Finite Group Databasebeta

← #29461038

Subgroups — #29461038

Order 15104.

1686 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21437486C211yesmaximal, characteristic
2#21435394C214yesmaximal, complemented
3#21435379C214yesmaximal, complemented
4#21435364C214yesmaximal, complemented
5#21435349C214yesmaximal, complemented
6#21434645C211yesmaximal, characteristic, complemented
7#21434638C211yesmaximal, characteristic, complemented
8#21434499C211yesmaximal, characteristic, complemented
9#21434492C211yesmaximal, characteristic, complemented
10#21434027C212yesmaximal, complemented
11#21434019C212yesmaximal, complemented
12#21433914C212yesmaximal, complemented
13#21433905C212yesmaximal, complemented
14#21432734C211yesmaximal, characteristic, complemented
15C2×C59×#544C211yesmaximal, characteristic, complemented
16#16838023C2212yes—
17#16838023C2212yes—
18#16838014C2212yes—
19#16838007C2212yes—
20#16837999—21no—
21#16837999—21no—
22#16837990—21no—
23#16837990—21no—
24#16837959C2211yescharacteristic
25#16837952C2211yescharacteristic
26#16837930—22no—
27#16837930—22no—
28#16837913C2212yes—
29C4×#11745685C2212yes—
30#16837812C2212yescomplemented
31#16837812C2212yescomplemented
32#16837808C2214yescomplemented
33#16837805C2212yescomplemented
34#16837801C2214yescomplemented
35#16837798C2212yescomplemented
36#16837772C2212yescomplemented
37#16837768C2212yescomplemented
38#16837764C2214yescomplemented
39#16837759C2214yescomplemented
40#16837754C2212yescomplemented
41#16837750C2212yescomplemented
42#16837743C2214yes—
43#16837743C2214yes—
44#16837737C2214yes—
45#16837732C2214yes—
46#16837726C2214yes—
47#16837726C2214yes—
48#16837720C2214yes—
49#16837715C2214yes—
50#16837706C2214yescomplemented
51#16837706C2214yescomplemented
52#16837699C2214yescomplemented
53#16837699C2214yescomplemented
54#16837694C2214yescomplemented
55#16837689C2214yescomplemented
56#16837684C2214yescomplemented
57#16837679C2214yescomplemented
58#16837463C2214yes—
59#16837463C2214yes—
60#16837442C2212yes—
61#16837442C2212yes—
62#16837442C2212yes—
63#16837442C2212yes—
64#16837426C2212yes—
65#16837401C2212yes—
66#16837401C2212yes—
67#16837401C2212yes—
68#16837401C2212yes—
69#16837366C2212yes—
70C4×#11745664C2211yescharacteristic
71C4×#11745664C2211yescharacteristic
72C59×#544—22no—
73C59×#544—22no—
74C59×#544C2214yes—
75C59×#544C2214yes—
76C2×C4⋊Q8×C59—21no—
77C2×C4⋊Q8×C59C2211yescharacteristic
78C2×C4⋊Q8×C59C2211yescharacteristic
79C2×#125×C59—21no—
80C2×#125×C59C2211yescharacteristic
81C2×#125×C59C2211yescharacteristic
82C2×C22⋊Q8×C59—21no—
83C2×C22⋊Q8×C59—21no—
84C2×#117×C59C2211yescharacteristic
85C2×#117×C59C2211yescharacteristic
86C22×C4⋊C4×C59C2211yescharacteristic
87C2×#11745685C2312yes—
88C2×#11745664C2312yes—
89C2×#11745664C2312yes—
90#14273727C2311yescharacteristic
91#14273727C2311yescharacteristic
92#14273727C2311yescharacteristic
93#14273724C2311yescharacteristic
94#14273722—22no—
95#14273722—22no—
96#14273720—22no—
97#14273720—22no—
98#14273719C2312yes—
99#14273717—22no—
100#14273717—22no—
101#14273715C2312yes—
102#14273713—22no—
103#14273713—22no—
104#14273712—22no—
105#14273712—22no—
106#14273710—22no—
107#14273709—22no—
108#14273709—22no—
109#14273706—21no—
110#14273706—21no—
111#14273706C2312yes—
112#14273706C2312yes—
113#14273705—22no—
114#14273705—22no—
115#14273701—21no—
116#14273701—21no—
117#14273701C2312yes—
118#14273701C2312yes—
119#14273700—22no—
120#14273700—22no—
121#14273696—22no—
122C4×Dic118—21no—
123C4×Dic118—21no—
124C4×Dic118C2312yes—
125C4×Dic118C2312yes—
126C4×D236—21no—
127C4×D236—21no—
128C4×D236C2312yes—
129C4×D236C2312yes—
130C4×C22⋊D59—22no—
131C4×C22⋊D59—22no—
132C4×C22⋊D59—22no—
133C4×C22⋊D59—22no—
134#14273686C2312yes—
135#14273684—22no—
136C42×D59—22no—
137#14273660C2314yes—
138#14273660C2314yes—
139#14273660C2314yes—
140#14273660C2314yes—
141#14273658C2314yes—
142#14273658C2314yes—
143#14273658C2314yes—
144#14273658C2314yes—
145C4⋊(C59⋊C8)C2314yes—
146C4⋊(C59⋊C8)C2314yes—
147#14273650C2314yes—
148#14273650C2314yes—
149#14273650C2314yes—
150#14273650C2314yes—
151#14273647C2314yes—
152#14273647C2314yes—
153#14273647C2314yes—
154#14273647C2314yes—
155C22⋊(C59⋊C8)C2314yes—
156C22⋊(C59⋊C8)C2314yes—
157#14273638C2312yes—
158#14273638C2312yes—
159C4×C59⋊C8C2312yes—
160C4×C59⋊C8C2312yes—
161C22×Q8×C59—21no—
162C22×Q8×C59—21no—
163C23×C4×C59—21no—
164C23×C4×C59C2311yescharacteristic
165C4⋊Q8×C59—24no—
166C4⋊Q8×C59—24no—
167C4⋊Q8×C59—22no—
168C4⋊Q8×C59—21no—
169C4⋊Q8×C59—21no—
170C4⋊Q8×C59C2314yes—
171C4⋊Q8×C59C2312yes—
172C4⋊Q8×C59C2312yes—
173#125×C59—24no—
174#125×C59—24no—
175#125×C59—22no—
176#125×C59—21no—
177#125×C59—21no—
178#125×C59C2314yes—
179#125×C59C2312yes—
180#125×C59C2312yes—
181C22⋊Q8×C59—24no—
182C22⋊Q8×C59—24no—
183C22⋊Q8×C59—24no—
184C22⋊Q8×C59—24no—
185#117×C59—22no—
186#117×C59D412yes—
187#117×C59D412yes—
188#117×C59C2314yes—
189#117×C59C2312yes—
190#117×C59C2312yes—
191C2×C4⋊C4×C59—21no—
192C2×C4⋊C4×C59—22no—
193C2×C4⋊C4×C59—21no—
194C2×C4⋊C4×C59—21no—
195C2×C4⋊C4×C59—21no—
196C2×C4⋊C4×C59—21no—
197C2×C4⋊C4×C59—21no—
198C2×C4⋊C4×C59—21no—
199C2×C4⋊C4×C59D411yescharacteristic
200C2×C4⋊C4×C59D411yescharacteristic
201C2×C4⋊C4×C59C2311yescharacteristic
202C2×C4⋊C4×C59C2311yescharacteristic
203C2×C4⋊C4×C59C2311yescharacteristic
204C2×C4⋊C4×C59C2311yescharacteristic
205C2×C4⋊C4×C59C2314yes—
206C2×C22⋊C4×C59—21no—
207C2×C22⋊C4×C59D411yescharacteristic
208C2×C22⋊C4×C59D411yescharacteristic
209C2×C42×C59—21no—
210C2×C42×C59C2311yescharacteristic
211C2×C42×C59C2311yescharacteristic
212C24×C59C2×D411yescharacteristic
213C2×Q8×C59—24no—
214C2×Q8×C59—22no—
215C2×Q8×C59—22no—
216C2×Q8×C59—82no—
217C2×Q8×C59—82no—
218C22×C4×C59—24no—
219C22×C4×C59—21no—
220C22×C4×C59—21no—
221C22×C4×C59—21no—
222C22×C4×C59—21no—
223C22×C4×C59—24no—
224C22×C4×C59—82no—
225C22×C4×C59C2×D411yescharacteristic
226C22×C4×C59C2×D412yes—
227C22×C4×C59C2×D411yescharacteristic
228C22×C4×C59C2×D411yescharacteristic
229C22×C4×C59C2×D411yescharacteristic
230C22×C4×C59C2×D411yescharacteristic
231C22×C4×C59C2412yes—
232C22×C4×C59C2411yescharacteristic
233C2×C22⋊D59—22no—
234C2×C22⋊D59—22no—
235C2×C22⋊D59—22no—
236#11745685—28no—
237C2×D236—21no—
238C2×D236—21no—
239C2×D236C2412yes—
240C2×C4×D59—22no—
241C2×C4×D59—22no—
242C2×C4×D59—22no—
243C2×Dic118—21no—
244C2×Dic118—21no—
245C2×Dic118C2412yes—
246C4⋊C4×C59—24no—
247C4⋊C4×C59—21no—
248C4⋊C4×C59—21no—
249C4⋊C4×C59—24no—
250C4⋊C4×C59—22no—
251C4⋊C4×C59—22no—
252C4⋊C4×C59—24no—
253C4⋊C4×C59—22no—
254C4⋊C4×C59—22no—
255C4⋊C4×C59—24no—
256C4⋊C4×C59—22no—
257C4⋊C4×C59—22no—
258C4⋊C4×C59—21no—
259C4⋊C4×C59—21no—
260C4⋊C4×C59C2×D412yes—
261C4⋊C4×C59C2×D412yes—
262C4⋊C4×C59C2×D412yes—
263C4⋊C4×C59C2×D412yes—
264C4⋊C4×C59C2412yes—
265C4⋊C4×C59C2412yes—
266C4⋊C4×C59C2412yes—
267C4⋊C4×C59C2412yes—
268C22⋊C4×C59—24no—
269C22⋊C4×C59C2×D412yes—
270C22⋊C4×C59C2×D412yes—
271C22⋊C4×C59C2×D412yes—
272C22⋊C4×C59C2×D412yes—
273C42×C59—24no—
274C42×C59C2×D412yes—
275C42×C59C2×D411yescharacteristic
276C42×C59C2×D411yescharacteristic
277C42×C59C2411yescharacteristic
278C42×C59C2411yescharacteristic
279C42×C59C2412yes—
280C22⋊Dic59—22no—
281C22⋊Dic59—22no—
282C22⋊Dic59—22no—
283(C2×D59)⋊C4—22no—
284(C2×D59)⋊C4—22no—
285(C2×D59)⋊C4—22no—
286(C2×D59)⋊C4—22no—
287(C2×D59)⋊C4—22no—
288(C2×D59)⋊C4—22no—
289C4⋊Dic59—21no—
290C4⋊Dic59—21no—
291C4⋊Dic59—21no—
292C4⋊Dic59—21no—
293C4⋊Dic59C2412yes—
294C4⋊Dic59C2412yes—
295Dic59⋊C4—22no—
296Dic59⋊C4—22no—
297Dic59⋊C4—22no—
298Dic59⋊C4—22no—
299Dic59⋊C4—22no—
300Dic59⋊C4—22no—
301C4×Dic59—22no—
302C4×Dic59—22no—
303C4×Dic59—22no—
304#11745664—24no—
305#11745664—24no—
306C2×C59⋊C8C2414yes—
307C2×C59⋊C8C2414yes—
308C23×C59—22no—
309C23×C59—41no—
310C23×C59—41no—
311C23×C59C22×D412yes—
312C23×C59C22×D411yescharacteristic
313C22×D59—22no—
314Q8×C59—82no—
315Q8×C59—84no—
316Q8×C59—82no—
317C2×C4×C59—22no—
318C2×C4×C59—24no—
319C2×C4×C59—24no—
320C2×C4×C59—22no—
321C2×C4×C59—22no—
322C2×C4×C59—22no—
323C2×C4×C59—22no—
324C2×C4×C59—41no—
325C2×C4×C59—41no—
326C2×C4×C59—41no—
327C2×C4×C59—41no—
328C2×C4×C59—42no—
329C2×C4×C59—42no—
330C2×C4×C59—42no—
331C2×C4×C59—42no—
332C2×C4×C59—84no—
333C2×C4×C59C22×D412yes—
334C2×C4×C59C22×D412yes—
335C2×C4×C59C22×D411yescharacteristic
336C2×C4×C59C22×D411yescharacteristic
337C2×C4×C59C22×D412yes—
338C2×C4×C59C22×D411yescharacteristic
339C2×C4×C59C22×D411yescharacteristic
340C2×C4×C59C22×D411yescharacteristic
341C2×C4×C592−1+414yes—
342C2×C4×C59C2511yescharacteristic
343C22⋊D59—44no—
344C22⋊D59—82no—
345C22⋊D59—82no—
346C2×Dic59—22no—
347C2×Dic59—22no—
348C2×Dic59—22no—
349D236—24no—
350D236—81no—
351D236—81no—
352C4×D59—44no—
353C4×D59—82no—
354C4×D59—82no—
355Dic118—24no—
356Dic118—81no—
357Dic118—81no—
358C59⋊C8—24no—
359C59⋊C8—24no—
360#60867—591nomaximal, Sylow
361C22×C59—21no—
362C22×C59—21no—
363C22×C59—22no—
364C22×C59—22no—
365C22×C59—22no—
366C22×C59—44no—
367C22×C59#53612yes—
368C22×C59C23×D411yescharacteristic
369C2×D59—42no—
370C2×D59—42no—
371C2×D59—42no—
372C4×C59—21no—
373C4×C59—22no—
374C4×C59—21no—
375C4×C59—21no—
376C4×C59—22no—
377C4×C59—21no—
378C4×C59—22no—
379C4×C59—42no—
380C4×C59—42no—
381C4×C59—42no—
382C4×C59—42no—
383C4×C59#53612yes—
384C4×C59C2×2−1+412yes—
385Dic59—42no—
386Dic59—42no—
387Dic59—42no—
388C2×#544D5911yescharacteristic, complemented
389#3455—591no—
390#3244—594no—
391#3243—594no—
392#3242—594no—
393#3241—594no—
394#3166—591no—
395#3165—591no—
396#3142—591no—
397#3141—591no—
398#3093—592no—
399#3092—592no—
400#3080—592no—
401#3079—592no—
402#2921—591no—
403C2×C59—22no—
404C2×C59—42no—
405C2×C59C2×#53611yescharacteristic
406C2×C59#358511yescharacteristic
407C2×C59#358611yescharacteristic
408D59—82no—
409#544—22no—
410#544—22no—
411#544C2×D5914yes—
412#544C2×D5914yes—
413#542—592no—
414#542—592no—
415#541—592no—
416#540—592no—
417#539—1181no—
418#539—1181no—
419#538—1181no—
420#538—1181no—
421#533—591no—
422#532—591no—
423C2×C4⋊Q8—21no—
424C2×C4⋊Q8C2×D5911yescharacteristic
425C2×C4⋊Q8C2×D5911yescharacteristic
426#529—1182no—
427#529—1182no—
428C2×#125—21no—
429C2×#125C2×D5911yescharacteristic
430C2×#125C2×D5911yescharacteristic
431#525—592no—
432C2×C22⋊Q8—21no—
433C2×C22⋊Q8—21no—
434C4×#41—592no—
435C2×#117C2×D5911yescharacteristic
436C2×#117C2×D5911yescharacteristic
437C22×C4⋊C4C2×D5911yescharacteristic
438#501—594no—
439#501—592no—
440#501—592no—
441#500—592no—
442#499—594no—
443#498—592no—
444#491—592no—
445#490—592no—
446#489—594no—
447#488—594no—
448#487—592no—
449#486—592no—
450#485—594no—
451#485—594no—
452#484—594no—
453#483—594no—
454#482—594no—
455#482—594no—
456#481—594no—
457#480—594no—
458#479—594no—
459#479—594no—
460#478—594no—
461#478—594no—
462#477—594no—
463#476—594no—
464#475—594no—
465#474—594no—
466#433—594no—
467#433—594no—
468#428—592no—
469#428—592no—
470#428—592no—
471#428—592no—
472#423—592no—
473#417—592no—
474#417—592no—
475#417—592no—
476#417—592no—
477#407—592no—
478C4×M16—591no—
479C4×M16—591no—
480C59#6086711yescharacteristic, complemented, Sylow
481C2×#41—592no—
482C22×Q8—21no—
483C22×Q8—21no—
484C23×C4—21no—
485C23×C4C22×D5911yescharacteristic
486C2×M16—592no—
487C2×M16—592no—
488C4⋊Q8—24no—
489C4⋊Q8—24no—
490C4⋊Q8—22no—
491C4⋊Q8—21no—
492C4⋊Q8—21no—
493C4⋊Q8—591no—
494C4⋊Q8—591no—
495C4⋊Q8—591no—
496C4⋊Q8C22×D5914yes—
497C4⋊Q8C22×D5912yes—
498C4⋊Q8C22×D5912yes—
499#127—591no—
500#126—1182no—
501#126—1182no—
502#126—1182no—
503#126—1182no—
504#125—24no—
505#125—24no—
506#125—22no—
507#125—21no—
508#125—21no—
509#125—592no—
510#125—1182no—
511#125—1182no—
512#125C22×D5914yes—
513#125C22×D5912yes—
514#125C22×D5912yes—
515#124—592no—
516#124—1182no—
517#124—1182no—
518#123—1182no—
519#123—1182no—
520#123—1182no—
521#123—1182no—
522#123—1182no—
523C22⋊Q8—24no—
524C22⋊Q8—24no—
525C22⋊Q8—24no—
526C22⋊Q8—24no—
527C22⋊Q8—592no—
528C22⋊Q8—592no—
529C22⋊Q8—1181no—
530C22⋊Q8—1181no—
531C22⋊Q8—1182no—
532C22⋊Q8—1182no—
533#121—592no—
534#121—592no—
535#121—1181no—
536#121—1181no—
537#121—1182no—
538#121—1182no—
539#120—1182no—
540C4×Q8—592no—
541C4×Q8—592no—
542C4×Q8—1181no—
543C4×Q8—1181no—
544C4×D4—592no—
545C4×D4—592no—
546C4×D4—1182no—
547C4×D4—1182no—
548C4×D4—1182no—
549C4×D4—1182no—
550C4×D4—1181no—
551C4×D4—1181no—
552#117—22no—
553#117—592no—
554#117—1182no—
555#117C22⋊D5912yes—
556#117C22⋊D5912yes—
557#117C22×D5914yes—
558#117C22×D5912yes—
559#117C22×D5912yes—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—22no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4C22⋊D5911yescharacteristic
569C2×C4⋊C4C22⋊D5911yescharacteristic
570C2×C4⋊C4C22×D5911yescharacteristic
571C2×C4⋊C4C22×D5911yescharacteristic
572C2×C4⋊C4C22×D5914yes—
573C2×C4⋊C4C22×D5911yescharacteristic
574C2×C4⋊C4C22×D5911yescharacteristic
575C2×C22⋊C4—21no—
576C2×C22⋊C4C22⋊D5911yescharacteristic
577C2×C22⋊C4C22⋊D5911yescharacteristic
578C2×C42—21no—
579C2×C42—1182no—
580C2×C42C22×D5911yescharacteristic
581C2×C42C22×D5911yescharacteristic
582#107—594no—
583#107—594no—
584#107—594no—
585#107—594no—
586#106—594no—
587#106—594no—
588#106—594no—
589#106—594no—
590C4⋊C8—594no—
591C4⋊C8—594no—
592#103—594no—
593#103—594no—
594#103—594no—
595#103—594no—
596#102—594no—
597#102—594no—
598#102—594no—
599#102—594no—
600C22⋊C8—594no—
601C22⋊C8—594no—
602#97—592no—
603#97—592no—
604C4×C8—592no—
605C4×C8—592no—
606C24C2×C22⋊D5911yescharacteristic
607#41—1188no—
608C2×Q8—24no—
609C2×Q8—22no—
610C2×Q8—22no—
611C2×Q8—82no—
612C2×Q8—82no—
613C2×Q8—592no—
614C2×Q8—1181no—
615C2×Q8—1181no—
616C2×D4—592no—
617C2×D4—1182no—
618C2×D4—1182no—
619C2×D4—1182no—
620C2×D4—1181no—
621C2×D4—1181no—
622C22×C4—24no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—24no—
628C22×C4—82no—
629C22×C4—1182no—
630C22×C4—1182no—
631C22×C4—1182no—
632C22×C4C2×C22⋊D5911yescharacteristic
633C22×C4C2×C22⋊D5912yes—
634C22×C4C2×C22⋊D5911yescharacteristic
635C22×C4C2×C22⋊D5911yescharacteristic
636C22×C4C2×C22⋊D5911yescharacteristic
637C22×C4C2×C22⋊D5911yescharacteristic
638C22×C4C23×D5912yes—
639C22×C4C23×D5911yescharacteristic
640M16—1184no—
641M16—1184no—
642C2×C8—594no—
643C2×C8—594no—
644C4⋊C4—24no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—24no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—24no—
651C4⋊C4—22no—
652C4⋊C4—22no—
653C4⋊C4—24no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—592no—
659C4⋊C4—592no—
660C4⋊C4—1182no—
661C4⋊C4—1182no—
662C4⋊C4—1181no—
663C4⋊C4—1181no—
664C4⋊C4—1182no—
665C4⋊C4—1182no—
666C4⋊C4—1182no—
667C4⋊C4—1182no—
668C4⋊C4—1181no—
669C4⋊C4—1181no—
670C4⋊C4C2×C22⋊D5912yes—
671C4⋊C4C2×C22⋊D5912yes—
672C4⋊C4C2×C22⋊D5912yes—
673C4⋊C4C2×C22⋊D5912yes—
674C4⋊C4C23×D5912yes—
675C4⋊C4C23×D5912yes—
676C4⋊C4C23×D5912yes—
677C4⋊C4C23×D5912yes—
678C22⋊C4—24no—
679C22⋊C4—1182no—
680C22⋊C4—1182no—
681C22⋊C4—1182no—
682C22⋊C4—1182no—
683C22⋊C4—1182no—
684C22⋊C4—1182no—
685C22⋊C4—1182no—
686C22⋊C4—1182no—
687C22⋊C4—1182no—
688C22⋊C4C2×C22⋊D5912yes—
689C22⋊C4C2×C22⋊D5912yes—
690C22⋊C4C2×C22⋊D5912yes—
691C22⋊C4C2×C22⋊D5912yes—
692C42—24no—
693C42—1182no—
694C42—1182no—
695C42—1182no—
696C42C2×C22⋊D5912yes—
697C42C2×C22⋊D5911yescharacteristic
698C42C2×C22⋊D5911yescharacteristic
699C42C23×D5911yescharacteristic
700C42C23×D5911yescharacteristic
701C42C23×D5912yes—
702C23—22no—
703C23—41no—
704C23—41no—
705C23—1182no—
706C23C22×C22⋊D5912yes—
707C23C22×C22⋊D5911yescharacteristic
708Q8—84no—
709Q8—82no—
710Q8—82no—
711Q8—1184no—
712Q8—4721no—
713Q8—4721no—
714D4—1184no—
715D4—4721no—
716D4—4721no—
717D4—4722no—
718D4—4722no—
719D4—2364no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—84no—
736C2×C4—1182no—
737C2×C4—1182no—
738C2×C4—1182no—
739C2×C4—4722no—
740C2×C4—4722no—
741C2×C4—2364no—
742C2×C4C22×C22⋊D5912yes—
743C2×C4C22×C22⋊D5912yes—
744C2×C4C22×C22⋊D5912yes—
745C2×C4C22×C22⋊D5911yescharacteristic
746C2×C4C22×C22⋊D5911yescharacteristic
747C2×C4C22×C22⋊D5911yescharacteristic
748C2×C4C22×C22⋊D5911yescharacteristic
749C2×C4C22×C22⋊D5911yescharacteristic
750C2×C4#1427377514yes—
751C2×C4C24×D5911yescharacteristic
752C8—1184no—
753C8—1184no—
754C22—21no—
755C22—21no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—44no—
760C22—2362no—
761C22—2362no—
762C22—2362no—
763C22#1683797612yes—
764C22C23×C22⋊D5911yescharacteristic
765C4—22no—
766C4—21no—
767C4—21no—
768C4—22no—
769C4—21no—
770C4—21no—
771C4—22no—
772C4—42no—
773C4—42no—
774C4—42no—
775C4—42no—
776C4—2362no—
777C4—2362no—
778C4—2362no—
779C4#1683797612yes—
780C4C2×#1427377512yes—
781C2—22no—
782C2—42no—
783C2—4722no—
784C2C2×#1683797611yescharacteristic
785C2#2143887611yescharacteristic
786C2#2143888311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#544C2
socleC22×C59C23×D4
prime radical#21437486C2
hypercenterC2×#544D59
hypocenterC59#60867
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×#117 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
2. #21435394C2semidirect
3. #21435379C2semidirect
4. #21435364C2semidirect
5. #21435349C2semidirect
6. #21434645C2semidirect
7. #21434638C2semidirect
8. #21434499C2semidirect
9. #21434492C2semidirect
10. #21434027C2semidirect
11. #21434019C2semidirect
12. #21433914C2semidirect
13. #21433905C2semidirect
14. #21432734C2semidirect
15. C2×C59×#544C2semidirect
30. #16837812C22semidirect
31. #16837812C22semidirect
32. #16837808C22semidirect
33. #16837805C22semidirect
34. #16837801C22semidirect
35. #16837798C22semidirect
36. #16837772C22semidirect
37. #16837768C22semidirect
38. #16837764C22semidirect
39. #16837759C22semidirect
40. #16837754C22semidirect
41. #16837750C22semidirect
50. #16837706C22semidirect
51. #16837706C22semidirect
52. #16837699C22semidirect
53. #16837699C22semidirect
54. #16837694C22semidirect
55. #16837689C22semidirect
56. #16837684C22semidirect
57. #16837679C22semidirect
388. C2×#544D59semidirect
480. C59#60867semidirect

Maximal subgroups

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

subgroupindex
#214374862
#214353942
#214353792
#214353642
#214353492
#214346452
#214346382
#214344992
#214344922
#214340272
#214340192
#214339142
#214339052
#214327342
C2×C59×#5442
#6086759