Finite Group Databasebeta

← C2×#20287463 #28263836

Subgroups — C2×#20287463 #28263836

Order 13568.

1950 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811359C211yesmaximal, characteristic, complemented
2C2×#16811329C211yesmaximal, characteristic, complemented
3#20287463C2116yesmaximal, direct product factor
4C2×#16810981C211yesmaximal, characteristic, complemented
5C2×#16810976C211yesmaximal, characteristic, complemented
6C2×#16810927C211yesmaximal, characteristic, complemented
7C2×#16810921C211yesmaximal, characteristic, complemented
8C2×#16810901C211yesmaximal, characteristic, complemented
9C2×#16810837C211yesmaximal, characteristic, complemented
10C2×#16810837C211yesmaximal, characteristic, complemented
11C2×#16810815C211yesmaximal, characteristic
12C2×#16810751C211yesmaximal, characteristic, complemented
13C2×#16810732C211yesmaximal, characteristic, complemented
14C2×#16810725C211yesmaximal, characteristic, complemented
15C2×#16810703C211yesmaximal, characteristic, complemented
16C2×C53×#490C211yesmaximal, characteristic, complemented
17C22×#11719913C2211yescharacteristic
18C22×#11719922C2211yescharacteristic
19C22×#11719922C2211yescharacteristic
20#16811359—24no—
21#16811359C2218yescomplemented
22#16811329—24no—
23#16811329C2218yescomplemented
24C2×#13133216C2211yescharacteristic
25C2×#13133208C2211yescharacteristic
26C2×#13133204—21no—
27C2×#13133204C2211yescharacteristic
28C2×#13133204C2211yescharacteristic
29C2×#13133198—21no—
30C2×#13133198—21no—
31C2×#13133197—21no—
32C2×#13133195—21no—
33C2×#13133195—21no—
34C2×C4×Dic106C2211yescharacteristic
35C2×C4×Dic106C2211yescharacteristic
36C2×C4×D212C2211yescharacteristic
37C2×D4×Dic53—21no—
38C2×D4×Dic53C2211yescharacteristic
39C2×D4×Dic53C2211yescharacteristic
40C2×#13133179C2211yescharacteristic
41C2×#13133179C2211yescharacteristic
42C2×C4⋊C4×D53—21no—
43#16810981C2218yescomplemented
44#16810976C2218yescomplemented
45#16810927C2218yescomplemented
46#16810921C2218yescomplemented
47#16810901C2218yescomplemented
48#16810837C2218yescomplemented
49#16810837C2218yescomplemented
50#16810815C2218yes—
51#16810751C2218yescomplemented
52#16810732C2218yescomplemented
53#16810725C2218yescomplemented
54#16810703C2218yescomplemented
55C2×#13133151C2211yescharacteristic
56C2×#13133150C2211yescharacteristic
57C2×#13133148C2211yescharacteristic
58C2×C4⋊#88322C2211yescharacteristic
59C2×#13133146C2211yescharacteristic
60C2×#13133146C2211yescharacteristic
61C2×#13133142C2211yescharacteristic
62C2×#13133140C2211yescharacteristic
63C2×#13133140C2211yescharacteristic
64C2×#13133139C2211yescharacteristic
65C2×#13133138C2211yescharacteristic
66C2×#13133138C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C2×#127×C53C2211yescharacteristic
70C2×#125×C53C2211yescharacteristic
71C53×#490C2218yescomplemented
72C2×#102×C53C2211yescharacteristic
73C2×#102×C53C2211yescharacteristic
74C2×#102×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×#97×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106D411yescharacteristic
79C22×Dic106C2311yescharacteristic
80C22×D212C2311yescharacteristic
81C23×Dic53—21no—
82C23×Dic53—21no—
83C22×C4×D53—21no—
84C22×C4×D53—21no—
85C22×C4×D53—21no—
86C2×#11719913—24no—
87C2×#11719913C2314yes—
88C2×#11719922—24no—
89C2×#11719922—24no—
90C2×#11719922C2314yes—
91C2×#11719922C2314yes—
92C22×#88322C2311yescharacteristic
93C22×#88322C2311yescharacteristic
94#13133216—22no—
95#13133216C2314yes—
96#13133208—22no—
97#13133208C2314yes—
98#13133204—22no—
99#13133204—22no—
100#13133204—28no—
101#13133204C2314yes—
102#13133204C2314yes—
103#13133198—28no—
104#13133198—28no—
105#13133197—28no—
106#13133195—28no—
107#13133195—28no—
108C4×Dic106—22no—
109C4×Dic106D414yes—
110C4×Dic106C2314yes—
111C4×Dic106C2314yes—
112C4×D212—22no—
113C4×D212C2314yes—
114D4×Dic53—28no—
115D4×Dic53—22no—
116D4×Dic53—22no—
117D4×Dic53C2314yes—
118D4×Dic53C2314yes—
119#13133179—22no—
120#13133179—22no—
121#13133179C2314yes—
122#13133179C2314yes—
123C2×C4⋊Dic53—21no—
124C2×C4⋊Dic53D411yescharacteristic
125C2×C4⋊Dic53C2311yescharacteristic
126C2×C4⋊Dic53C2311yescharacteristic
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919D411yescharacteristic
131C2×#11719919D411yescharacteristic
132C4⋊C4×D53—28no—
133C2×C22⋊Dic53—21no—
134C2×C22⋊Dic53—21no—
135C2×C22⋊Dic53—21no—
136C2×C22⋊Dic53—21no—
137C2×C22⋊Dic53—21no—
138C2×C22⋊Dic53—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×C4×Dic53—21no—
143C2×C4×Dic53C2311yescharacteristic
144C2×C4×Dic53C2311yescharacteristic
145#13133151C2314yes—
146#13133150C2314yes—
147#13133148C2314yes—
148C4⋊#88322C2314yes—
149#13133146C2314yes—
150#13133146C2314yes—
151#13133142C2314yes—
152#13133140C2314yes—
153#13133140C2314yes—
154#13133139C2314yes—
155#13133138C2314yes—
156#13133138C2314yes—
157#13133127C2314yes—
158C8×Dic53C2314yes—
159C22×D4×C53—21no—
160C22×D4×C53—21no—
161C22×D4×C53C2311yescharacteristic
162C22×D4×C53C2311yescharacteristic
163C22×C8×C53C2311yescharacteristic
164C22×C8×C53C2311yescharacteristic
165#127×C53—22no—
166#127×C53C2314yes—
167#125×C53—22no—
168#125×C53C2314yes—
169C2×C4⋊C4×C53—21no—
170C2×C4⋊C4×C53—21no—
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C42×C53C2311yescharacteristic
174#102×C53C2314yes—
175#102×C53C2314yes—
176#102×C53C2314yes—
177#102×C53C2314yes—
178#97×C53C2314yes—
179C24×C53—21no—
180C24×C53—21no—
181C23×D53—21no—
182C2×D4×C53—21no—
183C2×D4×C53—21no—
184C2×D4×C53—24no—
185C2×D4×C53—24no—
186C2×D4×C53—22no—
187C2×D4×C53—22no—
188C2×D4×C53—22no—
189C2×D4×C53—22no—
190C2×D4×C53—44no—
191C2×D4×C53—82no—
192C2×D4×C53C2412yes—
193C2×D4×C53C2412yes—
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53C2×D411yescharacteristic
197C22×C4×C53C2×D411yescharacteristic
198C22×C4×C53C2411yescharacteristic
199C22×Dic53—21no—
200C22×Dic53—21no—
201C22×Dic53—21no—
202C22×Dic53—24no—
203C22×Dic53—24no—
204C22×Dic53—82no—
205C22×Dic53—82no—
206C22×Dic53C2×D411yescharacteristic
207C22×Dic53C2×D411yescharacteristic
208C22×Dic53C2×D411yescharacteristic
209C22×Dic53C2×D411yescharacteristic
210C2×D212—21no—
211C2×D212—22no—
212C2×D212#4114yes—
213C2×D212C2412yes—
214C2×C4×D53—24no—
215C2×C4×D53—24no—
216C2×C4×D53—24no—
217C2×C4×D53—44no—
218C2×C4×D53—82no—
219C2×C4×D53—82no—
220C2×Dic106—22no—
221C2×Dic106—22no—
222C2×Dic106—21no—
223C2×Dic106—24no—
224C2×Dic106—42no—
225C2×Dic106—82no—
226C2×Dic106C2×D414yes—
227C2×Dic106C2412yes—
228C2×C8×C53—22no—
229C2×C8×C53—22no—
230C2×C8×C53C2412yes—
231C2×C8×C53C2412yes—
232C4⋊C4×C53—24no—
233C4⋊C4×C53—24no—
234C4⋊C4×C53—21no—
235C4⋊C4×C53—21no—
236C4⋊C4×C53C2412yes—
237C4⋊C4×C53C2412yes—
238C42×C53C2×D412yes—
239C42×C53C2412yes—
240C22⋊Dic53—24no—
241C22⋊Dic53—24no—
242C22⋊Dic53—24no—
243C22⋊Dic53—24no—
244C22⋊Dic53—24no—
245C22⋊Dic53—24no—
246#11719922—28no—
247#11719922—28no—
248#11719921—24no—
249#11719921—24no—
250#11719921—24no—
251C4⋊Dic53—21no—
252C4⋊Dic53—21no—
253C4⋊Dic53—24no—
254C4⋊Dic53C2×D414yes—
255C4⋊Dic53C2412yes—
256C4⋊Dic53C2412yes—
257#11719919—24no—
258#11719919—24no—
259#11719919—24no—
260#11719919C2×D414yes—
261#11719919C2×D414yes—
262C4×Dic53—24no—
263C4×Dic53C2×D412yes—
264C4×Dic53C2×D412yes—
265C4×Dic53C2412yes—
266C4×Dic53C2412yes—
267C2×#88322—22no—
268C2×#88322—22no—
269C2×#88322C2412yes—
270C2×#88322C2412yes—
271#11719913—28no—
272C23×C53—22no—
273C23×C53—22no—
274C23×C53—42no—
275C23×C53—42no—
276C23×C53—42no—
277C23×C53—42no—
278C23×C53—42no—
279C23×C53—42no—
280C23×C53C22×D411yescharacteristic
281C22×D53—24no—
282C22×D53—22no—
283C22×D53—42no—
284C22×D53—42no—
285D4×C53—22no—
286D4×C53—22no—
287D4×C53—22no—
288D4×C53—22no—
289D4×C53—48no—
290D4×C53—42no—
291D4×C53—42no—
292D4×C53—84no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53—42no—
298C2×C4×C53—42no—
299C2×C4×C53C22×D412yes—
300C2×C4×C53C22×D412yes—
301C2×C4×C53C22×D411yescharacteristic
302C2×C4×C53C2×#4112yes—
303C2×C4×C532−1+412yes—
304C2×C4×C53C2511yescharacteristic
305C2×Dic53—22no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—22no—
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—42no—
313C2×Dic53—42no—
314C2×Dic53—42no—
315C2×Dic53—84no—
316C2×Dic53—84no—
317C2×Dic53C22×D412yes—
318C2×Dic53C22×D412yes—
319C2×Dic53C22×D412yes—
320C2×Dic53C22×D412yes—
321D212—24no—
322D212—22no—
323D212C2×#4114yes—
324C4×D53—48no—
325C4×D53—84no—
326C4×D53—84no—
327Dic106—22no—
328Dic106—22no—
329Dic106—44no—
330Dic106—42no—
331Dic106—84no—
332C8×C53—22no—
333C8×C53—22no—
334#88322—22no—
335#88322—22no—
336C2×#3370—531nomaximal, Sylow
337C22×C53—42no—
338C22×C53—42no—
339C22×C53—42no—
340C22×C53—42no—
341C22×C53—42no—
342C22×C53—42no—
343C22×C53—84no—
344C22×C53—84no—
345C22×C53#54812yes—
346C22×C53#57512yes—
347C22×C53#57612yes—
348C22×C53C23×D411yescharacteristic
349C2×D53—24no—
350C2×D53—48no—
351C2×D53—42no—
352C2×D53—42no—
353C4×C53—22no—
354C4×C53—22no—
355C4×C53—42no—
356C4×C53—42no—
357C4×C53#54812yes—
358C4×C53C22×#4111yescharacteristic
359C4×C53C2×2−1+411yescharacteristic
360Dic53—22no—
361Dic53—22no—
362Dic53—22no—
363Dic53—22no—
364Dic53—42no—
365Dic53—42no—
366Dic53—42no—
367C2×#559—531no—
368C2×#554—531no—
369#3370—5316no—
370C2×#490D5311yescharacteristic, complemented
371C2×#489—531no—
372C2×#488—531no—
373C2×#479—531no—
374C2×#478—531no—
375C2×#474—531no—
376C2×#463—531no—
377C2×#463—531no—
378C2×#459—531no—
379C2×#446—531no—
380C2×#442—531no—
381C2×#440—531no—
382C2×C4×D8—531no—
383C2×C53—82no—
384C2×C53—82no—
385C2×C53#337014yescomplemented
386C2×C53C2×#54811yescharacteristic
387C2×C53C2×#57511yescharacteristic
388C2×C53C2×#57611yescharacteristic
389D53—44no—
390C22×SD16—531no—
391C22×D8—531no—
392C22×D8—531no—
393#559—538no—
394#559—1064no—
395#554—538no—
396#554—1064no—
397C2×C4⋊Q8—531no—
398C2×#127C2×D5311yescharacteristic
399C2×#125—531no—
400C2×#125C2×D5311yescharacteristic
401C2×#124—531no—
402C2×#124—531no—
403C2×#124—1061no—
404C2×#123—1061no—
405C2×#123—1061no—
406C2×C22⋊Q8—1061no—
407C2×C22⋊Q8—1061no—
408C2×C22⋊Q8—1061no—
409C2×C4×Q8—531no—
410C2×C4×Q8—531no—
411C2×C4×D4—531no—
412C2×C4×D4—531no—
413C2×C4×D4—531no—
414C2×C4×D4—531no—
415C2×C4×D4—531no—
416C2×C4×D4—1061no—
417C22×C4⋊C4—1061no—
418#490C2×D5318yescomplemented
419#489—538no—
420#488—538no—
421#479—538no—
422#478—538no—
423#474—538no—
424#463—538no—
425#463—538no—
426#459—538no—
427#446—538no—
428#442—538no—
429#440—538no—
430C4×D8—538no—
431C2×#107—531no—
432C2×#107—531no—
433C2×#106—531no—
434C2×C4⋊C8—531no—
435C2×C4⋊C8—531no—
436C2×C4⋊C8—531no—
437C2×#103—531no—
438C2×#103—531no—
439C2×#103—531no—
440C2×#102—531no—
441C2×#102—531no—
442C2×#102—531no—
443C2×#102C2×D5311yescharacteristic
444C2×#102C2×D5311yescharacteristic
445C2×#102C2×D5311yescharacteristic
446C2×#102C2×D5311yescharacteristic
447C2×#97—531no—
448C2×#97C2×D5311yescharacteristic
449C2×C4×C8—531no—
450C53C2×#337011yescharacteristic, complemented, Sylow
451C22×Q8—531no—
452C22×Q8—531no—
453C22×Q8—1061no—
454C22×D4—21no—
455C22×D4—21no—
456C22×D4—531no—
457C22×D4C22×D5311yescharacteristic
458C22×D4C22×D5311yescharacteristic
459C23×C4—1061no—
460C23×C4—1061no—
461C23×C4—1061no—
462C23×C4—1061no—
463C23×C4—1061no—
464C2×SD16—534no—
465C2×SD16—1064no—
466C2×D8—534no—
467C2×D8—534no—
468C2×D8—1064no—
469C2×D8—1064no—
470C22×C8—531no—
471C22×C8—531no—
472C22×C8C22×D5311yescharacteristic
473C22×C8C22×D5311yescharacteristic
474C4⋊Q8—534no—
475C4⋊Q8—1062no—
476#127—22no—
477#127C22×D5314yes—
478#125—22no—
479#125—534no—
480#125—1062no—
481#125C22×D5314yes—
482#124—534no—
483#124—534no—
484#124—1062no—
485#124—1062no—
486#124—1068no—
487#123—1068no—
488#123—1068no—
489C22⋊Q8—1068no—
490C22⋊Q8—1068no—
491C22⋊Q8—1068no—
492C4×Q8—534no—
493C4×Q8—534no—
494C4×Q8—534no—
495C4×Q8—1062no—
496C4×D4—534no—
497C4×D4—534no—
498C4×D4—534no—
499C4×D4—534no—
500C4×D4—534no—
501C4×D4—1062no—
502C4×D4—1062no—
503C4×D4—1062no—
504C4×D4—1062no—
505C4×D4—1068no—
506C4×D4—1062no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—531no—
510C2×C4⋊C4—531no—
511C2×C4⋊C4—531no—
512C2×C4⋊C4—531no—
513C2×C4⋊C4—531no—
514C2×C4⋊C4—1068no—
515C2×C4⋊C4—1061no—
516C2×C4⋊C4—1061no—
517C2×C4⋊C4—1061no—
518C2×C4⋊C4—1061no—
519C2×C4⋊C4C22×D5311yescharacteristic
520C2×C4⋊C4C22×D5311yescharacteristic
521C2×C22⋊C4—1061no—
522C2×C22⋊C4—1061no—
523C2×C22⋊C4—1061no—
524C2×C22⋊C4—1061no—
525C2×C22⋊C4—1061no—
526C2×C22⋊C4—1061no—
527C2×C22⋊C4—1061no—
528C2×C22⋊C4—1061no—
529C2×C22⋊C4—1061no—
530C2×C42—531no—
531C2×C42—531no—
532C2×C42—1061no—
533C2×C42C22×D5311yescharacteristic
534#107—534no—
535#107—534no—
536#106—534no—
537C4⋊C8—534no—
538C4⋊C8—534no—
539C4⋊C8—534no—
540#103—534no—
541#103—534no—
542#103—534no—
543#102—534no—
544#102—534no—
545#102—534no—
546#102C22×D5314yes—
547#102C22×D5314yes—
548#102C22×D5314yes—
549#102C22×D5314yes—
550#97—534no—
551#97C22×D5314yes—
552C4×C8—534no—
553C24—21no—
554C24—21no—
555C24—1061no—
556C2×Q8—534no—
557C2×Q8—532no—
558C2×Q8—1064no—
559C2×Q8—1061no—
560C2×Q8—1062no—
561C2×Q8—1062no—
562C2×Q8—4242no—
563C2×Q8—2122no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—24no—
567C2×D4—24no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—44no—
573C2×D4—82no—
574C2×D4—534no—
575C2×D4—532no—
576C2×D4—1061no—
577C2×D4—1062no—
578C2×D4C23×D5312yes—
579C2×D4C23×D5312yes—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—531no—
583C22×C4—531no—
584C22×C4—531no—
585C22×C4—531no—
586C22×C4—1064no—
587C22×C4—1064no—
588C22×C4—1064no—
589C22×C4—1064no—
590C22×C4—1061no—
591C22×C4—1061no—
592C22×C4—1061no—
593C22×C4—1064no—
594C22×C4—4242no—
595C22×C4—4242no—
596C22×C4—4242no—
597C22×C4—4242no—
598C22×C4—2124no—
599C22×C4D4×D5311yescharacteristic
600C22×C4D4×D5311yescharacteristic
601C22×C4C23×D5311yescharacteristic
602SD16—1068no—
603D8—1068no—
604D8—1068no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—532no—
608C2×C8—532no—
609C2×C8—1062no—
610C2×C8—1062no—
611C2×C8C23×D5312yes—
612C2×C8C23×D5312yes—
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—534no—
618C4⋊C4—534no—
619C4⋊C4—534no—
620C4⋊C4—532no—
621C4⋊C4—532no—
622C4⋊C4—1064no—
623C4⋊C4—1064no—
624C4⋊C4—1064no—
625C4⋊C4—1061no—
626C4⋊C4—1061no—
627C4⋊C4—1064no—
628C4⋊C4C23×D5312yes—
629C4⋊C4C23×D5312yes—
630C22⋊C4—1064no—
631C22⋊C4—1064no—
632C22⋊C4—1064no—
633C22⋊C4—1064no—
634C22⋊C4—1064no—
635C22⋊C4—1064no—
636C22⋊C4—1064no—
637C22⋊C4—1064no—
638C22⋊C4—1064no—
639C42—532no—
640C42—532no—
641C42—532no—
642C42—532no—
643C42—1064no—
644C42D4×D5312yes—
645C42C23×D5312yes—
646C23—22no—
647C23—22no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—1064no—
655C23—1062no—
656C23—2122no—
657C23—2122no—
658C23C2×D4×D5311yescharacteristic
659Q8—1062no—
660Q8—1062no—
661Q8—4244no—
662Q8—2124no—
663Q8—2122no—
664D4—22no—
665D4—22no—
666D4—22no—
667D4—22no—
668D4—48no—
669D4—42no—
670D4—42no—
671D4—84no—
672D4—534no—
673D4—1064no—
674D4—1062no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—532no—
682C2×C4—532no—
683C2×C4—532no—
684C2×C4—532no—
685C2×C4—1062no—
686C2×C4—1062no—
687C2×C4—1062no—
688C2×C4—1062no—
689C2×C4—1062no—
690C2×C4—1062no—
691C2×C4—1062no—
692C2×C4—4244no—
693C2×C4—4244no—
694C2×C4—4244no—
695C2×C4—4244no—
696C2×C4—2128no—
697C2×C4—2122no—
698C2×C4—2122no—
699C2×C4—2122no—
700C2×C4C2×D4×D5312yes—
701C2×C4C2×D4×D5312yes—
702C2×C4C2×D4×D5311yescharacteristic
703C2×C4#41×D5312yes—
704C2×C4#1313326412yes—
705C2×C4C24×D5311yescharacteristic
706C8—22no—
707C8—22no—
708C8—1062no—
709C8—1062no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—84no—
717C22—84no—
718C22—1064no—
719C22—2122no—
720C22—2122no—
721C22—2128no—
722C22#1681128112yes—
723C22#1681141912yes—
724C22#1681142712yes—
725C22C22×D4×D5311yescharacteristic
726C4—22no—
727C4—22no—
728C4—42no—
729C4—42no—
730C4—1062no—
731C4—1062no—
732C4—1062no—
733C4—1062no—
734C4—2122no—
735C4—2122no—
736C4—2122no—
737C4#1681128112yes—
738C4C2×#41×D5311yescharacteristic
739C4C2×#1313326411yescharacteristic
740C2—82no—
741C2—82no—
742C2—2124no—
743C2#2028746314yesdirect product factor
744C2C2×#1681128111yescharacteristic
745C2C2×#1681141911yescharacteristic
746C2C2×#1681142711yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#490C2
socleC23×C53C22×D4
prime radicalC2×#16810815C2
hypercenterC2×#490D53
hypocenterC53C2×#3370
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#490

Complements

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

NH ≅ G/Ntype
1. C2×#16811359C2semidirect
2. C2×#16811329C2semidirect
3. #20287463C2direct (N × H)
4. C2×#16810981C2semidirect
5. C2×#16810976C2semidirect
6. C2×#16810927C2semidirect
7. C2×#16810921C2semidirect
8. C2×#16810901C2semidirect
9. C2×#16810837C2semidirect
10. C2×#16810837C2semidirect
12. C2×#16810751C2semidirect
13. C2×#16810732C2semidirect
14. C2×#16810725C2semidirect
15. C2×#16810703C2semidirect
16. C2×C53×#490C2semidirect
21. #16811359C22semidirect
23. #16811329C22semidirect
43. #16810981C22semidirect
44. #16810976C22semidirect
45. #16810927C22semidirect
46. #16810921C22semidirect
47. #16810901C22semidirect
48. #16810837C22semidirect
49. #16810837C22semidirect
51. #16810751C22semidirect
52. #16810732C22semidirect
53. #16810725C22semidirect
54. #16810703C22semidirect
71. C53×#490C22semidirect
370. C2×#490D53semidirect
385. C2×C53#3370semidirect
418. #490C2×D53semidirect
450. C53C2×#3370semidirect
743. C2#20287463direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113592
C2×#168113292
#202874632
C2×#168109812
C2×#168109762
C2×#168109272
C2×#168109212
C2×#168109012
C2×#168108372
C2×#168108152
C2×#168107512
C2×#168107322
C2×#168107252
C2×#168107032
C2×C53×#4902
C2×#337053