Finite Group Databasebeta

← C2×#20284919 #28252344

Subgroups — C2×#20284919 #28252344

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×#16811229C211yesmaximal, characteristic, complemented
2C2×#16811102C211yesmaximal, characteristic, complemented
3#20284919C2116yesmaximal, direct product factor
4C2×#16810943C211yesmaximal, characteristic, complemented
5C2×#16810938C211yesmaximal, characteristic, complemented
6C2×#16810927C211yesmaximal, characteristic, complemented
7C2×#16810824C211yesmaximal, characteristic, complemented
8C2×#16810818C211yesmaximal, characteristic, complemented
9C2×#16810769C211yesmaximal, characteristic, complemented
10C2×#16810769C211yesmaximal, characteristic, complemented
11C2×#16810732C211yesmaximal, characteristic, complemented
12C2×#16810722C211yesmaximal, characteristic, complemented
13C2×#16810710C211yesmaximal, characteristic, complemented
14C2×#16810703C211yesmaximal, characteristic, complemented
15C2×#16810683C211yesmaximal, characteristic, complemented
16C2×C53×#478C211yesmaximal, characteristic, complemented
17C22×#11719947C2211yescharacteristic
18C22×#11719913C2211yescharacteristic
19C22×#11719913C2211yescharacteristic
20C22×#11719922C2211yescharacteristic
21C22×#11719922C2211yescharacteristic
22#16811229—24no—
23#16811229C2218yescomplemented
24C2×#13133214C2211yescharacteristic
25C2×#13133202—21no—
26C2×#13133202—21no—
27C2×#13133192—21no—
28C2×#13133192—21no—
29C2×#13133192C2211yescharacteristic
30C2×#13133192C2211yescharacteristic
31#16811102—24no—
32#16811102C2218yescomplemented
33C2×C4×Dic106C2211yescharacteristic
34C2×#13133182C2211yescharacteristic
35C2×D4×Dic53C2211yescharacteristic
36C2×#13133179C2211yescharacteristic
37C2×#13133179C2211yescharacteristic
38C2×C4×C22⋊D53—21no—
39C2×#13133177—21no—
40C2×#13133174C2211yescharacteristic
41C2×#13133173—21no—
42C22×#11719919—21no—
43C2×C4⋊C4×D53C2211yescharacteristic
44#16810943C2218yescomplemented
45#16810938C2218yescomplemented
46#16810927C2218yescomplemented
47#16810824C2218yescomplemented
48#16810818C2218yescomplemented
49#16810769C2218yescomplemented
50#16810769C2218yescomplemented
51#16810732C2218yescomplemented
52#16810722C2218yescomplemented
53#16810710C2218yescomplemented
54#16810703C2218yescomplemented
55#16810683C2218yescomplemented
56C2×#13133150C2211yescharacteristic
57C2×#13133148C2211yescharacteristic
58C2×C4⋊#88322C2211yescharacteristic
59C2×#13133140C2211yescharacteristic
60C2×#13133140C2211yescharacteristic
61C2×#13133139C2211yescharacteristic
62C2×#13133139C2211yescharacteristic
63C2×#13133137C2211yescharacteristic
64C2×#13133137C2211yescharacteristic
65C2×#13133129C2211yescharacteristic
66C2×#13133129C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
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
77C2×#11719947—24no—
78C2×#11719947—22no—
79C2×#11719947—24no—
80C2×#11719947C2314yes—
81C22×Dic106C2311yescharacteristic
82C22×D212—21no—
83C22×D212—21no—
84C22×D212—21no—
85C22×D212—21no—
86C22×D212C2311yescharacteristic
87C22×D212C2311yescharacteristic
88C22×C22⋊D53—21no—
89C23×Dic53—21no—
90C23×Dic53—21no—
91C22×C4×D53—21no—
92C22×C4×D53—21no—
93C22×C4×D53—21no—
94C22×C4×D53C2311yescharacteristic
95C2×#11719913—24no—
96C2×#11719913—24no—
97C2×#11719913C2314yes—
98C2×#11719913C2314yes—
99C2×#11719922—24no—
100C2×#11719922—24no—
101C2×#11719922C2314yes—
102C2×#11719922C2314yes—
103C22×#88322C2311yescharacteristic
104C22×#88322C2311yescharacteristic
105#13133214—22no—
106#13133214C2314yes—
107#13133202—28no—
108#13133202—28no—
109#13133192—28no—
110#13133192—28no—
111#13133192—22no—
112#13133192—22no—
113#13133192C2314yes—
114#13133192C2314yes—
115C4×Dic106—22no—
116C4×Dic106C2314yes—
117#13133182—22no—
118#13133182C2314yes—
119D4×Dic53—22no—
120D4×Dic53C2314yes—
121#13133179—22no—
122#13133179—22no—
123#13133179C2314yes—
124#13133179C2314yes—
125C4×C22⋊D53—28no—
126#13133177—28no—
127#13133174D414yes—
128#13133174C2314yes—
129#13133173—28no—
130C2×C4⋊Dic53C2311yescharacteristic
131C2×#11719919—28no—
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×#11719919—21no—
135C2×#11719919D411yescharacteristic
136C2×#11719919D411yescharacteristic
137C4⋊C4×D53—22no—
138C4⋊C4×D53C2314yes—
139C2×C22⋊Dic53—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×#11719921—21no—
143C2×#11719921—21no—
144C2×#11719921D411yescharacteristic
145C2×#11719921D411yescharacteristic
146C2×C4×Dic53—21no—
147C2×C4×Dic53—21no—
148C2×C4×Dic53C2311yescharacteristic
149#13133150C2314yes—
150#13133148C2314yes—
151C4⋊#88322C2314yes—
152#13133140C2314yes—
153#13133140C2314yes—
154#13133139C2314yes—
155#13133139C2314yes—
156#13133137C2314yes—
157#13133137C2314yes—
158#13133129C2314yes—
159#13133129C2314yes—
160#13133127C2314yes—
161C8×Dic53C2314yes—
162C22×D4×C53C2311yescharacteristic
163C23×C4×C53—21no—
164C22×C8×C53C2311yescharacteristic
165C22×C8×C53C2311yescharacteristic
166#125×C53—22no—
167#125×C53C2314yes—
168C4×D4×C53—22no—
169C4×D4×C53C2314yes—
170C2×C4⋊C4×C53—21no—
171C2×C4⋊C4×C53—21no—
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C22⋊C4×C53—21no—
176C2×C42×C53C2311yescharacteristic
177#107×C53C2314yes—
178#106×C53C2314yes—
179C4⋊C8×C53C2314yes—
180#102×C53C2314yes—
181#102×C53C2314yes—
182C24×C53—21no—
183C23×D53—21no—
184C23×D53—21no—
185C23×D53C2×D411yescharacteristic
186C2×D4×C53—21no—
187C2×D4×C53—22no—
188C2×D4×C53#4114yes—
189C2×D4×C53C2412yes—
190C22×C4×C53—21no—
191C22×C4×C53—21no—
192C22×C4×C53—21no—
193C22×C4×C53—24no—
194C22×C4×C53—82no—
195C22×C4×C53C2×D411yescharacteristic
196C22×C4×C53C2×D411yescharacteristic
197C22×C4×C53C2411yescharacteristic
198C2×C22⋊D53—28no—
199C2×C22⋊D53—24no—
200C22×Dic53—28no—
201C22×Dic53—21no—
202C22×Dic53—24no—
203C22×Dic53—21no—
204C22×Dic53—24no—
205C22×Dic53—82no—
206C22×Dic53C2×D411yescharacteristic
207C22×Dic53C2×D411yescharacteristic
208C22×Dic53C2×D411yescharacteristic
209#11719947—216no—
210#11719947—28no—
211#11719947—28no—
212C2×D212—22no—
213C2×D212—22no—
214C2×D212—22no—
215C2×D212—22no—
216C2×D212—21no—
217C2×D212—21no—
218C2×D212—24no—
219C2×D212—24no—
220C2×D212—24no—
221C2×D212—24no—
222C2×D212—82no—
223C2×D212—82no—
224C2×D212—82no—
225C2×D212—82no—
226C2×D212C2412yes—
227C2×D212C2412yes—
228C2×C4×D53—22no—
229C2×C4×D53—22no—
230C2×C4×D53—24no—
231C2×C4×D53—24no—
232C2×C4×D53—24no—
233C2×C4×D53—82no—
234C2×C4×D53—82no—
235C2×C4×D53—82no—
236C2×C4×D53C2×D412yes—
237C2×C4×D53C2412yes—
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—24no—
248C4⋊C4×C53—21no—
249C4⋊C4×C53—21no—
250C4⋊C4×C53—21no—
251C4⋊C4×C53C2412yes—
252C4⋊C4×C53C2412yes—
253C4⋊C4×C53C2412yes—
254C22⋊C4×C53—24no—
255C42×C53C2×D412yes—
256C42×C53C2412yes—
257C22⋊Dic53—24no—
258#11719922—28no—
259#11719922—28no—
260#11719921—24no—
261#11719921—24no—
262#11719921—24no—
263#11719921—24no—
264#11719921C2×D414yes—
265#11719921C2×D414yes—
266C4⋊Dic53—21no—
267C4⋊Dic53C2412yes—
268#11719919—24no—
269#11719919—24no—
270#11719919—24no—
271#11719919C2×D414yes—
272#11719919C2×D414yes—
273C4×Dic53—24no—
274C4×Dic53—24no—
275C4×Dic53C2×D412yes—
276C4×Dic53C2412yes—
277C2×#88322—22no—
278C2×#88322—22no—
279C2×#88322C2412yes—
280C2×#88322C2412yes—
281#11719913—28no—
282#11719913—28no—
283C23×C53—24no—
284C23×C53—22no—
285C23×C53—42no—
286C23×C53—42no—
287C23×C53C22×D411yescharacteristic
288C22×D53—22no—
289C22×D53—22no—
290C22×D53—22no—
291C22×D53—22no—
292C22×D53—22no—
293C22×D53—42no—
294C22×D53—42no—
295C22×D53—42no—
296C22×D53—42no—
297C22×D53—42no—
298C22×D53—42no—
299C22×D53C22×D412yes—
300D4×C53—24no—
301D4×C53—22no—
302D4×C53C2×#4114yes—
303C2×C4×C53—22no—
304C2×C4×C53—22no—
305C2×C4×C53—22no—
306C2×C4×C53—22no—
307C2×C4×C53—22no—
308C2×C4×C53—42no—
309C2×C4×C53—42no—
310C2×C4×C53—42no—
311C2×C4×C53—84no—
312C2×C4×C53C22×D412yes—
313C2×C4×C53C22×D412yes—
314C2×C4×C53C22×D411yescharacteristic
315C2×C4×C53C2×#4112yes—
316C2×C4×C53C2×#4112yes—
317C2×C4×C53C2511yescharacteristic
318C22⋊D53—216no—
319C2×Dic53—216no—
320C2×Dic53—24no—
321C2×Dic53—22no—
322C2×Dic53—22no—
323C2×Dic53—22no—
324C2×Dic53—22no—
325C2×Dic53—22no—
326C2×Dic53—42no—
327C2×Dic53—84no—
328C2×Dic53C22×D412yes—
329C2×Dic53C22×D412yes—
330C2×Dic53C22×D412yes—
331D212—22no—
332D212—22no—
333D212—22no—
334D212—22no—
335D212—42no—
336D212—42no—
337D212—84no—
338D212—84no—
339D212—84no—
340D212—84no—
341C4×D53—24no—
342C4×D53—22no—
343C4×D53—22no—
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—24no—
356C22×C53—48no—
357C22×C53—42no—
358C22×C53—42no—
359C22×C53#52512yes—
360C22×C53#57612yes—
361C22×C53#57712yes—
362C22×C53C23×D411yescharacteristic
363C2×D53—22no—
364C2×D53—22no—
365C2×D53—22no—
366C2×D53—44no—
367C2×D53—42no—
368C2×D53—42no—
369C2×D53—42no—
370C2×D53—42no—
371C2×D53—42no—
372C2×D53—42no—
373C2×D53—84no—
374C2×D53—84no—
375C4×C53—22no—
376C4×C53—22no—
377C4×C53—42no—
378C4×C53—42no—
379C4×C53—42no—
380C4×C53#52512yes—
381C4×C53C22×#4111yescharacteristic
382C4×C53C22×#4111yescharacteristic
383Dic53—24no—
384Dic53—22no—
385Dic53—22no—
386Dic53—22no—
387Dic53—42no—
388C2×#540—531no—
389C2×#520—531no—
390#3119—5316no—
391C2×#481—531no—
392C2×#480—531no—
393C2×#479—531no—
394C2×#478D5311yescharacteristic, complemented
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—44no—
405C2×C53#311914yescomplemented
406C2×C53C2×#52511yescharacteristic
407C2×C53C2×#57611yescharacteristic
408C2×C53C2×#57711yescharacteristic
409D53—42no—
410D53—82no—
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×#125C2×D5311yescharacteristic
421C2×#123—1061no—
422C2×#123—1061no—
423C2×#121—531no—
424C2×#121—531no—
425C2×#121—1061no—
426C2×#121—1061no—
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—1061no—
435C2×C4×D4—1061no—
436C2×C4×D4C2×D5311yescharacteristic
437C2×#117—531no—
438C2×#117—1061no—
439C22×C4⋊C4—531no—
440C22×C4⋊C4—1061no—
441#481—538no—
442#480—538no—
443#479—538no—
444#478C2×D5318yescomplemented
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×#107—531no—
455C2×#107C2×D5311yescharacteristic
456C2×#106—531no—
457C2×#106C2×D5311yescharacteristic
458C2×C4⋊C8—531no—
459C2×C4⋊C8C2×D5311yescharacteristic
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⋊C8—531no—
470C2×#97—531no—
471C2×C4×C8—531no—
472C53C2×#311911yescharacteristic, complemented, Sylow
473C2×#41—534no—
474C2×#41—1062no—
475C2×#41—1064no—
476C2×#41—1064no—
477C22×Q8—531no—
478C22×D4—531no—
479C22×D4—531no—
480C22×D4—1061no—
481C22×D4—1061no—
482C22×D4—1061no—
483C22×D4—1061no—
484C22×D4—1061no—
485C22×D4C22×D5311yescharacteristic
486C23×C4—21no—
487C23×C4—531no—
488C23×C4—1061no—
489C23×C4—1061no—
490C23×C4—1061no—
491C23×C4—1061no—
492C23×C4—1061no—
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—22no—
508#125C22×D5314yes—
509#123—1068no—
510#123—1068no—
511#121—534no—
512#121—534no—
513#121—1068no—
514#121—1068no—
515#121—1062no—
516#121—1062no—
517C4×Q8—534no—
518C4×Q8—534no—
519C4×Q8—1062no—
520C4×Q8—1062no—
521C4×D4—22no—
522C4×D4—534no—
523C4×D4—534no—
524C4×D4—534no—
525C4×D4—1062no—
526C4×D4—1062no—
527C4×D4—1062no—
528C4×D4—1068no—
529C4×D4—1068no—
530C4×D4C22×D5314yes—
531#117—534no—
532#117—534no—
533#117—1068no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—531no—
537C2×C4⋊C4—531no—
538C2×C4⋊C4—531no—
539C2×C4⋊C4—534no—
540C2×C4⋊C4—1062no—
541C2×C4⋊C4—1068no—
542C2×C4⋊C4—1061no—
543C2×C4⋊C4—1061no—
544C2×C4⋊C4—1061no—
545C2×C4⋊C4C22×D5311yescharacteristic
546C2×C4⋊C4C22×D5311yescharacteristic
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—1061no—
558C2×C42—1061no—
559C2×C42C22×D5311yescharacteristic
560#107—534no—
561#107C22×D5314yes—
562#106—534no—
563#106C22×D5314yes—
564C4⋊C8—534no—
565C4⋊C8C22×D5314yes—
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⋊C8—534no—
576#97—534no—
577C4×C8—534no—
578C24—21no—
579C24—531no—
580C24—1061no—
581C24—1061no—
582#41—1068no—
583#41—10616no—
584#41—1068no—
585C2×Q8—534no—
586C2×Q8—532no—
587C2×Q8—1061no—
588C2×Q8—1062no—
589C2×D4—21no—
590C2×D4—22no—
591C2×D4—532no—
592C2×D4—532no—
593C2×D4—1064no—
594C2×D4—1064no—
595C2×D4—1064no—
596C2×D4—1068no—
597C2×D4—1064no—
598C2×D4—1064no—
599C2×D4—1061no—
600C2×D4—1061no—
601C2×D4—1062no—
602C2×D4—1062no—
603C2×D4—1062no—
604C2×D4—1062no—
605C2×D4—4242no—
606C2×D4—4242no—
607C2×D4—4242no—
608C2×D4—4242no—
609C2×D4#1171994914yes—
610C2×D4C23×D5312yes—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—24no—
615C22×C4—82no—
616C22×C4—531no—
617C22×C4—531no—
618C22×C4—531no—
619C22×C4—532no—
620C22×C4—532no—
621C22×C4—1064no—
622C22×C4—1064no—
623C22×C4—1064no—
624C22×C4—1064no—
625C22×C4—1064no—
626C22×C4—1068no—
627C22×C4—1061no—
628C22×C4—1062no—
629C22×C4—1062no—
630C22×C4—1061no—
631C22×C4—4242no—
632C22×C4—4242no—
633C22×C4—4242no—
634C22×C4—4242no—
635C22×C4D4×D5311yescharacteristic
636C22×C4D4×D5311yescharacteristic
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—24no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—534no—
656C4⋊C4—534no—
657C4⋊C4—532no—
658C4⋊C4—1064no—
659C4⋊C4—1064no—
660C4⋊C4—1061no—
661C4⋊C4—1064no—
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—1064no—
676C42—1064no—
677C42D4×D5312yes—
678C42C23×D5312yes—
679C23—24no—
680C23—22no—
681C23—42no—
682C23—42no—
683C23—532no—
684C23—1062no—
685C23—1062no—
686C23—1062no—
687C23—1062no—
688C23—1062no—
689C23—2122no—
690C23—2122no—
691C23—2122no—
692C23—2122no—
693C23—2122no—
694C23—2122no—
695C23C2×D4×D5311yescharacteristic
696Q8—534no—
697Q8—1064no—
698Q8—1062no—
699D4—24no—
700D4—22no—
701D4—10616no—
702D4—1062no—
703D4—1062no—
704D4—1062no—
705D4—1062no—
706D4—4244no—
707D4—4244no—
708D4—4244no—
709D4—4244no—
710D4—2122no—
711D4—2122no—
712D4C2×#1171994914yes—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—84no—
722C2×C4—532no—
723C2×C4—532no—
724C2×C4—532no—
725C2×C4—10616no—
726C2×C4—1062no—
727C2×C4—1064no—
728C2×C4—1062no—
729C2×C4—1062no—
730C2×C4—1062no—
731C2×C4—1064no—
732C2×C4—1062no—
733C2×C4—1062no—
734C2×C4—1062no—
735C2×C4—4244no—
736C2×C4—4244no—
737C2×C4—4244no—
738C2×C4—4244no—
739C2×C4—2122no—
740C2×C4C2×D4×D5312yes—
741C2×C4C2×D4×D5312yes—
742C2×C4C2×D4×D5311yescharacteristic
743C2×C4#41×D5312yes—
744C2×C4C2×#1171994912yes—
745C2×C4C24×D5311yescharacteristic
746C8—22no—
747C8—22no—
748C8—1062no—
749C8—1062no—
750C22—24no—
751C22—42no—
752C22—42no—
753C22—48no—
754C22—1062no—
755C22—1062no—
756C22—1062no—
757C22—4244no—
758C22—4244no—
759C22—2122no—
760C22—2122no—
761C22—2122no—
762C22—2122no—
763C22—2122no—
764C22—2122no—
765C22—2124no—
766C22#1681113612yes—
767C22#1681142712yes—
768C22#1681143012yes—
769C22C22×D4×D5311yescharacteristic
770C4—22no—
771C4—22no—
772C4—42no—
773C4—42no—
774C4—42no—
775C4—1062no—
776C4—1062no—
777C4—1062no—
778C4—1064no—
779C4—2122no—
780C4#1681113612yes—
781C4C2×#41×D5311yescharacteristic
782C4C22×#1171994911yescharacteristic
783C2—44no—
784C2—4242no—
785C2—4242no—
786C2—2122no—
787C2#2028491914yesdirect product factor
788C2C2×#1681113611yescharacteristic
789C2C2×#1681142711yescharacteristic
790C2C2×#1681143011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#478C2
socleC23×C53C22×D4
hypercenterC2×#478D53
hypocenterC53C2×#3119
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×#16811229C2semidirect
2. C2×#16811102C2semidirect
3. #20284919C2direct (N × H)
4. C2×#16810943C2semidirect
5. C2×#16810938C2semidirect
6. C2×#16810927C2semidirect
7. C2×#16810824C2semidirect
8. C2×#16810818C2semidirect
9. C2×#16810769C2semidirect
10. C2×#16810769C2semidirect
11. C2×#16810732C2semidirect
12. C2×#16810722C2semidirect
13. C2×#16810710C2semidirect
14. C2×#16810703C2semidirect
15. C2×#16810683C2semidirect
16. C2×C53×#478C2semidirect
23. #16811229C22semidirect
32. #16811102C22semidirect
44. #16810943C22semidirect
45. #16810938C22semidirect
46. #16810927C22semidirect
47. #16810824C22semidirect
48. #16810818C22semidirect
49. #16810769C22semidirect
50. #16810769C22semidirect
51. #16810732C22semidirect
52. #16810722C22semidirect
53. #16810710C22semidirect
54. #16810703C22semidirect
55. #16810683C22semidirect
71. C53×#478C22semidirect
394. C2×#478D53semidirect
405. C2×C53#3119semidirect
444. #478C2×D53semidirect
472. C53C2×#3119semidirect
787. C2#20284919direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112292
C2×#168111022
#202849192
C2×#168109432
C2×#168109382
C2×#168109272
C2×#168108242
C2×#168108182
C2×#168107692
C2×#168107322
C2×#168107222
C2×#168107102
C2×#168107032
C2×#168106832
C2×C53×#4782
C2×#311953