Finite Group Databasebeta

← #28276451

Subgroups — #28276451

Order 13568.

2114 conjugacy classes of subgroups.

The subgroup lattice has 1842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288621C211yesmaximal, characteristic, complemented
2#20288202C211yesmaximal, characteristic, complemented
3#20287738C211yesmaximal, characteristic, complemented
4#20287736C211yesmaximal, characteristic, complemented
5#20287436C211yesmaximal, characteristic, complemented
6#20287430C211yesmaximal, characteristic, complemented
7#20287018C211yesmaximal, characteristic, complemented
8#20287016C211yesmaximal, characteristic, complemented
9#20286704C211yesmaximal, characteristic, complemented
10#20286702C211yesmaximal, characteristic, complemented
11#20286700C211yesmaximal, characteristic, complemented
12#20286312C211yesmaximal, characteristic, complemented
13#20286308C211yesmaximal, characteristic, complemented
14#20286215C211yesmaximal, characteristic, complemented
15#20286211C211yesmaximal, characteristic, complemented
16#20286207C211yesmaximal, characteristic, complemented
17#20286203C211yesmaximal, characteristic, complemented
18#20286101C211yesmaximal, characteristic, complemented
19#20286097C211yesmaximal, characteristic, complemented
20#20286021C211yesmaximal, characteristic, complemented
21#20285711C211yesmaximal, characteristic, complemented
22#20285707C211yesmaximal, characteristic, complemented
23#20285638C211yesmaximal, characteristic, complemented
24#20284812C211yesmaximal, characteristic, complemented
25#20284811C211yesmaximal, characteristic, complemented
26#20284712C211yesmaximal, characteristic, complemented
27#20284178C211yesmaximal, characteristic, complemented
28#20284177C211yesmaximal, characteristic, complemented
29C2×#16810827C211yesmaximal, characteristic, complemented
30#20283827C211yesmaximal, characteristic, complemented
31C53×#3308C211yesmaximal, characteristic, complemented
32C2×#41×D53—21no—
33C2×#13133245C2211yescharacteristic
34C2×#13133244C2211yescharacteristic
35C2×#13133242C2211yescharacteristic
36C2×#13133241C2211yescharacteristic
37C22×#11719913C2211yescharacteristic
38C22×#11719924C2211yescharacteristic
39#16811345C2211yescharacteristic, complemented
40#16811342C2211yescharacteristic, complemented
41#16811335—21no—
42#16811327—21no—
43#16811322—21no—
44#16811316—21no—
45#16811294C2211yescharacteristic
46#16811288C2211yescharacteristic
47#16811284C2211yescharacteristic, complemented
48#16811283—21no—
49#16811282C2211yescharacteristic, complemented
50#16811279C2211yescharacteristic, complemented
51#16811275C2211yescharacteristic, complemented
52#16811274C2211yescharacteristic
53#16811274C2211yescharacteristic
54#16811272C2211yescharacteristic, complemented
55#16811265—21no—
56#16811265—21no—
57#16811261—21no—
58D4×D212C2211yescharacteristic
59#16811257C2211yescharacteristic
60#16811257C2211yescharacteristic
61#16811243—21no—
62#16811237—21no—
63#16811200—21no—
64#16811177C2211yescharacteristic, complemented
65#16811175C2211yescharacteristic, complemented
66#16811174C2211yescharacteristic
67#16811172C2211yescharacteristic, complemented
68#16811169C2211yescharacteristic, complemented
69#16811168C2211yescharacteristic
70#16811168C2211yescharacteristic
71#16811168C2211yescharacteristic, complemented
72C2×#13133215C2211yescharacteristic, complemented
73#16811136—21no—
74#16811131—21no—
75#16811131—21no—
76#16811102—21no—
77C4×#11719947C2211yescharacteristic
78C2×#13133179C2211yescharacteristic
79C2×#13133179C2211yescharacteristic
80C4×D4×D53C2211yescharacteristic
81#16811013C2211yescharacteristic, complemented
82#16811012C2211yescharacteristic, complemented
83#16811011C2211yescharacteristic, complemented
84#16811009C2211yescharacteristic, complemented
85#16810994C2211yescharacteristic, complemented
86#16810994C2211yescharacteristic, complemented
87#16810985C2211yescharacteristic, complemented
88#16810984C2211yescharacteristic, complemented
89#16810981C2211yescharacteristic, complemented
90#16810972C2211yescharacteristic, complemented
91#16810972C2211yescharacteristic, complemented
92#16810960C2211yescharacteristic, complemented
93#16810958C2211yescharacteristic, complemented
94#16810957C2211yescharacteristic, complemented
95#16810936C2211yescharacteristic, complemented
96#16810917C2211yescharacteristic, complemented
97#16810916C2211yescharacteristic, complemented
98#16810915C2211yescharacteristic, complemented
99#16810902C2211yescharacteristic
100#16810902C2211yescharacteristic, complemented
101#16810902C2211yescharacteristic, complemented
102#16810902C2211yescharacteristic, complemented
103#16810901C2211yescharacteristic, complemented
104#16810901C2211yescharacteristic, complemented
105#16810872C2211yescharacteristic, complemented
106#16810872C2211yescharacteristic, complemented
107#16810871C2211yescharacteristic, complemented
108#16810870C2211yescharacteristic, complemented
109#16810870C2211yescharacteristic, complemented
110#16810869C2211yescharacteristic, complemented
111#16810867C2211yescharacteristic, complemented
112#16810859C2211yescharacteristic, complemented
113#16810857C2211yescharacteristic, complemented
114#16810857C2211yescharacteristic, complemented
115#16810841C2211yescharacteristic
116#16810841C2211yescharacteristic, complemented
117#16810839C2211yescharacteristic
118#16810838C2211yescharacteristic, complemented
119#16810837C2211yescharacteristic
120#16810837C2211yescharacteristic, complemented
121#16810835C2211yescharacteristic
122#16810827C2211yescharacteristic
123#16810827C2211yescharacteristic
124#16810827C2211yescharacteristic
125#16810827C2211yescharacteristic
126#16810827C2211yescharacteristic, complemented
127#16810827C2211yescharacteristic, complemented
128#16810827C2211yescharacteristic, complemented
129#16810827C2211yescharacteristic, complemented
130#16810827C2211yescharacteristic, complemented
131#16810827C2211yescharacteristic, complemented
132#16810826C2211yescharacteristic, complemented
133#16810826C2211yescharacteristic, complemented
134#16810824C2211yescharacteristic, complemented
135#16810823C2211yescharacteristic, complemented
136#16810822C2211yescharacteristic, complemented
137#16810821C2211yescharacteristic, complemented
138#16810817C2211yescharacteristic
139#16810817C2211yescharacteristic, complemented
140#16810817C2211yescharacteristic, complemented
141#16810817C2211yescharacteristic, complemented
142#16810816C2211yescharacteristic, complemented
143#16810816C2211yescharacteristic, complemented
144#16810776C2211yescharacteristic
145#16810775C2211yescharacteristic
146#16810773C2211yescharacteristic
147#16810772C2211yescharacteristic
148#16810771C2211yescharacteristic, complemented
149#16810771C2211yescharacteristic, complemented
150#16810770C2211yescharacteristic, complemented
151#16810769C2211yescharacteristic, complemented
152#16810769C2211yescharacteristic, complemented
153#16810768C2211yescharacteristic, complemented
154#16810766C2211yescharacteristic, complemented
155#16810764C2211yescharacteristic, complemented
156#16810762C2211yescharacteristic, complemented
157#16810761C2211yescharacteristic, complemented
158#16810759C2211yescharacteristic
159#16810756C2211yescharacteristic
160#16810752C2211yescharacteristic, complemented
161#16810751C2211yescharacteristic, complemented
162#16810726C2211yescharacteristic
163#16810726C2211yescharacteristic, complemented
164#16810725C2211yescharacteristic
165#16810723C2211yescharacteristic, complemented
166#16810722C2211yescharacteristic
167#16810722C2211yescharacteristic, complemented
168#16810721C2211yescharacteristic
169#16810705C2211yescharacteristic
170#16810705C2211yescharacteristic, complemented
171#16810703C2211yescharacteristic
172#16810703C2211yescharacteristic, complemented
173#16810699C2211yescharacteristic, complemented
174#16810698C2211yescharacteristic, complemented
175#16810695C2211yescharacteristic, complemented
176#16810694C2211yescharacteristic, complemented
177#16810691C2211yescharacteristic, complemented
178#16810678C2211yescharacteristic, complemented
179#16810677C2211yescharacteristic, complemented
180#16810673C2211yescharacteristic, complemented
181#16810646C2211yescharacteristic, complemented
182#16810645C2211yescharacteristic, complemented
183C2×#13133146C2211yescharacteristic, complemented
184#16810623C2211yescharacteristic, complemented
185#16810622C2211yescharacteristic, complemented
186#16810621C2211yescharacteristic, complemented
187C2×#13133140C2211yescharacteristic, complemented
188C53×#548C2211yescharacteristic, complemented
189C53×#547C2211yescharacteristic
190C53×#489C2211yescharacteristic, complemented
191C53×#484C2211yescharacteristic, complemented
192C53×#480C2211yescharacteristic, complemented
193C53×#477C2211yescharacteristic, complemented
194C53×#468C2211yescharacteristic, complemented
195C53×#466C2211yescharacteristic, complemented
196C53×#463C2211yescharacteristic, complemented
197C53×#449C2211yescharacteristic, complemented
198C53×#448C2211yescharacteristic, complemented
199C53×#440C2211yescharacteristic, complemented
200C53×#435C2211yescharacteristic, complemented
201C53×#417C2211yescharacteristic, complemented
202C2×#103×C53C2211yescharacteristic, complemented
203C2×#11719949—21no—
204C2×#11719949C2311yescharacteristic
205C2×#11719945—21no—
206C2×#11719945—21no—
207C2×#11719945—21no—
208C2×#11719945C2311yescharacteristic
209C2×#11719947—21no—
210C2×#11719947—21no—
211C2×#11719947—21no—
212C2×#11719947D411yescharacteristic
213C2×#11719947C2311yescharacteristic
214#41×D53—48no—
215C22×Dic106C2311yescharacteristic
216C2×Q8×D53—21no—
217C22×D212C2311yescharacteristic
218C22×D212C2311yescharacteristic
219C2×D4×D53—21no—
220C2×D4×D53—21no—
221C2×D4×D53—21no—
222C2×D4×D53C2311yescharacteristic
223C22×C4×D53—21no—
224C22×C4×D53—21no—
225C22×C4×D53—21no—
226#13133245—42no—
227#13133244—42no—
228#13133242—42no—
229#13133241—42no—
230C2×#11719913—42no—
231C2×#11719913C2311yescharacteristic
232C2×#11719913C2311yescharacteristic
233C2×#11719913C2311yescharacteristic
234C2×#11719913C2311yescharacteristic
235C2×#11719913C2311yescharacteristic
236C2×#11719913C2311yescharacteristic
237C2×#11719923C2311yescharacteristic
238C2×#11719923C2311yescharacteristic
239C2×#11719924—42no—
240C2×#11719924C2311yescharacteristic
241C2×#11719924C2311yescharacteristic
242C2×#11719924C2311yescharacteristic
243C2×#11719924C2311yescharacteristic
244C2×#11719924C2311yescharacteristic
245C2×#11719924C2311yescharacteristic
246C2×D424C2311yescharacteristic
247C2×D424C2311yescharacteristic
248C2×D424C2311yescharacteristic
249C2×#11719922C2311yescharacteristic
250C2×#11719922C2311yescharacteristic
251C2×#11719922C2311yescharacteristic
252C2×#11719922C2311yescharacteristic
253C2×#11719917C2311yescharacteristic
254C2×#11719912C2311yescharacteristic
255C2×#11719912C2311yescharacteristic
256C22×#88322C2311yescharacteristic
257#13133216C2311yescharacteristic
258#13133216C2311yescharacteristic
259#13133216C2311yescharacteristic
260#13133215—21no—
261#13133215—21no—
262#13133215C2311yescharacteristic
263#13133215C2311yescharacteristic
264#13133215C2311yescharacteristic
265#13133215C2311yescharacteristic
266#13133214C2311yescharacteristic
267#13133213C2311yescharacteristic
268#13133213C2311yescharacteristic
269#13133213C2311yescharacteristic
270#13133212—21no—
271#13133211—21no—
272#13133210—21no—
273#13133210—21no—
274#13133207—21no—
275#13133207—21no—
276#13133206—21no—
277#13133206—21no—
278#13133206C2311yescharacteristic
279#13133205C2311yescharacteristic
280#13133204C2311yescharacteristic
281#13133203—21no—
282#13133203—21no—
283#13133203—21no—
284#13133203—21no—
285#13133203—21no—
286#13133202—21no—
287#13133202—21no—
288#13133202—21no—
289#13133200—21no—
290#13133200—21no—
291#13133200—21no—
292#13133199—21no—
293#13133198—21no—
294#13133197C2311yescharacteristic
295#13133196C2311yescharacteristic
296#13133195—21no—
297#13133195—21no—
298#13133195—21no—
299#13133195—21no—
300#13133195—21no—
301#13133195—21no—
302#13133195—21no—
303#13133194—21no—
304#13133194—21no—
305#13133194—21no—
306#13133193—21no—
307#13133193—21no—
308#13133193C2311yescharacteristic
309#13133192—21no—
310#13133192—21no—
311#13133192C2311yescharacteristic
312#13133192C2311yescharacteristic
313#13133191—21no—
314#13133191—21no—
315#13133191C2311yescharacteristic
316#13133191C2311yescharacteristic
317#13133191C2311yescharacteristic
318#13133190—21no—
319#13133190—21no—
320#13133190—21no—
321#13133190—21no—
322#13133190—21no—
323#13133190—21no—
324#13133190—21no—
325#13133189—21no—
326#13133189—21no—
327#13133189—21no—
328#13133189—21no—
329#13133189—21no—
330#13133189—21no—
331#13133189—21no—
332#13133189—21no—
333#13133187—21no—
334#13133187—21no—
335#13133187—21no—
336#13133187—21no—
337#13133185—21no—
338#13133185—21no—
339Q8×Dic53C2311yescharacteristic
340C4×Dic106—21no—
341C4×Dic106C2311yescharacteristic
342C4×Dic106C2311yescharacteristic
343#13133182—21no—
344#13133182D411yescharacteristic
345#13133182C2311yescharacteristic
346C4×D212C2311yescharacteristic
347D4×Dic53—21no—
348D4×Dic53D411yescharacteristic
349D4×Dic53C2311yescharacteristic
350D4×Dic53C2311yescharacteristic
351#13133179—21no—
352#13133179—21no—
353#13133179—21no—
354#13133179—21no—
355#13133179—21no—
356#13133179C2311yescharacteristic
357#13133179C2311yescharacteristic
358#13133179C2311yescharacteristic
359#13133179C2311yescharacteristic
360#13133179C2311yescharacteristic
361#13133179C2311yescharacteristic
362#13133179C2311yescharacteristic
363#13133179C2311yescharacteristic
364C4×C22⋊D53—21no—
365C4×C22⋊D53—21no—
366C4×C22⋊D53—21no—
367C4×C22⋊D53—21no—
368C4×C22⋊D53C2311yescharacteristic
369C4×C22⋊D53C2311yescharacteristic
370#13133177—21no—
371#13133177—21no—
372#13133177—21no—
373#13133177—21no—
374#13133177—21no—
375#13133177—21no—
376#13133177—21no—
377#13133177D411yescharacteristic
378#13133177D411yescharacteristic
379#13133175D411yescharacteristic
380#13133174—21no—
381#13133174—21no—
382#13133173—21no—
383#13133173—21no—
384#13133173D411yescharacteristic
385#13133173D411yescharacteristic
386C2×#11719919—21no—
387C2×#11719919—21no—
388C2×#11719919—21no—
389C4⋊C4×D53—21no—
390C4⋊C4×D53C2311yescharacteristic
391C2×#11719921—21no—
392C2×#11719921—21no—
393C22⋊C4×D53—21no—
394C2×C4×Dic53C2311yescharacteristic
395C2×C4×Dic53C2311yescharacteristic
396C42×D53C2311yescharacteristic
397#13133151C2311yescharacteristic
398#13133150C2311yescharacteristic
399#13133150C2311yescharacteristic
400#13133150C2311yescharacteristic
401#13133150C2311yescharacteristic
402C4⋊#88322C2311yescharacteristic
403#13133146C2311yescharacteristic
404#13133146C2311yescharacteristic
405#13133146C2311yescharacteristic
406#13133146C2311yescharacteristic
407#13133146C2311yescharacteristic
408#13133146C2311yescharacteristic
409#13133146C2311yescharacteristic
410#13133146C2311yescharacteristic
411#13133142C2311yescharacteristic
412#13133142C2311yescharacteristic
413#13133141C2311yescharacteristic
414#13133141C2311yescharacteristic
415#13133140C2311yescharacteristic
416#13133140C2311yescharacteristic
417#13133140C2311yescharacteristic
418#13133140C2311yescharacteristic
419#13133140C2311yescharacteristic
420#13133140C2311yescharacteristic
421#13133139C2311yescharacteristic
422#13133139C2311yescharacteristic
423#13133139C2311yescharacteristic
424#13133139C2311yescharacteristic
425#13133138C2311yescharacteristic
426#13133138C2311yescharacteristic
427#13133137C2311yescharacteristic
428#13133137C2311yescharacteristic
429#13133137C2311yescharacteristic
430#13133137C2311yescharacteristic
431#13133137C2311yescharacteristic
432#13133137C2311yescharacteristic
433C22⋊#88322C2311yescharacteristic
434C22⋊#88322C2311yescharacteristic
435#13133129C2311yescharacteristic
436#13133129C2311yescharacteristic
437#13133128C2311yescharacteristic
438#13133127C2311yescharacteristic
439#13133127C2311yescharacteristic
440C8×Dic53C2311yescharacteristic
441C8×Dic53C2311yescharacteristic
442C2×#41×C53—21no—
443C2×#41×C53C2311yescharacteristic
444C22×Q8×C53C2311yescharacteristic
445C2×SD16×C53C2311yescharacteristic
446C2×SD16×C53C2311yescharacteristic
447C2×D8×C53C2311yescharacteristic
448C2×M16×C53C2311yescharacteristic
449C22×C8×C53C2311yescharacteristic
450C4⋊Q8×C53C2311yescharacteristic
451#124×C53—21no—
452#124×C53C2311yescharacteristic
453#123×C53—21no—
454#123×C53—21no—
455C22⋊Q8×C53—21no—
456C22⋊Q8×C53—21no—
457C22⋊Q8×C53C2311yescharacteristic
458#121×C53—21no—
459#121×C53C2311yescharacteristic
460#121×C53C2311yescharacteristic
461#121×C53C2311yescharacteristic
462C4×Q8×C53C2311yescharacteristic
463C4×D4×C53—21no—
464C4×D4×C53C2311yescharacteristic
465C4×D4×C53C2311yescharacteristic
466C2×C4⋊C4×C53C2311yescharacteristic
467C2×C4⋊C4×C53C2311yescharacteristic
468#107×C53C2311yescharacteristic
469#107×C53C2311yescharacteristic
470#107×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
480#102×C53C2311yescharacteristic
481#102×C53C2311yescharacteristic
482C22⋊C8×C53C2311yescharacteristic
483C22⋊C8×C53C2311yescharacteristic
484#97×C53C2311yescharacteristic
485C23×D53—21no—
486C23×D53—21no—
487C23×D53—21no—
488#41×C53—41no—
489#41×C53—41no—
490#41×C53—44no—
491C2×Q8×C53—21no—
492C2×Q8×C53—21no—
493C2×Q8×C53—41no—
494C2×Q8×C53—41no—
495C2×Q8×C53C2411yescharacteristic
496C2×Q8×C53C2411yescharacteristic
497C2×D4×C53—21no—
498C2×D4×C53—21no—
499C2×D4×C53—21no—
500C2×D4×C53—21no—
501C2×D4×C53C2×D411yescharacteristic
502C2×D4×C53C2411yescharacteristic
503C2×D4×C53C2411yescharacteristic
504C22×C4×C53—21no—
505C22×C4×C53—21no—
506C22×C4×C53—21no—
507C22×C4×C53—21no—
508C22×C4×C53—21no—
509C22×C4×C53C2411yescharacteristic
510C22×C4×C53C2411yescharacteristic
511C2×C22⋊D53—21no—
512C2×C22⋊D53—21no—
513C2×C22⋊D53—21no—
514C2×C22⋊D53—21no—
515C2×C22⋊D53—21no—
516C2×C22⋊D53—21no—
517C2×C22⋊D53—21no—
518C2×C22⋊D53—21no—
519C2×C22⋊D53—21no—
520C2×C22⋊D53—21no—
521C2×C22⋊D53—21no—
522C2×C22⋊D53—21no—
523C2×C22⋊D53C2×D411yescharacteristic
524C2×C22⋊D53C2×D411yescharacteristic
525C22×Dic53—21no—
526C22×Dic53—21no—
527C22×Dic53—21no—
528C22×Dic53—21no—
529C22×Dic53C2×D411yescharacteristic
530C22×Dic53C2×D411yescharacteristic
531C22×Dic53C2×D411yescharacteristic
532C22×Dic53C2×D411yescharacteristic
533#11719949—44no—
534#11719949—41no—
535#11719949—41no—
536Q8×D53—44no—
537#11719947—24no—
538#11719947—41no—
539#11719947—41no—
540#11719947—44no—
541#11719947—44no—
542#11719947—44no—
543D4×D53—22no—
544D4×D53—41no—
545D4×D53—44no—
546D4×D53—44no—
547D4×D53—44no—
548#11719945—44no—
549#11719945—41no—
550#11719945—41no—
551#11719945—44no—
552#11719945—44no—
553C2×D212—22no—
554C2×D212—22no—
555C2×D212—21no—
556C2×D212—21no—
557C2×D212—21no—
558C2×D212—21no—
559C2×D212—21no—
560C2×D212—21no—
561C2×D212—21no—
562C2×D212—41no—
563C2×D212—41no—
564C2×D212C2411yescharacteristic
565C2×D212C2411yescharacteristic
566C2×D212C2411yescharacteristic
567C2×D212C2411yescharacteristic
568C2×C4×D53—21no—
569C2×C4×D53—21no—
570C2×C4×D53—21no—
571C2×C4×D53—21no—
572C2×C4×D53—21no—
573C2×C4×D53—21no—
574C2×C4×D53—21no—
575C2×C4×D53—21no—
576C2×C4×D53—21no—
577C2×C4×D53—21no—
578C2×C4×D53—21no—
579C2×C4×D53—21no—
580C2×C4×D53—44no—
581C2×C4×D53—44no—
582C2×C4×D53—44no—
583C2×C4×D53C2×D411yescharacteristic
584C2×C4×D53C2×D411yescharacteristic
585C2×C4×D53C2411yescharacteristic
586C2×Dic106—21no—
587C2×Dic106—21no—
588C2×Dic106—21no—
589C2×Dic106—21no—
590C2×Dic106—41no—
591C2×Dic106—41no—
592C2×Dic106C2×D411yescharacteristic
593C2×Dic106C2411yescharacteristic
594C2×Dic106C2411yescharacteristic
595SD16×C53—41no—
596SD16×C53—41no—
597D8×C53—41no—
598M16×C53—41no—
599C2×C8×C53—41no—
600C2×C8×C53C2411yescharacteristic
601C2×C8×C53C2411yescharacteristic
602C2×C8×C53C2411yescharacteristic
603C2×C8×C53C2411yescharacteristic
604C4⋊C4×C53—21no—
605C4⋊C4×C53—21no—
606C4⋊C4×C53—21no—
607C4⋊C4×C53—21no—
608C4⋊C4×C53—21no—
609C4⋊C4×C53C2×D411yescharacteristic
610C4⋊C4×C53C2411yescharacteristic
611C4⋊C4×C53C2411yescharacteristic
612C4⋊C4×C53C2411yescharacteristic
613C4⋊C4×C53C2411yescharacteristic
614C22⋊C4×C53—21no—
615C22⋊C4×C53—21no—
616C22⋊C4×C53—21no—
617C22⋊C4×C53—21no—
618C22⋊C4×C53—21no—
619C22⋊C4×C53—21no—
620C22⋊C4×C53—21no—
621C22⋊C4×C53C2×D411yescharacteristic
622C22⋊C4×C53C2×D411yescharacteristic
623C42×C53—21no—
624C42×C53C2411yescharacteristic
625C22⋊Dic53—21no—
626C22⋊Dic53—21no—
627C22⋊Dic53—21no—
628C22⋊Dic53—21no—
629C22⋊Dic53—21no—
630C22⋊Dic53C2×D411yescharacteristic
631C22⋊Dic53C2×D411yescharacteristic
632#11719924—22no—
633#11719924—22no—
634#11719924—41no—
635#11719924—41no—
636#11719924—41no—
637#11719924—41no—
638#11719923—41no—
639#11719923—41no—
640#11719922—22no—
641#11719922—41no—
642#11719922—41no—
643#11719922—41no—
644#11719921—21no—
645#11719921—21no—
646#11719921—21no—
647#11719921—21no—
648#11719921—21no—
649#11719921—21no—
650#11719921—21no—
651#11719921—21no—
652#11719921—21no—
653#11719921—21no—
654#11719921—21no—
655#11719921—21no—
656#11719921—21no—
657#11719921—21no—
658#11719921—21no—
659#11719921—21no—
660#11719921—21no—
661#11719921—21no—
662#11719921—21no—
663#11719921—21no—
664#11719921C2×D411yescharacteristic
665#11719921C2×D411yescharacteristic
666C4⋊Dic53—21no—
667C4⋊Dic53—21no—
668C4⋊Dic53C2×D411yescharacteristic
669C4⋊Dic53C2411yescharacteristic
670C4⋊Dic53C2411yescharacteristic
671#11719919—21no—
672#11719919—21no—
673#11719919—21no—
674#11719919—21no—
675#11719919—21no—
676#11719919—21no—
677#11719919—21no—
678#11719919—21no—
679#11719919—21no—
680#11719919—21no—
681#11719919—21no—
682#11719919—21no—
683#11719919—21no—
684#11719919—21no—
685#11719919—21no—
686#11719919—21no—
687#11719919C2×D411yescharacteristic
688#11719919C2×D411yescharacteristic
689#11719919C2×D411yescharacteristic
690#11719919C2×D411yescharacteristic
691C4×Dic53—21no—
692C4×Dic53—21no—
693C4×Dic53—21no—
694C4×Dic53C2×D411yescharacteristic
695C4×Dic53C2×D411yescharacteristic
696C4×Dic53C2×D411yescharacteristic
697C4×Dic53C2×D411yescharacteristic
698C4×Dic53C2×D411yescharacteristic
699C4×Dic53C2×D411yescharacteristic
700C4×Dic53C2411yescharacteristic
701C4×Dic53C2411yescharacteristic
702C4×Dic53C2411yescharacteristic
703#11719917—41no—
704C2×#88322—41no—
705C2×#88322C2411yescharacteristic
706C2×#88322C2411yescharacteristic
707C2×#88322C2411yescharacteristic
708C2×#88322C2411yescharacteristic
709D424—22no—
710D424—41no—
711D424—41no—
712#11719913—22no—
713#11719913—22no—
714#11719913—41no—
715#11719913—41no—
716#11719913—41no—
717#11719913—41no—
718#11719912—41no—
719#11719912—41no—
720C23×C53—21no—
721C23×C53—21no—
722C23×C53C22×D411yescharacteristic
723C23×C53C22×D411yescharacteristic
724C22×D53—21no—
725C22×D53—21no—
726C22×D53—21no—
727C22×D53—21no—
728C22×D53—42no—
729C22×D53—42no—
730C22×D53—42no—
731C22×D53—42no—
732C22×D53—42no—
733C22×D53—42no—
734C22×D53—81no—
735C22×D53—81no—
736C22×D53—81no—
737C22×D53C22×D411yescharacteristic
738Q8×C53—21no—
739Q8×C53—21no—
740Q8×C53—21no—
741Q8×C53—21no—
742Q8×C53—42no—
743Q8×C53—81no—
744D4×C53—22no—
745D4×C53—21no—
746D4×C53—21no—
747D4×C53—21no—
748D4×C53—21no—
749D4×C53—42no—
750D4×C53—42no—
751D4×C53—42no—
752D4×C53—81no—
753C2×C4×C53—21no—
754C2×C4×C53—21no—
755C2×C4×C53—21no—
756C2×C4×C53—21no—
757C2×C4×C53—21no—
758C2×C4×C53—21no—
759C2×C4×C53—21no—
760C2×C4×C53—21no—
761C2×C4×C53—21no—
762C2×C4×C53—21no—
763C2×C4×C53—42no—
764C2×C4×C53—42no—
765C2×C4×C53—42no—
766C2×C4×C53—81no—
767C2×C4×C53—81no—
768C2×C4×C53C22×D411yescharacteristic
769C2×C4×C53C22×D411yescharacteristic
770C2×C4×C53C22×D411yescharacteristic
771C2×C4×C53C22×D411yescharacteristic
772C2×C4×C53C2511yescharacteristic
773C22⋊D53—22no—
774C22⋊D53—22no—
775C22⋊D53—42no—
776C22⋊D53—42no—
777C22⋊D53—42no—
778C22⋊D53—42no—
779C22⋊D53—42no—
780C22⋊D53—42no—
781C22⋊D53—42no—
782C22⋊D53—42no—
783C22⋊D53—81no—
784C22⋊D53—81no—
785C22⋊D53—81no—
786C22⋊D53—81no—
787C2×Dic53—22no—
788C2×Dic53—21no—
789C2×Dic53—21no—
790C2×Dic53—21no—
791C2×Dic53—21no—
792C2×Dic53—41no—
793C2×Dic53—41no—
794C2×Dic53—42no—
795C2×Dic53—42no—
796C2×Dic53—81no—
797C2×Dic53—81no—
798C2×Dic53AGL(1,ℤ/8)14yescomplemented
799C2×Dic53C22×D411yescharacteristic
800C2×Dic53C22×D411yescharacteristic
801C2×Dic53C22×D411yescharacteristic
802C2×Dic53C22×D411yescharacteristic
803C2×Dic53C22×D411yescharacteristic
804C2×Dic53C22×D411yescharacteristic
805C2×Dic53C22×D411yescharacteristic
806D212—21no—
807D212—21no—
808D212—21no—
809D212—21no—
810D212—21no—
811D212—21no—
812D212—21no—
813D212—42no—
814D212—42no—
815D212—42no—
816D212—42no—
817D212—42no—
818D212—81no—
819D212—81no—
820D212H(5,𝔽2)12yes—
821C4×D53—21no—
822C4×D53—21no—
823C4×D53—22no—
824C4×D53—41no—
825C4×D53—42no—
826C4×D53—42no—
827C4×D53—42no—
828C4×D53—42no—
829C4×D53—42no—
830C4×D53—42no—
831C4×D53—42no—
832C4×D53—42no—
833C4×D53—42no—
834C4×D53—42no—
835C4×D53—81no—
836C4×D53—81no—
837Dic106—22no—
838Dic106—21no—
839Dic106—21no—
840Dic106—21no—
841Dic106—21no—
842Dic106—42no—
843Dic106—42no—
844Dic106—42no—
845Dic106—81no—
846C8×C53—21no—
847C8×C53—21no—
848C8×C53—21no—
849C8×C53—21no—
850#88322—21no—
851#88322—21no—
852#88322—21no—
853#88322—21no—
854#61962—531nomaximal, Sylow
855C22×C53—21no—
856C22×C53—21no—
857C22×C53—21no—
858C22×C53—21no—
859C22×C53—21no—
860C22×C53—41no—
861C22×C53—41no—
862C22×C53—41no—
863C22×C53—41no—
864C22×C53—41no—
865C22×C53—41no—
866C22×C53C2×AGL(1,ℤ/8)12yes—
867C22×C53C23×D411yescharacteristic
868C2×D53—21no—
869C2×D53—21no—
870C2×D53—22no—
871C2×D53—21no—
872C2×D53—41no—
873C2×D53—41no—
874C2×D53—41no—
875C2×D53—41no—
876C2×D53—41no—
877C2×D53—41no—
878C2×D53—41no—
879C2×D53—41no—
880C2×D53—41no—
881C2×D53—41no—
882C2×D53—41no—
883C2×D53—84no—
884C2×D53—84no—
885C2×D53—84no—
886C4×C53—21no—
887C4×C53—21no—
888C4×C53—21no—
889C4×C53—21no—
890C4×C53—41no—
891C4×C53—41no—
892C4×C53—41no—
893C4×C53—41no—
894C4×C53—41no—
895C4×C53—41no—
896C4×C53C2×H(5,𝔽2)11yescharacteristic
897C4×C53#58511yescharacteristic
898Dic53—21no—
899Dic53—21no—
900Dic53—21no—
901Dic53—21no—
902Dic53—21no—
903Dic53—41no—
904Dic53—41no—
905Dic53—41no—
906Dic53—41no—
907Dic53C2×AGL(1,ℤ/8)12yes—
908Dic53C2×AGL(1,ℤ/8)12yes—
909#3511—531no—
910D4×#41—531no—
911#3397—531no—
912#3397—531no—
913#3367—531no—
914#3367—531no—
915#3330—531no—
916#3330—531no—
917#3308—531no—
918#3308—531no—
919#3308—531no—
920#3308D5311yescharacteristic, complemented
921#3272—531no—
922#3272—531no—
923#3265—531no—
924#3265—531no—
925#3265—531no—
926#3265—531no—
927#3254—531no—
928#3254—531no—
929#3245—531no—
930#3214—531no—
931#3214—531no—
932#3206—531no—
933#3110—531no—
934#3110—531no—
935#3100—531no—
936#3036—531no—
937#3036—531no—
938C2×#461—531no—
939#2989—531no—
940C2×C53—22no—
941C2×C53—41no—
942C2×C53—81no—
943C2×C53—81no—
944C2×C53#348811yescharacteristic
945C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
946C2×C53#358611yescharacteristic
947D53—41no—
948D53—42no—
949D53—81no—
950D53—81no—
951D53—81no—
952C22×#41—1061no—
953C2×AGL(1,ℤ/8)—531no—
954C2×AGL(1,ℤ/8)—531no—
955C2×AGL(1,ℤ/8)—531no—
956C2×AGL(1,ℤ/8)—531no—
957C22×SD16—531no—
958C22×SD16—531no—
959#556—531no—
960#556—531no—
961#555—1061no—
962#554—1061no—
963#553—1061no—
964#553—1061no—
965#550—531no—
966D4×Q8—531no—
967#548—531no—
968#548—531no—
969#548—531no—
970#548—1061no—
971#548C2×D5311yescharacteristic, complemented
972#547—531no—
973#547—531no—
974#547—531no—
975#547—531no—
976#547C2×D5311yescharacteristic
977#546—1061no—
978#546—1061no—
979#546—1061no—
980D42—531no—
981D42—531no—
982D42—531no—
983#542—1061no—
984#542—1061no—
985#537—1061no—
986#533—531no—
987#533—531no—
988#532—531no—
989#532—531no—
990#532—531no—
991#532—531no—
992#532—531no—
993#532—531no—
994C2×C4⋊Q8—531no—
995#525—1061no—
996#525—1061no—
997#525—1061no—
998#520—1061no—
999C4×#41—531no—
1000C2×C4×D4—531no—
1001C2×C4×D4—531no—
1002C2×C4×D4—531no—
1003#496—531no—
1004#496—531no—
1005#496—531no—
1006#496—531no—
1007#492—531no—
1008#492—531no—
1009#489—531no—
1010#489—531no—
1011#489—531no—
1012#489C2×D5311yescharacteristic, complemented
1013#487—531no—
1014#487—531no—
1015#484—531no—
1016#484—531no—
1017#484—531no—
1018#484C2×D5311yescharacteristic, complemented
1019#480—531no—
1020#480C2×D5311yescharacteristic, complemented
1021#477—531no—
1022#477—531no—
1023#477—531no—
1024#477C2×D5311yescharacteristic, complemented
1025#474—531no—
1026#474—531no—
1027#474—531no—
1028#474—531no—
1029#474—531no—
1030#474—531no—
1031#468—531no—
1032#468—531no—
1033#468—531no—
1034#468—531no—
1035#468—531no—
1036#468—531no—
1037#468—531no—
1038#468C2×D5311yescharacteristic, complemented
1039#466—531no—
1040#466—531no—
1041#466—531no—
1042#466C2×D5311yescharacteristic, complemented
1043#463—531no—
1044#463—531no—
1045#463—531no—
1046#463—531no—
1047#463—531no—
1048#463—531no—
1049#463—531no—
1050#463C2×D5311yescharacteristic, complemented
1051#461—531no—
1052#461—531no—
1053#461—531no—
1054#461—531no—
1055#461—531no—
1056#461—531no—
1057#461—531no—
1058#461—531no—
1059#461—531no—
1060#461—531no—
1061#461—531no—
1062#461—531no—
1063#460—531no—
1064#460—531no—
1065#460—531no—
1066#460—531no—
1067#459—531no—
1068#459—531no—
1069#459—531no—
1070#459—531no—
1071#459—531no—
1072#459—531no—
1073#450—531no—
1074#450—531no—
1075#450—531no—
1076#450—531no—
1077#449—531no—
1078#449—531no—
1079#449—531no—
1080#449—531no—
1081#449—531no—
1082#449—531no—
1083#449—531no—
1084#449C2×D5311yescharacteristic, complemented
1085#448—531no—
1086#448—531no—
1087#448—531no—
1088#448C2×D5311yescharacteristic, complemented
1089#447—531no—
1090#447—531no—
1091#446—531no—
1092#446—531no—
1093#440—531no—
1094#440—531no—
1095#440—531no—
1096#440—531no—
1097#440—531no—
1098#440—531no—
1099#440—531no—
1100#440C2×D5311yescharacteristic, complemented
1101C4×D8—531no—
1102C4×D8—531no—
1103C4×D8—531no—
1104C4×D8—531no—
1105#436—531no—
1106#436—531no—
1107#435—531no—
1108#435—531no—
1109#435—531no—
1110#435C2×D5311yescharacteristic, complemented
1111#432—531no—
1112#432—531no—
1113#431—531no—
1114#423—531no—
1115#423—531no—
1116C2×C4⋊C8—531no—
1117#417—531no—
1118#417—531no—
1119#417—531no—
1120#417C2×D5311yescharacteristic, complemented
1121C2×#103—531no—
1122C2×#103C2×D5311yescharacteristic, complemented
1123C53#6196211yescharacteristic, complemented, Sylow
1124C2×#41—21no—
1125C2×#41—531no—
1126C2×#41—531no—
1127C2×#41—531no—
1128C2×#41—531no—
1129C2×#41—1061no—
1130C2×#41—1061no—
1131C2×#41—1061no—
1132C2×#41—1061no—
1133C2×#41—1061no—
1134C2×#41—1061no—
1135C2×#41—1061no—
1136C2×#41—2128no—
1137C2×#41C22×D5311yescharacteristic
1138C22×Q8—531no—
1139C22×Q8—1061no—
1140C22×Q8C22×D5311yescharacteristic
1141C22×D4—531no—
1142C22×D4—531no—
1143C22×D4—531no—
1144C22×D4—1061no—
1145C22×D4—1061no—
1146C22×D4—1061no—
1147C23×C4—1061no—
1148C23×C4—1061no—
1149C23×C4—1061no—
1150AGL(1,ℤ/8)—2122no—
1151AGL(1,ℤ/8)—2122no—
1152AGL(1,ℤ/8)—2122no—
1153AGL(1,ℤ/8)—2122no—
1154C2×SD16—531no—
1155C2×SD16—531no—
1156C2×SD16—531no—
1157C2×SD16—531no—
1158C2×SD16—531no—
1159C2×SD16—531no—
1160C2×SD16—531no—
1161C2×SD16—531no—
1162C2×SD16—531no—
1163C2×SD16—531no—
1164C2×SD16—531no—
1165C2×SD16—531no—
1166C2×SD16—531no—
1167C2×SD16—531no—
1168C2×SD16—2122no—
1169C2×SD16—2122no—
1170C2×SD16C22×D5311yescharacteristic
1171C2×SD16C22×D5311yescharacteristic
1172C2×D8—531no—
1173C2×D8—531no—
1174C2×D8—531no—
1175C2×D8—531no—
1176C2×D8—531no—
1177C2×D8—531no—
1178C2×D8—531no—
1179C2×D8C22×D5311yescharacteristic
1180C2×M16—531no—
1181C2×M16—531no—
1182C2×M16—531no—
1183C2×M16C22×D5311yescharacteristic
1184C22×C8—531no—
1185C22×C8C22×D5311yescharacteristic
1186C4⋊Q8—531no—
1187C4⋊Q8—531no—
1188C4⋊Q8—531no—
1189C4⋊Q8—531no—
1190C4⋊Q8—531no—
1191C4⋊Q8—531no—
1192C4⋊Q8—531no—
1193C4⋊Q8—1061no—
1194C4⋊Q8—1061no—
1195C4⋊Q8C22×D5311yescharacteristic
1196#127—531no—
1197#127—531no—
1198#127—531no—
1199#127—531no—
1200#126—1061no—
1201#126—1061no—
1202#126—1061no—
1203#126—1061no—
1204#125—1061no—
1205#125—1061no—
1206#124—21no—
1207#124—531no—
1208#124—531no—
1209#124—531no—
1210#124—1061no—
1211#124—1061no—
1212#124—1061no—
1213#124—1061no—
1214#124—1061no—
1215#124—1061no—
1216#124—1061no—
1217#124C22×D5311yescharacteristic
1218#123—21no—
1219#123—21no—
1220#123—1061no—
1221#123—1061no—
1222#123—1061no—
1223#123—1061no—
1224#123—1061no—
1225#123—1061no—
1226#123—1061no—
1227#123—1061no—
1228C22⋊Q8—21no—
1229C22⋊Q8—21no—
1230C22⋊Q8—531no—
1231C22⋊Q8—531no—
1232C22⋊Q8—531no—
1233C22⋊Q8—1061no—
1234C22⋊Q8—1061no—
1235C22⋊Q8—1061no—
1236C22⋊Q8—1061no—
1237C22⋊Q8—1061no—
1238C22⋊Q8—1061no—
1239C22⋊Q8—1061no—
1240C22⋊Q8—1061no—
1241C22⋊Q8—1061no—
1242C22⋊Q8—1061no—
1243C22⋊Q8—1061no—
1244C22⋊Q8—1061no—
1245C22⋊Q8C22×D5311yescharacteristic
1246#121—21no—
1247#121—531no—
1248#121—531no—
1249#121—531no—
1250#121—531no—
1251#121—531no—
1252#121—1061no—
1253#121—1061no—
1254#121—1061no—
1255#121—1061no—
1256#121—1061no—
1257#121—1061no—
1258#121—1061no—
1259#121—1061no—
1260#121—1061no—
1261#121—1061no—
1262#121—1061no—
1263#121—1061no—
1264#121—1061no—
1265#121—1061no—
1266#121—1061no—
1267#121—1061no—
1268#121—1061no—
1269#121—1061no—
1270#121—1061no—
1271#121C22×D5311yescharacteristic
1272#121C22×D5311yescharacteristic
1273#121C22×D5311yescharacteristic
1274#120—1061no—
1275#120—1061no—
1276#120—1061no—
1277#120—1061no—
1278#120—1061no—
1279#120—1061no—
1280C4×Q8—531no—
1281C4×Q8—531no—
1282C4×Q8—531no—
1283C4×Q8—531no—
1284C4×Q8—531no—
1285C4×Q8—1061no—
1286C4×Q8—1061no—
1287C4×Q8C22×D5311yescharacteristic
1288C4×D4—21no—
1289C4×D4—531no—
1290C4×D4—531no—
1291C4×D4—531no—
1292C4×D4—531no—
1293C4×D4—531no—
1294C4×D4—531no—
1295C4×D4—531no—
1296C4×D4—531no—
1297C4×D4—531no—
1298C4×D4—531no—
1299C4×D4—531no—
1300C4×D4—531no—
1301C4×D4—531no—
1302C4×D4—531no—
1303C4×D4—531no—
1304C4×D4—531no—
1305C4×D4—1061no—
1306C4×D4—1061no—
1307C4×D4—1061no—
1308C4×D4—1061no—
1309C4×D4—1061no—
1310C4×D4—1061no—
1311C4×D4—1061no—
1312C4×D4—1061no—
1313C4×D4—1061no—
1314C4×D4—1061no—
1315C4×D4—1061no—
1316C4×D4—1061no—
1317C4×D4—1061no—
1318C4×D4—1061no—
1319C4×D4—1061no—
1320C4×D4—1061no—
1321C4×D4—1061no—
1322C4×D4C22×D5311yescharacteristic
1323C4×D4C22×D5311yescharacteristic
1324#117—531no—
1325#117—531no—
1326#117—531no—
1327#117—1061no—
1328#117—1061no—
1329#117—1061no—
1330#117—1061no—
1331C2×C4⋊C4—531no—
1332C2×C4⋊C4—1061no—
1333C2×C4⋊C4—1061no—
1334C2×C4⋊C4—1061no—
1335C2×C4⋊C4—1061no—
1336C2×C4⋊C4C22×D5311yescharacteristic
1337C2×C4⋊C4C22×D5311yescharacteristic
1338C2×C22⋊C4—1061no—
1339C2×C22⋊C4—1061no—
1340C2×C22⋊C4—1061no—
1341C2×C42—531no—
1342C2×C42—531no—
1343C2×C42—531no—
1344#107—531no—
1345#107—531no—
1346#107—531no—
1347#107—531no—
1348#107—531no—
1349#107C22×D5311yescharacteristic
1350#107C22×D5311yescharacteristic
1351#107C22×D5311yescharacteristic
1352C4⋊C8—531no—
1353C4⋊C8—531no—
1354C4⋊C8—531no—
1355C4⋊C8—531no—
1356C4⋊C8—531no—
1357C4⋊C8—531no—
1358C4⋊C8—531no—
1359C4⋊C8—531no—
1360C4⋊C8—531no—
1361C4⋊C8C22×D5311yescharacteristic
1362#103—531no—
1363#103—531no—
1364#103—531no—
1365#103—531no—
1366#103—531no—
1367#103—531no—
1368#103—531no—
1369#103—531no—
1370#103—531no—
1371#103—531no—
1372#103C22×D5311yescharacteristic
1373#103C22×D5311yescharacteristic
1374#103C22×D5311yescharacteristic
1375#103C22×D5311yescharacteristic
1376#103C22×D5311yescharacteristic
1377#103C22×D5311yescharacteristic
1378#102—531no—
1379#102—531no—
1380#102—531no—
1381#102—531no—
1382#102—531no—
1383#102—531no—
1384#102—531no—
1385#102—531no—
1386#102—531no—
1387#102—531no—
1388#102—531no—
1389#102—531no—
1390#102C22×D5311yescharacteristic
1391#102C22×D5311yescharacteristic
1392#102C22×D5311yescharacteristic
1393#102C22×D5311yescharacteristic
1394C22⋊C8—531no—
1395C22⋊C8—531no—
1396C22⋊C8—531no—
1397C22⋊C8—531no—
1398C22⋊C8C22×D5311yescharacteristic
1399C22⋊C8C22×D5311yescharacteristic
1400#97—531no—
1401#97—531no—
1402#97—531no—
1403#97C22×D5311yescharacteristic
1404C4×C8—531no—
1405C4×C8—531no—
1406C24—1061no—
1407C24—1061no—
1408C24—1061no—
1409#41—41no—
1410#41—41no—
1411#41—44no—
1412#41—1064no—
1413#41—2121no—
1414#41—2121no—
1415#41—2124no—
1416#41—2124no—
1417#41—2124no—
1418#41—2124no—
1419#41—2124no—
1420#41—2121no—
1421#41—2121no—
1422#41—2121no—
1423#41—2121no—
1424#41—2124no—
1425#41—2124no—
1426C2×Q8—21no—
1427C2×Q8—21no—
1428C2×Q8—41no—
1429C2×Q8—41no—
1430C2×Q8—531no—
1431C2×Q8—531no—
1432C2×Q8—531no—
1433C2×Q8—1061no—
1434C2×Q8—1061no—
1435C2×Q8—1061no—
1436C2×Q8—1061no—
1437C2×Q8—2121no—
1438C2×Q8—2121no—
1439C2×Q8—2124no—
1440C2×Q8C23×D5311yescharacteristic
1441C2×Q8C23×D5311yescharacteristic
1442C2×D4—21no—
1443C2×D4—21no—
1444C2×D4—21no—
1445C2×D4—21no—
1446C2×D4—531no—
1447C2×D4—531no—
1448C2×D4—531no—
1449C2×D4—531no—
1450C2×D4—531no—
1451C2×D4—531no—
1452C2×D4—1062no—
1453C2×D4—1062no—
1454C2×D4—1061no—
1455C2×D4—1061no—
1456C2×D4—1061no—
1457C2×D4—1061no—
1458C2×D4—1061no—
1459C2×D4—1061no—
1460C2×D4—1061no—
1461C2×D4—1061no—
1462C2×D4—1061no—
1463C2×D4—1061no—
1464C2×D4—1062no—
1465C2×D4—1061no—
1466C2×D4—1061no—
1467C2×D4—1061no—
1468C2×D4—1061no—
1469C2×D4—1061no—
1470C2×D4—1061no—
1471C2×D4—1061no—
1472C2×D4—1061no—
1473C2×D4—1061no—
1474C2×D4—2121no—
1475C2×D4—2121no—
1476C2×D4—2121no—
1477C2×D4—2124no—
1478C2×D4—2124no—
1479C2×D4—2124no—
1480C2×D4D4×D5311yescharacteristic
1481C2×D4C23×D5311yescharacteristic
1482C2×D4C23×D5311yescharacteristic
1483C22×C4—21no—
1484C22×C4—21no—
1485C22×C4—21no—
1486C22×C4—21no—
1487C22×C4—21no—
1488C22×C4—531no—
1489C22×C4—531no—
1490C22×C4—531no—
1491C22×C4—531no—
1492C22×C4—531no—
1493C22×C4—531no—
1494C22×C4—531no—
1495C22×C4—1061no—
1496C22×C4—1061no—
1497C22×C4—1061no—
1498C22×C4—1061no—
1499C22×C4—1061no—
1500C22×C4—1061no—
1501C22×C4—1061no—
1502C22×C4—1061no—
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—2124no—
1512C22×C4—2124no—
1513C22×C4—2124no—
1514C22×C4C23×D5311yescharacteristic
1515C22×C4C23×D5311yescharacteristic
1516SD16—41no—
1517SD16—41no—
1518SD16—1062no—
1519SD16—1062no—
1520SD16—1062no—
1521SD16—1062no—
1522SD16—2121no—
1523SD16—2121no—
1524SD16—2121no—
1525SD16—2121no—
1526SD16—2121no—
1527SD16—2121no—
1528SD16—2121no—
1529SD16—2121no—
1530SD16—2121no—
1531SD16—2121no—
1532D8—41no—
1533D8—1062no—
1534D8—1062no—
1535D8—2121no—
1536D8—2121no—
1537D8—2121no—
1538D8—2121no—
1539D8—2121no—
1540M16—41no—
1541M16—2121no—
1542M16—2121no—
1543M16—2121no—
1544C2×C8—41no—
1545C2×C8—531no—
1546C2×C8—531no—
1547C2×C8—531no—
1548C2×C8—531no—
1549C2×C8—2121no—
1550C2×C8C23×D5311yescharacteristic
1551C2×C8C23×D5311yescharacteristic
1552C2×C8C23×D5311yescharacteristic
1553C2×C8C23×D5311yescharacteristic
1554C4⋊C4—21no—
1555C4⋊C4—21no—
1556C4⋊C4—21no—
1557C4⋊C4—21no—
1558C4⋊C4—21no—
1559C4⋊C4—531no—
1560C4⋊C4—531no—
1561C4⋊C4—531no—
1562C4⋊C4—531no—
1563C4⋊C4—531no—
1564C4⋊C4—531no—
1565C4⋊C4—531no—
1566C4⋊C4—1061no—
1567C4⋊C4—1061no—
1568C4⋊C4—1061no—
1569C4⋊C4—1061no—
1570C4⋊C4—1061no—
1571C4⋊C4—1061no—
1572C4⋊C4—1061no—
1573C4⋊C4—1061no—
1574C4⋊C4—1061no—
1575C4⋊C4—1061no—
1576C4⋊C4—1061no—
1577C4⋊C4—1061no—
1578C4⋊C4—1061no—
1579C4⋊C4—1061no—
1580C4⋊C4—1061no—
1581C4⋊C4—1061no—
1582C4⋊C4—1061no—
1583C4⋊C4—1061no—
1584C4⋊C4D4×D5311yescharacteristic
1585C4⋊C4C23×D5311yescharacteristic
1586C4⋊C4C23×D5311yescharacteristic
1587C4⋊C4C23×D5311yescharacteristic
1588C4⋊C4C23×D5311yescharacteristic
1589C22⋊C4—21no—
1590C22⋊C4—21no—
1591C22⋊C4—21no—
1592C22⋊C4—21no—
1593C22⋊C4—21no—
1594C22⋊C4—21no—
1595C22⋊C4—21no—
1596C22⋊C4—531no—
1597C22⋊C4—531no—
1598C22⋊C4—531no—
1599C22⋊C4—531no—
1600C22⋊C4—1061no—
1601C22⋊C4—1061no—
1602C22⋊C4—1061no—
1603C22⋊C4—1061no—
1604C22⋊C4—1061no—
1605C22⋊C4—1061no—
1606C22⋊C4—1061no—
1607C22⋊C4—1061no—
1608C22⋊C4—1061no—
1609C22⋊C4—1061no—
1610C22⋊C4—1061no—
1611C22⋊C4—1061no—
1612C22⋊C4—1061no—
1613C22⋊C4—1061no—
1614C22⋊C4—1061no—
1615C22⋊C4—1061no—
1616C22⋊C4—1061no—
1617C22⋊C4—1061no—
1618C22⋊C4—1061no—
1619C22⋊C4—1061no—
1620C22⋊C4—1061no—
1621C22⋊C4—1061no—
1622C22⋊C4—1061no—
1623C22⋊C4—1061no—
1624C22⋊C4—1061no—
1625C22⋊C4D4×D5311yescharacteristic
1626C22⋊C4D4×D5311yescharacteristic
1627C42—21no—
1628C42—531no—
1629C42—531no—
1630C42—531no—
1631C42—531no—
1632C42—531no—
1633C42—531no—
1634C42—531no—
1635C42—531no—
1636C42—531no—
1637C42—1061no—
1638C42—1061no—
1639C42—1061no—
1640C42C23×D5311yescharacteristic
1641C23—21no—
1642C23—21no—
1643C23—531no—
1644C23—1061no—
1645C23—1061no—
1646C23—1061no—
1647C23—1061no—
1648C23—4241no—
1649C23—4241no—
1650C23—4241no—
1651C23—2122no—
1652C23—2122no—
1653C23—2122no—
1654C23—2122no—
1655C23—2122no—
1656C23—2122no—
1657C23C2×D4×D5311yescharacteristic
1658C23C2×D4×D5311yescharacteristic
1659Q8—21no—
1660Q8—21no—
1661Q8—21no—
1662Q8—21no—
1663Q8—42no—
1664Q8—81no—
1665Q8—1062no—
1666Q8—1061no—
1667Q8—1061no—
1668Q8—1061no—
1669Q8—1061no—
1670Q8—4241no—
1671Q8—2122no—
1672Q8—2122no—
1673Q8—2122no—
1674D4—22no—
1675D4—21no—
1676D4—21no—
1677D4—21no—
1678D4—21no—
1679D4—42no—
1680D4—42no—
1681D4—42no—
1682D4—81no—
1683D4—532no—
1684D4—1062no—
1685D4—1062no—
1686D4—1061no—
1687D4—1061no—
1688D4—1061no—
1689D4—1061no—
1690D4—1061no—
1691D4—1061no—
1692D4—1061no—
1693D4—4241no—
1694D4—4241no—
1695D4—4241no—
1696D4—4241no—
1697D4—4241no—
1698D4—4241no—
1699D4—2122no—
1700D4—2122no—
1701D4—2122no—
1702D4—2122no—
1703D4—2122no—
1704D4—2122no—
1705D4—2122no—
1706D4—2122no—
1707D4—2122no—
1708D4—2122no—
1709D4—2122no—
1710D4—2122no—
1711D4—2122no—
1712C2×C4—21no—
1713C2×C4—21no—
1714C2×C4—21no—
1715C2×C4—21no—
1716C2×C4—21no—
1717C2×C4—21no—
1718C2×C4—21no—
1719C2×C4—21no—
1720C2×C4—21no—
1721C2×C4—21no—
1722C2×C4—42no—
1723C2×C4—42no—
1724C2×C4—42no—
1725C2×C4—81no—
1726C2×C4—81no—
1727C2×C4—534no—
1728C2×C4—531no—
1729C2×C4—531no—
1730C2×C4—531no—
1731C2×C4—531no—
1732C2×C4—531no—
1733C2×C4—531no—
1734C2×C4—531no—
1735C2×C4—1062no—
1736C2×C4—1062no—
1737C2×C4—1061no—
1738C2×C4—1061no—
1739C2×C4—1061no—
1740C2×C4—1061no—
1741C2×C4—1061no—
1742C2×C4—1061no—
1743C2×C4—4241no—
1744C2×C4—4241no—
1745C2×C4—4241no—
1746C2×C4—4241no—
1747C2×C4—2121no—
1748C2×C4—2122no—
1749C2×C4—2122no—
1750C2×C4—2122no—
1751C2×C4—2122no—
1752C2×C4—2122no—
1753C2×C4—2122no—
1754C2×C4—2122no—
1755C2×C4—2122no—
1756C2×C4—2122no—
1757C2×C4—2122no—
1758C2×C4—2122no—
1759C2×C4—2122no—
1760C2×C4—2121no—
1761C2×C4—2121no—
1762C2×C4C2×D4×D5311yescharacteristic
1763C2×C4C2×D4×D5311yescharacteristic
1764C2×C4C2×D4×D5311yescharacteristic
1765C2×C4C2×D4×D5311yescharacteristic
1766C2×C4C24×D5311yescharacteristic
1767C8—21no—
1768C8—21no—
1769C8—21no—
1770C8—21no—
1771C8—1061no—
1772C8—1061no—
1773C8—1061no—
1774C8—1061no—
1775C22—21no—
1776C22—21no—
1777C22—21no—
1778C22—21no—
1779C22—21no—
1780C22—41no—
1781C22—41no—
1782C22—41no—
1783C22—41no—
1784C22—41no—
1785C22—41no—
1786C22—1061no—
1787C22—1062no—
1788C22—1061no—
1789C22—1061no—
1790C22—4244no—
1791C22—4244no—
1792C22—4244no—
1793C22—2121no—
1794C22—2121no—
1795C22—2121no—
1796C22—2121no—
1797C22—2121no—
1798C22—2121no—
1799C22—2121no—
1800C22—2121no—
1801C22—2121no—
1802C22—2121no—
1803C22—2121no—
1804C22AGL(1,ℤ/8)×D5312yes—
1805C22C22×D4×D5311yescharacteristic
1806C4—21no—
1807C4—21no—
1808C4—21no—
1809C4—21no—
1810C4—41no—
1811C4—41no—
1812C4—41no—
1813C4—41no—
1814C4—41no—
1815C4—41no—
1816C4—532no—
1817C4—532no—
1818C4—1061no—
1819C4—1061no—
1820C4—1061no—
1821C4—1061no—
1822C4—1061no—
1823C4—2121no—
1824C4—2121no—
1825C4—2121no—
1826C4—2121no—
1827C4H(5,𝔽2)×D5311yescharacteristic
1828C4#1681145911yescharacteristic
1829C2—22no—
1830C2—41no—
1831C2—81no—
1832C2—81no—
1833C2—4241no—
1834C2—4241no—
1835C2—4241no—
1836C2—2121no—
1837C2—2122no—
1838C2#2028837811yescharacteristic
1839C2C2×AGL(1,ℤ/8)×D5311yescharacteristic
1840C2#2028950011yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3308C2
socleC22×C53C23×D4
hypercenter#3308D53
hypocenterC53#61962
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3308

Complements

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

NH ≅ G/Ntype
1. #20288621C2semidirect
2. #20288202C2semidirect
3. #20287738C2semidirect
4. #20287736C2semidirect
5. #20287436C2semidirect
6. #20287430C2semidirect
7. #20287018C2semidirect
8. #20287016C2semidirect
9. #20286704C2semidirect
10. #20286702C2semidirect
11. #20286700C2semidirect
12. #20286312C2semidirect
13. #20286308C2semidirect
14. #20286215C2semidirect
15. #20286211C2semidirect
16. #20286207C2semidirect
17. #20286203C2semidirect
18. #20286101C2semidirect
19. #20286097C2semidirect
20. #20286021C2semidirect
21. #20285711C2semidirect
22. #20285707C2semidirect
23. #20285638C2semidirect
24. #20284812C2semidirect
25. #20284811C2semidirect
26. #20284712C2semidirect
27. #20284178C2semidirect
28. #20284177C2semidirect
29. C2×#16810827C2semidirect
30. #20283827C2semidirect
31. C53×#3308C2semidirect
39. #16811345C22semidirect
40. #16811342C22semidirect
47. #16811284C22semidirect
49. #16811282C22semidirect
50. #16811279C22semidirect
51. #16811275C22semidirect
54. #16811272C22semidirect
64. #16811177C22semidirect
65. #16811175C22semidirect
67. #16811172C22semidirect
68. #16811169C22semidirect
71. #16811168C22semidirect
72. C2×#13133215C22semidirect
81. #16811013C22semidirect
82. #16811012C22semidirect
83. #16811011C22semidirect
84. #16811009C22semidirect
85. #16810994C22semidirect
86. #16810994C22semidirect
87. #16810985C22semidirect
88. #16810984C22semidirect
89. #16810981C22semidirect
90. #16810972C22semidirect
91. #16810972C22semidirect
92. #16810960C22semidirect
93. #16810958C22semidirect
94. #16810957C22semidirect
95. #16810936C22semidirect
96. #16810917C22semidirect
97. #16810916C22semidirect
98. #16810915C22semidirect
100. #16810902C22semidirect
101. #16810902C22semidirect
102. #16810902C22semidirect
103. #16810901C22semidirect
104. #16810901C22semidirect
105. #16810872C22semidirect
106. #16810872C22semidirect
107. #16810871C22semidirect
108. #16810870C22semidirect
109. #16810870C22semidirect
110. #16810869C22semidirect
111. #16810867C22semidirect
112. #16810859C22semidirect
113. #16810857C22semidirect
114. #16810857C22semidirect
116. #16810841C22semidirect
118. #16810838C22semidirect
120. #16810837C22semidirect
126. #16810827C22semidirect
127. #16810827C22semidirect
128. #16810827C22semidirect
129. #16810827C22semidirect
130. #16810827C22semidirect
131. #16810827C22semidirect
132. #16810826C22semidirect
133. #16810826C22semidirect
134. #16810824C22semidirect
135. #16810823C22semidirect
136. #16810822C22semidirect
137. #16810821C22semidirect
139. #16810817C22semidirect
140. #16810817C22semidirect
141. #16810817C22semidirect
142. #16810816C22semidirect
143. #16810816C22semidirect
148. #16810771C22semidirect
149. #16810771C22semidirect
150. #16810770C22semidirect
151. #16810769C22semidirect
152. #16810769C22semidirect
153. #16810768C22semidirect
154. #16810766C22semidirect
155. #16810764C22semidirect
156. #16810762C22semidirect
157. #16810761C22semidirect
160. #16810752C22semidirect
161. #16810751C22semidirect
163. #16810726C22semidirect
165. #16810723C22semidirect
167. #16810722C22semidirect
170. #16810705C22semidirect
172. #16810703C22semidirect
173. #16810699C22semidirect
174. #16810698C22semidirect
175. #16810695C22semidirect
176. #16810694C22semidirect
177. #16810691C22semidirect
178. #16810678C22semidirect
179. #16810677C22semidirect
180. #16810673C22semidirect
181. #16810646C22semidirect
182. #16810645C22semidirect
183. C2×#13133146C22semidirect
184. #16810623C22semidirect
185. #16810622C22semidirect
186. #16810621C22semidirect
187. C2×#13133140C22semidirect
188. C53×#548C22semidirect
190. C53×#489C22semidirect
191. C53×#484C22semidirect
192. C53×#480C22semidirect
193. C53×#477C22semidirect
194. C53×#468C22semidirect
195. C53×#466C22semidirect
196. C53×#463C22semidirect
197. C53×#449C22semidirect
198. C53×#448C22semidirect
199. C53×#440C22semidirect
200. C53×#435C22semidirect
201. C53×#417C22semidirect
202. C2×#103×C53C22semidirect
798. C2×Dic53AGL(1,ℤ/8)semidirect
920. #3308D53semidirect
971. #548C2×D53semidirect
1012. #489C2×D53semidirect
1018. #484C2×D53semidirect
1020. #480C2×D53semidirect
1024. #477C2×D53semidirect
1038. #468C2×D53semidirect
1042. #466C2×D53semidirect
1050. #463C2×D53semidirect
1084. #449C2×D53semidirect
1088. #448C2×D53semidirect
1100. #440C2×D53semidirect
1110. #435C2×D53semidirect
1120. #417C2×D53semidirect
1122. C2×#103C2×D53semidirect
1123. C53#61962semidirect

Maximal subgroups

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

subgroupindex
#202886212
#202882022
#202877382
#202877362
#202874362
#202874302
#202870182
#202870162
#202867042
#202867022
#202867002
#202863122
#202863082
#202862152
#202862112
#202862072
#202862032
#202861012
#202860972
#202860212
#202857112
#202857072
#202856382
#202848122
#202848112
#202847122
#202841782
#202841772
C2×#168108272
#202838272
C53×#33082
#6196253