Finite Group Databasebeta

← #27395367

Subgroups — #27395367

Order 13568.

1080 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×#16810773C211yesmaximal, characteristic
2#20277295C211yesmaximal, characteristic
3#20275599C211yesmaximal, characteristic, complemented
4#20275572C211yesmaximal, characteristic, complemented
5#20275411C211yesmaximal, characteristic, complemented
6#20275397C211yesmaximal, characteristic, complemented
7#20275342C211yesmaximal, characteristic, complemented
8#20275335C211yesmaximal, characteristic, complemented
9#20275070C211yesmaximal, characteristic, complemented
10#20275070C211yesmaximal, characteristic, complemented
11#20275028C211yesmaximal, characteristic, complemented
12#20274912C211yesmaximal, characteristic, complemented
13#20274645C211yesmaximal, characteristic
14#20274481C211yesmaximal, characteristic, complemented
15C53×#2323C211yesmaximal, characteristic, complemented
16C23×D212C2211yescharacteristic
17C22×#11719924C2211yescharacteristic
18C22×#11719924C2211yescharacteristic
19C2×#13133176C2211yescharacteristic
20#16810773C418yescomplemented
21C2×#13133150C2211yescharacteristic, complemented
22C2×#13133148C2211yescharacteristic, complemented
23C2×#13133141C2211yescharacteristic, complemented
24C2×#13133141C2211yescharacteristic, complemented
25C2×#13133137C2211yescharacteristic
26C2×#13133137C2211yescharacteristic
27C2×#13133137C2211yescharacteristic
28C2×#13133137C2211yescharacteristic
29C2×#13133137C2211yescharacteristic
30C2×#13133137C2211yescharacteristic
31C2×C22⋊#88322C2211yescharacteristic
32C2×C22⋊#88322C2211yescharacteristic
33C2×#13133128C2211yescharacteristic, complemented
34C2×C4×#88322C2211yescharacteristic, complemented
35#16810525C2211yescharacteristic
36#16810525C2211yescharacteristic
37#16810525C2211yescharacteristic
38#16810525C2211yescharacteristic
39#16810524—21no—
40#16810524—21no—
41#16810478—21no—
42#16810478—21no—
43#16810385C2211yescharacteristic, complemented
44#16810385C2211yescharacteristic, complemented
45#16810385C2211yescharacteristic, complemented
46#16810385C2211yescharacteristic, complemented
47#16810378C2211yescharacteristic, complemented
48#16810378C2211yescharacteristic, complemented
49C2×C22⋊Q8×C53C2211yescharacteristic
50C2×C4×Q8×C53C2211yescharacteristic, complemented
51C2×#117×C53C2211yescharacteristic
52C53×#391C2211yescharacteristic, complemented
53C53×#389—21no—
54C53×#389C2211yescharacteristic, complemented
55C53×#388—21no—
56C53×#388—21no—
57C53×#387—21no—
58C53×#380C2211yescharacteristic
59C4×C4⋊C4×C53C2211yescharacteristic, complemented
60C24×D53—21no—
61C22×D212—21no—
62C22×D212—22no—
63C22×D212—41no—
64C22×D212—41no—
65C22×D212—41no—
66C22×D212—41no—
67C22×D212C2×C414yes—
68C22×D212C2311yescharacteristic
69C22×D212C2311yescharacteristic
70C2×#11719924—41no—
71C2×#11719924—41no—
72C2×#11719924—41no—
73C2×#11719924—41no—
74C2×#11719924C2×C414yes—
75C2×#11719924C2×C414yes—
76C22×#88322C2311yescharacteristic
77C22×#88322C2311yescharacteristic
78C22×#88322C2311yescharacteristic
79C22×#88322C2311yescharacteristic
80#13133176—41no—
81#13133176—41no—
82C2×C4⋊Dic53C2311yescharacteristic
83C2×C4⋊Dic53C2311yescharacteristic
84C2×C22⋊Dic53—21no—
85C2×#11719921—21no—
86C2×#11719921—21no—
87C2×#11719921—21no—
88C2×#11719921—21no—
89C2×#11719921—21no—
90C2×#11719921—21no—
91C2×#11719921—21no—
92C2×#11719921—21no—
93C2×C4×Dic53—21no—
94#13133150—41no—
95#13133148—41no—
96#13133141—41no—
97#13133141—41no—
98#13133137—41no—
99#13133137—41no—
100#13133137—41no—
101#13133137—41no—
102#13133137C2×C414yes—
103#13133137C2×C414yes—
104C22⋊#88322—22no—
105C22⋊#88322C2×C414yes—
106#13133128—41no—
107C4×#88322—41no—
108C22×Q8×C53C2311yescharacteristic
109C23×C4×C53C2311yescharacteristic
110C22⋊Q8×C53—22no—
111C22⋊Q8×C53C2×C414yes—
112C4×Q8×C53—41no—
113C4×Q8×C53—41no—
114#117×C53—41no—
115#117×C53—41no—
116C2×C4⋊C4×C53—21no—
117C2×C4⋊C4×C53—21no—
118C2×C4⋊C4×C53—21no—
119C2×C4⋊C4×C53D411yescharacteristic
120C2×C4⋊C4×C53D411yescharacteristic
121C2×C4⋊C4×C53C2311yescharacteristic
122C2×C4⋊C4×C53C2311yescharacteristic
123C2×C4⋊C4×C53C2311yescharacteristic
124C2×C22⋊C4×C53—21no—
125C2×C22⋊C4×C53—21no—
126C2×C22⋊C4×C53D411yescharacteristic
127C2×C22⋊C4×C53D411yescharacteristic
128C2×C42×C53—21no—
129C2×C42×C53—21no—
130C2×C42×C53C2311yescharacteristic
131C2×C42×C53C2311yescharacteristic
132#95×C53—21no—
133#95×C53—21no—
134#95×C53—21no—
135#95×C53—21no—
136#95×C53—21no—
137C24×C53C2×D411yescharacteristic
138C23×D53—21no—
139C23×D53—21no—
140C23×D53—24no—
141C23×D53—42no—
142C23×D53—42no—
143C23×D53—81no—
144C23×D53—81no—
145C23×D53—81no—
146C23×D53—81no—
147C2×Q8×C53—21no—
148C2×Q8×C53—21no—
149C2×Q8×C53—21no—
150C2×Q8×C53—21no—
151C2×Q8×C53—21no—
152C2×Q8×C53C22×C412yes—
153C22×C4×C53—21no—
154C22×C4×C53—21no—
155C22×C4×C53—21no—
156C22×C4×C53—21no—
157C22×C4×C53—21no—
158C22×C4×C53—21no—
159C22×C4×C53—21no—
160C22×C4×C53—21no—
161C22×C4×C53C22×C412yes—
162C22×C4×C53C2×D411yescharacteristic
163C22×C4×C53C2×D411yescharacteristic
164C22×C4×C53C2×D411yescharacteristic
165C22×C4×C53C2×D411yescharacteristic
166C22×C4×C53C2×D411yescharacteristic
167C22×C4×C53#4112yes—
168C22×C4×C53C2411yescharacteristic
169C22×Dic53—21no—
170C22×Dic53—21no—
171C2×D212—21no—
172C2×D212—21no—
173C2×D212—21no—
174C2×D212—21no—
175C2×D212—21no—
176C2×D212—21no—
177C2×D212—21no—
178C2×D212—21no—
179C2×D212—24no—
180C2×D212—21no—
181C2×D212—21no—
182C2×D212—44no—
183C2×D212—44no—
184C2×D212—42no—
185C2×D212—42no—
186C2×D212—44no—
187C2×D212—44no—
188C2×D212C22×C412yes—
189C2×D212C22×C412yes—
190C4⋊C4×C53—24no—
191C4⋊C4×C53—21no—
192C4⋊C4×C53—21no—
193C4⋊C4×C53—21no—
194C4⋊C4×C53—21no—
195C4⋊C4×C53—21no—
196C4⋊C4×C53—41no—
197C4⋊C4×C53—41no—
198C4⋊C4×C53—42no—
199C4⋊C4×C53—81no—
200C4⋊C4×C53C22×C412yes—
201C22⋊C4×C53—24no—
202C22⋊C4×C53—41no—
203C22⋊C4×C53—41no—
204C22⋊C4×C53—81no—
205C42×C53—21no—
206C42×C53—21no—
207C42×C53—21no—
208C42×C53—21no—
209C42×C53—42no—
210C42×C53—81no—
211C22⋊Dic53—42no—
212#11719924—44no—
213#11719924—44no—
214#11719921—81no—
215#11719921—81no—
216#11719921—81no—
217#11719921—81no—
218#11719921—81no—
219#11719921—81no—
220#11719921—81no—
221#11719921—81no—
222C4⋊Dic53—21no—
223C4⋊Dic53—21no—
224C4⋊Dic53—21no—
225C4⋊Dic53—21no—
226C4×Dic53—42no—
227C2×#88322—21no—
228C2×#88322—21no—
229C2×#88322—21no—
230C2×#88322—21no—
231C2×#88322—21no—
232C2×#88322—21no—
233C2×#88322—21no—
234C2×#88322—21no—
235C2×#88322—21no—
236C2×#88322—21no—
237C2×#88322C22×C412yes—
238C2×#88322C22×C412yes—
239C23×C53—21no—
240C23×C53—21no—
241C23×C53—21no—
242C23×C53—21no—
243C23×C53—21no—
244C23×C53—21no—
245C23×C53C4×D412yes—
246C23×C53C22×D411yescharacteristic
247C22×D53—22no—
248C22×D53—22no—
249C22×D53—48no—
250C22×D53—41no—
251C22×D53—41no—
252C22×D53—41no—
253C22×D53—41no—
254C22×D53—41no—
255C22×D53—41no—
256C22×D53—41no—
257C22×D53—41no—
258C22×D53—41no—
259C22×D53—41no—
260C22×D53—41no—
261C22×D53—41no—
262C22×D53—84no—
263C22×D53—84no—
264C22×D53—84no—
265C22×D53—84no—
266C22×D53—84no—
267C22×D53—84no—
268Q8×C53—22no—
269Q8×C53—22no—
270Q8×C53—41no—
271Q8×C53—41no—
272C2×C4×C53—21no—
273C2×C4×C53—21no—
274C2×C4×C53—22no—
275C2×C4×C53—22no—
276C2×C4×C53—22no—
277C2×C4×C53—22no—
278C2×C4×C53—22no—
279C2×C4×C53—22no—
280C2×C4×C53—21no—
281C2×C4×C53—21no—
282C2×C4×C53—21no—
283C2×C4×C53—21no—
284C2×C4×C53—21no—
285C2×C4×C53—21no—
286C2×C4×C53—21no—
287C2×C4×C53—21no—
288C2×C4×C53—21no—
289C2×C4×C53—21no—
290C2×C4×C53—21no—
291C2×C4×C53—21no—
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×C53—41no—
301C2×C4×C53—41no—
302C2×C4×C53C4×D412yes—
303C2×C4×C53C23×C411yescharacteristic
304C2×C4×C53C2×#4111yescharacteristic
305C2×C4×C53H(5,𝔽2)11yescharacteristic
306C2×C4×C53H(5,𝔽2)11yescharacteristic
307C2×C4×C53H(5,𝔽2)11yescharacteristic
308C2×C4×C53H(5,𝔽2)11yescharacteristic
309C2×Dic53—41no—
310C2×Dic53—41no—
311C2×Dic53—41no—
312C2×Dic53—41no—
313C2×Dic53—41no—
314C2×Dic53—41no—
315D212—22no—
316D212—22no—
317D212—22no—
318D212—22no—
319D212—48no—
320D212—41no—
321D212—41no—
322D212—41no—
323D212—41no—
324#88322—22no—
325#88322—22no—
326#88322—41no—
327#88322—41no—
328#22052—531nomaximal, Sylow
329C22×C53—22no—
330C22×C53—22no—
331C22×C53—22no—
332C22×C53—41no—
333C22×C53—41no—
334C22×C53—41no—
335C22×C53—41no—
336C22×C53C2×C4×D411yescharacteristic
337C22×C53#53411yescharacteristic
338C22×C53#53511yescharacteristic
339C22×C53#57611yescharacteristic
340C22×C53#57711yescharacteristic
341C22×C53#57711yescharacteristic
342C22×C53#57711yescharacteristic
343C2×D53—42no—
344C2×D53—42no—
345C2×D53—42no—
346C2×D53—42no—
347C2×D53—42no—
348C2×D53—42no—
349C2×D53—816no—
350C2×D53—81no—
351C2×D53—81no—
352C2×D53—81no—
353C2×D53—81no—
354C2×D53—81no—
355C2×D53—81no—
356C2×D53—81no—
357C2×D53—81no—
358C4×C53—22no—
359C4×C53—42no—
360C4×C53—41no—
361C4×C53—41no—
362C4×C53—41no—
363C4×C53—41no—
364C4×C53—42no—
365C4×C53—81no—
366C4×C53—81no—
367C4×C53#51811yescharacteristic
368C4×C53#51811yescharacteristic
369C4×C53#53811yescharacteristic
370C4×C53#53811yescharacteristic
371Dic53—81no—
372Dic53—81no—
373C2×#450—531no—
374#2323D5311yescharacteristic, complemented
375#2309—531no—
376#1973—531no—
377#1968—531no—
378#1936—531no—
379#1934—531no—
380#1926—531no—
381#1925—531no—
382#1880—531no—
383#1880—531no—
384#1873—531no—
385#1854—531no—
386#1786—531no—
387#1750—531no—
388C2×C53—42no—
389C2×C53#232111yescharacteristic
390C2×C53#294611yescharacteristic
391C2×C53#294911yescharacteristic
392C2×C53#319811yescharacteristic
393C2×C53#320011yescharacteristic
394C2×C53#322211yescharacteristic
395C2×C53#322411yescharacteristic
396D53—82no—
397D53—82no—
398C23×D4—531no—
399C22×SD16—531no—
400C22×SD16—531no—
401C2×C22⋊Q8C2×D5311yescharacteristic
402C2×C4×Q8C2×D5311yescharacteristic, complemented
403C2×#117—531no—
404C2×#117C2×D5311yescharacteristic
405#450—538no—
406C2×#107—531no—
407C2×#106—531no—
408C2×#103—531no—
409C2×#103—531no—
410C2×#102—531no—
411C2×#102—531no—
412C2×#102—531no—
413C2×#102—531no—
414C2×#102—531no—
415C2×#102—531no—
416C2×C22⋊C8—531no—
417C2×C22⋊C8—531no—
418C2×#97—531no—
419C2×C4×C8—531no—
420#391C2×D5311yescharacteristic, complemented
421#390—531no—
422#390—531no—
423#390—531no—
424#390—531no—
425#390—1061no—
426#390—1061no—
427#389—21no—
428#389C2×D5311yescharacteristic, complemented
429#388—21no—
430#388—21no—
431#387—21no—
432#380C2×D5311yescharacteristic
433#379—1061no—
434#379—1061no—
435C4×C4⋊C4C2×D5311yescharacteristic, complemented
436#340—531no—
437#340—531no—
438#340—531no—
439#340—531no—
440#336—531no—
441#336—531no—
442C53#2205211yescharacteristic, complemented, Sylow
443C25—1061no—
444C22×Q8C22×D5311yescharacteristic
445C22×D4—534no—
446C22×D4—531no—
447C22×D4—531no—
448C22×D4—1062no—
449C22×D4—1061no—
450C22×D4—2121no—
451C22×D4—2121no—
452C22×D4—2121no—
453C22×D4—2121no—
454C23×C4C22×D5311yescharacteristic
455C2×SD16—534no—
456C2×SD16—534no—
457C2×SD16—2121no—
458C2×SD16—2121no—
459C2×SD16—2121no—
460C2×SD16—2121no—
461C22×C8—531no—
462C22×C8—531no—
463C22×C8—531no—
464C22×C8—531no—
465C22⋊Q8—22no—
466C22⋊Q8C4×D5314yes—
467C4×Q8—41no—
468C4×Q8—41no—
469#117—41no—
470#117—41no—
471#117—2121no—
472#117—2121no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—531no—
477C2×C4⋊C4—531no—
478C2×C4⋊C4C22⋊D5311yescharacteristic
479C2×C4⋊C4C22⋊D5311yescharacteristic
480C2×C4⋊C4C22×D5311yescharacteristic
481C2×C4⋊C4C22×D5311yescharacteristic
482C2×C4⋊C4C22×D5311yescharacteristic
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—1061no—
486C2×C22⋊C4—1061no—
487C2×C22⋊C4—1061no—
488C2×C22⋊C4—1061no—
489C2×C22⋊C4—1061no—
490C2×C22⋊C4—1061no—
491C2×C22⋊C4—1061no—
492C2×C22⋊C4—1061no—
493C2×C22⋊C4—1061no—
494C2×C22⋊C4C22⋊D5311yescharacteristic
495C2×C22⋊C4C22⋊D5311yescharacteristic
496C2×C42—21no—
497C2×C42—21no—
498C2×C42—1061no—
499C2×C42C22×D5311yescharacteristic
500C2×C42C22×D5311yescharacteristic
501#107—2121no—
502#106—2121no—
503#103—2121no—
504#103—2121no—
505#102—534no—
506#102—534no—
507#102—2121no—
508#102—2121no—
509#102—2121no—
510#102—2121no—
511C22⋊C8—534no—
512C22⋊C8—1062no—
513#97—2121no—
514C4×C8—2121no—
515#95—21no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95—21no—
520C24—1064no—
521C24—1061no—
522C24—1061no—
523C24—4241no—
524C24—4241no—
525C24—4241no—
526C24—4241no—
527C24—2122no—
528C24—2122no—
529C24C2×C22⋊D5311yescharacteristic
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8C2×C4×D5312yes—
536C2×D4—532no—
537C2×D4—532no—
538C2×D4—1064no—
539C2×D4—1061no—
540C2×D4—1061no—
541C2×D4—1061no—
542C2×D4—1061no—
543C2×D4—1061no—
544C2×D4—1061no—
545C2×D4—1061no—
546C2×D4—1061no—
547C2×D4—1061no—
548C2×D4—1061no—
549C2×D4—2124no—
550C2×D4—2124no—
551C2×D4—2122no—
552C2×D4—2122no—
553C2×D4—2124no—
554C2×D4—2124no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—1061no—
564C22×C4—1061no—
565C22×C4C2×C4×D5312yes—
566C22×C4#1171994512yes—
567C22×C4C2×C22⋊D5311yescharacteristic
568C22×C4C2×C22⋊D5311yescharacteristic
569C22×C4C2×C22⋊D5311yescharacteristic
570C22×C4C2×C22⋊D5311yescharacteristic
571C22×C4C2×C22⋊D5311yescharacteristic
572C22×C4C23×D5311yescharacteristic
573SD16—2124no—
574SD16—2124no—
575C2×C8—532no—
576C2×C8—532no—
577C2×C8—1061no—
578C2×C8—1061no—
579C2×C8—1061no—
580C2×C8—1061no—
581C2×C8—1061no—
582C2×C8—1061no—
583C2×C8—1061no—
584C2×C8—1061no—
585C2×C8—1061no—
586C2×C8—1061no—
587C4⋊C4—24no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—41no—
594C4⋊C4—41no—
595C4⋊C4—42no—
596C4⋊C4—81no—
597C4⋊C4—1061no—
598C4⋊C4—1061no—
599C4⋊C4—1061no—
600C4⋊C4—1061no—
601C4⋊C4C2×C4×D5312yes—
602C22⋊C4—24no—
603C22⋊C4—41no—
604C22⋊C4—41no—
605C22⋊C4—81no—
606C22⋊C4—4241no—
607C22⋊C4—4241no—
608C22⋊C4—4241no—
609C22⋊C4—4241no—
610C22⋊C4—4241no—
611C22⋊C4—4241no—
612C22⋊C4—4241no—
613C22⋊C4—4241no—
614C22⋊C4—2122no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—21no—
619C42—42no—
620C42—81no—
621C42—2122no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—1062no—
629C23—1062no—
630C23—4244no—
631C23—4244no—
632C23—4244no—
633C23—4244no—
634C23—4244no—
635C23—4244no—
636C23—2128no—
637C23—2121no—
638C23—2121no—
639C23—2121no—
640C23—2121no—
641C23—2121no—
642C23—2121no—
643C23—2121no—
644C23—2121no—
645C23—2121no—
646C23—2121no—
647C23—2121no—
648C23—2121no—
649C23C4×C22⋊D5312yes—
650C23C22×C22⋊D5311yescharacteristic
651Q8—22no—
652Q8—22no—
653Q8—41no—
654Q8—41no—
655D4—1062no—
656D4—1062no—
657D4—1062no—
658D4—1062no—
659D4—2128no—
660D4—2121no—
661D4—2121no—
662D4—2121no—
663D4—2121no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—2121no—
695C2×C4—2121no—
696C2×C4—2121no—
697C2×C4—2121no—
698C2×C4—2121no—
699C2×C4—2121no—
700C2×C4C4×C22⋊D5312yes—
701C2×C4C22×C4×D5311yescharacteristic
702C2×C4C2×#1171994511yescharacteristic
703C2×C4#1313326211yescharacteristic
704C2×C4#1313326211yescharacteristic
705C2×C4#1313326311yescharacteristic
706C2×C4#1313326311yescharacteristic
707C8—1062no—
708C8—1062no—
709C8—2121no—
710C8—2121no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—42416no—
719C22—4241no—
720C22—4241no—
721C22—4241no—
722C22—4241no—
723C22—4241no—
724C22—4241no—
725C22—4241no—
726C22—4241no—
727C22—2122no—
728C22—2122no—
729C22—2122no—
730C22—2122no—
731C22—2122no—
732C22—2122no—
733C22C2×C4×C22⋊D5311yescharacteristic
734C22#1681118211yescharacteristic
735C22#1681118711yescharacteristic
736C22#1681142611yescharacteristic
737C22#1681143111yescharacteristic
738C22#1681143111yescharacteristic
739C22#1681143111yescharacteristic
740C4—22no—
741C4—42no—
742C4—41no—
743C4—41no—
744C4—41no—
745C4—41no—
746C4—42no—
747C4—81no—
748C4—81no—
749C4—4241no—
750C4—4241no—
751C4#1681109511yescharacteristic
752C4#1681109511yescharacteristic
753C4#1681120611yescharacteristic
754C4#1681120611yescharacteristic
755C2—42no—
756C2—4242no—
757C2—4242no—
758C2#2027736911yescharacteristic
759C2#2028354311yescharacteristic
760C2#2028357411yescharacteristic
761C2#2028556111yescharacteristic
762C2#2028558211yescharacteristic
763C2#2028578111yescharacteristic
764C2#2028580311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2323C2
socleC23×C53C22×D4
prime radicalC23×D212C22
cosocleC22×C4×C53C24
hypercenter#2323D53
hypocenterC53#22052
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2323

Complements

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

NH ≅ G/Ntype
3. #20275599C2semidirect
4. #20275572C2semidirect
5. #20275411C2semidirect
6. #20275397C2semidirect
7. #20275342C2semidirect
8. #20275335C2semidirect
9. #20275070C2semidirect
10. #20275070C2semidirect
11. #20275028C2semidirect
12. #20274912C2semidirect
14. #20274481C2semidirect
15. C53×#2323C2semidirect
20. #16810773C4semidirect
21. C2×#13133150C22semidirect
22. C2×#13133148C22semidirect
23. C2×#13133141C22semidirect
24. C2×#13133141C22semidirect
33. C2×#13133128C22semidirect
34. C2×C4×#88322C22semidirect
43. #16810385C22semidirect
44. #16810385C22semidirect
45. #16810385C22semidirect
46. #16810385C22semidirect
47. #16810378C22semidirect
48. #16810378C22semidirect
50. C2×C4×Q8×C53C22semidirect
52. C53×#391C22semidirect
54. C53×#389C22semidirect
59. C4×C4⋊C4×C53C22semidirect
374. #2323D53semidirect
402. C2×C4×Q8C2×D53semidirect
420. #391C2×D53semidirect
428. #389C2×D53semidirect
435. C4×C4⋊C4C2×D53semidirect
442. C53#22052semidirect

Maximal subgroups

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

subgroupindex
C2×#168107732
#202772952
#202755992
#202755722
#202754112
#202753972
#202753422
#202753352
#202750702
#202750282
#202749122
#202746452
#202744812
C53×#23232
#2205253