Finite Group Databasebeta

← #28761276

Subgroups — #28761276

Order 15104.

2866 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838028C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D59C211yesmaximal, characteristic
3#21432432C212yesmaximal, complemented
4#21432382C212yesmaximal, complemented
5#21429915C212yesmaximal, complemented
6#21429907C212yesmaximal, complemented
7#21427922C214yesmaximal, complemented
8#21427920C214yesmaximal, complemented
9#21427907C214yesmaximal, complemented
10#21427905C214yesmaximal, complemented
11#21426708C211yesmaximal, characteristic, complemented
12#21426671C211yesmaximal, characteristic
13#21426671C211yesmaximal, characteristic
14C2×#16837275C211yesmaximal, characteristic, complemented
15C2×C59×#385C211yesmaximal, characteristic, complemented
16C23×C22⋊D59C2211yescharacteristic
17C23×C4×D59C2211yescharacteristic
18#16838028—28no—
19C2×#14273706C2212yescomplemented
20C2×#14273706C2212yescomplemented
21C2×#14273705C2214yescomplemented
22C2×#14273704C2212yes—
23C2×#14273704C2212yes—
24C2×#14273704C2212yescomplemented
25C2×#14273704C2212yescomplemented
26C2×C4×C22⋊D59—28no—
27C2×C4×C22⋊D59C2214yes—
28C2×C4×C22⋊D59C2214yes—
29C22×Dic59⋊C4C2211yescharacteristic
30C22×Dic59⋊C4C2212yescomplemented
31C22×C22⋊Dic59C2211yescharacteristic
32C22×C22⋊Dic59C2211yescharacteristic
33C22×C22⋊Dic59C2211yescharacteristic
34C22×(C2×D59)⋊C4C2211yescharacteristic
35C22×C4×Dic59C2211yescharacteristic
36#16837343C2214yescomplemented
37#16837337C2214yescomplemented
38#16837336C2214yescomplemented
39#16837333C2214yescomplemented
40#16837326C2214yescomplemented
41#16837324C2214yescomplemented
42#16837322C2214yescomplemented
43#16837315C2214yescomplemented
44#16837306C2214yescomplemented
45#16837297C2214yescomplemented
46#16837288C2214yescomplemented
47#16837284C2214yescomplemented
48#16837281C2212yes—
49#16837281C2214yes—
50#16837281C2212yes—
51#16837279C2212yes—
52#16837279C2214yes—
53#16837279C2212yes—
54#16837276C2214yescomplemented
55#16837275C2212yes—
56#16837275C2212yes—
57#16837275C2214yescomplemented
58#16837275C2214yescomplemented
59#16837274C2214yescomplemented
60#16837273C2214yescomplemented
61#16837263C2212yes—
62#16837263C2212yes—
63#16837261C2214yescomplemented
64#16837260C2212yes—
65#16837260C2212yes—
66#16837257C2212yes—
67#16837257C2212yes—
68C2×C59⋊#95C2212yescomplemented
69C24×C4×C59C2211yescharacteristic
70C22×C4⋊C4×C59C2212yescomplemented
71C22×C22⋊C4×C59C2211yescharacteristic
72C22×C22⋊C4×C59C2211yescharacteristic
73C59×#385C2212yes—
74C59×#385C2212yes—
75C59×#385C2214yescomplemented
76C2×#95×C59C2212yescomplemented
77C24×D59C2311yescharacteristic
78C22×Dic118C2312yes—
79C22×Dic118C2312yes—
80C22×C22⋊D59—24no—
81C22×C22⋊D59—24no—
82C22×C22⋊D59Q818yescomplemented
83C22×C22⋊D59C2312yes—
84C22×C22⋊D59C2312yes—
85C23×Dic59C2311yescharacteristic
86C23×Dic59C2311yescharacteristic
87C23×Dic59C2311yescharacteristic
88C23×Dic59C2312yes—
89C23×Dic59C2311yescharacteristic
90C23×Dic59C2311yescharacteristic
91C22×C4×D59—24no—
92C22×C4×D59—44no—
93C22×C4×D59C2314yes—
94#14273706—28no—
95#14273706—28no—
96#14273705—48no—
97#14273704—28no—
98#14273704—28no—
99#14273704—28no—
100#14273704—28no—
101C4×C22⋊D59—216no—
102C4×C22⋊D59—216no—
103C2×C4⋊Dic59C2312yes—
104C2×C4⋊Dic59C2312yes—
105C2×Dic59⋊C4—24no—
106C2×Dic59⋊C4—44no—
107C2×Dic59⋊C4C2312yes—
108C2×Dic59⋊C4C2312yes—
109C2×Dic59⋊C4C2312yes—
110C2×Dic59⋊C4C2312yes—
111C2×Dic59⋊C4C2314yes—
112C2×Dic59⋊C4C2314yes—
113C2×Dic59⋊C4C2314yes—
114C2×Dic59⋊C4C2314yes—
115C2×Dic59⋊C4C2314yes—
116C2×C22⋊Dic59—24no—
117C2×C22⋊Dic59—24no—
118C2×C22⋊Dic59D418yes—
119C2×C22⋊Dic59C2312yes—
120C2×C22⋊Dic59C2312yes—
121C2×C22⋊Dic59C2312yes—
122C2×C22⋊Dic59C2312yes—
123C2×C22⋊Dic59C2312yes—
124C2×C22⋊Dic59C2312yes—
125C2×(C2×D59)⋊C4—24no—
126C2×(C2×D59)⋊C4C2314yes—
127C2×(C2×D59)⋊C4C2314yes—
128C2×(C2×D59)⋊C4C2314yes—
129C2×(C2×D59)⋊C4C2314yes—
130C2×(C2×D59)⋊C4C2314yes—
131C2×C4×Dic59—24no—
132C2×C4×Dic59C2314yes—
133C59⋊#95C2314yes—
134C59⋊#95C2314yes—
135C59⋊#95C2314yes—
136C59⋊#95C2314yes—
137C59⋊#95C2314yes—
138C59⋊#95C2314yes—
139C59⋊#95C2314yes—
140C59⋊#95C2314yes—
141C25×C59C2311yescharacteristic
142C23×C4×C59—24no—
143C23×C4×C59—44no—
144C23×C4×C59C2311yescharacteristic
145C23×C4×C59C2312yes—
146C23×C4×C59C2312yes—
147C23×C4×C59C2311yescharacteristic
148C23×C4×C59C2311yescharacteristic
149C23×C4×C59C2312yes—
150C23×C4×C59C2311yescharacteristic
151C2×C4⋊C4×C59—44no—
152C2×C4⋊C4×C59C2314yes—
153C2×C4⋊C4×C59C2314yes—
154C2×C22⋊C4×C59—24no—
155C2×C22⋊C4×C59—24no—
156C2×C22⋊C4×C59C2312yes—
157C2×C22⋊C4×C59C2312yes—
158C2×C22⋊C4×C59C2312yes—
159C2×C22⋊C4×C59C2312yes—
160#95×C59C2314yes—
161#95×C59C2314yes—
162C24×C59—42no—
163C24×C59—42no—
164C24×C59C2×D414yes—
165C24×C59C2×Q814yes—
166C24×C59#4114yes—
167C24×C59C2411yescharacteristic
168C24×C59C2411yescharacteristic
169C24×C59C2411yescharacteristic
170C23×D59—22no—
171C23×D59—22no—
172C23×D59—42no—
173C23×D59—42no—
174C23×D59C2×Q814yes—
175C23×D59C2412yes—
176C22×C4×C59—22no—
177C22×C4×C59—24no—
178C22×C4×C59—22no—
179C22×C4×C59—24no—
180C22×C4×C59—24no—
181C22×C4×C59—24no—
182C22×C4×C59—22no—
183C22×C4×C59—22no—
184C22×C4×C59—24no—
185C22×C4×C59—24no—
186C22×C4×C59—42no—
187C22×C4×C59—42no—
188C22×C4×C59—42no—
189C22×C4×C59—42no—
190C22×C4×C59—42no—
191C22×C4×C59—42no—
192C22×C4×C59—42no—
193C22×C4×C59—416no—
194C22×C4×C59C2412yes—
195C22×C4×C59C2414yes—
196C22×C4×C59C2412yes—
197C22×C4×C59C2412yes—
198C22×C4×C59C2412yes—
199C2×C22⋊D59—232no—
200C2×C22⋊D59—24no—
201C2×C22⋊D59—24no—
202C2×C22⋊D59—24no—
203C2×C22⋊D59—24no—
204C2×C22⋊D59C2×Q818yes—
205C2×C22⋊D59C2×Q818yes—
206C22×Dic59—22no—
207C22×Dic59—22no—
208C22×Dic59—24no—
209C22×Dic59—22no—
210C22×Dic59—22no—
211C22×Dic59—42no—
212C22×Dic59—42no—
213C22×Dic59—42no—
214C22×Dic59—42no—
215C22×Dic59—42no—
216C22×Dic59—42no—
217C22×Dic59C2×D414yes—
218C22×Dic59C2×D414yes—
219C22×Dic59C2×Q814yes—
220C22×Dic59C2414yes—
221C22×Dic59C2412yes—
222C22×Dic59C2412yes—
223C22×Dic59C2412yes—
224C22×Dic59C2412yes—
225C22×Dic59C2412yes—
226C2×C4×D59—28no—
227C2×C4×D59—28no—
228C2×C4×D59—44no—
229C2×C4×D59—416no—
230C2×Dic118—24no—
231C2×Dic118—24no—
232C2×Dic118—44no—
233C2×Dic118—44no—
234C4⋊C4×C59—28no—
235C4⋊C4×C59—44no—
236C22⋊C4×C59—24no—
237C22⋊C4×C59—24no—
238C22⋊C4×C59—24no—
239C22⋊C4×C59—24no—
240C22⋊Dic59—24no—
241C22⋊Dic59—24no—
242C22⋊Dic59—24no—
243C22⋊Dic59—24no—
244C22⋊Dic59C2×D418yes—
245C22⋊Dic59C2×D418yes—
246(C2×D59)⋊C4—28no—
247(C2×D59)⋊C4—44no—
248(C2×D59)⋊C4—44no—
249(C2×D59)⋊C4—44no—
250(C2×D59)⋊C4—44no—
251C4⋊Dic59—24no—
252C4⋊Dic59—24no—
253Dic59⋊C4—28no—
254Dic59⋊C4—28no—
255Dic59⋊C4—24no—
256Dic59⋊C4—24no—
257Dic59⋊C4—24no—
258Dic59⋊C4—24no—
259Dic59⋊C4—44no—
260Dic59⋊C4—44no—
261Dic59⋊C4—44no—
262C4×Dic59—28no—
263C23×C59—22no—
264C23×C59—22no—
265C23×C59—22no—
266C23×C59—22no—
267C23×C59—22no—
268C23×C59—22no—
269C23×C59—44no—
270C23×C59—44no—
271C23×C59—48no—
272C23×C59—48no—
273C23×C59C22⋊Q8116yescomplemented
274C23×C59C22×D412yes—
275C23×C59C22×D412yes—
276C23×C59C22×D412yes—
277C23×C59C22×Q812yes—
278C23×C59C22×Q812yes—
279C23×C59C22×Q812yes—
280C23×C59C2×#4112yes—
281C23×C59C2×#4112yes—
282C23×C59C2×#4112yes—
283C23×C59C2511yescharacteristic
284C22×D59—28no—
285C22×D59—22no—
286C22×D59—22no—
287C22×D59—24no—
288C22×D59—24no—
289C22×D59—48no—
290C22×D59—44no—
291C22×D59—48no—
292C22×D59—44no—
293C22×D59C22×Q814yes—
294C2×C4×C59—28no—
295C2×C4×C59—22no—
296C2×C4×C59—22no—
297C2×C4×C59—22no—
298C2×C4×C59—22no—
299C2×C4×C59—22no—
300C2×C4×C59—24no—
301C2×C4×C59—22no—
302C2×C4×C59—24no—
303C2×C4×C59—24no—
304C2×C4×C59—22no—
305C2×C4×C59—24no—
306C2×C4×C59—24no—
307C2×C4×C59—48no—
308C2×C4×C59—48no—
309C2×C4×C59—48no—
310C2×C4×C59—44no—
311C2×C4×C59—82no—
312C2×C4×C59—82no—
313C2×C4×C59H(5,𝔽2)14yes—
314C22⋊D59—216no—
315C22⋊D59—216no—
316C2×Dic59—28no—
317C2×Dic59—22no—
318C2×Dic59—22no—
319C2×Dic59—24no—
320C2×Dic59—24no—
321C2×Dic59—22no—
322C2×Dic59—22no—
323C2×Dic59—24no—
324C2×Dic59—24no—
325C2×Dic59—24no—
326C2×Dic59—24no—
327C2×Dic59—24no—
328C2×Dic59—44no—
329C2×Dic59—44no—
330C2×Dic59—48no—
331C2×Dic59—82no—
332C2×Dic59—82no—
333C2×Dic59C22×D414yes—
334C2×Dic59C22×D414yes—
335C2×Dic59C22×Q814yes—
336C4×D59—416no—
337Dic118—84no—
338Dic118—84no—
339#34985—591nomaximal, Sylow
340C22×C59—24no—
341C22×C59—24no—
342C22×C59—24no—
343C22×C59—22no—
344C22×C59—22no—
345C22×C59—22no—
346C22×C59—22no—
347C22×C59—22no—
348C22×C59—22no—
349C22×C59—24no—
350C22×C59—24no—
351C22×C59—24no—
352C22×C59—416no—
353C22×C59C2×C22⋊Q814yes—
354C22×C59C2×C22⋊Q814yes—
355C22×C59C2×C22⋊Q814yes—
356C22×C59C23×D411yescharacteristic
357C22×C59C23×Q811yescharacteristic
358C22×C59C22×#4111yescharacteristic
359C22×C59C2×H(5,𝔽2)12yes—
360C22×C59#58512yes—
361C2×D59—24no—
362C2×D59—28no—
363C2×D59—416no—
364C2×D59—44no—
365C2×D59—42no—
366C2×D59—42no—
367C4×C59—24no—
368C4×C59—44no—
369C4×C59—42no—
370C4×C59—42no—
371C4×C59—42no—
372Dic59—24no—
373Dic59—24no—
374Dic59—24no—
375Dic59—44no—
376Dic59—42no—
377Dic59—42no—
378C2×#543—591no—
379C22×C4×D4—591no—
380#2855—592no—
381#2848—592no—
382#2627—592no—
383#2626—592no—
384#2450—594no—
385#2450—594no—
386#2449—594no—
387#2449—594no—
388#2315—591no—
389#2308—591no—
390#2308—591no—
391C2×#385—591no—
392C2×#385D5911yescharacteristic, complemented
393C2×C59—24no—
394C2×C59—24no—
395C2×C59—24no—
396C2×C59C22×C22⋊Q811yescharacteristic
397C2×C59#345912yes—
398C2×C59#348411yescharacteristic
399C2×C59#348511yescharacteristic
400C2×C59#350112yes—
401D59—44no—
402C23×D4—591no—
403C24×C4—591no—
404C24×C4C2×D5911yescharacteristic
405#543—1188no—
406C2×C22⋊Q8—592no—
407C2×C22⋊Q8—592no—
408C2×C22⋊Q8—594no—
409C2×C22⋊Q8—592no—
410C2×C22⋊Q8—592no—
411C2×C22⋊Q8—592no—
412C2×C22⋊Q8—592no—
413C2×C4×D4—594no—
414C2×C4×D4—594no—
415C2×C4×D4—1188no—
416C22×C4⋊C4—591no—
417C22×C4⋊C4—592no—
418C22×C4⋊C4C2×D5912yescomplemented
419C22×C22⋊C4—591no—
420C22×C22⋊C4—591no—
421C22×C22⋊C4—591no—
422C22×C22⋊C4—591no—
423C22×C22⋊C4C2×D5911yescharacteristic
424C22×C22⋊C4C2×D5911yescharacteristic
425C22×C42—591no—
426#400—594no—
427#399—594no—
428#398—594no—
429#398—594no—
430#396—594no—
431#396—594no—
432#395—594no—
433#393—594no—
434#391—594no—
435#389—594no—
436#387—594no—
437#387—594no—
438#386—592no—
439#386—594no—
440#386—592no—
441#386—592no—
442#386—594no—
443#386—592no—
444#385—594no—
445#385—592no—
446#385—592no—
447#385—594no—
448#385—594no—
449#385—594no—
450#385—594no—
451#385C2×D5912yes—
452#385C2×D5912yes—
453#385C2×D5914yescomplemented
454#381—592no—
455#381—592no—
456#380—592no—
457#380—592no—
458#380—594no—
459#379—592no—
460#379—592no—
461C2×#95—592no—
462C2×#95C2×D5912yescomplemented
463C59#3498511yescharacteristic, complemented, Sylow
464C25—591no—
465C25C22×D5911yescharacteristic
466C22×Q8—592no—
467C22×Q8—592no—
468C22×D4—598no—
469C22×D4—592no—
470C22×D4—592no—
471C22×D4—1184no—
472C22×D4—1184no—
473C23×C4—24no—
474C23×C4—44no—
475C23×C4—591no—
476C23×C4—591no—
477C23×C4—591no—
478C23×C4—591no—
479C23×C4—592no—
480C23×C4—591no—
481C23×C4—594no—
482C23×C4—1184no—
483C23×C4—2364no—
484C23×C4C22×D5911yescharacteristic
485C23×C4C22×D5912yes—
486C23×C4C22×D5912yes—
487C23×C4C22×D5911yescharacteristic
488C23×C4C22×D5911yescharacteristic
489C23×C4C22×D5912yes—
490C23×C4C22×D5911yescharacteristic
491C22⋊Q8—1188no—
492C22⋊Q8—1188no—
493C22⋊Q8—1188no—
494C22⋊Q8—1188no—
495C22⋊Q8—1188no—
496C22⋊Q8—1188no—
497C22⋊Q8—2368no—
498C4×D4—11816no—
499C4×D4—11816no—
500C2×C4⋊C4—44no—
501C2×C4⋊C4—594no—
502C2×C4⋊C4—594no—
503C2×C4⋊C4—592no—
504C2×C4⋊C4—592no—
505C2×C4⋊C4—592no—
506C2×C4⋊C4—592no—
507C2×C4⋊C4—592no—
508C2×C4⋊C4—592no—
509C2×C4⋊C4—594no—
510C2×C4⋊C4—594no—
511C2×C4⋊C4—594no—
512C2×C4⋊C4—1184no—
513C2×C4⋊C4—2364no—
514C2×C4⋊C4C22×D5914yes—
515C2×C4⋊C4C22×D5914yes—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—598no—
519C2×C22⋊C4—592no—
520C2×C22⋊C4—592no—
521C2×C22⋊C4—592no—
522C2×C22⋊C4—592no—
523C2×C22⋊C4—592no—
524C2×C22⋊C4—592no—
525C2×C22⋊C4—594no—
526C2×C22⋊C4—594no—
527C2×C22⋊C4—594no—
528C2×C22⋊C4—594no—
529C2×C22⋊C4—594no—
530C2×C22⋊C4—1184no—
531C2×C22⋊C4—1184no—
532C2×C22⋊C4—1184no—
533C2×C22⋊C4C22×D5912yes—
534C2×C22⋊C4C22×D5912yes—
535C2×C22⋊C4C22×D5912yes—
536C2×C22⋊C4C22×D5912yes—
537C2×C42—594no—
538C2×C42—1184no—
539#95—594no—
540#95—594no—
541#95—594no—
542#95—594no—
543#95—594no—
544#95—594no—
545#95—594no—
546#95—594no—
547#95C22×D5914yes—
548#95C22×D5914yes—
549C24—42no—
550C24—42no—
551C24—592no—
552C24—594no—
553C24—1182no—
554C24—1182no—
555C24—2362no—
556C24—2362no—
557C24#1174568514yes—
558C24D4×D5914yes—
559C24Q8×D5914yes—
560C24C23×D5911yescharacteristic
561C24C23×D5911yescharacteristic
562C24C23×D5911yescharacteristic
563C2×Q8—1184no—
564C2×Q8—1184no—
565C2×Q8—2364no—
566C2×Q8—2364no—
567C2×D4—598no—
568C2×D4—598no—
569C2×D4—11832no—
570C2×D4—1184no—
571C2×D4—1184no—
572C2×D4—1184no—
573C2×D4—1184no—
574C22×C4—22no—
575C22×C4—24no—
576C22×C4—22no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—416no—
592C22×C4—594no—
593C22×C4—592no—
594C22×C4—592no—
595C22×C4—592no—
596C22×C4—594no—
597C22×C4—594no—
598C22×C4—594no—
599C22×C4—592no—
600C22×C4—592no—
601C22×C4—1188no—
602C22×C4—1182no—
603C22×C4—1182no—
604C22×C4—1182no—
605C22×C4—1182no—
606C22×C4—1184no—
607C22×C4—1188no—
608C22×C4—2364no—
609C22×C4—23616no—
610C22×C4—2362no—
611C22×C4—2362no—
612C22×C4—2362no—
613C22×C4—2362no—
614C22×C4—2362no—
615C22×C4—2362no—
616C22×C4C23×D5914yes—
617C22×C4C23×D5912yes—
618C22×C4C23×D5912yes—
619C22×C4C23×D5912yes—
620C22×C4C23×D5912yes—
621C4⋊C4—28no—
622C4⋊C4—44no—
623C4⋊C4—1188no—
624C4⋊C4—1184no—
625C4⋊C4—1184no—
626C4⋊C4—1184no—
627C4⋊C4—1184no—
628C4⋊C4—1184no—
629C4⋊C4—1184no—
630C4⋊C4—1188no—
631C4⋊C4—2364no—
632C4⋊C4—2364no—
633C4⋊C4—2364no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—598no—
639C22⋊C4—598no—
640C22⋊C4—1188no—
641C22⋊C4—1184no—
642C22⋊C4—1184no—
643C22⋊C4—1184no—
644C22⋊C4—1184no—
645C22⋊C4—2364no—
646C22⋊C4—2364no—
647C22⋊C4—2364no—
648C22⋊C4—2364no—
649C42—1188no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—44no—
657C23—48no—
658C23—44no—
659C23—48no—
660C23—594no—
661C23—1188no—
662C23—1182no—
663C23—1182no—
664C23—1184no—
665C23—1184no—
666C23—2368no—
667C23—2364no—
668C23—2364no—
669C23—2368no—
670C23#14273705116yescomplemented
671C23C2×D4×D5912yes—
672C23C2×D4×D5912yes—
673C23C2×D4×D5912yes—
674C23C2×Q8×D5912yes—
675C23C2×Q8×D5912yes—
676C23C2×Q8×D5912yes—
677C23C2×#1174568512yes—
678C23C2×#1174568512yes—
679C23C2×#1174568512yes—
680C23C24×D5911yescharacteristic
681Q8—4724no—
682Q8—4724no—
683D4—11816no—
684D4—11816no—
685C2×C4—28no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—48no—
699C2×C4—48no—
700C2×C4—48no—
701C2×C4—44no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4—594no—
705C2×C4—594no—
706C2×C4—594no—
707C2×C4—1188no—
708C2×C4—1182no—
709C2×C4—1182no—
710C2×C4—1184no—
711C2×C4—1184no—
712C2×C4—1182no—
713C2×C4—1182no—
714C2×C4—1184no—
715C2×C4—1184no—
716C2×C4—1184no—
717C2×C4—1184no—
718C2×C4—1184no—
719C2×C4—4722no—
720C2×C4—4722no—
721C2×C4—23616no—
722C2×C4—2364no—
723C2×C4—2364no—
724C2×C4—2368no—
725C2×C4#1427377214yes—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—24no—
733C22—24no—
734C22—24no—
735C22—24no—
736C22—24no—
737C22—24no—
738C22—416no—
739C22—1184no—
740C22—1188no—
741C22—23616no—
742C22—2362no—
743C22—2362no—
744C22—2364no—
745C22C2×#1427370514yes—
746C22C2×#1427370514yes—
747C22C2×#1427370514yes—
748C22C22×D4×D5911yescharacteristic
749C22C22×Q8×D5911yescharacteristic
750C22C22×#1174568511yescharacteristic
751C22C2×#1427377212yes—
752C22#1683823812yes—
753C4—24no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—44no—
758C4—1184no—
759C4—1184no—
760C4—1184no—
761C4—2362no—
762C4—2362no—
763C4—2364no—
764C2—24no—
765C2—24no—
766C2—24no—
767C2—2364no—
768C2C22×#1427370511yescharacteristic
769C2#2143750512yes—
770C2#2143772511yescharacteristic
771C2#2143773411yescharacteristic
772C2#2143789212yes—
subgroupG/H
center, FrattiniC23C24×D59
commutator, socle, cosocleC23×C59C25
FittingC2×C59×#385C2
prime radicalC23×C22⋊D59C22
hypercenterC2×#385D59
hypocenterC59#34985
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C2×#16838028C2semidirect
3. #21432432C2semidirect
4. #21432382C2semidirect
5. #21429915C2semidirect
6. #21429907C2semidirect
7. #21427922C2semidirect
8. #21427920C2semidirect
9. #21427907C2semidirect
10. #21427905C2semidirect
11. #21426708C2semidirect
14. C2×#16837275C2semidirect
15. C2×C59×#385C2semidirect
19. C2×#14273706C22semidirect
20. C2×#14273706C22semidirect
21. C2×#14273705C22semidirect
24. C2×#14273704C22semidirect
25. C2×#14273704C22semidirect
30. C22×Dic59⋊C4C22semidirect
36. #16837343C22semidirect
37. #16837337C22semidirect
38. #16837336C22semidirect
39. #16837333C22semidirect
40. #16837326C22semidirect
41. #16837324C22semidirect
42. #16837322C22semidirect
43. #16837315C22semidirect
44. #16837306C22semidirect
45. #16837297C22semidirect
46. #16837288C22semidirect
47. #16837284C22semidirect
54. #16837276C22semidirect
57. #16837275C22semidirect
58. #16837275C22semidirect
59. #16837274C22semidirect
60. #16837273C22semidirect
63. #16837261C22semidirect
68. C2×C59⋊#95C22semidirect
70. C22×C4⋊C4×C59C22semidirect
75. C59×#385C22semidirect
76. C2×#95×C59C22semidirect
82. C22×C22⋊D59Q8semidirect
273. C23×C59C22⋊Q8semidirect
392. C2×#385D59semidirect
418. C22×C4⋊C4C2×D59semidirect
453. #385C2×D59semidirect
462. C2×#95C2×D59semidirect
463. C59#34985semidirect
670. C23#14273705semidirect

Maximal subgroups

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

subgroupindex
C2×#168380282
C22×C4×C22⋊D592
#214324322
#214323822
#214299152
#214299072
#214279222
#214279202
#214279072
#214279052
#214267082
#214266712
C2×#168372752
C2×C59×#3852
#3498559