×C4—121no—
307C2×C3×C4—121no—
308C2×C3×C4—121no—
309C2×C3×C4C2×S411yescharacteristic
310C2×Dic3—31no—
311C2×Dic3—31no—
312C2×Dic3—31no—
313C2×Dic3—31no—
314C2×Dic3—31no—
315C2×Dic3—31no—
316C2×Dic3—31no—
317C2×Dic3—61no—
318C2×Dic3SL(2,ℤ/4)11yescharacteristic
319C4×D3—31no—
320C4×D3—31no—
321C4×D3—31no—
322C4×D3—31no—
323C4×D3—31no—
324C4×D3—31no—
325C4×D3—31no—
326C4×D3—31no—
327C4×D3—31no—
328C4×D3—31no—
329C4×D3—31no—
330C4×D3—31no—
331C4×D3—61no—
332C4×D3—61no—
333C4×D3—61no—
334C4×D3—61no—
335C4×D3SL(2,ℤ/4)11yescharacteristic
336C4×D3SL(2,ℤ/4)11yescharacteristic
337C4×D3C2×S411yescharacteristic
338C4×D3C2×S411yescharacteristic
339C3×C8—62no—
340C3×C8—62no—
341C3⋊C8—42no—
342C3⋊C8—62no—
343C3⋊C8—62no—
344C3⋊C8—122no—
345C3⋊C8—242no—
346C2×C32—41no—
347C2×C32—81no—
348C3×D3—42no—
349C3×D3—81no—
350C24—31no—
351C24—31no—
352C24—62no—
353C24—91no—
354C24—91no—
355C24—91no—
356C24—91no—
357C24—182no—
358C24D3×Dic311yescharacteristic
359C22×C4—31no—
360C22×C4—31no—
361C22×C4—31no—
362C22×C4—31no—
363C22×C4—31no—
364C22×C4—31no—
365C22×C4—31no—
366C22×C4—91no—
367C22×C4—91no—
368C22×C4—91no—
369C22×C4—91no—
370C22×C4—91no—
371C22×C4—91no—
372C22×C4—91no—
373C22×C4—91no—
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—91no—
386C22×C4—91no—
387C22×C4—91no—
388C22×C4—91no—
389C22×C4—91no—
390C22×C4—91no—
391C22×C4—91no—
392C22×C4—91no—
393C22×C4—181no—
394C22×C4—181no—
395C22×C4—181no—
396C22×C4—181no—
397C22×C4—181no—
398C22×C4—181no—
399C22×C4—181no—
400C22×C4D3×Dic311yescharacteristic
401C22×C4C2×D3211yescharacteristic
402M16—61no—
403M16—61no—
404M16—61no—
405M16—61no—
406M16—182no—
407M16—182no—
408M16—182no—
409M16—182no—
410M16—181no—
411M16—181no—
412M16—181no—
413M16—181no—
414C2×C8—32no—
415C2×C8—32no—
416C2×C8—92no—
417C2×C8—92no—
418C2×C8—182no—
419C2×C8—182no—
420C2×C8—182no—
421C2×C8—182no—
422C22×C3—31no—
423C22×C3—31no—
424C22×C3—32no—
425C22×C3—31no—
426C22×C3—41no—
427C22×C3—61no—
428C22×C3—61no—
429C22×C3—61no—
430C22×C3—81no—
431C22×C3—121no—
432C22×C3—121no—
433C22×C3—242no—
434C22×C3C2×#20811yescharacteristic, complemented
435C22×C3C2×SL(2,ℤ/4)11yescharacteristic
436C2×D3—22no—
437C2×D3—31no—
438C2×D3—32no—
439C2×D3—32no—
440C2×D3—32no—
441C2×D3—32no—
442C2×D3—31no—
443C2×D3—62no—
444C2×D3—61no—
445C2×D3—61no—
446C2×D3—61no—
447C2×D3—62no—
448C2×D3—64no—
449C2×D3—62no—
450C2×D3—61no—
451C2×D3C2×SL(2,ℤ/4)11yescharacteristic
452C2×D3C2×SL(2,ℤ/4)11yescharacteristic
453A4—21no—
454A4D3×M1611yescharacteristic, complemented
455C3×C4—31no—
456C3×C4—31no—
457C3×C4—41no—
458C3×C4—41no—
459C3×C4—81no—
460C3×C4—81no—
461C3×C4—121no—
462C3×C4—121no—
463C3×C4C2×SL(2,ℤ/4)11yescharacteristic
464C3×C4C22×S411yescharacteristic
465Dic3—31no—
466Dic3—31no—
467Dic3C2×SL(2,ℤ/4)11yescharacteristic
468Dic3C2×SL(2,ℤ/4)11yescharacteristic
469C32—41noSylow
470C23—21no—
471C23—31no—
472C23—31no—
473C23—31no—
474C23—32no—
475C23—61no—
476C23—61no—
477C23—91no—
478C23—91no—
479C23—91no—
480C23—91no—
481C23—91no—
482C23—91no—
483C23—92no—
484C23—94no—
485C23—91no—
486C23—181no—
487C23—181no—
488C23—182no—
489C23—182no—
490C23—182no—
491C23—182no—
492C23—182no—
493C23—182no—
494C23—182no—
495C23C2×D3×Dic311yescharacteristic
496C2×C4—31no—
497C2×C4—31no—
498C2×C4—31no—
499C2×C4—31no—
500C2×C4—31no—
501C2×C4—31no—
502C2×C4—31no—
503C2×C4—31no—
504C2×C4—31no—
505C2×C4—31no—
506C2×C4—31no—
507C2×C4—31no—
508C2×C4—61no—
509C2×C4—91no—
510C2×C4—91no—
511C2×C4—91no—
512C2×C4—91no—
513C2×C4—91no—
514C2×C4—91no—
515C2×C4—91no—
516C2×C4—91no—
517C2×C4—91no—
518C2×C4—91no—
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—181no—
529C2×C4—181no—
530C2×C4—181no—
531C2×C4—181no—
532C2×C4—181no—
533C2×C4D3×S411yescharacteristic
534C8—62no—
535C8—62no—
536C8—182no—
537C8—182no—
538C2×C3—21no—
539C2×C3—31no—
540C2×C3—31no—
541C2×C3—41no—
542C2×C3—61no—
543C2×C3—81no—
544C2×C3—81no—
545C2×C3—122no—
546C2×C3—161no—
547C2×C3—241no—
548C2×C3C22×SL(2,ℤ/4)11yescharacteristic
549D3—21no—
550D3—32no—
551D3—61no—
552D3#540912yesdirect product factor
553C22—31no—
554C22—31no—
555C22—31no—
556C22—32no—
557C22—31no—
558C22—31no—
559C22—61no—
560C22—61no—
561C22—62no—
562C22—61no—
563C22—92no—
564C22—92no—
565C22—92no—
566C22—92no—
567C22—91no—
568C22—91no—
569C22—182no—
570C22—181no—
571C22—182no—
572C22—181no—
573C22—181no—
574C22—181no—
575C22—182no—
576C22—184no—
577C22D3×#20811yescharacteristic, complemented
578C22D3×SL(2,ℤ/4)11yescharacteristic
579C4—31no—
580C4—31no—
581C4—31no—
582C4—31no—
583C4—91no—
584C4—91no—
585C4D3×SL(2,ℤ/4)11yescharacteristic
586C4C2×D3×S411yescharacteristic
587C3—41no—
588C3—81no—
589C3C2×#540911yescharacteristic, complemented
590C2—21no—
591C2—31no—
592C2—31no—
593C2—32no—
594C2—61no—
595C2—61no—
596C2—92no—
597C2—181no—
598C2C2×D3×SL(2,ℤ/4)11yescharacteristic
subgroupG/H
center, FrattiniC4C2×D3×S4
commutatorC2×C3×A4C22×C4
FittingC23×C3×C4C2×D3
socleC23×C3C22×Dic3
prime radicalC22×D3×A4C4
cosocleC3×C4×A4C23
hypercenterC2×C4D3×S4
hypocenterC3×A4C2×M16
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C4 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #10593643C2semidirect
3. C3×#5409C2semidirect
4. #10593182C2semidirect
5. D3×A4⋊C8C2semidirect
16. C3⋊(A4⋊C8)C22semidirect
17. C3×A4⋊C8C22semidirect
25. #5409D3direct (N × H)
91. A4⋊C8C2×D3semidirect
104. D3×A4M16semidirect
217. C3×A4C2×M16semidirect
286. C22×D3#208semidirect
434. C22×C3C2×#208semidirect
454. A4D3×M16semidirect
552. D3#5409direct (N × H)
577. C22D3×#208semidirect
589. C3C2×#5409semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D3×A42
#105936432
C3×#54092
#105931822
D3×A4⋊C82
C2×#54093
D3×#4073
D3×#2084