Finite Group Databasebeta

← D53⋊#1986 #28320530

Subgroups — D53⋊#1986 #28320530

Order 13568.

1290 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D53⋊M16C211yesmaximal, characteristic
2C2×C4×C4⋊#6157C211yesmaximal, characteristic
3#20290892C214yesmaximal, complemented
4#20290891C212yesmaximal, complemented
5#20290890C212yesmaximal, complemented
6#20290391C214yesmaximal
7#533×D53C211yesmaximal, characteristic
8C2×D53⋊M16C2212yes—
9C22×C4⋊#6157—21no—
10C22×C4×#6157C2212yes—
11C4×#11719936C2212yes—
12C4×#11719936C2212yes—
13C4×#11719940—21no—
14C4×#11719940—21no—
15#16811582—21no—
16C4×D53⋊C8—21no—
17C4×C4⋊#6157—21no—
18C4×C4⋊#6157—21no—
19C4×C4⋊#6157C2212yes—
20C4×C4⋊#6157C2212yes—
21C2×(C2×#6157)⋊C4—21no—
22#16811493C2218yes—
23#16811493C2218yes—
24#16811180C411yescharacteristic, complemented
25#16811179C2212yes—
26#16811178C2211yescharacteristic
27#16811178C2211yescharacteristic
28#16811177—21no—
29#16811177—21no—
30#16811176C412yescomplemented
31#16811175—21no—
32#16811175—21no—
33C4⋊Q8×D53C411yescharacteristic, complemented
34C4⋊Q8×D53C411yescharacteristic, complemented
35#125×D53C412yescomplemented
36C22⋊Q8×D53—21no—
37C22⋊Q8×D53—21no—
38C4×Q8×D53—21no—
39C4×Q8×D53—21no—
40#117×D53C2212yes—
41C2×C42×D53C2211yescharacteristic
42C53×#533C411yescharacteristic, complemented
43C23×#6157—22no—
44C2×#11719936C2314yes—
45D53⋊M16—24no—
46D53⋊M16Q818yescomplemented
47C2×#11719940—22no—
48C2×D53⋊C8—22no—
49C2×C4⋊#6157—28no—
50C2×C4⋊#6157—22no—
51C2×C4⋊#6157—22no—
52C2×C4×#6157—28no—
53C2×C4×#6157—22no—
54C2×C4×#6157C2314yes—
55#13133272—22no—
56#13133272—22no—
57C4×#88324—22no—
58C4×#88324—22no—
59(C2×#6157)⋊C4—22no—
60(C2×#6157)⋊C4—22no—
61C2×Q8×D53—21no—
62C2×Q8×D53—21no—
63C22×C4×D53D411yescharacteristic
64C22×C4×D53D411yescharacteristic
65C22×C4×D53C2311yescharacteristic
66#13133217C2×C411yescharacteristic, complemented
67#13133217C2×C411yescharacteristic, complemented
68#13133216—21no—
69#13133216—21no—
70#13133216C2×C412yescomplemented
71#13133216C2×C412yescomplemented
72#13133215—21no—
73#13133215—21no—
74#13133209C2×C412yescomplemented
75#13133208C2×C412yescomplemented
76#13133208C2×C412yescomplemented
77#13133207—22no—
78#13133207—22no—
79#13133197—21no—
80#13133197—21no—
81#13133196—21no—
82#13133196—21no—
83#13133195—22no—
84#13133195—22no—
85#13133194—22no—
86#13133194—22no—
87#13133193—21no—
88#13133193—21no—
89Q8×Dic53—21no—
90Q8×Dic53—21no—
91C4×Dic106—21no—
92C4×Dic106—21no—
93C4×Dic106—22no—
94C4×Dic106—22no—
95#13133182—21no—
96#13133182—21no—
97#13133182—22no—
98#13133182—22no—
99#13133176C2×C412yes—
100#13133175C2312yes—
101#13133175C2312yes—
102#13133174—22no—
103#13133173—22no—
104C4⋊C4×D53—22no—
105C4⋊C4×D53—22no—
106C4⋊C4×D53—21no—
107C4⋊C4×D53—21no—
108C4⋊C4×D53C2×C412yes—
109C4⋊C4×D53C2×C412yes—
110C22⋊C4×D53—22no—
111C2×C4×Dic53C2×C411yescharacteristic
112C2×C4×Dic53D411yescharacteristic
113C2×C4×Dic53D411yescharacteristic
114C42×D53—22no—
115C42×D53C2×C411yescharacteristic
116C42×D53C2×C411yescharacteristic
117C42×D53D411yescharacteristic
118C42×D53D411yescharacteristic
119C42×D53D411yescharacteristic
120C42×D53D411yescharacteristic
121C42×D53C2311yescharacteristic
122C42×D53C2311yescharacteristic
123C4⋊Q8×C53C2×C411yescharacteristic, complemented
124C4⋊Q8×C53C2×C411yescharacteristic, complemented
125#125×C53C2×C412yescomplemented
126C22⋊Q8×C53—21no—
127C22⋊Q8×C53—21no—
128C4×Q8×C53—21no—
129C4×Q8×C53—21no—
130#117×C53C2×C412yes—
131C2×C42×C53C2×C411yescharacteristic
132C23×D53C2×D411yescharacteristic
133C22×#6157—28no—
134C22×#6157—24no—
135C22×#6157—44no—
136C22×#6157—44no—
137C2×Q8×C53—21no—
138C2×Q8×C53—21no—
139C22×C4×C53C22⋊C411yescharacteristic
140C22×C4×C53C22⋊C411yescharacteristic
141C22×C4×C53C22×C411yescharacteristic
142C22×Dic53C22⋊C411yescharacteristic
143C22×Dic53C22⋊C411yescharacteristic
144C22×Dic53C2×D411yescharacteristic
145Q8×D53—44no—
146Q8×D53—44no—
147C2×C4×D53—24no—
148C2×C4×D53—22no—
149C2×C4×D53—22no—
150C2×C4×D53—42no—
151C2×C4×D53C22⋊C411yescharacteristic
152C2×C4×D53C22⋊C411yescharacteristic
153C2×C4×D53C22⋊C411yescharacteristic
154C2×C4×D53C22⋊C411yescharacteristic
155C2×C4×D53C22×C411yescharacteristic
156C2×C4×D53C2×D411yescharacteristic
157C2×C4×D53C2×D411yescharacteristic
158C2×C4×D53C2×D411yescharacteristic
159C2×C4×D53C2×D411yescharacteristic
160C2×C4×D53C2×D411yescharacteristic
161C2×C4×D53C2×D411yescharacteristic
162C2×C4×D53C2×Q814yes—
163C2×C4×D53#4114yes—
164C2×C4×D53C2411yescharacteristic
165C2×Dic106—21no—
166C2×Dic106—21no—
167C2×Dic106—22no—
168C2×Dic106—22no—
169#11719940—28no—
170C2×#88324—24no—
171C4⋊#6157—28no—
172C4⋊#6157—28no—
173C4×#6157—28no—
174C4×#6157—44no—
175#11719936—24no—
176#11719936C2×Q818yescomplemented
177D53⋊C8—28no—
178C4⋊C4×C53—22no—
179C4⋊C4×C53—22no—
180C4⋊C4×C53—21no—
181C4⋊C4×C53—21no—
182C4⋊C4×C53C22×C412yes—
183C4⋊C4×C53C22×C412yes—
184C22⋊C4×C53—22no—
185C42×C53—22no—
186C42×C53C22⋊C411yescharacteristic
187C42×C53C22⋊C411yescharacteristic
188C42×C53C22×C411yescharacteristic
189C42×C53C22×C411yescharacteristic
190C22⋊Dic53—22no—
191#11719921—22no—
192#11719921—22no—
193C4⋊Dic53—21no—
194C4⋊Dic53—21no—
195C4⋊Dic53—22no—
196C4⋊Dic53—22no—
197C4⋊Dic53C22×C412yes—
198C4⋊Dic53C22×C412yes—
199#11719919—22no—
200#11719919—22no—
201#11719919—22no—
202#11719919—22no—
203#11719919—22no—
204#11719919—22no—
205#11719919—22no—
206#11719919—22no—
207C4×Dic53—22no—
208C4×Dic53—22no—
209C4×Dic53—22no—
210C4×Dic53C22⋊C411yescharacteristic
211C4×Dic53C22⋊C411yescharacteristic
212C4×Dic53C22⋊C411yescharacteristic
213C4×Dic53C22⋊C411yescharacteristic
214C4×Dic53C22⋊C411yescharacteristic
215C4×Dic53C22⋊C411yescharacteristic
216C4×Dic53C22×C411yescharacteristic
217C4×Dic53C22×C411yescharacteristic
218C4×Dic53C2×D411yescharacteristic
219C4×Dic53C2×D411yescharacteristic
220C4×Dic53C2×D411yescharacteristic
221C4×Dic53C2×D411yescharacteristic
222C23×C53C2×C22⋊C411yescharacteristic
223C22×D53—22no—
224C22×D53—22no—
225C22×D53C2×C22⋊C411yescharacteristic
226C22×D53#12412yes—
227C22×D53C4⋊Q812yes—
228C22×D53C22×D411yescharacteristic
229C2×#6157—28no—
230C2×#6157—44no—
231C2×#6157—416no—
232C2×#6157—44no—
233Q8×C53—42no—
234Q8×C53—42no—
235C2×C4×C53—22no—
236C2×C4×C53—22no—
237C2×C4×C53—22no—
238C2×C4×C53—41no—
239C2×C4×C53C2×C22⋊C411yescharacteristic
240C2×C4×C53C2×C22⋊C411yescharacteristic
241C2×C4×C53C2×C22⋊C411yescharacteristic
242C2×C4×C53C2×C22⋊C411yescharacteristic
243C2×C4×C53C2×C22⋊C411yescharacteristic
244C2×C4×C53C4×Q814yes—
245C2×C4×C53C23×C411yescharacteristic
246C2×Dic53—22no—
247C2×Dic53—22no—
248C2×Dic53—22no—
249C2×Dic53—41no—
250C2×Dic53C2×C22⋊C411yescharacteristic
251C2×Dic53C2×C22⋊C411yescharacteristic
252C2×Dic53C2×C22⋊C411yescharacteristic
253C2×Dic53C2×C22⋊C411yescharacteristic
254C2×Dic53C2×C22⋊C411yescharacteristic
255C2×Dic53C22⋊Q814yes—
256C2×Dic53C22×D411yescharacteristic
257C4×D53—22no—
258C4×D53—22no—
259C4×D53—22no—
260C4×D53—22no—
261C4×D53—22no—
262C4×D53—41no—
263C4×D53—41no—
264C4×D53—44no—
265C4×D53—44no—
266C4×D53#10414yes—
267C4×D53C4×Q814yes—
268C4×D53C22⋊Q814yes—
269C4×D53#12412yes—
270C4×D53C4⋊Q812yes—
271C4×D53C22×Q812yes—
272C4×D53C2×#4112yes—
273Dic106—44no—
274Dic106—42no—
275Dic106—42no—
276Dic106—44no—
277#88324—28no—
278C2×#1986—531nomaximal, Sylow
279C22×C53—21no—
280C22×C53—21no—
281C22×C53#39112yes—
282C22×C53C22×C22⋊C411yescharacteristic
283C2×D53—21no—
284C2×D53—21no—
285C2×D53—24no—
286C2×D53—24no—
287C2×D53#39112yes—
288C2×D53C2×#10412yes—
289C2×D53#42112yes—
290C2×D53C2×#12411yescharacteristic
291C2×D53C2×C4⋊Q811yescharacteristic
292#6157—48no—
293C4×C53—21no—
294C4×C53—21no—
295C4×C53—21no—
296C4×C53—42no—
297C4×C53—42no—
298C4×C53#39112yes—
299C4×C53C2×#10412yes—
300C4×C53C2×C4×Q812yes—
301Dic53—21no—
302Dic53—21no—
303Dic53—21no—
304Dic53—42no—
305Dic53—42no—
306Dic53#39112yes—
307Dic53C2×#10412yes—
308Dic53C2×C22⋊Q812yes—
309C2×#533—531no—
310C2×C4×M16—531no—
311C2×C4×C4⋊C4—531no—
312#1986—532no—
313#1986—532no—
314#1986—534no—
315C2×#339—534no—
316C2×C53—22no—
317C2×C53C2×#39111yescharacteristic
318C2×C53C22×#10411yescharacteristic
319C2×C53C2×#42111yescharacteristic
320D53—21no—
321D53—21no—
322D53#198614yescomplemented
323C22×M16—532no—
324#533—531no—
325#533—531no—
326#533—532no—
327#533—532no—
328#533—531no—
329#533—1061no—
330#533—1061no—
331#533—1061no—
332#533—1061no—
333#533#615711yescharacteristic, complemented
334C2×C4⋊Q8—531no—
335C2×C4⋊Q8—531no—
336C2×#125—532no—
337C2×C22⋊Q8—1061no—
338C2×C22⋊Q8—1061no—
339C2×C4×Q8—1061no—
340C2×C4×Q8—1061no—
341C2×#117—532no—
342C22×C4⋊C4—1061no—
343C22×C42—531no—
344C22×C42—532no—
345C4×M16—532no—
346C4×M16—532no—
347C4×M16—1061no—
348C4×M16—1061no—
349C2×#97—1061no—
350C2×C4×C8—1061no—
351C4×C4⋊C4—532no—
352C4×C4⋊C4—532no—
353C4×C4⋊C4—1061no—
354C4×C4⋊C4—1061no—
355C2×#95—1061no—
356#339—538no—
357#339—538no—
358C53C2×#198611yescharacteristic, complemented, Sylow
359C22×Q8—1061no—
360C22×Q8—1061no—
361C23×C4—531no—
362C23×C4—531no—
363C23×C4—531no—
364C23×C4—1062no—
365C2×M16—534no—
366C2×M16—538no—
367C2×M16—1062no—
368C2×M16—1064no—
369C22×C8—1062no—
370C4⋊Q8—532no—
371C4⋊Q8—532no—
372C4⋊Q8—531no—
373C4⋊Q8—531no—
374C4⋊Q8—1061no—
375C4⋊Q8—1061no—
376C4⋊Q8—1061no—
377C4⋊Q8—1061no—
378C4⋊Q8C2×#615711yescharacteristic, complemented
379C4⋊Q8C2×#615711yescharacteristic, complemented
380#125—532no—
381#125—532no—
382#125—532no—
383#125—1062no—
384#125—1062no—
385#125C2×#615712yescomplemented
386C22⋊Q8—21no—
387C22⋊Q8—21no—
388C22⋊Q8—1062no—
389C22⋊Q8—1062no—
390C22⋊Q8—1062no—
391C22⋊Q8—1062no—
392C22⋊Q8—1061no—
393C22⋊Q8—1061no—
394C22⋊Q8—1061no—
395C22⋊Q8—1061no—
396C22⋊Q8—1061no—
397C22⋊Q8—1061no—
398C4×Q8—21no—
399C4×Q8—21no—
400C4×Q8—1062no—
401C4×Q8—1062no—
402C4×Q8—1062no—
403C4×Q8—1061no—
404C4×Q8—1062no—
405C4×Q8—1061no—
406C4×Q8—1061no—
407C4×Q8—1061no—
408C4×Q8—1061no—
409C4×Q8—1061no—
410#117—532no—
411#117—532no—
412#117—532no—
413#117—1062no—
414#117—1062no—
415#117C2×#615712yes—
416C2×C4⋊C4—532no—
417C2×C4⋊C4—532no—
418C2×C4⋊C4—1062no—
419C2×C4⋊C4—1062no—
420C2×C4⋊C4—1061no—
421C2×C4⋊C4—1061no—
422C2×C4⋊C4—1062no—
423C2×C4⋊C4—1062no—
424C2×C4⋊C4—1068no—
425C2×C22⋊C4—1062no—
426C2×C42—531no—
427C2×C42—531no—
428C2×C42—531no—
429C2×C42—531no—
430C2×C42—531no—
431C2×C42—531no—
432C2×C42—531no—
433C2×C42—531no—
434C2×C42—531no—
435C2×C42—531no—
436C2×C42—531no—
437C2×C42—534no—
438C2×C42—1062no—
439C2×C42—1068no—
440C2×C42—1062no—
441C2×C42C2×#615711yescharacteristic
442#97—1062no—
443#97—1062no—
444C4×C8—1062no—
445C4×C8—1062no—
446#95—1062no—
447#95—1062no—
448C24—531no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—1062no—
452C2×Q8—1062no—
453C2×Q8—1061no—
454C2×Q8—1061no—
455C2×Q8—2124no—
456C2×Q8—2124no—
457C22×C4—531no—
458C22×C4—531no—
459C22×C4—531no—
460C22×C4—531no—
461C22×C4—534no—
462C22×C4—534no—
463C22×C4—531no—
464C22×C4—531no—
465C22×C4—531no—
466C22×C4—531no—
467C22×C4—531no—
468C22×C4—531no—
469C22×C4—531no—
470C22×C4—531no—
471C22×C4—531no—
472C22×C4—531no—
473C22×C4—531no—
474C22×C4—1064no—
475C22×C4—1062no—
476C22×C4—1062no—
477C22×C4—1064no—
478C22×C4—1068no—
479C22×C4—2122no—
480C22×C4—2124no—
481C22×C4—2124no—
482C22×C4C22⋊#615711yescharacteristic
483C22×C4C22⋊#615711yescharacteristic
484C22×C4C22×#615711yescharacteristic
485M16—538no—
486M16—1064no—
487M16—1068no—
488C2×C8—1064no—
489C2×C8—1068no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—532no—
495C4⋊C4—532no—
496C4⋊C4—1062no—
497C4⋊C4—1062no—
498C4⋊C4—1062no—
499C4⋊C4—1062no—
500C4⋊C4—1062no—
501C4⋊C4—1062no—
502C4⋊C4—1062no—
503C4⋊C4—1062no—
504C4⋊C4—1068no—
505C4⋊C4—1068no—
506C4⋊C4—1062no—
507C4⋊C4—1062no—
508C4⋊C4—1061no—
509C4⋊C4—1061no—
510C4⋊C4C22×#615712yes—
511C4⋊C4C22×#615712yes—
512C22⋊C4—22no—
513C22⋊C4—1062no—
514C22⋊C4—1062no—
515C22⋊C4—1062no—
516C42—22no—
517C42—531no—
518C42—531no—
519C42—531no—
520C42—531no—
521C42—531no—
522C42—531no—
523C42—531no—
524C42—531no—
525C42—531no—
526C42—531no—
527C42—531no—
528C42—531no—
529C42—1062no—
530C42—1062no—
531C42—1068no—
532C42—1062no—
533C42—2124no—
534C42C22⋊#615711yescharacteristic
535C42C22⋊#615711yescharacteristic
536C42C22×#615711yescharacteristic
537C42C22×#615711yescharacteristic
538C23—531no—
539C23—532no—
540C23—532no—
541C23—531no—
542C23—1062no—
543C23—1062no—
544C23C2×C22⋊#615711yescharacteristic
545Q8—42no—
546Q8—42no—
547Q8—2122no—
548Q8—2124no—
549Q8—2124no—
550Q8—2122no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—41no—
555C2×C4—534no—
556C2×C4—531no—
557C2×C4—531no—
558C2×C4—531no—
559C2×C4—534no—
560C2×C4—532no—
561C2×C4—532no—
562C2×C4—534no—
563C2×C4—534no—
564C2×C4—532no—
565C2×C4—532no—
566C2×C4—531no—
567C2×C4—531no—
568C2×C4—531no—
569C2×C4—1062no—
570C2×C4—1062no—
571C2×C4—1062no—
572C2×C4—1062no—
573C2×C4—1062no—
574C2×C4—1062no—
575C2×C4—1068no—
576C2×C4—1062no—
577C2×C4—1062no—
578C2×C4—2121no—
579C2×C4—2121no—
580C2×C4—2124no—
581C2×C4—2124no—
582C2×C4—2121no—
583C2×C4—2124no—
584C2×C4—21216no—
585C2×C4—2124no—
586C2×C4C2×C22⋊#615711yescharacteristic
587C2×C4C2×C22⋊#615711yescharacteristic
588C2×C4C2×C22⋊#615711yescharacteristic
589C2×C4C2×C22⋊#615711yescharacteristic
590C2×C4C2×C22⋊#615711yescharacteristic
591C2×C4Q8×#615714yes—
592C2×C4C23×#615711yescharacteristic
593C8—1068no—
594C22—21no—
595C22—21no—
596C22—532no—
597C22—532no—
598C22—532no—
599C22—531no—
600C22—531no—
601C22—1064no—
602C22—1064no—
603C22—1061no—
604C22—1061no—
605C22(C2×#6157)⋊Q812yes—
606C22C22×C22⋊#615711yescharacteristic
607C4—21no—
608C4—21no—
609C4—21no—
610C4—42no—
611C4—42no—
612C4—532no—
613C4—532no—
614C4—532no—
615C4—1061no—
616C4—1061no—
617C4—1061no—
618C4—2128no—
619C4—2122no—
620C4—2122no—
621C4(C2×#6157)⋊Q812yes—
622C4D53⋊#10412yes—
623C4C2×Q8×#615712yes—
624C2—22no—
625C2—534no—
626C2—1061no—
627C2—1061no—
628C2C2×(C2×#6157)⋊Q811yescharacteristic
629C2C2×D53⋊#10411yescharacteristic
630C2D53⋊#42111yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6157
commutatorC2×C4×C53C23×C4
FrattiniC2×C4C23×#6157
FittingC53×#533C4
socleC22×C53C22×C22⋊C4
prime radicalC23×D53C2×D4
cosocleC2×C4×D53C24
hypercenter#533#6157
hypocenterC53C2×#1986
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
3. #20290892C2semidirect
4. #20290891C2semidirect
5. #20290890C2semidirect
24. #16811180C4semidirect
30. #16811176C4semidirect
33. C4⋊Q8×D53C4semidirect
34. C4⋊Q8×D53C4semidirect
35. #125×D53C4semidirect
42. C53×#533C4semidirect
46. D53⋊M16Q8semidirect
66. #13133217C2×C4semidirect
67. #13133217C2×C4semidirect
70. #13133216C2×C4semidirect
71. #13133216C2×C4semidirect
74. #13133209C2×C4semidirect
75. #13133208C2×C4semidirect
76. #13133208C2×C4semidirect
123. C4⋊Q8×C53C2×C4semidirect
124. C4⋊Q8×C53C2×C4semidirect
125. #125×C53C2×C4semidirect
176. #11719936C2×Q8semidirect
322. D53#1986semidirect
333. #533#6157semidirect
358. C53C2×#1986semidirect
378. C4⋊Q8C2×#6157semidirect
379. C4⋊Q8C2×#6157semidirect
385. #125C2×#6157semidirect

Maximal subgroups

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

subgroupindex
C4×D53⋊M162
C2×C4×C4⋊#61572
#202908922
#202908912
#202908902
#202903912
#533×D532
C2×#198653