Finite Group Databasebeta

← #27436778

Subgroups — #27436778

Order 13568.

1444 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810936C211yesmaximal, characteristic, complemented
2C2×#16810857C211yesmaximal, characteristic, complemented
3#20278155C211yesmaximal, characteristic, complemented
4#20276040C211yesmaximal, characteristic, complemented
5#20275894C211yesmaximal, characteristic, complemented
6#20275848C211yesmaximal, characteristic, complemented
7#20275711C211yesmaximal, characteristic, complemented
8#20275063C211yesmaximal, characteristic, complemented
9#20275033C211yesmaximal, characteristic, complemented
10#20275032C211yesmaximal, characteristic, complemented
11#20275008C211yesmaximal, characteristic, complemented
12#20274962C211yesmaximal, characteristic, complemented
13#20274903C211yesmaximal, characteristic, complemented
14C2×#16810385C211yesmaximal, characteristic, complemented
15C2×C53×#547C211yesmaximal, characteristic, complemented
16C22×#11719922C2211yescharacteristic
17C23×#88322C2211yescharacteristic
18C2×#13133191C2211yescharacteristic
19C2×#13133191C2211yescharacteristic
20C2×#13133189—21no—
21C22×C4⋊Dic53C2211yescharacteristic
22#16810936—24no—
23#16810857—24no—
24C2×#13133150C2211yescharacteristic
25C2×#13133150C2211yescharacteristic
26C2×#13133150C2211yescharacteristic
27C2×#13133138C2211yescharacteristic
28C2×#13133138C2211yescharacteristic
29C2×#13133138C2211yescharacteristic
30C2×#13133137C2211yescharacteristic
31C2×#13133137C2211yescharacteristic
32C2×#13133137C2211yescharacteristic
33C2×C22⋊#88322C2211yescharacteristic
34C2×C22⋊#88322C2211yescharacteristic
35C2×C22⋊#88322C2211yescharacteristic
36#16810545—21no—
37#16810539—21no—
38#16810525C2211yescharacteristic
39#16810521C2211yescharacteristic
40#16810500—21no—
41#16810483C2211yescharacteristic
42#16810385C2211yescharacteristic
43#16810385C2211yescharacteristic
44#16810385C2211yescharacteristic
45#16810385C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810378C2211yescharacteristic
49#16810378C2211yescharacteristic
50C22×#41×C53—21no—
51C53×#547—24no—
52C53×#547—24no—
53C2×C4⋊Q8×C53C2211yescharacteristic
54C2×#123×C53—21no—
55C2×#123×C53—21no—
56C2×C22⋊Q8×C53—21no—
57C2×#121×C53C2211yescharacteristic
58C2×#121×C53C2211yescharacteristic
59C2×C4×D4×C53C2211yescharacteristic
60C2×C4×D4×C53C2211yescharacteristic
61C22×C4⋊C4×C53C2211yescharacteristic
62C22×C4⋊C4×C53C2211yescharacteristic
63C22×D212C2311yescharacteristic
64C22×C22⋊D53—21no—
65C22×C22⋊D53—21no—
66C23×Dic53—21no—
67C2×#11719922—22no—
68C2×#11719922—22no—
69C2×#11719922—41no—
70C22×#88322—22no—
71C22×#88322—22no—
72C22×#88322—41no—
73C22×#88322C2311yescharacteristic
74C22×#88322C2311yescharacteristic
75C22×#88322C2311yescharacteristic
76C22×#88322C2311yescharacteristic
77#13133191—22no—
78#13133191—22no—
79#13133191—22no—
80#13133191—41no—
81#13133189—44no—
82C2×C4⋊Dic53—21no—
83C2×C4⋊Dic53—22no—
84C2×C4⋊Dic53—41no—
85C2×C4⋊Dic53C2311yescharacteristic
86C2×C4⋊Dic53C2311yescharacteristic
87C2×C4⋊Dic53C2311yescharacteristic
88C2×#11719919—21no—
89C2×C22⋊Dic53—21no—
90C2×#11719921—21no—
91C2×#11719921—21no—
92C2×#11719921—21no—
93C2×#11719921—21no—
94#13133150—22no—
95#13133150—22no—
96#13133150—22no—
97#13133138—22no—
98#13133138—22no—
99#13133138—41no—
100#13133137—22no—
101#13133137—22no—
102#13133137—22no—
103C22⋊#88322—22no—
104C22⋊#88322—22no—
105C22⋊#88322—41no—
106#13133124—21no—
107#13133124—21no—
108C2×#41×C53—28no—
109C2×#41×C53—44no—
110C2×#41×C53—44no—
111C22×Q8×C53—21no—
112C22×D4×C53—21no—
113C22×D4×C53—21no—
114C22×D4×C53D411yescharacteristic
115C22×D4×C53C2311yescharacteristic
116C23×C4×C53—21no—
117C23×C4×C53—21no—
118C23×C4×C53—21no—
119C23×C4×C53C2311yescharacteristic
120C23×C4×C53C2311yescharacteristic
121C4⋊Q8×C53—22no—
122C4⋊Q8×C53—22no—
123#123×C53—28no—
124#123×C53—28no—
125C22⋊Q8×C53—28no—
126#121×C53—22no—
127#121×C53—22no—
128#121×C53—22no—
129#121×C53D414yescomplemented
130C4×D4×C53—22no—
131C4×D4×C53—22no—
132C4×D4×C53—22no—
133C4×D4×C53—22no—
134C2×C4⋊C4×C53—22no—
135C2×C4⋊C4×C53—22no—
136C2×C4⋊C4×C53—21no—
137C2×C4⋊C4×C53—21no—
138C2×C4⋊C4×C53—22no—
139C2×C4⋊C4×C53—21no—
140C2×C4⋊C4×C53D411yescharacteristic
141C2×C4⋊C4×C53D414yescomplemented
142C2×C4⋊C4×C53C2311yescharacteristic
143C2×C4⋊C4×C53C2311yescharacteristic
144C2×C4⋊C4×C53C2311yescharacteristic
145C2×C22⋊C4×C53—21no—
146C2×C22⋊C4×C53—21no—
147C2×C22⋊C4×C53—21no—
148C2×C22⋊C4×C53D411yescharacteristic
149C2×C22⋊C4×C53D411yescharacteristic
150C2×C42×C53C2311yescharacteristic
151C24×C53—21no—
152C24×C53C2×D411yescharacteristic
153C24×C53C2×D411yescharacteristic
154C23×D53—21no—
155#41×C53—432no—
156C2×Q8×C53—24no—
157C2×Q8×C53—42no—
158C2×Q8×C53—42no—
159C2×D4×C53—22no—
160C2×D4×C53—22no—
161C2×D4×C53—24no—
162C2×D4×C53—24no—
163C2×D4×C53—21no—
164C2×D4×C53—21no—
165C2×D4×C53—21no—
166C2×D4×C53—21no—
167C2×D4×C53—21no—
168C2×D4×C53—42no—
169C2×D4×C53—42no—
170C2×D4×C53—42no—
171C2×D4×C53—42no—
172C2×D4×C53D814yescomplemented
173C2×D4×C53C2×D412yes—
174C22×C4×C53—21no—
175C22×C4×C53—21no—
176C22×C4×C53—21no—
177C22×C4×C53—21no—
178C22×C4×C53—24no—
179C22×C4×C53—24no—
180C22×C4×C53—24no—
181C22×C4×C53—21no—
182C22×C4×C53—21no—
183C22×C4×C53—21no—
184C22×C4×C53—21no—
185C22×C4×C53—21no—
186C22×C4×C53—21no—
187C22×C4×C53—21no—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53—42no—
191C22×C4×C53—42no—
192C22×C4×C53—42no—
193C22×C4×C53—42no—
194C22×C4×C53—42no—
195C22×C4×C53—42no—
196C22×C4×C53C2×D411yescharacteristic
197C22×C4×C53C2×D411yescharacteristic
198C22×C4×C53C2×D411yescharacteristic
199C22×C4×C53C2×D412yes—
200C22×C4×C53C2×D412yes—
201C22×C4×C53C2×D411yescharacteristic
202C22×C4×C53C2411yescharacteristic
203C2×C22⋊D53—42no—
204C2×C22⋊D53—42no—
205C2×C22⋊D53—42no—
206C2×C22⋊D53—42no—
207C2×C22⋊D53—42no—
208C2×C22⋊D53—81no—
209C22×Dic53—21no—
210C22×Dic53—21no—
211C22×Dic53—21no—
212C22×Dic53—42no—
213C22×Dic53—42no—
214C22×Dic53—81no—
215C2×D212—21no—
216C2×D212—21no—
217C2×D212—21no—
218C2×D212—21no—
219C2×D212—21no—
220C2×D212—21no—
221C4⋊C4×C53—24no—
222C4⋊C4×C53—24no—
223C4⋊C4×C53—24no—
224C4⋊C4×C53—22no—
225C4⋊C4×C53—21no—
226C4⋊C4×C53—21no—
227C4⋊C4×C53—21no—
228C4⋊C4×C53C2×D412yes—
229C4⋊C4×C53C2×D412yes—
230C4⋊C4×C53C2×D412yes—
231C22⋊C4×C53—24no—
232C22⋊C4×C53—24no—
233C22⋊C4×C53—22no—
234C22⋊C4×C53—24no—
235C22⋊C4×C53—22no—
236C42×C53—21no—
237C42×C53—21no—
238C22⋊Dic53—42no—
239#11719922—44no—
240#11719921—42no—
241#11719921—42no—
242#11719921—42no—
243#11719921—81no—
244C4⋊Dic53—21no—
245C4⋊Dic53—21no—
246C4⋊Dic53—21no—
247C4⋊Dic53—21no—
248C4⋊Dic53—21no—
249C4⋊Dic53—42no—
250C4⋊Dic53#4112yescomplemented
251#11719919—42no—
252C2×#88322—21no—
253C2×#88322—21no—
254C2×#88322—21no—
255C2×#88322—21no—
256C2×#88322—21no—
257C2×#88322—21no—
258C2×#88322—21no—
259C2×#88322—21no—
260C2×#88322—21no—
261C2×#88322—21no—
262C2×#88322—21no—
263C2×#88322—44no—
264C2×#88322#4112yescomplemented
265C23×C53—21no—
266C23×C53—21no—
267C23×C53—21no—
268C23×C53—21no—
269C23×C53—21no—
270C23×C53—21no—
271C23×C53—21no—
272C23×C53—21no—
273C23×C53—21no—
274C23×C53—21no—
275C23×C53—22no—
276C23×C53—41no—
277C23×C53—41no—
278C23×C53—41no—
279C23×C53—41no—
280C23×C53—41no—
281C23×C53—41no—
282C23×C53#12012yes—
283C23×C53C2×D812yes—
284C23×C53C2×D812yes—
285C23×C53AGL(1,ℤ/8)12yes—
286C23×C53C22×D411yescharacteristic
287C22×D53—41no—
288C22×D53—41no—
289C22×D53—41no—
290C22×D53—41no—
291C22×D53—41no—
292C22×D53—41no—
293C22×D53—41no—
294Q8×C53—48no—
295D4×C53—28no—
296D4×C53—22no—
297D4×C53—22no—
298D4×C53—48no—
299D4×C53—48no—
300D4×C53—41no—
301D4×C53—41no—
302C2×C4×C53—21no—
303C2×C4×C53—21no—
304C2×C4×C53—21no—
305C2×C4×C53—21no—
306C2×C4×C53—22no—
307C2×C4×C53—22no—
308C2×C4×C53—22no—
309C2×C4×C53—22no—
310C2×C4×C53—22no—
311C2×C4×C53—22no—
312C2×C4×C53—22no—
313C2×C4×C53—21no—
314C2×C4×C53—21no—
315C2×C4×C53—21no—
316C2×C4×C53—21no—
317C2×C4×C53—21no—
318C2×C4×C53—21no—
319C2×C4×C53—48no—
320C2×C4×C53—48no—
321C2×C4×C53—41no—
322C2×C4×C53—41no—
323C2×C4×C53—41no—
324C2×C4×C53—41no—
325C2×C4×C53—41no—
326C2×C4×C53—41no—
327C2×C4×C53—48no—
328C2×C4×C53—41no—
329C2×C4×C53—41no—
330C2×C4×C53—41no—
331C2×C4×C53—41no—
332C2×C4×C53#12012yes—
333C2×C4×C53C2×D812yes—
334C2×C4×C53C22×D411yescharacteristic
335C2×C4×C53C22×D411yescharacteristic
336C2×C4×C53C2×#4111yescharacteristic
337C2×C4×C53C2×#4111yescharacteristic
338C2×C4×C53H(5,𝔽2)11yescharacteristic
339C2×C4×C532−1+411yescharacteristic
340C22⋊D53—84no—
341C22⋊D53—84no—
342C2×Dic53—22no—
343C2×Dic53—41no—
344C2×Dic53—41no—
345C2×Dic53—41no—
346C2×Dic53—41no—
347C2×Dic53—41no—
348C2×Dic53—41no—
349C2×Dic53—41no—
350C2×Dic53—41no—
351C2×Dic53—84no—
352D212—41no—
353D212—41no—
354D212—41no—
355D212—41no—
356#88322—22no—
357#88322—41no—
358#88322—41no—
359#88322—41no—
360#25533—531nomaximal, Sylow
361C22×C53—22no—
362C22×C53—22no—
363C22×C53—22no—
364C22×C53—22no—
365C22×C53—22no—
366C22×C53—22no—
367C22×C53—22no—
368C22×C53—22no—
369C22×C53—22no—
370C22×C53—41no—
371C22×C53—41no—
372C22×C53—41no—
373C22×C53—41no—
374C22×C53—42no—
375C22×C53—42no—
376C22×C53—42no—
377C22×C53—81no—
378C22×C53—81no—
379C22×C53—81no—
380C22×C53—81no—
381C22×C53#44714yes—
382C22×C53C2×#12011yescharacteristic
383C22×C53#54611yescharacteristic
384C22×C53#54711yescharacteristic
385C22×C53C22×D811yescharacteristic
386C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
387C22×C53#57711yescharacteristic
388C22×C53#57811yescharacteristic
389C2×D53—81no—
390C2×D53—81no—
391C2×D53—81no—
392C2×D53—81no—
393C2×D53—81no—
394C2×D53—81no—
395C2×D53—81no—
396C4×C53—22no—
397C4×C53—22no—
398C4×C53—41no—
399C4×C53—42no—
400C4×C53—42no—
401C4×C53—42no—
402C4×C53—41no—
403C4×C53#53211yescharacteristic
404C4×C53#53711yescharacteristic
405C4×C53#54611yescharacteristic
406C4×C53#54711yescharacteristic
407Dic53—42no—
408Dic53—81no—
409Dic53—81no—
410C2×#547D5311yescharacteristic, complemented
411C2×#480—531no—
412C2×#466—531no—
413#2416—531no—
414#2057—531no—
415#2033—531no—
416#2023—531no—
417#1999—531no—
418#1879—531no—
419#1874—531no—
420#1874—531no—
421#1869—531no—
422#1862—531no—
423#1852—531no—
424C2×#340—531no—
425C2×C53—24no—
426C2×C53—42no—
427C2×C53—82no—
428C2×C53#243011yescharacteristic
429C2×C53C2×#44711yescharacteristic
430C2×C53#301311yescharacteristic
431C2×C53#329411yescharacteristic
432C2×C53#330811yescharacteristic
433C2×C53#333411yescharacteristic
434C2×C53#334511yescharacteristic
435D53—161no—
436C22×#41—21no—
437C22×D8—531no—
438C23×C8—531no—
439#547—24no—
440#547—24no—
441C2×C4⋊Q8C2×D5311yescharacteristic
442C2×#123—21no—
443C2×#123—21no—
444C2×C22⋊Q8—21no—
445C2×#121—531no—
446C2×#121—531no—
447C2×#121—1061no—
448C2×#121C2×D5311yescharacteristic
449C2×#121C2×D5311yescharacteristic
450C2×C4×D4C2×D5311yescharacteristic
451C2×C4×D4C2×D5311yescharacteristic
452C22×C4⋊C4—531no—
453C22×C4⋊C4C2×D5311yescharacteristic
454C22×C4⋊C4C2×D5311yescharacteristic
455#480—1064no—
456#466—1064no—
457C2×#107—531no—
458C2×#107—531no—
459C2×#107—531no—
460C2×#102—531no—
461C2×#102—531no—
462C2×#102—531no—
463C2×#102—531no—
464C2×#102—531no—
465C2×#102—531no—
466C2×C22⋊C8—531no—
467C2×C22⋊C8—531no—
468C2×C22⋊C8—531no—
469#396—1061no—
470#394—1061no—
471#390—531no—
472#389—531no—
473#386—1061no—
474#380—531no—
475#340—531no—
476#340—531no—
477#340—531no—
478#340—531no—
479#340—531no—
480#340—531no—
481#336—531no—
482#336—531no—
483C53#2553311yescharacteristic, complemented, Sylow
484C2×#41—28no—
485C2×#41—44no—
486C2×#41—44no—
487C22×Q8—21no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—531no—
491C22×D4—1061no—
492C22×D4—1061no—
493C22×D4C22⋊D5311yescharacteristic
494C22×D4C22×D5311yescharacteristic
495C23×C4—21no—
496C23×C4—21no—
497C23×C4—21no—
498C23×C4—1061no—
499C23×C4C22×D5311yescharacteristic
500C23×C4C22×D5311yescharacteristic
501C2×D8—1062no—
502C2×D8—1062no—
503C2×D8—2121no—
504C22×C8—531no—
505C22×C8—531no—
506C22×C8—531no—
507C22×C8—531no—
508C22×C8—1062no—
509C22×C8—1062no—
510C22×C8—2121no—
511C4⋊Q8—22no—
512C4⋊Q8—22no—
513#123—28no—
514#123—28no—
515C22⋊Q8—28no—
516#121—22no—
517#121—22no—
518#121—22no—
519#121—1062no—
520#121—1062no—
521#121—1062no—
522#121—2121no—
523#121—2124no—
524#121C22⋊D5314yescomplemented
525C4×D4—22no—
526C4×D4—22no—
527C4×D4—22no—
528C4×D4—22no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—22no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—22no—
534C2×C4⋊C4—22no—
535C2×C4⋊C4—531no—
536C2×C4⋊C4—531no—
537C2×C4⋊C4—531no—
538C2×C4⋊C4—1062no—
539C2×C4⋊C4—1061no—
540C2×C4⋊C4—1061no—
541C2×C4⋊C4—2121no—
542C2×C4⋊C4C22⋊D5311yescharacteristic
543C2×C4⋊C4C22⋊D5314yescomplemented
544C2×C4⋊C4C22×D5311yescharacteristic
545C2×C4⋊C4C22×D5311yescharacteristic
546C2×C4⋊C4C22×D5311yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—1061no—
551C2×C22⋊C4—1061no—
552C2×C22⋊C4—1061no—
553C2×C22⋊C4—1061no—
554C2×C22⋊C4—1061no—
555C2×C22⋊C4C22⋊D5311yescharacteristic
556C2×C22⋊C4C22⋊D5311yescharacteristic
557C2×C42C22×D5311yescharacteristic
558#107—1062no—
559#107—1062no—
560#107—1062no—
561#102—1062no—
562#102—1062no—
563#102—1062no—
564#102—1062no—
565#102—1062no—
566#102—2121no—
567C22⋊C8—1062no—
568C22⋊C8—1062no—
569C22⋊C8—2121no—
570#95—1061no—
571#95—1061no—
572C24—21no—
573C24—1061no—
574C24C2×C22⋊D5311yescharacteristic
575C24C2×C22⋊D5311yescharacteristic
576#41—432no—
577C2×Q8—24no—
578C2×Q8—42no—
579C2×Q8—42no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—24no—
583C2×D4—24no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—42no—
590C2×D4—42no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4—1061no—
594C2×D4—1061no—
595C2×D4—1061no—
596C2×D4—1061no—
597C2×D4—1061no—
598C2×D4—1061no—
599C2×D4—4241no—
600C2×D4—2122no—
601C2×D4—2122no—
602C2×D4—2122no—
603C2×D4—2122no—
604C2×D4—2122no—
605C2×D4#1171992214yescomplemented
606C2×D4C2×C22⋊D5312yes—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—24no—
612C22×C4—24no—
613C22×C4—24no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—1061no—
630C22×C4—1061no—
631C22×C4—1061no—
632C22×C4—4241no—
633C22×C4—2122no—
634C22×C4—2122no—
635C22×C4C2×C22⋊D5311yescharacteristic
636C22×C4C2×C22⋊D5311yescharacteristic
637C22×C4C2×C22⋊D5311yescharacteristic
638C22×C4C2×C22⋊D5312yes—
639C22×C4C2×C22⋊D5312yes—
640C22×C4C2×C22⋊D5311yescharacteristic
641C22×C4C23×D5311yescharacteristic
642D8—2124no—
643C2×C8—532no—
644C2×C8—1061no—
645C2×C8—1061no—
646C2×C8—1061no—
647C2×C8—1061no—
648C2×C8—1061no—
649C2×C8—1061no—
650C2×C8—1061no—
651C2×C8—1061no—
652C2×C8—1061no—
653C2×C8—1061no—
654C2×C8—1061no—
655C2×C8—2124no—
656C4⋊C4—24no—
657C4⋊C4—24no—
658C4⋊C4—24no—
659C4⋊C4—22no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—532no—
664C4⋊C4—1061no—
665C4⋊C4—1061no—
666C4⋊C4—1061no—
667C4⋊C4—1061no—
668C4⋊C4—1061no—
669C4⋊C4—2122no—
670C4⋊C4—2122no—
671C4⋊C4C2×C22⋊D5312yes—
672C4⋊C4C2×C22⋊D5312yes—
673C4⋊C4C2×C22⋊D5312yes—
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—22no—
677C22⋊C4—24no—
678C22⋊C4—22no—
679C22⋊C4—4241no—
680C22⋊C4—2122no—
681C22⋊C4—2122no—
682C22⋊C4—2122no—
683C22⋊C4—2122no—
684C42—21no—
685C42—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—22no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—2121no—
704C23—2121no—
705C23—2121no—
706C23—2121no—
707C23—2121no—
708C23—2121no—
709C23—2121no—
710C23#1313318612yes—
711C23C2×#1171992212yes—
712C23C2×#1171992212yes—
713C23#1313324312yes—
714C23C22×C22⋊D5311yescharacteristic
715Q8—48no—
716D4—28no—
717D4—22no—
718D4—22no—
719D4—48no—
720D4—48no—
721D4—41no—
722D4—41no—
723D4—4244no—
724D4—4244no—
725D4—2121no—
726D4—2121no—
727D4—2121no—
728D4—2121no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—48no—
747C2×C4—48no—
748C2×C4—48no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—1062no—
760C2×C4—4244no—
761C2×C4—2121no—
762C2×C4—2121no—
763C2×C4—2121no—
764C2×C4—2121no—
765C2×C4—2121no—
766C2×C4—2121no—
767C2×C4—2121no—
768C2×C4—2121no—
769C2×C4#1313318612yes—
770C2×C4C2×#1171992212yes—
771C2×C4C22×C22⋊D5311yescharacteristic
772C2×C4C22×C22⋊D5311yescharacteristic
773C2×C4#41×D5311yescharacteristic
774C2×C4#41×D5311yescharacteristic
775C2×C4#1313326311yescharacteristic
776C2×C4#1313326411yescharacteristic
777C8—1062no—
778C8—2121no—
779C8—2121no—
780C8—2121no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—4241no—
802C22—4241no—
803C22—4241no—
804C22—4241no—
805C22—4241no—
806C22—4241no—
807C22—4241no—
808C22#1681075714yes—
809C22C2×#1313318611yescharacteristic
810C22#1681126111yescharacteristic
811C22#1681127211yescharacteristic
812C22C22×#1171992211yescharacteristic
813C22C2×#1313324311yescharacteristic
814C22#1681143111yescharacteristic
815C22#1681143811yescharacteristic
816C4—22no—
817C4—22no—
818C4—41no—
819C4—41no—
820C4—42no—
821C4—42no—
822C4—42no—
823C4—4241no—
824C4—4241no—
825C4—2122no—
826C4#1681116911yescharacteristic
827C4#1681120111yescharacteristic
828C4#1681126111yescharacteristic
829C4#1681127211yescharacteristic
830C2—24no—
831C2—42no—
832C2—82no—
833C2—8481no—
834C2#2027831911yescharacteristic
835C2C2×#1681075711yescharacteristic
836C2#2028403011yescharacteristic
837C2#2028652211yescharacteristic
838C2#2028670011yescharacteristic
839C2#2028705811yescharacteristic
840C2#2028718511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
FittingC2×C53×#547C2
socleC23×C53C22×D4
hypercenterC2×#547D53
hypocenterC53#25533
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#16810936C2semidirect
2. C2×#16810857C2semidirect
3. #20278155C2semidirect
4. #20276040C2semidirect
5. #20275894C2semidirect
6. #20275848C2semidirect
7. #20275711C2semidirect
8. #20275063C2semidirect
9. #20275033C2semidirect
10. #20275032C2semidirect
11. #20275008C2semidirect
12. #20274962C2semidirect
13. #20274903C2semidirect
14. C2×#16810385C2semidirect
15. C2×C53×#547C2semidirect
129. #121×C53D4semidirect
141. C2×C4⋊C4×C53D4semidirect
172. C2×D4×C53D8semidirect
250. C4⋊Dic53#41semidirect
264. C2×#88322#41semidirect
410. C2×#547D53semidirect
483. C53#25533semidirect
524. #121C22⋊D53semidirect
543. C2×C4⋊C4C22⋊D53semidirect
605. C2×D4#11719922semidirect

Maximal subgroups

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

subgroupindex
C2×#168109362
C2×#168108572
#202781552
#202760402
#202758942
#202758482
#202757112
#202750632
#202750332
#202750322
#202750082
#202749622
#202749032
C2×#168103852
C2×C53×#5472
#2553353