Finite Group Databasebeta

← D3×#64688 #14280751

Subgroups — D3×#64688 #14280751

Order 1920.

912 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#685C211yesmaximal, characteristic
2C5×D3×C22⋊C8C211yesmaximal, characteristic, complemented
3D3×C22⋊#168C211yesmaximal, characteristic, complemented
4#11746289C211yesmaximal, characteristic, complemented
5C3×#64688C211yesmaximal, characteristic, complemented
6#11745950C211yesmaximal, characteristic, complemented
7#11745948C211yesmaximal, characteristic, complemented
8C2×#64688—31nomaximal, Hall
9C23×D3×D5C411yescharacteristic
10C22×C4×C5×D3C2211yescharacteristic
11C22×D3×Dic5C411yescharacteristic
12C2×#6714C2211yescharacteristic
13C2×C5×D3×C8—21no—
14C2×C3×#685C2211yescharacteristic
15C2×#6667C411yescharacteristic
16C2×#6665C411yescharacteristic
17D3×#685—21no—
18D3×#685—21no—
19D3×#685—21no—
20D3×#685—21no—
21C2×D3×#168—21no—
22C3×C5×C22⋊C8C2211yescharacteristic, complemented
23#91114C2211yescharacteristic, complemented
24C5×#830C2211yescharacteristic, complemented
25C5×(C2×D3)⋊C8—21no—
26C3×C22⋊#168C2211yescharacteristic, complemented
27(C2×D3)⋊#168—21no—
28D3×#323—51nomaximal, Hall
29C22×#685—31no—
30C2×C5×C22⋊C8—31no—
31C2×C22⋊#168—31no—
32#64688—31no—
33#64688—31no—
34#64688—31no—
35#64688D311yescharacteristic, direct product factor
36C23×D15C2×C411yescharacteristic
37C23×C5×D3C2×C411yescharacteristic
38C23×C3×D5C2×C411yescharacteristic
39C22×D3×D5—21no—
40C22×D3×D5—21no—
41C22×D3×D5—22no—
42C22×D3×D5—42no—
43C22×D3×D5—42no—
44C22×D3×D5C814yescomplemented
45C22×C3×C4×C5C2311yescharacteristic
46C22×Dic15C2×C411yescharacteristic
47C22×C5×Dic3C2×C411yescharacteristic
48C2×C4×C5×D3—42no—
49C2×C4×C5×D3D411yescharacteristic
50C2×C4×C5×D3D411yescharacteristic
51C2×C4×C5×D3D411yescharacteristic
52C2×C4×C5×D3D411yescharacteristic
53C22×C3×Dic5C2×C411yescharacteristic
54C2×D3×Dic5—21no—
55C2×D3×Dic5—21no—
56C2×D3×Dic5—42no—
57C2×C3×C5×C8—21no—
58#6714—21no—
59#6714—21no—
60C2×C3⋊#168—21no—
61C2×C5×C3⋊C8—21no—
62C5×D3×C8—42no—
63C3×#685—21no—
64C3×#685—21no—
65C2×C3×#168—21no—
66#6667—21no—
67#6667—21no—
68#6665—21no—
69#6665—21no—
70D3×#168—42no—
71C2×D3×C22⋊C4—51no—
72D3×C22⋊C8—51no—
73D3×C22⋊C8D511yescharacteristic, complemented
74C3×#323—51no—
75#4525—51no—
76#4468—51no—
77#4468—51no—
78C24×D5—31no—
79C23×C4×C5—31no—
80C23×Dic5—31no—
81C22×C5×C8—61no—
82C2×#685—31no—
83C2×#685—31no—
84C2×#685—31no—
85C2×#685—61no—
86C2×#685—61no—
87C2×#685—61no—
88C2×#685—61no—
89C2×#685C2×D311yescharacteristic
90C22×#168—61no—
91C5×C22⋊C8—31no—
92C5×C22⋊C8—61no—
93C5×C22⋊C8C2×D311yescharacteristic, complemented
94C22⋊#168—31no—
95C22⋊#168—61no—
96C22⋊#168C2×D311yescharacteristic, complemented
97C2×#323—151noSylow
98C23×C3×C5C22×C411yescharacteristic
99C22×D15—21no—
100C22×D15—21no—
101C22×D15—41no—
102C22×D15—41no—
103C22×D15C2×C812yescomplemented
104C22×C5×D3—22no—
105C22×C5×D3—22no—
106C22×C5×D3C22⋊C411yescharacteristic
107C22×C5×D3C22⋊C411yescharacteristic
108C22×C5×D3C2×C812yes—
109C22×C5×D3M1612yes—
110C22×C3×D5—21no—
111C22×C3×D5—21no—
112C22×C3×D5—41no—
113C22×C3×D5—41no—
114C22×C3×D5C2×C812yescomplemented
115C2×D3×D5—24no—
116C2×D3×D5—24no—
117C2×D3×D5—42no—
118C2×D3×D5—42no—
119C2×D3×D5—48no—
120C2×D3×D5—42no—
121C2×D3×D5—42no—
122C2×D3×D5—48no—
123C2×C3×C4×C5—41no—
124C2×C3×C4×C5C2×D411yescharacteristic
125C2×C3×C4×C5C2×D411yescharacteristic
126C2×Dic15—21no—
127C2×Dic15—41no—
128C2×C5×Dic3—41no—
129C2×C5×Dic3C22⋊C411yescharacteristic
130C2×C5×Dic3C22⋊C411yescharacteristic
131C4×C5×D3—22no—
132C4×C5×D3—22no—
133C4×C5×D3—41no—
134C4×C5×D3—41no—
135C2×C3×Dic5—21no—
136C2×C3×Dic5—41no—
137D3×Dic5—42no—
138D3×Dic5—42no—
139C3×C5×C8—41no—
140C3⋊#168—41no—
141C3×#168—41no—
142C5×C3⋊C8—41no—
143C24×D3—51no—
144C22×C4×D3—51no—
145C22×C4×D3C2×D511yescharacteristic
146C2×C3×C22⋊C4—51no—
147C2×#217—51no—
148C2×(C2×D3)⋊C4—51no—
149C2×(C2×D3)⋊C4—51no—
150C2×D3×C8—21no—
151C2×D3×C8—101no—
152D3×C22⋊C4—101no—
153D3×C22⋊C4—101no—
154D3×C22⋊C4—101no—
155D3×C22⋊C4—101no—
156C3×C22⋊C8—51no—
157C3×C22⋊C8C2×D511yescharacteristic, complemented
158#830—51no—
159#830C2×D511yescharacteristic, complemented
160(C2×D3)⋊C8—21no—
161(C2×D3)⋊C8—101no—
162C24×C5—31no—
163C23×D5—31no—
164C23×D5—34no—
165C23×D5—62no—
166C23×D5—61no—
167C23×D5—61no—
168C23×D5—122no—
169C23×D5—122no—
170C23×D5C4×D311yescharacteristic
171C22×C4×C5—31no—
172C22×C4×C5—31no—
173C22×C4×C5—31no—
174C22×C4×C5—31no—
175C22×C4×C5—31no—
176C22×C4×C5—122no—
177C22×C4×C5C22×D311yescharacteristic
178C22×Dic5—31no—
179C22×Dic5—61no—
180C22×Dic5—61no—
181C22×Dic5—122no—
182C22×Dic5C4×D311yescharacteristic
183C2×C5×C8—21no—
184C2×C5×C8—61no—
185C2×C5×C8—122no—
186#685—21no—
187#685—21no—
188#685—61no—
189#685—61no—
190#685—61no—
191#685—61no—
192#685—61no—
193#685—61no—
194C2×#168—21no—
195C2×#168—61no—
196C2×#168—122no—
197C22×C22⋊C4—151no—
198C2×C22⋊C8—31no—
199C2×C22⋊C8—151no—
200#323—51no—
201#323—151no—
202#323—151no—
203#323—151no—
204C22×C3×C5—21no—
205C22×C3×C5—21no—
206C22×C3×C5C2×C22⋊C411yescharacteristic
207C22×C3×C5C22×C811yescharacteristic
208C22×C3×C5C2×M1611yescharacteristic
209C2×D15—22no—
210C2×D15—42no—
211C2×D15—41no—
212C2×D15—41no—
213C2×D15—42no—
214C2×C5×D3—21no—
215C2×C5×D3—21no—
216C2×C5×D3—24no—
217C2×C5×D3—24no—
218C2×C5×D3C22⋊C812yes—
219C2×C5×D3C22⋊C812yes—
220C2×C5×D3#9912yes—
221C2×C5×D3#10012yes—
222C2×C3×D5—22no—
223C2×C3×D5—42no—
224C2×C3×D5—41no—
225C2×C3×D5—41no—
226C2×C3×D5—42no—
227D3×D5—48no—
228D3×D5—48no—
229C3×C4×C5—21no—
230C3×C4×C5—21no—
231Dic15—41no—
232C3×Dic5—41no—
233C5×Dic3—21no—
234C5×Dic3—21no—
235C24×C3—51no—
236C23×D3—51no—
237C23×D3—54no—
238C23×D3—102no—
239C23×D3—101no—
240C23×D3—101no—
241C23×D3—202no—
242C23×D3—202no—
243C23×D3C4×D511yescharacteristic
244C22×C3×C4—51no—
245C22×C3×C4C22×D511yescharacteristic
246C22×Dic3—51no—
247C22×Dic3C4×D511yescharacteristic
248C2×C4×D3—42no—
249C2×C4×D3—101no—
250C2×C4×D3—101no—
251C2×C4×D3—202no—
252C2×C4×D3D2011yescharacteristic
253C2×C4×D3D2011yescharacteristic
254C2×C4×D3C22⋊D511yescharacteristic
255C2×C4×D3C22⋊D511yescharacteristic
256C2×C3×C8—21no—
257C2×C3×C8—101no—
258C3×C22⋊C4—101no—
259C3×C22⋊C4—101no—
260#217—101no—
261#217—101no—
262(C2×D3)⋊C4—101no—
263(C2×D3)⋊C4—101no—
264(C2×D3)⋊C4—101no—
265(C2×D3)⋊C4—101no—
266C2×C3⋊C8—21no—
267C2×C3⋊C8—101no—
268D3×C8—42no—
269D3×C8—202no—
270C23×C5—31no—
271C23×C5—31no—
272C23×C5—32no—
273C23×C5—32no—
274C23×C5—62no—
275C23×C5—62no—
276C23×C5C2×C4×D311yescharacteristic
277C22×D5—21no—
278C22×D5—21no—
279C22×D5—32no—
280C22×D5—41no—
281C22×D5—41no—
282C22×D5—64no—
283C22×D5—64no—
284C22×D5—61no—
285C22×D5—61no—
286C22×D5—122no—
287C22×D5—122no—
288C22×D5—128no—
289C22×D5—122no—
290C22×D5—122no—
291C22×D5—128no—
292C22×D5—121no—
293C22×D5—121no—
294C22×D5D3×C812yescomplemented
295C2×C4×C5—31no—
296C2×C4×C5—31no—
297C2×C4×C5—41no—
298C2×C4×C5—62no—
299C2×C4×C5—62no—
300C2×C4×C5—121no—
301C2×C4×C5—121no—
302C2×C4×C5—121no—
303C2×C4×C5D3×D411yescharacteristic
304C2×C4×C5D3×D411yescharacteristic
305C2×Dic5—21no—
306C2×Dic5—41no—
307C2×Dic5—61no—
308C2×Dic5—122no—
309C2×Dic5—122no—
310C2×Dic5—121no—
311C5×C8—41no—
312C5×C8—121no—
313#168—41no—
314#168—121no—
315C25—151no—
316C23×C4—31no—
317C23×C4—151no—
318C22×C8—61no—
319C22×C8—301no—
320C2×C22⋊C4—51no—
321C2×C22⋊C4—151no—
322C2×C22⋊C4—151no—
323C2×C22⋊C4—151no—
324C2×C22⋊C4—301no—
325C2×C22⋊C4—301no—
326C2×C22⋊C4—301no—
327C2×C22⋊C4—301no—
328C22⋊C8—31no—
329C22⋊C8—51no—
330C22⋊C8—61no—
331C22⋊C8—151no—
332C22⋊C8—301no—
333C22⋊C8D3×D511yescharacteristic, complemented
334C2×C3×C5—21no—
335C2×C3×C5—21no—
336C2×C3×C5C2×C22⋊C811yescharacteristic
337C2×C3×C5C2×#9911yescharacteristic
338C2×C3×C5C2×#10011yescharacteristic
339D15—42no—
340C3×D5—42no—
341C5×D3—22no—
342C5×D3#32314yescomplemented
343C23×C3—52no—
344C23×C3—101no—
345C23×C3—101no—
346C23×C3—201no—
347C23×C3—201no—
348C23×C3C2×C4×D511yescharacteristic
349C22×D3—22no—
350C22×D3—22no—
351C22×D3—52no—
352C22×D3—101no—
353C22×D3—101no—
354C22×D3—104no—
355C22×D3—104no—
356C22×D3—202no—
357C22×D3—202no—
358C22×D3—208no—
359C22×D3—208no—
360C22×D3—202no—
361C22×D3—202no—
362C22×D3—201no—
363C22×D3—201no—
364C22×D3C8×D512yes—
365C22×D3#67612yes—
366C22×D3#68511yescharacteristic
367C22×D3#68511yescharacteristic
368C2×C3×C4—41no—
369C2×C3×C4—101no—
370C2×C3×C4—201no—
371C2×C3×C4C2×D2011yescharacteristic
372C2×C3×C4C2×C22⋊D511yescharacteristic
373C2×Dic3—41no—
374C2×Dic3—101no—
375C2×Dic3—201no—
376C2×Dic3#68511yescharacteristic
377C2×Dic3#68511yescharacteristic
378C4×D3—22no—
379C4×D3—22no—
380C4×D3—41no—
381C4×D3—41no—
382C4×D3—202no—
383C4×D3—202no—
384C3×C8—41no—
385C3×C8—201no—
386C3⋊C8—41no—
387C3⋊C8—201no—
388C22×C5—21no—
389C22×C5—21no—
390C22×C5—32no—
391C22×C5—32no—
392C22×C5—32no—
393C22×C5—32no—
394C22×C5—64no—
395C22×C5—64no—
396C22×C5—61no—
397C22×C5—61no—
398C22×C5D3×C22⋊C411yescharacteristic
399C22×C5C2×D3×C811yescharacteristic
400C22×C5D3×M1611yescharacteristic
401C2×D5—22no—
402C2×D5—42no—
403C2×D5—41no—
404C2×D5—41no—
405C2×D5—42no—
406C2×D5—62no—
407C2×D5—128no—
408C2×D5—128no—
409C2×D5—122no—
410C2×D5—121no—
411C2×D5—121no—
412C2×D5—122no—
413C4×C5—21no—
414C4×C5—21no—
415C4×C5—61no—
416C4×C5—61no—
417Dic5—41no—
418Dic5—121no—
419C24—31no—
420C24—51no—
421C24—154no—
422C24—151no—
423C24—301no—
424C24—301no—
425C24—302no—
426C24—602no—
427C24—602no—
428C22×C4—31no—
429C22×C4—31no—
430C22×C4—31no—
431C22×C4—31no—
432C22×C4—31no—
433C22×C4—51no—
434C22×C4—122no—
435C22×C4—151no—
436C22×C4—301no—
437C22×C4—301no—
438C22×C4—602no—
439C22×C4C2×D3×D511yescharacteristic
440C2×C8—21no—
441C2×C8—61no—
442C2×C8—101no—
443C2×C8—122no—
444C2×C8—301no—
445C2×C8—602no—
446C22⋊C4—101no—
447C22⋊C4—101no—
448C22⋊C4—301no—
449C22⋊C4—301no—
450C22⋊C4—301no—
451C22⋊C4—301no—
452C22⋊C4—301no—
453C22⋊C4—301no—
454C3×C5C2×#32311yescharacteristic, complemented, Hall
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—102no—
458C22×C3—202no—
459C22×C3—202no—
460C22×C3—201no—
461C22×C3—201no—
462C22×C3C2×C8×D511yescharacteristic
463C22×C3C2×#67611yescharacteristic
464C22×C3C2×#68511yescharacteristic
465C2×D3—21no—
466C2×D3—21no—
467C2×D3—24no—
468C2×D3—24no—
469C2×D3—102no—
470C2×D3—208no—
471C2×D3—202no—
472C2×D3—201no—
473C2×D3—201no—
474C2×D3—208no—
475C2×D3—202no—
476C2×D3#393812yes—
477C2×D3#395212yes—
478C2×D3#395212yes—
479C2×D3#395512yes—
480C3×C4—21no—
481C3×C4—21no—
482C3×C4—201no—
483Dic3—21no—
484Dic3—21no—
485Dic3—201no—
486C2×C5—21no—
487C2×C5—21no—
488C2×C5—34no—
489C2×C5—62no—
490C2×C5D3×C22⋊C811yescharacteristic
491C2×C5D3×#9911yescharacteristic
492C2×C5D3×#10011yescharacteristic
493D5—42no—
494D5—122no—
495C23—31no—
496C23—31no—
497C23—32no—
498C23—32no—
499C23—52no—
500C23—62no—
501C23—62no—
502C23—101no—
503C23—101no—
504C23—152no—
505C23—201no—
506C23—201no—
507C23—304no—
508C23—304no—
509C23—301no—
510C23—301no—
511C23—601no—
512C23—601no—
513C23—602no—
514C23—602no—
515C23—608no—
516C23—608no—
517C23—602no—
518C23—602no—
519C23C4×D3×D511yescharacteristic
520C2×C4—31no—
521C2×C4—31no—
522C2×C4—41no—
523C2×C4—62no—
524C2×C4—62no—
525C2×C4—101no—
526C2×C4—121no—
527C2×C4—121no—
528C2×C4—121no—
529C2×C4—201no—
530C2×C4—301no—
531C2×C4—602no—
532C2×C4—602no—
533C2×C4—601no—
534C2×C4D3×D2011yescharacteristic
535C2×C4D3×C22⋊D511yescharacteristic
536C8—41no—
537C8—121no—
538C8—201no—
539C8—601no—
540C2×C3—21no—
541C2×C3—21no—
542C2×C3—202no—
543C2×C3C2×#393811yescharacteristic
544C2×C3C2×#395211yescharacteristic
545C2×C3C2×#395511yescharacteristic
546D3—22no—
547D3—202no—
548D3#6468814yesdirect product factor
549C5D3×#32311yescharacteristic, complemented, Sylow
550C22—21no—
551C22—21no—
552C22—32no—
553C22—32no—
554C22—32no—
555C22—32no—
556C22—64no—
557C22—64no—
558C22—61no—
559C22—61no—
560C22—102no—
561C22—202no—
562C22—202no—
563C22—201no—
564C22—201no—
565C22—302no—
566C22—602no—
567C22—602no—
568C22—608no—
569C22—608no—
570C22—601no—
571C22—601no—
572C22D3×C8×D511yescharacteristic
573C22D3×#67611yescharacteristic
574C22D3×#68511yescharacteristic
575C4—21no—
576C4—21no—
577C4—61no—
578C4—61no—
579C4—201no—
580C4—601no—
581C3C2×#6468811yescharacteristic, complemented, Sylow
582C2—21no—
583C2—21no—
584C2—34no—
585C2—62no—
586C2—202no—
587C2—602no—
588C2D3×#393811yescharacteristic
589C2D3×#395211yescharacteristic
590C2D3×#395511yescharacteristic
subgroupG/H
centerC22D3×#685
commutatorC22×C3×C5C22×C8
FrattiniC22×C4C2×D3×D5
FittingC3×C5×C22⋊C8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×D3×D5C4
cosocleC22×C3×C4×C5C23
hypercenterC22⋊C8D3×D5
hypocenterC3×C5C2×#323
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C5×D3×C22⋊C8C2semidirect
3. D3×C22⋊#168C2semidirect
4. #11746289C2semidirect
5. C3×#64688C2semidirect
6. #11745950C2semidirect
7. #11745948C2semidirect
22. C3×C5×C22⋊C8C22semidirect
23. #91114C22semidirect
24. C5×#830C22semidirect
26. C3×C22⋊#168C22semidirect
35. #64688D3direct (N × H)
44. C22×D3×D5C8semidirect
73. D3×C22⋊C8D5semidirect
93. C5×C22⋊C8C2×D3semidirect
96. C22⋊#168C2×D3semidirect
103. C22×D15C2×C8semidirect
114. C22×C3×D5C2×C8semidirect
157. C3×C22⋊C8C2×D5semidirect
159. #830C2×D5semidirect
294. C22×D5D3×C8semidirect
333. C22⋊C8D3×D5semidirect
342. C5×D3#323semidirect
454. C3×C5C2×#323semidirect
548. D3#64688direct (N × H)
549. C5D3×#323semidirect
581. C3C2×#64688semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#6852
C5×D3×C22⋊C82
D3×C22⋊#1682
#117462892
C3×#646882
#117459502
#117459482
C2×#646883
D3×#3235