Finite Group Databasebeta

← #28292975

Subgroups — #28292975

Order 13568.

7050 conjugacy classes of subgroups.

The subgroup lattice has 1408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289155C214yesmaximal, complemented
2#20289151C214yesmaximal, complemented
3#20289149C218yesmaximal, complemented
4#20289059C211yesmaximal, characteristic, complemented
5#20289055C212yesmaximal, complemented
6#20289053C214yesmaximal, complemented
7#20288623C212yesmaximal, complemented
8#20288620C214yesmaximal, complemented
9#20288615C212yesmaximal, complemented
10#20288593C214yesmaximal, complemented
11#20288533C212yesmaximal, complemented
12#20288530C214yesmaximal, complemented
13#20288529C212yesmaximal, complemented
14#20288494C214yesmaximal, complemented
15#20288417C214yesmaximal, complemented
16#20288415C214yesmaximal, complemented
17#20288364C214yesmaximal, complemented
18#20288009C212yesmaximal, complemented
19C2×C4⋊Q8×D53C211yesmaximal, characteristic, complemented
20C53×#3544C211yesmaximal, characteristic, complemented
21C2×#13133264C2214yes—
22C22×Q8×D53C2212yes—
23#16811375C2218yescomplemented
24#16811374C2218yescomplemented
25#16811373C2214yescomplemented
26#16811372C2214yescomplemented
27#16811372C2214yescomplemented
28Q8×Dic106C2212yescomplemented
29#16811353C2211yescharacteristic, complemented
30#16811353C2214yescomplemented
31#16811350C2214yescomplemented
32#16811350C2218yescomplemented
33#16811349C2214yescomplemented
34#16811344C2214yescomplemented
35#16811341C2214yescomplemented
36#16811340C2218yescomplemented
37#16811339C2211yescharacteristic, complemented
38#16811338C2212yescomplemented
39#16811335C2214yescomplemented
40#16811334C2214yes—
41#16811334C2212yescomplemented
42#16811333C2214yes—
43#16811333C2212yescomplemented
44#16811331C2214yes—
45#16811330C2212yescomplemented
46#16811329C2218yes—
47#16811328C2214yes—
48#16811327C2218yes—
49#16811327C2218yescomplemented
50#16811326C2214yes—
51#16811324C2218yes—
52#16811323C2214yes—
53#16811320C2214yes—
54#16811318C2218yes—
55#16811317C2214yes—
56#16811315C2214yes—
57#16811313C2214yes—
58#16811310C2218yes—
59#16811308C2214yes—
60#16811306C2218yes—
61D4×Dic106C2214yescomplemented
62#16811288C2218yes—
63#16811288C2218yes—
64#16811288C2214yescomplemented
65#16811286C2218yes—
66#16811286C2218yes—
67#16811286C2218yescomplemented
68#16811283C2218yes—
69#16811283C2218yes—
70#16811281C2218yes—
71#16811281C2218yes—
72#16811277C2214yes—
73#16811274C2214yes—
74#16811274C2214yescomplemented
75#16811273C2214yes—
76#16811273C2214yescomplemented
77#16811272C2218yes—
78#16811271C2218yes—
79#16811271C2218yescomplemented
80#16811253C2214yes—
81#16811253C2214yescomplemented
82#16811252C2218yescomplemented
83#16811251C2214yescomplemented
84#16811250C2214yes—
85#16811250C2214yescomplemented
86#16811250C2218yescomplemented
87#16811247C2214yescomplemented
88#16811244C2214yescomplemented
89#16811243C2218yescomplemented
90#16811242C2214yescomplemented
91#16811237C2218yescomplemented
92#16811232C2218yescomplemented
93#16811230C2218yescomplemented
94#16811221C2218yes—
95#16811219C2218yes—
96#16811216C2218yes—
97#16811214C2218yes—
98#16811203C2214yes—
99#16811202C2214yes—
100#16811197C2214yes—
101#16811196C2218yescomplemented
102#16811195C2218yes—
103#16811195C2218yes—
104#16811195C2218yescomplemented
105#16811179C2212yes—
106#16811179C2214yescomplemented
107#16811177C2212yes—
108#16811177C2214yescomplemented
109#16811176C2214yescomplemented
110#16811175C2212yes—
111#16811175C2214yescomplemented
112#16811172C2212yes—
113#16811170C2212yes—
114#16811170C2214yescomplemented
115#16811168C2212yes—
116#16811168C2214yescomplemented
117C2×#13133217C2211yescharacteristic
118C2×#13133216C2214yes—
119C2×#13133216C2214yescomplemented
120C2×#13133215C2212yes—
121C4⋊Q8×D53C2212yes—
122C4⋊Q8×D53C2214yes—
123C4⋊Q8×D53C2212yes—
124C4⋊Q8×D53C2214yes—
125C4⋊Q8×D53C2214yes—
126C4⋊Q8×D53C2214yescomplemented
127#16811158C2212yes—
128#16811157C2212yes—
129#16811156C2214yes—
130#16811156C2214yes—
131#16811152C2212yes—
132#16811151C2214yes—
133#16811150C2214yes—
134#16811136C2212yes—
135#16811135C2214yes—
136#16811133C2212yes—
137#16811132C2214yes—
138#16811131C2214yes—
139#16811131C2218yes—
140#16811130C2214yes—
141#16811105C2214yes—
142#16811104C2214yes—
143#16811103C2214yes—
144#16811102C2214yes—
145#16811100C2214yes—
146C4×#11719949C2212yes—
147#16811091C2214yes—
148C4×#11719947C2212yes—
149C4×#11719947C2214yes—
150C2×C4⋊C4×D53C2214yes—
151C2×C42×D53C2211yescharacteristic
152C53×#563C2214yescomplemented
153Q82×C53C2211yescharacteristic, complemented
154C53×#555C2211yescharacteristic, complemented
155C53×#554C2212yescomplemented
156C53×#552C2214yes—
157C53×#547C2214yes—
158C53×#544C2214yescomplemented
159C53×#542C2214yescomplemented
160C53×#536C2214yes—
161C2×C4⋊Q8×C53C2211yescharacteristic
162C53×#529C2212yes—
163#13133264—416no—
164C2×#11719949C2312yes—
165C2×#11719945C2314yes—
166C2×#11719945C2314yes—
167C2×#11719945C2318yes—
168C2×#11719947C2312yes—
169C2×#11719947C2314yes—
170C2×#11719947C2318yes—
171C2×#11719947C2318yes—
172C22×Dic106C2314yes—
173C22×Dic106C2318yes—
174C22×Dic106C2312yes—
175C2×Q8×D53—48no—
176C2×Q8×D53C2314yes—
177C2×Q8×D53C2318yes—
178C2×Q8×D53C2314yes—
179C2×Q8×D53C2318yes—
180C22×C4×D53C2312yes—
181C22×C4×D53C2311yescharacteristic
182C22×C4×D53C2314yes—
183#13133217C2314yes—
184#13133217C2312yes—
185#13133217C2312yes—
186#13133217C2314yes—
187#13133216C2318yes—
188#13133216C2318yes—
189#13133216C2314yes—
190#13133216C2314yes—
191#13133216C2314yes—
192#13133216C2314yes—
193#13133216C2318yes—
194#13133216C2318yes—
195#13133216C2318yes—
196#13133216C2318yes—
197#13133216C2314yes—
198#13133216C2314yes—
199#13133216C2318yes—
200#13133216C2312yes—
201#13133216C2312yes—
202#13133215C2318yes—
203#13133215C2314yes—
204#13133215C2314yes—
205#13133215C2314yes—
206#13133215C2314yes—
207#13133215C2314yes—
208#13133215C2314yes—
209#13133215C2312yes—
210#13133213C2312yes—
211#13133212C2318yes—
212#13133212C2318yes—
213#13133212C2318yes—
214#13133212C2314yes—
215#13133211C2318yes—
216#13133211C2314yes—
217#13133210C2318yes—
218#13133210C2318yes—
219#13133210C2318yes—
220#13133210C2314yes—
221#13133209C2318yes—
222#13133209C2314yes—
223#13133209C2312yes—
224#13133208C2314yes—
225#13133208C2318yes—
226#13133208C2314yes—
227#13133208C2318yes—
228#13133207C2318yes—
229#13133207C2318yes—
230#13133207C2318yes—
231#13133207C2318yes—
232#13133207C2318yes—
233#13133207C2318yes—
234#13133207C2314yes—
235#13133207C2314yes—
236#13133206C2314yes—
237#13133206C2314yes—
238#13133205C2312yes—
239#13133203C2318yes—
240#13133203C2318yes—
241#13133203C2318yes—
242#13133203C2318yes—
243#13133203C2314yes—
244#13133203C2314yes—
245#13133202C2318yes—
246#13133202C2318yes—
247#13133202C2314yes—
248#13133202C2314yes—
249#13133201C2318yes—
250#13133201C2318yes—
251#13133200C2318yes—
252#13133200C2318yes—
253#13133200C2314yes—
254#13133199C2318yes—
255#13133199C2318yes—
256#13133199C2314yes—
257#13133199C2314yes—
258#13133198C2318yes—
259#13133198C2318yes—
260#13133197C2318yes—
261#13133197C2318yes—
262#13133197C2314yes—
263#13133197C2312yes—
264#13133196C2318yes—
265#13133196C2312yes—
266#13133196C2314yes—
267#13133195C2318yes—
268#13133195C2318yes—
269#13133195C2318yes—
270#13133195C2318yes—
271#13133195C2318yes—
272#13133195C2318yes—
273#13133195C2314yes—
274#13133195C2314yes—
275#13133195C2318yes—
276#13133195C2318yes—
277#13133195C2318yes—
278#13133195C2314yes—
279#13133194C2318yes—
280#13133194C2318yes—
281#13133194C2318yes—
282#13133194C2318yes—
283#13133194C2318yes—
284#13133194C2318yes—
285#13133194C2314yes—
286#13133194C2318yes—
287#13133193C2318yes—
288#13133193C2318yes—
289#13133193C2318yes—
290#13133193C2318yes—
291#13133193C2314yes—
292#13133193C2312yes—
293#13133192C2314yes—
294#13133192C2318yes—
295#13133192C2312yes—
296#13133191C2312yes—
297#13133191C2314yes—
298#13133190C2318yes—
299#13133190C2314yes—
300#13133190C2314yes—
301#13133190C2318yes—
302#13133190C2318yes—
303#13133190C2314yes—
304#13133189C2314yes—
305#13133189C2318yes—
306#13133188C2314yes—
307#13133188C2318yes—
308#13133188C2312yes—
309#13133187C2314yes—
310#13133185C2314yes—
311Q8×Dic53C2314yes—
312Q8×Dic53C2312yes—
313C4×Dic106C2318yes—
314C4×Dic106C2318yes—
315C4×Dic106C2314yes—
316C4×Dic106C2318yes—
317C4×Dic106C2314yes—
318C4×Dic106C2312yes—
319#13133182C2318yes—
320#13133182C2318yes—
321#13133182C2314yes—
322#13133182C2314yes—
323#13133182C2318yes—
324#13133182C2314yes—
325#13133182C2314yes—
326#13133182C2312yes—
327C4×D212C2314yes—
328C4×D212C2318yes—
329C4×D212C2318yes—
330C4×D212C2314yes—
331C4×D212C2312yes—
332D4×Dic53C2314yes—
333D4×Dic53C2314yes—
334D4×Dic53C2312yes—
335#13133179C2314yes—
336#13133179C2312yes—
337#13133179C2314yes—
338#13133179C2314yes—
339#13133179C2318yes—
340#13133179C2318yes—
341#13133179C2314yes—
342C4×C22⋊D53C2318yes—
343C4×C22⋊D53C2314yes—
344C4×C22⋊D53C2314yes—
345C4×C22⋊D53C2318yes—
346C4×C22⋊D53C2318yes—
347C4×C22⋊D53C2314yes—
348#13133177C2314yes—
349#13133177C2318yes—
350#13133177C2314yes—
351#13133177C2314yes—
352#13133177C2314yes—
353#13133177C2314yes—
354#13133177C2318yes—
355#13133177C2318yes—
356#13133177C2314yes—
357#13133177C2314yes—
358#13133176C2314yes—
359#13133176C2314yes—
360#13133175C2314yes—
361#13133175C2314yes—
362#13133175C2312yes—
363#13133175C2314yes—
364#13133175C2312yes—
365#13133175C2314yes—
366#13133174C2318yes—
367#13133174C2314yes—
368#13133174C2314yes—
369#13133173C2318yes—
370#13133173C2318yes—
371#13133173C2314yes—
372#13133173C2314yes—
373#13133173C2314yes—
374C2×C4⋊Dic53C2314yes—
375C2×C4⋊Dic53C2314yes—
376C2×#11719919C2318yes—
377C2×#11719919C2318yes—
378C4⋊C4×D53C2318yes—
379C4⋊C4×D53C2314yes—
380C4⋊C4×D53C2314yes—
381C4⋊C4×D53C2314yes—
382C4⋊C4×D53C2318yes—
383C4⋊C4×D53C2314yes—
384C4⋊C4×D53C2314yes—
385C4⋊C4×D53C2314yes—
386C4⋊C4×D53C2318yes—
387C2×C4×Dic53C2312yes—
388C2×C4×Dic53C2311yescharacteristic
389C2×C4×Dic53C2314yes—
390C42×D53C2312yes—
391C42×D53C2312yes—
392C42×D53C2312yes—
393C42×D53C2312yes—
394C42×D53C2314yes—
395C2×#41×C53C2314yes—
396C22×Q8×C53C2312yes—
397C4⋊Q8×C53C2314yes—
398C4⋊Q8×C53C2314yes—
399C4⋊Q8×C53C2314yes—
400C4⋊Q8×C53C2314yes—
401C4⋊Q8×C53C2311yescharacteristic
402C4⋊Q8×C53C2311yescharacteristic
403C4⋊Q8×C53C2312yes—
404#126×C53C2314yes—
405#126×C53C2318yes—
406#125×C53C2312yes—
407#125×C53C2314yes—
408#125×C53C2318yes—
409#124×C53C2314yes—
410#124×C53C2314yes—
411#124×C53C2312yes—
412#123×C53C2318yes—
413#123×C53C2318yes—
414#123×C53C2314yes—
415C22⋊Q8×C53C2318yes—
416C22⋊Q8×C53C2318yes—
417C22⋊Q8×C53C2318yes—
418C22⋊Q8×C53C2312yes—
419C22⋊Q8×C53C2314yes—
420#121×C53C2312yes—
421#121×C53C2314yes—
422C4×Q8×C53C2312yes—
423C4×Q8×C53C2314yes—
424C4×D4×C53C2314yes—
425C4×D4×C53C2314yes—
426C4×D4×C53C2312yes—
427#117×C53C2314yes—
428#117×C53C2314yes—
429#117×C53C2314yes—
430C2×C4⋊C4×C53C2314yes—
431C2×C4⋊C4×C53C2314yes—
432C2×C42×C53C2311yescharacteristic
433C23×D53C2411yescharacteristic
434#41×C53—48no—
435C2×Q8×C53—44no—
436C2×Q8×C53C2412yes—
437C2×Q8×C53C2412yes—
438C2×Q8×C53C2414yes—
439C2×Q8×C53C2414yes—
440C2×Q8×C53C2412yes—
441C2×D4×C53C2412yes—
442C2×D4×C53C2414yes—
443C2×D4×C53C2414yes—
444C22×C4×C53C2412yes—
445C22×C4×C53C2411yescharacteristic
446C22×C4×C53C2414yes—
447C22×C4×C53C2414yes—
448C22×C4×C53C2418yes—
449C2×C22⋊D53C2414yes—
450C2×C22⋊D53C2414yes—
451C2×C22⋊D53C2414yes—
452C2×C22⋊D53C2414yes—
453C2×C22⋊D53C2414yes—
454C2×C22⋊D53C2418yes—
455C22×Dic53C2412yes—
456C22×Dic53C2414yes—
457C22×Dic53C2414yes—
458C22×Dic53C2414yes—
459C22×Dic53C2418yes—
460C22×Dic53C2411yescharacteristic
461#11719949—28no—
462Q8×D53—48no—
463Q8×D53—416no—
464Q8×D53—48no—
465Q8×D53—416no—
466#11719947—216no—
467#11719947—28no—
468#11719947—416no—
469#11719947—416no—
470#11719945—216no—
471#11719945—416no—
472#11719945—48no—
473C2×D212C2414yes—
474C2×D212C2414yes—
475C2×D212C2412yes—
476C2×D212C2414yes—
477C2×C4×D53—24no—
478C2×C4×D53—28no—
479C2×C4×D53—48no—
480C2×C4×D53C2412yes—
481C2×C4×D53C2412yes—
482C2×C4×D53C2412yes—
483C2×C4×D53C2412yes—
484C2×C4×D53C2412yes—
485C2×C4×D53C2414yes—
486C2×C4×D53C2414yes—
487C2×C4×D53C2414yes—
488C2×C4×D53C2418yes—
489C2×C4×D53C2418yes—
490C2×C4×D53C2418yes—
491C2×C4×D53C2418yes—
492C2×C4×D53C2412yes—
493C2×Dic106—216no—
494C2×Dic106—416no—
495C2×Dic106—44no—
496C2×Dic106C2414yes—
497C2×Dic106C2412yes—
498C2×Dic106C2418yes—
499C2×Dic106C2414yes—
500C2×Dic106C2418yes—
501C2×Dic106C2414yes—
502C2×Dic106C2414yes—
503C2×Dic106C2414yes—
504C2×Dic106C2418yes—
505C4⋊C4×C53C2414yes—
506C4⋊C4×C53C2412yes—
507C4⋊C4×C53C2414yes—
508C4⋊C4×C53C2418yes—
509C4⋊C4×C53C2418yes—
510C4⋊C4×C53C2412yes—
511C4⋊C4×C53C2418yes—
512C4⋊C4×C53C2414yes—
513C4⋊C4×C53C2414yes—
514C4⋊C4×C53C2414yes—
515C4⋊C4×C53C2414yes—
516C4⋊C4×C53C2418yes—
517C22⋊C4×C53C2414yes—
518C22⋊C4×C53C2414yes—
519C22⋊C4×C53C2418yes—
520C22⋊C4×C53C2414yes—
521C22⋊C4×C53C2418yes—
522C22⋊C4×C53C2414yes—
523C22⋊C4×C53C2414yes—
524C42×C53C2412yes—
525C42×C53C2411yescharacteristic
526C42×C53C2411yescharacteristic
527C42×C53C2414yes—
528C42×C53C2414yes—
529C42×C53C2414yes—
530C22⋊Dic53C2414yes—
531C22⋊Dic53C2418yes—
532C22⋊Dic53C2414yes—
533C22⋊Dic53C2414yes—
534C22⋊Dic53C2418yes—
535#11719921C2414yes—
536#11719921C2414yes—
537#11719921C2414yes—
538#11719921C2414yes—
539#11719921C2418yes—
540#11719921C2418yes—
541#11719921C2414yes—
542#11719921C2414yes—
543#11719921C2414yes—
544#11719921C2418yes—
545#11719921C2414yes—
546#11719921C2418yes—
547#11719921C2414yes—
548#11719921C2414yes—
549C4⋊Dic53C2414yes—
550C4⋊Dic53C2412yes—
551C4⋊Dic53C2414yes—
552C4⋊Dic53C2418yes—
553C4⋊Dic53C2418yes—
554C4⋊Dic53C2418yes—
555C4⋊Dic53C2412yes—
556C4⋊Dic53C2414yes—
557C4⋊Dic53C2414yes—
558C4⋊Dic53C2418yes—
559#11719919C2418yes—
560#11719919C2418yes—
561#11719919C2414yes—
562#11719919C2418yes—
563#11719919C2418yes—
564#11719919C2418yes—
565#11719919C2418yes—
566#11719919C2418yes—
567#11719919C2418yes—
568#11719919C2414yes—
569#11719919C2414yes—
570#11719919C2414yes—
571#11719919C2414yes—
572#11719919C2414yes—
573#11719919C2414yes—
574#11719919C2414yes—
575#11719919C2418yes—
576#11719919C2418yes—
577#11719919C2414yes—
578#11719919C2414yes—
579C4×Dic53C2412yes—
580C4×Dic53C2412yes—
581C4×Dic53C2412yes—
582C4×Dic53C2411yescharacteristic
583C4×Dic53C2412yes—
584C4×Dic53C2412yes—
585C4×Dic53C2411yescharacteristic
586C4×Dic53C2414yes—
587C4×Dic53C2414yes—
588C4×Dic53C2414yes—
589C4×Dic53C2414yes—
590C4×Dic53C2414yes—
591C4×Dic53C2418yes—
592C4×Dic53C2414yes—
593C4×Dic53C2418yes—
594C4×Dic53C2414yes—
595C23×C53C2514yes—
596C23×C53C2511yescharacteristic
597C22×D53—22no—
598C22×D53—24no—
599C22×D53C2514yes—
600C22×D53C2512yes—
601Q8×C53—24no—
602Q8×C53—42no—
603Q8×C53—44no—
604Q8×C53—42no—
605Q8×C53—44no—
606D4×C53—28no—
607D4×C53—24no—
608D4×C53—44no—
609C2×C4×C53—28no—
610C2×C4×C53—22no—
611C2×C4×C53—24no—
612C2×C4×C53—28no—
613C2×C4×C53—48no—
614C2×C4×C53C2511yescharacteristic
615C2×C4×C53C2511yescharacteristic
616C2×C4×C53C2514yes—
617C2×C4×C53C2514yes—
618C2×C4×C53C2514yes—
619C2×C4×C53C2514yes—
620C2×C4×C53C2512yes—
621C2×C4×C53C2514yes—
622C2×C4×C53C2512yes—
623C22⋊D53—28no—
624C22⋊D53—28no—
625C22⋊D53—28no—
626C22⋊D53—28no—
627C22⋊D53—28no—
628C22⋊D53—48no—
629C2×Dic53—28no—
630C2×Dic53—28no—
631C2×Dic53—24no—
632C2×Dic53—28no—
633C2×Dic53—48no—
634C2×Dic53H(5,𝔽2)14yes—
635C2×Dic53C2518yes—
636C2×Dic53C2514yes—
637C2×Dic53C2514yes—
638C2×Dic53C2514yes—
639C2×Dic53C2512yes—
640C2×Dic53C2512yes—
641C2×Dic53C2512yes—
642D212—28no—
643D212—28no—
644D212—24no—
645D212—44no—
646C4×D53—24no—
647C4×D53—24no—
648C4×D53—28no—
649C4×D53—24no—
650C4×D53—24no—
651C4×D53—28no—
652C4×D53—24no—
653C4×D53—28no—
654C4×D53—48no—
655C4×D53—48no—
656C4×D53—48no—
657C4×D53—48no—
658C4×D532−1+418yescomplemented
659Dic106—24no—
660Dic106—216no—
661Dic106—216no—
662Dic106—28no—
663Dic106—28no—
664Dic106—44no—
665Dic106—48no—
666Dic106—44no—
667Dic106—44no—
668#62833—531nomaximal, Sylow
669C22×C53—22no—
670C22×C53—24no—
671C22×C53—24no—
672C22×C53—24no—
673C22×C53C2×H(5,𝔽2)12yes—
674C22×C53C2611yescharacteristic
675C2×D53—28no—
676C2×D53—22no—
677C2×D53—22no—
678C2×D53—24no—
679C2×D53—24no—
680C2×D53—24no—
681C2×D53C2×2−1+414yes—
682C4×C53—24no—
683C4×C53—24no—
684C4×C53—24no—
685C4×C53—21no—
686C4×C53—21no—
687C4×C53—24no—
688C4×C53—22no—
689C4×C53—24no—
690C4×C53C2×2−1+414yes—
691Dic53—28no—
692Dic53—24no—
693Dic53—24no—
694Dic53—24no—
695Dic53—22no—
696Dic53C2×H(5,𝔽2)14yes—
697Dic53C2×2−1+414yes—
698#3552—538no—
699#3552—534no—
700#3552—534no—
701#3544—534no—
702#3544—531no—
703#3544—532no—
704#3544D5311yescharacteristic, complemented
705#3511—532no—
706#3511—532no—
707#3511—534no—
708#3509—534no—
709#3503—532no—
710#3503—532no—
711#3503—534no—
712#3499—534no—
713#3492—534no—
714#3492—534no—
715#3486—534no—
716#3444—532no—
717C22×C4⋊Q8—531no—
718C2×C53—22no—
719C2×C53—44no—
720C2×C53C22×H(5,𝔽2)11yescharacteristic
721C2×C53C22×2−1+412yes—
722D53—24no—
723D53—44no—
724C2×2−1+4—534no—
725C23×Q8—532no—
726#563—534no—
727#563—534no—
728#563—538no—
729#563—534no—
730#563—538no—
731#563C2×D5314yescomplemented
732Q82—534no—
733Q82—531no—
734Q82—532no—
735Q82C2×D5311yescharacteristic, complemented
736#557—538no—
737#557—534no—
738#557—534no—
739#556—538no—
740#556—534no—
741#556—534no—
742#555—531no—
743#555—534no—
744#555—532no—
745#555C2×D5311yescharacteristic, complemented
746#554—534no—
747#554—532no—
748#554—538no—
749#554—538no—
750#554—538no—
751#554—534no—
752#554—534no—
753#554—532no—
754#554—532no—
755#554—534no—
756#554C2×D5312yescomplemented
757#553—538no—
758#553—534no—
759#553—538no—
760#553—534no—
761#553—534no—
762#553—534no—
763#552—538no—
764#552—534no—
765#552—534no—
766#552—538no—
767#552—534no—
768#552C2×D5314yes—
769D4×Q8—538no—
770D4×Q8—538no—
771D4×Q8—534no—
772D4×Q8—538no—
773D4×Q8—538no—
774D4×Q8—538no—
775D4×Q8—534no—
776#548—538no—
777#548—538no—
778#548—538no—
779#548—538no—
780#547—538no—
781#547—538no—
782#547—538no—
783#547—534no—
784#547—534no—
785#547—534no—
786#547—534no—
787#547—534no—
788#547C2×D5314yes—
789#544—534no—
790#544—538no—
791#544—534no—
792#544—534no—
793#544—534no—
794#544—538no—
795#544—534no—
796#544C2×D5314yescomplemented
797#542—534no—
798#542—538no—
799#542—534no—
800#542—538no—
801#542—534no—
802#542C2×D5314yescomplemented
803#541—538no—
804#541—538no—
805#539—538no—
806#539—538no—
807#539—538no—
808#539—538no—
809#537—534no—
810#537—534no—
811#536—534no—
812#536—538no—
813#536—538no—
814#536—538no—
815#536—538no—
816#536C2×D5314yes—
817#533—532no—
818#533—534no—
819#533—532no—
820#533—534no—
821#533—532no—
822#533—534no—
823#533—534no—
824#532—532no—
825#532—532no—
826#532—534no—
827#532—532no—
828#532—534no—
829C2×C4⋊Q8—532no—
830C2×C4⋊Q8—532no—
831C2×C4⋊Q8—532no—
832C2×C4⋊Q8—534no—
833C2×C4⋊Q8—534no—
834C2×C4⋊Q8—534no—
835C2×C4⋊Q8—534no—
836C2×C4⋊Q8—534no—
837C2×C4⋊Q8—534no—
838C2×C4⋊Q8—531no—
839C2×C4⋊Q8C2×D5311yescharacteristic
840#529—534no—
841#529—534no—
842#529—532no—
843#529—532no—
844#529—534no—
845#529—534no—
846#529—532no—
847#529C2×D5312yes—
848#525—534no—
849#525—534no—
850#525—538no—
851#525—532no—
852#525—532no—
853#525—534no—
854#525—534no—
855#520—534no—
856#520—534no—
857#520—534no—
858#520—534no—
859#519—534no—
860C4×#41—532no—
861C4×#41—534no—
862C4×#41—532no—
863C4×#41—534no—
864C22×C4⋊C4—534no—
865C22×C42—531no—
866C53#6283311yescharacteristic, complemented, Sylow
8672−1+4—21216no—
868C2×#41—532no—
869C2×#41—532no—
870C2×#41—534no—
871C2×#41—538no—
872C2×#41—538no—
873C2×#41—534no—
874C2×#41—534no—
875C2×#41—538no—
876C2×#41C22×D5314yes—
877C22×Q8—534no—
878C22×Q8—538no—
879C22×Q8—534no—
880C22×Q8—538no—
881C22×Q8—534no—
882C22×Q8—532no—
883C22×Q8—538no—
884C22×Q8—2128no—
885C22×Q8C22×D5312yes—
886C23×C4—532no—
887C23×C4—531no—
888C23×C4—534no—
889C4⋊Q8—534no—
890C4⋊Q8—534no—
891C4⋊Q8—534no—
892C4⋊Q8—534no—
893C4⋊Q8—538no—
894C4⋊Q8—532no—
895C4⋊Q8—534no—
896C4⋊Q8—534no—
897C4⋊Q8—534no—
898C4⋊Q8—532no—
899C4⋊Q8—534no—
900C4⋊Q8—538no—
901C4⋊Q8—538no—
902C4⋊Q8—534no—
903C4⋊Q8—534no—
904C4⋊Q8—538no—
905C4⋊Q8—538no—
906C4⋊Q8—538no—
907C4⋊Q8—534no—
908C4⋊Q8—534no—
909C4⋊Q8—532no—
910C4⋊Q8—538no—
911C4⋊Q8—538no—
912C4⋊Q8—534no—
913C4⋊Q8—532no—
914C4⋊Q8—532no—
915C4⋊Q8—534no—
916C4⋊Q8C22×D5314yes—
917C4⋊Q8C22×D5311yescharacteristic
918C4⋊Q8C22×D5311yescharacteristic
919C4⋊Q8C22×D5312yes—
920C4⋊Q8C22×D5314yes—
921C4⋊Q8C22×D5314yes—
922C4⋊Q8C22×D5314yes—
923#127—532no—
924#126—534no—
925#126—538no—
926#126—538no—
927#126—538no—
928#126—534no—
929#126—538no—
930#126—538no—
931#126—538no—
932#126—534no—
933#126—538no—
934#126C22×D5314yes—
935#126C22×D5318yes—
936#125—534no—
937#125—534no—
938#125—538no—
939#125—538no—
940#125—534no—
941#125—534no—
942#125—538no—
943#125—538no—
944#125—538no—
945#125—538no—
946#125—538no—
947#125—538no—
948#125—532no—
949#125—534no—
950#125—538no—
951#125C22×D5312yes—
952#125C22×D5314yes—
953#125C22×D5318yes—
954#124—534no—
955#124—534no—
956#124—534no—
957#124—534no—
958#124—538no—
959#124—538no—
960#124—538no—
961#124—538no—
962#124—532no—
963#124C22×D5312yes—
964#124C22×D5314yes—
965#124C22×D5314yes—
966#123—538no—
967#123—538no—
968#123—534no—
969#123—538no—
970#123—538no—
971#123—534no—
972#123—534no—
973#123—538no—
974#123—538no—
975#123—534no—
976#123—534no—
977#123—538no—
978#123—538no—
979#123—538no—
980#123—538no—
981#123C22×D5314yes—
982#123C22×D5318yes—
983#123C22×D5318yes—
984C22⋊Q8—532no—
985C22⋊Q8—538no—
986C22⋊Q8—534no—
987C22⋊Q8—538no—
988C22⋊Q8—538no—
989C22⋊Q8—538no—
990C22⋊Q8—532no—
991C22⋊Q8—534no—
992C22⋊Q8—538no—
993C22⋊Q8—534no—
994C22⋊Q8—534no—
995C22⋊Q8—534no—
996C22⋊Q8—532no—
997C22⋊Q8—538no—
998C22⋊Q8—538no—
999C22⋊Q8—538no—
1000C22⋊Q8—538no—
1001C22⋊Q8—538no—
1002C22⋊Q8—538no—
1003C22⋊Q8—534no—
1004C22⋊Q8—538no—
1005C22⋊Q8—538no—
1006C22⋊Q8—538no—
1007C22⋊Q8—538no—
1008C22⋊Q8—538no—
1009C22⋊Q8—534no—
1010C22⋊Q8—538no—
1011C22⋊Q8—538no—
1012C22⋊Q8—538no—
1013C22⋊Q8—538no—
1014C22⋊Q8—538no—
1015C22⋊Q8—538no—
1016C22⋊Q8—538no—
1017C22⋊Q8C22×D5312yes—
1018C22⋊Q8C22×D5314yes—
1019C22⋊Q8C22×D5318yes—
1020C22⋊Q8C22×D5318yes—
1021C22⋊Q8C22×D5318yes—
1022#121—534no—
1023#121—532no—
1024#121—538no—
1025#121—534no—
1026#121—538no—
1027#121—532no—
1028#121—534no—
1029#121—532no—
1030#121—538no—
1031#121—534no—
1032#121—534no—
1033#121—534no—
1034#121—534no—
1035#121—538no—
1036#121—538no—
1037#121—538no—
1038#121C22×D5312yes—
1039#121C22×D5314yes—
1040#120—534no—
1041#120—534no—
1042C4×Q8—532no—
1043C4×Q8—534no—
1044C4×Q8—534no—
1045C4×Q8—534no—
1046C4×Q8—534no—
1047C4×Q8—532no—
1048C4×Q8—538no—
1049C4×Q8—538no—
1050C4×Q8—538no—
1051C4×Q8—534no—
1052C4×Q8—534no—
1053C4×Q8—532no—
1054C4×Q8—538no—
1055C4×Q8—538no—
1056C4×Q8—538no—
1057C4×Q8—534no—
1058C4×Q8C22×D5312yes—
1059C4×Q8C22×D5314yes—
1060C4×D4—534no—
1061C4×D4—532no—
1062C4×D4—534no—
1063C4×D4—534no—
1064C4×D4—534no—
1065C4×D4—534no—
1066C4×D4—538no—
1067C4×D4—538no—
1068C4×D4—538no—
1069C4×D4—534no—
1070C4×D4—534no—
1071C4×D4—534no—
1072C4×D4—532no—
1073C4×D4—538no—
1074C4×D4—538no—
1075C4×D4—534no—
1076C4×D4—534no—
1077C4×D4—534no—
1078C4×D4—534no—
1079C4×D4—534no—
1080C4×D4—534no—
1081C4×D4—534no—
1082C4×D4—534no—
1083C4×D4—538no—
1084C4×D4—538no—
1085C4×D4—538no—
1086C4×D4—534no—
1087C4×D4—532no—
1088C4×D4—538no—
1089C4×D4—538no—
1090C4×D4—534no—
1091C4×D4C22×D5314yes—
1092C4×D4C22×D5312yes—
1093C4×D4C22×D5314yes—
1094#117—534no—
1095#117—534no—
1096#117—532no—
1097#117—532no—
1098#117—534no—
1099#117—534no—
1100#117—534no—
1101#117—534no—
1102#117—534no—
1103#117—534no—
1104#117—534no—
1105#117—538no—
1106#117—538no—
1107#117—534no—
1108#117—534no—
1109#117—538no—
1110#117C22×D5314yes—
1111#117C22×D5314yes—
1112#117C22×D5314yes—
1113C2×C4⋊C4—538no—
1114C2×C4⋊C4—534no—
1115C2×C4⋊C4—538no—
1116C2×C4⋊C4—534no—
1117C2×C4⋊C4—534no—
1118C2×C4⋊C4—534no—
1119C2×C4⋊C4—538no—
1120C2×C4⋊C4—538no—
1121C2×C4⋊C4—534no—
1122C2×C4⋊C4—534no—
1123C2×C4⋊C4—538no—
1124C2×C4⋊C4—534no—
1125C2×C4⋊C4—534no—
1126C2×C4⋊C4C22×D5314yes—
1127C2×C4⋊C4C22×D5314yes—
1128C2×C42—534no—
1129C2×C42—532no—
1130C2×C42—531no—
1131C2×C42—534no—
1132C2×C42—532no—
1133C2×C42—532no—
1134C2×C42—532no—
1135C2×C42—532no—
1136C2×C42C22×D5311yescharacteristic
1137C24—531no—
1138#41—48no—
1139#41—10616no—
1140#41—1068no—
1141#41—10616no—
1142#41—1068no—
1143#41—2128no—
1144#41—21216no—
1145#41—21216no—
1146#41—21216no—
1147C2×Q8—44no—
1148C2×Q8—534no—
1149C2×Q8—532no—
1150C2×Q8—538no—
1151C2×Q8—534no—
1152C2×Q8—538no—
1153C2×Q8—534no—
1154C2×Q8—538no—
1155C2×Q8—534no—
1156C2×Q8—534no—
1157C2×Q8—10616no—
1158C2×Q8—2124no—
1159C2×Q8—21216no—
1160C2×Q8—2128no—
1161C2×Q8—21216no—
1162C2×Q8—2128no—
1163C2×Q8—21216no—
1164C2×Q8C23×D5312yes—
1165C2×Q8C23×D5314yes—
1166C2×Q8C23×D5312yes—
1167C2×Q8C23×D5314yes—
1168C2×Q8C23×D5312yes—
1169C2×D4—534no—
1170C2×D4—534no—
1171C2×D4—534no—
1172C2×D4—534no—
1173C2×D4—534no—
1174C2×D4—538no—
1175C2×D4—534no—
1176C2×D4—534no—
1177C2×D4—532no—
1178C2×D4—534no—
1179C2×D4C23×D5312yes—
1180C2×D4C23×D5314yes—
1181C2×D4C23×D5314yes—
1182C22×C4—531no—
1183C22×C4—532no—
1184C22×C4—532no—
1185C22×C4—534no—
1186C22×C4—534no—
1187C22×C4—534no—
1188C22×C4—538no—
1189C22×C4—532no—
1190C22×C4—532no—
1191C22×C4—532no—
1192C22×C4—532no—
1193C22×C4—532no—
1194C22×C4—534no—
1195C22×C4—534no—
1196C22×C4—534no—
1197C22×C4—538no—
1198C22×C4—538no—
1199C22×C4—538no—
1200C22×C4—538no—
1201C22×C4—1068no—
1202C22×C4—1064no—
1203C22×C4—2128no—
1204C22×C4C23×D5312yes—
1205C22×C4C23×D5311yescharacteristic
1206C22×C4C23×D5314yes—
1207C22×C4C23×D5314yes—
1208C22×C4C23×D5318yes—
1209C4⋊C4—538no—
1210C4⋊C4—534no—
1211C4⋊C4—538no—
1212C4⋊C4—534no—
1213C4⋊C4—534no—
1214C4⋊C4—532no—
1215C4⋊C4—538no—
1216C4⋊C4—538no—
1217C4⋊C4—538no—
1218C4⋊C4—538no—
1219C4⋊C4—538no—
1220C4⋊C4—538no—
1221C4⋊C4—538no—
1222C4⋊C4—538no—
1223C4⋊C4—538no—
1224C4⋊C4—534no—
1225C4⋊C4—532no—
1226C4⋊C4—534no—
1227C4⋊C4—534no—
1228C4⋊C4—534no—
1229C4⋊C4—534no—
1230C4⋊C4—534no—
1231C4⋊C4—534no—
1232C4⋊C4—534no—
1233C4⋊C4—534no—
1234C4⋊C4—534no—
1235C4⋊C4—534no—
1236C4⋊C4—538no—
1237C4⋊C4—538no—
1238C4⋊C4—538no—
1239C4⋊C4C23×D5314yes—
1240C4⋊C4C23×D5312yes—
1241C4⋊C4C23×D5314yes—
1242C4⋊C4C23×D5318yes—
1243C4⋊C4C23×D5318yes—
1244C4⋊C4C23×D5318yes—
1245C4⋊C4C23×D5312yes—
1246C4⋊C4C23×D5314yes—
1247C4⋊C4C23×D5314yes—
1248C4⋊C4C23×D5314yes—
1249C4⋊C4C23×D5314yes—
1250C4⋊C4C23×D5318yes—
1251C22⋊C4—534no—
1252C22⋊C4—538no—
1253C22⋊C4—538no—
1254C22⋊C4—534no—
1255C22⋊C4—534no—
1256C22⋊C4—534no—
1257C22⋊C4—534no—
1258C22⋊C4—534no—
1259C22⋊C4—534no—
1260C22⋊C4—538no—
1261C22⋊C4—538no—
1262C22⋊C4—538no—
1263C22⋊C4—538no—
1264C22⋊C4—534no—
1265C22⋊C4—534no—
1266C22⋊C4—534no—
1267C22⋊C4—534no—
1268C22⋊C4—534no—
1269C22⋊C4—534no—
1270C22⋊C4C23×D5314yes—
1271C22⋊C4C23×D5318yes—
1272C22⋊C4C23×D5314yes—
1273C22⋊C4C23×D5314yes—
1274C22⋊C4C23×D5318yes—
1275C22⋊C4C23×D5314yes—
1276C22⋊C4C23×D5314yes—
1277C42—532no—
1278C42—532no—
1279C42—532no—
1280C42—531no—
1281C42—532no—
1282C42—532no—
1283C42—531no—
1284C42—534no—
1285C42—534no—
1286C42—534no—
1287C42—534no—
1288C42—534no—
1289C42—534no—
1290C42—534no—
1291C42—538no—
1292C42—538no—
1293C42C23×D5312yes—
1294C42C23×D5311yescharacteristic
1295C42C23×D5311yescharacteristic
1296C42C23×D5314yes—
1297C42C23×D5314yes—
1298C42C23×D5314yes—
1299C23—532no—
1300C23—534no—
1301C23—1064no—
1302C23—1062no—
1303C23C24×D5314yes—
1304C23C24×D5311yescharacteristic
1305Q8—24no—
1306Q8—42no—
1307Q8—44no—
1308Q8—42no—
1309Q8—44no—
1310Q8—10616no—
1311Q8—10616no—
1312Q8—1068no—
1313Q8—1068no—
1314Q8—1064no—
1315Q8—2124no—
1316Q8—2124no—
1317Q8—2124no—
1318Q8—2128no—
1319D4—28no—
1320D4—24no—
1321D4—44no—
1322D4—1068no—
1323D4—1068no—
1324D4—1068no—
1325D4—1068no—
1326D4—1068no—
1327D4—1068no—
1328D4—1068no—
1329D4—1064no—
1330D4—2124no—
1331D4—2128no—
1332C2×C4—22no—
1333C2×C4—28no—
1334C2×C4—24no—
1335C2×C4—28no—
1336C2×C4—48no—
1337C2×C4—534no—
1338C2×C4—532no—
1339C2×C4—532no—
1340C2×C4—538no—
1341C2×C4—534no—
1342C2×C4—534no—
1343C2×C4—532no—
1344C2×C4—534no—
1345C2×C4—538no—
1346C2×C4—1064no—
1347C2×C4—1064no—
1348C2×C4—1064no—
1349C2×C4—1068no—
1350C2×C4—1068no—
1351C2×C4—1064no—
1352C2×C4—1064no—
1353C2×C4—1068no—
1354C2×C4—1068no—
1355C2×C4—1068no—
1356C2×C4—1064no—
1357C2×C4—1068no—
1358C2×C4—2128no—
1359C2×C4—2128no—
1360C2×C4—2128no—
1361C2×C4—2128no—
1362C2×C4—2128no—
1363C2×C4C24×D5314yes—
1364C2×C4C24×D5314yes—
1365C2×C4C24×D5312yes—
1366C2×C4C24×D5311yescharacteristic
1367C2×C4C24×D5311yescharacteristic
1368C2×C4C24×D5314yes—
1369C2×C4C24×D5314yes—
1370C2×C4C24×D5314yes—
1371C2×C4C24×D5312yes—
1372C22—22no—
1373C22—24no—
1374C22—24no—
1375C22—24no—
1376C22—534no—
1377C22—1068no—
1378C22—1062no—
1379C22—1062no—
1380C22—1064no—
1381C22—1064no—
1382C22—1064no—
1383C22H(5,𝔽2)×D5312yes—
1384C22C25×D5311yescharacteristic
1385C4—24no—
1386C4—21no—
1387C4—21no—
1388C4—24no—
1389C4—24no—
1390C4—22no—
1391C4—24no—
1392C4—24no—
1393C4—534no—
1394C4—534no—
1395C4—1064no—
1396C4—1068no—
1397C4—1062no—
1398C4—1064no—
1399C4—1064no—
1400C42−1+4×D5314yes—
1401C2—22no—
1402C2—44no—
1403C2—1064no—
1404C2—2124no—
1405C2C2×H(5,𝔽2)×D5311yescharacteristic
1406C2C2×2−1+4×D5312yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3544C2
hypercenter#3544D53
hypocenterC53#62833
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3544

Complements

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

NH ≅ G/Ntype
1. #20289155C2semidirect
2. #20289151C2semidirect
3. #20289149C2semidirect
4. #20289059C2semidirect
5. #20289055C2semidirect
6. #20289053C2semidirect
7. #20288623C2semidirect
8. #20288620C2semidirect
9. #20288615C2semidirect
10. #20288593C2semidirect
11. #20288533C2semidirect
12. #20288530C2semidirect
13. #20288529C2semidirect
14. #20288494C2semidirect
15. #20288417C2semidirect
16. #20288415C2semidirect
17. #20288364C2semidirect
18. #20288009C2semidirect
19. C2×C4⋊Q8×D53C2semidirect
20. C53×#3544C2semidirect
23. #16811375C22semidirect
24. #16811374C22semidirect
25. #16811373C22semidirect
26. #16811372C22semidirect
27. #16811372C22semidirect
28. Q8×Dic106C22semidirect
29. #16811353C22semidirect
30. #16811353C22semidirect
31. #16811350C22semidirect
32. #16811350C22semidirect
33. #16811349C22semidirect
34. #16811344C22semidirect
35. #16811341C22semidirect
36. #16811340C22semidirect
37. #16811339C22semidirect
38. #16811338C22semidirect
39. #16811335C22semidirect
41. #16811334C22semidirect
43. #16811333C22semidirect
45. #16811330C22semidirect
49. #16811327C22semidirect
61. D4×Dic106C22semidirect
64. #16811288C22semidirect
67. #16811286C22semidirect
74. #16811274C22semidirect
76. #16811273C22semidirect
79. #16811271C22semidirect
81. #16811253C22semidirect
82. #16811252C22semidirect
83. #16811251C22semidirect
85. #16811250C22semidirect
86. #16811250C22semidirect
87. #16811247C22semidirect
88. #16811244C22semidirect
89. #16811243C22semidirect
90. #16811242C22semidirect
91. #16811237C22semidirect
92. #16811232C22semidirect
93. #16811230C22semidirect
101. #16811196C22semidirect
104. #16811195C22semidirect
106. #16811179C22semidirect
108. #16811177C22semidirect
109. #16811176C22semidirect
111. #16811175C22semidirect
114. #16811170C22semidirect
116. #16811168C22semidirect
119. C2×#13133216C22semidirect
126. C4⋊Q8×D53C22semidirect
152. C53×#563C22semidirect
153. Q82×C53C22semidirect
154. C53×#555C22semidirect
155. C53×#554C22semidirect
158. C53×#544C22semidirect
159. C53×#542C22semidirect
658. C4×D532−1+4semidirect
704. #3544D53semidirect
731. #563C2×D53semidirect
735. Q82C2×D53semidirect
745. #555C2×D53semidirect
756. #554C2×D53semidirect
796. #544C2×D53semidirect
802. #542C2×D53semidirect
866. C53#62833semidirect

Maximal subgroups

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

subgroupindex
#202891552
#202891512
#202891492
#202890592
#202890552
#202890532
#202886232
#202886202
#202886152
#202885932
#202885332
#202885302
#202885292
#202884942
#202884172
#202884152
#202883642
#202880092
C2×C4⋊Q8×D532
C53×#35442
#6283353