Finite Group Databasebeta

← #28252623

Subgroups — #28252623

Order 13568.

2010 conjugacy classes of subgroups.

The subgroup lattice has 1704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#541×D53C211yesmaximal, characteristic, complemented
2#20287915C211yesmaximal, characteristic
3#20285017C211yesmaximal, characteristic, complemented
4#20285014C211yesmaximal, characteristic, complemented
5#20285013C211yesmaximal, characteristic, complemented
6#20285012C211yesmaximal, characteristic, complemented
7#20284969C211yesmaximal, characteristic, complemented
8#20284966C211yesmaximal, characteristic, complemented
9#20284965C211yesmaximal, characteristic, complemented
10#20284964C211yesmaximal, characteristic, complemented
11#20284932C211yesmaximal, characteristic, complemented
12#20284931C211yesmaximal, characteristic, complemented
13#20284930C211yesmaximal, characteristic, complemented
14#20284929C211yesmaximal, characteristic, complemented
15#20284924C211yesmaximal, characteristic, complemented
16#20284923C211yesmaximal, characteristic, complemented
17#20284922C211yesmaximal, characteristic, complemented
18#20284660C211yesmaximal, characteristic, complemented
19#20284658C211yesmaximal, characteristic, complemented
20#20284534C211yesmaximal, characteristic, complemented
21#20284532C211yesmaximal, characteristic, complemented
22#20284199C211yesmaximal, characteristic, complemented
23#20284197C211yesmaximal, characteristic, complemented
24#20283972C211yesmaximal, characteristic
25#20283972C211yesmaximal, characteristic
26#20283537C211yesmaximal, characteristic, complemented
27C4×#13133249C211yesmaximal, characteristic, complemented
28#20283531C211yesmaximal, characteristic, complemented
29C4×#13133246C211yesmaximal, characteristic, complemented
30#20283349C211yesmaximal, characteristic, complemented
31C53×#3120C211yesmaximal, characteristic, complemented
32C2×#41×D53C2211yescharacteristic
33C2×#13133249C2211yescharacteristic
34C2×#13133249C2211yescharacteristic
35C2×#13133246C2211yescharacteristic
36C2×#13133246C2211yescharacteristic
37#16811236C2211yescharacteristic
38#16811235C2211yescharacteristic, complemented
39#16811234C2211yescharacteristic
40#16811233C2211yescharacteristic, complemented
41#16811233C2211yescharacteristic, complemented
42#16811232—21no—
43#16811232—21no—
44#16811231C2211yescharacteristic
45#16811231C2211yescharacteristic
46#16811230—21no—
47#16811230—21no—
48C4⋊Q8×D53C2211yescharacteristic, complemented
49#126×D53—21no—
50#126×D53—21no—
51#125×D53—21no—
52#125×D53—21no—
53#125×D53C2211yescharacteristic, complemented
54C22⋊Q8×D53C2211yescharacteristic
55C22⋊Q8×D53C2211yescharacteristic
56#16811106C2211yescharacteristic
57#16811104—21no—
58#16811104C2211yescharacteristic
59#16811103—21no—
60#16811103C2211yescharacteristic
61#16811099C2211yescharacteristic
62#16811099C2211yescharacteristic
63#16811095—21no—
64#16811095—21no—
65#16811095C2211yescharacteristic
66#16811095C2211yescharacteristic
67C4×#11719949C2211yescharacteristic
68C4×#11719949C2211yescharacteristic
69C4×#11719947—21no—
70C4×#11719947—21no—
71C4×#11719947C2211yescharacteristic
72C4×#11719947C2211yescharacteristic
73C4×Q8×D53C2211yescharacteristic, complemented
74C4×Q8×D53C2211yescharacteristic, complemented
75C2×#13133175—21no—
76C2×#13133175C2211yescharacteristic
77#117×D53—21no—
78#117×D53C2211yescharacteristic
79#16810967C2211yescharacteristic
80#16810967C2211yescharacteristic
81#16810966C2211yescharacteristic
82#16810966C2211yescharacteristic
83#16810963C2211yescharacteristic
84#16810963C2211yescharacteristic
85#16810962C2211yescharacteristic
86#16810962C2211yescharacteristic
87#16810959C2211yescharacteristic, complemented
88#16810958C2211yescharacteristic, complemented
89#16810956C2211yescharacteristic, complemented
90#16810954C2211yescharacteristic, complemented
91#16810953C2211yescharacteristic, complemented
92#16810951C2211yescharacteristic, complemented
93#16810933C2211yescharacteristic, complemented
94#16810932C2211yescharacteristic, complemented
95#16810931C2211yescharacteristic, complemented
96#16810930C2211yescharacteristic, complemented
97#16810929C2211yescharacteristic, complemented
98#16810928C2211yescharacteristic, complemented
99#16810927C2211yescharacteristic, complemented
100#16810926C2211yescharacteristic, complemented
101#16810925C2211yescharacteristic, complemented
102#16810924C2211yescharacteristic, complemented
103#16810923C2211yescharacteristic, complemented
104#16810922C2211yescharacteristic, complemented
105#16810921C2211yescharacteristic, complemented
106#16810920C2211yescharacteristic, complemented
107#16810834C2211yescharacteristic, complemented
108#16810833C2211yescharacteristic, complemented
109#16810832C2211yescharacteristic, complemented
110#16810832C2211yescharacteristic, complemented
111#16810831C2211yescharacteristic, complemented
112#16810831C2211yescharacteristic, complemented
113#16810830C2211yescharacteristic, complemented
114#16810829C2211yescharacteristic, complemented
115#16810828C2211yescharacteristic, complemented
116#16810827C2211yescharacteristic, complemented
117#16810827C2211yescharacteristic, complemented
118#16810826C2211yescharacteristic, complemented
119#16810826C2211yescharacteristic, complemented
120#16810825C2211yescharacteristic, complemented
121#16810787C2211yescharacteristic
122#16810787C2211yescharacteristic
123#16810785C2211yescharacteristic
124#16810785C2211yescharacteristic
125#16810783C2211yescharacteristic
126#16810783C2211yescharacteristic
127#16810780C2211yescharacteristic
128#16810780C2211yescharacteristic
129#16810777C2211yescharacteristic
130#16810777C2211yescharacteristic
131#16810775C2211yescharacteristic
132#16810775C2211yescharacteristic
133#16810772C2211yescharacteristic
134#16810772C2211yescharacteristic
135#16810731C2211yescharacteristic, complemented
136#16810730C2211yescharacteristic, complemented
137#16810729C2211yescharacteristic, complemented
138#16810728C2211yescharacteristic, complemented
139#16810728C2211yescharacteristic, complemented
140#16810727C2211yescharacteristic, complemented
141#16810727C2211yescharacteristic, complemented
142#16810726C2211yescharacteristic, complemented
143#16810725C2211yescharacteristic, complemented
144#16810724C2211yescharacteristic, complemented
145#16810723C2211yescharacteristic, complemented
146#16810722C2211yescharacteristic, complemented
147#16810721C2211yescharacteristic, complemented
148#16810720C2211yescharacteristic, complemented
149C4×Dic212C2211yescharacteristic, complemented
150Q16×Dic53C2211yescharacteristic, complemented
151#16810717C2211yescharacteristic, complemented
152C4×#11719925C2211yescharacteristic, complemented
153C4×#11719925C2211yescharacteristic, complemented
154#16810715C2211yescharacteristic, complemented
155#16810715C2211yescharacteristic, complemented
156#16810714C2211yescharacteristic, complemented
157C4×#11719913C2211yescharacteristic, complemented
158SD16×Dic53C2211yescharacteristic, complemented
159C4×#11719924C2211yescharacteristic, complemented
160#16810710C2211yescharacteristic, complemented
161C4×#11719923C2211yescharacteristic, complemented
162#16810708C2211yescharacteristic, complemented
163#16810685C2211yescharacteristic
164#16810684C2211yescharacteristic, complemented
165#16810683C2211yescharacteristic
166#16810683C2211yescharacteristic
167#16810682C2211yescharacteristic
168#16810681C2211yescharacteristic, complemented
169#16810681C2211yescharacteristic, complemented
170#16810664C2211yescharacteristic, complemented
171#16810664C2211yescharacteristic, complemented
172#16810662C2211yescharacteristic, complemented
173#16810662C2211yescharacteristic, complemented
174#16810645C2211yescharacteristic, complemented
175#16810645C2211yescharacteristic, complemented
176#16810630C2211yescharacteristic, complemented
177#16810630C2211yescharacteristic, complemented
178#16810630C2211yescharacteristic, complemented
179#16810630C2211yescharacteristic, complemented
180#16810623C2211yescharacteristic
181#16810623C2211yescharacteristic
182#16810621C2211yescharacteristic
183#16810621C2211yescharacteristic
184#16810585C2211yescharacteristic
185#16810585C2211yescharacteristic
186#16810575C2211yescharacteristic, complemented
187C4×#11719912C2211yescharacteristic, complemented
188C53×#541C2211yescharacteristic, complemented
189C53×#520C2211yescharacteristic
190C53×#484C2211yescharacteristic, complemented
191C53×#483C2211yescharacteristic, complemented
192C53×#479C2211yescharacteristic, complemented
193C53×#478C2211yescharacteristic, complemented
194C53×#462C2211yescharacteristic, complemented
195C53×#461C2211yescharacteristic, complemented
196C53×#452C2211yescharacteristic
197C53×#452C2211yescharacteristic
198C53×#441C2211yescharacteristic, complemented
199C53×#440C2211yescharacteristic, complemented
200C4×Q16×C53C2211yescharacteristic, complemented
201C4×SD16×C53C2211yescharacteristic, complemented
202C53×#433C2211yescharacteristic, complemented
203C2×#11719949C2311yescharacteristic
204C2×#11719945—21no—
205C2×#11719945C2311yescharacteristic
206C2×#11719947—21no—
207C2×#11719947C2311yescharacteristic
208#41×D53—24no—
209#41×D53—24no—
210C2×Q8×D53C2311yescharacteristic
211C2×Q8×D53C2311yescharacteristic
212C2×Q8×D53C2311yescharacteristic
213C2×D4×D53—21no—
214C2×D4×D53C2311yescharacteristic
215C22×C4×D53—21no—
216C22×C4×D53C2311yescharacteristic
217#13133249—24no—
218#13133249—24no—
219#13133246—24no—
220#13133246—24no—
221C2×Dic212C2311yescharacteristic
222C2×Dic212C2311yescharacteristic
223C2×#11719925C2311yescharacteristic
224C2×#11719925C2311yescharacteristic
225C2×#11719925C2311yescharacteristic
226C2×#11719925C2311yescharacteristic
227C2×#11719913C2311yescharacteristic
228C2×#11719913C2311yescharacteristic
229C2×#11719923C2311yescharacteristic
230C2×#11719923C2311yescharacteristic
231C2×#11719924C2311yescharacteristic
232C2×#11719924C2311yescharacteristic
233C2×#11719912C2311yescharacteristic
234C2×#11719912C2311yescharacteristic
235C2×#11719912C2311yescharacteristic
236C2×#11719912C2311yescharacteristic
237#13133217C2311yescharacteristic
238#13133216—21no—
239#13133216—21no—
240#13133215C2311yescharacteristic
241#13133215C2311yescharacteristic
242#13133212—21no—
243#13133212—21no—
244#13133212—21no—
245#13133212—21no—
246#13133212—21no—
247#13133212—21no—
248#13133211—21no—
249#13133211—21no—
250#13133210—21no—
251#13133210—21no—
252#13133210—21no—
253#13133210—21no—
254#13133210—21no—
255#13133210—21no—
256#13133209—21no—
257#13133209—21no—
258#13133209C2311yescharacteristic
259#13133208—21no—
260#13133208—21no—
261#13133208—21no—
262#13133208—21no—
263#13133208C2311yescharacteristic
264#13133208C2311yescharacteristic
265#13133207—21no—
266#13133207—21no—
267#13133207—21no—
268#13133207—21no—
269#13133207—21no—
270#13133207—21no—
271#13133207—21no—
272#13133207—21no—
273#13133207—21no—
274#13133207—21no—
275#13133197C2311yescharacteristic
276#13133197C2311yescharacteristic
277#13133196C2311yescharacteristic
278#13133196C2311yescharacteristic
279#13133195—21no—
280#13133195—21no—
281#13133194—21no—
282#13133194—21no—
283#13133193C2311yescharacteristic
284#13133193C2311yescharacteristic
285Q8×Dic53C2311yescharacteristic
286Q8×Dic53C2311yescharacteristic
287Q8×Dic53C2311yescharacteristic
288Q8×Dic53C2311yescharacteristic
289C4×Dic106—21no—
290C4×Dic106—21no—
291C4×Dic106—21no—
292C4×Dic106—21no—
293C4×Dic106C2311yescharacteristic
294C4×Dic106C2311yescharacteristic
295C4×Dic106C2311yescharacteristic
296C4×Dic106C2311yescharacteristic
297#13133182—21no—
298#13133182—21no—
299#13133182—21no—
300#13133182—21no—
301#13133182C2311yescharacteristic
302#13133182C2311yescharacteristic
303#13133182C2311yescharacteristic
304#13133182C2311yescharacteristic
305C4×D212—21no—
306C4×D212—21no—
307C4×D212C2311yescharacteristic
308C4×D212C2311yescharacteristic
309D4×Dic53—21no—
310D4×Dic53—21no—
311D4×Dic53C2311yescharacteristic
312D4×Dic53C2311yescharacteristic
313#13133179—21no—
314#13133179—21no—
315#13133179C2311yescharacteristic
316#13133179C2311yescharacteristic
317C4×C22⋊D53—21no—
318C4×C22⋊D53—21no—
319C4×C22⋊D53—21no—
320C4×C22⋊D53—21no—
321C4×C22⋊D53—21no—
322C4×C22⋊D53—21no—
323#13133177—21no—
324#13133177—21no—
325#13133177—21no—
326#13133177—21no—
327#13133177—21no—
328#13133177—21no—
329#13133176—21no—
330#13133176C2311yescharacteristic
331#13133175—21no—
332#13133175—21no—
333#13133175—21no—
334#13133175—21no—
335#13133175—21no—
336#13133175—21no—
337#13133175—21no—
338#13133175—21no—
339#13133175D411yescharacteristic
340#13133175D411yescharacteristic
341#13133175C2311yescharacteristic
342#13133175C2311yescharacteristic
343#13133175C2311yescharacteristic
344#13133175C2311yescharacteristic
345#13133174—21no—
346#13133174—21no—
347#13133174C2311yescharacteristic
348#13133174C2311yescharacteristic
349#13133173—21no—
350#13133173—21no—
351#13133173D411yescharacteristic
352#13133173D411yescharacteristic
353C2×C4⋊Dic53—21no—
354C2×C4⋊Dic53C2311yescharacteristic
355C4⋊C4×D53—21no—
356C4⋊C4×D53—21no—
357C4⋊C4×D53—21no—
358C4⋊C4×D53—21no—
359C4⋊C4×D53—21no—
360C4⋊C4×D53—21no—
361C4⋊C4×D53—21no—
362C4⋊C4×D53—21no—
363C4⋊C4×D53—21no—
364C4⋊C4×D53—21no—
365C4⋊C4×D53D411yescharacteristic
366C4⋊C4×D53D411yescharacteristic
367C4⋊C4×D53C2311yescharacteristic
368C4⋊C4×D53C2311yescharacteristic
369C2×#11719921—21no—
370C2×#11719921—21no—
371C2×#11719921—21no—
372C22⋊C4×D53—21no—
373C22⋊C4×D53—21no—
374C22⋊C4×D53—21no—
375C22⋊C4×D53—21no—
376C22⋊C4×D53D411yescharacteristic
377C22⋊C4×D53D411yescharacteristic
378C2×C4×Dic53—21no—
379C2×C4×Dic53—21no—
380C2×C4×Dic53—21no—
381C42×D53—21no—
382C42×D53—21no—
383C42×D53—21no—
384C42×D53—21no—
385C42×D53C2311yescharacteristic
386C42×D53C2311yescharacteristic
387#13133151C2311yescharacteristic
388#13133151C2311yescharacteristic
389#13133150C2311yescharacteristic
390#13133150C2311yescharacteristic
391#13133150C2311yescharacteristic
392#13133150C2311yescharacteristic
393#13133149C2311yescharacteristic
394#13133149C2311yescharacteristic
395#13133148C2311yescharacteristic
396#13133148C2311yescharacteristic
397#13133148C2311yescharacteristic
398#13133148C2311yescharacteristic
399C4⋊#88322C2311yescharacteristic
400C4⋊#88322C2311yescharacteristic
401#13133146C2311yescharacteristic
402#13133146C2311yescharacteristic
403#13133146C2311yescharacteristic
404#13133146C2311yescharacteristic
405#13133142C2311yescharacteristic
406#13133142C2311yescharacteristic
407#13133142C2311yescharacteristic
408#13133142C2311yescharacteristic
409#13133142C2311yescharacteristic
410#13133142C2311yescharacteristic
411#13133141C2311yescharacteristic
412#13133141C2311yescharacteristic
413#13133141C2311yescharacteristic
414#13133141C2311yescharacteristic
415#13133141C2311yescharacteristic
416#13133141C2311yescharacteristic
417#13133140C2311yescharacteristic
418#13133140C2311yescharacteristic
419#13133140C2311yescharacteristic
420#13133140C2311yescharacteristic
421#13133140C2311yescharacteristic
422#13133140C2311yescharacteristic
423#13133139C2311yescharacteristic
424#13133139C2311yescharacteristic
425#13133138C2311yescharacteristic
426#13133138C2311yescharacteristic
427#13133137C2311yescharacteristic
428#13133137C2311yescharacteristic
429C22⋊#88322C2311yescharacteristic
430C22⋊#88322C2311yescharacteristic
431#13133129C2311yescharacteristic
432#13133129C2311yescharacteristic
433#13133129C2311yescharacteristic
434#13133129C2311yescharacteristic
435#13133128C2311yescharacteristic
436#13133127C2311yescharacteristic
437#13133127C2311yescharacteristic
438C4×#88322C2311yescharacteristic
439C8×Dic53C2311yescharacteristic
440C8×Dic53C2311yescharacteristic
441C2×#41×C53C2311yescharacteristic
442C2×Q16×C53C2311yescharacteristic
443C2×Q16×C53C2311yescharacteristic
444C2×SD16×C53C2311yescharacteristic
445C2×SD16×C53C2311yescharacteristic
446C4⋊Q8×C53C2311yescharacteristic
447#126×C53—21no—
448#126×C53—21no—
449#125×C53—21no—
450#125×C53—21no—
451#125×C53C2311yescharacteristic
452C22⋊Q8×C53C2311yescharacteristic
453C22⋊Q8×C53C2311yescharacteristic
454C4×Q8×C53C2311yescharacteristic
455C4×Q8×C53C2311yescharacteristic
456C4×Q8×C53C2311yescharacteristic
457C4×Q8×C53C2311yescharacteristic
458C4×D4×C53—21no—
459C4×D4×C53—21no—
460C4×D4×C53C2311yescharacteristic
461C4×D4×C53C2311yescharacteristic
462#117×C53—21no—
463#117×C53C2311yescharacteristic
464C2×C4⋊C4×C53—21no—
465C2×C4⋊C4×C53C2311yescharacteristic
466#107×C53C2311yescharacteristic
467#107×C53C2311yescharacteristic
468#106×C53C2311yescharacteristic
469#106×C53C2311yescharacteristic
470C4⋊C8×C53C2311yescharacteristic
471C4⋊C8×C53C2311yescharacteristic
472#103×C53C2311yescharacteristic
473#103×C53C2311yescharacteristic
474#103×C53C2311yescharacteristic
475#103×C53C2311yescharacteristic
476#103×C53C2311yescharacteristic
477#103×C53C2311yescharacteristic
478#102×C53C2311yescharacteristic
479#102×C53C2311yescharacteristic
480C22⋊C8×C53C2311yescharacteristic
481C22⋊C8×C53C2311yescharacteristic
482#97×C53C2311yescharacteristic
483C4×C8×C53C2311yescharacteristic
484C23×D53—21no—
485C23×D53C2×D411yescharacteristic
486#41×C53—22no—
487#41×C53—22no—
488C2×Q8×C53C2411yescharacteristic
489C2×Q8×C53C2411yescharacteristic
490C2×Q8×C53C2411yescharacteristic
491C2×D4×C53—21no—
492C2×D4×C53C2411yescharacteristic
493C22×C4×C53—21no—
494C22×C4×C53—21no—
495C22×C4×C53—21no—
496C22×C4×C53—21no—
497C22×C4×C53C2411yescharacteristic
498C2×C22⋊D53—21no—
499C2×C22⋊D53—21no—
500C2×C22⋊D53—21no—
501C22×Dic53—21no—
502C22×Dic53—21no—
503C22×Dic53—21no—
504C22×Dic53—21no—
505C22×Dic53C2×D411yescharacteristic
506#11719949—22no—
507#11719949#4114yes—
508Q8×D53—22no—
509Q8×D53—22no—
510Q8×D53—22no—
511Q8×D53—22no—
512Q8×D53—22no—
513Q8×D53—22no—
514#11719947—28no—
515#11719947—22no—
516#11719947#4114yes—
517D4×D53—28no—
518D4×D53—22no—
519D4×D53—22no—
520#11719945—28no—
521#11719945—22no—
522#11719945—22no—
523C2×D212—21no—
524C2×D212C2411yescharacteristic
525C2×C4×D53—28no—
526C2×C4×D53—21no—
527C2×C4×D53—21no—
528C2×C4×D53—21no—
529C2×C4×D53—22no—
530C2×C4×D53—22no—
531C2×C4×D53—21no—
532C2×C4×D53—21no—
533C2×C4×D53—21no—
534C2×C4×D53—21no—
535C2×C4×D53—21no—
536C2×C4×D53—21no—
537C2×C4×D53—21no—
538C2×C4×D53—21no—
539C2×C4×D53C2×D411yescharacteristic
540C2×C4×D53C2×D411yescharacteristic
541C2×C4×D53C2×D411yescharacteristic
542C2×C4×D53C2×D411yescharacteristic
543C2×C4×D53C2×D411yescharacteristic
544C2×C4×D53C2×D411yescharacteristic
545C2×C4×D53C2411yescharacteristic
546C2×C4×D53C2411yescharacteristic
547C2×Dic106—21no—
548C2×Dic106—21no—
549C2×Dic106—21no—
550C2×Dic106C2411yescharacteristic
551C2×Dic106C2411yescharacteristic
552C2×Dic106C2411yescharacteristic
553Q16×C53—22no—
554Q16×C53—22no—
555SD16×C53—22no—
556SD16×C53—22no—
557C2×C8×C53C2411yescharacteristic
558C2×C8×C53C2411yescharacteristic
559C2×C8×C53C2411yescharacteristic
560C2×C8×C53C2411yescharacteristic
561C4⋊C4×C53—21no—
562C4⋊C4×C53—21no—
563C4⋊C4×C53—21no—
564C4⋊C4×C53—21no—
565C4⋊C4×C53—21no—
566C4⋊C4×C53—21no—
567C4⋊C4×C53—21no—
568C4⋊C4×C53—21no—
569C4⋊C4×C53—21no—
570C4⋊C4×C53—21no—
571C4⋊C4×C53—21no—
572C4⋊C4×C53C2×D411yescharacteristic
573C4⋊C4×C53C2×D411yescharacteristic
574C4⋊C4×C53C2411yescharacteristic
575C4⋊C4×C53C2411yescharacteristic
576C4⋊C4×C53C2411yescharacteristic
577C4⋊C4×C53C2411yescharacteristic
578C22⋊C4×C53—21no—
579C22⋊C4×C53—21no—
580C22⋊C4×C53—21no—
581C22⋊C4×C53—21no—
582C22⋊C4×C53C2×D411yescharacteristic
583C22⋊C4×C53C2×D411yescharacteristic
584C42×C53—21no—
585C42×C53—21no—
586C42×C53—21no—
587C42×C53—21no—
588C42×C53C2411yescharacteristic
589C42×C53C2411yescharacteristic
590C22⋊Dic53—21no—
591C22⋊Dic53—21no—
592C22⋊Dic53—21no—
593C22⋊Dic53—21no—
594C22⋊Dic53C2×D411yescharacteristic
595C22⋊Dic53C2×D411yescharacteristic
596#11719925—22no—
597#11719925—22no—
598#11719925—22no—
599#11719925—22no—
600#11719924—22no—
601#11719924—22no—
602#11719923—22no—
603#11719923—22no—
604#11719921—21no—
605#11719921—21no—
606#11719921—21no—
607#11719921—21no—
608#11719921—21no—
609#11719921—21no—
610#11719921—21no—
611#11719921—21no—
612#11719921—21no—
613#11719921—21no—
614#11719921—21no—
615#11719921—21no—
616#11719921C2×D411yescharacteristic
617#11719921C2×D411yescharacteristic
618#11719921C2×D411yescharacteristic
619#11719921C2×D411yescharacteristic
620C4⋊Dic53—21no—
621C4⋊Dic53—21no—
622C4⋊Dic53—21no—
623C4⋊Dic53—21no—
624C4⋊Dic53—21no—
625C4⋊Dic53—21no—
626C4⋊Dic53—21no—
627C4⋊Dic53—21no—
628C4⋊Dic53—21no—
629C4⋊Dic53—21no—
630C4⋊Dic53—21no—
631C4⋊Dic53C2×D411yescharacteristic
632C4⋊Dic53C2×D411yescharacteristic
633C4⋊Dic53C2411yescharacteristic
634C4⋊Dic53C2411yescharacteristic
635C4⋊Dic53C2411yescharacteristic
636C4⋊Dic53C2411yescharacteristic
637#11719919—21no—
638#11719919—21no—
639#11719919—21no—
640#11719919—21no—
641#11719919—21no—
642#11719919—21no—
643#11719919—21no—
644#11719919—21no—
645#11719919—21no—
646#11719919—21no—
647#11719919—21no—
648#11719919—21no—
649#11719919—21no—
650#11719919—21no—
651#11719919—21no—
652#11719919—21no—
653#11719919—21no—
654#11719919—21no—
655#11719919—21no—
656#11719919—21no—
657#11719919—21no—
658#11719919—21no—
659#11719919C2×D411yescharacteristic
660#11719919C2×D411yescharacteristic
661#11719919C2×D411yescharacteristic
662#11719919C2×D411yescharacteristic
663C4×Dic53—21no—
664C4×Dic53—21no—
665C4×Dic53—21no—
666C4×Dic53—21no—
667C4×Dic53—21no—
668C4×Dic53—21no—
669C4×Dic53—21no—
670C4×Dic53—21no—
671C4×Dic53—21no—
672C4×Dic53—21no—
673C4×Dic53—21no—
674C4×Dic53—21no—
675C4×Dic53—21no—
676C4×Dic53—21no—
677C4×Dic53—21no—
678C4×Dic53—21no—
679C4×Dic53C2×D411yescharacteristic
680C4×Dic53C2×D411yescharacteristic
681C4×Dic53C2×D411yescharacteristic
682C4×Dic53C2×D411yescharacteristic
683C4×Dic53C2411yescharacteristic
684C4×Dic53C2411yescharacteristic
685C2×#88322C2411yescharacteristic
686C2×#88322C2411yescharacteristic
687C2×#88322C2411yescharacteristic
688C2×#88322C2411yescharacteristic
689Dic212—22no—
690Dic212—22no—
691#11719913—22no—
692#11719913—22no—
693#11719912—22no—
694#11719912—22no—
695#11719912—22no—
696#11719912—22no—
697C23×C53—21no—
698C23×C53C22×D411yescharacteristic
699C22×D53—21no—
700C22×D53—24no—
701C22×D53—22no—
702C22×D53—41no—
703C22×D53—41no—
704C22×D53—81no—
705C22×D53—81no—
706C22×D53C22×D411yescharacteristic
707C22×D53C22×D411yescharacteristic
708Q8×C53—21no—
709Q8×C53—21no—
710Q8×C53—21no—
711Q8×C53—21no—
712Q8×C53—21no—
713Q8×C53C2×#4112yes—
714D4×C53—24no—
715D4×C53—21no—
716D4×C53C2×#4112yes—
717C2×C4×C53—24no—
718C2×C4×C53—21no—
719C2×C4×C53—21no—
720C2×C4×C53—21no—
721C2×C4×C53—21no—
722C2×C4×C53—21no—
723C2×C4×C53—21no—
724C2×C4×C53—21no—
725C2×C4×C53—21no—
726C2×C4×C53—21no—
727C2×C4×C53—81no—
728C2×C4×C53—81no—
729C2×C4×C53—81no—
730C2×C4×C53C22×D411yescharacteristic
731C2×C4×C53C22×D411yescharacteristic
732C2×C4×C53C22×D411yescharacteristic
733C2×C4×C53C22×D411yescharacteristic
734C2×C4×C53C22×D411yescharacteristic
735C2×C4×C53C2511yescharacteristic
736C22⋊D53—24no—
737C22⋊D53—24no—
738C22⋊D53—24no—
739C2×Dic53—21no—
740C2×Dic53—22no—
741C2×Dic53—24no—
742C2×Dic53—21no—
743C2×Dic53—21no—
744C2×Dic53—21no—
745C2×Dic53—21no—
746C2×Dic53—21no—
747C2×Dic53—21no—
748C2×Dic53—81no—
749C2×Dic53—81no—
750C2×Dic53—81no—
751C2×Dic53C22×D411yescharacteristic
752C2×Dic53C22×D411yescharacteristic
753C2×Dic53C22×D411yescharacteristic
754C2×Dic53C22×D411yescharacteristic
755C2×Dic53C22×D411yescharacteristic
756C2×Dic53C22×D411yescharacteristic
757D212—24no—
758D212—21no—
759D212C2×#4112yes—
760C4×D53—24no—
761C4×D53—24no—
762C4×D53—22no—
763C4×D53—21no—
764C4×D53—21no—
765C4×D53—22no—
766C4×D53—24no—
767C4×D53—41no—
768C4×D53—41no—
769C4×D53—41no—
770C4×D53—41no—
771C4×D53—42no—
772C4×D53—42no—
773C4×D53—42no—
774C4×D53—42no—
775C4×D53—81no—
776C4×D53—81no—
777C4×D53—81no—
778C4×D53—81no—
779C4×D53C2×#4112yes—
780C4×D53C2×#4112yes—
781Dic106—24no—
782Dic106—21no—
783Dic106—21no—
784Dic106—21no—
785Dic106—21no—
786Dic106—21no—
787Dic106—42no—
788Dic106—42no—
789Dic106C2×#4112yes—
790C8×C53—21no—
791C8×C53—21no—
792C8×C53—21no—
793C8×C53—21no—
794#88322—21no—
795#88322—21no—
796#88322—21no—
797#88322—21no—
798#60569—531nomaximal, Sylow
799C22×C53—21no—
800C22×C53—21no—
801C22×C53—21no—
802C22×C53—22no—
803C22×C53—41no—
804C22×C53—41no—
805C22×C53C23×D411yescharacteristic
806C2×D53—21no—
807C2×D53—21no—
808C2×D53—21no—
809C2×D53—21no—
810C2×D53—21no—
811C2×D53—22no—
812C2×D53—41no—
813C2×D53—41no—
814C2×D53—82no—
815C2×D53—84no—
816C2×D53#52512yes—
817C4×C53—21no—
818C4×C53—21no—
819C4×C53—21no—
820C4×C53—21no—
821C4×C53—22no—
822C4×C53—21no—
823C4×C53—41no—
824C4×C53—41no—
825C4×C53—41no—
826C4×C53—41no—
827C4×C53—41no—
828C4×C53—41no—
829C4×C53C22×#4111yescharacteristic
830C4×C53C22×#4111yescharacteristic
831Dic53—21no—
832Dic53—21no—
833Dic53—21no—
834Dic53—21no—
835Dic53—21no—
836Dic53—22no—
837Dic53—41no—
838Dic53—41no—
839Dic53—41no—
840Dic53—41no—
841Dic53—41no—
842Dic53—41no—
843Dic53#52512yes—
844C2×#541—531no—
845#3428—531no—
846#3127—531no—
847#3127—531no—
848#3127—531no—
849#3127—531no—
850#3123—531no—
851#3123—531no—
852#3123—531no—
853#3123—531no—
854#3120—531no—
855#3120—531no—
856#3120—531no—
857#3120—531no—
858#3120—531no—
859#3120—531no—
860#3120—531no—
861#3120D5311yescharacteristic, complemented
862#3095—531no—
863#3095—531no—
864#3080—531no—
865#3080—531no—
866#3039—531no—
867#3039—531no—
868#3007—531no—
869#3007—531no—
870C4×#137—531no—
871C4×#137—531no—
872C4×#137—531no—
873C4×#137—531no—
874#2921—531no—
875C2×C53—41no—
876C2×C53—42no—
877C2×C53C2×#52511yescharacteristic
878C2×C53#358611yescharacteristic
879C2×C53#358611yescharacteristic
880D53—22no—
881D53—41no—
882D53—42no—
883C22×#41—531no—
884C2×#137—531no—
885C2×#137—531no—
886C2×#137—531no—
887C2×#137—531no—
888#541—531no—
889#541—531no—
890#541—531no—
891#541—531no—
892#541—531no—
893#541—531no—
894#541—531no—
895#541—1061no—
896#541—1061no—
897#541—1061no—
898#541—1061no—
899#541C2×D5311yescharacteristic, complemented
900C2×C4⋊Q8—531no—
901C2×#126—1061no—
902C2×#126—1061no—
903C2×#125—531no—
904C2×#125—1061no—
905C2×#125—1061no—
906C2×C22⋊Q8—531no—
907C2×C22⋊Q8—531no—
908#520—531no—
909#520—531no—
910#520—531no—
911#520—1061no—
912#520—1061no—
913#520C2×D5311yescharacteristic
914#519—531no—
915#519—531no—
916#518—531no—
917#518—531no—
918#518—1061no—
919#518—1061no—
920C4×#41—531no—
921C4×#41—531no—
922C4×#41—531no—
923C4×#41—531no—
924C4×#41—1061no—
925C4×#41—1061no—
926C2×C4×Q8—531no—
927C2×C4×Q8—531no—
928C2×#117—531no—
929C2×#117—531no—
930C2×#117—1061no—
931C2×#117—1061no—
932#485—531no—
933#485—531no—
934#485—531no—
935#485—531no—
936#485—531no—
937#485—531no—
938#485—531no—
939#485—531no—
940#484—531no—
941#484—531no—
942#484—531no—
943#484C2×D5311yescharacteristic, complemented
944#483—531no—
945#483—531no—
946#483—531no—
947#483C2×D5311yescharacteristic, complemented
948#479—531no—
949#479—531no—
950#479—531no—
951#479—531no—
952#479—531no—
953#479—531no—
954#479—531no—
955#479C2×D5311yescharacteristic, complemented
956#478—531no—
957#478—531no—
958#478—531no—
959#478—531no—
960#478—531no—
961#478—531no—
962#478—531no—
963#478C2×D5311yescharacteristic, complemented
964#462—531no—
965#462—531no—
966#462—531no—
967#462—531no—
968#462—531no—
969#462—531no—
970#462—531no—
971#462C2×D5311yescharacteristic, complemented
972#461—531no—
973#461—531no—
974#461—531no—
975#461—531no—
976#461—531no—
977#461—531no—
978#461—531no—
979#461C2×D5311yescharacteristic, complemented
980#452—531no—
981#452—531no—
982#452—531no—
983#452—531no—
984#452—531no—
985#452—531no—
986#452C2×D5311yescharacteristic
987#452C2×D5311yescharacteristic
988#451—531no—
989#451—531no—
990#451—531no—
991#451—531no—
992#450—531no—
993#450—531no—
994#450—531no—
995#450—531no—
996#441—531no—
997#441—531no—
998#441—531no—
999#441—531no—
1000#441—531no—
1001#441—531no—
1002#441—531no—
1003#441C2×D5311yescharacteristic, complemented
1004#440—531no—
1005#440—531no—
1006#440—531no—
1007#440—531no—
1008#440—531no—
1009#440—531no—
1010#440—531no—
1011#440C2×D5311yescharacteristic, complemented
1012C4×Q16—531no—
1013C4×Q16—531no—
1014C4×Q16—531no—
1015C4×Q16—531no—
1016C4×Q16—531no—
1017C4×Q16—531no—
1018C4×Q16—531no—
1019C4×Q16C2×D5311yescharacteristic, complemented
1020C4×SD16—531no—
1021C4×SD16—531no—
1022C4×SD16—531no—
1023C4×SD16—531no—
1024C4×SD16—531no—
1025C4×SD16—531no—
1026C4×SD16—531no—
1027C4×SD16C2×D5311yescharacteristic, complemented
1028#433—531no—
1029#433—531no—
1030#433—531no—
1031#433—531no—
1032#433—531no—
1033#433—531no—
1034#433—531no—
1035#433C2×D5311yescharacteristic, complemented
1036#428—531no—
1037#428—531no—
1038#428—531no—
1039#428—531no—
1040#423—531no—
1041#423—531no—
1042#419—531no—
1043#419—531no—
1044#419—531no—
1045#419—531no—
1046#417—531no—
1047#417—531no—
1048#417—531no—
1049#417—531no—
1050#407—531no—
1051#407—531no—
1052C4×M16—531no—
1053C4×M16—531no—
1054C53#6056911yescharacteristic, complemented, Sylow
1055C2×#41—531no—
1056C2×#41—531no—
1057C2×#41—531no—
1058C2×#41—1061no—
1059C2×#41—1061no—
1060C2×#41—1064no—
1061C2×#41—1064no—
1062C2×#41C22×D5311yescharacteristic
1063C22×Q8—531no—
1064C22×Q8—531no—
1065C22×Q8—531no—
1066C22×D4—531no—
1067C22×D4—1061no—
1068C23×C4—531no—
1069C23×C4—1061no—
1070#137—1064no—
1071#137—1064no—
1072#137—1064no—
1073#137—1064no—
1074C2×Q16—531no—
1075C2×Q16—531no—
1076C2×Q16—531no—
1077C2×Q16—531no—
1078C2×Q16—531no—
1079C2×Q16—531no—
1080C2×Q16C22×D5311yescharacteristic
1081C2×Q16C22×D5311yescharacteristic
1082C2×SD16—531no—
1083C2×SD16—531no—
1084C2×SD16—531no—
1085C2×SD16—531no—
1086C2×SD16—531no—
1087C2×SD16—531no—
1088C2×SD16C22×D5311yescharacteristic
1089C2×SD16C22×D5311yescharacteristic
1090C2×M16—531no—
1091C2×M16—531no—
1092C2×M16—531no—
1093C2×M16—531no—
1094C4⋊Q8—531no—
1095C4⋊Q8—531no—
1096C4⋊Q8—531no—
1097C4⋊Q8—1061no—
1098C4⋊Q8—1061no—
1099C4⋊Q8C22×D5311yescharacteristic
1100#126—21no—
1101#126—21no—
1102#126—1061no—
1103#126—1061no—
1104#126—1061no—
1105#126—1061no—
1106#126—1061no—
1107#126—1061no—
1108#126—1061no—
1109#126—1061no—
1110#126—1061no—
1111#126—1061no—
1112#126—1061no—
1113#126—1061no—
1114#126—1061no—
1115#126—1061no—
1116#125—21no—
1117#125—21no—
1118#125—531no—
1119#125—531no—
1120#125—531no—
1121#125—1061no—
1122#125—1061no—
1123#125—1061no—
1124#125—1061no—
1125#125—1061no—
1126#125—1061no—
1127#125—1061no—
1128#125—1061no—
1129#125—1061no—
1130#125—1061no—
1131#125—1061no—
1132#125—1061no—
1133#125—1061no—
1134#125—1061no—
1135#125—1061no—
1136#125—1061no—
1137#125C22×D5311yescharacteristic
1138C22⋊Q8—531no—
1139C22⋊Q8—531no—
1140C22⋊Q8—531no—
1141C22⋊Q8—531no—
1142C22⋊Q8—531no—
1143C22⋊Q8—531no—
1144C22⋊Q8—1061no—
1145C22⋊Q8—1061no—
1146C22⋊Q8—1061no—
1147C22⋊Q8—1061no—
1148C22⋊Q8C22×D5311yescharacteristic
1149C22⋊Q8C22×D5311yescharacteristic
1150C4×Q8—531no—
1151C4×Q8—531no—
1152C4×Q8—531no—
1153C4×Q8—531no—
1154C4×Q8—531no—
1155C4×Q8—531no—
1156C4×Q8—531no—
1157C4×Q8—531no—
1158C4×Q8—531no—
1159C4×Q8—531no—
1160C4×Q8—531no—
1161C4×Q8—531no—
1162C4×Q8—1061no—
1163C4×Q8—1061no—
1164C4×Q8—1061no—
1165C4×Q8—1061no—
1166C4×Q8—1061no—
1167C4×Q8—1061no—
1168C4×Q8—1061no—
1169C4×Q8—1061no—
1170C4×Q8C22×D5311yescharacteristic
1171C4×Q8C22×D5311yescharacteristic
1172C4×Q8C22×D5311yescharacteristic
1173C4×Q8C22×D5311yescharacteristic
1174C4×D4—21no—
1175C4×D4—21no—
1176C4×D4—531no—
1177C4×D4—531no—
1178C4×D4—531no—
1179C4×D4—531no—
1180C4×D4—531no—
1181C4×D4—531no—
1182C4×D4—1061no—
1183C4×D4—1061no—
1184C4×D4—1061no—
1185C4×D4—1061no—
1186C4×D4—1061no—
1187C4×D4—1061no—
1188C4×D4—1061no—
1189C4×D4—1061no—
1190C4×D4—1061no—
1191C4×D4—1061no—
1192C4×D4—1061no—
1193C4×D4—1061no—
1194C4×D4—1061no—
1195C4×D4—1061no—
1196C4×D4—1061no—
1197C4×D4—1061no—
1198C4×D4—1061no—
1199C4×D4—1061no—
1200C4×D4C22×D5311yescharacteristic
1201C4×D4C22×D5311yescharacteristic
1202#117—21no—
1203#117—531no—
1204#117—531no—
1205#117—531no—
1206#117—531no—
1207#117—531no—
1208#117—531no—
1209#117—531no—
1210#117—531no—
1211#117—531no—
1212#117—531no—
1213#117—531no—
1214#117—1061no—
1215#117—1061no—
1216#117—1061no—
1217#117—1061no—
1218#117—1061no—
1219#117—1061no—
1220#117—1061no—
1221#117—1061no—
1222#117—1061no—
1223#117—1061no—
1224#117—1061no—
1225#117—1061no—
1226#117—1061no—
1227#117C22×D5311yescharacteristic
1228C2×C4⋊C4—21no—
1229C2×C4⋊C4—531no—
1230C2×C4⋊C4—531no—
1231C2×C4⋊C4—531no—
1232C2×C4⋊C4—531no—
1233C2×C4⋊C4—531no—
1234C2×C4⋊C4—1061no—
1235C2×C4⋊C4—1061no—
1236C2×C4⋊C4—1061no—
1237C2×C4⋊C4—1061no—
1238C2×C4⋊C4—1061no—
1239C2×C4⋊C4—1061no—
1240C2×C4⋊C4—1061no—
1241C2×C4⋊C4—1061no—
1242C2×C4⋊C4—1061no—
1243C2×C4⋊C4—1061no—
1244C2×C4⋊C4—1061no—
1245C2×C4⋊C4C22×D5311yescharacteristic
1246C2×C22⋊C4—531no—
1247C2×C22⋊C4—531no—
1248C2×C22⋊C4—1061no—
1249C2×C22⋊C4—1061no—
1250C2×C22⋊C4—1061no—
1251C2×C22⋊C4—1061no—
1252C2×C22⋊C4—1061no—
1253C2×C22⋊C4—1061no—
1254C2×C22⋊C4—1061no—
1255C2×C42—531no—
1256C2×C42—531no—
1257C2×C42—1061no—
1258C2×C42—1061no—
1259C2×C42—1061no—
1260C2×C42—1061no—
1261C2×C42—1061no—
1262C2×C42—1061no—
1263C2×C42—1061no—
1264#107—531no—
1265#107—531no—
1266#107—531no—
1267#107—531no—
1268#107—531no—
1269#107—531no—
1270#107C22×D5311yescharacteristic
1271#107C22×D5311yescharacteristic
1272#106—531no—
1273#106—531no—
1274#106—531no—
1275#106—531no—
1276#106—531no—
1277#106—531no—
1278#106C22×D5311yescharacteristic
1279#106C22×D5311yescharacteristic
1280C4⋊C8—531no—
1281C4⋊C8—531no—
1282C4⋊C8—531no—
1283C4⋊C8—531no—
1284C4⋊C8—531no—
1285C4⋊C8—531no—
1286C4⋊C8C22×D5311yescharacteristic
1287C4⋊C8C22×D5311yescharacteristic
1288#103—531no—
1289#103—531no—
1290#103—531no—
1291#103—531no—
1292#103—531no—
1293#103—531no—
1294#103—531no—
1295#103—531no—
1296#103—531no—
1297#103—531no—
1298#103—531no—
1299#103—531no—
1300#103—531no—
1301#103—531no—
1302#103—531no—
1303#103—531no—
1304#103—531no—
1305#103—531no—
1306#103C22×D5311yescharacteristic
1307#103C22×D5311yescharacteristic
1308#103C22×D5311yescharacteristic
1309#103C22×D5311yescharacteristic
1310#103C22×D5311yescharacteristic
1311#103C22×D5311yescharacteristic
1312#102—531no—
1313#102—531no—
1314#102—531no—
1315#102—531no—
1316#102—531no—
1317#102—531no—
1318#102C22×D5311yescharacteristic
1319#102C22×D5311yescharacteristic
1320C22⋊C8—531no—
1321C22⋊C8—531no—
1322C22⋊C8—531no—
1323C22⋊C8—531no—
1324C22⋊C8—531no—
1325C22⋊C8—531no—
1326C22⋊C8C22×D5311yescharacteristic
1327C22⋊C8C22×D5311yescharacteristic
1328#97—531no—
1329#97—531no—
1330#97—531no—
1331#97C22×D5311yescharacteristic
1332C4×C8—531no—
1333C4×C8—531no—
1334C4×C8—531no—
1335C4×C8C22×D5311yescharacteristic
1336C24—531no—
1337C24—1061no—
1338#41—22no—
1339#41—22no—
1340#41—534no—
1341#41—534no—
1342#41—1062no—
1343#41—1062no—
1344#41—1068no—
1345#41—1062no—
1346#41—1062no—
1347#41—1068no—
1348C2×Q8—531no—
1349C2×Q8—531no—
1350C2×Q8—531no—
1351C2×Q8—1061no—
1352C2×Q8—1061no—
1353C2×Q8—1061no—
1354C2×Q8—1062no—
1355C2×Q8—1062no—
1356C2×Q8—1062no—
1357C2×Q8—1062no—
1358C2×Q8—1062no—
1359C2×Q8—1062no—
1360C2×Q8C23×D5311yescharacteristic
1361C2×Q8C23×D5311yescharacteristic
1362C2×Q8C23×D5311yescharacteristic
1363C2×D4—21no—
1364C2×D4—531no—
1365C2×D4—1061no—
1366C2×D4—1061no—
1367C2×D4—1062no—
1368C2×D4—1068no—
1369C2×D4—1061no—
1370C2×D4—1061no—
1371C2×D4—1062no—
1372C2×D4C23×D5311yescharacteristic
1373C22×C4—21no—
1374C22×C4—21no—
1375C22×C4—21no—
1376C22×C4—21no—
1377C22×C4—531no—
1378C22×C4—531no—
1379C22×C4—531no—
1380C22×C4—531no—
1381C22×C4—531no—
1382C22×C4—531no—
1383C22×C4—531no—
1384C22×C4—531no—
1385C22×C4—531no—
1386C22×C4—1061no—
1387C22×C4—1062no—
1388C22×C4—1062no—
1389C22×C4—1061no—
1390C22×C4—1061no—
1391C22×C4—1061no—
1392C22×C4—1068no—
1393C22×C4—1061no—
1394C22×C4—1061no—
1395C22×C4—1061no—
1396C22×C4—1061no—
1397C22×C4—1061no—
1398C22×C4—1061no—
1399C22×C4—1061no—
1400C22×C4—1061no—
1401C22×C4—1061no—
1402C22×C4—1061no—
1403C22×C4—1061no—
1404C22×C4C23×D5311yescharacteristic
1405Q16—22no—
1406Q16—22no—
1407Q16—1062no—
1408Q16—1062no—
1409Q16—1062no—
1410Q16—1062no—
1411Q16—1062no—
1412Q16—1062no—
1413SD16—22no—
1414SD16—22no—
1415SD16—1062no—
1416SD16—1062no—
1417SD16—1062no—
1418SD16—1062no—
1419SD16—1062no—
1420SD16—1062no—
1421M16—1062no—
1422M16—1062no—
1423M16—1062no—
1424M16—1062no—
1425C2×C8—531no—
1426C2×C8—531no—
1427C2×C8—531no—
1428C2×C8—531no—
1429C2×C8C23×D5311yescharacteristic
1430C2×C8C23×D5311yescharacteristic
1431C2×C8C23×D5311yescharacteristic
1432C2×C8C23×D5311yescharacteristic
1433C4⋊C4—21no—
1434C4⋊C4—21no—
1435C4⋊C4—21no—
1436C4⋊C4—21no—
1437C4⋊C4—21no—
1438C4⋊C4—21no—
1439C4⋊C4—21no—
1440C4⋊C4—21no—
1441C4⋊C4—21no—
1442C4⋊C4—21no—
1443C4⋊C4—21no—
1444C4⋊C4—531no—
1445C4⋊C4—531no—
1446C4⋊C4—531no—
1447C4⋊C4—531no—
1448C4⋊C4—531no—
1449C4⋊C4—531no—
1450C4⋊C4—531no—
1451C4⋊C4—531no—
1452C4⋊C4—531no—
1453C4⋊C4—531no—
1454C4⋊C4—1061no—
1455C4⋊C4—1061no—
1456C4⋊C4—1061no—
1457C4⋊C4—1061no—
1458C4⋊C4—1061no—
1459C4⋊C4—1061no—
1460C4⋊C4—1061no—
1461C4⋊C4—1061no—
1462C4⋊C4—1061no—
1463C4⋊C4—1061no—
1464C4⋊C4—1061no—
1465C4⋊C4—1061no—
1466C4⋊C4—1061no—
1467C4⋊C4—1061no—
1468C4⋊C4—1061no—
1469C4⋊C4—1061no—
1470C4⋊C4—1061no—
1471C4⋊C4—1061no—
1472C4⋊C4—1061no—
1473C4⋊C4—1061no—
1474C4⋊C4—1061no—
1475C4⋊C4—1061no—
1476C4⋊C4—1061no—
1477C4⋊C4—1061no—
1478C4⋊C4—1061no—
1479C4⋊C4—1061no—
1480C4⋊C4—1061no—
1481C4⋊C4—1061no—
1482C4⋊C4—1061no—
1483C4⋊C4—1061no—
1484C4⋊C4—1061no—
1485C4⋊C4—1061no—
1486C4⋊C4—1061no—
1487C4⋊C4D4×D5311yescharacteristic
1488C4⋊C4D4×D5311yescharacteristic
1489C4⋊C4C23×D5311yescharacteristic
1490C4⋊C4C23×D5311yescharacteristic
1491C4⋊C4C23×D5311yescharacteristic
1492C4⋊C4C23×D5311yescharacteristic
1493C22⋊C4—21no—
1494C22⋊C4—21no—
1495C22⋊C4—21no—
1496C22⋊C4—21no—
1497C22⋊C4—531no—
1498C22⋊C4—531no—
1499C22⋊C4—531no—
1500C22⋊C4—531no—
1501C22⋊C4—531no—
1502C22⋊C4—531no—
1503C22⋊C4—1061no—
1504C22⋊C4—1061no—
1505C22⋊C4—1061no—
1506C22⋊C4—1061no—
1507C22⋊C4—1061no—
1508C22⋊C4—1061no—
1509C22⋊C4—1061no—
1510C22⋊C4—1061no—
1511C22⋊C4—1061no—
1512C22⋊C4—1061no—
1513C22⋊C4—1061no—
1514C22⋊C4—1061no—
1515C22⋊C4—1061no—
1516C22⋊C4—1061no—
1517C22⋊C4—1061no—
1518C22⋊C4—1061no—
1519C22⋊C4D4×D5311yescharacteristic
1520C22⋊C4D4×D5311yescharacteristic
1521C42—21no—
1522C42—21no—
1523C42—21no—
1524C42—21no—
1525C42—531no—
1526C42—531no—
1527C42—531no—
1528C42—531no—
1529C42—531no—
1530C42—531no—
1531C42—1061no—
1532C42—1061no—
1533C42—1061no—
1534C42—1061no—
1535C42—1061no—
1536C42—1061no—
1537C42—1061no—
1538C42—1061no—
1539C42—1061no—
1540C42—1061no—
1541C42—1061no—
1542C42—1061no—
1543C42—1061no—
1544C42—1061no—
1545C42—1061no—
1546C42—1061no—
1547C42C23×D5311yescharacteristic
1548C42C23×D5311yescharacteristic
1549C23—21no—
1550C23—531no—
1551C23—531no—
1552C23—1062no—
1553C23—1064no—
1554C23—1061no—
1555C23—4241no—
1556C23—4241no—
1557C23—2121no—
1558C23—2121no—
1559C23C2×D4×D5311yescharacteristic
1560Q8—21no—
1561Q8—21no—
1562Q8—21no—
1563Q8—21no—
1564Q8—21no—
1565Q8—532no—
1566Q8—1064no—
1567Q8—1061no—
1568Q8—1061no—
1569Q8—1061no—
1570Q8—1061no—
1571Q8—1061no—
1572Q8—2122no—
1573Q8—2122no—
1574Q8#41×D5312yes—
1575D4—24no—
1576D4—21no—
1577D4—532no—
1578D4—1064no—
1579D4—1064no—
1580D4—1064no—
1581D4—1064no—
1582D4—1061no—
1583D4#41×D5312yes—
1584C2×C4—24no—
1585C2×C4—21no—
1586C2×C4—21no—
1587C2×C4—21no—
1588C2×C4—21no—
1589C2×C4—21no—
1590C2×C4—21no—
1591C2×C4—21no—
1592C2×C4—21no—
1593C2×C4—21no—
1594C2×C4—81no—
1595C2×C4—81no—
1596C2×C4—81no—
1597C2×C4—531no—
1598C2×C4—532no—
1599C2×C4—532no—
1600C2×C4—531no—
1601C2×C4—531no—
1602C2×C4—531no—
1603C2×C4—531no—
1604C2×C4—531no—
1605C2×C4—1062no—
1606C2×C4—1064no—
1607C2×C4—1062no—
1608C2×C4—1064no—
1609C2×C4—1064no—
1610C2×C4—1062no—
1611C2×C4—1064no—
1612C2×C4—1061no—
1613C2×C4—1061no—
1614C2×C4—1061no—
1615C2×C4—1061no—
1616C2×C4—1061no—
1617C2×C4—1061no—
1618C2×C4—1061no—
1619C2×C4—1061no—
1620C2×C4—1061no—
1621C2×C4—4241no—
1622C2×C4—4241no—
1623C2×C4—4241no—
1624C2×C4—4241no—
1625C2×C4—4241no—
1626C2×C4—4241no—
1627C2×C4—4241no—
1628C2×C4—2121no—
1629C2×C4—2121no—
1630C2×C4—2121no—
1631C2×C4—2121no—
1632C2×C4—2122no—
1633C2×C4—2122no—
1634C2×C4—2122no—
1635C2×C4—2122no—
1636C2×C4C2×D4×D5311yescharacteristic
1637C2×C4C2×D4×D5311yescharacteristic
1638C2×C4C2×D4×D5311yescharacteristic
1639C2×C4C2×D4×D5311yescharacteristic
1640C2×C4C2×D4×D5311yescharacteristic
1641C2×C4C24×D5311yescharacteristic
1642C8—21no—
1643C8—21no—
1644C8—21no—
1645C8—21no—
1646C8—1061no—
1647C8—1061no—
1648C8—1061no—
1649C8—1061no—
1650C22—21no—
1651C22—22no—
1652C22—21no—
1653C22—21no—
1654C22—41no—
1655C22—41no—
1656C22—532no—
1657C22—1061no—
1658C22—1061no—
1659C22—1061no—
1660C22—1062no—
1661C22—1061no—
1662C22—1061no—
1663C22—4242no—
1664C22—4244no—
1665C22—2121no—
1666C22—2121no—
1667C22C22×D4×D5311yescharacteristic
1668C4—21no—
1669C4—22no—
1670C4—21no—
1671C4—21no—
1672C4—21no—
1673C4—21no—
1674C4—41no—
1675C4—41no—
1676C4—41no—
1677C4—41no—
1678C4—41no—
1679C4—41no—
1680C4—532no—
1681C4—1061no—
1682C4—1062no—
1683C4—1061no—
1684C4—1061no—
1685C4—1061no—
1686C4—1061no—
1687C4—2121no—
1688C4—2121no—
1689C4—2121no—
1690C4—2121no—
1691C4—2121no—
1692C4—2121no—
1693C4C2×#41×D5311yescharacteristic
1694C4C2×#41×D5311yescharacteristic
1695C2—41no—
1696C2—42no—
1697C2—1062no—
1698C2—2121no—
1699C2—2122no—
1700C2#525×D5311yescharacteristic
1701C2#2028949711yescharacteristic
1702C2#2028950011yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3120C2
socleC22×C53C23×D4
prime radicalC2×#41×D53C22
hypercenter#3120D53
hypocenterC53#60569
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ #117 ◁ #3120

Complements

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

NH ≅ G/Ntype
1. #541×D53C2semidirect
3. #20285017C2semidirect
4. #20285014C2semidirect
5. #20285013C2semidirect
6. #20285012C2semidirect
7. #20284969C2semidirect
8. #20284966C2semidirect
9. #20284965C2semidirect
10. #20284964C2semidirect
11. #20284932C2semidirect
12. #20284931C2semidirect
13. #20284930C2semidirect
14. #20284929C2semidirect
15. #20284924C2semidirect
16. #20284923C2semidirect
17. #20284922C2semidirect
18. #20284660C2semidirect
19. #20284658C2semidirect
20. #20284534C2semidirect
21. #20284532C2semidirect
22. #20284199C2semidirect
23. #20284197C2semidirect
26. #20283537C2semidirect
27. C4×#13133249C2semidirect
28. #20283531C2semidirect
29. C4×#13133246C2semidirect
30. #20283349C2semidirect
31. C53×#3120C2semidirect
38. #16811235C22semidirect
40. #16811233C22semidirect
41. #16811233C22semidirect
48. C4⋊Q8×D53C22semidirect
53. #125×D53C22semidirect
73. C4×Q8×D53C22semidirect
74. C4×Q8×D53C22semidirect
87. #16810959C22semidirect
88. #16810958C22semidirect
89. #16810956C22semidirect
90. #16810954C22semidirect
91. #16810953C22semidirect
92. #16810951C22semidirect
93. #16810933C22semidirect
94. #16810932C22semidirect
95. #16810931C22semidirect
96. #16810930C22semidirect
97. #16810929C22semidirect
98. #16810928C22semidirect
99. #16810927C22semidirect
100. #16810926C22semidirect
101. #16810925C22semidirect
102. #16810924C22semidirect
103. #16810923C22semidirect
104. #16810922C22semidirect
105. #16810921C22semidirect
106. #16810920C22semidirect
107. #16810834C22semidirect
108. #16810833C22semidirect
109. #16810832C22semidirect
110. #16810832C22semidirect
111. #16810831C22semidirect
112. #16810831C22semidirect
113. #16810830C22semidirect
114. #16810829C22semidirect
115. #16810828C22semidirect
116. #16810827C22semidirect
117. #16810827C22semidirect
118. #16810826C22semidirect
119. #16810826C22semidirect
120. #16810825C22semidirect
135. #16810731C22semidirect
136. #16810730C22semidirect
137. #16810729C22semidirect
138. #16810728C22semidirect
139. #16810728C22semidirect
140. #16810727C22semidirect
141. #16810727C22semidirect
142. #16810726C22semidirect
143. #16810725C22semidirect
144. #16810724C22semidirect
145. #16810723C22semidirect
146. #16810722C22semidirect
147. #16810721C22semidirect
148. #16810720C22semidirect
149. C4×Dic212C22semidirect
150. Q16×Dic53C22semidirect
151. #16810717C22semidirect
152. C4×#11719925C22semidirect
153. C4×#11719925C22semidirect
154. #16810715C22semidirect
155. #16810715C22semidirect
156. #16810714C22semidirect
157. C4×#11719913C22semidirect
158. SD16×Dic53C22semidirect
159. C4×#11719924C22semidirect
160. #16810710C22semidirect
161. C4×#11719923C22semidirect
162. #16810708C22semidirect
164. #16810684C22semidirect
168. #16810681C22semidirect
169. #16810681C22semidirect
170. #16810664C22semidirect
171. #16810664C22semidirect
172. #16810662C22semidirect
173. #16810662C22semidirect
174. #16810645C22semidirect
175. #16810645C22semidirect
176. #16810630C22semidirect
177. #16810630C22semidirect
178. #16810630C22semidirect
179. #16810630C22semidirect
186. #16810575C22semidirect
187. C4×#11719912C22semidirect
188. C53×#541C22semidirect
190. C53×#484C22semidirect
191. C53×#483C22semidirect
192. C53×#479C22semidirect
193. C53×#478C22semidirect
194. C53×#462C22semidirect
195. C53×#461C22semidirect
198. C53×#441C22semidirect
199. C53×#440C22semidirect
200. C4×Q16×C53C22semidirect
201. C4×SD16×C53C22semidirect
202. C53×#433C22semidirect
861. #3120D53semidirect
899. #541C2×D53semidirect
943. #484C2×D53semidirect
947. #483C2×D53semidirect
955. #479C2×D53semidirect
963. #478C2×D53semidirect
971. #462C2×D53semidirect
979. #461C2×D53semidirect
1003. #441C2×D53semidirect
1011. #440C2×D53semidirect
1019. C4×Q16C2×D53semidirect
1027. C4×SD16C2×D53semidirect
1035. #433C2×D53semidirect
1054. C53#60569semidirect

Maximal subgroups

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

subgroupindex
#541×D532
#202879152
#202850172
#202850142
#202850132
#202850122
#202849692
#202849662
#202849652
#202849642
#202849322
#202849312
#202849302
#202849292
#202849242
#202849232
#202849222
#202846602
#202846582
#202845342
#202845322
#202841992
#202841972
#202839722
#202835372
C4×#131332492
#202835312
C4×#131332462
#202833492
C53×#31202
#6056953