Finite Group Databasebeta

← C2×#20284983 #28252413

Subgroups — C2×#20284983 #28252413

Order 13568.

2134 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811245C211yesmaximal, characteristic, complemented
2C2×#16811105C211yesmaximal, characteristic, complemented
3#20284983C2116yesmaximal, direct product factor
4C2×#16810957C211yesmaximal, characteristic, complemented
5C2×#16810938C211yesmaximal, characteristic, complemented
6C2×#16810916C211yesmaximal, characteristic, complemented
7C2×#16810902C211yesmaximal, characteristic, complemented
8C2×#16810847C211yesmaximal, characteristic, complemented
9C2×#16810841C211yesmaximal, characteristic, complemented
10C2×#16810784C211yesmaximal, characteristic, complemented
11C2×#16810771C211yesmaximal, characteristic
12C2×#16810721C211yesmaximal, characteristic, complemented
13C2×#16810721C211yesmaximal, characteristic, complemented
14C2×C4×D424C211yesmaximal, characteristic, complemented
15C2×#16810682C211yesmaximal, characteristic, complemented
16C2×C4×Q16×C53C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C22×#11719924C2211yescharacteristic
19C22×#11719924C2211yescharacteristic
20C22×D424C2211yescharacteristic
21#16811245—24no—
22#16811245C2218yescomplemented
23C2×#13133216C2211yescharacteristic
24C2×#13133211—21no—
25C2×#13133206C2211yescharacteristic
26C2×#13133205—21no—
27C2×#13133202—21no—
28C2×#13133195—21no—
29C2×#13133193C2211yescharacteristic
30C2×#13133192C2211yescharacteristic
31#16811105—24no—
32#16811105C2218yescomplemented
33C2×Q8×Dic53C2211yescharacteristic
34C2×C4×D212—21no—
35C2×C4×D212C2211yescharacteristic
36C2×C4×D212C2211yescharacteristic
37C2×#13133179—21no—
38C2×#13133179C2211yescharacteristic
39C2×#13133174—21no—
40C2×#13133174C2211yescharacteristic
41C2×C4⋊C4×D53—21no—
42C2×C4⋊C4×D53C2211yescharacteristic
43#16810957C2218yescomplemented
44#16810938C2218yescomplemented
45#16810916C2218yescomplemented
46#16810902C2218yescomplemented
47#16810847C2218yescomplemented
48#16810841C2218yescomplemented
49#16810784C2218yescomplemented
50#16810771C2218yes—
51#16810721C2218yescomplemented
52#16810721C2218yescomplemented
53C4×D424C2218yescomplemented
54#16810682C2218yescomplemented
55C2×#13133151C2211yescharacteristic
56C2×#13133150C2211yescharacteristic
57C2×#13133150C2211yescharacteristic
58C2×#13133146C2211yescharacteristic
59C2×#13133146C2211yescharacteristic
60C2×#13133141C2211yescharacteristic
61C2×#13133141C2211yescharacteristic
62C2×#13133139C2211yescharacteristic
63C2×#13133139C2211yescharacteristic
64C2×#13133137C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×#13133129C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133128C2211yescharacteristic
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—24no—
78C2×#11719949—24no—
79C2×#11719949—22no—
80C2×#11719949C2314yes—
81C22×Dic106—21no—
82C22×D212—21no—
83C22×D212—21no—
84C22×D212C2311yescharacteristic
85C22×D212C2311yescharacteristic
86C22×C4×D53—21no—
87C22×C4×D53—21no—
88C22×C4×D53—21no—
89C22×C4×D53—21no—
90C22×C4×D53—21no—
91C22×C4×D53C2311yescharacteristic
92C2×#11719924—24no—
93C2×#11719924—24no—
94C2×#11719924C2314yes—
95C2×#11719924C2314yes—
96C2×D424—24no—
97C2×D424C2314yes—
98C22×#88322C2311yescharacteristic
99C22×#88322C2311yescharacteristic
100#13133216—22no—
101#13133216C2314yes—
102#13133211—28no—
103#13133206—22no—
104#13133206C2314yes—
105#13133205—28no—
106#13133202—28no—
107#13133195—28no—
108#13133193—22no—
109#13133193C2314yes—
110#13133192—22no—
111#13133192C2314yes—
112Q8×Dic53—22no—
113Q8×Dic53C2314yes—
114C4×D212—22no—
115C4×D212—22no—
116C4×D212—28no—
117C4×D212C2314yes—
118C4×D212C2314yes—
119#13133179—28no—
120#13133179—22no—
121#13133179C2314yes—
122#13133174—28no—
123#13133174D414yes—
124#13133174C2314yes—
125C2×C4⋊Dic53—21no—
126C2×C4⋊Dic53C2311yescharacteristic
127C2×C4⋊Dic53C2311yescharacteristic
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919D411yescharacteristic
132C2×#11719919D411yescharacteristic
133C4⋊C4×D53—28no—
134C4⋊C4×D53—22no—
135C4⋊C4×D53C2314yes—
136C2×#11719921—21no—
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×#11719921—21no—
143C2×#11719921D411yescharacteristic
144C2×#11719921D411yescharacteristic
145C2×C4×Dic53—21no—
146C2×C4×Dic53C2311yescharacteristic
147#13133151C2314yes—
148#13133150C2314yes—
149#13133150C2314yes—
150#13133146C2314yes—
151#13133146C2314yes—
152#13133141C2314yes—
153#13133141C2314yes—
154#13133139C2314yes—
155#13133139C2314yes—
156#13133137C2314yes—
157#13133137C2314yes—
158#13133129C2314yes—
159#13133129C2314yes—
160#13133128C2314yes—
161C22×Q8×C53C2311yescharacteristic
162C22×Q8×C53C2311yescharacteristic
163C2×Q16×C53—24no—
164C2×Q16×C53C2314yes—
165C22×C8×C53C2311yescharacteristic
166C22×C8×C53C2311yescharacteristic
167C4×Q8×C53—22no—
168C4×Q8×C53—22no—
169C4×Q8×C53C2314yes—
170C4×Q8×C53C2314yes—
171C2×C4⋊C4×C53—21no—
172C2×C4⋊C4×C53—21no—
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C42×C53—21no—
176C2×C42×C53—21no—
177C2×C42×C53C2311yescharacteristic
178#107×C53C2314yes—
179#103×C53C2314yes—
180#103×C53C2314yes—
181C4×C8×C53C2314yes—
182C23×D53—21no—
183C23×D53—21no—
184C23×D53C2×D411yescharacteristic
185C2×Q8×C53—21no—
186C2×Q8×C53—21no—
187C2×Q8×C53—22no—
188C2×Q8×C53—22no—
189C2×Q8×C53—22no—
190C2×Q8×C53#4114yes—
191C2×Q8×C53C2412yes—
192C2×Q8×C53C2412yes—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53C2×D411yescharacteristic
198C22×C4×C53C2×D411yescharacteristic
199C22×C4×C53C2411yescharacteristic
200C22×Dic53—21no—
201C22×Dic53—21no—
202C22×Dic53C2×D411yescharacteristic
203C22×Dic53C2×D411yescharacteristic
204C22×Dic53C2×D411yescharacteristic
205#11719949—216no—
206#11719949—28no—
207#11719949—28no—
208C2×D212—28no—
209C2×D212—24no—
210C2×D212—21no—
211C2×D212—22no—
212C2×D212—22no—
213C2×D212—22no—
214C2×D212—21no—
215C2×D212—24no—
216C2×D212—82no—
217C2×D212#4114yes—
218C2×D212C2412yes—
219C2×D212C2412yes—
220C2×C4×D53—28no—
221C2×C4×D53—22no—
222C2×C4×D53—22no—
223C2×C4×D53—24no—
224C2×C4×D53—24no—
225C2×C4×D53—24no—
226C2×C4×D53—24no—
227C2×C4×D53—24no—
228C2×C4×D53—82no—
229C2×C4×D53—82no—
230C2×C4×D53—82no—
231C2×C4×D53—82no—
232C2×C4×D53C2×D412yes—
233C2×C4×D53C2412yes—
234C2×Dic106—24no—
235C2×Dic106—82no—
236Q16×C53—28no—
237C2×C8×C53—22no—
238C2×C8×C53—22no—
239C2×C8×C53C2412yes—
240C2×C8×C53C2412yes—
241C4⋊C4×C53—24no—
242C4⋊C4×C53—24no—
243C4⋊C4×C53—21no—
244C4⋊C4×C53—21no—
245C4⋊C4×C53C2412yes—
246C4⋊C4×C53C2412yes—
247C42×C53—24no—
248C42×C53—24no—
249C42×C53C2×D412yes—
250C42×C53C2412yes—
251#11719924—28no—
252#11719924—28no—
253#11719921—24no—
254#11719921—24no—
255#11719921—24no—
256#11719921—24no—
257#11719921—24no—
258#11719921—24no—
259#11719921—24no—
260#11719921C2×D414yes—
261#11719921C2×D414yes—
262C4⋊Dic53—21no—
263C4⋊Dic53—21no—
264C4⋊Dic53—24no—
265C4⋊Dic53C2412yes—
266C4⋊Dic53C2412yes—
267#11719919—24no—
268#11719919—24no—
269#11719919—24no—
270#11719919C2×D414yes—
271#11719919C2×D414yes—
272C4×Dic53—24no—
273C4×Dic53C2×D412yes—
274C4×Dic53C2412yes—
275C2×#88322—22no—
276C2×#88322—22no—
277C2×#88322C2412yes—
278C2×#88322C2412yes—
279D424—28no—
280C23×C53C22×D411yescharacteristic
281C22×D53—22no—
282C22×D53—24no—
283C22×D53—22no—
284C22×D53—22no—
285C22×D53—22no—
286C22×D53—22no—
287C22×D53—42no—
288C22×D53—42no—
289C22×D53—42no—
290C22×D53—42no—
291C22×D53—42no—
292C22×D53C22×D412yes—
293Q8×C53—24no—
294Q8×C53—22no—
295Q8×C53—22no—
296Q8×C53—22no—
297Q8×C53—42no—
298Q8×C53C2×#4114yes—
299C2×C4×C53—24no—
300C2×C4×C53—22no—
301C2×C4×C53—22no—
302C2×C4×C53—22no—
303C2×C4×C53—22no—
304C2×C4×C53—22no—
305C2×C4×C53—22no—
306C2×C4×C53—42no—
307C2×C4×C53—42no—
308C2×C4×C53—42no—
309C2×C4×C53C22×D412yes—
310C2×C4×C53C22×D412yes—
311C2×C4×C53C22×D411yescharacteristic
312C2×C4×C53C2×#4112yes—
313C2×C4×C53C2×#4112yes—
314C2×C4×C53C2511yescharacteristic
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—22no—
319C2×Dic53—22no—
320C2×Dic53—42no—
321C2×Dic53—42no—
322C2×Dic53C22×D412yes—
323C2×Dic53C22×D412yes—
324C2×Dic53C22×D412yes—
325D212—216no—
326D212—24no—
327D212—22no—
328D212—22no—
329D212—22no—
330D212—42no—
331D212—84no—
332D212C2×#4114yes—
333C4×D53—216no—
334C4×D53—24no—
335C4×D53—22no—
336C4×D53—22no—
337C4×D53—84no—
338C4×D53—84no—
339C4×D53—84no—
340C4×D53—84no—
341Dic106—84no—
342C8×C53—22no—
343C8×C53—22no—
344#88322—22no—
345#88322—22no—
346C2×#3124—531nomaximal, Sylow
347C22×C53#52512yes—
348C22×C53#57612yes—
349C22×C53#57812yes—
350C22×C53C23×D411yescharacteristic
351C2×D53—22no—
352C2×D53—24no—
353C2×D53—22no—
354C2×D53—22no—
355C2×D53—44no—
356C2×D53—48no—
357C2×D53—42no—
358C2×D53—42no—
359C2×D53—42no—
360C2×D53—42no—
361C2×D53—42no—
362C2×D53—84no—
363C4×C53—24no—
364C4×C53—22no—
365C4×C53—22no—
366C4×C53—42no—
367C4×C53—42no—
368C4×C53—42no—
369C4×C53#52512yes—
370C4×C53C22×#4111yescharacteristic
371C4×C53C22×#4111yescharacteristic
372Dic53—22no—
373Dic53—22no—
374Dic53—22no—
375Dic53—42no—
376Dic53—42no—
377C2×#542—531no—
378C2×#520—531no—
379#3124—5316no—
380C2×#484—531no—
381C2×#480—531no—
382C2×#477—531no—
383C2×#474—531no—
384C2×#464—531no—
385C2×#463—531no—
386C2×#452—531no—
387C2×#449—531no—
388C2×#440—531no—
389C2×#440—531no—
390C2×C4×Q16D5311yescharacteristic, complemented
391C2×C4×D8—531no—
392C2×#433—531no—
393C2×C53#312414yescomplemented
394C2×C53C2×#52511yescharacteristic
395C2×C53C2×#57611yescharacteristic
396C2×C53C2×#57811yescharacteristic
397D53—42no—
398D53—44no—
399D53—82no—
400C22×#41—531no—
401C22×Q16C2×D5311yescharacteristic
402C22×SD16—531no—
403C22×SD16—531no—
404C22×D8—531no—
405#542—538no—
406#542—1064no—
407C2×C4⋊Q8—531no—
408C2×#126—1061no—
409C2×#124—531no—
410C2×#124—1061no—
411C2×#123—1061no—
412C2×C22⋊Q8—531no—
413C2×C22⋊Q8—1061no—
414C2×#121—531no—
415#520—538no—
416#520—1064no—
417C2×C4×Q8—531no—
418C2×C4×Q8C2×D5311yescharacteristic
419C2×C4×Q8C2×D5311yescharacteristic
420C2×C4×D4—531no—
421C2×C4×D4—531no—
422C2×C4×D4—531no—
423C2×C4×D4—1061no—
424C2×C4×D4—1061no—
425C2×#117—531no—
426C2×#117—1061no—
427C22×C4⋊C4—531no—
428C22×C4⋊C4—1061no—
429#484—538no—
430#480—538no—
431#477—538no—
432#474—538no—
433#464—538no—
434#463—538no—
435#452—538no—
436#449—538no—
437#440—538no—
438#440—538no—
439C4×Q16C2×D5318yescomplemented
440C4×D8—538no—
441#433—538no—
442C2×#107—531no—
443C2×#107—531no—
444C2×#107—531no—
445C2×#107C2×D5311yescharacteristic
446C2×C4⋊C8—531no—
447C2×C4⋊C8—531no—
448C2×#103—531no—
449C2×#103—531no—
450C2×#103C2×D5311yescharacteristic
451C2×#103C2×D5311yescharacteristic
452C2×#102—531no—
453C2×#102—531no—
454C2×#102—531no—
455C2×#102—531no—
456C2×C22⋊C8—531no—
457C2×C22⋊C8—531no—
458C2×#97—531no—
459C2×C4×C8C2×D5311yescharacteristic
460C53C2×#312411yescharacteristic, complemented, Sylow
461C2×#41—534no—
462C2×#41—1062no—
463C2×#41—1064no—
464C2×#41—1064no—
465C22×Q8—1061no—
466C22×Q8C22×D5311yescharacteristic
467C22×Q8C22×D5311yescharacteristic
468C22×D4—531no—
469C22×D4—531no—
470C22×D4—1061no—
471C22×D4—1061no—
472C23×C4—531no—
473C23×C4—1061no—
474C23×C4—1061no—
475C23×C4—1061no—
476C23×C4—1061no—
477C23×C4—1061no—
478C2×Q16—24no—
479C2×Q16C22×D5314yes—
480C2×SD16—534no—
481C2×SD16—534no—
482C2×SD16—1064no—
483C2×SD16—1064no—
484C2×D8—534no—
485C2×D8—1064no—
486C22×C8—531no—
487C22×C8—531no—
488C22×C8C22×D5311yescharacteristic
489C22×C8C22×D5311yescharacteristic
490C4⋊Q8—534no—
491C4⋊Q8—1062no—
492#126—1068no—
493#124—534no—
494#124—1068no—
495#124—1062no—
496#123—1068no—
497C22⋊Q8—534no—
498C22⋊Q8—1068no—
499C22⋊Q8—1062no—
500#121—534no—
501#121—1062no—
502C4×Q8—22no—
503C4×Q8—22no—
504C4×Q8—534no—
505C4×Q8—1062no—
506C4×Q8C22×D5314yes—
507C4×Q8C22×D5314yes—
508C4×D4—534no—
509C4×D4—534no—
510C4×D4—534no—
511C4×D4—1068no—
512C4×D4—1062no—
513C4×D4—1068no—
514C4×D4—1062no—
515C4×D4—1062no—
516#117—534no—
517#117—534no—
518#117—1068no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—531no—
522C2×C4⋊C4—531no—
523C2×C4⋊C4—531no—
524C2×C4⋊C4—531no—
525C2×C4⋊C4—534no—
526C2×C4⋊C4—1068no—
527C2×C4⋊C4—1062no—
528C2×C4⋊C4—1061no—
529C2×C4⋊C4—1061no—
530C2×C4⋊C4—1061no—
531C2×C4⋊C4—1061no—
532C2×C4⋊C4C22×D5311yescharacteristic
533C2×C4⋊C4C22×D5311yescharacteristic
534C2×C22⋊C4—531no—
535C2×C22⋊C4—531no—
536C2×C22⋊C4—1061no—
537C2×C22⋊C4—1061no—
538C2×C22⋊C4—1061no—
539C2×C22⋊C4—1061no—
540C2×C22⋊C4—1061no—
541C2×C22⋊C4—1061no—
542C2×C22⋊C4—1061no—
543C2×C42—21no—
544C2×C42—21no—
545C2×C42—531no—
546C2×C42—1061no—
547C2×C42C22×D5311yescharacteristic
548#107—534no—
549#107—534no—
550#107—534no—
551#107C22×D5314yes—
552C4⋊C8—534no—
553C4⋊C8—534no—
554#103—534no—
555#103—534no—
556#103C22×D5314yes—
557#103C22×D5314yes—
558#102—534no—
559#102—534no—
560#102—534no—
561#102—534no—
562C22⋊C8—534no—
563C22⋊C8—534no—
564#97—534no—
565C4×C8C22×D5314yes—
566C24—531no—
567C24—1061no—
568C24—1061no—
569#41—1068no—
570#41—10616no—
571#41—1068no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—22no—
575C2×Q8—22no—
576C2×Q8—22no—
577C2×Q8—1064no—
578C2×Q8—4242no—
579C2×Q8#1171994514yes—
580C2×Q8C23×D5312yes—
581C2×Q8C23×D5312yes—
582C2×D4—534no—
583C2×D4—532no—
584C2×D4—532no—
585C2×D4—1064no—
586C2×D4—1068no—
587C2×D4—1064no—
588C2×D4—1061no—
589C2×D4—1061no—
590C2×D4—1062no—
591C2×D4—1062no—
592C2×D4—1062no—
593C2×D4—4242no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—531no—
599C22×C4—531no—
600C22×C4—531no—
601C22×C4—532no—
602C22×C4—532no—
603C22×C4—1064no—
604C22×C4—1064no—
605C22×C4—1068no—
606C22×C4—1064no—
607C22×C4—1062no—
608C22×C4—1062no—
609C22×C4—1061no—
610C22×C4—1061no—
611C22×C4—1064no—
612C22×C4—1064no—
613C22×C4—4242no—
614C22×C4—4242no—
615C22×C4—4242no—
616C22×C4—4242no—
617C22×C4D4×D5311yescharacteristic
618C22×C4D4×D5311yescharacteristic
619C22×C4C23×D5311yescharacteristic
620Q16—28no—
621SD16—1068no—
622SD16—1068no—
623D8—1068no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—532no—
627C2×C8—532no—
628C2×C8—1062no—
629C2×C8—1062no—
630C2×C8C23×D5312yes—
631C2×C8C23×D5312yes—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—534no—
637C4⋊C4—534no—
638C4⋊C4—532no—
639C4⋊C4—532no—
640C4⋊C4—1064no—
641C4⋊C4—1064no—
642C4⋊C4—1064no—
643C4⋊C4—1064no—
644C4⋊C4—1061no—
645C4⋊C4—1061no—
646C4⋊C4C23×D5312yes—
647C4⋊C4C23×D5312yes—
648C22⋊C4—534no—
649C22⋊C4—534no—
650C22⋊C4—1064no—
651C22⋊C4—1064no—
652C22⋊C4—1064no—
653C22⋊C4—1064no—
654C22⋊C4—1064no—
655C22⋊C4—1064no—
656C22⋊C4—1064no—
657C42—24no—
658C42—24no—
659C42—532no—
660C42—532no—
661C42—1064no—
662C42D4×D5312yes—
663C42C23×D5312yes—
664C23—532no—
665C23—1064no—
666C23—1062no—
667C23—1062no—
668C23—1062no—
669C23—1062no—
670C23—1062no—
671C23—2122no—
672C23—2122no—
673C23—2122no—
674C23—2122no—
675C23—2122no—
676C23C2×D4×D5311yescharacteristic
677Q8—24no—
678Q8—22no—
679Q8—22no—
680Q8—22no—
681Q8—42no—
682Q8—4244no—
683Q8C2×#1171994514yes—
684D4—534no—
685D4—10616no—
686D4—1064no—
687D4—1062no—
688D4—1062no—
689D4—1062no—
690D4—4244no—
691D4—2122no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—532no—
703C2×C4—532no—
704C2×C4—532no—
705C2×C4—10616no—
706C2×C4—1062no—
707C2×C4—1062no—
708C2×C4—1062no—
709C2×C4—1064no—
710C2×C4—1062no—
711C2×C4—1062no—
712C2×C4—1062no—
713C2×C4—1062no—
714C2×C4—4244no—
715C2×C4—4244no—
716C2×C4—4244no—
717C2×C4—4244no—
718C2×C4—2122no—
719C2×C4—2122no—
720C2×C4C2×D4×D5312yes—
721C2×C4C2×D4×D5312yes—
722C2×C4C2×D4×D5311yescharacteristic
723C2×C4#41×D5312yes—
724C2×C4C2×#1171994512yes—
725C2×C4C24×D5311yescharacteristic
726C8—22no—
727C8—22no—
728C8—1062no—
729C8—1062no—
730C22—1062no—
731C22—1062no—
732C22—1064no—
733C22—1062no—
734C22—4244no—
735C22—2122no—
736C22—2122no—
737C22—2122no—
738C22—2124no—
739C22—2128no—
740C22—2122no—
741C22—2122no—
742C22#1681113212yes—
743C22#1681142512yes—
744C22#1681143612yes—
745C22C22×D4×D5311yescharacteristic
746C4—22no—
747C4—22no—
748C4—24no—
749C4—42no—
750C4—42no—
751C4—42no—
752C4—1062no—
753C4—1062no—
754C4—1062no—
755C4—2122no—
756C4—2122no—
757C4#1681113212yes—
758C4C2×#41×D5311yescharacteristic
759C4C22×#1171994511yescharacteristic
760C2—4242no—
761C2—2122no—
762C2—2124no—
763C2#2028498314yesdirect product factor
764C2C2×#1681113211yescharacteristic
765C2C2×#1681142511yescharacteristic
766C2C2×#1681143611yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C4×Q16×C53C2
socleC23×C53C22×D4
prime radicalC2×#16810771C2
hypercenterC2×C4×Q16D53
hypocenterC53C2×#3124
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×#16811245C2semidirect
2. C2×#16811105C2semidirect
3. #20284983C2direct (N × H)
4. C2×#16810957C2semidirect
5. C2×#16810938C2semidirect
6. C2×#16810916C2semidirect
7. C2×#16810902C2semidirect
8. C2×#16810847C2semidirect
9. C2×#16810841C2semidirect
10. C2×#16810784C2semidirect
12. C2×#16810721C2semidirect
13. C2×#16810721C2semidirect
14. C2×C4×D424C2semidirect
15. C2×#16810682C2semidirect
16. C2×C4×Q16×C53C2semidirect
22. #16811245C22semidirect
32. #16811105C22semidirect
43. #16810957C22semidirect
44. #16810938C22semidirect
45. #16810916C22semidirect
46. #16810902C22semidirect
47. #16810847C22semidirect
48. #16810841C22semidirect
49. #16810784C22semidirect
51. #16810721C22semidirect
52. #16810721C22semidirect
53. C4×D424C22semidirect
54. #16810682C22semidirect
72. C4×Q16×C53C22semidirect
390. C2×C4×Q16D53semidirect
393. C2×C53#3124semidirect
439. C4×Q16C2×D53semidirect
460. C53C2×#3124semidirect
763. C2#20284983direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112452
C2×#168111052
#202849832
C2×#168109572
C2×#168109382
C2×#168109162
C2×#168109022
C2×#168108472
C2×#168108412
C2×#168107842
C2×#168107712
C2×#168107212
C2×C4×D4242
C2×#168106822
C2×C4×Q16×C532
C2×#312453