Finite Group Databasebeta

← #28292380

Subgroups — #28292380

Order 13568.

7190 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288825C214yesmaximal, complemented
2#20288813C214yesmaximal, complemented
3#20288723C214yesmaximal, complemented
4#20288712C214yesmaximal, complemented
5#20288566C216yesmaximal, complemented
6#20288521C211yesmaximal, characteristic, complemented
7#20288482C211yesmaximal, characteristic, complemented
8#20288432C216yesmaximal, complemented
9#20288373C211yesmaximal, characteristic, complemented
10#20288338C214yesmaximal, complemented
11#20288331C214yesmaximal, complemented
12#20288314C214yesmaximal, complemented
13#20288305C214yesmaximal, complemented
14#20288128C216yesmaximal, complemented
15#20288007C216yesmaximal, complemented
162−1+4×Dic53C211yesmaximal, characteristic, complemented
17#20287924C211yesmaximal, characteristic, complemented
18C2×#41×Dic53C211yesmaximal, characteristic, complemented
19C53×#3487C211yesmaximal, characteristic, complemented
20C2×#13133265C2211yescharacteristic
21#16811359C22112yescomplemented
22#16811355C22112yescomplemented
23Q8×Dic106C2214yescomplemented
24#16811352C2214yescomplemented
25#16811349C2214yescomplemented
26#16811349C2214yescomplemented
27#16811344C22112yescomplemented
28#16811343C22112yescomplemented
29#16811342C22112yescomplemented
30#16811338C22112yescomplemented
31#16811337C22112yescomplemented
32#16811337C22112yescomplemented
33#16811325C22112yescomplemented
34#16811320C22112yescomplemented
35#16811320C22112yescomplemented
36#16811319C22112yescomplemented
37#16811313C22112yescomplemented
38#16811307C22112yescomplemented
39#16811293C22112yescomplemented
40#16811292C2214yes—
41#16811292C2214yes—
42#16811292C2214yescomplemented
43Q8×C22⋊D53C2214yescomplemented
44#16811284C2214yescomplemented
45#16811280C2214yes—
46#16811280C2214yes—
47#16811280C2214yescomplemented
48#16811273C22112yescomplemented
49#16811251C2216yes—
50#16811242C22112yescomplemented
51#16811240C22112yescomplemented
52#16811227C22112yescomplemented
53#16811226C22112yescomplemented
54#16811208C22124yes—
55#16811201C2216yes—
56#16811190C2216yes—
57#16811176C2216yes—
58#16811175C2216yescomplemented
59#16811175C2216yescomplemented
60#16811171C22112yescomplemented
61#16811169C2216yes—
62#16811168C2216yescomplemented
63#16811168C2216yescomplemented
64#16811168C22112yescomplemented
65#16811159C2216yescomplemented
66#16811159C2216yescomplemented
67#16811154C2216yescomplemented
68#16811154C2216yescomplemented
69#16811154C22112yescomplemented
70#16811153C22112yescomplemented
71#16811153C22112yescomplemented
72#16811152C22112yescomplemented
73#16811150C2214yes—
74#16811150C22112yes—
75#16811134C2216yes—
76#16811129C22112yes—
77#16811129C22112yes—
78#16811106C2216yes—
79#16811106C2214yescomplemented
80#16811105C2214yescomplemented
81#16811103C2216yes—
82#16811101C2211yescharacteristic
83#16811101C2214yescomplemented
84#16811099C2214yescomplemented
85#41×Dic53C2216yes—
86#41×Dic53C2214yes—
87#41×Dic53C2214yes—
88#41×Dic53C2214yes—
89#41×Dic53C2214yes—
90#41×Dic53C2214yescomplemented
91C4×#11719949C2214yescomplemented
92#16811091C2216yes—
93C4×#11719947C22112yescomplemented
94C4×#11719947C22112yescomplemented
95C2×Q8×Dic53C2211yescharacteristic
96C2×Q8×Dic53C2211yescharacteristic
97C2×Q8×Dic53C2214yescomplemented
98C4×Q8×D53C2214yescomplemented
99C2×D4×Dic53C2213yes—
100C2×D4×Dic53C2213yes—
101C2×#13133176C2213yes—
102C22×C4×Dic53C2213yes—
103C2×2−1+4×C53C2211yescharacteristic
104C22×#41×C53C2211yescharacteristic
105C53×#550C2214yes—
106C53×#550C2214yes—
107C53×#548C2214yes—
108C53×#548C2214yes—
109C53×#535C2216yes—
110C53×#525C2216yes—
111C53×#519C2211yescharacteristic
112#13133265—28no—
113C2×#11719949C2314yes—
114C2×#11719945C2316yes—
115C2×#11719947C23112yes—
116C2×#11719947C23112yes—
117C2×Q8×D53C2314yes—
118C23×Dic53C2313yes—
119C23×Dic53C2313yes—
120#13133217C23112yes—
121#13133216C2316yes—
122#13133216C2316yes—
123#13133216C23112yes—
124#13133215C2316yes—
125#13133213C23112yes—
126#13133213C2316yes—
127#13133212C23112yes—
128#13133212C2314yes—
129#13133210C23124yes—
130#13133210C23124yes—
131#13133210C23112yes—
132#13133210C2314yes—
133#13133209C23112yes—
134#13133208C23112yes—
135#13133208C2316yes—
136#13133208C2316yes—
137#13133207C23112yes—
138#13133207C2314yes—
139#13133206C2316yes—
140#13133204C23112yes—
141#13133204C2316yes—
142#13133204C23124yes—
143#13133203C23112yes—
144#13133203C23124yes—
145#13133203C2314yes—
146#13133201C23112yes—
147#13133201C23112yes—
148#13133200C2314yes—
149#13133199C23124yes—
150#13133198C23124yes—
151#13133198C23112yes—
152#13133198C23112yes—
153#13133196C2316yes—
154#13133196C2316yes—
155#13133196C23112yes—
156#13133194C23112yes—
157#13133194C2314yes—
158#13133194C23112yes—
159#13133194C23112yes—
160#13133193C23112yes—
161#13133191C23112yes—
162#13133191C2316yes—
163#13133191C2316yes—
164#13133189C23112yes—
165#13133189C23124yes—
166#13133189C2314yes—
167#13133189C23112yes—
168#13133189C23112yes—
169#13133188C23112yes—
170#13133188C23112yes—
171#13133188C23112yes—
172#13133188C23124yes—
173#13133186C23112yes—
174Q8×Dic53C2314yes—
175Q8×Dic53C2314yes—
176Q8×Dic53C2314yes—
177Q8×Dic53C2314yes—
178Q8×Dic53C23112yes—
179Q8×Dic53C2314yes—
180Q8×Dic53C2314yes—
181Q8×Dic53C2316yes—
182Q8×Dic53C2316yes—
183C4×Dic106C23112yes—
184C4×Dic106C23112yes—
185C4×Dic106C23112yes—
186#13133182C2316yes—
187#13133182C23112yes—
188#13133182C2314yes—
189#13133182C2316yes—
190C4×D212C23112yes—
191D4×Dic53C23112yes—
192D4×Dic53C23112yes—
193D4×Dic53C23112yes—
194D4×Dic53C23112yes—
195D4×Dic53C23112yes—
196D4×Dic53C23112yes—
197D4×Dic53C23112yes—
198D4×Dic53C2314yes—
199D4×Dic53C2316yes—
200D4×Dic53C23112yes—
201D4×Dic53C2316yes—
202#13133179C2316yes—
203#13133179C2316yes—
204C4×C22⋊D53C23112yes—
205C4×C22⋊D53C23112yes—
206C4×C22⋊D53C23112yes—
207C4×C22⋊D53C23112yes—
208#13133177C23112yes—
209#13133177C23112yes—
210#13133177C2314yes—
211#13133177C23112yes—
212#13133177C2314yes—
213#13133177C23112yes—
214#13133176C23112yes—
215#13133176C23112yes—
216#13133176C23112yes—
217#13133176C2316yes—
218#13133176C23112yes—
219#13133175C23112yes—
220#13133175C23112yes—
221#13133175C2314yes—
222#13133174C23112yes—
223#13133173C23112yes—
224#13133173C23112yes—
225#13133173C2314yes—
226#13133173C23112yes—
227C2×C4⋊Dic53C23112yes—
228C2×C4⋊Dic53C2313yes—
229C2×C4⋊Dic53C2313yes—
230C4⋊C4×D53C23112yes—
231C2×C22⋊Dic53C2316yes—
232C2×C4×Dic53C2311yescharacteristic
233C2×C4×Dic53C2313yes—
234C2×C4×Dic53C2313yes—
235C2×C4×Dic53C2313yes—
236C2×C4×Dic53C2316yes—
237C2×C4×Dic53C2316yes—
238C2×C4×Dic53C2316yes—
239C2×C4×Dic53C2316yes—
240C2×C4×Dic53C23112yes—
241C42×D53C23112yes—
2422−1+4×C53—28no—
243C2×#41×C53—28no—
244C2×#41×C53C2314yes—
245C2×#41×C53C2314yes—
246C2×#41×C53C2314yes—
247C2×#41×C53C2316yes—
248C22×Q8×C53C2314yes—
249C22×Q8×C53C2311yescharacteristic
250C22×D4×C53C2313yes—
251C23×C4×C53C2313yes—
252#127×C53C23112yes—
253#124×C53C23112yes—
254#123×C53C2314yes—
255C22⋊Q8×C53C2316yes—
256C22⋊Q8×C53C2316yes—
257#121×C53C23112yes—
258#121×C53C2316yes—
259#121×C53C2316yes—
260#121×C53C23112yes—
261#120×C53C23112yes—
262C4×Q8×C53C2314yes—
263C4×Q8×C53C2314yes—
264C4×D4×C53C23112yes—
265C4×D4×C53C23112yes—
266#117×C53C2316yes—
267C24×C53C2413yes—
268#41×C53—216no—
269#41×C53—216no—
270#41×C53—216no—
271#41×C53—224no—
272C2×Q8×C53—216no—
273C2×Q8×C53#4118yescomplemented
274C2×Q8×C53C2416yes—
275C2×Q8×C53C2414yes—
276C2×D4×C53—212no—
277C2×D4×C53C2414yes—
278C2×D4×C53C24112yes—
279C2×D4×C53C2416yes—
280C2×D4×C53C24112yes—
281C2×D4×C53C24112yes—
282C22×C4×C53—212no—
283C22×C4×C53C24112yes—
284C22×C4×C53C2416yes—
285C22×C4×C53C2416yes—
286C22×C4×C53C2411yescharacteristic
287C22×C4×C53C2413yes—
288C2×C22⋊D53C2414yes—
289C2×C22⋊D53C2414yes—
290C2×C22⋊D53C24112yes—
291C2×C22⋊D53C24112yes—
292C2×C22⋊D53C24112yes—
293C22×Dic53—46no—
294C22×Dic53—46no—
295C22×Dic53C2411yescharacteristic
296C22×Dic53C2411yescharacteristic
297C22×Dic53C2414yes—
298C22×Dic53C2416yes—
299C22×Dic53C2416yes—
300C22×Dic53C2413yes—
301C22×Dic53C2413yes—
302C22×Dic53C2416yes—
303C22×Dic53C2416yes—
304C22×Dic53C24112yes—
305#11719949—216no—
306Q8×D53—216no—
307#11719947—424no—
308#11719947—424no—
309#11719945—224no—
310C2×D212C2416yes—
311C2×C4×D53C2414yes—
312C2×C4×D53C24112yes—
313C2×C4×D53C24112yes—
314C2×Dic106C2416yes—
315C2×Dic106C2414yes—
316C2×Dic106C24112yes—
317C4⋊C4×C53C2416yes—
318C4⋊C4×C53C2416yes—
319C4⋊C4×C53C2414yes—
320C4⋊C4×C53C2414yes—
321C22⋊C4×C53C2414yes—
322C22⋊C4×C53C2414yes—
323C22⋊C4×C53C2414yes—
324C22⋊C4×C53C24112yes—
325C22⋊C4×C53C24112yes—
326C42×C53C24112yes—
327C22⋊Dic53C24124yes—
328C22⋊Dic53C2414yes—
329C22⋊Dic53C24112yes—
330C22⋊Dic53C24112yes—
331C22⋊Dic53C24112yes—
332C22⋊Dic53C2414yes—
333C22⋊Dic53C24112yes—
334C22⋊Dic53C2414yes—
335#11719921C2414yes—
336#11719921C24112yes—
337#11719921C2414yes—
338#11719921C2414yes—
339#11719921C2414yes—
340#11719921C24112yes—
341C4⋊Dic53C24112yes—
342C4⋊Dic53C2416yes—
343C4⋊Dic53C24112yes—
344C4⋊Dic53C24112yes—
345C4⋊Dic53C2414yes—
346C4⋊Dic53C24112yes—
347C4⋊Dic53C2416yes—
348C4⋊Dic53C2414yes—
349#11719919C24112yes—
350#11719919C2414yes—
351#11719919C2414yes—
352#11719919C2414yes—
353#11719919C2414yes—
354#11719919C24112yes—
355#11719919C24112yes—
356#11719919C2414yes—
357#11719919C24112yes—
358#11719919C2414yes—
359C4×Dic53C2414yes—
360C4×Dic53C2416yes—
361C4×Dic53C24112yes—
362C4×Dic53C2411yescharacteristic
363C4×Dic53C2411yescharacteristic
364C4×Dic53C2411yescharacteristic
365C4×Dic53C2411yescharacteristic
366C4×Dic53C2414yes—
367C4×Dic53C2416yes—
368C4×Dic53C2416yes—
369C4×Dic53C2416yes—
370C4×Dic53C2416yes—
371C4×Dic53C2416yes—
372C4×Dic53C24112yes—
373C4×Dic53C24112yes—
374C23×C53—26no—
375C23×C53—43no—
376C23×C53—43no—
377C23×C53C2514yes—
378C23×C53C2516yes—
379C23×C53C2511yescharacteristic
380C22×D53C2514yes—
381Q8×C53—212no—
382Q8×C53C2×#41116yes—
383D4×C53—28no—
384D4×C53—224no—
385D4×C53—212no—
386D4×C53—412no—
387D4×C53—412no—
388C2×C4×C53—22no—
389C2×C4×C53—212no—
390C2×C4×C53—212no—
391C2×C4×C53—224no—
392C2×C4×C53C2×#41112yes—
393C2×C4×C53C2514yes—
394C2×C4×C53C2514yes—
395C2×C4×C53C2511yescharacteristic
396C2×C4×C53C2511yescharacteristic
397C2×C4×C53C2514yes—
398C2×C4×C53C2516yes—
399C22⋊D53—28no—
400C22⋊D53—28no—
401C22⋊D53—412no—
402C22⋊D53—412no—
403C22⋊D53—412no—
404C2×Dic53—28no—
405C2×Dic53—212no—
406C2×Dic53—212no—
407C2×Dic53—22no—
408C2×Dic53—22no—
409C2×Dic53—412no—
410C2×Dic53—43no—
411C2×Dic53—46no—
412C2×Dic53—43no—
413C2×Dic53—46no—
414C2×Dic53C2514yes—
415C2×Dic53C2514yes—
416C2×Dic53C2516yes—
417C2×Dic53C2514yes—
418C2×Dic53C2516yes—
419C2×Dic53C2511yescharacteristic
420C2×Dic53C2511yescharacteristic
421C2×Dic53C2511yescharacteristic
422C2×Dic53C2511yescharacteristic
423D212—212no—
424C4×D53—224no—
425C4×D53—28no—
426C4×D53—412no—
427Dic106—212no—
428Dic106—28no—
429Dic106—412no—
430#62793—531nomaximal, Sylow
431C22×C53—21no—
432C22×C53—21no—
433C22×C53—24no—
434C22×C53—26no—
435C22×C53—26no—
436C22×C53—26no—
437C22×C53—24no—
438C22×C53—24no—
439C22×C53—412no—
440C22×C53C22×#4112yes—
441C22×C53C2611yescharacteristic
442C2×D53—24no—
443C2×D53—24no—
444C2×D53—24no—
445C4×C53—21no—
446C4×C53—21no—
447C4×C53—24no—
448C4×C53—24no—
449C4×C53—24no—
450C4×C53C22×#41112yes—
451Dic53—24no—
452Dic53—24no—
453Dic53—24no—
454Dic53—26no—
455Dic53—26no—
456Dic53—21no—
457Dic53—21no—
458Dic53#58512yes—
459Dic53#58512yes—
460#3524—534no—
461#3524—534no—
462#3518—534no—
463#3517—534no—
464#3506—536no—
465#3502—531no—
466#3497—531no—
467#3493—536no—
468#3487—531no—
469#3487D5311yescharacteristic, complemented
470#3483—534no—
471#3482—534no—
472#3480—534no—
473#3480—534no—
474#3460—536no—
475#3444—536no—
476C4×2−1+4—531no—
477C4×2−1+4—531no—
478C2×C4×#41—531no—
479C2×C53—22no—
480C2×C53—44no—
481C2×C53—46no—
482C2×C53C23×#4111yescharacteristic
483C2×C53C2×#58511yescharacteristic
484C2×C53C2×#58511yescharacteristic
485D53—44no—
486C2×2−1+4—531no—
487C2×2−1+4C2×D5311yescharacteristic
488C22×#41C2×D5311yescharacteristic
489#559—5312no—
490#559—5312no—
491Q82—534no—
492#557—534no—
493#557—534no—
494#557—534no—
495#556—5312no—
496#556—5312no—
497#556—5312no—
498#555—5312no—
499#555—5312no—
500#555—5312no—
501#553—5312no—
502#553—5312no—
503#553—5312no—
504#553—5312no—
505#552—5312no—
506#552—5312no—
507#550—534no—
508#550—534no—
509#550—534no—
510#550—5312no—
511#550C2×D5314yes—
512#550C2×D5314yes—
513D4×Q8—534no—
514#548—534no—
515#548—534no—
516#548—534no—
517#548—534no—
518#548C2×D5314yes—
519#548C2×D5314yes—
520#547—5312no—
521#544—536no—
522#542—5312no—
523#542—5312no—
524#540—5312no—
525#540—5312no—
526#538—5324no—
527#537—536no—
528#535—536no—
529#535C2×D5316yes—
530#533—536no—
531#533—536no—
532#533—536no—
533#532—536no—
534#532—5312no—
535#532—536no—
536#532—536no—
537#532—5312no—
538#529—5312no—
539#529—534no—
540#529—5312no—
541#529—536no—
542#529—536no—
543#529—536no—
544#529—536no—
545#529—5312no—
546#529—5312no—
547#529—5312no—
548#525—536no—
549#525—5312no—
550#525—5312no—
551#525C2×D5316yes—
552#520—536no—
553#520—534no—
554#520—534no—
555#520—536no—
556#519—531no—
557#519—534no—
558#519—534no—
559#519C2×D5311yescharacteristic
560C4×#41—534no—
561C4×#41—534no—
562C4×#41—534no—
563C4×#41—534no—
564C4×#41—536no—
565C4×#41—534no—
566C4×#41—534no—
567C4×#41—5312no—
568C4×#41—5312no—
569C4×#41—536no—
570C2×C4×Q8—531no—
571C2×C4×Q8—531no—
572C2×C4×Q8—534no—
573C2×C4×Q8—534no—
574C2×C4×D4—533no—
575C2×C4×D4—533no—
576C2×#117—533no—
577C22×C42—533no—
578C53#6279311yescharacteristic, complemented, Sylow
5792−1+4—28no—
5802−1+4—1068no—
581C2×#41—28no—
582C2×#41—534no—
583C2×#41—5312no—
584C2×#41—5312no—
585C2×#41—536no—
586C2×#41C22×D5314yes—
587C2×#41C22×D5314yes—
588C2×#41C22×D5316yes—
589C2×#41C22×D5314yes—
590C22×Q8—534no—
591C22×Q8C22×D5314yes—
592C22×Q8C22×D5311yescharacteristic
593C22×D4C22×D5313yes—
594C23×C4—533no—
595C23×C4—533no—
596C23×C4C22×D5313yes—
597C4⋊Q8—536no—
598C4⋊Q8—536no—
599C4⋊Q8—536no—
600C4⋊Q8—5312no—
601C4⋊Q8—5312no—
602#127—536no—
603#127—5312no—
604#127C22×D53112yes—
605#126—534no—
606#126—5312no—
607#126—534no—
608#126—5312no—
609#126—5324no—
610#126—5324no—
611#125—534no—
612#125—5312no—
613#125—536no—
614#125—536no—
615#125—5312no—
616#125—5312no—
617#124—536no—
618#124—536no—
619#124—5312no—
620#124—5324no—
621#124—534no—
622#124—5312no—
623#124—5324no—
624#124C22×D53112yes—
625#123—5312no—
626#123—5312no—
627#123—5324no—
628#123—534no—
629#123—5312no—
630#123—5312no—
631#123—5324no—
632#123C22×D5314yes—
633C22⋊Q8—5312no—
634C22⋊Q8—536no—
635C22⋊Q8—536no—
636C22⋊Q8—5312no—
637C22⋊Q8—534no—
638C22⋊Q8—5312no—
639C22⋊Q8—5312no—
640C22⋊Q8—5312no—
641C22⋊Q8C22×D5316yes—
642C22⋊Q8C22×D5316yes—
643#121—534no—
644#121—5312no—
645#121—5312no—
646#121—5312no—
647#121—5312no—
648#121—5312no—
649#121—5312no—
650#121—5324no—
651#121—5324no—
652#121—536no—
653#121—536no—
654#121—5312no—
655#121C22×D5316yes—
656#121C22×D5316yes—
657#121C22×D53112yes—
658#121C22×D53112yes—
659#120—5312no—
660#120C22×D53112yes—
661C4×Q8—534no—
662C4×Q8—536no—
663C4×Q8—534no—
664C4×Q8—534no—
665C4×Q8—534no—
666C4×Q8—534no—
667C4×Q8—5312no—
668C4×Q8—536no—
669C4×Q8—534no—
670C4×Q8—536no—
671C4×Q8—534no—
672C4×Q8—536no—
673C4×Q8—5312no—
674C4×Q8—5312no—
675C4×Q8—5312no—
676C4×Q8—5312no—
677C4×Q8C22×D5314yes—
678C4×Q8C22×D5314yes—
679C4×D4—5312no—
680C4×D4—5312no—
681C4×D4—5312no—
682C4×D4—5312no—
683C4×D4—534no—
684C4×D4—536no—
685C4×D4—5312no—
686C4×D4—536no—
687C4×D4—5312no—
688C4×D4—5312no—
689C4×D4—5312no—
690C4×D4—5312no—
691C4×D4—5312no—
692C4×D4—5312no—
693C4×D4—5312no—
694C4×D4—536no—
695C4×D4—536no—
696C4×D4—534no—
697C4×D4—534no—
698C4×D4—5312no—
699C4×D4—5312no—
700C4×D4—5312no—
701C4×D4—5312no—
702C4×D4—5312no—
703C4×D4C22×D53112yes—
704C4×D4C22×D53112yes—
705#117—5312no—
706#117—5312no—
707#117—536no—
708#117—5312no—
709#117—5312no—
710#117—534no—
711#117—5312no—
712#117—5312no—
713#117—534no—
714#117—5312no—
715#117—5312no—
716#117—5312no—
717#117—5312no—
718#117C22×D5316yes—
719C2×C4⋊C4—533no—
720C2×C4⋊C4—533no—
721C2×C4⋊C4—5312no—
722C2×C4⋊C4—5312no—
723C2×C22⋊C4—536no—
724C2×C42—533no—
725C2×C42—533no—
726C2×C42—533no—
727C2×C42—5312no—
728C2×C42—536no—
729C2×C42—536no—
730C2×C42—536no—
731C2×C42—536no—
732C2×C42—531no—
733C2×C42—5312no—
734C24C23×D5313yes—
735#41—216no—
736#41—216no—
737#41—216no—
738#41—224no—
739#41—10616no—
740#41—10624no—
741#41—21224no—
742#41—21224no—
743C2×Q8—216no—
744C2×Q8—536no—
745C2×Q8—534no—
746C2×Q8—5312no—
747C2×Q8—10616no—
748C2×Q8#1171994718yescomplemented
749C2×Q8C23×D5316yes—
750C2×Q8C23×D5314yes—
751C2×D4—212no—
752C2×D4—534no—
753C2×D4—534no—
754C2×D4—5312no—
755C2×D4—5312no—
756C2×D4—5312no—
757C2×D4—536no—
758C2×D4C23×D5314yes—
759C2×D4C23×D53112yes—
760C2×D4C23×D5316yes—
761C2×D4C23×D53112yes—
762C2×D4C23×D53112yes—
763C22×C4—212no—
764C22×C4—531no—
765C22×C4—531no—
766C22×C4—534no—
767C22×C4—536no—
768C22×C4—536no—
769C22×C4—533no—
770C22×C4—533no—
771C22×C4—536no—
772C22×C4—536no—
773C22×C4—5312no—
774C22×C4—534no—
775C22×C4—5312no—
776C22×C4—5312no—
777C22×C4—2126no—
778C22×C4—2126no—
779C22×C4C23×D5311yescharacteristic
780C22×C4C23×D5316yes—
781C22×C4C23×D5316yes—
782C22×C4C23×D53112yes—
783C22×C4C23×D5313yes—
784C4⋊C4—5312no—
785C4⋊C4—536no—
786C4⋊C4—5312no—
787C4⋊C4—5312no—
788C4⋊C4—5312no—
789C4⋊C4—534no—
790C4⋊C4—534no—
791C4⋊C4—534no—
792C4⋊C4—536no—
793C4⋊C4—534no—
794C4⋊C4—534no—
795C4⋊C4—534no—
796C4⋊C4—534no—
797C4⋊C4—534no—
798C4⋊C4—5312no—
799C4⋊C4—5312no—
800C4⋊C4—5312no—
801C4⋊C4—5312no—
802C4⋊C4C23×D5316yes—
803C4⋊C4C23×D5314yes—
804C4⋊C4C23×D5316yes—
805C4⋊C4C23×D5314yes—
806C22⋊C4—5324no—
807C22⋊C4—534no—
808C22⋊C4—534no—
809C22⋊C4—5312no—
810C22⋊C4—534no—
811C22⋊C4—5312no—
812C22⋊C4—5312no—
813C22⋊C4—5312no—
814C22⋊C4—534no—
815C22⋊C4—5312no—
816C22⋊C4—534no—
817C22⋊C4—534no—
818C22⋊C4—534no—
819C22⋊C4—5312no—
820C22⋊C4C23×D5314yes—
821C22⋊C4C23×D5314yes—
822C22⋊C4C23×D53112yes—
823C22⋊C4C23×D53112yes—
824C22⋊C4C23×D5314yes—
825C42—531no—
826C42—531no—
827C42—536no—
828C42—531no—
829C42—531no—
830C42—536no—
831C42—534no—
832C42—534no—
833C42—536no—
834C42—536no—
835C42—536no—
836C42—536no—
837C42—5312no—
838C42—5312no—
839C42—5312no—
840C42C23×D53112yes—
841C23—26no—
842C23—43no—
843C23—43no—
844C23—534no—
845C23C24×D5316yes—
846C23C24×D5314yes—
847C23C24×D5311yescharacteristic
848Q8—212no—
849Q8—1068no—
850Q8—10612no—
851Q8—21212no—
852Q8C2×#11719947116yes—
853D4—28no—
854D4—224no—
855D4—212no—
856D4—412no—
857D4—412no—
858D4—1068no—
859D4—1068no—
860D4—10612no—
861D4—21212no—
862D4—21212no—
863D4—21212no—
864C2×C4—22no—
865C2×C4—212no—
866C2×C4—212no—
867C2×C4—224no—
868C2×C4—531no—
869C2×C4—531no—
870C2×C4—536no—
871C2×C4—531no—
872C2×C4—531no—
873C2×C4—534no—
874C2×C4—534no—
875C2×C4—536no—
876C2×C4—534no—
877C2×C4—1068no—
878C2×C4—1062no—
879C2×C4—1062no—
880C2×C4—10612no—
881C2×C4—10612no—
882C2×C4—1068no—
883C2×C4—10624no—
884C2×C4—21212no—
885C2×C4—2123no—
886C2×C4—2126no—
887C2×C4—2126no—
888C2×C4—2123no—
889C2×C4—21212no—
890C2×C4C2×#11719947112yes—
891C2×C4C24×D5311yescharacteristic
892C2×C4C24×D5311yescharacteristic
893C2×C4C24×D5314yes—
894C2×C4C24×D5314yes—
895C2×C4C24×D5314yes—
896C2×C4C24×D5316yes—
897C22—21no—
898C22—21no—
899C22—24no—
900C22—26no—
901C22—26no—
902C22—26no—
903C22—24no—
904C22—24no—
905C22—412no—
906C22—1064no—
907C22—1064no—
908C22—1064no—
909C22C22×#1171994712yes—
910C22C25×D5311yescharacteristic
911C4—21no—
912C4—21no—
913C4—24no—
914C4—24no—
915C4—24no—
916C4—532no—
917C4—532no—
918C4—1064no—
919C4—1061no—
920C4—1061no—
921C4—1066no—
922C4—1066no—
923C4—1064no—
924C4—1064no—
925C4C22×#11719947112yes—
926C2—22no—
927C2—46no—
928C2—44no—
929C2—2124no—
930C2C23×#1171994711yescharacteristic
931C2#585×D5311yescharacteristic
932C2#585×D5311yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3487C2
hypercenter#3487D53
hypocenterC53#62793
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3487

Complements

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

NH ≅ G/Ntype
1. #20288825C2semidirect
2. #20288813C2semidirect
3. #20288723C2semidirect
4. #20288712C2semidirect
5. #20288566C2semidirect
6. #20288521C2semidirect
7. #20288482C2semidirect
8. #20288432C2semidirect
9. #20288373C2semidirect
10. #20288338C2semidirect
11. #20288331C2semidirect
12. #20288314C2semidirect
13. #20288305C2semidirect
14. #20288128C2semidirect
15. #20288007C2semidirect
16. 2−1+4×Dic53C2semidirect
17. #20287924C2semidirect
18. C2×#41×Dic53C2semidirect
19. C53×#3487C2semidirect
21. #16811359C22semidirect
22. #16811355C22semidirect
23. Q8×Dic106C22semidirect
24. #16811352C22semidirect
25. #16811349C22semidirect
26. #16811349C22semidirect
27. #16811344C22semidirect
28. #16811343C22semidirect
29. #16811342C22semidirect
30. #16811338C22semidirect
31. #16811337C22semidirect
32. #16811337C22semidirect
33. #16811325C22semidirect
34. #16811320C22semidirect
35. #16811320C22semidirect
36. #16811319C22semidirect
37. #16811313C22semidirect
38. #16811307C22semidirect
39. #16811293C22semidirect
42. #16811292C22semidirect
43. Q8×C22⋊D53C22semidirect
44. #16811284C22semidirect
47. #16811280C22semidirect
48. #16811273C22semidirect
50. #16811242C22semidirect
51. #16811240C22semidirect
52. #16811227C22semidirect
53. #16811226C22semidirect
58. #16811175C22semidirect
59. #16811175C22semidirect
60. #16811171C22semidirect
62. #16811168C22semidirect
63. #16811168C22semidirect
64. #16811168C22semidirect
65. #16811159C22semidirect
66. #16811159C22semidirect
67. #16811154C22semidirect
68. #16811154C22semidirect
69. #16811154C22semidirect
70. #16811153C22semidirect
71. #16811153C22semidirect
72. #16811152C22semidirect
79. #16811106C22semidirect
80. #16811105C22semidirect
83. #16811101C22semidirect
84. #16811099C22semidirect
90. #41×Dic53C22semidirect
91. C4×#11719949C22semidirect
93. C4×#11719947C22semidirect
94. C4×#11719947C22semidirect
97. C2×Q8×Dic53C22semidirect
98. C4×Q8×D53C22semidirect
273. C2×Q8×C53#41semidirect
469. #3487D53semidirect
578. C53#62793semidirect
748. C2×Q8#11719947semidirect

Maximal subgroups

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

subgroupindex
#202888252
#202888132
#202887232
#202887122
#202885662
#202885212
#202884822
#202884322
#202883732
#202883382
#202883312
#202883142
#202883052
#202881282
#202880072
2−1+4×Dic532
#202879242
C2×#41×Dic532
C53×#34872
#6279353