Finite Group Databasebeta

← #27438716

Subgroups — #27438716

Order 13568.

1092 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811022C211yesmaximal, characteristic, complemented
2C2×#16810923C211yesmaximal, characteristic, complemented
3#20279881C211yesmaximal, characteristic, complemented
4#20275901C211yesmaximal, characteristic, complemented
5#20275901C211yesmaximal, characteristic, complemented
6#20275894C211yesmaximal, characteristic, complemented
7#20275894C211yesmaximal, characteristic, complemented
8#20275673C211yesmaximal, characteristic, complemented
9#20275510C211yesmaximal, characteristic, complemented
10#20274914C211yesmaximal, characteristic, complemented
11#20274914C211yesmaximal, characteristic, complemented
12#20274908C211yesmaximal, characteristic, complemented
13#20274903C211yesmaximal, characteristic, complemented
14C4×#13133138C211yesmaximal, characteristic, complemented
15C2×C53×#553C211yesmaximal, characteristic
16C2×#13133209C2211yescharacteristic
17#16811022—24no—
18#16810923—24no—
19C2×#13133150C2211yescharacteristic
20C2×#13133150C2211yescharacteristic
21C2×#13133150C2211yescharacteristic
22C2×#13133148C2211yescharacteristic
23C2×#13133148C2211yescharacteristic
24C2×#13133148C2211yescharacteristic
25C2×C4⋊#88322C2211yescharacteristic
26C2×#13133138C2211yescharacteristic
27C2×#13133138C2211yescharacteristic
28C2×#13133138C2211yescharacteristic
29C2×#13133138C2211yescharacteristic
30C2×C22⋊#88322C2211yescharacteristic
31C2×C22⋊#88322C2211yescharacteristic
32C2×C22⋊#88322C2211yescharacteristic
33C2×C22⋊#88322C2211yescharacteristic
34C2×C4×#88322C2211yescharacteristic
35#16810561—21no—
36#16810537—21no—
37#16810517—21no—
38#16810517—21no—
39#16810483C2211yescharacteristic
40#16810483C2211yescharacteristic
41#16810483C2211yescharacteristic
42#16810483C2211yescharacteristic
43C4×C4⋊Dic53C2211yescharacteristic
44#16810385C2211yescharacteristic
45#16810385C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810385C2211yescharacteristic
49#16810385C2211yescharacteristic
50C53×#553—24no—
51C53×#553—24no—
52C2×#126×C53—21no—
53C2×#125×C53C2211yescharacteristic
54C2×#123×C53—21no—
55C2×#121×C53—21no—
56C2×#121×C53C2211yescharacteristic
57C2×#121×C53C2211yescharacteristic
58C2×C4×D4×C53—21no—
59C2×C4×D4×C53C2211yescharacteristic
60C2×C4×D4×C53C2211yescharacteristic
61C2×#117×C53C2211yescharacteristic
62C22×C4⋊C4×C53C2211yescharacteristic
63C22×#88322C2311yescharacteristic
64C22×#88322C2311yescharacteristic
65C22×#88322C2311yescharacteristic
66C22×#88322C2311yescharacteristic
67#13133209—22no—
68#13133209—22no—
69C2×C4⋊Dic53C2311yescharacteristic
70C2×C4⋊Dic53C2311yescharacteristic
71C2×C4⋊Dic53C2311yescharacteristic
72C2×C4⋊Dic53C2311yescharacteristic
73C2×#11719919—21no—
74C2×#11719919—21no—
75C2×C22⋊Dic53—21no—
76C2×C22⋊Dic53—21no—
77C2×C22⋊Dic53—21no—
78C2×C22⋊Dic53—21no—
79C2×C4×Dic53—21no—
80#13133150—22no—
81#13133150—22no—
82#13133150—22no—
83#13133148—22no—
84#13133148—22no—
85#13133148—22no—
86C4⋊#88322—22no—
87#13133138—22no—
88#13133138—22no—
89#13133138—22no—
90#13133138—22no—
91C22⋊#88322—22no—
92C22⋊#88322—22no—
93C22⋊#88322—22no—
94C22⋊#88322—22no—
95C4×#88322—22no—
96#13133124—21no—
97#13133124—21no—
98#13133124—21no—
99#13133124—21no—
100#13133124—21no—
101C22×D4×C53—21no—
102C22×D4×C53—21no—
103C22×D4×C53D411yescharacteristic
104C22×D4×C53C2311yescharacteristic
105C23×C4×C53—21no—
106C23×C4×C53—21no—
107C23×C4×C53C2311yescharacteristic
108C23×C4×C53C2311yescharacteristic
109#126×C53—28no—
110#125×C53—22no—
111#125×C53D414yes—
112#123×C53—28no—
113#121×C53—28no—
114#121×C53—22no—
115#121×C53—22no—
116#121×C53—22no—
117#121×C53—22no—
118C4×D4×C53—28no—
119C4×D4×C53—22no—
120C4×D4×C53—22no—
121C4×D4×C53—22no—
122C4×D4×C53D414yes—
123#117×C53—22no—
124#117×C53—22no—
125C2×C4⋊C4×C53—22no—
126C2×C4⋊C4×C53—22no—
127C2×C4⋊C4×C53—21no—
128C2×C4⋊C4×C53—21no—
129C2×C4⋊C4×C53—21no—
130C2×C4⋊C4×C53D411yescharacteristic
131C2×C4⋊C4×C53C2311yescharacteristic
132C2×C4⋊C4×C53C2311yescharacteristic
133C2×C4⋊C4×C53C2311yescharacteristic
134C2×C22⋊C4×C53—21no—
135C2×C22⋊C4×C53—21no—
136C2×C22⋊C4×C53—21no—
137C2×C22⋊C4×C53—21no—
138C2×C22⋊C4×C53D411yescharacteristic
139C2×C22⋊C4×C53D411yescharacteristic
140C2×C42×C53—21no—
141C2×C42×C53C2311yescharacteristic
142C24×C53—21no—
143C24×C53C2×D411yescharacteristic
144C24×C53C2×D411yescharacteristic
145C2×D4×C53—24no—
146C2×D4×C53—22no—
147C2×D4×C53—24no—
148C2×D4×C53—22no—
149C2×D4×C53—21no—
150C2×D4×C53—21no—
151C2×D4×C53—21no—
152C2×D4×C53—21no—
153C2×D4×C53—21no—
154C2×D4×C53—41no—
155C2×D4×C53—42no—
156C2×D4×C53—42no—
157C2×D4×C53—81no—
158C2×D4×C53—81no—
159C2×D4×C53C2×D412yes—
160C22×C4×C53—21no—
161C22×C4×C53—21no—
162C22×C4×C53—21no—
163C22×C4×C53—24no—
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×C53—21no—
173C22×C4×C53—21no—
174C22×C4×C53—21no—
175C22×C4×C53—21no—
176C22×C4×C53—24no—
177C22×C4×C53—81no—
178C22×C4×C53—81no—
179C22×C4×C53—81no—
180C22×C4×C53—81no—
181C22×C4×C53C2×D411yescharacteristic
182C22×C4×C53C2×D411yescharacteristic
183C22×C4×C53C2×D411yescharacteristic
184C22×C4×C53C2×D411yescharacteristic
185C22×C4×C53C2411yescharacteristic
186C22×Dic53—21no—
187C22×Dic53—21no—
188C22×Dic53—21no—
189C22×Dic53—21no—
190C4⋊C4×C53—24no—
191C4⋊C4×C53—24no—
192C4⋊C4×C53—24no—
193C4⋊C4×C53—22no—
194C4⋊C4×C53—21no—
195C4⋊C4×C53—21no—
196C4⋊C4×C53—21no—
197C4⋊C4×C53C2×D412yes—
198C4⋊C4×C53C2×D412yes—
199C4⋊C4×C53C2×D412yes—
200C22⋊C4×C53—24no—
201C22⋊C4×C53—24no—
202C22⋊C4×C53—24no—
203C22⋊C4×C53—24no—
204C22⋊C4×C53—22no—
205C22⋊C4×C53—22no—
206C42×C53—24no—
207C42×C53C2×D412yes—
208C42×C53C2×D412yes—
209C22⋊Dic53—42no—
210C22⋊Dic53—42no—
211C22⋊Dic53—81no—
212C22⋊Dic53—81no—
213C4⋊Dic53—21no—
214C4⋊Dic53—21no—
215C4⋊Dic53—21no—
216C4⋊Dic53—21no—
217C4⋊Dic53—21no—
218C4⋊Dic53—21no—
219C4⋊Dic53—21no—
220C4⋊Dic53—21no—
221#11719919—42no—
222#11719919—42no—
223C4×Dic53—81no—
224C2×#88322—21no—
225C2×#88322—21no—
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#4112yes—
235C2×#88322#4112yes—
236C23×C53—21no—
237C23×C53—21no—
238C23×C53—21no—
239C23×C53—21no—
240C23×C53—21no—
241C23×C53—21no—
242C23×C53—21no—
243C23×C53—22no—
244C23×C53—21no—
245C23×C53—21no—
246C23×C53—21no—
247C23×C53—21no—
248C23×C53—21no—
249C23×C53—21no—
250C23×C53—41no—
251C23×C53—41no—
252C23×C53—41no—
253C23×C53—41no—
254C23×C53—41no—
255C23×C53—41no—
256C23×C53#13512yes—
257C23×C53C22×D411yescharacteristic
258D4×C53—22no—
259D4×C53—22no—
260D4×C53—44no—
261D4×C53—48no—
262D4×C53—41no—
263D4×C53—41no—
264D4×C53—84no—
265C2×C4×C53—21no—
266C2×C4×C53—21no—
267C2×C4×C53—21no—
268C2×C4×C53—21no—
269C2×C4×C53—22no—
270C2×C4×C53—22no—
271C2×C4×C53—21no—
272C2×C4×C53—21no—
273C2×C4×C53—22no—
274C2×C4×C53—21no—
275C2×C4×C53—21no—
276C2×C4×C53—21no—
277C2×C4×C53—21no—
278C2×C4×C53—41no—
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—41no—
291C2×C4×C53—41no—
292C2×C4×C53—84no—
293C2×C4×C53—84no—
294C2×C4×C53#12012yes—
295C2×C4×C53#12012yes—
296C2×C4×C53C22×D411yescharacteristic
297C2×C4×C53C22×D411yescharacteristic
298C2×C4×C53C2×#4111yescharacteristic
299C2×C4×C53C2×#4111yescharacteristic
300C2×C4×C532−1+411yescharacteristic
301C2×C4×C532−1+411yescharacteristic
302C2×Dic53—41no—
303C2×Dic53—41no—
304C2×Dic53—41no—
305C2×Dic53—41no—
306C2×Dic53—41no—
307C2×Dic53—41no—
308C2×Dic53—41no—
309C2×Dic53—41no—
310C2×Dic53—41no—
311C2×Dic53—41no—
312C2×Dic53—41no—
313C2×Dic53—41no—
314#88322—22no—
315#88322—22no—
316#88322—41no—
317#88322—41no—
318#25707—531nomaximal, Sylow
319C22×C53—22no—
320C22×C53—22no—
321C22×C53—22no—
322C22×C53—41no—
323C22×C53—41no—
324C22×C53—41no—
325C22×C53—41no—
326C22×C53—41no—
327C22×C53—41no—
328C22×C53—41no—
329C22×C53—41no—
330C22×C53—41no—
331C22×C53—42no—
332C22×C53—41no—
333C22×C53—42no—
334C22×C53—42no—
335C22×C53—41no—
336C22×C53—81no—
337C22×C53—81no—
338C22×C53—81no—
339C22×C53—81no—
340C22×C53C2×#12011yescharacteristic
341C22×C53#54711yescharacteristic
342C22×C53#54711yescharacteristic
343C22×C53C2×#13511yescharacteristic
344C22×C53#57511yescharacteristic
345C22×C53#57611yescharacteristic
346C22×C53#57711yescharacteristic
347C4×C53—22no—
348C4×C53—22no—
349C4×C53—41no—
350C4×C53—41no—
351C4×C53—42no—
352C4×C53—42no—
353C4×C53—42no—
354C4×C53#53211yescharacteristic
355C4×C53#53611yescharacteristic
356C4×C53#54811yescharacteristic
357C4×C53#54811yescharacteristic
358Dic53—81no—
359Dic53—81no—
360Dic53—81no—
361Dic53—81no—
362C2×#553D5311yescharacteristic
363C2×#499—531no—
364C2×#478—531no—
365#2562—531no—
366#2034—531no—
367#2034—531no—
368#2033—531no—
369#2033—531no—
370#1989—531no—
371#1954—531no—
372#1854—531no—
373#1854—531no—
374#1853—531no—
375#1852—531no—
376C4×#102—531no—
377C2×C53—42no—
378C2×C53—81no—
379C2×C53—82no—
380C2×C53#243211yescharacteristic
381C2×C53#300211yescharacteristic
382C2×C53#301211yescharacteristic
383C2×C53#333711yescharacteristic
384C2×C53#333911yescharacteristic
385C2×C53#335111yescharacteristic
386C2×C53#335511yescharacteristic
387#553—24no—
388#553—24no—
389C2×#126—21no—
390C2×#125—531no—
391C2×#125C2×D5311yescharacteristic
392C2×#123—21no—
393C2×#121—21no—
394C2×#121C2×D5311yescharacteristic
395C2×#121C2×D5311yescharacteristic
396C2×C4×D4—21no—
397C2×C4×D4C2×D5311yescharacteristic
398C2×C4×D4C2×D5311yescharacteristic
399C2×#117C2×D5311yescharacteristic
400C22×C4⋊C4C2×D5311yescharacteristic
401#499—1064no—
402#478—1064no—
403C2×#107—531no—
404C2×#107—531no—
405C2×#107—531no—
406C2×#106—531no—
407C2×#106—531no—
408C2×#106—531no—
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×C22⋊C8—531no—
417C2×C22⋊C8—531no—
418C2×C4×C8—531no—
419#400—1061no—
420#394—1061no—
421#388—1061no—
422#388—1061no—
423#380—531no—
424#380—531no—
425#380—531no—
426#380—531no—
427C4×C4⋊C4—531no—
428#340—531no—
429#340—531no—
430#340—531no—
431#340—531no—
432#340—531no—
433#340—531no—
434C53#2570711yescharacteristic, complemented, Sylow
435C22×D4—21no—
436C22×D4—21no—
437C22×D4C22⋊D5311yescharacteristic
438C22×D4C22×D5311yescharacteristic
439C23×C4—21no—
440C23×C4—21no—
441C23×C4C22×D5311yescharacteristic
442C23×C4C22×D5311yescharacteristic
443C22×C8—531no—
444C22×C8—531no—
445C22×C8—531no—
446C22×C8—531no—
447#126—28no—
448#125—22no—
449#125—1062no—
450#125—1062no—
451#125C22⋊D5314yes—
452#123—28no—
453#121—28no—
454#121—22no—
455#121—22no—
456#121—22no—
457#121—22no—
458C4×D4—28no—
459C4×D4—22no—
460C4×D4—22no—
461C4×D4—22no—
462C4×D4C22⋊D5314yes—
463#117—22no—
464#117—22no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—531no—
471C2×C4⋊C4—531no—
472C2×C4⋊C4—531no—
473C2×C4⋊C4—531no—
474C2×C4⋊C4—1061no—
475C2×C4⋊C4—1061no—
476C2×C4⋊C4C22⋊D5311yescharacteristic
477C2×C4⋊C4C22×D5311yescharacteristic
478C2×C4⋊C4C22×D5311yescharacteristic
479C2×C4⋊C4C22×D5311yescharacteristic
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—1061no—
485C2×C22⋊C4—1061no—
486C2×C22⋊C4—1061no—
487C2×C22⋊C4—1061no—
488C2×C22⋊C4C22⋊D5311yescharacteristic
489C2×C22⋊C4C22⋊D5311yescharacteristic
490C2×C42—21no—
491C2×C42—1061no—
492C2×C42C22×D5311yescharacteristic
493#107—1062no—
494#107—1062no—
495#107—1062no—
496#106—1062no—
497#106—1062no—
498#106—1062no—
499C4⋊C8—1062no—
500#102—1062no—
501#102—1062no—
502#102—1062no—
503#102—1062no—
504C22⋊C8—1062no—
505C22⋊C8—1062no—
506C22⋊C8—1062no—
507C22⋊C8—1062no—
508C4×C8—1062no—
509#95—1061no—
510#95—1061no—
511#95—1061no—
512#95—1061no—
513#95—1061no—
514C24—21no—
515C24C2×C22⋊D5311yescharacteristic
516C24C2×C22⋊D5311yescharacteristic
517C2×D4—24no—
518C2×D4—22no—
519C2×D4—24no—
520C2×D4—22no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—41no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4—81no—
530C2×D4—81no—
531C2×D4C2×C22⋊D5312yes—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—24no—
536C22×C4—21no—
537C22×C4—21no—
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—24no—
549C22×C4—81no—
550C22×C4—81no—
551C22×C4—81no—
552C22×C4—81no—
553C22×C4—1061no—
554C22×C4—1061no—
555C22×C4—1061no—
556C22×C4—1061no—
557C22×C4C2×C22⋊D5311yescharacteristic
558C22×C4C2×C22⋊D5311yescharacteristic
559C22×C4C2×C22⋊D5311yescharacteristic
560C22×C4C2×C22⋊D5311yescharacteristic
561C22×C4C23×D5311yescharacteristic
562C2×C8—532no—
563C2×C8—532no—
564C2×C8—1061no—
565C2×C8—1061no—
566C2×C8—1061no—
567C2×C8—1061no—
568C2×C8—1061no—
569C2×C8—1061no—
570C2×C8—1061no—
571C2×C8—1061no—
572C2×C8—1061no—
573C2×C8—1061no—
574C4⋊C4—24no—
575C4⋊C4—24no—
576C4⋊C4—24no—
577C4⋊C4—22no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—1061no—
582C4⋊C4—1061no—
583C4⋊C4—1061no—
584C4⋊C4—1061no—
585C4⋊C4—1061no—
586C4⋊C4—1061no—
587C4⋊C4—1061no—
588C4⋊C4—1061no—
589C4⋊C4—2122no—
590C4⋊C4—2122no—
591C4⋊C4C2×C22⋊D5312yes—
592C4⋊C4C2×C22⋊D5312yes—
593C4⋊C4C2×C22⋊D5312yes—
594C22⋊C4—24no—
595C22⋊C4—24no—
596C22⋊C4—24no—
597C22⋊C4—24no—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—4241no—
601C22⋊C4—4241no—
602C22⋊C4—2122no—
603C22⋊C4—2122no—
604C42—24no—
605C42—4241no—
606C42C2×C22⋊D5312yes—
607C42C2×C22⋊D5312yes—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—22no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23#1313323712yes—
629C23C22×C22⋊D5311yescharacteristic
630D4—22no—
631D4—22no—
632D4—44no—
633D4—48no—
634D4—41no—
635D4—41no—
636D4—84no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—84no—
665C2×C4—84no—
666C2×C4—2121no—
667C2×C4—2121no—
668C2×C4—2121no—
669C2×C4—2121no—
670C2×C4—2121no—
671C2×C4—2121no—
672C2×C4—2121no—
673C2×C4—2121no—
674C2×C4—2121no—
675C2×C4—2121no—
676C2×C4—2121no—
677C2×C4—2121no—
678C2×C4#1313318612yes—
679C2×C4#1313318612yes—
680C2×C4C22×C22⋊D5311yescharacteristic
681C2×C4C22×C22⋊D5311yescharacteristic
682C2×C4#41×D5311yescharacteristic
683C2×C4#41×D5311yescharacteristic
684C2×C4#1313326411yescharacteristic
685C2×C4#1313326411yescharacteristic
686C8—1062no—
687C8—1062no—
688C8—2121no—
689C8—2121no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—42no—
699C22—41no—
700C22—41no—
701C22—42no—
702C22—41no—
703C22—41no—
704C22—42no—
705C22—41no—
706C22—41no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22C2×#1313318611yescharacteristic
712C22#1681127211yescharacteristic
713C22#1681127211yescharacteristic
714C22C2×#1313323711yescharacteristic
715C22#1681142111yescharacteristic
716C22#1681142611yescharacteristic
717C22#1681143411yescharacteristic
718C4—22no—
719C4—22no—
720C4—42no—
721C4—41no—
722C4—41no—
723C4—42no—
724C4—42no—
725C4—4241no—
726C4—4241no—
727C4—4241no—
728C4—4241no—
729C4#1681116911yescharacteristic
730C4#1681119411yescharacteristic
731C4#1681128011yescharacteristic
732C4#1681128011yescharacteristic
733C2—42no—
734C2—81no—
735C2—82no—
736C2#2027833911yescharacteristic
737C2#2028393311yescharacteristic
738C2#2028401911yescharacteristic
739C2#2028708811yescharacteristic
740C2#2028711111yescharacteristic
741C2#2028726911yescharacteristic
742C2#2028731511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
Fitting, prime radicalC2×C53×#553C2
socleC23×C53C22×D4
hypercenterC2×#553D53
hypocenterC53#25707
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#16811022C2semidirect
2. C2×#16810923C2semidirect
3. #20279881C2semidirect
4. #20275901C2semidirect
5. #20275901C2semidirect
6. #20275894C2semidirect
7. #20275894C2semidirect
8. #20275673C2semidirect
9. #20275510C2semidirect
10. #20274914C2semidirect
11. #20274914C2semidirect
12. #20274908C2semidirect
13. #20274903C2semidirect
14. C4×#13133138C2semidirect
434. C53#25707semidirect

Maximal subgroups

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

subgroupindex
C2×#168110222
C2×#168109232
#202798812
#202759012
#202758942
#202756732
#202755102
#202749142
#202749082
#202749032
C4×#131331382
C2×C53×#5532
#2570753