Finite Group Databasebeta

← #27531028

Subgroups — #27531028

Order 13568.

1062 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20283002C211yesmaximal, characteristic, complemented
2#20276152C211yesmaximal, characteristic, complemented
3#20276146C211yesmaximal, characteristic, complemented
4#20276141C211yesmaximal, characteristic, complemented
5#20275918C211yesmaximal, characteristic, complemented
6#20275918C211yesmaximal, characteristic, complemented
7#20275911C211yesmaximal, characteristic, complemented
8#20275901C211yesmaximal, characteristic, complemented
9#20275894C211yesmaximal, characteristic, complemented
10#20275894C211yesmaximal, characteristic, complemented
11#20275718C211yesmaximal, characteristic, complemented
12#20275718C211yesmaximal, characteristic, complemented
13#20275718C211yesmaximal, characteristic, complemented
14#20274625C211yesmaximal, characteristic, complemented
15C53×#2847C211yesmaximal, characteristic
16C22×#11719923C2211yescharacteristic, complemented
17C2×#13133196C2211yescharacteristic
18C2×#13133196C2211yescharacteristic
19C2×#13133196C2211yescharacteristic
20C2×#13133150C2211yescharacteristic, complemented
21C2×#13133150C2211yescharacteristic, complemented
22C2×#13133148C2211yescharacteristic, complemented
23C2×#13133140C2211yescharacteristic, complemented
24C2×#13133140C2211yescharacteristic, complemented
25C2×#13133140C2211yescharacteristic, complemented
26C2×#13133138C2211yescharacteristic, complemented
27C2×#13133138C2211yescharacteristic, complemented
28C2×#13133138C2211yescharacteristic, complemented
29C2×C22⋊#88322C2211yescharacteristic
30C2×C22⋊#88322C2211yescharacteristic
31C2×C22⋊#88322C2211yescharacteristic
32C2×C22⋊#88322C2211yescharacteristic
33C2×C22⋊#88322C2211yescharacteristic
34C2×C22⋊#88322C2211yescharacteristic
35#16810496—21no—
36#16810496—21no—
37#16810496—21no—
38#16810483C2211yescharacteristic
39#16810483C2211yescharacteristic
40#16810483C2211yescharacteristic
41#16810479—21no—
42#16810385C2211yescharacteristic, complemented
43#16810385C2211yescharacteristic, complemented
44#16810385C2211yescharacteristic, complemented
45#16810385C2211yescharacteristic, complemented
46#16810385C2211yescharacteristic, complemented
47#16810385C2211yescharacteristic, complemented
48C24×C4×C53C2211yescharacteristic
49C2×#121×C53C2211yescharacteristic
50C2×#121×C53C2211yescharacteristic
51C2×#121×C53C2211yescharacteristic
52C2×#120×C53—21no—
53C53×#386—21no—
54C53×#386—21no—
55C53×#386—21no—
56C53×#380C2211yescharacteristic
57C53×#380C2211yescharacteristic
58C53×#380C2211yescharacteristic
59C22×Dic106C2311yescharacteristic
60C2×#11719923—41no—
61C2×#11719923—41no—
62C2×#11719923—41no—
63C22×#88322C2311yescharacteristic
64C22×#88322C2311yescharacteristic
65C22×#88322C2311yescharacteristic
66C22×#88322C2311yescharacteristic
67#13133196—41no—
68#13133196—41no—
69#13133196—41no—
70#13133196—41no—
71#13133196—41no—
72#13133196—41no—
73C2×C4⋊Dic53C2311yescharacteristic
74C2×C4⋊Dic53C2311yescharacteristic
75C2×C4⋊Dic53C2311yescharacteristic
76C2×#11719919—21no—
77C2×#11719919—21no—
78C2×#11719919—21no—
79C2×C22⋊Dic53—21no—
80C2×C22⋊Dic53—21no—
81C2×C22⋊Dic53—21no—
82C2×C22⋊Dic53—21no—
83C2×C22⋊Dic53—21no—
84C2×C22⋊Dic53—21no—
85#13133150—41no—
86#13133150—41no—
87#13133148—41no—
88#13133140—41no—
89#13133140—41no—
90#13133140—41no—
91#13133138—41no—
92#13133138—41no—
93#13133138—41no—
94C22⋊#88322—41no—
95C22⋊#88322—41no—
96C22⋊#88322—41no—
97C22⋊#88322—41no—
98C22⋊#88322—41no—
99C22⋊#88322—41no—
100#13133124—21no—
101#13133124—21no—
102#13133124—21no—
103C25×C53D411yescharacteristic
104C22×D4×C53—21no—
105C22×D4×C53—21no—
106C22×D4×C53—21no—
107C22×D4×C53C2311yescharacteristic
108C23×C4×C53—41no—
109C23×C4×C53—41no—
110C23×C4×C53—41no—
111C23×C4×C53—41no—
112C23×C4×C53—41no—
113C23×C4×C53—41no—
114C23×C4×C53D411yescharacteristic
115C23×C4×C53D411yescharacteristic
116C23×C4×C53D411yescharacteristic
117C23×C4×C53C2311yescharacteristic
118C23×C4×C53C2311yescharacteristic
119C23×C4×C53C2311yescharacteristic
120#121×C53—41no—
121#121×C53—41no—
122#121×C53—41no—
123#121×C53—41no—
124#121×C53—41no—
125#121×C53—41no—
126#120×C53—44no—
127C2×C4⋊C4×C53C2311yescharacteristic
128C2×C4⋊C4×C53C2311yescharacteristic
129C2×C4⋊C4×C53C2311yescharacteristic
130C2×C22⋊C4×C53—21no—
131C2×C22⋊C4×C53—21no—
132C2×C22⋊C4×C53—21no—
133C2×C22⋊C4×C53—21no—
134C2×C22⋊C4×C53—21no—
135C2×C22⋊C4×C53—21no—
136#95×C53—21no—
137#95×C53—21no—
138#95×C53—21no—
139C24×C53—22no—
140C24×C53—22no—
141C24×C53—22no—
142C24×C53—21no—
143C24×C53—41no—
144C24×C53—41no—
145C24×C53—41no—
146C24×C53—41no—
147C24×C53C2×D411yescharacteristic
148C24×C53C2×D411yescharacteristic
149C24×C53C2×D411yescharacteristic
150C2×D4×C53—21no—
151C2×D4×C53—21no—
152C2×D4×C53—21no—
153C2×D4×C53—21no—
154C2×D4×C53—21no—
155C2×D4×C53—21no—
156C2×D4×C53—42no—
157C2×D4×C53—42no—
158C2×D4×C53—42no—
159C2×D4×C53—42no—
160C2×D4×C53—42no—
161C2×D4×C53—42no—
162C2×D4×C53—42no—
163C2×D4×C53—42no—
164C2×D4×C53—42no—
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—41no—
187C22×C4×C53—41no—
188C22×C4×C53—41no—
189C22×C4×C53—41no—
190C22×C4×C53—41no—
191C22×C4×C53—41no—
192C22×C4×C53—41no—
193C22×C4×C53—41no—
194C22×C4×C53—41no—
195C22×C4×C53—44no—
196C22×C4×C53—44no—
197C22×C4×C53—44no—
198C22×C4×C53—44no—
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53C2×D411yescharacteristic
201C22×C4×C53C2×D411yescharacteristic
202C22×C4×C53C2411yescharacteristic
203C22×Dic53—21no—
204C22×Dic53—21no—
205C22×Dic53—21no—
206C22×Dic53—21no—
207C2×Dic106—21no—
208C2×Dic106—21no—
209C2×Dic106—21no—
210C2×Dic106—21no—
211C2×Dic106—21no—
212C2×Dic106—21no—
213C4⋊C4×C53—21no—
214C4⋊C4×C53—21no—
215C4⋊C4×C53—21no—
216C4⋊C4×C53—21no—
217C4⋊C4×C53—21no—
218C4⋊C4×C53—21no—
219C22⋊C4×C53—42no—
220C22⋊C4×C53—42no—
221C22⋊C4×C53—42no—
222C22⋊C4×C53—42no—
223C22⋊C4×C53—42no—
224C22⋊C4×C53—42no—
225C22⋊Dic53—42no—
226C22⋊Dic53—42no—
227C22⋊Dic53—42no—
228C22⋊Dic53—42no—
229C22⋊Dic53—42no—
230C22⋊Dic53—42no—
231#11719923—44no—
232C4⋊Dic53—21no—
233C4⋊Dic53—21no—
234C4⋊Dic53—21no—
235C4⋊Dic53—21no—
236C4⋊Dic53—21no—
237C4⋊Dic53—21no—
238#11719919—42no—
239#11719919—42no—
240#11719919—42no—
241C2×#88322—21no—
242C2×#88322—21no—
243C2×#88322—21no—
244C2×#88322—21no—
245C2×#88322—21no—
246C2×#88322—21no—
247C2×#88322—21no—
248C2×#88322—21no—
249C2×#88322—21no—
250C2×#88322—21no—
251C2×#88322—21no—
252C2×#88322—21no—
253C23×C53—21no—
254C23×C53—21no—
255C23×C53—21no—
256C23×C53—21no—
257C23×C53—21no—
258C23×C53—21no—
259C23×C53—21no—
260C23×C53—21no—
261C23×C53—21no—
262C23×C53—21no—
263C23×C53—21no—
264C23×C53—21no—
265C23×C53—21no—
266C23×C53—21no—
267C23×C53—21no—
268C23×C53—21no—
269C23×C53—21no—
270C23×C53—21no—
271C23×C53—44no—
272C23×C53—44no—
273C23×C53—44no—
274C23×C53—44no—
275C23×C53—44no—
276C23×C53—44no—
277C23×C53—44no—
278C23×C53—41no—
279C23×C53—41no—
280C23×C53—41no—
281C23×C53—41no—
282C23×C53—41no—
283C23×C53—41no—
284C23×C53—41no—
285C23×C53#13512yes—
286C23×C53AGL(1,ℤ/8)12yes—
287C23×C53#13712yes—
288C23×C53C22×D411yescharacteristic
289D4×C53—41no—
290D4×C53—41no—
291D4×C53—41no—
292D4×C53—41no—
293D4×C53—84no—
294D4×C53—84no—
295D4×C53—84no—
296C2×C4×C53—21no—
297C2×C4×C53—21no—
298C2×C4×C53—21no—
299C2×C4×C53—21no—
300C2×C4×C53—21no—
301C2×C4×C53—21no—
302C2×C4×C53—21no—
303C2×C4×C53—21no—
304C2×C4×C53—21no—
305C2×C4×C53—44no—
306C2×C4×C53—44no—
307C2×C4×C53—44no—
308C2×C4×C53—41no—
309C2×C4×C53—41no—
310C2×C4×C53—41no—
311C2×C4×C53—41no—
312C2×C4×C53—41no—
313C2×C4×C53—41no—
314C2×C4×C53—41no—
315C2×C4×C53—41no—
316C2×C4×C53—41no—
317C2×C4×C53—41no—
318C2×C4×C53—41no—
319C2×C4×C53—41no—
320C2×C4×C53—41no—
321C2×C4×C53—41no—
322C2×C4×C53—41no—
323C2×C4×C53—41no—
324C2×C4×C53—41no—
325C2×C4×C53—41no—
326C2×C4×C53—41no—
327C2×C4×C53—41no—
328C2×C4×C53—41no—
329C2×C4×C53H(5,𝔽2)11yescharacteristic
330C2×C4×C53H(5,𝔽2)11yescharacteristic
331C2×C4×C53H(5,𝔽2)11yescharacteristic
332C2×C4×C53H(5,𝔽2)11yescharacteristic
333C2×C4×C53H(5,𝔽2)11yescharacteristic
334C2×C4×C53H(5,𝔽2)11yescharacteristic
335C2×Dic53—41no—
336C2×Dic53—41no—
337C2×Dic53—41no—
338C2×Dic53—41no—
339C2×Dic53—41no—
340C2×Dic53—41no—
341C2×Dic53—41no—
342C2×Dic53—41no—
343C2×Dic53—41no—
344C2×Dic53—41no—
345C2×Dic53—41no—
346C2×Dic53—41no—
347Dic106—41no—
348Dic106—41no—
349Dic106—41no—
350Dic106—41no—
351#88322—41no—
352#88322—41no—
353#88322—41no—
354#88322—41no—
355#32709—531nomaximal, Sylow
356C22×C53—22no—
357C22×C53—22no—
358C22×C53—22no—
359C22×C53—22no—
360C22×C53—22no—
361C22×C53—22no—
362C22×C53—22no—
363C22×C53—22no—
364C22×C53—22no—
365C22×C53—416no—
366C22×C53—41no—
367C22×C53—41no—
368C22×C53—41no—
369C22×C53—41no—
370C22×C53—41no—
371C22×C53—41no—
372C22×C53—41no—
373C22×C53—41no—
374C22×C53—41no—
375C22×C53—41no—
376C22×C53—41no—
377C22×C53—41no—
378C22×C53—81no—
379C22×C53—81no—
380C22×C53—81no—
381C22×C53—81no—
382C22×C53—81no—
383C22×C53—81no—
384C22×C53—81no—
385C22×C53#53411yescharacteristic
386C22×C53#53411yescharacteristic
387C22×C53#53411yescharacteristic
388C22×C53C2×#13511yescharacteristic
389C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
390C22×C53C2×#13711yescharacteristic
391C22×C53#57511yescharacteristic
392C4×C53—41no—
393C4×C53—41no—
394C4×C53—41no—
395C4×C53—81no—
396C4×C53—81no—
397C4×C53—81no—
398C4×C53#56011yescharacteristic
399C4×C53#56011yescharacteristic
400C4×C53#56011yescharacteristic
401C4×C53H(3,𝔽4)11yescharacteristic
402Dic53—81no—
403Dic53—81no—
404Dic53—81no—
405Dic53—81no—
406#2848—531no—
407#2847D5311yescharacteristic
408#2077—531no—
409#2076—531no—
410#2075—531no—
411#2036—531no—
412#2036—531no—
413#2035—531no—
414#2034—531no—
415#2033—531no—
416#2033—531no—
417#2000—531no—
418#2000—531no—
419#2000—531no—
420#1779—531no—
421C2×C53—42no—
422C2×C53—42no—
423C2×C53—42no—
424C2×C53—161no—
425C2×C53#281211yescharacteristic
426C2×C53#318811yescharacteristic
427C2×C53#319011yescharacteristic
428C2×C53#319111yescharacteristic
429C2×C53#319311yescharacteristic
430C2×C53#319411yescharacteristic
431C2×C53#319611yescharacteristic
432C24×C4C2×D5311yescharacteristic
433C22×SD16—531no—
434C2×C22⋊Q8—531no—
435C2×C22⋊Q8—531no—
436C2×C22⋊Q8—531no—
437C2×#121C2×D5311yescharacteristic
438C2×#121C2×D5311yescharacteristic
439C2×#121C2×D5311yescharacteristic
440C2×#120—21no—
441C2×#107—531no—
442C2×#107—531no—
443C2×#106—531no—
444C2×#103—531no—
445C2×#103—531no—
446C2×#103—531no—
447C2×#102—531no—
448C2×#102—531no—
449C2×#102—531no—
450C2×C22⋊C8—531no—
451C2×C22⋊C8—531no—
452C2×C22⋊C8—531no—
453C2×C22⋊C8—531no—
454C2×C22⋊C8—531no—
455C2×C22⋊C8—531no—
456#386—21no—
457#386—21no—
458#386—21no—
459#385—1061no—
460#385—1061no—
461#385—1061no—
462#380—531no—
463#380—531no—
464#380—531no—
465#380C2×D5311yescharacteristic
466#380C2×D5311yescharacteristic
467#380C2×D5311yescharacteristic
468#379—1061no—
469#340—531no—
470#340—531no—
471#340—531no—
472#340—531no—
473#340—531no—
474#340—531no—
475C53#3270911yescharacteristic, complemented, Sylow
476C25C22⋊D5311yescharacteristic
477C22×Q8—531no—
478C22×D4—21no—
479C22×D4—21no—
480C22×D4—21no—
481C22×D4C22×D5311yescharacteristic
482C23×C4—41no—
483C23×C4—41no—
484C23×C4—41no—
485C23×C4—41no—
486C23×C4—41no—
487C23×C4—41no—
488C23×C4C22⋊D5311yescharacteristic
489C23×C4C22⋊D5311yescharacteristic
490C23×C4C22⋊D5311yescharacteristic
491C23×C4C22×D5311yescharacteristic
492C23×C4C22×D5311yescharacteristic
493C23×C4C22×D5311yescharacteristic
494C2×SD16—2121no—
495C2×SD16—2121no—
496C2×SD16—2121no—
497C22×C8—531no—
498C22×C8—531no—
499C22×C8—531no—
500C22×C8—531no—
501C22⋊Q8—2121no—
502C22⋊Q8—2121no—
503C22⋊Q8—2121no—
504C22⋊Q8—2121no—
505C22⋊Q8—2121no—
506C22⋊Q8—2121no—
507#121—41no—
508#121—41no—
509#121—41no—
510#121—41no—
511#121—41no—
512#121—41no—
513#120—44no—
514C2×C4⋊C4—531no—
515C2×C4⋊C4—531no—
516C2×C4⋊C4—531no—
517C2×C4⋊C4—1061no—
518C2×C4⋊C4—1061no—
519C2×C4⋊C4—1061no—
520C2×C4⋊C4C22×D5311yescharacteristic
521C2×C4⋊C4C22×D5311yescharacteristic
522C2×C4⋊C4C22×D5311yescharacteristic
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—1061no—
530C2×C22⋊C4—1061no—
531C2×C22⋊C4—1061no—
532C2×C22⋊C4—1061no—
533C2×C22⋊C4—1061no—
534C2×C22⋊C4—1061no—
535#107—2121no—
536#107—2121no—
537#106—2121no—
538#103—2121no—
539#103—2121no—
540#103—2121no—
541#102—2121no—
542#102—2121no—
543#102—2121no—
544C22⋊C8—2121no—
545C22⋊C8—2121no—
546C22⋊C8—2121no—
547C22⋊C8—2121no—
548C22⋊C8—2121no—
549C22⋊C8—2121no—
550#95—21no—
551#95—21no—
552#95—21no—
553#95—1061no—
554#95—1061no—
555#95—1061no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—21no—
560C24—41no—
561C24—41no—
562C24—41no—
563C24—41no—
564C24C2×C22⋊D5311yescharacteristic
565C24C2×C22⋊D5311yescharacteristic
566C24C2×C22⋊D5311yescharacteristic
567C2×Q8—1061no—
568C2×Q8—1061no—
569C2×Q8—1061no—
570C2×Q8—1061no—
571C2×Q8—1061no—
572C2×Q8—1061no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—42no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—44no—
619C22×C4—44no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4—1061no—
623C22×C4—1061no—
624C22×C4—1061no—
625C22×C4—1061no—
626C22×C4C2×C22⋊D5311yescharacteristic
627C22×C4C2×C22⋊D5311yescharacteristic
628C22×C4C2×C22⋊D5311yescharacteristic
629C22×C4C23×D5311yescharacteristic
630SD16—2124no—
631C2×C8—1061no—
632C2×C8—1061no—
633C2×C8—1061no—
634C2×C8—1061no—
635C2×C8—1061no—
636C2×C8—1061no—
637C2×C8—1061no—
638C2×C8—1061no—
639C2×C8—1061no—
640C2×C8—1061no—
641C2×C8—1061no—
642C2×C8—1061no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—1061no—
650C4⋊C4—1061no—
651C4⋊C4—1061no—
652C4⋊C4—1061no—
653C4⋊C4—1061no—
654C4⋊C4—1061no—
655C4⋊C4—2122no—
656C4⋊C4—2122no—
657C4⋊C4—2122no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—2122no—
665C22⋊C4—2122no—
666C22⋊C4—2122no—
667C22⋊C4—2122no—
668C22⋊C4—2122no—
669C22⋊C4—2122no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23#1313323712yes—
703C23#1313324312yes—
704C23#1313324712yes—
705C23C22×C22⋊D5311yescharacteristic
706Q8—2121no—
707Q8—2121no—
708Q8—2121no—
709Q8—2121no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—41no—
714D4—84no—
715D4—84no—
716D4—84no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—2121no—
751C2×C4—2121no—
752C2×C4—2121no—
753C2×C4—2121no—
754C2×C4—2121no—
755C2×C4—2121no—
756C2×C4—2121no—
757C2×C4—2121no—
758C2×C4—2121no—
759C2×C4—2121no—
760C2×C4—2121no—
761C2×C4—2121no—
762C2×C4#1313326211yescharacteristic
763C2×C4#1313326211yescharacteristic
764C2×C4#1313326211yescharacteristic
765C2×C4#1313326211yescharacteristic
766C2×C4#1313326211yescharacteristic
767C2×C4#1313326211yescharacteristic
768C8—2121no—
769C8—2121no—
770C8—2121no—
771C8—2121no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—416no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22#1681118211yescharacteristic
802C22#1681118211yescharacteristic
803C22#1681118211yescharacteristic
804C22C2×#1313323711yescharacteristic
805C22C2×#1313324311yescharacteristic
806C22C2×#1313324711yescharacteristic
807C22#1681142111yescharacteristic
808C4—41no—
809C4—41no—
810C4—41no—
811C4—81no—
812C4—81no—
813C4—81no—
814C4—4241no—
815C4—4241no—
816C4—4241no—
817C4—4241no—
818C4#1681136211yescharacteristic
819C4#1681136211yescharacteristic
820C4#1681136211yescharacteristic
821C4#1681136611yescharacteristic
822C2—42no—
823C2—42no—
824C2—42no—
825C2—161no—
826C2#2028271011yescharacteristic
827C2#2028548011yescharacteristic
828C2#2028549211yescharacteristic
829C2#2028550311yescharacteristic
830C2#2028552111yescharacteristic
831C2#2028552911yescharacteristic
832C2#2028554111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
Fitting, prime radicalC53×#2847C2
socleC23×C53C22×D4
hypercenter#2847D53
hypocenterC53#32709
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C24×C4 ◁ #2847

Complements

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

NH ≅ G/Ntype
1. #20283002C2semidirect
2. #20276152C2semidirect
3. #20276146C2semidirect
4. #20276141C2semidirect
5. #20275918C2semidirect
6. #20275918C2semidirect
7. #20275911C2semidirect
8. #20275901C2semidirect
9. #20275894C2semidirect
10. #20275894C2semidirect
11. #20275718C2semidirect
12. #20275718C2semidirect
13. #20275718C2semidirect
14. #20274625C2semidirect
16. C22×#11719923C22semidirect
20. C2×#13133150C22semidirect
21. C2×#13133150C22semidirect
22. C2×#13133148C22semidirect
23. C2×#13133140C22semidirect
24. C2×#13133140C22semidirect
25. C2×#13133140C22semidirect
26. C2×#13133138C22semidirect
27. C2×#13133138C22semidirect
28. C2×#13133138C22semidirect
42. #16810385C22semidirect
43. #16810385C22semidirect
44. #16810385C22semidirect
45. #16810385C22semidirect
46. #16810385C22semidirect
47. #16810385C22semidirect
475. C53#32709semidirect

Maximal subgroups

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

subgroupindex
#202830022
#202761522
#202761462
#202761412
#202759182
#202759112
#202759012
#202758942
#202757182
#202746252
C53×#28472
#3270953