Finite Group Databasebeta

← #28292985

Subgroups — #28292985

Order 13568.

7900 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289237C218yesmaximal, complemented
2#20289120C212yesmaximal, complemented
3#20289115C211yesmaximal, characteristic, complemented
4#20289077C218yesmaximal, complemented
5#20288953C214yesmaximal, complemented
6#20288748C214yesmaximal, complemented
7#20288746C214yesmaximal, complemented
8#20288623C214yesmaximal, complemented
9#20288587C214yesmaximal, complemented
10#20288565C214yesmaximal, complemented
11#20288492C214yesmaximal, complemented
12#20288473C214yesmaximal, complemented
13#20288379C218yesmaximal, complemented
14#20288012C211yesmaximal, characteristic, complemented
15#532×D53C212yesmaximal, complemented
16C53×#3548C211yesmaximal, characteristic, complemented
17C2×#13133263C2218yescomplemented
18C2×#41×D53C2214yescomplemented
19#16811371C2214yescomplemented
20#16811365C2218yescomplemented
21#16811361C22116yescomplemented
22#16811357C22116yescomplemented
23#16811344C2218yescomplemented
24#16811339C2214yescomplemented
25#16811338C2214yescomplemented
26#16811338C2214yescomplemented
27#16811333C2214yescomplemented
28#16811326C2218yescomplemented
29#16811323C2218yescomplemented
30#16811321C2218yescomplemented
31#16811320C2218yescomplemented
32#16811295C2214yescomplemented
33#16811292C2218yescomplemented
34#16811291C22116yescomplemented
35#16811283C22116yescomplemented
36#16811276C2214yescomplemented
37#16811274C2218yescomplemented
38#16811265C22116yescomplemented
39#16811264C2218yescomplemented
40#16811264C22116yescomplemented
41#16811262C22116yescomplemented
42#16811262C22116yescomplemented
43#16811261C2218yescomplemented
44D4×D212C2214yescomplemented
45D4×D212C2214yescomplemented
46D4×D212C2218yescomplemented
47#16811258C2214yescomplemented
48#16811258C2218yescomplemented
49#16811257C2218yescomplemented
50#16811257C22116yescomplemented
51#16811257C22116yescomplemented
52#16811243C22116yescomplemented
53#16811229C2214yescomplemented
54#16811228C2214yescomplemented
55#16811227C2214yescomplemented
56#16811213C22116yescomplemented
57#16811209C22116yescomplemented
58#16811205C22116yescomplemented
59#16811203C2218yescomplemented
60#16811203C2218yescomplemented
61#16811189C2218yescomplemented
62#16811189C2218yescomplemented
63#16811189C22116yescomplemented
64#16811189C2218yescomplemented
65#16811187C2218yescomplemented
66#16811184C22116yescomplemented
67#16811179C2214yescomplemented
68#16811178C2212yescomplemented
69#16811174C2212yescomplemented
70#16811174C2212yescomplemented
71#16811173C2211yescharacteristic, complemented
72#16811173C2212yescomplemented
73#16811172C2214yescomplemented
74#16811171C2212yescomplemented
75#16811170C2214yescomplemented
76#16811170C2218yescomplemented
77#16811170C2214yescomplemented
78#16811169C2214yescomplemented
79#16811168C2214yescomplemented
80#16811168C2214yescomplemented
81C4⋊Q8×D53C2212yescomplemented
82#127×D53C2214yescomplemented
83#127×D53C2212yescomplemented
84#16811160C2214yescomplemented
85#16811159C2214yescomplemented
86#16811158C2214yescomplemented
87#124×D53C2214yescomplemented
88#16811136C2214yescomplemented
89#16811136C2218yescomplemented
90#16811135C2212yescomplemented
91#16811130C2218yescomplemented
92C2×#13133192C2218yescomplemented
93#121×D53C2214yescomplemented
94#121×D53C2218yescomplemented
95#121×D53C2214yescomplemented
96#16811104C2218yescomplemented
97#16811095C2218yescomplemented
98C4×#11719949C2214yescomplemented
99#16811091C2212yescomplemented
100C4×D4×D53C2214yescomplemented
101C4×D4×D53C2214yescomplemented
102C2×C42×D53C2211yescharacteristic, complemented
103C53×#562C2214yescomplemented
104C53×#554C2214yescomplemented
105C53×#550C2214yescomplemented
106C53×#547C2214yescomplemented
107C53×#540C2214yescomplemented
108C53×#537C2218yescomplemented
109C53×#533C2211yescharacteristic, complemented
110C53×#532C2212yescomplemented
111#13133263—432no—
112C2×#11719949C2314yes—
113C2×#11719949C2314yes—
114C2×#11719949C2318yes—
115C2×#11719945C2318yes—
116C2×#11719945C23116yes—
117C2×#11719945C2312yes—
118C2×#11719945C2314yes—
119C2×#11719947C2318yes—
120C2×#11719947C2314yes—
121#41×D53—416no—
122C2×Q8×D53C2314yes—
123C22×D212C23116yes—
124C22×D212C2318yes—
125C2×D4×D53C2314yes—
126C2×D4×D53C23116yes—
127C2×D4×D53C2314yes—
128C2×D4×D53C2318yes—
129C2×D4×D53C2318yes—
130C2×D4×D53C23116yes—
131C2×D4×D53C2318yes—
132C2×D4×D53C2314yes—
133C22×C4×D53C2312yes—
134C22×C4×D53C2311yescharacteristic
135C22×C4×D53C2318yes—
136#13133217C2312yes—
137#13133217C2311yescharacteristic
138#13133216C2314yes—
139#13133216C2314yes—
140#13133215C2314yes—
141#13133214C2312yes—
142#13133214C2314yes—
143#13133214C2311yescharacteristic
144#13133213C23116yes—
145#13133213C23116yes—
146#13133213C2314yes—
147#13133213C2314yes—
148#13133213C2314yes—
149#13133212C23116yes—
150#13133212C2318yes—
151#13133210C23116yes—
152#13133209C2314yes—
153#13133208C2314yes—
154#13133206C2314yes—
155#13133206C23116yes—
156#13133206C2314yes—
157#13133205C2312yes—
158#13133205C2314yes—
159#13133204C2314yes—
160#13133203C2318yes—
161#13133203C23116yes—
162#13133203C23116yes—
163#13133203C23116yes—
164#13133203C2318yes—
165#13133202C2318yes—
166#13133202C23116yes—
167#13133202C23116yes—
168#13133202C23116yes—
169#13133201C2314yes—
170#13133200C23116yes—
171#13133198C23116yes—
172#13133197C2314yes—
173#13133195C23116yes—
174#13133195C23116yes—
175#13133193C2318yes—
176#13133193C2314yes—
177#13133192C23116yes—
178#13133192C2318yes—
179#13133192C23116yes—
180#13133192C23116yes—
181#13133192C2318yes—
182#13133192C2314yes—
183#13133192C2318yes—
184#13133192C2314yes—
185#13133192C2314yes—
186#13133192C2314yes—
187#13133191C2318yes—
188#13133191C2318yes—
189#13133191C23116yes—
190#13133191C2314yes—
191#13133191C2314yes—
192#13133191C2314yes—
193#13133190C23116yes—
194#13133190C2318yes—
195#13133190C23116yes—
196#13133190C23116yes—
197#13133190C2318yes—
198#13133189C23116yes—
199#13133189C2318yes—
200#13133189C2318yes—
201#13133188C2318yes—
202#13133188C23116yes—
203#13133188C2314yes—
204#13133188C2318yes—
205#13133188C2314yes—
206#13133187C23116yes—
207#13133187C23116yes—
208#13133187C23116yes—
209#13133187C23116yes—
210#13133187C2314yes—
211#13133185C23116yes—
212#13133185C23116yes—
213#13133185C23116yes—
214#13133185C23116yes—
215Q8×Dic53C2314yes—
216#13133182C23116yes—
217#13133182C2314yes—
218C4×D212C2314yes—
219C4×D212C2318yes—
220C4×D212C2314yes—
221C4×D212C2318yes—
222C4×D212C2314yes—
223D4×Dic53C2314yes—
224D4×Dic53C2314yes—
225#13133179C2314yes—
226#13133179C23116yes—
227#13133179C2314yes—
228#13133179C2314yes—
229#13133179C2318yes—
230#13133179C2314yes—
231C4×C22⋊D53C23116yes—
232C4×C22⋊D53C2318yes—
233C4×C22⋊D53C2318yes—
234C4×C22⋊D53C23116yes—
235C4×C22⋊D53C23116yes—
236#13133177C2318yes—
237#13133177C2318yes—
238#13133177C23116yes—
239#13133177C2318yes—
240#13133176C2318yes—
241#13133175C2318yes—
242#13133175C2318yes—
243#13133175C2314yes—
244#13133175C2318yes—
245#13133174C2314yes—
246C4⋊C4×D53C2318yes—
247C4⋊C4×D53C2314yes—
248C4⋊C4×D53C2314yes—
249C2×#11719921C23116yes—
250C22⋊C4×D53C23116yes—
251C22⋊C4×D53C2318yes—
252C22⋊C4×D53C2318yes—
253C2×C4×Dic53C2311yescharacteristic
254C2×C4×Dic53C2312yes—
255C42×D53C2312yes—
256C42×D53C2312yes—
257C42×D53C2312yes—
258C42×D53C2312yes—
259C42×D53C2314yes—
260C2×#41×C53C2318yes—
261C2×#41×C53C2314yes—
262C4⋊Q8×C53C2312yes—
263C4⋊Q8×C53C2312yes—
264#127×C53C2312yes—
265#127×C53C2314yes—
266#125×C53C2312yes—
267#125×C53C2314yes—
268#124×C53C2314yes—
269#123×C53C23116yes—
270C22⋊Q8×C53C23116yes—
271C22⋊Q8×C53C2318yes—
272C22⋊Q8×C53C2314yes—
273#121×C53C23116yes—
274#121×C53C2314yes—
275#121×C53C2314yes—
276#121×C53C2318yes—
277#121×C53C23116yes—
278C4×Q8×C53C2314yes—
279C4×D4×C53C2314yes—
280C4×D4×C53C2314yes—
281C4×D4×C53C2318yes—
282#117×C53C2312yes—
283C2×C4⋊C4×C53C2318yes—
284C2×C42×C53C2311yescharacteristic
285C23×D53C2411yescharacteristic
286C23×D53C2418yes—
287C23×D53C24116yes—
288#41×C53—48no—
289#41×C53—416no—
290C2×Q8×C53C2414yes—
291C2×Q8×C53C2414yes—
292C2×D4×C53C2414yes—
293C2×D4×C53C2414yes—
294C2×D4×C53C2418yes—
295C2×D4×C53C24116yes—
296C2×D4×C53C2414yes—
297C22×C4×C53C2411yescharacteristic
298C22×C4×C53C2412yes—
299C22×C4×C53C2418yes—
300C22×C4×C53C24116yes—
301C2×C22⋊D53C2418yes—
302C2×C22⋊D53C2418yes—
303C2×C22⋊D53C2418yes—
304C2×C22⋊D53C2414yes—
305C2×C22⋊D53C2418yes—
306C2×C22⋊D53C24116yes—
307C2×C22⋊D53C24116yes—
308C2×C22⋊D53C2418yes—
309C22×Dic53C2412yes—
310C22×Dic53C2411yescharacteristic
311C22×Dic53C2418yes—
312#11719949—216no—
313#11719949—48no—
314#11719949—416no—
315Q8×D53—48no—
316#11719947—416no—
317#11719947—48no—
318D4×D53—216no—
319D4×D53—48no—
320D4×D53—416no—
321D4×D53—416no—
322D4×D53—48no—
323D4×D53—432no—
324D4×D53—416no—
325D4×D53—432no—
326#11719945—232no—
327#11719945—432no—
328#11719945—48no—
329#11719945—44no—
330C2×D212—416no—
331C2×D212—432no—
332C2×D212C2418yes—
333C2×D212C2414yes—
334C2×D212C2418yes—
335C2×D212C2414yes—
336C2×D212C2414yes—
337C2×D212C2412yes—
338C2×D212C2414yes—
339C2×D212C24116yes—
340C2×D212C24116yes—
341C2×C4×D53—28no—
342C2×C4×D53—42no—
343C2×C4×D53—416no—
344C2×C4×D53C2412yes—
345C2×C4×D53C2412yes—
346C2×C4×D53C2412yes—
347C2×C4×D53C2412yes—
348C2×C4×D53C2414yes—
349C2×C4×D53C2418yes—
350C2×C4×D53C2418yes—
351C2×C4×D53C2412yes—
352C2×C4×D53C2418yes—
353C2×C4×D53C2418yes—
354C2×C4×D53C24116yes—
355C2×C4×D53C2412yes—
356C2×Dic106C2418yes—
357C2×Dic106C2412yes—
358C2×Dic106C2414yes—
359C4⋊C4×C53C2414yes—
360C4⋊C4×C53C2414yes—
361C4⋊C4×C53C24116yes—
362C4⋊C4×C53C2414yes—
363C4⋊C4×C53C2414yes—
364C4⋊C4×C53C2418yes—
365C22⋊C4×C53C2414yes—
366C22⋊C4×C53C24116yes—
367C22⋊C4×C53C2418yes—
368C22⋊C4×C53C2418yes—
369C42×C53C2411yescharacteristic
370C42×C53C2412yes—
371C42×C53C2411yescharacteristic
372C42×C53C2414yes—
373C22⋊Dic53C2418yes—
374C22⋊Dic53C2418yes—
375C22⋊Dic53C24116yes—
376#11719921C2418yes—
377#11719921C2418yes—
378#11719921C24116yes—
379#11719921C2418yes—
380#11719921C2418yes—
381#11719921C2418yes—
382#11719921C24116yes—
383#11719921C2418yes—
384#11719921C24116yes—
385#11719921C2418yes—
386#11719921C2418yes—
387C4⋊Dic53C2414yes—
388C4⋊Dic53C2414yes—
389C4⋊Dic53C2414yes—
390C4⋊Dic53C2418yes—
391#11719919C2418yes—
392#11719919C2418yes—
393#11719919C24116yes—
394#11719919C2418yes—
395C4×Dic53C2411yescharacteristic
396C4×Dic53C2411yescharacteristic
397C4×Dic53C2412yes—
398C4×Dic53C2412yes—
399C4×Dic53C2412yes—
400C4×Dic53C2412yes—
401C4×Dic53C2412yes—
402C4×Dic53C2418yes—
403C4×Dic53C24116yes—
404C23×C53C2511yescharacteristic
405C23×C53C2518yes—
406C22×D53—24no—
407C22×D53—216no—
408C22×D53—41no—
409C22×D53—48no—
410C22×D53—48no—
411C22×D53—416no—
412C22×D53—416no—
413C22×D53—416no—
414C22×D53C2518yes—
415C22×D53C2514yes—
416C22×D53C2512yes—
417Q8×C53—28no—
418Q8×C53—44no—
419D4×C53—28no—
420D4×C53—28no—
421D4×C53—416no—
422D4×C53—48no—
423D4×C53—44no—
424C2×C4×C53—24no—
425C2×C4×C53—216no—
426C2×C4×C53—22no—
427C2×C4×C53—416no—
428C2×C4×C53C2512yes—
429C2×C4×C53C2511yescharacteristic
430C2×C4×C53C2518yes—
431C2×C4×C53C2518yes—
432C2×C4×C53C2512yes—
433C2×C4×C53C2511yescharacteristic
434C22⋊D53—216no—
435C22⋊D53—216no—
436C22⋊D53—216no—
437C22⋊D53—416no—
438C22⋊D53—48no—
439C22⋊D53—44no—
440C22⋊D53—416no—
441C22⋊D53—48no—
442C2×Dic53—24no—
443C2×Dic53—48no—
444C2×Dic53—41no—
445C2×Dic53C2518yes—
446C2×Dic53C2514yes—
447C2×Dic53C2512yes—
448C2×Dic53C2512yes—
449C2×Dic53C2512yes—
450D212—216no—
451D212—216no—
452D212—28no—
453D212—28no—
454D212—28no—
455D212—416no—
456D212—416no—
457D212—42no—
458D212—44no—
459C4×D53—24no—
460C4×D53—24no—
461C4×D53—216no—
462C4×D53—24no—
463C4×D53—28no—
464C4×D53—24no—
465C4×D53—216no—
466C4×D53—42no—
467C4×D53—48no—
468C4×D53—48no—
469C4×D53—416no—
470C4×D53H(5,𝔽2)18yescomplemented
471Dic106—216no—
472Dic106—42no—
473Dic106—44no—
474#62834—531nomaximal, Sylow
475C22×C53—22no—
476C22×C53—28no—
477C22×C53—28no—
478C22×C53—21no—
479C22×C53—28no—
480C22×C53C2611yescharacteristic
481C2×D53—22no—
482C2×D53—22no—
483C2×D53—28no—
484C2×D53—28no—
485C2×D53—28no—
486C2×D53—24no—
487C2×D53—28no—
488C2×D53—44no—
489C2×D53—816no—
490C2×D53—1616no—
491C2×D53C2×H(5,𝔽2)14yes—
492C4×C53—28no—
493C4×C53—22no—
494C4×C53—28no—
495C4×C53—21no—
496C4×C53C2×H(5,𝔽2)14yes—
497C4×C53#58512yes—
498Dic53—28no—
499Dic53—22no—
500Dic53—24no—
501Dic53—22no—
502Dic53C2×H(5,𝔽2)14yes—
503#3558—538no—
504#3549—532no—
505#3548—531no—
506#3548D5311yescharacteristic, complemented
507#3546—538no—
508#3537—534no—
509#3519—534no—
510#3519—534no—
511#3511—534no—
512#3508—534no—
513#3506—534no—
514#3498—534no—
515#3496—534no—
516#3488—538no—
517#3444—531no—
518C2×#532—532no—
519C2×C53—41no—
520C2×C53—48no—
521C2×C53C22×H(5,𝔽2)12yes—
522C2×C53C2×#58511yescharacteristic
523D53—24no—
524D53—48no—
525D53—44no—
526C2×H(5,𝔽2)—538no—
527C22×#41—534no—
528#562—534no—
529#562C2×D5314yescomplemented
530H(3,𝔽4)—538no—
531#560—5316no—
532#559—5316no—
533#556—538no—
534#555—534no—
535#555—534no—
536#555—534no—
537#554—534no—
538#554C2×D5314yescomplemented
539#553—538no—
540#553—538no—
541#553—538no—
542#553—538no—
543#550—538no—
544#550—5316no—
545#550—534no—
546#550C2×D5314yescomplemented
547#548—5316no—
548#547—534no—
549#547—538no—
550#547C2×D5314yescomplemented
551#546—538no—
552#546—5316no—
553#546—5316no—
554#546—538no—
555#546—5316no—
556#546—5316no—
557D42—538no—
558D42—534no—
559D42—5316no—
560D42—5316no—
561D42—538no—
562D42—534no—
563D42—538no—
564D42—534no—
565#542—5316no—
566#540—534no—
567#540—534no—
568#540—534no—
569#540C2×D5314yescomplemented
570#538—5316no—
571#538—5316no—
572#538—5316no—
573#537—538no—
574#537—538no—
575#537C2×D5318yescomplemented
576#535—538no—
577#535—538no—
578#535—538no—
579#535—5316no—
580#535—538no—
581#534—5316no—
582#533—532no—
583#533—534no—
584#533C2×D5311yescharacteristic, complemented
585#532—534no—
586#532—532no—
587#532—532no—
588#532—532no—
589#532—534no—
590#532—534no—
591#532—534no—
592#532—534no—
593#532—534no—
594#532—538no—
595#532—532no—
596#532—531no—
597#532C2×D5312yescomplemented
598C2×C4⋊Q8—532no—
599C2×#127—532no—
600C2×#127—534no—
601#529—534no—
602#529—534no—
603#529—534no—
604C2×#124—534no—
605#525—538no—
606#525—534no—
607#525—538no—
608#525—532no—
609C2×#121—534no—
610C2×#121—534no—
611C2×#121—538no—
612C2×#121—538no—
613#520—538no—
614#518—538no—
615C4×#41—534no—
616C4×#41—532no—
617C2×C4×D4—534no—
618C2×C4×D4—534no—
619C22×C42—531no—
620C53#6283411yescharacteristic, complemented, Sylow
621H(5,𝔽2)—21232no—
622C2×#41—534no—
623C2×#41—538no—
624C2×#41—534no—
625C2×#41—534no—
626C2×#41—538no—
627C2×#41—538no—
628C2×#41—532no—
629C2×#41—534no—
630C2×#41—5316no—
631C2×#41—21216no—
632C2×#41C22×D5318yes—
633C2×#41C22×D5314yes—
634C22×Q8—534no—
635C22×D4—534no—
636C22×D4—534no—
637C22×D4—538no—
638C22×D4—538no—
639C22×D4—5316no—
640C22×D4—538no—
641C22×D4—534no—
642C22×D4—5316no—
643C22×D4—5316no—
644C22×D4—538no—
645C23×C4—532no—
646C23×C4—538no—
647C23×C4—531no—
648C4⋊Q8—534no—
649C4⋊Q8—534no—
650C4⋊Q8—534no—
651C4⋊Q8—532no—
652C4⋊Q8—531no—
653C4⋊Q8C22×D5312yes—
654C4⋊Q8C22×D5312yes—
655#127—534no—
656#127—534no—
657#127—534no—
658#127—5316no—
659#127—5316no—
660#127—532no—
661#127—534no—
662#127—531no—
663#127C22×D5312yes—
664#127C22×D5314yes—
665#126—538no—
666#126—5316no—
667#126—5316no—
668#125—534no—
669#125—534no—
670#125C22×D5312yes—
671#125C22×D5314yes—
672#124—534no—
673#124—534no—
674#124—5316no—
675#124—534no—
676#124—538no—
677#124—538no—
678#124—5316no—
679#124—5316no—
680#124—5316no—
681#124—534no—
682#124—532no—
683#124C22×D5314yes—
684#123—5316no—
685#123—5316no—
686#123—538no—
687#123—5316no—
688#123—5316no—
689#123—5316no—
690#123—534no—
691#123C22×D53116yes—
692C22⋊Q8—534no—
693C22⋊Q8—538no—
694C22⋊Q8—534no—
695C22⋊Q8—5316no—
696C22⋊Q8—5316no—
697C22⋊Q8C22×D5314yes—
698C22⋊Q8C22×D5318yes—
699C22⋊Q8C22×D53116yes—
700#121—534no—
701#121—534no—
702#121—538no—
703#121—538no—
704#121—5316no—
705#121—538no—
706#121—538no—
707#121—5316no—
708#121—534no—
709#121—534no—
710#121—538no—
711#121—534no—
712#121—538no—
713#121—5316no—
714#121—534no—
715#121—534no—
716#121—534no—
717#121—5316no—
718#121—538no—
719#121—538no—
720#121—5316no—
721#121—534no—
722#121—538no—
723#121—5316no—
724#121—538no—
725#121—538no—
726#121—5316no—
727#121—5316no—
728#121—5316no—
729#121C22×D5314yes—
730#121C22×D5314yes—
731#121C22×D5318yes—
732#121C22×D53116yes—
733#121C22×D53116yes—
734#120—5316no—
735#120—5316no—
736#120—5316no—
737#120—5316no—
738#120—534no—
739#120—5316no—
740#120—5316no—
741#120—5316no—
742#120—5316no—
743C4×Q8—534no—
744C4×Q8—534no—
745C4×Q8—5316no—
746C4×Q8C22×D5314yes—
747C4×D4—534no—
748C4×D4—534no—
749C4×D4—538no—
750C4×D4—538no—
751C4×D4—5316no—
752C4×D4—5316no—
753C4×D4—5316no—
754C4×D4—534no—
755C4×D4—534no—
756C4×D4—538no—
757C4×D4—534no—
758C4×D4—534no—
759C4×D4—5316no—
760C4×D4—538no—
761C4×D4—538no—
762C4×D4—538no—
763C4×D4—5316no—
764C4×D4—534no—
765C4×D4—534no—
766C4×D4—538no—
767C4×D4—534no—
768C4×D4—538no—
769C4×D4C22×D5314yes—
770C4×D4C22×D5314yes—
771C4×D4C22×D5318yes—
772#117—538no—
773#117—534no—
774#117—538no—
775#117—538no—
776#117—538no—
777#117—534no—
778#117C22×D5312yes—
779C2×C4⋊C4—534no—
780C2×C4⋊C4—534no—
781C2×C4⋊C4—538no—
782C2×C4⋊C4C22×D5318yes—
783C2×C22⋊C4—5316no—
784C2×C22⋊C4—538no—
785C2×C22⋊C4—538no—
786C2×C22⋊C4—5316no—
787C2×C42—531no—
788C2×C42—532no—
789C2×C42—532no—
790C2×C42—532no—
791C2×C42—534no—
792C2×C42—532no—
793C2×C42—532no—
794C2×C42C22×D5311yescharacteristic
795C24—531no—
796C24—538no—
797C24—5316no—
798#41—48no—
799#41—416no—
800#41—10632no—
801#41—10616no—
802#41—2124no—
803#41—2128no—
804#41—21232no—
805#41—2128no—
806#41—21216no—
807#41—2128no—
808#41—21216no—
809C2×Q8—538no—
810C2×Q8—532no—
811C2×Q8—534no—
812C2×Q8—2128no—
813C2×Q8C23×D5314yes—
814C2×Q8C23×D5314yes—
815C2×D4—538no—
816C2×D4—538no—
817C2×D4—538no—
818C2×D4—534no—
819C2×D4—538no—
820C2×D4—5316no—
821C2×D4—5316no—
822C2×D4—538no—
823C2×D4—534no—
824C2×D4—538no—
825C2×D4—538no—
826C2×D4—534no—
827C2×D4—534no—
828C2×D4—532no—
829C2×D4—534no—
830C2×D4—5316no—
831C2×D4—5316no—
832C2×D4—10616no—
833C2×D4—21216no—
834C2×D4—21232no—
835C2×D4—2128no—
836C2×D4—21216no—
837C2×D4—21216no—
838C2×D4—2128no—
839C2×D4—21232no—
840C2×D4—21216no—
841C2×D4—21232no—
842C2×D4C23×D5314yes—
843C2×D4C23×D5314yes—
844C2×D4C23×D5314yes—
845C2×D4C23×D5318yes—
846C2×D4C23×D53116yes—
847C22×C4—532no—
848C22×C4—532no—
849C22×C4—531no—
850C22×C4—538no—
851C22×C4—532no—
852C22×C4—532no—
853C22×C4—532no—
854C22×C4—532no—
855C22×C4—534no—
856C22×C4—538no—
857C22×C4—538no—
858C22×C4—532no—
859C22×C4—538no—
860C22×C4—538no—
861C22×C4—5316no—
862C22×C4—1068no—
863C22×C4—2122no—
864C22×C4—21216no—
865C22×C4C23×D5311yescharacteristic
866C22×C4C23×D5312yes—
867C22×C4C23×D5318yes—
868C22×C4C23×D53116yes—
869C4⋊C4—534no—
870C4⋊C4—534no—
871C4⋊C4—538no—
872C4⋊C4—538no—
873C4⋊C4—5316no—
874C4⋊C4—534no—
875C4⋊C4—538no—
876C4⋊C4—538no—
877C4⋊C4C23×D5314yes—
878C4⋊C4C23×D5314yes—
879C4⋊C4C23×D5314yes—
880C4⋊C4C23×D53116yes—
881C4⋊C4C23×D5318yes—
882C4⋊C4C23×D5314yes—
883C22⋊C4—538no—
884C22⋊C4—538no—
885C22⋊C4—5316no—
886C22⋊C4—538no—
887C22⋊C4—538no—
888C22⋊C4—5316no—
889C22⋊C4—5316no—
890C22⋊C4—538no—
891C22⋊C4—538no—
892C22⋊C4—538no—
893C22⋊C4—538no—
894C22⋊C4—538no—
895C22⋊C4—538no—
896C22⋊C4—5316no—
897C22⋊C4C23×D53116yes—
898C22⋊C4C23×D5318yes—
899C22⋊C4C23×D5318yes—
900C22⋊C4C23×D5314yes—
901C42—531no—
902C42—531no—
903C42—532no—
904C42—532no—
905C42—532no—
906C42—532no—
907C42—532no—
908C42—538no—
909C42—5316no—
910C42C23×D5311yescharacteristic
911C42C23×D5312yes—
912C42C23×D5311yescharacteristic
913C42C23×D5314yes—
914C23—532no—
915C23—534no—
916C23—538no—
917C23—10616no—
918C23—1064no—
919C23—21216no—
920C23—21216no—
921C23—21216no—
922C23—2128no—
923C23—2128no—
924C23—2121no—
925C23C24×D5318yes—
926C23C24×D5311yescharacteristic
927Q8—28no—
928Q8—44no—
929Q8—10616no—
930Q8—2124no—
931Q8—2122no—
932D4—28no—
933D4—28no—
934D4—416no—
935D4—48no—
936D4—44no—
937D4—10616no—
938D4—10616no—
939D4—10616no—
940D4—10616no—
941D4—10616no—
942D4—1068no—
943D4—1068no—
944D4—1068no—
945D4—21216no—
946D4—21216no—
947D4—2124no—
948D4—2122no—
949D4—2128no—
950D4—21216no—
951D4—21216no—
952D4—2128no—
953D4—2124no—
954C2×C4—24no—
955C2×C4—216no—
956C2×C4—22no—
957C2×C4—416no—
958C2×C4—532no—
959C2×C4—538no—
960C2×C4—534no—
961C2×C4—532no—
962C2×C4—532no—
963C2×C4—538no—
964C2×C4—1064no—
965C2×C4—10616no—
966C2×C4—1064no—
967C2×C4—1064no—
968C2×C4—1064no—
969C2×C4—10616no—
970C2×C4—1064no—
971C2×C4—1068no—
972C2×C4—2122no—
973C2×C4—2128no—
974C2×C4—2128no—
975C2×C4—21216no—
976C2×C4—2121no—
977C2×C4—2128no—
978C2×C4C24×D5311yescharacteristic
979C2×C4C24×D5312yes—
980C2×C4C24×D5318yes—
981C2×C4C24×D5318yes—
982C2×C4C24×D5312yes—
983C2×C4C24×D5311yescharacteristic
984C22—22no—
985C22—28no—
986C22—28no—
987C22—21no—
988C22—28no—
989C22—534no—
990C22—84816no—
991C22—1062no—
992C22—1062no—
993C22—1068no—
994C22—1068no—
995C22—1068no—
996C22—1064no—
997C22—1068no—
998C22—42416no—
999C22—2124no—
1000C22C25×D5311yescharacteristic
1001C4—28no—
1002C4—22no—
1003C4—28no—
1004C4—21no—
1005C4—534no—
1006C4—1062no—
1007C4—1068no—
1008C4—1062no—
1009C4—1064no—
1010C4H(5,𝔽2)×D5314yes—
1011C4#1681146012yes—
1012C2—48no—
1013C2—41no—
1014C2—1064no—
1015C2—2124no—
1016C2—2128no—
1017C2C2×H(5,𝔽2)×D5312yes—
1018C2C2×#1681146011yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3548C2
hypercenter#3548D53
hypocenterC53#62834
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3548

Complements

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

NH ≅ G/Ntype
1. #20289237C2semidirect
2. #20289120C2semidirect
3. #20289115C2semidirect
4. #20289077C2semidirect
5. #20288953C2semidirect
6. #20288748C2semidirect
7. #20288746C2semidirect
8. #20288623C2semidirect
9. #20288587C2semidirect
10. #20288565C2semidirect
11. #20288492C2semidirect
12. #20288473C2semidirect
13. #20288379C2semidirect
14. #20288012C2semidirect
15. #532×D53C2semidirect
16. C53×#3548C2semidirect
17. C2×#13133263C22semidirect
18. C2×#41×D53C22semidirect
19. #16811371C22semidirect
20. #16811365C22semidirect
21. #16811361C22semidirect
22. #16811357C22semidirect
23. #16811344C22semidirect
24. #16811339C22semidirect
25. #16811338C22semidirect
26. #16811338C22semidirect
27. #16811333C22semidirect
28. #16811326C22semidirect
29. #16811323C22semidirect
30. #16811321C22semidirect
31. #16811320C22semidirect
32. #16811295C22semidirect
33. #16811292C22semidirect
34. #16811291C22semidirect
35. #16811283C22semidirect
36. #16811276C22semidirect
37. #16811274C22semidirect
38. #16811265C22semidirect
39. #16811264C22semidirect
40. #16811264C22semidirect
41. #16811262C22semidirect
42. #16811262C22semidirect
43. #16811261C22semidirect
44. D4×D212C22semidirect
45. D4×D212C22semidirect
46. D4×D212C22semidirect
47. #16811258C22semidirect
48. #16811258C22semidirect
49. #16811257C22semidirect
50. #16811257C22semidirect
51. #16811257C22semidirect
52. #16811243C22semidirect
53. #16811229C22semidirect
54. #16811228C22semidirect
55. #16811227C22semidirect
56. #16811213C22semidirect
57. #16811209C22semidirect
58. #16811205C22semidirect
59. #16811203C22semidirect
60. #16811203C22semidirect
61. #16811189C22semidirect
62. #16811189C22semidirect
63. #16811189C22semidirect
64. #16811189C22semidirect
65. #16811187C22semidirect
66. #16811184C22semidirect
67. #16811179C22semidirect
68. #16811178C22semidirect
69. #16811174C22semidirect
70. #16811174C22semidirect
71. #16811173C22semidirect
72. #16811173C22semidirect
73. #16811172C22semidirect
74. #16811171C22semidirect
75. #16811170C22semidirect
76. #16811170C22semidirect
77. #16811170C22semidirect
78. #16811169C22semidirect
79. #16811168C22semidirect
80. #16811168C22semidirect
81. C4⋊Q8×D53C22semidirect
82. #127×D53C22semidirect
83. #127×D53C22semidirect
84. #16811160C22semidirect
85. #16811159C22semidirect
86. #16811158C22semidirect
87. #124×D53C22semidirect
88. #16811136C22semidirect
89. #16811136C22semidirect
90. #16811135C22semidirect
91. #16811130C22semidirect
92. C2×#13133192C22semidirect
93. #121×D53C22semidirect
94. #121×D53C22semidirect
95. #121×D53C22semidirect
96. #16811104C22semidirect
97. #16811095C22semidirect
98. C4×#11719949C22semidirect
99. #16811091C22semidirect
100. C4×D4×D53C22semidirect
101. C4×D4×D53C22semidirect
102. C2×C42×D53C22semidirect
103. C53×#562C22semidirect
104. C53×#554C22semidirect
105. C53×#550C22semidirect
106. C53×#547C22semidirect
107. C53×#540C22semidirect
108. C53×#537C22semidirect
109. C53×#533C22semidirect
110. C53×#532C22semidirect
470. C4×D53H(5,𝔽2)semidirect
506. #3548D53semidirect
529. #562C2×D53semidirect
538. #554C2×D53semidirect
546. #550C2×D53semidirect
550. #547C2×D53semidirect
569. #540C2×D53semidirect
575. #537C2×D53semidirect
584. #533C2×D53semidirect
597. #532C2×D53semidirect
620. C53#62834semidirect

Maximal subgroups

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

subgroupindex
#202892372
#202891202
#202891152
#202890772
#202889532
#202887482
#202887462
#202886232
#202885872
#202885652
#202884922
#202884732
#202883792
#202880122
#532×D532
C53×#35482
#6283453