Finite Group Databasebeta

← D53×#3487 #28292332

Subgroups — D53×#3487 #28292332

Order 13568.

11510 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×2−1+4×D53C211yesmaximal, characteristic, complemented
2C22×#41×D53C211yesmaximal, characteristic, complemented
3#20288374C211yesmaximal, characteristic, complemented
4#20288373C211yesmaximal, characteristic, complemented
5#20288372C218yesmaximal, complemented
6#20288371C216yesmaximal, complemented
7#20288370C211yesmaximal, characteristic, complemented
8#20288369C216yesmaximal, complemented
9#20288368C218yesmaximal, complemented
10#550×D53C218yesmaximal, complemented
11#548×D53C218yesmaximal, complemented
12#535×D53C216yesmaximal, complemented
13#525×D53C216yesmaximal, complemented
14#519×D53C211yesmaximal, characteristic, complemented
15C53×#3487C211yesmaximal, characteristic, complemented
16C2×#13133265C2211yescharacteristic, complemented
17C2×#13133265C2214yescomplemented
18C2×#13133264C2216yescomplemented
19C2×#13133264C2214yescomplemented
202−1+4×D53—216no—
21C22×#11719949C2211yescharacteristic, complemented
22C22×#11719945C2213yescomplemented
23C22×#11719947C2213yescomplemented
24C2×#41×D53—216no—
25C2×#41×D53C2216yes—
26C2×#41×D53C2218yes—
27C2×#41×D53C2218yescomplemented
28C2×#41×D53C2214yescomplemented
29C22×Q8×D53C2211yescharacteristic
30C22×Q8×D53C2214yescomplemented
31C22×D4×D53C2213yes—
32C23×C4×D53C2213yes—
33#16811295C2218yescomplemented
34#16811294C22124yescomplemented
35#16811293C22124yescomplemented
36#16811292C2218yescomplemented
37#16811292C2218yescomplemented
38#16811291C22124yescomplemented
39#16811291C22124yescomplemented
40#16811285C2218yescomplemented
41#16811284C2218yescomplemented
42#16811283C22124yescomplemented
43#16811282C22124yescomplemented
44#16811281C22124yescomplemented
45#16811280C2218yescomplemented
46#16811279C22124yescomplemented
47#16811192C2216yescomplemented
48#16811191C22112yescomplemented
49#16811190C2216yescomplemented
50#16811189C22124yescomplemented
51#16811188C22124yescomplemented
52#16811187C2216yescomplemented
53#16811186C22112yescomplemented
54#127×D53C22112yescomplemented
55#124×D53C22112yescomplemented
56#16811136C22112yescomplemented
57#16811135C2216yescomplemented
58#16811134C2216yescomplemented
59#16811133C22112yescomplemented
60#16811132C22124yescomplemented
61#16811131C22112yescomplemented
62#16811130C2216yescomplemented
63#16811129C22112yescomplemented
64#123×D53C2214yes—
65C22⋊Q8×D53C22112yescomplemented
66#121×D53C22124yescomplemented
67#121×D53C22112yescomplemented
68#120×D53C22112yes—
69#16811101C2211yescharacteristic, complemented
70#16811100C2216yescomplemented
71#16811099C2218yescomplemented
72C4×Q8×D53C2218yescomplemented
73C4×D4×D53C22124yescomplemented
74#117×D53C2216yes—
75C2×2−1+4×C53C2211yescharacteristic, complemented
76C22×#41×C53C2211yescharacteristic, complemented
77C53×#550C2218yescomplemented
78C53×#548C2218yescomplemented
79C53×#535C2216yescomplemented
80C53×#525C2216yescomplemented
81C53×#519C2211yescharacteristic, complemented
82C24×D53C2313yes—
83#13133265—28no—
84#13133265—232no—
85#13133264—232no—
86#13133264—248no—
87C2×#11719949—28no—
88C2×#11719949C2318yes—
89C2×#11719949C2316yes—
90C2×#11719949C2314yescomplemented
91C2×#11719945—224no—
92C2×#11719945C23124yes—
93C2×#11719945C23112yes—
94C2×#11719945C2316yes—
95C2×#11719945C23112yescomplemented
96C2×#11719947—224no—
97C2×#11719947C23124yes—
98C2×#11719947C23112yes—
99C2×#11719947C2316yes—
100C2×#11719947C23112yescomplemented
101#41×D53—264no—
102#41×D53—232no—
103#41×D53—264no—
104#41×D53—248no—
105C22×Dic106C2313yes—
106C22×Dic106C23112yescomplemented
107C2×Q8×D53—232no—
108C2×Q8×D53D4116yescomplemented
109C2×Q8×D53C2316yes—
110C2×Q8×D53C2314yes—
111C2×Q8×D53C2314yes—
112C2×Q8×D53C2314yescomplemented
113C2×Q8×D53C23112yescomplemented
114C22×D212C2313yes—
115C22×C22⋊D53C2316yes—
116C2×D4×D53—224no—
117C2×D4×D53C2314yes—
118C2×D4×D53C23112yes—
119C2×D4×D53C2316yes—
120C2×D4×D53C23112yes—
121C2×D4×D53C23124yes—
122C23×Dic53C2313yes—
123C22×C4×D53—224no—
124C22×C4×D53C23112yes—
125C22×C4×D53C23112yes—
126C22×C4×D53C2311yescharacteristic
127C22×C4×D53C2313yes—
128C22×C4×D53C2313yes—
129C22×C4×D53C23112yes—
130C22×C4×D53C2313yes—
131#13133214C23112yescomplemented
132#13133213C23112yescomplemented
133#13133213C23112yescomplemented
134#13133213C23148yescomplemented
135#13133206C23112yescomplemented
136#13133205C23112yescomplemented
137#13133204C23112yescomplemented
138#13133203C23148yescomplemented
139#13133202C2318yes—
140#13133201C2314yes—
141#13133200C2314yes—
142#13133199C2318yes—
143#13133198C2314yes—
144#13133197C23112yescomplemented
145#13133196C23112yescomplemented
146#13133195C23124yescomplemented
147#13133194C23124yescomplemented
148#13133193C23112yescomplemented
149#13133192C23124yescomplemented
150#13133192C23112yescomplemented
151#13133191C23124yescomplemented
152#13133191C23112yescomplemented
153#13133190C23148yescomplemented
154#13133190C23124yescomplemented
155#13133189C23148yescomplemented
156#13133189C23124yescomplemented
157#13133188C23124yescomplemented
158#13133188C23112yescomplemented
159#13133187C23112yes—
160#13133187C23124yes—
161#13133186C23112yes—
162#13133185C23112yes—
163#13133185C23124yes—
164Q8×Dic53C2318yescomplemented
165C4×Dic106C23124yescomplemented
166#13133182C23124yescomplemented
167C4×D212C23124yescomplemented
168D4×Dic53C23124yescomplemented
169#13133179C23124yescomplemented
170C4×C22⋊D53C23124yescomplemented
171C4×C22⋊D53C23124yescomplemented
172#13133177C23124yescomplemented
173#13133177C23124yescomplemented
174#13133176C2316yes—
175#13133175C23112yes—
176#13133174C23112yes—
177#13133173C23112yes—
178C4⋊C4×D53C23112yes—
179C4⋊C4×D53C2318yes—
180C22⋊C4×D53C2314yes—
181C22⋊C4×D53C2318yes—
182C22⋊C4×D53C23124yes—
183C42×D53C23112yes—
1842−1+4×C53—28no—
185C2×#41×C53—28no—
186C2×#41×C53C2318yes—
187C2×#41×C53C2316yes—
188C2×#41×C53C2314yescomplemented
189C22×Q8×C53C2311yescharacteristic
190C22×Q8×C53C2314yescomplemented
191C22×D4×C53C2313yes—
192C23×C4×C53C2313yes—
193#127×C53C23112yescomplemented
194#124×C53C23112yescomplemented
195#123×C53C2314yes—
196C22⋊Q8×C53C23112yescomplemented
197#121×C53C23124yescomplemented
198#121×C53C23112yescomplemented
199#120×C53C23112yes—
200C4×Q8×C53C2318yescomplemented
201C4×D4×C53C23124yescomplemented
202#117×C53C2316yes—
203C24×C53C2413yes—
204C23×D53—212no—
205C23×D53—412no—
206C23×D53C2416yes—
207C23×D53C2414yes—
208C23×D53C2411yescharacteristic
209C23×D53C2416yes—
210C23×D53C2413yes—
211#41×C53—232no—
212#41×C53—216no—
213#41×C53—224no—
214C2×Q8×C53—216no—
215C2×Q8×C53C2×D418yescomplemented
216C2×Q8×C53C2416yes—
217C2×Q8×C53C2414yes—
218C2×D4×C53—212no—
219C2×D4×C53C2414yes—
220C2×D4×C53C24112yes—
221C2×D4×C53C2416yes—
222C2×D4×C53C24124yes—
223C22×C4×C53—212no—
224C22×C4×C53C24112yes—
225C22×C4×C53C24112yes—
226C22×C4×C53C2411yescharacteristic
227C22×C4×C53C2413yes—
228C2×C22⋊D53—224no—
229C2×C22⋊D53C2414yes—
230C2×C22⋊D53C2414yes—
231C2×C22⋊D53C24124yes—
232C2×C22⋊D53C24112yes—
233C2×C22⋊D53C24124yes—
234C2×C22⋊D53C24124yes—
235C22×Dic53—212no—
236C22×Dic53C24112yes—
237C22×Dic53C24112yes—
238C22×Dic53C2411yescharacteristic
239C22×Dic53C2413yes—
240#11719949—232no—
241#11719949—216no—
242#11719949—224no—
243Q8×D53—216no—
244Q8×D53—224no—
245Q8×D53—248no—
246Q8×D53C2×D4132yes—
247Q8×D53C2×D4132yescomplemented
248#11719947—248no—
249#11719947—224no—
250#11719947—296no—
251#11719947—248no—
252D4×D53—216no—
253D4×D53—248no—
254D4×D53—248no—
255D4×D53—224no—
256D4×D53—448no—
257#11719945—224no—
258#11719945—248no—
259#11719945—296no—
260#11719945—248no—
261C2×D212—212no—
262C2×D212C2414yes—
263C2×D212C24112yes—
264C2×D212C2416yes—
265C2×D212C24124yes—
266C2×C4×D53—24no—
267C2×C4×D53—212no—
268C2×C4×D53—212no—
269C2×C4×D53—248no—
270C2×C4×D53—248no—
271C2×C4×D53—248no—
272C2×C4×D53C2×D4124yes—
273C2×C4×D53C2418yes—
274C2×C4×D53C2414yes—
275C2×C4×D53C2412yes—
276C2×C4×D53C24112yes—
277C2×C4×D53C24112yes—
278C2×C4×D53C24112yes—
279C2×C4×D53C24112yes—
280C2×C4×D53C2412yes—
281C2×C4×D53C2416yes—
282C2×C4×D53C2416yes—
283C2×Dic106—248no—
284C2×Dic106C2×D4124yescomplemented
285C2×Dic106C24112yes—
286C2×Dic106C2416yes—
287C2×Dic106C24112yes—
288C4⋊C4×C53C24112yes—
289C4⋊C4×C53C2418yes—
290C22⋊C4×C53C2414yes—
291C22⋊C4×C53C2418yes—
292C22⋊C4×C53C24124yes—
293C42×C53C24112yes—
294C22⋊Dic53C2414yes—
295C22⋊Dic53C2418yes—
296C22⋊Dic53C24124yes—
297#11719921C2418yes—
298#11719921C2418yes—
299#11719921C24124yes—
300#11719921C2418yes—
301#11719921C24124yes—
302C4⋊Dic53C24112yes—
303C4⋊Dic53C2418yes—
304#11719919C24124yes—
305#11719919C2418yes—
306#11719919C2418yes—
307C4×Dic53C24124yes—
308C4×Dic53C24112yes—
309C23×C53—26no—
310C23×C53—46no—
311C23×C53C2514yes—
312C23×C53C2516yes—
313C23×C53C2511yescharacteristic
314C22×D53—24no—
315C22×D53—26no—
316C22×D53—28no—
317C22×D53—212no—
318C22×D53—212no—
319C22×D53—216no—
320C22×D53—224no—
321C22×D53—412no—
322C22×D53—46no—
323C22×D53—448no—
324C22×D53C22×D414yes—
325C22×D53C2514yes—
326C22×D53C2516yes—
327C22×D53C2511yescharacteristic
328C22×D53C2511yescharacteristic
329Q8×C53—212no—
330Q8×C53C22×D4116yes—
331D4×C53—28no—
332D4×C53—224no—
333D4×C53—212no—
334D4×C53—424no—
335C2×C4×C53—22no—
336C2×C4×C53—224no—
337C2×C4×C53—224no—
338C2×C4×C53C22×D4112yes—
339C2×C4×C53C2514yes—
340C2×C4×C53C2512yes—
341C2×C4×C53C2518yes—
342C2×C4×C53C2516yes—
343C22⋊D53—28no—
344C22⋊D53—28no—
345C22⋊D53—224no—
346C22⋊D53—248no—
347C22⋊D53—424no—
348C22⋊D53—424no—
349C2×Dic53—22no—
350C2×Dic53—224no—
351C2×Dic53—224no—
352C2×Dic53C22×D4112yes—
353C2×Dic53C2514yes—
354C2×Dic53C2512yes—
355C2×Dic53C2518yes—
356C2×Dic53C2516yes—
357D212—28no—
358D212—224no—
359D212—212no—
360D212—424no—
361C4×D53—24no—
362C4×D53—24no—
363C4×D53—28no—
364C4×D53—216no—
365C4×D53—224no—
366C4×D53—224no—
367C4×D53—224no—
368C4×D53—224no—
369C4×D53C22×D4124yes—
370C4×D53C22×D4124yes—
371Dic106—212no—
372Dic106—224no—
373Dic106C22×D4148yes—
374C2×#3487—531nomaximal, Sylow
375C22×C53—22no—
376C22×C53—24no—
377C22×C53—26no—
378C22×C53—28no—
379C22×C53—212no—
380C22×C53—412no—
381C22×C53C23×D412yes—
382C22×C53C2611yescharacteristic
383C2×D53—22no—
384C2×D53—28no—
385C2×D53—24no—
386C2×D53—26no—
387C2×D53—28no—
388C2×D53—212no—
389C2×D53—424no—
390C2×D53—412no—
391C2×D53—416no—
392C2×D53—424no—
393C2×D53C23×D412yes—
394C2×D53C23×D412yes—
395C2×D53#58514yes—
396C4×C53—24no—
397C4×C53—22no—
398C4×C53—28no—
399C4×C53C23×D4112yes—
400Dic53—24no—
401Dic53—22no—
402Dic53—28no—
403Dic53C23×D4112yes—
404C22×2−1+4—531no—
405C23×#41—531no—
406#3487—531no—
407#3487—531no—
408#3487—538no—
409#3487—538no—
410#3487—536no—
411#3487—536no—
412#3487—531no—
413#3487D5311yescharacteristic, direct product factor
414C2×#550—538no—
415C2×#548—538no—
416C2×#535—536no—
417C2×#525—536no—
418C2×#519—531no—
419C2×C53—22no—
420C2×C53—46no—
421C2×C53—44no—
422C2×C53C24×D411yescharacteristic
423C2×C53C2×#58512yes—
424D53—22no—
425D53—44no—
426D53—46no—
427D53#348714yesdirect product factor
428C2×2−1+4—536no—
429C2×2−1+4—534no—
430C2×2−1+4—531no—
431C2×2−1+4—534no—
432C2×2−1+4—10616no—
433C2×2−1+4C2×D5311yescharacteristic, complemented
434C22×#41—538no—
435C22×#41—538no—
436C22×#41—536no—
437C22×#41—534no—
438C22×#41—531no—
439C22×#41—533no—
440C22×#41—533no—
441C22×#41—10616no—
442C22×#41C2×D5311yescharacteristic, complemented
443C23×Q8—531no—
444C23×Q8—534no—
445C23×D4—533no—
446C24×C4—533no—
447#550—538no—
448#550—538no—
449#550—5324no—
450#550—5324no—
451#550—5324no—
452#550—538no—
453#550—5324no—
454#550C2×D5318yescomplemented
455#548—538no—
456#548—538no—
457#548—5324no—
458#548—5324no—
459#548—5324no—
460#548—538no—
461#548—5324no—
462#548C2×D5318yescomplemented
463#535—536no—
464#535—536no—
465#535—5312no—
466#535—5312no—
467#535—5324no—
468#535—5324no—
469#535—536no—
470#535C2×D5316yescomplemented
471C2×#127—5312no—
472C2×#124—5312no—
473#525—536no—
474#525—536no—
475#525—5312no—
476#525—5312no—
477#525—5312no—
478#525—5312no—
479#525—5324no—
480#525—536no—
481#525C2×D5316yescomplemented
482C2×#123—534no—
483C2×C22⋊Q8—5312no—
484C2×#121—5312no—
485C2×#121—5324no—
486C2×#120—5312no—
487#519—531no—
488#519—538no—
489#519—536no—
490#519C2×D5311yescharacteristic, complemented
491C2×C4×Q8—538no—
492C2×C4×D4—5324no—
493C2×#117—536no—
494C53C2×#348711yescharacteristic, complemented, Sylow
495C25—533no—
4962−1+4—28no—
4972−1+4—10632no—
4982−1+4—10632no—
4992−1+4—10648no—
5002−1+4—1068no—
501C2×#41—28no—
502C2×#41—536no—
503C2×#41—538no—
504C2×#41—534no—
505C2×#41—5312no—
506C2×#41—536no—
507C2×#41—5324no—
508C2×#41—5312no—
509C2×#41—5312no—
510C2×#41—536no—
511C2×#41—5324no—
512C2×#41—5312no—
513C2×#41—10624no—
514C2×#41—10648no—
515C2×#41—10624no—
516C2×#41—10664no—
517C2×#41—10664no—
518C2×#41—10632no—
519C2×#41—1068no—
520C2×#41C22×D5316yes—
521C2×#41C22×D5318yes—
522C2×#41C22×D5314yescomplemented
523C22×Q8—5316no—
524C22×Q8—534no—
525C22×Q8—534no—
526C22×Q8—536no—
527C22×Q8—5312no—
528C22×Q8—534no—
529C22×Q8—533no—
530C22×Q8—5312no—
531C22×Q8—10632no—
532C22×Q8C22×D5311yescharacteristic
533C22×Q8C22×D5314yescomplemented
534C22×D4—536no—
535C22×D4—534no—
536C22×D4—5312no—
537C22×D4—536no—
538C22×D4—5312no—
539C22×D4—5324no—
540C22×D4—533no—
541C22×D4—10624no—
542C22×D4C22×D5313yes—
543C23×C4—533no—
544C23×C4—533no—
545C23×C4—5312no—
546C23×C4—5312no—
547C23×C4—531no—
548C23×C4—533no—
549C23×C4—5312no—
550C23×C4—533no—
551C23×C4—10624no—
552C23×C4C22×D5313yes—
553#127—5348no—
554#127—5312no—
555#127—5312no—
556#127—5312no—
557#127C22×D53112yescomplemented
558#124—5312no—
559#124—5312no—
560#124—5348no—
561#124—5312no—
562#124C22×D53112yescomplemented
563#123—534no—
564#123—534no—
565#123—538no—
566#123—538no—
567#123—534no—
568#123C22×D5314yes—
569C22⋊Q8—5312no—
570C22⋊Q8—5312no—
571C22⋊Q8—5324no—
572C22⋊Q8—5312no—
573C22⋊Q8—5324no—
574C22⋊Q8C22×D53112yescomplemented
575#121—5312no—
576#121—5324no—
577#121—5324no—
578#121—5348no—
579#121—5312no—
580#121—5324no—
581#121—5312no—
582#121—5324no—
583#121—5324no—
584#121—5348no—
585#121C22×D53112yescomplemented
586#121C22×D53124yescomplemented
587#120—5312no—
588#120—5312no—
589#120—5324no—
590#120—5324no—
591#120—5312no—
592#120C22×D53112yes—
593C4×Q8—538no—
594C4×Q8—5324no—
595C4×Q8—5324no—
596C4×Q8C22×D5318yescomplemented
597C4×D4—5324no—
598C4×D4—5324no—
599C4×D4—5324no—
600C4×D4—5324no—
601C4×D4—5324no—
602C4×D4—5324no—
603C4×D4—5324no—
604C4×D4C22×D53124yescomplemented
605#117—536no—
606#117—5312no—
607#117—5312no—
608#117—5312no—
609#117C22×D5316yes—
610C2×C4⋊C4—5312no—
611C2×C4⋊C4—538no—
612C2×C22⋊C4—534no—
613C2×C22⋊C4—538no—
614C2×C22⋊C4—5324no—
615C2×C42—5312no—
616C24—531no—
617C24—536no—
618C24—534no—
619C24—536no—
620C24—533no—
621C24—10612no—
622C24—21212no—
623C24C23×D5313yes—
624#41—232no—
625#41—216no—
626#41—224no—
627#41—10648no—
628#41—10696no—
629#41—10648no—
630#41—10648no—
631#41—10624no—
632#41—10624no—
633#41—10696no—
634#41—10648no—
635#41—10632no—
636#41—10616no—
637#41—10624no—
638C2×Q8—216no—
639C2×Q8—5332no—
640C2×Q8—5332no—
641C2×Q8—5324no—
642C2×Q8—5312no—
643C2×Q8—5312no—
644C2×Q8—536no—
645C2×Q8—10648no—
646C2×Q8—10624no—
647C2×Q8—10648no—
648C2×Q8—10616no—
649C2×Q8D4×D5318yescomplemented
650C2×Q8C23×D5316yes—
651C2×Q8C23×D5314yes—
652C2×D4—212no—
653C2×D4—534no—
654C2×D4—534no—
655C2×D4—5324no—
656C2×D4—5312no—
657C2×D4—5324no—
658C2×D4—5324no—
659C2×D4—534no—
660C2×D4—5312no—
661C2×D4—536no—
662C2×D4—5324no—
663C2×D4—10648no—
664C2×D4—10648no—
665C2×D4—10624no—
666C2×D4—10624no—
667C2×D4—10616no—
668C2×D4—10612no—
669C2×D4—21248no—
670C2×D4C23×D5314yes—
671C2×D4C23×D53112yes—
672C2×D4C23×D5316yes—
673C2×D4C23×D53124yes—
674C22×C4—212no—
675C22×C4—533no—
676C22×C4—5324no—
677C22×C4—536no—
678C22×C4—536no—
679C22×C4—5312no—
680C22×C4—5312no—
681C22×C4—531no—
682C22×C4—538no—
683C22×C4—534no—
684C22×C4—532no—
685C22×C4—5312no—
686C22×C4—5312no—
687C22×C4—5312no—
688C22×C4—5312no—
689C22×C4—532no—
690C22×C4—10612no—
691C22×C4—10648no—
692C22×C4—10648no—
693C22×C4—10648no—
694C22×C4—1064no—
695C22×C4—10612no—
696C22×C4—10612no—
697C22×C4C23×D53112yes—
698C22×C4C23×D53112yes—
699C22×C4C23×D5311yescharacteristic
700C22×C4C23×D5313yes—
701C4⋊C4—5324no—
702C4⋊C4—5312no—
703C4⋊C4—538no—
704C4⋊C4—538no—
705C4⋊C4—538no—
706C4⋊C4C23×D53112yes—
707C4⋊C4C23×D5318yes—
708C22⋊C4—534no—
709C22⋊C4—538no—
710C22⋊C4—5324no—
711C22⋊C4—538no—
712C22⋊C4—538no—
713C22⋊C4—538no—
714C22⋊C4—5324no—
715C22⋊C4—5324no—
716C22⋊C4C23×D5314yes—
717C22⋊C4C23×D5318yes—
718C22⋊C4C23×D53124yes—
719C42—5324no—
720C42—5312no—
721C42C23×D53112yes—
722C23—26no—
723C23—46no—
724C23—531no—
725C23—534no—
726C23—531no—
727C23—536no—
728C23—534no—
729C23—1064no—
730C23—1068no—
731C23—10612no—
732C23—10612no—
733C23—10616no—
734C23—10624no—
735C23—1066no—
736C23—2126no—
737C23—21212no—
738C23—21248no—
739C23C24×D5316yes—
740C23C24×D5314yes—
741C23C24×D5311yescharacteristic
742Q8—212no—
743Q8—5348no—
744Q8—10624no—
745Q8—10612no—
746Q8C2×D4×D53116yes—
747D4—28no—
748D4—224no—
749D4—212no—
750D4—424no—
751D4—1068no—
752D4—10648no—
753D4—10624no—
754D4—1068no—
755D4—1068no—
756D4—10624no—
757D4—10612no—
758D4—21224no—
759D4—21224no—
760D4—21224no—
761C2×C4—22no—
762C2×C4—224no—
763C2×C4—224no—
764C2×C4—5312no—
765C2×C4—536no—
766C2×C4—5324no—
767C2×C4—5324no—
768C2×C4—538no—
769C2×C4—534no—
770C2×C4—532no—
771C2×C4—10624no—
772C2×C4—10624no—
773C2×C4—1064no—
774C2×C4—1064no—
775C2×C4—1068no—
776C2×C4—10616no—
777C2×C4—10624no—
778C2×C4—10624no—
779C2×C4—1062no—
780C2×C4—10624no—
781C2×C4—10624no—
782C2×C4C2×D4×D53112yes—
783C2×C4C24×D5318yes—
784C2×C4C24×D5314yes—
785C2×C4C24×D5312yes—
786C2×C4C24×D5316yes—
787C22—22no—
788C22—24no—
789C22—26no—
790C22—28no—
791C22—212no—
792C22—412no—
793C22—532no—
794C22—534no—
795C22—532no—
796C22—1068no—
797C22—1062no—
798C22—1064no—
799C22—1066no—
800C22—1068no—
801C22—10612no—
802C22—21212no—
803C22—21224no—
804C22—21216no—
805C22—21224no—
806C22C22×D4×D5312yes—
807C22C25×D5311yescharacteristic
808C4—22no—
809C4—24no—
810C4—28no—
811C4—5312no—
812C4—1062no—
813C4—1064no—
814C4—1068no—
815C4C22×D4×D53112yes—
816C2—22no—
817C2—46no—
818C2—44no—
819C2—534no—
820C2—1062no—
821C2—2126no—
822C2—2124no—
823C2C23×D4×D5311yescharacteristic
824C2#585×D5312yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3487C2
hypercenter#3487D53
hypocenterC53C2×#3487
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3487

Complements

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

NH ≅ G/Ntype
1. C2×2−1+4×D53C2semidirect
2. C22×#41×D53C2semidirect
3. #20288374C2semidirect
4. #20288373C2semidirect
5. #20288372C2semidirect
6. #20288371C2semidirect
7. #20288370C2semidirect
8. #20288369C2semidirect
9. #20288368C2semidirect
10. #550×D53C2semidirect
11. #548×D53C2semidirect
12. #535×D53C2semidirect
13. #525×D53C2semidirect
14. #519×D53C2semidirect
15. C53×#3487C2semidirect
16. C2×#13133265C22semidirect
17. C2×#13133265C22semidirect
18. C2×#13133264C22semidirect
19. C2×#13133264C22semidirect
21. C22×#11719949C22semidirect
22. C22×#11719945C22semidirect
23. C22×#11719947C22semidirect
27. C2×#41×D53C22semidirect
28. C2×#41×D53C22semidirect
30. C22×Q8×D53C22semidirect
33. #16811295C22semidirect
34. #16811294C22semidirect
35. #16811293C22semidirect
36. #16811292C22semidirect
37. #16811292C22semidirect
38. #16811291C22semidirect
39. #16811291C22semidirect
40. #16811285C22semidirect
41. #16811284C22semidirect
42. #16811283C22semidirect
43. #16811282C22semidirect
44. #16811281C22semidirect
45. #16811280C22semidirect
46. #16811279C22semidirect
47. #16811192C22semidirect
48. #16811191C22semidirect
49. #16811190C22semidirect
50. #16811189C22semidirect
51. #16811188C22semidirect
52. #16811187C22semidirect
53. #16811186C22semidirect
54. #127×D53C22semidirect
55. #124×D53C22semidirect
56. #16811136C22semidirect
57. #16811135C22semidirect
58. #16811134C22semidirect
59. #16811133C22semidirect
60. #16811132C22semidirect
61. #16811131C22semidirect
62. #16811130C22semidirect
63. #16811129C22semidirect
65. C22⋊Q8×D53C22semidirect
66. #121×D53C22semidirect
67. #121×D53C22semidirect
69. #16811101C22semidirect
70. #16811100C22semidirect
71. #16811099C22semidirect
72. C4×Q8×D53C22semidirect
73. C4×D4×D53C22semidirect
75. C2×2−1+4×C53C22semidirect
76. C22×#41×C53C22semidirect
77. C53×#550C22semidirect
78. C53×#548C22semidirect
79. C53×#535C22semidirect
80. C53×#525C22semidirect
81. C53×#519C22semidirect
90. C2×#11719949C23semidirect
95. C2×#11719945C23semidirect
100. C2×#11719947C23semidirect
106. C22×Dic106C23semidirect
108. C2×Q8×D53D4semidirect
112. C2×Q8×D53C23semidirect
113. C2×Q8×D53C23semidirect
131. #13133214C23semidirect
132. #13133213C23semidirect
133. #13133213C23semidirect
134. #13133213C23semidirect
135. #13133206C23semidirect
136. #13133205C23semidirect
137. #13133204C23semidirect
138. #13133203C23semidirect
144. #13133197C23semidirect
145. #13133196C23semidirect
146. #13133195C23semidirect
147. #13133194C23semidirect
148. #13133193C23semidirect
149. #13133192C23semidirect
150. #13133192C23semidirect
151. #13133191C23semidirect
152. #13133191C23semidirect
153. #13133190C23semidirect
154. #13133190C23semidirect
155. #13133189C23semidirect
156. #13133189C23semidirect
157. #13133188C23semidirect
158. #13133188C23semidirect
164. Q8×Dic53C23semidirect
165. C4×Dic106C23semidirect
166. #13133182C23semidirect
167. C4×D212C23semidirect
168. D4×Dic53C23semidirect
169. #13133179C23semidirect
170. C4×C22⋊D53C23semidirect
171. C4×C22⋊D53C23semidirect
172. #13133177C23semidirect
173. #13133177C23semidirect
188. C2×#41×C53C23semidirect
190. C22×Q8×C53C23semidirect
193. #127×C53C23semidirect
194. #124×C53C23semidirect
196. C22⋊Q8×C53C23semidirect
197. #121×C53C23semidirect
198. #121×C53C23semidirect
200. C4×Q8×C53C23semidirect
201. C4×D4×C53C23semidirect
215. C2×Q8×C53C2×D4semidirect
247. Q8×D53C2×D4semidirect
284. C2×Dic106C2×D4semidirect
413. #3487D53direct (N × H)
427. D53#3487direct (N × H)
433. C2×2−1+4C2×D53semidirect
442. C22×#41C2×D53semidirect
454. #550C2×D53semidirect
462. #548C2×D53semidirect
470. #535C2×D53semidirect
481. #525C2×D53semidirect
490. #519C2×D53semidirect
494. C53C2×#3487semidirect
522. C2×#41C22×D53semidirect
533. C22×Q8C22×D53semidirect
557. #127C22×D53semidirect
562. #124C22×D53semidirect
574. C22⋊Q8C22×D53semidirect
585. #121C22×D53semidirect
586. #121C22×D53semidirect
596. C4×Q8C22×D53semidirect
604. C4×D4C22×D53semidirect
649. C2×Q8D4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×2−1+4×D532
C22×#41×D532
#202883742
#202883732
#202883722
#202883712
#202883702
#202883692
#202883682
#550×D532
#548×D532
#535×D532
#525×D532
#519×D532
C53×#34872
C2×#348753