Finite Group Databasebeta

← C2×#20286785 #28260830

Subgroups — C2×#20286785 #28260830

Order 13568.

2114 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×#16811344C211yesmaximal, characteristic, complemented
2C2×#16811280C211yesmaximal, characteristic
3#20286785C2116yesmaximal, direct product factor
4C2×#16810981C211yesmaximal, characteristic, complemented
5C2×#16810965C211yesmaximal, characteristic, complemented
6C2×#16810946C211yesmaximal, characteristic, complemented
7C2×#16810916C211yesmaximal, characteristic, complemented
8C2×#16810866C211yesmaximal, characteristic, complemented
9C2×#16810862C211yesmaximal, characteristic, complemented
10C2×#16810843C211yesmaximal, characteristic, complemented
11C2×#16810777C211yesmaximal, characteristic, complemented
12C2×#16810730C211yesmaximal, characteristic, complemented
13C2×#16810691C211yesmaximal, characteristic, complemented
14C2×#16810630C211yesmaximal, characteristic, complemented
15C2×#16810619C211yesmaximal, characteristic, complemented
16C2×C53×#452C211yesmaximal, characteristic, complemented
17C22×Q8×D53C2211yescharacteristic
18C22×#11719925C2211yescharacteristic
19C22×#11719912C2211yescharacteristic
20C23×#88322C2211yescharacteristic
21#16811344—24no—
22#16811344C2218yescomplemented
23#16811280—24no—
24#16811280C2218yes—
25C2×#13133216C2211yescharacteristic
26C2×#13133212—21no—
27C2×#13133210—21no—
28C2×#13133204—21no—
29C2×#13133204C2211yescharacteristic
30C2×#13133203—21no—
31C2×#13133196—21no—
32C2×#13133196C2211yescharacteristic
33C2×#13133193C2211yescharacteristic
34C2×#13133188—21no—
35C2×#13133188C2211yescharacteristic
36C2×Q8×Dic53C2211yescharacteristic
37C2×Q8×Dic53C2211yescharacteristic
38C2×#13133182—21no—
39C2×C4×C22⋊D53—21no—
40C2×C4×C22⋊D53C2211yescharacteristic
41C2×#13133176C2211yescharacteristic
42C2×#13133175C2211yescharacteristic
43#16810981C2218yescomplemented
44#16810965C2218yescomplemented
45#16810946C2218yescomplemented
46#16810916C2218yescomplemented
47#16810866C2218yescomplemented
48#16810862C2218yescomplemented
49#16810843C2218yescomplemented
50#16810777C2218yescomplemented
51#16810730C2218yescomplemented
52#16810691C2218yescomplemented
53C2×#13133151C2211yescharacteristic
54C2×#13133150C2211yescharacteristic
55C2×#13133149C2211yescharacteristic
56C2×#13133146C2211yescharacteristic
57#16810630C2218yescomplemented
58#16810619C2218yescomplemented
59C2×#13133142C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133141C2211yescharacteristic
62C2×#13133141C2211yescharacteristic
63C2×#13133141C2211yescharacteristic
64C2×#13133140C2211yescharacteristic
65C2×#13133138C2211yescharacteristic
66C2×#13133138C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133127C2211yescharacteristic
69C22×#41×C53C2211yescharacteristic
70C22×Q16×C53C2211yescharacteristic
71C22×SD16×C53C2211yescharacteristic
72C2×C22⋊Q8×C53C2211yescharacteristic
73C53×#452C2218yescomplemented
74C2×#103×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106—21no—
79C22×Dic106C2311yescharacteristic
80C2×Q8×D53—22no—
81C2×Q8×D53—24no—
82C2×Q8×D53—42no—
83C2×Q8×D53C2314yes—
84C22×C22⋊D53—21no—
85C22×C22⋊D53D411yescharacteristic
86C22×C4×D53—21no—
87C22×C4×D53C2311yescharacteristic
88C2×#11719925—42no—
89C2×#11719925C2314yes—
90C2×#11719912—42no—
91C2×#11719912C2314yes—
92C22×#88322—42no—
93C22×#88322C2311yescharacteristic
94C22×#88322C2311yescharacteristic
95C22×#88322C2314yes—
96#13133216—22no—
97#13133216C2314yes—
98#13133212—28no—
99#13133210—28no—
100#13133204—28no—
101#13133204—22no—
102#13133204C2314yes—
103#13133203—28no—
104#13133196—28no—
105#13133196—22no—
106#13133196C2314yes—
107#13133193—22no—
108#13133193C2314yes—
109#13133188—28no—
110#13133188—22no—
111#13133188C2314yes—
112Q8×Dic53—22no—
113Q8×Dic53—22no—
114Q8×Dic53C2314yes—
115Q8×Dic53C2314yes—
116#13133182—28no—
117C4×C22⋊D53—28no—
118C4×C22⋊D53D414yes—
119C4×C22⋊D53C2314yes—
120#13133176—22no—
121#13133176C2314yes—
122#13133175—22no—
123#13133175C2314yes—
124C2×C4⋊Dic53—21no—
125C2×C4⋊Dic53—21no—
126C2×C4⋊Dic53C2311yescharacteristic
127C2×C4⋊Dic53C2311yescharacteristic
128C2×C4⋊Dic53C2311yescharacteristic
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919—21no—
132C2×#11719919D411yescharacteristic
133C2×C22⋊Dic53—21no—
134C2×C22⋊Dic53—21no—
135C2×C22⋊Dic53—21no—
136C2×C22⋊Dic53—21no—
137C2×C22⋊Dic53—21no—
138C2×C22⋊Dic53D411yescharacteristic
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921D411yescharacteristic
142C2×C4×Dic53—21no—
143C2×C4×Dic53—21no—
144C2×C4×Dic53—21no—
145C2×C4×Dic53—21no—
146C2×C4×Dic53C2311yescharacteristic
147#13133151C2314yes—
148#13133150C2314yes—
149#13133149C2314yes—
150#13133146C2314yes—
151#13133142C2314yes—
152#13133142C2314yes—
153#13133141C2314yes—
154#13133141C2314yes—
155#13133141C2314yes—
156#13133140C2314yes—
157#13133138C2314yes—
158#13133138C2314yes—
159#13133129C2314yes—
160#13133127C2314yes—
161C2×#41×C53—22no—
162C2×#41×C53—24no—
163C2×#41×C53—42no—
164C2×#41×C53C2314yes—
165C22×Q8×C53C2311yescharacteristic
166C22×Q8×C53C2311yescharacteristic
167C22×D4×C53—21no—
168C22×D4×C53C2311yescharacteristic
169C23×C4×C53—21no—
170C23×C4×C53C2311yescharacteristic
171C2×Q16×C53—24no—
172C2×Q16×C53C2314yes—
173C2×SD16×C53—42no—
174C2×SD16×C53C2314yes—
175C22×C8×C53C2311yescharacteristic
176C22×C8×C53C2311yescharacteristic
177C22⋊Q8×C53—22no—
178C22⋊Q8×C53C2314yes—
179C2×C4⋊C4×C53—21no—
180C2×C4⋊C4×C53C2311yescharacteristic
181C2×C22⋊C4×C53—21no—
182#103×C53C2314yes—
183#102×C53C2314yes—
184C22⋊C8×C53C2314yes—
185C24×C53—21no—
186C24×C53C2×D411yescharacteristic
187C23×D53C2×D411yescharacteristic
188#41×C53—28no—
189#41×C53—44no—
190#41×C53—48no—
191C2×Q8×C53—21no—
192C2×Q8×C53—21no—
193C2×Q8×C53—22no—
194C2×Q8×C53—22no—
195C2×Q8×C53—22no—
196C2×Q8×C53#4114yes—
197C2×Q8×C53C2412yes—
198C2×Q8×C53C2412yes—
199C2×D4×C53—24no—
200C2×D4×C53—21no—
201C2×D4×C53—22no—
202C2×D4×C53—22no—
203C2×D4×C53—44no—
204C2×D4×C53C2412yes—
205C22×C4×C53—21no—
206C22×C4×C53—22no—
207C22×C4×C53—22no—
208C22×C4×C53—21no—
209C22×C4×C53—21no—
210C22×C4×C53—24no—
211C22×C4×C53—44no—
212C22×C4×C53C2×D411yescharacteristic
213C22×C4×C53C2×D412yes—
214C22×C4×C53C2412yes—
215C22×C4×C53C2411yescharacteristic
216C2×C22⋊D53—24no—
217C2×C22⋊D53—42no—
218C2×C22⋊D53—44no—
219C2×C22⋊D53C2×D414yes—
220C22×Dic53—21no—
221C22×Dic53—21no—
222C22×Dic53—21no—
223C22×Dic53—21no—
224C22×Dic53C2×D411yescharacteristic
225C22×Dic53C2×D411yescharacteristic
226C22×Dic53C2×D411yescharacteristic
227Q8×D53—28no—
228Q8×D53—44no—
229Q8×D53—48no—
230C2×C4×D53—22no—
231C2×C4×D53—22no—
232C2×C4×D53—24no—
233C2×C4×D53—44no—
234C2×C4×D53C2×D412yes—
235C2×C4×D53C2412yes—
236C2×Dic106—22no—
237C2×Dic106—22no—
238C2×Dic106—21no—
239C2×Dic106—24no—
240C2×Dic106—24no—
241C2×Dic106—44no—
242C2×Dic106—44no—
243C2×Dic106C2412yes—
244Q16×C53—28no—
245SD16×C53—44no—
246C2×C8×C53—22no—
247C2×C8×C53—22no—
248C2×C8×C53C2412yes—
249C2×C8×C53C2412yes—
250C4⋊C4×C53—24no—
251C4⋊C4×C53—21no—
252C4⋊C4×C53C2412yes—
253C22⋊C4×C53—24no—
254C22⋊Dic53—24no—
255C22⋊Dic53—24no—
256C22⋊Dic53—24no—
257C22⋊Dic53—24no—
258C22⋊Dic53—24no—
259C22⋊Dic53C2×D414yes—
260#11719925—44no—
261#11719921—24no—
262#11719921—24no—
263#11719921C2×D414yes—
264C4⋊Dic53—21no—
265C4⋊Dic53—21no—
266C4⋊Dic53—21no—
267C4⋊Dic53—24no—
268C4⋊Dic53—24no—
269C4⋊Dic53C2412yes—
270C4⋊Dic53C2412yes—
271C4⋊Dic53C2412yes—
272#11719919—24no—
273#11719919—24no—
274#11719919—24no—
275#11719919C2×D414yes—
276C4×Dic53—24no—
277C4×Dic53—24no—
278C4×Dic53—24no—
279C4×Dic53—24no—
280C4×Dic53C2×D412yes—
281C4×Dic53C2412yes—
282C2×#88322—22no—
283C2×#88322—22no—
284C2×#88322—44no—
285C2×#88322C2412yes—
286C2×#88322C2412yes—
287#11719912—44no—
288C23×C53—22no—
289C23×C53—22no—
290C23×C53—22no—
291C23×C53—22no—
292C23×C53—42no—
293C23×C53—42no—
294C23×C53—42no—
295C23×C53C22×D412yes—
296C23×C53C22×D411yescharacteristic
297C22×D53—22no—
298C22×D53—22no—
299C22×D53—22no—
300C22×D53C22×D412yes—
301Q8×C53—24no—
302Q8×C53—22no—
303Q8×C53—22no—
304Q8×C53—22no—
305Q8×C53—42no—
306Q8×C53C2×#4114yes—
307D4×C53—22no—
308D4×C53—22no—
309D4×C53—48no—
310D4×C53—42no—
311C2×C4×C53—24no—
312C2×C4×C53—22no—
313C2×C4×C53—22no—
314C2×C4×C53—24no—
315C2×C4×C53—22no—
316C2×C4×C53—22no—
317C2×C4×C53—22no—
318C2×C4×C53—22no—
319C2×C4×C53—48no—
320C2×C4×C53—42no—
321C2×C4×C53—42no—
322C2×C4×C53C22×D412yes—
323C2×C4×C53C22×D411yescharacteristic
324C2×C4×C53C2×#4112yes—
325C2×C4×C53H(5,𝔽2)12yes—
326C2×C4×C53C2511yescharacteristic
327C22⋊D53—44no—
328C22⋊D53—48no—
329C2×Dic53—22no—
330C2×Dic53—22no—
331C2×Dic53—22no—
332C2×Dic53—22no—
333C2×Dic53—22no—
334C2×Dic53—22no—
335C2×Dic53—22no—
336C2×Dic53—42no—
337C2×Dic53—42no—
338C2×Dic53—42no—
339C2×Dic53—42no—
340C2×Dic53C22×D412yes—
341C2×Dic53C22×D412yes—
342C2×Dic53C22×D412yes—
343C4×D53—24no—
344C4×D53—22no—
345C4×D53—22no—
346C4×D53—48no—
347Dic106—22no—
348Dic106—22no—
349Dic106—48no—
350Dic106—48no—
351Dic106—42no—
352C8×C53—22no—
353C8×C53—22no—
354#88322—22no—
355#88322—22no—
356C2×#3313—531nomaximal, Sylow
357C22×C53—22no—
358C22×C53—22no—
359C22×C53—22no—
360C22×C53—44no—
361C22×C53—42no—
362C22×C53—42no—
363C22×C53—42no—
364C22×C53—84no—
365C22×C53#54612yes—
366C22×C53#57512yes—
367C22×C53#57812yes—
368C22×C53C23×D411yescharacteristic
369C2×D53—22no—
370C2×D53—22no—
371C2×D53—22no—
372C2×D53—44no—
373C4×C53—24no—
374C4×C53—22no—
375C4×C53—42no—
376C4×C53—42no—
377C4×C53#54612yes—
378C4×C53C22×#4111yescharacteristic
379C4×C53C2×H(5,𝔽2)11yescharacteristic
380Dic53—22no—
381Dic53—22no—
382Dic53—22no—
383Dic53—42no—
384Dic53—42no—
385Dic53—42no—
386Dic53—42no—
387C2×#556—531no—
388C2×#548—531no—
389#3313—5316no—
390C2×#489—531no—
391C2×#485—531no—
392C2×#482—531no—
393C2×#477—531no—
394C2×#468—531no—
395C2×#467—531no—
396C2×#464—531no—
397C2×#452D5311yescharacteristic, complemented
398C2×#451—531no—
399C2×#441—531no—
400C2×#435—531no—
401C2×#419—531no—
402C2×#416—531no—
403C2×C53—42no—
404C2×C53—82no—
405C2×C53#331314yescomplemented
406C2×C53C2×#54611yescharacteristic
407C2×C53C2×#57511yescharacteristic
408C2×C53C2×#57811yescharacteristic
409D53—42no—
410C22×#41C2×D5311yescharacteristic
411C23×Q8—531no—
412C22×Q16—531no—
413C22×Q16C2×D5311yescharacteristic
414C22×SD16C2×D5311yescharacteristic
415C22×M16—531no—
416C23×C8—531no—
417#556—538no—
418#556—1064no—
419#548—538no—
420#548—1064no—
421C2×C4⋊Q8—531no—
422C2×#126—1061no—
423C2×#126—1061no—
424C2×#124—531no—
425C2×#124—1061no—
426C2×#124—1061no—
427C2×C22⋊Q8—531no—
428C2×C22⋊Q8—531no—
429C2×C22⋊Q8—1061no—
430C2×C22⋊Q8C2×D5311yescharacteristic
431C2×#121—531no—
432C2×#121—1061no—
433C2×C4×Q8—531no—
434C2×C4×Q8—531no—
435C2×C4×Q8—1061no—
436C2×C4×D4—531no—
437C2×C4×D4—1061no—
438C2×#117—531no—
439C2×#117—531no—
440#489—538no—
441#485—538no—
442#482—538no—
443#477—538no—
444#468—538no—
445#467—538no—
446#464—538no—
447#452C2×D5318yescomplemented
448#451—538no—
449#441—538no—
450#435—538no—
451C2×#107—531no—
452C2×#107—531no—
453C2×#106—531no—
454C2×C4⋊C8—531no—
455#419—538no—
456#416—538no—
457C2×#103—531no—
458C2×#103—531no—
459C2×#103—531no—
460C2×#103—531no—
461C2×#103—531no—
462C2×#103—531no—
463C2×#103C2×D5311yescharacteristic
464C2×#102—531no—
465C2×#102—531no—
466C2×#102C2×D5311yescharacteristic
467C2×C22⋊C8—531no—
468C2×C22⋊C8C2×D5311yescharacteristic
469C2×#97—531no—
470C53C2×#331311yescharacteristic, complemented, Sylow
471C2×#41—22no—
472C2×#41—24no—
473C2×#41—42no—
474C2×#41C22×D5314yes—
475C22×Q8—534no—
476C22×Q8—531no—
477C22×Q8—1061no—
478C22×Q8—1061no—
479C22×Q8—1062no—
480C22×Q8—1064no—
481C22×Q8—2122no—
482C22×Q8C22×D5311yescharacteristic
483C22×Q8C22×D5311yescharacteristic
484C22×D4—21no—
485C22×D4—531no—
486C22×D4—1061no—
487C22×D4C22×D5311yescharacteristic
488C23×C4—21no—
489C23×C4—531no—
490C23×C4—1061no—
491C23×C4C22×D5311yescharacteristic
492C2×Q16—24no—
493C2×Q16—534no—
494C2×Q16—2122no—
495C2×Q16C22×D5314yes—
496C2×SD16—42no—
497C2×SD16C22×D5314yes—
498C2×M16—534no—
499C2×M16—2122no—
500C22×C8—531no—
501C22×C8—531no—
502C22×C8—534no—
503C22×C8—2122no—
504C22×C8C22×D5311yescharacteristic
505C22×C8C22×D5311yescharacteristic
506C4⋊Q8—534no—
507C4⋊Q8—1062no—
508#126—1068no—
509#126—1068no—
510#124—534no—
511#124—1062no—
512#124—1068no—
513#124—1068no—
514C22⋊Q8—22no—
515C22⋊Q8—534no—
516C22⋊Q8—534no—
517C22⋊Q8—1068no—
518C22⋊Q8—1062no—
519C22⋊Q8—1062no—
520C22⋊Q8C22×D5314yes—
521#121—534no—
522#121—1062no—
523#121—1068no—
524C4×Q8—534no—
525C4×Q8—534no—
526C4×Q8—1062no—
527C4×Q8—1062no—
528C4×Q8—1068no—
529C4×D4—534no—
530C4×D4—534no—
531C4×D4—1068no—
532#117—534no—
533#117—534no—
534#117—1062no—
535#117—1062no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—531no—
538C2×C4⋊C4—531no—
539C2×C4⋊C4—531no—
540C2×C4⋊C4—531no—
541C2×C4⋊C4—1061no—
542C2×C4⋊C4—1061no—
543C2×C4⋊C4—1061no—
544C2×C4⋊C4—1061no—
545C2×C4⋊C4—1061no—
546C2×C4⋊C4C22×D5311yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—531no—
549C2×C22⋊C4—531no—
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×C42—531no—
558C2×C42—1061no—
559C2×C42—1061no—
560C2×C42—1061no—
561C2×C42—1061no—
562#107—534no—
563#107—534no—
564#106—534no—
565C4⋊C8—534no—
566#103—534no—
567#103—534no—
568#103—534no—
569#103—534no—
570#103—534no—
571#103—534no—
572#103C22×D5314yes—
573#102—534no—
574#102—534no—
575#102C22×D5314yes—
576C22⋊C8—534no—
577C22⋊C8C22×D5314yes—
578#97—534no—
579C24—21no—
580C24—531no—
581C24D4×D5311yescharacteristic
582#41—28no—
583#41—44no—
584#41—48no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—22no—
588C2×Q8—22no—
589C2×Q8—22no—
590C2×Q8—532no—
591C2×Q8—1064no—
592C2×Q8—1064no—
593C2×Q8—1061no—
594C2×Q8—1068no—
595C2×Q8—1062no—
596C2×Q8—1062no—
597C2×Q8—2124no—
598C2×Q8—2124no—
599C2×Q8—2124no—
600C2×Q8—2128no—
601C2×Q8#1171994714yes—
602C2×Q8C23×D5312yes—
603C2×Q8C23×D5312yes—
604C2×D4—24no—
605C2×D4—21no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—44no—
609C2×D4—534no—
610C2×D4—1064no—
611C2×D4—2122no—
612C2×D4—2124no—
613C2×D4C23×D5312yes—
614C22×C4—21no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—24no—
620C22×C4—44no—
621C22×C4—531no—
622C22×C4—531no—
623C22×C4—531no—
624C22×C4—532no—
625C22×C4—532no—
626C22×C4—1064no—
627C22×C4—1062no—
628C22×C4—1062no—
629C22×C4—1061no—
630C22×C4—1061no—
631C22×C4—1061no—
632C22×C4—1061no—
633C22×C4—2124no—
634C22×C4D4×D5312yes—
635C22×C4D4×D5311yescharacteristic
636C22×C4C23×D5312yes—
637C22×C4C23×D5311yescharacteristic
638Q16—28no—
639Q16—2124no—
640SD16—44no—
641M16—2124no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—532no—
645C2×C8—532no—
646C2×C8—1062no—
647C2×C8—1062no—
648C2×C8—2124no—
649C2×C8C23×D5312yes—
650C2×C8C23×D5312yes—
651C4⋊C4—24no—
652C4⋊C4—21no—
653C4⋊C4—534no—
654C4⋊C4—532no—
655C4⋊C4—532no—
656C4⋊C4—532no—
657C4⋊C4—1064no—
658C4⋊C4—1064no—
659C4⋊C4—1064no—
660C4⋊C4—1064no—
661C4⋊C4—1061no—
662C4⋊C4—1061no—
663C4⋊C4—1061no—
664C4⋊C4—1064no—
665C4⋊C4C23×D5312yes—
666C22⋊C4—24no—
667C22⋊C4—534no—
668C22⋊C4—534no—
669C22⋊C4—1064no—
670C22⋊C4—1064no—
671C22⋊C4—1064no—
672C22⋊C4—1064no—
673C22⋊C4—1064no—
674C22⋊C4—1064no—
675C22⋊C4—1064no—
676C42—532no—
677C42—532no—
678C42—1064no—
679C42—1064no—
680C42—1064no—
681C42—1064no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—532no—
690C23—1062no—
691C23—1062no—
692C23—1062no—
693C23C2×D4×D5312yes—
694C23C2×D4×D5311yescharacteristic
695Q8—22no—
696Q8—24no—
697Q8—22no—
698Q8—22no—
699Q8—42no—
700Q8—1062no—
701Q8—1062no—
702Q8—2128no—
703Q8—2128no—
704Q8—2122no—
705Q8C2×#1171994714yes—
706D4—22no—
707D4—22no—
708D4—48no—
709D4—42no—
710D4—2124no—
711D4—2128no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—48no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—532no—
724C2×C4—532no—
725C2×C4—532no—
726C2×C4—1062no—
727C2×C4—1062no—
728C2×C4—1062no—
729C2×C4—1062no—
730C2×C4—1062no—
731C2×C4—1064no—
732C2×C4—1062no—
733C2×C4—1062no—
734C2×C4—1062no—
735C2×C4—1062no—
736C2×C4—2128no—
737C2×C4—2122no—
738C2×C4—2122no—
739C2×C4—2122no—
740C2×C4—2122no—
741C2×C4C2×D4×D5312yes—
742C2×C4C2×D4×D5311yescharacteristic
743C2×C4C2×#1171994712yes—
744C2×C4#1313326212yes—
745C2×C4C24×D5311yescharacteristic
746C8—22no—
747C8—22no—
748C8—1062no—
749C8—1062no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—44no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—84no—
758C22—1062no—
759C22—1062no—
760C22—1062no—
761C22—2124no—
762C22#1681126012yes—
763C22#1681142012yes—
764C22#1681143912yes—
765C22C22×D4×D5311yescharacteristic
766C4—22no—
767C4—24no—
768C4—42no—
769C4—42no—
770C4—1062no—
771C4—1062no—
772C4—1062no—
773C4—2122no—
774C4—2122no—
775C4—2122no—
776C4—2122no—
777C4#1681126012yes—
778C4C22×#1171994711yescharacteristic
779C4C2×#1313326211yescharacteristic
780C2—42no—
781C2—82no—
782C2—2122no—
783C2#2028678514yesdirect product factor
784C2C2×#1681126011yescharacteristic
785C2C2×#1681142011yescharacteristic
786C2C2×#1681143911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#452C2
socleC23×C53C22×D4
prime radicalC2×#16811280C2
hypercenterC2×#452D53
hypocenterC53C2×#3313
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#16811344C2semidirect
3. #20286785C2direct (N × H)
4. C2×#16810981C2semidirect
5. C2×#16810965C2semidirect
6. C2×#16810946C2semidirect
7. C2×#16810916C2semidirect
8. C2×#16810866C2semidirect
9. C2×#16810862C2semidirect
10. C2×#16810843C2semidirect
11. C2×#16810777C2semidirect
12. C2×#16810730C2semidirect
13. C2×#16810691C2semidirect
14. C2×#16810630C2semidirect
15. C2×#16810619C2semidirect
16. C2×C53×#452C2semidirect
22. #16811344C22semidirect
43. #16810981C22semidirect
44. #16810965C22semidirect
45. #16810946C22semidirect
46. #16810916C22semidirect
47. #16810866C22semidirect
48. #16810862C22semidirect
49. #16810843C22semidirect
50. #16810777C22semidirect
51. #16810730C22semidirect
52. #16810691C22semidirect
57. #16810630C22semidirect
58. #16810619C22semidirect
73. C53×#452C22semidirect
397. C2×#452D53semidirect
405. C2×C53#3313semidirect
447. #452C2×D53semidirect
470. C53C2×#3313semidirect
783. C2#20286785direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113442
C2×#168112802
#202867852
C2×#168109812
C2×#168109652
C2×#168109462
C2×#168109162
C2×#168108662
C2×#168108622
C2×#168108432
C2×#168107772
C2×#168107302
C2×#168106912
C2×#168106302
C2×#168106192
C2×C53×#4522
C2×#331353