Finite Group Databasebeta

← #27351097

Subgroups — #27351097

Order 13568.

1010 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288325C211yesmaximal, characteristic
2#20283359C211yesmaximal, characteristic, complemented
3#20273183C211yesmaximal, characteristic, complemented
4#20273178C211yesmaximal, characteristic, complemented
5#20273173C211yesmaximal, characteristic, complemented
6#20273157C211yesmaximal, characteristic, complemented
7#20273147C211yesmaximal, characteristic, complemented
8#20273139C211yesmaximal, characteristic, complemented
9#20273126C211yesmaximal, characteristic, complemented
10#20273121C211yesmaximal, characteristic, complemented
11#20273113C211yesmaximal, characteristic, complemented
12#20273105C211yesmaximal, characteristic, complemented
13#20273100C211yesmaximal, characteristic, complemented
14C2×#16810350C211yesmaximal, characteristic, complemented
15C53×#2990C211yesmaximal, characteristic, complemented
16#16811358C411yescharacteristic
17#16811333C411yescharacteristic
18#16811330C411yescharacteristic
19#16811319C411yescharacteristic
20#16811319C411yescharacteristic
21#16811317—21no—
22#16811297—21no—
23#16811297—21no—
24#16811269C411yescharacteristic
25#16811269C411yescharacteristic
26#16811261—21no—
27D4×D212C411yescharacteristic
28#16811173C2211yescharacteristic
29#16811160—21no—
30#16811157C2211yescharacteristic
31#16811157C2211yescharacteristic
32#16811132—21no—
33#16811132—21no—
34C4×#11719945C2211yescharacteristic
35C2×C4×D212C2211yescharacteristic
36C2×C4×D212C2211yescharacteristic
37C4×D4×D53—21no—
38#16810684—21no—
39#16810684—21no—
40#16810676C2211yescharacteristic, complemented
41#16810676C2211yescharacteristic, complemented
42#16810676C2211yescharacteristic, complemented
43#16810676C2211yescharacteristic, complemented
44#16810650—21no—
45#16810590—21no—
46C4×#11719917C2211yescharacteristic, complemented
47C2×C4×#88322C2211yescharacteristic, complemented
48#16810353C2211yescharacteristic, complemented
49#16810353C2211yescharacteristic, complemented
50#16810353C2211yescharacteristic, complemented
51#16810353C2211yescharacteristic, complemented
52#16810350C2211yescharacteristic
53#16810350C2211yescharacteristic
54#16810350C2211yescharacteristic
55#16810350C2211yescharacteristic
56#16810350C2211yescharacteristic, complemented
57#16810350C2211yescharacteristic, complemented
58#16810350C2211yescharacteristic, complemented
59#16810350C2211yescharacteristic, complemented
60#16810350C2211yescharacteristic, complemented
61#16810350C2211yescharacteristic, complemented
62#16810350C2211yescharacteristic, complemented
63#16810350C2211yescharacteristic, complemented
64C4×#41×C53C2211yescharacteristic
65C53×#446—21no—
66C53×#435—21no—
67C53×#435—21no—
68C8×D4×C53—21no—
69C53×#432C2211yescharacteristic, complemented
70C53×#432C2211yescharacteristic, complemented
71C53×#431C2211yescharacteristic, complemented
72C53×#423C2211yescharacteristic, complemented
73C2×C4⋊C8×C53C2211yescharacteristic, complemented
74C2×C4⋊C8×C53C2211yescharacteristic, complemented
75C2×#11719945—21no—
76C2×#11719945C2×C411yescharacteristic
77C22×D212C2×C411yescharacteristic
78C22×D212C2×C411yescharacteristic
79C2×D4×D53—21no—
80C22×C4×D53—21no—
81C22×C4×D53—21no—
82C2×#11719917—21no—
83C22×#88322—21no—
84#13133217C2×C411yescharacteristic
85#13133214C2×C411yescharacteristic
86#13133212—21no—
87#13133212—21no—
88#13133211—21no—
89#13133211—21no—
90#13133209C2×C411yescharacteristic
91#13133209C2×C411yescharacteristic
92#13133208—21no—
93#13133206—21no—
94#13133205—21no—
95#13133205C2×C411yescharacteristic
96#13133205C2×C411yescharacteristic
97#13133202—21no—
98#13133202—21no—
99#13133202—21no—
100#13133202—21no—
101#13133200—21no—
102#13133200—21no—
103#13133199—21no—
104#13133199—21no—
105#13133196C2×C411yescharacteristic
106#13133196C2×C411yescharacteristic
107#13133195—21no—
108#13133195—21no—
109#13133194—21no—
110#13133194—21no—
111#13133193—21no—
112#13133192—21no—
113#13133191—21no—
114#13133191C2×C411yescharacteristic
115#13133191C2×C411yescharacteristic
116#13133191C2×C411yescharacteristic
117#13133191C2×C411yescharacteristic
118#13133190—21no—
119#13133190—21no—
120#13133189—21no—
121#13133189—21no—
122#13133187—21no—
123#13133187—21no—
124#13133185—21no—
125#13133185—21no—
126C4×Dic106C2×C411yescharacteristic
127C4×Dic106C2311yescharacteristic
128C4×D212—21no—
129C4×D212—21no—
130C4×D212—21no—
131C4×D212—21no—
132C4×D212—21no—
133C4×D212C2×C411yescharacteristic
134C4×D212C2×C411yescharacteristic
135C4×D212C2×C411yescharacteristic
136C4×D212C2×C411yescharacteristic
137C4×D212C2×C411yescharacteristic
138C4×D212C2311yescharacteristic
139C4×D212C2311yescharacteristic
140C4×D212C2311yescharacteristic
141D4×Dic53—21no—
142#13133179—21no—
143C4×C22⋊D53—21no—
144C4×C22⋊D53—21no—
145C4×C22⋊D53—21no—
146C4×C22⋊D53—21no—
147#13133177—21no—
148#13133177—21no—
149#13133176C2×C411yescharacteristic
150#13133174—21no—
151#13133174—21no—
152#13133174—21no—
153C2×C4⋊Dic53C2×C411yescharacteristic
154C2×C4⋊Dic53C2×C411yescharacteristic
155C4⋊C4×D53—21no—
156C2×#11719921—21no—
157C2×#11719921—21no—
158C22⋊C4×D53—21no—
159C22⋊C4×D53—21no—
160C42×D53—21no—
161C4⋊#88322—21no—
162C4⋊#88322—21no—
163C4⋊#88322—21no—
164C4⋊#88322—21no—
165C22⋊#88322—21no—
166C22⋊#88322—21no—
167C22⋊#88322—21no—
168C22⋊#88322—21no—
169#13133128—21no—
170C4×#88322—21no—
171C4×#88322C2311yescharacteristic
172C4×#88322C2311yescharacteristic
173C4×#88322C2311yescharacteristic
174C4×#88322C2311yescharacteristic
175C2×#41×C53D411yescharacteristic
176C2×M16×C53—21no—
177C22×C8×C53—21no—
178C22×C8×C53—21no—
179C4×Q8×C53C2×C411yescharacteristic
180C4×Q8×C53D411yescharacteristic
181C4×D4×C53C2×C411yescharacteristic
182C4×D4×C53C2×C411yescharacteristic
183C4×D4×C53C2×C411yescharacteristic
184C4×D4×C53D411yescharacteristic
185C4×D4×C53D411yescharacteristic
186C4×D4×C53D411yescharacteristic
187#117×C53D411yescharacteristic
188#117×C53D411yescharacteristic
189#117×C53D411yescharacteristic
190C2×C42×C53C2311yescharacteristic
191C2×C42×C53C2311yescharacteristic
192C2×C42×C53C2311yescharacteristic
193C4⋊C8×C53—21no—
194C4⋊C8×C53—21no—
195C4⋊C8×C53—21no—
196C4⋊C8×C53C2311yescharacteristic
197C4⋊C8×C53C2311yescharacteristic
198C4⋊C8×C53C2311yescharacteristic
199C4⋊C8×C53C2311yescharacteristic
200C22⋊C8×C53—21no—
201C22⋊C8×C53—21no—
202C22⋊C8×C53—21no—
203#97×C53—21no—
204#97×C53—21no—
205C4×C8×C53—21no—
206C23×D53—21no—
207C23×D53—21no—
208#41×C53—42no—
209C2×Q8×C53C22⋊C411yescharacteristic
210C2×D4×C53C22⋊C411yescharacteristic
211C2×D4×C53C22⋊C411yescharacteristic
212C2×D4×C53C22⋊C411yescharacteristic
213C22×C4×C53C22×C411yescharacteristic
214C22×C4×C53C22×C411yescharacteristic
215C22×C4×C53C22×C411yescharacteristic
216C22×C4×C53C2×D411yescharacteristic
217C22×C4×C53C2×D411yescharacteristic
218C22×C4×C53C2×D411yescharacteristic
219C22×C4×C53C2×D411yescharacteristic
220C22×C4×C53C2×D411yescharacteristic
221C22×C4×C53C2×D411yescharacteristic
222C2×C22⋊D53—21no—
223C2×C22⋊D53—21no—
224C2×C22⋊D53—21no—
225C2×C22⋊D53—21no—
226C2×C22⋊D53—21no—
227C22×Dic53—21no—
228C22×Dic53—21no—
229D4×D53—44no—
230#11719945—22no—
231#11719945—41no—
232#11719945—81no—
233#11719945—81no—
234C2×D212—22no—
235C2×D212—22no—
236C2×D212—21no—
237C2×D212—21no—
238C2×D212—21no—
239C2×D212—21no—
240C2×D212—41no—
241C2×D212—41no—
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—21no—
251C2×C4×D53—21no—
252C2×C4×D53—21no—
253C2×C4×D53—21no—
254C2×C4×D53—81no—
255C2×C4×D53—81no—
256C2×C4×D53—81no—
257C2×C4×D53—81no—
258C2×Dic106—21no—
259C2×Dic106C22×C411yescharacteristic
260M16×C53—81no—
261C2×C8×C53—21no—
262C2×C8×C53—21no—
263C2×C8×C53—21no—
264C2×C8×C53—21no—
265C2×C8×C53—81no—
266C2×C8×C53—81no—
267C4⋊C4×C53C22⋊C411yescharacteristic
268C4⋊C4×C53C22⋊C411yescharacteristic
269C4⋊C4×C53C22⋊C411yescharacteristic
270C4⋊C4×C53C22⋊C411yescharacteristic
271C4⋊C4×C53C22⋊C411yescharacteristic
272C4⋊C4×C53C22⋊C411yescharacteristic
273C22⋊C4×C53C22⋊C411yescharacteristic
274C22⋊C4×C53C22⋊C411yescharacteristic
275C22⋊C4×C53C22⋊C411yescharacteristic
276C22⋊C4×C53C22⋊C411yescharacteristic
277C22⋊C4×C53C22⋊C411yescharacteristic
278C22⋊C4×C53C22⋊C411yescharacteristic
279C42×C53C22×C411yescharacteristic
280C42×C53C22×C411yescharacteristic
281C42×C53C22×C411yescharacteristic
282C42×C53C2×D411yescharacteristic
283C42×C53C2×D411yescharacteristic
284C42×C53C2×D411yescharacteristic
285C42×C53C2×D411yescharacteristic
286C42×C53C2×D411yescharacteristic
287C42×C53C2×D411yescharacteristic
288C42×C53C2411yescharacteristic
289C22⋊Dic53—21no—
290C22⋊Dic53—21no—
291C22⋊Dic53—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—21no—
303#11719921—21no—
304#11719921—21no—
305#11719921—21no—
306#11719921—21no—
307#11719921—21no—
308C4⋊Dic53—21no—
309C4⋊Dic53—21no—
310C4⋊Dic53—21no—
311C4⋊Dic53C22×C411yescharacteristic
312C4⋊Dic53C22×C411yescharacteristic
313C4⋊Dic53C22×C411yescharacteristic
314C4⋊Dic53C22×C411yescharacteristic
315#11719919—21no—
316#11719919—21no—
317#11719919—21no—
318#11719919—21no—
319#11719919—21no—
320#11719919—21no—
321#11719919—21no—
322#11719919—21no—
323C4×Dic53—21no—
324C4×Dic53—21no—
325C4×Dic53—21no—
326#11719917—42no—
327C2×#88322—21no—
328C2×#88322—21no—
329C2×#88322—21no—
330C2×#88322—21no—
331C2×#88322—42no—
332C23×C53C2×C22⋊C411yescharacteristic
333C23×C53C2×C22⋊C411yescharacteristic
334C23×C53C2×C22⋊C411yescharacteristic
335C22×D53—21no—
336C22×D53—21no—
337C22×D53—21no—
338C22×D53—42no—
339C22×D53—42no—
340C22×D53—42no—
341C22×D53—42no—
342C22×D53—81no—
343C22×D53—81no—
344Q8×C53—41no—
345D4×C53—22no—
346D4×C53—22no—
347D4×C53—41no—
348C2×C4×C53—22no—
349C2×C4×C53—21no—
350C2×C4×C53—21no—
351C2×C4×C53—21no—
352C2×C4×C53—21no—
353C2×C4×C53—21no—
354C2×C4×C53—21no—
355C2×C4×C53—21no—
356C2×C4×C53—21no—
357C2×C4×C53—21no—
358C2×C4×C53—21no—
359C2×C4×C53—21no—
360C2×C4×C53—21no—
361C2×C4×C53—41no—
362C2×C4×C53—41no—
363C2×C4×C53C2×C22⋊C411yescharacteristic
364C2×C4×C53C2×C22⋊C411yescharacteristic
365C2×C4×C53C2×C22⋊C411yescharacteristic
366C2×C4×C53C2×C22⋊C411yescharacteristic
367C2×C4×C53C2×C22⋊C411yescharacteristic
368C2×C4×C53C2×C22⋊C411yescharacteristic
369C2×C4×C53C2×C22⋊C411yescharacteristic
370C2×C4×C53C2×C22⋊C411yescharacteristic
371C2×C4×C53C2×C22⋊C411yescharacteristic
372C2×C4×C53C23×C411yescharacteristic
373C2×C4×C53C22×D411yescharacteristic
374C2×C4×C53C22×D411yescharacteristic
375C22⋊D53—42no—
376C22⋊D53—42no—
377C22⋊D53—42no—
378C22⋊D53—81no—
379C22⋊D53—81no—
380C2×Dic53—21no—
381C2×Dic53—21no—
382C2×Dic53—21no—
383C2×Dic53—21no—
384C2×Dic53—21no—
385C2×Dic53—81no—
386C2×Dic53—81no—
387D212—21no—
388D212—21no—
389D212—21no—
390D212—21no—
391D212—21no—
392D212—42no—
393D212—42no—
394D212—42no—
395D212—81no—
396D212#13112yes—
397C4×D53—42no—
398C4×D53—42no—
399C4×D53—41no—
400C4×D53—41no—
401C4×D53—41no—
402C4×D53—41no—
403C4×D53—41no—
404C4×D53—41no—
405C4×D53—81no—
406C4×D53—81no—
407C4×D53—81no—
408C4×D53—81no—
409Dic106—21no—
410Dic106—21no—
411Dic106—81no—
412C8×C53—41no—
413C8×C53—41no—
414C8×C53—41no—
415C8×C53—41no—
416#88322—41no—
417#88322—41no—
418#88322—41no—
419#88322—41no—
420#17521—531nomaximal, Sylow
421C22×C53—21no—
422C22×C53—21no—
423C22×C53—21no—
424C22×C53—21no—
425C22×C53—21no—
426C22×C53—21no—
427C22×C53—21no—
428C22×C53—21no—
429C22×C53#42112yes—
430C22×C53C22×C22⋊C411yescharacteristic
431C2×D53—22no—
432C2×D53—41no—
433C2×D53—41no—
434C2×D53—41no—
435C2×D53—41no—
436C2×D53—41no—
437C2×D53—41no—
438C2×D53—41no—
439C2×D53—41no—
440C2×D53—84no—
441C2×D53—84no—
442C4×C53—21no—
443C4×C53—21no—
444C4×C53—21no—
445C4×C53—21no—
446C4×C53—21no—
447C4×C53—21no—
448C4×C53—21no—
449C4×C53—21no—
450C4×C53—21no—
451C4×C53—21no—
452C4×C53C2×#13111yescharacteristic
453C4×C53#56811yescharacteristic
454C4×C53#57611yescharacteristic
455C4×C53#57711yescharacteristic
456Dic53—41no—
457Dic53—41no—
458Dic53—41no—
459Dic53—41no—
460Dic53—41no—
461#3481—531no—
462#2990D5311yescharacteristic, complemented
463#2922—531no—
464#1496—531no—
465#1495—531no—
466#1494—531no—
467#1490—531no—
468#1488—531no—
469#1486—531no—
470#1483—531no—
471#1482—531no—
472#1480—531no—
473#1478—531no—
474#1477—531no—
475C2×D4⋊C8—531no—
476C2×C53—22no—
477C2×C53—41no—
478C2×C53—41no—
479C2×C53#288011yescharacteristic
480C2×C53#289711yescharacteristic
481C2×C53C2×#42111yescharacteristic
482D53—42no—
483D53—81no—
484D53—81no—
485#559—531no—
486#554—531no—
487#554—531no—
488#553—531no—
489#553—531no—
490#553—1061no—
491#551—1061no—
492#551—1061no—
493#546—531no—
494#546—531no—
495#546—1061no—
496D42—531no—
497#532—531no—
498#529—531no—
499#529—531no—
500#529—1061no—
501#525—1061no—
502#525—1061no—
503C4×#41—531no—
504C4×#41C2×D5311yescharacteristic
505C2×C4×D4—531no—
506C2×C4×D4—531no—
507C2×C4×D4—1061no—
508#446—21no—
509#435—21no—
510#435—21no—
511C8×D4—21no—
512#433—1061no—
513#433—1061no—
514#432C2×D5311yescharacteristic, complemented
515#432C2×D5311yescharacteristic, complemented
516#431—531no—
517#431—531no—
518#431—531no—
519#431—531no—
520#431C2×D5311yescharacteristic, complemented
521#424—1061no—
522#423C2×D5311yescharacteristic, complemented
523C2×C4⋊C8C2×D5311yescharacteristic, complemented
524C2×C4⋊C8C2×D5311yescharacteristic, complemented
525#408—1061no—
526C4×M16—531no—
527C2×C4×C8—531no—
528Q8⋊C8—531no—
529Q8⋊C8—531no—
530Q8⋊C8—531no—
531Q8⋊C8—531no—
532D4⋊C8—531no—
533D4⋊C8—531no—
534D4⋊C8—531no—
535D4⋊C8—531no—
536D4⋊C8—531no—
537D4⋊C8—531no—
538D4⋊C8—531no—
539D4⋊C8—531no—
540D4⋊C8—531no—
541D4⋊C8—531no—
542D4⋊C8—531no—
543D4⋊C8—531no—
544C53#1752111yescharacteristic, complemented, Sylow
545C2×#41—531no—
546C2×#41—1061no—
547C2×#41D21211yescharacteristic
548C22×D4—531no—
549C22×D4—531no—
550C22×D4—1061no—
551C23×C4—1061no—
552C23×C4—1061no—
553C2×M16—21no—
554C2×M16—1061no—
555C22×C8—21no—
556C22×C8—21no—
557C22×C8—1061no—
558C4⋊Q8—531no—
559#127—531no—
560#126—1061no—
561#126—1061no—
562#126—1061no—
563#126—1061no—
564#125—531no—
565#125—531no—
566#125—1061no—
567#124—531no—
568#124—531no—
569#124—1061no—
570#124—1061no—
571#123—1061no—
572#123—1061no—
573#123—1061no—
574#123—1061no—
575#123—1061no—
576#123—1061no—
577#123—1061no—
578#123—1061no—
579C22⋊Q8—531no—
580C22⋊Q8—531no—
581C22⋊Q8—1061no—
582C22⋊Q8—1061no—
583C22⋊Q8—1061no—
584C22⋊Q8—1061no—
585C22⋊Q8—1061no—
586#121—531no—
587#121—531no—
588#121—531no—
589#121—531no—
590#121—1061no—
591#121—1061no—
592#121—1061no—
593#121—1061no—
594#121—1061no—
595#121—1061no—
596#120—1061no—
597#120—1061no—
598#120—1061no—
599#120—1061no—
600C4×Q8—531no—
601C4×Q8—531no—
602C4×Q8C4×D5311yescharacteristic
603C4×Q8C22⋊D5311yescharacteristic
604C4×D4—531no—
605C4×D4—531no—
606C4×D4—531no—
607C4×D4—531no—
608C4×D4—531no—
609C4×D4—531no—
610C4×D4—531no—
611C4×D4—531no—
612C4×D4—1061no—
613C4×D4—1061no—
614C4×D4—1061no—
615C4×D4—1061no—
616C4×D4—1061no—
617C4×D4—1061no—
618C4×D4—1061no—
619C4×D4—1061no—
620C4×D4—1061no—
621C4×D4—1061no—
622C4×D4—1061no—
623C4×D4—1061no—
624C4×D4—1061no—
625C4×D4C4×D5311yescharacteristic
626C4×D4C4×D5311yescharacteristic
627C4×D4C4×D5311yescharacteristic
628C4×D4C22⋊D5311yescharacteristic
629C4×D4C22⋊D5311yescharacteristic
630C4×D4C22⋊D5311yescharacteristic
631#117—531no—
632#117—1061no—
633#117—1061no—
634#117—1061no—
635#117D21211yescharacteristic
636#117D21211yescharacteristic
637#117D21211yescharacteristic
638C2×C4⋊C4—531no—
639C2×C4⋊C4—531no—
640C2×C4⋊C4—1061no—
641C2×C22⋊C4—1061no—
642C2×C22⋊C4—1061no—
643C2×C22⋊C4—1061no—
644C2×C22⋊C4—1061no—
645C2×C42—1061no—
646C2×C42C22×D5311yescharacteristic
647C2×C42C22×D5311yescharacteristic
648C2×C42C22×D5311yescharacteristic
649C4⋊C8—21no—
650C4⋊C8—21no—
651C4⋊C8—21no—
652C4⋊C8—1061no—
653C4⋊C8—1061no—
654C4⋊C8—1061no—
655C4⋊C8—1061no—
656C4⋊C8C22×D5311yescharacteristic
657C4⋊C8C22×D5311yescharacteristic
658C4⋊C8C22×D5311yescharacteristic
659C4⋊C8C22×D5311yescharacteristic
660C22⋊C8—21no—
661C22⋊C8—21no—
662C22⋊C8—21no—
663C22⋊C8—1061no—
664C22⋊C8—1061no—
665C22⋊C8—1061no—
666C22⋊C8—1061no—
667#97—21no—
668#97—21no—
669#97—1061no—
670C4×C8—21no—
671C4×C8—531no—
672C4×C8—531no—
673C4×C8—531no—
674C4×C8—531no—
675C4×C8—1061no—
676C24—1061no—
677C24—1061no—
678#41—42no—
679#41—1062no—
680#41—4241no—
681#41—4241no—
682#41—2121no—
683C2×Q8—531no—
684C2×Q8—1061no—
685C2×Q8#1171992111yescharacteristic
686C2×D4—531no—
687C2×D4—531no—
688C2×D4—531no—
689C2×D4—1062no—
690C2×D4—1062no—
691C2×D4—1061no—
692C2×D4—1061no—
693C2×D4—1061no—
694C2×D4—1061no—
695C2×D4—1061no—
696C2×D4—1061no—
697C2×D4—1061no—
698C2×D4—1061no—
699C2×D4—1061no—
700C2×D4—2121no—
701C2×D4—2121no—
702C2×D4—2124no—
703C2×D4#1171992111yescharacteristic
704C2×D4#1171992111yescharacteristic
705C2×D4#1171992111yescharacteristic
706C22×C4—1061no—
707C22×C4—1061no—
708C22×C4—1061no—
709C22×C4—1061no—
710C22×C4—1061no—
711C22×C4—1061no—
712C22×C4—1061no—
713C22×C4—1061no—
714C22×C4—1061no—
715C22×C4—1061no—
716C22×C4—1061no—
717C22×C4—4241no—
718C22×C4—4241no—
719C22×C4—4241no—
720C22×C4—4241no—
721C22×C4C2×C4×D5311yescharacteristic
722C22×C4C2×C4×D5311yescharacteristic
723C22×C4C2×C4×D5311yescharacteristic
724C22×C4C2×D21211yescharacteristic
725C22×C4C2×D21211yescharacteristic
726C22×C4C2×D21211yescharacteristic
727C22×C4C2×C22⋊D5311yescharacteristic
728C22×C4C2×C22⋊D5311yescharacteristic
729C22×C4C2×C22⋊D5311yescharacteristic
730M16—81no—
731M16—2122no—
732C2×C8—21no—
733C2×C8—21no—
734C2×C8—21no—
735C2×C8—21no—
736C2×C8—81no—
737C2×C8—81no—
738C2×C8—1061no—
739C2×C8—1061no—
740C2×C8—1061no—
741C2×C8—1061no—
742C2×C8—2122no—
743C4⋊C4—531no—
744C4⋊C4—531no—
745C4⋊C4—531no—
746C4⋊C4—531no—
747C4⋊C4—1061no—
748C4⋊C4—1061no—
749C4⋊C4—1061no—
750C4⋊C4—1061no—
751C4⋊C4—1061no—
752C4⋊C4—1061no—
753C4⋊C4—1061no—
754C4⋊C4—1061no—
755C4⋊C4—1061no—
756C4⋊C4—1061no—
757C4⋊C4—1061no—
758C4⋊C4#1171992111yescharacteristic
759C4⋊C4#1171992111yescharacteristic
760C4⋊C4#1171992111yescharacteristic
761C4⋊C4#1171992111yescharacteristic
762C4⋊C4#1171992111yescharacteristic
763C4⋊C4#1171992111yescharacteristic
764C22⋊C4—1061no—
765C22⋊C4—1061no—
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—1061no—
775C22⋊C4—1061no—
776C22⋊C4—1061no—
777C22⋊C4—1061no—
778C22⋊C4—1061no—
779C22⋊C4—1061no—
780C22⋊C4—1061no—
781C22⋊C4—1061no—
782C22⋊C4—1061no—
783C22⋊C4#1171992111yescharacteristic
784C22⋊C4#1171992111yescharacteristic
785C22⋊C4#1171992111yescharacteristic
786C22⋊C4#1171992111yescharacteristic
787C22⋊C4#1171992111yescharacteristic
788C22⋊C4#1171992111yescharacteristic
789C42—1061no—
790C42—1061no—
791C42—1061no—
792C42C2×C4×D5311yescharacteristic
793C42C2×C4×D5311yescharacteristic
794C42C2×C4×D5311yescharacteristic
795C42C2×D21211yescharacteristic
796C42C2×D21211yescharacteristic
797C42C2×D21211yescharacteristic
798C42C2×C22⋊D5311yescharacteristic
799C42C2×C22⋊D5311yescharacteristic
800C42C2×C22⋊D5311yescharacteristic
801C42C23×D5311yescharacteristic
802C23—1061no—
803C23—1061no—
804C23—1061no—
805C23—4241no—
806C23—4241no—
807C23—2122no—
808C23—2122no—
809C23—2122no—
810C23—2122no—
811C23C2×#1171992111yescharacteristic
812C23C2×#1171992111yescharacteristic
813C23C2×#1171992111yescharacteristic
814Q8—41no—
815Q8—1061no—
816Q8—1061no—
817Q8—4241no—
818D4—22no—
819D4—22no—
820D4—41no—
821D4—532no—
822D4—1061no—
823D4—1061no—
824D4—1061no—
825D4—1061no—
826D4—1061no—
827D4—4241no—
828D4—4241no—
829D4—4241no—
830D4—2122no—
831D4—2122no—
832D4—2122no—
833D4—2122no—
834D4—2122no—
835D4—2122no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—1061no—
852C2×C4—1061no—
853C2×C4—1061no—
854C2×C4—1061no—
855C2×C4—1061no—
856C2×C4—4241no—
857C2×C4—4241no—
858C2×C4—4241no—
859C2×C4—4241no—
860C2×C4—4241no—
861C2×C4—4241no—
862C2×C4—2122no—
863C2×C4—2122no—
864C2×C4—2121no—
865C2×C4—2121no—
866C2×C4—2121no—
867C2×C4—2121no—
868C2×C4—2121no—
869C2×C4—2121no—
870C2×C4C2×#1171992111yescharacteristic
871C2×C4C2×#1171992111yescharacteristic
872C2×C4C2×#1171992111yescharacteristic
873C2×C4C2×#1171992111yescharacteristic
874C2×C4C2×#1171992111yescharacteristic
875C2×C4C2×#1171992111yescharacteristic
876C2×C4C2×#1171992111yescharacteristic
877C2×C4C2×#1171992111yescharacteristic
878C2×C4C2×#1171992111yescharacteristic
879C2×C4C22×C4×D5311yescharacteristic
880C2×C4C22×C22⋊D5311yescharacteristic
881C2×C4C22×D21211yescharacteristic
882C8—41no—
883C8—41no—
884C8—41no—
885C8—41no—
886C8—2121no—
887C8—2121no—
888C8—2121no—
889C8—2121no—
890C22—21no—
891C22—21no—
892C22—21no—
893C22—21no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—1062no—
899C22—4244no—
900C22—4244no—
901C22—2121no—
902C22—2121no—
903C22—2121no—
904C22—2121no—
905C22—2121no—
906C22—2121no—
907C22—2121no—
908C22—2121no—
909C22#1681063912yes—
910C22C22×#1171992111yescharacteristic
911C4—21no—
912C4—21no—
913C4—21no—
914C4—21no—
915C4—21no—
916C4—21no—
917C4—21no—
918C4—21no—
919C4—21no—
920C4—21no—
921C4—2121no—
922C4—2121no—
923C4—2121no—
924C4—2121no—
925C4—2121no—
926C4#131×D5311yescharacteristic
927C4#1681138811yescharacteristic
928C4#1681142611yescharacteristic
929C4#1681143111yescharacteristic
930C2—22no—
931C2—41no—
932C2—41no—
933C2—4241no—
934C2—4241no—
935C2—2122no—
936C2#2028316211yescharacteristic
937C2#2028323811yescharacteristic
938C2C2×#1681063911yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC42C23×D53
FittingC53×#2990C2
socleC22×C53C22×C22⋊C4
prime radical#20288325C2
cosocleC42×C53C24
hypercenter#2990D53
hypocenterC53#17521
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2990

Complements

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

NH ≅ G/Ntype
2. #20283359C2semidirect
3. #20273183C2semidirect
4. #20273178C2semidirect
5. #20273173C2semidirect
6. #20273157C2semidirect
7. #20273147C2semidirect
8. #20273139C2semidirect
9. #20273126C2semidirect
10. #20273121C2semidirect
11. #20273113C2semidirect
12. #20273105C2semidirect
13. #20273100C2semidirect
14. C2×#16810350C2semidirect
15. C53×#2990C2semidirect
40. #16810676C22semidirect
41. #16810676C22semidirect
42. #16810676C22semidirect
43. #16810676C22semidirect
46. C4×#11719917C22semidirect
47. C2×C4×#88322C22semidirect
48. #16810353C22semidirect
49. #16810353C22semidirect
50. #16810353C22semidirect
51. #16810353C22semidirect
56. #16810350C22semidirect
57. #16810350C22semidirect
58. #16810350C22semidirect
59. #16810350C22semidirect
60. #16810350C22semidirect
61. #16810350C22semidirect
62. #16810350C22semidirect
63. #16810350C22semidirect
69. C53×#432C22semidirect
70. C53×#432C22semidirect
71. C53×#431C22semidirect
72. C53×#423C22semidirect
73. C2×C4⋊C8×C53C22semidirect
74. C2×C4⋊C8×C53C22semidirect
462. #2990D53semidirect
514. #432C2×D53semidirect
515. #432C2×D53semidirect
520. #431C2×D53semidirect
522. #423C2×D53semidirect
523. C2×C4⋊C8C2×D53semidirect
524. C2×C4⋊C8C2×D53semidirect
544. C53#17521semidirect

Maximal subgroups

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

subgroupindex
#202883252
#202833592
#202731832
#202731782
#202731732
#202731572
#202731472
#202731392
#202731262
#202731212
#202731132
#202731052
#202731002
C2×#168103502
C53×#29902
#1752153