Finite Group Databasebeta

← #27402239

Subgroups — #27402239

Order 13568.

1042 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810692C211yesmaximal, characteristic
2C2×#16810665C211yesmaximal, characteristic, complemented
3C2×#106×D53C211yesmaximal, characteristic, complemented
4#20277637C211yesmaximal, characteristic
5#20277611C211yesmaximal, characteristic
6#20275486C211yesmaximal, characteristic, complemented
7#20275477C211yesmaximal, characteristic, complemented
8#20274912C211yesmaximal, characteristic, complemented
9#20274909C211yesmaximal, characteristic, complemented
10#20274907C211yesmaximal, characteristic, complemented
11#20274904C211yesmaximal, characteristic, complemented
12#20274880C211yesmaximal, characteristic, complemented
13#20274741C211yesmaximal, characteristic, complemented
14#20274614C211yesmaximal, characteristic, complemented
15C53×#1809C211yesmaximal, characteristic, complemented
16C22×C8×D53C2211yescharacteristic
17C2×C4×C22⋊D53C2211yescharacteristic
18C2×#13133177—21no—
19C2×#13133176C2211yescharacteristic
20C22×C4⋊Dic53C2211yescharacteristic
21C2×C4⋊C4×D53C2211yescharacteristic
22C2×C4⋊C4×D53C2211yescharacteristic
23#16810692C418yescomplemented
24#16810665—24no—
25C2×#13133151C2211yescharacteristic
26C2×#13133151C2211yescharacteristic
27C2×#13133150C2211yescharacteristic
28C2×#13133149C2211yescharacteristic
29C2×#13133149C2211yescharacteristic
30C2×#13133148C2211yescharacteristic
31C2×#13133148C2211yescharacteristic
32C2×#13133148C2211yescharacteristic
33#106×D53—24no—
34C2×#13133146C2211yescharacteristic
35C2×C22⋊#88322C2211yescharacteristic
36C2×#13133129C2211yescharacteristic
37C2×#13133127C2211yescharacteristic
38#16810520—21no—
39#16810511—21no—
40#16810505—21no—
41#16810499—21no—
42#16810497—21no—
43#16810495—21no—
44#16810492C2211yescharacteristic
45#16810488C2211yescharacteristic
46#16810480C2211yescharacteristic
47#16810480C2211yescharacteristic
48C4⋊C4×Dic53C2211yescharacteristic
49C4⋊C4×Dic53C2211yescharacteristic
50#16810470—21no—
51#16810385C2211yescharacteristic
52#16810385C2211yescharacteristic
53#16810385C2211yescharacteristic
54#16810385C2211yescharacteristic
55C22×M16×C53C2211yescharacteristic
56C2×#107×C53C2211yescharacteristic
57C2×#106×C53C2211yescharacteristic
58C53×#380C2211yescharacteristic
59C53×#380C2211yescharacteristic
60C53×#340C2211yescharacteristic
61C53×#340C2211yescharacteristic
62C22×C22⋊D53D411yescharacteristic
63C23×Dic53—21no—
64C22×C4×D53—21no—
65C22×C4×D53—21no—
66C22×C4×D53C2311yescharacteristic
67C22×#88322C2311yescharacteristic
68C22×#88322C2311yescharacteristic
69C2×C8×D53—22no—
70C2×C8×D53—22no—
71C2×C8×D53C2×C414yescomplemented
72C4×C22⋊D53C2×C414yes—
73C4×C22⋊D53Q814yes—
74#13133177—44no—
75#13133176—22no—
76#13133176—41no—
77C2×C4⋊Dic53—21no—
78C2×C4⋊Dic53—22no—
79C2×C4⋊Dic53—41no—
80C2×C4⋊Dic53C2311yescharacteristic
81C2×C4⋊Dic53C2311yescharacteristic
82C2×C4⋊Dic53C2311yescharacteristic
83C2×C4⋊Dic53C2311yescharacteristic
84C2×#11719919—21no—
85C2×#11719919—21no—
86C2×#11719919—21no—
87C2×#11719919—21no—
88C2×#11719919D411yescharacteristic
89C4⋊C4×D53—22no—
90C4⋊C4×D53—22no—
91C4⋊C4×D53—41no—
92C4⋊C4×D53—41no—
93C2×C22⋊Dic53—21no—
94C2×C22⋊Dic53D411yescharacteristic
95C2×#11719921—21no—
96C2×#11719921—21no—
97C2×#11719921D411yescharacteristic
98C2×C4×Dic53—21no—
99C2×C4×Dic53—21no—
100C2×C4×Dic53—21no—
101C2×C4×Dic53C2311yescharacteristic
102#13133151—22no—
103#13133151—22no—
104#13133150—41no—
105#13133149—22no—
106#13133149D414yescomplemented
107#13133148—22no—
108#13133148—22no—
109#13133148—41no—
110#13133146C2×C414yescomplemented
111C22⋊#88322C2×C414yescomplemented
112#13133129C2×C414yescomplemented
113#13133127C2×C414yescomplemented
114#13133124—21no—
115#13133124—21no—
116#13133124—21no—
117#13133124—21no—
118#13133124—21no—
119#13133124—21no—
120C23×C4×C53C2311yescharacteristic
121C2×M16×C53—22no—
122C2×M16×C53—22no—
123C2×M16×C53C2×C414yescomplemented
124C22×C8×C53C2311yescharacteristic
125C22×C8×C53C2311yescharacteristic
126C2×C4⋊C4×C53C2311yescharacteristic
127C2×C4⋊C4×C53C2311yescharacteristic
128C2×C4⋊C4×C53C2311yescharacteristic
129C2×C4⋊C4×C53C2311yescharacteristic
130C2×C22⋊C4×C53—21no—
131C2×C22⋊C4×C53—21no—
132#107×C53—22no—
133#106×C53—22no—
134#95×C53—21no—
135#95×C53—21no—
136C24×C53C2×D411yescharacteristic
137C23×D53C2×D411yescharacteristic
138C22×C4×C53—21no—
139C22×C4×C53—21no—
140C22×C4×C53—21no—
141C22×C4×C53—21no—
142C22×C4×C53—21no—
143C22×C4×C53—21no—
144C22×C4×C53—21no—
145C22×C4×C53—21no—
146C22×C4×C53C22×C412yes—
147C22×C4×C53C2×D411yescharacteristic
148C22×C4×C53C2×Q812yes—
149C22×C4×C53C2411yescharacteristic
150C2×C22⋊D53—22no—
151C2×C22⋊D53—22no—
152C2×C22⋊D53C4⋊C414yes—
153C22×Dic53—21no—
154C22×Dic53—21no—
155C22×Dic53—21no—
156C22×Dic53—21no—
157C22×Dic53—42no—
158C22×Dic53—42no—
159C22×Dic53—81no—
160C22×Dic53C2×D411yescharacteristic
161C22×Dic53C2×D411yescharacteristic
162C22×Dic53C2×D411yescharacteristic
163C2×C4×D53—21no—
164C2×C4×D53—21no—
165C2×C4×D53—21no—
166C2×C4×D53—21no—
167C2×C4×D53—42no—
168C2×C4×D53—42no—
169C2×C4×D53—42no—
170C2×C4×D53—42no—
171C2×C4×D53—81no—
172C2×C4×D53—81no—
173C2×C4×D53C22×C412yes—
174C2×C4×D53C2×Q812yes—
175M16×C53—28no—
176C2×C8×C53—21no—
177C2×C8×C53—21no—
178C2×C8×C53C22×C412yes—
179C2×C8×C53C22×C412yes—
180C2×C8×C53C2×D412yes—
181C2×C8×C53#4112yes—
182C4⋊C4×C53—21no—
183C4⋊C4×C53—21no—
184C4⋊C4×C53—21no—
185C4⋊C4×C53—21no—
186C4⋊C4×C53—21no—
187C4⋊C4×C53—21no—
188C4⋊C4×C53—21no—
189C4⋊C4×C53—21no—
190C22⋊C4×C53—42no—
191C22⋊C4×C53—81no—
192C22⋊Dic53—42no—
193C22⋊Dic53C4⋊C414yes—
194#11719921—42no—
195#11719921—42no—
196#11719921C4⋊C414yes—
197C4⋊Dic53—21no—
198C4⋊Dic53—21no—
199C4⋊Dic53—21no—
200C4⋊Dic53—21no—
201C4⋊Dic53—21no—
202C4⋊Dic53—21no—
203C4⋊Dic53—42no—
204C4⋊Dic53C2×D412yes—
205C4⋊Dic53C2×D412yes—
206#11719919—42no—
207#11719919—42no—
208#11719919—42no—
209#11719919—81no—
210#11719919C4⋊C414yes—
211C4×Dic53—42no—
212C4×Dic53—42no—
213C4×Dic53—81no—
214C4×Dic53C22×C412yes—
215C4×Dic53C2×Q812yes—
216C2×#88322—21no—
217C2×#88322—21no—
218C2×#88322—21no—
219C2×#88322—21no—
220C2×#88322C22×C412yes—
221C2×#88322C22×C412yes—
222C8×D53—28no—
223C23×C53—21no—
224C23×C53—21no—
225C23×C53—21no—
226C23×C53—21no—
227C23×C53—21no—
228C23×C53—21no—
229C23×C53C2×C4⋊C412yes—
230C23×C53C22×D411yescharacteristic
231C22×D53—21no—
232C22×D53—21no—
233C22×D53—21no—
234C22×D53—21no—
235C22×D53C2×C4⋊C412yes—
236C22×D53AGL(1,ℤ/8)12yes—
237C22×D53#13712yes—
238C2×C4×C53—21no—
239C2×C4×C53—21no—
240C2×C4×C53—22no—
241C2×C4×C53—22no—
242C2×C4×C53—22no—
243C2×C4×C53—22no—
244C2×C4×C53—41no—
245C2×C4×C53—41no—
246C2×C4×C53—41no—
247C2×C4×C53—41no—
248C2×C4×C53—41no—
249C2×C4×C53—41no—
250C2×C4×C53—41no—
251C2×C4×C53—41no—
252C2×C4×C53—41no—
253C2×C4×C53—41no—
254C2×C4×C53—41no—
255C2×C4×C53—41no—
256C2×C4×C53C2×C4⋊C412yes—
257C2×C4×C53C23×C411yescharacteristic
258C2×C4×C53C22×D411yescharacteristic
259C2×C4×C53C22×Q811yescharacteristic
260C2×C4×C53C2×#4111yescharacteristic
261C2×C4×C53H(5,𝔽2)11yescharacteristic
262C2×C4×C532−1+411yescharacteristic
263C22⋊D53—28no—
264C2×Dic53—21no—
265C2×Dic53—21no—
266C2×Dic53—21no—
267C2×Dic53—21no—
268C2×Dic53—21no—
269C2×Dic53—21no—
270C2×Dic53—22no—
271C2×Dic53—22no—
272C2×Dic53—41no—
273C2×Dic53—41no—
274C2×Dic53—41no—
275C2×Dic53—41no—
276C2×Dic53—41no—
277C2×Dic53—41no—
278C2×Dic53—41no—
279C2×Dic53—41no—
280C2×Dic53—41no—
281C2×Dic53—41no—
282C2×Dic53—84no—
283C2×Dic53C2×C4⋊C412yes—
284C2×Dic53C2×C4⋊C412yes—
285C2×Dic53C2×C4⋊C412yes—
286C4×D53—22no—
287C4×D53—22no—
288C4×D53—22no—
289C4×D53—22no—
290C4×D53—84no—
291C4×D53—84no—
292C8×C53—22no—
293C8×C53C4×D414yescomplemented
294#88322—22no—
295#88322—22no—
296#22659—531nomaximal, Sylow
297C22×C53—22no—
298C22×C53—22no—
299C22×C53—22no—
300C22×C53—41no—
301C22×C53—41no—
302C22×C53—41no—
303C22×C53—41no—
304C22×C53C22×C4⋊C411yescharacteristic
305C22×C53D4211yescharacteristic
306C22×C53#54711yescharacteristic
307C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
308C22×C53C2×#13711yescharacteristic
309C22×C53#57711yescharacteristic
310C22×C53#57711yescharacteristic
311C2×D53—22no—
312C2×D53—22no—
313C2×D53—22no—
314C2×D53—22no—
315C2×D53—22no—
316C2×D53—22no—
317C2×D53#42814yescomplemented
318C4×C53—22no—
319C4×C53—81no—
320C4×C53—81no—
321C4×C53—81no—
322C4×C53—81no—
323C4×C53C2×C4×D411yescharacteristic
324C4×C53#52011yescharacteristic
325C4×C53D4×Q811yescharacteristic
326C4×C53#55411yescharacteristic
327Dic53—22no—
328Dic53—22no—
329Dic53—22no—
330Dic53—42no—
331Dic53—42no—
332Dic53—81no—
333Dic53—81no—
334C2×#435—531no—
335C2×#428—531no—
336C22×#106—531no—
337#2352—531no—
338D4×C4⋊C4—531no—
339#1949—531no—
340#1948—531no—
341#1854—531no—
342#1853—531no—
343#1853—531no—
344#1852—531no—
345#1847—531no—
346#1809D5311yescharacteristic, complemented
347#1808—531no—
348#1776—531no—
349C2×C53—42no—
350C2×C53D4×C4⋊C411yescharacteristic
351C2×C53C2×#42811yescharacteristic
352C2×C53#291211yescharacteristic
353C2×C53#326511yescharacteristic
354C2×C53#326611yescharacteristic
355C2×C53#334411yescharacteristic
356C2×C53#334511yescharacteristic
357D53—24no—
358C22×M16C2×D5311yescharacteristic
359C23×C8—531no—
360C2×C4×D4—531no—
361C2×C4×D4—1061no—
362C2×#117—531no—
363C22×C4⋊C4—531no—
364C22×C4⋊C4—531no—
365C22×C4⋊C4—531no—
366#435—538no—
367#428—1064no—
368C2×#107—531no—
369C2×#107—531no—
370C2×#107—531no—
371C2×#107C2×D5311yescharacteristic
372C2×#106—531no—
373C2×#106—531no—
374C2×#106—531no—
375C2×#106—531no—
376C2×#106—531no—
377C2×#106—1064no—
378C2×#106C2×D5311yescharacteristic
379C2×C4⋊C8—531no—
380C2×C22⋊C8—531no—
381C2×C22⋊C8—531no—
382C2×#97—531no—
383#389—1061no—
384#388—1061no—
385#387—1061no—
386#386—1061no—
387#385—1061no—
388#385—1061no—
389#384—531no—
390#382—531no—
391#380—531no—
392#380—531no—
393#380C2×D5311yescharacteristic
394#380C2×D5311yescharacteristic
395C4×C4⋊C4—531no—
396C4×C4⋊C4—531no—
397C4×C22⋊C4—1061no—
398#340—531no—
399#340—531no—
400#340—531no—
401#340—531no—
402#340C2×D5311yescharacteristic
403#340C2×D5311yescharacteristic
404C53#2265911yescharacteristic, complemented, Sylow
405C22×D4—531no—
406C23×C4—531no—
407C23×C4—1061no—
408C23×C4—1061no—
409C23×C4—1061no—
410C23×C4C22×D5311yescharacteristic
411C2×M16—22no—
412C2×M16—22no—
413C2×M16C4×D5314yescomplemented
414C22×C8—531no—
415C22×C8—531no—
416C22×C8—534no—
417C22×C8—1062no—
418C22×C8—1062no—
419C22×C8C22×D5311yescharacteristic
420C22×C8C22×D5311yescharacteristic
421C4×D4—534no—
422C4×D4—534no—
423C4×D4—2124no—
424#117—1062no—
425#117—2121no—
426C2×C4⋊C4—531no—
427C2×C4⋊C4—531no—
428C2×C4⋊C4—531no—
429C2×C4⋊C4—531no—
430C2×C4⋊C4—531no—
431C2×C4⋊C4—1062no—
432C2×C4⋊C4—1062no—
433C2×C4⋊C4—1062no—
434C2×C4⋊C4—1061no—
435C2×C4⋊C4—1061no—
436C2×C4⋊C4—1061no—
437C2×C4⋊C4—1061no—
438C2×C4⋊C4—1061no—
439C2×C4⋊C4—2121no—
440C2×C4⋊C4—2121no—
441C2×C4⋊C4—2121no—
442C2×C4⋊C4C22×D5311yescharacteristic
443C2×C4⋊C4C22×D5311yescharacteristic
444C2×C4⋊C4C22×D5311yescharacteristic
445C2×C4⋊C4C22×D5311yescharacteristic
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—531no—
449C2×C22⋊C4—531no—
450C2×C22⋊C4—1061no—
451C2×C22⋊C4—1061no—
452C2×C22⋊C4—1061no—
453C2×C42—531no—
454C2×C42—1061no—
455C2×C42—1061no—
456C2×C42—1061no—
457#107—22no—
458#107—1062no—
459#107—1062no—
460#107—2121no—
461#106—22no—
462#106—534no—
463#106—1062no—
464#106—1062no—
465#106—1062no—
466#106—2121no—
467C4⋊C8—534no—
468C22⋊C8—534no—
469C22⋊C8—534no—
470#97—534no—
471#95—21no—
472#95—21no—
473#95—1061no—
474#95—1061no—
475#95—1061no—
476#95—1061no—
477#95—1061no—
478#95—1061no—
479C24—531no—
480C24D4×D5311yescharacteristic
481C2×D4—534no—
482C2×D4—1062no—
483C2×D4—1062no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—531no—
493C22×C4—531no—
494C22×C4—531no—
495C22×C4—532no—
496C22×C4—532no—
497C22×C4—1061no—
498C22×C4—1061no—
499C22×C4—1061no—
500C22×C4—1061no—
501C22×C4—1061no—
502C22×C4—1061no—
503C22×C4—1061no—
504C22×C4—1061no—
505C22×C4—4241no—
506C22×C4—4241no—
507C22×C4—4241no—
508C22×C4—2122no—
509C22×C4—2122no—
510C22×C4—2122no—
511C22×C4—2122no—
512C22×C4—2122no—
513C22×C4—2122no—
514C22×C4C2×C4×D5312yes—
515C22×C4D4×D5311yescharacteristic
516C22×C4Q8×D5312yes—
517C22×C4C23×D5311yescharacteristic
518M16—28no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—532no—
522C2×C8—532no—
523C2×C8—1061no—
524C2×C8—1061no—
525C2×C8—1061no—
526C2×C8—1061no—
527C2×C8—1068no—
528C2×C8C2×C4×D5312yes—
529C2×C8C2×C4×D5312yes—
530C2×C8D4×D5312yes—
531C2×C8#1171994712yes—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—534no—
541C4⋊C4—532no—
542C4⋊C4—532no—
543C4⋊C4—1061no—
544C4⋊C4—1061no—
545C4⋊C4—1061no—
546C4⋊C4—1061no—
547C4⋊C4—1061no—
548C4⋊C4—1061no—
549C4⋊C4—4241no—
550C4⋊C4—2122no—
551C4⋊C4—2122no—
552C4⋊C4—2122no—
553C4⋊C4—2122no—
554C22⋊C4—42no—
555C22⋊C4—81no—
556C22⋊C4—534no—
557C22⋊C4—534no—
558C22⋊C4—2122no—
559C22⋊C4—2122no—
560C22⋊C4—2122no—
561C42—532no—
562C42—532no—
563C42—4241no—
564C42—2122no—
565C42—2122no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—532no—
573C23—532no—
574C23—532no—
575C23—1061no—
576C23—1061no—
577C23—1061no—
578C23—1061no—
579C23C4⋊C4×D5312yes—
580C23C2×D4×D5311yescharacteristic
581D4—1068no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—532no—
601C2×C4—532no—
602C2×C4—532no—
603C2×C4—1061no—
604C2×C4—1061no—
605C2×C4—1061no—
606C2×C4—1061no—
607C2×C4—1061no—
608C2×C4—1061no—
609C2×C4—1062no—
610C2×C4—1062no—
611C2×C4—1062no—
612C2×C4—1062no—
613C2×C4—1062no—
614C2×C4—1062no—
615C2×C4—4244no—
616C2×C4—4244no—
617C2×C4—4244no—
618C2×C4—2121no—
619C2×C4—2121no—
620C2×C4—2121no—
621C2×C4—2121no—
622C2×C4—2121no—
623C2×C4—2121no—
624C2×C4—2121no—
625C2×C4—2121no—
626C2×C4—2121no—
627C2×C4—2121no—
628C2×C4C4⋊C4×D5312yes—
629C2×C4C22×C4×D5311yescharacteristic
630C2×C4C2×D4×D5311yescharacteristic
631C2×C4C2×Q8×D5311yescharacteristic
632C2×C4C2×#1171994711yescharacteristic
633C2×C4#1313326311yescharacteristic
634C2×C4#1313326411yescharacteristic
635C8—22no—
636C8—1062no—
637C8—1062no—
638C8#1313317714yescomplemented
639C22—22no—
640C22—22no—
641C22—22no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—534no—
647C22—1062no—
648C22—1062no—
649C22—1062no—
650C22—1062no—
651C22—1062no—
652C22—1062no—
653C22C2×C4⋊C4×D5311yescharacteristic
654C22#1681125711yescharacteristic
655C22#1681127311yescharacteristic
656C22AGL(1,ℤ/8)×D5311yescharacteristic
657C22#137×D5311yescharacteristic
658C22#1681143211yescharacteristic
659C22#1681143311yescharacteristic
660C4—22no—
661C4—81no—
662C4—81no—
663C4—81no—
664C4—81no—
665C4—1062no—
666C4—1062no—
667C4—1062no—
668C4—4241no—
669C4—4241no—
670C4—2122no—
671C4—2122no—
672C4C2×#1313317711yescharacteristic
673C4#1681110311yescharacteristic
674C4#1681128611yescharacteristic
675C4#1681133111yescharacteristic
676C2—42no—
677C2—1064no—
678C2#2027761111yescharacteristic
679C2#428×D5311yescharacteristic
680C2#2028330911yescharacteristic
681C2#2028621711yescharacteristic
682C2#2028623211yescharacteristic
683C2#2028716511yescharacteristic
684C2#2028718011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1809C2
socleC23×C53C22×D4
prime radicalC22×C22⋊D53D4
cosocleC22×C4×C53C24
hypercenter#1809D53
hypocenterC53#22659
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1809

Complements

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

NH ≅ G/Ntype
2. C2×#16810665C2semidirect
3. C2×#106×D53C2semidirect
6. #20275486C2semidirect
7. #20275477C2semidirect
8. #20274912C2semidirect
9. #20274909C2semidirect
10. #20274907C2semidirect
11. #20274904C2semidirect
12. #20274880C2semidirect
13. #20274741C2semidirect
14. #20274614C2semidirect
15. C53×#1809C2semidirect
23. #16810692C4semidirect
71. C2×C8×D53C2×C4semidirect
106. #13133149D4semidirect
110. #13133146C2×C4semidirect
111. C22⋊#88322C2×C4semidirect
112. #13133129C2×C4semidirect
113. #13133127C2×C4semidirect
123. C2×M16×C53C2×C4semidirect
293. C8×C53C4×D4semidirect
317. C2×D53#428semidirect
346. #1809D53semidirect
404. C53#22659semidirect
413. C2×M16C4×D53semidirect
638. C8#13133177semidirect

Maximal subgroups

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

subgroupindex
C2×#168106922
C2×#168106652
C2×#106×D532
#202776372
#202776112
#202754862
#202754772
#202749122
#202749092
#202749072
#202749042
#202748802
#202747412
#202746142
C53×#18092
#2265953