Finite Group Databasebeta

← #27351623

Subgroups — #27351623

Order 13568.

1060 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288735C211yesmaximal, characteristic
2#20283746C211yesmaximal, characteristic, complemented
3#20277342C211yesmaximal, characteristic, complemented
4#20273291C211yesmaximal, characteristic, complemented
5#20273281C211yesmaximal, characteristic, complemented
6#20273273C211yesmaximal, characteristic, complemented
7#20273270C211yesmaximal, characteristic, complemented
8#20273260C211yesmaximal, characteristic, complemented
9#20273257C211yesmaximal, characteristic, complemented
10#20273252C211yesmaximal, characteristic, complemented
11#20273242C211yesmaximal, characteristic, complemented
12#20273230C211yesmaximal, characteristic, complemented
13#20273219C211yesmaximal, characteristic, complemented
14C2×#16810358C211yesmaximal, characteristic, complemented
15C53×#1501C211yesmaximal, characteristic, complemented
16#16811336C411yescharacteristic, complemented
17#16811331C411yescharacteristic, complemented
18#16811325C411yescharacteristic, complemented
19#16811322—21no—
20#16811317C411yescharacteristic, complemented
21#16811292C411yescharacteristic, complemented
22#16811268—21no—
23#16811264C411yescharacteristic, complemented
24#16811261C411yescharacteristic, complemented
25#16811260—21no—
26#16811257C411yescharacteristic, complemented
27#16811255—21no—
28#16811225—21no—
29#16811209—21no—
30#16811206—21no—
31#16811168C2211yescharacteristic
32#16811159C2211yescharacteristic
33#16811136C2211yescharacteristic
34C2×#13133191C2211yescharacteristic
35#121×D53C2211yescharacteristic
36#16811095—21no—
37C2×C4×C22⋊D53C2211yescharacteristic
38#16810698—21no—
39#16810697—21no—
40#16810694—21no—
41C8×C22⋊D53—21no—
42#16810677C2211yescharacteristic, complemented
43#16810673C2211yescharacteristic, complemented
44#16810587C2211yescharacteristic, complemented
45#16810585C2211yescharacteristic, complemented
46C22⋊C8×D53C2211yescharacteristic, complemented
47#16810514—21no—
48#16810507—21no—
49#16810500—21no—
50#16810495—21no—
51#16810490C2211yescharacteristic, complemented
52#16810487C2211yescharacteristic, complemented
53#16810485C2211yescharacteristic, complemented
54#16810482C2211yescharacteristic, complemented
55C2×#13133124C2211yescharacteristic, complemented
56#16810360C2211yescharacteristic, complemented
57#16810360C2211yescharacteristic, complemented
58#16810358C2211yescharacteristic
59#16810358C2211yescharacteristic
60#16810358C2211yescharacteristic, complemented
61#16810358C2211yescharacteristic, complemented
62#16810357C2211yescharacteristic, complemented
63#16810357C2211yescharacteristic, complemented
64#16810356C2211yescharacteristic
65#16810356C2211yescharacteristic
66#16810356C2211yescharacteristic, complemented
67#16810356C2211yescharacteristic, complemented
68C53×#525C2211yescharacteristic
69C2×C22⋊C8×C53C2211yescharacteristic, complemented
70C4×C22⋊C4×C53C2211yescharacteristic, complemented
71C53×#328C2211yescharacteristic, complemented
72C53×#328C2211yescharacteristic, complemented
73C53×#327C2211yescharacteristic, complemented
74C53×#327C2211yescharacteristic, complemented
75C2×#11719949C2×C411yescharacteristic, complemented
76C2×#11719947—21no—
77C22×D212C2×C411yescharacteristic
78C22×C22⋊D53—21no—
79C22×C22⋊D53D411yescharacteristic
80C2×D4×D53—21no—
81C2×D4×D53—21no—
82C2×D4×D53C2×C411yescharacteristic, complemented
83C23×Dic53—21no—
84C22×C4×D53C2311yescharacteristic
85C2×#11719917—21no—
86C2×#11719912—21no—
87C2×C8×D53—21no—
88#13133216C2×C411yescharacteristic, complemented
89#13133213—21no—
90#13133213C2×C411yescharacteristic, complemented
91#13133212—21no—
92#13133211—21no—
93#13133210—21no—
94#13133208C2×C411yescharacteristic, complemented
95#13133207—21no—
96#13133206C2×C411yescharacteristic, complemented
97#13133205—21no—
98#13133203—21no—
99#13133203—21no—
100#13133202—21no—
101#13133202—21no—
102#13133201—21no—
103#13133201—21no—
104#13133200—21no—
105#13133199—21no—
106#13133197—21no—
107#13133194—21no—
108#13133193C2×C411yescharacteristic, complemented
109#13133192—21no—
110#13133192C2×C411yescharacteristic, complemented
111#13133192C2×C411yescharacteristic, complemented
112#13133191—21no—
113#13133191—21no—
114#13133191—21no—
115#13133191C2×C411yescharacteristic
116#13133191C2×C411yescharacteristic
117#13133191C2311yescharacteristic
118#13133191C2311yescharacteristic
119#13133190—21no—
120#13133190—21no—
121#13133190—21no—
122#13133190—21no—
123#13133189—21no—
124#13133189—21no—
125#13133189—21no—
126#13133189—21no—
127#13133188—21no—
128#13133188C2×C411yescharacteristic, complemented
129#13133187—21no—
130#13133187—21no—
131#13133187—21no—
132#13133185—21no—
133#13133185—21no—
134Q8×Dic53C2×C411yescharacteristic, complemented
135C4×D212—21no—
136D4×Dic53—21no—
137D4×Dic53C2×C411yescharacteristic, complemented
138#13133179—21no—
139#13133179C2×C411yescharacteristic, complemented
140#13133179C2×C411yescharacteristic, complemented
141C4×C22⋊D53—21no—
142C4×C22⋊D53C2×C411yescharacteristic
143C4×C22⋊D53C2×C411yescharacteristic
144C4×C22⋊D53C2×C411yescharacteristic
145C4×C22⋊D53C2×C411yescharacteristic
146C4×C22⋊D53D411yescharacteristic
147C4×C22⋊D53D411yescharacteristic
148C4×C22⋊D53D411yescharacteristic
149C4×C22⋊D53D411yescharacteristic
150#13133177—21no—
151#13133177—21no—
152#13133177—21no—
153#13133177—21no—
154#13133175—21no—
155#13133175C2×C411yescharacteristic, complemented
156#13133174—21no—
157C2×C4⋊Dic53C2×C411yescharacteristic
158C2×#11719919—21no—
159C2×#11719919—21no—
160C2×#11719919D411yescharacteristic
161C4⋊C4×D53C2×C411yescharacteristic, complemented
162C2×C22⋊Dic53D411yescharacteristic
163C2×#11719921—21no—
164C2×#11719921—21no—
165C2×#11719921—21no—
166C2×#11719921—21no—
167C2×#11719921D411yescharacteristic
168C22⋊C4×D53—21no—
169C22⋊C4×D53—21no—
170C2×C4×Dic53C2311yescharacteristic
171#13133146—21no—
172#13133146—21no—
173C22⋊#88322—21no—
174C22⋊#88322C2311yescharacteristic
175C22⋊#88322C2311yescharacteristic
176#13133129—21no—
177#13133129—21no—
178#13133127—21no—
179C8×Dic53—21no—
180#13133124—21no—
181#13133124—21no—
182#13133124—21no—
183#13133124—21no—
184#13133124—21no—
185#13133124C2311yescharacteristic
186#13133124C2311yescharacteristic
187C2×#41×C53C2×C411yescharacteristic
188C23×C4×C53C2311yescharacteristic
189C22×C8×C53—21no—
190#123×C53—21no—
191C22⋊Q8×C53C2×C411yescharacteristic
192C22⋊Q8×C53C2311yescharacteristic
193#121×C53C2×C411yescharacteristic
194#121×C53C2311yescharacteristic
195#120×C53—21no—
196C4×D4×C53—21no—
197C4×D4×C53—21no—
198#117×C53C2×C411yescharacteristic
199C2×C22⋊C4×C53—21no—
200C2×C42×C53—21no—
201C22⋊C8×C53—21no—
202C22⋊C8×C53C2311yescharacteristic
203C22⋊C8×C53C2311yescharacteristic
204#95×C53C2311yescharacteristic
205#95×C53C2311yescharacteristic
206C24×C53C2×D411yescharacteristic
207C23×D53—21no—
208C23×D53—21no—
209C23×D53C2×D411yescharacteristic
210#41×C53—81no—
211C2×Q8×C53C22×C411yescharacteristic
212C2×D4×C53—21no—
213C2×D4×C53—21no—
214C2×D4×C53—21no—
215C2×D4×C53C22×C411yescharacteristic
216C22×C4×C53—21no—
217C22×C4×C53—21no—
218C22×C4×C53—21no—
219C22×C4×C53—81no—
220C22×C4×C53C22×C411yescharacteristic
221C22×C4×C53C22×C411yescharacteristic
222C22×C4×C53C2×D411yescharacteristic
223C22×C4×C53C2×D411yescharacteristic
224C22×C4×C53C2×D411yescharacteristic
225C22×C4×C53C2411yescharacteristic
226C2×C22⋊D53—21no—
227C2×C22⋊D53—21no—
228C2×C22⋊D53—21no—
229C2×C22⋊D53—21no—
230C2×C22⋊D53—21no—
231C2×C22⋊D53—21no—
232C2×C22⋊D53—21no—
233C2×C22⋊D53—21no—
234C2×C22⋊D53—42no—
235C2×C22⋊D53—81no—
236C2×C22⋊D53—81no—
237C2×C22⋊D53C22⋊C411yescharacteristic
238C2×C22⋊D53C22⋊C411yescharacteristic
239C2×C22⋊D53C22⋊C411yescharacteristic
240C2×C22⋊D53C22⋊C411yescharacteristic
241C22×Dic53—21no—
242C22×Dic53—21no—
243C22×Dic53—21no—
244C22×Dic53—21no—
245C22×Dic53—42no—
246C22×Dic53—81no—
247C22×Dic53—81no—
248C22×Dic53C2×D411yescharacteristic
249C22×Dic53C2×D411yescharacteristic
250C22×Dic53C2×D411yescharacteristic
251#11719949—81no—
252#11719947—81no—
253#11719947—81no—
254D4×D53—44no—
255D4×D53—81no—
256D4×D53—81no—
257D4×D53—81no—
258C2×D212—21no—
259C2×D212—21no—
260C2×D212—21no—
261C2×D212—21no—
262C2×D212—81no—
263C2×D212C22×C411yescharacteristic
264C2×D212C22×C411yescharacteristic
265C2×C4×D53—21no—
266C2×C4×D53—21no—
267C2×C4×D53—21no—
268C2×C4×D53—21no—
269C2×C4×D53—81no—
270C2×C4×D53C22×C411yescharacteristic
271C2×C4×D53C22×C411yescharacteristic
272C2×C4×D53C2×D411yescharacteristic
273C2×C4×D53C2×D411yescharacteristic
274C2×Dic106—21no—
275C2×C8×C53—21no—
276C2×C8×C53—21no—
277C2×C8×C53—81no—
278C4⋊C4×C53—21no—
279C4⋊C4×C53—21no—
280C4⋊C4×C53C22×C411yescharacteristic
281C4⋊C4×C53C22×C411yescharacteristic
282C22⋊C4×C53—21no—
283C22⋊C4×C53—21no—
284C22⋊C4×C53—21no—
285C22⋊C4×C53—21no—
286C22⋊C4×C53—21no—
287C22⋊C4×C53—42no—
288C42×C53—21no—
289C42×C53—81no—
290C22⋊Dic53—21no—
291C22⋊Dic53—21no—
292C22⋊Dic53C22⋊C411yescharacteristic
293C22⋊Dic53C22⋊C411yescharacteristic
294C22⋊Dic53C22⋊C411yescharacteristic
295C22⋊Dic53C22⋊C411yescharacteristic
296#11719921—21no—
297#11719921—21no—
298#11719921—21no—
299#11719921—21no—
300#11719921—21no—
301#11719921—21no—
302#11719921—21no—
303#11719921—21no—
304#11719921—21no—
305#11719921—21no—
306#11719921—21no—
307#11719921—21no—
308#11719921—81no—
309#11719921—81no—
310#11719921C22⋊C411yescharacteristic
311#11719921C22⋊C411yescharacteristic
312#11719921C22⋊C411yescharacteristic
313#11719921C22⋊C411yescharacteristic
314C4⋊Dic53—21no—
315C4⋊Dic53—21no—
316C4⋊Dic53—21no—
317C4⋊Dic53C22×C411yescharacteristic
318C4⋊Dic53C22×C411yescharacteristic
319#11719919—21no—
320#11719919—21no—
321#11719919—21no—
322#11719919—21no—
323#11719919—81no—
324#11719919—81no—
325#11719919C22⋊C411yescharacteristic
326#11719919C22⋊C411yescharacteristic
327#11719919C22⋊C411yescharacteristic
328#11719919C22⋊C411yescharacteristic
329C4×Dic53—21no—
330C4×Dic53—21no—
331C4×Dic53C22×C411yescharacteristic
332C4×Dic53C22×C411yescharacteristic
333C4×Dic53C2×D411yescharacteristic
334C4×Dic53C2×D411yescharacteristic
335#11719917—81no—
336C2×#88322—21no—
337C2×#88322—21no—
338#11719912—81no—
339C8×D53—81no—
340C23×C53—21no—
341C23×C53—21no—
342C23×C53—22no—
343C23×C53—21no—
344C23×C53—41no—
345C23×C53C2×C22⋊C411yescharacteristic
346C23×C53C2×C22⋊C411yescharacteristic
347C23×C53C22×D411yescharacteristic
348C22×D53—21no—
349C22×D53—21no—
350C22×D53—21no—
351C22×D53—21no—
352C22×D53—41no—
353C22×D53—41no—
354C22×D53—42no—
355C22×D53—42no—
356C22×D53—81no—
357C22×D53—81no—
358C22×D53—81no—
359C22×D53—81no—
360C22×D53C2×C22⋊C411yescharacteristic
361C22×D53C2×C22⋊C411yescharacteristic
362Q8×C53—41no—
363D4×C53—41no—
364D4×C53—41no—
365D4×C53—41no—
366D4×C53—42no—
367D4×C53—81no—
368C2×C4×C53—21no—
369C2×C4×C53—21no—
370C2×C4×C53—21no—
371C2×C4×C53—41no—
372C2×C4×C53—41no—
373C2×C4×C53—41no—
374C2×C4×C53—41no—
375C2×C4×C53—41no—
376C2×C4×C53—41no—
377C2×C4×C53—41no—
378C2×C4×C53—41no—
379C2×C4×C53—41no—
380C2×C4×C53—41no—
381C2×C4×C53—41no—
382C2×C4×C53—41no—
383C2×C4×C53—81no—
384C2×C4×C53C2×C22⋊C411yescharacteristic
385C2×C4×C53C2×C22⋊C411yescharacteristic
386C2×C4×C53C23×C411yescharacteristic
387C2×C4×C53C22×D411yescharacteristic
388C22⋊D53—22no—
389C22⋊D53—22no—
390C22⋊D53—41no—
391C22⋊D53—41no—
392C22⋊D53—42no—
393C22⋊D53—41no—
394C22⋊D53—41no—
395C22⋊D53—41no—
396C22⋊D53—41no—
397C22⋊D53—81no—
398C22⋊D53—81no—
399C22⋊D53—81no—
400C22⋊D53—81no—
401C22⋊D53—81no—
402C2×Dic53—21no—
403C2×Dic53—21no—
404C2×Dic53—21no—
405C2×Dic53—21no—
406C2×Dic53—41no—
407C2×Dic53—41no—
408C2×Dic53—41no—
409C2×Dic53—41no—
410C2×Dic53—41no—
411C2×Dic53—41no—
412C2×Dic53—41no—
413C2×Dic53—41no—
414C2×Dic53—81no—
415C2×Dic53—81no—
416C2×Dic53—84no—
417C2×Dic53C2×C22⋊C411yescharacteristic
418C2×Dic53C2×C22⋊C411yescharacteristic
419C2×Dic53C2×C22⋊C411yescharacteristic
420C2×Dic53C2×C22⋊C411yescharacteristic
421C2×Dic53C2×C22⋊C411yescharacteristic
422C2×Dic53C2×C22⋊C411yescharacteristic
423D212—41no—
424D212—41no—
425D212—42no—
426D212—81no—
427D212—81no—
428D212—81no—
429C4×D53—41no—
430C4×D53—41no—
431C4×D53—41no—
432C4×D53—41no—
433C4×D53—42no—
434C4×D53—81no—
435C4×D53—81no—
436C4×D53—81no—
437Dic106—81no—
438C8×C53—41no—
439C8×C53—41no—
440#88322—41no—
441#88322—41no—
442#17597—531nomaximal, Sylow
443C22×C53—21no—
444C22×C53—21no—
445C22×C53—21no—
446C22×C53—21no—
447C22×C53—21no—
448C22×C53—21no—
449C22×C53—21no—
450C22×C53—42no—
451C22×C53—42no—
452C22×C53—41no—
453C22×C53—41no—
454C22×C53—41no—
455C22×C53#42112yes—
456C22×C53C22×C22⋊C411yescharacteristic
457C22×C53#57611yescharacteristic
458C22×C53#57711yescharacteristic
459C2×D53—21no—
460C2×D53—21no—
461C2×D53—21no—
462C2×D53—21no—
463C2×D53—21no—
464C2×D53—21no—
465C2×D53—41no—
466C2×D53—41no—
467C2×D53—41no—
468C2×D53—41no—
469C2×D53—41no—
470C2×D53—41no—
471C2×D53—81no—
472C2×D53—81no—
473C2×D53—162no—
474C2×D53—162no—
475C4×C53—21no—
476C4×C53—21no—
477C4×C53—21no—
478C4×C53—21no—
479C4×C53—41no—
480C4×C53—41no—
481C4×C53—41no—
482C4×C53—81no—
483C4×C53—81no—
484Dic53—21no—
485Dic53—21no—
486Dic53—21no—
487Dic53—21no—
488Dic53—21no—
489Dic53—21no—
490Dic53—41no—
491Dic53—41no—
492Dic53—81no—
493Dic53—81no—
494#3519—531no—
495#2974—531no—
496#2318—531no—
497#1521—531no—
498#1519—531no—
499#1517—531no—
500#1516—531no—
501#1514—531no—
502#1513—531no—
503#1512—531no—
504#1510—531no—
505#1507—531no—
506#1504—531no—
507#1501D5311yescharacteristic, complemented
508C2×#327—531no—
509C2×C53—21no—
510C2×C53—21no—
511C2×C53—22no—
512C2×C53—41no—
513C2×C53—81no—
514C2×C53#288311yescharacteristic
515C2×C53#289711yescharacteristic
516C2×C53C2×#42111yescharacteristic
517D53—41no—
518D53—41no—
519D53—81no—
520D53—81no—
521#555—531no—
522#554—531no—
523#553—531no—
524#553—531no—
525#553—1061no—
526#550—531no—
527#546—531no—
528#546—531no—
529#546—1061no—
530#546—1061no—
531D42—531no—
532D42—1061no—
533#540—1061no—
534#538—1061no—
535#538—1061no—
536#532—531no—
537#529—531no—
538#525—531no—
539#525C2×D5311yescharacteristic
540C2×#121—531no—
541C2×#121—531no—
542#518—1061no—
543C2×C4×D4—531no—
544#436—1061no—
545#435—1061no—
546#435—1061no—
547C8×D4—1061no—
548#432—531no—
549#431—531no—
550#407—531no—
551#407—531no—
552C2×C22⋊C8—531no—
553C2×C22⋊C8C2×D5311yescharacteristic, complemented
554#388—1061no—
555#387—1061no—
556#386—1061no—
557#385—1061no—
558#383—531no—
559#382—531no—
560#381—531no—
561#380—531no—
562C4×C22⋊C4C2×D5311yescharacteristic, complemented
563C2×#95—531no—
564#328—531no—
565#328—531no—
566#328C2×D5311yescharacteristic, complemented
567#328C2×D5311yescharacteristic, complemented
568#327—531no—
569#327—531no—
570#327—531no—
571#327—531no—
572#327—531no—
573#327—531no—
574#327—531no—
575#327—531no—
576#327—531no—
577#327—531no—
578#327C2×D5311yescharacteristic, complemented
579#327C2×D5311yescharacteristic, complemented
580C53#1759711yescharacteristic, complemented, Sylow
581C2×#41—531no—
582C2×#41—1061no—
583C2×#41C4×D5311yescharacteristic
584C22×D4—531no—
585C22×D4—531no—
586C22×D4—531no—
587C22×D4—1061no—
588C22×D4—1061no—
589C22×D4—1061no—
590C23×C4—531no—
591C23×C4—1061no—
592C23×C4C22×D5311yescharacteristic
593C2×M16—1061no—
594C2×M16—1061no—
595C22×C8—21no—
596C22×C8—1061no—
597C4⋊Q8—531no—
598#127—531no—
599#127—1061no—
600#126—1061no—
601#126—1061no—
602#126—1061no—
603#125—531no—
604#125—1061no—
605#124—531no—
606#124—1061no—
607#124—1061no—
608#124—1061no—
609#123—21no—
610#123—1061no—
611#123—1061no—
612#123—1061no—
613#123—1061no—
614#123—1061no—
615#123—1061no—
616C22⋊Q8—531no—
617C22⋊Q8—1061no—
618C22⋊Q8—1061no—
619C22⋊Q8C4×D5311yescharacteristic
620C22⋊Q8C22×D5311yescharacteristic
621#121—531no—
622#121—531no—
623#121—531no—
624#121—531no—
625#121—531no—
626#121—531no—
627#121—531no—
628#121—1061no—
629#121—1061no—
630#121—1061no—
631#121—1061no—
632#121—1061no—
633#121—1061no—
634#121—1061no—
635#121—1061no—
636#121—1061no—
637#121—1061no—
638#121—1061no—
639#121—1061no—
640#121—1061no—
641#121C4×D5311yescharacteristic
642#121C22×D5311yescharacteristic
643#120—21no—
644#120—1061no—
645#120—1061no—
646#120—1061no—
647#120—1061no—
648#120—1061no—
649C4×Q8—531no—
650C4×D4—21no—
651C4×D4—21no—
652C4×D4—531no—
653C4×D4—531no—
654C4×D4—531no—
655C4×D4—531no—
656C4×D4—531no—
657C4×D4—531no—
658C4×D4—531no—
659C4×D4—531no—
660C4×D4—531no—
661C4×D4—531no—
662C4×D4—531no—
663C4×D4—1061no—
664C4×D4—1061no—
665C4×D4—1061no—
666C4×D4—1061no—
667C4×D4—1061no—
668C4×D4—1061no—
669C4×D4—1061no—
670C4×D4—1061no—
671#117—531no—
672#117—1061no—
673#117—1061no—
674#117C4×D5311yescharacteristic
675C2×C4⋊C4—531no—
676C2×C4⋊C4—531no—
677C2×C4⋊C4—531no—
678C2×C4⋊C4—1061no—
679C2×C4⋊C4—1061no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—531no—
682C2×C22⋊C4—531no—
683C2×C22⋊C4—1061no—
684C2×C22⋊C4—1061no—
685C2×C22⋊C4—1061no—
686C2×C22⋊C4—1061no—
687C2×C22⋊C4—1061no—
688C2×C22⋊C4—1061no—
689C2×C42—21no—
690C2×C42—531no—
691C4⋊C8—1061no—
692C4⋊C8—1061no—
693C22⋊C8—21no—
694C22⋊C8—531no—
695C22⋊C8—531no—
696C22⋊C8—1061no—
697C22⋊C8—1061no—
698C22⋊C8—1061no—
699C22⋊C8C22×D5311yescharacteristic
700C22⋊C8C22×D5311yescharacteristic
701#97—1061no—
702C4×C8—1061no—
703#95—531no—
704#95—531no—
705#95—1061no—
706#95—1061no—
707#95—1061no—
708#95—1061no—
709#95—1061no—
710#95C22×D5311yescharacteristic
711#95C22×D5311yescharacteristic
712C24—531no—
713C24—1061no—
714C24—1061no—
715C24D4×D5311yescharacteristic
716#41—81no—
717#41—4241no—
718#41—4241no—
719#41—4241no—
720C2×Q8—1061no—
721C2×Q8C2×C4×D5311yescharacteristic
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—531no—
726C2×D4—531no—
727C2×D4—531no—
728C2×D4—531no—
729C2×D4—531no—
730C2×D4—531no—
731C2×D4—1061no—
732C2×D4—1061no—
733C2×D4—1061no—
734C2×D4—1061no—
735C2×D4—1061no—
736C2×D4—1061no—
737C2×D4—1061no—
738C2×D4—1061no—
739C2×D4—1061no—
740C2×D4—1061no—
741C2×D4—1061no—
742C2×D4—1061no—
743C2×D4—4241no—
744C2×D4—4241no—
745C2×D4—4241no—
746C2×D4—4241no—
747C2×D4—4241no—
748C2×D4—4241no—
749C2×D4—2124no—
750C2×D4—2122no—
751C2×D4C2×C4×D5311yescharacteristic
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—81no—
756C22×C4—531no—
757C22×C4—531no—
758C22×C4—531no—
759C22×C4—531no—
760C22×C4—531no—
761C22×C4—531no—
762C22×C4—531no—
763C22×C4—1061no—
764C22×C4—1061no—
765C22×C4—1061no—
766C22×C4—1061no—
767C22×C4—1061no—
768C22×C4—1061no—
769C22×C4—1061no—
770C22×C4—1061no—
771C22×C4—4241no—
772C22×C4—4241no—
773C22×C4—4241no—
774C22×C4—2122no—
775C22×C4C2×C4×D5311yescharacteristic
776C22×C4C2×C4×D5311yescharacteristic
777C22×C4D4×D5311yescharacteristic
778C22×C4D4×D5311yescharacteristic
779C22×C4D4×D5311yescharacteristic
780C22×C4C23×D5311yescharacteristic
781M16—4241no—
782M16—4241no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—81no—
786C2×C8—1061no—
787C2×C8—1061no—
788C2×C8—4241no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—531no—
792C4⋊C4—531no—
793C4⋊C4—531no—
794C4⋊C4—531no—
795C4⋊C4—531no—
796C4⋊C4—531no—
797C4⋊C4—1061no—
798C4⋊C4—1061no—
799C4⋊C4—1061no—
800C4⋊C4—1061no—
801C4⋊C4—1061no—
802C4⋊C4—1061no—
803C4⋊C4—1061no—
804C4⋊C4—4241no—
805C4⋊C4—4241no—
806C4⋊C4C2×C4×D5311yescharacteristic
807C4⋊C4C2×C4×D5311yescharacteristic
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—42no—
814C22⋊C4—531no—
815C22⋊C4—531no—
816C22⋊C4—531no—
817C22⋊C4—531no—
818C22⋊C4—531no—
819C22⋊C4—531no—
820C22⋊C4—531no—
821C22⋊C4—531no—
822C22⋊C4—1061no—
823C22⋊C4—1061no—
824C22⋊C4—1061no—
825C22⋊C4—1061no—
826C22⋊C4—1061no—
827C22⋊C4—1061no—
828C22⋊C4—1061no—
829C22⋊C4—1061no—
830C22⋊C4—1061no—
831C22⋊C4—1061no—
832C22⋊C4—1061no—
833C22⋊C4—1061no—
834C22⋊C4—1061no—
835C22⋊C4—1061no—
836C22⋊C4—4241no—
837C22⋊C4—4241no—
838C42—21no—
839C42—81no—
840C42—531no—
841C42—531no—
842C42—531no—
843C42—531no—
844C42—1061no—
845C42—1061no—
846C23—22no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—41no—
851C23—531no—
852C23—531no—
853C23—1061no—
854C23—1061no—
855C23—1061no—
856C23—1061no—
857C23—4241no—
858C23—4241no—
859C23—4241no—
860C23—4241no—
861C23—2121no—
862C23—2121no—
863C23—2122no—
864C23—2122no—
865C23C22⋊C4×D5311yescharacteristic
866C23C22⋊C4×D5311yescharacteristic
867C23C2×D4×D5311yescharacteristic
868Q8—41no—
869Q8—4241no—
870D4—41no—
871D4—42no—
872D4—41no—
873D4—41no—
874D4—81no—
875D4—1062no—
876D4—1062no—
877D4—4241no—
878D4—4241no—
879D4—4241no—
880D4—4241no—
881D4—4241no—
882D4—4241no—
883D4—4241no—
884D4—4241no—
885D4—2121no—
886D4—2121no—
887D4—2122no—
888D4—2121no—
889D4—2121no—
890D4—2122no—
891D4—2121no—
892D4—2121no—
893D4—2121no—
894D4—2121no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—81no—
911C2×C4—531no—
912C2×C4—531no—
913C2×C4—531no—
914C2×C4—531no—
915C2×C4—531no—
916C2×C4—531no—
917C2×C4—1061no—
918C2×C4—1061no—
919C2×C4—1061no—
920C2×C4—1061no—
921C2×C4—4241no—
922C2×C4—4241no—
923C2×C4—4241no—
924C2×C4—4241no—
925C2×C4—4244no—
926C2×C4—4241no—
927C2×C4—2121no—
928C2×C4—2121no—
929C2×C4—2121no—
930C2×C4—2121no—
931C2×C4—2122no—
932C2×C4—2121no—
933C2×C4—2121no—
934C2×C4—2121no—
935C2×C4—2121no—
936C2×C4—2121no—
937C2×C4—2121no—
938C2×C4—2121no—
939C2×C4—2121no—
940C2×C4C22⋊C4×D5311yescharacteristic
941C2×C4C22⋊C4×D5311yescharacteristic
942C2×C4C22×C4×D5311yescharacteristic
943C2×C4C2×D4×D5311yescharacteristic
944C8—41no—
945C8—41no—
946C8—2121no—
947C8—2121no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—42no—
956C22—42no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—8482no—
961C22—8482no—
962C22—1061no—
963C22—1061no—
964C22—1061no—
965C22—1061no—
966C22—1061no—
967C22—1061no—
968C22—4241no—
969C22—4241no—
970C22—2121no—
971C22—2121no—
972C22—2121no—
973C22—2121no—
974C22—2121no—
975C22—2121no—
976C22#1681063812yes—
977C22C2×C22⋊C4×D5311yescharacteristic
978C22#1681142511yescharacteristic
979C22#1681143011yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—41no—
985C4—41no—
986C4—41no—
987C4—81no—
988C4—81no—
989C4—1061no—
990C4—1061no—
991C4—1061no—
992C4—1061no—
993C4—1061no—
994C4—1061no—
995C4—4241no—
996C4—4241no—
997C4—2121no—
998C4—2121no—
999C2—21no—
1000C2—21no—
1001C2—22no—
1002C2—41no—
1003C2—81no—
1004C2—4241no—
1005C2—4241no—
1006C2—2121no—
1007C2—2121no—
1008C2#2028317311yescharacteristic
1009C2#2028323711yescharacteristic
1010C2C2×#1681063811yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1501C2
socleC22×C53C22×C22⋊C4
prime radical#20288735C2
cosocleC22×C4×C53C24
hypercenter#1501D53
hypocenterC53#17597
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1501

Complements

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

NH ≅ G/Ntype
2. #20283746C2semidirect
3. #20277342C2semidirect
4. #20273291C2semidirect
5. #20273281C2semidirect
6. #20273273C2semidirect
7. #20273270C2semidirect
8. #20273260C2semidirect
9. #20273257C2semidirect
10. #20273252C2semidirect
11. #20273242C2semidirect
12. #20273230C2semidirect
13. #20273219C2semidirect
14. C2×#16810358C2semidirect
15. C53×#1501C2semidirect
16. #16811336C4semidirect
17. #16811331C4semidirect
18. #16811325C4semidirect
20. #16811317C4semidirect
21. #16811292C4semidirect
23. #16811264C4semidirect
24. #16811261C4semidirect
26. #16811257C4semidirect
42. #16810677C22semidirect
43. #16810673C22semidirect
44. #16810587C22semidirect
45. #16810585C22semidirect
46. C22⋊C8×D53C22semidirect
51. #16810490C22semidirect
52. #16810487C22semidirect
53. #16810485C22semidirect
54. #16810482C22semidirect
55. C2×#13133124C22semidirect
56. #16810360C22semidirect
57. #16810360C22semidirect
60. #16810358C22semidirect
61. #16810358C22semidirect
62. #16810357C22semidirect
63. #16810357C22semidirect
66. #16810356C22semidirect
67. #16810356C22semidirect
69. C2×C22⋊C8×C53C22semidirect
70. C4×C22⋊C4×C53C22semidirect
71. C53×#328C22semidirect
72. C53×#328C22semidirect
73. C53×#327C22semidirect
74. C53×#327C22semidirect
75. C2×#11719949C2×C4semidirect
82. C2×D4×D53C2×C4semidirect
88. #13133216C2×C4semidirect
90. #13133213C2×C4semidirect
94. #13133208C2×C4semidirect
96. #13133206C2×C4semidirect
108. #13133193C2×C4semidirect
110. #13133192C2×C4semidirect
111. #13133192C2×C4semidirect
128. #13133188C2×C4semidirect
134. Q8×Dic53C2×C4semidirect
137. D4×Dic53C2×C4semidirect
139. #13133179C2×C4semidirect
140. #13133179C2×C4semidirect
155. #13133175C2×C4semidirect
161. C4⋊C4×D53C2×C4semidirect
507. #1501D53semidirect
553. C2×C22⋊C8C2×D53semidirect
562. C4×C22⋊C4C2×D53semidirect
566. #328C2×D53semidirect
567. #328C2×D53semidirect
578. #327C2×D53semidirect
579. #327C2×D53semidirect
580. C53#17597semidirect

Maximal subgroups

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

subgroupindex
#202887352
#202837462
#202773422
#202732912
#202732812
#202732732
#202732702
#202732602
#202732572
#202732522
#202732422
#202732302
#202732192
C2×#168103582
C53×#15012
#1759753