Finite Group Databasebeta

← C2×#20287425 #28263746

Subgroups — C2×#20287425 #28263746

Order 13568.

2198 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811329C211yesmaximal, characteristic, complemented
2C2×#16811294C211yesmaximal, characteristic, complemented
3#20287425C2116yesmaximal, direct product factor
4C2×#16810989C211yesmaximal, characteristic, complemented
5C2×#16810986C211yesmaximal, characteristic, complemented
6C2×#16810968C211yesmaximal, characteristic, complemented
7C2×#16810926C211yesmaximal, characteristic, complemented
8C2×#16810912C211yesmaximal, characteristic, complemented
9C2×#16810819C211yesmaximal, characteristic, complemented
10C2×#16810817C211yesmaximal, characteristic, complemented
11C2×#16810817C211yesmaximal, characteristic, complemented
12C2×#16810752C211yesmaximal, characteristic, complemented
13C2×#16810734C211yesmaximal, characteristic, complemented
14C2×#16810733C211yesmaximal, characteristic, complemented
15C2×#16810705C211yesmaximal, characteristic, complemented
16C2×C53×#478C211yesmaximal, characteristic, complemented
17C22×#11719945—21no—
18C22×D424C2211yescharacteristic
19C22×D424C2211yescharacteristic
20C22×#11719922C2211yescharacteristic
21#16811329—24no—
22#16811329C2218yescomplemented
23#16811294—24no—
24#16811294C2218yescomplemented
25C2×#13133216C2211yescharacteristic
26C2×#13133214C2211yescharacteristic
27C2×#13133213C2211yescharacteristic
28C2×#13133213C2211yescharacteristic
29C2×#13133208C2211yescharacteristic
30C2×#13133197—21no—
31C2×#13133195—21no—
32C2×#13133195—21no—
33C2×#13133191—21no—
34C2×#13133190—21no—
35C2×#13133190—21no—
36C2×C4×Dic106C2211yescharacteristic
37C2×C4×D212C2211yescharacteristic
38C2×#13133179C2211yescharacteristic
39C2×#13133179C2211yescharacteristic
40C2×#13133179C2211yescharacteristic
41C2×#13133179C2211yescharacteristic
42C2×C4⋊C4×D53—21no—
43#16810989C2218yescomplemented
44#16810986C2218yescomplemented
45#16810968C2218yescomplemented
46#16810926C2218yescomplemented
47#16810912C2218yescomplemented
48#16810819C2218yescomplemented
49#16810817C2218yescomplemented
50#16810817C2218yescomplemented
51#16810752C2218yescomplemented
52#16810734C2218yescomplemented
53#16810733C2218yescomplemented
54#16810705C2218yescomplemented
55C2×#13133148C2211yescharacteristic
56C2×#13133146C2211yescharacteristic
57C2×#13133146C2211yescharacteristic
58C2×#13133139C2211yescharacteristic
59C2×#13133139C2211yescharacteristic
60C2×#13133138C2211yescharacteristic
61C2×#13133137C2211yescharacteristic
62C2×#13133137C2211yescharacteristic
63C2×#13133137C2211yescharacteristic
64C2×#13133137C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×#13133128C2211yescharacteristic
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×#11719945—28no—
78C2×#11719945—48no—
79C22×Dic106—21no—
80C22×Dic106D411yescharacteristic
81C22×D212—21no—
82C22×D212—21no—
83C22×D212C2311yescharacteristic
84C22×D212C2311yescharacteristic
85C22×D212C2311yescharacteristic
86C22×C22⋊D53—21no—
87C22×C22⋊D53—21no—
88C22×C22⋊D53—21no—
89C22×C22⋊D53—21no—
90C22×C4×D53—21no—
91C22×C4×D53—21no—
92C22×C4×D53—21no—
93C22×C4×D53—21no—
94C22×C4×D53—21no—
95C2×D424—24no—
96C2×D424—24no—
97C2×D424C2314yes—
98C2×D424C2314yes—
99C2×#11719922—24no—
100C2×#11719922C2314yes—
101C22×#88322C2311yescharacteristic
102C22×#88322C2311yescharacteristic
103#13133216—22no—
104#13133216C2314yes—
105#13133214—22no—
106#13133214C2314yes—
107#13133213—22no—
108#13133213—22no—
109#13133213C2314yes—
110#13133213C2314yes—
111#13133208—22no—
112#13133208C2314yes—
113#13133197—28no—
114#13133195—28no—
115#13133195—28no—
116#13133191—28no—
117#13133190—28no—
118#13133190—28no—
119C4×Dic106D414yes—
120C4×Dic106C2314yes—
121C4×D212—22no—
122C4×D212C2314yes—
123#13133179—22no—
124#13133179—22no—
125#13133179—22no—
126#13133179—22no—
127#13133179C2314yes—
128#13133179C2314yes—
129#13133179C2314yes—
130#13133179C2314yes—
131C2×C4⋊Dic53—21no—
132C2×C4⋊Dic53D411yescharacteristic
133C2×C4⋊Dic53C2311yescharacteristic
134C2×#11719919—21no—
135C2×#11719919—21no—
136C2×#11719919D411yescharacteristic
137C2×#11719919D411yescharacteristic
138C4⋊C4×D53—28no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×#11719921—21no—
143C2×#11719921—21no—
144C2×C4×Dic53C2311yescharacteristic
145C2×C4×Dic53C2311yescharacteristic
146#13133148C2314yes—
147#13133146C2314yes—
148#13133146C2314yes—
149#13133139C2314yes—
150#13133139C2314yes—
151#13133138C2314yes—
152#13133137C2314yes—
153#13133137C2314yes—
154#13133137C2314yes—
155#13133137C2314yes—
156#13133137C2314yes—
157#13133128C2314yes—
158#13133127C2314yes—
159C8×Dic53C2314yes—
160C22×D4×C53C2311yescharacteristic
161C23×C4×C53—21no—
162C22×C8×C53C2311yescharacteristic
163C22×C8×C53C2311yescharacteristic
164#125×C53—22no—
165#125×C53C2314yes—
166C4×D4×C53—22no—
167C4×D4×C53C2314yes—
168C2×C4⋊C4×C53—21no—
169C2×C4⋊C4×C53—21no—
170C2×C4⋊C4×C53C2311yescharacteristic
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C22⋊C4×C53—21no—
174C2×C42×C53C2311yescharacteristic
175#107×C53C2314yes—
176#106×C53C2314yes—
177C4⋊C8×C53C2314yes—
178#102×C53C2314yes—
179#102×C53C2314yes—
180C24×C53—21no—
181C23×D53—21no—
182C23×D53—21no—
183C23×D53—21no—
184C2×D4×C53—21no—
185C2×D4×C53—22no—
186C2×D4×C53—22no—
187C2×D4×C53C2412yes—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53—21no—
191C22×C4×C53—24no—
192C22×C4×C53—44no—
193C22×C4×C53C2×D411yescharacteristic
194C22×C4×C53C2×D411yescharacteristic
195C22×C4×C53C2411yescharacteristic
196C2×C22⋊D53—24no—
197C2×C22⋊D53—24no—
198C2×C22⋊D53—24no—
199C2×C22⋊D53—24no—
200C2×C22⋊D53—44no—
201C2×C22⋊D53—44no—
202C2×C22⋊D53—82no—
203C2×C22⋊D53—82no—
204C22×Dic53—21no—
205C22×Dic53C2×D411yescharacteristic
206C22×Dic53C2×D411yescharacteristic
207C22×Dic53C2×D411yescharacteristic
208C22×Dic53C2×D411yescharacteristic
209#11719945—432no—
210C2×D212—21no—
211C2×D212—22no—
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—44no—
221C2×D212—82no—
222C2×D212#4114yescomplemented
223C2×D212C2412yes—
224C2×D212C2412yes—
225C2×D212C2412yes—
226C2×C4×D53—24no—
227C2×C4×D53—24no—
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×D53—82no—
235C2×C4×D53—82no—
236C2×Dic106—24no—
237C2×Dic106—24no—
238C2×Dic106—82no—
239C2×Dic106C2×D414yes—
240C2×C8×C53—22no—
241C2×C8×C53—22no—
242C2×C8×C53C2412yes—
243C2×C8×C53C2412yes—
244C4⋊C4×C53—24no—
245C4⋊C4×C53—24no—
246C4⋊C4×C53—21no—
247C4⋊C4×C53—21no—
248C4⋊C4×C53—21no—
249C4⋊C4×C53C2412yes—
250C4⋊C4×C53C2412yes—
251C4⋊C4×C53C2412yes—
252C22⋊C4×C53—24no—
253C42×C53C2×D412yes—
254C42×C53C2412yes—
255#11719922—28no—
256#11719921—24no—
257#11719921—24no—
258#11719921—24no—
259#11719921—24no—
260#11719921—24no—
261C4⋊Dic53—21no—
262C4⋊Dic53—24no—
263C4⋊Dic53C2×D414yes—
264C4⋊Dic53C2412yes—
265#11719919—24no—
266#11719919—24no—
267#11719919C2×D414yes—
268#11719919C2×D414yes—
269C4×Dic53C2×D412yes—
270C4×Dic53C2×D412yes—
271C4×Dic53C2412yes—
272C4×Dic53C2412yes—
273C2×#88322—22no—
274C2×#88322—22no—
275C2×#88322C2412yes—
276C2×#88322C2412yes—
277D424—28no—
278D424—28no—
279C23×C53—22no—
280C23×C53—42no—
281C23×C53—42no—
282C23×C53—42no—
283C23×C53C22×D411yescharacteristic
284C22×D53—24no—
285C22×D53—22no—
286C22×D53—22no—
287C22×D53—22no—
288C22×D53—42no—
289C22×D53—42no—
290C22×D53—42no—
291C22×D53—42no—
292C22×D53—42no—
293C22×D53—42no—
294C22×D53—42no—
295C22×D53—42no—
296D4×C53—22no—
297D4×C53—22no—
298D4×C53—42no—
299C2×C4×C53—22no—
300C2×C4×C53—22no—
301C2×C4×C53—22no—
302C2×C4×C53—22no—
303C2×C4×C53—22no—
304C2×C4×C53—48no—
305C2×C4×C53—42no—
306C2×C4×C53—42no—
307C2×C4×C53—42no—
308C2×C4×C53C22×D412yes—
309C2×C4×C53C22×D412yes—
310C2×C4×C53C22×D411yescharacteristic
311C2×C4×C53C2×#4112yes—
312C2×C4×C532−1+412yes—
313C2×C4×C53C2511yescharacteristic
314C22⋊D53—48no—
315C22⋊D53—48no—
316C22⋊D53—84no—
317C22⋊D53—84no—
318C2×Dic53—22no—
319C2×Dic53—22no—
320C2×Dic53—22no—
321C2×Dic53—22no—
322C2×Dic53—42no—
323C2×Dic53AGL(1,ℤ/8)14yes—
324C2×Dic53C22×D412yes—
325C2×Dic53C22×D412yes—
326C2×Dic53C22×D412yes—
327C2×Dic53C22×D412yes—
328D212—24no—
329D212—22no—
330D212—22no—
331D212—22no—
332D212—22no—
333D212—22no—
334D212—48no—
335D212—42no—
336D212—42no—
337D212—84no—
338D212C2×#4114yescomplemented
339C4×D53—48no—
340C4×D53—48no—
341C4×D53—48no—
342C4×D53—84no—
343C4×D53—84no—
344Dic106—28no—
345Dic106—84no—
346C8×C53—22no—
347C8×C53—22no—
348#88322—22no—
349#88322—22no—
350C2×#3366—531nomaximal, Sylow
351C22×C53—42no—
352C22×C53—42no—
353C22×C53—42no—
354C22×C53—84no—
355C22×C53#54812yes—
356C22×C53C2×AGL(1,ℤ/8)12yes—
357C22×C53#57612yes—
358C22×C53C23×D411yescharacteristic
359C2×D53—24no—
360C2×D53—48no—
361C2×D53—42no—
362C2×D53—42no—
363C2×D53—42no—
364C2×D53—42no—
365C2×D53—42no—
366C2×D53—42no—
367C2×D53—42no—
368C2×D53—42no—
369C2×D53—84no—
370C2×D53—84no—
371C4×C53—22no—
372C4×C53—22no—
373C4×C53—42no—
374C4×C53—42no—
375C4×C53—42no—
376C4×C53#54812yes—
377C4×C53C22×#4111yescharacteristic
378C4×C53C2×2−1+411yescharacteristic
379Dic53—22no—
380Dic53—22no—
381Dic53—22no—
382Dic53—42no—
383Dic53C2×AGL(1,ℤ/8)14yes—
384C2×#554—531no—
385C2×#550—531no—
386#3366—5316no—
387C2×#490—531no—
388C2×#490—531no—
389C2×#486—531no—
390C2×#478—531no—
391C2×#478D5311yescharacteristic, complemented
392C2×#476—531no—
393C2×#459—531no—
394C2×#459—531no—
395C2×#459—531no—
396C2×#446—531no—
397C2×#442—531no—
398C2×#442—531no—
399C2×C4×D8—531no—
400C2×C53—82no—
401C2×C53#336614yescomplemented
402C2×C53C2×#54811yescharacteristic
403C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
404C2×C53C2×#57611yescharacteristic
405D53—44no—
406D53—82no—
407D53—82no—
408C22×#41—1061no—
409C22×D8—531no—
410C22×D8—531no—
411C22×D8—531no—
412#554—538no—
413#554—1064no—
414#550—538no—
415#550—1064no—
416C2×C4⋊Q8—531no—
417C2×#127—531no—
418C2×#127—531no—
419C2×#127—531no—
420C2×#125—531no—
421C2×#125C2×D5311yescharacteristic
422C2×C22⋊Q8—1061no—
423C2×C22⋊Q8—1061no—
424C2×C22⋊Q8—1061no—
425C2×#121—1061no—
426C2×#121—1061no—
427C2×#121—1061no—
428C2×C4×Q8—531no—
429C2×C4×D4—531no—
430C2×C4×D4—531no—
431C2×C4×D4—531no—
432C2×C4×D4—531no—
433C2×C4×D4—531no—
434C2×C4×D4C2×D5311yescharacteristic
435C22×C4⋊C4—1061no—
436#490—538no—
437#490—538no—
438#486—538no—
439#478—538no—
440#478C2×D5318yescomplemented
441#476—538no—
442#459—538no—
443#459—538no—
444#459—538no—
445#446—538no—
446#442—538no—
447#442—538no—
448C4×D8—538no—
449C2×#107C2×D5311yescharacteristic
450C2×#106—531no—
451C2×#106C2×D5311yescharacteristic
452C2×C4⋊C8—531no—
453C2×C4⋊C8—531no—
454C2×C4⋊C8C2×D5311yescharacteristic
455C2×#102—531no—
456C2×#102—531no—
457C2×#102—531no—
458C2×#102—531no—
459C2×#102—531no—
460C2×#102—531no—
461C2×#102—531no—
462C2×#102—531no—
463C2×#102C2×D5311yescharacteristic
464C2×#102C2×D5311yescharacteristic
465C2×#97—531no—
466C2×#97—531no—
467C2×C4×C8—531no—
468C53C2×#336611yescharacteristic, complemented, Sylow
469C2×#41—1068no—
470C2×#41—2128no—
471C22×Q8—531no—
472C22×Q8—1061no—
473C22×D4—531no—
474C22×D4—531no—
475C22×D4—531no—
476C22×D4—1061no—
477C22×D4—1061no—
478C22×D4—1061no—
479C22×D4—1061no—
480C22×D4—1061no—
481C22×D4—1061no—
482C22×D4C22×D5311yescharacteristic
483C23×C4—21no—
484C23×C4—1061no—
485C23×C4—1061no—
486C23×C4—1061no—
487C23×C4—1061no—
488C23×C4—1061no—
489C2×D8—534no—
490C2×D8—534no—
491C2×D8—534no—
492C2×D8—1064no—
493C2×D8—1064no—
494C2×D8—1064no—
495C22×C8—531no—
496C22×C8—531no—
497C22×C8C22×D5311yescharacteristic
498C22×C8C22×D5311yescharacteristic
499C4⋊Q8—534no—
500C4⋊Q8—1062no—
501#127—534no—
502#127—534no—
503#127—534no—
504#127—1062no—
505#127—1062no—
506#127—1062no—
507#125—22no—
508#125—534no—
509#125—1062no—
510#125C22×D5314yes—
511C22⋊Q8—1068no—
512C22⋊Q8—1068no—
513C22⋊Q8—1068no—
514#121—1068no—
515#121—1068no—
516#121—1068no—
517C4×Q8—534no—
518C4×Q8—534no—
519C4×D4—22no—
520C4×D4—534no—
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—1062no—
530C4×D4C22×D5314yes—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—531no—
534C2×C4⋊C4—531no—
535C2×C4⋊C4—531no—
536C2×C4⋊C4—531no—
537C2×C4⋊C4—1068no—
538C2×C4⋊C4—1061no—
539C2×C4⋊C4—1061no—
540C2×C4⋊C4—1061no—
541C2×C4⋊C4C22×D5311yescharacteristic
542C2×C4⋊C4C22×D5311yescharacteristic
543C2×C4⋊C4C22×D5311yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—1061no—
546C2×C22⋊C4—1061no—
547C2×C22⋊C4—1061no—
548C2×C22⋊C4—1061no—
549C2×C22⋊C4—1061no—
550C2×C42—531no—
551C2×C42—531no—
552C2×C42C22×D5311yescharacteristic
553#107C22×D5314yes—
554#106—534no—
555#106C22×D5314yes—
556C4⋊C8—534no—
557C4⋊C8—534no—
558C4⋊C8C22×D5314yes—
559#102—534no—
560#102—534no—
561#102—534no—
562#102—534no—
563#102—534no—
564#102—534no—
565#102—534no—
566#102—534no—
567#102C22×D5314yes—
568#102C22×D5314yes—
569#97—534no—
570#97—534no—
571C4×C8—534no—
572C24—21no—
573C24—1061no—
574C24—1061no—
575C24—1061no—
576#41—21232no—
577C2×Q8—534no—
578C2×Q8—1064no—
579C2×Q8—1064no—
580C2×Q8—4242no—
581C2×D4—21no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—534no—
585C2×D4—532no—
586C2×D4—532no—
587C2×D4—532no—
588C2×D4—1064no—
589C2×D4—1064no—
590C2×D4—1064no—
591C2×D4—1064no—
592C2×D4—1061no—
593C2×D4—1064no—
594C2×D4—1061no—
595C2×D4—1061no—
596C2×D4—1064no—
597C2×D4—1062no—
598C2×D4—1062no—
599C2×D4—1062no—
600C2×D4—1062no—
601C2×D4—1062no—
602C2×D4—4242no—
603C2×D4—4242no—
604C2×D4—4242no—
605C2×D4—2124no—
606C2×D4—2124no—
607C2×D4—2124no—
608C2×D4C23×D5312yes—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—24no—
613C22×C4—44no—
614C22×C4—531no—
615C22×C4—531no—
616C22×C4—531no—
617C22×C4—531no—
618C22×C4—1064no—
619C22×C4—1064no—
620C22×C4—1064no—
621C22×C4—1064no—
622C22×C4—1061no—
623C22×C4—1064no—
624C22×C4—4242no—
625C22×C4—4242no—
626C22×C4—2124no—
627C22×C4—2124no—
628C22×C4—2124no—
629C22×C4D4×D5311yescharacteristic
630C22×C4D4×D5311yescharacteristic
631C22×C4C23×D5311yescharacteristic
632D8—1068no—
633D8—1068no—
634D8—1068no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—532no—
638C2×C8—532no—
639C2×C8—1062no—
640C2×C8—1062no—
641C2×C8C23×D5312yes—
642C2×C8C23×D5312yes—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—534no—
649C4⋊C4—534no—
650C4⋊C4—534no—
651C4⋊C4—532no—
652C4⋊C4—1064no—
653C4⋊C4—1064no—
654C4⋊C4—1064no—
655C4⋊C4—1061no—
656C4⋊C4C23×D5312yes—
657C4⋊C4C23×D5312yes—
658C4⋊C4C23×D5312yes—
659C22⋊C4—24no—
660C22⋊C4—1064no—
661C22⋊C4—1064no—
662C22⋊C4—1064no—
663C22⋊C4—1064no—
664C22⋊C4—1064no—
665C42—532no—
666C42—532no—
667C42—532no—
668C42—532no—
669C42D4×D5312yes—
670C42C23×D5312yes—
671C23—22no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—1064no—
676C23—1062no—
677C23—1062no—
678C23—1062no—
679C23—2122no—
680C23—2122no—
681C23—2122no—
682C23—2122no—
683C23—2122no—
684C23—2122no—
685C23—2122no—
686C23—2122no—
687C23C2×D4×D5311yescharacteristic
688Q8—1068no—
689Q8—4244no—
690D4—22no—
691D4—22no—
692D4—42no—
693D4—534no—
694D4—1064no—
695D4—1062no—
696D4—1062no—
697D4—1062no—
698D4—1062no—
699D4—1062no—
700D4—4244no—
701D4—4244no—
702D4—4244no—
703D4—2128no—
704D4—2128no—
705D4—2128no—
706D4—2122no—
707D4—2122no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—48no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—534no—
718C2×C4—532no—
719C2×C4—532no—
720C2×C4—532no—
721C2×C4—532no—
722C2×C4—1062no—
723C2×C4—1062no—
724C2×C4—1062no—
725C2×C4—1062no—
726C2×C4—4244no—
727C2×C4—4244no—
728C2×C4—2128no—
729C2×C4—2128no—
730C2×C4—2128no—
731C2×C4—2122no—
732C2×C4C2×D4×D5312yes—
733C2×C4C2×D4×D5312yes—
734C2×C4C2×D4×D5311yescharacteristic
735C2×C4#41×D5312yes—
736C2×C4#1313326512yes—
737C2×C4C24×D5311yescharacteristic
738C8—22no—
739C8—22no—
740C8—1062no—
741C8—1062no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—84no—
746C22—1064no—
747C22—4244no—
748C22—4244no—
749C22—2122no—
750C22—2122no—
751C22—2122no—
752C22—2122no—
753C22—2122no—
754C22—2122no—
755C22—2122no—
756C22—2122no—
757C22—2128no—
758C22#1681128312yes—
759C22AGL(1,ℤ/8)×D5312yes—
760C22#1681142512yes—
761C22C22×D4×D5311yescharacteristic
762C4—22no—
763C4—22no—
764C4—42no—
765C4—42no—
766C4—42no—
767C4—534no—
768C4—1062no—
769C4—1062no—
770C4—1062no—
771C4—2122no—
772C4#1681128312yes—
773C4C2×#41×D5311yescharacteristic
774C4C2×#1313326511yescharacteristic
775C2—82no—
776C2—4242no—
777C2—4242no—
778C2—2124no—
779C2#2028742514yesdirect product factor
780C2C2×#1681128311yescharacteristic
781C2C2×AGL(1,ℤ/8)×D5311yescharacteristic
782C2C2×#1681142511yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#478C2
socleC23×C53C22×D4
hypercenterC2×#478D53
hypocenterC53C2×#3366
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×#16811329C2semidirect
2. C2×#16811294C2semidirect
3. #20287425C2direct (N × H)
4. C2×#16810989C2semidirect
5. C2×#16810986C2semidirect
6. C2×#16810968C2semidirect
7. C2×#16810926C2semidirect
8. C2×#16810912C2semidirect
9. C2×#16810819C2semidirect
10. C2×#16810817C2semidirect
11. C2×#16810817C2semidirect
12. C2×#16810752C2semidirect
13. C2×#16810734C2semidirect
14. C2×#16810733C2semidirect
15. C2×#16810705C2semidirect
16. C2×C53×#478C2semidirect
22. #16811329C22semidirect
24. #16811294C22semidirect
43. #16810989C22semidirect
44. #16810986C22semidirect
45. #16810968C22semidirect
46. #16810926C22semidirect
47. #16810912C22semidirect
48. #16810819C22semidirect
49. #16810817C22semidirect
50. #16810817C22semidirect
51. #16810752C22semidirect
52. #16810734C22semidirect
53. #16810733C22semidirect
54. #16810705C22semidirect
71. C53×#478C22semidirect
222. C2×D212#41semidirect
338. D212C2×#41semidirect
391. C2×#478D53semidirect
401. C2×C53#3366semidirect
440. #478C2×D53semidirect
468. C53C2×#3366semidirect
779. C2#20287425direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113292
C2×#168112942
#202874252
C2×#168109892
C2×#168109862
C2×#168109682
C2×#168109262
C2×#168109122
C2×#168108192
C2×#168108172
C2×#168107522
C2×#168107342
C2×#168107332
C2×#168107052
C2×C53×#4782
C2×#336653