Finite Group Databasebeta

← #27395284

Subgroups — #27395284

Order 13568.

1096 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810768C211yesmaximal, characteristic
2C4×#13133191C211yesmaximal, characteristic, complemented
3#20275580C211yesmaximal, characteristic, complemented
4#20275572C211yesmaximal, characteristic, complemented
5#20275401C211yesmaximal, characteristic, complemented
6#20275394C211yesmaximal, characteristic, complemented
7#20275353C211yesmaximal, characteristic, complemented
8#20275339C211yesmaximal, characteristic, complemented
9#20275066C211yesmaximal, characteristic, complemented
10#20275052C211yesmaximal, characteristic, complemented
11#20275037C211yesmaximal, characteristic, complemented
12#20274914C211yesmaximal, characteristic, complemented
13#20274655C211yesmaximal, characteristic, complemented
14C4×C22⋊#88322C211yesmaximal, characteristic, complemented
15C53×#2297C211yesmaximal, characteristic, complemented
16C22×#11719924C2211yescharacteristic
17C22×#11719922C2211yescharacteristic
18C2×#13133191C2211yescharacteristic
19C2×C4×D212C2211yescharacteristic
20C2×C4×C22⋊D53—21no—
21#16810768C418yescomplemented
22C2×#13133150C2211yescharacteristic
23C2×#13133148C2211yescharacteristic
24C2×#13133141C2211yescharacteristic
25C2×#13133141C2211yescharacteristic
26C2×#13133141C2211yescharacteristic
27C2×#13133138C2211yescharacteristic
28C2×#13133138C2211yescharacteristic
29C2×#13133138C2211yescharacteristic
30C2×#13133137C2211yescharacteristic
31C2×#13133137C2211yescharacteristic
32C2×C22⋊#88322C2211yescharacteristic
33C2×C22⋊#88322C2211yescharacteristic
34C2×C4×#88322C2211yescharacteristic
35C2×C4×#88322C2211yescharacteristic
36#16810525C2211yescharacteristic
37#16810521C2211yescharacteristic
38#16810514—21no—
39#16810502—21no—
40#16810483C2211yescharacteristic
41C4×C4⋊Dic53C2211yescharacteristic
42C4×#11719921—21no—
43#16810385C2211yescharacteristic
44#16810385C2211yescharacteristic
45#16810385C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810378C2211yescharacteristic
48#16810378C2211yescharacteristic
49C22×#41×C53C2211yescharacteristic
50C2×#117×C53C2211yescharacteristic
51C22×C42×C53C2211yescharacteristic
52C53×#391C2211yescharacteristic
53C53×#391C2211yescharacteristic
54C53×#390C2211yescharacteristic
55C53×#390C2211yescharacteristic
56C53×#386—21no—
57C53×#386—21no—
58C4×C22⋊C4×C53—21no—
59C4×C22⋊C4×C53—21no—
60C22×D212C2311yescharacteristic
61C22×C22⋊D53—21no—
62C22×C4×D53—21no—
63C2×#11719924—41no—
64C2×#11719924—41no—
65C2×#11719924C2×C414yescomplemented
66C2×#11719922—41no—
67C2×#11719922—41no—
68C2×#11719922C2×C414yescomplemented
69C22×#88322C2311yescharacteristic
70C22×#88322C2311yescharacteristic
71C22×#88322C2311yescharacteristic
72C22×#88322C2311yescharacteristic
73#13133191—22no—
74#13133191C2×C414yes—
75C4×D212—41no—
76C4×D212—41no—
77C4×C22⋊D53—44no—
78C2×C4⋊Dic53C2311yescharacteristic
79C2×C4⋊Dic53C2311yescharacteristic
80C2×C4⋊Dic53C2311yescharacteristic
81C2×#11719919—21no—
82C2×C22⋊Dic53—21no—
83C2×#11719921—21no—
84C2×#11719921—21no—
85C2×#11719921—21no—
86C2×#11719921—21no—
87C2×C4×Dic53—21no—
88#13133150—41no—
89#13133148—41no—
90#13133141—41no—
91#13133141—41no—
92#13133141C2×C414yescomplemented
93#13133138—41no—
94#13133138—41no—
95#13133138C2×C414yescomplemented
96#13133137—41no—
97#13133137—41no—
98C22⋊#88322—22no—
99C22⋊#88322C2×C414yescomplemented
100C4×#88322—41no—
101C4×#88322—41no—
102#13133124—21no—
103#13133124—21no—
104#13133124—21no—
105C2×#41×C53—22no—
106C2×#41×C53—41no—
107C2×#41×C53—41no—
108C2×#41×C53—41no—
109C2×#41×C53—41no—
110C2×#41×C53C2×C414yescomplemented
111C22×Q8×C53C2311yescharacteristic
112C22×D4×C53—21no—
113C22×D4×C53C2311yescharacteristic
114C23×C4×C53—21no—
115C23×C4×C53D411yescharacteristic
116C23×C4×C53D411yescharacteristic
117C23×C4×C53C2311yescharacteristic
118#117×C53—41no—
119#117×C53—41no—
120C2×C4⋊C4×C53C2311yescharacteristic
121C2×C4⋊C4×C53C2311yescharacteristic
122C2×C22⋊C4×C53—21no—
123C2×C22⋊C4×C53—21no—
124C2×C22⋊C4×C53—21no—
125C2×C22⋊C4×C53—21no—
126C2×C22⋊C4×C53—21no—
127C2×C42×C53—21no—
128C2×C42×C53—41no—
129C2×C42×C53—41no—
130C2×C42×C53D411yescharacteristic
131C2×C42×C53D411yescharacteristic
132C2×C42×C53C2311yescharacteristic
133C2×C42×C53C2311yescharacteristic
134#95×C53—21no—
135#95×C53—21no—
136#95×C53—21no—
137#95×C53—21no—
138C24×C53—21no—
139C24×C53C2×D411yescharacteristic
140C23×D53—21no—
141#41×C53—44no—
142#41×C53—44no—
143#41×C53—44no—
144#41×C53—44no—
145C2×Q8×C53—21no—
146C2×Q8×C53—21no—
147C2×Q8×C53—21no—
148C2×Q8×C53—21no—
149C2×Q8×C53—21no—
150C2×Q8×C53C22×C412yes—
151C2×D4×C53—24no—
152C2×D4×C53—21no—
153C2×D4×C53—21no—
154C2×D4×C53—21no—
155C2×D4×C53—21no—
156C2×D4×C53—21no—
157C2×D4×C53—42no—
158C2×D4×C53—42no—
159C2×D4×C53C22×C412yes—
160C22×C4×C53—21no—
161C22×C4×C53—21no—
162C22×C4×C53—21no—
163C22×C4×C53—21no—
164C22×C4×C53—21no—
165C22×C4×C53—24no—
166C22×C4×C53—22no—
167C22×C4×C53—22no—
168C22×C4×C53—22no—
169C22×C4×C53—21no—
170C22×C4×C53—21no—
171C22×C4×C53—41no—
172C22×C4×C53—41no—
173C22×C4×C53—41no—
174C22×C4×C53—42no—
175C22×C4×C53—42no—
176C22×C4×C53C22×C412yes—
177C22×C4×C53C2×D411yescharacteristic
178C22×C4×C53C2×D411yescharacteristic
179C22×C4×C53C2×D411yescharacteristic
180C22×C4×C53C2×D411yescharacteristic
181C22×C4×C53C2×D411yescharacteristic
182C22×C4×C53#4112yes—
183C22×C4×C53C2411yescharacteristic
184C2×C22⋊D53—24no—
185C2×C22⋊D53—42no—
186C2×C22⋊D53—42no—
187C22×Dic53—21no—
188C22×Dic53—21no—
189C22×Dic53—21no—
190C2×D212—21no—
191C2×D212—21no—
192C2×D212—21no—
193C2×D212—21no—
194C2×D212—21no—
195C2×D212C22×C412yes—
196C2×C4×D53—42no—
197C2×C4×D53—42no—
198C2×C4×D53—42no—
199C4⋊C4×C53—21no—
200C4⋊C4×C53—21no—
201C4⋊C4×C53—21no—
202C4⋊C4×C53—21no—
203C22⋊C4×C53—42no—
204C22⋊C4×C53—42no—
205C22⋊C4×C53—42no—
206C22⋊C4×C53—42no—
207C22⋊C4×C53—42no—
208C42×C53—21no—
209C42×C53—21no—
210C42×C53—21no—
211C42×C53—21no—
212C42×C53—41no—
213C42×C53—41no—
214C42×C53—42no—
215C22⋊Dic53—42no—
216#11719924—44no—
217#11719922—44no—
218#11719921—24no—
219#11719921—42no—
220#11719921—42no—
221#11719921—42no—
222C4⋊Dic53—21no—
223C4⋊Dic53—21no—
224C4⋊Dic53—21no—
225C4⋊Dic53—21no—
226C4⋊Dic53—21no—
227C4⋊Dic53C22×C412yes—
228#11719919—42no—
229C4×Dic53—42no—
230C2×#88322—21no—
231C2×#88322—21no—
232C2×#88322—21no—
233C2×#88322—21no—
234C2×#88322—21no—
235C2×#88322—21no—
236C2×#88322—21no—
237C2×#88322—21no—
238C2×#88322—21no—
239C2×#88322—21no—
240C2×#88322C22×C412yes—
241C2×#88322C22×C412yes—
242C23×C53—21no—
243C23×C53—21no—
244C23×C53—21no—
245C23×C53—21no—
246C23×C53—21no—
247C23×C53—21no—
248C23×C53—22no—
249C23×C53—41no—
250C23×C53—41no—
251C23×C53—41no—
252C23×C53—41no—
253C23×C53—41no—
254C23×C53—41no—
255C23×C53C4×D412yes—
256C23×C53C22×D411yescharacteristic
257C22×D53—22no—
258C22×D53—41no—
259C22×D53—41no—
260C22×D53—41no—
261C22×D53—41no—
262C22×D53—41no—
263C22×D53—41no—
264Q8×C53—22no—
265Q8×C53—22no—
266Q8×C53—41no—
267Q8×C53—41no—
268D4×C53—22no—
269D4×C53—22no—
270D4×C53—48no—
271D4×C53—41no—
272D4×C53—41no—
273C2×C4×C53—21no—
274C2×C4×C53—21no—
275C2×C4×C53—21no—
276C2×C4×C53—21no—
277C2×C4×C53—21no—
278C2×C4×C53—21no—
279C2×C4×C53—21no—
280C2×C4×C53—21no—
281C2×C4×C53—22no—
282C2×C4×C53—22no—
283C2×C4×C53—22no—
284C2×C4×C53—22no—
285C2×C4×C53—22no—
286C2×C4×C53—21no—
287C2×C4×C53—21no—
288C2×C4×C53—21no—
289C2×C4×C53—44no—
290C2×C4×C53—44no—
291C2×C4×C53—48no—
292C2×C4×C53—41no—
293C2×C4×C53—41no—
294C2×C4×C53—41no—
295C2×C4×C53—41no—
296C2×C4×C53—41no—
297C2×C4×C53—41no—
298C2×C4×C53—41no—
299C2×C4×C53—41no—
300C2×C4×C53C4×D412yes—
301C2×C4×C53#13512yes—
302C2×C4×C53#13512yes—
303C2×C4×C53AGL(1,ℤ/8)12yes—
304C2×C4×C53C23×C411yescharacteristic
305C2×C4×C53C2×#4111yescharacteristic
306C2×C4×C53H(5,𝔽2)11yescharacteristic
307C2×C4×C53H(5,𝔽2)11yescharacteristic
308C2×C4×C53H(5,𝔽2)11yescharacteristic
309C2×C4×C53H(5,𝔽2)11yescharacteristic
310C22⋊D53—48no—
311C2×Dic53—22no—
312C2×Dic53—41no—
313C2×Dic53—41no—
314C2×Dic53—41no—
315C2×Dic53—41no—
316C2×Dic53—41no—
317C2×Dic53—41no—
318C2×Dic53—41no—
319C2×Dic53—41no—
320D212—22no—
321D212—22no—
322D212—41no—
323D212—41no—
324C4×D53—84no—
325#88322—22no—
326#88322—22no—
327#88322—41no—
328#88322—41no—
329#22045—531nomaximal, Sylow
330C22×C53—22no—
331C22×C53—22no—
332C22×C53—22no—
333C22×C53—41no—
334C22×C53—41no—
335C22×C53—41no—
336C22×C53—41no—
337C22×C53—42no—
338C22×C53—42no—
339C22×C53—42no—
340C22×C53—81no—
341C22×C53—81no—
342C22×C53—81no—
343C22×C53—81no—
344C22×C53C2×C4×D411yescharacteristic
345C22×C53#53411yescharacteristic
346C22×C53#53511yescharacteristic
347C22×C53C2×#13511yescharacteristic
348C22×C53C2×#13511yescharacteristic
349C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
350C22×C53#57511yescharacteristic
351C2×D53—42no—
352C2×D53—42no—
353C2×D53—42no—
354C2×D53—81no—
355C2×D53—81no—
356C2×D53—81no—
357C2×D53—81no—
358C4×C53—22no—
359C4×C53—22no—
360C4×C53—22no—
361C4×C53—22no—
362C4×C53—42no—
363C4×C53—41no—
364C4×C53—81no—
365C4×C53—81no—
366C4×C53#51811yescharacteristic
367C4×C53#51811yescharacteristic
368C4×C53#53811yescharacteristic
369C4×C53#53811yescharacteristic
370Dic53—42no—
371Dic53—81no—
372Dic53—81no—
373C2×#449—531no—
374C4×#121—531no—
375#2297D5311yescharacteristic, complemented
376#1970—531no—
377#1968—531no—
378#1934—531no—
379#1933—531no—
380#1928—531no—
381#1926—531no—
382#1879—531no—
383#1877—531no—
384#1875—531no—
385#1854—531no—
386#1788—531no—
387C4×C22⋊C8—531no—
388C2×C53—42no—
389C2×C53—82no—
390C2×C53#232111yescharacteristic
391C2×C53C4×#13511yescharacteristic
392C2×C53C4×AGL(1,ℤ/8)11yescharacteristic
393C2×C53#318811yescharacteristic
394C2×C53#319111yescharacteristic
395C2×C53#320711yescharacteristic
396C2×C53#321211yescharacteristic
397D53—82no—
398C22×#41C2×D5311yescharacteristic
399C22×SD16—531no—
400C22×D8—531no—
401C2×#121—531no—
402C2×C4×D4—531no—
403C2×C4×D4—1061no—
404C2×#117C2×D5311yescharacteristic
405C22×C42C2×D5311yescharacteristic
406#449—538no—
407C2×#107—531no—
408C2×#106—531no—
409C2×#103—531no—
410C2×#103—531no—
411C2×#103—531no—
412C2×#102—531no—
413C2×#102—531no—
414C2×#102—531no—
415C2×#102—531no—
416C2×#102—531no—
417C2×C22⋊C8—531no—
418C2×C22⋊C8—531no—
419C2×C4×C8—531no—
420C2×C4×C8—531no—
421#391C2×D5311yescharacteristic
422#391C2×D5311yescharacteristic
423#390—531no—
424#390C2×D5311yescharacteristic
425#390C2×D5311yescharacteristic
426#389—531no—
427#388—1061no—
428#386—21no—
429#386—21no—
430#386—1061no—
431#380—531no—
432C4×C4⋊C4—531no—
433C4×C22⋊C4—21no—
434C4×C22⋊C4—21no—
435C4×C22⋊C4—1061no—
436#340—531no—
437#340—531no—
438#340—531no—
439#340—531no—
440#336—531no—
441#336—531no—
442C53#2204511yescharacteristic, complemented, Sylow
443C2×#41—22no—
444C2×#41—41no—
445C2×#41—41no—
446C2×#41—41no—
447C2×#41—41no—
448C2×#41C4×D5314yescomplemented
449C22×Q8C22×D5311yescharacteristic
450C22×D4—21no—
451C22×D4—531no—
452C22×D4—1061no—
453C22×D4C22×D5311yescharacteristic
454C23×C4—21no—
455C23×C4—1061no—
456C23×C4C22⋊D5311yescharacteristic
457C23×C4C22⋊D5311yescharacteristic
458C23×C4C22×D5311yescharacteristic
459C2×SD16—534no—
460C2×SD16—2121no—
461C2×SD16—2121no—
462C2×D8—534no—
463C2×D8—2121no—
464C2×D8—2121no—
465C22×C8—531no—
466C22×C8—531no—
467C22×C8—531no—
468C22×C8—531no—
469#121—534no—
470#121—1062no—
471C4×D4—2121no—
472C4×D4—2121no—
473C4×D4—2124no—
474#117—41no—
475#117—41no—
476C2×C4⋊C4—531no—
477C2×C4⋊C4—531no—
478C2×C4⋊C4—531no—
479C2×C4⋊C4—1061no—
480C2×C4⋊C4C22×D5311yescharacteristic
481C2×C4⋊C4C22×D5311yescharacteristic
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—1061no—
488C2×C22⋊C4—1061no—
489C2×C22⋊C4—1061no—
490C2×C22⋊C4—1061no—
491C2×C22⋊C4—1061no—
492C2×C42—21no—
493C2×C42—41no—
494C2×C42—41no—
495C2×C42—1061no—
496C2×C42C22⋊D5311yescharacteristic
497C2×C42C22⋊D5311yescharacteristic
498C2×C42C22×D5311yescharacteristic
499C2×C42C22×D5311yescharacteristic
500#107—2121no—
501#106—2121no—
502#103—534no—
503#103—2121no—
504#103—2121no—
505#102—534no—
506#102—2121no—
507#102—2121no—
508#102—2121no—
509#102—2121no—
510C22⋊C8—534no—
511C22⋊C8—1062no—
512C4×C8—2121no—
513C4×C8—2121no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—21no—
518#95—1061no—
519#95—1061no—
520#95—1061no—
521C24—21no—
522C24—1061no—
523C24C2×C22⋊D5311yescharacteristic
524#41—44no—
525#41—44no—
526#41—44no—
527#41—44no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8C2×C4×D5312yes—
534C2×D4—24no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—532no—
543C2×D4—1064no—
544C2×D4—1061no—
545C2×D4—1061no—
546C2×D4—1061no—
547C2×D4—1061no—
548C2×D4—1061no—
549C2×D4—2122no—
550C2×D4—2122no—
551C2×D4C2×C4×D5312yes—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—24no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—1061no—
569C22×C4—1061no—
570C22×C4—1061no—
571C22×C4—2122no—
572C22×C4—2122no—
573C22×C4—2122no—
574C22×C4C2×C4×D5312yes—
575C22×C4#1171994512yes—
576C22×C4C2×C22⋊D5311yescharacteristic
577C22×C4C2×C22⋊D5311yescharacteristic
578C22×C4C2×C22⋊D5311yescharacteristic
579C22×C4C2×C22⋊D5311yescharacteristic
580C22×C4C2×C22⋊D5311yescharacteristic
581C22×C4C23×D5311yescharacteristic
582SD16—2124no—
583D8—2124no—
584C2×C8—532no—
585C2×C8—532no—
586C2×C8—1061no—
587C2×C8—1061no—
588C2×C8—1061no—
589C2×C8—1061no—
590C2×C8—1061no—
591C2×C8—1061no—
592C2×C8—1061no—
593C2×C8—1061no—
594C2×C8—1061no—
595C2×C8—1061no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—532no—
601C4⋊C4—1061no—
602C4⋊C4—1061no—
603C4⋊C4—1061no—
604C4⋊C4—1061no—
605C4⋊C4—1061no—
606C4⋊C4—2122no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—42no—
612C22⋊C4—1064no—
613C22⋊C4—2122no—
614C22⋊C4—2122no—
615C22⋊C4—2122no—
616C22⋊C4—2122no—
617C42—21no—
618C42—21no—
619C42—21no—
620C42—21no—
621C42—41no—
622C42—41no—
623C42—42no—
624C42—2122no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—22no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—1062no—
639C23—2121no—
640C23—2121no—
641C23—2121no—
642C23—2121no—
643C23—2121no—
644C23—2121no—
645C23C4×C22⋊D5312yes—
646C23C22×C22⋊D5311yescharacteristic
647Q8—22no—
648Q8—22no—
649Q8—41no—
650Q8—41no—
651D4—22no—
652D4—22no—
653D4—48no—
654D4—41no—
655D4—41no—
656D4—1062no—
657D4—1062no—
658D4—2128no—
659D4—2121no—
660D4—2121no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—44no—
678C2×C4—44no—
679C2×C4—48no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—1062no—
689C2×C4—4244no—
690C2×C4—2121no—
691C2×C4—2121no—
692C2×C4—2121no—
693C2×C4—2121no—
694C2×C4—2121no—
695C2×C4—2121no—
696C2×C4—2121no—
697C2×C4—2121no—
698C2×C4C4×C22⋊D5312yes—
699C2×C4#1313323712yes—
700C2×C4#1313323712yes—
701C2×C4#1313324212yes—
702C2×C4C22×C4×D5311yescharacteristic
703C2×C4C2×#1171994511yescharacteristic
704C2×C4#1313326211yescharacteristic
705C2×C4#1313326211yescharacteristic
706C2×C4#1313326211yescharacteristic
707C2×C4#1313326211yescharacteristic
708C8—1062no—
709C8—1062no—
710C8—2121no—
711C8—2121no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—4241no—
727C22—4241no—
728C22—4241no—
729C22—4241no—
730C22—2122no—
731C22—2122no—
732C22—2122no—
733C22C2×C4×C22⋊D5311yescharacteristic
734C22#1681118211yescharacteristic
735C22#1681119011yescharacteristic
736C22C2×#1313323711yescharacteristic
737C22C2×#1313323711yescharacteristic
738C22C2×#1313324211yescharacteristic
739C22#1681142111yescharacteristic
740C4—22no—
741C4—22no—
742C4—22no—
743C4—22no—
744C4—41no—
745C4—42no—
746C4—81no—
747C4—81no—
748C4—4241no—
749C4—4241no—
750C4—2122no—
751C4#1681109611yescharacteristic
752C4#1681109611yescharacteristic
753C4#1681121111yescharacteristic
754C4#1681121111yescharacteristic
755C2—42no—
756C2—82no—
757C2—4242no—
758C2#2027737311yescharacteristic
759C2C4×#1313323711yescharacteristic
760C2C4×#1313324211yescharacteristic
761C2#2028547611yescharacteristic
762C2#2028550311yescharacteristic
763C2#2028564811yescharacteristic
764C2#2028569111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2297C2
socleC23×C53C22×D4
prime radicalC2×#16810768C2
cosocleC22×C4×C53C24
hypercenter#2297D53
hypocenterC53#22045
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2297

Complements

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

NH ≅ G/Ntype
2. C4×#13133191C2semidirect
3. #20275580C2semidirect
4. #20275572C2semidirect
5. #20275401C2semidirect
6. #20275394C2semidirect
7. #20275353C2semidirect
8. #20275339C2semidirect
9. #20275066C2semidirect
10. #20275052C2semidirect
11. #20275037C2semidirect
12. #20274914C2semidirect
13. #20274655C2semidirect
14. C4×C22⋊#88322C2semidirect
15. C53×#2297C2semidirect
21. #16810768C4semidirect
65. C2×#11719924C2×C4semidirect
68. C2×#11719922C2×C4semidirect
92. #13133141C2×C4semidirect
95. #13133138C2×C4semidirect
99. C22⋊#88322C2×C4semidirect
110. C2×#41×C53C2×C4semidirect
375. #2297D53semidirect
442. C53#22045semidirect
448. C2×#41C4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168107682
C4×#131331912
#202755802
#202755722
#202754012
#202753942
#202753532
#202753392
#202750662
#202750522
#202750372
#202749142
#202746552
C4×C22⋊#883222
C53×#22972
#2204553