Finite Group Databasebeta

← #27395452

Subgroups — #27395452

Order 13568.

968 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20277399C211yesmaximal, characteristic, complemented
2#20277307C211yesmaximal, characteristic
3#20275598C211yesmaximal, characteristic, complemented
4#20275577C211yesmaximal, characteristic, complemented
5#20275407C211yesmaximal, characteristic, complemented
6#20275400C211yesmaximal, characteristic, complemented
7#20275358C211yesmaximal, characteristic, complemented
8#20275337C211yesmaximal, characteristic, complemented
9#20275072C211yesmaximal, characteristic, complemented
10#20275058C211yesmaximal, characteristic, complemented
11#20275023C211yesmaximal, characteristic, complemented
12#20274905C211yesmaximal, characteristic, complemented
13#20274655C211yesmaximal, characteristic
14#20274483C211yesmaximal, characteristic, complemented
15C2×C53×#452C211yesmaximal, characteristic
16C2×Q8×Dic53C2211yescharacteristic
17C2×#13133176C2211yescharacteristic
18C22×C4⋊Dic53C2211yescharacteristic
19C2×#13133151C2211yescharacteristic
20C2×#13133151C2211yescharacteristic
21C2×#13133141C2211yescharacteristic
22C2×#13133141C2211yescharacteristic
23C2×#13133141C2211yescharacteristic
24C2×#13133141C2211yescharacteristic
25C2×#13133138C2211yescharacteristic
26C2×#13133138C2211yescharacteristic
27C2×C22⋊#88322C2211yescharacteristic
28C2×#13133127C2211yescharacteristic
29C2×C8×Dic53C2211yescharacteristic
30#16810530C2211yescharacteristic
31#16810530C2211yescharacteristic
32#16810530C2211yescharacteristic
33#16810526C2211yescharacteristic
34#16810526C2211yescharacteristic
35#16810522—21no—
36#16810522C2211yescharacteristic
37#16810516—21no—
38#16810516—21no—
39#16810509—21no—
40#16810503—21no—
41#16810503—21no—
42#16810483—21no—
43#16810483—21no—
44#16810483C2211yescharacteristic
45C4⋊C4×Dic53C2211yescharacteristic
46#16810386C2211yescharacteristic
47#16810386C2211yescharacteristic
48#16810385C2211yescharacteristic
49#16810385C2211yescharacteristic
50#16810377C2211yescharacteristic
51#16810377C2211yescharacteristic
52C22×#41×C53C2211yescharacteristic
53C22×Q16×C53C2211yescharacteristic
54C22×SD16×C53C2211yescharacteristic
55C2×C22⋊Q8×C53C2211yescharacteristic
56C53×#452C418yescomplemented
57C2×#103×C53C2211yescharacteristic
58C2×#102×C53C2211yescharacteristic
59C2×C22⋊C8×C53C2211yescharacteristic
60C23×Dic53—21no—
61C22×#88322C2311yescharacteristic
62C22×#88322C2311yescharacteristic
63Q8×Dic53—41no—
64Q8×Dic53—41no—
65#13133176—41no—
66#13133176—41no—
67C2×C4⋊Dic53—21no—
68C2×C4⋊Dic53—21no—
69C2×C4⋊Dic53—21no—
70C2×C4⋊Dic53—41no—
71C2×C4⋊Dic53—41no—
72C2×C4⋊Dic53D411yescharacteristic
73C2×C4⋊Dic53D411yescharacteristic
74C2×C4⋊Dic53C2311yescharacteristic
75C2×C4⋊Dic53C2311yescharacteristic
76C2×C4⋊Dic53C2311yescharacteristic
77C2×C4⋊Dic53C2311yescharacteristic
78C2×C22⋊Dic53—21no—
79C2×C22⋊Dic53—21no—
80C2×C22⋊Dic53—21no—
81C2×C22⋊Dic53—21no—
82C2×C22⋊Dic53—21no—
83C2×C22⋊Dic53D411yescharacteristic
84C2×C22⋊Dic53D411yescharacteristic
85C2×C4×Dic53—21no—
86C2×C4×Dic53—21no—
87C2×C4×Dic53C2311yescharacteristic
88C2×C4×Dic53C2311yescharacteristic
89#13133151—41no—
90#13133151—41no—
91#13133141—41no—
92#13133141—41no—
93#13133141—41no—
94#13133141—41no—
95#13133138—41no—
96#13133138—41no—
97C22⋊#88322—22no—
98#13133127—41no—
99C8×Dic53—41no—
100#13133124—21no—
101#13133124—21no—
102#13133124—21no—
103#13133124—21no—
104#13133124—21no—
105#13133124—21no—
106#13133124—21no—
107#13133124—21no—
108#13133124—21no—
109C2×#41×C53—22no—
110C2×#41×C53—41no—
111C2×#41×C53—41no—
112C2×#41×C53—41no—
113C2×#41×C53—41no—
114C2×#41×C53C2×C414yes—
115C22×Q8×C53C2311yescharacteristic
116C22×Q8×C53C2311yescharacteristic
117C22×D4×C53—21no—
118C22×D4×C53C2311yescharacteristic
119C23×C4×C53—21no—
120C23×C4×C53C2311yescharacteristic
121C2×Q16×C53—41no—
122C2×Q16×C53—41no—
123C2×Q16×C53C2×C414yescomplemented
124C2×SD16×C53—41no—
125C2×SD16×C53—41no—
126C2×SD16×C53C2×C414yescomplemented
127C22×C8×C53C2311yescharacteristic
128C22×C8×C53C2311yescharacteristic
129C22⋊Q8×C53—22no—
130C22⋊Q8×C53C2×C414yes—
131C2×C4⋊C4×C53—21no—
132C2×C4⋊C4×C53C2311yescharacteristic
133C2×C22⋊C4×C53—21no—
134#103×C53C2×C414yescomplemented
135#102×C53C2×C414yescomplemented
136C22⋊C8×C53C2×C414yes—
137C24×C53—21no—
138C24×C53C2×D411yescharacteristic
139#41×C53—44no—
140#41×C53—44no—
141#41×C53—44no—
142#41×C53—44no—
143C2×Q8×C53—21no—
144C2×Q8×C53—21no—
145C2×Q8×C53—21no—
146C2×Q8×C53—21no—
147C2×Q8×C53—21no—
148C2×Q8×C53—21no—
149C2×Q8×C53—21no—
150C2×Q8×C53—21no—
151C2×Q8×C53—21no—
152C2×Q8×C53—21no—
153C2×Q8×C53C22×C412yes—
154C2×Q8×C53C22×C412yes—
155C2×D4×C53—24no—
156C2×D4×C53—21no—
157C2×D4×C53—21no—
158C2×D4×C53—21no—
159C2×D4×C53—21no—
160C2×D4×C53—21no—
161C2×D4×C53—42no—
162C2×D4×C53—42no—
163C2×D4×C53C22×C412yes—
164C22×C4×C53—21no—
165C22×C4×C53—21no—
166C22×C4×C53—21no—
167C22×C4×C53—21no—
168C22×C4×C53—21no—
169C22×C4×C53—21no—
170C22×C4×C53—21no—
171C22×C4×C53—24no—
172C22×C4×C53—42no—
173C22×C4×C53—42no—
174C22×C4×C53C22×C412yes—
175C22×C4×C53C2×D411yescharacteristic
176C22×C4×C53#4112yes—
177C22×C4×C53C2411yescharacteristic
178C22×Dic53—21no—
179C22×Dic53—21no—
180C22×Dic53—21no—
181C22×Dic53—21no—
182C22×Dic53—42no—
183C22×Dic53—81no—
184C22×Dic53—81no—
185C22×Dic53C2×D411yescharacteristic
186C22×Dic53C2×D411yescharacteristic
187C22×Dic53C2×D411yescharacteristic
188C22×Dic53C2×D411yescharacteristic
189Q16×C53—44no—
190SD16×C53—44no—
191C2×C8×C53—21no—
192C2×C8×C53—21no—
193C2×C8×C53—21no—
194C2×C8×C53—21no—
195C2×C8×C53C22×C412yes—
196C2×C8×C53C22×C412yes—
197C4⋊C4×C53—24no—
198C4⋊C4×C53—21no—
199C4⋊C4×C53C22×C412yes—
200C22⋊C4×C53—24no—
201C22⋊Dic53—41no—
202C22⋊Dic53—41no—
203C22⋊Dic53—81no—
204C22⋊Dic53—81no—
205C22⋊Dic53—81no—
206C22⋊Dic53—81no—
207C22⋊Dic53—81no—
208C4⋊Dic53—21no—
209C4⋊Dic53—21no—
210C4⋊Dic53—21no—
211C4⋊Dic53—21no—
212C4⋊Dic53—21no—
213C4⋊Dic53—21no—
214C4⋊Dic53—21no—
215C4⋊Dic53—21no—
216C4⋊Dic53—41no—
217C4⋊Dic53—41no—
218C4⋊Dic53—42no—
219C4⋊Dic53—42no—
220C4⋊Dic53—81no—
221C4×Dic53—21no—
222C4×Dic53—21no—
223C4×Dic53—21no—
224C4×Dic53—21no—
225C4×Dic53—42no—
226C4×Dic53—81no—
227C2×#88322—21no—
228C2×#88322—21no—
229C2×#88322—21no—
230C2×#88322—21no—
231C2×#88322—21no—
232C2×#88322—21no—
233C23×C53—21no—
234C23×C53—21no—
235C23×C53—21no—
236C23×C53—21no—
237C23×C53—21no—
238C23×C53—21no—
239C23×C53—22no—
240C23×C53—41no—
241C23×C53—41no—
242C23×C53—41no—
243C23×C53—41no—
244C23×C53—41no—
245C23×C53—41no—
246C23×C53C4×D412yes—
247C23×C53C22×D411yescharacteristic
248Q8×C53—22no—
249Q8×C53—22no—
250Q8×C53—22no—
251Q8×C53—22no—
252Q8×C53—41no—
253Q8×C53—41no—
254Q8×C53—41no—
255Q8×C53—41no—
256D4×C53—22no—
257D4×C53—22no—
258D4×C53—48no—
259D4×C53—41no—
260D4×C53—41no—
261C2×C4×C53—21no—
262C2×C4×C53—21no—
263C2×C4×C53—22no—
264C2×C4×C53—22no—
265C2×C4×C53—22no—
266C2×C4×C53—22no—
267C2×C4×C53—22no—
268C2×C4×C53—22no—
269C2×C4×C53—22no—
270C2×C4×C53—48no—
271C2×C4×C53—41no—
272C2×C4×C53—41no—
273C2×C4×C53—41no—
274C2×C4×C53—41no—
275C2×C4×C53—41no—
276C2×C4×C53—41no—
277C2×C4×C53C4×D412yes—
278C2×C4×C53C23×C411yescharacteristic
279C2×C4×C53C2×#4111yescharacteristic
280C2×C4×C53H(5,𝔽2)11yescharacteristic
281C2×C4×C53H(5,𝔽2)11yescharacteristic
282C2×C4×C53H(5,𝔽2)11yescharacteristic
283C2×C4×C53H(5,𝔽2)11yescharacteristic
284C2×Dic53—21no—
285C2×Dic53—21no—
286C2×Dic53—21no—
287C2×Dic53—21no—
288C2×Dic53—21no—
289C2×Dic53—21no—
290C2×Dic53—21no—
291C2×Dic53—21no—
292C2×Dic53—21no—
293C2×Dic53—21no—
294C2×Dic53—21no—
295C2×Dic53—21no—
296C2×Dic53—41no—
297C2×Dic53—41no—
298C2×Dic53—41no—
299C2×Dic53—41no—
300C2×Dic53—41no—
301C2×Dic53—41no—
302C2×Dic53—41no—
303C2×Dic53—41no—
304C2×Dic53—41no—
305C2×Dic53—41no—
306C2×Dic53—41no—
307C2×Dic53—41no—
308C2×Dic53—84no—
309C8×C53—22no—
310C8×C53—22no—
311#88322—41no—
312#88322—41no—
313#22057—531nomaximal, Sylow
314C22×C53—22no—
315C22×C53—22no—
316C22×C53—22no—
317C22×C53—41no—
318C22×C53—41no—
319C22×C53—41no—
320C22×C53—41no—
321C22×C53—42no—
322C22×C53—42no—
323C22×C53—42no—
324C22×C53—81no—
325C22×C53—81no—
326C22×C53—81no—
327C22×C53—81no—
328C22×C53C2×C4×D411yescharacteristic
329C22×C53#53411yescharacteristic
330C22×C53#53511yescharacteristic
331C22×C53#57611yescharacteristic
332C22×C53#57711yescharacteristic
333C22×C53#57811yescharacteristic
334C22×C53#57811yescharacteristic
335C4×C53—22no—
336C4×C53—42no—
337C4×C53—42no—
338C4×C53—42no—
339C4×C53#51811yescharacteristic
340C4×C53#51811yescharacteristic
341C4×C53#53811yescharacteristic
342C4×C53#53811yescharacteristic
343Dic53—41no—
344Dic53—41no—
345Dic53—41no—
346Dic53—41no—
347Dic53—81no—
348Dic53—81no—
349Dic53—81no—
350Dic53—81no—
351C2×#452D5311yescharacteristic
352#2323—531no—
353#2311—531no—
354#1973—531no—
355#1969—531no—
356#1935—531no—
357#1934—531no—
358#1928—531no—
359#1925—531no—
360#1880—531no—
361#1878—531no—
362#1872—531no—
363#1852—531no—
364#1788—531no—
365#1750—531no—
366C2×C53—42no—
367C2×C53—82no—
368C2×C53#232111yescharacteristic
369C2×C53#294711yescharacteristic
370C2×C53#295111yescharacteristic
371C2×C53#320111yescharacteristic
372C2×C53#320311yescharacteristic
373C2×C53#322311yescharacteristic
374C2×C53#322411yescharacteristic
375C22×#41C2×D5311yescharacteristic
376C22×Q16C2×D5311yescharacteristic
377C22×SD16C2×D5311yescharacteristic
378C2×C22⋊Q8C2×D5311yescharacteristic
379C2×C4×Q8—531no—
380C2×#117—531no—
381C22×C4⋊C4—531no—
382#452Dic5318yescomplemented
383C2×#107—531no—
384C2×#107—531no—
385C2×#103—531no—
386C2×#103—531no—
387C2×#103—531no—
388C2×#103—531no—
389C2×#103C2×D5311yescharacteristic
390C2×#102—531no—
391C2×#102—531no—
392C2×#102C2×D5311yescharacteristic
393C2×C22⋊C8—531no—
394C2×C22⋊C8C2×D5311yescharacteristic
395C2×#97—531no—
396C2×C4×C8—531no—
397#391—531no—
398#391—531no—
399#391—531no—
400#390—531no—
401#390—531no—
402#389—531no—
403#389—1061no—
404#388—1061no—
405#388—1061no—
406#387—1061no—
407#386—1061no—
408#386—1061no—
409#380—531no—
410#380—1061no—
411#380—1061no—
412C4×C4⋊C4—531no—
413#340—531no—
414#340—531no—
415#340—531no—
416#340—531no—
417#336—531no—
418#336—531no—
419C53#2205711yescharacteristic, complemented, Sylow
420C2×#41—22no—
421C2×#41—41no—
422C2×#41—41no—
423C2×#41—41no—
424C2×#41—41no—
425C2×#41C2×Dic5314yes—
426C22×Q8C22×D5311yescharacteristic
427C22×Q8C22×D5311yescharacteristic
428C22×D4—21no—
429C22×D4C22×D5311yescharacteristic
430C23×C4—21no—
431C23×C4—1061no—
432C23×C4C22×D5311yescharacteristic
433C2×Q16—41no—
434C2×Q16—41no—
435C2×Q16C2×Dic5314yescomplemented
436C2×SD16—41no—
437C2×SD16—41no—
438C2×SD16C2×Dic5314yescomplemented
439C22×C8—531no—
440C22×C8—531no—
441C22×C8C22×D5311yescharacteristic
442C22×C8C22×D5311yescharacteristic
443C22⋊Q8—22no—
444C22⋊Q8C2×Dic5314yes—
445C4×Q8—2121no—
446C4×Q8—2121no—
447#117—2121no—
448#117—2121no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—531no—
451C2×C4⋊C4—531no—
452C2×C4⋊C4—531no—
453C2×C4⋊C4—531no—
454C2×C4⋊C4—531no—
455C2×C4⋊C4—531no—
456C2×C4⋊C4—1061no—
457C2×C4⋊C4—1061no—
458C2×C4⋊C4—1061no—
459C2×C4⋊C4—2121no—
460C2×C4⋊C4—2121no—
461C2×C4⋊C4C22×D5311yescharacteristic
462C2×C22⋊C4—21no—
463C2×C22⋊C4—531no—
464C2×C22⋊C4—531no—
465C2×C22⋊C4—1061no—
466C2×C22⋊C4—1061no—
467C2×C22⋊C4—1061no—
468C2×C22⋊C4—1061no—
469C2×C22⋊C4—1061no—
470C2×C42—531no—
471C2×C42—531no—
472C2×C42—1061no—
473C2×C42—1061no—
474#107—2121no—
475#107—2121no—
476#103—2121no—
477#103—2121no—
478#103—2121no—
479#103—2121no—
480#103C2×Dic5314yescomplemented
481#102—2121no—
482#102—2121no—
483#102C2×Dic5314yescomplemented
484C22⋊C8—1062no—
485C22⋊C8C2×Dic5314yes—
486#97—2121no—
487C4×C8—2121no—
488#95—1061no—
489#95—1061no—
490#95—1061no—
491#95—1061no—
492#95—1061no—
493#95—1061no—
494#95—1061no—
495#95—1061no—
496#95—1061no—
497C24—21no—
498C24D4×D5311yescharacteristic
499#41—44no—
500#41—44no—
501#41—44no—
502#41—44no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8C22×Dic5312yes—
514C2×Q8C22×Dic5312yes—
515C2×D4—24no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4C22×Dic5312yes—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—24no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—531no—
535C22×C4—531no—
536C22×C4—531no—
537C22×C4—531no—
538C22×C4—1061no—
539C22×C4—1061no—
540C22×C4—1061no—
541C22×C4—1061no—
542C22×C4—4241no—
543C22×C4—4241no—
544C22×C4—2122no—
545C22×C4D4×D5311yescharacteristic
546C22×C4#1171994712yes—
547C22×C4C22×Dic5312yes—
548C22×C4C23×D5311yescharacteristic
549Q16—44no—
550SD16—44no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—1061no—
556C2×C8—1061no—
557C2×C8—1061no—
558C2×C8—1061no—
559C2×C8—1061no—
560C2×C8—1061no—
561C2×C8C22×Dic5312yes—
562C2×C8C22×Dic5312yes—
563C4⋊C4—24no—
564C4⋊C4—21no—
565C4⋊C4—1061no—
566C4⋊C4—1061no—
567C4⋊C4—1061no—
568C4⋊C4—1061no—
569C4⋊C4—1061no—
570C4⋊C4—1061no—
571C4⋊C4—1061no—
572C4⋊C4—1061no—
573C4⋊C4—4241no—
574C4⋊C4—2121no—
575C4⋊C4—2121no—
576C4⋊C4—2122no—
577C4⋊C4—2122no—
578C4⋊C4C22×Dic5312yes—
579C22⋊C4—24no—
580C22⋊C4—4241no—
581C22⋊C4—4241no—
582C22⋊C4—4241no—
583C22⋊C4—4241no—
584C22⋊C4—4241no—
585C22⋊C4—2121no—
586C22⋊C4—2121no—
587C42—1061no—
588C42—1061no—
589C42—1061no—
590C42—1061no—
591C42—4241no—
592C42—2122no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—22no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23D4×Dic5312yes—
607C23C2×D4×D5311yescharacteristic
608Q8—22no—
609Q8—22no—
610Q8—22no—
611Q8—22no—
612Q8—41no—
613Q8—41no—
614Q8—41no—
615Q8—41no—
616D4—22no—
617D4—22no—
618D4—48no—
619D4—41no—
620D4—41no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—48no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—1061no—
638C2×C4—1061no—
639C2×C4—1061no—
640C2×C4—1061no—
641C2×C4—1061no—
642C2×C4—1061no—
643C2×C4—1061no—
644C2×C4—1061no—
645C2×C4—1061no—
646C2×C4—1061no—
647C2×C4—1061no—
648C2×C4—1061no—
649C2×C4—4244no—
650C2×C4—2121no—
651C2×C4—2121no—
652C2×C4—2121no—
653C2×C4—2121no—
654C2×C4—2121no—
655C2×C4—2121no—
656C2×C4—2121no—
657C2×C4—2121no—
658C2×C4—2121no—
659C2×C4—2121no—
660C2×C4—2121no—
661C2×C4—2121no—
662C2×C4D4×Dic5312yes—
663C2×C4C23×Dic5311yescharacteristic
664C2×C4C2×#1171994711yescharacteristic
665C2×C4#1313326211yescharacteristic
666C2×C4#1313326211yescharacteristic
667C2×C4#1313326211yescharacteristic
668C2×C4#1313326211yescharacteristic
669C8—22no—
670C8—22no—
671C8—2121no—
672C8—2121no—
673C22—22no—
674C22—22no—
675C22—22no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—42no—
681C22—42no—
682C22—42no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22C2×D4×Dic5311yescharacteristic
688C22#1681118311yescharacteristic
689C22#1681118811yescharacteristic
690C22#1681142511yescharacteristic
691C22#1681143211yescharacteristic
692C22#1681143711yescharacteristic
693C22#1681143911yescharacteristic
694C4—22no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—4241no—
699C4—4241no—
700C4—4241no—
701C4—4241no—
702C4—2121no—
703C4—2121no—
704C4—2121no—
705C4—2121no—
706C4#1681109811yescharacteristic
707C4#1681109811yescharacteristic
708C4#1681120811yescharacteristic
709C4#1681120811yescharacteristic
710C2—42no—
711C2—82no—
712C2#2027737611yescharacteristic
713C2#2028355911yescharacteristic
714C2#2028359111yescharacteristic
715C2#2028559611yescharacteristic
716C2#2028561611yescharacteristic
717C2#2028579611yescharacteristic
718C2#2028581511yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#452C2
socleC23×C53C22×D4
prime radicalC22×#41×C53C22
cosocleC22×C4×C53C24
hypercenterC2×#452D53
hypocenterC53#22057
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. #20277399C2semidirect
3. #20275598C2semidirect
4. #20275577C2semidirect
5. #20275407C2semidirect
6. #20275400C2semidirect
7. #20275358C2semidirect
8. #20275337C2semidirect
9. #20275072C2semidirect
10. #20275058C2semidirect
11. #20275023C2semidirect
12. #20274905C2semidirect
14. #20274483C2semidirect
56. C53×#452C4semidirect
123. C2×Q16×C53C2×C4semidirect
126. C2×SD16×C53C2×C4semidirect
134. #103×C53C2×C4semidirect
135. #102×C53C2×C4semidirect
382. #452Dic53semidirect
419. C53#22057semidirect
435. C2×Q16C2×Dic53semidirect
438. C2×SD16C2×Dic53semidirect
480. #103C2×Dic53semidirect
483. #102C2×Dic53semidirect

Maximal subgroups

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

subgroupindex
#202773992
#202773072
#202755982
#202755772
#202754072
#202754002
#202753582
#202753372
#202750722
#202750582
#202750232
#202749052
#202746552
#202744832
C2×C53×#4522
#2205753