Finite Group Databasebeta

← #28261476

Subgroups — #28261476

Order 13568.

2230 conjugacy classes of subgroups.

The subgroup lattice has 1898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288431C211yesmaximal, characteristic, complemented
2#20288343C211yesmaximal, characteristic, complemented
3#20286960C211yesmaximal, characteristic, complemented
4#20286950C211yesmaximal, characteristic, complemented
5#20286946C211yesmaximal, characteristic, complemented
6#20286944C211yesmaximal, characteristic, complemented
7#20286934C211yesmaximal, characteristic, complemented
8#20286928C211yesmaximal, characteristic, complemented
9#20286920C211yesmaximal, characteristic, complemented
10#20286910C211yesmaximal, characteristic, complemented
11#20286877C211yesmaximal, characteristic, complemented
12#20286876C211yesmaximal, characteristic, complemented
13#20286851C211yesmaximal, characteristic, complemented
14#20286753C211yesmaximal, characteristic, complemented
15#20286752C211yesmaximal, characteristic, complemented
16#20286735C211yesmaximal, characteristic, complemented
17#20286732C211yesmaximal, characteristic, complemented
18#20285070C211yesmaximal, characteristic, complemented
19#20284672C211yesmaximal, characteristic, complemented
20#20284643C211yesmaximal, characteristic, complemented
21#20284545C211yesmaximal, characteristic, complemented
22#20284394C211yesmaximal, characteristic, complemented
23#20284322C211yesmaximal, characteristic, complemented
24#20284249C211yesmaximal, characteristic, complemented
25#20284014C211yesmaximal, characteristic, complemented
26#20283939C211yesmaximal, characteristic, complemented
27#20283544C211yesmaximal, characteristic, complemented
28#20283413C211yesmaximal, characteristic, complemented
29#20283236C211yesmaximal, characteristic, complemented
30#418×D53C211yesmaximal, characteristic, complemented
31C53×#3318C211yesmaximal, characteristic, complemented
32C2×#13133262C2211yescharacteristic
33C22×D4×D53C2211yescharacteristic
34C2×#13133241C2211yescharacteristic
35C2×#13133241C2211yescharacteristic, complemented
36C2×#13133236C2211yescharacteristic, complemented
37C2×#13133223C2211yescharacteristic, complemented
38C2×M16×D53C2211yescharacteristic, complemented
39#16811343C2211yescharacteristic, complemented
40#16811341C2211yescharacteristic, complemented
41#16811340—21no—
42#16811338C2211yescharacteristic, complemented
43#16811337—21no—
44#16811337C2211yescharacteristic, complemented
45#16811322—21no—
46#16811320C2211yescharacteristic, complemented
47#16811311C2211yescharacteristic, complemented
48#16811310—21no—
49#16811308C2211yescharacteristic, complemented
50#16811270C2211yescharacteristic
51#16811269C2211yescharacteristic
52#16811268C2211yescharacteristic
53#16811267C2211yescharacteristic
54#16811262—21no—
55#16811260—21no—
56#16811258C2211yescharacteristic
57#16811257C2211yescharacteristic
58D4×C22⋊D53—21no—
59D4×C22⋊D53C2211yescharacteristic
60#16811255—21no—
61#16811253C2211yescharacteristic, complemented
62#16811209—21no—
63#16811205—21no—
64#16811202C2211yescharacteristic, complemented
65#16811189C2211yescharacteristic
66#16811186C2211yescharacteristic
67#16811183—21no—
68#16811181—21no—
69#16811156—21no—
70#16811155—21no—
71#16811133C2211yescharacteristic
72#16811133C2211yescharacteristic, complemented
73#16811132C2211yescharacteristic
74C2×#13133185—21no—
75#120×D53—21no—
76#16811104C2211yescharacteristic, complemented
77#16811102C2211yescharacteristic, complemented
78#16811095C2211yescharacteristic
79#117×D53C2211yescharacteristic, complemented
80#16810986C2211yescharacteristic, complemented
81#16810983C2211yescharacteristic, complemented
82#16810981C2211yescharacteristic, complemented
83#16810980C2211yescharacteristic, complemented
84#16810976C2211yescharacteristic, complemented
85#16810969C2211yescharacteristic, complemented
86#16810968C2211yescharacteristic, complemented
87#16810967C2211yescharacteristic, complemented
88#16810966C2211yescharacteristic, complemented
89#16810965C2211yescharacteristic, complemented
90#16810964C2211yescharacteristic, complemented
91#16810949C2211yescharacteristic, complemented
92#16810948C2211yescharacteristic, complemented
93#16810946C2211yescharacteristic, complemented
94#16810946C2211yescharacteristic, complemented
95#16810945C2211yescharacteristic, complemented
96#16810944C2211yescharacteristic, complemented
97#16810944C2211yescharacteristic, complemented
98#16810943C2211yescharacteristic, complemented
99#16810936C2211yescharacteristic, complemented
100#16810935C2211yescharacteristic, complemented
101#16810925C2211yescharacteristic, complemented
102#16810922C2211yescharacteristic, complemented
103#16810920C2211yescharacteristic, complemented
104#16810914C2211yescharacteristic, complemented
105#16810911C2211yescharacteristic, complemented
106#16810903C2211yescharacteristic, complemented
107#16810902C2211yescharacteristic, complemented
108#16810882C2211yescharacteristic, complemented
109#16810881C2211yescharacteristic, complemented
110#16810874C2211yescharacteristic, complemented
111#16810873C2211yescharacteristic, complemented
112#16810873C2211yescharacteristic, complemented
113#16810870C2211yescharacteristic, complemented
114#16810868C2211yescharacteristic, complemented
115#16810868C2211yescharacteristic, complemented
116#16810867C2211yescharacteristic, complemented
117#16810867C2211yescharacteristic, complemented
118#16810867C2211yescharacteristic, complemented
119#16810858C2211yescharacteristic, complemented
120#16810852C2211yescharacteristic, complemented
121#16810851C2211yescharacteristic, complemented
122#16810846C2211yescharacteristic, complemented
123#16810844C2211yescharacteristic, complemented
124#16810838C2211yescharacteristic, complemented
125#16810836C2211yescharacteristic, complemented
126#16810822C2211yescharacteristic, complemented
127#16810820C2211yescharacteristic, complemented
128#16810816C2211yescharacteristic, complemented
129#16810787C2211yescharacteristic, complemented
130#16810786C2211yescharacteristic, complemented
131#16810776C2211yescharacteristic, complemented
132#16810775C2211yescharacteristic, complemented
133#16810775C2211yescharacteristic, complemented
134#16810775C2211yescharacteristic, complemented
135#16810774C2211yescharacteristic, complemented
136#16810774C2211yescharacteristic, complemented
137#16810766C2211yescharacteristic, complemented
138#16810765C2211yescharacteristic, complemented
139#16810756C2211yescharacteristic, complemented
140#16810755C2211yescharacteristic, complemented
141#16810755C2211yescharacteristic, complemented
142#16810755C2211yescharacteristic, complemented
143#16810732C2211yescharacteristic, complemented
144#16810725C2211yescharacteristic, complemented
145#16810720C2211yescharacteristic, complemented
146#16810710C2211yescharacteristic, complemented
147C4×#11719923C2211yescharacteristic, complemented
148D8×Dic53C2211yescharacteristic, complemented
149C4×#11719922C2211yescharacteristic, complemented
150#16810701C2211yescharacteristic, complemented
151#16810700C2211yescharacteristic, complemented
152#16810698C2211yescharacteristic, complemented
153#16810698C2211yescharacteristic, complemented
154#16810696C2211yescharacteristic, complemented
155#16810694C2211yescharacteristic, complemented
156#16810692C2211yescharacteristic, complemented
157#16810664C2211yescharacteristic, complemented
158#16810662C2211yescharacteristic, complemented
159#16810658C2211yescharacteristic, complemented
160#16810648C2211yescharacteristic, complemented
161#16810629C2211yescharacteristic, complemented
162#16810628C2211yescharacteristic, complemented
163#16810628C2211yescharacteristic, complemented
164#16810627C2211yescharacteristic, complemented
165#16810626C2211yescharacteristic
166#16810626C2211yescharacteristic, complemented
167#16810626C2211yescharacteristic, complemented
168#16810626C2211yescharacteristic, complemented
169#16810626C2211yescharacteristic, complemented
170#16810626C2211yescharacteristic, complemented
171#16810626C2211yescharacteristic, complemented
172#16810622C2211yescharacteristic, complemented
173#16810621C2211yescharacteristic, complemented
174#16810621C2211yescharacteristic, complemented
175#16810621C2211yescharacteristic, complemented
176#16810620C2211yescharacteristic, complemented
177#16810616C2211yescharacteristic, complemented
178#16810616C2211yescharacteristic, complemented
179#16810616C2211yescharacteristic, complemented
180#102×D53C2211yescharacteristic
181#102×D53C2211yescharacteristic
182#102×D53C2211yescharacteristic, complemented
183#102×D53C2211yescharacteristic, complemented
184#102×D53C2211yescharacteristic, complemented
185#16810588C2211yescharacteristic, complemented
186#16810585C2211yescharacteristic, complemented
187#16810580C2211yescharacteristic, complemented
188C53×#553C2211yescharacteristic, complemented
189D42×C53C2211yescharacteristic
190C53×#490C2211yescharacteristic, complemented
191C53×#482C2211yescharacteristic, complemented
192C53×#481C2211yescharacteristic, complemented
193C53×#478C2211yescharacteristic, complemented
194C53×#469C2211yescharacteristic, complemented
195C53×#466C2211yescharacteristic, complemented
196C53×#459C2211yescharacteristic, complemented
197C53×#447C2211yescharacteristic, complemented
198C53×#447C2211yescharacteristic, complemented
199C53×#442C2211yescharacteristic, complemented
200C53×#435C2211yescharacteristic, complemented
201C53×#418C2211yescharacteristic, complemented
202C2×#102×C53C2211yescharacteristic, complemented
203C24×D53—21no—
204#13133262—24no—
205#13133262—42no—
206C2×#11719945C2311yescharacteristic
207C2×#11719945C2311yescharacteristic
208C2×#11719947—21no—
209C2×#11719947C2311yescharacteristic
210C2×#11719947C2311yescharacteristic
211C2×#11719947C2311yescharacteristic
212C22×D212C2311yescharacteristic
213C22×C22⋊D53—21no—
214C22×C22⋊D53—21no—
215C22×C22⋊D53—21no—
216C22×C22⋊D53—21no—
217C2×D4×D53—24no—
218C2×D4×D53—21no—
219C2×D4×D53—21no—
220C2×D4×D53—21no—
221C2×D4×D53—21no—
222C2×D4×D53—21no—
223C2×D4×D53—42no—
224C2×D4×D53C2311yescharacteristic
225C2×D4×D53C2311yescharacteristic
226C2×D4×D53C2311yescharacteristic
227C2×D4×D53C2311yescharacteristic
228C2×D4×D53C2311yescharacteristic
229C22×C4×D53C2311yescharacteristic
230#13133241—24no—
231#13133241—42no—
232#13133236—42no—
233C2×Dic212C2311yescharacteristic, complemented
234C2×#11719913C2311yescharacteristic
235C2×#11719913C2311yescharacteristic
236C2×#11719923C2311yescharacteristic
237C2×#11719923C2311yescharacteristic
238C2×#11719923C2311yescharacteristic, complemented
239C2×#11719923C2311yescharacteristic, complemented
240C2×#11719922C2311yescharacteristic
241C2×#11719922C2311yescharacteristic
242#13133223—42no—
243C2×#11719917C2311yescharacteristic
244C2×#11719917C2311yescharacteristic, complemented
245C2×#11719912C2311yescharacteristic
246C2×#11719912C2311yescharacteristic
247C2×#11719912C2311yescharacteristic
248C2×#11719912C2311yescharacteristic
249C2×#11719912C2311yescharacteristic, complemented
250M16×D53—42no—
251C2×C8×D53C2311yescharacteristic
252C2×C8×D53C2311yescharacteristic
253C2×C8×D53C2311yescharacteristic, complemented
254#13133217C2311yescharacteristic, complemented
255#13133216—21no—
256#13133216C2311yescharacteristic, complemented
257#13133213—21no—
258#13133213C2311yescharacteristic
259#13133212—21no—
260#13133212—21no—
261#13133211—21no—
262#13133210—21no—
263#13133210—21no—
264#13133210—21no—
265#13133210—21no—
266#13133208—21no—
267#13133208C2311yescharacteristic, complemented
268#13133207—21no—
269#13133207—21no—
270#13133205C2311yescharacteristic
271#13133204—21no—
272#13133204—21no—
273#13133204C2311yescharacteristic
274#13133203—21no—
275#13133203—21no—
276#13133203—21no—
277#13133203—21no—
278#13133203—21no—
279#13133202—21no—
280#13133202—21no—
281#13133202D411yescharacteristic
282#13133201—21no—
283#13133200—21no—
284#13133199—21no—
285#13133199—21no—
286#13133199—21no—
287#13133199D411yescharacteristic
288#13133198—21no—
289#13133198—21no—
290#13133197—21no—
291#13133197C2311yescharacteristic
292#13133197C2311yescharacteristic
293#13133197C2311yescharacteristic, complemented
294#13133196C2311yescharacteristic
295#13133196C2311yescharacteristic
296#13133196C2311yescharacteristic, complemented
297#13133195—21no—
298#13133195D411yescharacteristic
299#13133194—21no—
300#13133194D411yescharacteristic
301#13133192C2311yescharacteristic
302#13133191—21no—
303#13133191—21no—
304#13133191C2311yescharacteristic
305#13133190—21no—
306#13133190—21no—
307#13133190—21no—
308#13133190D411yescharacteristic
309#13133189—21no—
310#13133189—21no—
311#13133189—21no—
312#13133189—21no—
313#13133189—21no—
314#13133189—21no—
315#13133189D411yescharacteristic
316#13133188—21no—
317#13133188—21no—
318#13133188—21no—
319#13133188—21no—
320#13133188C2311yescharacteristic
321#13133188C2311yescharacteristic
322#13133188C2311yescharacteristic
323#13133188C2311yescharacteristic, complemented
324#13133187—21no—
325#13133187—21no—
326#13133187—21no—
327#13133187D411yescharacteristic
328#13133186—21no—
329#13133186—21no—
330#13133185—21no—
331#13133185—21no—
332#13133185—21no—
333#13133185—21no—
334#13133185—21no—
335#13133185—21no—
336#13133185—21no—
337#13133185—21no—
338#13133185—21no—
339#13133185—21no—
340#13133185—21no—
341#13133185D411yescharacteristic
342C4×Dic106—21no—
343C4×Dic106C2311yescharacteristic, complemented
344#13133182—21no—
345#13133182—21no—
346#13133182C2311yescharacteristic, complemented
347C4×D212C2311yescharacteristic
348C4×D212C2311yescharacteristic
349D4×Dic53—21no—
350D4×Dic53—21no—
351D4×Dic53C2311yescharacteristic
352D4×Dic53C2311yescharacteristic, complemented
353#13133179—21no—
354#13133179C2311yescharacteristic
355C4×C22⋊D53—21no—
356C4×C22⋊D53—21no—
357C4×C22⋊D53—21no—
358C4×C22⋊D53—21no—
359C4×C22⋊D53C2311yescharacteristic
360C4×C22⋊D53C2311yescharacteristic
361#13133177—21no—
362#13133177—21no—
363#13133177—21no—
364#13133177—21no—
365#13133177—21no—
366#13133176—21no—
367#13133176—21no—
368#13133176C2311yescharacteristic
369#13133176C2311yescharacteristic, complemented
370#13133175—21no—
371#13133175C2311yescharacteristic
372#13133175C2311yescharacteristic
373#13133175C2311yescharacteristic
374#13133175C2311yescharacteristic
375#13133175C2311yescharacteristic, complemented
376#13133174—21no—
377#13133174C2311yescharacteristic
378#13133173—21no—
379#13133173—21no—
380#13133173—21no—
381C2×#11719919—21no—
382C4⋊C4×D53C2311yescharacteristic
383C4⋊C4×D53C2311yescharacteristic
384C4⋊C4×D53C2311yescharacteristic, complemented
385C2×C22⋊Dic53—21no—
386C2×#11719921—21no—
387C2×#11719921—21no—
388C22⋊C4×D53—21no—
389C22⋊C4×D53—21no—
390C22⋊C4×D53—21no—
391C22⋊C4×D53—21no—
392C42×D53—21no—
393#13133151C2311yescharacteristic, complemented
394#13133150C2311yescharacteristic, complemented
395#13133150C2311yescharacteristic, complemented
396#13133150C2311yescharacteristic, complemented
397#13133150C2311yescharacteristic, complemented
398#13133149C2311yescharacteristic, complemented
399#13133149C2311yescharacteristic, complemented
400#13133148C2311yescharacteristic, complemented
401#13133148C2311yescharacteristic, complemented
402C4⋊#88322C2311yescharacteristic, complemented
403#13133146C2311yescharacteristic, complemented
404#13133146C2311yescharacteristic, complemented
405#13133142C2311yescharacteristic, complemented
406#13133142C2311yescharacteristic, complemented
407#13133142C2311yescharacteristic, complemented
408#13133142C2311yescharacteristic, complemented
409#13133140C2311yescharacteristic, complemented
410#13133140C2311yescharacteristic, complemented
411#13133140C2311yescharacteristic, complemented
412#13133140C2311yescharacteristic, complemented
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, complemented
426#13133138C2311yescharacteristic, complemented
427#13133138C2311yescharacteristic, complemented
428#13133138C2311yescharacteristic, complemented
429#13133137C2311yescharacteristic
430#13133137C2311yescharacteristic
431#13133137C2311yescharacteristic
432#13133137C2311yescharacteristic
433#13133137C2311yescharacteristic
434#13133137C2311yescharacteristic
435C22⋊#88322C2311yescharacteristic
436C22⋊#88322C2311yescharacteristic, complemented
437#13133129C2311yescharacteristic
438#13133129C2311yescharacteristic
439#13133129C2311yescharacteristic, complemented
440#13133129C2311yescharacteristic, complemented
441#13133127C2311yescharacteristic, complemented
442C4×#88322C2311yescharacteristic, complemented
443C8×Dic53C2311yescharacteristic, complemented
444C22×D4×C53—21no—
445C22×D4×C53C2311yescharacteristic
446C22×D4×C53C2311yescharacteristic
447C2×D8×C53C2311yescharacteristic
448C2×D8×C53C2311yescharacteristic
449C2×D8×C53C2311yescharacteristic, complemented
450C2×M16×C53C2311yescharacteristic
451C22×C8×C53C2311yescharacteristic, complemented
452#127×C53C2311yescharacteristic
453#126×C53—21no—
454#125×C53C2311yescharacteristic, complemented
455#123×C53—21no—
456#121×C53—21no—
457#121×C53—21no—
458#121×C53C2311yescharacteristic
459#121×C53C2311yescharacteristic
460#121×C53C2311yescharacteristic
461#121×C53C2311yescharacteristic, complemented
462#120×C53—21no—
463#120×C53—21no—
464C4×D4×C53—21no—
465C4×D4×C53C2311yescharacteristic
466C4×D4×C53C2311yescharacteristic
467C4×D4×C53C2311yescharacteristic, complemented
468#117×C53C2311yescharacteristic
469C2×C4⋊C4×C53C2311yescharacteristic, complemented
470#107×C53C2311yescharacteristic, complemented
471#106×C53C2311yescharacteristic, complemented
472#106×C53C2311yescharacteristic, complemented
473C4⋊C8×C53C2311yescharacteristic, complemented
474#102×C53C2311yescharacteristic
475#102×C53C2311yescharacteristic
476#102×C53C2311yescharacteristic
477#102×C53C2311yescharacteristic
478#102×C53C2311yescharacteristic
479#102×C53C2311yescharacteristic
480#102×C53C2311yescharacteristic, complemented
481#102×C53C2311yescharacteristic, complemented
482#102×C53C2311yescharacteristic, complemented
483#102×C53C2311yescharacteristic, complemented
484C22⋊C8×C53C2311yescharacteristic
485C22⋊C8×C53C2311yescharacteristic, complemented
486#97×C53C2311yescharacteristic, complemented
487C24×C53—21no—
488C24×C53—21no—
489C23×D53—21no—
490C23×D53—21no—
491C23×D53—21no—
492C23×D53—21no—
493C23×D53—21no—
494C23×D53—21no—
495C23×D53—44no—
496C23×D53—82no—
497C23×D53—82no—
498C23×D53C2×D411yescharacteristic
499C2×D4×C53—22no—
500C2×D4×C53—22no—
501C2×D4×C53—21no—
502C2×D4×C53—21no—
503C2×D4×C53—21no—
504C2×D4×C53—21no—
505C2×D4×C53—21no—
506C2×D4×C53—21no—
507C2×D4×C53—21no—
508C2×D4×C53—21no—
509C2×D4×C53—41no—
510C2×D4×C53—41no—
511C2×D4×C53—82no—
512C2×D4×C53C2×D411yescharacteristic
513C2×D4×C53C2411yescharacteristic
514C2×D4×C53C2411yescharacteristic
515C2×D4×C53C2411yescharacteristic
516C2×D4×C53C2411yescharacteristic
517C22×C4×C53—21no—
518C22×C4×C53—21no—
519C22×C4×C53—21no—
520C22×C4×C53C2411yescharacteristic
521C22×C4×C53C2411yescharacteristic
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—44no—
539C2×C22⋊D53—44no—
540C2×C22⋊D53—44no—
541C2×C22⋊D53—82no—
542C2×C22⋊D53C2×D411yescharacteristic
543C2×C22⋊D53C2×D411yescharacteristic
544C2×C22⋊D53C2×D411yescharacteristic
545C2×C22⋊D53C2×D411yescharacteristic
546C22×Dic53—21no—
547C22×Dic53—21no—
548C22×Dic53—21no—
549C22×Dic53—21no—
550C22×Dic53—21no—
551C22×Dic53C2×D411yescharacteristic
552#11719947—22no—
553#11719947—22no—
554#11719947—22no—
555#11719947—22no—
556#11719947—22no—
557#11719947—41no—
558#11719947—44no—
559D4×D53—22no—
560D4×D53—22no—
561D4×D53—22no—
562D4×D53—22no—
563D4×D53—22no—
564D4×D53—22no—
565D4×D53—41no—
566D4×D53—41no—
567D4×D53—41no—
568D4×D53—44no—
569D4×D53—44no—
570D4×D53—44no—
571D4×D53—82no—
572D4×D53—82no—
573D4×D53#4114yes—
574#11719945—22no—
575#11719945—22no—
576#11719945—22no—
577#11719945—41no—
578C2×D212—22no—
579C2×D212—21no—
580C2×D212—21no—
581C2×D212—41no—
582C2×D212C2×D411yescharacteristic
583C2×D212C2×D411yescharacteristic
584C2×D212C2411yescharacteristic
585C2×D212C2411yescharacteristic
586C2×C4×D53—22no—
587C2×C4×D53—22no—
588C2×C4×D53—21no—
589C2×C4×D53—21no—
590C2×C4×D53—21no—
591C2×C4×D53—21no—
592C2×C4×D53—21no—
593C2×C4×D53—21no—
594C2×C4×D53C2×D411yescharacteristic
595C2×C4×D53C2×D411yescharacteristic
596C2×C4×D53C2411yescharacteristic
597C2×C4×D53C2411yescharacteristic
598C2×C4×D53C2411yescharacteristic
599C2×Dic106—21no—
600C2×Dic106—21no—
601C2×Dic106C2×D411yescharacteristic
602C2×Dic106C2411yescharacteristic
603C2×Dic106C2411yescharacteristic
604D8×C53—22no—
605D8×C53—41no—
606D8×C53—41no—
607M16×C53—41no—
608C2×C8×C53—41no—
609C2×C8×C53C2411yescharacteristic
610C2×C8×C53C2411yescharacteristic
611C2×C8×C53C2411yescharacteristic
612C2×C8×C53C2411yescharacteristic
613C4⋊C4×C53—21no—
614C4⋊C4×C53—21no—
615C4⋊C4×C53—21no—
616C4⋊C4×C53C2×D411yescharacteristic
617C4⋊C4×C53C2411yescharacteristic
618C4⋊C4×C53C2411yescharacteristic
619C4⋊C4×C53C2411yescharacteristic
620C4⋊C4×C53C2411yescharacteristic
621C22⋊C4×C53—21no—
622C22⋊C4×C53—21no—
623C22⋊C4×C53—21no—
624C22⋊C4×C53—21no—
625C22⋊C4×C53—21no—
626C22⋊C4×C53—21no—
627C22⋊C4×C53—21no—
628C22⋊C4×C53C2×D411yescharacteristic
629C22⋊C4×C53C2×D411yescharacteristic
630C42×C53—21no—
631C42×C53C2411yescharacteristic
632C22⋊Dic53—21no—
633C22⋊Dic53—21no—
634C22⋊Dic53—21no—
635C22⋊Dic53—21no—
636C22⋊Dic53—21no—
637C22⋊Dic53—21no—
638C22⋊Dic53—21no—
639C22⋊Dic53—21no—
640C22⋊Dic53—21no—
641C22⋊Dic53—21no—
642C22⋊Dic53—21no—
643C22⋊Dic53—21no—
644C22⋊Dic53—21no—
645C22⋊Dic53C2×D411yescharacteristic
646C22⋊Dic53C2×D411yescharacteristic
647#11719923—22no—
648#11719923—41no—
649#11719923—41no—
650#11719923—41no—
651#11719922—22no—
652#11719922—41no—
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#11719921—21no—
665#11719921—21no—
666#11719921—21no—
667#11719921C2×D411yescharacteristic
668#11719921C2×D411yescharacteristic
669#11719921C2×D411yescharacteristic
670#11719921C2×D411yescharacteristic
671#11719921C2×D411yescharacteristic
672#11719921C2×D411yescharacteristic
673C4⋊Dic53—21no—
674C4⋊Dic53—21no—
675C4⋊Dic53—21no—
676C4⋊Dic53—21no—
677C4⋊Dic53—21no—
678C4⋊Dic53C2×D411yescharacteristic
679C4⋊Dic53C2411yescharacteristic
680C4⋊Dic53C2411yescharacteristic
681C4⋊Dic53C2411yescharacteristic
682C4⋊Dic53C2411yescharacteristic
683#11719919—21no—
684#11719919—21no—
685#11719919—21no—
686#11719919—21no—
687#11719919—21no—
688#11719919—21no—
689#11719919—21no—
690#11719919—21no—
691#11719919—21no—
692#11719919—21no—
693#11719919C2×D411yescharacteristic
694#11719919C2×D411yescharacteristic
695#11719919C2×D411yescharacteristic
696#11719919C2×D411yescharacteristic
697C4×Dic53—21no—
698C4×Dic53—21no—
699C4×Dic53—21no—
700C4×Dic53—21no—
701C4×Dic53—21no—
702C4×Dic53—21no—
703C4×Dic53—21no—
704C4×Dic53—21no—
705C4×Dic53—21no—
706C4×Dic53C2411yescharacteristic
707#11719917—41no—
708#11719917—41no—
709C2×#88322C2411yescharacteristic
710C2×#88322C2411yescharacteristic
711C2×#88322C2411yescharacteristic
712C2×#88322C2411yescharacteristic
713Dic212—41no—
714#11719913—22no—
715#11719913—41no—
716#11719912—22no—
717#11719912—22no—
718#11719912—41no—
719#11719912—41no—
720#11719912—41no—
721C8×D53—22no—
722C8×D53—22no—
723C8×D53—41no—
724C23×C53—21no—
725C23×C53—21no—
726C23×C53—21no—
727C23×C53—21no—
728C23×C53—42no—
729C23×C53—42no—
730C23×C53—42no—
731C23×C53—81no—
732C23×C53—81no—
733C23×C53—81no—
734C23×C53C22×D411yescharacteristic
735C23×C53C22×D411yescharacteristic
736C22×D53—21no—
737C22×D53—22no—
738C22×D53—24no—
739C22×D53—21no—
740C22×D53—41no—
741C22×D53—41no—
742C22×D53—42no—
743C22×D53—42no—
744C22×D53—42no—
745C22×D53—42no—
746C22×D53—42no—
747C22×D53—42no—
748C22×D53—42no—
749C22×D53—42no—
750C22×D53—81no—
751C22×D53—81no—
752C22×D53—81no—
753C22×D53—81no—
754C22×D53—81no—
755C22×D53—81no—
756C22×D53—81no—
757C22×D53—81no—
758C22×D53—81no—
759C22×D53—816no—
760C22×D53C22×D411yescharacteristic
761C22×D53C22×D411yescharacteristic
762C22×D53C22×D411yescharacteristic
763D4×C53—21no—
764D4×C53—21no—
765D4×C53—21no—
766D4×C53—21no—
767D4×C53—21no—
768D4×C53—21no—
769D4×C53—21no—
770D4×C53—41no—
771D4×C53—42no—
772D4×C53—42no—
773D4×C53—42no—
774D4×C53—81no—
775D4×C53—81no—
776D4×C53—81no—
777D4×C53—81no—
778D4×C53—81no—
779D4×C53C2×#4112yes—
780C2×C4×C53—21no—
781C2×C4×C53—21no—
782C2×C4×C53—21no—
783C2×C4×C53—21no—
784C2×C4×C53—21no—
785C2×C4×C53—21no—
786C2×C4×C53—21no—
787C2×C4×C53—21no—
788C2×C4×C53—81no—
789C2×C4×C53—81no—
790C2×C4×C53—81no—
791C2×C4×C53C22×D411yescharacteristic
792C2×C4×C53C22×D411yescharacteristic
793C2×C4×C53C22×D411yescharacteristic
794C2×C4×C53C22×D411yescharacteristic
795C2×C4×C53C2511yescharacteristic
796C22⋊D53—22no—
797C22⋊D53—22no—
798C22⋊D53—24no—
799C22⋊D53—41no—
800C22⋊D53—41no—
801C22⋊D53—42no—
802C22⋊D53—42no—
803C22⋊D53—42no—
804C22⋊D53—42no—
805C22⋊D53—42no—
806C22⋊D53—42no—
807C22⋊D53—42no—
808C22⋊D53—42no—
809C22⋊D53—42no—
810C22⋊D53—81no—
811C22⋊D53—81no—
812C22⋊D53—81no—
813C22⋊D53—81no—
814C22⋊D53—81no—
815C22⋊D53—81no—
816C2×Dic53—22no—
817C2×Dic53—21no—
818C2×Dic53—21no—
819C2×Dic53—21no—
820C2×Dic53—21no—
821C2×Dic53—21no—
822C2×Dic53—21no—
823C2×Dic53—42no—
824C2×Dic53—42no—
825C2×Dic53—42no—
826C2×Dic53—81no—
827C2×Dic53—81no—
828C2×Dic53C22×D411yescharacteristic
829C2×Dic53C22×D411yescharacteristic
830C2×Dic53C22×D411yescharacteristic
831C2×Dic53C22×D411yescharacteristic
832C2×Dic53C22×D411yescharacteristic
833D212—22no—
834D212—21no—
835D212—21no—
836D212—21no—
837D212—41no—
838D212—42no—
839D212—81no—
840D212C2×#4112yes—
841C4×D53—22no—
842C4×D53—21no—
843C4×D53—21no—
844C4×D53—21no—
845C4×D53—21no—
846C4×D53—22no—
847C4×D53—42no—
848C4×D53—81no—
849C4×D53—81no—
850C4×D53—81no—
851C4×D53—81no—
852C4×D53—81no—
853C4×D53C2×#4112yes—
854C4×D53H(5,𝔽2)12yes—
855Dic106—22no—
856Dic106—21no—
857Dic106—21no—
858Dic106—21no—
859Dic106—21no—
860Dic106—81no—
861Dic106—81no—
862C8×C53—21no—
863C8×C53—21no—
864C8×C53—21no—
865C8×C53—21no—
866#88322—21no—
867#88322—21no—
868#88322—21no—
869#88322—21no—
870#61175—531nomaximal, Sylow
871C22×C53—21no—
872C22×C53—21no—
873C22×C53—21no—
874C22×C53—21no—
875C22×C53—21no—
876C22×C53—22no—
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—84no—
890C22×C53—162no—
891C22×C53C23×D411yescharacteristic
892C2×D53—21no—
893C2×D53—21no—
894C2×D53—21no—
895C2×D53—21no—
896C2×D53—21no—
897C2×D53—21no—
898C2×D53—21no—
899C2×D53—21no—
900C2×D53—22no—
901C2×D53—44no—
902C2×D53—41no—
903C2×D53—41no—
904C2×D53—41no—
905C2×D53—41no—
906C2×D53—41no—
907C2×D53—84no—
908C2×D53—84no—
909C2×D53—84no—
910C2×D53—84no—
911C2×D53—84no—
912C2×D53—162no—
913C2×D53#54612yes—
914C4×C53—21no—
915C4×C53—21no—
916C4×C53—21no—
917C4×C53—21no—
918C4×C53—41no—
919C4×C53—41no—
920C4×C53—41no—
921C4×C53—41no—
922C4×C53C22×#4111yescharacteristic
923C4×C53C2×H(5,𝔽2)11yescharacteristic
924Dic53—21no—
925Dic53—21no—
926Dic53—21no—
927Dic53—21no—
928Dic53—41no—
929Dic53—41no—
930Dic53—41no—
931Dic53—41no—
932Dic53—41no—
933Dic53—41no—
934Dic53#54612yes—
935#3493—531no—
936#3484—531no—
937#3325—531no—
938#3325—531no—
939#3324—531no—
940#3324—531no—
941#3323—531no—
942#3323—531no—
943#3322—531no—
944#3322—531no—
945#3319—531no—
946#3319—531no—
947#3318—531no—
948#3318D5311yescharacteristic, complemented
949#3311—531no—
950#3311—531no—
951#3310—531no—
952#3310—531no—
953#3136—531no—
954#3096—531no—
955#3093—531no—
956#3081—531no—
957#3062—531no—
958#3054—531no—
959#3045—531no—
960#3012—531no—
961#3003—531no—
962#2946—531no—
963#2930—531no—
964#2897—531no—
965C2×#418—531no—
966C2×C53—41no—
967C2×C53—42no—
968C2×C53—41no—
969C2×C53—81no—
970C2×C53—81no—
971C2×C53—81no—
972C2×C53C2×#54611yescharacteristic
973C2×C53#358511yescharacteristic
974C2×C53#358511yescharacteristic
975D53—22no—
976D53—41no—
977D53—41no—
978D53—42no—
979D53—81no—
980C2×H(5,𝔽2)—531no—
981C23×D4—531no—
982C2×AGL(1,ℤ/8)—531no—
983C2×AGL(1,ℤ/8)—531no—
984C2×#135—531no—
985C2×#131—531no—
986C22×M16—531no—
987#556—531no—
988#556—531no—
989#556—1061no—
990#555—531no—
991#555—531no—
992#555—1061no—
993#553—531no—
994#553—1061no—
995#553C2×D5311yescharacteristic, complemented
996#552—531no—
997#552—531no—
998#552—1061no—
999#546—531no—
1000#546—531no—
1001#546—531no—
1002#546—531no—
1003#546—1061no—
1004#546—1061no—
1005D42—531no—
1006D42—531no—
1007D42—531no—
1008D42—1061no—
1009D42—1061no—
1010D42C2×D5311yescharacteristic
1011#544—531no—
1012#538—1061no—
1013#538—1061no—
1014#537—531no—
1015#535—531no—
1016#535—531no—
1017#534—1061no—
1018#534—1061no—
1019#529—1061no—
1020#529—1061no—
1021#525—531no—
1022#525—531no—
1023#525—531no—
1024C2×#120—1061no—
1025C2×#120—1061no—
1026#520—531no—
1027#520—531no—
1028#518—531no—
1029C2×#117—531no—
1030#490—531no—
1031#490C2×D5311yescharacteristic, complemented
1032#489—531no—
1033#489—531no—
1034#488—531no—
1035#488—531no—
1036#486—531no—
1037#486—531no—
1038#485—531no—
1039#485—531no—
1040#485—531no—
1041#485—531no—
1042#482—531no—
1043#482—531no—
1044#482—531no—
1045#482—531no—
1046#482—531no—
1047#482—531no—
1048#482—531no—
1049#482C2×D5311yescharacteristic, complemented
1050#481—531no—
1051#481C2×D5311yescharacteristic, complemented
1052#480—531no—
1053#480—531no—
1054#478—531no—
1055#478—531no—
1056#478—531no—
1057#478C2×D5311yescharacteristic, complemented
1058#476—531no—
1059#476—531no—
1060#474—531no—
1061#474—531no—
1062#470—531no—
1063#470—531no—
1064#469—531no—
1065#469—531no—
1066#469—531no—
1067#469C2×D5311yescharacteristic, complemented
1068#468—531no—
1069#468—531no—
1070#468—531no—
1071#468—531no—
1072#468—531no—
1073#468—531no—
1074#466—531no—
1075#466C2×D5311yescharacteristic, complemented
1076#465—531no—
1077#465—531no—
1078#464—531no—
1079#464—531no—
1080#463—531no—
1081#463—531no—
1082#460—531no—
1083#460—531no—
1084#459—531no—
1085#459C2×D5311yescharacteristic, complemented
1086#452—531no—
1087#452—531no—
1088#450—531no—
1089#450—531no—
1090#450—531no—
1091#450—531no—
1092#450—531no—
1093#450—531no—
1094#449—531no—
1095#449—531no—
1096#447—531no—
1097#447—531no—
1098#447—531no—
1099#447—531no—
1100#447C2×D5311yescharacteristic, complemented
1101#447C2×D5311yescharacteristic, complemented
1102#442—531no—
1103#442C2×D5311yescharacteristic, complemented
1104#440—531no—
1105#440—531no—
1106C4×SD16—531no—
1107C4×SD16—531no—
1108C4×D8—531no—
1109C4×D8—531no—
1110#436—531no—
1111#436—531no—
1112#436—531no—
1113#436—531no—
1114#435—531no—
1115#435—531no—
1116#435—531no—
1117#435C2×D5311yescharacteristic, complemented
1118#428—531no—
1119#428—531no—
1120#427—531no—
1121#424—531no—
1122#418—531no—
1123#418—531no—
1124#418—531no—
1125#418—531no—
1126#418—531no—
1127#418—531no—
1128#418—531no—
1129#418—531no—
1130#418—531no—
1131#418—531no—
1132#418—531no—
1133#418C2×D5311yescharacteristic, complemented
1134#417—531no—
1135#417—531no—
1136#417—531no—
1137#417—531no—
1138#416—531no—
1139#416—531no—
1140#416—531no—
1141#416—531no—
1142C2×#102—531no—
1143C2×#102—531no—
1144C2×#102—531no—
1145C2×#102—531no—
1146C2×#102—531no—
1147C2×#102C2×D5311yescharacteristic, complemented
1148#408—531no—
1149#407—531no—
1150#405—531no—
1151C53#6117511yescharacteristic, complemented, Sylow
1152C25—1061no—
1153H(5,𝔽2)—1064no—
1154H(5,𝔽2)—2122no—
1155C2×#41—531no—
1156C2×#41—531no—
1157C2×#41—531no—
1158C2×#41—531no—
1159C2×#41—531no—
1160C2×#41—1061no—
1161C22×D4—21no—
1162C22×D4—531no—
1163C22×D4—531no—
1164C22×D4—531no—
1165C22×D4—531no—
1166C22×D4—531no—
1167C22×D4—531no—
1168C22×D4—1061no—
1169C22×D4—1061no—
1170C22×D4—1061no—
1171C22×D4—1064no—
1172C22×D4—1061no—
1173C22×D4—1061no—
1174C22×D4—1061no—
1175C22×D4—1061no—
1176C22×D4—1061no—
1177C22×D4—1061no—
1178C22×D4—2122no—
1179C22×D4C22×D5311yescharacteristic
1180C22×D4C22×D5311yescharacteristic
1181C23×C4—531no—
1182AGL(1,ℤ/8)—1064no—
1183AGL(1,ℤ/8)—2122no—
1184#135—2122no—
1185C2×Q16—531no—
1186C2×SD16—531no—
1187C2×SD16—531no—
1188C2×SD16—531no—
1189C2×SD16—531no—
1190C2×SD16—531no—
1191C2×SD16—531no—
1192C2×D8—531no—
1193C2×D8—531no—
1194C2×D8C22×D5311yescharacteristic
1195C2×D8C22×D5311yescharacteristic
1196C2×D8C22×D5311yescharacteristic, complemented
1197#131—2122no—
1198C2×M16—531no—
1199C2×M16—531no—
1200C2×M16—531no—
1201C2×M16—531no—
1202C2×M16—531no—
1203C2×M16—531no—
1204C2×M16—531no—
1205C2×M16—2122no—
1206C2×M16C22×D5311yescharacteristic
1207C22×C8—531no—
1208C22×C8—531no—
1209C22×C8—531no—
1210C22×C8C22×D5311yescharacteristic, complemented
1211C4⋊Q8—531no—
1212C4⋊Q8—531no—
1213C4⋊Q8—1061no—
1214#127—531no—
1215#127—1061no—
1216#127C22×D5311yescharacteristic
1217#126—21no—
1218#126—1061no—
1219#126—1061no—
1220#126—1061no—
1221#126—1061no—
1222#126—1061no—
1223#126—1061no—
1224#126—1061no—
1225#125—531no—
1226#125—1061no—
1227#125—1061no—
1228#125—1061no—
1229#125C22×D5311yescharacteristic, complemented
1230#124—531no—
1231#124—531no—
1232#124—1061no—
1233#124—1061no—
1234#124—1061no—
1235#124—1061no—
1236#124—1061no—
1237#124—1061no—
1238#124—1061no—
1239#123—21no—
1240#123—531no—
1241#123—531no—
1242#123—1061no—
1243#123—1061no—
1244#123—1061no—
1245#123—1061no—
1246#123—1061no—
1247#123—1061no—
1248#123—1061no—
1249#123—1061no—
1250#123—1061no—
1251C22⋊Q8—531no—
1252C22⋊Q8—531no—
1253C22⋊Q8—531no—
1254C22⋊Q8—531no—
1255C22⋊Q8—531no—
1256C22⋊Q8—531no—
1257C22⋊Q8—531no—
1258C22⋊Q8—531no—
1259C22⋊Q8—1061no—
1260C22⋊Q8—1061no—
1261C22⋊Q8—1061no—
1262#121—21no—
1263#121—21no—
1264#121—531no—
1265#121—531no—
1266#121—531no—
1267#121—531no—
1268#121—531no—
1269#121—531no—
1270#121—531no—
1271#121—531no—
1272#121—1061no—
1273#121—1061no—
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#121C22×D5311yescharacteristic
1288#121C22×D5311yescharacteristic
1289#121C22×D5311yescharacteristic
1290#121C22×D5311yescharacteristic, complemented
1291#120—21no—
1292#120—21no—
1293#120—531no—
1294#120—531no—
1295#120—1061no—
1296#120—1061no—
1297#120—1061no—
1298#120—1061no—
1299#120—1061no—
1300#120—1061no—
1301#120—1061no—
1302#120—1061no—
1303#120—1061no—
1304#120—1061no—
1305#120—1061no—
1306#120—1061no—
1307#120—1061no—
1308#120—1061no—
1309#120—1061no—
1310#120—1061no—
1311C4×Q8—531no—
1312C4×Q8—531no—
1313C4×Q8—1061no—
1314C4×Q8—1061no—
1315C4×Q8—1061no—
1316C4×D4—21no—
1317C4×D4—531no—
1318C4×D4—531no—
1319C4×D4—531no—
1320C4×D4—531no—
1321C4×D4—531no—
1322C4×D4—531no—
1323C4×D4—531no—
1324C4×D4—1061no—
1325C4×D4—1061no—
1326C4×D4—1061no—
1327C4×D4—1061no—
1328C4×D4—1061no—
1329C4×D4—1061no—
1330C4×D4—1061no—
1331C4×D4—1061no—
1332C4×D4—1061no—
1333C4×D4—1061no—
1334C4×D4—1061no—
1335C4×D4—1061no—
1336C4×D4C22×D5311yescharacteristic
1337C4×D4C22×D5311yescharacteristic
1338C4×D4C22×D5311yescharacteristic, complemented
1339#117—531no—
1340#117—531no—
1341#117—531no—
1342#117—531no—
1343#117—531no—
1344#117—531no—
1345#117—531no—
1346#117—531no—
1347#117—1061no—
1348#117—1061no—
1349#117—1061no—
1350#117—1061no—
1351#117—1061no—
1352#117—1061no—
1353#117—1061no—
1354#117C22×D5311yescharacteristic
1355C2×C4⋊C4—531no—
1356C2×C4⋊C4—531no—
1357C2×C4⋊C4—531no—
1358C2×C4⋊C4—1061no—
1359C2×C4⋊C4C22×D5311yescharacteristic, complemented
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×C22⋊C4—1061no—
1367C2×C42—1061no—
1368#107—531no—
1369#107—531no—
1370#107—531no—
1371#107—531no—
1372#107—531no—
1373#107C22×D5311yescharacteristic, complemented
1374#106—531no—
1375#106—531no—
1376#106—531no—
1377#106—531no—
1378#106C22×D5311yescharacteristic, complemented
1379#106C22×D5311yescharacteristic, complemented
1380C4⋊C8—531no—
1381C4⋊C8—531no—
1382C4⋊C8—531no—
1383C4⋊C8C22×D5311yescharacteristic, complemented
1384#103—531no—
1385#103—531no—
1386#103—531no—
1387#103—531no—
1388#103—531no—
1389#103—531no—
1390#103—531no—
1391#103—531no—
1392#102—531no—
1393#102—531no—
1394#102—531no—
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
1419#102C22×D5311yescharacteristic
1420#102C22×D5311yescharacteristic, complemented
1421#102C22×D5311yescharacteristic, complemented
1422#102C22×D5311yescharacteristic, complemented
1423#102C22×D5311yescharacteristic, complemented
1424C22⋊C8—531no—
1425C22⋊C8—531no—
1426C22⋊C8—531no—
1427C22⋊C8—531no—
1428C22⋊C8—531no—
1429C22⋊C8—531no—
1430C22⋊C8C22×D5311yescharacteristic
1431C22⋊C8C22×D5311yescharacteristic, complemented
1432#97—531no—
1433#97C22×D5311yescharacteristic, complemented
1434C4×C8—531no—
1435C4×C8—531no—
1436C24—21no—
1437C24—21no—
1438C24—531no—
1439C24—1061no—
1440C24—1061no—
1441C24—1061no—
1442C24—1061no—
1443C24—1061no—
1444C24—1061no—
1445C24—4242no—
1446C24—4242no—
1447C24—2124no—
1448#41—1062no—
1449#41—1062no—
1450#41—1062no—
1451#41—1062no—
1452#41—1062no—
1453#41—1062no—
1454#41—1062no—
1455#41—1062no—
1456#41—2121no—
1457#41—2121no—
1458#41—2124no—
1459C2×Q8—531no—
1460C2×Q8—531no—
1461C2×Q8—531no—
1462C2×Q8—1061no—
1463C2×Q8—1061no—
1464C2×D4—22no—
1465C2×D4—22no—
1466C2×D4—21no—
1467C2×D4—21no—
1468C2×D4—21no—
1469C2×D4—21no—
1470C2×D4—21no—
1471C2×D4—21no—
1472C2×D4—21no—
1473C2×D4—21no—
1474C2×D4—41no—
1475C2×D4—41no—
1476C2×D4—82no—
1477C2×D4—534no—
1478C2×D4—531no—
1479C2×D4—531no—
1480C2×D4—531no—
1481C2×D4—531no—
1482C2×D4—531no—
1483C2×D4—531no—
1484C2×D4—531no—
1485C2×D4—531no—
1486C2×D4—1062no—
1487C2×D4—1061no—
1488C2×D4—1062no—
1489C2×D4—1062no—
1490C2×D4—1062no—
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—1062no—
1500C2×D4—1062no—
1501C2×D4—1061no—
1502C2×D4—1061no—
1503C2×D4—1061no—
1504C2×D4—1061no—
1505C2×D4—1061no—
1506C2×D4—1061no—
1507C2×D4—1061no—
1508C2×D4—1061no—
1509C2×D4—1061no—
1510C2×D4—1061no—
1511C2×D4—4242no—
1512C2×D4—4242no—
1513C2×D4—4242no—
1514C2×D4—2121no—
1515C2×D4—2121no—
1516C2×D4—2121no—
1517C2×D4—2121no—
1518C2×D4—2124no—
1519C2×D4—2124no—
1520C2×D4—2124no—
1521C2×D4—2124no—
1522C2×D4—2124no—
1523C2×D4—2124no—
1524C2×D4D4×D5311yescharacteristic
1525C2×D4C23×D5311yescharacteristic
1526C2×D4C23×D5311yescharacteristic
1527C2×D4C23×D5311yescharacteristic
1528C2×D4C23×D5311yescharacteristic
1529C22×C4—21no—
1530C22×C4—21no—
1531C22×C4—21no—
1532C22×C4—531no—
1533C22×C4—531no—
1534C22×C4—531no—
1535C22×C4—531no—
1536C22×C4—531no—
1537C22×C4—531no—
1538C22×C4—1062no—
1539C22×C4—1062no—
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—1061no—
1550C22×C4—1061no—
1551C22×C4C23×D5311yescharacteristic
1552C22×C4C23×D5311yescharacteristic
1553Q16—2121no—
1554SD16—1062no—
1555SD16—1062no—
1556SD16—2121no—
1557SD16—2121no—
1558SD16—2121no—
1559SD16—2121no—
1560D8—22no—
1561D8—41no—
1562D8—41no—
1563D8—1062no—
1564D8—2121no—
1565M16—41no—
1566M16—1062no—
1567M16—1062no—
1568M16—2121no—
1569M16—2121no—
1570M16—2121no—
1571M16—2121no—
1572M16—2121no—
1573C2×C8—41no—
1574C2×C8—531no—
1575C2×C8—531no—
1576C2×C8—531no—
1577C2×C8—531no—
1578C2×C8—1062no—
1579C2×C8—1062no—
1580C2×C8—2121no—
1581C2×C8C23×D5311yescharacteristic
1582C2×C8C23×D5311yescharacteristic
1583C2×C8C23×D5311yescharacteristic
1584C2×C8C23×D5311yescharacteristic
1585C4⋊C4—21no—
1586C4⋊C4—21no—
1587C4⋊C4—21no—
1588C4⋊C4—531no—
1589C4⋊C4—531no—
1590C4⋊C4—531no—
1591C4⋊C4—531no—
1592C4⋊C4—531no—
1593C4⋊C4—531no—
1594C4⋊C4—531no—
1595C4⋊C4—531no—
1596C4⋊C4—531no—
1597C4⋊C4—1061no—
1598C4⋊C4—1061no—
1599C4⋊C4—1061no—
1600C4⋊C4—1061no—
1601C4⋊C4—1061no—
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⋊C4D4×D5311yescharacteristic
1613C4⋊C4C23×D5311yescharacteristic
1614C4⋊C4C23×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—531no—
1625C22⋊C4—531no—
1626C22⋊C4—531no—
1627C22⋊C4—531no—
1628C22⋊C4—531no—
1629C22⋊C4—531no—
1630C22⋊C4—531no—
1631C22⋊C4—531no—
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⋊C4—1061no—
1656C22⋊C4—1061no—
1657C22⋊C4—1061no—
1658C22⋊C4—1061no—
1659C22⋊C4D4×D5311yescharacteristic
1660C22⋊C4D4×D5311yescharacteristic
1661C42—21no—
1662C42—531no—
1663C42—1061no—
1664C42—1061no—
1665C42—1061no—
1666C42—1061no—
1667C42—1061no—
1668C42—1061no—
1669C42—1061no—
1670C42—1061no—
1671C42—1061no—
1672C42C23×D5311yescharacteristic
1673C23—21no—
1674C23—21no—
1675C23—21no—
1676C23—21no—
1677C23—42no—
1678C23—42no—
1679C23—42no—
1680C23—81no—
1681C23—81no—
1682C23—81no—
1683C23—531no—
1684C23—531no—
1685C23—531no—
1686C23—1064no—
1687C23—1062no—
1688C23—1061no—
1689C23—1061no—
1690C23—4241no—
1691C23—4241no—
1692C23—4241no—
1693C23—4241no—
1694C23—4241no—
1695C23—4241no—
1696C23—4241no—
1697C23—4241no—
1698C23—4241no—
1699C23—42416no—
1700C23—2121no—
1701C23—2121no—
1702C23—2122no—
1703C23—2122no—
1704C23—2122no—
1705C23—2122no—
1706C23—2122no—
1707C23—2122no—
1708C23—2122no—
1709C23—2122no—
1710C23C2×D4×D5311yescharacteristic
1711C23C2×D4×D5311yescharacteristic
1712Q8—1062no—
1713Q8—1061no—
1714Q8—1061no—
1715Q8—1061no—
1716Q8—1061no—
1717Q8—4241no—
1718Q8—4241no—
1719D4—21no—
1720D4—21no—
1721D4—21no—
1722D4—21no—
1723D4—21no—
1724D4—21no—
1725D4—21no—
1726D4—41no—
1727D4—42no—
1728D4—42no—
1729D4—42no—
1730D4—81no—
1731D4—81no—
1732D4—81no—
1733D4—81no—
1734D4—81no—
1735D4—532no—
1736D4—1062no—
1737D4—1064no—
1738D4—1062no—
1739D4—1062no—
1740D4—1061no—
1741D4—1061no—
1742D4—1061no—
1743D4—4241no—
1744D4—4241no—
1745D4—4241no—
1746D4—4241no—
1747D4—4241no—
1748D4—4241no—
1749D4—4241no—
1750D4—2121no—
1751D4—2122no—
1752D4—2122no—
1753D4—2121no—
1754D4—2121no—
1755D4—2122no—
1756D4—2122no—
1757D4—2122no—
1758D4—2122no—
1759D4—2122no—
1760D4—2122no—
1761D4—2122no—
1762D4—2122no—
1763D4#41×D5312yes—
1764C2×C4—21no—
1765C2×C4—21no—
1766C2×C4—21no—
1767C2×C4—21no—
1768C2×C4—21no—
1769C2×C4—21no—
1770C2×C4—21no—
1771C2×C4—21no—
1772C2×C4—81no—
1773C2×C4—81no—
1774C2×C4—81no—
1775C2×C4—531no—
1776C2×C4—532no—
1777C2×C4—532no—
1778C2×C4—531no—
1779C2×C4—531no—
1780C2×C4—531no—
1781C2×C4—531no—
1782C2×C4—1062no—
1783C2×C4—1062no—
1784C2×C4—1062no—
1785C2×C4—1061no—
1786C2×C4—1061no—
1787C2×C4—1061no—
1788C2×C4—1061no—
1789C2×C4—1061no—
1790C2×C4—1061no—
1791C2×C4—1061no—
1792C2×C4—1061no—
1793C2×C4—1061no—
1794C2×C4—1061no—
1795C2×C4—4241no—
1796C2×C4—4241no—
1797C2×C4—4241no—
1798C2×C4—4241no—
1799C2×C4—4241no—
1800C2×C4—4241no—
1801C2×C4—4241no—
1802C2×C4—2122no—
1803C2×C4—2122no—
1804C2×C4—2122no—
1805C2×C4—2122no—
1806C2×C4C2×D4×D5311yescharacteristic
1807C2×C4C2×D4×D5311yescharacteristic
1808C2×C4C2×D4×D5311yescharacteristic
1809C2×C4C2×D4×D5311yescharacteristic
1810C2×C4C24×D5311yescharacteristic
1811C8—21no—
1812C8—21no—
1813C8—21no—
1814C8—21no—
1815C8—1061no—
1816C8—1061no—
1817C8—1061no—
1818C8—1061no—
1819C22—21no—
1820C22—21no—
1821C22—22no—
1822C22—21no—
1823C22—21no—
1824C22—21no—
1825C22—21no—
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—162no—
1839C22—532no—
1840C22—8482no—
1841C22—1061no—
1842C22—1061no—
1843C22—1061no—
1844C22—1061no—
1845C22—1062no—
1846C22—1061no—
1847C22—1061no—
1848C22—1061no—
1849C22—1061no—
1850C22—4244no—
1851C22—4244no—
1852C22—4244no—
1853C22—4244no—
1854C22—4244no—
1855C22—2124no—
1856C22—2121no—
1857C22—2121no—
1858C22—2121no—
1859C22—2121no—
1860C22—2121no—
1861C22C22×D4×D5311yescharacteristic
1862C4—21no—
1863C4—21no—
1864C4—21no—
1865C4—21no—
1866C4—41no—
1867C4—41no—
1868C4—41no—
1869C4—41no—
1870C4—532no—
1871C4—1061no—
1872C4—1061no—
1873C4—1061no—
1874C4—1061no—
1875C4—2121no—
1876C4—2121no—
1877C4—2121no—
1878C4—2121no—
1879C4—2121no—
1880C4—2121no—
1881C4C2×#41×D5311yescharacteristic
1882C4H(5,𝔽2)×D5311yescharacteristic
1883C2—41no—
1884C2—41no—
1885C2—42no—
1886C2—81no—
1887C2—81no—
1888C2—81no—
1889C2—1062no—
1890C2—4241no—
1891C2—2121no—
1892C2—2122no—
1893C2—2121no—
1894C2#546×D5311yescharacteristic
1895C2#2028949011yescharacteristic
1896C2#2028949111yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3318C2
socleC22×C53C23×D4
hypercenter#3318D53
hypocenterC53#61175
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3318

Complements

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

NH ≅ G/Ntype
1. #20288431C2semidirect
2. #20288343C2semidirect
3. #20286960C2semidirect
4. #20286950C2semidirect
5. #20286946C2semidirect
6. #20286944C2semidirect
7. #20286934C2semidirect
8. #20286928C2semidirect
9. #20286920C2semidirect
10. #20286910C2semidirect
11. #20286877C2semidirect
12. #20286876C2semidirect
13. #20286851C2semidirect
14. #20286753C2semidirect
15. #20286752C2semidirect
16. #20286735C2semidirect
17. #20286732C2semidirect
18. #20285070C2semidirect
19. #20284672C2semidirect
20. #20284643C2semidirect
21. #20284545C2semidirect
22. #20284394C2semidirect
23. #20284322C2semidirect
24. #20284249C2semidirect
25. #20284014C2semidirect
26. #20283939C2semidirect
27. #20283544C2semidirect
28. #20283413C2semidirect
29. #20283236C2semidirect
30. #418×D53C2semidirect
31. C53×#3318C2semidirect
35. C2×#13133241C22semidirect
36. C2×#13133236C22semidirect
37. C2×#13133223C22semidirect
38. C2×M16×D53C22semidirect
39. #16811343C22semidirect
40. #16811341C22semidirect
42. #16811338C22semidirect
44. #16811337C22semidirect
46. #16811320C22semidirect
47. #16811311C22semidirect
49. #16811308C22semidirect
61. #16811253C22semidirect
64. #16811202C22semidirect
72. #16811133C22semidirect
76. #16811104C22semidirect
77. #16811102C22semidirect
79. #117×D53C22semidirect
80. #16810986C22semidirect
81. #16810983C22semidirect
82. #16810981C22semidirect
83. #16810980C22semidirect
84. #16810976C22semidirect
85. #16810969C22semidirect
86. #16810968C22semidirect
87. #16810967C22semidirect
88. #16810966C22semidirect
89. #16810965C22semidirect
90. #16810964C22semidirect
91. #16810949C22semidirect
92. #16810948C22semidirect
93. #16810946C22semidirect
94. #16810946C22semidirect
95. #16810945C22semidirect
96. #16810944C22semidirect
97. #16810944C22semidirect
98. #16810943C22semidirect
99. #16810936C22semidirect
100. #16810935C22semidirect
101. #16810925C22semidirect
102. #16810922C22semidirect
103. #16810920C22semidirect
104. #16810914C22semidirect
105. #16810911C22semidirect
106. #16810903C22semidirect
107. #16810902C22semidirect
108. #16810882C22semidirect
109. #16810881C22semidirect
110. #16810874C22semidirect
111. #16810873C22semidirect
112. #16810873C22semidirect
113. #16810870C22semidirect
114. #16810868C22semidirect
115. #16810868C22semidirect
116. #16810867C22semidirect
117. #16810867C22semidirect
118. #16810867C22semidirect
119. #16810858C22semidirect
120. #16810852C22semidirect
121. #16810851C22semidirect
122. #16810846C22semidirect
123. #16810844C22semidirect
124. #16810838C22semidirect
125. #16810836C22semidirect
126. #16810822C22semidirect
127. #16810820C22semidirect
128. #16810816C22semidirect
129. #16810787C22semidirect
130. #16810786C22semidirect
131. #16810776C22semidirect
132. #16810775C22semidirect
133. #16810775C22semidirect
134. #16810775C22semidirect
135. #16810774C22semidirect
136. #16810774C22semidirect
137. #16810766C22semidirect
138. #16810765C22semidirect
139. #16810756C22semidirect
140. #16810755C22semidirect
141. #16810755C22semidirect
142. #16810755C22semidirect
143. #16810732C22semidirect
144. #16810725C22semidirect
145. #16810720C22semidirect
146. #16810710C22semidirect
147. C4×#11719923C22semidirect
148. D8×Dic53C22semidirect
149. C4×#11719922C22semidirect
150. #16810701C22semidirect
151. #16810700C22semidirect
152. #16810698C22semidirect
153. #16810698C22semidirect
154. #16810696C22semidirect
155. #16810694C22semidirect
156. #16810692C22semidirect
157. #16810664C22semidirect
158. #16810662C22semidirect
159. #16810658C22semidirect
160. #16810648C22semidirect
161. #16810629C22semidirect
162. #16810628C22semidirect
163. #16810628C22semidirect
164. #16810627C22semidirect
166. #16810626C22semidirect
167. #16810626C22semidirect
168. #16810626C22semidirect
169. #16810626C22semidirect
170. #16810626C22semidirect
171. #16810626C22semidirect
172. #16810622C22semidirect
173. #16810621C22semidirect
174. #16810621C22semidirect
175. #16810621C22semidirect
176. #16810620C22semidirect
177. #16810616C22semidirect
178. #16810616C22semidirect
179. #16810616C22semidirect
182. #102×D53C22semidirect
183. #102×D53C22semidirect
184. #102×D53C22semidirect
185. #16810588C22semidirect
186. #16810585C22semidirect
187. #16810580C22semidirect
188. C53×#553C22semidirect
190. C53×#490C22semidirect
191. C53×#482C22semidirect
192. C53×#481C22semidirect
193. C53×#478C22semidirect
194. C53×#469C22semidirect
195. C53×#466C22semidirect
196. C53×#459C22semidirect
197. C53×#447C22semidirect
198. C53×#447C22semidirect
199. C53×#442C22semidirect
200. C53×#435C22semidirect
201. C53×#418C22semidirect
202. C2×#102×C53C22semidirect
233. C2×Dic212C23semidirect
238. C2×#11719923C23semidirect
239. C2×#11719923C23semidirect
244. C2×#11719917C23semidirect
249. C2×#11719912C23semidirect
253. C2×C8×D53C23semidirect
254. #13133217C23semidirect
256. #13133216C23semidirect
267. #13133208C23semidirect
293. #13133197C23semidirect
296. #13133196C23semidirect
323. #13133188C23semidirect
343. C4×Dic106C23semidirect
346. #13133182C23semidirect
352. D4×Dic53C23semidirect
369. #13133176C23semidirect
375. #13133175C23semidirect
384. C4⋊C4×D53C23semidirect
393. #13133151C23semidirect
394. #13133150C23semidirect
395. #13133150C23semidirect
396. #13133150C23semidirect
397. #13133150C23semidirect
398. #13133149C23semidirect
399. #13133149C23semidirect
400. #13133148C23semidirect
401. #13133148C23semidirect
402. C4⋊#88322C23semidirect
403. #13133146C23semidirect
404. #13133146C23semidirect
405. #13133142C23semidirect
406. #13133142C23semidirect
407. #13133142C23semidirect
408. #13133142C23semidirect
409. #13133140C23semidirect
410. #13133140C23semidirect
411. #13133140C23semidirect
412. #13133140C23semidirect
425. #13133138C23semidirect
426. #13133138C23semidirect
427. #13133138C23semidirect
428. #13133138C23semidirect
436. C22⋊#88322C23semidirect
439. #13133129C23semidirect
440. #13133129C23semidirect
441. #13133127C23semidirect
442. C4×#88322C23semidirect
443. C8×Dic53C23semidirect
449. C2×D8×C53C23semidirect
451. C22×C8×C53C23semidirect
454. #125×C53C23semidirect
461. #121×C53C23semidirect
467. C4×D4×C53C23semidirect
469. C2×C4⋊C4×C53C23semidirect
470. #107×C53C23semidirect
471. #106×C53C23semidirect
472. #106×C53C23semidirect
473. C4⋊C8×C53C23semidirect
480. #102×C53C23semidirect
481. #102×C53C23semidirect
482. #102×C53C23semidirect
483. #102×C53C23semidirect
485. C22⋊C8×C53C23semidirect
486. #97×C53C23semidirect
948. #3318D53semidirect
995. #553C2×D53semidirect
1031. #490C2×D53semidirect
1049. #482C2×D53semidirect
1051. #481C2×D53semidirect
1057. #478C2×D53semidirect
1067. #469C2×D53semidirect
1075. #466C2×D53semidirect
1085. #459C2×D53semidirect
1100. #447C2×D53semidirect
1101. #447C2×D53semidirect
1103. #442C2×D53semidirect
1117. #435C2×D53semidirect
1133. #418C2×D53semidirect
1147. C2×#102C2×D53semidirect
1151. C53#61175semidirect
1196. C2×D8C22×D53semidirect
1210. C22×C8C22×D53semidirect
1229. #125C22×D53semidirect
1290. #121C22×D53semidirect
1338. C4×D4C22×D53semidirect
1359. C2×C4⋊C4C22×D53semidirect
1373. #107C22×D53semidirect
1378. #106C22×D53semidirect
1379. #106C22×D53semidirect
1383. C4⋊C8C22×D53semidirect
1420. #102C22×D53semidirect
1421. #102C22×D53semidirect
1422. #102C22×D53semidirect
1423. #102C22×D53semidirect
1431. C22⋊C8C22×D53semidirect
1433. #97C22×D53semidirect

Maximal subgroups

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

subgroupindex
#202884312
#202883432
#202869602
#202869502
#202869462
#202869442
#202869342
#202869282
#202869202
#202869102
#202868772
#202868762
#202868512
#202867532
#202867522
#202867352
#202867322
#202850702
#202846722
#202846432
#202845452
#202843942
#202843222
#202842492
#202840142
#202839392
#202835442
#202834132
#202832362
#418×D532
C53×#33182
#6117553