Finite Group Databasebeta

← #27544589

Subgroups — #27544589

Order 13568.

2230 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811158C211yesmaximal, characteristic
2#20277841C212yesmaximal, complemented
3#20277829C212yesmaximal, complemented
4#20277825C211yesmaximal, characteristic, complemented
5#20277825C211yesmaximal, characteristic, complemented
6#20277821C211yesmaximal, characteristic, complemented
7#20277677C212yesmaximal, complemented
8#20277654C212yesmaximal, complemented
9#20277596C212yesmaximal, complemented
10#20277570C212yesmaximal, complemented
11#20277444C212yesmaximal, complemented
12#20277414C212yesmaximal
13#20277347C212yesmaximal, complemented
14C4×#13133202C212yesmaximal, complemented
15#20277236C212yesmaximal, complemented
16#20277107C211yesmaximal, characteristic, complemented
17#20277075C212yesmaximal, complemented
18#376×D53C211yesmaximal, characteristic, complemented
19C53×#2371C211yesmaximal, characteristic, complemented
20#16811158C4116yescomplemented
21C2×#13133212C2212yes—
22C2×#13133205C2211yescharacteristic
23C2×#13133202C2212yes—
24C2×#13133197C2211yescharacteristic
25C2×#13133192C2211yescharacteristic
26C2×#13133182C2211yescharacteristic
27C2×C4×D212C2212yes—
28C2×#13133179C2212yes—
29C2×#13133179C2212yes—
30C2×#13133179C2211yescharacteristic
31C2×#13133175C2212yes—
32C2×C42×D53C2212yes—
33C2×C42×D53C2211yescharacteristic
34#16810527C2212yes—
35#16810527C2212yes—
36#16810521C2212yes—
37#16810519C2212yes—
38#16810515C2212yes—
39#16810514C2212yes—
40#16810514C2212yes—
41#16810514C2212yes—
42#16810513C2212yes—
43#16810512C2212yes—
44#16810512C2212yes—
45#16810512C2212yes—
46#16810510C2212yes—
47#16810509C2212yes—
48#16810509C2212yes—
49#16810509C2212yes—
50#16810509C2212yes—
51#16810508C2212yes—
52#16810506C2212yes—
53#16810504C2212yes—
54#16810501C2212yes—
55#16810501C2212yes—
56#16810501C2212yes—
57#16810501C2212yes—
58#16810497C2212yes—
59#16810497C2212yes—
60#16810494C2212yes—
61#16810494C2212yes—
62#16810490C2212yes—
63#16810490C2212yes—
64#16810487C2211yescharacteristic
65#16810487C2211yescharacteristic
66#16810487C2212yes—
67#16810485C2212yes—
68#16810485C2211yescharacteristic
69#16810485C2211yescharacteristic
70#16810482C2212yes—
71#16810480C2212yes—
72C4⋊C4×Dic53C2212yes—
73C4⋊C4×Dic53C2212yes—
74C4⋊C4×Dic53C2212yes—
75C4×#11719919C2212yes—
76C4×#11719919C2212yes—
77#16810474C2212yes—
78C4×#11719921C2212yes—
79C4×#11719921C2212yes—
80C4×#11719921C2212yes—
81C4×#11719921C2212yes—
82C4×#11719921C2212yes—
83C4×#11719921C2212yes—
84#16810470C2212yes—
85#16810470C2212yes—
86#16810470C2212yes—
87#16810470C2212yes—
88#16810469C2211yescharacteristic
89#16810469C2212yes—
90#16810469C2211yescharacteristic
91#16810469C2212yes—
92#16810468C2211yescharacteristic
93#16810468C2211yescharacteristic
94#16810468C2212yes—
95#95×D53C2211yescharacteristic
96#95×D53C2211yescharacteristic
97#95×D53C2212yes—
98#95×D53C2212yes—
99C2×#125×C53C2211yescharacteristic
100C53×#387C2212yes—
101C53×#387C2212yes—
102C53×#387C2212yes—
103C53×#387C2212yes—
104C4×C4⋊C4×C53C2212yes—
105C4×C4⋊C4×C53C2212yes—
106C53×#376C2211yescharacteristic
107C53×#376C2211yescharacteristic
108C22×Dic106C2311yescharacteristic
109C22×D212C2312yes—
110C22×D212C2311yescharacteristic
111C22×C4×D53C2311yescharacteristic
112C22×C4×D53C2312yes—
113C22×C4×D53C2312yes—
114C22×C4×D53C2312yes—
115C22×C4×D53C2311yescharacteristic
116C22×C4×D53C2311yescharacteristic
117C22×C4×D53C2312yes—
118C22×C4×D53C2312yes—
119#13133212C2×C4116yescomplemented
120#13133205C2×C418yescomplemented
121#13133202C2×C4116yescomplemented
122#13133197C2×C418yescomplemented
123#13133192C2×C418yes—
124#13133182C2×C418yescomplemented
125C4×D212—28no—
126#13133179—28no—
127#13133179C2×C4116yescomplemented
128#13133179C2×C418yescomplemented
129#13133175C2×C4116yescomplemented
130C2×C4⋊Dic53C2312yes—
131C2×C4⋊Dic53C2312yes—
132C2×C4⋊Dic53C2312yes—
133C2×#11719919C2312yes—
134C2×#11719919C2312yes—
135C2×#11719919C2312yes—
136C2×#11719919C2312yes—
137C2×#11719919C2312yes—
138C2×#11719921C2312yes—
139C2×#11719921C2312yes—
140C2×#11719921C2312yes—
141C2×#11719921C2312yes—
142C2×#11719921C2312yes—
143C2×#11719921C2312yes—
144C2×#11719921C2312yes—
145C2×#11719921C2312yes—
146C2×#11719921C2312yes—
147C2×#11719921C2312yes—
148C2×#11719921C2312yes—
149C2×#11719921C2312yes—
150C2×#11719921C2312yes—
151C2×C4×Dic53C2312yes—
152C2×C4×Dic53C2312yes—
153C2×C4×Dic53C2312yes—
154C2×C4×Dic53C2312yes—
155C2×C4×Dic53C2312yes—
156C2×C4×Dic53C2312yes—
157C2×C4×Dic53C2312yes—
158C2×C4×Dic53C2312yes—
159C2×C4×Dic53C2311yescharacteristic
160C2×C4×Dic53C2311yescharacteristic
161C2×C4×Dic53C2311yescharacteristic
162C2×C4×Dic53C2312yes—
163C42×D53—28no—
164C42×D53C2×C418yescomplemented
165#13133124C2312yes—
166#13133124C2312yes—
167#13133124C2312yes—
168#13133124C2312yes—
169#13133124C2312yes—
170#13133124C2312yes—
171#13133124C2312yes—
172#13133124C2312yes—
173#13133124C2312yes—
174#13133124C2312yes—
175#13133124C2312yes—
176#13133124C2312yes—
177#13133124C2311yescharacteristic
178#13133124C2311yescharacteristic
179#13133124C2312yes—
180#13133124C2312yes—
181#13133124C2311yescharacteristic
182#13133124C2312yes—
183#13133124C2311yescharacteristic
184#13133124C2312yes—
185#13133124C2312yes—
186#13133124C2312yes—
187#125×C53C2×C418yescomplemented
188C2×C4⋊C4×C53C2312yes—
189C2×C4⋊C4×C53C2312yes—
190C2×C4⋊C4×C53C2311yescharacteristic
191C2×C4⋊C4×C53C2311yescharacteristic
192C2×C4⋊C4×C53C2312yes—
193C2×C4⋊C4×C53C2312yes—
194C2×C42×C53C2312yes—
195C2×C42×C53C2312yes—
196C2×C42×C53C2312yes—
197C2×C42×C53C2312yes—
198C2×C42×C53C2311yescharacteristic
199#95×C53C2312yes—
200#95×C53C2312yes—
201#95×C53C2312yes—
202#95×C53C2312yes—
203#95×C53C2312yes—
204#95×C53C2312yes—
205#95×C53C2311yescharacteristic
206#95×C53C2311yescharacteristic
207#95×C53C2311yescharacteristic
208#95×C53C2311yescharacteristic
209C23×D53C2412yes—
210C23×D53C2411yescharacteristic
211C22×C4×C53C2412yes—
212C22×C4×C53C2412yes—
213C22×C4×C53C2412yes—
214C22×C4×C53C2411yescharacteristic
215C22×C4×C53C2411yescharacteristic
216C22×C4×C53C2411yescharacteristic
217C22×C4×C53C2412yes—
218C22×C4×C53C2412yes—
219C22×C4×C53C2412yes—
220C22×Dic53C2412yes—
221C22×Dic53C2412yes—
222C22×Dic53C2412yes—
223C22×Dic53C2411yescharacteristic
224C22×Dic53C2411yescharacteristic
225C22×Dic53C2412yes—
226C22×Dic53C2411yescharacteristic
227C22×Dic53C2412yes—
228C2×D212—24no—
229C2×D212—24no—
230C2×D212—41no—
231C2×D212—41no—
232C2×D212C22×C418yes—
233C2×D212C22×C414yes—
234C2×C4×D53—24no—
235C2×C4×D53—24no—
236C2×C4×D53—24no—
237C2×C4×D53—24no—
238C2×C4×D53—42no—
239C2×C4×D53—42no—
240C2×C4×D53—42no—
241C2×C4×D53—41no—
242C2×C4×D53—41no—
243C2×C4×D53—42no—
244C2×C4×D53—42no—
245C2×C4×D53—42no—
246C2×C4×D53—42no—
247C2×C4×D53—42no—
248C2×C4×D53—42no—
249C2×C4×D53—42no—
250C2×C4×D53—42no—
251C2×C4×D53C22×C414yes—
252C2×C4×D53C22×C414yes—
253C2×C4×D53C22×C414yes—
254C2×C4×D53C22×C418yes—
255C2×C4×D53#4118yes—
256C2×Dic106—41no—
257C2×Dic106—41no—
258C2×Dic106C22×C414yes—
259C4⋊C4×C53—24no—
260C4⋊C4×C53—42no—
261C4⋊C4×C53C22×C418yes—
262C4⋊C4×C53C22×C414yes—
263C4⋊C4×C53C22×C418yes—
264C4⋊C4×C53C22×C414yes—
265C42×C53—24no—
266C42×C53—24no—
267C42×C53—42no—
268C42×C53—42no—
269C42×C53C22×C414yes—
270#11719921—24no—
271#11719921—24no—
272#11719921—24no—
273#11719921—24no—
274#11719921—42no—
275#11719921—42no—
276#11719921—42no—
277#11719921—42no—
278#11719921C22×C418yes—
279#11719921C22×C418yes—
280#11719921C22×C418yes—
281#11719921C22×C418yes—
282#11719921C22×C418yes—
283C4⋊Dic53—24no—
284C4⋊Dic53—42no—
285C4⋊Dic53C22×C418yes—
286#11719919—42no—
287#11719919—42no—
288#11719919—42no—
289#11719919—42no—
290#11719919C22×C418yes—
291C4×Dic53—24no—
292C4×Dic53—24no—
293C4×Dic53—24no—
294C4×Dic53—24no—
295C4×Dic53—42no—
296C4×Dic53—42no—
297C4×Dic53—42no—
298C4×Dic53—42no—
299C4×Dic53C22×C414yes—
300C4×Dic53C22×C414yes—
301C4×Dic53C22×C414yes—
302C4×Dic53C22×C418yes—
303C23×C53C2511yescharacteristic
304C22×D53—22no—
305C22×D53—21no—
306C22×D53—21no—
307C22×D53—22no—
308C22×D53—22no—
309C22×D53—22no—
310C22×D53—22no—
311C22×D53—22no—
312C22×D53—22no—
313C22×D53C23×C414yes—
314C22×D53C23×C412yes—
315C22×D53C2×#4114yes—
316C2×C4×C53—22no—
317C2×C4×C53—22no—
318C2×C4×C53—22no—
319C2×C4×C53—21no—
320C2×C4×C53—21no—
321C2×C4×C53—22no—
322C2×C4×C53—22no—
323C2×C4×C53—22no—
324C2×C4×C53—22no—
325C2×C4×C53—22no—
326C2×C4×C53—22no—
327C2×C4×C53—22no—
328C2×C4×C53—22no—
329C2×C4×C53—22no—
330C2×C4×C53—22no—
331C2×C4×C53—22no—
332C2×C4×C53—22no—
333C2×C4×C53—22no—
334C2×C4×C53—22no—
335C2×C4×C53C23×C412yes—
336C2×C4×C53C23×C412yes—
337C2×C4×C53C23×C412yes—
338C2×C4×C53C23×C414yes—
339C2×C4×C53C23×C414yes—
340C2×C4×C53C2×#4114yes—
341C2×Dic53—22no—
342C2×Dic53—22no—
343C2×Dic53—22no—
344C2×Dic53—22no—
345C2×Dic53—22no—
346C2×Dic53—22no—
347C2×Dic53—21no—
348C2×Dic53—21no—
349C2×Dic53—22no—
350C2×Dic53—22no—
351C2×Dic53—22no—
352C2×Dic53—22no—
353C2×Dic53—22no—
354C2×Dic53—22no—
355C2×Dic53—22no—
356C2×Dic53—22no—
357C2×Dic53—22no—
358C2×Dic53C23×C414yes—
359C2×Dic53C23×C412yes—
360C2×Dic53C23×C412yes—
361C2×Dic53C23×C412yes—
362C2×Dic53C2×#4114yes—
363D212—216no—
364D212—44no—
365C4×D53—28no—
366C4×D53—44no—
367C4×D53—48no—
368C4×D53—44no—
369C4×D53—48no—
370C4×D53—48no—
371C4×D53—84no—
372C4×D53—84no—
373Dic106—44no—
374#34219—531nomaximal, Sylow
375C22×C53C24×C411yescharacteristic
376C22×C53C22×#4112yes—
377C22×C53#58512yes—
378C22×C53#58511yescharacteristic
379C22×C53#58511yescharacteristic
380C2×D53—22no—
381C2×D53—22no—
382C2×D53—24no—
383C2×D53—24no—
384C2×D53—24no—
385C2×D53—24no—
386C2×D53—24no—
387C2×D53—42no—
388C2×D53—42no—
389C2×D53—42no—
390C2×D53—42no—
391C2×D53C4×#4114yes—
392C4×C53—22no—
393C4×C53—24no—
394C4×C53—22no—
395C4×C53—22no—
396C4×C53—24no—
397C4×C53—24no—
398C4×C53—42no—
399C4×C53—42no—
400C4×C53—42no—
401Dic53—22no—
402Dic53—24no—
403Dic53—22no—
404Dic53—22no—
405Dic53—24no—
406Dic53—42no—
407Dic53—42no—
408Dic53—42no—
409C2×#529—531no—
410#2373—532no—
411#2373—532no—
412#2372—531no—
413#2372—531no—
414#2371—531no—
415#2371D5311yescharacteristic, complemented
416#2356—532no—
417#2353—532no—
418#2346—532no—
419#2343—532no—
420#2329—532no—
421#2325—532no—
422#2318—532no—
423C4×#123—532no—
424C4×#123—532no—
425#2283—531no—
426#2275—532no—
427C2×#376—531no—
428C2×C53C2×C4×#4111yescharacteristic
429C2×C53#342811yescharacteristic
430C2×C53#342811yescharacteristic
431C2×C53#349112yes—
432C2×C53#349312yes—
433D53—24no—
434D53—44no—
435#529—5316no—
436C2×#126—532no—
437C2×#125C2×D5311yescharacteristic
438C2×#124—531no—
439C2×#123—532no—
440C2×C22⋊Q8—531no—
441C2×#121—531no—
442C2×C4×Q8—531no—
443C2×C4×D4—532no—
444C2×C4×D4—531no—
445C2×C4×D4—532no—
446C2×C4×D4—532no—
447C2×#117—532no—
448C22×C42—531no—
449C22×C42—532no—
450#391—532no—
451#391—532no—
452#389—532no—
453#389—532no—
454#388—532no—
455#388—532no—
456#388—532no—
457#388—532no—
458#388—532no—
459#388—532no—
460#388—532no—
461#388—532no—
462#387—532no—
463#387—532no—
464#387—532no—
465#387—532no—
466#387—532no—
467#387—532no—
468#387—532no—
469#387—532no—
470#387C2×D5312yes—
471#387C2×D5312yes—
472#387C2×D5312yes—
473#387C2×D5312yes—
474#386—532no—
475#386—532no—
476#386—532no—
477#386—532no—
478#385—532no—
479#385—532no—
480#385—532no—
481#385—532no—
482#383—532no—
483#383—532no—
484#382—532no—
485#382—531no—
486#382—531no—
487#381—532no—
488#381—531no—
489#381—531no—
490#380—532no—
491#380—532no—
492C4×C4⋊C4—532no—
493C4×C4⋊C4—532no—
494C4×C4⋊C4—532no—
495C4×C4⋊C4—532no—
496C4×C4⋊C4—532no—
497C4×C4⋊C4—532no—
498C4×C4⋊C4C2×D5312yes—
499C4×C4⋊C4C2×D5312yes—
500C4×C22⋊C4—532no—
501C4×C22⋊C4—532no—
502C4×C22⋊C4—532no—
503C4×C22⋊C4—532no—
504C4×C22⋊C4—532no—
505C4×C22⋊C4—532no—
506C4×C22⋊C4—532no—
507C4×C22⋊C4—532no—
508C4×C22⋊C4—532no—
509C4×C22⋊C4—532no—
510#376—532no—
511#376—532no—
512#376—531no—
513#376—531no—
514#376—532no—
515#376—531no—
516#376—531no—
517#376C2×D5311yescharacteristic
518#376C2×D5311yescharacteristic
519C2×#95—531no—
520C2×#95—532no—
521C2×#95—532no—
522C2×#95—531no—
523C53#3421911yescharacteristic, complemented, Sylow
524C22×Q8—531no—
525C22×D4—532no—
526C22×D4—531no—
527C23×C4—531no—
528C23×C4—532no—
529C23×C4—531no—
530C23×C4—532no—
531C23×C4—531no—
532C23×C4—532no—
533C23×C4—532no—
534C23×C4—532no—
535#126—5316no—
536#125C4×D5318yescomplemented
537#124—538no—
538#123—5316no—
539C22⋊Q8—538no—
540#121—538no—
541C4×Q8—538no—
542C4×D4—538no—
543C4×D4—5316no—
544C4×D4—1068no—
545C4×D4—1068no—
546#117—5316no—
547C2×C4⋊C4—532no—
548C2×C4⋊C4—532no—
549C2×C4⋊C4—532no—
550C2×C4⋊C4—532no—
551C2×C4⋊C4—532no—
552C2×C4⋊C4—532no—
553C2×C4⋊C4—532no—
554C2×C4⋊C4—532no—
555C2×C4⋊C4C22×D5312yes—
556C2×C4⋊C4C22×D5312yes—
557C2×C4⋊C4C22×D5312yes—
558C2×C4⋊C4C22×D5311yescharacteristic
559C2×C4⋊C4C22×D5312yes—
560C2×C4⋊C4C22×D5311yescharacteristic
561C2×C22⋊C4—532no—
562C2×C22⋊C4—532no—
563C2×C22⋊C4—532no—
564C2×C22⋊C4—532no—
565C2×C22⋊C4—532no—
566C2×C22⋊C4—532no—
567C2×C22⋊C4—532no—
568C2×C22⋊C4—532no—
569C2×C22⋊C4—532no—
570C2×C22⋊C4—532no—
571C2×C22⋊C4—532no—
572C2×C22⋊C4—532no—
573C2×C22⋊C4—532no—
574C2×C42—531no—
575C2×C42—532no—
576C2×C42—531no—
577C2×C42—531no—
578C2×C42—538no—
579C2×C42—532no—
580C2×C42—532no—
581C2×C42—532no—
582C2×C42—532no—
583C2×C42—532no—
584C2×C42—532no—
585C2×C42—532no—
586C2×C42—532no—
587C2×C42—1068no—
588C2×C42C22×D5312yes—
589C2×C42C22×D5312yes—
590C2×C42C22×D5312yes—
591C2×C42C22×D5312yes—
592C2×C42C22×D5311yescharacteristic
593#95—532no—
594#95—531no—
595#95—532no—
596#95—532no—
597#95—532no—
598#95—532no—
599#95—531no—
600#95—532no—
601#95—532no—
602#95—532no—
603#95—531no—
604#95—532no—
605#95—532no—
606#95—531no—
607#95—532no—
608#95—532no—
609#95—532no—
610#95—532no—
611#95—532no—
612#95—532no—
613#95—532no—
614#95—532no—
615#95C22×D5311yescharacteristic
616#95C22×D5312yes—
617#95C22×D5311yescharacteristic
618#95C22×D5312yes—
619#95C22×D5311yescharacteristic
620#95C22×D5311yescharacteristic
621#95C22×D5312yes—
622#95C22×D5312yes—
623#95C22×D5312yes—
624#95C22×D5312yes—
625C24—531no—
626C24—532no—
627C2×Q8—534no—
628C2×Q8—2121no—
629C2×Q8—2121no—
630C2×D4—538no—
631C2×D4—534no—
632C2×D4—1064no—
633C2×D4—1064no—
634C2×D4—2121no—
635C2×D4—2121no—
636C22×C4—531no—
637C22×C4—532no—
638C22×C4—531no—
639C22×C4—532no—
640C22×C4—531no—
641C22×C4—534no—
642C22×C4—534no—
643C22×C4—534no—
644C22×C4—538no—
645C22×C4—538no—
646C22×C4—532no—
647C22×C4—532no—
648C22×C4—532no—
649C22×C4—1064no—
650C22×C4—1064no—
651C22×C4—1064no—
652C22×C4—1064no—
653C22×C4—2122no—
654C22×C4—2122no—
655C22×C4—2122no—
656C22×C4—2122no—
657C22×C4—2122no—
658C22×C4—2122no—
659C22×C4—2122no—
660C22×C4—2122no—
661C22×C4—2122no—
662C22×C4—2121no—
663C22×C4—2121no—
664C22×C4—2122no—
665C22×C4—2122no—
666C22×C4C23×D5312yes—
667C22×C4C23×D5312yes—
668C22×C4C23×D5312yes—
669C22×C4C23×D5311yescharacteristic
670C22×C4C23×D5311yescharacteristic
671C22×C4C23×D5311yescharacteristic
672C22×C4C23×D5312yes—
673C22×C4C23×D5312yes—
674C22×C4C23×D5312yes—
675C4⋊C4—24no—
676C4⋊C4—42no—
677C4⋊C4—538no—
678C4⋊C4—538no—
679C4⋊C4—1064no—
680C4⋊C4—2122no—
681C4⋊C4—2122no—
682C4⋊C4—2122no—
683C4⋊C4—2122no—
684C4⋊C4—2122no—
685C4⋊C4C2×C4×D5318yes—
686C4⋊C4C2×C4×D5314yes—
687C4⋊C4C2×C4×D5318yes—
688C4⋊C4C2×C4×D5314yes—
689C22⋊C4—538no—
690C22⋊C4—538no—
691C22⋊C4—538no—
692C22⋊C4—538no—
693C22⋊C4—538no—
694C22⋊C4—1064no—
695C22⋊C4—1064no—
696C22⋊C4—1064no—
697C22⋊C4—1064no—
698C22⋊C4—2122no—
699C22⋊C4—2122no—
700C22⋊C4—2122no—
701C22⋊C4—2122no—
702C42—24no—
703C42—24no—
704C42—42no—
705C42—42no—
706C42—534no—
707C42—534no—
708C42—534no—
709C42—538no—
710C42—1064no—
711C42—1064no—
712C42—1064no—
713C42—1064no—
714C42—2122no—
715C42—2122no—
716C42—2122no—
717C42—2122no—
718C42C2×C4×D5314yes—
719C23—532no—
720C23—534no—
721C23—534no—
722C23—1062no—
723C23—1061no—
724C23—1061no—
725C23—1062no—
726C23—1062no—
727C23—1062no—
728C23—1062no—
729C23—1062no—
730C23—1062no—
731C23C24×D5311yescharacteristic
732Q8—2124no—
733D4—10616no—
734D4—2124no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—532no—
755C2×C4—532no—
756C2×C4—532no—
757C2×C4—534no—
758C2×C4—534no—
759C2×C4—1068no—
760C2×C4—1062no—
761C2×C4—1062no—
762C2×C4—1062no—
763C2×C4—1062no—
764C2×C4—1062no—
765C2×C4—1061no—
766C2×C4—1061no—
767C2×C4—1062no—
768C2×C4—1062no—
769C2×C4—1062no—
770C2×C4—1062no—
771C2×C4—1062no—
772C2×C4—1062no—
773C2×C4—1062no—
774C2×C4—1062no—
775C2×C4—1062no—
776C2×C4—1062no—
777C2×C4—4244no—
778C2×C4—4244no—
779C2×C4—2128no—
780C2×C4—2124no—
781C2×C4—2128no—
782C2×C4—2124no—
783C2×C4—2128no—
784C2×C4C22×C4×D5312yes—
785C2×C4C22×C4×D5312yes—
786C2×C4C22×C4×D5312yes—
787C2×C4C22×C4×D5314yes—
788C2×C4C22×C4×D5314yes—
789C2×C4#41×D5314yes—
790C22—534no—
791C22—1064no—
792C22—1062no—
793C22—1062no—
794C22—1064no—
795C22—1064no—
796C22—1064no—
797C22—1064no—
798C22—2122no—
799C22—2122no—
800C22—2122no—
801C22—2122no—
802C22C23×C4×D5311yescharacteristic
803C22C2×#41×D5312yes—
804C22#1681145912yes—
805C22#1681146011yescharacteristic
806C22#1681146011yescharacteristic
807C4—22no—
808C4—24no—
809C4—24no—
810C4—22no—
811C4—24no—
812C4—22no—
813C4—42no—
814C4—42no—
815C4—42no—
816C4—1062no—
817C4—1064no—
818C4—1062no—
819C4—1062no—
820C4—1064no—
821C4—2122no—
822C4—2122no—
823C4—2122no—
824C2—1064no—
825C2—2124no—
826C2C4×#41×D5311yescharacteristic
827C2#2028791411yescharacteristic
828C2#2028791711yescharacteristic
829C2#2028841012yes—
830C2#2028843312yes—
subgroupG/H
center, FrattiniC23C24×D53
commutatorC22×C53C24×C4
FittingC53×#2371C2
socle, cosocleC23×C53C25
prime radicalC2×#13133192C22
hypercenter#2371D53
hypocenterC53#34219
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ #2371

Complements

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

NH ≅ G/Ntype
2. #20277841C2semidirect
3. #20277829C2semidirect
4. #20277825C2semidirect
5. #20277825C2semidirect
6. #20277821C2semidirect
7. #20277677C2semidirect
8. #20277654C2semidirect
9. #20277596C2semidirect
10. #20277570C2semidirect
11. #20277444C2semidirect
13. #20277347C2semidirect
14. C4×#13133202C2semidirect
15. #20277236C2semidirect
16. #20277107C2semidirect
17. #20277075C2semidirect
18. #376×D53C2semidirect
19. C53×#2371C2semidirect
20. #16811158C4semidirect
119. #13133212C2×C4semidirect
120. #13133205C2×C4semidirect
121. #13133202C2×C4semidirect
122. #13133197C2×C4semidirect
124. #13133182C2×C4semidirect
127. #13133179C2×C4semidirect
128. #13133179C2×C4semidirect
129. #13133175C2×C4semidirect
164. C42×D53C2×C4semidirect
187. #125×C53C2×C4semidirect
415. #2371D53semidirect
523. C53#34219semidirect
536. #125C4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168111582
#202778412
#202778292
#202778252
#202778212
#202776772
#202776542
#202775962
#202775702
#202774442
#202774142
#202773472
C4×#131332022
#202772362
#202771072
#202770752
#376×D532
C53×#23712
#3421953