Finite Group Databasebeta

← #27385146

Subgroups — #27385146

Order 13568.

1342 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#131×D53C211yesmaximal, characteristic
2C2×#16810670C211yesmaximal, characteristic, complemented
3#424×D53C211yesmaximal, characteristic, complemented
4C2×#16810638C211yesmaximal, characteristic
5#20283230C211yesmaximal, characteristic
6#20274993C211yesmaximal, characteristic, complemented
7#20274992C211yesmaximal, characteristic, complemented
8#20274991C211yesmaximal, characteristic, complemented
9#20274990C211yesmaximal, characteristic, complemented
10#20274989C211yesmaximal, characteristic, complemented
11#20274988C211yesmaximal, characteristic, complemented
12#20274987C211yesmaximal, characteristic, complemented
13#20274423C211yesmaximal, characteristic, complemented
14#20274410C211yesmaximal, characteristic, complemented
15C53×#1866C211yesmaximal, characteristic, complemented
16C2×#41×D53C2211yescharacteristic
17C2×#13133225—21no—
18C2×#13133225C2211yescharacteristic
19C2×#13133224C2211yescharacteristic
20C2×#13133223—21no—
21C2×#13133223C2211yescharacteristic
22#131×D53—24no—
23#131×D53—24no—
24C22×#11719912C2211yescharacteristic
25C2×M16×D53—21no—
26C2×M16×D53C2211yescharacteristic
27C2×M16×D53C2211yescharacteristic
28C22×C8×D53—21no—
29C22×C8×D53C2211yescharacteristic
30C2×#13133174C2211yescharacteristic
31#117×D53C2211yescharacteristic
32#16810670—24no—
33C2×#13133153C2211yescharacteristic, complemented
34C2×#13133152C2211yescharacteristic, complemented
35C2×#13133152C2211yescharacteristic, complemented
36#16810651C2211yescharacteristic, complemented
37#16810650C2211yescharacteristic, complemented
38#16810649C2211yescharacteristic, complemented
39#16810648—21no—
40#16810648—21no—
41C4⋊C8×D53—21no—
42C4⋊C8×D53—21no—
43#16810638—24no—
44C2×#13133145C2211yescharacteristic
45C2×#13133144C2211yescharacteristic
46C2×#13133143C2211yescharacteristic
47#16810630C411yescharacteristic, complemented
48#16810630C411yescharacteristic, complemented
49#16810626C411yescharacteristic, complemented
50#16810626C411yescharacteristic, complemented
51#16810623C411yescharacteristic, complemented
52#16810623C411yescharacteristic, complemented
53#16810621C411yescharacteristic, complemented
54#16810621C411yescharacteristic, complemented
55#16810620C2211yescharacteristic
56#16810619C2211yescharacteristic
57#16810617C2211yescharacteristic
58#16810384C2211yescharacteristic, complemented
59#16810383C2211yescharacteristic, complemented
60#16810382C2211yescharacteristic, complemented
61#16810378C2211yescharacteristic, complemented
62#16810377C2211yescharacteristic, complemented
63#16810377C2211yescharacteristic, complemented
64C2×#131×C53C2211yescharacteristic
65C2×#108×C53C2211yescharacteristic, complemented
66C53×#424C2211yescharacteristic, complemented
67C2×#104×C53C2211yescharacteristic
68C53×#416C2211yescharacteristic
69C53×#339C2211yescharacteristic, complemented
70C53×#336C2211yescharacteristic, complemented
71C2×#11719949C2×C411yescharacteristic
72C2×#11719945—21no—
73C2×#11719945C2311yescharacteristic
74C2×#11719947—21no—
75C2×#11719947C2×C411yescharacteristic
76#41×D53—22no—
77#41×D53—22no—
78#41×D53D414yes—
79#41×D53Q814yes—
80C2×Q8×D53C2×C411yescharacteristic
81C2×D4×D53—21no—
82C2×D4×D53C2×C411yescharacteristic
83C22×C4×D53—21no—
84C22×C4×D53C2311yescharacteristic
85#13133225—28no—
86#13133225—22no—
87#13133225—22no—
88#13133224—22no—
89#13133224—22no—
90#13133223—28no—
91#13133223—22no—
92#13133223—22no—
93C2×#11719917—21no—
94C2×#11719917C2311yescharacteristic
95C2×#11719917C2311yescharacteristic
96C2×#11719912—21no—
97C2×#11719912—21no—
98C2×#11719912—21no—
99C2×#11719912—22no—
100C2×#11719912—21no—
101C2×#11719912—22no—
102C2×#11719912C2×C411yescharacteristic
103C2×#11719912C2×C411yescharacteristic
104C2×#11719912C2×C411yescharacteristic
105C2×#11719912C2×C411yescharacteristic
106M16×D53—28no—
107M16×D53—22no—
108M16×D53—22no—
109M16×D53—22no—
110M16×D53D414yes—
111C22×#88322—21no—
112C22×#88322C2311yescharacteristic
113C22×#88322C2311yescharacteristic
114C2×C8×D53—28no—
115C2×C8×D53—21no—
116C2×C8×D53—21no—
117C2×C8×D53—21no—
118C2×C8×D53—22no—
119C2×C8×D53—22no—
120C2×C8×D53—21no—
121C2×C8×D53D411yescharacteristic
122C2×C8×D53D411yescharacteristic
123C2×C8×D53D411yescharacteristic
124C2×C8×D53D411yescharacteristic
125#13133176C2311yescharacteristic
126#13133175C2×C411yescharacteristic
127#13133175C2×C411yescharacteristic
128#13133174—21no—
129#13133174—22no—
130#13133174—22no—
131#13133173—21no—
132C2×#11719919—21no—
133C4⋊C4×D53C2×C411yescharacteristic
134C4⋊C4×D53C2×C411yescharacteristic
135C2×#11719921—21no—
136C22⋊C4×D53—21no—
137C2×C4×Dic53C2311yescharacteristic
138C42×D53—21no—
139#13133153—22no—
140#13133152—22no—
141#13133152—22no—
142C4⋊#88322—21no—
143C4⋊#88322—21no—
144#13133146—21no—
145#13133146—21no—
146#13133146—21no—
147#13133146—21no—
148#13133145—22no—
149#13133144—22no—
150#13133143—22no—
151#13133142C2×C411yescharacteristic
152#13133142C2×C411yescharacteristic
153#13133141C2×C411yescharacteristic
154#13133141C2×C411yescharacteristic
155#13133140C2×C411yescharacteristic
156#13133140C2×C411yescharacteristic
157#13133139C2×C411yescharacteristic
158#13133139C2×C411yescharacteristic
159#13133138C2×C411yescharacteristic
160#13133138C2×C411yescharacteristic
161#13133137C2×C411yescharacteristic
162#13133137C2×C411yescharacteristic
163C2×#41×C53C2311yescharacteristic
164#131×C53—22no—
165#131×C53—22no—
166C2×M16×C53—21no—
167C2×M16×C53C2311yescharacteristic
168C2×M16×C53C2311yescharacteristic
169C22×C8×C53—21no—
170C22×C8×C53C2311yescharacteristic
171C22×C8×C53C2311yescharacteristic
172#117×C53C2311yescharacteristic
173C2×C42×C53C2311yescharacteristic
174#108×C53—22no—
175C4⋊C8×C53—21no—
176C4⋊C8×C53—21no—
177#104×C53—22no—
178#103×C53C2×C411yescharacteristic
179#103×C53C2×C411yescharacteristic
180#102×C53C2×C411yescharacteristic
181#102×C53C2×C411yescharacteristic
182C23×D53—21no—
183C23×D53#4111yescharacteristic
184#41×C53—21no—
185#41×C53—21no—
186#41×C53C2×D412yes—
187#41×C53C2×Q812yes—
188C2×Q8×C53C22×C411yescharacteristic
189C2×D4×C53—21no—
190C2×D4×C53C22×C411yescharacteristic
191C22×C4×C53—21no—
192C22×C4×C53—21no—
193C22×C4×C53C2411yescharacteristic
194C2×C22⋊D53—21no—
195C2×C22⋊D53—21no—
196C2×C22⋊D53—21no—
197C22×Dic53—21no—
198C22×Dic53—21no—
199C22×Dic53#4111yescharacteristic
200#11719949—22no—
201#11719949C4⋊C414yes—
202Q8×D53—22no—
203Q8×D53C4⋊C414yes—
204#11719947—24no—
205#11719947—24no—
206#11719947—22no—
207#11719947C4⋊C414yes—
208D4×D53—24no—
209D4×D53—24no—
210D4×D53—22no—
211D4×D53C4⋊C414yes—
212#11719945—21no—
213#11719945—21no—
214#11719945—24no—
215#11719945—24no—
216#11719945C2×D412yes—
217#11719945C2×Q812yes—
218C2×D212—21no—
219C2×D212C22×C411yescharacteristic
220C2×C4×D53—21no—
221C2×C4×D53—21no—
222C2×C4×D53—21no—
223C2×C4×D53—24no—
224C2×C4×D53—24no—
225C2×C4×D53—21no—
226C2×C4×D53—21no—
227C2×C4×D53C22×C411yescharacteristic
228C2×C4×D53C22×C411yescharacteristic
229C2×C4×D53C2×D412yes—
230C2×C4×D53C2×D412yes—
231C2×C4×D53C2×D411yescharacteristic
232C2×C4×D53C2×D411yescharacteristic
233C2×C4×D53C2×Q812yes—
234C2×C4×D53#4112yes—
235C2×Dic106—21no—
236C2×Dic106C22×C411yescharacteristic
237M16×C53—24no—
238M16×C53—21no—
239M16×C53—21no—
240M16×C53—21no—
241M16×C53C2×D412yes—
242C2×C8×C53—24no—
243C2×C8×C53—21no—
244C2×C8×C53—21no—
245C2×C8×C53—21no—
246C2×C8×C53—21no—
247C2×C8×C53—21no—
248C2×C8×C53—21no—
249C2×C8×C53C22×C411yescharacteristic
250C2×C8×C53C22×C411yescharacteristic
251C2×C8×C53C2×D411yescharacteristic
252C2×C8×C53C2×D411yescharacteristic
253C4⋊C4×C53C22×C411yescharacteristic
254C4⋊C4×C53C22×C411yescharacteristic
255C22⋊C4×C53—21no—
256C42×C53—21no—
257C42×C53—21no—
258C42×C53—21no—
259C22⋊Dic53—21no—
260#11719921—21no—
261#11719921—21no—
262#11719921—42no—
263C4⋊Dic53C22×C411yescharacteristic
264C4⋊Dic53C22×C411yescharacteristic
265#11719919—21no—
266#11719919—21no—
267#11719919—42no—
268C4×Dic53—21no—
269C4×Dic53—21no—
270C4×Dic53—21no—
271C4×Dic53—21no—
272C4×Dic53—21no—
273#11719917—24no—
274#11719917—21no—
275#11719917—21no—
276#11719917—21no—
277#11719917C2×D412yes—
278C2×#88322—24no—
279C2×#88322—21no—
280C2×#88322—21no—
281C2×#88322—21no—
282C2×#88322—21no—
283C2×#88322—21no—
284C2×#88322—21no—
285C2×#88322C22×C411yescharacteristic
286C2×#88322C22×C411yescharacteristic
287C2×#88322C2×D411yescharacteristic
288C2×#88322C2×D411yescharacteristic
289#11719912—24no—
290#11719912—24no—
291#11719912—22no—
292#11719912—22no—
293#11719912—22no—
294#11719912—22no—
295#11719912—24no—
296#11719912—42no—
297C8×D53—24no—
298C8×D53—24no—
299C8×D53—22no—
300C8×D53—24no—
301C8×D53—22no—
302C8×D53—22no—
303C8×D53—22no—
304C8×D53—42no—
305C23×C53—21no—
306C23×C53C2×#4111yescharacteristic
307C22×D53—21no—
308C22×D53—24no—
309C22×D53—41no—
310C22×D53—41no—
311C22×D53—42no—
312C22×D53—42no—
313C22×D53C4×D411yescharacteristic
314C22×D53C4×D411yescharacteristic
315C22×D53C22⋊Q812yes—
316C22×D53#12312yes—
317Q8×C53—21no—
318Q8×C53C2×C4⋊C412yes—
319D4×C53—22no—
320D4×C53—22no—
321D4×C53—21no—
322D4×C53C2×C4⋊C412yes—
323C2×C4×C53—21no—
324C2×C4×C53—22no—
325C2×C4×C53—22no—
326C2×C4×C53—21no—
327C2×C4×C53—21no—
328C2×C4×C53—41no—
329C2×C4×C53—41no—
330C2×C4×C53—41no—
331C2×C4×C53C23×C411yescharacteristic
332C2×C4×C53C22×D411yescharacteristic
333C2×C4×C53C22×D411yescharacteristic
334C2×C4×C53C22×D411yescharacteristic
335C2×C4×C53C22×Q811yescharacteristic
336C2×C4×C53C2×#4111yescharacteristic
337C22⋊D53—22no—
338C22⋊D53—22no—
339C22⋊D53—24no—
340C22⋊D53—24no—
341C2×Dic53—21no—
342C2×Dic53—24no—
343C2×Dic53—21no—
344C2×Dic53—21no—
345C2×Dic53—41no—
346C2×Dic53—41no—
347C2×Dic53—41no—
348C2×Dic53C4×D411yescharacteristic
349C2×Dic53C4×D411yescharacteristic
350C2×Dic53C22⋊Q812yes—
351C2×Dic53#12312yes—
352D212—24no—
353D212—21no—
354D212C2×C4⋊C412yes—
355C4×D53—24no—
356C4×D53—22no—
357C4×D53—22no—
358C4×D53—24no—
359C4×D53—42no—
360C4×D53—42no—
361C4×D53C2×C4⋊C412yes—
362C4×D53C2×C4⋊C412yes—
363C4×D53C4×D412yes—
364C4×D53C4×D412yes—
365C4×D53#12012yes—
366C4×D53#12012yes—
367C4×D53C22⋊Q812yes—
368C4×D53C22⋊Q812yes—
369Dic106—21no—
370Dic106—24no—
371Dic106C2×C4⋊C412yes—
372C8×C53—21no—
373C8×C53—21no—
374C8×C53—21no—
375C8×C53—22no—
376C8×C53—21no—
377C8×C53—41no—
378#88322—21no—
379#88322—21no—
380#88322—21no—
381#88322—22no—
382#88322—21no—
383#88322—41no—
384#20884—531nomaximal, Sylow
385C22×C53—21no—
386C22×C53—21no—
387C22×C53—22no—
388C22×C53—41no—
389C22×C53—41no—
390C22×C53C2×C4×D411yescharacteristic
391C22×C53C2×C22⋊Q811yescharacteristic
392C22×C53C2×#12311yescharacteristic
393C2×D53—21no—
394C2×D53—21no—
395C2×D53—21no—
396C2×D53—21no—
397C2×D53—22no—
398C2×D53—42no—
399C2×D53—42no—
400C2×D53—48no—
401C2×D53—41no—
402C2×D53—41no—
403C2×D53#38512yes—
404C2×D53#38512yes—
405C4×C53—22no—
406C4×C53—41no—
407C4×C53—41no—
408C4×C53—81no—
409C4×C53C22×C4⋊C411yescharacteristic
410C4×C53C2×C4×D411yescharacteristic
411C4×C53C2×#12011yescharacteristic
412C4×C53C2×C22⋊Q811yescharacteristic
413Dic53—22no—
414Dic53—41no—
415Dic53—41no—
416Dic53—81no—
417Dic53#38512yes—
418Dic53#38512yes—
419C22×#131—531no—
420C2×#430—531no—
421C2×#424—531no—
422C2×#421—531no—
423#2896—531no—
424#1866—531no—
425#1866—531no—
426#1866—531no—
427#1866—531no—
428#1866—531no—
429#1866—531no—
430#1866—531no—
431#1866D5311yescharacteristic, complemented
432#1733—531no—
433#1729—531no—
434C2×C53—21no—
435C2×C53—21no—
436C2×C53—42no—
437C2×C53C2×#38511yescharacteristic
438C2×C53#295511yescharacteristic
439C2×C53#295511yescharacteristic
440D53—22no—
441D53—22no—
442D53—42no—
443C22×#41—531no—
444C2×#131—531no—
445C2×#131—531no—
446C2×#131—531no—
447C2×#131—1061no—
448C2×#131—1061no—
449C2×#131—1064no—
450C2×#131—1064no—
451C2×#131C2×D5311yescharacteristic
452C22×M16—531no—
453C22×M16—531no—
454C22×M16—531no—
455C22×M16—1061no—
456C23×C8—531no—
457C23×C8—1061no—
458C2×#117—531no—
459C2×#117—531no—
460#430—1064no—
461C2×#108—531no—
462C2×#108—531no—
463C2×#108—531no—
464C2×#108C2×D5311yescharacteristic, complemented
465#424—531no—
466#424—531no—
467#424—531no—
468#424—1061no—
469#424—1061no—
470#424C2×D5311yescharacteristic, complemented
471C2×C4⋊C8—1061no—
472C2×C4⋊C8—1061no—
473#421—1064no—
474C2×#104—531no—
475C2×#104—531no—
476C2×#104—531no—
477C2×#104C2×D5311yescharacteristic
478#419—531no—
479#419—531no—
480#418—531no—
481#418—531no—
482#417—531no—
483#417—531no—
484#417—531no—
485#417—531no—
486#416—531no—
487#416—531no—
488#416—531no—
489#416C2×D5311yescharacteristic
490#339—531no—
491#339—531no—
492#339—531no—
493#339C2×D5311yescharacteristic, complemented
494#336—531no—
495#336—531no—
496#336—531no—
497#336C2×D5311yescharacteristic, complemented
498C53#2088411yescharacteristic, complemented, Sylow
499C2×#41—534no—
500C2×#41—534no—
501C2×#41—531no—
502C2×#41—531no—
503C2×#41—531no—
504C2×#41—1061no—
505C2×#41—1061no—
506C2×#41—1062no—
507C2×#41—1062no—
508C2×#41C22×D5311yescharacteristic
509C22×Q8—531no—
510C22×D4—531no—
511C22×D4—1061no—
512C23×C4—531no—
513C23×C4—1061no—
514#131—22no—
515#131—22no—
516#131—1062no—
517#131—1062no—
518#131—1068no—
519#131—1062no—
520#131—1068no—
521#131—1062no—
522#131—1062no—
523#131—1062no—
524C2×M16—21no—
525C2×M16—531no—
526C2×M16—531no—
527C2×M16—531no—
528C2×M16—531no—
529C2×M16—531no—
530C2×M16—534no—
531C2×M16—531no—
532C2×M16—1061no—
533C2×M16—1061no—
534C2×M16—1062no—
535C2×M16—1062no—
536C2×M16—1061no—
537C2×M16—1061no—
538C2×M16—1062no—
539C2×M16—1068no—
540C2×M16—1061no—
541C2×M16—1062no—
542C2×M16—1062no—
543C2×M16C22×D5311yescharacteristic
544C2×M16C22×D5311yescharacteristic
545C22×C8—21no—
546C22×C8—531no—
547C22×C8—531no—
548C22×C8—531no—
549C22×C8—531no—
550C22×C8—531no—
551C22×C8—531no—
552C22×C8—1061no—
553C22×C8—1062no—
554C22×C8—1062no—
555C22×C8—1061no—
556C22×C8—1068no—
557C22×C8—1061no—
558C22×C8—1061no—
559C22×C8—1061no—
560C22×C8C22×D5311yescharacteristic
561C22×C8C22×D5311yescharacteristic
562#117—531no—
563#117—531no—
564#117—531no—
565#117—1061no—
566#117—1062no—
567#117—1062no—
568#117—1061no—
569#117C22×D5311yescharacteristic
570C2×C4⋊C4—531no—
571C2×C4⋊C4—531no—
572C2×C4⋊C4—1061no—
573C2×C22⋊C4—1061no—
574C2×C22⋊C4—1061no—
575C2×C42—531no—
576C2×C42—1061no—
577C2×C42C22×D5311yescharacteristic
578#108—22no—
579#108—1062no—
580#108—1062no—
581#108—1062no—
582C4⋊C8—21no—
583C4⋊C8—21no—
584C4⋊C8—1061no—
585C4⋊C8—1061no—
586C4⋊C8—1061no—
587C4⋊C8—1061no—
588C4⋊C8—1061no—
589C4⋊C8—1061no—
590#104—22no—
591#104—1062no—
592#104—1062no—
593#104—1062no—
594#103—531no—
595#103—531no—
596#103—531no—
597#103—531no—
598#103—531no—
599#103—531no—
600#103C4×D5311yescharacteristic
601#103C4×D5311yescharacteristic
602#102—531no—
603#102—531no—
604#102—531no—
605#102—531no—
606#102—531no—
607#102—531no—
608#102C4×D5311yescharacteristic
609#102C4×D5311yescharacteristic
610C24—531no—
611C24—1061no—
612#41—21no—
613#41—21no—
614#41—534no—
615#41—534no—
616#41—532no—
617#41—532no—
618#41—1064no—
619#41—1064no—
620#41—1064no—
621#41—1064no—
622#41—1062no—
623#41—1062no—
624#41—1061no—
625#41—1061no—
626#41D4×D5312yes—
627#41Q8×D5312yes—
628C2×Q8—534no—
629C2×Q8—531no—
630C2×Q8—1061no—
631C2×Q8—1062no—
632C2×Q8C2×C4×D5311yescharacteristic
633C2×D4—21no—
634C2×D4—534no—
635C2×D4—531no—
636C2×D4—1061no—
637C2×D4—1062no—
638C2×D4—1061no—
639C2×D4—1064no—
640C2×D4—1064no—
641C2×D4—1061no—
642C2×D4—1061no—
643C2×D4C2×C4×D5311yescharacteristic
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—531no—
647C22×C4—531no—
648C22×C4—531no—
649C22×C4—532no—
650C22×C4—532no—
651C22×C4—531no—
652C22×C4—531no—
653C22×C4—532no—
654C22×C4—532no—
655C22×C4—1064no—
656C22×C4—1061no—
657C22×C4—1064no—
658C22×C4—1061no—
659C22×C4—1061no—
660C22×C4—1061no—
661C22×C4—1061no—
662C22×C4—1061no—
663C22×C4—1061no—
664C22×C4C23×D5311yescharacteristic
665M16—24no—
666M16—21no—
667M16—21no—
668M16—21no—
669M16—532no—
670M16—1064no—
671M16—1062no—
672M16—1062no—
673M16—1062no—
674M16—1062no—
675M16—1064no—
676M16—1064no—
677M16—1064no—
678M16—1061no—
679M16—1061no—
680M16—1061no—
681M16—2122no—
682M16D4×D5312yes—
683C2×C8—24no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—531no—
691C2×C8—531no—
692C2×C8—531no—
693C2×C8—531no—
694C2×C8—1062no—
695C2×C8—1062no—
696C2×C8—1062no—
697C2×C8—1062no—
698C2×C8—1064no—
699C2×C8—1064no—
700C2×C8—1064no—
701C2×C8—1064no—
702C2×C8—1061no—
703C2×C8—1061no—
704C2×C8—1061no—
705C2×C8—1061no—
706C2×C8—1061no—
707C2×C8—1061no—
708C2×C8—2122no—
709C2×C8C2×C4×D5311yescharacteristic
710C2×C8C2×C4×D5311yescharacteristic
711C2×C8D4×D5311yescharacteristic
712C2×C8D4×D5311yescharacteristic
713C4⋊C4—531no—
714C4⋊C4—531no—
715C4⋊C4—1061no—
716C4⋊C4—1061no—
717C4⋊C4—2122no—
718C4⋊C4C2×C4×D5311yescharacteristic
719C4⋊C4C2×C4×D5311yescharacteristic
720C22⋊C4—21no—
721C22⋊C4—1061no—
722C22⋊C4—1061no—
723C22⋊C4—1061no—
724C22⋊C4—2122no—
725C42—21no—
726C42—21no—
727C42—21no—
728C42—1061no—
729C42—1061no—
730C42—1061no—
731C42—1061no—
732C42—1061no—
733C23—21no—
734C23—531no—
735C23—531no—
736C23—532no—
737C23—532no—
738C23—1064no—
739C23—1061no—
740C23—2121no—
741C23—2121no—
742C23—2122no—
743C23—2122no—
744C23#41×D5311yescharacteristic
745Q8—21no—
746Q8—532no—
747Q8—1064no—
748Q8—1061no—
749Q8C4⋊C4×D5312yes—
750D4—22no—
751D4—22no—
752D4—21no—
753D4—532no—
754D4—1064no—
755D4—1064no—
756D4—1064no—
757D4—1062no—
758D4—1062no—
759D4—1061no—
760D4C4⋊C4×D5312yes—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—531no—
770C2×C4—531no—
771C2×C4—532no—
772C2×C4—532no—
773C2×C4—532no—
774C2×C4—532no—
775C2×C4—532no—
776C2×C4—532no—
777C2×C4—532no—
778C2×C4—532no—
779C2×C4—532no—
780C2×C4—532no—
781C2×C4—1064no—
782C2×C4—1064no—
783C2×C4—1064no—
784C2×C4—1061no—
785C2×C4—1062no—
786C2×C4—1062no—
787C2×C4—1061no—
788C2×C4—1061no—
789C2×C4—2122no—
790C2×C4—2122no—
791C2×C4—2121no—
792C2×C4—2121no—
793C2×C4—2121no—
794C2×C4C22×C4×D5311yescharacteristic
795C2×C4C2×D4×D5311yescharacteristic
796C2×C4C2×D4×D5311yescharacteristic
797C2×C4C2×D4×D5311yescharacteristic
798C2×C4C2×Q8×D5311yescharacteristic
799C2×C4#41×D5311yescharacteristic
800C8—21no—
801C8—21no—
802C8—21no—
803C8—22no—
804C8—21no—
805C8—41no—
806C8—1061no—
807C8—1061no—
808C8—1061no—
809C8—1061no—
810C8—1062no—
811C8—2121no—
812C22—21no—
813C22—21no—
814C22—22no—
815C22—41no—
816C22—41no—
817C22—532no—
818C22—532no—
819C22—1061no—
820C22—1061no—
821C22—1061no—
822C22—1061no—
823C22—1062no—
824C22—2122no—
825C22—2122no—
826C22—2128no—
827C22—2121no—
828C22—2121no—
829C22C4×D4×D5311yescharacteristic
830C22C22⋊Q8×D5311yescharacteristic
831C22#123×D5311yescharacteristic
832C4—22no—
833C4—41no—
834C4—41no—
835C4—81no—
836C4—532no—
837C4—532no—
838C4—1062no—
839C4—4241no—
840C4—2121no—
841C4—2121no—
842C4C2×C4⋊C4×D5311yescharacteristic
843C4C4×D4×D5311yescharacteristic
844C4#120×D5311yescharacteristic
845C4C22⋊Q8×D5311yescharacteristic
846C2—21no—
847C2—21no—
848C2—42no—
849C2—1062no—
850C2—1062no—
851C2—2122no—
852C2#385×D5311yescharacteristic
853C2#2028361311yescharacteristic
854C2#2028361511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1866C2
socleC22×C53C2×C4×D4
prime radicalC2×#41×D53C22
cosocleC22×C4×C53C24
hypercenter#1866D53
hypocenterC53#20884
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1866

Complements

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

NH ≅ G/Ntype
2. C2×#16810670C2semidirect
3. #424×D53C2semidirect
6. #20274993C2semidirect
7. #20274992C2semidirect
8. #20274991C2semidirect
9. #20274990C2semidirect
10. #20274989C2semidirect
11. #20274988C2semidirect
12. #20274987C2semidirect
13. #20274423C2semidirect
14. #20274410C2semidirect
15. C53×#1866C2semidirect
33. C2×#13133153C22semidirect
34. C2×#13133152C22semidirect
35. C2×#13133152C22semidirect
36. #16810651C22semidirect
37. #16810650C22semidirect
38. #16810649C22semidirect
47. #16810630C4semidirect
48. #16810630C4semidirect
49. #16810626C4semidirect
50. #16810626C4semidirect
51. #16810623C4semidirect
52. #16810623C4semidirect
53. #16810621C4semidirect
54. #16810621C4semidirect
58. #16810384C22semidirect
59. #16810383C22semidirect
60. #16810382C22semidirect
61. #16810378C22semidirect
62. #16810377C22semidirect
63. #16810377C22semidirect
65. C2×#108×C53C22semidirect
66. C53×#424C22semidirect
69. C53×#339C22semidirect
70. C53×#336C22semidirect
431. #1866D53semidirect
464. C2×#108C2×D53semidirect
470. #424C2×D53semidirect
493. #339C2×D53semidirect
497. #336C2×D53semidirect
498. C53#20884semidirect

Maximal subgroups

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

subgroupindex
C2×#131×D532
C2×#168106702
#424×D532
C2×#168106382
#202832302
#202749932
#202749922
#202749912
#202749902
#202749892
#202749882
#202749872
#202744232
#202744102
C53×#18662
#2088453