Finite Group Databasebeta

← #28270653

Subgroups — #28270653

Order 13568.

2100 conjugacy classes of subgroups.

The subgroup lattice has 1902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289011C211yesmaximal, characteristic, complemented
2#20288375C211yesmaximal, characteristic, complemented
3#20287051C211yesmaximal, characteristic, complemented
4#20286977C211yesmaximal, characteristic, complemented
5#20286942C211yesmaximal, characteristic, complemented
6#20286913C211yesmaximal, characteristic, complemented
7#20286792C211yesmaximal, characteristic, complemented
8#20286784C211yesmaximal, characteristic, complemented
9#20286720C211yesmaximal, characteristic, complemented
10#20286384C211yesmaximal, characteristic, complemented
11#20286369C211yesmaximal, characteristic, complemented
12#20286350C211yesmaximal, characteristic, complemented
13#20286311C211yesmaximal, characteristic, complemented
14#20286297C211yesmaximal, characteristic, complemented
15#20286275C211yesmaximal, characteristic, complemented
16#20286227C211yesmaximal, characteristic, complemented
17#20286208C211yesmaximal, characteristic, complemented
18#20285814C211yesmaximal, characteristic, complemented
19#20285788C211yesmaximal, characteristic, complemented
20#20285615C211yesmaximal, characteristic, complemented
21#20285590C211yesmaximal, characteristic, complemented
22#20285533C211yesmaximal, characteristic, complemented
23#20285516C211yesmaximal, characteristic, complemented
24#20284981C211yesmaximal, characteristic, complemented
25#20284934C211yesmaximal, characteristic, complemented
26#20284024C211yesmaximal, characteristic, complemented
27#20283987C211yesmaximal, characteristic, complemented
28#20283970C211yesmaximal, characteristic, complemented
29#20283959C211yesmaximal, characteristic, complemented
30#20283774C211yesmaximal, characteristic, complemented
31C53×#3310C211yesmaximal, characteristic, complemented
32C2×#13133262C2211yescharacteristic
33C22×#11719947C2211yescharacteristic
34C2×#13133250C2211yescharacteristic, complemented
35C2×#13133246C2211yescharacteristic, complemented
36C2×#13133246C2211yescharacteristic, complemented
37C2×#13133246C2211yescharacteristic, complemented
38C2×#13133243C2211yescharacteristic, complemented
39C2×#13133243C2211yescharacteristic, complemented
40C2×#13133239C2211yescharacteristic, complemented
41C2×SD16×D53C2211yescharacteristic, complemented
42#16811375—21no—
43#16811370—21no—
44#16811341C2211yescharacteristic, complemented
45#16811329—21no—
46#16811328C2211yescharacteristic, complemented
47#16811326C2211yescharacteristic, complemented
48#16811317—21no—
49#16811293C2211yescharacteristic
50#16811291C2211yescharacteristic
51Q8×D212C2211yescharacteristic, complemented
52#16811283C2211yescharacteristic, complemented
53#16811283C2211yescharacteristic, complemented
54#16811282C2211yescharacteristic
55#16811279C2211yescharacteristic
56#16811278C2211yescharacteristic, complemented
57#16811268C2211yescharacteristic
58#16811267C2211yescharacteristic
59#16811262—21no—
60#16811260—21no—
61D4×C22⋊D53—21no—
62D4×C22⋊D53C2211yescharacteristic
63#16811255—21no—
64#16811245C2211yescharacteristic, complemented
65#16811244—21no—
66#16811236C2211yescharacteristic, complemented
67#16811221—21no—
68#16811212—21no—
69#16811209—21no—
70#16811204C2211yescharacteristic, complemented
71#16811202C2211yescharacteristic
72#16811200—21no—
73#16811196C2211yescharacteristic, complemented
74#16811188—21no—
75#16811186C2211yescharacteristic
76#16811135C2211yescharacteristic, complemented
77#16811132C2211yescharacteristic
78#16811129—21no—
79C22⋊Q8×D53C2211yescharacteristic, complemented
80C2×#13133189—21no—
81#121×D53C2211yescharacteristic
82#16811102C2211yescharacteristic
83#16811017C2211yescharacteristic, complemented
84#16811009C2211yescharacteristic, complemented
85#16811004C2211yescharacteristic, complemented
86#16810995C2211yescharacteristic, complemented
87#16810981C2211yescharacteristic, complemented
88#16810980C2211yescharacteristic, complemented
89#16810968C2211yescharacteristic, complemented
90#16810967C2211yescharacteristic, complemented
91#16810960C2211yescharacteristic, complemented
92#16810958C2211yescharacteristic, complemented
93#16810957C2211yescharacteristic, complemented
94#16810955C2211yescharacteristic, complemented
95#16810947C2211yescharacteristic, complemented
96#16810945C2211yescharacteristic, complemented
97#16810938C2211yescharacteristic, complemented
98#16810938C2211yescharacteristic, complemented
99#16810935C2211yescharacteristic, complemented
100#16810927C2211yescharacteristic, complemented
101#16810917C2211yescharacteristic, complemented
102#16810901C2211yescharacteristic, complemented
103#16810879C2211yescharacteristic, complemented
104#16810877C2211yescharacteristic, complemented
105#16810875C2211yescharacteristic, complemented
106#16810871C2211yescharacteristic, complemented
107#16810870C2211yescharacteristic, complemented
108#16810870C2211yescharacteristic, complemented
109#16810869C2211yescharacteristic, complemented
110#16810868C2211yescharacteristic, complemented
111#16810868C2211yescharacteristic, complemented
112#16810867C2211yescharacteristic, complemented
113#16810867C2211yescharacteristic, complemented
114#16810865C2211yescharacteristic, complemented
115#16810864C2211yescharacteristic, complemented
116#16810858C2211yescharacteristic, complemented
117#16810848C2211yescharacteristic, complemented
118#16810845C2211yescharacteristic, complemented
119#16810844C2211yescharacteristic, complemented
120#16810844C2211yescharacteristic, complemented
121#16810840C2211yescharacteristic, complemented
122#16810839C2211yescharacteristic, complemented
123#16810834C2211yescharacteristic, complemented
124#16810828C2211yescharacteristic, complemented
125#16810822C2211yescharacteristic, complemented
126#16810822C2211yescharacteristic, complemented
127#16810815C2211yescharacteristic, complemented
128#16810787C2211yescharacteristic, complemented
129#16810787C2211yescharacteristic, complemented
130#16810786C2211yescharacteristic
131#16810786C2211yescharacteristic
132#16810786C2211yescharacteristic, complemented
133#16810786C2211yescharacteristic, complemented
134#16810786C2211yescharacteristic, complemented
135#16810786C2211yescharacteristic, complemented
136#16810786C2211yescharacteristic, complemented
137#16810783C2211yescharacteristic, complemented
138#16810782C2211yescharacteristic
139#16810782C2211yescharacteristic, complemented
140#16810781C2211yescharacteristic, complemented
141#16810780C2211yescharacteristic, complemented
142#16810778C2211yescharacteristic, complemented
143#16810775C2211yescharacteristic, complemented
144#16810775C2211yescharacteristic, complemented
145#16810775C2211yescharacteristic, complemented
146#16810774C2211yescharacteristic, complemented
147#16810774C2211yescharacteristic, complemented
148#16810772C2211yescharacteristic, complemented
149#16810770C2211yescharacteristic, complemented
150#16810769C2211yescharacteristic
151#16810769C2211yescharacteristic, complemented
152#16810769C2211yescharacteristic, complemented
153#16810769C2211yescharacteristic, complemented
154#16810769C2211yescharacteristic, complemented
155#16810766C2211yescharacteristic, complemented
156#16810766C2211yescharacteristic, complemented
157#16810763C2211yescharacteristic, complemented
158#16810760C2211yescharacteristic, complemented
159#16810760C2211yescharacteristic, complemented
160#16810758C2211yescharacteristic, complemented
161#16810758C2211yescharacteristic, complemented
162#16810729C2211yescharacteristic, complemented
163#16810725C2211yescharacteristic, complemented
164#16810720C2211yescharacteristic, complemented
165#16810717C2211yescharacteristic, complemented
166C4×#11719925C2211yescharacteristic, complemented
167#16810714C2211yescharacteristic, complemented
168C4×#11719922C2211yescharacteristic, complemented
169#16810701C2211yescharacteristic, complemented
170#16810700C2211yescharacteristic, complemented
171#16810699C2211yescharacteristic, complemented
172#16810698C2211yescharacteristic, complemented
173#16810697C2211yescharacteristic, complemented
174#16810696C2211yescharacteristic, complemented
175#16810694C2211yescharacteristic, complemented
176#16810685C2211yescharacteristic, complemented
177#16810683C2211yescharacteristic, complemented
178#16810631C2211yescharacteristic, complemented
179#16810626C2211yescharacteristic, complemented
180#16810622C2211yescharacteristic, complemented
181#16810621C2211yescharacteristic, complemented
182#16810621C2211yescharacteristic, complemented
183#16810616C2211yescharacteristic, complemented
184#16810589C2211yescharacteristic, complemented
185#16810588C2211yescharacteristic, complemented
186#16810586C2211yescharacteristic, complemented
187#16810585C2211yescharacteristic, complemented
188C53×#552C2211yescharacteristic, complemented
189D42×C53C2211yescharacteristic
190C53×#490C2211yescharacteristic, complemented
191C53×#482C2211yescharacteristic, complemented
192C53×#480C2211yescharacteristic, complemented
193C53×#478C2211yescharacteristic, complemented
194C53×#468C2211yescharacteristic, complemented
195C53×#465C2211yescharacteristic, complemented
196C53×#460C2211yescharacteristic, complemented
197C53×#450C2211yescharacteristic, complemented
198C53×#450C2211yescharacteristic, complemented
199C53×#440C2211yescharacteristic, complemented
200C53×#435C2211yescharacteristic, complemented
201C53×#418C2211yescharacteristic, complemented
202C2×#102×C53C2211yescharacteristic, complemented
203#13133262—42no—
204#13133262—42no—
205C2×#11719945C2311yescharacteristic
206C2×#11719945C2311yescharacteristic
207C2×#11719945C2311yescharacteristic
208C2×#11719945C2311yescharacteristic
209C2×#11719947—21no—
210C2×#11719947—21no—
211C2×#11719947—21no—
212C2×#11719947—42no—
213C2×#11719947—42no—
214C2×#11719947C2311yescharacteristic
215C2×#11719947C2311yescharacteristic
216C2×#11719947C2311yescharacteristic
217C2×#11719947C2311yescharacteristic
218C2×#11719947C2311yescharacteristic
219C22×Dic106C2311yescharacteristic
220C2×Q8×D53C2311yescharacteristic
221C2×Q8×D53C2311yescharacteristic
222C22×C22⋊D53—21no—
223C22×C22⋊D53—21no—
224C22×C22⋊D53—21no—
225C22×C22⋊D53—21no—
226C2×D4×D53—21no—
227C2×D4×D53—21no—
228C2×D4×D53C2311yescharacteristic
229C2×D4×D53C2311yescharacteristic
230C23×Dic53—21no—
231C22×C4×D53C2311yescharacteristic
232#13133250—42no—
233#13133246—42no—
234#13133246—42no—
235#13133246—42no—
236#13133243—42no—
237#13133243—42no—
238#13133239—42no—
239C2×Dic212C2311yescharacteristic
240C2×Dic212C2311yescharacteristic
241C2×Dic212C2311yescharacteristic
242C2×Dic212C2311yescharacteristic
243C2×#11719925C2311yescharacteristic
244C2×#11719925C2311yescharacteristic
245C2×#11719913C2311yescharacteristic
246C2×#11719913C2311yescharacteristic
247C2×#11719913C2311yescharacteristic
248C2×#11719913C2311yescharacteristic
249C2×#11719923C2311yescharacteristic
250C2×#11719923C2311yescharacteristic
251C2×#11719923C2311yescharacteristic
252C2×#11719923C2311yescharacteristic
253C2×#11719923C2311yescharacteristic
254C2×#11719923C2311yescharacteristic
255C2×#11719924C2311yescharacteristic
256SD16×D53—42no—
257C2×D424C2311yescharacteristic
258C2×#11719922C2311yescharacteristic
259C2×#11719922C2311yescharacteristic
260C2×#11719922C2311yescharacteristic
261C2×#11719917C2311yescharacteristic
262C2×#11719917C2311yescharacteristic
263C2×#11719912C2311yescharacteristic
264C2×#11719912C2311yescharacteristic
265C2×#11719912C2311yescharacteristic
266C2×C8×D53C2311yescharacteristic
267#13133217—21no—
268#13133217C2311yescharacteristic
269#13133216—21no—
270#13133216C2311yescharacteristic
271#13133213—21no—
272#13133213—21no—
273#13133213C2311yescharacteristic
274#13133212—21no—
275#13133212—21no—
276#13133212—21no—
277#13133211—21no—
278#13133211—21no—
279#13133210—21no—
280#13133208—21no—
281#13133208—21no—
282#13133207—21no—
283#13133206C2311yescharacteristic
284#13133205—21no—
285#13133205C2311yescharacteristic
286#13133204C2311yescharacteristic
287#13133203—21no—
288#13133203—21no—
289#13133203—21no—
290#13133203—21no—
291#13133203—21no—
292#13133203—21no—
293#13133202—21no—
294#13133202—21no—
295#13133202—21no—
296#13133202D411yescharacteristic
297#13133201—21no—
298#13133201—21no—
299#13133199—21no—
300#13133199—21no—
301#13133199—21no—
302#13133199D411yescharacteristic
303#13133198—21no—
304#13133197—21no—
305#13133197—21no—
306#13133197—21no—
307#13133197C2311yescharacteristic
308#13133197C2311yescharacteristic
309#13133197C2311yescharacteristic
310#13133197C2311yescharacteristic
311#13133197C2311yescharacteristic
312#13133196—21no—
313#13133196C2311yescharacteristic
314#13133196C2311yescharacteristic
315#13133196C2311yescharacteristic
316#13133195—21no—
317#13133195—21no—
318#13133195—21no—
319#13133195—21no—
320#13133195—21no—
321#13133195—21no—
322#13133195D411yescharacteristic
323#13133194—21no—
324#13133194—21no—
325#13133194—21no—
326#13133194D411yescharacteristic
327#13133193C2311yescharacteristic
328#13133192—21no—
329#13133192—21no—
330#13133192C2311yescharacteristic
331#13133192C2311yescharacteristic
332#13133192C2311yescharacteristic
333#13133192C2311yescharacteristic
334#13133191—21no—
335#13133191—21no—
336#13133191—21no—
337#13133191C2311yescharacteristic
338#13133190—21no—
339#13133190—21no—
340#13133190—21no—
341#13133190—21no—
342#13133190—21no—
343#13133190D411yescharacteristic
344#13133189—21no—
345#13133189—21no—
346#13133189—21no—
347#13133189—21no—
348#13133189—21no—
349#13133189—21no—
350#13133189—21no—
351#13133189—21no—
352#13133189—21no—
353#13133189—21no—
354#13133189—21no—
355#13133189D411yescharacteristic
356#13133188—21no—
357#13133188—21no—
358#13133188C2311yescharacteristic
359#13133188C2311yescharacteristic
360#13133187—21no—
361#13133187—21no—
362#13133187D411yescharacteristic
363#13133186—21no—
364#13133186—21no—
365#13133185—21no—
366#13133185—21no—
367#13133185—21no—
368#13133185D411yescharacteristic
369C4×Dic106—21no—
370C4×Dic106C2311yescharacteristic
371#13133182C2311yescharacteristic
372#13133182C2311yescharacteristic
373#13133182C2311yescharacteristic
374C4×D212—21no—
375C4×D212—21no—
376C4×D212—21no—
377C4×D212C2311yescharacteristic
378C4×D212C2311yescharacteristic
379D4×Dic53—21no—
380D4×Dic53—21no—
381D4×Dic53C2311yescharacteristic
382#13133179—21no—
383#13133179—21no—
384#13133179—21no—
385C4×C22⋊D53—21no—
386C4×C22⋊D53—21no—
387C4×C22⋊D53C2311yescharacteristic
388C4×C22⋊D53C2311yescharacteristic
389#13133177—21no—
390#13133177—21no—
391#13133177—21no—
392#13133175C2311yescharacteristic
393#13133174C2311yescharacteristic
394#13133173—21no—
395C2×#11719919—21no—
396C4⋊C4×D53—21no—
397C4⋊C4×D53—21no—
398C4⋊C4×D53C2311yescharacteristic
399C4⋊C4×D53C2311yescharacteristic
400C2×C22⋊Dic53—21no—
401C2×#11719921—21no—
402C22⋊C4×D53—21no—
403C22⋊C4×D53—21no—
404#13133151C2311yescharacteristic
405#13133150C2311yescharacteristic
406#13133150C2311yescharacteristic
407#13133150C2311yescharacteristic
408#13133148C2311yescharacteristic
409C4⋊#88322C2311yescharacteristic
410#13133146C2311yescharacteristic
411#13133146C2311yescharacteristic
412#13133142C2311yescharacteristic
413#13133142C2311yescharacteristic
414#13133142C2311yescharacteristic
415#13133142C2311yescharacteristic
416#13133141C2311yescharacteristic
417#13133140C2311yescharacteristic
418#13133140C2311yescharacteristic
419#13133140C2311yescharacteristic
420#13133140C2311yescharacteristic
421#13133140C2311yescharacteristic
422#13133140C2311yescharacteristic
423#13133140C2311yescharacteristic
424#13133140C2311yescharacteristic
425#13133139C2311yescharacteristic
426#13133139C2311yescharacteristic
427#13133138C2311yescharacteristic
428#13133138C2311yescharacteristic
429#13133138C2311yescharacteristic
430#13133137C2311yescharacteristic
431#13133137C2311yescharacteristic
432#13133137C2311yescharacteristic
433#13133137C2311yescharacteristic
434C22⋊#88322C2311yescharacteristic
435C22⋊#88322C2311yescharacteristic
436#13133129C2311yescharacteristic
437#13133129C2311yescharacteristic
438#13133129C2311yescharacteristic
439#13133129C2311yescharacteristic
440#13133129C2311yescharacteristic
441#13133129C2311yescharacteristic
442#13133129C2311yescharacteristic
443#13133129C2311yescharacteristic
444#13133127C2311yescharacteristic
445C4×#88322C2311yescharacteristic
446C8×Dic53C2311yescharacteristic
447C22×D4×C53—21no—
448C22×D4×C53C2311yescharacteristic
449C22×D4×C53C2311yescharacteristic
450C2×SD16×C53C2311yescharacteristic
451C2×SD16×C53C2311yescharacteristic
452C2×SD16×C53C2311yescharacteristic
453C2×M16×C53C2311yescharacteristic
454C22×C8×C53C2311yescharacteristic
455#127×C53C2311yescharacteristic
456#126×C53—21no—
457#125×C53—21no—
458#125×C53C2311yescharacteristic
459#123×C53—21no—
460C22⋊Q8×C53C2311yescharacteristic
461C22⋊Q8×C53C2311yescharacteristic
462#121×C53—21no—
463#121×C53C2311yescharacteristic
464#121×C53C2311yescharacteristic
465#120×C53—21no—
466#120×C53—21no—
467C4×Q8×C53C2311yescharacteristic
468C4×D4×C53C2311yescharacteristic
469C4×D4×C53C2311yescharacteristic
470#117×C53—21no—
471#117×C53C2311yescharacteristic
472C2×C4⋊C4×C53C2311yescharacteristic
473#107×C53C2311yescharacteristic
474#107×C53C2311yescharacteristic
475#106×C53C2311yescharacteristic
476C4⋊C8×C53C2311yescharacteristic
477#103×C53C2311yescharacteristic
478#102×C53C2311yescharacteristic
479#102×C53C2311yescharacteristic
480#102×C53C2311yescharacteristic
481#102×C53C2311yescharacteristic
482#102×C53C2311yescharacteristic
483#102×C53C2311yescharacteristic
484#102×C53C2311yescharacteristic
485#102×C53C2311yescharacteristic
486#102×C53C2311yescharacteristic
487C22⋊C8×C53C2311yescharacteristic
488C22⋊C8×C53C2311yescharacteristic
489#97×C53C2311yescharacteristic
490C24×C53—21no—
491C24×C53—21no—
492C23×D53—21no—
493C23×D53—21no—
494C23×D53C2×D411yescharacteristic
495C2×Q8×C53C2411yescharacteristic
496C2×D4×C53—22no—
497C2×D4×C53—22no—
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—82no—
507C2×D4×C53C2×D411yescharacteristic
508C2×D4×C53C2411yescharacteristic
509C2×D4×C53C2411yescharacteristic
510C2×D4×C53C2411yescharacteristic
511C22×C4×C53—21no—
512C22×C4×C53—21no—
513C22×C4×C53C2411yescharacteristic
514C22×C4×C53C2411yescharacteristic
515C2×C22⋊D53—21no—
516C2×C22⋊D53—21no—
517C2×C22⋊D53—21no—
518C2×C22⋊D53—21no—
519C2×C22⋊D53—21no—
520C2×C22⋊D53—21no—
521C2×C22⋊D53—21no—
522C2×C22⋊D53—21no—
523C2×C22⋊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—44no—
531C2×C22⋊D53—44no—
532C2×C22⋊D53—44no—
533C2×C22⋊D53—82no—
534C2×C22⋊D53C2×D411yescharacteristic
535C2×C22⋊D53C2×D411yescharacteristic
536C2×C22⋊D53C2×D411yescharacteristic
537C2×C22⋊D53C2×D411yescharacteristic
538C22×Dic53—21no—
539C22×Dic53—21no—
540C22×Dic53—21no—
541C22×Dic53—21no—
542C22×Dic53—21no—
543C22×Dic53—21no—
544C22×Dic53—21no—
545C22×Dic53—44no—
546C22×Dic53C2×D411yescharacteristic
547Q8×D53—41no—
548Q8×D53—41no—
549Q8×D53—41no—
550Q8×D53—41no—
551#11719947—22no—
552#11719947—22no—
553#11719947—22no—
554#11719947—22no—
555#11719947—22no—
556#11719947—41no—
557#11719947—41no—
558#11719947—41no—
559#11719947—41no—
560#11719947—41no—
561#11719947—44no—
562#11719947—44no—
563#11719947—44no—
564D4×D53—22no—
565D4×D53—41no—
566D4×D53—41no—
567D4×D53—41no—
568D4×D53—44no—
569D4×D53—82no—
570#11719945—22no—
571#11719945—41no—
572#11719945—41no—
573#11719945—41no—
574#11719945—41no—
575#11719945—41no—
576#11719945—41no—
577#11719945—41no—
578C2×D212—21no—
579C2×D212—21no—
580C2×D212—21no—
581C2×D212—21no—
582C2×D212C2×D411yescharacteristic
583C2×D212C2×D411yescharacteristic
584C2×D212C2411yescharacteristic
585C2×D212C2411yescharacteristic
586C2×C4×D53—21no—
587C2×C4×D53—21no—
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×D53—41no—
595C2×C4×D53—41no—
596C2×C4×D53C2×D411yescharacteristic
597C2×C4×D53C2×D411yescharacteristic
598C2×C4×D53C2411yescharacteristic
599C2×C4×D53C2411yescharacteristic
600C2×C4×D53C2411yescharacteristic
601C2×Dic106—22no—
602C2×Dic106—21no—
603C2×Dic106—21no—
604C2×Dic106—21no—
605C2×Dic106—21no—
606C2×Dic106—41no—
607C2×Dic106C2×D411yescharacteristic
608C2×Dic106C2411yescharacteristic
609C2×Dic106C2411yescharacteristic
610C2×Dic106C2411yescharacteristic
611C2×Dic106C2411yescharacteristic
612SD16×C53—22no—
613SD16×C53—41no—
614SD16×C53—41no—
615M16×C53—41no—
616C2×C8×C53—41no—
617C2×C8×C53C2411yescharacteristic
618C2×C8×C53C2411yescharacteristic
619C2×C8×C53C2411yescharacteristic
620C2×C8×C53C2411yescharacteristic
621C4⋊C4×C53—21no—
622C4⋊C4×C53—21no—
623C4⋊C4×C53—21no—
624C4⋊C4×C53—21no—
625C4⋊C4×C53—21no—
626C4⋊C4×C53—21no—
627C4⋊C4×C53C2×D411yescharacteristic
628C4⋊C4×C53C2411yescharacteristic
629C4⋊C4×C53C2411yescharacteristic
630C4⋊C4×C53C2411yescharacteristic
631C4⋊C4×C53C2411yescharacteristic
632C22⋊C4×C53—21no—
633C22⋊C4×C53—21no—
634C22⋊C4×C53—21no—
635C22⋊C4×C53—21no—
636C22⋊C4×C53—21no—
637C22⋊C4×C53—21no—
638C22⋊C4×C53C2×D411yescharacteristic
639C22⋊C4×C53C2×D411yescharacteristic
640C42×C53—21no—
641C42×C53—21no—
642C42×C53C2411yescharacteristic
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⋊Dic53C2×D411yescharacteristic
652C22⋊Dic53C2×D411yescharacteristic
653#11719925—22no—
654#11719925—41no—
655#11719924—41no—
656#11719923—22no—
657#11719923—22no—
658#11719923—41no—
659#11719923—41no—
660#11719923—41no—
661#11719923—41no—
662#11719922—22no—
663#11719922—41no—
664#11719922—41no—
665#11719921—21no—
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#11719921—21no—
679#11719921—21no—
680#11719921—21no—
681#11719921—21no—
682#11719921C2×D411yescharacteristic
683#11719921C2×D411yescharacteristic
684#11719921C2×D411yescharacteristic
685#11719921C2×D411yescharacteristic
686#11719921C2×D411yescharacteristic
687#11719921C2×D411yescharacteristic
688C4⋊Dic53—21no—
689C4⋊Dic53—21no—
690C4⋊Dic53—21no—
691C4⋊Dic53—21no—
692C4⋊Dic53—21no—
693C4⋊Dic53—21no—
694C4⋊Dic53—21no—
695C4⋊Dic53C2×D411yescharacteristic
696C4⋊Dic53C2411yescharacteristic
697C4⋊Dic53C2411yescharacteristic
698#11719919—21no—
699#11719919—21no—
700#11719919—21no—
701#11719919—21no—
702#11719919—21no—
703#11719919—21no—
704#11719919—21no—
705#11719919—21no—
706#11719919—21no—
707#11719919—21no—
708#11719919—21no—
709#11719919C2×D411yescharacteristic
710#11719919C2×D411yescharacteristic
711#11719919C2×D411yescharacteristic
712#11719919C2×D411yescharacteristic
713C4×Dic53—21no—
714C4×Dic53—21no—
715C4×Dic53—21no—
716C4×Dic53—21no—
717C4×Dic53—21no—
718C4×Dic53C2411yescharacteristic
719#11719917—41no—
720#11719917—41no—
721C2×#88322C2411yescharacteristic
722C2×#88322C2411yescharacteristic
723C2×#88322C2411yescharacteristic
724C2×#88322C2411yescharacteristic
725Dic212—22no—
726Dic212—22no—
727Dic212—41no—
728Dic212—41no—
729D424—41no—
730#11719913—22no—
731#11719913—41no—
732#11719913—41no—
733#11719913—41no—
734#11719912—41no—
735#11719912—41no—
736#11719912—41no—
737C8×D53—41no—
738C23×C53—21no—
739C23×C53—21no—
740C23×C53—21no—
741C23×C53—42no—
742C23×C53—42no—
743C23×C53—42no—
744C23×C53—81no—
745C23×C53—81no—
746C23×C53—81no—
747C23×C53C22×D411yescharacteristic
748C23×C53C22×D411yescharacteristic
749C22×D53—21no—
750C22×D53—21no—
751C22×D53—41no—
752C22×D53—41no—
753C22×D53—41no—
754C22×D53—42no—
755C22×D53—42no—
756C22×D53—81no—
757C22×D53—81no—
758C22×D53—81no—
759C22×D53—81no—
760C22×D53C22×D411yescharacteristic
761C22×D53C22×D411yescharacteristic
762C22×D53C22×D411yescharacteristic
763Q8×C53—21no—
764Q8×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×C53H(5,𝔽2)12yes—
778C2×C4×C53—21no—
779C2×C4×C53—21no—
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—81no—
788C2×C4×C53—81no—
789C2×C4×C53C22×D411yescharacteristic
790C2×C4×C53C22×D411yescharacteristic
791C2×C4×C53C22×D411yescharacteristic
792C2×C4×C53C22×D411yescharacteristic
793C2×C4×C53C2511yescharacteristic
794C22⋊D53—24no—
795C22⋊D53—41no—
796C22⋊D53—41no—
797C22⋊D53—41no—
798C22⋊D53—41no—
799C22⋊D53—42no—
800C22⋊D53—42no—
801C22⋊D53—42no—
802C22⋊D53—42no—
803C22⋊D53—42no—
804C22⋊D53—42no—
805C22⋊D53—42no—
806C22⋊D53—42no—
807C22⋊D53—81no—
808C22⋊D53—81no—
809C22⋊D53—81no—
810C22⋊D53—81no—
811C22⋊D53—81no—
812C22⋊D53—81no—
813C2×Dic53—24no—
814C2×Dic53—21no—
815C2×Dic53—21no—
816C2×Dic53—21no—
817C2×Dic53—21no—
818C2×Dic53—21no—
819C2×Dic53—21no—
820C2×Dic53—41no—
821C2×Dic53—42no—
822C2×Dic53—42no—
823C2×Dic53—42no—
824C2×Dic53—42no—
825C2×Dic53—42no—
826C2×Dic53—81no—
827C2×Dic53C22×D411yescharacteristic
828C2×Dic53C22×D411yescharacteristic
829C2×Dic53C22×D411yescharacteristic
830C2×Dic53C22×D411yescharacteristic
831C2×Dic53C22×D411yescharacteristic
832D212—21no—
833D212—21no—
834D212—21no—
835D212—21no—
836D212—41no—
837D212—41no—
838D212—42no—
839D212—81no—
840D212—81no—
841D212—81no—
842C4×D53—21no—
843C4×D53—21no—
844C4×D53—21no—
845C4×D53—21no—
846C4×D53—21no—
847C4×D53—21no—
848C4×D53—41no—
849C4×D53—41no—
850C4×D53—42no—
851C4×D53—81no—
852C4×D53—81no—
853C4×D53—81no—
854C4×D53—81no—
855C4×D53—81no—
856C4×D53—81no—
857C4×D53—81no—
858Dic106—21no—
859Dic106—21no—
860Dic106—21no—
861Dic106—21no—
862Dic106—21no—
863Dic106—21no—
864Dic106—21no—
865Dic106—41no—
866Dic106—42no—
867Dic106—81no—
868Dic106—81no—
869Dic106—81no—
870Dic106H(5,𝔽2)12yes—
871C8×C53—21no—
872C8×C53—21no—
873C8×C53—21no—
874C8×C53—21no—
875#88322—21no—
876#88322—21no—
877#88322—21no—
878#88322—21no—
879#61654—531nomaximal, Sylow
880C22×C53—21no—
881C22×C53—21no—
882C22×C53—21no—
883C22×C53—21no—
884C22×C53—22no—
885C22×C53—21no—
886C22×C53—21no—
887C22×C53—41no—
888C22×C53—41no—
889C22×C53—41no—
890C22×C53—41no—
891C22×C53—41no—
892C22×C53—41no—
893C22×C53—41no—
894C22×C53—41no—
895C22×C53—84no—
896C22×C53—162no—
897C22×C53C23×D411yescharacteristic
898C2×D53—21no—
899C2×D53—21no—
900C2×D53—21no—
901C2×D53—21no—
902C2×D53—21no—
903C2×D53—21no—
904C2×D53—21no—
905C2×D53—21no—
906C2×D53—21no—
907C2×D53—41no—
908C2×D53—41no—
909C2×D53—41no—
910C2×D53—41no—
911C2×D53—41no—
912C2×D53—41no—
913C2×D53—82no—
914C2×D53—162no—
915C2×D53—162no—
916C4×C53—21no—
917C4×C53—21no—
918C4×C53—21no—
919C4×C53—21no—
920C4×C53—41no—
921C4×C53—41no—
922C4×C53—41no—
923C4×C53—41no—
924C4×C53—41no—
925C4×C53C2×H(5,𝔽2)11yescharacteristic
926C4×C53C2×H(5,𝔽2)11yescharacteristic
927Dic53—21no—
928Dic53—21no—
929Dic53—22no—
930Dic53—21no—
931Dic53—21no—
932Dic53—21no—
933Dic53—41no—
934Dic53—41no—
935Dic53—41no—
936Dic53—41no—
937Dic53—41no—
938#3541—531no—
939#3488—531no—
940#3333—531no—
941#3327—531no—
942#3324—531no—
943#3322—531no—
944#3314—531no—
945#3313—531no—
946#3310D5311yescharacteristic, complemented
947#3309—531no—
948#3278—531no—
949#3277—531no—
950#3275—531no—
951#3272—531no—
952#3271—531no—
953#3269—531no—
954#3266—531no—
955#3265—531no—
956#3224—531no—
957#3222—531no—
958#3203—531no—
959#3201—531no—
960#3194—531no—
961#3193—531no—
962#3124—531no—
963#3120—531no—
964#3012—531no—
965#3009—531no—
966#3007—531no—
967#3005—531no—
968#2978—531no—
969C2×C53—41no—
970C2×C53—42no—
971C2×C53—41no—
972C2×C53—81no—
973C2×C53—81no—
974C2×C53#348411yescharacteristic
975C2×C53#358511yescharacteristic
976C2×C53#358611yescharacteristic
977D53—41no—
978D53—41no—
979D53—41no—
980D53—81no—
981D53—81no—
982C2×H(5,𝔽2)—531no—
983C22×#41—531no—
984C2×#137—531no—
985C2×#137—531no—
986C2×#137—531no—
987C2×#137—531no—
988C2×AGL(1,ℤ/8)—531no—
989C2×AGL(1,ℤ/8)—531no—
990C2×#135—531no—
991C22×SD16—531no—
992#563—1061no—
993#562—1061no—
994#556—531no—
995#554—531no—
996#554—1061no—
997#553—531no—
998#553—1061no—
999#552C2×D5311yescharacteristic, complemented
1000#550—531no—
1001#550—531no—
1002D4×Q8—531no—
1003#548—531no—
1004#548—531no—
1005#548—531no—
1006#548—531no—
1007#547—531no—
1008#546—531no—
1009#546—531no—
1010#546—1061no—
1011#546—1061no—
1012D42—531no—
1013D42—1061no—
1014D42—1061no—
1015D42C2×D5311yescharacteristic
1016#542—531no—
1017#542—1061no—
1018#541—531no—
1019#539—1061no—
1020#538—1061no—
1021#538—1061no—
1022#537—531no—
1023#537—531no—
1024#537—1061no—
1025#536—531no—
1026#535—531no—
1027#535—1061no—
1028#525—531no—
1029#525—531no—
1030#525—1061no—
1031C2×C22⋊Q8—531no—
1032C2×#121—531no—
1033C2×#121—1061no—
1034#520—531no—
1035#497—531no—
1036#496—531no—
1037#495—531no—
1038#492—531no—
1039#490C2×D5311yescharacteristic, complemented
1040#489—531no—
1041#488—531no—
1042#486—531no—
1043#485—531no—
1044#484—531no—
1045#484—531no—
1046#484—531no—
1047#483—531no—
1048#482—531no—
1049#482—531no—
1050#482C2×D5311yescharacteristic, complemented
1051#480—531no—
1052#480—531no—
1053#480—531no—
1054#480C2×D5311yescharacteristic, complemented
1055#479—531no—
1056#478C2×D5311yescharacteristic, complemented
1057#477—531no—
1058#474—531no—
1059#470—531no—
1060#469—531no—
1061#469—531no—
1062#468—531no—
1063#468—531no—
1064#468—531no—
1065#468—531no—
1066#468—531no—
1067#468—531no—
1068#468—531no—
1069#468—531no—
1070#468C2×D5311yescharacteristic, complemented
1071#467—531no—
1072#467—531no—
1073#466—531no—
1074#465C2×D5311yescharacteristic, complemented
1075#464—531no—
1076#464—531no—
1077#464—531no—
1078#464—531no—
1079#463—531no—
1080#463—531no—
1081#462—531no—
1082#461—531no—
1083#460—531no—
1084#460—531no—
1085#460C2×D5311yescharacteristic, complemented
1086#459—531no—
1087#452—531no—
1088#452—531no—
1089#452—531no—
1090#452—531no—
1091#452—531no—
1092#452—531no—
1093#452—531no—
1094#452—531no—
1095#452—531no—
1096#452—531no—
1097#452—531no—
1098#452—531no—
1099#451—531no—
1100#451—531no—
1101#451—531no—
1102#450—531no—
1103#450—531no—
1104#450—531no—
1105#450—531no—
1106#450—531no—
1107#450—531no—
1108#450C2×D5311yescharacteristic, complemented
1109#450C2×D5311yescharacteristic, complemented
1110#449—531no—
1111#449—531no—
1112#449—531no—
1113#449—531no—
1114#449—531no—
1115#449—531no—
1116#449—531no—
1117#449—531no—
1118#448—531no—
1119#448—531no—
1120#448—531no—
1121#447—531no—
1122#447—531no—
1123#441—531no—
1124#440—531no—
1125#440—531no—
1126#440C2×D5311yescharacteristic, complemented
1127C4×Q16—531no—
1128C4×Q16—531no—
1129C4×SD16—531no—
1130C4×D8—531no—
1131#436—531no—
1132#436—531no—
1133#436—531no—
1134#436—531no—
1135#435—531no—
1136#435—531no—
1137#435—531no—
1138#435C2×D5311yescharacteristic, complemented
1139#433—531no—
1140#433—531no—
1141#419—531no—
1142#418—531no—
1143#418C2×D5311yescharacteristic, complemented
1144#417—531no—
1145#417—531no—
1146#417—531no—
1147#416—531no—
1148C2×#102C2×D5311yescharacteristic, complemented
1149#408—531no—
1150#408—531no—
1151#407—531no—
1152#407—531no—
1153C53#6165411yescharacteristic, complemented, Sylow
1154H(5,𝔽2)—2122no—
1155H(5,𝔽2)—2122no—
1156C2×#41—531no—
1157C2×#41—531no—
1158C2×#41—531no—
1159C2×#41—531no—
1160C2×#41—531no—
1161C2×#41—531no—
1162C2×#41—531no—
1163C2×#41—531no—
1164C2×#41—531no—
1165C2×#41—1061no—
1166C2×#41—1061no—
1167C2×#41—1061no—
1168C2×#41—2122no—
1169C2×#41—2122no—
1170C22×Q8—531no—
1171C22×Q8—531no—
1172C22×Q8—531no—
1173C22×D4—21no—
1174C22×D4—531no—
1175C22×D4—531no—
1176C22×D4—1061no—
1177C22×D4—1061no—
1178C22×D4—1061no—
1179C22×D4—1061no—
1180C22×D4—1061no—
1181C22×D4—1061no—
1182C22×D4C22×D5311yescharacteristic
1183C22×D4C22×D5311yescharacteristic
1184C23×C4—531no—
1185C23×C4—1061no—
1186#137—2122no—
1187#137—2122no—
1188#137—2122no—
1189#137—2122no—
1190AGL(1,ℤ/8)—2122no—
1191AGL(1,ℤ/8)—2122no—
1192#135—2122no—
1193C2×Q16—531no—
1194C2×Q16—531no—
1195C2×Q16—531no—
1196C2×Q16—531no—
1197C2×Q16—531no—
1198C2×Q16—531no—
1199C2×SD16—531no—
1200C2×SD16—531no—
1201C2×SD16—531no—
1202C2×SD16—531no—
1203C2×SD16—531no—
1204C2×SD16—531no—
1205C2×SD16—531no—
1206C2×SD16—531no—
1207C2×SD16—531no—
1208C2×SD16—531no—
1209C2×SD16—531no—
1210C2×SD16—2122no—
1211C2×SD16C22×D5311yescharacteristic
1212C2×SD16C22×D5311yescharacteristic
1213C2×SD16C22×D5311yescharacteristic
1214C2×D8—531no—
1215C2×D8—531no—
1216C2×D8—531no—
1217C2×D8—531no—
1218C2×M16—531no—
1219C2×M16—531no—
1220C2×M16—531no—
1221C2×M16—531no—
1222C2×M16—531no—
1223C2×M16C22×D5311yescharacteristic
1224C22×C8—531no—
1225C22×C8C22×D5311yescharacteristic
1226C4⋊Q8—531no—
1227C4⋊Q8—531no—
1228C4⋊Q8—1061no—
1229C4⋊Q8—1061no—
1230#127—531no—
1231#127—1061no—
1232#127—1061no—
1233#127C22×D5311yescharacteristic
1234#126—21no—
1235#126—1061no—
1236#126—1061no—
1237#126—1061no—
1238#126—1061no—
1239#126—1061no—
1240#126—1061no—
1241#125—21no—
1242#125—1061no—
1243#125—1061no—
1244#125—1061no—
1245#125C22×D5311yescharacteristic
1246#124—531no—
1247#124—531no—
1248#124—531no—
1249#124—1061no—
1250#124—1061no—
1251#124—1061no—
1252#124—1061no—
1253#124—1061no—
1254#124—1061no—
1255#124—1061no—
1256#123—21no—
1257#123—531no—
1258#123—531no—
1259#123—1061no—
1260#123—1061no—
1261#123—1061no—
1262#123—1061no—
1263#123—1061no—
1264#123—1061no—
1265#123—1061no—
1266#123—1061no—
1267#123—1061no—
1268C22⋊Q8—531no—
1269C22⋊Q8—531no—
1270C22⋊Q8—531no—
1271C22⋊Q8—531no—
1272C22⋊Q8—531no—
1273C22⋊Q8—531no—
1274C22⋊Q8—531no—
1275C22⋊Q8—531no—
1276C22⋊Q8—531no—
1277C22⋊Q8—531no—
1278C22⋊Q8—531no—
1279C22⋊Q8—1061no—
1280C22⋊Q8—1061no—
1281C22⋊Q8—1061no—
1282C22⋊Q8—1061no—
1283C22⋊Q8—1061no—
1284C22⋊Q8—1061no—
1285C22⋊Q8—1061no—
1286C22⋊Q8—1061no—
1287C22⋊Q8—1061no—
1288C22⋊Q8—1061no—
1289C22⋊Q8—1061no—
1290C22⋊Q8—1061no—
1291C22⋊Q8—1061no—
1292C22⋊Q8C22×D5311yescharacteristic
1293C22⋊Q8C22×D5311yescharacteristic
1294#121—21no—
1295#121—531no—
1296#121—531no—
1297#121—531no—
1298#121—531no—
1299#121—531no—
1300#121—531no—
1301#121—531no—
1302#121—531no—
1303#121—531no—
1304#121—1061no—
1305#121—1061no—
1306#121—1061no—
1307#121—1061no—
1308#121—1061no—
1309#121—1061no—
1310#121—1061no—
1311#121—1061no—
1312#121—1061no—
1313#121—1061no—
1314#121—1061no—
1315#121—1061no—
1316#121—1061no—
1317#121—1061no—
1318#121—1061no—
1319#121—1061no—
1320#121—1061no—
1321#121—1061no—
1322#121—1061no—
1323#121—1061no—
1324#121—1061no—
1325#121—1061no—
1326#121—1061no—
1327#121C22×D5311yescharacteristic
1328#121C22×D5311yescharacteristic
1329#120—21no—
1330#120—21no—
1331#120—531no—
1332#120—531no—
1333#120—1061no—
1334#120—1061no—
1335#120—1061no—
1336#120—1061no—
1337#120—1061no—
1338#120—1061no—
1339#120—1061no—
1340C4×Q8—531no—
1341C4×Q8—531no—
1342C4×Q8—531no—
1343C4×Q8—531no—
1344C4×Q8—1061no—
1345C4×Q8C22×D5311yescharacteristic
1346C4×D4—531no—
1347C4×D4—531no—
1348C4×D4—531no—
1349C4×D4—531no—
1350C4×D4—531no—
1351C4×D4—1061no—
1352C4×D4—1061no—
1353C4×D4—1061no—
1354C4×D4—1061no—
1355C4×D4—1061no—
1356C4×D4—1061no—
1357C4×D4—1061no—
1358C4×D4—1061no—
1359C4×D4—1061no—
1360C4×D4—1061no—
1361C4×D4—1061no—
1362C4×D4—1061no—
1363C4×D4—1061no—
1364C4×D4C22×D5311yescharacteristic
1365C4×D4C22×D5311yescharacteristic
1366#117—21no—
1367#117—531no—
1368#117—531no—
1369#117—1061no—
1370#117C22×D5311yescharacteristic
1371C2×C4⋊C4—531no—
1372C2×C4⋊C4—531no—
1373C2×C4⋊C4—1061no—
1374C2×C4⋊C4—1061no—
1375C2×C4⋊C4—1061no—
1376C2×C4⋊C4C22×D5311yescharacteristic
1377C2×C22⋊C4—1061no—
1378C2×C22⋊C4—1061no—
1379C2×C22⋊C4—1061no—
1380C2×C22⋊C4—1061no—
1381#107—531no—
1382#107—531no—
1383#107—531no—
1384#107—531no—
1385#107C22×D5311yescharacteristic
1386#107C22×D5311yescharacteristic
1387#106—531no—
1388#106C22×D5311yescharacteristic
1389C4⋊C8—531no—
1390C4⋊C8—531no—
1391C4⋊C8—531no—
1392C4⋊C8C22×D5311yescharacteristic
1393#103—531no—
1394#103—531no—
1395#103—531no—
1396#103—531no—
1397#103—531no—
1398#103—531no—
1399#103—531no—
1400#103—531no—
1401#103—531no—
1402#103—531no—
1403#103—531no—
1404#103—531no—
1405#103—531no—
1406#103C22×D5311yescharacteristic
1407#102—531no—
1408#102—531no—
1409#102—531no—
1410#102—531no—
1411#102—531no—
1412#102—531no—
1413#102—531no—
1414#102—531no—
1415#102—531no—
1416#102C22×D5311yescharacteristic
1417#102C22×D5311yescharacteristic
1418#102C22×D5311yescharacteristic
1419#102C22×D5311yescharacteristic
1420#102C22×D5311yescharacteristic
1421#102C22×D5311yescharacteristic
1422#102C22×D5311yescharacteristic
1423#102C22×D5311yescharacteristic
1424#102C22×D5311yescharacteristic
1425C22⋊C8—531no—
1426C22⋊C8—531no—
1427C22⋊C8—531no—
1428C22⋊C8—531no—
1429C22⋊C8—531no—
1430C22⋊C8—531no—
1431C22⋊C8—531no—
1432C22⋊C8—531no—
1433C22⋊C8—531no—
1434C22⋊C8—531no—
1435C22⋊C8C22×D5311yescharacteristic
1436C22⋊C8C22×D5311yescharacteristic
1437#97—531no—
1438#97C22×D5311yescharacteristic
1439C4×C8—531no—
1440C4×C8—531no—
1441C24—21no—
1442C24—21no—
1443C24—531no—
1444C24—1061no—
1445C24—1061no—
1446#41—1062no—
1447#41—1062no—
1448#41—1062no—
1449#41—1062no—
1450#41—1062no—
1451#41—1062no—
1452#41—2121no—
1453#41—2121no—
1454#41—2121no—
1455#41—2121no—
1456#41—2121no—
1457#41—2121no—
1458#41—2121no—
1459#41—2121no—
1460#41—2121no—
1461#41—2121no—
1462#41—2121no—
1463#41—2121no—
1464#41—2124no—
1465#41—2124no—
1466#41—2124no—
1467C2×Q8—531no—
1468C2×Q8—531no—
1469C2×Q8—531no—
1470C2×Q8—531no—
1471C2×Q8—531no—
1472C2×Q8—1061no—
1473C2×Q8—1061no—
1474C2×Q8—1061no—
1475C2×Q8—1062no—
1476C2×Q8—1061no—
1477C2×Q8—2121no—
1478C2×Q8—2121no—
1479C2×Q8—2121no—
1480C2×Q8—2121no—
1481C2×Q8—2121no—
1482C2×Q8C23×D5311yescharacteristic
1483C2×D4—22no—
1484C2×D4—22no—
1485C2×D4—21no—
1486C2×D4—21no—
1487C2×D4—21no—
1488C2×D4—21no—
1489C2×D4—21no—
1490C2×D4—21no—
1491C2×D4—41no—
1492C2×D4—41no—
1493C2×D4—82no—
1494C2×D4—531no—
1495C2×D4—531no—
1496C2×D4—531no—
1497C2×D4—531no—
1498C2×D4—531no—
1499C2×D4—531no—
1500C2×D4—531no—
1501C2×D4—531no—
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—1062no—
1512C2×D4—1061no—
1513C2×D4—1061no—
1514C2×D4—1061no—
1515C2×D4—1061no—
1516C2×D4—1061no—
1517C2×D4—1061no—
1518C2×D4—1061no—
1519C2×D4—1061no—
1520C2×D4—1061no—
1521C2×D4—1061no—
1522C2×D4—4242no—
1523C2×D4—4242no—
1524C2×D4—2121no—
1525C2×D4—2121no—
1526C2×D4—2121no—
1527C2×D4—2124no—
1528C2×D4—2124no—
1529C2×D4—2124no—
1530C2×D4—2124no—
1531C2×D4D4×D5311yescharacteristic
1532C2×D4C23×D5311yescharacteristic
1533C2×D4C23×D5311yescharacteristic
1534C2×D4C23×D5311yescharacteristic
1535C22×C4—21no—
1536C22×C4—21no—
1537C22×C4—531no—
1538C22×C4—531no—
1539C22×C4—531no—
1540C22×C4—531no—
1541C22×C4—531no—
1542C22×C4—531no—
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×C4—1061no—
1552C22×C4—1061no—
1553C22×C4—1061no—
1554C22×C4—1061no—
1555C22×C4—1061no—
1556C22×C4—1061no—
1557C22×C4—1061no—
1558C22×C4—2121no—
1559C22×C4—2121no—
1560C22×C4—2124no—
1561C22×C4C23×D5311yescharacteristic
1562C22×C4C23×D5311yescharacteristic
1563Q16—1062no—
1564Q16—1062no—
1565Q16—1062no—
1566Q16—2121no—
1567Q16—2121no—
1568Q16—2121no—
1569SD16—22no—
1570SD16—41no—
1571SD16—41no—
1572SD16—1062no—
1573SD16—1062no—
1574SD16—1062no—
1575SD16—2121no—
1576SD16—2121no—
1577SD16—2121no—
1578SD16—2121no—
1579SD16—2121no—
1580SD16—2121no—
1581SD16—2121no—
1582SD16—2121no—
1583D8—1062no—
1584D8—2121no—
1585D8—2121no—
1586D8—2121no—
1587M16—41no—
1588M16—2121no—
1589M16—2121no—
1590M16—2121no—
1591M16—2121no—
1592M16—2121no—
1593C2×C8—41no—
1594C2×C8—531no—
1595C2×C8—531no—
1596C2×C8—531no—
1597C2×C8—531no—
1598C2×C8—2121no—
1599C2×C8C23×D5311yescharacteristic
1600C2×C8C23×D5311yescharacteristic
1601C2×C8C23×D5311yescharacteristic
1602C2×C8C23×D5311yescharacteristic
1603C4⋊C4—21no—
1604C4⋊C4—21no—
1605C4⋊C4—21no—
1606C4⋊C4—21no—
1607C4⋊C4—21no—
1608C4⋊C4—21no—
1609C4⋊C4—531no—
1610C4⋊C4—531no—
1611C4⋊C4—531no—
1612C4⋊C4—531no—
1613C4⋊C4—531no—
1614C4⋊C4—531no—
1615C4⋊C4—531no—
1616C4⋊C4—1061no—
1617C4⋊C4—1061no—
1618C4⋊C4—1061no—
1619C4⋊C4—1061no—
1620C4⋊C4—1061no—
1621C4⋊C4—1061no—
1622C4⋊C4—1061no—
1623C4⋊C4—1061no—
1624C4⋊C4—1061no—
1625C4⋊C4—1061no—
1626C4⋊C4—1061no—
1627C4⋊C4—1061no—
1628C4⋊C4—1061no—
1629C4⋊C4—1061no—
1630C4⋊C4—1061no—
1631C4⋊C4—1061no—
1632C4⋊C4—1061no—
1633C4⋊C4—1061no—
1634C4⋊C4D4×D5311yescharacteristic
1635C4⋊C4C23×D5311yescharacteristic
1636C4⋊C4C23×D5311yescharacteristic
1637C4⋊C4C23×D5311yescharacteristic
1638C4⋊C4C23×D5311yescharacteristic
1639C22⋊C4—21no—
1640C22⋊C4—21no—
1641C22⋊C4—21no—
1642C22⋊C4—21no—
1643C22⋊C4—21no—
1644C22⋊C4—21no—
1645C22⋊C4—531no—
1646C22⋊C4—531no—
1647C22⋊C4—531no—
1648C22⋊C4—531no—
1649C22⋊C4—531no—
1650C22⋊C4—531no—
1651C22⋊C4—531no—
1652C22⋊C4—531no—
1653C22⋊C4—1061no—
1654C22⋊C4—1061no—
1655C22⋊C4—1061no—
1656C22⋊C4—1061no—
1657C22⋊C4—1061no—
1658C22⋊C4—1061no—
1659C22⋊C4—1061no—
1660C22⋊C4—1061no—
1661C22⋊C4—1061no—
1662C22⋊C4—1061no—
1663C22⋊C4—1061no—
1664C22⋊C4—1061no—
1665C22⋊C4—1061no—
1666C22⋊C4—1061no—
1667C22⋊C4—1061no—
1668C22⋊C4—1061no—
1669C22⋊C4—1061no—
1670C22⋊C4—1061no—
1671C22⋊C4—1061no—
1672C22⋊C4—1061no—
1673C22⋊C4—1061no—
1674C22⋊C4—1061no—
1675C22⋊C4—1061no—
1676C22⋊C4—1061no—
1677C22⋊C4—1061no—
1678C22⋊C4D4×D5311yescharacteristic
1679C22⋊C4D4×D5311yescharacteristic
1680C42—21no—
1681C42—21no—
1682C42—531no—
1683C42—1061no—
1684C42—1061no—
1685C42—1061no—
1686C42—1061no—
1687C42—1061no—
1688C42C23×D5311yescharacteristic
1689C23—21no—
1690C23—21no—
1691C23—21no—
1692C23—42no—
1693C23—42no—
1694C23—42no—
1695C23—81no—
1696C23—81no—
1697C23—81no—
1698C23—531no—
1699C23—531no—
1700C23—531no—
1701C23—1061no—
1702C23—1061no—
1703C23—4241no—
1704C23—4241no—
1705C23—4241no—
1706C23—4241no—
1707C23—2122no—
1708C23—2121no—
1709C23—2121no—
1710C23—2121no—
1711C23—2122no—
1712C23C2×D4×D5311yescharacteristic
1713C23C2×D4×D5311yescharacteristic
1714Q8—21no—
1715Q8—21no—
1716Q8—532no—
1717Q8—1061no—
1718Q8—1061no—
1719Q8—1061no—
1720Q8—1061no—
1721Q8—1061no—
1722Q8—1061no—
1723Q8—1061no—
1724Q8—4241no—
1725Q8—4241no—
1726Q8—4241no—
1727Q8—2121no—
1728Q8—2122no—
1729D4—21no—
1730D4—21no—
1731D4—21no—
1732D4—21no—
1733D4—21no—
1734D4—41no—
1735D4—42no—
1736D4—42no—
1737D4—42no—
1738D4—81no—
1739D4—81no—
1740D4—81no—
1741D4—1064no—
1742D4—1061no—
1743D4—1061no—
1744D4—1061no—
1745D4—1061no—
1746D4—4241no—
1747D4—4241no—
1748D4—4241no—
1749D4—4241no—
1750D4—4241no—
1751D4—4241no—
1752D4—4241no—
1753D4—4241no—
1754D4—4241no—
1755D4—2121no—
1756D4—2121no—
1757D4—2122no—
1758D4—2121no—
1759D4—2121no—
1760D4—2121no—
1761D4—2121no—
1762D4—2122no—
1763D4—2122no—
1764D4—2122no—
1765D4—2122no—
1766D4—2122no—
1767D4—2122no—
1768D4—2122no—
1769D4—2122no—
1770D4#1313326312yes—
1771C2×C4—21no—
1772C2×C4—21no—
1773C2×C4—21no—
1774C2×C4—21no—
1775C2×C4—21no—
1776C2×C4—21no—
1777C2×C4—21no—
1778C2×C4—21no—
1779C2×C4—21no—
1780C2×C4—81no—
1781C2×C4—81no—
1782C2×C4—531no—
1783C2×C4—531no—
1784C2×C4—531no—
1785C2×C4—531no—
1786C2×C4—531no—
1787C2×C4—1064no—
1788C2×C4—1061no—
1789C2×C4—1061no—
1790C2×C4—1061no—
1791C2×C4—1061no—
1792C2×C4—1061no—
1793C2×C4—1061no—
1794C2×C4—1061no—
1795C2×C4—1061no—
1796C2×C4—1061no—
1797C2×C4—1061no—
1798C2×C4—1061no—
1799C2×C4—1061no—
1800C2×C4—4241no—
1801C2×C4—4241no—
1802C2×C4—4241no—
1803C2×C4—4241no—
1804C2×C4—4241no—
1805C2×C4—4241no—
1806C2×C4—4241no—
1807C2×C4—4241no—
1808C2×C4—2121no—
1809C2×C4—2121no—
1810C2×C4—2122no—
1811C2×C4—2121no—
1812C2×C4—2122no—
1813C2×C4—2122no—
1814C2×C4—2122no—
1815C2×C4—2122no—
1816C2×C4—2122no—
1817C2×C4C2×D4×D5311yescharacteristic
1818C2×C4C2×D4×D5311yescharacteristic
1819C2×C4C2×D4×D5311yescharacteristic
1820C2×C4C2×D4×D5311yescharacteristic
1821C2×C4C24×D5311yescharacteristic
1822C8—21no—
1823C8—21no—
1824C8—21no—
1825C8—21no—
1826C8—1061no—
1827C8—1061no—
1828C8—1061no—
1829C8—1061no—
1830C22—21no—
1831C22—21no—
1832C22—22no—
1833C22—21no—
1834C22—21no—
1835C22—21no—
1836C22—21no—
1837C22—41no—
1838C22—41no—
1839C22—41no—
1840C22—41no—
1841C22—41no—
1842C22—41no—
1843C22—41no—
1844C22—41no—
1845C22—84no—
1846C22—162no—
1847C22—8482no—
1848C22—8482no—
1849C22—1061no—
1850C22—1061no—
1851C22—1061no—
1852C22—1061no—
1853C22—1061no—
1854C22—1061no—
1855C22—1061no—
1856C22—1061no—
1857C22—1061no—
1858C22—4242no—
1859C22—2121no—
1860C22—2121no—
1861C22—2121no—
1862C22—2121no—
1863C22—2121no—
1864C22—2121no—
1865C22C22×D4×D5311yescharacteristic
1866C4—21no—
1867C4—21no—
1868C4—21no—
1869C4—21no—
1870C4—41no—
1871C4—41no—
1872C4—41no—
1873C4—41no—
1874C4—41no—
1875C4—1061no—
1876C4—1061no—
1877C4—1061no—
1878C4—1062no—
1879C4—1061no—
1880C4—1061no—
1881C4—2121no—
1882C4—2121no—
1883C4—2121no—
1884C4—2121no—
1885C4—2121no—
1886C4H(5,𝔽2)×D5311yescharacteristic
1887C4C2×#1313326311yescharacteristic
1888C2—41no—
1889C2—41no—
1890C2—42no—
1891C2—81no—
1892C2—81no—
1893C2—4241no—
1894C2—4241no—
1895C2—2121no—
1896C2—2121no—
1897C2—2121no—
1898C2#2028834511yescharacteristic
1899C2#2028949111yescharacteristic
1900C2#2028949711yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3310C2
socleC22×C53C23×D4
hypercenter#3310D53
hypocenterC53#61654
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3310

Complements

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

NH ≅ G/Ntype
1. #20289011C2semidirect
2. #20288375C2semidirect
3. #20287051C2semidirect
4. #20286977C2semidirect
5. #20286942C2semidirect
6. #20286913C2semidirect
7. #20286792C2semidirect
8. #20286784C2semidirect
9. #20286720C2semidirect
10. #20286384C2semidirect
11. #20286369C2semidirect
12. #20286350C2semidirect
13. #20286311C2semidirect
14. #20286297C2semidirect
15. #20286275C2semidirect
16. #20286227C2semidirect
17. #20286208C2semidirect
18. #20285814C2semidirect
19. #20285788C2semidirect
20. #20285615C2semidirect
21. #20285590C2semidirect
22. #20285533C2semidirect
23. #20285516C2semidirect
24. #20284981C2semidirect
25. #20284934C2semidirect
26. #20284024C2semidirect
27. #20283987C2semidirect
28. #20283970C2semidirect
29. #20283959C2semidirect
30. #20283774C2semidirect
31. C53×#3310C2semidirect
34. C2×#13133250C22semidirect
35. C2×#13133246C22semidirect
36. C2×#13133246C22semidirect
37. C2×#13133246C22semidirect
38. C2×#13133243C22semidirect
39. C2×#13133243C22semidirect
40. C2×#13133239C22semidirect
41. C2×SD16×D53C22semidirect
44. #16811341C22semidirect
46. #16811328C22semidirect
47. #16811326C22semidirect
51. Q8×D212C22semidirect
52. #16811283C22semidirect
53. #16811283C22semidirect
56. #16811278C22semidirect
64. #16811245C22semidirect
66. #16811236C22semidirect
70. #16811204C22semidirect
73. #16811196C22semidirect
76. #16811135C22semidirect
79. C22⋊Q8×D53C22semidirect
83. #16811017C22semidirect
84. #16811009C22semidirect
85. #16811004C22semidirect
86. #16810995C22semidirect
87. #16810981C22semidirect
88. #16810980C22semidirect
89. #16810968C22semidirect
90. #16810967C22semidirect
91. #16810960C22semidirect
92. #16810958C22semidirect
93. #16810957C22semidirect
94. #16810955C22semidirect
95. #16810947C22semidirect
96. #16810945C22semidirect
97. #16810938C22semidirect
98. #16810938C22semidirect
99. #16810935C22semidirect
100. #16810927C22semidirect
101. #16810917C22semidirect
102. #16810901C22semidirect
103. #16810879C22semidirect
104. #16810877C22semidirect
105. #16810875C22semidirect
106. #16810871C22semidirect
107. #16810870C22semidirect
108. #16810870C22semidirect
109. #16810869C22semidirect
110. #16810868C22semidirect
111. #16810868C22semidirect
112. #16810867C22semidirect
113. #16810867C22semidirect
114. #16810865C22semidirect
115. #16810864C22semidirect
116. #16810858C22semidirect
117. #16810848C22semidirect
118. #16810845C22semidirect
119. #16810844C22semidirect
120. #16810844C22semidirect
121. #16810840C22semidirect
122. #16810839C22semidirect
123. #16810834C22semidirect
124. #16810828C22semidirect
125. #16810822C22semidirect
126. #16810822C22semidirect
127. #16810815C22semidirect
128. #16810787C22semidirect
129. #16810787C22semidirect
132. #16810786C22semidirect
133. #16810786C22semidirect
134. #16810786C22semidirect
135. #16810786C22semidirect
136. #16810786C22semidirect
137. #16810783C22semidirect
139. #16810782C22semidirect
140. #16810781C22semidirect
141. #16810780C22semidirect
142. #16810778C22semidirect
143. #16810775C22semidirect
144. #16810775C22semidirect
145. #16810775C22semidirect
146. #16810774C22semidirect
147. #16810774C22semidirect
148. #16810772C22semidirect
149. #16810770C22semidirect
151. #16810769C22semidirect
152. #16810769C22semidirect
153. #16810769C22semidirect
154. #16810769C22semidirect
155. #16810766C22semidirect
156. #16810766C22semidirect
157. #16810763C22semidirect
158. #16810760C22semidirect
159. #16810760C22semidirect
160. #16810758C22semidirect
161. #16810758C22semidirect
162. #16810729C22semidirect
163. #16810725C22semidirect
164. #16810720C22semidirect
165. #16810717C22semidirect
166. C4×#11719925C22semidirect
167. #16810714C22semidirect
168. C4×#11719922C22semidirect
169. #16810701C22semidirect
170. #16810700C22semidirect
171. #16810699C22semidirect
172. #16810698C22semidirect
173. #16810697C22semidirect
174. #16810696C22semidirect
175. #16810694C22semidirect
176. #16810685C22semidirect
177. #16810683C22semidirect
178. #16810631C22semidirect
179. #16810626C22semidirect
180. #16810622C22semidirect
181. #16810621C22semidirect
182. #16810621C22semidirect
183. #16810616C22semidirect
184. #16810589C22semidirect
185. #16810588C22semidirect
186. #16810586C22semidirect
187. #16810585C22semidirect
188. C53×#552C22semidirect
190. C53×#490C22semidirect
191. C53×#482C22semidirect
192. C53×#480C22semidirect
193. C53×#478C22semidirect
194. C53×#468C22semidirect
195. C53×#465C22semidirect
196. C53×#460C22semidirect
197. C53×#450C22semidirect
198. C53×#450C22semidirect
199. C53×#440C22semidirect
200. C53×#435C22semidirect
201. C53×#418C22semidirect
202. C2×#102×C53C22semidirect
946. #3310D53semidirect
999. #552C2×D53semidirect
1039. #490C2×D53semidirect
1050. #482C2×D53semidirect
1054. #480C2×D53semidirect
1056. #478C2×D53semidirect
1070. #468C2×D53semidirect
1074. #465C2×D53semidirect
1085. #460C2×D53semidirect
1108. #450C2×D53semidirect
1109. #450C2×D53semidirect
1126. #440C2×D53semidirect
1138. #435C2×D53semidirect
1143. #418C2×D53semidirect
1148. C2×#102C2×D53semidirect
1153. C53#61654semidirect

Maximal subgroups

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

subgroupindex
#202890112
#202883752
#202870512
#202869772
#202869422
#202869132
#202867922
#202867842
#202867202
#202863842
#202863692
#202863502
#202863112
#202862972
#202862752
#202862272
#202862082
#202858142
#202857882
#202856152
#202855902
#202855332
#202855162
#202849812
#202849342
#202840242
#202839872
#202839702
#202839592
#202837742
C53×#33102
#6165453