Finite Group Databasebeta

← C2×#20287057 #28262499

Subgroups — C2×#20287057 #28262499

Order 13568.

2374 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×#16811274C211yesmaximal, characteristic, complemented
2C2×#16811273C211yesmaximal, characteristic, complemented
3#20287057C2116yesmaximal, direct product factor
4C2×#16811027C211yesmaximal, characteristic, complemented
5C2×#16810938C211yesmaximal, characteristic, complemented
6C2×#16810937C211yesmaximal, characteristic, complemented
7C2×#16810935C211yesmaximal, characteristic, complemented
8C2×#16810902C211yesmaximal, characteristic, complemented
9C2×#16810901C211yesmaximal, characteristic, complemented
10C2×#16810858C211yesmaximal, characteristic, complemented
11C2×#16810857C211yesmaximal, characteristic, complemented
12C2×#16810703C211yesmaximal, characteristic, complemented
13C2×#16810686C211yesmaximal, characteristic, complemented
14C22×#13133150C211yesmaximal, characteristic, complemented
15C2×#107×D53C211yesmaximal, characteristic, complemented
16C2×C53×#480C211yesmaximal, characteristic, complemented
17C22×#11719945—21no—
18C22×#11719947—21no—
19C22×#11719922C2211yescharacteristic
20C23×#88322C2211yescharacteristic
21C22×C8×D53C2211yescharacteristic
22#16811274—24no—
23#16811274C2218yescomplemented
24#16811273—24no—
25#16811273C2218yescomplemented
26C2×#13133216C2211yescharacteristic
27C2×#13133216C2211yescharacteristic
28C2×#13133202—21no—
29C2×#13133200—21no—
30C2×#13133199—21no—
31C2×#13133198—21no—
32C2×#13133195—21no—
33C2×#13133194—21no—
34C2×#13133192C2211yescharacteristic
35C2×#13133191C2211yescharacteristic
36C2×#13133188C2211yescharacteristic
37C2×D4×Dic53C2211yescharacteristic
38C2×#13133179C2211yescharacteristic
39C2×C4×C22⋊D53C2211yescharacteristic
40C22×C4⋊Dic53C2211yescharacteristic
41C2×C4⋊C4×D53C2211yescharacteristic
42C2×C4⋊C4×D53C2211yescharacteristic
43#16811027C2218yescomplemented
44#16810938C2218yescomplemented
45#16810937C2218yescomplemented
46#16810935C2218yescomplemented
47#16810902C2218yescomplemented
48#16810901C2218yescomplemented
49#16810858C2218yescomplemented
50#16810857C2218yescomplemented
51#16810703C2218yescomplemented
52#16810686C2218yescomplemented
53C2×#13133151C2211yescharacteristic
54C2×#13133151C2211yescharacteristic
55C2×#13133150C2211yescharacteristic
56C2×#13133150C2211yescharacteristic
57C2×#13133150C2211yescharacteristic
58C2×#13133150C2211yescharacteristic
59C2×#13133150C2211yescharacteristic
60C2×#13133150C2218yescomplemented
61#107×D53C2218yescomplemented
62C2×#13133146C2211yescharacteristic
63C2×#13133139C2211yescharacteristic
64C2×#13133139C2211yescharacteristic
65C2×#13133138C2211yescharacteristic
66C2×#13133137C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
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—28no—
78C2×#11719945—48no—
79C2×#11719947—28no—
80C2×#11719947—48no—
81C22×Dic106—21no—
82C22×Dic106—21no—
83C22×D212—21no—
84C22×D212C2311yescharacteristic
85C22×C22⋊D53—21no—
86C22×C22⋊D53—21no—
87C22×C22⋊D53D411yescharacteristic
88C23×Dic53—21no—
89C23×Dic53—21no—
90C22×C4×D53—21no—
91C22×C4×D53—21no—
92C22×C4×D53—21no—
93C22×C4×D53C2311yescharacteristic
94C2×#11719922—24no—
95C2×#11719922C2314yes—
96C22×#88322—24no—
97C22×#88322C2311yescharacteristic
98C22×#88322C2314yes—
99C22×#88322C2311yescharacteristic
100C2×C8×D53—24no—
101C2×C8×D53C2314yes—
102#13133216—22no—
103#13133216—22no—
104#13133216C2314yes—
105#13133216C2314yes—
106#13133202—28no—
107#13133200—28no—
108#13133199—28no—
109#13133198—28no—
110#13133195—28no—
111#13133194—28no—
112#13133192—22no—
113#13133192C2314yes—
114#13133191—22no—
115#13133191C2314yes—
116#13133188—22no—
117#13133188C2314yes—
118D4×Dic53—22no—
119D4×Dic53C2314yes—
120#13133179—22no—
121#13133179C2314yes—
122C4×C22⋊D53D414yes—
123C4×C22⋊D53C2314yes—
124C2×C4⋊Dic53—22no—
125C2×C4⋊Dic53—21no—
126C2×C4⋊Dic53C2314yes—
127C2×C4⋊Dic53C2311yescharacteristic
128C2×C4⋊Dic53C2311yescharacteristic
129C2×C4⋊Dic53C2311yescharacteristic
130C2×#11719919—21no—
131C2×#11719919—21no—
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×#11719919D411yescharacteristic
135C4⋊C4×D53—22no—
136C4⋊C4×D53—22no—
137C4⋊C4×D53C2314yes—
138C4⋊C4×D53C2314yes—
139C2×C22⋊Dic53—21no—
140C2×C22⋊Dic53—21no—
141C2×C22⋊Dic53D411yescharacteristic
142C2×#11719921—21no—
143C2×#11719921—21no—
144C2×#11719921—21no—
145C2×#11719921D411yescharacteristic
146C2×C4×Dic53C2311yescharacteristic
147#13133151C2314yes—
148#13133151C2314yes—
149#13133150C2314yes—
150#13133150C2314yes—
151#13133150C2314yes—
152#13133150C2314yes—
153#13133150C2314yes—
154#13133146C2314yes—
155#13133139C2314yes—
156#13133139C2314yes—
157#13133138C2314yes—
158#13133137C2314yes—
159#13133129C2314yes—
160C8×Dic53C2314yes—
161C22×D4×C53—21no—
162C22×D4×C53C2311yescharacteristic
163C23×C4×C53—21no—
164C23×C4×C53C2311yescharacteristic
165C22×C8×C53C2311yescharacteristic
166C22×C8×C53C2311yescharacteristic
167#121×C53—22no—
168#121×C53C2314yes—
169C2×C4⋊C4×C53—22no—
170C2×C4⋊C4×C53—21no—
171C2×C4⋊C4×C53C2314yes—
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C22⋊C4×C53—21no—
176#107×C53C2314yes—
177#107×C53C2314yes—
178#102×C53C2314yes—
179#102×C53C2314yes—
180C22⋊C8×C53C2314yes—
181C24×C53—21no—
182C24×C53C2×D411yescharacteristic
183C23×D53—21no—
184C23×D53C2×D411yescharacteristic
185C2×D4×C53—24no—
186C2×D4×C53—21no—
187C2×D4×C53—22no—
188C2×D4×C53—22no—
189C2×D4×C53—44no—
190C2×D4×C53C2412yes—
191C22×C4×C53—22no—
192C22×C4×C53—22no—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53—24no—
197C22×C4×C53—44no—
198C22×C4×C53C2×D411yescharacteristic
199C22×C4×C53C2×D412yes—
200C22×C4×C53C2412yes—
201C22×C4×C53C2411yescharacteristic
202C2×C22⋊D53—24no—
203C2×C22⋊D53—24no—
204C2×C22⋊D53—44no—
205C2×C22⋊D53—44no—
206C2×C22⋊D53D818yescomplemented
207C2×C22⋊D53C2×D414yes—
208C22×Dic53—21no—
209C22×Dic53—21no—
210C22×Dic53—21no—
211C22×Dic53—24no—
212C22×Dic53—24no—
213C22×Dic53—44no—
214C22×Dic53—44no—
215C22×Dic53C2×D411yescharacteristic
216C22×Dic53C2×D411yescharacteristic
217C22×Dic53C2×D411yescharacteristic
218#11719947—432no—
219#11719945—432no—
220C2×D212—22no—
221C2×D212—22no—
222C2×D212—24no—
223C2×D212—21no—
224C2×D212—44no—
225C2×D212C2412yes—
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×D53C2412yes—
236C2×Dic106—24no—
237C2×Dic106—24no—
238C2×Dic106—44no—
239C2×Dic106—44no—
240C2×C8×C53—22no—
241C2×C8×C53—22no—
242C2×C8×C53C2412yes—
243C2×C8×C53C2412yes—
244C4⋊C4×C53—21no—
245C4⋊C4×C53—21no—
246C4⋊C4×C53—24no—
247C4⋊C4×C53—21no—
248C4⋊C4×C53C2412yes—
249C4⋊C4×C53C2412yes—
250C4⋊C4×C53C2412yes—
251C22⋊C4×C53—24no—
252C22⋊Dic53—24no—
253C22⋊Dic53—24no—
254C22⋊Dic53C2×D414yes—
255#11719922—28no—
256#11719921—24no—
257#11719921—24no—
258#11719921—24no—
259#11719921C2×D414yes—
260C4⋊Dic53—21no—
261C4⋊Dic53—21no—
262C4⋊Dic53—21no—
263C4⋊Dic53—24no—
264C4⋊Dic53C2412yes—
265C4⋊Dic53C2412yes—
266C4⋊Dic53C2412yes—
267#11719919—24no—
268#11719919—24no—
269#11719919—24no—
270#11719919—24no—
271#11719919C2×D414yes—
272C4×Dic53C2×D412yes—
273C4×Dic53C2412yes—
274C2×#88322—22no—
275C2×#88322—28no—
276C2×#88322#4114yescomplemented
277C2×#88322C2412yes—
278C2×#88322C2412yes—
279C8×D53—28no—
280C23×C53—22no—
281C23×C53—22no—
282C23×C53—22no—
283C23×C53—42no—
284C23×C53—42no—
285C23×C53—42no—
286C23×C53C2×D814yes—
287C23×C53C22×D412yes—
288C23×C53C22×D411yescharacteristic
289C22×D53—22no—
290C22×D53—22no—
291C22×D53—22no—
292C22×D53—42no—
293C22×D53—42no—
294C22×D53—42no—
295C22×D53C2×D814yes—
296C22×D53C22×D412yes—
297D4×C53—22no—
298D4×C53—22no—
299D4×C53—48no—
300D4×C53—42no—
301C2×C4×C53—22no—
302C2×C4×C53—24no—
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—48no—
312C2×C4×C53C22×D412yes—
313C2×C4×C53C22×D411yescharacteristic
314C2×C4×C53C2×#4112yes—
315C2×C4×C532−1+412yes—
316C2×C4×C53C2511yescharacteristic
317C22⋊D53—48no—
318C22⋊D53—48no—
319C22⋊D53C2×D8116yescomplemented
320C2×Dic53—22no—
321C2×Dic53—22no—
322C2×Dic53—22no—
323C2×Dic53—22no—
324C2×Dic53—22no—
325C2×Dic53—42no—
326C2×Dic53—42no—
327C2×Dic53—42no—
328C2×Dic53—48no—
329C2×Dic53—48no—
330C2×Dic53C2×D814yes—
331C2×Dic53C22×D412yes—
332C2×Dic53C22×D412yes—
333C2×Dic53C22×D412yes—
334D212—22no—
335D212—22no—
336D212—48no—
337D212—42no—
338C4×D53—24no—
339C4×D53—22no—
340C4×D53—22no—
341C4×D53—48no—
342C4×D53—48no—
343C4×D53—48no—
344Dic106—48no—
345Dic106—48no—
346C8×C53—22no—
347C8×C53—22no—
348#88322—22no—
349#88322C2×#4114yescomplemented
350C2×#3334—531nomaximal, Sylow
351C22×C53—28no—
352C22×C53—22no—
353C22×C53—22no—
354C22×C53—42no—
355C22×C53—42no—
356C22×C53—42no—
357C22×C53—84no—
358C22×C53#54712yes—
359C22×C53C22×D814yes—
360C22×C53C22×D812yes—
361C22×C53#57812yes—
362C22×C53C23×D411yescharacteristic
363C2×D53—28no—
364C2×D53—22no—
365C2×D53—22no—
366C2×D53—42no—
367C2×D53—42no—
368C2×D53—42no—
369C2×D53—84no—
370C2×D53C22×D814yes—
371C4×C53—22no—
372C4×C53—42no—
373C4×C53—42no—
374C4×C53—42no—
375C4×C53#54712yes—
376C4×C53C22×#4111yescharacteristic
377C4×C53C2×2−1+411yescharacteristic
378Dic53—22no—
379Dic53—22no—
380Dic53—42no—
381Dic53—42no—
382Dic53—42no—
383Dic53C22×D814yes—
384C2×#547—531no—
385C2×#547—531no—
386#3334—5316no—
387C2×#500—531no—
388C2×#480—531no—
389C2×#480—531no—
390C2×#480—531no—
391C2×#480D5311yescharacteristic, complemented
392C2×#474—531no—
393C2×#474—531no—
394C2×#466—531no—
395C2×#466—531no—
396C2×C4×D8—531no—
397C2×C8×D4—531no—
398C22×#107—531no—
399C22×#107—531no—
400C2×C53—24no—
401C2×C53—82no—
402C2×C53#333414yescomplemented
403C2×C53C2×#54711yescharacteristic
404C2×C53C23×D811yescharacteristic
405C2×C53C2×#57811yescharacteristic
406D53—24no—
407D53—82no—
408C22×#41—1061no—
409C22×#41—1061no—
410C22×D8—531no—
411C23×C8—531no—
412C23×C8—531no—
413#547—538no—
414#547—538no—
415#547—1064no—
416#547—1064no—
417C2×C4⋊Q8—531no—
418C2×C4⋊Q8—531no—
419C2×#123—1061no—
420C2×#123—1061no—
421C2×#123—1061no—
422C2×#123—1061no—
423C2×C22⋊Q8—1061no—
424C2×C22⋊Q8—1061no—
425C2×#121—531no—
426C2×#121—531no—
427C2×#121—531no—
428C2×#121C2×D5311yescharacteristic
429C2×C4×D4—531no—
430C2×C4×D4—531no—
431C2×C4×D4—531no—
432C22×C4⋊C4—531no—
433C22×C4⋊C4—531no—
434C22×C4⋊C4—531no—
435C22×C4⋊C4C2×D5311yescharacteristic
436#500—538no—
437#480—538no—
438#480—538no—
439#480—538no—
440#480C2×D5318yescomplemented
441#474—538no—
442#474—538no—
443#466—538no—
444#466—538no—
445C4×D8—538no—
446C8×D4—538no—
447C2×#107—531no—
448C2×#107—531no—
449C2×#107—538no—
450C2×#107—531no—
451C2×#107—531no—
452C2×#107—531no—
453C2×#107—531no—
454C2×#107—531no—
455C2×#107—538no—
456C2×#107C2×D5311yescharacteristic
457C2×#107C2×D5311yescharacteristic
458C2×C4⋊C8—531no—
459C2×#102—531no—
460C2×#102—531no—
461C2×#102—531no—
462C2×#102—531no—
463C2×#102C2×D5311yescharacteristic
464C2×#102C2×D5311yescharacteristic
465C2×C22⋊C8—531no—
466C2×C22⋊C8C2×D5311yescharacteristic
467C2×C4×C8—531no—
468C53C2×#333411yescharacteristic, complemented, Sylow
469C2×#41—1068no—
470C2×#41—1068no—
471C2×#41—2128no—
472C2×#41—2128no—
473C22×Q8—1061no—
474C22×Q8—1061no—
475C22×D4—21no—
476C22×D4—531no—
477C22×D4—531no—
478C22×D4—1061no—
479C22×D4—1061no—
480C22×D4—1061no—
481C22×D4C22×D5311yescharacteristic
482C23×C4—21no—
483C23×C4—531no—
484C23×C4—1061no—
485C23×C4—1061no—
486C23×C4—1061no—
487C23×C4—1061no—
488C23×C4—1061no—
489C23×C4C22×D5311yescharacteristic
490C2×D8—534no—
491C2×D8—1064no—
492C22×C8—531no—
493C22×C8—531no—
494C22×C8—534no—
495C22×C8—534no—
496C22×C8—1064no—
497C22×C8—1064no—
498C22×C8C22×D5311yescharacteristic
499C22×C8C22×D5311yescharacteristic
500C4⋊Q8—534no—
501C4⋊Q8—534no—
502C4⋊Q8—1062no—
503C4⋊Q8—1062no—
504#123—1068no—
505#123—1068no—
506#123—1068no—
507#123—1068no—
508C22⋊Q8—1068no—
509C22⋊Q8—1068no—
510#121—22no—
511#121—534no—
512#121—534no—
513#121—534no—
514#121—1062no—
515#121—1062no—
516#121—1062no—
517#121C22×D5314yes—
518C4×D4—534no—
519C4×D4—534no—
520C4×D4—534no—
521C4×D4—534no—
522C4×D4—1062no—
523C4×D4—1062no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—22no—
526C2×C4⋊C4—531no—
527C2×C4⋊C4—531no—
528C2×C4⋊C4—531no—
529C2×C4⋊C4—531no—
530C2×C4⋊C4—534no—
531C2×C4⋊C4—534no—
532C2×C4⋊C4—534no—
533C2×C4⋊C4—1062no—
534C2×C4⋊C4—1062no—
535C2×C4⋊C4—1061no—
536C2×C4⋊C4—1061no—
537C2×C4⋊C4—1061no—
538C2×C4⋊C4—1061no—
539C2×C4⋊C4—1061no—
540C2×C4⋊C4—1062no—
541C2×C4⋊C4C22×D5311yescharacteristic
542C2×C4⋊C4C22×D5311yescharacteristic
543C2×C4⋊C4C22×D5311yescharacteristic
544C2×C4⋊C4C22×D5314yes—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—531no—
547C2×C22⋊C4—531no—
548C2×C22⋊C4—1061no—
549C2×C22⋊C4—1061no—
550C2×C22⋊C4—1061no—
551C2×C22⋊C4—1061no—
552C2×C22⋊C4—1061no—
553C2×C42—531no—
554#107—534no—
555#107—534no—
556#107—534no—
557#107—534no—
558#107—534no—
559#107—534no—
560#107—534no—
561#107C22×D5314yes—
562#107C22×D5314yes—
563C4⋊C8—534no—
564#102—534no—
565#102—534no—
566#102—534no—
567#102—534no—
568#102C22×D5314yes—
569#102C22×D5314yes—
570C22⋊C8—534no—
571C22⋊C8C22×D5314yes—
572C4×C8—534no—
573C24—21no—
574C24—531no—
575C24—1061no—
576C24D4×D5311yescharacteristic
577#41—21232no—
578#41—21232no—
579C2×Q8—1064no—
580C2×Q8—1064no—
581C2×Q8—2124no—
582C2×Q8—2124no—
583C2×D4—24no—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—44no—
588C2×D4—538no—
589C2×D4—534no—
590C2×D4—532no—
591C2×D4—1064no—
592C2×D4—1064no—
593C2×D4—1064no—
594C2×D4—1061no—
595C2×D4—1062no—
596C2×D4—1062no—
597C2×D4—2124no—
598C2×D4—2124no—
599C2×D4—2124no—
600C2×D4C23×D5312yes—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—24no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—44no—
608C22×C4—531no—
609C22×C4—531no—
610C22×C4—531no—
611C22×C4—532no—
612C22×C4—532no—
613C22×C4—1064no—
614C22×C4—1064no—
615C22×C4—1064no—
616C22×C4—1064no—
617C22×C4—1062no—
618C22×C4—1062no—
619C22×C4—1064no—
620C22×C4—1061no—
621C22×C4—1061no—
622C22×C4—1061no—
623C22×C4—2124no—
624C22×C4—2124no—
625C22×C4—2124no—
626C22×C4—2124no—
627C22×C4—2124no—
628C22×C4D4×D5312yes—
629C22×C4D4×D5311yescharacteristic
630C22×C4C23×D5312yes—
631C22×C4C23×D5311yescharacteristic
632D8—1068no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—534no—
636C2×C8—532no—
637C2×C8—532no—
638C2×C8—1068no—
639C2×C8—1068no—
640C2×C8—1062no—
641C2×C8C23×D5312yes—
642C2×C8C23×D5312yes—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—24no—
646C4⋊C4—21no—
647C4⋊C4—534no—
648C4⋊C4—532no—
649C4⋊C4—532no—
650C4⋊C4—532no—
651C4⋊C4—1064no—
652C4⋊C4—1064no—
653C4⋊C4—1064no—
654C4⋊C4—1064no—
655C4⋊C4—1061no—
656C4⋊C4—1061no—
657C4⋊C4—1061no—
658C4⋊C4—1064no—
659C4⋊C4C23×D5312yes—
660C4⋊C4C23×D5312yes—
661C4⋊C4C23×D5312yes—
662C22⋊C4—24no—
663C22⋊C4—534no—
664C22⋊C4—534no—
665C22⋊C4—1064no—
666C22⋊C4—1064no—
667C22⋊C4—1064no—
668C22⋊C4—1064no—
669C22⋊C4—1064no—
670C42—532no—
671C42—532no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—534no—
679C23—532no—
680C23—1062no—
681C23—1062no—
682C23—1062no—
683C23—2122no—
684C23—2122no—
685C23—2122no—
686C23D8×D5314yes—
687C23C2×D4×D5312yes—
688C23C2×D4×D5311yescharacteristic
689Q8—2128no—
690Q8—2128no—
691D4—22no—
692D4—22no—
693D4—48no—
694D4—42no—
695D4—5316no—
696D4—1062no—
697D4—1062no—
698D4—2128no—
699D4—2128no—
700D4—2128no—
701D4—2122no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—48no—
712C2×C4—42no—
713C2×C4—534no—
714C2×C4—532no—
715C2×C4—532no—
716C2×C4—532no—
717C2×C4—1062no—
718C2×C4—1062no—
719C2×C4—1064no—
720C2×C4—1062no—
721C2×C4—1062no—
722C2×C4—1062no—
723C2×C4—1062no—
724C2×C4—1062no—
725C2×C4—2128no—
726C2×C4—2128no—
727C2×C4—2128no—
728C2×C4—2128no—
729C2×C4—2122no—
730C2×C4—2122no—
731C2×C4—2122no—
732C2×C4—2128no—
733C2×C4C2×D4×D5312yes—
734C2×C4C2×D4×D5311yescharacteristic
735C2×C4#41×D5312yes—
736C2×C4#1313326412yes—
737C2×C4C24×D5311yescharacteristic
738C8—22no—
739C8—22no—
740C8—534no—
741C8—1062no—
742C22—28no—
743C22—22no—
744C22—22no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—84no—
749C22—534no—
750C22—1068no—
751C22—1062no—
752C22—1062no—
753C22—4244no—
754C22—2122no—
755C22—2122no—
756C22—2122no—
757C22#1681127112yes—
758C22C2×D8×D5314yes—
759C22C2×D8×D5312yes—
760C22#1681143912yes—
761C22C22×D4×D5311yescharacteristic
762C4—22no—
763C4—42no—
764C4—42no—
765C4—42no—
766C4—534no—
767C4—1062no—
768C4—1062no—
769C4—2122no—
770C4—2122no—
771C4—2122no—
772C4#1681127112yes—
773C4C2×#41×D5311yescharacteristic
774C4C2×#1313326411yescharacteristic
775C2—24no—
776C2—82no—
777C2—1064no—
778C2—4242no—
779C2#2028705714yesdirect product factor
780C2C2×#1681127111yescharacteristic
781C2C22×D8×D5311yescharacteristic
782C2C2×#1681143911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#480C2
socleC23×C53C22×D4
hypercenterC2×#480D53
hypocenterC53C2×#3334
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×#16811274C2semidirect
2. C2×#16811273C2semidirect
3. #20287057C2direct (N × H)
4. C2×#16811027C2semidirect
5. C2×#16810938C2semidirect
6. C2×#16810937C2semidirect
7. C2×#16810935C2semidirect
8. C2×#16810902C2semidirect
9. C2×#16810901C2semidirect
10. C2×#16810858C2semidirect
11. C2×#16810857C2semidirect
12. C2×#16810703C2semidirect
13. C2×#16810686C2semidirect
14. C22×#13133150C2semidirect
15. C2×#107×D53C2semidirect
16. C2×C53×#480C2semidirect
23. #16811274C22semidirect
25. #16811273C22semidirect
43. #16811027C22semidirect
44. #16810938C22semidirect
45. #16810937C22semidirect
46. #16810935C22semidirect
47. #16810902C22semidirect
48. #16810901C22semidirect
49. #16810858C22semidirect
50. #16810857C22semidirect
51. #16810703C22semidirect
52. #16810686C22semidirect
60. C2×#13133150C22semidirect
61. #107×D53C22semidirect
71. C53×#480C22semidirect
206. C2×C22⋊D53D8semidirect
276. C2×#88322#41semidirect
319. C22⋊D53C2×D8semidirect
349. #88322C2×#41semidirect
391. C2×#480D53semidirect
402. C2×C53#3334semidirect
440. #480C2×D53semidirect
468. C53C2×#3334semidirect
779. C2#20287057direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112742
C2×#168112732
#202870572
C2×#168110272
C2×#168109382
C2×#168109372
C2×#168109352
C2×#168109022
C2×#168109012
C2×#168108582
C2×#168108572
C2×#168107032
C2×#168106862
C22×#131331502
C2×#107×D532
C2×C53×#4802
C2×#333453