Finite Group Databasebeta

← #28270359

Subgroups — #28270359

Order 13568.

2110 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289013C211yesmaximal, characteristic, complemented
2#20288381C211yesmaximal, characteristic, complemented
3#20286858C211yesmaximal, characteristic, complemented
4#20286846C211yesmaximal, characteristic, complemented
5#20286830C211yesmaximal, characteristic, complemented
6#20286746C211yesmaximal, characteristic, complemented
7#20286647C211yesmaximal, characteristic, complemented
8#20286617C211yesmaximal, characteristic, complemented
9#20286557C211yesmaximal, characteristic, complemented
10#20286534C211yesmaximal, characteristic, complemented
11#20286456C211yesmaximal, characteristic, complemented
12#20286440C211yesmaximal, characteristic, complemented
13#20286415C211yesmaximal, characteristic, complemented
14D4×#11719924C211yesmaximal, characteristic, complemented
15#20286294C211yesmaximal, characteristic, complemented
16#20286239C211yesmaximal, characteristic, complemented
17#20286203C211yesmaximal, characteristic, complemented
18#20285816C211yesmaximal, characteristic, complemented
19#20285782C211yesmaximal, characteristic, complemented
20#20285622C211yesmaximal, characteristic, complemented
21#20285601C211yesmaximal, characteristic, complemented
22#20285481C211yesmaximal, characteristic, complemented
23#20285470C211yesmaximal, characteristic, complemented
24#20284990C211yesmaximal, characteristic, complemented
25#20284928C211yesmaximal, characteristic, complemented
26#20284023C211yesmaximal, characteristic, complemented
27#20283991C211yesmaximal, characteristic, complemented
28#20283938C211yesmaximal, characteristic, complemented
29C2×#16810784C211yesmaximal, characteristic, complemented
30#20283766C211yesmaximal, characteristic, complemented
31C53×#3270C211yesmaximal, characteristic, complemented
32C2×#13133263C2211yescharacteristic
33C22×#11719949C2211yescharacteristic
34C2×#13133244C2211yescharacteristic, complemented
35C2×#13133240C2211yescharacteristic, complemented
36C2×#13133240C2211yescharacteristic, complemented
37C2×#13133240C2211yescharacteristic, complemented
38C22×#11719924C2211yescharacteristic, complemented
39C22×#11719924C2211yescharacteristic, complemented
40#16811372—21no—
41#16811369—21no—
42#16811344C2211yescharacteristic, complemented
43#16811331C2211yescharacteristic, complemented
44#16811327—21no—
45#16811322—21no—
46#16811319C2211yescharacteristic, complemented
47#16811314C2211yescharacteristic, complemented
48#16811295C2211yescharacteristic
49#16811292C2211yescharacteristic
50#16811284C2211yescharacteristic
51#16811284C2211yescharacteristic, complemented
52#16811284C2211yescharacteristic, complemented
53#16811276C2211yescharacteristic, complemented
54#16811266—21no—
55#16811266C2211yescharacteristic
56#16811264—21no—
57#16811264C2211yescharacteristic
58D4×D212—21no—
59D4×D212C2211yescharacteristic
60#16811257—21no—
61#16811257C2211yescharacteristic
62#16811247—21no—
63#16811245C2211yescharacteristic, complemented
64#16811234C2211yescharacteristic, complemented
65#16811219—21no—
66#16811213—21no—
67#16811206—21no—
68#16811203—21no—
69#16811203C2211yescharacteristic
70#16811203C2211yescharacteristic, complemented
71#16811197C2211yescharacteristic, complemented
72#16811191—21no—
73#16811191C2211yescharacteristic
74#16811136C2211yescharacteristic, complemented
75#16811132—21no—
76#16811132C2211yescharacteristic
77C2×#13133193C2211yescharacteristic, complemented
78#121×D53—21no—
79#121×D53C2211yescharacteristic
80#16811105C2211yescharacteristic
81#16811009C2211yescharacteristic, complemented
82#16811008C2211yescharacteristic, complemented
83#16810997C2211yescharacteristic, complemented
84#16810988C2211yescharacteristic, complemented
85#16810984C2211yescharacteristic, complemented
86#16810977C2211yescharacteristic, complemented
87#16810968C2211yescharacteristic, complemented
88#16810961C2211yescharacteristic, complemented
89#16810957C2211yescharacteristic, complemented
90#16810952C2211yescharacteristic, complemented
91#16810952C2211yescharacteristic, complemented
92#16810952C2211yescharacteristic, complemented
93#16810949C2211yescharacteristic, complemented
94#16810948C2211yescharacteristic, complemented
95#16810945C2211yescharacteristic, complemented
96#16810943C2211yescharacteristic, complemented
97#16810943C2211yescharacteristic, complemented
98#16810942C2211yescharacteristic, complemented
99#16810939C2211yescharacteristic, complemented
100#16810930C2211yescharacteristic, complemented
101#16810924C2211yescharacteristic, complemented
102#16810912C2211yescharacteristic, complemented
103#16810906C2211yescharacteristic, complemented
104#16810878C2211yescharacteristic, complemented
105#16810876C2211yescharacteristic, complemented
106#16810872C2211yescharacteristic, complemented
107#16810861C2211yescharacteristic, complemented
108#16810859C2211yescharacteristic, complemented
109#16810857C2211yescharacteristic, complemented
110#16810855C2211yescharacteristic, complemented
111#16810855C2211yescharacteristic, complemented
112#16810855C2211yescharacteristic, complemented
113#16810854C2211yescharacteristic, complemented
114#16810854C2211yescharacteristic, complemented
115#16810854C2211yescharacteristic, complemented
116#16810849C2211yescharacteristic, complemented
117#16810849C2211yescharacteristic, complemented
118#16810847C2211yescharacteristic, complemented
119#16810847C2211yescharacteristic, complemented
120#16810847C2211yescharacteristic, complemented
121#16810841C2211yescharacteristic, complemented
122#16810835C2211yescharacteristic, complemented
123#16810825C2211yescharacteristic, complemented
124#16810823C2211yescharacteristic, complemented
125#16810821C2211yescharacteristic, complemented
126#16810821C2211yescharacteristic, complemented
127#16810819C2211yescharacteristic, complemented
128#16810784C2211yescharacteristic
129#16810784C2211yescharacteristic
130#16810784C2211yescharacteristic
131#16810784C2211yescharacteristic, complemented
132#16810784C2211yescharacteristic, complemented
133#16810784C2211yescharacteristic, complemented
134#16810784C2211yescharacteristic, complemented
135#16810784C2211yescharacteristic, complemented
136#16810784C2211yescharacteristic, complemented
137#16810784C2211yescharacteristic, complemented
138#16810784C2211yescharacteristic, complemented
139#16810784C2211yescharacteristic, complemented
140#16810784C2211yescharacteristic, complemented
141#16810773C2211yescharacteristic, complemented
142#16810773C2211yescharacteristic, complemented
143#16810772C2211yescharacteristic, complemented
144#16810772C2211yescharacteristic, complemented
145#16810772C2211yescharacteristic, complemented
146#16810772C2211yescharacteristic, complemented
147#16810772C2211yescharacteristic, complemented
148#16810771C2211yescharacteristic
149#16810771C2211yescharacteristic, complemented
150#16810771C2211yescharacteristic, complemented
151#16810771C2211yescharacteristic, complemented
152#16810768C2211yescharacteristic, complemented
153#16810767C2211yescharacteristic, complemented
154#16810762C2211yescharacteristic, complemented
155#16810762C2211yescharacteristic, complemented
156#16810762C2211yescharacteristic, complemented
157#16810759C2211yescharacteristic, complemented
158#16810759C2211yescharacteristic, complemented
159#16810758C2211yescharacteristic, complemented
160#16810736C2211yescharacteristic, complemented
161#16810730C2211yescharacteristic, complemented
162#16810726C2211yescharacteristic, complemented
163Q16×Dic53C2211yescharacteristic, complemented
164C4×#11719924C2211yescharacteristic, complemented
165C4×#11719924C2211yescharacteristic, complemented
166#16810708C2211yescharacteristic, complemented
167#16810696C2211yescharacteristic, complemented
168#16810692C2211yescharacteristic, complemented
169#16810691C2211yescharacteristic, complemented
170D4×#88322C2211yescharacteristic, complemented
171#16810688C2211yescharacteristic, complemented
172C8×C22⋊D53C2211yescharacteristic, complemented
173#16810686C2211yescharacteristic, complemented
174#16810685C2211yescharacteristic, complemented
175#16810683C2211yescharacteristic, complemented
176#16810629C2211yescharacteristic, complemented
177#16810623C2211yescharacteristic, complemented
178#16810619C2211yescharacteristic, complemented
179#16810618C2211yescharacteristic, complemented
180#16810618C2211yescharacteristic, complemented
181C2×#13133141C2211yescharacteristic, complemented
182C2×#13133139C2211yescharacteristic, complemented
183#102×D53C2211yescharacteristic, complemented
184#16810591C2211yescharacteristic, complemented
185#16810588C2211yescharacteristic, complemented
186C2×#13133129C2211yescharacteristic, complemented
187C22⋊C8×D53C2211yescharacteristic, complemented
188C2×#137×C53C2211yescharacteristic, complemented
189C22×Q16×C53C2211yescharacteristic, complemented
190D4×Q8×C53C2211yescharacteristic, complemented
191C53×#548C2211yescharacteristic
192C53×#497C2211yescharacteristic, complemented
193C53×#470C2211yescharacteristic, complemented
194C53×#465C2211yescharacteristic, complemented
195C53×#464C2211yescharacteristic, complemented
196C53×#462C2211yescharacteristic, complemented
197C53×#452C2211yescharacteristic, complemented
198C53×#451C2211yescharacteristic, complemented
199C53×#451C2211yescharacteristic, complemented
200C53×#448C2211yescharacteristic, complemented
201C53×#441C2211yescharacteristic, complemented
202C53×#435C2211yescharacteristic, complemented
203#13133263—42no—
204#13133263—42no—
205C2×#11719949—21no—
206C2×#11719949—21no—
207C2×#11719949—42no—
208C2×#11719949—42no—
209C2×#11719949C2311yescharacteristic
210C2×#11719949C2311yescharacteristic
211C2×#11719949C2311yescharacteristic
212C2×#11719949C2311yescharacteristic
213C2×#11719949C2311yescharacteristic
214C2×#11719949C2311yescharacteristic
215C2×#11719949C2311yescharacteristic
216C2×#11719945—21no—
217C2×#11719945C2311yescharacteristic
218C22×D212—21no—
219C22×D212—21no—
220C22×D212C2311yescharacteristic
221C22×D212C2311yescharacteristic
222C2×D4×D53—21no—
223C2×D4×D53—21no—
224C2×D4×D53—21no—
225C2×D4×D53—21no—
226C2×D4×D53—21no—
227C2×D4×D53C2311yescharacteristic
228C2×D4×D53C2311yescharacteristic
229C22×C4×D53—21no—
230C22×C4×D53C2311yescharacteristic
231#13133244—42no—
232#13133240—42no—
233#13133240—42no—
234#13133240—42no—
235C2×#11719924—42no—
236C2×#11719924—42no—
237C2×#11719924C2311yescharacteristic
238C2×#11719924C2311yescharacteristic
239C2×#11719924C2311yescharacteristic
240C2×#11719924C2311yescharacteristic
241C2×#11719924C2311yescharacteristic
242C2×#11719924C2311yescharacteristic
243C2×#11719924C2311yescharacteristic
244C2×#11719924C2311yescharacteristic
245C2×#11719924C2311yescharacteristic
246C2×#11719924C2311yescharacteristic
247C2×#11719924C2311yescharacteristic
248C2×D424C2311yescharacteristic
249C2×D424C2311yescharacteristic
250C2×D424C2311yescharacteristic
251C2×#11719922C2311yescharacteristic
252C2×#11719912C2311yescharacteristic
253C22×#88322C2311yescharacteristic
254C22×#88322C2311yescharacteristic
255C2×C8×D53C2311yescharacteristic
256C2×C8×D53C2311yescharacteristic
257C2×C8×D53C2311yescharacteristic
258#13133216C2311yescharacteristic
259#13133215—21no—
260#13133214—21no—
261#13133214C2311yescharacteristic
262#13133213—21no—
263#13133213C2311yescharacteristic
264#13133212—21no—
265#13133212—21no—
266#13133212—21no—
267#13133212—21no—
268#13133211—21no—
269#13133211—21no—
270#13133210—21no—
271#13133209C2311yescharacteristic
272#13133207—21no—
273#13133207—21no—
274#13133207—21no—
275#13133207—21no—
276#13133206—21no—
277#13133206—21no—
278#13133206—21no—
279#13133206—21no—
280#13133206C2311yescharacteristic
281#13133206C2311yescharacteristic
282#13133205—21no—
283#13133203—21no—
284#13133202—21no—
285#13133202—21no—
286#13133202—21no—
287#13133202—21no—
288#13133202—21no—
289#13133202—21no—
290#13133202D411yescharacteristic
291#13133200—21no—
292#13133200—21no—
293#13133199—21no—
294#13133199—21no—
295#13133199D411yescharacteristic
296#13133197—21no—
297#13133195—21no—
298#13133195—21no—
299#13133195—21no—
300#13133195D411yescharacteristic
301#13133194—21no—
302#13133194D411yescharacteristic
303#13133193—21no—
304#13133193—21no—
305#13133193—21no—
306#13133193—21no—
307#13133193—21no—
308#13133193C2311yescharacteristic
309#13133193C2311yescharacteristic
310#13133193C2311yescharacteristic
311#13133193C2311yescharacteristic
312#13133193C2311yescharacteristic
313#13133193C2311yescharacteristic
314#13133193C2311yescharacteristic
315#13133193C2311yescharacteristic
316#13133192—21no—
317#13133192—21no—
318#13133192—21no—
319#13133192—21no—
320#13133192—21no—
321#13133192—21no—
322#13133192—21no—
323#13133192C2311yescharacteristic
324#13133192C2311yescharacteristic
325#13133192C2311yescharacteristic
326#13133191—21no—
327#13133191—21no—
328#13133191—21no—
329#13133191—21no—
330#13133191C2311yescharacteristic
331#13133191C2311yescharacteristic
332#13133191C2311yescharacteristic
333#13133191C2311yescharacteristic
334#13133190—21no—
335#13133190—21no—
336#13133190—21no—
337#13133190—21no—
338#13133190—21no—
339#13133190—21no—
340#13133190—21no—
341#13133190—21no—
342#13133190—21no—
343#13133190D411yescharacteristic
344#13133189—21no—
345#13133189—21no—
346#13133189D411yescharacteristic
347#13133188—21no—
348#13133188C2311yescharacteristic
349#13133187—21no—
350#13133187—21no—
351#13133187—21no—
352#13133187—21no—
353#13133187—21no—
354#13133187—21no—
355#13133187—21no—
356#13133187—21no—
357#13133187D411yescharacteristic
358#13133185—21no—
359#13133185D411yescharacteristic
360Q8×Dic53C2311yescharacteristic
361Q8×Dic53C2311yescharacteristic
362Q8×Dic53C2311yescharacteristic
363#13133182—21no—
364C4×D212—21no—
365C4×D212—21no—
366C4×D212C2311yescharacteristic
367C4×D212C2311yescharacteristic
368C4×D212C2311yescharacteristic
369#13133179—21no—
370#13133179—21no—
371#13133179C2311yescharacteristic
372C4×C22⋊D53—21no—
373C4×C22⋊D53—21no—
374C4×C22⋊D53—21no—
375C4×C22⋊D53—21no—
376C4×C22⋊D53C2311yescharacteristic
377C4×C22⋊D53C2311yescharacteristic
378#13133177—21no—
379#13133177—21no—
380#13133177—21no—
381#13133176C2311yescharacteristic
382#13133175C2311yescharacteristic
383#13133174—21no—
384#13133174—21no—
385#13133174C2311yescharacteristic
386C2×C4⋊Dic53C2311yescharacteristic
387C2×#11719919—21no—
388C4⋊C4×D53—21no—
389C4⋊C4×D53—21no—
390C4⋊C4×D53C2311yescharacteristic
391C4⋊C4×D53C2311yescharacteristic
392C2×#11719921—21no—
393C22⋊C4×D53—21no—
394C22⋊C4×D53—21no—
395C22⋊C4×D53—21no—
396#13133151C2311yescharacteristic
397#13133150C2311yescharacteristic
398#13133149C2311yescharacteristic
399#13133149C2311yescharacteristic
400#13133148C2311yescharacteristic
401#13133148C2311yescharacteristic
402#13133148C2311yescharacteristic
403C4⋊#88322C2311yescharacteristic
404#13133146C2311yescharacteristic
405#13133146C2311yescharacteristic
406#13133141C2311yescharacteristic
407#13133141C2311yescharacteristic
408#13133141C2311yescharacteristic
409#13133141C2311yescharacteristic
410#13133141C2311yescharacteristic
411#13133141C2311yescharacteristic
412#13133141C2311yescharacteristic
413#13133141C2311yescharacteristic
414#13133141C2311yescharacteristic
415#13133139C2311yescharacteristic
416#13133139C2311yescharacteristic
417#13133139C2311yescharacteristic
418#13133139C2311yescharacteristic
419#13133139C2311yescharacteristic
420#13133139C2311yescharacteristic
421#13133139C2311yescharacteristic
422#13133139C2311yescharacteristic
423#13133139C2311yescharacteristic
424#13133139C2311yescharacteristic
425#13133138C2311yescharacteristic
426#13133138C2311yescharacteristic
427#13133138C2311yescharacteristic
428#13133137C2311yescharacteristic
429#13133137C2311yescharacteristic
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#13133127C2311yescharacteristic
443C4×#88322C2311yescharacteristic
444C8×Dic53C2311yescharacteristic
445C2×#41×C53C2311yescharacteristic
446C22×Q8×C53C2311yescharacteristic
447C22×Q8×C53C2311yescharacteristic
448C22×Q8×C53C2311yescharacteristic
449#137×C53—42no—
450C2×Q16×C53—42no—
451C2×Q16×C53C2311yescharacteristic
452C2×Q16×C53C2311yescharacteristic
453C2×Q16×C53C2311yescharacteristic
454C2×Q16×C53C2311yescharacteristic
455C2×Q16×C53C2311yescharacteristic
456C2×Q16×C53C2311yescharacteristic
457C2×SD16×C53C2311yescharacteristic
458C2×SD16×C53C2311yescharacteristic
459C2×SD16×C53C2311yescharacteristic
460C2×M16×C53C2311yescharacteristic
461C22×C8×C53C2311yescharacteristic
462C4⋊Q8×C53—21no—
463C4⋊Q8×C53C2311yescharacteristic
464#124×C53—21no—
465#124×C53C2311yescharacteristic
466C22⋊Q8×C53—21no—
467C22⋊Q8×C53—21no—
468C22⋊Q8×C53—21no—
469C22⋊Q8×C53C2311yescharacteristic
470C22⋊Q8×C53C2311yescharacteristic
471C22⋊Q8×C53C2311yescharacteristic
472#121×C53—21no—
473#121×C53C2311yescharacteristic
474C4×Q8×C53C2311yescharacteristic
475C4×Q8×C53C2311yescharacteristic
476C4×D4×C53—21no—
477C4×D4×C53—21no—
478C4×D4×C53C2311yescharacteristic
479#106×C53C2311yescharacteristic
480C4⋊C8×C53C2311yescharacteristic
481#103×C53C2311yescharacteristic
482#103×C53C2311yescharacteristic
483#103×C53C2311yescharacteristic
484#103×C53C2311yescharacteristic
485#103×C53C2311yescharacteristic
486#102×C53C2311yescharacteristic
487C22⋊C8×C53C2311yescharacteristic
488C22⋊C8×C53C2311yescharacteristic
489#97×C53C2311yescharacteristic
490C23×D53—21no—
491C23×D53—21no—
492C23×D53—21no—
493C23×D53—21no—
494C23×D53C2×D411yescharacteristic
495#41×C53—22no—
496#41×C53—41no—
497C2×Q8×C53—21no—
498C2×Q8×C53—21no—
499C2×Q8×C53—21no—
500C2×Q8×C53—22no—
501C2×Q8×C53—41no—
502C2×Q8×C53—41no—
503C2×Q8×C53—41no—
504C2×Q8×C53—41no—
505C2×Q8×C53—41no—
506C2×Q8×C53C2411yescharacteristic
507C2×Q8×C53C2411yescharacteristic
508C2×Q8×C53C2411yescharacteristic
509C2×Q8×C53C2411yescharacteristic
510C2×Q8×C53C2411yescharacteristic
511C2×D4×C53—21no—
512C2×D4×C53—21no—
513C2×D4×C53C2×D411yescharacteristic
514C2×D4×C53C2411yescharacteristic
515C22×C4×C53—21no—
516C22×C4×C53—21no—
517C22×C4×C53—21no—
518C22×C4×C53—21no—
519C22×C4×C53C2411yescharacteristic
520C22×C4×C53C2411yescharacteristic
521C2×C22⋊D53—21no—
522C2×C22⋊D53—21no—
523C2×C22⋊D53—21no—
524C2×C22⋊D53—21no—
525C2×C22⋊D53—21no—
526C2×C22⋊D53—21no—
527C2×C22⋊D53—21no—
528C2×C22⋊D53—21no—
529C2×C22⋊D53—21no—
530C2×C22⋊D53C2×D411yescharacteristic
531C2×C22⋊D53C2×D411yescharacteristic
532C2×C22⋊D53C2×D411yescharacteristic
533C2×C22⋊D53C2×D411yescharacteristic
534C22×Dic53—21no—
535C22×Dic53C2×D411yescharacteristic
536#11719949—22no—
537#11719949—22no—
538#11719949—22no—
539#11719949—22no—
540#11719949—22no—
541#11719949—41no—
542#11719949—41no—
543#11719949—41no—
544#11719949—41no—
545#11719949—41no—
546#11719949—44no—
547#11719949—41no—
548#11719949—41no—
549#11719949—41no—
550#11719949—41no—
551#11719949—44no—
552D4×D53—22no—
553D4×D53—41no—
554D4×D53—41no—
555D4×D53—41no—
556D4×D53—44no—
557D4×D53—44no—
558D4×D53—82no—
559D4×D53—82no—
560D4×D53—82no—
561#11719945—41no—
562#11719945—41no—
563#11719945—44no—
564C2×D212—21no—
565C2×D212—22no—
566C2×D212—22no—
567C2×D212—21no—
568C2×D212—21no—
569C2×D212—21no—
570C2×D212—21no—
571C2×D212—21no—
572C2×D212—21no—
573C2×D212—21no—
574C2×D212—21no—
575C2×D212—21no—
576C2×D212—21no—
577C2×D212—21no—
578C2×D212—21no—
579C2×D212—21no—
580C2×D212—41no—
581C2×D212—41no—
582C2×D212—44no—
583C2×D212—44no—
584C2×D212C2×D411yescharacteristic
585C2×D212C2×D411yescharacteristic
586C2×D212C2411yescharacteristic
587C2×D212C2411yescharacteristic
588C2×D212C2411yescharacteristic
589C2×D212C2411yescharacteristic
590C2×C4×D53—21no—
591C2×C4×D53—21no—
592C2×C4×D53—21no—
593C2×C4×D53—21no—
594C2×C4×D53—21no—
595C2×C4×D53—21no—
596C2×C4×D53—21no—
597C2×C4×D53—21no—
598C2×C4×D53—21no—
599C2×C4×D53—21no—
600C2×C4×D53—21no—
601C2×C4×D53—21no—
602C2×C4×D53—41no—
603C2×C4×D53—41no—
604C2×C4×D53—44no—
605C2×C4×D53C2×D411yescharacteristic
606C2×C4×D53C2×D411yescharacteristic
607C2×C4×D53C2411yescharacteristic
608C2×C4×D53C2411yescharacteristic
609C2×C4×D53C2411yescharacteristic
610C2×Dic106—21no—
611C2×Dic106C2×D411yescharacteristic
612Q16×C53—22no—
613Q16×C53—22no—
614Q16×C53—22no—
615Q16×C53—41no—
616Q16×C53—41no—
617Q16×C53—41no—
618SD16×C53—41no—
619SD16×C53—41no—
620SD16×C53—41no—
621M16×C53—41no—
622C2×C8×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×C53—21no—
631C4⋊C4×C53—21no—
632C4⋊C4×C53—21no—
633C4⋊C4×C53—21no—
634C4⋊C4×C53C2×D411yescharacteristic
635C4⋊C4×C53C2411yescharacteristic
636C4⋊C4×C53C2411yescharacteristic
637C22⋊C4×C53—21no—
638C22⋊C4×C53—21no—
639C22⋊C4×C53—21no—
640C22⋊C4×C53—21no—
641C22⋊C4×C53—21no—
642C22⋊C4×C53—21no—
643C22⋊C4×C53C2×D411yescharacteristic
644C22⋊C4×C53C2×D411yescharacteristic
645C42×C53—21no—
646C42×C53—21no—
647C42×C53C2411yescharacteristic
648C22⋊Dic53—21no—
649C22⋊Dic53—21no—
650C22⋊Dic53C2×D411yescharacteristic
651C22⋊Dic53C2×D411yescharacteristic
652#11719924—22no—
653#11719924—22no—
654#11719924—22no—
655#11719924—22no—
656#11719924—41no—
657#11719924—41no—
658#11719924—41no—
659#11719924—41no—
660#11719924—41no—
661#11719924—41no—
662#11719924—41no—
663#11719922—41no—
664#11719921—21no—
665#11719921—21no—
666#11719921—21no—
667#11719921—21no—
668#11719921—21no—
669#11719921—21no—
670#11719921—21no—
671#11719921—21no—
672#11719921—21no—
673#11719921—21no—
674#11719921—21no—
675#11719921—21no—
676#11719921—21no—
677#11719921—21no—
678#11719921—21no—
679#11719921—21no—
680#11719921—21no—
681#11719921—21no—
682#11719921—21no—
683#11719921—21no—
684#11719921—21no—
685#11719921—21no—
686#11719921—21no—
687#11719921C2×D411yescharacteristic
688#11719921C2×D411yescharacteristic
689#11719921C2×D411yescharacteristic
690#11719921C2×D411yescharacteristic
691#11719921C2×D411yescharacteristic
692#11719921C2×D411yescharacteristic
693C4⋊Dic53—21no—
694C4⋊Dic53—21no—
695C4⋊Dic53—21no—
696C4⋊Dic53—21no—
697C4⋊Dic53C2×D411yescharacteristic
698C4⋊Dic53C2411yescharacteristic
699C4⋊Dic53C2411yescharacteristic
700C4⋊Dic53C2411yescharacteristic
701C4⋊Dic53C2411yescharacteristic
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#11719919—21no—
715#11719919C2×D411yescharacteristic
716#11719919C2×D411yescharacteristic
717#11719919C2×D411yescharacteristic
718#11719919C2×D411yescharacteristic
719C4×Dic53—21no—
720C4×Dic53—21no—
721C4×Dic53—21no—
722C4×Dic53—21no—
723C4×Dic53—21no—
724C4×Dic53C2411yescharacteristic
725C2×#88322—41no—
726C2×#88322—41no—
727C2×#88322C2411yescharacteristic
728C2×#88322C2411yescharacteristic
729C2×#88322C2411yescharacteristic
730C2×#88322C2411yescharacteristic
731D424—22no—
732D424—41no—
733D424—41no—
734#11719912—41no—
735C8×D53—41no—
736C8×D53—41no—
737C8×D53—41no—
738C23×C53—21no—
739C23×C53C22×D411yescharacteristic
740C23×C53C22×D411yescharacteristic
741C22×D53—21no—
742C22×D53—22no—
743C22×D53—21no—
744C22×D53—21no—
745C22×D53—21no—
746C22×D53—41no—
747C22×D53—41no—
748C22×D53—42no—
749C22×D53—42no—
750C22×D53—42no—
751C22×D53—42no—
752C22×D53—42no—
753C22×D53—81no—
754C22×D53—81no—
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—21no—
770Q8×C53—21no—
771Q8×C53—21no—
772Q8×C53—42no—
773Q8×C53—81no—
774Q8×C53—81no—
775Q8×C53H(5,𝔽2)12yes—
776D4×C53—22no—
777D4×C53—21no—
778D4×C53—21no—
779D4×C53—42no—
780D4×C53—42no—
781C2×C4×C53—21no—
782C2×C4×C53—21no—
783C2×C4×C53—21no—
784C2×C4×C53—21no—
785C2×C4×C53—21no—
786C2×C4×C53—21no—
787C2×C4×C53—21no—
788C2×C4×C53—21no—
789C2×C4×C53—21no—
790C2×C4×C53—21no—
791C2×C4×C53—21no—
792C2×C4×C53—42no—
793C2×C4×C53—42no—
794C2×C4×C53—81no—
795C2×C4×C53—81no—
796C2×C4×C53C22×D411yescharacteristic
797C2×C4×C53C22×D411yescharacteristic
798C2×C4×C53C22×D411yescharacteristic
799C2×C4×C53C22×D411yescharacteristic
800C2×C4×C53C2511yescharacteristic
801C22⋊D53—22no—
802C22⋊D53—41no—
803C22⋊D53—41no—
804C22⋊D53—41no—
805C22⋊D53—42no—
806C22⋊D53—42no—
807C22⋊D53—42no—
808C22⋊D53—42no—
809C22⋊D53—81no—
810C22⋊D53—81no—
811C22⋊D53—81no—
812C22⋊D53—81no—
813C22⋊D53—81no—
814C2×Dic53—21no—
815C2×Dic53—21no—
816C2×Dic53—21no—
817C2×Dic53—21no—
818C2×Dic53—41no—
819C2×Dic53—81no—
820C2×Dic53C22×D411yescharacteristic
821C2×Dic53C22×D411yescharacteristic
822C2×Dic53C22×D411yescharacteristic
823C2×Dic53C22×D411yescharacteristic
824C2×Dic53C22×D411yescharacteristic
825D212—24no—
826D212—21no—
827D212—21no—
828D212—21no—
829D212—21no—
830D212—21no—
831D212—21no—
832D212—21no—
833D212—41no—
834D212—41no—
835D212—42no—
836D212—42no—
837D212—42no—
838D212—42no—
839D212—42no—
840D212—42no—
841D212—81no—
842D212—81no—
843D212—81no—
844D212—81no—
845D212—81no—
846D212—81no—
847D212—81no—
848D212H(5,𝔽2)12yes—
849C4×D53—24no—
850C4×D53—21no—
851C4×D53—21no—
852C4×D53—21no—
853C4×D53—21no—
854C4×D53—21no—
855C4×D53—21no—
856C4×D53—41no—
857C4×D53—41no—
858C4×D53—42no—
859C4×D53—42no—
860C4×D53—42no—
861C4×D53—42no—
862C4×D53—81no—
863C4×D53—81no—
864C4×D53—81no—
865C4×D53—81no—
866C4×D53—81no—
867C4×D53—81no—
868C4×D53—81no—
869Dic106—41no—
870Dic106—81no—
871C8×C53—21no—
872C8×C53—21no—
873C8×C53—21no—
874C8×C53—21no—
875#88322—21no—
876#88322—21no—
877#88322—21no—
878#88322—21no—
879#61640—531nomaximal, Sylow
880C22×C53—21no—
881C22×C53—21no—
882C22×C53—21no—
883C22×C53—21no—
884C22×C53—21no—
885C22×C53—41no—
886C22×C53—41no—
887C22×C53—41no—
888C22×C53#57712yes—
889C22×C53C23×D411yescharacteristic
890C2×D53—21no—
891C2×D53—21no—
892C2×D53—21no—
893C2×D53—21no—
894C2×D53—22no—
895C2×D53—21no—
896C2×D53—21no—
897C2×D53—21no—
898C2×D53—21no—
899C2×D53—21no—
900C2×D53—41no—
901C2×D53—41no—
902C2×D53—41no—
903C2×D53—41no—
904C2×D53—41no—
905C2×D53—41no—
906C2×D53—41no—
907C2×D53—41no—
908C2×D53—41no—
909C2×D53—41no—
910C2×D53—41no—
911C2×D53—82no—
912C2×D53—84no—
913C2×D53—162no—
914C2×D53—162no—
915C2×D53—162no—
916C4×C53—21no—
917C4×C53—21no—
918C4×C53—22no—
919C4×C53—21no—
920C4×C53—21no—
921C4×C53—41no—
922C4×C53—41no—
923C4×C53—41no—
924C4×C53—41no—
925C4×C53—41no—
926C4×C53—41no—
927C4×C53C2×H(5,𝔽2)11yescharacteristic
928C4×C53C2×H(5,𝔽2)11yescharacteristic
929Dic53—21no—
930Dic53—21no—
931Dic53—21no—
932Dic53—21no—
933Dic53—21no—
934Dic53—41no—
935Dic53—41no—
936Dic53—41no—
937Dic53—41no—
938#3541—531no—
939#3488—531no—
940#3318—531no—
941#3317—531no—
942#3316—531no—
943#3311—531no—
944#3304—531no—
945#3301—531no—
946#3296—531no—
947#3295—531no—
948#3285—531no—
949#3284—531no—
950#3282—531no—
951D4×SD16—531no—
952#3271—531no—
953#3270D5311yescharacteristic, complemented
954#3267—531no—
955#3265—531no—
956#3224—531no—
957#3222—531no—
958#3204—531no—
959#3201—531no—
960#3188—531no—
961#3187—531no—
962#3125—531no—
963#3120—531no—
964#3012—531no—
965#3009—531no—
966#3002—531no—
967C2×#452—531no—
968#2977—531no—
969C2×C53—22no—
970C2×C53—41no—
971C2×C53—81no—
972C2×C53#348411yescharacteristic
973C2×C53C2×#57711yescharacteristic
974C2×C53#358411yescharacteristic
975D53—41no—
976D53—41no—
977D53—41no—
978D53—42no—
979D53—81no—
980D53—81no—
981D53—81no—
982C2×H(5,𝔽2)—531no—
983C22×#41—531no—
984C2×#137C2×D5311yescharacteristic, complemented
985C2×AGL(1,ℤ/8)—531no—
986C2×#135—531no—
987C2×#135—531no—
988C2×#135—531no—
989C22×Q16C2×D5311yescharacteristic, complemented
990C22×SD16—531no—
991C22×SD16—531no—
992#563—1061no—
993#562—1061no—
994#556—531no—
995#554—531no—
996#554—1061no—
997#553—531no—
998#553—1061no—
999#552—531no—
1000#550—531no—
1001#550—531no—
1002D4×Q8C2×D5311yescharacteristic, complemented
1003#548—531no—
1004#548—531no—
1005#548—531no—
1006#548C2×D5311yescharacteristic
1007#547—531no—
1008#546—531no—
1009#546—531no—
1010#546—1061no—
1011#546—1061no—
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#497C2×D5311yescharacteristic, complemented
1036#496—531no—
1037#495—531no—
1038#492—531no—
1039#490—531no—
1040#489—531no—
1041#488—531no—
1042#486—531no—
1043#485—531no—
1044#484—531no—
1045#483—531no—
1046#483—531no—
1047#483—531no—
1048#482—531no—
1049#482—531no—
1050#482—531no—
1051#481—531no—
1052#481—531no—
1053#481—531no—
1054#481—531no—
1055#479—531no—
1056#478—531no—
1057#476—531no—
1058#475—531no—
1059#470—531no—
1060#470C2×D5311yescharacteristic, complemented
1061#469—531no—
1062#468—531no—
1063#467—531no—
1064#466—531no—
1065#466—531no—
1066#465—531no—
1067#465—531no—
1068#465—531no—
1069#465—531no—
1070#465—531no—
1071#465—531no—
1072#465—531no—
1073#465—531no—
1074#465C2×D5311yescharacteristic, complemented
1075#464—531no—
1076#464—531no—
1077#464—531no—
1078#464C2×D5311yescharacteristic, complemented
1079#463—531no—
1080#463—531no—
1081#462C2×D5311yescharacteristic, complemented
1082#461—531no—
1083#460—531no—
1084#460—531no—
1085#460—531no—
1086#459—531no—
1087#452—531no—
1088#452—531no—
1089#452—531no—
1090#452—531no—
1091#452—531no—
1092#452—531no—
1093#452—531no—
1094#452—531no—
1095#452—531no—
1096#452—531no—
1097#452—531no—
1098#452—531no—
1099#452—531no—
1100#452C2×D5311yescharacteristic, complemented
1101#451C2×D5311yescharacteristic, complemented
1102#451C2×D5311yescharacteristic, complemented
1103#450—531no—
1104#450—531no—
1105#450—531no—
1106#450—531no—
1107#450—531no—
1108#450—531no—
1109#450—531no—
1110#449—531no—
1111#449—531no—
1112#449—531no—
1113#449—531no—
1114#449—531no—
1115#449—531no—
1116#448—531no—
1117#448—531no—
1118#448—531no—
1119#448C2×D5311yescharacteristic, complemented
1120#447—531no—
1121#447—531no—
1122#447—531no—
1123#442—531no—
1124#441—531no—
1125#441C2×D5311yescharacteristic, complemented
1126#440—531no—
1127C4×Q16—531no—
1128C4×SD16—531no—
1129C4×SD16—531no—
1130C4×SD16—531no—
1131#435—531no—
1132#435—531no—
1133#435—531no—
1134#435C2×D5311yescharacteristic, complemented
1135C8×D4—531no—
1136C8×D4—531no—
1137C8×D4—531no—
1138C8×D4—531no—
1139#433—531no—
1140#433—531no—
1141#418—531no—
1142#417—531no—
1143#416—531no—
1144#416—531no—
1145#416—531no—
1146C2×#103—531no—
1147C2×#102—531no—
1148C2×#102—531no—
1149#408—531no—
1150#408—531no—
1151C2×C22⋊C8—531no—
1152C2×C22⋊C8—531no—
1153C53#6164011yescharacteristic, complemented, Sylow
1154H(5,𝔽2)—2122no—
1155H(5,𝔽2)—2122no—
1156C2×#41—531no—
1157C2×#41—531no—
1158C2×#41—531no—
1159C2×#41—531no—
1160C2×#41—531no—
1161C2×#41—531no—
1162C2×#41—531no—
1163C2×#41—531no—
1164C2×#41—1061no—
1165C2×#41—1061no—
1166C2×#41—1061no—
1167C2×#41—2122no—
1168C2×#41—2122no—
1169C2×#41C22×D5311yescharacteristic
1170C22×Q8C22×D5311yescharacteristic
1171C22×Q8C22×D5311yescharacteristic
1172C22×Q8C22×D5311yescharacteristic
1173C22×D4—531no—
1174C22×D4—531no—
1175C22×D4—531no—
1176C22×D4—531no—
1177C22×D4—1061no—
1178C22×D4—1061no—
1179C22×D4—1061no—
1180C22×D4—1061no—
1181C22×D4—1061no—
1182C22×D4—1061no—
1183C22×D4—1061no—
1184C23×C4—531no—
1185C23×C4—1061no—
1186#137—42no—
1187AGL(1,ℤ/8)—2122no—
1188#135—2122no—
1189#135—2122no—
1190#135—2122no—
1191C2×Q16—42no—
1192C2×Q16C22×D5311yescharacteristic
1193C2×Q16C22×D5311yescharacteristic
1194C2×Q16C22×D5311yescharacteristic
1195C2×Q16C22×D5311yescharacteristic
1196C2×Q16C22×D5311yescharacteristic
1197C2×Q16C22×D5311yescharacteristic
1198C2×SD16—531no—
1199C2×SD16—531no—
1200C2×SD16—531no—
1201C2×SD16—531no—
1202C2×SD16—531no—
1203C2×SD16—531no—
1204C2×SD16—531no—
1205C2×SD16—531no—
1206C2×SD16—531no—
1207C2×SD16—531no—
1208C2×SD16—531no—
1209C2×SD16—2122no—
1210C2×SD16—2122no—
1211C2×SD16C22×D5311yescharacteristic
1212C2×SD16C22×D5311yescharacteristic
1213C2×SD16C22×D5311yescharacteristic
1214C2×D8—531no—
1215C2×D8—531no—
1216C2×D8—531no—
1217C2×D8—531no—
1218C2×M16—531no—
1219C2×M16C22×D5311yescharacteristic
1220C22×C8—531no—
1221C22×C8—531no—
1222C22×C8—531no—
1223C22×C8—531no—
1224C22×C8—531no—
1225C22×C8C22×D5311yescharacteristic
1226C4⋊Q8—21no—
1227C4⋊Q8—531no—
1228C4⋊Q8—1061no—
1229C4⋊Q8C22×D5311yescharacteristic
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—531no—
1249#124—1061no—
1250#124—1061no—
1251#124—1061no—
1252#124—1061no—
1253#124—1061no—
1254#124—1061no—
1255#124C22×D5311yescharacteristic
1256#123—531no—
1257#123—531no—
1258#123—1061no—
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—21no—
1270C22⋊Q8—21no—
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—531no—
1281C22⋊Q8—1061no—
1282C22⋊Q8—1061no—
1283C22⋊Q8—1061no—
1284C22⋊Q8—1061no—
1285C22⋊Q8—1061no—
1286C22⋊Q8—1061no—
1287C22⋊Q8—1061no—
1288C22⋊Q8—1061no—
1289C22⋊Q8—1061no—
1290C22⋊Q8—1061no—
1291C22⋊Q8C22×D5311yescharacteristic
1292C22⋊Q8C22×D5311yescharacteristic
1293C22⋊Q8C22×D5311yescharacteristic
1294#121—21no—
1295#121—531no—
1296#121—531no—
1297#121—531no—
1298#121—531no—
1299#121—531no—
1300#121—531no—
1301#121—531no—
1302#121—531no—
1303#121—531no—
1304#121—531no—
1305#121—1061no—
1306#121—1061no—
1307#121—1061no—
1308#121—1061no—
1309#121—1061no—
1310#121—1061no—
1311#121—1061no—
1312#121—1061no—
1313#121—1061no—
1314#121—1061no—
1315#121—1061no—
1316#121—1061no—
1317#121—1061no—
1318#121—1061no—
1319#121—1061no—
1320#121—1061no—
1321#121—1061no—
1322#121—1061no—
1323#121—1061no—
1324#121—1061no—
1325#121—1061no—
1326#121—1061no—
1327#121—1061no—
1328#121C22×D5311yescharacteristic
1329#120—531no—
1330#120—531no—
1331#120—1061no—
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—1061no—
1344C4×Q8C22×D5311yescharacteristic
1345C4×Q8C22×D5311yescharacteristic
1346C4×D4—21no—
1347C4×D4—21no—
1348C4×D4—531no—
1349C4×D4—531no—
1350C4×D4—531no—
1351C4×D4—531no—
1352C4×D4—531no—
1353C4×D4—531no—
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×D4—1061no—
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—1061no—
1378C2×C22⋊C4—1061no—
1379C2×C22⋊C4—1061no—
1380C2×C22⋊C4—1061no—
1381#107—531no—
1382#107—531no—
1383#106—531no—
1384#106—531no—
1385#106—531no—
1386#106—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#103C22×D5311yescharacteristic
1403#103C22×D5311yescharacteristic
1404#103C22×D5311yescharacteristic
1405#103C22×D5311yescharacteristic
1406#103C22×D5311yescharacteristic
1407#102—531no—
1408#102—531no—
1409#102—531no—
1410#102—531no—
1411#102—531no—
1412#102—531no—
1413#102—531no—
1414#102—531no—
1415#102—531no—
1416#102—531no—
1417#102—531no—
1418#102—531no—
1419#102—531no—
1420#102—531no—
1421#102—531no—
1422#102—531no—
1423#102—531no—
1424#102C22×D5311yescharacteristic
1425C22⋊C8—531no—
1426C22⋊C8—531no—
1427C22⋊C8—531no—
1428C22⋊C8—531no—
1429C22⋊C8—531no—
1430C22⋊C8—531no—
1431C22⋊C8—531no—
1432C22⋊C8—531no—
1433C22⋊C8—531no—
1434C22⋊C8—531no—
1435C22⋊C8C22×D5311yescharacteristic
1436C22⋊C8C22×D5311yescharacteristic
1437#97—531no—
1438#97C22×D5311yescharacteristic
1439C4×C8—531no—
1440C4×C8—531no—
1441C24—531no—
1442C24—1061no—
1443C24—1061no—
1444C24—1061no—
1445C24—1061no—
1446#41—22no—
1447#41—41no—
1448#41—1062no—
1449#41—1062no—
1450#41—1062no—
1451#41—1062no—
1452#41—1062no—
1453#41—2121no—
1454#41—2121no—
1455#41—2124no—
1456#41—2121no—
1457#41—2121no—
1458#41—2121no—
1459#41—2121no—
1460#41—2121no—
1461#41—2121no—
1462#41—2121no—
1463#41—2121no—
1464#41—2121no—
1465#41—2124no—
1466#41—2124no—
1467C2×Q8—21no—
1468C2×Q8—21no—
1469C2×Q8—21no—
1470C2×Q8—22no—
1471C2×Q8—41no—
1472C2×Q8—41no—
1473C2×Q8—41no—
1474C2×Q8—41no—
1475C2×Q8—41no—
1476C2×Q8—531no—
1477C2×Q8—1061no—
1478C2×Q8C23×D5311yescharacteristic
1479C2×Q8C23×D5311yescharacteristic
1480C2×Q8C23×D5311yescharacteristic
1481C2×Q8C23×D5311yescharacteristic
1482C2×Q8C23×D5311yescharacteristic
1483C2×D4—21no—
1484C2×D4—21no—
1485C2×D4—531no—
1486C2×D4—531no—
1487C2×D4—531no—
1488C2×D4—531no—
1489C2×D4—531no—
1490C2×D4—531no—
1491C2×D4—531no—
1492C2×D4—531no—
1493C2×D4—531no—
1494C2×D4—531no—
1495C2×D4—1062no—
1496C2×D4—1062no—
1497C2×D4—1061no—
1498C2×D4—1061no—
1499C2×D4—1061no—
1500C2×D4—1061no—
1501C2×D4—1061no—
1502C2×D4—1061no—
1503C2×D4—1061no—
1504C2×D4—1061no—
1505C2×D4—1061no—
1506C2×D4—1061no—
1507C2×D4—1061no—
1508C2×D4—1061no—
1509C2×D4—1061no—
1510C2×D4—1061no—
1511C2×D4—1062no—
1512C2×D4—1061no—
1513C2×D4—1061no—
1514C2×D4—1061no—
1515C2×D4—1061no—
1516C2×D4—1061no—
1517C2×D4—1061no—
1518C2×D4—1061no—
1519C2×D4—1061no—
1520C2×D4—1061no—
1521C2×D4—4242no—
1522C2×D4—4242no—
1523C2×D4—4242no—
1524C2×D4—2121no—
1525C2×D4—2121no—
1526C2×D4—2124no—
1527C2×D4—2124no—
1528C2×D4—2121no—
1529C2×D4—2121no—
1530C2×D4—2121no—
1531C2×D4—2124no—
1532C2×D4—2124no—
1533C2×D4D4×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—22no—
1564Q16—22no—
1565Q16—22no—
1566Q16—41no—
1567Q16—41no—
1568Q16—41no—
1569SD16—41no—
1570SD16—41no—
1571SD16—41no—
1572SD16—1062no—
1573SD16—1062no—
1574SD16—1062no—
1575SD16—1062no—
1576SD16—2121no—
1577SD16—2121no—
1578SD16—2121no—
1579SD16—2121no—
1580SD16—2121no—
1581SD16—2121no—
1582SD16—2121no—
1583D8—1062no—
1584D8—2121no—
1585D8—2121no—
1586D8—2121no—
1587M16—41no—
1588M16—2121no—
1589C2×C8—41no—
1590C2×C8—531no—
1591C2×C8—531no—
1592C2×C8—531no—
1593C2×C8—531no—
1594C2×C8—2121no—
1595C2×C8—2121no—
1596C2×C8—2121no—
1597C2×C8—2121no—
1598C2×C8—2121no—
1599C2×C8C23×D5311yescharacteristic
1600C2×C8C23×D5311yescharacteristic
1601C2×C8C23×D5311yescharacteristic
1602C2×C8C23×D5311yescharacteristic
1603C4⋊C4—21no—
1604C4⋊C4—21no—
1605C4⋊C4—21no—
1606C4⋊C4—21no—
1607C4⋊C4—21no—
1608C4⋊C4—21no—
1609C4⋊C4—21no—
1610C4⋊C4—531no—
1611C4⋊C4—531no—
1612C4⋊C4—531no—
1613C4⋊C4—531no—
1614C4⋊C4—531no—
1615C4⋊C4—531no—
1616C4⋊C4—531no—
1617C4⋊C4—531no—
1618C4⋊C4—531no—
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—531no—
1646C22⋊C4—531no—
1647C22⋊C4—531no—
1648C22⋊C4—531no—
1649C22⋊C4—531no—
1650C22⋊C4—531no—
1651C22⋊C4—531no—
1652C22⋊C4—531no—
1653C22⋊C4—1061no—
1654C22⋊C4—1061no—
1655C22⋊C4—1061no—
1656C22⋊C4—1061no—
1657C22⋊C4—1061no—
1658C22⋊C4—1061no—
1659C22⋊C4—1061no—
1660C22⋊C4—1061no—
1661C22⋊C4—1061no—
1662C22⋊C4—1061no—
1663C22⋊C4—1061no—
1664C22⋊C4—1061no—
1665C22⋊C4—1061no—
1666C22⋊C4—1061no—
1667C22⋊C4—1061no—
1668C22⋊C4—1061no—
1669C22⋊C4—1061no—
1670C22⋊C4—1061no—
1671C22⋊C4—1061no—
1672C22⋊C4—1061no—
1673C22⋊C4—1061no—
1674C22⋊C4—1061no—
1675C22⋊C4—1061no—
1676C22⋊C4—1061no—
1677C22⋊C4—1061no—
1678C22⋊C4D4×D5311yescharacteristic
1679C22⋊C4D4×D5311yescharacteristic
1680C42—21no—
1681C42—21no—
1682C42—531no—
1683C42—1061no—
1684C42—1061no—
1685C42—1061no—
1686C42—1061no—
1687C42—1061no—
1688C42C23×D5311yescharacteristic
1689C23—21no—
1690C23—531no—
1691C23—531no—
1692C23—531no—
1693C23—1062no—
1694C23—1061no—
1695C23—1061no—
1696C23—1061no—
1697C23—1061no—
1698C23—4241no—
1699C23—4241no—
1700C23—4241no—
1701C23—4241no—
1702C23—4241no—
1703C23—4241no—
1704C23—4241no—
1705C23—2122no—
1706C23—2121no—
1707C23—2121no—
1708C23—2122no—
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—21no—
1721Q8—21no—
1722Q8—21no—
1723Q8—42no—
1724Q8—81no—
1725Q8—81no—
1726Q8—4241no—
1727Q8—2121no—
1728Q8#1313326212yes—
1729D4—22no—
1730D4—21no—
1731D4—21no—
1732D4—42no—
1733D4—42no—
1734D4—532no—
1735D4—1064no—
1736D4—1062no—
1737D4—1061no—
1738D4—1061no—
1739D4—1061no—
1740D4—1061no—
1741D4—1061no—
1742D4—1061no—
1743D4—1061no—
1744D4—4241no—
1745D4—4241no—
1746D4—4241no—
1747D4—4241no—
1748D4—4241no—
1749D4—4241no—
1750D4—4241no—
1751D4—4241no—
1752D4—4241no—
1753D4—4241no—
1754D4—4241no—
1755D4—4241no—
1756D4—2121no—
1757D4—2121no—
1758D4—2122no—
1759D4—2122no—
1760D4—2122no—
1761D4—2122no—
1762D4—2122no—
1763D4—2122no—
1764D4—2121no—
1765D4—2121no—
1766D4—2121no—
1767D4—2122no—
1768D4—2122no—
1769D4—2122no—
1770D4—2122no—
1771C2×C4—21no—
1772C2×C4—21no—
1773C2×C4—21no—
1774C2×C4—21no—
1775C2×C4—21no—
1776C2×C4—21no—
1777C2×C4—21no—
1778C2×C4—21no—
1779C2×C4—21no—
1780C2×C4—21no—
1781C2×C4—21no—
1782C2×C4—42no—
1783C2×C4—42no—
1784C2×C4—81no—
1785C2×C4—81no—
1786C2×C4—531no—
1787C2×C4—531no—
1788C2×C4—531no—
1789C2×C4—531no—
1790C2×C4—531no—
1791C2×C4—1064no—
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—4241no—
1810C2×C4—2121no—
1811C2×C4—2121no—
1812C2×C4—2122no—
1813C2×C4—2122no—
1814C2×C4—2122no—
1815C2×C4—2122no—
1816C2×C4—2121no—
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—21no—
1833C22—21no—
1834C22—21no—
1835C22—41no—
1836C22—41no—
1837C22—41no—
1838C22—8482no—
1839C22—8482no—
1840C22—8482no—
1841C22—1062no—
1842C22—1061no—
1843C22—1061no—
1844C22—1061no—
1845C22—1061no—
1846C22—1061no—
1847C22—1061no—
1848C22—1061no—
1849C22—1061no—
1850C22—1061no—
1851C22—4244no—
1852C22—4242no—
1853C22—2121no—
1854C22—2121no—
1855C22—2121no—
1856C22—2121no—
1857C22—2121no—
1858C22—2121no—
1859C22—2121no—
1860C22—2121no—
1861C22—2121no—
1862C22—2121no—
1863C22—2121no—
1864C22#1681143212yes—
1865C22C22×D4×D5311yescharacteristic
1866C4—21no—
1867C4—21no—
1868C4—22no—
1869C4—21no—
1870C4—21no—
1871C4—41no—
1872C4—41no—
1873C4—41no—
1874C4—41no—
1875C4—41no—
1876C4—41no—
1877C4—1061no—
1878C4—1061no—
1879C4—1061no—
1880C4—1061no—
1881C4—1061no—
1882C4—2121no—
1883C4—2121no—
1884C4—2121no—
1885C4—2121no—
1886C4H(5,𝔽2)×D5311yescharacteristic
1887C4C2×#1313326211yescharacteristic
1888C2—22no—
1889C2—41no—
1890C2—81no—
1891C2—4241no—
1892C2—4241no—
1893C2—4241no—
1894C2—2121no—
1895C2—2121no—
1896C2—2122no—
1897C2—2121no—
1898C2#2028834311yescharacteristic
1899C2C2×#1681143211yescharacteristic
1900C2#2028948511yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3270C2
socleC22×C53C23×D4
hypercenter#3270D53
hypocenterC53#61640
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3270

Complements

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

NH ≅ G/Ntype
1. #20289013C2semidirect
2. #20288381C2semidirect
3. #20286858C2semidirect
4. #20286846C2semidirect
5. #20286830C2semidirect
6. #20286746C2semidirect
7. #20286647C2semidirect
8. #20286617C2semidirect
9. #20286557C2semidirect
10. #20286534C2semidirect
11. #20286456C2semidirect
12. #20286440C2semidirect
13. #20286415C2semidirect
14. D4×#11719924C2semidirect
15. #20286294C2semidirect
16. #20286239C2semidirect
17. #20286203C2semidirect
18. #20285816C2semidirect
19. #20285782C2semidirect
20. #20285622C2semidirect
21. #20285601C2semidirect
22. #20285481C2semidirect
23. #20285470C2semidirect
24. #20284990C2semidirect
25. #20284928C2semidirect
26. #20284023C2semidirect
27. #20283991C2semidirect
28. #20283938C2semidirect
29. C2×#16810784C2semidirect
30. #20283766C2semidirect
31. C53×#3270C2semidirect
34. C2×#13133244C22semidirect
35. C2×#13133240C22semidirect
36. C2×#13133240C22semidirect
37. C2×#13133240C22semidirect
38. C22×#11719924C22semidirect
39. C22×#11719924C22semidirect
42. #16811344C22semidirect
43. #16811331C22semidirect
46. #16811319C22semidirect
47. #16811314C22semidirect
51. #16811284C22semidirect
52. #16811284C22semidirect
53. #16811276C22semidirect
63. #16811245C22semidirect
64. #16811234C22semidirect
70. #16811203C22semidirect
71. #16811197C22semidirect
74. #16811136C22semidirect
77. C2×#13133193C22semidirect
81. #16811009C22semidirect
82. #16811008C22semidirect
83. #16810997C22semidirect
84. #16810988C22semidirect
85. #16810984C22semidirect
86. #16810977C22semidirect
87. #16810968C22semidirect
88. #16810961C22semidirect
89. #16810957C22semidirect
90. #16810952C22semidirect
91. #16810952C22semidirect
92. #16810952C22semidirect
93. #16810949C22semidirect
94. #16810948C22semidirect
95. #16810945C22semidirect
96. #16810943C22semidirect
97. #16810943C22semidirect
98. #16810942C22semidirect
99. #16810939C22semidirect
100. #16810930C22semidirect
101. #16810924C22semidirect
102. #16810912C22semidirect
103. #16810906C22semidirect
104. #16810878C22semidirect
105. #16810876C22semidirect
106. #16810872C22semidirect
107. #16810861C22semidirect
108. #16810859C22semidirect
109. #16810857C22semidirect
110. #16810855C22semidirect
111. #16810855C22semidirect
112. #16810855C22semidirect
113. #16810854C22semidirect
114. #16810854C22semidirect
115. #16810854C22semidirect
116. #16810849C22semidirect
117. #16810849C22semidirect
118. #16810847C22semidirect
119. #16810847C22semidirect
120. #16810847C22semidirect
121. #16810841C22semidirect
122. #16810835C22semidirect
123. #16810825C22semidirect
124. #16810823C22semidirect
125. #16810821C22semidirect
126. #16810821C22semidirect
127. #16810819C22semidirect
131. #16810784C22semidirect
132. #16810784C22semidirect
133. #16810784C22semidirect
134. #16810784C22semidirect
135. #16810784C22semidirect
136. #16810784C22semidirect
137. #16810784C22semidirect
138. #16810784C22semidirect
139. #16810784C22semidirect
140. #16810784C22semidirect
141. #16810773C22semidirect
142. #16810773C22semidirect
143. #16810772C22semidirect
144. #16810772C22semidirect
145. #16810772C22semidirect
146. #16810772C22semidirect
147. #16810772C22semidirect
149. #16810771C22semidirect
150. #16810771C22semidirect
151. #16810771C22semidirect
152. #16810768C22semidirect
153. #16810767C22semidirect
154. #16810762C22semidirect
155. #16810762C22semidirect
156. #16810762C22semidirect
157. #16810759C22semidirect
158. #16810759C22semidirect
159. #16810758C22semidirect
160. #16810736C22semidirect
161. #16810730C22semidirect
162. #16810726C22semidirect
163. Q16×Dic53C22semidirect
164. C4×#11719924C22semidirect
165. C4×#11719924C22semidirect
166. #16810708C22semidirect
167. #16810696C22semidirect
168. #16810692C22semidirect
169. #16810691C22semidirect
170. D4×#88322C22semidirect
171. #16810688C22semidirect
172. C8×C22⋊D53C22semidirect
173. #16810686C22semidirect
174. #16810685C22semidirect
175. #16810683C22semidirect
176. #16810629C22semidirect
177. #16810623C22semidirect
178. #16810619C22semidirect
179. #16810618C22semidirect
180. #16810618C22semidirect
181. C2×#13133141C22semidirect
182. C2×#13133139C22semidirect
183. #102×D53C22semidirect
184. #16810591C22semidirect
185. #16810588C22semidirect
186. C2×#13133129C22semidirect
187. C22⋊C8×D53C22semidirect
188. C2×#137×C53C22semidirect
189. C22×Q16×C53C22semidirect
190. D4×Q8×C53C22semidirect
192. C53×#497C22semidirect
193. C53×#470C22semidirect
194. C53×#465C22semidirect
195. C53×#464C22semidirect
196. C53×#462C22semidirect
197. C53×#452C22semidirect
198. C53×#451C22semidirect
199. C53×#451C22semidirect
200. C53×#448C22semidirect
201. C53×#441C22semidirect
202. C53×#435C22semidirect
953. #3270D53semidirect
984. C2×#137C2×D53semidirect
989. C22×Q16C2×D53semidirect
1002. D4×Q8C2×D53semidirect
1035. #497C2×D53semidirect
1060. #470C2×D53semidirect
1074. #465C2×D53semidirect
1078. #464C2×D53semidirect
1081. #462C2×D53semidirect
1100. #452C2×D53semidirect
1101. #451C2×D53semidirect
1102. #451C2×D53semidirect
1119. #448C2×D53semidirect
1125. #441C2×D53semidirect
1134. #435C2×D53semidirect
1153. C53#61640semidirect

Maximal subgroups

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

subgroupindex
#202890132
#202883812
#202868582
#202868462
#202868302
#202867462
#202866472
#202866172
#202865572
#202865342
#202864562
#202864402
#202864152
D4×#117199242
#202862942
#202862392
#202862032
#202858162
#202857822
#202856222
#202856012
#202854812
#202854702
#202849902
#202849282
#202840232
#202839912
#202839382
C2×#168107842
#202837662
C53×#32702
#6164053