Finite Group Databasebeta

← #28293290

Subgroups — #28293290

Order 13568.

10986 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811460C211yesmaximal, characteristic, complemented
2C22×#13133265C211yesmaximal, characteristic, complemented
3#20288506C218yesmaximal, complemented
4#20288499C218yesmaximal, complemented
5#20288394C218yesmaximal, complemented
6#20288392C218yesmaximal, complemented
7#20288367C211yesmaximal, characteristic, complemented
8#20288366C211yesmaximal, characteristic, complemented
9#20288363C211yesmaximal, characteristic, complemented
10#20288358C216yesmaximal, complemented
11#20288357C216yesmaximal, complemented
12#20288045C216yesmaximal, complemented
13#536×D53C216yesmaximal, complemented
14#20287917C211yesmaximal, characteristic, complemented
15C53×#3486C211yesmaximal, characteristic, complemented
16#16811460—216no—
17C2×#13133265—216no—
18C2×#13133265C2211yescharacteristic
19C2×#13133265C2218yescomplemented
20C2×#13133265C2218yescomplemented
21C2×#13133265C2214yescomplemented
22C2×#13133263C2216yes—
23C2×#13133263C2214yescomplemented
24C22×#11719949C2211yescharacteristic
25C22×#11719949C2213yescomplemented
26C22×#11719949C2214yescomplemented
27C22×#11719945C2213yescomplemented
28C22×#11719945C2213yescomplemented
29C2×#41×D53C2216yes—
30C2×#41×D53C2214yescomplemented
31C22×Q8×D53C2213yescomplemented
32C22×Q8×D53C2211yescharacteristic, complemented
33Q8×D212C2218yescomplemented
34Q8×C22⋊D53C2218yescomplemented
35Q8×C22⋊D53C2218yescomplemented
36#16811285C2218yescomplemented
37#16811284C2218yescomplemented
38#16811280C2218yescomplemented
39#16811278C22124yescomplemented
40#16811276C22124yescomplemented
41#16811275C22124yescomplemented
42#16811275C22124yescomplemented
43#16811270C22124yescomplemented
44#16811269C22124yescomplemented
45#16811266C22124yescomplemented
46#16811264C22124yescomplemented
47#16811203C22112yescomplemented
48#16811202C22112yescomplemented
49#16811199C2216yescomplemented
50#16811198C22112yescomplemented
51#16811197C2216yescomplemented
52#16811196C22124yescomplemented
53#16811196C22112yescomplemented
54#16811195C22112yescomplemented
55#16811194C2216yescomplemented
56#16811193C22112yescomplemented
57#16811189C22112yescomplemented
58#16811188C2214yescomplemented
59#16811184C22112yescomplemented
60#16811183C22112yescomplemented
61#16811170C22124yescomplemented
62C4⋊Q8×D53C22112yescomplemented
63#124×D53C22112yescomplemented
64#16811135C2216yescomplemented
65#16811134C2216yescomplemented
66#16811132C22124yescomplemented
67#16811130C2216yescomplemented
68#123×D53C22124yescomplemented
69C22⋊Q8×D53C22124yescomplemented
70#16811105C2218yescomplemented
71#16811101C2211yescharacteristic, complemented
72#16811097C2216yescomplemented
73C4×#11719949C2218yescomplemented
74#117×D53C2216yescomplemented
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—264no—
84#13133265—264no—
85#13133265—232no—
86#13133263—232no—
87#13133263—248no—
88C2×#11719949—232no—
89C2×#11719949—224no—
90C2×#11719949D4116yescomplemented
91C2×#11719949C23124yes—
92C2×#11719949C23112yes—
93C2×#11719949C2314yes—
94C2×#11719949C2316yes—
95C2×#11719949C2314yes—
96C2×#11719949C2314yes—
97C2×#11719945—224no—
98C2×#11719945—224no—
99C2×#11719945C23124yes—
100C2×#11719945C23112yes—
101C2×#11719945C23112yes—
102C2×#11719945C2316yes—
103C2×#11719945C23112yes—
104C2×#11719945C23112yes—
105C2×#11719947C2314yes—
106C2×#11719947C2316yes—
107#41×D53—232no—
108#41×D53—248no—
109C22×Dic106C2313yes—
110C22×Dic106C2313yes—
111C2×Q8×D53—28no—
112C2×Q8×D53—224no—
113C2×Q8×D53C2318yes—
114C2×Q8×D53C2314yes—
115C2×Q8×D53C23112yes—
116C2×Q8×D53C23112yes—
117C2×Q8×D53C2316yes—
118C22×D212C23112yes—
119C22×D212C2313yes—
120C22×D212C2313yes—
121C22×C22⋊D53C2313yes—
122C22×C22⋊D53C2311yescharacteristic
123C2×D4×D53C23112yes—
124C2×D4×D53C23112yes—
125C2×D4×D53C2316yes—
126C22×C4×D53C23112yes—
127C22×C4×D53C2316yes—
128C22×C4×D53C2313yes—
129C22×C4×D53C2313yes—
130#13133217C23112yes—
131#13133216C23124yes—
132#13133215C23112yes—
133#13133215C23112yes—
134#13133213C2318yes—
135#13133206C23112yes—
136#13133205C23112yes—
137#13133204C23112yes—
138#13133203C23124yes—
139#13133203C2318yes—
140#13133202C23148yes—
141#13133202C23124yes—
142#13133201C23112yes—
143#13133200C23112yes—
144#13133199C23148yes—
145#13133199C23124yes—
146#13133198C23112yes—
147#13133197C23124yes—
148#13133197C23112yes—
149#13133196C23124yes—
150#13133196C23112yes—
151#13133195C23124yes—
152#13133194C23124yes—
153#13133193C23124yes—
154#13133193C23112yes—
155#13133192C23124yes—
156#13133192C23112yes—
157#13133191C23112yes—
158#13133190C23124yes—
159#13133190C23124yes—
160#13133190C2318yes—
161#13133189C2318yes—
162#13133188C23112yes—
163#13133188C23124yes—
164#13133187C23124yes—
165#13133187C2314yes—
166#13133186C2314yes—
167#13133185C23124yes—
168#13133185C2314yes—
169Q8×Dic53C2318yes—
170C4×D212C23124yes—
171C4×D212C23124yes—
172#13133179C23124yes—
173C4×C22⋊D53C23124yes—
174C4×C22⋊D53C23124yes—
175#13133176C2316yes—
176#13133175C23112yes—
177#13133174C23112yes—
178#13133173C2314yes—
179C4⋊C4×D53C23148yes—
180C4⋊C4×D53C23112yes—
181C22⋊C4×D53C23148yes—
182C22⋊C4×D53C23112yes—
183C42×D53C23112yes—
1842−1+4×C53—28no—
185C2×#41×C53C2314yes—
186C2×#41×C53C2316yes—
187C22×Q8×C53—28no—
188C22×Q8×C53C2318yes—
189C22×Q8×C53C2314yes—
190C22×Q8×C53C2313yes—
191C22×Q8×C53C2311yescharacteristic
192C23×C4×C53C2313yes—
193C4⋊Q8×C53C23112yes—
194#124×C53C23112yes—
195#123×C53C23112yes—
196C22⋊Q8×C53C23124yes—
197C22⋊Q8×C53C23112yes—
198#121×C53C23112yes—
199#120×C53C2314yes—
200C4×Q8×C53C2318yes—
201C4×D4×C53C23124yes—
202#117×C53C2316yes—
203C24×C53C2411yescharacteristic
204C23×D53C24112yes—
205C23×D53C2411yescharacteristic
206C23×D53C2413yes—
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—212no—
225C2×C22⋊D53—24no—
226C2×C22⋊D53C24112yes—
227C2×C22⋊D53C2414yes—
228C2×C22⋊D53C24112yes—
229C2×C22⋊D53C2412yes—
230C2×C22⋊D53C2414yes—
231C2×C22⋊D53C2412yes—
232C2×C22⋊D53C2418yes—
233C2×C22⋊D53C2418yes—
234C22×Dic53C2414yes—
235C22×Dic53C2413yes—
236C22×Dic53C2411yescharacteristic
237#11719949—216no—
238#11719949—248no—
239#11719949—296no—
240#11719949—224no—
241#11719949C2×D4132yes—
242#11719949C2×D4132yes—
243Q8×D53—232no—
244Q8×D53—216no—
245Q8×D53—248no—
246Q8×D53—248no—
247Q8×D53—224no—
248#11719947—216no—
249#11719947—224no—
250D4×D53—248no—
251D4×D53—248no—
252D4×D53—224no—
253#11719945—224no—
254#11719945—248no—
255#11719945—296no—
256#11719945—248no—
257#11719945—248no—
258#11719945—248no—
259C2×D212—212no—
260C2×D212—248no—
261C2×D212C2×D4124yes—
262C2×D212C24112yes—
263C2×D212C24112yes—
264C2×D212C2416yes—
265C2×D212C2418yes—
266C2×D212C24112yes—
267C2×C4×D53—224no—
268C2×C4×D53—212no—
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×D53C24124yes—
277C2×C4×D53C2416yes—
278C2×C4×D53C2416yes—
279C2×Dic106—212no—
280C2×Dic106—212no—
281C2×Dic106C2416yes—
282C2×Dic106C24112yes—
283C2×Dic106C2416yes—
284C2×Dic106C2416yes—
285C2×Dic106C2414yes—
286C4⋊C4×C53C24112yes—
287C4⋊C4×C53C24124yes—
288C22⋊C4×C53C2414yes—
289C22⋊C4×C53C2418yes—
290C22⋊C4×C53C24124yes—
291C42×C53C24112yes—
292C22⋊Dic53C2414yes—
293C22⋊Dic53C24124yes—
294C22⋊Dic53C2418yes—
295#11719921C24124yes—
296#11719921C24124yes—
297#11719921C24124yes—
298#11719921C2418yes—
299#11719921C2418yes—
300C4⋊Dic53C24124yes—
301C4⋊Dic53C24112yes—
302#11719919C2418yes—
303#11719919C24124yes—
304#11719919C24124yes—
305C4×Dic53C2418yes—
306C4×Dic53C24112yes—
307C23×C53—22no—
308C23×C53—42no—
309C23×C53C2514yes—
310C23×C53C2512yes—
311C23×C53C2511yescharacteristic
312C22×D53—22no—
313C22×D53—224no—
314C22×D53—46no—
315C22×D53—42no—
316C22×D53—424no—
317C22×D53C22×D4112yes—
318C22×D53C2512yes—
319C22×D53C2514yes—
320C22×D53C2516yes—
321Q8×C53—224no—
322Q8×C53—212no—
323Q8×C53C22×D4116yes—
324D4×C53—28no—
325D4×C53—212no—
326D4×C53—48no—
327C2×C4×C53—26no—
328C2×C4×C53—224no—
329C2×C4×C53—224no—
330C2×C4×C53C22×D4112yes—
331C2×C4×C53C2516yes—
332C2×C4×C53C2514yes—
333C2×C4×C53C2518yes—
334C2×C4×C53C2516yes—
335C22⋊D53—28no—
336C22⋊D53—224no—
337C22⋊D53—224no—
338C22⋊D53—24no—
339C22⋊D53—24no—
340C22⋊D53—28no—
341C22⋊D53—48no—
342C22⋊D53—48no—
343C2×Dic53—26no—
344C2×Dic53—28no—
345C2×Dic53C22×D414yes—
346C2×Dic53C2516yes—
347C2×Dic53C2514yes—
348C2×Dic53C2518yes—
349C2×Dic53C2511yescharacteristic
350C2×Dic53C2511yescharacteristic
351D212—224no—
352D212—224no—
353D212—212no—
354D212—48no—
355D212C22×D4148yes—
356C4×D53—224no—
357C4×D53—248no—
358C4×D53—224no—
359C4×D53—224no—
360C4×D53—28no—
361C4×D53—424no—
362C4×D53C22×D4124yes—
363C4×D53C22×D4124yes—
364Dic106—224no—
365Dic106—212no—
366Dic106—212no—
367Dic106—212no—
368Dic106—28no—
369#62859—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—212no—
380C2×D53—22no—
381C2×D53—24no—
382C2×D53—22no—
383C2×D53—28no—
384C2×D53—22no—
385C2×D53—412no—
386C2×D53—44no—
387C2×D53—824no—
388C2×D53C23×D4112yes—
389C4×C53—26no—
390C4×C53—24no—
391C4×C53—28no—
392C4×C53C23×D4112yes—
393Dic53—26no—
394Dic53—24no—
395Dic53—28no—
396Dic53C23×D412yes—
397Dic53C23×D412yes—
398C2×#585—531no—
399C22×2−1+4—531no—
400#3500—538no—
401#3499—538no—
402#3489—538no—
403#3489—538no—
404#3486—531no—
405#3486—531no—
406#3486—531no—
407#3486D5311yescharacteristic, complemented
408#3485—536no—
409#3485—536no—
410#3449—536no—
411C2×#536—536no—
412#3428—531no—
413C2×C53—22no—
414C2×C53—44no—
415C2×C53—42no—
416C2×C53C24×D411yescharacteristic
417C2×C532−1+612yes—
418D53—212no—
419D53—42no—
420D53—44no—
421#585—10616no—
422C2×2−1+4—538no—
423C2×2−1+4—538no—
424C2×2−1+4—531no—
425C2×2−1+4—534no—
426C2×2−1+4—10616no—
427C2×2−1+4C2×D5311yescharacteristic
428C2×H(5,𝔽2)—536no—
429C2×H(5,𝔽2)—534no—
430C22×#41—536no—
431C22×#41—534no—
432C22×#41—531no—
433C22×#41—533no—
434C22×#41—534no—
435C22×#41—533no—
436C22×#41—533no—
437C23×Q8—533no—
438C23×Q8—531no—
439C23×Q8C2×D5311yescharacteristic, complemented
440D4×Q8—538no—
441D4×Q8—538no—
442D4×Q8—538no—
443D4×Q8C2×D5318yescomplemented
444#548—538no—
445#548—538no—
446#548—538no—
447#548C2×D5318yescomplemented
448#547—5324no—
449#547—5324no—
450#547—5324no—
451#547—5324no—
452#546—5324no—
453#546—5324no—
454#546—5324no—
455#546—5324no—
456#537—5312no—
457#537—5312no—
458#536—536no—
459#536—536no—
460#536—5312no—
461#536—5312no—
462#536—5312no—
463#536—5324no—
464#536—5312no—
465#536—536no—
466#536C2×D5316yescomplemented
467#535—5312no—
468#535—534no—
469#534—5312no—
470#534—5312no—
471#532—5324no—
472C2×C4⋊Q8—5312no—
473C2×#124—5312no—
474#525—536no—
475#525—536no—
476#525—5324no—
477#525—536no—
478#525C2×D5316yescomplemented
479C2×#123—5324no—
480C2×C22⋊Q8—5324no—
481#520—538no—
482#519—531no—
483#519C2×D5311yescharacteristic, complemented
484#518—536no—
485C4×#41—538no—
486C2×#117—536no—
487C53#6285911yescharacteristic, complemented, Sylow
4882−1+4—28no—
4892−1+4—10664no—
4902−1+4—10664no—
4912−1+4—10632no—
4922−1+4—1068no—
493H(5,𝔽2)—10648no—
494H(5,𝔽2)—10632no—
495C2×#41—5316no—
496C2×#41—534no—
497C2×#41—534no—
498C2×#41—536no—
499C2×#41—5324no—
500C2×#41—5312no—
501C2×#41—534no—
502C2×#41—534no—
503C2×#41—536no—
504C2×#41—536no—
505C2×#41—5312no—
506C2×#41—5312no—
507C2×#41—5312no—
508C2×#41—5324no—
509C2×#41—5312no—
510C2×#41—10624no—
511C2×#41—10624no—
512C2×#41—10648no—
513C2×#41—10624no—
514C2×#41—10632no—
515C2×#41—10632no—
516C2×#41C22×D5316yes—
517C2×#41C22×D5314yes—
518C22×Q8—28no—
519C22×Q8—5312no—
520C22×Q8—5312no—
521C22×Q8—536no—
522C22×Q8—538no—
523C22×Q8—534no—
524C22×Q8—533no—
525C22×Q8—533no—
526C22×Q8—10624no—
527C22×Q8—1068no—
528C22×Q8C22×D5313yes—
529C22×Q8C22×D5318yes—
530C22×Q8C22×D5314yes—
531C22×Q8C22×D5311yescharacteristic
532C22×D4—533no—
533C22×D4—531no—
534C22×D4—5312no—
535C22×D4—536no—
536C22×D4—5312no—
537C22×D4—533no—
538C22×D4—533no—
539C22×D4—5312no—
540C23×C4—533no—
541C23×C4—5312no—
542C23×C4—536no—
543C23×C4—533no—
544C23×C4C22×D5313yes—
545C4⋊Q8—5312no—
546C4⋊Q8—5312no—
547C4⋊Q8—5324no—
548C4⋊Q8—5312no—
549C4⋊Q8C22×D53112yes—
550#127—538no—
551#124—5312no—
552#124—5312no—
553#124—5324no—
554#124—538no—
555#124—5312no—
556#124C22×D53112yes—
557#123—5312no—
558#123—5312no—
559#123—5348no—
560#123—5324no—
561#123—5312no—
562#123—5348no—
563#123—5324no—
564#123C22×D53112yes—
565C22⋊Q8—5324no—
566C22⋊Q8—5312no—
567C22⋊Q8—5324no—
568C22⋊Q8—5312no—
569C22⋊Q8—5324no—
570C22⋊Q8—5324no—
571C22⋊Q8—5312no—
572C22⋊Q8—5324no—
573C22⋊Q8C22×D53124yes—
574C22⋊Q8C22×D53112yes—
575#121—538no—
576#121—5312no—
577#121—5324no—
578#121—5312no—
579#121—5312no—
580#121—5324no—
581#121—538no—
582#121—5324no—
583#121—5324no—
584#121C22×D53112yes—
585#120—534no—
586#120—534no—
587#120—5324no—
588#120—534no—
589#120—5324no—
590#120C22×D5314yes—
591C4×Q8—538no—
592C4×Q8C22×D5318yes—
593C4×D4—5324no—
594C4×D4—5324no—
595C4×D4—5324no—
596C4×D4—5324no—
597C4×D4—5324no—
598C4×D4C22×D53124yes—
599#117—536no—
600#117—5312no—
601#117—534no—
602#117—5312no—
603#117C22×D5316yes—
604C2×C4⋊C4—5312no—
605C2×C4⋊C4—5348no—
606C2×C22⋊C4—5312no—
607C2×C22⋊C4—5348no—
608C2×C42—5312no—
609C24—533no—
610C24—5312no—
611C24—531no—
612C24C23×D5311yescharacteristic
613#41—216no—
614#41—224no—
615#41—5332no—
616#41—5332no—
617#41—10648no—
618#41—10648no—
619#41—10648no—
620#41—10648no—
621#41—10696no—
622#41—10616no—
623#41—10624no—
624#41—10624no—
625#41—10648no—
626#41—10696no—
627#41—10616no—
628#41—10624no—
629C2×Q8—232no—
630C2×Q8—216no—
631C2×Q8—212no—
632C2×Q8—536no—
633C2×Q8—5312no—
634C2×Q8—536no—
635C2×Q8—536no—
636C2×Q8—534no—
637C2×Q8—10612no—
638C2×Q8—10648no—
639C2×Q8—10648no—
640C2×Q8—10624no—
641C2×Q8—10632no—
642C2×Q8—10616no—
643C2×Q8—10612no—
644C2×Q8D4×D5318yes—
645C2×Q8C23×D53112yes—
646C2×Q8C23×D5316yes—
647C2×Q8C23×D5314yes—
648C2×D4—5312no—
649C2×D4—534no—
650C2×D4—532no—
651C2×D4—5312no—
652C2×D4—534no—
653C2×D4—532no—
654C2×D4—538no—
655C2×D4—538no—
656C2×D4—5324no—
657C2×D4—5312no—
658C2×D4—5312no—
659C2×D4—5312no—
660C2×D4—536no—
661C2×D4—538no—
662C2×D4—10648no—
663C2×D4—10612no—
664C2×D4—10624no—
665C2×D4—1064no—
666C2×D4—10648no—
667C2×D4—10648no—
668C2×D4—10612no—
669C2×D4C23×D5314yes—
670C2×D4C23×D5316yes—
671C2×D4C23×D5318yes—
672C22×C4—212no—
673C22×C4—531no—
674C22×C4—5324no—
675C22×C4—536no—
676C22×C4—536no—
677C22×C4—534no—
678C22×C4—533no—
679C22×C4—5324no—
680C22×C4—5312no—
681C22×C4—5312no—
682C22×C4—5312no—
683C22×C4—534no—
684C22×C4—5324no—
685C22×C4—10648no—
686C22×C4—10624no—
687C22×C4—10612no—
688C22×C4C23×D53112yes—
689C22×C4C23×D53112yes—
690C22×C4C23×D5313yes—
691C22×C4C23×D5313yes—
692C4⋊C4—538no—
693C4⋊C4—5324no—
694C4⋊C4—5324no—
695C4⋊C4—5324no—
696C4⋊C4—5312no—
697C4⋊C4C23×D53124yes—
698C4⋊C4C23×D53112yes—
699C22⋊C4—534no—
700C22⋊C4—5324no—
701C22⋊C4—538no—
702C22⋊C4—5324no—
703C22⋊C4—5324no—
704C22⋊C4—5324no—
705C22⋊C4—538no—
706C22⋊C4—538no—
707C22⋊C4C23×D5314yes—
708C22⋊C4C23×D53124yes—
709C22⋊C4C23×D5318yes—
710C42—538no—
711C42—5312no—
712C42C23×D53112yes—
713C23—22no—
714C23—42no—
715C23—536no—
716C23—5312no—
717C23—534no—
718C23—532no—
719C23—10624no—
720C23—1062no—
721C23—21224no—
722C23—2126no—
723C23—2122no—
724C23C24×D5314yes—
725C23C24×D5312yes—
726C23C24×D5311yescharacteristic
727Q8—224no—
728Q8—212no—
729Q8—10612no—
730Q8—10612no—
731Q8—1068no—
732Q8—10624no—
733Q8—10612no—
734Q8C2×D4×D53116yes—
735D4—28no—
736D4—212no—
737D4—48no—
738D4—5348no—
739D4—10624no—
740D4—10624no—
741D4—1068no—
742D4—1064no—
743D4—1064no—
744D4—10624no—
745D4—10624no—
746D4—1068no—
747D4—10612no—
748D4—2128no—
749D4—2128no—
750D4—2128no—
751C2×C4—26no—
752C2×C4—224no—
753C2×C4—224no—
754C2×C4—534no—
755C2×C4—531no—
756C2×C4—531no—
757C2×C4—5324no—
758C2×C4—5324no—
759C2×C4—538no—
760C2×C4—536no—
761C2×C4—534no—
762C2×C4—1068no—
763C2×C4—10624no—
764C2×C4—10648no—
765C2×C4—1068no—
766C2×C4—1066no—
767C2×C4—10624no—
768C2×C4—10624no—
769C2×C4—21224no—
770C2×C4C2×D4×D53112yes—
771C2×C4C24×D5318yes—
772C2×C4C24×D5316yes—
773C2×C4C24×D5314yes—
774C2×C4C24×D5316yes—
775C22—22no—
776C22—22no—
777C22—24no—
778C22—22no—
779C22—28no—
780C22—22no—
781C22—44no—
782C22—5312no—
783C22—10612no—
784C22—1062no—
785C22—1064no—
786C22—1062no—
787C22—1062no—
788C22—1068no—
789C22—42424no—
790C22—21212no—
791C22—2124no—
792C22C22×D4×D5312yes—
793C22C25×D5311yescharacteristic
794C4—24no—
795C4—26no—
796C4—28no—
797C4—532no—
798C4—532no—
799C4—1064no—
800C4—1066no—
801C4—1068no—
802C4C22×D4×D53112yes—
803C2—22no—
804C2—42no—
805C2—44no—
806C2—10612no—
807C2—2124no—
808C2—2122no—
809C2C23×D4×D5311yescharacteristic
810C2#2028952712yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3486C2
hypercenter#3486D53
hypocenterC53#62859
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3486

Complements

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

NH ≅ G/Ntype
1. C2×#16811460C2semidirect
2. C22×#13133265C2semidirect
3. #20288506C2semidirect
4. #20288499C2semidirect
5. #20288394C2semidirect
6. #20288392C2semidirect
7. #20288367C2semidirect
8. #20288366C2semidirect
9. #20288363C2semidirect
10. #20288358C2semidirect
11. #20288357C2semidirect
12. #20288045C2semidirect
13. #536×D53C2semidirect
14. #20287917C2semidirect
15. C53×#3486C2semidirect
19. C2×#13133265C22semidirect
20. C2×#13133265C22semidirect
21. C2×#13133265C22semidirect
23. C2×#13133263C22semidirect
25. C22×#11719949C22semidirect
26. C22×#11719949C22semidirect
27. C22×#11719945C22semidirect
28. C22×#11719945C22semidirect
30. C2×#41×D53C22semidirect
31. C22×Q8×D53C22semidirect
32. C22×Q8×D53C22semidirect
33. Q8×D212C22semidirect
34. Q8×C22⋊D53C22semidirect
35. Q8×C22⋊D53C22semidirect
36. #16811285C22semidirect
37. #16811284C22semidirect
38. #16811280C22semidirect
39. #16811278C22semidirect
40. #16811276C22semidirect
41. #16811275C22semidirect
42. #16811275C22semidirect
43. #16811270C22semidirect
44. #16811269C22semidirect
45. #16811266C22semidirect
46. #16811264C22semidirect
47. #16811203C22semidirect
48. #16811202C22semidirect
49. #16811199C22semidirect
50. #16811198C22semidirect
51. #16811197C22semidirect
52. #16811196C22semidirect
53. #16811196C22semidirect
54. #16811195C22semidirect
55. #16811194C22semidirect
56. #16811193C22semidirect
57. #16811189C22semidirect
58. #16811188C22semidirect
59. #16811184C22semidirect
60. #16811183C22semidirect
61. #16811170C22semidirect
62. C4⋊Q8×D53C22semidirect
63. #124×D53C22semidirect
64. #16811135C22semidirect
65. #16811134C22semidirect
66. #16811132C22semidirect
67. #16811130C22semidirect
68. #123×D53C22semidirect
69. C22⋊Q8×D53C22semidirect
70. #16811105C22semidirect
71. #16811101C22semidirect
72. #16811097C22semidirect
73. C4×#11719949C22semidirect
74. #117×D53C22semidirect
76. C23×Q8×C53C22semidirect
77. D4×Q8×C53C22semidirect
78. C53×#548C22semidirect
79. C53×#536C22semidirect
80. C53×#525C22semidirect
81. C53×#519C22semidirect
90. C2×#11719949D4semidirect
407. #3486D53semidirect
439. C23×Q8C2×D53semidirect
443. D4×Q8C2×D53semidirect
447. #548C2×D53semidirect
466. #536C2×D53semidirect
478. #525C2×D53semidirect
483. #519C2×D53semidirect
487. C53#62859semidirect

Maximal subgroups

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

subgroupindex
C2×#168114602
C22×#131332652
#202885062
#202884992
#202883942
#202883922
#202883672
#202883662
#202883632
#202883582
#202883572
#202880452
#536×D532
#202879172
C53×#34862
#6285953