Finite Group Databasebeta

← D53×#1491 #27350511

Subgroups — D53×#1491 #27350511

Order 13568.

1302 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D53C211yesmaximal, characteristic
2#432×D53C211yesmaximal, characteristic
3C4×M16×D53C211yesmaximal, characteristic
4#20273163C211yesmaximal, characteristic, complemented
5#20273162C211yesmaximal, characteristic, complemented
6#20273161C211yesmaximal, characteristic, complemented
7#20273160C214yesmaximal, complemented
8Q8⋊C8×D53C214yesmaximal, complemented
9C53×#1491C211yesmaximal, characteristic, complemented
10C22×Q8×D53C411yescharacteristic
11C2×M16×D53—21no—
12C2×Q8×Dic53C411yescharacteristic
13C2×C4×Dic106—21no—
14C2×C4×Dic106C2211yescharacteristic
15C2×#13133182—21no—
16C2×#13133182C411yescharacteristic
17C4×Q8×D53—21no—
18C4×Q8×D53—21no—
19C4×Q8×D53—21no—
20C4×Q8×D53—21no—
21C4×Q8×D53C412yes—
22C4×Q8×D53C412yes—
23C4×Q8×D53C2212yes—
24C4×Q8×D53C2212yes—
25C2×C4⋊C4×D53—21no—
26C2×C4⋊C4×D53C411yescharacteristic
27C2×C42×D53—21no—
28C2×C42×D53C2211yescharacteristic
29#16810680C2211yescharacteristic
30#16810679C2212yes—
31#16810678—21no—
32#16810677—21no—
33C4⋊C8×D53C2212yes—
34C22⋊C8×D53—21no—
35C4×#11719917C2211yescharacteristic
36#16810575—21no—
37M16×Dic53—21no—
38C4×#11719912C2212yes—
39#97×D53—21no—
40#97×D53—21no—
41C4×C8×D53C2212yes—
42#16810355C2214yescomplemented
43Q8⋊#88322C2214yescomplemented
44#16810353C2214yescomplemented
45C2×C4×Q8×C53C2211yescharacteristic
46C53×#432C2211yescharacteristic
47C4×M16×C53C2211yescharacteristic
48C53×Q8⋊C8C2214yescomplemented
49C22×Dic106—21no—
50C22×Dic106C2×C411yescharacteristic
51C2×Q8×D53—28no—
52C2×Q8×D53—21no—
53C2×Q8×D53—21no—
54C2×Q8×D53C2×C412yes—
55C2×Q8×D53C2×C412yes—
56C22×C4×D53—21no—
57C22×C4×D53—21no—
58C22×C4×D53C2×C411yescharacteristic
59C22×C4×D53D411yescharacteristic
60C22×C4×D53D411yescharacteristic
61C2×#11719917—21no—
62C2×#11719912—22no—
63M16×D53—28no—
64C2×C8×D53—22no—
65C2×C8×D53—22no—
66Q8×Dic53—21no—
67Q8×Dic53—21no—
68Q8×Dic53C2×C412yes—
69Q8×Dic53C2×C412yes—
70C4×Dic106—21no—
71C4×Dic106—21no—
72C4×Dic106—22no—
73C4×Dic106—22no—
74C4×Dic106—22no—
75C4×Dic106—22no—
76C4×Dic106C2×C412yes—
77C4×Dic106C2312yes—
78#13133182—21no—
79#13133182—21no—
80#13133182—22no—
81#13133182—22no—
82#13133182—22no—
83#13133182—22no—
84#13133182C2×C412yes—
85#13133182C2×C412yes—
86C2×C4⋊Dic53—21no—
87C2×C4⋊Dic53C2×C411yescharacteristic
88C2×#11719919—21no—
89C2×#11719919—21no—
90C2×#11719919—21no—
91C4⋊C4×D53—22no—
92C4⋊C4×D53—22no—
93C4⋊C4×D53—21no—
94C4⋊C4×D53—21no—
95C4⋊C4×D53—22no—
96C4⋊C4×D53—22no—
97C4⋊C4×D53C2×C412yes—
98C4⋊C4×D53C2×C412yes—
99C2×C4×Dic53—21no—
100C2×C4×Dic53—21no—
101C2×C4×Dic53—21no—
102C2×C4×Dic53C2×C411yescharacteristic
103C2×C4×Dic53D411yescharacteristic
104C2×C4×Dic53D411yescharacteristic
105C42×D53—22no—
106C42×D53—22no—
107C42×D53—22no—
108C42×D53—22no—
109C42×D53C2×C411yescharacteristic
110C42×D53C2×C411yescharacteristic
111C42×D53D411yescharacteristic
112C42×D53D411yescharacteristic
113C42×D53D411yescharacteristic
114C42×D53D411yescharacteristic
115C42×D53C2311yescharacteristic
116C42×D53C2311yescharacteristic
117C4⋊#88322C2312yes—
118#13133146—22no—
119C22⋊#88322—21no—
120#13133129—22no—
121#13133128—21no—
122#13133128—21no—
123#13133127—22no—
124#13133127—22no—
125C4×#88322C2312yes—
126C8×Dic53—22no—
127C22×Q8×C53C2×C411yescharacteristic
128C2×M16×C53—21no—
129C4×Q8×C53—21no—
130C4×Q8×C53—21no—
131C4×Q8×C53C2×C412yes—
132C4×Q8×C53C2312yes—
133C2×C4⋊C4×C53—21no—
134C2×C4⋊C4×C53C2×C411yescharacteristic
135C2×C42×C53—21no—
136C2×C42×C53C2311yescharacteristic
137C4⋊C8×C53C2312yes—
138C22⋊C8×C53—21no—
139#97×C53—21no—
140#97×C53—21no—
141C4×C8×C53C2312yes—
142C23×D53C22⋊C411yescharacteristic
143C2×Q8×C53—24no—
144C2×Q8×C53—21no—
145C2×Q8×C53C22×C412yes—
146C22×C4×C53—21no—
147C22×C4×C53—21no—
148C22×C4×C53C22×C411yescharacteristic
149C22×C4×C53C2×D411yescharacteristic
150C22×C4×C53C2×D411yescharacteristic
151C22×Dic53—21no—
152C22×Dic53—21no—
153C22×Dic53C22⋊C411yescharacteristic
154C22×Dic53C22⋊C411yescharacteristic
155C22×Dic53C22⋊C411yescharacteristic
156Q8×D53—28no—
157Q8×D53—28no—
158Q8×D53—24no—
159Q8×D53—24no—
160Q8×D53—24no—
161Q8×D53M1618yescomplemented
162C2×C4×D53—28no—
163C2×C4×D53—24no—
164C2×C4×D53—22no—
165C2×C4×D53—22no—
166C2×C4×D53—24no—
167C2×C4×D53—24no—
168C2×C4×D53—22no—
169C2×C4×D53—22no—
170C2×C4×D53—44no—
171C2×C4×D53C22⋊C411yescharacteristic
172C2×C4×D53C22⋊C411yescharacteristic
173C2×C4×D53C22⋊C411yescharacteristic
174C2×C4×D53C22⋊C411yescharacteristic
175C2×C4×D53C22⋊C411yescharacteristic
176C2×C4×D53C22⋊C411yescharacteristic
177C2×C4×D53C22×C411yescharacteristic
178C2×C4×D53C22×C411yescharacteristic
179C2×C4×D53C2×D411yescharacteristic
180C2×C4×D53C2×D411yescharacteristic
181C2×C4×D53C2×D411yescharacteristic
182C2×C4×D53C2×D411yescharacteristic
183C2×Dic106—28no—
184C2×Dic106—21no—
185C2×Dic106—22no—
186C2×Dic106—22no—
187C2×Dic106—24no—
188C2×Dic106C22×C412yes—
189M16×C53—24no—
190C2×C8×C53—22no—
191C2×C8×C53—22no—
192C4⋊C4×C53—22no—
193C4⋊C4×C53—21no—
194C4⋊C4×C53—22no—
195C4⋊C4×C53C22×C412yes—
196C42×C53—22no—
197C42×C53—22no—
198C42×C53C22×C411yescharacteristic
199C42×C53C2×D411yescharacteristic
200C42×C53C2×D411yescharacteristic
201C42×C53C2411yescharacteristic
202C4⋊Dic53—21no—
203C4⋊Dic53—22no—
204C4⋊Dic53—22no—
205C4⋊Dic53C22×C412yes—
206#11719919—22no—
207#11719919—22no—
208#11719919—22no—
209#11719919—22no—
210#11719919—22no—
211#11719919—22no—
212C4×Dic53—22no—
213C4×Dic53—22no—
214C4×Dic53—22no—
215C4×Dic53—22no—
216C4×Dic53—22no—
217C4×Dic53—22no—
218C4×Dic53C22⋊C411yescharacteristic
219C4×Dic53C22⋊C411yescharacteristic
220C4×Dic53C22⋊C411yescharacteristic
221C4×Dic53C22⋊C411yescharacteristic
222C4×Dic53C22⋊C411yescharacteristic
223C4×Dic53C22⋊C411yescharacteristic
224C4×Dic53C22×C411yescharacteristic
225C4×Dic53C22×C411yescharacteristic
226C4×Dic53C2×D411yescharacteristic
227C4×Dic53C2×D411yescharacteristic
228C4×Dic53C2×D411yescharacteristic
229C4×Dic53C2×D411yescharacteristic
230#11719917—24no—
231C2×#88322—22no—
232C2×#88322—22no—
233#11719912—28no—
234C8×D53—28no—
235C8×D53—44no—
236C23×C53C2×C22⋊C411yescharacteristic
237C22×D53—22no—
238C22×D53—22no—
239C22×D53#10414yes—
240C22×D53C2×C22⋊C411yescharacteristic
241C22×D53C2×C22⋊C411yescharacteristic
242Q8×C53—24no—
243Q8×C53—22no—
244Q8×C53C2×M1614yescomplemented
245C2×C4×C53—24no—
246C2×C4×C53—22no—
247C2×C4×C53—22no—
248C2×C4×C53—22no—
249C2×C4×C53—22no—
250C2×C4×C53—22no—
251C2×C4×C53—42no—
252C2×C4×C53C2×C22⋊C411yescharacteristic
253C2×C4×C53C2×C22⋊C411yescharacteristic
254C2×C4×C53C2×C22⋊C411yescharacteristic
255C2×C4×C53C23×C411yescharacteristic
256C2×C4×C53C22×D411yescharacteristic
257C2×C4×C53C22×D411yescharacteristic
258C2×Dic53—24no—
259C2×Dic53—22no—
260C2×Dic53—22no—
261C2×Dic53—22no—
262C2×Dic53—22no—
263C2×Dic53—22no—
264C2×Dic53—42no—
265C2×Dic53C2×C22⋊C411yescharacteristic
266C2×Dic53C2×C22⋊C411yescharacteristic
267C2×Dic53C2×C22⋊C411yescharacteristic
268C2×Dic53C2×C22⋊C411yescharacteristic
269C2×Dic53C2×C22⋊C411yescharacteristic
270C2×Dic53C2×C22⋊C411yescharacteristic
271C4×D53—28no—
272C4×D53—28no—
273C4×D53—22no—
274C4×D53—22no—
275C4×D53—22no—
276C4×D53—22no—
277C4×D53—22no—
278C4×D53—22no—
279C4×D53—22no—
280C4×D53—22no—
281C4×D53—22no—
282C4×D53—22no—
283C4×D53—44no—
284C4×D53—44no—
285C4×D53C2×M1614yes—
286C4×D53#13714yes—
287Dic106—28no—
288Dic106—24no—
289Dic106—22no—
290Dic106—28no—
291Dic106C2×M1614yescomplemented
292C8×C53—24no—
293C8×C53—42no—
294#88322—24no—
295#88322—42no—
296C2×#1491—531nomaximal, Sylow
297C22×C53—21no—
298C22×C53—21no—
299C22×C53C2×#10412yes—
300C22×C53C22×C22⋊C411yescharacteristic
301C2×D53—21no—
302C2×D53—21no—
303C2×D53—28no—
304C2×D53#40712yes—
305C2×D53#41912yes—
306C2×D53C2×#10412yes—
307C2×D53C2×#10412yes—
308C4×C53—24no—
309C4×C53—21no—
310C4×C53—21no—
311C4×C53—21no—
312C4×C53—21no—
313C4×C53—42no—
314C4×C53C22×M1612yes—
315C4×C53C2×#13712yes—
316Dic53—21no—
317Dic53—24no—
318Dic53—21no—
319Dic53—21no—
320Dic53—21no—
321Dic53—42no—
322Dic53#40712yes—
323Dic53#41912yes—
324C22×C4×Q8—531no—
325C2×#432—531no—
326C2×C4×M16—531no—
327#1491—531no—
328#1491—531no—
329#1491—534no—
330#1491—531no—
331#1491D5311yescharacteristic, direct product factor
332C2×Q8⋊C8—534no—
333C2×C53—22no—
334C2×C53C2×#40711yescharacteristic
335C2×C53C2×#41911yescharacteristic
336C2×C53C22×#10411yescharacteristic
337D53—22no—
338D53#149114yesdirect product factor
339C23×Q8—531no—
340C22×M16—1061no—
341C2×C4×Q8—531no—
342C2×C4×Q8—532no—
343C2×C4×Q8—532no—
344C2×C4×Q8—532no—
345C2×C4×Q8—532no—
346C2×C4×Q8—531no—
347C2×C4×Q8—531no—
348C2×C4×Q8—1061no—
349C2×C4×Q8—1061no—
350C2×C4×Q8—1061no—
351C2×C4×Q8—1061no—
352C2×C4×Q8—1061no—
353C2×C4×Q8—1061no—
354C2×C4×Q8C2×D5311yescharacteristic
355C22×C4⋊C4—531no—
356C22×C4⋊C4—1061no—
357C22×C42—531no—
358C22×C42—1061no—
359#432—531no—
360#432—532no—
361#432—1061no—
362#432—1061no—
363#432C2×D5311yescharacteristic
364C2×C4⋊C8—532no—
365C2×C22⋊C8—1061no—
366C4×M16—531no—
367C4×M16—532no—
368C4×M16—1061no—
369C4×M16—1061no—
370C4×M16C2×D5311yescharacteristic
371C2×#97—1061no—
372C2×#97—1061no—
373C2×C4×C8—532no—
374Q8⋊C8—534no—
375Q8⋊C8—534no—
376Q8⋊C8—534no—
377Q8⋊C8C2×D5314yescomplemented
378C53C2×#149111yescharacteristic, complemented, Sylow
379C22×Q8—532no—
380C22×Q8—532no—
381C22×Q8—531no—
382C22×Q8—1061no—
383C22×Q8—1061no—
384C22×Q8—1061no—
385C22×Q8—1068no—
386C22×Q8C4×D5311yescharacteristic
387C23×C4—531no—
388C23×C4—531no—
389C23×C4—531no—
390C23×C4—1061no—
391C23×C4—1061no—
392C2×M16—21no—
393C2×M16—1062no—
394C2×M16—1068no—
395C2×M16—1061no—
396C22×C8—1062no—
397C22×C8—1062no—
398C4×Q8—21no—
399C4×Q8—21no—
400C4×Q8—532no—
401C4×Q8—532no—
402C4×Q8—532no—
403C4×Q8—532no—
404C4×Q8—532no—
405C4×Q8—532no—
406C4×Q8—1062no—
407C4×Q8—1062no—
408C4×Q8—1062no—
409C4×Q8—1062no—
410C4×Q8—1062no—
411C4×Q8—1062no—
412C4×Q8—1061no—
413C4×Q8—1061no—
414C4×Q8—1062no—
415C4×Q8—1062no—
416C4×Q8—1061no—
417C4×Q8—1061no—
418C4×Q8—1061no—
419C4×Q8—1061no—
420C4×Q8C4×D5312yes—
421C4×Q8C22×D5312yes—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—531no—
424C2×C4⋊C4—532no—
425C2×C4⋊C4—532no—
426C2×C4⋊C4—1061no—
427C2×C4⋊C4—1061no—
428C2×C4⋊C4—1062no—
429C2×C4⋊C4—1062no—
430C2×C4⋊C4—1062no—
431C2×C4⋊C4—1062no—
432C2×C4⋊C4—1061no—
433C2×C4⋊C4—1061no—
434C2×C4⋊C4—1061no—
435C2×C4⋊C4—1061no—
436C2×C4⋊C4C4×D5311yescharacteristic
437C2×C42—21no—
438C2×C42—531no—
439C2×C42—531no—
440C2×C42—531no—
441C2×C42—531no—
442C2×C42—531no—
443C2×C42—531no—
444C2×C42—531no—
445C2×C42—531no—
446C2×C42—531no—
447C2×C42—531no—
448C2×C42—531no—
449C2×C42—1062no—
450C2×C42—1062no—
451C2×C42—1062no—
452C2×C42—1062no—
453C2×C42—1061no—
454C2×C42—1061no—
455C2×C42—1061no—
456C2×C42C22×D5311yescharacteristic
457C4⋊C8—532no—
458C4⋊C8—1062no—
459C4⋊C8C22×D5312yes—
460C22⋊C8—21no—
461C22⋊C8—1062no—
462C22⋊C8—1061no—
463#97—21no—
464#97—21no—
465#97—1062no—
466#97—1062no—
467#97—1061no—
468#97—1061no—
469C4×C8—532no—
470C4×C8—1062no—
471C4×C8C22×D5312yes—
472C24—531no—
473C2×Q8—24no—
474C2×Q8—21no—
475C2×Q8—538no—
476C2×Q8—532no—
477C2×Q8—1062no—
478C2×Q8—1062no—
479C2×Q8—1064no—
480C2×Q8—1068no—
481C2×Q8—1064no—
482C2×Q8—1064no—
483C2×Q8—1068no—
484C2×Q8—1068no—
485C2×Q8—1064no—
486C2×Q8—1061no—
487C2×Q8C2×C4×D5312yes—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—531no—
491C22×C4—531no—
492C22×C4—531no—
493C22×C4—531no—
494C22×C4—531no—
495C22×C4—531no—
496C22×C4—531no—
497C22×C4—531no—
498C22×C4—531no—
499C22×C4—531no—
500C22×C4—531no—
501C22×C4—531no—
502C22×C4—531no—
503C22×C4—531no—
504C22×C4—531no—
505C22×C4—1064no—
506C22×C4—1064no—
507C22×C4—1062no—
508C22×C4—1062no—
509C22×C4—1064no—
510C22×C4—1068no—
511C22×C4—1062no—
512C22×C4—1062no—
513C22×C4—1061no—
514C22×C4—1061no—
515C22×C4—2124no—
516C22×C4C2×C4×D5311yescharacteristic
517C22×C4D4×D5311yescharacteristic
518C22×C4D4×D5311yescharacteristic
519M16—24no—
520M16—1068no—
521M16—1064no—
522C2×C8—22no—
523C2×C8—22no—
524C2×C8—1068no—
525C2×C8—1062no—
526C2×C8—1062no—
527C2×C8—2124no—
528C4⋊C4—22no—
529C4⋊C4—21no—
530C4⋊C4—22no—
531C4⋊C4—532no—
532C4⋊C4—1062no—
533C4⋊C4—1062no—
534C4⋊C4—1062no—
535C4⋊C4—1062no—
536C4⋊C4—1062no—
537C4⋊C4—1062no—
538C4⋊C4—1061no—
539C4⋊C4—1062no—
540C4⋊C4—1062no—
541C4⋊C4C2×C4×D5312yes—
542C42—22no—
543C42—22no—
544C42—531no—
545C42—531no—
546C42—531no—
547C42—531no—
548C42—531no—
549C42—531no—
550C42—531no—
551C42—531no—
552C42—531no—
553C42—531no—
554C42—531no—
555C42—531no—
556C42—1062no—
557C42—1062no—
558C42—1062no—
559C42—1062no—
560C42—1062no—
561C42—1062no—
562C42C2×C4×D5311yescharacteristic
563C42D4×D5311yescharacteristic
564C42D4×D5311yescharacteristic
565C42C23×D5311yescharacteristic
566C23—531no—
567C23—531no—
568C23—534no—
569C23—1062no—
570C23—1062no—
571C23C22⋊C4×D5311yescharacteristic
572Q8—24no—
573Q8—22no—
574Q8—534no—
575Q8—1068no—
576Q8—1068no—
577Q8—1064no—
578Q8—1062no—
579Q8M16×D5314yescomplemented
580C2×C4—24no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—42no—
587C2×C4—531no—
588C2×C4—531no—
589C2×C4—534no—
590C2×C4—534no—
591C2×C4—531no—
592C2×C4—531no—
593C2×C4—531no—
594C2×C4—531no—
595C2×C4—1062no—
596C2×C4—1062no—
597C2×C4—1062no—
598C2×C4—1062no—
599C2×C4—1062no—
600C2×C4—1062no—
601C2×C4—1062no—
602C2×C4—1062no—
603C2×C4—1068no—
604C2×C4—1068no—
605C2×C4—1062no—
606C2×C4—1062no—
607C2×C4—1064no—
608C2×C4—1062no—
609C2×C4—1062no—
610C2×C4—1062no—
611C2×C4—1062no—
612C2×C4—1062no—
613C2×C4—2124no—
614C2×C4—2124no—
615C2×C4—2122no—
616C2×C4C22⋊C4×D5311yescharacteristic
617C2×C4C22⋊C4×D5311yescharacteristic
618C2×C4C22⋊C4×D5311yescharacteristic
619C2×C4C22×C4×D5311yescharacteristic
620C2×C4C2×D4×D5311yescharacteristic
621C2×C4C2×D4×D5311yescharacteristic
622C8—24no—
623C8—42no—
624C8—1064no—
625C8—2122no—
626C22—21no—
627C22—21no—
628C22—532no—
629C22—532no—
630C22—532no—
631C22—532no—
632C22—1068no—
633C22—1061no—
634C22—1061no—
635C22#104×D5312yes—
636C22C2×C22⋊C4×D5311yescharacteristic
637C4—24no—
638C4—21no—
639C4—21no—
640C4—21no—
641C4—21no—
642C4—42no—
643C4—532no—
644C4—532no—
645C4—1061no—
646C4—1064no—
647C4—1061no—
648C4—1061no—
649C4—1061no—
650C4—2122no—
651C4C2×M16×D5312yes—
652C4#137×D5312yes—
653C2—22no—
654C2—534no—
655C2—1062no—
656C2#407×D5311yescharacteristic
657C2#419×D5311yescharacteristic
658C2C2×#104×D5311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC42C23×D53
FittingC53×#1491C2
socleC22×C53C22×C22⋊C4
prime radicalC23×D53C22⋊C4
cosocleC42×C53C24
hypercenter#1491D53
hypocenterC53C2×#1491
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1491

Complements

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

NH ≅ G/Ntype
4. #20273163C2semidirect
5. #20273162C2semidirect
6. #20273161C2semidirect
7. #20273160C2semidirect
8. Q8⋊C8×D53C2semidirect
9. C53×#1491C2semidirect
42. #16810355C22semidirect
43. Q8⋊#88322C22semidirect
44. #16810353C22semidirect
48. C53×Q8⋊C8C22semidirect
161. Q8×D53M16semidirect
244. Q8×C53C2×M16semidirect
291. Dic106C2×M16semidirect
331. #1491D53direct (N × H)
338. D53#1491direct (N × H)
377. Q8⋊C8C2×D53semidirect
378. C53C2×#1491semidirect
579. Q8M16×D53semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D532
#432×D532
C4×M16×D532
#202731632
#202731622
#202731612
#202731602
Q8⋊C8×D532
C53×#14912
C2×#149153