Finite Group Databasebeta

← #28256433

Subgroups — #28256433

Order 13568.

1686 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×#16811251C211yesmaximal, characteristic, complemented
2#20286007C214yesmaximal, complemented
3#20285992C214yesmaximal, complemented
4#20285977C214yesmaximal, complemented
5#20285962C214yesmaximal, complemented
6#20285268C211yesmaximal, characteristic, complemented
7#20285262C211yesmaximal, characteristic, complemented
8#20285115C211yesmaximal, characteristic, complemented
9#20285108C211yesmaximal, characteristic, complemented
10#20284644C212yesmaximal, complemented
11#20284635C212yesmaximal, complemented
12#20284537C212yesmaximal, complemented
13#20284530C212yesmaximal, complemented
14#20283353C211yesmaximal, characteristic, complemented
15C53×#3455C211yesmaximal, characteristic
16#16811251—22no—
17#16811251—22no—
18#16811251C2214yes—
19#16811251C2214yes—
20C2×#13133217C2211yescharacteristic
21C2×#13133217C2211yescharacteristic
22C2×#13133216—21no—
23C2×#13133209C2211yescharacteristic
24C2×#13133209C2211yescharacteristic
25C2×#13133208—21no—
26C2×#13133194—21no—
27C2×#13133194—21no—
28C2×#13133176C2211yescharacteristic
29C22×C4⋊Dic53C2211yescharacteristic
30#16811033C2214yescomplemented
31#16811029C2212yescomplemented
32#16811029C2212yescomplemented
33#16811026C2212yescomplemented
34#16811022C2214yescomplemented
35#16811019C2212yescomplemented
36#16810991C2212yescomplemented
37#16810987C2212yescomplemented
38#16810982C2214yescomplemented
39#16810977C2214yescomplemented
40#16810973C2212yescomplemented
41#16810969C2212yescomplemented
42#16810961C2214yes—
43#16810961C2214yes—
44#16810956C2214yes—
45#16810951C2214yes—
46#16810944C2214yes—
47#16810944C2214yes—
48#16810939C2214yes—
49#16810934C2214yes—
50#16810930C2214yescomplemented
51#16810930C2214yescomplemented
52#16810923C2214yescomplemented
53#16810923C2214yescomplemented
54#16810918C2214yescomplemented
55#16810913C2214yescomplemented
56#16810908C2214yescomplemented
57#16810903C2214yescomplemented
58#16810684C2214yes—
59#16810684C2214yes—
60#16810666C2212yes—
61#16810666C2212yes—
62#16810666C2212yes—
63#16810666C2212yes—
64#16810647C2212yes—
65#16810624C2212yes—
66#16810624C2212yes—
67#16810624C2212yes—
68#16810624C2212yes—
69#16810587C2212yes—
70C4×#11719917C2211yescharacteristic
71C4×#11719917C2211yescharacteristic
72C53×#542C2212yes—
73C53×#542C2212yes—
74C53×#541C2212yes—
75C53×#540C2212yes—
76C53×#539—21no—
77C53×#539—21no—
78C53×#538—21no—
79C53×#538—21no—
80C53×#533C2211yescharacteristic
81C53×#532C2211yescharacteristic
82C53×#529—22no—
83C53×#529—22no—
84C53×#525C2212yes—
85C4×#41×C53C2212yes—
86C2×#117×C53C2211yescharacteristic
87C22×Dic106—21no—
88C22×Dic106—21no—
89C23×Dic53—21no—
90C2×#11719917C2312yes—
91C2×#11719917C2312yes—
92#13133217—22no—
93#13133217—21no—
94#13133217—21no—
95#13133217C2312yes—
96#13133217C2312yes—
97#13133217C2314yes—
98#13133216—24no—
99#13133216—24no—
100#13133209—22no—
101#13133209—21no—
102#13133209—21no—
103#13133209C2312yes—
104#13133209C2312yes—
105#13133209C2314yes—
106#13133208—24no—
107#13133208—24no—
108#13133194—24no—
109#13133194—24no—
110#13133194—24no—
111#13133194—24no—
112#13133176—22no—
113#13133176C2314yes—
114C2×C4⋊Dic53—21no—
115C2×C4⋊Dic53—22no—
116C2×C4⋊Dic53—21no—
117C2×C4⋊Dic53—21no—
118C2×C4⋊Dic53C2311yescharacteristic
119C2×C4⋊Dic53C2311yescharacteristic
120C2×C4⋊Dic53C2314yes—
121C2×C4⋊Dic53C2311yescharacteristic
122C2×C4⋊Dic53C2311yescharacteristic
123C2×#11719919—21no—
124C2×#11719919—21no—
125C2×#11719919—21no—
126C2×#11719919—21no—
127C2×C22⋊Dic53—21no—
128C2×C4×Dic53—21no—
129#13133150C2314yes—
130#13133150C2314yes—
131#13133150C2314yes—
132#13133150C2314yes—
133#13133148C2314yes—
134#13133148C2314yes—
135#13133148C2314yes—
136#13133148C2314yes—
137C4⋊#88322C2314yes—
138C4⋊#88322C2314yes—
139#13133141C2314yes—
140#13133141C2314yes—
141#13133141C2314yes—
142#13133141C2314yes—
143#13133138C2314yes—
144#13133138C2314yes—
145#13133138C2314yes—
146#13133138C2314yes—
147C22⋊#88322C2314yes—
148C22⋊#88322C2314yes—
149#13133128C2312yes—
150#13133128C2312yes—
151C4×#88322C2312yes—
152C4×#88322C2312yes—
153C2×#41×C53C2312yes—
154C23×C4×C53C2311yescharacteristic
155C4⋊Q8×C53C2311yescharacteristic
156C4⋊Q8×C53C2311yescharacteristic
157C4⋊Q8×C53C2311yescharacteristic
158#127×C53C2311yescharacteristic
159#126×C53—22no—
160#126×C53—22no—
161#126×C53—22no—
162#126×C53—22no—
163#125×C53—22no—
164#125×C53—22no—
165#125×C53C2312yes—
166#124×C53—22no—
167#124×C53—22no—
168#124×C53C2312yes—
169#123×C53—22no—
170#123×C53—22no—
171#123×C53—22no—
172#123×C53—22no—
173#123×C53—22no—
174C22⋊Q8×C53—22no—
175C22⋊Q8×C53—22no—
176C22⋊Q8×C53—21no—
177C22⋊Q8×C53—21no—
178C22⋊Q8×C53C2312yes—
179C22⋊Q8×C53C2312yes—
180#121×C53—22no—
181#121×C53—22no—
182#121×C53—21no—
183#121×C53—21no—
184#121×C53C2312yes—
185#121×C53C2312yes—
186#120×C53—22no—
187C4×Q8×C53—21no—
188C4×Q8×C53—21no—
189C4×Q8×C53C2312yes—
190C4×Q8×C53C2312yes—
191C4×D4×C53—21no—
192C4×D4×C53—21no—
193C4×D4×C53—22no—
194C4×D4×C53—22no—
195C4×D4×C53—22no—
196C4×D4×C53—22no—
197C4×D4×C53C2312yes—
198C4×D4×C53C2312yes—
199#117×C53—22no—
200#117×C53D412yes—
201#117×C53D412yes—
202#117×C53C2312yes—
203#117×C53C2312yes—
204#117×C53C2312yes—
205C2×C4⋊C4×C53D411yescharacteristic
206C2×C4⋊C4×C53D411yescharacteristic
207C2×C22⋊C4×C53D411yescharacteristic
208C2×C22⋊C4×C53D411yescharacteristic
209C2×C42×C53—22no—
210C2×C42×C53C2311yescharacteristic
211C2×C42×C53C2311yescharacteristic
212C24×C53C2×D411yescharacteristic
213#41×C53—28no—
214C2×Q8×C53—21no—
215C2×Q8×C53—21no—
216C2×Q8×C53C2412yes—
217C2×D4×C53—22no—
218C2×D4×C53—22no—
219C2×D4×C53—22no—
220C2×D4×C53—21no—
221C2×D4×C53—21no—
222C2×D4×C53C2412yes—
223C22×C4×C53—24no—
224C22×C4×C53—22no—
225C22×C4×C53—22no—
226C22×C4×C53—22no—
227C22×C4×C53C2×D411yescharacteristic
228C22×C4×C53C2×D412yes—
229C22×C4×C53C2×D411yescharacteristic
230C22×C4×C53C2×D411yescharacteristic
231C22×C4×C53C2×D411yescharacteristic
232C22×C4×C53C2×D411yescharacteristic
233C22×C4×C53C2412yes—
234C22×C4×C53C2411yescharacteristic
235C22×Dic53—21no—
236C22×Dic53—21no—
237C22×Dic53—21no—
238C22×Dic53—21no—
239C22×Dic53—24no—
240C22×Dic53—82no—
241C2×Dic106—24no—
242C2×Dic106—22no—
243C2×Dic106—22no—
244C2×Dic106—82no—
245C2×Dic106—82no—
246C4⋊C4×C53—22no—
247C4⋊C4×C53—22no—
248C4⋊C4×C53—21no—
249C4⋊C4×C53—21no—
250C4⋊C4×C53—22no—
251C4⋊C4×C53—22no—
252C4⋊C4×C53—22no—
253C4⋊C4×C53—22no—
254C4⋊C4×C53—21no—
255C4⋊C4×C53—21no—
256C4⋊C4×C53C2×D412yes—
257C4⋊C4×C53C2×D412yes—
258C4⋊C4×C53C2×D412yes—
259C4⋊C4×C53C2×D412yes—
260C4⋊C4×C53C2412yes—
261C4⋊C4×C53C2412yes—
262C22⋊C4×C53—22no—
263C22⋊C4×C53—22no—
264C22⋊C4×C53—22no—
265C22⋊C4×C53—22no—
266C22⋊C4×C53—22no—
267C22⋊C4×C53—22no—
268C22⋊C4×C53—22no—
269C22⋊C4×C53—22no—
270C22⋊C4×C53—22no—
271C22⋊C4×C53C2×D412yes—
272C22⋊C4×C53C2×D412yes—
273C22⋊C4×C53C2×D412yes—
274C22⋊C4×C53C2×D412yes—
275C42×C53—22no—
276C42×C53—22no—
277C42×C53—22no—
278C42×C53C2×D412yes—
279C42×C53C2×D411yescharacteristic
280C42×C53C2×D411yescharacteristic
281C42×C53C2412yes—
282C42×C53C2411yescharacteristic
283C42×C53C2411yescharacteristic
284C22⋊Dic53—24no—
285C4⋊Dic53—24no—
286C4⋊Dic53—21no—
287C4⋊Dic53—21no—
288C4⋊Dic53—24no—
289C4⋊Dic53—22no—
290C4⋊Dic53—22no—
291C4⋊Dic53—21no—
292C4⋊Dic53—21no—
293C4⋊Dic53C2412yes—
294C4⋊Dic53C2412yes—
295C4⋊Dic53C2412yes—
296C4⋊Dic53C2412yes—
297#11719919—24no—
298#11719919—22no—
299#11719919—22no—
300#11719919—24no—
301#11719919—22no—
302#11719919—22no—
303C4×Dic53—24no—
304#11719917—24no—
305#11719917—24no—
306C2×#88322C2414yes—
307C2×#88322C2414yes—
308C23×C53—22no—
309C23×C53—22no—
310C23×C53—41no—
311C23×C53—41no—
312C23×C53C22×D412yes—
313C23×C53C22×D411yescharacteristic
314Q8×C53—24no—
315Q8×C53—81no—
316Q8×C53—81no—
317D4×C53—24no—
318D4×C53—44no—
319D4×C53—81no—
320D4×C53—81no—
321D4×C53—82no—
322D4×C53—82no—
323C2×C4×C53—22no—
324C2×C4×C53—24no—
325C2×C4×C53—24no—
326C2×C4×C53—22no—
327C2×C4×C53—22no—
328C2×C4×C53—22no—
329C2×C4×C53—41no—
330C2×C4×C53—41no—
331C2×C4×C53—41no—
332C2×C4×C53—41no—
333C2×C4×C53—44no—
334C2×C4×C53—82no—
335C2×C4×C53—82no—
336C2×C4×C53C22×D412yes—
337C2×C4×C53C22×D411yescharacteristic
338C2×C4×C53C22×D411yescharacteristic
339C2×C4×C53C22×D412yes—
340C2×C4×C53C22×D412yes—
341C2×C4×C53C22×D411yescharacteristic
342C2×C4×C53C22×D411yescharacteristic
343C2×C4×C53C22×D411yescharacteristic
344C2×C4×C532−1+414yes—
345C2×C4×C53C2511yescharacteristic
346C2×Dic53—22no—
347C2×Dic53—22no—
348C2×Dic53—22no—
349C2×Dic53—22no—
350C2×Dic53—42no—
351C2×Dic53—42no—
352C2×Dic53—42no—
353C2×Dic53—42no—
354C2×Dic53—84no—
355Dic106—84no—
356Dic106—82no—
357Dic106—82no—
358#88322—24no—
359#88322—24no—
360#60867—531nomaximal, Sylow
361C22×C53—21no—
362C22×C53—21no—
363C22×C53—22no—
364C22×C53—22no—
365C22×C53—22no—
366C22×C53—44no—
367C22×C53—42no—
368C22×C53—42no—
369C22×C53—42no—
370C22×C53#53612yes—
371C22×C53C23×D411yescharacteristic
372C4×C53—22no—
373C4×C53—21no—
374C4×C53—21no—
375C4×C53—22no—
376C4×C53—21no—
377C4×C53—21no—
378C4×C53—22no—
379C4×C53—42no—
380C4×C53—42no—
381C4×C53—42no—
382C4×C53#53612yes—
383C4×C53C2×2−1+412yes—
384Dic53—42no—
385Dic53—42no—
386Dic53—42no—
387Dic53—42no—
388C2×#544—531no—
389#3455D5311yescharacteristic
390#3244—534no—
391#3243—534no—
392#3242—534no—
393#3241—534no—
394#3166—531no—
395#3165—531no—
396#3142—531no—
397#3141—531no—
398#3093—532no—
399#3092—532no—
400#3080—532no—
401#3079—532no—
402#2921—531no—
403C2×C53—22no—
404C2×C53—42no—
405C2×C53—82no—
406C2×C53C2×#53611yescharacteristic
407C2×C53#358511yescharacteristic
408C2×C53#358611yescharacteristic
409#544—534no—
410#544—534no—
411#544—1062no—
412#544—1062no—
413#542C2×D5312yes—
414#542C2×D5312yes—
415#541C2×D5312yes—
416#540C2×D5312yes—
417#539—21no—
418#539—21no—
419#538—21no—
420#538—21no—
421#533C2×D5311yescharacteristic
422#532C2×D5311yescharacteristic
423C2×C4⋊Q8—531no—
424C2×C4⋊Q8—531no—
425C2×C4⋊Q8—1061no—
426#529—22no—
427#529—22no—
428C2×#125—531no—
429C2×#125—531no—
430C2×#125—1061no—
431#525C2×D5312yes—
432C2×C22⋊Q8—1061no—
433C2×C22⋊Q8—1061no—
434C4×#41C2×D5312yes—
435C2×#117—531no—
436C2×#117C2×D5311yescharacteristic
437C22×C4⋊C4—531no—
438#501—532no—
439#501—532no—
440#501—534no—
441#500—532no—
442#499—534no—
443#498—532no—
444#491—532no—
445#490—532no—
446#489—534no—
447#488—534no—
448#487—532no—
449#486—532no—
450#485—534no—
451#485—534no—
452#484—534no—
453#483—534no—
454#482—534no—
455#482—534no—
456#481—534no—
457#480—534no—
458#479—534no—
459#479—534no—
460#478—534no—
461#478—534no—
462#477—534no—
463#476—534no—
464#475—534no—
465#474—534no—
466#433—534no—
467#433—534no—
468#428—532no—
469#428—532no—
470#428—532no—
471#428—532no—
472#423—532no—
473#417—532no—
474#417—532no—
475#417—532no—
476#417—532no—
477#407—532no—
478C4×M16—531no—
479C4×M16—531no—
480C53#6086711yescharacteristic, complemented, Sylow
481C2×#41C22×D5312yes—
482C22×Q8—1061no—
483C22×Q8—1061no—
484C23×C4—1061no—
485C23×C4C22×D5311yescharacteristic
486C2×M16—532no—
487C2×M16—532no—
488C4⋊Q8—534no—
489C4⋊Q8—532no—
490C4⋊Q8—532no—
491C4⋊Q8—1064no—
492C4⋊Q8—1064no—
493C4⋊Q8—1062no—
494C4⋊Q8—1061no—
495C4⋊Q8—1061no—
496C4⋊Q8C22×D5311yescharacteristic
497C4⋊Q8C22×D5311yescharacteristic
498C4⋊Q8C22×D5311yescharacteristic
499#127C22×D5311yescharacteristic
500#126—22no—
501#126—22no—
502#126—22no—
503#126—22no—
504#125—22no—
505#125—22no—
506#125—534no—
507#125—532no—
508#125—532no—
509#125—1064no—
510#125—1064no—
511#125—1062no—
512#125—1061no—
513#125—1061no—
514#125C22×D5312yes—
515#124—22no—
516#124—22no—
517#124C22×D5312yes—
518#123—22no—
519#123—22no—
520#123—22no—
521#123—22no—
522#123—22no—
523C22⋊Q8—21no—
524C22⋊Q8—21no—
525C22⋊Q8—22no—
526C22⋊Q8—22no—
527C22⋊Q8—1064no—
528C22⋊Q8—1064no—
529C22⋊Q8—1064no—
530C22⋊Q8—1064no—
531C22⋊Q8C22×D5312yes—
532C22⋊Q8C22×D5312yes—
533#121—21no—
534#121—21no—
535#121—22no—
536#121—22no—
537#121C22×D5312yes—
538#121C22×D5312yes—
539#120—22no—
540C4×Q8—21no—
541C4×Q8—21no—
542C4×Q8C22×D5312yes—
543C4×Q8C22×D5312yes—
544C4×D4—22no—
545C4×D4—22no—
546C4×D4—22no—
547C4×D4—22no—
548C4×D4—21no—
549C4×D4—21no—
550C4×D4C22×D5312yes—
551C4×D4C22×D5312yes—
552#117—22no—
553#117—534no—
554#117—1062no—
555#117C22⋊D5312yes—
556#117C22⋊D5312yes—
557#117C22×D5312yes—
558#117C22×D5312yes—
559#117C22×D5312yes—
560C2×C4⋊C4—531no—
561C2×C4⋊C4—531no—
562C2×C4⋊C4—534no—
563C2×C4⋊C4—531no—
564C2×C4⋊C4—531no—
565C2×C4⋊C4—1061no—
566C2×C4⋊C4—1062no—
567C2×C4⋊C4—1061no—
568C2×C4⋊C4—1061no—
569C2×C4⋊C4—1061no—
570C2×C4⋊C4—1061no—
571C2×C4⋊C4—1061no—
572C2×C4⋊C4—1061no—
573C2×C4⋊C4C22⋊D5311yescharacteristic
574C2×C4⋊C4C22⋊D5311yescharacteristic
575C2×C22⋊C4—1061no—
576C2×C22⋊C4C22⋊D5311yescharacteristic
577C2×C22⋊C4C22⋊D5311yescharacteristic
578C2×C42—22no—
579C2×C42—1061no—
580C2×C42C22×D5311yescharacteristic
581C2×C42C22×D5311yescharacteristic
582#107—534no—
583#107—534no—
584#107—534no—
585#107—534no—
586#106—534no—
587#106—534no—
588#106—534no—
589#106—534no—
590C4⋊C8—534no—
591C4⋊C8—534no—
592#103—534no—
593#103—534no—
594#103—534no—
595#103—534no—
596#102—534no—
597#102—534no—
598#102—534no—
599#102—534no—
600C22⋊C8—534no—
601C22⋊C8—534no—
602#97—532no—
603#97—532no—
604C4×C8—532no—
605C4×C8—532no—
606C24C2×C22⋊D5311yescharacteristic
607#41—28no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—1064no—
611C2×Q8—1062no—
612C2×Q8—1062no—
613C2×Q8—4242no—
614C2×Q8—4242no—
615C2×Q8C23×D5312yes—
616C2×D4—22no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4C23×D5312yes—
622C22×C4—24no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—1064no—
627C22×C4—1061no—
628C22×C4—1061no—
629C22×C4—1061no—
630C22×C4—1061no—
631C22×C4—4242no—
632C22×C4C2×C22⋊D5311yescharacteristic
633C22×C4C2×C22⋊D5312yes—
634C22×C4C2×C22⋊D5311yescharacteristic
635C22×C4C2×C22⋊D5311yescharacteristic
636C22×C4C2×C22⋊D5311yescharacteristic
637C22×C4C2×C22⋊D5311yescharacteristic
638C22×C4C23×D5312yes—
639C22×C4C23×D5311yescharacteristic
640M16—1064no—
641M16—1064no—
642C2×C8—534no—
643C2×C8—534no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—532no—
655C4⋊C4—532no—
656C4⋊C4—532no—
657C4⋊C4—532no—
658C4⋊C4—1064no—
659C4⋊C4—1061no—
660C4⋊C4—1061no—
661C4⋊C4—1061no—
662C4⋊C4—1061no—
663C4⋊C4—1064no—
664C4⋊C4—1062no—
665C4⋊C4—1062no—
666C4⋊C4—1064no—
667C4⋊C4—1062no—
668C4⋊C4—1062no—
669C4⋊C4—1064no—
670C4⋊C4—1062no—
671C4⋊C4—1062no—
672C4⋊C4C2×C22⋊D5312yes—
673C4⋊C4C2×C22⋊D5312yes—
674C4⋊C4C2×C22⋊D5312yes—
675C4⋊C4C2×C22⋊D5312yes—
676C4⋊C4C23×D5312yes—
677C4⋊C4C23×D5312yes—
678C22⋊C4—22no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—22no—
683C22⋊C4—22no—
684C22⋊C4—22no—
685C22⋊C4—22no—
686C22⋊C4—22no—
687C22⋊C4—1064no—
688C22⋊C4C2×C22⋊D5312yes—
689C22⋊C4C2×C22⋊D5312yes—
690C22⋊C4C2×C22⋊D5312yes—
691C22⋊C4C2×C22⋊D5312yes—
692C42—22no—
693C42—22no—
694C42—22no—
695C42—1064no—
696C42C2×C22⋊D5312yes—
697C42C2×C22⋊D5311yescharacteristic
698C42C2×C22⋊D5311yescharacteristic
699C42C23×D5311yescharacteristic
700C42C23×D5311yescharacteristic
701C42C23×D5312yes—
702C23—22no—
703C23—22no—
704C23—41no—
705C23—41no—
706C23C22×C22⋊D5312yes—
707C23C22×C22⋊D5311yescharacteristic
708Q8—24no—
709Q8—81no—
710Q8—81no—
711Q8—4244no—
712Q8—4242no—
713Q8—4242no—
714D4—24no—
715D4—44no—
716D4—81no—
717D4—81no—
718D4—82no—
719D4—82no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—44no—
731C2×C4—82no—
732C2×C4—82no—
733C2×C4—1062no—
734C2×C4—1062no—
735C2×C4—1062no—
736C2×C4—1062no—
737C2×C4—4244no—
738C2×C4—2122no—
739C2×C4—2122no—
740C2×C4—2122no—
741C2×C4—2122no—
742C2×C4C22×C22⋊D5312yes—
743C2×C4C22×C22⋊D5312yes—
744C2×C4C22×C22⋊D5312yes—
745C2×C4C22×C22⋊D5311yescharacteristic
746C2×C4C22×C22⋊D5311yescharacteristic
747C2×C4C22×C22⋊D5311yescharacteristic
748C2×C4C22×C22⋊D5311yescharacteristic
749C2×C4C22×C22⋊D5311yescharacteristic
750C2×C4#1313326414yes—
751C2×C4C24×D5311yescharacteristic
752C8—1064no—
753C8—1064no—
754C22—21no—
755C22—21no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—44no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22#1681119412yes—
764C22C23×C22⋊D5311yescharacteristic
765C4—22no—
766C4—22no—
767C4—21no—
768C4—21no—
769C4—22no—
770C4—21no—
771C4—21no—
772C4—42no—
773C4—42no—
774C4—42no—
775C4—2122no—
776C4—2122no—
777C4—2122no—
778C4—2122no—
779C4#1681119412yes—
780C4C2×#1313326412yes—
781C2—22no—
782C2—42no—
783C2—82no—
784C2C2×#1681119411yescharacteristic
785C2#2028949411yescharacteristic
786C2#2028950111yescharacteristic
subgroupG/H
centerC22C23×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
Fitting, prime radicalC53×#3455C2
socleC22×C53C23×D4
hypercenter#3455D53
hypocenterC53#60867
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×#117 ◁ #3455

Complements

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

NH ≅ G/Ntype
1. C2×#16811251C2semidirect
2. #20286007C2semidirect
3. #20285992C2semidirect
4. #20285977C2semidirect
5. #20285962C2semidirect
6. #20285268C2semidirect
7. #20285262C2semidirect
8. #20285115C2semidirect
9. #20285108C2semidirect
10. #20284644C2semidirect
11. #20284635C2semidirect
12. #20284537C2semidirect
13. #20284530C2semidirect
14. #20283353C2semidirect
30. #16811033C22semidirect
31. #16811029C22semidirect
32. #16811029C22semidirect
33. #16811026C22semidirect
34. #16811022C22semidirect
35. #16811019C22semidirect
36. #16810991C22semidirect
37. #16810987C22semidirect
38. #16810982C22semidirect
39. #16810977C22semidirect
40. #16810973C22semidirect
41. #16810969C22semidirect
50. #16810930C22semidirect
51. #16810930C22semidirect
52. #16810923C22semidirect
53. #16810923C22semidirect
54. #16810918C22semidirect
55. #16810913C22semidirect
56. #16810908C22semidirect
57. #16810903C22semidirect
480. C53#60867semidirect

Maximal subgroups

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

subgroupindex
C2×#168112512
#202860072
#202859922
#202859772
#202859622
#202852682
#202852622
#202851152
#202851082
#202846442
#202846352
#202845372
#202845302
#202833532
C53×#34552
#6086753