Finite Group Databasebeta

← #28276037

Subgroups — #28276037

Order 13568.

1810 conjugacy classes of subgroups.

The subgroup lattice has 1740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289123C211yesmaximal, characteristic, complemented
2#20288590C211yesmaximal, characteristic, complemented
3#20287760C211yesmaximal, characteristic, complemented
4#20287754C211yesmaximal, characteristic, complemented
5#20287732C211yesmaximal, characteristic, complemented
6#20287730C211yesmaximal, characteristic, complemented
7#20287724C211yesmaximal, characteristic, complemented
8#20287722C211yesmaximal, characteristic, complemented
9#20287708C211yesmaximal, characteristic, complemented
10#20287706C211yesmaximal, characteristic, complemented
11#20287526C211yesmaximal, characteristic, complemented
12#20287524C211yesmaximal, characteristic, complemented
13#20287504C211yesmaximal, characteristic, complemented
14#20287502C211yesmaximal, characteristic, complemented
15#20287383C211yesmaximal, characteristic, complemented
16#20287381C211yesmaximal, characteristic, complemented
17#20287347C211yesmaximal, characteristic, complemented
18#20287345C211yesmaximal, characteristic, complemented
19#20285815C211yesmaximal, characteristic, complemented
20#20285809C211yesmaximal, characteristic, complemented
21#20285807C211yesmaximal, characteristic, complemented
22#20285654C211yesmaximal, characteristic, complemented
23#20285631C211yesmaximal, characteristic, complemented
24#20284901C211yesmaximal, characteristic, complemented
25#20284900C211yesmaximal, characteristic, complemented
26#20284893C211yesmaximal, characteristic, complemented
27#20284892C211yesmaximal, characteristic, complemented
28#20284779C211yesmaximal, characteristic, complemented
29#20284768C211yesmaximal, characteristic, complemented
30#20283814C211yesmaximal, characteristic, complemented
31C53×#3224C211yesmaximal, characteristic, complemented
32#16811375—21no—
33#16811374—21no—
34#16811356C2211yescharacteristic, complemented
35#16811355C2211yescharacteristic
36#16811355C2211yescharacteristic
37#16811355C2211yescharacteristic
38#16811355C2211yescharacteristic
39#16811355C2211yescharacteristic, complemented
40Q8×Dic106C2211yescharacteristic, complemented
41#16811353C2211yescharacteristic, complemented
42#16811345C2211yescharacteristic, complemented
43#16811342C2211yescharacteristic, complemented
44#16811340—21no—
45#16811293C2211yescharacteristic
46#16811293C2211yescharacteristic
47#16811293C2211yescharacteristic
48#16811293C2211yescharacteristic
49D4×Dic106C2211yescharacteristic, complemented
50#16811288C2211yescharacteristic, complemented
51#16811286—21no—
52#16811260—21no—
53#16811260—21no—
54#16811260—21no—
55#16811260—21no—
56#16811246C2211yescharacteristic
57#16811244C2211yescharacteristic
58#16811241—21no—
59#16811240C2211yescharacteristic
60#16811237—21no—
61#16811226—21no—
62#16811226—21no—
63#16811195—21no—
64#16811193—21no—
65#16811187C2211yescharacteristic
66#16811176C2211yescharacteristic
67#16811175C2211yescharacteristic
68#16811168—21no—
69#16811168—21no—
70#16811168C2211yescharacteristic
71C2×#13133213C2211yescharacteristic
72#16811098C2211yescharacteristic
73#16811097C2211yescharacteristic
74#41×Dic53C2211yescharacteristic
75#16811011C2211yescharacteristic, complemented
76#16811010C2211yescharacteristic, complemented
77#16811009C2211yescharacteristic, complemented
78#16811008C2211yescharacteristic, complemented
79#16811005C2211yescharacteristic, complemented
80#16811004C2211yescharacteristic, complemented
81#16810998C2211yescharacteristic
82#16810998C2211yescharacteristic
83#16810994C2211yescharacteristic
84#16810994C2211yescharacteristic
85#16810984C2211yescharacteristic, complemented
86#16810984C2211yescharacteristic, complemented
87#16810982C2211yescharacteristic, complemented
88#16810969C2211yescharacteristic, complemented
89#16810968C2211yescharacteristic
90#16810968C2211yescharacteristic
91#16810968C2211yescharacteristic
92#16810968C2211yescharacteristic
93#16810968C2211yescharacteristic, complemented
94#16810968C2211yescharacteristic, complemented
95#16810965C2211yescharacteristic
96#16810961C2211yescharacteristic
97#16810948C2211yescharacteristic
98#16810944C2211yescharacteristic
99#16810916C2211yescharacteristic, complemented
100#16810914C2211yescharacteristic, complemented
101#16810911C2211yescharacteristic, complemented
102#16810911C2211yescharacteristic, complemented
103#16810911C2211yescharacteristic, complemented
104#16810910C2211yescharacteristic, complemented
105#16810906C2211yescharacteristic, complemented
106#16810904C2211yescharacteristic, complemented
107#16810901C2211yescharacteristic, complemented
108#16810901C2211yescharacteristic, complemented
109#16810901C2211yescharacteristic, complemented
110#16810900C2211yescharacteristic, complemented
111#16810848C2211yescharacteristic, complemented
112#16810847C2211yescharacteristic, complemented
113#16810842C2211yescharacteristic, complemented
114#16810841C2211yescharacteristic, complemented
115#16810840C2211yescharacteristic, complemented
116#16810840C2211yescharacteristic, complemented
117#16810840C2211yescharacteristic, complemented
118#16810839C2211yescharacteristic, complemented
119#16810839C2211yescharacteristic, complemented
120#16810836C2211yescharacteristic, complemented
121#16810836C2211yescharacteristic, complemented
122#16810835C2211yescharacteristic, complemented
123#16810835C2211yescharacteristic, complemented
124#16810835C2211yescharacteristic, complemented
125#16810831C2211yescharacteristic, complemented
126#16810826C2211yescharacteristic, complemented
127#16810822C2211yescharacteristic
128#16810822C2211yescharacteristic
129#16810822C2211yescharacteristic, complemented
130#16810821C2211yescharacteristic
131#16810821C2211yescharacteristic
132#16810821C2211yescharacteristic, complemented
133#16810821C2211yescharacteristic, complemented
134#16810820C2211yescharacteristic, complemented
135#16810817C2211yescharacteristic
136#16810817C2211yescharacteristic
137#16810817C2211yescharacteristic, complemented
138#16810816C2211yescharacteristic
139#16810816C2211yescharacteristic
140#16810816C2211yescharacteristic, complemented
141#16810816C2211yescharacteristic, complemented
142#16810815C2211yescharacteristic, complemented
143#16810785C2211yescharacteristic
144#16810776C2211yescharacteristic
145#16810774C2211yescharacteristic
146#16810773C2211yescharacteristic
147#16810768C2211yescharacteristic
148#16810759C2211yescharacteristic
149#16810757C2211yescharacteristic
150#16810756C2211yescharacteristic
151#16810752C2211yescharacteristic, complemented
152#16810752C2211yescharacteristic, complemented
153#16810751C2211yescharacteristic, complemented
154#16810751C2211yescharacteristic, complemented
155C8×Dic106C2211yescharacteristic, complemented
156C8×Dic106C2211yescharacteristic, complemented
157#16810747C2211yescharacteristic, complemented
158#16810747C2211yescharacteristic, complemented
159#16810736C2211yescharacteristic, complemented
160#16810735C2211yescharacteristic, complemented
161#16810733C2211yescharacteristic, complemented
162#16810732C2211yescharacteristic, complemented
163#16810725C2211yescharacteristic, complemented
164#16810724C2211yescharacteristic, complemented
165#16810721C2211yescharacteristic, complemented
166#16810720C2211yescharacteristic, complemented
167Q16×Dic53C2211yescharacteristic, complemented
168#16810715C2211yescharacteristic, complemented
169#16810714C2211yescharacteristic, complemented
170#16810714C2211yescharacteristic, complemented
171C4×#11719913C2211yescharacteristic, complemented
172SD16×Dic53C2211yescharacteristic, complemented
173SD16×Dic53C2211yescharacteristic, complemented
174SD16×Dic53C2211yescharacteristic, complemented
175C4×#11719924C2211yescharacteristic, complemented
176#16810708C2211yescharacteristic, complemented
177C4×D424C2211yescharacteristic, complemented
178D8×Dic53C2211yescharacteristic, complemented
179D8×Dic53C2211yescharacteristic, complemented
180C4×#11719922C2211yescharacteristic, complemented
181#16810703C2211yescharacteristic, complemented
182#16810703C2211yescharacteristic, complemented
183#16810684C2211yescharacteristic
184#16810681C2211yescharacteristic
185#16810681C2211yescharacteristic
186#16810673C2211yescharacteristic
187#16810673C2211yescharacteristic
188C53×#542C2211yescharacteristic
189C53×#535C2211yescharacteristic
190C53×#496C2211yescharacteristic, complemented
191C53×#495C2211yescharacteristic, complemented
192C53×#489C2211yescharacteristic, complemented
193C53×#486C2211yescharacteristic, complemented
194C53×#464C2211yescharacteristic, complemented
195C53×#463C2211yescharacteristic, complemented
196C53×#460C2211yescharacteristic, complemented
197C53×#459C2211yescharacteristic, complemented
198C53×#452C2211yescharacteristic
199C53×#450C2211yescharacteristic
200C53×#449C2211yescharacteristic
201C53×#447C2211yescharacteristic
202C53×#433C2211yescharacteristic
203C2×#11719947—21no—
204C2×#11719947—21no—
205C2×#11719947—21no—
206C2×#11719947—21no—
207C2×#11719947—21no—
208C22×Dic106—21no—
209C2×Q8×D53—21no—
210C22×D212C2311yescharacteristic
211C22×C22⋊D53—21no—
212C22×C22⋊D53—21no—
213C2×#11719925C2311yescharacteristic
214C2×#11719913C2311yescharacteristic
215C2×#11719913C2311yescharacteristic
216C2×#11719923C2311yescharacteristic
217C2×#11719923C2311yescharacteristic
218C2×#11719923C2311yescharacteristic
219C2×#11719924C2311yescharacteristic
220C2×#11719924C2311yescharacteristic
221C2×#11719924C2311yescharacteristic
222C2×D424C2311yescharacteristic
223C2×D424C2311yescharacteristic
224C2×#11719922C2311yescharacteristic
225C2×#11719922C2311yescharacteristic
226C2×#11719922C2311yescharacteristic
227C2×#11719922C2311yescharacteristic
228C2×#11719922C2311yescharacteristic
229#13133217—21no—
230#13133217C2311yescharacteristic
231#13133216—21no—
232#13133216—21no—
233#13133216—21no—
234#13133216D411yescharacteristic
235#13133216D411yescharacteristic
236#13133216C2311yescharacteristic
237#13133216C2311yescharacteristic
238#13133216C2311yescharacteristic
239#13133216C2311yescharacteristic
240#13133215—21no—
241#13133215—21no—
242#13133215C2311yescharacteristic
243#13133213—21no—
244#13133213—21no—
245#13133213C2311yescharacteristic
246#13133213C2311yescharacteristic
247#13133213C2311yescharacteristic
248#13133213C2311yescharacteristic
249#13133213C2311yescharacteristic
250#13133213C2311yescharacteristic
251#13133213C2311yescharacteristic
252#13133212—21no—
253#13133212—21no—
254#13133212—21no—
255#13133211—21no—
256#13133210—21no—
257#13133210—21no—
258#13133210—21no—
259#13133208D411yescharacteristic
260#13133208D411yescharacteristic
261#13133207—21no—
262#13133206C2311yescharacteristic
263#13133206C2311yescharacteristic
264#13133206C2311yescharacteristic
265#13133205C2311yescharacteristic
266#13133204—21no—
267#13133204C2311yescharacteristic
268#13133203—21no—
269#13133203—21no—
270#13133203—21no—
271#13133203—21no—
272#13133203—21no—
273#13133203—21no—
274#13133203—21no—
275#13133203—21no—
276#13133203—21no—
277#13133201—21no—
278#13133201—21no—
279#13133201—21no—
280#13133201—21no—
281#13133201—21no—
282#13133200—21no—
283#13133199—21no—
284#13133199—21no—
285#13133199—21no—
286#13133199—21no—
287#13133199—21no—
288#13133199—21no—
289#13133199—21no—
290#13133199—21no—
291#13133198—21no—
292#13133197—21no—
293#13133196—21no—
294#13133196C2311yescharacteristic
295#13133195—21no—
296#13133195—21no—
297#13133195—21no—
298#13133195—21no—
299#13133194—21no—
300#13133194—21no—
301#13133194—21no—
302#13133194—21no—
303#13133194—21no—
304#13133194D411yescharacteristic
305#13133194D411yescharacteristic
306#13133194D411yescharacteristic
307#13133194D411yescharacteristic
308#13133193—21no—
309#13133191—21no—
310#13133191—21no—
311#13133191C2311yescharacteristic
312#13133189—21no—
313#13133189—21no—
314#13133189—21no—
315#13133189—21no—
316#13133189—21no—
317#13133189—21no—
318#13133189—21no—
319#13133189—21no—
320#13133189—21no—
321#13133188—21no—
322#13133188—21no—
323#13133188—21no—
324#13133188—21no—
325#13133185—21no—
326#13133185—21no—
327Q8×Dic53C2311yescharacteristic
328Q8×Dic53C2311yescharacteristic
329Q8×Dic53C2311yescharacteristic
330Q8×Dic53C2311yescharacteristic
331C4×Dic106—21no—
332C4×Dic106C2311yescharacteristic
333C4×Dic106C2311yescharacteristic
334C4×Dic106C2311yescharacteristic
335C4×Dic106C2311yescharacteristic
336C4×Dic106C2311yescharacteristic
337#13133182—21no—
338#13133182—21no—
339#13133182C2311yescharacteristic
340#13133182C2311yescharacteristic
341C4×D212C2311yescharacteristic
342C4×D212C2311yescharacteristic
343C4×D212C2311yescharacteristic
344C4×D212C2311yescharacteristic
345C4×D212C2311yescharacteristic
346D4×Dic53—21no—
347D4×Dic53—21no—
348D4×Dic53—21no—
349D4×Dic53—21no—
350D4×Dic53C2311yescharacteristic
351D4×Dic53C2311yescharacteristic
352D4×Dic53C2311yescharacteristic
353D4×Dic53C2311yescharacteristic
354D4×Dic53C2311yescharacteristic
355D4×Dic53C2311yescharacteristic
356D4×Dic53C2311yescharacteristic
357D4×Dic53C2311yescharacteristic
358#13133179—21no—
359#13133179—21no—
360#13133179C2311yescharacteristic
361#13133179C2311yescharacteristic
362C4×C22⋊D53—21no—
363#13133177—21no—
364#13133177—21no—
365#13133177—21no—
366#13133177—21no—
367#13133177—21no—
368#13133177—21no—
369#13133176—21no—
370#13133176C2311yescharacteristic
371#13133176C2311yescharacteristic
372#13133174—21no—
373#13133173—21no—
374#13133173—21no—
375C2×C22⋊Dic53—21no—
376C2×C22⋊Dic53—21no—
377C22⋊C4×D53—21no—
378C22⋊C4×D53—21no—
379C2×C4×Dic53—21no—
380C2×C4×Dic53C2311yescharacteristic
381#13133151C2311yescharacteristic
382#13133151C2311yescharacteristic
383#13133150C2311yescharacteristic
384#13133150C2311yescharacteristic
385#13133149C2311yescharacteristic
386#13133149C2311yescharacteristic
387#13133148C2311yescharacteristic
388#13133148C2311yescharacteristic
389C4⋊#88322C2311yescharacteristic
390C4⋊#88322C2311yescharacteristic
391#13133146C2311yescharacteristic
392#13133146C2311yescharacteristic
393#13133146C2311yescharacteristic
394#13133146C2311yescharacteristic
395#13133146C2311yescharacteristic
396#13133146C2311yescharacteristic
397#13133146C2311yescharacteristic
398#13133146C2311yescharacteristic
399#13133142C2311yescharacteristic
400#13133142C2311yescharacteristic
401#13133141C2311yescharacteristic
402#13133141C2311yescharacteristic
403#13133141C2311yescharacteristic
404#13133141C2311yescharacteristic
405#13133139C2311yescharacteristic
406#13133139C2311yescharacteristic
407#13133139C2311yescharacteristic
408#13133139C2311yescharacteristic
409#13133139C2311yescharacteristic
410#13133139C2311yescharacteristic
411#13133138C2311yescharacteristic
412#13133138C2311yescharacteristic
413#13133138C2311yescharacteristic
414#13133138C2311yescharacteristic
415#13133138C2311yescharacteristic
416#13133138C2311yescharacteristic
417#13133138C2311yescharacteristic
418#13133138C2311yescharacteristic
419#13133137C2311yescharacteristic
420#13133137C2311yescharacteristic
421#13133137C2311yescharacteristic
422#13133137C2311yescharacteristic
423C22⋊#88322C2311yescharacteristic
424C22⋊#88322C2311yescharacteristic
425#13133128C2311yescharacteristic
426#13133127C2311yescharacteristic
427#13133127C2311yescharacteristic
428C4×#88322C2311yescharacteristic
429C8×Dic53C2311yescharacteristic
430C8×Dic53C2311yescharacteristic
431C8×Dic53C2311yescharacteristic
432C8×Dic53C2311yescharacteristic
433C8×Dic53C2311yescharacteristic
434C8×Dic53C2311yescharacteristic
435C2×#41×C53C2311yescharacteristic
436C22×D4×C53C2311yescharacteristic
437C2×Q16×C53C2311yescharacteristic
438C2×SD16×C53C2311yescharacteristic
439C2×SD16×C53C2311yescharacteristic
440C2×SD16×C53C2311yescharacteristic
441C2×SD16×C53C2311yescharacteristic
442C2×D8×C53C2311yescharacteristic
443C2×D8×C53C2311yescharacteristic
444C2×D8×C53C2311yescharacteristic
445C4⋊Q8×C53C2311yescharacteristic
446#127×C53C2311yescharacteristic
447#127×C53C2311yescharacteristic
448#126×C53—21no—
449#124×C53—21no—
450#124×C53C2311yescharacteristic
451#124×C53C2311yescharacteristic
452#124×C53C2311yescharacteristic
453#123×C53—21no—
454C22⋊Q8×C53—21no—
455C22⋊Q8×C53C2311yescharacteristic
456#121×C53—21no—
457#121×C53—21no—
458#121×C53C2311yescharacteristic
459#120×C53—21no—
460#120×C53—21no—
461C4×Q8×C53C2311yescharacteristic
462C4×D4×C53C2311yescharacteristic
463#117×C53C2311yescharacteristic
464C4⋊C8×C53C2311yescharacteristic
465C4⋊C8×C53C2311yescharacteristic
466#103×C53C2311yescharacteristic
467#103×C53C2311yescharacteristic
468#102×C53C2311yescharacteristic
469#102×C53C2311yescharacteristic
470#102×C53C2311yescharacteristic
471#102×C53C2311yescharacteristic
472#102×C53C2311yescharacteristic
473#102×C53C2311yescharacteristic
474C22⋊C8×C53C2311yescharacteristic
475C22⋊C8×C53C2311yescharacteristic
476#97×C53C2311yescharacteristic
477C4×C8×C53C2311yescharacteristic
478C24×C53—21no—
479C23×D53—21no—
480#41×C53—41no—
481#41×C53—41no—
482C2×Q8×C53—21no—
483C2×Q8×C53C2411yescharacteristic
484C2×Q8×C53C2411yescharacteristic
485C2×D4×C53—21no—
486C2×D4×C53—21no—
487C2×D4×C53—21no—
488C2×D4×C53—21no—
489C2×D4×C53—21no—
490C2×D4×C53—21no—
491C2×D4×C53—21no—
492C2×D4×C53—41no—
493C2×D4×C53—41no—
494C2×D4×C53C2411yescharacteristic
495C2×D4×C53C2411yescharacteristic
496C2×D4×C53C2411yescharacteristic
497C2×D4×C53C2411yescharacteristic
498C22×C4×C53—21no—
499C22×C4×C53—21no—
500C22×C4×C53C2411yescharacteristic
501C2×C22⋊D53—21no—
502C2×C22⋊D53—21no—
503C2×C22⋊D53—21no—
504C2×C22⋊D53—21no—
505C2×C22⋊D53—21no—
506C2×C22⋊D53—21no—
507C2×C22⋊D53—21no—
508C2×C22⋊D53—21no—
509C2×C22⋊D53—21no—
510C2×C22⋊D53—21no—
511C2×C22⋊D53—21no—
512C2×C22⋊D53—21no—
513C2×C22⋊D53—21no—
514C2×C22⋊D53—21no—
515C2×C22⋊D53—21no—
516C2×C22⋊D53—82no—
517C2×C22⋊D53—82no—
518C22×Dic53—21no—
519C22×Dic53—21no—
520C22×Dic53—21no—
521C22×Dic53—21no—
522C22×Dic53—21no—
523C22×Dic53—21no—
524C22×Dic53—21no—
525C22×Dic53—21no—
526C22×Dic53C2×D411yescharacteristic
527C22×Dic53C2×D411yescharacteristic
528Q8×D53—82no—
529#11719947—82no—
530#11719947—82no—
531#11719947—82no—
532#11719947—82no—
533#11719947—82no—
534C2×D212—21no—
535C2×D212—41no—
536C2×D212—41no—
537C2×D212C2411yescharacteristic
538C2×D212C2411yescharacteristic
539C2×D212C2411yescharacteristic
540C2×C4×D53—21no—
541C2×C4×D53—21no—
542C2×C4×D53—21no—
543C2×C4×D53—21no—
544C2×C4×D53—21no—
545C2×C4×D53—21no—
546C2×C4×D53—21no—
547C2×Dic106—21no—
548C2×Dic106—21no—
549C2×Dic106—21no—
550C2×Dic106—21no—
551C2×Dic106—21no—
552C2×Dic106—82no—
553C2×Dic106C2×D411yescharacteristic
554C2×Dic106C2×D411yescharacteristic
555C2×Dic106C2×D411yescharacteristic
556C2×Dic106C2×D411yescharacteristic
557C2×Dic106C2411yescharacteristic
558Q16×C53—41no—
559SD16×C53—41no—
560SD16×C53—41no—
561SD16×C53—41no—
562SD16×C53—41no—
563D8×C53—41no—
564D8×C53—41no—
565D8×C53—41no—
566C2×C8×C53C2411yescharacteristic
567C2×C8×C53C2411yescharacteristic
568C2×C8×C53C2411yescharacteristic
569C2×C8×C53C2411yescharacteristic
570C4⋊C4×C53—21no—
571C4⋊C4×C53—21no—
572C4⋊C4×C53—21no—
573C4⋊C4×C53C2×D411yescharacteristic
574C4⋊C4×C53C2×D411yescharacteristic
575C4⋊C4×C53C2411yescharacteristic
576C4⋊C4×C53C2411yescharacteristic
577C22⋊C4×C53—21no—
578C22⋊C4×C53—21no—
579C22⋊C4×C53—21no—
580C22⋊C4×C53—21no—
581C22⋊C4×C53—21no—
582C22⋊C4×C53—21no—
583C22⋊C4×C53—21no—
584C22⋊C4×C53—21no—
585C22⋊C4×C53—21no—
586C22⋊C4×C53C2×D411yescharacteristic
587C22⋊C4×C53C2×D411yescharacteristic
588C42×C53—21no—
589C42×C53C2411yescharacteristic
590C42×C53C2411yescharacteristic
591C22⋊Dic53—21no—
592C22⋊Dic53—21no—
593C22⋊Dic53—21no—
594C22⋊Dic53—21no—
595C22⋊Dic53—21no—
596C22⋊Dic53—21no—
597C22⋊Dic53—21no—
598C22⋊Dic53—21no—
599C22⋊Dic53—21no—
600C22⋊Dic53—21no—
601C22⋊Dic53—21no—
602C22⋊Dic53—21no—
603C22⋊Dic53C2×D411yescharacteristic
604C22⋊Dic53C2×D411yescharacteristic
605#11719925—41no—
606#11719924—41no—
607#11719924—41no—
608#11719924—41no—
609#11719923—41no—
610#11719923—41no—
611#11719923—41no—
612#11719922—41no—
613#11719922—41no—
614#11719922—41no—
615#11719922—41no—
616#11719922—41no—
617#11719921—21no—
618#11719921—21no—
619#11719921—21no—
620#11719921—21no—
621#11719921—21no—
622#11719921—21no—
623#11719921—21no—
624#11719921—21no—
625#11719921—21no—
626#11719921—21no—
627#11719921—21no—
628#11719921—21no—
629#11719921—21no—
630#11719921—21no—
631#11719921—21no—
632#11719921—21no—
633C4⋊Dic53—21no—
634C4⋊Dic53—21no—
635C4⋊Dic53—21no—
636C4⋊Dic53—21no—
637C4⋊Dic53—21no—
638C4⋊Dic53C2×D411yescharacteristic
639C4⋊Dic53C2×D411yescharacteristic
640C4⋊Dic53C2×D411yescharacteristic
641C4⋊Dic53C2×D411yescharacteristic
642C4⋊Dic53C2×D411yescharacteristic
643C4⋊Dic53C2×D411yescharacteristic
644C4⋊Dic53C2411yescharacteristic
645C4⋊Dic53C2411yescharacteristic
646C4⋊Dic53C2411yescharacteristic
647C4⋊Dic53C2411yescharacteristic
648#11719919—21no—
649#11719919—21no—
650#11719919—21no—
651#11719919—21no—
652#11719919—21no—
653#11719919—21no—
654#11719919—21no—
655#11719919—21no—
656#11719919—21no—
657#11719919—21no—
658#11719919C2×D411yescharacteristic
659#11719919C2×D411yescharacteristic
660#11719919C2×D411yescharacteristic
661#11719919C2×D411yescharacteristic
662#11719919C2×D411yescharacteristic
663#11719919C2×D411yescharacteristic
664#11719919C2×D411yescharacteristic
665#11719919C2×D411yescharacteristic
666C4×Dic53—21no—
667C4×Dic53—21no—
668C4×Dic53—21no—
669C4×Dic53—21no—
670C4×Dic53—21no—
671C4×Dic53—21no—
672C4×Dic53—21no—
673C4×Dic53—21no—
674C4×Dic53C2×D411yescharacteristic
675C4×Dic53C2×D411yescharacteristic
676C4×Dic53C2411yescharacteristic
677C4×Dic53C2411yescharacteristic
678C4×Dic53C2411yescharacteristic
679C4×Dic53C2411yescharacteristic
680C2×#88322C2411yescharacteristic
681C2×#88322C2411yescharacteristic
682C2×#88322C2411yescharacteristic
683C2×#88322C2411yescharacteristic
684D424—41no—
685D424—41no—
686#11719913—41no—
687#11719913—41no—
688C23×C53—21no—
689C23×C53—21no—
690C23×C53—21no—
691C23×C53—21no—
692C23×C53—42no—
693C23×C53—81no—
694C23×C53—81no—
695C23×C53C22×D411yescharacteristic
696C22×D53—21no—
697C22×D53—21no—
698C22×D53—21no—
699C22×D53—42no—
700C22×D53—81no—
701C22×D53—81no—
702Q8×C53—21no—
703Q8×C53—21no—
704Q8×C53—21no—
705Q8×C53—21no—
706Q8×C53—81no—
707D4×C53—21no—
708D4×C53—21no—
709D4×C53—21no—
710D4×C53—21no—
711D4×C53—21no—
712D4×C53—21no—
713D4×C53—21no—
714D4×C53—21no—
715D4×C53—42no—
716D4×C53—42no—
717D4×C53—81no—
718D4×C53—81no—
719D4×C53—81no—
720D4×C53—81no—
721D4×C53—81no—
722C2×C4×C53—21no—
723C2×C4×C53—21no—
724C2×C4×C53—21no—
725C2×C4×C53—21no—
726C2×C4×C53—21no—
727C2×C4×C53—21no—
728C2×C4×C53—42no—
729C2×C4×C53—81no—
730C2×C4×C53C22×D411yescharacteristic
731C2×C4×C53C22×D411yescharacteristic
732C2×C4×C53C22×D411yescharacteristic
733C2×C4×C53C22×D411yescharacteristic
734C2×C4×C53C22×D411yescharacteristic
735C2×C4×C53C2511yescharacteristic
736C22⋊D53—42no—
737C22⋊D53—42no—
738C22⋊D53—42no—
739C22⋊D53—42no—
740C22⋊D53—42no—
741C22⋊D53—81no—
742C22⋊D53—81no—
743C22⋊D53—81no—
744C22⋊D53—81no—
745C22⋊D53—81no—
746C22⋊D53—81no—
747C22⋊D53—81no—
748C22⋊D53—81no—
749C22⋊D53—81no—
750C22⋊D53—81no—
751C2×Dic53—22no—
752C2×Dic53—22no—
753C2×Dic53—21no—
754C2×Dic53—21no—
755C2×Dic53—21no—
756C2×Dic53—21no—
757C2×Dic53—21no—
758C2×Dic53—42no—
759C2×Dic53—42no—
760C2×Dic53—42no—
761C2×Dic53—81no—
762C2×Dic53—81no—
763C2×Dic53—81no—
764C2×Dic53—81no—
765C2×Dic53—81no—
766C2×Dic53C22×D411yescharacteristic
767C2×Dic53C22×D411yescharacteristic
768C2×Dic53C22×D411yescharacteristic
769C2×Dic53C22×D411yescharacteristic
770C2×Dic53C22×D411yescharacteristic
771C2×Dic53C22×D411yescharacteristic
772C2×Dic53C22×D411yescharacteristic
773C2×Dic53C22×D411yescharacteristic
774D212—21no—
775D212—21no—
776D212—21no—
777D212—21no—
778D212—21no—
779D212—21no—
780D212—42no—
781C4×D53—42no—
782C4×D53—81no—
783C4×D53—81no—
784C4×D53—81no—
785C4×D53—81no—
786C4×D53—81no—
787C4×D53—81no—
788Dic106—22no—
789Dic106—22no—
790Dic106—22no—
791Dic106—22no—
792Dic106—21no—
793Dic106—21no—
794Dic106—42no—
795Dic106—81no—
796Dic106—81no—
797Dic106—81no—
798Dic106—81no—
799C8×C53—21no—
800C8×C53—21no—
801C8×C53—21no—
802C8×C53—21no—
803#88322—21no—
804#88322—21no—
805#88322—21no—
806#88322—21no—
807#61937—531nomaximal, Sylow
808C22×C53—21no—
809C22×C53—21no—
810C22×C53—21no—
811C22×C53—41no—
812C22×C53—41no—
813C22×C53—41no—
814C22×C53—41no—
815C22×C53—41no—
816C22×C53—41no—
817C22×C53—41no—
818C22×C53—41no—
819C22×C53—41no—
820C22×C53—41no—
821C22×C53—41no—
822C22×C53—41no—
823C22×C53—162no—
824C22×C53C23×D411yescharacteristic
825C2×D53—41no—
826C2×D53—41no—
827C2×D53—41no—
828C2×D53—41no—
829C2×D53—41no—
830C2×D53—41no—
831C2×D53—41no—
832C2×D53—41no—
833C2×D53—41no—
834C2×D53—162no—
835C4×C53—21no—
836C4×C53—21no—
837C4×C53—21no—
838C4×C53—21no—
839C4×C53—21no—
840C4×C53—41no—
841C4×C53—41no—
842C4×C53—41no—
843C4×C53—41no—
844C4×C53#58511yescharacteristic
845C4×C53#58511yescharacteristic
846Dic53—21no—
847Dic53—21no—
848Dic53—21no—
849Dic53—21no—
850Dic53—21no—
851Dic53—21no—
852Dic53—41no—
853Dic53—41no—
854Dic53—41no—
855Dic53—41no—
856Dic53—41no—
857Dic53#57612yes—
858Dic53#57712yes—
859#3550—531no—
860#3508—531no—
861#3399—531no—
862#3399—531no—
863#3397—531no—
864#3397—531no—
865#3396—531no—
866#3396—531no—
867#3394—531no—
868#3394—531no—
869#3375—531no—
870#3375—531no—
871#3373—531no—
872#3373—531no—
873#3362—531no—
874#3362—531no—
875#3358—531no—
876#3358—531no—
877#3224—531no—
878#3224—531no—
879#3224—531no—
880#3224D5311yescharacteristic, complemented
881#3208—531no—
882#3205—531no—
883#3118—531no—
884#3118—531no—
885#3118—531no—
886#3118—531no—
887#3107—531no—
888#3106—531no—
889#2986—531no—
890C2×C53—41no—
891C2×C53—81no—
892C2×C53—81no—
893C2×C53—81no—
894C2×C53—81no—
895C2×C53#348711yescharacteristic
896C2×C53C2×#57611yescharacteristic
897C2×C53C2×#57711yescharacteristic
898D53—81no—
899D53—81no—
900D53—81no—
901#563—1061no—
902#563—1061no—
903#559—531no—
904#559—531no—
905#559—531no—
906#559—531no—
907#559—531no—
908#559—531no—
909Q82—531no—
910Q82—531no—
911#556—531no—
912#556—531no—
913#556—1061no—
914#550—531no—
915#550—531no—
916#550—531no—
917#550—531no—
918D4×Q8—531no—
919D4×Q8—531no—
920D4×Q8—1061no—
921#546—1061no—
922#546—1061no—
923#546—1061no—
924#546—1061no—
925#542—531no—
926#542—531no—
927#542—531no—
928#542—1061no—
929#542—1061no—
930#542C2×D5311yescharacteristic
931#540—1061no—
932#540—1061no—
933#536—1061no—
934#536—1061no—
935#535—531no—
936#535C2×D5311yescharacteristic
937#533—531no—
938#533—531no—
939#532—531no—
940#532—1061no—
941#532—1061no—
942C2×#127—531no—
943#518—531no—
944#518—531no—
945C4×#41—531no—
946#496—531no—
947#496—531no—
948#496—531no—
949#496C2×D5311yescharacteristic, complemented
950#495—531no—
951#495—531no—
952#495—531no—
953#495C2×D5311yescharacteristic, complemented
954#493—531no—
955#493—531no—
956#492—531no—
957#492—531no—
958#489—531no—
959#489—531no—
960#489—531no—
961#489C2×D5311yescharacteristic, complemented
962#486—531no—
963#486—531no—
964#486—531no—
965#486—531no—
966#486—531no—
967#486—531no—
968#486—531no—
969#486C2×D5311yescharacteristic, complemented
970#485—531no—
971#485—531no—
972#482—531no—
973#482—531no—
974#477—531no—
975#476—531no—
976#476—531no—
977#476—531no—
978#476—531no—
979#476—531no—
980#475—531no—
981#474—531no—
982#474—531no—
983#474—531no—
984#474—531no—
985#474—531no—
986#464—531no—
987#464—531no—
988#464—531no—
989#464C2×D5311yescharacteristic, complemented
990#463—531no—
991#463—531no—
992#463—531no—
993#463—531no—
994#463—531no—
995#463—531no—
996#463—531no—
997#463—531no—
998#463—531no—
999#463—531no—
1000#463—531no—
1001#463C2×D5311yescharacteristic, complemented
1002#462—531no—
1003#461—531no—
1004#460—531no—
1005#460—531no—
1006#460—531no—
1007#460—531no—
1008#460—531no—
1009#460—531no—
1010#460—531no—
1011#460—531no—
1012#460C2×D5311yescharacteristic, complemented
1013#459—531no—
1014#459—531no—
1015#459—531no—
1016#459—531no—
1017#459—531no—
1018#459—531no—
1019#459—531no—
1020#459—531no—
1021#459C2×D5311yescharacteristic, complemented
1022#452—531no—
1023#452C2×D5311yescharacteristic
1024#450—531no—
1025#450—531no—
1026#450—531no—
1027#450C2×D5311yescharacteristic
1028#449—531no—
1029#449C2×D5311yescharacteristic
1030#447—531no—
1031#447—531no—
1032#447—531no—
1033#447C2×D5311yescharacteristic
1034#446—531no—
1035#446—531no—
1036#446—531no—
1037#446—531no—
1038C8×Q8—531no—
1039C8×Q8—531no—
1040C8×Q8—531no—
1041C8×Q8—531no—
1042#442—531no—
1043#442—531no—
1044#442—531no—
1045#442—531no—
1046#440—531no—
1047#440—531no—
1048#440—531no—
1049#440—531no—
1050C4×Q16—531no—
1051C4×Q16—531no—
1052C4×SD16—531no—
1053C4×SD16—531no—
1054C4×SD16—531no—
1055C4×SD16—531no—
1056C4×SD16—531no—
1057C4×SD16—531no—
1058C4×SD16—531no—
1059C4×SD16—531no—
1060C4×D8—531no—
1061C4×D8—531no—
1062C4×D8—531no—
1063C4×D8—531no—
1064C4×D8—531no—
1065C4×D8—531no—
1066#433—531no—
1067#433—531no—
1068#433—531no—
1069#433C2×D5311yescharacteristic
1070#431—531no—
1071#431—531no—
1072C53#6193711yescharacteristic, complemented, Sylow
1073C2×#41—1061no—
1074C2×#41—1061no—
1075C2×#41—1061no—
1076C2×#41—1061no—
1077C2×#41—1061no—
1078C2×#41C22×D5311yescharacteristic
1079C22×Q8—1061no—
1080C22×Q8—1061no—
1081C22×D4—531no—
1082C22×D4—1061no—
1083C22×D4—1061no—
1084C22×D4C22×D5311yescharacteristic
1085C2×Q16—531no—
1086C2×Q16C22×D5311yescharacteristic
1087C2×SD16—531no—
1088C2×SD16—531no—
1089C2×SD16—531no—
1090C2×SD16—531no—
1091C2×SD16—531no—
1092C2×SD16—531no—
1093C2×SD16—531no—
1094C2×SD16—531no—
1095C2×SD16C22×D5311yescharacteristic
1096C2×SD16C22×D5311yescharacteristic
1097C2×SD16C22×D5311yescharacteristic
1098C2×SD16C22×D5311yescharacteristic
1099C2×D8—531no—
1100C2×D8—531no—
1101C2×D8—531no—
1102C2×D8—531no—
1103C2×D8—531no—
1104C2×D8—531no—
1105C2×D8—531no—
1106C2×D8C22×D5311yescharacteristic
1107C2×D8C22×D5311yescharacteristic
1108C2×D8C22×D5311yescharacteristic
1109C4⋊Q8—531no—
1110C4⋊Q8—531no—
1111C4⋊Q8—531no—
1112C4⋊Q8—531no—
1113C4⋊Q8—531no—
1114C4⋊Q8—531no—
1115C4⋊Q8—531no—
1116C4⋊Q8—531no—
1117C4⋊Q8—1061no—
1118C4⋊Q8—1061no—
1119C4⋊Q8—1061no—
1120C4⋊Q8—1061no—
1121C4⋊Q8—1061no—
1122C4⋊Q8—1061no—
1123C4⋊Q8C22×D5311yescharacteristic
1124#127—531no—
1125#127—531no—
1126#127—531no—
1127#127—531no—
1128#127—531no—
1129#127—531no—
1130#127—531no—
1131#127—1061no—
1132#127—1061no—
1133#127C22×D5311yescharacteristic
1134#127C22×D5311yescharacteristic
1135#126—21no—
1136#126—1061no—
1137#126—1061no—
1138#126—1061no—
1139#126—1061no—
1140#126—1061no—
1141#126—1061no—
1142#126—1061no—
1143#125—531no—
1144#125—531no—
1145#125—1061no—
1146#124—21no—
1147#124—531no—
1148#124—531no—
1149#124—531no—
1150#124—531no—
1151#124—531no—
1152#124—1061no—
1153#124—1061no—
1154#124—1061no—
1155#124—1061no—
1156#124—1061no—
1157#124—1061no—
1158#124—1061no—
1159#124—1061no—
1160#124—1061no—
1161#124—1061no—
1162#124C22×D5311yescharacteristic
1163#124C22×D5311yescharacteristic
1164#124C22×D5311yescharacteristic
1165#123—21no—
1166#123—1061no—
1167#123—1061no—
1168#123—1061no—
1169#123—1061no—
1170#123—1061no—
1171#123—1061no—
1172#123—1061no—
1173#123—1061no—
1174#123—1061no—
1175#123—1061no—
1176#123—1061no—
1177#123—1061no—
1178#123—1061no—
1179#123—1061no—
1180#123—1061no—
1181C22⋊Q8—21no—
1182C22⋊Q8—531no—
1183C22⋊Q8—531no—
1184C22⋊Q8—531no—
1185C22⋊Q8—531no—
1186C22⋊Q8—531no—
1187C22⋊Q8—1061no—
1188C22⋊Q8—1061no—
1189C22⋊Q8—1061no—
1190C22⋊Q8—1061no—
1191C22⋊Q8—1061no—
1192C22⋊Q8—1061no—
1193C22⋊Q8—1061no—
1194C22⋊Q8—1061no—
1195C22⋊Q8—1061no—
1196C22⋊Q8—1061no—
1197C22⋊Q8—1061no—
1198C22⋊Q8—1061no—
1199C22⋊Q8C22×D5311yescharacteristic
1200#121—21no—
1201#121—21no—
1202#121—531no—
1203#121—1061no—
1204#121—1061no—
1205#121—1061no—
1206#121—1061no—
1207#121—1061no—
1208#121—1061no—
1209#121—1061no—
1210#121—1061no—
1211#121—1061no—
1212#121—1061no—
1213#121—1061no—
1214#121—1061no—
1215#121—1061no—
1216#121—1061no—
1217#121—1061no—
1218#121C22×D5311yescharacteristic
1219#120—21no—
1220#120—21no—
1221#120—1061no—
1222#120—1061no—
1223C4×Q8—531no—
1224C4×Q8—531no—
1225C4×Q8—531no—
1226C4×Q8—531no—
1227C4×Q8—531no—
1228C4×Q8—531no—
1229C4×Q8—531no—
1230C4×Q8—531no—
1231C4×Q8—531no—
1232C4×Q8—531no—
1233C4×Q8—531no—
1234C4×Q8—1061no—
1235C4×Q8—1061no—
1236C4×Q8—1061no—
1237C4×Q8C22×D5311yescharacteristic
1238C4×D4—531no—
1239C4×D4—531no—
1240C4×D4—531no—
1241C4×D4—531no—
1242C4×D4—531no—
1243C4×D4—531no—
1244C4×D4—531no—
1245C4×D4—531no—
1246C4×D4—531no—
1247C4×D4—531no—
1248C4×D4—531no—
1249C4×D4—531no—
1250C4×D4—531no—
1251C4×D4—531no—
1252C4×D4—531no—
1253C4×D4—1061no—
1254C4×D4—1061no—
1255C4×D4—1061no—
1256C4×D4—1061no—
1257C4×D4—1061no—
1258C4×D4—1061no—
1259C4×D4—1061no—
1260C4×D4—1061no—
1261C4×D4—1061no—
1262C4×D4—1061no—
1263C4×D4—1061no—
1264C4×D4—1061no—
1265C4×D4—1061no—
1266C4×D4C22×D5311yescharacteristic
1267#117—531no—
1268#117—531no—
1269#117—1061no—
1270#117—1061no—
1271#117—1061no—
1272#117—1061no—
1273#117C22×D5311yescharacteristic
1274C2×C22⋊C4—1061no—
1275C2×C22⋊C4—1061no—
1276C2×C22⋊C4—1061no—
1277C2×C22⋊C4—1061no—
1278C2×C42—531no—
1279C2×C42—1061no—
1280#107—531no—
1281#107—531no—
1282#107—531no—
1283#107—531no—
1284#106—531no—
1285#106—531no—
1286#106—531no—
1287#106—531no—
1288C4⋊C8—531no—
1289C4⋊C8—531no—
1290C4⋊C8—531no—
1291C4⋊C8—531no—
1292C4⋊C8—531no—
1293C4⋊C8—531no—
1294C4⋊C8—531no—
1295C4⋊C8—531no—
1296C4⋊C8—531no—
1297C4⋊C8—531no—
1298C4⋊C8C22×D5311yescharacteristic
1299C4⋊C8C22×D5311yescharacteristic
1300#103—531no—
1301#103—531no—
1302#103—531no—
1303#103—531no—
1304#103—531no—
1305#103—531no—
1306#103C22×D5311yescharacteristic
1307#103C22×D5311yescharacteristic
1308#102—531no—
1309#102—531no—
1310#102—531no—
1311#102—531no—
1312#102—531no—
1313#102—531no—
1314#102—531no—
1315#102—531no—
1316#102—531no—
1317#102—531no—
1318#102—531no—
1319#102—531no—
1320#102—531no—
1321#102—531no—
1322#102—531no—
1323#102—531no—
1324#102—531no—
1325#102—531no—
1326#102C22×D5311yescharacteristic
1327#102C22×D5311yescharacteristic
1328#102C22×D5311yescharacteristic
1329#102C22×D5311yescharacteristic
1330#102C22×D5311yescharacteristic
1331#102C22×D5311yescharacteristic
1332C22⋊C8—531no—
1333C22⋊C8—531no—
1334C22⋊C8C22×D5311yescharacteristic
1335C22⋊C8C22×D5311yescharacteristic
1336#97—531no—
1337#97—531no—
1338#97—531no—
1339#97C22×D5311yescharacteristic
1340C4×C8—531no—
1341C4×C8—531no—
1342C4×C8—531no—
1343C4×C8—531no—
1344C4×C8—531no—
1345C4×C8—531no—
1346C4×C8—531no—
1347C4×C8C22×D5311yescharacteristic
1348C24—21no—
1349C24—1061no—
1350#41—41no—
1351#41—41no—
1352#41—4242no—
1353#41—4242no—
1354#41—4242no—
1355#41—4242no—
1356#41—4242no—
1357C2×Q8—21no—
1358C2×Q8—531no—
1359C2×Q8—531no—
1360C2×Q8—531no—
1361C2×Q8—531no—
1362C2×Q8—531no—
1363C2×Q8—1061no—
1364C2×Q8—1061no—
1365C2×Q8—1061no—
1366C2×Q8—1061no—
1367C2×Q8—1061no—
1368C2×Q8—4242no—
1369C2×Q8—4242no—
1370C2×Q8C23×D5311yescharacteristic
1371C2×Q8C23×D5311yescharacteristic
1372C2×D4—21no—
1373C2×D4—21no—
1374C2×D4—21no—
1375C2×D4—21no—
1376C2×D4—21no—
1377C2×D4—21no—
1378C2×D4—21no—
1379C2×D4—41no—
1380C2×D4—41no—
1381C2×D4—531no—
1382C2×D4—531no—
1383C2×D4—531no—
1384C2×D4—1061no—
1385C2×D4—1061no—
1386C2×D4—1061no—
1387C2×D4—1061no—
1388C2×D4—1061no—
1389C2×D4—1061no—
1390C2×D4—1061no—
1391C2×D4—1061no—
1392C2×D4—1061no—
1393C2×D4—1061no—
1394C2×D4—1061no—
1395C2×D4—1061no—
1396C2×D4—1061no—
1397C2×D4—1061no—
1398C2×D4—1061no—
1399C2×D4—1061no—
1400C2×D4—4242no—
1401C2×D4—4242no—
1402C2×D4—2121no—
1403C2×D4—2121no—
1404C2×D4C23×D5311yescharacteristic
1405C2×D4C23×D5311yescharacteristic
1406C2×D4C23×D5311yescharacteristic
1407C2×D4C23×D5311yescharacteristic
1408C22×C4—21no—
1409C22×C4—21no—
1410C22×C4—531no—
1411C22×C4—531no—
1412C22×C4—1061no—
1413C22×C4—1061no—
1414C22×C4—1061no—
1415C22×C4—1061no—
1416C22×C4—1061no—
1417C22×C4—1061no—
1418C22×C4—1061no—
1419C22×C4—1061no—
1420C22×C4—1061no—
1421C22×C4—1061no—
1422C22×C4—1061no—
1423C22×C4—1061no—
1424C22×C4—1061no—
1425C22×C4—1061no—
1426C22×C4—1061no—
1427C22×C4C23×D5311yescharacteristic
1428Q16—41no—
1429Q16—2121no—
1430SD16—41no—
1431SD16—41no—
1432SD16—41no—
1433SD16—41no—
1434SD16—2121no—
1435SD16—2121no—
1436SD16—2121no—
1437SD16—2121no—
1438SD16—2121no—
1439SD16—2121no—
1440SD16—2121no—
1441SD16—2121no—
1442D8—41no—
1443D8—41no—
1444D8—41no—
1445D8—2121no—
1446D8—2121no—
1447D8—2121no—
1448D8—2121no—
1449D8—2121no—
1450D8—2121no—
1451D8—2121no—
1452C2×C8—531no—
1453C2×C8—531no—
1454C2×C8—531no—
1455C2×C8—531no—
1456C2×C8C23×D5311yescharacteristic
1457C2×C8C23×D5311yescharacteristic
1458C2×C8C23×D5311yescharacteristic
1459C2×C8C23×D5311yescharacteristic
1460C4⋊C4—21no—
1461C4⋊C4—21no—
1462C4⋊C4—21no—
1463C4⋊C4—531no—
1464C4⋊C4—531no—
1465C4⋊C4—531no—
1466C4⋊C4—531no—
1467C4⋊C4—531no—
1468C4⋊C4—531no—
1469C4⋊C4—531no—
1470C4⋊C4—531no—
1471C4⋊C4—531no—
1472C4⋊C4—531no—
1473C4⋊C4—531no—
1474C4⋊C4—531no—
1475C4⋊C4—531no—
1476C4⋊C4—531no—
1477C4⋊C4—531no—
1478C4⋊C4—531no—
1479C4⋊C4—531no—
1480C4⋊C4—531no—
1481C4⋊C4—1061no—
1482C4⋊C4—1061no—
1483C4⋊C4—1061no—
1484C4⋊C4—1061no—
1485C4⋊C4—1061no—
1486C4⋊C4—1061no—
1487C4⋊C4—1061no—
1488C4⋊C4—1061no—
1489C4⋊C4—1061no—
1490C4⋊C4—1061no—
1491C4⋊C4—1061no—
1492C4⋊C4—1061no—
1493C4⋊C4—1061no—
1494C4⋊C4—1061no—
1495C4⋊C4—1061no—
1496C4⋊C4D4×D5311yescharacteristic
1497C4⋊C4D4×D5311yescharacteristic
1498C4⋊C4C23×D5311yescharacteristic
1499C4⋊C4C23×D5311yescharacteristic
1500C22⋊C4—21no—
1501C22⋊C4—21no—
1502C22⋊C4—21no—
1503C22⋊C4—21no—
1504C22⋊C4—21no—
1505C22⋊C4—21no—
1506C22⋊C4—21no—
1507C22⋊C4—21no—
1508C22⋊C4—21no—
1509C22⋊C4—531no—
1510C22⋊C4—531no—
1511C22⋊C4—1061no—
1512C22⋊C4—1061no—
1513C22⋊C4—1061no—
1514C22⋊C4—1061no—
1515C22⋊C4—1061no—
1516C22⋊C4—1061no—
1517C22⋊C4—1061no—
1518C22⋊C4—1061no—
1519C22⋊C4—1061no—
1520C22⋊C4—1061no—
1521C22⋊C4—1061no—
1522C22⋊C4—1061no—
1523C22⋊C4—1061no—
1524C22⋊C4—1061no—
1525C22⋊C4—1061no—
1526C22⋊C4—1061no—
1527C22⋊C4—1061no—
1528C22⋊C4—1061no—
1529C22⋊C4—1061no—
1530C22⋊C4—1061no—
1531C22⋊C4—1061no—
1532C22⋊C4—1061no—
1533C22⋊C4—1061no—
1534C22⋊C4—1061no—
1535C22⋊C4—1061no—
1536C22⋊C4—1061no—
1537C22⋊C4—1061no—
1538C22⋊C4—1061no—
1539C22⋊C4D4×D5311yescharacteristic
1540C22⋊C4D4×D5311yescharacteristic
1541C42—21no—
1542C42—531no—
1543C42—531no—
1544C42—531no—
1545C42—531no—
1546C42—531no—
1547C42—531no—
1548C42—1061no—
1549C42—1061no—
1550C42—1061no—
1551C42—1061no—
1552C42—1061no—
1553C42—1061no—
1554C42—1061no—
1555C42—1061no—
1556C42C23×D5311yescharacteristic
1557C42C23×D5311yescharacteristic
1558C23—21no—
1559C23—21no—
1560C23—21no—
1561C23—21no—
1562C23—42no—
1563C23—81no—
1564C23—81no—
1565C23—1061no—
1566C23—1061no—
1567C23—1061no—
1568C23—4241no—
1569C23—4241no—
1570C23—2122no—
1571C23C2×D4×D5311yescharacteristic
1572Q8—21no—
1573Q8—21no—
1574Q8—21no—
1575Q8—21no—
1576Q8—81no—
1577Q8—1062no—
1578Q8—1062no—
1579Q8—1062no—
1580Q8—1062no—
1581Q8—1061no—
1582Q8—1061no—
1583Q8—4241no—
1584Q8—4241no—
1585Q8—4241no—
1586Q8—4241no—
1587Q8—2122no—
1588D4—21no—
1589D4—21no—
1590D4—21no—
1591D4—21no—
1592D4—21no—
1593D4—21no—
1594D4—21no—
1595D4—21no—
1596D4—42no—
1597D4—42no—
1598D4—81no—
1599D4—81no—
1600D4—81no—
1601D4—81no—
1602D4—81no—
1603D4—1061no—
1604D4—1061no—
1605D4—1061no—
1606D4—1061no—
1607D4—1061no—
1608D4—1061no—
1609D4—4241no—
1610D4—4241no—
1611D4—4241no—
1612D4—4241no—
1613D4—4241no—
1614D4—4241no—
1615D4—4241no—
1616D4—4241no—
1617D4—4241no—
1618D4—4241no—
1619D4—2122no—
1620D4—2122no—
1621D4—2122no—
1622D4—2122no—
1623D4—2122no—
1624D4—2122no—
1625C2×C4—21no—
1626C2×C4—21no—
1627C2×C4—21no—
1628C2×C4—21no—
1629C2×C4—21no—
1630C2×C4—21no—
1631C2×C4—42no—
1632C2×C4—81no—
1633C2×C4—531no—
1634C2×C4—531no—
1635C2×C4—531no—
1636C2×C4—531no—
1637C2×C4—531no—
1638C2×C4—531no—
1639C2×C4—531no—
1640C2×C4—531no—
1641C2×C4—1062no—
1642C2×C4—1062no—
1643C2×C4—1061no—
1644C2×C4—1061no—
1645C2×C4—1061no—
1646C2×C4—1061no—
1647C2×C4—1061no—
1648C2×C4—4241no—
1649C2×C4—4241no—
1650C2×C4—4241no—
1651C2×C4—4241no—
1652C2×C4—4241no—
1653C2×C4—4241no—
1654C2×C4—4241no—
1655C2×C4—4241no—
1656C2×C4—4241no—
1657C2×C4—4241no—
1658C2×C4—4241no—
1659C2×C4—2122no—
1660C2×C4—2122no—
1661C2×C4—2122no—
1662C2×C4—2122no—
1663C2×C4C2×D4×D5311yescharacteristic
1664C2×C4C2×D4×D5311yescharacteristic
1665C2×C4C2×D4×D5311yescharacteristic
1666C2×C4C2×D4×D5311yescharacteristic
1667C2×C4C2×D4×D5311yescharacteristic
1668C2×C4C24×D5311yescharacteristic
1669C8—21no—
1670C8—21no—
1671C8—21no—
1672C8—21no—
1673C8—1061no—
1674C8—1061no—
1675C8—1061no—
1676C8—1061no—
1677C22—21no—
1678C22—21no—
1679C22—21no—
1680C22—41no—
1681C22—41no—
1682C22—41no—
1683C22—41no—
1684C22—41no—
1685C22—41no—
1686C22—41no—
1687C22—41no—
1688C22—41no—
1689C22—41no—
1690C22—41no—
1691C22—41no—
1692C22—162no—
1693C22—8482no—
1694C22—2121no—
1695C22—2121no—
1696C22—2121no—
1697C22—2121no—
1698C22—2121no—
1699C22—2121no—
1700C22—2121no—
1701C22—2121no—
1702C22—2121no—
1703C22C22×D4×D5311yescharacteristic
1704C4—21no—
1705C4—21no—
1706C4—21no—
1707C4—21no—
1708C4—21no—
1709C4—41no—
1710C4—41no—
1711C4—41no—
1712C4—41no—
1713C4—532no—
1714C4—532no—
1715C4—1061no—
1716C4—1061no—
1717C4—1061no—
1718C4—1061no—
1719C4—1061no—
1720C4—1061no—
1721C4—2121no—
1722C4—2121no—
1723C4—2121no—
1724C4—2121no—
1725C4—2121no—
1726C4#1681145811yescharacteristic
1727C4#1681145811yescharacteristic
1728C2—41no—
1729C2—81no—
1730C2—81no—
1731C2—81no—
1732C2—81no—
1733C2—4241no—
1734C2—4241no—
1735C2—4241no—
1736C2#2028837111yescharacteristic
1737C2#576×D5311yescharacteristic
1738C2#577×D5311yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3224C2
socleC22×C53C23×D4
hypercenter#3224D53
hypocenterC53#61937
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ #117 ◁ #3224

Complements

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

NH ≅ G/Ntype
1. #20289123C2semidirect
2. #20288590C2semidirect
3. #20287760C2semidirect
4. #20287754C2semidirect
5. #20287732C2semidirect
6. #20287730C2semidirect
7. #20287724C2semidirect
8. #20287722C2semidirect
9. #20287708C2semidirect
10. #20287706C2semidirect
11. #20287526C2semidirect
12. #20287524C2semidirect
13. #20287504C2semidirect
14. #20287502C2semidirect
15. #20287383C2semidirect
16. #20287381C2semidirect
17. #20287347C2semidirect
18. #20287345C2semidirect
19. #20285815C2semidirect
20. #20285809C2semidirect
21. #20285807C2semidirect
22. #20285654C2semidirect
23. #20285631C2semidirect
24. #20284901C2semidirect
25. #20284900C2semidirect
26. #20284893C2semidirect
27. #20284892C2semidirect
28. #20284779C2semidirect
29. #20284768C2semidirect
30. #20283814C2semidirect
31. C53×#3224C2semidirect
34. #16811356C22semidirect
39. #16811355C22semidirect
40. Q8×Dic106C22semidirect
41. #16811353C22semidirect
42. #16811345C22semidirect
43. #16811342C22semidirect
49. D4×Dic106C22semidirect
50. #16811288C22semidirect
75. #16811011C22semidirect
76. #16811010C22semidirect
77. #16811009C22semidirect
78. #16811008C22semidirect
79. #16811005C22semidirect
80. #16811004C22semidirect
85. #16810984C22semidirect
86. #16810984C22semidirect
87. #16810982C22semidirect
88. #16810969C22semidirect
93. #16810968C22semidirect
94. #16810968C22semidirect
99. #16810916C22semidirect
100. #16810914C22semidirect
101. #16810911C22semidirect
102. #16810911C22semidirect
103. #16810911C22semidirect
104. #16810910C22semidirect
105. #16810906C22semidirect
106. #16810904C22semidirect
107. #16810901C22semidirect
108. #16810901C22semidirect
109. #16810901C22semidirect
110. #16810900C22semidirect
111. #16810848C22semidirect
112. #16810847C22semidirect
113. #16810842C22semidirect
114. #16810841C22semidirect
115. #16810840C22semidirect
116. #16810840C22semidirect
117. #16810840C22semidirect
118. #16810839C22semidirect
119. #16810839C22semidirect
120. #16810836C22semidirect
121. #16810836C22semidirect
122. #16810835C22semidirect
123. #16810835C22semidirect
124. #16810835C22semidirect
125. #16810831C22semidirect
126. #16810826C22semidirect
129. #16810822C22semidirect
132. #16810821C22semidirect
133. #16810821C22semidirect
134. #16810820C22semidirect
137. #16810817C22semidirect
140. #16810816C22semidirect
141. #16810816C22semidirect
142. #16810815C22semidirect
151. #16810752C22semidirect
152. #16810752C22semidirect
153. #16810751C22semidirect
154. #16810751C22semidirect
155. C8×Dic106C22semidirect
156. C8×Dic106C22semidirect
157. #16810747C22semidirect
158. #16810747C22semidirect
159. #16810736C22semidirect
160. #16810735C22semidirect
161. #16810733C22semidirect
162. #16810732C22semidirect
163. #16810725C22semidirect
164. #16810724C22semidirect
165. #16810721C22semidirect
166. #16810720C22semidirect
167. Q16×Dic53C22semidirect
168. #16810715C22semidirect
169. #16810714C22semidirect
170. #16810714C22semidirect
171. C4×#11719913C22semidirect
172. SD16×Dic53C22semidirect
173. SD16×Dic53C22semidirect
174. SD16×Dic53C22semidirect
175. C4×#11719924C22semidirect
176. #16810708C22semidirect
177. C4×D424C22semidirect
178. D8×Dic53C22semidirect
179. D8×Dic53C22semidirect
180. C4×#11719922C22semidirect
181. #16810703C22semidirect
182. #16810703C22semidirect
190. C53×#496C22semidirect
191. C53×#495C22semidirect
192. C53×#489C22semidirect
193. C53×#486C22semidirect
194. C53×#464C22semidirect
195. C53×#463C22semidirect
196. C53×#460C22semidirect
197. C53×#459C22semidirect
880. #3224D53semidirect
949. #496C2×D53semidirect
953. #495C2×D53semidirect
961. #489C2×D53semidirect
969. #486C2×D53semidirect
989. #464C2×D53semidirect
1001. #463C2×D53semidirect
1012. #460C2×D53semidirect
1021. #459C2×D53semidirect
1072. C53#61937semidirect

Maximal subgroups

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

subgroupindex
#202891232
#202885902
#202877602
#202877542
#202877322
#202877302
#202877242
#202877222
#202877082
#202877062
#202875262
#202875242
#202875042
#202875022
#202873832
#202873812
#202873472
#202873452
#202858152
#202858092
#202858072
#202856542
#202856312
#202849012
#202849002
#202848932
#202848922
#202847792
#202847682
#202838142
C53×#32242
#6193753