Finite Group Databasebeta

← D3×#65176 #14427752

Subgroups — D3×#65176 #14427752

Order 1920.

1024 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×Dic20C211yesmaximal, characteristic, complemented
2C2×D3×C8×D5C211yesmaximal, characteristic
3D3×#4043C212yesmaximal
4#11750988C211yesmaximal, characteristic, complemented
5C5×D3×#107C211yesmaximal, characteristic, complemented
6C3×#65176C211yesmaximal, characteristic, complemented
7#11747958C211yesmaximal, characteristic, complemented
8#11747943C211yesmaximal, characteristic, complemented
9D3×#3942C212yesmaximal, complemented
10#11747445C212yesmaximal, complemented
11#11747359C212yesmaximal, complemented
12C2×#65176—31nomaximal, Hall
13C2×C4×D3×D5C2211yescharacteristic
14C2×D3×Dic10C2212yes—
15C2×Dic60C2211yescharacteristic, complemented
16C2×C8×D15C2211yescharacteristic
17#91786C2212yes—
18C2×C5×D3×C8C2211yescharacteristic
19C5×D3×C4⋊C4C2212yes—
20C2×C3×Dic20C2211yescharacteristic, complemented
21C2×C3×C8×D5C2211yescharacteristic
22C3×#4043C2212yes—
23D3×#685—22no—
24#91429—22no—
25D3×C4⋊Dic5—22no—
26#91422—22no—
27#91390C2212yes—
28#91360C2212yes—
29C2×#6662C2212yescomplemented
30C2×#6648C2211yescharacteristic
31C2×D3×#168C2211yescharacteristic
32C2×D5×C3⋊C8C2211yescharacteristic
33D3×Dic20—24no—
34D3×C8×D5—24no—
35C3×C5×#107C2211yescharacteristic, complemented
36#91094C2212yescomplemented
37C5×#818C2211yescharacteristic, complemented
38C5×#807C2212yescomplemented
39C3×#3942C2212yescomplemented
40#90975C2212yescomplemented
41#90970C2212yescomplemented
42D3×#467—51nomaximal, Hall
43C22×Dic20—31no—
44C22×C8×D5—31no—
45C2×#4043—32no—
46C2×C5×#107—31no—
47C2×#3942—32no—
48#65176—31no—
49#65176—31no—
50#65176—32no—
51#65176—31no—
52#65176—32no—
53#65176D311yescharacteristic, direct product factor
54C22×D3×D5D411yescharacteristic
55C2×C4×D15C2311yescharacteristic
56C2×Dic30C2312yes—
57C2×C4×C5×D3—22no—
58C2×C4×C5×D3C2311yescharacteristic
59C2×C3×C4×D5C2311yescharacteristic
60C2×C3×Dic10C2312yes—
61C2×#1204—22no—
62C2×#1200D411yescharacteristic
63C2×D3×Dic5—22no—
64C2×D3×Dic5D411yescharacteristic
65C2×D5×Dic3D411yescharacteristic
66C4×D3×D5—22no—
67C4×D3×D5—22no—
68D3×Dic10—24no—
69D3×Dic10—24no—
70C2×C3×C5×C8C2311yescharacteristic
71C3×C5×C4⋊C4C2312yes—
72#6714—22no—
73C4⋊Dic15—22no—
74C2×C3⋊#168C2311yescharacteristic
75Dic60—22no—
76C8×D15—22no—
77C5×C4⋊Dic3C2312yes—
78C5×Dic3⋊C4—22no—
79C2×C5×C3⋊C8C2311yescharacteristic
80C5×D3×C8D414yes—
81C3×#685—22no—
82C3×C4⋊Dic5—22no—
83C2×C3×#168C2311yescharacteristic
84C3×Dic20—22no—
85C3×C8×D5—22no—
86Dic3⋊Dic5—22no—
87Dic3⋊Dic5—22no—
88#6667—22no—
89#6665—22no—
90#6662—24no—
91#6648—22no—
92D3×#168—22no—
93D5×C3⋊C8—22no—
94C2×D3×Q16—51no—
95C22×D3×C8—51no—
96D3×C22⋊Q8—52no—
97C3×#467—51no—
98#5188—51no—
99#5116—51no—
100#5051—52no—
101#4887—51no—
102D3×#107D511yescharacteristic, complemented
103#4813—52no—
104D3×#103—52no—
105C22×C4×D5—31no—
106C22×Dic10—32no—
107C22×C5×C8—31no—
108C2×C5×C4⋊C4—32no—
109C2×#685—62no—
110C2×C4⋊Dic5—62no—
111C22×#168—31no—
112C2×Dic20—32no—
113C2×Dic20—31no—
114C2×Dic20—64no—
115C2×Dic20C2×D311yescharacteristic, complemented
116C2×C8×D5—31no—
117C2×C8×D5—31no—
118C2×C8×D5—31no—
119C2×C8×D5—64no—
120C2×C8×D5C2×D311yescharacteristic
121#4043—32no—
122#4043—32no—
123#4043—32no—
124#4043—62no—
125#4043—62no—
126#4043C2×D312yes—
127C5×#107—31no—
128C5×#107—32no—
129C5×#107C2×D311yescharacteristic, complemented
130#3942—32no—
131#3942—32no—
132#3942—32no—
133#3942C2×D312yescomplemented
134C2×#467—151noSylow
135C22×D15C2×D411yescharacteristic
136C22×C5×D3C2×D411yescharacteristic
137C22×C3×D5C2×D411yescharacteristic
138C2×D3×D5—22no—
139C2×D3×D5—22no—
140C2×D3×D5Q1614yescomplemented
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5C2411yescharacteristic
143C2×Dic15—22no—
144C2×Dic15C2×D411yescharacteristic
145C4×D15—21no—
146C4×D15—21no—
147Dic30—22no—
148Dic30—22no—
149C2×C5×Dic3—22no—
150C2×C5×Dic3C2×D411yescharacteristic
151C4×C5×D3—44no—
152C4×C5×D3C2×D412yes—
153C4×C5×D3#4112yes—
154C2×C3×Dic5—22no—
155C2×C3×Dic5C2×D411yescharacteristic
156C3×C4×D5—21no—
157C3×C4×D5—21no—
158C3×Dic10—22no—
159C3×Dic10—22no—
160#1204—44no—
161#1200—22no—
162D3×Dic5—22no—
163D3×Dic5—44no—
164D5×Dic3—22no—
165C3×C5×C8C2×D412yes—
166C3⋊#168—21no—
167C3×#168—21no—
168C5×C3⋊C8C2×D412yes—
169C2×D3×Q8—52no—
170C22×C4×D3—51no—
171C2×C3×Q16—51no—
172C22×C3×C8—51no—
173C3×C22⋊Q8—52no—
174#946—52no—
175C2×#216—52no—
176#924—52no—
177C22×C3⋊C8—51no—
178D3×Q16—104no—
179C2×Dic12—51no—
180C2×D3×C8—51no—
181C2×D3×C8—51no—
182C2×D3×C8—51no—
183C2×D3×C8—104no—
184C2×D3×C8C2×D511yescharacteristic
185#897—52no—
186#896—102no—
187D3×C4⋊C4—102no—
188D3×C4⋊C4C2×D512yes—
189D3×C22⋊C4—102no—
190#878—102no—
191C3×#107C2×D511yescharacteristic, complemented
192C3×#103—52no—
193#835—52no—
194#818C2×D511yescharacteristic, complemented
195#816—52no—
196#810—52no—
197#807C2×D512yescomplemented
198C23×D5—31no—
199C22×C4×C5—31no—
200C22×C4×C5—62no—
201C22×Dic5—31no—
202C22×Dic5—62no—
203C2×C4×D5—31no—
204C2×C4×D5—31no—
205C2×C4×D5—31no—
206C2×C4×D5—62no—
207C2×C4×D5—62no—
208C2×C4×D5C22×D311yescharacteristic
209C2×Dic10—32no—
210C2×Dic10—64no—
211C2×Dic10—64no—
212C2×Dic10—62no—
213C2×Dic10C22×D312yes—
214C2×C5×C8—31no—
215C2×C5×C8—34no—
216C2×C5×C8C22×D311yescharacteristic
217C5×C4⋊C4—32no—
218C5×C4⋊C4—62no—
219C5×C4⋊C4C22×D312yes—
220#685—22no—
221#685—62no—
222#685—62no—
223#685—62no—
224C4⋊Dic5—22no—
225C4⋊Dic5—62no—
226C4⋊Dic5—62no—
227C4⋊Dic5—62no—
228C2×#168—31no—
229C2×#168—62no—
230C2×#168C22×D311yescharacteristic
231Dic20—22no—
232Dic20—64no—
233Dic20—62no—
234C8×D5—22no—
235C8×D5—62no—
236C8×D5—62no—
237C8×D5—62no—
238C22×Q16—151no—
239C23×C8—151no—
240C2×C22⋊Q8—152no—
241#467—51no—
242#467—152no—
243#467—152no—
244#467—151no—
245#467—151no—
246#467—151no—
247C2×#107—31no—
248C2×#103—152no—
249C22×C3×C5C22×D411yescharacteristic
250C2×D15—21no—
251C2×D15—21no—
252C2×D15C2×Q1612yescomplemented
253C2×C5×D3#12112yes—
254C2×C5×D3C2×Q1612yes—
255C2×C5×D3#13512yes—
256C2×C3×D5—21no—
257C2×C3×D5—21no—
258C2×C3×D5C2×Q1612yescomplemented
259D3×D5—28no—
260C3×C4×C5—42no—
261C3×C4×C5C22×D411yescharacteristic
262C3×C4×C5C2×#4111yescharacteristic
263Dic15—21no—
264Dic15—42no—
265C3×Dic5—21no—
266C3×Dic5—42no—
267C5×Dic3—42no—
268C5×Dic3#12112yes—
269C23×D3—51no—
270C2×C3×Q8—52no—
271C22×C3×C4—51no—
272C22×Dic3—51no—
273D3×Q8—104no—
274D3×Q8—104no—
275C2×C4×D3—22no—
276C2×C4×D3—51no—
277C2×C4×D3—51no—
278C2×C4×D3—51no—
279C2×C4×D3—102no—
280C2×C4×D3—102no—
281C2×C4×D3—102no—
282C2×C4×D3C22×D511yescharacteristic
283C2×Dic6—52no—
284C2×Dic6—102no—
285C3×Q16—102no—
286C2×C3×C8—51no—
287C2×C3×C8—102no—
288C2×C3×C8C22×D511yescharacteristic
289C3×C4⋊C4—102no—
290C3×C4⋊C4C22×D512yes—
291C3×C22⋊C4—102no—
292#217—102no—
293#216—104no—
294(C2×D3)⋊C4—102no—
295(C2×D3)⋊C4—102no—
296C4⋊Dic3—102no—
297C4⋊Dic3C22×D512yes—
298Dic3⋊C4—22no—
299Dic3⋊C4—102no—
300Dic3⋊C4—102no—
301C2×C3⋊C8—51no—
302C2×C3⋊C8—102no—
303C2×C3⋊C8C22×D511yescharacteristic
304Dic12—102no—
305D3×C8—102no—
306D3×C8—102no—
307D3×C8—102no—
308D3×C8D2014yes—
309C23×C5—31no—
310C22×D5—31no—
311C22×D5—34no—
312C22×D5—62no—
313C22×D5—62no—
314C22×D5D3×D411yescharacteristic
315C2×C4×C5—22no—
316C2×C4×C5—31no—
317C2×C4×C5—32no—
318C2×C4×C5—32no—
319C2×C4×C5—62no—
320C2×C4×C5—124no—
321C2×C4×C5C23×D311yescharacteristic
322C2×Dic5—22no—
323C2×Dic5—31no—
324C2×Dic5—62no—
325C2×Dic5—62no—
326C2×Dic5—124no—
327C2×Dic5D3×D411yescharacteristic
328C4×D5—21no—
329C4×D5—21no—
330C4×D5—62no—
331C4×D5—62no—
332C4×D5—61no—
333C4×D5—61no—
334Dic10—22no—
335Dic10—22no—
336Dic10—62no—
337Dic10—62no—
338Dic10—124no—
339C5×C8—32no—
340C5×C8D3×D412yes—
341#168—21no—
342#168—61no—
343C22×Q8—152no—
344C23×C4—151no—
345C2×Q16—51no—
346C2×Q16—152no—
347C2×Q16—151no—
348C2×Q16—304no—
349C22×C8—31no—
350C22×C8—51no—
351C22×C8—151no—
352C22×C8—151no—
353C22×C8—151no—
354C22×C8—151no—
355C22×C8—304no—
356C22⋊Q8—52no—
357C22⋊Q8—152no—
358C22⋊Q8—152no—
359C22⋊Q8—152no—
360C22⋊Q8—302no—
361C22⋊Q8—302no—
362C2×C4⋊C4—32no—
363C2×C4⋊C4—302no—
364C2×C22⋊C4—302no—
365#107—31no—
366#107—32no—
367#107D3×D511yescharacteristic, complemented
368#103—52no—
369#103—152no—
370#103—152no—
371#103—152no—
372C2×C3×C5C2×#12111yescharacteristic
373C2×C3×C5C22×Q1611yescharacteristic
374C2×C3×C5C2×#13511yescharacteristic
375D15—22no—
376C3×D5—22no—
377C5×D3#46714yescomplemented
378C23×C3—51no—
379C22×D3—51no—
380C22×D3—54no—
381C22×D3—102no—
382C22×D3—102no—
383C22×D3D4×D511yescharacteristic
384C3×Q8—102no—
385C3×Q8—102no—
386C2×C3×C4—22no—
387C2×C3×C4—51no—
388C2×C3×C4—101no—
389C2×C3×C4—101no—
390C2×C3×C4—102no—
391C2×C3×C4C23×D511yescharacteristic
392C2×Dic3—22no—
393C2×Dic3—51no—
394C2×Dic3—102no—
395C2×Dic3—102no—
396C2×Dic3D4×D511yescharacteristic
397C4×D3—44no—
398C4×D3—102no—
399C4×D3—101no—
400C4×D3—101no—
401C4×D3—102no—
402C4×D3—204no—
403C4×D3C2×D2012yes—
404C4×D3#71312yes—
405Dic6—102no—
406Dic6—102no—
407Dic6—204no—
408C3×C8—101no—
409C3×C8C2×D2012yes—
410C3⋊C8—101no—
411C3⋊C8C2×D2012yes—
412C22×C5—32no—
413C22×C5—32no—
414C22×C5—32no—
415C22×C5C2×D3×D411yescharacteristic
416C2×D5—21no—
417C2×D5—21no—
418C2×D5—32no—
419C2×D5—68no—
420C2×D5—61no—
421C2×D5—61no—
422C2×D5D3×Q1612yescomplemented
423C4×C5—32no—
424C4×C5—42no—
425C4×C5—122no—
426C4×C5C2×D3×D411yescharacteristic
427C4×C5D3×#4111yescharacteristic
428Dic5—21no—
429Dic5—42no—
430Dic5—61no—
431Dic5—122no—
432C24—151no—
433C2×Q8—52no—
434C2×Q8—152no—
435C2×Q8—302no—
436C2×Q8—304no—
437C2×Q8—304no—
438C22×C4—31no—
439C22×C4—51no—
440C22×C4—62no—
441C22×C4—151no—
442C22×C4—151no—
443C22×C4—151no—
444C22×C4—151no—
445C22×C4—302no—
446C22×C4—302no—
447C22×C4—302no—
448Q16—102no—
449Q16—304no—
450Q16—302no—
451C2×C8—31no—
452C2×C8—34no—
453C2×C8—51no—
454C2×C8—102no—
455C2×C8—151no—
456C2×C8—302no—
457C2×C8—302no—
458C2×C8—302no—
459C2×C8—302no—
460C2×C8C2×D3×D511yescharacteristic
461C4⋊C4—32no—
462C4⋊C4—62no—
463C4⋊C4—102no—
464C4⋊C4—302no—
465C4⋊C4—302no—
466C4⋊C4—302no—
467C4⋊C4C2×D3×D512yes—
468C22⋊C4—102no—
469C22⋊C4—302no—
470C22⋊C4—302no—
471C22⋊C4—302no—
472C3×C5C2×#46711yescharacteristic, complemented, Hall
473C22×C3—52no—
474C22×C3—101no—
475C22×C3—101no—
476C22×C3C2×D4×D511yescharacteristic
477C2×D3—52no—
478C2×D3—101no—
479C2×D3—101no—
480C2×D3—108no—
481C2×D3#404112yes—
482C2×D3#405812yes—
483C2×D3D5×Q1612yes—
484C3×C4—42no—
485C3×C4—101no—
486C3×C4—202no—
487C3×C4C22×D2011yescharacteristic
488C3×C4C2×#71311yescharacteristic
489Dic3—42no—
490Dic3—101no—
491Dic3—202no—
492Dic3#404112yes—
493C2×C5—34no—
494C2×C5D3×#12111yescharacteristic
495C2×C5C2×D3×Q1611yescharacteristic
496C2×C5D3×#13511yescharacteristic
497D5—22no—
498D5—62no—
499C23—31no—
500C23—51no—
501C23—154no—
502C23—151no—
503C23—302no—
504C23—302no—
505Q8—102no—
506Q8—102no—
507Q8—302no—
508Q8—302no—
509Q8—604no—
510C2×C4—22no—
511C2×C4—31no—
512C2×C4—32no—
513C2×C4—32no—
514C2×C4—51no—
515C2×C4—62no—
516C2×C4—101no—
517C2×C4—101no—
518C2×C4—102no—
519C2×C4—124no—
520C2×C4—151no—
521C2×C4—302no—
522C2×C4—302no—
523C2×C4—302no—
524C2×C4—301no—
525C2×C4—301no—
526C2×C4—302no—
527C2×C4—604no—
528C2×C4C22×D3×D511yescharacteristic
529C8—32no—
530C8—101no—
531C8—301no—
532C8D3×D2012yes—
533C2×C3—102no—
534C2×C3C2×#404111yescharacteristic
535C2×C3C2×#405811yescharacteristic
536C2×C3C2×D5×Q1611yescharacteristic
537D3—102no—
538D3#6517614yesdirect product factor
539C5D3×#46711yescharacteristic, complemented, Sylow
540C22—32no—
541C22—32no—
542C22—32no—
543C22—52no—
544C22—101no—
545C22—101no—
546C22—152no—
547C22—308no—
548C22—301no—
549C22—301no—
550C22D3×D4×D511yescharacteristic
551C4—32no—
552C4—42no—
553C4—101no—
554C4—122no—
555C4—202no—
556C4—301no—
557C4—602no—
558C4C2×D3×D2011yescharacteristic
559C4D3×#71311yescharacteristic
560C3C2×#6517611yescharacteristic, complemented, Sylow
561C2—34no—
562C2—102no—
563C2—302no—
564C2D3×#404111yescharacteristic
565C2D3×#405811yescharacteristic
566C2D3×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×D3×D5D4
hypercenter#107D3×D5
hypocenterC3×C5C2×#467
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
1. C2×D3×Dic20C2semidirect
4. #11750988C2semidirect
5. C5×D3×#107C2semidirect
6. C3×#65176C2semidirect
7. #11747958C2semidirect
8. #11747943C2semidirect
9. D3×#3942C2semidirect
10. #11747445C2semidirect
11. #11747359C2semidirect
15. C2×Dic60C22semidirect
20. C2×C3×Dic20C22semidirect
29. C2×#6662C22semidirect
35. C3×C5×#107C22semidirect
36. #91094C22semidirect
37. C5×#818C22semidirect
38. C5×#807C22semidirect
39. C3×#3942C22semidirect
40. #90975C22semidirect
41. #90970C22semidirect
53. #65176D3direct (N × H)
102. D3×#107D5semidirect
115. C2×Dic20C2×D3semidirect
129. C5×#107C2×D3semidirect
133. #3942C2×D3semidirect
140. C2×D3×D5Q16semidirect
191. C3×#107C2×D5semidirect
194. #818C2×D5semidirect
197. #807C2×D5semidirect
252. C2×D15C2×Q16semidirect
258. C2×C3×D5C2×Q16semidirect
367. #107D3×D5semidirect
377. C5×D3#467semidirect
422. C2×D5D3×Q16semidirect
472. C3×C5C2×#467semidirect
538. D3#65176direct (N × H)
539. C5D3×#467semidirect
560. C3C2×#65176semidirect

Maximal subgroups

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

subgroupindex
C2×D3×Dic202
C2×D3×C8×D52
D3×#40432
#117509882
C5×D3×#1072
C3×#651762
#117479582
#117479432
D3×#39422
#117474452
#117473592
C2×#651763
D3×#4675