Finite Group Databasebeta

← #27306997

Subgroups — #27306997

Order 13568.

1962 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810507C211yesmaximal, characteristic, complemented
2C2×#16810495C211yesmaximal, characteristic
3C2×#16810481C211yesmaximal, characteristic
4C22×#13133124C211yesmaximal, characteristic
5#20272981C211yesmaximal, characteristic, complemented
6#20272976C211yesmaximal, characteristic, complemented
7#20272973C211yesmaximal, characteristic, complemented
8#20272966C211yesmaximal, characteristic, complemented
9#20272948C211yesmaximal, characteristic, complemented
10#20272948C211yesmaximal, characteristic, complemented
11#20272942C211yesmaximal, characteristic, complemented
12#20272938C211yesmaximal, characteristic
13#20272937C211yesmaximal, characteristic
14#20272937C211yesmaximal, characteristic
15C2×C4×C22⋊C4×C53C211yesmaximal, characteristic
16C24×Dic53C2211yescharacteristic
17C24×Dic53C2211yescharacteristic
18C22×#11719919C2211yescharacteristic
19C22×#11719919C2211yescharacteristic
20C22×#11719919C2211yescharacteristic
21C22×#11719919C2211yescharacteristic
22C22×C22⋊Dic53C2211yescharacteristic
23C22×C22⋊Dic53C2211yescharacteristic
24#16810507—24no—
25#16810495C418yescomplemented
26#16810481—24no—
27C2×#13133124—24no—
28C2×#13133124C2211yescharacteristic
29C2×#13133124C2211yescharacteristic
30C2×#13133124C2211yescharacteristic
31C2×#13133124C2211yescharacteristic
32C2×#13133124C2211yescharacteristic
33C2×#13133124C2211yescharacteristic
34C2×#13133124C2211yescharacteristic
35C2×#13133124C2211yescharacteristic
36C2×#13133124C2211yescharacteristic
37C2×#13133124C2211yescharacteristic
38C2×#13133124C2211yescharacteristic
39C2×#13133124C2211yescharacteristic
40C2×#13133124C2211yescharacteristic
41C2×#13133124C2211yescharacteristic
42C2×#13133124C2211yescharacteristic
43C2×#13133124C2211yescharacteristic
44C2×#13133124C2211yescharacteristic
45C2×#13133124C2211yescharacteristic
46C2×#13133124C2211yescharacteristic
47C2×#13133124C2211yescharacteristic
48C24×C4×C53C2211yescharacteristic
49C22×C22⋊C4×C53C2211yescharacteristic
50C22×C22⋊C4×C53C2211yescharacteristic
51C22×C42×C53C2211yescharacteristic
52C22×C42×C53C2211yescharacteristic
53C4×C22⋊C4×C53—24no—
54C2×#95×C53C2211yescharacteristic
55C2×#95×C53C2211yescharacteristic
56C23×Dic53—22no—
57C23×Dic53—22no—
58C23×Dic53—22no—
59C23×Dic53—22no—
60C23×Dic53—22no—
61C23×Dic53—22no—
62C23×Dic53—22no—
63C23×Dic53—22no—
64C23×Dic53—22no—
65C23×Dic53—41no—
66C23×Dic53—41no—
67C23×Dic53—41no—
68C23×Dic53—41no—
69C23×Dic53C2×C414yes—
70C23×Dic53C2311yescharacteristic
71C23×Dic53C2311yescharacteristic
72C23×Dic53C2311yescharacteristic
73C23×Dic53C2311yescharacteristic
74C23×Dic53C2311yescharacteristic
75C23×Dic53C2311yescharacteristic
76C23×Dic53C2311yescharacteristic
77C23×Dic53C2311yescharacteristic
78C2×#11719919—22no—
79C2×#11719919—22no—
80C2×#11719919—22no—
81C2×#11719919—22no—
82C2×#11719919—22no—
83C2×#11719919—22no—
84C2×#11719919—41no—
85C2×#11719919—41no—
86C2×#11719919—41no—
87C2×#11719919—41no—
88C2×#11719919C2×C414yescomplemented
89C2×#11719919C2×C414yescomplemented
90C2×C22⋊Dic53—22no—
91C2×C22⋊Dic53—22no—
92C2×C22⋊Dic53—22no—
93C2×C22⋊Dic53—22no—
94C2×C22⋊Dic53—22no—
95C2×C22⋊Dic53C2×C414yes—
96#13133124—22no—
97#13133124—22no—
98#13133124—22no—
99#13133124—22no—
100#13133124—22no—
101#13133124—22no—
102#13133124—22no—
103#13133124—22no—
104#13133124—22no—
105#13133124—22no—
106#13133124—22no—
107#13133124—41no—
108#13133124—41no—
109#13133124—41no—
110#13133124—41no—
111#13133124—41no—
112#13133124—41no—
113#13133124C2×C414yescomplemented
114#13133124C2×C414yescomplemented
115#13133124D414yes—
116C25×C53C2311yescharacteristic
117C23×C4×C53—22no—
118C23×C4×C53—22no—
119C23×C4×C53—22no—
120C23×C4×C53—22no—
121C23×C4×C53—41no—
122C23×C4×C53—41no—
123C23×C4×C53Q814yes—
124C23×C4×C53C2311yescharacteristic
125C23×C4×C53C2311yescharacteristic
126C23×C4×C53C2311yescharacteristic
127C23×C4×C53C2311yescharacteristic
128C23×C4×C53C2311yescharacteristic
129C23×C4×C53C2311yescharacteristic
130C2×C22⋊C4×C53—22no—
131C2×C22⋊C4×C53—22no—
132C2×C22⋊C4×C53—22no—
133C2×C22⋊C4×C53—22no—
134C2×C22⋊C4×C53C2×C414yes—
135C2×C22⋊C4×C53D414yes—
136C2×C42×C53—22no—
137C2×C42×C53—22no—
138C2×C42×C53—22no—
139C2×C42×C53—22no—
140C2×C42×C53—41no—
141C2×C42×C53—41no—
142#95×C53—22no—
143#95×C53—22no—
144C24×C53—21no—
145C24×C53—21no—
146C24×C53—21no—
147C24×C53—21no—
148C24×C53—21no—
149C24×C53—21no—
150C24×C53—21no—
151C24×C53—21no—
152C24×C53C22×C412yes—
153C24×C53C2×D412yes—
154C24×C53C2×Q812yes—
155C24×C53#4112yes—
156C24×C53#4112yes—
157C24×C53#4112yes—
158C24×C53#4112yes—
159C24×C53C2411yescharacteristic
160C22×C4×C53—21no—
161C22×C4×C53—21no—
162C22×C4×C53—21no—
163C22×C4×C53—21no—
164C22×C4×C53—28no—
165C22×C4×C53—21no—
166C22×C4×C53—21no—
167C22×C4×C53—21no—
168C22×C4×C53—21no—
169C22×C4×C53—21no—
170C22×C4×C53—21no—
171C22×C4×C53—21no—
172C22×C4×C53—21no—
173C22×C4×C53—21no—
174C22×C4×C53—21no—
175C22×C4×C53—21no—
176C22×C4×C53—21no—
177C22×C4×C53—21no—
178C22×C4×C53—21no—
179C22×C4×C53—21no—
180C22×C4×C53—21no—
181C22×C4×C53—21no—
182C22×C4×C53—21no—
183C22×C4×C53—21no—
184C22×C4×C53—21no—
185C22×C4×C53—21no—
186C22×C4×C53—21no—
187C22×C4×C53—21no—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53—21no—
191C22×C4×C53—21no—
192C22×C4×C53—21no—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53—28no—
196C22×C4×C53—44no—
197C22×C4×C53—44no—
198C22×C4×C53—44no—
199C22×C4×C53—44no—
200C22×C4×C53—44no—
201C22×C4×C53C22×C412yes—
202C22×C4×C53C22×C412yes—
203C22×C4×C53C2×D412yes—
204C22×C4×C53C2×D412yes—
205C22×C4×C53C2×D412yes—
206C22×C4×C53C2×Q812yes—
207C22×C4×C53C2×Q812yes—
208C22×C4×C53#4112yes—
209C22×Dic53—21no—
210C22×Dic53—21no—
211C22×Dic53—21no—
212C22×Dic53—21no—
213C22×Dic53—28no—
214C22×Dic53—28no—
215C22×Dic53—21no—
216C22×Dic53—21no—
217C22×Dic53—21no—
218C22×Dic53—21no—
219C22×Dic53—21no—
220C22×Dic53—21no—
221C22×Dic53—21no—
222C22×Dic53—21no—
223C22×Dic53—21no—
224C22×Dic53—21no—
225C22×Dic53—21no—
226C22×Dic53—21no—
227C22×Dic53—21no—
228C22×Dic53—21no—
229C22×Dic53—21no—
230C22×Dic53—21no—
231C22×Dic53—21no—
232C22×Dic53—21no—
233C22×Dic53—21no—
234C22×Dic53—21no—
235C22×Dic53—21no—
236C22×Dic53—21no—
237C22×Dic53—21no—
238C22×Dic53—21no—
239C22×Dic53—21no—
240C22×Dic53—21no—
241C22×Dic53—21no—
242C22×Dic53—21no—
243C22×Dic53—21no—
244C22×Dic53—21no—
245C22×Dic53—28no—
246C22×Dic53—21no—
247C22×Dic53—21no—
248C22×Dic53—21no—
249C22×Dic53—21no—
250C22×Dic53—21no—
251C22×Dic53—21no—
252C22×Dic53—21no—
253C22×Dic53—21no—
254C22×Dic53—21no—
255C22×Dic53—21no—
256C22×Dic53—21no—
257C22×Dic53—21no—
258C22×Dic53—21no—
259C22×Dic53—21no—
260C22×Dic53—44no—
261C22×Dic53—44no—
262C22×Dic53—44no—
263C22×Dic53—44no—
264C22×Dic53—44no—
265C22×Dic53—44no—
266C22×Dic53—44no—
267C22×Dic53—44no—
268C22×Dic53—44no—
269C22×Dic53—44no—
270C22×Dic53—44no—
271C22×Dic53C22×C412yes—
272C22×Dic53C22×C412yes—
273C22×Dic53C22×C412yes—
274C22×Dic53C22×C412yes—
275C22×Dic53C2×D412yes—
276C22×Dic53C2×D412yes—
277C22×Dic53#4112yes—
278C22×Dic53#4112yes—
279C22⋊C4×C53—28no—
280C22⋊C4×C53—28no—
281C42×C53—44no—
282C42×C53—44no—
283C22⋊Dic53—28no—
284C22⋊Dic53—44no—
285#11719919—28no—
286#11719919—44no—
287#11719919—44no—
288#11719919—44no—
289C23×C53—22no—
290C23×C53—22no—
291C23×C53—22no—
292C23×C53—22no—
293C23×C53—22no—
294C23×C53—22no—
295C23×C53—22no—
296C23×C53—22no—
297C23×C53—22no—
298C23×C53—22no—
299C23×C53—22no—
300C23×C53—22no—
301C23×C53—22no—
302C23×C53—22no—
303C23×C53—22no—
304C23×C53—22no—
305C23×C53—22no—
306C23×C53—22no—
307C23×C53—22no—
308C23×C53—22no—
309C23×C53—22no—
310C23×C53—22no—
311C23×C53—22no—
312C23×C53—22no—
313C23×C53—22no—
314C23×C53—22no—
315C23×C53—22no—
316C23×C53—22no—
317C23×C53#11714yes—
318C23×C53C4×D414yes—
319C23×C53C4×Q814yes—
320C23×C53C22⋊Q814yes—
321C23×C53#12314yes—
322C23×C53#12514yes—
323C23×C53#12614yes—
324C23×C53C23×C411yescharacteristic
325C23×C53C22×D411yescharacteristic
326C23×C53C22×D411yescharacteristic
327C23×C53C22×Q811yescharacteristic
328C23×C53C2×#4111yescharacteristic
329C23×C53C2×#4111yescharacteristic
330C23×C53C2×#4111yescharacteristic
331C23×C53C2×#4111yescharacteristic
332C23×C53C2×#4111yescharacteristic
333C23×C53C2×#4111yescharacteristic
334C23×C53C2×#4111yescharacteristic
335C23×C53H(5,𝔽2)11yescharacteristic
336C23×C53H(5,𝔽2)11yescharacteristic
337C23×C53H(5,𝔽2)11yescharacteristic
338C23×C532−1+411yescharacteristic
339C2×C4×C53—22no—
340C2×C4×C53—22no—
341C2×C4×C53—22no—
342C2×C4×C53—22no—
343C2×C4×C53—22no—
344C2×C4×C53—22no—
345C2×C4×C53—22no—
346C2×C4×C53—22no—
347C2×C4×C53—22no—
348C2×C4×C53—22no—
349C2×C4×C53—22no—
350C2×C4×C53—22no—
351C2×C4×C53—22no—
352C2×C4×C53—22no—
353C2×C4×C53—22no—
354C2×C4×C53—22no—
355C2×C4×C53—22no—
356C2×C4×C53—22no—
357C2×C4×C53—22no—
358C2×C4×C53—22no—
359C2×C4×C53—22no—
360C2×C4×C53—416no—
361C2×C4×C53—41no—
362C2×C4×C53—41no—
363C2×C4×C53—41no—
364C2×C4×C53—41no—
365C2×C4×C53—41no—
366C2×C4×C53—41no—
367C2×C4×C53—41no—
368C2×C4×C53—41no—
369C2×C4×C53—41no—
370C2×C4×C53—41no—
371C2×C4×C53—41no—
372C2×C4×C53—41no—
373C2×C4×C53—41no—
374C2×C4×C53—41no—
375C2×C4×C53—41no—
376C2×C4×C53—41no—
377C2×C4×C53—41no—
378C2×C4×C53—41no—
379C2×C4×C53—41no—
380C2×C4×C53—41no—
381C2×C4×C53C22⋊Q814yes—
382C2×Dic53—22no—
383C2×Dic53—22no—
384C2×Dic53—22no—
385C2×Dic53—22no—
386C2×Dic53—22no—
387C2×Dic53—22no—
388C2×Dic53—22no—
389C2×Dic53—22no—
390C2×Dic53—22no—
391C2×Dic53—22no—
392C2×Dic53—22no—
393C2×Dic53—22no—
394C2×Dic53—22no—
395C2×Dic53—22no—
396C2×Dic53—22no—
397C2×Dic53—22no—
398C2×Dic53—22no—
399C2×Dic53—22no—
400C2×Dic53—22no—
401C2×Dic53—22no—
402C2×Dic53—22no—
403C2×Dic53—416no—
404C2×Dic53—416no—
405C2×Dic53—41no—
406C2×Dic53—41no—
407C2×Dic53—41no—
408C2×Dic53—41no—
409C2×Dic53—41no—
410C2×Dic53—41no—
411C2×Dic53—41no—
412C2×Dic53—41no—
413C2×Dic53—41no—
414C2×Dic53—41no—
415C2×Dic53—41no—
416C2×Dic53—41no—
417C2×Dic53—41no—
418C2×Dic53—41no—
419C2×Dic53—41no—
420C2×Dic53—41no—
421C2×Dic53—41no—
422C2×Dic53—41no—
423C2×Dic53—41no—
424C2×Dic53—41no—
425C2×Dic53—41no—
426C2×Dic53—41no—
427C2×Dic53—41no—
428C2×Dic53—41no—
429C2×Dic53—41no—
430C2×Dic53—41no—
431C2×Dic53—41no—
432C2×Dic53—41no—
433C2×Dic53—41no—
434C2×Dic53—41no—
435C2×Dic53—41no—
436C2×Dic53—41no—
437C2×Dic53—41no—
438C2×Dic53—41no—
439C2×Dic53C4×D414yes—
440#13980—531nomaximal, Sylow
441C22×C53—24no—
442C22×C53—24no—
443C22×C53—24no—
444C22×C53—24no—
445C22×C53—24no—
446C22×C53—24no—
447C22×C53—24no—
448C22×C53—24no—
449C22×C53—24no—
450C22×C53—24no—
451C22×C53—24no—
452C22×C53—24no—
453C22×C53—24no—
454C22×C53—24no—
455C22×C53#38718yescomplemented
456C22×C53C2×#11711yescharacteristic
457C22×C53C2×C4×D411yescharacteristic
458C22×C53C2×C4×D411yescharacteristic
459C22×C53C2×C4×Q811yescharacteristic
460C22×C53C4×#4111yescharacteristic
461C22×C53#51811yescharacteristic
462C22×C53#52011yescharacteristic
463C22×C53C2×C22⋊Q811yescharacteristic
464C22×C53C2×C22⋊Q811yescharacteristic
465C22×C53C2×#12311yescharacteristic
466C22×C53#52511yescharacteristic
467C22×C53C2×#12511yescharacteristic
468C22×C53C2×#12611yescharacteristic
469C22×C53#52911yescharacteristic
470C22×C53#53311yescharacteristic
471C22×C53#53811yescharacteristic
472C22×C53#53911yescharacteristic
473C22×C53#54311yescharacteristic
474C22×C53#54411yescharacteristic
475C22×C53D4211yescharacteristic
476C22×C53#54611yescharacteristic
477C22×C53#54611yescharacteristic
478C22×C53#54611yescharacteristic
479C22×C53#54611yescharacteristic
480C22×C53#54711yescharacteristic
481C22×C53#54811yescharacteristic
482C22×C53#55111yescharacteristic
483C22×C53#55111yescharacteristic
484C22×C53#55111yescharacteristic
485C22×C53#55111yescharacteristic
486C22×C53#55211yescharacteristic
487C22×C53#55211yescharacteristic
488C22×C53#55311yescharacteristic
489C22×C53#55311yescharacteristic
490C22×C53#55311yescharacteristic
491C4×C53—24no—
492C4×C53—42no—
493C4×C53—42no—
494C4×C53—42no—
495C4×C53—42no—
496C4×C53—42no—
497Dic53—24no—
498Dic53—42no—
499Dic53—42no—
500Dic53—42no—
501Dic53—42no—
502Dic53—42no—
503Dic53—81no—
504Dic53—81no—
505C2×#387—531no—
506C2×#385—531no—
507C2×#380—531no—
508C2×C4×C22⋊C4D5311yescharacteristic
509C22×#95—531no—
510#1445—531no—
511#1443—531no—
512#1442—531no—
513#1441—531no—
514#1436—531no—
515#1436—531no—
516#1434—531no—
517C22⋊#95—531no—
518C22⋊#95—531no—
519C22⋊#95—531no—
520C2×C53—28no—
521C2×C53C2×#38711yescharacteristic
522C2×C53C4×C22⋊Q811yescharacteristic
523C2×C53#232911yescharacteristic
524C2×C53#235211yescharacteristic
525C2×C53#235311yescharacteristic
526C2×C53#235811yescharacteristic
527C2×C53#235911yescharacteristic
528C2×C53#243711yescharacteristic
529C2×C53#243811yescharacteristic
530C2×C53#244211yescharacteristic
531C2×C53#244311yescharacteristic
532C2×C53#244411yescharacteristic
533C2×C53#248011yescharacteristic
534C2×C53#249311yescharacteristic
535C2×C53#256911yescharacteristic
536C24×C4—531no—
537C24×C4—531no—
538C24×C4C2×D5311yescharacteristic
539C22×C4⋊C4—531no—
540C22×C4⋊C4—531no—
541C22×C4⋊C4—531no—
542C22×C4⋊C4—531no—
543C22×C22⋊C4—531no—
544C22×C22⋊C4—531no—
545C22×C22⋊C4C2×D5311yescharacteristic
546C22×C22⋊C4C2×D5311yescharacteristic
547C22×C42C2×D5311yescharacteristic
548C22×C42C2×D5311yescharacteristic
549#387—1064no—
550#385—538no—
551#380—1064no—
552C4×C22⋊C4—24no—
553C2×#95—531no—
554C2×#95—531no—
555C2×#95—531no—
556C2×#95—531no—
557C2×#95—531no—
558C2×#95—531no—
559C2×#95—531no—
560C2×#95—531no—
561C2×#95—531no—
562C2×#95—531no—
563C2×#95—531no—
564C2×#95—531no—
565C2×#95—531no—
566C2×#95—531no—
567C2×#95—531no—
568C2×#95—531no—
569C2×#95—531no—
570C2×#95—531no—
571C2×#95—531no—
572C2×#95—531no—
573C2×#95—1064no—
574C2×#95C2×D5311yescharacteristic
575C2×#95C2×D5311yescharacteristic
576C53#1398011yescharacteristic, complemented, Sylow
577C25C22×D5311yescharacteristic
578C23×C4—22no—
579C23×C4—22no—
580C23×C4—22no—
581C23×C4—22no—
582C23×C4—41no—
583C23×C4—41no—
584C23×C4—531no—
585C23×C4—531no—
586C23×C4—531no—
587C23×C4—531no—
588C23×C4—531no—
589C23×C4—531no—
590C23×C4—534no—
591C23×C4—531no—
592C23×C4—531no—
593C23×C4—1062no—
594C23×C4—1062no—
595C23×C4—1062no—
596C23×C4—1062no—
597C23×C4—1062no—
598C23×C4—1062no—
599C23×C4—1062no—
600C23×C4—1062no—
601C23×C4—1062no—
602C23×C4—2121no—
603C23×C4—2121no—
604C23×C4—2121no—
605C23×C4—2121no—
606C23×C4Dic10614yes—
607C23×C4C22×D5311yescharacteristic
608C23×C4C22×D5311yescharacteristic
609C23×C4C22×D5311yescharacteristic
610C23×C4C22×D5311yescharacteristic
611C23×C4C22×D5311yescharacteristic
612C23×C4C22×D5311yescharacteristic
613C2×C4⋊C4—534no—
614C2×C4⋊C4—534no—
615C2×C4⋊C4—1062no—
616C2×C4⋊C4—1062no—
617C2×C4⋊C4—1062no—
618C2×C4⋊C4—1062no—
619C2×C4⋊C4—1062no—
620C2×C4⋊C4—1062no—
621C2×C4⋊C4—2121no—
622C2×C4⋊C4—2121no—
623C2×C4⋊C4—2121no—
624C2×C4⋊C4—2121no—
625C2×C22⋊C4—22no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—534no—
630C2×C22⋊C4—1062no—
631C2×C22⋊C4—1062no—
632C2×C22⋊C4—1062no—
633C2×C22⋊C4—1062no—
634C2×C22⋊C4—1062no—
635C2×C22⋊C4C4×D5314yes—
636C2×C22⋊C4C22⋊D5314yes—
637C2×C42—22no—
638C2×C42—22no—
639C2×C42—22no—
640C2×C42—22no—
641C2×C42—41no—
642C2×C42—41no—
643#95—22no—
644#95—22no—
645#95—534no—
646#95—534no—
647#95—534no—
648#95—1062no—
649#95—1062no—
650#95—1062no—
651#95—1062no—
652#95—1062no—
653#95—1062no—
654#95—1062no—
655#95—1062no—
656#95—1062no—
657#95—1062no—
658#95—1062no—
659#95—2121no—
660#95—2121no—
661#95—2121no—
662#95—2121no—
663#95—2121no—
664#95—2121no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24C2×Dic10612yes—
674C24C2×C4×D5312yes—
675C24#1171994512yes—
676C24#1171994512yes—
677C24#1171994512yes—
678C24#1171994512yes—
679C24C2×C22⋊D5312yes—
680C24C23×D5311yescharacteristic
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—28no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—28no—
717C22×C4—44no—
718C22×C4—44no—
719C22×C4—44no—
720C22×C4—44no—
721C22×C4—44no—
722C22×C4—532no—
723C22×C4—532no—
724C22×C4—532no—
725C22×C4—532no—
726C22×C4—532no—
727C22×C4—532no—
728C22×C4—532no—
729C22×C4—532no—
730C22×C4—1068no—
731C22×C4—1061no—
732C22×C4—1061no—
733C22×C4—1061no—
734C22×C4—1061no—
735C22×C4—1068no—
736C22×C4—1068no—
737C22×C4—1061no—
738C22×C4—1061no—
739C22×C4—1061no—
740C22×C4—1061no—
741C22×C4—1061no—
742C22×C4—1061no—
743C22×C4—1061no—
744C22×C4—1061no—
745C22×C4—1061no—
746C22×C4—1061no—
747C22×C4—1061no—
748C22×C4—1061no—
749C22×C4—1061no—
750C22×C4—1061no—
751C22×C4—1061no—
752C22×C4—1061no—
753C22×C4—1061no—
754C22×C4—1061no—
755C22×C4—1061no—
756C22×C4—1061no—
757C22×C4—1061no—
758C22×C4—1061no—
759C22×C4—1061no—
760C22×C4—1061no—
761C22×C4—1061no—
762C22×C4—1061no—
763C22×C4—1061no—
764C22×C4—1061no—
765C22×C4—1061no—
766C22×C4—1061no—
767C22×C4—1061no—
768C22×C4—1061no—
769C22×C4—1061no—
770C22×C4—1061no—
771C22×C4—1061no—
772C22×C4—1061no—
773C22×C4—1061no—
774C22×C4—1061no—
775C22×C4—1061no—
776C22×C4—1061no—
777C22×C4—1061no—
778C22×C4—1061no—
779C22×C4—1061no—
780C22×C4—1061no—
781C22×C4—2124no—
782C22×C4—2124no—
783C22×C4—2124no—
784C22×C4—2124no—
785C22×C4—2124no—
786C22×C4—2124no—
787C22×C4—2124no—
788C22×C4—2124no—
789C22×C4—2124no—
790C22×C4—2124no—
791C22×C4—2124no—
792C22×C4C2×Dic10612yes—
793C22×C4C2×Dic10612yes—
794C22×C4C2×C4×D5312yes—
795C22×C4C2×C4×D5312yes—
796C22×C4D4×D5312yes—
797C22×C4#1171994712yes—
798C22×C4C2×C22⋊D5312yes—
799C22×C4C2×C22⋊D5312yes—
800C4⋊C4—1068no—
801C4⋊C4—2124no—
802C4⋊C4—2124no—
803C4⋊C4—2124no—
804C22⋊C4—28no—
805C22⋊C4—28no—
806C22⋊C4—1068no—
807C22⋊C4—2124no—
808C42—44no—
809C42—44no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23#1313317414yes—
839C23C4×C22⋊D5314yes—
840C23C4×Dic10614yes—
841C23#1313319614yes—
842C23#1313320014yes—
843C23#1313320914yes—
844C23#1313321114yes—
845C23C22×C4×D5311yescharacteristic
846C23C2×D4×D5311yescharacteristic
847C23C22×C22⋊D5311yescharacteristic
848C23C22×Dic10611yescharacteristic
849C23#41×D5311yescharacteristic
850C23#41×D5311yescharacteristic
851C23C2×#1171994711yescharacteristic
852C23C2×#1171994511yescharacteristic
853C23C2×#1171994511yescharacteristic
854C23C2×#1171994511yescharacteristic
855C23C2×#1171994511yescharacteristic
856C23#1313326211yescharacteristic
857C23#1313326211yescharacteristic
858C23#1313326311yescharacteristic
859C23#1313326411yescharacteristic
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—416no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—534no—
903C2×C4—1062no—
904C2×C4—1062no—
905C2×C4—1062no—
906C2×C4—1062no—
907C2×C4—1062no—
908C2×C4—1062no—
909C2×C4—1062no—
910C2×C4—1062no—
911C2×C4—1062no—
912C2×C4—1062no—
913C2×C4—1062no—
914C2×C4—1062no—
915C2×C4—1062no—
916C2×C4—1062no—
917C2×C4—1062no—
918C2×C4—1062no—
919C2×C4—1062no—
920C2×C4—1062no—
921C2×C4—1062no—
922C2×C4—1062no—
923C2×C4—1062no—
924C2×C4—21216no—
925C2×C4—2121no—
926C2×C4—2121no—
927C2×C4—2121no—
928C2×C4—2121no—
929C2×C4—2121no—
930C2×C4—2121no—
931C2×C4—2121no—
932C2×C4—2121no—
933C2×C4—2121no—
934C2×C4—2121no—
935C2×C4—2121no—
936C2×C4—2121no—
937C2×C4—2121no—
938C2×C4—2121no—
939C2×C4—21216no—
940C2×C4—2121no—
941C2×C4—2121no—
942C2×C4—2121no—
943C2×C4—2121no—
944C2×C4—2121no—
945C2×C4—2121no—
946C2×C4—2121no—
947C2×C4—2121no—
948C2×C4—2121no—
949C2×C4—2121no—
950C2×C4—2121no—
951C2×C4—2121no—
952C2×C4—2121no—
953C2×C4—2121no—
954C2×C4—2121no—
955C2×C4—2121no—
956C2×C4—2121no—
957C2×C4—2121no—
958C2×C4—2121no—
959C2×C4—2121no—
960C2×C4#1313319414yes—
961C22—24no—
962C22—24no—
963C22—24no—
964C22—24no—
965C22—24no—
966C22—24no—
967C22—24no—
968C22—24no—
969C22—24no—
970C22—24no—
971C22—24no—
972C22—24no—
973C22—24no—
974C22—24no—
975C22#1681050718yescomplemented
976C22C2×#1313317411yescharacteristic
977C22C4×D4×D5311yescharacteristic
978C22C2×C4×C22⋊D5311yescharacteristic
979C22C2×C4×Dic10611yescharacteristic
980C22C4×#1171994711yescharacteristic
981C22#1681109511yescharacteristic
982C22#1681110211yescharacteristic
983C22C2×#1313319411yescharacteristic
984C22C2×#1313319611yescharacteristic
985C22C2×#1313320011yescharacteristic
986C22#1681113211yescharacteristic
987C22C2×#1313320911yescharacteristic
988C22C2×#1313321111yescharacteristic
989C22#1681115311yescharacteristic
990C22#1681117611yescharacteristic
991C22#1681120611yescharacteristic
992C22#1681121511yescharacteristic
993C22#1681124911yescharacteristic
994C22#1681125111yescharacteristic
995C22D4×C22⋊D5311yescharacteristic
996C22#1681126111yescharacteristic
997C22#1681126311yescharacteristic
998C22#1681126711yescharacteristic
999C22#1681126911yescharacteristic
1000C22#1681127211yescharacteristic
1001C22#1681128211yescharacteristic
1002C22#1681129711yescharacteristic
1003C22#1681129911yescharacteristic
1004C22#1681130211yescharacteristic
1005C22#1681130211yescharacteristic
1006C22#1681130611yescharacteristic
1007C22#1681131311yescharacteristic
1008C22#1681131911yescharacteristic
1009C22#1681132211yescharacteristic
1010C22#1681132211yescharacteristic
1011C4—24no—
1012C4—42no—
1013C4—42no—
1014C4—42no—
1015C4—42no—
1016C4—42no—
1017C4—1064no—
1018C4—4241no—
1019C4—4241no—
1020C4—2122no—
1021C4—2122no—
1022C4—2122no—
1023C4—2122no—
1024C4—2122no—
1025C2—28no—
1026C2C2×#1681050711yescharacteristic
1027C2C4×#1313319411yescharacteristic
1028C2#2027744311yescharacteristic
1029C2#2027763811yescharacteristic
1030C2#2027764911yescharacteristic
1031C2#2027769211yescharacteristic
1032C2#2027770111yescharacteristic
1033C2#2027837611yescharacteristic
1034C2#2027838511yescharacteristic
1035C2#2027843911yescharacteristic
1036C2#2027844411yescharacteristic
1037C2#2027845911yescharacteristic
1038C2#2027896111yescharacteristic
1039C2#2027909411yescharacteristic
1040C2#2027993411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C4×C22⋊C4×C53C2
socle, cosocleC24×C53C24
prime radicalC25×C53C23
hypercenterC2×C4×C22⋊C4D53
hypocenterC53#13980
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#16810507C2semidirect
5. #20272981C2semidirect
6. #20272976C2semidirect
7. #20272973C2semidirect
8. #20272966C2semidirect
9. #20272948C2semidirect
10. #20272948C2semidirect
11. #20272942C2semidirect
25. #16810495C4semidirect
88. C2×#11719919C2×C4semidirect
89. C2×#11719919C2×C4semidirect
113. #13133124C2×C4semidirect
114. #13133124C2×C4semidirect
455. C22×C53#387semidirect
576. C53#13980semidirect
975. C22#16810507semidirect

Maximal subgroups

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

subgroupindex
C2×#168105072
C2×#168104952
C2×#168104812
C22×#131331242
#202729812
#202729762
#202729732
#202729662
#202729482
#202729422
#202729382
#202729372
C2×C4×C22⋊C4×C532
#1398053