Finite Group Databasebeta

← #27400474

Subgroups — #27400474

Order 13568.

1174 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811328C211yesmaximal, characteristic
2C2×#16810691C211yesmaximal, characteristic
3#20277646C211yesmaximal, characteristic
4#20275686C211yesmaximal, characteristic, complemented
5#20275665C211yesmaximal, characteristic, complemented
6#20275147C211yesmaximal, characteristic, complemented
7#20275136C211yesmaximal, characteristic, complemented
8#20275026C211yesmaximal, characteristic, complemented
9#20275020C211yesmaximal, characteristic, complemented
10#20274800C211yesmaximal, characteristic, complemented
11#20274729C211yesmaximal, characteristic, complemented
12#20274544C211yesmaximal, characteristic, complemented
13#20274433C211yesmaximal, characteristic, complemented
14C2×#16810385C211yesmaximal, characteristic, complemented
15C53×#1824C211yesmaximal, characteristic, complemented
16C22×#11719912C2211yescharacteristic
17C23×#88322C2211yescharacteristic
18#16811328—24no—
19#16811328C418yescomplemented
20C2×#13133216C2211yescharacteristic
21C2×#13133207—21no—
22C2×#13133197C2211yescharacteristic
23C2×#13133196—21no—
24C2×#13133196C2211yescharacteristic
25C2×#13133195—21no—
26C2×#13133182C2211yescharacteristic
27C2×C4×C22⋊D53—21no—
28C2×C4×C22⋊D53C2211yescharacteristic
29C2×#13133175C2211yescharacteristic
30C22×C4⋊Dic53C2211yescharacteristic
31C2×C4⋊C4×D53C2211yescharacteristic
32#16810691—24no—
33C2×#13133146C2211yescharacteristic
34C2×#13133142C2211yescharacteristic
35C2×#13133142C2211yescharacteristic
36C2×#13133140C2211yescharacteristic
37C2×#13133140C2211yescharacteristic
38C2×#13133129C2211yescharacteristic
39C2×#13133127C2211yescharacteristic
40#16810515—21no—
41#16810510—21no—
42#16810500—21no—
43#16810488C2211yescharacteristic
44#16810480C2211yescharacteristic
45C4⋊C4×Dic53C2211yescharacteristic
46C22⋊C4×Dic53—21no—
47#16810386C2211yescharacteristic
48#16810386C2211yescharacteristic
49#16810385C2211yescharacteristic
50#16810385C2211yescharacteristic
51#16810385C2211yescharacteristic
52#16810385C2211yescharacteristic
53#16810385C2211yescharacteristic
54#16810385C2211yescharacteristic
55C22×C4⋊C4×C53C2211yescharacteristic
56C2×C22⋊C8×C53C2211yescharacteristic
57C53×#380C2211yescharacteristic
58C53×#340C2211yescharacteristic
59C53×#340C2211yescharacteristic
60C53×#340C2211yescharacteristic
61C53×#340C2211yescharacteristic
62C22×Dic106—21no—
63C22×Dic106C2311yescharacteristic
64C22×C22⋊D53D411yescharacteristic
65C23×Dic53—21no—
66C22×C4×D53—21no—
67C22×C4×D53C2311yescharacteristic
68C2×#11719912—22no—
69C2×#11719912—22no—
70C2×#11719912—41no—
71C22×#88322—22no—
72C22×#88322—22no—
73C22×#88322—41no—
74C22×#88322C2311yescharacteristic
75C22×#88322C2311yescharacteristic
76#13133216—22no—
77#13133216C2×C414yescomplemented
78#13133207—28no—
79#13133197—22no—
80#13133197C2×C414yescomplemented
81#13133196—28no—
82#13133196—22no—
83#13133196C2×C414yes—
84#13133195—28no—
85#13133182—22no—
86#13133182C2×C414yescomplemented
87C4×C22⋊D53—28no—
88C4×C22⋊D53C2×C414yes—
89C4×C22⋊D53D414yes—
90#13133175—22no—
91#13133175—41no—
92C2×C4⋊Dic53—21no—
93C2×C4⋊Dic53—21no—
94C2×C4⋊Dic53—22no—
95C2×C4⋊Dic53—41no—
96C2×C4⋊Dic53C2311yescharacteristic
97C2×C4⋊Dic53C2311yescharacteristic
98C2×C4⋊Dic53C2311yescharacteristic
99C2×#11719919—21no—
100C2×#11719919—21no—
101C2×#11719919—21no—
102C2×#11719919—21no—
103C2×#11719919D411yescharacteristic
104C4⋊C4×D53—22no—
105C4⋊C4×D53C2×C414yescomplemented
106C2×C22⋊Dic53—21no—
107C2×C22⋊Dic53D411yescharacteristic
108C2×#11719921—21no—
109C2×#11719921—21no—
110C2×#11719921—21no—
111C2×#11719921D411yescharacteristic
112C2×C4×Dic53—21no—
113C2×C4×Dic53—21no—
114C2×C4×Dic53—21no—
115C2×C4×Dic53C2311yescharacteristic
116#13133146—22no—
117#13133142—22no—
118#13133142—41no—
119#13133140—22no—
120#13133140—41no—
121#13133129—22no—
122#13133127—22no—
123#13133124—21no—
124#13133124—21no—
125#13133124—21no—
126#13133124—21no—
127C23×C4×C53—21no—
128C23×C4×C53C2311yescharacteristic
129C22×C8×C53C2311yescharacteristic
130C22×C8×C53C2311yescharacteristic
131C2×C4⋊C4×C53—22no—
132C2×C4⋊C4×C53—21no—
133C2×C4⋊C4×C53C2×C414yes—
134C2×C4⋊C4×C53C2311yescharacteristic
135C2×C4⋊C4×C53C2311yescharacteristic
136C2×C4⋊C4×C53C2311yescharacteristic
137C2×C4⋊C4×C53C2311yescharacteristic
138C2×C22⋊C4×C53—21no—
139C22⋊C8×C53—22no—
140#95×C53—21no—
141C24×C53C2×D411yescharacteristic
142C23×D53C2×D411yescharacteristic
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—24no—
150C22×C4×C53—21no—
151C22×C4×C53—21no—
152C22×C4×C53—81no—
153C22×C4×C53—81no—
154C22×C4×C53C22×C412yes—
155C22×C4×C53C2×D411yescharacteristic
156C22×C4×C53C2×D412yes—
157C22×C4×C53C2411yescharacteristic
158C2×C22⋊D53—22no—
159C2×C22⋊D53—22no—
160C2×C22⋊D53C22⋊C414yes—
161C22×Dic53—21no—
162C22×Dic53—21no—
163C22×Dic53—21no—
164C22×Dic53—21no—
165C22×Dic53—42no—
166C22×Dic53—42no—
167C22×Dic53—81no—
168C22×Dic53C2×D411yescharacteristic
169C22×Dic53C2×D411yescharacteristic
170C22×Dic53C2×D411yescharacteristic
171C2×C4×D53—21no—
172C2×C4×D53—21no—
173C2×C4×D53—21no—
174C2×C4×D53—21no—
175C2×C4×D53—24no—
176C2×C4×D53—81no—
177C2×C4×D53—81no—
178C2×C4×D53C22×C412yes—
179C2×C4×D53C2×D412yes—
180C2×Dic106—21no—
181C2×Dic106—21no—
182C2×Dic106—21no—
183C2×Dic106—21no—
184C2×Dic106—21no—
185C2×Dic106—24no—
186C2×Dic106—81no—
187C2×Dic106—81no—
188C2×Dic106C22×C412yes—
189C2×C8×C53—21no—
190C2×C8×C53—21no—
191C2×C8×C53—21no—
192C2×C8×C53—21no—
193C2×C8×C53—21no—
194C2×C8×C53—21no—
195C4⋊C4×C53—24no—
196C4⋊C4×C53—21no—
197C4⋊C4×C53—21no—
198C4⋊C4×C53—21no—
199C4⋊C4×C53—21no—
200C4⋊C4×C53—21no—
201C4⋊C4×C53—21no—
202C4⋊C4×C53C22×C412yes—
203C4⋊C4×C53C22×C412yes—
204C22⋊C4×C53—42no—
205C22⋊Dic53—24no—
206C22⋊Dic53C22⋊C414yes—
207#11719921—24no—
208#11719921—42no—
209#11719921—81no—
210#11719921C22⋊C414yes—
211C4⋊Dic53—21no—
212C4⋊Dic53—21no—
213C4⋊Dic53—24no—
214C4⋊Dic53—21no—
215C4⋊Dic53—21no—
216C4⋊Dic53—42no—
217C4⋊Dic53C22×C412yes—
218C4⋊Dic53#4112yes—
219#11719919—24no—
220#11719919—24no—
221#11719919—24no—
222#11719919—24no—
223#11719919C22⋊C414yes—
224C4×Dic53—24no—
225C4×Dic53—42no—
226C4×Dic53—81no—
227C4×Dic53C22×C412yes—
228C4×Dic53C2×D412yes—
229C2×#88322—21no—
230C2×#88322—21no—
231C2×#88322—21no—
232C2×#88322—21no—
233C2×#88322—21no—
234C2×#88322—44no—
235C2×#88322#4112yes—
236#11719912—44no—
237C23×C53—21no—
238C23×C53—21no—
239C23×C53—21no—
240C23×C53—21no—
241C23×C53C2×C22⋊C412yes—
242C23×C53#13712yes—
243C23×C53#13712yes—
244C23×C53C22×D411yescharacteristic
245C22×D53—21no—
246C22×D53—21no—
247C22×D53—21no—
248C22×D53—21no—
249C22×D53—21no—
250C22×D53—21no—
251C22×D53C2×C22⋊C412yes—
252C2×C4×C53—21no—
253C2×C4×C53—21no—
254C2×C4×C53—22no—
255C2×C4×C53—22no—
256C2×C4×C53—22no—
257C2×C4×C53—22no—
258C2×C4×C53—22no—
259C2×C4×C53—22no—
260C2×C4×C53—41no—
261C2×C4×C53—41no—
262C2×C4×C53—41no—
263C2×C4×C53—41no—
264C2×C4×C53—41no—
265C2×C4×C53—41no—
266C2×C4×C53—41no—
267C2×C4×C53—41no—
268C2×C4×C53—41no—
269C2×C4×C53—41no—
270C2×C4×C53—84no—
271C2×C4×C53C2×C22⋊C412yes—
272C2×C4×C53C23×C411yescharacteristic
273C2×C4×C53C22×D411yescharacteristic
274C2×C4×C53C2×#4111yescharacteristic
275C2×C4×C53C2×#4111yescharacteristic
276C2×C4×C53H(5,𝔽2)11yescharacteristic
277C2×C4×C532−1+411yescharacteristic
278C22⋊D53—28no—
279C2×Dic53—21no—
280C2×Dic53—21no—
281C2×Dic53—21no—
282C2×Dic53—21no—
283C2×Dic53—21no—
284C2×Dic53—21no—
285C2×Dic53—22no—
286C2×Dic53—22no—
287C2×Dic53—22no—
288C2×Dic53—41no—
289C2×Dic53—41no—
290C2×Dic53—41no—
291C2×Dic53—41no—
292C2×Dic53—41no—
293C2×Dic53—41no—
294C2×Dic53—41no—
295C2×Dic53—41no—
296C2×Dic53—41no—
297C2×Dic53—84no—
298C2×Dic53C2×C22⋊C412yes—
299C2×Dic53C2×C22⋊C412yes—
300C2×Dic53C2×C22⋊C412yes—
301C4×D53—22no—
302C4×D53—22no—
303C4×D53—22no—
304C4×D53—22no—
305C4×D53—84no—
306Dic106—22no—
307Dic106—22no—
308Dic106—41no—
309Dic106—41no—
310Dic106—84no—
311C8×C53—41no—
312C8×C53—41no—
313#88322—22no—
314#88322—41no—
315#22497—531nomaximal, Sylow
316C22×C53—22no—
317C22×C53—22no—
318C22×C53—22no—
319C22×C53—22no—
320C22×C53—22no—
321C22×C53—22no—
322C22×C53#41914yes—
323C22×C53C22×C22⋊C411yescharacteristic
324C22×C53#54611yescharacteristic
325C22×C53#54711yescharacteristic
326C22×C53C2×#13711yescharacteristic
327C22×C53C2×#13711yescharacteristic
328C22×C53#57611yescharacteristic
329C22×C53#57711yescharacteristic
330C2×D53—22no—
331C2×D53—22no—
332C2×D53—22no—
333C2×D53—41no—
334C2×D53—41no—
335C2×D53—41no—
336C2×D53—41no—
337C4×C53—22no—
338C4×C53—42no—
339C4×C53—42no—
340C4×C53—81no—
341C4×C53—81no—
342C4×C53C4×#4111yescharacteristic
343C4×C53#52011yescharacteristic
344C4×C53#54611yescharacteristic
345C4×C53#54711yescharacteristic
346Dic53—22no—
347Dic53—22no—
348Dic53—22no—
349Dic53—42no—
350Dic53—42no—
351Dic53—42no—
352Dic53—81no—
353C2×#554—531no—
354C2×#435—531no—
355#2352—531no—
356#1993—531no—
357#1988—531no—
358#1894—531no—
359#1892—531no—
360#1873—531no—
361#1872—531no—
362#1824D5311yescharacteristic, complemented
363#1823—531no—
364#1805—531no—
365#1763—531no—
366#1736—531no—
367C2×#340—531no—
368C2×C53—24no—
369C2×C53#233911yescharacteristic
370C2×C53C2×#41911yescharacteristic
371C2×C53#289711yescharacteristic
372C2×C53#331411yescharacteristic
373C2×C53#331611yescharacteristic
374C2×C53#334411yescharacteristic
375C2×C53#334611yescharacteristic
376D53—42no—
377C22×M16—531no—
378C23×C8—531no—
379#554—538no—
380#554—1064no—
381C2×C4⋊Q8—531no—
382C2×#125—1061no—
383C2×C22⋊Q8—531no—
384C2×C22⋊Q8—531no—
385C2×C22⋊Q8—1061no—
386C2×C22⋊Q8—1061no—
387C2×C4×Q8—531no—
388C2×C4×D4—531no—
389C2×C4×D4—1061no—
390C2×#117—531no—
391C22×C4⋊C4—531no—
392C22×C4⋊C4—531no—
393C22×C4⋊C4C2×D5311yescharacteristic
394#435—1064no—
395C2×C4⋊C8—531no—
396C2×#103—531no—
397C2×#103—531no—
398C2×#103—531no—
399C2×#103—531no—
400C2×C22⋊C8—531no—
401C2×C22⋊C8C2×D5311yescharacteristic
402C2×#97—531no—
403#388—1061no—
404#387—1061no—
405#386—1061no—
406#382—531no—
407#380—531no—
408#380C2×D5311yescharacteristic
409C4×C4⋊C4—531no—
410C4×C22⋊C4—1061no—
411#340—531no—
412#340—531no—
413#340—531no—
414#340—531no—
415#340—531no—
416#340—531no—
417#340—531no—
418#340—531no—
419#340C2×D5311yescharacteristic
420#340C2×D5311yescharacteristic
421#340C2×D5311yescharacteristic
422#340C2×D5311yescharacteristic
423C53#2249711yescharacteristic, complemented, Sylow
424C22×Q8—531no—
425C22×Q8—1061no—
426C22×D4—531no—
427C23×C4—21no—
428C23×C4—531no—
429C23×C4—1061no—
430C23×C4—1061no—
431C23×C4C22×D5311yescharacteristic
432C2×M16—1062no—
433C2×M16—1062no—
434C2×M16—2121no—
435C22×C8—531no—
436C22×C8—531no—
437C22×C8—1062no—
438C22×C8—1062no—
439C22×C8—2121no—
440C22×C8C22×D5311yescharacteristic
441C22×C8C22×D5311yescharacteristic
442C4⋊Q8—534no—
443C4⋊Q8—1062no—
444#125—1068no—
445C22⋊Q8—534no—
446C22⋊Q8—534no—
447C22⋊Q8—1068no—
448C22⋊Q8—1068no—
449C22⋊Q8—1062no—
450C22⋊Q8—1062no—
451C4×Q8—534no—
452C4×Q8—1062no—
453C4×D4—534no—
454C4×D4—534no—
455C4×D4—1068no—
456#117—1062no—
457#117—2121no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—531no—
461C2×C4⋊C4—531no—
462C2×C4⋊C4—531no—
463C2×C4⋊C4—534no—
464C2×C4⋊C4—531no—
465C2×C4⋊C4—1062no—
466C2×C4⋊C4—1062no—
467C2×C4⋊C4—1061no—
468C2×C4⋊C4—1061no—
469C2×C4⋊C4—1061no—
470C2×C4⋊C4—1061no—
471C2×C4⋊C4—1061no—
472C2×C4⋊C4—1061no—
473C2×C4⋊C4—2121no—
474C2×C4⋊C4C4×D5314yes—
475C2×C4⋊C4C22×D5311yescharacteristic
476C2×C4⋊C4C22×D5311yescharacteristic
477C2×C4⋊C4C22×D5311yescharacteristic
478C2×C4⋊C4C22×D5311yescharacteristic
479C2×C22⋊C4—21no—
480C2×C22⋊C4—531no—
481C2×C22⋊C4—531no—
482C2×C22⋊C4—1061no—
483C2×C22⋊C4—1061no—
484C2×C22⋊C4—1061no—
485C2×C22⋊C4—1061no—
486C2×C42—531no—
487C2×C42—1061no—
488C2×C42—1061no—
489C2×C42—1061no—
490C4⋊C8—1062no—
491#103—1062no—
492#103—1062no—
493#103—2121no—
494#103—2121no—
495C22⋊C8—22no—
496C22⋊C8—1062no—
497#97—1062no—
498#95—21no—
499#95—1061no—
500#95—1061no—
501#95—1061no—
502#95—1061no—
503C24—531no—
504C24D4×D5311yescharacteristic
505C2×Q8—532no—
506C2×Q8—1064no—
507C2×Q8—1061no—
508C2×Q8—1061no—
509C2×Q8—1061no—
510C2×Q8—1061no—
511C2×Q8—1061no—
512C2×Q8—4241no—
513C2×Q8—4241no—
514C2×D4—534no—
515C2×D4—1062no—
516C2×D4—1062no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—24no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—81no—
527C22×C4—81no—
528C22×C4—531no—
529C22×C4—531no—
530C22×C4—531no—
531C22×C4—532no—
532C22×C4—532no—
533C22×C4—1064no—
534C22×C4—1061no—
535C22×C4—1061no—
536C22×C4—1061no—
537C22×C4—1061no—
538C22×C4—1061no—
539C22×C4—1061no—
540C22×C4—1061no—
541C22×C4—1061no—
542C22×C4—4241no—
543C22×C4—4241no—
544C22×C4—4241no—
545C22×C4—2122no—
546C22×C4—2122no—
547C22×C4C2×C4×D5312yes—
548C22×C4D4×D5311yescharacteristic
549C22×C4D4×D5312yes—
550C22×C4C23×D5311yescharacteristic
551M16—2124no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—532no—
559C2×C8—1061no—
560C2×C8—1061no—
561C2×C8—1061no—
562C2×C8—1061no—
563C2×C8—1061no—
564C2×C8—2124no—
565C4⋊C4—24no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—534no—
573C4⋊C4—532no—
574C4⋊C4—532no—
575C4⋊C4—1064no—
576C4⋊C4—1064no—
577C4⋊C4—1064no—
578C4⋊C4—1064no—
579C4⋊C4—1064no—
580C4⋊C4—1061no—
581C4⋊C4—1061no—
582C4⋊C4—1061no—
583C4⋊C4—1061no—
584C4⋊C4—2122no—
585C4⋊C4C2×C4×D5312yes—
586C4⋊C4C2×C4×D5312yes—
587C22⋊C4—42no—
588C22⋊C4—534no—
589C22⋊C4—534no—
590C22⋊C4—1064no—
591C22⋊C4—1064no—
592C22⋊C4—4241no—
593C22⋊C4—2122no—
594C42—532no—
595C42—532no—
596C42—1064no—
597C42—4241no—
598C42—2122no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—532no—
604C23—1061no—
605C23—1061no—
606C23—1061no—
607C23—1061no—
608C23—1061no—
609C23—1061no—
610C23C22⋊C4×D5312yes—
611C23#1313324612yes—
612C23#1313324912yes—
613C23C2×D4×D5311yescharacteristic
614Q8—1062no—
615Q8—1062no—
616Q8—4244no—
617Q8—2121no—
618Q8—2121no—
619D4—1068no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—84no—
639C2×C4—532no—
640C2×C4—532no—
641C2×C4—532no—
642C2×C4—1061no—
643C2×C4—1061no—
644C2×C4—1061no—
645C2×C4—1061no—
646C2×C4—1061no—
647C2×C4—1061no—
648C2×C4—1062no—
649C2×C4—1062no—
650C2×C4—1062no—
651C2×C4—1062no—
652C2×C4—1062no—
653C2×C4—1062no—
654C2×C4—1062no—
655C2×C4—4244no—
656C2×C4—4244no—
657C2×C4—2121no—
658C2×C4—2121no—
659C2×C4—2121no—
660C2×C4—2121no—
661C2×C4—2121no—
662C2×C4—2121no—
663C2×C4—2121no—
664C2×C4—2121no—
665C2×C4—2121no—
666C2×C4C22⋊C4×D5312yes—
667C2×C4C22×C4×D5311yescharacteristic
668C2×C4C2×D4×D5311yescharacteristic
669C2×C4#41×D5311yescharacteristic
670C2×C4#41×D5311yescharacteristic
671C2×C4#1313326311yescharacteristic
672C2×C4#1313326411yescharacteristic
673C8—41no—
674C8—41no—
675C8—1062no—
676C8—2121no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—1062no—
684C22—1062no—
685C22—1062no—
686C22—2121no—
687C22—2121no—
688C22—2121no—
689C22—2121no—
690C22#1681063014yes—
691C22C2×C22⋊C4×D5311yescharacteristic
692C22#1681126511yescharacteristic
693C22#1681127111yescharacteristic
694C22C2×#1313324611yescharacteristic
695C22C2×#1313324911yescharacteristic
696C22#1681142711yescharacteristic
697C22#1681143311yescharacteristic
698C4—22no—
699C4—42no—
700C4—42no—
701C4—81no—
702C4—81no—
703C4—1062no—
704C4—1062no—
705C4—1062no—
706C4—4241no—
707C4—2122no—
708C4—2122no—
709C4—2122no—
710C4#1681109111yescharacteristic
711C4#1681110311yescharacteristic
712C4#1681126511yescharacteristic
713C4#1681127111yescharacteristic
714C2—24no—
715C2—2122no—
716C2#2027753911yescharacteristic
717C2C2×#1681063011yescharacteristic
718C2#2028324011yescharacteristic
719C2#2028679411yescharacteristic
720C2#2028682411yescharacteristic
721C2#2028716811yescharacteristic
722C2#2028719811yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1824C2
socleC23×C53C22×D4
prime radicalC22×C22⋊D53D4
cosocleC22×C4×C53C24
hypercenter#1824D53
hypocenterC53#22497
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1824

Complements

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

NH ≅ G/Ntype
4. #20275686C2semidirect
5. #20275665C2semidirect
6. #20275147C2semidirect
7. #20275136C2semidirect
8. #20275026C2semidirect
9. #20275020C2semidirect
10. #20274800C2semidirect
11. #20274729C2semidirect
12. #20274544C2semidirect
13. #20274433C2semidirect
14. C2×#16810385C2semidirect
15. C53×#1824C2semidirect
19. #16811328C4semidirect
77. #13133216C2×C4semidirect
80. #13133197C2×C4semidirect
86. #13133182C2×C4semidirect
105. C4⋊C4×D53C2×C4semidirect
362. #1824D53semidirect
423. C53#22497semidirect

Maximal subgroups

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

subgroupindex
C2×#168113282
C2×#168106912
#202776462
#202756862
#202756652
#202751472
#202751362
#202750262
#202750202
#202748002
#202747292
#202745442
#202744332
C2×#168103852
C53×#18242
#2249753