Finite Group Databasebeta

← C2×#20286981 #28260959

Subgroups — C2×#20286981 #28260959

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×#16811312C211yesmaximal, characteristic, complemented
2C2×#16811279C211yesmaximal, characteristic
3#20286981C2116yesmaximal, direct product factor
4C2×#16810976C211yesmaximal, characteristic, complemented
5C2×#16810960C211yesmaximal, characteristic, complemented
6C2×#16810933C211yesmaximal, characteristic, complemented
7C2×#16810882C211yesmaximal, characteristic, complemented
8C2×#16810867C211yesmaximal, characteristic, complemented
9C2×#16810844C211yesmaximal, characteristic, complemented
10C2×#16810786C211yesmaximal, characteristic, complemented
11C2×#16810781C211yesmaximal, characteristic, complemented
12C2×#16810717C211yesmaximal, characteristic, complemented
13C2×#16810698C211yesmaximal, characteristic, complemented
14C2×#16810621C211yesmaximal, characteristic, complemented
15C2×#16810631C211yesmaximal, characteristic, complemented
16C2×C53×#482C211yesmaximal, characteristic, complemented
17C22×#11719947C2211yescharacteristic
18C23×Dic106C2211yescharacteristic
19C22×Dic212C2211yescharacteristic
20C22×Dic212C2211yescharacteristic
21C22×#11719923C2211yescharacteristic
22C22×#11719917C2211yescharacteristic
23C22×#11719912C2211yescharacteristic
24#16811312—24no—
25#16811312C2218yescomplemented
26#16811279—24no—
27#16811279C2218yes—
28C2×#13133210—21no—
29C2×#13133209—21no—
30C2×#13133208C2211yescharacteristic
31C2×#13133204C2211yescharacteristic
32C2×#13133203—21no—
33C2×#13133199—21no—
34C2×#13133197C2211yescharacteristic
35C2×#13133197C2211yescharacteristic
36C2×#13133196C2211yescharacteristic
37C2×#13133194—21no—
38C2×#13133189—21no—
39C2×#13133182C2211yescharacteristic
40C2×#13133182C2211yescharacteristic
41C2×D4×Dic53—21no—
42C2×C4×C22⋊D53C2211yescharacteristic
43C2×#13133174—21no—
44C2×C4⋊C4×D53C2211yescharacteristic
45#16810976C2218yescomplemented
46#16810960C2218yescomplemented
47#16810933C2218yescomplemented
48#16810882C2218yescomplemented
49#16810867C2218yescomplemented
50#16810844C2218yescomplemented
51#16810786C2218yescomplemented
52#16810781C2218yescomplemented
53#16810717C2218yescomplemented
54#16810698C2218yescomplemented
55C2×#13133150C2211yescharacteristic
56C2×#13133146C2211yescharacteristic
57#16810631C2218yescomplemented
58#16810621C2218yescomplemented
59C2×#13133142C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133140C2211yescharacteristic
62C2×#13133140C2211yescharacteristic
63C2×#13133140C2211yescharacteristic
64C2×#13133140C2211yescharacteristic
65C2×#13133140C2211yescharacteristic
66C2×#13133138C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C2×#121×C53C2211yescharacteristic
70C2×#117×C53C2211yescharacteristic
71C53×#482C2218yescomplemented
72C2×#107×C53C2211yescharacteristic
73C2×#106×C53C2211yescharacteristic
74C2×#102×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic
77C2×#11719947—22no—
78C2×#11719947—24no—
79C2×#11719947—42no—
80C2×#11719947C2314yes—
81C22×Dic106—24no—
82C22×Dic106—22no—
83C22×Dic106—21no—
84C22×Dic106—42no—
85C22×Dic106C2311yescharacteristic
86C22×Dic106C2311yescharacteristic
87C22×Dic106C2314yes—
88C22×Dic106C2311yescharacteristic
89C22×C22⋊D53—21no—
90C22×C22⋊D53D411yescharacteristic
91C23×Dic53—21no—
92C23×Dic53—21no—
93C22×C4×D53—21no—
94C22×C4×D53C2311yescharacteristic
95C2×Dic212—24no—
96C2×Dic212—42no—
97C2×Dic212C2314yes—
98C2×Dic212C2314yes—
99C2×#11719923—42no—
100C2×#11719923C2314yes—
101C2×#11719917—42no—
102C2×#11719917C2314yes—
103C2×#11719912—42no—
104C2×#11719912C2314yes—
105C22×#88322C2311yescharacteristic
106C22×#88322C2311yescharacteristic
107#13133210—28no—
108#13133209—28no—
109#13133208—22no—
110#13133208C2314yes—
111#13133204—22no—
112#13133204C2314yes—
113#13133203—28no—
114#13133199—28no—
115#13133197—22no—
116#13133197—22no—
117#13133197C2314yes—
118#13133197C2314yes—
119#13133196—22no—
120#13133196C2314yes—
121#13133194—28no—
122#13133189—28no—
123#13133182—22no—
124#13133182—22no—
125#13133182C2314yes—
126#13133182C2314yes—
127D4×Dic53—28no—
128C4×C22⋊D53D414yes—
129C4×C22⋊D53C2314yes—
130#13133174—28no—
131C2×C4⋊Dic53—21no—
132C2×C4⋊Dic53—21no—
133C2×C4⋊Dic53—21no—
134C2×C4⋊Dic53C2311yescharacteristic
135C2×#11719919—21no—
136C2×#11719919—21no—
137C2×#11719919—21no—
138C2×#11719919—21no—
139C2×#11719919—21no—
140C2×#11719919D411yescharacteristic
141C4⋊C4×D53—22no—
142C4⋊C4×D53C2314yes—
143C2×C22⋊Dic53—21no—
144C2×C22⋊Dic53—21no—
145C2×C22⋊Dic53—21no—
146C2×C22⋊Dic53D411yescharacteristic
147C2×#11719921—21no—
148C2×#11719921—21no—
149C2×#11719921D411yescharacteristic
150C2×C4×Dic53—21no—
151C2×C4×Dic53—21no—
152C2×C4×Dic53C2311yescharacteristic
153#13133150C2314yes—
154#13133146C2314yes—
155#13133142C2314yes—
156#13133142C2314yes—
157#13133140C2314yes—
158#13133140C2314yes—
159#13133140C2314yes—
160#13133140C2314yes—
161#13133140C2314yes—
162#13133138C2314yes—
163#13133129C2314yes—
164C8×Dic53C2314yes—
165C22×D4×C53—21no—
166C22×D4×C53C2311yescharacteristic
167C23×C4×C53C2311yescharacteristic
168C22×C8×C53C2311yescharacteristic
169C22×C8×C53C2311yescharacteristic
170#121×C53—22no—
171#121×C53C2314yes—
172#117×C53—22no—
173#117×C53C2314yes—
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C4⋊C4×C53C2311yescharacteristic
176C2×C4⋊C4×C53C2311yescharacteristic
177C2×C22⋊C4×C53—21no—
178C2×C22⋊C4×C53—21no—
179C2×C42×C53—21no—
180#107×C53C2314yes—
181#106×C53C2314yes—
182#102×C53C2314yes—
183#102×C53C2314yes—
184C22⋊C8×C53C2314yes—
185C24×C53—21no—
186C24×C53C2×D411yescharacteristic
187C23×D53C2×D411yescharacteristic
188C2×D4×C53—24no—
189C2×D4×C53—21no—
190C2×D4×C53—22no—
191C2×D4×C53—22no—
192C2×D4×C53—44no—
193C2×D4×C53C2412yes—
194C22×C4×C53—22no—
195C22×C4×C53—22no—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53C2×D412yes—
201C22×C4×C53C2412yes—
202C22×C4×C53C2411yescharacteristic
203C2×C22⋊D53—24no—
204C2×C22⋊D53—42no—
205C2×C22⋊D53—44no—
206C2×C22⋊D53C2×D414yes—
207C22×Dic53—21no—
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—28no—
219#11719947—44no—
220#11719947—48no—
221C2×C4×D53—22no—
222C2×C4×D53—22no—
223C2×C4×D53—24no—
224C2×C4×D53—44no—
225C2×C4×D53C2×D412yes—
226C2×C4×D53C2412yes—
227C2×Dic106—21no—
228C2×Dic106—22no—
229C2×Dic106—22no—
230C2×Dic106—22no—
231C2×Dic106—22no—
232C2×Dic106—22no—
233C2×Dic106—28no—
234C2×Dic106—21no—
235C2×Dic106—24no—
236C2×Dic106—21no—
237C2×Dic106—44no—
238C2×Dic106—48no—
239C2×Dic106—44no—
240C2×Dic106#4114yes—
241C2×Dic106C2412yes—
242C2×Dic106C2412yes—
243C2×Dic106C2412yes—
244C2×C8×C53—22no—
245C2×C8×C53—22no—
246C2×C8×C53C2412yes—
247C2×C8×C53C2412yes—
248C4⋊C4×C53—21no—
249C4⋊C4×C53—21no—
250C4⋊C4×C53—21no—
251C4⋊C4×C53C2412yes—
252C4⋊C4×C53C2412yes—
253C4⋊C4×C53C2412yes—
254C22⋊C4×C53—24no—
255C22⋊C4×C53—24no—
256C42×C53—24no—
257C22⋊Dic53—24no—
258C22⋊Dic53—24no—
259C22⋊Dic53—24no—
260C22⋊Dic53C2×D414yes—
261#11719923—44no—
262#11719921—24no—
263#11719921—24no—
264#11719921C2×D414yes—
265C4⋊Dic53—21no—
266C4⋊Dic53—24no—
267C4⋊Dic53—24no—
268C4⋊Dic53—24no—
269C4⋊Dic53C2412yes—
270#11719919—24no—
271#11719919—24no—
272#11719919—24no—
273#11719919—24no—
274#11719919—24no—
275#11719919C2×D414yes—
276C4×Dic53—24no—
277C4×Dic53—24no—
278C4×Dic53C2×D412yes—
279C4×Dic53C2412yes—
280#11719917—44no—
281C2×#88322—22no—
282C2×#88322—22no—
283C2×#88322C2412yes—
284C2×#88322C2412yes—
285Dic212—28no—
286Dic212—44no—
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—
301D4×C53—22no—
302D4×C53—22no—
303D4×C53—48no—
304D4×C53—42no—
305C2×C4×C53—22no—
306C2×C4×C53—24no—
307C2×C4×C53—22no—
308C2×C4×C53—22no—
309C2×C4×C53—22no—
310C2×C4×C53—22no—
311C2×C4×C53—22no—
312C2×C4×C53—42no—
313C2×C4×C53—42no—
314C2×C4×C53—42no—
315C2×C4×C53C22×D412yes—
316C2×C4×C53C22×D411yescharacteristic
317C2×C4×C53C2×#4112yes—
318C2×C4×C53H(5,𝔽2)12yes—
319C2×C4×C53C2511yescharacteristic
320C22⋊D53—44no—
321C22⋊D53—48no—
322C2×Dic53—24no—
323C2×Dic53—22no—
324C2×Dic53—22no—
325C2×Dic53—22no—
326C2×Dic53—22no—
327C2×Dic53—22no—
328C2×Dic53—22no—
329C2×Dic53—22no—
330C2×Dic53—48no—
331C2×Dic53—48no—
332C2×Dic53—42no—
333C2×Dic53—42no—
334C2×Dic53—42no—
335C2×Dic53C22×D412yes—
336C2×Dic53C22×D412yes—
337C2×Dic53C22×D412yes—
338C4×D53—24no—
339C4×D53—22no—
340C4×D53—22no—
341C4×D53—48no—
342Dic106—24no—
343Dic106—22no—
344Dic106—22no—
345Dic106—22no—
346Dic106—22no—
347Dic106—22no—
348Dic106—48no—
349Dic106—42no—
350Dic106—42no—
351Dic106C2×#4114yes—
352C8×C53—22no—
353C8×C53—22no—
354#88322—22no—
355#88322—22no—
356C2×#3327—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—22no—
374C4×C53—42no—
375C4×C53—42no—
376C4×C53—42no—
377C4×C53#54612yes—
378C4×C53C22×#4111yescharacteristic
379C4×C53C2×H(5,𝔽2)11yescharacteristic
380Dic53—24no—
381Dic53—22no—
382Dic53—22no—
383Dic53—22no—
384Dic53—42no—
385Dic53—42no—
386Dic53—42no—
387C2×#552—531no—
388C2×#548—531no—
389#3327—5316no—
390C2×#488—531no—
391C2×#484—531no—
392C2×#482D5311yescharacteristic, complemented
393C2×#479—531no—
394C2×#470—531no—
395C2×#468—531no—
396C2×#464—531no—
397C2×#452—531no—
398C2×#451—531no—
399C2×C4×Q16—531no—
400C2×#436—531no—
401C2×#417—531no—
402C2×#419—531no—
403C2×C53—42no—
404C2×C53—82no—
405C2×C53#332714yescomplemented
406C2×C53C2×#54611yescharacteristic
407C2×C53C2×#57511yescharacteristic
408C2×C53C2×#57811yescharacteristic
409D53—42no—
410C22×#41—531no—
411C23×Q8—531no—
412C22×Q16—531no—
413C22×Q16—531no—
414C22×SD16—531no—
415C22×M16—531no—
416C22×M16—531no—
417#552—538no—
418#552—1064no—
419#548—538no—
420#548—1064no—
421C2×#126—1061no—
422C2×#125—531no—
423C2×#125—1061no—
424C2×#124—531no—
425C2×#124—1061no—
426C2×#123—1061no—
427C2×C22⋊Q8—531no—
428C2×C22⋊Q8—531no—
429C2×C22⋊Q8—531no—
430C2×C22⋊Q8—1061no—
431C2×#121—1061no—
432C2×#121C2×D5311yescharacteristic
433C2×C4×Q8—531no—
434C2×C4×Q8—531no—
435C2×C4×D4—531no—
436C2×C4×D4—1061no—
437C2×#117—1061no—
438C2×#117C2×D5311yescharacteristic
439C22×C4⋊C4—531no—
440#488—538no—
441#484—538no—
442#482C2×D5318yescomplemented
443#479—538no—
444#470—538no—
445#468—538no—
446#464—538no—
447#452—538no—
448#451—538no—
449C4×Q16—538no—
450#436—538no—
451C2×#107—531no—
452C2×#107C2×D5311yescharacteristic
453C2×#106C2×D5311yescharacteristic
454C2×C4⋊C8—531no—
455#419—538no—
456#417—538no—
457C2×#103—531no—
458C2×#103—531no—
459C2×#103—531no—
460C2×#103—531no—
461C2×#103—531no—
462C2×#103—531no—
463C2×#103—531no—
464C2×#102—531no—
465C2×#102C2×D5311yescharacteristic
466C2×#102C2×D5311yescharacteristic
467C2×C22⋊C8—531no—
468C2×C22⋊C8C2×D5311yescharacteristic
469C2×C4×C8—531no—
470C53C2×#332711yescharacteristic, complemented, Sylow
471C2×#41—534no—
472C2×#41—1062no—
473C2×#41—1064no—
474C2×#41—2122no—
475C22×Q8—531no—
476C22×Q8—531no—
477C22×Q8—531no—
478C22×Q8—534no—
479C22×Q8—1064no—
480C22×Q8—1061no—
481C22×Q8—1062no—
482C22×Q8—2122no—
483C22×D4—21no—
484C22×D4—531no—
485C22×D4—1061no—
486C22×D4C22×D5311yescharacteristic
487C23×C4—531no—
488C23×C4—1061no—
489C23×C4—1061no—
490C23×C4—1061no—
491C23×C4C22×D5311yescharacteristic
492C2×Q16—534no—
493C2×Q16—534no—
494C2×Q16—1064no—
495C2×Q16—2122no—
496C2×SD16—534no—
497C2×SD16—2122no—
498C2×M16—534no—
499C2×M16—534no—
500C2×M16—2122no—
501C2×M16—2122no—
502C22×C8—531no—
503C22×C8—531no—
504C22×C8C22×D5311yescharacteristic
505C22×C8C22×D5311yescharacteristic
506#126—1068no—
507#125—534no—
508#125—1068no—
509#125—1062no—
510#124—534no—
511#124—1062no—
512#124—1068no—
513#123—1068no—
514C22⋊Q8—534no—
515C22⋊Q8—534no—
516C22⋊Q8—534no—
517C22⋊Q8—1068no—
518C22⋊Q8—1062no—
519C22⋊Q8—1062no—
520C22⋊Q8—1062no—
521#121—22no—
522#121—1068no—
523#121C22×D5314yes—
524C4×Q8—534no—
525C4×Q8—534no—
526C4×Q8—1062no—
527C4×Q8—1062no—
528C4×D4—534no—
529C4×D4—534no—
530C4×D4—1068no—
531#117—22no—
532#117—1068no—
533#117C22×D5314yes—
534C2×C4⋊C4—531no—
535C2×C4⋊C4—531no—
536C2×C4⋊C4—534no—
537C2×C4⋊C4—1062no—
538C2×C4⋊C4—1061no—
539C2×C4⋊C4—1061no—
540C2×C4⋊C4—1061no—
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×C4⋊C4C22×D5311yescharacteristic
548C2×C4⋊C4C22×D5311yescharacteristic
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—531no—
552C2×C22⋊C4—531no—
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—1061no—
561C2×C42—1061no—
562#107—534no—
563#107C22×D5314yes—
564#106C22×D5314yes—
565C4⋊C8—534no—
566#103—534no—
567#103—534no—
568#103—534no—
569#103—534no—
570#103—534no—
571#103—534no—
572#103—534no—
573#102—534no—
574#102C22×D5314yes—
575#102C22×D5314yes—
576C22⋊C8—534no—
577C22⋊C8C22×D5314yes—
578C4×C8—534no—
579C24—21no—
580C24—531no—
581C24D4×D5311yescharacteristic
582#41—1068no—
583#41—2124no—
584#41—2128no—
585C2×Q8—534no—
586C2×Q8—532no—
587C2×Q8—532no—
588C2×Q8—532no—
589C2×Q8—1068no—
590C2×Q8—1061no—
591C2×Q8—1061no—
592C2×Q8—1064no—
593C2×Q8—1061no—
594C2×Q8—1062no—
595C2×Q8—1062no—
596C2×Q8—1062no—
597C2×Q8—1062no—
598C2×Q8—1062no—
599C2×Q8—2124no—
600C2×Q8—2124no—
601C2×Q8—2128no—
602C2×D4—24no—
603C2×D4—21no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—44no—
607C2×D4—534no—
608C2×D4—1064no—
609C2×D4—2122no—
610C2×D4—2124no—
611C2×D4C23×D5312yes—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—531no—
618C22×C4—531no—
619C22×C4—531no—
620C22×C4—532no—
621C22×C4—532no—
622C22×C4—1064no—
623C22×C4—1064no—
624C22×C4—1061no—
625C22×C4—1062no—
626C22×C4—1062no—
627C22×C4—1064no—
628C22×C4—1061no—
629C22×C4—1061no—
630C22×C4—1061no—
631C22×C4—2124no—
632C22×C4—2124no—
633C22×C4—2124no—
634C22×C4D4×D5312yes—
635C22×C4D4×D5311yescharacteristic
636C22×C4C23×D5312yes—
637C22×C4C23×D5311yescharacteristic
638Q16—1068no—
639Q16—2124no—
640SD16—2124no—
641M16—2124no—
642M16—2124no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—532no—
646C2×C8—532no—
647C2×C8—1062no—
648C2×C8—1062no—
649C2×C8C23×D5312yes—
650C2×C8C23×D5312yes—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—534no—
655C4⋊C4—532no—
656C4⋊C4—1064no—
657C4⋊C4—1064no—
658C4⋊C4—1064no—
659C4⋊C4—1064no—
660C4⋊C4—1064no—
661C4⋊C4—1064no—
662C4⋊C4—1064no—
663C4⋊C4—1061no—
664C4⋊C4—1064no—
665C4⋊C4C23×D5312yes—
666C4⋊C4C23×D5312yes—
667C4⋊C4C23×D5312yes—
668C22⋊C4—24no—
669C22⋊C4—24no—
670C22⋊C4—534no—
671C22⋊C4—534no—
672C22⋊C4—1064no—
673C22⋊C4—1064no—
674C22⋊C4—1064no—
675C22⋊C4—1064no—
676C22⋊C4—1064no—
677C42—24no—
678C42—532no—
679C42—532no—
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—534no—
696Q8—1064no—
697Q8—1062no—
698Q8—1062no—
699Q8—1062no—
700Q8—1062no—
701Q8—1062no—
702Q8—2128no—
703Q8—2122no—
704Q8—2122no—
705D4—22no—
706D4—22no—
707D4—48no—
708D4—42no—
709D4—2124no—
710D4—2128no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—532no—
722C2×C4—532no—
723C2×C4—532no—
724C2×C4—1062no—
725C2×C4—1064no—
726C2×C4—1062no—
727C2×C4—1062no—
728C2×C4—1062no—
729C2×C4—1064no—
730C2×C4—1062no—
731C2×C4—1062no—
732C2×C4—1062no—
733C2×C4—1062no—
734C2×C4—1062no—
735C2×C4—2128no—
736C2×C4—2128no—
737C2×C4—2128no—
738C2×C4—2122no—
739C2×C4—2122no—
740C2×C4—2122no—
741C2×C4C2×D4×D5312yes—
742C2×C4C2×D4×D5311yescharacteristic
743C2×C4#41×D5312yes—
744C2×C4#1313326312yes—
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#1681126512yes—
763C22#1681141912yes—
764C22#1681143712yes—
765C22C22×D4×D5311yescharacteristic
766C4—22no—
767C4—42no—
768C4—42no—
769C4—42no—
770C4—1062no—
771C4—1064no—
772C4—1062no—
773C4—1062no—
774C4—2122no—
775C4—2122no—
776C4—2122no—
777C4#1681126512yes—
778C4C2×#41×D5311yescharacteristic
779C4C2×#1313326311yescharacteristic
780C2—42no—
781C2—82no—
782C2—2122no—
783C2#2028698114yesdirect product factor
784C2C2×#1681126511yescharacteristic
785C2C2×#1681141911yescharacteristic
786C2C2×#1681143711yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#482C2
socleC23×C53C22×D4
prime radicalC2×#16811279C2
hypercenterC2×#482D53
hypocenterC53C2×#3327
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#16811312C2semidirect
3. #20286981C2direct (N × H)
4. C2×#16810976C2semidirect
5. C2×#16810960C2semidirect
6. C2×#16810933C2semidirect
7. C2×#16810882C2semidirect
8. C2×#16810867C2semidirect
9. C2×#16810844C2semidirect
10. C2×#16810786C2semidirect
11. C2×#16810781C2semidirect
12. C2×#16810717C2semidirect
13. C2×#16810698C2semidirect
14. C2×#16810621C2semidirect
15. C2×#16810631C2semidirect
16. C2×C53×#482C2semidirect
25. #16811312C22semidirect
45. #16810976C22semidirect
46. #16810960C22semidirect
47. #16810933C22semidirect
48. #16810882C22semidirect
49. #16810867C22semidirect
50. #16810844C22semidirect
51. #16810786C22semidirect
52. #16810781C22semidirect
53. #16810717C22semidirect
54. #16810698C22semidirect
57. #16810631C22semidirect
58. #16810621C22semidirect
71. C53×#482C22semidirect
392. C2×#482D53semidirect
405. C2×C53#3327semidirect
442. #482C2×D53semidirect
470. C53C2×#3327semidirect
783. C2#20286981direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113122
C2×#168112792
#202869812
C2×#168109762
C2×#168109602
C2×#168109332
C2×#168108822
C2×#168108672
C2×#168108442
C2×#168107862
C2×#168107812
C2×#168107172
C2×#168106982
C2×#168106212
C2×#168106312
C2×C53×#4822
C2×#332753