Finite Group Databasebeta

← #28293161

Subgroups — #28293161

Order 13568.

10962 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133265C211yesmaximal, characteristic, complemented
2C2×2−1+4×D53C211yesmaximal, characteristic, complemented
3#20288485C218yesmaximal, complemented
4#20288483C218yesmaximal, complemented
5#20288374C211yesmaximal, characteristic, complemented
6#20288372C218yesmaximal, complemented
7#20288370C211yesmaximal, characteristic, complemented
8#20288369C216yesmaximal, complemented
9#20288366C211yesmaximal, characteristic, complemented
10#20288365C218yesmaximal, complemented
11#20288364C216yesmaximal, complemented
12#20288047C216yesmaximal, complemented
13#20288045C216yesmaximal, complemented
14#519×D53C211yesmaximal, characteristic, complemented
15C53×#3486C211yesmaximal, characteristic, complemented
16C2×#13133265—216no—
17C2×#13133265C2218yes—
18C2×#13133265C2211yescharacteristic
19C2×#13133265C2218yescomplemented
20C2×#13133265C2214yescomplemented
21C2×#13133264C2216yes—
22C2×#13133264C2214yescomplemented
232−1+4×D53—216no—
24C22×#11719949C2213yes—
25C22×#11719949C2211yescharacteristic, complemented
26C22×#11719945C2213yes—
27C22×#11719945C2213yescomplemented
28C2×#41×D53C2216yes—
29C2×#41×D53C2214yescomplemented
30C22×Q8×D53C2211yescharacteristic
31C22×Q8×D53C2213yescomplemented
32C22×Q8×D53C2214yescomplemented
33#16811295C2218yescomplemented
34#16811294C22124yescomplemented
35#16811292C2218yescomplemented
36#16811291C22124yescomplemented
37#16811288C22124yescomplemented
38Q8×C22⋊D53C2218yescomplemented
39#16811286C22124yescomplemented
40#16811285C2218yescomplemented
41#16811284C2218yescomplemented
42#16811284C2218yescomplemented
43#16811283C22124yescomplemented
44#16811283C22124yescomplemented
45#16811282C22124yescomplemented
46#16811281C22124yescomplemented
47#16811203C22112yescomplemented
48#16811203C22124yescomplemented
49#16811202C22112yescomplemented
50#16811198C22112yescomplemented
51#16811197C2216yescomplemented
52#16811196C22112yescomplemented
53#16811195C22112yescomplemented
54#16811192C2216yescomplemented
55#16811191C22112yescomplemented
56#16811189C22112yescomplemented
57#16811188C22112yescomplemented
58#16811187C2216yescomplemented
59#16811184C22112yes—
60#16811183C2214yes—
61#16811174C22112yescomplemented
62#16811172C22112yescomplemented
63#16811170C22124yescomplemented
64#16811136C22124yescomplemented
65#16811135C2216yescomplemented
66#16811134C2216yescomplemented
67#16811132C22124yescomplemented
68#16811131C22124yescomplemented
69#16811130C2216yescomplemented
70#16811101C2211yescharacteristic, complemented
71#16811100C2216yescomplemented
72#16811099C2218yescomplemented
73C4×Q8×D53C2218yescomplemented
74#117×D53C2216yes—
75C2×2−1+4×C53C2211yescharacteristic
76C23×Q8×C53C2211yescharacteristic, complemented
77D4×Q8×C53C2218yescomplemented
78C53×#548C2218yescomplemented
79C53×#536C2216yescomplemented
80C53×#525C2216yescomplemented
81C53×#519C2211yescharacteristic, complemented
82#13133265—28no—
83#13133265—232no—
84#13133265—264no—
85#13133265—264no—
86#13133264—232no—
87#13133264—248no—
88C2×#11719949—28no—
89C2×#11719949—224no—
90C2×#11719949C2314yes—
91C2×#11719949C2318yes—
92C2×#11719949C23112yes—
93C2×#11719949C23112yes—
94C2×#11719949C2316yes—
95C2×#11719945—224no—
96C2×#11719945—224no—
97C2×#11719945C23124yes—
98C2×#11719945C23112yes—
99C2×#11719945C23112yes—
100C2×#11719945C2316yes—
101C2×#11719945C23112yes—
102C2×#11719945C23112yes—
103C2×#11719947C23112yes—
104C2×#11719947C23112yes—
105C2×#11719947C2316yes—
106#41×D53—232no—
107#41×D53—248no—
108C22×Dic106C23112yes—
109C22×Dic106C2313yes—
110C22×Dic106C2313yes—
111C2×Q8×D53—232no—
112C2×Q8×D53—224no—
113C2×Q8×D53D4116yescomplemented
114C2×Q8×D53C23124yes—
115C2×Q8×D53C23112yes—
116C2×Q8×D53C2314yes—
117C2×Q8×D53C2316yes—
118C2×Q8×D53C2314yes—
119C2×Q8×D53C2314yes—
120C22×D212C2313yes—
121C22×D212C2313yes—
122C22×C22⋊D53C2311yescharacteristic
123C22×C22⋊D53C2313yes—
124C2×D4×D53C2314yes—
125C2×D4×D53C2316yes—
126C22×C4×D53C2313yes—
127C22×C4×D53C2316yes—
128C22×C4×D53C23112yes—
129C22×C4×D53C2313yes—
130#13133216C23124yes—
131#13133215C23112yes—
132#13133214C23112yes—
133#13133213C23112yes—
134#13133213C23124yes—
135#13133206C23112yes—
136#13133206C23112yes—
137#13133205C23112yes—
138#13133203C23124yes—
139#13133203C23124yes—
140#13133202C23124yes—
141#13133201C2314yes—
142#13133200C23112yes—
143#13133199C2318yes—
144#13133198C2314yes—
145#13133197C23112yes—
146#13133196C23112yes—
147#13133195C23148yes—
148#13133195C23124yes—
149#13133194C23124yes—
150#13133193C23124yes—
151#13133193C23112yes—
152#13133192C23112yes—
153#13133192C23124yes—
154#13133192C23124yes—
155#13133191C23124yes—
156#13133191C23112yes—
157#13133190C23148yes—
158#13133190C23124yes—
159#13133190C2318yes—
160#13133190C23124yes—
161#13133189C23124yes—
162#13133188C23112yes—
163#13133188C2318yes—
164#13133187C23112yes—
165#13133187C23124yes—
166#13133186C2314yes—
167#13133185C23112yes—
168#13133185C2318yes—
169Q8×Dic53C2318yes—
170C4×Dic106C23124yes—
171#13133182C23124yes—
172C4×D212C23124yes—
173#13133179C23148yes—
174C4×C22⋊D53C23124yes—
175C4×C22⋊D53C23124yes—
176#13133177C23148yes—
177#13133176C2316yes—
178#13133175C23112yes—
179#13133174C23112yes—
180#13133173C23112yes—
181C4⋊C4×D53C23112yes—
182C22⋊C4×D53C2314yes—
183C42×D53C23112yes—
1842−1+4×C53—28no—
185C2×#41×C53C2314yes—
186C2×#41×C53C2316yes—
187C22×Q8×C53—28no—
188C22×Q8×C53C2314yes—
189C22×Q8×C53C2318yes—
190C22×Q8×C53C2313yes—
191C22×Q8×C53C2311yescharacteristic
192C23×C4×C53C2313yes—
193C4⋊Q8×C53C23112yes—
194#124×C53C23112yes—
195#123×C53C23112yes—
196C22⋊Q8×C53C23112yes—
197C22⋊Q8×C53C23124yes—
198#121×C53C23112yes—
199#120×C53C2314yes—
200C4×Q8×C53C2318yes—
201C4×D4×C53C23124yes—
202#117×C53C2316yes—
203C24×C53C2411yescharacteristic
204C23×D53C2413yes—
205C23×D53C2414yes—
206C23×D53C2411yescharacteristic
207#41×C53—216no—
208#41×C53—224no—
209C2×Q8×C53—232no—
210C2×Q8×C53—216no—
211C2×Q8×C53—212no—
212C2×Q8×C53C2×D418yes—
213C2×Q8×C53C24112yes—
214C2×Q8×C53C2416yes—
215C2×Q8×C53C2414yes—
216C2×D4×C53C2414yes—
217C2×D4×C53C2416yes—
218C2×D4×C53C2418yes—
219C22×C4×C53—212no—
220C22×C4×C53C24112yes—
221C22×C4×C53C24112yes—
222C22×C4×C53C2413yes—
223C22×C4×C53C2413yes—
224C2×C22⋊D53—24no—
225C2×C22⋊D53—212no—
226C2×C22⋊D53C2412yes—
227C2×C22⋊D53C2414yes—
228C2×C22⋊D53C2412yes—
229C2×C22⋊D53C2414yes—
230C2×C22⋊D53C24112yes—
231C2×C22⋊D53C24112yes—
232C2×C22⋊D53C24124yes—
233C2×C22⋊D53C2418yes—
234C22×Dic53C24112yes—
235C22×Dic53C2411yescharacteristic
236C22×Dic53C2413yes—
237#11719949—216no—
238#11719949—232no—
239#11719949—224no—
240#11719949—248no—
241#11719949—248no—
242Q8×D53—216no—
243Q8×D53—224no—
244Q8×D53—248no—
245Q8×D53—296no—
246Q8×D53C2×D4132yes—
247Q8×D53C2×D4132yes—
248#11719947—248no—
249#11719947—224no—
250#11719947—248no—
251D4×D53—216no—
252D4×D53—224no—
253#11719945—224no—
254#11719945—248no—
255#11719945—248no—
256#11719945—248no—
257#11719945—248no—
258#11719945—296no—
259C2×D212—212no—
260C2×D212—212no—
261C2×D212C2416yes—
262C2×D212C2416yes—
263C2×D212C2414yes—
264C2×D212C24112yes—
265C2×D212C2416yes—
266C2×D212C24124yes—
267C2×C4×D53—212no—
268C2×C4×D53—224no—
269C2×C4×D53—248no—
270C2×C4×D53C2×D4124yes—
271C2×C4×D53C24124yes—
272C2×C4×D53C24112yes—
273C2×C4×D53C24112yes—
274C2×C4×D53C24112yes—
275C2×C4×D53C2414yes—
276C2×C4×D53C2418yes—
277C2×C4×D53C2416yes—
278C2×C4×D53C2416yes—
279C2×Dic106—212no—
280C2×Dic106—248no—
281C2×Dic106C2×D4124yes—
282C2×Dic106C24112yes—
283C2×Dic106C24112yes—
284C2×Dic106C2416yes—
285C2×Dic106C24112yes—
286C4⋊C4×C53C24112yes—
287C4⋊C4×C53C24124yes—
288C22⋊C4×C53C2414yes—
289C22⋊C4×C53C2418yes—
290C22⋊C4×C53C24124yes—
291C42×C53C24112yes—
292C22⋊Dic53C2414yes—
293C22⋊Dic53C2418yes—
294C22⋊Dic53C2418yes—
295#11719921C2418yes—
296#11719921C24124yes—
297#11719921C24124yes—
298#11719921C24124yes—
299#11719921C2418yes—
300C4⋊Dic53C24112yes—
301C4⋊Dic53C2418yes—
302#11719919C24124yes—
303#11719919C24124yes—
304#11719919C2418yes—
305C4×Dic53C24124yes—
306C4×Dic53C24112yes—
307C23×C53—22no—
308C23×C53—42no—
309C23×C53C2514yes—
310C23×C53C2512yes—
311C23×C53C2511yescharacteristic
312C22×D53—26no—
313C22×D53—28no—
314C22×D53—42no—
315C22×D53—48no—
316C22×D53—46no—
317C22×D53C22×D414yes—
318C22×D53C2516yes—
319C22×D53C2514yes—
320C22×D53C2511yescharacteristic
321C22×D53C2511yescharacteristic
322Q8×C53—212no—
323Q8×C53—224no—
324Q8×C53C22×D4116yes—
325D4×C53—28no—
326D4×C53—212no—
327D4×C53—48no—
328C2×C4×C53—26no—
329C2×C4×C53—224no—
330C2×C4×C53—224no—
331C2×C4×C53C22×D4112yes—
332C2×C4×C53C2514yes—
333C2×C4×C53C2516yes—
334C2×C4×C53C2518yes—
335C2×C4×C53C2516yes—
336C22⋊D53—28no—
337C22⋊D53—24no—
338C22⋊D53—24no—
339C22⋊D53—28no—
340C22⋊D53—224no—
341C22⋊D53—224no—
342C22⋊D53—48no—
343C22⋊D53—424no—
344C2×Dic53—22no—
345C2×Dic53—224no—
346C2×Dic53C22×D4112yes—
347C2×Dic53C2512yes—
348C2×Dic53C2514yes—
349C2×Dic53C2518yes—
350C2×Dic53C2516yes—
351D212—212no—
352D212—212no—
353D212—28no—
354D212—224no—
355D212—212no—
356D212—424no—
357C4×D53—28no—
358C4×D53—224no—
359C4×D53—224no—
360C4×D53—224no—
361C4×D53—248no—
362C4×D53—48no—
363C4×D53C22×D4124yes—
364C4×D53C22×D4124yes—
365Dic106—212no—
366Dic106—224no—
367Dic106—224no—
368Dic106C22×D4148yes—
369#62848—531nomaximal, Sylow
370C22×C53—22no—
371C22×C53—24no—
372C22×C53—22no—
373C22×C53—22no—
374C22×C53—28no—
375C22×C53—22no—
376C22×C53—44no—
377C22×C53C23×D412yes—
378C22×C53C2611yescharacteristic
379C2×D53—22no—
380C2×D53—22no—
381C2×D53—26no—
382C2×D53—24no—
383C2×D53—28no—
384C2×D53—212no—
385C2×D53—44no—
386C2×D53—416no—
387C2×D53—412no—
388C2×D53C23×D412yes—
389C2×D53C23×D412yes—
390C4×C53—24no—
391C4×C53—26no—
392C4×C53—28no—
393C4×C53C23×D4112yes—
394Dic53—22no—
395Dic53—24no—
396Dic53—28no—
397Dic53C23×D4112yes—
398C22×2−1+4—531no—
399C22×2−1+4—531no—
400#3497—538no—
401#3497—538no—
402#3487—531no—
403#3487—538no—
404#3487—536no—
405#3487—531no—
406#3486—531no—
407#3486—538no—
408#3486—536no—
409#3486D5311yescharacteristic, complemented
410#3449—536no—
411#3449—536no—
412C2×#519—531no—
413C2×C53—22no—
414C2×C53—44no—
415C2×C53—42no—
416C2×C53C24×D411yescharacteristic
417C2×C532−1+612yes—
418D53—22no—
419D53—22no—
420D53—46no—
421D53—44no—
422C2×2−1+4—536no—
423C2×2−1+4—534no—
424C2×2−1+4—538no—
425C2×2−1+4—531no—
426C2×2−1+4—534no—
427C2×2−1+4—538no—
428C2×2−1+4—10616no—
429C2×2−1+4—10616no—
430C2×2−1+4C2×D5311yescharacteristic
431C22×#41—536no—
432C22×#41—534no—
433C22×#41—533no—
434C22×#41—531no—
435C22×#41—533no—
436C22×#41—533no—
437C23×Q8—531no—
438C23×Q8—534no—
439C23×Q8—533no—
440C23×Q8C2×D5311yescharacteristic, complemented
441#550—538no—
442#550—5324no—
443#550—538no—
444#550—5324no—
445D4×Q8—538no—
446D4×Q8—5324no—
447D4×Q8—5324no—
448D4×Q8C2×D5318yescomplemented
449#548—538no—
450#548—538no—
451#548—5324no—
452#548—5324no—
453#548—5324no—
454#548—538no—
455#548—5324no—
456#548C2×D5318yescomplemented
457#537—5324no—
458#537—5312no—
459#537—5312no—
460#536—536no—
461#536—5312no—
462#536—5312no—
463#536—5312no—
464#536C2×D5316yescomplemented
465#535—536no—
466#535—5312no—
467#535—5312no—
468#535—5312no—
469#535—536no—
470#534—5312no—
471#534—534no—
472#532—5312no—
473#532—5312no—
474#532—5324no—
475#525—536no—
476#525—536no—
477#525—5324no—
478#525—5324no—
479#525—5324no—
480#525—536no—
481#525C2×D5316yescomplemented
482#519—531no—
483#519—538no—
484#519—536no—
485#519C2×D5311yescharacteristic, complemented
486C2×C4×Q8—538no—
487C2×#117—536no—
488C53#6284811yescharacteristic, complemented, Sylow
4892−1+4—28no—
4902−1+4—10664no—
4912−1+4—10664no—
4922−1+4—10632no—
4932−1+4—10632no—
4942−1+4—10648no—
4952−1+4—1068no—
496C2×#41—5312no—
497C2×#41—536no—
498C2×#41—5312no—
499C2×#41—534no—
500C2×#41—538no—
501C2×#41—5312no—
502C2×#41—536no—
503C2×#41—5312no—
504C2×#41—5312no—
505C2×#41—536no—
506C2×#41—5312no—
507C2×#41—5312no—
508C2×#41—5312no—
509C2×#41—5324no—
510C2×#41—10624no—
511C2×#41—10624no—
512C2×#41—10624no—
513C2×#41—10648no—
514C2×#41—10632no—
515C2×#41—1068no—
516C2×#41C22×D5316yes—
517C2×#41C22×D5314yes—
518C22×Q8—28no—
519C22×Q8—5316no—
520C22×Q8—534no—
521C22×Q8—534no—
522C22×Q8—536no—
523C22×Q8—5312no—
524C22×Q8—5324no—
525C22×Q8—534no—
526C22×Q8—533no—
527C22×Q8—533no—
528C22×Q8—5312no—
529C22×Q8—10632no—
530C22×Q8—10624no—
531C22×Q8C22×D5313yes—
532C22×Q8C22×D5314yes—
533C22×Q8C22×D5318yes—
534C22×Q8C22×D5311yescharacteristic
535C22×D4—531no—
536C22×D4—533no—
537C22×D4—534no—
538C22×D4—536no—
539C22×D4—533no—
540C22×D4—533no—
541C23×C4—533no—
542C23×C4—536no—
543C23×C4—5312no—
544C23×C4—533no—
545C23×C4C22×D5313yes—
546C4⋊Q8—5312no—
547C4⋊Q8—5324no—
548C4⋊Q8C22×D53112yes—
549#127—5324no—
550#127—5312no—
551#127—5312no—
552#124—5312no—
553#124—5312no—
554#124—5324no—
555#124—5324no—
556#124—5312no—
557#124C22×D53112yes—
558#123—534no—
559#123—5312no—
560#123—5324no—
561#123—538no—
562#123—534no—
563#123C22×D53112yes—
564C22⋊Q8—5312no—
565C22⋊Q8—5324no—
566C22⋊Q8—5312no—
567C22⋊Q8—5348no—
568C22⋊Q8—5324no—
569C22⋊Q8—5312no—
570C22⋊Q8—5324no—
571C22⋊Q8C22×D53124yes—
572C22⋊Q8C22×D53112yes—
573#121—5312no—
574#121—5324no—
575#121—538no—
576#121—5324no—
577#121—5312no—
578#121—5324no—
579#121—5312no—
580#121—5324no—
581#121—5348no—
582#121—5324no—
583#121—5324no—
584#121—538no—
585#121C22×D53112yes—
586#120—534no—
587#120—5312no—
588#120—538no—
589#120—5324no—
590#120—5312no—
591#120C22×D5314yes—
592C4×Q8—538no—
593C4×Q8—5324no—
594C4×Q8—5324no—
595C4×Q8C22×D5318yes—
596C4×D4—5324no—
597C4×D4—5324no—
598C4×D4—5348no—
599C4×D4—5348no—
600C4×D4—5324no—
601C4×D4C22×D53124yes—
602#117—536no—
603#117—5312no—
604#117—5312no—
605#117—5312no—
606#117C22×D5316yes—
607C2×C4⋊C4—5312no—
608C2×C22⋊C4—534no—
609C2×C42—5312no—
610C24—531no—
611C24—534no—
612C24—533no—
613C24C23×D5311yescharacteristic
614#41—216no—
615#41—224no—
616#41—10648no—
617#41—10648no—
618#41—10648no—
619#41—10696no—
620#41—10648no—
621#41—10648no—
622#41—10624no—
623#41—10648no—
624#41—10648no—
625#41—10624no—
626#41—10648no—
627#41—10616no—
628#41—10632no—
629#41—10624no—
630C2×Q8—232no—
631C2×Q8—216no—
632C2×Q8—212no—
633C2×Q8—5332no—
634C2×Q8—5332no—
635C2×Q8—5324no—
636C2×Q8—5312no—
637C2×Q8—5312no—
638C2×Q8—5312no—
639C2×Q8—536no—
640C2×Q8—10612no—
641C2×Q8—10648no—
642C2×Q8—10624no—
643C2×Q8—10696no—
644C2×Q8—10648no—
645C2×Q8—10616no—
646C2×Q8D4×D5318yes—
647C2×Q8C23×D5316yes—
648C2×Q8C23×D53112yes—
649C2×Q8C23×D5314yes—
650C2×D4—532no—
651C2×D4—534no—
652C2×D4—532no—
653C2×D4—534no—
654C2×D4—5312no—
655C2×D4—5312no—
656C2×D4—538no—
657C2×D4—5324no—
658C2×D4—536no—
659C2×D4—534no—
660C2×D4—536no—
661C2×D4—5312no—
662C2×D4—536no—
663C2×D4—5324no—
664C2×D4—10612no—
665C2×D4—10624no—
666C2×D4—10612no—
667C2×D4—10616no—
668C2×D4—1064no—
669C2×D4—10612no—
670C2×D4C23×D5314yes—
671C2×D4C23×D5316yes—
672C2×D4C23×D5318yes—
673C22×C4—212no—
674C22×C4—533no—
675C22×C4—5324no—
676C22×C4—536no—
677C22×C4—536no—
678C22×C4—5312no—
679C22×C4—531no—
680C22×C4—5312no—
681C22×C4—5324no—
682C22×C4—5312no—
683C22×C4—5312no—
684C22×C4—534no—
685C22×C4—538no—
686C22×C4—10624no—
687C22×C4—10648no—
688C22×C4—10612no—
689C22×C4C23×D53112yes—
690C22×C4C23×D53112yes—
691C22×C4C23×D5313yes—
692C22×C4C23×D5313yes—
693C4⋊C4—5324no—
694C4⋊C4—5312no—
695C4⋊C4—538no—
696C4⋊C4—5324no—
697C4⋊C4—538no—
698C4⋊C4C23×D53112yes—
699C4⋊C4C23×D53124yes—
700C22⋊C4—534no—
701C22⋊C4—538no—
702C22⋊C4—538no—
703C22⋊C4—538no—
704C22⋊C4—5324no—
705C22⋊C4—5324no—
706C22⋊C4—5324no—
707C22⋊C4—538no—
708C22⋊C4C23×D5314yes—
709C22⋊C4C23×D53124yes—
710C22⋊C4C23×D5318yes—
711C42—5324no—
712C42—5312no—
713C42C23×D53112yes—
714C23—22no—
715C23—42no—
716C23—531no—
717C23—531no—
718C23—534no—
719C23—534no—
720C23—536no—
721C23—1068no—
722C23—1066no—
723C23—2122no—
724C23—2126no—
725C23—2128no—
726C23C24×D5312yes—
727C23C24×D5314yes—
728C23C24×D5311yescharacteristic
729Q8—224no—
730Q8—212no—
731Q8—5348no—
732Q8—10624no—
733Q8—10624no—
734Q8—10612no—
735Q8C2×D4×D53116yes—
736D4—28no—
737D4—212no—
738D4—48no—
739D4—1068no—
740D4—10612no—
741D4—10612no—
742D4—10624no—
743D4—10624no—
744D4—1064no—
745D4—1064no—
746D4—1068no—
747D4—1068no—
748D4—10624no—
749D4—10612no—
750D4—21224no—
751D4—21224no—
752D4—2128no—
753C2×C4—26no—
754C2×C4—224no—
755C2×C4—224no—
756C2×C4—5312no—
757C2×C4—536no—
758C2×C4—5324no—
759C2×C4—5324no—
760C2×C4—538no—
761C2×C4—532no—
762C2×C4—534no—
763C2×C4—10624no—
764C2×C4—10648no—
765C2×C4—1068no—
766C2×C4—10624no—
767C2×C4—1062no—
768C2×C4—10624no—
769C2×C4—10624no—
770C2×C4—2128no—
771C2×C4C2×D4×D53112yes—
772C2×C4C24×D5318yes—
773C2×C4C24×D5314yes—
774C2×C4C24×D5316yes—
775C2×C4C24×D5316yes—
776C22—22no—
777C22—22no—
778C22—24no—
779C22—22no—
780C22—28no—
781C22—22no—
782C22—44no—
783C22—532no—
784C22—532no—
785C22—1062no—
786C22—1062no—
787C22—1066no—
788C22—1064no—
789C22—1068no—
790C22—10612no—
791C22—2124no—
792C22—21212no—
793C22—21216no—
794C22C22×D4×D5312yes—
795C22C25×D5311yescharacteristic
796C4—24no—
797C4—26no—
798C4—28no—
799C4—5312no—
800C4—1064no—
801C4—1062no—
802C4—1068no—
803C4C22×D4×D53112yes—
804C2—22no—
805C2—42no—
806C2—44no—
807C2—1062no—
808C2—1062no—
809C2—2126no—
810C2—2124no—
811C2C23×D4×D5311yescharacteristic
812C2#2028952712yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3486C2
hypercenter#3486D53
hypocenterC53#62848
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3486

Complements

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

NH ≅ G/Ntype
1. C22×#13133265C2semidirect
2. C2×2−1+4×D53C2semidirect
3. #20288485C2semidirect
4. #20288483C2semidirect
5. #20288374C2semidirect
6. #20288372C2semidirect
7. #20288370C2semidirect
8. #20288369C2semidirect
9. #20288366C2semidirect
10. #20288365C2semidirect
11. #20288364C2semidirect
12. #20288047C2semidirect
13. #20288045C2semidirect
14. #519×D53C2semidirect
15. C53×#3486C2semidirect
19. C2×#13133265C22semidirect
20. C2×#13133265C22semidirect
22. C2×#13133264C22semidirect
25. C22×#11719949C22semidirect
27. C22×#11719945C22semidirect
29. C2×#41×D53C22semidirect
31. C22×Q8×D53C22semidirect
32. C22×Q8×D53C22semidirect
33. #16811295C22semidirect
34. #16811294C22semidirect
35. #16811292C22semidirect
36. #16811291C22semidirect
37. #16811288C22semidirect
38. Q8×C22⋊D53C22semidirect
39. #16811286C22semidirect
40. #16811285C22semidirect
41. #16811284C22semidirect
42. #16811284C22semidirect
43. #16811283C22semidirect
44. #16811283C22semidirect
45. #16811282C22semidirect
46. #16811281C22semidirect
47. #16811203C22semidirect
48. #16811203C22semidirect
49. #16811202C22semidirect
50. #16811198C22semidirect
51. #16811197C22semidirect
52. #16811196C22semidirect
53. #16811195C22semidirect
54. #16811192C22semidirect
55. #16811191C22semidirect
56. #16811189C22semidirect
57. #16811188C22semidirect
58. #16811187C22semidirect
61. #16811174C22semidirect
62. #16811172C22semidirect
63. #16811170C22semidirect
64. #16811136C22semidirect
65. #16811135C22semidirect
66. #16811134C22semidirect
67. #16811132C22semidirect
68. #16811131C22semidirect
69. #16811130C22semidirect
70. #16811101C22semidirect
71. #16811100C22semidirect
72. #16811099C22semidirect
73. C4×Q8×D53C22semidirect
76. C23×Q8×C53C22semidirect
77. D4×Q8×C53C22semidirect
78. C53×#548C22semidirect
79. C53×#536C22semidirect
80. C53×#525C22semidirect
81. C53×#519C22semidirect
113. C2×Q8×D53D4semidirect
409. #3486D53semidirect
440. C23×Q8C2×D53semidirect
448. D4×Q8C2×D53semidirect
456. #548C2×D53semidirect
464. #536C2×D53semidirect
481. #525C2×D53semidirect
485. #519C2×D53semidirect
488. C53#62848semidirect

Maximal subgroups

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

subgroupindex
C22×#131332652
C2×2−1+4×D532
#202884852
#202884832
#202883742
#202883722
#202883702
#202883692
#202883662
#202883652
#202883642
#202880472
#202880452
#519×D532
C53×#34862
#6284853