Finite Group Databasebeta

← #28262047

Subgroups — #28262047

Order 13568.

2152 conjugacy classes of subgroups.

The subgroup lattice has 1872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288619C211yesmaximal, characteristic, complemented
2#20288475C211yesmaximal, characteristic, complemented
3#20287026C211yesmaximal, characteristic, complemented
4#20287024C211yesmaximal, characteristic, complemented
5#20286955C211yesmaximal, characteristic, complemented
6#20286953C211yesmaximal, characteristic, complemented
7#20286758C211yesmaximal, characteristic, complemented
8#20286756C211yesmaximal, characteristic, complemented
9#20286745C211yesmaximal, characteristic, complemented
10#20286678C211yesmaximal, characteristic, complemented
11#20286676C211yesmaximal, characteristic, complemented
12#20286675C211yesmaximal, characteristic, complemented
13#20286673C211yesmaximal, characteristic, complemented
14#20286641C211yesmaximal, characteristic, complemented
15#20286639C211yesmaximal, characteristic, complemented
16#20286534C211yesmaximal, characteristic, complemented
17#20286532C211yesmaximal, characteristic, complemented
18#20285107C211yesmaximal, characteristic, complemented
19#20284707C211yesmaximal, characteristic, complemented
20#20284701C211yesmaximal, characteristic, complemented
21#476×D53C211yesmaximal, characteristic, complemented
22#20284379C211yesmaximal, characteristic, complemented
23#20284372C211yesmaximal, characteristic, complemented
24#20284169C211yesmaximal, characteristic, complemented
25#20284023C211yesmaximal, characteristic, complemented
26#20284020C211yesmaximal, characteristic, complemented
27#20283520C211yesmaximal, characteristic, complemented
28#20283456C211yesmaximal, characteristic, complemented
29#20283240C211yesmaximal, characteristic, complemented
30#20283237C211yesmaximal, characteristic, complemented
31C53×#3311C211yesmaximal, characteristic, complemented
32C2×#13133263C2211yescharacteristic
33C2×#13133262C2211yescharacteristic
34C2×#13133244C2211yescharacteristic
35C2×#13133240C2211yescharacteristic, complemented
36C2×#13133238C2211yescharacteristic, complemented
37C2×#13133225C2211yescharacteristic, complemented
38C2×#13133223C2211yescharacteristic, complemented
39#16811346C2211yescharacteristic, complemented
40#16811336C2211yescharacteristic, complemented
41#16811336C2211yescharacteristic, complemented
42#16811331C2211yescharacteristic, complemented
43#16811331C2211yescharacteristic, complemented
44#16811324—21no—
45#16811324—21no—
46#16811285—21no—
47#16811281—21no—
48#16811277C2211yescharacteristic, complemented
49#16811276C2211yescharacteristic, complemented
50#16811275C2211yescharacteristic
51#16811272C2211yescharacteristic
52#16811271—21no—
53#16811269C2211yescharacteristic
54#16811268C2211yescharacteristic
55#16811266C2211yescharacteristic
56#16811263—21no—
57#16811262—21no—
58#16811257C2211yescharacteristic
59D4×C22⋊D53C2211yescharacteristic
60#16811255—21no—
61#16811239—21no—
62#16811239—21no—
63#16811203C2211yescharacteristic
64#16811203C2211yescharacteristic, complemented
65#16811203C2211yescharacteristic, complemented
66#16811202C2211yescharacteristic
67#16811184—21no—
68#16811183—21no—
69#16811177—21no—
70#16811172—21no—
71#16811172C2211yescharacteristic
72#16811170C2211yescharacteristic
73C4⋊Q8×D53C2211yescharacteristic, complemented
74C2×#13133190—21no—
75#121×D53—21no—
76#16811103C2211yescharacteristic, complemented
77#16811103C2211yescharacteristic, complemented
78C4×#11719949C2211yescharacteristic, complemented
79C4×D4×D53C2211yescharacteristic
80#16810985C2211yescharacteristic, complemented
81#16810983C2211yescharacteristic, complemented
82#16810982C2211yescharacteristic, complemented
83#16810972C2211yescharacteristic, complemented
84#16810972C2211yescharacteristic, complemented
85#16810968C2211yescharacteristic, complemented
86#16810968C2211yescharacteristic, complemented
87#16810966C2211yescharacteristic, complemented
88#16810964C2211yescharacteristic, complemented
89#16810962C2211yescharacteristic, complemented
90#16810955C2211yescharacteristic, complemented
91#16810954C2211yescharacteristic, complemented
92#16810952C2211yescharacteristic, complemented
93#16810951C2211yescharacteristic, complemented
94#16810950C2211yescharacteristic, complemented
95#16810947C2211yescharacteristic, complemented
96#16810946C2211yescharacteristic, complemented
97#16810943C2211yescharacteristic, complemented
98#16810942C2211yescharacteristic, complemented
99#16810940C2211yescharacteristic, complemented
100#16810939C2211yescharacteristic, complemented
101#16810914C2211yescharacteristic, complemented
102#16810913C2211yescharacteristic, complemented
103#16810912C2211yescharacteristic, complemented
104#16810912C2211yescharacteristic, complemented
105#16810911C2211yescharacteristic, complemented
106#16810911C2211yescharacteristic, complemented
107#16810910C2211yescharacteristic, complemented
108#16810880C2211yescharacteristic, complemented
109#16810879C2211yescharacteristic, complemented
110#16810878C2211yescharacteristic, complemented
111#16810877C2211yescharacteristic, complemented
112#16810876C2211yescharacteristic, complemented
113#16810875C2211yescharacteristic, complemented
114#16810874C2211yescharacteristic, complemented
115#16810855C2211yescharacteristic, complemented
116#16810855C2211yescharacteristic, complemented
117#16810854C2211yescharacteristic, complemented
118#16810854C2211yescharacteristic, complemented
119#16810853C2211yescharacteristic, complemented
120#16810852C2211yescharacteristic, complemented
121#16810849C2211yescharacteristic, complemented
122#16810845C2211yescharacteristic, complemented
123#16810839C2211yescharacteristic, complemented
124#16810835C2211yescharacteristic, complemented
125#16810831C2211yescharacteristic, complemented
126#16810827C2211yescharacteristic, complemented
127#16810821C2211yescharacteristic, complemented
128#16810817C2211yescharacteristic, complemented
129#16810784C2211yescharacteristic, complemented
130#16810783C2211yescharacteristic, complemented
131#16810782C2211yescharacteristic, complemented
132#16810773C2211yescharacteristic, complemented
133#16810772C2211yescharacteristic, complemented
134#16810772C2211yescharacteristic, complemented
135#16810771C2211yescharacteristic, complemented
136#16810770C2211yescharacteristic, complemented
137#16810769C2211yescharacteristic, complemented
138#16810768C2211yescharacteristic, complemented
139#16810759C2211yescharacteristic, complemented
140#16810758C2211yescharacteristic, complemented
141#16810758C2211yescharacteristic, complemented
142#16810757C2211yescharacteristic, complemented
143#16810736C2211yescharacteristic, complemented
144#16810733C2211yescharacteristic, complemented
145#16810721C2211yescharacteristic, complemented
146SD16×Dic53C2211yescharacteristic, complemented
147#16810708C2211yescharacteristic, complemented
148#16810705C2211yescharacteristic, complemented
149#16810703C2211yescharacteristic, complemented
150#16810699C2211yescharacteristic, complemented
151#16810698C2211yescharacteristic, complemented
152#16810696C2211yescharacteristic, complemented
153#16810695C2211yescharacteristic, complemented
154#16810693C2211yescharacteristic, complemented
155C8×C22⋊D53C2211yescharacteristic, complemented
156#16810686C2211yescharacteristic, complemented
157#16810664C2211yescharacteristic, complemented
158#106×D53C2211yescharacteristic, complemented
159#106×D53C2211yescharacteristic, complemented
160C4⋊C8×D53C2211yescharacteristic, complemented
161#16810627C2211yescharacteristic, complemented
162#16810626C2211yescharacteristic
163#16810626C2211yescharacteristic, complemented
164#16810626C2211yescharacteristic, complemented
165#16810625C2211yescharacteristic, complemented
166#16810624C2211yescharacteristic, complemented
167#16810623C2211yescharacteristic, complemented
168#16810623C2211yescharacteristic, complemented
169#16810623C2211yescharacteristic, complemented
170#16810623C2211yescharacteristic, complemented
171#16810621C2211yescharacteristic, complemented
172#16810621C2211yescharacteristic, complemented
173#16810621C2211yescharacteristic, complemented
174#16810618C2211yescharacteristic, complemented
175#16810618C2211yescharacteristic, complemented
176#16810617C2211yescharacteristic, complemented
177#16810616C2211yescharacteristic, complemented
178#16810616C2211yescharacteristic, complemented
179C2×#13133139C2211yescharacteristic, complemented
180C2×#13133138C2211yescharacteristic, complemented
181#102×D53C2211yescharacteristic
182#102×D53C2211yescharacteristic
183#102×D53C2211yescharacteristic, complemented
184#102×D53C2211yescharacteristic, complemented
185#16810588C2211yescharacteristic, complemented
186#16810588C2211yescharacteristic, complemented
187#16810575C2211yescharacteristic, complemented
188C53×#556C2211yescharacteristic, complemented
189C53×#546C2211yescharacteristic
190C53×#489C2211yescharacteristic, complemented
191C53×#485C2211yescharacteristic, complemented
192C53×#482C2211yescharacteristic, complemented
193C53×#476C2211yescharacteristic, complemented
194C53×#470C2211yescharacteristic, complemented
195C53×#465C2211yescharacteristic, complemented
196C53×#464C2211yescharacteristic, complemented
197C53×#452C2211yescharacteristic, complemented
198C53×#450C2211yescharacteristic, complemented
199C53×#440C2211yescharacteristic, complemented
200C53×#435C2211yescharacteristic, complemented
201C53×#418C2211yescharacteristic, complemented
202C53×#416C2211yescharacteristic, complemented
203#13133263—24no—
204#13133263—42no—
205#13133262—24no—
206#13133262—42no—
207C2×#11719949—21no—
208C2×#11719949C2311yescharacteristic
209C2×#11719949C2311yescharacteristic
210C2×#11719949C2311yescharacteristic
211C2×#11719945—21no—
212C2×#11719945C2311yescharacteristic
213C2×#11719945C2311yescharacteristic
214C2×#11719945C2311yescharacteristic
215C2×#11719947—21no—
216C2×#11719947—21no—
217C2×#11719947C2311yescharacteristic
218C2×#11719947C2311yescharacteristic
219C2×Q8×D53—21no—
220C22×D212—21no—
221C22×D212C2311yescharacteristic
222C22×C22⋊D53—21no—
223C22×C22⋊D53—21no—
224C22×C22⋊D53—21no—
225C2×D4×D53—21no—
226C2×D4×D53—21no—
227C2×D4×D53—21no—
228C2×D4×D53—21no—
229C2×D4×D53C2311yescharacteristic
230C2×D4×D53C2311yescharacteristic
231C2×D4×D53C2311yescharacteristic
232C22×C4×D53—21no—
233#13133244—24no—
234#13133240—42no—
235#13133238—42no—
236C2×#11719925C2311yescharacteristic
237C2×#11719913C2311yescharacteristic
238C2×#11719924C2311yescharacteristic
239C2×#11719924C2311yescharacteristic
240C2×#11719924C2311yescharacteristic
241C2×D424C2311yescharacteristic
242C2×D424C2311yescharacteristic
243C2×#11719922C2311yescharacteristic
244C2×#11719922C2311yescharacteristic
245#13133225—42no—
246#13133223—42no—
247C2×#11719917C2311yescharacteristic
248C2×#11719912C2311yescharacteristic
249C2×#11719912C2311yescharacteristic
250C2×#11719912C2311yescharacteristic
251C2×#11719912C2311yescharacteristic
252C22×#88322C2311yescharacteristic
253C2×C8×D53C2311yescharacteristic
254C2×C8×D53C2311yescharacteristic
255C2×C8×D53C2311yescharacteristic
256C2×C8×D53C2311yescharacteristic
257#13133217C2311yescharacteristic
258#13133216—21no—
259#13133216D411yescharacteristic
260#13133216C2311yescharacteristic
261#13133216C2311yescharacteristic
262#13133215—21no—
263#13133215C2311yescharacteristic
264#13133213D411yescharacteristic
265#13133213C2311yescharacteristic
266#13133212—21no—
267#13133212—21no—
268#13133207—21no—
269#13133207—21no—
270#13133205—21no—
271#13133205—21no—
272#13133205—21no—
273#13133205C2311yescharacteristic
274#13133203—21no—
275#13133203—21no—
276#13133203D411yescharacteristic
277#13133203D411yescharacteristic
278#13133202—21no—
279#13133202—21no—
280#13133202—21no—
281#13133202—21no—
282#13133201—21no—
283#13133201—21no—
284#13133201—21no—
285#13133200—21no—
286#13133199—21no—
287#13133199—21no—
288#13133198—21no—
289#13133197—21no—
290#13133197—21no—
291#13133197—21no—
292#13133197C2311yescharacteristic
293#13133196C2311yescharacteristic
294#13133195—21no—
295#13133195—21no—
296#13133195—21no—
297#13133194—21no—
298#13133194—21no—
299#13133194—21no—
300#13133193—21no—
301#13133193C2311yescharacteristic
302#13133193C2311yescharacteristic
303#13133193C2311yescharacteristic
304#13133192—21no—
305#13133192—21no—
306#13133192—21no—
307#13133192D411yescharacteristic
308#13133192C2311yescharacteristic
309#13133192C2311yescharacteristic
310#13133192C2311yescharacteristic
311#13133191—21no—
312#13133191C2311yescharacteristic
313#13133191C2311yescharacteristic
314#13133191C2311yescharacteristic
315#13133190—21no—
316#13133190—21no—
317#13133190—21no—
318#13133190—21no—
319#13133190—21no—
320#13133190—21no—
321#13133190—21no—
322#13133190—21no—
323#13133190—21no—
324#13133190—21no—
325#13133190—21no—
326#13133190—21no—
327#13133190—21no—
328#13133190—21no—
329#13133190—21no—
330#13133190D411yescharacteristic
331#13133190D411yescharacteristic
332#13133189—21no—
333#13133189—21no—
334#13133189—21no—
335#13133188—21no—
336#13133188D411yescharacteristic
337#13133188C2311yescharacteristic
338#13133187—21no—
339#13133187—21no—
340#13133187—21no—
341#13133186—21no—
342#13133185—21no—
343#13133185—21no—
344#13133185—21no—
345Q8×Dic53C2311yescharacteristic
346C4×Dic106—21no—
347C4×Dic106—21no—
348C4×Dic106—21no—
349C4×D212—21no—
350C4×D212—21no—
351C4×D212—21no—
352C4×D212C2311yescharacteristic
353C4×D212C2311yescharacteristic
354C4×D212C2311yescharacteristic
355D4×Dic53C2311yescharacteristic
356#13133179—21no—
357#13133179C2311yescharacteristic
358#13133179C2311yescharacteristic
359C4×C22⋊D53—21no—
360C4×C22⋊D53C2311yescharacteristic
361C4×C22⋊D53C2311yescharacteristic
362#13133177—21no—
363#13133177—21no—
364#13133177—21no—
365#13133177—21no—
366#13133177—21no—
367#13133177—21no—
368#13133177—21no—
369#13133177—21no—
370#13133177—21no—
371#13133175—21no—
372#13133175C2311yescharacteristic
373#13133175C2311yescharacteristic
374#13133175C2311yescharacteristic
375#13133174—21no—
376#13133174—21no—
377C2×C4⋊Dic53C2311yescharacteristic
378C2×C4⋊Dic53C2311yescharacteristic
379C2×#11719919—21no—
380C4⋊C4×D53—21no—
381C4⋊C4×D53—21no—
382C4⋊C4×D53C2311yescharacteristic
383C4⋊C4×D53C2311yescharacteristic
384C4⋊C4×D53C2311yescharacteristic
385C4⋊C4×D53C2311yescharacteristic
386C4⋊C4×D53C2311yescharacteristic
387C2×#11719921—21no—
388C22⋊C4×D53—21no—
389C22⋊C4×D53—21no—
390C22⋊C4×D53—21no—
391C42×D53—21no—
392C42×D53C2311yescharacteristic
393#13133150C2311yescharacteristic
394#13133149C2311yescharacteristic
395#13133149C2311yescharacteristic
396#13133149C2311yescharacteristic
397#13133148C2311yescharacteristic
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#13133140C2311yescharacteristic
413#13133140C2311yescharacteristic
414#13133140C2311yescharacteristic
415#13133139C2311yescharacteristic
416#13133139C2311yescharacteristic
417#13133139C2311yescharacteristic
418#13133139C2311yescharacteristic
419#13133139C2311yescharacteristic
420#13133139C2311yescharacteristic
421#13133139C2311yescharacteristic
422#13133138C2311yescharacteristic
423#13133138C2311yescharacteristic
424#13133138C2311yescharacteristic
425#13133138C2311yescharacteristic
426#13133138C2311yescharacteristic
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#13133128C2311yescharacteristic
442C8×Dic53C2311yescharacteristic
443C8×Dic53C2311yescharacteristic
444C2×#41×C53C2311yescharacteristic
445C22×D4×C53C2311yescharacteristic
446C2×Q16×C53C2311yescharacteristic
447C2×SD16×C53C2311yescharacteristic
448C2×SD16×C53C2311yescharacteristic
449C2×M16×C53C2311yescharacteristic
450C22×C8×C53C2311yescharacteristic
451C4⋊Q8×C53C2311yescharacteristic
452#126×C53—21no—
453#126×C53—21no—
454#124×C53—21no—
455#124×C53C2311yescharacteristic
456#123×C53—21no—
457C22⋊Q8×C53C2311yescharacteristic
458C22⋊Q8×C53C2311yescharacteristic
459C22⋊Q8×C53C2311yescharacteristic
460#121×C53—21no—
461#121×C53C2311yescharacteristic
462#120×C53—21no—
463C4×Q8×C53—21no—
464C4×Q8×C53C2311yescharacteristic
465C4×D4×C53C2311yescharacteristic
466C4×D4×C53C2311yescharacteristic
467#117×C53C2311yescharacteristic
468#117×C53C2311yescharacteristic
469C2×C22⋊C4×C53—21no—
470#107×C53C2311yescharacteristic
471#106×C53C2311yescharacteristic
472#106×C53C2311yescharacteristic
473C4⋊C8×C53C2311yescharacteristic
474#103×C53C2311yescharacteristic
475#103×C53C2311yescharacteristic
476#103×C53C2311yescharacteristic
477#103×C53C2311yescharacteristic
478#102×C53C2311yescharacteristic
479#102×C53C2311yescharacteristic
480#102×C53C2311yescharacteristic
481#102×C53C2311yescharacteristic
482#102×C53C2311yescharacteristic
483#102×C53C2311yescharacteristic
484C22⋊C8×C53C2311yescharacteristic
485C22⋊C8×C53C2311yescharacteristic
486#97×C53C2311yescharacteristic
487C24×C53—21no—
488C23×D53—21no—
489C23×D53—21no—
490C23×D53—21no—
491C23×D53—21no—
492#41×C53—22no—
493#41×C53—41no—
494C2×Q8×C53—21no—
495C2×Q8×C53C2411yescharacteristic
496C2×Q8×C53C2411yescharacteristic
497C2×D4×C53—22no—
498C2×D4×C53—21no—
499C2×D4×C53—21no—
500C2×D4×C53—21no—
501C2×D4×C53—41no—
502C2×D4×C53C2×D411yescharacteristic
503C2×D4×C53C2411yescharacteristic
504C2×D4×C53C2411yescharacteristic
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⋊D53—21no—
517C2×C22⋊D53—21no—
518C2×C22⋊D53—21no—
519C2×C22⋊D53—21no—
520C2×C22⋊D53—21no—
521C2×C22⋊D53—44no—
522C2×C22⋊D53—44no—
523C2×C22⋊D53—82no—
524C2×C22⋊D53C2×D411yescharacteristic
525C2×C22⋊D53C2×D411yescharacteristic
526C2×C22⋊D53C2×D411yescharacteristic
527C2×C22⋊D53C2×D411yescharacteristic
528C2×C22⋊D53C2×D411yescharacteristic
529C2×C22⋊D53C2×D411yescharacteristic
530C22×Dic53—21no—
531C22×Dic53—21no—
532C22×Dic53—21no—
533C22×Dic53—21no—
534C22×Dic53—21no—
535#11719949—22no—
536#11719949—22no—
537#11719949—22no—
538#11719949—22no—
539#11719949—22no—
540#11719949—41no—
541#11719949—82no—
542Q8×D53—82no—
543#11719947—22no—
544#11719947—22no—
545#11719947—22no—
546#11719947—41no—
547#11719947—44no—
548#11719947—82no—
549D4×D53—22no—
550D4×D53—22no—
551D4×D53—22no—
552D4×D53—41no—
553D4×D53—41no—
554D4×D53—44no—
555D4×D53—44no—
556D4×D53—44no—
557D4×D53—82no—
558D4×D53#4114yescomplemented
559#11719945—22no—
560#11719945—22no—
561#11719945—22no—
562#11719945—22no—
563#11719945—22no—
564#11719945—41no—
565#11719945—44no—
566C2×D212—22no—
567C2×D212—21no—
568C2×D212—21no—
569C2×D212—21no—
570C2×D212—21no—
571C2×D212—21no—
572C2×D212—21no—
573C2×D212—21no—
574C2×D212—41no—
575C2×D212—44no—
576C2×D212C2×D411yescharacteristic
577C2×D212C2×D411yescharacteristic
578C2×D212C2×D411yescharacteristic
579C2×D212C2411yescharacteristic
580C2×D212C2411yescharacteristic
581C2×D212C2411yescharacteristic
582C2×C4×D53—21no—
583C2×C4×D53—21no—
584C2×C4×D53—21no—
585C2×C4×D53—21no—
586C2×C4×D53—21no—
587C2×C4×D53—21no—
588C2×C4×D53—21no—
589C2×C4×D53—21no—
590C2×C4×D53—21no—
591C2×C4×D53—21no—
592C2×C4×D53—21no—
593C2×C4×D53—21no—
594C2×C4×D53—21no—
595C2×C4×D53—82no—
596C2×C4×D53C2×D411yescharacteristic
597C2×C4×D53C2×D411yescharacteristic
598C2×C4×D53C2411yescharacteristic
599C2×C4×D53C2411yescharacteristic
600C2×C4×D53C2411yescharacteristic
601C2×Dic106—21no—
602C2×Dic106—21no—
603C2×Dic106—21no—
604C2×Dic106C2×D411yescharacteristic
605C2×Dic106C2×D411yescharacteristic
606C2×Dic106C2411yescharacteristic
607Q16×C53—41no—
608SD16×C53—22no—
609SD16×C53—41no—
610M16×C53—41no—
611C2×C8×C53—41no—
612C2×C8×C53C2411yescharacteristic
613C2×C8×C53C2411yescharacteristic
614C2×C8×C53C2411yescharacteristic
615C2×C8×C53C2411yescharacteristic
616C4⋊C4×C53—21no—
617C4⋊C4×C53—21no—
618C4⋊C4×C53—21no—
619C4⋊C4×C53—21no—
620C4⋊C4×C53—21no—
621C4⋊C4×C53C2×D411yescharacteristic
622C4⋊C4×C53C2411yescharacteristic
623C4⋊C4×C53C2411yescharacteristic
624C4⋊C4×C53C2411yescharacteristic
625C4⋊C4×C53C2411yescharacteristic
626C22⋊C4×C53—21no—
627C22⋊C4×C53—21no—
628C22⋊C4×C53—21no—
629C22⋊C4×C53—21no—
630C22⋊C4×C53—21no—
631C22⋊C4×C53—21no—
632C22⋊C4×C53—21no—
633C22⋊C4×C53—21no—
634C22⋊C4×C53—21no—
635C22⋊C4×C53C2×D411yescharacteristic
636C22⋊C4×C53C2×D411yescharacteristic
637C42×C53—21no—
638C42×C53—21no—
639C42×C53—21no—
640C42×C53C2411yescharacteristic
641C22⋊Dic53—21no—
642C22⋊Dic53—21no—
643C22⋊Dic53—21no—
644C22⋊Dic53C2×D411yescharacteristic
645C22⋊Dic53C2×D411yescharacteristic
646#11719925—41no—
647#11719924—22no—
648#11719924—41no—
649#11719924—41no—
650#11719922—22no—
651#11719922—41no—
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#11719921—21no—
667#11719921—21no—
668#11719921—21no—
669#11719921—21no—
670#11719921—21no—
671#11719921C2×D411yescharacteristic
672#11719921C2×D411yescharacteristic
673#11719921C2×D411yescharacteristic
674#11719921C2×D411yescharacteristic
675C4⋊Dic53—21no—
676C4⋊Dic53—21no—
677C4⋊Dic53—21no—
678C4⋊Dic53—21no—
679C4⋊Dic53—21no—
680C4⋊Dic53C2×D411yescharacteristic
681C4⋊Dic53C2411yescharacteristic
682C4⋊Dic53C2411yescharacteristic
683C4⋊Dic53C2411yescharacteristic
684C4⋊Dic53C2411yescharacteristic
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#11719919—21no—
694#11719919—21no—
695#11719919—21no—
696#11719919—21no—
697#11719919—21no—
698#11719919C2×D411yescharacteristic
699#11719919C2×D411yescharacteristic
700C4×Dic53—21no—
701C4×Dic53—21no—
702C4×Dic53—21no—
703C4×Dic53—21no—
704C4×Dic53C2×D411yescharacteristic
705C4×Dic53C2×D411yescharacteristic
706C4×Dic53C2411yescharacteristic
707#11719917—41no—
708C2×#88322—41no—
709C2×#88322C2411yescharacteristic
710C2×#88322C2411yescharacteristic
711C2×#88322C2411yescharacteristic
712C2×#88322C2411yescharacteristic
713D424—22no—
714D424—41no—
715#11719913—41no—
716#11719912—22no—
717#11719912—22no—
718#11719912—41no—
719#11719912—41no—
720C8×D53—22no—
721C8×D53—22no—
722C8×D53—41no—
723C8×D53—41no—
724C23×C53—21no—
725C23×C53—21no—
726C23×C53—42no—
727C23×C53—81no—
728C23×C53—81no—
729C23×C53C22×D411yescharacteristic
730C23×C53C22×D411yescharacteristic
731C22×D53—21no—
732C22×D53—24no—
733C22×D53—21no—
734C22×D53—21no—
735C22×D53—42no—
736C22×D53—42no—
737C22×D53—42no—
738C22×D53—81no—
739C22×D53—81no—
740C22×D53—81no—
741C22×D53—81no—
742C22×D53—81no—
743C22×D53—81no—
744C22×D53—81no—
745C22×D53—81no—
746C22×D53C22×D411yescharacteristic
747C22×D53C22×D411yescharacteristic
748C22×D53C22×D411yescharacteristic
749Q8×C53—21no—
750Q8×C53—21no—
751Q8×C53—21no—
752Q8×C53—21no—
753Q8×C53—42no—
754D4×C53—21no—
755D4×C53—21no—
756D4×C53—21no—
757D4×C53—41no—
758D4×C53—42no—
759D4×C53—42no—
760D4×C53—81no—
761D4×C53C2×#4112yes—
762C2×C4×C53—21no—
763C2×C4×C53—21no—
764C2×C4×C53—21no—
765C2×C4×C53—21no—
766C2×C4×C53—21no—
767C2×C4×C53—21no—
768C2×C4×C53—21no—
769C2×C4×C53—21no—
770C2×C4×C53—21no—
771C2×C4×C53—21no—
772C2×C4×C53—42no—
773C2×C4×C53—81no—
774C2×C4×C53C22×D411yescharacteristic
775C2×C4×C53C22×D411yescharacteristic
776C2×C4×C53C22×D411yescharacteristic
777C2×C4×C53C22×D411yescharacteristic
778C2×C4×C53C2511yescharacteristic
779C22⋊D53—22no—
780C22⋊D53—22no—
781C22⋊D53—22no—
782C22⋊D53—22no—
783C22⋊D53—24no—
784C22⋊D53—22no—
785C22⋊D53—22no—
786C22⋊D53—42no—
787C22⋊D53—42no—
788C22⋊D53—42no—
789C22⋊D53—42no—
790C22⋊D53—42no—
791C22⋊D53—42no—
792C22⋊D53—81no—
793C22⋊D53—81no—
794C22⋊D53—81no—
795C22⋊D53—81no—
796C22⋊D53—81no—
797C2×Dic53—21no—
798C2×Dic53—21no—
799C2×Dic53—21no—
800C2×Dic53—21no—
801C2×Dic53—21no—
802C2×Dic53—42no—
803C2×Dic53—42no—
804C2×Dic53—42no—
805C2×Dic53—81no—
806C2×Dic53—81no—
807C2×Dic53C22×D411yescharacteristic
808C2×Dic53C22×D411yescharacteristic
809C2×Dic53C22×D411yescharacteristic
810C2×Dic53C22×D411yescharacteristic
811C2×Dic53C22×D411yescharacteristic
812D212—22no—
813D212—22no—
814D212—21no—
815D212—21no—
816D212—21no—
817D212—21no—
818D212—21no—
819D212—41no—
820D212—42no—
821D212—42no—
822D212—42no—
823D212—42no—
824D212—81no—
825D212—81no—
826D212—81no—
827D212C2×#4112yes—
828C4×D53—21no—
829C4×D53—21no—
830C4×D53—21no—
831C4×D53—21no—
832C4×D53—22no—
833C4×D53—41no—
834C4×D53—42no—
835C4×D53—42no—
836C4×D53—42no—
837C4×D53—42no—
838C4×D53—42no—
839C4×D53—42no—
840C4×D53—42no—
841C4×D53—81no—
842C4×D53—81no—
843C4×D53—81no—
844C4×D53—81no—
845C4×D53—81no—
846C4×D53—81no—
847C4×D53C2×#4112yes—
848C4×D53H(5,𝔽2)12yes—
849Dic106—22no—
850Dic106—22no—
851Dic106—21no—
852Dic106—21no—
853Dic106—42no—
854Dic106—81no—
855Dic106—81no—
856C8×C53—21no—
857C8×C53—21no—
858C8×C53—21no—
859C8×C53—21no—
860#88322—21no—
861#88322—21no—
862#88322—21no—
863#88322—21no—
864#61200—531nomaximal, Sylow
865C22×C53—21no—
866C22×C53—21no—
867C22×C53—22no—
868C22×C53—21no—
869C22×C53—21no—
870C22×C53—21no—
871C22×C53—21no—
872C22×C53—41no—
873C22×C53—41no—
874C22×C53—41no—
875C22×C53—41no—
876C22×C53—41no—
877C22×C53—162no—
878C22×C53C23×D411yescharacteristic
879C2×D53—21no—
880C2×D53—21no—
881C2×D53—21no—
882C2×D53—21no—
883C2×D53—21no—
884C2×D53—21no—
885C2×D53—22no—
886C2×D53—21no—
887C2×D53—21no—
888C2×D53—41no—
889C2×D53—41no—
890C2×D53—41no—
891C2×D53—41no—
892C2×D53—41no—
893C2×D53—41no—
894C2×D53—41no—
895C2×D53—41no—
896C2×D53—84no—
897C2×D53—162no—
898C2×D53—162no—
899C2×D53—162no—
900C2×D53#54612yes—
901C4×C53—21no—
902C4×C53—21no—
903C4×C53—21no—
904C4×C53—21no—
905C4×C53—41no—
906C4×C53—41no—
907C4×C53—41no—
908C4×C53—41no—
909C4×C53—41no—
910C4×C53—41no—
911C4×C53C22×#4111yescharacteristic
912C4×C53C2×H(5,𝔽2)11yescharacteristic
913Dic53—21no—
914Dic53—21no—
915Dic53—21no—
916Dic53—41no—
917Dic53—41no—
918Dic53—41no—
919Dic53—41no—
920Dic53—41no—
921Dic53#54612yes—
922Dic53#57712yes—
923#3511—531no—
924#3496—531no—
925#3331—531no—
926#3331—531no—
927#3325—531no—
928#3325—531no—
929#3311—531no—
930#3311—531no—
931#3311—531no—
932#3311D5311yescharacteristic, complemented
933#3306—531no—
934#3306—531no—
935#3306—531no—
936#3306—531no—
937#3303—531no—
938#3303—531no—
939#3295—531no—
940#3295—531no—
941#3141—531no—
942#3099—531no—
943#3099—531no—
944C2×#476—531no—
945#3060—531no—
946#3060—531no—
947#3035—531no—
948#3012—531no—
949#3012—531no—
950C4×AGL(1,ℤ/8)—531no—
951#2935—531no—
952#2897—531no—
953#2897—531no—
954C2×C53—42no—
955C2×C53—41no—
956C2×C53—41no—
957C2×C53—81no—
958C2×C53C2×#54611yescharacteristic
959C2×C53C2×#57711yescharacteristic
960C2×C53#358511yescharacteristic
961D53—22no—
962D53—41no—
963D53—41no—
964D53—42no—
965D53—81no—
966D53—81no—
967C2×H(5,𝔽2)—531no—
968C2×H(5,𝔽2)—531no—
969C2×AGL(1,ℤ/8)—531no—
970C2×#135—531no—
971C2×#135—531no—
972C2×#131—531no—
973C2×#131—531no—
974#556—531no—
975#556C2×D5311yescharacteristic, complemented
976#555—531no—
977#555—531no—
978#554—531no—
979#554—531no—
980#553—1061no—
981#553—1061no—
982#548—1061no—
983#548—1061no—
984#547—531no—
985#547—531no—
986#547—531no—
987#547—531no—
988#547—1061no—
989#546—531no—
990#546—531no—
991#546—531no—
992#546—1061no—
993#546—1061no—
994#546C2×D5311yescharacteristic
995D42—531no—
996D42—531no—
997D42—1061no—
998#542—1061no—
999#542—1061no—
1000#537—531no—
1001#537—531no—
1002#537—531no—
1003#537—531no—
1004#534—1061no—
1005#534—1061no—
1006#533—1061no—
1007#532—531no—
1008#532—531no—
1009#532—1061no—
1010C2×C4⋊Q8—531no—
1011C2×#121—1061no—
1012C2×#121—1061no—
1013#520—531no—
1014#520—531no—
1015C4×#41—531no—
1016C2×C4×D4—531no—
1017#489—531no—
1018#489—531no—
1019#489—531no—
1020#489C2×D5311yescharacteristic, complemented
1021#487—531no—
1022#487—531no—
1023#486—531no—
1024#486—531no—
1025#485—531no—
1026#485—531no—
1027#485—531no—
1028#485C2×D5311yescharacteristic, complemented
1029#483—531no—
1030#483—531no—
1031#483—531no—
1032#483—531no—
1033#482—531no—
1034#482—531no—
1035#482—531no—
1036#482C2×D5311yescharacteristic, complemented
1037#481—531no—
1038#481—531no—
1039#481—531no—
1040#481—531no—
1041#476—531no—
1042#476—531no—
1043#476—531no—
1044#476—531no—
1045#476—531no—
1046#476—531no—
1047#476—531no—
1048#476C2×D5311yescharacteristic, complemented
1049#470—531no—
1050#470—531no—
1051#470—531no—
1052#470C2×D5311yescharacteristic, complemented
1053#469—531no—
1054#469—531no—
1055#469—531no—
1056#469—531no—
1057#465—531no—
1058#465—531no—
1059#465—531no—
1060#465—531no—
1061#465—531no—
1062#465—531no—
1063#465—531no—
1064#465C2×D5311yescharacteristic, complemented
1065#464—531no—
1066#464C2×D5311yescharacteristic, complemented
1067#463—531no—
1068#463—531no—
1069#462—531no—
1070#461—531no—
1071#460—531no—
1072#459—531no—
1073#452—531no—
1074#452—531no—
1075#452—531no—
1076#452C2×D5311yescharacteristic, complemented
1077#450—531no—
1078#450—531no—
1079#450—531no—
1080#450C2×D5311yescharacteristic, complemented
1081#449—531no—
1082#449—531no—
1083#449—531no—
1084#449—531no—
1085#447—531no—
1086#447—531no—
1087#447—531no—
1088#447—531no—
1089#442—531no—
1090#442—531no—
1091#440—531no—
1092#440C2×D5311yescharacteristic, complemented
1093C4×SD16—531no—
1094C4×SD16—531no—
1095C4×D8—531no—
1096C4×D8—531no—
1097#436—531no—
1098#436—531no—
1099#435—531no—
1100#435—531no—
1101#435—531no—
1102#435C2×D5311yescharacteristic, complemented
1103C8×D4—531no—
1104C8×D4—531no—
1105#428—531no—
1106C2×#106—531no—
1107C2×#106—531no—
1108C2×C4⋊C8—531no—
1109#418—531no—
1110#418—531no—
1111#418—531no—
1112#418—531no—
1113#418C2×D5311yescharacteristic, complemented
1114#417—531no—
1115#417—531no—
1116#417—531no—
1117#417—531no—
1118#417—531no—
1119#417—531no—
1120#417—531no—
1121#417—531no—
1122#417—531no—
1123#416—531no—
1124#416—531no—
1125#416—531no—
1126#416—531no—
1127#416—531no—
1128#416C2×D5311yescharacteristic, complemented
1129C2×#102—531no—
1130C2×#102—531no—
1131C2×#102—531no—
1132C2×#102—531no—
1133C2×#102—531no—
1134C2×#102—531no—
1135#408—531no—
1136#408—531no—
1137C4×M16—531no—
1138C53#6120011yescharacteristic, complemented, Sylow
1139H(5,𝔽2)—1064no—
1140H(5,𝔽2)—1064no—
1141H(5,𝔽2)—2122no—
1142H(5,𝔽2)—2122no—
1143C2×#41—531no—
1144C2×#41—531no—
1145C2×#41—531no—
1146C2×#41—531no—
1147C2×#41—531no—
1148C2×#41—531no—
1149C2×#41—531no—
1150C2×#41—531no—
1151C2×#41—1061no—
1152C2×#41—1061no—
1153C2×#41—1061no—
1154C2×#41—1061no—
1155C2×#41C22×D5311yescharacteristic
1156C22×Q8—1061no—
1157C22×D4—531no—
1158C22×D4—531no—
1159C22×D4—531no—
1160C22×D4—531no—
1161C22×D4—1061no—
1162C22×D4—1061no—
1163C22×D4—1061no—
1164C22×D4—1061no—
1165C22×D4—1061no—
1166C22×D4—1061no—
1167C22×D4—1061no—
1168C22×D4—1061no—
1169C22×D4C22×D5311yescharacteristic
1170C23×C4—1061no—
1171AGL(1,ℤ/8)—1064no—
1172#135—2122no—
1173#135—2122no—
1174C2×Q16—531no—
1175C2×Q16C22×D5311yescharacteristic
1176C2×SD16—531no—
1177C2×SD16—531no—
1178C2×SD16—531no—
1179C2×SD16—531no—
1180C2×SD16C22×D5311yescharacteristic
1181C2×SD16C22×D5311yescharacteristic
1182C2×D8—531no—
1183C2×D8—531no—
1184C2×D8—531no—
1185C2×D8—531no—
1186#131—2122no—
1187#131—2122no—
1188C2×M16—531no—
1189C2×M16—531no—
1190C2×M16—531no—
1191C2×M16—531no—
1192C2×M16—531no—
1193C2×M16C22×D5311yescharacteristic
1194C22×C8—531no—
1195C22×C8—531no—
1196C22×C8—531no—
1197C22×C8—531no—
1198C22×C8—531no—
1199C22×C8C22×D5311yescharacteristic
1200C4⋊Q8—531no—
1201C4⋊Q8—531no—
1202C4⋊Q8—531no—
1203C4⋊Q8—531no—
1204C4⋊Q8—531no—
1205C4⋊Q8—1061no—
1206C4⋊Q8—1061no—
1207C4⋊Q8C22×D5311yescharacteristic
1208#127—531no—
1209#127—531no—
1210#126—21no—
1211#126—21no—
1212#126—1061no—
1213#126—1061no—
1214#125—1061no—
1215#125—1061no—
1216#124—21no—
1217#124—531no—
1218#124—531no—
1219#124—531no—
1220#124—1061no—
1221#124—1061no—
1222#124—1061no—
1223#124—1061no—
1224#124—1061no—
1225#124C22×D5311yescharacteristic
1226#123—21no—
1227#123—1061no—
1228#123—1061no—
1229#123—1061no—
1230#123—1061no—
1231#123—1061no—
1232#123—1061no—
1233#123—1061no—
1234#123—1061no—
1235#123—1061no—
1236#123—1061no—
1237#123—1061no—
1238C22⋊Q8—531no—
1239C22⋊Q8—531no—
1240C22⋊Q8—531no—
1241C22⋊Q8—531no—
1242C22⋊Q8—531no—
1243C22⋊Q8—1061no—
1244C22⋊Q8—1061no—
1245C22⋊Q8—1061no—
1246C22⋊Q8—1061no—
1247C22⋊Q8—1061no—
1248C22⋊Q8—1061no—
1249C22⋊Q8—1061no—
1250C22⋊Q8—1061no—
1251C22⋊Q8—1061no—
1252C22⋊Q8—1061no—
1253C22⋊Q8C22×D5311yescharacteristic
1254C22⋊Q8C22×D5311yescharacteristic
1255C22⋊Q8C22×D5311yescharacteristic
1256#121—21no—
1257#121—531no—
1258#121—531no—
1259#121—531no—
1260#121—531no—
1261#121—531no—
1262#121—531no—
1263#121—531no—
1264#121—531no—
1265#121—531no—
1266#121—531no—
1267#121—531no—
1268#121—1061no—
1269#121—1061no—
1270#121—1061no—
1271#121—1061no—
1272#121—1061no—
1273#121—1061no—
1274#121—1061no—
1275#121—1061no—
1276#121—1061no—
1277#121—1061no—
1278#121—1061no—
1279#121—1061no—
1280#121—1061no—
1281#121—1061no—
1282#121—1061no—
1283#121—1061no—
1284#121—1061no—
1285#121—1061no—
1286#121—1061no—
1287#121—1061no—
1288#121—1061no—
1289#121—1061no—
1290#121—1061no—
1291#121C22×D5311yescharacteristic
1292#120—21no—
1293#120—1061no—
1294#120—1061no—
1295#120—1061no—
1296#120—1061no—
1297#120—1061no—
1298#120—1061no—
1299#120—1061no—
1300C4×Q8—21no—
1301C4×Q8—531no—
1302C4×Q8—1061no—
1303C4×Q8—1061no—
1304C4×Q8—1061no—
1305C4×Q8C22×D5311yescharacteristic
1306C4×D4—531no—
1307C4×D4—531no—
1308C4×D4—531no—
1309C4×D4—531no—
1310C4×D4—531no—
1311C4×D4—531no—
1312C4×D4—531no—
1313C4×D4—531no—
1314C4×D4—1061no—
1315C4×D4—1061no—
1316C4×D4—1061no—
1317C4×D4—1061no—
1318C4×D4—1061no—
1319C4×D4—1061no—
1320C4×D4—1061no—
1321C4×D4—1061no—
1322C4×D4—1061no—
1323C4×D4—1061no—
1324C4×D4—1061no—
1325C4×D4—1061no—
1326C4×D4—1061no—
1327C4×D4—1061no—
1328C4×D4C22×D5311yescharacteristic
1329C4×D4C22×D5311yescharacteristic
1330#117—531no—
1331#117—531no—
1332#117—531no—
1333#117—1061no—
1334#117—1061no—
1335#117—1061no—
1336#117C22×D5311yescharacteristic
1337#117C22×D5311yescharacteristic
1338C2×C4⋊C4—531no—
1339C2×C4⋊C4—531no—
1340C2×C4⋊C4—531no—
1341C2×C4⋊C4—531no—
1342C2×C4⋊C4—531no—
1343C2×C4⋊C4—531no—
1344C2×C4⋊C4—531no—
1345C2×C4⋊C4—1061no—
1346C2×C4⋊C4—1061no—
1347C2×C4⋊C4—1061no—
1348C2×C22⋊C4—21no—
1349C2×C22⋊C4—1061no—
1350C2×C22⋊C4—1061no—
1351C2×C22⋊C4—1061no—
1352C2×C22⋊C4—1061no—
1353C2×C42—531no—
1354C2×C42—1061no—
1355#107—531no—
1356#107C22×D5311yescharacteristic
1357#106—531no—
1358#106—531no—
1359#106—531no—
1360#106—531no—
1361#106—531no—
1362#106—531no—
1363#106—531no—
1364#106—531no—
1365#106C22×D5311yescharacteristic
1366#106C22×D5311yescharacteristic
1367C4⋊C8—531no—
1368C4⋊C8—531no—
1369C4⋊C8—531no—
1370C4⋊C8C22×D5311yescharacteristic
1371#103—531no—
1372#103—531no—
1373#103—531no—
1374#103—531no—
1375#103—531no—
1376#103—531no—
1377#103—531no—
1378#103—531no—
1379#103—531no—
1380#103—531no—
1381#103C22×D5311yescharacteristic
1382#103C22×D5311yescharacteristic
1383#103C22×D5311yescharacteristic
1384#103C22×D5311yescharacteristic
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#102—531no—
1394#102—531no—
1395#102—531no—
1396#102—531no—
1397#102—531no—
1398#102—531no—
1399#102—531no—
1400#102—531no—
1401#102—531no—
1402#102—531no—
1403#102—531no—
1404#102—531no—
1405#102C22×D5311yescharacteristic
1406#102C22×D5311yescharacteristic
1407#102C22×D5311yescharacteristic
1408#102C22×D5311yescharacteristic
1409#102C22×D5311yescharacteristic
1410#102C22×D5311yescharacteristic
1411C22⋊C8—531no—
1412C22⋊C8—531no—
1413C22⋊C8—531no—
1414C22⋊C8—531no—
1415C22⋊C8—531no—
1416C22⋊C8—531no—
1417C22⋊C8C22×D5311yescharacteristic
1418C22⋊C8C22×D5311yescharacteristic
1419#97—531no—
1420#97C22×D5311yescharacteristic
1421C4×C8—531no—
1422C4×C8—531no—
1423C24—21no—
1424C24—1061no—
1425C24—1061no—
1426C24—1061no—
1427C24—1061no—
1428#41—22no—
1429#41—41no—
1430#41—1062no—
1431#41—1062no—
1432#41—1062no—
1433#41—1062no—
1434#41—1062no—
1435#41—1062no—
1436#41—1062no—
1437#41—1062no—
1438#41—1062no—
1439#41—1062no—
1440#41—1062no—
1441#41—1062no—
1442#41—1062no—
1443#41—4242no—
1444#41—4242no—
1445#41—2121no—
1446#41—2124no—
1447#41—2121no—
1448#41—2121no—
1449#41—2124no—
1450C2×Q8—21no—
1451C2×Q8—531no—
1452C2×Q8—531no—
1453C2×Q8—531no—
1454C2×Q8—1061no—
1455C2×Q8—1061no—
1456C2×Q8—1061no—
1457C2×Q8—4242no—
1458C2×Q8C23×D5311yescharacteristic
1459C2×Q8C23×D5311yescharacteristic
1460C2×D4—22no—
1461C2×D4—21no—
1462C2×D4—21no—
1463C2×D4—21no—
1464C2×D4—41no—
1465C2×D4—534no—
1466C2×D4—531no—
1467C2×D4—531no—
1468C2×D4—531no—
1469C2×D4—531no—
1470C2×D4—531no—
1471C2×D4—531no—
1472C2×D4—531no—
1473C2×D4—531no—
1474C2×D4—531no—
1475C2×D4—531no—
1476C2×D4—531no—
1477C2×D4—531no—
1478C2×D4—1062no—
1479C2×D4—1061no—
1480C2×D4—1061no—
1481C2×D4—1061no—
1482C2×D4—1061no—
1483C2×D4—1061no—
1484C2×D4—1061no—
1485C2×D4—1062no—
1486C2×D4—1061no—
1487C2×D4—1061no—
1488C2×D4—1061no—
1489C2×D4—1061no—
1490C2×D4—1061no—
1491C2×D4—1062no—
1492C2×D4—1062no—
1493C2×D4—1061no—
1494C2×D4—1061no—
1495C2×D4—1061no—
1496C2×D4—1061no—
1497C2×D4—1061no—
1498C2×D4—1061no—
1499C2×D4—1061no—
1500C2×D4—1061no—
1501C2×D4—4242no—
1502C2×D4—4242no—
1503C2×D4—2121no—
1504C2×D4—2124no—
1505C2×D4—2121no—
1506C2×D4—2121no—
1507C2×D4—2124no—
1508C2×D4—2124no—
1509C2×D4—2124no—
1510C2×D4—2124no—
1511C2×D4—2124no—
1512C2×D4D4×D5311yescharacteristic
1513C2×D4C23×D5311yescharacteristic
1514C2×D4C23×D5311yescharacteristic
1515C22×C4—21no—
1516C22×C4—21no—
1517C22×C4—531no—
1518C22×C4—531no—
1519C22×C4—531no—
1520C22×C4—531no—
1521C22×C4—531no—
1522C22×C4—1061no—
1523C22×C4—1061no—
1524C22×C4—1061no—
1525C22×C4—1061no—
1526C22×C4—1061no—
1527C22×C4—1061no—
1528C22×C4—1061no—
1529C22×C4—1061no—
1530C22×C4—1061no—
1531C22×C4—1061no—
1532C22×C4—1061no—
1533C22×C4—1061no—
1534C22×C4—1061no—
1535C22×C4—1061no—
1536C22×C4—1061no—
1537C22×C4—1061no—
1538C22×C4—1061no—
1539C22×C4—1061no—
1540C22×C4—4242no—
1541C22×C4C23×D5311yescharacteristic
1542C22×C4C23×D5311yescharacteristic
1543Q16—41no—
1544Q16—2121no—
1545SD16—22no—
1546SD16—41no—
1547SD16—1062no—
1548SD16—2121no—
1549SD16—2121no—
1550SD16—2121no—
1551D8—1062no—
1552D8—1062no—
1553D8—2121no—
1554D8—2121no—
1555M16—41no—
1556M16—1062no—
1557M16—1062no—
1558M16—2121no—
1559M16—2121no—
1560M16—2121no—
1561C2×C8—41no—
1562C2×C8—531no—
1563C2×C8—531no—
1564C2×C8—531no—
1565C2×C8—531no—
1566C2×C8—1062no—
1567C2×C8—1062no—
1568C2×C8—2121no—
1569C2×C8—2121no—
1570C2×C8—2121no—
1571C2×C8C23×D5311yescharacteristic
1572C2×C8C23×D5311yescharacteristic
1573C2×C8C23×D5311yescharacteristic
1574C2×C8C23×D5311yescharacteristic
1575C4⋊C4—21no—
1576C4⋊C4—21no—
1577C4⋊C4—21no—
1578C4⋊C4—21no—
1579C4⋊C4—21no—
1580C4⋊C4—531no—
1581C4⋊C4—531no—
1582C4⋊C4—531no—
1583C4⋊C4—531no—
1584C4⋊C4—531no—
1585C4⋊C4—531no—
1586C4⋊C4—531no—
1587C4⋊C4—1061no—
1588C4⋊C4—1061no—
1589C4⋊C4—1061no—
1590C4⋊C4—1061no—
1591C4⋊C4—1061no—
1592C4⋊C4—1061no—
1593C4⋊C4—1061no—
1594C4⋊C4—1061no—
1595C4⋊C4—1061no—
1596C4⋊C4—1061no—
1597C4⋊C4—1061no—
1598C4⋊C4—1061no—
1599C4⋊C4—1061no—
1600C4⋊C4—1061no—
1601C4⋊C4—1061no—
1602C4⋊C4—1061no—
1603C4⋊C4—1061no—
1604C4⋊C4—1061no—
1605C4⋊C4D4×D5311yescharacteristic
1606C4⋊C4C23×D5311yescharacteristic
1607C4⋊C4C23×D5311yescharacteristic
1608C4⋊C4C23×D5311yescharacteristic
1609C4⋊C4C23×D5311yescharacteristic
1610C22⋊C4—21no—
1611C22⋊C4—21no—
1612C22⋊C4—21no—
1613C22⋊C4—21no—
1614C22⋊C4—21no—
1615C22⋊C4—21no—
1616C22⋊C4—21no—
1617C22⋊C4—21no—
1618C22⋊C4—21no—
1619C22⋊C4—531no—
1620C22⋊C4—531no—
1621C22⋊C4—531no—
1622C22⋊C4—531no—
1623C22⋊C4—531no—
1624C22⋊C4—531no—
1625C22⋊C4—1061no—
1626C22⋊C4—1061no—
1627C22⋊C4—1061no—
1628C22⋊C4—1061no—
1629C22⋊C4—1061no—
1630C22⋊C4—1061no—
1631C22⋊C4—1061no—
1632C22⋊C4—1061no—
1633C22⋊C4—1061no—
1634C22⋊C4—1061no—
1635C22⋊C4—1061no—
1636C22⋊C4—1061no—
1637C22⋊C4—1061no—
1638C22⋊C4—1061no—
1639C22⋊C4—1061no—
1640C22⋊C4—1061no—
1641C22⋊C4—1061no—
1642C22⋊C4—1061no—
1643C22⋊C4—1061no—
1644C22⋊C4—1061no—
1645C22⋊C4—1061no—
1646C22⋊C4—1061no—
1647C22⋊C4D4×D5311yescharacteristic
1648C22⋊C4D4×D5311yescharacteristic
1649C42—21no—
1650C42—21no—
1651C42—21no—
1652C42—531no—
1653C42—531no—
1654C42—531no—
1655C42—1061no—
1656C42—1061no—
1657C42—1061no—
1658C42—1061no—
1659C42C23×D5311yescharacteristic
1660C23—21no—
1661C23—21no—
1662C23—42no—
1663C23—81no—
1664C23—81no—
1665C23—531no—
1666C23—531no—
1667C23—531no—
1668C23—1064no—
1669C23—1061no—
1670C23—1061no—
1671C23—1061no—
1672C23—4241no—
1673C23—4241no—
1674C23—4241no—
1675C23—4241no—
1676C23—4241no—
1677C23—4241no—
1678C23—4241no—
1679C23—4241no—
1680C23—2122no—
1681C23—2122no—
1682C23—2122no—
1683C23C2×D4×D5311yescharacteristic
1684C23C2×D4×D5311yescharacteristic
1685Q8—21no—
1686Q8—21no—
1687Q8—21no—
1688Q8—21no—
1689Q8—42no—
1690Q8—1062no—
1691Q8—1062no—
1692Q8—1061no—
1693Q8—1061no—
1694Q8—4241no—
1695Q8—4241no—
1696Q8—2122no—
1697D4—21no—
1698D4—21no—
1699D4—21no—
1700D4—41no—
1701D4—42no—
1702D4—42no—
1703D4—81no—
1704D4—532no—
1705D4—1062no—
1706D4—1062no—
1707D4—1064no—
1708D4—1062no—
1709D4—1062no—
1710D4—1062no—
1711D4—1062no—
1712D4—1062no—
1713D4—1062no—
1714D4—1061no—
1715D4—1061no—
1716D4—1061no—
1717D4—1061no—
1718D4—1061no—
1719D4—4241no—
1720D4—4241no—
1721D4—4241no—
1722D4—4241no—
1723D4—4241no—
1724D4—4241no—
1725D4—4241no—
1726D4—4241no—
1727D4—2121no—
1728D4—2122no—
1729D4—2122no—
1730D4—2122no—
1731D4—2122no—
1732D4—2122no—
1733D4—2122no—
1734D4—2122no—
1735D4—2122no—
1736D4—2122no—
1737D4—2122no—
1738D4#41×D5312yes—
1739C2×C4—21no—
1740C2×C4—21no—
1741C2×C4—21no—
1742C2×C4—21no—
1743C2×C4—21no—
1744C2×C4—21no—
1745C2×C4—21no—
1746C2×C4—21no—
1747C2×C4—21no—
1748C2×C4—21no—
1749C2×C4—42no—
1750C2×C4—81no—
1751C2×C4—531no—
1752C2×C4—531no—
1753C2×C4—532no—
1754C2×C4—532no—
1755C2×C4—531no—
1756C2×C4—531no—
1757C2×C4—531no—
1758C2×C4—1062no—
1759C2×C4—1061no—
1760C2×C4—1061no—
1761C2×C4—1061no—
1762C2×C4—1061no—
1763C2×C4—1061no—
1764C2×C4—1061no—
1765C2×C4—1061no—
1766C2×C4—1061no—
1767C2×C4—1061no—
1768C2×C4—4241no—
1769C2×C4—4241no—
1770C2×C4—4241no—
1771C2×C4—4241no—
1772C2×C4—4241no—
1773C2×C4—4241no—
1774C2×C4—4241no—
1775C2×C4—4241no—
1776C2×C4—2121no—
1777C2×C4—2122no—
1778C2×C4—2122no—
1779C2×C4—2122no—
1780C2×C4—2122no—
1781C2×C4—2122no—
1782C2×C4—2122no—
1783C2×C4—2122no—
1784C2×C4—2122no—
1785C2×C4—2122no—
1786C2×C4—2122no—
1787C2×C4C2×D4×D5311yescharacteristic
1788C2×C4C2×D4×D5311yescharacteristic
1789C2×C4C2×D4×D5311yescharacteristic
1790C2×C4C2×D4×D5311yescharacteristic
1791C2×C4C24×D5311yescharacteristic
1792C8—21no—
1793C8—21no—
1794C8—21no—
1795C8—21no—
1796C8—1061no—
1797C8—1061no—
1798C8—1061no—
1799C8—1061no—
1800C22—21no—
1801C22—21no—
1802C22—22no—
1803C22—21no—
1804C22—21no—
1805C22—21no—
1806C22—21no—
1807C22—41no—
1808C22—41no—
1809C22—41no—
1810C22—41no—
1811C22—41no—
1812C22—162no—
1813C22—532no—
1814C22—8482no—
1815C22—8482no—
1816C22—8482no—
1817C22—1061no—
1818C22—1061no—
1819C22—1061no—
1820C22—1061no—
1821C22—1062no—
1822C22—1061no—
1823C22—1061no—
1824C22—1061no—
1825C22—1061no—
1826C22—4244no—
1827C22—2121no—
1828C22—2121no—
1829C22—2121no—
1830C22—2121no—
1831C22—2121no—
1832C22—2121no—
1833C22—2121no—
1834C22—2121no—
1835C22C22×D4×D5311yescharacteristic
1836C4—21no—
1837C4—21no—
1838C4—21no—
1839C4—21no—
1840C4—41no—
1841C4—41no—
1842C4—41no—
1843C4—41no—
1844C4—41no—
1845C4—41no—
1846C4—532no—
1847C4—532no—
1848C4—1061no—
1849C4—1061no—
1850C4—1061no—
1851C4—2121no—
1852C4—2121no—
1853C4—2121no—
1854C4—2121no—
1855C4—2121no—
1856C4C2×#41×D5311yescharacteristic
1857C4H(5,𝔽2)×D5311yescharacteristic
1858C2—41no—
1859C2—41no—
1860C2—42no—
1861C2—81no—
1862C2—1062no—
1863C2—4241no—
1864C2—4241no—
1865C2—2121no—
1866C2—2121no—
1867C2—2122no—
1868C2#546×D5311yescharacteristic
1869C2#577×D5311yescharacteristic
1870C2#2028949211yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3311C2
socleC22×C53C23×D4
hypercenter#3311D53
hypocenterC53#61200
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3311

Complements

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

NH ≅ G/Ntype
1. #20288619C2semidirect
2. #20288475C2semidirect
3. #20287026C2semidirect
4. #20287024C2semidirect
5. #20286955C2semidirect
6. #20286953C2semidirect
7. #20286758C2semidirect
8. #20286756C2semidirect
9. #20286745C2semidirect
10. #20286678C2semidirect
11. #20286676C2semidirect
12. #20286675C2semidirect
13. #20286673C2semidirect
14. #20286641C2semidirect
15. #20286639C2semidirect
16. #20286534C2semidirect
17. #20286532C2semidirect
18. #20285107C2semidirect
19. #20284707C2semidirect
20. #20284701C2semidirect
21. #476×D53C2semidirect
22. #20284379C2semidirect
23. #20284372C2semidirect
24. #20284169C2semidirect
25. #20284023C2semidirect
26. #20284020C2semidirect
27. #20283520C2semidirect
28. #20283456C2semidirect
29. #20283240C2semidirect
30. #20283237C2semidirect
31. C53×#3311C2semidirect
35. C2×#13133240C22semidirect
36. C2×#13133238C22semidirect
37. C2×#13133225C22semidirect
38. C2×#13133223C22semidirect
39. #16811346C22semidirect
40. #16811336C22semidirect
41. #16811336C22semidirect
42. #16811331C22semidirect
43. #16811331C22semidirect
48. #16811277C22semidirect
49. #16811276C22semidirect
64. #16811203C22semidirect
65. #16811203C22semidirect
73. C4⋊Q8×D53C22semidirect
76. #16811103C22semidirect
77. #16811103C22semidirect
78. C4×#11719949C22semidirect
80. #16810985C22semidirect
81. #16810983C22semidirect
82. #16810982C22semidirect
83. #16810972C22semidirect
84. #16810972C22semidirect
85. #16810968C22semidirect
86. #16810968C22semidirect
87. #16810966C22semidirect
88. #16810964C22semidirect
89. #16810962C22semidirect
90. #16810955C22semidirect
91. #16810954C22semidirect
92. #16810952C22semidirect
93. #16810951C22semidirect
94. #16810950C22semidirect
95. #16810947C22semidirect
96. #16810946C22semidirect
97. #16810943C22semidirect
98. #16810942C22semidirect
99. #16810940C22semidirect
100. #16810939C22semidirect
101. #16810914C22semidirect
102. #16810913C22semidirect
103. #16810912C22semidirect
104. #16810912C22semidirect
105. #16810911C22semidirect
106. #16810911C22semidirect
107. #16810910C22semidirect
108. #16810880C22semidirect
109. #16810879C22semidirect
110. #16810878C22semidirect
111. #16810877C22semidirect
112. #16810876C22semidirect
113. #16810875C22semidirect
114. #16810874C22semidirect
115. #16810855C22semidirect
116. #16810855C22semidirect
117. #16810854C22semidirect
118. #16810854C22semidirect
119. #16810853C22semidirect
120. #16810852C22semidirect
121. #16810849C22semidirect
122. #16810845C22semidirect
123. #16810839C22semidirect
124. #16810835C22semidirect
125. #16810831C22semidirect
126. #16810827C22semidirect
127. #16810821C22semidirect
128. #16810817C22semidirect
129. #16810784C22semidirect
130. #16810783C22semidirect
131. #16810782C22semidirect
132. #16810773C22semidirect
133. #16810772C22semidirect
134. #16810772C22semidirect
135. #16810771C22semidirect
136. #16810770C22semidirect
137. #16810769C22semidirect
138. #16810768C22semidirect
139. #16810759C22semidirect
140. #16810758C22semidirect
141. #16810758C22semidirect
142. #16810757C22semidirect
143. #16810736C22semidirect
144. #16810733C22semidirect
145. #16810721C22semidirect
146. SD16×Dic53C22semidirect
147. #16810708C22semidirect
148. #16810705C22semidirect
149. #16810703C22semidirect
150. #16810699C22semidirect
151. #16810698C22semidirect
152. #16810696C22semidirect
153. #16810695C22semidirect
154. #16810693C22semidirect
155. C8×C22⋊D53C22semidirect
156. #16810686C22semidirect
157. #16810664C22semidirect
158. #106×D53C22semidirect
159. #106×D53C22semidirect
160. C4⋊C8×D53C22semidirect
161. #16810627C22semidirect
163. #16810626C22semidirect
164. #16810626C22semidirect
165. #16810625C22semidirect
166. #16810624C22semidirect
167. #16810623C22semidirect
168. #16810623C22semidirect
169. #16810623C22semidirect
170. #16810623C22semidirect
171. #16810621C22semidirect
172. #16810621C22semidirect
173. #16810621C22semidirect
174. #16810618C22semidirect
175. #16810618C22semidirect
176. #16810617C22semidirect
177. #16810616C22semidirect
178. #16810616C22semidirect
179. C2×#13133139C22semidirect
180. C2×#13133138C22semidirect
183. #102×D53C22semidirect
184. #102×D53C22semidirect
185. #16810588C22semidirect
186. #16810588C22semidirect
187. #16810575C22semidirect
188. C53×#556C22semidirect
190. C53×#489C22semidirect
191. C53×#485C22semidirect
192. C53×#482C22semidirect
193. C53×#476C22semidirect
194. C53×#470C22semidirect
195. C53×#465C22semidirect
196. C53×#464C22semidirect
197. C53×#452C22semidirect
198. C53×#450C22semidirect
199. C53×#440C22semidirect
200. C53×#435C22semidirect
201. C53×#418C22semidirect
202. C53×#416C22semidirect
558. D4×D53#41semidirect
932. #3311D53semidirect
975. #556C2×D53semidirect
1020. #489C2×D53semidirect
1028. #485C2×D53semidirect
1036. #482C2×D53semidirect
1048. #476C2×D53semidirect
1052. #470C2×D53semidirect
1064. #465C2×D53semidirect
1066. #464C2×D53semidirect
1076. #452C2×D53semidirect
1080. #450C2×D53semidirect
1092. #440C2×D53semidirect
1102. #435C2×D53semidirect
1113. #418C2×D53semidirect
1128. #416C2×D53semidirect
1138. C53#61200semidirect

Maximal subgroups

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

subgroupindex
#202886192
#202884752
#202870262
#202870242
#202869552
#202869532
#202867582
#202867562
#202867452
#202866782
#202866762
#202866752
#202866732
#202866412
#202866392
#202865342
#202865322
#202851072
#202847072
#202847012
#476×D532
#202843792
#202843722
#202841692
#202840232
#202840202
#202835202
#202834562
#202832402
#202832372
C53×#33112
#6120053