Finite Group Databasebeta

← #27351050

Subgroups — #27351050

Order 13568.

948 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20283682C211yesmaximal, characteristic, complemented
2#20283381C211yesmaximal, characteristic, complemented
3#20273184C211yesmaximal, characteristic, complemented
4#20273180C211yesmaximal, characteristic, complemented
5#20273175C211yesmaximal, characteristic, complemented
6#20273162C211yesmaximal, characteristic, complemented
7#20273154C211yesmaximal, characteristic, complemented
8#20273149C211yesmaximal, characteristic, complemented
9#20273132C211yesmaximal, characteristic, complemented
10#20273128C211yesmaximal, characteristic, complemented
11#20273123C211yesmaximal, characteristic, complemented
12#20273110C211yesmaximal, characteristic, complemented
13#20273102C211yesmaximal, characteristic, complemented
14#20273097C211yesmaximal, characteristic, complemented
15C53×#3480C211yesmaximal, characteristic
16#16810754—21no—
17#16810701—21no—
18#16810695—21no—
19#16810695—21no—
20#16810684—21no—
21#16810684—21no—
22#16810680C2211yescharacteristic
23#16810680C2211yescharacteristic
24#16810676C2211yescharacteristic
25#16810676C2211yescharacteristic
26#16810676C2211yescharacteristic
27#16810676C2211yescharacteristic
28#16810676C2211yescharacteristic
29#16810647C2211yescharacteristic
30C2×C4⋊#88322C2211yescharacteristic
31#16810590—21no—
32#16810579—21no—
33C4×#11719917C2211yescharacteristic
34C4×#11719917C2211yescharacteristic
35C2×C4×#88322C2211yescharacteristic
36Q8⋊#88322C2211yescharacteristic
37Q8⋊#88322C2211yescharacteristic
38Q8⋊#88322C2211yescharacteristic
39Q8⋊#88322C2211yescharacteristic
40Q8⋊#88322C2211yescharacteristic
41Q8⋊#88322C2211yescharacteristic
42Q8⋊#88322C2211yescharacteristic
43Q8⋊#88322C2211yescharacteristic
44D4⋊#88322C2211yescharacteristic
45D4⋊#88322C2211yescharacteristic
46D4⋊#88322C2211yescharacteristic
47D4⋊#88322C2211yescharacteristic
48D4⋊#88322C2211yescharacteristic
49D4⋊#88322C2211yescharacteristic
50D4⋊#88322C2211yescharacteristic
51D4⋊#88322C2211yescharacteristic
52C53×#559—21no—
53C53×#559C411yescharacteristic
54C53×#557C411yescharacteristic
55C53×#556—21no—
56C53×#556C411yescharacteristic
57C53×#553—21no—
58C53×#553—21no—
59C53×#553C411yescharacteristic
60C53×#553C411yescharacteristic
61C53×#550C411yescharacteristic
62C53×#548C411yescharacteristic
63C53×#548C411yescharacteristic
64C53×#532—21no—
65C53×#532C2211yescharacteristic
66C53×#529—21no—
67C53×#529—21no—
68C53×#529C2211yescharacteristic
69C53×#529C2211yescharacteristic
70C4×#41×C53—21no—
71C4×#41×C53C2211yescharacteristic
72C4×#41×C53C2211yescharacteristic
73C4×#41×C53C2211yescharacteristic
74C2×C4×Q8×C53C2211yescharacteristic
75C2×#11719917—21no—
76C2×#11719917—21no—
77C2×#11719917—21no—
78C22×#88322—21no—
79C22×#88322—21no—
80C4⋊#88322—21no—
81C4⋊#88322—21no—
82C4⋊#88322—21no—
83C4⋊#88322—21no—
84C4⋊#88322—21no—
85C4⋊#88322C2311yescharacteristic
86C4⋊#88322C2311yescharacteristic
87C4⋊#88322C2311yescharacteristic
88C4⋊#88322C2311yescharacteristic
89C22⋊#88322—21no—
90C22⋊#88322—21no—
91C22⋊#88322—21no—
92C22⋊#88322—21no—
93C22⋊#88322—21no—
94C22⋊#88322—21no—
95C22⋊#88322—21no—
96#13133128—21no—
97#13133128—21no—
98#13133128—21no—
99#13133128—21no—
100C4×#88322—21no—
101C4×#88322—21no—
102C4×#88322—21no—
103C4×#88322C2311yescharacteristic
104C4×#88322C2311yescharacteristic
105C4×#88322C2311yescharacteristic
106C4×#88322C2311yescharacteristic
107C2×#41×C53—21no—
108C2×#41×C53C2×C411yescharacteristic
109C2×#41×C53C2×C411yescharacteristic
110C2×#41×C53D411yescharacteristic
111C22×Q8×C53C2×C411yescharacteristic
112C4⋊Q8×C53—21no—
113C4⋊Q8×C53C2×C411yescharacteristic
114#127×C53—21no—
115#127×C53C2×C411yescharacteristic
116#126×C53—21no—
117#126×C53—21no—
118#126×C53—21no—
119#126×C53—21no—
120#126×C53—21no—
121#126×C53—21no—
122#125×C53—21no—
123#125×C53—21no—
124#125×C53C2×C411yescharacteristic
125#125×C53C2×C411yescharacteristic
126#124×C53—21no—
127#124×C53—21no—
128#124×C53—21no—
129#124×C53—21no—
130#124×C53—21no—
131#124×C53C2×C411yescharacteristic
132#124×C53C2×C411yescharacteristic
133#123×C53—21no—
134#123×C53—21no—
135#123×C53—21no—
136#123×C53—21no—
137#123×C53—21no—
138#123×C53—21no—
139C22⋊Q8×C53—21no—
140C22⋊Q8×C53—21no—
141C22⋊Q8×C53C2×C411yescharacteristic
142C22⋊Q8×C53C2×C411yescharacteristic
143#121×C53—21no—
144#121×C53—21no—
145#121×C53—21no—
146#121×C53—21no—
147#121×C53—21no—
148#121×C53—21no—
149#121×C53—21no—
150#121×C53C2×C411yescharacteristic
151#121×C53C2×C411yescharacteristic
152#121×C53C2×C411yescharacteristic
153#121×C53C2×C411yescharacteristic
154C4×Q8×C53—21no—
155C4×Q8×C53—21no—
156C4×Q8×C53—21no—
157C4×Q8×C53—21no—
158C4×Q8×C53C2×C411yescharacteristic
159C4×Q8×C53C2×C411yescharacteristic
160C4×Q8×C53C2×C411yescharacteristic
161C4×Q8×C53C2×C411yescharacteristic
162C4×Q8×C53C2×C411yescharacteristic
163C4×Q8×C53D411yescharacteristic
164C4×Q8×C53C2311yescharacteristic
165C4×Q8×C53C2311yescharacteristic
166C4×D4×C53—21no—
167C4×D4×C53—21no—
168C4×D4×C53—21no—
169C4×D4×C53—21no—
170C4×D4×C53—21no—
171C4×D4×C53—21no—
172C4×D4×C53—21no—
173C4×D4×C53—21no—
174C4×D4×C53—21no—
175C4×D4×C53—21no—
176C4×D4×C53—21no—
177C4×D4×C53—21no—
178C4×D4×C53—21no—
179C4×D4×C53C2×C411yescharacteristic
180C4×D4×C53C2×C411yescharacteristic
181C4×D4×C53C2×C411yescharacteristic
182C4×D4×C53C2×C411yescharacteristic
183C4×D4×C53C2×C411yescharacteristic
184C4×D4×C53D411yescharacteristic
185C4×D4×C53D411yescharacteristic
186C4×D4×C53D411yescharacteristic
187C4×D4×C53C2311yescharacteristic
188C4×D4×C53C2311yescharacteristic
189#117×C53—21no—
190#117×C53—21no—
191#117×C53—21no—
192#117×C53—21no—
193#117×C53C2×C411yescharacteristic
194#117×C53C2×C411yescharacteristic
195#117×C53D411yescharacteristic
196#117×C53D411yescharacteristic
197#117×C53D411yescharacteristic
198C2×C4⋊C4×C53—21no—
199C2×C4⋊C4×C53C2×C411yescharacteristic
200C2×C42×C53—21no—
201C2×C42×C53—21no—
202C2×C42×C53—21no—
203C2×C42×C53C2311yescharacteristic
204C2×C42×C53C2311yescharacteristic
205C2×C42×C53C2311yescharacteristic
206#41×C53—22no—
207#41×C53—22no—
208#41×C53—41no—
209#41×C53—41no—
210#41×C53—41no—
211#41×C53—41no—
212#41×C53—42no—
213#41×C53—42no—
214C2×Q8×C53—21no—
215C2×Q8×C53—21no—
216C2×Q8×C53—22no—
217C2×Q8×C53—41no—
218C2×Q8×C53C22⋊C411yescharacteristic
219C2×Q8×C53C22×C411yescharacteristic
220C2×Q8×C53C22×C411yescharacteristic
221C2×D4×C53—21no—
222C2×D4×C53—21no—
223C2×D4×C53—21no—
224C2×D4×C53—21no—
225C2×D4×C53—21no—
226C2×D4×C53—21no—
227C2×D4×C53—21no—
228C2×D4×C53—21no—
229C2×D4×C53C22⋊C411yescharacteristic
230C2×D4×C53C22⋊C411yescharacteristic
231C2×D4×C53C22⋊C411yescharacteristic
232C2×D4×C53C22×C411yescharacteristic
233C2×D4×C53C22×C411yescharacteristic
234C22×C4×C53—21no—
235C22×C4×C53—21no—
236C22×C4×C53—21no—
237C22×C4×C53—21no—
238C22×C4×C53—21no—
239C22×C4×C53—21no—
240C22×C4×C53—21no—
241C22×C4×C53—21no—
242C22×C4×C53C22×C411yescharacteristic
243C22×C4×C53C22×C411yescharacteristic
244C22×C4×C53C22×C411yescharacteristic
245C22×C4×C53C2×D411yescharacteristic
246C22×C4×C53C2×D411yescharacteristic
247C22×C4×C53C2×D411yescharacteristic
248C22×C4×C53C2×D411yescharacteristic
249C22×C4×C53C2×D411yescharacteristic
250C22×C4×C53C2×D411yescharacteristic
251C4⋊C4×C53—21no—
252C4⋊C4×C53—21no—
253C4⋊C4×C53—21no—
254C4⋊C4×C53—21no—
255C4⋊C4×C53—21no—
256C4⋊C4×C53—21no—
257C4⋊C4×C53—21no—
258C4⋊C4×C53—21no—
259C4⋊C4×C53—21no—
260C4⋊C4×C53—21no—
261C4⋊C4×C53—21no—
262C4⋊C4×C53—21no—
263C4⋊C4×C53—21no—
264C4⋊C4×C53—21no—
265C4⋊C4×C53C22⋊C411yescharacteristic
266C4⋊C4×C53C22⋊C411yescharacteristic
267C4⋊C4×C53C22⋊C411yescharacteristic
268C4⋊C4×C53C22⋊C411yescharacteristic
269C4⋊C4×C53C22⋊C411yescharacteristic
270C4⋊C4×C53C22⋊C411yescharacteristic
271C4⋊C4×C53C22×C411yescharacteristic
272C4⋊C4×C53C22×C411yescharacteristic
273C4⋊C4×C53C22×C411yescharacteristic
274C4⋊C4×C53C22×C411yescharacteristic
275C22⋊C4×C53—21no—
276C22⋊C4×C53—21no—
277C22⋊C4×C53—21no—
278C22⋊C4×C53—21no—
279C22⋊C4×C53—21no—
280C22⋊C4×C53—21no—
281C22⋊C4×C53—21no—
282C22⋊C4×C53—21no—
283C22⋊C4×C53—21no—
284C22⋊C4×C53—21no—
285C22⋊C4×C53—21no—
286C22⋊C4×C53—21no—
287C22⋊C4×C53—21no—
288C22⋊C4×C53—21no—
289C22⋊C4×C53—21no—
290C22⋊C4×C53—21no—
291C22⋊C4×C53C22⋊C411yescharacteristic
292C22⋊C4×C53C22⋊C411yescharacteristic
293C22⋊C4×C53C22⋊C411yescharacteristic
294C22⋊C4×C53C22⋊C411yescharacteristic
295C22⋊C4×C53C22⋊C411yescharacteristic
296C22⋊C4×C53C22⋊C411yescharacteristic
297C42×C53—21no—
298C42×C53—21no—
299C42×C53—21no—
300C42×C53—21no—
301C42×C53—21no—
302C42×C53—21no—
303C42×C53—21no—
304C42×C53—21no—
305C42×C53C22×C411yescharacteristic
306C42×C53C22×C411yescharacteristic
307C42×C53C22×C411yescharacteristic
308C42×C53C2×D411yescharacteristic
309C42×C53C2×D411yescharacteristic
310C42×C53C2×D411yescharacteristic
311C42×C53C2×D411yescharacteristic
312C42×C53C2×D411yescharacteristic
313C42×C53C2×D411yescharacteristic
314C42×C53C2411yescharacteristic
315#11719917—42no—
316#11719917—42no—
317#11719917—42no—
318C2×#88322—21no—
319C2×#88322—21no—
320C2×#88322—21no—
321C2×#88322—21no—
322C2×#88322—21no—
323C2×#88322—21no—
324C2×#88322—21no—
325C2×#88322—21no—
326C2×#88322—42no—
327C2×#88322—42no—
328C23×C53—21no—
329C23×C53—21no—
330C23×C53C2×C22⋊C411yescharacteristic
331C23×C53C2×C22⋊C411yescharacteristic
332C23×C53C2×C22⋊C411yescharacteristic
333Q8×C53—21no—
334Q8×C53—21no—
335Q8×C53—21no—
336Q8×C53—41no—
337Q8×C53—42no—
338Q8×C53—42no—
339Q8×C53#13112yes—
340D4×C53—21no—
341D4×C53—21no—
342D4×C53—21no—
343D4×C53—21no—
344D4×C53—41no—
345D4×C53—41no—
346D4×C53—41no—
347D4×C53—42no—
348D4×C53—42no—
349D4×C53—42no—
350D4×C53—42no—
351D4×C53—42no—
352D4×C53—81no—
353D4×C53—81no—
354D4×C53—81no—
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—21no—
362C2×C4×C53—21no—
363C2×C4×C53—21no—
364C2×C4×C53—21no—
365C2×C4×C53—21no—
366C2×C4×C53—21no—
367C2×C4×C53—21no—
368C2×C4×C53—21no—
369C2×C4×C53—21no—
370C2×C4×C53—21no—
371C2×C4×C53—21no—
372C2×C4×C53—21no—
373C2×C4×C53—41no—
374C2×C4×C53—41no—
375C2×C4×C53—41no—
376C2×C4×C53—42no—
377C2×C4×C53—42no—
378C2×C4×C53—42no—
379C2×C4×C53—41no—
380C2×C4×C53—41no—
381C2×C4×C53—41no—
382C2×C4×C53—41no—
383C2×C4×C53—81no—
384C2×C4×C53—81no—
385C2×C4×C53—81no—
386C2×C4×C53C2×C22⋊C411yescharacteristic
387C2×C4×C53C2×C22⋊C411yescharacteristic
388C2×C4×C53C2×C22⋊C411yescharacteristic
389C2×C4×C53C2×C22⋊C411yescharacteristic
390C2×C4×C53C2×C22⋊C411yescharacteristic
391C2×C4×C53C2×C22⋊C411yescharacteristic
392C2×C4×C53C2×C22⋊C411yescharacteristic
393C2×C4×C53C2×C22⋊C411yescharacteristic
394C2×C4×C53C2×C22⋊C411yescharacteristic
395C2×C4×C53C23×C411yescharacteristic
396C2×C4×C53C22×D411yescharacteristic
397C2×C4×C53C22×D411yescharacteristic
398#88322—22no—
399#88322—41no—
400#88322—41no—
401#88322—41no—
402#88322—41no—
403#88322—41no—
404#88322—41no—
405#88322—41no—
406#17516—531nomaximal, Sylow
407C22×C53—21no—
408C22×C53—21no—
409C22×C53—21no—
410C22×C53—21no—
411C22×C53—21no—
412C22×C53—21no—
413C22×C53—21no—
414C22×C53—21no—
415C22×C53—21no—
416C22×C53—41no—
417C22×C53—41no—
418C22×C53—41no—
419C22×C53—41no—
420C22×C53—41no—
421C22×C53—41no—
422C22×C53C22×C22⋊C411yescharacteristic
423C4×C53—21no—
424C4×C53—21no—
425C4×C53—21no—
426C4×C53—22no—
427C4×C53—21no—
428C4×C53—21no—
429C4×C53—21no—
430C4×C53—21no—
431C4×C53—21no—
432C4×C53—21no—
433C4×C53—21no—
434C4×C53—41no—
435C4×C53—41no—
436C4×C53—41no—
437C4×C53—41no—
438C4×C53—41no—
439C4×C53C2×#13111yescharacteristic
440C4×C53#56811yescharacteristic
441C4×C53#57511yescharacteristic
442C4×C53#57511yescharacteristic
443#3480D5311yescharacteristic
444#2965—531no—
445#2925—531no—
446#1496—531no—
447#1495—531no—
448#1494—531no—
449#1491—531no—
450#1489—531no—
451#1488—531no—
452#1484—531no—
453#1483—531no—
454#1482—531no—
455#1479—531no—
456#1477—531no—
457#1476—531no—
458C2×C53—41no—
459C2×C53—41no—
460C2×C53—41no—
461C2×C53—81no—
462C2×C53—81no—
463C2×C53#288011yescharacteristic
464C2×C53#289611yescharacteristic
465C2×C53#290111yescharacteristic
466#559—21no—
467#559Dic5311yescharacteristic
468#557Dic5311yescharacteristic
469#556—21no—
470#556Dic5311yescharacteristic
471#553—21no—
472#553—21no—
473#553Dic5311yescharacteristic
474#553Dic5311yescharacteristic
475#550Dic5311yescharacteristic
476#548Dic5311yescharacteristic
477#548Dic5311yescharacteristic
478#532—21no—
479#532C2×D5311yescharacteristic
480#529—21no—
481#529—21no—
482#529C2×D5311yescharacteristic
483#529C2×D5311yescharacteristic
484C4×#41—21no—
485C4×#41C2×D5311yescharacteristic
486C4×#41C2×D5311yescharacteristic
487C4×#41C2×D5311yescharacteristic
488C2×C4×Q8C2×D5311yescharacteristic
489#446—1061no—
490#436—1061no—
491#435—1061no—
492#435—1061no—
493#433—1061no—
494#433—1061no—
495#432—531no—
496#432—531no—
497#431—531no—
498#431—531no—
499#431—531no—
500#431—531no—
501#431—531no—
502#423—531no—
503C2×C4⋊C8—531no—
504#408—1061no—
505#405—1061no—
506C4×M16—531no—
507C4×M16—531no—
508C2×C4×C8—531no—
509Q8⋊C8—531no—
510Q8⋊C8—531no—
511Q8⋊C8—531no—
512Q8⋊C8—531no—
513Q8⋊C8—531no—
514Q8⋊C8—531no—
515Q8⋊C8—531no—
516Q8⋊C8—531no—
517D4⋊C8—531no—
518D4⋊C8—531no—
519D4⋊C8—531no—
520D4⋊C8—531no—
521D4⋊C8—531no—
522D4⋊C8—531no—
523D4⋊C8—531no—
524D4⋊C8—531no—
525C53#1751611yescharacteristic, complemented, Sylow
526C2×#41—21no—
527C2×#41C2×Dic5311yescharacteristic
528C2×#41C2×Dic5311yescharacteristic
529C2×#41C22⋊D5311yescharacteristic
530C22×Q8C2×Dic5311yescharacteristic
531C2×M16—1061no—
532C2×M16—1061no—
533C2×M16—1061no—
534C22×C8—1061no—
535C22×C8—1061no—
536C4⋊Q8—21no—
537C4⋊Q8C2×Dic5311yescharacteristic
538#127—21no—
539#127C2×Dic5311yescharacteristic
540#126—21no—
541#126—21no—
542#126—21no—
543#126—21no—
544#126—21no—
545#126—21no—
546#125—21no—
547#125—21no—
548#125C2×Dic5311yescharacteristic
549#125C2×Dic5311yescharacteristic
550#124—21no—
551#124—21no—
552#124—21no—
553#124—21no—
554#124—21no—
555#124C2×Dic5311yescharacteristic
556#124C2×Dic5311yescharacteristic
557#123—21no—
558#123—21no—
559#123—21no—
560#123—21no—
561#123—21no—
562#123—21no—
563C22⋊Q8—21no—
564C22⋊Q8—21no—
565C22⋊Q8C2×Dic5311yescharacteristic
566C22⋊Q8C2×Dic5311yescharacteristic
567#121—21no—
568#121—21no—
569#121—21no—
570#121—21no—
571#121—21no—
572#121—21no—
573#121—21no—
574#121C2×Dic5311yescharacteristic
575#121C2×Dic5311yescharacteristic
576#121C2×Dic5311yescharacteristic
577#121C2×Dic5311yescharacteristic
578C4×Q8—21no—
579C4×Q8—21no—
580C4×Q8—21no—
581C4×Q8—21no—
582C4×Q8C2×Dic5311yescharacteristic
583C4×Q8C2×Dic5311yescharacteristic
584C4×Q8C2×Dic5311yescharacteristic
585C4×Q8C2×Dic5311yescharacteristic
586C4×Q8C2×Dic5311yescharacteristic
587C4×Q8C22⋊D5311yescharacteristic
588C4×Q8C22×D5311yescharacteristic
589C4×Q8C22×D5311yescharacteristic
590C4×D4—21no—
591C4×D4—21no—
592C4×D4—21no—
593C4×D4—21no—
594C4×D4—21no—
595C4×D4—21no—
596C4×D4—21no—
597C4×D4—21no—
598C4×D4—21no—
599C4×D4—21no—
600C4×D4—21no—
601C4×D4—21no—
602C4×D4—21no—
603C4×D4C2×Dic5311yescharacteristic
604C4×D4C2×Dic5311yescharacteristic
605C4×D4C2×Dic5311yescharacteristic
606C4×D4C2×Dic5311yescharacteristic
607C4×D4C2×Dic5311yescharacteristic
608C4×D4C22⋊D5311yescharacteristic
609C4×D4C22⋊D5311yescharacteristic
610C4×D4C22⋊D5311yescharacteristic
611C4×D4C22×D5311yescharacteristic
612C4×D4C22×D5311yescharacteristic
613#117—21no—
614#117—21no—
615#117—21no—
616#117—21no—
617#117C2×Dic5311yescharacteristic
618#117C2×Dic5311yescharacteristic
619#117C22⋊D5311yescharacteristic
620#117C22⋊D5311yescharacteristic
621#117C22⋊D5311yescharacteristic
622C2×C4⋊C4—21no—
623C2×C4⋊C4C2×Dic5311yescharacteristic
624C2×C42—21no—
625C2×C42—21no—
626C2×C42—21no—
627C2×C42C22×D5311yescharacteristic
628C2×C42C22×D5311yescharacteristic
629C2×C42C22×D5311yescharacteristic
630C4⋊C8—531no—
631C4⋊C8—531no—
632C4⋊C8—531no—
633C4⋊C8—531no—
634C4⋊C8—1061no—
635C4⋊C8—1061no—
636C4⋊C8—1061no—
637C4⋊C8—1061no—
638C4⋊C8—1061no—
639C22⋊C8—1061no—
640C22⋊C8—1061no—
641C22⋊C8—1061no—
642C22⋊C8—1061no—
643C22⋊C8—1061no—
644C22⋊C8—1061no—
645C22⋊C8—1061no—
646#97—1061no—
647#97—1061no—
648#97—1061no—
649#97—1061no—
650C4×C8—531no—
651C4×C8—531no—
652C4×C8—531no—
653C4×C8—531no—
654C4×C8—1061no—
655C4×C8—1061no—
656C4×C8—1061no—
657#41—22no—
658#41—22no—
659#41—41no—
660#41—41no—
661#41—41no—
662#41—41no—
663#41—42no—
664#41—42no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8—22no—
668C2×Q8—41no—
669C2×Q8C22⋊Dic5311yescharacteristic
670C2×Q8C22×Dic5311yescharacteristic
671C2×Q8C22×Dic5311yescharacteristic
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4C22⋊Dic5311yescharacteristic
681C2×D4C22⋊Dic5311yescharacteristic
682C2×D4C22⋊Dic5311yescharacteristic
683C2×D4C22×Dic5311yescharacteristic
684C2×D4C22×Dic5311yescharacteristic
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4C22×Dic5311yescharacteristic
694C22×C4C22×Dic5311yescharacteristic
695C22×C4C22×Dic5311yescharacteristic
696C22×C4C2×C22⋊D5311yescharacteristic
697C22×C4C2×C22⋊D5311yescharacteristic
698C22×C4C2×C22⋊D5311yescharacteristic
699C22×C4C2×C22⋊D5311yescharacteristic
700C22×C4C2×C22⋊D5311yescharacteristic
701C22×C4C2×C22⋊D5311yescharacteristic
702M16—2122no—
703M16—2122no—
704M16—2122no—
705C2×C8—1061no—
706C2×C8—1061no—
707C2×C8—1061no—
708C2×C8—1061no—
709C2×C8—1061no—
710C2×C8—1061no—
711C2×C8—1061no—
712C2×C8—1061no—
713C2×C8—2122no—
714C2×C8—2122no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4C22⋊Dic5311yescharacteristic
730C4⋊C4C22⋊Dic5311yescharacteristic
731C4⋊C4C22⋊Dic5311yescharacteristic
732C4⋊C4C22⋊Dic5311yescharacteristic
733C4⋊C4C22⋊Dic5311yescharacteristic
734C4⋊C4C22⋊Dic5311yescharacteristic
735C4⋊C4C22×Dic5311yescharacteristic
736C4⋊C4C22×Dic5311yescharacteristic
737C4⋊C4C22×Dic5311yescharacteristic
738C4⋊C4C22×Dic5311yescharacteristic
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4C22⋊Dic5311yescharacteristic
756C22⋊C4C22⋊Dic5311yescharacteristic
757C22⋊C4C22⋊Dic5311yescharacteristic
758C22⋊C4C22⋊Dic5311yescharacteristic
759C22⋊C4C22⋊Dic5311yescharacteristic
760C22⋊C4C22⋊Dic5311yescharacteristic
761C42—21no—
762C42—21no—
763C42—21no—
764C42—21no—
765C42—21no—
766C42—21no—
767C42—21no—
768C42—21no—
769C42C22×Dic5311yescharacteristic
770C42C22×Dic5311yescharacteristic
771C42C22×Dic5311yescharacteristic
772C42C2×C22⋊D5311yescharacteristic
773C42C2×C22⋊D5311yescharacteristic
774C42C2×C22⋊D5311yescharacteristic
775C42C2×C22⋊D5311yescharacteristic
776C42C2×C22⋊D5311yescharacteristic
777C42C2×C22⋊D5311yescharacteristic
778C42C23×D5311yescharacteristic
779C23—21no—
780C23—21no—
781C23C2×C22⋊Dic5311yescharacteristic
782C23C2×C22⋊Dic5311yescharacteristic
783C23C2×C22⋊Dic5311yescharacteristic
784Q8—21no—
785Q8—21no—
786Q8—21no—
787Q8—41no—
788Q8—42no—
789Q8—42no—
790Q8#1313322412yes—
791D4—21no—
792D4—21no—
793D4—21no—
794D4—21no—
795D4—41no—
796D4—41no—
797D4—41no—
798D4—42no—
799D4—42no—
800D4—42no—
801D4—42no—
802D4—42no—
803D4—81no—
804D4—81no—
805D4—81no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—81no—
835C2×C4—81no—
836C2×C4—81no—
837C2×C4C2×C22⋊Dic5311yescharacteristic
838C2×C4C2×C22⋊Dic5311yescharacteristic
839C2×C4C2×C22⋊Dic5311yescharacteristic
840C2×C4C2×C22⋊Dic5311yescharacteristic
841C2×C4C2×C22⋊Dic5311yescharacteristic
842C2×C4C2×C22⋊Dic5311yescharacteristic
843C2×C4C2×C22⋊Dic5311yescharacteristic
844C2×C4C2×C22⋊Dic5311yescharacteristic
845C2×C4C2×C22⋊Dic5311yescharacteristic
846C2×C4C23×Dic5311yescharacteristic
847C2×C4C22×C22⋊D5311yescharacteristic
848C2×C4C22×C22⋊D5311yescharacteristic
849C8—1062no—
850C8—2121no—
851C8—2121no—
852C8—2121no—
853C8—2121no—
854C8—2121no—
855C8—2121no—
856C8—2121no—
857C22—21no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22C22×C22⋊Dic5311yescharacteristic
873C4—21no—
874C4—21no—
875C4—21no—
876C4—22no—
877C4—21no—
878C4—21no—
879C4—21no—
880C4—21no—
881C4—21no—
882C4—21no—
883C4—21no—
884C4—41no—
885C4—41no—
886C4—41no—
887C4—41no—
888C4—41no—
889C4C2×#1313322411yescharacteristic
890C4#1681139011yescharacteristic
891C4#1681142111yescharacteristic
892C4#1681142111yescharacteristic
893C2—41no—
894C2—41no—
895C2—41no—
896C2—81no—
897C2—81no—
898C2#2028316411yescharacteristic
899C2#2028323411yescharacteristic
900C2#2028326211yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC42C23×D53
Fitting, prime radicalC53×#3480C2
socleC22×C53C22×C22⋊C4
cosocleC42×C53C24
hypercenter#3480D53
hypocenterC53#17516
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #3480

Complements

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

NH ≅ G/Ntype
1. #20283682C2semidirect
2. #20283381C2semidirect
3. #20273184C2semidirect
4. #20273180C2semidirect
5. #20273175C2semidirect
6. #20273162C2semidirect
7. #20273154C2semidirect
8. #20273149C2semidirect
9. #20273132C2semidirect
10. #20273128C2semidirect
11. #20273123C2semidirect
12. #20273110C2semidirect
13. #20273102C2semidirect
14. #20273097C2semidirect
525. C53#17516semidirect

Maximal subgroups

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

subgroupindex
#202836822
#202833812
#202731842
#202731802
#202731752
#202731622
#202731542
#202731492
#202731322
#202731282
#202731232
#202731102
#202731022
#202730972
C53×#34802
#1751653