Finite Group Databasebeta

← D59×#1809 #28588258

Subgroups — D59×#1809 #28588258

Order 15104.

1662 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M16×D59C211yesmaximal, characteristic
2C2×#107×D59C211yesmaximal, characteristic, complemented
3C2×#106×D59C211yesmaximal, characteristic, complemented
4#380×D59C212yesmaximal
5#21424130C211yesmaximal, characteristic, complemented
6#21424129C211yesmaximal, characteristic, complemented
7#21424128C212yesmaximal, complemented
8#21424127C212yesmaximal, complemented
9#21424126C211yesmaximal, characteristic, complemented
10#340×D59C212yesmaximal, complemented
11C59×#1809C211yesmaximal, characteristic, complemented
12C23×C4×D59C2211yescharacteristic
13C22×#11745664C2211yescharacteristic
14C22×#11745659C2211yescharacteristic
15C22×#11745659C2211yescharacteristic
16C2×M16×D59—24no—
17C2×M16×D59—24no—
18C2×M16×D59C418yescomplemented
19C22×C8×D59C2211yescharacteristic
20C22×C8×D59C2211yescharacteristic
21C2×C4⋊C4×D59C2212yes—
22C2×C4⋊C4×D59C2212yes—
23C2×C22⋊C4×D59—22no—
24C2×#14273661C2211yescharacteristic, complemented
25C2×#14273660C2212yescomplemented
26#107×D59—24no—
27C2×#14273659C2211yescharacteristic, complemented
28C2×#14273658C2212yescomplemented
29#106×D59—24no—
30#16837262C2212yes—
31#16837261—22no—
32#16837260—22no—
33#16837259C2212yes—
34#16837259C2212yes—
35#95×D59—22no—
36#16837165C2212yescomplemented
37#16837164C2212yescomplemented
38#16837164C2212yescomplemented
39C22×M16×C59C2211yescharacteristic
40C2×#107×C59C2211yescharacteristic, complemented
41C2×#106×C59C2211yescharacteristic, complemented
42C59×#380C2212yes—
43C59×#340C2212yescomplemented
44C24×D59D411yescharacteristic
45C23×Dic59D411yescharacteristic
46C22×C4×D59—22no—
47C22×C4×D59—22no—
48C22×C4×D59—22no—
49C22×C4×D59—22no—
50C22×C4×D59—22no—
51C22×C4×D59—22no—
52C22×C4×D59C2×C414yes—
53C22×C4×D59D411yescharacteristic
54C22×C4×D59D411yescharacteristic
55C22×C4×D59Q814yes—
56C22×C4×D59C2311yescharacteristic
57C22×C4×D59C2311yescharacteristic
58C2×#11745664—22no—
59C2×#11745664—22no—
60C2×#11745664C2×C414yescomplemented
61C2×#11745659—22no—
62C2×#11745659—22no—
63C2×#11745659—22no—
64C2×#11745659—22no—
65C2×#11745659C2×C414yescomplemented
66C2×#11745659C2×C414yescomplemented
67M16×D59—232no—
68C22×C59⋊C8C2311yescharacteristic
69C22×C59⋊C8C2311yescharacteristic
70C2×C8×D59—22no—
71C2×C8×D59—22no—
72C2×C8×D59C2×C414yes—
73C2×C8×D59C2×C414yes—
74C2×C8×D59D414yes—
75C2×C8×D59D414yes—
76C2×C4⋊Dic59C2312yes—
77C2×C4⋊Dic59C2312yes—
78C2×Dic59⋊C4—22no—
79C2×Dic59⋊C4—22no—
80C4⋊C4×D59—24no—
81C4⋊C4×D59—24no—
82C4⋊C4×D59—24no—
83C4⋊C4×D59—24no—
84C2×C22⋊Dic59—22no—
85C2×(C2×D59)⋊C4—22no—
86C2×(C2×D59)⋊C4—22no—
87C22⋊C4×D59—48no—
88#14273661—22no—
89#14273660—24no—
90#14273659—22no—
91#14273658—24no—
92C59⋊#95—22no—
93C59⋊#95—22no—
94C59⋊#95—22no—
95C23×C4×C59C2311yescharacteristic
96C2×M16×C59—22no—
97C2×M16×C59—22no—
98C2×M16×C59C2×C414yescomplemented
99C22×C8×C59C2311yescharacteristic
100C22×C8×C59C2311yescharacteristic
101C2×C4⋊C4×C59C2312yes—
102C2×C4⋊C4×C59C2312yes—
103C2×C22⋊C4×C59—22no—
104#107×C59—22no—
105#106×C59—22no—
106#95×C59—22no—
107C24×C59C2×D411yescharacteristic
108C23×D59—22no—
109C23×D59—22no—
110C23×D59—24no—
111C23×D59—24no—
112C23×D59C4⋊C414yes—
113C23×D59C2×D411yescharacteristic
114C23×D59C2×D411yescharacteristic
115C22×C4×C59—21no—
116C22×C4×C59—21no—
117C22×C4×C59—21no—
118C22×C4×C59—21no—
119C22×C4×C59—22no—
120C22×C4×C59—22no—
121C22×C4×C59C22×C412yes—
122C22×C4×C59C2×D411yescharacteristic
123C22×C4×C59C2×Q812yes—
124C22×C4×C59C2411yescharacteristic
125C22×Dic59—22no—
126C22×Dic59—22no—
127C22×Dic59—22no—
128C22×Dic59—22no—
129C22×Dic59C4⋊C414yes—
130C22×Dic59C2×D411yescharacteristic
131C22×Dic59C2×D411yescharacteristic
132C2×C4×D59—22no—
133C2×C4×D59—22no—
134C2×C4×D59—21no—
135C2×C4×D59—21no—
136C2×C4×D59—21no—
137C2×C4×D59—21no—
138C2×C4×D59—22no—
139C2×C4×D59—22no—
140C2×C4×D59—28no—
141C2×C4×D59—28no—
142C2×C4×D59—28no—
143C2×C4×D59—28no—
144C2×C4×D59—44no—
145C2×C4×D59—44no—
146C2×C4×D59—44no—
147C2×C4×D59—44no—
148C2×C4×D59—44no—
149C2×C4×D59—44no—
150C2×C4×D59C4⋊C414yes—
151C2×C4×D59C4⋊C414yes—
152C2×C4×D59C22×C412yes—
153C2×C4×D59C22×C412yes—
154C2×C4×D59C2×D412yes—
155C2×C4×D59C2×D412yes—
156C2×C4×D59C2×Q812yes—
157C2×C4×D59C2×Q812yes—
158C2×C4×D59#4112yes—
159C2×C4×D59#4112yes—
160M16×C59—28no—
161C2×C8×C59—21no—
162C2×C8×C59—21no—
163C2×C8×C59C22×C412yes—
164C2×C8×C59C22×C412yes—
165C2×C8×C59C2×D412yes—
166C2×C8×C59C2×D412yes—
167C4⋊C4×C59—22no—
168C4⋊C4×C59—22no—
169C4⋊C4×C59—22no—
170C4⋊C4×C59—22no—
171C22⋊C4×C59—44no—
172C22⋊Dic59—44no—
173(C2×D59)⋊C4—44no—
174(C2×D59)⋊C4—44no—
175C4⋊Dic59—22no—
176C4⋊Dic59—22no—
177C4⋊Dic59—22no—
178C4⋊Dic59—22no—
179Dic59⋊C4—44no—
180Dic59⋊C4—44no—
181#11745664—28no—
182C2×C59⋊C8—21no—
183C2×C59⋊C8—21no—
184C2×C59⋊C8C22×C412yes—
185C2×C59⋊C8C22×C412yes—
186C2×C59⋊C8C2×D412yes—
187C2×C59⋊C8C2×D412yes—
188#11745659—28no—
189#11745659—28no—
190C8×D59—28no—
191C8×D59C22⋊C4116yescomplemented
192C23×C59—21no—
193C23×C59—21no—
194C23×C59—22no—
195C23×C59—22no—
196C23×C59C2×C4⋊C412yes—
197C23×C59C22×D411yescharacteristic
198C22×D59—21no—
199C22×D59—21no—
200C22×D59—22no—
201C22×D59—22no—
202C22×D59—28no—
203C22×D59—216no—
204C22×D59—48no—
205C22×D59—44no—
206C22×D59—44no—
207C22×D59C2×C4⋊C412yes—
208C22×D59C2×C4⋊C412yes—
209C22×D59#12112yes—
210C22×D59#12112yes—
211C22×D59AGL(1,ℤ/8)14yes—
212C22×D59#13714yes—
213C2×C4×C59—21no—
214C2×C4×C59—21no—
215C2×C4×C59—22no—
216C2×C4×C59—22no—
217C2×C4×C59—22no—
218C2×C4×C59—22no—
219C2×C4×C59—42no—
220C2×C4×C59—42no—
221C2×C4×C59—42no—
222C2×C4×C59—42no—
223C2×C4×C59—42no—
224C2×C4×C59—42no—
225C2×C4×C59C2×C4⋊C412yes—
226C2×C4×C59C23×C411yescharacteristic
227C2×C4×C59C22×D411yescharacteristic
228C2×C4×C59C22×D411yescharacteristic
229C2×C4×C59C22×Q811yescharacteristic
230C2×C4×C59C2×#4111yescharacteristic
231C2×C4×C59C2×#4111yescharacteristic
232C2×Dic59—21no—
233C2×Dic59—21no—
234C2×Dic59—28no—
235C2×Dic59—42no—
236C2×Dic59—42no—
237C2×Dic59—42no—
238C2×Dic59—42no—
239C2×Dic59—42no—
240C2×Dic59—42no—
241C2×Dic59C2×C4⋊C412yes—
242C2×Dic59C2×C4⋊C412yes—
243C2×Dic59#12112yes—
244C2×Dic59#12112yes—
245C4×D59—28no—
246C4×D59—22no—
247C4×D59—22no—
248C4×D59—22no—
249C4×D59—22no—
250C4×D59—28no—
251C4×D59—88no—
252C4×D59—88no—
253C4×D59C2×C22⋊C414yes—
254C4×D59#11714yes—
255C4×D59C22⋊Q814yes—
256C4×D59C22⋊Q814yes—
257C8×C59—22no—
258C8×C59C2×C22⋊C414yescomplemented
259C59⋊C8—22no—
260C59⋊C8C2×C22⋊C414yescomplemented
261C2×#1809—591nomaximal, Sylow
262C22×C59—24no—
263C22×C59—22no—
264C22×C59—42no—
265C22×C59—41no—
266C22×C59—41no—
267C22×C59C22×C4⋊C411yescharacteristic
268C22×C59C2×#12111yescharacteristic
269C22×C59C2×#12111yescharacteristic
270C22×C59C2×AGL(1,ℤ/8)12yes—
271C22×C59C2×#13712yes—
272C2×D59—24no—
273C2×D59—22no—
274C2×D59—42no—
275C2×D59—41no—
276C2×D59—41no—
277C2×D59—416no—
278C2×D59#38014yes—
279C2×D59#42818yes—
280C2×D59#46818yes—
281C2×D59#46914yes—
282C2×D59#47014yes—
283C4×C59—22no—
284C4×C59—82no—
285C4×C59—82no—
286C4×C59C22×C22⋊C411yescharacteristic
287C4×C59C2×#11711yescharacteristic
288C4×C59C2×C22⋊Q811yescharacteristic
289C4×C59C2×C22⋊Q811yescharacteristic
290Dic59—22no—
291Dic59—82no—
292Dic59—82no—
293Dic59#38014yes—
294C23×M16—591no—
295C22×#107—591no—
296C22×#106—591no—
297C2×#380—592no—
298#1809—591no—
299#1809—591no—
300#1809—592no—
301#1809—592no—
302#1809—591no—
303#1809D5911yescharacteristic, direct product factor
304C2×#340—592no—
305C2×C59—42no—
306C2×C59C2×#38011yescharacteristic
307C2×C59C2×#42812yes—
308C2×C59C2×#46812yes—
309C2×C59C2×#46911yescharacteristic
310C2×C59C2×#47011yescharacteristic
311D59—42no—
312D59#180918yesdirect product factor
313C24×C4—591no—
314C22×M16—591no—
315C22×M16—598no—
316C22×M16—591no—
317C22×M16—591no—
318C22×M16—1184no—
319C22×M16—1184no—
320C22×M16C2×D5911yescharacteristic
321C23×C8—591no—
322C23×C8—591no—
323C22×C4⋊C4—592no—
324C22×C4⋊C4—592no—
325C22×C22⋊C4—1182no—
326C2×#107—591no—
327C2×#107—592no—
328C2×#107—1184no—
329C2×#107C2×D5911yescharacteristic, complemented
330C2×#106—591no—
331C2×#106—592no—
332C2×#106—1184no—
333C2×#106C2×D5911yescharacteristic, complemented
334#380—592no—
335#380—592no—
336#380—592no—
337#380—1182no—
338#380—1182no—
339#380C2×D5912yes—
340C2×#95—1182no—
341#340—592no—
342#340—592no—
343#340—592no—
344#340C2×D5912yescomplemented
345C59C2×#180911yescharacteristic, complemented, Sylow
346C25—591no—
347C23×C4—591no—
348C23×C4—591no—
349C23×C4—594no—
350C23×C4—591no—
351C23×C4—591no—
352C23×C4—594no—
353C23×C4—591no—
354C23×C4—1182no—
355C23×C4—1182no—
356C23×C4—1182no—
357C23×C4—1182no—
358C23×C4—1182no—
359C23×C4—1182no—
360C23×C4C22×D5911yescharacteristic
361C2×M16—22no—
362C2×M16—22no—
363C2×M16—594no—
364C2×M16—594no—
365C2×M16—594no—
366C2×M16—1182no—
367C2×M16—1182no—
368C2×M16—11832no—
369C2×M16—1182no—
370C2×M16—1182no—
371C2×M16—1182no—
372C2×M16—1182no—
373C2×M16C4×D5914yescomplemented
374C22×C8—591no—
375C22×C8—594no—
376C22×C8—594no—
377C22×C8—594no—
378C22×C8—591no—
379C22×C8—594no—
380C22×C8—1182no—
381C22×C8—1182no—
382C22×C8C22×D5911yescharacteristic
383C22×C8C22×D5911yescharacteristic
384C2×C4⋊C4—592no—
385C2×C4⋊C4—592no—
386C2×C4⋊C4—1184no—
387C2×C4⋊C4—1184no—
388C2×C4⋊C4—1184no—
389C2×C4⋊C4—1184no—
390C2×C4⋊C4—1182no—
391C2×C4⋊C4—1182no—
392C2×C4⋊C4C22×D5912yes—
393C2×C4⋊C4C22×D5912yes—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—1182no—
396C2×C22⋊C4—1182no—
397C2×C22⋊C4—1182no—
398C2×C22⋊C4—2368no—
399#107—22no—
400#107—1184no—
401#107—1182no—
402#106—22no—
403#106—1184no—
404#106—1182no—
405#95—22no—
406#95—1182no—
407#95—1182no—
408#95—1182no—
409C24—591no—
410C24—594no—
411C24—591no—
412C24—1184no—
413C24—1182no—
414C24—1182no—
415C24—1184no—
416C24D4×D5911yescharacteristic
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—591no—
424C22×C4—592no—
425C22×C4—592no—
426C22×C4—592no—
427C22×C4—592no—
428C22×C4—592no—
429C22×C4—592no—
430C22×C4—594no—
431C22×C4—591no—
432C22×C4—594no—
433C22×C4—594no—
434C22×C4—592no—
435C22×C4—592no—
436C22×C4—1188no—
437C22×C4—1182no—
438C22×C4—1182no—
439C22×C4—1188no—
440C22×C4—1188no—
441C22×C4—1188no—
442C22×C4—1182no—
443C22×C4—1182no—
444C22×C4—1182no—
445C22×C4—1182no—
446C22×C4—1181no—
447C22×C4—1181no—
448C22×C4—1181no—
449C22×C4—1181no—
450C22×C4—1182no—
451C22×C4—1182no—
452C22×C4—2364no—
453C22×C4—2364no—
454C22×C4—2364no—
455C22×C4—2364no—
456C22×C4—2364no—
457C22×C4—2364no—
458C22×C4C2×C4×D5912yes—
459C22×C4D4×D5911yescharacteristic
460C22×C4Q8×D5912yes—
461C22×C4C23×D5911yescharacteristic
462M16—28no—
463M16—1188no—
464M16—1188no—
465M16—1188no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—592no—
469C2×C8—592no—
470C2×C8—592no—
471C2×C8—5916no—
472C2×C8—592no—
473C2×C8—1188no—
474C2×C8—1181no—
475C2×C8—1181no—
476C2×C8C2×C4×D5912yes—
477C2×C8C2×C4×D5912yes—
478C2×C8D4×D5912yes—
479C2×C8D4×D5912yes—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—1182no—
485C4⋊C4—1182no—
486C4⋊C4—1182no—
487C4⋊C4—1182no—
488C4⋊C4—2364no—
489C4⋊C4—2364no—
490C22⋊C4—44no—
491C22⋊C4—2364no—
492C22⋊C4—2364no—
493C22⋊C4—2364no—
494C23—21no—
495C23—21no—
496C23—22no—
497C23—22no—
498C23—592no—
499C23—592no—
500C23—594no—
501C23—594no—
502C23—592no—
503C23—592no—
504C23—1188no—
505C23—11816no—
506C23—1181no—
507C23—1181no—
508C23—1182no—
509C23—1182no—
510C23—2368no—
511C23—2364no—
512C23—2364no—
513C23C4⋊C4×D5912yes—
514C23C2×D4×D5911yescharacteristic
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—592no—
528C2×C4—592no—
529C2×C4—592no—
530C2×C4—594no—
531C2×C4—594no—
532C2×C4—594no—
533C2×C4—594no—
534C2×C4—592no—
535C2×C4—1188no—
536C2×C4—1188no—
537C2×C4—1188no—
538C2×C4—1181no—
539C2×C4—1181no—
540C2×C4—1182no—
541C2×C4—1182no—
542C2×C4—1182no—
543C2×C4—1182no—
544C2×C4—4728no—
545C2×C4—4728no—
546C2×C4—2362no—
547C2×C4—2362no—
548C2×C4—2362no—
549C2×C4—2362no—
550C2×C4—2362no—
551C2×C4—2362no—
552C2×C4C4⋊C4×D5912yes—
553C2×C4C22×C4×D5911yescharacteristic
554C2×C4C2×D4×D5911yescharacteristic
555C2×C4C2×D4×D5911yescharacteristic
556C2×C4C2×Q8×D5911yescharacteristic
557C2×C4#41×D5911yescharacteristic
558C2×C4#41×D5911yescharacteristic
559C8—22no—
560C8—594no—
561C8—1182no—
562C8C22⋊C4×D5914yescomplemented
563C22—22no—
564C22—24no—
565C22—42no—
566C22—41no—
567C22—41no—
568C22—594no—
569C22—598no—
570C22—594no—
571C22—594no—
572C22—598no—
573C22—1182no—
574C22—1184no—
575C22—23616no—
576C22—2362no—
577C22—2361no—
578C22—2361no—
579C22C2×C4⋊C4×D5911yescharacteristic
580C22#121×D5911yescharacteristic
581C22#121×D5911yescharacteristic
582C22AGL(1,ℤ/8)×D5912yes—
583C22#137×D5912yes—
584C4—22no—
585C4—82no—
586C4—82no—
587C4—594no—
588C4—1182no—
589C4—4722no—
590C4—4722no—
591C4C2×C22⋊C4×D5911yescharacteristic
592C4#117×D5911yescharacteristic
593C4C22⋊Q8×D5911yescharacteristic
594C4C22⋊Q8×D5911yescharacteristic
595C2—42no—
596C2—598no—
597C2—2362no—
598C2#380×D5911yescharacteristic
599C2#428×D5912yes—
600C2#468×D5912yes—
601C2#469×D5911yescharacteristic
602C2#470×D5911yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#1809C2
socleC23×C59C22×D4
prime radicalC24×D59D4
cosocleC22×C4×C59C24
hypercenter#1809D59
hypocenterC59C2×#1809
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1809

Complements

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

NH ≅ G/Ntype
2. C2×#107×D59C2semidirect
3. C2×#106×D59C2semidirect
5. #21424130C2semidirect
6. #21424129C2semidirect
7. #21424128C2semidirect
8. #21424127C2semidirect
9. #21424126C2semidirect
10. #340×D59C2semidirect
11. C59×#1809C2semidirect
18. C2×M16×D59C4semidirect
24. C2×#14273661C22semidirect
25. C2×#14273660C22semidirect
27. C2×#14273659C22semidirect
28. C2×#14273658C22semidirect
36. #16837165C22semidirect
37. #16837164C22semidirect
38. #16837164C22semidirect
40. C2×#107×C59C22semidirect
41. C2×#106×C59C22semidirect
43. C59×#340C22semidirect
60. C2×#11745664C2×C4semidirect
65. C2×#11745659C2×C4semidirect
66. C2×#11745659C2×C4semidirect
98. C2×M16×C59C2×C4semidirect
191. C8×D59C22⋊C4semidirect
258. C8×C59C2×C22⋊C4semidirect
260. C59⋊C8C2×C22⋊C4semidirect
303. #1809D59direct (N × H)
312. D59#1809direct (N × H)
329. C2×#107C2×D59semidirect
333. C2×#106C2×D59semidirect
344. #340C2×D59semidirect
345. C59C2×#1809semidirect
373. C2×M16C4×D59semidirect
562. C8C22⋊C4×D59semidirect

Maximal subgroups

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

subgroupindex
C22×M16×D592
C2×#107×D592
C2×#106×D592
#380×D592
#214241302
#214241292
#214241282
#214241272
#214241262
#340×D592
C59×#18092
C2×#180959