Finite Group Databasebeta

← #27351287

Subgroups — #27351287

Order 13568.

1166 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288735C211yesmaximal, characteristic
2#20283751C211yesmaximal, characteristic, complemented
3#20277073C211yesmaximal, characteristic, complemented
4#20273239C211yesmaximal, characteristic, complemented
5#20273232C211yesmaximal, characteristic, complemented
6#20273229C211yesmaximal, characteristic, complemented
7#20273221C211yesmaximal, characteristic, complemented
8#20273218C211yesmaximal, characteristic, complemented
9#20273208C211yesmaximal, characteristic, complemented
10#20273206C211yesmaximal, characteristic, complemented
11#20273205C211yesmaximal, characteristic, complemented
12#20273200C211yesmaximal, characteristic, complemented
13C2×#16810356C211yesmaximal, characteristic, complemented
14#327×D53C211yesmaximal, characteristic, complemented
15C53×#1504C211yesmaximal, 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⋊D53—21no—
38C2×C4×C22⋊D53C2211yescharacteristic
39#16810699—21no—
40#16810692—21no—
41#16810691—21no—
42#16810686—21no—
43#16810677C2211yescharacteristic, complemented
44#16810673C2211yescharacteristic, complemented
45#16810585C2211yescharacteristic, complemented
46C2×C22⋊#88322C2211yescharacteristic, complemented
47C22⋊C8×D53C2211yescharacteristic, complemented
48#16810474—21no—
49#16810474C2211yescharacteristic, complemented
50C4×C22⋊Dic53—21no—
51C4×C22⋊Dic53C2211yescharacteristic, complemented
52#16810470—21no—
53#16810470C2211yescharacteristic, complemented
54#16810468C2211yescharacteristic, complemented
55#95×D53C2211yescharacteristic, 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
69C53×#407C2211yescharacteristic, complemented
70C2×#95×C53C2211yescharacteristic, complemented
71C53×#328C2211yescharacteristic, complemented
72C53×#328C2211yescharacteristic, complemented
73C53×#327C2211yescharacteristic, complemented
74C53×#327C2211yescharacteristic, complemented
75C2×#11719949C2×C411yescharacteristic, complemented
76C2×#11719947—21no—
77C22×D212C2×C411yescharacteristic, complemented
78C22×C22⋊D53—21no—
79C22×C22⋊D53D411yescharacteristic
80C2×D4×D53—21no—
81C2×D4×D53—21no—
82C2×D4×D53C2×C411yescharacteristic, complemented
83C22×C4×D53—21no—
84C22×C4×D53C2311yescharacteristic
85C2×#11719912—21no—
86C22×#88322—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, complemented
116#13133191C2×C411yescharacteristic, complemented
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—28no—
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#13133175—21no—
156#13133175C2×C411yescharacteristic, complemented
157#13133174—21no—
158C2×C4⋊Dic53C2×C411yescharacteristic, complemented
159C2×#11719919—21no—
160C2×#11719919D411yescharacteristic
161C4⋊C4×D53C2×C411yescharacteristic, complemented
162C2×C22⋊Dic53—21no—
163C2×C22⋊Dic53D411yescharacteristic
164C2×#11719921—21no—
165C2×#11719921—21no—
166C2×#11719921—21no—
167C2×#11719921D411yescharacteristic
168C22⋊C4×D53—21no—
169C22⋊C4×D53—21no—
170C2×C4×Dic53—21no—
171C2×C4×Dic53—21no—
172C2×C4×Dic53—21no—
173C2×C4×Dic53—21no—
174C2×C4×Dic53C2311yescharacteristic
175#13133146—21no—
176#13133146—21no—
177C22⋊#88322—21no—
178C22⋊#88322C2311yescharacteristic
179C22⋊#88322C2311yescharacteristic
180#13133129—21no—
181#13133129—21no—
182#13133127—21no—
183C8×Dic53—21no—
184#13133124—21no—
185#13133124—21no—
186#13133124C2311yescharacteristic
187#13133124C2311yescharacteristic
188C2×#41×C53C2×C411yescharacteristic, complemented
189C23×C4×C53—21no—
190C23×C4×C53C2311yescharacteristic
191C2×M16×C53—21no—
192#123×C53—21no—
193C22⋊Q8×C53C2×C411yescharacteristic, complemented
194C22⋊Q8×C53C2311yescharacteristic
195#121×C53C2×C411yescharacteristic, complemented
196#121×C53C2311yescharacteristic
197#120×C53—21no—
198C4×D4×C53—21no—
199C4×D4×C53—21no—
200#117×C53C2×C411yescharacteristic, complemented
201C22⋊C8×C53—21no—
202C22⋊C8×C53C2311yescharacteristic
203C22⋊C8×C53C2311yescharacteristic
204#95×C53—21no—
205#95×C53C2311yescharacteristic
206#95×C53C2311yescharacteristic
207C24×C53C2×D411yescharacteristic
208C23×D53—21no—
209C23×D53—21no—
210C23×D53C2×D411yescharacteristic
211#41×C53—81no—
212C2×Q8×C53C22×C411yescharacteristic
213C2×D4×C53—21no—
214C2×D4×C53—21no—
215C2×D4×C53—21no—
216C2×D4×C53C22×C411yescharacteristic
217C22×C4×C53—21no—
218C22×C4×C53—21no—
219C22×C4×C53—24no—
220C22×C4×C53—21no—
221C22×C4×C53—81no—
222C22×C4×C53—81no—
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—24no—
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—81no—
240C2×C22⋊D53—81no—
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×Dic53C2×D411yescharacteristic
250C22×Dic53C2×D411yescharacteristic
251C22×Dic53C2×D411yescharacteristic
252#11719949—81no—
253#11719947—81no—
254#11719947—81no—
255D4×D53—44no—
256D4×D53—81no—
257D4×D53—81no—
258D4×D53—81no—
259C2×D212—21no—
260C2×D212—21no—
261C2×D212—21no—
262C2×D212—21no—
263C2×D212—81no—
264C2×D212C22×C411yescharacteristic
265C2×D212C22×C411yescharacteristic
266C2×C4×D53—21no—
267C2×C4×D53—24no—
268C2×C4×D53—21no—
269C2×C4×D53—21no—
270C2×C4×D53—21no—
271C2×C4×D53—81no—
272C2×C4×D53—81no—
273C2×C4×D53—81no—
274C2×C4×D53C22×C411yescharacteristic
275C2×C4×D53C22×C411yescharacteristic
276C2×C4×D53C2×D411yescharacteristic
277C2×C4×D53C2×D411yescharacteristic
278C2×Dic106—21no—
279M16×C53—81no—
280C2×C8×C53—21no—
281C2×C8×C53—21no—
282C4⋊C4×C53—21no—
283C4⋊C4×C53—21no—
284C4⋊C4×C53C22×C411yescharacteristic
285C4⋊C4×C53C22×C411yescharacteristic
286C22⋊C4×C53—21no—
287C22⋊C4×C53—21no—
288C22⋊C4×C53—21no—
289C22⋊C4×C53—21no—
290C22⋊C4×C53—21no—
291C42×C53—21no—
292C22⋊Dic53—24no—
293C22⋊Dic53—21no—
294C22⋊Dic53—21no—
295C22⋊Dic53C22⋊C411yescharacteristic
296C22⋊Dic53C22⋊C411yescharacteristic
297C22⋊Dic53C22⋊C411yescharacteristic
298C22⋊Dic53C22⋊C411yescharacteristic
299#11719921—24no—
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—21no—
309#11719921—21no—
310#11719921—21no—
311#11719921—21no—
312#11719921C22⋊C411yescharacteristic
313#11719921C22⋊C411yescharacteristic
314#11719921C22⋊C411yescharacteristic
315#11719921C22⋊C411yescharacteristic
316C4⋊Dic53—21no—
317C4⋊Dic53—21no—
318C4⋊Dic53—21no—
319C4⋊Dic53C22×C411yescharacteristic
320C4⋊Dic53C22×C411yescharacteristic
321#11719919—24no—
322#11719919—21no—
323#11719919—21no—
324#11719919—21no—
325#11719919—21no—
326#11719919C22⋊C411yescharacteristic
327#11719919C22⋊C411yescharacteristic
328#11719919C22⋊C411yescharacteristic
329#11719919C22⋊C411yescharacteristic
330C4×Dic53—24no—
331C4×Dic53—21no—
332C4×Dic53—21no—
333C4×Dic53—81no—
334C4×Dic53—81no—
335C4×Dic53—81no—
336C4×Dic53C22×C411yescharacteristic
337C4×Dic53C22×C411yescharacteristic
338C4×Dic53C2×D411yescharacteristic
339C4×Dic53C2×D411yescharacteristic
340C2×#88322—21no—
341C2×#88322—21no—
342C2×#88322—81no—
343#11719912—81no—
344C8×D53—81no—
345C23×C53—21no—
346C23×C53—21no—
347C23×C53—22no—
348C23×C53—21no—
349C23×C53—41no—
350C23×C53C2×C22⋊C411yescharacteristic
351C23×C53C2×C22⋊C411yescharacteristic
352C23×C53C22×D411yescharacteristic
353C22×D53—21no—
354C22×D53—21no—
355C22×D53—22no—
356C22×D53—21no—
357C22×D53—21no—
358C22×D53—41no—
359C22×D53—42no—
360C22×D53—42no—
361C22×D53—81no—
362C22×D53—81no—
363C22×D53—81no—
364C22×D53—81no—
365C22×D53C2×C22⋊C411yescharacteristic
366C22×D53C2×C22⋊C411yescharacteristic
367Q8×C53—41no—
368D4×C53—41no—
369D4×C53—41no—
370D4×C53—41no—
371D4×C53—42no—
372D4×C53—81no—
373C2×C4×C53—22no—
374C2×C4×C53—22no—
375C2×C4×C53—21no—
376C2×C4×C53—21no—
377C2×C4×C53—21no—
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—41no—
386C2×C4×C53—41no—
387C2×C4×C53—41no—
388C2×C4×C53—81no—
389C2×C4×C53—84no—
390C2×C4×C53C2×C22⋊C411yescharacteristic
391C2×C4×C53C2×C22⋊C411yescharacteristic
392C2×C4×C53C23×C411yescharacteristic
393C2×C4×C53C22×D411yescharacteristic
394C22⋊D53—22no—
395C22⋊D53—22no—
396C22⋊D53—22no—
397C22⋊D53—41no—
398C22⋊D53—41no—
399C22⋊D53—41no—
400C22⋊D53—41no—
401C22⋊D53—42no—
402C22⋊D53—81no—
403C22⋊D53—81no—
404C22⋊D53—81no—
405C22⋊D53—81no—
406C22⋊D53—81no—
407C22⋊D53#10414yes—
408C2×Dic53—21no—
409C2×Dic53—21no—
410C2×Dic53—22no—
411C2×Dic53—22no—
412C2×Dic53—22no—
413C2×Dic53—21no—
414C2×Dic53—21no—
415C2×Dic53—41no—
416C2×Dic53—41no—
417C2×Dic53—41no—
418C2×Dic53—41no—
419C2×Dic53—41no—
420C2×Dic53—81no—
421C2×Dic53—81no—
422C2×Dic53C2×C22⋊C411yescharacteristic
423C2×Dic53C2×C22⋊C411yescharacteristic
424C2×Dic53C2×C22⋊C411yescharacteristic
425C2×Dic53C2×C22⋊C411yescharacteristic
426C2×Dic53C2×C22⋊C411yescharacteristic
427C2×Dic53C2×C22⋊C411yescharacteristic
428D212—41no—
429D212—41no—
430D212—42no—
431D212—81no—
432D212—81no—
433D212—81no—
434C4×D53—41no—
435C4×D53—41no—
436C4×D53—41no—
437C4×D53—41no—
438C4×D53—42no—
439C4×D53—81no—
440C4×D53—81no—
441C4×D53—81no—
442C4×D53—84no—
443Dic106—81no—
444C8×C53—41no—
445C8×C53—41no—
446#88322—41no—
447#88322—41no—
448#17547—531nomaximal, Sylow
449C22×C53—21no—
450C22×C53—21no—
451C22×C53—21no—
452C22×C53—21no—
453C22×C53—21no—
454C22×C53—21no—
455C22×C53—21no—
456C22×C53—42no—
457C22×C53—42no—
458C22×C53—41no—
459C22×C53—41no—
460C22×C53—41no—
461C22×C53C2×#10412yes—
462C22×C53C22×C22⋊C411yescharacteristic
463C22×C53#57611yescharacteristic
464C22×C53#57711yescharacteristic
465C2×D53—21no—
466C2×D53—21no—
467C2×D53—21no—
468C2×D53—21no—
469C2×D53—21no—
470C2×D53—42no—
471C2×D53—42no—
472C2×D53—41no—
473C2×D53—41no—
474C2×D53—41no—
475C2×D53—41no—
476C2×D53—41no—
477C2×D53—41no—
478C2×D53—162no—
479C2×D53—162no—
480C2×D53C2×#10412yes—
481C4×C53—21no—
482C4×C53—21no—
483C4×C53—21no—
484C4×C53—21no—
485C4×C53—42no—
486C4×C53—42no—
487C4×C53—41no—
488C4×C53—41no—
489C4×C53—41no—
490Dic53—21no—
491Dic53—21no—
492Dic53—21no—
493Dic53—21no—
494Dic53—21no—
495Dic53—42no—
496Dic53—42no—
497Dic53—41no—
498Dic53—41no—
499Dic53C2×#10412yes—
500#3519—531no—
501#2974—531no—
502#2275—531no—
503#1509—531no—
504#1507—531no—
505#1507—531no—
506#1505—531no—
507#1504—531no—
508#1504D5311yescharacteristic, complemented
509#1502—531no—
510#1501—531no—
511#1501—531no—
512#1500—531no—
513C2×#327—531no—
514C2×#327—531no—
515C2×C53—21no—
516C2×C53—21no—
517C2×C53—22no—
518C2×C53—41no—
519C2×C53—81no—
520C2×C53#288311yescharacteristic
521C2×C53#289711yescharacteristic
522C2×C53C22×#10411yescharacteristic
523D53—22no—
524D53—41no—
525D53—81no—
526D53—81no—
527#555—531no—
528#554—531no—
529#553—531no—
530#553—531no—
531#553—1061no—
532#550—531no—
533#546—531no—
534#546—531no—
535#546—1061no—
536#546—1061no—
537D42—531no—
538D42—1061no—
539#540—1061no—
540#538—1061no—
541#538—1061no—
542#532—531no—
543#529—531no—
544#525—531no—
545#525C2×D5311yescharacteristic
546C2×#121—531no—
547C2×#121—531no—
548#518—1061no—
549C2×C4×D4—531no—
550C2×C4×D4—1061no—
551#436—1061no—
552#435—1061no—
553#435—1061no—
554C8×D4—1061no—
555#432—531no—
556#431—531no—
557#407—531no—
558#407C2×D5311yescharacteristic, complemented
559C2×C22⋊C8—531no—
560C2×C22⋊C8—531no—
561C4×C4⋊C4—531no—
562C4×C4⋊C4—1061no—
563C4×C22⋊C4—531no—
564C4×C22⋊C4—531no—
565C4×C22⋊C4—1061no—
566C4×C22⋊C4—1061no—
567#376—531no—
568C2×#95—531no—
569C2×#95C2×D5311yescharacteristic, complemented
570#328—531no—
571#328—531no—
572#328C2×D5311yescharacteristic, complemented
573#328C2×D5311yescharacteristic, complemented
574#327—531no—
575#327—531no—
576#327—531no—
577#327—531no—
578#327—531no—
579#327—531no—
580#327—531no—
581#327—531no—
582#327—531no—
583#327—531no—
584#327C2×D5311yescharacteristic, complemented
585#327C2×D5311yescharacteristic, complemented
586C53#1754711yescharacteristic, complemented, Sylow
587C2×#41—531no—
588C2×#41—1061no—
589C2×#41C4×D5311yescharacteristic, complemented
590C22×D4—531no—
591C22×D4—531no—
592C22×D4—531no—
593C22×D4—1061no—
594C22×D4—1061no—
595C22×D4—1061no—
596C23×C4—21no—
597C23×C4—531no—
598C23×C4—1061no—
599C23×C4C22×D5311yescharacteristic
600C2×M16—21no—
601C2×M16—1061no—
602C22×C8—1061no—
603C22×C8—1061no—
604C4⋊Q8—531no—
605#127—531no—
606#127—1061no—
607#126—1061no—
608#126—1061no—
609#126—1061no—
610#125—531no—
611#125—1061no—
612#124—531no—
613#124—1061no—
614#124—1061no—
615#124—1061no—
616#123—21no—
617#123—1061no—
618#123—1061no—
619#123—1061no—
620#123—1061no—
621#123—1061no—
622#123—1061no—
623C22⋊Q8—531no—
624C22⋊Q8—1061no—
625C22⋊Q8—1061no—
626C22⋊Q8C4×D5311yescharacteristic, complemented
627C22⋊Q8C22×D5311yescharacteristic
628#121—531no—
629#121—531no—
630#121—531no—
631#121—531no—
632#121—531no—
633#121—531no—
634#121—531no—
635#121—1061no—
636#121—1061no—
637#121—1061no—
638#121—1061no—
639#121—1061no—
640#121—1061no—
641#121—1061no—
642#121—1061no—
643#121—1061no—
644#121—1061no—
645#121—1061no—
646#121—1061no—
647#121—1061no—
648#121C4×D5311yescharacteristic, complemented
649#121C22×D5311yescharacteristic
650#120—21no—
651#120—1061no—
652#120—1061no—
653#120—1061no—
654#120—1061no—
655#120—1061no—
656C4×Q8—531no—
657C4×D4—21no—
658C4×D4—21no—
659C4×D4—531no—
660C4×D4—531no—
661C4×D4—531no—
662C4×D4—531no—
663C4×D4—531no—
664C4×D4—531no—
665C4×D4—531no—
666C4×D4—531no—
667C4×D4—531no—
668C4×D4—531no—
669C4×D4—531no—
670C4×D4—1061no—
671C4×D4—1061no—
672C4×D4—1061no—
673C4×D4—1061no—
674C4×D4—1061no—
675C4×D4—1061no—
676C4×D4—1061no—
677C4×D4—1061no—
678C4×D4—1068no—
679#117—531no—
680#117—1061no—
681#117—1061no—
682#117C4×D5311yescharacteristic, complemented
683C2×C4⋊C4—531no—
684C2×C4⋊C4—531no—
685C2×C4⋊C4—531no—
686C2×C4⋊C4—1061no—
687C2×C22⋊C4—531no—
688C2×C22⋊C4—531no—
689C2×C22⋊C4—1061no—
690C2×C22⋊C4—1061no—
691C2×C22⋊C4—1061no—
692C2×C22⋊C4—1061no—
693C2×C22⋊C4—1061no—
694C2×C22⋊C4—1061no—
695C2×C42—531no—
696C2×C42—1061no—
697C2×C42—1061no—
698C2×C42—1061no—
699C2×C42—1061no—
700C4⋊C8—1061no—
701C4⋊C8—1061no—
702C22⋊C8—21no—
703C22⋊C8—531no—
704C22⋊C8—531no—
705C22⋊C8—1061no—
706C22⋊C8—1061no—
707C22⋊C8—1061no—
708C22⋊C8C22×D5311yescharacteristic
709C22⋊C8C22×D5311yescharacteristic
710#97—1061no—
711C4×C8—1061no—
712#95—21no—
713#95—531no—
714#95—531no—
715#95—1061no—
716#95—1061no—
717#95C22×D5311yescharacteristic
718#95C22×D5311yescharacteristic
719C24—531no—
720C24—1061no—
721C24—1061no—
722C24D4×D5311yescharacteristic
723#41—81no—
724#41—4241no—
725#41—4241no—
726#41—4241no—
727C2×Q8—1061no—
728C2×Q8C2×C4×D5311yescharacteristic
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—531no—
733C2×D4—531no—
734C2×D4—531no—
735C2×D4—531no—
736C2×D4—531no—
737C2×D4—531no—
738C2×D4—1061no—
739C2×D4—1061no—
740C2×D4—1061no—
741C2×D4—1061no—
742C2×D4—1061no—
743C2×D4—1061no—
744C2×D4—1064no—
745C2×D4—1061no—
746C2×D4—1061no—
747C2×D4—1061no—
748C2×D4—1061no—
749C2×D4—1061no—
750C2×D4—1061no—
751C2×D4—4241no—
752C2×D4—4241no—
753C2×D4—4241no—
754C2×D4—4241no—
755C2×D4—4241no—
756C2×D4—4241no—
757C2×D4—2124no—
758C2×D4C2×C4×D5311yescharacteristic
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—24no—
762C22×C4—21no—
763C22×C4—81no—
764C22×C4—81no—
765C22×C4—81no—
766C22×C4—531no—
767C22×C4—531no—
768C22×C4—531no—
769C22×C4—531no—
770C22×C4—531no—
771C22×C4—531no—
772C22×C4—531no—
773C22×C4—1061no—
774C22×C4—1061no—
775C22×C4—1061no—
776C22×C4—1061no—
777C22×C4—1064no—
778C22×C4—1061no—
779C22×C4—1061no—
780C22×C4—1061no—
781C22×C4—1061no—
782C22×C4—4241no—
783C22×C4—4241no—
784C22×C4—4241no—
785C22×C4C2×C4×D5311yescharacteristic
786C22×C4C2×C4×D5311yescharacteristic
787C22×C4D4×D5311yescharacteristic
788C22×C4D4×D5311yescharacteristic
789C22×C4D4×D5311yescharacteristic
790C22×C4C23×D5311yescharacteristic
791M16—81no—
792M16—4241no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—1061no—
796C2×C8—1061no—
797C2×C8—4241no—
798C2×C8—4241no—
799C4⋊C4—21no—
800C4⋊C4—21no—
801C4⋊C4—531no—
802C4⋊C4—531no—
803C4⋊C4—531no—
804C4⋊C4—531no—
805C4⋊C4—531no—
806C4⋊C4—531no—
807C4⋊C4—1061no—
808C4⋊C4—1061no—
809C4⋊C4—1061no—
810C4⋊C4—1061no—
811C4⋊C4—1061no—
812C4⋊C4—1061no—
813C4⋊C4—1064no—
814C4⋊C4—1061no—
815C4⋊C4C2×C4×D5311yescharacteristic
816C4⋊C4C2×C4×D5311yescharacteristic
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—531no—
823C22⋊C4—531no—
824C22⋊C4—531no—
825C22⋊C4—531no—
826C22⋊C4—531no—
827C22⋊C4—531no—
828C22⋊C4—531no—
829C22⋊C4—531no—
830C22⋊C4—1061no—
831C22⋊C4—1061no—
832C22⋊C4—1061no—
833C22⋊C4—1061no—
834C22⋊C4—1061no—
835C22⋊C4—1061no—
836C22⋊C4—1061no—
837C22⋊C4—1061no—
838C22⋊C4—1064no—
839C22⋊C4—1061no—
840C22⋊C4—1061no—
841C22⋊C4—1064no—
842C22⋊C4—1061no—
843C22⋊C4—1061no—
844C22⋊C4—1061no—
845C22⋊C4—1061no—
846C42—21no—
847C42—531no—
848C42—531no—
849C42—531no—
850C42—531no—
851C42—1061no—
852C42—1061no—
853C42—1064no—
854C42—4241no—
855C42—4241no—
856C42—4241no—
857C23—22no—
858C23—21no—
859C23—21no—
860C23—21no—
861C23—41no—
862C23—531no—
863C23—531no—
864C23—1062no—
865C23—1061no—
866C23—1061no—
867C23—1061no—
868C23—1061no—
869C23—4241no—
870C23—4241no—
871C23—4241no—
872C23—4241no—
873C23—2121no—
874C23—2122no—
875C23—2122no—
876C23C22⋊C4×D5311yescharacteristic
877C23C22⋊C4×D5311yescharacteristic
878C23C2×D4×D5311yescharacteristic
879Q8—41no—
880Q8—4241no—
881D4—41no—
882D4—42no—
883D4—41no—
884D4—41no—
885D4—81no—
886D4—534no—
887D4—1062no—
888D4—1062no—
889D4—1062no—
890D4—4241no—
891D4—4241no—
892D4—4241no—
893D4—4241no—
894D4—4241no—
895D4—4241no—
896D4—4241no—
897D4—4241no—
898D4—2121no—
899D4—2121no—
900D4—2122no—
901D4—2122no—
902D4—2121no—
903D4—2121no—
904D4—2121no—
905D4—2121no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—81no—
922C2×C4—84no—
923C2×C4—531no—
924C2×C4—531no—
925C2×C4—531no—
926C2×C4—531no—
927C2×C4—531no—
928C2×C4—531no—
929C2×C4—1062no—
930C2×C4—1061no—
931C2×C4—1061no—
932C2×C4—1062no—
933C2×C4—1062no—
934C2×C4—1061no—
935C2×C4—1061no—
936C2×C4—4241no—
937C2×C4—4241no—
938C2×C4—4241no—
939C2×C4—4244no—
940C2×C4—4241no—
941C2×C4—4241no—
942C2×C4—2121no—
943C2×C4—2121no—
944C2×C4—2121no—
945C2×C4—2121no—
946C2×C4—2122no—
947C2×C4—2121no—
948C2×C4—2121no—
949C2×C4—2121no—
950C2×C4—2121no—
951C2×C4—2121no—
952C2×C4C22⋊C4×D5311yescharacteristic
953C2×C4C22⋊C4×D5311yescharacteristic
954C2×C4C22×C4×D5311yescharacteristic
955C2×C4C2×D4×D5311yescharacteristic
956C8—41no—
957C8—41no—
958C8—2121no—
959C8—2121no—
960C22—21no—
961C22—21no—
962C22—21no—
963C22—21no—
964C22—21no—
965C22—21no—
966C22—21no—
967C22—42no—
968C22—42no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—532no—
973C22—8482no—
974C22—8482no—
975C22—1061no—
976C22—1061no—
977C22—1061no—
978C22—1061no—
979C22—1061no—
980C22—2122no—
981C22—2122no—
982C22—2121no—
983C22—2121no—
984C22—2121no—
985C22—2121no—
986C22—2121no—
987C22—2121no—
988C22#104×D5312yes—
989C22C2×C22⋊C4×D5311yescharacteristic
990C22#1681142711yescharacteristic
991C22#1681143211yescharacteristic
992C4—21no—
993C4—21no—
994C4—21no—
995C4—21no—
996C4—42no—
997C4—42no—
998C4—41no—
999C4—41no—
1000C4—41no—
1001C4—532no—
1002C4—1061no—
1003C4—1061no—
1004C4—1061no—
1005C4—1061no—
1006C4—1061no—
1007C4—2122no—
1008C4—2122no—
1009C4—2121no—
1010C4—2121no—
1011C2—21no—
1012C2—21no—
1013C2—22no—
1014C2—41no—
1015C2—81no—
1016C2—1062no—
1017C2—4241no—
1018C2—4241no—
1019C2—2121no—
1020C2#2028317311yescharacteristic
1021C2#2028323911yescharacteristic
1022C2C2×#104×D5311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1504C2
socleC22×C53C22×C22⋊C4
prime radical#20288735C2
cosocleC22×C4×C53C24
hypercenter#1504D53
hypocenterC53#17547
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1504

Complements

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

NH ≅ G/Ntype
2. #20283751C2semidirect
3. #20277073C2semidirect
4. #20273239C2semidirect
5. #20273232C2semidirect
6. #20273229C2semidirect
7. #20273221C2semidirect
8. #20273218C2semidirect
9. #20273208C2semidirect
10. #20273206C2semidirect
11. #20273205C2semidirect
12. #20273200C2semidirect
13. C2×#16810356C2semidirect
14. #327×D53C2semidirect
15. C53×#1504C2semidirect
16. #16811336C4semidirect
17. #16811331C4semidirect
18. #16811325C4semidirect
20. #16811317C4semidirect
21. #16811292C4semidirect
23. #16811264C4semidirect
24. #16811261C4semidirect
26. #16811257C4semidirect
43. #16810677C22semidirect
44. #16810673C22semidirect
45. #16810585C22semidirect
46. C2×C22⋊#88322C22semidirect
47. C22⋊C8×D53C22semidirect
49. #16810474C22semidirect
51. C4×C22⋊Dic53C22semidirect
53. #16810470C22semidirect
54. #16810468C22semidirect
55. #95×D53C22semidirect
56. #16810360C22semidirect
57. #16810360C22semidirect
60. #16810358C22semidirect
61. #16810358C22semidirect
62. #16810357C22semidirect
63. #16810357C22semidirect
66. #16810356C22semidirect
67. #16810356C22semidirect
69. C53×#407C22semidirect
70. C2×#95×C53C22semidirect
71. C53×#328C22semidirect
72. C53×#328C22semidirect
73. C53×#327C22semidirect
74. C53×#327C22semidirect
75. C2×#11719949C2×C4semidirect
77. C22×D212C2×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
115. #13133191C2×C4semidirect
116. #13133191C2×C4semidirect
128. #13133188C2×C4semidirect
134. Q8×Dic53C2×C4semidirect
137. D4×Dic53C2×C4semidirect
139. #13133179C2×C4semidirect
140. #13133179C2×C4semidirect
156. #13133175C2×C4semidirect
158. C2×C4⋊Dic53C2×C4semidirect
161. C4⋊C4×D53C2×C4semidirect
188. C2×#41×C53C2×C4semidirect
193. C22⋊Q8×C53C2×C4semidirect
195. #121×C53C2×C4semidirect
200. #117×C53C2×C4semidirect
508. #1504D53semidirect
558. #407C2×D53semidirect
569. C2×#95C2×D53semidirect
572. #328C2×D53semidirect
573. #328C2×D53semidirect
584. #327C2×D53semidirect
585. #327C2×D53semidirect
586. C53#17547semidirect
589. C2×#41C4×D53semidirect
626. C22⋊Q8C4×D53semidirect
648. #121C4×D53semidirect
682. #117C4×D53semidirect

Maximal subgroups

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

subgroupindex
#202887352
#202837512
#202770732
#202732392
#202732322
#202732292
#202732212
#202732182
#202732082
#202732062
#202732052
#202732002
C2×#168103562
#327×D532
C53×#15042
#1754753