Finite Group Databasebeta

← #28735623

Subgroups — #28735623

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#21432378C211yesmaximal, characteristic
2#21425532C211yesmaximal, characteristic, complemented
3#21425527C211yesmaximal, characteristic, complemented
4#21425522C211yesmaximal, characteristic, complemented
5#21425296C211yesmaximal, characteristic, complemented
6#21425296C211yesmaximal, characteristic, complemented
7#21425289C211yesmaximal, characteristic, complemented
8#21425285C211yesmaximal, characteristic, complemented
9#21425278C211yesmaximal, characteristic, complemented
10#21425278C211yesmaximal, characteristic, complemented
11#21425097C211yesmaximal, characteristic, complemented
12#21425097C211yesmaximal, characteristic, complemented
13#21425097C211yesmaximal, characteristic, complemented
14#21424006C211yesmaximal, characteristic, complemented
15C59×#2848C211yesmaximal, characteristic, complemented
16C22×#11745671C2211yescharacteristic, complemented
17C2×#14273701C2211yescharacteristic
18C2×#14273701C2211yescharacteristic
19C2×#14273701C2211yescharacteristic
20C2×#14273696—21no—
21C2×#14273660C2211yescharacteristic, complemented
22C2×#14273660C2211yescharacteristic, complemented
23C2×#14273658C2211yescharacteristic, complemented
24C2×#14273651C2211yescharacteristic, complemented
25C2×#14273651C2211yescharacteristic, complemented
26C2×#14273651C2211yescharacteristic, complemented
27C2×#14273647C2211yescharacteristic, complemented
28C2×#14273647C2211yescharacteristic, complemented
29C2×#14273647C2211yescharacteristic, complemented
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
35C2×C22⋊(C59⋊C8)C2211yescharacteristic
36#16837281—21no—
37#16837281—21no—
38#16837281—21no—
39#16837262C2211yescharacteristic
40#16837262C2211yescharacteristic
41#16837262C2211yescharacteristic
42#16837164C2211yescharacteristic, complemented
43#16837164C2211yescharacteristic, complemented
44#16837164C2211yescharacteristic, complemented
45#16837164C2211yescharacteristic, complemented
46#16837164C2211yescharacteristic, complemented
47#16837164C2211yescharacteristic, complemented
48C24×C4×C59C2211yescharacteristic
49C2×C22⋊Q8×C59C2211yescharacteristic
50C2×C22⋊Q8×C59C2211yescharacteristic
51C2×C22⋊Q8×C59C2211yescharacteristic
52C59×#385—21no—
53C59×#385—21no—
54C59×#385—21no—
55C59×#380C2211yescharacteristic
56C59×#380C2211yescharacteristic
57C59×#380C2211yescharacteristic
58C59×#379—21no—
59C22×D236C2311yescharacteristic
60C22×C22⋊D59—21no—
61C22×C22⋊D59—21no—
62C22×C22⋊D59—21no—
63C2×#11745671—41no—
64C2×#11745671—41no—
65C2×#11745671—41no—
66C22×C59⋊C8C2311yescharacteristic
67C22×C59⋊C8C2311yescharacteristic
68C22×C59⋊C8C2311yescharacteristic
69C22×C59⋊C8C2311yescharacteristic
70#14273701—41no—
71#14273701—41no—
72#14273701—41no—
73#14273701—41no—
74#14273701—41no—
75#14273701—41no—
76#14273696—44no—
77C2×C4⋊Dic59C2311yescharacteristic
78C2×C4⋊Dic59C2311yescharacteristic
79C2×C4⋊Dic59C2311yescharacteristic
80C2×C22⋊Dic59—21no—
81C2×C22⋊Dic59—21no—
82C2×C22⋊Dic59—21no—
83C2×(C2×D59)⋊C4—21no—
84C2×(C2×D59)⋊C4—21no—
85C2×(C2×D59)⋊C4—21no—
86#14273660—41no—
87#14273660—41no—
88#14273658—41no—
89#14273651—41no—
90#14273651—41no—
91#14273651—41no—
92#14273647—41no—
93#14273647—41no—
94#14273647—41no—
95C22⋊(C59⋊C8)—41no—
96C22⋊(C59⋊C8)—41no—
97C22⋊(C59⋊C8)—41no—
98C22⋊(C59⋊C8)—41no—
99C22⋊(C59⋊C8)—41no—
100C22⋊(C59⋊C8)—41no—
101C59⋊#95—21no—
102C59⋊#95—21no—
103C59⋊#95—21no—
104C25×C59D411yescharacteristic
105C22×Q8×C59C2311yescharacteristic
106C23×C4×C59—41no—
107C23×C4×C59—41no—
108C23×C4×C59—41no—
109C23×C4×C59—41no—
110C23×C4×C59—41no—
111C23×C4×C59—41no—
112C23×C4×C59D411yescharacteristic
113C23×C4×C59D411yescharacteristic
114C23×C4×C59D411yescharacteristic
115C23×C4×C59C2311yescharacteristic
116C23×C4×C59C2311yescharacteristic
117C23×C4×C59C2311yescharacteristic
118C22⋊Q8×C59—41no—
119C22⋊Q8×C59—41no—
120C22⋊Q8×C59—41no—
121C22⋊Q8×C59—41no—
122C22⋊Q8×C59—41no—
123C22⋊Q8×C59—41no—
124C2×C4⋊C4×C59—21no—
125C2×C4⋊C4×C59—21no—
126C2×C4⋊C4×C59—21no—
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—41no—
143C24×C59—41no—
144C24×C59—41no—
145C24×C59—41no—
146C24×C59C2×D411yescharacteristic
147C24×C59C2×D411yescharacteristic
148C24×C59C2×D411yescharacteristic
149C23×D59—21no—
150C2×Q8×C59—21no—
151C2×Q8×C59—21no—
152C2×Q8×C59—21no—
153C2×Q8×C59—21no—
154C2×Q8×C59—21no—
155C2×Q8×C59—21no—
156C22×C4×C59—21no—
157C22×C4×C59—21no—
158C22×C4×C59—21no—
159C22×C4×C59—21no—
160C22×C4×C59—21no—
161C22×C4×C59—21no—
162C22×C4×C59—21no—
163C22×C4×C59—21no—
164C22×C4×C59—21no—
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—41no—
179C22×C4×C59—41no—
180C22×C4×C59—41no—
181C22×C4×C59—41no—
182C22×C4×C59—41no—
183C22×C4×C59—41no—
184C22×C4×C59—41no—
185C22×C4×C59—41no—
186C22×C4×C59—41no—
187C22×C4×C59—44no—
188C22×C4×C59—44no—
189C22×C4×C59—44no—
190C22×C4×C59—44no—
191C22×C4×C59C2×D411yescharacteristic
192C22×C4×C59C2×D411yescharacteristic
193C22×C4×C59C2×D411yescharacteristic
194C22×C4×C59C2411yescharacteristic
195C2×C22⋊D59—42no—
196C2×C22⋊D59—42no—
197C2×C22⋊D59—42no—
198C2×C22⋊D59—42no—
199C2×C22⋊D59—42no—
200C2×C22⋊D59—42no—
201C2×C22⋊D59—42no—
202C2×C22⋊D59—42no—
203C2×C22⋊D59—42no—
204C22×Dic59—21no—
205C22×Dic59—21no—
206C22×Dic59—21no—
207C2×D236—21no—
208C2×D236—21no—
209C2×D236—21no—
210C2×D236—21no—
211C2×D236—21no—
212C2×D236—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—
219C4⋊C4×C59—42no—
220C4⋊C4×C59—42no—
221C4⋊C4×C59—42no—
222C22⋊C4×C59—42no—
223C22⋊C4×C59—42no—
224C22⋊C4×C59—42no—
225C22⋊C4×C59—42no—
226C22⋊C4×C59—42no—
227C22⋊C4×C59—42no—
228C22⋊Dic59—42no—
229C22⋊Dic59—42no—
230C22⋊Dic59—42no—
231#11745671—44no—
232(C2×D59)⋊C4—42no—
233(C2×D59)⋊C4—42no—
234(C2×D59)⋊C4—42no—
235C4⋊Dic59—21no—
236C4⋊Dic59—21no—
237C4⋊Dic59—21no—
238C4⋊Dic59—21no—
239C4⋊Dic59—21no—
240C4⋊Dic59—21no—
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#13512yes—
279C23×C59AGL(1,ℤ/8)12yes—
280C23×C59#13712yes—
281C23×C59C22×D411yescharacteristic
282C22×D59—41no—
283C22×D59—41no—
284C22×D59—41no—
285C22×D59—41no—
286C22×D59—41no—
287C22×D59—41no—
288C22×D59—41no—
289Q8×C59—41no—
290Q8×C59—41no—
291Q8×C59—41no—
292Q8×C59—41no—
293C2×C4×C59—21no—
294C2×C4×C59—21no—
295C2×C4×C59—21no—
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—44no—
303C2×C4×C59—44no—
304C2×C4×C59—44no—
305C2×C4×C59—41no—
306C2×C4×C59—41no—
307C2×C4×C59—41no—
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
335C22⋊D59—84no—
336C22⋊D59—84no—
337C22⋊D59—84no—
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—
347D236—41no—
348D236—41no—
349D236—41no—
350D236—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#53411yescharacteristic
379C22×C59#53411yescharacteristic
380C22×C59#53411yescharacteristic
381C22×C59C2×#13511yescharacteristic
382C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
383C22×C59C2×#13711yescharacteristic
384C22×C59#57511yescharacteristic
385C2×D59—81no—
386C2×D59—81no—
387C2×D59—81no—
388C2×D59—81no—
389C2×D59—81no—
390C2×D59—81no—
391C2×D59—81no—
392C4×C59—41no—
393C4×C59—41no—
394C4×C59—41no—
395C4×C59—81no—
396C4×C59—81no—
397C4×C59—81no—
398C4×C59—81no—
399C4×C59#56011yescharacteristic
400C4×C59#56011yescharacteristic
401C4×C59#56011yescharacteristic
402C4×C59H(3,𝔽4)11yescharacteristic
403Dic59—81no—
404Dic59—81no—
405Dic59—81no—
406#2848D5911yescharacteristic, complemented
407#2847—591no—
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#281211yescharacteristic
425C2×C59#318811yescharacteristic
426C2×C59#319011yescharacteristic
427C2×C59#319111yescharacteristic
428C2×C59#319311yescharacteristic
429C2×C59#319411yescharacteristic
430C2×C59#319611yescharacteristic
431D59—161no—
432C24×C4C2×D5911yescharacteristic
433C22×SD16—591no—
434C2×C22⋊Q8C2×D5911yescharacteristic
435C2×C22⋊Q8C2×D5911yescharacteristic
436C2×C22⋊Q8C2×D5911yescharacteristic
437C2×#121—591no—
438C2×#121—591no—
439C2×#121—591no—
440C2×#120—1181no—
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—1181no—
457#386—1181no—
458#386—1181no—
459#385—21no—
460#385—21no—
461#385—21no—
462#380—591no—
463#380—591no—
464#380—591no—
465#380C2×D5911yescharacteristic
466#380C2×D5911yescharacteristic
467#380C2×D5911yescharacteristic
468#379—21no—
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×Q8C22×D5911yescharacteristic
478C22×D4—591no—
479C22×D4—1181no—
480C22×D4—1181no—
481C22×D4—1181no—
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—41no—
502C22⋊Q8—41no—
503C22⋊Q8—41no—
504C22⋊Q8—41no—
505C22⋊Q8—41no—
506C22⋊Q8—41no—
507#121—2361no—
508#121—2361no—
509#121—2361no—
510#121—2361no—
511#121—2361no—
512#121—2361no—
513#120—2364no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—591no—
518C2×C4⋊C4—591no—
519C2×C4⋊C4—591no—
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—41no—
560C24—41no—
561C24—41no—
562C24—41no—
563C24—1181no—
564C24C2×C22⋊D5911yescharacteristic
565C24C2×C22⋊D5911yescharacteristic
566C24C2×C22⋊D5911yescharacteristic
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×D4—1181no—
574C2×D4—1181no—
575C2×D4—1181no—
576C2×D4—1181no—
577C2×D4—1181no—
578C2×D4—1181no—
579C2×D4—2362no—
580C2×D4—2362no—
581C2×D4—2362no—
582C2×D4—2362no—
583C2×D4—2362no—
584C2×D4—2362no—
585C2×D4—2362no—
586C2×D4—2362no—
587C2×D4—2362no—
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—21no—
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—41no—
619C22×C4—44no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4—44no—
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—42no—
650C4⋊C4—42no—
651C4⋊C4—42no—
652C4⋊C4—1181no—
653C4⋊C4—1181no—
654C4⋊C4—1181no—
655C4⋊C4—1181no—
656C4⋊C4—1181no—
657C4⋊C4—1181no—
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—2361no—
696C23—2361no—
697C23—2361no—
698C23—2361no—
699C23—2361no—
700C23—2361no—
701C23—2361no—
702C23#1427374712yes—
703C23#1427375212yes—
704C23#1427375812yes—
705C23C22×C22⋊D5911yescharacteristic
706Q8—41no—
707Q8—41no—
708Q8—41no—
709Q8—41no—
710D4—4724no—
711D4—4724no—
712D4—4724no—
713D4—2361no—
714D4—2361no—
715D4—2361no—
716D4—2361no—
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—41no—
751C2×C4—41no—
752C2×C4—41no—
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—4721no—
795C22—4721no—
796C22—4721no—
797C22—4721no—
798C22—4721no—
799C22—4721no—
800C22—4721no—
801C22#1683796111yescharacteristic
802C22#1683796111yescharacteristic
803C22#1683796111yescharacteristic
804C22C2×#1427374711yescharacteristic
805C22C2×#1427375211yescharacteristic
806C22C2×#1427375811yescharacteristic
807C22#1683820011yescharacteristic
808C4—41no—
809C4—41no—
810C4—41no—
811C4—81no—
812C4—81no—
813C4—81no—
814C4—81no—
815C4—4721no—
816C4—4721no—
817C4—4721no—
818C4#1683814111yescharacteristic
819C4#1683814111yescharacteristic
820C4#1683814111yescharacteristic
821C4#1683814511yescharacteristic
822C2—42no—
823C2—42no—
824C2—42no—
825C2—9441no—
826C2#2143209111yescharacteristic
827C2#2143485711yescharacteristic
828C2#2143487711yescharacteristic
829C2#2143488411yescharacteristic
830C2#2143489811yescharacteristic
831C2#2143490611yescharacteristic
832C2#2143492611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC59×#2848C2
socleC23×C59C22×D4
prime radical#21432378C2
hypercenter#2848D59
hypocenterC59#32709
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C24×C4 ◁ #2848

Complements

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

NH ≅ G/Ntype
2. #21425532C2semidirect
3. #21425527C2semidirect
4. #21425522C2semidirect
5. #21425296C2semidirect
6. #21425296C2semidirect
7. #21425289C2semidirect
8. #21425285C2semidirect
9. #21425278C2semidirect
10. #21425278C2semidirect
11. #21425097C2semidirect
12. #21425097C2semidirect
13. #21425097C2semidirect
14. #21424006C2semidirect
15. C59×#2848C2semidirect
16. C22×#11745671C22semidirect
21. C2×#14273660C22semidirect
22. C2×#14273660C22semidirect
23. C2×#14273658C22semidirect
24. C2×#14273651C22semidirect
25. C2×#14273651C22semidirect
26. C2×#14273651C22semidirect
27. C2×#14273647C22semidirect
28. C2×#14273647C22semidirect
29. C2×#14273647C22semidirect
42. #16837164C22semidirect
43. #16837164C22semidirect
44. #16837164C22semidirect
45. #16837164C22semidirect
46. #16837164C22semidirect
47. #16837164C22semidirect
406. #2848D59semidirect
475. C59#32709semidirect

Maximal subgroups

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

subgroupindex
#214323782
#214255322
#214255272
#214255222
#214252962
#214252892
#214252852
#214252782
#214250972
#214240062
C59×#28482
#3270959