Finite Group Databasebeta

← #28292996

Subgroups — #28292996

Order 13568.

7900 conjugacy classes of subgroups.

The subgroup lattice has 1052 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289228C218yesmaximal, complemented
2#20289120C211yesmaximal, characteristic, complemented
3#20289113C212yesmaximal, complemented
4#20289085C218yesmaximal, complemented
5#20288948C214yesmaximal, complemented
6#20288750C214yesmaximal, complemented
7#20288738C214yesmaximal, complemented
8#20288615C214yesmaximal, complemented
9#20288590C214yesmaximal, complemented
10#20288557C214yesmaximal, complemented
11#20288487C214yesmaximal, complemented
12#20288471C214yesmaximal, complemented
13#20288382C218yesmaximal, complemented
14#20288010C211yesmaximal, characteristic, complemented
15#532×D53C212yesmaximal, complemented
16C53×#3549C211yesmaximal, characteristic, complemented
17C2×#13133262C2218yescomplemented
18C2×#41×D53C2214yescomplemented
19#16811367C2218yescomplemented
20#16811365C2214yescomplemented
21#16811362C2218yescomplemented
22#16811360C2218yescomplemented
23#16811355C22116yescomplemented
24#16811341C2218yescomplemented
25#16811339C2212yescomplemented
26#16811338C2214yescomplemented
27#16811334C2214yescomplemented
28#16811330C2214yescomplemented
29#16811325C2218yescomplemented
30#16811320C2218yescomplemented
31#16811317C2218yescomplemented
32#16811317C2218yescomplemented
33#16811294C2214yescomplemented
34#16811293C22116yescomplemented
35#16811293C2214yescomplemented
36#16811291C2218yescomplemented
37#16811281C22116yescomplemented
38#16811278C2214yescomplemented
39#16811277C2214yescomplemented
40#16811273C2218yescomplemented
41#16811270C2218yescomplemented
42#16811267C2218yescomplemented
43#16811266C22116yescomplemented
44#16811260C22116yescomplemented
45#16811260C22116yescomplemented
46#16811260C22116yescomplemented
47D4×D212C2214yescomplemented
48#16811258C2212yescomplemented
49#16811258C2218yescomplemented
50#16811257C2218yescomplemented
51D4×C22⋊D53C2218yescomplemented
52D4×C22⋊D53C2218yescomplemented
53#16811255C2218yescomplemented
54#16811255C22116yescomplemented
55#16811237C22116yescomplemented
56#16811226C2218yescomplemented
57#16811226C2218yescomplemented
58#16811208C22116yescomplemented
59#16811207C22116yescomplemented
60#16811207C22116yescomplemented
61#16811202C2218yescomplemented
62#16811202C2218yescomplemented
63#16811201C2218yescomplemented
64#16811189C2218yescomplemented
65#16811189C2218yescomplemented
66#16811188C22116yescomplemented
67#16811187C2214yescomplemented
68#16811183C22116yescomplemented
69#16811180C2211yescharacteristic, complemented
70#16811178C2212yescomplemented
71#16811176C2214yescomplemented
72#16811174C2212yescomplemented
73#16811173C2212yescomplemented
74#16811172C2214yescomplemented
75#16811171C2212yescomplemented
76#16811171C2212yescomplemented
77#16811170C2214yescomplemented
78#16811170C2214yescomplemented
79#16811169C2214yescomplemented
80#16811168C2214yescomplemented
81#16811168C2214yescomplemented
82#16811168C2218yescomplemented
83C4⋊Q8×D53C2212yescomplemented
84C2×#13133213C2214yescomplemented
85#127×D53C2212yescomplemented
86#16811155C2214yescomplemented
87#16811154C2214yescomplemented
88#16811152C2214yescomplemented
89#124×D53C2214yescomplemented
90#16811135C2218yescomplemented
91#16811133C2214yescomplemented
92#16811133C2218yescomplemented
93#16811130C2212yescomplemented
94C2×#13133188C2218yescomplemented
95#121×D53C2214yescomplemented
96#121×D53C2218yescomplemented
97#121×D53C2214yescomplemented
98#16811103C2218yescomplemented
99#16811098C2214yescomplemented
100#16811097C2214yescomplemented
101#41×Dic53C2212yescomplemented
102C4×#11719947C2214yescomplemented
103C4×D4×D53C2214yescomplemented
104C4×D4×D53C2214yescomplemented
105C2×C42×D53C2211yescharacteristic, complemented
106C53×H(3,𝔽4)C2214yescomplemented
107C53×#555C2212yescomplemented
108C53×#555C2214yescomplemented
109D42×C53C2212yescomplemented
110D42×C53C2214yescomplemented
111C53×#535C2218yescomplemented
112C53×#535C2214yescomplemented
113C53×#532C2211yescharacteristic, complemented
114C53×#532C2212yescomplemented
115#13133262—432no—
116C2×#11719949C2314yes—
117C2×#11719945C2318yes—
118C2×#11719945C2318yes—
119C2×#11719945C2314yes—
120C2×#11719947C2314yes—
121C2×#11719947C2318yes—
122C2×#11719947C23116yes—
123C2×#11719947C2318yes—
124C2×#11719947C2314yes—
125#41×D53—416no—
126C2×Q8×D53C2314yes—
127C22×D212C2314yes—
128C22×C22⋊D53C23116yes—
129C22×C22⋊D53C23116yes—
130C2×D4×D53C2314yes—
131C2×D4×D53C23116yes—
132C2×D4×D53C2318yes—
133C2×D4×D53C2314yes—
134C2×D4×D53C2318yes—
135C2×D4×D53C2314yes—
136C22×C4×D53C2312yes—
137C22×C4×D53C2311yescharacteristic
138C22×C4×D53C2318yes—
139#13133217C2312yes—
140#13133217C2312yes—
141#13133216C2314yes—
142#13133216C2314yes—
143#13133215C2314yes—
144#13133214C2312yes—
145#13133213C2314yes—
146#13133213C23116yes—
147#13133213C2318yes—
148#13133213C2318yes—
149#13133213C2314yes—
150#13133213C2314yes—
151#13133211C23116yes—
152#13133210C23116yes—
153#13133210C2318yes—
154#13133209C2312yes—
155#13133208C2314yes—
156#13133208C2318yes—
157#13133206C2318yes—
158#13133206C2314yes—
159#13133205C2314yes—
160#13133204C2314yes—
161#13133204C2314yes—
162#13133203C23116yes—
163#13133203C23116yes—
164#13133203C2318yes—
165#13133203C2318yes—
166#13133201C23116yes—
167#13133201C23116yes—
168#13133199C2318yes—
169#13133199C23116yes—
170#13133199C23116yes—
171#13133199C23116yes—
172#13133198C23116yes—
173#13133198C2314yes—
174#13133197C2318yes—
175#13133197C2314yes—
176#13133196C2318yes—
177#13133196C2314yes—
178#13133194C23116yes—
179#13133194C23116yes—
180#13133193C23116yes—
181#13133193C2314yes—
182#13133192C2318yes—
183#13133192C2314yes—
184#13133192C2314yes—
185#13133191C2318yes—
186#13133191C2318yes—
187#13133191C2314yes—
188#13133191C2314yes—
189#13133190C23116yes—
190#13133190C23116yes—
191#13133190C2318yes—
192#13133190C23116yes—
193#13133190C2318yes—
194#13133189C23116yes—
195#13133189C23116yes—
196#13133189C2318yes—
197#13133189C23116yes—
198#13133189C23116yes—
199#13133189C23116yes—
200#13133189C2318yes—
201#13133188C23116yes—
202#13133188C2318yes—
203#13133188C2318yes—
204#13133188C23116yes—
205#13133188C23116yes—
206#13133188C2314yes—
207#13133188C2314yes—
208#13133188C2314yes—
209#13133188C2314yes—
210#13133187C23116yes—
211#13133187C23116yes—
212#13133186C23116yes—
213#13133185C23116yes—
214#13133185C2318yes—
215#13133185C2318yes—
216#13133185C2314yes—
217#13133185C23116yes—
218Q8×Dic53C2314yes—
219C4×Dic106C23116yes—
220C4×Dic106C2314yes—
221#13133182C2314yes—
222C4×D212C23116yes—
223C4×D212C23116yes—
224C4×D212C2314yes—
225C4×D212C2314yes—
226D4×Dic53C2314yes—
227D4×Dic53C2314yes—
228D4×Dic53C2318yes—
229D4×Dic53C2318yes—
230D4×Dic53C23116yes—
231D4×Dic53C2314yes—
232D4×Dic53C2314yes—
233#13133179C2314yes—
234#13133179C2318yes—
235#13133179C2314yes—
236C4×C22⋊D53C2318yes—
237C4×C22⋊D53C2318yes—
238C4×C22⋊D53C2318yes—
239#13133177C2318yes—
240#13133177C23116yes—
241#13133177C23116yes—
242#13133177C2318yes—
243#13133177C2318yes—
244#13133176C2314yes—
245#13133176C2314yes—
246#13133176C2312yes—
247#13133175C2318yes—
248#13133175C2314yes—
249#13133173C2318yes—
250C2×C4⋊Dic53C2318yes—
251C4⋊C4×D53C2318yes—
252C4⋊C4×D53C2314yes—
253C4⋊C4×D53C2314yes—
254C2×C22⋊Dic53C23116yes—
255C22⋊C4×D53C2318yes—
256C22⋊C4×D53C23116yes—
257C22⋊C4×D53C2318yes—
258C2×C4×Dic53C2311yescharacteristic
259C2×C4×Dic53C2312yes—
260C2×C4×Dic53C2314yes—
261C42×D53C2312yes—
262C42×D53C2312yes—
263C42×D53C2312yes—
264C42×D53C2312yes—
265C2×#41×C53C2312yes—
266C2×#41×C53C2314yes—
267C22×D4×C53C2318yes—
268C22×D4×C53C2314yes—
269C4⋊Q8×C53C2312yes—
270C4⋊Q8×C53C2311yescharacteristic
271#127×C53C2312yes—
272#127×C53C2318yes—
273#127×C53C2311yescharacteristic
274#124×C53C23116yes—
275#124×C53C2312yes—
276#124×C53C2314yes—
277#124×C53C2318yes—
278#121×C53C2318yes—
279#121×C53C2318yes—
280#121×C53C2314yes—
281#121×C53C2314yes—
282#121×C53C2314yes—
283#121×C53C2318yes—
284#120×C53C2318yes—
285#120×C53C2318yes—
286#120×C53C23116yes—
287C4×D4×C53C2314yes—
288C4×D4×C53C2314yes—
289C4×D4×C53C2314yes—
290#117×C53C2314yes—
291#117×C53C2318yes—
292C2×C42×C53C2311yescharacteristic
293C24×C53C2418yes—
294C23×D53C2411yescharacteristic
295C23×D53C2418yes—
296C23×D53C2418yes—
297#41×C53—44no—
298#41×C53—48no—
299C2×Q8×C53C2412yes—
300C2×Q8×C53C2414yes—
301C2×D4×C53—48no—
302C2×D4×C53—416no—
303C2×D4×C53C2414yes—
304C2×D4×C53C2414yes—
305C2×D4×C53C2414yes—
306C2×D4×C53C2412yes—
307C2×D4×C53C2414yes—
308C2×D4×C53C2418yes—
309C2×D4×C53C24116yes—
310C2×D4×C53C2414yes—
311C2×D4×C53C2418yes—
312C22×C4×C53C2411yescharacteristic
313C22×C4×C53C2412yes—
314C22×C4×C53C2414yes—
315C22×C4×C53C2418yes—
316C2×C22⋊D53—432no—
317C2×C22⋊D53—432no—
318C2×C22⋊D53C2418yes—
319C2×C22⋊D53C2418yes—
320C2×C22⋊D53C2418yes—
321C2×C22⋊D53C2418yes—
322C2×C22⋊D53C2418yes—
323C2×C22⋊D53C2418yes—
324C2×C22⋊D53C24116yes—
325C2×C22⋊D53C24116yes—
326C2×C22⋊D53C24116yes—
327C22×Dic53C2412yes—
328C22×Dic53C2418yes—
329C22×Dic53C2411yescharacteristic
330C22×Dic53C2418yes—
331C22×Dic53C24116yes—
332#11719949—48no—
333Q8×D53—48no—
334#11719947—216no—
335#11719947—416no—
336#11719947—416no—
337#11719947—432no—
338#11719947—48no—
339D4×D53—216no—
340D4×D53—48no—
341D4×D53—416no—
342D4×D53—48no—
343D4×D53—416no—
344D4×D53—432no—
345#11719945—232no—
346#11719945—416no—
347#11719945—48no—
348C2×D212—48no—
349C2×D212C2414yes—
350C2×D212C2414yes—
351C2×D212C2418yes—
352C2×D212C2418yes—
353C2×D212C2414yes—
354C2×C4×D53—28no—
355C2×C4×D53—42no—
356C2×C4×D53—416no—
357C2×C4×D53C2412yes—
358C2×C4×D53C2412yes—
359C2×C4×D53C2412yes—
360C2×C4×D53C2412yes—
361C2×C4×D53C2418yes—
362C2×C4×D53C2412yes—
363C2×C4×D53C2418yes—
364C2×C4×D53C2418yes—
365C2×C4×D53C24116yes—
366C2×C4×D53C2412yes—
367C2×Dic106C2414yes—
368C2×Dic106C2418yes—
369C2×Dic106C2414yes—
370C4⋊C4×C53C2414yes—
371C4⋊C4×C53C2414yes—
372C4⋊C4×C53C2414yes—
373C22⋊C4×C53C2418yes—
374C22⋊C4×C53C24116yes—
375C22⋊C4×C53C2418yes—
376C22⋊C4×C53C2418yes—
377C22⋊C4×C53C2418yes—
378C42×C53C2411yescharacteristic
379C42×C53C2412yes—
380C42×C53C2411yescharacteristic
381C42×C53C2418yes—
382C22⋊Dic53C2418yes—
383C22⋊Dic53C2418yes—
384C22⋊Dic53C2418yes—
385C22⋊Dic53C2418yes—
386C22⋊Dic53C24116yes—
387C22⋊Dic53C2418yes—
388C22⋊Dic53C2414yes—
389#11719921C2418yes—
390#11719921C2418yes—
391#11719921C2418yes—
392#11719921C2418yes—
393#11719921C24116yes—
394#11719921C2418yes—
395#11719921C24116yes—
396C4⋊Dic53C2414yes—
397C4⋊Dic53C2414yes—
398C4⋊Dic53C2414yes—
399C4⋊Dic53C24116yes—
400C4⋊Dic53C2418yes—
401C4⋊Dic53C2414yes—
402#11719919C2418yes—
403#11719919C2418yes—
404#11719919C24116yes—
405#11719919C2418yes—
406#11719919C2418yes—
407C4×Dic53C2411yescharacteristic
408C4×Dic53C2412yes—
409C4×Dic53C2411yescharacteristic
410C4×Dic53C2412yes—
411C4×Dic53C2412yes—
412C4×Dic53C2412yes—
413C4×Dic53C2412yes—
414C4×Dic53C2418yes—
415C4×Dic53C2414yes—
416C4×Dic53C2418yes—
417C23×C53—416no—
418C23×C53—48no—
419C23×C53C2511yescharacteristic
420C23×C53C2518yes—
421C23×C53C2514yes—
422C22×D53—24no—
423C22×D53—216no—
424C22×D53—41no—
425C22×D53—48no—
426C22×D53—48no—
427C22×D53—48no—
428C22×D53—416no—
429C22×D53C2518yes—
430C22×D53C2512yes—
431Q8×C53—44no—
432Q8×C53—42no—
433D4×C53—28no—
434D4×C53—28no—
435D4×C53—28no—
436D4×C53—416no—
437D4×C53—48no—
438D4×C53—44no—
439D4×C53—48no—
440D4×C53—42no—
441D4×C53—44no—
442C2×C4×C53—24no—
443C2×C4×C53—216no—
444C2×C4×C53—22no—
445C2×C4×C53—28no—
446C2×C4×C53C2512yes—
447C2×C4×C53C2518yes—
448C2×C4×C53C2511yescharacteristic
449C2×C4×C53C2514yes—
450C2×C4×C53C2512yes—
451C2×C4×C53C2511yescharacteristic
452C22⋊D53—216no—
453C22⋊D53—216no—
454C22⋊D53—216no—
455C22⋊D53—216no—
456C22⋊D53—48no—
457C22⋊D53—416no—
458C22⋊D53—416no—
459C22⋊D53—416no—
460C22⋊D53—48no—
461C2×Dic53—24no—
462C2×Dic53—216no—
463C2×Dic53—48no—
464C2×Dic53—41no—
465C2×Dic53—416no—
466C2×Dic53C2518yes—
467C2×Dic53C2518yes—
468C2×Dic53C2512yes—
469C2×Dic53C2512yes—
470C2×Dic53C2512yes—
471D212—216no—
472D212—28no—
473D212—28no—
474D212—48no—
475D212—44no—
476C4×D53—24no—
477C4×D53—24no—
478C4×D53—216no—
479C4×D53—24no—
480C4×D53—24no—
481C4×D53—42no—
482C4×D53—48no—
483C4×D53—48no—
484C4×D53—416no—
485C4×D53H(5,𝔽2)18yescomplemented
486Dic106—28no—
487Dic106—216no—
488Dic106—44no—
489#62834—531nomaximal, Sylow
490C22×C53—28no—
491C22×C53—22no—
492C22×C53—28no—
493C22×C53—28no—
494C22×C53—21no—
495C22×C53—28no—
496C22×C53—24no—
497C22×C53—168no—
498C22×C53C2611yescharacteristic
499C2×D53—22no—
500C2×D53—22no—
501C2×D53—28no—
502C2×D53—28no—
503C2×D53—28no—
504C2×D53—44no—
505C2×D53—816no—
506C2×D53—168no—
507C2×D53C2×H(5,𝔽2)14yes—
508C4×C53—28no—
509C4×C53—22no—
510C4×C53—21no—
511C4×C53—24no—
512C4×C53C2×H(5,𝔽2)14yes—
513C4×C53#58512yes—
514Dic53—28no—
515Dic53—28no—
516Dic53—22no—
517Dic53—22no—
518Dic53C2×H(5,𝔽2)14yes—
519#3558—538no—
520#3549—531no—
521#3549D5311yescharacteristic, complemented
522#3548—532no—
523#3546—538no—
524#3537—534no—
525#3519—534no—
526#3519—534no—
527#3511—534no—
528#3508—534no—
529#3506—534no—
530#3498—534no—
531#3496—534no—
532#3488—538no—
533#3444—531no—
534C2×#532—532no—
535C2×C53—41no—
536C2×C53—48no—
537C2×C53—44no—
538C2×C53C22×H(5,𝔽2)12yes—
539C2×C53C2×#58511yescharacteristic
540D53—24no—
541D53—48no—
542C2×H(5,𝔽2)—538no—
543C22×#41—534no—
544#562—538no—
545H(3,𝔽4)—534no—
546H(3,𝔽4)C2×D5314yescomplemented
547#560—538no—
548#560—538no—
549#559—5316no—
550#556—538no—
551#555—532no—
552#555—534no—
553#555C2×D5312yescomplemented
554#555C2×D5314yescomplemented
555#554—534no—
556#554—534no—
557#553—538no—
558#553—538no—
559#553—538no—
560#553—538no—
561#550—5316no—
562#550—534no—
563#550—538no—
564#550—534no—
565#548—5316no—
566#547—538no—
567#547—534no—
568#547—534no—
569#546—538no—
570#546—5316no—
571#546—538no—
572#546—5316no—
573#546—5316no—
574#546—5316no—
575D42—538no—
576D42—538no—
577D42—538no—
578D42—532no—
579D42—538no—
580D42—538no—
581D42—5316no—
582D42—534no—
583D42C2×D5312yescomplemented
584D42C2×D5314yescomplemented
585#542—5316no—
586#540—538no—
587#540—538no—
588#538—5316no—
589#538—5316no—
590#538—5316no—
591#537—538no—
592#537—538no—
593#537—538no—
594#535—534no—
595#535—538no—
596#535—538no—
597#535—5316no—
598#535C2×D5318yescomplemented
599#535C2×D5314yescomplemented
600#534—5316no—
601#533—532no—
602#533—534no—
603#533—531no—
604#532—534no—
605#532—532no—
606#532—532no—
607#532—532no—
608#532—534no—
609#532—534no—
610#532—534no—
611#532—538no—
612#532—534no—
613#532—534no—
614#532—532no—
615#532C2×D5312yescomplemented
616#532C2×D5311yescharacteristic, complemented
617C2×C4⋊Q8—532no—
618C2×#127—534no—
619C2×#127—532no—
620#529—534no—
621#529—534no—
622#529—534no—
623C2×#124—534no—
624#525—532no—
625#525—534no—
626#525—538no—
627#525—538no—
628C2×#121—538no—
629C2×#121—534no—
630C2×#121—534no—
631C2×#121—538no—
632#520—538no—
633#518—534no—
634#518—534no—
635C4×#41—532no—
636C4×#41—534no—
637C2×C4×D4—534no—
638C2×C4×D4—534no—
639C22×C42—531no—
640C53#6283411yescharacteristic, complemented, Sylow
641H(5,𝔽2)—21232no—
642C2×#41—534no—
643C2×#41—534no—
644C2×#41—538no—
645C2×#41—534no—
646C2×#41—538no—
647C2×#41—5316no—
648C2×#41—538no—
649C2×#41—538no—
650C2×#41—534no—
651C2×#41—21216no—
652C2×#41C22×D5312yes—
653C2×#41C22×D5314yes—
654C22×Q8—534no—
655C22×D4—5316no—
656C22×D4—5316no—
657C22×D4—534no—
658C22×D4—534no—
659C22×D4—538no—
660C22×D4—5316no—
661C22×D4—538no—
662C22×D4—534no—
663C22×D4—534no—
664C22×D4C22×D5314yes—
665C22×D4C22×D5318yes—
666C23×C4—532no—
667C23×C4—538no—
668C23×C4—531no—
669C4⋊Q8—534no—
670C4⋊Q8—534no—
671C4⋊Q8—534no—
672C4⋊Q8—532no—
673C4⋊Q8—532no—
674C4⋊Q8C22×D5312yes—
675C4⋊Q8C22×D5311yescharacteristic
676#127—534no—
677#127—534no—
678#127—534no—
679#127—5316no—
680#127—538no—
681#127—538no—
682#127—532no—
683#127C22×D5312yes—
684#127C22×D5311yescharacteristic
685#127C22×D5318yes—
686#126—538no—
687#126—5316no—
688#126—5316no—
689#125—534no—
690#125—538no—
691#125—532no—
692#124—534no—
693#124—538no—
694#124—534no—
695#124—534no—
696#124—538no—
697#124—538no—
698#124—5316no—
699#124—5316no—
700#124—534no—
701#124C22×D5314yes—
702#124C22×D5312yes—
703#124C22×D5318yes—
704#124C22×D53116yes—
705#123—534no—
706#123—5316no—
707#123—538no—
708#123—5316no—
709#123—5316no—
710#123—5316no—
711#123—5316no—
712#123—5316no—
713C22⋊Q8—534no—
714C22⋊Q8—5316no—
715C22⋊Q8—534no—
716C22⋊Q8—538no—
717C22⋊Q8—534no—
718C22⋊Q8—538no—
719C22⋊Q8—5316no—
720C22⋊Q8—5316no—
721#121—534no—
722#121—534no—
723#121—534no—
724#121—538no—
725#121—538no—
726#121—5316no—
727#121—538no—
728#121—538no—
729#121—5316no—
730#121—5316no—
731#121—534no—
732#121—5316no—
733#121—5316no—
734#121—5316no—
735#121—5316no—
736#121—5316no—
737#121—534no—
738#121—534no—
739#121—538no—
740#121—538no—
741#121—534no—
742#121—534no—
743#121—538no—
744#121—538no—
745#121—538no—
746#121—5316no—
747#121—5316no—
748#121—5316no—
749#121C22×D5314yes—
750#121C22×D5314yes—
751#121C22×D5318yes—
752#121C22×D5314yes—
753#121C22×D5318yes—
754#121C22×D5318yes—
755#120—5316no—
756#120—534no—
757#120—5316no—
758#120—538no—
759#120—5316no—
760#120—538no—
761#120—5316no—
762#120—5316no—
763#120C22×D5318yes—
764#120C22×D53116yes—
765#120C22×D5318yes—
766C4×Q8—534no—
767C4×Q8—534no—
768C4×Q8—534no—
769C4×Q8—5316no—
770C4×D4—534no—
771C4×D4—534no—
772C4×D4—538no—
773C4×D4—534no—
774C4×D4—534no—
775C4×D4—5316no—
776C4×D4—538no—
777C4×D4—538no—
778C4×D4—538no—
779C4×D4—538no—
780C4×D4—534no—
781C4×D4—534no—
782C4×D4—538no—
783C4×D4—538no—
784C4×D4—538no—
785C4×D4—538no—
786C4×D4—5316no—
787C4×D4—5316no—
788C4×D4—534no—
789C4×D4—534no—
790C4×D4—5316no—
791C4×D4—5316no—
792C4×D4C22×D5314yes—
793C4×D4C22×D5314yes—
794C4×D4C22×D5314yes—
795#117—534no—
796#117—532no—
797#117—534no—
798#117—534no—
799#117—538no—
800#117—538no—
801#117C22×D5314yes—
802#117C22×D5318yes—
803C2×C4⋊C4—538no—
804C2×C4⋊C4—534no—
805C2×C4⋊C4—534no—
806C2×C4⋊C4—538no—
807C2×C22⋊C4—5316no—
808C2×C22⋊C4—538no—
809C2×C22⋊C4—538no—
810C2×C22⋊C4—5316no—
811C2×C42—534no—
812C2×C42—531no—
813C2×C42—532no—
814C2×C42—532no—
815C2×C42—532no—
816C2×C42—532no—
817C2×C42—532no—
818C2×C42C22×D5311yescharacteristic
819C24—531no—
820C24—538no—
821C24—538no—
822C24C23×D5318yes—
823#41—48no—
824#41—44no—
825#41—10632no—
826#41—10616no—
827#41—2128no—
828#41—21216no—
829#41—21216no—
830#41—2128no—
831#41—21216no—
832#41—21232no—
833#41—2128no—
834C2×Q8—534no—
835C2×Q8—538no—
836C2×Q8—534no—
837C2×Q8—2128no—
838C2×Q8C23×D5312yes—
839C2×Q8C23×D5314yes—
840C2×D4—48no—
841C2×D4—416no—
842C2×D4—538no—
843C2×D4—538no—
844C2×D4—538no—
845C2×D4—538no—
846C2×D4—538no—
847C2×D4—5316no—
848C2×D4—538no—
849C2×D4—5316no—
850C2×D4—5316no—
851C2×D4—534no—
852C2×D4—538no—
853C2×D4—534no—
854C2×D4—538no—
855C2×D4—534no—
856C2×D4—10616no—
857C2×D4—2128no—
858C2×D4—2128no—
859C2×D4—21216no—
860C2×D4—2128no—
861C2×D4—21232no—
862C2×D4—21216no—
863C2×D4—21232no—
864C2×D4—21232no—
865C2×D4C23×D5314yes—
866C2×D4C23×D5314yes—
867C2×D4C23×D5314yes—
868C2×D4C23×D5312yes—
869C2×D4C23×D5314yes—
870C2×D4C23×D5318yes—
871C2×D4C23×D53116yes—
872C2×D4C23×D5314yes—
873C2×D4C23×D5318yes—
874C22×C4—532no—
875C22×C4—532no—
876C22×C4—538no—
877C22×C4—531no—
878C22×C4—538no—
879C22×C4—5316no—
880C22×C4—532no—
881C22×C4—532no—
882C22×C4—532no—
883C22×C4—532no—
884C22×C4—538no—
885C22×C4—532no—
886C22×C4—538no—
887C22×C4—538no—
888C22×C4—5316no—
889C22×C4—1068no—
890C22×C4—2122no—
891C22×C4—21216no—
892C22×C4C23×D5311yescharacteristic
893C22×C4C23×D5312yes—
894C22×C4C23×D5314yes—
895C22×C4C23×D5318yes—
896C4⋊C4—534no—
897C4⋊C4—534no—
898C4⋊C4—534no—
899C4⋊C4—538no—
900C4⋊C4—538no—
901C4⋊C4—5316no—
902C4⋊C4—5316no—
903C4⋊C4—538no—
904C4⋊C4—538no—
905C4⋊C4—538no—
906C4⋊C4—534no—
907C4⋊C4C23×D5314yes—
908C4⋊C4C23×D5314yes—
909C4⋊C4C23×D5314yes—
910C22⋊C4—538no—
911C22⋊C4—538no—
912C22⋊C4—538no—
913C22⋊C4—5316no—
914C22⋊C4—538no—
915C22⋊C4—538no—
916C22⋊C4—534no—
917C22⋊C4—538no—
918C22⋊C4—5316no—
919C22⋊C4—538no—
920C22⋊C4—538no—
921C22⋊C4—538no—
922C22⋊C4—538no—
923C22⋊C4—5316no—
924C22⋊C4C23×D5318yes—
925C22⋊C4C23×D5318yes—
926C22⋊C4C23×D5318yes—
927C22⋊C4C23×D5318yes—
928C22⋊C4C23×D53116yes—
929C42—531no—
930C42—531no—
931C42—532no—
932C42—532no—
933C42—532no—
934C42—532no—
935C42—532no—
936C42—534no—
937C42—538no—
938C42—538no—
939C42C23×D5311yescharacteristic
940C42C23×D5312yes—
941C42C23×D5311yescharacteristic
942C42C23×D5318yes—
943C23—416no—
944C23—48no—
945C23—532no—
946C23—538no—
947C23—10616no—
948C23—1064no—
949C23—21216no—
950C23—2128no—
951C23—2128no—
952C23—2128no—
953C23—2121no—
954C23C24×D5314yes—
955C23C24×D5318yes—
956C23C24×D5311yescharacteristic
957Q8—44no—
958Q8—42no—
959Q8—10616no—
960Q8—1068no—
961Q8—2124no—
962D4—28no—
963D4—28no—
964D4—28no—
965D4—416no—
966D4—48no—
967D4—44no—
968D4—48no—
969D4—42no—
970D4—44no—
971D4—10616no—
972D4—10616no—
973D4—10616no—
974D4—10616no—
975D4—10616no—
976D4—1068no—
977D4—1068no—
978D4—2128no—
979D4—2124no—
980D4—2128no—
981D4—21216no—
982D4—21216no—
983D4—21216no—
984D4—2128no—
985C2×C4—24no—
986C2×C4—216no—
987C2×C4—22no—
988C2×C4—28no—
989C2×C4—532no—
990C2×C4—538no—
991C2×C4—532no—
992C2×C4—532no—
993C2×C4—538no—
994C2×C4—538no—
995C2×C4—1064no—
996C2×C4—1064no—
997C2×C4—1064no—
998C2×C4—10616no—
999C2×C4—1064no—
1000C2×C4—10616no—
1001C2×C4—1064no—
1002C2×C4—2122no—
1003C2×C4—2128no—
1004C2×C4—2128no—
1005C2×C4—21216no—
1006C2×C4—2121no—
1007C2×C4—2128no—
1008C2×C4—21216no—
1009C2×C4C24×D5314yes—
1010C2×C4C24×D5311yescharacteristic
1011C2×C4C24×D5312yes—
1012C2×C4C24×D5318yes—
1013C2×C4C24×D5312yes—
1014C2×C4C24×D5311yescharacteristic
1015C22—22no—
1016C22—28no—
1017C22—28no—
1018C22—28no—
1019C22—21no—
1020C22—24no—
1021C22—28no—
1022C22—168no—
1023C22—534no—
1024C22—8488no—
1025C22—1062no—
1026C22—1062no—
1027C22—1068no—
1028C22—1068no—
1029C22—1068no—
1030C22—42416no—
1031C22—2124no—
1032C22C25×D5311yescharacteristic
1033C4—22no—
1034C4—28no—
1035C4—21no—
1036C4—24no—
1037C4—534no—
1038C4—1062no—
1039C4—1068no—
1040C4—1068no—
1041C4—1062no—
1042C4H(5,𝔽2)×D5314yes—
1043C4#1681145812yes—
1044C2—44no—
1045C2—48no—
1046C2—41no—
1047C2—1064no—
1048C2—2128no—
1049C2C2×H(5,𝔽2)×D5312yes—
1050C2C2×#1681145811yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3549C2
hypercenter#3549D53
hypocenterC53#62834
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3549

Complements

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

NH ≅ G/Ntype
1. #20289228C2semidirect
2. #20289120C2semidirect
3. #20289113C2semidirect
4. #20289085C2semidirect
5. #20288948C2semidirect
6. #20288750C2semidirect
7. #20288738C2semidirect
8. #20288615C2semidirect
9. #20288590C2semidirect
10. #20288557C2semidirect
11. #20288487C2semidirect
12. #20288471C2semidirect
13. #20288382C2semidirect
14. #20288010C2semidirect
15. #532×D53C2semidirect
16. C53×#3549C2semidirect
17. C2×#13133262C22semidirect
18. C2×#41×D53C22semidirect
19. #16811367C22semidirect
20. #16811365C22semidirect
21. #16811362C22semidirect
22. #16811360C22semidirect
23. #16811355C22semidirect
24. #16811341C22semidirect
25. #16811339C22semidirect
26. #16811338C22semidirect
27. #16811334C22semidirect
28. #16811330C22semidirect
29. #16811325C22semidirect
30. #16811320C22semidirect
31. #16811317C22semidirect
32. #16811317C22semidirect
33. #16811294C22semidirect
34. #16811293C22semidirect
35. #16811293C22semidirect
36. #16811291C22semidirect
37. #16811281C22semidirect
38. #16811278C22semidirect
39. #16811277C22semidirect
40. #16811273C22semidirect
41. #16811270C22semidirect
42. #16811267C22semidirect
43. #16811266C22semidirect
44. #16811260C22semidirect
45. #16811260C22semidirect
46. #16811260C22semidirect
47. D4×D212C22semidirect
48. #16811258C22semidirect
49. #16811258C22semidirect
50. #16811257C22semidirect
51. D4×C22⋊D53C22semidirect
52. D4×C22⋊D53C22semidirect
53. #16811255C22semidirect
54. #16811255C22semidirect
55. #16811237C22semidirect
56. #16811226C22semidirect
57. #16811226C22semidirect
58. #16811208C22semidirect
59. #16811207C22semidirect
60. #16811207C22semidirect
61. #16811202C22semidirect
62. #16811202C22semidirect
63. #16811201C22semidirect
64. #16811189C22semidirect
65. #16811189C22semidirect
66. #16811188C22semidirect
67. #16811187C22semidirect
68. #16811183C22semidirect
69. #16811180C22semidirect
70. #16811178C22semidirect
71. #16811176C22semidirect
72. #16811174C22semidirect
73. #16811173C22semidirect
74. #16811172C22semidirect
75. #16811171C22semidirect
76. #16811171C22semidirect
77. #16811170C22semidirect
78. #16811170C22semidirect
79. #16811169C22semidirect
80. #16811168C22semidirect
81. #16811168C22semidirect
82. #16811168C22semidirect
83. C4⋊Q8×D53C22semidirect
84. C2×#13133213C22semidirect
85. #127×D53C22semidirect
86. #16811155C22semidirect
87. #16811154C22semidirect
88. #16811152C22semidirect
89. #124×D53C22semidirect
90. #16811135C22semidirect
91. #16811133C22semidirect
92. #16811133C22semidirect
93. #16811130C22semidirect
94. C2×#13133188C22semidirect
95. #121×D53C22semidirect
96. #121×D53C22semidirect
97. #121×D53C22semidirect
98. #16811103C22semidirect
99. #16811098C22semidirect
100. #16811097C22semidirect
101. #41×Dic53C22semidirect
102. C4×#11719947C22semidirect
103. C4×D4×D53C22semidirect
104. C4×D4×D53C22semidirect
105. C2×C42×D53C22semidirect
106. C53×H(3,𝔽4)C22semidirect
107. C53×#555C22semidirect
108. C53×#555C22semidirect
109. D42×C53C22semidirect
110. D42×C53C22semidirect
111. C53×#535C22semidirect
112. C53×#535C22semidirect
113. C53×#532C22semidirect
114. C53×#532C22semidirect
485. C4×D53H(5,𝔽2)semidirect
521. #3549D53semidirect
546. H(3,𝔽4)C2×D53semidirect
553. #555C2×D53semidirect
554. #555C2×D53semidirect
583. D42C2×D53semidirect
584. D42C2×D53semidirect
598. #535C2×D53semidirect
599. #535C2×D53semidirect
615. #532C2×D53semidirect
616. #532C2×D53semidirect
640. C53#62834semidirect

Maximal subgroups

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

subgroupindex
#202892282
#202891202
#202891132
#202890852
#202889482
#202887502
#202887382
#202886152
#202885902
#202885572
#202884872
#202884712
#202883822
#202880102
#532×D532
C53×#35492
#6283453