Finite Group Databasebeta

← #27384210

Subgroups — #27384210

Order 13568.

1428 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×Dic53C211yesmaximal, characteristic
2#20283344C211yesmaximal, characteristic, complemented
3C4×#13133173C211yesmaximal, characteristic, complemented
4#20274815C211yesmaximal, characteristic, complemented
5#20274812C211yesmaximal, characteristic, complemented
6#20274733C214yesmaximal, complemented
7#20274659C211yesmaximal, characteristic
8#104×Dic53C214yesmaximal, complemented
9C53×#1789C211yesmaximal, characteristic
10#41×Dic53—21no—
11#41×Dic53—21no—
12#41×Dic53—21no—
13#41×Dic53—21no—
14#41×Dic53C412yescomplemented
15#41×Dic53C412yescomplemented
16#41×Dic53C2212yes—
17#41×Dic53C2212yes—
18C2×Q8×Dic53C411yescharacteristic, complemented
19C2×Q8×Dic53C411yescharacteristic, complemented
20C2×D4×Dic53—21no—
21C2×D4×Dic53—21no—
22C2×D4×Dic53C411yescharacteristic, complemented
23C2×D4×Dic53C411yescharacteristic, complemented
24C2×#13133176—21no—
25C2×#13133176C2211yescharacteristic
26C2×#13133173—21no—
27C22×C4×Dic53—21no—
28C22×C4×Dic53C2211yescharacteristic
29#16810677—21no—
30#16810677—21no—
31#16810673—21no—
32#16810673—21no—
33#16810646C2212yescomplemented
34C2×#13133144C2214yes—
35#16810587C2211yescharacteristic
36M16×Dic53C2212yescomplemented
37C4×#11719919C2212yescomplemented
38#16810474—21no—
39C22⋊C4×Dic53—21no—
40C4×C22⋊Dic53C2211yescharacteristic
41#16810468—21no—
42C42×Dic53C2212yescomplemented
43#16810384C2214yescomplemented
44#16810383C2214yescomplemented
45C22×#41×C53C2211yescharacteristic
46C2×#104×C53C2214yes—
47C53×#407C2211yescharacteristic
48C4×C22⋊C4×C53C2211yescharacteristic
49C23×Dic53—21no—
50C23×Dic53—21no—
51C23×Dic53D411yescharacteristic
52C23×Dic53D411yescharacteristic
53C2×#11719917C2312yes—
54Q8×Dic53—21no—
55Q8×Dic53—21no—
56Q8×Dic53—21no—
57Q8×Dic53—21no—
58Q8×Dic53C2×C412yes—
59Q8×Dic53C2×C412yes—
60Q8×Dic53C2×C412yes—
61Q8×Dic53C2×C412yes—
62D4×Dic53—21no—
63D4×Dic53—21no—
64D4×Dic53—21no—
65D4×Dic53—21no—
66D4×Dic53—22no—
67D4×Dic53—22no—
68D4×Dic53—22no—
69D4×Dic53—22no—
70D4×Dic53—22no—
71D4×Dic53—22no—
72D4×Dic53—22no—
73D4×Dic53—22no—
74D4×Dic53C2×C412yes—
75D4×Dic53C2×C412yes—
76D4×Dic53C2×C412yes—
77D4×Dic53C2×C412yes—
78#13133176—22no—
79#13133176—22no—
80#13133176—22no—
81#13133176—22no—
82#13133176—21no—
83#13133176—21no—
84#13133176C2×C412yes—
85#13133176C2312yes—
86#13133173—28no—
87C2×C4⋊Dic53—21no—
88C2×C4⋊Dic53—21no—
89C2×C4⋊Dic53C2×C411yescharacteristic
90C2×C4⋊Dic53C2×C411yescharacteristic
91C2×#11719919—22no—
92C2×C22⋊Dic53—21no—
93C2×C22⋊Dic53—21no—
94C2×C22⋊Dic53—21no—
95C2×C22⋊Dic53—21no—
96C2×C4×Dic53—22no—
97C2×C4×Dic53—22no—
98C2×C4×Dic53—22no—
99C2×C4×Dic53—22no—
100C2×C4×Dic53—21no—
101C2×C4×Dic53—21no—
102C2×C4×Dic53—21no—
103C2×C4×Dic53—22no—
104C2×C4×Dic53—22no—
105C2×C4×Dic53C2×C411yescharacteristic
106C2×C4×Dic53C2×C411yescharacteristic
107C2×C4×Dic53C2×C411yescharacteristic
108C2×C4×Dic53C2×C411yescharacteristic
109C2×C4×Dic53D411yescharacteristic
110C2×C4×Dic53D411yescharacteristic
111C2×C4×Dic53D411yescharacteristic
112C2×C4×Dic53D411yescharacteristic
113C2×C4×Dic53D411yescharacteristic
114C2×C4×Dic53D411yescharacteristic
115C2×C4×Dic53C2312yes—
116C2×C4×Dic53C2311yescharacteristic
117C2×C4×Dic53C2311yescharacteristic
118#13133146—22no—
119#13133146—22no—
120#13133144—28no—
121C22⋊#88322—21no—
122C22⋊#88322—21no—
123#13133127—22no—
124C8×Dic53—22no—
125#13133124—21no—
126#13133124—22no—
127C2×#41×C53—28no—
128C2×#41×C53—21no—
129C2×#41×C53—21no—
130C2×#41×C53C2×C412yes—
131C2×#41×C53C2312yes—
132C22×Q8×C53C2×C411yescharacteristic
133C22×D4×C53—21no—
134C22×D4×C53C2×C411yescharacteristic
135C23×C4×C53—21no—
136C23×C4×C53C2311yescharacteristic
137C2×M16×C53C2312yes—
138C2×C22⋊C4×C53—21no—
139C2×C42×C53C2312yes—
140#104×C53—28no—
141C22⋊C8×C53—21no—
142C22⋊C8×C53—21no—
143#95×C53—21no—
144C24×C53—21no—
145C24×C53C2×D411yescharacteristic
146#41×C53—28no—
147#41×C53—28no—
148#41×C53—24no—
149#41×C53—24no—
150#41×C53—24no—
151#41×C53#4118yes—
152C2×Q8×C53—24no—
153C2×Q8×C53—21no—
154C2×Q8×C53C22×C412yes—
155C2×D4×C53—28no—
156C2×D4×C53—22no—
157C2×D4×C53—22no—
158C2×D4×C53—24no—
159C2×D4×C53—21no—
160C2×D4×C53C22×C412yes—
161C22×C4×C53—28no—
162C22×C4×C53—21no—
163C22×C4×C53—22no—
164C22×C4×C53—22no—
165C22×C4×C53—24no—
166C22×C4×C53—22no—
167C22×C4×C53C22×C411yescharacteristic
168C22×C4×C53C22×C411yescharacteristic
169C22×C4×C53C2×D411yescharacteristic
170C22×C4×C53C2×D411yescharacteristic
171C22×C4×C53C2×D411yescharacteristic
172C22×C4×C53C2411yescharacteristic
173C22×Dic53—24no—
174C22×Dic53—21no—
175C22×Dic53—21no—
176C22×Dic53—22no—
177C22×Dic53—22no—
178C22×Dic53—22no—
179C22×Dic53—22no—
180C22×Dic53—22no—
181C22×Dic53—42no—
182C22×Dic53—44no—
183C22×Dic53—44no—
184C22×Dic53C22⋊C411yescharacteristic
185C22×Dic53C22⋊C411yescharacteristic
186C22×Dic53C22⋊C411yescharacteristic
187C22×Dic53C22⋊C411yescharacteristic
188C22×Dic53C22⋊C411yescharacteristic
189C22×Dic53C22⋊C411yescharacteristic
190C22×Dic53C22⋊C411yescharacteristic
191C22×Dic53C22⋊C411yescharacteristic
192C22×Dic53C2×D411yescharacteristic
193C22×Dic53C2×D411yescharacteristic
194C22×Dic53C2×D411yescharacteristic
195C22×Dic53C2×D411yescharacteristic
196M16×C53—24no—
197C2×C8×C53—22no—
198C22⋊C4×C53—24no—
199C42×C53—24no—
200C22⋊Dic53—24no—
201C22⋊Dic53—22no—
202C22⋊Dic53—22no—
203C22⋊Dic53—22no—
204C22⋊Dic53—22no—
205C22⋊Dic53—22no—
206C22⋊Dic53—22no—
207C4⋊Dic53—21no—
208C4⋊Dic53—21no—
209C4⋊Dic53—22no—
210C4⋊Dic53—22no—
211C4⋊Dic53—22no—
212C4⋊Dic53—22no—
213C4⋊Dic53C22×C412yes—
214C4⋊Dic53C22×C412yes—
215#11719919—28no—
216C4×Dic53—28no—
217C4×Dic53—22no—
218C4×Dic53—22no—
219C4×Dic53—22no—
220C4×Dic53—22no—
221C4×Dic53—22no—
222C4×Dic53—22no—
223C4×Dic53—24no—
224C4×Dic53—44no—
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×Dic53C22×C411yescharacteristic
234C4×Dic53C22×C411yescharacteristic
235C4×Dic53C22×C411yescharacteristic
236C4×Dic53C22×C411yescharacteristic
237C4×Dic53C2×D411yescharacteristic
238C4×Dic53C2×D411yescharacteristic
239C4×Dic53C2×D411yescharacteristic
240C4×Dic53C2×D411yescharacteristic
241#11719917—24no—
242C2×#88322—22no—
243C23×C53—24no—
244C23×C53—22no—
245C23×C53—22no—
246C23×C53—22no—
247C23×C53—41no—
248C23×C53—42no—
249C23×C53—42no—
250C23×C53C2×C22⋊C411yescharacteristic
251C23×C53C2×C22⋊C411yescharacteristic
252C23×C53C22×D411yescharacteristic
253Q8×C53—24no—
254Q8×C53—22no—
255Q8×C53#11714yescomplemented
256D4×C53—28no—
257D4×C53—24no—
258D4×C53—28no—
259D4×C53—22no—
260D4×C53#11714yescomplemented
261C2×C4×C53—24no—
262C2×C4×C53—28no—
263C2×C4×C53—22no—
264C2×C4×C53—22no—
265C2×C4×C53—22no—
266C2×C4×C53—22no—
267C2×C4×C53—22no—
268C2×C4×C53—28no—
269C2×C4×C53—22no—
270C2×C4×C53—24no—
271C2×C4×C53—42no—
272C2×C4×C53—42no—
273C2×C4×C53C2×C22⋊C411yescharacteristic
274C2×C4×C53C2×C22⋊C411yescharacteristic
275C2×C4×C53C23×C411yescharacteristic
276C2×C4×C53C22×D411yescharacteristic
277C2×C4×C53C2×#4114yes—
278C2×Dic53—22no—
279C2×Dic53—22no—
280C2×Dic53—22no—
281C2×Dic53—22no—
282C2×Dic53—22no—
283C2×Dic53—22no—
284C2×Dic53—22no—
285C2×Dic53—22no—
286C2×Dic53—24no—
287C2×Dic53—22no—
288C2×Dic53—22no—
289C2×Dic53—41no—
290C2×Dic53—41no—
291C2×Dic53—41no—
292C2×Dic53—44no—
293C2×Dic53—42no—
294C2×Dic53—42no—
295C2×Dic53—42no—
296C2×Dic53—42no—
297C2×Dic53—44no—
298C2×Dic53—44no—
299C2×Dic53—44no—
300C2×Dic53#10414yescomplemented
301C2×Dic53C2×C22⋊C411yescharacteristic
302C2×Dic53C2×C22⋊C411yescharacteristic
303C2×Dic53C2×C22⋊C411yescharacteristic
304C2×Dic53C2×C22⋊C411yescharacteristic
305C2×Dic53C2×C22⋊C411yescharacteristic
306C2×Dic53C2×C22⋊C411yescharacteristic
307C2×Dic53C2×C22⋊C411yescharacteristic
308C2×Dic53C2×C22⋊C411yescharacteristic
309C8×C53—42no—
310#88322—42no—
311#20747—531nomaximal, Sylow
312C22×C53—21no—
313C22×C53—21no—
314C22×C53—21no—
315C22×C53—21no—
316C22×C53—21no—
317C22×C53—21no—
318C22×C53—21no—
319C22×C53—24no—
320C22×C53—44no—
321C22×C53—48no—
322C22×C53—42no—
323C22×C53—42no—
324C22×C53C2×#10412yes—
325C22×C53C22×C22⋊C411yescharacteristic
326C22×C53#52512yes—
327C4×C53—21no—
328C4×C53—24no—
329C4×C53—21no—
330C4×C53—44no—
331C4×C53C2×#11712yes—
332C4×C53#52512yes—
333Dic53—21no—
334Dic53—21no—
335Dic53—21no—
336Dic53—21no—
337Dic53—21no—
338Dic53—44no—
339Dic53—42no—
340Dic53—42no—
341Dic53C2×#10412yes—
342Dic53C2×#10412yes—
343Dic53#42112yes—
344C2×C4×#41—531no—
345#2920—531no—
346C4×#117—531no—
347#1826—531no—
348#1826—531no—
349#1806—534no—
350#1789—531no—
351#1789D5311yescharacteristic
352C4×#104—534no—
353C2×C53—22no—
354C2×C53—22no—
355C2×C53—41no—
356C2×C53—44no—
357C2×C53#228011yescharacteristic
358C2×C53C22×#10411yescharacteristic
359C2×C53C2×#42111yescharacteristic
360C22×#41C2×D5311yescharacteristic
361C4×#41—532no—
362C4×#41—532no—
363C4×#41—532no—
364C4×#41—532no—
365C4×#41—1061no—
366C4×#41—1061no—
367C4×#41—1061no—
368C4×#41—1061no—
369C2×C4×Q8—531no—
370C2×C4×Q8—531no—
371C2×C4×D4—531no—
372C2×C4×D4—531no—
373C2×C4×D4—1061no—
374C2×C4×D4—1061no—
375C2×#117—531no—
376C2×#117—1061no—
377C2×#117—1061no—
378C22×C42—531no—
379C22×C42—1061no—
380#432—1061no—
381#432—1061no—
382#431—1061no—
383#431—1061no—
384#423—532no—
385C2×#104—534no—
386C2×#104C2×D5314yes—
387#407—531no—
388#407C2×D5311yescharacteristic
389C4×M16—532no—
390C4×C4⋊C4—532no—
391C4×C4⋊C4—1061no—
392C4×C22⋊C4—531no—
393C4×C22⋊C4—1061no—
394C4×C22⋊C4C2×D5311yescharacteristic
395#376—1061no—
396C43—532no—
397#339—534no—
398#339—534no—
399C53#2074711yescharacteristic, complemented, Sylow
400C2×#41—28no—
401C2×#41—21no—
402C2×#41—21no—
403C2×#41C4×D5312yes—
404C2×#41C22×D5312yes—
405C22×Q8C4×D5311yescharacteristic
406C22×D4—21no—
407C22×D4C4×D5311yescharacteristic
408C23×C4—21no—
409C23×C4—531no—
410C23×C4—531no—
411C23×C4—1061no—
412C23×C4—1061no—
413C23×C4C22×D5311yescharacteristic
414C2×M16—532no—
415C2×M16C22×D5312yes—
416C4×Q8—532no—
417C4×Q8—532no—
418C4×Q8—532no—
419C4×Q8—532no—
420C4×Q8—1061no—
421C4×Q8—1061no—
422C4×Q8—1061no—
423C4×Q8—1061no—
424C4×D4—532no—
425C4×D4—532no—
426C4×D4—532no—
427C4×D4—532no—
428C4×D4—1061no—
429C4×D4—1061no—
430C4×D4—1061no—
431C4×D4—1061no—
432C4×D4—1062no—
433C4×D4—1062no—
434C4×D4—1062no—
435C4×D4—1062no—
436C4×D4—1062no—
437C4×D4—1062no—
438C4×D4—1062no—
439C4×D4—1062no—
440#117—532no—
441#117—532no—
442#117—1062no—
443#117—1062no—
444#117—1062no—
445#117—1062no—
446#117—1068no—
447#117—1061no—
448#117—1061no—
449C2×C4⋊C4—531no—
450C2×C4⋊C4—531no—
451C2×C4⋊C4—1061no—
452C2×C4⋊C4—1061no—
453C2×C4⋊C4—1062no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—1061no—
456C2×C22⋊C4—1061no—
457C2×C22⋊C4—1061no—
458C2×C22⋊C4—1061no—
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—531no—
469C2×C42—531no—
470C2×C42—531no—
471C2×C42—532no—
472C2×C42—1062no—
473C2×C42—1062no—
474C2×C42—1062no—
475C2×C42—1062no—
476C2×C42—1062no—
477C2×C42—1061no—
478C2×C42—1061no—
479C2×C42—1061no—
480C2×C42—1062no—
481C2×C42C22×D5312yes—
482C4⋊C8—1062no—
483C4⋊C8—1062no—
484#104—28no—
485#104—1068no—
486C22⋊C8—21no—
487C22⋊C8—21no—
488C22⋊C8—1061no—
489C22⋊C8—1061no—
490#97—1062no—
491C4×C8—1062no—
492#95—21no—
493#95—1062no—
494#95—1061no—
495C24—21no—
496C24D4×D5311yescharacteristic
497#41—28no—
498#41—28no—
499#41—24no—
500#41—24no—
501#41—24no—
502#41#1171994718yes—
503C2×Q8—24no—
504C2×Q8—21no—
505C2×Q8C2×C4×D5312yes—
506C2×D4—28no—
507C2×D4—22no—
508C2×D4—22no—
509C2×D4—24no—
510C2×D4—21no—
511C2×D4C2×C4×D5312yes—
512C22×C4—28no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—24no—
517C22×C4—22no—
518C22×C4—531no—
519C22×C4—531no—
520C22×C4—531no—
521C22×C4—531no—
522C22×C4—531no—
523C22×C4—531no—
524C22×C4—531no—
525C22×C4—531no—
526C22×C4—531no—
527C22×C4—531no—
528C22×C4—531no—
529C22×C4—531no—
530C22×C4—1064no—
531C22×C4—1062no—
532C22×C4—1062no—
533C22×C4—1062no—
534C22×C4—1062no—
535C22×C4—1061no—
536C22×C4—1061no—
537C22×C4—1062no—
538C22×C4—2124no—
539C22×C4—2122no—
540C22×C4—2124no—
541C22×C4C2×C4×D5311yescharacteristic
542C22×C4C2×C4×D5311yescharacteristic
543C22×C4D4×D5311yescharacteristic
544C22×C4D4×D5311yescharacteristic
545C22×C4D4×D5311yescharacteristic
546C22×C4C23×D5311yescharacteristic
547M16—24no—
548M16—1064no—
549C2×C8—22no—
550C2×C8—1062no—
551C4⋊C4—532no—
552C4⋊C4—532no—
553C4⋊C4—1062no—
554C4⋊C4—1062no—
555C4⋊C4—1062no—
556C4⋊C4—1062no—
557C4⋊C4—1068no—
558C4⋊C4—1061no—
559C4⋊C4—1061no—
560C22⋊C4—24no—
561C22⋊C4—1062no—
562C22⋊C4—1062no—
563C22⋊C4—1062no—
564C22⋊C4—1062no—
565C22⋊C4—1064no—
566C22⋊C4—1062no—
567C22⋊C4—1062no—
568C42—24no—
569C42—531no—
570C42—531no—
571C42—531no—
572C42—531no—
573C42—531no—
574C42—531no—
575C42—531no—
576C42—531no—
577C42—531no—
578C42—531no—
579C42—531no—
580C42—531no—
581C42—531no—
582C42—531no—
583C42—531no—
584C42—531no—
585C42—1062no—
586C42—1062no—
587C42—1062no—
588C42—1062no—
589C42—1068no—
590C42—1062no—
591C42—1062no—
592C42—1064no—
593C42—2124no—
594C23—24no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—41no—
599C23—42no—
600C23—42no—
601C23C22⋊C4×D5311yescharacteristic
602C23C22⋊C4×D5311yescharacteristic
603C23C2×D4×D5311yescharacteristic
604Q8—24no—
605Q8—22no—
606Q8#1313317314yescomplemented
607D4—28no—
608D4—24no—
609D4—28no—
610D4—22no—
611D4#1313317314yescomplemented
612C2×C4—24no—
613C2×C4—28no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—28no—
620C2×C4—22no—
621C2×C4—24no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—531no—
625C2×C4—531no—
626C2×C4—531no—
627C2×C4—534no—
628C2×C4—531no—
629C2×C4—531no—
630C2×C4—531no—
631C2×C4—531no—
632C2×C4—531no—
633C2×C4—1062no—
634C2×C4—1062no—
635C2×C4—1062no—
636C2×C4—1062no—
637C2×C4—1062no—
638C2×C4—1062no—
639C2×C4—1062no—
640C2×C4—1062no—
641C2×C4—1064no—
642C2×C4—1062no—
643C2×C4—1062no—
644C2×C4—2124no—
645C2×C4—2124no—
646C2×C4—2124no—
647C2×C4—2121no—
648C2×C4—2121no—
649C2×C4—2121no—
650C2×C4—2124no—
651C2×C4—2122no—
652C2×C4—2122no—
653C2×C4—2122no—
654C2×C4—2122no—
655C2×C4C22⋊C4×D5311yescharacteristic
656C2×C4C22⋊C4×D5311yescharacteristic
657C2×C4C22×C4×D5311yescharacteristic
658C2×C4C2×D4×D5311yescharacteristic
659C2×C4C2×#1171994714yes—
660C8—42no—
661C8—2122no—
662C22—21no—
663C22—21no—
664C22—21no—
665C22—21no—
666C22—21no—
667C22—24no—
668C22—21no—
669C22—21no—
670C22—44no—
671C22—48no—
672C22—42no—
673C22—42no—
674C22#104×D5312yes—
675C22C2×C22⋊C4×D5311yescharacteristic
676C22#1681112912yes—
677C4—21no—
678C4—24no—
679C4—21no—
680C4—44no—
681C4—532no—
682C4—532no—
683C4—532no—
684C4—1061no—
685C4—1061no—
686C4—1061no—
687C4—1061no—
688C4—1061no—
689C4—2124no—
690C4—2122no—
691C4—2122no—
692C4C2×#1313317312yes—
693C4#1681112912yes—
694C2—22no—
695C2—22no—
696C2—41no—
697C2—44no—
698C2#2027709311yescharacteristic
699C2C2×#104×D5311yescharacteristic
700C2#421×D5311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1789C2
socleC22×C53C22×C22⋊C4
prime radicalC22×#41×C53C22
cosocleC22×C4×C53C24
hypercenter#1789D53
hypocenterC53#20747
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1789

Complements

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

NH ≅ G/Ntype
2. #20283344C2semidirect
3. C4×#13133173C2semidirect
4. #20274815C2semidirect
5. #20274812C2semidirect
6. #20274733C2semidirect
8. #104×Dic53C2semidirect
14. #41×Dic53C4semidirect
15. #41×Dic53C4semidirect
18. C2×Q8×Dic53C4semidirect
19. C2×Q8×Dic53C4semidirect
22. C2×D4×Dic53C4semidirect
23. C2×D4×Dic53C4semidirect
33. #16810646C22semidirect
36. M16×Dic53C22semidirect
37. C4×#11719919C22semidirect
42. C42×Dic53C22semidirect
43. #16810384C22semidirect
44. #16810383C22semidirect
255. Q8×C53#117semidirect
260. D4×C53#117semidirect
300. C2×Dic53#104semidirect
399. C53#20747semidirect
606. Q8#13133173semidirect
611. D4#13133173semidirect

Maximal subgroups

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

subgroupindex
C2×#41×Dic532
#202833442
C4×#131331732
#202748152
#202748122
#202747332
#202746592
#104×Dic532
C53×#17892
#2074753