Finite Group Databasebeta

← D3×#65146 #14430203

Subgroups — D3×#65146 #14430203

Order 1920.

768 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#4036C211yesmaximal, characteristic
2D3×#4033C211yesmaximal, characteristic
3#11750958C211yesmaximal, characteristic, complemented
4C5×D3×#106C211yesmaximal, characteristic
5C3×#65146C211yesmaximal, characteristic, complemented
6#11747877C211yesmaximal, characteristic, complemented
7#11747852C211yesmaximal, characteristic, complemented
8D3×#3948C211yesmaximal, characteristic
9D3×#3946C211yesmaximal, characteristic
10D3×#3942C211yesmaximal, characteristic
11D3×#3939C211yesmaximal, characteristic
12#11747390C211yesmaximal, characteristic, complemented
13#11747302C211yesmaximal, characteristic, complemented
14#11747286C211yesmaximal, characteristic, complemented
15#11747184C211yesmaximal, characteristic, complemented
16C2×#65146—31nomaximal, Hall
17C2×D3×Dic10C2211yescharacteristic
18#91779C2211yescharacteristic
19#91776C2211yescharacteristic
20C2×C5×D3×C8C2211yescharacteristic
21C5×D3×C4⋊C4C2211yescharacteristic
22C5×D3×C4⋊C4C2211yescharacteristic
23C3×#4036C2211yescharacteristic
24C3×#4033C2211yescharacteristic
25D3×C4⋊Dic5—21no—
26D3×C4⋊Dic5C2211yescharacteristic
27D3×#683—21no—
28D3×#683—21no—
29C4×D3×Dic5—21no—
30C4×D3×Dic5C2211yescharacteristic
31#91388C2211yescharacteristic
32#91384C2211yescharacteristic
33#91346—21no—
34#91343—21no—
35#91333C2211yescharacteristic
36#91331C2211yescharacteristic
37#91325—21no—
38#91323—21no—
39C2×D3×#168C2211yescharacteristic
40C3×C5×#106C2211yescharacteristic
41#91100C2211yescharacteristic
42#91098C2211yescharacteristic
43#91094C2211yescharacteristic
44#91091C2211yescharacteristic
45C5×#817C2211yescharacteristic
46C5×#808C2211yescharacteristic
47C5×#808C2211yescharacteristic
48C3×#3948C2211yescharacteristic
49C3×#3946C2211yescharacteristic
50C3×#3942C2211yescharacteristic
51C3×#3939C2211yescharacteristic
52#90989C2211yescharacteristic
53#90988C2211yescharacteristic
54#90983C2211yescharacteristic
55#90982C2211yescharacteristic
56#90975C2211yescharacteristic
57#90974C2211yescharacteristic
58#90971C2211yescharacteristic
59#90970C2211yescharacteristic
60D3×#479—51nomaximal, Hall
61C2×#4036—31no—
62C2×#4033—31no—
63C2×C5×#106—31no—
64C2×#3948—31no—
65C2×#3946—31no—
66C2×#3942—31no—
67C2×#3939—31no—
68#65146—31no—
69#65146—31no—
70#65146—31no—
71#65146—31no—
72#65146—31no—
73#65146—31no—
74#65146—31no—
75#65146D311yescharacteristic, direct product factor
76C2×Dic30C2311yescharacteristic
77C2×C4×C5×D3—21no—
78C2×C4×C5×D3—21no—
79C2×C4×C5×D3C2311yescharacteristic
80C2×C3×Dic10C2311yescharacteristic
81C2×#1204—21no—
82C2×D3×Dic5—21no—
83C2×D3×Dic5—21no—
84C2×D3×Dic5D411yescharacteristic
85C2×D3×Dic5D411yescharacteristic
86D3×Dic10—22no—
87D3×Dic10Q814yes—
88C2×C3×C5×C8C2311yescharacteristic
89C3×C5×C4⋊C4C2311yescharacteristic
90C3×C5×C4⋊C4C2311yescharacteristic
91C4⋊Dic15—21no—
92C4⋊Dic15C2311yescharacteristic
93#6712—21no—
94#6712—21no—
95C4×Dic15—21no—
96C4×Dic15C2311yescharacteristic
97C2×C3⋊#168C2311yescharacteristic
98C5×C4⋊Dic3C2311yescharacteristic
99C5×C4⋊Dic3C2311yescharacteristic
100C5×Dic3⋊C4—21no—
101C5×Dic3⋊C4—21no—
102C2×C5×C3⋊C8C2311yescharacteristic
103C5×D3×C8—22no—
104C3×C4⋊Dic5—21no—
105C3×C4⋊Dic5C2311yescharacteristic
106C3×#683—21no—
107C3×#683—21no—
108C3×C4×Dic5—21no—
109C3×C4×Dic5C2311yescharacteristic
110C2×C3×#168C2311yescharacteristic
111Dic3⋊Dic5—21no—
112Dic3⋊Dic5—21no—
113Dic3⋊Dic5—21no—
114#6669—21no—
115#6669—21no—
116#6668—21no—
117#6668—21no—
118Dic3×Dic5—21no—
119Dic3×Dic5—21no—
120Dic3×Dic5D411yescharacteristic
121Dic3×Dic5D411yescharacteristic
122D3×#168—22no—
123D3×#125—51no—
124C4×D3×Q8—51no—
125C3×#479—51no—
126#5063—51no—
127#5022—51no—
128D3×#107—51no—
129#4877—51no—
130D3×#106D511yescharacteristic
131#4857—51no—
132D3×C4⋊C8—51no—
133#4829—51no—
134D3×#103—51no—
135D3×#103—51no—
136#4799—51no—
137#4796—51no—
138C22×Dic10—31no—
139C22×C5×C8—31no—
140C2×C5×C4⋊C4—31no—
141C2×C5×C4⋊C4—31no—
142C2×C4⋊Dic5—31no—
143C2×C4⋊Dic5—61no—
144C2×#683—61no—
145C2×#683—61no—
146C2×C4×Dic5—31no—
147C2×C4×Dic5—61no—
148C22×#168—31no—
149#4036—31no—
150#4036—31no—
151#4036—31no—
152#4036—61no—
153#4036—61no—
154#4036C2×D311yescharacteristic
155#4033—31no—
156#4033—31no—
157#4033—31no—
158#4033—61no—
159#4033—61no—
160#4033C2×D311yescharacteristic
161C5×#106—31no—
162C5×#106—31no—
163C5×#106—31no—
164C5×#106C2×D311yescharacteristic
165#3948—31no—
166#3948—31no—
167#3948—31no—
168#3948C2×D311yescharacteristic
169#3946—31no—
170#3946—31no—
171#3946—31no—
172#3946C2×D311yescharacteristic
173#3942—31no—
174#3942—31no—
175#3942—31no—
176#3942C2×D311yescharacteristic
177#3939—31no—
178#3939—31no—
179#3939—31no—
180#3939C2×D311yescharacteristic
181C2×#479—151noSylow
182C22×C5×D3C2×D411yescharacteristic
183C2×C3×C4×C5—21no—
184C2×C3×C4×C5—21no—
185C2×C3×C4×C5C2411yescharacteristic
186C2×Dic15—21no—
187C2×Dic15—21no—
188C2×Dic15C2×D411yescharacteristic
189C2×Dic15C2×D411yescharacteristic
190Dic30—21no—
191Dic30C2×Q812yes—
192C2×C5×Dic3—21no—
193C2×C5×Dic3—21no—
194C2×C5×Dic3C2×D411yescharacteristic
195C4×C5×D3—42no—
196C4×C5×D3—42no—
197C4×C5×D3C2×Q812yes—
198C4×C5×D3#4112yes—
199C2×C3×Dic5—21no—
200C2×C3×Dic5—21no—
201C2×C3×Dic5C2×D411yescharacteristic
202C2×C3×Dic5C2×D411yescharacteristic
203C3×Dic10—21no—
204C3×Dic10C2×Q812yes—
205#1204—24no—
206D3×Dic5—24no—
207D3×Dic5—22no—
208D3×Dic5—22no—
209D3×Dic5—42no—
210C3×C5×C8—21no—
211C3⋊#168—21no—
212C3×#168—21no—
213C5×C3⋊C8—21no—
214C2×D3×Q8—51no—
215C3×#125—51no—
216C3×C4×Q8—51no—
217Q8×Dic3—51no—
218C2×D3×C8—51no—
219C2×D3×C8C2×D511yescharacteristic
220D3×C4⋊C4—51no—
221D3×C4⋊C4—101no—
222D3×C4⋊C4—101no—
223D3×C4⋊C4—101no—
224D3×C4⋊C4C2×D511yescharacteristic
225D3×C4⋊C4C2×D511yescharacteristic
226#890—51no—
227#890—51no—
228#889—101no—
229#889—101no—
230#887—51no—
231#887—101no—
232C42×D3—51no—
233C42×D3—101no—
234#870—51no—
235C4×Dic6—51no—
236C4×Dic6—101no—
237C3×#107—51no—
238C3×#106C2×D511yescharacteristic
239C3×C4⋊C8—51no—
240C3×#103—51no—
241C3×#103—51no—
242#835—51no—
243#835—51no—
244#818—51no—
245#817C2×D511yescharacteristic
246#816—51no—
247#816—51no—
248Dic3⋊C8—51no—
249Dic3⋊C8—51no—
250#810—51no—
251#810—51no—
252#808C2×D511yescharacteristic
253#808C2×D511yescharacteristic
254#807—51no—
255#807—51no—
256C4⋊(C3⋊C8)—51no—
257C22×C4×C5—31no—
258C22×C4×C5—61no—
259C22×C4×C5—61no—
260C22×Dic5—31no—
261C22×Dic5—31no—
262C22×Dic5—61no—
263C22×Dic5—61no—
264C2×Dic10—31no—
265C2×Dic10—34no—
266C2×Dic10—62no—
267C2×Dic10—61no—
268C2×Dic10C22×D311yescharacteristic
269C2×C5×C8—31no—
270C2×C5×C8—62no—
271C2×C5×C8C22×D311yescharacteristic
272C5×C4⋊C4—31no—
273C5×C4⋊C4—31no—
274C5×C4⋊C4—61no—
275C5×C4⋊C4—61no—
276C5×C4⋊C4C22×D311yescharacteristic
277C5×C4⋊C4C22×D311yescharacteristic
278C4⋊Dic5—21no—
279C4⋊Dic5—31no—
280C4⋊Dic5—61no—
281C4⋊Dic5—61no—
282C4⋊Dic5—61no—
283C4⋊Dic5—61no—
284C4⋊Dic5C22×D311yescharacteristic
285#683—21no—
286#683—21no—
287#683—61no—
288#683—61no—
289#683—61no—
290#683—61no—
291#683—61no—
292#683—61no—
293C4×Dic5—21no—
294C4×Dic5—31no—
295C4×Dic5—31no—
296C4×Dic5—31no—
297C4×Dic5—61no—
298C4×Dic5—61no—
299C4×Dic5—61no—
300C4×Dic5C22×D311yescharacteristic
301C2×#168—31no—
302C2×#168—62no—
303C2×#168C22×D311yescharacteristic
304C2×#125—151no—
305C2×C4×Q8—151no—
306#479—51no—
307#479—151no—
308#479—151no—
309#479—151no—
310#479—151no—
311#479—151no—
312#479—151no—
313#479—151no—
314C2×#107—151no—
315C2×#106—31no—
316C2×C4⋊C8—151no—
317C2×#103—151no—
318C2×#103—151no—
319C22×C3×C5C22×D411yescharacteristic
320C2×C5×D3C22⋊Q812yes—
321C2×C5×D3#13512yes—
322C2×C5×D3#13712yes—
323C3×C4×C5—41no—
324C3×C4×C5—41no—
325C3×C4×C5C22×Q811yescharacteristic
326C3×C4×C5C2×#4111yescharacteristic
327Dic15—22no—
328Dic15—21no—
329Dic15—21no—
330Dic15—41no—
331C3×Dic5—22no—
332C3×Dic5—21no—
333C3×Dic5—21no—
334C3×Dic5—41no—
335C5×Dic3—41no—
336C5×Dic3—41no—
337C5×Dic3C22⋊Q812yes—
338C2×C3×Q8—51no—
339D3×Q8—54no—
340D3×Q8—102no—
341C2×C4×D3—21no—
342C2×C4×D3—21no—
343C2×C4×D3—51no—
344C2×C4×D3—51no—
345C2×C4×D3—101no—
346C2×C4×D3—101no—
347C2×C4×D3C22×D511yescharacteristic
348C2×Dic6—51no—
349C2×Dic6—101no—
350C2×C3×C8—51no—
351C2×C3×C8C22×D511yescharacteristic
352C3×C4⋊C4—51no—
353C3×C4⋊C4—101no—
354C3×C4⋊C4—101no—
355C3×C4⋊C4—101no—
356C3×C4⋊C4C22×D511yescharacteristic
357C3×C4⋊C4C22×D511yescharacteristic
358C3×C42—51no—
359C3×C42—101no—
360C4⋊Dic3—51no—
361C4⋊Dic3—101no—
362C4⋊Dic3—101no—
363C4⋊Dic3—101no—
364C4⋊Dic3C22×D511yescharacteristic
365C4⋊Dic3C22×D511yescharacteristic
366Dic3⋊C4—21no—
367Dic3⋊C4—21no—
368Dic3⋊C4—101no—
369Dic3⋊C4—101no—
370Dic3⋊C4—101no—
371Dic3⋊C4—101no—
372Dic3⋊C4—101no—
373Dic3⋊C4—101no—
374Dic3⋊C4—101no—
375C4×Dic3—51no—
376C4×Dic3—51no—
377C4×Dic3—51no—
378C4×Dic3—101no—
379C4×Dic3—101no—
380C4×Dic3—101no—
381C2×C3⋊C8—51no—
382C2×C3⋊C8C22×D511yescharacteristic
383D3×C8—22no—
384D3×C8—102no—
385C23×C5—31no—
386C2×C4×C5—21no—
387C2×C4×C5—21no—
388C2×C4×C5—31no—
389C2×C4×C5—32no—
390C2×C4×C5—32no—
391C2×C4×C5—61no—
392C2×C4×C5—61no—
393C2×C4×C5—122no—
394C2×C4×C5—122no—
395C2×C4×C5C23×D311yescharacteristic
396C2×Dic5—21no—
397C2×Dic5—21no—
398C2×Dic5—31no—
399C2×Dic5—31no—
400C2×Dic5—64no—
401C2×Dic5—62no—
402C2×Dic5—62no—
403C2×Dic5—61no—
404C2×Dic5—61no—
405C2×Dic5—122no—
406C2×Dic5D3×D411yescharacteristic
407C2×Dic5D3×D411yescharacteristic
408Dic10—21no—
409Dic10—32no—
410Dic10—64no—
411Dic10—61no—
412Dic10D3×Q812yes—
413C5×C8—21no—
414C5×C8—61no—
415#168—21no—
416#168—61no—
417C22×Q8—151no—
418C22×C8—31no—
419C22×C8—151no—
420#125—51no—
421#125—151no—
422#125—151no—
423#125—151no—
424#125—301no—
425#125—301no—
426C4×Q8—51no—
427C4×Q8—151no—
428C4×Q8—151no—
429C4×Q8—151no—
430C4×Q8—301no—
431C4×Q8—301no—
432C2×C4⋊C4—31no—
433C2×C4⋊C4—31no—
434C2×C4⋊C4—151no—
435C2×C4⋊C4—301no—
436C2×C4⋊C4—301no—
437C2×C4⋊C4—301no—
438C2×C42—151no—
439C2×C42—301no—
440#107—51no—
441#107—151no—
442#107—151no—
443#107—151no—
444#106—31no—
445#106—31no—
446#106—31no—
447#106D3×D511yescharacteristic
448C4⋊C8—51no—
449C4⋊C8—151no—
450C4⋊C8—151no—
451C4⋊C8—151no—
452#103—51no—
453#103—51no—
454#103—151no—
455#103—151no—
456#103—151no—
457#103—151no—
458#103—151no—
459#103—151no—
460C2×C3×C5C2×C22⋊Q811yescharacteristic
461C2×C3×C5C2×#13511yescharacteristic
462C2×C3×C5C2×#13711yescharacteristic
463C5×D3#47914yescomplemented
464C22×D3D4×D511yescharacteristic
465C3×Q8—52no—
466C3×Q8—101no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—51no—
470C2×C3×C4—51no—
471C2×C3×C4—101no—
472C2×C3×C4—101no—
473C2×C3×C4C23×D511yescharacteristic
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—51no—
477C2×Dic3—51no—
478C2×Dic3—101no—
479C2×Dic3—101no—
480C2×Dic3D4×D511yescharacteristic
481C4×D3—42no—
482C4×D3—42no—
483C4×D3—104no—
484C4×D3—102no—
485C4×D3—102no—
486C4×D3—202no—
487C4×D3#70912yes—
488C4×D3Q8×D512yes—
489Dic6—52no—
490Dic6—101no—
491Dic6—104no—
492C3×C8—21no—
493C3×C8—101no—
494C3⋊C8—21no—
495C3⋊C8—101no—
496C22×C5—32no—
497C22×C5—32no—
498C22×C5—32no—
499C22×C5C2×D3×D411yescharacteristic
500C4×C5—32no—
501C4×C5—41no—
502C4×C5—41no—
503C4×C5—121no—
504C4×C5—121no—
505C4×C5C2×D3×Q811yescharacteristic
506C4×C5D3×#4111yescharacteristic
507Dic5—21no—
508Dic5—21no—
509Dic5—22no—
510Dic5—41no—
511Dic5—61no—
512Dic5—61no—
513Dic5—62no—
514Dic5—121no—
515C2×Q8—51no—
516C2×Q8—154no—
517C2×Q8—151no—
518C2×Q8—301no—
519C2×Q8—302no—
520C22×C4—31no—
521C22×C4—61no—
522C22×C4—61no—
523C22×C4—151no—
524C22×C4—151no—
525C22×C4—301no—
526C22×C4—301no—
527C2×C8—31no—
528C2×C8—51no—
529C2×C8—62no—
530C2×C8—151no—
531C2×C8—302no—
532C2×C8C2×D3×D511yescharacteristic
533C4⋊C4—31no—
534C4⋊C4—31no—
535C4⋊C4—51no—
536C4⋊C4—61no—
537C4⋊C4—61no—
538C4⋊C4—101no—
539C4⋊C4—101no—
540C4⋊C4—101no—
541C4⋊C4—151no—
542C4⋊C4—301no—
543C4⋊C4—301no—
544C4⋊C4—301no—
545C4⋊C4—301no—
546C4⋊C4—301no—
547C4⋊C4—301no—
548C4⋊C4—301no—
549C4⋊C4—301no—
550C4⋊C4—301no—
551C4⋊C4—301no—
552C4⋊C4C2×D3×D511yescharacteristic
553C4⋊C4C2×D3×D511yescharacteristic
554C42—51no—
555C42—101no—
556C42—151no—
557C42—151no—
558C42—151no—
559C42—301no—
560C42—301no—
561C42—301no—
562C3×C5C2×#47911yescharacteristic, complemented, Hall
563C22×C3C2×D4×D511yescharacteristic
564C2×D3#404212yes—
565C2×D3#406112yes—
566C2×D3#406212yes—
567C3×C4—41no—
568C3×C4—41no—
569C3×C4—101no—
570C3×C4—101no—
571C3×C4—102no—
572C3×C4—201no—
573C3×C4C2×#70911yescharacteristic
574C3×C4C2×Q8×D511yescharacteristic
575Dic3—41no—
576Dic3—41no—
577Dic3—101no—
578Dic3—101no—
579Dic3—102no—
580Dic3—201no—
581Dic3#404212yes—
582C2×C5—34no—
583C2×C5D3×C22⋊Q811yescharacteristic
584C2×C5D3×#13511yescharacteristic
585C2×C5D3×#13711yescharacteristic
586C23—31no—
587Q8—52no—
588Q8—101no—
589Q8—152no—
590Q8—304no—
591Q8—301no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—31no—
595C2×C4—32no—
596C2×C4—32no—
597C2×C4—51no—
598C2×C4—51no—
599C2×C4—61no—
600C2×C4—61no—
601C2×C4—101no—
602C2×C4—101no—
603C2×C4—122no—
604C2×C4—122no—
605C2×C4—151no—
606C2×C4—151no—
607C2×C4—302no—
608C2×C4—302no—
609C2×C4—304no—
610C2×C4—301no—
611C2×C4—301no—
612C2×C4—602no—
613C2×C4C22×D3×D511yescharacteristic
614C8—21no—
615C8—61no—
616C8—101no—
617C8—301no—
618C2×C3C2×#404211yescharacteristic
619C2×C3C2×#406111yescharacteristic
620C2×C3C2×#406211yescharacteristic
621D3#6514614yesdirect product factor
622C5D3×#47911yescharacteristic, complemented, Sylow
623C22—32no—
624C22—32no—
625C22—32no—
626C22D3×D4×D511yescharacteristic
627C4—32no—
628C4—41no—
629C4—41no—
630C4—101no—
631C4—101no—
632C4—102no—
633C4—121no—
634C4—121no—
635C4—201no—
636C4—301no—
637C4—301no—
638C4—302no—
639C4—601no—
640C4D3×#70911yescharacteristic
641C4D3×Q8×D511yescharacteristic
642C3C2×#6514611yescharacteristic, complemented, Sylow
643C2—34no—
644C2D3×#404211yescharacteristic
645C2D3×#406111yescharacteristic
646C2D3×#406211yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#106C22
socleC22×C3×C5C22×D4
prime radicalC22×C5×D3C2×D4
hypercenter#106D3×D5
hypocenterC3×C5C2×#479
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
3. #11750958C2semidirect
5. C3×#65146C2semidirect
6. #11747877C2semidirect
7. #11747852C2semidirect
12. #11747390C2semidirect
13. #11747302C2semidirect
14. #11747286C2semidirect
15. #11747184C2semidirect
75. #65146D3direct (N × H)
463. C5×D3#479semidirect
562. C3×C5C2×#479semidirect
621. D3#65146direct (N × H)
622. C5D3×#479semidirect
642. C3C2×#65146semidirect

Maximal subgroups

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

subgroupindex
D3×#40362
D3×#40332
#117509582
C5×D3×#1062
C3×#651462
#117478772
#117478522
D3×#39482
D3×#39462
D3×#39422
D3×#39392
#117473902
#117473022
#117472862
#117471842
C2×#651463
D3×#4795