Finite Group Databasebeta

← #28276430

Subgroups — #28276430

Order 13568.

2178 conjugacy classes of subgroups.

The subgroup lattice has 1892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288583C211yesmaximal, characteristic, complemented
2D4×#11719947C211yesmaximal, characteristic, complemented
3#20287760C211yesmaximal, characteristic, complemented
4#20287754C211yesmaximal, characteristic, complemented
5#20287508C211yesmaximal, characteristic, complemented
6#20287502C211yesmaximal, characteristic, complemented
7#20287037C211yesmaximal, characteristic, complemented
8#20287035C211yesmaximal, characteristic, complemented
9#20286682C211yesmaximal, characteristic, complemented
10#20286680C211yesmaximal, characteristic, complemented
11#20286678C211yesmaximal, characteristic, complemented
12#20286676C211yesmaximal, characteristic, complemented
13#20286333C211yesmaximal, characteristic, complemented
14#20286329C211yesmaximal, characteristic, complemented
15#20286199C211yesmaximal, characteristic, complemented
16#20286195C211yesmaximal, characteristic, complemented
17#20286191C211yesmaximal, characteristic, complemented
18#20286094C211yesmaximal, characteristic, complemented
19#20286092C211yesmaximal, characteristic, complemented
20#20286026C211yesmaximal, characteristic, complemented
21#20285707C211yesmaximal, characteristic, complemented
22#20285705C211yesmaximal, characteristic, complemented
23#20285631C211yesmaximal, characteristic, complemented
24#20284804C211yesmaximal, characteristic, complemented
25#20284801C211yesmaximal, characteristic, complemented
26#20284718C211yesmaximal, characteristic, complemented
27#20284177C211yesmaximal, characteristic, complemented
28#20284176C211yesmaximal, characteristic, complemented
29C2×#16810816C211yesmaximal, characteristic, complemented
30#20283827C211yesmaximal, characteristic, complemented
31C53×#3264C211yesmaximal, characteristic, complemented
32C22×#11719947—21no—
33C2×#13133244C2211yescharacteristic, complemented
34C2×#13133243C2211yescharacteristic, complemented
35C2×#13133241C2211yescharacteristic, complemented
36C22×#11719922C2211yescharacteristic
37#16811357—21no—
38#16811356C2211yescharacteristic, complemented
39#16811355C2211yescharacteristic, complemented
40#16811293C2211yescharacteristic, complemented
41#16811292C2211yescharacteristic, complemented
42#16811291—21no—
43#16811291C2211yescharacteristic, complemented
44D4×Dic106C2211yescharacteristic, complemented
45#16811279—21no—
46#16811277C2211yescharacteristic
47#16811273C2211yescharacteristic
48#16811273C2211yescharacteristic, complemented
49#16811269C2211yescharacteristic, complemented
50#16811267—21no—
51#16811267C2211yescharacteristic, complemented
52#16811264C2211yescharacteristic, complemented
53#16811263—21no—
54#16811260—21no—
55#16811260—21no—
56#16811260—21no—
57D4×C22⋊D53C2211yescharacteristic
58D4×C22⋊D53C2211yescharacteristic, complemented
59#16811225—21no—
60#16811223—21no—
61#16811188—21no—
62#16811175C2211yescharacteristic, complemented
63#16811172C2211yescharacteristic, complemented
64#16811171C2211yescharacteristic, complemented
65#16811170C2211yescharacteristic, complemented
66#16811169C2211yescharacteristic, complemented
67#16811168C2211yescharacteristic
68#16811168C2211yescharacteristic, complemented
69#16811168C2211yescharacteristic, complemented
70C2×#13133213C2211yescharacteristic, complemented
71#16811133—21no—
72#16811129—21no—
73#16811129—21no—
74#16811096—21no—
75C4×#11719947C2211yescharacteristic
76C2×D4×Dic53C2211yescharacteristic
77C2×D4×Dic53C2211yescharacteristic, complemented
78C4×D4×D53C2211yescharacteristic, complemented
79#16811011C2211yescharacteristic, complemented
80#16811010C2211yescharacteristic, complemented
81#16811009C2211yescharacteristic, complemented
82#16810998C2211yescharacteristic, complemented
83#16810998C2211yescharacteristic, complemented
84#16810984C2211yescharacteristic, complemented
85#16810983C2211yescharacteristic, complemented
86#16810982C2211yescharacteristic, complemented
87#16810981C2211yescharacteristic, complemented
88#16810968C2211yescharacteristic, complemented
89#16810968C2211yescharacteristic, complemented
90#16810954C2211yescharacteristic, complemented
91#16810951C2211yescharacteristic, complemented
92#16810943C2211yescharacteristic, complemented
93#16810942C2211yescharacteristic, complemented
94#16810940C2211yescharacteristic, complemented
95#16810939C2211yescharacteristic, complemented
96#16810914C2211yescharacteristic, complemented
97#16810913C2211yescharacteristic, complemented
98#16810912C2211yescharacteristic, complemented
99#16810912C2211yescharacteristic, complemented
100#16810911C2211yescharacteristic, complemented
101#16810911C2211yescharacteristic, complemented
102#16810911C2211yescharacteristic, complemented
103#16810911C2211yescharacteristic, complemented
104#16810907C2211yescharacteristic, complemented
105#16810906C2211yescharacteristic, complemented
106#16810876C2211yescharacteristic, complemented
107#16810875C2211yescharacteristic, complemented
108#16810875C2211yescharacteristic, complemented
109#16810874C2211yescharacteristic, complemented
110#16810874C2211yescharacteristic, complemented
111#16810873C2211yescharacteristic, complemented
112#16810873C2211yescharacteristic, complemented
113#16810854C2211yescharacteristic, complemented
114#16810852C2211yescharacteristic, complemented
115#16810850C2211yescharacteristic, complemented
116#16810840C2211yescharacteristic, complemented
117#16810840C2211yescharacteristic, complemented
118#16810839C2211yescharacteristic, complemented
119#16810838C2211yescharacteristic, complemented
120#16810836C2211yescharacteristic, complemented
121#16810836C2211yescharacteristic, complemented
122#16810835C2211yescharacteristic, complemented
123#16810827C2211yescharacteristic, complemented
124#16810826C2211yescharacteristic, complemented
125#16810826C2211yescharacteristic, complemented
126#16810826C2211yescharacteristic, complemented
127#16810822C2211yescharacteristic, complemented
128#16810821C2211yescharacteristic, complemented
129#16810817C2211yescharacteristic, complemented
130#16810817C2211yescharacteristic, complemented
131#16810817C2211yescharacteristic, complemented
132#16810816C2211yescharacteristic
133#16810816C2211yescharacteristic
134#16810816C2211yescharacteristic
135#16810816C2211yescharacteristic
136#16810816C2211yescharacteristic, complemented
137#16810816C2211yescharacteristic, complemented
138#16810816C2211yescharacteristic, complemented
139#16810816C2211yescharacteristic, complemented
140#16810816C2211yescharacteristic, complemented
141#16810816C2211yescharacteristic, complemented
142#16810816C2211yescharacteristic, complemented
143#16810815C2211yescharacteristic, complemented
144#16810774C2211yescharacteristic
145#16810770C2211yescharacteristic, complemented
146#16810768C2211yescharacteristic, complemented
147#16810767C2211yescharacteristic, complemented
148#16810767C2211yescharacteristic, complemented
149#16810766C2211yescharacteristic, complemented
150#16810765C2211yescharacteristic, complemented
151#16810765C2211yescharacteristic, complemented
152#16810759C2211yescharacteristic, complemented
153#16810758C2211yescharacteristic, complemented
154#16810757C2211yescharacteristic, complemented
155#16810757C2211yescharacteristic, complemented
156#16810756C2211yescharacteristic, complemented
157#16810755C2211yescharacteristic, complemented
158#16810752C2211yescharacteristic, complemented
159#16810751C2211yescharacteristic, complemented
160#16810736C2211yescharacteristic, complemented
161#16810735C2211yescharacteristic, complemented
162#16810735C2211yescharacteristic, complemented
163#16810733C2211yescharacteristic, complemented
164#16810733C2211yescharacteristic, complemented
165#16810732C2211yescharacteristic, complemented
166#16810732C2211yescharacteristic, complemented
167#16810714C2211yescharacteristic, complemented
168#16810714C2211yescharacteristic, complemented
169SD16×Dic53C2211yescharacteristic, complemented
170SD16×Dic53C2211yescharacteristic, complemented
171#16810699C2211yescharacteristic, complemented
172#16810698C2211yescharacteristic, complemented
173#16810695C2211yescharacteristic, complemented
174#16810694C2211yescharacteristic, complemented
175#16810691C2211yescharacteristic, complemented
176#16810678C2211yescharacteristic, complemented
177#16810677C2211yescharacteristic, complemented
178#16810673C2211yescharacteristic, complemented
179#16810646C2211yescharacteristic, complemented
180#16810645C2211yescharacteristic, complemented
181C2×#13133146C2211yescharacteristic, complemented
182#16810625C2211yescharacteristic, complemented
183#16810624C2211yescharacteristic, complemented
184#16810623C2211yescharacteristic, complemented
185#16810621C2211yescharacteristic, complemented
186C2×#13133139C2211yescharacteristic, complemented
187C2×#13133138C2211yescharacteristic, complemented
188C2×AGL(1,ℤ/8)×C53C2211yescharacteristic, complemented
189C22×D8×C53C2211yescharacteristic
190C53×#546C2211yescharacteristic, complemented
191D42×C53C2211yescharacteristic
192C53×#496C2211yescharacteristic, complemented
193C53×#469C2211yescharacteristic, complemented
194C53×#465C2211yescharacteristic, complemented
195C53×#463C2211yescharacteristic, complemented
196C53×#459C2211yescharacteristic, complemented
197C53×#450C2211yescharacteristic
198C53×#449C2211yescharacteristic, complemented
199C53×#447C2211yescharacteristic, complemented
200C53×#447C2211yescharacteristic, complemented
201C53×#442C2211yescharacteristic, complemented
202C53×#435C2211yescharacteristic, complemented
203C2×#11719949C2311yescharacteristic
204C2×#11719945—21no—
205C2×#11719945C2311yescharacteristic
206C2×#11719947—21no—
207C2×#11719947—21no—
208C2×#11719947—21no—
209C2×#11719947—21no—
210C2×#11719947—21no—
211C2×#11719947—21no—
212C2×#11719947—21no—
213C2×#11719947—21no—
214C2×#11719947—48no—
215C2×#11719947D411yescharacteristic
216C2×#11719947C2311yescharacteristic
217C22×Dic106—21no—
218C22×D212C2311yescharacteristic
219C22×C22⋊D53—21no—
220C22×C22⋊D53—21no—
221C22×C22⋊D53—21no—
222C22×C22⋊D53—21no—
223C2×D4×D53C2311yescharacteristic
224C23×Dic53—21no—
225C23×Dic53—21no—
226C22×C4×D53—21no—
227#13133244—42no—
228#13133243—42no—
229#13133241—42no—
230C2×#11719913C2311yescharacteristic
231C2×#11719923C2311yescharacteristic
232C2×#11719923C2311yescharacteristic
233C2×#11719923C2311yescharacteristic
234C2×#11719924C2311yescharacteristic
235C2×D424C2311yescharacteristic
236C2×D424C2311yescharacteristic
237C2×#11719922—42no—
238C2×#11719922C2311yescharacteristic
239C2×#11719922C2311yescharacteristic
240C2×#11719922C2311yescharacteristic
241C2×#11719922C2311yescharacteristic
242C2×#11719922C2311yescharacteristic
243C2×#11719922C2311yescharacteristic
244C2×#11719922C2311yescharacteristic
245C2×#11719922C2311yescharacteristic
246C2×#11719917C2311yescharacteristic
247C2×#11719912C2311yescharacteristic
248C2×#11719912C2311yescharacteristic
249C22×#88322C2311yescharacteristic
250#13133217C2311yescharacteristic
251#13133216C2311yescharacteristic
252#13133216C2311yescharacteristic
253#13133216C2311yescharacteristic
254#13133215C2311yescharacteristic
255#13133213—21no—
256#13133213—21no—
257#13133213—21no—
258#13133213—21no—
259#13133213C2311yescharacteristic
260#13133213C2311yescharacteristic
261#13133213C2311yescharacteristic
262#13133213C2311yescharacteristic
263#13133213C2311yescharacteristic
264#13133213C2311yescharacteristic
265#13133207—21no—
266#13133206C2311yescharacteristic
267#13133205C2311yescharacteristic
268#13133204—21no—
269#13133204C2311yescharacteristic
270#13133203—21no—
271#13133203—21no—
272#13133203—21no—
273#13133203—21no—
274#13133203—21no—
275#13133203—21no—
276#13133202—21no—
277#13133202—21no—
278#13133201—21no—
279#13133201—21no—
280#13133201—21no—
281#13133200—21no—
282#13133199—21no—
283#13133199—21no—
284#13133199—21no—
285#13133199—21no—
286#13133198—21no—
287#13133198—21no—
288#13133198—21no—
289#13133197—21no—
290#13133196—21no—
291#13133196C2311yescharacteristic
292#13133194—21no—
293#13133194—21no—
294#13133194—21no—
295#13133194—21no—
296#13133194—21no—
297#13133192—21no—
298#13133192C2311yescharacteristic
299#13133191—21no—
300#13133191C2311yescharacteristic
301#13133191C2311yescharacteristic
302#13133191C2311yescharacteristic
303#13133190—21no—
304#13133190—21no—
305#13133190—21no—
306#13133190—21no—
307#13133190—21no—
308#13133189—21no—
309#13133189—21no—
310#13133189—21no—
311#13133189—21no—
312#13133189—21no—
313#13133189—21no—
314#13133189—21no—
315#13133189—21no—
316#13133189—21no—
317#13133189—21no—
318#13133189—21no—
319#13133188—21no—
320#13133188—21no—
321#13133188—21no—
322#13133188C2311yescharacteristic
323#13133188C2311yescharacteristic
324#13133188C2311yescharacteristic
325#13133187—21no—
326#13133186—21no—
327#13133186—21no—
328#13133186—21no—
329#13133185—21no—
330#13133185—21no—
331#13133185—21no—
332Q8×Dic53C2311yescharacteristic
333C4×Dic106C2311yescharacteristic
334#13133182—21no—
335#13133182D411yescharacteristic
336#13133182C2311yescharacteristic
337C4×D212C2311yescharacteristic
338C4×D212C2311yescharacteristic
339D4×Dic53—21no—
340D4×Dic53—21no—
341D4×Dic53—21no—
342D4×Dic53—21no—
343D4×Dic53—21no—
344D4×Dic53D411yescharacteristic
345D4×Dic53C2311yescharacteristic
346D4×Dic53C2311yescharacteristic
347D4×Dic53C2311yescharacteristic
348D4×Dic53C2311yescharacteristic
349D4×Dic53C2311yescharacteristic
350D4×Dic53C2311yescharacteristic
351D4×Dic53C2311yescharacteristic
352D4×Dic53C2311yescharacteristic
353#13133179C2311yescharacteristic
354#13133179C2311yescharacteristic
355C4×C22⋊D53—21no—
356C4×C22⋊D53—21no—
357C4×C22⋊D53—21no—
358C4×C22⋊D53—21no—
359C4×C22⋊D53—21no—
360C4×C22⋊D53—21no—
361C4×C22⋊D53C2311yescharacteristic
362C4×C22⋊D53C2311yescharacteristic
363#13133177—21no—
364#13133177—21no—
365#13133177—21no—
366#13133177—21no—
367#13133177—21no—
368#13133177—21no—
369#13133177—21no—
370#13133177—21no—
371#13133177D411yescharacteristic
372#13133177D411yescharacteristic
373#13133175D411yescharacteristic
374#13133173—21no—
375#13133173D411yescharacteristic
376#13133173D411yescharacteristic
377C2×C4⋊Dic53C2311yescharacteristic
378C2×C4⋊Dic53C2311yescharacteristic
379C4⋊C4×D53C2311yescharacteristic
380C2×C22⋊Dic53—21no—
381C2×C22⋊Dic53—21no—
382C2×C22⋊Dic53—21no—
383C22⋊C4×D53—21no—
384C22⋊C4×D53—21no—
385C22⋊C4×D53—21no—
386C2×C4×Dic53C2311yescharacteristic
387C2×C4×Dic53C2311yescharacteristic
388C42×D53C2311yescharacteristic
389#13133149C2311yescharacteristic
390#13133149C2311yescharacteristic
391#13133149C2311yescharacteristic
392#13133148C2311yescharacteristic
393#13133148C2311yescharacteristic
394#13133148C2311yescharacteristic
395#13133148C2311yescharacteristic
396C4⋊#88322C2311yescharacteristic
397#13133146C2311yescharacteristic
398#13133146C2311yescharacteristic
399#13133146C2311yescharacteristic
400#13133146C2311yescharacteristic
401#13133146C2311yescharacteristic
402#13133146C2311yescharacteristic
403#13133146C2311yescharacteristic
404#13133146C2311yescharacteristic
405#13133142C2311yescharacteristic
406#13133142C2311yescharacteristic
407#13133142C2311yescharacteristic
408#13133141C2311yescharacteristic
409#13133141C2311yescharacteristic
410#13133141C2311yescharacteristic
411#13133140C2311yescharacteristic
412#13133139C2311yescharacteristic
413#13133139C2311yescharacteristic
414#13133139C2311yescharacteristic
415#13133139C2311yescharacteristic
416#13133139C2311yescharacteristic
417#13133139C2311yescharacteristic
418#13133139C2311yescharacteristic
419#13133138C2311yescharacteristic
420#13133138C2311yescharacteristic
421#13133138C2311yescharacteristic
422#13133138C2311yescharacteristic
423#13133138C2311yescharacteristic
424#13133138C2311yescharacteristic
425#13133138C2311yescharacteristic
426#13133138C2311yescharacteristic
427#13133138C2311yescharacteristic
428#13133137C2311yescharacteristic
429#13133137C2311yescharacteristic
430#13133137C2311yescharacteristic
431C22⋊#88322C2311yescharacteristic
432C22⋊#88322C2311yescharacteristic
433#13133129C2311yescharacteristic
434#13133129C2311yescharacteristic
435#13133128C2311yescharacteristic
436#13133127C2311yescharacteristic
437#13133127C2311yescharacteristic
438C8×Dic53C2311yescharacteristic
439C8×Dic53C2311yescharacteristic
440C2×#41×C53C2311yescharacteristic
441C22×D4×C53—21no—
442C22×D4×C53C2311yescharacteristic
443C22×D4×C53C2311yescharacteristic
444C22×D4×C53C2311yescharacteristic
445AGL(1,ℤ/8)×C53—42no—
446C2×SD16×C53C2311yescharacteristic
447C2×SD16×C53C2311yescharacteristic
448C2×SD16×C53C2311yescharacteristic
449C2×D8×C53—42no—
450C2×D8×C53C2311yescharacteristic
451C2×D8×C53C2311yescharacteristic
452C2×D8×C53C2311yescharacteristic
453C2×D8×C53C2311yescharacteristic
454C2×D8×C53C2311yescharacteristic
455C2×D8×C53C2311yescharacteristic
456C2×M16×C53C2311yescharacteristic
457C22×C8×C53C2311yescharacteristic
458#127×C53C2311yescharacteristic
459#124×C53C2311yescharacteristic
460#123×C53—21no—
461C22⋊Q8×C53C2311yescharacteristic
462#121×C53—21no—
463#121×C53—21no—
464#121×C53C2311yescharacteristic
465#121×C53C2311yescharacteristic
466#121×C53C2311yescharacteristic
467#120×C53—21no—
468#120×C53—21no—
469#120×C53—21no—
470C4×D4×C53C2311yescharacteristic
471C4×D4×C53C2311yescharacteristic
472C4×D4×C53C2311yescharacteristic
473C2×C22⋊C4×C53—21no—
474#106×C53C2311yescharacteristic
475C4⋊C8×C53C2311yescharacteristic
476#103×C53C2311yescharacteristic
477#102×C53C2311yescharacteristic
478#102×C53C2311yescharacteristic
479#102×C53C2311yescharacteristic
480#102×C53C2311yescharacteristic
481#102×C53C2311yescharacteristic
482C22⋊C8×C53C2311yescharacteristic
483C22⋊C8×C53C2311yescharacteristic
484#97×C53C2311yescharacteristic
485C24×C53—21no—
486C24×C53—21no—
487C24×C53—21no—
488C23×D53—21no—
489C23×D53—21no—
490#41×C53—41no—
491#41×C53—41no—
492C2×Q8×C53C2411yescharacteristic
493C2×D4×C53—22no—
494C2×D4×C53—22no—
495C2×D4×C53—21no—
496C2×D4×C53—21no—
497C2×D4×C53—21no—
498C2×D4×C53—21no—
499C2×D4×C53—21no—
500C2×D4×C53—21no—
501C2×D4×C53—21no—
502C2×D4×C53—21no—
503C2×D4×C53—21no—
504C2×D4×C53—41no—
505C2×D4×C53—41no—
506C2×D4×C53—41no—
507C2×D4×C53—41no—
508C2×D4×C53—44no—
509C2×D4×C53C2×D411yescharacteristic
510C2×D4×C53C2411yescharacteristic
511C2×D4×C53C2411yescharacteristic
512C2×D4×C53C2411yescharacteristic
513C2×D4×C53C2411yescharacteristic
514C2×D4×C53C2411yescharacteristic
515C22×C4×C53—21no—
516C22×C4×C53—21no—
517C22×C4×C53—21no—
518C22×C4×C53C2411yescharacteristic
519C22×C4×C53C2411yescharacteristic
520C2×C22⋊D53—21no—
521C2×C22⋊D53—21no—
522C2×C22⋊D53—21no—
523C2×C22⋊D53—21no—
524C2×C22⋊D53—21no—
525C2×C22⋊D53—21no—
526C2×C22⋊D53—21no—
527C2×C22⋊D53—21no—
528C2×C22⋊D53—21no—
529C2×C22⋊D53—21no—
530C2×C22⋊D53—21no—
531C2×C22⋊D53—21no—
532C2×C22⋊D53—21no—
533C2×C22⋊D53—21no—
534C2×C22⋊D53—21no—
535C2×C22⋊D53—21no—
536C2×C22⋊D53—21no—
537C2×C22⋊D53—21no—
538C2×C22⋊D53—21no—
539C2×C22⋊D53—21no—
540C2×C22⋊D53—21no—
541C2×C22⋊D53—44no—
542C2×C22⋊D53—44no—
543C2×C22⋊D53—44no—
544C2×C22⋊D53—82no—
545C2×C22⋊D53C2×D411yescharacteristic
546C2×C22⋊D53C2×D411yescharacteristic
547C22×Dic53—21no—
548C22×Dic53—21no—
549C22×Dic53—21no—
550C22×Dic53—21no—
551C22×Dic53—21no—
552C22×Dic53—21no—
553C22×Dic53—21no—
554C22×Dic53—21no—
555C22×Dic53—21no—
556C22×Dic53—21no—
557C22×Dic53—21no—
558C22×Dic53—44no—
559C22×Dic53—44no—
560C22×Dic53C2×D411yescharacteristic
561C22×Dic53C2×D411yescharacteristic
562C22×Dic53C2×D411yescharacteristic
563C22×Dic53C2×D411yescharacteristic
564#11719949—41no—
565#11719949—41no—
566#11719947—24no—
567#11719947—41no—
568#11719947—41no—
569#11719947—44no—
570#11719947—44no—
571#11719947—44no—
572#11719947—44no—
573#11719947—44no—
574#11719947—44no—
575#11719947—44no—
576#11719947—82no—
577D4×D53—22no—
578D4×D53—41no—
579#11719945—41no—
580#11719945—41no—
581#11719945—82no—
582C2×D212—21no—
583C2×D212—21no—
584C2×D212—21no—
585C2×D212—41no—
586C2×D212—41no—
587C2×D212C2411yescharacteristic
588C2×D212C2411yescharacteristic
589C2×D212C2411yescharacteristic
590C2×C4×D53—21no—
591C2×C4×D53—21no—
592C2×C4×D53—21no—
593C2×C4×D53—21no—
594C2×C4×D53—21no—
595C2×C4×D53—21no—
596C2×C4×D53—21no—
597C2×C4×D53—44no—
598C2×C4×D53C2×D411yescharacteristic
599C2×C4×D53C2×D411yescharacteristic
600C2×C4×D53C2411yescharacteristic
601C2×Dic106—21no—
602C2×Dic106—21no—
603C2×Dic106—21no—
604C2×Dic106—21no—
605C2×Dic106—44no—
606C2×Dic106C2×D411yescharacteristic
607C2×Dic106C2411yescharacteristic
608SD16×C53—22no—
609SD16×C53—41no—
610SD16×C53—41no—
611D8×C53—22no—
612D8×C53—22no—
613D8×C53—41no—
614D8×C53—41no—
615D8×C53—41no—
616D8×C53—41no—
617M16×C53—41no—
618C2×C8×C53—41no—
619C2×C8×C53C2411yescharacteristic
620C2×C8×C53C2411yescharacteristic
621C2×C8×C53C2411yescharacteristic
622C2×C8×C53C2411yescharacteristic
623C4⋊C4×C53—21no—
624C4⋊C4×C53C2×D411yescharacteristic
625C4⋊C4×C53C2411yescharacteristic
626C4⋊C4×C53C2411yescharacteristic
627C22⋊C4×C53—21no—
628C22⋊C4×C53—21no—
629C22⋊C4×C53—21no—
630C22⋊C4×C53—21no—
631C22⋊C4×C53—21no—
632C22⋊C4×C53—21no—
633C22⋊C4×C53—21no—
634C22⋊C4×C53—21no—
635C22⋊C4×C53C2×D411yescharacteristic
636C22⋊C4×C53C2×D411yescharacteristic
637C42×C53C2411yescharacteristic
638C22⋊Dic53—21no—
639C22⋊Dic53—21no—
640C22⋊Dic53—21no—
641C22⋊Dic53—21no—
642C22⋊Dic53—21no—
643C22⋊Dic53—21no—
644C22⋊Dic53—21no—
645C22⋊Dic53—21no—
646C22⋊Dic53—21no—
647C22⋊Dic53—21no—
648C22⋊Dic53—21no—
649C22⋊Dic53—21no—
650C22⋊Dic53—21no—
651C22⋊Dic53—21no—
652C22⋊Dic53C2×D411yescharacteristic
653C22⋊Dic53C2×D411yescharacteristic
654#11719924—41no—
655#11719923—22no—
656#11719923—41no—
657#11719923—41no—
658#11719922—22no—
659#11719922—22no—
660#11719922—41no—
661#11719922—41no—
662#11719922—41no—
663#11719922—41no—
664#11719922—41no—
665#11719922—41no—
666#11719921—21no—
667#11719921—21no—
668#11719921—21no—
669#11719921—21no—
670#11719921—21no—
671#11719921—21no—
672#11719921—21no—
673#11719921—21no—
674#11719921—21no—
675#11719921—21no—
676#11719921—21no—
677#11719921—21no—
678#11719921C2×D411yescharacteristic
679#11719921C2×D411yescharacteristic
680C4⋊Dic53—21no—
681C4⋊Dic53—21no—
682C4⋊Dic53—21no—
683C4⋊Dic53—21no—
684C4⋊Dic53C2×D411yescharacteristic
685C4⋊Dic53C2411yescharacteristic
686C4⋊Dic53C2411yescharacteristic
687C4⋊Dic53C2411yescharacteristic
688C4⋊Dic53C2411yescharacteristic
689#11719919—21no—
690#11719919—21no—
691#11719919—21no—
692#11719919—21no—
693#11719919—21no—
694#11719919—21no—
695#11719919—21no—
696#11719919—21no—
697#11719919C2×D411yescharacteristic
698#11719919C2×D411yescharacteristic
699#11719919C2×D411yescharacteristic
700#11719919C2×D411yescharacteristic
701C4×Dic53—21no—
702C4×Dic53—21no—
703C4×Dic53C2×D411yescharacteristic
704C4×Dic53C2×D411yescharacteristic
705C4×Dic53C2×D411yescharacteristic
706C4×Dic53C2×D411yescharacteristic
707C4×Dic53C2×D411yescharacteristic
708C4×Dic53C2×D411yescharacteristic
709C4×Dic53C2411yescharacteristic
710C4×Dic53C2411yescharacteristic
711C4×Dic53C2411yescharacteristic
712#11719917—41no—
713C2×#88322—41no—
714C2×#88322C2411yescharacteristic
715C2×#88322C2411yescharacteristic
716C2×#88322C2411yescharacteristic
717C2×#88322C2411yescharacteristic
718D424—41no—
719D424—41no—
720#11719913—41no—
721#11719912—41no—
722#11719912—41no—
723C23×C53—21no—
724C23×C53—21no—
725C23×C53—21no—
726C23×C53—21no—
727C23×C53—21no—
728C23×C53—42no—
729C23×C53—42no—
730C23×C53—42no—
731C23×C53—42no—
732C23×C53—42no—
733C23×C53—81no—
734C23×C53—81no—
735C23×C53—81no—
736C23×C53—81no—
737C23×C53C22×D411yescharacteristic
738C23×C53C22×D411yescharacteristic
739C22×D53—21no—
740C22×D53—21no—
741C22×D53—21no—
742C22×D53—42no—
743C22×D53—42no—
744C22×D53—42no—
745C22×D53—81no—
746C22×D53—81no—
747C22×D53—81no—
748C22×D53C22×D411yescharacteristic
749Q8×C53—21no—
750Q8×C53—21no—
751D4×C53—22no—
752D4×C53—21no—
753D4×C53—21no—
754D4×C53—21no—
755D4×C53—21no—
756D4×C53—21no—
757D4×C53—21no—
758D4×C53—21no—
759D4×C53—21no—
760D4×C53—21no—
761D4×C53—42no—
762D4×C53—42no—
763D4×C53—42no—
764D4×C53—42no—
765D4×C53—42no—
766D4×C53—81no—
767D4×C53—81no—
768D4×C53—81no—
769D4×C53—81no—
770D4×C53H(5,𝔽2)12yes—
771C2×C4×C53—21no—
772C2×C4×C53—21no—
773C2×C4×C53—21no—
774C2×C4×C53—21no—
775C2×C4×C53—21no—
776C2×C4×C53—21no—
777C2×C4×C53—21no—
778C2×C4×C53—42no—
779C2×C4×C53—81no—
780C2×C4×C53—81no—
781C2×C4×C53C22×D411yescharacteristic
782C2×C4×C53C22×D411yescharacteristic
783C2×C4×C53C22×D411yescharacteristic
784C2×C4×C53C22×D411yescharacteristic
785C2×C4×C53C2511yescharacteristic
786C22⋊D53—22no—
787C22⋊D53—22no—
788C22⋊D53—42no—
789C22⋊D53—42no—
790C22⋊D53—42no—
791C22⋊D53—42no—
792C22⋊D53—42no—
793C22⋊D53—42no—
794C22⋊D53—42no—
795C22⋊D53—42no—
796C22⋊D53—42no—
797C22⋊D53—42no—
798C22⋊D53—42no—
799C22⋊D53—42no—
800C22⋊D53—42no—
801C22⋊D53—81no—
802C22⋊D53—81no—
803C22⋊D53—81no—
804C22⋊D53—81no—
805C22⋊D53—81no—
806C22⋊D53—81no—
807C22⋊D53—81no—
808C22⋊D53—81no—
809C2×Dic53—22no—
810C2×Dic53—21no—
811C2×Dic53—21no—
812C2×Dic53—21no—
813C2×Dic53—21no—
814C2×Dic53—21no—
815C2×Dic53—41no—
816C2×Dic53—41no—
817C2×Dic53—42no—
818C2×Dic53—42no—
819C2×Dic53—42no—
820C2×Dic53—42no—
821C2×Dic53—42no—
822C2×Dic53—42no—
823C2×Dic53—42no—
824C2×Dic53—42no—
825C2×Dic53—42no—
826C2×Dic53—81no—
827C2×Dic53—81no—
828C2×Dic53AGL(1,ℤ/8)14yescomplemented
829C2×Dic53C22×D411yescharacteristic
830C2×Dic53C22×D411yescharacteristic
831C2×Dic53C22×D411yescharacteristic
832C2×Dic53C22×D411yescharacteristic
833C2×Dic53C22×D411yescharacteristic
834C2×Dic53C22×D411yescharacteristic
835C2×Dic53C22×D411yescharacteristic
836D212—21no—
837D212—21no—
838D212—21no—
839D212—21no—
840D212—21no—
841D212—21no—
842D212—81no—
843D212—81no—
844D212—81no—
845C4×D53—21no—
846C4×D53—21no—
847C4×D53—22no—
848C4×D53—41no—
849C4×D53—42no—
850C4×D53—42no—
851C4×D53—42no—
852C4×D53—81no—
853C4×D53—81no—
854C4×D53—81no—
855C4×D53—81no—
856Dic106—22no—
857Dic106—21no—
858Dic106—21no—
859Dic106—42no—
860Dic106—42no—
861Dic106—42no—
862Dic106—42no—
863C8×C53—21no—
864C8×C53—21no—
865C8×C53—21no—
866C8×C53—21no—
867#88322—21no—
868#88322—21no—
869#88322—21no—
870#88322—21no—
871#61961—531nomaximal, Sylow
872C22×C53—21no—
873C22×C53—21no—
874C22×C53—21no—
875C22×C53—22no—
876C22×C53—21no—
877C22×C53—21no—
878C22×C53—41no—
879C22×C53—41no—
880C22×C53—41no—
881C22×C53—41no—
882C22×C53—41no—
883C22×C53—41no—
884C22×C53—41no—
885C22×C53—41no—
886C22×C53—41no—
887C22×C53—41no—
888C22×C53—41no—
889C22×C53—41no—
890C22×C53—41no—
891C22×C53—41no—
892C22×C53—84no—
893C22×C53—84no—
894C22×C53—162no—
895C22×C53C2×AGL(1,ℤ/8)12yes—
896C22×C53C23×D411yescharacteristic
897C2×D53—21no—
898C2×D53—21no—
899C2×D53—21no—
900C2×D53—41no—
901C2×D53—41no—
902C2×D53—41no—
903C2×D53—41no—
904C2×D53—41no—
905C2×D53—41no—
906C2×D53—41no—
907C2×D53—41no—
908C2×D53—41no—
909C2×D53—84no—
910C2×D53—162no—
911C4×C53—21no—
912C4×C53—21no—
913C4×C53—21no—
914C4×C53—21no—
915C4×C53—41no—
916C4×C53—41no—
917C4×C53—41no—
918C4×C53C2×H(5,𝔽2)11yescharacteristic
919C4×C53#58511yescharacteristic
920Dic53—21no—
921Dic53—21no—
922Dic53—21no—
923Dic53—21no—
924Dic53—21no—
925Dic53—41no—
926Dic53—41no—
927Dic53—41no—
928Dic53—41no—
929Dic53—41no—
930Dic53C2×AGL(1,ℤ/8)12yes—
931Dic53C2×AGL(1,ℤ/8)12yes—
932#3508—531no—
933D4×#41—531no—
934#3399—531no—
935#3399—531no—
936#3373—531no—
937#3373—531no—
938#3332—531no—
939#3332—531no—
940#3306—531no—
941#3306—531no—
942#3306—531no—
943#3306—531no—
944#3274—531no—
945#3274—531no—
946#3264—531no—
947#3264—531no—
948#3264—531no—
949#3264D5311yescharacteristic, complemented
950#3253—531no—
951#3253—531no—
952#3246—531no—
953#3214—531no—
954#3214—531no—
955#3205—531no—
956#3109—531no—
957#3109—531no—
958#3101—531no—
959#3036—531no—
960#3036—531no—
961C2×#459—531no—
962#2989—531no—
963C2×C53—22no—
964C2×C53—42no—
965C2×C53—41no—
966C2×C53—81no—
967C2×C53—81no—
968C2×C53—81no—
969C2×C53—81no—
970C2×C53#348811yescharacteristic
971C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
972C2×C53#358511yescharacteristic
973D53—41no—
974D53—81no—
975D53—81no—
976D53—81no—
977C22×#41—1061no—
978C2×AGL(1,ℤ/8)—531no—
979C2×AGL(1,ℤ/8)—531no—
980C2×AGL(1,ℤ/8)—531no—
981C2×AGL(1,ℤ/8)C2×D5311yescharacteristic, complemented
982C22×D8—531no—
983C22×D8C2×D5311yescharacteristic
984#559—531no—
985#559—531no—
986#559—1061no—
987#550—531no—
988#550—531no—
989#550—531no—
990#550—1061no—
991D4×Q8—531no—
992#548—1061no—
993#547—531no—
994#547—531no—
995#547—531no—
996#546—531no—
997#546—531no—
998#546—531no—
999#546—1061no—
1000#546—1061no—
1001#546—1061no—
1002#546—1061no—
1003#546—1061no—
1004#546C2×D5311yescharacteristic, complemented
1005D42—531no—
1006D42—531no—
1007D42C2×D5311yescharacteristic
1008#540—1061no—
1009#540—1061no—
1010#535—1061no—
1011#533—531no—
1012#532—531no—
1013#532—531no—
1014#532—531no—
1015#532—531no—
1016#532—531no—
1017#532—531no—
1018#532—531no—
1019C2×#127—531no—
1020#525—1061no—
1021#525—1061no—
1022#525—1061no—
1023#518—1061no—
1024C4×#41—531no—
1025C2×C4×D4—531no—
1026C2×C4×D4—531no—
1027C2×C4×D4—531no—
1028#496—531no—
1029#496—531no—
1030#496—531no—
1031#496C2×D5311yescharacteristic, complemented
1032#493—531no—
1033#493—531no—
1034#489—531no—
1035#489—531no—
1036#489—531no—
1037#489—531no—
1038#486—531no—
1039#486—531no—
1040#483—531no—
1041#483—531no—
1042#481—531no—
1043#481—531no—
1044#481—531no—
1045#481—531no—
1046#476—531no—
1047#476—531no—
1048#476—531no—
1049#476—531no—
1050#476—531no—
1051#476—531no—
1052#476—531no—
1053#476—531no—
1054#475—531no—
1055#475—531no—
1056#469—531no—
1057#469—531no—
1058#469—531no—
1059#469—531no—
1060#469—531no—
1061#469—531no—
1062#469—531no—
1063#469C2×D5311yescharacteristic, complemented
1064#465—531no—
1065#465—531no—
1066#465—531no—
1067#465C2×D5311yescharacteristic, complemented
1068#463—531no—
1069#463—531no—
1070#463—531no—
1071#463—531no—
1072#463—531no—
1073#463—531no—
1074#463—531no—
1075#463C2×D5311yescharacteristic, complemented
1076#461—531no—
1077#461—531no—
1078#461—531no—
1079#461—531no—
1080#460—531no—
1081#460—531no—
1082#459—531no—
1083#459—531no—
1084#459—531no—
1085#459—531no—
1086#459—531no—
1087#459—531no—
1088#459—531no—
1089#459—531no—
1090#459—531no—
1091#459—531no—
1092#459—531no—
1093#459—531no—
1094#459—531no—
1095#459—531no—
1096#459—531no—
1097#459C2×D5311yescharacteristic, complemented
1098#450—531no—
1099#450C2×D5311yescharacteristic
1100#449—531no—
1101#449—531no—
1102#449—531no—
1103#449—531no—
1104#449—531no—
1105#449—531no—
1106#449—531no—
1107#449C2×D5311yescharacteristic, complemented
1108#447—531no—
1109#447—531no—
1110#447—531no—
1111#447—531no—
1112#447—531no—
1113#447—531no—
1114#447C2×D5311yescharacteristic, complemented
1115#447C2×D5311yescharacteristic, complemented
1116#446—531no—
1117#446—531no—
1118#442—531no—
1119#442—531no—
1120#442—531no—
1121#442—531no—
1122#442—531no—
1123#442—531no—
1124#442—531no—
1125#442C2×D5311yescharacteristic, complemented
1126C4×SD16—531no—
1127C4×SD16—531no—
1128C4×SD16—531no—
1129C4×SD16—531no—
1130#436—531no—
1131#436—531no—
1132#435—531no—
1133#435—531no—
1134#435—531no—
1135#435C2×D5311yescharacteristic, complemented
1136#432—531no—
1137#432—531no—
1138#431—531no—
1139#423—531no—
1140#423—531no—
1141C2×C4⋊C8—531no—
1142#417—531no—
1143#417—531no—
1144#417—531no—
1145#417—531no—
1146C2×#102—531no—
1147C2×#102—531no—
1148C53#6196111yescharacteristic, complemented, Sylow
1149C2×#41—531no—
1150C2×#41—531no—
1151C2×#41—531no—
1152C2×#41—531no—
1153C2×#41—1061no—
1154C2×#41—1061no—
1155C2×#41—1061no—
1156C2×#41—1061no—
1157C2×#41—1061no—
1158C2×#41—1061no—
1159C2×#41—1061no—
1160C2×#41—1061no—
1161C2×#41—1061no—
1162C2×#41—2128no—
1163C2×#41C22×D5311yescharacteristic
1164C22×Q8—1061no—
1165C22×D4—21no—
1166C22×D4—531no—
1167C22×D4—531no—
1168C22×D4—1061no—
1169C22×D4—1061no—
1170C22×D4—1061no—
1171C22×D4—1061no—
1172C22×D4C22×D5311yescharacteristic
1173C22×D4C22×D5311yescharacteristic
1174C22×D4C22×D5311yescharacteristic
1175C23×C4—1061no—
1176C23×C4—1061no—
1177C23×C4—1061no—
1178AGL(1,ℤ/8)—42no—
1179AGL(1,ℤ/8)—2122no—
1180AGL(1,ℤ/8)—2122no—
1181AGL(1,ℤ/8)—2122no—
1182C2×SD16—531no—
1183C2×SD16—531no—
1184C2×SD16—531no—
1185C2×SD16—531no—
1186C2×SD16—531no—
1187C2×SD16C22×D5311yescharacteristic
1188C2×SD16C22×D5311yescharacteristic
1189C2×SD16C22×D5311yescharacteristic
1190C2×D8—42no—
1191C2×D8—531no—
1192C2×D8—531no—
1193C2×D8—531no—
1194C2×D8—531no—
1195C2×D8—531no—
1196C2×D8—531no—
1197C2×D8—531no—
1198C2×D8—531no—
1199C2×D8—531no—
1200C2×D8—531no—
1201C2×D8—2122no—
1202C2×D8C22×D5311yescharacteristic
1203C2×D8C22×D5311yescharacteristic
1204C2×D8C22×D5311yescharacteristic
1205C2×D8C22×D5311yescharacteristic
1206C2×D8C22×D5311yescharacteristic
1207C2×D8C22×D5311yescharacteristic
1208C2×M16—531no—
1209C2×M16—531no—
1210C2×M16—531no—
1211C2×M16C22×D5311yescharacteristic
1212C22×C8—531no—
1213C22×C8C22×D5311yescharacteristic
1214C4⋊Q8—531no—
1215C4⋊Q8—531no—
1216C4⋊Q8—531no—
1217C4⋊Q8—531no—
1218C4⋊Q8—531no—
1219#127—531no—
1220#127—531no—
1221#127—531no—
1222#127—531no—
1223#127—531no—
1224#127—531no—
1225#127—1061no—
1226#127—1061no—
1227#127—1061no—
1228#127—1061no—
1229#127C22×D5311yescharacteristic
1230#125—1061no—
1231#124—531no—
1232#124—531no—
1233#124—531no—
1234#124—1061no—
1235#124—1061no—
1236#124—1061no—
1237#124—1061no—
1238#124—1061no—
1239#124—1061no—
1240#124—1061no—
1241#124C22×D5311yescharacteristic
1242#123—21no—
1243#123—1061no—
1244#123—1061no—
1245#123—1061no—
1246#123—1061no—
1247#123—1061no—
1248#123—1061no—
1249#123—1061no—
1250#123—1061no—
1251#123—1061no—
1252#123—1061no—
1253#123—1061no—
1254#123—1061no—
1255#123—1061no—
1256C22⋊Q8—531no—
1257C22⋊Q8—1061no—
1258C22⋊Q8—1061no—
1259C22⋊Q8—1061no—
1260C22⋊Q8—1061no—
1261C22⋊Q8—1061no—
1262C22⋊Q8—1061no—
1263C22⋊Q8—1061no—
1264C22⋊Q8C22×D5311yescharacteristic
1265#121—21no—
1266#121—21no—
1267#121—531no—
1268#121—531no—
1269#121—531no—
1270#121—531no—
1271#121—531no—
1272#121—531no—
1273#121—531no—
1274#121—1061no—
1275#121—1061no—
1276#121—1061no—
1277#121—1061no—
1278#121—1061no—
1279#121—1061no—
1280#121—1061no—
1281#121—1061no—
1282#121—1061no—
1283#121—1061no—
1284#121—1061no—
1285#121—1061no—
1286#121—1061no—
1287#121—1061no—
1288#121—1061no—
1289#121—1061no—
1290#121—1061no—
1291#121—1061no—
1292#121—1061no—
1293#121—1061no—
1294#121—1061no—
1295#121C22×D5311yescharacteristic
1296#121C22×D5311yescharacteristic
1297#121C22×D5311yescharacteristic
1298#120—21no—
1299#120—21no—
1300#120—21no—
1301#120—1061no—
1302#120—1061no—
1303#120—1061no—
1304#120—1061no—
1305#120—1061no—
1306#120—1061no—
1307#120—1061no—
1308C4×Q8—531no—
1309C4×Q8—531no—
1310C4×Q8—531no—
1311C4×Q8—531no—
1312C4×Q8—1061no—
1313C4×D4—531no—
1314C4×D4—531no—
1315C4×D4—531no—
1316C4×D4—531no—
1317C4×D4—531no—
1318C4×D4—531no—
1319C4×D4—531no—
1320C4×D4—531no—
1321C4×D4—531no—
1322C4×D4—531no—
1323C4×D4—531no—
1324C4×D4—531no—
1325C4×D4—531no—
1326C4×D4—531no—
1327C4×D4—531no—
1328C4×D4—531no—
1329C4×D4—531no—
1330C4×D4—1061no—
1331C4×D4—1061no—
1332C4×D4—1061no—
1333C4×D4—1061no—
1334C4×D4—1061no—
1335C4×D4—1061no—
1336C4×D4—1061no—
1337C4×D4—1061no—
1338C4×D4—1061no—
1339C4×D4—1061no—
1340C4×D4—1061no—
1341C4×D4—1061no—
1342C4×D4—1061no—
1343C4×D4—1061no—
1344C4×D4—1061no—
1345C4×D4—1061no—
1346C4×D4—1061no—
1347C4×D4—1061no—
1348C4×D4—1061no—
1349C4×D4C22×D5311yescharacteristic
1350C4×D4C22×D5311yescharacteristic
1351C4×D4C22×D5311yescharacteristic
1352#117—531no—
1353#117—531no—
1354#117—531no—
1355#117—1061no—
1356C2×C4⋊C4—531no—
1357C2×C4⋊C4—531no—
1358C2×C4⋊C4—531no—
1359C2×C22⋊C4—21no—
1360C2×C22⋊C4—1061no—
1361C2×C22⋊C4—1061no—
1362C2×C22⋊C4—1061no—
1363C2×C22⋊C4—1061no—
1364C2×C22⋊C4—1061no—
1365C2×C22⋊C4—1061no—
1366C2×C42—531no—
1367C2×C42—531no—
1368C2×C42—531no—
1369#106—531no—
1370#106—531no—
1371#106—531no—
1372#106—531no—
1373#106—531no—
1374#106—531no—
1375#106—531no—
1376#106C22×D5311yescharacteristic
1377C4⋊C8—531no—
1378C4⋊C8—531no—
1379C4⋊C8—531no—
1380C4⋊C8—531no—
1381C4⋊C8—531no—
1382C4⋊C8—531no—
1383C4⋊C8—531no—
1384C4⋊C8—531no—
1385C4⋊C8—531no—
1386C4⋊C8C22×D5311yescharacteristic
1387#103—531no—
1388#103—531no—
1389#103—531no—
1390#103—531no—
1391#103—531no—
1392#103—531no—
1393#103—531no—
1394#103C22×D5311yescharacteristic
1395#102—531no—
1396#102—531no—
1397#102—531no—
1398#102—531no—
1399#102—531no—
1400#102—531no—
1401#102—531no—
1402#102—531no—
1403#102—531no—
1404#102—531no—
1405#102—531no—
1406#102—531no—
1407#102—531no—
1408#102—531no—
1409#102—531no—
1410#102—531no—
1411#102—531no—
1412#102—531no—
1413#102—531no—
1414#102C22×D5311yescharacteristic
1415#102C22×D5311yescharacteristic
1416#102C22×D5311yescharacteristic
1417#102C22×D5311yescharacteristic
1418#102C22×D5311yescharacteristic
1419C22⋊C8—531no—
1420C22⋊C8—531no—
1421C22⋊C8—531no—
1422C22⋊C8—531no—
1423C22⋊C8C22×D5311yescharacteristic
1424C22⋊C8C22×D5311yescharacteristic
1425#97—531no—
1426#97—531no—
1427#97—531no—
1428#97C22×D5311yescharacteristic
1429C4×C8—531no—
1430C4×C8—531no—
1431C24—21no—
1432C24—21no—
1433C24—21no—
1434C24—1061no—
1435C24—1061no—
1436#41—41no—
1437#41—41no—
1438#41—1064no—
1439#41—4242no—
1440#41—4242no—
1441#41—2121no—
1442#41—2121no—
1443#41—2124no—
1444#41—2121no—
1445#41—2121no—
1446#41—2121no—
1447#41—2121no—
1448#41—2124no—
1449#41—2124no—
1450#41—2124no—
1451#41—2124no—
1452#41—2124no—
1453#41—2124no—
1454C2×Q8—531no—
1455C2×Q8—531no—
1456C2×Q8—1061no—
1457C2×Q8—1061no—
1458C2×Q8—1061no—
1459C2×Q8—1061no—
1460C2×Q8—2124no—
1461C2×Q8C23×D5311yescharacteristic
1462C2×D4—22no—
1463C2×D4—22no—
1464C2×D4—21no—
1465C2×D4—21no—
1466C2×D4—21no—
1467C2×D4—21no—
1468C2×D4—21no—
1469C2×D4—21no—
1470C2×D4—21no—
1471C2×D4—21no—
1472C2×D4—21no—
1473C2×D4—41no—
1474C2×D4—41no—
1475C2×D4—41no—
1476C2×D4—41no—
1477C2×D4—44no—
1478C2×D4—531no—
1479C2×D4—531no—
1480C2×D4—531no—
1481C2×D4—531no—
1482C2×D4—531no—
1483C2×D4—1061no—
1484C2×D4—1061no—
1485C2×D4—1061no—
1486C2×D4—1061no—
1487C2×D4—1061no—
1488C2×D4—1061no—
1489C2×D4—1061no—
1490C2×D4—1061no—
1491C2×D4—1061no—
1492C2×D4—1061no—
1493C2×D4—1061no—
1494C2×D4—1061no—
1495C2×D4—1061no—
1496C2×D4—1061no—
1497C2×D4—1061no—
1498C2×D4—1062no—
1499C2×D4—1061no—
1500C2×D4—1061no—
1501C2×D4—1061no—
1502C2×D4—1061no—
1503C2×D4—1061no—
1504C2×D4—1061no—
1505C2×D4—1061no—
1506C2×D4—1061no—
1507C2×D4—1061no—
1508C2×D4—4242no—
1509C2×D4—2121no—
1510C2×D4—2121no—
1511C2×D4—2124no—
1512C2×D4—2121no—
1513C2×D4—2124no—
1514C2×D4—2124no—
1515C2×D4D4×D5311yescharacteristic
1516C2×D4C23×D5311yescharacteristic
1517C2×D4C23×D5311yescharacteristic
1518C2×D4C23×D5311yescharacteristic
1519C2×D4C23×D5311yescharacteristic
1520C2×D4C23×D5311yescharacteristic
1521C22×C4—21no—
1522C22×C4—21no—
1523C22×C4—21no—
1524C22×C4—531no—
1525C22×C4—531no—
1526C22×C4—531no—
1527C22×C4—531no—
1528C22×C4—531no—
1529C22×C4—531no—
1530C22×C4—531no—
1531C22×C4—1061no—
1532C22×C4—1061no—
1533C22×C4—1061no—
1534C22×C4—1061no—
1535C22×C4—1061no—
1536C22×C4—1061no—
1537C22×C4—1061no—
1538C22×C4—1061no—
1539C22×C4—1061no—
1540C22×C4—1061no—
1541C22×C4—1061no—
1542C22×C4—1061no—
1543C22×C4—1061no—
1544C22×C4—1061no—
1545C22×C4—1061no—
1546C22×C4—1061no—
1547C22×C4—1061no—
1548C22×C4—1061no—
1549C22×C4—2124no—
1550C22×C4—2124no—
1551C22×C4—2124no—
1552C22×C4C23×D5311yescharacteristic
1553C22×C4C23×D5311yescharacteristic
1554SD16—22no—
1555SD16—41no—
1556SD16—41no—
1557SD16—1062no—
1558SD16—2121no—
1559SD16—2121no—
1560SD16—2121no—
1561SD16—2121no—
1562D8—22no—
1563D8—22no—
1564D8—41no—
1565D8—41no—
1566D8—41no—
1567D8—41no—
1568D8—1062no—
1569D8—1062no—
1570D8—2121no—
1571D8—2121no—
1572D8—2121no—
1573D8—2121no—
1574D8—2121no—
1575D8—2121no—
1576D8—2121no—
1577D8—2121no—
1578M16—41no—
1579M16—2121no—
1580M16—2121no—
1581M16—2121no—
1582C2×C8—41no—
1583C2×C8—531no—
1584C2×C8—531no—
1585C2×C8—531no—
1586C2×C8—531no—
1587C2×C8—2121no—
1588C2×C8C23×D5311yescharacteristic
1589C2×C8C23×D5311yescharacteristic
1590C2×C8C23×D5311yescharacteristic
1591C2×C8C23×D5311yescharacteristic
1592C4⋊C4—21no—
1593C4⋊C4—531no—
1594C4⋊C4—531no—
1595C4⋊C4—531no—
1596C4⋊C4—531no—
1597C4⋊C4—531no—
1598C4⋊C4—531no—
1599C4⋊C4—531no—
1600C4⋊C4—531no—
1601C4⋊C4—531no—
1602C4⋊C4—1061no—
1603C4⋊C4—1061no—
1604C4⋊C4—1061no—
1605C4⋊C4—1061no—
1606C4⋊C4—1061no—
1607C4⋊C4—1061no—
1608C4⋊C4—1061no—
1609C4⋊C4—1061no—
1610C4⋊C4—1061no—
1611C4⋊C4—1061no—
1612C4⋊C4—1061no—
1613C4⋊C4—1061no—
1614C4⋊C4D4×D5311yescharacteristic
1615C4⋊C4C23×D5311yescharacteristic
1616C4⋊C4C23×D5311yescharacteristic
1617C22⋊C4—21no—
1618C22⋊C4—21no—
1619C22⋊C4—21no—
1620C22⋊C4—21no—
1621C22⋊C4—21no—
1622C22⋊C4—21no—
1623C22⋊C4—21no—
1624C22⋊C4—21no—
1625C22⋊C4—531no—
1626C22⋊C4—531no—
1627C22⋊C4—531no—
1628C22⋊C4—531no—
1629C22⋊C4—1061no—
1630C22⋊C4—1061no—
1631C22⋊C4—1061no—
1632C22⋊C4—1061no—
1633C22⋊C4—1061no—
1634C22⋊C4—1061no—
1635C22⋊C4—1061no—
1636C22⋊C4—1061no—
1637C22⋊C4—1061no—
1638C22⋊C4—1061no—
1639C22⋊C4—1061no—
1640C22⋊C4—1061no—
1641C22⋊C4—1061no—
1642C22⋊C4—1061no—
1643C22⋊C4—1061no—
1644C22⋊C4—1061no—
1645C22⋊C4—1061no—
1646C22⋊C4—1061no—
1647C22⋊C4—1061no—
1648C22⋊C4—1061no—
1649C22⋊C4—1061no—
1650C22⋊C4—1061no—
1651C22⋊C4—1061no—
1652C22⋊C4—1061no—
1653C22⋊C4—1061no—
1654C22⋊C4—1061no—
1655C22⋊C4D4×D5311yescharacteristic
1656C22⋊C4D4×D5311yescharacteristic
1657C42—531no—
1658C42—531no—
1659C42—531no—
1660C42—531no—
1661C42—531no—
1662C42—531no—
1663C42—531no—
1664C42—531no—
1665C42—531no—
1666C42—1061no—
1667C42—1061no—
1668C42C23×D5311yescharacteristic
1669C23—21no—
1670C23—21no—
1671C23—21no—
1672C23—21no—
1673C23—21no—
1674C23—42no—
1675C23—42no—
1676C23—42no—
1677C23—42no—
1678C23—42no—
1679C23—81no—
1680C23—81no—
1681C23—81no—
1682C23—81no—
1683C23—531no—
1684C23—1061no—
1685C23—1061no—
1686C23—1061no—
1687C23—4241no—
1688C23—4241no—
1689C23—4241no—
1690C23—2122no—
1691C23—2122no—
1692C23—2122no—
1693C23C2×D4×D5311yescharacteristic
1694C23C2×D4×D5311yescharacteristic
1695Q8—21no—
1696Q8—21no—
1697Q8—1062no—
1698Q8—1061no—
1699Q8—1061no—
1700Q8—2122no—
1701Q8—2122no—
1702Q8—2122no—
1703Q8—2122no—
1704D4—22no—
1705D4—21no—
1706D4—21no—
1707D4—21no—
1708D4—21no—
1709D4—21no—
1710D4—21no—
1711D4—21no—
1712D4—21no—
1713D4—21no—
1714D4—42no—
1715D4—42no—
1716D4—42no—
1717D4—42no—
1718D4—42no—
1719D4—81no—
1720D4—81no—
1721D4—81no—
1722D4—81no—
1723D4—1062no—
1724D4—1062no—
1725D4—1061no—
1726D4—1061no—
1727D4—1061no—
1728D4—1061no—
1729D4—1061no—
1730D4—1061no—
1731D4—4241no—
1732D4—4241no—
1733D4—4241no—
1734D4—4241no—
1735D4—4241no—
1736D4—4241no—
1737D4—4241no—
1738D4—4241no—
1739D4—4241no—
1740D4—4241no—
1741D4—4241no—
1742D4—2122no—
1743D4—2122no—
1744D4—2122no—
1745D4—2122no—
1746D4—2122no—
1747D4—2122no—
1748D4—2122no—
1749D4—2122no—
1750D4—2122no—
1751D4—2122no—
1752D4—2122no—
1753D4—2122no—
1754D4—2122no—
1755D4#1313326212yes—
1756C2×C4—21no—
1757C2×C4—21no—
1758C2×C4—21no—
1759C2×C4—21no—
1760C2×C4—21no—
1761C2×C4—21no—
1762C2×C4—21no—
1763C2×C4—42no—
1764C2×C4—81no—
1765C2×C4—81no—
1766C2×C4—534no—
1767C2×C4—531no—
1768C2×C4—531no—
1769C2×C4—531no—
1770C2×C4—531no—
1771C2×C4—531no—
1772C2×C4—531no—
1773C2×C4—531no—
1774C2×C4—1062no—
1775C2×C4—1062no—
1776C2×C4—1061no—
1777C2×C4—1061no—
1778C2×C4—1061no—
1779C2×C4—1061no—
1780C2×C4—1061no—
1781C2×C4—1061no—
1782C2×C4—1061no—
1783C2×C4—4241no—
1784C2×C4—4241no—
1785C2×C4—4241no—
1786C2×C4—4241no—
1787C2×C4—4241no—
1788C2×C4—4241no—
1789C2×C4—2121no—
1790C2×C4—2122no—
1791C2×C4—2122no—
1792C2×C4—2122no—
1793C2×C4—2122no—
1794C2×C4—2122no—
1795C2×C4—2122no—
1796C2×C4—2122no—
1797C2×C4—2122no—
1798C2×C4—2121no—
1799C2×C4—2121no—
1800C2×C4—2122no—
1801C2×C4—2122no—
1802C2×C4—2122no—
1803C2×C4—2122no—
1804C2×C4C2×D4×D5311yescharacteristic
1805C2×C4C2×D4×D5311yescharacteristic
1806C2×C4C2×D4×D5311yescharacteristic
1807C2×C4C2×D4×D5311yescharacteristic
1808C2×C4C24×D5311yescharacteristic
1809C8—21no—
1810C8—21no—
1811C8—21no—
1812C8—21no—
1813C8—1061no—
1814C8—1061no—
1815C8—1061no—
1816C8—1061no—
1817C22—21no—
1818C22—21no—
1819C22—21no—
1820C22—22no—
1821C22—21no—
1822C22—21no—
1823C22—41no—
1824C22—41no—
1825C22—41no—
1826C22—41no—
1827C22—41no—
1828C22—41no—
1829C22—41no—
1830C22—41no—
1831C22—41no—
1832C22—41no—
1833C22—41no—
1834C22—41no—
1835C22—41no—
1836C22—41no—
1837C22—84no—
1838C22—84no—
1839C22—162no—
1840C22—8482no—
1841C22—1061no—
1842C22—1061no—
1843C22—1061no—
1844C22—4244no—
1845C22—2121no—
1846C22—2121no—
1847C22—2121no—
1848C22—2121no—
1849C22—2121no—
1850C22—2121no—
1851C22—2121no—
1852C22—2121no—
1853C22—2121no—
1854C22AGL(1,ℤ/8)×D5312yes—
1855C22C22×D4×D5311yescharacteristic
1856C4—21no—
1857C4—21no—
1858C4—21no—
1859C4—21no—
1860C4—41no—
1861C4—41no—
1862C4—41no—
1863C4—532no—
1864C4—532no—
1865C4—1061no—
1866C4—1061no—
1867C4—1061no—
1868C4—1061no—
1869C4—1061no—
1870C4—2121no—
1871C4—2121no—
1872C4—2121no—
1873C4—2121no—
1874C4—2121no—
1875C4C2×#1313326211yescharacteristic
1876C4#1681145811yescharacteristic
1877C2—22no—
1878C2—41no—
1879C2—42no—
1880C2—81no—
1881C2—81no—
1882C2—81no—
1883C2—81no—
1884C2—4241no—
1885C2—4241no—
1886C2—4241no—
1887C2—2121no—
1888C2#2028837511yescharacteristic
1889C2C2×AGL(1,ℤ/8)×D5311yescharacteristic
1890C2#2028949011yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3264C2
socleC22×C53C23×D4
hypercenter#3264D53
hypocenterC53#61961
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3264

Complements

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

NH ≅ G/Ntype
1. #20288583C2semidirect
2. D4×#11719947C2semidirect
3. #20287760C2semidirect
4. #20287754C2semidirect
5. #20287508C2semidirect
6. #20287502C2semidirect
7. #20287037C2semidirect
8. #20287035C2semidirect
9. #20286682C2semidirect
10. #20286680C2semidirect
11. #20286678C2semidirect
12. #20286676C2semidirect
13. #20286333C2semidirect
14. #20286329C2semidirect
15. #20286199C2semidirect
16. #20286195C2semidirect
17. #20286191C2semidirect
18. #20286094C2semidirect
19. #20286092C2semidirect
20. #20286026C2semidirect
21. #20285707C2semidirect
22. #20285705C2semidirect
23. #20285631C2semidirect
24. #20284804C2semidirect
25. #20284801C2semidirect
26. #20284718C2semidirect
27. #20284177C2semidirect
28. #20284176C2semidirect
29. C2×#16810816C2semidirect
30. #20283827C2semidirect
31. C53×#3264C2semidirect
33. C2×#13133244C22semidirect
34. C2×#13133243C22semidirect
35. C2×#13133241C22semidirect
38. #16811356C22semidirect
39. #16811355C22semidirect
40. #16811293C22semidirect
41. #16811292C22semidirect
43. #16811291C22semidirect
44. D4×Dic106C22semidirect
48. #16811273C22semidirect
49. #16811269C22semidirect
51. #16811267C22semidirect
52. #16811264C22semidirect
58. D4×C22⋊D53C22semidirect
62. #16811175C22semidirect
63. #16811172C22semidirect
64. #16811171C22semidirect
65. #16811170C22semidirect
66. #16811169C22semidirect
68. #16811168C22semidirect
69. #16811168C22semidirect
70. C2×#13133213C22semidirect
77. C2×D4×Dic53C22semidirect
78. C4×D4×D53C22semidirect
79. #16811011C22semidirect
80. #16811010C22semidirect
81. #16811009C22semidirect
82. #16810998C22semidirect
83. #16810998C22semidirect
84. #16810984C22semidirect
85. #16810983C22semidirect
86. #16810982C22semidirect
87. #16810981C22semidirect
88. #16810968C22semidirect
89. #16810968C22semidirect
90. #16810954C22semidirect
91. #16810951C22semidirect
92. #16810943C22semidirect
93. #16810942C22semidirect
94. #16810940C22semidirect
95. #16810939C22semidirect
96. #16810914C22semidirect
97. #16810913C22semidirect
98. #16810912C22semidirect
99. #16810912C22semidirect
100. #16810911C22semidirect
101. #16810911C22semidirect
102. #16810911C22semidirect
103. #16810911C22semidirect
104. #16810907C22semidirect
105. #16810906C22semidirect
106. #16810876C22semidirect
107. #16810875C22semidirect
108. #16810875C22semidirect
109. #16810874C22semidirect
110. #16810874C22semidirect
111. #16810873C22semidirect
112. #16810873C22semidirect
113. #16810854C22semidirect
114. #16810852C22semidirect
115. #16810850C22semidirect
116. #16810840C22semidirect
117. #16810840C22semidirect
118. #16810839C22semidirect
119. #16810838C22semidirect
120. #16810836C22semidirect
121. #16810836C22semidirect
122. #16810835C22semidirect
123. #16810827C22semidirect
124. #16810826C22semidirect
125. #16810826C22semidirect
126. #16810826C22semidirect
127. #16810822C22semidirect
128. #16810821C22semidirect
129. #16810817C22semidirect
130. #16810817C22semidirect
131. #16810817C22semidirect
136. #16810816C22semidirect
137. #16810816C22semidirect
138. #16810816C22semidirect
139. #16810816C22semidirect
140. #16810816C22semidirect
141. #16810816C22semidirect
142. #16810816C22semidirect
143. #16810815C22semidirect
145. #16810770C22semidirect
146. #16810768C22semidirect
147. #16810767C22semidirect
148. #16810767C22semidirect
149. #16810766C22semidirect
150. #16810765C22semidirect
151. #16810765C22semidirect
152. #16810759C22semidirect
153. #16810758C22semidirect
154. #16810757C22semidirect
155. #16810757C22semidirect
156. #16810756C22semidirect
157. #16810755C22semidirect
158. #16810752C22semidirect
159. #16810751C22semidirect
160. #16810736C22semidirect
161. #16810735C22semidirect
162. #16810735C22semidirect
163. #16810733C22semidirect
164. #16810733C22semidirect
165. #16810732C22semidirect
166. #16810732C22semidirect
167. #16810714C22semidirect
168. #16810714C22semidirect
169. SD16×Dic53C22semidirect
170. SD16×Dic53C22semidirect
171. #16810699C22semidirect
172. #16810698C22semidirect
173. #16810695C22semidirect
174. #16810694C22semidirect
175. #16810691C22semidirect
176. #16810678C22semidirect
177. #16810677C22semidirect
178. #16810673C22semidirect
179. #16810646C22semidirect
180. #16810645C22semidirect
181. C2×#13133146C22semidirect
182. #16810625C22semidirect
183. #16810624C22semidirect
184. #16810623C22semidirect
185. #16810621C22semidirect
186. C2×#13133139C22semidirect
187. C2×#13133138C22semidirect
188. C2×AGL(1,ℤ/8)×C53C22semidirect
190. C53×#546C22semidirect
192. C53×#496C22semidirect
193. C53×#469C22semidirect
194. C53×#465C22semidirect
195. C53×#463C22semidirect
196. C53×#459C22semidirect
198. C53×#449C22semidirect
199. C53×#447C22semidirect
200. C53×#447C22semidirect
201. C53×#442C22semidirect
202. C53×#435C22semidirect
828. C2×Dic53AGL(1,ℤ/8)semidirect
949. #3264D53semidirect
981. C2×AGL(1,ℤ/8)C2×D53semidirect
1004. #546C2×D53semidirect
1031. #496C2×D53semidirect
1063. #469C2×D53semidirect
1067. #465C2×D53semidirect
1075. #463C2×D53semidirect
1097. #459C2×D53semidirect
1107. #449C2×D53semidirect
1114. #447C2×D53semidirect
1115. #447C2×D53semidirect
1125. #442C2×D53semidirect
1135. #435C2×D53semidirect
1148. C53#61961semidirect

Maximal subgroups

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

subgroupindex
#202885832
D4×#117199472
#202877602
#202877542
#202875082
#202875022
#202870372
#202870352
#202866822
#202866802
#202866782
#202866762
#202863332
#202863292
#202861992
#202861952
#202861912
#202860942
#202860922
#202860262
#202857072
#202857052
#202856312
#202848042
#202848012
#202847182
#202841772
#202841762
C2×#168108162
#202838272
C53×#32642
#6196153