Finite Group Databasebeta

← #27417673

Subgroups — #27417673

Order 13568.

1122 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810944C211yesmaximal, characteristic, complemented
2C2×#16810659C211yesmaximal, characteristic, complemented
3#20279012C211yesmaximal, characteristic, complemented
4#20276050C211yesmaximal, characteristic, complemented
5#20276050C211yesmaximal, characteristic, complemented
6#20275901C211yesmaximal, characteristic, complemented
7#20275894C211yesmaximal, characteristic, complemented
8#20275144C211yesmaximal, characteristic, complemented
9#20275008C211yesmaximal, characteristic, complemented
10#20274976C211yesmaximal, characteristic, complemented
11#20274962C211yesmaximal, characteristic, complemented
12#20274908C211yesmaximal, characteristic, complemented
13#20274903C211yesmaximal, characteristic, complemented
14#20274810C211yesmaximal, characteristic, complemented
15C2×C53×#553C211yesmaximal, characteristic
16C23×#88322C2211yescharacteristic
17C2×#13133176C2211yescharacteristic
18#16810944—24no—
19#16810659—24no—
20C2×#13133150C2211yescharacteristic
21C2×#13133150C2211yescharacteristic
22C2×#13133150C2211yescharacteristic
23C2×#13133148C2211yescharacteristic
24C2×#13133148C2211yescharacteristic
25C2×#13133148C2211yescharacteristic
26C2×#13133138C2211yescharacteristic
27C2×#13133138C2211yescharacteristic
28C2×#13133138C2211yescharacteristic
29C2×#13133138C2211yescharacteristic
30C2×C22⋊#88322C2211yescharacteristic
31C2×C22⋊#88322C2211yescharacteristic
32C2×C22⋊#88322C2211yescharacteristic
33#16810551—21no—
34#16810537—21no—
35#16810521C2211yescharacteristic
36#16810521C2211yescharacteristic
37#16810511—21no—
38#16810504—21no—
39#16810483C2211yescharacteristic
40#16810483C2211yescharacteristic
41#16810483C2211yescharacteristic
42#16810385C2211yescharacteristic
43#16810385C2211yescharacteristic
44#16810385C2211yescharacteristic
45#16810385C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810378C2211yescharacteristic
49#16810378C2211yescharacteristic
50C53×#553—24no—
51C53×#553—24no—
52C2×#126×C53—21no—
53C2×#125×C53C2211yescharacteristic
54C2×#123×C53—21no—
55C2×#121×C53—21no—
56C2×#121×C53C2211yescharacteristic
57C2×#121×C53C2211yescharacteristic
58C2×C4×D4×C53—21no—
59C2×C4×D4×C53C2211yescharacteristic
60C2×C4×D4×C53C2211yescharacteristic
61C2×#117×C53C2211yescharacteristic
62C22×C4⋊C4×C53C2211yescharacteristic
63C22×#88322—22no—
64C22×#88322—22no—
65C22×#88322—22no—
66C22×#88322C2311yescharacteristic
67C22×#88322C2311yescharacteristic
68C22×#88322C2311yescharacteristic
69C22×#88322C2311yescharacteristic
70#13133176—22no—
71#13133176—22no—
72C2×C4⋊Dic53C2311yescharacteristic
73C2×C4⋊Dic53C2311yescharacteristic
74C2×C4⋊Dic53C2311yescharacteristic
75C2×C4⋊Dic53C2311yescharacteristic
76C2×#11719919—21no—
77C2×#11719919—21no—
78C2×C22⋊Dic53—21no—
79C2×C22⋊Dic53—21no—
80C2×C22⋊Dic53—21no—
81C2×C22⋊Dic53—21no—
82C2×C4×Dic53—21no—
83#13133150—22no—
84#13133150—22no—
85#13133150—22no—
86#13133148—22no—
87#13133148—22no—
88#13133148—22no—
89#13133138—22no—
90#13133138—22no—
91#13133138—22no—
92#13133138—22no—
93C22⋊#88322—22no—
94C22⋊#88322—22no—
95C22⋊#88322—22no—
96#13133124—21no—
97#13133124—21no—
98#13133124—21no—
99#13133124—21no—
100#13133124—21no—
101C22×D4×C53—21no—
102C22×D4×C53—21no—
103C22×D4×C53D411yescharacteristic
104C22×D4×C53C2311yescharacteristic
105C23×C4×C53—21no—
106C23×C4×C53—21no—
107C23×C4×C53C2311yescharacteristic
108C23×C4×C53C2311yescharacteristic
109#126×C53—28no—
110#125×C53—22no—
111#125×C53—22no—
112#123×C53—28no—
113#121×C53—28no—
114#121×C53—22no—
115#121×C53—22no—
116#121×C53—22no—
117#121×C53D414yes—
118C4×D4×C53—28no—
119C4×D4×C53—22no—
120C4×D4×C53—22no—
121C4×D4×C53—22no—
122C4×D4×C53—22no—
123#117×C53—22no—
124#117×C53D414yes—
125C2×C4⋊C4×C53—22no—
126C2×C4⋊C4×C53—22no—
127C2×C4⋊C4×C53—21no—
128C2×C4⋊C4×C53—21no—
129C2×C4⋊C4×C53—21no—
130C2×C4⋊C4×C53D411yescharacteristic
131C2×C4⋊C4×C53C2311yescharacteristic
132C2×C4⋊C4×C53C2311yescharacteristic
133C2×C4⋊C4×C53C2311yescharacteristic
134C2×C22⋊C4×C53—21no—
135C2×C22⋊C4×C53—21no—
136C2×C22⋊C4×C53—21no—
137C2×C22⋊C4×C53—21no—
138C2×C22⋊C4×C53D411yescharacteristic
139C2×C22⋊C4×C53D411yescharacteristic
140C2×C42×C53—21no—
141C2×C42×C53C2311yescharacteristic
142C24×C53—21no—
143C24×C53C2×D411yescharacteristic
144C24×C53C2×D411yescharacteristic
145C2×D4×C53—24no—
146C2×D4×C53—22no—
147C2×D4×C53—22no—
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—41no—
155C2×D4×C53—42no—
156C2×D4×C53—42no—
157C2×D4×C53—81no—
158C2×D4×C53—81no—
159C2×D4×C53C2×D412yes—
160C22×C4×C53—21no—
161C22×C4×C53—21no—
162C22×C4×C53—21no—
163C22×C4×C53—21no—
164C22×C4×C53—21no—
165C22×C4×C53—21no—
166C22×C4×C53—21no—
167C22×C4×C53—24no—
168C22×C4×C53—24no—
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—81no—
176C22×C4×C53—81no—
177C22×C4×C53—81no—
178C22×C4×C53—81no—
179C22×C4×C53C2×D411yescharacteristic
180C22×C4×C53C2×D411yescharacteristic
181C22×C4×C53C2×D411yescharacteristic
182C22×C4×C53C2×D411yescharacteristic
183C22×C4×C53C2×D412yes—
184C22×C4×C53C2×D412yes—
185C22×C4×C53C2411yescharacteristic
186C22×Dic53—21no—
187C22×Dic53—21no—
188C22×Dic53—21no—
189C22×Dic53—21no—
190C4⋊C4×C53—24no—
191C4⋊C4×C53—24no—
192C4⋊C4×C53—24no—
193C4⋊C4×C53—22no—
194C4⋊C4×C53—21no—
195C4⋊C4×C53—21no—
196C4⋊C4×C53—21no—
197C4⋊C4×C53C2×D412yes—
198C4⋊C4×C53C2×D412yes—
199C4⋊C4×C53C2×D412yes—
200C22⋊C4×C53—24no—
201C22⋊C4×C53—24no—
202C22⋊C4×C53—24no—
203C22⋊C4×C53—22no—
204C22⋊C4×C53—24no—
205C22⋊C4×C53—22no—
206C42×C53—24no—
207C42×C53—21no—
208C42×C53—21no—
209C22⋊Dic53—42no—
210C22⋊Dic53—42no—
211C22⋊Dic53—81no—
212C22⋊Dic53—81no—
213C4⋊Dic53—21no—
214C4⋊Dic53—21no—
215C4⋊Dic53—21no—
216C4⋊Dic53—21no—
217C4⋊Dic53—21no—
218C4⋊Dic53—21no—
219C4⋊Dic53—21no—
220C4⋊Dic53—21no—
221#11719919—42no—
222#11719919—81no—
223C4×Dic53—42no—
224C2×#88322—28no—
225C2×#88322—21no—
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#4112yes—
236C2×#88322#4112yes—
237C23×C53—21no—
238C23×C53—21no—
239C23×C53—21no—
240C23×C53—21no—
241C23×C53—21no—
242C23×C53—21no—
243C23×C53—21no—
244C23×C53—21no—
245C23×C53—21no—
246C23×C53—21no—
247C23×C53—21no—
248C23×C53—21no—
249C23×C53—22no—
250C23×C53—41no—
251C23×C53—41no—
252C23×C53—41no—
253C23×C53—41no—
254C23×C53—41no—
255C23×C53—41no—
256C23×C53#12012yes—
257C23×C53#13512yes—
258C23×C53C22×D411yescharacteristic
259D4×C53—22no—
260D4×C53—22no—
261D4×C53—44no—
262D4×C53—48no—
263D4×C53—41no—
264D4×C53—41no—
265D4×C53—84no—
266C2×C4×C53—21no—
267C2×C4×C53—21no—
268C2×C4×C53—22no—
269C2×C4×C53—22no—
270C2×C4×C53—22no—
271C2×C4×C53—22no—
272C2×C4×C53—22no—
273C2×C4×C53—21no—
274C2×C4×C53—22no—
275C2×C4×C53—21no—
276C2×C4×C53—22no—
277C2×C4×C53—21no—
278C2×C4×C53—21no—
279C2×C4×C53—21no—
280C2×C4×C53—21no—
281C2×C4×C53—21no—
282C2×C4×C53—21no—
283C2×C4×C53—21no—
284C2×C4×C53—41no—
285C2×C4×C53—41no—
286C2×C4×C53—41no—
287C2×C4×C53—41no—
288C2×C4×C53—41no—
289C2×C4×C53—41no—
290C2×C4×C53—41no—
291C2×C4×C53—41no—
292C2×C4×C53—41no—
293C2×C4×C53—41no—
294C2×C4×C53—84no—
295C2×C4×C53—84no—
296C2×C4×C53#12012yes—
297C2×C4×C53C22×D411yescharacteristic
298C2×C4×C53C22×D411yescharacteristic
299C2×C4×C53C2×#4111yescharacteristic
300C2×C4×C53C2×#4111yescharacteristic
301C2×C4×C532−1+411yescharacteristic
302C2×C4×C532−1+411yescharacteristic
303C2×Dic53—41no—
304C2×Dic53—41no—
305C2×Dic53—41no—
306C2×Dic53—41no—
307C2×Dic53—41no—
308C2×Dic53—41no—
309C2×Dic53—41no—
310C2×Dic53—41no—
311C2×Dic53—41no—
312C2×Dic53—41no—
313C2×Dic53—41no—
314C2×Dic53—41no—
315#88322—22no—
316#88322—22no—
317#88322—41no—
318#88322—41no—
319#24090—531nomaximal, Sylow
320C22×C53—22no—
321C22×C53—22no—
322C22×C53—22no—
323C22×C53—22no—
324C22×C53—22no—
325C22×C53—22no—
326C22×C53—41no—
327C22×C53—41no—
328C22×C53—41no—
329C22×C53—41no—
330C22×C53—41no—
331C22×C53—41no—
332C22×C53—41no—
333C22×C53—41no—
334C22×C53—42no—
335C22×C53—42no—
336C22×C53—42no—
337C22×C53—81no—
338C22×C53—81no—
339C22×C53—81no—
340C22×C53—81no—
341C22×C53C2×#12011yescharacteristic
342C22×C53#54711yescharacteristic
343C22×C53#54711yescharacteristic
344C22×C53C2×#13511yescharacteristic
345C22×C53#57511yescharacteristic
346C22×C53#57611yescharacteristic
347C22×C53#57711yescharacteristic
348C4×C53—22no—
349C4×C53—41no—
350C4×C53—41no—
351C4×C53—42no—
352C4×C53—41no—
353C4×C53—42no—
354C4×C53—42no—
355C4×C53#52511yescharacteristic
356C4×C53#53611yescharacteristic
357C4×C53#54711yescharacteristic
358C4×C53#54711yescharacteristic
359Dic53—81no—
360Dic53—81no—
361Dic53—81no—
362Dic53—81no—
363C2×#553D5311yescharacteristic
364C2×#482—531no—
365C2×#427—531no—
366#2485—531no—
367#2059—531no—
368#2059—531no—
369#2034—531no—
370#2033—531no—
371#1893—531no—
372#1869—531no—
373#1864—531no—
374#1862—531no—
375#1853—531no—
376#1852—531no—
377#1825—531no—
378C2×C53—42no—
379C2×C53—42no—
380C2×C53—82no—
381C2×C53#240611yescharacteristic
382C2×C53#300211yescharacteristic
383C2×C53#301211yescharacteristic
384C2×C53#333711yescharacteristic
385C2×C53#333911yescharacteristic
386C2×C53#334711yescharacteristic
387C2×C53#335011yescharacteristic
388C23×C8—531no—
389#553—24no—
390#553—24no—
391C2×#126—21no—
392C2×#125C2×D5311yescharacteristic
393C2×#123—21no—
394C2×#121—21no—
395C2×#121C2×D5311yescharacteristic
396C2×#121C2×D5311yescharacteristic
397C2×C4×D4—21no—
398C2×C4×D4C2×D5311yescharacteristic
399C2×C4×D4C2×D5311yescharacteristic
400C2×#117—531no—
401C2×#117C2×D5311yescharacteristic
402C22×C4⋊C4C2×D5311yescharacteristic
403#482—1064no—
404#427—1064no—
405C2×#107—531no—
406C2×#107—531no—
407C2×#107—531no—
408C2×#106—531no—
409C2×#106—531no—
410C2×#106—531no—
411C2×#102—531no—
412C2×#102—531no—
413C2×#102—531no—
414C2×#102—531no—
415C2×C22⋊C8—531no—
416C2×C22⋊C8—531no—
417C2×C22⋊C8—531no—
418#397—1061no—
419#394—1061no—
420#389—531no—
421#389—531no—
422#388—1061no—
423#387—1061no—
424#380—531no—
425#380—531no—
426#380—531no—
427#340—531no—
428#340—531no—
429#340—531no—
430#340—531no—
431#340—531no—
432#340—531no—
433#336—531no—
434#336—531no—
435C53#2409011yescharacteristic, complemented, Sylow
436C22×D4—21no—
437C22×D4—21no—
438C22×D4C22⋊D5311yescharacteristic
439C22×D4C22×D5311yescharacteristic
440C23×C4—21no—
441C23×C4—21no—
442C23×C4C22×D5311yescharacteristic
443C23×C4C22×D5311yescharacteristic
444C22×C8—531no—
445C22×C8—531no—
446C22×C8—531no—
447C22×C8—531no—
448C22×C8—1062no—
449C22×C8—1062no—
450C22×C8—1062no—
451#126—28no—
452#125—22no—
453#125—22no—
454#123—28no—
455#121—28no—
456#121—22no—
457#121—22no—
458#121—22no—
459#121C22⋊D5314yes—
460C4×D4—28no—
461C4×D4—22no—
462C4×D4—22no—
463C4×D4—22no—
464C4×D4—22no—
465#117—22no—
466#117—1062no—
467#117—1062no—
468#117C22⋊D5314yes—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—531no—
475C2×C4⋊C4—531no—
476C2×C4⋊C4—531no—
477C2×C4⋊C4—531no—
478C2×C4⋊C4—1061no—
479C2×C4⋊C4—1061no—
480C2×C4⋊C4C22⋊D5311yescharacteristic
481C2×C4⋊C4C22×D5311yescharacteristic
482C2×C4⋊C4C22×D5311yescharacteristic
483C2×C4⋊C4C22×D5311yescharacteristic
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—1061no—
489C2×C22⋊C4—1061no—
490C2×C22⋊C4—1061no—
491C2×C22⋊C4—1061no—
492C2×C22⋊C4C22⋊D5311yescharacteristic
493C2×C22⋊C4C22⋊D5311yescharacteristic
494C2×C42—21no—
495C2×C42—1061no—
496C2×C42C22×D5311yescharacteristic
497#107—1062no—
498#107—1062no—
499#107—1062no—
500#106—1062no—
501#106—1062no—
502#106—1062no—
503#102—1062no—
504#102—1062no—
505#102—1062no—
506#102—1062no—
507C22⋊C8—1062no—
508C22⋊C8—1062no—
509C22⋊C8—1062no—
510#95—1061no—
511#95—1061no—
512#95—1061no—
513#95—1061no—
514#95—1061no—
515C24—21no—
516C24C2×C22⋊D5311yescharacteristic
517C24C2×C22⋊D5311yescharacteristic
518C2×D4—24no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—24no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—41no—
528C2×D4—42no—
529C2×D4—42no—
530C2×D4—81no—
531C2×D4—81no—
532C2×D4C2×C22⋊D5312yes—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—81no—
549C22×C4—81no—
550C22×C4—81no—
551C22×C4—81no—
552C22×C4—1061no—
553C22×C4—1061no—
554C22×C4—1061no—
555C22×C4—1061no—
556C22×C4C2×C22⋊D5311yescharacteristic
557C22×C4C2×C22⋊D5311yescharacteristic
558C22×C4C2×C22⋊D5311yescharacteristic
559C22×C4C2×C22⋊D5311yescharacteristic
560C22×C4C2×C22⋊D5312yes—
561C22×C4C2×C22⋊D5312yes—
562C22×C4C23×D5311yescharacteristic
563C2×C8—532no—
564C2×C8—532no—
565C2×C8—1068no—
566C2×C8—1061no—
567C2×C8—1061no—
568C2×C8—1061no—
569C2×C8—1061no—
570C2×C8—1061no—
571C2×C8—1061no—
572C2×C8—1061no—
573C2×C8—1061no—
574C2×C8—1061no—
575C2×C8—1061no—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—22no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—1061no—
584C4⋊C4—1061no—
585C4⋊C4—1061no—
586C4⋊C4—1061no—
587C4⋊C4—1061no—
588C4⋊C4—1061no—
589C4⋊C4—1061no—
590C4⋊C4—1061no—
591C4⋊C4—4241no—
592C4⋊C4—2122no—
593C4⋊C4C2×C22⋊D5312yes—
594C4⋊C4C2×C22⋊D5312yes—
595C4⋊C4C2×C22⋊D5312yes—
596C22⋊C4—24no—
597C22⋊C4—24no—
598C22⋊C4—24no—
599C22⋊C4—22no—
600C22⋊C4—24no—
601C22⋊C4—22no—
602C22⋊C4—4241no—
603C22⋊C4—4241no—
604C22⋊C4—2122no—
605C22⋊C4—2122no—
606C42—24no—
607C42—21no—
608C42—21no—
609C42—2122no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—22no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23#1313318612yes—
630C23#1313323712yes—
631C23C22×C22⋊D5311yescharacteristic
632D4—22no—
633D4—22no—
634D4—44no—
635D4—48no—
636D4—41no—
637D4—41no—
638D4—84no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—22no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—84no—
668C2×C4—84no—
669C2×C4—2121no—
670C2×C4—2121no—
671C2×C4—2121no—
672C2×C4—2121no—
673C2×C4—2121no—
674C2×C4—2121no—
675C2×C4—2121no—
676C2×C4—2121no—
677C2×C4—2121no—
678C2×C4—2121no—
679C2×C4—2121no—
680C2×C4—2121no—
681C2×C4#1313318612yes—
682C2×C4C22×C22⋊D5311yescharacteristic
683C2×C4C22×C22⋊D5311yescharacteristic
684C2×C4#41×D5311yescharacteristic
685C2×C4#41×D5311yescharacteristic
686C2×C4#1313326411yescharacteristic
687C2×C4#1313326411yescharacteristic
688C8—1062no—
689C8—1062no—
690C8—2121no—
691C8—2121no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22C2×#1313318611yescharacteristic
714C22#1681127211yescharacteristic
715C22#1681127211yescharacteristic
716C22C2×#1313323711yescharacteristic
717C22#1681142111yescharacteristic
718C22#1681142611yescharacteristic
719C22#1681143411yescharacteristic
720C4—22no—
721C4—41no—
722C4—42no—
723C4—41no—
724C4—41no—
725C4—42no—
726C4—42no—
727C4—4241no—
728C4—4241no—
729C4—4241no—
730C4—4241no—
731C4#1681113011yescharacteristic
732C4#1681119411yescharacteristic
733C4#1681127211yescharacteristic
734C4#1681127211yescharacteristic
735C2—42no—
736C2—42no—
737C2—82no—
738C2#2027804611yescharacteristic
739C2#2028393311yescharacteristic
740C2#2028401911yescharacteristic
741C2#2028708811yescharacteristic
742C2#2028711111yescharacteristic
743C2#2028720911yescharacteristic
744C2#2028725411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
Fitting, prime radicalC2×C53×#553C2
socleC23×C53C22×D4
hypercenterC2×#553D53
hypocenterC53#24090
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#16810944C2semidirect
2. C2×#16810659C2semidirect
3. #20279012C2semidirect
4. #20276050C2semidirect
5. #20276050C2semidirect
6. #20275901C2semidirect
7. #20275894C2semidirect
8. #20275144C2semidirect
9. #20275008C2semidirect
10. #20274976C2semidirect
11. #20274962C2semidirect
12. #20274908C2semidirect
13. #20274903C2semidirect
14. #20274810C2semidirect
435. C53#24090semidirect

Maximal subgroups

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

subgroupindex
C2×#168109442
C2×#168106592
#202790122
#202760502
#202759012
#202758942
#202751442
#202750082
#202749762
#202749622
#202749082
#202749032
#202748102
C2×C53×#5532
#2409053