Finite Group Databasebeta

← #28270349

Subgroups — #28270349

Order 13568.

2110 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#20288378C211yesmaximal, characteristic, complemented
3#20286853C211yesmaximal, characteristic, complemented
4#20286835C211yesmaximal, characteristic, complemented
5#20286829C211yesmaximal, characteristic, complemented
6#20286747C211yesmaximal, characteristic, complemented
7#20286652C211yesmaximal, characteristic, complemented
8#20286616C211yesmaximal, characteristic, complemented
9#20286535C211yesmaximal, characteristic, complemented
10#20286459C211yesmaximal, characteristic, complemented
11#20286447C211yesmaximal, characteristic, complemented
12#20286420C211yesmaximal, characteristic, complemented
13SD16×D212C211yesmaximal, characteristic, complemented
14#20286297C211yesmaximal, characteristic, complemented
15#20286280C211yesmaximal, characteristic, complemented
16#20286236C211yesmaximal, characteristic, complemented
17#20286208C211yesmaximal, characteristic, complemented
18#20285816C211yesmaximal, characteristic, complemented
19#20285790C211yesmaximal, characteristic, complemented
20#20285625C211yesmaximal, characteristic, complemented
21#20285600C211yesmaximal, characteristic, complemented
22#20285484C211yesmaximal, characteristic, complemented
23#20285467C211yesmaximal, characteristic, complemented
24#20284988C211yesmaximal, characteristic, complemented
25#20284934C211yesmaximal, characteristic, complemented
26#20284024C211yesmaximal, characteristic, complemented
27#20283987C211yesmaximal, characteristic, complemented
28#20283935C211yesmaximal, characteristic, complemented
29#452×D53C211yesmaximal, characteristic, complemented
30#20283768C211yesmaximal, characteristic, complemented
31C53×#3296C211yesmaximal, characteristic, complemented
32C2×#13133262C2211yescharacteristic
33C2×#41×D53C2211yescharacteristic
34C2×#13133246C2211yescharacteristic, complemented
35C2×#13133243C2211yescharacteristic, complemented
36C2×#13133239C2211yescharacteristic, complemented
37C2×#13133239C2211yescharacteristic, complemented
38C2×#13133237C2211yescharacteristic, complemented
39C2×Q16×D53C2211yescharacteristic, complemented
40C2×SD16×D53C2211yescharacteristic, 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#16811294C2211yescharacteristic
50#16811291C2211yescharacteristic
51Q8×D212C2211yescharacteristic, complemented
52#16811283C2211yescharacteristic
53#16811283C2211yescharacteristic, complemented
54#16811283C2211yescharacteristic, complemented
55#16811281C2211yescharacteristic
56#16811278C2211yescharacteristic, complemented
57#16811265—21no—
58#16811263—21no—
59#16811261C2211yescharacteristic
60D4×D212C2211yescharacteristic
61#16811257—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#16811203C2211yescharacteristic
72#16811200—21no—
73#16811196C2211yescharacteristic, complemented
74#16811191C2211yescharacteristic
75#16811188—21no—
76#16811135C2211yescharacteristic, complemented
77#16811132C2211yescharacteristic
78#16811131—21no—
79C22⋊Q8×D53C2211yescharacteristic, complemented
80C2×#13133190—21no—
81#121×D53C2211yescharacteristic
82#16811102C2211yescharacteristic
83#16811018C2211yescharacteristic, complemented
84#16811009C2211yescharacteristic, complemented
85#16811008C2211yescharacteristic, complemented
86#16810996C2211yescharacteristic, complemented
87#16810989C2211yescharacteristic, complemented
88#16810984C2211yescharacteristic, complemented
89#16810968C2211yescharacteristic, complemented
90#16810962C2211yescharacteristic, complemented
91#16810960C2211yescharacteristic, complemented
92#16810955C2211yescharacteristic, complemented
93#16810952C2211yescharacteristic, complemented
94#16810950C2211yescharacteristic, complemented
95#16810947C2211yescharacteristic, complemented
96#16810943C2211yescharacteristic, complemented
97#16810943C2211yescharacteristic, complemented
98#16810941C2211yescharacteristic, complemented
99#16810940C2211yescharacteristic, complemented
100#16810927C2211yescharacteristic, complemented
101#16810911C2211yescharacteristic, complemented
102#16810907C2211yescharacteristic, complemented
103#16810880C2211yescharacteristic, complemented
104#16810879C2211yescharacteristic, complemented
105#16810877C2211yescharacteristic, complemented
106#16810871C2211yescharacteristic, complemented
107#16810860C2211yescharacteristic, complemented
108#16810858C2211yescharacteristic, complemented
109#16810855C2211yescharacteristic, complemented
110#16810854C2211yescharacteristic, complemented
111#16810853C2211yescharacteristic, complemented
112#16810853C2211yescharacteristic, complemented
113#16810852C2211yescharacteristic, complemented
114#16810852C2211yescharacteristic, complemented
115#16810851C2211yescharacteristic, complemented
116#16810850C2211yescharacteristic, complemented
117#16810848C2211yescharacteristic, complemented
118#16810848C2211yescharacteristic, complemented
119#16810848C2211yescharacteristic, complemented
120#16810840C2211yescharacteristic, complemented
121#16810835C2211yescharacteristic, complemented
122#16810834C2211yescharacteristic, complemented
123#16810828C2211yescharacteristic, complemented
124#16810823C2211yescharacteristic, complemented
125#16810822C2211yescharacteristic, complemented
126#16810822C2211yescharacteristic, complemented
127#16810819C2211yescharacteristic, complemented
128#16810788C2211yescharacteristic, complemented
129#16810788C2211yescharacteristic, complemented
130#16810787C2211yescharacteristic, complemented
131#16810787C2211yescharacteristic, complemented
132#16810786C2211yescharacteristic
133#16810786C2211yescharacteristic
134#16810786C2211yescharacteristic, complemented
135#16810785C2211yescharacteristic, complemented
136#16810784C2211yescharacteristic, complemented
137#16810783C2211yescharacteristic, complemented
138#16810783C2211yescharacteristic, complemented
139#16810783C2211yescharacteristic, complemented
140#16810782C2211yescharacteristic
141#16810780C2211yescharacteristic, complemented
142#16810777C2211yescharacteristic, complemented
143#16810775C2211yescharacteristic, complemented
144#16810775C2211yescharacteristic, complemented
145#16810775C2211yescharacteristic, complemented
146#16810775C2211yescharacteristic, complemented
147#16810774C2211yescharacteristic, complemented
148#16810772C2211yescharacteristic, complemented
149#16810771C2211yescharacteristic, complemented
150#16810770C2211yescharacteristic, complemented
151#16810770C2211yescharacteristic, complemented
152#16810769C2211yescharacteristic
153#16810769C2211yescharacteristic, complemented
154#16810766C2211yescharacteristic, complemented
155#16810763C2211yescharacteristic, complemented
156#16810763C2211yescharacteristic, complemented
157#16810763C2211yescharacteristic, complemented
158#16810760C2211yescharacteristic, complemented
159#16810758C2211yescharacteristic, complemented
160#16810758C2211yescharacteristic, complemented
161#16810758C2211yescharacteristic, complemented
162#16810733C2211yescharacteristic, complemented
163#16810729C2211yescharacteristic, complemented
164#16810728C2211yescharacteristic, complemented
165#16810720C2211yescharacteristic, complemented
166#16810717C2211yescharacteristic, complemented
167#16810714C2211yescharacteristic, complemented
168C4×#11719913C2211yescharacteristic, complemented
169#16810697C2211yescharacteristic, complemented
170#16810695C2211yescharacteristic, complemented
171#16810694C2211yescharacteristic, complemented
172#16810693C2211yescharacteristic, complemented
173C8×D212C2211yescharacteristic, complemented
174C8×C22⋊D53C2211yescharacteristic, complemented
175#16810686C2211yescharacteristic, complemented
176#16810683C2211yescharacteristic, complemented
177#16810682C2211yescharacteristic, complemented
178#16810626C2211yescharacteristic, complemented
179#16810622C2211yescharacteristic, complemented
180#16810617C2211yescharacteristic, complemented
181#16810616C2211yescharacteristic, complemented
182#103×D53C2211yescharacteristic, complemented
183#102×D53C2211yescharacteristic, complemented
184#16810589C2211yescharacteristic, complemented
185#16810588C2211yescharacteristic, complemented
186C2×#13133129C2211yescharacteristic, complemented
187C22⋊C8×D53C2211yescharacteristic, complemented
188C53×#552C2211yescharacteristic, complemented
189C53×#546C2211yescharacteristic
190C53×#488C2211yescharacteristic, complemented
191C53×#483C2211yescharacteristic, complemented
192C53×#482C2211yescharacteristic, complemented
193C53×#478C2211yescharacteristic, complemented
194C53×#467C2211yescharacteristic, complemented
195C53×#465C2211yescharacteristic, complemented
196C53×#464C2211yescharacteristic, complemented
197C53×#452C2211yescharacteristic, complemented
198C53×#450C2211yescharacteristic, complemented
199C4×SD16×C53C2211yescharacteristic, complemented
200C8×D4×C53C2211yescharacteristic, complemented
201C53×#416C2211yescharacteristic, complemented
202C2×#102×C53C2211yescharacteristic, complemented
203#13133262—42no—
204#13133262—42no—
205C2×#11719949C2311yescharacteristic
206C2×#11719945—21no—
207C2×#11719945C2311yescharacteristic
208C2×#11719945C2311yescharacteristic
209C2×#11719945C2311yescharacteristic
210C2×#11719945C2311yescharacteristic
211C2×#11719945C2311yescharacteristic
212C2×#11719947—21no—
213C2×#11719947—21no—
214C2×#11719947C2311yescharacteristic
215C2×#11719947C2311yescharacteristic
216#41×D53—42no—
217#41×D53—42no—
218C2×Q8×D53C2311yescharacteristic
219C2×Q8×D53C2311yescharacteristic
220C2×Q8×D53C2311yescharacteristic
221C22×D212—21no—
222C22×C22⋊D53—21no—
223C22×C22⋊D53—21no—
224C22×C22⋊D53—21no—
225C2×D4×D53—21no—
226C2×D4×D53—21no—
227C2×D4×D53—21no—
228C2×D4×D53C2311yescharacteristic
229C2×D4×D53C2311yescharacteristic
230C2×D4×D53C2311yescharacteristic
231C22×C4×D53—21no—
232C22×C4×D53C2311yescharacteristic
233#13133246—42no—
234#13133243—42no—
235#13133239—42no—
236#13133239—42no—
237#13133237—42no—
238C2×Dic212C2311yescharacteristic
239C2×Dic212C2311yescharacteristic
240C2×#11719925C2311yescharacteristic
241C2×#11719925C2311yescharacteristic
242C2×#11719925C2311yescharacteristic
243Q16×D53—42no—
244C2×#11719913C2311yescharacteristic
245C2×#11719913C2311yescharacteristic
246C2×#11719913C2311yescharacteristic
247C2×#11719913C2311yescharacteristic
248C2×#11719913C2311yescharacteristic
249C2×#11719923C2311yescharacteristic
250C2×#11719923C2311yescharacteristic
251C2×#11719923C2311yescharacteristic
252C2×#11719923C2311yescharacteristic
253C2×#11719924C2311yescharacteristic
254C2×#11719924C2311yescharacteristic
255C2×#11719924C2311yescharacteristic
256SD16×D53—42no—
257SD16×D53—42no—
258C2×D424C2311yescharacteristic
259C2×D424C2311yescharacteristic
260C2×#11719922C2311yescharacteristic
261C2×#11719922C2311yescharacteristic
262C2×#11719917C2311yescharacteristic
263C2×#11719912C2311yescharacteristic
264C22×#88322C2311yescharacteristic
265C2×C8×D53C2311yescharacteristic
266C2×C8×D53C2311yescharacteristic
267C2×C8×D53C2311yescharacteristic
268#13133217—21no—
269#13133217C2311yescharacteristic
270#13133216—21no—
271#13133216C2311yescharacteristic
272#13133214C2311yescharacteristic
273#13133213—21no—
274#13133213—21no—
275#13133213C2311yescharacteristic
276#13133212—21no—
277#13133212—21no—
278#13133212—21no—
279#13133211—21no—
280#13133211—21no—
281#13133210—21no—
282#13133208—21no—
283#13133208—21no—
284#13133207—21no—
285#13133206C2311yescharacteristic
286#13133206C2311yescharacteristic
287#13133205—21no—
288#13133203—21no—
289#13133203—21no—
290#13133203—21no—
291#13133203—21no—
292#13133203—21no—
293#13133203—21no—
294#13133202—21no—
295#13133202—21no—
296#13133202—21no—
297#13133202D411yescharacteristic
298#13133201—21no—
299#13133200—21no—
300#13133199—21no—
301#13133199—21no—
302#13133199—21no—
303#13133199D411yescharacteristic
304#13133197—21no—
305#13133197—21no—
306#13133197—21no—
307#13133197C2311yescharacteristic
308#13133197C2311yescharacteristic
309#13133197C2311yescharacteristic
310#13133197C2311yescharacteristic
311#13133196—21no—
312#13133196C2311yescharacteristic
313#13133196C2311yescharacteristic
314#13133195—21no—
315#13133195—21no—
316#13133195—21no—
317#13133195—21no—
318#13133195—21no—
319#13133195—21no—
320#13133195—21no—
321#13133195D411yescharacteristic
322#13133194—21no—
323#13133194—21no—
324#13133194D411yescharacteristic
325#13133193C2311yescharacteristic
326#13133193C2311yescharacteristic
327#13133192—21no—
328#13133192—21no—
329#13133192—21no—
330#13133192C2311yescharacteristic
331#13133192C2311yescharacteristic
332#13133192C2311yescharacteristic
333#13133192C2311yescharacteristic
334#13133192C2311yescharacteristic
335#13133191—21no—
336#13133191—21no—
337#13133191—21no—
338#13133191C2311yescharacteristic
339#13133191C2311yescharacteristic
340#13133190—21no—
341#13133190—21no—
342#13133190—21no—
343#13133190—21no—
344#13133190—21no—
345#13133190—21no—
346#13133190—21no—
347#13133190—21no—
348#13133190—21no—
349#13133190—21no—
350#13133190—21no—
351#13133190—21no—
352#13133190D411yescharacteristic
353#13133189—21no—
354#13133189—21no—
355#13133189—21no—
356#13133189—21no—
357#13133189D411yescharacteristic
358#13133188—21no—
359#13133188C2311yescharacteristic
360#13133187—21no—
361#13133187—21no—
362#13133187—21no—
363#13133187—21no—
364#13133187—21no—
365#13133187D411yescharacteristic
366#13133186—21no—
367#13133185—21no—
368#13133185—21no—
369#13133185D411yescharacteristic
370C4×Dic106—21no—
371C4×Dic106C2311yescharacteristic
372#13133182C2311yescharacteristic
373#13133182C2311yescharacteristic
374#13133182C2311yescharacteristic
375C4×D212—21no—
376C4×D212—21no—
377C4×D212—21no—
378C4×D212C2311yescharacteristic
379C4×D212C2311yescharacteristic
380D4×Dic53C2311yescharacteristic
381#13133179—21no—
382#13133179—21no—
383#13133179—21no—
384#13133179—21no—
385#13133179—21no—
386C4×C22⋊D53—21no—
387C4×C22⋊D53—21no—
388C4×C22⋊D53C2311yescharacteristic
389C4×C22⋊D53C2311yescharacteristic
390#13133177—21no—
391#13133177—21no—
392#13133177—21no—
393#13133175C2311yescharacteristic
394#13133174C2311yescharacteristic
395#13133173—21no—
396C2×#11719919—21no—
397C4⋊C4×D53—21no—
398C4⋊C4×D53—21no—
399C4⋊C4×D53C2311yescharacteristic
400C4⋊C4×D53C2311yescharacteristic
401C2×#11719921—21no—
402C22⋊C4×D53—21no—
403C22⋊C4×D53—21no—
404#13133150C2311yescharacteristic
405#13133149C2311yescharacteristic
406#13133148C2311yescharacteristic
407#13133148C2311yescharacteristic
408#13133148C2311yescharacteristic
409C4⋊#88322C2311yescharacteristic
410#13133146C2311yescharacteristic
411#13133146C2311yescharacteristic
412#13133142C2311yescharacteristic
413#13133142C2311yescharacteristic
414#13133142C2311yescharacteristic
415#13133141C2311yescharacteristic
416#13133141C2311yescharacteristic
417#13133140C2311yescharacteristic
418#13133140C2311yescharacteristic
419#13133140C2311yescharacteristic
420#13133140C2311yescharacteristic
421#13133140C2311yescharacteristic
422#13133139C2311yescharacteristic
423#13133139C2311yescharacteristic
424#13133139C2311yescharacteristic
425#13133138C2311yescharacteristic
426#13133138C2311yescharacteristic
427#13133137C2311yescharacteristic
428#13133137C2311yescharacteristic
429#13133137C2311yescharacteristic
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#13133128C2311yescharacteristic
445#13133127C2311yescharacteristic
446C8×Dic53C2311yescharacteristic
447C2×#41×C53C2311yescharacteristic
448C22×D4×C53C2311yescharacteristic
449C2×Q16×C53C2311yescharacteristic
450C2×SD16×C53C2311yescharacteristic
451C2×SD16×C53C2311yescharacteristic
452C22×C8×C53C2311yescharacteristic
453C22×C8×C53C2311yescharacteristic
454#126×C53—21no—
455#125×C53—21no—
456#125×C53C2311yescharacteristic
457#124×C53C2311yescharacteristic
458#123×C53—21no—
459#123×C53—21no—
460C22⋊Q8×C53C2311yescharacteristic
461C22⋊Q8×C53C2311yescharacteristic
462C22⋊Q8×C53C2311yescharacteristic
463#121×C53—21no—
464#121×C53C2311yescharacteristic
465#120×C53—21no—
466C4×Q8×C53C2311yescharacteristic
467C4×D4×C53C2311yescharacteristic
468C4×D4×C53C2311yescharacteristic
469#117×C53—21no—
470#117×C53C2311yescharacteristic
471C2×C4⋊C4×C53C2311yescharacteristic
472C2×C22⋊C4×C53—21no—
473#107×C53C2311yescharacteristic
474#106×C53C2311yescharacteristic
475#106×C53C2311yescharacteristic
476C4⋊C8×C53C2311yescharacteristic
477#103×C53C2311yescharacteristic
478#103×C53C2311yescharacteristic
479#103×C53C2311yescharacteristic
480#103×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
489C4×C8×C53C2311yescharacteristic
490C24×C53—21no—
491C23×D53—21no—
492C23×D53—21no—
493C23×D53—21no—
494C23×D53C2×D411yescharacteristic
495#41×C53—22no—
496#41×C53—41no—
497C2×Q8×C53C2411yescharacteristic
498C2×Q8×C53C2411yescharacteristic
499C2×D4×C53—22no—
500C2×D4×C53—21no—
501C2×D4×C53—21no—
502C2×D4×C53—21no—
503C2×D4×C53—41no—
504C2×D4×C53C2×D411yescharacteristic
505C2×D4×C53C2411yescharacteristic
506C2×D4×C53C2411yescharacteristic
507C22×C4×C53—21no—
508C22×C4×C53—21no—
509C22×C4×C53—21no—
510C22×C4×C53C2411yescharacteristic
511C22×C4×C53C2411yescharacteristic
512C2×C22⋊D53—21no—
513C2×C22⋊D53—21no—
514C2×C22⋊D53—21no—
515C2×C22⋊D53—21no—
516C2×C22⋊D53—21no—
517C2×C22⋊D53—21no—
518C2×C22⋊D53—21no—
519C2×C22⋊D53—21no—
520C2×C22⋊D53—21no—
521C2×C22⋊D53—21no—
522C2×C22⋊D53—21no—
523C2×C22⋊D53—21no—
524C2×C22⋊D53—21no—
525C2×C22⋊D53—21no—
526C2×C22⋊D53—44no—
527C2×C22⋊D53—44no—
528C2×C22⋊D53—82no—
529C2×C22⋊D53C2×D411yescharacteristic
530C2×C22⋊D53C2×D411yescharacteristic
531C2×C22⋊D53C2×D411yescharacteristic
532C2×C22⋊D53C2×D411yescharacteristic
533C22×Dic53—21no—
534C22×Dic53—21no—
535C22×Dic53—21no—
536C22×Dic53C2×D411yescharacteristic
537#11719949—41no—
538#11719949—41no—
539Q8×D53—22no—
540Q8×D53—41no—
541Q8×D53—41no—
542Q8×D53—41no—
543Q8×D53—41no—
544Q8×D53—41no—
545#11719947—22no—
546#11719947—22no—
547#11719947—22no—
548#11719947—41no—
549#11719947—44no—
550#11719947—44no—
551D4×D53—22no—
552D4×D53—22no—
553D4×D53—41no—
554D4×D53—41no—
555D4×D53—41no—
556D4×D53—41no—
557D4×D53—44no—
558D4×D53—44no—
559D4×D53—82no—
560#11719945—22no—
561#11719945—22no—
562#11719945—41no—
563#11719945—41no—
564#11719945—41no—
565#11719945—41no—
566#11719945—41no—
567#11719945—41no—
568#11719945—41no—
569#11719945—41no—
570#11719945—44no—
571C2×D212—21no—
572C2×D212—21no—
573C2×D212—21no—
574C2×D212—21no—
575C2×D212—21no—
576C2×D212—21no—
577C2×D212—21no—
578C2×D212—21no—
579C2×D212—82no—
580C2×D212C2×D411yescharacteristic
581C2×D212C2×D411yescharacteristic
582C2×D212C2411yescharacteristic
583C2×D212C2411yescharacteristic
584C2×D212C2411yescharacteristic
585C2×C4×D53—21no—
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—21no—
595C2×C4×D53—21no—
596C2×C4×D53—41no—
597C2×C4×D53—41no—
598C2×C4×D53—44no—
599C2×C4×D53C2×D411yescharacteristic
600C2×C4×D53C2×D411yescharacteristic
601C2×C4×D53C2411yescharacteristic
602C2×C4×D53C2411yescharacteristic
603C2×C4×D53C2411yescharacteristic
604C2×Dic106—21no—
605C2×Dic106—21no—
606C2×Dic106—21no—
607C2×Dic106—21no—
608C2×Dic106C2×D411yescharacteristic
609C2×Dic106C2411yescharacteristic
610C2×Dic106C2411yescharacteristic
611C2×Dic106C2411yescharacteristic
612Q16×C53—41no—
613SD16×C53—22no—
614SD16×C53—41no—
615C2×C8×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×C53—21no—
628C4⋊C4×C53C2×D411yescharacteristic
629C4⋊C4×C53C2411yescharacteristic
630C4⋊C4×C53C2411yescharacteristic
631C4⋊C4×C53C2411yescharacteristic
632C4⋊C4×C53C2411yescharacteristic
633C22⋊C4×C53—21no—
634C22⋊C4×C53—21no—
635C22⋊C4×C53—21no—
636C22⋊C4×C53—21no—
637C22⋊C4×C53—21no—
638C22⋊C4×C53—21no—
639C22⋊C4×C53—21no—
640C22⋊C4×C53—21no—
641C22⋊C4×C53C2×D411yescharacteristic
642C22⋊C4×C53C2×D411yescharacteristic
643C42×C53—21no—
644C42×C53—21no—
645C42×C53C2411yescharacteristic
646C22⋊Dic53—21no—
647C22⋊Dic53—21no—
648C22⋊Dic53—21no—
649C22⋊Dic53—21no—
650C22⋊Dic53C2×D411yescharacteristic
651C22⋊Dic53C2×D411yescharacteristic
652#11719925—22no—
653#11719925—41no—
654#11719925—41no—
655#11719924—41no—
656#11719924—41no—
657#11719924—41no—
658#11719923—22no—
659#11719923—22no—
660#11719923—41no—
661#11719923—41no—
662#11719922—22no—
663#11719922—41no—
664#11719921—21no—
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#11719921—21no—
683#11719921C2×D411yescharacteristic
684#11719921C2×D411yescharacteristic
685#11719921C2×D411yescharacteristic
686#11719921C2×D411yescharacteristic
687#11719921C2×D411yescharacteristic
688#11719921C2×D411yescharacteristic
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—
720C2×#88322—41no—
721C2×#88322C2411yescharacteristic
722C2×#88322C2411yescharacteristic
723C2×#88322C2411yescharacteristic
724C2×#88322C2411yescharacteristic
725Dic212—22no—
726Dic212—22no—
727D424—41no—
728D424—41no—
729#11719913—22no—
730#11719913—41no—
731#11719913—41no—
732#11719913—41no—
733#11719913—41no—
734#11719912—41no—
735C8×D53—41no—
736C8×D53—41no—
737C8×D53—41no—
738C23×C53—21no—
739C23×C53—21no—
740C23×C53—42no—
741C23×C53—81no—
742C23×C53—81no—
743C23×C53C22×D411yescharacteristic
744C23×C53C22×D411yescharacteristic
745C22×D53—22no—
746C22×D53—21no—
747C22×D53—21no—
748C22×D53—21no—
749C22×D53—41no—
750C22×D53—41no—
751C22×D53—42no—
752C22×D53—42no—
753C22×D53—42no—
754C22×D53—42no—
755C22×D53—81no—
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—
765Q8×C53—21no—
766Q8×C53—21no—
767D4×C53—21no—
768D4×C53—21no—
769D4×C53—21no—
770D4×C53—41no—
771D4×C53—42no—
772D4×C53—42no—
773D4×C53—81no—
774D4×C53H(5,𝔽2)12yes—
775C2×C4×C53—21no—
776C2×C4×C53—21no—
777C2×C4×C53—21no—
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—42no—
786C2×C4×C53—81no—
787C2×C4×C53—81no—
788C2×C4×C53C22×D411yescharacteristic
789C2×C4×C53C22×D411yescharacteristic
790C2×C4×C53C22×D411yescharacteristic
791C2×C4×C53C22×D411yescharacteristic
792C2×C4×C53C2511yescharacteristic
793C22⋊D53—24no—
794C22⋊D53—22no—
795C22⋊D53—41no—
796C22⋊D53—41no—
797C22⋊D53—41no—
798C22⋊D53—42no—
799C22⋊D53—42no—
800C22⋊D53—42no—
801C22⋊D53—42no—
802C22⋊D53—42no—
803C22⋊D53—42no—
804C22⋊D53—42no—
805C22⋊D53—81no—
806C22⋊D53—81no—
807C22⋊D53—81no—
808C22⋊D53—81no—
809C22⋊D53—81no—
810C22⋊D53—81no—
811C2×Dic53—24no—
812C2×Dic53—21no—
813C2×Dic53—21no—
814C2×Dic53—21no—
815C2×Dic53—21no—
816C2×Dic53—21no—
817C2×Dic53—41no—
818C2×Dic53—42no—
819C2×Dic53—81no—
820C2×Dic53C22×D411yescharacteristic
821C2×Dic53C22×D411yescharacteristic
822C2×Dic53C22×D411yescharacteristic
823C2×Dic53C22×D411yescharacteristic
824C2×Dic53C22×D411yescharacteristic
825D212—22no—
826D212—21no—
827D212—21no—
828D212—21no—
829D212—21no—
830D212—21no—
831D212—21no—
832D212—41no—
833D212—42no—
834D212—42no—
835D212—42no—
836D212—81no—
837D212—81no—
838D212—81no—
839D212—81no—
840D212—81no—
841C4×D53—21no—
842C4×D53—21no—
843C4×D53—21no—
844C4×D53—21no—
845C4×D53—21no—
846C4×D53—21no—
847C4×D53—41no—
848C4×D53—41no—
849C4×D53—42no—
850C4×D53—42no—
851C4×D53—42no—
852C4×D53—42no—
853C4×D53—81no—
854C4×D53—81no—
855C4×D53—81no—
856C4×D53—81no—
857C4×D53—81no—
858C4×D53—81no—
859C4×D53—81no—
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#61640—531nomaximal, Sylow
880C22×C53—21no—
881C22×C53—21no—
882C22×C53—22no—
883C22×C53—21no—
884C22×C53—21no—
885C22×C53—21no—
886C22×C53—21no—
887C22×C53—41no—
888C22×C53—41no—
889C22×C53—41no—
890C22×C53—41no—
891C22×C53—41no—
892C22×C53—162no—
893C22×C53C23×D411yescharacteristic
894C2×D53—21no—
895C2×D53—21no—
896C2×D53—21no—
897C2×D53—21no—
898C2×D53—21no—
899C2×D53—21no—
900C2×D53—21no—
901C2×D53—21no—
902C2×D53—41no—
903C2×D53—41no—
904C2×D53—41no—
905C2×D53—41no—
906C2×D53—41no—
907C2×D53—41no—
908C2×D53—41no—
909C2×D53—41no—
910C2×D53—41no—
911C2×D53—82no—
912C2×D53—84no—
913C2×D53—162no—
914C2×D53—162no—
915C2×D53#57712yes—
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×C53—41no—
926C4×C53C2×H(5,𝔽2)11yescharacteristic
927C4×C53C2×H(5,𝔽2)11yescharacteristic
928Dic53—21no—
929Dic53—22no—
930Dic53—21no—
931Dic53—21no—
932Dic53—21no—
933Dic53—21no—
934Dic53—41no—
935Dic53—41no—
936Dic53—41no—
937Dic53—41no—
938#3541—531no—
939#3488—531no—
940#3318—531no—
941#3317—531no—
942#3316—531no—
943#3311—531no—
944#3304—531no—
945#3301—531no—
946#3296D5311yescharacteristic, complemented
947#3295—531no—
948#3285—531no—
949#3284—531no—
950#3282—531no—
951D4×SD16—531no—
952#3271—531no—
953#3270—531no—
954#3267—531no—
955#3265—531no—
956#3224—531no—
957#3222—531no—
958#3204—531no—
959#3201—531no—
960#3188—531no—
961#3187—531no—
962#3125—531no—
963#3120—531no—
964#3012—531no—
965#3009—531no—
966#3002—531no—
967C2×#452—531no—
968#2977—531no—
969C2×C53—42no—
970C2×C53—41no—
971C2×C53—41no—
972C2×C53—81no—
973C2×C53#348411yescharacteristic
974C2×C53C2×#57711yescharacteristic
975C2×C53#358411yescharacteristic
976D53—22no—
977D53—41no—
978D53—41no—
979D53—81no—
980D53—81no—
981D53—81no—
982C2×H(5,𝔽2)—531no—
983C22×#41—531no—
984C2×#137—531no—
985C2×AGL(1,ℤ/8)—531no—
986C2×#135—531no—
987C2×#135—531no—
988C2×#135—531no—
989C22×Q16—531no—
990C22×SD16—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—1061no—
1010#546—1061no—
1011#546C2×D5311yescharacteristic
1012D42—531no—
1013D42—531no—
1014D42—1061no—
1015D42—1061no—
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#490—531no—
1040#489—531no—
1041#488C2×D5311yescharacteristic, complemented
1042#486—531no—
1043#485—531no—
1044#484—531no—
1045#483—531no—
1046#483—531no—
1047#483C2×D5311yescharacteristic, complemented
1048#482—531no—
1049#482—531no—
1050#482C2×D5311yescharacteristic, complemented
1051#481—531no—
1052#481—531no—
1053#481—531no—
1054#481—531no—
1055#479—531no—
1056#478C2×D5311yescharacteristic, complemented
1057#476—531no—
1058#475—531no—
1059#470—531no—
1060#470—531no—
1061#469—531no—
1062#468—531no—
1063#467C2×D5311yescharacteristic, complemented
1064#466—531no—
1065#466—531no—
1066#465—531no—
1067#465—531no—
1068#465—531no—
1069#465—531no—
1070#465—531no—
1071#465—531no—
1072#465—531no—
1073#465—531no—
1074#465C2×D5311yescharacteristic, complemented
1075#464—531no—
1076#464—531no—
1077#464—531no—
1078#464C2×D5311yescharacteristic, complemented
1079#463—531no—
1080#463—531no—
1081#462—531no—
1082#461—531no—
1083#460—531no—
1084#460—531no—
1085#460—531no—
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#452—531no—
1100#452C2×D5311yescharacteristic, complemented
1101#451—531no—
1102#451—531no—
1103#450—531no—
1104#450—531no—
1105#450—531no—
1106#450—531no—
1107#450—531no—
1108#450—531no—
1109#450C2×D5311yescharacteristic, complemented
1110#449—531no—
1111#449—531no—
1112#449—531no—
1113#449—531no—
1114#449—531no—
1115#449—531no—
1116#448—531no—
1117#448—531no—
1118#448—531no—
1119#448—531no—
1120#447—531no—
1121#447—531no—
1122#447—531no—
1123#442—531no—
1124#441—531no—
1125#441—531no—
1126#440—531no—
1127C4×Q16—531no—
1128C4×SD16—531no—
1129C4×SD16—531no—
1130C4×SD16C2×D5311yescharacteristic, complemented
1131#435—531no—
1132#435—531no—
1133#435—531no—
1134#435—531no—
1135C8×D4—531no—
1136C8×D4—531no—
1137C8×D4—531no—
1138C8×D4C2×D5311yescharacteristic, complemented
1139#433—531no—
1140#433—531no—
1141#418—531no—
1142#417—531no—
1143#416—531no—
1144#416—531no—
1145#416C2×D5311yescharacteristic, complemented
1146C2×#103—531no—
1147C2×#102—531no—
1148C2×#102C2×D5311yescharacteristic, complemented
1149#408—531no—
1150#408—531no—
1151C2×C22⋊C8—531no—
1152C2×C22⋊C8—531no—
1153C53#6164011yescharacteristic, 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—1061no—
1165C2×#41—1061no—
1166C2×#41—1061no—
1167C2×#41—2122no—
1168C2×#41—2122no—
1169C2×#41C22×D5311yescharacteristic
1170C22×Q8—531no—
1171C22×Q8—531no—
1172C22×Q8—531no—
1173C22×D4—531no—
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×D4—1061no—
1183C22×D4C22×D5311yescharacteristic
1184C23×C4—531no—
1185C23×C4—1061no—
1186#137—2122no—
1187AGL(1,ℤ/8)—2122no—
1188#135—2122no—
1189#135—2122no—
1190#135—2122no—
1191C2×Q16—531no—
1192C2×Q16—531no—
1193C2×Q16—531no—
1194C2×Q16—531no—
1195C2×Q16—531no—
1196C2×Q16—2122no—
1197C2×Q16C22×D5311yescharacteristic
1198C2×SD16—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×SD16—2122no—
1212C2×SD16C22×D5311yescharacteristic
1213C2×SD16C22×D5311yescharacteristic
1214C2×D8—531no—
1215C2×D8—531no—
1216C2×D8—531no—
1217C2×D8—531no—
1218C2×M16—531no—
1219C2×M16—531no—
1220C22×C8—531no—
1221C22×C8—531no—
1222C22×C8—531no—
1223C22×C8—531no—
1224C22×C8C22×D5311yescharacteristic
1225C22×C8C22×D5311yescharacteristic
1226C4⋊Q8—531no—
1227C4⋊Q8—531no—
1228C4⋊Q8—1061no—
1229C4⋊Q8—1061no—
1230#127—531no—
1231#127—531no—
1232#127—1061no—
1233#127—1061no—
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—1061no—
1249#124—1061no—
1250#124—1061no—
1251#124—1061no—
1252#124—1061no—
1253#124—1061no—
1254#124—1061no—
1255#124C22×D5311yescharacteristic
1256#123—21no—
1257#123—21no—
1258#123—531no—
1259#123—531no—
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—1061no—
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⋊Q8C22×D5311yescharacteristic
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—531no—
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#121—1061no—
1328#121C22×D5311yescharacteristic
1329#120—21no—
1330#120—531no—
1331#120—531no—
1332#120—1061no—
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—21no—
1378C2×C22⋊C4—1061no—
1379C2×C22⋊C4—1061no—
1380C2×C22⋊C4—1061no—
1381#107—531no—
1382#107C22×D5311yescharacteristic
1383#106—531no—
1384#106—531no—
1385#106—531no—
1386#106—531no—
1387#106C22×D5311yescharacteristic
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#103C22×D5311yescharacteristic
1404#103C22×D5311yescharacteristic
1405#103C22×D5311yescharacteristic
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#102—531no—
1417#102—531no—
1418#102—531no—
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#97—531no—
1439C4×C8—531no—
1440C4×C8C22×D5311yescharacteristic
1441C24—21no—
1442C24—531no—
1443C24—1061no—
1444C24—1061no—
1445C24—1061no—
1446#41—22no—
1447#41—41no—
1448#41—1062no—
1449#41—1062no—
1450#41—1062no—
1451#41—1062no—
1452#41—1062no—
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—2124no—
1462#41—2121no—
1463#41—2124no—
1464#41—2124no—
1465#41—2121no—
1466#41—2121no—
1467C2×Q8—531no—
1468C2×Q8—531no—
1469C2×Q8—531no—
1470C2×Q8—531no—
1471C2×Q8—1061no—
1472C2×Q8—1061no—
1473C2×Q8—1061no—
1474C2×Q8—1061no—
1475C2×Q8—1062no—
1476C2×Q8—2121no—
1477C2×Q8—2121no—
1478C2×Q8—2121no—
1479C2×Q8—2121no—
1480C2×Q8—2121no—
1481C2×Q8C23×D5311yescharacteristic
1482C2×Q8C23×D5311yescharacteristic
1483C2×D4—22no—
1484C2×D4—21no—
1485C2×D4—21no—
1486C2×D4—21no—
1487C2×D4—41no—
1488C2×D4—531no—
1489C2×D4—531no—
1490C2×D4—531no—
1491C2×D4—531no—
1492C2×D4—531no—
1493C2×D4—531no—
1494C2×D4—531no—
1495C2×D4—531no—
1496C2×D4—531no—
1497C2×D4—1061no—
1498C2×D4—1061no—
1499C2×D4—1061no—
1500C2×D4—1061no—
1501C2×D4—1061no—
1502C2×D4—1061no—
1503C2×D4—1061no—
1504C2×D4—1061no—
1505C2×D4—1061no—
1506C2×D4—1061no—
1507C2×D4—1061no—
1508C2×D4—1061no—
1509C2×D4—1062no—
1510C2×D4—1062no—
1511C2×D4—1061no—
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—4242no—
1522C2×D4—4242no—
1523C2×D4—4242no—
1524C2×D4—2121no—
1525C2×D4—2121no—
1526C2×D4—2121no—
1527C2×D4—2121no—
1528C2×D4—2124no—
1529C2×D4—2124no—
1530C2×D4—2124no—
1531C2×D4—2124no—
1532C2×D4D4×D5311yescharacteristic
1533C2×D4C23×D5311yescharacteristic
1534C2×D4C23×D5311yescharacteristic
1535C22×C4—21no—
1536C22×C4—21no—
1537C22×C4—21no—
1538C22×C4—531no—
1539C22×C4—531no—
1540C22×C4—531no—
1541C22×C4—531no—
1542C22×C4—531no—
1543C22×C4—531no—
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—41no—
1564Q16—1062no—
1565Q16—1062no—
1566Q16—1062no—
1567Q16—2121no—
1568Q16—2121no—
1569SD16—22no—
1570SD16—41no—
1571SD16—1062no—
1572SD16—1062no—
1573SD16—1062no—
1574SD16—2121no—
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—2121no—
1588M16—2121no—
1589C2×C8—41no—
1590C2×C8—41no—
1591C2×C8—531no—
1592C2×C8—531no—
1593C2×C8—531no—
1594C2×C8—531no—
1595C2×C8—2121no—
1596C2×C8—2121no—
1597C2×C8—2121no—
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—21no—
1610C4⋊C4—531no—
1611C4⋊C4—531no—
1612C4⋊C4—531no—
1613C4⋊C4—531no—
1614C4⋊C4—531no—
1615C4⋊C4—531no—
1616C4⋊C4—531no—
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—21no—
1646C22⋊C4—21no—
1647C22⋊C4—531no—
1648C22⋊C4—531no—
1649C22⋊C4—531no—
1650C22⋊C4—531no—
1651C22⋊C4—531no—
1652C22⋊C4—531no—
1653C22⋊C4—531no—
1654C22⋊C4—531no—
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—42no—
1692C23—81no—
1693C23—81no—
1694C23—531no—
1695C23—531no—
1696C23—531no—
1697C23—1062no—
1698C23—1061no—
1699C23—1061no—
1700C23—1061no—
1701C23—4241no—
1702C23—4241no—
1703C23—4241no—
1704C23—4241no—
1705C23—4241no—
1706C23—2122no—
1707C23—2121no—
1708C23—2121no—
1709C23—2122no—
1710C23—2122no—
1711C23—2122no—
1712C23C2×D4×D5311yescharacteristic
1713C23C2×D4×D5311yescharacteristic
1714Q8—21no—
1715Q8—21no—
1716Q8—21no—
1717Q8—21no—
1718Q8—532no—
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—41no—
1733D4—42no—
1734D4—42no—
1735D4—81no—
1736D4—1062no—
1737D4—1062no—
1738D4—1064no—
1739D4—1061no—
1740D4—1061no—
1741D4—1061no—
1742D4—1061no—
1743D4—1061no—
1744D4—1061no—
1745D4—4241no—
1746D4—4241no—
1747D4—4241no—
1748D4—4241no—
1749D4—4241no—
1750D4—4241no—
1751D4—4241no—
1752D4—4241no—
1753D4—4241no—
1754D4—4241no—
1755D4—4241no—
1756D4—2121no—
1757D4—2122no—
1758D4—2122no—
1759D4—2122no—
1760D4—2121no—
1761D4—2121no—
1762D4—2121no—
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—21no—
1781C2×C4—42no—
1782C2×C4—81no—
1783C2×C4—81no—
1784C2×C4—531no—
1785C2×C4—531no—
1786C2×C4—531no—
1787C2×C4—531no—
1788C2×C4—531no—
1789C2×C4—1064no—
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—1061no—
1801C2×C4—4241no—
1802C2×C4—4241no—
1803C2×C4—4241no—
1804C2×C4—4241no—
1805C2×C4—4241no—
1806C2×C4—4241no—
1807C2×C4—4241no—
1808C2×C4—4241no—
1809C2×C4—2121no—
1810C2×C4—2121no—
1811C2×C4—2122no—
1812C2×C4—2122no—
1813C2×C4—2122no—
1814C2×C4—2122no—
1815C2×C4—2121no—
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—162no—
1843C22—532no—
1844C22—8482no—
1845C22—8482no—
1846C22—1061no—
1847C22—1061no—
1848C22—1061no—
1849C22—1061no—
1850C22—1061no—
1851C22—1061no—
1852C22—1061no—
1853C22—1061no—
1854C22—4244no—
1855C22—4242no—
1856C22—2121no—
1857C22—2121no—
1858C22—2121no—
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—41no—
1876C4—1061no—
1877C4—1061no—
1878C4—1061no—
1879C4—1062no—
1880C4—1061no—
1881C4—1061no—
1882C4—2121no—
1883C4—2121no—
1884C4—2121no—
1885C4—2121no—
1886C4H(5,𝔽2)×D5311yescharacteristic
1887C4C2×#1313326311yescharacteristic
1888C2—41no—
1889C2—41no—
1890C2—42no—
1891C2—81no—
1892C2—1062no—
1893C2—4241no—
1894C2—4241no—
1895C2—4241no—
1896C2—2121no—
1897C2—2121no—
1898C2#2028834511yescharacteristic
1899C2#577×D5311yescharacteristic
1900C2#2028948411yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3296C2
socleC22×C53C23×D4
hypercenter#3296D53
hypocenterC53#61640
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3296

Complements

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

NH ≅ G/Ntype
1. #20289011C2semidirect
2. #20288378C2semidirect
3. #20286853C2semidirect
4. #20286835C2semidirect
5. #20286829C2semidirect
6. #20286747C2semidirect
7. #20286652C2semidirect
8. #20286616C2semidirect
9. #20286535C2semidirect
10. #20286459C2semidirect
11. #20286447C2semidirect
12. #20286420C2semidirect
13. SD16×D212C2semidirect
14. #20286297C2semidirect
15. #20286280C2semidirect
16. #20286236C2semidirect
17. #20286208C2semidirect
18. #20285816C2semidirect
19. #20285790C2semidirect
20. #20285625C2semidirect
21. #20285600C2semidirect
22. #20285484C2semidirect
23. #20285467C2semidirect
24. #20284988C2semidirect
25. #20284934C2semidirect
26. #20284024C2semidirect
27. #20283987C2semidirect
28. #20283935C2semidirect
29. #452×D53C2semidirect
30. #20283768C2semidirect
31. C53×#3296C2semidirect
34. C2×#13133246C22semidirect
35. C2×#13133243C22semidirect
36. C2×#13133239C22semidirect
37. C2×#13133239C22semidirect
38. C2×#13133237C22semidirect
39. C2×Q16×D53C22semidirect
40. C2×SD16×D53C22semidirect
41. C2×SD16×D53C22semidirect
44. #16811341C22semidirect
46. #16811328C22semidirect
47. #16811326C22semidirect
51. Q8×D212C22semidirect
53. #16811283C22semidirect
54. #16811283C22semidirect
56. #16811278C22semidirect
64. #16811245C22semidirect
66. #16811236C22semidirect
70. #16811204C22semidirect
73. #16811196C22semidirect
76. #16811135C22semidirect
79. C22⋊Q8×D53C22semidirect
83. #16811018C22semidirect
84. #16811009C22semidirect
85. #16811008C22semidirect
86. #16810996C22semidirect
87. #16810989C22semidirect
88. #16810984C22semidirect
89. #16810968C22semidirect
90. #16810962C22semidirect
91. #16810960C22semidirect
92. #16810955C22semidirect
93. #16810952C22semidirect
94. #16810950C22semidirect
95. #16810947C22semidirect
96. #16810943C22semidirect
97. #16810943C22semidirect
98. #16810941C22semidirect
99. #16810940C22semidirect
100. #16810927C22semidirect
101. #16810911C22semidirect
102. #16810907C22semidirect
103. #16810880C22semidirect
104. #16810879C22semidirect
105. #16810877C22semidirect
106. #16810871C22semidirect
107. #16810860C22semidirect
108. #16810858C22semidirect
109. #16810855C22semidirect
110. #16810854C22semidirect
111. #16810853C22semidirect
112. #16810853C22semidirect
113. #16810852C22semidirect
114. #16810852C22semidirect
115. #16810851C22semidirect
116. #16810850C22semidirect
117. #16810848C22semidirect
118. #16810848C22semidirect
119. #16810848C22semidirect
120. #16810840C22semidirect
121. #16810835C22semidirect
122. #16810834C22semidirect
123. #16810828C22semidirect
124. #16810823C22semidirect
125. #16810822C22semidirect
126. #16810822C22semidirect
127. #16810819C22semidirect
128. #16810788C22semidirect
129. #16810788C22semidirect
130. #16810787C22semidirect
131. #16810787C22semidirect
134. #16810786C22semidirect
135. #16810785C22semidirect
136. #16810784C22semidirect
137. #16810783C22semidirect
138. #16810783C22semidirect
139. #16810783C22semidirect
141. #16810780C22semidirect
142. #16810777C22semidirect
143. #16810775C22semidirect
144. #16810775C22semidirect
145. #16810775C22semidirect
146. #16810775C22semidirect
147. #16810774C22semidirect
148. #16810772C22semidirect
149. #16810771C22semidirect
150. #16810770C22semidirect
151. #16810770C22semidirect
153. #16810769C22semidirect
154. #16810766C22semidirect
155. #16810763C22semidirect
156. #16810763C22semidirect
157. #16810763C22semidirect
158. #16810760C22semidirect
159. #16810758C22semidirect
160. #16810758C22semidirect
161. #16810758C22semidirect
162. #16810733C22semidirect
163. #16810729C22semidirect
164. #16810728C22semidirect
165. #16810720C22semidirect
166. #16810717C22semidirect
167. #16810714C22semidirect
168. C4×#11719913C22semidirect
169. #16810697C22semidirect
170. #16810695C22semidirect
171. #16810694C22semidirect
172. #16810693C22semidirect
173. C8×D212C22semidirect
174. C8×C22⋊D53C22semidirect
175. #16810686C22semidirect
176. #16810683C22semidirect
177. #16810682C22semidirect
178. #16810626C22semidirect
179. #16810622C22semidirect
180. #16810617C22semidirect
181. #16810616C22semidirect
182. #103×D53C22semidirect
183. #102×D53C22semidirect
184. #16810589C22semidirect
185. #16810588C22semidirect
186. C2×#13133129C22semidirect
187. C22⋊C8×D53C22semidirect
188. C53×#552C22semidirect
190. C53×#488C22semidirect
191. C53×#483C22semidirect
192. C53×#482C22semidirect
193. C53×#478C22semidirect
194. C53×#467C22semidirect
195. C53×#465C22semidirect
196. C53×#464C22semidirect
197. C53×#452C22semidirect
198. C53×#450C22semidirect
199. C4×SD16×C53C22semidirect
200. C8×D4×C53C22semidirect
201. C53×#416C22semidirect
202. C2×#102×C53C22semidirect
946. #3296D53semidirect
999. #552C2×D53semidirect
1041. #488C2×D53semidirect
1047. #483C2×D53semidirect
1050. #482C2×D53semidirect
1056. #478C2×D53semidirect
1063. #467C2×D53semidirect
1074. #465C2×D53semidirect
1078. #464C2×D53semidirect
1100. #452C2×D53semidirect
1109. #450C2×D53semidirect
1130. C4×SD16C2×D53semidirect
1138. C8×D4C2×D53semidirect
1145. #416C2×D53semidirect
1148. C2×#102C2×D53semidirect
1153. C53#61640semidirect

Maximal subgroups

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

subgroupindex
#202890112
#202883782
#202868532
#202868352
#202868292
#202867472
#202866522
#202866162
#202865352
#202864592
#202864472
#202864202
SD16×D2122
#202862972
#202862802
#202862362
#202862082
#202858162
#202857902
#202856252
#202856002
#202854842
#202854672
#202849882
#202849342
#202840242
#202839872
#202839352
#452×D532
#202837682
C53×#32962
#6164053