Finite Group Databasebeta

← C2×#20284902 #28252326

Subgroups — C2×#20284902 #28252326

Order 13568.

2274 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811246C211yesmaximal, characteristic, complemented
2C2×#16811097C211yesmaximal, characteristic, complemented
3#20284902C2116yesmaximal, direct product factor
4C2×#16810947C211yesmaximal, characteristic, complemented
5C2×#16810912C211yesmaximal, characteristic, complemented
6C2×#16810902C211yesmaximal, characteristic, complemented
7C2×#16810841C211yesmaximal, characteristic, complemented
8C2×#16810841C211yesmaximal, characteristic, complemented
9C2×#16810773C211yesmaximal, characteristic, complemented
10C2×#16810759C211yesmaximal, characteristic
11C2×#16810734C211yesmaximal, characteristic, complemented
12C2×#16810726C211yesmaximal, characteristic, complemented
13C2×#16810708C211yesmaximal, characteristic, complemented
14C2×#16810705C211yesmaximal, characteristic, complemented
15C2×#16810681C211yesmaximal, characteristic, complemented
16C2×C53×#485C211yesmaximal, characteristic, complemented
17C23×D212C2211yescharacteristic
18C22×#11719924C2211yescharacteristic
19C22×#11719924C2211yescharacteristic
20C22×D424C2211yescharacteristic
21C22×D424C2211yescharacteristic
22#16811246—24no—
23#16811246C2218yescomplemented
24C2×#13133216C2211yescharacteristic, complemented
25C2×#13133212—21no—
26C2×#13133206C2211yescharacteristic, complemented
27C2×#13133203—21no—
28C2×#13133199—21no—
29C2×#13133197—21no—
30C2×#13133191C2211yescharacteristic
31#16811097—24no—
32#16811097C2218yescomplemented
33C2×Q8×Dic53C2211yescharacteristic, complemented
34C2×C4×D212—21no—
35C2×C4×D212—21no—
36C2×#13133179C2211yescharacteristic
37C2×#13133179C2211yescharacteristic
38C2×#13133179C2211yescharacteristic
39C2×#13133179C2211yescharacteristic
40C2×#13133179C2211yescharacteristic, complemented
41C2×#13133176C2211yescharacteristic
42C2×C22⋊C4×D53—21no—
43C2×C22⋊C4×D53—21no—
44#16810947C2218yescomplemented
45#16810912C2218yescomplemented
46#16810902C2218yescomplemented
47#16810841C2218yescomplemented
48#16810841C2218yescomplemented
49#16810773C2218yescomplemented
50#16810759C2218yes—
51#16810734C2218yescomplemented
52#16810726C2218yescomplemented
53#16810708C2218yescomplemented
54#16810705C2218yescomplemented
55#16810681C2218yescomplemented
56C2×#13133150C2211yescharacteristic, complemented
57C2×#13133148C2211yescharacteristic, complemented
58C2×#13133146C2211yescharacteristic, complemented
59C2×#13133146C2211yescharacteristic, complemented
60C2×#13133139C2211yescharacteristic
61C2×#13133139C2211yescharacteristic
62C2×#13133137C2211yescharacteristic
63C2×#13133137C2211yescharacteristic
64C2×#13133137C2211yescharacteristic, complemented
65C2×#13133137C2211yescharacteristic, complemented
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133127C2211yescharacteristic, complemented
68C2×C8×Dic53C2211yescharacteristic, complemented
69C2×C22⋊Q8×C53C2211yescharacteristic
70C2×#117×C53C2211yescharacteristic
71C53×#485C2218yescomplemented
72C2×#107×C53C2211yescharacteristic, complemented
73C2×#106×C53C2211yescharacteristic, complemented
74C2×#103×C53C2211yescharacteristic, complemented
75C2×#103×C53C2211yescharacteristic, complemented
76C2×C22⋊C8×C53C2211yescharacteristic
77C24×D53—21no—
78C22×Dic106—21no—
79C22×D212—21no—
80C22×D212—22no—
81C22×D212—24no—
82C22×D212—24no—
83C22×D212C2314yes—
84C22×D212C2311yescharacteristic
85C22×D212C2311yescharacteristic
86C22×D212C2311yescharacteristic
87C22×C22⋊D53—21no—
88C22×C4×D53—21no—
89C22×C4×D53—21no—
90C22×C4×D53—21no—
91C22×C4×D53—21no—
92C22×C4×D53—21no—
93C2×#11719924—24no—
94C2×#11719924—24no—
95C2×#11719924C2314yes—
96C2×#11719924C2314yes—
97C2×D424—24no—
98C2×D424—24no—
99C2×D424C2314yes—
100C2×D424C2314yes—
101C22×#88322C2311yescharacteristic
102C22×#88322C2311yescharacteristic
103#13133216—22no—
104#13133216C2314yescomplemented
105#13133212—28no—
106#13133206—22no—
107#13133206C2314yescomplemented
108#13133203—28no—
109#13133199—28no—
110#13133197—28no—
111#13133191—22no—
112#13133191C2314yes—
113Q8×Dic53—22no—
114Q8×Dic53C2314yescomplemented
115C4×D212—28no—
116C4×D212—28no—
117#13133179—22no—
118#13133179—22no—
119#13133179—22no—
120#13133179—22no—
121#13133179—22no—
122#13133179C2314yes—
123#13133179C2314yes—
124#13133179C2314yes—
125#13133179C2314yes—
126#13133179C2314yescomplemented
127#13133176D414yes—
128#13133176C2314yes—
129C2×C4⋊Dic53—21no—
130C2×C4⋊Dic53D411yescharacteristic
131C2×C4⋊Dic53D411yescharacteristic
132C2×C4⋊Dic53C2311yescharacteristic
133C2×#11719919—21no—
134C2×C22⋊Dic53D411yescharacteristic
135C2×C22⋊Dic53D411yescharacteristic
136C2×#11719921—21no—
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×#11719921—21no—
143C2×#11719921—21no—
144C22⋊C4×D53—28no—
145C22⋊C4×D53—28no—
146C2×C4×Dic53—21no—
147C2×C4×Dic53C2311yescharacteristic
148C2×C4×Dic53C2311yescharacteristic
149#13133150C2314yescomplemented
150#13133148C2314yescomplemented
151#13133146C2314yescomplemented
152#13133146C2314yescomplemented
153#13133139C2314yes—
154#13133139C2314yes—
155#13133137C2314yes—
156#13133137C2314yes—
157#13133137C2314yescomplemented
158#13133137C2314yescomplemented
159C22⋊#88322C2314yes—
160#13133127C2314yescomplemented
161C8×Dic53C2314yescomplemented
162C22×Q8×C53C2311yescharacteristic
163C23×C4×C53C2311yescharacteristic
164C22×C8×C53C2311yescharacteristic
165C22×C8×C53C2311yescharacteristic
166C22⋊Q8×C53—22no—
167C22⋊Q8×C53C2314yes—
168#117×C53—22no—
169#117×C53C2314yes—
170C2×C4⋊C4×C53—21no—
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C22⋊C4×C53—21no—
175C2×C22⋊C4×C53—21no—
176C2×C42×C53—21no—
177#107×C53C2314yescomplemented
178#106×C53C2314yescomplemented
179#103×C53C2314yescomplemented
180#103×C53C2314yescomplemented
181C22⋊C8×C53C2314yes—
182C24×C53C2×D411yescharacteristic
183C23×D53—21no—
184C23×D53—21no—
185C23×D53—28no—
186C23×D53—24no—
187C23×D53—21no—
188C23×D53—82no—
189C23×D53—82no—
190C2×Q8×C53—21no—
191C2×Q8×C53—22no—
192C2×Q8×C53—22no—
193C2×Q8×C53C2412yes—
194C22×C4×C53—22no—
195C22×C4×C53—22no—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53C2×D411yescharacteristic
201C22×C4×C53C2×D412yes—
202C22×C4×C53C2412yes—
203C22×C4×C53C2411yescharacteristic
204C2×C22⋊D53—24no—
205C2×C22⋊D53—82no—
206C22×Dic53—21no—
207C22×Dic53C2×D411yescharacteristic
208C22×Dic53C2×D411yescharacteristic
209C22×Dic53C2×D411yescharacteristic
210C22×Dic53C2×D411yescharacteristic
211C2×D212—28no—
212C2×D212—216no—
213C2×D212—21no—
214C2×D212—21no—
215C2×D212—24no—
216C2×D212—22no—
217C2×D212—22no—
218C2×D212—28no—
219C2×D212—28no—
220C2×D212—22no—
221C2×D212—22no—
222C2×D212—21no—
223C2×D212#4114yes—
224C2×D212#4114yes—
225C2×D212C2412yes—
226C2×D212C2412yes—
227C2×D212C2412yes—
228C2×C4×D53—24no—
229C2×C4×D53—24no—
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×D53—82no—
237C2×C4×D53—82no—
238C2×Dic106—24no—
239C2×Dic106—82no—
240C2×C8×C53—22no—
241C2×C8×C53—22no—
242C2×C8×C53C2412yes—
243C2×C8×C53C2412yes—
244C4⋊C4×C53—24no—
245C4⋊C4×C53—21no—
246C4⋊C4×C53—21no—
247C4⋊C4×C53—21no—
248C4⋊C4×C53C2412yes—
249C4⋊C4×C53C2412yes—
250C4⋊C4×C53C2412yes—
251C22⋊C4×C53—24no—
252C22⋊C4×C53—24no—
253C42×C53—24no—
254C22⋊Dic53C2×D414yes—
255C22⋊Dic53C2×D414yes—
256#11719924—28no—
257#11719924—28no—
258#11719921—24no—
259#11719921—24no—
260#11719921—24no—
261#11719921—24no—
262#11719921—24no—
263#11719921—24no—
264#11719921—24no—
265#11719921—24no—
266C4⋊Dic53—21no—
267C4⋊Dic53—24no—
268C4⋊Dic53C2×D414yes—
269C4⋊Dic53C2×D414yes—
270C4⋊Dic53C2412yes—
271#11719919—24no—
272C4×Dic53—24no—
273C4×Dic53C2×D412yes—
274C4×Dic53C2×D412yes—
275C4×Dic53C2412yes—
276C4×Dic53C2412yes—
277C2×#88322—22no—
278C2×#88322—22no—
279C2×#88322C2412yes—
280C2×#88322C2412yes—
281D424—28no—
282D424—28no—
283C23×C53—22no—
284C23×C53—22no—
285C23×C53—22no—
286C23×C53C22×D412yes—
287C23×C53C22×D411yescharacteristic
288C22×D53—24no—
289C22×D53—24no—
290C22×D53—22no—
291C22×D53—22no—
292C22×D53—216no—
293C22×D53—22no—
294C22×D53—42no—
295C22×D53—42no—
296C22×D53—42no—
297C22×D53—42no—
298C22×D53—42no—
299C22×D53—42no—
300C22×D53—42no—
301C22×D53—84no—
302C22×D53—84no—
303C22×D53—816no—
304Q8×C53—22no—
305Q8×C53—22no—
306Q8×C53—42no—
307C2×C4×C53—22no—
308C2×C4×C53—24no—
309C2×C4×C53—22no—
310C2×C4×C53—22no—
311C2×C4×C53—22no—
312C2×C4×C53—22no—
313C2×C4×C53—22no—
314C2×C4×C53—22no—
315C2×C4×C53—42no—
316C2×C4×C53—42no—
317C2×C4×C53—42no—
318C2×C4×C53—42no—
319C2×C4×C53C22×D412yes—
320C2×C4×C53C22×D411yescharacteristic
321C2×C4×C53C2×#4112yes—
322C2×C4×C53C2×#4112yes—
323C2×C4×C53C2511yescharacteristic
324C22⋊D53—84no—
325C2×Dic53—22no—
326C2×Dic53—22no—
327C2×Dic53—22no—
328C2×Dic53—22no—
329C2×Dic53—22no—
330C2×Dic53—42no—
331C2×Dic53C22×D412yes—
332C2×Dic53C22×D412yes—
333C2×Dic53C22×D412yes—
334C2×Dic53C22×D412yes—
335D212—216no—
336D212—24no—
337D212—24no—
338D212—22no—
339D212—22no—
340D212—22no—
341D212—22no—
342D212—42no—
343D212C2×#4114yes—
344D212C2×#4114yes—
345C4×D53—84no—
346C4×D53—84no—
347C4×D53—84no—
348C4×D53—84no—
349C4×D53—84no—
350Dic106—84no—
351C8×C53—22no—
352C8×C53—22no—
353#88322—22no—
354#88322—22no—
355C2×#3118—531nomaximal, Sylow
356C22×C53—22no—
357C22×C53—22no—
358C22×C53—22no—
359C22×C53—44no—
360C22×C53#52512yes—
361C22×C53#57612yes—
362C22×C53#57712yes—
363C22×C53C23×D411yescharacteristic
364C2×D53—24no—
365C2×D53—24no—
366C2×D53—48no—
367C2×D53—48no—
368C2×D53—42no—
369C2×D53—42no—
370C2×D53—42no—
371C2×D53—42no—
372C2×D53—42no—
373C2×D53—42no—
374C2×D53—42no—
375C2×D53—816no—
376C2×D53—84no—
377C4×C53—22no—
378C4×C53—42no—
379C4×C53—42no—
380C4×C53—42no—
381C4×C53—42no—
382C4×C53#52512yes—
383C4×C53C22×#4111yescharacteristic
384C4×C53C22×#4111yescharacteristic
385Dic53—22no—
386Dic53—22no—
387Dic53—22no—
388Dic53—22no—
389Dic53—42no—
390C2×#542—531no—
391C2×#518—531no—
392#3118—5316no—
393C2×#485D5311yescharacteristic, complemented
394C2×#482—531no—
395C2×#476—531no—
396C2×#474—531no—
397C2×#463—531no—
398C2×#463—531no—
399C2×#450—531no—
400C2×#447—531no—
401C2×#442—531no—
402C2×#440—531no—
403C2×C4×SD16—531no—
404C2×C4×D8—531no—
405C2×#433—531no—
406C2×C53—42no—
407C2×C53#311814yescomplemented
408C2×C53C2×#52511yescharacteristic
409C2×C53C2×#57611yescharacteristic
410C2×C53C2×#57711yescharacteristic
411D53—44no—
412D53—44no—
413D53—82no—
414C23×D4—531no—
415C22×SD16—531no—
416C22×SD16—531no—
417C22×D8—531no—
418C22×D8—531no—
419#542—538no—
420#542—1064no—
421C2×C4⋊Q8—531no—
422C2×#126—1061no—
423C2×#124—531no—
424C2×#124—1061no—
425C2×#123—1061no—
426C2×C22⋊Q8—1061no—
427C2×C22⋊Q8C2×D5311yescharacteristic
428C2×#121—531no—
429#518—538no—
430#518—1064no—
431C2×C4×Q8—531no—
432C2×C4×D4—531no—
433C2×C4×D4—531no—
434C2×C4×D4—531no—
435C2×C4×D4—531no—
436C2×C4×D4—531no—
437C2×C4×D4—1061no—
438C2×C4×D4—1061no—
439C2×#117—531no—
440C2×#117C2×D5311yescharacteristic
441C22×C22⋊C4—1061no—
442C22×C22⋊C4—1061no—
443#485C2×D5318yescomplemented
444#482—538no—
445#476—538no—
446#474—538no—
447#463—538no—
448#463—538no—
449#450—538no—
450#447—538no—
451#442—538no—
452#440—538no—
453C4×SD16—538no—
454C4×D8—538no—
455#433—538no—
456C2×#107—531no—
457C2×#107C2×D5311yescharacteristic, complemented
458C2×#106—531no—
459C2×#106C2×D5311yescharacteristic, complemented
460C2×C4⋊C8—531no—
461C2×C4⋊C8—531no—
462C2×#103C2×D5311yescharacteristic, complemented
463C2×#103C2×D5311yescharacteristic, complemented
464C2×#102—531no—
465C2×#102—531no—
466C2×#102—531no—
467C2×#102—531no—
468C2×#102—531no—
469C2×#102—531no—
470C2×C22⋊C8—531no—
471C2×C22⋊C8C2×D5311yescharacteristic
472C2×#97—531no—
473C2×C4×C8—531no—
474C53C2×#311811yescharacteristic, complemented, Sylow
475C25—1061no—
476C22×Q8—1061no—
477C22×Q8C22×D5311yescharacteristic
478C22×D4—531no—
479C22×D4—531no—
480C22×D4—531no—
481C22×D4—534no—
482C22×D4—1064no—
483C22×D4—1064no—
484C22×D4—1061no—
485C22×D4—1061no—
486C22×D4—1062no—
487C23×C4—1061no—
488C23×C4—1061no—
489C23×C4—1061no—
490C23×C4—1061no—
491C23×C4—1061no—
492C23×C4C22×D5311yescharacteristic
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
505C4⋊Q8—534no—
506C4⋊Q8—1062no—
507#126—1068no—
508#124—534no—
509#124—1062no—
510#124—1068no—
511#123—1068no—
512C22⋊Q8—22no—
513C22⋊Q8—1068no—
514C22⋊Q8C22×D5314yes—
515#121—534no—
516#121—1062no—
517C4×Q8—534no—
518C4×Q8—1062no—
519C4×D4—534no—
520C4×D4—534no—
521C4×D4—534no—
522C4×D4—534no—
523C4×D4—534no—
524C4×D4—1068no—
525C4×D4—1068no—
526C4×D4—1062no—
527C4×D4—1062no—
528C4×D4—1062no—
529C4×D4—1062no—
530C4×D4—1062no—
531#117—22no—
532#117—534no—
533#117—534no—
534#117C22×D5314yes—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—531no—
537C2×C4⋊C4—531no—
538C2×C4⋊C4—531no—
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—21no—
546C2×C22⋊C4—531no—
547C2×C22⋊C4—531no—
548C2×C22⋊C4—1068no—
549C2×C22⋊C4—1068no—
550C2×C22⋊C4—1061no—
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—531no—
560C2×C42—531no—
561C2×C42—1061no—
562#107—534no—
563#107C22×D5314yescomplemented
564#106—534no—
565#106C22×D5314yescomplemented
566C4⋊C8—534no—
567C4⋊C8—534no—
568#103C22×D5314yescomplemented
569#103C22×D5314yescomplemented
570#102—534no—
571#102—534no—
572#102—534no—
573#102—534no—
574#102—534no—
575#102—534no—
576C22⋊C8—534no—
577C22⋊C8C22×D5314yes—
578#97—534no—
579C4×C8—534no—
580C24—1068no—
581C24—1064no—
582C24—1061no—
583C24—1061no—
584C24—1061no—
585C24—4242no—
586C24—4242no—
587C24D4×D5311yescharacteristic
588C2×Q8—21no—
589C2×Q8—22no—
590C2×Q8—22no—
591C2×Q8—1064no—
592C2×Q8—4242no—
593C2×Q8C23×D5312yes—
594C2×D4—534no—
595C2×D4—534no—
596C2×D4—532no—
597C2×D4—532no—
598C2×D4—532no—
599C2×D4—1068no—
600C2×D4—1068no—
601C2×D4—1068no—
602C2×D4—10616no—
603C2×D4—1064no—
604C2×D4—1064no—
605C2×D4—1061no—
606C2×D4—1061no—
607C2×D4—1061no—
608C2×D4—1062no—
609C2×D4—1062no—
610C2×D4—1062no—
611C2×D4—1062no—
612C2×D4—4242no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—531no—
620C22×C4—531no—
621C22×C4—531no—
622C22×C4—531no—
623C22×C4—1064no—
624C22×C4—1064no—
625C22×C4—1064no—
626C22×C4—1064no—
627C22×C4—1064no—
628C22×C4—1061no—
629C22×C4—4242no—
630C22×C4—4242no—
631C22×C4—4242no—
632C22×C4—4242no—
633C22×C4—4242no—
634C22×C4D4×D5312yes—
635C22×C4D4×D5311yescharacteristic
636C22×C4C23×D5312yes—
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—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—534no—
655C4⋊C4—534no—
656C4⋊C4—532no—
657C4⋊C4—1064no—
658C4⋊C4—1064no—
659C4⋊C4—1061no—
660C4⋊C4C23×D5312yes—
661C4⋊C4C23×D5312yes—
662C4⋊C4C23×D5312yes—
663C22⋊C4—24no—
664C22⋊C4—24no—
665C22⋊C4—534no—
666C22⋊C4—534no—
667C22⋊C4—1064no—
668C22⋊C4—1064no—
669C22⋊C4—1064no—
670C22⋊C4—1064no—
671C22⋊C4—1064no—
672C22⋊C4—1064no—
673C22⋊C4—1064no—
674C22⋊C4—1064no—
675C42—24no—
676C42—532no—
677C42—532no—
678C42—532no—
679C42—532no—
680C42—1064no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—10616no—
685C23—1064no—
686C23—1064no—
687C23—1062no—
688C23—1062no—
689C23—1062no—
690C23—4244no—
691C23—4244no—
692C23—42416no—
693C23—2122no—
694C23—2122no—
695C23—2122no—
696C23—2122no—
697C23—2122no—
698C23—2122no—
699C23—2122no—
700C23C2×D4×D5312yes—
701C23C2×D4×D5311yescharacteristic
702Q8—22no—
703Q8—22no—
704Q8—42no—
705Q8—4244no—
706D4—534no—
707D4—534no—
708D4—10616no—
709D4—1064no—
710D4—1064no—
711D4—1062no—
712D4—1062no—
713D4—1062no—
714D4—1062no—
715D4—4244no—
716D4—2122no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—532no—
730C2×C4—532no—
731C2×C4—532no—
732C2×C4—532no—
733C2×C4—1062no—
734C2×C4—1062no—
735C2×C4—1062no—
736C2×C4—1062no—
737C2×C4—1062no—
738C2×C4—4244no—
739C2×C4—4244no—
740C2×C4—4244no—
741C2×C4—4244no—
742C2×C4—4244no—
743C2×C4—2122no—
744C2×C4C2×D4×D5312yes—
745C2×C4C2×D4×D5311yescharacteristic
746C2×C4#41×D5312yes—
747C2×C4#41×D5312yes—
748C2×C4C24×D5311yescharacteristic
749C8—22no—
750C8—22no—
751C8—1062no—
752C8—1062no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—44no—
757C22—1064no—
758C22—1064no—
759C22—42416no—
760C22—4244no—
761C22—2122no—
762C22—2122no—
763C22—2122no—
764C22—2122no—
765C22—2122no—
766C22—2122no—
767C22—2122no—
768C22—2128no—
769C22—2128no—
770C22#1681113112yes—
771C22#1681142512yes—
772C22#1681143212yes—
773C22C22×D4×D5311yescharacteristic
774C4—22no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—1062no—
780C4—1062no—
781C4—1062no—
782C4—1062no—
783C4—2122no—
784C4#1681113112yes—
785C4C2×#41×D5311yescharacteristic
786C4C2×#41×D5311yescharacteristic
787C2—42no—
788C2—4242no—
789C2—2124no—
790C2—2124no—
791C2#2028490214yesdirect product factor
792C2C2×#1681113111yescharacteristic
793C2C2×#1681142511yescharacteristic
794C2C2×#1681143211yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#485C2
socleC23×C53C22×D4
prime radicalC2×#16810759C2
hypercenterC2×#485D53
hypocenterC53C2×#3118
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
1. C2×#16811246C2semidirect
2. C2×#16811097C2semidirect
3. #20284902C2direct (N × H)
4. C2×#16810947C2semidirect
5. C2×#16810912C2semidirect
6. C2×#16810902C2semidirect
7. C2×#16810841C2semidirect
8. C2×#16810841C2semidirect
9. C2×#16810773C2semidirect
11. C2×#16810734C2semidirect
12. C2×#16810726C2semidirect
13. C2×#16810708C2semidirect
14. C2×#16810705C2semidirect
15. C2×#16810681C2semidirect
16. C2×C53×#485C2semidirect
23. #16811246C22semidirect
24. C2×#13133216C22semidirect
26. C2×#13133206C22semidirect
32. #16811097C22semidirect
33. C2×Q8×Dic53C22semidirect
40. C2×#13133179C22semidirect
44. #16810947C22semidirect
45. #16810912C22semidirect
46. #16810902C22semidirect
47. #16810841C22semidirect
48. #16810841C22semidirect
49. #16810773C22semidirect
51. #16810734C22semidirect
52. #16810726C22semidirect
53. #16810708C22semidirect
54. #16810705C22semidirect
55. #16810681C22semidirect
56. C2×#13133150C22semidirect
57. C2×#13133148C22semidirect
58. C2×#13133146C22semidirect
59. C2×#13133146C22semidirect
64. C2×#13133137C22semidirect
65. C2×#13133137C22semidirect
67. C2×#13133127C22semidirect
68. C2×C8×Dic53C22semidirect
71. C53×#485C22semidirect
72. C2×#107×C53C22semidirect
73. C2×#106×C53C22semidirect
74. C2×#103×C53C22semidirect
75. C2×#103×C53C22semidirect
104. #13133216C23semidirect
107. #13133206C23semidirect
114. Q8×Dic53C23semidirect
126. #13133179C23semidirect
149. #13133150C23semidirect
150. #13133148C23semidirect
151. #13133146C23semidirect
152. #13133146C23semidirect
157. #13133137C23semidirect
158. #13133137C23semidirect
160. #13133127C23semidirect
161. C8×Dic53C23semidirect
177. #107×C53C23semidirect
178. #106×C53C23semidirect
179. #103×C53C23semidirect
180. #103×C53C23semidirect
393. C2×#485D53semidirect
407. C2×C53#3118semidirect
443. #485C2×D53semidirect
457. C2×#107C2×D53semidirect
459. C2×#106C2×D53semidirect
462. C2×#103C2×D53semidirect
463. C2×#103C2×D53semidirect
474. C53C2×#3118semidirect
563. #107C22×D53semidirect
565. #106C22×D53semidirect
568. #103C22×D53semidirect
569. #103C22×D53semidirect
791. C2#20284902direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112462
C2×#168110972
#202849022
C2×#168109472
C2×#168109122
C2×#168109022
C2×#168108412
C2×#168107732
C2×#168107592
C2×#168107342
C2×#168107262
C2×#168107082
C2×#168107052
C2×#168106812
C2×C53×#4852
C2×#311853