Finite Group Databasebeta

← #28292631

Subgroups — #28292631

Order 13568.

11534 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811460C211yesmaximal, characteristic, complemented
2C22×#41×D53C211yesmaximal, characteristic, complemented
3#20288394C218yesmaximal, complemented
4#20288383C218yesmaximal, complemented
5#20288373C211yesmaximal, characteristic, complemented
6#20288367C211yesmaximal, characteristic, complemented
7#20288363C211yesmaximal, characteristic, complemented
8#20288357C216yesmaximal, complemented
9#20288349C216yesmaximal, complemented
10#20288205C218yesmaximal, complemented
11#20288204C218yesmaximal, complemented
12#20288046C216yesmaximal, complemented
13#525×D53C216yesmaximal, complemented
14#20287917C211yesmaximal, characteristic, complemented
15C53×#3487C211yesmaximal, characteristic, complemented
16#16811460—216no—
17C2×#13133265C2211yescharacteristic, complemented
18C2×#13133265C2214yescomplemented
19C2×#13133263C2216yescomplemented
20C2×#13133263C2214yescomplemented
21C22×#11719949C2211yescharacteristic
22C22×#11719949C2214yescomplemented
23C22×#11719945C2213yescomplemented
24C22×#11719947C2213yescomplemented
25C2×#41×D53—216no—
26C2×#41×D53C2218yescomplemented
27C2×#41×D53C2218yescomplemented
28C2×#41×D53C2216yescomplemented
29C2×#41×D53C2214yescomplemented
30C22×Q8×D53C2211yescharacteristic, complemented
31C22×D4×D53C2213yescomplemented
32C23×C4×D53C2213yescomplemented
33#16811292C2218yescomplemented
34Q8×D212C2218yescomplemented
35Q8×C22⋊D53C2218yescomplemented
36#16811285C2218yescomplemented
37#16811280C2218yescomplemented
38#16811280C2218yescomplemented
39#16811278C22124yescomplemented
40#16811275C22124yescomplemented
41#16811270C22124yescomplemented
42#16811270C22124yescomplemented
43#16811269C22124yescomplemented
44#16811266C22124yescomplemented
45#16811258C22124yescomplemented
46#16811257C22124yescomplemented
47#16811202C22124yescomplemented
48#16811199C2216yescomplemented
49#16811194C2216yescomplemented
50#16811193C22112yescomplemented
51#16811190C2216yescomplemented
52#16811186C22112yescomplemented
53#16811183C22124yescomplemented
54#16811172C22112yescomplemented
55#16811171C22112yescomplemented
56#16811136C22112yescomplemented
57#16811135C2216yescomplemented
58#16811134C2216yescomplemented
59#16811133C22112yescomplemented
60#16811133C22124yescomplemented
61#16811132C22124yescomplemented
62#16811131C2214yescomplemented
63#16811130C2216yescomplemented
64#16811129C22112yescomplemented
65#123×D53C22112yescomplemented
66C22⋊Q8×D53C22112yescomplemented
67#121×D53C22112yescomplemented
68#120×D53C22112yescomplemented
69#16811105C2218yescomplemented
70#16811101C2211yescharacteristic, complemented
71#16811097C2216yescomplemented
72C4×#11719949C2218yescomplemented
73C4×D4×D53C22124yescomplemented
74#117×D53C2216yescomplemented
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#13133263—232no—
86#13133263—248no—
87C2×#11719949—232no—
88C2×#11719949D4116yescomplemented
89C2×#11719949C2314yes—
90C2×#11719949C2314yes—
91C2×#11719949C23112yescomplemented
92C2×#11719949C2314yescomplemented
93C2×#11719949C2316yescomplemented
94C2×#11719945—224no—
95C2×#11719945C23124yes—
96C2×#11719945C2316yes—
97C2×#11719945C23112yescomplemented
98C2×#11719945C23112yescomplemented
99C2×#11719947—224no—
100C2×#11719947C2314yes—
101C2×#11719947C23112yes—
102C2×#11719947C23112yes—
103C2×#11719947C2316yescomplemented
104#41×D53—264no—
105#41×D53—264no—
106#41×D53—232no—
107#41×D53—248no—
108C22×Dic106C2313yes—
109C2×Q8×D53—28no—
110C2×Q8×D53C2318yes—
111C2×Q8×D53C2314yescomplemented
112C2×Q8×D53C2316yescomplemented
113C22×D212C2313yes—
114C22×D212C23112yescomplemented
115C22×C22⋊D53C2316yes—
116C2×D4×D53—224no—
117C2×D4×D53C23124yes—
118C2×D4×D53C23112yes—
119C2×D4×D53C23124yes—
120C2×D4×D53C23112yescomplemented
121C2×D4×D53C2316yescomplemented
122C23×Dic53C2313yes—
123C22×C4×D53—224no—
124C22×C4×D53C23112yes—
125C22×C4×D53C23112yes—
126C22×C4×D53C2313yes—
127C22×C4×D53C2313yes—
128C22×C4×D53C2311yescharacteristic
129C22×C4×D53C2313yes—
130C22×C4×D53C23112yescomplemented
131#13133217C23112yescomplemented
132#13133215C23112yescomplemented
133#13133213C23112yescomplemented
134#13133205C23112yescomplemented
135#13133204C23112yescomplemented
136#13133204C23112yescomplemented
137#13133202C23124yescomplemented
138#13133201C23112yes—
139#13133200C2314yes—
140#13133199C23148yescomplemented
141#13133199C23124yescomplemented
142#13133198C23112yes—
143#13133197C23112yes—
144#13133197C23124yescomplemented
145#13133196C23124yescomplemented
146#13133196C23112yescomplemented
147#13133195C2318yes—
148#13133194C23124yescomplemented
149#13133193C23112yes—
150#13133192C23112yes—
151#13133191C23112yescomplemented
152#13133190C2318yes—
153#13133190C23148yescomplemented
154#13133189C23124yescomplemented
155#13133188C23112yes—
156#13133188C23124yescomplemented
157#13133188C23148yescomplemented
158#13133187C23124yes—
159#13133187C2314yes—
160#13133186C23112yes—
161#13133185C23124yes—
162#13133185C2314yes—
163#13133185C23148yescomplemented
164Q8×Dic53C2318yescomplemented
165C4×D212C23124yes—
166C4×D212C23124yescomplemented
167D4×Dic53C23124yescomplemented
168#13133179C2318yes—
169#13133179C23124yescomplemented
170C4×C22⋊D53C23124yes—
171C4×C22⋊D53C23124yescomplemented
172#13133177C2318yes—
173#13133177C23124yescomplemented
174#13133176C2316yes—
175#13133175C23112yescomplemented
176#13133174C23112yescomplemented
177#13133173C2314yes—
178C4⋊C4×D53C23124yescomplemented
179C4⋊C4×D53C23112yescomplemented
180C22⋊C4×D53C23124yes—
181C22⋊C4×D53C23112yes—
182C22⋊C4×D53C23124yescomplemented
183C42×D53C23112yescomplemented
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×C53C23112yescomplemented
198#121×C53C23124yescomplemented
199#120×C53C23112yes—
200C4×Q8×C53C2318yescomplemented
201C4×D4×C53C23124yescomplemented
202#117×C53C2316yes—
203C24×C53C2413yes—
204C23×D53—212no—
205C23×D53—412no—
206C23×D53C2411yescharacteristic
207C23×D53C24112yes—
208C23×D53C24112yes—
209C23×D53C2413yes—
210#41×C53—232no—
211#41×C53—216no—
212#41×C53—224no—
213C2×Q8×C53—216no—
214C2×Q8×C53C2×D418yescomplemented
215C2×Q8×C53C2416yes—
216C2×Q8×C53C2414yes—
217C2×D4×C53—212no—
218C2×D4×C53C2414yes—
219C2×D4×C53C24112yes—
220C2×D4×C53C2416yes—
221C2×D4×C53C24124yes—
222C22×C4×C53—212no—
223C22×C4×C53C24112yes—
224C22×C4×C53C24112yes—
225C22×C4×C53C2411yescharacteristic
226C22×C4×C53C2413yes—
227C2×C22⋊D53—224no—
228C2×C22⋊D53C2418yes—
229C2×C22⋊D53C24112yes—
230C2×C22⋊D53C24124yes—
231C2×C22⋊D53C2414yes—
232C2×C22⋊D53C2414yes—
233C2×C22⋊D53C24124yes—
234C22×Dic53—212no—
235C22×Dic53C2414yes—
236C22×Dic53C2416yes—
237C22×Dic53C2416yes—
238C22×Dic53C2413yes—
239C22×Dic53C2411yescharacteristic
240#11719949—216no—
241#11719949—248no—
242#11719949—224no—
243#11719949C2×D4132yescomplemented
244#11719949C2×D4132yescomplemented
245Q8×D53—232no—
246Q8×D53—216no—
247Q8×D53—224no—
248#11719947—216no—
249#11719947—224no—
250#11719947—248no—
251#11719947—248no—
252D4×D53—248no—
253D4×D53—296no—
254D4×D53—248no—
255D4×D53—224no—
256D4×D53—448no—
257#11719945—224no—
258#11719945—296no—
259#11719945—248no—
260#11719945—248no—
261C2×D212—248no—
262C2×D212C2×D4124yescomplemented
263C2×D212C2418yes—
264C2×D212C24112yes—
265C2×D212C2416yes—
266C2×D212C24112yes—
267C2×C4×D53—212no—
268C2×C4×D53—212no—
269C2×C4×D53—24no—
270C2×C4×D53—248no—
271C2×C4×D53—248no—
272C2×C4×D53—248no—
273C2×C4×D53C2×D4124yescomplemented
274C2×C4×D53C24112yes—
275C2×C4×D53C24112yes—
276C2×C4×D53C2412yes—
277C2×C4×D53C2414yes—
278C2×C4×D53C24112yes—
279C2×C4×D53C24112yes—
280C2×C4×D53C2412yes—
281C2×C4×D53C24124yes—
282C2×C4×D53C2416yes—
283C2×C4×D53C2416yes—
284C2×Dic106—212no—
285C2×Dic106C2414yes—
286C2×Dic106C2416yes—
287C2×Dic106C24112yes—
288C4⋊C4×C53C24112yes—
289C4⋊C4×C53C2418yes—
290C22⋊C4×C53C2414yes—
291C22⋊C4×C53C2418yes—
292C22⋊C4×C53C24124yes—
293C42×C53C24112yes—
294C22⋊Dic53C2414yes—
295C22⋊Dic53C24124yes—
296C22⋊Dic53C24124yes—
297#11719921C2418yes—
298#11719921C2418yes—
299#11719921C24124yes—
300#11719921C2418yes—
301#11719921C24124yes—
302C4⋊Dic53C24112yes—
303C4⋊Dic53C24124yes—
304#11719919C2418yes—
305#11719919C2418yes—
306#11719919C24124yes—
307C4×Dic53C2418yes—
308C4×Dic53C24112yes—
309C23×C53—26no—
310C23×C53—46no—
311C23×C53C2516yes—
312C23×C53C2514yes—
313C23×C53C2511yescharacteristic
314C22×D53—22no—
315C22×D53—24no—
316C22×D53—224no—
317C22×D53—224no—
318C22×D53—224no—
319C22×D53—46no—
320C22×D53—412no—
321C22×D53—424no—
322C22×D53—448no—
323C22×D53C22×D4112yes—
324C22×D53C2514yes—
325C22×D53C2516yes—
326C22×D53C2512yes—
327Q8×C53—212no—
328Q8×C53C22×D4116yes—
329D4×C53—28no—
330D4×C53—212no—
331D4×C53—224no—
332D4×C53—424no—
333C2×C4×C53—22no—
334C2×C4×C53—224no—
335C2×C4×C53—224no—
336C2×C4×C53C22×D4112yes—
337C2×C4×C53C2514yes—
338C2×C4×C53C2512yes—
339C2×C4×C53C2518yes—
340C2×C4×C53C2516yes—
341C22⋊D53—28no—
342C22⋊D53—224no—
343C22⋊D53—248no—
344C22⋊D53—216no—
345C22⋊D53—28no—
346C22⋊D53—424no—
347C2×Dic53—26no—
348C2×Dic53—28no—
349C2×Dic53—212no—
350C2×Dic53—212no—
351C2×Dic53C22×D414yes—
352C2×Dic53C2514yes—
353C2×Dic53C2516yes—
354C2×Dic53C2518yes—
355C2×Dic53C2511yescharacteristic
356C2×Dic53C2511yescharacteristic
357D212—224no—
358D212—216no—
359D212—212no—
360D212C22×D4148yes—
361C4×D53—224no—
362C4×D53—224no—
363C4×D53—224no—
364C4×D53—224no—
365C4×D53—24no—
366C4×D53—24no—
367C4×D53—28no—
368C4×D53—424no—
369C4×D53C22×D4124yes—
370C4×D53C22×D4124yes—
371Dic106—224no—
372Dic106—212no—
373Dic106—28no—
374#62811—531nomaximal, Sylow
375C22×C53—22no—
376C22×C53—26no—
377C22×C53—24no—
378C22×C53—28no—
379C22×C53—212no—
380C22×C53—412no—
381C22×C53C23×D412yes—
382C22×C53C2611yescharacteristic
383C2×D53—28no—
384C2×D53—22no—
385C2×D53—212no—
386C2×D53—22no—
387C2×D53—24no—
388C2×D53—28no—
389C2×D53—412no—
390C2×D53—448no—
391C2×D53—824no—
392C2×D53C23×D4112yes—
393C2×D53#58514yescomplemented
394C4×C53—24no—
395C4×C53—22no—
396C4×C53—28no—
397C4×C53C23×D4112yes—
398Dic53—24no—
399Dic53—26no—
400Dic53—28no—
401Dic53C23×D412yes—
402Dic53C23×D412yes—
403C2×#585—531no—
404C23×#41—531no—
405#3489—538no—
406#3488—538no—
407#3487—531no—
408#3487D5311yescharacteristic, complemented
409#3486—531no—
410#3486—531no—
411#3485—536no—
412#3484—536no—
413D4×#41—538no—
414D4×#41—538no—
415#3449—536no—
416C2×#525—536no—
417#3428—531no—
418C2×C53—22no—
419C2×C53—46no—
420C2×C53—44no—
421C2×C53C24×D411yescharacteristic
422C2×C53C2×#58512yes—
423D53—24no—
424D53—212no—
425D53—44no—
426#585—10616no—
427C2×2−1+4—531no—
428C2×2−1+4—534no—
429C2×2−1+4C2×D5311yescharacteristic, complemented
430C2×H(5,𝔽2)—536no—
431C2×H(5,𝔽2)—534no—
432C22×#41—538no—
433C22×#41—538no—
434C22×#41—536no—
435C22×#41—534no—
436C22×#41—531no—
437C22×#41—534no—
438C22×#41—533no—
439C22×#41—533no—
440C22×#41—10616no—
441C22×#41C2×D5311yescharacteristic, complemented
442C23×Q8—531no—
443C23×D4—533no—
444C24×C4—533no—
445#550—538no—
446#550C2×D5318yescomplemented
447D4×Q8—538no—
448D4×Q8—538no—
449#548—538no—
450#548—538no—
451#548—538no—
452#548C2×D5318yescomplemented
453#547—5324no—
454#547—5324no—
455#546—5324no—
456#546—5324no—
457#546—5324no—
458#546—5324no—
459D42—5324no—
460D42—5324no—
461#537—5324no—
462#536—536no—
463#536—5312no—
464#536—536no—
465#535—536no—
466#535—5312no—
467#535C2×D5316yescomplemented
468#534—5324no—
469#532—5312no—
470#532—5312no—
471#525—536no—
472#525—536no—
473#525—534no—
474#525—5312no—
475#525—5312no—
476#525—5324no—
477#525—5312no—
478#525—5324no—
479#525—536no—
480#525C2×D5316yescomplemented
481C2×#123—5312no—
482C2×C22⋊Q8—5312no—
483C2×#121—5312no—
484C2×#120—5312no—
485#520—538no—
486#519—531no—
487#519C2×D5311yescharacteristic, complemented
488#518—536no—
489C4×#41—538no—
490C2×C4×D4—5324no—
491C2×#117—536no—
492C53#6281111yescharacteristic, complemented, Sylow
493C25—533no—
4942−1+4—28no—
4952−1+4—10632no—
4962−1+4—1068no—
497H(5,𝔽2)—10648no—
498H(5,𝔽2)—10632no—
499C2×#41—28no—
500C2×#41—5316no—
501C2×#41—534no—
502C2×#41—534no—
503C2×#41—536no—
504C2×#41—5312no—
505C2×#41—534no—
506C2×#41—534no—
507C2×#41—5312no—
508C2×#41—536no—
509C2×#41—5312no—
510C2×#41—536no—
511C2×#41—5312no—
512C2×#41—5324no—
513C2×#41—5312no—
514C2×#41—10624no—
515C2×#41—10624no—
516C2×#41—10648no—
517C2×#41—10632no—
518C2×#41—10664no—
519C2×#41—10664no—
520C2×#41—10632no—
521C2×#41C22×D5316yes—
522C2×#41C22×D5318yes—
523C2×#41C22×D5314yescomplemented
524C22×Q8—536no—
525C22×Q8—538no—
526C22×Q8—534no—
527C22×Q8—533no—
528C22×Q8—1068no—
529C22×Q8C22×D5311yescharacteristic
530C22×Q8C22×D5314yescomplemented
531C22×D4—536no—
532C22×D4—5312no—
533C22×D4—536no—
534C22×D4—5324no—
535C22×D4—5312no—
536C22×D4—5324no—
537C22×D4—533no—
538C22×D4—5312no—
539C22×D4—10624no—
540C22×D4C22×D5313yes—
541C23×C4—533no—
542C23×C4—533no—
543C23×C4—5312no—
544C23×C4—5312no—
545C23×C4—5312no—
546C23×C4—533no—
547C23×C4—531no—
548C23×C4—533no—
549C23×C4—10624no—
550C23×C4C22×D5313yes—
551C4⋊Q8—5312no—
552C4⋊Q8—5312no—
553#127—5312no—
554#127C22×D53112yescomplemented
555#124—5312no—
556#124—5312no—
557#124—5312no—
558#124C22×D53112yescomplemented
559#123—5312no—
560#123—534no—
561#123—5324no—
562#123—5312no—
563#123—5324no—
564#123—5348no—
565#123C22×D5314yes—
566C22⋊Q8—5312no—
567C22⋊Q8—5312no—
568C22⋊Q8—5324no—
569C22⋊Q8—538no—
570C22⋊Q8—5312no—
571C22⋊Q8—5324no—
572C22⋊Q8—5324no—
573C22⋊Q8C22×D53112yescomplemented
574#121—5324no—
575#121—5312no—
576#121—5324no—
577#121—5348no—
578#121—5312no—
579#121—5312no—
580#121—538no—
581#121—5348no—
582#121C22×D53112yescomplemented
583#121C22×D53124yescomplemented
584#120—5312no—
585#120—534no—
586#120—5324no—
587#120—5348no—
588#120—534no—
589#120—5324no—
590#120C22×D53112yes—
591C4×Q8—538no—
592C4×Q8C22×D5318yescomplemented
593C4×D4—5324no—
594C4×D4—5324no—
595C4×D4—5324no—
596C4×D4—538no—
597C4×D4—5324no—
598C4×D4—538no—
599C4×D4—5324no—
600C4×D4—5324no—
601C4×D4—5324no—
602C4×D4C22×D53124yescomplemented
603#117—536no—
604#117—5312no—
605#117—534no—
606#117—5312no—
607#117C22×D5316yes—
608C2×C4⋊C4—5312no—
609C2×C4⋊C4—5324no—
610C2×C22⋊C4—5312no—
611C2×C22⋊C4—5324no—
612C2×C22⋊C4—5324no—
613C2×C42—5312no—
614C24—533no—
615C24—531no—
616C24—5312no—
617C24—5312no—
618C24—10612no—
619C24—21212no—
620C24C23×D5313yes—
621#41—232no—
622#41—216no—
623#41—224no—
624#41—5332no—
625#41—5332no—
626#41—10648no—
627#41—10696no—
628#41—10648no—
629#41—10616no—
630#41—10648no—
631#41—10624no—
632#41—10648no—
633#41—10624no—
634#41—10648no—
635#41—10616no—
636#41—10624no—
637C2×Q8—216no—
638C2×Q8—534no—
639C2×Q8—536no—
640C2×Q8—5312no—
641C2×Q8—10624no—
642C2×Q8—10632no—
643C2×Q8—10616no—
644C2×Q8—10612no—
645C2×Q8D4×D5318yescomplemented
646C2×Q8C23×D5316yes—
647C2×Q8C23×D5314yes—
648C2×D4—212no—
649C2×D4—538no—
650C2×D4—534no—
651C2×D4—5312no—
652C2×D4—5324no—
653C2×D4—534no—
654C2×D4—5324no—
655C2×D4—5324no—
656C2×D4—5312no—
657C2×D4—538no—
658C2×D4—5312no—
659C2×D4—536no—
660C2×D4—10648no—
661C2×D4—10624no—
662C2×D4—10696no—
663C2×D4—10648no—
664C2×D4—10648no—
665C2×D4—10624no—
666C2×D4—21248no—
667C2×D4C23×D5314yes—
668C2×D4C23×D5316yes—
669C2×D4C23×D53112yes—
670C2×D4C23×D53124yes—
671C22×C4—212no—
672C22×C4—531no—
673C22×C4—5324no—
674C22×C4—536no—
675C22×C4—536no—
676C22×C4—534no—
677C22×C4—536no—
678C22×C4—536no—
679C22×C4—533no—
680C22×C4—5312no—
681C22×C4—5312no—
682C22×C4—532no—
683C22×C4—534no—
684C22×C4—5312no—
685C22×C4—5312no—
686C22×C4—532no—
687C22×C4—5324no—
688C22×C4—1064no—
689C22×C4—10648no—
690C22×C4—10648no—
691C22×C4—10648no—
692C22×C4—10612no—
693C22×C4—10612no—
694C22×C4—10612no—
695C22×C4C23×D53112yes—
696C22×C4C23×D53112yes—
697C22×C4C23×D5311yescharacteristic
698C22×C4C23×D5313yes—
699C4⋊C4—538no—
700C4⋊C4—538no—
701C4⋊C4—5312no—
702C4⋊C4—5324no—
703C4⋊C4—5324no—
704C4⋊C4C23×D5318yes—
705C4⋊C4C23×D53112yes—
706C22⋊C4—534no—
707C22⋊C4—5324no—
708C22⋊C4—5324no—
709C22⋊C4—538no—
710C22⋊C4—538no—
711C22⋊C4—538no—
712C22⋊C4—5324no—
713C22⋊C4—5324no—
714C22⋊C4C23×D5314yes—
715C22⋊C4C23×D5318yes—
716C22⋊C4C23×D53124yes—
717C42—538no—
718C42—5312no—
719C42C23×D53112yes—
720C23—26no—
721C23—46no—
722C23—532no—
723C23—536no—
724C23—5312no—
725C23—534no—
726C23—1064no—
727C23—10624no—
728C23—10624no—
729C23—10624no—
730C23—1062no—
731C23—21224no—
732C23—2126no—
733C23—21212no—
734C23—21248no—
735C23C24×D5314yes—
736C23C24×D5316yes—
737C23C24×D5311yescharacteristic
738Q8—212no—
739Q8—1068no—
740Q8—10624no—
741Q8—10612no—
742Q8C2×D4×D53116yes—
743D4—28no—
744D4—224no—
745D4—212no—
746D4—424no—
747D4—5348no—
748D4—10624no—
749D4—10616no—
750D4—1068no—
751D4—10624no—
752D4—10648no—
753D4—10616no—
754D4—1068no—
755D4—10612no—
756D4—21224no—
757C2×C4—22no—
758C2×C4—224no—
759C2×C4—224no—
760C2×C4—534no—
761C2×C4—531no—
762C2×C4—531no—
763C2×C4—5324no—
764C2×C4—5324no—
765C2×C4—538no—
766C2×C4—534no—
767C2×C4—536no—
768C2×C4—1064no—
769C2×C4—1064no—
770C2×C4—1068no—
771C2×C4—10624no—
772C2×C4—10624no—
773C2×C4—1068no—
774C2×C4—10612no—
775C2×C4—10612no—
776C2×C4—1066no—
777C2×C4—10624no—
778C2×C4—10624no—
779C2×C4—21224no—
780C2×C4C2×D4×D53112yes—
781C2×C4C24×D5318yes—
782C2×C4C24×D5312yes—
783C2×C4C24×D5314yes—
784C2×C4C24×D5316yes—
785C22—22no—
786C22—24no—
787C22—26no—
788C22—28no—
789C22—212no—
790C22—412no—
791C22—5312no—
792C22—534no—
793C22—1068no—
794C22—1062no—
795C22—10612no—
796C22—1062no—
797C22—1064no—
798C22—1068no—
799C22—42424no—
800C22—21212no—
801C22—21248no—
802C22C22×D4×D5312yes—
803C22C25×D5311yescharacteristic
804C4—22no—
805C4—24no—
806C4—28no—
807C4—532no—
808C4—532no—
809C4—1066no—
810C4—1064no—
811C4—1068no—
812C4C22×D4×D53112yes—
813C2—22no—
814C2—46no—
815C2—44no—
816C2—1064no—
817C2—10612no—
818C2—2124no—
819C2C23×D4×D5311yescharacteristic
820C2#585×D5312yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3487C2
hypercenter#3487D53
hypocenterC53#62811
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3487

Complements

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

NH ≅ G/Ntype
1. C2×#16811460C2semidirect
2. C22×#41×D53C2semidirect
3. #20288394C2semidirect
4. #20288383C2semidirect
5. #20288373C2semidirect
6. #20288367C2semidirect
7. #20288363C2semidirect
8. #20288357C2semidirect
9. #20288349C2semidirect
10. #20288205C2semidirect
11. #20288204C2semidirect
12. #20288046C2semidirect
13. #525×D53C2semidirect
14. #20287917C2semidirect
15. C53×#3487C2semidirect
17. C2×#13133265C22semidirect
18. C2×#13133265C22semidirect
19. C2×#13133263C22semidirect
20. C2×#13133263C22semidirect
22. C22×#11719949C22semidirect
23. C22×#11719945C22semidirect
24. C22×#11719947C22semidirect
26. C2×#41×D53C22semidirect
27. C2×#41×D53C22semidirect
28. C2×#41×D53C22semidirect
29. C2×#41×D53C22semidirect
30. C22×Q8×D53C22semidirect
31. C22×D4×D53C22semidirect
32. C23×C4×D53C22semidirect
33. #16811292C22semidirect
34. Q8×D212C22semidirect
35. Q8×C22⋊D53C22semidirect
36. #16811285C22semidirect
37. #16811280C22semidirect
38. #16811280C22semidirect
39. #16811278C22semidirect
40. #16811275C22semidirect
41. #16811270C22semidirect
42. #16811270C22semidirect
43. #16811269C22semidirect
44. #16811266C22semidirect
45. #16811258C22semidirect
46. #16811257C22semidirect
47. #16811202C22semidirect
48. #16811199C22semidirect
49. #16811194C22semidirect
50. #16811193C22semidirect
51. #16811190C22semidirect
52. #16811186C22semidirect
53. #16811183C22semidirect
54. #16811172C22semidirect
55. #16811171C22semidirect
56. #16811136C22semidirect
57. #16811135C22semidirect
58. #16811134C22semidirect
59. #16811133C22semidirect
60. #16811133C22semidirect
61. #16811132C22semidirect
62. #16811131C22semidirect
63. #16811130C22semidirect
64. #16811129C22semidirect
65. #123×D53C22semidirect
66. C22⋊Q8×D53C22semidirect
67. #121×D53C22semidirect
68. #120×D53C22semidirect
69. #16811105C22semidirect
70. #16811101C22semidirect
71. #16811097C22semidirect
72. C4×#11719949C22semidirect
73. C4×D4×D53C22semidirect
74. #117×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
88. C2×#11719949D4semidirect
91. C2×#11719949C23semidirect
92. C2×#11719949C23semidirect
93. C2×#11719949C23semidirect
97. C2×#11719945C23semidirect
98. C2×#11719945C23semidirect
103. C2×#11719947C23semidirect
111. C2×Q8×D53C23semidirect
112. C2×Q8×D53C23semidirect
114. C22×D212C23semidirect
120. C2×D4×D53C23semidirect
121. C2×D4×D53C23semidirect
130. C22×C4×D53C23semidirect
131. #13133217C23semidirect
132. #13133215C23semidirect
133. #13133213C23semidirect
134. #13133205C23semidirect
135. #13133204C23semidirect
136. #13133204C23semidirect
137. #13133202C23semidirect
140. #13133199C23semidirect
141. #13133199C23semidirect
144. #13133197C23semidirect
145. #13133196C23semidirect
146. #13133196C23semidirect
148. #13133194C23semidirect
151. #13133191C23semidirect
153. #13133190C23semidirect
154. #13133189C23semidirect
156. #13133188C23semidirect
157. #13133188C23semidirect
163. #13133185C23semidirect
164. Q8×Dic53C23semidirect
166. C4×D212C23semidirect
167. D4×Dic53C23semidirect
169. #13133179C23semidirect
171. C4×C22⋊D53C23semidirect
173. #13133177C23semidirect
175. #13133175C23semidirect
176. #13133174C23semidirect
178. C4⋊C4×D53C23semidirect
179. C4⋊C4×D53C23semidirect
182. C22⋊C4×D53C23semidirect
183. C42×D53C23semidirect
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
214. C2×Q8×C53C2×D4semidirect
243. #11719949C2×D4semidirect
244. #11719949C2×D4semidirect
262. C2×D212C2×D4semidirect
273. C2×C4×D53C2×D4semidirect
393. C2×D53#585semidirect
408. #3487D53semidirect
429. C2×2−1+4C2×D53semidirect
441. C22×#41C2×D53semidirect
446. #550C2×D53semidirect
452. #548C2×D53semidirect
467. #535C2×D53semidirect
480. #525C2×D53semidirect
487. #519C2×D53semidirect
492. C53#62811semidirect
523. C2×#41C22×D53semidirect
530. C22×Q8C22×D53semidirect
554. #127C22×D53semidirect
558. #124C22×D53semidirect
573. C22⋊Q8C22×D53semidirect
582. #121C22×D53semidirect
583. #121C22×D53semidirect
592. C4×Q8C22×D53semidirect
602. C4×D4C22×D53semidirect
645. C2×Q8D4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168114602
C22×#41×D532
#202883942
#202883832
#202883732
#202883672
#202883632
#202883572
#202883492
#202882052
#202882042
#202880462
#525×D532
#202879172
C53×#34872
#6281153