Finite Group Databasebeta

← D53×#2097 #27413877

Subgroups — D53×#2097 #27413877

Order 13568.

1150 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#107×D53C211yesmaximal, characteristic
2C2×#106×D53C211yesmaximal, characteristic
3C2×#103×D53C211yesmaximal, characteristic
4C2×#103×D53C211yesmaximal, characteristic
5#391×D53C211yesmaximal, characteristic
6#382×D53C211yesmaximal, characteristic
7#20276266C211yesmaximal, characteristic, complemented
8#20276265C211yesmaximal, characteristic, complemented
9#20276264C211yesmaximal, characteristic, complemented
10#20276263C211yesmaximal, characteristic, complemented
11#20276262C211yesmaximal, characteristic, complemented
12#20276261C211yesmaximal, characteristic, complemented
13#20276260C211yesmaximal, characteristic, complemented
14#336×D53C211yesmaximal, characteristic
15C53×#2097C211yesmaximal, characteristic, complemented
16C22×Q8×D53C2211yescharacteristic
17C22×C8×D53C2211yescharacteristic
18C22×C8×D53C2211yescharacteristic
19C2×C4⋊C4×D53C2211yescharacteristic
20C2×C4⋊C4×D53C2211yescharacteristic
21C2×C4⋊C4×D53C2211yescharacteristic
22C2×C42×D53C2211yescharacteristic
23C2×#13133151C2211yescharacteristic
24C2×#13133150C2211yescharacteristic
25C2×#13133150C2211yescharacteristic
26#107×D53—24no—
27C2×#13133149C2211yescharacteristic
28C2×#13133148C2211yescharacteristic
29C2×#13133148C2211yescharacteristic
30#106×D53—24no—
31C2×#13133142C2211yescharacteristic
32C2×#13133142C2211yescharacteristic
33C2×#13133141C2211yescharacteristic
34C2×#13133141C2211yescharacteristic
35C2×#13133140C2211yescharacteristic
36C2×#13133140C2211yescharacteristic
37#103×D53—24no—
38#103×D53—24no—
39#16810530C2211yescharacteristic
40#16810529C2211yescharacteristic
41#16810528C2211yescharacteristic
42#16810527—22no—
43#16810489C2211yescharacteristic
44#16810488C2211yescharacteristic
45#16810488C2211yescharacteristic
46#16810487—22no—
47#95×D53—22no—
48#95×D53—22no—
49#16810378C2211yescharacteristic
50#16810377C2211yescharacteristic
51#16810377C2211yescharacteristic
52C2×#107×C53C2211yescharacteristic
53C2×#106×C53C2211yescharacteristic
54C2×#103×C53C2211yescharacteristic
55C2×#103×C53C2211yescharacteristic
56C53×#391C2211yescharacteristic
57C53×#382C2211yescharacteristic
58C53×#336C2211yescharacteristic
59C22×Dic106—21no—
60C22×Dic106C2311yescharacteristic
61C2×Q8×D53—22no—
62C2×Q8×D53—22no—
63C2×Q8×D53—22no—
64C2×Q8×D53—22no—
65C2×Q8×D53—22no—
66C2×Q8×D53Q814yes—
67C22×C4×D53—21no—
68C22×C4×D53—21no—
69C22×C4×D53—21no—
70C22×C4×D53—21no—
71C22×C4×D53D412yes—
72C22×C4×D53C2311yescharacteristic
73C22×#88322C2311yescharacteristic
74C22×#88322C2311yescharacteristic
75C2×C8×D53—22no—
76C2×C8×D53—22no—
77C2×C8×D53—22no—
78C2×C8×D53—22no—
79C2×C8×D53D414yes—
80C2×C8×D53D414yes—
81C2×C4⋊Dic53C2311yescharacteristic
82C2×C4⋊Dic53C2311yescharacteristic
83C2×C4⋊Dic53C2311yescharacteristic
84C2×#11719919—21no—
85C2×#11719919—21no—
86C2×#11719919—21no—
87C4⋊C4×D53—22no—
88C4⋊C4×D53—22no—
89C4⋊C4×D53—22no—
90C4⋊C4×D53—22no—
91C4⋊C4×D53—22no—
92C4⋊C4×D53—22no—
93C2×C4×Dic53D412yes—
94C2×C4×Dic53C2311yescharacteristic
95C42×D53—22no—
96C42×D53—22no—
97#13133151—22no—
98#13133150—22no—
99#13133150—22no—
100#13133149—22no—
101#13133148—22no—
102#13133148—22no—
103#13133142—22no—
104#13133142—22no—
105#13133141—22no—
106#13133141—22no—
107#13133140—22no—
108#13133140—22no—
109#13133124—22no—
110#13133124—22no—
111#13133124—22no—
112#13133124—22no—
113#13133124—22no—
114#13133124—22no—
115C22×Q8×C53C2311yescharacteristic
116C22×C8×C53C2311yescharacteristic
117C22×C8×C53C2311yescharacteristic
118C2×C4⋊C4×C53C2311yescharacteristic
119C2×C4⋊C4×C53C2311yescharacteristic
120C2×C4⋊C4×C53C2311yescharacteristic
121C2×C42×C53C2311yescharacteristic
122#107×C53—22no—
123#106×C53—22no—
124#103×C53—22no—
125#103×C53—22no—
126#95×C53—22no—
127#95×C53—22no—
128C23×D53C2×D411yescharacteristic
129C2×Q8×C53—21no—
130C2×Q8×C53—21no—
131C2×Q8×C53—21no—
132C2×Q8×C53—21no—
133C2×Q8×C53—21no—
134C2×Q8×C53C2×Q812yes—
135C22×C4×C53—21no—
136C22×C4×C53—21no—
137C22×C4×C53—21no—
138C22×C4×C53—21no—
139C22×C4×C53C2×D412yes—
140C22×C4×C53C2411yescharacteristic
141C22×Dic53—21no—
142C22×Dic53—21no—
143C22×Dic53—21no—
144C22×Dic53—21no—
145C22×Dic53C2×D412yes—
146C22×Dic53C2×D411yescharacteristic
147Q8×D53—28no—
148Q8×D53—28no—
149Q8×D53—44no—
150Q8×D53—44no—
151C2×C4×D53—24no—
152C2×C4×D53—24no—
153C2×C4×D53—24no—
154C2×C4×D53—24no—
155C2×C4×D53—42no—
156C2×C4×D53—42no—
157C2×C4×D53—42no—
158C2×C4×D53—42no—
159C2×C4×D53—42no—
160C2×C4×D53—44no—
161C2×C4×D53—44no—
162C2×C4×D53—44no—
163C2×C4×D53C2×D412yes—
164C2×C4×D53C2×D412yes—
165C2×C4×D53C2×Q812yes—
166C2×C4×D53#4112yes—
167C2×C4×D53#4112yes—
168C2×C4×D53#4112yes—
169C2×Dic106—21no—
170C2×Dic106—21no—
171C2×Dic106—21no—
172C2×Dic106—21no—
173C2×Dic106—21no—
174C2×Dic106—24no—
175C2×Dic106—42no—
176C2×Dic106—42no—
177C2×Dic106C2×Q812yes—
178C2×C8×C53—21no—
179C2×C8×C53—21no—
180C2×C8×C53—21no—
181C2×C8×C53—21no—
182C2×C8×C53C2×D412yes—
183C2×C8×C53C2×D412yes—
184C4⋊C4×C53—21no—
185C4⋊C4×C53—21no—
186C4⋊C4×C53—21no—
187C4⋊C4×C53—21no—
188C4⋊C4×C53—21no—
189C4⋊C4×C53—21no—
190C42×C53—21no—
191C42×C53—21no—
192C4⋊Dic53—21no—
193C4⋊Dic53—21no—
194C4⋊Dic53—21no—
195C4⋊Dic53—21no—
196C4⋊Dic53—21no—
197C4⋊Dic53—21no—
198#11719919—42no—
199#11719919—42no—
200#11719919—42no—
201C4×Dic53—21no—
202C4×Dic53—21no—
203C4×Dic53—24no—
204C2×#88322—21no—
205C2×#88322—21no—
206C2×#88322—21no—
207C2×#88322—21no—
208C2×#88322C2×D412yes—
209C2×#88322C2×D412yes—
210C8×D53—28no—
211C8×D53—28no—
212C23×C53C22×D411yescharacteristic
213C22×D53C22⋊Q812yes—
214C22×D53#12312yes—
215C22×D53#12712yes—
216C22×D53#13514yes—
217C22×D53#13714yes—
218Q8×C53—22no—
219Q8×C53—22no—
220Q8×C53—41no—
221Q8×C53—41no—
222C2×C4×C53—22no—
223C2×C4×C53—22no—
224C2×C4×C53—22no—
225C2×C4×C53—22no—
226C2×C4×C53—41no—
227C2×C4×C53—41no—
228C2×C4×C53—41no—
229C2×C4×C53—41no—
230C2×C4×C53—41no—
231C2×C4×C53—42no—
232C2×C4×C53—42no—
233C2×C4×C53—42no—
234C2×C4×C53C22×D411yescharacteristic
235C2×C4×C53C22×D411yescharacteristic
236C2×C4×C53C22×Q811yescharacteristic
237C2×C4×C53C2×#4111yescharacteristic
238C2×C4×C53C2×#4111yescharacteristic
239C2×C4×C53C2×#4111yescharacteristic
240C2×Dic53—22no—
241C2×Dic53—22no—
242C2×Dic53—22no—
243C2×Dic53—22no—
244C2×Dic53—41no—
245C2×Dic53—41no—
246C2×Dic53—41no—
247C2×Dic53—41no—
248C2×Dic53—41no—
249C2×Dic53—42no—
250C2×Dic53—42no—
251C2×Dic53—42no—
252C2×Dic53C22⋊Q812yes—
253C2×Dic53#12312yes—
254C2×Dic53#12712yes—
255C4×D53—48no—
256C4×D53—48no—
257C4×D53—84no—
258C4×D53—84no—
259C4×D53—84no—
260C4×D53C22⋊Q814yes—
261C4×D53C22⋊Q814yes—
262C4×D53#12314yes—
263C4×D53#12314yes—
264Dic106—22no—
265Dic106—22no—
266Dic106—41no—
267Dic106—41no—
268Dic106—48no—
269C8×C53—22no—
270C8×C53—22no—
271#88322—22no—
272#88322—22no—
273C2×#2097—531nomaximal, Sylow
274C22×C53C2×C22⋊Q811yescharacteristic
275C22×C53C2×#12311yescharacteristic
276C22×C53C2×#12711yescharacteristic
277C22×C53C2×#13512yes—
278C22×C53C2×#13712yes—
279C2×D53#39914yes—
280C2×D53#47918yes—
281C2×D53#48518yes—
282C2×D53#49514yes—
283C2×D53#49714yes—
284C4×C53—42no—
285C4×C53—42no—
286C4×C53—81no—
287C4×C53—81no—
288C4×C53—81no—
289C4×C53C2×C22⋊Q811yescharacteristic
290C4×C53C2×C22⋊Q811yescharacteristic
291C4×C53C2×#12311yescharacteristic
292C4×C53C2×#12311yescharacteristic
293Dic53—42no—
294Dic53—42no—
295Dic53—81no—
296Dic53—81no—
297Dic53—81no—
298Dic53#39914yes—
299C22×#107—531no—
300C22×#106—531no—
301C22×#103—531no—
302C22×#103—531no—
303C2×#391—531no—
304C2×#382—531no—
305#2097—531no—
306#2097—531no—
307#2097—531no—
308#2097—531no—
309#2097—531no—
310#2097—531no—
311#2097—531no—
312#2097D5311yescharacteristic, direct product factor
313C2×#336—531no—
314C2×C53C2×#39911yescharacteristic
315C2×C53C2×#47912yes—
316C2×C53C2×#48512yes—
317C2×C53C2×#49511yescharacteristic
318C2×C53C2×#49711yescharacteristic
319D53#209718yesdirect product factor
320C23×Q8—531no—
321C23×C8—531no—
322C23×C8—531no—
323C22×C4⋊C4—531no—
324C22×C4⋊C4—531no—
325C22×C4⋊C4—531no—
326C22×C42—531no—
327C2×#107—531no—
328C2×#107—531no—
329C2×#107—531no—
330C2×#107—1064no—
331C2×#107C2×D5311yescharacteristic
332C2×#106—531no—
333C2×#106—531no—
334C2×#106—531no—
335C2×#106—1064no—
336C2×#106C2×D5311yescharacteristic
337C2×#103—531no—
338C2×#103—531no—
339C2×#103—531no—
340C2×#103—531no—
341C2×#103—531no—
342C2×#103—531no—
343C2×#103—1064no—
344C2×#103—1064no—
345C2×#103C2×D5311yescharacteristic
346C2×#103C2×D5311yescharacteristic
347#391—531no—
348#391—531no—
349#391—531no—
350#391—1062no—
351#391C2×D5311yescharacteristic
352#382—531no—
353#382—531no—
354#382—531no—
355#382—1062no—
356#382C2×D5311yescharacteristic
357C2×#95—1062no—
358C2×#95—1062no—
359#336—531no—
360#336—531no—
361#336—531no—
362#336C2×D5311yescharacteristic
363C53C2×#209711yescharacteristic, complemented, Sylow
364C22×Q8—534no—
365C22×Q8—531no—
366C22×Q8—1061no—
367C22×Q8—1062no—
368C22×Q8—1062no—
369C22×Q8—1062no—
370C22×Q8—1062no—
371C22×Q8—1062no—
372C22×Q8C22×D5311yescharacteristic
373C23×C4—531no—
374C23×C4—532no—
375C23×C4—1061no—
376C23×C4—1061no—
377C23×C4—1061no—
378C23×C4—1061no—
379C22×C8—531no—
380C22×C8—531no—
381C22×C8—534no—
382C22×C8—534no—
383C22×C8—1062no—
384C22×C8—1062no—
385C22×C8—1062no—
386C22×C8—1062no—
387C22×C8C22×D5311yescharacteristic
388C22×C8C22×D5311yescharacteristic
389C2×C4⋊C4—531no—
390C2×C4⋊C4—531no—
391C2×C4⋊C4—531no—
392C2×C4⋊C4—1062no—
393C2×C4⋊C4—1062no—
394C2×C4⋊C4—1062no—
395C2×C4⋊C4—1062no—
396C2×C4⋊C4—1062no—
397C2×C4⋊C4—1062no—
398C2×C4⋊C4—1061no—
399C2×C4⋊C4—1061no—
400C2×C4⋊C4—1061no—
401C2×C4⋊C4C22×D5311yescharacteristic
402C2×C4⋊C4C22×D5311yescharacteristic
403C2×C4⋊C4C22×D5311yescharacteristic
404C2×C42—532no—
405C2×C42—531no—
406C2×C42—1062no—
407C2×C42—1062no—
408C2×C42C22×D5311yescharacteristic
409#107—22no—
410#107—1062no—
411#107—1062no—
412#107—1062no—
413#106—22no—
414#106—1062no—
415#106—1062no—
416#106—1062no—
417#103—22no—
418#103—22no—
419#103—1062no—
420#103—1062no—
421#103—1062no—
422#103—1062no—
423#103—1062no—
424#103—1062no—
425#95—22no—
426#95—22no—
427#95—1062no—
428#95—1062no—
429#95—1062no—
430#95—1062no—
431#95—1062no—
432#95—1062no—
433C24—531no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—532no—
440C2×Q8—1064no—
441C2×Q8—1068no—
442C2×Q8—1068no—
443C2×Q8—1061no—
444C2×Q8—1061no—
445C2×Q8—1061no—
446C2×Q8—1061no—
447C2×Q8—1061no—
448C2×Q8—2122no—
449C2×Q8—2122no—
450C2×Q8—2124no—
451C2×Q8—2124no—
452C2×Q8Q8×D5312yes—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—531no—
458C22×C4—532no—
459C22×C4—532no—
460C22×C4—532no—
461C22×C4—532no—
462C22×C4—532no—
463C22×C4—532no—
464C22×C4—532no—
465C22×C4—1064no—
466C22×C4—1064no—
467C22×C4—1064no—
468C22×C4—1064no—
469C22×C4—1061no—
470C22×C4—1061no—
471C22×C4—1061no—
472C22×C4—1061no—
473C22×C4—2122no—
474C22×C4—2122no—
475C22×C4—2122no—
476C22×C4—2124no—
477C22×C4—2124no—
478C22×C4—2124no—
479C22×C4—2122no—
480C22×C4—2122no—
481C22×C4D4×D5312yes—
482C22×C4C23×D5311yescharacteristic
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—532no—
488C2×C8—532no—
489C2×C8—1068no—
490C2×C8—1068no—
491C2×C8—1061no—
492C2×C8—1061no—
493C2×C8—1061no—
494C2×C8—1061no—
495C2×C8D4×D5312yes—
496C2×C8D4×D5312yes—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—1061no—
504C4⋊C4—1061no—
505C4⋊C4—1061no—
506C4⋊C4—1061no—
507C4⋊C4—1061no—
508C4⋊C4—1061no—
509C4⋊C4—2122no—
510C4⋊C4—2122no—
511C4⋊C4—2122no—
512C42—21no—
513C42—21no—
514C42—1064no—
515C42—1061no—
516C42—1061no—
517C23—532no—
518C23—532no—
519C23—534no—
520C23—534no—
521C23—532no—
522C23C2×D4×D5311yescharacteristic
523Q8—22no—
524Q8—22no—
525Q8—41no—
526Q8—41no—
527Q8—1062no—
528Q8—1062no—
529Q8—2128no—
530Q8—2121no—
531Q8—2121no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—532no—
545C2×C4—532no—
546C2×C4—532no—
547C2×C4—534no—
548C2×C4—534no—
549C2×C4—534no—
550C2×C4—534no—
551C2×C4—1062no—
552C2×C4—1062no—
553C2×C4—1062no—
554C2×C4—1062no—
555C2×C4—4244no—
556C2×C4—4244no—
557C2×C4—4244no—
558C2×C4—2128no—
559C2×C4—2128no—
560C2×C4—2122no—
561C2×C4—2122no—
562C2×C4—2122no—
563C2×C4—2121no—
564C2×C4—2121no—
565C2×C4—2121no—
566C2×C4—2121no—
567C2×C4—2121no—
568C2×C4C2×D4×D5311yescharacteristic
569C2×C4C2×D4×D5311yescharacteristic
570C2×C4C2×Q8×D5311yescharacteristic
571C2×C4#41×D5311yescharacteristic
572C2×C4#41×D5311yescharacteristic
573C2×C4#41×D5311yescharacteristic
574C8—22no—
575C8—22no—
576C8—1062no—
577C8—1062no—
578C22—538no—
579C22—538no—
580C22—534no—
581C22—534no—
582C22—534no—
583C22C22⋊Q8×D5311yescharacteristic
584C22#123×D5311yescharacteristic
585C22#127×D5311yescharacteristic
586C22#135×D5312yes—
587C22#137×D5312yes—
588C4—42no—
589C4—42no—
590C4—81no—
591C4—81no—
592C4—81no—
593C4—534no—
594C4—4241no—
595C4—4241no—
596C4—4241no—
597C4—2122no—
598C4—2122no—
599C4C22⋊Q8×D5311yescharacteristic
600C4C22⋊Q8×D5311yescharacteristic
601C4#123×D5311yescharacteristic
602C4#123×D5311yescharacteristic
603C2—538no—
604C2#399×D5311yescharacteristic
605C2#479×D5312yes—
606C2#485×D5312yes—
607C2#495×D5311yescharacteristic
608C2#497×D5311yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
FittingC53×#2097C2
socleC23×C53C22×D4
prime radicalC23×D53C2×D4
hypercenter#2097D53
hypocenterC53C2×#2097
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2097

Complements

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

NH ≅ G/Ntype
7. #20276266C2semidirect
8. #20276265C2semidirect
9. #20276264C2semidirect
10. #20276263C2semidirect
11. #20276262C2semidirect
12. #20276261C2semidirect
13. #20276260C2semidirect
15. C53×#2097C2semidirect
312. #2097D53direct (N × H)
319. D53#2097direct (N × H)
363. C53C2×#2097semidirect

Maximal subgroups

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

subgroupindex
C2×#107×D532
C2×#106×D532
C2×#103×D532
#391×D532
#382×D532
#202762662
#202762652
#202762642
#202762632
#202762622
#202762612
#202762602
#336×D532
C53×#20972
C2×#209753