Finite Group Databasebeta

← D53×#3189 #28254632

Subgroups — D53×#3189 #28254632

Order 13568.

2354 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×D53C212yesmaximal
2#20285490C211yesmaximal, characteristic, complemented
3#20285489C214yesmaximal, complemented
4#20285488C214yesmaximal, complemented
5#20285487C212yesmaximal, complemented
6#20285486C214yesmaximal, complemented
7#484×D53C214yesmaximal, complemented
8#467×D53C214yesmaximal, complemented
9#451×D53C214yesmaximal, complemented
10C2×C22⋊C8×D53C211yesmaximal, characteristic
11C53×#3189C211yesmaximal, characteristic, complemented
12C22×Q8×D53C2212yes—
13C23×C4×D53C2211yescharacteristic
14C2×Q16×D53C2214yescomplemented
15C22×C8×D53C2212yes—
16C2×#13133197C2212yes—
17C2×#13133196C2212yes—
18C2×#13133195—22no—
19C2×#13133194—22no—
20C2×#13133193C2212yes—
21C22⋊Q8×D53—22no—
22C22⋊Q8×D53—22no—
23C22⋊Q8×D53—22no—
24C22⋊Q8×D53—22no—
25C22⋊Q8×D53C2214yes—
26C22⋊Q8×D53C2214yes—
27C22⋊Q8×D53C2214yes—
28C22⋊Q8×D53C2214yes—
29C2×C4⋊C4×D53—22no—
30C2×C4⋊C4×D53C2212yes—
31C2×C22⋊C4×D53—22no—
32#16810960C2218yescomplemented
33#16810959C2214yescomplemented
34#16810958C2214yescomplemented
35#16810957C2218yescomplemented
36#16810956C2214yescomplemented
37#16810865C2214yescomplemented
38#16810864C2214yescomplemented
39#16810863C2218yescomplemented
40#16810862C2218yescomplemented
41#16810861C2214yescomplemented
42#16810781C2214yescomplemented
43#16810780C2218yescomplemented
44#16810779C2214yescomplemented
45#16810778C2214yescomplemented
46#16810777C2218yescomplemented
47#107×D53C2214yescomplemented
48#103×D53C2218yescomplemented
49C2×C22⋊#88322C2211yescharacteristic
50C2×#13133129C2212yes—
51C22⋊C8×D53C2214yes—
52C22⋊C8×D53C2214yes—
53C2×C22⋊Q8×C53C2212yes—
54C53×#484C2214yescomplemented
55C53×#467C2214yescomplemented
56C53×#451C2214yescomplemented
57C2×C22⋊C8×C53C2211yescharacteristic
58C24×D53D411yescharacteristic
59C22×Dic106—22no—
60C22×Dic106C2312yes—
61C2×Q8×D53—22no—
62C2×Q8×D53—22no—
63C2×Q8×D53—48no—
64C2×Q8×D53C2314yes—
65C2×Q8×D53C2314yes—
66C23×Dic53D411yescharacteristic
67C22×C4×D53—22no—
68C22×C4×D53—22no—
69C22×C4×D53—44no—
70C22×C4×D53D412yes—
71C22×C4×D53D411yescharacteristic
72C22×C4×D53D411yescharacteristic
73C22×C4×D53D412yes—
74C22×C4×D53C2312yes—
75C22×C4×D53C2311yescharacteristic
76C22×C4×D53C2312yes—
77C22×C4×D53C2311yescharacteristic
78C2×Dic212C2314yescomplemented
79C2×#11719925C2318yescomplemented
80Q16×D53—48no—
81C22×#88322C2312yes—
82C2×C8×D53—44no—
83C2×C8×D53C2314yes—
84C2×C8×D53C2314yes—
85#13133197—22no—
86#13133197—22no—
87#13133197C2314yes—
88#13133197C2314yes—
89#13133196—22no—
90#13133196—22no—
91#13133196C2314yes—
92#13133196C2314yes—
93#13133195—24no—
94#13133195—24no—
95#13133195—24no—
96#13133195—24no—
97#13133194—24no—
98#13133194—24no—
99#13133194—24no—
100#13133194—24no—
101#13133193—22no—
102#13133193—22no—
103#13133193C2314yes—
104#13133193C2314yes—
105C2×C4⋊Dic53—22no—
106C2×C4⋊Dic53C2312yes—
107C2×#11719919—22no—
108C2×#11719919—22no—
109C2×#11719919—22no—
110C4⋊C4×D53—24no—
111C4⋊C4×D53—24no—
112C4⋊C4×D53—24no—
113C4⋊C4×D53—24no—
114C4⋊C4×D53—22no—
115C4⋊C4×D53—22no—
116C4⋊C4×D53C2314yes—
117C4⋊C4×D53C2314yes—
118C2×C22⋊Dic53—22no—
119C2×#11719921—22no—
120C2×#11719921—22no—
121C22⋊C4×D53—24no—
122C22⋊C4×D53—24no—
123C22⋊C4×D53—24no—
124C22⋊C4×D53—24no—
125#13133151C2314yescomplemented
126#13133150C2318yescomplemented
127#13133142C2318yescomplemented
128#13133141C2318yescomplemented
129#13133140C2318yescomplemented
130C22⋊#88322C2314yes—
131#13133129C2318yes—
132C22×Q8×C53C2312yes—
133C23×C4×C53C2311yescharacteristic
134C2×Q16×C53C2314yescomplemented
135C22×C8×C53C2312yes—
136C22⋊Q8×C53—22no—
137C22⋊Q8×C53—22no—
138C22⋊Q8×C53C2314yes—
139C22⋊Q8×C53C2314yes—
140C2×C4⋊C4×C53—22no—
141C2×C4⋊C4×C53C2312yes—
142C2×C22⋊C4×C53—22no—
143#107×C53C2314yescomplemented
144#103×C53C2318yescomplemented
145C22⋊C8×C53C2314yes—
146C24×C53C2×D411yescharacteristic
147C23×D53—42no—
148C23×D53—42no—
149C23×D53Q1618yescomplemented
150C23×D53C2×D411yescharacteristic
151C23×D53C2×D412yes—
152C23×D53C2×D411yescharacteristic
153C23×D53C2×D412yes—
154C2×Q8×C53—22no—
155C2×Q8×C53—44no—
156C2×Q8×C53C2414yes—
157C22×C4×C53—22no—
158C22×C4×C53—22no—
159C22×C4×C53—42no—
160C22×C4×C53C2×D412yes—
161C22×C4×C53C2×D411yescharacteristic
162C22×C4×C53C2412yes—
163C22×C4×C53C2411yescharacteristic
164C22×Dic53—22no—
165C22×Dic53—22no—
166C22×Dic53—42no—
167C22×Dic53C2×D412yes—
168C22×Dic53C2×D411yescharacteristic
169C22×Dic53C2×D412yes—
170C22×Dic53C2×D411yescharacteristic
171Q8×D53—216no—
172Q8×D53—48no—
173Q8×D53—48no—
174Q8×D53—48no—
175C2×C4×D53—24no—
176C2×C4×D53—28no—
177C2×C4×D53—24no—
178C2×C4×D53—24no—
179C2×C4×D53—24no—
180C2×C4×D53—24no—
181C2×C4×D53—44no—
182C2×C4×D53—42no—
183C2×C4×D53—42no—
184C2×C4×D53—44no—
185C2×C4×D53—44no—
186C2×C4×D53—42no—
187C2×C4×D53—48no—
188C2×C4×D53—48no—
189C2×C4×D53C2×D411yescharacteristic
190C2×C4×D53C2×D412yes—
191C2×C4×D53C2×D412yes—
192C2×C4×D53C2×D411yescharacteristic
193C2×C4×D53C2×D412yes—
194C2×C4×D53C2×D412yes—
195C2×C4×D53C2×D412yes—
196C2×C4×D53C2412yes—
197C2×C4×D53C2411yescharacteristic
198C2×C4×D53C2411yescharacteristic
199C2×Dic106—22no—
200C2×Dic106—24no—
201C2×Dic106—24no—
202C2×Dic106—44no—
203C2×Dic106—48no—
204C2×Dic106C2414yes—
205Q16×C53—44no—
206C2×C8×C53—42no—
207C2×C8×C53C2414yes—
208C4⋊C4×C53—24no—
209C4⋊C4×C53—24no—
210C4⋊C4×C53—22no—
211C4⋊C4×C53C2414yes—
212C22⋊C4×C53—24no—
213C22⋊C4×C53—24no—
214C22⋊Dic53—24no—
215C22⋊Dic53—24no—
216#11719925—48no—
217#11719921—24no—
218#11719921—24no—
219#11719921—24no—
220#11719921—24no—
221C4⋊Dic53—22no—
222C4⋊Dic53—24no—
223C4⋊Dic53—24no—
224C4⋊Dic53C2414yes—
225#11719919—24no—
226#11719919—24no—
227#11719919—24no—
228#11719919—24no—
229#11719919—24no—
230#11719919—24no—
231C2×#88322—42no—
232C2×#88322C2414yes—
233Dic212—44no—
234C8×D53—28no—
235C8×D53—44no—
236C23×C53—41no—
237C23×C53—41no—
238C23×C53C2×Q1614yescomplemented
239C23×C53C22×D412yes—
240C23×C53C22×D411yescharacteristic
241C22×D53—24no—
242C22×D53—22no—
243C22×D53—24no—
244C22×D53—22no—
245C22×D53—416no—
246C22×D53—41no—
247C22×D53—42no—
248C22×D53—41no—
249C22×D53—42no—
250C22×D53C2×Q1614yes—
251C22×D53C2×Q1618yes—
252C22×D53C2×Q1614yescomplemented
253C22×D53C2×Q1618yescomplemented
254C22×D53C22×D412yes—
255C22×D53C22×D411yescharacteristic
256C22×D53C22×D411yescharacteristic
257Q8×C53—28no—
258Q8×C53—44no—
259C2×C4×C53—24no—
260C2×C4×C53—22no—
261C2×C4×C53—24no—
262C2×C4×C53—24no—
263C2×C4×C53—41no—
264C2×C4×C53—42no—
265C2×C4×C53—44no—
266C2×C4×C53—44no—
267C2×C4×C53C22×D412yes—
268C2×C4×C53C22×D411yescharacteristic
269C2×C4×C53C2511yescharacteristic
270C2×Dic53—24no—
271C2×Dic53—22no—
272C2×Dic53—24no—
273C2×Dic53—24no—
274C2×Dic53—41no—
275C2×Dic53—42no—
276C2×Dic53—44no—
277C2×Dic53—44no—
278C2×Dic53C22×D412yes—
279C2×Dic53C22×D411yescharacteristic
280C2×Dic53C22×D411yescharacteristic
281C4×D53—22no—
282C4×D53—24no—
283C4×D53—24no—
284C4×D53—22no—
285C4×D53—22no—
286C4×D53—24no—
287C4×D53—42no—
288C4×D53—42no—
289C4×D53—42no—
290C4×D53—48no—
291C4×D53—48no—
292C4×D53—48no—
293C4×D53—48no—
294C4×D53H(5,𝔽2)14yes—
295Dic106—28no—
296Dic106—48no—
297Dic106—44no—
298Dic106—48no—
299C8×C53—24no—
300#88322—24no—
301C2×#3189—531nomaximal, Sylow
302C22×C53—22no—
303C22×C53—21no—
304C22×C53—22no—
305C22×C53—21no—
306C22×C53—44no—
307C22×C53C22×Q1614yes—
308C22×C53C22×Q1612yes—
309C22×C53C23×D411yescharacteristic
310C2×D53—22no—
311C2×D53—21no—
312C2×D53—22no—
313C2×D53—21no—
314C2×D53—216no—
315C2×D53—28no—
316C2×D53—44no—
317C2×D53—48no—
318C2×D53#53412yes—
319C2×D53C22×Q1614yes—
320C2×D53C22×Q1612yes—
321C2×D53C22×Q1612yes—
322C2×D53#57512yes—
323C4×C53—22no—
324C4×C53—21no—
325C4×C53—44no—
326C4×C53—44no—
327C4×C53C2×H(5,𝔽2)12yes—
328Dic53—22no—
329Dic53—21no—
330Dic53—44no—
331Dic53—44no—
332Dic53#53412yes—
333C22×C22⋊Q8—532no—
334#3189—534no—
335#3189—534no—
336#3189—534no—
337#3189—531no—
338#3189—532no—
339#3189D5311yescharacteristic, direct product factor
340C2×#484—534no—
341C2×#467—534no—
342C2×#451—534no—
343C22×C22⋊C8—531no—
344C2×C53—24no—
345C2×C53—22no—
346C2×C53C2×#53411yescharacteristic
347C2×C53C23×Q1611yescharacteristic
348C2×C53C2×#57511yescharacteristic
349D53—24no—
350D53—22no—
351D53#318914yesdirect product factor
352C23×Q8—532no—
353C24×C4—531no—
354C22×Q16—534no—
355C23×C8—532no—
356C2×C22⋊Q8—532no—
357C2×C22⋊Q8—532no—
358C2×C22⋊Q8—534no—
359C2×C22⋊Q8—534no—
360C2×C22⋊Q8—534no—
361C2×C22⋊Q8—534no—
362C2×C22⋊Q8—532no—
363C2×C22⋊Q8—1062no—
364C2×C22⋊Q8—1062no—
365C2×C22⋊Q8—1062no—
366C2×C22⋊Q8—1062no—
367C2×C22⋊Q8—1062no—
368C2×C22⋊Q8—1062no—
369C2×C22⋊Q8C2×D5312yes—
370C22×C4⋊C4—532no—
371C22×C4⋊C4—1062no—
372C22×C22⋊C4—1062no—
373#484—534no—
374#484—534no—
375#484—538no—
376#484—538no—
377#484—534no—
378#484C2×D5314yescomplemented
379#467—534no—
380#467—534no—
381#467—538no—
382#467—534no—
383#467—538no—
384#467C2×D5314yescomplemented
385#451—534no—
386#451—538no—
387#451—534no—
388#451—538no—
389#451—534no—
390#451C2×D5314yescomplemented
391C2×#107—534no—
392C2×#103—538no—
393C2×C22⋊C8—531no—
394C2×C22⋊C8—532no—
395C2×C22⋊C8—534no—
396C2×C22⋊C8—534no—
397C2×C22⋊C8C2×D5311yescharacteristic
398C53C2×#318911yescharacteristic, complemented, Sylow
399C25—531no—
400C22×Q8—534no—
401C22×Q8—534no—
402C22×Q8—532no—
403C22×Q8—1062no—
404C22×Q8—1062no—
405C22×Q8—1062no—
406C22×Q8—2128no—
407C22×Q8C22×D5312yes—
408C23×C4—531no—
409C23×C4—532no—
410C23×C4—531no—
411C23×C4—532no—
412C23×C4—532no—
413C23×C4—531no—
414C23×C4—531no—
415C23×C4—532no—
416C23×C4—531no—
417C23×C4—1062no—
418C23×C4—1062no—
419C23×C4—2124no—
420C23×C4C22×D5311yescharacteristic
421C2×Q16—538no—
422C2×Q16—534no—
423C2×Q16—2128no—
424C2×Q16C22×D5314yescomplemented
425C22×C8—532no—
426C22×C8—534no—
427C22×C8—534no—
428C22×C8—2124no—
429C22×C8C22×D5312yes—
430C22⋊Q8—22no—
431C22⋊Q8—22no—
432C22⋊Q8—534no—
433C22⋊Q8—534no—
434C22⋊Q8—534no—
435C22⋊Q8—534no—
436C22⋊Q8—534no—
437C22⋊Q8—534no—
438C22⋊Q8—1064no—
439C22⋊Q8—1064no—
440C22⋊Q8—1064no—
441C22⋊Q8—1064no—
442C22⋊Q8—1064no—
443C22⋊Q8—1064no—
444C22⋊Q8—1064no—
445C22⋊Q8—1064no—
446C22⋊Q8—1062no—
447C22⋊Q8—1062no—
448C22⋊Q8—1062no—
449C22⋊Q8—1062no—
450C22⋊Q8—1062no—
451C22⋊Q8—1062no—
452C22⋊Q8C22×D5314yes—
453C22⋊Q8C22×D5314yes—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—532no—
456C2×C4⋊C4—534no—
457C2×C4⋊C4—534no—
458C2×C4⋊C4—1062no—
459C2×C4⋊C4—1062no—
460C2×C4⋊C4—1064no—
461C2×C4⋊C4—1064no—
462C2×C4⋊C4—1064no—
463C2×C4⋊C4—1064no—
464C2×C4⋊C4—1062no—
465C2×C4⋊C4—1062no—
466C2×C4⋊C4—1062no—
467C2×C4⋊C4—1062no—
468C2×C4⋊C4C22×D5312yes—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—1064no—
471C2×C22⋊C4—1064no—
472C2×C22⋊C4—1064no—
473C2×C22⋊C4—1064no—
474C2×C22⋊C4—1062no—
475C2×C22⋊C4—1062no—
476C2×C22⋊C4—1062no—
477#107—534no—
478#107—538no—
479#107C22×D5314yescomplemented
480#103—538no—
481#103—538no—
482#103—538no—
483#103C22×D5318yescomplemented
484C22⋊C8—534no—
485C22⋊C8—538no—
486C22⋊C8C22×D5314yes—
487C24—531no—
488C24—532no—
489C24—538no—
490C24—532no—
491C24—531no—
492C24—2122no—
493C24—2122no—
494C24D4×D5311yescharacteristic
495C2×Q8—22no—
496C2×Q8—44no—
497C2×Q8—534no—
498C2×Q8—1064no—
499C2×Q8—1064no—
500C2×Q8—10616no—
501C2×Q8—1062no—
502C2×Q8—2124no—
503C2×Q8—2128no—
504C2×Q8—2128no—
505C2×Q8—2128no—
506C2×Q8—2128no—
507C2×Q8C23×D5314yes—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—42no—
511C22×C4—531no—
512C22×C4—532no—
513C22×C4—531no—
514C22×C4—532no—
515C22×C4—531no—
516C22×C4—531no—
517C22×C4—532no—
518C22×C4—532no—
519C22×C4—531no—
520C22×C4—532no—
521C22×C4—531no—
522C22×C4—532no—
523C22×C4—532no—
524C22×C4—532no—
525C22×C4—1064no—
526C22×C4—1068no—
527C22×C4—1064no—
528C22×C4—1064no—
529C22×C4—1064no—
530C22×C4—1064no—
531C22×C4—1062no—
532C22×C4—1062no—
533C22×C4—2122no—
534C22×C4—2124no—
535C22×C4—2124no—
536C22×C4—2122no—
537C22×C4—2124no—
538C22×C4—2122no—
539C22×C4—2128no—
540C22×C4—2128no—
541C22×C4—2122no—
542C22×C4D4×D5312yes—
543C22×C4D4×D5311yescharacteristic
544C22×C4C23×D5312yes—
545C22×C4C23×D5311yescharacteristic
546Q16—44no—
547Q16—2124no—
548Q16—2128no—
549C2×C8—42no—
550C2×C8—534no—
551C2×C8—1068no—
552C2×C8—2124no—
553C2×C8—2122no—
554C2×C8C23×D5314yes—
555C4⋊C4—24no—
556C4⋊C4—24no—
557C4⋊C4—22no—
558C4⋊C4—534no—
559C4⋊C4—1064no—
560C4⋊C4—1064no—
561C4⋊C4—1064no—
562C4⋊C4—1064no—
563C4⋊C4—1064no—
564C4⋊C4—1064no—
565C4⋊C4—1062no—
566C4⋊C4—1064no—
567C4⋊C4—1064no—
568C4⋊C4C23×D5314yes—
569C22⋊C4—24no—
570C22⋊C4—24no—
571C22⋊C4—1064no—
572C22⋊C4—1064no—
573C22⋊C4—1064no—
574C22⋊C4—1064no—
575C22⋊C4—1064no—
576C22⋊C4—1064no—
577C23—41no—
578C23—41no—
579C23—531no—
580C23—534no—
581C23—538no—
582C23—531no—
583C23—532no—
584C23—538no—
585C23—534no—
586C23—1064no—
587C23—1062no—
588C23—1064no—
589C23—1062no—
590C23—2122no—
591C23—2121no—
592C23—2122no—
593C23—2121no—
594C23—21216no—
595C23Q16×D5314yescomplemented
596C23C2×D4×D5311yescharacteristic
597C23C2×D4×D5312yes—
598Q8—28no—
599Q8—44no—
600Q8—1068no—
601Q8—2124no—
602Q8—2128no—
603Q8—2128no—
604C2×C4—22no—
605C2×C4—24no—
606C2×C4—24no—
607C2×C4—24no—
608C2×C4—42no—
609C2×C4—41no—
610C2×C4—44no—
611C2×C4—44no—
612C2×C4—531no—
613C2×C4—534no—
614C2×C4—531no—
615C2×C4—532no—
616C2×C4—1062no—
617C2×C4—1064no—
618C2×C4—1062no—
619C2×C4—1064no—
620C2×C4—1062no—
621C2×C4—1064no—
622C2×C4—1062no—
623C2×C4—1064no—
624C2×C4—1064no—
625C2×C4—1064no—
626C2×C4—2122no—
627C2×C4—2122no—
628C2×C4—2122no—
629C2×C4—2128no—
630C2×C4—2128no—
631C2×C4—2128no—
632C2×C4—2128no—
633C2×C4—2122no—
634C2×C4—2121no—
635C2×C4—2124no—
636C2×C4—2124no—
637C2×C4C2×D4×D5311yescharacteristic
638C2×C4C2×D4×D5312yes—
639C2×C4C24×D5311yescharacteristic
640C8—24no—
641C8—1064no—
642C22—22no—
643C22—21no—
644C22—22no—
645C22—21no—
646C22—44no—
647C22—532no—
648C22—532no—
649C22—532no—
650C22—532no—
651C22—534no—
652C22—10616no—
653C22—1068no—
654C22—1062no—
655C22—1061no—
656C22—1062no—
657C22—1061no—
658C22—2128no—
659C22—2124no—
660C22C2×Q16×D5312yes—
661C22C2×Q16×D5314yes—
662C22C22×D4×D5311yescharacteristic
663C4—21no—
664C4—22no—
665C4—44no—
666C4—44no—
667C4—532no—
668C4—1061no—
669C4—1062no—
670C4—2124no—
671C4—2124no—
672C4H(5,𝔽2)×D5312yes—
673C2—24no—
674C2—22no—
675C2—534no—
676C2—1064no—
677C2—1062no—
678C2#534×D5311yescharacteristic
679C2C22×Q16×D5311yescharacteristic
680C2#575×D5311yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3189C2
socleC22×C53C23×D4
prime radicalC24×D53D4
hypercenter#3189D53
hypocenterC53C2×#3189
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3189

Complements

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

NH ≅ G/Ntype
2. #20285490C2semidirect
3. #20285489C2semidirect
4. #20285488C2semidirect
5. #20285487C2semidirect
6. #20285486C2semidirect
7. #484×D53C2semidirect
8. #467×D53C2semidirect
9. #451×D53C2semidirect
11. C53×#3189C2semidirect
14. C2×Q16×D53C22semidirect
32. #16810960C22semidirect
33. #16810959C22semidirect
34. #16810958C22semidirect
35. #16810957C22semidirect
36. #16810956C22semidirect
37. #16810865C22semidirect
38. #16810864C22semidirect
39. #16810863C22semidirect
40. #16810862C22semidirect
41. #16810861C22semidirect
42. #16810781C22semidirect
43. #16810780C22semidirect
44. #16810779C22semidirect
45. #16810778C22semidirect
46. #16810777C22semidirect
47. #107×D53C22semidirect
48. #103×D53C22semidirect
54. C53×#484C22semidirect
55. C53×#467C22semidirect
56. C53×#451C22semidirect
78. C2×Dic212C23semidirect
79. C2×#11719925C23semidirect
125. #13133151C23semidirect
126. #13133150C23semidirect
127. #13133142C23semidirect
128. #13133141C23semidirect
129. #13133140C23semidirect
134. C2×Q16×C53C23semidirect
143. #107×C53C23semidirect
144. #103×C53C23semidirect
149. C23×D53Q16semidirect
238. C23×C53C2×Q16semidirect
252. C22×D53C2×Q16semidirect
253. C22×D53C2×Q16semidirect
339. #3189D53direct (N × H)
351. D53#3189direct (N × H)
378. #484C2×D53semidirect
384. #467C2×D53semidirect
390. #451C2×D53semidirect
398. C53C2×#3189semidirect
424. C2×Q16C22×D53semidirect
479. #107C22×D53semidirect
483. #103C22×D53semidirect
595. C23Q16×D53semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×D532
#202854902
#202854892
#202854882
#202854872
#202854862
#484×D532
#467×D532
#451×D532
C2×C22⋊C8×D532
C53×#31892
C2×#318953