Finite Group Databasebeta

← #27384196

Subgroups — #27384196

Order 13568.

1298 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811103C211yesmaximal, characteristic
2C2×#16810684C211yesmaximal, characteristic, complemented
3#20274803C211yesmaximal, characteristic, complemented
4#20274799C211yesmaximal, characteristic, complemented
5#20274727C211yesmaximal, characteristic, complemented
6#20274722C211yesmaximal, characteristic, complemented
7#20274717C211yesmaximal, characteristic, complemented
8#20274712C211yesmaximal, characteristic, complemented
9#20274653C211yesmaximal, characteristic
10#20274653C211yesmaximal, characteristic
11#20274548C211yesmaximal, characteristic, complemented
12#20274543C211yesmaximal, characteristic, complemented
13C4×#13133140C211yesmaximal, characteristic, complemented
14C4×#13133137C211yesmaximal, characteristic, complemented
15C53×#2314C211yesmaximal, characteristic, complemented
16C22×#11719945C2211yescharacteristic
17#16811103—24no—
18#16811103C418yescomplemented
19C2×C4×Dic106C2211yescharacteristic
20C2×C4×Dic106C2211yescharacteristic
21C2×C4×D212C2211yescharacteristic
22C2×C4×D212C2211yescharacteristic
23C2×#13133177—21no—
24C2×#13133177—21no—
25C2×#13133175—21no—
26C22×C4⋊Dic53C2211yescharacteristic
27C2×C4⋊C4×D53—21no—
28#16810684—24no—
29C2×C4⋊#88322C2211yescharacteristic
30C2×C4⋊#88322C2211yescharacteristic
31C2×#13133140C2211yescharacteristic
32C2×#13133140C2211yescharacteristic
33C2×#13133140C2211yescharacteristic
34C2×#13133140C2211yescharacteristic
35C2×#13133137C2211yescharacteristic
36C2×#13133137C2211yescharacteristic
37C2×#13133137C2211yescharacteristic
38C2×#13133137C2211yescharacteristic
39C2×C22⋊#88322C2211yescharacteristic
40C2×C22⋊#88322C2211yescharacteristic
41C2×#13133128C2211yescharacteristic
42C2×C4×#88322C2211yescharacteristic
43#16810385C2211yescharacteristic
44#16810385C2211yescharacteristic
45#16810385C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810385C2211yescharacteristic
49#16810385C2211yescharacteristic
50#16810385C2211yescharacteristic
51C2×#117×C53C2211yescharacteristic
52C53×#388—21no—
53C53×#388—21no—
54C53×#387—21no—
55C53×#387—21no—
56C53×#384C2211yescharacteristic
57C53×#382C2211yescharacteristic
58C53×#380C2211yescharacteristic
59C53×#380C2211yescharacteristic
60C4×C4⋊C4×C53C2211yescharacteristic
61C4×C4⋊C4×C53C2211yescharacteristic
62C2×#11719945—22no—
63C2×#11719945—22no—
64C2×#11719945—22no—
65C2×#11719945—22no—
66C2×#11719945—22no—
67C2×#11719945C2×C414yes—
68C22×Dic106C2311yescharacteristic
69C22×D212C2311yescharacteristic
70C22×C22⋊D53—21no—
71C23×Dic53—21no—
72C22×C4×D53—21no—
73C22×C4×D53—21no—
74C22×C4×D53—21no—
75C22×#88322C2311yescharacteristic
76C22×#88322C2311yescharacteristic
77C22×#88322C2311yescharacteristic
78C22×#88322C2311yescharacteristic
79C4×Dic106—22no—
80C4×Dic106—22no—
81C4×Dic106C2×C414yes—
82C4×Dic106C2×C414yes—
83C4×D212—22no—
84C4×D212—22no—
85C4×D212C2×C414yes—
86C4×D212C2×C414yes—
87#13133177—28no—
88#13133177—28no—
89#13133175—28no—
90C2×C4⋊Dic53—21no—
91C2×C4⋊Dic53—22no—
92C2×C4⋊Dic53C2×C414yes—
93C2×C4⋊Dic53C2311yescharacteristic
94C2×C4⋊Dic53C2311yescharacteristic
95C2×#11719919—21no—
96C2×#11719919—21no—
97C4⋊C4×D53—28no—
98C2×#11719921—21no—
99C2×#11719921—21no—
100C2×C4×Dic53—21no—
101C2×C4×Dic53—21no—
102C4⋊#88322—22no—
103C4⋊#88322—22no—
104#13133140—22no—
105#13133140—22no—
106#13133140—22no—
107#13133140—22no—
108#13133137—22no—
109#13133137—22no—
110#13133137—22no—
111#13133137—22no—
112C22⋊#88322—22no—
113C22⋊#88322—22no—
114#13133128—22no—
115C4×#88322—22no—
116C23×C4×C53C2311yescharacteristic
117#117×C53C2×C414yes—
118#117×C53D414yes—
119C2×C4⋊C4×C53—21no—
120C2×C4⋊C4×C53—21no—
121C2×C4⋊C4×C53D411yescharacteristic
122C2×C4⋊C4×C53D411yescharacteristic
123C2×C4⋊C4×C53C2311yescharacteristic
124C2×C4⋊C4×C53C2311yescharacteristic
125C2×C4⋊C4×C53C2311yescharacteristic
126C2×C4⋊C4×C53C2311yescharacteristic
127C2×C22⋊C4×C53—21no—
128C2×C22⋊C4×C53—21no—
129C2×C22⋊C4×C53D411yescharacteristic
130C2×C22⋊C4×C53D411yescharacteristic
131C2×C42×C53—21no—
132C2×C42×C53—21no—
133C2×C42×C53C2311yescharacteristic
134C2×C42×C53C2311yescharacteristic
135#95×C53—21no—
136#95×C53—21no—
137#95×C53—21no—
138#95×C53—21no—
139#95×C53—21no—
140#95×C53—21no—
141C24×C53C2×D411yescharacteristic
142C23×D53—21no—
143C22×C4×C53—21no—
144C22×C4×C53—21no—
145C22×C4×C53—21no—
146C22×C4×C53—21no—
147C22×C4×C53—21no—
148C22×C4×C53—21no—
149C22×C4×C53—21no—
150C22×C4×C53—21no—
151C22×C4×C53C22×C412yes—
152C22×C4×C53C2×D411yescharacteristic
153C22×C4×C53C2×D411yescharacteristic
154C22×C4×C53C2×D411yescharacteristic
155C22×C4×C53C2×D411yescharacteristic
156C22×C4×C53C2×D411yescharacteristic
157C22×C4×C53C2×D412yes—
158C22×C4×C53C2411yescharacteristic
159C2×C22⋊D53—24no—
160C2×C22⋊D53—24no—
161C2×C22⋊D53—24no—
162C22×Dic53—21no—
163C22×Dic53—21no—
164C22×Dic53—21no—
165C22×Dic53—24no—
166C22×Dic53—81no—
167C22×Dic53—81no—
168#11719945—28no—
169#11719945—28no—
170#11719945—28no—
171#11719945—28no—
172C2×D212—21no—
173C2×D212—21no—
174C2×D212—21no—
175C2×D212C22×C412yes—
176C2×D212#4112yes—
177C2×D212#4112yes—
178C2×C4×D53—24no—
179C2×C4×D53—24no—
180C2×C4×D53—24no—
181C2×C4×D53—24no—
182C2×C4×D53—24no—
183C2×C4×D53—81no—
184C2×C4×D53—81no—
185C2×C4×D53—81no—
186C2×C4×D53—81no—
187C2×Dic106—21no—
188C2×Dic106—21no—
189C2×Dic106—21no—
190C2×Dic106C22×C412yes—
191C2×Dic106#4112yes—
192C2×Dic106#4112yes—
193C4⋊C4×C53—21no—
194C4⋊C4×C53—21no—
195C4⋊C4×C53—21no—
196C4⋊C4×C53—21no—
197C4⋊C4×C53—21no—
198C4⋊C4×C53—21no—
199C4⋊C4×C53—21no—
200C4⋊C4×C53—21no—
201C4⋊C4×C53—81no—
202C4⋊C4×C53—81no—
203C4⋊C4×C53C22⋊C414yes—
204C4⋊C4×C53C22⋊C414yes—
205C22⋊C4×C53—81no—
206C22⋊C4×C53—81no—
207C22⋊C4×C53C22⋊C414yes—
208C22⋊C4×C53C22⋊C414yes—
209C42×C53—81no—
210C42×C53—81no—
211C42×C53C22×C412yes—
212C42×C53C22×C412yes—
213C42×C53C2×D412yes—
214C42×C53C2×D412yes—
215#11719921—24no—
216#11719921—24no—
217C4⋊Dic53—24no—
218C4⋊Dic53—21no—
219C4⋊Dic53—21no—
220C4⋊Dic53C22×C412yes—
221C4⋊Dic53C22×C412yes—
222#11719919—24no—
223#11719919—24no—
224C4×Dic53—24no—
225C4×Dic53—24no—
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×#88322—21no—
237C2×#88322—21no—
238C23×C53—21no—
239C23×C53—21no—
240C23×C53—21no—
241C23×C53—21no—
242C23×C53—21no—
243C23×C53—21no—
244C23×C53C2×C22⋊C412yes—
245C23×C53C22×D411yescharacteristic
246C22×D53—22no—
247C22×D53—22no—
248C22×D53—22no—
249C22×D53—41no—
250C22×D53—41no—
251C22×D53—41no—
252C22×D53—41no—
253C2×C4×C53—21no—
254C2×C4×C53—21no—
255C2×C4×C53—21no—
256C2×C4×C53—21no—
257C2×C4×C53—21no—
258C2×C4×C53—21no—
259C2×C4×C53—21no—
260C2×C4×C53—21no—
261C2×C4×C53—21no—
262C2×C4×C53—21no—
263C2×C4×C53—22no—
264C2×C4×C53—22no—
265C2×C4×C53—22no—
266C2×C4×C53—22no—
267C2×C4×C53—41no—
268C2×C4×C53—41no—
269C2×C4×C53—41no—
270C2×C4×C53—41no—
271C2×C4×C53—41no—
272C2×C4×C53—41no—
273C2×C4×C53—41no—
274C2×C4×C53—41no—
275C2×C4×C53—41no—
276C2×C4×C53—41no—
277C2×C4×C53—41no—
278C2×C4×C53—41no—
279C2×C4×C53C2×C22⋊C412yes—
280C2×C4×C53C2×C22⋊C412yes—
281C2×C4×C53C2×C22⋊C412yes—
282C2×C4×C53C2×C22⋊C412yes—
283C2×C4×C53C2×C22⋊C412yes—
284C2×C4×C53C23×C411yescharacteristic
285C2×C4×C53C22×D411yescharacteristic
286C2×C4×C53C2×#4111yescharacteristic
287C2×C4×C53C2×#4111yescharacteristic
288C2×C4×C53C2×#4111yescharacteristic
289C2×C4×C53C2×#4111yescharacteristic
290C22⋊D53—216no—
291C2×Dic53—22no—
292C2×Dic53—22no—
293C2×Dic53—22no—
294C2×Dic53—22no—
295C2×Dic53—22no—
296C2×Dic53—41no—
297C2×Dic53—41no—
298C2×Dic53—41no—
299C2×Dic53—41no—
300C2×Dic53—84no—
301D212—22no—
302D212—22no—
303D212—22no—
304D212#11714yes—
305C4×D53—216no—
306C4×D53—84no—
307C4×D53—84no—
308Dic106—22no—
309Dic106—22no—
310Dic106—22no—
311Dic106#11714yes—
312#88322—41no—
313#88322—41no—
314#88322—41no—
315#88322—41no—
316#20746—531nomaximal, Sylow
317C22×C53—22no—
318C22×C53—22no—
319C22×C53—22no—
320C22×C53—41no—
321C22×C53—41no—
322C22×C53—41no—
323C22×C53—41no—
324C22×C53C22×C22⋊C411yescharacteristic
325C22×C53#52511yescharacteristic
326C22×C53#52511yescharacteristic
327C22×C53#57611yescharacteristic
328C22×C53#57711yescharacteristic
329C22×C53#57711yescharacteristic
330C22×C53#57811yescharacteristic
331C2×D53—24no—
332C2×D53—42no—
333C2×D53—42no—
334C2×D53—42no—
335C2×D53—42no—
336C2×D53—42no—
337C2×D53—42no—
338C4×C53—22no—
339C4×C53—22no—
340C4×C53—22no—
341C4×C53—22no—
342C4×C53—22no—
343C4×C53—81no—
344C4×C53—81no—
345C4×C53—81no—
346C4×C53—81no—
347C4×C53C2×#11711yescharacteristic
348C4×C53C2×#11711yescharacteristic
349C4×C53#52511yescharacteristic
350C4×C53#52511yescharacteristic
351Dic53—24no—
352Dic53—42no—
353Dic53—42no—
354C2×#520—531no—
355C2×#433—531no—
356#2314D5311yescharacteristic, complemented
357#1824—531no—
358#1823—531no—
359#1805—531no—
360#1804—531no—
361#1803—531no—
362#1802—531no—
363#1788—531no—
364#1788—531no—
365#1763—531no—
366#1762—531no—
367C4×#103—531no—
368C4×#102—531no—
369C2×C53—42no—
370C2×C53#228011yescharacteristic
371C2×C53#289711yescharacteristic
372C2×C53#289811yescharacteristic
373C2×C53#311911yescharacteristic
374C2×C53#312011yescharacteristic
375C2×C53#312411yescharacteristic
376C2×C53#312511yescharacteristic
377D53—44no—
378C22×#41—531no—
379#520—538no—
380#520—1064no—
381C2×C4×Q8—531no—
382C2×C4×Q8—531no—
383C2×C4×D4—531no—
384C2×C4×D4—531no—
385C2×C4×D4—1061no—
386C2×C4×D4—1061no—
387C2×#117—1061no—
388C2×#117C2×D5311yescharacteristic
389C22×C4⋊C4—531no—
390C22×C4⋊C4—1061no—
391#433—1064no—
392C2×C4⋊C8—531no—
393C2×C4⋊C8—531no—
394C2×#103—531no—
395C2×#103—531no—
396C2×#103—531no—
397C2×#103—531no—
398C2×#102—531no—
399C2×#102—531no—
400C2×#102—531no—
401C2×#102—531no—
402C2×C22⋊C8—531no—
403C2×C22⋊C8—531no—
404C2×#97—531no—
405C2×C4×C8—531no—
406#388—21no—
407#388—21no—
408#387—21no—
409#387—21no—
410#384C2×D5311yescharacteristic
411#382C2×D5311yescharacteristic
412#380C2×D5311yescharacteristic
413#380C2×D5311yescharacteristic
414C4×C4⋊C4C2×D5311yescharacteristic
415C4×C4⋊C4C2×D5311yescharacteristic
416#340—531no—
417#340—531no—
418#340—531no—
419#340—531no—
420#340—531no—
421#340—531no—
422#340—531no—
423#340—531no—
424C53#2074611yescharacteristic, complemented, Sylow
425C2×#41—534no—
426C2×#41—1062no—
427C2×#41—1062no—
428C2×#41—1062no—
429C2×#41—1062no—
430C2×#41—1062no—
431C22×Q8—531no—
432C22×D4—531no—
433C22×D4—1061no—
434C23×C4—1061no—
435C23×C4—1061no—
436C23×C4—1061no—
437C23×C4—1061no—
438C23×C4C22×D5311yescharacteristic
439C22×C8—531no—
440C22×C8—531no—
441C22×C8—531no—
442C22×C8—531no—
443C4×Q8—534no—
444C4×Q8—534no—
445C4×Q8—1062no—
446C4×Q8—1062no—
447C4×D4—534no—
448C4×D4—534no—
449C4×D4—1068no—
450C4×D4—1068no—
451C4×D4—1062no—
452C4×D4—1062no—
453#117—1068no—
454#117C4×D5314yes—
455#117D21214yes—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—534no—
459C2×C4⋊C4—531no—
460C2×C4⋊C4—531no—
461C2×C4⋊C4—1062no—
462C2×C4⋊C4—1061no—
463C2×C4⋊C4—1061no—
464C2×C4⋊C4—1061no—
465C2×C4⋊C4—1068no—
466C2×C4⋊C4C22⋊D5311yescharacteristic
467C2×C4⋊C4C22⋊D5311yescharacteristic
468C2×C4⋊C4C22×D5311yescharacteristic
469C2×C4⋊C4C22×D5311yescharacteristic
470C2×C4⋊C4C22×D5311yescharacteristic
471C2×C4⋊C4C22×D5311yescharacteristic
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—1061no—
475C2×C22⋊C4—1061no—
476C2×C22⋊C4C22⋊D5311yescharacteristic
477C2×C22⋊C4C22⋊D5311yescharacteristic
478C2×C42—21no—
479C2×C42—21no—
480C2×C42—1061no—
481C2×C42—1061no—
482C2×C42C22×D5311yescharacteristic
483C2×C42C22×D5311yescharacteristic
484C4⋊C8—1062no—
485C4⋊C8—1062no—
486#103—1062no—
487#103—1062no—
488#103—1062no—
489#103—1062no—
490#102—1062no—
491#102—1062no—
492#102—1062no—
493#102—1062no—
494C22⋊C8—1062no—
495C22⋊C8—1062no—
496#97—1062no—
497C4×C8—1062no—
498#95—21no—
499#95—21no—
500#95—21no—
501#95—21no—
502#95—21no—
503#95—21no—
504C24—1061no—
505C24C2×C22⋊D5311yescharacteristic
506#41—1068no—
507#41—1068no—
508#41—1068no—
509#41—1068no—
510C2×Q8—532no—
511C2×Q8—532no—
512C2×Q8—532no—
513C2×Q8—1061no—
514C2×Q8—1061no—
515C2×Q8—1061no—
516C2×D4—532no—
517C2×D4—532no—
518C2×D4—532no—
519C2×D4—1064no—
520C2×D4—1064no—
521C2×D4—1064no—
522C2×D4—1061no—
523C2×D4—1061no—
524C2×D4—1061no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—1064no—
534C22×C4—1064no—
535C22×C4—1061no—
536C22×C4—1064no—
537C22×C4—1064no—
538C22×C4—1061no—
539C22×C4—1061no—
540C22×C4—1064no—
541C22×C4—1064no—
542C22×C4—4241no—
543C22×C4—4241no—
544C22×C4—4241no—
545C22×C4—4241no—
546C22×C4—4241no—
547C22×C4—4241no—
548C22×C4C2×C4×D5312yes—
549C22×C4C2×D21212yes—
550C22×C4C2×C22⋊D5311yescharacteristic
551C22×C4C2×C22⋊D5311yescharacteristic
552C22×C4C2×C22⋊D5311yescharacteristic
553C22×C4C2×C22⋊D5311yescharacteristic
554C22×C4C2×C22⋊D5311yescharacteristic
555C22×C4C23×D5311yescharacteristic
556C2×C8—1061no—
557C2×C8—1061no—
558C2×C8—1061no—
559C2×C8—1061no—
560C2×C8—1061no—
561C2×C8—1061no—
562C2×C8—1061no—
563C2×C8—1061no—
564C2×C8—1061no—
565C2×C8—1061no—
566C2×C8—1061no—
567C2×C8—1061no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—81no—
577C4⋊C4—81no—
578C4⋊C4—532no—
579C4⋊C4—532no—
580C4⋊C4—1064no—
581C4⋊C4—1064no—
582C4⋊C4—1064no—
583C4⋊C4—1061no—
584C4⋊C4—1061no—
585C4⋊C4#1171992114yes—
586C4⋊C4#1171992114yes—
587C22⋊C4—81no—
588C22⋊C4—81no—
589C22⋊C4—1064no—
590C22⋊C4—1064no—
591C22⋊C4#1171992114yes—
592C22⋊C4#1171992114yes—
593C42—81no—
594C42—81no—
595C42—1064no—
596C42—1064no—
597C42C2×C4×D5312yes—
598C42C2×C4×D5312yes—
599C42C2×D21212yes—
600C42C2×D21212yes—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—1062no—
608C23—1062no—
609C23—1062no—
610C23—2121no—
611C23—2121no—
612C23—2121no—
613C23—2121no—
614C23C2×#1171992112yes—
615C23C22×C22⋊D5311yescharacteristic
616Q8—534no—
617Q8—1062no—
618Q8—1062no—
619Q8—1062no—
620D4—534no—
621D4—10616no—
622D4—1062no—
623D4—1062no—
624D4—1062no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—10616no—
652C2×C4—1062no—
653C2×C4—1062no—
654C2×C4—1062no—
655C2×C4—1062no—
656C2×C4—1062no—
657C2×C4—4244no—
658C2×C4—4244no—
659C2×C4—4244no—
660C2×C4—2121no—
661C2×C4—2121no—
662C2×C4—2121no—
663C2×C4—2121no—
664C2×C4C2×#1171992112yes—
665C2×C4C2×#1171992112yes—
666C2×C4C2×#1171992112yes—
667C2×C4C2×#1171992112yes—
668C2×C4C2×#1171992112yes—
669C2×C4C22×C4×D5311yescharacteristic
670C2×C4C22×D21211yescharacteristic
671C2×C4#41×D5311yescharacteristic
672C2×C4#41×D5311yescharacteristic
673C2×C4#41×D5311yescharacteristic
674C2×C4#41×D5311yescharacteristic
675C8—2121no—
676C8—2121no—
677C8—2121no—
678C8—2121no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—1064no—
687C22—2122no—
688C22—2122no—
689C22—2122no—
690C22—2122no—
691C22—2122no—
692C22—2122no—
693C22C22×#1171992111yescharacteristic
694C22#1681113011yescharacteristic
695C22#1681113011yescharacteristic
696C22#1681142611yescharacteristic
697C22#1681143111yescharacteristic
698C22#1681143411yescharacteristic
699C22#1681143811yescharacteristic
700C4—22no—
701C4—22no—
702C4—22no—
703C4—22no—
704C4—22no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4—81no—
709C4—1064no—
710C4—2122no—
711C4—2122no—
712C4#117×D5311yescharacteristic
713C4#117×D5311yescharacteristic
714C4#1681113511yescharacteristic
715C4#1681113511yescharacteristic
716C2—42no—
717C2—2124no—
718C2#2027709411yescharacteristic
719C2#2028323811yescharacteristic
720C2#2028324511yescharacteristic
721C2#2028490811yescharacteristic
722C2#2028492311yescharacteristic
723C2#2028497111yescharacteristic
724C2#2028498611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2314C2
socleC23×C53C22×D4
prime radicalC22×#11719945C22
cosocleC22×C4×C53C24
hypercenter#2314D53
hypocenterC53#20746
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2314

Complements

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

NH ≅ G/Ntype
2. C2×#16810684C2semidirect
3. #20274803C2semidirect
4. #20274799C2semidirect
5. #20274727C2semidirect
6. #20274722C2semidirect
7. #20274717C2semidirect
8. #20274712C2semidirect
11. #20274548C2semidirect
12. #20274543C2semidirect
13. C4×#13133140C2semidirect
14. C4×#13133137C2semidirect
15. C53×#2314C2semidirect
18. #16811103C4semidirect
356. #2314D53semidirect
424. C53#20746semidirect

Maximal subgroups

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

subgroupindex
C2×#168111032
C2×#168106842
#202748032
#202747992
#202747272
#202747222
#202747172
#202747122
#202746532
#202745482
#202745432
C4×#131331402
C4×#131331372
C53×#23142
#2074653