Finite Group Databasebeta

← D3×#65164 #14430116

Subgroups — D3×#65164 #14430116

Order 1920.

832 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#4034C211yesmaximal, characteristic
2D3×#4033C211yesmaximal, characteristic
3#11750976C211yesmaximal, characteristic, complemented
4C5×D3×#107C211yesmaximal, characteristic
5C3×#65164C211yesmaximal, characteristic, complemented
6#11747879C211yesmaximal, characteristic, complemented
7#11747849C211yesmaximal, characteristic, complemented
8D3×#3948C211yesmaximal, characteristic
9D3×#3946C211yesmaximal, characteristic
10D3×#3942C211yesmaximal, characteristic
11D3×#3939C211yesmaximal, characteristic
12#11747413C211yesmaximal, characteristic, complemented
13#11747303C211yesmaximal, characteristic, complemented
14#11747285C211yesmaximal, characteristic, complemented
15#11747182C211yesmaximal, characteristic, complemented
16C2×#65164—31nomaximal, Hall
17C2×D3×Dic10—21no—
18C2×D3×Dic10C2211yescharacteristic
19#91777C2211yescharacteristic
20#91776C2211yescharacteristic
21C2×C5×D3×C8C2211yescharacteristic
22C5×D3×C4⋊C4C2211yescharacteristic
23C5×D3×C4⋊C4C2211yescharacteristic
24C3×#4034C2211yescharacteristic
25C3×#4033C2211yescharacteristic
26#91470C2211yescharacteristic
27#91468C2211yescharacteristic
28D3×C4⋊Dic5C2211yescharacteristic
29D3×#683—21no—
30D3×#683—21no—
31C4×D3×Dic5—21no—
32C4×D3×Dic5C2211yescharacteristic
33#91333C2211yescharacteristic
34#91331C2211yescharacteristic
35#91328—21no—
36#91327—21no—
37#91325—21no—
38#91323—21no—
39C2×D3×#168C2211yescharacteristic
40C3×C5×#107C2211yescharacteristic
41#91100C2211yescharacteristic
42#91098C2211yescharacteristic
43#91094C2211yescharacteristic
44#91091C2211yescharacteristic
45C5×#818C2211yescharacteristic
46C5×#807C2211yescharacteristic
47C5×#807C2211yescharacteristic
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×#477—51nomaximal, Hall
61C2×#4034—31no—
62C2×#4033—31no—
63C2×C5×#107—31no—
64C2×#3948—31no—
65C2×#3946—31no—
66C2×#3942—31no—
67C2×#3939—31no—
68#65164—31no—
69#65164—31no—
70#65164—31no—
71#65164—31no—
72#65164—31no—
73#65164—31no—
74#65164—31no—
75#65164D311yescharacteristic, direct product factor
76C2×Dic30—21no—
77C2×Dic30C2311yescharacteristic
78C2×C4×C5×D3—21no—
79C2×C4×C5×D3—21no—
80C2×C4×C5×D3C2311yescharacteristic
81C2×C3×Dic10—21no—
82C2×C3×Dic10C2311yescharacteristic
83C2×#1204—21no—
84C2×#1204—21no—
85C2×#1204—21no—
86C2×D3×Dic5—21no—
87C2×D3×Dic5—21no—
88C2×D3×Dic5D411yescharacteristic
89C2×D3×Dic5D411yescharacteristic
90D3×Dic10—22no—
91D3×Dic10—44no—
92D3×Dic10Q814yescomplemented
93C2×C3×C5×C8C2311yescharacteristic
94C3×C5×C4⋊C4C2311yescharacteristic
95C3×C5×C4⋊C4C2311yescharacteristic
96C4⋊Dic15C2311yescharacteristic
97#6712—21no—
98#6712—21no—
99C4×Dic15—21no—
100C4×Dic15C2311yescharacteristic
101C2×C3⋊#168C2311yescharacteristic
102C5×C4⋊Dic3C2311yescharacteristic
103C5×C4⋊Dic3C2311yescharacteristic
104C5×Dic3⋊C4—21no—
105C5×Dic3⋊C4—21no—
106C2×C5×C3⋊C8C2311yescharacteristic
107C5×D3×C8—22no—
108C3×C4⋊Dic5C2311yescharacteristic
109C3×#683—21no—
110C3×#683—21no—
111C3×C4×Dic5—21no—
112C3×C4×Dic5C2311yescharacteristic
113C2×C3×#168C2311yescharacteristic
114Dic3⋊Dic5—21no—
115#6669—21no—
116#6669—21no—
117#6668—21no—
118#6668—21no—
119Dic3×Dic5—21no—
120Dic3×Dic5—21no—
121Dic3×Dic5D411yescharacteristic
122Dic3×Dic5D411yescharacteristic
123D3×#168—22no—
124D3×C4⋊Q8—51no—
125C4×D3×Q8—51no—
126C3×#477—51no—
127#5091—51no—
128#5021—51no—
129D3×#107—51no—
130D3×#107D511yescharacteristic
131#4875—51no—
132#4875—51no—
133#4850—51no—
134D3×C4⋊C8—51no—
135D3×#103—51no—
136D3×#103—51no—
137#4793—51no—
138#4793—51no—
139C22×Dic10—31no—
140C22×Dic10—61no—
141C22×C5×C8—31no—
142C2×C5×C4⋊C4—31no—
143C2×C5×C4⋊C4—31no—
144C2×C4⋊Dic5—31no—
145C2×#683—61no—
146C2×#683—61no—
147C2×C4×Dic5—31no—
148C2×C4×Dic5—61no—
149C22×#168—31no—
150#4034—31no—
151#4034—31no—
152#4034—31no—
153#4034—61no—
154#4034—61no—
155#4034C2×D311yescharacteristic
156#4033—31no—
157#4033—31no—
158#4033—31no—
159#4033—61no—
160#4033—61no—
161#4033C2×D311yescharacteristic
162C5×#107—31no—
163C5×#107—31no—
164C5×#107—31no—
165C5×#107C2×D311yescharacteristic
166#3948—31no—
167#3948—31no—
168#3948—31no—
169#3948C2×D311yescharacteristic
170#3946—31no—
171#3946—31no—
172#3946—31no—
173#3946C2×D311yescharacteristic
174#3942—31no—
175#3942—31no—
176#3942—31no—
177#3942C2×D311yescharacteristic
178#3939—31no—
179#3939—31no—
180#3939—31no—
181#3939C2×D311yescharacteristic
182C2×#477—151noSylow
183C22×C5×D3C2×D411yescharacteristic
184C2×C3×C4×C5—21no—
185C2×C3×C4×C5—21no—
186C2×C3×C4×C5C2411yescharacteristic
187C2×Dic15—21no—
188C2×Dic15—21no—
189C2×Dic15C2×D411yescharacteristic
190C2×Dic15C2×D411yescharacteristic
191Dic30—21no—
192Dic30—42no—
193Dic30C2×Q812yescomplemented
194C2×C5×Dic3—21no—
195C2×C5×Dic3—21no—
196C2×C5×Dic3C2×D411yescharacteristic
197C4×C5×D3—42no—
198C4×C5×D3—42no—
199C4×C5×D3C2×Q812yes—
200C4×C5×D3#4112yes—
201C2×C3×Dic5—21no—
202C2×C3×Dic5—21no—
203C2×C3×Dic5C2×D411yescharacteristic
204C2×C3×Dic5C2×D411yescharacteristic
205C3×Dic10—21no—
206C3×Dic10—42no—
207C3×Dic10C2×Q812yescomplemented
208#1204—24no—
209#1204—42no—
210#1204—42no—
211D3×Dic5—24no—
212D3×Dic5—22no—
213D3×Dic5—42no—
214D3×Dic5Q1614yes—
215C3×C5×C8—21no—
216C3⋊#168—21no—
217C3×#168—21no—
218C5×C3⋊C8—21no—
219C2×D3×Q8—51no—
220C2×D3×Q8—101no—
221C3×C4⋊Q8—51no—
222C3×C4×Q8—51no—
223Q8×Dic3—51no—
224#944—101no—
225C2×D3×C8—51no—
226C2×D3×C8C2×D511yescharacteristic
227D3×C4⋊C4—51no—
228D3×C4⋊C4—101no—
229D3×C4⋊C4—101no—
230D3×C4⋊C4C2×D511yescharacteristic
231D3×C4⋊C4C2×D511yescharacteristic
232#888—51no—
233#888—51no—
234#888—101no—
235#887—51no—
236#887—101no—
237C42×D3—51no—
238C42×D3—101no—
239#869—51no—
240C4×Dic6—51no—
241C4×Dic6—101no—
242C3×#107—51no—
243C3×#107C2×D511yescharacteristic
244C3×C4⋊C8—51no—
245C3×#103—51no—
246C3×#103—51no—
247#835—51no—
248#835—51no—
249#818—51no—
250#818C2×D511yescharacteristic
251#816—51no—
252#816—51no—
253Dic3⋊C8—51no—
254Dic3⋊C8—51no—
255#810—51no—
256#810—51no—
257#807—51no—
258#807—51no—
259#807C2×D511yescharacteristic
260#807C2×D511yescharacteristic
261C4⋊(C3⋊C8)—51no—
262C22×C4×C5—31no—
263C22×C4×C5—61no—
264C22×C4×C5—61no—
265C22×Dic5—31no—
266C22×Dic5—31no—
267C22×Dic5—61no—
268C22×Dic5—61no—
269C2×Dic10—21no—
270C2×Dic10—31no—
271C2×Dic10—34no—
272C2×Dic10—62no—
273C2×Dic10—61no—
274C2×Dic10—61no—
275C2×Dic10—61no—
276C2×Dic10—61no—
277C2×Dic10—124no—
278C2×Dic10C22×D311yescharacteristic
279C2×C5×C8—31no—
280C2×C5×C8—62no—
281C2×C5×C8C22×D311yescharacteristic
282C5×C4⋊C4—31no—
283C5×C4⋊C4—31no—
284C5×C4⋊C4—61no—
285C5×C4⋊C4—61no—
286C5×C4⋊C4C22×D311yescharacteristic
287C5×C4⋊C4C22×D311yescharacteristic
288C4⋊Dic5—31no—
289C4⋊Dic5—61no—
290C4⋊Dic5C22×D311yescharacteristic
291#683—21no—
292#683—21no—
293#683—61no—
294#683—61no—
295#683—61no—
296#683—61no—
297#683—61no—
298#683—61no—
299C4×Dic5—21no—
300C4×Dic5—31no—
301C4×Dic5—31no—
302C4×Dic5—31no—
303C4×Dic5—61no—
304C4×Dic5—61no—
305C4×Dic5—61no—
306C4×Dic5C22×D311yescharacteristic
307C2×#168—31no—
308C2×#168—62no—
309C2×#168C22×D311yescharacteristic
310C2×C4⋊Q8—151no—
311C2×C4×Q8—151no—
312#477—51no—
313#477—151no—
314#477—151no—
315#477—151no—
316#477—151no—
317#477—151no—
318#477—151no—
319#477—151no—
320C2×#107—31no—
321C2×#107—151no—
322C2×C4⋊C8—151no—
323C2×#103—151no—
324C2×#103—151no—
325C22×C3×C5C22×D411yescharacteristic
326C2×C5×D3C22⋊Q812yes—
327C2×C5×D3C2×Q1612yes—
328C2×C5×D3AGL(1,ℤ/8)12yes—
329C3×C4×C5—41no—
330C3×C4×C5—41no—
331C3×C4×C5C22×Q811yescharacteristic
332C3×C4×C5C2×#4111yescharacteristic
333Dic15—22no—
334Dic15—21no—
335Dic15—41no—
336Dic15C2×Q1612yes—
337C3×Dic5—22no—
338C3×Dic5—21no—
339C3×Dic5—41no—
340C3×Dic5C2×Q1612yes—
341C5×Dic3—41no—
342C5×Dic3—41no—
343C5×Dic3C22⋊Q812yes—
344C2×C3×Q8—51no—
345C2×C3×Q8—101no—
346D3×Q8—54no—
347D3×Q8—102no—
348D3×Q8—204no—
349C2×C4×D3—21no—
350C2×C4×D3—21no—
351C2×C4×D3—51no—
352C2×C4×D3—51no—
353C2×C4×D3—101no—
354C2×C4×D3—101no—
355C2×C4×D3C22×D511yescharacteristic
356C2×Dic6—51no—
357C2×Dic6—101no—
358C2×Dic6—101no—
359C2×Dic6—101no—
360C2×Dic6—101no—
361C2×C3×C8—51no—
362C2×C3×C8C22×D511yescharacteristic
363C3×C4⋊C4—51no—
364C3×C4⋊C4—101no—
365C3×C4⋊C4—101no—
366C3×C4⋊C4C22×D511yescharacteristic
367C3×C4⋊C4C22×D511yescharacteristic
368C3×C42—51no—
369C3×C42—101no—
370C4⋊Dic3—51no—
371C4⋊Dic3—101no—
372C4⋊Dic3—101no—
373C4⋊Dic3C22×D511yescharacteristic
374C4⋊Dic3C22×D511yescharacteristic
375Dic3⋊C4—21no—
376Dic3⋊C4—21no—
377Dic3⋊C4—101no—
378Dic3⋊C4—101no—
379Dic3⋊C4—101no—
380Dic3⋊C4—101no—
381Dic3⋊C4—101no—
382C4×Dic3—51no—
383C4×Dic3—51no—
384C4×Dic3—51no—
385C4×Dic3—101no—
386C4×Dic3—101no—
387C4×Dic3—101no—
388C2×C3⋊C8—51no—
389C2×C3⋊C8C22×D511yescharacteristic
390D3×C8—22no—
391D3×C8—102no—
392C23×C5—31no—
393C2×C4×C5—21no—
394C2×C4×C5—21no—
395C2×C4×C5—31no—
396C2×C4×C5—32no—
397C2×C4×C5—32no—
398C2×C4×C5—61no—
399C2×C4×C5—61no—
400C2×C4×C5—122no—
401C2×C4×C5—122no—
402C2×C4×C5C23×D311yescharacteristic
403C2×Dic5—21no—
404C2×Dic5—21no—
405C2×Dic5—31no—
406C2×Dic5—34no—
407C2×Dic5—31no—
408C2×Dic5—64no—
409C2×Dic5—62no—
410C2×Dic5—61no—
411C2×Dic5—61no—
412C2×Dic5—122no—
413C2×Dic5D3×D411yescharacteristic
414C2×Dic5D3×D411yescharacteristic
415Dic10—21no—
416Dic10—32no—
417Dic10—42no—
418Dic10—64no—
419Dic10—61no—
420Dic10—122no—
421Dic10—122no—
422Dic10—122no—
423Dic10D3×Q812yescomplemented
424C5×C8—21no—
425C5×C8—61no—
426#168—21no—
427#168—61no—
428C22×Q8—151no—
429C22×Q8—301no—
430C22×C8—31no—
431C22×C8—151no—
432C4⋊Q8—51no—
433C4⋊Q8—151no—
434C4⋊Q8—151no—
435C4⋊Q8—151no—
436C4⋊Q8—301no—
437C4⋊Q8—301no—
438C4×Q8—51no—
439C4×Q8—151no—
440C4×Q8—151no—
441C4×Q8—151no—
442C4×Q8—301no—
443C4×Q8—301no—
444C2×C4⋊C4—31no—
445C2×C4⋊C4—31no—
446C2×C4⋊C4—151no—
447C2×C4⋊C4—301no—
448C2×C4⋊C4—301no—
449C2×C42—151no—
450C2×C42—301no—
451#107—31no—
452#107—31no—
453#107—31no—
454#107—51no—
455#107—151no—
456#107—151no—
457#107—151no—
458#107D3×D511yescharacteristic
459C4⋊C8—51no—
460C4⋊C8—151no—
461C4⋊C8—151no—
462C4⋊C8—151no—
463#103—51no—
464#103—51no—
465#103—151no—
466#103—151no—
467#103—151no—
468#103—151no—
469#103—151no—
470#103—151no—
471C2×C3×C5C2×C22⋊Q811yescharacteristic
472C2×C3×C5C22×Q1611yescharacteristic
473C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
474C5×D3#47714yescomplemented
475C22×D3D4×D511yescharacteristic
476C3×Q8—52no—
477C3×Q8—101no—
478C3×Q8—202no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—51no—
482C2×C3×C4—51no—
483C2×C3×C4—101no—
484C2×C3×C4—101no—
485C2×C3×C4C23×D511yescharacteristic
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—51no—
489C2×Dic3—51no—
490C2×Dic3—101no—
491C2×Dic3—101no—
492C2×Dic3D4×D511yescharacteristic
493C4×D3—42no—
494C4×D3—42no—
495C4×D3—54no—
496C4×D3—104no—
497C4×D3—102no—
498C4×D3—202no—
499C4×D3#70912yes—
500C4×D3Q8×D512yes—
501Dic6—52no—
502Dic6—101no—
503Dic6—104no—
504Dic6—202no—
505Dic6—202no—
506Dic6—202no—
507C3×C8—21no—
508C3×C8—101no—
509C3⋊C8—21no—
510C3⋊C8—101no—
511C22×C5—32no—
512C22×C5—32no—
513C22×C5—32no—
514C22×C5C2×D3×D411yescharacteristic
515C4×C5—32no—
516C4×C5—41no—
517C4×C5—41no—
518C4×C5—121no—
519C4×C5—121no—
520C4×C5C2×D3×Q811yescharacteristic
521C4×C5D3×#4111yescharacteristic
522Dic5—21no—
523Dic5—22no—
524Dic5—32no—
525Dic5—41no—
526Dic5—61no—
527Dic5—62no—
528Dic5—121no—
529Dic5D3×Q1612yes—
530C2×Q8—51no—
531C2×Q8—101no—
532C2×Q8—154no—
533C2×Q8—151no—
534C2×Q8—301no—
535C2×Q8—301no—
536C2×Q8—302no—
537C2×Q8—301no—
538C2×Q8—301no—
539C2×Q8—604no—
540C22×C4—31no—
541C22×C4—61no—
542C22×C4—61no—
543C22×C4—151no—
544C22×C4—151no—
545C22×C4—301no—
546C22×C4—301no—
547C2×C8—31no—
548C2×C8—51no—
549C2×C8—62no—
550C2×C8—151no—
551C2×C8—302no—
552C2×C8C2×D3×D511yescharacteristic
553C4⋊C4—31no—
554C4⋊C4—31no—
555C4⋊C4—51no—
556C4⋊C4—61no—
557C4⋊C4—61no—
558C4⋊C4—101no—
559C4⋊C4—101no—
560C4⋊C4—151no—
561C4⋊C4—301no—
562C4⋊C4—301no—
563C4⋊C4—301no—
564C4⋊C4—301no—
565C4⋊C4—301no—
566C4⋊C4—301no—
567C4⋊C4—301no—
568C4⋊C4C2×D3×D511yescharacteristic
569C4⋊C4C2×D3×D511yescharacteristic
570C42—51no—
571C42—101no—
572C42—151no—
573C42—151no—
574C42—151no—
575C42—301no—
576C42—301no—
577C42—301no—
578C3×C5C2×#47711yescharacteristic, complemented, Hall
579C22×C3C2×D4×D511yescharacteristic
580C2×D3#404212yes—
581C2×D3#405712yes—
582C2×D3D5×Q1612yes—
583C3×C4—41no—
584C3×C4—41no—
585C3×C4—52no—
586C3×C4—101no—
587C3×C4—102no—
588C3×C4—201no—
589C3×C4C2×#70911yescharacteristic
590C3×C4C2×Q8×D511yescharacteristic
591Dic3—41no—
592Dic3—41no—
593Dic3—52no—
594Dic3—101no—
595Dic3—102no—
596Dic3—201no—
597Dic3#404212yes—
598C2×C5—34no—
599C2×C5D3×C22⋊Q811yescharacteristic
600C2×C5C2×D3×Q1611yescharacteristic
601C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
602C23—31no—
603Q8—52no—
604Q8—101no—
605Q8—152no—
606Q8—202no—
607Q8—304no—
608Q8—301no—
609Q8—602no—
610Q8—602no—
611Q8—602no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—31no—
615C2×C4—32no—
616C2×C4—32no—
617C2×C4—51no—
618C2×C4—51no—
619C2×C4—61no—
620C2×C4—61no—
621C2×C4—101no—
622C2×C4—101no—
623C2×C4—122no—
624C2×C4—122no—
625C2×C4—154no—
626C2×C4—151no—
627C2×C4—151no—
628C2×C4—302no—
629C2×C4—304no—
630C2×C4—301no—
631C2×C4—301no—
632C2×C4—602no—
633C2×C4C22×D3×D511yescharacteristic
634C8—21no—
635C8—61no—
636C8—101no—
637C8—301no—
638C2×C3C2×#404211yescharacteristic
639C2×C3C2×#405711yescharacteristic
640C2×C3C2×D5×Q1611yescharacteristic
641D3#6516414yesdirect product factor
642C5D3×#47711yescharacteristic, complemented, Sylow
643C22—32no—
644C22—32no—
645C22—32no—
646C22D3×D4×D511yescharacteristic
647C4—32no—
648C4—41no—
649C4—41no—
650C4—52no—
651C4—101no—
652C4—102no—
653C4—121no—
654C4—121no—
655C4—152no—
656C4—201no—
657C4—301no—
658C4—302no—
659C4—601no—
660C4D3×#70911yescharacteristic
661C4D3×Q8×D511yescharacteristic
662C3C2×#6516411yescharacteristic, complemented, Sylow
663C2—34no—
664C2D3×#404211yescharacteristic
665C2D3×#405711yescharacteristic
666C2D3×D5×Q1611yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#107C22
socleC22×C3×C5C22×D4
prime radicalC22×C5×D3C2×D4
hypercenter#107D3×D5
hypocenterC3×C5C2×#477
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
3. #11750976C2semidirect
5. C3×#65164C2semidirect
6. #11747879C2semidirect
7. #11747849C2semidirect
12. #11747413C2semidirect
13. #11747303C2semidirect
14. #11747285C2semidirect
15. #11747182C2semidirect
75. #65164D3direct (N × H)
92. D3×Dic10Q8semidirect
193. Dic30C2×Q8semidirect
207. C3×Dic10C2×Q8semidirect
423. Dic10D3×Q8semidirect
474. C5×D3#477semidirect
578. C3×C5C2×#477semidirect
641. D3#65164direct (N × H)
642. C5D3×#477semidirect
662. C3C2×#65164semidirect

Maximal subgroups

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

subgroupindex
D3×#40342
D3×#40332
#117509762
C5×D3×#1072
C3×#651642
#117478792
#117478492
D3×#39482
D3×#39462
D3×#39422
D3×#39392
#117474132
#117473032
#117472852
#117471822
C2×#651643
D3×#4775