Finite Group Databasebeta

← #27543020

Subgroups — #27543020

Order 13568.

2202 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811158C211yesmaximal, characteristic
2#20277528C211yesmaximal, characteristic, complemented
3#20277525C211yesmaximal, characteristic, complemented
4#20277521C211yesmaximal, characteristic, complemented
5#20277511C212yesmaximal, complemented
6#20277499C212yesmaximal, complemented
7#20277495C212yesmaximal, complemented
8#20277483C212yesmaximal, complemented
9#20277479C212yesmaximal
10#20277467C212yesmaximal, complemented
11#20277207C212yesmaximal, complemented
12#20277188C212yesmaximal, complemented
13#20277173C212yesmaximal, complemented
14#20277153C212yesmaximal, complemented
15#20277153C212yesmaximal, complemented
16#20277112C211yesmaximal, characteristic, complemented
17C4×#13133175C212yesmaximal, complemented
18C4×#13133175C211yesmaximal, characteristic, complemented
19C53×#2336C211yesmaximal, characteristic, complemented
20#16811158C4116yescomplemented
21C2×#13133212C2212yes—
22C2×#13133205C2211yescharacteristic
23C2×#13133202C2212yes—
24C2×#13133197C2211yescharacteristic
25C2×#13133192C2211yescharacteristic
26C2×#13133182C2211yescharacteristic
27C2×#13133179C2211yescharacteristic
28C2×#13133179C2212yes—
29C2×#13133175C2212yes—
30C2×#13133175C2212yes—
31C2×#13133175C2212yes—
32C2×C42×D53C2212yes—
33C2×C42×D53C2211yescharacteristic
34#16810527C2212yes—
35#16810527C2212yes—
36#16810525C2212yes—
37#16810524C2212yes—
38#16810522C2212yes—
39#16810520C2212yes—
40#16810518C2212yes—
41#16810515C2212yes—
42#16810515C2212yes—
43#16810515C2212yes—
44#16810514C2212yes—
45#16810514C2212yes—
46#16810514C2212yes—
47#16810513C2212yes—
48#16810513C2212yes—
49#16810513C2212yes—
50#16810512C2212yes—
51#16810512C2212yes—
52#16810512C2212yes—
53#16810509C2212yes—
54#16810509C2212yes—
55#16810509C2212yes—
56#16810509C2212yes—
57#16810508C2212yes—
58#16810507C2212yes—
59#16810506C2212yes—
60#16810505C2212yes—
61#16810501C2212yes—
62#16810501C2212yes—
63#16810501C2212yes—
64#16810501C2212yes—
65#16810497C2212yes—
66#16810497C2212yes—
67#16810494C2212yes—
68#16810494C2212yes—
69#16810491C2211yescharacteristic
70#16810487C2211yescharacteristic
71#16810487C2211yescharacteristic
72#16810485C2212yes—
73#16810482C2212yes—
74C4⋊C4×Dic53C2212yes—
75C4⋊C4×Dic53C2212yes—
76C4⋊C4×Dic53C2212yes—
77C4⋊C4×Dic53C2212yes—
78C4×C4⋊Dic53C2211yescharacteristic
79C4×C4⋊Dic53C2212yes—
80#16810474C2212yes—
81#16810474C2212yes—
82C4×#11719921C2211yescharacteristic
83C4×#11719921C2212yes—
84C4×#11719921C2212yes—
85C4×#11719921C2211yescharacteristic
86#16810470C2212yes—
87#16810470C2212yes—
88#16810470C2212yes—
89#16810470C2211yescharacteristic
90#16810470C2211yescharacteristic
91#16810470C2212yes—
92#16810470C2212yes—
93#16810468C2212yes—
94#16810468C2212yes—
95#16810468C2212yes—
96C42×Dic53C2211yescharacteristic
97C42×Dic53C2212yes—
98C42×Dic53C2211yescharacteristic
99C2×#125×C53C2211yescharacteristic
100C53×#389C2212yes—
101C53×#387C2212yes—
102C53×#387C2212yes—
103C53×#387C2212yes—
104C53×#387C2212yes—
105C53×#383C2211yescharacteristic
106C4×C4⋊C4×C53C2211yescharacteristic
107C4×C4⋊C4×C53C2212yes—
108C22×Dic106C2311yescharacteristic
109C22×D212C2311yescharacteristic
110C22×D212C2312yes—
111C22×C4×D53C2312yes—
112C22×C4×D53C2311yescharacteristic
113C22×C4×D53C2312yes—
114C22×C4×D53C2312yes—
115C22×C4×D53C2311yescharacteristic
116C22×C4×D53C2311yescharacteristic
117#13133212C2×C4116yescomplemented
118#13133205C2×C418yes—
119#13133202C2×C4116yescomplemented
120#13133197C2×C418yescomplemented
121#13133192C2×C418yes—
122#13133182C2×C418yescomplemented
123#13133179C2×C418yes—
124#13133179C2×C4116yescomplemented
125#13133175—28no—
126#13133175—28no—
127#13133175C2×C4116yescomplemented
128C2×C4⋊Dic53C2312yes—
129C2×C4⋊Dic53C2312yes—
130C2×C4⋊Dic53C2312yes—
131C2×C4⋊Dic53C2312yes—
132C2×#11719919C2312yes—
133C2×#11719919C2312yes—
134C2×#11719919C2312yes—
135C2×#11719919C2312yes—
136C2×#11719919C2312yes—
137C2×#11719921C2312yes—
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×#11719921C2312yes—
152C2×C4×Dic53C2312yes—
153C2×C4×Dic53C2312yes—
154C2×C4×Dic53C2312yes—
155C2×C4×Dic53C2312yes—
156C2×C4×Dic53C2312yes—
157C2×C4×Dic53C2312yes—
158C2×C4×Dic53C2311yescharacteristic
159C2×C4×Dic53C2312yes—
160C2×C4×Dic53C2312yes—
161C2×C4×Dic53C2312yes—
162C2×C4×Dic53C2311yescharacteristic
163C2×C4×Dic53C2311yescharacteristic
164C2×C4×Dic53C2311yescharacteristic
165C2×C4×Dic53C2311yescharacteristic
166C2×C4×Dic53C2312yes—
167C2×C4×Dic53C2312yes—
168C42×D53—28no—
169C42×D53C2×C418yescomplemented
170#13133124C2312yes—
171#13133124C2312yes—
172#13133124C2312yes—
173#13133124C2312yes—
174#13133124C2312yes—
175#13133124C2312yes—
176#13133124C2312yes—
177#13133124C2312yes—
178#13133124C2312yes—
179#13133124C2312yes—
180#13133124C2312yes—
181#13133124C2312yes—
182#13133124C2312yes—
183#13133124C2312yes—
184#13133124C2311yescharacteristic
185#13133124C2312yes—
186#13133124C2311yescharacteristic
187#125×C53C2×C418yescomplemented
188C2×C4⋊C4×C53C2312yes—
189C2×C4⋊C4×C53C2312yes—
190C2×C4⋊C4×C53C2312yes—
191C2×C4⋊C4×C53C2311yescharacteristic
192C2×C4⋊C4×C53C2311yescharacteristic
193C2×C4⋊C4×C53C2312yes—
194C2×C4⋊C4×C53C2312yes—
195C2×C42×C53C2312yes—
196C2×C42×C53C2312yes—
197C2×C42×C53C2311yescharacteristic
198C2×C42×C53C2311yescharacteristic
199C2×C42×C53C2311yescharacteristic
200#95×C53C2311yescharacteristic
201#95×C53C2312yes—
202#95×C53C2312yes—
203#95×C53C2312yes—
204#95×C53C2312yes—
205#95×C53C2312yes—
206#95×C53C2312yes—
207#95×C53C2312yes—
208#95×C53C2311yescharacteristic
209C23×D53C2412yes—
210C23×D53C2411yescharacteristic
211C22×C4×C53C2412yes—
212C22×C4×C53C2412yes—
213C22×C4×C53C2412yes—
214C22×C4×C53C2411yescharacteristic
215C22×C4×C53C2411yescharacteristic
216C22×C4×C53C2412yes—
217C22×C4×C53C2412yes—
218C22×C4×C53C2411yescharacteristic
219C22×C4×C53C2412yes—
220C22×Dic53C2412yes—
221C22×Dic53C2412yes—
222C22×Dic53C2412yes—
223C22×Dic53C2411yescharacteristic
224C22×Dic53C2412yes—
225C22×Dic53C2411yescharacteristic
226C22×Dic53C2412yes—
227C22×Dic53C2411yescharacteristic
228C2×D212—42no—
229C2×D212—42no—
230C2×D212—42no—
231C2×D212C22×C414yes—
232C2×D212C22×C418yes—
233C2×C4×D53—24no—
234C2×C4×D53—24no—
235C2×C4×D53—24no—
236C2×C4×D53—24no—
237C2×C4×D53—24no—
238C2×C4×D53—42no—
239C2×C4×D53—41no—
240C2×C4×D53—41no—
241C2×C4×D53—42no—
242C2×C4×D53—42no—
243C2×C4×D53—42no—
244C2×C4×D53—42no—
245C2×C4×D53C22×C414yes—
246C2×C4×D53C22×C418yes—
247C2×C4×D53C22×C414yes—
248C2×C4×D53C22×C414yes—
249C2×Dic106—42no—
250C2×Dic106C22×C414yes—
251C4⋊C4×C53—24no—
252C4⋊C4×C53—24no—
253C4⋊C4×C53—42no—
254C4⋊C4×C53C22×C418yes—
255C4⋊C4×C53C22×C414yes—
256C4⋊C4×C53C22×C418yes—
257C4⋊C4×C53C22×C414yes—
258C42×C53—24no—
259C42×C53—41no—
260C42×C53—42no—
261C42×C53—41no—
262C42×C53C22×C414yes—
263#11719921—24no—
264#11719921—24no—
265#11719921—24no—
266#11719921—24no—
267#11719921—42no—
268#11719921—42no—
269#11719921—42no—
270#11719921—42no—
271#11719921—42no—
272#11719921—42no—
273#11719921C22×C418yes—
274#11719921C22×C418yes—
275#11719921C22×C418yes—
276#11719921C22×C418yes—
277#11719921C22×C418yes—
278C4⋊Dic53—24no—
279C4⋊Dic53—24no—
280C4⋊Dic53—42no—
281C4⋊Dic53C22×C418yes—
282#11719919—42no—
283#11719919—42no—
284#11719919—42no—
285#11719919—42no—
286#11719919C22×C418yes—
287C4×Dic53—24no—
288C4×Dic53—24no—
289C4×Dic53—24no—
290C4×Dic53—24no—
291C4×Dic53—42no—
292C4×Dic53—42no—
293C4×Dic53—42no—
294C4×Dic53—41no—
295C4×Dic53—42no—
296C4×Dic53—42no—
297C4×Dic53—41no—
298C4×Dic53C22×C414yes—
299C4×Dic53C22×C414yes—
300C4×Dic53C22×C414yes—
301C4×Dic53C22×C418yes—
302C4×Dic53#4118yes—
303C23×C53C2511yescharacteristic
304C22×D53—22no—
305C22×D53—22no—
306C22×D53—22no—
307C22×D53—21no—
308C22×D53—21no—
309C22×D53—22no—
310C22×D53—22no—
311C22×D53—22no—
312C22×D53—22no—
313C22×D53—22no—
314C22×D53C23×C412yes—
315C22×D53C23×C414yes—
316C2×C4×C53—22no—
317C2×C4×C53—22no—
318C2×C4×C53—22no—
319C2×C4×C53—22no—
320C2×C4×C53—21no—
321C2×C4×C53—22no—
322C2×C4×C53—21no—
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—21no—
347C2×Dic53—21no—
348C2×Dic53—22no—
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×Dic53C23×C414yes—
358C2×Dic53C23×C412yes—
359C2×Dic53C23×C412yes—
360C2×Dic53C23×C412yes—
361C2×Dic53C2×#4114yes—
362C2×Dic53C2×#4114yes—
363D212—44no—
364D212—48no—
365C4×D53—216no—
366C4×D53—28no—
367C4×D53—44no—
368C4×D53—44no—
369C4×D53—48no—
370C4×D53—48no—
371Dic106—44no—
372#34081—531nomaximal, Sylow
373C22×C53C24×C411yescharacteristic
374C22×C53C22×#4112yes—
375C22×C53#58511yescharacteristic
376C22×C53#58512yes—
377C22×C53#58511yescharacteristic
378C2×D53—24no—
379C2×D53—22no—
380C2×D53—22no—
381C2×D53—22no—
382C2×D53—24no—
383C2×D53—24no—
384C2×D53—42no—
385C2×D53—42no—
386C2×D53—42no—
387C2×D53—42no—
388C2×D53—42no—
389C2×D53—42no—
390C4×C53—24no—
391C4×C53—22no—
392C4×C53—22no—
393C4×C53—22no—
394C4×C53—24no—
395C4×C53—24no—
396C4×C53—42no—
397C4×C53—42no—
398C4×C53—42no—
399Dic53—24no—
400Dic53—22no—
401Dic53—22no—
402Dic53—24no—
403Dic53—42no—
404Dic53—42no—
405Dic53—42no—
406Dic53C4×#4114yes—
407C2×#529—531no—
408#2337—531no—
409#2337—531no—
410#2336—531no—
411#2336D5311yescharacteristic, complemented
412#2335—532no—
413#2335—532no—
414#2334—532no—
415#2334—532no—
416#2333—532no—
417#2332—532no—
418#2298—532no—
419#2295—532no—
420#2293—532no—
421#2290—532no—
422#2290—532no—
423#2283—531no—
424C4×#117—532no—
425C4×#117—531no—
426C2×C53C2×C4×#4111yescharacteristic
427C2×C53#342811yescharacteristic
428C2×C53#342811yescharacteristic
429C2×C53#345512yes—
430C2×C53#345512yes—
431D53—42no—
432D53—44no—
433#529—5316no—
434C2×#126—532no—
435C2×#125C2×D5311yescharacteristic
436C2×#124—531no—
437C2×#123—532no—
438C2×C22⋊Q8—531no—
439C2×#121—531no—
440C2×C4×Q8—531no—
441C2×C4×D4—531no—
442C2×C4×D4—532no—
443C2×#117—532no—
444C2×#117—532no—
445C2×#117—532no—
446C22×C42—531no—
447C22×C42—532no—
448#391—532no—
449#391—532no—
450#390—532no—
451#390—532no—
452#389—532no—
453#389—532no—
454#389—532no—
455#389C2×D5312yes—
456#388—532no—
457#388—532no—
458#388—532no—
459#388—532no—
460#388—532no—
461#388—532no—
462#388—532no—
463#388—532no—
464#388—532no—
465#388—532no—
466#388—532no—
467#388—532no—
468#387—532no—
469#387—532no—
470#387—532no—
471#387—532no—
472#387—532no—
473#387—532no—
474#387—532no—
475#387—532no—
476#387C2×D5312yes—
477#387C2×D5312yes—
478#387C2×D5312yes—
479#387C2×D5312yes—
480#386—532no—
481#386—532no—
482#386—532no—
483#386—532no—
484#385—532no—
485#385—532no—
486#385—532no—
487#385—532no—
488#383—531no—
489#383C2×D5311yescharacteristic
490#382—531no—
491#382—531no—
492#381—532no—
493#380—532no—
494C4×C4⋊C4—532no—
495C4×C4⋊C4—532no—
496C4×C4⋊C4—532no—
497C4×C4⋊C4—532no—
498C4×C4⋊C4—532no—
499C4×C4⋊C4—531no—
500C4×C4⋊C4—532no—
501C4×C4⋊C4—532no—
502C4×C4⋊C4C2×D5312yes—
503C4×C4⋊C4C2×D5311yescharacteristic
504C4×C22⋊C4—532no—
505C4×C22⋊C4—531no—
506C4×C22⋊C4—531no—
507C4×C22⋊C4—532no—
508C4×C22⋊C4—532no—
509C4×C22⋊C4—532no—
510C4×C22⋊C4—532no—
511C4×C22⋊C4—531no—
512C4×C22⋊C4—531no—
513C4×C22⋊C4—532no—
514C4×C22⋊C4—532no—
515#376—532no—
516#376—532no—
517#376—532no—
518C43—531no—
519C43—532no—
520C43—531no—
521C53#3408111yescharacteristic, complemented, Sylow
522C22×Q8—531no—
523C22×D4—532no—
524C22×D4—531no—
525C23×C4—531no—
526C23×C4—532no—
527C23×C4—531no—
528C23×C4—531no—
529C23×C4—532no—
530C23×C4—532no—
531#126—5316no—
532#125C4×D5318yescomplemented
533#124—538no—
534#123—5316no—
535C22⋊Q8—538no—
536#121—538no—
537C4×Q8—538no—
538C4×D4—538no—
539C4×D4—5316no—
540#117—5316no—
541#117—1068no—
542#117—1068no—
543C2×C4⋊C4—532no—
544C2×C4⋊C4—532no—
545C2×C4⋊C4—532no—
546C2×C4⋊C4—532no—
547C2×C4⋊C4—532no—
548C2×C4⋊C4—532no—
549C2×C4⋊C4—532no—
550C2×C4⋊C4—532no—
551C2×C4⋊C4—532no—
552C2×C4⋊C4C22×D5312yes—
553C2×C4⋊C4C22×D5312yes—
554C2×C4⋊C4C22×D5312yes—
555C2×C4⋊C4C22×D5312yes—
556C2×C4⋊C4C22×D5311yescharacteristic
557C2×C4⋊C4C22×D5312yes—
558C2×C4⋊C4C22×D5311yescharacteristic
559C2×C22⋊C4—532no—
560C2×C22⋊C4—532no—
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—532no—
577C2×C42—531no—
578C2×C42—531no—
579C2×C42—538no—
580C2×C42—532no—
581C2×C42—532no—
582C2×C42—532no—
583C2×C42—532no—
584C2×C42—531no—
585C2×C42—532no—
586C2×C42—532no—
587C2×C42—531no—
588C2×C42—532no—
589C2×C42—532no—
590C2×C42—532no—
591C2×C42—1068no—
592C2×C42C22×D5312yes—
593C2×C42C22×D5311yescharacteristic
594C2×C42C22×D5312yes—
595C2×C42C22×D5311yescharacteristic
596C2×C42C22×D5311yescharacteristic
597#95—532no—
598#95—532no—
599#95—532no—
600#95—532no—
601#95—532no—
602#95—532no—
603#95—532no—
604#95—532no—
605#95—532no—
606#95—531no—
607#95—531no—
608#95—532no—
609#95—532no—
610#95—532no—
611#95—532no—
612#95—532no—
613#95—532no—
614#95C22×D5312yes—
615#95C22×D5312yes—
616#95C22×D5312yes—
617#95C22×D5311yescharacteristic
618#95C22×D5311yescharacteristic
619#95C22×D5312yes—
620#95C22×D5312yes—
621#95C22×D5312yes—
622#95C22×D5312yes—
623C24—532no—
624C24—531no—
625C2×Q8—534no—
626C2×Q8—2122no—
627C2×D4—538no—
628C2×D4—534no—
629C2×D4—2122no—
630C2×D4—2122no—
631C2×D4—2122no—
632C22×C4—531no—
633C22×C4—531no—
634C22×C4—532no—
635C22×C4—532no—
636C22×C4—531no—
637C22×C4—534no—
638C22×C4—538no—
639C22×C4—534no—
640C22×C4—534no—
641C22×C4—532no—
642C22×C4—532no—
643C22×C4—532no—
644C22×C4—1064no—
645C22×C4—1064no—
646C22×C4—1064no—
647C22×C4—1064no—
648C22×C4—1064no—
649C22×C4—2121no—
650C22×C4—2122no—
651C22×C4—2121no—
652C22×C4—2122no—
653C22×C4—2122no—
654C22×C4—2122no—
655C22×C4—2122no—
656C22×C4C23×D5312yes—
657C22×C4C23×D5312yes—
658C22×C4C23×D5312yes—
659C22×C4C23×D5311yescharacteristic
660C22×C4C23×D5311yescharacteristic
661C22×C4C23×D5312yes—
662C22×C4C23×D5312yes—
663C22×C4C23×D5311yescharacteristic
664C22×C4C23×D5312yes—
665C4⋊C4—24no—
666C4⋊C4—24no—
667C4⋊C4—42no—
668C4⋊C4—538no—
669C4⋊C4—538no—
670C4⋊C4—1064no—
671C4⋊C4—1064no—
672C4⋊C4—2122no—
673C4⋊C4—2122no—
674C4⋊C4—2122no—
675C4⋊C4—2122no—
676C4⋊C4—2122no—
677C4⋊C4C2×C4×D5318yes—
678C4⋊C4C2×C4×D5314yes—
679C4⋊C4C2×C4×D5318yes—
680C4⋊C4C2×C4×D5314yes—
681C22⋊C4—538no—
682C22⋊C4—538no—
683C22⋊C4—538no—
684C22⋊C4—538no—
685C22⋊C4—538no—
686C22⋊C4—1064no—
687C22⋊C4—1064no—
688C22⋊C4—1064no—
689C22⋊C4—1064no—
690C22⋊C4—2122no—
691C22⋊C4—2122no—
692C22⋊C4—2122no—
693C22⋊C4—2122no—
694C22⋊C4—2122no—
695C22⋊C4—2122no—
696C42—24no—
697C42—41no—
698C42—42no—
699C42—41no—
700C42—534no—
701C42—534no—
702C42—534no—
703C42—538no—
704C42—538no—
705C42—1064no—
706C42—1064no—
707C42—1064no—
708C42—1064no—
709C42—2122no—
710C42—2121no—
711C42—2122no—
712C42—2121no—
713C42—2122no—
714C42—2122no—
715C42—2122no—
716C42C2×C4×D5314yes—
717C23—534no—
718C23—532no—
719C23—1062no—
720C23—1062no—
721C23—1062no—
722C23—1062no—
723C23—1061no—
724C23—1062no—
725C23—1062no—
726C23—1062no—
727C23—1062no—
728C23—1061no—
729C23C24×D5311yescharacteristic
730Q8—2124no—
731D4—2128no—
732D4—2124no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—21no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—532no—
753C2×C4—534no—
754C2×C4—532no—
755C2×C4—532no—
756C2×C4—534no—
757C2×C4—534no—
758C2×C4—1068no—
759C2×C4—10616no—
760C2×C4—1061no—
761C2×C4—1062no—
762C2×C4—1062no—
763C2×C4—1062no—
764C2×C4—1062no—
765C2×C4—1062no—
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—2124no—
777C2×C4—2124no—
778C2×C4—2128no—
779C2×C4—2128no—
780C2×C4C22×C4×D5312yes—
781C2×C4C22×C4×D5312yes—
782C2×C4C22×C4×D5312yes—
783C2×C4C22×C4×D5314yes—
784C2×C4C22×C4×D5314yes—
785C2×C4#41×D5314yes—
786C22—1064no—
787C22—1062no—
788C22—1062no—
789C22—1064no—
790C22—1062no—
791C22—1064no—
792C22—2122no—
793C22—2122no—
794C22—2122no—
795C22—2122no—
796C22—2122no—
797C22—2122no—
798C22C23×C4×D5311yescharacteristic
799C22C2×#41×D5312yes—
800C22#1681145811yescharacteristic
801C22#1681146012yes—
802C22#1681146011yescharacteristic
803C4—24no—
804C4—24no—
805C4—22no—
806C4—22no—
807C4—24no—
808C4—22no—
809C4—42no—
810C4—42no—
811C4—42no—
812C4—534no—
813C4—1064no—
814C4—1062no—
815C4—1062no—
816C4—1064no—
817C4—2122no—
818C4—2122no—
819C4—2122no—
820C2—2122no—
821C2—2124no—
822C2C4×#41×D5311yescharacteristic
823C2#2028791511yescharacteristic
824C2#2028791711yescharacteristic
825C2#2028810112yes—
826C2#2028810612yes—
subgroupG/H
center, FrattiniC23C24×D53
commutatorC22×C53C24×C4
FittingC53×#2336C2
socle, cosocleC23×C53C25
prime radicalC2×#13133192C22
hypercenter#2336D53
hypocenterC53#34081
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ #2336

Complements

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

NH ≅ G/Ntype
2. #20277528C2semidirect
3. #20277525C2semidirect
4. #20277521C2semidirect
5. #20277511C2semidirect
6. #20277499C2semidirect
7. #20277495C2semidirect
8. #20277483C2semidirect
10. #20277467C2semidirect
11. #20277207C2semidirect
12. #20277188C2semidirect
13. #20277173C2semidirect
14. #20277153C2semidirect
15. #20277153C2semidirect
16. #20277112C2semidirect
17. C4×#13133175C2semidirect
18. C4×#13133175C2semidirect
19. C53×#2336C2semidirect
20. #16811158C4semidirect
117. #13133212C2×C4semidirect
119. #13133202C2×C4semidirect
120. #13133197C2×C4semidirect
122. #13133182C2×C4semidirect
124. #13133179C2×C4semidirect
127. #13133175C2×C4semidirect
169. C42×D53C2×C4semidirect
187. #125×C53C2×C4semidirect
411. #2336D53semidirect
521. C53#34081semidirect
532. #125C4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168111582
#202775282
#202775252
#202775212
#202775112
#202774992
#202774952
#202774832
#202774792
#202774672
#202772072
#202771882
#202771732
#202771532
#202771122
C4×#131331752
C53×#23362
#3408153