Finite Group Databasebeta

← #28735625

Subgroups — #28735625

Order 15104.

1062 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21432383C211yesmaximal, characteristic, complemented
2#21425533C211yesmaximal, characteristic, complemented
3#21425527C211yesmaximal, characteristic, complemented
4#21425522C211yesmaximal, characteristic, complemented
5#21425299C211yesmaximal, characteristic, complemented
6#21425299C211yesmaximal, characteristic, complemented
7#21425292C211yesmaximal, characteristic, complemented
8#21425282C211yesmaximal, characteristic, complemented
9#21425275C211yesmaximal, characteristic, complemented
10#21425275C211yesmaximal, characteristic, complemented
11#21425099C211yesmaximal, characteristic, complemented
12#21425099C211yesmaximal, characteristic, complemented
13#21425099C211yesmaximal, characteristic, complemented
14#21424006C211yesmaximal, characteristic, complemented
15C59×#2847C211yesmaximal, characteristic
16C22×#11745670C2211yescharacteristic, complemented
17C2×#14273706C2211yescharacteristic
18C2×#14273706C2211yescharacteristic
19C2×#14273706C2211yescharacteristic
20C2×#14273660C2211yescharacteristic, complemented
21C2×#14273660C2211yescharacteristic, complemented
22C2×#14273658C2211yescharacteristic, complemented
23C2×#14273650C2211yescharacteristic, complemented
24C2×#14273650C2211yescharacteristic, complemented
25C2×#14273650C2211yescharacteristic, complemented
26C2×#14273648C2211yescharacteristic, complemented
27C2×#14273648C2211yescharacteristic, complemented
28C2×#14273648C2211yescharacteristic, complemented
29C2×C22⋊(C59⋊C8)C2211yescharacteristic
30C2×C22⋊(C59⋊C8)C2211yescharacteristic
31C2×C22⋊(C59⋊C8)C2211yescharacteristic
32C2×C22⋊(C59⋊C8)C2211yescharacteristic
33C2×C22⋊(C59⋊C8)C2211yescharacteristic
34C2×C22⋊(C59⋊C8)C2211yescharacteristic
35#16837275—21no—
36#16837275—21no—
37#16837275—21no—
38#16837262C2211yescharacteristic
39#16837262C2211yescharacteristic
40#16837262C2211yescharacteristic
41#16837258—21no—
42#16837164C2211yescharacteristic, complemented
43#16837164C2211yescharacteristic, complemented
44#16837164C2211yescharacteristic, complemented
45#16837164C2211yescharacteristic, complemented
46#16837164C2211yescharacteristic, complemented
47#16837164C2211yescharacteristic, complemented
48C24×C4×C59C2211yescharacteristic
49C2×#121×C59C2211yescharacteristic
50C2×#121×C59C2211yescharacteristic
51C2×#121×C59C2211yescharacteristic
52C2×#120×C59—21no—
53C59×#386—21no—
54C59×#386—21no—
55C59×#386—21no—
56C59×#380C2211yescharacteristic
57C59×#380C2211yescharacteristic
58C59×#380C2211yescharacteristic
59C22×Dic118C2311yescharacteristic
60C2×#11745670—41no—
61C2×#11745670—41no—
62C2×#11745670—41no—
63C22×C59⋊C8C2311yescharacteristic
64C22×C59⋊C8C2311yescharacteristic
65C22×C59⋊C8C2311yescharacteristic
66C22×C59⋊C8C2311yescharacteristic
67#14273706—41no—
68#14273706—41no—
69#14273706—41no—
70#14273706—41no—
71#14273706—41no—
72#14273706—41no—
73C2×C4⋊Dic59C2311yescharacteristic
74C2×C4⋊Dic59C2311yescharacteristic
75C2×C4⋊Dic59C2311yescharacteristic
76C2×Dic59⋊C4—21no—
77C2×Dic59⋊C4—21no—
78C2×Dic59⋊C4—21no—
79C2×C22⋊Dic59—21no—
80C2×C22⋊Dic59—21no—
81C2×C22⋊Dic59—21no—
82C2×C22⋊Dic59—21no—
83C2×C22⋊Dic59—21no—
84C2×C22⋊Dic59—21no—
85#14273660—41no—
86#14273660—41no—
87#14273658—41no—
88#14273650—41no—
89#14273650—41no—
90#14273650—41no—
91#14273648—41no—
92#14273648—41no—
93#14273648—41no—
94C22⋊(C59⋊C8)—41no—
95C22⋊(C59⋊C8)—41no—
96C22⋊(C59⋊C8)—41no—
97C22⋊(C59⋊C8)—41no—
98C22⋊(C59⋊C8)—41no—
99C22⋊(C59⋊C8)—41no—
100C59⋊#95—21no—
101C59⋊#95—21no—
102C59⋊#95—21no—
103C25×C59D411yescharacteristic
104C22×D4×C59—21no—
105C22×D4×C59—21no—
106C22×D4×C59—21no—
107C22×D4×C59C2311yescharacteristic
108C23×C4×C59—41no—
109C23×C4×C59—41no—
110C23×C4×C59—41no—
111C23×C4×C59—41no—
112C23×C4×C59—41no—
113C23×C4×C59—41no—
114C23×C4×C59D411yescharacteristic
115C23×C4×C59D411yescharacteristic
116C23×C4×C59D411yescharacteristic
117C23×C4×C59C2311yescharacteristic
118C23×C4×C59C2311yescharacteristic
119C23×C4×C59C2311yescharacteristic
120#121×C59—41no—
121#121×C59—41no—
122#121×C59—41no—
123#121×C59—41no—
124#121×C59—41no—
125#121×C59—41no—
126#120×C59—44no—
127C2×C4⋊C4×C59C2311yescharacteristic
128C2×C4⋊C4×C59C2311yescharacteristic
129C2×C4⋊C4×C59C2311yescharacteristic
130C2×C22⋊C4×C59—21no—
131C2×C22⋊C4×C59—21no—
132C2×C22⋊C4×C59—21no—
133C2×C22⋊C4×C59—21no—
134C2×C22⋊C4×C59—21no—
135C2×C22⋊C4×C59—21no—
136#95×C59—21no—
137#95×C59—21no—
138#95×C59—21no—
139C24×C59—22no—
140C24×C59—22no—
141C24×C59—22no—
142C24×C59—21no—
143C24×C59—41no—
144C24×C59—41no—
145C24×C59—41no—
146C24×C59—41no—
147C24×C59C2×D411yescharacteristic
148C24×C59C2×D411yescharacteristic
149C24×C59C2×D411yescharacteristic
150C2×D4×C59—21no—
151C2×D4×C59—21no—
152C2×D4×C59—21no—
153C2×D4×C59—21no—
154C2×D4×C59—21no—
155C2×D4×C59—21no—
156C2×D4×C59—42no—
157C2×D4×C59—42no—
158C2×D4×C59—42no—
159C2×D4×C59—42no—
160C2×D4×C59—42no—
161C2×D4×C59—42no—
162C2×D4×C59—42no—
163C2×D4×C59—42no—
164C2×D4×C59—42no—
165C22×C4×C59—21no—
166C22×C4×C59—21no—
167C22×C4×C59—21no—
168C22×C4×C59—21no—
169C22×C4×C59—21no—
170C22×C4×C59—21no—
171C22×C4×C59—21no—
172C22×C4×C59—21no—
173C22×C4×C59—21no—
174C22×C4×C59—21no—
175C22×C4×C59—21no—
176C22×C4×C59—21no—
177C22×C4×C59—21no—
178C22×C4×C59—21no—
179C22×C4×C59—21no—
180C22×C4×C59—21no—
181C22×C4×C59—21no—
182C22×C4×C59—21no—
183C22×C4×C59—21no—
184C22×C4×C59—21no—
185C22×C4×C59—21no—
186C22×C4×C59—41no—
187C22×C4×C59—41no—
188C22×C4×C59—41no—
189C22×C4×C59—41no—
190C22×C4×C59—41no—
191C22×C4×C59—41no—
192C22×C4×C59—41no—
193C22×C4×C59—41no—
194C22×C4×C59—41no—
195C22×C4×C59—44no—
196C22×C4×C59—44no—
197C22×C4×C59—44no—
198C22×C4×C59—44no—
199C22×C4×C59C2×D411yescharacteristic
200C22×C4×C59C2×D411yescharacteristic
201C22×C4×C59C2×D411yescharacteristic
202C22×C4×C59C2411yescharacteristic
203C22×Dic59—21no—
204C22×Dic59—21no—
205C22×Dic59—21no—
206C22×Dic59—21no—
207C2×Dic118—21no—
208C2×Dic118—21no—
209C2×Dic118—21no—
210C2×Dic118—21no—
211C2×Dic118—21no—
212C2×Dic118—21no—
213C4⋊C4×C59—21no—
214C4⋊C4×C59—21no—
215C4⋊C4×C59—21no—
216C4⋊C4×C59—21no—
217C4⋊C4×C59—21no—
218C4⋊C4×C59—21no—
219C22⋊C4×C59—42no—
220C22⋊C4×C59—42no—
221C22⋊C4×C59—42no—
222C22⋊C4×C59—42no—
223C22⋊C4×C59—42no—
224C22⋊C4×C59—42no—
225C22⋊Dic59—42no—
226C22⋊Dic59—42no—
227C22⋊Dic59—42no—
228C22⋊Dic59—42no—
229C22⋊Dic59—42no—
230C22⋊Dic59—42no—
231#11745670—44no—
232C4⋊Dic59—21no—
233C4⋊Dic59—21no—
234C4⋊Dic59—21no—
235C4⋊Dic59—21no—
236C4⋊Dic59—21no—
237C4⋊Dic59—21no—
238Dic59⋊C4—42no—
239Dic59⋊C4—42no—
240Dic59⋊C4—42no—
241C2×C59⋊C8—21no—
242C2×C59⋊C8—21no—
243C2×C59⋊C8—21no—
244C2×C59⋊C8—21no—
245C2×C59⋊C8—21no—
246C2×C59⋊C8—21no—
247C2×C59⋊C8—21no—
248C2×C59⋊C8—21no—
249C2×C59⋊C8—21no—
250C2×C59⋊C8—21no—
251C2×C59⋊C8—21no—
252C2×C59⋊C8—21no—
253C23×C59—21no—
254C23×C59—21no—
255C23×C59—21no—
256C23×C59—21no—
257C23×C59—21no—
258C23×C59—21no—
259C23×C59—21no—
260C23×C59—21no—
261C23×C59—21no—
262C23×C59—21no—
263C23×C59—21no—
264C23×C59—21no—
265C23×C59—21no—
266C23×C59—21no—
267C23×C59—21no—
268C23×C59—21no—
269C23×C59—21no—
270C23×C59—21no—
271C23×C59—44no—
272C23×C59—44no—
273C23×C59—44no—
274C23×C59—44no—
275C23×C59—44no—
276C23×C59—44no—
277C23×C59—44no—
278C23×C59—41no—
279C23×C59—41no—
280C23×C59—41no—
281C23×C59—41no—
282C23×C59—41no—
283C23×C59—41no—
284C23×C59—41no—
285C23×C59#13512yes—
286C23×C59AGL(1,ℤ/8)12yes—
287C23×C59#13712yes—
288C23×C59C22×D411yescharacteristic
289D4×C59—41no—
290D4×C59—41no—
291D4×C59—41no—
292D4×C59—41no—
293D4×C59—84no—
294D4×C59—84no—
295D4×C59—84no—
296C2×C4×C59—21no—
297C2×C4×C59—21no—
298C2×C4×C59—21no—
299C2×C4×C59—21no—
300C2×C4×C59—21no—
301C2×C4×C59—21no—
302C2×C4×C59—21no—
303C2×C4×C59—21no—
304C2×C4×C59—21no—
305C2×C4×C59—44no—
306C2×C4×C59—44no—
307C2×C4×C59—44no—
308C2×C4×C59—41no—
309C2×C4×C59—41no—
310C2×C4×C59—41no—
311C2×C4×C59—41no—
312C2×C4×C59—41no—
313C2×C4×C59—41no—
314C2×C4×C59—41no—
315C2×C4×C59—41no—
316C2×C4×C59—41no—
317C2×C4×C59—41no—
318C2×C4×C59—41no—
319C2×C4×C59—41no—
320C2×C4×C59—41no—
321C2×C4×C59—41no—
322C2×C4×C59—41no—
323C2×C4×C59—41no—
324C2×C4×C59—41no—
325C2×C4×C59—41no—
326C2×C4×C59—41no—
327C2×C4×C59—41no—
328C2×C4×C59—41no—
329C2×C4×C59H(5,𝔽2)11yescharacteristic
330C2×C4×C59H(5,𝔽2)11yescharacteristic
331C2×C4×C59H(5,𝔽2)11yescharacteristic
332C2×C4×C59H(5,𝔽2)11yescharacteristic
333C2×C4×C59H(5,𝔽2)11yescharacteristic
334C2×C4×C59H(5,𝔽2)11yescharacteristic
335C2×Dic59—41no—
336C2×Dic59—41no—
337C2×Dic59—41no—
338C2×Dic59—41no—
339C2×Dic59—41no—
340C2×Dic59—41no—
341C2×Dic59—41no—
342C2×Dic59—41no—
343C2×Dic59—41no—
344C2×Dic59—41no—
345C2×Dic59—41no—
346C2×Dic59—41no—
347Dic118—41no—
348Dic118—41no—
349Dic118—41no—
350Dic118—41no—
351C59⋊C8—41no—
352C59⋊C8—41no—
353C59⋊C8—41no—
354C59⋊C8—41no—
355#32709—591nomaximal, Sylow
356C22×C59—22no—
357C22×C59—22no—
358C22×C59—22no—
359C22×C59—22no—
360C22×C59—22no—
361C22×C59—22no—
362C22×C59—22no—
363C22×C59—22no—
364C22×C59—22no—
365C22×C59—416no—
366C22×C59—41no—
367C22×C59—41no—
368C22×C59—41no—
369C22×C59—41no—
370C22×C59—41no—
371C22×C59—41no—
372C22×C59—41no—
373C22×C59—41no—
374C22×C59—41no—
375C22×C59—41no—
376C22×C59—41no—
377C22×C59—41no—
378C22×C59—81no—
379C22×C59—81no—
380C22×C59—81no—
381C22×C59—81no—
382C22×C59—81no—
383C22×C59—81no—
384C22×C59—81no—
385C22×C59#53411yescharacteristic
386C22×C59#53411yescharacteristic
387C22×C59#53411yescharacteristic
388C22×C59C2×#13511yescharacteristic
389C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
390C22×C59C2×#13711yescharacteristic
391C22×C59#57511yescharacteristic
392C4×C59—41no—
393C4×C59—41no—
394C4×C59—41no—
395C4×C59—81no—
396C4×C59—81no—
397C4×C59—81no—
398C4×C59#56011yescharacteristic
399C4×C59#56011yescharacteristic
400C4×C59#56011yescharacteristic
401C4×C59H(3,𝔽4)11yescharacteristic
402Dic59—81no—
403Dic59—81no—
404Dic59—81no—
405Dic59—81no—
406#2848—591no—
407#2847D5911yescharacteristic
408#2077—591no—
409#2076—591no—
410#2075—591no—
411#2036—591no—
412#2036—591no—
413#2035—591no—
414#2034—591no—
415#2033—591no—
416#2033—591no—
417#2000—591no—
418#2000—591no—
419#2000—591no—
420#1779—591no—
421C2×C59—42no—
422C2×C59—42no—
423C2×C59—42no—
424C2×C59—161no—
425C2×C59#281211yescharacteristic
426C2×C59#318811yescharacteristic
427C2×C59#319011yescharacteristic
428C2×C59#319111yescharacteristic
429C2×C59#319311yescharacteristic
430C2×C59#319411yescharacteristic
431C2×C59#319611yescharacteristic
432C24×C4C2×D5911yescharacteristic
433C22×SD16—591no—
434C2×C22⋊Q8—591no—
435C2×C22⋊Q8—591no—
436C2×C22⋊Q8—591no—
437C2×#121C2×D5911yescharacteristic
438C2×#121C2×D5911yescharacteristic
439C2×#121C2×D5911yescharacteristic
440C2×#120—21no—
441C2×#107—591no—
442C2×#107—591no—
443C2×#106—591no—
444C2×#103—591no—
445C2×#103—591no—
446C2×#103—591no—
447C2×#102—591no—
448C2×#102—591no—
449C2×#102—591no—
450C2×C22⋊C8—591no—
451C2×C22⋊C8—591no—
452C2×C22⋊C8—591no—
453C2×C22⋊C8—591no—
454C2×C22⋊C8—591no—
455C2×C22⋊C8—591no—
456#386—21no—
457#386—21no—
458#386—21no—
459#385—1181no—
460#385—1181no—
461#385—1181no—
462#380—591no—
463#380—591no—
464#380—591no—
465#380C2×D5911yescharacteristic
466#380C2×D5911yescharacteristic
467#380C2×D5911yescharacteristic
468#379—1181no—
469#340—591no—
470#340—591no—
471#340—591no—
472#340—591no—
473#340—591no—
474#340—591no—
475C59#3270911yescharacteristic, complemented, Sylow
476C25C22⋊D5911yescharacteristic
477C22×Q8—591no—
478C22×D4—21no—
479C22×D4—21no—
480C22×D4—21no—
481C22×D4C22×D5911yescharacteristic
482C23×C4—41no—
483C23×C4—41no—
484C23×C4—41no—
485C23×C4—41no—
486C23×C4—41no—
487C23×C4—41no—
488C23×C4C22⋊D5911yescharacteristic
489C23×C4C22⋊D5911yescharacteristic
490C23×C4C22⋊D5911yescharacteristic
491C23×C4C22×D5911yescharacteristic
492C23×C4C22×D5911yescharacteristic
493C23×C4C22×D5911yescharacteristic
494C2×SD16—2361no—
495C2×SD16—2361no—
496C2×SD16—2361no—
497C22×C8—591no—
498C22×C8—591no—
499C22×C8—591no—
500C22×C8—591no—
501C22⋊Q8—2361no—
502C22⋊Q8—2361no—
503C22⋊Q8—2361no—
504C22⋊Q8—2361no—
505C22⋊Q8—2361no—
506C22⋊Q8—2361no—
507#121—41no—
508#121—41no—
509#121—41no—
510#121—41no—
511#121—41no—
512#121—41no—
513#120—44no—
514C2×C4⋊C4—591no—
515C2×C4⋊C4—591no—
516C2×C4⋊C4—591no—
517C2×C4⋊C4—1181no—
518C2×C4⋊C4—1181no—
519C2×C4⋊C4—1181no—
520C2×C4⋊C4C22×D5911yescharacteristic
521C2×C4⋊C4C22×D5911yescharacteristic
522C2×C4⋊C4C22×D5911yescharacteristic
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—1181no—
530C2×C22⋊C4—1181no—
531C2×C22⋊C4—1181no—
532C2×C22⋊C4—1181no—
533C2×C22⋊C4—1181no—
534C2×C22⋊C4—1181no—
535#107—2361no—
536#107—2361no—
537#106—2361no—
538#103—2361no—
539#103—2361no—
540#103—2361no—
541#102—2361no—
542#102—2361no—
543#102—2361no—
544C22⋊C8—2361no—
545C22⋊C8—2361no—
546C22⋊C8—2361no—
547C22⋊C8—2361no—
548C22⋊C8—2361no—
549C22⋊C8—2361no—
550#95—21no—
551#95—21no—
552#95—21no—
553#95—1181no—
554#95—1181no—
555#95—1181no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—21no—
560C24—41no—
561C24—41no—
562C24—41no—
563C24—41no—
564C24C2×C22⋊D5911yescharacteristic
565C24C2×C22⋊D5911yescharacteristic
566C24C2×C22⋊D5911yescharacteristic
567C2×Q8—1181no—
568C2×Q8—1181no—
569C2×Q8—1181no—
570C2×Q8—1181no—
571C2×Q8—1181no—
572C2×Q8—1181no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—42no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—44no—
619C22×C4—44no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4—1181no—
623C22×C4—1181no—
624C22×C4—1181no—
625C22×C4—1181no—
626C22×C4C2×C22⋊D5911yescharacteristic
627C22×C4C2×C22⋊D5911yescharacteristic
628C22×C4C2×C22⋊D5911yescharacteristic
629C22×C4C23×D5911yescharacteristic
630SD16—2364no—
631C2×C8—1181no—
632C2×C8—1181no—
633C2×C8—1181no—
634C2×C8—1181no—
635C2×C8—1181no—
636C2×C8—1181no—
637C2×C8—1181no—
638C2×C8—1181no—
639C2×C8—1181no—
640C2×C8—1181no—
641C2×C8—1181no—
642C2×C8—1181no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—1181no—
650C4⋊C4—1181no—
651C4⋊C4—1181no—
652C4⋊C4—1181no—
653C4⋊C4—1181no—
654C4⋊C4—1181no—
655C4⋊C4—2362no—
656C4⋊C4—2362no—
657C4⋊C4—2362no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—2362no—
665C22⋊C4—2362no—
666C22⋊C4—2362no—
667C22⋊C4—2362no—
668C22⋊C4—2362no—
669C22⋊C4—2362no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23#1427374712yes—
703C23#1427375312yes—
704C23#1427375712yes—
705C23C22×C22⋊D5911yescharacteristic
706Q8—2361no—
707Q8—2361no—
708Q8—2361no—
709Q8—2361no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—41no—
714D4—84no—
715D4—84no—
716D4—84no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—2361no—
751C2×C4—2361no—
752C2×C4—2361no—
753C2×C4—2361no—
754C2×C4—2361no—
755C2×C4—2361no—
756C2×C4—2361no—
757C2×C4—2361no—
758C2×C4—2361no—
759C2×C4—2361no—
760C2×C4—2361no—
761C2×C4—2361no—
762C2×C4#1427377211yescharacteristic
763C2×C4#1427377211yescharacteristic
764C2×C4#1427377211yescharacteristic
765C2×C4#1427377211yescharacteristic
766C2×C4#1427377211yescharacteristic
767C2×C4#1427377211yescharacteristic
768C8—2361no—
769C8—2361no—
770C8—2361no—
771C8—2361no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—416no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22#1683796111yescharacteristic
802C22#1683796111yescharacteristic
803C22#1683796111yescharacteristic
804C22C2×#1427374711yescharacteristic
805C22C2×#1427375311yescharacteristic
806C22C2×#1427375711yescharacteristic
807C22#1683820011yescharacteristic
808C4—41no—
809C4—41no—
810C4—41no—
811C4—81no—
812C4—81no—
813C4—81no—
814C4—4721no—
815C4—4721no—
816C4—4721no—
817C4—4721no—
818C4#1683814111yescharacteristic
819C4#1683814111yescharacteristic
820C4#1683814111yescharacteristic
821C4#1683814511yescharacteristic
822C2—42no—
823C2—42no—
824C2—42no—
825C2—161no—
826C2#2143209111yescharacteristic
827C2#2143486111yescharacteristic
828C2#2143487311yescharacteristic
829C2#2143488411yescharacteristic
830C2#2143490211yescharacteristic
831C2#2143491011yescharacteristic
832C2#2143492211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
Fitting, prime radicalC59×#2847C2
socleC23×C59C22×D4
hypercenter#2847D59
hypocenterC59#32709
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C24×C4 ◁ #2847

Complements

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

NH ≅ G/Ntype
1. #21432383C2semidirect
2. #21425533C2semidirect
3. #21425527C2semidirect
4. #21425522C2semidirect
5. #21425299C2semidirect
6. #21425299C2semidirect
7. #21425292C2semidirect
8. #21425282C2semidirect
9. #21425275C2semidirect
10. #21425275C2semidirect
11. #21425099C2semidirect
12. #21425099C2semidirect
13. #21425099C2semidirect
14. #21424006C2semidirect
16. C22×#11745670C22semidirect
20. C2×#14273660C22semidirect
21. C2×#14273660C22semidirect
22. C2×#14273658C22semidirect
23. C2×#14273650C22semidirect
24. C2×#14273650C22semidirect
25. C2×#14273650C22semidirect
26. C2×#14273648C22semidirect
27. C2×#14273648C22semidirect
28. C2×#14273648C22semidirect
42. #16837164C22semidirect
43. #16837164C22semidirect
44. #16837164C22semidirect
45. #16837164C22semidirect
46. #16837164C22semidirect
47. #16837164C22semidirect
475. C59#32709semidirect

Maximal subgroups

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

subgroupindex
#214323832
#214255332
#214255272
#214255222
#214252992
#214252922
#214252822
#214252752
#214250992
#214240062
C59×#28472
#3270959