Finite Group Databasebeta

← C2×#20286607 #28260504

Subgroups — C2×#20286607 #28260504

Order 13568.

2146 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811314C211yesmaximal, characteristic, complemented
2C2×#16811285C211yesmaximal, characteristic
3#20286607C2116yesmaximal, direct product factor
4C2×#16810978C211yesmaximal, characteristic, complemented
5C2×#16810966C211yesmaximal, characteristic, complemented
6C2×#16810938C211yesmaximal, characteristic, complemented
7C2×#16810930C211yesmaximal, characteristic, complemented
8C2×#16810863C211yesmaximal, characteristic, complemented
9C2×#16810855C211yesmaximal, characteristic, complemented
10C2×#16810845C211yesmaximal, characteristic, complemented
11C2×#16810784C211yesmaximal, characteristic, complemented
12C2×#16810777C211yesmaximal, characteristic, complemented
13C2×C8×D212C211yesmaximal, characteristic, complemented
14C2×#16810618C211yesmaximal, characteristic, complemented
15C2×#103×D53C211yesmaximal, characteristic, complemented
16C2×C4×Q16×C53C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C22×Q8×D53C2211yescharacteristic
19C22×#11719925C2211yescharacteristic
20C22×#11719924C2211yescharacteristic
21C22×C8×D53C2211yescharacteristic
22C22×C8×D53C2211yescharacteristic
23#16811314—24no—
24#16811314C2218yescomplemented
25#16811285—24no—
26#16811285C2218yes—
27C2×#13133211—21no—
28C2×#13133209C2211yescharacteristic
29C2×#13133207—21no—
30C2×#13133205—21no—
31C2×#13133205C2211yescharacteristic
32C2×#13133202—21no—
33C2×#13133197—21no—
34C2×#13133197C2211yescharacteristic
35C2×#13133193C2211yescharacteristic
36C2×#13133193C2211yescharacteristic
37C2×#13133192—21no—
38C2×#13133192C2211yescharacteristic
39C2×C4×D212—21no—
40C2×C4×D212C2211yescharacteristic
41C2×#13133175C2211yescharacteristic
42C2×#13133174—21no—
43C2×C4⋊C4×D53C2211yescharacteristic
44#16810978C2218yescomplemented
45#16810966C2218yescomplemented
46#16810938C2218yescomplemented
47#16810930C2218yescomplemented
48#16810863C2218yescomplemented
49#16810855C2218yescomplemented
50#16810845C2218yescomplemented
51#16810784C2218yescomplemented
52#16810777C2218yescomplemented
53C8×D212C2218yescomplemented
54C2×#13133150C2211yescharacteristic
55C2×#13133148C2211yescharacteristic
56C2×C4⋊#88322C2211yescharacteristic
57#16810618C2218yescomplemented
58C2×#13133142C2211yescharacteristic
59C2×#13133142C2211yescharacteristic
60C2×#13133141C2211yescharacteristic
61C2×#13133141C2211yescharacteristic
62C2×#13133140C2211yescharacteristic
63#103×D53C2218yescomplemented
64C2×#13133139C2211yescharacteristic
65C2×#13133139C2211yescharacteristic
66C2×#13133137C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133129C2211yescharacteristic
69C22×Q16×C53C2211yescharacteristic
70C2×C4×Q8×C53C2211yescharacteristic
71C2×C4×Q8×C53C2211yescharacteristic
72C4×Q16×C53C2218yescomplemented
73C2×#107×C53C2211yescharacteristic
74C2×#103×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×C4×C8×C53C2211yescharacteristic
77C2×#11719949—22no—
78C2×#11719949—24no—
79C2×#11719949—42no—
80C2×#11719949C2314yes—
81C22×Dic106—21no—
82C22×Dic106C2311yescharacteristic
83C2×Q8×D53—22no—
84C2×Q8×D53—24no—
85C2×Q8×D53—42no—
86C2×Q8×D53C2314yes—
87C22×D212—21no—
88C22×D212—21no—
89C22×D212D411yescharacteristic
90C22×D212C2311yescharacteristic
91C22×C4×D53—21no—
92C22×C4×D53—21no—
93C22×C4×D53—21no—
94C22×C4×D53C2311yescharacteristic
95C22×C4×D53C2311yescharacteristic
96C2×#11719925—42no—
97C2×#11719925C2314yes—
98C2×#11719924—42no—
99C2×#11719924C2314yes—
100C22×#88322C2311yescharacteristic
101C22×#88322C2311yescharacteristic
102C2×C8×D53—42no—
103C2×C8×D53—42no—
104C2×C8×D53C2314yes—
105C2×C8×D53C2314yes—
106#13133211—28no—
107#13133209—22no—
108#13133209C2314yes—
109#13133207—28no—
110#13133205—22no—
111#13133205—28no—
112#13133205C2314yes—
113#13133202—28no—
114#13133197—28no—
115#13133197—22no—
116#13133197C2314yes—
117#13133193—22no—
118#13133193—22no—
119#13133193C2314yes—
120#13133193C2314yes—
121#13133192—28no—
122#13133192—22no—
123#13133192C2314yes—
124C4×D212—28no—
125C4×D212D414yes—
126C4×D212C2314yes—
127#13133175—22no—
128#13133175C2314yes—
129#13133174—28no—
130C2×C4⋊Dic53—21no—
131C2×C4⋊Dic53D411yescharacteristic
132C2×C4⋊Dic53C2311yescharacteristic
133C2×C4⋊Dic53C2311yescharacteristic
134C2×#11719919—21no—
135C2×#11719919—21no—
136C2×#11719919—21no—
137C2×#11719919—21no—
138C2×#11719919—21no—
139C4⋊C4×D53—22no—
140C4⋊C4×D53C2314yes—
141C2×#11719921—21no—
142C2×#11719921—21no—
143C2×#11719921—21no—
144C2×#11719921—21no—
145C2×#11719921—21no—
146C2×#11719921—21no—
147C2×#11719921—21no—
148C2×#11719921D411yescharacteristic
149C2×#11719921D411yescharacteristic
150C2×C4×Dic53—21no—
151#13133150C2314yes—
152#13133148C2314yes—
153C4⋊#88322C2314yes—
154#13133142C2314yes—
155#13133142C2314yes—
156#13133141C2314yes—
157#13133141C2314yes—
158#13133140C2314yes—
159#13133139C2314yes—
160#13133139C2314yes—
161#13133137C2314yes—
162#13133129C2314yes—
163#13133129C2314yes—
164C22×Q8×C53C2311yescharacteristic
165C22×Q8×C53C2311yescharacteristic
166C2×Q16×C53—24no—
167C2×Q16×C53C2314yes—
168C22×C8×C53C2311yescharacteristic
169C22×C8×C53C2311yescharacteristic
170C4×Q8×C53—22no—
171C4×Q8×C53—22no—
172C4×Q8×C53C2314yes—
173C4×Q8×C53C2314yes—
174C2×C4⋊C4×C53—21no—
175C2×C4⋊C4×C53—21no—
176C2×C4⋊C4×C53C2311yescharacteristic
177C2×C4⋊C4×C53C2311yescharacteristic
178C2×C42×C53—21no—
179C2×C42×C53—21no—
180C2×C42×C53C2311yescharacteristic
181#107×C53C2314yes—
182#103×C53C2314yes—
183#103×C53C2314yes—
184C4×C8×C53C2314yes—
185C23×D53—21no—
186C23×D53C2×D411yescharacteristic
187C23×D53C2×D411yescharacteristic
188C2×Q8×C53—21no—
189C2×Q8×C53—21no—
190C2×Q8×C53—22no—
191C2×Q8×C53—22no—
192C2×Q8×C53—22no—
193C2×Q8×C53#4114yes—
194C2×Q8×C53C2412yes—
195C2×Q8×C53C2412yes—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53C2×D411yescharacteristic
201C22×C4×C53C2×D411yescharacteristic
202C22×C4×C53C2411yescharacteristic
203C22×Dic53—21no—
204C22×Dic53—21no—
205C22×Dic53—21no—
206C22×Dic53C2×D411yescharacteristic
207C22×Dic53C2×D411yescharacteristic
208#11719949—28no—
209#11719949—44no—
210#11719949—48no—
211Q8×D53—28no—
212Q8×D53—44no—
213Q8×D53—48no—
214C2×D212—24no—
215C2×D212—22no—
216C2×D212—22no—
217C2×D212—24no—
218C2×D212—24no—
219C2×D212—21no—
220C2×D212—44no—
221C2×D212—44no—
222C2×D212C2×D414yes—
223C2×D212C2412yes—
224C2×C4×D53—22no—
225C2×C4×D53—22no—
226C2×C4×D53—22no—
227C2×C4×D53—22no—
228C2×C4×D53—24no—
229C2×C4×D53—24no—
230C2×C4×D53—24no—
231C2×C4×D53—44no—
232C2×C4×D53—44no—
233C2×C4×D53—44no—
234C2×C4×D53C2×D412yes—
235C2×C4×D53C2×D412yes—
236C2×C4×D53C2412yes—
237C2×C4×D53C2412yes—
238C2×Dic106—22no—
239C2×Dic106—22no—
240C2×Dic106—21no—
241C2×Dic106—24no—
242C2×Dic106—44no—
243C2×Dic106C2412yes—
244Q16×C53—28no—
245C2×C8×C53—22no—
246C2×C8×C53—22no—
247C2×C8×C53C2412yes—
248C2×C8×C53C2412yes—
249C4⋊C4×C53—24no—
250C4⋊C4×C53—24no—
251C4⋊C4×C53—21no—
252C4⋊C4×C53—21no—
253C4⋊C4×C53C2412yes—
254C4⋊C4×C53C2412yes—
255C42×C53—24no—
256C42×C53—24no—
257C42×C53C2×D412yes—
258C42×C53C2412yes—
259#11719925—44no—
260#11719924—44no—
261#11719921—24no—
262#11719921—24no—
263#11719921—24no—
264#11719921—24no—
265#11719921—24no—
266#11719921—24no—
267#11719921—24no—
268#11719921C2×D414yes—
269#11719921C2×D414yes—
270C4⋊Dic53—21no—
271C4⋊Dic53—21no—
272C4⋊Dic53—24no—
273C4⋊Dic53C2×D414yes—
274C4⋊Dic53C2412yes—
275C4⋊Dic53C2412yes—
276#11719919—24no—
277#11719919—24no—
278#11719919—24no—
279#11719919—24no—
280#11719919—24no—
281C4×Dic53—24no—
282C2×#88322—22no—
283C2×#88322—22no—
284C2×#88322C2412yes—
285C2×#88322C2412yes—
286C8×D53—44no—
287C8×D53—44no—
288C23×C53C22×D411yescharacteristic
289C22×D53—22no—
290C22×D53—22no—
291C22×D53—22no—
292C22×D53—22no—
293C22×D53—22no—
294C22×D53—22no—
295C22×D53—42no—
296C22×D53—42no—
297C22×D53—42no—
298C22×D53#13514yes—
299C22×D53C22×D412yes—
300C22×D53C22×D412yes—
301Q8×C53—24no—
302Q8×C53—22no—
303Q8×C53—22no—
304Q8×C53—22no—
305Q8×C53—42no—
306Q8×C53C2×#4114yes—
307C2×C4×C53—24no—
308C2×C4×C53—22no—
309C2×C4×C53—22no—
310C2×C4×C53—22no—
311C2×C4×C53—22no—
312C2×C4×C53—22no—
313C2×C4×C53—22no—
314C2×C4×C53—42no—
315C2×C4×C53—42no—
316C2×C4×C53—42no—
317C2×C4×C53C22×D412yes—
318C2×C4×C53C22×D412yes—
319C2×C4×C53C22×D411yescharacteristic
320C2×C4×C53C2×#4112yes—
321C2×C4×C53H(5,𝔽2)12yes—
322C2×C4×C53C2511yescharacteristic
323C2×Dic53—22no—
324C2×Dic53—22no—
325C2×Dic53—22no—
326C2×Dic53—22no—
327C2×Dic53—22no—
328C2×Dic53—42no—
329C2×Dic53—42no—
330C2×Dic53—42no—
331C2×Dic53C22×D412yes—
332C2×Dic53C22×D412yes—
333D212—28no—
334D212—22no—
335D212—22no—
336D212—48no—
337D212—48no—
338D212—42no—
339C4×D53—24no—
340C4×D53—24no—
341C4×D53—22no—
342C4×D53—22no—
343C4×D53—22no—
344C4×D53—22no—
345C4×D53—48no—
346C4×D53—48no—
347C4×D53—48no—
348Dic106—22no—
349Dic106—22no—
350Dic106—48no—
351Dic106—42no—
352C8×C53—22no—
353C8×C53—22no—
354#88322—22no—
355#88322—22no—
356C2×#3300—531nomaximal, Sylow
357C22×C53#54612yes—
358C22×C53C2×#13512yes—
359C22×C53#57812yes—
360C22×C53C23×D411yescharacteristic
361C2×D53—22no—
362C2×D53—28no—
363C2×D53—22no—
364C2×D53—22no—
365C2×D53—22no—
366C2×D53—22no—
367C2×D53—44no—
368C2×D53—42no—
369C2×D53—42no—
370C2×D53—42no—
371C2×D53—84no—
372C2×D53C2×#13514yes—
373C4×C53—24no—
374C4×C53—22no—
375C4×C53—22no—
376C4×C53—42no—
377C4×C53—42no—
378C4×C53—42no—
379C4×C53#54612yes—
380C4×C53C22×#4111yescharacteristic
381C4×C53C2×H(5,𝔽2)11yescharacteristic
382Dic53—22no—
383Dic53—22no—
384Dic53—42no—
385Dic53—42no—
386Dic53—42no—
387C2×#552—531no—
388C2×#548—531no—
389#3300—5316no—
390C2×#488—531no—
391C2×#485—531no—
392C2×#480—531no—
393C2×#479—531no—
394C2×#467—531no—
395C2×#465—531no—
396C2×#464—531no—
397C2×#452—531no—
398C2×#451—531no—
399C2×C4×Q16D5311yescharacteristic, complemented
400C2×C8×D4—531no—
401C2×#416—531no—
402C22×#103—531no—
403C2×C53#330014yescomplemented
404C2×C53C2×#54611yescharacteristic
405C2×C53C22×#13511yescharacteristic
406C2×C53C2×#57811yescharacteristic
407D53—24no—
408D53—42no—
409D53—82no—
410C22×#41—531no—
411C23×Q8—531no—
412C22×Q16—531no—
413C22×Q16C2×D5311yescharacteristic
414C22×SD16—531no—
415C23×C8—531no—
416C23×C8—531no—
417#552—538no—
418#552—1064no—
419#548—538no—
420#548—1064no—
421C2×#126—1061no—
422C2×#125—531no—
423C2×#125—1061no—
424C2×#124—531no—
425C2×#124—1061no—
426C2×#123—1061no—
427C2×C22⋊Q8—531no—
428C2×C22⋊Q8—531no—
429C2×C22⋊Q8—531no—
430C2×C22⋊Q8—1061no—
431C2×#121—531no—
432C2×#121—1061no—
433C2×C4×Q8C2×D5311yescharacteristic
434C2×C4×Q8C2×D5311yescharacteristic
435C2×C4×D4—531no—
436C2×C4×D4—1061no—
437C2×#117—531no—
438C2×#117—1061no—
439C22×C4⋊C4—531no—
440#488—538no—
441#485—538no—
442#480—538no—
443#479—538no—
444#467—538no—
445#465—538no—
446#464—538no—
447#452—538no—
448#451—538no—
449C4×Q16C2×D5318yescomplemented
450C8×D4—538no—
451C2×#107—531no—
452C2×#107C2×D5311yescharacteristic
453C2×#106—531no—
454C2×C4⋊C8—531no—
455#416—538no—
456C2×#103—531no—
457C2×#103—531no—
458C2×#103—531no—
459C2×#103—531no—
460C2×#103—531no—
461C2×#103—538no—
462C2×#103C2×D5311yescharacteristic
463C2×#103C2×D5311yescharacteristic
464C2×#102—531no—
465C2×#102—531no—
466C2×#102—531no—
467C2×C22⋊C8—531no—
468C2×C22⋊C8—531no—
469C2×C4×C8C2×D5311yescharacteristic
470C53C2×#330011yescharacteristic, complemented, Sylow
471C2×#41—534no—
472C2×#41—1062no—
473C2×#41—1064no—
474C2×#41—2122no—
475C22×Q8—534no—
476C22×Q8—531no—
477C22×Q8—1061no—
478C22×Q8—1062no—
479C22×Q8—1064no—
480C22×Q8—2122no—
481C22×Q8C22×D5311yescharacteristic
482C22×Q8C22×D5311yescharacteristic
483C22×D4—531no—
484C22×D4—531no—
485C22×D4—1061no—
486C22×D4—1061no—
487C23×C4—531no—
488C23×C4—531no—
489C23×C4—1061no—
490C23×C4—1061no—
491C23×C4—1061no—
492C2×Q16—24no—
493C2×Q16—534no—
494C2×Q16—2122no—
495C2×Q16C22×D5314yes—
496C2×SD16—534no—
497C2×SD16—2122no—
498C22×C8—531no—
499C22×C8—531no—
500C22×C8—534no—
501C22×C8—534no—
502C22×C8—2122no—
503C22×C8—2122no—
504C22×C8C22×D5311yescharacteristic
505C22×C8C22×D5311yescharacteristic
506#126—1068no—
507#125—534no—
508#125—1068no—
509#125—1062no—
510#124—534no—
511#124—1068no—
512#124—1062no—
513#123—1068no—
514C22⋊Q8—534no—
515C22⋊Q8—534no—
516C22⋊Q8—534no—
517C22⋊Q8—1068no—
518C22⋊Q8—1062no—
519C22⋊Q8—1062no—
520C22⋊Q8—1062no—
521#121—534no—
522#121—1062no—
523#121—1068no—
524C4×Q8—22no—
525C4×Q8—22no—
526C4×Q8C22×D5314yes—
527C4×Q8C22×D5314yes—
528C4×D4—534no—
529C4×D4—534no—
530C4×D4—1068no—
531#117—534no—
532#117—1068no—
533#117—1062no—
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—1061no—
542C2×C4⋊C4—1061no—
543C2×C4⋊C4—1061no—
544C2×C4⋊C4—1061no—
545C2×C4⋊C4—1061no—
546C2×C4⋊C4—1061no—
547C2×C4⋊C4C22×D5311yescharacteristic
548C2×C4⋊C4C22×D5311yescharacteristic
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×C22⋊C4—1061no—
557C2×C22⋊C4—1061no—
558C2×C42—21no—
559C2×C42—21no—
560C2×C42—1061no—
561C2×C42C22×D5311yescharacteristic
562#107—534no—
563#107C22×D5314yes—
564#106—534no—
565C4⋊C8—534no—
566#103—534no—
567#103—534no—
568#103—534no—
569#103—534no—
570#103—534no—
571#103C22×D5314yes—
572#103C22×D5314yes—
573#102—534no—
574#102—534no—
575#102—534no—
576C22⋊C8—534no—
577C22⋊C8—534no—
578C4×C8C22×D5314yes—
579C24—531no—
580C24—531no—
581C24—1061no—
582#41—1068no—
583#41—2124no—
584#41—2128no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—22no—
588C2×Q8—22no—
589C2×Q8—22no—
590C2×Q8—532no—
591C2×Q8—1064no—
592C2×Q8—1061no—
593C2×Q8—1068no—
594C2×Q8—1062no—
595C2×Q8—1062no—
596C2×Q8—2124no—
597C2×Q8—2124no—
598C2×Q8—2128no—
599C2×Q8#1171994514yes—
600C2×Q8C23×D5312yes—
601C2×Q8C23×D5312yes—
602C2×D4—534no—
603C2×D4—532no—
604C2×D4—1064no—
605C2×D4—1064no—
606C2×D4—1064no—
607C2×D4—1061no—
608C2×D4—1062no—
609C2×D4—1062no—
610C2×D4—2124no—
611C2×D4—2124no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—531no—
617C22×C4—531no—
618C22×C4—532no—
619C22×C4—532no—
620C22×C4—532no—
621C22×C4—532no—
622C22×C4—1064no—
623C22×C4—1064no—
624C22×C4—1064no—
625C22×C4—1062no—
626C22×C4—1062no—
627C22×C4—1062no—
628C22×C4—1062no—
629C22×C4—1061no—
630C22×C4—1061no—
631C22×C4—1061no—
632C22×C4—2124no—
633C22×C4—2124no—
634C22×C4—2124no—
635C22×C4D4×D5311yescharacteristic
636C22×C4D4×D5311yescharacteristic
637C22×C4C23×D5311yescharacteristic
638Q16—28no—
639Q16—2124no—
640SD16—2124no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—532no—
644C2×C8—532no—
645C2×C8—1062no—
646C2×C8—1062no—
647C2×C8—2124no—
648C2×C8—2124no—
649C2×C8C23×D5312yes—
650C2×C8C23×D5312yes—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—534no—
656C4⋊C4—532no—
657C4⋊C4—532no—
658C4⋊C4—1064no—
659C4⋊C4—1064no—
660C4⋊C4—1064no—
661C4⋊C4—1064no—
662C4⋊C4—1061no—
663C4⋊C4—1061no—
664C4⋊C4—1064no—
665C4⋊C4—1064no—
666C4⋊C4C23×D5312yes—
667C4⋊C4C23×D5312yes—
668C22⋊C4—534no—
669C22⋊C4—534no—
670C22⋊C4—1064no—
671C22⋊C4—1064no—
672C22⋊C4—1064no—
673C22⋊C4—1064no—
674C22⋊C4—1064no—
675C22⋊C4—1064no—
676C22⋊C4—1064no—
677C42—24no—
678C42—24no—
679C42—1064no—
680C42D4×D5312yes—
681C42C23×D5312yes—
682C23—534no—
683C23—532no—
684C23—532no—
685C23—1062no—
686C23—1062no—
687C23—1062no—
688C23—1062no—
689C23—1062no—
690C23—1062no—
691C23—2122no—
692C23—2122no—
693C23—2122no—
694C23C2×D4×D5311yescharacteristic
695Q8—24no—
696Q8—22no—
697Q8—22no—
698Q8—22no—
699Q8—42no—
700Q8—1062no—
701Q8—1062no—
702Q8—2128no—
703Q8—2122no—
704Q8C2×#1171994514yes—
705D4—1068no—
706D4—1062no—
707D4—1062no—
708D4—2128no—
709D4—2128no—
710D4—2122no—
711C2×C4—24no—
712C2×C4—22no—
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—532no—
722C2×C4—532no—
723C2×C4—1062no—
724C2×C4—1062no—
725C2×C4—1064no—
726C2×C4—1064no—
727C2×C4—1062no—
728C2×C4—1062no—
729C2×C4—1062no—
730C2×C4—1062no—
731C2×C4—1062no—
732C2×C4—1062no—
733C2×C4—1062no—
734C2×C4—2128no—
735C2×C4—2128no—
736C2×C4—2128no—
737C2×C4—2122no—
738C2×C4—2122no—
739C2×C4—2122no—
740C2×C4C2×D4×D5312yes—
741C2×C4C2×D4×D5312yes—
742C2×C4C2×D4×D5311yescharacteristic
743C2×C4C2×#1171994512yes—
744C2×C4#1313326312yes—
745C2×C4C24×D5311yescharacteristic
746C8—22no—
747C8—22no—
748C8—1062no—
749C8—1062no—
750C22—534no—
751C22—1068no—
752C22—1062no—
753C22—1062no—
754C22—1062no—
755C22—1062no—
756C22—1062no—
757C22—4244no—
758C22—2122no—
759C22—2122no—
760C22—2122no—
761C22—2124no—
762C22#1681126912yes—
763C22#135×D5312yes—
764C22#1681143612yes—
765C22C22×D4×D5311yescharacteristic
766C4—22no—
767C4—24no—
768C4—22no—
769C4—42no—
770C4—42no—
771C4—42no—
772C4—1062no—
773C4—1062no—
774C4—2122no—
775C4—2122no—
776C4—2122no—
777C4#1681126912yes—
778C4C22×#1171994511yescharacteristic
779C4C2×#1313326311yescharacteristic
780C2—1064no—
781C2—4242no—
782C2—2122no—
783C2#2028660714yesdirect product factor
784C2C2×#1681126911yescharacteristic
785C2C2×#135×D5311yescharacteristic
786C2C2×#1681143611yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C4×Q16×C53C2
socleC23×C53C22×D4
prime radicalC2×#16811285C2
hypercenterC2×C4×Q16D53
hypocenterC53C2×#3300
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
1. C2×#16811314C2semidirect
3. #20286607C2direct (N × H)
4. C2×#16810978C2semidirect
5. C2×#16810966C2semidirect
6. C2×#16810938C2semidirect
7. C2×#16810930C2semidirect
8. C2×#16810863C2semidirect
9. C2×#16810855C2semidirect
10. C2×#16810845C2semidirect
11. C2×#16810784C2semidirect
12. C2×#16810777C2semidirect
13. C2×C8×D212C2semidirect
14. C2×#16810618C2semidirect
15. C2×#103×D53C2semidirect
16. C2×C4×Q16×C53C2semidirect
24. #16811314C22semidirect
44. #16810978C22semidirect
45. #16810966C22semidirect
46. #16810938C22semidirect
47. #16810930C22semidirect
48. #16810863C22semidirect
49. #16810855C22semidirect
50. #16810845C22semidirect
51. #16810784C22semidirect
52. #16810777C22semidirect
53. C8×D212C22semidirect
57. #16810618C22semidirect
63. #103×D53C22semidirect
72. C4×Q16×C53C22semidirect
399. C2×C4×Q16D53semidirect
403. C2×C53#3300semidirect
449. C4×Q16C2×D53semidirect
470. C53C2×#3300semidirect
783. C2#20286607direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113142
C2×#168112852
#202866072
C2×#168109782
C2×#168109662
C2×#168109382
C2×#168109302
C2×#168108632
C2×#168108552
C2×#168108452
C2×#168107842
C2×#168107772
C2×C8×D2122
C2×#168106182
C2×#103×D532
C2×C4×Q16×C532
C2×#330053