Finite Group Databasebeta

← #27351816

Subgroups — #27351816

Order 13568.

1038 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288543C211yesmaximal, characteristic
2#20283737C211yesmaximal, characteristic, complemented
3#20277652C211yesmaximal, characteristic, complemented
4#20273291C211yesmaximal, characteristic, complemented
5#20273289C211yesmaximal, characteristic, complemented
6#20273285C211yesmaximal, characteristic, complemented
7#20273281C211yesmaximal, characteristic, complemented
8#20273269C211yesmaximal, characteristic, complemented
9#20273207C211yesmaximal, characteristic, complemented
10#20273206C211yesmaximal, characteristic, complemented
11#20273200C211yesmaximal, characteristic, complemented
12#20273198C211yesmaximal, characteristic, complemented
13#328×D53C211yesmaximal, characteristic, complemented
14#327×D53C211yesmaximal, characteristic, complemented
15C53×#1516C211yesmaximal, characteristic, complemented
16#16811323—21no—
17#16811320C411yescharacteristic, complemented
18#16811318—21no—
19#16811317C411yescharacteristic, complemented
20#16811312C411yescharacteristic, complemented
21#16811307C411yescharacteristic, complemented
22#16811302—21no—
23#16811301—21no—
24#16811283C411yescharacteristic, complemented
25#16811280C411yescharacteristic, complemented
26#16811270C411yescharacteristic, complemented
27#16811261C411yescharacteristic, complemented
28#16811215—21no—
29#16811208—21no—
30#16811183—21no—
31#16811159C2211yescharacteristic
32#16811154C2211yescharacteristic
33#16811134C2211yescharacteristic
34C22⋊Q8×D53C2211yescharacteristic
35#121×D53C2211yescharacteristic
36#16811095—21no—
37C2×C4×C22⋊D53C2211yescharacteristic
38C8×C22⋊D53—21no—
39C8×C22⋊D53—21no—
40#16810686—21no—
41#16810686—21no—
42#16810673C2211yescharacteristic, complemented
43#16810673C2211yescharacteristic, complemented
44C2×C22⋊#88322C2211yescharacteristic, complemented
45C22⋊C8×D53C2211yescharacteristic
46C22⋊C8×D53C2211yescharacteristic
47#16810517—21no—
48#16810505—21no—
49#16810499—21no—
50#16810490C2211yescharacteristic, complemented
51#16810482C2211yescharacteristic
52C4×C22⋊Dic53C2211yescharacteristic, complemented
53#16810470—21no—
54#16810468C2211yescharacteristic, complemented
55#95×D53C2211yescharacteristic
56#16810361C2211yescharacteristic, complemented
57#16810361C2211yescharacteristic, complemented
58#16810360C2211yescharacteristic, complemented
59#16810360C2211yescharacteristic, complemented
60#16810359C2211yescharacteristic, complemented
61#16810359C2211yescharacteristic, complemented
62#16810358C2211yescharacteristic
63#16810358C2211yescharacteristic
64#16810357C2211yescharacteristic
65#16810357C2211yescharacteristic
66#16810356C2211yescharacteristic
67#16810356C2211yescharacteristic
68C53×#525C2211yescharacteristic
69C2×C22⋊C8×C53C2211yescharacteristic, complemented
70C53×#381C2211yescharacteristic, complemented
71C53×#328C2211yescharacteristic, complemented
72C53×#328C2211yescharacteristic, complemented
73C53×#327C2211yescharacteristic
74C53×#327C2211yescharacteristic
75C2×#11719945C2×C411yescharacteristic, complemented
76C2×Q8×D53C2×C411yescharacteristic
77C22×C22⋊D53D411yescharacteristic
78C2×D4×D53—21no—
79C2×D4×D53C2×C411yescharacteristic
80C22×C4×D53—21no—
81C22×C4×D53C2311yescharacteristic
82C22×#88322—21no—
83C2×C8×D53—21no—
84C2×C8×D53—21no—
85#13133212—21no—
86#13133211—21no—
87#13133210—21no—
88#13133210—21no—
89#13133210—21no—
90#13133210—21no—
91#13133209—21no—
92#13133208C2×C411yescharacteristic, complemented
93#13133208C2×C411yescharacteristic, complemented
94#13133207—21no—
95#13133206C2×C411yescharacteristic, complemented
96#13133204—21no—
97#13133204C2×C411yescharacteristic, complemented
98#13133203—21no—
99#13133201—21no—
100#13133200—21no—
101#13133200—21no—
102#13133199—21no—
103#13133199—21no—
104#13133199—21no—
105#13133199—21no—
106#13133198—21no—
107#13133198—21no—
108#13133197C2×C411yescharacteristic
109#13133196—21no—
110#13133196C2×C411yescharacteristic, complemented
111#13133196C2311yescharacteristic
112#13133195—21no—
113#13133195—21no—
114#13133194—21no—
115#13133193C2×C411yescharacteristic
116#13133192C2×C411yescharacteristic
117#13133191C2×C411yescharacteristic, complemented
118#13133191C2311yescharacteristic
119#13133190—21no—
120#13133190—21no—
121#13133190—21no—
122#13133189—21no—
123#13133189—21no—
124#13133188—21no—
125#13133188—21no—
126#13133188—21no—
127#13133188C2×C411yescharacteristic
128#13133186—21no—
129#13133185—21no—
130#13133185—21no—
131Q8×Dic53C2×C411yescharacteristic, complemented
132#13133182C2×C411yescharacteristic, complemented
133C4×D212—21no—
134D4×Dic53—21no—
135D4×Dic53C2×C411yescharacteristic, complemented
136#13133179—21no—
137#13133179C2×C411yescharacteristic, complemented
138C4×C22⋊D53—21no—
139C4×C22⋊D53—21no—
140C4×C22⋊D53—21no—
141C4×C22⋊D53C2×C411yescharacteristic
142C4×C22⋊D53C2×C411yescharacteristic
143C4×C22⋊D53C2×C411yescharacteristic
144C4×C22⋊D53C2×C411yescharacteristic
145C4×C22⋊D53D411yescharacteristic
146C4×C22⋊D53D411yescharacteristic
147C4×C22⋊D53D411yescharacteristic
148C4×C22⋊D53D411yescharacteristic
149#13133177—21no—
150#13133177—21no—
151#13133176C2×C411yescharacteristic, complemented
152#13133175—21no—
153#13133175—21no—
154#13133174—21no—
155#13133173—21no—
156C2×#11719919—21no—
157C2×#11719919D411yescharacteristic
158C4⋊C4×D53—21no—
159C4⋊C4×D53C2×C411yescharacteristic
160C4⋊C4×D53C2×C411yescharacteristic
161C2×C22⋊Dic53—21no—
162C2×C22⋊Dic53D411yescharacteristic
163C2×#11719921—21no—
164C2×#11719921—21no—
165C2×#11719921D411yescharacteristic
166C22⋊C4×D53—21no—
167C22⋊C4×D53—21no—
168C22⋊C4×D53—21no—
169C2×C4×Dic53—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—
179C8×Dic53—21no—
180C8×Dic53—21no—
181#13133124—21no—
182#13133124—21no—
183#13133124—21no—
184#13133124—21no—
185#13133124C2311yescharacteristic
186#13133124C2311yescharacteristic
187C2×#41×C53C2×C411yescharacteristic, complemented
188C23×C4×C53C2311yescharacteristic
189C22×C8×C53—21no—
190#123×C53—21no—
191C22⋊Q8×C53C2×C411yescharacteristic, complemented
192C22⋊Q8×C53C2311yescharacteristic
193#121×C53C2×C411yescharacteristic, complemented
194#121×C53C2311yescharacteristic
195#120×C53—21no—
196C4×D4×C53—21no—
197C4×D4×C53—21no—
198#117×C53C2×C411yescharacteristic, complemented
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×C53C2×D411yescharacteristic
207C23×D53—21no—
208C23×D53C2×D411yescharacteristic
209#41×C53—81no—
210C2×Q8×C53C22×C411yescharacteristic
211C2×D4×C53—21no—
212C2×D4×C53—21no—
213C2×D4×C53—21no—
214C2×D4×C53C22×C411yescharacteristic
215C22×C4×C53—21no—
216C22×C4×C53—21no—
217C22×C4×C53—21no—
218C22×C4×C53—81no—
219C22×C4×C53C22×C411yescharacteristic
220C22×C4×C53C22×C411yescharacteristic
221C22×C4×C53C2×D411yescharacteristic
222C22×C4×C53C2×D411yescharacteristic
223C22×C4×C53C2×D411yescharacteristic
224C22×C4×C53C2411yescharacteristic
225C2×C22⋊D53—22no—
226C2×C22⋊D53—22no—
227C2×C22⋊D53—21no—
228C2×C22⋊D53—21no—
229C2×C22⋊D53—21no—
230C2×C22⋊D53—21no—
231C2×C22⋊D53—21no—
232C2×C22⋊D53C22⋊C411yescharacteristic
233C2×C22⋊D53C22⋊C411yescharacteristic
234C2×C22⋊D53C22⋊C411yescharacteristic
235C2×C22⋊D53C22⋊C411yescharacteristic
236C22×Dic53—21no—
237C22×Dic53—21no—
238C22×Dic53—21no—
239C22×Dic53C2×D411yescharacteristic
240C22×Dic53C2×D411yescharacteristic
241C22×Dic53C2×D411yescharacteristic
242Q8×D53—81no—
243D4×D53—42no—
244D4×D53—42no—
245D4×D53—81no—
246#11719945—81no—
247C2×D212—21no—
248C2×D212C22×C411yescharacteristic
249C2×C4×D53—21no—
250C2×C4×D53—21no—
251C2×C4×D53—21no—
252C2×C4×D53—21no—
253C2×C4×D53—21no—
254C2×C4×D53—42no—
255C2×C4×D53—42no—
256C2×C4×D53—81no—
257C2×C4×D53—81no—
258C2×C4×D53C22×C411yescharacteristic
259C2×C4×D53C22×C411yescharacteristic
260C2×C4×D53C2×D411yescharacteristic
261C2×C4×D53C2×D411yescharacteristic
262C2×Dic106—21no—
263C2×Dic106C22×C411yescharacteristic
264C2×C8×C53—21no—
265C2×C8×C53—21no—
266C2×C8×C53—81no—
267C4⋊C4×C53—21no—
268C4⋊C4×C53—21no—
269C4⋊C4×C53C22×C411yescharacteristic
270C4⋊C4×C53C22×C411yescharacteristic
271C22⋊C4×C53—21no—
272C22⋊C4×C53—21no—
273C22⋊C4×C53—21no—
274C22⋊C4×C53—21no—
275C22⋊C4×C53—21no—
276C22⋊C4×C53—81no—
277C42×C53—21no—
278C22⋊Dic53—21no—
279C22⋊Dic53—21no—
280C22⋊Dic53—21no—
281C22⋊Dic53—21no—
282C22⋊Dic53—21no—
283C22⋊Dic53—21no—
284C22⋊Dic53—21no—
285C22⋊Dic53—42no—
286C22⋊Dic53C22⋊C411yescharacteristic
287C22⋊Dic53C22⋊C411yescharacteristic
288C22⋊Dic53C22⋊C411yescharacteristic
289C22⋊Dic53C22⋊C411yescharacteristic
290#11719921—21no—
291#11719921—21no—
292#11719921—21no—
293#11719921—21no—
294#11719921—21no—
295#11719921—21no—
296#11719921—21no—
297#11719921—21no—
298#11719921—42no—
299#11719921C22⋊C411yescharacteristic
300#11719921C22⋊C411yescharacteristic
301#11719921C22⋊C411yescharacteristic
302#11719921C22⋊C411yescharacteristic
303C4⋊Dic53—21no—
304C4⋊Dic53—21no—
305C4⋊Dic53—21no—
306C4⋊Dic53—21no—
307C4⋊Dic53C22×C411yescharacteristic
308C4⋊Dic53C22×C411yescharacteristic
309#11719919—21no—
310#11719919—21no—
311#11719919—21no—
312#11719919—21no—
313#11719919—21no—
314#11719919—21no—
315#11719919—21no—
316#11719919—21no—
317#11719919—81no—
318#11719919C22⋊C411yescharacteristic
319#11719919C22⋊C411yescharacteristic
320#11719919C22⋊C411yescharacteristic
321#11719919C22⋊C411yescharacteristic
322C4×Dic53—21no—
323C4×Dic53—21no—
324C4×Dic53—21no—
325C4×Dic53—42no—
326C4×Dic53—81no—
327C4×Dic53C22×C411yescharacteristic
328C4×Dic53C22×C411yescharacteristic
329C4×Dic53C2×D411yescharacteristic
330C4×Dic53C2×D411yescharacteristic
331C2×#88322—21no—
332C2×#88322—21no—
333C2×#88322—81no—
334C8×D53—81no—
335C8×D53—81no—
336C23×C53—21no—
337C23×C53—21no—
338C23×C53—21no—
339C23×C53—41no—
340C23×C53—41no—
341C23×C53C2×C22⋊C411yescharacteristic
342C23×C53C2×C22⋊C411yescharacteristic
343C23×C53C22×D411yescharacteristic
344C22×D53—21no—
345C22×D53—41no—
346C22×D53—41no—
347C22×D53—42no—
348C22×D53—81no—
349C22×D53—81no—
350C22×D53C2×C22⋊C411yescharacteristic
351C22×D53C2×C22⋊C411yescharacteristic
352C22×D53#13512yes—
353C22×D53#13512yes—
354Q8×C53—41no—
355D4×C53—41no—
356D4×C53—41no—
357D4×C53—41no—
358D4×C53—81no—
359D4×C53—81no—
360C2×C4×C53—21no—
361C2×C4×C53—21no—
362C2×C4×C53—21no—
363C2×C4×C53—41no—
364C2×C4×C53—41no—
365C2×C4×C53—41no—
366C2×C4×C53—41no—
367C2×C4×C53—41no—
368C2×C4×C53—41no—
369C2×C4×C53—41no—
370C2×C4×C53—41no—
371C2×C4×C53—41no—
372C2×C4×C53—41no—
373C2×C4×C53—41no—
374C2×C4×C53—41no—
375C2×C4×C53—81no—
376C2×C4×C53C2×C22⋊C411yescharacteristic
377C2×C4×C53C2×C22⋊C411yescharacteristic
378C2×C4×C53C23×C411yescharacteristic
379C2×C4×C53C22×D411yescharacteristic
380C22⋊D53—22no—
381C22⋊D53—22no—
382C22⋊D53—22no—
383C22⋊D53—22no—
384C22⋊D53—41no—
385C22⋊D53—41no—
386C22⋊D53—42no—
387C22⋊D53—81no—
388C22⋊D53—81no—
389C22⋊D53—81no—
390C2×Dic53—21no—
391C2×Dic53—21no—
392C2×Dic53—22no—
393C2×Dic53—21no—
394C2×Dic53—21no—
395C2×Dic53—21no—
396C2×Dic53—41no—
397C2×Dic53—41no—
398C2×Dic53—41no—
399C2×Dic53—41no—
400C2×Dic53—41no—
401C2×Dic53—41no—
402C2×Dic53—41no—
403C2×Dic53—81no—
404C2×Dic53C2×C22⋊C411yescharacteristic
405C2×Dic53C2×C22⋊C411yescharacteristic
406C2×Dic53C2×C22⋊C411yescharacteristic
407C2×Dic53C2×C22⋊C411yescharacteristic
408C2×Dic53C2×C22⋊C411yescharacteristic
409C2×Dic53C2×C22⋊C411yescharacteristic
410D212—41no—
411D212—42no—
412C4×D53—41no—
413C4×D53—41no—
414C4×D53—41no—
415C4×D53—41no—
416C4×D53—42no—
417C4×D53—81no—
418C4×D53—81no—
419C4×D53—81no—
420C4×D53—81no—
421C4×D53—84no—
422Dic106—41no—
423Dic106—81no—
424C8×C53—41no—
425C8×C53—41no—
426#88322—41no—
427#88322—41no—
428#17615—531nomaximal, Sylow
429C22×C53—21no—
430C22×C53—21no—
431C22×C53—21no—
432C22×C53—21no—
433C22×C53—21no—
434C22×C53—21no—
435C22×C53—21no—
436C22×C53—21no—
437C22×C53—41no—
438C22×C53—41no—
439C22×C53—41no—
440C22×C53—81no—
441C22×C53—81no—
442C22×C53C22×C22⋊C411yescharacteristic
443C22×C53C2×#13511yescharacteristic
444C22×C53C2×#13511yescharacteristic
445C2×D53—21no—
446C2×D53—21no—
447C2×D53—21no—
448C2×D53—21no—
449C2×D53—42no—
450C2×D53—42no—
451C2×D53—41no—
452C2×D53—41no—
453C2×D53—41no—
454C2×D53—162no—
455C2×D53#41612yes—
456C2×D53#41612yes—
457C4×C53—21no—
458C4×C53—21no—
459C4×C53—21no—
460C4×C53—21no—
461C4×C53—41no—
462C4×C53—41no—
463C4×C53—41no—
464C4×C53—81no—
465C4×C53—81no—
466Dic53—21no—
467Dic53—21no—
468Dic53—21no—
469Dic53—21no—
470Dic53—21no—
471Dic53—21no—
472Dic53—42no—
473Dic53—41no—
474Dic53—41no—
475Dic53—41no—
476Dic53—81no—
477#3505—531no—
478#2972—531no—
479#2353—531no—
480#1521—531no—
481#1521—531no—
482#1520—531no—
483#1519—531no—
484#1516—531no—
485#1516D5311yescharacteristic, complemented
486#1501—531no—
487#1501—531no—
488#1500—531no—
489#1500—531no—
490C2×#328—531no—
491C2×#327—531no—
492C2×C53—21no—
493C2×C53—21no—
494C2×C53—41no—
495C2×C53—41no—
496C2×C53—81no—
497C2×C53#288311yescharacteristic
498C2×C53C2×#41611yescharacteristic
499C2×C53#290111yescharacteristic
500D53—22no—
501D53—22no—
502D53—81no—
503#553—531no—
504#553—531no—
505#553—1061no—
506#553—1061no—
507#552—531no—
508#552—531no—
509#551—1061no—
510#551—1061no—
511#548—531no—
512#548—531no—
513#546—531no—
514#546—531no—
515#539—1061no—
516#538—1061no—
517#534—1061no—
518#529—531no—
519#529—531no—
520#525—531no—
521#525C2×D5311yescharacteristic
522C2×C22⋊Q8—531no—
523C2×#121—531no—
524#518—1061no—
525C2×C4×D4—531no—
526C8×D4—1061no—
527C8×D4—1061no—
528C8×D4—1061no—
529C8×D4—1061no—
530#431—531no—
531#431—531no—
532C2×C22⋊C8—531no—
533C2×C22⋊C8—531no—
534C2×C22⋊C8—531no—
535C2×C22⋊C8C2×D5311yescharacteristic, complemented
536#388—1061no—
537#387—1061no—
538#386—1061no—
539#383—531no—
540#381C2×D5311yescharacteristic, complemented
541#380—531no—
542C4×C22⋊C4—531no—
543C4×C22⋊C4—1061no—
544#376—531no—
545C2×#95—531no—
546#328—531no—
547#328—531no—
548#328—531no—
549#328—531no—
550#328—531no—
551#328—531no—
552#328C2×D5311yescharacteristic, complemented
553#328C2×D5311yescharacteristic, complemented
554#327—531no—
555#327—531no—
556#327—531no—
557#327—531no—
558#327—531no—
559#327—531no—
560#327C2×D5311yescharacteristic
561#327C2×D5311yescharacteristic
562C53#1761511yescharacteristic, complemented, Sylow
563C2×#41—531no—
564C2×#41C4×D5311yescharacteristic, complemented
565C22×Q8—531no—
566C22×D4—531no—
567C22×D4—531no—
568C22×D4—1061no—
569C23×C4—531no—
570C23×C4—1061no—
571C23×C4C22×D5311yescharacteristic
572C22×C8—21no—
573C22×C8—1061no—
574C22×C8—1061no—
575C22×C8—1061no—
576#126—1061no—
577#126—1061no—
578#126—1061no—
579#126—1061no—
580#126—1061no—
581#126—1061no—
582#125—531no—
583#125—531no—
584#125—1061no—
585#125—1061no—
586#124—531no—
587#124—531no—
588#124—1061no—
589#124—1061no—
590#123—21no—
591#123—1061no—
592#123—1061no—
593#123—1061no—
594#123—1061no—
595#123—1061no—
596#123—1061no—
597#123—1061no—
598#123—1061no—
599#123—1061no—
600C22⋊Q8—531no—
601C22⋊Q8—531no—
602C22⋊Q8—531no—
603C22⋊Q8—531no—
604C22⋊Q8—1061no—
605C22⋊Q8—1061no—
606C22⋊Q8—1061no—
607C22⋊Q8—1061no—
608C22⋊Q8C4×D5311yescharacteristic, complemented
609C22⋊Q8C22×D5311yescharacteristic
610#121—531no—
611#121—531no—
612#121—531no—
613#121—531no—
614#121—1061no—
615#121—1061no—
616#121—1061no—
617#121—1061no—
618#121—1061no—
619#121—1061no—
620#121—1061no—
621#121—1061no—
622#121C4×D5311yescharacteristic, complemented
623#121C22×D5311yescharacteristic
624#120—21no—
625#120—1061no—
626#120—1061no—
627#120—1061no—
628C4×Q8—531no—
629C4×Q8—531no—
630C4×D4—21no—
631C4×D4—21no—
632C4×D4—531no—
633C4×D4—531no—
634C4×D4—531no—
635C4×D4—531no—
636C4×D4—531no—
637C4×D4—531no—
638C4×D4—531no—
639C4×D4—531no—
640C4×D4—531no—
641C4×D4—531no—
642C4×D4—1061no—
643C4×D4—1061no—
644C4×D4—1061no—
645C4×D4—1061no—
646C4×D4—1061no—
647C4×D4—1061no—
648C4×D4—1061no—
649C4×D4—1061no—
650#117—531no—
651#117—1061no—
652#117—1061no—
653#117—1061no—
654#117—1061no—
655#117C4×D5311yescharacteristic, complemented
656C2×C4⋊C4—531no—
657C2×C4⋊C4—531no—
658C2×C4⋊C4—531no—
659C2×C4⋊C4—1061no—
660C2×C4⋊C4—1061no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—531no—
663C2×C22⋊C4—531no—
664C2×C22⋊C4—1061no—
665C2×C22⋊C4—1061no—
666C2×C22⋊C4—1061no—
667C2×C22⋊C4—1061no—
668C2×C22⋊C4—1061no—
669C2×C22⋊C4—1061no—
670C2×C42—531no—
671C2×C42—1061no—
672C2×C42—1061no—
673C4⋊C8—1061no—
674C4⋊C8—1061no—
675C22⋊C8—21no—
676C22⋊C8—531no—
677C22⋊C8—531no—
678C22⋊C8—1061no—
679C22⋊C8—1061no—
680C22⋊C8—1061no—
681C22⋊C8C22×D5311yescharacteristic
682C22⋊C8C22×D5311yescharacteristic
683C4×C8—1061no—
684C4×C8—1061no—
685#95—21no—
686#95—531no—
687#95—531no—
688#95—1061no—
689#95—1061no—
690#95—1061no—
691#95—1061no—
692#95C22×D5311yescharacteristic
693#95C22×D5311yescharacteristic
694C24—531no—
695C24—1061no—
696C24D4×D5311yescharacteristic
697#41—81no—
698#41—4241no—
699C2×Q8—531no—
700C2×Q8—1061no—
701C2×Q8—4241no—
702C2×Q8C2×C4×D5311yescharacteristic
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—531no—
707C2×D4—531no—
708C2×D4—531no—
709C2×D4—531no—
710C2×D4—531no—
711C2×D4—1061no—
712C2×D4—1061no—
713C2×D4—1062no—
714C2×D4—1062no—
715C2×D4—1061no—
716C2×D4—1061no—
717C2×D4—1061no—
718C2×D4—1061no—
719C2×D4—4241no—
720C2×D4—2122no—
721C2×D4—2122no—
722C2×D4C2×C4×D5311yescharacteristic
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—81no—
727C22×C4—531no—
728C22×C4—531no—
729C22×C4—531no—
730C22×C4—531no—
731C22×C4—531no—
732C22×C4—531no—
733C22×C4—531no—
734C22×C4—1061no—
735C22×C4—1061no—
736C22×C4—1061no—
737C22×C4—1061no—
738C22×C4—1061no—
739C22×C4—1061no—
740C22×C4—1061no—
741C22×C4—1061no—
742C22×C4—4241no—
743C22×C4—4241no—
744C22×C4—2122no—
745C22×C4—2122no—
746C22×C4C2×C4×D5311yescharacteristic
747C22×C4C2×C4×D5311yescharacteristic
748C22×C4D4×D5311yescharacteristic
749C22×C4D4×D5311yescharacteristic
750C22×C4D4×D5311yescharacteristic
751C22×C4C23×D5311yescharacteristic
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—81no—
755C2×C8—1061no—
756C2×C8—1061no—
757C2×C8—4241no—
758C2×C8—4241no—
759C2×C8—4241no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—531no—
763C4⋊C4—531no—
764C4⋊C4—531no—
765C4⋊C4—531no—
766C4⋊C4—531no—
767C4⋊C4—531no—
768C4⋊C4—1061no—
769C4⋊C4—1061no—
770C4⋊C4—1061no—
771C4⋊C4—1061no—
772C4⋊C4—1061no—
773C4⋊C4—1061no—
774C4⋊C4—1061no—
775C4⋊C4—1061no—
776C4⋊C4—1061no—
777C4⋊C4—1061no—
778C4⋊C4—1061no—
779C4⋊C4—1061no—
780C4⋊C4—4241no—
781C4⋊C4C2×C4×D5311yescharacteristic
782C4⋊C4C2×C4×D5311yescharacteristic
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—81no—
789C22⋊C4—531no—
790C22⋊C4—531no—
791C22⋊C4—531no—
792C22⋊C4—531no—
793C22⋊C4—531no—
794C22⋊C4—531no—
795C22⋊C4—531no—
796C22⋊C4—531no—
797C22⋊C4—1061no—
798C22⋊C4—1061no—
799C22⋊C4—1061no—
800C22⋊C4—1061no—
801C22⋊C4—1061no—
802C22⋊C4—1061no—
803C22⋊C4—1061no—
804C22⋊C4—1061no—
805C22⋊C4—1061no—
806C22⋊C4—1061no—
807C22⋊C4—1061no—
808C22⋊C4—1061no—
809C22⋊C4—1061no—
810C22⋊C4—1061no—
811C22⋊C4—1061no—
812C22⋊C4—2122no—
813C22⋊C4—2122no—
814C42—21no—
815C42—531no—
816C42—531no—
817C42—531no—
818C42—531no—
819C42—1061no—
820C42—1061no—
821C42—1061no—
822C42—4241no—
823C42—2122no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—41no—
828C23—41no—
829C23—531no—
830C23—531no—
831C23—532no—
832C23—532no—
833C23—1061no—
834C23—4241no—
835C23—4241no—
836C23—2121no—
837C23—2121no—
838C23—2122no—
839C23C22⋊C4×D5311yescharacteristic
840C23C22⋊C4×D5311yescharacteristic
841C23C2×D4×D5311yescharacteristic
842Q8—41no—
843Q8—4241no—
844Q8—2121no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—81no—
849D4—81no—
850D4—1062no—
851D4—1062no—
852D4—1062no—
853D4—1062no—
854D4—4241no—
855D4—4241no—
856D4—4241no—
857D4—2121no—
858D4—2122no—
859D4—2122no—
860D4—2121no—
861D4—2121no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—81no—
878C2×C4—531no—
879C2×C4—531no—
880C2×C4—531no—
881C2×C4—531no—
882C2×C4—531no—
883C2×C4—531no—
884C2×C4—1061no—
885C2×C4—1061no—
886C2×C4—1062no—
887C2×C4—1061no—
888C2×C4—1061no—
889C2×C4—1061no—
890C2×C4—4241no—
891C2×C4—4241no—
892C2×C4—4241no—
893C2×C4—4241no—
894C2×C4—4244no—
895C2×C4—4241no—
896C2×C4—2121no—
897C2×C4—2121no—
898C2×C4—2121no—
899C2×C4—2121no—
900C2×C4—2122no—
901C2×C4—2121no—
902C2×C4—2121no—
903C2×C4—2121no—
904C2×C4—2121no—
905C2×C4—2121no—
906C2×C4—2121no—
907C2×C4—2121no—
908C2×C4C22⋊C4×D5311yescharacteristic
909C2×C4C22⋊C4×D5311yescharacteristic
910C2×C4C22×C4×D5311yescharacteristic
911C2×C4C2×D4×D5311yescharacteristic
912C8—41no—
913C8—41no—
914C8—2121no—
915C8—2121no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—21no—
922C22—21no—
923C22—21no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—81no—
928C22—81no—
929C22—532no—
930C22—532no—
931C22—8482no—
932C22—1061no—
933C22—1061no—
934C22—1061no—
935C22—1061no—
936C22—2122no—
937C22—2122no—
938C22—2121no—
939C22—2121no—
940C22—2121no—
941C22C2×C22⋊C4×D5311yescharacteristic
942C22#135×D5311yescharacteristic
943C22#135×D5311yescharacteristic
944C4—21no—
945C4—21no—
946C4—21no—
947C4—21no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—81no—
952C4—81no—
953C4—1061no—
954C4—1061no—
955C4—1061no—
956C4—1061no—
957C4—1061no—
958C4—1061no—
959C4—4241no—
960C4—2122no—
961C4—2121no—
962C4—2121no—
963C4—2121no—
964C2—21no—
965C2—21no—
966C2—41no—
967C2—41no—
968C2—81no—
969C2—1062no—
970C2—1062no—
971C2—4241no—
972C2#2028317311yescharacteristic
973C2#416×D5311yescharacteristic
974C2#2028326111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1516C2
socleC22×C53C22×C22⋊C4
prime radical#20288543C2
cosocleC22×C4×C53C24
hypercenter#1516D53
hypocenterC53#17615
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1516

Complements

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

NH ≅ G/Ntype
2. #20283737C2semidirect
3. #20277652C2semidirect
4. #20273291C2semidirect
5. #20273289C2semidirect
6. #20273285C2semidirect
7. #20273281C2semidirect
8. #20273269C2semidirect
9. #20273207C2semidirect
10. #20273206C2semidirect
11. #20273200C2semidirect
12. #20273198C2semidirect
13. #328×D53C2semidirect
14. #327×D53C2semidirect
15. C53×#1516C2semidirect
17. #16811320C4semidirect
19. #16811317C4semidirect
20. #16811312C4semidirect
21. #16811307C4semidirect
24. #16811283C4semidirect
25. #16811280C4semidirect
26. #16811270C4semidirect
27. #16811261C4semidirect
42. #16810673C22semidirect
43. #16810673C22semidirect
44. C2×C22⋊#88322C22semidirect
50. #16810490C22semidirect
52. C4×C22⋊Dic53C22semidirect
54. #16810468C22semidirect
56. #16810361C22semidirect
57. #16810361C22semidirect
58. #16810360C22semidirect
59. #16810360C22semidirect
60. #16810359C22semidirect
61. #16810359C22semidirect
69. C2×C22⋊C8×C53C22semidirect
70. C53×#381C22semidirect
71. C53×#328C22semidirect
72. C53×#328C22semidirect
75. C2×#11719945C2×C4semidirect
92. #13133208C2×C4semidirect
93. #13133208C2×C4semidirect
95. #13133206C2×C4semidirect
97. #13133204C2×C4semidirect
110. #13133196C2×C4semidirect
117. #13133191C2×C4semidirect
131. Q8×Dic53C2×C4semidirect
132. #13133182C2×C4semidirect
135. D4×Dic53C2×C4semidirect
137. #13133179C2×C4semidirect
151. #13133176C2×C4semidirect
187. C2×#41×C53C2×C4semidirect
191. C22⋊Q8×C53C2×C4semidirect
193. #121×C53C2×C4semidirect
198. #117×C53C2×C4semidirect
485. #1516D53semidirect
535. C2×C22⋊C8C2×D53semidirect
540. #381C2×D53semidirect
552. #328C2×D53semidirect
553. #328C2×D53semidirect
562. C53#17615semidirect
564. C2×#41C4×D53semidirect
608. C22⋊Q8C4×D53semidirect
622. #121C4×D53semidirect
655. #117C4×D53semidirect

Maximal subgroups

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

subgroupindex
#202885432
#202837372
#202776522
#202732912
#202732892
#202732852
#202732812
#202732692
#202732072
#202732062
#202732002
#202731982
#328×D532
#327×D532
C53×#15162
#1761553