Finite Group Databasebeta

← #28270097

Subgroups — #28270097

Order 13568.

2050 conjugacy classes of subgroups.

The subgroup lattice has 1868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288987C211yesmaximal, characteristic, complemented
2#20288396C211yesmaximal, characteristic, complemented
3#20287011C211yesmaximal, characteristic, complemented
4#20286995C211yesmaximal, characteristic, complemented
5#20286898C211yesmaximal, characteristic, complemented
6#20286876C211yesmaximal, characteristic, complemented
7#20286786C211yesmaximal, characteristic, complemented
8#20286748C211yesmaximal, characteristic, complemented
9#20286640C211yesmaximal, characteristic, complemented
10#20286634C211yesmaximal, characteristic, complemented
11#20286451C211yesmaximal, characteristic, complemented
12#20286424C211yesmaximal, characteristic, complemented
13#20286348C211yesmaximal, characteristic, complemented
14#20286321C211yesmaximal, characteristic, complemented
15#20286287C211yesmaximal, characteristic, complemented
16#20286276C211yesmaximal, characteristic, complemented
17#20286242C211yesmaximal, characteristic, complemented
18#20286220C211yesmaximal, characteristic, complemented
19#20285826C211yesmaximal, characteristic, complemented
20#20285818C211yesmaximal, characteristic, complemented
21#20285604C211yesmaximal, characteristic, complemented
22#20285572C211yesmaximal, characteristic, complemented
23#20285544C211yesmaximal, characteristic, complemented
24#20285501C211yesmaximal, characteristic, complemented
25#20284977C211yesmaximal, characteristic, complemented
26#20284007C211yesmaximal, characteristic, complemented
27#20283998C211yesmaximal, characteristic, complemented
28#20283958C211yesmaximal, characteristic, complemented
29#20283930C211yesmaximal, characteristic, complemented
30#20283761C211yesmaximal, characteristic, complemented
31C53×#3125C211yesmaximal, characteristic, complemented
32C2×#13133264C2211yescharacteristic
33C2×#41×D53C2211yescharacteristic, complemented
34C2×#13133249C2211yescharacteristic
35C2×#13133246C2211yescharacteristic, complemented
36C2×#13133244C2211yescharacteristic
37C2×#13133241C2211yescharacteristic, complemented
38C2×#13133238C2211yescharacteristic
39C2×#13133236C2211yescharacteristic
40C2×Q16×D53C2211yescharacteristic, complemented
41C2×SD16×D53C2211yescharacteristic, complemented
42#16811365—21no—
43#16811363—21no—
44#16811355—21no—
45#16811347C2211yescharacteristic
46#16811346C2211yescharacteristic, complemented
47#16811339C2211yescharacteristic, complemented
48#16811338C2211yescharacteristic
49#16811296—21no—
50Q8×D212C2211yescharacteristic
51Q8×D212C2211yescharacteristic, complemented
52#16811285C2211yescharacteristic
53#16811285C2211yescharacteristic
54#16811285C2211yescharacteristic, complemented
55#16811281C2211yescharacteristic, complemented
56#16811277—21no—
57#16811277—21no—
58#16811277C2211yescharacteristic
59#16811277C2211yescharacteristic, complemented
60#16811268—21no—
61#16811268—21no—
62#16811268C2211yescharacteristic
63#16811268C2211yescharacteristic, complemented
64#16811268C2211yescharacteristic, complemented
65#16811266C2211yescharacteristic
66#16811246—21no—
67#16811244C2211yescharacteristic, complemented
68#16811239—21no—
69#16811213—21no—
70#16811212—21no—
71#16811204—21no—
72#16811204C2211yescharacteristic
73#16811199—21no—
74#16811199C2211yescharacteristic, complemented
75#16811196C2211yescharacteristic, complemented
76#16811189C2211yescharacteristic, complemented
77#16811136C2211yescharacteristic
78#16811135—21no—
79#16811135C2211yescharacteristic
80#16811133C2211yescharacteristic
81C2×#13133197—21no—
82C2×#13133197C2211yescharacteristic, complemented
83#16811018C2211yescharacteristic, complemented
84#16811017C2211yescharacteristic, complemented
85#16811007C2211yescharacteristic, complemented
86#16811005C2211yescharacteristic, complemented
87#16810985C2211yescharacteristic, complemented
88#16810983C2211yescharacteristic, complemented
89#16810975C2211yescharacteristic, complemented
90#16810974C2211yescharacteristic, complemented
91#16810967C2211yescharacteristic, complemented
92#16810967C2211yescharacteristic, complemented
93#16810967C2211yescharacteristic, complemented
94#16810967C2211yescharacteristic, complemented
95#16810967C2211yescharacteristic, complemented
96#16810967C2211yescharacteristic, complemented
97#16810958C2211yescharacteristic, complemented
98#16810949C2211yescharacteristic, complemented
99#16810949C2211yescharacteristic, complemented
100#16810936C2211yescharacteristic, complemented
101#16810918C2211yescharacteristic, complemented
102#16810903C2211yescharacteristic, complemented
103#16810882C2211yescharacteristic, complemented
104#16810882C2211yescharacteristic, complemented
105#16810882C2211yescharacteristic, complemented
106#16810877C2211yescharacteristic, complemented
107#16810872C2211yescharacteristic, complemented
108#16810868C2211yescharacteristic
109#16810868C2211yescharacteristic
110#16810868C2211yescharacteristic, complemented
111#16810863C2211yescharacteristic, complemented
112#16810863C2211yescharacteristic, complemented
113#16810863C2211yescharacteristic, complemented
114#16810858C2211yescharacteristic, complemented
115#16810853C2211yescharacteristic, complemented
116#16810853C2211yescharacteristic, complemented
117#16810853C2211yescharacteristic, complemented
118#16810853C2211yescharacteristic, complemented
119#16810846C2211yescharacteristic, complemented
120#16810845C2211yescharacteristic, complemented
121#16810845C2211yescharacteristic, complemented
122#16810839C2211yescharacteristic, complemented
123#16810838C2211yescharacteristic, complemented
124#16810838C2211yescharacteristic, complemented
125#16810834C2211yescharacteristic, complemented
126#16810833C2211yescharacteristic, complemented
127#16810829C2211yescharacteristic, complemented
128#16810828C2211yescharacteristic, complemented
129#16810788C2211yescharacteristic
130#16810788C2211yescharacteristic
131#16810787C2211yescharacteristic, complemented
132#16810786C2211yescharacteristic, complemented
133#16810786C2211yescharacteristic, complemented
134#16810786C2211yescharacteristic, complemented
135#16810785C2211yescharacteristic, complemented
136#16810784C2211yescharacteristic, complemented
137#16810783C2211yescharacteristic, complemented
138#16810782C2211yescharacteristic, complemented
139#16810782C2211yescharacteristic, complemented
140#16810781C2211yescharacteristic, complemented
141#16810780C2211yescharacteristic, complemented
142#16810780C2211yescharacteristic, complemented
143#16810780C2211yescharacteristic, complemented
144#16810778C2211yescharacteristic, complemented
145#16810777C2211yescharacteristic, complemented
146#16810775C2211yescharacteristic, complemented
147#16810775C2211yescharacteristic, complemented
148#16810771C2211yescharacteristic
149#16810770C2211yescharacteristic
150#16810769C2211yescharacteristic
151#16810769C2211yescharacteristic, complemented
152#16810768C2211yescharacteristic
153#16810766C2211yescharacteristic
154#16810765C2211yescharacteristic, complemented
155#16810764C2211yescharacteristic, complemented
156#16810763C2211yescharacteristic, complemented
157#16810763C2211yescharacteristic, complemented
158#16810761C2211yescharacteristic, complemented
159#16810760C2211yescharacteristic
160#16810760C2211yescharacteristic, complemented
161#16810758C2211yescharacteristic, complemented
162#16810755C2211yescharacteristic
163#16810723C2211yescharacteristic, complemented
164#16810721C2211yescharacteristic, complemented
165C4×#11719925C2211yescharacteristic, complemented
166C4×#11719922C2211yescharacteristic, complemented
167#16810702C2211yescharacteristic, complemented
168#16810700C2211yescharacteristic
169#16810696C2211yescharacteristic, complemented
170#16810696C2211yescharacteristic, complemented
171#16810693C2211yescharacteristic
172#16810693C2211yescharacteristic, complemented
173C8×D212C2211yescharacteristic, complemented
174#16810688C2211yescharacteristic, complemented
175#16810684C2211yescharacteristic, complemented
176#16810630C2211yescharacteristic, complemented
177#16810630C2211yescharacteristic, complemented
178#16810630C2211yescharacteristic, complemented
179#16810626C2211yescharacteristic, complemented
180#16810618C2211yescharacteristic, complemented
181#16810616C2211yescharacteristic, complemented
182#16810616C2211yescharacteristic, complemented
183#16810616C2211yescharacteristic, complemented
184#16810588C2211yescharacteristic, complemented
185#16810588C2211yescharacteristic, complemented
186#16810585C2211yescharacteristic, complemented
187C22⋊C8×D53C2211yescharacteristic, complemented
188C53×#542C2211yescharacteristic, complemented
189C53×#520C2211yescharacteristic, complemented
190C53×#483C2211yescharacteristic, complemented
191C53×#481C2211yescharacteristic, complemented
192C53×#476C2211yescharacteristic, complemented
193C53×#475C2211yescharacteristic, complemented
194C53×#464C2211yescharacteristic, complemented
195C53×#463C2211yescharacteristic, complemented
196C53×#452C2211yescharacteristic, complemented
197C53×#449C2211yescharacteristic
198C53×#442C2211yescharacteristic, complemented
199C53×#441C2211yescharacteristic, complemented
200C4×SD16×C53C2211yescharacteristic, complemented
201C4×SD16×C53C2211yescharacteristic, complemented
202C53×#433C2211yescharacteristic, complemented
203#13133264—42no—
204#13133264—42no—
205C2×#11719949C2311yescharacteristic
206C2×#11719949C2311yescharacteristic
207C2×#11719945—21no—
208C2×#11719945—21no—
209C2×#11719945C2311yescharacteristic
210C2×#11719945C2311yescharacteristic
211C2×#11719947—21no—
212C2×#11719947—21no—
213C2×#11719947—21no—
214C2×#11719947C2311yescharacteristic
215C2×#11719947C2311yescharacteristic
216C2×#11719947C2311yescharacteristic
217C2×#11719947C2311yescharacteristic
218#41×D53—42no—
219#41×D53—42no—
220C22×Dic106—21no—
221C22×Dic106C2311yescharacteristic
222C2×Q8×D53C2311yescharacteristic
223C2×Q8×D53C2311yescharacteristic
224C2×Q8×D53C2311yescharacteristic
225C2×Q8×D53C2311yescharacteristic
226C2×D4×D53—21no—
227C2×D4×D53C2311yescharacteristic
228C2×D4×D53C2311yescharacteristic
229C22×C4×D53—21no—
230C22×C4×D53C2311yescharacteristic
231#13133249—42no—
232#13133246—42no—
233#13133244—42no—
234#13133241—42no—
235#13133238—42no—
236#13133236—42no—
237C2×Dic212C2311yescharacteristic
238C2×Dic212C2311yescharacteristic
239C2×Dic212C2311yescharacteristic
240C2×#11719925C2311yescharacteristic
241C2×#11719925C2311yescharacteristic
242C2×#11719925C2311yescharacteristic
243C2×#11719925C2311yescharacteristic
244Q16×D53—42no—
245C2×#11719913C2311yescharacteristic
246C2×#11719913C2311yescharacteristic
247C2×#11719913C2311yescharacteristic
248C2×#11719913C2311yescharacteristic
249C2×#11719923C2311yescharacteristic
250C2×#11719923C2311yescharacteristic
251C2×#11719923C2311yescharacteristic
252C2×#11719923C2311yescharacteristic
253C2×#11719924C2311yescharacteristic
254C2×#11719924C2311yescharacteristic
255SD16×D53—42no—
256C2×D424C2311yescharacteristic
257C2×#11719922C2311yescharacteristic
258C2×#11719922C2311yescharacteristic
259C2×#11719912C2311yescharacteristic
260C2×#11719912C2311yescharacteristic
261C2×#11719912C2311yescharacteristic
262C2×#11719912C2311yescharacteristic
263C2×C8×D53C2311yescharacteristic
264C2×C8×D53C2311yescharacteristic
265C2×C8×D53C2311yescharacteristic
266C2×C8×D53C2311yescharacteristic
267#13133217—21no—
268#13133217—21no—
269#13133217C2311yescharacteristic
270#13133217C2311yescharacteristic
271#13133217C2311yescharacteristic
272#13133216—21no—
273#13133213—21no—
274#13133212—21no—
275#13133212—21no—
276#13133212—21no—
277#13133212—21no—
278#13133212—21no—
279#13133206—21no—
280#13133206—21no—
281#13133206—21no—
282#13133205—21no—
283#13133205—21no—
284#13133205—21no—
285#13133205—21no—
286#13133205C2311yescharacteristic
287#13133205C2311yescharacteristic
288#13133205C2311yescharacteristic
289#13133203—21no—
290#13133203—21no—
291#13133203—21no—
292#13133203—21no—
293#13133203—21no—
294#13133203—21no—
295#13133202—21no—
296#13133202—21no—
297#13133201—21no—
298#13133201—21no—
299#13133201—21no—
300#13133201—21no—
301#13133201—21no—
302#13133201—21no—
303#13133201—21no—
304#13133201—21no—
305#13133201—21no—
306#13133201D411yescharacteristic
307#13133201D411yescharacteristic
308#13133199—21no—
309#13133199—21no—
310#13133199—21no—
311#13133199—21no—
312#13133197—21no—
313#13133197—21no—
314#13133197—21no—
315#13133197—21no—
316#13133197—21no—
317#13133197—21no—
318#13133197—21no—
319#13133197—21no—
320#13133197—21no—
321#13133197—21no—
322#13133197—21no—
323#13133197—21no—
324#13133197D411yescharacteristic
325#13133197D411yescharacteristic
326#13133197C2311yescharacteristic
327#13133197C2311yescharacteristic
328#13133197C2311yescharacteristic
329#13133197C2311yescharacteristic
330#13133197C2311yescharacteristic
331#13133197C2311yescharacteristic
332#13133197C2311yescharacteristic
333#13133197C2311yescharacteristic
334#13133196C2311yescharacteristic
335#13133195—21no—
336#13133194—21no—
337#13133193C2311yescharacteristic
338#13133193C2311yescharacteristic
339#13133192—21no—
340#13133192—21no—
341#13133192—21no—
342#13133192—21no—
343#13133192—21no—
344#13133192D411yescharacteristic
345#13133192D411yescharacteristic
346#13133192C2311yescharacteristic
347#13133192C2311yescharacteristic
348#13133192C2311yescharacteristic
349#13133192C2311yescharacteristic
350#13133191—21no—
351#13133191—21no—
352#13133191—21no—
353#13133191—21no—
354#13133191—21no—
355#13133191—21no—
356#13133191—21no—
357#13133191—21no—
358#13133191C2311yescharacteristic
359#13133190—21no—
360#13133190—21no—
361#13133188C2311yescharacteristic
362#13133188C2311yescharacteristic
363#13133187—21no—
364#13133187—21no—
365#13133187—21no—
366#13133187—21no—
367#13133187—21no—
368#13133187—21no—
369#13133187D411yescharacteristic
370#13133187D411yescharacteristic
371#13133185—21no—
372#13133185—21no—
373Q8×Dic53—21no—
374C4×Dic106—21no—
375C4×Dic106C2311yescharacteristic
376C4×D212—21no—
377C4×D212—21no—
378C4×D212—21no—
379C4×D212—21no—
380C4×D212—21no—
381C4×D212C2311yescharacteristic
382C4×D212C2311yescharacteristic
383C4×D212C2311yescharacteristic
384C4×D212C2311yescharacteristic
385C4×D212C2311yescharacteristic
386D4×Dic53—21no—
387#13133179—21no—
388#13133177—21no—
389#13133177—21no—
390#13133177—21no—
391#13133176—21no—
392#13133175—21no—
393#13133175C2311yescharacteristic
394#13133175C2311yescharacteristic
395#13133175C2311yescharacteristic
396#13133175C2311yescharacteristic
397C2×C4⋊Dic53—21no—
398C2×C4⋊Dic53—21no—
399C2×C4⋊Dic53—21no—
400C2×#11719921—21no—
401C2×#11719921—21no—
402C2×#11719921—21no—
403C2×#11719921—21no—
404C22⋊C4×D53—21no—
405#13133150C2311yescharacteristic
406#13133150C2311yescharacteristic
407#13133150C2311yescharacteristic
408#13133150C2311yescharacteristic
409C4⋊#88322C2311yescharacteristic
410C4⋊#88322C2311yescharacteristic
411#13133142C2311yescharacteristic
412#13133142C2311yescharacteristic
413#13133142C2311yescharacteristic
414#13133142C2311yescharacteristic
415#13133142C2311yescharacteristic
416#13133142C2311yescharacteristic
417#13133141C2311yescharacteristic
418#13133141C2311yescharacteristic
419#13133140C2311yescharacteristic
420#13133140C2311yescharacteristic
421#13133140C2311yescharacteristic
422#13133140C2311yescharacteristic
423#13133140C2311yescharacteristic
424#13133140C2311yescharacteristic
425#13133140C2311yescharacteristic
426#13133140C2311yescharacteristic
427#13133139C2311yescharacteristic
428#13133139C2311yescharacteristic
429#13133138C2311yescharacteristic
430#13133138C2311yescharacteristic
431#13133137C2311yescharacteristic
432#13133137C2311yescharacteristic
433#13133137C2311yescharacteristic
434#13133137C2311yescharacteristic
435C22⋊#88322C2311yescharacteristic
436C22⋊#88322C2311yescharacteristic
437#13133129C2311yescharacteristic
438#13133129C2311yescharacteristic
439#13133129C2311yescharacteristic
440#13133129C2311yescharacteristic
441#13133129C2311yescharacteristic
442#13133129C2311yescharacteristic
443#13133129C2311yescharacteristic
444#13133129C2311yescharacteristic
445#13133128C2311yescharacteristic
446C4×#88322C2311yescharacteristic
447C2×#41×C53C2311yescharacteristic
448C2×Q16×C53C2311yescharacteristic
449C2×SD16×C53C2311yescharacteristic
450C2×SD16×C53C2311yescharacteristic
451C2×D8×C53C2311yescharacteristic
452C4⋊Q8×C53C2311yescharacteristic
453#126×C53—21no—
454#124×C53—21no—
455#124×C53C2311yescharacteristic
456#123×C53—21no—
457C22⋊Q8×C53—21no—
458C22⋊Q8×C53C2311yescharacteristic
459#121×C53C2311yescharacteristic
460C4×Q8×C53C2311yescharacteristic
461C4×Q8×C53C2311yescharacteristic
462C4×Q8×C53C2311yescharacteristic
463C4×D4×C53—21no—
464C4×D4×C53—21no—
465C4×D4×C53C2311yescharacteristic
466C4×D4×C53C2311yescharacteristic
467C4×D4×C53C2311yescharacteristic
468#117×C53—21no—
469#117×C53C2311yescharacteristic
470C2×C4⋊C4×C53—21no—
471C2×C4⋊C4×C53C2311yescharacteristic
472#106×C53C2311yescharacteristic
473#106×C53C2311yescharacteristic
474#106×C53C2311yescharacteristic
475#106×C53C2311yescharacteristic
476C4⋊C8×C53C2311yescharacteristic
477C4⋊C8×C53C2311yescharacteristic
478#103×C53C2311yescharacteristic
479#103×C53C2311yescharacteristic
480#103×C53C2311yescharacteristic
481#103×C53C2311yescharacteristic
482#102×C53C2311yescharacteristic
483#102×C53C2311yescharacteristic
484#102×C53C2311yescharacteristic
485#102×C53C2311yescharacteristic
486C22⋊C8×C53C2311yescharacteristic
487C22⋊C8×C53C2311yescharacteristic
488#97×C53C2311yescharacteristic
489C4×C8×C53C2311yescharacteristic
490C23×D53—21no—
491C23×D53—21no—
492C23×D53C2×D411yescharacteristic
493#41×C53—22no—
494#41×C53—22no—
495C2×Q8×C53—21no—
496C2×Q8×C53C2411yescharacteristic
497C2×Q8×C53C2411yescharacteristic
498C2×D4×C53—21no—
499C2×D4×C53—21no—
500C2×D4×C53C2411yescharacteristic
501C2×D4×C53C2411yescharacteristic
502C22×C4×C53—21no—
503C22×C4×C53—21no—
504C22×C4×C53—21no—
505C22×C4×C53—21no—
506C22×C4×C53—21no—
507C22×C4×C53C2411yescharacteristic
508C2×C22⋊D53—21no—
509C2×C22⋊D53—21no—
510C2×C22⋊D53—21no—
511C2×C22⋊D53—21no—
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⋊D53C2×D411yescharacteristic
519C2×C22⋊D53C2×D411yescharacteristic
520C22×Dic53—21no—
521C22×Dic53—21no—
522C22×Dic53—21no—
523C22×Dic53—21no—
524C22×Dic53—21no—
525C22×Dic53C2×D411yescharacteristic
526#11719949—22no—
527#11719949—41no—
528#11719949—41no—
529#11719949—41no—
530Q8×D53—22no—
531Q8×D53—22no—
532Q8×D53—22no—
533Q8×D53—41no—
534Q8×D53—41no—
535Q8×D53—41no—
536Q8×D53—41no—
537Q8×D53—41no—
538#11719947—22no—
539#11719947—22no—
540#11719947—22no—
541#11719947—41no—
542#11719947—41no—
543#11719947—41no—
544#11719947—41no—
545#11719947—41no—
546#11719947—44no—
547#11719947—44no—
548#11719947—44no—
549D4×D53—22no—
550D4×D53—41no—
551D4×D53—41no—
552D4×D53—41no—
553D4×D53—44no—
554#11719945—41no—
555#11719945—41no—
556#11719945—41no—
557#11719945—41no—
558#11719945—44no—
559#11719945—44no—
560C2×D212—21no—
561C2×D212—21no—
562C2×D212—21no—
563C2×D212—21no—
564C2×D212—21no—
565C2×D212—21no—
566C2×D212C2×D411yescharacteristic
567C2×D212C2×D411yescharacteristic
568C2×D212C2×D411yescharacteristic
569C2×D212C2×D411yescharacteristic
570C2×D212C2×D411yescharacteristic
571C2×D212C2411yescharacteristic
572C2×D212C2411yescharacteristic
573C2×C4×D53—21no—
574C2×C4×D53—21no—
575C2×C4×D53—21no—
576C2×C4×D53—21no—
577C2×C4×D53—21no—
578C2×C4×D53—21no—
579C2×C4×D53—21no—
580C2×C4×D53—21no—
581C2×C4×D53—41no—
582C2×C4×D53—41no—
583C2×C4×D53—44no—
584C2×C4×D53C2×D411yescharacteristic
585C2×C4×D53C2×D411yescharacteristic
586C2×C4×D53C2411yescharacteristic
587C2×C4×D53C2411yescharacteristic
588C2×C4×D53C2411yescharacteristic
589C2×C4×D53C2411yescharacteristic
590C2×Dic106—21no—
591C2×Dic106—21no—
592C2×Dic106—21no—
593C2×Dic106—21no—
594C2×Dic106—21no—
595C2×Dic106—21no—
596C2×Dic106—41no—
597C2×Dic106—41no—
598C2×Dic106—44no—
599C2×Dic106C2×D411yescharacteristic
600C2×Dic106C2411yescharacteristic
601C2×Dic106C2411yescharacteristic
602C2×Dic106C2411yescharacteristic
603C2×Dic106C2411yescharacteristic
604Q16×C53—22no—
605SD16×C53—22no—
606SD16×C53—22no—
607D8×C53—22no—
608C2×C8×C53C2411yescharacteristic
609C2×C8×C53C2411yescharacteristic
610C2×C8×C53C2411yescharacteristic
611C2×C8×C53C2411yescharacteristic
612C4⋊C4×C53—21no—
613C4⋊C4×C53—21no—
614C4⋊C4×C53—21no—
615C4⋊C4×C53—21no—
616C4⋊C4×C53—21no—
617C4⋊C4×C53—21no—
618C4⋊C4×C53C2×D411yescharacteristic
619C4⋊C4×C53C2×D411yescharacteristic
620C4⋊C4×C53C2411yescharacteristic
621C4⋊C4×C53C2411yescharacteristic
622C4⋊C4×C53C2411yescharacteristic
623C4⋊C4×C53C2411yescharacteristic
624C22⋊C4×C53—21no—
625C22⋊C4×C53—21no—
626C22⋊C4×C53—21no—
627C22⋊C4×C53—21no—
628C22⋊C4×C53—21no—
629C22⋊C4×C53—21no—
630C22⋊C4×C53—21no—
631C22⋊C4×C53C2×D411yescharacteristic
632C22⋊C4×C53C2×D411yescharacteristic
633C42×C53—21no—
634C42×C53—21no—
635C42×C53—21no—
636C42×C53C2411yescharacteristic
637C42×C53C2411yescharacteristic
638C22⋊Dic53—21no—
639C22⋊Dic53—21no—
640C22⋊Dic53—21no—
641#11719925—22no—
642#11719925—41no—
643#11719925—41no—
644#11719925—41no—
645#11719924—22no—
646#11719924—41no—
647#11719923—22no—
648#11719923—41no—
649#11719923—41no—
650#11719923—41no—
651#11719922—22no—
652#11719922—41no—
653#11719921—21no—
654#11719921—21no—
655#11719921—21no—
656#11719921—21no—
657#11719921—21no—
658#11719921—21no—
659#11719921—21no—
660#11719921—21no—
661#11719921—21no—
662#11719921—21no—
663#11719921—21no—
664#11719921—21no—
665#11719921—21no—
666#11719921—21no—
667#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#11719921C2×D411yescharacteristic
680#11719921C2×D411yescharacteristic
681#11719921C2×D411yescharacteristic
682#11719921C2×D411yescharacteristic
683#11719921C2×D411yescharacteristic
684#11719921C2×D411yescharacteristic
685#11719921C2×D411yescharacteristic
686#11719921C2×D411yescharacteristic
687C4⋊Dic53—21no—
688C4⋊Dic53—21no—
689C4⋊Dic53—21no—
690C4⋊Dic53—21no—
691C4⋊Dic53—21no—
692C4⋊Dic53—21no—
693C4⋊Dic53—21no—
694C4⋊Dic53—21no—
695C4⋊Dic53—21no—
696C4⋊Dic53—21no—
697C4⋊Dic53—21no—
698C4⋊Dic53—21no—
699C4⋊Dic53—21no—
700C4⋊Dic53C2×D411yescharacteristic
701C4⋊Dic53C2×D411yescharacteristic
702C4⋊Dic53C2×D411yescharacteristic
703C4⋊Dic53C2×D411yescharacteristic
704C4⋊Dic53C2411yescharacteristic
705C4⋊Dic53C2411yescharacteristic
706#11719919—21no—
707#11719919—21no—
708#11719919—21no—
709#11719919—21no—
710C4×Dic53—21no—
711C4×Dic53—21no—
712C4×Dic53—21no—
713C4×Dic53—21no—
714C4×Dic53—21no—
715C2×#88322C2411yescharacteristic
716C2×#88322C2411yescharacteristic
717C2×#88322C2411yescharacteristic
718C2×#88322C2411yescharacteristic
719Dic212—41no—
720Dic212—41no—
721Dic212—41no—
722D424—41no—
723#11719913—41no—
724#11719913—41no—
725#11719913—41no—
726#11719913—41no—
727#11719912—41no—
728#11719912—41no—
729#11719912—41no—
730#11719912—41no—
731C8×D53—41no—
732C8×D53—41no—
733C8×D53—41no—
734C8×D53—41no—
735C23×C53—21no—
736C23×C53—21no—
737C23×C53C22×D411yescharacteristic
738C22×D53—21no—
739C22×D53—21no—
740C22×D53—41no—
741C22×D53—41no—
742C22×D53—41no—
743C22×D53—42no—
744C22×D53—42no—
745C22×D53—81no—
746C22×D53—81no—
747C22×D53—81no—
748C22×D53—81no—
749C22×D53C22×D411yescharacteristic
750C22×D53C22×D411yescharacteristic
751C22×D53C22×D411yescharacteristic
752C22×D53C22×D411yescharacteristic
753Q8×C53—21no—
754Q8×C53—21no—
755Q8×C53—21no—
756Q8×C53—81no—
757Q8×C53H(5,𝔽2)12yes—
758D4×C53—24no—
759D4×C53—21no—
760D4×C53—21no—
761D4×C53—21no—
762D4×C53—81no—
763D4×C53H(5,𝔽2)12yes—
764C2×C4×C53—24no—
765C2×C4×C53—21no—
766C2×C4×C53—21no—
767C2×C4×C53—21no—
768C2×C4×C53—21no—
769C2×C4×C53—21no—
770C2×C4×C53—21no—
771C2×C4×C53—21no—
772C2×C4×C53—21no—
773C2×C4×C53—81no—
774C2×C4×C53—81no—
775C2×C4×C53—81no—
776C2×C4×C53—81no—
777C2×C4×C53C22×D411yescharacteristic
778C2×C4×C53C22×D411yescharacteristic
779C2×C4×C53C22×D411yescharacteristic
780C2×C4×C53C22×D411yescharacteristic
781C2×C4×C53C22×D411yescharacteristic
782C2×C4×C53C2511yescharacteristic
783C22⋊D53—41no—
784C22⋊D53—41no—
785C22⋊D53—42no—
786C22⋊D53—42no—
787C22⋊D53—42no—
788C22⋊D53—42no—
789C22⋊D53—42no—
790C22⋊D53—81no—
791C22⋊D53—81no—
792C22⋊D53—81no—
793C22⋊D53—81no—
794C22⋊D53—81no—
795C2×Dic53—21no—
796C2×Dic53—21no—
797C2×Dic53—21no—
798C2×Dic53—21no—
799C2×Dic53—21no—
800C2×Dic53—21no—
801C2×Dic53—41no—
802C2×Dic53—42no—
803C2×Dic53—42no—
804C2×Dic53—42no—
805C2×Dic53—42no—
806C2×Dic53—81no—
807C2×Dic53C22×D411yescharacteristic
808C2×Dic53C22×D411yescharacteristic
809C2×Dic53C22×D411yescharacteristic
810C2×Dic53C22×D411yescharacteristic
811D212—21no—
812D212—21no—
813D212—21no—
814D212—21no—
815D212—41no—
816D212—41no—
817D212—41no—
818D212—41no—
819D212—41no—
820D212—42no—
821D212—81no—
822D212—81no—
823D212—81no—
824D212—81no—
825D212—81no—
826C4×D53—21no—
827C4×D53—21no—
828C4×D53—21no—
829C4×D53—21no—
830C4×D53—21no—
831C4×D53—21no—
832C4×D53—21no—
833C4×D53—21no—
834C4×D53—41no—
835C4×D53—41no—
836C4×D53—42no—
837C4×D53—42no—
838C4×D53—42no—
839C4×D53—42no—
840C4×D53—42no—
841C4×D53—81no—
842C4×D53—81no—
843C4×D53—81no—
844Dic106—21no—
845Dic106—21no—
846Dic106—21no—
847Dic106—21no—
848Dic106—21no—
849Dic106—21no—
850Dic106—21no—
851Dic106—21no—
852Dic106—41no—
853Dic106—42no—
854Dic106—42no—
855Dic106—42no—
856Dic106—42no—
857Dic106—81no—
858Dic106—81no—
859C8×C53—21no—
860C8×C53—21no—
861C8×C53—21no—
862C8×C53—21no—
863#88322—21no—
864#88322—21no—
865#88322—21no—
866#88322—21no—
867#61627—531nomaximal, Sylow
868C22×C53—21no—
869C22×C53—21no—
870C22×C53—21no—
871C22×C53—22no—
872C22×C53—41no—
873C22×C53—41no—
874C22×C53—41no—
875C22×C53—41no—
876C22×C53—41no—
877C22×C53C23×D411yescharacteristic
878C2×D53—21no—
879C2×D53—21no—
880C2×D53—21no—
881C2×D53—21no—
882C2×D53—21no—
883C2×D53—21no—
884C2×D53—21no—
885C2×D53—21no—
886C2×D53—21no—
887C2×D53—21no—
888C2×D53—21no—
889C2×D53—21no—
890C2×D53—41no—
891C2×D53—41no—
892C2×D53—41no—
893C2×D53—41no—
894C2×D53—41no—
895C2×D53—41no—
896C2×D53—82no—
897C2×D53—84no—
898C2×D53—162no—
899C4×C53—21no—
900C4×C53—21no—
901C4×C53—21no—
902C4×C53—21no—
903C4×C53—21no—
904C4×C53—22no—
905C4×C53—41no—
906C4×C53—41no—
907C4×C53—41no—
908C4×C53—41no—
909C4×C53—41no—
910C4×C53C2×H(5,𝔽2)11yescharacteristic
911C4×C53C2×H(5,𝔽2)11yescharacteristic
912Dic53—21no—
913Dic53—21no—
914Dic53—21no—
915Dic53—21no—
916Dic53—41no—
917Dic53—41no—
918Dic53—41no—
919Dic53—41no—
920Dic53—41no—
921Dic53—41no—
922#3540—531no—
923#3489—531no—
924#3329—531no—
925#3328—531no—
926#3321—531no—
927#3319—531no—
928#3313—531no—
929#3311—531no—
930#3303—531no—
931#3302—531no—
932#3285—531no—
933#3282—531no—
934#3275—531no—
935#3273—531no—
936#3270—531no—
937#3269—531no—
938#3267—531no—
939#3266—531no—
940#3225—531no—
941#3225—531no—
942#3201—531no—
943#3198—531no—
944#3196—531no—
945#3190—531no—
946#3125D5311yescharacteristic, complemented
947#3124—531no—
948#3011—531no—
949#3010—531no—
950#3005—531no—
951#3002—531no—
952#2976—531no—
953C2×C53—41no—
954C2×C53—42no—
955C2×C53—81no—
956C2×C53#348411yescharacteristic
957C2×C53#358411yescharacteristic
958C2×C53#358611yescharacteristic
959D53—41no—
960D53—41no—
961D53—41no—
962D53—41no—
963D53—81no—
964D53—81no—
965C2×2−1+4—531no—
966C22×#41—531no—
967C2×#137—531no—
968C2×#137—531no—
969C2×AGL(1,ℤ/8)—531no—
970C2×AGL(1,ℤ/8)—531no—
971C2×#135—531no—
972C2×#135—531no—
973C22×Q16—531no—
974C22×SD16—531no—
975H(3,𝔽4)—1061no—
976#560—1061no—
977#559—1061no—
978#556—531no—
979#556—531no—
980#555—531no—
981#555—531no—
982#551—1061no—
983D4×Q8—531no—
984D4×Q8—531no—
985#548—531no—
986#548—531no—
987#548—531no—
988#548—531no—
989#547—531no—
990#547—531no—
991#547—1061no—
992#547—1061no—
993#546—531no—
994#546—531no—
995#546—531no—
996#546—531no—
997#546—1061no—
998#546—1061no—
999#542—531no—
1000#542—1061no—
1001#542—1061no—
1002#542C2×D5311yescharacteristic, complemented
1003#538—1061no—
1004#538—1061no—
1005#537—531no—
1006#537—1061no—
1007#536—531no—
1008#536—531no—
1009#536—1061no—
1010#535—531no—
1011#525—531no—
1012#525—531no—
1013#525—531no—
1014#525—1061no—
1015C2×C22⋊Q8—531no—
1016C2×C22⋊Q8—1061no—
1017#520C2×D5311yescharacteristic, complemented
1018#497—531no—
1019#497—531no—
1020#495—531no—
1021#495—531no—
1022#489—531no—
1023#489—531no—
1024#487—531no—
1025#487—531no—
1026#485—531no—
1027#485—531no—
1028#485—531no—
1029#485—531no—
1030#485—531no—
1031#485—531no—
1032#484—531no—
1033#483C2×D5311yescharacteristic, complemented
1034#482—531no—
1035#482—531no—
1036#481C2×D5311yescharacteristic, complemented
1037#480—531no—
1038#477—531no—
1039#476C2×D5311yescharacteristic, complemented
1040#475C2×D5311yescharacteristic, complemented
1041#474—531no—
1042#470—531no—
1043#470—531no—
1044#470—531no—
1045#469—531no—
1046#468—531no—
1047#468—531no—
1048#468—531no—
1049#468—531no—
1050#467—531no—
1051#467—531no—
1052#467—531no—
1053#466—531no—
1054#465—531no—
1055#465—531no—
1056#465—531no—
1057#465—531no—
1058#464—531no—
1059#464—531no—
1060#464—531no—
1061#464C2×D5311yescharacteristic, complemented
1062#463—531no—
1063#463—531no—
1064#463—531no—
1065#463C2×D5311yescharacteristic, complemented
1066#462—531no—
1067#462—531no—
1068#461—531no—
1069#461—531no—
1070#452—531no—
1071#452—531no—
1072#452—531no—
1073#452—531no—
1074#452—531no—
1075#452—531no—
1076#452—531no—
1077#452—531no—
1078#452—531no—
1079#452—531no—
1080#452—531no—
1081#452C2×D5311yescharacteristic, complemented
1082#451—531no—
1083#451—531no—
1084#451—531no—
1085#451—531no—
1086#451—531no—
1087#451—531no—
1088#450—531no—
1089#450—531no—
1090#449—531no—
1091#449—531no—
1092#449—531no—
1093#449—531no—
1094#449—531no—
1095#449—531no—
1096#449—531no—
1097#449C2×D5311yescharacteristic
1098#448—531no—
1099#448—531no—
1100#448—531no—
1101#448—531no—
1102#448—531no—
1103#448—531no—
1104#447—531no—
1105#447—531no—
1106#442C2×D5311yescharacteristic, complemented
1107#441C2×D5311yescharacteristic, complemented
1108#440—531no—
1109#440—531no—
1110C4×Q16—531no—
1111C4×SD16C2×D5311yescharacteristic, complemented
1112C4×SD16C2×D5311yescharacteristic, complemented
1113C4×D8—531no—
1114#436—531no—
1115#436—531no—
1116#435—531no—
1117#435—531no—
1118#435—531no—
1119#435—531no—
1120C8×D4—531no—
1121C8×D4—531no—
1122#433—531no—
1123#433C2×D5311yescharacteristic, complemented
1124#419—531no—
1125#419—531no—
1126#419—531no—
1127#418—531no—
1128#416—531no—
1129#416—531no—
1130#416—531no—
1131#416—531no—
1132#408—531no—
1133#408—531no—
1134#407—531no—
1135C2×C22⋊C8—531no—
1136C53#6162711yescharacteristic, complemented, Sylow
11372−1+4—2122no—
11382−1+4—2122no—
1139C2×#41—531no—
1140C2×#41—531no—
1141C2×#41—531no—
1142C2×#41—531no—
1143C2×#41—531no—
1144C2×#41—531no—
1145C2×#41—531no—
1146C2×#41—531no—
1147C2×#41—1061no—
1148C2×#41—1061no—
1149C2×#41—1061no—
1150C2×#41—1061no—
1151C2×#41—1061no—
1152C2×#41—2122no—
1153C2×#41—2122no—
1154C2×#41C22×D5311yescharacteristic
1155C22×Q8—531no—
1156C22×Q8—531no—
1157C22×Q8—531no—
1158C22×Q8—531no—
1159C22×Q8—531no—
1160C22×Q8—1061no—
1161C22×D4—531no—
1162C22×D4—531no—
1163C22×D4—1061no—
1164C23×C4—531no—
1165C23×C4—1061no—
1166#137—2122no—
1167#137—2122no—
1168AGL(1,ℤ/8)—2122no—
1169AGL(1,ℤ/8)—2122no—
1170#135—2122no—
1171#135—2122no—
1172C2×Q16—531no—
1173C2×Q16—531no—
1174C2×Q16—531no—
1175C2×Q16—531no—
1176C2×Q16—531no—
1177C2×Q16—531no—
1178C2×Q16—531no—
1179C2×Q16—2122no—
1180C2×Q16C22×D5311yescharacteristic
1181C2×SD16—531no—
1182C2×SD16—531no—
1183C2×SD16—531no—
1184C2×SD16—531no—
1185C2×SD16—531no—
1186C2×SD16—531no—
1187C2×SD16—531no—
1188C2×SD16—531no—
1189C2×SD16—531no—
1190C2×SD16—531no—
1191C2×SD16—2122no—
1192C2×SD16C22×D5311yescharacteristic
1193C2×SD16C22×D5311yescharacteristic
1194C2×D8—531no—
1195C2×D8—531no—
1196C2×D8—531no—
1197C2×D8C22×D5311yescharacteristic
1198C2×M16—531no—
1199C2×M16—531no—
1200C2×M16—531no—
1201C2×M16—531no—
1202C22×C8—531no—
1203C22×C8—531no—
1204C22×C8—531no—
1205C22×C8—531no—
1206C4⋊Q8—531no—
1207C4⋊Q8—531no—
1208C4⋊Q8—531no—
1209C4⋊Q8—1061no—
1210C4⋊Q8—1061no—
1211C4⋊Q8—1061no—
1212C4⋊Q8C22×D5311yescharacteristic
1213#127—1061no—
1214#126—21no—
1215#126—1061no—
1216#126—1061no—
1217#126—1061no—
1218#126—1061no—
1219#126—1061no—
1220#124—21no—
1221#124—531no—
1222#124—531no—
1223#124—531no—
1224#124—1061no—
1225#124—1061no—
1226#124—1061no—
1227#124—1061no—
1228#124—1061no—
1229#124—1061no—
1230#124—1061no—
1231#124—1061no—
1232#124—1061no—
1233#124—1061no—
1234#124—1061no—
1235#124—1061no—
1236#124—1061no—
1237#124C22×D5311yescharacteristic
1238#123—21no—
1239#123—531no—
1240#123—531no—
1241#123—1061no—
1242#123—1061no—
1243#123—1061no—
1244#123—1061no—
1245#123—1061no—
1246#123—1061no—
1247#123—1061no—
1248#123—1061no—
1249#123—1061no—
1250#123—1061no—
1251#123—1061no—
1252#123—1061no—
1253#123—1061no—
1254#123—1061no—
1255#123—1061no—
1256C22⋊Q8—21no—
1257C22⋊Q8—531no—
1258C22⋊Q8—531no—
1259C22⋊Q8—531no—
1260C22⋊Q8—531no—
1261C22⋊Q8—531no—
1262C22⋊Q8—531no—
1263C22⋊Q8—531no—
1264C22⋊Q8—531no—
1265C22⋊Q8—531no—
1266C22⋊Q8—531no—
1267C22⋊Q8—531no—
1268C22⋊Q8—531no—
1269C22⋊Q8—531no—
1270C22⋊Q8—1061no—
1271C22⋊Q8—1061no—
1272C22⋊Q8—1061no—
1273C22⋊Q8—1061no—
1274C22⋊Q8—1061no—
1275C22⋊Q8—1061no—
1276C22⋊Q8—1061no—
1277C22⋊Q8—1061no—
1278C22⋊Q8—1061no—
1279C22⋊Q8—1061no—
1280C22⋊Q8—1061no—
1281C22⋊Q8—1061no—
1282C22⋊Q8—1061no—
1283C22⋊Q8—1061no—
1284C22⋊Q8C22×D5311yescharacteristic
1285#121—531no—
1286#121—531no—
1287#121—531no—
1288#121—531no—
1289#121—531no—
1290#121—531no—
1291#121—531no—
1292#121—531no—
1293#121—531no—
1294#121—1061no—
1295#121—1061no—
1296#121—1061no—
1297#121—1061no—
1298#121—1061no—
1299#121—1061no—
1300#121—1061no—
1301#121—1061no—
1302#121—1061no—
1303#121—1061no—
1304#121—1061no—
1305#121—1061no—
1306#121—1061no—
1307#121—1061no—
1308#121—1061no—
1309#121C22×D5311yescharacteristic
1310#120—531no—
1311#120—531no—
1312#120—1061no—
1313#120—1061no—
1314#120—1061no—
1315#120—1061no—
1316#120—1061no—
1317#120—1061no—
1318#120—1061no—
1319#120—1061no—
1320C4×Q8—531no—
1321C4×Q8—1061no—
1322C4×Q8—1061no—
1323C4×Q8C22×D5311yescharacteristic
1324C4×Q8C22×D5311yescharacteristic
1325C4×Q8C22×D5311yescharacteristic
1326C4×D4—21no—
1327C4×D4—21no—
1328C4×D4—531no—
1329C4×D4—531no—
1330C4×D4—531no—
1331C4×D4—531no—
1332C4×D4—531no—
1333C4×D4—1061no—
1334C4×D4—1061no—
1335C4×D4—1061no—
1336C4×D4—1061no—
1337C4×D4—1061no—
1338C4×D4—1061no—
1339C4×D4—1061no—
1340C4×D4—1061no—
1341C4×D4—1061no—
1342C4×D4—1061no—
1343C4×D4C22×D5311yescharacteristic
1344C4×D4C22×D5311yescharacteristic
1345C4×D4C22×D5311yescharacteristic
1346#117—21no—
1347#117—531no—
1348#117—531no—
1349#117—531no—
1350#117—531no—
1351#117—1061no—
1352#117—1061no—
1353#117C22×D5311yescharacteristic
1354C2×C4⋊C4—21no—
1355C2×C4⋊C4—1061no—
1356C2×C4⋊C4—1061no—
1357C2×C4⋊C4—1061no—
1358C2×C4⋊C4C22×D5311yescharacteristic
1359C2×C22⋊C4—1061no—
1360C2×C22⋊C4—1061no—
1361C2×C22⋊C4—1061no—
1362C2×C22⋊C4—1061no—
1363C2×C22⋊C4—1061no—
1364#107—531no—
1365#107—531no—
1366#107—531no—
1367#107—531no—
1368#106C22×D5311yescharacteristic
1369#106C22×D5311yescharacteristic
1370#106C22×D5311yescharacteristic
1371#106C22×D5311yescharacteristic
1372C4⋊C8—531no—
1373C4⋊C8—531no—
1374C4⋊C8C22×D5311yescharacteristic
1375C4⋊C8C22×D5311yescharacteristic
1376#103—531no—
1377#103—531no—
1378#103—531no—
1379#103—531no—
1380#103—531no—
1381#103—531no—
1382#103—531no—
1383#103—531no—
1384#103—531no—
1385#103—531no—
1386#103—531no—
1387#103—531no—
1388#103—531no—
1389#103—531no—
1390#103—531no—
1391#103—531no—
1392#103C22×D5311yescharacteristic
1393#103C22×D5311yescharacteristic
1394#103C22×D5311yescharacteristic
1395#103C22×D5311yescharacteristic
1396#102—531no—
1397#102—531no—
1398#102—531no—
1399#102—531no—
1400#102—531no—
1401#102—531no—
1402#102—531no—
1403#102—531no—
1404#102C22×D5311yescharacteristic
1405#102C22×D5311yescharacteristic
1406#102C22×D5311yescharacteristic
1407#102C22×D5311yescharacteristic
1408C22⋊C8—531no—
1409C22⋊C8—531no—
1410C22⋊C8—531no—
1411C22⋊C8—531no—
1412C22⋊C8—531no—
1413C22⋊C8—531no—
1414C22⋊C8—531no—
1415C22⋊C8—531no—
1416C22⋊C8—531no—
1417C22⋊C8—531no—
1418C22⋊C8C22×D5311yescharacteristic
1419C22⋊C8C22×D5311yescharacteristic
1420#97—531no—
1421#97C22×D5311yescharacteristic
1422C4×C8—531no—
1423C4×C8C22×D5311yescharacteristic
1424C24—531no—
1425C24—1061no—
1426C24—1061no—
1427#41—22no—
1428#41—22no—
1429#41—1062no—
1430#41—1062no—
1431#41—1062no—
1432#41—1062no—
1433#41—2121no—
1434#41—2121no—
1435#41—2121no—
1436#41—2121no—
1437#41—2124no—
1438#41—2124no—
1439#41—2121no—
1440#41—2121no—
1441#41—2121no—
1442#41—2121no—
1443#41—2121no—
1444#41—2121no—
1445#41—2121no—
1446#41—2121no—
1447#41—2124no—
1448#41—2124no—
1449#41—2124no—
1450C2×Q8—21no—
1451C2×Q8—531no—
1452C2×Q8—531no—
1453C2×Q8—531no—
1454C2×Q8—531no—
1455C2×Q8—531no—
1456C2×Q8—1061no—
1457C2×Q8—1061no—
1458C2×Q8—1061no—
1459C2×Q8—1061no—
1460C2×Q8—1061no—
1461C2×Q8—1061no—
1462C2×Q8—1062no—
1463C2×Q8—1062no—
1464C2×Q8—1062no—
1465C2×Q8—2121no—
1466C2×Q8—2121no—
1467C2×Q8—2124no—
1468C2×Q8—2121no—
1469C2×Q8—2121no—
1470C2×Q8—2121no—
1471C2×Q8—2121no—
1472C2×Q8—2121no—
1473C2×Q8C23×D5311yescharacteristic
1474C2×Q8C23×D5311yescharacteristic
1475C2×D4—21no—
1476C2×D4—21no—
1477C2×D4—531no—
1478C2×D4—531no—
1479C2×D4—531no—
1480C2×D4—531no—
1481C2×D4—531no—
1482C2×D4—531no—
1483C2×D4—531no—
1484C2×D4—531no—
1485C2×D4—531no—
1486C2×D4—1061no—
1487C2×D4—1061no—
1488C2×D4—1061no—
1489C2×D4—1061no—
1490C2×D4—1061no—
1491C2×D4—1061no—
1492C2×D4—1061no—
1493C2×D4—1061no—
1494C2×D4—1062no—
1495C2×D4—1061no—
1496C2×D4—1061no—
1497C2×D4—1061no—
1498C2×D4—1061no—
1499C2×D4—1061no—
1500C2×D4—1061no—
1501C2×D4—1061no—
1502C2×D4—1061no—
1503C2×D4—2121no—
1504C2×D4—2121no—
1505C2×D4—2121no—
1506C2×D4—2124no—
1507C2×D4C23×D5311yescharacteristic
1508C2×D4C23×D5311yescharacteristic
1509C22×C4—21no—
1510C22×C4—21no—
1511C22×C4—21no—
1512C22×C4—21no—
1513C22×C4—21no—
1514C22×C4—531no—
1515C22×C4—531no—
1516C22×C4—531no—
1517C22×C4—531no—
1518C22×C4—531no—
1519C22×C4—531no—
1520C22×C4—531no—
1521C22×C4—1061no—
1522C22×C4—1061no—
1523C22×C4—1061no—
1524C22×C4—1061no—
1525C22×C4—1061no—
1526C22×C4—1061no—
1527C22×C4—1061no—
1528C22×C4—1061no—
1529C22×C4—1061no—
1530C22×C4—1061no—
1531C22×C4—1061no—
1532C22×C4—1061no—
1533C22×C4—1061no—
1534C22×C4—2121no—
1535C22×C4—2121no—
1536C22×C4—2124no—
1537C22×C4C23×D5311yescharacteristic
1538Q16—22no—
1539Q16—1062no—
1540Q16—2121no—
1541Q16—2121no—
1542Q16—2121no—
1543Q16—2121no—
1544Q16—2121no—
1545Q16—2121no—
1546SD16—22no—
1547SD16—22no—
1548SD16—1062no—
1549SD16—1062no—
1550SD16—2121no—
1551SD16—2121no—
1552SD16—2121no—
1553SD16—2121no—
1554SD16—2121no—
1555SD16—2121no—
1556SD16—2121no—
1557SD16—2121no—
1558D8—22no—
1559D8—1062no—
1560D8—2121no—
1561D8—2121no—
1562M16—2121no—
1563M16—2121no—
1564M16—2121no—
1565M16—2121no—
1566C2×C8—531no—
1567C2×C8—531no—
1568C2×C8—531no—
1569C2×C8—531no—
1570C2×C8—2121no—
1571C2×C8—2121no—
1572C2×C8—2121no—
1573C2×C8—2121no—
1574C2×C8C23×D5311yescharacteristic
1575C2×C8C23×D5311yescharacteristic
1576C2×C8C23×D5311yescharacteristic
1577C2×C8C23×D5311yescharacteristic
1578C4⋊C4—21no—
1579C4⋊C4—21no—
1580C4⋊C4—21no—
1581C4⋊C4—21no—
1582C4⋊C4—21no—
1583C4⋊C4—21no—
1584C4⋊C4—531no—
1585C4⋊C4—531no—
1586C4⋊C4—531no—
1587C4⋊C4—531no—
1588C4⋊C4—531no—
1589C4⋊C4—531no—
1590C4⋊C4—1061no—
1591C4⋊C4—1061no—
1592C4⋊C4—1061no—
1593C4⋊C4—1061no—
1594C4⋊C4—1061no—
1595C4⋊C4—1061no—
1596C4⋊C4—1061no—
1597C4⋊C4—1061no—
1598C4⋊C4—1061no—
1599C4⋊C4—1061no—
1600C4⋊C4—1061no—
1601C4⋊C4—1061no—
1602C4⋊C4—1061no—
1603C4⋊C4—1061no—
1604C4⋊C4—1061no—
1605C4⋊C4—1061no—
1606C4⋊C4—1061no—
1607C4⋊C4D4×D5311yescharacteristic
1608C4⋊C4D4×D5311yescharacteristic
1609C4⋊C4C23×D5311yescharacteristic
1610C4⋊C4C23×D5311yescharacteristic
1611C4⋊C4C23×D5311yescharacteristic
1612C4⋊C4C23×D5311yescharacteristic
1613C22⋊C4—21no—
1614C22⋊C4—21no—
1615C22⋊C4—21no—
1616C22⋊C4—21no—
1617C22⋊C4—21no—
1618C22⋊C4—21no—
1619C22⋊C4—21no—
1620C22⋊C4—531no—
1621C22⋊C4—531no—
1622C22⋊C4—531no—
1623C22⋊C4—531no—
1624C22⋊C4—531no—
1625C22⋊C4—531no—
1626C22⋊C4—531no—
1627C22⋊C4—531no—
1628C22⋊C4—1061no—
1629C22⋊C4—1061no—
1630C22⋊C4—1061no—
1631C22⋊C4—1061no—
1632C22⋊C4—1061no—
1633C22⋊C4—1061no—
1634C22⋊C4—1061no—
1635C22⋊C4—1061no—
1636C22⋊C4—1061no—
1637C22⋊C4—1061no—
1638C22⋊C4—1061no—
1639C22⋊C4—1061no—
1640C22⋊C4—1061no—
1641C22⋊C4—1061no—
1642C22⋊C4—1061no—
1643C22⋊C4—1061no—
1644C22⋊C4—1061no—
1645C22⋊C4—1061no—
1646C22⋊C4—1061no—
1647C22⋊C4—1061no—
1648C22⋊C4—1061no—
1649C22⋊C4—1061no—
1650C22⋊C4—1061no—
1651C22⋊C4—1061no—
1652C22⋊C4—1061no—
1653C22⋊C4—1061no—
1654C22⋊C4—1061no—
1655C22⋊C4—1061no—
1656C22⋊C4—1061no—
1657C22⋊C4D4×D5311yescharacteristic
1658C22⋊C4D4×D5311yescharacteristic
1659C42—21no—
1660C42—21no—
1661C42—21no—
1662C42—1061no—
1663C42—1061no—
1664C42—1061no—
1665C42—1061no—
1666C42—1061no—
1667C42C23×D5311yescharacteristic
1668C42C23×D5311yescharacteristic
1669C23—21no—
1670C23—21no—
1671C23—531no—
1672C23—531no—
1673C23—531no—
1674C23—531no—
1675C23—1061no—
1676C23—1061no—
1677C23—4241no—
1678C23—4241no—
1679C23—4241no—
1680C23—4241no—
1681C23—2121no—
1682C23—2121no—
1683C23—2121no—
1684C23—2122no—
1685C23—2122no—
1686C23C2×D4×D5311yescharacteristic
1687Q8—21no—
1688Q8—21no—
1689Q8—21no—
1690Q8—81no—
1691Q8—1061no—
1692Q8—1061no—
1693Q8—1061no—
1694Q8—1061no—
1695Q8—1061no—
1696Q8—1061no—
1697Q8—1061no—
1698Q8—1061no—
1699Q8—4241no—
1700Q8—4241no—
1701Q8—2121no—
1702Q8—2122no—
1703Q8—2122no—
1704Q8—2122no—
1705Q8—2122no—
1706Q8#1313326312yes—
1707D4—24no—
1708D4—21no—
1709D4—21no—
1710D4—21no—
1711D4—81no—
1712D4—1061no—
1713D4—1061no—
1714D4—1061no—
1715D4—1061no—
1716D4—4241no—
1717D4—4241no—
1718D4—4241no—
1719D4—4241no—
1720D4—4241no—
1721D4—4241no—
1722D4—4241no—
1723D4—4241no—
1724D4—4241no—
1725D4—4241no—
1726D4—2121no—
1727D4—2121no—
1728D4—2121no—
1729D4—2121no—
1730D4—2121no—
1731D4—2122no—
1732D4—2121no—
1733D4—2121no—
1734D4—2122no—
1735D4—2122no—
1736D4—2122no—
1737D4—2122no—
1738D4—2122no—
1739D4#1313326312yes—
1740C2×C4—24no—
1741C2×C4—21no—
1742C2×C4—21no—
1743C2×C4—21no—
1744C2×C4—21no—
1745C2×C4—21no—
1746C2×C4—21no—
1747C2×C4—21no—
1748C2×C4—21no—
1749C2×C4—81no—
1750C2×C4—81no—
1751C2×C4—81no—
1752C2×C4—81no—
1753C2×C4—531no—
1754C2×C4—531no—
1755C2×C4—531no—
1756C2×C4—531no—
1757C2×C4—1061no—
1758C2×C4—1061no—
1759C2×C4—1061no—
1760C2×C4—1061no—
1761C2×C4—1061no—
1762C2×C4—1061no—
1763C2×C4—1061no—
1764C2×C4—1061no—
1765C2×C4—1061no—
1766C2×C4—1061no—
1767C2×C4—1061no—
1768C2×C4—1061no—
1769C2×C4—1061no—
1770C2×C4—1061no—
1771C2×C4—4241no—
1772C2×C4—4241no—
1773C2×C4—4241no—
1774C2×C4—4241no—
1775C2×C4—2121no—
1776C2×C4—2121no—
1777C2×C4—2122no—
1778C2×C4—2122no—
1779C2×C4—2122no—
1780C2×C4—2122no—
1781C2×C4—2122no—
1782C2×C4—2121no—
1783C2×C4—2122no—
1784C2×C4—2122no—
1785C2×C4—2122no—
1786C2×C4—2122no—
1787C2×C4C2×D4×D5311yescharacteristic
1788C2×C4C2×D4×D5311yescharacteristic
1789C2×C4C2×D4×D5311yescharacteristic
1790C2×C4C2×D4×D5311yescharacteristic
1791C2×C4C2×D4×D5311yescharacteristic
1792C2×C4C24×D5311yescharacteristic
1793C8—21no—
1794C8—21no—
1795C8—21no—
1796C8—21no—
1797C8—1061no—
1798C8—1061no—
1799C8—1061no—
1800C8—1061no—
1801C22—21no—
1802C22—22no—
1803C22—21no—
1804C22—21no—
1805C22—41no—
1806C22—41no—
1807C22—41no—
1808C22—41no—
1809C22—41no—
1810C22—8482no—
1811C22—1061no—
1812C22—1061no—
1813C22—1061no—
1814C22—1061no—
1815C22—1061no—
1816C22—1061no—
1817C22—1061no—
1818C22—1061no—
1819C22—1061no—
1820C22—1061no—
1821C22—1061no—
1822C22—1061no—
1823C22—4244no—
1824C22—4242no—
1825C22—2121no—
1826C22—2121no—
1827C22—2121no—
1828C22—2121no—
1829C22—2121no—
1830C22—2121no—
1831C22C22×D4×D5311yescharacteristic
1832C4—21no—
1833C4—22no—
1834C4—21no—
1835C4—21no—
1836C4—21no—
1837C4—21no—
1838C4—41no—
1839C4—41no—
1840C4—41no—
1841C4—41no—
1842C4—41no—
1843C4—1061no—
1844C4—1061no—
1845C4—1061no—
1846C4—1061no—
1847C4—2121no—
1848C4—2121no—
1849C4—2121no—
1850C4—2121no—
1851C4—2121no—
1852C4—2121no—
1853C4C2×#1313326311yescharacteristic
1854C4C2×#1313326311yescharacteristic
1855C2—41no—
1856C2—42no—
1857C2—81no—
1858C2—4241no—
1859C2—4241no—
1860C2—2121no—
1861C2—2121no—
1862C2—2121no—
1863C2—2121no—
1864C2#2028834811yescharacteristic
1865C2#2028948711yescharacteristic
1866C2#2028949711yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3125C2
socleC22×C53C23×D4
hypercenter#3125D53
hypocenterC53#61627
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ #117 ◁ #3125

Complements

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

NH ≅ G/Ntype
1. #20288987C2semidirect
2. #20288396C2semidirect
3. #20287011C2semidirect
4. #20286995C2semidirect
5. #20286898C2semidirect
6. #20286876C2semidirect
7. #20286786C2semidirect
8. #20286748C2semidirect
9. #20286640C2semidirect
10. #20286634C2semidirect
11. #20286451C2semidirect
12. #20286424C2semidirect
13. #20286348C2semidirect
14. #20286321C2semidirect
15. #20286287C2semidirect
16. #20286276C2semidirect
17. #20286242C2semidirect
18. #20286220C2semidirect
19. #20285826C2semidirect
20. #20285818C2semidirect
21. #20285604C2semidirect
22. #20285572C2semidirect
23. #20285544C2semidirect
24. #20285501C2semidirect
25. #20284977C2semidirect
26. #20284007C2semidirect
27. #20283998C2semidirect
28. #20283958C2semidirect
29. #20283930C2semidirect
30. #20283761C2semidirect
31. C53×#3125C2semidirect
33. C2×#41×D53C22semidirect
35. C2×#13133246C22semidirect
37. C2×#13133241C22semidirect
40. C2×Q16×D53C22semidirect
41. C2×SD16×D53C22semidirect
46. #16811346C22semidirect
47. #16811339C22semidirect
51. Q8×D212C22semidirect
54. #16811285C22semidirect
55. #16811281C22semidirect
59. #16811277C22semidirect
63. #16811268C22semidirect
64. #16811268C22semidirect
67. #16811244C22semidirect
74. #16811199C22semidirect
75. #16811196C22semidirect
76. #16811189C22semidirect
82. C2×#13133197C22semidirect
83. #16811018C22semidirect
84. #16811017C22semidirect
85. #16811007C22semidirect
86. #16811005C22semidirect
87. #16810985C22semidirect
88. #16810983C22semidirect
89. #16810975C22semidirect
90. #16810974C22semidirect
91. #16810967C22semidirect
92. #16810967C22semidirect
93. #16810967C22semidirect
94. #16810967C22semidirect
95. #16810967C22semidirect
96. #16810967C22semidirect
97. #16810958C22semidirect
98. #16810949C22semidirect
99. #16810949C22semidirect
100. #16810936C22semidirect
101. #16810918C22semidirect
102. #16810903C22semidirect
103. #16810882C22semidirect
104. #16810882C22semidirect
105. #16810882C22semidirect
106. #16810877C22semidirect
107. #16810872C22semidirect
110. #16810868C22semidirect
111. #16810863C22semidirect
112. #16810863C22semidirect
113. #16810863C22semidirect
114. #16810858C22semidirect
115. #16810853C22semidirect
116. #16810853C22semidirect
117. #16810853C22semidirect
118. #16810853C22semidirect
119. #16810846C22semidirect
120. #16810845C22semidirect
121. #16810845C22semidirect
122. #16810839C22semidirect
123. #16810838C22semidirect
124. #16810838C22semidirect
125. #16810834C22semidirect
126. #16810833C22semidirect
127. #16810829C22semidirect
128. #16810828C22semidirect
131. #16810787C22semidirect
132. #16810786C22semidirect
133. #16810786C22semidirect
134. #16810786C22semidirect
135. #16810785C22semidirect
136. #16810784C22semidirect
137. #16810783C22semidirect
138. #16810782C22semidirect
139. #16810782C22semidirect
140. #16810781C22semidirect
141. #16810780C22semidirect
142. #16810780C22semidirect
143. #16810780C22semidirect
144. #16810778C22semidirect
145. #16810777C22semidirect
146. #16810775C22semidirect
147. #16810775C22semidirect
151. #16810769C22semidirect
154. #16810765C22semidirect
155. #16810764C22semidirect
156. #16810763C22semidirect
157. #16810763C22semidirect
158. #16810761C22semidirect
160. #16810760C22semidirect
161. #16810758C22semidirect
163. #16810723C22semidirect
164. #16810721C22semidirect
165. C4×#11719925C22semidirect
166. C4×#11719922C22semidirect
167. #16810702C22semidirect
169. #16810696C22semidirect
170. #16810696C22semidirect
172. #16810693C22semidirect
173. C8×D212C22semidirect
174. #16810688C22semidirect
175. #16810684C22semidirect
176. #16810630C22semidirect
177. #16810630C22semidirect
178. #16810630C22semidirect
179. #16810626C22semidirect
180. #16810618C22semidirect
181. #16810616C22semidirect
182. #16810616C22semidirect
183. #16810616C22semidirect
184. #16810588C22semidirect
185. #16810588C22semidirect
186. #16810585C22semidirect
187. C22⋊C8×D53C22semidirect
188. C53×#542C22semidirect
189. C53×#520C22semidirect
190. C53×#483C22semidirect
191. C53×#481C22semidirect
192. C53×#476C22semidirect
193. C53×#475C22semidirect
194. C53×#464C22semidirect
195. C53×#463C22semidirect
196. C53×#452C22semidirect
198. C53×#442C22semidirect
199. C53×#441C22semidirect
200. C4×SD16×C53C22semidirect
201. C4×SD16×C53C22semidirect
202. C53×#433C22semidirect
946. #3125D53semidirect
1002. #542C2×D53semidirect
1017. #520C2×D53semidirect
1033. #483C2×D53semidirect
1036. #481C2×D53semidirect
1039. #476C2×D53semidirect
1040. #475C2×D53semidirect
1061. #464C2×D53semidirect
1065. #463C2×D53semidirect
1081. #452C2×D53semidirect
1106. #442C2×D53semidirect
1107. #441C2×D53semidirect
1111. C4×SD16C2×D53semidirect
1112. C4×SD16C2×D53semidirect
1123. #433C2×D53semidirect
1136. C53#61627semidirect

Maximal subgroups

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

subgroupindex
#202889872
#202883962
#202870112
#202869952
#202868982
#202868762
#202867862
#202867482
#202866402
#202866342
#202864512
#202864242
#202863482
#202863212
#202862872
#202862762
#202862422
#202862202
#202858262
#202858182
#202856042
#202855722
#202855442
#202855012
#202849772
#202840072
#202839982
#202839582
#202839302
#202837612
C53×#31252
#6162753