Finite Group Databasebeta

← C2×#20284917 #28252342

Subgroups — C2×#20284917 #28252342

Order 13568.

2198 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811226C211yesmaximal, characteristic, complemented
2C2×#16811104C211yesmaximal, characteristic, complemented
3#20284917C2116yesmaximal, direct product factor
4C2×#16810941C211yesmaximal, characteristic, complemented
5C2×#16810929C211yesmaximal, characteristic, complemented
6C2×#16810926C211yesmaximal, characteristic, complemented
7C2×#16810822C211yesmaximal, characteristic, complemented
8C2×#16810817C211yesmaximal, characteristic, complemented
9C2×#16810770C211yesmaximal, characteristic, complemented
10C2×#16810766C211yesmaximal, characteristic, complemented
11C2×#16810732C211yesmaximal, characteristic, complemented
12C2×#16810722C211yesmaximal, characteristic, complemented
13C2×#16810714C211yesmaximal, characteristic, complemented
14C2×#16810705C211yesmaximal, characteristic, complemented
15C2×#16810681C211yesmaximal, characteristic, complemented
16C2×C53×#480C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C22×#11719913C2211yescharacteristic
19C22×#11719923C2211yescharacteristic
20C22×D424C2211yescharacteristic
21C22×#11719922C2211yescharacteristic
22#16811226—24no—
23#16811226C2218yescomplemented
24C2×#13133213C2211yescharacteristic
25C2×#13133208C2211yescharacteristic
26C2×#13133201—21no—
27C2×#13133199—21no—
28C2×#13133191C2211yescharacteristic
29C2×#13133189—21no—
30C2×#13133188—21no—
31#16811104—24no—
32#16811104C2218yescomplemented
33C2×#13133182C2211yescharacteristic
34C2×#13133182C2211yescharacteristic
35C2×D4×Dic53C2211yescharacteristic
36C2×#13133179C2211yescharacteristic
37C2×#13133179C2211yescharacteristic
38C2×#13133179C2211yescharacteristic
39C2×C4×C22⋊D53—21no—
40C2×C4×C22⋊D53—21no—
41C2×#13133176C2211yescharacteristic
42C2×#13133175—21no—
43C2×C4⋊C4×D53—21no—
44#16810941C2218yescomplemented
45#16810929C2218yescomplemented
46#16810926C2218yescomplemented
47#16810822C2218yescomplemented
48#16810817C2218yescomplemented
49#16810770C2218yescomplemented
50#16810766C2218yescomplemented
51#16810732C2218yescomplemented
52#16810722C2218yescomplemented
53#16810714C2218yescomplemented
54#16810705C2218yescomplemented
55#16810681C2218yescomplemented
56C2×#13133148C2211yescharacteristic
57C2×#13133148C2211yescharacteristic
58C2×#13133146C2211yescharacteristic
59C2×#13133146C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133140C2211yescharacteristic
62C2×#13133139C2211yescharacteristic
63C2×#13133137C2211yescharacteristic
64C2×#13133137C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C2×#121×C53C2211yescharacteristic
70C22×C4⋊C4×C53C2211yescharacteristic
71C53×#480C2218yescomplemented
72C2×#107×C53C2211yescharacteristic
73C2×#107×C53C2211yescharacteristic
74C2×#102×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic
77C2×#11719945—22no—
78C2×#11719945—24no—
79C2×#11719945—24no—
80C2×#11719945C2314yes—
81C22×Dic106C2311yescharacteristic
82C22×D212C2311yescharacteristic
83C22×D212C2311yescharacteristic
84C22×C22⋊D53—21no—
85C22×C22⋊D53—21no—
86C22×C22⋊D53—21no—
87C22×C22⋊D53—21no—
88C23×Dic53—21no—
89C22×C4×D53—21no—
90C22×C4×D53—21no—
91C22×C4×D53—21no—
92C22×C4×D53—21no—
93C2×#11719913—24no—
94C2×#11719913C2314yes—
95C2×#11719923—24no—
96C2×#11719923C2314yes—
97C2×D424—24no—
98C2×D424C2314yes—
99C2×#11719922—24no—
100C2×#11719922C2314yes—
101C22×#88322C2311yescharacteristic
102C22×#88322C2311yescharacteristic
103#13133213—22no—
104#13133213C2314yes—
105#13133208—22no—
106#13133208C2314yes—
107#13133201—28no—
108#13133199—28no—
109#13133191—22no—
110#13133191C2314yes—
111#13133189—28no—
112#13133188—28no—
113#13133182—22no—
114#13133182—22no—
115#13133182C2314yes—
116#13133182C2314yes—
117D4×Dic53—22no—
118D4×Dic53C2314yes—
119#13133179—22no—
120#13133179—22no—
121#13133179—22no—
122#13133179C2314yes—
123#13133179C2314yes—
124#13133179C2314yes—
125C4×C22⋊D53—28no—
126C4×C22⋊D53—28no—
127#13133176D414yes—
128#13133176C2314yes—
129#13133175—28no—
130C2×C4⋊Dic53—21no—
131C2×C4⋊Dic53D411yescharacteristic
132C2×C4⋊Dic53D411yescharacteristic
133C2×C4⋊Dic53C2311yescharacteristic
134C2×#11719919—21no—
135C2×#11719919—21no—
136C2×#11719919—21no—
137C4⋊C4×D53—28no—
138C2×C22⋊Dic53—21no—
139C2×C22⋊Dic53D411yescharacteristic
140C2×C22⋊Dic53D411yescharacteristic
141C2×#11719921—21no—
142C2×#11719921—21no—
143C2×#11719921—21no—
144C2×#11719921—21no—
145C2×C4×Dic53—21no—
146C2×C4×Dic53—21no—
147C2×C4×Dic53C2311yescharacteristic
148C2×C4×Dic53C2311yescharacteristic
149#13133148C2314yes—
150#13133148C2314yes—
151#13133146C2314yes—
152#13133146C2314yes—
153#13133142C2314yes—
154#13133140C2314yes—
155#13133139C2314yes—
156#13133137C2314yes—
157#13133137C2314yes—
158#13133137C2314yes—
159C22⋊#88322C2314yes—
160#13133127C2314yes—
161C8×Dic53C2314yes—
162C22×D4×C53—21no—
163C22×D4×C53C2311yescharacteristic
164C23×C4×C53—21no—
165C23×C4×C53C2311yescharacteristic
166C22×C8×C53C2311yescharacteristic
167C22×C8×C53C2311yescharacteristic
168#121×C53—22no—
169#121×C53C2314yes—
170C2×C4⋊C4×C53—21no—
171C2×C4⋊C4×C53—22no—
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C4⋊C4×C53C2314yes—
175C2×C4⋊C4×C53C2311yescharacteristic
176C2×C22⋊C4×C53—21no—
177#107×C53C2314yes—
178#107×C53C2314yes—
179#102×C53C2314yes—
180#102×C53C2314yes—
181C22⋊C8×C53C2314yes—
182C24×C53—21no—
183C24×C53C2×D411yescharacteristic
184C23×D53—21no—
185C23×D53—21no—
186C2×D4×C53—24no—
187C2×D4×C53—21no—
188C2×D4×C53—22no—
189C2×D4×C53—22no—
190C2×D4×C53—82no—
191C2×D4×C53C2412yes—
192C22×C4×C53—22no—
193C22×C4×C53—22no—
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—24no—
198C22×C4×C53—82no—
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53C2×D412yes—
201C22×C4×C53C2412yes—
202C22×C4×C53C2411yescharacteristic
203C2×C22⋊D53—28no—
204C2×C22⋊D53—24no—
205C2×C22⋊D53—24no—
206C2×C22⋊D53—24no—
207C2×C22⋊D53—24no—
208C2×C22⋊D53—82no—
209C2×C22⋊D53—82no—
210C2×C22⋊D53—82no—
211C22×Dic53—21no—
212C22×Dic53—21no—
213C22×Dic53—24no—
214C22×Dic53—82no—
215C22×Dic53C2×D411yescharacteristic
216C22×Dic53C2×D411yescharacteristic
217C22×Dic53C2×D411yescharacteristic
218C22×Dic53C2×D411yescharacteristic
219#11719945—216no—
220#11719945—28no—
221#11719945—28no—
222C2×D212—21no—
223C2×D212—22no—
224C2×D212—22no—
225C2×D212—22no—
226C2×D212—21no—
227C2×D212#4114yes—
228C2×D212C2412yes—
229C2×D212C2412yes—
230C2×C4×D53—28no—
231C2×C4×D53—24no—
232C2×C4×D53—24no—
233C2×C4×D53—24no—
234C2×C4×D53—24no—
235C2×C4×D53—82no—
236C2×C4×D53—82no—
237C2×C4×D53—82no—
238C2×Dic106—21no—
239C2×Dic106—22no—
240C2×Dic106#4114yes—
241C2×Dic106C2412yes—
242C2×C8×C53—22no—
243C2×C8×C53—22no—
244C2×C8×C53C2412yes—
245C2×C8×C53C2412yes—
246C4⋊C4×C53—24no—
247C4⋊C4×C53—21no—
248C4⋊C4×C53—21no—
249C4⋊C4×C53—21no—
250C4⋊C4×C53C2412yes—
251C4⋊C4×C53C2412yes—
252C4⋊C4×C53C2412yes—
253C22⋊C4×C53—24no—
254C22⋊Dic53—24no—
255C22⋊Dic53C2×D414yes—
256C22⋊Dic53C2×D414yes—
257#11719923—28no—
258#11719922—28no—
259#11719921—24no—
260#11719921—24no—
261#11719921—24no—
262#11719921—24no—
263C4⋊Dic53—21no—
264C4⋊Dic53—24no—
265C4⋊Dic53C2×D414yes—
266C4⋊Dic53C2×D414yes—
267C4⋊Dic53C2412yes—
268#11719919—24no—
269#11719919—24no—
270#11719919—24no—
271C4×Dic53—24no—
272C4×Dic53—24no—
273C4×Dic53C2×D412yes—
274C4×Dic53C2×D412yes—
275C4×Dic53C2412yes—
276C4×Dic53C2412yes—
277C2×#88322—22no—
278C2×#88322—22no—
279C2×#88322C2412yes—
280C2×#88322C2412yes—
281D424—28no—
282#11719913—28no—
283C23×C53—22no—
284C23×C53—22no—
285C23×C53—22no—
286C23×C53—22no—
287C23×C53—42no—
288C23×C53—42no—
289C23×C53—42no—
290C23×C53C22×D412yes—
291C23×C53C22×D411yescharacteristic
292C22×D53—24no—
293C22×D53—22no—
294C22×D53—22no—
295C22×D53—42no—
296C22×D53—42no—
297C22×D53—42no—
298C22×D53—42no—
299C22×D53—42no—
300D4×C53—22no—
301D4×C53—22no—
302D4×C53—42no—
303D4×C53—84no—
304C2×C4×C53—22no—
305C2×C4×C53—24no—
306C2×C4×C53—22no—
307C2×C4×C53—22no—
308C2×C4×C53—22no—
309C2×C4×C53—22no—
310C2×C4×C53—22no—
311C2×C4×C53—42no—
312C2×C4×C53—42no—
313C2×C4×C53—42no—
314C2×C4×C53—84no—
315C2×C4×C53C22×D412yes—
316C2×C4×C53C22×D411yescharacteristic
317C2×C4×C53C2×#4112yes—
318C2×C4×C53C2×#4112yes—
319C2×C4×C53C2511yescharacteristic
320C22⋊D53—216no—
321C22⋊D53—84no—
322C22⋊D53—84no—
323C22⋊D53—84no—
324C2×Dic53—24no—
325C2×Dic53—22no—
326C2×Dic53—22no—
327C2×Dic53—22no—
328C2×Dic53—22no—
329C2×Dic53—22no—
330C2×Dic53—22no—
331C2×Dic53—42no—
332C2×Dic53—84no—
333C2×Dic53C22×D412yes—
334C2×Dic53C22×D412yes—
335C2×Dic53C22×D412yes—
336C2×Dic53C22×D412yes—
337D212—24no—
338D212—22no—
339D212—22no—
340D212—22no—
341D212—42no—
342D212C2×#4114yes—
343C4×D53—216no—
344C4×D53—84no—
345C4×D53—84no—
346C4×D53—84no—
347Dic106—24no—
348Dic106—22no—
349Dic106C2×#4114yes—
350C8×C53—22no—
351C8×C53—22no—
352#88322—22no—
353#88322—22no—
354C2×#3119—531nomaximal, Sylow
355C22×C53—22no—
356C22×C53—22no—
357C22×C53—22no—
358C22×C53—44no—
359C22×C53—42no—
360C22×C53—42no—
361C22×C53—42no—
362C22×C53—84no—
363C22×C53#52512yes—
364C22×C53#57612yes—
365C22×C53#57712yes—
366C22×C53C23×D411yescharacteristic
367C2×D53—24no—
368C2×D53—48no—
369C2×D53—42no—
370C2×D53—42no—
371C2×D53—42no—
372C2×D53—42no—
373C2×D53—42no—
374C2×D53—84no—
375C4×C53—22no—
376C4×C53—42no—
377C4×C53—42no—
378C4×C53—42no—
379C4×C53#52512yes—
380C4×C53C22×#4111yescharacteristic
381C4×C53C22×#4111yescharacteristic
382Dic53—24no—
383Dic53—22no—
384Dic53—22no—
385Dic53—22no—
386Dic53—22no—
387Dic53—42no—
388C2×#540—531no—
389C2×#520—531no—
390#3119—5316no—
391C2×#481—531no—
392C2×#480D5311yescharacteristic, complemented
393C2×#479—531no—
394C2×#478—531no—
395C2×#460—531no—
396C2×#459—531no—
397C2×#449—531no—
398C2×#449—531no—
399C2×#442—531no—
400C2×#440—531no—
401C2×C4×SD16—531no—
402C2×C4×D8—531no—
403C2×#433—531no—
404C2×C53—42no—
405C2×C53—82no—
406C2×C53#311914yescomplemented
407C2×C53C2×#52511yescharacteristic
408C2×C53C2×#57611yescharacteristic
409C2×C53C2×#57711yescharacteristic
410D53—44no—
411D53—82no—
412C22×#41—531no—
413C22×SD16—531no—
414C22×SD16—531no—
415C22×D8—531no—
416C22×D8—531no—
417#540—538no—
418#540—1064no—
419C2×#127—531no—
420C2×#125—531no—
421C2×#123—1061no—
422C2×#123—1061no—
423C2×#121—531no—
424C2×#121—1061no—
425C2×#121—1061no—
426C2×#121C2×D5311yescharacteristic
427#520—538no—
428#520—1064no—
429C2×C4×Q8—531no—
430C2×C4×Q8—531no—
431C2×C4×D4—531no—
432C2×C4×D4—531no—
433C2×C4×D4—531no—
434C2×C4×D4—531no—
435C2×C4×D4—1061no—
436C2×C4×D4—1061no—
437C2×#117—531no—
438C2×#117—1061no—
439C22×C4⋊C4—1061no—
440C22×C4⋊C4C2×D5311yescharacteristic
441#481—538no—
442#480C2×D5318yescomplemented
443#479—538no—
444#478—538no—
445#460—538no—
446#459—538no—
447#449—538no—
448#449—538no—
449#442—538no—
450#440—538no—
451C4×SD16—538no—
452C4×D8—538no—
453#433—538no—
454C2×#107C2×D5311yescharacteristic
455C2×#107C2×D5311yescharacteristic
456C2×#106—531no—
457C2×#106—531no—
458C2×C4⋊C8—531no—
459C2×C4⋊C8—531no—
460C2×#103—531no—
461C2×#103—531no—
462C2×#102—531no—
463C2×#102—531no—
464C2×#102—531no—
465C2×#102—531no—
466C2×#102C2×D5311yescharacteristic
467C2×#102C2×D5311yescharacteristic
468C2×C22⋊C8—531no—
469C2×C22⋊C8C2×D5311yescharacteristic
470C2×#97—531no—
471C2×C4×C8—531no—
472C53C2×#311911yescharacteristic, complemented, Sylow
473C2×#41—534no—
474C2×#41—1064no—
475C2×#41—1064no—
476C2×#41—1062no—
477C22×Q8—531no—
478C22×D4—21no—
479C22×D4—531no—
480C22×D4—531no—
481C22×D4—1061no—
482C22×D4—1061no—
483C22×D4—1061no—
484C22×D4—1061no—
485C22×D4C22×D5311yescharacteristic
486C23×C4—21no—
487C23×C4—1061no—
488C23×C4—1061no—
489C23×C4—1061no—
490C23×C4—1061no—
491C23×C4—1061no—
492C23×C4C22×D5311yescharacteristic
493C2×SD16—534no—
494C2×SD16—534no—
495C2×SD16—1064no—
496C2×SD16—1064no—
497C2×D8—534no—
498C2×D8—534no—
499C2×D8—1064no—
500C2×D8—1064no—
501C22×C8—531no—
502C22×C8—531no—
503C22×C8C22×D5311yescharacteristic
504C22×C8C22×D5311yescharacteristic
505#127—534no—
506#127—1062no—
507#125—534no—
508#125—1062no—
509#123—1068no—
510#123—1068no—
511#121—22no—
512#121—534no—
513#121—1068no—
514#121—1068no—
515#121—1062no—
516#121C22×D5314yes—
517C4×Q8—534no—
518C4×Q8—534no—
519C4×Q8—1062no—
520C4×Q8—1062no—
521C4×D4—534no—
522C4×D4—534no—
523C4×D4—534no—
524C4×D4—534no—
525C4×D4—1062no—
526C4×D4—1062no—
527C4×D4—1062no—
528C4×D4—1062no—
529C4×D4—1068no—
530C4×D4—1068no—
531#117—534no—
532#117—534no—
533#117—1068no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—22no—
536C2×C4⋊C4—531no—
537C2×C4⋊C4—531no—
538C2×C4⋊C4—531no—
539C2×C4⋊C4—1068no—
540C2×C4⋊C4—1061no—
541C2×C4⋊C4—1061no—
542C2×C4⋊C4—1061no—
543C2×C4⋊C4—1061no—
544C2×C4⋊C4C22×D5311yescharacteristic
545C2×C4⋊C4C22×D5311yescharacteristic
546C2×C4⋊C4C22×D5314yes—
547C2×C4⋊C4C22×D5311yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—531no—
550C2×C22⋊C4—531no—
551C2×C22⋊C4—1061no—
552C2×C22⋊C4—1061no—
553C2×C22⋊C4—1061no—
554C2×C22⋊C4—1061no—
555C2×C22⋊C4—1061no—
556C2×C42—531no—
557C2×C42—531no—
558C2×C42—1061no—
559C2×C42—1061no—
560#107C22×D5314yes—
561#107C22×D5314yes—
562#106—534no—
563#106—534no—
564C4⋊C8—534no—
565C4⋊C8—534no—
566#103—534no—
567#103—534no—
568#102—534no—
569#102—534no—
570#102—534no—
571#102—534no—
572#102C22×D5314yes—
573#102C22×D5314yes—
574C22⋊C8—534no—
575C22⋊C8C22×D5314yes—
576#97—534no—
577C4×C8—534no—
578C24—21no—
579C24—1061no—
580C24—1061no—
581C24D4×D5311yescharacteristic
582#41—1068no—
583#41—1068no—
584#41—10616no—
585C2×Q8—534no—
586C2×Q8—532no—
587C2×Q8—1061no—
588C2×Q8—1062no—
589C2×D4—24no—
590C2×D4—21no—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—82no—
594C2×D4—534no—
595C2×D4—532no—
596C2×D4—532no—
597C2×D4—1064no—
598C2×D4—1064no—
599C2×D4—1068no—
600C2×D4—1064no—
601C2×D4—1064no—
602C2×D4—1061no—
603C2×D4—1061no—
604C2×D4—1062no—
605C2×D4—1062no—
606C2×D4—1062no—
607C2×D4—4242no—
608C2×D4—4242no—
609C2×D4—4242no—
610C2×D4C23×D5312yes—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—24no—
617C22×C4—82no—
618C22×C4—531no—
619C22×C4—531no—
620C22×C4—531no—
621C22×C4—531no—
622C22×C4—1064no—
623C22×C4—1064no—
624C22×C4—1064no—
625C22×C4—1068no—
626C22×C4—1064no—
627C22×C4—1061no—
628C22×C4—1064no—
629C22×C4—1061no—
630C22×C4—4242no—
631C22×C4—4242no—
632C22×C4—4242no—
633C22×C4—4242no—
634C22×C4D4×D5312yes—
635C22×C4D4×D5311yescharacteristic
636C22×C4C23×D5312yes—
637C22×C4C23×D5311yescharacteristic
638SD16—1068no—
639SD16—1068no—
640D8—1068no—
641D8—1068no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—532no—
645C2×C8—532no—
646C2×C8—1062no—
647C2×C8—1062no—
648C2×C8C23×D5312yes—
649C2×C8C23×D5312yes—
650C4⋊C4—24no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—534no—
655C4⋊C4—534no—
656C4⋊C4—532no—
657C4⋊C4—1064no—
658C4⋊C4—1064no—
659C4⋊C4—1064no—
660C4⋊C4—1064no—
661C4⋊C4—1061no—
662C4⋊C4C23×D5312yes—
663C4⋊C4C23×D5312yes—
664C4⋊C4C23×D5312yes—
665C22⋊C4—24no—
666C22⋊C4—534no—
667C22⋊C4—534no—
668C22⋊C4—1064no—
669C22⋊C4—1064no—
670C22⋊C4—1064no—
671C22⋊C4—1064no—
672C22⋊C4—1064no—
673C42—532no—
674C42—532no—
675C42—532no—
676C42—532no—
677C42—1064no—
678C42—1064no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—1064no—
687C23—1062no—
688C23—1062no—
689C23—2122no—
690C23—2122no—
691C23—2122no—
692C23—2122no—
693C23—2122no—
694C23C2×D4×D5312yes—
695C23C2×D4×D5311yescharacteristic
696Q8—534no—
697Q8—1064no—
698Q8—1062no—
699D4—22no—
700D4—22no—
701D4—42no—
702D4—84no—
703D4—534no—
704D4—10616no—
705D4—1064no—
706D4—1062no—
707D4—1062no—
708D4—1062no—
709D4—4244no—
710D4—4244no—
711D4—4244no—
712D4—2122no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—84no—
724C2×C4—532no—
725C2×C4—532no—
726C2×C4—532no—
727C2×C4—532no—
728C2×C4—10616no—
729C2×C4—1064no—
730C2×C4—1062no—
731C2×C4—1062no—
732C2×C4—1062no—
733C2×C4—1062no—
734C2×C4—1062no—
735C2×C4—1062no—
736C2×C4—4244no—
737C2×C4—4244no—
738C2×C4—4244no—
739C2×C4—4244no—
740C2×C4—2122no—
741C2×C4C2×D4×D5312yes—
742C2×C4C2×D4×D5311yescharacteristic
743C2×C4#41×D5312yes—
744C2×C4#41×D5312yes—
745C2×C4C24×D5311yescharacteristic
746C8—22no—
747C8—22no—
748C8—1062no—
749C8—1062no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—44no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—84no—
758C22—1064no—
759C22—4244no—
760C22—2122no—
761C22—2122no—
762C22—2122no—
763C22—2122no—
764C22—2122no—
765C22—2128no—
766C22#1681113112yes—
767C22#1681142412yes—
768C22#1681143212yes—
769C22C22×D4×D5311yescharacteristic
770C4—22no—
771C4—42no—
772C4—42no—
773C4—42no—
774C4—1062no—
775C4—1062no—
776C4—1062no—
777C4—1062no—
778C4—1064no—
779C4—2122no—
780C4#1681113112yes—
781C4C2×#41×D5311yescharacteristic
782C4C2×#41×D5311yescharacteristic
783C2—42no—
784C2—82no—
785C2—4242no—
786C2—2124no—
787C2#2028491714yesdirect product factor
788C2C2×#1681113111yescharacteristic
789C2C2×#1681142411yescharacteristic
790C2C2×#1681143211yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#480C2
socleC23×C53C22×D4
hypercenterC2×#480D53
hypocenterC53C2×#3119
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
1. C2×#16811226C2semidirect
2. C2×#16811104C2semidirect
3. #20284917C2direct (N × H)
4. C2×#16810941C2semidirect
5. C2×#16810929C2semidirect
6. C2×#16810926C2semidirect
7. C2×#16810822C2semidirect
8. C2×#16810817C2semidirect
9. C2×#16810770C2semidirect
10. C2×#16810766C2semidirect
11. C2×#16810732C2semidirect
12. C2×#16810722C2semidirect
13. C2×#16810714C2semidirect
14. C2×#16810705C2semidirect
15. C2×#16810681C2semidirect
16. C2×C53×#480C2semidirect
23. #16811226C22semidirect
32. #16811104C22semidirect
44. #16810941C22semidirect
45. #16810929C22semidirect
46. #16810926C22semidirect
47. #16810822C22semidirect
48. #16810817C22semidirect
49. #16810770C22semidirect
50. #16810766C22semidirect
51. #16810732C22semidirect
52. #16810722C22semidirect
53. #16810714C22semidirect
54. #16810705C22semidirect
55. #16810681C22semidirect
71. C53×#480C22semidirect
392. C2×#480D53semidirect
406. C2×C53#3119semidirect
442. #480C2×D53semidirect
472. C53C2×#3119semidirect
787. C2#20284917direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112262
C2×#168111042
#202849172
C2×#168109412
C2×#168109292
C2×#168109262
C2×#168108222
C2×#168108172
C2×#168107702
C2×#168107662
C2×#168107322
C2×#168107222
C2×#168107142
C2×#168107052
C2×#168106812
C2×C53×#4802
C2×#311953