Finite Group Databasebeta

← #27351871

Subgroups — #27351871

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#20288550C211yesmaximal, characteristic
2#20283743C211yesmaximal, characteristic, complemented
3#20277623C211yesmaximal, characteristic, complemented
4#20273285C211yesmaximal, characteristic, complemented
5#20273281C211yesmaximal, characteristic, complemented
6#20273257C211yesmaximal, characteristic, complemented
7#20273255C211yesmaximal, characteristic, complemented
8#20273251C211yesmaximal, characteristic, complemented
9#20273241C211yesmaximal, characteristic, complemented
10#20273240C211yesmaximal, characteristic, complemented
11#20273218C211yesmaximal, characteristic, complemented
12#20273216C211yesmaximal, characteristic, complemented
13#328×D53C211yesmaximal, characteristic, complemented
14#327×D53C211yesmaximal, characteristic, complemented
15C53×#1512C211yesmaximal, characteristic, complemented
16#16811326C411yescharacteristic, complemented
17#16811324—21no—
18#16811323C411yescharacteristic, complemented
19#16811317—21no—
20#16811314C411yescharacteristic, complemented
21#16811311C411yescharacteristic, complemented
22#16811298—21no—
23#16811297—21no—
24#16811285C411yescharacteristic, complemented
25#16811281C411yescharacteristic, complemented
26#16811268C411yescharacteristic, complemented
27#16811266C411yescharacteristic, complemented
28#16811217—21no—
29#16811206—21no—
30#16811184—21no—
31#16811157C2211yescharacteristic
32#16811136C2211yescharacteristic
33#16811133C2211yescharacteristic
34C22⋊Q8×D53C2211yescharacteristic
35#121×D53C2211yescharacteristic
36#16811095—21no—
37C2×C4×D212C2211yescharacteristic
38C2×#13133179—21no—
39#16810696—21no—
40#16810696—21no—
41#16810693—21no—
42#16810693—21no—
43#16810680C2211yescharacteristic, complemented
44#16810585C2211yescharacteristic, complemented
45#16810585C2211yescharacteristic, complemented
46C22⋊C8×D53C2211yescharacteristic
47C22⋊C8×D53C2211yescharacteristic
48#16810519—21no—
49#16810497—21no—
50#16810497—21no—
51#16810482C2211yescharacteristic
52#16810482C2211yescharacteristic, complemented
53C4×C4⋊Dic53C2211yescharacteristic, complemented
54#95×D53C2211yescharacteristic
55#95×D53C2211yescharacteristic, complemented
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×#529C2211yescharacteristic
69C53×#432C2211yescharacteristic, complemented
70C53×#382C2211yescharacteristic, complemented
71C53×#328C2211yescharacteristic, complemented
72C53×#328C2211yescharacteristic, complemented
73C53×#327C2211yescharacteristic
74C53×#327C2211yescharacteristic
75C2×#11719949C2×C411yescharacteristic, complemented
76C2×#11719947C2×C411yescharacteristic, complemented
77C2×Q8×D53C2×C411yescharacteristic, complemented
78C22×D212D411yescharacteristic
79C2×D4×D53—21no—
80C2×D4×D53C2×C411yescharacteristic, complemented
81C22×C4×D53—21no—
82C22×C4×D53—21no—
83C22×C4×D53C2311yescharacteristic
84C22×C4×D53C2311yescharacteristic
85C2×#11719912—21no—
86C2×#11719912—21no—
87C2×C8×D53—21no—
88C2×C8×D53—21no—
89#13133212—21no—
90#13133212—21no—
91#13133211—21no—
92#13133211—21no—
93#13133210—21no—
94#13133209C2×C411yescharacteristic, complemented
95#13133208—21no—
96#13133207—21no—
97#13133205—21no—
98#13133205C2×C411yescharacteristic, complemented
99#13133203—21no—
100#13133202—21no—
101#13133202—21no—
102#13133202—21no—
103#13133202—21no—
104#13133201—21no—
105#13133200—21no—
106#13133200—21no—
107#13133199—21no—
108#13133199—21no—
109#13133197—21no—
110#13133197C2×C411yescharacteristic, complemented
111#13133197C2×C411yescharacteristic, complemented
112#13133196C2311yescharacteristic
113#13133195—21no—
114#13133194—21no—
115#13133194—21no—
116#13133193C2×C411yescharacteristic, complemented
117#13133193C2×C411yescharacteristic, complemented
118#13133192—21no—
119#13133192—21no—
120#13133192C2×C411yescharacteristic, complemented
121#13133192C2×C411yescharacteristic, complemented
122#13133191—21no—
123#13133191C2311yescharacteristic
124#13133190—21no—
125#13133190—21no—
126#13133190—21no—
127#13133190—21no—
128#13133189—21no—
129#13133188C2×C411yescharacteristic, complemented
130#13133188C2×C411yescharacteristic, complemented
131#13133187—21no—
132#13133187—21no—
133#13133187—21no—
134#13133185—21no—
135C4×Dic106C2×C411yescharacteristic, complemented
136C4×D212—21no—
137C4×D212C2×C411yescharacteristic
138C4×D212C2×C411yescharacteristic
139C4×D212C2×C411yescharacteristic
140C4×D212C2×C411yescharacteristic
141C4×D212C2×C411yescharacteristic, complemented
142C4×D212D411yescharacteristic
143C4×D212D411yescharacteristic
144C4×D212D411yescharacteristic
145C4×D212D411yescharacteristic
146D4×Dic53—21no—
147#13133179—21no—
148#13133179—21no—
149#13133179—44no—
150C4×C22⋊D53—21no—
151C4×C22⋊D53—21no—
152#13133177—21no—
153#13133177—21no—
154#13133177—21no—
155#13133175—21no—
156#13133175C2×C411yescharacteristic, complemented
157#13133175C2×C411yescharacteristic, complemented
158#13133174—21no—
159#13133174—21no—
160C2×C4⋊Dic53—21no—
161C2×C4⋊Dic53D411yescharacteristic
162C2×#11719919—21no—
163C2×#11719919—21no—
164C4⋊C4×D53—21no—
165C4⋊C4×D53C2×C411yescharacteristic, complemented
166C4⋊C4×D53C2×C411yescharacteristic, complemented
167C2×#11719921—21no—
168C2×#11719921—21no—
169C2×#11719921—21no—
170C2×#11719921D411yescharacteristic
171C2×#11719921D411yescharacteristic
172C22⋊C4×D53—21no—
173C22⋊C4×D53—21no—
174C22⋊C4×D53—21no—
175C2×C4×Dic53—21no—
176C4⋊#88322—21no—
177C22⋊#88322C2311yescharacteristic
178C22⋊#88322C2311yescharacteristic
179#13133129—21no—
180#13133129—21no—
181#13133129—21no—
182#13133129—21no—
183#13133128—21no—
184#13133124—21no—
185#13133124—21no—
186#13133124C2311yescharacteristic
187#13133124C2311yescharacteristic
188#126×C53—21no—
189#125×C53C2×C411yescharacteristic, complemented
190#124×C53C2×C411yescharacteristic, complemented
191#123×C53—21no—
192C22⋊Q8×C53C2311yescharacteristic
193#121×C53C2311yescharacteristic
194C4×Q8×C53C2×C411yescharacteristic, complemented
195C4×D4×C53—21no—
196C4×D4×C53C2×C411yescharacteristic, complemented
197#117×C53—21no—
198C2×C4⋊C4×C53—21no—
199C2×C42×C53C2311yescharacteristic
200C4⋊C8×C53—21no—
201C22⋊C8×C53C2311yescharacteristic
202C22⋊C8×C53C2311yescharacteristic
203#97×C53—21no—
204#95×C53—21no—
205#95×C53C2311yescharacteristic
206#95×C53C2311yescharacteristic
207C23×D53—21no—
208C23×D53C2×D411yescharacteristic
209C23×D53C2×D411yescharacteristic
210C2×Q8×C53C22×C411yescharacteristic
211C2×D4×C53—21no—
212C2×D4×C53C22×C411yescharacteristic
213C22×C4×C53—21no—
214C22×C4×C53—21no—
215C22×C4×C53—21no—
216C22×C4×C53C2×D411yescharacteristic
217C22×C4×C53C2×D411yescharacteristic
218C22×C4×C53C2411yescharacteristic
219C2×C22⋊D53—21no—
220C2×C22⋊D53—21no—
221C2×C22⋊D53—21no—
222C2×C22⋊D53—21no—
223C2×C22⋊D53—21no—
224C22×Dic53—21no—
225C22×Dic53—21no—
226C22×Dic53—21no—
227C22×Dic53C2×D411yescharacteristic
228C22×Dic53C2×D411yescharacteristic
229#11719949—81no—
230Q8×D53—81no—
231#11719947—81no—
232D4×D53—42no—
233D4×D53—42no—
234D4×D53—81no—
235C2×D212—22no—
236C2×D212—22no—
237C2×D212—21no—
238C2×D212—21no—
239C2×D212—21no—
240C2×D212C22⋊C411yescharacteristic
241C2×D212C22⋊C411yescharacteristic
242C2×D212C22⋊C411yescharacteristic
243C2×D212C22⋊C411yescharacteristic
244C2×D212C22×C411yescharacteristic
245C2×C4×D53—21no—
246C2×C4×D53—21no—
247C2×C4×D53—21no—
248C2×C4×D53—21no—
249C2×C4×D53—21no—
250C2×C4×D53—42no—
251C2×C4×D53—42no—
252C2×C4×D53—42no—
253C2×C4×D53—42no—
254C2×C4×D53—81no—
255C2×C4×D53—81no—
256C2×C4×D53—81no—
257C2×C4×D53—81no—
258C2×C4×D53C22×C411yescharacteristic
259C2×C4×D53C22×C411yescharacteristic
260C2×C4×D53C22×C411yescharacteristic
261C2×C4×D53C22×C411yescharacteristic
262C2×C4×D53C2×D411yescharacteristic
263C2×C4×D53C2×D411yescharacteristic
264C2×C4×D53C2×D411yescharacteristic
265C2×C4×D53C2×D411yescharacteristic
266C2×Dic106—21no—
267C2×Dic106C22×C411yescharacteristic
268C2×C8×C53—21no—
269C2×C8×C53—21no—
270C4⋊C4×C53—21no—
271C4⋊C4×C53—21no—
272C4⋊C4×C53—21no—
273C4⋊C4×C53—21no—
274C4⋊C4×C53—42no—
275C4⋊C4×C53C22×C411yescharacteristic
276C4⋊C4×C53C22×C411yescharacteristic
277C22⋊C4×C53—21no—
278C22⋊C4×C53—21no—
279C22⋊C4×C53—21no—
280C22⋊C4×C53—21no—
281C22⋊C4×C53—21no—
282C42×C53—21no—
283C42×C53C22×C411yescharacteristic
284C42×C53C22×C411yescharacteristic
285C42×C53C2×D411yescharacteristic
286C42×C53C2×D411yescharacteristic
287C22⋊Dic53—21no—
288C22⋊Dic53—21no—
289C22⋊Dic53—21no—
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—21no—
299#11719921—21no—
300#11719921—21no—
301#11719921—21no—
302#11719921—42no—
303#11719921—42no—
304#11719921C22⋊C411yescharacteristic
305#11719921C22⋊C411yescharacteristic
306#11719921C22⋊C411yescharacteristic
307#11719921C22⋊C411yescharacteristic
308#11719921C22⋊C411yescharacteristic
309#11719921C22⋊C411yescharacteristic
310#11719921C22⋊C411yescharacteristic
311#11719921C22⋊C411yescharacteristic
312C4⋊Dic53—21no—
313C4⋊Dic53—21no—
314C4⋊Dic53—42no—
315C4⋊Dic53C22⋊C411yescharacteristic
316C4⋊Dic53C22⋊C411yescharacteristic
317C4⋊Dic53C22⋊C411yescharacteristic
318C4⋊Dic53C22⋊C411yescharacteristic
319C4⋊Dic53C22×C411yescharacteristic
320C4⋊Dic53C22×C411yescharacteristic
321#11719919—21no—
322#11719919—21no—
323#11719919—21no—
324#11719919—21no—
325#11719919—21no—
326#11719919—21no—
327#11719919—21no—
328#11719919—21no—
329#11719919—81no—
330#11719919—81no—
331C4×Dic53—21no—
332C4×Dic53—21no—
333C4×Dic53—21no—
334C4×Dic53—42no—
335C2×#88322—21no—
336C2×#88322—21no—
337#11719912—81no—
338#11719912—81no—
339C8×D53—81no—
340C8×D53—81no—
341C23×C53—21no—
342C23×C53C22×D411yescharacteristic
343C22×D53—21no—
344C22×D53—21no—
345C22×D53—21no—
346C22×D53—41no—
347C22×D53—41no—
348C22×D53—41no—
349C22×D53—41no—
350C22×D53—42no—
351C22×D53—81no—
352C22×D53—81no—
353C22×D53C2×C22⋊C411yescharacteristic
354C22×D53C2×C22⋊C411yescharacteristic
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—
363C2×C4×C53—21no—
364C2×C4×C53—21no—
365C2×C4×C53—21no—
366C2×C4×C53—21no—
367C2×C4×C53—21no—
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—41no—
376C2×C4×C53—81no—
377C2×C4×C53C2×C22⋊C411yescharacteristic
378C2×C4×C53C2×C22⋊C411yescharacteristic
379C2×C4×C53C2×C22⋊C411yescharacteristic
380C2×C4×C53C2×C22⋊C411yescharacteristic
381C2×C4×C53C23×C411yescharacteristic
382C2×C4×C53C22×D411yescharacteristic
383C22⋊D53—41no—
384C22⋊D53—41no—
385C22⋊D53—42no—
386C22⋊D53—81no—
387C22⋊D53—81no—
388C22⋊D53—81no—
389C2×Dic53—22no—
390C2×Dic53—21no—
391C2×Dic53—21no—
392C2×Dic53—21no—
393C2×Dic53—41no—
394C2×Dic53—41no—
395C2×Dic53—41no—
396C2×Dic53—41no—
397C2×Dic53—41no—
398C2×Dic53—41no—
399C2×Dic53—41no—
400C2×Dic53—81no—
401C2×Dic53C2×C22⋊C411yescharacteristic
402C2×Dic53C2×C22⋊C411yescharacteristic
403C2×Dic53C2×C22⋊C411yescharacteristic
404C2×Dic53C2×C22⋊C411yescharacteristic
405D212—22no—
406D212—22no—
407D212—22no—
408D212—22no—
409D212—41no—
410D212—42no—
411D212—81no—
412D212—81no—
413C4×D53—41no—
414C4×D53—41no—
415C4×D53—41no—
416C4×D53—41no—
417C4×D53—41no—
418C4×D53—41no—
419C4×D53—41no—
420C4×D53—41no—
421C4×D53—42no—
422C4×D53—81no—
423C4×D53—81no—
424C4×D53—81no—
425C4×D53—81no—
426C4×D53—84no—
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—41no—
438C22×C53—41no—
439C22×C53—41no—
440C22×C53C22×C22⋊C411yescharacteristic
441C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
442C22×C53C2×#13711yescharacteristic
443C2×D53—21no—
444C2×D53—21no—
445C2×D53—21no—
446C2×D53—21no—
447C2×D53—21no—
448C2×D53—21no—
449C2×D53—21no—
450C2×D53—21no—
451C2×D53—21no—
452C2×D53—21no—
453C2×D53—42no—
454C2×D53—42no—
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—21no—
468C4×C53—21no—
469C4×C53—41no—
470C4×C53—41no—
471C4×C53—41no—
472C4×C53—81no—
473C4×C53—81no—
474Dic53—21no—
475Dic53—21no—
476Dic53—21no—
477Dic53—21no—
478Dic53—42no—
479Dic53—41no—
480Dic53—41no—
481Dic53—41no—
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#1512D5311yescharacteristic, complemented
492#1509—531no—
493#1509—531no—
494#1504—531no—
495#1504—531no—
496C2×#328—531no—
497C2×#327—531no—
498C2×C53—21no—
499C2×C53—21no—
500C2×C53—81no—
501C2×C53#288311yescharacteristic
502C2×C53C2×#41711yescharacteristic
503C2×C53#290111yescharacteristic
504D53—22no—
505D53—22no—
506D53—41no—
507D53—41no—
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#529C2×D5311yescharacteristic
526#525—531no—
527#525—531no—
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#432C2×D5311yescharacteristic, complemented
539#407—531no—
540#407—531no—
541C2×C22⋊C8—531no—
542C2×C22⋊C8—531no—
543#389—1061no—
544#385—1061no—
545#385—1061no—
546#382C2×D5311yescharacteristic, complemented
547#380—531no—
548#380—531no—
549C4×C4⋊C4—531no—
550C2×#95—531no—
551C2×#95—531no—
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×#41—531no—
571C22×Q8—531no—
572C22×D4—531no—
573C22×D4—531no—
574C22×D4—1061no—
575C23×C4—531no—
576C23×C4—531no—
577C23×C4—1061no—
578C23×C4—1061no—
579C2×M16—1061no—
580C2×M16—1061no—
581C22×C8—1061no—
582C22×C8—1061no—
583#126—21no—
584#126—1061no—
585#126—1061no—
586#126—1061no—
587#126—1061no—
588#126—1061no—
589#125—531no—
590#125—1061no—
591#125—1061no—
592#125C4×D5311yescharacteristic, complemented
593#124—531no—
594#124—1061no—
595#124—1061no—
596#124C4×D5311yescharacteristic, complemented
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—531no—
612C22⋊Q8—1061no—
613C22⋊Q8—1061no—
614C22⋊Q8—1061no—
615C22⋊Q8—1061no—
616C22⋊Q8C22×D5311yescharacteristic
617#121—531no—
618#121—531no—
619#121—531no—
620#121—531no—
621#121—531no—
622#121—1061no—
623#121—1061no—
624#121—1061no—
625#121—1061no—
626#121—1061no—
627#121—1061no—
628#121—1061no—
629#121—1061no—
630#121C22×D5311yescharacteristic
631#120—1061no—
632#120—1061no—
633#120—1061no—
634#120—1061no—
635C4×Q8—531no—
636C4×Q8C4×D5311yescharacteristic, complemented
637C4×D4—21no—
638C4×D4—531no—
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—1061no—
648C4×D4—1061no—
649C4×D4—1061no—
650C4×D4—1061no—
651C4×D4—1061no—
652C4×D4—1061no—
653C4×D4—1061no—
654C4×D4—1061no—
655C4×D4—1061no—
656C4×D4—2124no—
657C4×D4C4×D5311yescharacteristic, complemented
658#117—21no—
659#117—531no—
660#117—531no—
661#117—1061no—
662#117—1061no—
663#117—1061no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—531no—
666C2×C4⋊C4—531no—
667C2×C4⋊C4—531no—
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—1061no—
681C2×C42C22×D5311yescharacteristic
682C4⋊C8—21no—
683C4⋊C8—1061no—
684C22⋊C8—531no—
685C22⋊C8—531no—
686C22⋊C8—1061no—
687C22⋊C8—1061no—
688C22⋊C8—1061no—
689C22⋊C8—1061no—
690C22⋊C8C22×D5311yescharacteristic
691C22⋊C8C22×D5311yescharacteristic
692#97—21no—
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—531no—
703C24—1061no—
704#41—4241no—
705#41—4241no—
706C2×Q8—531no—
707C2×Q8—1061no—
708C2×Q8—4241no—
709C2×Q8C2×C4×D5311yescharacteristic
710C2×D4—21no—
711C2×D4—531no—
712C2×D4—531no—
713C2×D4—531no—
714C2×D4—531no—
715C2×D4—531no—
716C2×D4—1062no—
717C2×D4—1062no—
718C2×D4—1061no—
719C2×D4—1061no—
720C2×D4—1061no—
721C2×D4—1061no—
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—531no—
734C22×C4—531no—
735C22×C4—531no—
736C22×C4—531no—
737C22×C4—531no—
738C22×C4—531no—
739C22×C4—531no—
740C22×C4—531no—
741C22×C4—531no—
742C22×C4—531no—
743C22×C4—1061no—
744C22×C4—1061no—
745C22×C4—1061no—
746C22×C4—1061no—
747C22×C4—1061no—
748C22×C4—1061no—
749C22×C4—1061no—
750C22×C4—1061no—
751C22×C4—4241no—
752C22×C4—4241no—
753C22×C4—4241no—
754C22×C4—4241no—
755C22×C4—2122no—
756C22×C4—2122no—
757C22×C4—2122no—
758C22×C4—2122no—
759C22×C4D4×D5311yescharacteristic
760C22×C4D4×D5311yescharacteristic
761C22×C4C23×D5311yescharacteristic
762M16—4241no—
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—21no—
773C4⋊C4—21no—
774C4⋊C4—42no—
775C4⋊C4—531no—
776C4⋊C4—531no—
777C4⋊C4—531no—
778C4⋊C4—531no—
779C4⋊C4—531no—
780C4⋊C4—531no—
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—1061no—
791C4⋊C4—4241no—
792C4⋊C4—4241no—
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—1061no—
828C42—1061no—
829C42—1061no—
830C42—2122no—
831C42C2×C4×D5311yescharacteristic
832C42C2×C4×D5311yescharacteristic
833C42D4×D5311yescharacteristic
834C42D4×D5311yescharacteristic
835C23—21no—
836C23—531no—
837C23—531no—
838C23—532no—
839C23—532no—
840C23—531no—
841C23—531no—
842C23—1061no—
843C23—1061no—
844C23—1061no—
845C23—4241no—
846C23—4241no—
847C23—2121no—
848C23—2121no—
849C23—2121no—
850C23—2121no—
851C23—2122no—
852C23C2×D4×D5311yescharacteristic
853Q8—41no—
854Q8—4241no—
855Q8—2121no—
856D4—41no—
857D4—41no—
858D4—41no—
859D4—1062no—
860D4—1062no—
861D4—1062no—
862D4—1062no—
863D4—4241no—
864D4—4241no—
865D4—4241no—
866D4—4241no—
867D4—4241no—
868D4—2121no—
869D4—2122no—
870D4—2122no—
871D4—2121no—
872D4—2121no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
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—81no—
887C2×C4—531no—
888C2×C4—531no—
889C2×C4—531no—
890C2×C4—531no—
891C2×C4—1062no—
892C2×C4—1061no—
893C2×C4—1061no—
894C2×C4—1061no—
895C2×C4—4241no—
896C2×C4—4241no—
897C2×C4—4241no—
898C2×C4—4241no—
899C2×C4—4244no—
900C2×C4—4244no—
901C2×C4—4241no—
902C2×C4—2121no—
903C2×C4—2121no—
904C2×C4—2121no—
905C2×C4—2121no—
906C2×C4—2121no—
907C2×C4—2121no—
908C2×C4—2121no—
909C2×C4—2121no—
910C2×C4—2122no—
911C2×C4—2121no—
912C2×C4—2121no—
913C2×C4—2121no—
914C2×C4—2121no—
915C2×C4—2121no—
916C2×C4—2121no—
917C2×C4—2121no—
918C2×C4C22⋊C4×D5311yescharacteristic
919C2×C4C22⋊C4×D5311yescharacteristic
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—41no—
931C22—41no—
932C22—41no—
933C22—532no—
934C22—532no—
935C22—8482no—
936C22—1061no—
937C22—1061no—
938C22—1061no—
939C22—1061no—
940C22—1061no—
941C22—1061no—
942C22—1061no—
943C22—1061no—
944C22—1061no—
945C22—1061no—
946C22—2122no—
947C22—2122no—
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—21no—
961C4—21no—
962C4—41no—
963C4—41no—
964C4—41no—
965C4—81no—
966C4—81no—
967C4—1061no—
968C4—1061no—
969C4—1061no—
970C4—1061no—
971C4—4241no—
972C4—2122no—
973C4—2121no—
974C4—2121no—
975C4—2121no—
976C2—21no—
977C2—21no—
978C2—81no—
979C2—1062no—
980C2—1062no—
981C2—4241no—
982C2—2121no—
983C2—2121no—
984C2#2028317411yescharacteristic
985C2#417×D5311yescharacteristic
986C2#2028326111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1512C2
socleC22×C53C22×C22⋊C4
prime radical#20288550C2
cosocleC22×C4×C53C24
hypercenter#1512D53
hypocenterC53#17622
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1512

Complements

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

NH ≅ G/Ntype
2. #20283743C2semidirect
3. #20277623C2semidirect
4. #20273285C2semidirect
5. #20273281C2semidirect
6. #20273257C2semidirect
7. #20273255C2semidirect
8. #20273251C2semidirect
9. #20273241C2semidirect
10. #20273240C2semidirect
11. #20273218C2semidirect
12. #20273216C2semidirect
13. #328×D53C2semidirect
14. #327×D53C2semidirect
15. C53×#1512C2semidirect
16. #16811326C4semidirect
18. #16811323C4semidirect
20. #16811314C4semidirect
21. #16811311C4semidirect
24. #16811285C4semidirect
25. #16811281C4semidirect
26. #16811268C4semidirect
27. #16811266C4semidirect
43. #16810680C22semidirect
44. #16810585C22semidirect
45. #16810585C22semidirect
52. #16810482C22semidirect
53. C4×C4⋊Dic53C22semidirect
55. #95×D53C22semidirect
56. #16810361C22semidirect
57. #16810361C22semidirect
58. #16810360C22semidirect
59. #16810360C22semidirect
60. #16810359C22semidirect
61. #16810359C22semidirect
69. C53×#432C22semidirect
70. C53×#382C22semidirect
71. C53×#328C22semidirect
72. C53×#328C22semidirect
75. C2×#11719949C2×C4semidirect
76. C2×#11719947C2×C4semidirect
77. C2×Q8×D53C2×C4semidirect
80. C2×D4×D53C2×C4semidirect
94. #13133209C2×C4semidirect
98. #13133205C2×C4semidirect
110. #13133197C2×C4semidirect
111. #13133197C2×C4semidirect
116. #13133193C2×C4semidirect
117. #13133193C2×C4semidirect
120. #13133192C2×C4semidirect
121. #13133192C2×C4semidirect
129. #13133188C2×C4semidirect
130. #13133188C2×C4semidirect
135. C4×Dic106C2×C4semidirect
141. C4×D212C2×C4semidirect
156. #13133175C2×C4semidirect
157. #13133175C2×C4semidirect
165. C4⋊C4×D53C2×C4semidirect
166. C4⋊C4×D53C2×C4semidirect
189. #125×C53C2×C4semidirect
190. #124×C53C2×C4semidirect
194. C4×Q8×C53C2×C4semidirect
196. C4×D4×C53C2×C4semidirect
491. #1512D53semidirect
538. #432C2×D53semidirect
546. #382C2×D53semidirect
558. #328C2×D53semidirect
559. #328C2×D53semidirect
568. C53#17622semidirect
592. #125C4×D53semidirect
596. #124C4×D53semidirect
636. C4×Q8C4×D53semidirect
657. C4×D4C4×D53semidirect

Maximal subgroups

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

subgroupindex
#202885502
#202837432
#202776232
#202732852
#202732812
#202732572
#202732552
#202732512
#202732412
#202732402
#202732182
#202732162
#328×D532
#327×D532
C53×#15122
#1762253