Finite Group Databasebeta

← #27389236

Subgroups — #27389236

Order 13568.

1150 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811244C211yesmaximal, characteristic
2C2×#16810684C211yesmaximal, characteristic, complemented
3#20275667C211yesmaximal, characteristic, complemented
4#20275663C211yesmaximal, characteristic, complemented
5#20275647C211yesmaximal, characteristic, complemented
6#20275647C211yesmaximal, characteristic, complemented
7#20275037C211yesmaximal, characteristic
8#20275032C211yesmaximal, characteristic
9#20275027C211yesmaximal, characteristic, complemented
10#20275022C211yesmaximal, characteristic, complemented
11#20274548C211yesmaximal, characteristic, complemented
12#20274543C211yesmaximal, characteristic, complemented
13C4×#13133140C211yesmaximal, characteristic, complemented
14C4×#13133137C211yesmaximal, characteristic, complemented
15C53×#2274C211yesmaximal, characteristic, complemented
16#16811244—24no—
17#16811244C418yescomplemented
18C2×#13133217C2211yescharacteristic
19C2×#13133212—21no—
20C2×#13133205C2211yescharacteristic
21C2×#13133203—21no—
22C2×#13133199—21no—
23C2×#13133196C2211yescharacteristic
24C2×#13133195—21no—
25C2×#13133191C2211yescharacteristic
26C2×C4×Dic106C2211yescharacteristic
27C2×C4×D212C2211yescharacteristic
28#16810684—24no—
29C2×C4⋊#88322C2211yescharacteristic
30C2×C4⋊#88322C2211yescharacteristic
31C2×#13133140C2211yescharacteristic
32C2×#13133140C2211yescharacteristic
33C2×#13133140C2211yescharacteristic
34C2×#13133140C2211yescharacteristic
35C2×#13133137C2211yescharacteristic
36C2×#13133137C2211yescharacteristic
37C2×#13133137C2211yescharacteristic
38C2×#13133137C2211yescharacteristic
39C2×C22⋊#88322C2211yescharacteristic
40C2×C22⋊#88322C2211yescharacteristic
41C2×#13133128C2211yescharacteristic
42C2×C4×#88322C2211yescharacteristic
43#16810385C2211yescharacteristic
44#16810385C2211yescharacteristic
45#16810385C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810385C2211yescharacteristic
49#16810385C2211yescharacteristic
50#16810385C2211yescharacteristic
51C2×#117×C53C2211yescharacteristic
52C2×#117×C53C2211yescharacteristic
53C22×C4⋊C4×C53C2211yescharacteristic
54C4×C4⋊C4×C53—21no—
55C4×C4⋊C4×C53—21no—
56C4×C4⋊C4×C53C2211yescharacteristic
57C4×C4⋊C4×C53C2211yescharacteristic
58C4×C4⋊C4×C53C2211yescharacteristic
59C4×C4⋊C4×C53C2211yescharacteristic
60C4×C22⋊C4×C53—21no—
61C4×C22⋊C4×C53—21no—
62C22×Dic106—21no—
63C22×Dic106C2311yescharacteristic
64C22×D212C2311yescharacteristic
65C22×C22⋊D53—21no—
66C22×C4×D53—21no—
67C22×#88322C2311yescharacteristic
68C22×#88322C2311yescharacteristic
69C22×#88322C2311yescharacteristic
70C22×#88322C2311yescharacteristic
71#13133217—22no—
72#13133217C2×C414yescomplemented
73#13133212—28no—
74#13133205—22no—
75#13133205C2×C414yescomplemented
76#13133203—28no—
77#13133199—28no—
78#13133196—22no—
79#13133196C2×C414yes—
80#13133195—28no—
81#13133191—22no—
82#13133191C2×C414yes—
83C4×Dic106—22no—
84C4×Dic106C2×C414yescomplemented
85C4×D212—22no—
86C4×D212C2×C414yescomplemented
87C2×C4⋊Dic53—21no—
88C2×C4⋊Dic53C2311yescharacteristic
89C2×C4⋊Dic53C2311yescharacteristic
90C2×#11719919—21no—
91C2×#11719919—21no—
92C2×C22⋊Dic53—21no—
93C2×#11719921—21no—
94C2×#11719921—21no—
95C2×#11719921—21no—
96C2×#11719921—21no—
97C2×C4×Dic53—21no—
98C4⋊#88322—22no—
99C4⋊#88322—22no—
100#13133140—22no—
101#13133140—22no—
102#13133140—22no—
103#13133140—22no—
104#13133137—22no—
105#13133137—22no—
106#13133137—22no—
107#13133137—22no—
108C22⋊#88322—22no—
109C22⋊#88322—22no—
110#13133128—22no—
111C4×#88322—22no—
112C23×C4×C53—21no—
113C23×C4×C53C2311yescharacteristic
114#117×C53—22no—
115#117×C53—22no—
116#117×C53C2×C414yes—
117#117×C53D414yes—
118C2×C4⋊C4×C53—22no—
119C2×C4⋊C4×C53—22no—
120C2×C4⋊C4×C53—21no—
121C2×C4⋊C4×C53D411yescharacteristic
122C2×C4⋊C4×C53D411yescharacteristic
123C2×C4⋊C4×C53C2311yescharacteristic
124C2×C4⋊C4×C53C2311yescharacteristic
125C2×C4⋊C4×C53C2311yescharacteristic
126C2×C4⋊C4×C53C2311yescharacteristic
127C2×C22⋊C4×C53—21no—
128C2×C22⋊C4×C53D411yescharacteristic
129C2×C22⋊C4×C53D411yescharacteristic
130C2×C42×C53—21no—
131C2×C42×C53—21no—
132C2×C42×C53—21no—
133C2×C42×C53—21no—
134C2×C42×C53—21no—
135C2×C42×C53C2311yescharacteristic
136C2×C42×C53C2311yescharacteristic
137#95×C53—21no—
138#95×C53—21no—
139#95×C53—21no—
140#95×C53—21no—
141C24×C53C2×D411yescharacteristic
142C23×D53—21no—
143C22×C4×C53—21no—
144C22×C4×C53—21no—
145C22×C4×C53—21no—
146C22×C4×C53—21no—
147C22×C4×C53—21no—
148C22×C4×C53—21no—
149C22×C4×C53—21no—
150C22×C4×C53—21no—
151C22×C4×C53—24no—
152C22×C4×C53—81no—
153C22×C4×C53—81no—
154C22×C4×C53C22×C412yes—
155C22×C4×C53C2×D411yescharacteristic
156C22×C4×C53C2×D411yescharacteristic
157C22×C4×C53C2×D411yescharacteristic
158C22×C4×C53C2×D411yescharacteristic
159C22×C4×C53C2×D411yescharacteristic
160C22×C4×C53C2×D412yes—
161C22×C4×C53C2411yescharacteristic
162C2×C22⋊D53—24no—
163C2×C22⋊D53—81no—
164C2×C22⋊D53—81no—
165C22×Dic53—21no—
166C22×Dic53—21no—
167C22×Dic53—21no—
168C2×D212—21no—
169C2×D212—21no—
170C2×D212—21no—
171C2×D212—21no—
172C2×D212—21no—
173C2×D212C22×C412yes—
174C2×C4×D53—24no—
175C2×C4×D53—81no—
176C2×C4×D53—81no—
177C2×Dic106—21no—
178C2×Dic106—21no—
179C2×Dic106—21no—
180C2×Dic106—21no—
181C2×Dic106—21no—
182C2×Dic106—24no—
183C2×Dic106—81no—
184C2×Dic106—81no—
185C2×Dic106C22×C412yes—
186C4⋊C4×C53—24no—
187C4⋊C4×C53—21no—
188C4⋊C4×C53—21no—
189C4⋊C4×C53—21no—
190C4⋊C4×C53—21no—
191C4⋊C4×C53C22⋊C414yes—
192C4⋊C4×C53C22⋊C414yes—
193C4⋊C4×C53#4112yes—
194C4⋊C4×C53#4112yes—
195C4⋊C4×C53#4112yes—
196C4⋊C4×C53#4112yes—
197C22⋊C4×C53—24no—
198C22⋊C4×C53C22⋊C414yes—
199C22⋊C4×C53C22⋊C414yes—
200C42×C53—24no—
201C42×C53—81no—
202C42×C53—81no—
203C42×C53—81no—
204C42×C53—81no—
205C42×C53C22×C412yes—
206C42×C53C22×C412yes—
207C42×C53C2×D412yes—
208C42×C53C2×D412yes—
209C22⋊Dic53—24no—
210#11719921—24no—
211#11719921—24no—
212#11719921—24no—
213#11719921—24no—
214C4⋊Dic53—24no—
215C4⋊Dic53—21no—
216C4⋊Dic53—21no—
217C4⋊Dic53C22×C412yes—
218C4⋊Dic53C22×C412yes—
219#11719919—24no—
220#11719919—24no—
221C4×Dic53—24no—
222C2×#88322—21no—
223C2×#88322—21no—
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—
234C23×C53—21no—
235C23×C53—21no—
236C23×C53—21no—
237C23×C53—21no—
238C23×C53—21no—
239C23×C53—21no—
240C23×C53C2×C22⋊C412yes—
241C23×C53C22×D411yescharacteristic
242C22×D53—22no—
243C22×D53—41no—
244C22×D53—41no—
245C22×D53—41no—
246C22×D53—41no—
247C22×D53—41no—
248C22×D53—41no—
249C2×C4×C53—21no—
250C2×C4×C53—21no—
251C2×C4×C53—21no—
252C2×C4×C53—21no—
253C2×C4×C53—21no—
254C2×C4×C53—21no—
255C2×C4×C53—21no—
256C2×C4×C53—21no—
257C2×C4×C53—21no—
258C2×C4×C53—21no—
259C2×C4×C53—22no—
260C2×C4×C53—22no—
261C2×C4×C53—22no—
262C2×C4×C53—22no—
263C2×C4×C53—22no—
264C2×C4×C53—22no—
265C2×C4×C53—22no—
266C2×C4×C53—22no—
267C2×C4×C53—41no—
268C2×C4×C53—41no—
269C2×C4×C53—41no—
270C2×C4×C53—41no—
271C2×C4×C53—41no—
272C2×C4×C53—41no—
273C2×C4×C53—41no—
274C2×C4×C53—41no—
275C2×C4×C53—84no—
276C2×C4×C53C2×C22⋊C412yes—
277C2×C4×C53C2×C22⋊C412yes—
278C2×C4×C53C2×C22⋊C412yes—
279C2×C4×C53C2×C22⋊C412yes—
280C2×C4×C53C2×C22⋊C412yes—
281C2×C4×C53C23×C411yescharacteristic
282C2×C4×C53C22×D411yescharacteristic
283C2×C4×C53C2×#4111yescharacteristic
284C2×C4×C53C2×#4111yescharacteristic
285C2×C4×C53C2×#4111yescharacteristic
286C2×C4×C53C2×#4111yescharacteristic
287C22⋊D53—84no—
288C2×Dic53—22no—
289C2×Dic53—22no—
290C2×Dic53—22no—
291C2×Dic53—41no—
292C2×Dic53—41no—
293C2×Dic53—41no—
294C2×Dic53—41no—
295C2×Dic53—41no—
296C2×Dic53—41no—
297D212—22no—
298D212—22no—
299D212—41no—
300D212—41no—
301C4×D53—84no—
302Dic106—22no—
303Dic106—22no—
304Dic106—41no—
305Dic106—41no—
306Dic106—84no—
307#88322—41no—
308#88322—41no—
309#88322—41no—
310#88322—41no—
311#21397—531nomaximal, Sylow
312C22×C53—22no—
313C22×C53—22no—
314C22×C53—22no—
315C22×C53—41no—
316C22×C53—41no—
317C22×C53—41no—
318C22×C53—41no—
319C22×C53C22×C22⋊C411yescharacteristic
320C22×C53#52511yescharacteristic
321C22×C53#52511yescharacteristic
322C22×C53#57611yescharacteristic
323C22×C53#57711yescharacteristic
324C22×C53#57711yescharacteristic
325C22×C53#57811yescharacteristic
326C2×D53—42no—
327C2×D53—42no—
328C2×D53—42no—
329C2×D53—81no—
330C2×D53—81no—
331C2×D53—81no—
332C2×D53—81no—
333C4×C53—22no—
334C4×C53—22no—
335C4×C53—22no—
336C4×C53—22no—
337C4×C53—22no—
338C4×C53—42no—
339C4×C53—42no—
340C4×C53—42no—
341C4×C53—42no—
342C4×C53C4×#4111yescharacteristic
343C4×C53C4×#4111yescharacteristic
344C4×C53#53211yescharacteristic
345C4×C53#53211yescharacteristic
346Dic53—42no—
347Dic53—42no—
348Dic53—42no—
349C2×#542—531no—
350C2×#433—531no—
351#2274D5311yescharacteristic, complemented
352#1988—531no—
353#1987—531no—
354#1983—531no—
355#1983—531no—
356#1875—531no—
357#1874—531no—
358#1873—531no—
359#1872—531no—
360#1763—531no—
361#1762—531no—
362C4×#103—531no—
363C4×#102—531no—
364C2×C53—42no—
365C2×C53#229711yescharacteristic
366C2×C53#289711yescharacteristic
367C2×C53#289811yescharacteristic
368C2×C53#311811yescharacteristic
369C2×C53#312111yescharacteristic
370C2×C53#312411yescharacteristic
371C2×C53#312511yescharacteristic
372D53—82no—
373#542—538no—
374#542—1064no—
375C2×C4⋊Q8—531no—
376C2×#126—1061no—
377C2×#124—531no—
378C2×#124—1061no—
379C2×#123—1061no—
380C2×C22⋊Q8—531no—
381C2×C22⋊Q8—1061no—
382C2×#121—531no—
383C2×C4×Q8—531no—
384C2×C4×D4—531no—
385C2×#117C2×D5311yescharacteristic
386C2×#117C2×D5311yescharacteristic
387C22×C4⋊C4C2×D5311yescharacteristic
388#433—1064no—
389C2×C4⋊C8—531no—
390C2×C4⋊C8—531no—
391C2×#103—531no—
392C2×#103—531no—
393C2×#103—531no—
394C2×#103—531no—
395C2×#102—531no—
396C2×#102—531no—
397C2×#102—531no—
398C2×#102—531no—
399C2×C22⋊C8—531no—
400C2×C22⋊C8—531no—
401C2×#97—531no—
402C2×C4×C8—531no—
403C4×C4⋊C4—21no—
404C4×C4⋊C4—21no—
405C4×C4⋊C4C2×D5311yescharacteristic
406C4×C4⋊C4C2×D5311yescharacteristic
407C4×C4⋊C4C2×D5311yescharacteristic
408C4×C4⋊C4C2×D5311yescharacteristic
409C4×C22⋊C4—21no—
410C4×C22⋊C4—21no—
411#340—531no—
412#340—531no—
413#340—531no—
414#340—531no—
415#340—531no—
416#340—531no—
417#340—531no—
418#340—531no—
419C53#2139711yescharacteristic, complemented, Sylow
420C22×Q8—531no—
421C22×Q8—1061no—
422C22×D4—531no—
423C22×D4—1061no—
424C23×C4—21no—
425C23×C4—1061no—
426C23×C4C22×D5311yescharacteristic
427C22×C8—531no—
428C22×C8—531no—
429C22×C8—531no—
430C22×C8—531no—
431C4⋊Q8—534no—
432C4⋊Q8—1062no—
433#126—1068no—
434#124—534no—
435#124—1068no—
436#124—1062no—
437#123—1068no—
438C22⋊Q8—534no—
439C22⋊Q8—1062no—
440C22⋊Q8—1068no—
441#121—534no—
442#121—1062no—
443C4×Q8—534no—
444C4×Q8—1062no—
445C4×D4—534no—
446C4×D4—1062no—
447#117—22no—
448#117—22no—
449#117C4×D5314yes—
450#117D21214yes—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—531no—
455C2×C4⋊C4—531no—
456C2×C4⋊C4—1061no—
457C2×C4⋊C4—1061no—
458C2×C4⋊C4—1061no—
459C2×C4⋊C4C22⋊D5311yescharacteristic
460C2×C4⋊C4C22⋊D5311yescharacteristic
461C2×C4⋊C4C22×D5311yescharacteristic
462C2×C4⋊C4C22×D5311yescharacteristic
463C2×C4⋊C4C22×D5311yescharacteristic
464C2×C4⋊C4C22×D5311yescharacteristic
465C2×C22⋊C4—21no—
466C2×C22⋊C4—1061no—
467C2×C22⋊C4—1061no—
468C2×C22⋊C4—1061no—
469C2×C22⋊C4—1061no—
470C2×C22⋊C4—1061no—
471C2×C22⋊C4C22⋊D5311yescharacteristic
472C2×C22⋊C4C22⋊D5311yescharacteristic
473C2×C42—21no—
474C2×C42—21no—
475C2×C42—21no—
476C2×C42—21no—
477C2×C42—21no—
478C2×C42—1061no—
479C2×C42C22×D5311yescharacteristic
480C2×C42C22×D5311yescharacteristic
481C4⋊C8—1062no—
482C4⋊C8—1062no—
483#103—1062no—
484#103—1062no—
485#103—1062no—
486#103—1062no—
487#102—1062no—
488#102—1062no—
489#102—1062no—
490#102—1062no—
491C22⋊C8—1062no—
492C22⋊C8—1062no—
493#97—1062no—
494C4×C8—1062no—
495#95—21no—
496#95—21no—
497#95—21no—
498#95—21no—
499C24—1061no—
500C24C2×C22⋊D5311yescharacteristic
501C2×Q8—532no—
502C2×Q8—1064no—
503C2×Q8—1061no—
504C2×Q8—1061no—
505C2×Q8—1061no—
506C2×Q8—1061no—
507C2×Q8—1061no—
508C2×Q8—4241no—
509C2×Q8—4241no—
510C2×D4—532no—
511C2×D4—1064no—
512C2×D4—1061no—
513C2×D4—1061no—
514C2×D4—1061no—
515C2×D4—1061no—
516C2×D4—1061no—
517C2×D4—4241no—
518C2×D4—4241no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—24no—
528C22×C4—81no—
529C22×C4—81no—
530C22×C4—1061no—
531C22×C4—1061no—
532C22×C4—1061no—
533C22×C4—1064no—
534C22×C4—4241no—
535C22×C4—4241no—
536C22×C4C2×C4×D5312yes—
537C22×C4C2×D21212yes—
538C22×C4C2×C22⋊D5311yescharacteristic
539C22×C4C2×C22⋊D5311yescharacteristic
540C22×C4C2×C22⋊D5311yescharacteristic
541C22×C4C2×C22⋊D5311yescharacteristic
542C22×C4C2×C22⋊D5311yescharacteristic
543C22×C4C23×D5311yescharacteristic
544C2×C8—1061no—
545C2×C8—1061no—
546C2×C8—1061no—
547C2×C8—1061no—
548C2×C8—1061no—
549C2×C8—1061no—
550C2×C8—1061no—
551C2×C8—1061no—
552C2×C8—1061no—
553C2×C8—1061no—
554C2×C8—1061no—
555C2×C8—1061no—
556C4⋊C4—24no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—532no—
562C4⋊C4—532no—
563C4⋊C4—1064no—
564C4⋊C4—1064no—
565C4⋊C4—1064no—
566C4⋊C4—1061no—
567C4⋊C4—1061no—
568C4⋊C4#1171992114yes—
569C4⋊C4#1171992114yes—
570C4⋊C4#1171994512yes—
571C4⋊C4#1171994512yes—
572C4⋊C4#1171994512yes—
573C4⋊C4#1171994512yes—
574C22⋊C4—24no—
575C22⋊C4—1064no—
576C22⋊C4—1064no—
577C22⋊C4—1064no—
578C22⋊C4—1064no—
579C22⋊C4—1064no—
580C22⋊C4#1171992114yes—
581C22⋊C4#1171992114yes—
582C42—24no—
583C42—81no—
584C42—81no—
585C42—81no—
586C42—81no—
587C42—1064no—
588C42C2×C4×D5312yes—
589C42C2×C4×D5312yes—
590C42C2×D21212yes—
591C42C2×D21212yes—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—1062no—
599C23—2121no—
600C23—2121no—
601C23—2121no—
602C23—2121no—
603C23—2121no—
604C23—2121no—
605C23C2×#1171992112yes—
606C23C22×C22⋊D5311yescharacteristic
607Q8—1062no—
608Q8—1062no—
609Q8—4244no—
610Q8—2121no—
611Q8—2121no—
612D4—1062no—
613D4—1062no—
614D4—4244no—
615D4—2121no—
616D4—2121no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—84no—
644C2×C4—1062no—
645C2×C4—1062no—
646C2×C4—1062no—
647C2×C4—4244no—
648C2×C4—2121no—
649C2×C4—2121no—
650C2×C4—2121no—
651C2×C4—2121no—
652C2×C4—2121no—
653C2×C4—2121no—
654C2×C4C2×#1171992112yes—
655C2×C4C2×#1171992112yes—
656C2×C4C2×#1171992112yes—
657C2×C4C2×#1171992112yes—
658C2×C4C2×#1171992112yes—
659C2×C4C22×C4×D5311yescharacteristic
660C2×C4C22×D21211yescharacteristic
661C2×C4C2×#1171994511yescharacteristic
662C2×C4C2×#1171994511yescharacteristic
663C2×C4C2×#1171994511yescharacteristic
664C2×C4C2×#1171994511yescharacteristic
665C8—2121no—
666C8—2121no—
667C8—2121no—
668C8—2121no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—4241no—
677C22—4241no—
678C22—4241no—
679C22—4241no—
680C22—2122no—
681C22—2122no—
682C22—2122no—
683C22C22×#1171992111yescharacteristic
684C22#1681113411yescharacteristic
685C22#1681113411yescharacteristic
686C22#1681142611yescharacteristic
687C22#1681143111yescharacteristic
688C22#1681143411yescharacteristic
689C22#1681143811yescharacteristic
690C4—22no—
691C4—22no—
692C4—22no—
693C4—22no—
694C4—22no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—42no—
699C4—2122no—
700C4—2122no—
701C4—2122no—
702C4C4×#1171994511yescharacteristic
703C4C4×#1171994511yescharacteristic
704C4#1681117311yescharacteristic
705C4#1681117311yescharacteristic
706C2—42no—
707C2—4242no—
708C2#2027720511yescharacteristic
709C2#2028323811yescharacteristic
710C2#2028324511yescharacteristic
711C2#2028489911yescharacteristic
712C2#2028494411yescharacteristic
713C2#2028497711yescharacteristic
714C2#2028499211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2274C2
socleC23×C53C22×D4
prime radicalC2×#13133191C22
cosocleC22×C4×C53C24
hypercenter#2274D53
hypocenterC53#21397
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2274

Complements

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

NH ≅ G/Ntype
2. C2×#16810684C2semidirect
3. #20275667C2semidirect
4. #20275663C2semidirect
5. #20275647C2semidirect
6. #20275647C2semidirect
9. #20275027C2semidirect
10. #20275022C2semidirect
11. #20274548C2semidirect
12. #20274543C2semidirect
13. C4×#13133140C2semidirect
14. C4×#13133137C2semidirect
15. C53×#2274C2semidirect
17. #16811244C4semidirect
72. #13133217C2×C4semidirect
75. #13133205C2×C4semidirect
84. C4×Dic106C2×C4semidirect
86. C4×D212C2×C4semidirect
351. #2274D53semidirect
419. C53#21397semidirect

Maximal subgroups

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

subgroupindex
C2×#168112442
C2×#168106842
#202756672
#202756632
#202756472
#202750372
#202750322
#202750272
#202750222
#202745482
#202745432
C4×#131331402
C4×#131331372
C53×#22742
#2139753