Finite Group Databasebeta

← D3×#65352 #14430143

Subgroups — D3×#65352 #14430143

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
1C5×D3×#125C211yesmaximal, characteristic
2C4×D3×Dic10C211yesmaximal, characteristic
3#11751164C211yesmaximal, characteristic, complemented
4C3×#65352C211yesmaximal, characteristic, complemented
5D3×#3942C211yesmaximal, characteristic
6D3×#3942C211yesmaximal, characteristic
7D3×#3940C211yesmaximal, characteristic
8D3×#3939C211yesmaximal, characteristic
9#11747296C211yesmaximal, characteristic, complemented
10#11747295C211yesmaximal, characteristic, complemented
11#11747291C211yesmaximal, characteristic, complemented
12#11747290C211yesmaximal, characteristic, complemented
13D3×C4⋊#168C211yesmaximal, characteristic
14#11746967C211yesmaximal, characteristic, complemented
15#11746919C211yesmaximal, characteristic, complemented
16C2×#65352—31nomaximal, Hall
17C2×D3×Dic10C2211yescharacteristic
18C3×C5×#125C2211yescharacteristic
19C4×Dic30C2211yescharacteristic
20C5×D3×C4⋊C4—21no—
21C5×D3×C4⋊C4—21no—
22C5×D3×C4⋊C4C2211yescharacteristic
23C5×D3×C4⋊C4C2211yescharacteristic
24C5×#890C2211yescharacteristic
25C5×#890C2211yescharacteristic
26C5×#889—21no—
27C5×#889—21no—
28C42×C5×D3C2211yescharacteristic
29C5×#870C2211yescharacteristic
30C3×C4×Dic10C2211yescharacteristic
31C4×#1204—21no—
32D3×C4⋊Dic5C2211yescharacteristic
33D3×#683—21no—
34C4×D3×Dic5—21no—
35#91340C2211yescharacteristic
36Dic3×Dic10C2211yescharacteristic
37#91324—21no—
38C2×D3×#168C2211yescharacteristic
39C2×D3×#168C2211yescharacteristic
40#91094C2211yescharacteristic
41#91094C2211yescharacteristic
42#91092C2211yescharacteristic
43#91091C2211yescharacteristic
44C4⋊(C3⋊#168)C2211yescharacteristic
45C3×#3942C2211yescharacteristic
46C3×#3942C2211yescharacteristic
47C3×#3940C2211yescharacteristic
48C3×#3939C2211yescharacteristic
49C3×C4⋊#168C2211yescharacteristic
50#90989C2211yescharacteristic
51#90988C2211yescharacteristic
52#90986C2211yescharacteristic
53#90985C2211yescharacteristic
54Dic3⋊#168C2211yescharacteristic
55Dic3⋊#168C2211yescharacteristic
56#90975C2211yescharacteristic
57#90975C2211yescharacteristic
58#90970C2211yescharacteristic
59#90970C2211yescharacteristic
60D3×#479—51nomaximal, Hall
61C2×C5×#125—31no—
62C2×C4×Dic10—31no—
63#65352—31no—
64#65352—31no—
65#65352—31no—
66#65352—31no—
67#65352—31no—
68#65352—31no—
69#65352—31no—
70#65352D311yescharacteristic, direct product factor
71C2×#3942—31no—
72C2×#3942—31no—
73C2×#3940—31no—
74C2×#3939—31no—
75C2×C4⋊#168—31no—
76C2×Dic30C2311yescharacteristic
77C2×C4×C5×D3—21no—
78C2×C4×C5×D3—21no—
79C2×C4×C5×D3D411yescharacteristic
80C2×C4×C5×D3D411yescharacteristic
81C2×C4×C5×D3C2311yescharacteristic
82C2×C3×Dic10C2311yescharacteristic
83C2×#1204—21no—
84C2×D3×Dic5—21no—
85C2×D3×Dic5—21no—
86D3×Dic10—22no—
87D3×Dic10Q814yes—
88C3×C5×C4⋊C4—21no—
89C3×C5×C4⋊C4—21no—
90C3×C5×C4⋊C4C2311yescharacteristic
91C3×C5×C4⋊C4C2311yescharacteristic
92C3×C42×C5C2311yescharacteristic
93C4⋊Dic15C2311yescharacteristic
94#6712—21no—
95C4×Dic15—21no—
96C2×C3⋊#168C2311yescharacteristic
97C2×C3⋊#168C2311yescharacteristic
98C5×C4⋊Dic3—21no—
99C5×C4⋊Dic3—21no—
100C5×C4⋊Dic3C2311yescharacteristic
101C5×C4⋊Dic3C2311yescharacteristic
102C5×Dic3⋊C4—21no—
103C5×Dic3⋊C4—21no—
104C5×Dic3⋊C4—21no—
105C5×Dic3⋊C4—21no—
106C5×Dic3⋊C4—21no—
107C5×Dic3⋊C4—21no—
108C4×C5×Dic3D411yescharacteristic
109C4×C5×Dic3D411yescharacteristic
110C4×C5×Dic3C2311yescharacteristic
111C3×C4⋊Dic5C2311yescharacteristic
112C3×#683—21no—
113C3×C4×Dic5—21no—
114C2×C3×#168C2311yescharacteristic
115C2×C3×#168C2311yescharacteristic
116Dic3⋊Dic5—21no—
117#6669—21no—
118#6668—21no—
119Dic3×Dic5—21no—
120Dic3×Dic5—21no—
121D3×#168—22no—
122D3×#168—22no—
123D3×#125D511yescharacteristic
124C4×D3×Q8—51no—
125C3×#479—51no—
126#5063—51no—
127#5022—51no—
128D3×#107—51no—
129#4877—51no—
130D3×#106—51no—
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—
139C5×#125—31no—
140C5×#125—31no—
141C5×#125—31no—
142C5×#125—61no—
143C5×#125—61no—
144C5×#125C2×D311yescharacteristic
145C2×C5×C4⋊C4—31no—
146C2×C5×C4⋊C4—31no—
147C2×C5×C4⋊C4—61no—
148C2×C5×C4⋊C4—61no—
149C2×C42×C5—31no—
150C2×C4⋊Dic5—31no—
151C2×#683—61no—
152C2×C4×Dic5—61no—
153C22×#168—31no—
154C22×#168—31no—
155C4×Dic10—31no—
156C4×Dic10—31no—
157C4×Dic10—31no—
158C4×Dic10—61no—
159C4×Dic10—61no—
160C4×Dic10C2×D311yescharacteristic
161#3942—31no—
162#3942—31no—
163#3942—31no—
164#3942—31no—
165#3942—31no—
166#3942—31no—
167#3942C2×D311yescharacteristic
168#3942C2×D311yescharacteristic
169#3940—31no—
170#3940—31no—
171#3940—31no—
172#3940C2×D311yescharacteristic
173#3939—31no—
174#3939—31no—
175#3939—31no—
176#3939C2×D311yescharacteristic
177C4⋊#168—31no—
178C4⋊#168—31no—
179C4⋊#168—31no—
180C4⋊#168C2×D311yescharacteristic
181C2×#479—151noSylow
182C22×C5×D3C2×D411yescharacteristic
183C2×C3×C4×C5—21no—
184C2×C3×C4×C5—21no—
185C2×C3×C4×C5C2×D411yescharacteristic
186C2×C3×C4×C5C2×D411yescharacteristic
187C2×C3×C4×C5C2411yescharacteristic
188C2×Dic15—21no—
189C2×Dic15—21no—
190Dic30—21no—
191Dic30C2×Q812yes—
192C2×C5×Dic3—21no—
193C2×C5×Dic3—21no—
194C2×C5×Dic3C2×D411yescharacteristic
195C2×C5×Dic3C2×D411yescharacteristic
196C2×C5×Dic3C2×D411yescharacteristic
197C4×C5×D3—22no—
198C4×C5×D3—22no—
199C4×C5×D3—42no—
200C4×C5×D3—42no—
201C4×C5×D3C2×Q812yes—
202C4×C5×D3#4112yes—
203C2×C3×Dic5—21no—
204C2×C3×Dic5—21no—
205C3×Dic10—21no—
206C3×Dic10C2×Q812yes—
207#1204—24no—
208D3×Dic5—24no—
209D3×Dic5—42no—
210C3⋊#168—21no—
211C3⋊#168—21no—
212C3×#168—21no—
213C3×#168—21no—
214C2×D3×Q8—51no—
215C3×#125C2×D511yescharacteristic
216C3×C4×Q8—51no—
217Q8×Dic3—51no—
218C2×D3×C8—51no—
219C2×D3×C8—51no—
220D3×C4⋊C4—21no—
221D3×C4⋊C4—21no—
222D3×C4⋊C4—51no—
223D3×C4⋊C4—101no—
224D3×C4⋊C4C2×D511yescharacteristic
225D3×C4⋊C4C2×D511yescharacteristic
226#890C2×D511yescharacteristic
227#890C2×D511yescharacteristic
228#889—21no—
229#889—21no—
230#887—51no—
231#887—101no—
232C42×D3—101no—
233C42×D3C2×D511yescharacteristic
234#870C2×D511yescharacteristic
235C4×Dic6—51no—
236C4×Dic6—101no—
237C3×#107—51no—
238C3×#106—51no—
239C3×C4⋊C8—51no—
240C3×#103—51no—
241C3×#103—51no—
242#835—51no—
243#835—51no—
244#818—51no—
245#817—51no—
246#816—51no—
247#816—51no—
248Dic3⋊C8—51no—
249Dic3⋊C8—51no—
250#810—51no—
251#810—51no—
252#808—51no—
253#808—51no—
254#807—51no—
255#807—51no—
256C4⋊(C3⋊C8)—51no—
257C22×C4×C5—31no—
258C22×C4×C5—31no—
259C22×C4×C5—31no—
260C22×C4×C5—61no—
261C22×C4×C5—61no—
262C22×Dic5—61no—
263C22×Dic5—61no—
264C2×Dic10—31no—
265C2×Dic10—34no—
266C2×Dic10—62no—
267C2×Dic10—61no—
268C2×Dic10C22×D311yescharacteristic
269C5×C4⋊C4—21no—
270C5×C4⋊C4—21no—
271C5×C4⋊C4—31no—
272C5×C4⋊C4—31no—
273C5×C4⋊C4—61no—
274C5×C4⋊C4—61no—
275C5×C4⋊C4—61no—
276C5×C4⋊C4—61no—
277C5×C4⋊C4—61no—
278C5×C4⋊C4—61no—
279C5×C4⋊C4—61no—
280C5×C4⋊C4—61no—
281C5×C4⋊C4C22×D311yescharacteristic
282C5×C4⋊C4C22×D311yescharacteristic
283C42×C5—31no—
284C42×C5—31no—
285C42×C5—31no—
286C42×C5C22×D311yescharacteristic
287C4⋊Dic5—31no—
288C4⋊Dic5—61no—
289C4⋊Dic5C22×D311yescharacteristic
290#683—21no—
291#683—61no—
292#683—61no—
293#683—61no—
294C4×Dic5—21no—
295C4×Dic5—61no—
296C4×Dic5—61no—
297C4×Dic5—61no—
298C2×#168—31no—
299C2×#168—31no—
300C2×#168—62no—
301C2×#168—62no—
302C2×#168C22×D311yescharacteristic
303C2×#168C22×D311yescharacteristic
304C2×#125—31no—
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—151no—
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—21no—
324C3×C4×C5—21no—
325C3×C4×C5—41no—
326C3×C4×C5—41no—
327C3×C4×C5C22×Q811yescharacteristic
328C3×C4×C5C2×#4111yescharacteristic
329Dic15—22no—
330Dic15—41no—
331C3×Dic5—22no—
332C3×Dic5—41no—
333C5×Dic3—21no—
334C5×Dic3—21no—
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—101no—
344C2×C4×D3—101no—
345C2×C4×D3C22⋊D511yescharacteristic
346C2×C4×D3C22⋊D511yescharacteristic
347C2×C4×D3C22×D511yescharacteristic
348C2×Dic6—51no—
349C2×Dic6—101no—
350C2×C3×C8—51no—
351C2×C3×C8—51no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—21no—
354C3×C4⋊C4—51no—
355C3×C4⋊C4—101no—
356C3×C4⋊C4C22×D511yescharacteristic
357C3×C4⋊C4C22×D511yescharacteristic
358C3×C42—101no—
359C3×C42C22×D511yescharacteristic
360C4⋊Dic3—21no—
361C4⋊Dic3—21no—
362C4⋊Dic3—51no—
363C4⋊Dic3—101no—
364C4⋊Dic3C22×D511yescharacteristic
365C4⋊Dic3C22×D511yescharacteristic
366Dic3⋊C4—21no—
367Dic3⋊C4—21no—
368Dic3⋊C4—21no—
369Dic3⋊C4—21no—
370Dic3⋊C4—21no—
371Dic3⋊C4—21no—
372Dic3⋊C4—101no—
373Dic3⋊C4—101no—
374Dic3⋊C4—101no—
375C4×Dic3—101no—
376C4×Dic3—101no—
377C4×Dic3—101no—
378C4×Dic3C22⋊D511yescharacteristic
379C4×Dic3C22⋊D511yescharacteristic
380C4×Dic3C22×D511yescharacteristic
381C2×C3⋊C8—51no—
382C2×C3⋊C8—51no—
383D3×C8—102no—
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—31no—
392C2×C4×C5—31no—
393C2×C4×C5—62no—
394C2×C4×C5—62no—
395C2×C4×C5—61no—
396C2×C4×C5—61no—
397C2×C4×C5—122no—
398C2×C4×C5—122no—
399C2×C4×C5D3×D411yescharacteristic
400C2×C4×C5D3×D411yescharacteristic
401C2×C4×C5C23×D311yescharacteristic
402C2×Dic5—21no—
403C2×Dic5—21no—
404C2×Dic5—64no—
405C2×Dic5—61no—
406C2×Dic5—61no—
407C2×Dic5—122no—
408Dic10—21no—
409Dic10—32no—
410Dic10—64no—
411Dic10—61no—
412Dic10D3×Q812yes—
413#168—21no—
414#168—21no—
415#168—61no—
416#168—61no—
417C22×Q8—151no—
418C22×C8—151no—
419C22×C8—151no—
420#125—31no—
421#125—31no—
422#125—31no—
423#125—61no—
424#125—61no—
425#125D3×D511yescharacteristic
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—61no—
435C2×C4⋊C4—61no—
436C2×C4⋊C4—151no—
437C2×C4⋊C4—301no—
438C2×C42—31no—
439C2×C42—301no—
440#107—51no—
441#107—151no—
442#107—151no—
443#107—151no—
444#106—51no—
445#106—151no—
446#106—151no—
447#106—151no—
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×D3C2×C22⋊D511yescharacteristic
465C3×Q8—52no—
466C3×Q8—101no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—101no—
470C2×C3×C4—101no—
471C2×C3×C4C2×C22⋊D511yescharacteristic
472C2×C3×C4C2×C22⋊D511yescharacteristic
473C2×C3×C4C23×D511yescharacteristic
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—101no—
477C2×Dic3—101no—
478C2×Dic3C2×C22⋊D511yescharacteristic
479C2×Dic3C2×C22⋊D511yescharacteristic
480C2×Dic3C2×C22⋊D511yescharacteristic
481C4×D3—22no—
482C4×D3—22no—
483C4×D3—42no—
484C4×D3—42no—
485C4×D3—104no—
486C4×D3—202no—
487C4×D3Q8×D512yes—
488C4×D3#71312yes—
489Dic6—52no—
490Dic6—101no—
491Dic6—104no—
492C3×C8—101no—
493C3×C8—101no—
494C3⋊C8—101no—
495C3⋊C8—101no—
496C22×C5—32no—
497C22×C5—32no—
498C22×C5—32no—
499C22×C5C2×D3×D411yescharacteristic
500C4×C5—21no—
501C4×C5—21no—
502C4×C5—32no—
503C4×C5—41no—
504C4×C5—41no—
505C4×C5—61no—
506C4×C5—61no—
507C4×C5—121no—
508C4×C5—121no—
509C4×C5C2×D3×Q811yescharacteristic
510C4×C5D3×#4111yescharacteristic
511Dic5—22no—
512Dic5—41no—
513Dic5—62no—
514Dic5—121no—
515C2×Q8—51no—
516C2×Q8—154no—
517C2×Q8—151no—
518C2×Q8—301no—
519C2×Q8—302no—
520C22×C4—31no—
521C22×C4—31no—
522C22×C4—31no—
523C22×C4—61no—
524C22×C4—61no—
525C22×C4—301no—
526C22×C4—301no—
527C2×C8—51no—
528C2×C8—51no—
529C2×C8—151no—
530C2×C8—151no—
531C2×C8—302no—
532C2×C8—302no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—31no—
536C4⋊C4—31no—
537C4⋊C4—51no—
538C4⋊C4—61no—
539C4⋊C4—61no—
540C4⋊C4—61no—
541C4⋊C4—61no—
542C4⋊C4—61no—
543C4⋊C4—61no—
544C4⋊C4—61no—
545C4⋊C4—61no—
546C4⋊C4—101no—
547C4⋊C4—151no—
548C4⋊C4—301no—
549C4⋊C4—301no—
550C4⋊C4—301no—
551C4⋊C4—301no—
552C4⋊C4C2×D3×D511yescharacteristic
553C4⋊C4C2×D3×D511yescharacteristic
554C42—31no—
555C42—31no—
556C42—31no—
557C42—101no—
558C42—301no—
559C42—301no—
560C42—301no—
561C42C2×D3×D511yescharacteristic
562C3×C5C2×#47911yescharacteristic, complemented, Hall
563C22×C3C22×C22⋊D511yescharacteristic
564C2×D3#409212yes—
565C2×D3#409612yes—
566C2×D3#409712yes—
567C3×C4—21no—
568C3×C4—21no—
569C3×C4—41no—
570C3×C4—41no—
571C3×C4—102no—
572C3×C4—201no—
573C3×C4C2×Q8×D511yescharacteristic
574C3×C4C2×#71311yescharacteristic
575Dic3—21no—
576Dic3—21no—
577Dic3—41no—
578Dic3—41no—
579Dic3—102no—
580Dic3—201no—
581Dic3#409212yes—
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—31no—
598C2×C4—31no—
599C2×C4—62no—
600C2×C4—62no—
601C2×C4—61no—
602C2×C4—61no—
603C2×C4—101no—
604C2×C4—101no—
605C2×C4—122no—
606C2×C4—122no—
607C2×C4—304no—
608C2×C4—301no—
609C2×C4—301no—
610C2×C4—602no—
611C2×C4D3×C22⋊D511yescharacteristic
612C2×C4D3×C22⋊D511yescharacteristic
613C2×C4C22×D3×D511yescharacteristic
614C8—101no—
615C8—101no—
616C8—301no—
617C8—301no—
618C2×C3C2×#409211yescharacteristic
619C2×C3C2×#409611yescharacteristic
620C2×C3C2×#409711yescharacteristic
621D3#6535214yesdirect product factor
622C5D3×#47911yescharacteristic, complemented, Sylow
623C22—32no—
624C22—32no—
625C22—32no—
626C22C2×D3×C22⋊D511yescharacteristic
627C4—21no—
628C4—21no—
629C4—32no—
630C4—41no—
631C4—41no—
632C4—61no—
633C4—61no—
634C4—102no—
635C4—121no—
636C4—121no—
637C4—201no—
638C4—302no—
639C4—601no—
640C4D3×Q8×D511yescharacteristic
641C4D3×#71311yescharacteristic
642C3C2×#6535211yescharacteristic, complemented, Sylow
643C2—34no—
644C2D3×#409211yescharacteristic
645C2D3×#409611yescharacteristic
646C2D3×#409711yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#125C22
socleC22×C3×C5C22×D4
prime radicalC22×C5×D3C2×D4
hypercenter#125D3×D5
hypocenterC3×C5C2×#479
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
3. #11751164C2semidirect
4. C3×#65352C2semidirect
9. #11747296C2semidirect
10. #11747295C2semidirect
11. #11747291C2semidirect
12. #11747290C2semidirect
14. #11746967C2semidirect
15. #11746919C2semidirect
70. #65352D3direct (N × H)
463. C5×D3#479semidirect
562. C3×C5C2×#479semidirect
621. D3#65352direct (N × H)
622. C5D3×#479semidirect
642. C3C2×#65352semidirect

Maximal subgroups

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

subgroupindex
C5×D3×#1252
C4×D3×Dic102
#117511642
C3×#653522
D3×#39422
D3×#39402
D3×#39392
#117472962
#117472952
#117472912
#117472902
D3×C4⋊#1682
#117469672
#117469192
C2×#653523
D3×#4795