Finite Group Databasebeta

← #27351759

Subgroups — #27351759

Order 13568.

944 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288461C211yesmaximal, characteristic
2#20283375C211yesmaximal, characteristic, complemented
3#20277577C211yesmaximal, characteristic, complemented
4#20273291C211yesmaximal, characteristic, complemented
5#20273277C211yesmaximal, characteristic, complemented
6#20273269C211yesmaximal, characteristic
7#20273264C211yesmaximal, characteristic, complemented
8#20273252C211yesmaximal, characteristic, complemented
9#20273239C211yesmaximal, characteristic, complemented
10#20273225C211yesmaximal, characteristic, complemented
11#20273220C211yesmaximal, characteristic
12#20273212C211yesmaximal, characteristic, complemented
13#20273200C211yesmaximal, characteristic, complemented
14C2×#16810360C211yesmaximal, characteristic, complemented
15C53×#1511C211yesmaximal, characteristic, complemented
16#16811344—21no—
17#16811331—21no—
18#16811315—21no—
19#16811308—21no—
20#16811308—21no—
21#16811307—21no—
22#16811299—21no—
23#16811299—21no—
24#16811254C411yescharacteristic, complemented
25#16811246C411yescharacteristic, complemented
26#16811246C411yescharacteristic, complemented
27#16811233C411yescharacteristic, complemented
28#16811233C411yescharacteristic, complemented
29#16811197C411yescharacteristic, complemented
30#16811175C2211yescharacteristic
31#16811175C2211yescharacteristic
32#16811159C2211yescharacteristic
33#16811159C2211yescharacteristic
34#16811134C2211yescharacteristic
35#16811104C411yescharacteristic, complemented
36#16811101C411yescharacteristic, complemented
37C2×#13133176C2211yescharacteristic
38#16810681—21no—
39#16810681—21no—
40#16810677C2211yescharacteristic
41#16810677C2211yescharacteristic
42#16810673C2211yescharacteristic
43#16810673C2211yescharacteristic
44#16810651—21no—
45C2×C22⋊#88322C2211yescharacteristic
46#16810581—21no—
47#16810508—21no—
48#16810506—21no—
49#16810495—21no—
50#16810490C2211yescharacteristic
51#16810487C2211yescharacteristic
52#16810474C2211yescharacteristic
53C22⋊C4×Dic53—21no—
54#16810468C2211yescharacteristic
55C2×#13133124C2211yescharacteristic
56#16810361C2211yescharacteristic
57#16810361C2211yescharacteristic
58#16810360C2211yescharacteristic
59#16810360C2211yescharacteristic
60#16810360C2211yescharacteristic
61#16810360C2211yescharacteristic
62#16810359C2211yescharacteristic
63#16810359C2211yescharacteristic
64#16810358C2211yescharacteristic
65#16810358C2211yescharacteristic
66#16810356C2211yescharacteristic
67#16810356C2211yescharacteristic
68C2×C22⋊Q8×C53C2211yescharacteristic
69C53×#407C2211yescharacteristic
70C53×#381C2211yescharacteristic
71C53×#328C2211yescharacteristic
72C53×#328C2211yescharacteristic
73C53×#328C2211yescharacteristic
74C53×#328C2211yescharacteristic
75C2×#11719945C2×C411yescharacteristic
76C23×Dic53—21no—
77C22×#88322—21no—
78#13133216—21no—
79#13133216C2×C411yescharacteristic, complemented
80#13133216C2×C411yescharacteristic, complemented
81#13133215C2×C411yescharacteristic, complemented
82#13133215C2×C411yescharacteristic, complemented
83#13133212—21no—
84#13133212—21no—
85#13133212—21no—
86#13133212—21no—
87#13133210—21no—
88#13133210—21no—
89#13133210—21no—
90#13133210—21no—
91#13133208—21no—
92#13133208—21no—
93#13133208—21no—
94#13133208C2×C411yescharacteristic, complemented
95#13133208C2×C411yescharacteristic, complemented
96#13133207—21no—
97#13133207—21no—
98#13133207—21no—
99#13133207—21no—
100#13133206C2×C411yescharacteristic, complemented
101#13133206C2×C411yescharacteristic, complemented
102#13133203—21no—
103#13133203—21no—
104#13133201—21no—
105#13133201—21no—
106#13133200—21no—
107#13133200—21no—
108#13133200—21no—
109#13133199—21no—
110#13133199—21no—
111#13133197—21no—
112#13133197—21no—
113#13133196—21no—
114#13133196—21no—
115#13133196C2×C411yescharacteristic
116#13133196C2311yescharacteristic
117#13133194—21no—
118#13133194—21no—
119#13133193—21no—
120#13133193—21no—
121#13133191C2×C411yescharacteristic
122#13133191C2311yescharacteristic
123#13133186—21no—
124Q8×Dic53—21no—
125Q8×Dic53—21no—
126Q8×Dic53C2×C411yescharacteristic, complemented
127Q8×Dic53C2×C411yescharacteristic, complemented
128Q8×Dic53C2×C411yescharacteristic, complemented
129Q8×Dic53C2×C411yescharacteristic, complemented
130#13133182—21no—
131#13133182—21no—
132#13133182C2×C411yescharacteristic, complemented
133#13133182C2×C411yescharacteristic, complemented
134#13133179C2×C411yescharacteristic, complemented
135#13133179C2×C411yescharacteristic, complemented
136C4×C22⋊D53—21no—
137C4×C22⋊D53—21no—
138C4×C22⋊D53—21no—
139C4×C22⋊D53—21no—
140#13133177—21no—
141#13133177—21no—
142#13133176—21no—
143#13133176—21no—
144#13133176C2×C411yescharacteristic
145#13133176C2×C411yescharacteristic
146#13133176C2×C411yescharacteristic
147#13133176C2×C411yescharacteristic
148#13133176C2×C411yescharacteristic
149#13133176D411yescharacteristic
150#13133176D411yescharacteristic
151#13133176D411yescharacteristic
152#13133176D411yescharacteristic
153#13133175—21no—
154#13133175—21no—
155#13133175—21no—
156#13133173—21no—
157#13133173—21no—
158C2×C4⋊Dic53D411yescharacteristic
159C2×C4⋊Dic53D411yescharacteristic
160C2×#11719919—21no—
161C2×#11719919—21no—
162C4⋊C4×D53—21no—
163C2×C22⋊Dic53D411yescharacteristic
164C2×C22⋊Dic53D411yescharacteristic
165C2×C4×Dic53—21no—
166C2×C4×Dic53—21no—
167C2×C4×Dic53C2311yescharacteristic
168C2×C4×Dic53C2311yescharacteristic
169#13133146—21no—
170#13133146—21no—
171#13133146—21no—
172#13133146—21no—
173C22⋊#88322—21no—
174C22⋊#88322C2311yescharacteristic
175C22⋊#88322C2311yescharacteristic
176#13133127—21no—
177#13133127—21no—
178C8×Dic53—21no—
179C8×Dic53—21no—
180#13133124—21no—
181#13133124—21no—
182#13133124—21no—
183#13133124—21no—
184#13133124—21no—
185#13133124C2311yescharacteristic
186#13133124C2311yescharacteristic
187C22×Q8×C53C2×C411yescharacteristic
188C23×C4×C53C2311yescharacteristic
189C2×M16×C53—21no—
190C22⋊Q8×C53—21no—
191C22⋊Q8×C53—21no—
192C22⋊Q8×C53C2×C411yescharacteristic
193C22⋊Q8×C53C2×C411yescharacteristic
194C22⋊Q8×C53C2311yescharacteristic
195C22⋊Q8×C53C2311yescharacteristic
196C2×C4⋊C4×C53—21no—
197C2×C4⋊C4×C53C2×C411yescharacteristic
198C2×C22⋊C4×C53—21no—
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
207C2×Q8×C53—21no—
208C2×Q8×C53—42no—
209C2×Q8×C53C22×C411yescharacteristic
210C2×Q8×C53C22×C411yescharacteristic
211C22×C4×C53—21no—
212C22×C4×C53—21no—
213C22×C4×C53—21no—
214C22×C4×C53—21no—
215C22×C4×C53—42no—
216C22×C4×C53C22×C411yescharacteristic
217C22×C4×C53C22×C411yescharacteristic
218C22×C4×C53C2×D411yescharacteristic
219C22×C4×C53C2×D411yescharacteristic
220C22×C4×C53C2×D411yescharacteristic
221C22×C4×C53C2411yescharacteristic
222C2×C22⋊D53—21no—
223C2×C22⋊D53—21no—
224C2×C22⋊D53—21no—
225C22×Dic53—21no—
226C22×Dic53—21no—
227C22×Dic53—42no—
228C22×Dic53—42no—
229C22×Dic53—81no—
230C22×Dic53C2×D411yescharacteristic
231C22×Dic53C2×D411yescharacteristic
232C22×Dic53C2×D411yescharacteristic
233C22×Dic53C2×D411yescharacteristic
234#11719945—42no—
235C2×D212C22×C411yescharacteristic
236C2×C4×D53—21no—
237C2×C4×D53—21no—
238C2×C4×D53—21no—
239C2×Dic106—21no—
240C2×Dic106—21no—
241C2×Dic106C22×C411yescharacteristic
242M16×C53—42no—
243C2×C8×C53—21no—
244C2×C8×C53—21no—
245C4⋊C4×C53—21no—
246C4⋊C4×C53—21no—
247C4⋊C4×C53—21no—
248C4⋊C4×C53—21no—
249C4⋊C4×C53—21no—
250C4⋊C4×C53C22×C411yescharacteristic
251C4⋊C4×C53C22×C411yescharacteristic
252C22⋊C4×C53—21no—
253C22⋊C4×C53—21no—
254C22⋊C4×C53—21no—
255C22⋊C4×C53—21no—
256C22⋊C4×C53—42no—
257C22⋊Dic53—21no—
258C22⋊Dic53—21no—
259C22⋊Dic53—21no—
260C22⋊Dic53C22⋊C411yescharacteristic
261C22⋊Dic53C22⋊C411yescharacteristic
262C22⋊Dic53C22⋊C411yescharacteristic
263C22⋊Dic53C22⋊C411yescharacteristic
264C22⋊Dic53C22⋊C411yescharacteristic
265C22⋊Dic53C22⋊C411yescharacteristic
266C22⋊Dic53C22⋊C411yescharacteristic
267C22⋊Dic53C22⋊C411yescharacteristic
268#11719921—21no—
269#11719921—21no—
270#11719921—21no—
271#11719921—21no—
272#11719921—21no—
273#11719921—21no—
274#11719921—21no—
275#11719921—21no—
276C4⋊Dic53—21no—
277C4⋊Dic53—21no—
278C4⋊Dic53—21no—
279C4⋊Dic53—21no—
280C4⋊Dic53—21no—
281C4⋊Dic53—21no—
282C4⋊Dic53C22⋊C411yescharacteristic
283C4⋊Dic53C22⋊C411yescharacteristic
284C4⋊Dic53C22⋊C411yescharacteristic
285C4⋊Dic53C22⋊C411yescharacteristic
286C4⋊Dic53C22⋊C411yescharacteristic
287C4⋊Dic53C22⋊C411yescharacteristic
288C4⋊Dic53C22⋊C411yescharacteristic
289C4⋊Dic53C22⋊C411yescharacteristic
290C4⋊Dic53C22×C411yescharacteristic
291C4⋊Dic53C22×C411yescharacteristic
292#11719919—21no—
293#11719919—21no—
294#11719919—21no—
295#11719919—21no—
296#11719919—21no—
297#11719919—21no—
298#11719919—21no—
299#11719919—21no—
300#11719919—21no—
301#11719919—21no—
302#11719919—21no—
303#11719919—21no—
304#11719919—42no—
305#11719919—81no—
306C4×Dic53—21no—
307C4×Dic53—21no—
308C4×Dic53—21no—
309C4×Dic53—21no—
310C4×Dic53—21no—
311C4×Dic53—21no—
312C4×Dic53—21no—
313C4×Dic53—42no—
314C4×Dic53—81no—
315C4×Dic53C22×C411yescharacteristic
316C4×Dic53C22×C411yescharacteristic
317C4×Dic53C22×C411yescharacteristic
318C4×Dic53C22×C411yescharacteristic
319C4×Dic53C2×D411yescharacteristic
320C4×Dic53C2×D411yescharacteristic
321C4×Dic53C2×D411yescharacteristic
322C4×Dic53C2×D411yescharacteristic
323C2×#88322—21no—
324C2×#88322—21no—
325C2×#88322—42no—
326C23×C53—21no—
327C23×C53—21no—
328C23×C53—22no—
329C23×C53—41no—
330C23×C53C2×C22⋊C411yescharacteristic
331C23×C53C2×C22⋊C411yescharacteristic
332C23×C53C22×D411yescharacteristic
333C22×D53—21no—
334Q8×C53—42no—
335Q8×C53—41no—
336Q8×C53—41no—
337C2×C4×C53—22no—
338C2×C4×C53—22no—
339C2×C4×C53—21no—
340C2×C4×C53—21no—
341C2×C4×C53—21no—
342C2×C4×C53—21no—
343C2×C4×C53—41no—
344C2×C4×C53—41no—
345C2×C4×C53—41no—
346C2×C4×C53—41no—
347C2×C4×C53—42no—
348C2×C4×C53—41no—
349C2×C4×C53—41no—
350C2×C4×C53—41no—
351C2×C4×C53—41no—
352C2×C4×C53—41no—
353C2×C4×C53—41no—
354C2×C4×C53—81no—
355C2×C4×C53C2×C22⋊C411yescharacteristic
356C2×C4×C53C2×C22⋊C411yescharacteristic
357C2×C4×C53C23×C411yescharacteristic
358C2×C4×C53C22×D411yescharacteristic
359C22⋊D53—41no—
360C22⋊D53—41no—
361C22⋊D53—42no—
362C22⋊D53—81no—
363C2×Dic53—21no—
364C2×Dic53—21no—
365C2×Dic53—21no—
366C2×Dic53—21no—
367C2×Dic53—22no—
368C2×Dic53—21no—
369C2×Dic53—21no—
370C2×Dic53—21no—
371C2×Dic53—41no—
372C2×Dic53—41no—
373C2×Dic53—41no—
374C2×Dic53—41no—
375C2×Dic53—41no—
376C2×Dic53—41no—
377C2×Dic53—41no—
378C2×Dic53—84no—
379C2×Dic53C2×C22⋊C411yescharacteristic
380C2×Dic53C2×C22⋊C411yescharacteristic
381C2×Dic53C2×C22⋊C411yescharacteristic
382C2×Dic53C2×C22⋊C411yescharacteristic
383C2×Dic53C2×C22⋊C411yescharacteristic
384C2×Dic53C2×C22⋊C411yescharacteristic
385C2×Dic53C2×C22⋊C411yescharacteristic
386C2×Dic53C2×C22⋊C411yescharacteristic
387D212—41no—
388C4×D53—42no—
389C4×D53—81no—
390C4×D53—81no—
391Dic106—41no—
392Dic106—81no—
393Dic106—81no—
394C8×C53—41no—
395C8×C53—41no—
396#88322—41no—
397#88322—41no—
398#17609—531nomaximal, Sylow
399C22×C53—21no—
400C22×C53—21no—
401C22×C53—21no—
402C22×C53—21no—
403C22×C53—21no—
404C22×C53—21no—
405C22×C53—21no—
406C22×C53—42no—
407C22×C53—42no—
408C22×C53#41012yes—
409C22×C53C22×C22⋊C411yescharacteristic
410C22×C53#57711yescharacteristic
411C22×C53#57811yescharacteristic
412C2×D53—41no—
413C2×D53—41no—
414C2×D53—41no—
415C4×C53—21no—
416C4×C53—21no—
417C4×C53—21no—
418C4×C53—21no—
419C4×C53—41no—
420C4×C53—41no—
421C4×C53—41no—
422C4×C53—41no—
423C4×C53—81no—
424C4×C53—81no—
425Dic53—21no—
426Dic53—21no—
427Dic53—21no—
428Dic53—21no—
429Dic53—21no—
430Dic53—21no—
431Dic53—21no—
432Dic53—21no—
433Dic53—42no—
434Dic53—41no—
435Dic53—41no—
436Dic53—41no—
437Dic53—81no—
438#3495—531no—
439#2924—531no—
440#2343—531no—
441#1521—531no—
442#1518—531no—
443#1516—531no—
444#1515—531no—
445#1512—531no—
446#1511D5311yescharacteristic, complemented
447#1509—531no—
448#1506—531no—
449#1504—531no—
450#1503—531no—
451#1500—531no—
452C2×#328—531no—
453C2×C53—21no—
454C2×C53—21no—
455C2×C53—22no—
456C2×C53—41no—
457C2×C53C2×#41011yescharacteristic
458C2×C53#289811yescharacteristic
459C2×C53#290111yescharacteristic
460D53—81no—
461#556—1061no—
462#554—1061no—
463#552—1061no—
464#552—1061no—
465#552—1061no—
466#552—1061no—
467#551—1061no—
468#551—1061no—
469#544—531no—
470#542—531no—
471#542—531no—
472#541—531no—
473#541—531no—
474#536—531no—
475#533—531no—
476#533—531no—
477#529—531no—
478#529—531no—
479#525—531no—
480C2×C22⋊Q8C2×D5311yescharacteristic
481#520—531no—
482#519—531no—
483C2×#117—531no—
484#433—1061no—
485#433—1061no—
486#432—531no—
487#432—531no—
488#431—531no—
489#431—531no—
490#424—1061no—
491#407C2×D5311yescharacteristic
492C2×C22⋊C8—531no—
493#405—1061no—
494#387—1061no—
495#387—1061no—
496#385—1061no—
497#383—531no—
498#382—531no—
499#381C2×D5311yescharacteristic
500C4×C4⋊C4—531no—
501C4×C22⋊C4—1061no—
502#376—531no—
503C2×#95—531no—
504#328—531no—
505#328—531no—
506#328—531no—
507#328—531no—
508#328—531no—
509#328—531no—
510#328—531no—
511#328—531no—
512#328C2×D5311yescharacteristic
513#328C2×D5311yescharacteristic
514#328C2×D5311yescharacteristic
515#328C2×D5311yescharacteristic
516#327—531no—
517#327—531no—
518#327—531no—
519#327—531no—
520C53#1760911yescharacteristic, complemented, Sylow
521C2×#41—531no—
522C22×Q8C4×D5311yescharacteristic
523C23×C4—1061no—
524C23×C4C22×D5311yescharacteristic
525C2×M16—21no—
526C22×C8—1061no—
527C4⋊Q8—531no—
528C4⋊Q8—531no—
529C4⋊Q8—531no—
530C4⋊Q8—531no—
531C4⋊Q8—1061no—
532#126—1061no—
533#126—1061no—
534#126—1061no—
535#126—1061no—
536#126—1061no—
537#126—1061no—
538#126—1061no—
539#126—1061no—
540#125—531no—
541#125—531no—
542#125—1061no—
543#125—1061no—
544#125—1061no—
545#125—1061no—
546#125—1061no—
547#125—1061no—
548#125—1061no—
549#124—531no—
550#124—531no—
551#124—1061no—
552#124—1061no—
553#123—1061no—
554#123—1061no—
555#123—1061no—
556#123—1061no—
557#123—1061no—
558#123—1061no—
559#123—1061no—
560C22⋊Q8—21no—
561C22⋊Q8—21no—
562C22⋊Q8—531no—
563C22⋊Q8—531no—
564C22⋊Q8—1061no—
565C22⋊Q8—1061no—
566C22⋊Q8—1061no—
567C22⋊Q8—1061no—
568C22⋊Q8—1061no—
569C22⋊Q8—1061no—
570C22⋊Q8—1061no—
571C22⋊Q8—1061no—
572C22⋊Q8C4×D5311yescharacteristic
573C22⋊Q8C4×D5311yescharacteristic
574C22⋊Q8C22×D5311yescharacteristic
575C22⋊Q8C22×D5311yescharacteristic
576#121—531no—
577#121—531no—
578#120—1061no—
579C4×Q8—531no—
580C4×Q8—531no—
581C4×Q8—531no—
582C4×Q8—531no—
583C4×Q8—531no—
584C4×Q8—531no—
585C4×Q8—1061no—
586C4×Q8—1061no—
587C4×Q8—1061no—
588C4×Q8—1061no—
589C4×D4—531no—
590C4×D4—531no—
591C4×D4—1061no—
592C4×D4—1061no—
593C4×D4—1061no—
594C4×D4—1061no—
595C4×D4—1061no—
596C4×D4—1061no—
597#117—531no—
598#117—531no—
599#117—531no—
600#117—531no—
601#117—531no—
602#117—531no—
603#117—531no—
604#117—531no—
605#117—531no—
606#117—1061no—
607#117—1061no—
608#117—1061no—
609#117—1061no—
610#117—1061no—
611#117—1061no—
612#117—1061no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—531no—
615C2×C4⋊C4—531no—
616C2×C4⋊C4—1061no—
617C2×C4⋊C4—1061no—
618C2×C4⋊C4—1061no—
619C2×C4⋊C4C4×D5311yescharacteristic
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—531no—
623C2×C22⋊C4—531no—
624C2×C42—531no—
625C2×C42—531no—
626C2×C42—1061no—
627C2×C42—1061no—
628C4⋊C8—1061no—
629C4⋊C8—1061no—
630C4⋊C8—1061no—
631C4⋊C8—1061no—
632C22⋊C8—21no—
633C22⋊C8—531no—
634C22⋊C8—531no—
635C22⋊C8—1061no—
636C22⋊C8C22×D5311yescharacteristic
637C22⋊C8C22×D5311yescharacteristic
638#97—1061no—
639#97—1061no—
640C4×C8—1061no—
641C4×C8—1061no—
642#95—21no—
643#95—531no—
644#95—531no—
645#95—1061no—
646#95—1061no—
647#95—1061no—
648#95—1061no—
649#95—1061no—
650#95C22×D5311yescharacteristic
651#95C22×D5311yescharacteristic
652C24D4×D5311yescharacteristic
653#41—2122no—
654C2×Q8—21no—
655C2×Q8—42no—
656C2×Q8—531no—
657C2×Q8—1061no—
658C2×Q8—1061no—
659C2×Q8C2×C4×D5311yescharacteristic
660C2×Q8C2×C4×D5311yescharacteristic
661C2×D4—531no—
662C2×D4—1061no—
663C2×D4—1061no—
664C2×D4—1061no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—42no—
670C22×C4—531no—
671C22×C4—531no—
672C22×C4—531no—
673C22×C4—531no—
674C22×C4—1061no—
675C22×C4—1061no—
676C22×C4—1061no—
677C22×C4—1061no—
678C22×C4—1061no—
679C22×C4—4241no—
680C22×C4—2122no—
681C22×C4—2122no—
682C22×C4C2×C4×D5311yescharacteristic
683C22×C4C2×C4×D5311yescharacteristic
684C22×C4D4×D5311yescharacteristic
685C22×C4D4×D5311yescharacteristic
686C22×C4D4×D5311yescharacteristic
687C22×C4C23×D5311yescharacteristic
688M16—42no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—1061no—
692C2×C8—1061no—
693C2×C8—2122no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—531no—
700C4⋊C4—531no—
701C4⋊C4—531no—
702C4⋊C4—531no—
703C4⋊C4—531no—
704C4⋊C4—531no—
705C4⋊C4—531no—
706C4⋊C4—531no—
707C4⋊C4—531no—
708C4⋊C4—531no—
709C4⋊C4—1061no—
710C4⋊C4—1061no—
711C4⋊C4—1061no—
712C4⋊C4—1061no—
713C4⋊C4—1061no—
714C4⋊C4—1061no—
715C4⋊C4—1061no—
716C4⋊C4—1061no—
717C4⋊C4—1061no—
718C4⋊C4—1061no—
719C4⋊C4—1061no—
720C4⋊C4—1061no—
721C4⋊C4—1061no—
722C4⋊C4—1061no—
723C4⋊C4—1061no—
724C4⋊C4—1061no—
725C4⋊C4—1061no—
726C4⋊C4—1061no—
727C4⋊C4—4241no—
728C4⋊C4—2122no—
729C4⋊C4C2×C4×D5311yescharacteristic
730C4⋊C4C2×C4×D5311yescharacteristic
731C22⋊C4—21no—
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—42no—
736C22⋊C4—531no—
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—1061no—
753C22⋊C4—1061no—
754C22⋊C4—1061no—
755C42—531no—
756C42—531no—
757C42—531no—
758C42—531no—
759C42—531no—
760C42—531no—
761C42—531no—
762C42—531no—
763C42—1061no—
764C42—1061no—
765C42—1061no—
766C42—1061no—
767C42—1061no—
768C42—1061no—
769C42—1061no—
770C42—4241no—
771C42—2122no—
772C23—22no—
773C23—21no—
774C23—21no—
775C23—41no—
776C23—1061no—
777C23C22⋊C4×D5311yescharacteristic
778C23C22⋊C4×D5311yescharacteristic
779C23C2×D4×D5311yescharacteristic
780Q8—41no—
781Q8—41no—
782Q8—42no—
783Q8—4241no—
784Q8—4241no—
785Q8—2121no—
786D4—4241no—
787D4—2121no—
788D4—2122no—
789D4—2121no—
790D4—2121no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—81no—
809C2×C4—531no—
810C2×C4—531no—
811C2×C4—531no—
812C2×C4—531no—
813C2×C4—531no—
814C2×C4—531no—
815C2×C4—531no—
816C2×C4—531no—
817C2×C4—1061no—
818C2×C4—1061no—
819C2×C4—1061no—
820C2×C4—1061no—
821C2×C4—1062no—
822C2×C4—1061no—
823C2×C4—1061no—
824C2×C4—1061no—
825C2×C4—4241no—
826C2×C4—4241no—
827C2×C4—4244no—
828C2×C4—2122no—
829C2×C4—2121no—
830C2×C4—2121no—
831C2×C4—2121no—
832C2×C4—2121no—
833C2×C4—2121no—
834C2×C4—2121no—
835C2×C4—2121no—
836C2×C4C22⋊C4×D5311yescharacteristic
837C2×C4C22⋊C4×D5311yescharacteristic
838C2×C4C22×C4×D5311yescharacteristic
839C2×C4C2×D4×D5311yescharacteristic
840C8—41no—
841C8—41no—
842C8—2121no—
843C8—2121no—
844C22—21no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—42no—
852C22—42no—
853C22—2121no—
854C22—2121no—
855C22—2121no—
856C22#1681059512yes—
857C22C2×C22⋊C4×D5311yescharacteristic
858C22#1681143211yescharacteristic
859C22#1681143911yescharacteristic
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—41no—
865C4—41no—
866C4—41no—
867C4—41no—
868C4—81no—
869C4—81no—
870C4—1061no—
871C4—1061no—
872C4—1061no—
873C4—1061no—
874C4—1061no—
875C4—1061no—
876C4—1061no—
877C4—1061no—
878C4—4241no—
879C4—2122no—
880C4—2121no—
881C4—2121no—
882C4—2121no—
883C2—21no—
884C2—21no—
885C2—22no—
886C2—41no—
887C2—4241no—
888C2C2×#1681059511yescharacteristic
889C2#2028324711yescharacteristic
890C2#2028326111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1511C2
socleC22×C53C22×C22⋊C4
prime radical#16811134C22
cosocleC22×C4×C53C24
hypercenter#1511D53
hypocenterC53#17609
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1511

Complements

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

NH ≅ G/Ntype
2. #20283375C2semidirect
3. #20277577C2semidirect
4. #20273291C2semidirect
5. #20273277C2semidirect
7. #20273264C2semidirect
8. #20273252C2semidirect
9. #20273239C2semidirect
10. #20273225C2semidirect
12. #20273212C2semidirect
13. #20273200C2semidirect
14. C2×#16810360C2semidirect
15. C53×#1511C2semidirect
24. #16811254C4semidirect
25. #16811246C4semidirect
26. #16811246C4semidirect
27. #16811233C4semidirect
28. #16811233C4semidirect
29. #16811197C4semidirect
35. #16811104C4semidirect
36. #16811101C4semidirect
79. #13133216C2×C4semidirect
80. #13133216C2×C4semidirect
81. #13133215C2×C4semidirect
82. #13133215C2×C4semidirect
94. #13133208C2×C4semidirect
95. #13133208C2×C4semidirect
100. #13133206C2×C4semidirect
101. #13133206C2×C4semidirect
126. Q8×Dic53C2×C4semidirect
127. Q8×Dic53C2×C4semidirect
128. Q8×Dic53C2×C4semidirect
129. Q8×Dic53C2×C4semidirect
132. #13133182C2×C4semidirect
133. #13133182C2×C4semidirect
134. #13133179C2×C4semidirect
135. #13133179C2×C4semidirect
446. #1511D53semidirect
520. C53#17609semidirect

Maximal subgroups

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

subgroupindex
#202884612
#202833752
#202775772
#202732912
#202732772
#202732692
#202732642
#202732522
#202732392
#202732252
#202732202
#202732122
#202732002
C2×#168103602
C53×#15112
#1760953