Finite Group Databasebeta

← #28270347

Subgroups — #28270347

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#20288994C211yesmaximal, characteristic, complemented
2#20288375C211yesmaximal, characteristic, complemented
3#20286860C211yesmaximal, characteristic, complemented
4#20286836C211yesmaximal, characteristic, complemented
5#20286828C211yesmaximal, characteristic, complemented
6#20286756C211yesmaximal, characteristic, complemented
7#20286657C211yesmaximal, characteristic, complemented
8#20286623C211yesmaximal, characteristic, complemented
9#20286554C211yesmaximal, characteristic, complemented
10#20286539C211yesmaximal, characteristic, complemented
11#20286452C211yesmaximal, characteristic, complemented
12#20286443C211yesmaximal, characteristic, complemented
13#20286428C211yesmaximal, characteristic, complemented
14SD16×C22⋊D53C211yesmaximal, characteristic, complemented
15#20286299C211yesmaximal, characteristic, complemented
16#20286278C211yesmaximal, characteristic, complemented
17#20286234C211yesmaximal, characteristic, complemented
18#20285804C211yesmaximal, characteristic, complemented
19#20285786C211yesmaximal, characteristic, complemented
20#20285624C211yesmaximal, characteristic, complemented
21#20285592C211yesmaximal, characteristic, complemented
22#20285475C211yesmaximal, characteristic, complemented
23#20285470C211yesmaximal, characteristic, complemented
24#20284989C211yesmaximal, characteristic, complemented
25#20284933C211yesmaximal, characteristic, complemented
26#20284018C211yesmaximal, characteristic, complemented
27#20283987C211yesmaximal, characteristic, complemented
28#20283928C211yesmaximal, characteristic, complemented
29C2×#16810782C211yesmaximal, characteristic, complemented
30#20283766C211yesmaximal, characteristic, complemented
31C53×#3265C211yesmaximal, characteristic, complemented
32C2×#13133262C2211yescharacteristic
33C22×#11719947C2211yescharacteristic
34C2×#13133246C2211yescharacteristic, complemented
35C2×#13133237C2211yescharacteristic, complemented
36C2×#13133236C2211yescharacteristic, complemented
37C2×#13133236C2211yescharacteristic, complemented
38C22×#11719925C2211yescharacteristic, complemented
39C2×SD16×D53C2211yescharacteristic, complemented
40#16811374—21no—
41#16811367—21no—
42#16811346C2211yescharacteristic, complemented
43#16811332—21no—
44#16811330C2211yescharacteristic, complemented
45#16811325C2211yescharacteristic, complemented
46#16811316—21no—
47#16811315C2211yescharacteristic, complemented
48#16811293C2211yescharacteristic
49#16811291C2211yescharacteristic
50Q8×C22⋊D53C2211yescharacteristic, complemented
51#16811282C2211yescharacteristic
52#16811281C2211yescharacteristic, complemented
53#16811279C2211yescharacteristic
54#16811272C2211yescharacteristic, complemented
55#16811268C2211yescharacteristic
56#16811267C2211yescharacteristic
57#16811262—21no—
58#16811260—21no—
59D4×C22⋊D53—21no—
60D4×C22⋊D53C2211yescharacteristic
61#16811255—21no—
62#16811242C2211yescharacteristic, complemented
63#16811237—21no—
64#16811231C2211yescharacteristic, complemented
65#16811222—21no—
66#16811210—21no—
67#16811206—21no—
68#16811202C2211yescharacteristic
69#16811201C2211yescharacteristic, complemented
70#16811200—21no—
71#16811196C2211yescharacteristic, complemented
72#16811188—21no—
73#16811186C2211yescharacteristic
74#16811133C2211yescharacteristic, complemented
75#16811132C2211yescharacteristic
76#16811129—21no—
77C2×#13133193C2211yescharacteristic, complemented
78C2×#13133189—21no—
79#121×D53C2211yescharacteristic
80#16811102C2211yescharacteristic
81#16811014C2211yescharacteristic, complemented
82#16811005C2211yescharacteristic, complemented
83#16810994C2211yescharacteristic, complemented
84#16810986C2211yescharacteristic, complemented
85#16810983C2211yescharacteristic, complemented
86#16810976C2211yescharacteristic, complemented
87#16810969C2211yescharacteristic, complemented
88#16810966C2211yescharacteristic, complemented
89#16810960C2211yescharacteristic, complemented
90#16810954C2211yescharacteristic, complemented
91#16810952C2211yescharacteristic, complemented
92#16810952C2211yescharacteristic, complemented
93#16810950C2211yescharacteristic, complemented
94#16810946C2211yescharacteristic, complemented
95#16810946C2211yescharacteristic, complemented
96#16810942C2211yescharacteristic, complemented
97#16810940C2211yescharacteristic, complemented
98#16810939C2211yescharacteristic, complemented
99#16810939C2211yescharacteristic, complemented
100#16810929C2211yescharacteristic, complemented
101#16810925C2211yescharacteristic, complemented
102#16810913C2211yescharacteristic, complemented
103#16810909C2211yescharacteristic, complemented
104#16810881C2211yescharacteristic, complemented
105#16810880C2211yescharacteristic, complemented
106#16810873C2211yescharacteristic, complemented
107#16810862C2211yescharacteristic, complemented
108#16810857C2211yescharacteristic, complemented
109#16810855C2211yescharacteristic, complemented
110#16810855C2211yescharacteristic, complemented
111#16810852C2211yescharacteristic, complemented
112#16810851C2211yescharacteristic, complemented
113#16810850C2211yescharacteristic, complemented
114#16810850C2211yescharacteristic, complemented
115#16810849C2211yescharacteristic, complemented
116#16810849C2211yescharacteristic, complemented
117#16810849C2211yescharacteristic, complemented
118#16810846C2211yescharacteristic, complemented
119#16810845C2211yescharacteristic, complemented
120#16810843C2211yescharacteristic, complemented
121#16810842C2211yescharacteristic, complemented
122#16810836C2211yescharacteristic, complemented
123#16810832C2211yescharacteristic, complemented
124#16810826C2211yescharacteristic, complemented
125#16810821C2211yescharacteristic, complemented
126#16810820C2211yescharacteristic, complemented
127#16810816C2211yescharacteristic, complemented
128#16810787C2211yescharacteristic, complemented
129#16810786C2211yescharacteristic
130#16810786C2211yescharacteristic, complemented
131#16810785C2211yescharacteristic, complemented
132#16810783C2211yescharacteristic, complemented
133#16810782C2211yescharacteristic
134#16810782C2211yescharacteristic
135#16810782C2211yescharacteristic, complemented
136#16810782C2211yescharacteristic, complemented
137#16810782C2211yescharacteristic, complemented
138#16810782C2211yescharacteristic, complemented
139#16810782C2211yescharacteristic, complemented
140#16810782C2211yescharacteristic, complemented
141#16810782C2211yescharacteristic, complemented
142#16810781C2211yescharacteristic, complemented
143#16810780C2211yescharacteristic, complemented
144#16810775C2211yescharacteristic, complemented
145#16810774C2211yescharacteristic, complemented
146#16810774C2211yescharacteristic, complemented
147#16810772C2211yescharacteristic, complemented
148#16810772C2211yescharacteristic, complemented
149#16810772C2211yescharacteristic, complemented
150#16810769C2211yescharacteristic, complemented
151#16810765C2211yescharacteristic
152#16810765C2211yescharacteristic, complemented
153#16810765C2211yescharacteristic, complemented
154#16810765C2211yescharacteristic, complemented
155#16810762C2211yescharacteristic, complemented
156#16810761C2211yescharacteristic, complemented
157#16810760C2211yescharacteristic, complemented
158#16810755C2211yescharacteristic, complemented
159#16810755C2211yescharacteristic, complemented
160#16810735C2211yescharacteristic, complemented
161#16810731C2211yescharacteristic, complemented
162#16810727C2211yescharacteristic, complemented
163C4×#11719925C2211yescharacteristic, complemented
164#16810714C2211yescharacteristic, complemented
165SD16×Dic53C2211yescharacteristic, complemented
166C4×#11719923C2211yescharacteristic, 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#16810626C2211yescharacteristic, complemented
177#16810625C2211yescharacteristic, complemented
178#16810616C2211yescharacteristic, complemented
179#16810616C2211yescharacteristic, complemented
180#16810616C2211yescharacteristic, complemented
181C2×#13133142C2211yescharacteristic, complemented
182C2×#13133138C2211yescharacteristic, complemented
183C2×#13133138C2211yescharacteristic, complemented
184#16810591C2211yescharacteristic, complemented
185#16810588C2211yescharacteristic, complemented
186C2×#13133129C2211yescharacteristic, complemented
187C22⋊C8×D53C2211yescharacteristic, complemented
188C2×AGL(1,ℤ/8)×C53C2211yescharacteristic, complemented
189C22×SD16×C53C2211yescharacteristic, complemented
190C53×#548C2211yescharacteristic, complemented
191D42×C53C2211yescharacteristic
192C53×#496C2211yescharacteristic, complemented
193C53×#468C2211yescharacteristic, complemented
194C53×#466C2211yescharacteristic, complemented
195C53×#463C2211yescharacteristic, complemented
196C53×#460C2211yescharacteristic, complemented
197C53×#450C2211yescharacteristic, complemented
198C53×#449C2211yescharacteristic, complemented
199C53×#448C2211yescharacteristic, complemented
200C53×#447C2211yescharacteristic, complemented
201C53×#440C2211yescharacteristic, complemented
202C53×#435C2211yescharacteristic, complemented
203#13133262—42no—
204#13133262—42no—
205C2×#11719945C2311yescharacteristic
206C2×#11719945C2311yescharacteristic
207C2×#11719947—21no—
208C2×#11719947—21no—
209C2×#11719947—21no—
210C2×#11719947—42no—
211C2×#11719947—42no—
212C2×#11719947C2311yescharacteristic
213C2×#11719947C2311yescharacteristic
214C2×#11719947C2311yescharacteristic
215C2×#11719947C2311yescharacteristic
216C2×#11719947C2311yescharacteristic
217C2×#11719947C2311yescharacteristic
218C22×Dic106C2311yescharacteristic
219C2×Q8×D53C2311yescharacteristic
220C22×C22⋊D53—21no—
221C22×C22⋊D53—21no—
222C22×C22⋊D53—21no—
223C22×C22⋊D53—21no—
224C2×D4×D53—21no—
225C2×D4×D53—21no—
226C2×D4×D53C2311yescharacteristic
227C2×D4×D53C2311yescharacteristic
228C23×Dic53—21no—
229C22×C4×D53C2311yescharacteristic
230#13133246—42no—
231#13133237—42no—
232#13133236—42no—
233#13133236—42no—
234C2×Dic212C2311yescharacteristic
235C2×Dic212C2311yescharacteristic
236C2×#11719925—42no—
237C2×#11719925C2311yescharacteristic
238C2×#11719925C2311yescharacteristic
239C2×#11719925C2311yescharacteristic
240C2×#11719925C2311yescharacteristic
241C2×#11719913C2311yescharacteristic
242C2×#11719923C2311yescharacteristic
243C2×#11719923C2311yescharacteristic
244C2×#11719923C2311yescharacteristic
245C2×#11719923C2311yescharacteristic
246C2×#11719923C2311yescharacteristic
247C2×#11719924C2311yescharacteristic
248C2×#11719924C2311yescharacteristic
249SD16×D53—42no—
250C2×#11719922C2311yescharacteristic
251C2×#11719912C2311yescharacteristic
252C22×#88322C2311yescharacteristic
253C22×#88322C2311yescharacteristic
254C2×C8×D53C2311yescharacteristic
255C2×C8×D53C2311yescharacteristic
256C2×C8×D53C2311yescharacteristic
257#13133217C2311yescharacteristic
258#13133216—21no—
259#13133215—21no—
260#13133215C2311yescharacteristic
261#13133213—21no—
262#13133213—21no—
263#13133213C2311yescharacteristic
264#13133212—21no—
265#13133212—21no—
266#13133212—21no—
267#13133212—21no—
268#13133211—21no—
269#13133210—21no—
270#13133210—21no—
271#13133209—21no—
272#13133208—21no—
273#13133208—21no—
274#13133208C2311yescharacteristic
275#13133207—21no—
276#13133205—21no—
277#13133205C2311yescharacteristic
278#13133204C2311yescharacteristic
279#13133203—21no—
280#13133203—21no—
281#13133203—21no—
282#13133203—21no—
283#13133203—21no—
284#13133202—21no—
285#13133202D411yescharacteristic
286#13133201—21no—
287#13133201—21no—
288#13133201—21no—
289#13133201—21no—
290#13133200—21no—
291#13133199—21no—
292#13133199—21no—
293#13133199D411yescharacteristic
294#13133198—21no—
295#13133198—21no—
296#13133197C2311yescharacteristic
297#13133197C2311yescharacteristic
298#13133196—21no—
299#13133196—21no—
300#13133196C2311yescharacteristic
301#13133196C2311yescharacteristic
302#13133196C2311yescharacteristic
303#13133195—21no—
304#13133195D411yescharacteristic
305#13133194—21no—
306#13133194—21no—
307#13133194—21no—
308#13133194—21no—
309#13133194—21no—
310#13133194—21no—
311#13133194D411yescharacteristic
312#13133193—21no—
313#13133193—21no—
314#13133193—21no—
315#13133193C2311yescharacteristic
316#13133193C2311yescharacteristic
317#13133193C2311yescharacteristic
318#13133193C2311yescharacteristic
319#13133193C2311yescharacteristic
320#13133192C2311yescharacteristic
321#13133191—21no—
322#13133191—21no—
323#13133191C2311yescharacteristic
324#13133190—21no—
325#13133190—21no—
326#13133190—21no—
327#13133190—21no—
328#13133190D411yescharacteristic
329#13133189—21no—
330#13133189—21no—
331#13133189—21no—
332#13133189—21no—
333#13133189—21no—
334#13133189—21no—
335#13133189—21no—
336#13133189—21no—
337#13133189—21no—
338#13133189—21no—
339#13133189—21no—
340#13133189—21no—
341#13133189—21no—
342#13133189—21no—
343#13133189—21no—
344#13133189D411yescharacteristic
345#13133188—21no—
346#13133188C2311yescharacteristic
347#13133188C2311yescharacteristic
348#13133188C2311yescharacteristic
349#13133188C2311yescharacteristic
350#13133187—21no—
351#13133187D411yescharacteristic
352#13133186—21no—
353#13133186—21no—
354#13133185—21no—
355#13133185—21no—
356#13133185—21no—
357#13133185—21no—
358#13133185D411yescharacteristic
359Q8×Dic53C2311yescharacteristic
360C4×Dic106—21no—
361C4×Dic106C2311yescharacteristic
362C4×Dic106C2311yescharacteristic
363#13133182C2311yescharacteristic
364C4×D212C2311yescharacteristic
365D4×Dic53—21no—
366D4×Dic53—21no—
367D4×Dic53—21no—
368D4×Dic53—21no—
369D4×Dic53—21no—
370D4×Dic53C2311yescharacteristic
371D4×Dic53C2311yescharacteristic
372C4×C22⋊D53—21no—
373C4×C22⋊D53—21no—
374C4×C22⋊D53C2311yescharacteristic
375C4×C22⋊D53C2311yescharacteristic
376#13133177—21no—
377#13133177—21no—
378#13133177—21no—
379#13133177—21no—
380#13133177—21no—
381#13133175C2311yescharacteristic
382#13133175C2311yescharacteristic
383#13133174C2311yescharacteristic
384#13133173—21no—
385#13133173—21no—
386C2×C4⋊Dic53C2311yescharacteristic
387C2×C4⋊Dic53C2311yescharacteristic
388C2×#11719919—21no—
389C2×#11719919—21no—
390C2×#11719919—21no—
391C4⋊C4×D53C2311yescharacteristic
392C2×C22⋊Dic53—21no—
393C2×#11719921—21no—
394C2×#11719921—21no—
395C22⋊C4×D53—21no—
396#13133150C2311yescharacteristic
397#13133149C2311yescharacteristic
398#13133149C2311yescharacteristic
399#13133149C2311yescharacteristic
400#13133148C2311yescharacteristic
401#13133148C2311yescharacteristic
402#13133148C2311yescharacteristic
403C4⋊#88322C2311yescharacteristic
404#13133146C2311yescharacteristic
405#13133146C2311yescharacteristic
406#13133142C2311yescharacteristic
407#13133142C2311yescharacteristic
408#13133142C2311yescharacteristic
409#13133142C2311yescharacteristic
410#13133142C2311yescharacteristic
411#13133142C2311yescharacteristic
412#13133142C2311yescharacteristic
413#13133141C2311yescharacteristic
414#13133141C2311yescharacteristic
415#13133140C2311yescharacteristic
416#13133140C2311yescharacteristic
417#13133140C2311yescharacteristic
418#13133139C2311yescharacteristic
419#13133139C2311yescharacteristic
420#13133139C2311yescharacteristic
421#13133138C2311yescharacteristic
422#13133138C2311yescharacteristic
423#13133138C2311yescharacteristic
424#13133138C2311yescharacteristic
425#13133138C2311yescharacteristic
426#13133138C2311yescharacteristic
427#13133138C2311yescharacteristic
428#13133138C2311yescharacteristic
429#13133138C2311yescharacteristic
430#13133138C2311yescharacteristic
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×D4×C53—21no—
448C22×D4×C53C2311yescharacteristic
449C22×D4×C53C2311yescharacteristic
450AGL(1,ℤ/8)×C53—42no—
451C2×SD16×C53—42no—
452C2×SD16×C53C2311yescharacteristic
453C2×SD16×C53C2311yescharacteristic
454C2×SD16×C53C2311yescharacteristic
455C2×SD16×C53C2311yescharacteristic
456C2×SD16×C53C2311yescharacteristic
457C2×SD16×C53C2311yescharacteristic
458C2×D8×C53C2311yescharacteristic
459C2×D8×C53C2311yescharacteristic
460C2×D8×C53C2311yescharacteristic
461C2×M16×C53C2311yescharacteristic
462C22×C8×C53C2311yescharacteristic
463#127×C53C2311yescharacteristic
464#124×C53—21no—
465#124×C53C2311yescharacteristic
466C22⋊Q8×C53—21no—
467C22⋊Q8×C53C2311yescharacteristic
468#121×C53—21no—
469#121×C53—21no—
470#121×C53C2311yescharacteristic
471#121×C53C2311yescharacteristic
472#121×C53C2311yescharacteristic
473#120×C53—21no—
474#120×C53—21no—
475C4×Q8×C53C2311yescharacteristic
476C4×D4×C53—21no—
477C4×D4×C53C2311yescharacteristic
478C4×D4×C53C2311yescharacteristic
479#107×C53C2311yescharacteristic
480C4⋊C8×C53C2311yescharacteristic
481#103×C53C2311yescharacteristic
482#103×C53C2311yescharacteristic
483#102×C53C2311yescharacteristic
484#102×C53C2311yescharacteristic
485#102×C53C2311yescharacteristic
486#102×C53C2311yescharacteristic
487C22⋊C8×C53C2311yescharacteristic
488C22⋊C8×C53C2311yescharacteristic
489#97×C53C2311yescharacteristic
490C24×C53—21no—
491C24×C53—21no—
492C23×D53—21no—
493C23×D53—21no—
494C23×D53C2×D411yescharacteristic
495#41×C53—41no—
496#41×C53—41no—
497C2×Q8×C53—21no—
498C2×Q8×C53—41no—
499C2×Q8×C53—41no—
500C2×Q8×C53C2411yescharacteristic
501C2×Q8×C53C2411yescharacteristic
502C2×D4×C53—22no—
503C2×D4×C53—22no—
504C2×D4×C53—21no—
505C2×D4×C53—21no—
506C2×D4×C53—21no—
507C2×D4×C53—21no—
508C2×D4×C53—21no—
509C2×D4×C53—21no—
510C2×D4×C53—21no—
511C2×D4×C53—21no—
512C2×D4×C53—41no—
513C2×D4×C53—41no—
514C2×D4×C53—82no—
515C2×D4×C53C2×D411yescharacteristic
516C2×D4×C53C2411yescharacteristic
517C2×D4×C53C2411yescharacteristic
518C2×D4×C53C2411yescharacteristic
519C2×D4×C53C2411yescharacteristic
520C22×C4×C53—21no—
521C22×C4×C53—21no—
522C22×C4×C53—21no—
523C22×C4×C53C2411yescharacteristic
524C22×C4×C53C2411yescharacteristic
525C2×C22⋊D53—21no—
526C2×C22⋊D53—21no—
527C2×C22⋊D53—21no—
528C2×C22⋊D53—21no—
529C2×C22⋊D53—21no—
530C2×C22⋊D53—21no—
531C2×C22⋊D53—21no—
532C2×C22⋊D53—21no—
533C2×C22⋊D53—21no—
534C2×C22⋊D53—21no—
535C2×C22⋊D53—21no—
536C2×C22⋊D53—21no—
537C2×C22⋊D53—21no—
538C2×C22⋊D53—21no—
539C2×C22⋊D53—21no—
540C2×C22⋊D53—21no—
541C2×C22⋊D53—44no—
542C2×C22⋊D53—44no—
543C2×C22⋊D53—44no—
544C2×C22⋊D53—82no—
545C2×C22⋊D53C2×D411yescharacteristic
546C2×C22⋊D53C2×D411yescharacteristic
547C2×C22⋊D53C2×D411yescharacteristic
548C2×C22⋊D53C2×D411yescharacteristic
549C22×Dic53—21no—
550C22×Dic53—21no—
551C22×Dic53—21no—
552C22×Dic53—21no—
553C22×Dic53—21no—
554C22×Dic53—21no—
555C22×Dic53—21no—
556C22×Dic53—21no—
557C22×Dic53—21no—
558C22×Dic53—21no—
559C22×Dic53—21no—
560C22×Dic53—44no—
561C22×Dic53C2×D411yescharacteristic
562Q8×D53—41no—
563Q8×D53—41no—
564#11719947—22no—
565#11719947—22no—
566#11719947—22no—
567#11719947—22no—
568#11719947—22no—
569#11719947—41no—
570#11719947—41no—
571#11719947—41no—
572#11719947—41no—
573#11719947—41no—
574#11719947—41no—
575#11719947—41no—
576#11719947—44no—
577#11719947—44no—
578#11719947—44no—
579D4×D53—22no—
580D4×D53—41no—
581D4×D53—41no—
582D4×D53—41no—
583D4×D53—44no—
584D4×D53—82no—
585#11719945—22no—
586#11719945—41no—
587#11719945—41no—
588#11719945—41no—
589C2×D212—21no—
590C2×D212C2×D411yescharacteristic
591C2×D212C2×D411yescharacteristic
592C2×D212C2411yescharacteristic
593C2×C4×D53—21no—
594C2×C4×D53—21no—
595C2×C4×D53—21no—
596C2×C4×D53—41no—
597C2×C4×D53—41no—
598C2×C4×D53C2×D411yescharacteristic
599C2×C4×D53C2×D411yescharacteristic
600C2×C4×D53C2411yescharacteristic
601C2×C4×D53C2411yescharacteristic
602C2×C4×D53C2411yescharacteristic
603C2×Dic106—22no—
604C2×Dic106—21no—
605C2×Dic106—21no—
606C2×Dic106—21no—
607C2×Dic106—41no—
608C2×Dic106C2×D411yescharacteristic
609C2×Dic106C2411yescharacteristic
610C2×Dic106C2411yescharacteristic
611C2×Dic106C2411yescharacteristic
612SD16×C53—22no—
613SD16×C53—22no—
614SD16×C53—41no—
615SD16×C53—41no—
616SD16×C53—41no—
617SD16×C53—41no—
618D8×C53—22no—
619D8×C53—41no—
620D8×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×C53C2×D411yescharacteristic
630C4⋊C4×C53C2411yescharacteristic
631C4⋊C4×C53C2411yescharacteristic
632C22⋊C4×C53—21no—
633C22⋊C4×C53—21no—
634C22⋊C4×C53—21no—
635C22⋊C4×C53—21no—
636C22⋊C4×C53—21no—
637C22⋊C4×C53—21no—
638C22⋊C4×C53—21no—
639C22⋊C4×C53C2×D411yescharacteristic
640C22⋊C4×C53C2×D411yescharacteristic
641C42×C53—21no—
642C42×C53C2411yescharacteristic
643C22⋊Dic53—21no—
644C22⋊Dic53—21no—
645C22⋊Dic53—21no—
646C22⋊Dic53—21no—
647C22⋊Dic53—21no—
648C22⋊Dic53—21no—
649C22⋊Dic53—21no—
650C22⋊Dic53—21no—
651C22⋊Dic53—21no—
652C22⋊Dic53—21no—
653C22⋊Dic53—21no—
654C22⋊Dic53C2×D411yescharacteristic
655C22⋊Dic53C2×D411yescharacteristic
656#11719925—22no—
657#11719925—22no—
658#11719925—41no—
659#11719925—41no—
660#11719924—41no—
661#11719924—41no—
662#11719923—22no—
663#11719923—22no—
664#11719923—41no—
665#11719923—41no—
666#11719923—41no—
667#11719922—41no—
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#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⋊Dic53C2×D411yescharacteristic
695C4⋊Dic53C2411yescharacteristic
696C4⋊Dic53C2411yescharacteristic
697C4⋊Dic53C2411yescharacteristic
698C4⋊Dic53C2411yescharacteristic
699#11719919—21no—
700#11719919—21no—
701#11719919—21no—
702#11719919—21no—
703#11719919—21no—
704#11719919—21no—
705#11719919—21no—
706#11719919—21no—
707#11719919—21no—
708#11719919—21no—
709#11719919—21no—
710#11719919—21no—
711#11719919—21no—
712#11719919—21no—
713#11719919—21no—
714#11719919C2×D411yescharacteristic
715#11719919C2×D411yescharacteristic
716#11719919C2×D411yescharacteristic
717#11719919C2×D411yescharacteristic
718C4×Dic53—21no—
719C4×Dic53—21no—
720C4×Dic53—21no—
721C4×Dic53—21no—
722C4×Dic53—21no—
723C4×Dic53—21no—
724C4×Dic53C2411yescharacteristic
725C2×#88322—41no—
726C2×#88322—41no—
727C2×#88322C2411yescharacteristic
728C2×#88322C2411yescharacteristic
729C2×#88322C2411yescharacteristic
730C2×#88322C2411yescharacteristic
731Dic212—22no—
732Dic212—41no—
733#11719913—41no—
734#11719912—41no—
735C8×D53—41no—
736C8×D53—41no—
737C8×D53—41no—
738C23×C53—21no—
739C23×C53—21no—
740C23×C53—21no—
741C23×C53—21no—
742C23×C53—42no—
743C23×C53—42no—
744C23×C53—42no—
745C23×C53—81no—
746C23×C53—81no—
747C23×C53—81no—
748C23×C53C22×D411yescharacteristic
749C23×C53C22×D411yescharacteristic
750C22×D53—22no—
751C22×D53—21no—
752C22×D53—41no—
753C22×D53—41no—
754C22×D53—42no—
755C22×D53—42no—
756C22×D53—81no—
757C22×D53—81no—
758C22×D53—81no—
759C22×D53—81no—
760C22×D53C22×D411yescharacteristic
761C22×D53C22×D411yescharacteristic
762C22×D53C22×D411yescharacteristic
763Q8×C53—21no—
764Q8×C53—21no—
765Q8×C53—21no—
766Q8×C53—21no—
767Q8×C53—81no—
768D4×C53—22no—
769D4×C53—21no—
770D4×C53—21no—
771D4×C53—21no—
772D4×C53—21no—
773D4×C53—21no—
774D4×C53—21no—
775D4×C53—21no—
776D4×C53—42no—
777D4×C53—42no—
778D4×C53—42no—
779D4×C53—42no—
780D4×C53—81no—
781D4×C53—81no—
782D4×C53—81no—
783D4×C53—81no—
784D4×C53H(5,𝔽2)12yes—
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—21no—
793C2×C4×C53—81no—
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—24no—
802C22⋊D53—22no—
803C22⋊D53—41no—
804C22⋊D53—41no—
805C22⋊D53—41no—
806C22⋊D53—42no—
807C22⋊D53—42no—
808C22⋊D53—42no—
809C22⋊D53—42no—
810C22⋊D53—42no—
811C22⋊D53—42no—
812C22⋊D53—42no—
813C22⋊D53—42no—
814C22⋊D53—81no—
815C22⋊D53—81no—
816C22⋊D53—81no—
817C22⋊D53—81no—
818C22⋊D53—81no—
819C22⋊D53—81no—
820C22⋊D53—81no—
821C2×Dic53—24no—
822C2×Dic53—21no—
823C2×Dic53—21no—
824C2×Dic53—21no—
825C2×Dic53—21no—
826C2×Dic53—21no—
827C2×Dic53—21no—
828C2×Dic53—21no—
829C2×Dic53—41no—
830C2×Dic53—42no—
831C2×Dic53—42no—
832C2×Dic53—42no—
833C2×Dic53—42no—
834C2×Dic53—42no—
835C2×Dic53—81no—
836C2×Dic53—81no—
837C2×Dic53—81no—
838C2×Dic53—81no—
839C2×Dic53—81no—
840C2×Dic53C22×D411yescharacteristic
841C2×Dic53C22×D411yescharacteristic
842C2×Dic53C22×D411yescharacteristic
843C2×Dic53C22×D411yescharacteristic
844C2×Dic53C22×D411yescharacteristic
845D212—21no—
846D212—21no—
847D212—41no—
848D212—41no—
849D212—81no—
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—81no—
860C4×D53—81no—
861Dic106—21no—
862Dic106—21no—
863Dic106—21no—
864Dic106—21no—
865Dic106—21no—
866Dic106—41no—
867Dic106—42no—
868Dic106—81no—
869Dic106—81no—
870Dic106H(5,𝔽2)12yes—
871C8×C53—21no—
872C8×C53—21no—
873C8×C53—21no—
874C8×C53—21no—
875#88322—21no—
876#88322—21no—
877#88322—21no—
878#88322—21no—
879#61640—531nomaximal, Sylow
880C22×C53—21no—
881C22×C53—21no—
882C22×C53—21no—
883C22×C53—22no—
884C22×C53—21no—
885C22×C53—21no—
886C22×C53—41no—
887C22×C53—41no—
888C22×C53—41no—
889C22×C53—41no—
890C22×C53—41no—
891C22×C53—41no—
892C22×C53—41no—
893C22×C53—41no—
894C22×C53—41no—
895C22×C53—41no—
896C22×C53—41no—
897C22×C53—84no—
898C22×C53—162no—
899C22×C53#57712yes—
900C22×C53C23×D411yescharacteristic
901C2×D53—21no—
902C2×D53—21no—
903C2×D53—21no—
904C2×D53—21no—
905C2×D53—21no—
906C2×D53—21no—
907C2×D53—21no—
908C2×D53—21no—
909C2×D53—21no—
910C2×D53—41no—
911C2×D53—41no—
912C2×D53—41no—
913C2×D53—82no—
914C2×D53—162no—
915C2×D53—162no—
916C4×C53—21no—
917C4×C53—21no—
918C4×C53—21no—
919C4×C53—21no—
920C4×C53—41no—
921C4×C53—41no—
922C4×C53—41no—
923C4×C53—41no—
924C4×C53C2×H(5,𝔽2)11yescharacteristic
925C4×C53C2×H(5,𝔽2)11yescharacteristic
926Dic53—21no—
927Dic53—22no—
928Dic53—21no—
929Dic53—21no—
930Dic53—21no—
931Dic53—21no—
932Dic53—41no—
933Dic53—41no—
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#3270—531no—
954#3267—531no—
955#3265D5311yescharacteristic, complemented
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—42no—
971C2×C53—41no—
972C2×C53—81no—
973C2×C53—81no—
974C2×C53—81no—
975C2×C53#348411yescharacteristic
976C2×C53C2×#57711yescharacteristic
977C2×C53#358411yescharacteristic
978D53—41no—
979D53—41no—
980D53—41no—
981D53—81no—
982C2×H(5,𝔽2)—531no—
983C22×#41—531no—
984C2×#137—531no—
985C2×AGL(1,ℤ/8)C2×D5311yescharacteristic, complemented
986C2×#135—531no—
987C2×#135—531no—
988C2×#135—531no—
989C22×Q16—531no—
990C22×SD16—531no—
991C22×SD16C2×D5311yescharacteristic, complemented
992#563—1061no—
993#562—1061no—
994#556—531no—
995#554—531no—
996#554—1061no—
997#553—531no—
998#553—1061no—
999#552—531no—
1000#550—531no—
1001#550—531no—
1002D4×Q8—531no—
1003#548—531no—
1004#548—531no—
1005#548—531no—
1006#548C2×D5311yescharacteristic, complemented
1007#547—531no—
1008#546—531no—
1009#546—531no—
1010#546—1061no—
1011#546—1061no—
1012D42—531no—
1013D42—1061no—
1014D42—1061no—
1015D42C2×D5311yescharacteristic
1016#542—531no—
1017#542—1061no—
1018#541—531no—
1019#539—1061no—
1020#538—1061no—
1021#538—1061no—
1022#537—531no—
1023#537—531no—
1024#537—1061no—
1025#536—531no—
1026#535—531no—
1027#535—1061no—
1028#525—531no—
1029#525—531no—
1030#525—1061no—
1031C2×C22⋊Q8—531no—
1032C2×#121—531no—
1033C2×#121—1061no—
1034#520—531no—
1035#497—531no—
1036#496C2×D5311yescharacteristic, complemented
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#470—531no—
1061#469—531no—
1062#468C2×D5311yescharacteristic, complemented
1063#467—531no—
1064#466—531no—
1065#466C2×D5311yescharacteristic, complemented
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#465—531no—
1075#464—531no—
1076#464—531no—
1077#464—531no—
1078#464—531no—
1079#463—531no—
1080#463C2×D5311yescharacteristic, complemented
1081#462—531no—
1082#461—531no—
1083#460—531no—
1084#460—531no—
1085#460C2×D5311yescharacteristic, complemented
1086#459—531no—
1087#452—531no—
1088#452—531no—
1089#452—531no—
1090#452—531no—
1091#452—531no—
1092#452—531no—
1093#452—531no—
1094#452—531no—
1095#452—531no—
1096#452—531no—
1097#452—531no—
1098#452—531no—
1099#452—531no—
1100#452—531no—
1101#451—531no—
1102#451—531no—
1103#450—531no—
1104#450—531no—
1105#450—531no—
1106#450—531no—
1107#450—531no—
1108#450—531no—
1109#450C2×D5311yescharacteristic, complemented
1110#449—531no—
1111#449—531no—
1112#449—531no—
1113#449—531no—
1114#449—531no—
1115#449C2×D5311yescharacteristic, complemented
1116#448—531no—
1117#448—531no—
1118#448—531no—
1119#448C2×D5311yescharacteristic, complemented
1120#447—531no—
1121#447—531no—
1122#447C2×D5311yescharacteristic, complemented
1123#442—531no—
1124#441—531no—
1125#441—531no—
1126#440C2×D5311yescharacteristic, complemented
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×Q8—531no—
1171C22×Q8—531no—
1172C22×Q8C22×D5311yescharacteristic
1173C22×D4—21no—
1174C22×D4—531no—
1175C22×D4—531no—
1176C22×D4—1061no—
1177C22×D4—1061no—
1178C22×D4—1061no—
1179C22×D4—1061no—
1180C22×D4—1061no—
1181C22×D4—1061no—
1182C22×D4C22×D5311yescharacteristic
1183C22×D4C22×D5311yescharacteristic
1184C23×C4—531no—
1185C23×C4—1061no—
1186#137—2122no—
1187AGL(1,ℤ/8)—42no—
1188#135—2122no—
1189#135—2122no—
1190#135—2122no—
1191C2×Q16—531no—
1192C2×Q16—531no—
1193C2×Q16—531no—
1194C2×Q16—531no—
1195C2×Q16—531no—
1196C2×Q16—531no—
1197C2×Q16—2122no—
1198C2×SD16—42no—
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—2122no—
1208C2×SD16C22×D5311yescharacteristic
1209C2×SD16C22×D5311yescharacteristic
1210C2×SD16C22×D5311yescharacteristic
1211C2×SD16C22×D5311yescharacteristic
1212C2×SD16C22×D5311yescharacteristic
1213C2×SD16C22×D5311yescharacteristic
1214C2×D8—531no—
1215C2×D8C22×D5311yescharacteristic
1216C2×D8C22×D5311yescharacteristic
1217C2×D8C22×D5311yescharacteristic
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—531no—
1227C4⋊Q8—531no—
1228C4⋊Q8—1061no—
1229C4⋊Q8—1061no—
1230#127—531no—
1231#127—1061no—
1232#127—1061no—
1233#127C22×D5311yescharacteristic
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—531no—
1270C22⋊Q8—531no—
1271C22⋊Q8—531no—
1272C22⋊Q8—531no—
1273C22⋊Q8—531no—
1274C22⋊Q8—531no—
1275C22⋊Q8—531no—
1276C22⋊Q8—531no—
1277C22⋊Q8—531no—
1278C22⋊Q8—531no—
1279C22⋊Q8—531no—
1280C22⋊Q8—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⋊Q8—1061no—
1292C22⋊Q8—1061no—
1293C22⋊Q8C22×D5311yescharacteristic
1294#121—21no—
1295#121—21no—
1296#121—531no—
1297#121—531no—
1298#121—531no—
1299#121—531no—
1300#121—531no—
1301#121—531no—
1302#121—531no—
1303#121—531no—
1304#121—1061no—
1305#121—1061no—
1306#121—1061no—
1307#121—1061no—
1308#121—1061no—
1309#121—1061no—
1310#121—1061no—
1311#121—1061no—
1312#121—1061no—
1313#121—1061no—
1314#121—1061no—
1315#121—1061no—
1316#121—1061no—
1317#121—1061no—
1318#121—1061no—
1319#121—1061no—
1320#121—1061no—
1321#121—1061no—
1322#121—1061no—
1323#121—1061no—
1324#121—1061no—
1325#121—1061no—
1326#121C22×D5311yescharacteristic
1327#121C22×D5311yescharacteristic
1328#121C22×D5311yescharacteristic
1329#120—21no—
1330#120—21no—
1331#120—531no—
1332#120—531no—
1333#120—1061no—
1334#120—1061no—
1335#120—1061no—
1336#120—1061no—
1337#120—1061no—
1338#120—1061no—
1339#120—1061no—
1340C4×Q8—531no—
1341C4×Q8—531no—
1342C4×Q8—531no—
1343C4×Q8—531no—
1344C4×Q8—1061no—
1345C4×Q8C22×D5311yescharacteristic
1346C4×D4—21no—
1347C4×D4—531no—
1348C4×D4—531no—
1349C4×D4—531no—
1350C4×D4—531no—
1351C4×D4—531no—
1352C4×D4—1061no—
1353C4×D4—1061no—
1354C4×D4—1061no—
1355C4×D4—1061no—
1356C4×D4—1061no—
1357C4×D4—1061no—
1358C4×D4—1061no—
1359C4×D4—1061no—
1360C4×D4—1061no—
1361C4×D4—1061no—
1362C4×D4—1061no—
1363C4×D4—1061no—
1364C4×D4C22×D5311yescharacteristic
1365C4×D4C22×D5311yescharacteristic
1366#117—531no—
1367#117—531no—
1368#117—531no—
1369#117—1061no—
1370#117—1061no—
1371C2×C4⋊C4—531no—
1372C2×C4⋊C4—531no—
1373C2×C4⋊C4—531no—
1374C2×C4⋊C4—1061no—
1375C2×C4⋊C4—1061no—
1376C2×C4⋊C4—1061no—
1377C2×C22⋊C4—1061no—
1378C2×C22⋊C4—1061no—
1379C2×C22⋊C4—1061no—
1380C2×C22⋊C4—1061no—
1381#107—531no—
1382#107C22×D5311yescharacteristic
1383#106—531no—
1384#106—531no—
1385#106—531no—
1386#106—531no—
1387#106—531no—
1388#106—531no—
1389C4⋊C8—531no—
1390C4⋊C8—531no—
1391C4⋊C8—531no—
1392C4⋊C8C22×D5311yescharacteristic
1393#103—531no—
1394#103—531no—
1395#103—531no—
1396#103—531no—
1397#103—531no—
1398#103—531no—
1399#103—531no—
1400#103—531no—
1401#103—531no—
1402#103—531no—
1403#103—531no—
1404#103—531no—
1405#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#102C22×D5311yescharacteristic
1422#102C22×D5311yescharacteristic
1423#102C22×D5311yescharacteristic
1424#102C22×D5311yescharacteristic
1425C22⋊C8—531no—
1426C22⋊C8—531no—
1427C22⋊C8—531no—
1428C22⋊C8—531no—
1429C22⋊C8—531no—
1430C22⋊C8—531no—
1431C22⋊C8—531no—
1432C22⋊C8—531no—
1433C22⋊C8—531no—
1434C22⋊C8—531no—
1435C22⋊C8C22×D5311yescharacteristic
1436C22⋊C8C22×D5311yescharacteristic
1437#97—531no—
1438#97C22×D5311yescharacteristic
1439C4×C8—531no—
1440C4×C8—531no—
1441C24—21no—
1442C24—21no—
1443C24—531no—
1444C24—1061no—
1445C24—1061no—
1446#41—41no—
1447#41—41no—
1448#41—1062no—
1449#41—1062no—
1450#41—1062no—
1451#41—1062no—
1452#41—1062no—
1453#41—1062no—
1454#41—2121no—
1455#41—2121no—
1456#41—2121no—
1457#41—2121no—
1458#41—2121no—
1459#41—2121no—
1460#41—2121no—
1461#41—2121no—
1462#41—2121no—
1463#41—2121no—
1464#41—2124no—
1465#41—2124no—
1466#41—2124no—
1467C2×Q8—21no—
1468C2×Q8—41no—
1469C2×Q8—41no—
1470C2×Q8—531no—
1471C2×Q8—531no—
1472C2×Q8—531no—
1473C2×Q8—531no—
1474C2×Q8—1061no—
1475C2×Q8—1062no—
1476C2×Q8—1061no—
1477C2×Q8—1061no—
1478C2×Q8—2121no—
1479C2×Q8—2121no—
1480C2×Q8—2121no—
1481C2×Q8C23×D5311yescharacteristic
1482C2×Q8C23×D5311yescharacteristic
1483C2×D4—22no—
1484C2×D4—22no—
1485C2×D4—21no—
1486C2×D4—21no—
1487C2×D4—21no—
1488C2×D4—21no—
1489C2×D4—21no—
1490C2×D4—21no—
1491C2×D4—21no—
1492C2×D4—21no—
1493C2×D4—41no—
1494C2×D4—41no—
1495C2×D4—82no—
1496C2×D4—531no—
1497C2×D4—531no—
1498C2×D4—531no—
1499C2×D4—531no—
1500C2×D4—531no—
1501C2×D4—531no—
1502C2×D4—531no—
1503C2×D4—1061no—
1504C2×D4—1061no—
1505C2×D4—1061no—
1506C2×D4—1061no—
1507C2×D4—1061no—
1508C2×D4—1061no—
1509C2×D4—1062no—
1510C2×D4—1061no—
1511C2×D4—1061no—
1512C2×D4—1061no—
1513C2×D4—1061no—
1514C2×D4—1061no—
1515C2×D4—1061no—
1516C2×D4—1061no—
1517C2×D4—1061no—
1518C2×D4—1061no—
1519C2×D4—1061no—
1520C2×D4—1061no—
1521C2×D4—4242no—
1522C2×D4—4242no—
1523C2×D4—2121no—
1524C2×D4—2121no—
1525C2×D4—2121no—
1526C2×D4—2124no—
1527C2×D4—2124no—
1528C2×D4—2124no—
1529C2×D4—2124no—
1530C2×D4D4×D5311yescharacteristic
1531C2×D4C23×D5311yescharacteristic
1532C2×D4C23×D5311yescharacteristic
1533C2×D4C23×D5311yescharacteristic
1534C2×D4C23×D5311yescharacteristic
1535C22×C4—21no—
1536C22×C4—21no—
1537C22×C4—21no—
1538C22×C4—531no—
1539C22×C4—531no—
1540C22×C4—531no—
1541C22×C4—531no—
1542C22×C4—531no—
1543C22×C4—531no—
1544C22×C4—1061no—
1545C22×C4—1061no—
1546C22×C4—1061no—
1547C22×C4—1061no—
1548C22×C4—1061no—
1549C22×C4—1061no—
1550C22×C4—1061no—
1551C22×C4—1061no—
1552C22×C4—1061no—
1553C22×C4—1061no—
1554C22×C4—1061no—
1555C22×C4—1061no—
1556C22×C4—1061no—
1557C22×C4—1061no—
1558C22×C4—2121no—
1559C22×C4—2121no—
1560C22×C4—2124no—
1561C22×C4C23×D5311yescharacteristic
1562C22×C4C23×D5311yescharacteristic
1563Q16—1062no—
1564Q16—1062no—
1565Q16—1062no—
1566Q16—2121no—
1567Q16—2121no—
1568Q16—2121no—
1569SD16—22no—
1570SD16—22no—
1571SD16—41no—
1572SD16—41no—
1573SD16—41no—
1574SD16—41no—
1575SD16—1062no—
1576SD16—1062no—
1577SD16—2121no—
1578SD16—2121no—
1579SD16—2121no—
1580SD16—2121no—
1581SD16—2121no—
1582SD16—2121no—
1583D8—22no—
1584D8—41no—
1585D8—41no—
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—531no—
1606C4⋊C4—531no—
1607C4⋊C4—531no—
1608C4⋊C4—531no—
1609C4⋊C4—531no—
1610C4⋊C4—531no—
1611C4⋊C4—531no—
1612C4⋊C4—531no—
1613C4⋊C4—531no—
1614C4⋊C4—1061no—
1615C4⋊C4—1061no—
1616C4⋊C4—1061no—
1617C4⋊C4—1061no—
1618C4⋊C4—1061no—
1619C4⋊C4—1061no—
1620C4⋊C4—1061no—
1621C4⋊C4—1061no—
1622C4⋊C4—1061no—
1623C4⋊C4—1061no—
1624C4⋊C4—1061no—
1625C4⋊C4—1061no—
1626C4⋊C4—1061no—
1627C4⋊C4—1061no—
1628C4⋊C4—1061no—
1629C4⋊C4—1061no—
1630C4⋊C4—1061no—
1631C4⋊C4—1061no—
1632C4⋊C4—1061no—
1633C4⋊C4—1061no—
1634C4⋊C4—1061no—
1635C4⋊C4—1061no—
1636C4⋊C4D4×D5311yescharacteristic
1637C4⋊C4C23×D5311yescharacteristic
1638C4⋊C4C23×D5311yescharacteristic
1639C22⋊C4—21no—
1640C22⋊C4—21no—
1641C22⋊C4—21no—
1642C22⋊C4—21no—
1643C22⋊C4—21no—
1644C22⋊C4—21no—
1645C22⋊C4—21no—
1646C22⋊C4—531no—
1647C22⋊C4—531no—
1648C22⋊C4—531no—
1649C22⋊C4—531no—
1650C22⋊C4—531no—
1651C22⋊C4—531no—
1652C22⋊C4—531no—
1653C22⋊C4—531no—
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—531no—
1682C42—1061no—
1683C42—1061no—
1684C42—1061no—
1685C42—1061no—
1686C42—1061no—
1687C42—1061no—
1688C42C23×D5311yescharacteristic
1689C23—21no—
1690C23—21no—
1691C23—21no—
1692C23—21no—
1693C23—42no—
1694C23—42no—
1695C23—42no—
1696C23—81no—
1697C23—81no—
1698C23—81no—
1699C23—531no—
1700C23—531no—
1701C23—531no—
1702C23—1062no—
1703C23—1061no—
1704C23—4241no—
1705C23—4241no—
1706C23—4241no—
1707C23—4241no—
1708C23—2122no—
1709C23—2121no—
1710C23—2121no—
1711C23—2122no—
1712C23C2×D4×D5311yescharacteristic
1713C23C2×D4×D5311yescharacteristic
1714Q8—21no—
1715Q8—21no—
1716Q8—21no—
1717Q8—21no—
1718Q8—81no—
1719Q8—532no—
1720Q8—1061no—
1721Q8—1061no—
1722Q8—1061no—
1723Q8—1061no—
1724Q8—1061no—
1725Q8—4241no—
1726Q8—4241no—
1727Q8—2121no—
1728Q8—2122no—
1729D4—22no—
1730D4—21no—
1731D4—21no—
1732D4—21no—
1733D4—21no—
1734D4—21no—
1735D4—21no—
1736D4—21no—
1737D4—42no—
1738D4—42no—
1739D4—42no—
1740D4—42no—
1741D4—81no—
1742D4—81no—
1743D4—81no—
1744D4—81no—
1745D4—1064no—
1746D4—1062no—
1747D4—1061no—
1748D4—1061no—
1749D4—4241no—
1750D4—4241no—
1751D4—4241no—
1752D4—4241no—
1753D4—4241no—
1754D4—4241no—
1755D4—4241no—
1756D4—4241no—
1757D4—2121no—
1758D4—2121no—
1759D4—2121no—
1760D4—2121no—
1761D4—2121no—
1762D4—2122no—
1763D4—2122no—
1764D4—2122no—
1765D4—2122no—
1766D4—2122no—
1767D4—2122no—
1768D4—2122no—
1769D4—2122no—
1770D4#1313326212yes—
1771C2×C4—21no—
1772C2×C4—21no—
1773C2×C4—21no—
1774C2×C4—21no—
1775C2×C4—21no—
1776C2×C4—21no—
1777C2×C4—21no—
1778C2×C4—21no—
1779C2×C4—81no—
1780C2×C4—81no—
1781C2×C4—81no—
1782C2×C4—531no—
1783C2×C4—531no—
1784C2×C4—531no—
1785C2×C4—531no—
1786C2×C4—531no—
1787C2×C4—1064no—
1788C2×C4—1061no—
1789C2×C4—1061no—
1790C2×C4—1061no—
1791C2×C4—1061no—
1792C2×C4—1061no—
1793C2×C4—1061no—
1794C2×C4—1061no—
1795C2×C4—1061no—
1796C2×C4—1061no—
1797C2×C4—1061no—
1798C2×C4—1061no—
1799C2×C4—1061no—
1800C2×C4—1061no—
1801C2×C4—4241no—
1802C2×C4—4241no—
1803C2×C4—4241no—
1804C2×C4—4241no—
1805C2×C4—4241no—
1806C2×C4—4241no—
1807C2×C4—4241no—
1808C2×C4—2121no—
1809C2×C4—2121no—
1810C2×C4—2122no—
1811C2×C4—2121no—
1812C2×C4—2122no—
1813C2×C4—2122no—
1814C2×C4—2122no—
1815C2×C4—2122no—
1816C2×C4—2122no—
1817C2×C4C2×D4×D5311yescharacteristic
1818C2×C4C2×D4×D5311yescharacteristic
1819C2×C4C2×D4×D5311yescharacteristic
1820C2×C4C2×D4×D5311yescharacteristic
1821C2×C4C24×D5311yescharacteristic
1822C8—21no—
1823C8—21no—
1824C8—21no—
1825C8—21no—
1826C8—1061no—
1827C8—1061no—
1828C8—1061no—
1829C8—1061no—
1830C22—21no—
1831C22—21no—
1832C22—21no—
1833C22—22no—
1834C22—21no—
1835C22—21no—
1836C22—41no—
1837C22—41no—
1838C22—41no—
1839C22—41no—
1840C22—41no—
1841C22—41no—
1842C22—41no—
1843C22—41no—
1844C22—41no—
1845C22—41no—
1846C22—41no—
1847C22—84no—
1848C22—162no—
1849C22—8482no—
1850C22—8482no—
1851C22—1061no—
1852C22—1061no—
1853C22—1061no—
1854C22—1061no—
1855C22—1061no—
1856C22—1061no—
1857C22—1061no—
1858C22—1061no—
1859C22—1061no—
1860C22—4242no—
1861C22—2121no—
1862C22—2121no—
1863C22—2121no—
1864C22#1681143312yes—
1865C22C22×D4×D5311yescharacteristic
1866C4—21no—
1867C4—21no—
1868C4—21no—
1869C4—21no—
1870C4—41no—
1871C4—41no—
1872C4—41no—
1873C4—41no—
1874C4—1061no—
1875C4—1061no—
1876C4—1061no—
1877C4—1062no—
1878C4—1061no—
1879C4—1061no—
1880C4—2121no—
1881C4—2121no—
1882C4—2121no—
1883C4—2121no—
1884C4—2121no—
1885C4—2121no—
1886C4H(5,𝔽2)×D5311yescharacteristic
1887C4C2×#1313326211yescharacteristic
1888C2—22no—
1889C2—41no—
1890C2—42no—
1891C2—81no—
1892C2—81no—
1893C2—81no—
1894C2—4241no—
1895C2—2121no—
1896C2—2121no—
1897C2—2121no—
1898C2#2028834311yescharacteristic
1899C2C2×#1681143311yescharacteristic
1900C2#2028948711yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3265C2
socleC22×C53C23×D4
hypercenter#3265D53
hypocenterC53#61640
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3265

Complements

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

NH ≅ G/Ntype
1. #20288994C2semidirect
2. #20288375C2semidirect
3. #20286860C2semidirect
4. #20286836C2semidirect
5. #20286828C2semidirect
6. #20286756C2semidirect
7. #20286657C2semidirect
8. #20286623C2semidirect
9. #20286554C2semidirect
10. #20286539C2semidirect
11. #20286452C2semidirect
12. #20286443C2semidirect
13. #20286428C2semidirect
14. SD16×C22⋊D53C2semidirect
15. #20286299C2semidirect
16. #20286278C2semidirect
17. #20286234C2semidirect
18. #20285804C2semidirect
19. #20285786C2semidirect
20. #20285624C2semidirect
21. #20285592C2semidirect
22. #20285475C2semidirect
23. #20285470C2semidirect
24. #20284989C2semidirect
25. #20284933C2semidirect
26. #20284018C2semidirect
27. #20283987C2semidirect
28. #20283928C2semidirect
29. C2×#16810782C2semidirect
30. #20283766C2semidirect
31. C53×#3265C2semidirect
34. C2×#13133246C22semidirect
35. C2×#13133237C22semidirect
36. C2×#13133236C22semidirect
37. C2×#13133236C22semidirect
38. C22×#11719925C22semidirect
39. C2×SD16×D53C22semidirect
42. #16811346C22semidirect
44. #16811330C22semidirect
45. #16811325C22semidirect
47. #16811315C22semidirect
50. Q8×C22⋊D53C22semidirect
52. #16811281C22semidirect
54. #16811272C22semidirect
62. #16811242C22semidirect
64. #16811231C22semidirect
69. #16811201C22semidirect
71. #16811196C22semidirect
74. #16811133C22semidirect
77. C2×#13133193C22semidirect
81. #16811014C22semidirect
82. #16811005C22semidirect
83. #16810994C22semidirect
84. #16810986C22semidirect
85. #16810983C22semidirect
86. #16810976C22semidirect
87. #16810969C22semidirect
88. #16810966C22semidirect
89. #16810960C22semidirect
90. #16810954C22semidirect
91. #16810952C22semidirect
92. #16810952C22semidirect
93. #16810950C22semidirect
94. #16810946C22semidirect
95. #16810946C22semidirect
96. #16810942C22semidirect
97. #16810940C22semidirect
98. #16810939C22semidirect
99. #16810939C22semidirect
100. #16810929C22semidirect
101. #16810925C22semidirect
102. #16810913C22semidirect
103. #16810909C22semidirect
104. #16810881C22semidirect
105. #16810880C22semidirect
106. #16810873C22semidirect
107. #16810862C22semidirect
108. #16810857C22semidirect
109. #16810855C22semidirect
110. #16810855C22semidirect
111. #16810852C22semidirect
112. #16810851C22semidirect
113. #16810850C22semidirect
114. #16810850C22semidirect
115. #16810849C22semidirect
116. #16810849C22semidirect
117. #16810849C22semidirect
118. #16810846C22semidirect
119. #16810845C22semidirect
120. #16810843C22semidirect
121. #16810842C22semidirect
122. #16810836C22semidirect
123. #16810832C22semidirect
124. #16810826C22semidirect
125. #16810821C22semidirect
126. #16810820C22semidirect
127. #16810816C22semidirect
128. #16810787C22semidirect
130. #16810786C22semidirect
131. #16810785C22semidirect
132. #16810783C22semidirect
135. #16810782C22semidirect
136. #16810782C22semidirect
137. #16810782C22semidirect
138. #16810782C22semidirect
139. #16810782C22semidirect
140. #16810782C22semidirect
141. #16810782C22semidirect
142. #16810781C22semidirect
143. #16810780C22semidirect
144. #16810775C22semidirect
145. #16810774C22semidirect
146. #16810774C22semidirect
147. #16810772C22semidirect
148. #16810772C22semidirect
149. #16810772C22semidirect
150. #16810769C22semidirect
152. #16810765C22semidirect
153. #16810765C22semidirect
154. #16810765C22semidirect
155. #16810762C22semidirect
156. #16810761C22semidirect
157. #16810760C22semidirect
158. #16810755C22semidirect
159. #16810755C22semidirect
160. #16810735C22semidirect
161. #16810731C22semidirect
162. #16810727C22semidirect
163. C4×#11719925C22semidirect
164. #16810714C22semidirect
165. SD16×Dic53C22semidirect
166. C4×#11719923C22semidirect
167. #16810696C22semidirect
168. #16810692C22semidirect
169. #16810691C22semidirect
170. D4×#88322C22semidirect
171. #16810688C22semidirect
172. C8×C22⋊D53C22semidirect
173. #16810686C22semidirect
174. #16810685C22semidirect
175. #16810683C22semidirect
176. #16810626C22semidirect
177. #16810625C22semidirect
178. #16810616C22semidirect
179. #16810616C22semidirect
180. #16810616C22semidirect
181. C2×#13133142C22semidirect
182. C2×#13133138C22semidirect
183. C2×#13133138C22semidirect
184. #16810591C22semidirect
185. #16810588C22semidirect
186. C2×#13133129C22semidirect
187. C22⋊C8×D53C22semidirect
188. C2×AGL(1,ℤ/8)×C53C22semidirect
189. C22×SD16×C53C22semidirect
190. C53×#548C22semidirect
192. C53×#496C22semidirect
193. C53×#468C22semidirect
194. C53×#466C22semidirect
195. C53×#463C22semidirect
196. C53×#460C22semidirect
197. C53×#450C22semidirect
198. C53×#449C22semidirect
199. C53×#448C22semidirect
200. C53×#447C22semidirect
201. C53×#440C22semidirect
202. C53×#435C22semidirect
955. #3265D53semidirect
985. C2×AGL(1,ℤ/8)C2×D53semidirect
991. C22×SD16C2×D53semidirect
1006. #548C2×D53semidirect
1036. #496C2×D53semidirect
1062. #468C2×D53semidirect
1065. #466C2×D53semidirect
1080. #463C2×D53semidirect
1085. #460C2×D53semidirect
1109. #450C2×D53semidirect
1115. #449C2×D53semidirect
1119. #448C2×D53semidirect
1122. #447C2×D53semidirect
1126. #440C2×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
#202889942
#202883752
#202868602
#202868362
#202868282
#202867562
#202866572
#202866232
#202865542
#202865392
#202864522
#202864432
#202864282
SD16×C22⋊D532
#202862992
#202862782
#202862342
#202858042
#202857862
#202856242
#202855922
#202854752
#202854702
#202849892
#202849332
#202840182
#202839872
#202839282
C2×#168107822
#202837662
C53×#32652
#6164053