Finite Group Databasebeta

← #27351618

Subgroups — #27351618

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#20277350C211yesmaximal, characteristic, complemented
4#20273289C211yesmaximal, characteristic, complemented
5#20273273C211yesmaximal, characteristic, complemented
6#20273272C211yesmaximal, characteristic, complemented
7#20273260C211yesmaximal, characteristic, complemented
8#20273256C211yesmaximal, characteristic, complemented
9#20273250C211yesmaximal, characteristic, complemented
10#20273244C211yesmaximal, characteristic, complemented
11#20273229C211yesmaximal, characteristic, complemented
12#20273216C211yesmaximal, characteristic, complemented
13#20273203C211yesmaximal, characteristic, complemented
14#327×D53C211yesmaximal, characteristic, complemented
15C53×#1519C211yesmaximal, 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#16810517—21no—
48#16810504—21no—
49#16810499—21no—
50#16810494—21no—
51#16810490C2211yescharacteristic, complemented
52#16810487C2211yescharacteristic, complemented
53#16810486C2211yescharacteristic, complemented
54#16810470C2211yescharacteristic, complemented
55#95×D53C2211yescharacteristic, 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
70C53×#380C2211yescharacteristic, complemented
71C53×#327C2211yescharacteristic
72C53×#327C2211yescharacteristic
73C53×#327C2211yescharacteristic, complemented
74C53×#327C2211yescharacteristic, complemented
75C2×#11719945C2×C411yescharacteristic, complemented
76C2×#11719947—21no—
77C2×#11719947C2×C411yescharacteristic
78C22×C22⋊D53—21no—
79C22×C22⋊D53D411yescharacteristic
80C2×D4×D53—21no—
81C2×D4×D53C2×C411yescharacteristic
82C22×C4×D53—21no—
83C22×C4×D53C2311yescharacteristic
84C2×#11719917—21no—
85C2×#11719912—21no—
86C2×C8×D53—21no—
87#13133216C2×C411yescharacteristic, complemented
88#13133213—21no—
89#13133213C2×C411yescharacteristic, complemented
90#13133212—21no—
91#13133210—21no—
92#13133210—21no—
93#13133208C2×C411yescharacteristic, complemented
94#13133207—21no—
95#13133204—21no—
96#13133204C2×C411yescharacteristic, complemented
97#13133203—21no—
98#13133203—21no—
99#13133202—21no—
100#13133200—21no—
101#13133199—21no—
102#13133199—21no—
103#13133198—21no—
104#13133198—21no—
105#13133198—21no—
106#13133197C2×C411yescharacteristic
107#13133196—21no—
108#13133196C2×C411yescharacteristic, complemented
109#13133196C2311yescharacteristic
110#13133195—21no—
111#13133192C2×C411yescharacteristic
112#13133191—21no—
113#13133191C2×C411yescharacteristic, complemented
114#13133191C2311yescharacteristic
115#13133190—21no—
116#13133190—21no—
117#13133189—21no—
118#13133189—21no—
119#13133189—21no—
120#13133189—21no—
121#13133189—21no—
122#13133189—21no—
123#13133188—21no—
124#13133188—21no—
125#13133188C2×C411yescharacteristic
126#13133188C2×C411yescharacteristic
127#13133186—21no—
128#13133186—21no—
129#13133186—21no—
130#13133185—21no—
131#13133185—21no—
132#13133185—21no—
133#13133182C2×C411yescharacteristic, complemented
134D4×Dic53—21no—
135D4×Dic53—21no—
136D4×Dic53C2×C411yescharacteristic, complemented
137D4×Dic53C2×C411yescharacteristic, complemented
138#13133179C2×C411yescharacteristic, complemented
139C4×C22⋊D53—21no—
140C4×C22⋊D53—21no—
141C4×C22⋊D53—21no—
142C4×C22⋊D53—21no—
143C4×C22⋊D53C2×C411yescharacteristic
144C4×C22⋊D53C2×C411yescharacteristic
145C4×C22⋊D53C2×C411yescharacteristic
146C4×C22⋊D53C2×C411yescharacteristic
147C4×C22⋊D53D411yescharacteristic
148C4×C22⋊D53D411yescharacteristic
149C4×C22⋊D53D411yescharacteristic
150C4×C22⋊D53D411yescharacteristic
151#13133177—21no—
152#13133177—21no—
153#13133177—21no—
154#13133177—21no—
155#13133176C2×C411yescharacteristic, complemented
156#13133175C2×C411yescharacteristic
157#13133173—21no—
158#13133173—21no—
159C2×#11719919—21no—
160C2×#11719919D411yescharacteristic
161C4⋊C4×D53C2×C411yescharacteristic
162C2×C22⋊Dic53—21no—
163C2×C22⋊Dic53—21no—
164C2×C22⋊Dic53D411yescharacteristic
165C2×#11719921—21no—
166C2×#11719921D411yescharacteristic
167C22⋊C4×D53—21no—
168C22⋊C4×D53—21no—
169C2×C4×Dic53—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
187C22×D4×C53—21no—
188C22×D4×C53C2×C411yescharacteristic, complemented
189C23×C4×C53C2311yescharacteristic
190C22×C8×C53—21no—
191#121×C53—21no—
192#121×C53—21no—
193#121×C53C2×C411yescharacteristic, complemented
194#121×C53C2×C411yescharacteristic, complemented
195#121×C53C2311yescharacteristic
196#121×C53C2311yescharacteristic
197C2×C4⋊C4×C53—21no—
198C2×C4⋊C4×C53C2×C411yescharacteristic, complemented
199C2×C22⋊C4×C53—21no—
200C2×C22⋊C4×C53—21no—
201C22⋊C8×C53—21no—
202C22⋊C8×C53C2311yescharacteristic
203C22⋊C8×C53C2311yescharacteristic
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—81no—
224C22×C4×C53C22×C411yescharacteristic
225C22×C4×C53C22×C411yescharacteristic
226C22×C4×C53C2×D411yescharacteristic
227C22×C4×C53C2×D411yescharacteristic
228C22×C4×C53C2×D411yescharacteristic
229C22×C4×C53C2411yescharacteristic
230C2×C22⋊D53—21no—
231C2×C22⋊D53—21no—
232C2×C22⋊D53—21no—
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—42no—
240C2×C22⋊D53—44no—
241C2×C22⋊D53C22⋊C411yescharacteristic
242C2×C22⋊D53C22⋊C411yescharacteristic
243C2×C22⋊D53C22⋊C411yescharacteristic
244C2×C22⋊D53C22⋊C411yescharacteristic
245C22×Dic53—21no—
246C22×Dic53—21no—
247C22×Dic53—21no—
248C22×Dic53—21no—
249C22×Dic53—21no—
250C22×Dic53C2×D411yescharacteristic
251C22×Dic53C2×D411yescharacteristic
252C22×Dic53C2×D411yescharacteristic
253#11719947—81no—
254#11719947—81no—
255#11719947—81no—
256D4×D53—81no—
257D4×D53—81no—
258D4×D53—81no—
259#11719945—81no—
260C2×D212—21no—
261C2×D212C22×C411yescharacteristic
262C2×C4×D53—21no—
263C2×C4×D53—21no—
264C2×C4×D53—21no—
265C2×C4×D53—42no—
266C2×C4×D53—81no—
267C2×C4×D53—81no—
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×C53—81no—
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—81no—
287C22⋊Dic53—21no—
288C22⋊Dic53—21no—
289C22⋊Dic53—21no—
290C22⋊Dic53—21no—
291C22⋊Dic53—21no—
292C22⋊Dic53—21no—
293C22⋊Dic53—21no—
294C22⋊Dic53—21no—
295C22⋊Dic53—21no—
296C22⋊Dic53—81no—
297C22⋊Dic53C22⋊C411yescharacteristic
298C22⋊Dic53C22⋊C411yescharacteristic
299C22⋊Dic53C22⋊C411yescharacteristic
300C22⋊Dic53C22⋊C411yescharacteristic
301#11719921—21no—
302#11719921—21no—
303#11719921—21no—
304#11719921—21no—
305#11719921—21no—
306#11719921—21no—
307#11719921—42no—
308#11719921C22⋊C411yescharacteristic
309#11719921C22⋊C411yescharacteristic
310#11719921C22⋊C411yescharacteristic
311#11719921C22⋊C411yescharacteristic
312C4⋊Dic53—21no—
313C4⋊Dic53—21no—
314C4⋊Dic53C22×C411yescharacteristic
315C4⋊Dic53C22×C411yescharacteristic
316#11719919—21no—
317#11719919—21no—
318#11719919—21no—
319#11719919—21no—
320#11719919—21no—
321#11719919—21no—
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—21no—
343C23×C53—21no—
344C23×C53—41no—
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—22no—
355C22×D53—21no—
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×C53C2×C22⋊C411yescharacteristic
387C2×C4×C53C2×C22⋊C411yescharacteristic
388C2×C4×C53C23×C411yescharacteristic
389C2×C4×C53C22×D411yescharacteristic
390C22⋊D53—22no—
391C22⋊D53—22no—
392C22⋊D53—41no—
393C22⋊D53—41no—
394C22⋊D53—42no—
395C22⋊D53—42no—
396C22⋊D53—41no—
397C22⋊D53—41no—
398C22⋊D53—42no—
399C22⋊D53—81no—
400C22⋊D53—81no—
401C22⋊D53—81no—
402C22⋊D53—81no—
403C22⋊D53—81no—
404C2×Dic53—21no—
405C2×Dic53—21no—
406C2×Dic53—21no—
407C2×Dic53—21no—
408C2×Dic53—21no—
409C2×Dic53—41no—
410C2×Dic53—41no—
411C2×Dic53—42no—
412C2×Dic53—41no—
413C2×Dic53—41no—
414C2×Dic53—41no—
415C2×Dic53—41no—
416C2×Dic53—41no—
417C2×Dic53—41no—
418C2×Dic53—81no—
419C2×Dic53—81no—
420C2×Dic53C2×C22⋊C411yescharacteristic
421C2×Dic53C2×C22⋊C411yescharacteristic
422C2×Dic53C2×C22⋊C411yescharacteristic
423C2×Dic53C2×C22⋊C411yescharacteristic
424C2×Dic53C2×C22⋊C411yescharacteristic
425C2×Dic53C2×C22⋊C411yescharacteristic
426D212—41no—
427D212—81no—
428C4×D53—41no—
429C4×D53—41no—
430C4×D53—41no—
431C4×D53—41no—
432C4×D53—81no—
433C4×D53—81no—
434C4×D53—81no—
435C4×D53—84no—
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—21no—
451C22×C53—41no—
452C22×C53—41no—
453C22×C53—41no—
454C22×C53—41no—
455C22×C53—41no—
456C22×C53—41no—
457C22×C53—81no—
458C22×C53—81no—
459C22×C53—162no—
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—42no—
469C2×D53—42no—
470C2×D53—41no—
471C2×D53—41no—
472C2×D53—41no—
473C2×D53—162no—
474C2×D53#42112yes—
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#1519D5311yescharacteristic, complemented
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×#327—531no—
509C2×C53—21no—
510C2×C53—21no—
511C2×C53—41no—
512C2×C53—41no—
513C2×C53—81no—
514C2×C53—81no—
515C2×C53#288311yescharacteristic
516C2×C53#289711yescharacteristic
517C2×C53C2×#42111yescharacteristic
518D53—22no—
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#380C2×D5311yescharacteristic, complemented
562C4×C22⋊C4—531no—
563C2×#95—531no—
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, complemented
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—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, complemented
640#121C4×D5311yescharacteristic, complemented
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—21no—
676C2×C4⋊C4—531no—
677C2×C4⋊C4—531no—
678C2×C4⋊C4—1061no—
679C2×C4⋊C4C4×D5311yescharacteristic, complemented
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—531no—
683C2×C22⋊C4—531no—
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—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—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—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—81no—
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—1061no—
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—81no—
813C22⋊C4—531no—
814C22⋊C4—531no—
815C22⋊C4—531no—
816C22⋊C4—531no—
817C22⋊C4—531no—
818C22⋊C4—531no—
819C22⋊C4—531no—
820C22⋊C4—531no—
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—1061no—
836C22⋊C4—4241no—
837C22⋊C4—2122no—
838C42—531no—
839C42—531no—
840C42—531no—
841C42—531no—
842C42—1061no—
843C42—1061no—
844C42—1061no—
845C42—4241no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—41no—
851C23—41no—
852C23—42no—
853C23—81no—
854C23—81no—
855C23—531no—
856C23—531no—
857C23—1062no—
858C23—1061no—
859C23—1061no—
860C23—1061no—
861C23—4241no—
862C23—4241no—
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—531no—
911C2×C4—531no—
912C2×C4—531no—
913C2×C4—531no—
914C2×C4—531no—
915C2×C4—531no—
916C2×C4—1061no—
917C2×C4—1061no—
918C2×C4—1061no—
919C2×C4—1061no—
920C2×C4—1061no—
921C2×C4—4241no—
922C2×C4—4241no—
923C2×C4—4241no—
924C2×C4—4244no—
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—21no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—81no—
963C22—81no—
964C22—162no—
965C22—532no—
966C22—8482no—
967C22—1061no—
968C22—1061no—
969C22—1061no—
970C22—1061no—
971C22—1061no—
972C22—2122no—
973C22—2122no—
974C22—2121no—
975C22—2121no—
976C22—2121no—
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—41no—
1002C2—41no—
1003C2—81no—
1004C2—81no—
1005C2—1062no—
1006C2—4241no—
1007C2—2121no—
1008C2#2028317311yescharacteristic
1009C2#2028323611yescharacteristic
1010C2#421×D5311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1519C2
socleC22×C53C22×C22⋊C4
prime radical#20288741C2
cosocleC22×C4×C53C24
hypercenter#1519D53
hypocenterC53#17597
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1519

Complements

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

NH ≅ G/Ntype
2. #20283746C2semidirect
3. #20277350C2semidirect
4. #20273289C2semidirect
5. #20273273C2semidirect
6. #20273272C2semidirect
7. #20273260C2semidirect
8. #20273256C2semidirect
9. #20273250C2semidirect
10. #20273244C2semidirect
11. #20273229C2semidirect
12. #20273216C2semidirect
13. #20273203C2semidirect
14. #327×D53C2semidirect
15. C53×#1519C2semidirect
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. #16810486C22semidirect
54. #16810470C22semidirect
55. #95×D53C22semidirect
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. C53×#380C22semidirect
73. C53×#327C22semidirect
74. C53×#327C22semidirect
75. C2×#11719945C2×C4semidirect
87. #13133216C2×C4semidirect
89. #13133213C2×C4semidirect
93. #13133208C2×C4semidirect
96. #13133204C2×C4semidirect
108. #13133196C2×C4semidirect
113. #13133191C2×C4semidirect
133. #13133182C2×C4semidirect
136. D4×Dic53C2×C4semidirect
137. D4×Dic53C2×C4semidirect
138. #13133179C2×C4semidirect
155. #13133176C2×C4semidirect
188. C22×D4×C53C2×C4semidirect
193. #121×C53C2×C4semidirect
194. #121×C53C2×C4semidirect
198. C2×C4⋊C4×C53C2×C4semidirect
498. #1519D53semidirect
553. C2×C22⋊C8C2×D53semidirect
561. #380C2×D53semidirect
578. #327C2×D53semidirect
579. #327C2×D53semidirect
580. C53#17597semidirect
589. C22×D4C4×D53semidirect
639. #121C4×D53semidirect
640. #121C4×D53semidirect
679. C2×C4⋊C4C4×D53semidirect

Maximal subgroups

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

subgroupindex
#202887412
#202837462
#202773502
#202732892
#202732732
#202732722
#202732602
#202732562
#202732502
#202732442
#202732292
#202732162
#202732032
#327×D532
C53×#15192
#1759753