Finite Group Databasebeta

← #28761612

Subgroups — #28761612

Order 15104.

2642 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837989C212yesmaximal, complemented
2#21432448C211yesmaximal, characteristic, complemented
3#21432375C212yesmaximal, complemented
4#21430029C212yesmaximal, complemented
5#21429832C212yesmaximal, complemented
6#21429230C214yesmaximal, complemented
7#21429200C214yesmaximal, complemented
8#21428521C212yesmaximal, complemented
9#21428457C212yesmaximal, complemented
10#21427687C212yesmaximal, complemented
11#21427608C212yesmaximal, complemented
12#21426801C212yesmaximal, complemented
13#121×Dic59C212yesmaximal, complemented
14C2×C4×(C2×D59)⋊C4C211yesmaximal, characteristic, complemented
15C59×#2856C211yesmaximal, characteristic, complemented
16C23×C4×D59C2211yescharacteristic
17#16837989—216no—
18C2×#14273727C2211yescharacteristic, complemented
19C2×#14273722C2214yes—
20C2×#14273713C2214yes—
21C2×#14273711C2214yes—
22C2×#14273706C2212yes—
23C2×#14273699C2214yes—
24C2×#14273698C2212yes—
25C2×#14273698C2212yes—
26C2×#14273695C2214yes—
27C2×D4×Dic59C2214yes—
28C2×D4×Dic59C2212yescomplemented
29C22×(C2×D59)⋊C4C2211yescharacteristic
30C22×(C2×D59)⋊C4C2211yescharacteristic
31C22×C4×Dic59C2211yescharacteristic
32#16837340C2214yescomplemented
33#16837328C2214yes—
34#16837327C2214yescomplemented
35#16837318C2214yes—
36#16837318C2214yes—
37#16837316C2214yescomplemented
38#16837314C2214yescomplemented
39#16837310C2214yes—
40#16837308C2212yescomplemented
41#16837305C2212yescomplemented
42#16837301C2212yescomplemented
43#16837300C2212yescomplemented
44#16837300C2212yescomplemented
45#16837295C2214yescomplemented
46#16837295C2214yescomplemented
47#16837288C2214yescomplemented
48#16837282C2214yes—
49#16837282C2214yes—
50#16837282C2214yescomplemented
51#16837278C2214yes—
52#16837278C2214yes—
53#16837277C2214yescomplemented
54#16837272C2211yescharacteristic, complemented
55#16837262C2212yes—
56#16837262C2212yes—
57#16837259C2212yes—
58#16837259C2212yes—
59C4⋊C4×Dic59C2212yescomplemented
60C22⋊C4×Dic59C2214yescomplemented
61C4×(C2×D59)⋊C4C2212yes—
62C4×(C2×D59)⋊C4C2212yes—
63C4×(C2×D59)⋊C4C2212yes—
64C4×(C2×D59)⋊C4C2212yes—
65C2×C59⋊#95C2211yescharacteristic
66C2×C59⋊#95C2211yescharacteristic
67C2×#127×C59C2211yescharacteristic, complemented
68C2×#121×C59C2212yes—
69C2×#121×C59C2212yes—
70C2×#121×C59C2212yes—
71C22×C42×C59C2211yescharacteristic
72C59×#390C2212yescomplemented
73C59×#390C2212yescomplemented
74C59×#390C2212yescomplemented
75C59×#384C2211yescharacteristic, complemented
76C24×D59C2311yescharacteristic
77C22×Dic118C2312yes—
78C22×C22⋊D59C2314yes—
79C22×C22⋊D59C2314yes—
80C23×Dic59C2314yes—
81C23×Dic59C2311yescharacteristic
82C23×Dic59C2311yescharacteristic
83C23×Dic59C2311yescharacteristic
84C22×C4×D59—24no—
85C22×C4×D59—42no—
86C22×C4×D59—42no—
87C22×C4×D59C2312yes—
88C22×C4×D59C2312yes—
89#14273727—42no—
90#14273722—216no—
91#14273713—216no—
92#14273711—216no—
93#14273706—28no—
94#14273699—216no—
95#14273698—44no—
96#14273698—44no—
97#14273695—216no—
98D4×Dic59—216no—
99D4×Dic59—44no—
100C2×C4⋊Dic59C2312yes—
101C2×C4⋊Dic59C2312yes—
102C2×C4⋊Dic59C2312yes—
103C2×C4⋊Dic59C2314yes—
104C2×C4⋊Dic59C2312yes—
105C2×C4⋊Dic59C2312yes—
106C2×Dic59⋊C4C2314yes—
107C2×C22⋊Dic59C2314yes—
108C2×C22⋊Dic59C2314yes—
109C2×C22⋊Dic59C2314yes—
110C2×C22⋊Dic59C2314yes—
111C2×C22⋊Dic59C2314yes—
112C2×C22⋊Dic59C2314yes—
113C2×(C2×D59)⋊C4—24no—
114C2×(C2×D59)⋊C4D418yescomplemented
115C2×(C2×D59)⋊C4C2314yes—
116C2×(C2×D59)⋊C4C2314yes—
117C2×(C2×D59)⋊C4C2312yes—
118C2×(C2×D59)⋊C4C2312yes—
119C2×(C2×D59)⋊C4C2312yes—
120C2×(C2×D59)⋊C4C2312yes—
121C2×C4×Dic59—42no—
122C2×C4×Dic59C2314yes—
123C2×C4×Dic59C2312yes—
124C2×C4×Dic59C2312yes—
125C59⋊#95C2312yes—
126C59⋊#95C2312yes—
127C59⋊#95C2312yes—
128C59⋊#95C2312yes—
129C59⋊#95C2314yes—
130C59⋊#95C2314yes—
131C59⋊#95C2314yes—
132C59⋊#95C2314yes—
133C59⋊#95C2314yes—
134C59⋊#95C2314yes—
135C22×D4×C59C2312yes—
136C22×D4×C59C2314yes—
137C22×D4×C59C2312yes—
138C22×D4×C59C2312yes—
139C23×C4×C59C2311yescharacteristic
140C23×C4×C59C2311yescharacteristic
141C23×C4×C59C2311yescharacteristic
142#127×C59—42no—
143#121×C59—28no—
144#121×C59—28no—
145#121×C59—28no—
146C2×C4⋊C4×C59C2312yes—
147C2×C4⋊C4×C59C2312yes—
148C2×C4⋊C4×C59C2312yes—
149C2×C22⋊C4×C59C2314yes—
150C2×C22⋊C4×C59C2314yes—
151C2×C22⋊C4×C59C2314yes—
152C2×C42×C59—42no—
153C2×C42×C59C2311yescharacteristic
154C2×C42×C59C2311yescharacteristic
155C2×C42×C59C2311yescharacteristic
156C2×C42×C59C2311yescharacteristic
157C24×C59C2414yes—
158C24×C59C2411yescharacteristic
159C23×D59—22no—
160C23×D59—22no—
161C23×D59—41no—
162C23×D59—41no—
163C23×D59—41no—
164C23×D59—41no—
165C23×D59C2×D414yes—
166C23×D59C2412yes—
167C2×D4×C59—28no—
168C2×D4×C59—28no—
169C2×D4×C59—28no—
170C2×D4×C59—24no—
171C2×D4×C59—24no—
172C2×D4×C59—24no—
173C2×D4×C59—24no—
174C2×D4×C59—24no—
175C2×D4×C59—42no—
176C2×D4×C59—42no—
177C2×D4×C59—42no—
178C2×D4×C59—42no—
179C22×C4×C59—22no—
180C22×C4×C59—22no—
181C22×C4×C59—41no—
182C22×C4×C59—41no—
183C22×C4×C59—41no—
184C22×C4×C59—41no—
185C22×C4×C59C2×D414yes—
186C22×C4×C59#4114yes—
187C22×C4×C59#4114yes—
188C22×C4×C59C2414yes—
189C22×C4×C59C2411yescharacteristic
190C22×C4×C59C2411yescharacteristic
191C22×C4×C59C2411yescharacteristic
192C22×C4×C59C2411yescharacteristic
193C22×C4×C59C2411yescharacteristic
194C22×C4×C59C2411yescharacteristic
195C2×C22⋊D59—28no—
196C2×C22⋊D59—28no—
197C2×C22⋊D59—44no—
198C2×C22⋊D59—44no—
199C2×C22⋊D59—44no—
200C2×C22⋊D59—44no—
201C22×Dic59—22no—
202C22×Dic59—22no—
203C22×Dic59—28no—
204C22×Dic59—41no—
205C22×Dic59—41no—
206C22×Dic59—41no—
207C22×Dic59—41no—
208C22×Dic59—41no—
209C22×Dic59—41no—
210C22×Dic59—44no—
211C22×Dic59—44no—
212C22×Dic59C2×D414yes—
213C22×Dic59C2412yes—
214C22×Dic59C2412yes—
215C22×Dic59C2414yes—
216C22×Dic59C2414yes—
217C22×Dic59C2412yes—
218C2×C4×D59—24no—
219C2×C4×D59—24no—
220C2×C4×D59—24no—
221C2×C4×D59—24no—
222C2×C4×D59—42no—
223C2×C4×D59—42no—
224C2×C4×D59—416no—
225C2×Dic118—24no—
226C2×Dic118—42no—
227C2×Dic118—42no—
228C4⋊C4×C59—24no—
229C4⋊C4×C59—24no—
230C4⋊C4×C59—24no—
231C22⋊C4×C59—28no—
232C22⋊C4×C59—28no—
233C22⋊C4×C59—28no—
234C42×C59—22no—
235C42×C59—22no—
236C42×C59—41no—
237C42×C59—41no—
238C22⋊Dic59—28no—
239C22⋊Dic59—28no—
240C22⋊Dic59—44no—
241C22⋊Dic59—44no—
242C22⋊Dic59—44no—
243C22⋊Dic59—44no—
244(C2×D59)⋊C4—28no—
245(C2×D59)⋊C4—28no—
246(C2×D59)⋊C4—24no—
247(C2×D59)⋊C4—24no—
248(C2×D59)⋊C4C2×D418yes—
249(C2×D59)⋊C4C2×D418yes—
250C4⋊Dic59—24no—
251C4⋊Dic59—24no—
252C4⋊Dic59—24no—
253C4⋊Dic59—28no—
254C4⋊Dic59—42no—
255C4⋊Dic59—42no—
256Dic59⋊C4—28no—
257C4×Dic59—24no—
258C4×Dic59—28no—
259C4×Dic59—42no—
260C23×C59—21no—
261C23×C59—21no—
262C23×C59—21no—
263C23×C59—21no—
264C23×C59—24no—
265C23×C59—24no—
266C23×C59—24no—
267C23×C59—24no—
268C23×C59—24no—
269C23×C59—24no—
270C23×C59—24no—
271C23×C59C22×D412yes—
272C23×C59C2×#4112yes—
273C23×C59C2×#4112yes—
274C23×C59C2511yescharacteristic
275C22×D59—28no—
276C22×D59—22no—
277C22×D59—22no—
278C22×D59—22no—
279C22×D59—22no—
280C22×D59—22no—
281C22×D59—22no—
282C22×D59—44no—
283C22×D59—44no—
284C22×D59—44no—
285C22×D59—44no—
286C22×D59—44no—
287C22×D59—44no—
288C22×D59C22×D414yes—
289D4×C59—416no—
290D4×C59—48no—
291D4×C59—84no—
292D4×C59—84no—
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—21no—
303C2×C4×C59—28no—
304C2×C4×C59—24no—
305C2×C4×C59—24no—
306C2×C4×C59—24no—
307C2×C4×C59—44no—
308C2×C4×C59—44no—
309C2×C4×C59C22×D412yes—
310C2×C4×C59C22×D412yes—
311C2×C4×C59C2×#4112yes—
312C2×C4×C59C2×#4112yes—
313C2×C4×C59C2×#4112yes—
314C2×C4×C59C2×#4112yes—
315C2×C4×C59H(5,𝔽2)12yes—
316C2×C4×C59H(5,𝔽2)12yes—
317C22⋊D59—88no—
318C22⋊D59—88no—
319C2×Dic59—22no—
320C2×Dic59—22no—
321C2×Dic59—24no—
322C2×Dic59—24no—
323C2×Dic59—22no—
324C2×Dic59—22no—
325C2×Dic59—22no—
326C2×Dic59—24no—
327C2×Dic59—24no—
328C2×Dic59—22no—
329C2×Dic59—22no—
330C2×Dic59—24no—
331C2×Dic59—22no—
332C2×Dic59—24no—
333C2×Dic59—44no—
334C2×Dic59—44no—
335C2×Dic59—44no—
336C2×Dic59—88no—
337C2×Dic59C22×D414yes—
338C4×D59—48no—
339C4×D59—48no—
340Dic118—84no—
341#35005—591nomaximal, Sylow
342C22×C59—22no—
343C22×C59—22no—
344C22×C59—22no—
345C22×C59—22no—
346C22×C59—22no—
347C22×C59—22no—
348C22×C59—44no—
349C22×C59—44no—
350C22×C59—44no—
351C22×C59—44no—
352C22×C59—44no—
353C22×C59—44no—
354C22×C59—44no—
355C22×C59#53214yes—
356C22×C59C23×D411yescharacteristic
357C22×C59C22×#4111yescharacteristic
358C22×C59C22×#4111yescharacteristic
359C22×C59C2×H(5,𝔽2)11yescharacteristic
360C22×C59C2×H(5,𝔽2)11yescharacteristic
361C22×C59#58511yescharacteristic
362C22×C59#58511yescharacteristic
363C2×D59—24no—
364C2×D59—24no—
365C2×D59—24no—
366C2×D59—416no—
367C2×D59—42no—
368C2×D59—42no—
369C2×D59—42no—
370C2×D59—42no—
371C4×C59—22no—
372C4×C59—22no—
373C4×C59—22no—
374C4×C59—22no—
375C4×C59—22no—
376C4×C59—44no—
377C4×C59#53814yescomplemented
378Dic59—24no—
379Dic59—42no—
380Dic59—44no—
381Dic59—44no—
382Dic59—42no—
383C2×#538—592no—
384#2857—591no—
385#2856D5911yescharacteristic, complemented
386#2847—592no—
387#2639—592no—
388#2617—592no—
389#2559—594no—
390#2557—594no—
391#2496—592no—
392#2491—592no—
393#2428—592no—
394#2422—592no—
395#2325—592no—
396C4×#121—592no—
397C2×C4×C22⋊C4—591no—
398C2×C59—24no—
399C2×C59—84no—
400C2×C59C2×#53211yescharacteristic
401C2×C59C2×#53811yescharacteristic
402C2×C59#345511yescharacteristic
403C2×C59#349611yescharacteristic
404C2×C59#349611yescharacteristic
405C2×C59#350511yescharacteristic
406C2×C59#350611yescharacteristic
407D59—44no—
408C24×C4—591no—
409#538—11816no—
410C2×C4⋊Q8—591no—
411C2×#127C2×D5911yescharacteristic, complemented
412C2×#126—594no—
413C2×#124—594no—
414C2×#123—594no—
415C2×C22⋊Q8—592no—
416C2×#121—594no—
417C2×#121—592no—
418C2×#121—592no—
419C2×#121C2×D5912yes—
420C2×#121C2×D5912yes—
421C2×#121C2×D5912yes—
422C2×#120—594no—
423C2×C4×D4—594no—
424C2×C4×D4—592no—
425C22×C22⋊C4—591no—
426C22×C22⋊C4—591no—
427C22×C42—591no—
428C22×C42C2×D5911yescharacteristic
429#400—594no—
430#397—594no—
431#397—594no—
432#394—594no—
433#394—594no—
434#394—594no—
435#393—594no—
436#392—594no—
437#391—592no—
438#390—592no—
439#390C2×D5912yescomplemented
440#390C2×D5912yescomplemented
441#390C2×D5912yescomplemented
442#389—592no—
443#389—592no—
444#389—592no—
445#388—594no—
446#388—594no—
447#387—594no—
448#386—594no—
449#386—594no—
450#386—594no—
451#386—594no—
452#386—594no—
453#385—594no—
454#384—591no—
455#384C2×D5911yescharacteristic, complemented
456#380—592no—
457#380—592no—
458#380—592no—
459#380—592no—
460C4×C4⋊C4—592no—
461C4×C22⋊C4—594no—
462C4×C22⋊C4—592no—
463C4×C22⋊C4—592no—
464C4×C22⋊C4—592no—
465C4×C22⋊C4—592no—
466C2×#95—591no—
467C2×#95—591no—
468C59#3500511yescharacteristic, complemented, Sylow
469C25—591no—
470C22×Q8—592no—
471C22×D4—594no—
472C22×D4—594no—
473C22×D4C22×D5914yes—
474C22×D4C22×D5912yes—
475C22×D4C22×D5912yes—
476C22×D4C22×D5912yes—
477C23×C4—591no—
478C23×C4—591no—
479C23×C4—594no—
480C23×C4—591no—
481C23×C4—592no—
482C23×C4—592no—
483C23×C4—1184no—
484C23×C4—2362no—
485C23×C4—2362no—
486C23×C4C22×D5911yescharacteristic
487C23×C4C22×D5911yescharacteristic
488C23×C4C22×D5911yescharacteristic
489C4⋊Q8—2362no—
490#127—42no—
491#126—11816no—
492#124—11816no—
493#123—11816no—
494C22⋊Q8—1188no—
495#121—28no—
496#121—28no—
497#121—28no—
498#121—11816no—
499#121—2364no—
500#121—2364no—
501#120—11816no—
502C4×D4—11816no—
503C4×D4—2364no—
504C2×C4⋊C4—592no—
505C2×C4⋊C4—594no—
506C2×C4⋊C4—594no—
507C2×C4⋊C4—592no—
508C2×C4⋊C4—592no—
509C2×C4⋊C4—592no—
510C2×C4⋊C4—592no—
511C2×C4⋊C4C22×D5912yes—
512C2×C4⋊C4C22×D5912yes—
513C2×C4⋊C4C22×D5912yes—
514C2×C22⋊C4—598no—
515C2×C22⋊C4—592no—
516C2×C22⋊C4—592no—
517C2×C22⋊C4—594no—
518C2×C22⋊C4—594no—
519C2×C22⋊C4—592no—
520C2×C22⋊C4—592no—
521C2×C22⋊C4—594no—
522C2×C22⋊C4—594no—
523C2×C22⋊C4—594no—
524C2×C22⋊C4—594no—
525C2×C22⋊C4—594no—
526C2×C22⋊C4—594no—
527C2×C22⋊C4—1184no—
528C2×C22⋊C4C22×D5914yes—
529C2×C22⋊C4C22×D5914yes—
530C2×C22⋊C4C22×D5914yes—
531C2×C42—42no—
532C2×C42—594no—
533C2×C42—592no—
534C2×C42—592no—
535C2×C42—2362no—
536C2×C42C22×D5911yescharacteristic
537C2×C42C22×D5911yescharacteristic
538C2×C42C22×D5911yescharacteristic
539C2×C42C22×D5911yescharacteristic
540#95—592no—
541#95—592no—
542#95—592no—
543#95—592no—
544#95—594no—
545#95—594no—
546#95—594no—
547#95—594no—
548#95—594no—
549#95—594no—
550C24—592no—
551C24—594no—
552C24—1182no—
553C24—1182no—
554C24—2361no—
555C24—2361no—
556C24—2361no—
557C24—2361no—
558C24C23×D5914yes—
559C24C23×D5911yescharacteristic
560C2×Q8—1184no—
561C2×Q8—2362no—
562C2×Q8—2362no—
563C2×D4—28no—
564C2×D4—28no—
565C2×D4—28no—
566C2×D4—24no—
567C2×D4—24no—
568C2×D4—24no—
569C2×D4—24no—
570C2×D4—24no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—42no—
574C2×D4—42no—
575C2×D4—1188no—
576C2×D4—1188no—
577C2×D4—2364no—
578C2×D4—2364no—
579C2×D4—2364no—
580C2×D4—2364no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—592no—
588C22×C4—594no—
589C22×C4—592no—
590C22×C4—592no—
591C22×C4—594no—
592C22×C4—594no—
593C22×C4—1188no—
594C22×C4—1182no—
595C22×C4—1182no—
596C22×C4—1184no—
597C22×C4—1184no—
598C22×C4—1184no—
599C22×C4—1184no—
600C22×C4—2362no—
601C22×C4—2362no—
602C22×C4—23616no—
603C22×C4—2364no—
604C22×C4—2364no—
605C22×C4—2361no—
606C22×C4—2361no—
607C22×C4—2361no—
608C22×C4—2361no—
609C22×C4—2361no—
610C22×C4—2361no—
611C22×C4D4×D5914yes—
612C22×C4#1174568714yes—
613C22×C4#1174568714yes—
614C22×C4C23×D5914yes—
615C22×C4C23×D5911yescharacteristic
616C22×C4C23×D5911yescharacteristic
617C22×C4C23×D5911yescharacteristic
618C22×C4C23×D5911yescharacteristic
619C22×C4C23×D5911yescharacteristic
620C22×C4C23×D5911yescharacteristic
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—1188no—
625C4⋊C4—1188no—
626C4⋊C4—1184no—
627C4⋊C4—1184no—
628C4⋊C4—1184no—
629C4⋊C4—2362no—
630C4⋊C4—2362no—
631C22⋊C4—28no—
632C22⋊C4—28no—
633C22⋊C4—28no—
634C22⋊C4—598no—
635C22⋊C4—598no—
636C22⋊C4—1188no—
637C22⋊C4—1188no—
638C22⋊C4—1188no—
639C22⋊C4—1188no—
640C22⋊C4—1184no—
641C22⋊C4—1184no—
642C22⋊C4—2364no—
643C22⋊C4—2364no—
644C22⋊C4—2364no—
645C22⋊C4—2364no—
646C42—22no—
647C42—22no—
648C42—41no—
649C42—41no—
650C42—1188no—
651C42—1184no—
652C42—2362no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—594no—
665C23—1188no—
666C23—1182no—
667C23—1182no—
668C23—1182no—
669C23—1182no—
670C23—1182no—
671C23—1182no—
672C23—2364no—
673C23—2364no—
674C23—2364no—
675C23—2364no—
676C23—2364no—
677C23—2364no—
678C23C2×D4×D5912yes—
679C23C2×#1174568712yes—
680C23C2×#1174568712yes—
681C23C24×D5911yescharacteristic
682Q8—4724no—
683D4—416no—
684D4—48no—
685D4—84no—
686D4—84no—
687D4—4728no—
688D4—4728no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—28no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—594no—
706C2×C4—1182no—
707C2×C4—1182no—
708C2×C4—1184no—
709C2×C4—1184no—
710C2×C4—1182no—
711C2×C4—1182no—
712C2×C4—1182no—
713C2×C4—1184no—
714C2×C4—1182no—
715C2×C4—1184no—
716C2×C4—1182no—
717C2×C4—1182no—
718C2×C4—1184no—
719C2×C4—1184no—
720C2×C4—4728no—
721C2×C4—2368no—
722C2×C4—2364no—
723C2×C4—2364no—
724C2×C4—2364no—
725C2×C4—2368no—
726C2×C4C2×D4×D5912yes—
727C2×C4C2×D4×D5912yes—
728C2×C4C2×#1174568712yes—
729C2×C4C2×#1174568712yes—
730C2×C4C2×#1174568712yes—
731C2×C4C2×#1174568712yes—
732C2×C4#1427377212yes—
733C2×C4#1427377312yes—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—22no—
739C22—22no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—44no—
744C22—44no—
745C22—44no—
746C22—44no—
747C22—1184no—
748C22—1184no—
749C22—1184no—
750C22—23616no—
751C22—2362no—
752C22—2362no—
753C22—2362no—
754C22—2362no—
755C22#1683795014yes—
756C22C22×D4×D5911yescharacteristic
757C22C22×#1174568711yescharacteristic
758C22C22×#1174568711yescharacteristic
759C22C2×#1427377211yescharacteristic
760C22C2×#1427377311yescharacteristic
761C22#1683823811yescharacteristic
762C22#1683823811yescharacteristic
763C4—22no—
764C4—22no—
765C4—22no—
766C4—22no—
767C4—22no—
768C4—44no—
769C4—1184no—
770C4—2364no—
771C4—2364no—
772C4—2362no—
773C4—2362no—
774C4#1683798914yescomplemented
775C2—24no—
776C2—84no—
777C2—2364no—
778C2C2×#1683795011yescharacteristic
779C2C2×#1683798911yescharacteristic
780C2#2143748511yescharacteristic
781C2#2143785311yescharacteristic
782C2#2143785811yescharacteristic
783C2#2143793011yescharacteristic
784C2#2143794511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D59
commutator, socle, cosocleC23×C59C25
FittingC59×#2856C2
hypercenter#2856D59
hypocenterC59#35005
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #2856

Complements

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

NH ≅ G/Ntype
1. C2×#16837989C2semidirect
2. #21432448C2semidirect
3. #21432375C2semidirect
4. #21430029C2semidirect
5. #21429832C2semidirect
6. #21429230C2semidirect
7. #21429200C2semidirect
8. #21428521C2semidirect
9. #21428457C2semidirect
10. #21427687C2semidirect
11. #21427608C2semidirect
12. #21426801C2semidirect
13. #121×Dic59C2semidirect
14. C2×C4×(C2×D59)⋊C4C2semidirect
15. C59×#2856C2semidirect
18. C2×#14273727C22semidirect
28. C2×D4×Dic59C22semidirect
32. #16837340C22semidirect
34. #16837327C22semidirect
37. #16837316C22semidirect
38. #16837314C22semidirect
40. #16837308C22semidirect
41. #16837305C22semidirect
42. #16837301C22semidirect
43. #16837300C22semidirect
44. #16837300C22semidirect
45. #16837295C22semidirect
46. #16837295C22semidirect
47. #16837288C22semidirect
50. #16837282C22semidirect
53. #16837277C22semidirect
54. #16837272C22semidirect
59. C4⋊C4×Dic59C22semidirect
60. C22⋊C4×Dic59C22semidirect
67. C2×#127×C59C22semidirect
72. C59×#390C22semidirect
73. C59×#390C22semidirect
74. C59×#390C22semidirect
75. C59×#384C22semidirect
114. C2×(C2×D59)⋊C4D4semidirect
377. C4×C59#538semidirect
385. #2856D59semidirect
411. C2×#127C2×D59semidirect
439. #390C2×D59semidirect
440. #390C2×D59semidirect
441. #390C2×D59semidirect
455. #384C2×D59semidirect
468. C59#35005semidirect
774. C4#16837989semidirect

Maximal subgroups

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

subgroupindex
C2×#168379892
#214324482
#214323752
#214300292
#214298322
#214292302
#214292002
#214285212
#214284572
#214276872
#214276082
#214268012
#121×Dic592
C2×C4×(C2×D59)⋊C42
C59×#28562
#3500559