Finite Group Databasebeta

← #27422937

Subgroups — #27422937

Order 13568.

1056 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810774C211yesmaximal, characteristic
2C2×#16810684C211yesmaximal, characteristic, complemented
3#20280512C211yesmaximal, characteristic, complemented
4#20276103C211yesmaximal, characteristic, complemented
5#20276089C211yesmaximal, characteristic, complemented
6#20276032C211yesmaximal, characteristic, complemented
7#20276032C211yesmaximal, characteristic, complemented
8#20275595C211yesmaximal, characteristic, complemented
9#20275568C211yesmaximal, characteristic, complemented
10#20275415C211yesmaximal, characteristic, complemented
11#20275401C211yesmaximal, characteristic, complemented
12#20275027C211yesmaximal, characteristic, complemented
13#20274914C211yesmaximal, characteristic, complemented
14#20274646C211yesmaximal, characteristic
15C53×#2309C211yesmaximal, characteristic
16C22×#11719923C2211yescharacteristic
17C22×#11719923C2211yescharacteristic
18C2×#13133196C2211yescharacteristic
19#16810774—24no—
20#16810684—24no—
21C2×#13133150C2211yescharacteristic, complemented
22C2×#13133148C2211yescharacteristic, complemented
23C2×C4⋊#88322C2211yescharacteristic, complemented
24C2×C4⋊#88322C2211yescharacteristic, complemented
25C2×#13133140C2211yescharacteristic, complemented
26C2×#13133140C2211yescharacteristic, complemented
27C2×#13133138C2211yescharacteristic
28C2×#13133138C2211yescharacteristic
29C2×#13133138C2211yescharacteristic
30C2×#13133138C2211yescharacteristic
31C2×#13133138C2211yescharacteristic
32C2×#13133138C2211yescharacteristic
33C2×C22⋊#88322C2211yescharacteristic
34C2×C22⋊#88322C2211yescharacteristic
35C2×#13133128C2211yescharacteristic, complemented
36C2×C4×#88322C2211yescharacteristic, complemented
37#16810561—21no—
38#16810554—21no—
39#16810551—21no—
40#16810551—21no—
41#16810529C2211yescharacteristic, complemented
42#16810529C2211yescharacteristic, complemented
43#16810521C2211yescharacteristic, complemented
44#16810521C2211yescharacteristic, complemented
45#16810483C2211yescharacteristic
46#16810385C2211yescharacteristic, complemented
47#16810385C2211yescharacteristic, complemented
48#16810385C2211yescharacteristic, complemented
49#16810385C2211yescharacteristic, complemented
50C23×D4×C53C2211yescharacteristic
51C2×#117×C53C2211yescharacteristic
52C2×#117×C53C2211yescharacteristic
53C53×#390—21no—
54C53×#390—21no—
55C53×#390C2211yescharacteristic
56C53×#390C2211yescharacteristic
57C53×#390C2211yescharacteristic
58C53×#390C2211yescharacteristic
59C53×#379—21no—
60C53×#379—21no—
61C22×Dic106C2311yescharacteristic
62C2×#11719923—22no—
63C2×#11719923—22no—
64C2×#11719923—22no—
65C2×#11719923—22no—
66C2×#11719923—41no—
67C2×#11719923—41no—
68C22×#88322C2311yescharacteristic
69C22×#88322C2311yescharacteristic
70C22×#88322C2311yescharacteristic
71C22×#88322C2311yescharacteristic
72#13133196—22no—
73#13133196—22no—
74C2×C4⋊Dic53C2311yescharacteristic
75C2×C4⋊Dic53C2311yescharacteristic
76C2×C4⋊Dic53C2311yescharacteristic
77C2×#11719919—21no—
78C2×#11719919—21no—
79C2×#11719919—21no—
80C2×C22⋊Dic53—21no—
81C2×C22⋊Dic53—21no—
82#13133150—41no—
83#13133148—41no—
84C4⋊#88322—22no—
85C4⋊#88322—22no—
86#13133140—41no—
87#13133140—41no—
88#13133138—22no—
89#13133138—22no—
90#13133138—22no—
91#13133138—22no—
92#13133138—41no—
93#13133138—41no—
94C22⋊#88322—22no—
95C22⋊#88322D414yes—
96#13133128—22no—
97C4×#88322—22no—
98#13133124—21no—
99#13133124—21no—
100#13133124—21no—
101#13133124—21no—
102#13133124—21no—
103#13133124—21no—
104#13133124—21no—
105C25×C53—21no—
106C22×D4×C53—22no—
107C22×D4×C53—22no—
108C22×D4×C53—21no—
109C22×D4×C53—22no—
110C22×D4×C53—22no—
111C22×D4×C53—41no—
112C22×D4×C53—41no—
113C22×D4×C53C2311yescharacteristic
114C22×D4×C53C2311yescharacteristic
115C23×C4×C53C2311yescharacteristic
116#117×C53—22no—
117#117×C53—22no—
118#117×C53—41no—
119#117×C53—41no—
120C2×C4⋊C4×C53D411yescharacteristic
121C2×C4⋊C4×C53D411yescharacteristic
122C2×C4⋊C4×C53C2311yescharacteristic
123C2×C4⋊C4×C53C2311yescharacteristic
124C2×C22⋊C4×C53—21no—
125C2×C22⋊C4×C53—21no—
126C2×C22⋊C4×C53—21no—
127C2×C22⋊C4×C53—21no—
128C2×C22⋊C4×C53—21no—
129C2×C22⋊C4×C53—21no—
130C2×C22⋊C4×C53—21no—
131C2×C22⋊C4×C53—21no—
132C2×C22⋊C4×C53—21no—
133C2×C22⋊C4×C53D411yescharacteristic
134C2×C22⋊C4×C53D411yescharacteristic
135C2×C42×C53—21no—
136C2×C42×C53C2311yescharacteristic
137C2×C42×C53C2311yescharacteristic
138C24×C53—24no—
139C24×C53—21no—
140C24×C53—21no—
141C24×C53—42no—
142C24×C53—42no—
143C24×C53—81no—
144C24×C53—81no—
145C24×C53—81no—
146C24×C53—81no—
147C24×C53C2×D411yescharacteristic
148C2×D4×C53—24no—
149C2×D4×C53—21no—
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—21no—
157C2×D4×C53—21no—
158C2×D4×C53—21no—
159C2×D4×C53—44no—
160C2×D4×C53—44no—
161C2×D4×C53—44no—
162C2×D4×C53—44no—
163C2×D4×C53—42no—
164C2×D4×C53—42no—
165C2×D4×C53#4112yes—
166C2×D4×C53#4112yes—
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×C53C2×D411yescharacteristic
174C22×C4×C53C2×D411yescharacteristic
175C22×C4×C53C2×D411yescharacteristic
176C22×C4×C53C2×D411yescharacteristic
177C22×C4×C53C2×D411yescharacteristic
178C22×C4×C53C2×D412yes—
179C22×C4×C53#4112yes—
180C22×C4×C53C2411yescharacteristic
181C22×Dic53—21no—
182C22×Dic53—21no—
183C22×Dic53—21no—
184C22×Dic53—21no—
185C2×Dic106—21no—
186C2×Dic106—21no—
187C2×Dic106—21no—
188C2×Dic106—21no—
189C2×Dic106—21no—
190C2×Dic106—21no—
191C4⋊C4×C53—22no—
192C4⋊C4×C53—22no—
193C4⋊C4×C53—21no—
194C4⋊C4×C53—21no—
195C4⋊C4×C53—21no—
196C4⋊C4×C53—21no—
197C22⋊C4×C53—22no—
198C22⋊C4×C53—22no—
199C22⋊C4×C53—42no—
200C22⋊C4×C53—81no—
201C22⋊C4×C53—81no—
202C22⋊C4×C53—81no—
203C22⋊C4×C53—81no—
204C22⋊C4×C53—81no—
205C22⋊C4×C53—81no—
206C22⋊C4×C53—81no—
207C22⋊C4×C53—81no—
208C42×C53—21no—
209C42×C53—21no—
210C42×C53—21no—
211C42×C53—21no—
212C42×C53—42no—
213C22⋊Dic53—42no—
214C22⋊Dic53—81no—
215#11719923—44no—
216#11719923—44no—
217C4⋊Dic53—21no—
218C4⋊Dic53—21no—
219C4⋊Dic53—21no—
220C4⋊Dic53—21no—
221C4⋊Dic53—21no—
222C4⋊Dic53—21no—
223#11719919—42no—
224#11719919—81no—
225#11719919—81no—
226C2×#88322—21no—
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×#88322C2×D412yes—
237C2×#88322C2×D412yes—
238C23×C53—21no—
239C23×C53—21no—
240C23×C53—21no—
241C23×C53—21no—
242C23×C53—21no—
243C23×C53—21no—
244C23×C53—22no—
245C23×C53—22no—
246C23×C53—48no—
247C23×C53—41no—
248C23×C53—41no—
249C23×C53—41no—
250C23×C53—41no—
251C23×C53—41no—
252C23×C53—41no—
253C23×C53—41no—
254C23×C53—41no—
255C23×C53—41no—
256C23×C53—41no—
257C23×C53—41no—
258C23×C53—41no—
259C23×C53—84no—
260C23×C53—84no—
261C23×C53—84no—
262C23×C53—84no—
263C23×C53—84no—
264C23×C53—84no—
265C23×C53#12112yes—
266C23×C53C22×D411yescharacteristic
267D4×C53—22no—
268D4×C53—22no—
269D4×C53—22no—
270D4×C53—22no—
271D4×C53—48no—
272D4×C53—41no—
273D4×C53—41no—
274D4×C53—41no—
275D4×C53—41no—
276C2×C4×C53—21no—
277C2×C4×C53—21no—
278C2×C4×C53—22no—
279C2×C4×C53—22no—
280C2×C4×C53—22no—
281C2×C4×C53—22no—
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—21no—
293C2×C4×C53—21no—
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#12112yes—
301C2×C4×C53C22×D411yescharacteristic
302C2×C4×C53C2×#4111yescharacteristic
303C2×C4×C53C2×#4111yescharacteristic
304C2×C4×C53C2×#4111yescharacteristic
305C2×C4×C53H(5,𝔽2)11yescharacteristic
306C2×C4×C53H(5,𝔽2)11yescharacteristic
307C2×Dic53—41no—
308C2×Dic53—41no—
309C2×Dic53—41no—
310C2×Dic53—41no—
311C2×Dic53—41no—
312C2×Dic53—41no—
313C2×Dic53—41no—
314C2×Dic53—41no—
315C2×Dic53—41no—
316C2×Dic53—41no—
317C2×Dic53—41no—
318C2×Dic53—41no—
319Dic106—41no—
320Dic106—41no—
321Dic106—41no—
322Dic106—41no—
323#88322—22no—
324#88322—22no—
325#88322—41no—
326#88322—41no—
327#24516—531nomaximal, Sylow
328C22×C53—22no—
329C22×C53—22no—
330C22×C53—22no—
331C22×C53—41no—
332C22×C53—41no—
333C22×C53—41no—
334C22×C53—41no—
335C22×C53—42no—
336C22×C53—42no—
337C22×C53—42no—
338C22×C53—42no—
339C22×C53—42no—
340C22×C53—42no—
341C22×C53—816no—
342C22×C53—81no—
343C22×C53—81no—
344C22×C53—81no—
345C22×C53—81no—
346C22×C53—81no—
347C22×C53—81no—
348C22×C53—81no—
349C22×C53—81no—
350C22×C53C2×#12111yescharacteristic
351C22×C53#52511yescharacteristic
352C22×C53#53511yescharacteristic
353C22×C53#57611yescharacteristic
354C22×C53#57711yescharacteristic
355C22×C53#57711yescharacteristic
356C22×C53#57711yescharacteristic
357C4×C53—22no—
358C4×C53—41no—
359C4×C53—41no—
360C4×C53—41no—
361C4×C53—41no—
362C4×C53—81no—
363C4×C53—81no—
364C4×C53#54611yescharacteristic
365C4×C53#54611yescharacteristic
366C4×C53#55111yescharacteristic
367C4×C53#55111yescharacteristic
368Dic53—81no—
369Dic53—81no—
370Dic53—81no—
371Dic53—81no—
372C2×#450—531no—
373C2×#433—531no—
374#2625—531no—
375#2309D5311yescharacteristic
376#2067—531no—
377#2065—531no—
378#2055—531no—
379#2055—531no—
380#1973—531no—
381#1968—531no—
382#1936—531no—
383#1934—531no—
384#1873—531no—
385#1854—531no—
386#1786—531no—
387C2×C53—42no—
388C2×C53—82no—
389C2×C53—82no—
390C2×C53#241111yescharacteristic
391C2×C53#305711yescharacteristic
392C2×C53#306211yescharacteristic
393C2×C53#311811yescharacteristic
394C2×C53#312311yescharacteristic
395C2×C53#322211yescharacteristic
396C2×C53#322411yescharacteristic
397C23×D4C2×D5311yescharacteristic
398C22×SD16—531no—
399C22×SD16—531no—
400C2×C22⋊Q8—531no—
401C2×#117C2×D5311yescharacteristic
402C2×#117C2×D5311yescharacteristic
403#450—1064no—
404#433—1064no—
405C2×#107—531no—
406C2×#106—531no—
407C2×C4⋊C8—531no—
408C2×C4⋊C8—531no—
409C2×#103—531no—
410C2×#103—531no—
411C2×#102—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×#97—531no—
420C2×C4×C8—531no—
421#400—1061no—
422#398—1061no—
423#397—1061no—
424#397—1061no—
425#391—531no—
426#391—531no—
427#390—21no—
428#390—21no—
429#390C2×D5311yescharacteristic
430#390C2×D5311yescharacteristic
431#390C2×D5311yescharacteristic
432#390C2×D5311yescharacteristic
433#389—531no—
434#389—531no—
435#380—531no—
436#379—21no—
437#379—21no—
438#340—531no—
439#340—531no—
440#340—531no—
441#340—531no—
442C53#2451611yescharacteristic, complemented, Sylow
443C25—21no—
444C22×Q8—531no—
445C22×D4—22no—
446C22×D4—22no—
447C22×D4—22no—
448C22×D4—22no—
449C22×D4—21no—
450C22×D4—41no—
451C22×D4—41no—
452C22×D4C22×D5311yescharacteristic
453C22×D4C22×D5311yescharacteristic
454C23×C4C22×D5311yescharacteristic
455C2×SD16—1062no—
456C2×SD16—1062no—
457C2×SD16—1062no—
458C2×SD16—1062no—
459C2×SD16—2121no—
460C2×SD16—2121no—
461C22×C8—531no—
462C22×C8—531no—
463C22×C8—531no—
464C22×C8—531no—
465C22⋊Q8—1062no—
466C22⋊Q8—1062no—
467#117—22no—
468#117—22no—
469#117—41no—
470#117—41no—
471C2×C4⋊C4—531no—
472C2×C4⋊C4—531no—
473C2×C4⋊C4—531no—
474C2×C4⋊C4—1061no—
475C2×C4⋊C4—1061no—
476C2×C4⋊C4—1061no—
477C2×C4⋊C4C22⋊D5311yescharacteristic
478C2×C4⋊C4C22⋊D5311yescharacteristic
479C2×C4⋊C4C22×D5311yescharacteristic
480C2×C4⋊C4C22×D5311yescharacteristic
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—1061no—
491C2×C22⋊C4—1061no—
492C2×C22⋊C4C22⋊D5311yescharacteristic
493C2×C22⋊C4C22⋊D5311yescharacteristic
494C2×C42—21no—
495C2×C42C22×D5311yescharacteristic
496C2×C42C22×D5311yescharacteristic
497#107—2121no—
498#106—2121no—
499C4⋊C8—1062no—
500C4⋊C8—1062no—
501#103—2121no—
502#103—2121no—
503#102—1062no—
504#102—1062no—
505#102—1062no—
506#102—1062no—
507#102—2121no—
508#102—2121no—
509C22⋊C8—534no—
510C22⋊C8—1062no—
511#97—1062no—
512C4×C8—1062no—
513#95—1061no—
514#95—1061no—
515#95—1061no—
516#95—1061no—
517#95—1061no—
518#95—1061no—
519#95—1061no—
520C24—24no—
521C24—21no—
522C24—21no—
523C24—42no—
524C24—42no—
525C24—81no—
526C24—81no—
527C24—81no—
528C24—81no—
529C24C2×C22⋊D5311yescharacteristic
530C2×Q8—1061no—
531C2×Q8—1061no—
532C2×Q8—1061no—
533C2×Q8—1061no—
534C2×Q8—1061no—
535C2×Q8—1061no—
536C2×D4—24no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4—44no—
550C2×D4—44no—
551C2×D4—42no—
552C2×D4—42no—
553C2×D4#1171994512yes—
554C2×D4#1171994512yes—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—1061no—
562C22×C4—1061no—
563C22×C4—1061no—
564C22×C4—1061no—
565C22×C4D4×D5312yes—
566C22×C4#1171994712yes—
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—22no—
588C4⋊C4—22no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—1061no—
594C4⋊C4—1061no—
595C4⋊C4—1061no—
596C4⋊C4—1061no—
597C4⋊C4—1061no—
598C4⋊C4—1061no—
599C4⋊C4—4241no—
600C4⋊C4—4241no—
601C4⋊C4—2122no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—42no—
605C22⋊C4—81no—
606C22⋊C4—81no—
607C22⋊C4—81no—
608C22⋊C4—81no—
609C22⋊C4—81no—
610C22⋊C4—81no—
611C22⋊C4—81no—
612C22⋊C4—81no—
613C22⋊C4—4241no—
614C22⋊C4—2122no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—21no—
619C42—42no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—22no—
627C23—22no—
628C23—48no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—84no—
642C23—84no—
643C23—84no—
644C23—84no—
645C23—84no—
646C23—84no—
647C23#1313318912yes—
648C23C22×C22⋊D5311yescharacteristic
649Q8—2121no—
650Q8—2121no—
651Q8—2121no—
652Q8—2121no—
653D4—22no—
654D4—22no—
655D4—22no—
656D4—22no—
657D4—48no—
658D4—41no—
659D4—41no—
660D4—41no—
661D4—41no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
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—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—2121no—
687C2×C4—2121no—
688C2×C4—2121no—
689C2×C4—2121no—
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×C4#1313318912yes—
699C2×C4C2×D4×D5311yescharacteristic
700C2×C4C2×#1171994711yescharacteristic
701C2×C4C2×#1171994511yescharacteristic
702C2×C4C2×#1171994511yescharacteristic
703C2×C4#1313326211yescharacteristic
704C2×C4#1313326211yescharacteristic
705C8—1062no—
706C8—1062no—
707C8—2121no—
708C8—2121no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—816no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22C2×#1313318911yescharacteristic
732C22#1681113411yescharacteristic
733C22#1681119011yescharacteristic
734C22#1681142611yescharacteristic
735C22#1681143411yescharacteristic
736C22#1681143411yescharacteristic
737C22#1681143411yescharacteristic
738C4—22no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—81no—
744C4—81no—
745C4—4241no—
746C4—4241no—
747C4—4241no—
748C4—4241no—
749C4#1681126311yescharacteristic
750C4#1681126311yescharacteristic
751C4#1681129911yescharacteristic
752C4#1681129911yescharacteristic
753C2—42no—
754C2—82no—
755C2—82no—
756C2#2027810011yescharacteristic
757C2#2028435111yescharacteristic
758C2#2028439111yescharacteristic
759C2#2028489911yescharacteristic
760C2#2028496711yescharacteristic
761C2#2028578711yescharacteristic
762C2#2028580911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
FittingC53×#2309C2
socleC23×C53C22×D4
prime radicalC23×D4×C53C22
hypercenter#2309D53
hypocenterC53#24516
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2309

Complements

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

NH ≅ G/Ntype
2. C2×#16810684C2semidirect
3. #20280512C2semidirect
4. #20276103C2semidirect
5. #20276089C2semidirect
6. #20276032C2semidirect
7. #20276032C2semidirect
8. #20275595C2semidirect
9. #20275568C2semidirect
10. #20275415C2semidirect
11. #20275401C2semidirect
12. #20275027C2semidirect
13. #20274914C2semidirect
21. C2×#13133150C22semidirect
22. C2×#13133148C22semidirect
23. C2×C4⋊#88322C22semidirect
24. C2×C4⋊#88322C22semidirect
25. C2×#13133140C22semidirect
26. C2×#13133140C22semidirect
35. C2×#13133128C22semidirect
36. C2×C4×#88322C22semidirect
41. #16810529C22semidirect
42. #16810529C22semidirect
43. #16810521C22semidirect
44. #16810521C22semidirect
46. #16810385C22semidirect
47. #16810385C22semidirect
48. #16810385C22semidirect
49. #16810385C22semidirect
442. C53#24516semidirect

Maximal subgroups

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

subgroupindex
C2×#168107742
C2×#168106842
#202805122
#202761032
#202760892
#202760322
#202755952
#202755682
#202754152
#202754012
#202750272
#202749142
#202746462
C53×#23092
#2451653