Finite Group Databasebeta

← #28261457

Subgroups — #28261457

Order 13568.

2106 conjugacy classes of subgroups.

The subgroup lattice has 1838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288446C211yesmaximal, characteristic, complemented
2#20288392C211yesmaximal, characteristic, complemented
3#20286906C211yesmaximal, characteristic, complemented
4#20286902C211yesmaximal, characteristic, complemented
5#20286882C211yesmaximal, characteristic, complemented
6#20286690C211yesmaximal, characteristic, complemented
7#20286686C211yesmaximal, characteristic, complemented
8#20286682C211yesmaximal, characteristic, complemented
9#20286678C211yesmaximal, characteristic, complemented
10#20286646C211yesmaximal, characteristic, complemented
11#20286641C211yesmaximal, characteristic, complemented
12#20286621C211yesmaximal, characteristic, complemented
13#20286614C211yesmaximal, characteristic, complemented
14#20286580C211yesmaximal, characteristic, complemented
15#20286573C211yesmaximal, characteristic, complemented
16#20286563C211yesmaximal, characteristic, complemented
17#20286559C211yesmaximal, characteristic, complemented
18#20285081C211yesmaximal, characteristic, complemented
19#20284701C211yesmaximal, characteristic, complemented
20#20284660C211yesmaximal, characteristic, complemented
21#20284580C211yesmaximal, characteristic, complemented
22#20284390C211yesmaximal, characteristic, complemented
23#465×D53C211yesmaximal, characteristic, complemented
24#20284222C211yesmaximal, characteristic, complemented
25#20283996C211yesmaximal, characteristic, complemented
26#20283966C211yesmaximal, characteristic, complemented
27#20283546C211yesmaximal, characteristic, complemented
28#20283406C211yesmaximal, characteristic, complemented
29#20283247C211yesmaximal, characteristic, complemented
30C2×#16810618C211yesmaximal, characteristic, complemented
31C53×#3320C211yesmaximal, characteristic, complemented
32C2×#13133265C2211yescharacteristic
33C22×#11719949C2211yescharacteristic
34C2×#13133244C2211yescharacteristic
35C2×#13133244C2211yescharacteristic
36C2×SD16×D53C2211yescharacteristic, complemented
37C2×#13133225C2211yescharacteristic, complemented
38C22×C8×D53C2211yescharacteristic
39#16811338C2211yescharacteristic, complemented
40#16811336C2211yescharacteristic, complemented
41#16811326C2211yescharacteristic, complemented
42#16811325C2211yescharacteristic, complemented
43#16811321C2211yescharacteristic
44#16811298—21no—
45#16811296—21no—
46Q8×C22⋊D53C2211yescharacteristic, complemented
47#16811285C2211yescharacteristic, complemented
48#16811284C2211yescharacteristic, complemented
49#16811277C2211yescharacteristic
50#16811276—21no—
51#16811276C2211yescharacteristic, complemented
52#16811275—21no—
53#16811275C2211yescharacteristic, complemented
54#16811273C2211yescharacteristic
55#16811269—21no—
56#16811269C2211yescharacteristic, complemented
57#16811268—21no—
58#16811264—21no—
59#16811264C2211yescharacteristic, complemented
60#16811262—21no—
61#16811253C2211yescharacteristic, complemented
62#16811239—21no—
63#16811225—21no—
64#16811203—21no—
65#16811203C2211yescharacteristic
66#16811198—21no—
67#16811198C2211yescharacteristic
68#16811189C2211yescharacteristic, complemented
69#16811168—21no—
70#16811153—21no—
71#16811132—21no—
72#16811132C2211yescharacteristic
73C22⋊Q8×D53—21no—
74C22⋊Q8×D53C2211yescharacteristic
75#121×D53C2211yescharacteristic
76#16811105C2211yescharacteristic
77#16811103C2211yescharacteristic, complemented
78#16811095C2211yescharacteristic, complemented
79C2×#13133175C2211yescharacteristic
80#16810990C2211yescharacteristic, complemented
81#16810984C2211yescharacteristic, complemented
82#16810983C2211yescharacteristic, complemented
83#16810980C2211yescharacteristic, complemented
84#16810979C2211yescharacteristic, complemented
85#16810973C2211yescharacteristic, complemented
86#16810972C2211yescharacteristic, complemented
87#16810966C2211yescharacteristic, complemented
88#16810966C2211yescharacteristic, complemented
89#16810962C2211yescharacteristic, complemented
90#16810962C2211yescharacteristic, complemented
91#16810962C2211yescharacteristic, complemented
92#16810958C2211yescharacteristic, complemented
93#16810954C2211yescharacteristic, complemented
94#16810952C2211yescharacteristic, complemented
95#16810951C2211yescharacteristic, complemented
96#16810951C2211yescharacteristic, complemented
97#16810950C2211yescharacteristic, complemented
98#16810947C2211yescharacteristic, complemented
99#16810943C2211yescharacteristic, complemented
100#16810942C2211yescharacteristic, complemented
101#16810928C2211yescharacteristic, complemented
102#16810926C2211yescharacteristic, complemented
103#16810920C2211yescharacteristic, complemented
104#16810914C2211yescharacteristic, complemented
105#16810912C2211yescharacteristic, complemented
106#16810908C2211yescharacteristic, complemented
107#16810906C2211yescharacteristic, complemented
108#16810876C2211yescharacteristic, complemented
109#16810875C2211yescharacteristic, complemented
110#16810872C2211yescharacteristic, complemented
111#16810860C2211yescharacteristic, complemented
112#16810857C2211yescharacteristic, complemented
113#16810855C2211yescharacteristic, complemented
114#16810854C2211yescharacteristic
115#16810854C2211yescharacteristic, complemented
116#16810853C2211yescharacteristic, complemented
117#16810852C2211yescharacteristic
118#16810851C2211yescharacteristic, complemented
119#16810850C2211yescharacteristic
120#16810849C2211yescharacteristic, complemented
121#16810849C2211yescharacteristic, complemented
122#16810841C2211yescharacteristic, complemented
123#16810840C2211yescharacteristic, complemented
124#16810839C2211yescharacteristic, complemented
125#16810838C2211yescharacteristic, complemented
126#16810827C2211yescharacteristic, complemented
127#16810826C2211yescharacteristic, complemented
128#16810825C2211yescharacteristic, complemented
129#16810771C2211yescharacteristic
130#16810771C2211yescharacteristic
131#16810771C2211yescharacteristic, complemented
132#16810770C2211yescharacteristic, complemented
133#16810767C2211yescharacteristic
134#16810767C2211yescharacteristic
135#16810767C2211yescharacteristic, complemented
136#16810766C2211yescharacteristic, complemented
137#16810763C2211yescharacteristic, complemented
138#16810762C2211yescharacteristic
139#16810762C2211yescharacteristic, complemented
140#16810760C2211yescharacteristic, complemented
141#16810759C2211yescharacteristic
142#16810756C2211yescharacteristic
143#16810736C2211yescharacteristic, complemented
144#16810732C2211yescharacteristic, complemented
145#16810726C2211yescharacteristic, complemented
146SD16×Dic53C2211yescharacteristic, complemented
147C4×#11719924C2211yescharacteristic, complemented
148#16810705C2211yescharacteristic, complemented
149C4×#11719922C2211yescharacteristic, complemented
150#16810696C2211yescharacteristic, complemented
151#16810694C2211yescharacteristic, complemented
152#16810692C2211yescharacteristic, complemented
153D4×#88322C2211yescharacteristic, complemented
154#16810688C2211yescharacteristic, complemented
155#16810686C2211yescharacteristic, complemented
156#16810686C2211yescharacteristic, complemented
157#16810664C2211yescharacteristic, complemented
158#16810664C2211yescharacteristic, complemented
159#106×D53C2211yescharacteristic, complemented
160#16810648C2211yescharacteristic, complemented
161#16810630C2211yescharacteristic, complemented
162#16810630C2211yescharacteristic, complemented
163#16810630C2211yescharacteristic, complemented
164#16810625C2211yescharacteristic, complemented
165#16810623C2211yescharacteristic
166#16810623C2211yescharacteristic
167#16810623C2211yescharacteristic, complemented
168#16810618C2211yescharacteristic
169#16810618C2211yescharacteristic
170#16810618C2211yescharacteristic
171#16810618C2211yescharacteristic
172#16810618C2211yescharacteristic, complemented
173#16810618C2211yescharacteristic, complemented
174#16810618C2211yescharacteristic, complemented
175#16810618C2211yescharacteristic, complemented
176#16810618C2211yescharacteristic, complemented
177#16810617C2211yescharacteristic, complemented
178C2×#13133141C2211yescharacteristic, complemented
179C2×#13133141C2211yescharacteristic, complemented
180#103×D53C2211yescharacteristic, complemented
181#103×D53C2211yescharacteristic, complemented
182C2×#13133139C2211yescharacteristic, complemented
183C2×#13133137C2211yescharacteristic, complemented
184#102×D53C2211yescharacteristic, complemented
185#16810588C2211yescharacteristic, complemented
186#16810585C2211yescharacteristic
187#16810580C2211yescharacteristic, complemented
188C53×#553C2211yescharacteristic
189D4×Q8×C53C2211yescharacteristic, complemented
190C53×#491C2211yescharacteristic, complemented
191C53×#485C2211yescharacteristic, complemented
192C53×#484C2211yescharacteristic, complemented
193C53×#479C2211yescharacteristic, complemented
194C53×#468C2211yescharacteristic, complemented
195C53×#465C2211yescharacteristic
196C53×#461C2211yescharacteristic, complemented
197C53×#448C2211yescharacteristic
198C53×#448C2211yescharacteristic, complemented
199C53×#440C2211yescharacteristic, complemented
200C53×#435C2211yescharacteristic, complemented
201C53×#419C2211yescharacteristic, complemented
202C2×#103×C53C2211yescharacteristic, complemented
203#13133265—24no—
204#13133265—42no—
205C2×#11719949—21no—
206C2×#11719949—21no—
207C2×#11719949—21no—
208C2×#11719949—24no—
209C2×#11719949—42no—
210C2×#11719949C2311yescharacteristic
211C2×#11719949C2311yescharacteristic
212C2×#11719949C2311yescharacteristic
213C2×#11719949C2311yescharacteristic
214C2×#11719949C2311yescharacteristic
215C2×#11719945—21no—
216C2×#11719945—21no—
217C2×#11719945C2311yescharacteristic
218C2×#11719945C2311yescharacteristic
219C2×#11719947—21no—
220C2×#11719947—21no—
221C2×Q8×D53—21no—
222C2×Q8×D53C2311yescharacteristic
223C2×Q8×D53C2311yescharacteristic
224C22×D212—21no—
225C22×D212C2311yescharacteristic
226C2×D4×D53—21no—
227C2×D4×D53C2311yescharacteristic
228C22×C4×D53—21no—
229C22×C4×D53C2311yescharacteristic
230#13133244—24no—
231#13133244—42no—
232C2×#11719913C2311yescharacteristic
233C2×#11719923C2311yescharacteristic
234C2×#11719924C2311yescharacteristic
235C2×#11719924C2311yescharacteristic
236C2×#11719924C2311yescharacteristic
237SD16×D53—42no—
238C2×D424C2311yescharacteristic
239C2×D424C2311yescharacteristic
240C2×#11719922C2311yescharacteristic
241C2×#11719922C2311yescharacteristic
242#13133225—42no—
243C2×#11719912C2311yescharacteristic
244C2×#11719912C2311yescharacteristic
245C2×#11719912C2311yescharacteristic
246C22×#88322C2311yescharacteristic
247C22×#88322C2311yescharacteristic
248C2×C8×D53—42no—
249C2×C8×D53C2311yescharacteristic
250C2×C8×D53C2311yescharacteristic
251C2×C8×D53C2311yescharacteristic
252C2×C8×D53C2311yescharacteristic
253C2×C8×D53C2311yescharacteristic
254#13133217C2311yescharacteristic
255#13133216—21no—
256#13133216C2311yescharacteristic
257#13133215—21no—
258#13133215C2311yescharacteristic
259#13133213—21no—
260#13133212—21no—
261#13133212—21no—
262#13133210—21no—
263#13133208C2311yescharacteristic
264#13133207—21no—
265#13133206—21no—
266#13133206C2311yescharacteristic
267#13133205—21no—
268#13133205—21no—
269#13133205C2311yescharacteristic
270#13133203—21no—
271#13133203—21no—
272#13133203—21no—
273#13133203—21no—
274#13133202—21no—
275#13133202—21no—
276#13133202—21no—
277#13133202—21no—
278#13133202—21no—
279#13133202—21no—
280#13133202—21no—
281#13133202—21no—
282#13133202—21no—
283#13133202D411yescharacteristic
284#13133201—21no—
285#13133201—21no—
286#13133201—21no—
287#13133199—21no—
288#13133199—21no—
289#13133199D411yescharacteristic
290#13133198—21no—
291#13133197—21no—
292#13133197—21no—
293#13133197—21no—
294#13133197C2311yescharacteristic
295#13133196—21no—
296#13133196C2311yescharacteristic
297#13133195—21no—
298#13133195—21no—
299#13133195—21no—
300#13133195—21no—
301#13133195—21no—
302#13133195D411yescharacteristic
303#13133194—21no—
304#13133194—21no—
305#13133194D411yescharacteristic
306#13133193—21no—
307#13133193—21no—
308#13133193C2311yescharacteristic
309#13133193C2311yescharacteristic
310#13133192—21no—
311#13133192—21no—
312#13133192—21no—
313#13133192—21no—
314#13133192—21no—
315#13133192C2311yescharacteristic
316#13133192C2311yescharacteristic
317#13133192C2311yescharacteristic
318#13133191—21no—
319#13133191—21no—
320#13133191—21no—
321#13133191C2311yescharacteristic
322#13133191C2311yescharacteristic
323#13133191C2311yescharacteristic
324#13133190—21no—
325#13133190—21no—
326#13133190—21no—
327#13133190—21no—
328#13133190—21no—
329#13133190—21no—
330#13133190D411yescharacteristic
331#13133189—21no—
332#13133189—21no—
333#13133189D411yescharacteristic
334#13133188C2311yescharacteristic
335#13133188C2311yescharacteristic
336#13133187—21no—
337#13133187—21no—
338#13133187D411yescharacteristic
339#13133185—21no—
340#13133185—21no—
341#13133185D411yescharacteristic
342Q8×Dic53C2311yescharacteristic
343C4×Dic106—21no—
344C4×D212—21no—
345C4×D212—21no—
346C4×D212—21no—
347C4×D212C2311yescharacteristic
348C4×D212C2311yescharacteristic
349C4×D212C2311yescharacteristic
350D4×Dic53—21no—
351D4×Dic53C2311yescharacteristic
352#13133179—21no—
353#13133179—21no—
354#13133179C2311yescharacteristic
355#13133179C2311yescharacteristic
356C4×C22⋊D53—21no—
357C4×C22⋊D53—21no—
358C4×C22⋊D53—21no—
359C4×C22⋊D53—21no—
360C4×C22⋊D53C2311yescharacteristic
361C4×C22⋊D53C2311yescharacteristic
362#13133177—21no—
363#13133177—21no—
364#13133177—21no—
365#13133176—21no—
366#13133175—21no—
367#13133175—21no—
368#13133175C2311yescharacteristic
369#13133175C2311yescharacteristic
370#13133175C2311yescharacteristic
371#13133175C2311yescharacteristic
372#13133175C2311yescharacteristic
373#13133174—21no—
374#13133174—21no—
375#13133174C2311yescharacteristic
376C2×C4⋊Dic53C2311yescharacteristic
377C2×C4⋊Dic53C2311yescharacteristic
378C4⋊C4×D53—21no—
379C4⋊C4×D53—21no—
380C4⋊C4×D53—21no—
381C4⋊C4×D53—21no—
382C4⋊C4×D53C2311yescharacteristic
383C4⋊C4×D53C2311yescharacteristic
384C4⋊C4×D53C2311yescharacteristic
385C2×#11719921—21no—
386C2×#11719921—21no—
387C22⋊C4×D53—21no—
388C22⋊C4×D53—21no—
389C22⋊C4×D53—21no—
390C22⋊C4×D53—21no—
391C22⋊C4×D53—21no—
392C2×C4×Dic53—21no—
393#13133150C2311yescharacteristic
394#13133150C2311yescharacteristic
395#13133149C2311yescharacteristic
396#13133149C2311yescharacteristic
397#13133149C2311yescharacteristic
398#13133148C2311yescharacteristic
399#13133148C2311yescharacteristic
400#13133148C2311yescharacteristic
401#13133148C2311yescharacteristic
402C4⋊#88322C2311yescharacteristic
403#13133146C2311yescharacteristic
404#13133146C2311yescharacteristic
405#13133142C2311yescharacteristic
406#13133142C2311yescharacteristic
407#13133142C2311yescharacteristic
408#13133141C2311yescharacteristic
409#13133141C2311yescharacteristic
410#13133141C2311yescharacteristic
411#13133141C2311yescharacteristic
412#13133141C2311yescharacteristic
413#13133141C2311yescharacteristic
414#13133141C2311yescharacteristic
415#13133141C2311yescharacteristic
416#13133141C2311yescharacteristic
417#13133140C2311yescharacteristic
418#13133140C2311yescharacteristic
419#13133140C2311yescharacteristic
420#13133139C2311yescharacteristic
421#13133139C2311yescharacteristic
422#13133139C2311yescharacteristic
423#13133139C2311yescharacteristic
424#13133139C2311yescharacteristic
425#13133139C2311yescharacteristic
426#13133139C2311yescharacteristic
427#13133138C2311yescharacteristic
428#13133137C2311yescharacteristic
429#13133137C2311yescharacteristic
430#13133137C2311yescharacteristic
431#13133137C2311yescharacteristic
432#13133137C2311yescharacteristic
433#13133137C2311yescharacteristic
434#13133137C2311yescharacteristic
435C22⋊#88322C2311yescharacteristic
436C22⋊#88322C2311yescharacteristic
437#13133129C2311yescharacteristic
438#13133129C2311yescharacteristic
439#13133129C2311yescharacteristic
440#13133129C2311yescharacteristic
441#13133127C2311yescharacteristic
442C4×#88322C2311yescharacteristic
443C8×Dic53C2311yescharacteristic
444C22×Q8×C53C2311yescharacteristic
445C22×Q8×C53C2311yescharacteristic
446C2×SD16×C53C2311yescharacteristic
447C2×SD16×C53C2311yescharacteristic
448C2×SD16×C53C2311yescharacteristic
449C2×M16×C53C2311yescharacteristic
450C22×C8×C53C2311yescharacteristic
451C4⋊Q8×C53—21no—
452C4⋊Q8×C53C2311yescharacteristic
453#126×C53—21no—
454#125×C53C2311yescharacteristic
455#123×C53—21no—
456C22⋊Q8×C53—21no—
457C22⋊Q8×C53—21no—
458C22⋊Q8×C53C2311yescharacteristic
459C22⋊Q8×C53C2311yescharacteristic
460#121×C53—21no—
461#121×C53C2311yescharacteristic
462#121×C53C2311yescharacteristic
463C4×Q8×C53C2311yescharacteristic
464C4×D4×C53—21no—
465C4×D4×C53—21no—
466C4×D4×C53C2311yescharacteristic
467C4×D4×C53C2311yescharacteristic
468#117×C53C2311yescharacteristic
469C2×C4⋊C4×C53C2311yescharacteristic
470#107×C53C2311yescharacteristic
471#107×C53C2311yescharacteristic
472#106×C53C2311yescharacteristic
473C4⋊C8×C53C2311yescharacteristic
474#103×C53C2311yescharacteristic
475#103×C53C2311yescharacteristic
476#103×C53C2311yescharacteristic
477#103×C53C2311yescharacteristic
478#103×C53C2311yescharacteristic
479#103×C53C2311yescharacteristic
480#103×C53C2311yescharacteristic
481#103×C53C2311yescharacteristic
482#103×C53C2311yescharacteristic
483#102×C53C2311yescharacteristic
484C22⋊C8×C53C2311yescharacteristic
485C22⋊C8×C53C2311yescharacteristic
486#97×C53C2311yescharacteristic
487C23×D53—21no—
488C23×D53—21no—
489C23×D53C2×D411yescharacteristic
490C2×Q8×C53—21no—
491C2×Q8×C53—21no—
492C2×Q8×C53—22no—
493C2×Q8×C53—22no—
494C2×Q8×C53—41no—
495C2×Q8×C53—41no—
496C2×Q8×C53C2411yescharacteristic
497C2×Q8×C53C2411yescharacteristic
498C2×Q8×C53C2411yescharacteristic
499C2×D4×C53—21no—
500C2×D4×C53—21no—
501C2×D4×C53C2×D411yescharacteristic
502C2×D4×C53C2411yescharacteristic
503C22×C4×C53—21no—
504C22×C4×C53—21no—
505C22×C4×C53—21no—
506C22×C4×C53—21no—
507C22×C4×C53C2411yescharacteristic
508C22×C4×C53C2411yescharacteristic
509C2×C22⋊D53—21no—
510C2×C22⋊D53—21no—
511C2×C22⋊D53—21no—
512C2×C22⋊D53—21no—
513C2×C22⋊D53—21no—
514C2×C22⋊D53—21no—
515C2×C22⋊D53—21no—
516C2×C22⋊D53C2×D411yescharacteristic
517C2×C22⋊D53C2×D411yescharacteristic
518C2×C22⋊D53C2×D411yescharacteristic
519C2×C22⋊D53C2×D411yescharacteristic
520C22×Dic53—21no—
521C22×Dic53—21no—
522C22×Dic53—21no—
523C22×Dic53C2×D411yescharacteristic
524#11719949—22no—
525#11719949—22no—
526#11719949—22no—
527#11719949—22no—
528#11719949—22no—
529#11719949—22no—
530#11719949—44no—
531#11719949—41no—
532#11719949—41no—
533#11719949—41no—
534#11719949—44no—
535#11719949—44no—
536#11719949#4114yescomplemented
537Q8×D53—22no—
538Q8×D53—22no—
539Q8×D53—22no—
540Q8×D53—41no—
541Q8×D53—44no—
542#11719947—82no—
543#11719947—82no—
544D4×D53—22no—
545D4×D53—22no—
546D4×D53—82no—
547#11719945—22no—
548#11719945—22no—
549#11719945—22no—
550#11719945—41no—
551#11719945—44no—
552#11719945—44no—
553C2×D212—21no—
554C2×D212—22no—
555C2×D212—21no—
556C2×D212—21no—
557C2×D212—21no—
558C2×D212—21no—
559C2×D212—21no—
560C2×D212—21no—
561C2×D212—21no—
562C2×D212—21no—
563C2×D212—41no—
564C2×D212—44no—
565C2×D212C2×D411yescharacteristic
566C2×D212C2×D411yescharacteristic
567C2×D212C2411yescharacteristic
568C2×D212C2411yescharacteristic
569C2×D212C2411yescharacteristic
570C2×C4×D53—21no—
571C2×C4×D53—22no—
572C2×C4×D53—22no—
573C2×C4×D53—21no—
574C2×C4×D53—21no—
575C2×C4×D53—21no—
576C2×C4×D53—21no—
577C2×C4×D53—21no—
578C2×C4×D53—21no—
579C2×C4×D53—21no—
580C2×C4×D53—21no—
581C2×C4×D53—21no—
582C2×C4×D53—21no—
583C2×C4×D53—21no—
584C2×C4×D53—21no—
585C2×C4×D53—21no—
586C2×C4×D53—21no—
587C2×C4×D53—44no—
588C2×C4×D53C2×D411yescharacteristic
589C2×C4×D53C2×D411yescharacteristic
590C2×C4×D53C2411yescharacteristic
591C2×C4×D53C2411yescharacteristic
592C2×C4×D53C2411yescharacteristic
593C2×Dic106—21no—
594C2×Dic106—21no—
595C2×Dic106—21no—
596C2×Dic106—21no—
597C2×Dic106C2×D411yescharacteristic
598C2×Dic106C2411yescharacteristic
599SD16×C53—22no—
600SD16×C53—41no—
601SD16×C53—41no—
602M16×C53—41no—
603C2×C8×C53—41no—
604C2×C8×C53C2411yescharacteristic
605C2×C8×C53C2411yescharacteristic
606C2×C8×C53C2411yescharacteristic
607C2×C8×C53C2411yescharacteristic
608C4⋊C4×C53—21no—
609C4⋊C4×C53—21no—
610C4⋊C4×C53—21no—
611C4⋊C4×C53—21no—
612C4⋊C4×C53—21no—
613C4⋊C4×C53—21no—
614C4⋊C4×C53—21no—
615C4⋊C4×C53—21no—
616C4⋊C4×C53C2×D411yescharacteristic
617C4⋊C4×C53C2411yescharacteristic
618C4⋊C4×C53C2411yescharacteristic
619C4⋊C4×C53C2411yescharacteristic
620C4⋊C4×C53C2411yescharacteristic
621C22⋊C4×C53—21no—
622C22⋊C4×C53—21no—
623C22⋊C4×C53—21no—
624C22⋊C4×C53—21no—
625C22⋊C4×C53—21no—
626C22⋊C4×C53—21no—
627C22⋊C4×C53C2×D411yescharacteristic
628C22⋊C4×C53C2×D411yescharacteristic
629C42×C53—21no—
630C42×C53—21no—
631C42×C53C2411yescharacteristic
632C22⋊Dic53—21no—
633C22⋊Dic53—21no—
634C22⋊Dic53—21no—
635C22⋊Dic53—21no—
636C22⋊Dic53C2×D411yescharacteristic
637C22⋊Dic53C2×D411yescharacteristic
638#11719924—22no—
639#11719924—41no—
640#11719924—41no—
641#11719923—41no—
642#11719922—22no—
643#11719922—41no—
644#11719921—21no—
645#11719921—21no—
646#11719921—21no—
647#11719921—21no—
648#11719921—21no—
649#11719921—21no—
650#11719921—21no—
651#11719921—21no—
652#11719921—21no—
653#11719921—21no—
654#11719921—21no—
655#11719921—21no—
656#11719921—21no—
657#11719921—21no—
658#11719921—21no—
659#11719921—21no—
660#11719921—21no—
661#11719921—21no—
662#11719921—21no—
663#11719921—21no—
664#11719921—21no—
665#11719921—21no—
666#11719921C2×D411yescharacteristic
667#11719921C2×D411yescharacteristic
668#11719921C2×D411yescharacteristic
669#11719921C2×D411yescharacteristic
670#11719921C2×D411yescharacteristic
671#11719921C2×D411yescharacteristic
672C4⋊Dic53—21no—
673C4⋊Dic53—21no—
674C4⋊Dic53—21no—
675C4⋊Dic53—21no—
676C4⋊Dic53—21no—
677C4⋊Dic53—21no—
678C4⋊Dic53C2×D411yescharacteristic
679C4⋊Dic53C2411yescharacteristic
680C4⋊Dic53C2411yescharacteristic
681C4⋊Dic53C2411yescharacteristic
682C4⋊Dic53C2411yescharacteristic
683#11719919—21no—
684#11719919—21no—
685#11719919—21no—
686#11719919—21no—
687#11719919—21no—
688#11719919—21no—
689#11719919—21no—
690#11719919—21no—
691#11719919—21no—
692#11719919—21no—
693#11719919C2×D411yescharacteristic
694#11719919C2×D411yescharacteristic
695#11719919C2×D411yescharacteristic
696#11719919C2×D411yescharacteristic
697C4×Dic53—21no—
698C4×Dic53—21no—
699C4×Dic53—21no—
700C4×Dic53—21no—
701C4×Dic53—21no—
702C4×Dic53—21no—
703C4×Dic53C2411yescharacteristic
704C2×#88322—41no—
705C2×#88322—41no—
706C2×#88322C2411yescharacteristic
707C2×#88322C2411yescharacteristic
708C2×#88322C2411yescharacteristic
709C2×#88322C2411yescharacteristic
710D424—22no—
711D424—41no—
712#11719913—41no—
713#11719912—22no—
714#11719912—22no—
715#11719912—41no—
716C8×D53—22no—
717C8×D53—22no—
718C8×D53—41no—
719C8×D53—41no—
720C8×D53—41no—
721C23×C53—21no—
722C23×C53C22×D411yescharacteristic
723C23×C53C22×D411yescharacteristic
724C22×D53—22no—
725C22×D53—21no—
726C22×D53—22no—
727C22×D53—21no—
728C22×D53—21no—
729C22×D53—41no—
730C22×D53—42no—
731C22×D53—42no—
732C22×D53—42no—
733C22×D53—81no—
734C22×D53—81no—
735C22×D53—81no—
736C22×D53C22×D411yescharacteristic
737C22×D53C22×D411yescharacteristic
738C22×D53C22×D411yescharacteristic
739Q8×C53—21no—
740Q8×C53—21no—
741Q8×C53—21no—
742Q8×C53—21no—
743Q8×C53—21no—
744Q8×C53—42no—
745Q8×C53—42no—
746Q8×C53C2×#4112yes—
747D4×C53—22no—
748D4×C53—21no—
749D4×C53—21no—
750D4×C53—42no—
751D4×C53—81no—
752C2×C4×C53—21no—
753C2×C4×C53—21no—
754C2×C4×C53—21no—
755C2×C4×C53—21no—
756C2×C4×C53—21no—
757C2×C4×C53—21no—
758C2×C4×C53—21no—
759C2×C4×C53—21no—
760C2×C4×C53—21no—
761C2×C4×C53—21no—
762C2×C4×C53—21no—
763C2×C4×C53—42no—
764C2×C4×C53—42no—
765C2×C4×C53—81no—
766C2×C4×C53—81no—
767C2×C4×C53C22×D411yescharacteristic
768C2×C4×C53C22×D411yescharacteristic
769C2×C4×C53C22×D411yescharacteristic
770C2×C4×C53C22×D411yescharacteristic
771C2×C4×C53C2511yescharacteristic
772C22⋊D53—22no—
773C22⋊D53—22no—
774C22⋊D53—22no—
775C22⋊D53—41no—
776C22⋊D53—42no—
777C22⋊D53—42no—
778C22⋊D53—42no—
779C22⋊D53—81no—
780C22⋊D53—81no—
781C22⋊D53—81no—
782C22⋊D53—81no—
783C2×Dic53—22no—
784C2×Dic53—21no—
785C2×Dic53—21no—
786C2×Dic53—21no—
787C2×Dic53—21no—
788C2×Dic53—21no—
789C2×Dic53—42no—
790C2×Dic53—81no—
791C2×Dic53—81no—
792C2×Dic53C22×D411yescharacteristic
793C2×Dic53C22×D411yescharacteristic
794C2×Dic53C22×D411yescharacteristic
795C2×Dic53C22×D411yescharacteristic
796C2×Dic53C22×D411yescharacteristic
797D212—24no—
798D212—22no—
799D212—21no—
800D212—21no—
801D212—21no—
802D212—21no—
803D212—21no—
804D212—41no—
805D212—42no—
806D212—42no—
807D212—42no—
808D212—42no—
809D212—42no—
810D212—81no—
811D212—81no—
812D212—81no—
813D212C2×#4112yes—
814C4×D53—22no—
815C4×D53—21no—
816C4×D53—21no—
817C4×D53—21no—
818C4×D53—21no—
819C4×D53—22no—
820C4×D53—24no—
821C4×D53—42no—
822C4×D53—42no—
823C4×D53—42no—
824C4×D53—42no—
825C4×D53—42no—
826C4×D53—42no—
827C4×D53—42no—
828C4×D53—81no—
829C4×D53—81no—
830C4×D53—81no—
831C4×D53—81no—
832C4×D53—81no—
833C4×D53—81no—
834C4×D53—81no—
835C4×D53C2×#4112yes—
836C4×D53H(5,𝔽2)12yes—
837Dic106—22no—
838Dic106—21no—
839Dic106—21no—
840Dic106—42no—
841Dic106—42no—
842Dic106—81no—
843Dic106—81no—
844C8×C53—21no—
845C8×C53—21no—
846C8×C53—21no—
847C8×C53—21no—
848#88322—21no—
849#88322—21no—
850#88322—21no—
851#88322—21no—
852#61174—531nomaximal, Sylow
853C22×C53—21no—
854C22×C53—21no—
855C22×C53—21no—
856C22×C53—21no—
857C22×C53—21no—
858C22×C53—41no—
859C22×C53—41no—
860C22×C53—41no—
861C22×C53#57712yes—
862C22×C53C23×D411yescharacteristic
863C2×D53—21no—
864C2×D53—21no—
865C2×D53—21no—
866C2×D53—21no—
867C2×D53—21no—
868C2×D53—22no—
869C2×D53—21no—
870C2×D53—21no—
871C2×D53—21no—
872C2×D53—44no—
873C2×D53—41no—
874C2×D53—41no—
875C2×D53—41no—
876C2×D53—41no—
877C2×D53—41no—
878C2×D53—41no—
879C2×D53—41no—
880C2×D53—41no—
881C2×D53—84no—
882C2×D53—162no—
883C2×D53#54612yes—
884C4×C53—21no—
885C4×C53—21no—
886C4×C53—22no—
887C4×C53—21no—
888C4×C53—21no—
889C4×C53—41no—
890C4×C53—41no—
891C4×C53—41no—
892C4×C53—41no—
893C4×C53—41no—
894C4×C53—41no—
895C4×C53C22×#4111yescharacteristic
896C4×C53C2×H(5,𝔽2)11yescharacteristic
897Dic53—21no—
898Dic53—21no—
899Dic53—21no—
900Dic53—21no—
901Dic53—41no—
902Dic53—41no—
903Dic53—41no—
904Dic53—41no—
905Dic53—41no—
906Dic53#54612yes—
907#3494—531no—
908#3489—531no—
909#3321—531no—
910#3321—531no—
911#3320—531no—
912#3320D5311yescharacteristic, complemented
913#3307—531no—
914#3307—531no—
915#3306—531no—
916#3306—531no—
917#3303—531no—
918#3303—531no—
919#3301—531no—
920#3301—531no—
921#3298—531no—
922#3298—531no—
923#3297—531no—
924#3297—531no—
925#3137—531no—
926#3099—531no—
927#3095—531no—
928#3084—531no—
929#3062—531no—
930C2×#465—531no—
931#3042—531no—
932#3010—531no—
933#3006—531no—
934#2946—531no—
935#2929—531no—
936#2898—531no—
937C2×#416—531no—
938C2×C53—22no—
939C2×C53—41no—
940C2×C53—81no—
941C2×C53C2×#54611yescharacteristic
942C2×C53C2×#57711yescharacteristic
943C2×C53#358411yescharacteristic
944D53—22no—
945D53—41no—
946D53—41no—
947D53—42no—
948D53—81no—
949D53—81no—
950C2×2−1+4—531no—
951C22×#41—531no—
952C2×AGL(1,ℤ/8)—531no—
953C2×AGL(1,ℤ/8)—531no—
954C22×SD16—531no—
955C2×#131—531no—
956C23×C8—531no—
957#555—531no—
958#555—531no—
959#553—531no—
960#553—531no—
961#553—531no—
962#553C2×D5311yescharacteristic
963#551—1061no—
964#551—1061no—
965D4×Q8—531no—
966D4×Q8C2×D5311yescharacteristic, complemented
967#548—531no—
968#548—531no—
969#547—531no—
970#547—531no—
971#547—531no—
972#547—531no—
973#547—1061no—
974#547—1061no—
975#546—531no—
976#546—531no—
977#546—1061no—
978#546—1061no—
979#546—1061no—
980#546—1061no—
981#544—531no—
982#542—1061no—
983#540—1061no—
984#537—531no—
985#537—1061no—
986#536—531no—
987#536—1061no—
988#535—531no—
989#532—1061no—
990#529—1061no—
991#525—531no—
992#525—1061no—
993C2×C22⋊Q8—531no—
994C2×C22⋊Q8—1061no—
995C2×#121—531no—
996#520—531no—
997#520—531no—
998#518—531no—
999C2×#117—531no—
1000#491—531no—
1001#491C2×D5311yescharacteristic, complemented
1002#489—531no—
1003#489—531no—
1004#488—531no—
1005#488—531no—
1006#487—531no—
1007#487—531no—
1008#485—531no—
1009#485—531no—
1010#485—531no—
1011#485—531no—
1012#485—531no—
1013#485C2×D5311yescharacteristic, complemented
1014#484—531no—
1015#484C2×D5311yescharacteristic, complemented
1016#483—531no—
1017#483—531no—
1018#483—531no—
1019#483—531no—
1020#482—531no—
1021#482—531no—
1022#481—531no—
1023#481—531no—
1024#479—531no—
1025#479C2×D5311yescharacteristic, complemented
1026#478—531no—
1027#478—531no—
1028#476—531no—
1029#476—531no—
1030#475—531no—
1031#475—531no—
1032#469—531no—
1033#469—531no—
1034#468—531no—
1035#468C2×D5311yescharacteristic, complemented
1036#466—531no—
1037#466—531no—
1038#465—531no—
1039#465—531no—
1040#465—531no—
1041#465—531no—
1042#465—531no—
1043#465—531no—
1044#465—531no—
1045#465—531no—
1046#465—531no—
1047#465C2×D5311yescharacteristic
1048#463—531no—
1049#463—531no—
1050#463—531no—
1051#463—531no—
1052#461—531no—
1053#461—531no—
1054#461—531no—
1055#461C2×D5311yescharacteristic, complemented
1056#449—531no—
1057#449—531no—
1058#449—531no—
1059#449—531no—
1060#449—531no—
1061#449—531no—
1062#449—531no—
1063#449—531no—
1064#448—531no—
1065#448—531no—
1066#448—531no—
1067#448—531no—
1068#448C2×D5311yescharacteristic
1069#448C2×D5311yescharacteristic, complemented
1070#447—531no—
1071#447—531no—
1072#442—531no—
1073#442—531no—
1074#440—531no—
1075#440C2×D5311yescharacteristic, complemented
1076C4×SD16—531no—
1077C4×SD16—531no—
1078C4×D8—531no—
1079C4×D8—531no—
1080#435—531no—
1081#435—531no—
1082#435—531no—
1083#435C2×D5311yescharacteristic, complemented
1084C8×D4—531no—
1085C8×D4—531no—
1086C8×D4—531no—
1087C8×D4—531no—
1088#428—531no—
1089#428—531no—
1090C2×#106—531no—
1091#424—531no—
1092#419—531no—
1093#419—531no—
1094#419—531no—
1095#419C2×D5311yescharacteristic, complemented
1096#417—531no—
1097#417—531no—
1098#417—531no—
1099#417—531no—
1100#416—531no—
1101#416—531no—
1102#416—531no—
1103#416—531no—
1104#416—531no—
1105#416—531no—
1106#416—531no—
1107#416—531no—
1108#416—531no—
1109#416—531no—
1110C2×#103—531no—
1111C2×#103—531no—
1112C2×#103—531no—
1113C2×#103—531no—
1114C2×#103C2×D5311yescharacteristic, complemented
1115C2×#102—531no—
1116C2×#102—531no—
1117C2×#102—531no—
1118#408—531no—
1119#407—531no—
1120#405—531no—
1121C53#6117411yescharacteristic, complemented, Sylow
11222−1+4—1064no—
11232−1+4—2122no—
1124C2×#41—531no—
1125C2×#41—531no—
1126C2×#41—531no—
1127C2×#41—531no—
1128C2×#41—531no—
1129C2×#41—531no—
1130C2×#41—531no—
1131C2×#41—1061no—
1132C2×#41—1061no—
1133C2×#41—1061no—
1134C2×#41—1061no—
1135C2×#41—1061no—
1136C2×#41—1061no—
1137C2×#41—1061no—
1138C2×#41—1064no—
1139C2×#41—2122no—
1140C22×Q8—531no—
1141C22×Q8—531no—
1142C22×Q8—1061no—
1143C22×Q8C22×D5311yescharacteristic
1144C22×Q8C22×D5311yescharacteristic
1145C22×D4—531no—
1146C22×D4—531no—
1147C22×D4—1061no—
1148C22×D4—1061no—
1149C23×C4—531no—
1150C23×C4—1061no—
1151AGL(1,ℤ/8)—1064no—
1152AGL(1,ℤ/8)—2122no—
1153C2×SD16—531no—
1154C2×SD16—531no—
1155C2×SD16—531no—
1156C2×SD16—531no—
1157C2×SD16—531no—
1158C2×SD16—2122no—
1159C2×SD16C22×D5311yescharacteristic
1160C2×SD16C22×D5311yescharacteristic
1161C2×SD16C22×D5311yescharacteristic
1162C2×D8—531no—
1163C2×D8—531no—
1164C2×D8—531no—
1165C2×D8—531no—
1166#131—2122no—
1167C2×M16—531no—
1168C2×M16—531no—
1169C2×M16—531no—
1170C2×M16C22×D5311yescharacteristic
1171C22×C8—531no—
1172C22×C8—531no—
1173C22×C8—531no—
1174C22×C8—531no—
1175C22×C8—531no—
1176C22×C8—531no—
1177C22×C8—531no—
1178C22×C8—2122no—
1179C22×C8C22×D5311yescharacteristic
1180C4⋊Q8—21no—
1181C4⋊Q8—531no—
1182C4⋊Q8—531no—
1183C4⋊Q8—531no—
1184C4⋊Q8—1061no—
1185C4⋊Q8—1061no—
1186C4⋊Q8C22×D5311yescharacteristic
1187#127—1061no—
1188#126—21no—
1189#126—1061no—
1190#126—1061no—
1191#126—1061no—
1192#125—531no—
1193#125—1061no—
1194#125C22×D5311yescharacteristic
1195#124—531no—
1196#124—531no—
1197#124—1061no—
1198#124—1061no—
1199#124—1061no—
1200#124—1061no—
1201#124—1061no—
1202#124—1061no—
1203#124—1061no—
1204#123—21no—
1205#123—531no—
1206#123—531no—
1207#123—1061no—
1208#123—1061no—
1209#123—1061no—
1210#123—1061no—
1211#123—1061no—
1212#123—1061no—
1213#123—1061no—
1214#123—1061no—
1215#123—1061no—
1216#123—1061no—
1217#123—1061no—
1218#123—1061no—
1219#123—1061no—
1220#123—1061no—
1221#123—1061no—
1222C22⋊Q8—21no—
1223C22⋊Q8—21no—
1224C22⋊Q8—531no—
1225C22⋊Q8—531no—
1226C22⋊Q8—531no—
1227C22⋊Q8—531no—
1228C22⋊Q8—531no—
1229C22⋊Q8—531no—
1230C22⋊Q8—1061no—
1231C22⋊Q8—1061no—
1232C22⋊Q8—1061no—
1233C22⋊Q8—1061no—
1234C22⋊Q8—1061no—
1235C22⋊Q8—1061no—
1236C22⋊Q8—1061no—
1237C22⋊Q8—1061no—
1238C22⋊Q8—1061no—
1239C22⋊Q8—1061no—
1240C22⋊Q8—1061no—
1241C22⋊Q8—1061no—
1242C22⋊Q8—1061no—
1243C22⋊Q8C22×D5311yescharacteristic
1244C22⋊Q8C22×D5311yescharacteristic
1245#121—21no—
1246#121—531no—
1247#121—531no—
1248#121—531no—
1249#121—531no—
1250#121—531no—
1251#121—531no—
1252#121—531no—
1253#121—531no—
1254#121—531no—
1255#121—531no—
1256#121—1061no—
1257#121—1061no—
1258#121—1061no—
1259#121—1061no—
1260#121—1061no—
1261#121—1061no—
1262#121—1061no—
1263#121—1061no—
1264#121—1061no—
1265#121—1061no—
1266#121—1061no—
1267#121—1061no—
1268#121—1061no—
1269#121—1061no—
1270#121—1061no—
1271#121—1061no—
1272#121C22×D5311yescharacteristic
1273#121C22×D5311yescharacteristic
1274#120—531no—
1275#120—531no—
1276#120—1061no—
1277#120—1061no—
1278#120—1061no—
1279#120—1061no—
1280C4×Q8—531no—
1281C4×Q8—1061no—
1282C4×Q8C22×D5311yescharacteristic
1283C4×D4—21no—
1284C4×D4—21no—
1285C4×D4—531no—
1286C4×D4—531no—
1287C4×D4—531no—
1288C4×D4—531no—
1289C4×D4—531no—
1290C4×D4—531no—
1291C4×D4—531no—
1292C4×D4—531no—
1293C4×D4—1061no—
1294C4×D4—1061no—
1295C4×D4—1061no—
1296C4×D4—1061no—
1297C4×D4—1061no—
1298C4×D4—1061no—
1299C4×D4—1061no—
1300C4×D4—1061no—
1301C4×D4—1061no—
1302C4×D4—1061no—
1303C4×D4—1061no—
1304C4×D4—1061no—
1305C4×D4—1061no—
1306C4×D4C22×D5311yescharacteristic
1307C4×D4C22×D5311yescharacteristic
1308#117—531no—
1309#117—531no—
1310#117—531no—
1311#117—531no—
1312#117—531no—
1313#117—531no—
1314#117—1061no—
1315#117—1061no—
1316#117—1061no—
1317#117—1061no—
1318#117—1061no—
1319#117C22×D5311yescharacteristic
1320C2×C4⋊C4—531no—
1321C2×C4⋊C4—531no—
1322C2×C4⋊C4—531no—
1323C2×C4⋊C4—531no—
1324C2×C4⋊C4—531no—
1325C2×C4⋊C4—1061no—
1326C2×C4⋊C4—1061no—
1327C2×C4⋊C4—1061no—
1328C2×C4⋊C4—1061no—
1329C2×C4⋊C4C22×D5311yescharacteristic
1330C2×C22⋊C4—1061no—
1331C2×C22⋊C4—1061no—
1332C2×C22⋊C4—1061no—
1333C2×C22⋊C4—1061no—
1334C2×C22⋊C4—1061no—
1335C2×C22⋊C4—1061no—
1336C2×C22⋊C4—1061no—
1337C2×C42—1061no—
1338#107—531no—
1339#107—531no—
1340#107C22×D5311yescharacteristic
1341#107C22×D5311yescharacteristic
1342#106—531no—
1343#106—531no—
1344#106—531no—
1345#106—531no—
1346#106—531no—
1347#106—531no—
1348#106—531no—
1349#106C22×D5311yescharacteristic
1350C4⋊C8—531no—
1351C4⋊C8—531no—
1352C4⋊C8—531no—
1353C4⋊C8C22×D5311yescharacteristic
1354#103—531no—
1355#103—531no—
1356#103—531no—
1357#103—531no—
1358#103—531no—
1359#103—531no—
1360#103—531no—
1361#103—531no—
1362#103—531no—
1363#103—531no—
1364#103—531no—
1365#103—531no—
1366#103—531no—
1367#103—531no—
1368#103—531no—
1369#103C22×D5311yescharacteristic
1370#103C22×D5311yescharacteristic
1371#103C22×D5311yescharacteristic
1372#103C22×D5311yescharacteristic
1373#103C22×D5311yescharacteristic
1374#103C22×D5311yescharacteristic
1375#103C22×D5311yescharacteristic
1376#103C22×D5311yescharacteristic
1377#103C22×D5311yescharacteristic
1378#102—531no—
1379#102—531no—
1380#102—531no—
1381#102—531no—
1382#102—531no—
1383#102—531no—
1384#102—531no—
1385#102—531no—
1386#102—531no—
1387#102—531no—
1388#102—531no—
1389#102—531no—
1390#102—531no—
1391#102—531no—
1392#102—531no—
1393#102C22×D5311yescharacteristic
1394C22⋊C8—531no—
1395C22⋊C8—531no—
1396C22⋊C8—531no—
1397C22⋊C8—531no—
1398C22⋊C8—531no—
1399C22⋊C8—531no—
1400C22⋊C8C22×D5311yescharacteristic
1401C22⋊C8C22×D5311yescharacteristic
1402#97—531no—
1403#97C22×D5311yescharacteristic
1404C4×C8—531no—
1405C4×C8—531no—
1406C24—531no—
1407C24—1061no—
1408C24—1061no—
1409#41—534no—
1410#41—1062no—
1411#41—1062no—
1412#41—1062no—
1413#41—1062no—
1414#41—1062no—
1415#41—1062no—
1416#41—1062no—
1417#41—1062no—
1418#41—1062no—
1419#41—4242no—
1420#41—4242no—
1421#41—2121no—
1422#41—2124no—
1423#41—2124no—
1424#41—2124no—
1425#41—2121no—
1426#41—2121no—
1427#41—2121no—
1428#41—2124no—
1429#41—2124no—
1430C2×Q8—21no—
1431C2×Q8—21no—
1432C2×Q8—22no—
1433C2×Q8—22no—
1434C2×Q8—41no—
1435C2×Q8—41no—
1436C2×Q8—531no—
1437C2×Q8—531no—
1438C2×Q8—1061no—
1439C2×Q8—1061no—
1440C2×Q8—1061no—
1441C2×Q8—1062no—
1442C2×Q8—1062no—
1443C2×Q8—1061no—
1444C2×Q8—1062no—
1445C2×Q8—2121no—
1446C2×Q8—2124no—
1447C2×Q8C23×D5311yescharacteristic
1448C2×Q8C23×D5311yescharacteristic
1449C2×Q8C23×D5311yescharacteristic
1450C2×D4—21no—
1451C2×D4—21no—
1452C2×D4—531no—
1453C2×D4—531no—
1454C2×D4—531no—
1455C2×D4—531no—
1456C2×D4—531no—
1457C2×D4—531no—
1458C2×D4—531no—
1459C2×D4—531no—
1460C2×D4—531no—
1461C2×D4—1062no—
1462C2×D4—1061no—
1463C2×D4—1061no—
1464C2×D4—1061no—
1465C2×D4—1061no—
1466C2×D4—1061no—
1467C2×D4—1061no—
1468C2×D4—1061no—
1469C2×D4—1061no—
1470C2×D4—1062no—
1471C2×D4—1062no—
1472C2×D4—1061no—
1473C2×D4—1061no—
1474C2×D4—1061no—
1475C2×D4—1061no—
1476C2×D4—1061no—
1477C2×D4—1061no—
1478C2×D4—1061no—
1479C2×D4—1061no—
1480C2×D4—4242no—
1481C2×D4—2121no—
1482C2×D4—2124no—
1483C2×D4D4×D5311yescharacteristic
1484C2×D4C23×D5311yescharacteristic
1485C22×C4—21no—
1486C22×C4—21no—
1487C22×C4—21no—
1488C22×C4—21no—
1489C22×C4—531no—
1490C22×C4—531no—
1491C22×C4—531no—
1492C22×C4—531no—
1493C22×C4—531no—
1494C22×C4—531no—
1495C22×C4—1061no—
1496C22×C4—1062no—
1497C22×C4—1062no—
1498C22×C4—1061no—
1499C22×C4—1061no—
1500C22×C4—1061no—
1501C22×C4—1061no—
1502C22×C4—1061no—
1503C22×C4—1061no—
1504C22×C4—1061no—
1505C22×C4—1061no—
1506C22×C4—1061no—
1507C22×C4—1061no—
1508C22×C4—1061no—
1509C22×C4—1061no—
1510C22×C4—1061no—
1511C22×C4—1061no—
1512C22×C4—1061no—
1513C22×C4—1061no—
1514C22×C4—1061no—
1515C22×C4—2124no—
1516C22×C4C23×D5311yescharacteristic
1517C22×C4C23×D5311yescharacteristic
1518SD16—22no—
1519SD16—41no—
1520SD16—41no—
1521SD16—1062no—
1522SD16—2121no—
1523SD16—2121no—
1524SD16—2121no—
1525SD16—2121no—
1526D8—1062no—
1527D8—1062no—
1528D8—2121no—
1529D8—2121no—
1530M16—41no—
1531M16—1062no—
1532M16—1062no—
1533M16—2121no—
1534C2×C8—41no—
1535C2×C8—531no—
1536C2×C8—531no—
1537C2×C8—531no—
1538C2×C8—531no—
1539C2×C8—1062no—
1540C2×C8—1062no—
1541C2×C8—2121no—
1542C2×C8—2121no—
1543C2×C8—2121no—
1544C2×C8—2121no—
1545C2×C8—2121no—
1546C2×C8C23×D5311yescharacteristic
1547C2×C8C23×D5311yescharacteristic
1548C2×C8C23×D5311yescharacteristic
1549C2×C8C23×D5311yescharacteristic
1550C4⋊C4—21no—
1551C4⋊C4—21no—
1552C4⋊C4—21no—
1553C4⋊C4—21no—
1554C4⋊C4—21no—
1555C4⋊C4—21no—
1556C4⋊C4—21no—
1557C4⋊C4—21no—
1558C4⋊C4—531no—
1559C4⋊C4—531no—
1560C4⋊C4—531no—
1561C4⋊C4—531no—
1562C4⋊C4—531no—
1563C4⋊C4—531no—
1564C4⋊C4—531no—
1565C4⋊C4—531no—
1566C4⋊C4—531no—
1567C4⋊C4—1061no—
1568C4⋊C4—1061no—
1569C4⋊C4—1061no—
1570C4⋊C4—1061no—
1571C4⋊C4—1061no—
1572C4⋊C4—1061no—
1573C4⋊C4—1061no—
1574C4⋊C4—1061no—
1575C4⋊C4—1061no—
1576C4⋊C4—1061no—
1577C4⋊C4—1061no—
1578C4⋊C4—1061no—
1579C4⋊C4—1061no—
1580C4⋊C4—1061no—
1581C4⋊C4—1061no—
1582C4⋊C4—1061no—
1583C4⋊C4D4×D5311yescharacteristic
1584C4⋊C4C23×D5311yescharacteristic
1585C4⋊C4C23×D5311yescharacteristic
1586C4⋊C4C23×D5311yescharacteristic
1587C4⋊C4C23×D5311yescharacteristic
1588C22⋊C4—21no—
1589C22⋊C4—21no—
1590C22⋊C4—21no—
1591C22⋊C4—21no—
1592C22⋊C4—21no—
1593C22⋊C4—21no—
1594C22⋊C4—531no—
1595C22⋊C4—531no—
1596C22⋊C4—531no—
1597C22⋊C4—531no—
1598C22⋊C4—531no—
1599C22⋊C4—531no—
1600C22⋊C4—531no—
1601C22⋊C4—531no—
1602C22⋊C4—1061no—
1603C22⋊C4—1061no—
1604C22⋊C4—1061no—
1605C22⋊C4—1061no—
1606C22⋊C4—1061no—
1607C22⋊C4—1061no—
1608C22⋊C4—1061no—
1609C22⋊C4—1061no—
1610C22⋊C4—1061no—
1611C22⋊C4—1061no—
1612C22⋊C4—1061no—
1613C22⋊C4—1061no—
1614C22⋊C4—1061no—
1615C22⋊C4—1061no—
1616C22⋊C4—1061no—
1617C22⋊C4—1061no—
1618C22⋊C4—1061no—
1619C22⋊C4—1061no—
1620C22⋊C4—1061no—
1621C22⋊C4—1061no—
1622C22⋊C4—1061no—
1623C22⋊C4—1061no—
1624C22⋊C4—1061no—
1625C22⋊C4—1061no—
1626C22⋊C4—1061no—
1627C22⋊C4—1061no—
1628C22⋊C4D4×D5311yescharacteristic
1629C22⋊C4D4×D5311yescharacteristic
1630C42—21no—
1631C42—21no—
1632C42—531no—
1633C42—1061no—
1634C42—1061no—
1635C42—1061no—
1636C42—1061no—
1637C42—1061no—
1638C42—1061no—
1639C42C23×D5311yescharacteristic
1640C23—21no—
1641C23—531no—
1642C23—531no—
1643C23—531no—
1644C23—1062no—
1645C23—1062no—
1646C23—1061no—
1647C23—1061no—
1648C23—1061no—
1649C23—4241no—
1650C23—4241no—
1651C23—4241no—
1652C23—2121no—
1653C23—2122no—
1654C23—2122no—
1655C23—2122no—
1656C23C2×D4×D5311yescharacteristic
1657C23C2×D4×D5311yescharacteristic
1658Q8—21no—
1659Q8—21no—
1660Q8—21no—
1661Q8—21no—
1662Q8—21no—
1663Q8—42no—
1664Q8—42no—
1665Q8—1062no—
1666Q8—1061no—
1667Q8—1061no—
1668Q8—4241no—
1669Q8—4241no—
1670Q8—2122no—
1671Q8—2122no—
1672Q8#41×D5312yes—
1673D4—22no—
1674D4—21no—
1675D4—21no—
1676D4—42no—
1677D4—81no—
1678D4—532no—
1679D4—1062no—
1680D4—1064no—
1681D4—1062no—
1682D4—1062no—
1683D4—1062no—
1684D4—1061no—
1685D4—1061no—
1686D4—1061no—
1687D4—1061no—
1688D4—1061no—
1689D4—4241no—
1690D4—4241no—
1691D4—4241no—
1692D4—4241no—
1693D4—4241no—
1694D4—4241no—
1695D4—4241no—
1696D4—2121no—
1697D4—2122no—
1698D4—2122no—
1699D4—2122no—
1700D4—2122no—
1701D4—2122no—
1702D4—2122no—
1703D4—2121no—
1704D4—2122no—
1705D4—2122no—
1706C2×C4—21no—
1707C2×C4—21no—
1708C2×C4—21no—
1709C2×C4—21no—
1710C2×C4—21no—
1711C2×C4—21no—
1712C2×C4—21no—
1713C2×C4—21no—
1714C2×C4—21no—
1715C2×C4—21no—
1716C2×C4—21no—
1717C2×C4—42no—
1718C2×C4—42no—
1719C2×C4—81no—
1720C2×C4—81no—
1721C2×C4—531no—
1722C2×C4—532no—
1723C2×C4—532no—
1724C2×C4—531no—
1725C2×C4—531no—
1726C2×C4—531no—
1727C2×C4—531no—
1728C2×C4—1062no—
1729C2×C4—1064no—
1730C2×C4—1062no—
1731C2×C4—1062no—
1732C2×C4—1061no—
1733C2×C4—1061no—
1734C2×C4—1061no—
1735C2×C4—1061no—
1736C2×C4—1061no—
1737C2×C4—1061no—
1738C2×C4—1061no—
1739C2×C4—1061no—
1740C2×C4—1061no—
1741C2×C4—4241no—
1742C2×C4—4241no—
1743C2×C4—4241no—
1744C2×C4—4241no—
1745C2×C4—4241no—
1746C2×C4—4241no—
1747C2×C4—4241no—
1748C2×C4—4241no—
1749C2×C4—4241no—
1750C2×C4—2122no—
1751C2×C4—2122no—
1752C2×C4—2122no—
1753C2×C4—2122no—
1754C2×C4—2122no—
1755C2×C4—2122no—
1756C2×C4—2122no—
1757C2×C4—2122no—
1758C2×C4C2×D4×D5311yescharacteristic
1759C2×C4C2×D4×D5311yescharacteristic
1760C2×C4C2×D4×D5311yescharacteristic
1761C2×C4C2×D4×D5311yescharacteristic
1762C2×C4C24×D5311yescharacteristic
1763C8—21no—
1764C8—21no—
1765C8—21no—
1766C8—21no—
1767C8—1061no—
1768C8—1061no—
1769C8—1061no—
1770C8—1061no—
1771C22—21no—
1772C22—21no—
1773C22—21no—
1774C22—21no—
1775C22—21no—
1776C22—41no—
1777C22—41no—
1778C22—41no—
1779C22—532no—
1780C22—8482no—
1781C22—1061no—
1782C22—1061no—
1783C22—1061no—
1784C22—1062no—
1785C22—1061no—
1786C22—1061no—
1787C22—1061no—
1788C22—1061no—
1789C22—1061no—
1790C22—4244no—
1791C22—2124no—
1792C22—2121no—
1793C22—2121no—
1794C22—2121no—
1795C22—2121no—
1796C22—2121no—
1797C22—2121no—
1798C22—2121no—
1799C22—2121no—
1800C22#1681143212yes—
1801C22C22×D4×D5311yescharacteristic
1802C4—21no—
1803C4—21no—
1804C4—22no—
1805C4—21no—
1806C4—21no—
1807C4—41no—
1808C4—41no—
1809C4—41no—
1810C4—41no—
1811C4—41no—
1812C4—41no—
1813C4—532no—
1814C4—1061no—
1815C4—1061no—
1816C4—1061no—
1817C4—1061no—
1818C4—2121no—
1819C4—2121no—
1820C4—2121no—
1821C4—2121no—
1822C4—2121no—
1823C4C2×#41×D5311yescharacteristic
1824C4H(5,𝔽2)×D5311yescharacteristic
1825C2—22no—
1826C2—41no—
1827C2—81no—
1828C2—1062no—
1829C2—4241no—
1830C2—4241no—
1831C2—2121no—
1832C2—2121no—
1833C2—2122no—
1834C2#546×D5311yescharacteristic
1835C2C2×#1681143211yescharacteristic
1836C2#2028948711yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3320C2
socleC22×C53C23×D4
hypercenter#3320D53
hypocenterC53#61174
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3320

Complements

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

NH ≅ G/Ntype
1. #20288446C2semidirect
2. #20288392C2semidirect
3. #20286906C2semidirect
4. #20286902C2semidirect
5. #20286882C2semidirect
6. #20286690C2semidirect
7. #20286686C2semidirect
8. #20286682C2semidirect
9. #20286678C2semidirect
10. #20286646C2semidirect
11. #20286641C2semidirect
12. #20286621C2semidirect
13. #20286614C2semidirect
14. #20286580C2semidirect
15. #20286573C2semidirect
16. #20286563C2semidirect
17. #20286559C2semidirect
18. #20285081C2semidirect
19. #20284701C2semidirect
20. #20284660C2semidirect
21. #20284580C2semidirect
22. #20284390C2semidirect
23. #465×D53C2semidirect
24. #20284222C2semidirect
25. #20283996C2semidirect
26. #20283966C2semidirect
27. #20283546C2semidirect
28. #20283406C2semidirect
29. #20283247C2semidirect
30. C2×#16810618C2semidirect
31. C53×#3320C2semidirect
36. C2×SD16×D53C22semidirect
37. C2×#13133225C22semidirect
39. #16811338C22semidirect
40. #16811336C22semidirect
41. #16811326C22semidirect
42. #16811325C22semidirect
46. Q8×C22⋊D53C22semidirect
47. #16811285C22semidirect
48. #16811284C22semidirect
51. #16811276C22semidirect
53. #16811275C22semidirect
56. #16811269C22semidirect
59. #16811264C22semidirect
61. #16811253C22semidirect
68. #16811189C22semidirect
77. #16811103C22semidirect
78. #16811095C22semidirect
80. #16810990C22semidirect
81. #16810984C22semidirect
82. #16810983C22semidirect
83. #16810980C22semidirect
84. #16810979C22semidirect
85. #16810973C22semidirect
86. #16810972C22semidirect
87. #16810966C22semidirect
88. #16810966C22semidirect
89. #16810962C22semidirect
90. #16810962C22semidirect
91. #16810962C22semidirect
92. #16810958C22semidirect
93. #16810954C22semidirect
94. #16810952C22semidirect
95. #16810951C22semidirect
96. #16810951C22semidirect
97. #16810950C22semidirect
98. #16810947C22semidirect
99. #16810943C22semidirect
100. #16810942C22semidirect
101. #16810928C22semidirect
102. #16810926C22semidirect
103. #16810920C22semidirect
104. #16810914C22semidirect
105. #16810912C22semidirect
106. #16810908C22semidirect
107. #16810906C22semidirect
108. #16810876C22semidirect
109. #16810875C22semidirect
110. #16810872C22semidirect
111. #16810860C22semidirect
112. #16810857C22semidirect
113. #16810855C22semidirect
115. #16810854C22semidirect
116. #16810853C22semidirect
118. #16810851C22semidirect
120. #16810849C22semidirect
121. #16810849C22semidirect
122. #16810841C22semidirect
123. #16810840C22semidirect
124. #16810839C22semidirect
125. #16810838C22semidirect
126. #16810827C22semidirect
127. #16810826C22semidirect
128. #16810825C22semidirect
131. #16810771C22semidirect
132. #16810770C22semidirect
135. #16810767C22semidirect
136. #16810766C22semidirect
137. #16810763C22semidirect
139. #16810762C22semidirect
140. #16810760C22semidirect
143. #16810736C22semidirect
144. #16810732C22semidirect
145. #16810726C22semidirect
146. SD16×Dic53C22semidirect
147. C4×#11719924C22semidirect
148. #16810705C22semidirect
149. C4×#11719922C22semidirect
150. #16810696C22semidirect
151. #16810694C22semidirect
152. #16810692C22semidirect
153. D4×#88322C22semidirect
154. #16810688C22semidirect
155. #16810686C22semidirect
156. #16810686C22semidirect
157. #16810664C22semidirect
158. #16810664C22semidirect
159. #106×D53C22semidirect
160. #16810648C22semidirect
161. #16810630C22semidirect
162. #16810630C22semidirect
163. #16810630C22semidirect
164. #16810625C22semidirect
167. #16810623C22semidirect
172. #16810618C22semidirect
173. #16810618C22semidirect
174. #16810618C22semidirect
175. #16810618C22semidirect
176. #16810618C22semidirect
177. #16810617C22semidirect
178. C2×#13133141C22semidirect
179. C2×#13133141C22semidirect
180. #103×D53C22semidirect
181. #103×D53C22semidirect
182. C2×#13133139C22semidirect
183. C2×#13133137C22semidirect
184. #102×D53C22semidirect
185. #16810588C22semidirect
187. #16810580C22semidirect
189. D4×Q8×C53C22semidirect
190. C53×#491C22semidirect
191. C53×#485C22semidirect
192. C53×#484C22semidirect
193. C53×#479C22semidirect
194. C53×#468C22semidirect
196. C53×#461C22semidirect
198. C53×#448C22semidirect
199. C53×#440C22semidirect
200. C53×#435C22semidirect
201. C53×#419C22semidirect
202. C2×#103×C53C22semidirect
536. #11719949#41semidirect
912. #3320D53semidirect
966. D4×Q8C2×D53semidirect
1001. #491C2×D53semidirect
1013. #485C2×D53semidirect
1015. #484C2×D53semidirect
1025. #479C2×D53semidirect
1035. #468C2×D53semidirect
1055. #461C2×D53semidirect
1069. #448C2×D53semidirect
1075. #440C2×D53semidirect
1083. #435C2×D53semidirect
1095. #419C2×D53semidirect
1114. C2×#103C2×D53semidirect
1121. C53#61174semidirect

Maximal subgroups

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

subgroupindex
#202884462
#202883922
#202869062
#202869022
#202868822
#202866902
#202866862
#202866822
#202866782
#202866462
#202866412
#202866212
#202866142
#202865802
#202865732
#202865632
#202865592
#202850812
#202847012
#202846602
#202845802
#202843902
#465×D532
#202842222
#202839962
#202839662
#202835462
#202834062
#202832472
C2×#168106182
C53×#33202
#6117453