Finite Group Databasebeta

← #27547377

Subgroups — #27547377

Order 13568.

2118 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811158C211yesmaximal, characteristic
2#20277906C212yesmaximal, complemented
3#20277905C212yesmaximal, complemented
4#20277712C212yesmaximal, complemented
5#20277700C212yesmaximal, complemented
6#20277654C212yesmaximal, complemented
7#20277624C212yesmaximal, complemented
8#20277604C212yesmaximal, complemented
9#20277574C212yesmaximal, complemented
10#20277528C211yesmaximal, characteristic, complemented
11#20277525C211yesmaximal, characteristic, complemented
12#20277521C211yesmaximal, characteristic, complemented
13#20277444C212yesmaximal, complemented
14#20277414C212yesmaximal
15#20277364C212yesmaximal, complemented
16#20277347C212yesmaximal, complemented
17#20277119C211yesmaximal, characteristic, complemented
18#383×D53C211yesmaximal, characteristic, complemented
19C53×#2336C211yesmaximal, characteristic, complemented
20#16811158C4116yescomplemented
21C2×#13133212C2212yes—
22C2×#13133205C2211yescharacteristic
23C2×#13133202C2212yes—
24C2×#13133197C2211yescharacteristic
25C2×#13133192C2211yescharacteristic
26C2×#13133182C2211yescharacteristic
27C2×C4×D212C2212yes—
28C2×#13133179C2212yes—
29C2×#13133179C2211yescharacteristic
30C2×#13133179C2212yes—
31C2×#13133175C2212yes—
32C2×#13133174C2211yescharacteristic
33C2×#13133174C2211yescharacteristic
34C2×C42×D53C2211yescharacteristic
35#16810527C2212yes—
36#16810527C2212yes—
37#16810522C2212yes—
38#16810521C2212yes—
39#16810520C2212yes—
40#16810519C2212yes—
41#16810518C2212yes—
42#16810515C2212yes—
43#16810514C2212yes—
44#16810514C2212yes—
45#16810514C2212yes—
46#16810513C2212yes—
47#16810512C2212yes—
48#16810512C2212yes—
49#16810512C2212yes—
50#16810509C2212yes—
51#16810509C2212yes—
52#16810509C2212yes—
53#16810509C2212yes—
54#16810508C2212yes—
55#16810507C2212yes—
56#16810506C2212yes—
57#16810505C2212yes—
58#16810501C2212yes—
59#16810501C2212yes—
60#16810501C2212yes—
61#16810501C2212yes—
62#16810497C2212yes—
63#16810497C2212yes—
64#16810497C2212yes—
65#16810497C2212yes—
66#16810494C2212yes—
67#16810494C2212yes—
68#16810494C2212yes—
69#16810494C2212yes—
70#16810492C2212yes—
71#16810491C2211yescharacteristic
72#16810490C2212yes—
73#16810490C2212yes—
74#16810490C2212yes—
75#16810490C2211yescharacteristic
76#16810490C2211yescharacteristic
77#16810488C2212yes—
78#16810487C2212yes—
79#16810485C2212yes—
80#16810482C2212yes—
81#16810480C2212yes—
82#16810480C2212yes—
83C4⋊C4×Dic53C2212yes—
84C4×#11719919C2211yescharacteristic
85C4×#11719919C2211yescharacteristic
86C4×#11719919C2212yes—
87C4×C4⋊Dic53C2211yescharacteristic
88C4×#11719921C2212yes—
89C4×#11719921C2212yes—
90C4×#11719921C2212yes—
91#16810470C2212yes—
92#16810470C2212yes—
93#16810468C2212yes—
94#95×D53C2212yes—
95#95×D53C2211yescharacteristic
96#95×D53C2211yescharacteristic
97#95×D53C2212yes—
98#95×D53C2212yes—
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×D212C2312yes—
110C22×D212C2311yescharacteristic
111C22×C4×D53C2311yescharacteristic
112C22×C4×D53C2312yes—
113C22×C4×D53C2312yes—
114C22×C4×D53C2312yes—
115C22×C4×D53C2312yes—
116C22×C4×D53C2311yescharacteristic
117C22×C4×D53C2311yescharacteristic
118C22×C4×D53C2312yes—
119#13133212C2×C4116yescomplemented
120#13133205C2×C418yescomplemented
121#13133202C2×C4116yescomplemented
122#13133197C2×C418yescomplemented
123#13133192C2×C418yes—
124#13133182C2×C418yescomplemented
125C4×D212—44no—
126#13133179—44no—
127#13133179C2×C4116yescomplemented
128#13133179C2×C418yescomplemented
129#13133175C2×C4116yescomplemented
130#13133174—42no—
131#13133174—42no—
132C2×C4⋊Dic53C2312yes—
133C2×C4⋊Dic53C2312yes—
134C2×C4⋊Dic53C2312yes—
135C2×C4⋊Dic53C2312yes—
136C2×#11719919C2312yes—
137C2×#11719919C2312yes—
138C2×#11719919C2312yes—
139C2×#11719919C2312yes—
140C2×#11719919C2312yes—
141C2×#11719919C2312yes—
142C2×#11719919C2312yes—
143C2×#11719921C2312yes—
144C2×#11719921C2312yes—
145C2×#11719921C2312yes—
146C2×#11719921C2312yes—
147C2×#11719921C2312yes—
148C2×#11719921C2312yes—
149C2×#11719921C2312yes—
150C2×#11719921C2312yes—
151C2×#11719921C2312yes—
152C2×#11719921C2312yes—
153C2×#11719921C2312yes—
154C2×#11719921C2312yes—
155C2×#11719921C2312yes—
156C2×C4×Dic53C2312yes—
157C2×C4×Dic53C2312yes—
158C2×C4×Dic53C2312yes—
159C2×C4×Dic53C2312yes—
160C2×C4×Dic53C2311yescharacteristic
161C2×C4×Dic53C2311yescharacteristic
162C2×C4×Dic53C2311yescharacteristic
163C2×C4×Dic53C2311yescharacteristic
164C2×C4×Dic53C2311yescharacteristic
165C2×C4×Dic53C2312yes—
166C42×D53C2×C418yescomplemented
167#13133124C2312yes—
168#13133124C2312yes—
169#13133124C2312yes—
170#13133124C2312yes—
171#13133124C2312yes—
172#13133124C2312yes—
173#13133124C2312yes—
174#13133124C2312yes—
175#13133124C2312yes—
176#13133124C2312yes—
177#13133124C2312yes—
178#13133124C2312yes—
179#13133124C2312yes—
180#13133124C2312yes—
181#13133124C2311yescharacteristic
182#13133124C2312yes—
183#13133124C2311yescharacteristic
184#13133124C2312yes—
185#13133124C2312yes—
186#13133124C2312yes—
187#13133124C2312yes—
188#125×C53C2×C418yescomplemented
189C2×C4⋊C4×C53C2312yes—
190C2×C4⋊C4×C53C2312yes—
191C2×C4⋊C4×C53C2312yes—
192C2×C4⋊C4×C53C2311yescharacteristic
193C2×C4⋊C4×C53C2311yescharacteristic
194C2×C4⋊C4×C53C2312yes—
195C2×C4⋊C4×C53C2312yes—
196C2×C42×C53C2312yes—
197C2×C42×C53C2311yescharacteristic
198C2×C42×C53C2312yes—
199C2×C42×C53C2311yescharacteristic
200C2×C42×C53C2311yescharacteristic
201#95×C53C2311yescharacteristic
202#95×C53C2312yes—
203#95×C53C2312yes—
204#95×C53C2312yes—
205#95×C53C2312yes—
206#95×C53C2312yes—
207#95×C53C2312yes—
208#95×C53C2312yes—
209#95×C53C2311yescharacteristic
210C23×D53C2412yes—
211C23×D53C2411yescharacteristic
212C22×C4×C53C2412yes—
213C22×C4×C53C2412yes—
214C22×C4×C53C2412yes—
215C22×C4×C53C2412yes—
216C22×C4×C53C2411yescharacteristic
217C22×C4×C53C2411yescharacteristic
218C22×C4×C53C2412yes—
219C22×C4×C53C2412yes—
220C22×C4×C53C2411yescharacteristic
221C22×Dic53C2412yes—
222C22×Dic53C2412yes—
223C22×Dic53C2412yes—
224C22×Dic53C2412yes—
225C22×Dic53C2411yescharacteristic
226C22×Dic53C2412yes—
227C22×Dic53C2411yescharacteristic
228C22×Dic53C2411yescharacteristic
229C2×D212—24no—
230C2×D212—24no—
231C2×D212—42no—
232C2×D212C22×C418yes—
233C2×D212C22×C414yes—
234C2×C4×D53—22no—
235C2×C4×D53—22no—
236C2×C4×D53—24no—
237C2×C4×D53—24no—
238C2×C4×D53—42no—
239C2×C4×D53—42no—
240C2×C4×D53—42no—
241C2×C4×D53—42no—
242C2×C4×D53—42no—
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×D53—42no—
252C2×C4×D53C22×C414yes—
253C2×C4×D53C22×C414yes—
254C2×C4×D53C22×C414yes—
255C2×C4×D53C22×C418yes—
256C2×Dic106—42no—
257C2×Dic106C22×C414yes—
258C4⋊C4×C53—42no—
259C4⋊C4×C53—42no—
260C4⋊C4×C53—42no—
261C4⋊C4×C53C22×C418yes—
262C4⋊C4×C53C22×C414yes—
263C4⋊C4×C53C22×C418yes—
264C4⋊C4×C53C22×C414yes—
265C42×C53—42no—
266C42×C53—41no—
267C42×C53—41no—
268C42×C53—42no—
269C42×C53C22×C414yes—
270#11719921—24no—
271#11719921—24no—
272#11719921—42no—
273#11719921—42no—
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—42no—
284C4⋊Dic53—42no—
285C4⋊Dic53—42no—
286C4⋊Dic53C22×C418yes—
287#11719919—42no—
288#11719919—42no—
289#11719919—42no—
290#11719919—42no—
291#11719919—42no—
292#11719919—42no—
293#11719919C22×C418yes—
294C4×Dic53—42no—
295C4×Dic53—42no—
296C4×Dic53—42no—
297C4×Dic53—41no—
298C4×Dic53—41no—
299C4×Dic53—42no—
300C4×Dic53C22×C414yes—
301C4×Dic53C22×C414yes—
302C4×Dic53C22×C414yes—
303C4×Dic53C22×C418yes—
304C23×C53C2511yescharacteristic
305C22×D53—22no—
306C22×D53—22no—
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×D53H(5,𝔽2)12yes—
316C22×D532−1+412yes—
317C2×C4×C53—21no—
318C2×C4×C53—22no—
319C2×C4×C53—21no—
320C2×C4×C53—22no—
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×C53—22no—
336C2×C4×C53—22no—
337C2×C4×C53C23×C412yes—
338C2×C4×C53C23×C412yes—
339C2×C4×C53C23×C412yes—
340C2×C4×C53C23×C414yes—
341C2×C4×C53C23×C414yes—
342C2×Dic53—21no—
343C2×Dic53—21no—
344C2×Dic53—22no—
345C2×Dic53—22no—
346C2×Dic53—22no—
347C2×Dic53—22no—
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×Dic53—22no—
358C2×Dic53—22no—
359C2×Dic53—22no—
360C2×Dic53C23×C414yes—
361C2×Dic53C23×C412yes—
362C2×Dic53C23×C412yes—
363C2×Dic53C23×C412yes—
364D212—216no—
365D212—44no—
366C4×D53—28no—
367C4×D53—44no—
368C4×D53—48no—
369C4×D53—44no—
370C4×D53—84no—
371C4×D53—84no—
372C4×D53—84no—
373C4×D53—84no—
374Dic106—44no—
375#34401—531nomaximal, Sylow
376C22×C53C24×C411yescharacteristic
377C22×C53C2×H(5,𝔽2)11yescharacteristic
378C22×C53C2×2−1+411yescharacteristic
379C22×C53#58512yes—
380C22×C53#58512yes—
381C2×D53—22no—
382C2×D53—22no—
383C2×D53—24no—
384C2×D53—24no—
385C2×D53—24no—
386C2×D53—24no—
387C2×D53—24no—
388C2×D53—42no—
389C2×D53—42no—
390C2×D53—42no—
391C2×D53—42no—
392C2×D53#52014yes—
393C4×C53—22no—
394C4×C53—24no—
395C4×C53—22no—
396C4×C53—24no—
397C4×C53—22no—
398C4×C53—42no—
399C4×C53—42no—
400C4×C53—42no—
401C4×C53—42no—
402Dic53—22no—
403Dic53—24no—
404Dic53—22no—
405Dic53—22no—
406Dic53—42no—
407Dic53—42no—
408Dic53—42no—
409Dic53—42no—
410C2×#529—531no—
411#2383—532no—
412#2383—532no—
413#2359—532no—
414#2359—532no—
415#2353—532no—
416#2349—532no—
417#2347—532no—
418#2343—532no—
419#2337—531no—
420#2337—531no—
421#2336—531no—
422#2336D5311yescharacteristic, complemented
423#2329—532no—
424#2325—532no—
425#2320—532no—
426#2318—532no—
427#2285—531no—
428C2×#383—531no—
429C2×C53C2×#52011yescharacteristic
430C2×C53#342811yescharacteristic
431C2×C53#342811yescharacteristic
432C2×C53#356012yes—
433C2×C53#356412yes—
434D53—24no—
435D53—44no—
436#529—5316no—
437C2×#126—532no—
438C2×#125C2×D5311yescharacteristic
439C2×#124—531no—
440C2×#123—532no—
441C2×C22⋊Q8—531no—
442C2×#121—531no—
443C2×C4×Q8—531no—
444C2×C4×D4—531no—
445C2×C4×D4—532no—
446C2×C4×D4—532no—
447C2×C4×D4—532no—
448C2×#117—532no—
449C2×#117—531no—
450C2×#117—531no—
451C22×C42—531no—
452#391—532no—
453#391—532no—
454#389—532no—
455#389—532no—
456#389—532no—
457#389—532no—
458#389—532no—
459#389C2×D5312yes—
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#385—532no—
489#385—532no—
490#385—532no—
491#385—532no—
492#384—532no—
493#383—531no—
494#383—532no—
495#383—532no—
496#383—532no—
497#383—531no—
498#383—531no—
499#383C2×D5311yescharacteristic
500#382—532no—
501#382—532no—
502#381—532no—
503#380—532no—
504#380—532no—
505#380—532no—
506C4×C4⋊C4—532no—
507C4×C4⋊C4—532no—
508C4×C4⋊C4—531no—
509C4×C4⋊C4—531no—
510C4×C4⋊C4—531no—
511C4×C4⋊C4C2×D5311yescharacteristic
512C4×C4⋊C4C2×D5312yes—
513C4×C22⋊C4—532no—
514C4×C22⋊C4—532no—
515C4×C22⋊C4—532no—
516C4×C22⋊C4—532no—
517C4×C22⋊C4—532no—
518#376—532no—
519C2×#95—532no—
520C2×#95—532no—
521C2×#95—531no—
522C2×#95—531no—
523C2×#95—532no—
524C53#3440111yescharacteristic, complemented, Sylow
525C22×Q8—531no—
526C22×D4—532no—
527C22×D4—531no—
528C23×C4—531no—
529C23×C4—532no—
530C23×C4—531no—
531C23×C4—531no—
532C23×C4—532no—
533C23×C4—532no—
534C23×C4—532no—
535C23×C4—532no—
536#126—5316no—
537#125C4×D5318yescomplemented
538#124—538no—
539#123—5316no—
540C22⋊Q8—538no—
541#121—538no—
542C4×Q8—538no—
543C4×D4—538no—
544C4×D4—5316no—
545C4×D4—2124no—
546C4×D4—2124no—
547#117—5316no—
548#117—2122no—
549#117—2122no—
550C2×C4⋊C4—532no—
551C2×C4⋊C4—532no—
552C2×C4⋊C4—532no—
553C2×C4⋊C4—532no—
554C2×C4⋊C4—532no—
555C2×C4⋊C4—532no—
556C2×C4⋊C4—532no—
557C2×C4⋊C4—532no—
558C2×C4⋊C4—532no—
559C2×C4⋊C4—532no—
560C2×C4⋊C4—532no—
561C2×C4⋊C4C22×D5312yes—
562C2×C4⋊C4C22×D5312yes—
563C2×C4⋊C4C22×D5312yes—
564C2×C4⋊C4C22×D5312yes—
565C2×C4⋊C4C22×D5311yescharacteristic
566C2×C4⋊C4C22×D5312yes—
567C2×C4⋊C4C22×D5311yescharacteristic
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×C22⋊C4—532no—
575C2×C22⋊C4—532no—
576C2×C22⋊C4—532no—
577C2×C22⋊C4—532no—
578C2×C22⋊C4—532no—
579C2×C22⋊C4—532no—
580C2×C22⋊C4—532no—
581C2×C42—531no—
582C2×C42—532no—
583C2×C42—531no—
584C2×C42—531no—
585C2×C42—538no—
586C2×C42—531no—
587C2×C42—531no—
588C2×C42—532no—
589C2×C42—532no—
590C2×C42—532no—
591C2×C42—532no—
592C2×C42C22×D5311yescharacteristic
593C2×C42C22×D5311yescharacteristic
594C2×C42C22×D5312yes—
595C2×C42C22×D5312yes—
596C2×C42C22×D5311yescharacteristic
597#95—532no—
598#95—532no—
599#95—532no—
600#95—532no—
601#95—531no—
602#95—532no—
603#95—532no—
604#95—532no—
605#95—532no—
606#95—532no—
607#95—531no—
608#95—532no—
609#95—532no—
610#95—532no—
611#95—532no—
612#95—532no—
613#95—532no—
614#95—532no—
615#95—532no—
616#95—532no—
617#95—532no—
618#95C22×D5312yes—
619#95C22×D5311yescharacteristic
620#95C22×D5312yes—
621#95C22×D5311yescharacteristic
622#95C22×D5312yes—
623#95C22×D5312yes—
624#95C22×D5312yes—
625#95C22×D5312yes—
626#95C22×D5312yes—
627C24—531no—
628C24—532no—
629C2×Q8—534no—
630C2×Q8—2122no—
631C2×D4—538no—
632C2×D4—534no—
633C2×D4—1064no—
634C2×D4—1064no—
635C2×D4—2122no—
636C22×C4—531no—
637C22×C4—532no—
638C22×C4—531no—
639C22×C4—531no—
640C22×C4—534no—
641C22×C4—534no—
642C22×C4—534no—
643C22×C4—538no—
644C22×C4—532no—
645C22×C4—532no—
646C22×C4—532no—
647C22×C4—532no—
648C22×C4—1062no—
649C22×C4—1062no—
650C22×C4—1064no—
651C22×C4—1064no—
652C22×C4—2122no—
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—2122no—
663C22×C4—2122no—
664C22×C4—2122no—
665C22×C4—2122no—
666C22×C4C23×D5312yes—
667C22×C4C23×D5312yes—
668C22×C4C23×D5312yes—
669C22×C4C23×D5312yes—
670C22×C4C23×D5311yescharacteristic
671C22×C4C23×D5311yescharacteristic
672C22×C4C23×D5312yes—
673C22×C4C23×D5312yes—
674C22×C4C23×D5311yescharacteristic
675C4⋊C4—42no—
676C4⋊C4—42no—
677C4⋊C4—42no—
678C4⋊C4—538no—
679C4⋊C4—538no—
680C4⋊C4—2122no—
681C4⋊C4—2122no—
682C4⋊C4—2122no—
683C4⋊C4—2122no—
684C4⋊C4—2122no—
685C4⋊C4—2122no—
686C4⋊C4—2122no—
687C4⋊C4—2122no—
688C4⋊C4—2122no—
689C4⋊C4C2×C4×D5318yes—
690C4⋊C4C2×C4×D5314yes—
691C4⋊C4C2×C4×D5318yes—
692C4⋊C4C2×C4×D5314yes—
693C22⋊C4—538no—
694C22⋊C4—538no—
695C22⋊C4—538no—
696C22⋊C4—538no—
697C22⋊C4—538no—
698C22⋊C4—1064no—
699C22⋊C4—1064no—
700C22⋊C4—2122no—
701C22⋊C4—2122no—
702C22⋊C4—2122no—
703C22⋊C4—2122no—
704C22⋊C4—2122no—
705C22⋊C4—2122no—
706C42—41no—
707C42—41no—
708C42—42no—
709C42—42no—
710C42—534no—
711C42—534no—
712C42—534no—
713C42—538no—
714C42—2121no—
715C42—2121no—
716C42—2122no—
717C42—2122no—
718C42—2122no—
719C42—2122no—
720C42C2×C4×D5314yes—
721C23—532no—
722C23—532no—
723C23—532no—
724C23—534no—
725C23—1062no—
726C23—1062no—
727C23—1062no—
728C23—1062no—
729C23—1062no—
730C23—1062no—
731C23—1062no—
732C23—1062no—
733C23C24×D5311yescharacteristic
734Q8—2124no—
735D4—10616no—
736D4—2124no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—21no—
740C2×C4—22no—
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—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—532no—
758C2×C4—532no—
759C2×C4—532no—
760C2×C4—534no—
761C2×C4—1068no—
762C2×C4—1061no—
763C2×C4—1061no—
764C2×C4—1062no—
765C2×C4—1062no—
766C2×C4—1062no—
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—1062no—
778C2×C4—1062no—
779C2×C4—1062no—
780C2×C4—4244no—
781C2×C4—4244no—
782C2×C4—4244no—
783C2×C4—4244no—
784C2×C4—2124no—
785C2×C4—2128no—
786C2×C4—2124no—
787C2×C4C22×C4×D5312yes—
788C2×C4C22×C4×D5312yes—
789C2×C4C22×C4×D5312yes—
790C2×C4C22×C4×D5314yes—
791C2×C4C22×C4×D5314yes—
792C22—534no—
793C22—1064no—
794C22—1062no—
795C22—1062no—
796C22—1064no—
797C22—1064no—
798C22—1064no—
799C22—1064no—
800C22—2122no—
801C22—2122no—
802C22—2122no—
803C22—2122no—
804C22C23×C4×D5311yescharacteristic
805C22H(5,𝔽2)×D5311yescharacteristic
806C222−1+4×D5311yescharacteristic
807C22#1681145912yes—
808C22#1681146012yes—
809C4—22no—
810C4—24no—
811C4—24no—
812C4—22no—
813C4—22no—
814C4—42no—
815C4—42no—
816C4—42no—
817C4—42no—
818C4—1062no—
819C4—1062no—
820C4—1062no—
821C4—1064no—
822C4—2122no—
823C4—2122no—
824C4—2122no—
825C4—2122no—
826C2—1064no—
827C2—2124no—
828C2#520×D5311yescharacteristic
829C2#2028791411yescharacteristic
830C2#2028791711yescharacteristic
831C2#2028926812yes—
832C2#2028932812yes—
subgroupG/H
center, FrattiniC23C24×D53
commutatorC22×C53C24×C4
FittingC53×#2336C2
socle, cosocleC23×C53C25
prime radicalC2×#13133192C22
hypercenter#2336D53
hypocenterC53#34401
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ #2336

Complements

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

NH ≅ G/Ntype
2. #20277906C2semidirect
3. #20277905C2semidirect
4. #20277712C2semidirect
5. #20277700C2semidirect
6. #20277654C2semidirect
7. #20277624C2semidirect
8. #20277604C2semidirect
9. #20277574C2semidirect
10. #20277528C2semidirect
11. #20277525C2semidirect
12. #20277521C2semidirect
13. #20277444C2semidirect
15. #20277364C2semidirect
16. #20277347C2semidirect
17. #20277119C2semidirect
18. #383×D53C2semidirect
19. C53×#2336C2semidirect
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
166. C42×D53C2×C4semidirect
188. #125×C53C2×C4semidirect
422. #2336D53semidirect
524. C53#34401semidirect
537. #125C4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168111582
#202779062
#202779052
#202777122
#202777002
#202776542
#202776242
#202776042
#202775742
#202775282
#202775252
#202775212
#202774442
#202774142
#202773642
#202773472
#202771192
#383×D532
C53×#23362
#3440153