Finite Group Databasebeta

← D3×#65086 #14437964

Subgroups — D3×#65086 #14437964

Order 1920.

768 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#4090C211yesmaximal, characteristic
2D3×#4036C211yesmaximal, characteristic
3#11750898C211yesmaximal, characteristic, complemented
4C5×D3×#103C211yesmaximal, characteristic
5C3×#65086C211yesmaximal, characteristic, complemented
6#11749336C211yesmaximal, characteristic, complemented
7#11749330C211yesmaximal, characteristic, complemented
8D3×#3967C211yesmaximal, characteristic
9#11748040C211yesmaximal, characteristic, complemented
10#11748025C211yesmaximal, characteristic, complemented
11D3×#3948C211yesmaximal, characteristic
12D3×#3947C211yesmaximal, characteristic
13D3×#3942C211yesmaximal, characteristic
14#11747429C211yesmaximal, characteristic, complemented
15#11747156C211yesmaximal, characteristic, complemented
16C2×#65086—31nomaximal, Hall
17C2×C5×D3×Q8C2211yescharacteristic
18C2×D3×Dic10C2211yescharacteristic
19#91833C2211yescharacteristic
20#91779C2211yescharacteristic
21C2×C5×D3×C8C2211yescharacteristic
22C5×D3×C4⋊C4C2211yescharacteristic
23C3×#4090C2211yescharacteristic
24C3×#4036C2211yescharacteristic
25D3×C4⋊Dic5—21no—
26D3×C4⋊Dic5C2211yescharacteristic
27D3×#683—21no—
28D3×#683—21no—
29D3×#683—21no—
30C4×D3×Dic5C2211yescharacteristic
31#91388C2211yescharacteristic
32#91385C2211yescharacteristic
33#91384C2211yescharacteristic
34#91376C2211yescharacteristic
35#91346—21no—
36#91343—21no—
37#91329—21no—
38#91329—21no—
39C2×D3×#168C2211yescharacteristic
40C3×C5×#103C2211yescharacteristic
41#91119C2211yescharacteristic
42#91100C2211yescharacteristic
43#91099C2211yescharacteristic
44#91094C2211yescharacteristic
45C5×#835C2211yescharacteristic
46C5×#816C2211yescharacteristic
47C5×#810C2211yescharacteristic
48C3×#3967C2211yescharacteristic
49C3×#3948C2211yescharacteristic
50C3×#3947C2211yescharacteristic
51C3×#3942C2211yescharacteristic
52#90975C2211yescharacteristic
53#90974C2211yescharacteristic
54#90973C2211yescharacteristic
55#90972C2211yescharacteristic
56#90971C2211yescharacteristic
57#90970C2211yescharacteristic
58#90954C2211yescharacteristic
59#90952C2211yescharacteristic
60D3×#491—51nomaximal, Hall
61C2×#4090—31no—
62C2×#4036—31no—
63C2×C5×#103—31no—
64C2×#3967—31no—
65C2×#3948—31no—
66C2×#3947—31no—
67C2×#3942—31no—
68#65086—31no—
69#65086—31no—
70#65086—31no—
71#65086—31no—
72#65086—31no—
73#65086—31no—
74#65086—31no—
75#65086D311yescharacteristic, direct product factor
76C2×C3×C5×Q8C2311yescharacteristic
77C2×Dic30C2311yescharacteristic
78C5×D3×Q8—22no—
79C5×D3×Q8—22no—
80C2×C4×C5×D3—21no—
81C2×C4×C5×D3—21no—
82C2×C4×C5×D3C2311yescharacteristic
83C2×C5×Dic6—21no—
84C2×C5×Dic6C2311yescharacteristic
85C2×C3×Dic10C2311yescharacteristic
86C2×#1204—21no—
87C2×D3×Dic5—21no—
88C2×D3×Dic5—21no—
89C2×D3×Dic5D411yescharacteristic
90C2×D3×Dic5D411yescharacteristic
91D3×Dic10—22no—
92D3×Dic10—22no—
93C2×C3×C5×C8C2311yescharacteristic
94C3×C5×C4⋊C4C2311yescharacteristic
95C4⋊Dic15—21no—
96C4⋊Dic15C2311yescharacteristic
97#6712—21no—
98#6712—21no—
99#6712—21no—
100C4×Dic15C2311yescharacteristic
101C2×C3⋊#168C2311yescharacteristic
102C5×C4⋊Dic3C2311yescharacteristic
103C5×Dic3⋊C4—21no—
104C2×C5×C3⋊C8C2311yescharacteristic
105C5×D3×C8—22no—
106C3×C4⋊Dic5—21no—
107C3×C4⋊Dic5C2311yescharacteristic
108C3×#683—21no—
109C3×#683—21no—
110C3×#683—21no—
111C3×C4×Dic5C2311yescharacteristic
112C2×C3×#168C2311yescharacteristic
113Dic3⋊Dic5—21no—
114Dic3⋊Dic5—21no—
115Dic3⋊Dic5—21no—
116#6669—21no—
117#6669—21no—
118#6669—21no—
119#6668—21no—
120#6668—21no—
121#6668—21no—
122Dic3×Dic5D411yescharacteristic
123Dic3×Dic5D411yescharacteristic
124D3×#168—22no—
125D3×C4⋊Q8—51no—
126D3×#125—51no—
127C3×#491—51no—
128#5082—51no—
129#5069—51no—
130D3×#103—51no—
131D3×#103—51no—
132D3×#103—51no—
133D3×#103D511yescharacteristic
134#4797—51no—
135#4797—51no—
136#4797—51no—
137#4797—51no—
138D3×#97—51no—
139#4703—51no—
140C22×C5×Q8—31no—
141C22×Dic10—31no—
142C22×C5×C8—31no—
143C2×C5×C4⋊C4—31no—
144#4090—31no—
145#4090—31no—
146#4090—31no—
147#4090—61no—
148#4090—61no—
149#4090C2×D311yescharacteristic
150C2×C4⋊Dic5—31no—
151C2×C4⋊Dic5—61no—
152C2×#683—61no—
153C2×#683—61no—
154C2×#683—61no—
155C2×C4×Dic5—31no—
156C22×#168—31no—
157#4036—31no—
158#4036—31no—
159#4036—31no—
160#4036—61no—
161#4036—61no—
162#4036C2×D311yescharacteristic
163C5×#103—31no—
164C5×#103—31no—
165C5×#103—31no—
166C5×#103C2×D311yescharacteristic
167#3967—31no—
168#3967—31no—
169#3967—31no—
170#3967C2×D311yescharacteristic
171#3948—31no—
172#3948—31no—
173#3948—31no—
174#3948C2×D311yescharacteristic
175#3947—31no—
176#3947—31no—
177#3947—31no—
178#3947C2×D311yescharacteristic
179#3942—31no—
180#3942—31no—
181#3942—31no—
182#3942C2×D311yescharacteristic
183C2×#491—151noSylow
184C22×C5×D3C2×D411yescharacteristic
185C3×C5×Q8—21no—
186C3×C5×Q8—21no—
187C2×C3×C4×C5—21no—
188C2×C3×C4×C5—21no—
189C2×C3×C4×C5C2411yescharacteristic
190C2×Dic15—21no—
191C2×Dic15—21no—
192C2×Dic15C2×D411yescharacteristic
193C2×Dic15C2×D411yescharacteristic
194Dic30—21no—
195Dic30—21no—
196C2×C5×Dic3—21no—
197C2×C5×Dic3—21no—
198C2×C5×Dic3C2×D411yescharacteristic
199C4×C5×D3—42no—
200C4×C5×D3—42no—
201C4×C5×D3#4112yes—
202C4×C5×D3#4112yes—
203C5×Dic6—21no—
204C5×Dic6—21no—
205C5×Dic6—42no—
206C2×C3×Dic5—21no—
207C2×C3×Dic5—21no—
208C2×C3×Dic5C2×D411yescharacteristic
209C2×C3×Dic5C2×D411yescharacteristic
210C3×Dic10—21no—
211C3×Dic10—21no—
212#1204—42no—
213D3×Dic5—22no—
214D3×Dic5—22no—
215D3×Dic5—42no—
216D3×Dic5—42no—
217C3×C5×C8—21no—
218C3⋊#168—21no—
219C3×#168—21no—
220C5×C3⋊C8—21no—
221C2×D3×Q8—51no—
222C2×D3×Q8C2×D511yescharacteristic
223C3×C4⋊Q8—51no—
224C3×#125—51no—
225#944—51no—
226#944—51no—
227C2×D3×C8—51no—
228C2×D3×C8C2×D511yescharacteristic
229D3×C4⋊C4—51no—
230D3×C4⋊C4—101no—
231D3×C4⋊C4—101no—
232D3×C4⋊C4—101no—
233D3×C4⋊C4—101no—
234D3×C4⋊C4C2×D511yescharacteristic
235#890—51no—
236#890—51no—
237#889—101no—
238#889—101no—
239#888—101no—
240#888—101no—
241C42×D3—51no—
242#870—51no—
243#869—51no—
244C3×#103—51no—
245C3×#103—51no—
246C3×#103—51no—
247C3×#103C2×D511yescharacteristic
248C3×#97—51no—
249#835—51no—
250#835—51no—
251#835—51no—
252#835C2×D511yescharacteristic
253#816—51no—
254#816—51no—
255#816—51no—
256#816C2×D511yescharacteristic
257#815—51no—
258#815—51no—
259#810—51no—
260#810—51no—
261#810—51no—
262#810C2×D511yescharacteristic
263#803—51no—
264C2×C5×Q8—31no—
265C2×C5×Q8—61no—
266C2×C5×Q8—62no—
267C2×C5×Q8—62no—
268C2×C5×Q8C22×D311yescharacteristic
269C22×C4×C5—31no—
270C22×C4×C5—61no—
271C22×C4×C5—61no—
272C22×Dic5—31no—
273C22×Dic5—31no—
274C22×Dic5—61no—
275C22×Dic5—61no—
276C2×Dic10—31no—
277C2×Dic10—62no—
278C2×Dic10—62no—
279C2×Dic10—61no—
280C2×Dic10C22×D311yescharacteristic
281C2×C5×C8—31no—
282C2×C5×C8—62no—
283C2×C5×C8C22×D311yescharacteristic
284C5×C4⋊C4—31no—
285C5×C4⋊C4—61no—
286C5×C4⋊C4C22×D311yescharacteristic
287C4⋊Dic5—21no—
288C4⋊Dic5—31no—
289C4⋊Dic5—61no—
290C4⋊Dic5—61no—
291C4⋊Dic5—61no—
292C4⋊Dic5—61no—
293C4⋊Dic5C22×D311yescharacteristic
294#683—21no—
295#683—21no—
296#683—21no—
297#683—61no—
298#683—61no—
299#683—61no—
300#683—61no—
301#683—61no—
302#683—61no—
303#683—61no—
304#683—61no—
305#683—61no—
306C4×Dic5—31no—
307C4×Dic5—31no—
308C4×Dic5—31no—
309C4×Dic5C22×D311yescharacteristic
310C2×#168—31no—
311C2×#168—62no—
312C2×#168C22×D311yescharacteristic
313C2×C4⋊Q8—151no—
314C2×#125—151no—
315#491—51no—
316#491—151no—
317#491—151no—
318#491—151no—
319#491—151no—
320#491—151no—
321#491—151no—
322#491—151no—
323C2×#103—31no—
324C2×#103—151no—
325C2×#103—151no—
326C2×#103—151no—
327C2×#97—151no—
328C22×C3×C5C22×D411yescharacteristic
329C2×C5×D3#12412yes—
330C2×C5×D3#13712yes—
331C2×C5×D3#13712yes—
332C3×C4×C5—41no—
333C3×C4×C5—41no—
334C3×C4×C5C2×#4111yescharacteristic
335C3×C4×C5C2×#4111yescharacteristic
336Dic15—21no—
337Dic15—21no—
338Dic15—41no—
339Dic15—41no—
340C3×Dic5—21no—
341C3×Dic5—21no—
342C3×Dic5—41no—
343C3×Dic5—41no—
344C5×Dic3—41no—
345C5×Dic3—41no—
346C5×Dic3#12412yes—
347C2×C3×Q8—51no—
348C2×C3×Q8C22×D511yescharacteristic
349D3×Q8—22no—
350D3×Q8—22no—
351D3×Q8—102no—
352D3×Q8—102no—
353C2×C4×D3—21no—
354C2×C4×D3—21no—
355C2×C4×D3—51no—
356C2×C4×D3—51no—
357C2×C4×D3—101no—
358C2×C4×D3—101no—
359C2×C4×D3C22×D511yescharacteristic
360C2×Dic6—21no—
361C2×Dic6—51no—
362C2×Dic6—101no—
363C2×Dic6C22×D511yescharacteristic
364C2×C3×C8—51no—
365C2×C3×C8C22×D511yescharacteristic
366C3×C4⋊C4—51no—
367C3×C4⋊C4—101no—
368C3×C4⋊C4—101no—
369C3×C4⋊C4—101no—
370C3×C4⋊C4—101no—
371C3×C4⋊C4C22×D511yescharacteristic
372C3×C42—51no—
373C4⋊Dic3—51no—
374C4⋊Dic3—101no—
375C4⋊Dic3—101no—
376C4⋊Dic3—101no—
377C4⋊Dic3—101no—
378C4⋊Dic3C22×D511yescharacteristic
379Dic3⋊C4—21no—
380Dic3⋊C4—101no—
381Dic3⋊C4—101no—
382Dic3⋊C4—101no—
383Dic3⋊C4—101no—
384Dic3⋊C4—101no—
385Dic3⋊C4—101no—
386Dic3⋊C4—101no—
387Dic3⋊C4—101no—
388Dic3⋊C4—101no—
389C4×Dic3—51no—
390C4×Dic3—51no—
391C4×Dic3—51no—
392C2×C3⋊C8—51no—
393C2×C3⋊C8C22×D511yescharacteristic
394D3×C8—22no—
395D3×C8—102no—
396C23×C5—31no—
397C5×Q8—21no—
398C5×Q8—21no—
399C5×Q8—61no—
400C5×Q8—61no—
401C5×Q8—122no—
402C2×C4×C5—21no—
403C2×C4×C5—21no—
404C2×C4×C5—31no—
405C2×C4×C5—32no—
406C2×C4×C5—32no—
407C2×C4×C5—61no—
408C2×C4×C5—61no—
409C2×C4×C5—122no—
410C2×C4×C5—122no—
411C2×C4×C5C23×D311yescharacteristic
412C2×Dic5—21no—
413C2×Dic5—21no—
414C2×Dic5—31no—
415C2×Dic5—31no—
416C2×Dic5—62no—
417C2×Dic5—62no—
418C2×Dic5—61no—
419C2×Dic5—61no—
420C2×Dic5—122no—
421C2×Dic5—122no—
422C2×Dic5D3×D411yescharacteristic
423C2×Dic5D3×D411yescharacteristic
424Dic10—21no—
425Dic10—21no—
426Dic10—61no—
427Dic10—61no—
428Dic10—122no—
429C5×C8—21no—
430C5×C8—61no—
431#168—21no—
432#168—61no—
433C22×Q8—31no—
434C22×Q8—151no—
435C22×C8—31no—
436C22×C8—151no—
437C4⋊Q8—51no—
438C4⋊Q8—151no—
439C4⋊Q8—151no—
440C4⋊Q8—151no—
441C4⋊Q8—301no—
442C4⋊Q8—301no—
443#125—51no—
444#125—151no—
445#125—151no—
446#125—151no—
447#125—301no—
448#125—301no—
449C2×C4⋊C4—31no—
450C2×C4⋊C4—151no—
451C2×C4⋊C4—301no—
452C2×C4⋊C4—301no—
453C2×C4⋊C4—301no—
454C2×C4⋊C4—301no—
455C2×C42—151no—
456#103—31no—
457#103—31no—
458#103—31no—
459#103—51no—
460#103—51no—
461#103—51no—
462#103—151no—
463#103—151no—
464#103—151no—
465#103—151no—
466#103—151no—
467#103—151no—
468#103—151no—
469#103—151no—
470#103—151no—
471#103D3×D511yescharacteristic
472#97—51no—
473#97—151no—
474#97—151no—
475#97—151no—
476C2×C3×C5C2×#12411yescharacteristic
477C2×C3×C5C2×#13711yescharacteristic
478C2×C3×C5C2×#13711yescharacteristic
479C5×D3#49114yescomplemented
480C22×D3D4×D511yescharacteristic
481C3×Q8—21no—
482C3×Q8—21no—
483C3×Q8—101no—
484C3×Q8—101no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—51no—
488C2×C3×C4—51no—
489C2×C3×C4—101no—
490C2×C3×C4—101no—
491C2×C3×C4C23×D511yescharacteristic
492C2×Dic3—21no—
493C2×Dic3—21no—
494C2×Dic3—51no—
495C2×Dic3—51no—
496C2×Dic3—101no—
497C2×Dic3—101no—
498C2×Dic3D4×D511yescharacteristic
499C4×D3—42no—
500C4×D3—42no—
501C4×D3—102no—
502C4×D3—102no—
503C4×D3—202no—
504C4×D3—202no—
505C4×D3#70912yes—
506C4×D3#71112yes—
507Dic6—21no—
508Dic6—21no—
509Dic6—42no—
510Dic6—101no—
511Dic6—101no—
512Dic6—202no—
513C3×C8—21no—
514C3×C8—101no—
515C3⋊C8—21no—
516C3⋊C8—101no—
517C22×C5—32no—
518C22×C5—32no—
519C22×C5—32no—
520C22×C5C2×D3×D411yescharacteristic
521C4×C5—32no—
522C4×C5—41no—
523C4×C5—41no—
524C4×C5—121no—
525C4×C5—121no—
526C4×C5D3×#4111yescharacteristic
527C4×C5D3×#4111yescharacteristic
528Dic5—21no—
529Dic5—21no—
530Dic5—41no—
531Dic5—41no—
532Dic5—61no—
533Dic5—61no—
534Dic5—121no—
535Dic5—121no—
536C2×Q8—31no—
537C2×Q8—51no—
538C2×Q8—61no—
539C2×Q8—62no—
540C2×Q8—62no—
541C2×Q8—151no—
542C2×Q8—301no—
543C2×Q8—302no—
544C2×Q8—302no—
545C2×Q8C2×D3×D511yescharacteristic
546C22×C4—31no—
547C22×C4—61no—
548C22×C4—61no—
549C22×C4—151no—
550C22×C4—151no—
551C22×C4—301no—
552C22×C4—301no—
553C2×C8—31no—
554C2×C8—51no—
555C2×C8—62no—
556C2×C8—151no—
557C2×C8—302no—
558C2×C8C2×D3×D511yescharacteristic
559C4⋊C4—31no—
560C4⋊C4—51no—
561C4⋊C4—61no—
562C4⋊C4—101no—
563C4⋊C4—101no—
564C4⋊C4—101no—
565C4⋊C4—101no—
566C4⋊C4—151no—
567C4⋊C4—301no—
568C4⋊C4—301no—
569C4⋊C4—301no—
570C4⋊C4—301no—
571C4⋊C4—301no—
572C4⋊C4—301no—
573C4⋊C4—301no—
574C4⋊C4—301no—
575C4⋊C4—301no—
576C4⋊C4—301no—
577C4⋊C4—301no—
578C4⋊C4—301no—
579C4⋊C4—301no—
580C4⋊C4C2×D3×D511yescharacteristic
581C42—51no—
582C42—151no—
583C42—151no—
584C42—151no—
585C3×C5C2×#49111yescharacteristic, complemented, Hall
586C22×C3C2×D4×D511yescharacteristic
587C2×D3#403112yes—
588C2×D3#406112yes—
589C2×D3#406412yes—
590C3×C4—41no—
591C3×C4—41no—
592C3×C4—101no—
593C3×C4—101no—
594C3×C4—201no—
595C3×C4—201no—
596C3×C4C2×#70911yescharacteristic
597C3×C4C2×#71111yescharacteristic
598Dic3—41no—
599Dic3—41no—
600Dic3—101no—
601Dic3—101no—
602Dic3—201no—
603Dic3—201no—
604Dic3#403112yes—
605C2×C5—34no—
606C2×C5D3×#12411yescharacteristic
607C2×C5D3×#13711yescharacteristic
608C2×C5D3×#13711yescharacteristic
609C23—31no—
610Q8—21no—
611Q8—21no—
612Q8—61no—
613Q8—61no—
614Q8—101no—
615Q8—101no—
616Q8—122no—
617Q8—301no—
618Q8—301no—
619Q8—602no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—31no—
623C2×C4—32no—
624C2×C4—32no—
625C2×C4—51no—
626C2×C4—51no—
627C2×C4—61no—
628C2×C4—61no—
629C2×C4—101no—
630C2×C4—101no—
631C2×C4—122no—
632C2×C4—122no—
633C2×C4—151no—
634C2×C4—151no—
635C2×C4—302no—
636C2×C4—302no—
637C2×C4—301no—
638C2×C4—301no—
639C2×C4—602no—
640C2×C4—602no—
641C2×C4C22×D3×D511yescharacteristic
642C8—21no—
643C8—61no—
644C8—101no—
645C8—301no—
646C2×C3C2×#403111yescharacteristic
647C2×C3C2×#406111yescharacteristic
648C2×C3C2×#406411yescharacteristic
649D3#6508614yesdirect product factor
650C5D3×#49111yescharacteristic, complemented, Sylow
651C22—32no—
652C22—32no—
653C22—32no—
654C22D3×D4×D511yescharacteristic
655C4—32no—
656C4—41no—
657C4—41no—
658C4—101no—
659C4—101no—
660C4—121no—
661C4—121no—
662C4—201no—
663C4—201no—
664C4—301no—
665C4—301no—
666C4—601no—
667C4—601no—
668C4D3×#70911yescharacteristic
669C4D3×#71111yescharacteristic
670C3C2×#6508611yescharacteristic, complemented, Sylow
671C2—34no—
672C2D3×#403111yescharacteristic
673C2D3×#406111yescharacteristic
674C2D3×#406411yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#103C22
socleC22×C3×C5C22×D4
prime radicalC22×C5×D3C2×D4
hypercenter#103D3×D5
hypocenterC3×C5C2×#491
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
3. #11750898C2semidirect
5. C3×#65086C2semidirect
6. #11749336C2semidirect
7. #11749330C2semidirect
9. #11748040C2semidirect
10. #11748025C2semidirect
14. #11747429C2semidirect
15. #11747156C2semidirect
75. #65086D3direct (N × H)
479. C5×D3#491semidirect
585. C3×C5C2×#491semidirect
649. D3#65086direct (N × H)
650. C5D3×#491semidirect
670. C3C2×#65086semidirect

Maximal subgroups

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

subgroupindex
D3×#40902
D3×#40362
#117508982
C5×D3×#1032
C3×#650862
#117493362
#117493302
D3×#39672
#117480402
#117480252
D3×#39482
D3×#39472
D3×#39422
#117474292
#117471562
C2×#650863
D3×#4915