Finite Group Databasebeta

← D59×#2085 #28617653

Subgroups — D59×#2085 #28617653

Order 15104.

998 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#107×D59C211yesmaximal, characteristic
2C2×#106×D59C211yesmaximal, characteristic
3#389×D59C211yesmaximal, characteristic
4#382×D59C211yesmaximal, characteristic
5#21425583C211yesmaximal, characteristic, complemented
6#21425582C211yesmaximal, characteristic, complemented
7#21425581C211yesmaximal, characteristic, complemented
8#21425580C211yesmaximal, characteristic, complemented
9#21425579C211yesmaximal, characteristic, complemented
10#21425578C211yesmaximal, characteristic, complemented
11#21425577C211yesmaximal, characteristic, complemented
12#340×D59C211yesmaximal, characteristic
13#340×D59C211yesmaximal, characteristic
14#336×D59C211yesmaximal, characteristic
15C59×#2085C211yesmaximal, characteristic, complemented
16C22×C8×D59C2211yescharacteristic
17C22×C8×D59C2211yescharacteristic
18C2×C4⋊C4×D59—21no—
19C2×C4⋊C4×D59C2211yescharacteristic
20C2×C4⋊C4×D59C2211yescharacteristic
21C2×C4⋊C4×D59C2211yescharacteristic
22C2×C4⋊C4×D59C2211yescharacteristic
23C2×C42×D59C2211yescharacteristic
24C2×#14273661C2211yescharacteristic
25C2×#14273660C2211yescharacteristic
26C2×#14273660C2211yescharacteristic
27#107×D59—24no—
28C2×#14273659C2211yescharacteristic
29C2×#14273658C2211yescharacteristic
30C2×#14273658C2211yescharacteristic
31#106×D59—24no—
32#16837301C2211yescharacteristic
33#16837300C2211yescharacteristic
34#16837299—21no—
35#16837298C2211yescharacteristic
36#16837297—21no—
37#16837268C2211yescharacteristic
38#16837267C2211yescharacteristic
39#16837267C2211yescharacteristic
40#16837266—21no—
41#16837266—21no—
42#95×D59—21no—
43#95×D59—21no—
44#95×D59—21no—
45#16837165C2211yescharacteristic
46#16837165C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837164C2211yescharacteristic
50#16837164C2211yescharacteristic
51#16837157C2211yescharacteristic
52#16837156C2211yescharacteristic
53#16837156C2211yescharacteristic
54C2×#107×C59C2211yescharacteristic
55C2×#106×C59C2211yescharacteristic
56C59×#389C2211yescharacteristic
57C59×#382C2211yescharacteristic
58C59×#340C2211yescharacteristic
59C59×#340C2211yescharacteristic
60C59×#336C2211yescharacteristic
61C22×C4×D59—21no—
62C22×C4×D59—21no—
63C22×C4×D59—21no—
64C22×C4×D59—21no—
65C22×C4×D59D411yescharacteristic
66C22×C4×D59D411yescharacteristic
67C22×C4×D59C2311yescharacteristic
68C22×C59⋊C8C2311yescharacteristic
69C22×C59⋊C8C2311yescharacteristic
70C2×C8×D59—22no—
71C2×C8×D59—22no—
72C2×C8×D59—22no—
73C2×C8×D59—22no—
74C2×C8×D59Q814yes—
75C2×C8×D59Q814yes—
76C2×C4⋊Dic59—21no—
77C2×C4⋊Dic59C2311yescharacteristic
78C2×C4⋊Dic59C2311yescharacteristic
79C2×C4⋊Dic59C2311yescharacteristic
80C2×C4⋊Dic59C2311yescharacteristic
81C2×Dic59⋊C4—21no—
82C2×Dic59⋊C4—21no—
83C2×Dic59⋊C4—21no—
84C2×Dic59⋊C4—21no—
85C2×Dic59⋊C4—21no—
86C2×Dic59⋊C4—21no—
87C4⋊C4×D59—22no—
88C4⋊C4×D59—22no—
89C4⋊C4×D59—22no—
90C4⋊C4×D59—22no—
91C4⋊C4×D59—22no—
92C4⋊C4×D59—22no—
93C4⋊C4×D59—22no—
94C4⋊C4×D59—44no—
95C4⋊C4×D59D414yes—
96C2×C4×Dic59D411yescharacteristic
97C2×C4×Dic59D411yescharacteristic
98C2×C4×Dic59C2311yescharacteristic
99C42×D59—22no—
100C42×D59—22no—
101#14273661—22no—
102#14273660—22no—
103#14273660—22no—
104#14273659—22no—
105#14273658—22no—
106#14273658—22no—
107C59⋊#95—21no—
108C59⋊#95—21no—
109C59⋊#95—21no—
110C59⋊#95—21no—
111C59⋊#95—21no—
112C59⋊#95—21no—
113C59⋊#95—21no—
114C59⋊#95—21no—
115C59⋊#95—21no—
116C22×C8×C59C2311yescharacteristic
117C22×C8×C59C2311yescharacteristic
118C2×C4⋊C4×C59—21no—
119C2×C4⋊C4×C59C2311yescharacteristic
120C2×C4⋊C4×C59C2311yescharacteristic
121C2×C4⋊C4×C59C2311yescharacteristic
122C2×C4⋊C4×C59C2311yescharacteristic
123C2×C42×C59C2311yescharacteristic
124#107×C59—22no—
125#106×C59—22no—
126#95×C59—21no—
127#95×C59—21no—
128#95×C59—21no—
129C23×D59C2×D411yescharacteristic
130C22×C4×C59—21no—
131C22×C4×C59—21no—
132C22×C4×C59—21no—
133C22×C4×C59—21no—
134C22×C4×C59C2×D411yescharacteristic
135C22×C4×C59C2×D411yescharacteristic
136C22×C4×C59C2411yescharacteristic
137C22×Dic59—21no—
138C22×Dic59—21no—
139C22×Dic59—21no—
140C22×Dic59—21no—
141C22×Dic59C2×D411yescharacteristic
142C22×Dic59C2×D411yescharacteristic
143C22×Dic59C2×D411yescharacteristic
144C2×C4×D59—24no—
145C2×C4×D59—22no—
146C2×C4×D59—22no—
147C2×C4×D59—22no—
148C2×C4×D59—22no—
149C2×C4×D59—22no—
150C2×C4×D59—22no—
151C2×C4×D59—42no—
152C2×C4×D59—42no—
153C2×C4×D59—42no—
154C2×C4×D59—42no—
155C2×C4×D59—42no—
156C2×C4×D59—42no—
157C2×C4×D59—42no—
158C2×C4×D59—42no—
159C2×C4×D59—42no—
160C2×C4×D59—42no—
161C2×C4×D59—42no—
162C2×C4×D59C2×D412yes—
163C2×C4×D59C2×Q812yes—
164C2×C4×D59C2×Q812yes—
165C2×C4×D59#4112yes—
166C2×C4×D59#4112yes—
167C2×C4×D59#4112yes—
168C2×C8×C59—21no—
169C2×C8×C59—21no—
170C2×C8×C59—21no—
171C2×C8×C59—21no—
172C2×C8×C59C2×Q812yes—
173C2×C8×C59C2×Q812yes—
174C4⋊C4×C59—21no—
175C4⋊C4×C59—21no—
176C4⋊C4×C59—21no—
177C4⋊C4×C59—21no—
178C4⋊C4×C59—21no—
179C4⋊C4×C59—21no—
180C4⋊C4×C59—21no—
181C4⋊C4×C59—42no—
182C4⋊C4×C59C2×D412yes—
183C42×C59—21no—
184C42×C59—21no—
185C4⋊Dic59—21no—
186C4⋊Dic59—21no—
187C4⋊Dic59—21no—
188C4⋊Dic59—21no—
189C4⋊Dic59—21no—
190C4⋊Dic59—21no—
191C4⋊Dic59—21no—
192C4⋊Dic59—42no—
193C4⋊Dic59C2×D412yes—
194Dic59⋊C4—24no—
195Dic59⋊C4—42no—
196Dic59⋊C4—42no—
197Dic59⋊C4—42no—
198Dic59⋊C4—42no—
199Dic59⋊C4—42no—
200C4×Dic59—21no—
201C4×Dic59—21no—
202C4×Dic59—22no—
203C4×Dic59—22no—
204C2×C59⋊C8—21no—
205C2×C59⋊C8—21no—
206C2×C59⋊C8—21no—
207C2×C59⋊C8—21no—
208C2×C59⋊C8C2×Q812yes—
209C2×C59⋊C8C2×Q812yes—
210C8×D59—28no—
211C8×D59—28no—
212C23×C59C22×D411yescharacteristic
213C22×D59#12112yes—
214C22×D59#12312yes—
215C22×D59C4⋊Q812yes—
216C22×D59#13512yes—
217C22×D59#13512yes—
218C22×D59AGL(1,ℤ/8)12yes—
219C22×D59#13712yes—
220C2×C4×C59—22no—
221C2×C4×C59—21no—
222C2×C4×C59—21no—
223C2×C4×C59—21no—
224C2×C4×C59—21no—
225C2×C4×C59—21no—
226C2×C4×C59—21no—
227C2×C4×C59—41no—
228C2×C4×C59—41no—
229C2×C4×C59—41no—
230C2×C4×C59—41no—
231C2×C4×C59—41no—
232C2×C4×C59—41no—
233C2×C4×C59—41no—
234C2×C4×C59—41no—
235C2×C4×C59—41no—
236C2×C4×C59—41no—
237C2×C4×C59—41no—
238C2×C4×C59C22×D411yescharacteristic
239C2×C4×C59C22×Q811yescharacteristic
240C2×C4×C59C22×Q811yescharacteristic
241C2×C4×C59C2×#4111yescharacteristic
242C2×C4×C59C2×#4111yescharacteristic
243C2×C4×C59C2×#4111yescharacteristic
244C2×Dic59—22no—
245C2×Dic59—21no—
246C2×Dic59—21no—
247C2×Dic59—21no—
248C2×Dic59—21no—
249C2×Dic59—21no—
250C2×Dic59—21no—
251C2×Dic59—41no—
252C2×Dic59—41no—
253C2×Dic59—41no—
254C2×Dic59—41no—
255C2×Dic59—41no—
256C2×Dic59—41no—
257C2×Dic59—41no—
258C2×Dic59—41no—
259C2×Dic59—41no—
260C2×Dic59—41no—
261C2×Dic59—41no—
262C2×Dic59#12112yes—
263C2×Dic59#12312yes—
264C2×Dic59C4⋊Q812yes—
265C4×D59—48no—
266C4×D59—44no—
267C4×D59—44no—
268C4×D59—84no—
269C4×D59—84no—
270C4×D59—84no—
271C4×D59C22⋊Q814yes—
272C4×D59C22⋊Q814yes—
273C4×D59#12514yes—
274C4×D59#12514yes—
275C8×C59—22no—
276C8×C59—22no—
277C59⋊C8—22no—
278C59⋊C8—22no—
279C2×#2085—591nomaximal, Sylow
280C22×C59C2×#12111yescharacteristic
281C22×C59C2×#12311yescharacteristic
282C22×C59C2×C4⋊Q811yescharacteristic
283C22×C59C2×#13511yescharacteristic
284C22×C59C2×#13511yescharacteristic
285C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
286C22×C59C2×#13711yescharacteristic
287C2×D59#39814yes—
288C2×D59#46314yes—
289C2×D59#46414yes—
290C2×D59#48214yes—
291C2×D59#48514yes—
292C2×D59#49914yes—
293C2×D59#50114yes—
294C4×C59—41no—
295C4×C59—41no—
296C4×C59—42no—
297C4×C59—81no—
298C4×C59—81no—
299C4×C59—81no—
300C4×C59C2×C22⋊Q811yescharacteristic
301C4×C59C2×C22⋊Q811yescharacteristic
302C4×C59C2×#12511yescharacteristic
303C4×C59C2×#12511yescharacteristic
304Dic59—41no—
305Dic59—41no—
306Dic59—42no—
307Dic59—81no—
308Dic59—81no—
309Dic59—81no—
310Dic59#39814yes—
311C22×#107—591no—
312C22×#106—591no—
313C2×#389—591no—
314C2×#382—591no—
315#2085—591no—
316#2085—591no—
317#2085—591no—
318#2085—591no—
319#2085—591no—
320#2085—591no—
321#2085—591no—
322#2085D5911yescharacteristic, direct product factor
323C2×#340—591no—
324C2×#340—591no—
325C2×#336—591no—
326C2×C59C2×#39811yescharacteristic
327C2×C59C2×#46311yescharacteristic
328C2×C59C2×#46411yescharacteristic
329C2×C59C2×#48211yescharacteristic
330C2×C59C2×#48511yescharacteristic
331C2×C59C2×#49911yescharacteristic
332C2×C59C2×#50111yescharacteristic
333D59#208518yesdirect product factor
334C23×C8—591no—
335C23×C8—591no—
336C22×C4⋊C4—591no—
337C22×C4⋊C4—591no—
338C22×C4⋊C4—591no—
339C22×C4⋊C4—591no—
340C22×C4⋊C4—1181no—
341C22×C42—591no—
342C2×#107—591no—
343C2×#107—591no—
344C2×#107—591no—
345C2×#107—1184no—
346C2×#107C2×D5911yescharacteristic
347C2×#106—591no—
348C2×#106—591no—
349C2×#106—591no—
350C2×#106—1184no—
351C2×#106C2×D5911yescharacteristic
352#389—591no—
353#389—591no—
354#389—591no—
355#389—1181no—
356#389—1181no—
357#389C2×D5911yescharacteristic
358#382—591no—
359#382—591no—
360#382—591no—
361#382—1181no—
362#382—1181no—
363#382C2×D5911yescharacteristic
364C2×#95—1181no—
365C2×#95—1181no—
366C2×#95—1181no—
367#340—591no—
368#340—591no—
369#340—591no—
370#340—591no—
371#340—591no—
372#340—591no—
373#340C2×D5911yescharacteristic
374#340C2×D5911yescharacteristic
375#336—591no—
376#336—591no—
377#336—591no—
378#336C2×D5911yescharacteristic
379C59C2×#208511yescharacteristic, complemented, Sylow
380C23×C4—591no—
381C23×C4—591no—
382C23×C4—591no—
383C23×C4—1181no—
384C23×C4—1181no—
385C23×C4—1181no—
386C23×C4—1181no—
387C22×C8—591no—
388C22×C8—591no—
389C22×C8—594no—
390C22×C8—594no—
391C22×C8—1182no—
392C22×C8—1182no—
393C22×C8—1182no—
394C22×C8—1182no—
395C22×C8C22×D5911yescharacteristic
396C22×C8C22×D5911yescharacteristic
397C2×C4⋊C4—21no—
398C2×C4⋊C4—591no—
399C2×C4⋊C4—594no—
400C2×C4⋊C4—591no—
401C2×C4⋊C4—591no—
402C2×C4⋊C4—591no—
403C2×C4⋊C4—1182no—
404C2×C4⋊C4—1182no—
405C2×C4⋊C4—1182no—
406C2×C4⋊C4—1182no—
407C2×C4⋊C4—1182no—
408C2×C4⋊C4—1182no—
409C2×C4⋊C4—1182no—
410C2×C4⋊C4—1181no—
411C2×C4⋊C4—1181no—
412C2×C4⋊C4—1181no—
413C2×C4⋊C4—1181no—
414C2×C4⋊C4—1181no—
415C2×C4⋊C4—1181no—
416C2×C4⋊C4—1181no—
417C2×C4⋊C4—2364no—
418C2×C4⋊C4C22×D5911yescharacteristic
419C2×C4⋊C4C22×D5911yescharacteristic
420C2×C4⋊C4C22×D5911yescharacteristic
421C2×C4⋊C4C22×D5911yescharacteristic
422C2×C42—591no—
423C2×C42—591no—
424C2×C42—591no—
425C2×C42—1182no—
426C2×C42—1182no—
427C2×C42C22×D5911yescharacteristic
428#107—22no—
429#107—1182no—
430#107—1182no—
431#107—1182no—
432#106—22no—
433#106—1182no—
434#106—1182no—
435#106—1182no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—1181no—
440#95—1181no—
441#95—1181no—
442#95—1181no—
443#95—1181no—
444#95—1181no—
445#95—1181no—
446#95—1181no—
447#95—1181no—
448C24—591no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—591no—
454C22×C4—592no—
455C22×C4—592no—
456C22×C4—592no—
457C22×C4—592no—
458C22×C4—592no—
459C22×C4—592no—
460C22×C4—591no—
461C22×C4—591no—
462C22×C4—1182no—
463C22×C4—1182no—
464C22×C4—1184no—
465C22×C4—1182no—
466C22×C4—1182no—
467C22×C4—1182no—
468C22×C4—1182no—
469C22×C4—1181no—
470C22×C4—1181no—
471C22×C4—1181no—
472C22×C4—1181no—
473C22×C4—2362no—
474C22×C4—2362no—
475C22×C4—2362no—
476C22×C4—2362no—
477C22×C4—2362no—
478C22×C4—2362no—
479C22×C4—2362no—
480C22×C4—2362no—
481C22×C4—2362no—
482C22×C4—2362no—
483C22×C4—2362no—
484C22×C4D4×D5911yescharacteristic
485C22×C4D4×D5911yescharacteristic
486C22×C4C23×D5911yescharacteristic
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—592no—
492C2×C8—592no—
493C2×C8—1188no—
494C2×C8—1188no—
495C2×C8—1181no—
496C2×C8—1181no—
497C2×C8—1181no—
498C2×C8—1181no—
499C2×C8Q8×D5912yes—
500C2×C8Q8×D5912yes—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—42no—
509C4⋊C4—592no—
510C4⋊C4—1184no—
511C4⋊C4—1181no—
512C4⋊C4—1181no—
513C4⋊C4—1181no—
514C4⋊C4—1181no—
515C4⋊C4—1181no—
516C4⋊C4—1181no—
517C4⋊C4—1181no—
518C4⋊C4—2362no—
519C4⋊C4—2362no—
520C4⋊C4—2362no—
521C4⋊C4—2362no—
522C4⋊C4—2362no—
523C4⋊C4—2362no—
524C4⋊C4D4×D5912yes—
525C42—21no—
526C42—21no—
527C42—1182no—
528C42—1182no—
529C42—1181no—
530C42—1181no—
531C23—592no—
532C23—592no—
533C23—592no—
534C23—592no—
535C23—592no—
536C23—592no—
537C23—592no—
538C23C2×D4×D5911yescharacteristic
539C2×C4—22no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—592no—
558C2×C4—592no—
559C2×C4—592no—
560C2×C4—594no—
561C2×C4—594no—
562C2×C4—594no—
563C2×C4—594no—
564C2×C4—1182no—
565C2×C4—1181no—
566C2×C4—1181no—
567C2×C4—1181no—
568C2×C4—1181no—
569C2×C4—1181no—
570C2×C4—1181no—
571C2×C4—4724no—
572C2×C4—4724no—
573C2×C4—4724no—
574C2×C4—2364no—
575C2×C4—2364no—
576C2×C4—2368no—
577C2×C4—2361no—
578C2×C4—2361no—
579C2×C4—2361no—
580C2×C4—2361no—
581C2×C4—2361no—
582C2×C4—2361no—
583C2×C4—2361no—
584C2×C4—2361no—
585C2×C4—2361no—
586C2×C4—2361no—
587C2×C4—2361no—
588C2×C4C2×D4×D5911yescharacteristic
589C2×C4C2×Q8×D5911yescharacteristic
590C2×C4C2×Q8×D5911yescharacteristic
591C2×C4#41×D5911yescharacteristic
592C2×C4#41×D5911yescharacteristic
593C2×C4#41×D5911yescharacteristic
594C8—22no—
595C8—22no—
596C8—1182no—
597C8—1182no—
598C22—594no—
599C22—594no—
600C22—594no—
601C22—594no—
602C22—594no—
603C22—594no—
604C22—594no—
605C22#121×D5911yescharacteristic
606C22#123×D5911yescharacteristic
607C22C4⋊Q8×D5911yescharacteristic
608C22#135×D5911yescharacteristic
609C22#135×D5911yescharacteristic
610C22AGL(1,ℤ/8)×D5911yescharacteristic
611C22#137×D5911yescharacteristic
612C4—41no—
613C4—41no—
614C4—42no—
615C4—81no—
616C4—81no—
617C4—81no—
618C4—594no—
619C4—4721no—
620C4—4721no—
621C4—4721no—
622C4—2361no—
623C4—2361no—
624C4—2362no—
625C4C22⋊Q8×D5911yescharacteristic
626C4C22⋊Q8×D5911yescharacteristic
627C4#125×D5911yescharacteristic
628C4#125×D5911yescharacteristic
629C2—598no—
630C2#398×D5911yescharacteristic
631C2#463×D5911yescharacteristic
632C2#464×D5911yescharacteristic
633C2#482×D5911yescharacteristic
634C2#485×D5911yescharacteristic
635C2#499×D5911yescharacteristic
636C2#501×D5911yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC59×#2085C2
socleC23×C59C22×D4
prime radicalC23×D59C2×D4
hypercenter#2085D59
hypocenterC59C2×#2085
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2085

Complements

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

NH ≅ G/Ntype
5. #21425583C2semidirect
6. #21425582C2semidirect
7. #21425581C2semidirect
8. #21425580C2semidirect
9. #21425579C2semidirect
10. #21425578C2semidirect
11. #21425577C2semidirect
15. C59×#2085C2semidirect
322. #2085D59direct (N × H)
333. D59#2085direct (N × H)
379. C59C2×#2085semidirect

Maximal subgroups

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

subgroupindex
C2×#107×D592
C2×#106×D592
#389×D592
#382×D592
#214255832
#214255822
#214255812
#214255802
#214255792
#214255782
#214255772
#340×D592
#336×D592
C59×#20852
C2×#208559