Finite Group Databasebeta

← #27351615

Subgroups — #27351615

Order 13568.

1060 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288735C211yesmaximal, characteristic
2#20283751C211yesmaximal, characteristic, complemented
3#20277349C211yesmaximal, characteristic, complemented
4#20273291C211yesmaximal, characteristic, complemented
5#20273281C211yesmaximal, characteristic, complemented
6#20273273C211yesmaximal, characteristic, complemented
7#20273270C211yesmaximal, characteristic, complemented
8#20273260C211yesmaximal, characteristic, complemented
9#20273257C211yesmaximal, characteristic, complemented
10#20273252C211yesmaximal, characteristic, complemented
11#20273242C211yesmaximal, characteristic, complemented
12#20273232C211yesmaximal, characteristic, complemented
13#20273206C211yesmaximal, characteristic, complemented
14C2×#16810356C211yesmaximal, characteristic, complemented
15C53×#1504C211yesmaximal, characteristic, complemented
16#16811336C411yescharacteristic, complemented
17#16811331C411yescharacteristic, complemented
18#16811325C411yescharacteristic, complemented
19#16811322—21no—
20#16811317C411yescharacteristic, complemented
21#16811292C411yescharacteristic, complemented
22#16811268—21no—
23#16811264C411yescharacteristic, complemented
24#16811261C411yescharacteristic, complemented
25#16811260—21no—
26#16811257C411yescharacteristic, complemented
27#16811255—21no—
28#16811225—21no—
29#16811209—21no—
30#16811206—21no—
31#16811168C2211yescharacteristic
32#16811159C2211yescharacteristic
33#16811136C2211yescharacteristic
34C2×#13133191C2211yescharacteristic
35#121×D53C2211yescharacteristic
36#16811095—21no—
37C2×C4×C22⋊D53C2211yescharacteristic
38#16810699—21no—
39#16810692—21no—
40#16810691—21no—
41#16810686—21no—
42#16810677C2211yescharacteristic, complemented
43#16810673C2211yescharacteristic, complemented
44#16810585C2211yescharacteristic, complemented
45C2×C22⋊#88322C2211yescharacteristic, complemented
46C22⋊C8×D53C2211yescharacteristic, complemented
47#16810512—21no—
48#16810505—21no—
49#16810502—21no—
50#16810496—21no—
51#16810490C2211yescharacteristic, complemented
52#16810487C2211yescharacteristic, complemented
53#16810485C2211yescharacteristic, complemented
54#16810482C2211yescharacteristic, complemented
55C4×C22⋊Dic53C2211yescharacteristic, complemented
56#16810360C2211yescharacteristic, complemented
57#16810360C2211yescharacteristic, complemented
58#16810358C2211yescharacteristic
59#16810358C2211yescharacteristic
60#16810358C2211yescharacteristic, complemented
61#16810358C2211yescharacteristic, complemented
62#16810357C2211yescharacteristic, complemented
63#16810357C2211yescharacteristic, complemented
64#16810356C2211yescharacteristic
65#16810356C2211yescharacteristic
66#16810356C2211yescharacteristic, complemented
67#16810356C2211yescharacteristic, complemented
68C53×#525C2211yescharacteristic
69C53×#407C2211yescharacteristic, complemented
70C2×#95×C53C2211yescharacteristic, complemented
71C53×#328C2211yescharacteristic, complemented
72C53×#328C2211yescharacteristic, complemented
73C53×#327C2211yescharacteristic, complemented
74C53×#327C2211yescharacteristic, complemented
75C2×#11719949C2×C411yescharacteristic, complemented
76C2×#11719947—21no—
77C22×D212C2×C411yescharacteristic
78C22×C22⋊D53—21no—
79C22×C22⋊D53D411yescharacteristic
80C2×D4×D53—21no—
81C2×D4×D53—21no—
82C2×D4×D53C2×C411yescharacteristic, complemented
83C22×C4×D53C2311yescharacteristic
84C2×#11719912—21no—
85C22×#88322—21no—
86C2×C8×D53—21no—
87#13133216C2×C411yescharacteristic, complemented
88#13133213—21no—
89#13133213C2×C411yescharacteristic, complemented
90#13133212—21no—
91#13133211—21no—
92#13133210—21no—
93#13133208C2×C411yescharacteristic, complemented
94#13133207—21no—
95#13133206C2×C411yescharacteristic, complemented
96#13133205—21no—
97#13133203—21no—
98#13133203—21no—
99#13133202—21no—
100#13133202—21no—
101#13133201—21no—
102#13133201—21no—
103#13133200—21no—
104#13133199—21no—
105#13133197—21no—
106#13133194—21no—
107#13133193C2×C411yescharacteristic, complemented
108#13133192—21no—
109#13133192C2×C411yescharacteristic, complemented
110#13133192C2×C411yescharacteristic, complemented
111#13133191—21no—
112#13133191—21no—
113#13133191—21no—
114#13133191C2×C411yescharacteristic
115#13133191C2×C411yescharacteristic
116#13133191C2311yescharacteristic
117#13133191C2311yescharacteristic
118#13133190—21no—
119#13133190—21no—
120#13133190—21no—
121#13133190—21no—
122#13133189—21no—
123#13133189—21no—
124#13133189—21no—
125#13133189—21no—
126#13133188—21no—
127#13133188C2×C411yescharacteristic, complemented
128#13133187—21no—
129#13133187—21no—
130#13133187—21no—
131#13133185—21no—
132#13133185—21no—
133Q8×Dic53C2×C411yescharacteristic, complemented
134C4×D212—21no—
135D4×Dic53—21no—
136D4×Dic53C2×C411yescharacteristic, complemented
137#13133179—21no—
138#13133179C2×C411yescharacteristic, complemented
139#13133179C2×C411yescharacteristic, complemented
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#13133177—21no—
152#13133177—21no—
153#13133175—21no—
154#13133175C2×C411yescharacteristic, complemented
155#13133174—21no—
156C2×C4⋊Dic53C2×C411yescharacteristic
157C2×#11719919—21no—
158C2×#11719919—21no—
159C2×#11719919D411yescharacteristic
160C4⋊C4×D53C2×C411yescharacteristic, complemented
161C2×C22⋊Dic53—21no—
162C2×C22⋊Dic53D411yescharacteristic
163C2×#11719921—21no—
164C2×#11719921—21no—
165C2×#11719921—21no—
166C2×#11719921—21no—
167C2×#11719921D411yescharacteristic
168C22⋊C4×D53—21no—
169C22⋊C4×D53—21no—
170C2×C4×Dic53—21no—
171C2×C4×Dic53C2311yescharacteristic
172#13133146—21no—
173#13133146—21no—
174C22⋊#88322—21no—
175C22⋊#88322C2311yescharacteristic
176C22⋊#88322C2311yescharacteristic
177#13133129—21no—
178#13133129—21no—
179#13133127—21no—
180C8×Dic53—21no—
181#13133124—21no—
182#13133124—21no—
183#13133124—21no—
184#13133124—21no—
185#13133124C2311yescharacteristic
186#13133124C2311yescharacteristic
187C2×#41×C53C2×C411yescharacteristic
188C23×C4×C53—21no—
189C23×C4×C53C2311yescharacteristic
190C2×M16×C53—21no—
191#123×C53—21no—
192C22⋊Q8×C53C2×C411yescharacteristic
193C22⋊Q8×C53C2311yescharacteristic
194#121×C53C2×C411yescharacteristic
195#121×C53C2311yescharacteristic
196#120×C53—21no—
197C4×D4×C53—21no—
198C4×D4×C53—21no—
199#117×C53C2×C411yescharacteristic
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×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—81no—
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—21no—
230C2×C22⋊D53—21no—
231C2×C22⋊D53—21no—
232C2×C22⋊D53—21no—
233C2×C22⋊D53—21no—
234C2×C22⋊D53—21no—
235C2×C22⋊D53—21no—
236C2×C22⋊D53—21no—
237C2×C22⋊D53—42no—
238C2×C22⋊D53—81no—
239C2×C22⋊D53—81no—
240C2×C22⋊D53C22⋊C411yescharacteristic
241C2×C22⋊D53C22⋊C411yescharacteristic
242C2×C22⋊D53C22⋊C411yescharacteristic
243C2×C22⋊D53C22⋊C411yescharacteristic
244C22×Dic53—21no—
245C22×Dic53—21no—
246C22×Dic53—21no—
247C22×Dic53—21no—
248C22×Dic53C2×D411yescharacteristic
249C22×Dic53C2×D411yescharacteristic
250C22×Dic53C2×D411yescharacteristic
251#11719949—81no—
252#11719947—81no—
253#11719947—81no—
254D4×D53—44no—
255D4×D53—81no—
256D4×D53—81no—
257D4×D53—81no—
258C2×D212—21no—
259C2×D212—21no—
260C2×D212—21no—
261C2×D212—21no—
262C2×D212—81no—
263C2×D212C22×C411yescharacteristic
264C2×D212C22×C411yescharacteristic
265C2×C4×D53—21no—
266C2×C4×D53—21no—
267C2×C4×D53—21no—
268C2×C4×D53—21no—
269C2×C4×D53—81no—
270C2×C4×D53C22×C411yescharacteristic
271C2×C4×D53C22×C411yescharacteristic
272C2×C4×D53C2×D411yescharacteristic
273C2×C4×D53C2×D411yescharacteristic
274C2×Dic106—21no—
275M16×C53—81no—
276C2×C8×C53—21no—
277C2×C8×C53—21no—
278C4⋊C4×C53—21no—
279C4⋊C4×C53—21no—
280C4⋊C4×C53C22×C411yescharacteristic
281C4⋊C4×C53C22×C411yescharacteristic
282C22⋊C4×C53—21no—
283C22⋊C4×C53—21no—
284C22⋊C4×C53—21no—
285C22⋊C4×C53—21no—
286C22⋊C4×C53—21no—
287C42×C53—21no—
288C22⋊Dic53—21no—
289C22⋊Dic53—21no—
290C22⋊Dic53—42no—
291C22⋊Dic53C22⋊C411yescharacteristic
292C22⋊Dic53C22⋊C411yescharacteristic
293C22⋊Dic53C22⋊C411yescharacteristic
294C22⋊Dic53C22⋊C411yescharacteristic
295#11719921—21no—
296#11719921—21no—
297#11719921—21no—
298#11719921—21no—
299#11719921—21no—
300#11719921—21no—
301#11719921—21no—
302#11719921—21no—
303#11719921—21no—
304#11719921—21no—
305#11719921—21no—
306#11719921—21no—
307#11719921—81no—
308#11719921—81no—
309#11719921C22⋊C411yescharacteristic
310#11719921C22⋊C411yescharacteristic
311#11719921C22⋊C411yescharacteristic
312#11719921C22⋊C411yescharacteristic
313C4⋊Dic53—21no—
314C4⋊Dic53—21no—
315C4⋊Dic53—21no—
316C4⋊Dic53C22×C411yescharacteristic
317C4⋊Dic53C22×C411yescharacteristic
318#11719919—21no—
319#11719919—21no—
320#11719919—21no—
321#11719919—21no—
322#11719919—81no—
323#11719919—81no—
324#11719919C22⋊C411yescharacteristic
325#11719919C22⋊C411yescharacteristic
326#11719919C22⋊C411yescharacteristic
327#11719919C22⋊C411yescharacteristic
328C4×Dic53—21no—
329C4×Dic53—21no—
330C4×Dic53—81no—
331C4×Dic53C22×C411yescharacteristic
332C4×Dic53C22×C411yescharacteristic
333C4×Dic53C2×D411yescharacteristic
334C4×Dic53C2×D411yescharacteristic
335C2×#88322—21no—
336C2×#88322—21no—
337C2×#88322—81no—
338#11719912—81no—
339C8×D53—81no—
340C23×C53—21no—
341C23×C53—21no—
342C23×C53—22no—
343C23×C53—21no—
344C23×C53—41no—
345C23×C53C2×C22⋊C411yescharacteristic
346C23×C53C2×C22⋊C411yescharacteristic
347C23×C53C22×D411yescharacteristic
348C22×D53—21no—
349C22×D53—21no—
350C22×D53—21no—
351C22×D53—21no—
352C22×D53—41no—
353C22×D53—41no—
354C22×D53—42no—
355C22×D53—42no—
356C22×D53—81no—
357C22×D53—81no—
358C22×D53—81no—
359C22×D53—81no—
360C22×D53C2×C22⋊C411yescharacteristic
361C22×D53C2×C22⋊C411yescharacteristic
362Q8×C53—41no—
363D4×C53—41no—
364D4×C53—41no—
365D4×C53—41no—
366D4×C53—42no—
367D4×C53—81no—
368C2×C4×C53—21no—
369C2×C4×C53—21no—
370C2×C4×C53—21no—
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—41no—
381C2×C4×C53—41no—
382C2×C4×C53—41no—
383C2×C4×C53—81no—
384C2×C4×C53—84no—
385C2×C4×C53C2×C22⋊C411yescharacteristic
386C2×C4×C53C2×C22⋊C411yescharacteristic
387C2×C4×C53C23×C411yescharacteristic
388C2×C4×C53C22×D411yescharacteristic
389C22⋊D53—22no—
390C22⋊D53—22no—
391C22⋊D53—41no—
392C22⋊D53—41no—
393C22⋊D53—42no—
394C22⋊D53—41no—
395C22⋊D53—41no—
396C22⋊D53—41no—
397C22⋊D53—41no—
398C22⋊D53—81no—
399C22⋊D53—81no—
400C22⋊D53—81no—
401C22⋊D53—81no—
402C22⋊D53—81no—
403C2×Dic53—21no—
404C2×Dic53—21no—
405C2×Dic53—21no—
406C2×Dic53—21no—
407C2×Dic53—41no—
408C2×Dic53—41no—
409C2×Dic53—41no—
410C2×Dic53—41no—
411C2×Dic53—41no—
412C2×Dic53—41no—
413C2×Dic53—41no—
414C2×Dic53—41no—
415C2×Dic53—81no—
416C2×Dic53—81no—
417C2×Dic53C2×C22⋊C411yescharacteristic
418C2×Dic53C2×C22⋊C411yescharacteristic
419C2×Dic53C2×C22⋊C411yescharacteristic
420C2×Dic53C2×C22⋊C411yescharacteristic
421C2×Dic53C2×C22⋊C411yescharacteristic
422C2×Dic53C2×C22⋊C411yescharacteristic
423D212—41no—
424D212—41no—
425D212—42no—
426D212—81no—
427D212—81no—
428D212—81no—
429C4×D53—41no—
430C4×D53—41no—
431C4×D53—41no—
432C4×D53—41no—
433C4×D53—42no—
434C4×D53—81no—
435C4×D53—81no—
436C4×D53—81no—
437Dic106—81no—
438C8×C53—41no—
439C8×C53—41no—
440#88322—41no—
441#88322—41no—
442#17597—531nomaximal, Sylow
443C22×C53—21no—
444C22×C53—21no—
445C22×C53—21no—
446C22×C53—21no—
447C22×C53—21no—
448C22×C53—21no—
449C22×C53—21no—
450C22×C53—42no—
451C22×C53—42no—
452C22×C53—41no—
453C22×C53—41no—
454C22×C53—41no—
455C22×C53#42112yes—
456C22×C53C22×C22⋊C411yescharacteristic
457C22×C53#57611yescharacteristic
458C22×C53#57711yescharacteristic
459C2×D53—21no—
460C2×D53—21no—
461C2×D53—21no—
462C2×D53—21no—
463C2×D53—21no—
464C2×D53—21no—
465C2×D53—41no—
466C2×D53—41no—
467C2×D53—41no—
468C2×D53—41no—
469C2×D53—41no—
470C2×D53—41no—
471C2×D53—81no—
472C2×D53—81no—
473C2×D53—162no—
474C2×D53—162no—
475C4×C53—21no—
476C4×C53—21no—
477C4×C53—21no—
478C4×C53—21no—
479C4×C53—41no—
480C4×C53—41no—
481C4×C53—41no—
482C4×C53—81no—
483C4×C53—81no—
484Dic53—21no—
485Dic53—21no—
486Dic53—21no—
487Dic53—21no—
488Dic53—21no—
489Dic53—21no—
490Dic53—41no—
491Dic53—41no—
492Dic53—81no—
493Dic53—81no—
494#3519—531no—
495#2974—531no—
496#2318—531no—
497#1521—531no—
498#1519—531no—
499#1517—531no—
500#1516—531no—
501#1514—531no—
502#1513—531no—
503#1512—531no—
504#1510—531no—
505#1507—531no—
506#1504D5311yescharacteristic, complemented
507#1501—531no—
508C2×#327—531no—
509C2×C53—21no—
510C2×C53—21no—
511C2×C53—22no—
512C2×C53—41no—
513C2×C53—81no—
514C2×C53#288311yescharacteristic
515C2×C53#289711yescharacteristic
516C2×C53C2×#42111yescharacteristic
517D53—41no—
518D53—41no—
519D53—81no—
520D53—81no—
521#555—531no—
522#554—531no—
523#553—531no—
524#553—531no—
525#553—1061no—
526#550—531no—
527#546—531no—
528#546—531no—
529#546—1061no—
530#546—1061no—
531D42—531no—
532D42—1061no—
533#540—1061no—
534#538—1061no—
535#538—1061no—
536#532—531no—
537#529—531no—
538#525—531no—
539#525C2×D5311yescharacteristic
540C2×#121—531no—
541C2×#121—531no—
542#518—1061no—
543C2×C4×D4—531no—
544#436—1061no—
545#435—1061no—
546#435—1061no—
547C8×D4—1061no—
548#432—531no—
549#431—531no—
550#407—531no—
551#407C2×D5311yescharacteristic, complemented
552C2×C22⋊C8—531no—
553C2×C22⋊C8—531no—
554#388—1061no—
555#387—1061no—
556#386—1061no—
557#385—1061no—
558#383—531no—
559#382—531no—
560#381—531no—
561#380—531no—
562C4×C22⋊C4—531no—
563C2×#95C2×D5311yescharacteristic, complemented
564#328—531no—
565#328—531no—
566#328C2×D5311yescharacteristic, complemented
567#328C2×D5311yescharacteristic, complemented
568#327—531no—
569#327—531no—
570#327—531no—
571#327—531no—
572#327—531no—
573#327—531no—
574#327—531no—
575#327—531no—
576#327—531no—
577#327—531no—
578#327C2×D5311yescharacteristic, complemented
579#327C2×D5311yescharacteristic, complemented
580C53#1759711yescharacteristic, complemented, Sylow
581C2×#41—531no—
582C2×#41—1061no—
583C2×#41C4×D5311yescharacteristic
584C22×D4—531no—
585C22×D4—531no—
586C22×D4—531no—
587C22×D4—1061no—
588C22×D4—1061no—
589C22×D4—1061no—
590C23×C4—21no—
591C23×C4—531no—
592C23×C4C22×D5311yescharacteristic
593C2×M16—21no—
594C2×M16—1061no—
595C22×C8—1061no—
596C22×C8—1061no—
597C4⋊Q8—531no—
598#127—531no—
599#127—1061no—
600#126—1061no—
601#126—1061no—
602#126—1061no—
603#125—531no—
604#125—1061no—
605#124—531no—
606#124—1061no—
607#124—1061no—
608#124—1061no—
609#123—21no—
610#123—1061no—
611#123—1061no—
612#123—1061no—
613#123—1061no—
614#123—1061no—
615#123—1061no—
616C22⋊Q8—531no—
617C22⋊Q8—1061no—
618C22⋊Q8—1061no—
619C22⋊Q8C4×D5311yescharacteristic
620C22⋊Q8C22×D5311yescharacteristic
621#121—531no—
622#121—531no—
623#121—531no—
624#121—531no—
625#121—531no—
626#121—531no—
627#121—531no—
628#121—1061no—
629#121—1061no—
630#121—1061no—
631#121—1061no—
632#121—1061no—
633#121—1061no—
634#121—1061no—
635#121—1061no—
636#121—1061no—
637#121—1061no—
638#121—1061no—
639#121—1061no—
640#121—1061no—
641#121C4×D5311yescharacteristic
642#121C22×D5311yescharacteristic
643#120—21no—
644#120—1061no—
645#120—1061no—
646#120—1061no—
647#120—1061no—
648#120—1061no—
649C4×Q8—531no—
650C4×D4—21no—
651C4×D4—21no—
652C4×D4—531no—
653C4×D4—531no—
654C4×D4—531no—
655C4×D4—531no—
656C4×D4—531no—
657C4×D4—531no—
658C4×D4—531no—
659C4×D4—531no—
660C4×D4—531no—
661C4×D4—531no—
662C4×D4—531no—
663C4×D4—1061no—
664C4×D4—1061no—
665C4×D4—1061no—
666C4×D4—1061no—
667C4×D4—1061no—
668C4×D4—1061no—
669C4×D4—1061no—
670C4×D4—1061no—
671#117—531no—
672#117—1061no—
673#117—1061no—
674#117C4×D5311yescharacteristic
675C2×C4⋊C4—531no—
676C2×C4⋊C4—531no—
677C2×C4⋊C4—531no—
678C2×C4⋊C4—1061no—
679C2×C4⋊C4—1061no—
680C2×C22⋊C4—531no—
681C2×C22⋊C4—531no—
682C2×C22⋊C4—1061no—
683C2×C22⋊C4—1061no—
684C2×C22⋊C4—1061no—
685C2×C22⋊C4—1061no—
686C2×C22⋊C4—1061no—
687C2×C22⋊C4—1061no—
688C2×C22⋊C4—1061no—
689C2×C42—531no—
690C2×C42—1061no—
691C4⋊C8—1061no—
692C4⋊C8—1061no—
693C22⋊C8—21no—
694C22⋊C8—531no—
695C22⋊C8—531no—
696C22⋊C8—1061no—
697C22⋊C8—1061no—
698C22⋊C8—1061no—
699C22⋊C8C22×D5311yescharacteristic
700C22⋊C8C22×D5311yescharacteristic
701#97—1061no—
702C4×C8—1061no—
703#95—21no—
704#95—531no—
705#95—531no—
706#95—1061no—
707#95—1061no—
708#95—1061no—
709#95—1061no—
710#95C22×D5311yescharacteristic
711#95C22×D5311yescharacteristic
712C24—531no—
713C24—1061no—
714C24—1061no—
715C24D4×D5311yescharacteristic
716#41—81no—
717#41—4241no—
718#41—4241no—
719#41—4241no—
720C2×Q8—1061no—
721C2×Q8C2×C4×D5311yescharacteristic
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—531no—
726C2×D4—531no—
727C2×D4—531no—
728C2×D4—531no—
729C2×D4—531no—
730C2×D4—531no—
731C2×D4—1061no—
732C2×D4—1061no—
733C2×D4—1061no—
734C2×D4—1061no—
735C2×D4—1061no—
736C2×D4—1061no—
737C2×D4—1061no—
738C2×D4—1061no—
739C2×D4—1061no—
740C2×D4—1061no—
741C2×D4—1061no—
742C2×D4—1061no—
743C2×D4—4241no—
744C2×D4—4241no—
745C2×D4—4241no—
746C2×D4—4241no—
747C2×D4—4241no—
748C2×D4—4241no—
749C2×D4—2124no—
750C2×D4—2122no—
751C2×D4C2×C4×D5311yescharacteristic
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—42no—
756C22×C4—81no—
757C22×C4—81no—
758C22×C4—81no—
759C22×C4—531no—
760C22×C4—531no—
761C22×C4—531no—
762C22×C4—531no—
763C22×C4—531no—
764C22×C4—531no—
765C22×C4—531no—
766C22×C4—1061no—
767C22×C4—1061no—
768C22×C4—1061no—
769C22×C4—1061no—
770C22×C4—1061no—
771C22×C4—1061no—
772C22×C4—1061no—
773C22×C4—1061no—
774C22×C4—4241no—
775C22×C4C2×C4×D5311yescharacteristic
776C22×C4C2×C4×D5311yescharacteristic
777C22×C4D4×D5311yescharacteristic
778C22×C4D4×D5311yescharacteristic
779C22×C4D4×D5311yescharacteristic
780C22×C4C23×D5311yescharacteristic
781M16—81no—
782M16—4241no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—1061no—
786C2×C8—1061no—
787C2×C8—4241no—
788C2×C8—4241no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—531no—
792C4⋊C4—531no—
793C4⋊C4—531no—
794C4⋊C4—531no—
795C4⋊C4—531no—
796C4⋊C4—531no—
797C4⋊C4—1061no—
798C4⋊C4—1061no—
799C4⋊C4—1061no—
800C4⋊C4—1061no—
801C4⋊C4—1061no—
802C4⋊C4—1061no—
803C4⋊C4—1061no—
804C4⋊C4—4241no—
805C4⋊C4—4241no—
806C4⋊C4C2×C4×D5311yescharacteristic
807C4⋊C4C2×C4×D5311yescharacteristic
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—531no—
814C22⋊C4—531no—
815C22⋊C4—531no—
816C22⋊C4—531no—
817C22⋊C4—531no—
818C22⋊C4—531no—
819C22⋊C4—531no—
820C22⋊C4—531no—
821C22⋊C4—1061no—
822C22⋊C4—1061no—
823C22⋊C4—1061no—
824C22⋊C4—1061no—
825C22⋊C4—1061no—
826C22⋊C4—1061no—
827C22⋊C4—1061no—
828C22⋊C4—1061no—
829C22⋊C4—1061no—
830C22⋊C4—1061no—
831C22⋊C4—1061no—
832C22⋊C4—1061no—
833C22⋊C4—1061no—
834C22⋊C4—1061no—
835C22⋊C4—4241no—
836C22⋊C4—4241no—
837C22⋊C4—2122no—
838C42—21no—
839C42—531no—
840C42—531no—
841C42—531no—
842C42—531no—
843C42—1061no—
844C42—1061no—
845C42—4241no—
846C23—22no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—41no—
851C23—531no—
852C23—531no—
853C23—1061no—
854C23—1061no—
855C23—1061no—
856C23—1061no—
857C23—4241no—
858C23—4241no—
859C23—4241no—
860C23—4241no—
861C23—2121no—
862C23—2121no—
863C23—2122no—
864C23—2122no—
865C23C22⋊C4×D5311yescharacteristic
866C23C22⋊C4×D5311yescharacteristic
867C23C2×D4×D5311yescharacteristic
868Q8—41no—
869Q8—4241no—
870D4—41no—
871D4—42no—
872D4—41no—
873D4—41no—
874D4—81no—
875D4—1062no—
876D4—1062no—
877D4—4241no—
878D4—4241no—
879D4—4241no—
880D4—4241no—
881D4—4241no—
882D4—4241no—
883D4—4241no—
884D4—4241no—
885D4—2121no—
886D4—2121no—
887D4—2122no—
888D4—2121no—
889D4—2121no—
890D4—2122no—
891D4—2121no—
892D4—2121no—
893D4—2121no—
894D4—2121no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—81no—
911C2×C4—84no—
912C2×C4—531no—
913C2×C4—531no—
914C2×C4—531no—
915C2×C4—531no—
916C2×C4—531no—
917C2×C4—531no—
918C2×C4—1061no—
919C2×C4—1061no—
920C2×C4—1061no—
921C2×C4—1061no—
922C2×C4—4241no—
923C2×C4—4241no—
924C2×C4—4241no—
925C2×C4—4241no—
926C2×C4—4241no—
927C2×C4—2121no—
928C2×C4—2121no—
929C2×C4—2121no—
930C2×C4—2121no—
931C2×C4—2122no—
932C2×C4—2121no—
933C2×C4—2121no—
934C2×C4—2121no—
935C2×C4—2121no—
936C2×C4—2121no—
937C2×C4—2121no—
938C2×C4—2121no—
939C2×C4—2121no—
940C2×C4C22⋊C4×D5311yescharacteristic
941C2×C4C22⋊C4×D5311yescharacteristic
942C2×C4C22×C4×D5311yescharacteristic
943C2×C4C2×D4×D5311yescharacteristic
944C8—41no—
945C8—41no—
946C8—2121no—
947C8—2121no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—42no—
956C22—42no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—8482no—
961C22—8482no—
962C22—1061no—
963C22—1061no—
964C22—1061no—
965C22—1061no—
966C22—1061no—
967C22—1061no—
968C22—4241no—
969C22—4241no—
970C22—2121no—
971C22—2121no—
972C22—2121no—
973C22—2121no—
974C22—2121no—
975C22—2121no—
976C22#1681063812yes—
977C22C2×C22⋊C4×D5311yescharacteristic
978C22#1681142711yescharacteristic
979C22#1681143211yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—41no—
985C4—41no—
986C4—41no—
987C4—81no—
988C4—81no—
989C4—1061no—
990C4—1061no—
991C4—1061no—
992C4—1061no—
993C4—1061no—
994C4—1061no—
995C4—4241no—
996C4—4241no—
997C4—2121no—
998C4—2121no—
999C2—21no—
1000C2—21no—
1001C2—22no—
1002C2—41no—
1003C2—81no—
1004C2—4241no—
1005C2—4241no—
1006C2—2121no—
1007C2—2121no—
1008C2#2028317311yescharacteristic
1009C2#2028323911yescharacteristic
1010C2C2×#1681063811yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1504C2
socleC22×C53C22×C22⋊C4
prime radical#20288735C2
cosocleC22×C4×C53C24
hypercenter#1504D53
hypocenterC53#17597
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1504

Complements

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

NH ≅ G/Ntype
2. #20283751C2semidirect
3. #20277349C2semidirect
4. #20273291C2semidirect
5. #20273281C2semidirect
6. #20273273C2semidirect
7. #20273270C2semidirect
8. #20273260C2semidirect
9. #20273257C2semidirect
10. #20273252C2semidirect
11. #20273242C2semidirect
12. #20273232C2semidirect
13. #20273206C2semidirect
14. C2×#16810356C2semidirect
15. C53×#1504C2semidirect
16. #16811336C4semidirect
17. #16811331C4semidirect
18. #16811325C4semidirect
20. #16811317C4semidirect
21. #16811292C4semidirect
23. #16811264C4semidirect
24. #16811261C4semidirect
26. #16811257C4semidirect
42. #16810677C22semidirect
43. #16810673C22semidirect
44. #16810585C22semidirect
45. C2×C22⋊#88322C22semidirect
46. C22⋊C8×D53C22semidirect
51. #16810490C22semidirect
52. #16810487C22semidirect
53. #16810485C22semidirect
54. #16810482C22semidirect
55. C4×C22⋊Dic53C22semidirect
56. #16810360C22semidirect
57. #16810360C22semidirect
60. #16810358C22semidirect
61. #16810358C22semidirect
62. #16810357C22semidirect
63. #16810357C22semidirect
66. #16810356C22semidirect
67. #16810356C22semidirect
69. C53×#407C22semidirect
70. C2×#95×C53C22semidirect
71. C53×#328C22semidirect
72. C53×#328C22semidirect
73. C53×#327C22semidirect
74. C53×#327C22semidirect
75. C2×#11719949C2×C4semidirect
82. C2×D4×D53C2×C4semidirect
87. #13133216C2×C4semidirect
89. #13133213C2×C4semidirect
93. #13133208C2×C4semidirect
95. #13133206C2×C4semidirect
107. #13133193C2×C4semidirect
109. #13133192C2×C4semidirect
110. #13133192C2×C4semidirect
127. #13133188C2×C4semidirect
133. Q8×Dic53C2×C4semidirect
136. D4×Dic53C2×C4semidirect
138. #13133179C2×C4semidirect
139. #13133179C2×C4semidirect
154. #13133175C2×C4semidirect
160. C4⋊C4×D53C2×C4semidirect
506. #1504D53semidirect
551. #407C2×D53semidirect
563. C2×#95C2×D53semidirect
566. #328C2×D53semidirect
567. #328C2×D53semidirect
578. #327C2×D53semidirect
579. #327C2×D53semidirect
580. C53#17597semidirect

Maximal subgroups

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

subgroupindex
#202887352
#202837512
#202773492
#202732912
#202732812
#202732732
#202732702
#202732602
#202732572
#202732522
#202732422
#202732322
#202732062
C2×#168103562
C53×#15042
#1759753