Finite Group Databasebeta

← #28600015

Subgroups — #28600015

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×#16837547C211yesmaximal, characteristic
2#21426789C211yesmaximal, characteristic, complemented
3#21424980C211yesmaximal, characteristic, complemented
4#21424961C211yesmaximal, characteristic, complemented
5#21424796C211yesmaximal, characteristic, complemented
6#21424775C211yesmaximal, characteristic, complemented
7#21424734C211yesmaximal, characteristic, complemented
8#21424713C211yesmaximal, characteristic, complemented
9#21424447C211yesmaximal, characteristic, complemented
10#21424433C211yesmaximal, characteristic, complemented
11#21424413C211yesmaximal, characteristic, complemented
12#21424284C211yesmaximal, characteristic, complemented
13#21424036C211yesmaximal, characteristic, complemented
14#21423862C211yesmaximal, characteristic, complemented
15C59×#2311C211yesmaximal, characteristic, complemented
16C22×#11745671C2211yescharacteristic
17C22×#11745669C2211yescharacteristic
18C2×#14273701C2211yescharacteristic
19C2×C4×D236C2211yescharacteristic
20#16837547C418yescomplemented
21C2×#14273660C2211yescharacteristic
22C2×#14273660C2211yescharacteristic
23C2×#14273651C2211yescharacteristic
24C2×#14273651C2211yescharacteristic
25C2×#14273651C2211yescharacteristic
26C2×#14273648C2211yescharacteristic
27C2×#14273648C2211yescharacteristic
28C2×#14273648C2211yescharacteristic
29C2×#14273647C2211yescharacteristic
30C2×#14273647C2211yescharacteristic
31C2×C22⋊(C59⋊C8)C2211yescharacteristic
32C2×C22⋊(C59⋊C8)C2211yescharacteristic
33C2×#14273638C2211yescharacteristic
34C2×C4×C59⋊C8C2211yescharacteristic
35#16837304C2211yescharacteristic
36#16837302—21no—
37#16837300C2211yescharacteristic
38#16837292—21no—
39#16837278—21no—
40#16837273—21no—
41#16837262C2211yescharacteristic
42C4×C4⋊Dic59C2211yescharacteristic
43#16837164C2211yescharacteristic
44#16837164C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837157C2211yescharacteristic
48#16837157C2211yescharacteristic
49C22×#41×C59C2211yescharacteristic
50C2×#117×C59C2211yescharacteristic
51C22×C4⋊C4×C59C2211yescharacteristic
52C59×#391C2211yescharacteristic
53C59×#391C2211yescharacteristic
54C59×#390C2211yescharacteristic
55C59×#390C2211yescharacteristic
56C59×#386—21no—
57C59×#386—21no—
58C59×#380—21no—
59C59×#380—21no—
60C22×D236C2311yescharacteristic
61C22×C22⋊D59—21no—
62C22×C4×D59—21no—
63C2×#11745671—41no—
64C2×#11745671—41no—
65C2×#11745671C2×C414yescomplemented
66C2×#11745669—41no—
67C2×#11745669—41no—
68C2×#11745669C2×C414yescomplemented
69C22×C59⋊C8C2311yescharacteristic
70C22×C59⋊C8C2311yescharacteristic
71C22×C59⋊C8C2311yescharacteristic
72C22×C59⋊C8C2311yescharacteristic
73#14273701—22no—
74#14273701C2×C414yes—
75C4×D236—41no—
76C4×D236—41no—
77C2×C4⋊Dic59C2311yescharacteristic
78C2×C4⋊Dic59C2311yescharacteristic
79C2×C4⋊Dic59C2311yescharacteristic
80C2×Dic59⋊C4—21no—
81C2×C22⋊Dic59—21no—
82C2×(C2×D59)⋊C4—21no—
83C2×(C2×D59)⋊C4—21no—
84C2×(C2×D59)⋊C4—21no—
85C2×(C2×D59)⋊C4—21no—
86C2×C4×Dic59—21no—
87#14273660—41no—
88#14273660—41no—
89#14273651—41no—
90#14273651—41no—
91#14273651C2×C414yescomplemented
92#14273648—41no—
93#14273648—41no—
94#14273648C2×C414yescomplemented
95#14273647—41no—
96#14273647—41no—
97C22⋊(C59⋊C8)—22no—
98C22⋊(C59⋊C8)C2×C414yescomplemented
99#14273638—41no—
100C4×C59⋊C8—41no—
101C59⋊#95—21no—
102C59⋊#95—21no—
103C59⋊#95—21no—
104C2×#41×C59—22no—
105C2×#41×C59—41no—
106C2×#41×C59—41no—
107C2×#41×C59—41no—
108C2×#41×C59—41no—
109C2×#41×C59C2×C414yescomplemented
110C22×Q8×C59C2311yescharacteristic
111C22×D4×C59—21no—
112C22×D4×C59C2311yescharacteristic
113C23×C4×C59—21no—
114C23×C4×C59—21no—
115C23×C4×C59C2311yescharacteristic
116#117×C59—41no—
117#117×C59—41no—
118C2×C4⋊C4×C59—21no—
119C2×C4⋊C4×C59—41no—
120C2×C4⋊C4×C59—41no—
121C2×C4⋊C4×C59D411yescharacteristic
122C2×C4⋊C4×C59D411yescharacteristic
123C2×C4⋊C4×C59C2311yescharacteristic
124C2×C4⋊C4×C59C2311yescharacteristic
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×C59C2311yescharacteristic
132C2×C42×C59C2311yescharacteristic
133#95×C59—21no—
134#95×C59—21no—
135#95×C59—21no—
136#95×C59—21no—
137C24×C59—21no—
138C24×C59C2×D411yescharacteristic
139C23×D59—21no—
140#41×C59—44no—
141#41×C59—44no—
142#41×C59—44no—
143#41×C59—44no—
144C2×Q8×C59—21no—
145C2×Q8×C59—21no—
146C2×Q8×C59—21no—
147C2×Q8×C59—21no—
148C2×Q8×C59—21no—
149C2×Q8×C59C22×C412yes—
150C2×D4×C59—24no—
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×C59C22×C412yes—
159C22×C4×C59—21no—
160C22×C4×C59—21no—
161C22×C4×C59—21no—
162C22×C4×C59—21no—
163C22×C4×C59—21no—
164C22×C4×C59—24no—
165C22×C4×C59—21no—
166C22×C4×C59—21no—
167C22×C4×C59—42no—
168C22×C4×C59—42no—
169C22×C4×C59—42no—
170C22×C4×C59—81no—
171C22×C4×C59—81no—
172C22×C4×C59C22×C412yes—
173C22×C4×C59C2×D411yescharacteristic
174C22×C4×C59C2×D411yescharacteristic
175C22×C4×C59C2×D411yescharacteristic
176C22×C4×C59C2×D411yescharacteristic
177C22×C4×C59C2×D411yescharacteristic
178C22×C4×C59#4112yes—
179C22×C4×C59C2411yescharacteristic
180C2×C22⋊D59—24no—
181C2×C22⋊D59—81no—
182C2×C22⋊D59—81no—
183C22×Dic59—21no—
184C22×Dic59—21no—
185C22×Dic59—21no—
186C2×D236—21no—
187C2×D236—21no—
188C2×D236—21no—
189C2×D236—21no—
190C2×D236—21no—
191C2×D236C22×C412yes—
192C2×C4×D59—42no—
193C2×C4×D59—81no—
194C2×C4×D59—81no—
195C4⋊C4×C59—21no—
196C4⋊C4×C59—21no—
197C4⋊C4×C59—21no—
198C4⋊C4×C59—21no—
199C4⋊C4×C59—41no—
200C4⋊C4×C59—41no—
201C4⋊C4×C59—42no—
202C22⋊C4×C59—41no—
203C22⋊C4×C59—41no—
204C22⋊C4×C59—81no—
205C22⋊C4×C59—81no—
206C22⋊C4×C59—81no—
207C22⋊C4×C59—81no—
208C42×C59—21no—
209C42×C59—21no—
210C42×C59—21no—
211C42×C59—21no—
212C22⋊Dic59—81no—
213#11745671—44no—
214#11745669—44no—
215(C2×D59)⋊C4—24no—
216(C2×D59)⋊C4—42no—
217(C2×D59)⋊C4—81no—
218(C2×D59)⋊C4—81no—
219C4⋊Dic59—21no—
220C4⋊Dic59—21no—
221C4⋊Dic59—21no—
222C4⋊Dic59—21no—
223C4⋊Dic59—21no—
224C4⋊Dic59C22×C412yes—
225Dic59⋊C4—81no—
226C4×Dic59—81no—
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—
261Q8×C59—22no—
262Q8×C59—22no—
263Q8×C59—41no—
264Q8×C59—41no—
265D4×C59—22no—
266D4×C59—22no—
267D4×C59—48no—
268D4×C59—41no—
269D4×C59—41no—
270C2×C4×C59—21no—
271C2×C4×C59—21no—
272C2×C4×C59—22no—
273C2×C4×C59—22no—
274C2×C4×C59—22no—
275C2×C4×C59—22no—
276C2×C4×C59—22no—
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—21no—
286C2×C4×C59—21no—
287C2×C4×C59—21no—
288C2×C4×C59—21no—
289C2×C4×C59—48no—
290C2×C4×C59—41no—
291C2×C4×C59—41no—
292C2×C4×C59—41no—
293C2×C4×C59—41no—
294C2×C4×C59—41no—
295C2×C4×C59—41no—
296C2×C4×C59—41no—
297C2×C4×C59—41no—
298C2×C4×C59—84no—
299C2×C4×C59C4×D412yes—
300C2×C4×C59C23×C411yescharacteristic
301C2×C4×C59C2×#4111yescharacteristic
302C2×C4×C59H(5,𝔽2)11yescharacteristic
303C2×C4×C59H(5,𝔽2)11yescharacteristic
304C2×C4×C59H(5,𝔽2)11yescharacteristic
305C2×C4×C59H(5,𝔽2)11yescharacteristic
306C22⋊D59—84no—
307C2×Dic59—22no—
308C2×Dic59—41no—
309C2×Dic59—41no—
310C2×Dic59—41no—
311C2×Dic59—41no—
312C2×Dic59—41no—
313C2×Dic59—41no—
314C2×Dic59—41no—
315C2×Dic59—41no—
316D236—22no—
317D236—22no—
318D236—41no—
319D236—41no—
320C4×D59—84no—
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—42no—
356C4×C59—41no—
357C4×C59—41no—
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#2324—591no—
371#2311D5911yescharacteristic, complemented
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×#41C2×D5911yescharacteristic
395C22×SD16—591no—
396C22×D8—591no—
397C2×#121—591no—
398C2×C4×D4—591no—
399C2×#117C2×D5911yescharacteristic
400C22×C4⋊C4C2×D5911yescharacteristic
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#391C2×D5911yescharacteristic
417#391C2×D5911yescharacteristic
418#390—591no—
419#390—1181no—
420#390C2×D5911yescharacteristic
421#390C2×D5911yescharacteristic
422#389—591no—
423#388—1181no—
424#386—21no—
425#386—21no—
426#386—1181no—
427#385—1181no—
428#380—21no—
429#380—21no—
430#380—591no—
431C4×C4⋊C4—591no—
432#340—591no—
433#340—591no—
434#340—591no—
435#340—591no—
436#336—591no—
437#336—591no—
438C59#2205511yescharacteristic, complemented, Sylow
439C2×#41—22no—
440C2×#41—41no—
441C2×#41—41no—
442C2×#41—41no—
443C2×#41—41no—
444C2×#41C4×D5914yescomplemented
445C22×Q8C22×D5911yescharacteristic
446C22×D4—21no—
447C22×D4—591no—
448C22×D4—1181no—
449C22×D4C22×D5911yescharacteristic
450C23×C4—21no—
451C23×C4—21no—
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—594no—
465#121—1182no—
466C4×D4—2361no—
467C4×D4—2361no—
468#117—41no—
469#117—41no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—41no—
472C2×C4⋊C4—41no—
473C2×C4⋊C4—591no—
474C2×C4⋊C4—591no—
475C2×C4⋊C4—591no—
476C2×C4⋊C4—1181no—
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—1181no—
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—1181no—
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—21no—
513#95—1181no—
514#95—1181no—
515#95—1181no—
516C24—21no—
517C24—1181no—
518C24C2×C22⋊D5911yescharacteristic
519#41—44no—
520#41—44no—
521#41—44no—
522#41—44no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8C2×C4×D5912yes—
529C2×D4—24no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—592no—
538C2×D4—1184no—
539C2×D4—1181no—
540C2×D4—1181no—
541C2×D4—1181no—
542C2×D4—1181no—
543C2×D4—1181no—
544C2×D4—4721no—
545C2×D4—4721no—
546C2×D4C2×C4×D5912yes—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—24no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—81no—
559C22×C4—81no—
560C22×C4—1181no—
561C22×C4—1181no—
562C22×C4—1181no—
563C22×C4—4721no—
564C22×C4—4721no—
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—41no—
593C4⋊C4—41no—
594C4⋊C4—42no—
595C4⋊C4—592no—
596C4⋊C4—1181no—
597C4⋊C4—1181no—
598C4⋊C4—1181no—
599C4⋊C4—1181no—
600C4⋊C4—1181no—
601C4⋊C4—4721no—
602C22⋊C4—41no—
603C22⋊C4—41no—
604C22⋊C4—81no—
605C22⋊C4—81no—
606C22⋊C4—81no—
607C22⋊C4—81no—
608C22⋊C4—1184no—
609C22⋊C4—4721no—
610C22⋊C4—4721no—
611C22⋊C4—4721no—
612C22⋊C4—2362no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—4721no—
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—22no—
641Q8—22no—
642Q8—41no—
643Q8—41no—
644D4—22no—
645D4—22no—
646D4—48no—
647D4—41no—
648D4—41no—
649D4—1182no—
650D4—1182no—
651D4—4724no—
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—48no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—84no—
683C2×C4—1182no—
684C2×C4—4724no—
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#1427377211yescharacteristic
699C2×C4#1427377211yescharacteristic
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#1683796911yescharacteristic
728C22#1683820511yescharacteristic
729C22#1683820511yescharacteristic
730C22#1683821011yescharacteristic
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#1683787511yescharacteristic
744C4#1683787511yescharacteristic
745C4#1683799011yescharacteristic
746C4#1683799011yescharacteristic
747C2—42no—
748C2—82no—
749C2—4722no—
750C2#2142675411yescharacteristic
751C2#2143292411yescharacteristic
752C2#2143296911yescharacteristic
753C2#2143494211yescharacteristic
754C2#2143499311yescharacteristic
755C2#2143514611yescharacteristic
756C2#2143520511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2311C2
socleC23×C59C22×D4
prime radicalC2×#16837547C2
cosocleC22×C4×C59C24
hypercenter#2311D59
hypocenterC59#22055
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2311

Complements

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

NH ≅ G/Ntype
2. #21426789C2semidirect
3. #21424980C2semidirect
4. #21424961C2semidirect
5. #21424796C2semidirect
6. #21424775C2semidirect
7. #21424734C2semidirect
8. #21424713C2semidirect
9. #21424447C2semidirect
10. #21424433C2semidirect
11. #21424413C2semidirect
12. #21424284C2semidirect
13. #21424036C2semidirect
14. #21423862C2semidirect
15. C59×#2311C2semidirect
20. #16837547C4semidirect
65. C2×#11745671C2×C4semidirect
68. C2×#11745669C2×C4semidirect
91. #14273651C2×C4semidirect
94. #14273648C2×C4semidirect
98. C22⋊(C59⋊C8)C2×C4semidirect
109. C2×#41×C59C2×C4semidirect
371. #2311D59semidirect
438. C59#22055semidirect
444. C2×#41C4×D59semidirect

Maximal subgroups

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

subgroupindex
C2×#168375472
#214267892
#214249802
#214249612
#214247962
#214247752
#214247342
#214247132
#214244472
#214244332
#214244132
#214242842
#214240362
#214238622
C59×#23112
#2205559