Finite Group Databasebeta

← #27351867

Subgroups — #27351867

Order 13568.

1074 conjugacy classes of subgroups.

The subgroup lattice has 988 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288543C211yesmaximal, characteristic
2#20283742C211yesmaximal, characteristic, complemented
3#20277622C211yesmaximal, characteristic, complemented
4#20273285C211yesmaximal, characteristic, complemented
5#20273281C211yesmaximal, characteristic, complemented
6#20273259C211yesmaximal, characteristic, complemented
7#20273258C211yesmaximal, characteristic, complemented
8#20273252C211yesmaximal, characteristic, complemented
9#20273250C211yesmaximal, characteristic, complemented
10#20273239C211yesmaximal, characteristic, complemented
11#20273237C211yesmaximal, characteristic, complemented
12#20273217C211yesmaximal, characteristic, complemented
13#328×D53C211yesmaximal, characteristic, complemented
14#327×D53C211yesmaximal, characteristic, complemented
15C53×#1504C211yesmaximal, 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⋊D53—21no—
38C2×C4×C22⋊D53C2211yescharacteristic
39#16810697—21no—
40#16810697—21no—
41#16810692—21no—
42#16810692—21no—
43#16810677C2211yescharacteristic, complemented
44#16810677C2211yescharacteristic, complemented
45#16810587C2211yescharacteristic, complemented
46C22⋊C8×D53C2211yescharacteristic
47C22⋊C8×D53C2211yescharacteristic
48#16810520—21no—
49#16810497—21no—
50#16810496—21no—
51#16810487C2211yescharacteristic, complemented
52#16810483C2211yescharacteristic, complemented
53#16810482C2211yescharacteristic
54#16810474C2211yescharacteristic, 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
69C53×#407C2211yescharacteristic, complemented
70C2×#95×C53C2211yescharacteristic, complemented
71C53×#328C2211yescharacteristic, complemented
72C53×#328C2211yescharacteristic, complemented
73C53×#327C2211yescharacteristic
74C53×#327C2211yescharacteristic
75C2×#11719945C2×C411yescharacteristic, complemented
76C2×Q8×D53C2×C411yescharacteristic, complemented
77C22×C22⋊D53D411yescharacteristic
78C2×D4×D53—21no—
79C2×D4×D53C2×C411yescharacteristic, complemented
80C22×C4×D53—21no—
81C22×C4×D53C2311yescharacteristic
82C2×#11719917—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, complemented
109#13133196—21no—
110#13133196C2×C411yescharacteristic, complemented
111#13133196C2311yescharacteristic
112#13133195—21no—
113#13133195—21no—
114#13133194—21no—
115#13133193C2×C411yescharacteristic, complemented
116#13133192C2×C411yescharacteristic, complemented
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, complemented
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⋊D53—44no—
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#13133176C2×C411yescharacteristic, complemented
153#13133175—21no—
154#13133175—21no—
155#13133174—21no—
156#13133173—21no—
157C2×C4⋊Dic53—21no—
158C2×#11719919—21no—
159C2×#11719919—21no—
160C2×#11719919—21no—
161C2×#11719919D411yescharacteristic
162C4⋊C4×D53—21no—
163C4⋊C4×D53C2×C411yescharacteristic, complemented
164C4⋊C4×D53C2×C411yescharacteristic, complemented
165C2×C22⋊Dic53—21no—
166C2×C22⋊Dic53D411yescharacteristic
167C2×#11719921—21no—
168C2×#11719921—21no—
169C2×#11719921D411yescharacteristic
170C22⋊C4×D53—21no—
171C22⋊C4×D53—21no—
172C22⋊C4×D53—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—
183#13133127—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×D53C2×D411yescharacteristic
210#41×C53—81no—
211C2×Q8×C53C22×C411yescharacteristic
212C2×D4×C53—21no—
213C2×D4×C53—21no—
214C2×D4×C53—21no—
215C2×D4×C53C22×C411yescharacteristic
216C22×C4×C53—21no—
217C22×C4×C53—21no—
218C22×C4×C53—21no—
219C22×C4×C53—42no—
220C22×C4×C53—42no—
221C22×C4×C53—81no—
222C22×C4×C53—81no—
223C22×C4×C53C22×C411yescharacteristic
224C22×C4×C53C22×C411yescharacteristic
225C22×C4×C53C2×D411yescharacteristic
226C22×C4×C53C2×D411yescharacteristic
227C22×C4×C53C2×D411yescharacteristic
228C22×C4×C53C2411yescharacteristic
229C2×C22⋊D53—22no—
230C2×C22⋊D53—22no—
231C2×C22⋊D53—21no—
232C2×C22⋊D53—21no—
233C2×C22⋊D53—21no—
234C2×C22⋊D53—21no—
235C2×C22⋊D53—21no—
236C2×C22⋊D53C22⋊C411yescharacteristic
237C2×C22⋊D53C22⋊C411yescharacteristic
238C2×C22⋊D53C22⋊C411yescharacteristic
239C2×C22⋊D53C22⋊C411yescharacteristic
240C22×Dic53—21no—
241C22×Dic53—21no—
242C22×Dic53—21no—
243C22×Dic53C2×D411yescharacteristic
244C22×Dic53C2×D411yescharacteristic
245C22×Dic53C2×D411yescharacteristic
246Q8×D53—81no—
247D4×D53—42no—
248D4×D53—42no—
249D4×D53—81no—
250#11719945—81no—
251C2×D212—21no—
252C2×D212C22×C411yescharacteristic
253C2×C4×D53—21no—
254C2×C4×D53—21no—
255C2×C4×D53—21no—
256C2×C4×D53—21no—
257C2×C4×D53—21no—
258C2×C4×D53—42no—
259C2×C4×D53—42no—
260C2×C4×D53—81no—
261C2×C4×D53—81no—
262C2×C4×D53C22×C411yescharacteristic
263C2×C4×D53C22×C411yescharacteristic
264C2×C4×D53C2×D411yescharacteristic
265C2×C4×D53C2×D411yescharacteristic
266C2×Dic106—21no—
267C2×Dic106C22×C411yescharacteristic
268M16×C53—81no—
269C2×C8×C53—21no—
270C2×C8×C53—21no—
271C4⋊C4×C53—21no—
272C4⋊C4×C53—21no—
273C4⋊C4×C53C22×C411yescharacteristic
274C4⋊C4×C53C22×C411yescharacteristic
275C22⋊C4×C53—21no—
276C22⋊C4×C53—21no—
277C22⋊C4×C53—21no—
278C22⋊C4×C53—21no—
279C22⋊C4×C53—21no—
280C42×C53—21no—
281C22⋊Dic53—21no—
282C22⋊Dic53—21no—
283C22⋊Dic53—21no—
284C22⋊Dic53—21no—
285C22⋊Dic53—21no—
286C22⋊Dic53—21no—
287C22⋊Dic53—21no—
288C22⋊Dic53—42no—
289C22⋊Dic53C22⋊C411yescharacteristic
290C22⋊Dic53C22⋊C411yescharacteristic
291C22⋊Dic53C22⋊C411yescharacteristic
292C22⋊Dic53C22⋊C411yescharacteristic
293#11719921—21no—
294#11719921—21no—
295#11719921—21no—
296#11719921—21no—
297#11719921—21no—
298#11719921—21no—
299#11719921—21no—
300#11719921—21no—
301#11719921—42no—
302#11719921C22⋊C411yescharacteristic
303#11719921C22⋊C411yescharacteristic
304#11719921C22⋊C411yescharacteristic
305#11719921C22⋊C411yescharacteristic
306C4⋊Dic53—21no—
307C4⋊Dic53—21no—
308C4⋊Dic53—21no—
309C4⋊Dic53—21no—
310C4⋊Dic53—81no—
311C4⋊Dic53C22×C411yescharacteristic
312C4⋊Dic53C22×C411yescharacteristic
313#11719919—21no—
314#11719919—21no—
315#11719919—21no—
316#11719919—21no—
317#11719919—21no—
318#11719919—21no—
319#11719919—21no—
320#11719919—21no—
321#11719919—42no—
322#11719919—42no—
323#11719919—81no—
324#11719919C22⋊C411yescharacteristic
325#11719919C22⋊C411yescharacteristic
326#11719919C22⋊C411yescharacteristic
327#11719919C22⋊C411yescharacteristic
328C4×Dic53—21no—
329C4×Dic53—21no—
330C4×Dic53—21no—
331C4×Dic53—42no—
332C4×Dic53C22×C411yescharacteristic
333C4×Dic53C22×C411yescharacteristic
334C4×Dic53C2×D411yescharacteristic
335C4×Dic53C2×D411yescharacteristic
336#11719917—81no—
337C2×#88322—21no—
338C2×#88322—21no—
339C8×D53—81no—
340C8×D53—81no—
341C23×C53—21no—
342C23×C53—21no—
343C23×C53—21no—
344C23×C53—41no—
345C23×C53—41no—
346C23×C53C2×C22⋊C411yescharacteristic
347C23×C53C2×C22⋊C411yescharacteristic
348C23×C53C22×D411yescharacteristic
349C22×D53—21no—
350C22×D53—41no—
351C22×D53—41no—
352C22×D53—42no—
353C22×D53—81no—
354C22×D53—81no—
355C22×D53C2×C22⋊C411yescharacteristic
356C22×D53C2×C22⋊C411yescharacteristic
357C22×D53AGL(1,ℤ/8)12yes—
358C22×D53#13712yes—
359Q8×C53—41no—
360D4×C53—41no—
361D4×C53—41no—
362D4×C53—41no—
363D4×C53—81no—
364D4×C53—81no—
365C2×C4×C53—22no—
366C2×C4×C53—21no—
367C2×C4×C53—21no—
368C2×C4×C53—21no—
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—41no—
376C2×C4×C53—41no—
377C2×C4×C53—41no—
378C2×C4×C53—41no—
379C2×C4×C53—41no—
380C2×C4×C53—81no—
381C2×C4×C53—84no—
382C2×C4×C53C2×C22⋊C411yescharacteristic
383C2×C4×C53C2×C22⋊C411yescharacteristic
384C2×C4×C53C23×C411yescharacteristic
385C2×C4×C53C22×D411yescharacteristic
386C22⋊D53—22no—
387C22⋊D53—22no—
388C22⋊D53—22no—
389C22⋊D53—22no—
390C22⋊D53—41no—
391C22⋊D53—41no—
392C22⋊D53—42no—
393C22⋊D53—81no—
394C22⋊D53—81no—
395C22⋊D53—81no—
396C2×Dic53—21no—
397C2×Dic53—21no—
398C2×Dic53—21no—
399C2×Dic53—21no—
400C2×Dic53—21no—
401C2×Dic53—41no—
402C2×Dic53—41no—
403C2×Dic53—41no—
404C2×Dic53—41no—
405C2×Dic53—41no—
406C2×Dic53—41no—
407C2×Dic53—41no—
408C2×Dic53—41no—
409C2×Dic53—81no—
410C2×Dic53C2×C22⋊C411yescharacteristic
411C2×Dic53C2×C22⋊C411yescharacteristic
412C2×Dic53C2×C22⋊C411yescharacteristic
413C2×Dic53C2×C22⋊C411yescharacteristic
414C2×Dic53C2×C22⋊C411yescharacteristic
415C2×Dic53C2×C22⋊C411yescharacteristic
416D212—41no—
417D212—42no—
418C4×D53—41no—
419C4×D53—41no—
420C4×D53—41no—
421C4×D53—41no—
422C4×D53—42no—
423C4×D53—81no—
424C4×D53—81no—
425C4×D53—81no—
426C4×D53—81no—
427C4×D53—84no—
428Dic106—41no—
429Dic106—81no—
430C8×C53—41no—
431C8×C53—41no—
432#88322—41no—
433#88322—41no—
434#17622—531nomaximal, Sylow
435C22×C53—21no—
436C22×C53—21no—
437C22×C53—21no—
438C22×C53—21no—
439C22×C53—21no—
440C22×C53—21no—
441C22×C53—21no—
442C22×C53—21no—
443C22×C53—42no—
444C22×C53—42no—
445C22×C53—41no—
446C22×C53—41no—
447C22×C53—41no—
448C22×C53C22×C22⋊C411yescharacteristic
449C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
450C22×C53C2×#13711yescharacteristic
451C2×D53—21no—
452C2×D53—21no—
453C2×D53—21no—
454C2×D53—21no—
455C2×D53—42no—
456C2×D53—42no—
457C2×D53—41no—
458C2×D53—41no—
459C2×D53—41no—
460C2×D53—162no—
461C2×D53#41712yes—
462C2×D53#41712yes—
463C4×C53—21no—
464C4×C53—21no—
465C4×C53—21no—
466C4×C53—21no—
467C4×C53—42no—
468C4×C53—41no—
469C4×C53—41no—
470C4×C53—41no—
471C4×C53—81no—
472Dic53—21no—
473Dic53—21no—
474Dic53—21no—
475Dic53—21no—
476Dic53—21no—
477Dic53—21no—
478Dic53—41no—
479Dic53—41no—
480Dic53—41no—
481Dic53—81no—
482Dic53—81no—
483#3505—531no—
484#2973—531no—
485#2349—531no—
486#1520—531no—
487#1519—531no—
488#1513—531no—
489#1513—531no—
490#1512—531no—
491#1512—531no—
492#1509—531no—
493#1509—531no—
494#1504—531no—
495#1504D5311yescharacteristic, complemented
496C2×#328—531no—
497C2×#327—531no—
498C2×C53—21no—
499C2×C53—21no—
500C2×C53—41no—
501C2×C53—41no—
502C2×C53—81no—
503C2×C53#288311yescharacteristic
504C2×C53C2×#41711yescharacteristic
505C2×C53#290111yescharacteristic
506D53—22no—
507D53—22no—
508D53—81no—
509#553—531no—
510#553—531no—
511#553—1061no—
512#553—1061no—
513#552—531no—
514#552—531no—
515#551—1061no—
516#551—1061no—
517#548—531no—
518#548—531no—
519#546—531no—
520#546—531no—
521#539—1061no—
522#538—1061no—
523#534—1061no—
524#529—531no—
525#529—531no—
526#525—531no—
527#525C2×D5311yescharacteristic
528C2×C22⋊Q8—531no—
529C2×#121—531no—
530#518—1061no—
531C2×C4×D4—531no—
532C2×C4×D4—1061no—
533#435—1061no—
534#435—1061no—
535#435—1061no—
536#435—1061no—
537#432—531no—
538#432—531no—
539#407—531no—
540#407C2×D5311yescharacteristic, complemented
541C2×C22⋊C8—531no—
542C2×C22⋊C8—531no—
543#389—1061no—
544#385—1061no—
545#385—1061no—
546#382—531no—
547#380—531no—
548#380—531no—
549C4×C4⋊C4—531no—
550C2×#95—531no—
551C2×#95C2×D5311yescharacteristic, complemented
552#328—531no—
553#328—531no—
554#328—531no—
555#328—531no—
556#328—531no—
557#328—531no—
558#328C2×D5311yescharacteristic, complemented
559#328C2×D5311yescharacteristic, complemented
560#327—531no—
561#327—531no—
562#327—531no—
563#327—531no—
564#327—531no—
565#327—531no—
566#327C2×D5311yescharacteristic
567#327C2×D5311yescharacteristic
568C53#1762211yescharacteristic, complemented, Sylow
569C2×#41—531no—
570C2×#41C4×D5311yescharacteristic, complemented
571C22×Q8—531no—
572C22×D4—531no—
573C22×D4—531no—
574C22×D4—1061no—
575C23×C4—21no—
576C23×C4—531no—
577C23×C4—1061no—
578C23×C4C22×D5311yescharacteristic
579C2×M16—21no—
580C2×M16—1061no—
581C22×C8—1061no—
582C22×C8—1061no—
583#126—1061no—
584#126—1061no—
585#126—1061no—
586#126—1061no—
587#126—1061no—
588#126—1061no—
589#125—531no—
590#125—531no—
591#125—1061no—
592#125—1061no—
593#124—531no—
594#124—531no—
595#124—1061no—
596#124—1061no—
597#123—21no—
598#123—1061no—
599#123—1061no—
600#123—1061no—
601#123—1061no—
602#123—1061no—
603#123—1061no—
604#123—1061no—
605#123—1061no—
606#123—1061no—
607C22⋊Q8—531no—
608C22⋊Q8—531no—
609C22⋊Q8—531no—
610C22⋊Q8—531no—
611C22⋊Q8—1061no—
612C22⋊Q8—1061no—
613C22⋊Q8—1061no—
614C22⋊Q8—1061no—
615C22⋊Q8C4×D5311yescharacteristic, complemented
616C22⋊Q8C22×D5311yescharacteristic
617#121—531no—
618#121—531no—
619#121—531no—
620#121—531no—
621#121—1061no—
622#121—1061no—
623#121—1061no—
624#121—1061no—
625#121—1061no—
626#121—1061no—
627#121—1061no—
628#121—1061no—
629#121C4×D5311yescharacteristic, complemented
630#121C22×D5311yescharacteristic
631#120—21no—
632#120—1061no—
633#120—1061no—
634#120—1061no—
635C4×Q8—531no—
636C4×Q8—531no—
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—531no—
640C4×D4—531no—
641C4×D4—531no—
642C4×D4—531no—
643C4×D4—531no—
644C4×D4—531no—
645C4×D4—531no—
646C4×D4—531no—
647C4×D4—531no—
648C4×D4—531no—
649C4×D4—1061no—
650C4×D4—1061no—
651C4×D4—1061no—
652C4×D4—1061no—
653C4×D4—1061no—
654C4×D4—1061no—
655C4×D4—1061no—
656C4×D4—1061no—
657C4×D4—2124no—
658#117—531no—
659#117—1061no—
660#117—1061no—
661#117—1061no—
662#117—1061no—
663#117C4×D5311yescharacteristic, complemented
664C2×C4⋊C4—531no—
665C2×C4⋊C4—531no—
666C2×C4⋊C4—531no—
667C2×C4⋊C4—1061no—
668C2×C4⋊C4—1061no—
669C2×C4⋊C4—1061no—
670C2×C4⋊C4—1061no—
671C2×C4⋊C4—1061no—
672C2×C22⋊C4—531no—
673C2×C22⋊C4—531no—
674C2×C22⋊C4—1061no—
675C2×C22⋊C4—1061no—
676C2×C22⋊C4—1061no—
677C2×C22⋊C4—1061no—
678C2×C22⋊C4—1061no—
679C2×C22⋊C4—1061no—
680C2×C42—531no—
681C2×C42—1061no—
682C4⋊C8—1061no—
683C4⋊C8—1061no—
684C22⋊C8—21no—
685C22⋊C8—531no—
686C22⋊C8—531no—
687C22⋊C8—1061no—
688C22⋊C8—1061no—
689C22⋊C8—1061no—
690C22⋊C8C22×D5311yescharacteristic
691C22⋊C8C22×D5311yescharacteristic
692#97—1061no—
693#97—1061no—
694#95—21no—
695#95—531no—
696#95—531no—
697#95—1061no—
698#95—1061no—
699#95C22×D5311yescharacteristic
700#95C22×D5311yescharacteristic
701C24—531no—
702C24—1061no—
703C24D4×D5311yescharacteristic
704#41—81no—
705#41—4241no—
706C2×Q8—531no—
707C2×Q8—1061no—
708C2×Q8—4241no—
709C2×Q8C2×C4×D5311yescharacteristic
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—531no—
714C2×D4—531no—
715C2×D4—531no—
716C2×D4—531no—
717C2×D4—531no—
718C2×D4—1061no—
719C2×D4—1061no—
720C2×D4—1062no—
721C2×D4—1062no—
722C2×D4—1061no—
723C2×D4—1061no—
724C2×D4—1061no—
725C2×D4—1061no—
726C2×D4—4241no—
727C2×D4—2122no—
728C2×D4—2122no—
729C2×D4C2×C4×D5311yescharacteristic
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—42no—
734C22×C4—42no—
735C22×C4—81no—
736C22×C4—81no—
737C22×C4—531no—
738C22×C4—531no—
739C22×C4—531no—
740C22×C4—531no—
741C22×C4—531no—
742C22×C4—531no—
743C22×C4—531no—
744C22×C4—1061no—
745C22×C4—1061no—
746C22×C4—1061no—
747C22×C4—1061no—
748C22×C4—1061no—
749C22×C4—1061no—
750C22×C4—1061no—
751C22×C4—1061no—
752C22×C4—4241no—
753C22×C4—4241no—
754C22×C4—2122no—
755C22×C4—2122no—
756C22×C4C2×C4×D5311yescharacteristic
757C22×C4C2×C4×D5311yescharacteristic
758C22×C4D4×D5311yescharacteristic
759C22×C4D4×D5311yescharacteristic
760C22×C4D4×D5311yescharacteristic
761C22×C4C23×D5311yescharacteristic
762M16—81no—
763M16—4241no—
764C2×C8—21no—
765C2×C8—21no—
766C2×C8—1061no—
767C2×C8—1061no—
768C2×C8—4241no—
769C2×C8—4241no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—531no—
773C4⋊C4—531no—
774C4⋊C4—531no—
775C4⋊C4—531no—
776C4⋊C4—531no—
777C4⋊C4—531no—
778C4⋊C4—1061no—
779C4⋊C4—1061no—
780C4⋊C4—1061no—
781C4⋊C4—1061no—
782C4⋊C4—1061no—
783C4⋊C4—1061no—
784C4⋊C4—1061no—
785C4⋊C4—1061no—
786C4⋊C4—1061no—
787C4⋊C4—1061no—
788C4⋊C4—1061no—
789C4⋊C4—1061no—
790C4⋊C4—4241no—
791C4⋊C4—4241no—
792C4⋊C4—2122no—
793C4⋊C4—2122no—
794C4⋊C4C2×C4×D5311yescharacteristic
795C4⋊C4C2×C4×D5311yescharacteristic
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—531no—
802C22⋊C4—531no—
803C22⋊C4—531no—
804C22⋊C4—531no—
805C22⋊C4—531no—
806C22⋊C4—531no—
807C22⋊C4—531no—
808C22⋊C4—531no—
809C22⋊C4—1061no—
810C22⋊C4—1061no—
811C22⋊C4—1061no—
812C22⋊C4—1061no—
813C22⋊C4—1061no—
814C22⋊C4—1061no—
815C22⋊C4—1061no—
816C22⋊C4—1061no—
817C22⋊C4—1061no—
818C22⋊C4—1061no—
819C22⋊C4—1061no—
820C22⋊C4—1061no—
821C22⋊C4—1061no—
822C22⋊C4—1061no—
823C22⋊C4—1061no—
824C22⋊C4—2122no—
825C22⋊C4—2122no—
826C42—21no—
827C42—531no—
828C42—531no—
829C42—531no—
830C42—531no—
831C42—1061no—
832C42—1061no—
833C42—1061no—
834C42—2122no—
835C23—21no—
836C23—21no—
837C23—21no—
838C23—41no—
839C23—41no—
840C23—531no—
841C23—531no—
842C23—532no—
843C23—532no—
844C23—1061no—
845C23—4241no—
846C23—4241no—
847C23—2121no—
848C23—2121no—
849C23—2122no—
850C23C22⋊C4×D5311yescharacteristic
851C23C22⋊C4×D5311yescharacteristic
852C23C2×D4×D5311yescharacteristic
853Q8—41no—
854Q8—4241no—
855Q8—2121no—
856D4—41no—
857D4—41no—
858D4—41no—
859D4—81no—
860D4—81no—
861D4—1062no—
862D4—1062no—
863D4—1062no—
864D4—1062no—
865D4—4241no—
866D4—4241no—
867D4—4241no—
868D4—2121no—
869D4—2122no—
870D4—2122no—
871D4—2121no—
872D4—2121no—
873C2×C4—22no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—81no—
889C2×C4—84no—
890C2×C4—531no—
891C2×C4—531no—
892C2×C4—531no—
893C2×C4—531no—
894C2×C4—531no—
895C2×C4—531no—
896C2×C4—1061no—
897C2×C4—1061no—
898C2×C4—1061no—
899C2×C4—1061no—
900C2×C4—1061no—
901C2×C4—4241no—
902C2×C4—4241no—
903C2×C4—4244no—
904C2×C4—4241no—
905C2×C4—4241no—
906C2×C4—4241no—
907C2×C4—2121no—
908C2×C4—2121no—
909C2×C4—2121no—
910C2×C4—2121no—
911C2×C4—2122no—
912C2×C4—2121no—
913C2×C4—2121no—
914C2×C4—2121no—
915C2×C4—2121no—
916C2×C4—2121no—
917C2×C4—2121no—
918C2×C4—2121no—
919C2×C4—2121no—
920C2×C4C22⋊C4×D5311yescharacteristic
921C2×C4C22⋊C4×D5311yescharacteristic
922C2×C4C22×C4×D5311yescharacteristic
923C2×C4C2×D4×D5311yescharacteristic
924C8—41no—
925C8—41no—
926C8—2121no—
927C8—2121no—
928C22—21no—
929C22—21no—
930C22—21no—
931C22—21no—
932C22—21no—
933C22—21no—
934C22—21no—
935C22—21no—
936C22—42no—
937C22—42no—
938C22—41no—
939C22—41no—
940C22—41no—
941C22—532no—
942C22—532no—
943C22—8482no—
944C22—1061no—
945C22—1061no—
946C22—1061no—
947C22—1061no—
948C22—2122no—
949C22—2122no—
950C22—2121no—
951C22—2121no—
952C22—2121no—
953C22C2×C22⋊C4×D5311yescharacteristic
954C22AGL(1,ℤ/8)×D5311yescharacteristic
955C22#137×D5311yescharacteristic
956C4—21no—
957C4—21no—
958C4—21no—
959C4—21no—
960C4—42no—
961C4—41no—
962C4—41no—
963C4—41no—
964C4—81no—
965C4—1061no—
966C4—1061no—
967C4—1061no—
968C4—1061no—
969C4—1061no—
970C4—1061no—
971C4—4241no—
972C4—4241no—
973C4—2121no—
974C4—2121no—
975C4—2121no—
976C2—21no—
977C2—21no—
978C2—41no—
979C2—41no—
980C2—81no—
981C2—1062no—
982C2—1062no—
983C2—4241no—
984C2#2028317311yescharacteristic
985C2#417×D5311yescharacteristic
986C2#2028325911yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1504C2
socleC22×C53C22×C22⋊C4
prime radical#20288543C2
cosocleC22×C4×C53C24
hypercenter#1504D53
hypocenterC53#17622
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. #20283742C2semidirect
3. #20277622C2semidirect
4. #20273285C2semidirect
5. #20273281C2semidirect
6. #20273259C2semidirect
7. #20273258C2semidirect
8. #20273252C2semidirect
9. #20273250C2semidirect
10. #20273239C2semidirect
11. #20273237C2semidirect
12. #20273217C2semidirect
13. #328×D53C2semidirect
14. #327×D53C2semidirect
15. C53×#1504C2semidirect
17. #16811320C4semidirect
19. #16811317C4semidirect
20. #16811312C4semidirect
21. #16811307C4semidirect
24. #16811283C4semidirect
25. #16811280C4semidirect
26. #16811270C4semidirect
27. #16811261C4semidirect
43. #16810677C22semidirect
44. #16810677C22semidirect
45. #16810587C22semidirect
51. #16810487C22semidirect
52. #16810483C22semidirect
54. #16810474C22semidirect
56. #16810361C22semidirect
57. #16810361C22semidirect
58. #16810360C22semidirect
59. #16810360C22semidirect
60. #16810359C22semidirect
61. #16810359C22semidirect
69. C53×#407C22semidirect
70. C2×#95×C53C22semidirect
71. C53×#328C22semidirect
72. C53×#328C22semidirect
75. C2×#11719945C2×C4semidirect
76. C2×Q8×D53C2×C4semidirect
79. C2×D4×D53C2×C4semidirect
92. #13133208C2×C4semidirect
93. #13133208C2×C4semidirect
95. #13133206C2×C4semidirect
97. #13133204C2×C4semidirect
108. #13133197C2×C4semidirect
110. #13133196C2×C4semidirect
115. #13133193C2×C4semidirect
116. #13133192C2×C4semidirect
117. #13133191C2×C4semidirect
127. #13133188C2×C4semidirect
131. Q8×Dic53C2×C4semidirect
132. #13133182C2×C4semidirect
135. D4×Dic53C2×C4semidirect
137. #13133179C2×C4semidirect
152. #13133176C2×C4semidirect
163. C4⋊C4×D53C2×C4semidirect
164. C4⋊C4×D53C2×C4semidirect
188. C2×#41×C53C2×C4semidirect
193. C22⋊Q8×C53C2×C4semidirect
195. #121×C53C2×C4semidirect
200. #117×C53C2×C4semidirect
495. #1504D53semidirect
540. #407C2×D53semidirect
551. C2×#95C2×D53semidirect
558. #328C2×D53semidirect
559. #328C2×D53semidirect
568. C53#17622semidirect
570. C2×#41C4×D53semidirect
615. C22⋊Q8C4×D53semidirect
629. #121C4×D53semidirect
663. #117C4×D53semidirect

Maximal subgroups

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

subgroupindex
#202885432
#202837422
#202776222
#202732852
#202732812
#202732592
#202732582
#202732522
#202732502
#202732392
#202732372
#202732172
#328×D532
#327×D532
C53×#15042
#1762253