Finite Group Databasebeta

← D53×#2314 #27542681

Subgroups — D53×#2314 #27542681

Order 13568.

2678 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#117×D53C211yesmaximal, characteristic
2#20277325C211yesmaximal, characteristic, complemented
3#20277324C211yesmaximal, characteristic, complemented
4#20277323C211yesmaximal, characteristic, complemented
5#20277322C212yesmaximal, complemented
6#20277321C214yesmaximal, complemented
7#20277320C212yesmaximal, complemented
8#20277319C214yesmaximal, complemented
9#388×D53C214yesmaximal
10#387×D53C214yesmaximal, complemented
11#384×D53C211yesmaximal, characteristic, complemented
12#382×D53C211yesmaximal, characteristic, complemented
13#380×D53C212yesmaximal
14C4×C4⋊C4×D53C212yesmaximal, complemented
15C53×#2314C211yesmaximal, characteristic, complemented
16C23×C4×D53C2211yescharacteristic
17C2×#13133176C2211yescharacteristic
18C2×#13133175C2212yes—
19C2×#13133174C2211yescharacteristic
20C2×#13133174C2211yescharacteristic
21C2×#13133173C2212yes—
22#117×D53C4116yescomplemented
23C2×C4⋊C4×D53C2212yes—
24C2×C4⋊C4×D53C2212yes—
25C2×C4⋊C4×D53C2214yes—
26C2×C4⋊C4×D53C2212yes—
27C2×C22⋊C4×D53C2214yes—
28C2×C22⋊C4×D53C2212yes—
29C2×C42×D53C2214yes—
30C2×C42×D53C2211yescharacteristic
31C2×C42×D53C2211yescharacteristic
32#16810517C2214yes—
33#16810516C2214yes—
34#16810515C2214yes—
35#16810514C2214yes—
36#16810513C2214yes—
37#16810512C2214yes—
38#16810511C2214yes—
39#16810510C2214yescomplemented
40#16810509C2214yescomplemented
41#16810508C2214yescomplemented
42#16810507C2214yescomplemented
43#16810506C2214yescomplemented
44#16810505C2214yescomplemented
45#16810504C2214yescomplemented
46#16810493C2211yescharacteristic, complemented
47#16810492C2214yescomplemented
48#16810492C2212yescomplemented
49#16810489C2211yescharacteristic, complemented
50#16810488C2212yescomplemented
51#16810487C2214yescomplemented
52#16810483C2212yes—
53#16810482C2214yes—
54#16810481C2214yes—
55#16810480C2212yes—
56#16810480C2212yes—
57C4⋊C4×Dic53C2212yescomplemented
58C4⋊C4×Dic53C2212yescomplemented
59C4×#11719919C2214yescomplemented
60C4×C4⋊Dic53C2212yescomplemented
61#16810474C2214yescomplemented
62#95×D53C2214yes—
63#95×D53C2214yes—
64#95×D53C2214yes—
65C2×#117×C53C2211yescharacteristic
66C53×#388C2214yes—
67C53×#387C2214yescomplemented
68C53×#384C2211yescharacteristic, complemented
69C53×#382C2211yescharacteristic, complemented
70C53×#380C2212yes—
71C4×C4⋊C4×C53C2212yescomplemented
72C24×D53C2311yescharacteristic
73C23×Dic53C2311yescharacteristic
74C22×C4×D53—24no—
75C22×C4×D53—24no—
76C22×C4×D53C2×C418yes—
77C22×C4×D53C2314yes—
78C22×C4×D53C2314yes—
79C22×C4×D53C2312yes—
80C22×C4×D53C2312yes—
81C22×C4×D53C2311yescharacteristic
82C22×C4×D53C2311yescharacteristic
83C22×C4×D53C2311yescharacteristic
84C22×C4×D53C2311yescharacteristic
85#13133176C2×C418yescomplemented
86#13133175C2×C4116yescomplemented
87#13133174C2×C418yescomplemented
88#13133174C2×C418yescomplemented
89#13133173C2×C4116yescomplemented
90C2×C4⋊Dic53C2312yes—
91C2×C4⋊Dic53C2312yes—
92C2×C4⋊Dic53C2314yes—
93C2×C4⋊Dic53C2312yes—
94C2×#11719919C2314yes—
95C2×#11719919C2314yes—
96C2×#11719919C2314yes—
97C2×#11719919C2314yes—
98C2×#11719919C2312yes—
99C2×#11719919C2312yes—
100C4⋊C4×D53—28no—
101C4⋊C4×D53—28no—
102C4⋊C4×D53—48no—
103C4⋊C4×D53C2×C4116yes—
104C2×C22⋊Dic53C2314yes—
105C2×C22⋊Dic53C2312yes—
106C2×#11719921C2314yes—
107C2×#11719921C2314yes—
108C2×#11719921C2312yes—
109C2×#11719921C2312yes—
110C22⋊C4×D53—48no—
111C22⋊C4×D53C2×C4116yes—
112C2×C4×Dic53C2314yes—
113C2×C4×Dic53C2314yes—
114C2×C4×Dic53C2314yes—
115C2×C4×Dic53C2312yes—
116C2×C4×Dic53C2312yes—
117C2×C4×Dic53C2311yescharacteristic
118C2×C4×Dic53C2311yescharacteristic
119C42×D53—48no—
120C42×D53C2×C418yes—
121C42×D53C2×C418yes—
122#13133124C2314yes—
123#13133124C2314yes—
124#13133124C2314yes—
125#13133124C2314yes—
126#13133124C2314yes—
127#13133124C2314yes—
128#13133124C2314yes—
129#13133124C2314yes—
130#13133124C2314yes—
131C23×C4×C53C2311yescharacteristic
132#117×C53C2×C418yescomplemented
133C2×C4⋊C4×C53C2312yes—
134C2×C4⋊C4×C53C2312yes—
135C2×C4⋊C4×C53C2314yes—
136C2×C4⋊C4×C53C2312yes—
137C2×C22⋊C4×C53C2314yes—
138C2×C22⋊C4×C53C2312yes—
139C2×C42×C53C2314yes—
140C2×C42×C53C2311yescharacteristic
141C2×C42×C53C2311yescharacteristic
142#95×C53C2314yes—
143#95×C53C2314yes—
144#95×C53C2314yes—
145C24×C53C2411yescharacteristic
146C23×D53—22no—
147C23×D53—22no—
148C23×D53—24no—
149C23×D53—24no—
150C23×D53C22×C414yes—
151C23×D53C2411yescharacteristic
152C23×D53C2411yescharacteristic
153C22×C4×C53—22no—
154C22×C4×C53—22no—
155C22×C4×C53C22×C414yes—
156C22×C4×C53C2414yes—
157C22×C4×C53C2414yes—
158C22×C4×C53C2411yescharacteristic
159C22×C4×C53C2412yes—
160C22×C4×C53C2412yes—
161C22×C4×C53C2411yescharacteristic
162C22×Dic53—22no—
163C22×Dic53—22no—
164C22×Dic53C22×C414yes—
165C22×Dic53C2414yes—
166C22×Dic53C2414yes—
167C22×Dic53C2411yescharacteristic
168C22×Dic53C2412yes—
169C22×Dic53C2412yes—
170C22×Dic53C2411yescharacteristic
171C2×C4×D53—22no—
172C2×C4×D53—22no—
173C2×C4×D53—24no—
174C2×C4×D53—24no—
175C2×C4×D53—24no—
176C2×C4×D53—24no—
177C2×C4×D53—22no—
178C2×C4×D53—22no—
179C2×C4×D53—22no—
180C2×C4×D53—22no—
181C2×C4×D53—232no—
182C2×C4×D53—28no—
183C2×C4×D53—28no—
184C2×C4×D53—28no—
185C2×C4×D53—28no—
186C2×C4×D53—28no—
187C2×C4×D53—28no—
188C2×C4×D53C22×C418yes—
189C2×C4×D53C22×C418yes—
190C2×C4×D53C22×C414yes—
191C2×C4×D53C22×C414yes—
192C2×C4×D53C22×C414yes—
193C2×C4×D53C22×C414yes—
194C2×C4×D53#4114yes—
195C2×C4×D53#4114yes—
196C4⋊C4×C53—24no—
197C4⋊C4×C53—24no—
198C4⋊C4×C53—44no—
199C4⋊C4×C53C22×C418yes—
200C22⋊C4×C53—44no—
201C22⋊C4×C53C22×C418yes—
202C42×C53—44no—
203C42×C53C22×C414yes—
204C42×C53C22×C414yes—
205C22⋊Dic53—44no—
206C22⋊Dic53C22×C418yes—
207#11719921—44no—
208#11719921—44no—
209#11719921C22×C418yes—
210#11719921C22×C418yes—
211C4⋊Dic53—24no—
212C4⋊Dic53—24no—
213C4⋊Dic53—44no—
214C4⋊Dic53C22×C418yes—
215#11719919—28no—
216#11719919—28no—
217#11719919—44no—
218#11719919—44no—
219#11719919C22×C418yes—
220#11719919C22×C418yes—
221C4×Dic53—44no—
222C4×Dic53—44no—
223C4×Dic53—44no—
224C4×Dic53C22×C418yes—
225C4×Dic53C22×C418yes—
226C4×Dic53C22×C414yes—
227C4×Dic53C22×C414yes—
228C23×C53—21no—
229C23×C53—21no—
230C23×C53—22no—
231C23×C53—22no—
232C23×C53C23×C412yes—
233C23×C53C2511yescharacteristic
234C22×D53—21no—
235C22×D53—21no—
236C22×D53—22no—
237C22×D53—22no—
238C22×D53—28no—
239C22×D53—216no—
240C22×D53—44no—
241C22×D53—44no—
242C22×D53—48no—
243C22×D53C23×C412yes—
244C22×D53C23×C412yes—
245C22×D53C2×#4112yes—
246C22×D53C2×#4112yes—
247C22×D53H(5,𝔽2)14yes—
248C22×D532−1+414yes—
249C2×C4×C53—21no—
250C2×C4×C53—21no—
251C2×C4×C53—22no—
252C2×C4×C53—22no—
253C2×C4×C53—22no—
254C2×C4×C53—22no—
255C2×C4×C53—28no—
256C2×C4×C53—24no—
257C2×C4×C53—24no—
258C2×C4×C53—24no—
259C2×C4×C53—24no—
260C2×C4×C53—24no—
261C2×C4×C53—24no—
262C2×C4×C53C23×C412yes—
263C2×C4×C53C23×C414yes—
264C2×C4×C53C23×C414yes—
265C2×C4×C53C23×C412yes—
266C2×C4×C53C2×#4112yes—
267C2×C4×C53C2×#4112yes—
268C2×Dic53—21no—
269C2×Dic53—21no—
270C2×Dic53—22no—
271C2×Dic53—22no—
272C2×Dic53—22no—
273C2×Dic53—22no—
274C2×Dic53—28no—
275C2×Dic53—24no—
276C2×Dic53—24no—
277C2×Dic53—24no—
278C2×Dic53—24no—
279C2×Dic53—24no—
280C2×Dic53—24no—
281C2×Dic53C23×C412yes—
282C2×Dic53C23×C414yes—
283C2×Dic53C23×C414yes—
284C2×Dic53C23×C412yes—
285C2×Dic53C2×#4112yes—
286C2×Dic53C2×#4112yes—
287C4×D53—28no—
288C4×D53—216no—
289C4×D53—216no—
290C4×D53—28no—
291C4×D53—28no—
292C4×D53—416no—
293C4×D53—416no—
294C4×D53#117116yes—
295C2×#2314—531nomaximal, Sylow
296C22×C53—22no—
297C22×C53—24no—
298C22×C53—41no—
299C22×C53—41no—
300C22×C53—42no—
301C22×C53C24×C411yescharacteristic
302C22×C53C22×#4111yescharacteristic
303C22×C53C22×#4111yescharacteristic
304C22×C53C2×H(5,𝔽2)12yes—
305C22×C53C2×2−1+412yes—
306C2×D53—22no—
307C2×D53—24no—
308C2×D53—41no—
309C2×D53—41no—
310C2×D53—42no—
311C2×D53—416no—
312C2×D53C2×#11714yes—
313C2×D53#52018yes—
314C2×D53#54014yes—
315C2×D53#54114yes—
316C2×D53#54218yes—
317C4×C53—22no—
318C4×C53—24no—
319C4×C53—24no—
320C4×C53—44no—
321C4×C53—44no—
322C4×C53C2×#11714yes—
323Dic53—22no—
324Dic53—24no—
325Dic53—24no—
326Dic53—44no—
327Dic53—44no—
328Dic53C2×#11714yes—
329C22×#117—531no—
330#2314—534no—
331#2314—534no—
332#2314—531no—
333#2314—531no—
334#2314—532no—
335#2314—532no—
336#2314—531no—
337#2314D5311yescharacteristic, direct product factor
338C2×#388—534no—
339C2×#387—534no—
340C2×#384—531no—
341C2×#382—531no—
342C2×#380—532no—
343C2×C4×C4⋊C4—532no—
344C2×C53—42no—
345C2×C53C22×#11711yescharacteristic
346C2×C53C2×#52012yes—
347C2×C53C2×#54011yescharacteristic
348C2×C53C2×#54111yescharacteristic
349C2×C53C2×#54212yes—
350D53—42no—
351D53#231418yesdirect product factor
352C24×C4—531no—
353C2×#117—531no—
354C2×#117—5316no—
355C2×#117—532no—
356C2×#117—532no—
357C2×#117—531no—
358C2×#117—531no—
359C2×#117C2×D5311yescharacteristic
360C22×C4⋊C4—532no—
361C22×C4⋊C4—532no—
362C22×C4⋊C4—532no—
363C22×C4⋊C4—534no—
364C22×C22⋊C4—532no—
365C22×C22⋊C4—534no—
366C22×C42—531no—
367C22×C42—531no—
368C22×C42—534no—
369#388—534no—
370#388—534no—
371#388—534no—
372#388—534no—
373#388—534no—
374#388—534no—
375#388—534no—
376#388C2×D5314yes—
377#387—534no—
378#387—534no—
379#387—534no—
380#387—534no—
381#387—534no—
382#387—534no—
383#387—534no—
384#387C2×D5314yescomplemented
385#384—534no—
386#384—532no—
387#384—531no—
388#384C2×D5311yescharacteristic, complemented
389#382—532no—
390#382—531no—
391#382—534no—
392#382C2×D5311yescharacteristic, complemented
393#380—532no—
394#380—532no—
395#380—532no—
396#380—534no—
397#380—534no—
398#380C2×D5312yes—
399C4×C4⋊C4—532no—
400C4×C4⋊C4—532no—
401C4×C4⋊C4—532no—
402C4×C4⋊C4—534no—
403C4×C4⋊C4—534no—
404C4×C4⋊C4C2×D5312yescomplemented
405C2×#95—534no—
406C2×#95—534no—
407C2×#95—534no—
408C53C2×#231411yescharacteristic, complemented, Sylow
409C25—531no—
410C23×C4—531no—
411C23×C4—531no—
412C23×C4—538no—
413C23×C4—532no—
414C23×C4—532no—
415C23×C4—531no—
416C23×C4—531no—
417C23×C4—531no—
418C23×C4—534no—
419C23×C4—534no—
420C23×C4—1064no—
421C23×C4—1064no—
422C23×C4C22×D5311yescharacteristic
423#117—538no—
424#117—5316no—
425#117—5316no—
426#117—538no—
427#117—538no—
428#117C4×D5318yescomplemented
429C2×C4⋊C4—532no—
430C2×C4⋊C4—532no—
431C2×C4⋊C4—532no—
432C2×C4⋊C4—5316no—
433C2×C4⋊C4—534no—
434C2×C4⋊C4—534no—
435C2×C4⋊C4—532no—
436C2×C4⋊C4—532no—
437C2×C4⋊C4—534no—
438C2×C4⋊C4—534no—
439C2×C4⋊C4—534no—
440C2×C4⋊C4—1068no—
441C2×C4⋊C4—1068no—
442C2×C4⋊C4—2128no—
443C2×C4⋊C4C22×D5312yes—
444C2×C4⋊C4C22×D5312yes—
445C2×C4⋊C4C22×D5314yes—
446C2×C4⋊C4C22×D5312yes—
447C2×C22⋊C4—532no—
448C2×C22⋊C4—532no—
449C2×C22⋊C4—532no—
450C2×C22⋊C4—5316no—
451C2×C22⋊C4—534no—
452C2×C22⋊C4—534no—
453C2×C22⋊C4—534no—
454C2×C22⋊C4—2128no—
455C2×C22⋊C4C22×D5314yes—
456C2×C22⋊C4C22×D5312yes—
457C2×C42—532no—
458C2×C42—531no—
459C2×C42—532no—
460C2×C42—531no—
461C2×C42—538no—
462C2×C42—538no—
463C2×C42—534no—
464C2×C42—534no—
465C2×C42—534no—
466C2×C42—2128no—
467C2×C42C22×D5314yes—
468C2×C42C22×D5311yescharacteristic
469C2×C42C22×D5311yescharacteristic
470#95—534no—
471#95—534no—
472#95—534no—
473#95—534no—
474#95—534no—
475#95—534no—
476#95—534no—
477#95—534no—
478#95—534no—
479#95C22×D5314yes—
480#95C22×D5314yes—
481#95C22×D5314yes—
482C24—531no—
483C24—534no—
484C24—531no—
485C24—1064no—
486C24—1062no—
487C24—1062no—
488C24—1064no—
489C24C23×D5311yescharacteristic
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—531no—
493C22×C4—534no—
494C22×C4—534no—
495C22×C4—534no—
496C22×C4—534no—
497C22×C4—531no—
498C22×C4—532no—
499C22×C4—532no—
500C22×C4—538no—
501C22×C4—538no—
502C22×C4—534no—
503C22×C4—534no—
504C22×C4—534no—
505C22×C4—534no—
506C22×C4—534no—
507C22×C4—1062no—
508C22×C4—1062no—
509C22×C4—10632no—
510C22×C4—1064no—
511C22×C4—1064no—
512C22×C4—1064no—
513C22×C4—1064no—
514C22×C4—1062no—
515C22×C4—1062no—
516C22×C4—1068no—
517C22×C4—1068no—
518C22×C4—1068no—
519C22×C4—1068no—
520C22×C4—1068no—
521C22×C4—1068no—
522C22×C4—1062no—
523C22×C4—1062no—
524C22×C4—1062no—
525C22×C4—1062no—
526C22×C4C2×C4×D5314yes—
527C22×C4C23×D5314yes—
528C22×C4C23×D5314yes—
529C22×C4C23×D5311yescharacteristic
530C22×C4C23×D5312yes—
531C22×C4C23×D5312yes—
532C22×C4C23×D5311yescharacteristic
533C4⋊C4—24no—
534C4⋊C4—24no—
535C4⋊C4—44no—
536C4⋊C4—538no—
537C4⋊C4—538no—
538C4⋊C4—538no—
539C4⋊C4—1068no—
540C4⋊C4—1068no—
541C4⋊C4—1064no—
542C4⋊C4—1064no—
543C4⋊C4—2124no—
544C4⋊C4—2124no—
545C4⋊C4—2124no—
546C4⋊C4C2×C4×D5318yes—
547C22⋊C4—44no—
548C22⋊C4—538no—
549C22⋊C4—538no—
550C22⋊C4—538no—
551C22⋊C4—2124no—
552C22⋊C4—2124no—
553C22⋊C4—2124no—
554C22⋊C4C2×C4×D5318yes—
555C42—44no—
556C42—538no—
557C42—538no—
558C42—534no—
559C42—534no—
560C42—2124no—
561C42—2124no—
562C42—2124no—
563C42C2×C4×D5314yes—
564C42C2×C4×D5314yes—
565C23—21no—
566C23—21no—
567C23—22no—
568C23—22no—
569C23—532no—
570C23—532no—
571C23—532no—
572C23—534no—
573C23—534no—
574C23—532no—
575C23—1068no—
576C23—10616no—
577C23—1061no—
578C23—1061no—
579C23—1062no—
580C23—1062no—
581C23—2124no—
582C23—2124no—
583C23—2128no—
584C23C22×C4×D5312yes—
585C23C24×D5311yescharacteristic
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—28no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—24no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—532no—
600C2×C4—532no—
601C2×C4—532no—
602C2×C4—5316no—
603C2×C4—534no—
604C2×C4—534no—
605C2×C4—532no—
606C2×C4—1068no—
607C2×C4—10616no—
608C2×C4—10616no—
609C2×C4—1068no—
610C2×C4—1068no—
611C2×C4—1061no—
612C2×C4—1061no—
613C2×C4—1062no—
614C2×C4—1062no—
615C2×C4—1062no—
616C2×C4—1062no—
617C2×C4—1068no—
618C2×C4—1064no—
619C2×C4—1064no—
620C2×C4—1064no—
621C2×C4—1064no—
622C2×C4—1064no—
623C2×C4—1064no—
624C2×C4—21216no—
625C2×C4—21216no—
626C2×C4C22×C4×D5314yes—
627C2×C4C22×C4×D5314yes—
628C2×C4C22×C4×D5312yes—
629C2×C4C22×C4×D5312yes—
630C2×C4#41×D5312yes—
631C2×C4#41×D5312yes—
632C22—22no—
633C22—24no—
634C22—41no—
635C22—41no—
636C22—42no—
637C22—534no—
638C22—534no—
639C22—538no—
640C22—534no—
641C22—538no—
642C22—1062no—
643C22—1064no—
644C22—21216no—
645C22—2121no—
646C22—2121no—
647C22—2122no—
648C22C23×C4×D5311yescharacteristic
649C22C2×#41×D5311yescharacteristic
650C22C2×#41×D5311yescharacteristic
651C22H(5,𝔽2)×D5312yes—
652C222−1+4×D5312yes—
653C4—22no—
654C4—24no—
655C4—24no—
656C4—44no—
657C4—44no—
658C4—534no—
659C4—1062no—
660C4—1064no—
661C4—1064no—
662C4—2124no—
663C4—2124no—
664C4#117×D5314yes—
665C2—42no—
666C2—538no—
667C2—2122no—
668C2C2×#117×D5311yescharacteristic
669C2#520×D5312yes—
670C2#540×D5311yescharacteristic
671C2#541×D5311yescharacteristic
672C2#542×D5312yes—
subgroupG/H
center, FrattiniC23C24×D53
commutatorC22×C53C24×C4
FittingC53×#2314C2
socle, cosocleC23×C53C25
prime radicalC24×D53C23
hypercenter#2314D53
hypocenterC53C2×#2314
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ #2314

Complements

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

NH ≅ G/Ntype
2. #20277325C2semidirect
3. #20277324C2semidirect
4. #20277323C2semidirect
5. #20277322C2semidirect
6. #20277321C2semidirect
7. #20277320C2semidirect
8. #20277319C2semidirect
10. #387×D53C2semidirect
11. #384×D53C2semidirect
12. #382×D53C2semidirect
14. C4×C4⋊C4×D53C2semidirect
15. C53×#2314C2semidirect
22. #117×D53C4semidirect
39. #16810510C22semidirect
40. #16810509C22semidirect
41. #16810508C22semidirect
42. #16810507C22semidirect
43. #16810506C22semidirect
44. #16810505C22semidirect
45. #16810504C22semidirect
46. #16810493C22semidirect
47. #16810492C22semidirect
48. #16810492C22semidirect
49. #16810489C22semidirect
50. #16810488C22semidirect
51. #16810487C22semidirect
57. C4⋊C4×Dic53C22semidirect
58. C4⋊C4×Dic53C22semidirect
59. C4×#11719919C22semidirect
60. C4×C4⋊Dic53C22semidirect
61. #16810474C22semidirect
67. C53×#387C22semidirect
68. C53×#384C22semidirect
69. C53×#382C22semidirect
71. C4×C4⋊C4×C53C22semidirect
85. #13133176C2×C4semidirect
86. #13133175C2×C4semidirect
87. #13133174C2×C4semidirect
88. #13133174C2×C4semidirect
89. #13133173C2×C4semidirect
132. #117×C53C2×C4semidirect
337. #2314D53direct (N × H)
351. D53#2314direct (N × H)
384. #387C2×D53semidirect
388. #384C2×D53semidirect
392. #382C2×D53semidirect
404. C4×C4⋊C4C2×D53semidirect
408. C53C2×#2314semidirect
428. #117C4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×#117×D532
#202773252
#202773242
#202773232
#202773222
#202773212
#202773202
#202773192
#388×D532
#387×D532
#384×D532
#382×D532
#380×D532
C4×C4⋊C4×D532
C53×#23142
C2×#231453