Finite Group Databasebeta

← #27400346

Subgroups — #27400346

Order 13568.

1226 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×#16811320C211yesmaximal, characteristic
2C2×#16810686C211yesmaximal, characteristic, complemented
3#20277645C211yesmaximal, characteristic, complemented
4#20275678C211yesmaximal, characteristic, complemented
5#20275669C211yesmaximal, characteristic, complemented
6#20275144C211yesmaximal, characteristic, complemented
7#20275140C211yesmaximal, characteristic, complemented
8#20275029C211yesmaximal, characteristic, complemented
9#20274811C211yesmaximal, characteristic, complemented
10#20274804C211yesmaximal, characteristic, complemented
11#20274723C211yesmaximal, characteristic, complemented
12#102×Dic53C211yesmaximal, characteristic, complemented
13#20274431C211yesmaximal, characteristic, complemented
14#340×D53C211yesmaximal, characteristic, complemented
15C53×#1875C211yesmaximal, characteristic, complemented
16C23×#88322C2211yescharacteristic
17C22×C8×D53C2211yescharacteristic
18#16811320—24no—
19#16811320C418yescomplemented
20C2×#13133210—21no—
21C2×#13133208C2211yescharacteristic
22C2×#13133198—21no—
23C2×#13133188—21no—
24C2×#13133188C2211yescharacteristic
25C2×D4×Dic53C2211yescharacteristic
26C2×C4×C22⋊D53C2211yescharacteristic
27C2×#13133177—21no—
28C2×#13133176C2211yescharacteristic
29C2×C4⋊C4×D53C2211yescharacteristic
30C2×C4⋊C4×D53C2211yescharacteristic
31#16810686—24no—
32C2×#13133146C2211yescharacteristic
33C2×#13133138C2211yescharacteristic
34C2×#13133138C2211yescharacteristic
35C2×#13133129C2211yescharacteristic
36C2×C8×Dic53C2211yescharacteristic
37#16810517—21no—
38#16810507—21no—
39#16810499—21no—
40#16810488C2211yescharacteristic
41#16810483C2211yescharacteristic
42#16810480C2211yescharacteristic
43C4⋊C4×Dic53C2211yescharacteristic
44C4×#11719921—21no—
45#16810386C2211yescharacteristic
46#16810386C2211yescharacteristic
47#16810386C2211yescharacteristic
48#16810386C2211yescharacteristic
49#16810385C2211yescharacteristic
50#16810385C2211yescharacteristic
51#16810385C2211yescharacteristic
52#16810385C2211yescharacteristic
53#16810385C2211yescharacteristic
54#16810385C2211yescharacteristic
55C2×#121×C53C2211yescharacteristic
56C2×#117×C53C2211yescharacteristic
57C2×#102×C53C2211yescharacteristic
58C2×#102×C53C2211yescharacteristic
59C2×C22⋊C8×C53C2211yescharacteristic
60C53×#340C2211yescharacteristic
61C53×#340C2211yescharacteristic
62C22×C22⋊D53—21no—
63C22×C22⋊D53D411yescharacteristic
64C23×Dic53—21no—
65C22×C4×D53—21no—
66C22×C4×D53—21no—
67C22×C4×D53C2311yescharacteristic
68C22×#88322—22no—
69C22×#88322—22no—
70C22×#88322—41no—
71C22×#88322C2311yescharacteristic
72C22×#88322C2311yescharacteristic
73C2×C8×D53—22no—
74C2×C8×D53—22no—
75C2×C8×D53—41no—
76#13133210—28no—
77#13133208—22no—
78#13133208C2×C414yescomplemented
79#13133198—28no—
80#13133188—28no—
81#13133188—22no—
82#13133188C2×C414yes—
83D4×Dic53—22no—
84D4×Dic53C2×C414yescomplemented
85C4×C22⋊D53C2×C414yes—
86C4×C22⋊D53D414yes—
87#13133177—28no—
88#13133176—22no—
89#13133176C2×C414yescomplemented
90C2×C4⋊Dic53—21no—
91C2×C4⋊Dic53C2311yescharacteristic
92C2×C4⋊Dic53C2311yescharacteristic
93C2×C4⋊Dic53C2311yescharacteristic
94C2×C4⋊Dic53C2311yescharacteristic
95C2×#11719919—21no—
96C2×#11719919—21no—
97C2×#11719919—21no—
98C2×#11719919D411yescharacteristic
99C4⋊C4×D53—22no—
100C4⋊C4×D53—22no—
101C4⋊C4×D53—41no—
102C4⋊C4×D53C2×C414yes—
103C2×C22⋊Dic53—21no—
104C2×C22⋊Dic53—21no—
105C2×C22⋊Dic53—21no—
106C2×C22⋊Dic53—21no—
107C2×C22⋊Dic53D411yescharacteristic
108C2×#11719921—21no—
109C2×#11719921D411yescharacteristic
110C2×C4×Dic53—21no—
111C2×C4×Dic53—21no—
112C2×C4×Dic53C2311yescharacteristic
113#13133146—22no—
114#13133138—22no—
115#13133138—41no—
116#13133129—22no—
117C8×Dic53—22no—
118#13133124—21no—
119#13133124—21no—
120#13133124—21no—
121#13133124—21no—
122#13133124—21no—
123C22×D4×C53—21no—
124C22×D4×C53C2311yescharacteristic
125C23×C4×C53C2311yescharacteristic
126C22×C8×C53C2311yescharacteristic
127C22×C8×C53C2311yescharacteristic
128#121×C53—22no—
129#121×C53C2×C414yescomplemented
130#117×C53—22no—
131#117×C53—41no—
132C2×C4⋊C4×C53C2311yescharacteristic
133C2×C4⋊C4×C53C2311yescharacteristic
134C2×C4⋊C4×C53C2311yescharacteristic
135C2×C22⋊C4×C53—21no—
136C2×C22⋊C4×C53—21no—
137C2×C42×C53—21no—
138#102×C53—22no—
139#102×C53—41no—
140C22⋊C8×C53—22no—
141C24×C53—21no—
142C24×C53C2×D411yescharacteristic
143C23×D53C2×D411yescharacteristic
144C2×D4×C53—24no—
145C2×D4×C53—21no—
146C2×D4×C53—21no—
147C2×D4×C53—21no—
148C2×D4×C53—21no—
149C2×D4×C53—21no—
150C2×D4×C53—81no—
151C2×D4×C53—81no—
152C2×D4×C53C22×C412yes—
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×C53C22×C412yes—
161C22×C4×C53C2×D411yescharacteristic
162C22×C4×C53C2×D412yes—
163C22×C4×C53C2411yescharacteristic
164C2×C22⋊D53—22no—
165C2×C22⋊D53—22no—
166C2×C22⋊D53—24no—
167C2×C22⋊D53—42no—
168C2×C22⋊D53—42no—
169C2×C22⋊D53C22⋊C414yes—
170C22×Dic53—21no—
171C22×Dic53—21no—
172C22×Dic53—24no—
173C22×Dic53—21no—
174C22×Dic53—21no—
175C22×Dic53—81no—
176C22×Dic53—81no—
177C22×Dic53C2×D411yescharacteristic
178C22×Dic53C2×D411yescharacteristic
179C22×Dic53C2×D411yescharacteristic
180C2×C4×D53—21no—
181C2×C4×D53—21no—
182C2×C4×D53—21no—
183C2×C4×D53—21no—
184C2×C4×D53—24no—
185C2×C4×D53—42no—
186C2×C4×D53—42no—
187C2×C4×D53—81no—
188C2×C4×D53—81no—
189C2×C4×D53—81no—
190C2×C4×D53C22×C412yes—
191C2×C4×D53C2×D412yes—
192C2×C8×C53—21no—
193C2×C8×C53—21no—
194C2×C8×C53—21no—
195C2×C8×C53—21no—
196C2×C8×C53—21no—
197C2×C8×C53—21no—
198C4⋊C4×C53—21no—
199C4⋊C4×C53—21no—
200C4⋊C4×C53—21no—
201C4⋊C4×C53—21no—
202C4⋊C4×C53C22×C412yes—
203C4⋊C4×C53#4112yes—
204C22⋊C4×C53—24no—
205C22⋊C4×C53—42no—
206C42×C53—42no—
207C22⋊Dic53—24no—
208C22⋊Dic53—24no—
209C22⋊Dic53—24no—
210C22⋊Dic53—81no—
211C22⋊Dic53C22⋊C414yes—
212#11719921—42no—
213#11719921C22⋊C414yes—
214C4⋊Dic53—21no—
215C4⋊Dic53—21no—
216C4⋊Dic53—24no—
217C4⋊Dic53—21no—
218C4⋊Dic53—21no—
219C4⋊Dic53—21no—
220C4⋊Dic53—21no—
221C4⋊Dic53C22×C412yes—
222C4⋊Dic53C22×C412yes—
223#11719919—24no—
224#11719919—24no—
225#11719919—42no—
226#11719919C22⋊C414yes—
227C4×Dic53—24no—
228C4×Dic53—81no—
229C4×Dic53C22×C412yes—
230C4×Dic53C2×D412yes—
231C2×#88322—21no—
232C2×#88322—21no—
233C2×#88322—21no—
234C2×#88322—21no—
235C2×#88322—21no—
236C2×#88322—44no—
237C2×#88322#4112yes—
238C8×D53—44no—
239C23×C53—21no—
240C23×C53—21no—
241C23×C53—21no—
242C23×C53—21no—
243C23×C53—21no—
244C23×C53—21no—
245C23×C53—22no—
246C23×C53—41no—
247C23×C53—41no—
248C23×C53—41no—
249C23×C53—41no—
250C23×C53—41no—
251C23×C53—41no—
252C23×C53C2×C22⋊C412yes—
253C23×C53C22×D411yescharacteristic
254C22×D53—21no—
255C22×D53—21no—
256C22×D53—21no—
257C22×D53—21no—
258C22×D53C2×C22⋊C412yes—
259C22×D53#13512yes—
260C22×D53#13512yes—
261D4×C53—22no—
262D4×C53—22no—
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—22no—
274C2×C4×C53—41no—
275C2×C4×C53—41no—
276C2×C4×C53—41no—
277C2×C4×C53—41no—
278C2×C4×C53—41no—
279C2×C4×C53—41no—
280C2×C4×C53—41no—
281C2×C4×C53C2×C22⋊C412yes—
282C2×C4×C53C23×C411yescharacteristic
283C2×C4×C53C22×D411yescharacteristic
284C2×C4×C53C2×#4111yescharacteristic
285C2×C4×C53C2×#4111yescharacteristic
286C2×C4×C53H(5,𝔽2)11yescharacteristic
287C2×C4×C532−1+411yescharacteristic
288C22⋊D53—28no—
289C22⋊D53—48no—
290C2×Dic53—21no—
291C2×Dic53—21no—
292C2×Dic53—21no—
293C2×Dic53—21no—
294C2×Dic53—21no—
295C2×Dic53—21no—
296C2×Dic53—22no—
297C2×Dic53—22no—
298C2×Dic53—41no—
299C2×Dic53—41no—
300C2×Dic53—41no—
301C2×Dic53—41no—
302C2×Dic53—41no—
303C2×Dic53—41no—
304C2×Dic53—41no—
305C2×Dic53—41no—
306C2×Dic53—41no—
307C2×Dic53—41no—
308C2×Dic53—84no—
309C2×Dic53C2×C22⋊C412yes—
310C2×Dic53C2×C22⋊C412yes—
311C2×Dic53C2×C22⋊C412yes—
312C4×D53—22no—
313C4×D53—22no—
314C4×D53—22no—
315C4×D53—22no—
316C4×D53—84no—
317C4×D53—84no—
318C8×C53—41no—
319C8×C53—41no—
320#88322—22no—
321#88322—41no—
322#22488—531nomaximal, Sylow
323C22×C53—22no—
324C22×C53—22no—
325C22×C53—22no—
326C22×C53—41no—
327C22×C53—41no—
328C22×C53—41no—
329C22×C53—41no—
330C22×C53—42no—
331C22×C53—42no—
332C22×C53—42no—
333C22×C53—81no—
334C22×C53—81no—
335C22×C53—81no—
336C22×C53—81no—
337C22×C53C22×C22⋊C411yescharacteristic
338C22×C53#54611yescharacteristic
339C22×C53#54711yescharacteristic
340C22×C53C2×#13511yescharacteristic
341C22×C53C2×#13511yescharacteristic
342C22×C53#57611yescharacteristic
343C22×C53#57711yescharacteristic
344C2×D53—22no—
345C2×D53—22no—
346C2×D53—22no—
347C2×D53—22no—
348C2×D53—22no—
349C2×D53—22no—
350C2×D53#41614yes—
351C4×C53—22no—
352C4×C53—42no—
353C4×C53—42no—
354C4×C53—81no—
355C4×C53C4×#4111yescharacteristic
356C4×C53#52011yescharacteristic
357C4×C53#54611yescharacteristic
358C4×C53#54711yescharacteristic
359Dic53—22no—
360Dic53—22no—
361Dic53—22no—
362Dic53—42no—
363Dic53—42no—
364Dic53—81no—
365Dic53—81no—
366C2×#553—531no—
367C2×C8×D4—531no—
368#2352—531no—
369#1991—531no—
370#1989—531no—
371#1893—531no—
372#1893—531no—
373#1875D5311yescharacteristic, complemented
374#1874—531no—
375#1825—531no—
376#1824—531no—
377#1804—531no—
378C4×#102—531no—
379#1735—531no—
380C2×#340—531no—
381C2×C53—42no—
382C2×C53—82no—
383C2×C53#233911yescharacteristic
384C2×C53C2×#41611yescharacteristic
385C2×C53#289711yescharacteristic
386C2×C53#329711yescharacteristic
387C2×C53#330111yescharacteristic
388C2×C53#333711yescharacteristic
389C2×C53#333911yescharacteristic
390D53—24no—
391C23×C8—531no—
392C23×C8—531no—
393#553—538no—
394#553—1064no—
395C2×#126—1061no—
396C2×#125—531no—
397C2×#123—1061no—
398C2×#121—531no—
399C2×#121—1061no—
400C2×#121C2×D5311yescharacteristic
401C2×C4×D4—531no—
402C2×C4×D4—531no—
403C2×C4×D4—1061no—
404C2×#117—531no—
405C2×#117C2×D5311yescharacteristic
406C22×C4⋊C4—531no—
407C22×C4⋊C4—531no—
408C8×D4—1064no—
409C2×C4⋊C8—531no—
410C2×#102—531no—
411C2×#102—531no—
412C2×#102C2×D5311yescharacteristic
413C2×#102C2×D5311yescharacteristic
414C2×C22⋊C8—531no—
415C2×C22⋊C8C2×D5311yescharacteristic
416C2×C4×C8—531no—
417#388—1061no—
418#387—1061no—
419#386—1061no—
420#382—531no—
421#380—531no—
422#380—531no—
423C4×C4⋊C4—531no—
424C4×C22⋊C4—1061no—
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#340C2×D5311yescharacteristic
436#340C2×D5311yescharacteristic
437C53#2248811yescharacteristic, complemented, Sylow
438C22×D4—21no—
439C22×D4—531no—
440C22×D4—1061no—
441C22×D4C22×D5311yescharacteristic
442C23×C4—531no—
443C23×C4—1061no—
444C23×C4—1061no—
445C23×C4—1061no—
446C23×C4C22×D5311yescharacteristic
447C22×C8—531no—
448C22×C8—531no—
449C22×C8—1062no—
450C22×C8—1062no—
451C22×C8—1062no—
452C22×C8—1062no—
453C22×C8—2121no—
454C22×C8—2121no—
455C22×C8C22×D5311yescharacteristic
456C22×C8C22×D5311yescharacteristic
457#126—1068no—
458#125—534no—
459#125—1062no—
460#123—1068no—
461#121—22no—
462#121—534no—
463#121—1062no—
464#121—1068no—
465#121C4×D5314yescomplemented
466C4×D4—534no—
467C4×D4—534no—
468C4×D4—534no—
469C4×D4—1062no—
470C4×D4—1068no—
471#117—22no—
472#117—41no—
473#117—534no—
474#117—1062no—
475C2×C4⋊C4—531no—
476C2×C4⋊C4—531no—
477C2×C4⋊C4—531no—
478C2×C4⋊C4—534no—
479C2×C4⋊C4—531no—
480C2×C4⋊C4—531no—
481C2×C4⋊C4—1062no—
482C2×C4⋊C4—1061no—
483C2×C4⋊C4—1061no—
484C2×C4⋊C4—1061no—
485C2×C4⋊C4—1062no—
486C2×C4⋊C4—1061no—
487C2×C4⋊C4—2121no—
488C2×C4⋊C4C22×D5311yescharacteristic
489C2×C4⋊C4C22×D5311yescharacteristic
490C2×C4⋊C4C22×D5311yescharacteristic
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—531no—
494C2×C22⋊C4—531no—
495C2×C22⋊C4—1061no—
496C2×C22⋊C4—1061no—
497C2×C22⋊C4—1061no—
498C2×C22⋊C4—1061no—
499C2×C22⋊C4—1061no—
500C2×C42—21no—
501C2×C42—531no—
502C2×C42—1061no—
503C2×C42—1061no—
504C4⋊C8—1062no—
505#102—22no—
506#102—41no—
507#102—1062no—
508#102—2121no—
509C22⋊C8—22no—
510C22⋊C8—1062no—
511C4×C8—1062no—
512#95—1061no—
513#95—1061no—
514#95—1061no—
515#95—1061no—
516#95—1061no—
517C24—21no—
518C24—531no—
519C24D4×D5311yescharacteristic
520C2×D4—24no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—81no—
527C2×D4—81no—
528C2×D4—534no—
529C2×D4—1062no—
530C2×D4—1062no—
531C2×D4—1064no—
532C2×D4—2122no—
533C2×D4—2122no—
534C2×D4C2×C4×D5312yes—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—531no—
543C22×C4—531no—
544C22×C4—531no—
545C22×C4—532no—
546C22×C4—532no—
547C22×C4—1064no—
548C22×C4—1064no—
549C22×C4—1061no—
550C22×C4—1061no—
551C22×C4—1061no—
552C22×C4—1061no—
553C22×C4—1061no—
554C22×C4—1061no—
555C22×C4—1061no—
556C22×C4—1061no—
557C22×C4—4241no—
558C22×C4—4241no—
559C22×C4—4241no—
560C22×C4—4241no—
561C22×C4—4241no—
562C22×C4—2122no—
563C22×C4—2122no—
564C22×C4C2×C4×D5312yes—
565C22×C4D4×D5311yescharacteristic
566C22×C4D4×D5312yes—
567C22×C4C23×D5311yescharacteristic
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—532no—
575C2×C8—1061no—
576C2×C8—1061no—
577C2×C8—1061no—
578C2×C8—1061no—
579C2×C8—1061no—
580C2×C8—2124no—
581C2×C8—2124no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—534no—
587C4⋊C4—532no—
588C4⋊C4—532no—
589C4⋊C4—1064no—
590C4⋊C4—1064no—
591C4⋊C4—1064no—
592C4⋊C4—1061no—
593C4⋊C4—1061no—
594C4⋊C4—1061no—
595C4⋊C4—1061no—
596C4⋊C4—1061no—
597C4⋊C4—1061no—
598C4⋊C4—2122no—
599C4⋊C4C2×C4×D5312yes—
600C4⋊C4#1171994712yes—
601C22⋊C4—24no—
602C22⋊C4—42no—
603C22⋊C4—534no—
604C22⋊C4—534no—
605C22⋊C4—1064no—
606C22⋊C4—1064no—
607C22⋊C4—1064no—
608C22⋊C4—4241no—
609C22⋊C4—2122no—
610C42—42no—
611C42—532no—
612C42—532no—
613C42—1064no—
614C42—4241no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—22no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—532no—
629C23—532no—
630C23—532no—
631C23—1061no—
632C23—1061no—
633C23—1061no—
634C23—1061no—
635C23C22⋊C4×D5312yes—
636C23C2×D4×D5311yescharacteristic
637D4—22no—
638D4—22no—
639D4—41no—
640D4—41no—
641D4—84no—
642D4—1068no—
643D4—2128no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—532no—
660C2×C4—532no—
661C2×C4—532no—
662C2×C4—1061no—
663C2×C4—1061no—
664C2×C4—1061no—
665C2×C4—1061no—
666C2×C4—1061no—
667C2×C4—1061no—
668C2×C4—1062no—
669C2×C4—1062no—
670C2×C4—1062no—
671C2×C4—1062no—
672C2×C4—1062no—
673C2×C4—1062no—
674C2×C4—4244no—
675C2×C4—4244no—
676C2×C4—4244no—
677C2×C4—2121no—
678C2×C4—2121no—
679C2×C4—2121no—
680C2×C4—2121no—
681C2×C4—2121no—
682C2×C4—2121no—
683C2×C4—2121no—
684C2×C4—2121no—
685C2×C4—2121no—
686C2×C4—2121no—
687C2×C4C22⋊C4×D5312yes—
688C2×C4C22×C4×D5311yescharacteristic
689C2×C4C2×D4×D5311yescharacteristic
690C2×C4#41×D5311yescharacteristic
691C2×C4C2×#1171994711yescharacteristic
692C2×C4#1313326211yescharacteristic
693C2×C4#1313326411yescharacteristic
694C8—41no—
695C8—41no—
696C8—1062no—
697C8—2121no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22—534no—
713C22—1062no—
714C22—1062no—
715C22—1062no—
716C22—1062no—
717C22—1062no—
718C22—1062no—
719C22C2×C22⋊C4×D5311yescharacteristic
720C22#1681126011yescharacteristic
721C22#1681127111yescharacteristic
722C22#135×D5311yescharacteristic
723C22#135×D5311yescharacteristic
724C22#1681142711yescharacteristic
725C22#1681143311yescharacteristic
726C4—22no—
727C4—42no—
728C4—42no—
729C4—81no—
730C4—1062no—
731C4—1062no—
732C4—1062no—
733C4—4241no—
734C4—4241no—
735C4—2122no—
736C4—2122no—
737C4C4×#1171994711yescharacteristic
738C4#1681110211yescharacteristic
739C4#1681126211yescharacteristic
740C4#1681127311yescharacteristic
741C2—42no—
742C2—82no—
743C2—1064no—
744C2#2027754111yescharacteristic
745C2#416×D5311yescharacteristic
746C2#2028324011yescharacteristic
747C2#2028655811yescharacteristic
748C2#2028661011yescharacteristic
749C2#2028708711yescharacteristic
750C2#2028711011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1875C2
socleC23×C53C22×D4
prime radicalC2×#16811320C2
cosocleC22×C4×C53C24
hypercenter#1875D53
hypocenterC53#22488
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1875

Complements

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

NH ≅ G/Ntype
2. C2×#16810686C2semidirect
3. #20277645C2semidirect
4. #20275678C2semidirect
5. #20275669C2semidirect
6. #20275144C2semidirect
7. #20275140C2semidirect
8. #20275029C2semidirect
9. #20274811C2semidirect
10. #20274804C2semidirect
11. #20274723C2semidirect
12. #102×Dic53C2semidirect
13. #20274431C2semidirect
14. #340×D53C2semidirect
15. C53×#1875C2semidirect
19. #16811320C4semidirect
78. #13133208C2×C4semidirect
84. D4×Dic53C2×C4semidirect
89. #13133176C2×C4semidirect
129. #121×C53C2×C4semidirect
373. #1875D53semidirect
437. C53#22488semidirect
465. #121C4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168113202
C2×#168106862
#202776452
#202756782
#202756692
#202751442
#202751402
#202750292
#202748112
#202748042
#202747232
#102×Dic532
#202744312
#340×D532
C53×#18752
#2248853