Finite Group Databasebeta

← #28599875

Subgroups — #28599875

Order 15104.

1096 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837545C211yesmaximal, characteristic
2#21426586C211yesmaximal, characteristic, complemented
3#21424961C211yesmaximal, characteristic, complemented
4#21424949C211yesmaximal, characteristic, complemented
5#21424778C211yesmaximal, characteristic, complemented
6#21424771C211yesmaximal, characteristic, complemented
7#21424737C211yesmaximal, characteristic, complemented
8#21424723C211yesmaximal, characteristic, complemented
9#21424444C211yesmaximal, characteristic, complemented
10#21424430C211yesmaximal, characteristic, complemented
11#21424419C211yesmaximal, characteristic, complemented
12#21424293C211yesmaximal, characteristic, complemented
13#21424034C211yesmaximal, characteristic, complemented
14C4×C22⋊(C59⋊C8)C211yesmaximal, characteristic, complemented
15C4×#121×C59C211yesmaximal, characteristic, complemented
16C22×#11745685C2211yescharacteristic
17C22×#11745670C2211yescharacteristic
18C22×#11745669C2211yescharacteristic
19C2×#14273686C2211yescharacteristic
20#16837545C418yescomplemented
21C2×#14273660C2211yescharacteristic
22C2×#14273658C2211yescharacteristic
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×C4×C59⋊C8C2211yescharacteristic
34C2×C4×C59⋊C8C2211yescharacteristic
35#16837308C2211yescharacteristic
36#16837308C2211yescharacteristic
37#16837304C2211yescharacteristic
38#16837304C2211yescharacteristic
39#16837281—21no—
40#16837281—21no—
41C4×(C2×D59)⋊C4—21no—
42C4×(C2×D59)⋊C4—21no—
43#16837164C2211yescharacteristic
44#16837164C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837157C2211yescharacteristic
48#16837157C2211yescharacteristic
49C2×#121×C59C2211yescharacteristic
50C2×C4×D4×C59—21no—
51C2×C4×D4×C59C2211yescharacteristic
52C22×C42×C59C2211yescharacteristic
53C59×#390C2211yescharacteristic
54C59×#389C2211yescharacteristic
55C59×#388—21no—
56C59×#386—21no—
57C59×#380C2211yescharacteristic
58C4×C4⋊C4×C59C2211yescharacteristic
59C4×C22⋊C4×C59—21no—
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—
69C22×C4×D59—21no—
70C2×#11745670—41no—
71C2×#11745670—41no—
72C2×#11745670C2×C414yescomplemented
73C2×#11745669—41no—
74C2×#11745669—41no—
75C2×#11745669C2×C414yescomplemented
76C22×C59⋊C8C2311yescharacteristic
77C22×C59⋊C8C2311yescharacteristic
78C22×C59⋊C8C2311yescharacteristic
79C22×C59⋊C8C2311yescharacteristic
80#14273686—41no—
81#14273686—41no—
82C2×C4⋊Dic59C2311yescharacteristic
83C2×C4⋊Dic59C2311yescharacteristic
84C2×C22⋊Dic59—21no—
85C2×(C2×D59)⋊C4—21no—
86C2×(C2×D59)⋊C4—21no—
87C2×(C2×D59)⋊C4—21no—
88C2×(C2×D59)⋊C4—21no—
89C2×C4×Dic59—21no—
90#14273660—41no—
91#14273658—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
102C4×C59⋊C8—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×C59D411yescharacteristic
112C23×C4×C59D411yescharacteristic
113C23×C4×C59C2311yescharacteristic
114#121×C59—22no—
115#121×C59C2×C414yes—
116C4×D4×C59—41no—
117C4×D4×C59—41no—
118C4×D4×C59—44no—
119C2×C4⋊C4×C59—21no—
120C2×C4⋊C4×C59C2311yescharacteristic
121C2×C4⋊C4×C59C2311yescharacteristic
122C2×C4⋊C4×C59C2311yescharacteristic
123C2×C22⋊C4×C59—21no—
124C2×C22⋊C4×C59—21no—
125C2×C22⋊C4×C59—21no—
126C2×C22⋊C4×C59—21no—
127C2×C22⋊C4×C59—21no—
128C2×C42×C59—21no—
129C2×C42×C59—41no—
130C2×C42×C59—41no—
131C2×C42×C59D411yescharacteristic
132C2×C42×C59D411yescharacteristic
133C2×C42×C59C2311yescharacteristic
134C2×C42×C59C2311yescharacteristic
135#95×C59—21no—
136#95×C59—21no—
137#95×C59—21no—
138C24×C59—21no—
139C24×C59C2×D411yescharacteristic
140C23×D59—21no—
141C2×D4×C59—24no—
142C2×D4×C59—21no—
143C2×D4×C59—21no—
144C2×D4×C59—21no—
145C2×D4×C59—21no—
146C2×D4×C59—21no—
147C2×D4×C59—42no—
148C2×D4×C59—42no—
149C2×D4×C59C22×C412yes—
150C22×C4×C59—21no—
151C22×C4×C59—21no—
152C22×C4×C59—21no—
153C22×C4×C59—21no—
154C22×C4×C59—21no—
155C22×C4×C59—22no—
156C22×C4×C59—22no—
157C22×C4×C59—22no—
158C22×C4×C59—21no—
159C22×C4×C59—21no—
160C22×C4×C59—41no—
161C22×C4×C59—41no—
162C22×C4×C59—41no—
163C22×C4×C59—42no—
164C22×C4×C59—42no—
165C22×C4×C59—42no—
166C22×C4×C59C22×C412yes—
167C22×C4×C59C2×D411yescharacteristic
168C22×C4×C59C2×D411yescharacteristic
169C22×C4×C59C2×D411yescharacteristic
170C22×C4×C59C2×D411yescharacteristic
171C22×C4×C59C2×D411yescharacteristic
172C22×C4×C59#4112yes—
173C22×C4×C59C2411yescharacteristic
174C2×C22⋊D59—24no—
175C2×C22⋊D59—42no—
176C2×C22⋊D59—42no—
177C22×Dic59—21no—
178C22×Dic59—21no—
179C22×Dic59—21no—
180#11745685—44no—
181#11745685—44no—
182#11745685—44no—
183#11745685—44no—
184C2×D236—21no—
185C2×D236—21no—
186C2×D236—21no—
187C2×D236—21no—
188C2×D236—21no—
189C2×D236C22×C412yes—
190C2×C4×D59—24no—
191C2×C4×D59—42no—
192C2×C4×D59—42no—
193C2×Dic118—21no—
194C2×Dic118—21no—
195C2×Dic118—21no—
196C2×Dic118—21no—
197C2×Dic118—21no—
198C2×Dic118C22×C412yes—
199C4⋊C4×C59—21no—
200C4⋊C4×C59—21no—
201C4⋊C4×C59—21no—
202C4⋊C4×C59—21no—
203C4⋊C4×C59—21no—
204C4⋊C4×C59—42no—
205C4⋊C4×C59C22×C412yes—
206C22⋊C4×C59—24no—
207C22⋊C4×C59—42no—
208C22⋊C4×C59—42no—
209C22⋊C4×C59—42no—
210C22⋊C4×C59—42no—
211C42×C59—21no—
212C42×C59—21no—
213C42×C59—21no—
214C42×C59—21no—
215C42×C59—41no—
216C42×C59—41no—
217C42×C59—42no—
218C22⋊Dic59—42no—
219#11745670—44no—
220#11745669—44no—
221(C2×D59)⋊C4—42no—
222(C2×D59)⋊C4—42no—
223(C2×D59)⋊C4—42no—
224(C2×D59)⋊C4—42no—
225C4⋊Dic59—21no—
226C4⋊Dic59—21no—
227C4⋊Dic59—21no—
228C4⋊Dic59—21no—
229C4×Dic59—42no—
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⋊C8—21no—
238C2×C59⋊C8—21no—
239C2×C59⋊C8—21no—
240C2×C59⋊C8C22×C412yes—
241C2×C59⋊C8C22×C412yes—
242C23×C59—21no—
243C23×C59—21no—
244C23×C59—21no—
245C23×C59—21no—
246C23×C59—21no—
247C23×C59—21no—
248C23×C59—22no—
249C23×C59—41no—
250C23×C59—41no—
251C23×C59—41no—
252C23×C59—41no—
253C23×C59—41no—
254C23×C59—41no—
255C23×C59C4×D412yes—
256C23×C59C22×D411yescharacteristic
257C22×D59—22no—
258C22×D59—41no—
259C22×D59—41no—
260C22×D59—41no—
261C22×D59—41no—
262C22×D59—41no—
263C22×D59—41no—
264D4×C59—22no—
265D4×C59—22no—
266D4×C59—48no—
267D4×C59—41no—
268D4×C59—41no—
269C2×C4×C59—21no—
270C2×C4×C59—21no—
271C2×C4×C59—21no—
272C2×C4×C59—21no—
273C2×C4×C59—21no—
274C2×C4×C59—21no—
275C2×C4×C59—21no—
276C2×C4×C59—21no—
277C2×C4×C59—22no—
278C2×C4×C59—22no—
279C2×C4×C59—22no—
280C2×C4×C59—22no—
281C2×C4×C59—22no—
282C2×C4×C59—21no—
283C2×C4×C59—21no—
284C2×C4×C59—21no—
285C2×C4×C59—44no—
286C2×C4×C59—44no—
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—41no—
294C2×C4×C59—41no—
295C2×C4×C59—84no—
296C2×C4×C59C4×D412yes—
297C2×C4×C59#13512yes—
298C2×C4×C59#13512yes—
299C2×C4×C59AGL(1,ℤ/8)12yes—
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—48no—
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—48no—
321Dic118—22no—
322Dic118—22no—
323Dic118—41no—
324Dic118—41no—
325C59⋊C8—22no—
326C59⋊C8—22no—
327C59⋊C8—41no—
328C59⋊C8—41no—
329#22045—591nomaximal, Sylow
330C22×C59—22no—
331C22×C59—22no—
332C22×C59—22no—
333C22×C59—41no—
334C22×C59—41no—
335C22×C59—41no—
336C22×C59—41no—
337C22×C59—42no—
338C22×C59—42no—
339C22×C59—42no—
340C22×C59—81no—
341C22×C59—81no—
342C22×C59—81no—
343C22×C59—81no—
344C22×C59C2×C4×D411yescharacteristic
345C22×C59#53411yescharacteristic
346C22×C59#53511yescharacteristic
347C22×C59C2×#13511yescharacteristic
348C22×C59C2×#13511yescharacteristic
349C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
350C22×C59#57511yescharacteristic
351C2×D59—42no—
352C2×D59—42no—
353C2×D59—42no—
354C2×D59—81no—
355C2×D59—81no—
356C2×D59—81no—
357C2×D59—81no—
358C4×C59—22no—
359C4×C59—22no—
360C4×C59—22no—
361C4×C59—22no—
362C4×C59—41no—
363C4×C59—42no—
364C4×C59—81no—
365C4×C59—81no—
366C4×C59#51811yescharacteristic
367C4×C59#51811yescharacteristic
368C4×C59#53811yescharacteristic
369C4×C59#53811yescharacteristic
370Dic59—42no—
371Dic59—81no—
372Dic59—81no—
373C2×#449—591no—
374C4×#121D5911yescharacteristic, complemented
375#2297—591no—
376#1970—591no—
377#1968—591no—
378#1934—591no—
379#1933—591no—
380#1928—591no—
381#1926—591no—
382#1879—591no—
383#1877—591no—
384#1875—591no—
385#1854—591no—
386#1788—591no—
387C4×C22⋊C8—591no—
388C2×C59—42no—
389C2×C59—82no—
390C2×C59#232111yescharacteristic
391C2×C59C4×#13511yescharacteristic
392C2×C59C4×AGL(1,ℤ/8)11yescharacteristic
393C2×C59#318811yescharacteristic
394C2×C59#319111yescharacteristic
395C2×C59#320711yescharacteristic
396C2×C59#321211yescharacteristic
397D59—82no—
398C22×#41—591no—
399C22×SD16—591no—
400C22×D8—591no—
401C2×#121C2×D5911yescharacteristic
402C2×C4×D4—21no—
403C2×C4×D4C2×D5911yescharacteristic
404C2×#117—591no—
405C22×C42C2×D5911yescharacteristic
406#449—598no—
407C2×#107—591no—
408C2×#106—591no—
409C2×#103—591no—
410C2×#103—591no—
411C2×#103—591no—
412C2×#102—591no—
413C2×#102—591no—
414C2×#102—591no—
415C2×#102—591no—
416C2×#102—591no—
417C2×C22⋊C8—591no—
418C2×C22⋊C8—591no—
419C2×C4×C8—591no—
420C2×C4×C8—591no—
421#391—591no—
422#391—591no—
423#390—591no—
424#390—591no—
425#390C2×D5911yescharacteristic
426#389C2×D5911yescharacteristic
427#388—21no—
428#386—21no—
429#386—1181no—
430#386—1181no—
431#380C2×D5911yescharacteristic
432C4×C4⋊C4C2×D5911yescharacteristic
433C4×C22⋊C4—21no—
434C4×C22⋊C4—1181no—
435C4×C22⋊C4—1181no—
436#340—591no—
437#340—591no—
438#340—591no—
439#340—591no—
440#336—591no—
441#336—591no—
442C59#2204511yescharacteristic, complemented, Sylow
443C2×#41—594no—
444C2×#41—1182no—
445C2×#41—2361no—
446C2×#41—2361no—
447C2×#41—2361no—
448C2×#41—2361no—
449C22×Q8—591no—
450C22×D4—21no—
451C22×D4—591no—
452C22×D4—1181no—
453C22×D4C22×D5911yescharacteristic
454C23×C4—21no—
455C23×C4—1181no—
456C23×C4C22⋊D5911yescharacteristic
457C23×C4C22⋊D5911yescharacteristic
458C23×C4C22×D5911yescharacteristic
459C2×SD16—594no—
460C2×SD16—2361no—
461C2×SD16—2361no—
462C2×D8—594no—
463C2×D8—2361no—
464C2×D8—2361no—
465C22×C8—591no—
466C22×C8—591no—
467C22×C8—591no—
468C22×C8—591no—
469#121—22no—
470#121C4×D5914yes—
471C4×D4—41no—
472C4×D4—41no—
473C4×D4—44no—
474#117—2361no—
475#117—2361no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—591no—
478C2×C4⋊C4—591no—
479C2×C4⋊C4C22×D5911yescharacteristic
480C2×C4⋊C4C22×D5911yescharacteristic
481C2×C4⋊C4C22×D5911yescharacteristic
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—1181no—
488C2×C22⋊C4—1181no—
489C2×C22⋊C4—1181no—
490C2×C22⋊C4—1181no—
491C2×C22⋊C4—1181no—
492C2×C42—21no—
493C2×C42—41no—
494C2×C42—41no—
495C2×C42—1181no—
496C2×C42C22⋊D5911yescharacteristic
497C2×C42C22⋊D5911yescharacteristic
498C2×C42C22×D5911yescharacteristic
499C2×C42C22×D5911yescharacteristic
500#107—2361no—
501#106—2361no—
502#103—594no—
503#103—2361no—
504#103—2361no—
505#102—594no—
506#102—2361no—
507#102—2361no—
508#102—2361no—
509#102—2361no—
510C22⋊C8—594no—
511C22⋊C8—1182no—
512C4×C8—2361no—
513C4×C8—2361no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—1181no—
518#95—1181no—
519#95—1181no—
520#95—1181no—
521C24—21no—
522C24—1181no—
523C24C2×C22⋊D5911yescharacteristic
524#41—2364no—
525#41—2364no—
526#41—2364no—
527#41—2364no—
528C2×Q8—592no—
529C2×Q8—1181no—
530C2×Q8—1181no—
531C2×Q8—1181no—
532C2×Q8—1181no—
533C2×Q8—1181no—
534C2×D4—24no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—592no—
543C2×D4—1184no—
544C2×D4—1181no—
545C2×D4—1181no—
546C2×D4—1181no—
547C2×D4—1181no—
548C2×D4—1181no—
549C2×D4—2362no—
550C2×D4—2362no—
551C2×D4C2×C4×D5912yes—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—1181no—
569C22×C4—1184no—
570C22×C4—1181no—
571C22×C4—1181no—
572C22×C4—2362no—
573C22×C4—2362no—
574C22×C4C2×C4×D5912yes—
575C22×C4#1174568512yes—
576C22×C4C2×C22⋊D5911yescharacteristic
577C22×C4C2×C22⋊D5911yescharacteristic
578C22×C4C2×C22⋊D5911yescharacteristic
579C22×C4C2×C22⋊D5911yescharacteristic
580C22×C4C2×C22⋊D5911yescharacteristic
581C22×C4C23×D5911yescharacteristic
582SD16—2364no—
583D8—2364no—
584C2×C8—592no—
585C2×C8—592no—
586C2×C8—1181no—
587C2×C8—1181no—
588C2×C8—1181no—
589C2×C8—1181no—
590C2×C8—1181no—
591C2×C8—1181no—
592C2×C8—1181no—
593C2×C8—1181no—
594C2×C8—1181no—
595C2×C8—1181no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—42no—
602C4⋊C4—1181no—
603C4⋊C4—1181no—
604C4⋊C4—1181no—
605C4⋊C4—1181no—
606C4⋊C4C2×C4×D5912yes—
607C22⋊C4—24no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—42no—
612C22⋊C4—2362no—
613C22⋊C4—2362no—
614C22⋊C4—2362no—
615C22⋊C4—2362no—
616C22⋊C4—2362no—
617C42—21no—
618C42—21no—
619C42—21no—
620C42—21no—
621C42—41no—
622C42—41no—
623C42—42no—
624C42—2362no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—22no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—1182no—
639C23—2361no—
640C23—2361no—
641C23—2361no—
642C23—2361no—
643C23—2361no—
644C23—2361no—
645C23C4×C22⋊D5912yes—
646C23C22×C22⋊D5911yescharacteristic
647Q8—1182no—
648Q8—1182no—
649Q8—2361no—
650Q8—2361no—
651D4—22no—
652D4—22no—
653D4—48no—
654D4—41no—
655D4—41no—
656D4—1182no—
657D4—1182no—
658D4—2368no—
659D4—2361no—
660D4—2361no—
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—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—44no—
678C2×C4—44no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—84no—
688C2×C4—1182no—
689C2×C4—2368no—
690C2×C4—2361no—
691C2×C4—2361no—
692C2×C4—2361no—
693C2×C4—2361no—
694C2×C4—2361no—
695C2×C4—2361no—
696C2×C4—2361no—
697C2×C4—2361no—
698C2×C4C4×C22⋊D5912yes—
699C2×C4#1427374712yes—
700C2×C4#1427374712yes—
701C2×C4#1427375312yes—
702C2×C4C22×C4×D5911yescharacteristic
703C2×C4C2×#1174568511yescharacteristic
704C2×C4#1427377211yescharacteristic
705C2×C4#1427377211yescharacteristic
706C2×C4#1427377311yescharacteristic
707C2×C4#1427377311yescharacteristic
708C8—1182no—
709C8—1182no—
710C8—2361no—
711C8—2361no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—4721no—
727C22—4721no—
728C22—4721no—
729C22—4721no—
730C22—2362no—
731C22—2362no—
732C22—2362no—
733C22C2×C4×C22⋊D5911yescharacteristic
734C22#1683796111yescharacteristic
735C22#1683796611yescharacteristic
736C22C2×#1427374711yescharacteristic
737C22C2×#1427374711yescharacteristic
738C22C2×#1427375311yescharacteristic
739C22#1683820011yescharacteristic
740C4—22no—
741C4—22no—
742C4—22no—
743C4—22no—
744C4—41no—
745C4—42no—
746C4—81no—
747C4—81no—
748C4—4721no—
749C4—4721no—
750C4—2362no—
751C4#1683787411yescharacteristic
752C4#1683787411yescharacteristic
753C4#1683798511yescharacteristic
754C4#1683798511yescharacteristic
755C2—42no—
756C2—82no—
757C2—4722no—
758C2#2142675011yescharacteristic
759C2C4×#1427374711yescharacteristic
760C2C4×#1427375311yescharacteristic
761C2#2143486111yescharacteristic
762C2#2143488411yescharacteristic
763C2#2143502511yescharacteristic
764C2#2143506811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC4×#121×C59C2
socleC23×C59C22×D4
prime radicalC2×#16837545C2
cosocleC22×C4×C59C24
hypercenterC4×#121D59
hypocenterC59#22045
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
2. #21426586C2semidirect
3. #21424961C2semidirect
4. #21424949C2semidirect
5. #21424778C2semidirect
6. #21424771C2semidirect
7. #21424737C2semidirect
8. #21424723C2semidirect
9. #21424444C2semidirect
10. #21424430C2semidirect
11. #21424419C2semidirect
12. #21424293C2semidirect
13. #21424034C2semidirect
14. C4×C22⋊(C59⋊C8)C2semidirect
15. C4×#121×C59C2semidirect
20. #16837545C4semidirect
65. C2×#11745685C2×C4semidirect
72. C2×#11745670C2×C4semidirect
75. C2×#11745669C2×C4semidirect
94. #14273650C2×C4semidirect
99. #14273647C2×C4semidirect
101. C22⋊(C59⋊C8)C2×C4semidirect
374. C4×#121D59semidirect
442. C59#22045semidirect

Maximal subgroups

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

subgroupindex
C2×#168375452
#214265862
#214249612
#214249492
#214247782
#214247712
#214247372
#214247232
#214244442
#214244302
#214244192
#214242932
#214240342
C4×C22⋊(C59⋊C8)2
C4×#121×C592
#2204559