Finite Group Databasebeta

← #28600009

Subgroups — #28600009

Order 15104.

1024 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837545C211yesmaximal, characteristic
2#21426684C211yesmaximal, characteristic, complemented
3#21424976C211yesmaximal, characteristic, complemented
4#21424961C211yesmaximal, characteristic, complemented
5#21424792C211yesmaximal, characteristic, complemented
6#21424771C211yesmaximal, characteristic, complemented
7#21424737C211yesmaximal, characteristic, complemented
8#21424716C211yesmaximal, characteristic, complemented
9#21424444C211yesmaximal, characteristic, complemented
10#21424430C211yesmaximal, characteristic, complemented
11#21424414C211yesmaximal, characteristic, complemented
12#21424283C211yesmaximal, characteristic, complemented
13#21424034C211yesmaximal, characteristic, complemented
14#21423862C211yesmaximal, characteristic, complemented
15C59×#2324C211yesmaximal, characteristic, complemented
16C22×#11745685C2211yescharacteristic
17C22×#11745670C2211yescharacteristic
18C22×#11745669C2211yescharacteristic
19C22×C4⋊Dic59C2211yescharacteristic
20#16837545C418yescomplemented
21C2×#14273660C2211yescharacteristic
22C2×#14273660C2211yescharacteristic
23C2×#14273650C2211yescharacteristic
24C2×#14273650C2211yescharacteristic
25C2×#14273650C2211yescharacteristic
26C2×#14273648C2211yescharacteristic
27C2×#14273648C2211yescharacteristic
28C2×#14273647C2211yescharacteristic
29C2×#14273647C2211yescharacteristic
30C2×#14273647C2211yescharacteristic
31C2×C22⋊(C59⋊C8)C2211yescharacteristic
32C2×C22⋊(C59⋊C8)C2211yescharacteristic
33C2×#14273638C2211yescharacteristic
34C2×C4×C59⋊C8C2211yescharacteristic
35#16837308C2211yescharacteristic
36#16837308C2211yescharacteristic
37#16837304C2211yescharacteristic
38#16837304C2211yescharacteristic
39#16837279—21no—
40#16837279—21no—
41#16837259—21no—
42#16837259—21no—
43#16837164C2211yescharacteristic
44#16837164C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837157C2211yescharacteristic
48#16837157C2211yescharacteristic
49C2×#121×C59C2211yescharacteristic
50C2×C4×D4×C59C2211yescharacteristic
51C2×#117×C59C2211yescharacteristic
52C59×#390—21no—
53C59×#390C2211yescharacteristic
54C59×#389C2211yescharacteristic
55C59×#388—21no—
56C59×#386—21no—
57C59×#385—21no—
58C59×#380C2211yescharacteristic
59C4×C4⋊C4×C59C2211yescharacteristic
60C2×#11745685—22no—
61C2×#11745685—41no—
62C2×#11745685—41no—
63C2×#11745685—41no—
64C2×#11745685—41no—
65C2×#11745685C2×C414yescomplemented
66C22×Dic118C2311yescharacteristic
67C22×D236C2311yescharacteristic
68C22×C22⋊D59—21no—
69C23×Dic59—21no—
70C22×C4×D59—21no—
71C2×#11745670—41no—
72C2×#11745670—41no—
73C2×#11745670C2×C414yescomplemented
74C2×#11745669—41no—
75C2×#11745669—41no—
76C2×#11745669C2×C414yescomplemented
77C22×C59⋊C8C2311yescharacteristic
78C22×C59⋊C8C2311yescharacteristic
79C22×C59⋊C8C2311yescharacteristic
80C22×C59⋊C8C2311yescharacteristic
81C2×C4⋊Dic59—21no—
82C2×C4⋊Dic59—41no—
83C2×C4⋊Dic59—41no—
84C2×C4⋊Dic59C2311yescharacteristic
85C2×C4⋊Dic59C2311yescharacteristic
86C2×(C2×D59)⋊C4—21no—
87C2×(C2×D59)⋊C4—21no—
88C2×(C2×D59)⋊C4—21no—
89C2×(C2×D59)⋊C4—21no—
90#14273660—41no—
91#14273660—41no—
92#14273650—41no—
93#14273650—41no—
94#14273650C2×C414yescomplemented
95#14273648—41no—
96#14273648—41no—
97#14273647—41no—
98#14273647—41no—
99#14273647C2×C414yescomplemented
100C22⋊(C59⋊C8)—22no—
101C22⋊(C59⋊C8)C2×C414yescomplemented
102#14273638—41no—
103C4×C59⋊C8—41no—
104C59⋊#95—21no—
105C59⋊#95—21no—
106C59⋊#95—21no—
107C59⋊#95—21no—
108C22×D4×C59—21no—
109C22×D4×C59C2311yescharacteristic
110C23×C4×C59—21no—
111C23×C4×C59C2311yescharacteristic
112#121×C59—22no—
113#121×C59C2×C414yes—
114C4×D4×C59—41no—
115C4×D4×C59—41no—
116#117×C59—41no—
117#117×C59—41no—
118C2×C4⋊C4×C59—21no—
119C2×C4⋊C4×C59D411yescharacteristic
120C2×C4⋊C4×C59D411yescharacteristic
121C2×C4⋊C4×C59C2311yescharacteristic
122C2×C4⋊C4×C59C2311yescharacteristic
123C2×C4⋊C4×C59C2311yescharacteristic
124C2×C22⋊C4×C59—21no—
125C2×C22⋊C4×C59—21no—
126C2×C22⋊C4×C59—21no—
127C2×C22⋊C4×C59—21no—
128C2×C22⋊C4×C59—21no—
129C2×C22⋊C4×C59D411yescharacteristic
130C2×C22⋊C4×C59D411yescharacteristic
131C2×C42×C59—21no—
132C2×C42×C59C2311yescharacteristic
133C2×C42×C59C2311yescharacteristic
134#95×C59—21no—
135#95×C59—21no—
136#95×C59—21no—
137C24×C59—21no—
138C24×C59C2×D411yescharacteristic
139C23×D59—21no—
140C2×D4×C59—24no—
141C2×D4×C59—21no—
142C2×D4×C59—21no—
143C2×D4×C59—21no—
144C2×D4×C59—21no—
145C2×D4×C59—21no—
146C2×D4×C59—81no—
147C2×D4×C59—81no—
148C2×D4×C59C22×C412yes—
149C22×C4×C59—21no—
150C22×C4×C59—21no—
151C22×C4×C59—21no—
152C22×C4×C59—21no—
153C22×C4×C59—21no—
154C22×C4×C59—21no—
155C22×C4×C59—21no—
156C22×C4×C59—42no—
157C22×C4×C59—81no—
158C22×C4×C59—81no—
159C22×C4×C59C22×C412yes—
160C22×C4×C59C2×D411yescharacteristic
161C22×C4×C59C2×D411yescharacteristic
162C22×C4×C59C2×D411yescharacteristic
163C22×C4×C59C2×D411yescharacteristic
164C22×C4×C59C2×D411yescharacteristic
165C22×C4×C59#4112yes—
166C22×C4×C59C2411yescharacteristic
167C2×C22⋊D59—24no—
168C2×C22⋊D59—42no—
169C2×C22⋊D59—42no—
170C22×Dic59—21no—
171C22×Dic59—21no—
172C22×Dic59—21no—
173C22×Dic59—42no—
174C22×Dic59—81no—
175C22×Dic59—81no—
176#11745685—44no—
177#11745685—44no—
178#11745685—44no—
179#11745685—44no—
180C2×D236—21no—
181C2×D236—21no—
182C2×D236—21no—
183C2×D236—21no—
184C2×D236—21no—
185C2×D236C22×C412yes—
186C2×C4×D59—24no—
187C2×C4×D59—42no—
188C2×C4×D59—42no—
189C2×Dic118—21no—
190C2×Dic118—21no—
191C2×Dic118—21no—
192C2×Dic118—21no—
193C2×Dic118—21no—
194C2×Dic118C22×C412yes—
195C4⋊C4×C59—21no—
196C4⋊C4×C59—21no—
197C4⋊C4×C59—21no—
198C4⋊C4×C59—21no—
199C4⋊C4×C59—21no—
200C4⋊C4×C59—41no—
201C4⋊C4×C59—41no—
202C4⋊C4×C59—81no—
203C4⋊C4×C59C22×C412yes—
204C22⋊C4×C59—24no—
205C22⋊C4×C59—41no—
206C22⋊C4×C59—41no—
207C22⋊C4×C59—42no—
208C22⋊C4×C59—81no—
209C22⋊C4×C59—81no—
210C22⋊C4×C59—81no—
211C42×C59—21no—
212C42×C59—21no—
213C42×C59—21no—
214C42×C59—21no—
215C42×C59—81no—
216#11745670—44no—
217#11745669—44no—
218(C2×D59)⋊C4—81no—
219(C2×D59)⋊C4—81no—
220(C2×D59)⋊C4—81no—
221(C2×D59)⋊C4—81no—
222C4⋊Dic59—21no—
223C4⋊Dic59—21no—
224C4⋊Dic59—21no—
225C4⋊Dic59—21no—
226C4⋊Dic59—42no—
227C2×C59⋊C8—21no—
228C2×C59⋊C8—21no—
229C2×C59⋊C8—21no—
230C2×C59⋊C8—21no—
231C2×C59⋊C8—21no—
232C2×C59⋊C8—21no—
233C2×C59⋊C8—21no—
234C2×C59⋊C8—21no—
235C2×C59⋊C8—21no—
236C2×C59⋊C8—21no—
237C2×C59⋊C8C22×C412yes—
238C2×C59⋊C8C22×C412yes—
239C23×C59—21no—
240C23×C59—21no—
241C23×C59—21no—
242C23×C59—21no—
243C23×C59—21no—
244C23×C59—21no—
245C23×C59—22no—
246C23×C59—41no—
247C23×C59—41no—
248C23×C59—41no—
249C23×C59—41no—
250C23×C59—41no—
251C23×C59—41no—
252C23×C59C4×D412yes—
253C23×C59C22×D411yescharacteristic
254C22×D59—22no—
255C22×D59—41no—
256C22×D59—41no—
257C22×D59—41no—
258C22×D59—41no—
259C22×D59—41no—
260C22×D59—41no—
261D4×C59—22no—
262D4×C59—22no—
263D4×C59—41no—
264D4×C59—41no—
265D4×C59—84no—
266C2×C4×C59—21no—
267C2×C4×C59—21no—
268C2×C4×C59—22no—
269C2×C4×C59—22no—
270C2×C4×C59—22no—
271C2×C4×C59—22no—
272C2×C4×C59—22no—
273C2×C4×C59—21no—
274C2×C4×C59—21no—
275C2×C4×C59—21no—
276C2×C4×C59—21no—
277C2×C4×C59—21no—
278C2×C4×C59—21no—
279C2×C4×C59—21no—
280C2×C4×C59—21no—
281C2×C4×C59—21no—
282C2×C4×C59—21no—
283C2×C4×C59—21no—
284C2×C4×C59—21no—
285C2×C4×C59—41no—
286C2×C4×C59—41no—
287C2×C4×C59—41no—
288C2×C4×C59—41no—
289C2×C4×C59—41no—
290C2×C4×C59—41no—
291C2×C4×C59—41no—
292C2×C4×C59—41no—
293C2×C4×C59—84no—
294C2×C4×C59C4×D412yes—
295C2×C4×C59C23×C411yescharacteristic
296C2×C4×C59C2×#4111yescharacteristic
297C2×C4×C59H(5,𝔽2)11yescharacteristic
298C2×C4×C59H(5,𝔽2)11yescharacteristic
299C2×C4×C59H(5,𝔽2)11yescharacteristic
300C2×C4×C59H(5,𝔽2)11yescharacteristic
301C22⋊D59—48no—
302C2×Dic59—22no—
303C2×Dic59—41no—
304C2×Dic59—41no—
305C2×Dic59—41no—
306C2×Dic59—41no—
307C2×Dic59—41no—
308C2×Dic59—41no—
309C2×Dic59—41no—
310C2×Dic59—41no—
311C2×Dic59—84no—
312D236—22no—
313D236—22no—
314D236—41no—
315D236—41no—
316C4×D59—48no—
317Dic118—22no—
318Dic118—22no—
319Dic118—41no—
320Dic118—41no—
321C59⋊C8—22no—
322C59⋊C8—22no—
323C59⋊C8—41no—
324C59⋊C8—41no—
325#22055—591nomaximal, Sylow
326C22×C59—22no—
327C22×C59—22no—
328C22×C59—22no—
329C22×C59—41no—
330C22×C59—41no—
331C22×C59—41no—
332C22×C59—41no—
333C22×C59—42no—
334C22×C59—42no—
335C22×C59—42no—
336C22×C59—81no—
337C22×C59—81no—
338C22×C59—81no—
339C22×C59—81no—
340C22×C59C2×C4×D411yescharacteristic
341C22×C59#53411yescharacteristic
342C22×C59#53511yescharacteristic
343C22×C59#57611yescharacteristic
344C22×C59#57611yescharacteristic
345C22×C59#57711yescharacteristic
346C22×C59#57811yescharacteristic
347C2×D59—42no—
348C2×D59—42no—
349C2×D59—42no—
350C2×D59—81no—
351C2×D59—81no—
352C2×D59—81no—
353C2×D59—81no—
354C4×C59—22no—
355C4×C59—41no—
356C4×C59—41no—
357C4×C59—42no—
358C4×C59—41no—
359C4×C59—41no—
360C4×C59—81no—
361C4×C59—81no—
362C4×C59#51811yescharacteristic
363C4×C59#51811yescharacteristic
364C4×C59#53811yescharacteristic
365C4×C59#53811yescharacteristic
366Dic59—42no—
367Dic59—81no—
368Dic59—81no—
369C2×#449—591no—
370#2324D5911yescharacteristic, complemented
371#2311—591no—
372#1973—591no—
373#1970—591no—
374#1936—591no—
375#1933—591no—
376#1928—591no—
377#1925—591no—
378#1879—591no—
379#1877—591no—
380#1874—591no—
381#1852—591no—
382#1788—591no—
383#1750—591no—
384C2×C59—42no—
385C2×C59—82no—
386C2×C59#232111yescharacteristic
387C2×C59#294611yescharacteristic
388C2×C59#295111yescharacteristic
389C2×C59#319811yescharacteristic
390C2×C59#320311yescharacteristic
391C2×C59#322011yescharacteristic
392C2×C59#322511yescharacteristic
393D59—82no—
394C22×#41—591no—
395C22×SD16—591no—
396C22×D8—591no—
397C2×#121C2×D5911yescharacteristic
398C2×C4×D4C2×D5911yescharacteristic
399C2×#117C2×D5911yescharacteristic
400C22×C4⋊C4—591no—
401#449—598no—
402C2×#107—591no—
403C2×#107—591no—
404C2×#103—591no—
405C2×#103—591no—
406C2×#103—591no—
407C2×#102—591no—
408C2×#102—591no—
409C2×#102—591no—
410C2×#102—591no—
411C2×#102—591no—
412C2×C22⋊C8—591no—
413C2×C22⋊C8—591no—
414C2×#97—591no—
415C2×C4×C8—591no—
416#391—591no—
417#391—591no—
418#390—21no—
419#390—591no—
420#390—591no—
421#390C2×D5911yescharacteristic
422#389C2×D5911yescharacteristic
423#388—21no—
424#386—21no—
425#386—1181no—
426#386—1181no—
427#385—21no—
428#380—1181no—
429#380—1181no—
430#380C2×D5911yescharacteristic
431C4×C4⋊C4C2×D5911yescharacteristic
432#340—591no—
433#340—591no—
434#340—591no—
435#340—591no—
436#336—591no—
437#336—591no—
438C59#2205511yescharacteristic, complemented, Sylow
439C2×#41—594no—
440C2×#41—1182no—
441C2×#41—2361no—
442C2×#41—2361no—
443C2×#41—2361no—
444C2×#41—2361no—
445C22×Q8—591no—
446C22×D4—21no—
447C22×D4—591no—
448C22×D4—1181no—
449C22×D4C22×D5911yescharacteristic
450C23×C4—21no—
451C23×C4—1181no—
452C23×C4—1181no—
453C23×C4C22×D5911yescharacteristic
454C2×SD16—594no—
455C2×SD16—2361no—
456C2×SD16—2361no—
457C2×D8—594no—
458C2×D8—2361no—
459C2×D8—2361no—
460C22×C8—591no—
461C22×C8—591no—
462C22×C8—591no—
463C22×C8—591no—
464#121—22no—
465#121C4×D5914yes—
466C4×D4—41no—
467C4×D4—41no—
468#117—41no—
469#117—41no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—591no—
472C2×C4⋊C4—591no—
473C2×C4⋊C4—1181no—
474C2×C4⋊C4—2361no—
475C2×C4⋊C4—2361no—
476C2×C4⋊C4C22⋊D5911yescharacteristic
477C2×C4⋊C4C22⋊D5911yescharacteristic
478C2×C4⋊C4C22×D5911yescharacteristic
479C2×C4⋊C4C22×D5911yescharacteristic
480C2×C4⋊C4C22×D5911yescharacteristic
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—1181no—
487C2×C22⋊C4—1181no—
488C2×C22⋊C4—1181no—
489C2×C22⋊C4—1181no—
490C2×C22⋊C4C22⋊D5911yescharacteristic
491C2×C22⋊C4C22⋊D5911yescharacteristic
492C2×C42—21no—
493C2×C42C22×D5911yescharacteristic
494C2×C42C22×D5911yescharacteristic
495#107—2361no—
496#107—2361no—
497#103—594no—
498#103—2361no—
499#103—2361no—
500#102—594no—
501#102—2361no—
502#102—2361no—
503#102—2361no—
504#102—2361no—
505C22⋊C8—594no—
506C22⋊C8—1182no—
507#97—2361no—
508C4×C8—2361no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—1181no—
513#95—1181no—
514#95—1181no—
515#95—1181no—
516C24—21no—
517C24—1181no—
518C24C2×C22⋊D5911yescharacteristic
519#41—2364no—
520#41—2364no—
521#41—2364no—
522#41—2364no—
523C2×Q8—592no—
524C2×Q8—1181no—
525C2×Q8—1181no—
526C2×Q8—1181no—
527C2×Q8—1181no—
528C2×Q8—1181no—
529C2×D4—24no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—81no—
536C2×D4—81no—
537C2×D4—592no—
538C2×D4—1184no—
539C2×D4—1181no—
540C2×D4—1181no—
541C2×D4—1181no—
542C2×D4—1181no—
543C2×D4—1181no—
544C2×D4—2362no—
545C2×D4—2362no—
546C2×D4C2×C4×D5912yes—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—42no—
555C22×C4—81no—
556C22×C4—81no—
557C22×C4—1181no—
558C22×C4—1184no—
559C22×C4—1181no—
560C22×C4—1181no—
561C22×C4—4721no—
562C22×C4—4721no—
563C22×C4—2362no—
564C22×C4—2362no—
565C22×C4—2362no—
566C22×C4C2×C4×D5912yes—
567C22×C4#1174568512yes—
568C22×C4C2×C22⋊D5911yescharacteristic
569C22×C4C2×C22⋊D5911yescharacteristic
570C22×C4C2×C22⋊D5911yescharacteristic
571C22×C4C2×C22⋊D5911yescharacteristic
572C22×C4C2×C22⋊D5911yescharacteristic
573C22×C4C23×D5911yescharacteristic
574SD16—2364no—
575D8—2364no—
576C2×C8—592no—
577C2×C8—592no—
578C2×C8—1181no—
579C2×C8—1181no—
580C2×C8—1181no—
581C2×C8—1181no—
582C2×C8—1181no—
583C2×C8—1181no—
584C2×C8—1181no—
585C2×C8—1181no—
586C2×C8—1181no—
587C2×C8—1181no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—41no—
594C4⋊C4—41no—
595C4⋊C4—81no—
596C4⋊C4—1181no—
597C4⋊C4—1181no—
598C4⋊C4—1181no—
599C4⋊C4—1181no—
600C4⋊C4—2362no—
601C4⋊C4C2×C4×D5912yes—
602C22⋊C4—24no—
603C22⋊C4—41no—
604C22⋊C4—41no—
605C22⋊C4—42no—
606C22⋊C4—81no—
607C22⋊C4—81no—
608C22⋊C4—81no—
609C22⋊C4—4721no—
610C22⋊C4—4721no—
611C22⋊C4—4721no—
612C22⋊C4—4721no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—81no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—22no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—1182no—
632C23—2361no—
633C23—2361no—
634C23—2361no—
635C23—2361no—
636C23—2361no—
637C23—2361no—
638C23C4×C22⋊D5912yes—
639C23C22×C22⋊D5911yescharacteristic
640Q8—1182no—
641Q8—1182no—
642Q8—2361no—
643Q8—2361no—
644D4—22no—
645D4—22no—
646D4—41no—
647D4—41no—
648D4—84no—
649D4—1182no—
650D4—1182no—
651D4—2368no—
652D4—2361no—
653D4—2361no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—22no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—84no—
682C2×C4—1182no—
683C2×C4—4724no—
684C2×C4—2368no—
685C2×C4—2361no—
686C2×C4—2361no—
687C2×C4—2361no—
688C2×C4—2361no—
689C2×C4—2361no—
690C2×C4—2361no—
691C2×C4—2361no—
692C2×C4—2361no—
693C2×C4C4×C22⋊D5912yes—
694C2×C4C22×C4×D5911yescharacteristic
695C2×C4C2×#1174568511yescharacteristic
696C2×C4#1427377211yescharacteristic
697C2×C4#1427377211yescharacteristic
698C2×C4#1427377311yescharacteristic
699C2×C4#1427377311yescharacteristic
700C8—1182no—
701C8—1182no—
702C8—2361no—
703C8—2361no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—4721no—
719C22—4721no—
720C22—4721no—
721C22—4721no—
722C22—2362no—
723C22—2362no—
724C22—2362no—
725C22C2×C4×C22⋊D5911yescharacteristic
726C22#1683796111yescharacteristic
727C22#1683796611yescharacteristic
728C22#1683820511yescharacteristic
729C22#1683820511yescharacteristic
730C22#1683821311yescharacteristic
731C22#1683821711yescharacteristic
732C4—22no—
733C4—41no—
734C4—41no—
735C4—42no—
736C4—41no—
737C4—41no—
738C4—81no—
739C4—81no—
740C4—4721no—
741C4—4721no—
742C4—2362no—
743C4#1683787411yescharacteristic
744C4#1683787411yescharacteristic
745C4#1683798511yescharacteristic
746C4#1683798511yescharacteristic
747C2—42no—
748C2—82no—
749C2—4722no—
750C2#2142675011yescharacteristic
751C2#2143292811yescharacteristic
752C2#2143296911yescharacteristic
753C2#2143494811yescharacteristic
754C2#2143499311yescharacteristic
755C2#2143514011yescharacteristic
756C2#2143519911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2324C2
socleC23×C59C22×D4
prime radicalC2×#16837545C2
cosocleC22×C4×C59C24
hypercenter#2324D59
hypocenterC59#22055
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2324

Complements

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

NH ≅ G/Ntype
2. #21426684C2semidirect
3. #21424976C2semidirect
4. #21424961C2semidirect
5. #21424792C2semidirect
6. #21424771C2semidirect
7. #21424737C2semidirect
8. #21424716C2semidirect
9. #21424444C2semidirect
10. #21424430C2semidirect
11. #21424414C2semidirect
12. #21424283C2semidirect
13. #21424034C2semidirect
14. #21423862C2semidirect
15. C59×#2324C2semidirect
20. #16837545C4semidirect
65. C2×#11745685C2×C4semidirect
73. C2×#11745670C2×C4semidirect
76. C2×#11745669C2×C4semidirect
94. #14273650C2×C4semidirect
99. #14273647C2×C4semidirect
101. C22⋊(C59⋊C8)C2×C4semidirect
370. #2324D59semidirect
438. C59#22055semidirect

Maximal subgroups

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

subgroupindex
C2×#168375452
#214266842
#214249762
#214249612
#214247922
#214247712
#214247372
#214247162
#214244442
#214244302
#214244142
#214242832
#214240342
#214238622
C59×#23242
#2205559