Finite Group Databasebeta

← #27412460

Subgroups — #27412460

Order 13568.

1114 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810721C211yesmaximal, characteristic, complemented
2C2×C4×#11719924C211yesmaximal, characteristic, complemented
3#20277408C211yesmaximal, characteristic
4#20276050C211yesmaximal, characteristic, complemented
5#20275958C211yesmaximal, characteristic, complemented
6#20275915C211yesmaximal, characteristic, complemented
7#20275908C211yesmaximal, characteristic, complemented
8#20275858C211yesmaximal, characteristic, complemented
9#20275798C211yesmaximal, characteristic, complemented
10#20275716C211yesmaximal, characteristic
11#20275716C211yesmaximal, characteristic
12#20274545C211yesmaximal, characteristic, complemented
13C4×#13133141C211yesmaximal, characteristic, complemented
14#20274481C211yesmaximal, characteristic, complemented
15C2×C53×#541C211yesmaximal, characteristic, complemented
16C22×#11719924C2211yescharacteristic
17C22×#11719924C2211yescharacteristic
18C2×#13133191C2211yescharacteristic
19C2×C4×D212C2211yescharacteristic
20#16810721—24no—
21C4×#11719924—24no—
22C2×#13133150C2211yescharacteristic
23C2×#13133148C2211yescharacteristic
24C2×#13133141C2211yescharacteristic
25C2×#13133141C2211yescharacteristic
26C2×#13133141C2211yescharacteristic
27C2×#13133141C2211yescharacteristic
28C2×#13133141C2211yescharacteristic
29C2×#13133141C2211yescharacteristic
30C2×#13133137C2211yescharacteristic
31C2×#13133137C2211yescharacteristic
32C2×C22⋊#88322C2211yescharacteristic
33C2×C22⋊#88322C2211yescharacteristic
34C2×#13133128C2211yescharacteristic
35C2×C4×#88322C2211yescharacteristic
36#16810525C2211yescharacteristic
37#16810523—21no—
38#16810521C2211yescharacteristic
39#16810513—21no—
40#16810499—21no—
41#16810494—21no—
42#16810483C2211yescharacteristic
43C4×C4⋊Dic53C2211yescharacteristic
44#16810385C2211yescharacteristic
45#16810385C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810378C2211yescharacteristic
49#16810378C2211yescharacteristic
50C53×#541—24no—
51C53×#541—24no—
52C2×C4⋊Q8×C53C2211yescharacteristic
53C2×#126×C53—21no—
54C2×#126×C53—21no—
55C2×#125×C53—21no—
56C2×#125×C53—21no—
57C2×#125×C53C2211yescharacteristic
58C2×C22⋊Q8×C53C2211yescharacteristic
59C2×C22⋊Q8×C53C2211yescharacteristic
60C2×C4×Q8×C53C2211yescharacteristic
61C2×C4×Q8×C53C2211yescharacteristic
62C2×#117×C53C2211yescharacteristic
63C22×D212C2311yescharacteristic
64C22×C22⋊D53—21no—
65C22×C4×D53—21no—
66C2×#11719924—22no—
67C2×#11719924—22no—
68C2×#11719924—22no—
69C2×#11719924—22no—
70C2×#11719924—22no—
71C2×#11719924—22no—
72C22×#88322C2311yescharacteristic
73C22×#88322C2311yescharacteristic
74C22×#88322C2311yescharacteristic
75C22×#88322C2311yescharacteristic
76#13133191—22no—
77#13133191—22no—
78C4×D212—22no—
79C4×D212—22no—
80C2×C4⋊Dic53C2311yescharacteristic
81C2×C4⋊Dic53C2311yescharacteristic
82C2×C4⋊Dic53C2311yescharacteristic
83C2×#11719919—21no—
84C2×C22⋊Dic53—21no—
85C2×#11719921—21no—
86C2×#11719921—21no—
87C2×#11719921—21no—
88C2×#11719921—21no—
89C2×C4×Dic53—21no—
90#13133150—22no—
91#13133148—22no—
92#13133141—22no—
93#13133141—22no—
94#13133141—22no—
95#13133141—22no—
96#13133141—22no—
97#13133141—22no—
98#13133137—22no—
99#13133137—22no—
100C22⋊#88322—22no—
101C22⋊#88322—22no—
102#13133128—22no—
103C4×#88322—22no—
104#13133124—21no—
105#13133124—21no—
106#13133124—21no—
107C22×Q8×C53C2311yescharacteristic
108C22×Q8×C53C2311yescharacteristic
109C23×C4×C53C2311yescharacteristic
110C4⋊Q8×C53—22no—
111C4⋊Q8×C53—22no—
112#126×C53—28no—
113#126×C53—28no—
114#125×C53—28no—
115#125×C53—28no—
116#125×C53—22no—
117#125×C53—22no—
118C22⋊Q8×C53—22no—
119C22⋊Q8×C53—22no—
120C22⋊Q8×C53—22no—
121C22⋊Q8×C53—22no—
122C4×Q8×C53—22no—
123C4×Q8×C53—22no—
124C4×Q8×C53D414yescomplemented
125C4×Q8×C53D414yescomplemented
126#117×C53—22no—
127#117×C53—22no—
128C2×C4⋊C4×C53—21no—
129C2×C4⋊C4×C53—21no—
130C2×C4⋊C4×C53—21no—
131C2×C4⋊C4×C53—21no—
132C2×C4⋊C4×C53—21no—
133C2×C4⋊C4×C53—21no—
134C2×C4⋊C4×C53—21no—
135C2×C4⋊C4×C53—21no—
136C2×C4⋊C4×C53D411yescharacteristic
137C2×C4⋊C4×C53D411yescharacteristic
138C2×C4⋊C4×C53C2311yescharacteristic
139C2×C4⋊C4×C53C2311yescharacteristic
140C2×C22⋊C4×C53—21no—
141C2×C22⋊C4×C53—21no—
142C2×C22⋊C4×C53D411yescharacteristic
143C2×C22⋊C4×C53D411yescharacteristic
144C2×C42×C53—21no—
145C2×C42×C53—21no—
146C2×C42×C53C2311yescharacteristic
147C2×C42×C53C2311yescharacteristic
148C24×C53C2×D411yescharacteristic
149C23×D53—21no—
150C2×Q8×C53—21no—
151C2×Q8×C53—21no—
152C2×Q8×C53—21no—
153C2×Q8×C53—21no—
154C2×Q8×C53—21no—
155C2×Q8×C53—21no—
156C2×Q8×C53—21no—
157C2×Q8×C53—21no—
158C2×Q8×C53—21no—
159C2×Q8×C53—21no—
160C2×Q8×C53C2×D412yes—
161C2×Q8×C53C2×D412yes—
162C22×C4×C53—21no—
163C22×C4×C53—21no—
164C22×C4×C53—21no—
165C22×C4×C53—21no—
166C22×C4×C53—21no—
167C22×C4×C53—21no—
168C22×C4×C53—21no—
169C22×C4×C53—21no—
170C22×C4×C53—21no—
171C22×C4×C53—21no—
172C22×C4×C53C2×D411yescharacteristic
173C22×C4×C53C2×D411yescharacteristic
174C22×C4×C53C2×D411yescharacteristic
175C22×C4×C53C2×D411yescharacteristic
176C22×C4×C53C2×D411yescharacteristic
177C22×C4×C53C2411yescharacteristic
178C2×C22⋊D53—24no—
179C2×C22⋊D53—81no—
180C2×C22⋊D53—81no—
181C22×Dic53—21no—
182C22×Dic53—21no—
183C22×Dic53—21no—
184C2×D212—21no—
185C2×D212—21no—
186C2×D212—21no—
187C2×D212—21no—
188C2×D212—21no—
189C2×D212#4112yes—
190C2×C4×D53—42no—
191C2×C4×D53—81no—
192C2×C4×D53—81no—
193C4⋊C4×C53—24no—
194C4⋊C4×C53—24no—
195C4⋊C4×C53—24no—
196C4⋊C4×C53—24no—
197C4⋊C4×C53—24no—
198C4⋊C4×C53—24no—
199C4⋊C4×C53—24no—
200C4⋊C4×C53—24no—
201C4⋊C4×C53—22no—
202C4⋊C4×C53—22no—
203C4⋊C4×C53—21no—
204C4⋊C4×C53—21no—
205C4⋊C4×C53C2×D412yes—
206C4⋊C4×C53C2×D412yes—
207C22⋊C4×C53—24no—
208C22⋊C4×C53—24no—
209C22⋊C4×C53—22no—
210C22⋊C4×C53—22no—
211C42×C53—24no—
212C42×C53—24no—
213C42×C53—21no—
214C42×C53—21no—
215C42×C53C2×D412yes—
216C42×C53C2×D412yes—
217C22⋊Dic53—81no—
218#11719924—28no—
219#11719924—28no—
220#11719921—24no—
221#11719921—42no—
222#11719921—81no—
223#11719921—81no—
224C4⋊Dic53—21no—
225C4⋊Dic53—21no—
226C4⋊Dic53—21no—
227C4⋊Dic53—21no—
228C4⋊Dic53—21no—
229C4⋊Dic53#4112yes—
230#11719919—81no—
231C4×Dic53—81no—
232C2×#88322—21no—
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#4112yes—
243C2×#88322#4112yes—
244C23×C53—21no—
245C23×C53—21no—
246C23×C53—21no—
247C23×C53—21no—
248C23×C53—21no—
249C23×C53—21no—
250C23×C53—21no—
251C23×C53C22×D411yescharacteristic
252C22×D53—22no—
253C22×D53—41no—
254C22×D53—41no—
255C22×D53—41no—
256C22×D53—41no—
257C22×D53—41no—
258C22×D53—41no—
259Q8×C53—22no—
260Q8×C53—22no—
261Q8×C53—22no—
262Q8×C53—22no—
263Q8×C53—41no—
264Q8×C53—41no—
265Q8×C53—41no—
266Q8×C53—41no—
267C2×C4×C53—21no—
268C2×C4×C53—21no—
269C2×C4×C53—21no—
270C2×C4×C53—21no—
271C2×C4×C53—21no—
272C2×C4×C53—22no—
273C2×C4×C53—22no—
274C2×C4×C53—22no—
275C2×C4×C53—22no—
276C2×C4×C53—21no—
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—41no—
295C2×C4×C53—41no—
296C2×C4×C53#12012yes—
297C2×C4×C53#12012yes—
298C2×C4×C53C22×D411yescharacteristic
299C2×C4×C53C22×D411yescharacteristic
300C2×C4×C53C2×#4111yescharacteristic
301C2×C4×C53C2×#4111yescharacteristic
302C2×C4×C53C2×#4111yescharacteristic
303C2×C4×C53C2×#4111yescharacteristic
304C22⋊D53—84no—
305C2×Dic53—22no—
306C2×Dic53—41no—
307C2×Dic53—41no—
308C2×Dic53—41no—
309C2×Dic53—41no—
310C2×Dic53—41no—
311C2×Dic53—41no—
312C2×Dic53—41no—
313C2×Dic53—41no—
314D212—22no—
315D212—22no—
316D212—41no—
317D212—41no—
318C4×D53—84no—
319#88322—22no—
320#88322—22no—
321#88322—41no—
322#88322—41no—
323#23584—531nomaximal, Sylow
324C22×C53—41no—
325C22×C53—41no—
326C22×C53—41no—
327C22×C53—41no—
328C22×C53—41no—
329C22×C53—41no—
330C22×C53—41no—
331C22×C53C2×#12011yescharacteristic
332C22×C53#52511yescharacteristic
333C22×C53#53211yescharacteristic
334C22×C53#57711yescharacteristic
335C22×C53#57711yescharacteristic
336C22×C53#57711yescharacteristic
337C22×C53#57811yescharacteristic
338C2×D53—42no—
339C2×D53—42no—
340C2×D53—42no—
341C2×D53—81no—
342C2×D53—81no—
343C2×D53—81no—
344C2×D53—81no—
345C4×C53—22no—
346C4×C53—22no—
347C4×C53—41no—
348C4×C53—42no—
349C4×C53—42no—
350C4×C53—41no—
351C4×C53—42no—
352C4×C53—41no—
353C4×C53—42no—
354C4×C53#52511yescharacteristic
355C4×C53#52511yescharacteristic
356C4×C53#53211yescharacteristic
357C4×C53#53211yescharacteristic
358Dic53—42no—
359Dic53—81no—
360Dic53—81no—
361C2×#541D5311yescharacteristic, complemented
362C2×#440—531no—
363C2×C4×SD16—531no—
364#2324—531no—
365#2059—531no—
366#2043—531no—
367#2036—531no—
368#2035—531no—
369#2025—531no—
370#2013—531no—
371#2000—531no—
372#2000—531no—
373#1763—531no—
374C4×#103—531no—
375#1750—531no—
376C2×C53—81no—
377C2×C53#238811yescharacteristic
378C2×C53#301011yescharacteristic
379C2×C53#301311yescharacteristic
380C2×C53#312011yescharacteristic
381C2×C53#312311yescharacteristic
382C2×C53#317411yescharacteristic
383C2×C53#317811yescharacteristic
384D53—82no—
385C22×SD16—531no—
386C22×SD16—531no—
387#541—24no—
388#541—24no—
389C2×C4⋊Q8C2×D5311yescharacteristic
390C2×#126—21no—
391C2×#126—21no—
392C2×#125—21no—
393C2×#125—21no—
394C2×#125C2×D5311yescharacteristic
395C2×C22⋊Q8C2×D5311yescharacteristic
396C2×C22⋊Q8C2×D5311yescharacteristic
397C2×#121—531no—
398C2×C4×Q8C2×D5311yescharacteristic
399C2×C4×Q8C2×D5311yescharacteristic
400C2×C4×D4—531no—
401C2×#117C2×D5311yescharacteristic
402#440—1064no—
403C4×SD16—1064no—
404C2×#107—531no—
405C2×#106—531no—
406C2×#103—531no—
407C2×#103—531no—
408C2×#103—531no—
409C2×#103—531no—
410C2×#103—531no—
411C2×#103—531no—
412C2×#102—531no—
413C2×#102—531no—
414C2×C22⋊C8—531no—
415C2×C22⋊C8—531no—
416C2×#97—531no—
417C2×C4×C8—531no—
418#390—531no—
419#390—1061no—
420#389—531no—
421#388—1061no—
422#386—1061no—
423#385—1061no—
424#380—531no—
425C4×C4⋊C4—531no—
426#340—531no—
427#340—531no—
428#340—531no—
429#340—531no—
430#336—531no—
431#336—531no—
432C53#2358411yescharacteristic, complemented, Sylow
433C22×Q8C22×D5311yescharacteristic
434C22×Q8C22×D5311yescharacteristic
435C22×D4—531no—
436C22×D4—1061no—
437C23×C4—1061no—
438C23×C4C22×D5311yescharacteristic
439C2×SD16—1062no—
440C2×SD16—1062no—
441C2×SD16—1062no—
442C2×SD16—1062no—
443C2×SD16—1062no—
444C2×SD16—1062no—
445C22×C8—531no—
446C22×C8—531no—
447C22×C8—531no—
448C22×C8—531no—
449C4⋊Q8—22no—
450C4⋊Q8—22no—
451#126—28no—
452#126—28no—
453#125—28no—
454#125—28no—
455#125—22no—
456#125—22no—
457C22⋊Q8—22no—
458C22⋊Q8—22no—
459C22⋊Q8—22no—
460C22⋊Q8—22no—
461#121—1062no—
462#121—1062no—
463C4×Q8—22no—
464C4×Q8—22no—
465C4×Q8C22⋊D5314yescomplemented
466C4×Q8C22⋊D5314yescomplemented
467C4×D4—1062no—
468C4×D4—1062no—
469#117—22no—
470#117—22no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—531no—
480C2×C4⋊C4—531no—
481C2×C4⋊C4—531no—
482C2×C4⋊C4—1061no—
483C2×C4⋊C4C22⋊D5311yescharacteristic
484C2×C4⋊C4C22⋊D5311yescharacteristic
485C2×C4⋊C4C22×D5311yescharacteristic
486C2×C4⋊C4C22×D5311yescharacteristic
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—1061no—
490C2×C22⋊C4—1061no—
491C2×C22⋊C4—1061no—
492C2×C22⋊C4—1061no—
493C2×C22⋊C4—1061no—
494C2×C22⋊C4C22⋊D5311yescharacteristic
495C2×C22⋊C4C22⋊D5311yescharacteristic
496C2×C42—21no—
497C2×C42—21no—
498C2×C42—1061no—
499C2×C42C22×D5311yescharacteristic
500C2×C42C22×D5311yescharacteristic
501#107—1062no—
502#106—1062no—
503#103—1062no—
504#103—1062no—
505#103—1062no—
506#103—1062no—
507#103—1062no—
508#103—1062no—
509#102—1062no—
510#102—1062no—
511C22⋊C8—1062no—
512C22⋊C8—1062no—
513#97—1062no—
514C4×C8—1062no—
515#95—1061no—
516#95—1061no—
517#95—1061no—
518C24—1061no—
519C24C2×C22⋊D5311yescharacteristic
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8C2×C22⋊D5312yes—
531C2×Q8C2×C22⋊D5312yes—
532C2×D4—532no—
533C2×D4—1064no—
534C2×D4—1061no—
535C2×D4—1061no—
536C2×D4—1061no—
537C2×D4—1061no—
538C2×D4—1061no—
539C2×D4—4241no—
540C2×D4—4241no—
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—21no—
551C22×C4—1061no—
552C22×C4—1061no—
553C22×C4—1061no—
554C22×C4—4241no—
555C22×C4—4241no—
556C22×C4—2122no—
557C22×C4C2×C22⋊D5311yescharacteristic
558C22×C4C2×C22⋊D5311yescharacteristic
559C22×C4C2×C22⋊D5311yescharacteristic
560C22×C4C2×C22⋊D5311yescharacteristic
561C22×C4C2×C22⋊D5311yescharacteristic
562C22×C4C23×D5311yescharacteristic
563SD16—1068no—
564SD16—1068no—
565C2×C8—532no—
566C2×C8—532no—
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—
576C2×C8—1061no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—24no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—532no—
590C4⋊C4—1061no—
591C4⋊C4—1061no—
592C4⋊C4—1061no—
593C4⋊C4—1061no—
594C4⋊C4—1061no—
595C4⋊C4—4241no—
596C4⋊C4C2×C22⋊D5312yes—
597C4⋊C4C2×C22⋊D5312yes—
598C22⋊C4—24no—
599C22⋊C4—24no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—1064no—
603C22⋊C4—4241no—
604C22⋊C4—4241no—
605C22⋊C4—4241no—
606C22⋊C4—2122no—
607C42—24no—
608C42—24no—
609C42—21no—
610C42—21no—
611C42—4241no—
612C42C2×C22⋊D5312yes—
613C42C2×C22⋊D5312yes—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—1062no—
622C23—2121no—
623C23—2121no—
624C23—2121no—
625C23—2121no—
626C23—2121no—
627C23—2121no—
628C23C22×C22⋊D5311yescharacteristic
629Q8—22no—
630Q8—22no—
631Q8—22no—
632Q8—22no—
633Q8—41no—
634Q8—41no—
635Q8—41no—
636Q8—41no—
637D4—1062no—
638D4—1062no—
639D4—4244no—
640D4—2121no—
641D4—2121no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
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—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—1062no—
672C2×C4—4244no—
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×C4#1313318612yes—
683C2×C4C22×C22⋊D5311yescharacteristic
684C2×C4C22×C22⋊D5311yescharacteristic
685C2×C4#41×D5311yescharacteristic
686C2×C4#41×D5311yescharacteristic
687C2×C4#41×D5311yescharacteristic
688C2×C4#41×D5311yescharacteristic
689C8—1062no—
690C8—1062no—
691C8—2121no—
692C8—2121no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—4241no—
701C22—4241no—
702C22—4241no—
703C22—4241no—
704C22—2122no—
705C22—2122no—
706C22—2122no—
707C22C2×#1313318611yescharacteristic
708C22#1681113011yescharacteristic
709C22#1681116911yescharacteristic
710C22#1681143111yescharacteristic
711C22#1681143111yescharacteristic
712C22#1681143111yescharacteristic
713C22#1681143811yescharacteristic
714C4—22no—
715C4—22no—
716C4—41no—
717C4—42no—
718C4—41no—
719C4—42no—
720C4—41no—
721C4—42no—
722C4—42no—
723C4—4241no—
724C4—4241no—
725C4—2122no—
726C4#1681113011yescharacteristic
727C4#1681113011yescharacteristic
728C4#1681116911yescharacteristic
729C4#1681116911yescharacteristic
730C2—81no—
731C2—4242no—
732C2#2027792811yescharacteristic
733C2#2028400111yescharacteristic
734C2#2028403011yescharacteristic
735C2#2028492311yescharacteristic
736C2#2028496211yescharacteristic
737C2#2028534411yescharacteristic
738C2#2028538511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
FittingC2×C53×#541C2
socleC23×C53C22×D4
prime radicalC2×#13133191C22
hypercenterC2×#541D53
hypocenterC53#23584
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
1. C2×#16810721C2semidirect
2. C2×C4×#11719924C2semidirect
4. #20276050C2semidirect
5. #20275958C2semidirect
6. #20275915C2semidirect
7. #20275908C2semidirect
8. #20275858C2semidirect
9. #20275798C2semidirect
12. #20274545C2semidirect
13. C4×#13133141C2semidirect
14. #20274481C2semidirect
15. C2×C53×#541C2semidirect
124. C4×Q8×C53D4semidirect
125. C4×Q8×C53D4semidirect
361. C2×#541D53semidirect
432. C53#23584semidirect
465. C4×Q8C22⋊D53semidirect
466. C4×Q8C22⋊D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168107212
C2×C4×#117199242
#202774082
#202760502
#202759582
#202759152
#202759082
#202758582
#202757982
#202757162
#202745452
C4×#131331412
#202744812
C2×C53×#5412
#2358453