Finite Group Databasebeta

← #27400389

Subgroups — #27400389

Order 13568.

1194 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811338C211yesmaximal, characteristic
2C2×#16810695C211yesmaximal, characteristic, complemented
3#20275687C211yesmaximal, characteristic, complemented
4#20275667C211yesmaximal, characteristic, complemented
5#20275151C211yesmaximal, characteristic, complemented
6#20275141C211yesmaximal, characteristic, complemented
7#20275037C211yesmaximal, characteristic, complemented
8#20275032C211yesmaximal, characteristic, complemented
9#20274807C211yesmaximal, characteristic, complemented
10#20274807C211yesmaximal, characteristic, complemented
11#20274722C211yesmaximal, characteristic, complemented
12#20274543C211yesmaximal, characteristic, complemented
13#20274434C211yesmaximal, characteristic, complemented
14#20274431C211yesmaximal, characteristic, complemented
15C53×#2352C211yesmaximal, characteristic, complemented
16C22×#11719917C2211yescharacteristic
17C23×#88322C2211yescharacteristic
18#16811338—24no—
19#16811338C418yescomplemented
20C2×#13133217C2211yescharacteristic
21C2×#13133203—21no—
22C2×#13133203—21no—
23C2×#13133191C2211yescharacteristic
24C2×#13133191C2211yescharacteristic
25C2×#13133188—21no—
26C2×C4×D212C2211yescharacteristic
27C2×#13133176C2211yescharacteristic
28C2×#13133176C2211yescharacteristic
29C2×#13133175—21no—
30#16810695—24no—
31C2×C4⋊#88322C2211yescharacteristic
32C2×#13133137C2211yescharacteristic
33C2×#13133137C2211yescharacteristic
34C2×#13133137C2211yescharacteristic
35C2×#13133137C2211yescharacteristic
36C2×C22⋊#88322C2211yescharacteristic
37C2×C22⋊#88322C2211yescharacteristic
38C2×#13133128C2211yescharacteristic
39#16810385C2211yescharacteristic
40#16810385C2211yescharacteristic
41#16810385C2211yescharacteristic
42#16810385C2211yescharacteristic
43#16810385C2211yescharacteristic
44#16810385C2211yescharacteristic
45#16810385C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810385C2211yescharacteristic
49#16810385C2211yescharacteristic
50#16810385C2211yescharacteristic
51C2×C4×D4×C53C2211yescharacteristic
52C2×#117×C53C2211yescharacteristic
53C22×C4⋊C4×C53C2211yescharacteristic
54C53×#388—21no—
55C53×#387—21no—
56C53×#386—21no—
57C53×#382C2211yescharacteristic
58C53×#380C2211yescharacteristic
59C53×#380C2211yescharacteristic
60C4×C4⋊C4×C53C2211yescharacteristic
61C4×C22⋊C4×C53—21no—
62C22×Dic106—21no—
63C22×D212C2311yescharacteristic
64C22×C22⋊D53—21no—
65C22×C22⋊D53—21no—
66C22×C4×D53—21no—
67C2×#11719917—22no—
68C2×#11719917—22no—
69C2×#11719917—41no—
70C22×#88322—22no—
71C22×#88322—22no—
72C22×#88322—41no—
73C22×#88322C2311yescharacteristic
74C22×#88322C2311yescharacteristic
75C22×#88322C2311yescharacteristic
76C22×#88322C2311yescharacteristic
77#13133217—22no—
78#13133217C2×C414yescomplemented
79#13133203—28no—
80#13133203—28no—
81#13133191—22no—
82#13133191—22no—
83#13133191C2×C414yes—
84#13133191C2×C414yescomplemented
85#13133188—28no—
86C4×D212—22no—
87C4×D212C2×C414yescomplemented
88#13133176—22no—
89#13133176—22no—
90#13133176C2×C414yes—
91#13133176C2×C414yescomplemented
92#13133175—28no—
93C2×C4⋊Dic53—21no—
94C2×C4⋊Dic53C2311yescharacteristic
95C2×C4⋊Dic53C2311yescharacteristic
96C2×C4⋊Dic53C2311yescharacteristic
97C2×C22⋊Dic53—21no—
98C2×C22⋊Dic53—21no—
99C2×#11719921—21no—
100C2×#11719921—21no—
101C2×#11719921—21no—
102C2×C4×Dic53—21no—
103C2×C4×Dic53—21no—
104C4⋊#88322—22no—
105#13133137—22no—
106#13133137—22no—
107#13133137—41no—
108#13133137—41no—
109C22⋊#88322—22no—
110C22⋊#88322—22no—
111#13133128—22no—
112C22×D4×C53D411yescharacteristic
113C23×C4×C53—21no—
114C23×C4×C53C2311yescharacteristic
115C23×C4×C53C2311yescharacteristic
116C4×D4×C53C2×C414yes—
117C4×D4×C53D414yes—
118#117×C53—22no—
119#117×C53—41no—
120C2×C4⋊C4×C53—21no—
121C2×C4⋊C4×C53—22no—
122C2×C4⋊C4×C53—41no—
123C2×C4⋊C4×C53D411yescharacteristic
124C2×C4⋊C4×C53C2311yescharacteristic
125C2×C4⋊C4×C53C2311yescharacteristic
126C2×C4⋊C4×C53C2311yescharacteristic
127C2×C4⋊C4×C53C2311yescharacteristic
128C2×C22⋊C4×C53—21no—
129C2×C22⋊C4×C53—21no—
130C2×C22⋊C4×C53—21no—
131C2×C22⋊C4×C53D411yescharacteristic
132C2×C22⋊C4×C53D411yescharacteristic
133C2×C42×C53—21no—
134C2×C42×C53—21no—
135C2×C42×C53C2311yescharacteristic
136#95×C53—21no—
137#95×C53—21no—
138#95×C53—21no—
139#95×C53—21no—
140#95×C53—21no—
141C24×C53C2×D411yescharacteristic
142C24×C53C2×D411yescharacteristic
143C23×D53—21no—
144C2×D4×C53—41no—
145C2×D4×C53—41no—
146C2×D4×C53C22⋊C414yes—
147C22×C4×C53—21no—
148C22×C4×C53—21no—
149C22×C4×C53—21no—
150C22×C4×C53—21no—
151C22×C4×C53—21no—
152C22×C4×C53—21no—
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—42no—
160C22×C4×C53—42no—
161C22×C4×C53—81no—
162C22×C4×C53C22×C412yes—
163C22×C4×C53C22×C412yes—
164C22×C4×C53C2×D411yescharacteristic
165C22×C4×C53C2×D411yescharacteristic
166C22×C4×C53C2×D411yescharacteristic
167C22×C4×C53C2×D411yescharacteristic
168C22×C4×C53C2×D412yes—
169C22×C4×C53C2×D412yes—
170C22×C4×C53C2411yescharacteristic
171C2×C22⋊D53—24no—
172C2×C22⋊D53—24no—
173C2×C22⋊D53—81no—
174C2×C22⋊D53—81no—
175C2×C22⋊D53—81no—
176C2×C22⋊D53—81no—
177C22×Dic53—21no—
178C22×Dic53—21no—
179C22×Dic53—21no—
180C2×D212—21no—
181C2×D212—21no—
182C2×D212—21no—
183C2×D212—21no—
184C2×D212—21no—
185C2×D212C22×C412yes—
186C2×C4×D53—24no—
187C2×C4×D53—42no—
188C2×C4×D53—42no—
189C2×Dic106—24no—
190C2×Dic106—81no—
191C2×Dic106—81no—
192C4⋊C4×C53—21no—
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—42no—
200C4⋊C4×C53C22⋊C414yes—
201C4⋊C4×C53#4112yes—
202C22⋊C4×C53—42no—
203C22⋊C4×C53—42no—
204C22⋊C4×C53—81no—
205C22⋊C4×C53C22⋊C414yes—
206C22⋊C4×C53C22⋊C414yes—
207C42×C53—42no—
208C42×C53—81no—
209C42×C53C22×C412yes—
210C42×C53C2×D412yes—
211C22⋊Dic53—24no—
212C22⋊Dic53—24no—
213#11719921—24no—
214#11719921—24no—
215#11719921—24no—
216C4⋊Dic53—24no—
217C4⋊Dic53—21no—
218C4⋊Dic53—21no—
219C4⋊Dic53—21no—
220C4⋊Dic53C22×C412yes—
221C4⋊Dic53C22×C412yes—
222C4⋊Dic53C22×C412yes—
223C4×Dic53—24no—
224C4×Dic53—24no—
225#11719917—44no—
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—44no—
238C2×#88322#4112yes—
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—21no—
250C23×C53—21no—
251C23×C53C2×C22⋊C412yes—
252C23×C53C2×C22⋊C412yes—
253C23×C53C22×D411yescharacteristic
254C22×D53—22no—
255C22×D53—41no—
256C22×D53—41no—
257C22×D53—41no—
258C22×D53—41no—
259C22×D53—41no—
260C22×D53—41no—
261D4×C53—44no—
262C2×C4×C53—21no—
263C2×C4×C53—21no—
264C2×C4×C53—21no—
265C2×C4×C53—21no—
266C2×C4×C53—21no—
267C2×C4×C53—21no—
268C2×C4×C53—21no—
269C2×C4×C53—21no—
270C2×C4×C53—22no—
271C2×C4×C53—22no—
272C2×C4×C53—22no—
273C2×C4×C53—22no—
274C2×C4×C53—22no—
275C2×C4×C53—22no—
276C2×C4×C53—22no—
277C2×C4×C53—22no—
278C2×C4×C53—22no—
279C2×C4×C53—41no—
280C2×C4×C53—41no—
281C2×C4×C53—41no—
282C2×C4×C53—41no—
283C2×C4×C53—41no—
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—84no—
291C2×C4×C53C2×C22⋊C412yes—
292C2×C4×C53C2×C22⋊C412yes—
293C2×C4×C53C2×C22⋊C412yes—
294C2×C4×C53C2×C22⋊C412yes—
295C2×C4×C53C23×C411yescharacteristic
296C2×C4×C53C22×D411yescharacteristic
297C2×C4×C53C2×#4111yescharacteristic
298C2×C4×C53C2×#4111yescharacteristic
299C2×C4×C53H(5,𝔽2)11yescharacteristic
300C2×C4×C532−1+411yescharacteristic
301C22⋊D53—84no—
302C22⋊D53—84no—
303C2×Dic53—22no—
304C2×Dic53—22no—
305C2×Dic53—22no—
306C2×Dic53—41no—
307C2×Dic53—41no—
308C2×Dic53—41no—
309C2×Dic53—41no—
310C2×Dic53—41no—
311C2×Dic53—41no—
312D212—22no—
313D212—22no—
314D212—41no—
315D212—41no—
316C4×D53—48no—
317Dic106—84no—
318#88322—22no—
319#88322—41no—
320#88322—41no—
321#88322—41no—
322#22492—531nomaximal, Sylow
323C22×C53—22no—
324C22×C53—22no—
325C22×C53—22no—
326C22×C53—22no—
327C22×C53—22no—
328C22×C53—22no—
329C22×C53—41no—
330C22×C53—41no—
331C22×C53—41no—
332C22×C53—41no—
333C22×C53—41no—
334C22×C53—41no—
335C22×C53—41no—
336C22×C53—41no—
337C22×C53C22×C22⋊C411yescharacteristic
338C22×C53#54611yescharacteristic
339C22×C53#54711yescharacteristic
340C22×C53#57511yescharacteristic
341C22×C53#57511yescharacteristic
342C22×C53#57611yescharacteristic
343C22×C53#57711yescharacteristic
344C2×D53—42no—
345C2×D53—42no—
346C2×D53—42no—
347C2×D53—81no—
348C2×D53—81no—
349C2×D53—81no—
350C2×D53—81no—
351C4×C53—22no—
352C4×C53—22no—
353C4×C53—22no—
354C4×C53—22no—
355C4×C53—42no—
356C4×C53—81no—
357C4×C53—81no—
358C4×C53—81no—
359C4×C53C4×#4111yescharacteristic
360C4×C53#52011yescharacteristic
361C4×C53#54611yescharacteristic
362C4×C53#54711yescharacteristic
363Dic53—42no—
364Dic53—42no—
365Dic53—42no—
366C2×#555—531no—
367C2×#435—531no—
368#2352D5311yescharacteristic, complemented
369#1993—531no—
370#1988—531no—
371#1895—531no—
372#1893—531no—
373#1875—531no—
374#1874—531no—
375#1825—531no—
376#1825—531no—
377#1804—531no—
378#1762—531no—
379#1736—531no—
380#1735—531no—
381C2×C53—42no—
382C2×C53—42no—
383C2×C53#233911yescharacteristic
384C2×C53#289611yescharacteristic
385C2×C53#289711yescharacteristic
386C2×C53#331911yescharacteristic
387C2×C53#332111yescharacteristic
388C2×C53#334711yescharacteristic
389C2×C53#334811yescharacteristic
390D53—82no—
391C22×M16—531no—
392C23×C8—531no—
393#555—538no—
394#555—1064no—
395C2×C4⋊Q8—531no—
396C2×#124—1061no—
397C2×#124—1061no—
398C2×#121—531no—
399C2×#121—531no—
400C2×#121—1061no—
401C2×C4×D4—531no—
402C2×C4×D4C2×D5311yescharacteristic
403C2×#117—531no—
404C2×#117—531no—
405C2×#117—1061no—
406C2×#117C2×D5311yescharacteristic
407C22×C4⋊C4C2×D5311yescharacteristic
408#435—1064no—
409C2×C4⋊C8—531no—
410C2×#102—531no—
411C2×#102—531no—
412C2×#102—531no—
413C2×#102—531no—
414C2×C22⋊C8—531no—
415C2×C22⋊C8—531no—
416C2×#97—531no—
417#388—21no—
418#387—21no—
419#386—21no—
420#382C2×D5311yescharacteristic
421#380C2×D5311yescharacteristic
422#380C2×D5311yescharacteristic
423C4×C4⋊C4C2×D5311yescharacteristic
424C4×C22⋊C4—21no—
425#340—531no—
426#340—531no—
427#340—531no—
428#340—531no—
429#340—531no—
430#340—531no—
431#340—531no—
432#340—531no—
433#340—531no—
434#340—531no—
435#340—531no—
436#340—531no—
437C53#2249211yescharacteristic, complemented, Sylow
438C22×Q8—1061no—
439C22×D4—531no—
440C22×D4—1061no—
441C22×D4—1061no—
442C22×D4C22⋊D5311yescharacteristic
443C23×C4—21no—
444C23×C4—1061no—
445C23×C4C22×D5311yescharacteristic
446C23×C4C22×D5311yescharacteristic
447C2×M16—1062no—
448C2×M16—1062no—
449C2×M16—2121no—
450C22×C8—531no—
451C22×C8—531no—
452C22×C8—531no—
453C22×C8—531no—
454C22×C8—1062no—
455C22×C8—1062no—
456C22×C8—2121no—
457C4⋊Q8—534no—
458C4⋊Q8—1062no—
459#124—1068no—
460#124—1068no—
461#121—534no—
462#121—534no—
463#121—1068no—
464#121—1062no—
465#121—1062no—
466C4×D4—534no—
467C4×D4—1062no—
468C4×D4C4×D5314yes—
469C4×D4D21214yes—
470#117—22no—
471#117—41no—
472#117—534no—
473#117—534no—
474#117—1062no—
475#117—1062no—
476#117—1068no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—41no—
480C2×C4⋊C4—531no—
481C2×C4⋊C4—531no—
482C2×C4⋊C4—531no—
483C2×C4⋊C4—1061no—
484C2×C4⋊C4C22⋊D5311yescharacteristic
485C2×C4⋊C4C22×D5311yescharacteristic
486C2×C4⋊C4C22×D5311yescharacteristic
487C2×C4⋊C4C22×D5311yescharacteristic
488C2×C4⋊C4C22×D5311yescharacteristic
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—1061no—
493C2×C22⋊C4—1061no—
494C2×C22⋊C4—1061no—
495C2×C22⋊C4—1061no—
496C2×C22⋊C4—1061no—
497C2×C22⋊C4C22⋊D5311yescharacteristic
498C2×C22⋊C4C22⋊D5311yescharacteristic
499C2×C42—21no—
500C2×C42—21no—
501C2×C42—1061no—
502C2×C42—1061no—
503C2×C42C22×D5311yescharacteristic
504C4⋊C8—1062no—
505#102—1062no—
506#102—1062no—
507#102—2121no—
508#102—2121no—
509C22⋊C8—1062no—
510C22⋊C8—1062no—
511#97—1062no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95—21no—
517C24—1061no—
518C24C2×C22⋊D5311yescharacteristic
519C24C2×C22⋊D5311yescharacteristic
520C2×Q8—1064no—
521C2×Q8—4241no—
522C2×Q8—4241no—
523C2×D4—41no—
524C2×D4—41no—
525C2×D4—532no—
526C2×D4—1064no—
527C2×D4—1064no—
528C2×D4—1061no—
529C2×D4—1061no—
530C2×D4—1061no—
531C2×D4—1061no—
532C2×D4—1061no—
533C2×D4—4241no—
534C2×D4—4241no—
535C2×D4—4241no—
536C2×D4—4241no—
537C2×D4#1171992114yes—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—81no—
553C22×C4—1061no—
554C22×C4—1061no—
555C22×C4—1061no—
556C22×C4—1064no—
557C22×C4—2122no—
558C22×C4—2122no—
559C22×C4C2×C4×D5312yes—
560C22×C4C2×C4×D5312yes—
561C22×C4C2×D21212yes—
562C22×C4C2×D21212yes—
563C22×C4C2×C22⋊D5311yescharacteristic
564C22×C4C2×C22⋊D5311yescharacteristic
565C22×C4C2×C22⋊D5311yescharacteristic
566C22×C4C2×C22⋊D5311yescharacteristic
567C22×C4C23×D5311yescharacteristic
568M16—2124no—
569C2×C8—532no—
570C2×C8—1061no—
571C2×C8—1061no—
572C2×C8—1061no—
573C2×C8—1061no—
574C2×C8—1061no—
575C2×C8—1061no—
576C2×C8—1061no—
577C2×C8—1061no—
578C2×C8—1061no—
579C2×C8—1061no—
580C2×C8—1061no—
581C2×C8—2124no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—42no—
590C4⋊C4—532no—
591C4⋊C4—532no—
592C4⋊C4—532no—
593C4⋊C4—1064no—
594C4⋊C4—1061no—
595C4⋊C4—1061no—
596C4⋊C4—1061no—
597C4⋊C4#1171992114yes—
598C4⋊C4#1171994712yes—
599C22⋊C4—42no—
600C22⋊C4—42no—
601C22⋊C4—81no—
602C22⋊C4—1064no—
603C22⋊C4—1064no—
604C22⋊C4—1064no—
605C22⋊C4—1064no—
606C22⋊C4—1064no—
607C22⋊C4#1171992114yes—
608C22⋊C4#1171992114yes—
609C42—42no—
610C42—81no—
611C42—1064no—
612C42—1064no—
613C42C2×C4×D5312yes—
614C42C2×D21212yes—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—1062no—
628C23—2121no—
629C23—2121no—
630C23—2121no—
631C23—2121no—
632C23—2121no—
633C23—2121no—
634C23C2×#1171992112yes—
635C23C2×#1171992112yes—
636C23C22×C22⋊D5311yescharacteristic
637Q8—4244no—
638D4—44no—
639D4—1062no—
640D4—1062no—
641D4—4244no—
642D4—4244no—
643D4—2121no—
644D4—2121no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—84no—
674C2×C4—1062no—
675C2×C4—1062no—
676C2×C4—1062no—
677C2×C4—2128no—
678C2×C4—2121no—
679C2×C4—2121no—
680C2×C4—2121no—
681C2×C4—2121no—
682C2×C4—2121no—
683C2×C4—2121no—
684C2×C4C2×#1171992112yes—
685C2×C4C2×#1171992112yes—
686C2×C4C2×#1171992112yes—
687C2×C4C2×#1171992112yes—
688C2×C4C22×C4×D5311yescharacteristic
689C2×C4C22×D21211yescharacteristic
690C2×C4#41×D5311yescharacteristic
691C2×C4C2×#1171994711yescharacteristic
692C2×C4#1313326211yescharacteristic
693C2×C4#1313326411yescharacteristic
694C8—1062no—
695C8—2121no—
696C8—2121no—
697C8—2121no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—4241no—
713C22—4241no—
714C22—4241no—
715C22—4241no—
716C22—2122no—
717C22—2122no—
718C22—2122no—
719C22C22×#1171992111yescharacteristic
720C22#1681126711yescharacteristic
721C22#1681127211yescharacteristic
722C22#1681142111yescharacteristic
723C22#1681142111yescharacteristic
724C22#1681142611yescharacteristic
725C22#1681143111yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—42no—
731C4—81no—
732C4—81no—
733C4—81no—
734C4—2122no—
735C4—2122no—
736C4—2122no—
737C4C4×#1171994711yescharacteristic
738C4#1681110211yescharacteristic
739C4#1681126811yescharacteristic
740C4#1681127711yescharacteristic
741C2—42no—
742C2—42no—
743C2—4242no—
744C2#2027754011yescharacteristic
745C2#2028323211yescharacteristic
746C2#2028323811yescharacteristic
747C2#2028687111yescharacteristic
748C2#2028690111yescharacteristic
749C2#2028720911yescharacteristic
750C2#2028722411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2352C2
socleC23×C53C22×D4
prime radicalC2×#16811338C2
cosocleC22×C4×C53C24
hypercenter#2352D53
hypocenterC53#22492
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
2. C2×#16810695C2semidirect
3. #20275687C2semidirect
4. #20275667C2semidirect
5. #20275151C2semidirect
6. #20275141C2semidirect
7. #20275037C2semidirect
8. #20275032C2semidirect
9. #20274807C2semidirect
10. #20274807C2semidirect
11. #20274722C2semidirect
12. #20274543C2semidirect
13. #20274434C2semidirect
14. #20274431C2semidirect
15. C53×#2352C2semidirect
19. #16811338C4semidirect
78. #13133217C2×C4semidirect
84. #13133191C2×C4semidirect
87. C4×D212C2×C4semidirect
91. #13133176C2×C4semidirect
368. #2352D53semidirect
437. C53#22492semidirect

Maximal subgroups

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

subgroupindex
C2×#168113382
C2×#168106952
#202756872
#202756672
#202751512
#202751412
#202750372
#202750322
#202748072
#202747222
#202745432
#202744342
#202744312
C53×#23522
#2249253