Finite Group Databasebeta

← D53×#1986 #27388571

Subgroups — D53×#1986 #27388571

Order 13568.

1290 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D53C211yesmaximal, characteristic
2C4×M16×D53C211yesmaximal, characteristic
3C4×C4⋊C4×D53C211yesmaximal, characteristic
4#20275660C211yesmaximal, characteristic, complemented
5#20275659C211yesmaximal, characteristic, complemented
6#20275658C211yesmaximal, characteristic, complemented
7#20275657C214yesmaximal, complemented
8#339×D53C214yesmaximal
9C53×#1986C211yesmaximal, characteristic, complemented
10C2×M16×D53C2212yes—
11#16811180C2211yescharacteristic
12#16811179C412yescomplemented
13#16811178C411yescharacteristic, complemented
14#16811178C411yescharacteristic, complemented
15#16811177—21no—
16#16811177—21no—
17#16811176C2212yes—
18#16811175—21no—
19#16811175—21no—
20C4⋊Q8×D53C411yescharacteristic, complemented
21C4⋊Q8×D53C411yescharacteristic, complemented
22#125×D53C412yescomplemented
23C22⋊Q8×D53—21no—
24C22⋊Q8×D53—21no—
25C4×Q8×D53—21no—
26C4×Q8×D53—21no—
27#117×D53C2212yes—
28C2×C4⋊C4×D53—21no—
29C2×C42×D53C2212yes—
30C2×C42×D53C2211yescharacteristic
31C4×#11719917C2211yescharacteristic
32#16810575—21no—
33M16×Dic53C2212yes—
34C4×#11719912—21no—
35#97×D53—21no—
36C4×C8×D53—21no—
37C4⋊C4×Dic53—21no—
38C4×#11719919C2212yes—
39C4×C4⋊Dic53C2211yescharacteristic
40#16810474—21no—
41#95×D53—21no—
42#16810384C2214yes—
43#16810383C2214yes—
44#16810382C2214yes—
45C53×#533C2211yescharacteristic
46C4×M16×C53C2211yescharacteristic
47C4×C4⋊C4×C53C2211yescharacteristic
48C53×#339C2214yes—
49C2×Q8×D53—21no—
50C2×Q8×D53—21no—
51C22×C4×D53—22no—
52C22×C4×D53D411yescharacteristic
53C22×C4×D53D411yescharacteristic
54C22×C4×D53C2311yescharacteristic
55C2×#11719917C2312yes—
56C2×#11719912—22no—
57M16×D53—24no—
58M16×D53Q818yescomplemented
59C2×C8×D53—22no—
60#13133217C2×C411yescharacteristic, complemented
61#13133217C2×C411yescharacteristic, complemented
62#13133216—21no—
63#13133216—21no—
64#13133216C2×C412yescomplemented
65#13133216C2×C412yescomplemented
66#13133215—21no—
67#13133215—21no—
68#13133209C2×C412yescomplemented
69#13133208C2×C412yescomplemented
70#13133208C2×C412yescomplemented
71#13133207—22no—
72#13133207—22no—
73#13133197—21no—
74#13133197—21no—
75#13133196—21no—
76#13133196—21no—
77#13133195—22no—
78#13133195—22no—
79#13133194—22no—
80#13133194—22no—
81#13133193—21no—
82#13133193—21no—
83Q8×Dic53—21no—
84Q8×Dic53—21no—
85C4×Dic106—21no—
86C4×Dic106—21no—
87C4×Dic106—22no—
88C4×Dic106—22no—
89#13133182—21no—
90#13133182—21no—
91#13133182—22no—
92#13133182—22no—
93#13133176C2312yes—
94#13133175C2×C412yes—
95#13133175C2×C412yes—
96#13133174—22no—
97#13133173—22no—
98C2×C4⋊Dic53—21no—
99C2×#11719919—22no—
100C4⋊C4×D53—28no—
101C4⋊C4×D53—22no—
102C4⋊C4×D53—22no—
103C4⋊C4×D53—21no—
104C4⋊C4×D53—21no—
105C4⋊C4×D53C2×C412yes—
106C4⋊C4×D53C2×C412yes—
107C22⋊C4×D53—22no—
108C2×C4×Dic53—22no—
109C2×C4×Dic53D411yescharacteristic
110C2×C4×Dic53D411yescharacteristic
111C2×C4×Dic53C2312yes—
112C2×C4×Dic53C2311yescharacteristic
113C42×D53—22no—
114C42×D53—28no—
115C42×D53C2×C411yescharacteristic
116C42×D53C2×C411yescharacteristic
117C42×D53C2×C411yescharacteristic
118C42×D53C2×C411yescharacteristic
119C42×D53D411yescharacteristic
120C42×D53D411yescharacteristic
121C42×D53D411yescharacteristic
122C42×D53D411yescharacteristic
123#13133128—21no—
124#13133127—22no—
125C4×#88322—21no—
126C8×Dic53—22no—
127#13133124—21no—
128#13133124—22no—
129C2×M16×C53C2312yes—
130C4⋊Q8×C53C2×C411yescharacteristic, complemented
131C4⋊Q8×C53C2×C411yescharacteristic, complemented
132#125×C53C2×C412yescomplemented
133C22⋊Q8×C53—21no—
134C22⋊Q8×C53—21no—
135C4×Q8×C53—21no—
136C4×Q8×C53—21no—
137#117×C53C2312yes—
138C2×C4⋊C4×C53—21no—
139C2×C42×C53C2312yes—
140C2×C42×C53C2311yescharacteristic
141#97×C53—21no—
142C4×C8×C53—21no—
143#95×C53—21no—
144C23×D53C2×D411yescharacteristic
145C2×Q8×C53—21no—
146C2×Q8×C53—21no—
147C22×C4×C53—22no—
148C22×C4×C53C2×D411yescharacteristic
149C22×C4×C53C2×D411yescharacteristic
150C22×C4×C53C2411yescharacteristic
151C22×Dic53—22no—
152C22×Dic53C2×D411yescharacteristic
153C22×Dic53C2×D411yescharacteristic
154C22×Dic53C2×D411yescharacteristic
155Q8×D53—44no—
156Q8×D53—44no—
157C2×C4×D53—24no—
158C2×C4×D53—28no—
159C2×C4×D53—22no—
160C2×C4×D53—22no—
161C2×C4×D53—42no—
162C2×C4×D53—44no—
163C2×C4×D53—44no—
164C2×C4×D53C22⋊C411yescharacteristic
165C2×C4×D53C22⋊C411yescharacteristic
166C2×C4×D53C22⋊C411yescharacteristic
167C2×C4×D53C22⋊C411yescharacteristic
168C2×C4×D53C22⋊C411yescharacteristic
169C2×C4×D53C22⋊C411yescharacteristic
170C2×C4×D53C22⋊C411yescharacteristic
171C2×C4×D53C22⋊C411yescharacteristic
172C2×C4×D53C22×C411yescharacteristic
173C2×C4×D53C22×C411yescharacteristic
174C2×C4×D53C2×D411yescharacteristic
175C2×C4×D53C2×D411yescharacteristic
176C2×C4×D53C2×Q814yes—
177C2×C4×D53#4114yes—
178C2×Dic106—21no—
179C2×Dic106—21no—
180C2×Dic106—22no—
181C2×Dic106—22no—
182M16×C53—22no—
183M16×C53C2×Q814yescomplemented
184C2×C8×C53—22no—
185C4⋊C4×C53—24no—
186C4⋊C4×C53—22no—
187C4⋊C4×C53—22no—
188C4⋊C4×C53—21no—
189C4⋊C4×C53—21no—
190C4⋊C4×C53C22×C412yes—
191C4⋊C4×C53C22×C412yes—
192C22⋊C4×C53—22no—
193C42×C53—22no—
194C42×C53—24no—
195C42×C53C22×C411yescharacteristic
196C42×C53C22×C411yescharacteristic
197C42×C53C2×D411yescharacteristic
198C42×C53C2×D411yescharacteristic
199C22⋊Dic53—22no—
200#11719921—22no—
201#11719921—22no—
202C4⋊Dic53—24no—
203C4⋊Dic53—21no—
204C4⋊Dic53—21no—
205C4⋊Dic53—22no—
206C4⋊Dic53—22no—
207C4⋊Dic53C22×C412yes—
208C4⋊Dic53C22×C412yes—
209#11719919—28no—
210#11719919—22no—
211#11719919—22no—
212#11719919—22no—
213#11719919—22no—
214#11719919—22no—
215#11719919—22no—
216#11719919—22no—
217#11719919—22no—
218C4×Dic53—22no—
219C4×Dic53—22no—
220C4×Dic53—22no—
221C4×Dic53—24no—
222C4×Dic53—44no—
223C4×Dic53C22⋊C411yescharacteristic
224C4×Dic53C22⋊C411yescharacteristic
225C4×Dic53C22⋊C411yescharacteristic
226C4×Dic53C22⋊C411yescharacteristic
227C4×Dic53C22⋊C411yescharacteristic
228C4×Dic53C22⋊C411yescharacteristic
229C4×Dic53C22⋊C411yescharacteristic
230C4×Dic53C22⋊C411yescharacteristic
231C4×Dic53C22×C411yescharacteristic
232C4×Dic53C22×C411yescharacteristic
233C4×Dic53C2×D411yescharacteristic
234C4×Dic53C2×D411yescharacteristic
235#11719917—22no—
236#11719917C2×Q814yescomplemented
237C2×#88322—22no—
238#11719912—28no—
239C8×D53—28no—
240C23×C53C22×D411yescharacteristic
241C22×D53—22no—
242C22×D53—22no—
243C22×D53C2×C22⋊C411yescharacteristic
244C22×D53C2×C22⋊C411yescharacteristic
245C22×D53#12412yes—
246C22×D53C4⋊Q812yes—
247Q8×C53—42no—
248Q8×C53—42no—
249C2×C4×C53—22no—
250C2×C4×C53—24no—
251C2×C4×C53—22no—
252C2×C4×C53—22no—
253C2×C4×C53—41no—
254C2×C4×C53—42no—
255C2×C4×C53—42no—
256C2×C4×C53C2×C22⋊C411yescharacteristic
257C2×C4×C53C2×C22⋊C411yescharacteristic
258C2×C4×C53C2×C22⋊C411yescharacteristic
259C2×C4×C53C2×C22⋊C411yescharacteristic
260C2×C4×C53C23×C411yescharacteristic
261C2×C4×C53C22×D411yescharacteristic
262C2×C4×C53C22×Q812yes—
263C2×C4×C53C2×#4112yes—
264C2×Dic53—22no—
265C2×Dic53—24no—
266C2×Dic53—22no—
267C2×Dic53—22no—
268C2×Dic53—41no—
269C2×Dic53—42no—
270C2×Dic53—42no—
271C2×Dic53C2×C22⋊C411yescharacteristic
272C2×Dic53C2×C22⋊C411yescharacteristic
273C2×Dic53C2×C22⋊C411yescharacteristic
274C2×Dic53C2×C22⋊C411yescharacteristic
275C2×Dic53C2×C22⋊C411yescharacteristic
276C2×Dic53C2×C22⋊C411yescharacteristic
277C2×Dic53#12412yes—
278C2×Dic53C4⋊Q812yes—
279C4×D53—22no—
280C4×D53—22no—
281C4×D53—22no—
282C4×D53—22no—
283C4×D53—22no—
284C4×D53—41no—
285C4×D53—41no—
286C4×D53—416no—
287C4×D53—44no—
288C4×D53—44no—
289C4×D53#10414yes—
290C4×D53C4×Q814yes—
291C4×D53C4×Q814yes—
292C4×D53C22⋊Q814yes—
293C4×D53C22⋊Q814yes—
294Dic106—44no—
295Dic106—42no—
296Dic106—42no—
297Dic106—44no—
298C8×C53—24no—
299#88322—24no—
300C2×#1986—531nomaximal, Sylow
301C22×C53—21no—
302C22×C53—21no—
303C22×C53C22×C22⋊C411yescharacteristic
304C22×C53C2×#12411yescharacteristic
305C22×C53C2×C4⋊Q811yescharacteristic
306C2×D53—21no—
307C2×D53—21no—
308C2×D53—24no—
309C2×D53—24no—
310C2×D53#39112yes—
311C2×D53#39112yes—
312C2×D53C2×#10412yes—
313C2×D53#42112yes—
314C4×C53—21no—
315C4×C53—21no—
316C4×C53—21no—
317C4×C53—44no—
318C4×C53—42no—
319C4×C53—42no—
320C4×C53C2×#10412yes—
321C4×C53C2×C4×Q812yes—
322C4×C53C2×C22⋊Q812yes—
323Dic53—21no—
324Dic53—21no—
325Dic53—21no—
326Dic53—44no—
327Dic53—42no—
328Dic53—42no—
329Dic53#39112yes—
330Dic53#39112yes—
331Dic53C2×#10412yes—
332C2×#533—531no—
333C2×C4×M16—531no—
334C2×C4×C4⋊C4—531no—
335#1986—531no—
336#1986—531no—
337#1986—534no—
338#1986—531no—
339#1986D5311yescharacteristic, direct product factor
340C2×#339—534no—
341C2×C53—21no—
342C2×C53—21no—
343C2×C53C2×#39111yescharacteristic
344C2×C53C22×#10411yescharacteristic
345C2×C53C2×#42111yescharacteristic
346D53—22no—
347D53#198614yesdirect product factor
348C22×M16—532no—
349#533—531no—
350#533—531no—
351#533—532no—
352#533—532no—
353#533—531no—
354#533—1061no—
355#533—1061no—
356#533—1061no—
357#533—1061no—
358#533C2×D5311yescharacteristic
359C2×C4⋊Q8—531no—
360C2×C4⋊Q8—531no—
361C2×#125—532no—
362C2×C22⋊Q8—1061no—
363C2×C22⋊Q8—1061no—
364C2×C4×Q8—1061no—
365C2×C4×Q8—1061no—
366C2×#117—532no—
367C22×C4⋊C4—1061no—
368C22×C42—531no—
369C22×C42—532no—
370C4×M16—532no—
371C4×M16—531no—
372C4×M16—1061no—
373C4×M16—1061no—
374C4×M16C2×D5311yescharacteristic
375C2×#97—1061no—
376C2×C4×C8—1061no—
377C4×C4⋊C4—532no—
378C4×C4⋊C4—531no—
379C4×C4⋊C4—1061no—
380C4×C4⋊C4—1061no—
381C4×C4⋊C4C2×D5311yescharacteristic
382C2×#95—1061no—
383#339—534no—
384#339—534no—
385#339—534no—
386#339C2×D5314yes—
387C53C2×#198611yescharacteristic, complemented, Sylow
388C22×Q8—1061no—
389C22×Q8—1061no—
390C23×C4—531no—
391C23×C4—531no—
392C23×C4—531no—
393C23×C4—1062no—
394C2×M16—532no—
395C2×M16—538no—
396C2×M16—1062no—
397C2×M16—1064no—
398C2×M16C22×D5312yes—
399C22×C8—1062no—
400C4⋊Q8—532no—
401C4⋊Q8—532no—
402C4⋊Q8—531no—
403C4⋊Q8—531no—
404C4⋊Q8—1061no—
405C4⋊Q8—1061no—
406C4⋊Q8—1061no—
407C4⋊Q8—1061no—
408C4⋊Q8C4×D5311yescharacteristic, complemented
409C4⋊Q8C4×D5311yescharacteristic, complemented
410#125—532no—
411#125—532no—
412#125—532no—
413#125—1062no—
414#125—1062no—
415#125C4×D5312yescomplemented
416C22⋊Q8—21no—
417C22⋊Q8—21no—
418C22⋊Q8—1062no—
419C22⋊Q8—1062no—
420C22⋊Q8—1062no—
421C22⋊Q8—1062no—
422C22⋊Q8—1061no—
423C22⋊Q8—1061no—
424C22⋊Q8—1061no—
425C22⋊Q8—1061no—
426C22⋊Q8—1061no—
427C22⋊Q8—1061no—
428C4×Q8—21no—
429C4×Q8—21no—
430C4×Q8—1062no—
431C4×Q8—1062no—
432C4×Q8—1062no—
433C4×Q8—1062no—
434C4×Q8—1061no—
435C4×Q8—1061no—
436C4×Q8—1061no—
437C4×Q8—1061no—
438C4×Q8—1061no—
439C4×Q8—1061no—
440#117—532no—
441#117—532no—
442#117—532no—
443#117—1062no—
444#117—1062no—
445#117C22×D5312yes—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—532no—
448C2×C4⋊C4—532no—
449C2×C4⋊C4—1062no—
450C2×C4⋊C4—1062no—
451C2×C4⋊C4—1061no—
452C2×C4⋊C4—1061no—
453C2×C4⋊C4—1068no—
454C2×C4⋊C4—1062no—
455C2×C4⋊C4—1061no—
456C2×C22⋊C4—1062no—
457C2×C42—531no—
458C2×C42—531no—
459C2×C42—531no—
460C2×C42—531no—
461C2×C42—531no—
462C2×C42—531no—
463C2×C42—531no—
464C2×C42—531no—
465C2×C42—531no—
466C2×C42—531no—
467C2×C42—531no—
468C2×C42—532no—
469C2×C42—1062no—
470C2×C42—1068no—
471C2×C42—1062no—
472C2×C42C22×D5312yes—
473C2×C42C22×D5311yescharacteristic
474#97—21no—
475#97—1062no—
476#97—1061no—
477C4×C8—21no—
478C4×C8—1062no—
479C4×C8—1061no—
480#95—21no—
481#95—1062no—
482#95—1061no—
483C24—531no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—1062no—
487C2×Q8—1062no—
488C2×Q8—1061no—
489C2×Q8—1061no—
490C2×Q8—2124no—
491C2×Q8—2124no—
492C22×C4—22no—
493C22×C4—531no—
494C22×C4—531no—
495C22×C4—531no—
496C22×C4—531no—
497C22×C4—531no—
498C22×C4—531no—
499C22×C4—534no—
500C22×C4—534no—
501C22×C4—531no—
502C22×C4—531no—
503C22×C4—531no—
504C22×C4—531no—
505C22×C4—531no—
506C22×C4—531no—
507C22×C4—531no—
508C22×C4—531no—
509C22×C4—531no—
510C22×C4—1064no—
511C22×C4—1062no—
512C22×C4—1062no—
513C22×C4—1068no—
514C22×C4—1062no—
515C22×C4—2122no—
516C22×C4—2124no—
517C22×C4—2124no—
518C22×C4D4×D5311yescharacteristic
519C22×C4D4×D5311yescharacteristic
520C22×C4C23×D5311yescharacteristic
521M16—22no—
522M16—534no—
523M16—1068no—
524M16—1062no—
525M16Q8×D5314yescomplemented
526C2×C8—22no—
527C2×C8—1068no—
528C2×C8—1062no—
529C4⋊C4—24no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—532no—
535C4⋊C4—532no—
536C4⋊C4—1062no—
537C4⋊C4—1062no—
538C4⋊C4—1062no—
539C4⋊C4—1062no—
540C4⋊C4—1062no—
541C4⋊C4—1062no—
542C4⋊C4—1062no—
543C4⋊C4—1062no—
544C4⋊C4—1068no—
545C4⋊C4—1064no—
546C4⋊C4—1062no—
547C4⋊C4—1062no—
548C4⋊C4—1061no—
549C4⋊C4—1061no—
550C4⋊C4C2×C4×D5312yes—
551C4⋊C4C2×C4×D5312yes—
552C22⋊C4—22no—
553C22⋊C4—1062no—
554C22⋊C4—1062no—
555C22⋊C4—1062no—
556C42—22no—
557C42—24no—
558C42—531no—
559C42—531no—
560C42—531no—
561C42—531no—
562C42—531no—
563C42—531no—
564C42—531no—
565C42—531no—
566C42—531no—
567C42—531no—
568C42—531no—
569C42—531no—
570C42—1062no—
571C42—1062no—
572C42—1062no—
573C42—1064no—
574C42—2124no—
575C42C2×C4×D5311yescharacteristic
576C42C2×C4×D5311yescharacteristic
577C42D4×D5311yescharacteristic
578C42D4×D5311yescharacteristic
579C23—531no—
580C23—531no—
581C23—532no—
582C23—532no—
583C23—1062no—
584C23—1062no—
585C23C2×D4×D5311yescharacteristic
586Q8—42no—
587Q8—42no—
588Q8—2122no—
589Q8—2124no—
590Q8—2124no—
591Q8—2122no—
592C2×C4—22no—
593C2×C4—24no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—41no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—531no—
600C2×C4—531no—
601C2×C4—531no—
602C2×C4—532no—
603C2×C4—532no—
604C2×C4—534no—
605C2×C4—534no—
606C2×C4—534no—
607C2×C4—534no—
608C2×C4—534no—
609C2×C4—531no—
610C2×C4—531no—
611C2×C4—531no—
612C2×C4—1062no—
613C2×C4—1062no—
614C2×C4—1062no—
615C2×C4—1062no—
616C2×C4—1062no—
617C2×C4—1062no—
618C2×C4—1064no—
619C2×C4—1062no—
620C2×C4—1062no—
621C2×C4—2121no—
622C2×C4—2121no—
623C2×C4—2124no—
624C2×C4—2124no—
625C2×C4—21216no—
626C2×C4—2121no—
627C2×C4—2122no—
628C2×C4—2122no—
629C2×C4C22⋊C4×D5311yescharacteristic
630C2×C4C22⋊C4×D5311yescharacteristic
631C2×C4C22⋊C4×D5311yescharacteristic
632C2×C4C22⋊C4×D5311yescharacteristic
633C2×C4C22×C4×D5311yescharacteristic
634C2×C4C2×D4×D5311yescharacteristic
635C2×C4C2×Q8×D5312yes—
636C2×C4#41×D5312yes—
637C8—24no—
638C8—1064no—
639C22—21no—
640C22—21no—
641C22—532no—
642C22—532no—
643C22—532no—
644C22—532no—
645C22—1064no—
646C22—1064no—
647C22—1061no—
648C22—1061no—
649C22C2×C22⋊C4×D5311yescharacteristic
650C22#124×D5311yescharacteristic
651C22C4⋊Q8×D5311yescharacteristic
652C4—21no—
653C4—21no—
654C4—21no—
655C4—44no—
656C4—42no—
657C4—42no—
658C4—532no—
659C4—532no—
660C4—532no—
661C4—1061no—
662C4—1061no—
663C4—1061no—
664C4—2124no—
665C4—2122no—
666C4—2122no—
667C4#104×D5312yes—
668C4C4×Q8×D5312yes—
669C4C22⋊Q8×D5312yes—
670C2—21no—
671C2—21no—
672C2—534no—
673C2—1062no—
674C2#391×D5311yescharacteristic
675C2C2×#104×D5311yescharacteristic
676C2#421×D5311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1986C2
socleC22×C53C22×C22⋊C4
prime radicalC23×D53C2×D4
cosocleC22×C4×C53C24
hypercenter#1986D53
hypocenterC53C2×#1986
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1986

Complements

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

NH ≅ G/Ntype
4. #20275660C2semidirect
5. #20275659C2semidirect
6. #20275658C2semidirect
7. #20275657C2semidirect
9. C53×#1986C2semidirect
12. #16811179C4semidirect
13. #16811178C4semidirect
14. #16811178C4semidirect
20. C4⋊Q8×D53C4semidirect
21. C4⋊Q8×D53C4semidirect
22. #125×D53C4semidirect
58. M16×D53Q8semidirect
60. #13133217C2×C4semidirect
61. #13133217C2×C4semidirect
64. #13133216C2×C4semidirect
65. #13133216C2×C4semidirect
68. #13133209C2×C4semidirect
69. #13133208C2×C4semidirect
70. #13133208C2×C4semidirect
130. C4⋊Q8×C53C2×C4semidirect
131. C4⋊Q8×C53C2×C4semidirect
132. #125×C53C2×C4semidirect
183. M16×C53C2×Q8semidirect
236. #11719917C2×Q8semidirect
339. #1986D53direct (N × H)
347. D53#1986direct (N × H)
387. C53C2×#1986semidirect
408. C4⋊Q8C4×D53semidirect
409. C4⋊Q8C4×D53semidirect
415. #125C4×D53semidirect
525. M16Q8×D53semidirect

Maximal subgroups

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

subgroupindex
#533×D532
C4×M16×D532
C4×C4⋊C4×D532
#202756602
#202756592
#202756582
#202756572
#339×D532
C53×#19862
C2×#198653