Finite Group Databasebeta

← D53×#1892 #27385751

Subgroups — D53×#1892 #27385751

Order 13568.

2094 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C8×D53C211yesmaximal, characteristic
2C2×C22⋊Q8×D53C211yesmaximal, characteristic
3C2×#103×D53C212yesmaximal, complemented
4#380×D53C211yesmaximal, characteristic
5#20275139C211yesmaximal, characteristic, complemented
6#20275138C211yesmaximal, characteristic, complemented
7#20275137C212yesmaximal, complemented
8#20275136C211yesmaximal, characteristic, complemented
9#20275135C212yesmaximal, complemented
10#340×D53C212yesmaximal, complemented
11C53×#1892C211yesmaximal, characteristic, complemented
12C22×Q8×D53C2211yescharacteristic
13C23×C4×D53C2211yescharacteristic
14C23×#88322C2211yescharacteristic
15C22×C8×D53—24no—
16C22×C8×D53—28no—
17C22×C8×D53C2212yes—
18C22×C8×D53C2212yes—
19C2×#13133197C2211yescharacteristic
20C2×#13133196C2211yescharacteristic
21C2×#13133195—21no—
22C2×#13133194—21no—
23C2×#13133193C2211yescharacteristic
24C22⋊Q8×D53—24no—
25C22⋊Q8×D53C418yescomplemented
26C2×C4⋊C4×D53—21no—
27C2×C4⋊C4×D53C2212yes—
28C2×C4⋊C4×D53C2211yescharacteristic
29C2×C22⋊C4×D53—21no—
30C2×C22⋊C4×D53—21no—
31C2×#13133142C2212yescomplemented
32C2×#13133141C2212yescomplemented
33C2×#13133140C2212yescomplemented
34#103×D53—28no—
35#16810483C2211yescharacteristic
36#16810482—21no—
37#16810481—21no—
38#16810480C2212yes—
39#95×D53—21no—
40#16810386C2212yescomplemented
41#16810385C2212yescomplemented
42#16810385C2212yescomplemented
43C23×C8×C53C2211yescharacteristic
44C2×C22⋊Q8×C53C2211yescharacteristic
45C2×#103×C53C2212yescomplemented
46C53×#380C2211yescharacteristic
47C53×#340C2212yescomplemented
48C24×D53D411yescharacteristic
49C22×Dic106—21no—
50C22×Dic106C2311yescharacteristic
51C2×Q8×D53—22no—
52C2×Q8×D53—24no—
53C2×Q8×D53—24no—
54C2×Q8×D53C2×C414yes—
55C23×Dic53D411yescharacteristic
56C22×C4×D53—24no—
57C22×C4×D53—24no—
58C22×C4×D53—21no—
59C22×C4×D53—21no—
60C22×C4×D53—22no—
61C22×C4×D53C2×C414yes—
62C22×C4×D53D411yescharacteristic
63C22×C4×D53D411yescharacteristic
64C22×C4×D53D414yes—
65C22×C4×D53C2311yescharacteristic
66C22×C4×D53C2311yescharacteristic
67C22×#88322—24no—
68C22×#88322—22no—
69C22×#88322C2312yes—
70C2×C8×D53—232no—
71C2×C8×D53—24no—
72C2×C8×D53—24no—
73C2×C8×D53—24no—
74C2×C8×D53—24no—
75C2×C8×D53—24no—
76C2×C8×D53D418yes—
77#13133197—22no—
78#13133197C2×C414yescomplemented
79#13133196—22no—
80#13133196C2×C414yescomplemented
81#13133195—28no—
82#13133194—28no—
83#13133193—22no—
84#13133193C2×C414yescomplemented
85C2×C4⋊Dic53—21no—
86C2×C4⋊Dic53C2312yes—
87C2×C4⋊Dic53C2311yescharacteristic
88C2×#11719919—21no—
89C2×#11719919—21no—
90C2×#11719919—21no—
91C2×#11719919—22no—
92C4⋊C4×D53—28no—
93C4⋊C4×D53—22no—
94C4⋊C4×D53—24no—
95C4⋊C4×D53—24no—
96C4⋊C4×D53C2×C414yes—
97C2×C22⋊Dic53—21no—
98C2×C22⋊Dic53—21no—
99C2×#11719921—21no—
100C2×#11719921—21no—
101C2×#11719921—22no—
102C22⋊C4×D53—28no—
103C22⋊C4×D53—44no—
104#13133142—24no—
105#13133141—24no—
106#13133140—24no—
107#13133124—21no—
108#13133124—22no—
109C22×Q8×C53C2311yescharacteristic
110C23×C4×C53C2311yescharacteristic
111C22×C8×C53—24no—
112C22×C8×C53—22no—
113C22×C8×C53C2312yes—
114C22⋊Q8×C53—22no—
115C22⋊Q8×C53C2×C414yescomplemented
116C2×C4⋊C4×C53—21no—
117C2×C4⋊C4×C53C2312yes—
118C2×C4⋊C4×C53C2311yescharacteristic
119C2×C22⋊C4×C53—21no—
120C2×C22⋊C4×C53—21no—
121#103×C53—24no—
122#95×C53—21no—
123C24×C53C2×D411yescharacteristic
124C23×D53—24no—
125C23×D53—24no—
126C23×D53C22⋊C414yes—
127C23×D53SD1614yes—
128C23×D53Q1614yes—
129C23×D53C2×D411yescharacteristic
130C23×D53C2×D411yescharacteristic
131C2×Q8×C53—21no—
132C2×Q8×C53—22no—
133C2×Q8×C53—22no—
134C2×Q8×C53C22×C412yes—
135C22×C4×C53—22no—
136C22×C4×C53—22no—
137C22×C4×C53—21no—
138C22×C4×C53—21no—
139C22×C4×C53—22no—
140C22×C4×C53C22×C412yes—
141C22×C4×C53C2×D411yescharacteristic
142C22×C4×C53C2×D412yes—
143C22×C4×C53C2411yescharacteristic
144C22×Dic53—24no—
145C22×Dic53—21no—
146C22×Dic53—21no—
147C22×Dic53—22no—
148C22×Dic53C22⋊C414yes—
149C22×Dic53C2×D411yescharacteristic
150C22×Dic53C2×D411yescharacteristic
151Q8×D53—216no—
152Q8×D53—44no—
153Q8×D53—44no—
154C2×C4×D53—24no—
155C2×C4×D53—22no—
156C2×C4×D53—22no—
157C2×C4×D53—24no—
158C2×C4×D53—216no—
159C2×C4×D53—28no—
160C2×C4×D53—28no—
161C2×C4×D53—24no—
162C2×C4×D53—24no—
163C2×C4×D53—44no—
164C2×C4×D53—44no—
165C2×C4×D53—44no—
166C2×C4×D53—44no—
167C2×C4×D53—44no—
168C2×C4×D53C22⋊C414yes—
169C2×C4×D53C22⋊C414yes—
170C2×C4×D53C22×C412yes—
171C2×C4×D53C22×C412yes—
172C2×C4×D53C2×D412yes—
173C2×C4×D53C2×D414yes—
174C2×C4×D53C2×D412yes—
175C2×C4×D53#4114yes—
176C2×Dic106—22no—
177C2×Dic106—22no—
178C2×Dic106—21no—
179C2×Dic106—24no—
180C2×Dic106—44no—
181C2×Dic106C22×C412yes—
182C2×C8×C53—28no—
183C2×C8×C53—22no—
184C2×C8×C53—22no—
185C2×C8×C53C2×D414yes—
186C4⋊C4×C53—24no—
187C4⋊C4×C53—21no—
188C4⋊C4×C53—22no—
189C4⋊C4×C53—22no—
190C4⋊C4×C53C22×C412yes—
191C22⋊C4×C53—24no—
192C22⋊C4×C53—42no—
193C22⋊Dic53—24no—
194C22⋊Dic53—42no—
195#11719921—24no—
196#11719921—24no—
197#11719921—44no—
198C4⋊Dic53—21no—
199C4⋊Dic53—24no—
200C4⋊Dic53—22no—
201C4⋊Dic53—22no—
202C4⋊Dic53C22×C412yes—
203#11719919—24no—
204#11719919—24no—
205#11719919—24no—
206#11719919—44no—
207C2×#88322—28no—
208C2×#88322—22no—
209C2×#88322—22no—
210C2×#88322C2×D414yes—
211C8×D53—216no—
212C8×D53—216no—
213C23×C53—22no—
214C23×C53—22no—
215C23×C53C2×C22⋊C412yes—
216C23×C53C2×SD1612yes—
217C23×C53C2×Q1612yes—
218C23×C53C22×D411yescharacteristic
219C22×D53—22no—
220C22×D53—22no—
221C22×D53—28no—
222C22×D53—28no—
223C22×D53—216no—
224C22×D53—216no—
225C22×D53#103116yescomplemented
226C22×D53C2×C22⋊C412yes—
227C22×D53C2×C22⋊C412yes—
228C22×D53#12114yes—
229C22×D53C2×SD1612yes—
230C22×D53C2×SD1612yes—
231C22×D53C2×Q1612yes—
232C22×D53C2×Q1612yes—
233C22×D53#13514yes—
234Q8×C53—24no—
235Q8×C53—41no—
236Q8×C53—41no—
237C2×C4×C53—22no—
238C2×C4×C53—24no—
239C2×C4×C53—22no—
240C2×C4×C53—22no—
241C2×C4×C53—22no—
242C2×C4×C53—22no—
243C2×C4×C53—42no—
244C2×C4×C53—42no—
245C2×C4×C53—42no—
246C2×C4×C53—42no—
247C2×C4×C53—42no—
248C2×C4×C53C2×C22⋊C412yes—
249C2×C4×C53C23×C411yescharacteristic
250C2×C4×C53C22×D412yes—
251C2×C4×C53C22×D411yescharacteristic
252C2×C4×C53C2×#4112yes—
253C2×Dic53—22no—
254C2×Dic53—28no—
255C2×Dic53—22no—
256C2×Dic53—22no—
257C2×Dic53—42no—
258C2×Dic53—42no—
259C2×Dic53—42no—
260C2×Dic53—42no—
261C2×Dic53—42no—
262C2×Dic53C2×C22⋊C412yes—
263C2×Dic53C2×C22⋊C412yes—
264C2×Dic53#12114yes—
265C4×D53—28no—
266C4×D53—24no—
267C4×D53—22no—
268C4×D53—22no—
269C4×D53—28no—
270C4×D53—48no—
271C4×D53—48no—
272C4×D53—88no—
273C4×D53C4×D418yes—
274C4×D53#12014yes—
275C4×D53#12314yes—
276Dic106—24no—
277Dic106—41no—
278Dic106—41no—
279Dic106—48no—
280C8×C53—24no—
281#88322—24no—
282C2×#1892—531nomaximal, Sylow
283C22×C53—22no—
284C22×C53—24no—
285C22×C53—24no—
286C22×C53—22no—
287C22×C53C2×#10314yescomplemented
288C22×C53C22×C22⋊C411yescharacteristic
289C22×C53C2×#12112yes—
290C22×C53C22×SD1611yescharacteristic
291C22×C53C22×Q1611yescharacteristic
292C22×C53C2×#13512yes—
293C2×D53—22no—
294C2×D53—24no—
295C2×D53—24no—
296C2×D53—22no—
297C2×D53—232no—
298C2×D53#38614yes—
299C2×D53C2×#10314yes—
300C2×D53C2×#10314yescomplemented
301C2×D53#41614yes—
302C2×D53#46518yes—
303C2×D53#46718yes—
304C4×C53—22no—
305C4×C53—42no—
306C4×C53—42no—
307C4×C53—82no—
308C4×C53C2×C4×D412yes—
309C4×C53C2×#12011yescharacteristic
310C4×C53C2×#12311yescharacteristic
311Dic53—22no—
312Dic53—42no—
313Dic53—42no—
314Dic53—82no—
315Dic53#38614yes—
316C24×C8—531no—
317C22×C22⋊Q8—531no—
318C22×#103—532no—
319C2×#380—531no—
320#1892—532no—
321#1892—531no—
322#1892—532no—
323#1892—531no—
324#1892—531no—
325#1892D5311yescharacteristic, direct product factor
326C2×#340—532no—
327C2×C53—24no—
328C2×C53C2×#38611yescharacteristic
329C2×C53C22×#10311yescharacteristic
330C2×C53C2×#41611yescharacteristic
331C2×C53C2×#46512yes—
332C2×C53C2×#46712yes—
333D53—24no—
334D53#189218yesdirect product factor
335C23×Q8—531no—
336C24×C4—531no—
337C23×C8—532no—
338C23×C8—531no—
339C23×C8—532no—
340C23×C8—1068no—
341C23×C8—1064no—
342C23×C8C2×D5311yescharacteristic
343C2×C22⋊Q8—531no—
344C2×C22⋊Q8—531no—
345C2×C22⋊Q8—538no—
346C2×C22⋊Q8—531no—
347C2×C22⋊Q8—1061no—
348C2×C22⋊Q8—1061no—
349C2×C22⋊Q8—1064no—
350C2×C22⋊Q8C2×D5311yescharacteristic
351C22×C4⋊C4—531no—
352C22×C4⋊C4—532no—
353C22×C4⋊C4—1061no—
354C22×C22⋊C4—1061no—
355C22×C22⋊C4—1061no—
356C2×#103—532no—
357C2×#103—532no—
358C2×#103—532no—
359C2×#103—1068no—
360C2×#103C2×D5312yescomplemented
361#380—531no—
362#380—532no—
363#380—1061no—
364#380—1061no—
365#380C2×D5311yescharacteristic
366C2×#95—1061no—
367#340—532no—
368#340—532no—
369#340—532no—
370#340C2×D5312yescomplemented
371C53C2×#189211yescharacteristic, complemented, Sylow
372C25—531no—
373C22×Q8—534no—
374C22×Q8—531no—
375C22×Q8—1061no—
376C22×Q8—1062no—
377C22×Q8—1064no—
378C22×Q8—1064no—
379C22×Q8C22×D5311yescharacteristic
380C23×C4—531no—
381C23×C4—531no—
382C23×C4—534no—
383C23×C4—531no—
384C23×C4—534no—
385C23×C4—531no—
386C23×C4—531no—
387C23×C4—1064no—
388C23×C4—1064no—
389C23×C4—1061no—
390C23×C4—1061no—
391C23×C4—1062no—
392C23×C4C22×D5311yescharacteristic
393C22×C8—22no—
394C22×C8—24no—
395C22×C8—532no—
396C22×C8—538no—
397C22×C8—1064no—
398C22×C8—1064no—
399C22×C8—1064no—
400C22×C8—1064no—
401C22×C8—10632no—
402C22×C8—1064no—
403C22×C8—1062no—
404C22×C8—1064no—
405C22×C8C22×D5312yes—
406C22⋊Q8—22no—
407C22⋊Q8—534no—
408C22⋊Q8—534no—
409C22⋊Q8—534no—
410C22⋊Q8—1068no—
411C22⋊Q8—1068no—
412C22⋊Q8—1062no—
413C22⋊Q8—1062no—
414C22⋊Q8—1062no—
415C22⋊Q8C4×D5314yescomplemented
416C2×C4⋊C4—21no—
417C2×C4⋊C4—531no—
418C2×C4⋊C4—534no—
419C2×C4⋊C4—532no—
420C2×C4⋊C4—1062no—
421C2×C4⋊C4—1068no—
422C2×C4⋊C4—1064no—
423C2×C4⋊C4—1064no—
424C2×C4⋊C4—1061no—
425C2×C4⋊C4—1061no—
426C2×C4⋊C4—1061no—
427C2×C4⋊C4—1061no—
428C2×C4⋊C4—1062no—
429C2×C4⋊C4C22×D5312yes—
430C2×C4⋊C4C22×D5311yescharacteristic
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—1068no—
434C2×C22⋊C4—1061no—
435C2×C22⋊C4—1061no—
436C2×C22⋊C4—1061no—
437C2×C22⋊C4—1062no—
438C2×C22⋊C4—1061no—
439C2×C22⋊C4—2124no—
440#103—24no—
441#103—1064no—
442#103—1064no—
443#103—1064no—
444#95—21no—
445#95—1062no—
446#95—1061no—
447C24—531no—
448C24—534no—
449C24—534no—
450C24—534no—
451C24—531no—
452C24—1064no—
453C24—1064no—
454C24D4×D5311yescharacteristic
455C2×Q8—21no—
456C2×Q8—22no—
457C2×Q8—22no—
458C2×Q8—532no—
459C2×Q8—1064no—
460C2×Q8—10616no—
461C2×Q8—1061no—
462C2×Q8—1062no—
463C2×Q8—1062no—
464C2×Q8—2124no—
465C2×Q8—2124no—
466C2×Q8—2124no—
467C2×Q8C2×C4×D5312yes—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—531no—
474C22×C4—532no—
475C22×C4—534no—
476C22×C4—532no—
477C22×C4—534no—
478C22×C4—534no—
479C22×C4—531no—
480C22×C4—534no—
481C22×C4—534no—
482C22×C4—532no—
483C22×C4—532no—
484C22×C4—1068no—
485C22×C4—1064no—
486C22×C4—10616no—
487C22×C4—1068no—
488C22×C4—1064no—
489C22×C4—1064no—
490C22×C4—1064no—
491C22×C4—1064no—
492C22×C4—1062no—
493C22×C4—1062no—
494C22×C4—1061no—
495C22×C4—1061no—
496C22×C4—1062no—
497C22×C4—2124no—
498C22×C4—2124no—
499C22×C4—2124no—
500C22×C4—2124no—
501C22×C4—2124no—
502C22×C4C2×C4×D5312yes—
503C22×C4D4×D5311yescharacteristic
504C22×C4D4×D5312yes—
505C22×C4C23×D5311yescharacteristic
506C2×C8—28no—
507C2×C8—22no—
508C2×C8—22no—
509C2×C8—534no—
510C2×C8—10616no—
511C2×C8—10616no—
512C2×C8—1068no—
513C2×C8—1062no—
514C2×C8—1062no—
515C2×C8D4×D5314yes—
516C4⋊C4—24no—
517C4⋊C4—21no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—532no—
521C4⋊C4—1064no—
522C4⋊C4—1064no—
523C4⋊C4—1064no—
524C4⋊C4—1064no—
525C4⋊C4—1061no—
526C4⋊C4—1062no—
527C4⋊C4—1062no—
528C4⋊C4—2124no—
529C4⋊C4C2×C4×D5312yes—
530C22⋊C4—24no—
531C22⋊C4—42no—
532C22⋊C4—1064no—
533C22⋊C4—1064no—
534C22⋊C4—1064no—
535C22⋊C4—2124no—
536C22⋊C4—2122no—
537C23—22no—
538C23—22no—
539C23—532no—
540C23—534no—
541C23—532no—
542C23—532no—
543C23—534no—
544C23—532no—
545C23—5316no—
546C23—532no—
547C23—532no—
548C23—1068no—
549C23—1068no—
550C23—10616no—
551C23—10616no—
552C23—1062no—
553C23—1062no—
554C23C22⋊C4×D5312yes—
555C23SD16×D5312yes—
556C23Q16×D5312yes—
557C23C2×D4×D5311yescharacteristic
558Q8—24no—
559Q8—41no—
560Q8—41no—
561Q8—1064no—
562Q8—2128no—
563Q8—2121no—
564Q8—2121no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—532no—
577C2×C4—534no—
578C2×C4—538no—
579C2×C4—534no—
580C2×C4—534no—
581C2×C4—532no—
582C2×C4—1068no—
583C2×C4—1068no—
584C2×C4—1068no—
585C2×C4—1062no—
586C2×C4—1064no—
587C2×C4—1062no—
588C2×C4—1062no—
589C2×C4—1062no—
590C2×C4—1062no—
591C2×C4—4248no—
592C2×C4—2128no—
593C2×C4—2128no—
594C2×C4—2122no—
595C2×C4—2122no—
596C2×C4—2122no—
597C2×C4—2122no—
598C2×C4—2122no—
599C2×C4C22⋊C4×D5312yes—
600C2×C4C22×C4×D5311yescharacteristic
601C2×C4C2×D4×D5312yes—
602C2×C4C2×D4×D5311yescharacteristic
603C2×C4#41×D5312yes—
604C8—24no—
605C8—1064no—
606C22—22no—
607C22—24no—
608C22—24no—
609C22—22no—
610C22—534no—
611C22—534no—
612C22—538no—
613C22—538no—
614C22—534no—
615C22—534no—
616C22—10632no—
617C22—1062no—
618C22—1064no—
619C22—1064no—
620C22—1062no—
621C22#103×D5314yescomplemented
622C22C2×C22⋊C4×D5311yescharacteristic
623C22#121×D5312yes—
624C22C2×SD16×D5311yescharacteristic
625C22C2×Q16×D5311yescharacteristic
626C22#135×D5312yes—
627C4—22no—
628C4—42no—
629C4—42no—
630C4—82no—
631C4—534no—
632C4—1062no—
633C4—4242no—
634C4—2122no—
635C4—2122no—
636C4C4×D4×D5312yes—
637C4#120×D5311yescharacteristic
638C4#123×D5311yescharacteristic
639C2—24no—
640C2—538no—
641C2—1064no—
642C2#386×D5311yescharacteristic
643C2C2×#103×D5311yescharacteristic
644C2#416×D5311yescharacteristic
645C2#465×D5312yes—
646C2#467×D5312yes—
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1892C2
socleC23×C53C22×D4
prime radicalC24×D53D4
cosocleC22×C4×C53C24
hypercenter#1892D53
hypocenterC53C2×#1892
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1892

Complements

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

NH ≅ G/Ntype
3. C2×#103×D53C2semidirect
5. #20275139C2semidirect
6. #20275138C2semidirect
7. #20275137C2semidirect
8. #20275136C2semidirect
9. #20275135C2semidirect
10. #340×D53C2semidirect
11. C53×#1892C2semidirect
25. C22⋊Q8×D53C4semidirect
31. C2×#13133142C22semidirect
32. C2×#13133141C22semidirect
33. C2×#13133140C22semidirect
40. #16810386C22semidirect
41. #16810385C22semidirect
42. #16810385C22semidirect
45. C2×#103×C53C22semidirect
47. C53×#340C22semidirect
78. #13133197C2×C4semidirect
80. #13133196C2×C4semidirect
84. #13133193C2×C4semidirect
115. C22⋊Q8×C53C2×C4semidirect
225. C22×D53#103semidirect
287. C22×C53C2×#103semidirect
300. C2×D53C2×#103semidirect
325. #1892D53direct (N × H)
334. D53#1892direct (N × H)
360. C2×#103C2×D53semidirect
370. #340C2×D53semidirect
371. C53C2×#1892semidirect
415. C22⋊Q8C4×D53semidirect
621. C22#103×D53semidirect

Maximal subgroups

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

subgroupindex
C23×C8×D532
C2×C22⋊Q8×D532
C2×#103×D532
#380×D532
#202751392
#202751382
#202751372
#202751362
#202751352
#340×D532
C53×#18922
C2×#189253