Finite Group Databasebeta

← #28292638

Subgroups — #28292638

Order 13568.

11346 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×#16811460C212yesmaximal, complemented
2#20288509C212yesmaximal, complemented
3#20288504C216yesmaximal, complemented
4#20288498C213yesmaximal, complemented
5#20288493C211yesmaximal, characteristic, complemented
6#20288488C213yesmaximal, complemented
7#20288485C214yesmaximal, complemented
8#20288473C2112yesmaximal, complemented
9D4×#11719949C214yesmaximal, complemented
10#20288202C2112yesmaximal, complemented
11#20288047C216yesmaximal, complemented
12C2×#16811174C213yesmaximal, complemented
13#532×D53C213yesmaximal, complemented
14C4×#41×D53C211yesmaximal, characteristic, complemented
15C53×#3499C211yesmaximal, characteristic, complemented
16#16811460—232no—
17C2×#13133265C2214yescomplemented
18C2×#13133265C2216yescomplemented
19C2×#13133263C22112yescomplemented
20C2×#13133263C2216yescomplemented
21C2×#13133263C2212yescomplemented
22C22×#11719949C2216yescomplemented
23C22×#11719949C2214yescomplemented
24C2×#41×D53C2211yescharacteristic
25C2×#41×D53C2216yescomplemented
26C2×#41×D53C22112yescomplemented
27#16811295C2214yescomplemented
28#16811294C22112yescomplemented
29#16811288C22112yescomplemented
30#16811284C2218yescomplemented
31#16811283C22124yescomplemented
32#16811276C22112yescomplemented
33#16811274C22124yescomplemented
34#16811265C22148yescomplemented
35#16811264C22124yescomplemented
36#16811261C22124yescomplemented
37D4×D212C22112yescomplemented
38D4×D212C22112yescomplemented
39#16811257C22124yescomplemented
40#16811203C22124yescomplemented
41#16811198C22112yescomplemented
42#16811197C2216yescomplemented
43#16811192C2216yescomplemented
44#16811191C22112yescomplemented
45#16811187C2216yescomplemented
46#16811184C22124yescomplemented
47#16811174C2216yescomplemented
48#16811174C22112yescomplemented
49#16811174C22112yescomplemented
50#16811174C2216yescomplemented
51#16811174C2213yescomplemented
52#16811174C2216yescomplemented
53#16811173C2213yescomplemented
54#16811172C2216yescomplemented
55#16811171C2211yescharacteristic, complemented
56#16811170C22112yescomplemented
57#16811169C2216yescomplemented
58#16811168C22112yescomplemented
59C4⋊Q8×D53C2213yescomplemented
60C2×#13133214C2213yescomplemented
61#127×D53C2213yescomplemented
62C2×#13133206C2216yescomplemented
63#124×D53C2216yescomplemented
64#16811136C22124yescomplemented
65#16811131C22124yescomplemented
66C2×#13133192C22112yescomplemented
67#121×D53C22112yescomplemented
68#41×Dic53C2211yescharacteristic, complemented
69C4×#11719949C2212yescomplemented
70C4×#11719945C2213yescomplemented
71#16811091C2213yescomplemented
72C4×#11719947C2216yescomplemented
73C4×Q8×D53C2212yescomplemented
74C2×#13133179C22112yescomplemented
75C4×D4×D53C2216yescomplemented
76C4×D4×D53C22112yescomplemented
77#117×D53C2213yescomplemented
78C2×C42×D53C2213yescomplemented
79C2×2−1+4×C53C2212yescomplemented
80D4×Q8×C53C2214yescomplemented
81C53×#547C22112yescomplemented
82C53×#536C2216yescomplemented
83C53×#532C2213yescomplemented
84C2×C4⋊Q8×C53C2213yescomplemented
85C4×#41×C53C2211yescharacteristic, complemented
86#13133265—232no—
87#13133265—248no—
88#13133263—216no—
89#13133263—296no—
90#13133263—248no—
91C2×#11719949—232no—
92C2×#11719949—248no—
93C2×#11719949C23112yes—
94C2×#11719949C2314yes—
95C2×#11719949C23112yes—
96C2×#11719949C2316yes—
97C2×#11719949C23112yes—
98C2×#11719949C23112yes—
99C2×#11719949C2311yescharacteristic
100C2×#11719945C23124yes—
101C2×#11719945C23112yes—
102C2×#11719945C2316yes—
103C2×#11719945C23112yes—
104C2×#11719945C2313yes—
105C2×#11719947C23112yes—
106C2×#11719947C2312yes—
107C2×#11719947C2313yes—
108#41×D53—296no—
109#41×D53—248no—
110#41×D53D4116yescomplemented
111C2×Q8×D53C23112yes—
112C2×Q8×D53C2316yes—
113C2×Q8×D53C2311yescharacteristic
114C22×D212C23112yes—
115C22×D212C23112yes—
116C22×D212C2316yes—
117C22×D212C23112yes—
118C2×D4×D53C23124yes—
119C2×D4×D53C23112yes—
120C2×D4×D53C2316yes—
121C2×D4×D53C23112yes—
122C2×D4×D53C23112yes—
123C2×D4×D53C2313yes—
124C22×C4×D53C23112yes—
125C22×C4×D53C23112yes—
126C22×C4×D53C2316yes—
127C22×C4×D53C2313yes—
128#13133217C2311yescharacteristic
129#13133216C23112yes—
130#13133215C2316yes—
131#13133214C23112yes—
132#13133214C2313yes—
133#13133214C2316yes—
134#13133213C23112yes—
135#13133213C2316yes—
136#13133206C23124yes—
137#13133206C2316yes—
138#13133206C23112yes—
139#13133205C2316yes—
140#13133204C2312yes—
141#13133203C23124yes—
142#13133202C23148yes—
143#13133200C23124yes—
144#13133195C23148yes—
145#13133193C23124yes—
146#13133192C23124yes—
147#13133192C23124yes—
148#13133192C23124yes—
149#13133192C23112yes—
150#13133192C23124yes—
151#13133191C23112yes—
152#13133191C23124yes—
153#13133190C23148yes—
154#13133190C23124yes—
155#13133189C23124yes—
156#13133188C2314yes—
157#13133187C23148yes—
158#13133187C23124yes—
159#13133185C23124yes—
160Q8×Dic53C2312yes—
161C4×Dic106C2316yes—
162#13133182C2316yes—
163C4×D212C2316yes—
164C4×D212C23112yes—
165D4×Dic53C2314yes—
166D4×Dic53C2316yes—
167#13133179C2316yes—
168#13133179C23124yes—
169#13133179C23124yes—
170#13133179C23112yes—
171#13133179C23124yes—
172C4×C22⋊D53C23124yes—
173C4×C22⋊D53C23112yes—
174#13133177C23112yes—
175#13133177C23124yes—
176#13133176C2313yes—
177#13133175C2316yes—
178#13133174C2316yes—
179#13133173C2316yes—
180C4⋊C4×D53C23112yes—
181C4⋊C4×D53C2316yes—
182C2×#11719921C23124yes—
183C22⋊C4×D53C23124yes—
184C22⋊C4×D53C2316yes—
185C2×C4×Dic53C2316yes—
186C2×C4×Dic53C2313yes—
187C42×D53C2311yescharacteristic
188C42×D53C2313yes—
189C42×D53C2316yes—
190C42×D53C2316yes—
191C42×D53C2313yes—
192C42×D53C2313yes—
1932−1+4×C53—216no—
194C2×#41×C53C2316yes—
195C2×#41×C53C23112yes—
196C2×#41×C53C2311yescharacteristic
197C22×Q8×C53C2314yes—
198C22×Q8×C53C2316yes—
199C4⋊Q8×C53C23112yes—
200C4⋊Q8×C53C2313yes—
201C4⋊Q8×C53C2316yes—
202#127×C53C2311yescharacteristic
203#124×C53C2316yes—
204#123×C53C23124yes—
205C22⋊Q8×C53C23124yes—
206#121×C53C23112yes—
207C4×Q8×C53C2312yes—
208C4×D4×C53C23112yes—
209C4×D4×C53C2316yes—
210#117×C53C2313yes—
211C2×C4⋊C4×C53C23112yes—
212C2×C42×C53C2313yes—
213C23×D53C24112yes—
214C23×D53C24112yes—
215C23×D53C2413yes—
216#41×C53—248no—
217#41×C53—224no—
218#41×C53C2×D418yescomplemented
219C2×Q8×C53—216no—
220C2×Q8×C53—224no—
221C2×Q8×C53C24112yes—
222C2×Q8×C53C2416yes—
223C2×Q8×C53C2411yescharacteristic
224C2×D4×C53C2414yes—
225C2×D4×C53C24112yes—
226C2×D4×C53C2412yes—
227C2×D4×C53C2413yes—
228C22×C4×C53C2416yes—
229C22×C4×C53C24112yes—
230C22×C4×C53C24112yes—
231C22×C4×C53C2413yes—
232C2×C22⋊D53C24112yes—
233C2×C22⋊D53C2414yes—
234C2×C22⋊D53C24112yes—
235C2×C22⋊D53C24124yes—
236C2×C22⋊D53C2416yes—
237C22×Dic53C2414yes—
238C22×Dic53C2416yes—
239C22×Dic53C2413yes—
240#11719949—216no—
241#11719949—248no—
242#11719949—248no—
243#11719949—224no—
244#11719949—248no—
245#11719949—248no—
246#11719949C2×D418yescomplemented
247Q8×D53—224no—
248Q8×D53—248no—
249Q8×D53C2×D418yescomplemented
250#11719947—248no—
251#11719947—28no—
252#11719947C2×D4124yescomplemented
253D4×D53—248no—
254D4×D53—248no—
255D4×D53—296no—
256D4×D53—224no—
257D4×D53—424no—
258D4×D53C2×D4124yescomplemented
259#11719945—224no—
260#11719945—296no—
261#11719945—248no—
262#11719945—248no—
263#11719945C2×D4124yescomplemented
264C2×D212—248no—
265C2×D212—224no—
266C2×D212—248no—
267C2×D212—424no—
268C2×D212C24112yes—
269C2×D212C24124yes—
270C2×D212C24112yes—
271C2×D212C24112yes—
272C2×D212C2416yes—
273C2×D212C24124yes—
274C2×D212C2413yes—
275C2×C4×D53—248no—
276C2×C4×D53—248no—
277C2×C4×D53—412no—
278C2×C4×D53C2×D4124yescomplemented
279C2×C4×D53C2412yes—
280C2×C4×D53C2416yes—
281C2×C4×D53C24112yes—
282C2×C4×D53C24112yes—
283C2×C4×D53C24112yes—
284C2×C4×D53C24124yes—
285C2×C4×D53C2416yes—
286C2×C4×D53C2416yes—
287C2×C4×D53C2411yescharacteristic
288C2×C4×D53C2413yes—
289C2×C4×D53C2413yes—
290C2×C4×D53C2413yes—
291C2×Dic106C24112yes—
292C2×Dic106C2412yes—
293C2×Dic106C2413yes—
294C4⋊C4×C53C24112yes—
295C4⋊C4×C53C24124yes—
296C4⋊C4×C53C2416yes—
297C22⋊C4×C53C2416yes—
298C22⋊C4×C53C24124yes—
299C42×C53C2411yescharacteristic
300C42×C53C2413yes—
301C42×C53C2416yes—
302C22⋊Dic53C2418yes—
303C22⋊Dic53C2416yes—
304#11719921C24124yes—
305#11719921C24112yes—
306#11719921C24124yes—
307#11719921C24148yes—
308C4⋊Dic53C2414yes—
309C4⋊Dic53C2416yes—
310#11719919C24112yes—
311#11719919C24124yes—
312C4×Dic53C2412yes—
313C4×Dic53C2411yescharacteristic
314C4×Dic53C2416yes—
315C4×Dic53C2413yes—
316C4×Dic53C2416yes—
317C4×Dic53C2416yes—
318C4×Dic53C2416yes—
319C23×C53C2514yes—
320C23×C53C2513yes—
321C22×D53—224no—
322C22×D53—224no—
323C22×D53—46no—
324C22×D53—424no—
325C22×D53—424no—
326C22×D53C22×D4112yes—
327C22×D53C25112yes—
328C22×D53C2511yescharacteristic
329C22×D53C2513yes—
330Q8×C53—212no—
331Q8×C53—224no—
332Q8×C53C22×D414yes—
333D4×C53—224no—
334D4×C53—24no—
335D4×C53—28no—
336D4×C53C22×D4112yes—
337C2×C4×C53—224no—
338C2×C4×C53—224no—
339C2×C4×C53—212no—
340C2×C4×C53C22×D4112yes—
341C2×C4×C53C25112yes—
342C2×C4×C53C2516yes—
343C2×C4×C53C2511yescharacteristic
344C2×C4×C53C2513yes—
345C2×C4×C53C2512yes—
346C22⋊D53—224no—
347C22⋊D53—28no—
348C22⋊D53—224no—
349C22⋊D53—424no—
350C22⋊D53C22×D4124yes—
351C2×Dic53—28no—
352C2×Dic53—46no—
353C2×Dic53C22×D4112yes—
354C2×Dic53C2514yes—
355C2×Dic53C2512yes—
356C2×Dic53C2516yes—
357C2×Dic53C2513yes—
358C2×Dic53C2511yescharacteristic
359D212—248no—
360D212—224no—
361D212—212no—
362D212—224no—
363D212—224no—
364D212—424no—
365D212C22×D4112yes—
366C4×D53—224no—
367C4×D53—224no—
368C4×D53—24no—
369C4×D53—212no—
370C4×D53—224no—
371C4×D53—248no—
372C4×D53—46no—
373C4×D53—46no—
374C4×D53C22×D4112yes—
375C4×D53C22×D414yes—
376C4×D53C22×D4112yes—
377C4×D53C22×D4112yes—
378Dic106—24no—
379Dic106—224no—
380Dic106C22×D4112yes—
381#62812—531nomaximal, Sylow
382C22×C53—26no—
383C22×C53—24no—
384C22×C53—28no—
385C22×C53C23×D416yes—
386C22×C53C2611yescharacteristic
387C2×D53—22no—
388C2×D53—26no—
389C2×D53—212no—
390C2×D53—224no—
391C2×D53—412no—
392C2×D53—824no—
393C2×D53—824no—
394C2×D53C23×D416yes—
395C2×D53C23×D412yes—
396C4×C53—212no—
397C4×C53—26no—
398C4×C53C23×D412yes—
399C4×C53C23×D416yes—
400C4×C53#58514yescomplemented
401Dic53—24no—
402Dic53—22no—
403Dic53—26no—
404Dic53C23×D416yes—
405Dic53C23×D412yes—
406C2×#585—532no—
407#3500—532no—
408#3500—536no—
409#3499—533no—
410#3499D5311yescharacteristic, complemented
411#3498—533no—
412#3498—531no—
413#3497—534no—
414#3496—5312no—
415D4×#41—534no—
416D4×#41—5312no—
417#3449—536no—
418C2×#532—533no—
419C2×#532—533no—
420C2×C4×#41—531no—
421C2×C53—26no—
422C2×C53—44no—
423C2×C53C24×D411yescharacteristic
424C2×C53C2×#58512yes—
425D53—22no—
426D53—26no—
427D53—412no—
428#585—10632no—
429C2×2−1+4—534no—
430C2×2−1+4—536no—
431C2×2−1+4C2×D5312yescomplemented
432C2×H(5,𝔽2)—5312no—
433C2×H(5,𝔽2)—536no—
434C2×H(5,𝔽2)—532no—
435C22×#41—531no—
436C22×#41—536no—
437C22×#41—5312no—
438C22×#41—536no—
439C22×#41—534no—
440#550—534no—
441#550—5312no—
442D4×Q8—5312no—
443D4×Q8C2×D5314yescomplemented
444#548—538no—
445#548—5324no—
446#547—5312no—
447#547—5324no—
448#547C2×D53112yescomplemented
449#546—5324no—
450#546—5348no—
451#546—5324no—
452D42—5324no—
453D42—5312no—
454D42—5312no—
455#537—5324no—
456#536—536no—
457#536—5312no—
458#536C2×D5316yescomplemented
459#535—536no—
460#535—5312no—
461#535—536no—
462#534—5324no—
463#532—536no—
464#532—533no—
465#532—536no—
466#532—5312no—
467#532—5312no—
468#532—536no—
469#532—536no—
470#532—531no—
471#532—536no—
472#532—5312no—
473#532—5312no—
474#532—533no—
475#532C2×D5313yescomplemented
476C2×C4⋊Q8—533no—
477C2×C4⋊Q8C2×D5313yescomplemented
478C2×#127—533no—
479C2×#127—533no—
480C2×#124—536no—
481C2×#124—536no—
482#525—5324no—
483#525—5324no—
484C2×#121—5312no—
485C2×#121—5312no—
486C4×#41—531no—
487C4×#41—532no—
488C4×#41—536no—
489C4×#41—533no—
490C4×#41—533no—
491C4×#41C2×D5311yescharacteristic, complemented
492C2×C4×Q8—532no—
493C2×C4×D4—536no—
494C2×C4×D4—5312no—
495C2×C4×D4—5312no—
496C2×#117—533no—
497C22×C42—533no—
498C53#6281211yescharacteristic, complemented, Sylow
4992−1+4—216no—
5002−1+4—10632no—
5012−1+4—10648no—
502H(5,𝔽2)—10696no—
503H(5,𝔽2)—10648no—
504H(5,𝔽2)—10616no—
505C2×#41—5316no—
506C2×#41—531no—
507C2×#41—5312no—
508C2×#41—536no—
509C2×#41—5312no—
510C2×#41—5312no—
511C2×#41—5312no—
512C2×#41—534no—
513C2×#41—533no—
514C2×#41—5312no—
515C2×#41—532no—
516C2×#41—533no—
517C2×#41—536no—
518C2×#41—5312no—
519C2×#41—5324no—
520C2×#41—5312no—
521C2×#41—10648no—
522C2×#41—10648no—
523C2×#41—10632no—
524C2×#41—10696no—
525C2×#41C22×D5316yes—
526C2×#41C22×D53112yes—
527C2×#41C22×D5311yescharacteristic
528C22×Q8—531no—
529C22×Q8—536no—
530C22×Q8—5312no—
531C22×Q8C22×D5316yes—
532C22×Q8C22×D5314yes—
533C22×D4—533no—
534C22×D4—5312no—
535C22×D4—536no—
536C22×D4—5324no—
537C22×D4—5312no—
538C22×D4—5312no—
539C22×D4—5312no—
540C22×D4—536no—
541C22×D4—5312no—
542C22×D4—5312no—
543C23×C4—533no—
544C23×C4—5312no—
545C23×C4—5312no—
546C23×C4—536no—
547C4⋊Q8—536no—
548C4⋊Q8—5312no—
549C4⋊Q8—531no—
550C4⋊Q8C22×D5313yes—
551C4⋊Q8C22×D5316yes—
552C4⋊Q8C22×D53112yes—
553#127—536no—
554#127—5312no—
555#127—533no—
556#127—536no—
557#127—5312no—
558#127C22×D5311yescharacteristic
559#124—536no—
560#124—5312no—
561#124—5324no—
562#124—532no—
563#124—5324no—
564#124—536no—
565#124C22×D5316yes—
566#123—5324no—
567#123—5348no—
568#123C22×D53124yes—
569C22⋊Q8—5324no—
570C22⋊Q8—5348no—
571C22⋊Q8C22×D53124yes—
572#121—534no—
573#121—5324no—
574#121—5312no—
575#121—5324no—
576#121—5312no—
577#121—5324no—
578#121—5324no—
579#121—5324no—
580#121—5324no—
581#121—5324no—
582#121—5348no—
583#121C22×D53112yes—
584#120—5324no—
585#120—5348no—
586#120—5324no—
587C4×Q8—532no—
588C4×Q8—536no—
589C4×Q8—536no—
590C4×Q8C22×D5312yes—
591C4×D4—534no—
592C4×D4—536no—
593C4×D4—5312no—
594C4×D4—5324no—
595C4×D4—5312no—
596C4×D4—536no—
597C4×D4—5324no—
598C4×D4—5324no—
599C4×D4—5324no—
600C4×D4—5312no—
601C4×D4—5324no—
602C4×D4—536no—
603C4×D4—5312no—
604C4×D4C22×D5316yes—
605C4×D4C22×D53112yes—
606#117—533no—
607#117—536no—
608#117—536no—
609#117—536no—
610#117C22×D5313yes—
611C2×C4⋊C4—536no—
612C2×C4⋊C4—5312no—
613C2×C4⋊C4C22×D53112yes—
614C2×C22⋊C4—5324no—
615C2×C22⋊C4—536no—
616C2×C22⋊C4—5324no—
617C2×C42—536no—
618C2×C42—533no—
619C2×C42—533no—
620C2×C42—536no—
621C2×C42—536no—
622C2×C42—533no—
623C2×C42—533no—
624C2×C42—531no—
625C2×C42C22×D5313yes—
626C24—533no—
627C24—5312no—
628C24—5312no—
629#41—248no—
630#41—224no—
631#41—538no—
632#41—5324no—
633#41—5324no—
634#41—10648no—
635#41—10696no—
636#41—10648no—
637#41—10648no—
638#41—1068no—
639#41—10624no—
640#41—10648no—
641#41—10648no—
642#41—10648no—
643#41—10648no—
644#41—10616no—
645#41—10624no—
646#41D4×D5318yescomplemented
647C2×Q8—216no—
648C2×Q8—224no—
649C2×Q8—538no—
650C2×Q8—533no—
651C2×Q8—5312no—
652C2×Q8—532no—
653C2×Q8—10624no—
654C2×Q8—10648no—
655C2×Q8C23×D53112yes—
656C2×Q8C23×D5316yes—
657C2×Q8C23×D5311yescharacteristic
658C2×D4—536no—
659C2×D4—5324no—
660C2×D4—5312no—
661C2×D4—534no—
662C2×D4—5312no—
663C2×D4—5324no—
664C2×D4—533no—
665C2×D4—5312no—
666C2×D4—5324no—
667C2×D4—5312no—
668C2×D4—5312no—
669C2×D4—536no—
670C2×D4—5324no—
671C2×D4—10648no—
672C2×D4—10648no—
673C2×D4—10624no—
674C2×D4—10696no—
675C2×D4—10648no—
676C2×D4—10648no—
677C2×D4—10624no—
678C2×D4—21224no—
679C2×D4—21224no—
680C2×D4C23×D5314yes—
681C2×D4C23×D53112yes—
682C2×D4C23×D5312yes—
683C2×D4C23×D5313yes—
684C22×C4—533no—
685C22×C4—5324no—
686C22×C4—531no—
687C22×C4—533no—
688C22×C4—533no—
689C22×C4—533no—
690C22×C4—534no—
691C22×C4—536no—
692C22×C4—532no—
693C22×C4—536no—
694C22×C4—5312no—
695C22×C4—5312no—
696C22×C4—5324no—
697C22×C4—5312no—
698C22×C4—536no—
699C22×C4—536no—
700C22×C4—10648no—
701C22×C4—10648no—
702C22×C4—21212no—
703C22×C4C23×D5316yes—
704C22×C4C23×D53112yes—
705C22×C4C23×D53112yes—
706C22×C4C23×D5313yes—
707C4⋊C4—534no—
708C4⋊C4—5312no—
709C4⋊C4—536no—
710C4⋊C4—5324no—
711C4⋊C4C23×D53112yes—
712C4⋊C4C23×D5316yes—
713C4⋊C4C23×D53124yes—
714C22⋊C4—538no—
715C22⋊C4—536no—
716C22⋊C4—5324no—
717C22⋊C4—5312no—
718C22⋊C4—5348no—
719C22⋊C4—5324no—
720C22⋊C4C23×D5316yes—
721C22⋊C4C23×D53124yes—
722C42—532no—
723C42—531no—
724C42—536no—
725C42—533no—
726C42—536no—
727C42—536no—
728C42—536no—
729C42C23×D5311yescharacteristic
730C42C23×D5313yes—
731C42C23×D5316yes—
732C23—533no—
733C23—531no—
734C23—5312no—
735C23—5312no—
736C23—10624no—
737C23—10624no—
738C23—21224no—
739C23—21224no—
740C23—2126no—
741C23C24×D5314yes—
742C23C24×D5313yes—
743Q8—224no—
744Q8—212no—
745Q8—5312no—
746Q8—10624no—
747Q8—1064no—
748Q8C2×D4×D5314yes—
749D4—224no—
750D4—24no—
751D4—28no—
752D4—5324no—
753D4—5312no—
754D4—10624no—
755D4—10648no—
756D4—10624no—
757D4—1068no—
758D4—10624no—
759D4—10624no—
760D4—10612no—
761D4—10624no—
762D4—21224no—
763D4—21224no—
764D4C2×D4×D53112yes—
765C2×C4—224no—
766C2×C4—224no—
767C2×C4—212no—
768C2×C4—5312no—
769C2×C4—531no—
770C2×C4—533no—
771C2×C4—534no—
772C2×C4—5312no—
773C2×C4—5312no—
774C2×C4—5312no—
775C2×C4—532no—
776C2×C4—536no—
777C2×C4—534no—
778C2×C4—10624no—
779C2×C4—10648no—
780C2×C4—10624no—
781C2×C4—1068no—
782C2×C4—10624no—
783C2×C4—1064no—
784C2×C4—10612no—
785C2×C4—2126no—
786C2×C4—2126no—
787C2×C4—2126no—
788C2×C4C2×D4×D53112yes—
789C2×C4C24×D5316yes—
790C2×C4C24×D53112yes—
791C2×C4C24×D5311yescharacteristic
792C2×C4C24×D5313yes—
793C2×C4C24×D5312yes—
794C22—26no—
795C22—24no—
796C22—28no—
797C22—532no—
798C22—536no—
799C22—1062no—
800C22—1066no—
801C22—10612no—
802C22—10624no—
803C22—42424no—
804C22—42424no—
805C22—21212no—
806C22C22×D4×D5316yes—
807C22C25×D5311yescharacteristic
808C4—212no—
809C4—26no—
810C4—532no—
811C4—536no—
812C4—1064no—
813C4—1062no—
814C4—1066no—
815C4C22×D4×D5316yes—
816C4C22×D4×D5312yes—
817C4#1681146014yescomplemented
818C2—26no—
819C2—44no—
820C2—1066no—
821C2—1062no—
822C2—21212no—
823C2C23×D4×D5311yescharacteristic
824C2C2×#1681146012yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3499C2
hypercenter#3499D53
hypocenterC53#62812
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3499

Complements

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

NH ≅ G/Ntype
1. C2×#16811460C2semidirect
2. #20288509C2semidirect
3. #20288504C2semidirect
4. #20288498C2semidirect
5. #20288493C2semidirect
6. #20288488C2semidirect
7. #20288485C2semidirect
8. #20288473C2semidirect
9. D4×#11719949C2semidirect
10. #20288202C2semidirect
11. #20288047C2semidirect
12. C2×#16811174C2semidirect
13. #532×D53C2semidirect
14. C4×#41×D53C2semidirect
15. C53×#3499C2semidirect
17. C2×#13133265C22semidirect
18. C2×#13133265C22semidirect
19. C2×#13133263C22semidirect
20. C2×#13133263C22semidirect
21. C2×#13133263C22semidirect
22. C22×#11719949C22semidirect
23. C22×#11719949C22semidirect
25. C2×#41×D53C22semidirect
26. C2×#41×D53C22semidirect
27. #16811295C22semidirect
28. #16811294C22semidirect
29. #16811288C22semidirect
30. #16811284C22semidirect
31. #16811283C22semidirect
32. #16811276C22semidirect
33. #16811274C22semidirect
34. #16811265C22semidirect
35. #16811264C22semidirect
36. #16811261C22semidirect
37. D4×D212C22semidirect
38. D4×D212C22semidirect
39. #16811257C22semidirect
40. #16811203C22semidirect
41. #16811198C22semidirect
42. #16811197C22semidirect
43. #16811192C22semidirect
44. #16811191C22semidirect
45. #16811187C22semidirect
46. #16811184C22semidirect
47. #16811174C22semidirect
48. #16811174C22semidirect
49. #16811174C22semidirect
50. #16811174C22semidirect
51. #16811174C22semidirect
52. #16811174C22semidirect
53. #16811173C22semidirect
54. #16811172C22semidirect
55. #16811171C22semidirect
56. #16811170C22semidirect
57. #16811169C22semidirect
58. #16811168C22semidirect
59. C4⋊Q8×D53C22semidirect
60. C2×#13133214C22semidirect
61. #127×D53C22semidirect
62. C2×#13133206C22semidirect
63. #124×D53C22semidirect
64. #16811136C22semidirect
65. #16811131C22semidirect
66. C2×#13133192C22semidirect
67. #121×D53C22semidirect
68. #41×Dic53C22semidirect
69. C4×#11719949C22semidirect
70. C4×#11719945C22semidirect
71. #16811091C22semidirect
72. C4×#11719947C22semidirect
73. C4×Q8×D53C22semidirect
74. C2×#13133179C22semidirect
75. C4×D4×D53C22semidirect
76. C4×D4×D53C22semidirect
77. #117×D53C22semidirect
78. C2×C42×D53C22semidirect
79. C2×2−1+4×C53C22semidirect
80. D4×Q8×C53C22semidirect
81. C53×#547C22semidirect
82. C53×#536C22semidirect
83. C53×#532C22semidirect
84. C2×C4⋊Q8×C53C22semidirect
85. C4×#41×C53C22semidirect
110. #41×D53D4semidirect
218. #41×C53C2×D4semidirect
246. #11719949C2×D4semidirect
249. Q8×D53C2×D4semidirect
252. #11719947C2×D4semidirect
258. D4×D53C2×D4semidirect
263. #11719945C2×D4semidirect
278. C2×C4×D53C2×D4semidirect
400. C4×C53#585semidirect
410. #3499D53semidirect
431. C2×2−1+4C2×D53semidirect
443. D4×Q8C2×D53semidirect
448. #547C2×D53semidirect
458. #536C2×D53semidirect
475. #532C2×D53semidirect
477. C2×C4⋊Q8C2×D53semidirect
491. C4×#41C2×D53semidirect
498. C53#62812semidirect
646. #41D4×D53semidirect
817. C4#16811460semidirect

Maximal subgroups

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

subgroupindex
C2×#168114602
#202885092
#202885042
#202884982
#202884932
#202884882
#202884852
#202884732
D4×#117199492
#202882022
#202880472
C2×#168111742
#532×D532
C4×#41×D532
C53×#34992
#6281253