Finite Group Databasebeta

← #28270655

Subgroups — #28270655

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#20288994C211yesmaximal, characteristic, complemented
2#20288378C211yesmaximal, characteristic, complemented
3#20287054C211yesmaximal, characteristic, complemented
4#20286978C211yesmaximal, characteristic, complemented
5#20286948C211yesmaximal, characteristic, complemented
6#20286909C211yesmaximal, characteristic, complemented
7#20286796C211yesmaximal, characteristic, complemented
8#20286788C211yesmaximal, characteristic, complemented
9#20286740C211yesmaximal, characteristic, complemented
10#20286716C211yesmaximal, characteristic, complemented
11#20286379C211yesmaximal, characteristic, complemented
12#20286370C211yesmaximal, characteristic, complemented
13#20286309C211yesmaximal, characteristic, complemented
14#20286301C211yesmaximal, characteristic, complemented
15#20286274C211yesmaximal, characteristic, complemented
16#20286219C211yesmaximal, characteristic, complemented
17#20286216C211yesmaximal, characteristic, complemented
18#20285802C211yesmaximal, characteristic, complemented
19#20285784C211yesmaximal, characteristic, complemented
20#20285616C211yesmaximal, characteristic, complemented
21#20285598C211yesmaximal, characteristic, complemented
22#20285524C211yesmaximal, characteristic, complemented
23#20285519C211yesmaximal, characteristic, complemented
24#20284974C211yesmaximal, characteristic, complemented
25#20284925C211yesmaximal, characteristic, complemented
26#20284018C211yesmaximal, characteristic, complemented
27#20283987C211yesmaximal, characteristic, complemented
28#20283971C211yesmaximal, characteristic, complemented
29#20283953C211yesmaximal, characteristic, complemented
30#20283772C211yesmaximal, characteristic, complemented
31C53×#3275C211yesmaximal, characteristic, complemented
32C2×#13133262C2211yescharacteristic
33C2×#41×D53C2211yescharacteristic
34C2×#13133248C2211yescharacteristic, complemented
35C2×#13133246C2211yescharacteristic, complemented
36C2×#13133246C2211yescharacteristic, complemented
37C2×#13133241C2211yescharacteristic, complemented
38C2×#13133237C2211yescharacteristic, complemented
39C2×SD16×D53C2211yescharacteristic, complemented
40#16811374—21no—
41#16811367—21no—
42#16811346C2211yescharacteristic, complemented
43#16811332—21no—
44#16811330C2211yescharacteristic, complemented
45#16811325C2211yescharacteristic, complemented
46#16811316—21no—
47#16811315C2211yescharacteristic, complemented
48#16811294C2211yescharacteristic
49#16811291C2211yescharacteristic
50Q8×C22⋊D53C2211yescharacteristic, complemented
51#16811283C2211yescharacteristic
52#16811281C2211yescharacteristic
53#16811281C2211yescharacteristic, complemented
54#16811272C2211yescharacteristic, complemented
55#16811265—21no—
56#16811263—21no—
57#16811261C2211yescharacteristic
58D4×D212C2211yescharacteristic
59#16811257—21no—
60D4×C22⋊D53C2211yescharacteristic
61#16811255—21no—
62#16811242C2211yescharacteristic, complemented
63#16811237—21no—
64#16811231C2211yescharacteristic, complemented
65#16811222—21no—
66#16811210—21no—
67#16811206—21no—
68#16811203C2211yescharacteristic
69#16811201C2211yescharacteristic, complemented
70#16811200—21no—
71#16811196C2211yescharacteristic, complemented
72#16811191C2211yescharacteristic
73#16811188—21no—
74#16811133C2211yescharacteristic, complemented
75#16811132C2211yescharacteristic
76#16811131—21no—
77C2×#13133193C2211yescharacteristic, complemented
78C2×#13133190—21no—
79#121×D53C2211yescharacteristic
80#16811102C2211yescharacteristic
81#16811016C2211yescharacteristic, complemented
82#16811013C2211yescharacteristic, complemented
83#16810994C2211yescharacteristic, complemented
84#16810986C2211yescharacteristic, complemented
85#16810982C2211yescharacteristic, complemented
86#16810979C2211yescharacteristic, complemented
87#16810970C2211yescharacteristic, complemented
88#16810963C2211yescharacteristic, complemented
89#16810957C2211yescharacteristic, complemented
90#16810957C2211yescharacteristic, complemented
91#16810956C2211yescharacteristic, complemented
92#16810955C2211yescharacteristic, complemented
93#16810949C2211yescharacteristic, complemented
94#16810949C2211yescharacteristic, complemented
95#16810945C2211yescharacteristic, complemented
96#16810937C2211yescharacteristic, complemented
97#16810937C2211yescharacteristic, complemented
98#16810935C2211yescharacteristic, complemented
99#16810934C2211yescharacteristic, complemented
100#16810933C2211yescharacteristic, complemented
101#16810921C2211yescharacteristic, complemented
102#16810919C2211yescharacteristic, complemented
103#16810903C2211yescharacteristic, complemented
104#16810874C2211yescharacteristic, complemented
105#16810872C2211yescharacteristic, complemented
106#16810872C2211yescharacteristic, complemented
107#16810872C2211yescharacteristic, complemented
108#16810869C2211yescharacteristic, complemented
109#16810869C2211yescharacteristic, complemented
110#16810867C2211yescharacteristic, complemented
111#16810866C2211yescharacteristic, complemented
112#16810866C2211yescharacteristic, complemented
113#16810866C2211yescharacteristic, complemented
114#16810862C2211yescharacteristic, complemented
115#16810861C2211yescharacteristic, complemented
116#16810858C2211yescharacteristic, complemented
117#16810854C2211yescharacteristic, complemented
118#16810847C2211yescharacteristic, complemented
119#16810842C2211yescharacteristic, complemented
120#16810842C2211yescharacteristic, complemented
121#16810840C2211yescharacteristic, complemented
122#16810832C2211yescharacteristic, complemented
123#16810826C2211yescharacteristic, complemented
124#16810824C2211yescharacteristic, complemented
125#16810823C2211yescharacteristic, complemented
126#16810821C2211yescharacteristic, complemented
127#16810816C2211yescharacteristic, complemented
128#16810788C2211yescharacteristic, complemented
129#16810787C2211yescharacteristic, complemented
130#16810787C2211yescharacteristic, complemented
131#16810786C2211yescharacteristic
132#16810785C2211yescharacteristic, complemented
133#16810784C2211yescharacteristic, complemented
134#16810784C2211yescharacteristic, complemented
135#16810783C2211yescharacteristic, complemented
136#16810782C2211yescharacteristic
137#16810782C2211yescharacteristic
138#16810782C2211yescharacteristic, complemented
139#16810777C2211yescharacteristic, complemented
140#16810777C2211yescharacteristic, complemented
141#16810777C2211yescharacteristic, complemented
142#16810775C2211yescharacteristic, complemented
143#16810774C2211yescharacteristic, complemented
144#16810772C2211yescharacteristic, complemented
145#16810772C2211yescharacteristic, complemented
146#16810772C2211yescharacteristic, complemented
147#16810772C2211yescharacteristic, complemented
148#16810772C2211yescharacteristic, complemented
149#16810769C2211yescharacteristic, complemented
150#16810768C2211yescharacteristic, complemented
151#16810767C2211yescharacteristic, complemented
152#16810766C2211yescharacteristic, complemented
153#16810765C2211yescharacteristic
154#16810765C2211yescharacteristic, complemented
155#16810765C2211yescharacteristic, complemented
156#16810763C2211yescharacteristic, complemented
157#16810762C2211yescharacteristic, complemented
158#16810755C2211yescharacteristic, complemented
159#16810755C2211yescharacteristic, complemented
160#16810728C2211yescharacteristic, complemented
161#16810724C2211yescharacteristic, complemented
162#16810723C2211yescharacteristic, complemented
163#16810720C2211yescharacteristic, complemented
164C4×Dic212C2211yescharacteristic, complemented
165#16810715C2211yescharacteristic, complemented
166D8×Dic53C2211yescharacteristic, complemented
167#16810702C2211yescharacteristic, complemented
168#16810699C2211yescharacteristic, complemented
169#16810698C2211yescharacteristic, complemented
170#16810695C2211yescharacteristic, complemented
171#16810693C2211yescharacteristic, complemented
172#16810692C2211yescharacteristic, complemented
173#16810691C2211yescharacteristic, complemented
174#16810683C2211yescharacteristic, complemented
175#16810682C2211yescharacteristic, complemented
176#16810630C2211yescharacteristic, complemented
177#16810626C2211yescharacteristic, complemented
178#16810626C2211yescharacteristic, complemented
179#16810625C2211yescharacteristic, complemented
180#16810625C2211yescharacteristic, complemented
181#16810624C2211yescharacteristic, complemented
182#16810616C2211yescharacteristic, complemented
183C2×#13133138C2211yescharacteristic, complemented
184#16810591C2211yescharacteristic, complemented
185#16810588C2211yescharacteristic, complemented
186#16810586C2211yescharacteristic, complemented
187#16810585C2211yescharacteristic, complemented
188C2×#137×C53C2211yescharacteristic, complemented
189C2×AGL(1,ℤ/8)×C53C2211yescharacteristic, complemented
190C53×#548C2211yescharacteristic, complemented
191C53×#546C2211yescharacteristic
192C53×#495C2211yescharacteristic, complemented
193C53×#470C2211yescharacteristic, complemented
194C53×#469C2211yescharacteristic, complemented
195C53×#464C2211yescharacteristic, complemented
196C53×#463C2211yescharacteristic, complemented
197C53×#452C2211yescharacteristic, complemented
198C53×#450C2211yescharacteristic, complemented
199C53×#449C2211yescharacteristic, complemented
200C53×#448C2211yescharacteristic, complemented
201C4×SD16×C53C2211yescharacteristic, complemented
202C53×#436C2211yescharacteristic, complemented
203#13133262—42no—
204#13133262—42no—
205C2×#11719949C2311yescharacteristic
206C2×#11719945—21no—
207C2×#11719945C2311yescharacteristic
208C2×#11719945C2311yescharacteristic
209C2×#11719945C2311yescharacteristic
210C2×#11719947—21no—
211C2×#11719947—21no—
212C2×#11719947C2311yescharacteristic
213C2×#11719947C2311yescharacteristic
214C2×#11719947C2311yescharacteristic
215#41×D53—42no—
216#41×D53—42no—
217C2×Q8×D53C2311yescharacteristic
218C2×Q8×D53C2311yescharacteristic
219C22×D212—21no—
220C22×C22⋊D53—21no—
221C22×C22⋊D53—21no—
222C22×C22⋊D53—21no—
223C2×D4×D53—21no—
224C2×D4×D53—21no—
225C2×D4×D53—21no—
226C2×D4×D53C2311yescharacteristic
227C2×D4×D53C2311yescharacteristic
228C2×D4×D53C2311yescharacteristic
229C22×C4×D53—21no—
230C22×C4×D53C2311yescharacteristic
231#13133248—42no—
232#13133246—42no—
233#13133246—42no—
234#13133241—42no—
235#13133237—42no—
236C2×Dic212C2311yescharacteristic
237C2×#11719925C2311yescharacteristic
238C2×#11719925C2311yescharacteristic
239C2×#11719925C2311yescharacteristic
240C2×#11719913C2311yescharacteristic
241C2×#11719913C2311yescharacteristic
242C2×#11719923C2311yescharacteristic
243C2×#11719923C2311yescharacteristic
244C2×#11719923C2311yescharacteristic
245C2×#11719924C2311yescharacteristic
246C2×#11719924C2311yescharacteristic
247C2×#11719924C2311yescharacteristic
248C2×#11719924C2311yescharacteristic
249SD16×D53—42no—
250C2×#11719922C2311yescharacteristic
251C2×#11719922C2311yescharacteristic
252C2×#11719917C2311yescharacteristic
253C2×#11719912C2311yescharacteristic
254C2×#11719912C2311yescharacteristic
255C2×#11719912C2311yescharacteristic
256C22×#88322C2311yescharacteristic
257C2×C8×D53C2311yescharacteristic
258#13133217C2311yescharacteristic
259#13133216—21no—
260#13133215—21no—
261#13133215C2311yescharacteristic
262#13133214C2311yescharacteristic
263#13133213—21no—
264#13133213—21no—
265#13133213C2311yescharacteristic
266#13133212—21no—
267#13133212—21no—
268#13133212—21no—
269#13133212—21no—
270#13133211—21no—
271#13133210—21no—
272#13133210—21no—
273#13133209—21no—
274#13133208—21no—
275#13133208—21no—
276#13133208C2311yescharacteristic
277#13133207—21no—
278#13133206C2311yescharacteristic
279#13133205—21no—
280#13133203—21no—
281#13133203—21no—
282#13133203—21no—
283#13133203—21no—
284#13133203—21no—
285#13133202—21no—
286#13133202D411yescharacteristic
287#13133201—21no—
288#13133201—21no—
289#13133201—21no—
290#13133200—21no—
291#13133200—21no—
292#13133199—21no—
293#13133199—21no—
294#13133199D411yescharacteristic
295#13133198—21no—
296#13133197C2311yescharacteristic
297#13133196—21no—
298#13133196—21no—
299#13133196C2311yescharacteristic
300#13133196C2311yescharacteristic
301#13133195—21no—
302#13133195—21no—
303#13133195D411yescharacteristic
304#13133194—21no—
305#13133194—21no—
306#13133194—21no—
307#13133194—21no—
308#13133194—21no—
309#13133194D411yescharacteristic
310#13133193—21no—
311#13133193—21no—
312#13133193—21no—
313#13133193C2311yescharacteristic
314#13133193C2311yescharacteristic
315#13133193C2311yescharacteristic
316#13133193C2311yescharacteristic
317#13133193C2311yescharacteristic
318#13133193C2311yescharacteristic
319#13133192—21no—
320#13133192C2311yescharacteristic
321#13133192C2311yescharacteristic
322#13133191—21no—
323#13133191—21no—
324#13133191C2311yescharacteristic
325#13133191C2311yescharacteristic
326#13133190—21no—
327#13133190—21no—
328#13133190—21no—
329#13133190—21no—
330#13133190—21no—
331#13133190—21no—
332#13133190—21no—
333#13133190—21no—
334#13133190—21no—
335#13133190—21no—
336#13133190—21no—
337#13133190D411yescharacteristic
338#13133189—21no—
339#13133189—21no—
340#13133189—21no—
341#13133189—21no—
342#13133189—21no—
343#13133189—21no—
344#13133189—21no—
345#13133189—21no—
346#13133189D411yescharacteristic
347#13133188C2311yescharacteristic
348#13133188C2311yescharacteristic
349#13133188C2311yescharacteristic
350#13133187—21no—
351#13133187—21no—
352#13133187—21no—
353#13133187—21no—
354#13133187D411yescharacteristic
355#13133186—21no—
356#13133185—21no—
357#13133185—21no—
358#13133185—21no—
359#13133185D411yescharacteristic
360Q8×Dic53C2311yescharacteristic
361C4×Dic106—21no—
362C4×Dic106C2311yescharacteristic
363C4×Dic106C2311yescharacteristic
364#13133182C2311yescharacteristic
365C4×D212C2311yescharacteristic
366D4×Dic53—21no—
367D4×Dic53—21no—
368D4×Dic53—21no—
369D4×Dic53C2311yescharacteristic
370D4×Dic53C2311yescharacteristic
371#13133179—21no—
372#13133179—21no—
373C4×C22⋊D53—21no—
374C4×C22⋊D53—21no—
375C4×C22⋊D53C2311yescharacteristic
376C4×C22⋊D53C2311yescharacteristic
377#13133177—21no—
378#13133177—21no—
379#13133177—21no—
380#13133177—21no—
381#13133177—21no—
382#13133175C2311yescharacteristic
383#13133175C2311yescharacteristic
384#13133174C2311yescharacteristic
385#13133173—21no—
386#13133173—21no—
387C2×C4⋊Dic53C2311yescharacteristic
388C2×C4⋊Dic53C2311yescharacteristic
389C2×#11719919—21no—
390C2×#11719919—21no—
391C2×#11719919—21no—
392C4⋊C4×D53C2311yescharacteristic
393C2×#11719921—21no—
394C2×#11719921—21no—
395C22⋊C4×D53—21no—
396#13133151C2311yescharacteristic
397#13133151C2311yescharacteristic
398#13133151C2311yescharacteristic
399#13133150C2311yescharacteristic
400#13133150C2311yescharacteristic
401#13133150C2311yescharacteristic
402#13133148C2311yescharacteristic
403C4⋊#88322C2311yescharacteristic
404#13133146C2311yescharacteristic
405#13133146C2311yescharacteristic
406#13133142C2311yescharacteristic
407#13133142C2311yescharacteristic
408#13133142C2311yescharacteristic
409#13133142C2311yescharacteristic
410#13133141C2311yescharacteristic
411#13133141C2311yescharacteristic
412#13133141C2311yescharacteristic
413#13133141C2311yescharacteristic
414#13133141C2311yescharacteristic
415#13133140C2311yescharacteristic
416#13133140C2311yescharacteristic
417#13133139C2311yescharacteristic
418#13133139C2311yescharacteristic
419#13133139C2311yescharacteristic
420#13133139C2311yescharacteristic
421#13133139C2311yescharacteristic
422#13133139C2311yescharacteristic
423#13133138C2311yescharacteristic
424#13133138C2311yescharacteristic
425#13133138C2311yescharacteristic
426#13133138C2311yescharacteristic
427#13133138C2311yescharacteristic
428#13133138C2311yescharacteristic
429#13133138C2311yescharacteristic
430#13133137C2311yescharacteristic
431#13133137C2311yescharacteristic
432C22⋊#88322C2311yescharacteristic
433C22⋊#88322C2311yescharacteristic
434#13133129C2311yescharacteristic
435#13133129C2311yescharacteristic
436#13133129C2311yescharacteristic
437#13133129C2311yescharacteristic
438#13133129C2311yescharacteristic
439#13133129C2311yescharacteristic
440#13133129C2311yescharacteristic
441#13133129C2311yescharacteristic
442#13133128C2311yescharacteristic
443#13133127C2311yescharacteristic
444C8×Dic53C2311yescharacteristic
445C2×#41×C53C2311yescharacteristic
446C2×#41×C53C2311yescharacteristic
447C22×Q8×C53C2311yescharacteristic
448C22×D4×C53C2311yescharacteristic
449#137×C53—42no—
450AGL(1,ℤ/8)×C53—42no—
451C2×Q16×C53C2311yescharacteristic
452C2×Q16×C53C2311yescharacteristic
453C2×SD16×C53C2311yescharacteristic
454C2×SD16×C53C2311yescharacteristic
455C2×SD16×C53C2311yescharacteristic
456C2×SD16×C53C2311yescharacteristic
457C2×SD16×C53C2311yescharacteristic
458C2×D8×C53C2311yescharacteristic
459C2×D8×C53C2311yescharacteristic
460C2×M16×C53C2311yescharacteristic
461C2×M16×C53C2311yescharacteristic
462#124×C53—21no—
463#124×C53C2311yescharacteristic
464#124×C53C2311yescharacteristic
465#123×C53—21no—
466C22⋊Q8×C53—21no—
467C22⋊Q8×C53C2311yescharacteristic
468C22⋊Q8×C53C2311yescharacteristic
469#121×C53—21no—
470#121×C53—21no—
471#121×C53C2311yescharacteristic
472#121×C53C2311yescharacteristic
473#120×C53—21no—
474C4×Q8×C53C2311yescharacteristic
475C4×D4×C53—21no—
476C4×D4×C53C2311yescharacteristic
477C4×D4×C53C2311yescharacteristic
478C2×C22⋊C4×C53—21no—
479#106×C53C2311yescharacteristic
480C4⋊C8×C53C2311yescharacteristic
481#103×C53C2311yescharacteristic
482#103×C53C2311yescharacteristic
483#103×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—
497#41×C53—41no—
498#41×C53—41no—
499C2×Q8×C53—21no—
500C2×Q8×C53—41no—
501C2×Q8×C53—41no—
502C2×Q8×C53C2411yescharacteristic
503C2×Q8×C53C2411yescharacteristic
504C2×Q8×C53C2411yescharacteristic
505C2×D4×C53—22no—
506C2×D4×C53—21no—
507C2×D4×C53—21no—
508C2×D4×C53—21no—
509C2×D4×C53—21no—
510C2×D4×C53—21no—
511C2×D4×C53—41no—
512C2×D4×C53C2×D411yescharacteristic
513C2×D4×C53C2411yescharacteristic
514C2×D4×C53C2411yescharacteristic
515C2×D4×C53C2411yescharacteristic
516C22×C4×C53—21no—
517C22×C4×C53—21no—
518C22×C4×C53—21no—
519C22×C4×C53—21no—
520C22×C4×C53C2411yescharacteristic
521C22×C4×C53C2411yescharacteristic
522C2×C22⋊D53—21no—
523C2×C22⋊D53—21no—
524C2×C22⋊D53—21no—
525C2×C22⋊D53—21no—
526C2×C22⋊D53—21no—
527C2×C22⋊D53—21no—
528C2×C22⋊D53—21no—
529C2×C22⋊D53—21no—
530C2×C22⋊D53—21no—
531C2×C22⋊D53—21no—
532C2×C22⋊D53—21no—
533C2×C22⋊D53—21no—
534C2×C22⋊D53—21no—
535C2×C22⋊D53—21no—
536C2×C22⋊D53—21no—
537C2×C22⋊D53—44no—
538C2×C22⋊D53—44no—
539C2×C22⋊D53—82no—
540C2×C22⋊D53C2×D411yescharacteristic
541C2×C22⋊D53C2×D411yescharacteristic
542C2×C22⋊D53C2×D411yescharacteristic
543C2×C22⋊D53C2×D411yescharacteristic
544C22×Dic53—21no—
545C22×Dic53—21no—
546C22×Dic53—21no—
547C22×Dic53—21no—
548C22×Dic53—21no—
549C22×Dic53—21no—
550C22×Dic53—21no—
551C22×Dic53C2×D411yescharacteristic
552#11719949—41no—
553#11719949—41no—
554Q8×D53—22no—
555Q8×D53—41no—
556Q8×D53—41no—
557Q8×D53—41no—
558#11719947—22no—
559#11719947—22no—
560#11719947—22no—
561#11719947—41no—
562#11719947—41no—
563#11719947—41no—
564#11719947—44no—
565#11719947—44no—
566D4×D53—22no—
567D4×D53—22no—
568D4×D53—41no—
569D4×D53—41no—
570D4×D53—41no—
571D4×D53—41no—
572D4×D53—44no—
573D4×D53—44no—
574D4×D53—82no—
575#11719945—22no—
576#11719945—22no—
577#11719945—41no—
578#11719945—41no—
579#11719945—41no—
580#11719945—41no—
581#11719945—44no—
582C2×D212—21no—
583C2×D212—21no—
584C2×D212—21no—
585C2×D212—21no—
586C2×D212—21no—
587C2×D212—82no—
588C2×D212C2×D411yescharacteristic
589C2×D212C2×D411yescharacteristic
590C2×D212C2411yescharacteristic
591C2×D212C2411yescharacteristic
592C2×C4×D53—21no—
593C2×C4×D53—21no—
594C2×C4×D53—21no—
595C2×C4×D53—21no—
596C2×C4×D53—21no—
597C2×C4×D53—21no—
598C2×C4×D53—41no—
599C2×C4×D53—41no—
600C2×C4×D53—44no—
601C2×C4×D53C2×D411yescharacteristic
602C2×C4×D53C2×D411yescharacteristic
603C2×C4×D53C2411yescharacteristic
604C2×C4×D53C2411yescharacteristic
605C2×C4×D53C2411yescharacteristic
606C2×Dic106—21no—
607C2×Dic106—21no—
608C2×Dic106—21no—
609C2×Dic106C2×D411yescharacteristic
610C2×Dic106C2411yescharacteristic
611C2×Dic106C2411yescharacteristic
612Q16×C53—41no—
613Q16×C53—41no—
614SD16×C53—22no—
615SD16×C53—22no—
616SD16×C53—41no—
617SD16×C53—41no—
618SD16×C53—41no—
619D8×C53—22no—
620D8×C53—41no—
621M16×C53—41no—
622M16×C53—41no—
623C2×C8×C53C2411yescharacteristic
624C2×C8×C53C2411yescharacteristic
625C2×C8×C53C2411yescharacteristic
626C2×C8×C53C2411yescharacteristic
627C4⋊C4×C53—21no—
628C4⋊C4×C53—21no—
629C4⋊C4×C53—21no—
630C4⋊C4×C53C2×D411yescharacteristic
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×C53—21no—
642C22⋊C4×C53C2×D411yescharacteristic
643C22⋊C4×C53C2×D411yescharacteristic
644C42×C53—21no—
645C42×C53C2411yescharacteristic
646C22⋊Dic53—21no—
647C22⋊Dic53—21no—
648C22⋊Dic53—21no—
649C22⋊Dic53—21no—
650C22⋊Dic53—21no—
651C22⋊Dic53—21no—
652C22⋊Dic53—21no—
653C22⋊Dic53C2×D411yescharacteristic
654C22⋊Dic53C2×D411yescharacteristic
655#11719925—22no—
656#11719925—22no—
657#11719925—41no—
658#11719924—41no—
659#11719924—41no—
660#11719924—41no—
661#11719924—41no—
662#11719923—22no—
663#11719923—22no—
664#11719923—41no—
665#11719922—41no—
666#11719922—41no—
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⋊Dic53C2×D411yescharacteristic
695C4⋊Dic53C2411yescharacteristic
696C4⋊Dic53C2411yescharacteristic
697C4⋊Dic53C2411yescharacteristic
698C4⋊Dic53C2411yescharacteristic
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#11719919—21no—
710#11719919—21no—
711#11719919—21no—
712#11719919—21no—
713#11719919—21no—
714#11719919C2×D411yescharacteristic
715#11719919C2×D411yescharacteristic
716#11719919C2×D411yescharacteristic
717#11719919C2×D411yescharacteristic
718C4×Dic53—21no—
719C4×Dic53—21no—
720C4×Dic53—21no—
721C4×Dic53—21no—
722C4×Dic53—21no—
723C4×Dic53—21no—
724C4×Dic53C2411yescharacteristic
725#11719917—41no—
726C2×#88322—41no—
727C2×#88322C2411yescharacteristic
728C2×#88322C2411yescharacteristic
729C2×#88322C2411yescharacteristic
730C2×#88322C2411yescharacteristic
731Dic212—22no—
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—81no—
743C23×C53—81no—
744C23×C53C22×D411yescharacteristic
745C23×C53C22×D411yescharacteristic
746C22×D53—21no—
747C22×D53—21no—
748C22×D53—41no—
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—
767Q8×C53—21no—
768Q8×C53—21no—
769Q8×C53—81no—
770D4×C53—21no—
771D4×C53—21no—
772D4×C53—21no—
773D4×C53—21no—
774D4×C53—21no—
775D4×C53—41no—
776D4×C53—42no—
777D4×C53—42no—
778D4×C53—42no—
779D4×C53—81no—
780D4×C53—81no—
781D4×C53H(5,𝔽2)12yes—
782C2×C4×C53—21no—
783C2×C4×C53—21no—
784C2×C4×C53—21no—
785C2×C4×C53—21no—
786C2×C4×C53—21no—
787C2×C4×C53—21no—
788C2×C4×C53—21no—
789C2×C4×C53—21no—
790C2×C4×C53—21no—
791C2×C4×C53—42no—
792C2×C4×C53—81no—
793C2×C4×C53—81no—
794C2×C4×C53—81no—
795C2×C4×C53C22×D411yescharacteristic
796C2×C4×C53C22×D411yescharacteristic
797C2×C4×C53C22×D411yescharacteristic
798C2×C4×C53C22×D411yescharacteristic
799C2×C4×C53C2511yescharacteristic
800C22⋊D53—24no—
801C22⋊D53—41no—
802C22⋊D53—41no—
803C22⋊D53—41no—
804C22⋊D53—41no—
805C22⋊D53—42no—
806C22⋊D53—42no—
807C22⋊D53—42no—
808C22⋊D53—42no—
809C22⋊D53—42no—
810C22⋊D53—42no—
811C22⋊D53—42no—
812C22⋊D53—81no—
813C22⋊D53—81no—
814C22⋊D53—81no—
815C22⋊D53—81no—
816C22⋊D53—81no—
817C22⋊D53—81no—
818C22⋊D53—81no—
819C2×Dic53—24no—
820C2×Dic53—21no—
821C2×Dic53—21no—
822C2×Dic53—21no—
823C2×Dic53—21no—
824C2×Dic53—21no—
825C2×Dic53—21no—
826C2×Dic53—41no—
827C2×Dic53—42no—
828C2×Dic53—81no—
829C2×Dic53—81no—
830C2×Dic53—81no—
831C2×Dic53—81no—
832C2×Dic53—81no—
833C2×Dic53C22×D411yescharacteristic
834C2×Dic53C22×D411yescharacteristic
835C2×Dic53C22×D411yescharacteristic
836C2×Dic53C22×D411yescharacteristic
837C2×Dic53C22×D411yescharacteristic
838D212—21no—
839D212—21no—
840D212—21no—
841D212—21no—
842D212—41no—
843D212—41no—
844D212—42no—
845D212—42no—
846D212—81no—
847D212—81no—
848D212—81no—
849C4×D53—21no—
850C4×D53—21no—
851C4×D53—21no—
852C4×D53—21no—
853C4×D53—21no—
854C4×D53—21no—
855C4×D53—41no—
856C4×D53—41no—
857C4×D53—42no—
858C4×D53—42no—
859C4×D53—42no—
860C4×D53—42no—
861C4×D53—81no—
862C4×D53—81no—
863Dic106—21no—
864Dic106—21no—
865Dic106—21no—
866Dic106—41no—
867Dic106—42no—
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—162no—
896C22×C53C23×D411yescharacteristic
897C2×D53—21no—
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—41no—
907C2×D53—41no—
908C2×D53—41no—
909C2×D53—41no—
910C2×D53—41no—
911C2×D53—41no—
912C2×D53—82no—
913C2×D53—84no—
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#3310—531no—
947#3309—531no—
948#3278—531no—
949#3277—531no—
950#3275D5311yescharacteristic, complemented
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—42no—
970C2×C53—41no—
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×#137C2×D5311yescharacteristic, complemented
988C2×AGL(1,ℤ/8)—531no—
989C2×AGL(1,ℤ/8)C2×D5311yescharacteristic, complemented
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#552—531no—
1000#550—531no—
1001#550—531no—
1002D4×Q8—531no—
1003#548—531no—
1004#548—531no—
1005#548—531no—
1006#548C2×D5311yescharacteristic, complemented
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#495C2×D5311yescharacteristic, complemented
1038#492—531no—
1039#490—531no—
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#482—531no—
1051#480—531no—
1052#480—531no—
1053#480—531no—
1054#480—531no—
1055#479—531no—
1056#478—531no—
1057#477—531no—
1058#474—531no—
1059#470C2×D5311yescharacteristic, complemented
1060#469—531no—
1061#469C2×D5311yescharacteristic, complemented
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#468—531no—
1071#467—531no—
1072#467—531no—
1073#466—531no—
1074#465—531no—
1075#464—531no—
1076#464—531no—
1077#464—531no—
1078#464C2×D5311yescharacteristic, complemented
1079#463—531no—
1080#463C2×D5311yescharacteristic, complemented
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#452C2×D5311yescharacteristic, complemented
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#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#449—531no—
1117#449C2×D5311yescharacteristic, complemented
1118#448—531no—
1119#448—531no—
1120#448C2×D5311yescharacteristic, complemented
1121#447—531no—
1122#447—531no—
1123#441—531no—
1124#440—531no—
1125#440—531no—
1126#440—531no—
1127C4×Q16—531no—
1128C4×Q16—531no—
1129C4×SD16C2×D5311yescharacteristic, complemented
1130C4×D8—531no—
1131#436—531no—
1132#436—531no—
1133#436—531no—
1134#436C2×D5311yescharacteristic, complemented
1135#435—531no—
1136#435—531no—
1137#435—531no—
1138#435—531no—
1139#433—531no—
1140#433—531no—
1141#419—531no—
1142#418—531no—
1143#418—531no—
1144#417—531no—
1145#417—531no—
1146#417—531no—
1147#416—531no—
1148C2×#102—531no—
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—1061no—
1164C2×#41—1061no—
1165C2×#41—1061no—
1166C2×#41—2122no—
1167C2×#41—2122no—
1168C2×#41C22×D5311yescharacteristic
1169C2×#41C22×D5311yescharacteristic
1170C22×Q8—531no—
1171C22×Q8—531no—
1172C22×Q8C22×D5311yescharacteristic
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—42no—
1187#137—2122no—
1188#137—2122no—
1189#137—2122no—
1190AGL(1,ℤ/8)—42no—
1191AGL(1,ℤ/8)—2122no—
1192#135—2122no—
1193C2×Q16—531no—
1194C2×Q16—531no—
1195C2×Q16—531no—
1196C2×Q16—531no—
1197C2×Q16C22×D5311yescharacteristic
1198C2×Q16C22×D5311yescharacteristic
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—2122no—
1209C2×SD16C22×D5311yescharacteristic
1210C2×SD16C22×D5311yescharacteristic
1211C2×SD16C22×D5311yescharacteristic
1212C2×SD16C22×D5311yescharacteristic
1213C2×SD16C22×D5311yescharacteristic
1214C2×D8—531no—
1215C2×D8—531no—
1216C2×D8C22×D5311yescharacteristic
1217C2×D8C22×D5311yescharacteristic
1218C2×M16—531no—
1219C2×M16—531no—
1220C2×M16—531no—
1221C2×M16—531no—
1222C2×M16C22×D5311yescharacteristic
1223C2×M16C22×D5311yescharacteristic
1224C22×C8—531no—
1225C22×C8—531no—
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—1061no—
1235#126—1061no—
1236#126—1061no—
1237#126—1061no—
1238#126—1061no—
1239#126—1061no—
1240#126—1061no—
1241#125—531no—
1242#125—1061no—
1243#125—1061no—
1244#125—1061no—
1245#125—1061no—
1246#124—21no—
1247#124—531no—
1248#124—1061no—
1249#124—1061no—
1250#124—1061no—
1251#124—1061no—
1252#124—1061no—
1253#124—1061no—
1254#124C22×D5311yescharacteristic
1255#124C22×D5311yescharacteristic
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—21no—
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—531no—
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—21no—
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#121C22×D5311yescharacteristic
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—21no—
1347C4×D4—531no—
1348C4×D4—531no—
1349C4×D4—531no—
1350C4×D4—531no—
1351C4×D4—531no—
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—531no—
1367#117—531no—
1368#117—531no—
1369#117—1061no—
1370#117—1061no—
1371C2×C4⋊C4—531no—
1372C2×C4⋊C4—531no—
1373C2×C4⋊C4—531no—
1374C2×C4⋊C4—1061no—
1375C2×C4⋊C4—1061no—
1376C2×C4⋊C4—1061no—
1377C2×C22⋊C4—21no—
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#107—531no—
1386#107—531no—
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#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#102—531no—
1420#102—531no—
1421#102—531no—
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—41no—
1449#41—41no—
1450#41—1062no—
1451#41—1062no—
1452#41—1062no—
1453#41—1062no—
1454#41—1062no—
1455#41—2121no—
1456#41—2121no—
1457#41—2121no—
1458#41—2121no—
1459#41—2124no—
1460#41—2121no—
1461#41—2121no—
1462#41—2121no—
1463#41—2124no—
1464#41—2124no—
1465#41—2121no—
1466#41—2121no—
1467C2×Q8—21no—
1468C2×Q8—41no—
1469C2×Q8—41no—
1470C2×Q8—531no—
1471C2×Q8—531no—
1472C2×Q8—531no—
1473C2×Q8—1061no—
1474C2×Q8—1061no—
1475C2×Q8—1061no—
1476C2×Q8—1062no—
1477C2×Q8—2121no—
1478C2×Q8—2121no—
1479C2×Q8—2121no—
1480C2×Q8C23×D5311yescharacteristic
1481C2×Q8C23×D5311yescharacteristic
1482C2×Q8C23×D5311yescharacteristic
1483C2×D4—22no—
1484C2×D4—21no—
1485C2×D4—21no—
1486C2×D4—21no—
1487C2×D4—21no—
1488C2×D4—21no—
1489C2×D4—41no—
1490C2×D4—531no—
1491C2×D4—531no—
1492C2×D4—531no—
1493C2×D4—531no—
1494C2×D4—531no—
1495C2×D4—531no—
1496C2×D4—531no—
1497C2×D4—531no—
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—1062no—
1508C2×D4—1062no—
1509C2×D4—1061no—
1510C2×D4—1061no—
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—4242no—
1521C2×D4—4242no—
1522C2×D4—4242no—
1523C2×D4—2121no—
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—21no—
1538C22×C4—21no—
1539C22×C4—531no—
1540C22×C4—531no—
1541C22×C4—531no—
1542C22×C4—531no—
1543C22×C4—531no—
1544C22×C4—531no—
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—41no—
1565Q16—1062no—
1566Q16—1062no—
1567Q16—1062no—
1568Q16—2121no—
1569SD16—22no—
1570SD16—22no—
1571SD16—41no—
1572SD16—41no—
1573SD16—41no—
1574SD16—1062no—
1575SD16—1062no—
1576SD16—2121no—
1577SD16—2121no—
1578SD16—2121no—
1579SD16—2121no—
1580SD16—2121no—
1581SD16—2121no—
1582SD16—2121no—
1583D8—22no—
1584D8—41no—
1585D8—2121no—
1586D8—2121no—
1587M16—41no—
1588M16—41no—
1589M16—2121no—
1590M16—2121no—
1591M16—2121no—
1592M16—2121no—
1593C2×C8—531no—
1594C2×C8—531no—
1595C2×C8—531no—
1596C2×C8—531no—
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—531no—
1607C4⋊C4—531no—
1608C4⋊C4—531no—
1609C4⋊C4—531no—
1610C4⋊C4—531no—
1611C4⋊C4—531no—
1612C4⋊C4—531no—
1613C4⋊C4—531no—
1614C4⋊C4—531no—
1615C4⋊C4—1061no—
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⋊C4—1061no—
1635C4⋊C4—1061no—
1636C4⋊C4D4×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—21no—
1648C22⋊C4—531no—
1649C22⋊C4—531no—
1650C22⋊C4—531no—
1651C22⋊C4—531no—
1652C22⋊C4—531no—
1653C22⋊C4—531no—
1654C22⋊C4—531no—
1655C22⋊C4—531no—
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—531no—
1682C42—1061no—
1683C42—1061no—
1684C42—1061no—
1685C42—1061no—
1686C42—1061no—
1687C42—1061no—
1688C42C23×D5311yescharacteristic
1689C23—21no—
1690C23—21no—
1691C23—21no—
1692C23—42no—
1693C23—81no—
1694C23—81no—
1695C23—531no—
1696C23—531no—
1697C23—531no—
1698C23—1061no—
1699C23—1061no—
1700C23—4241no—
1701C23—4241no—
1702C23—4241no—
1703C23—4241no—
1704C23—4241no—
1705C23—2122no—
1706C23—2121no—
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—21no—
1719Q8—21no—
1720Q8—81no—
1721Q8—532no—
1722Q8—1061no—
1723Q8—1061no—
1724Q8—1061no—
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—1064no—
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—2121no—
1756D4—2121no—
1757D4—2122no—
1758D4—2122no—
1759D4—2121no—
1760D4—2121no—
1761D4—2121no—
1762D4—2121no—
1763D4—2122no—
1764D4—2122no—
1765D4—2122no—
1766D4—2122no—
1767D4—2122no—
1768D4—2122no—
1769D4—2122no—
1770D4#1313326212yes—
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—42no—
1781C2×C4—81no—
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—1061no—
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—41no—
1843C22—41no—
1844C22—41no—
1845C22—162no—
1846C22—8482no—
1847C22—8482no—
1848C22—1061no—
1849C22—1061no—
1850C22—1061no—
1851C22—1061no—
1852C22—1061no—
1853C22—1061no—
1854C22—1061no—
1855C22—1061no—
1856C22—1061no—
1857C22—4244no—
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×#1313326211yescharacteristic
1888C2—41no—
1889C2—41no—
1890C2—42no—
1891C2—81no—
1892C2—81no—
1893C2—4241no—
1894C2—4241no—
1895C2—2121no—
1896C2—2121no—
1897C2—2121no—
1898C2#2028834311yescharacteristic
1899C2#2028949311yescharacteristic
1900C2#2028949911yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3275C2
socleC22×C53C23×D4
hypercenter#3275D53
hypocenterC53#61654
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3275

Complements

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

NH ≅ G/Ntype
1. #20288994C2semidirect
2. #20288378C2semidirect
3. #20287054C2semidirect
4. #20286978C2semidirect
5. #20286948C2semidirect
6. #20286909C2semidirect
7. #20286796C2semidirect
8. #20286788C2semidirect
9. #20286740C2semidirect
10. #20286716C2semidirect
11. #20286379C2semidirect
12. #20286370C2semidirect
13. #20286309C2semidirect
14. #20286301C2semidirect
15. #20286274C2semidirect
16. #20286219C2semidirect
17. #20286216C2semidirect
18. #20285802C2semidirect
19. #20285784C2semidirect
20. #20285616C2semidirect
21. #20285598C2semidirect
22. #20285524C2semidirect
23. #20285519C2semidirect
24. #20284974C2semidirect
25. #20284925C2semidirect
26. #20284018C2semidirect
27. #20283987C2semidirect
28. #20283971C2semidirect
29. #20283953C2semidirect
30. #20283772C2semidirect
31. C53×#3275C2semidirect
34. C2×#13133248C22semidirect
35. C2×#13133246C22semidirect
36. C2×#13133246C22semidirect
37. C2×#13133241C22semidirect
38. C2×#13133237C22semidirect
39. C2×SD16×D53C22semidirect
42. #16811346C22semidirect
44. #16811330C22semidirect
45. #16811325C22semidirect
47. #16811315C22semidirect
50. Q8×C22⋊D53C22semidirect
53. #16811281C22semidirect
54. #16811272C22semidirect
62. #16811242C22semidirect
64. #16811231C22semidirect
69. #16811201C22semidirect
71. #16811196C22semidirect
74. #16811133C22semidirect
77. C2×#13133193C22semidirect
81. #16811016C22semidirect
82. #16811013C22semidirect
83. #16810994C22semidirect
84. #16810986C22semidirect
85. #16810982C22semidirect
86. #16810979C22semidirect
87. #16810970C22semidirect
88. #16810963C22semidirect
89. #16810957C22semidirect
90. #16810957C22semidirect
91. #16810956C22semidirect
92. #16810955C22semidirect
93. #16810949C22semidirect
94. #16810949C22semidirect
95. #16810945C22semidirect
96. #16810937C22semidirect
97. #16810937C22semidirect
98. #16810935C22semidirect
99. #16810934C22semidirect
100. #16810933C22semidirect
101. #16810921C22semidirect
102. #16810919C22semidirect
103. #16810903C22semidirect
104. #16810874C22semidirect
105. #16810872C22semidirect
106. #16810872C22semidirect
107. #16810872C22semidirect
108. #16810869C22semidirect
109. #16810869C22semidirect
110. #16810867C22semidirect
111. #16810866C22semidirect
112. #16810866C22semidirect
113. #16810866C22semidirect
114. #16810862C22semidirect
115. #16810861C22semidirect
116. #16810858C22semidirect
117. #16810854C22semidirect
118. #16810847C22semidirect
119. #16810842C22semidirect
120. #16810842C22semidirect
121. #16810840C22semidirect
122. #16810832C22semidirect
123. #16810826C22semidirect
124. #16810824C22semidirect
125. #16810823C22semidirect
126. #16810821C22semidirect
127. #16810816C22semidirect
128. #16810788C22semidirect
129. #16810787C22semidirect
130. #16810787C22semidirect
132. #16810785C22semidirect
133. #16810784C22semidirect
134. #16810784C22semidirect
135. #16810783C22semidirect
138. #16810782C22semidirect
139. #16810777C22semidirect
140. #16810777C22semidirect
141. #16810777C22semidirect
142. #16810775C22semidirect
143. #16810774C22semidirect
144. #16810772C22semidirect
145. #16810772C22semidirect
146. #16810772C22semidirect
147. #16810772C22semidirect
148. #16810772C22semidirect
149. #16810769C22semidirect
150. #16810768C22semidirect
151. #16810767C22semidirect
152. #16810766C22semidirect
154. #16810765C22semidirect
155. #16810765C22semidirect
156. #16810763C22semidirect
157. #16810762C22semidirect
158. #16810755C22semidirect
159. #16810755C22semidirect
160. #16810728C22semidirect
161. #16810724C22semidirect
162. #16810723C22semidirect
163. #16810720C22semidirect
164. C4×Dic212C22semidirect
165. #16810715C22semidirect
166. D8×Dic53C22semidirect
167. #16810702C22semidirect
168. #16810699C22semidirect
169. #16810698C22semidirect
170. #16810695C22semidirect
171. #16810693C22semidirect
172. #16810692C22semidirect
173. #16810691C22semidirect
174. #16810683C22semidirect
175. #16810682C22semidirect
176. #16810630C22semidirect
177. #16810626C22semidirect
178. #16810626C22semidirect
179. #16810625C22semidirect
180. #16810625C22semidirect
181. #16810624C22semidirect
182. #16810616C22semidirect
183. C2×#13133138C22semidirect
184. #16810591C22semidirect
185. #16810588C22semidirect
186. #16810586C22semidirect
187. #16810585C22semidirect
188. C2×#137×C53C22semidirect
189. C2×AGL(1,ℤ/8)×C53C22semidirect
190. C53×#548C22semidirect
192. C53×#495C22semidirect
193. C53×#470C22semidirect
194. C53×#469C22semidirect
195. C53×#464C22semidirect
196. C53×#463C22semidirect
197. C53×#452C22semidirect
198. C53×#450C22semidirect
199. C53×#449C22semidirect
200. C53×#448C22semidirect
201. C4×SD16×C53C22semidirect
202. C53×#436C22semidirect
950. #3275D53semidirect
987. C2×#137C2×D53semidirect
989. C2×AGL(1,ℤ/8)C2×D53semidirect
1006. #548C2×D53semidirect
1037. #495C2×D53semidirect
1059. #470C2×D53semidirect
1061. #469C2×D53semidirect
1078. #464C2×D53semidirect
1080. #463C2×D53semidirect
1098. #452C2×D53semidirect
1109. #450C2×D53semidirect
1117. #449C2×D53semidirect
1120. #448C2×D53semidirect
1129. C4×SD16C2×D53semidirect
1134. #436C2×D53semidirect
1153. C53#61654semidirect

Maximal subgroups

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

subgroupindex
#202889942
#202883782
#202870542
#202869782
#202869482
#202869092
#202867962
#202867882
#202867402
#202867162
#202863792
#202863702
#202863092
#202863012
#202862742
#202862192
#202862162
#202858022
#202857842
#202856162
#202855982
#202855242
#202855192
#202849742
#202849252
#202840182
#202839872
#202839712
#202839532
#202837722
C53×#32752
#6165453