Finite Group Databasebeta

← C2×#20287466 #28263839

Subgroups — C2×#20287466 #28263839

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×#16811356C211yesmaximal, characteristic, complemented
2C2×#16811329C211yesmaximal, characteristic, complemented
3#20287466C2116yesmaximal, direct product factor
4C2×#16810986C211yesmaximal, characteristic, complemented
5C2×#16810981C211yesmaximal, characteristic, complemented
6C2×#16810980C211yesmaximal, characteristic, complemented
7C2×#16810933C211yesmaximal, characteristic, complemented
8C2×#16810902C211yesmaximal, characteristic, complemented
9C2×#16810839C211yesmaximal, characteristic, complemented
10C2×#16810837C211yesmaximal, characteristic, complemented
11C2×#16810817C211yesmaximal, characteristic
12C2×#16810750C211yesmaximal, characteristic, complemented
13C2×#16810734C211yesmaximal, characteristic, complemented
14C2×#16810722C211yesmaximal, characteristic, complemented
15C2×C4×#11719922C211yesmaximal, characteristic, complemented
16C2×C53×#478C211yesmaximal, characteristic, complemented
17C22×#11719913C2211yescharacteristic
18C22×D424C2211yescharacteristic
19C22×#11719922C2211yescharacteristic
20#16811356—24no—
21#16811356C2218yescomplemented
22#16811329—24no—
23#16811329C2218yescomplemented
24C2×#13133216C2211yescharacteristic
25C2×#13133213C2211yescharacteristic
26C2×#13133208C2211yescharacteristic
27C2×#13133205C2211yescharacteristic
28C2×#13133204C2211yescharacteristic
29C2×#13133203—21no—
30C2×#13133200—21no—
31C2×#13133199—21no—
32C2×#13133197—21no—
33C2×#13133195—21no—
34C2×#13133195—21no—
35C2×C4×Dic106C2211yescharacteristic
36C2×#13133182C2211yescharacteristic
37C2×C4×D212C2211yescharacteristic
38C2×#13133179C2211yescharacteristic
39C2×#13133179C2211yescharacteristic
40C2×#13133179C2211yescharacteristic
41C2×C4×C22⋊D53—21no—
42C2×C4⋊C4×D53—21no—
43#16810986C2218yescomplemented
44#16810981C2218yescomplemented
45#16810980C2218yescomplemented
46#16810933C2218yescomplemented
47#16810902C2218yescomplemented
48#16810839C2218yescomplemented
49#16810837C2218yescomplemented
50#16810817C2218yes—
51#16810750C2218yescomplemented
52#16810734C2218yescomplemented
53#16810722C2218yescomplemented
54C4×#11719922C2218yescomplemented
55C2×#13133150C2211yescharacteristic
56C2×#13133146C2211yescharacteristic
57C2×#13133146C2211yescharacteristic
58C2×#13133142C2211yescharacteristic
59C2×#13133140C2211yescharacteristic
60C2×#13133140C2211yescharacteristic
61C2×#13133139C2211yescharacteristic
62C2×#13133138C2211yescharacteristic
63C2×#13133137C2211yescharacteristic
64C2×#13133137C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×#13133127C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68C2×C4×#88322C2211yescharacteristic
69C2×#125×C53C2211yescharacteristic
70C2×C4×D4×C53C2211yescharacteristic
71C53×#478C2218yescomplemented
72C2×#107×C53C2211yescharacteristic
73C2×#106×C53C2211yescharacteristic
74C2×C4⋊C8×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×#102×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106D411yescharacteristic
79C22×Dic106C2311yescharacteristic
80C22×D212C2311yescharacteristic
81C22×D212C2311yescharacteristic
82C22×C22⋊D53—21no—
83C22×C22⋊D53—21no—
84C22×C4×D53—21no—
85C22×C4×D53—21no—
86C22×C4×D53—21no—
87C22×C4×D53—21no—
88C2×#11719913—24no—
89C2×#11719913C2314yes—
90C2×D424—24no—
91C2×D424C2314yes—
92C2×#11719922—24no—
93C2×#11719922C2314yes—
94C22×#88322C2311yescharacteristic
95C22×#88322C2311yescharacteristic
96#13133216—22no—
97#13133216C2314yes—
98#13133213—22no—
99#13133213C2314yes—
100#13133208—22no—
101#13133208C2314yes—
102#13133205—22no—
103#13133205C2314yes—
104#13133204—22no—
105#13133204C2314yes—
106#13133203—28no—
107#13133200—28no—
108#13133199—28no—
109#13133197—28no—
110#13133195—28no—
111#13133195—28no—
112C4×Dic106D414yes—
113C4×Dic106C2314yes—
114#13133182—22no—
115#13133182C2314yes—
116C4×D212—22no—
117C4×D212C2314yes—
118#13133179—22no—
119#13133179—22no—
120#13133179—22no—
121#13133179C2314yes—
122#13133179C2314yes—
123#13133179C2314yes—
124C4×C22⋊D53—28no—
125C2×C4⋊Dic53—21no—
126C2×C4⋊Dic53D411yescharacteristic
127C2×C4⋊Dic53C2311yescharacteristic
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919D411yescharacteristic
132C2×#11719919D411yescharacteristic
133C4⋊C4×D53—28no—
134C2×C22⋊Dic53—21no—
135C2×C22⋊Dic53—21no—
136C2×#11719921—21no—
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×C4×Dic53—21no—
143C2×C4×Dic53C2311yescharacteristic
144C2×C4×Dic53C2311yescharacteristic
145#13133150C2314yes—
146#13133146C2314yes—
147#13133146C2314yes—
148#13133142C2314yes—
149#13133140C2314yes—
150#13133140C2314yes—
151#13133139C2314yes—
152#13133138C2314yes—
153#13133137C2314yes—
154#13133137C2314yes—
155#13133137C2314yes—
156#13133127C2314yes—
157#13133127C2314yes—
158C4×#88322C2314yes—
159C22×D4×C53C2311yescharacteristic
160C23×C4×C53—21no—
161C22×C8×C53C2311yescharacteristic
162C22×C8×C53C2311yescharacteristic
163#125×C53—22no—
164#125×C53C2314yes—
165C4×D4×C53—22no—
166C4×D4×C53C2314yes—
167C2×C4⋊C4×C53—21no—
168C2×C4⋊C4×C53—21no—
169C2×C4⋊C4×C53C2311yescharacteristic
170C2×C4⋊C4×C53C2311yescharacteristic
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C22⋊C4×C53—21no—
173C2×C42×C53C2311yescharacteristic
174#107×C53C2314yes—
175#106×C53C2314yes—
176C4⋊C8×C53C2314yes—
177#102×C53C2314yes—
178#102×C53C2314yes—
179C24×C53—21no—
180C23×D53—21no—
181C23×D53—21no—
182C2×D4×C53—21no—
183C2×D4×C53—22no—
184C2×D4×C53—22no—
185C2×D4×C53C2412yes—
186C22×C4×C53—21no—
187C22×C4×C53—21no—
188C22×C4×C53—21no—
189C22×C4×C53—24no—
190C22×C4×C53—82no—
191C22×C4×C53C2×D411yescharacteristic
192C22×C4×C53C2×D411yescharacteristic
193C22×C4×C53C2411yescharacteristic
194C2×C22⋊D53—24no—
195C2×C22⋊D53—24no—
196C2×C22⋊D53—44no—
197C2×C22⋊D53—82no—
198C22×Dic53—21no—
199C22×Dic53—21no—
200C22×Dic53C2×D411yescharacteristic
201C22×Dic53C2×D411yescharacteristic
202C22×Dic53C2×D411yescharacteristic
203C22×Dic53C2×D411yescharacteristic
204C2×D212—21no—
205C2×D212—22no—
206C2×D212—22no—
207C2×D212—22no—
208C2×D212—21no—
209C2×D212#4114yes—
210C2×D212C2412yes—
211C2×D212C2412yes—
212C2×C4×D53—24no—
213C2×C4×D53—24no—
214C2×C4×D53—24no—
215C2×C4×D53—24no—
216C2×C4×D53—44no—
217C2×C4×D53—82no—
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×C53—21no—
237C4⋊C4×C53C2412yes—
238C4⋊C4×C53C2412yes—
239C4⋊C4×C53C2412yes—
240C22⋊C4×C53—24no—
241C42×C53C2×D412yes—
242C42×C53C2412yes—
243C22⋊Dic53—24no—
244C22⋊Dic53—24no—
245#11719922—28no—
246#11719921—24no—
247#11719921—24no—
248#11719921—24no—
249#11719921—24no—
250#11719921—24no—
251#11719921—24no—
252C4⋊Dic53—21no—
253C4⋊Dic53—24no—
254C4⋊Dic53C2×D414yes—
255C4⋊Dic53C2412yes—
256#11719919—24no—
257#11719919—24no—
258#11719919—24no—
259#11719919C2×D414yes—
260#11719919C2×D414yes—
261C4×Dic53—24no—
262C4×Dic53C2×D412yes—
263C4×Dic53C2×D412yes—
264C4×Dic53C2412yes—
265C4×Dic53C2412yes—
266C2×#88322—22no—
267C2×#88322—22no—
268C2×#88322C2412yes—
269C2×#88322C2412yes—
270D424—28no—
271#11719913—28no—
272C23×C53—22no—
273C23×C53—42no—
274C23×C53—42no—
275C23×C53—42no—
276C23×C53C22×D411yescharacteristic
277C22×D53—24no—
278C22×D53—22no—
279C22×D53—22no—
280C22×D53—42no—
281C22×D53—42no—
282C22×D53—42no—
283C22×D53—42no—
284C22×D53—42no—
285D4×C53—22no—
286D4×C53—22no—
287D4×C53—42no—
288C2×C4×C53—22no—
289C2×C4×C53—22no—
290C2×C4×C53—22no—
291C2×C4×C53—22no—
292C2×C4×C53—22no—
293C2×C4×C53—42no—
294C2×C4×C53—42no—
295C2×C4×C53—42no—
296C2×C4×C53—84no—
297C2×C4×C53C22×D412yes—
298C2×C4×C53C22×D412yes—
299C2×C4×C53C22×D411yescharacteristic
300C2×C4×C53C2×#4112yes—
301C2×C4×C532−1+412yes—
302C2×C4×C53C2511yescharacteristic
303C22⋊D53—48no—
304C22⋊D53—84no—
305C2×Dic53—22no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—22no—
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—42no—
312C2×Dic53—42no—
313C2×Dic53C22×D412yes—
314C2×Dic53C22×D412yes—
315C2×Dic53C22×D412yes—
316C2×Dic53C22×D412yes—
317D212—24no—
318D212—22no—
319D212—22no—
320D212—22no—
321D212—42no—
322D212C2×#4114yes—
323C4×D53—48no—
324C4×D53—84no—
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—84no—
341C22×C53#54812yes—
342C22×C53#57512yes—
343C22×C53#57612yes—
344C22×C53C23×D411yescharacteristic
345C2×D53—24no—
346C2×D53—48no—
347C2×D53—42no—
348C2×D53—42no—
349C2×D53—42no—
350C2×D53—42no—
351C2×D53—42no—
352C2×D53—84no—
353C4×C53—22no—
354C4×C53—22no—
355C4×C53—42no—
356C4×C53—42no—
357C4×C53—42no—
358C4×C53#54812yes—
359C4×C53C22×#4111yescharacteristic
360C4×C53C2×2−1+411yescharacteristic
361Dic53—22no—
362Dic53—22no—
363Dic53—22no—
364Dic53—22no—
365Dic53—42no—
366Dic53—42no—
367C2×#559—531no—
368C2×#554—531no—
369#3370—5316no—
370C2×#490—531no—
371C2×#489—531no—
372C2×#488—531no—
373C2×#479—531no—
374C2×#478D5311yescharacteristic, complemented
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#337014yescomplemented
385C2×C53C2×#54811yescharacteristic
386C2×C53C2×#57511yescharacteristic
387C2×C53C2×#57611yescharacteristic
388D53—44no—
389D53—82no—
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×#127—531no—
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—1061no—
416C2×C4×D4C2×D5311yescharacteristic
417C22×C4⋊C4—1061no—
418#490—538no—
419#489—538no—
420#488—538no—
421#479—538no—
422#478C2×D5318yescomplemented
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×#107C2×D5311yescharacteristic
433C2×#106C2×D5311yescharacteristic
434C2×C4⋊C8—531no—
435C2×C4⋊C8—531no—
436C2×C4⋊C8C2×D5311yescharacteristic
437C2×#103—531no—
438C2×#103—531no—
439C2×#103—531no—
440C2×#102—531no—
441C2×#102—531no—
442C2×#102—531no—
443C2×#102—531no—
444C2×#102—531no—
445C2×#102C2×D5311yescharacteristic
446C2×#102C2×D5311yescharacteristic
447C2×#97—531no—
448C2×#97—531no—
449C2×C4×C8—531no—
450C53C2×#337011yescharacteristic, complemented, Sylow
451C22×Q8—531no—
452C22×Q8—531no—
453C22×Q8—1061no—
454C22×D4—531no—
455C22×D4—531no—
456C22×D4—1061no—
457C22×D4—1061no—
458C22×D4C22×D5311yescharacteristic
459C23×C4—21no—
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—534no—
477#127—1062no—
478#125—22no—
479#125—534no—
480#125—1062no—
481#125C22×D5314yes—
482#124—534no—
483#124—534no—
484#124—1062no—
485#124—1068no—
486#124—1062no—
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—22no—
497C4×D4—534no—
498C4×D4—534no—
499C4×D4—534no—
500C4×D4—534no—
501C4×D4—1062no—
502C4×D4—1062no—
503C4×D4—1062no—
504C4×D4—1068no—
505C4×D4—1062no—
506C4×D4C22×D5314yes—
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—1068no—
514C2×C4⋊C4—1061no—
515C2×C4⋊C4—1061no—
516C2×C4⋊C4—1061no—
517C2×C4⋊C4—1061no—
518C2×C4⋊C4C22×D5311yescharacteristic
519C2×C4⋊C4C22×D5311yescharacteristic
520C2×C4⋊C4C22×D5311yescharacteristic
521C2×C22⋊C4—21no—
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#107C22×D5314yes—
536#106C22×D5314yes—
537C4⋊C8—534no—
538C4⋊C8—534no—
539C4⋊C8C22×D5314yes—
540#103—534no—
541#103—534no—
542#103—534no—
543#102—534no—
544#102—534no—
545#102—534no—
546#102—534no—
547#102—534no—
548#102C22×D5314yes—
549#102C22×D5314yes—
550#97—534no—
551#97—534no—
552C4×C8—534no—
553C24—21no—
554C24—1061no—
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—22no—
566C2×D4—22no—
567C2×D4—534no—
568C2×D4—532no—
569C2×D4—532no—
570C2×D4—1064no—
571C2×D4—1064no—
572C2×D4—1061no—
573C2×D4—1061no—
574C2×D4—1062no—
575C2×D4—1062no—
576C2×D4—1062no—
577C2×D4—4242no—
578C2×D4—2124no—
579C2×D4C23×D5312yes—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—24no—
584C22×C4—82no—
585C22×C4—531no—
586C22×C4—531no—
587C22×C4—531no—
588C22×C4—531no—
589C22×C4—1064no—
590C22×C4—1064no—
591C22×C4—1064no—
592C22×C4—1061no—
593C22×C4—1061no—
594C22×C4—1064no—
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—21no—
618C4⋊C4—534no—
619C4⋊C4—534no—
620C4⋊C4—534no—
621C4⋊C4—532no—
622C4⋊C4—1064no—
623C4⋊C4—1064no—
624C4⋊C4—1064no—
625C4⋊C4—1064no—
626C4⋊C4—1061no—
627C4⋊C4C23×D5312yes—
628C4⋊C4C23×D5312yes—
629C4⋊C4C23×D5312yes—
630C22⋊C4—24no—
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—42no—
648C23—42no—
649C23—42no—
650C23—1064no—
651C23—1062no—
652C23—1062no—
653C23—2122no—
654C23—2122no—
655C23—2122no—
656C23—2122no—
657C23—2122no—
658C23C2×D4×D5311yescharacteristic
659Q8—1062no—
660Q8—1062no—
661Q8—4244no—
662Q8—2124no—
663Q8—2122no—
664D4—22no—
665D4—22no—
666D4—42no—
667D4—534no—
668D4—1064no—
669D4—1062no—
670D4—1062no—
671D4—1062no—
672D4—4244no—
673D4—2128no—
674D4—2122no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—84no—
684C2×C4—532no—
685C2×C4—532no—
686C2×C4—532no—
687C2×C4—532no—
688C2×C4—1062no—
689C2×C4—1062no—
690C2×C4—1062no—
691C2×C4—1062no—
692C2×C4—1062no—
693C2×C4—1062no—
694C2×C4—4244no—
695C2×C4—4244no—
696C2×C4—4244no—
697C2×C4—2128no—
698C2×C4—2122no—
699C2×C4—2122no—
700C2×C4C2×D4×D5312yes—
701C2×C4C2×D4×D5312yes—
702C2×C4C2×D4×D5311yescharacteristic
703C2×C4#41×D5312yes—
704C2×C4#1313326512yes—
705C2×C4C24×D5311yescharacteristic
706C8—22no—
707C8—22no—
708C8—1062no—
709C8—1062no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—84no—
714C22—1064no—
715C22—4244no—
716C22—2122no—
717C22—2122no—
718C22—2122no—
719C22—2122no—
720C22—2122no—
721C22—2128no—
722C22#1681128312yes—
723C22#1681142012yes—
724C22#1681142712yes—
725C22C22×D4×D5311yescharacteristic
726C4—22no—
727C4—22no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—1062no—
732C4—1062no—
733C4—1062no—
734C4—1062no—
735C4—2122no—
736C4—2122no—
737C4#1681128312yes—
738C4C2×#41×D5311yescharacteristic
739C4C2×#1313326511yescharacteristic
740C2—82no—
741C2—4242no—
742C2—2124no—
743C2#2028746614yesdirect product factor
744C2C2×#1681128311yescharacteristic
745C2C2×#1681142011yescharacteristic
746C2C2×#1681142711yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#478C2
socleC23×C53C22×D4
prime radicalC2×#16810817C2
hypercenterC2×#478D53
hypocenterC53C2×#3370
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#16811356C2semidirect
2. C2×#16811329C2semidirect
3. #20287466C2direct (N × H)
4. C2×#16810986C2semidirect
5. C2×#16810981C2semidirect
6. C2×#16810980C2semidirect
7. C2×#16810933C2semidirect
8. C2×#16810902C2semidirect
9. C2×#16810839C2semidirect
10. C2×#16810837C2semidirect
12. C2×#16810750C2semidirect
13. C2×#16810734C2semidirect
14. C2×#16810722C2semidirect
15. C2×C4×#11719922C2semidirect
16. C2×C53×#478C2semidirect
21. #16811356C22semidirect
23. #16811329C22semidirect
43. #16810986C22semidirect
44. #16810981C22semidirect
45. #16810980C22semidirect
46. #16810933C22semidirect
47. #16810902C22semidirect
48. #16810839C22semidirect
49. #16810837C22semidirect
51. #16810750C22semidirect
52. #16810734C22semidirect
53. #16810722C22semidirect
54. C4×#11719922C22semidirect
71. C53×#478C22semidirect
374. C2×#478D53semidirect
384. C2×C53#3370semidirect
422. #478C2×D53semidirect
450. C53C2×#3370semidirect
743. C2#20287466direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113562
C2×#168113292
#202874662
C2×#168109862
C2×#168109812
C2×#168109802
C2×#168109332
C2×#168109022
C2×#168108392
C2×#168108372
C2×#168108172
C2×#168107502
C2×#168107342
C2×#168107222
C2×C4×#117199222
C2×C53×#4782
C2×#337053