Finite Group Databasebeta

← #27351704

Subgroups — #27351704

Order 13568.

1004 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288444C211yesmaximal, characteristic
2#20283375C211yesmaximal, characteristic, complemented
3#20277577C211yesmaximal, characteristic, complemented
4#20273289C211yesmaximal, characteristic, complemented
5#20273273C211yesmaximal, characteristic, complemented
6#20273269C211yesmaximal, characteristic, complemented
7#20273260C211yesmaximal, characteristic, complemented
8#20273250C211yesmaximal, characteristic, complemented
9#20273237C211yesmaximal, characteristic, complemented
10#20273221C211yesmaximal, characteristic, complemented
11#20273220C211yesmaximal, characteristic, complemented
12#20273208C211yesmaximal, characteristic, complemented
13#20273198C211yesmaximal, characteristic, complemented
14C2×#16810357C211yesmaximal, characteristic, complemented
15C53×#1510C211yesmaximal, characteristic, complemented
16#16811337—21no—
17#16811325—21no—
18#16811320—21no—
19#16811299—21no—
20#16811299—21no—
21#16811273—21no—
22#16811267—21no—
23#16811267—21no—
24#16811254C411yescharacteristic, complemented
25#16811240C411yescharacteristic, complemented
26#16811240C411yescharacteristic, complemented
27#16811226C411yescharacteristic, complemented
28#16811226C411yescharacteristic, complemented
29#16811190C411yescharacteristic, complemented
30#16811168C2211yescharacteristic
31#16811168C2211yescharacteristic
32#16811154C2211yescharacteristic
33#16811154C2211yescharacteristic
34#16811134C2211yescharacteristic
35#16811104C411yescharacteristic, complemented
36#16811098C411yescharacteristic, complemented
37C2×#13133176C2211yescharacteristic
38#16810681—21no—
39#16810681—21no—
40#16810677C2211yescharacteristic, complemented
41#16810677C2211yescharacteristic, complemented
42#16810673C2211yescharacteristic, complemented
43#16810673C2211yescharacteristic, complemented
44#16810651—21no—
45C2×C22⋊#88322C2211yescharacteristic
46#16810581—21no—
47#16810508—21no—
48#16810506—21no—
49#16810495—21no—
50#16810490C2211yescharacteristic, complemented
51#16810487C2211yescharacteristic, complemented
52#16810474C2211yescharacteristic, complemented
53C22⋊C4×Dic53—21no—
54#16810468C2211yescharacteristic, complemented
55C2×#13133124C2211yescharacteristic
56#16810361C2211yescharacteristic, complemented
57#16810361C2211yescharacteristic, complemented
58#16810359C2211yescharacteristic, complemented
59#16810359C2211yescharacteristic, complemented
60#16810358C2211yescharacteristic, complemented
61#16810358C2211yescharacteristic, complemented
62#16810357C2211yescharacteristic
63#16810357C2211yescharacteristic
64#16810357C2211yescharacteristic
65#16810357C2211yescharacteristic
66#16810356C2211yescharacteristic, complemented
67#16810356C2211yescharacteristic, complemented
68C2×#121×C53C2211yescharacteristic
69C53×#407C2211yescharacteristic
70C53×#381C2211yescharacteristic
71C53×#327C2211yescharacteristic
72C53×#327C2211yescharacteristic
73C53×#327C2211yescharacteristic
74C53×#327C2211yescharacteristic
75C2×#11719945C2×C411yescharacteristic
76C2×#11719947—21no—
77C2×#11719947—21no—
78C23×Dic53—21no—
79C22×#88322—21no—
80#13133216—21no—
81#13133216C2×C411yescharacteristic, complemented
82#13133216C2×C411yescharacteristic, complemented
83#13133213C2×C411yescharacteristic, complemented
84#13133213C2×C411yescharacteristic, complemented
85#13133210—21no—
86#13133210—21no—
87#13133210—21no—
88#13133210—21no—
89#13133208—21no—
90#13133208C2×C411yescharacteristic, complemented
91#13133208C2×C411yescharacteristic, complemented
92#13133204—21no—
93#13133204—21no—
94#13133204C2×C411yescharacteristic, complemented
95#13133204C2×C411yescharacteristic, complemented
96#13133203—21no—
97#13133203—21no—
98#13133201—21no—
99#13133201—21no—
100#13133200—21no—
101#13133199—21no—
102#13133199—21no—
103#13133198—21no—
104#13133198—21no—
105#13133198—21no—
106#13133198—21no—
107#13133196—21no—
108#13133196—21no—
109#13133196C2×C411yescharacteristic
110#13133196C2311yescharacteristic
111#13133194—21no—
112#13133194—21no—
113#13133191C2×C411yescharacteristic
114#13133191C2311yescharacteristic
115#13133189—21no—
116#13133189—21no—
117#13133189—21no—
118#13133189—21no—
119#13133188—21no—
120#13133188—21no—
121#13133188—21no—
122#13133188—21no—
123#13133186—21no—
124#13133186—21no—
125#13133186—21no—
126#13133182C2×C411yescharacteristic, complemented
127#13133182C2×C411yescharacteristic, complemented
128D4×Dic53—21no—
129D4×Dic53—21no—
130D4×Dic53—21no—
131D4×Dic53—21no—
132D4×Dic53C2×C411yescharacteristic, complemented
133D4×Dic53C2×C411yescharacteristic, complemented
134D4×Dic53C2×C411yescharacteristic, complemented
135D4×Dic53C2×C411yescharacteristic, complemented
136#13133179C2×C411yescharacteristic, complemented
137#13133179C2×C411yescharacteristic, complemented
138C4×C22⋊D53—21no—
139C4×C22⋊D53—21no—
140C4×C22⋊D53—21no—
141C4×C22⋊D53—21no—
142#13133177—21no—
143#13133177—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#13133173—21no—
155#13133173—21no—
156C2×C4⋊Dic53D411yescharacteristic
157C2×C4⋊Dic53D411yescharacteristic
158C2×#11719919—21no—
159C2×#11719919—21no—
160C4⋊C4×D53—21no—
161C2×C22⋊Dic53—21no—
162C2×C22⋊Dic53—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×D4×C53—21no—
188C22×D4×C53C2×C411yescharacteristic
189C23×C4×C53C2311yescharacteristic
190C2×M16×C53—21no—
191#121×C53—21no—
192#121×C53—21no—
193#121×C53C2×C411yescharacteristic
194#121×C53C2×C411yescharacteristic
195#121×C53C2311yescharacteristic
196#121×C53C2311yescharacteristic
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×C53—21no—
207C24×C53C2×D411yescharacteristic
208C2×D4×C53—21no—
209C2×D4×C53—21no—
210C2×D4×C53—21no—
211C2×D4×C53—21no—
212C2×D4×C53—21no—
213C2×D4×C53—42no—
214C2×D4×C53—81no—
215C2×D4×C53—81no—
216C2×D4×C53C22×C411yescharacteristic
217C2×D4×C53C22×C411yescharacteristic
218C22×C4×C53—21no—
219C22×C4×C53—21no—
220C22×C4×C53—21no—
221C22×C4×C53—42no—
222C22×C4×C53C22×C411yescharacteristic
223C22×C4×C53C22×C411yescharacteristic
224C22×C4×C53C2×D411yescharacteristic
225C22×C4×C53C2×D411yescharacteristic
226C22×C4×C53C2×D411yescharacteristic
227C22×C4×C53C2411yescharacteristic
228C2×C22⋊D53—21no—
229C2×C22⋊D53—21no—
230C2×C22⋊D53—21no—
231C2×C22⋊D53—21no—
232C2×C22⋊D53—21no—
233C2×C22⋊D53—21no—
234C2×C22⋊D53—21no—
235C22×Dic53—21no—
236C22×Dic53—21no—
237C22×Dic53—21no—
238C22×Dic53—21no—
239C22×Dic53—21no—
240C22×Dic53—21no—
241C22×Dic53—42no—
242C22×Dic53—42no—
243C22×Dic53—81no—
244C22×Dic53C2×D411yescharacteristic
245C22×Dic53C2×D411yescharacteristic
246C22×Dic53C2×D411yescharacteristic
247C22×Dic53C2×D411yescharacteristic
248#11719947—81no—
249#11719947—81no—
250#11719947—81no—
251#11719947—81no—
252#11719945—42no—
253C2×D212C22×C411yescharacteristic
254C2×C4×D53—21no—
255C2×C4×D53—21no—
256C2×C4×D53—21no—
257C2×Dic106—21no—
258C2×Dic106—21no—
259C2×Dic106C22×C411yescharacteristic
260M16×C53—42no—
261C2×C8×C53—21no—
262C2×C8×C53—21no—
263C4⋊C4×C53—21no—
264C4⋊C4×C53C22×C411yescharacteristic
265C4⋊C4×C53C22×C411yescharacteristic
266C22⋊C4×C53—21no—
267C22⋊C4×C53—21no—
268C22⋊C4×C53—21no—
269C22⋊C4×C53—21no—
270C22⋊C4×C53—42no—
271C22⋊Dic53—21no—
272C22⋊Dic53—21no—
273C22⋊Dic53—21no—
274C22⋊Dic53—21no—
275C22⋊Dic53—21no—
276C22⋊Dic53—21no—
277C22⋊Dic53—21no—
278C22⋊Dic53—21no—
279C22⋊Dic53—21no—
280C22⋊Dic53—21no—
281C22⋊Dic53—21no—
282C22⋊Dic53C22⋊C411yescharacteristic
283C22⋊Dic53C22⋊C411yescharacteristic
284C22⋊Dic53C22⋊C411yescharacteristic
285C22⋊Dic53C22⋊C411yescharacteristic
286C22⋊Dic53C22⋊C411yescharacteristic
287C22⋊Dic53C22⋊C411yescharacteristic
288C22⋊Dic53C22⋊C411yescharacteristic
289C22⋊Dic53C22⋊C411yescharacteristic
290#11719921—21no—
291#11719921—21no—
292#11719921—21no—
293#11719921—21no—
294C4⋊Dic53—21no—
295C4⋊Dic53—21no—
296C4⋊Dic53C22⋊C411yescharacteristic
297C4⋊Dic53C22⋊C411yescharacteristic
298C4⋊Dic53C22⋊C411yescharacteristic
299C4⋊Dic53C22⋊C411yescharacteristic
300C4⋊Dic53C22⋊C411yescharacteristic
301C4⋊Dic53C22⋊C411yescharacteristic
302C4⋊Dic53C22⋊C411yescharacteristic
303C4⋊Dic53C22⋊C411yescharacteristic
304C4⋊Dic53C22×C411yescharacteristic
305C4⋊Dic53C22×C411yescharacteristic
306#11719919—21no—
307#11719919—21no—
308#11719919—21no—
309#11719919—21no—
310#11719919—21no—
311#11719919—21no—
312#11719919—21no—
313#11719919—21no—
314#11719919—42no—
315#11719919—81no—
316C4×Dic53—21no—
317C4×Dic53—21no—
318C4×Dic53—21no—
319C4×Dic53—42no—
320C4×Dic53—81no—
321C4×Dic53C22×C411yescharacteristic
322C4×Dic53C22×C411yescharacteristic
323C4×Dic53C22×C411yescharacteristic
324C4×Dic53C22×C411yescharacteristic
325C4×Dic53C2×D411yescharacteristic
326C4×Dic53C2×D411yescharacteristic
327C4×Dic53C2×D411yescharacteristic
328C4×Dic53C2×D411yescharacteristic
329C2×#88322—21no—
330C2×#88322—21no—
331C2×#88322—42no—
332C23×C53—21no—
333C23×C53—21no—
334C23×C53—22no—
335C23×C53—21no—
336C23×C53—21no—
337C23×C53—41no—
338C23×C53—42no—
339C23×C53—81no—
340C23×C53—81no—
341C23×C53C2×C22⋊C411yescharacteristic
342C23×C53C2×C22⋊C411yescharacteristic
343C23×C53C22×D411yescharacteristic
344C22×D53—21no—
345D4×C53—41no—
346D4×C53—41no—
347D4×C53—42no—
348D4×C53—41no—
349D4×C53—41no—
350D4×C53—41no—
351D4×C53—41no—
352D4×C53—81no—
353D4×C53—81no—
354C2×C4×C53—22no—
355C2×C4×C53—22no—
356C2×C4×C53—21no—
357C2×C4×C53—21no—
358C2×C4×C53—41no—
359C2×C4×C53—41no—
360C2×C4×C53—41no—
361C2×C4×C53—41no—
362C2×C4×C53—41no—
363C2×C4×C53—41no—
364C2×C4×C53—41no—
365C2×C4×C53—41no—
366C2×C4×C53—41no—
367C2×C4×C53—41no—
368C2×C4×C53—81no—
369C2×C4×C53C2×C22⋊C411yescharacteristic
370C2×C4×C53C2×C22⋊C411yescharacteristic
371C2×C4×C53C23×C411yescharacteristic
372C2×C4×C53C22×D411yescharacteristic
373C22⋊D53—41no—
374C22⋊D53—41no—
375C22⋊D53—42no—
376C22⋊D53—81no—
377C22⋊D53—81no—
378C22⋊D53—81no—
379C22⋊D53—81no—
380C22⋊D53—81no—
381C2×Dic53—21no—
382C2×Dic53—21no—
383C2×Dic53—21no—
384C2×Dic53—21no—
385C2×Dic53—22no—
386C2×Dic53—21no—
387C2×Dic53—21no—
388C2×Dic53—21no—
389C2×Dic53—41no—
390C2×Dic53—41no—
391C2×Dic53—41no—
392C2×Dic53—41no—
393C2×Dic53—41no—
394C2×Dic53—41no—
395C2×Dic53—41no—
396C2×Dic53—81no—
397C2×Dic53—81no—
398C2×Dic53—81no—
399C2×Dic53—81no—
400C2×Dic53—84no—
401C2×Dic53C2×C22⋊C411yescharacteristic
402C2×Dic53C2×C22⋊C411yescharacteristic
403C2×Dic53C2×C22⋊C411yescharacteristic
404C2×Dic53C2×C22⋊C411yescharacteristic
405C2×Dic53C2×C22⋊C411yescharacteristic
406C2×Dic53C2×C22⋊C411yescharacteristic
407C2×Dic53C2×C22⋊C411yescharacteristic
408C2×Dic53C2×C22⋊C411yescharacteristic
409D212—41no—
410C4×D53—42no—
411C4×D53—81no—
412C4×D53—81no—
413Dic106—41no—
414Dic106—81no—
415Dic106—81no—
416C8×C53—41no—
417C8×C53—41no—
418#88322—41no—
419#88322—41no—
420#17604—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—42no—
429C22×C53—42no—
430C22×C53—41no—
431C22×C53—41no—
432C22×C53—41no—
433C22×C53—41no—
434C22×C53—41no—
435C22×C53—41no—
436C22×C53—162no—
437C22×C53#41012yes—
438C22×C53C22×C22⋊C411yescharacteristic
439C22×C53#57611yescharacteristic
440C22×C53#57711yescharacteristic
441C2×D53—41no—
442C2×D53—41no—
443C2×D53—41no—
444C4×C53—21no—
445C4×C53—21no—
446C4×C53—21no—
447C4×C53—21no—
448C4×C53—41no—
449C4×C53—41no—
450C4×C53—81no—
451C4×C53—81no—
452Dic53—21no—
453Dic53—21no—
454Dic53—21no—
455Dic53—21no—
456Dic53—21no—
457Dic53—21no—
458Dic53—21no—
459Dic53—21no—
460Dic53—42no—
461Dic53—41no—
462Dic53—41no—
463Dic53—41no—
464Dic53—81no—
465#3494—531no—
466#2924—531no—
467#2343—531no—
468#1521—531no—
469#1517—531no—
470#1516—531no—
471#1514—531no—
472#1512—531no—
473#1510D5311yescharacteristic, complemented
474#1509—531no—
475#1505—531no—
476#1504—531no—
477#1502—531no—
478#1500—531no—
479C2×#327—531no—
480C2×C53—21no—
481C2×C53—21no—
482C2×C53—22no—
483C2×C53—41no—
484C2×C53—81no—
485C2×C53—81no—
486C2×C53C2×#41011yescharacteristic
487C2×C53#289711yescharacteristic
488C2×C53#290111yescharacteristic
489D53—81no—
490#555—1061no—
491#553—1061no—
492#553—1061no—
493#551—1061no—
494#551—1061no—
495#547—1061no—
496#546—1061no—
497#546—1061no—
498#544—531no—
499#542—531no—
500#542—531no—
501#540—531no—
502#540—531no—
503#535—531no—
504#532—531no—
505#532—531no—
506#529—531no—
507#529—531no—
508#525—531no—
509C2×#121C2×D5311yescharacteristic
510#520—531no—
511#518—531no—
512C2×#117—531no—
513#433—1061no—
514#433—1061no—
515#432—531no—
516#432—531no—
517#431—531no—
518#431—531no—
519#424—1061no—
520#407C2×D5311yescharacteristic
521C2×C22⋊C8—531no—
522#405—1061no—
523#387—1061no—
524#387—1061no—
525#385—1061no—
526#383—531no—
527#382—531no—
528#381C2×D5311yescharacteristic
529C4×C4⋊C4—531no—
530C4×C22⋊C4—1061no—
531#376—531no—
532C2×#95—531no—
533#328—531no—
534#328—531no—
535#328—531no—
536#328—531no—
537#327—531no—
538#327—531no—
539#327—531no—
540#327—531no—
541#327—531no—
542#327—531no—
543#327—531no—
544#327—531no—
545#327C2×D5311yescharacteristic
546#327C2×D5311yescharacteristic
547#327C2×D5311yescharacteristic
548#327C2×D5311yescharacteristic
549C53#1760411yescharacteristic, complemented, Sylow
550C2×#41—531no—
551C2×#41—1061no—
552C2×#41—1061no—
553C22×D4—21no—
554C22×D4C4×D5311yescharacteristic
555C23×C4—1061no—
556C23×C4C22×D5311yescharacteristic
557C2×M16—21no—
558C22×C8—1061no—
559C4⋊Q8—531no—
560C4⋊Q8—531no—
561C4⋊Q8—1061no—
562#127—531no—
563#127—531no—
564#126—1061no—
565#126—1061no—
566#126—1061no—
567#126—1061no—
568#125—531no—
569#125—531no—
570#125—1061no—
571#124—531no—
572#124—531no—
573#124—1061no—
574#124—1061no—
575#124—1061no—
576#124—1061no—
577#123—1061no—
578#123—1061no—
579#123—1061no—
580#123—1061no—
581#123—1061no—
582#123—1061no—
583#123—1061no—
584#123—1061no—
585#123—1061no—
586C22⋊Q8—531no—
587C22⋊Q8—531no—
588C22⋊Q8—1061no—
589C22⋊Q8—1061no—
590C22⋊Q8—1061no—
591C22⋊Q8—1061no—
592#121—21no—
593#121—21no—
594#121—531no—
595#121—531no—
596#121—1061no—
597#121—1061no—
598#121—1061no—
599#121—1061no—
600#121—1061no—
601#121—1061no—
602#121—1061no—
603#121—1061no—
604#121C4×D5311yescharacteristic
605#121C4×D5311yescharacteristic
606#121C22×D5311yescharacteristic
607#121C22×D5311yescharacteristic
608#120—1061no—
609#120—1061no—
610#120—1061no—
611C4×Q8—531no—
612C4×Q8—531no—
613C4×D4—531no—
614C4×D4—531no—
615C4×D4—531no—
616C4×D4—531no—
617C4×D4—531no—
618C4×D4—531no—
619C4×D4—1061no—
620C4×D4—1061no—
621C4×D4—1061no—
622C4×D4—1061no—
623C4×D4—1061no—
624C4×D4—1061no—
625C4×D4—1061no—
626C4×D4—1061no—
627C4×D4—1061no—
628C4×D4—1061no—
629#117—531no—
630#117—531no—
631#117—531no—
632#117—531no—
633#117—531no—
634#117—531no—
635#117—531no—
636#117—531no—
637#117—531no—
638#117—1061no—
639#117—1061no—
640#117—1061no—
641C2×C4⋊C4—531no—
642C2×C4⋊C4—531no—
643C2×C4⋊C4—1061no—
644C2×C4⋊C4—1061no—
645C2×C4⋊C4—1061no—
646C2×C4⋊C4C4×D5311yescharacteristic
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—531no—
650C2×C22⋊C4—531no—
651C2×C22⋊C4—1061no—
652C2×C22⋊C4—1061no—
653C2×C42—531no—
654C2×C42—531no—
655C2×C42—1061no—
656C2×C42—1061no—
657C4⋊C8—1061no—
658C4⋊C8—1061no—
659C4⋊C8—1061no—
660C4⋊C8—1061no—
661C22⋊C8—21no—
662C22⋊C8—531no—
663C22⋊C8—531no—
664C22⋊C8—1061no—
665C22⋊C8C22×D5311yescharacteristic
666C22⋊C8C22×D5311yescharacteristic
667#97—1061no—
668#97—1061no—
669C4×C8—1061no—
670C4×C8—1061no—
671#95—21no—
672#95—531no—
673#95—531no—
674#95—1061no—
675#95—1061no—
676#95—1061no—
677#95—1061no—
678#95—1061no—
679#95C22×D5311yescharacteristic
680#95C22×D5311yescharacteristic
681C24—21no—
682C24D4×D5311yescharacteristic
683#41—4241no—
684#41—4241no—
685#41—4241no—
686#41—4241no—
687#41—2122no—
688C2×Q8—531no—
689C2×Q8—1061no—
690C2×Q8—1061no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—42no—
697C2×D4—81no—
698C2×D4—81no—
699C2×D4—531no—
700C2×D4—1061no—
701C2×D4—1061no—
702C2×D4—1061no—
703C2×D4—1061no—
704C2×D4—1061no—
705C2×D4—1061no—
706C2×D4—1061no—
707C2×D4C2×C4×D5311yescharacteristic
708C2×D4C2×C4×D5311yescharacteristic
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—42no—
713C22×C4—531no—
714C22×C4—531no—
715C22×C4—531no—
716C22×C4—531no—
717C22×C4—1061no—
718C22×C4—1061no—
719C22×C4—1061no—
720C22×C4—1061no—
721C22×C4—1061no—
722C22×C4—1061no—
723C22×C4—1061no—
724C22×C4—1061no—
725C22×C4—1061no—
726C22×C4—4241no—
727C22×C4—2122no—
728C22×C4—2122no—
729C22×C4C2×C4×D5311yescharacteristic
730C22×C4C2×C4×D5311yescharacteristic
731C22×C4D4×D5311yescharacteristic
732C22×C4D4×D5311yescharacteristic
733C22×C4D4×D5311yescharacteristic
734C22×C4C23×D5311yescharacteristic
735M16—42no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—1061no—
739C2×C8—1061no—
740C2×C8—2122no—
741C4⋊C4—21no—
742C4⋊C4—531no—
743C4⋊C4—531no—
744C4⋊C4—531no—
745C4⋊C4—531no—
746C4⋊C4—531no—
747C4⋊C4—531no—
748C4⋊C4—531no—
749C4⋊C4—531no—
750C4⋊C4—531no—
751C4⋊C4—531no—
752C4⋊C4—1061no—
753C4⋊C4—1061no—
754C4⋊C4—1061no—
755C4⋊C4—1061no—
756C4⋊C4—1061no—
757C4⋊C4—1061no—
758C4⋊C4—1061no—
759C4⋊C4—1061no—
760C4⋊C4—1061no—
761C4⋊C4—1061no—
762C4⋊C4—4241no—
763C4⋊C4—2122no—
764C4⋊C4C2×C4×D5311yescharacteristic
765C4⋊C4C2×C4×D5311yescharacteristic
766C22⋊C4—21no—
767C22⋊C4—21no—
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—42no—
771C22⋊C4—531no—
772C22⋊C4—531no—
773C22⋊C4—531no—
774C22⋊C4—531no—
775C22⋊C4—531no—
776C22⋊C4—531no—
777C22⋊C4—531no—
778C22⋊C4—531no—
779C22⋊C4—1061no—
780C22⋊C4—1061no—
781C22⋊C4—1061no—
782C22⋊C4—1061no—
783C22⋊C4—1061no—
784C22⋊C4—1061no—
785C22⋊C4—1061no—
786C22⋊C4—1061no—
787C22⋊C4—1061no—
788C22⋊C4—1061no—
789C22⋊C4—1061no—
790C22⋊C4—1061no—
791C22⋊C4—1061no—
792C22⋊C4—1061no—
793C22⋊C4—1061no—
794C42—531no—
795C42—531no—
796C42—531no—
797C42—531no—
798C42—531no—
799C42—531no—
800C42—531no—
801C42—531no—
802C42—1061no—
803C42—1061no—
804C42—1061no—
805C42—4241no—
806C42—2122no—
807C23—22no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—41no—
813C23—42no—
814C23—81no—
815C23—81no—
816C23—1061no—
817C23C22⋊C4×D5311yescharacteristic
818C23C22⋊C4×D5311yescharacteristic
819C23C2×D4×D5311yescharacteristic
820Q8—4241no—
821Q8—4241no—
822Q8—2121no—
823D4—41no—
824D4—41no—
825D4—42no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—81no—
831D4—81no—
832D4—4241no—
833D4—4241no—
834D4—4241no—
835D4—4241no—
836D4—4241no—
837D4—2121no—
838D4—2122no—
839D4—2121no—
840D4—2121no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—81no—
856C2×C4—531no—
857C2×C4—531no—
858C2×C4—531no—
859C2×C4—531no—
860C2×C4—531no—
861C2×C4—531no—
862C2×C4—531no—
863C2×C4—531no—
864C2×C4—1061no—
865C2×C4—1061no—
866C2×C4—1061no—
867C2×C4—1061no—
868C2×C4—1062no—
869C2×C4—1061no—
870C2×C4—1061no—
871C2×C4—1061no—
872C2×C4—4241no—
873C2×C4—4241no—
874C2×C4—4241no—
875C2×C4—4241no—
876C2×C4—4241no—
877C2×C4—4241no—
878C2×C4—4244no—
879C2×C4—2122no—
880C2×C4—2121no—
881C2×C4—2121no—
882C2×C4—2121no—
883C2×C4—2121no—
884C2×C4—2121no—
885C2×C4—2121no—
886C2×C4—2121no—
887C2×C4C22⋊C4×D5311yescharacteristic
888C2×C4C22⋊C4×D5311yescharacteristic
889C2×C4C22×C4×D5311yescharacteristic
890C2×C4C2×D4×D5311yescharacteristic
891C8—41no—
892C8—41no—
893C8—2121no—
894C8—2121no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—42no—
903C22—42no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—162no—
911C22—2121no—
912C22—2121no—
913C22—2121no—
914C22#1681059512yes—
915C22C2×C22⋊C4×D5311yescharacteristic
916C22#1681142711yescharacteristic
917C22#1681143311yescharacteristic
918C4—21no—
919C4—21no—
920C4—21no—
921C4—21no—
922C4—41no—
923C4—41no—
924C4—81no—
925C4—81no—
926C4—1061no—
927C4—1061no—
928C4—1061no—
929C4—1061no—
930C4—1061no—
931C4—1061no—
932C4—1061no—
933C4—1061no—
934C4—4241no—
935C4—2122no—
936C4—2121no—
937C4—2121no—
938C4—2121no—
939C2—21no—
940C2—21no—
941C2—22no—
942C2—41no—
943C2—81no—
944C2—81no—
945C2—4241no—
946C2C2×#1681059511yescharacteristic
947C2#2028324011yescharacteristic
948C2#2028326111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1510C2
socleC22×C53C22×C22⋊C4
prime radical#20288444C2
cosocleC22×C4×C53C24
hypercenter#1510D53
hypocenterC53#17604
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1510

Complements

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

NH ≅ G/Ntype
2. #20283375C2semidirect
3. #20277577C2semidirect
4. #20273289C2semidirect
5. #20273273C2semidirect
6. #20273269C2semidirect
7. #20273260C2semidirect
8. #20273250C2semidirect
9. #20273237C2semidirect
10. #20273221C2semidirect
11. #20273220C2semidirect
12. #20273208C2semidirect
13. #20273198C2semidirect
14. C2×#16810357C2semidirect
15. C53×#1510C2semidirect
24. #16811254C4semidirect
25. #16811240C4semidirect
26. #16811240C4semidirect
27. #16811226C4semidirect
28. #16811226C4semidirect
29. #16811190C4semidirect
35. #16811104C4semidirect
36. #16811098C4semidirect
40. #16810677C22semidirect
41. #16810677C22semidirect
42. #16810673C22semidirect
43. #16810673C22semidirect
50. #16810490C22semidirect
51. #16810487C22semidirect
52. #16810474C22semidirect
54. #16810468C22semidirect
56. #16810361C22semidirect
57. #16810361C22semidirect
58. #16810359C22semidirect
59. #16810359C22semidirect
60. #16810358C22semidirect
61. #16810358C22semidirect
66. #16810356C22semidirect
67. #16810356C22semidirect
81. #13133216C2×C4semidirect
82. #13133216C2×C4semidirect
83. #13133213C2×C4semidirect
84. #13133213C2×C4semidirect
90. #13133208C2×C4semidirect
91. #13133208C2×C4semidirect
94. #13133204C2×C4semidirect
95. #13133204C2×C4semidirect
126. #13133182C2×C4semidirect
127. #13133182C2×C4semidirect
132. D4×Dic53C2×C4semidirect
133. D4×Dic53C2×C4semidirect
134. D4×Dic53C2×C4semidirect
135. D4×Dic53C2×C4semidirect
136. #13133179C2×C4semidirect
137. #13133179C2×C4semidirect
473. #1510D53semidirect
549. C53#17604semidirect

Maximal subgroups

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

subgroupindex
#202884442
#202833752
#202775772
#202732892
#202732732
#202732692
#202732602
#202732502
#202732372
#202732212
#202732202
#202732082
#202731982
C2×#168103572
C53×#15102
#1760453