Finite Group Databasebeta

← #27395422

Subgroups — #27395422

Order 13568.

1024 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20277410C211yesmaximal, characteristic, complemented
2#20277307C211yesmaximal, characteristic, complemented
3#20275598C211yesmaximal, characteristic, complemented
4#20275582C211yesmaximal, characteristic, complemented
5#20275414C211yesmaximal, characteristic, complemented
6#20275393C211yesmaximal, characteristic, complemented
7#20275358C211yesmaximal, characteristic, complemented
8#20275337C211yesmaximal, characteristic, complemented
9#20275065C211yesmaximal, characteristic, complemented
10#20275051C211yesmaximal, characteristic, complemented
11#20275033C211yesmaximal, characteristic, complemented
12#20274905C211yesmaximal, characteristic, complemented
13#20274655C211yesmaximal, characteristic, complemented
14#20274483C211yesmaximal, characteristic, complemented
15C2×C53×#449C211yesmaximal, characteristic
16C2×D4×Dic53C2211yescharacteristic
17C2×#13133176C2211yescharacteristic
18C22×C4⋊Dic53C2211yescharacteristic
19C2×#13133151C2211yescharacteristic
20C2×#13133151C2211yescharacteristic
21C2×#13133141C2211yescharacteristic
22C2×#13133141C2211yescharacteristic
23C2×#13133138C2211yescharacteristic
24C2×#13133138C2211yescharacteristic
25C2×#13133138C2211yescharacteristic
26C2×#13133138C2211yescharacteristic
27C2×C22⋊#88322C2211yescharacteristic
28C2×#13133127C2211yescharacteristic
29C2×C8×Dic53C2211yescharacteristic
30#16810530C2211yescharacteristic
31#16810530C2211yescharacteristic
32#16810526—21no—
33#16810526C2211yescharacteristic
34#16810526C2211yescharacteristic
35#16810526C2211yescharacteristic
36#16810522C2211yescharacteristic
37#16810516—21no—
38#16810503—21no—
39#16810503—21no—
40#16810503—21no—
41#16810498—21no—
42#16810483—21no—
43#16810483—21no—
44#16810483C2211yescharacteristic
45C4⋊C4×Dic53C2211yescharacteristic
46#16810386C2211yescharacteristic
47#16810386C2211yescharacteristic
48#16810385C2211yescharacteristic
49#16810385C2211yescharacteristic
50#16810377C2211yescharacteristic
51#16810377C2211yescharacteristic
52C22×#41×C53C2211yescharacteristic
53C22×SD16×C53C2211yescharacteristic
54C22×D8×C53C2211yescharacteristic
55C2×#121×C53C2211yescharacteristic
56C53×#449C418yescomplemented
57C2×#103×C53C2211yescharacteristic
58C2×#102×C53C2211yescharacteristic
59C2×C22⋊C8×C53C2211yescharacteristic
60C23×Dic53—21no—
61C23×Dic53—21no—
62C22×#88322C2311yescharacteristic
63C22×#88322C2311yescharacteristic
64D4×Dic53—41no—
65D4×Dic53—41no—
66#13133176—41no—
67#13133176—41no—
68C2×C4⋊Dic53—21no—
69C2×C4⋊Dic53—21no—
70C2×C4⋊Dic53—41no—
71C2×C4⋊Dic53—41no—
72C2×C4⋊Dic53D411yescharacteristic
73C2×C4⋊Dic53D411yescharacteristic
74C2×C4⋊Dic53C2311yescharacteristic
75C2×C4⋊Dic53C2311yescharacteristic
76C2×C4⋊Dic53C2311yescharacteristic
77C2×C4⋊Dic53C2311yescharacteristic
78C2×C22⋊Dic53—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—
85C2×C22⋊Dic53—21no—
86C2×C22⋊Dic53D411yescharacteristic
87C2×C22⋊Dic53D411yescharacteristic
88C2×C4×Dic53—21no—
89C2×C4×Dic53C2311yescharacteristic
90C2×C4×Dic53C2311yescharacteristic
91#13133151—41no—
92#13133151—41no—
93#13133141—41no—
94#13133141—41no—
95#13133138—41no—
96#13133138—41no—
97#13133138—41no—
98#13133138—41no—
99C22⋊#88322—22no—
100#13133127—41no—
101C8×Dic53—41no—
102#13133124—21no—
103#13133124—21no—
104#13133124—21no—
105#13133124—21no—
106#13133124—21no—
107#13133124—21no—
108#13133124—21no—
109C2×#41×C53—22no—
110C2×#41×C53—41no—
111C2×#41×C53—41no—
112C2×#41×C53—41no—
113C2×#41×C53—41no—
114C2×#41×C53C2×C414yescomplemented
115C22×Q8×C53C2311yescharacteristic
116C22×D4×C53—21no—
117C22×D4×C53—21no—
118C22×D4×C53C2311yescharacteristic
119C22×D4×C53C2311yescharacteristic
120C23×C4×C53—21no—
121C23×C4×C53C2311yescharacteristic
122C2×SD16×C53—41no—
123C2×SD16×C53—41no—
124C2×SD16×C53C2×C414yescomplemented
125C2×D8×C53—41no—
126C2×D8×C53—41no—
127C2×D8×C53C2×C414yescomplemented
128C22×C8×C53C2311yescharacteristic
129C22×C8×C53C2311yescharacteristic
130#121×C53—22no—
131#121×C53C2×C414yes—
132C2×C4⋊C4×C53C2311yescharacteristic
133C2×C22⋊C4×C53—21no—
134#103×C53C2×C414yescomplemented
135#102×C53C2×C414yescomplemented
136C22⋊C8×C53C2×C414yescomplemented
137C24×C53—21no—
138C24×C53—21no—
139C24×C53C2×D411yescharacteristic
140#41×C53—44no—
141#41×C53—44no—
142#41×C53—44no—
143#41×C53—44no—
144C2×Q8×C53—21no—
145C2×Q8×C53—21no—
146C2×Q8×C53—21no—
147C2×Q8×C53—21no—
148C2×Q8×C53—21no—
149C2×Q8×C53C22×C412yes—
150C2×D4×C53—24no—
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—21no—
158C2×D4×C53—21no—
159C2×D4×C53—21no—
160C2×D4×C53—21no—
161C2×D4×C53—21no—
162C2×D4×C53—42no—
163C2×D4×C53—42no—
164C2×D4×C53—81no—
165C2×D4×C53—81no—
166C2×D4×C53C22×C412yes—
167C2×D4×C53C22×C412yes—
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—24no—
175C22×C4×C53—42no—
176C22×C4×C53—42no—
177C22×C4×C53C22×C412yes—
178C22×C4×C53C2×D411yescharacteristic
179C22×C4×C53#4112yes—
180C22×C4×C53C2411yescharacteristic
181C22×Dic53—21no—
182C22×Dic53—21no—
183C22×Dic53—21no—
184C22×Dic53—21no—
185C22×Dic53—42no—
186C22×Dic53—42no—
187C22×Dic53—81no—
188C22×Dic53—81no—
189C22×Dic53—81no—
190C22×Dic53—81no—
191C22×Dic53C2×D411yescharacteristic
192C22×Dic53C2×D411yescharacteristic
193C22×Dic53C2×D411yescharacteristic
194C22×Dic53C2×D411yescharacteristic
195SD16×C53—44no—
196D8×C53—44no—
197C2×C8×C53—21no—
198C2×C8×C53—21no—
199C2×C8×C53—21no—
200C2×C8×C53—21no—
201C2×C8×C53C22×C412yes—
202C2×C8×C53C22×C412yes—
203C4⋊C4×C53—21no—
204C4⋊C4×C53C22×C412yes—
205C22⋊C4×C53—24no—
206C22⋊Dic53—41no—
207C22⋊Dic53—41no—
208C22⋊Dic53—42no—
209C22⋊Dic53—81no—
210C22⋊Dic53—81no—
211C22⋊Dic53—81no—
212C22⋊Dic53—81no—
213C22⋊Dic53—81no—
214C22⋊Dic53—81no—
215C22⋊Dic53—81no—
216C4⋊Dic53—21no—
217C4⋊Dic53—21no—
218C4⋊Dic53—21no—
219C4⋊Dic53—21no—
220C4⋊Dic53—21no—
221C4⋊Dic53—21no—
222C4⋊Dic53—21no—
223C4⋊Dic53—21no—
224C4⋊Dic53—41no—
225C4⋊Dic53—41no—
226C4⋊Dic53—42no—
227C4⋊Dic53—81no—
228C4×Dic53—21no—
229C4×Dic53—21no—
230C4×Dic53—21no—
231C4×Dic53—21no—
232C4×Dic53—81no—
233C2×#88322—21no—
234C2×#88322—21no—
235C2×#88322—21no—
236C2×#88322—21no—
237C2×#88322—21no—
238C2×#88322—21no—
239C23×C53—21no—
240C23×C53—21no—
241C23×C53—21no—
242C23×C53—21no—
243C23×C53—21no—
244C23×C53—21no—
245C23×C53—22no—
246C23×C53—22no—
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×C53C4×D412yes—
260C23×C53C22×D411yescharacteristic
261Q8×C53—22no—
262Q8×C53—22no—
263Q8×C53—41no—
264Q8×C53—41no—
265D4×C53—22no—
266D4×C53—22no—
267D4×C53—22no—
268D4×C53—22no—
269D4×C53—48no—
270D4×C53—41no—
271D4×C53—41no—
272D4×C53—41no—
273D4×C53—41no—
274D4×C53—84no—
275C2×C4×C53—21no—
276C2×C4×C53—21no—
277C2×C4×C53—22no—
278C2×C4×C53—22no—
279C2×C4×C53—22no—
280C2×C4×C53—22no—
281C2×C4×C53—22no—
282C2×C4×C53—22no—
283C2×C4×C53—48no—
284C2×C4×C53—41no—
285C2×C4×C53—41no—
286C2×C4×C53—41no—
287C2×C4×C53—41no—
288C2×C4×C53C4×D412yes—
289C2×C4×C53C23×C411yescharacteristic
290C2×C4×C53C2×#4111yescharacteristic
291C2×C4×C53H(5,𝔽2)11yescharacteristic
292C2×C4×C53H(5,𝔽2)11yescharacteristic
293C2×C4×C53H(5,𝔽2)11yescharacteristic
294C2×C4×C53H(5,𝔽2)11yescharacteristic
295C2×Dic53—21no—
296C2×Dic53—21no—
297C2×Dic53—21no—
298C2×Dic53—21no—
299C2×Dic53—21no—
300C2×Dic53—21no—
301C2×Dic53—21no—
302C2×Dic53—21no—
303C2×Dic53—21no—
304C2×Dic53—21no—
305C2×Dic53—21no—
306C2×Dic53—21no—
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—
319C2×Dic53—84no—
320C2×Dic53—84no—
321C8×C53—22no—
322C8×C53—22no—
323#88322—41no—
324#88322—41no—
325#22055—531nomaximal, Sylow
326C22×C53—22no—
327C22×C53—22no—
328C22×C53—22no—
329C22×C53—41no—
330C22×C53—41no—
331C22×C53—41no—
332C22×C53—41no—
333C22×C53—42no—
334C22×C53—42no—
335C22×C53—42no—
336C22×C53—42no—
337C22×C53—42no—
338C22×C53—42no—
339C22×C53—81no—
340C22×C53—81no—
341C22×C53—81no—
342C22×C53—81no—
343C22×C53—81no—
344C22×C53—81no—
345C22×C53—81no—
346C22×C53—81no—
347C22×C53C2×C4×D411yescharacteristic
348C22×C53#53411yescharacteristic
349C22×C53#53511yescharacteristic
350C22×C53#57611yescharacteristic
351C22×C53#57611yescharacteristic
352C22×C53#57711yescharacteristic
353C22×C53#57811yescharacteristic
354C4×C53—22no—
355C4×C53—42no—
356C4×C53—42no—
357C4×C53#51811yescharacteristic
358C4×C53#51811yescharacteristic
359C4×C53#53811yescharacteristic
360C4×C53#53811yescharacteristic
361Dic53—41no—
362Dic53—41no—
363Dic53—41no—
364Dic53—41no—
365Dic53—81no—
366Dic53—81no—
367Dic53—81no—
368Dic53—81no—
369C2×#449D5311yescharacteristic
370#2324—531no—
371#2311—531no—
372#1973—531no—
373#1970—531no—
374#1936—531no—
375#1933—531no—
376#1928—531no—
377#1925—531no—
378#1879—531no—
379#1877—531no—
380#1874—531no—
381#1852—531no—
382#1788—531no—
383#1750—531no—
384C2×C53—42no—
385C2×C53—82no—
386C2×C53—82no—
387C2×C53#232111yescharacteristic
388C2×C53#294611yescharacteristic
389C2×C53#295111yescharacteristic
390C2×C53#319811yescharacteristic
391C2×C53#320311yescharacteristic
392C2×C53#322011yescharacteristic
393C2×C53#322511yescharacteristic
394C22×#41C2×D5311yescharacteristic
395C22×SD16C2×D5311yescharacteristic
396C22×D8C2×D5311yescharacteristic
397C2×#121C2×D5311yescharacteristic
398C2×C4×D4—531no—
399C2×#117—531no—
400C22×C4⋊C4—531no—
401#449Dic5318yescomplemented
402C2×#107—531no—
403C2×#107—531no—
404C2×#103—531no—
405C2×#103—531no—
406C2×#103C2×D5311yescharacteristic
407C2×#102—531no—
408C2×#102—531no—
409C2×#102—531no—
410C2×#102—531no—
411C2×#102C2×D5311yescharacteristic
412C2×C22⋊C8—531no—
413C2×C22⋊C8C2×D5311yescharacteristic
414C2×#97—531no—
415C2×C4×C8—531no—
416#391—531no—
417#391—531no—
418#390—531no—
419#390—531no—
420#390—531no—
421#390—1061no—
422#389—531no—
423#388—1061no—
424#386—1061no—
425#386—1061no—
426#386—1061no—
427#385—1061no—
428#380—531no—
429#380—1061no—
430#380—1061no—
431C4×C4⋊C4—531no—
432#340—531no—
433#340—531no—
434#340—531no—
435#340—531no—
436#336—531no—
437#336—531no—
438C53#2205511yescharacteristic, complemented, Sylow
439C2×#41—22no—
440C2×#41—41no—
441C2×#41—41no—
442C2×#41—41no—
443C2×#41—41no—
444C2×#41C2×Dic5314yescomplemented
445C22×Q8C22×D5311yescharacteristic
446C22×D4—21no—
447C22×D4—21no—
448C22×D4C22×D5311yescharacteristic
449C22×D4C22×D5311yescharacteristic
450C23×C4—21no—
451C23×C4—1061no—
452C23×C4—1061no—
453C23×C4C22×D5311yescharacteristic
454C2×SD16—41no—
455C2×SD16—41no—
456C2×SD16C2×Dic5314yescomplemented
457C2×D8—41no—
458C2×D8—41no—
459C2×D8C2×Dic5314yescomplemented
460C22×C8—531no—
461C22×C8—531no—
462C22×C8C22×D5311yescharacteristic
463C22×C8C22×D5311yescharacteristic
464#121—22no—
465#121C2×Dic5314yes—
466C4×D4—2121no—
467C4×D4—2121no—
468#117—2121no—
469#117—2121no—
470C2×C4⋊C4—531no—
471C2×C4⋊C4—531no—
472C2×C4⋊C4—531no—
473C2×C4⋊C4—531no—
474C2×C4⋊C4—531no—
475C2×C4⋊C4—531no—
476C2×C4⋊C4—1061no—
477C2×C4⋊C4—1061no—
478C2×C4⋊C4—2121no—
479C2×C4⋊C4—2121no—
480C2×C4⋊C4C22×D5311yescharacteristic
481C2×C22⋊C4—21no—
482C2×C22⋊C4—531no—
483C2×C22⋊C4—531no—
484C2×C22⋊C4—1061no—
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×C42—531no—
493C2×C42—531no—
494C2×C42—1061no—
495#107—2121no—
496#107—2121no—
497#103—2121no—
498#103—2121no—
499#103C2×Dic5314yescomplemented
500#102—2121no—
501#102—2121no—
502#102—2121no—
503#102—2121no—
504#102C2×Dic5314yescomplemented
505C22⋊C8—1062no—
506C22⋊C8C2×Dic5314yescomplemented
507#97—2121no—
508C4×C8—2121no—
509#95—1061no—
510#95—1061no—
511#95—1061no—
512#95—1061no—
513#95—1061no—
514#95—1061no—
515#95—1061no—
516C24—21no—
517C24—21no—
518C24D4×D5311yescharacteristic
519#41—44no—
520#41—44no—
521#41—44no—
522#41—44no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8C22×Dic5312yes—
529C2×D4—24no—
530C2×D4—24no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—42no—
542C2×D4—42no—
543C2×D4—81no—
544C2×D4—81no—
545C2×D4C22×Dic5312yes—
546C2×D4C22×Dic5312yes—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—24no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—531no—
557C22×C4—531no—
558C22×C4—531no—
559C22×C4—531no—
560C22×C4—1061no—
561C22×C4—1061no—
562C22×C4—1061no—
563C22×C4—1061no—
564C22×C4—4241no—
565C22×C4—4241no—
566C22×C4—4241no—
567C22×C4—4241no—
568C22×C4—2122no—
569C22×C4—2122no—
570C22×C4D4×D5311yescharacteristic
571C22×C4#1171994712yes—
572C22×C4C22×Dic5312yes—
573C22×C4C23×D5311yescharacteristic
574SD16—44no—
575D8—44no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—1061no—
581C2×C8—1061no—
582C2×C8—1061no—
583C2×C8—1061no—
584C2×C8—1061no—
585C2×C8—1061no—
586C2×C8C22×Dic5312yes—
587C2×C8C22×Dic5312yes—
588C4⋊C4—21no—
589C4⋊C4—1061no—
590C4⋊C4—1061no—
591C4⋊C4—1061no—
592C4⋊C4—1061no—
593C4⋊C4—1061no—
594C4⋊C4—1061no—
595C4⋊C4—1061no—
596C4⋊C4—1061no—
597C4⋊C4—4241no—
598C4⋊C4—2121no—
599C4⋊C4—2121no—
600C4⋊C4—2122no—
601C4⋊C4C22×Dic5312yes—
602C22⋊C4—24no—
603C22⋊C4—4241no—
604C22⋊C4—4241no—
605C22⋊C4—4241no—
606C22⋊C4—4241no—
607C22⋊C4—4241no—
608C22⋊C4—4241no—
609C22⋊C4—4241no—
610C22⋊C4—2121no—
611C22⋊C4—2121no—
612C22⋊C4—2122no—
613C42—1061no—
614C42—1061no—
615C42—1061no—
616C42—1061no—
617C42—4241no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—22no—
625C23—22no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23D4×Dic5312yes—
639C23C2×D4×D5311yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—41no—
643Q8—41no—
644D4—22no—
645D4—22no—
646D4—22no—
647D4—22no—
648D4—48no—
649D4—41no—
650D4—41no—
651D4—41no—
652D4—41no—
653D4—84no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—48no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—1061no—
668C2×C4—1061no—
669C2×C4—1061no—
670C2×C4—1061no—
671C2×C4—1061no—
672C2×C4—1061no—
673C2×C4—1061no—
674C2×C4—1061no—
675C2×C4—1061no—
676C2×C4—1061no—
677C2×C4—1061no—
678C2×C4—1061no—
679C2×C4—4244no—
680C2×C4—4244no—
681C2×C4—2121no—
682C2×C4—2121no—
683C2×C4—2121no—
684C2×C4—2121no—
685C2×C4—2121no—
686C2×C4—2121no—
687C2×C4—2121no—
688C2×C4—2121no—
689C2×C4—2121no—
690C2×C4—2121no—
691C2×C4—2121no—
692C2×C4—2121no—
693C2×C4D4×Dic5312yes—
694C2×C4C23×Dic5311yescharacteristic
695C2×C4C2×#1171994711yescharacteristic
696C2×C4#1313326211yescharacteristic
697C2×C4#1313326211yescharacteristic
698C2×C4#1313326211yescharacteristic
699C2×C4#1313326211yescharacteristic
700C8—22no—
701C8—22no—
702C8—2121no—
703C8—2121no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22C2×D4×Dic5311yescharacteristic
726C22#1681118311yescharacteristic
727C22#1681118811yescharacteristic
728C22#1681142511yescharacteristic
729C22#1681142711yescharacteristic
730C22#1681143311yescharacteristic
731C22#1681143711yescharacteristic
732C4—22no—
733C4—42no—
734C4—42no—
735C4—4241no—
736C4—4241no—
737C4—4241no—
738C4—4241no—
739C4—2121no—
740C4—2121no—
741C4—2121no—
742C4—2121no—
743C4#1681109811yescharacteristic
744C4#1681109811yescharacteristic
745C4#1681120811yescharacteristic
746C4#1681120811yescharacteristic
747C2—42no—
748C2—82no—
749C2—82no—
750C2#2027737611yescharacteristic
751C2#2028354811yescharacteristic
752C2#2028359111yescharacteristic
753C2#2028556411yescharacteristic
754C2#2028561411yescharacteristic
755C2#2028576311yescharacteristic
756C2#2028582011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
Fitting, prime radicalC2×C53×#449C2
socleC23×C53C22×D4
cosocleC22×C4×C53C24
hypercenterC2×#449D53
hypocenterC53#22055
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. #20277410C2semidirect
2. #20277307C2semidirect
3. #20275598C2semidirect
4. #20275582C2semidirect
5. #20275414C2semidirect
6. #20275393C2semidirect
7. #20275358C2semidirect
8. #20275337C2semidirect
9. #20275065C2semidirect
10. #20275051C2semidirect
11. #20275033C2semidirect
12. #20274905C2semidirect
13. #20274655C2semidirect
14. #20274483C2semidirect
56. C53×#449C4semidirect
114. C2×#41×C53C2×C4semidirect
124. C2×SD16×C53C2×C4semidirect
127. C2×D8×C53C2×C4semidirect
134. #103×C53C2×C4semidirect
135. #102×C53C2×C4semidirect
136. C22⋊C8×C53C2×C4semidirect
401. #449Dic53semidirect
438. C53#22055semidirect
444. C2×#41C2×Dic53semidirect
456. C2×SD16C2×Dic53semidirect
459. C2×D8C2×Dic53semidirect
499. #103C2×Dic53semidirect
504. #102C2×Dic53semidirect
506. C22⋊C8C2×Dic53semidirect

Maximal subgroups

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

subgroupindex
#202774102
#202773072
#202755982
#202755822
#202754142
#202753932
#202753582
#202753372
#202750652
#202750512
#202750332
#202749052
#202746552
#202744832
C2×C53×#4492
#2205553