Finite Group Databasebeta

← #27351611

Subgroups — #27351611

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#20288741C211yesmaximal, characteristic
2#20283746C211yesmaximal, characteristic, complemented
3#20277349C211yesmaximal, characteristic, complemented
4#20273289C211yesmaximal, characteristic, complemented
5#20273281C211yesmaximal, characteristic, complemented
6#20273273C211yesmaximal, characteristic, complemented
7#20273268C211yesmaximal, characteristic, complemented
8#20273260C211yesmaximal, characteristic, complemented
9#20273255C211yesmaximal, characteristic, complemented
10#20273250C211yesmaximal, characteristic, complemented
11#20273242C211yesmaximal, characteristic, complemented
12#20273231C211yesmaximal, characteristic, complemented
13#20273217C211yesmaximal, characteristic, complemented
14#20273207C211yesmaximal, characteristic, complemented
15C2×C53×#327C211yesmaximal, characteristic, complemented
16#16811337C411yescharacteristic, complemented
17#16811328C411yescharacteristic, complemented
18#16811321C411yescharacteristic, complemented
19#16811320C411yescharacteristic, complemented
20#16811316—21no—
21#16811291C411yescharacteristic, complemented
22#16811270C411yescharacteristic, complemented
23#16811267—21no—
24#16811267C411yescharacteristic, complemented
25#16811262—21no—
26D4×C22⋊D53—21no—
27D4×C22⋊D53C411yescharacteristic, complemented
28#16811223—21no—
29#16811211—21no—
30#16811205—21no—
31#16811168C2211yescharacteristic
32#16811154C2211yescharacteristic
33#16811134C2211yescharacteristic
34#16811133C2211yescharacteristic
35#121×D53C2211yescharacteristic
36#16811096—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#16810512—21no—
48#16810505—21no—
49#16810502—21no—
50#16810496—21no—
51#16810490C2211yescharacteristic, complemented
52#16810487C2211yescharacteristic, complemented
53#16810485C2211yescharacteristic, complemented
54#16810482C2211yescharacteristic, complemented
55C4×C22⋊Dic53C2211yescharacteristic, complemented
56#16810361C2211yescharacteristic, complemented
57#16810361C2211yescharacteristic, complemented
58#16810359C2211yescharacteristic, complemented
59#16810359C2211yescharacteristic, complemented
60#16810358C2211yescharacteristic, complemented
61#16810358C2211yescharacteristic, complemented
62#16810357C2211yescharacteristic
63#16810357C2211yescharacteristic
64#16810357C2211yescharacteristic, complemented
65#16810357C2211yescharacteristic, complemented
66#16810356C2211yescharacteristic, complemented
67#16810356C2211yescharacteristic, complemented
68C2×#121×C53C2211yescharacteristic
69C2×C22⋊C8×C53C2211yescharacteristic, complemented
70C2×#95×C53C2211yescharacteristic, complemented
71C53×#327C2211yescharacteristic
72C53×#327C2211yescharacteristic
73C53×#327C2211yescharacteristic, complemented
74C53×#327C2211yescharacteristic, complemented
75C2×#11719945C2×C411yescharacteristic
76C2×#11719947—21no—
77C2×#11719947C2×C411yescharacteristic, complemented
78C22×C22⋊D53—21no—
79C22×C22⋊D53D411yescharacteristic
80C2×D4×D53—21no—
81C2×D4×D53C2×C411yescharacteristic, complemented
82C22×C4×D53C2311yescharacteristic
83C2×#11719917—21no—
84C2×#11719912—21no—
85C2×C8×D53—21no—
86#13133216C2×C411yescharacteristic, complemented
87#13133213—21no—
88#13133213C2×C411yescharacteristic, complemented
89#13133212—21no—
90#13133210—21no—
91#13133210—21no—
92#13133208C2×C411yescharacteristic, complemented
93#13133207—21no—
94#13133204—21no—
95#13133204C2×C411yescharacteristic, complemented
96#13133203—21no—
97#13133203—21no—
98#13133202—21no—
99#13133200—21no—
100#13133199—21no—
101#13133199—21no—
102#13133198—21no—
103#13133198—21no—
104#13133198—21no—
105#13133197C2×C411yescharacteristic, complemented
106#13133196—21no—
107#13133196C2×C411yescharacteristic
108#13133196C2311yescharacteristic
109#13133195—21no—
110#13133192C2×C411yescharacteristic, complemented
111#13133191—21no—
112#13133191C2×C411yescharacteristic
113#13133191C2311yescharacteristic
114#13133190—21no—
115#13133190—21no—
116#13133189—21no—
117#13133189—21no—
118#13133189—21no—
119#13133189—21no—
120#13133189—21no—
121#13133189—21no—
122#13133188—21no—
123#13133188—21no—
124#13133188C2×C411yescharacteristic, complemented
125#13133188C2×C411yescharacteristic, complemented
126#13133186—21no—
127#13133186—21no—
128#13133186—21no—
129#13133185—21no—
130#13133185—21no—
131#13133185—21no—
132#13133182C2×C411yescharacteristic, complemented
133D4×Dic53—21no—
134D4×Dic53—21no—
135D4×Dic53C2×C411yescharacteristic, complemented
136D4×Dic53C2×C411yescharacteristic, complemented
137#13133179C2×C411yescharacteristic, complemented
138C4×C22⋊D53—21no—
139C4×C22⋊D53—21no—
140C4×C22⋊D53—21no—
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#13133176C2×C411yescharacteristic
155#13133175C2×C411yescharacteristic, complemented
156#13133173—21no—
157#13133173—21no—
158C2×#11719919—21no—
159C2×#11719919—21no—
160C2×#11719919D411yescharacteristic
161C4⋊C4×D53C2×C411yescharacteristic, complemented
162C2×C22⋊Dic53—21no—
163C2×C22⋊Dic53—21no—
164C2×C22⋊Dic53D411yescharacteristic
165C2×#11719921—21no—
166C2×#11719921—21no—
167C2×#11719921D411yescharacteristic
168C22⋊C4×D53—21no—
169C22⋊C4×D53—21no—
170C2×C4×Dic53—21no—
171C2×C4×Dic53C2311yescharacteristic
172#13133146—21no—
173#13133146—21no—
174C22⋊#88322—21no—
175C22⋊#88322C2311yescharacteristic
176C22⋊#88322C2311yescharacteristic
177#13133129—21no—
178#13133129—21no—
179#13133127—21no—
180C8×Dic53—21no—
181#13133124—21no—
182#13133124—21no—
183#13133124—21no—
184#13133124—21no—
185#13133124C2311yescharacteristic
186#13133124C2311yescharacteristic
187C22×D4×C53—21no—
188C22×D4×C53C2×C411yescharacteristic
189C23×C4×C53—21no—
190C23×C4×C53C2311yescharacteristic
191C22×C8×C53—21no—
192#121×C53—21no—
193#121×C53—21no—
194#121×C53C2×C411yescharacteristic
195#121×C53C2×C411yescharacteristic
196#121×C53C2311yescharacteristic
197#121×C53C2311yescharacteristic
198C2×C4⋊C4×C53C2×C411yescharacteristic
199C2×C22⋊C4×C53—21no—
200C22⋊C8×C53—21no—
201C22⋊C8×C53C2311yescharacteristic
202C22⋊C8×C53C2311yescharacteristic
203#95×C53—21no—
204#95×C53C2311yescharacteristic
205#95×C53C2311yescharacteristic
206C24×C53—21no—
207C24×C53C2×D411yescharacteristic
208C23×D53—21no—
209C23×D53C2×D411yescharacteristic
210C2×D4×C53—21no—
211C2×D4×C53—21no—
212C2×D4×C53—21no—
213C2×D4×C53—21no—
214C2×D4×C53—21no—
215C2×D4×C53—81no—
216C2×D4×C53—81no—
217C2×D4×C53—81no—
218C2×D4×C53C22×C411yescharacteristic
219C2×D4×C53C22×C411yescharacteristic
220C22×C4×C53—21no—
221C22×C4×C53—21no—
222C22×C4×C53—21no—
223C22×C4×C53—42no—
224C22×C4×C53—81no—
225C22×C4×C53—81no—
226C22×C4×C53—81no—
227C22×C4×C53C22×C411yescharacteristic
228C22×C4×C53C22×C411yescharacteristic
229C22×C4×C53C2×D411yescharacteristic
230C22×C4×C53C2×D411yescharacteristic
231C22×C4×C53C2×D411yescharacteristic
232C22×C4×C53C2411yescharacteristic
233C2×C22⋊D53—21no—
234C2×C22⋊D53—21no—
235C2×C22⋊D53—21no—
236C2×C22⋊D53—21no—
237C2×C22⋊D53—21no—
238C2×C22⋊D53—21no—
239C2×C22⋊D53—21no—
240C2×C22⋊D53—21no—
241C2×C22⋊D53—21no—
242C2×C22⋊D53—42no—
243C2×C22⋊D53—44no—
244C2×C22⋊D53C22⋊C411yescharacteristic
245C2×C22⋊D53C22⋊C411yescharacteristic
246C2×C22⋊D53C22⋊C411yescharacteristic
247C2×C22⋊D53C22⋊C411yescharacteristic
248C22×Dic53—21no—
249C22×Dic53—21no—
250C22×Dic53—21no—
251C22×Dic53—21no—
252C22×Dic53—21no—
253C22×Dic53C2×D411yescharacteristic
254C22×Dic53C2×D411yescharacteristic
255C22×Dic53C2×D411yescharacteristic
256#11719947—81no—
257#11719947—81no—
258#11719947—81no—
259D4×D53—81no—
260D4×D53—81no—
261D4×D53—81no—
262#11719945—81no—
263C2×D212—21no—
264C2×D212C22×C411yescharacteristic
265C2×C4×D53—21no—
266C2×C4×D53—21no—
267C2×C4×D53—21no—
268C2×C4×D53—81no—
269C2×C4×D53C22×C411yescharacteristic
270C2×C4×D53C22×C411yescharacteristic
271C2×C4×D53C2×D411yescharacteristic
272C2×C4×D53C2×D411yescharacteristic
273C2×Dic106—21no—
274C2×Dic106C22×C411yescharacteristic
275C2×C8×C53—21no—
276C2×C8×C53—21no—
277C2×C8×C53—81no—
278C4⋊C4×C53—21no—
279C4⋊C4×C53C22×C411yescharacteristic
280C4⋊C4×C53C22×C411yescharacteristic
281C22⋊C4×C53—21no—
282C22⋊C4×C53—21no—
283C22⋊C4×C53—21no—
284C22⋊C4×C53—21no—
285C22⋊Dic53—21no—
286C22⋊Dic53—21no—
287C22⋊Dic53—21no—
288C22⋊Dic53—21no—
289C22⋊Dic53—21no—
290C22⋊Dic53—21no—
291C22⋊Dic53—21no—
292C22⋊Dic53—21no—
293C22⋊Dic53—21no—
294C22⋊Dic53—42no—
295C22⋊Dic53C22⋊C411yescharacteristic
296C22⋊Dic53C22⋊C411yescharacteristic
297C22⋊Dic53C22⋊C411yescharacteristic
298C22⋊Dic53C22⋊C411yescharacteristic
299#11719921—21no—
300#11719921—21no—
301#11719921—21no—
302#11719921—21no—
303#11719921—21no—
304#11719921—21no—
305#11719921—81no—
306#11719921—81no—
307#11719921C22⋊C411yescharacteristic
308#11719921C22⋊C411yescharacteristic
309#11719921C22⋊C411yescharacteristic
310#11719921C22⋊C411yescharacteristic
311C4⋊Dic53—21no—
312C4⋊Dic53—21no—
313C4⋊Dic53C22×C411yescharacteristic
314C4⋊Dic53C22×C411yescharacteristic
315#11719919—21no—
316#11719919—21no—
317#11719919—21no—
318#11719919—21no—
319#11719919—21no—
320#11719919—21no—
321#11719919—81no—
322#11719919—81no—
323#11719919C22⋊C411yescharacteristic
324#11719919C22⋊C411yescharacteristic
325#11719919C22⋊C411yescharacteristic
326#11719919C22⋊C411yescharacteristic
327C4×Dic53—21no—
328C4×Dic53—21no—
329C4×Dic53—21no—
330C4×Dic53—81no—
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—21no—
345C23×C53—41no—
346C23×C53—42no—
347C23×C53—81no—
348C23×C53—81no—
349C23×C53C2×C22⋊C411yescharacteristic
350C23×C53C2×C22⋊C411yescharacteristic
351C23×C53C22×D411yescharacteristic
352C22×D53—21no—
353C22×D53—21no—
354C22×D53—21no—
355C22×D53—41no—
356C22×D53—41no—
357C22×D53—42no—
358C22×D53—81no—
359C22×D53—81no—
360C22×D53C2×C22⋊C411yescharacteristic
361C22×D53C2×C22⋊C411yescharacteristic
362D4×C53—41no—
363D4×C53—41no—
364D4×C53—41no—
365D4×C53—41no—
366D4×C53—41no—
367D4×C53—41no—
368D4×C53—81no—
369D4×C53—81no—
370D4×C53—81no—
371C2×C4×C53—21no—
372C2×C4×C53—21no—
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—41no—
384C2×C4×C53—41no—
385C2×C4×C53—81no—
386C2×C4×C53—84no—
387C2×C4×C53C2×C22⋊C411yescharacteristic
388C2×C4×C53C2×C22⋊C411yescharacteristic
389C2×C4×C53C23×C411yescharacteristic
390C2×C4×C53C22×D411yescharacteristic
391C22⋊D53—22no—
392C22⋊D53—22no—
393C22⋊D53—41no—
394C22⋊D53—41no—
395C22⋊D53—42no—
396C22⋊D53—42no—
397C22⋊D53—41no—
398C22⋊D53—41no—
399C22⋊D53—42no—
400C22⋊D53—81no—
401C22⋊D53—81no—
402C22⋊D53—81no—
403C22⋊D53—81no—
404C22⋊D53—81no—
405C2×Dic53—21no—
406C2×Dic53—21no—
407C2×Dic53—21no—
408C2×Dic53—21no—
409C2×Dic53—21no—
410C2×Dic53—41no—
411C2×Dic53—41no—
412C2×Dic53—42no—
413C2×Dic53—41no—
414C2×Dic53—41no—
415C2×Dic53—41no—
416C2×Dic53—41no—
417C2×Dic53—41no—
418C2×Dic53—41no—
419C2×Dic53—81no—
420C2×Dic53—81no—
421C2×Dic53C2×C22⋊C411yescharacteristic
422C2×Dic53C2×C22⋊C411yescharacteristic
423C2×Dic53C2×C22⋊C411yescharacteristic
424C2×Dic53C2×C22⋊C411yescharacteristic
425C2×Dic53C2×C22⋊C411yescharacteristic
426C2×Dic53C2×C22⋊C411yescharacteristic
427D212—41no—
428D212—81no—
429C4×D53—41no—
430C4×D53—41no—
431C4×D53—41no—
432C4×D53—41no—
433C4×D53—81no—
434C4×D53—81no—
435C4×D53—81no—
436Dic106—41no—
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—41no—
456C22×C53—41no—
457C22×C53—41no—
458C22×C53—162no—
459C22×C53#42112yes—
460C22×C53C22×C22⋊C411yescharacteristic
461C22×C53#57611yescharacteristic
462C22×C53#57711yescharacteristic
463C2×D53—21no—
464C2×D53—21no—
465C2×D53—21no—
466C2×D53—21no—
467C2×D53—21no—
468C2×D53—21no—
469C2×D53—41no—
470C2×D53—41no—
471C2×D53—41no—
472C2×D53—81no—
473C2×D53—81no—
474C2×D53—162no—
475C4×C53—21no—
476C4×C53—21no—
477C4×C53—21no—
478C4×C53—21no—
479C4×C53—41no—
480C4×C53—41no—
481C4×C53—81no—
482C4×C53—81no—
483Dic53—21no—
484Dic53—21no—
485Dic53—21no—
486Dic53—21no—
487Dic53—21no—
488Dic53—21no—
489Dic53—41no—
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#1501—531no—
508C2×#327D5311yescharacteristic, complemented
509C2×C53—21no—
510C2×C53—21no—
511C2×C53—22no—
512C2×C53—41no—
513C2×C53—81no—
514C2×C53—81no—
515C2×C53#288311yescharacteristic
516C2×C53#289711yescharacteristic
517C2×C53C2×#42111yescharacteristic
518D53—41no—
519D53—41no—
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#525—531no—
540C2×#121—531no—
541C2×#121C2×D5311yescharacteristic
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⋊C4—531no—
563C2×#95C2×D5311yescharacteristic, complemented
564#328—531no—
565#328—531no—
566#328—531no—
567#328—531no—
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#327C2×D5311yescharacteristic
577#327C2×D5311yescharacteristic
578#327C2×D5311yescharacteristic, complemented
579#327C2×D5311yescharacteristic, complemented
580C53#1759711yescharacteristic, complemented, Sylow
581C2×#41—531no—
582C2×#41—531no—
583C2×#41—1061no—
584C22×D4—21no—
585C22×D4—531no—
586C22×D4—531no—
587C22×D4—1061no—
588C22×D4—1061no—
589C22×D4C4×D5311yescharacteristic
590C23×C4—21no—
591C23×C4—531no—
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—1061no—
610#123—1061no—
611#123—1061no—
612#123—1061no—
613#123—1061no—
614#123—1061no—
615#123—1061no—
616C22⋊Q8—531no—
617C22⋊Q8—531no—
618C22⋊Q8—531no—
619C22⋊Q8—1061no—
620C22⋊Q8—1061no—
621#121—21no—
622#121—21no—
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#121C4×D5311yescharacteristic
640#121C4×D5311yescharacteristic
641#121C22×D5311yescharacteristic
642#121C22×D5311yescharacteristic
643#120—1061no—
644#120—1061no—
645#120—1061no—
646#120—1061no—
647#120—1061no—
648#120—1061no—
649C4×Q8—531no—
650C4×D4—531no—
651C4×D4—531no—
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—1061no—
662C4×D4—1061no—
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—531no—
673#117—1061no—
674#117—1061no—
675C2×C4⋊C4—531no—
676C2×C4⋊C4—531no—
677C2×C4⋊C4—1061no—
678C2×C4⋊C4—1061no—
679C2×C4⋊C4C4×D5311yescharacteristic
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—531no—
690C2×C42—1061no—
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—21no—
704#95—531no—
705#95—531no—
706#95—1061no—
707#95—1061no—
708#95—1061no—
709#95—1061no—
710#95C22×D5311yescharacteristic
711#95C22×D5311yescharacteristic
712C24—21no—
713C24—531no—
714C24—1061no—
715C24D4×D5311yescharacteristic
716#41—4241no—
717#41—4241no—
718#41—4241no—
719#41—4241no—
720C2×Q8—531no—
721C2×Q8—1061no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—81no—
728C2×D4—81no—
729C2×D4—81no—
730C2×D4—531no—
731C2×D4—531no—
732C2×D4—531no—
733C2×D4—531no—
734C2×D4—531no—
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—1061no—
744C2×D4—1061no—
745C2×D4—4241no—
746C2×D4—4241no—
747C2×D4—4241no—
748C2×D4—2122no—
749C2×D4—2124no—
750C2×D4C2×C4×D5311yescharacteristic
751C2×D4C2×C4×D5311yescharacteristic
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—42no—
756C22×C4—81no—
757C22×C4—81no—
758C22×C4—81no—
759C22×C4—531no—
760C22×C4—531no—
761C22×C4—531no—
762C22×C4—531no—
763C22×C4—531no—
764C22×C4—531no—
765C22×C4—531no—
766C22×C4—1061no—
767C22×C4—1061no—
768C22×C4—1061no—
769C22×C4—1061no—
770C22×C4—1061no—
771C22×C4—1061no—
772C22×C4—1061no—
773C22×C4—1061no—
774C22×C4—4241no—
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—531no—
791C4⋊C4—531no—
792C4⋊C4—531no—
793C4⋊C4—531no—
794C4⋊C4—531no—
795C4⋊C4—531no—
796C4⋊C4—1061no—
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—531no—
813C22⋊C4—531no—
814C22⋊C4—531no—
815C22⋊C4—531no—
816C22⋊C4—531no—
817C22⋊C4—531no—
818C22⋊C4—531no—
819C22⋊C4—531no—
820C22⋊C4—1061no—
821C22⋊C4—1061no—
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—4241no—
836C22⋊C4—4241no—
837C22⋊C4—2122no—
838C42—531no—
839C42—531no—
840C42—531no—
841C42—531no—
842C42—1061no—
843C42—1061no—
844C42—1061no—
845C42—4241no—
846C23—22no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—41no—
852C23—42no—
853C23—81no—
854C23—81no—
855C23—531no—
856C23—531no—
857C23—1061no—
858C23—1061no—
859C23—1061no—
860C23—4241no—
861C23—4241no—
862C23—2121no—
863C23—2121no—
864C23—2122no—
865C23C22⋊C4×D5311yescharacteristic
866C23C22⋊C4×D5311yescharacteristic
867C23C2×D4×D5311yescharacteristic
868Q8—4241no—
869Q8—2121no—
870D4—41no—
871D4—41no—
872D4—41no—
873D4—41no—
874D4—41no—
875D4—41no—
876D4—81no—
877D4—81no—
878D4—81no—
879D4—1062no—
880D4—1062no—
881D4—4241no—
882D4—4241no—
883D4—4241no—
884D4—4241no—
885D4—4241no—
886D4—4241no—
887D4—2121no—
888D4—2121no—
889D4—2121no—
890D4—2122no—
891D4—2122no—
892D4—2122no—
893D4—2121no—
894D4—2121no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—41no—
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—81no—
910C2×C4—84no—
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—1061no—
922C2×C4—4241no—
923C2×C4—4241no—
924C2×C4—4241no—
925C2×C4—4241no—
926C2×C4—4241no—
927C2×C4—2121no—
928C2×C4—2121no—
929C2×C4—2121no—
930C2×C4—2121no—
931C2×C4—2121no—
932C2×C4—2121no—
933C2×C4—2122no—
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—41no—
961C22—41no—
962C22—41no—
963C22—162no—
964C22—8482no—
965C22—1061no—
966C22—1061no—
967C22—1061no—
968C22—1061no—
969C22—1061no—
970C22—1061no—
971C22—4241no—
972C22—4241no—
973C22—2121no—
974C22—2121no—
975C22—2121no—
976C22#1681063812yes—
977C22C2×C22⋊C4×D5311yescharacteristic
978C22#1681142411yescharacteristic
979C22#1681142911yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—41no—
985C4—41no—
986C4—81no—
987C4—81no—
988C4—1061no—
989C4—1061no—
990C4—1061no—
991C4—1061no—
992C4—1061no—
993C4—1061no—
994C4—4241no—
995C4—4241no—
996C4—2121no—
997C4—2121no—
998C4—2121no—
999C2—21no—
1000C2—21no—
1001C2—22no—
1002C2—41no—
1003C2—81no—
1004C2—81no—
1005C2—4241no—
1006C2—2121no—
1007C2—2121no—
1008C2#2028317311yescharacteristic
1009C2#2028323611yescharacteristic
1010C2C2×#1681063811yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#327C2
socleC22×C53C22×C22⋊C4
prime radical#20288741C2
cosocleC22×C4×C53C24
hypercenterC2×#327D53
hypocenterC53#17597
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. #20283746C2semidirect
3. #20277349C2semidirect
4. #20273289C2semidirect
5. #20273281C2semidirect
6. #20273273C2semidirect
7. #20273268C2semidirect
8. #20273260C2semidirect
9. #20273255C2semidirect
10. #20273250C2semidirect
11. #20273242C2semidirect
12. #20273231C2semidirect
13. #20273217C2semidirect
14. #20273207C2semidirect
15. C2×C53×#327C2semidirect
16. #16811337C4semidirect
17. #16811328C4semidirect
18. #16811321C4semidirect
19. #16811320C4semidirect
21. #16811291C4semidirect
22. #16811270C4semidirect
24. #16811267C4semidirect
27. D4×C22⋊D53C4semidirect
42. #16810677C22semidirect
43. #16810673C22semidirect
44. #16810587C22semidirect
45. #16810585C22semidirect
46. C22⋊C8×D53C22semidirect
51. #16810490C22semidirect
52. #16810487C22semidirect
53. #16810485C22semidirect
54. #16810482C22semidirect
55. C4×C22⋊Dic53C22semidirect
56. #16810361C22semidirect
57. #16810361C22semidirect
58. #16810359C22semidirect
59. #16810359C22semidirect
60. #16810358C22semidirect
61. #16810358C22semidirect
64. #16810357C22semidirect
65. #16810357C22semidirect
66. #16810356C22semidirect
67. #16810356C22semidirect
69. C2×C22⋊C8×C53C22semidirect
70. C2×#95×C53C22semidirect
73. C53×#327C22semidirect
74. C53×#327C22semidirect
77. C2×#11719947C2×C4semidirect
81. C2×D4×D53C2×C4semidirect
86. #13133216C2×C4semidirect
88. #13133213C2×C4semidirect
92. #13133208C2×C4semidirect
95. #13133204C2×C4semidirect
105. #13133197C2×C4semidirect
110. #13133192C2×C4semidirect
124. #13133188C2×C4semidirect
125. #13133188C2×C4semidirect
132. #13133182C2×C4semidirect
135. D4×Dic53C2×C4semidirect
136. D4×Dic53C2×C4semidirect
137. #13133179C2×C4semidirect
155. #13133175C2×C4semidirect
161. C4⋊C4×D53C2×C4semidirect
508. C2×#327D53semidirect
553. C2×C22⋊C8C2×D53semidirect
563. C2×#95C2×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
#202887412
#202837462
#202773492
#202732892
#202732812
#202732732
#202732682
#202732602
#202732552
#202732502
#202732422
#202732312
#202732172
#202732072
C2×C53×#3272
#1759753