Finite Group Databasebeta

← D3×#65282 #14331744

Subgroups — D3×#65282 #14331744

Order 1920.

1640 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×D3×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×D3×#685C212yesmaximal
3C2×D3×#685C211yesmaximal, characteristic
4#11751093C211yesmaximal, characteristic, complemented
5C3×#65282C211yesmaximal, characteristic, complemented
6D3×#3963C212yesmaximal, complemented
7D3×#3963C211yesmaximal, characteristic, complemented
8#11748760C211yesmaximal, characteristic, complemented
9#11748739C212yesmaximal, complemented
10#11748608C211yesmaximal, characteristic, complemented
11#11748597C212yesmaximal, complemented
12C2×#65282—31nomaximal, Hall
13C23×D3×D5C2211yescharacteristic
14C22×C4×C5×D3C2212yes—
15C22×C4×C5×D3C2211yescharacteristic
16C22×D3×Dic5C2212yes—
17C22×D3×Dic5C2211yescharacteristic
18C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
19C2×#6714C2211yescharacteristic
20C2×#6714C2212yes—
21C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
22C2×C5×Dic3⋊C4C2212yescomplemented
23C5×D3×C4⋊C4—24no—
24C2×C3×#685C2212yes—
25C2×C3×#685C2211yescharacteristic
26C2×#6667C2212yes—
27C2×#6667C2211yescharacteristic
28C2×#6665C2211yescharacteristic
29C2×#6665C2212yes—
30D3×#685—28no—
31D3×#685—24no—
32#91115C2212yescomplemented
33#91115C2211yescharacteristic, complemented
34C3×#3963C2211yescharacteristic, complemented
35C3×#3963C2212yescomplemented
36#90994C2212yescomplemented
37#90994C2212yescomplemented
38#90994C2212yescomplemented
39D3×#397—51nomaximal, Hall
40C22×C5×C4⋊C4—31no—
41C22×#685—31no—
42C22×#685—32no—
43C2×#3963—31no—
44C2×#3963—32no—
45#65282—32no—
46#65282—31no—
47#65282—31no—
48#65282—32no—
49#65282—31no—
50#65282D311yescharacteristic, direct product factor
51C23×D15C2311yescharacteristic
52C23×C5×D3C2311yescharacteristic
53C23×C3×D5C2311yescharacteristic
54C22×D3×D5—22no—
55C22×D3×D5—22no—
56C22×D3×D5—24no—
57C22×D3×D5—24no—
58C22×D3×D5D414yes—
59C22×C3×C4×C5C2312yes—
60C22×C3×C4×C5C2311yescharacteristic
61C22×Dic15C2311yescharacteristic
62C22×Dic15C2312yes—
63C22×C5×Dic3C2312yes—
64C22×C5×Dic3C2311yescharacteristic
65C2×C4×C5×D3—24no—
66C2×C4×C5×D3—24no—
67C2×C4×C5×D3—24no—
68C2×C4×C5×D3—24no—
69C2×C4×C5×D3D414yes—
70C22×C3×Dic5C2312yes—
71C22×C3×Dic5C2311yescharacteristic
72C2×D3×Dic5—24no—
73C2×D3×Dic5—22no—
74C2×D3×Dic5—24no—
75C2×D3×Dic5—24no—
76C2×D3×Dic5—24no—
77C3×C5×C4⋊C4—22no—
78#6714—24no—
79#6714—22no—
80C5×C4⋊Dic3—22no—
81C5×Dic3⋊C4—24no—
82C3×#685—24no—
83C3×#685—22no—
84#6667—24no—
85#6667—22no—
86#6665—24no—
87#6665—22no—
88C2×D3×C4⋊C4D511yescharacteristic, complemented
89C2×D3×C22⋊C4—52no—
90C2×D3×C22⋊C4—51no—
91C3×#397—51no—
92#4992—51no—
93#4953—51no—
94#4952—52no—
95#4675—52no—
96#4674—51no—
97D3×#95—52no—
98D3×#95—51no—
99C24×D5—31no—
100C23×C4×C5—31no—
101C23×C4×C5—32no—
102C23×Dic5—31no—
103C23×Dic5—32no—
104C2×C5×C4⋊C4—32no—
105C2×C5×C4⋊C4—31no—
106C2×C5×C4⋊C4—64no—
107C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
108C2×#685—31no—
109C2×#685—32no—
110C2×#685—32no—
111C2×#685—31no—
112C2×#685—31no—
113C2×#685—32no—
114C2×#685—64no—
115C2×#685—68no—
116C2×#685C2×D312yes—
117C2×#685C2×D311yescharacteristic
118#3963—32no—
119#3963—31no—
120#3963—32no—
121#3963—32no—
122#3963—32no—
123#3963C2×D312yescomplemented
124#3963C2×D311yescharacteristic, complemented
125C2×#397—151noSylow
126C23×C3×C5C2411yescharacteristic
127C22×D15—21no—
128C22×D15—21no—
129C22×D15—22no—
130C22×D15—22no—
131C22×D15C2×D412yes—
132C22×C5×D3C2×D412yes—
133C22×C5×D3C2×D412yes—
134C22×C5×D3#4112yes—
135C22×C5×D3#4114yes—
136C22×C5×D3#4114yes—
137C22×C3×D5—21no—
138C22×C3×D5—21no—
139C22×C3×D5—22no—
140C22×C3×D5—22no—
141C22×C3×D5C2×D412yes—
142C2×D3×D5—28no—
143C2×D3×D5—216no—
144C2×D3×D5—44no—
145C2×D3×D5—44no—
146C2×D3×D5—48no—
147C2×C3×C4×C5—22no—
148C2×C3×C4×C5—22no—
149C2×C3×C4×C5—22no—
150C2×C3×C4×C5—22no—
151C2×C3×C4×C5C2×D412yes—
152C2×Dic15—22no—
153C2×Dic15—21no—
154C2×Dic15—22no—
155C2×Dic15—22no—
156C2×Dic15—22no—
157C2×C5×Dic3—22no—
158C2×C5×Dic3—22no—
159C2×C5×Dic3—22no—
160C2×C5×Dic3—22no—
161C2×C5×Dic3C2×D412yes—
162C4×C5×D3—28no—
163C4×C5×D3—48no—
164C2×C3×Dic5—22no—
165C2×C3×Dic5—21no—
166C2×C3×Dic5—22no—
167C2×C3×Dic5—22no—
168C2×C3×Dic5—22no—
169D3×Dic5—48no—
170D3×Dic5—44no—
171C24×D3—51no—
172C22×C4×D3—52no—
173C22×C4×D3—51no—
174C22×C4×D3C2×D512yes—
175C22×C4×D3C2×D511yescharacteristic
176C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
177C2×C3×C22⋊C4—52no—
178C2×C3×C22⋊C4—51no—
179C2×#217—51no—
180C2×#217—52no—
181C2×(C2×D3)⋊C4—51no—
182C2×(C2×D3)⋊C4—52no—
183C2×(C2×D3)⋊C4—52no—
184C2×(C2×D3)⋊C4—51no—
185C2×C4⋊Dic3C2×D511yescharacteristic, complemented
186C2×Dic3⋊C4C2×D512yescomplemented
187D3×C4⋊C4—24no—
188D3×C22⋊C4—108no—
189D3×C22⋊C4—104no—
190C3×#95—51no—
191C3×#95—52no—
192C3⋊#95—52no—
193C3⋊#95—51no—
194C3⋊#95—52no—
195C3⋊#95—52no—
196C3⋊#95—52no—
197C24×C5—31no—
198C23×D5—31no—
199C23×D5—34no—
200C23×D5—64no—
201C23×D5—64no—
202C23×D5—62no—
203C23×D5—62no—
204C23×D5C22×D311yescharacteristic
205C22×C4×C5—31no—
206C22×C4×C5—34no—
207C22×C4×C5—32no—
208C22×C4×C5—64no—
209C22×C4×C5—64no—
210C22×C4×C5—64no—
211C22×C4×C5—64no—
212C22×C4×C5C22×D312yes—
213C22×C4×C5C22×D311yescharacteristic
214C22×Dic5—32no—
215C22×Dic5—31no—
216C22×Dic5—64no—
217C22×Dic5—64no—
218C22×Dic5—64no—
219C22×Dic5—64no—
220C22×Dic5—62no—
221C22×Dic5C22×D312yes—
222C22×Dic5C22×D311yescharacteristic
223C5×C4⋊C4—22no—
224C5×C4⋊C4—64no—
225C5×C4⋊C4—62no—
226#685—24no—
227#685—22no—
228#685—62no—
229#685—64no—
230#685—64no—
231#685—62no—
232#685—64no—
233#685—62no—
234C22×C4⋊C4—31no—
235C22×C22⋊C4—151no—
236C22×C22⋊C4—152no—
237#397—51no—
238#397—151no—
239#397—152no—
240#397—152no—
241#397—151no—
242#397—151no—
243C2×#95—151no—
244C2×#95—152no—
245C22×C3×C5C22×D411yescharacteristic
246C22×C3×C5C22×D411yescharacteristic
247C22×C3×C5C2×#4112yes—
248C22×C3×C5C2×#4111yescharacteristic
249C22×C3×C5C2×#4112yes—
250C2×D15—22no—
251C2×D15—24no—
252C2×D15—41no—
253C2×D15—41no—
254C2×D15—42no—
255C2×C5×D3#12114yes—
256C2×C5×D3#12318yes—
257C2×C5×D3#12314yes—
258C2×C5×D3#12414yes—
259C2×C5×D3#12618yes—
260C2×C3×D5—22no—
261C2×C3×D5—24no—
262C2×C3×D5—41no—
263C2×C3×D5—41no—
264C2×C3×D5—42no—
265D3×D5—416no—
266C3×C4×C5—22no—
267C3×C4×C5—42no—
268Dic15—42no—
269Dic15—41no—
270C3×Dic5—42no—
271C3×Dic5—41no—
272C5×Dic3—22no—
273C5×Dic3—42no—
274C24×C3—51no—
275C23×D3—51no—
276C23×D3—54no—
277C23×D3—104no—
278C23×D3—102no—
279C23×D3—104no—
280C23×D3—102no—
281C23×D3C22×D511yescharacteristic
282C22×C3×C4—52no—
283C22×C3×C4—51no—
284C22×C3×C4C22×D512yes—
285C22×C3×C4C22×D511yescharacteristic
286C22×Dic3—52no—
287C22×Dic3—51no—
288C22×Dic3C22×D512yes—
289C22×Dic3C22×D511yescharacteristic
290C2×C4×D3—24no—
291C2×C4×D3—24no—
292C2×C4×D3—24no—
293C2×C4×D3—24no—
294C2×C4×D3—104no—
295C2×C4×D3—104no—
296C2×C4×D3—104no—
297C2×C4×D3—104no—
298C2×C4×D3—102no—
299C2×C4×D3C22⋊D514yes—
300C3×C4⋊C4—22no—
301C3×C22⋊C4—104no—
302C3×C22⋊C4—102no—
303#217—104no—
304#217—102no—
305(C2×D3)⋊C4—104no—
306(C2×D3)⋊C4—104no—
307(C2×D3)⋊C4—102no—
308(C2×D3)⋊C4—102no—
309C4⋊Dic3—22no—
310Dic3⋊C4—24no—
311C23×C5—32no—
312C23×C5—32no—
313C23×C5—34no—
314C23×C5—34no—
315C23×C5—32no—
316C23×C5C23×D311yescharacteristic
317C22×D5—21no—
318C22×D5—22no—
319C22×D5—21no—
320C22×D5—22no—
321C22×D5—32no—
322C22×D5—616no—
323C22×D5—68no—
324C22×D5—61no—
325C22×D5—62no—
326C22×D5—61no—
327C22×D5—62no—
328C22×D5—124no—
329C22×D5—124no—
330C22×D5—128no—
331C22×D5D3×D412yes—
332C2×C4×C5—22no—
333C2×C4×C5—22no—
334C2×C4×C5—22no—
335C2×C4×C5—22no—
336C2×C4×C5—32no—
337C2×C4×C5—68no—
338C2×C4×C5—62no—
339C2×C4×C5—62no—
340C2×C4×C5—62no—
341C2×C4×C5—62no—
342C2×C4×C5—128no—
343C2×C4×C5D3×D412yes—
344C2×Dic5—22no—
345C2×Dic5—21no—
346C2×Dic5—22no—
347C2×Dic5—22no—
348C2×Dic5—22no—
349C2×Dic5—62no—
350C2×Dic5—61no—
351C2×Dic5—62no—
352C2×Dic5—62no—
353C2×Dic5—62no—
354C2×Dic5—128no—
355C2×Dic5—124no—
356C25—151no—
357C23×C4—31no—
358C23×C4—32no—
359C23×C4—152no—
360C23×C4—151no—
361C2×C4⋊C4—32no—
362C2×C4⋊C4—31no—
363C2×C4⋊C4—64no—
364C2×C4⋊C4D3×D511yescharacteristic, complemented
365C2×C22⋊C4—52no—
366C2×C22⋊C4—51no—
367C2×C22⋊C4—151no—
368C2×C22⋊C4—152no—
369C2×C22⋊C4—151no—
370C2×C22⋊C4—152no—
371C2×C22⋊C4—152no—
372C2×C22⋊C4—151no—
373C2×C22⋊C4—304no—
374C2×C22⋊C4—308no—
375#95—52no—
376#95—51no—
377#95—152no—
378#95—152no—
379#95—152no—
380#95—152no—
381#95—151no—
382C2×C3×C5C2×#12111yescharacteristic
383C2×C3×C5C2×#12312yes—
384C2×C3×C5C2×#12311yescharacteristic
385C2×C3×C5C2×#12411yescharacteristic
386C2×C3×C5C2×#12612yes—
387D15—42no—
388C3×D5—42no—
389C5×D3#39718yescomplemented
390C23×C3—52no—
391C23×C3—102no—
392C23×C3—101no—
393C23×C3—102no—
394C23×C3—101no—
395C23×C3C23×D511yescharacteristic
396C22×D3—52no—
397C22×D3—102no—
398C22×D3—101no—
399C22×D3—102no—
400C22×D3—101no—
401C22×D3—1016no—
402C22×D3—108no—
403C22×D3—208no—
404C22×D3—204no—
405C22×D3—204no—
406C22×D3#70914yes—
407C22×D3D4×D512yes—
408C22×D3#71112yes—
409C22×D3#71314yes—
410C22×D3C2×C22⋊D512yes—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—102no—
416C2×C3×C4—102no—
417C2×C3×C4—102no—
418C2×C3×C4—102no—
419C2×C3×C4—101no—
420C2×C3×C4C2×C22⋊D512yes—
421C2×Dic3—22no—
422C2×Dic3—22no—
423C2×Dic3—22no—
424C2×Dic3—22no—
425C2×Dic3—102no—
426C2×Dic3—102no—
427C2×Dic3—102no—
428C2×Dic3—102no—
429C2×Dic3—101no—
430C2×Dic3C2×C22⋊D512yes—
431C4×D3—28no—
432C4×D3—48no—
433C4×D3—208no—
434C4×D3—204no—
435C22×C5—38no—
436C22×C5—34no—
437C22×C5—34no—
438C22×C5—38no—
439C22×C5—34no—
440C22×C5C2×D3×D411yescharacteristic
441C22×C5C2×D3×D411yescharacteristic
442C22×C5D3×#4112yes—
443C22×C5D3×#4111yescharacteristic
444C22×C5D3×#4112yes—
445C2×D5—24no—
446C2×D5—22no—
447C2×D5—41no—
448C2×D5—41no—
449C2×D5—42no—
450C2×D5—64no—
451C2×D5—62no—
452C2×D5—1216no—
453C2×D5—121no—
454C2×D5—121no—
455C2×D5—122no—
456C4×C5—22no—
457C4×C5—42no—
458C4×C5—62no—
459C4×C5—122no—
460Dic5—42no—
461Dic5—41no—
462Dic5—122no—
463Dic5—121no—
464C24—31no—
465C24—51no—
466C24—154no—
467C24—151no—
468C24—302no—
469C24—304no—
470C24—302no—
471C24—304no—
472C22×C4—31no—
473C22×C4—34no—
474C22×C4—32no—
475C22×C4—52no—
476C22×C4—51no—
477C22×C4—64no—
478C22×C4—64no—
479C22×C4—64no—
480C22×C4—64no—
481C22×C4—152no—
482C22×C4—151no—
483C22×C4—304no—
484C22×C4—302no—
485C22×C4—304no—
486C22×C4—304no—
487C22×C4—304no—
488C22×C4C2×D3×D512yes—
489C22×C4C2×D3×D511yescharacteristic
490C4⋊C4—22no—
491C4⋊C4—64no—
492C4⋊C4—62no—
493C22⋊C4—104no—
494C22⋊C4—102no—
495C22⋊C4—304no—
496C22⋊C4—302no—
497C22⋊C4—302no—
498C22⋊C4—304no—
499C22⋊C4—304no—
500C22⋊C4—302no—
501C3×C5C2×#39711yescharacteristic, complemented, Hall
502C22×C3—104no—
503C22×C3—102no—
504C22×C3—202no—
505C22×C3—201no—
506C22×C3—201no—
507C22×C3C2×#70912yes—
508C22×C3C2×D4×D511yescharacteristic
509C22×C3C2×#71111yescharacteristic
510C22×C3C2×#71312yes—
511C22×C3C22×C22⋊D511yescharacteristic
512C2×D3—104no—
513C2×D3—102no—
514C2×D3—202no—
515C2×D3—201no—
516C2×D3—201no—
517C2×D3—2016no—
518C2×D3#404018yes—
519C2×D3#404418yes—
520C2×D3#407514yes—
521C2×D3#408414yes—
522C2×D3#409314yes—
523C3×C4—22no—
524C3×C4—42no—
525C3×C4—202no—
526C3×C4—201no—
527Dic3—22no—
528Dic3—42no—
529Dic3—202no—
530Dic3—201no—
531C2×C5—38no—
532C2×C5D3×#12111yescharacteristic
533C2×C5D3×#12312yes—
534C2×C5D3×#12311yescharacteristic
535C2×C5D3×#12411yescharacteristic
536C2×C5D3×#12612yes—
537D5—42no—
538D5—122no—
539C23—34no—
540C23—32no—
541C23—32no—
542C23—34no—
543C23—32no—
544C23—52no—
545C23—102no—
546C23—101no—
547C23—102no—
548C23—101no—
549C23—152no—
550C23—308no—
551C23—3016no—
552C23—302no—
553C23—301no—
554C23—302no—
555C23—301no—
556C23—604no—
557C23—604no—
558C23—608no—
559C23C22×D3×D511yescharacteristic
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—32no—
565C2×C4—68no—
566C2×C4—62no—
567C2×C4—62no—
568C2×C4—62no—
569C2×C4—62no—
570C2×C4—102no—
571C2×C4—102no—
572C2×C4—102no—
573C2×C4—102no—
574C2×C4—101no—
575C2×C4—128no—
576C2×C4—302no—
577C2×C4—302no—
578C2×C4—302no—
579C2×C4—302no—
580C2×C4—301no—
581C2×C4—604no—
582C2×C4—608no—
583C2×C4D3×C22⋊D512yes—
584C2×C3—202no—
585C2×C3C2×#404012yes—
586C2×C3C2×#404412yes—
587C2×C3C2×#407511yescharacteristic
588C2×C3C2×#408411yescharacteristic
589C2×C3C2×#409311yescharacteristic
590D3—202no—
591D3#6528218yesdirect product factor
592C5D3×#39711yescharacteristic, complemented, Sylow
593C22—34no—
594C22—34no—
595C22—38no—
596C22—34no—
597C22—38no—
598C22—102no—
599C22—104no—
600C22—201no—
601C22—201no—
602C22—202no—
603C22—302no—
604C22—304no—
605C22—6016no—
606C22—601no—
607C22—601no—
608C22—602no—
609C22D3×#70912yes—
610C22D3×D4×D511yescharacteristic
611C22D3×#71111yescharacteristic
612C22D3×#71312yes—
613C22C2×D3×C22⋊D511yescharacteristic
614C4—22no—
615C4—42no—
616C4—62no—
617C4—122no—
618C4—201no—
619C4—202no—
620C4—601no—
621C4—602no—
622C3C2×#6528211yescharacteristic, complemented, Sylow
623C2—38no—
624C2—202no—
625C2—602no—
626C2D3×#404012yes—
627C2D3×#404412yes—
628C2D3×#407511yescharacteristic
629C2D3×#408411yescharacteristic
630C2D3×#409311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutator, socle, cosocleC23×C3×C5C24
FittingC2×C3×C5×C4⋊C4C22
prime radicalC23×D3×D5C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#397
LCSG ▷ C23×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C5×D3×C4⋊C4C2semidirect
4. #11751093C2semidirect
5. C3×#65282C2semidirect
6. D3×#3963C2semidirect
7. D3×#3963C2semidirect
8. #11748760C2semidirect
9. #11748739C2semidirect
10. #11748608C2semidirect
11. #11748597C2semidirect
18. C2×C3×C5×C4⋊C4C22semidirect
21. C2×C5×C4⋊Dic3C22semidirect
22. C2×C5×Dic3⋊C4C22semidirect
32. #91115C22semidirect
33. #91115C22semidirect
34. C3×#3963C22semidirect
35. C3×#3963C22semidirect
36. #90994C22semidirect
37. #90994C22semidirect
38. #90994C22semidirect
50. #65282D3direct (N × H)
88. C2×D3×C4⋊C4D5semidirect
107. C2×C5×C4⋊C4C2×D3semidirect
123. #3963C2×D3semidirect
124. #3963C2×D3semidirect
176. C2×C3×C4⋊C4C2×D5semidirect
185. C2×C4⋊Dic3C2×D5semidirect
186. C2×Dic3⋊C4C2×D5semidirect
364. C2×C4⋊C4D3×D5semidirect
389. C5×D3#397semidirect
501. C3×C5C2×#397semidirect
591. D3#65282direct (N × H)
592. C5D3×#397semidirect
622. C3C2×#65282semidirect

Maximal subgroups

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

subgroupindex
C2×C5×D3×C4⋊C42
C2×D3×#6852
#117510932
C3×#652822
D3×#39632
#117487602
#117487392
#117486082
#117485972
C2×#652823
D3×#3975