Finite Group Databasebeta

← #27400434

Subgroups — #27400434

Order 13568.

1390 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811277C211yesmaximal, characteristic
2C2×#16810695C211yesmaximal, characteristic, complemented
3#20275687C211yesmaximal, characteristic, complemented
4#20275663C211yesmaximal, characteristic, complemented
5#20275151C211yesmaximal, characteristic, complemented
6#20275141C211yesmaximal, characteristic, complemented
7#20275037C211yesmaximal, characteristic, complemented
8#20275032C211yesmaximal, characteristic, complemented
9#20274803C211yesmaximal, characteristic, complemented
10#20274799C211yesmaximal, characteristic, complemented
11#20274722C211yesmaximal, characteristic, complemented
12#20274543C211yesmaximal, characteristic, complemented
13#20274436C211yesmaximal, characteristic, complemented
14C2×#16810385C211yesmaximal, characteristic, complemented
15C53×#2352C211yesmaximal, characteristic, complemented
16C22×#11719947—21no—
17C22×#11719917C2211yescharacteristic
18C23×#88322C2211yescharacteristic
19#16811277—24no—
20#16811277C418yescomplemented
21C2×#13133217C2211yescharacteristic
22C2×#13133201—21no—
23C2×#13133201—21no—
24C2×#13133197—21no—
25C2×#13133191C2211yescharacteristic
26C2×#13133191C2211yescharacteristic
27C2×C4×D212C2211yescharacteristic
28C22×C4⋊Dic53C2211yescharacteristic
29C22×C4⋊Dic53C2211yescharacteristic
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—
62C2×#11719947—28no—
63C2×#11719947—44no—
64C2×#11719947—44no—
65C22×Dic106—21no—
66C22×D212C2311yescharacteristic
67C22×C22⋊D53—21no—
68C22×C22⋊D53—21no—
69C23×Dic53—21no—
70C23×Dic53—21no—
71C22×C4×D53—21no—
72C2×#11719917—22no—
73C2×#11719917—22no—
74C2×#11719917—41no—
75C22×#88322—22no—
76C22×#88322—22no—
77C22×#88322—41no—
78C22×#88322C2311yescharacteristic
79C22×#88322C2311yescharacteristic
80C22×#88322C2311yescharacteristic
81C22×#88322C2311yescharacteristic
82#13133217—22no—
83#13133217C2×C414yescomplemented
84#13133201—28no—
85#13133201—28no—
86#13133197—28no—
87#13133191—22no—
88#13133191—22no—
89#13133191C2×C414yes—
90#13133191C2×C414yescomplemented
91C4×D212—22no—
92C4×D212C2×C414yescomplemented
93C2×C4⋊Dic53—22no—
94C2×C4⋊Dic53—22no—
95C2×C4⋊Dic53—21no—
96C2×C4⋊Dic53—21no—
97C2×C4⋊Dic53—21no—
98C2×C4⋊Dic53C2×C414yes—
99C2×C4⋊Dic53C2×C414yescomplemented
100C2×C4⋊Dic53C2311yescharacteristic
101C2×C4⋊Dic53C2311yescharacteristic
102C2×C4⋊Dic53C2311yescharacteristic
103C2×#11719921—21no—
104C2×#11719921—21no—
105C2×#11719921—21no—
106C4⋊#88322—22no—
107#13133137—22no—
108#13133137—22no—
109#13133137—41no—
110#13133137—41no—
111C22⋊#88322—22no—
112C22⋊#88322—22no—
113#13133128—22no—
114C22×D4×C53D411yescharacteristic
115C23×C4×C53—21no—
116C23×C4×C53C2311yescharacteristic
117C23×C4×C53C2311yescharacteristic
118C4×D4×C53C2×C414yes—
119C4×D4×C53D414yes—
120#117×C53—22no—
121#117×C53—41no—
122C2×C4⋊C4×C53—21no—
123C2×C4⋊C4×C53—22no—
124C2×C4⋊C4×C53—41no—
125C2×C4⋊C4×C53D411yescharacteristic
126C2×C4⋊C4×C53C2311yescharacteristic
127C2×C4⋊C4×C53C2311yescharacteristic
128C2×C4⋊C4×C53C2311yescharacteristic
129C2×C4⋊C4×C53C2311yescharacteristic
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×C53—21no—
137C2×C42×C53C2311yescharacteristic
138#95×C53—21no—
139#95×C53—21no—
140#95×C53—21no—
141#95×C53—21no—
142#95×C53—21no—
143C24×C53C2×D411yescharacteristic
144C24×C53C2×D411yescharacteristic
145C23×D53—21no—
146C2×D4×C53—22no—
147C2×D4×C53—22no—
148C2×D4×C53C22⋊C414yes—
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—21no—
160C22×C4×C53—21no—
161C22×C4×C53—42no—
162C22×C4×C53—42no—
163C22×C4×C53—81no—
164C22×C4×C53C22×C412yes—
165C22×C4×C53C22×C412yes—
166C22×C4×C53C2×D411yescharacteristic
167C22×C4×C53C2×D411yescharacteristic
168C22×C4×C53C2×D411yescharacteristic
169C22×C4×C53C2×D411yescharacteristic
170C22×C4×C53C2×D412yes—
171C22×C4×C53C2×D412yes—
172C22×C4×C53C2411yescharacteristic
173C2×C22⋊D53—24no—
174C2×C22⋊D53—24no—
175C2×C22⋊D53—42no—
176C2×C22⋊D53—42no—
177C2×C22⋊D53—42no—
178C2×C22⋊D53—42no—
179C22×Dic53—24no—
180C22×Dic53—24no—
181C22×Dic53—21no—
182C22×Dic53—21no—
183C22×Dic53—21no—
184C22×Dic53—42no—
185C22×Dic53—42no—
186C22×Dic53—42no—
187C22×Dic53—42no—
188#11719947—432no—
189C2×D212—21no—
190C2×D212—21no—
191C2×D212—21no—
192C2×D212—21no—
193C2×D212—21no—
194C2×D212C22×C412yes—
195C2×C4×D53—24no—
196C2×C4×D53—42no—
197C2×C4×D53—42no—
198C2×Dic106—24no—
199C2×Dic106—42no—
200C2×Dic106—42no—
201C4⋊C4×C53—21no—
202C4⋊C4×C53—21no—
203C4⋊C4×C53—21no—
204C4⋊C4×C53—21no—
205C4⋊C4×C53—21no—
206C4⋊C4×C53—21no—
207C4⋊C4×C53—21no—
208C4⋊C4×C53—42no—
209C4⋊C4×C53C22⋊C414yes—
210C4⋊C4×C53#4112yescomplemented
211C22⋊C4×C53—42no—
212C22⋊C4×C53—42no—
213C22⋊C4×C53—81no—
214C22⋊C4×C53C22⋊C414yes—
215C22⋊C4×C53C22⋊C414yes—
216C42×C53—42no—
217C42×C53—81no—
218C42×C53C22×C412yes—
219C42×C53C2×D412yes—
220#11719921—24no—
221#11719921—24no—
222#11719921—24no—
223C4⋊Dic53—24no—
224C4⋊Dic53—24no—
225C4⋊Dic53—24no—
226C4⋊Dic53—21no—
227C4⋊Dic53—21no—
228C4⋊Dic53—21no—
229C4⋊Dic53C22×C412yes—
230C4⋊Dic53C22×C412yes—
231C4⋊Dic53C22×C412yes—
232#11719917—44no—
233C2×#88322—21no—
234C2×#88322—21no—
235C2×#88322—21no—
236C2×#88322—21no—
237C2×#88322—21no—
238C2×#88322—21no—
239C2×#88322—21no—
240C2×#88322—21no—
241C2×#88322—21no—
242C2×#88322—21no—
243C2×#88322—21no—
244C2×#88322—44no—
245C2×#88322#4112yescomplemented
246C23×C53—21no—
247C23×C53—21no—
248C23×C53—21no—
249C23×C53—21no—
250C23×C53—21no—
251C23×C53—21no—
252C23×C53—21no—
253C23×C53—21no—
254C23×C53—21no—
255C23×C53—21no—
256C23×C53C2×C22⋊C412yes—
257C23×C53C2×C22⋊C412yes—
258C23×C53AGL(1,ℤ/8)12yes—
259C23×C53AGL(1,ℤ/8)12yes—
260C23×C53C22×D411yescharacteristic
261C22×D53—22no—
262C22×D53—41no—
263C22×D53—41no—
264C22×D53—41no—
265C22×D53—41no—
266C22×D53—41no—
267C22×D53—41no—
268D4×C53—28no—
269C2×C4×C53—21no—
270C2×C4×C53—21no—
271C2×C4×C53—21no—
272C2×C4×C53—21no—
273C2×C4×C53—21no—
274C2×C4×C53—21no—
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—22no—
284C2×C4×C53—22no—
285C2×C4×C53—22no—
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—41no—
295C2×C4×C53—41no—
296C2×C4×C53—41no—
297C2×C4×C53—84no—
298C2×C4×C53C2×C22⋊C412yes—
299C2×C4×C53C2×C22⋊C412yes—
300C2×C4×C53C2×C22⋊C412yes—
301C2×C4×C53C2×C22⋊C412yes—
302C2×C4×C53C23×C411yescharacteristic
303C2×C4×C53C22×D411yescharacteristic
304C2×C4×C53C2×#4111yescharacteristic
305C2×C4×C53C2×#4111yescharacteristic
306C2×C4×C53H(5,𝔽2)11yescharacteristic
307C2×C4×C532−1+411yescharacteristic
308C22⋊D53—48no—
309C22⋊D53—48no—
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—22no—
313C2×Dic53—48no—
314C2×Dic53—41no—
315C2×Dic53—41no—
316C2×Dic53—41no—
317C2×Dic53—41no—
318C2×Dic53—41no—
319C2×Dic53—41no—
320C2×Dic53—48no—
321D212—22no—
322D212—22no—
323D212—41no—
324D212—41no—
325C4×D53—48no—
326Dic106—48no—
327#88322—22no—
328#88322—41no—
329#88322—41no—
330#88322—41no—
331#22495—531nomaximal, Sylow
332C22×C53—22no—
333C22×C53—22no—
334C22×C53—22no—
335C22×C53—22no—
336C22×C53—22no—
337C22×C53—22no—
338C22×C53—22no—
339C22×C53—22no—
340C22×C53—22no—
341C22×C53—41no—
342C22×C53—41no—
343C22×C53—41no—
344C22×C53—41no—
345C22×C53#41814yes—
346C22×C53C22×C22⋊C411yescharacteristic
347C22×C53#54611yescharacteristic
348C22×C53#54711yescharacteristic
349C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
350C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
351C22×C53#57711yescharacteristic
352C22×C53#57811yescharacteristic
353C2×D53—42no—
354C2×D53—42no—
355C2×D53—42no—
356C2×D53—81no—
357C2×D53—81no—
358C2×D53—81no—
359C2×D53—81no—
360C4×C53—22no—
361C4×C53—22no—
362C4×C53—22no—
363C4×C53—22no—
364C4×C53—42no—
365C4×C53—81no—
366C4×C53—81no—
367C4×C53—81no—
368C4×C53C4×#4111yescharacteristic
369C4×C53#52011yescharacteristic
370C4×C53#54611yescharacteristic
371C4×C53#54711yescharacteristic
372Dic53—42no—
373Dic53—42no—
374Dic53—42no—
375C2×#547—531no—
376C2×#435—531no—
377#2352D5311yescharacteristic, complemented
378#1993—531no—
379#1987—531no—
380#1895—531no—
381#1893—531no—
382#1875—531no—
383#1874—531no—
384#1824—531no—
385#1823—531no—
386#1804—531no—
387#1762—531no—
388#1736—531no—
389C2×#340—531no—
390C2×C53—24no—
391C2×C53—42no—
392C2×C53#233911yescharacteristic
393C2×C53C2×#41811yescharacteristic
394C2×C53#289811yescharacteristic
395C2×C53#330611yescharacteristic
396C2×C53#330811yescharacteristic
397C2×C53#334311yescharacteristic
398C2×C53#334511yescharacteristic
399D53—82no—
400C22×#41—1061no—
401C22×M16—531no—
402C23×C8—531no—
403#547—538no—
404#547—1064no—
405C2×C4⋊Q8—531no—
406C2×#123—1061no—
407C2×#123—1061no—
408C2×C22⋊Q8—1061no—
409C2×#121—531no—
410C2×#121—531no—
411C2×C4×D4—531no—
412C2×C4×D4C2×D5311yescharacteristic
413C2×#117C2×D5311yescharacteristic
414C22×C4⋊C4—531no—
415C22×C4⋊C4—531no—
416C22×C4⋊C4C2×D5311yescharacteristic
417#435—1064no—
418C2×C4⋊C8—531no—
419C2×#102—531no—
420C2×#102—531no—
421C2×#102—531no—
422C2×#102—531no—
423C2×C22⋊C8—531no—
424C2×C22⋊C8—531no—
425C2×#97—531no—
426#388—21no—
427#387—21no—
428#386—21no—
429#382C2×D5311yescharacteristic
430#380C2×D5311yescharacteristic
431#380C2×D5311yescharacteristic
432C4×C4⋊C4C2×D5311yescharacteristic
433C4×C22⋊C4—21no—
434#340—531no—
435#340—531no—
436#340—531no—
437#340—531no—
438#340—531no—
439#340—531no—
440#340—531no—
441#340—531no—
442#340—531no—
443#340—531no—
444#340—531no—
445#340—531no—
446C53#2249511yescharacteristic, complemented, Sylow
447C2×#41—1068no—
448C2×#41—2124no—
449C2×#41—2124no—
450C22×Q8—1061no—
451C22×D4—531no—
452C22×D4—1061no—
453C22×D4—1061no—
454C22×D4C22⋊D5311yescharacteristic
455C23×C4—21no—
456C23×C4—1061no—
457C23×C4—1061no—
458C23×C4—1061no—
459C23×C4C22×D5311yescharacteristic
460C23×C4C22×D5311yescharacteristic
461C2×M16—1062no—
462C2×M16—1062no—
463C2×M16—2121no—
464C22×C8—531no—
465C22×C8—531no—
466C22×C8—531no—
467C22×C8—531no—
468C22×C8—1062no—
469C22×C8—1062no—
470C22×C8—2121no—
471C4⋊Q8—534no—
472C4⋊Q8—1062no—
473#123—1068no—
474#123—1068no—
475C22⋊Q8—1068no—
476#121—534no—
477#121—534no—
478#121—1062no—
479#121—1062no—
480C4×D4—534no—
481C4×D4—1062no—
482C4×D4C4×D5314yes—
483C4×D4D21214yes—
484#117—22no—
485#117—41no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—41no—
489C2×C4⋊C4—534no—
490C2×C4⋊C4—534no—
491C2×C4⋊C4—531no—
492C2×C4⋊C4—531no—
493C2×C4⋊C4—531no—
494C2×C4⋊C4—1062no—
495C2×C4⋊C4—1062no—
496C2×C4⋊C4—1061no—
497C2×C4⋊C4—1061no—
498C2×C4⋊C4—1061no—
499C2×C4⋊C4C22⋊D5311yescharacteristic
500C2×C4⋊C4C22×D5311yescharacteristic
501C2×C4⋊C4C22×D5311yescharacteristic
502C2×C4⋊C4C22×D5311yescharacteristic
503C2×C4⋊C4C22×D5311yescharacteristic
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—1061no—
508C2×C22⋊C4—1061no—
509C2×C22⋊C4—1061no—
510C2×C22⋊C4C22⋊D5311yescharacteristic
511C2×C22⋊C4C22⋊D5311yescharacteristic
512C2×C42—21no—
513C2×C42—21no—
514C2×C42C22×D5311yescharacteristic
515C4⋊C8—1062no—
516#102—1062no—
517#102—1062no—
518#102—2121no—
519#102—2121no—
520C22⋊C8—1062no—
521C22⋊C8—1062no—
522#97—1062no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95—21no—
527#95—21no—
528C24—1061no—
529C24C2×C22⋊D5311yescharacteristic
530C24C2×C22⋊D5311yescharacteristic
531#41—21232no—
532C2×Q8—1064no—
533C2×Q8—2122no—
534C2×Q8—2122no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—532no—
538C2×D4—1064no—
539C2×D4—1064no—
540C2×D4—1061no—
541C2×D4—1061no—
542C2×D4—1061no—
543C2×D4—1061no—
544C2×D4—1061no—
545C2×D4—2122no—
546C2×D4—2122no—
547C2×D4—2122no—
548C2×D4—2122no—
549C2×D4#1171992114yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—81no—
565C22×C4—1064no—
566C22×C4—1064no—
567C22×C4—1061no—
568C22×C4—1061no—
569C22×C4—1061no—
570C22×C4—1064no—
571C22×C4—2122no—
572C22×C4—2122no—
573C22×C4—2122no—
574C22×C4—2122no—
575C22×C4—2122no—
576C22×C4—2122no—
577C22×C4C2×C4×D5312yes—
578C22×C4C2×C4×D5312yes—
579C22×C4C2×D21212yes—
580C22×C4C2×D21212yes—
581C22×C4C2×C22⋊D5311yescharacteristic
582C22×C4C2×C22⋊D5311yescharacteristic
583C22×C4C2×C22⋊D5311yescharacteristic
584C22×C4C2×C22⋊D5311yescharacteristic
585C22×C4C23×D5311yescharacteristic
586M16—2124no—
587C2×C8—532no—
588C2×C8—1061no—
589C2×C8—1061no—
590C2×C8—1061no—
591C2×C8—1061no—
592C2×C8—1061no—
593C2×C8—1061no—
594C2×C8—1061no—
595C2×C8—1061no—
596C2×C8—1061no—
597C2×C8—1061no—
598C2×C8—1061no—
599C2×C8—2124no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—42no—
608C4⋊C4—532no—
609C4⋊C4—532no—
610C4⋊C4—532no—
611C4⋊C4—1064no—
612C4⋊C4—1064no—
613C4⋊C4—1064no—
614C4⋊C4—1061no—
615C4⋊C4—1061no—
616C4⋊C4—1061no—
617C4⋊C4#1171992114yes—
618C4⋊C4#1171994712yescomplemented
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—81no—
622C22⋊C4—1064no—
623C22⋊C4—1064no—
624C22⋊C4—1064no—
625C22⋊C4#1171992114yes—
626C22⋊C4#1171992114yes—
627C42—42no—
628C42—81no—
629C42C2×C4×D5312yes—
630C42C2×D21212yes—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—1062no—
642C23—2121no—
643C23—2121no—
644C23—2121no—
645C23—2121no—
646C23—2121no—
647C23—2121no—
648C23C2×#1171992112yes—
649C23C2×#1171992112yes—
650C23#1313324212yes—
651C23#1313324212yes—
652C23C22×C22⋊D5311yescharacteristic
653Q8—2128no—
654D4—28no—
655D4—1062no—
656D4—1062no—
657D4—2128no—
658D4—2128no—
659D4—2121no—
660D4—2121no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—84no—
690C2×C4—1062no—
691C2×C4—1062no—
692C2×C4—1062no—
693C2×C4—2128no—
694C2×C4—2128no—
695C2×C4—2128no—
696C2×C4—2121no—
697C2×C4—2121no—
698C2×C4—2121no—
699C2×C4—2121no—
700C2×C4—2121no—
701C2×C4—2121no—
702C2×C4C2×#1171992112yes—
703C2×C4C2×#1171992112yes—
704C2×C4C2×#1171992112yes—
705C2×C4C2×#1171992112yes—
706C2×C4C22×C4×D5311yescharacteristic
707C2×C4C22×D21211yescharacteristic
708C2×C4#41×D5311yescharacteristic
709C2×C4C2×#1171994711yescharacteristic
710C2×C4#1313326211yescharacteristic
711C2×C4#1313326411yescharacteristic
712C8—1062no—
713C8—2121no—
714C8—2121no—
715C8—2121no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—4241no—
730C22—4241no—
731C22—4241no—
732C22—4241no—
733C22—2122no—
734C22—2122no—
735C22—2122no—
736C22#1681062714yes—
737C22C22×#1171992111yescharacteristic
738C22#1681126711yescharacteristic
739C22#1681127211yescharacteristic
740C22C2×#1313324211yescharacteristic
741C22C2×#1313324211yescharacteristic
742C22#1681143411yescharacteristic
743C22#1681143811yescharacteristic
744C4—22no—
745C4—22no—
746C4—22no—
747C4—22no—
748C4—42no—
749C4—81no—
750C4—81no—
751C4—81no—
752C4—2122no—
753C4—2122no—
754C4—2122no—
755C4C4×#1171994711yescharacteristic
756C4#1681110211yescharacteristic
757C4#1681126811yescharacteristic
758C4#1681127711yescharacteristic
759C2—24no—
760C2—42no—
761C2—4242no—
762C2#2027754011yescharacteristic
763C2C2×#1681062711yescharacteristic
764C2#2028324511yescharacteristic
765C2#2028667611yescharacteristic
766C2#2028670611yescharacteristic
767C2#2028715511yescharacteristic
768C2#2028717911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2352C2
socleC23×C53C22×D4
prime radicalC2×#16811277C2
cosocleC22×C4×C53C24
hypercenter#2352D53
hypocenterC53#22495
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. #20275663C2semidirect
5. #20275151C2semidirect
6. #20275141C2semidirect
7. #20275037C2semidirect
8. #20275032C2semidirect
9. #20274803C2semidirect
10. #20274799C2semidirect
11. #20274722C2semidirect
12. #20274543C2semidirect
13. #20274436C2semidirect
14. C2×#16810385C2semidirect
15. C53×#2352C2semidirect
20. #16811277C4semidirect
83. #13133217C2×C4semidirect
90. #13133191C2×C4semidirect
92. C4×D212C2×C4semidirect
99. C2×C4⋊Dic53C2×C4semidirect
210. C4⋊C4×C53#41semidirect
245. C2×#88322#41semidirect
377. #2352D53semidirect
446. C53#22495semidirect
618. C4⋊C4#11719947semidirect

Maximal subgroups

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

subgroupindex
C2×#168112772
C2×#168106952
#202756872
#202756632
#202751512
#202751412
#202750372
#202750322
#202748032
#202747992
#202747222
#202745432
#202744362
C2×#168103852
C53×#23522
#2249553