Finite Group Databasebeta

← #28274769

Subgroups — #28274769

Order 13568.

1730 conjugacy classes of subgroups.

The subgroup lattice has 1648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289184C211yesmaximal, characteristic, complemented
2#20288517C211yesmaximal, characteristic, complemented
3#20287670C211yesmaximal, characteristic, complemented
4#20287668C211yesmaximal, characteristic, complemented
5#20287639C211yesmaximal, characteristic, complemented
6#20287611C211yesmaximal, characteristic, complemented
7#20287593C211yesmaximal, characteristic, complemented
8#20287584C211yesmaximal, characteristic, complemented
9#20287577C211yesmaximal, characteristic, complemented
10#20287567C211yesmaximal, characteristic, complemented
11#20287504C211yesmaximal, characteristic, complemented
12#20287471C211yesmaximal, characteristic, complemented
13#20287467C211yesmaximal, characteristic, complemented
14#20287425C211yesmaximal, characteristic, complemented
15#20287374C211yesmaximal, characteristic, complemented
16#20287372C211yesmaximal, characteristic, complemented
17#20287372C211yesmaximal, characteristic, complemented
18#20287349C211yesmaximal, characteristic, complemented
19#20286002C211yesmaximal, characteristic, complemented
20#20285968C211yesmaximal, characteristic, complemented
21#20285964C211yesmaximal, characteristic, complemented
22#20285897C211yesmaximal, characteristic, complemented
23#20285849C211yesmaximal, characteristic, complemented
24#20284959C211yesmaximal, characteristic, complemented
25#20284954C211yesmaximal, characteristic, complemented
26#20284902C211yesmaximal, characteristic, complemented
27#20284893C211yesmaximal, characteristic, complemented
28#20284765C211yesmaximal, characteristic, complemented
29#20284712C211yesmaximal, characteristic, complemented
30#20283814C211yesmaximal, characteristic, complemented
31C53×#3243C211yesmaximal, characteristic, complemented
32#16811370—21no—
33#16811367—21no—
34#16811358C2211yescharacteristic, complemented
35#16811355C2211yescharacteristic, complemented
36#16811355C2211yescharacteristic, complemented
37#16811349C2211yescharacteristic, complemented
38#16811334—21no—
39#16811334C2211yescharacteristic
40#16811334C2211yescharacteristic
41#16811334C2211yescharacteristic, complemented
42#16811332C2211yescharacteristic, complemented
43#16811329—21no—
44#16811329—21no—
45#16811329C2211yescharacteristic
46#16811329C2211yescharacteristic
47#16811329C2211yescharacteristic
48#16811329C2211yescharacteristic
49#16811294C2211yescharacteristic, complemented
50#16811288—21no—
51#16811288C2211yescharacteristic
52#16811288C2211yescharacteristic
53#16811288C2211yescharacteristic, complemented
54#16811281—21no—
55#16811271—21no—
56#16811254C2211yescharacteristic
57#16811248—21no—
58#16811248—21no—
59#16811246C2211yescharacteristic
60#16811239—21no—
61#16811228C2211yescharacteristic
62#16811226C2211yescharacteristic
63#16811222—21no—
64#16811214—21no—
65#16811196—21no—
66#16811176C2211yescharacteristic
67#16811176C2211yescharacteristic
68#16811168C2211yescharacteristic
69#16811159C2211yescharacteristic
70C22⋊Q8×D53—21no—
71C22⋊Q8×D53—21no—
72#16811097C2211yescharacteristic
73#16811097C2211yescharacteristic
74C2×#13133179C2211yescharacteristic
75#16811031C2211yescharacteristic, complemented
76#16811031C2211yescharacteristic, complemented
77#16811029C2211yescharacteristic, complemented
78#16811027C2211yescharacteristic, complemented
79#16811027C2211yescharacteristic, complemented
80#16811024C2211yescharacteristic, complemented
81#16811024C2211yescharacteristic, complemented
82#16811023C2211yescharacteristic, complemented
83#16811022C2211yescharacteristic, complemented
84#16811020C2211yescharacteristic, complemented
85#16810989C2211yescharacteristic, complemented
86#16810986C2211yescharacteristic, complemented
87#16810984C2211yescharacteristic, complemented
88#16810979C2211yescharacteristic, complemented
89#16810979C2211yescharacteristic, complemented
90#16810979C2211yescharacteristic, complemented
91#16810971C2211yescharacteristic, complemented
92#16810968C2211yescharacteristic, complemented
93#16810968C2211yescharacteristic, complemented
94#16810968C2211yescharacteristic, complemented
95#16810961C2211yescharacteristic
96#16810948C2211yescharacteristic
97#16810948C2211yescharacteristic
98#16810947C2211yescharacteristic
99#16810947C2211yescharacteristic
100#16810944C2211yescharacteristic
101#16810941C2211yescharacteristic
102#16810936C2211yescharacteristic
103#16810928C2211yescharacteristic, complemented
104#16810926C2211yescharacteristic
105#16810926C2211yescharacteristic
106#16810926C2211yescharacteristic
107#16810926C2211yescharacteristic, complemented
108#16810926C2211yescharacteristic, complemented
109#16810926C2211yescharacteristic, complemented
110#16810925C2211yescharacteristic, complemented
111#16810924C2211yescharacteristic
112#16810924C2211yescharacteristic
113#16810922C2211yescharacteristic
114#16810922C2211yescharacteristic, complemented
115#16810921C2211yescharacteristic, complemented
116#16810921C2211yescharacteristic, complemented
117#16810920C2211yescharacteristic, complemented
118#16810920C2211yescharacteristic, complemented
119#16810916C2211yescharacteristic, complemented
120#16810916C2211yescharacteristic, complemented
121#16810912C2211yescharacteristic
122#16810912C2211yescharacteristic, complemented
123#16810911C2211yescharacteristic, complemented
124#16810910C2211yescharacteristic
125#16810910C2211yescharacteristic, complemented
126#16810906C2211yescharacteristic, complemented
127#16810902C2211yescharacteristic
128#16810902C2211yescharacteristic
129#16810902C2211yescharacteristic
130#16810902C2211yescharacteristic, complemented
131#16810902C2211yescharacteristic, complemented
132#16810902C2211yescharacteristic, complemented
133#16810900C2211yescharacteristic
134#16810900C2211yescharacteristic, complemented
135#16810841C2211yescharacteristic
136#16810841C2211yescharacteristic
137#16810841C2211yescharacteristic
138#16810841C2211yescharacteristic
139#16810835C2211yescharacteristic
140#16810835C2211yescharacteristic
141#16810819C2211yescharacteristic
142#16810819C2211yescharacteristic
143#16810817C2211yescharacteristic
144#16810817C2211yescharacteristic
145#16810817C2211yescharacteristic
146#16810817C2211yescharacteristic
147#16810773C2211yescharacteristic
148#16810759C2211yescharacteristic
149#16810759C2211yescharacteristic
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
160#16810736C2211yescharacteristic
161#16810734C2211yescharacteristic
162#16810734C2211yescharacteristic
163#16810733C2211yescharacteristic
164#16810732C2211yescharacteristic
165#16810726C2211yescharacteristic
166#16810721C2211yescharacteristic
167C4×#11719924C2211yescharacteristic
168#16810708C2211yescharacteristic
169#16810708C2211yescharacteristic
170#16810708C2211yescharacteristic
171C4×D424C2211yescharacteristic
172C4×D424C2211yescharacteristic
173#16810705C2211yescharacteristic
174#16810705C2211yescharacteristic
175#16810705C2211yescharacteristic
176#16810705C2211yescharacteristic
177#16810705C2211yescharacteristic
178#16810705C2211yescharacteristic
179C4×#11719922C2211yescharacteristic
180#16810703C2211yescharacteristic
181#16810703C2211yescharacteristic
182#16810703C2211yescharacteristic
183#16810684C2211yescharacteristic
184#16810681C2211yescharacteristic
185#16810681C2211yescharacteristic
186#16810673C2211yescharacteristic
187#16810673C2211yescharacteristic
188C53×#544C2211yescharacteristic
189C53×#542C2211yescharacteristic
190C53×#501C2211yescharacteristic, complemented
191C53×#500C2211yescharacteristic, complemented
192C53×#489C2211yescharacteristic, complemented
193C53×#488C2211yescharacteristic, complemented
194C53×#485C2211yescharacteristic
195C53×#484C2211yescharacteristic
196C53×#482C2211yescharacteristic
197C53×#480C2211yescharacteristic
198C53×#479C2211yescharacteristic, complemented
199C53×#478C2211yescharacteristic, complemented
200C53×#477C2211yescharacteristic, complemented
201C53×#474C2211yescharacteristic, complemented
202C53×#433C2211yescharacteristic
203C2×#11719945—21no—
204C2×#11719947—21no—
205C2×Q8×D53—21no—
206C2×Q8×D53—21no—
207C2×Q8×D53—21no—
208C22×D212C2311yescharacteristic
209C22×C4×D53—21no—
210C2×#11719924C2311yescharacteristic
211C2×#11719924C2311yescharacteristic
212C2×D424C2311yescharacteristic
213C2×D424C2311yescharacteristic
214C2×D424C2311yescharacteristic
215C2×D424C2311yescharacteristic
216C2×#11719922C2311yescharacteristic
217C2×#11719922C2311yescharacteristic
218#13133216—21no—
219#13133216—21no—
220#13133216D411yescharacteristic
221#13133216D411yescharacteristic
222#13133216C2311yescharacteristic
223#13133216C2311yescharacteristic
224#13133216C2311yescharacteristic
225#13133216C2311yescharacteristic
226#13133216C2311yescharacteristic
227#13133216C2311yescharacteristic
228#13133214C2311yescharacteristic
229#13133213C2311yescharacteristic
230#13133213C2311yescharacteristic
231#13133212—21no—
232#13133212—21no—
233#13133209—21no—
234#13133209C2311yescharacteristic
235#13133208—21no—
236#13133208—21no—
237#13133208D411yescharacteristic
238#13133208D411yescharacteristic
239#13133208C2311yescharacteristic
240#13133208C2311yescharacteristic
241#13133208C2311yescharacteristic
242#13133208C2311yescharacteristic
243#13133208C2311yescharacteristic
244#13133208C2311yescharacteristic
245#13133206C2311yescharacteristic
246#13133206C2311yescharacteristic
247#13133205—21no—
248#13133203—21no—
249#13133203—21no—
250#13133203—21no—
251#13133203—21no—
252#13133202—21no—
253#13133202—21no—
254#13133202—21no—
255#13133202—21no—
256#13133201—21no—
257#13133201—21no—
258#13133201—21no—
259#13133201—21no—
260#13133199—21no—
261#13133199—21no—
262#13133199—21no—
263#13133199—21no—
264#13133197—21no—
265#13133197—21no—
266#13133197—21no—
267#13133197—21no—
268#13133197—21no—
269#13133197—21no—
270#13133197—21no—
271#13133197—21no—
272#13133196—21no—
273#13133196—21no—
274#13133196—21no—
275#13133195—21no—
276#13133195—21no—
277#13133195—21no—
278#13133195—21no—
279#13133195—21no—
280#13133195—21no—
281#13133195—21no—
282#13133195—21no—
283#13133195—21no—
284#13133195—21no—
285#13133195—21no—
286#13133195—21no—
287#13133195—21no—
288#13133195—21no—
289#13133194—21no—
290#13133194—21no—
291#13133194—21no—
292#13133194—21no—
293#13133194D411yescharacteristic
294#13133194D411yescharacteristic
295#13133194D411yescharacteristic
296#13133194D411yescharacteristic
297#13133193—21no—
298#13133193—21no—
299#13133193—21no—
300#13133193—21no—
301#13133193—21no—
302#13133193—21no—
303#13133193—21no—
304#13133193—21no—
305#13133193—21no—
306#13133191—21no—
307#13133191C2311yescharacteristic
308#13133191C2311yescharacteristic
309#13133190—21no—
310#13133190—21no—
311#13133190—21no—
312#13133190—21no—
313#13133189—21no—
314#13133189—21no—
315#13133188—21no—
316Q8×Dic53C2311yescharacteristic
317Q8×Dic53C2311yescharacteristic
318C4×Dic106—21no—
319C4×Dic106—21no—
320C4×Dic106—21no—
321C4×Dic106C2311yescharacteristic
322C4×Dic106C2311yescharacteristic
323C4×Dic106C2311yescharacteristic
324C4×Dic106C2311yescharacteristic
325C4×D212—21no—
326C4×D212—21no—
327C4×D212—21no—
328C4×D212C2311yescharacteristic
329C4×D212C2311yescharacteristic
330C4×D212C2311yescharacteristic
331C4×D212C2311yescharacteristic
332C4×D212C2311yescharacteristic
333C4×D212C2311yescharacteristic
334D4×Dic53C2311yescharacteristic
335D4×Dic53C2311yescharacteristic
336#13133179—21no—
337#13133179—21no—
338#13133179—21no—
339#13133179—21no—
340#13133179C2311yescharacteristic
341#13133179C2311yescharacteristic
342#13133179C2311yescharacteristic
343#13133179C2311yescharacteristic
344#13133179C2311yescharacteristic
345#13133179C2311yescharacteristic
346#13133179C2311yescharacteristic
347#13133179C2311yescharacteristic
348#13133179C2311yescharacteristic
349#13133179C2311yescharacteristic
350#13133179C2311yescharacteristic
351#13133179C2311yescharacteristic
352#13133177—21no—
353#13133177—21no—
354#13133177—21no—
355#13133177—21no—
356#13133176C2311yescharacteristic
357#13133176C2311yescharacteristic
358#13133175—21no—
359C2×#11719919—21no—
360C4⋊C4×D53—21no—
361C4⋊C4×D53—21no—
362C4⋊C4×D53—21no—
363C4⋊C4×D53—21no—
364C4⋊C4×D53—21no—
365C4⋊C4×D53—21no—
366C4⋊C4×D53—21no—
367C2×#11719921—21no—
368C22⋊C4×D53—21no—
369C22⋊C4×D53—21no—
370C22⋊C4×D53—21no—
371C22⋊C4×D53—21no—
372C2×C4×Dic53C2311yescharacteristic
373#13133151C2311yescharacteristic
374#13133151C2311yescharacteristic
375#13133150C2311yescharacteristic
376#13133150C2311yescharacteristic
377#13133150C2311yescharacteristic
378#13133150C2311yescharacteristic
379#13133150C2311yescharacteristic
380#13133150C2311yescharacteristic
381#13133149C2311yescharacteristic
382#13133149C2311yescharacteristic
383#13133148C2311yescharacteristic
384#13133148C2311yescharacteristic
385#13133148C2311yescharacteristic
386#13133148C2311yescharacteristic
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#13133141C2311yescharacteristic
400#13133141C2311yescharacteristic
401#13133139C2311yescharacteristic
402#13133139C2311yescharacteristic
403#13133139C2311yescharacteristic
404#13133139C2311yescharacteristic
405#13133139C2311yescharacteristic
406#13133139C2311yescharacteristic
407#13133139C2311yescharacteristic
408#13133139C2311yescharacteristic
409#13133138C2311yescharacteristic
410#13133138C2311yescharacteristic
411#13133137C2311yescharacteristic
412#13133137C2311yescharacteristic
413#13133137C2311yescharacteristic
414#13133137C2311yescharacteristic
415#13133137C2311yescharacteristic
416#13133137C2311yescharacteristic
417#13133137C2311yescharacteristic
418#13133137C2311yescharacteristic
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
435C4⋊Q8×C53—21no—
436C4⋊Q8×C53C2311yescharacteristic
437C4⋊Q8×C53C2311yescharacteristic
438C4⋊Q8×C53C2311yescharacteristic
439#126×C53—21no—
440#125×C53—21no—
441#125×C53C2311yescharacteristic
442#125×C53C2311yescharacteristic
443#124×C53—21no—
444#124×C53C2311yescharacteristic
445#123×C53—21no—
446C22⋊Q8×C53—21no—
447C22⋊Q8×C53—21no—
448C22⋊Q8×C53—21no—
449C22⋊Q8×C53C2311yescharacteristic
450#121×C53C2311yescharacteristic
451C4×Q8×C53C2311yescharacteristic
452C4×D4×C53C2311yescharacteristic
453#117×C53C2311yescharacteristic
454#117×C53C2311yescharacteristic
455C2×C4⋊C4×C53C2311yescharacteristic
456#107×C53C2311yescharacteristic
457#107×C53C2311yescharacteristic
458#107×C53C2311yescharacteristic
459#107×C53C2311yescharacteristic
460#107×C53C2311yescharacteristic
461#107×C53C2311yescharacteristic
462#106×C53C2311yescharacteristic
463#106×C53C2311yescharacteristic
464C4⋊C8×C53C2311yescharacteristic
465C4⋊C8×C53C2311yescharacteristic
466#103×C53C2311yescharacteristic
467#103×C53C2311yescharacteristic
468#103×C53C2311yescharacteristic
469#103×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
478C23×D53—21no—
479C2×Q8×C53—21no—
480C2×Q8×C53—21no—
481C2×Q8×C53—21no—
482C2×Q8×C53C2411yescharacteristic
483C2×D4×C53—21no—
484C2×D4×C53C2411yescharacteristic
485C22×C4×C53—21no—
486C22×C4×C53—21no—
487C22×C4×C53C2411yescharacteristic
488C2×C22⋊D53—21no—
489C2×C22⋊D53—21no—
490C2×C22⋊D53—21no—
491C2×C22⋊D53—21no—
492C2×C22⋊D53—21no—
493C2×C22⋊D53—21no—
494C22×Dic53—21no—
495C22×Dic53—21no—
496C22×Dic53C2×D411yescharacteristic
497C22×Dic53C2×D411yescharacteristic
498Q8×D53—82no—
499Q8×D53—82no—
500Q8×D53—82no—
501#11719947—82no—
502#11719945—82no—
503C2×D212—21no—
504C2×D212—22no—
505C2×D212—22no—
506C2×D212—21no—
507C2×D212—21no—
508C2×D212C2411yescharacteristic
509C2×D212C2411yescharacteristic
510C2×D212C2411yescharacteristic
511C2×D212C2411yescharacteristic
512C2×C4×D53—21no—
513C2×C4×D53—21no—
514C2×C4×D53—21no—
515C2×C4×D53—21no—
516C2×C4×D53—21no—
517C2×C4×D53—21no—
518C2×C4×D53—21no—
519C2×C4×D53—21no—
520C2×C4×D53—21no—
521C2×C4×D53—21no—
522C2×C4×D53—21no—
523C2×C4×D53—21no—
524C2×C4×D53—21no—
525C2×C4×D53—21no—
526C2×C4×D53—21no—
527C2×C4×D53—21no—
528C2×C4×D53—21no—
529C2×C4×D53—21no—
530C2×C4×D53—82no—
531C2×Dic106—21no—
532C2×Dic106—21no—
533C2×Dic106—21no—
534C2×Dic106—21no—
535C2×Dic106—21no—
536C2×Dic106—21no—
537C2×Dic106C2×D411yescharacteristic
538C2×Dic106C2×D411yescharacteristic
539C2×Dic106C2×D411yescharacteristic
540C2×Dic106C2×D411yescharacteristic
541C2×C8×C53C2411yescharacteristic
542C2×C8×C53C2411yescharacteristic
543C2×C8×C53C2411yescharacteristic
544C2×C8×C53C2411yescharacteristic
545C4⋊C4×C53—21no—
546C4⋊C4×C53—21no—
547C4⋊C4×C53—21no—
548C4⋊C4×C53—21no—
549C4⋊C4×C53—21no—
550C4⋊C4×C53—21no—
551C4⋊C4×C53—21no—
552C4⋊C4×C53—21no—
553C4⋊C4×C53—21no—
554C4⋊C4×C53—21no—
555C4⋊C4×C53C2×D411yescharacteristic
556C4⋊C4×C53C2×D411yescharacteristic
557C4⋊C4×C53C2411yescharacteristic
558C4⋊C4×C53C2411yescharacteristic
559C4⋊C4×C53C2411yescharacteristic
560C4⋊C4×C53C2411yescharacteristic
561C4⋊C4×C53C2411yescharacteristic
562C4⋊C4×C53C2411yescharacteristic
563C22⋊C4×C53—21no—
564C22⋊C4×C53—21no—
565C22⋊C4×C53—21no—
566C22⋊C4×C53—21no—
567C22⋊C4×C53—21no—
568C22⋊C4×C53—21no—
569C22⋊C4×C53C2×D411yescharacteristic
570C22⋊C4×C53C2×D411yescharacteristic
571C42×C53—21no—
572C42×C53—21no—
573C42×C53C2411yescharacteristic
574C42×C53C2411yescharacteristic
575C22⋊Dic53—21no—
576C22⋊Dic53—21no—
577C22⋊Dic53—21no—
578C22⋊Dic53C2×D411yescharacteristic
579C22⋊Dic53C2×D411yescharacteristic
580#11719924—22no—
581#11719924—22no—
582#11719922—22no—
583#11719922—22no—
584#11719921—21no—
585#11719921—21no—
586#11719921—21no—
587#11719921—21no—
588#11719921—21no—
589#11719921—21no—
590#11719921—21no—
591#11719921—21no—
592#11719921—21no—
593#11719921—21no—
594#11719921—21no—
595#11719921—21no—
596#11719921—21no—
597#11719921—21no—
598#11719921—21no—
599#11719921—21no—
600#11719921—21no—
601#11719921—21no—
602#11719921—21no—
603#11719921—21no—
604#11719921—21no—
605#11719921—21no—
606#11719921—21no—
607#11719921—21no—
608C4⋊Dic53—21no—
609C4⋊Dic53—21no—
610C4⋊Dic53—21no—
611C4⋊Dic53—21no—
612C4⋊Dic53—21no—
613C4⋊Dic53—21no—
614C4⋊Dic53—21no—
615C4⋊Dic53—21no—
616C4⋊Dic53C2×D411yescharacteristic
617C4⋊Dic53C2×D411yescharacteristic
618C4⋊Dic53C2×D411yescharacteristic
619C4⋊Dic53C2×D411yescharacteristic
620C4⋊Dic53C2×D411yescharacteristic
621C4⋊Dic53C2×D411yescharacteristic
622C4⋊Dic53C2411yescharacteristic
623C4⋊Dic53C2411yescharacteristic
624C4⋊Dic53C2411yescharacteristic
625C4⋊Dic53C2411yescharacteristic
626#11719919—21no—
627#11719919—21no—
628#11719919—21no—
629#11719919—21no—
630#11719919—21no—
631#11719919—21no—
632#11719919—21no—
633#11719919—21no—
634#11719919—21no—
635#11719919—21no—
636#11719919—21no—
637#11719919—21no—
638#11719919—21no—
639#11719919—21no—
640#11719919C2×D411yescharacteristic
641#11719919C2×D411yescharacteristic
642#11719919C2×D411yescharacteristic
643#11719919C2×D411yescharacteristic
644#11719919C2×D411yescharacteristic
645#11719919C2×D411yescharacteristic
646#11719919C2×D411yescharacteristic
647#11719919C2×D411yescharacteristic
648C4×Dic53—21no—
649C4×Dic53—21no—
650C4×Dic53—21no—
651C4×Dic53C2×D411yescharacteristic
652C4×Dic53C2×D411yescharacteristic
653C4×Dic53C2411yescharacteristic
654C4×Dic53C2411yescharacteristic
655C4×Dic53C2411yescharacteristic
656C4×Dic53C2411yescharacteristic
657C2×#88322C2411yescharacteristic
658C2×#88322C2411yescharacteristic
659C2×#88322C2411yescharacteristic
660C2×#88322C2411yescharacteristic
661D424—22no—
662D424—22no—
663D424—22no—
664D424—22no—
665C23×C53—21no—
666C23×C53C22×D411yescharacteristic
667C22×D53—21no—
668C22×D53—21no—
669C22×D53—24no—
670C22×D53—21no—
671C22×D53—21no—
672C22×D53—81no—
673C22×D53—81no—
674Q8×C53—21no—
675Q8×C53—21no—
676Q8×C53—81no—
677Q8×C53—81no—
678Q8×C53—81no—
679D4×C53—21no—
680D4×C53—21no—
681D4×C53—81no—
682C2×C4×C53—21no—
683C2×C4×C53—21no—
684C2×C4×C53—21no—
685C2×C4×C53—21no—
686C2×C4×C53—21no—
687C2×C4×C53—21no—
688C2×C4×C53—21no—
689C2×C4×C53—21no—
690C2×C4×C53—21no—
691C2×C4×C53—81no—
692C2×C4×C53—81no—
693C2×C4×C53C22×D411yescharacteristic
694C2×C4×C53C22×D411yescharacteristic
695C2×C4×C53C22×D411yescharacteristic
696C2×C4×C53C22×D411yescharacteristic
697C2×C4×C53C22×D411yescharacteristic
698C2×C4×C53C2511yescharacteristic
699C22⋊D53—42no—
700C22⋊D53—81no—
701C22⋊D53—81no—
702C22⋊D53—81no—
703C22⋊D53—81no—
704C22⋊D53—81no—
705C2×Dic53—22no—
706C2×Dic53—21no—
707C2×Dic53—21no—
708C2×Dic53—21no—
709C2×Dic53—21no—
710C2×Dic53—41no—
711C2×Dic53—81no—
712C2×Dic53—81no—
713C2×Dic53C22×D411yescharacteristic
714C2×Dic53C22×D411yescharacteristic
715C2×Dic53C22×D411yescharacteristic
716C2×Dic53C22×D411yescharacteristic
717C2×Dic53C22×D411yescharacteristic
718C2×Dic53C22×D411yescharacteristic
719C2×Dic53C22×D411yescharacteristic
720C2×Dic53C22×D411yescharacteristic
721D212—24no—
722D212—21no—
723D212—21no—
724D212—21no—
725D212—21no—
726D212—21no—
727D212—21no—
728D212—81no—
729D212—81no—
730D2122−1+412yes—
731D2122−1+412yes—
732C4×D53—42no—
733C4×D53—42no—
734C4×D53—42no—
735C4×D53—81no—
736C4×D53—81no—
737C4×D53—81no—
738C4×D53—81no—
739C4×D53—81no—
740C4×D53—81no—
741C4×D53—81no—
742C4×D53—81no—
743C4×D53—81no—
744C4×D53—81no—
745C4×D53—81no—
746C4×D53—81no—
747C4×D53—81no—
748C4×D53—81no—
749C4×D53—81no—
750Dic106—22no—
751Dic106—22no—
752Dic106—41no—
753Dic106—41no—
754Dic106—42no—
755Dic106—42no—
756Dic106—81no—
757Dic106—81no—
758Dic106—81no—
759Dic106—81no—
760C8×C53—21no—
761C8×C53—21no—
762C8×C53—21no—
763C8×C53—21no—
764#88322—21no—
765#88322—21no—
766#88322—21no—
767#88322—21no—
768#61863—531nomaximal, Sylow
769C22×C53—21no—
770C22×C53—21no—
771C22×C53—21no—
772C22×C53—41no—
773C22×C53—41no—
774C22×C53—41no—
775C22×C53C23×D411yescharacteristic
776C2×D53—22no—
777C2×D53—22no—
778C2×D53—41no—
779C2×D53—41no—
780C2×D53—41no—
781C2×D53—41no—
782C2×D53—41no—
783C2×D53—41no—
784C2×D53—41no—
785C2×D53—41no—
786C2×D53—41no—
787C2×D53—41no—
788C2×D53—84no—
789C4×C53—21no—
790C4×C53—21no—
791C4×C53—21no—
792C4×C53—21no—
793C4×C53—21no—
794C4×C53—41no—
795C4×C53—41no—
796C4×C53—41no—
797C4×C53—41no—
798C4×C53—41no—
799C4×C53—41no—
800C4×C53—41no—
801C4×C53C2×2−1+411yescharacteristic
802C4×C53C2×2−1+411yescharacteristic
803Dic53—21no—
804Dic53—21no—
805Dic53—21no—
806Dic53—21no—
807Dic53—21no—
808Dic53—21no—
809Dic53—21no—
810Dic53—41no—
811Dic53—41no—
812Dic53—41no—
813Dic53—41no—
814Dic53#57612yes—
815#3554—531no—
816#3501—531no—
817#3389—531no—
818#3389—531no—
819#3386—531no—
820#3384—531no—
821#3381—531no—
822#3380—531no—
823#3380—531no—
824Q8×D8—531no—
825#3373—531no—
826#3370—531no—
827#3370—531no—
828#3366—531no—
829#3361—531no—
830#3361—531no—
831#3361—531no—
832#3358—531no—
833#3243—531no—
834#3243D5311yescharacteristic, complemented
835#3241—531no—
836#3241—531no—
837#3233—531no—
838#3228—531no—
839#3122—531no—
840#3122—531no—
841#3118—531no—
842#3118—531no—
843#3105—531no—
844#3100—531no—
845#2986—531no—
846C2×C53—41no—
847C2×C53—81no—
848C2×C53#348611yescharacteristic
849C2×C53C2×#57611yescharacteristic
850C2×C53#358411yescharacteristic
851D53—42no—
852D53—42no—
853D53—81no—
854D53—81no—
855#562—1061no—
856#562—1061no—
857#559—531no—
858#559—531no—
859#559—531no—
860#557—531no—
861#554—531no—
862#554—531no—
863#554—531no—
864#554—531no—
865#554—531no—
866#554—531no—
867#554—531no—
868#554—531no—
869#554—1061no—
870#554—1061no—
871#554—1061no—
872#550—531no—
873D4×Q8—531no—
874D4×Q8—531no—
875D4×Q8—531no—
876D4×Q8—1061no—
877#548—1061no—
878#547—1061no—
879#544—531no—
880#544C2×D5311yescharacteristic
881#543—1061no—
882#543—1061no—
883#542—531no—
884#542—1061no—
885#542C2×D5311yescharacteristic
886#540—531no—
887#540—531no—
888#539—1061no—
889#539—1061no—
890#536—1061no—
891#533—531no—
892#533—531no—
893#532—531no—
894#529—531no—
895C2×C22⋊Q8—1061no—
896C2×C22⋊Q8—1061no—
897#518—531no—
898#518—531no—
899C2×C4×D4—531no—
900#501—531no—
901#501—531no—
902#501—531no—
903#501C2×D5311yescharacteristic, complemented
904#500—531no—
905#500—531no—
906#500C2×D5311yescharacteristic, complemented
907#499—531no—
908#499—531no—
909#499—531no—
910#499—531no—
911#498—531no—
912#490—531no—
913#490—531no—
914#489—531no—
915#489C2×D5311yescharacteristic, complemented
916#488—531no—
917#488—531no—
918#488—531no—
919#488C2×D5311yescharacteristic, complemented
920#486—531no—
921#486—531no—
922#486—531no—
923#486—531no—
924#485—531no—
925#485C2×D5311yescharacteristic
926#484C2×D5311yescharacteristic
927#482—531no—
928#482—531no—
929#482—531no—
930#482—531no—
931#482—531no—
932#482C2×D5311yescharacteristic
933#481—531no—
934#480—531no—
935#480C2×D5311yescharacteristic
936#479—531no—
937#479C2×D5311yescharacteristic, complemented
938#478—531no—
939#478—531no—
940#478—531no—
941#478—531no—
942#478—531no—
943#478—531no—
944#478—531no—
945#478—531no—
946#478—531no—
947#478—531no—
948#478—531no—
949#478—531no—
950#478—531no—
951#478—531no—
952#478—531no—
953#478C2×D5311yescharacteristic, complemented
954#477—531no—
955#477—531no—
956#477C2×D5311yescharacteristic, complemented
957#476—531no—
958#476—531no—
959#476—531no—
960#476—531no—
961#476—531no—
962#475—531no—
963#474—531no—
964#474—531no—
965#474—531no—
966#474—531no—
967#474—531no—
968#474—531no—
969#474—531no—
970#474—531no—
971#474C2×D5311yescharacteristic, complemented
972#463—531no—
973#463—531no—
974#463—531no—
975#463—531no—
976#463—531no—
977#463—531no—
978#459—531no—
979#459—531no—
980#459—531no—
981#459—531no—
982#459—531no—
983#459—531no—
984#450—531no—
985#447—531no—
986#447—531no—
987#447—531no—
988#446—531no—
989#446—531no—
990#446—531no—
991#446—531no—
992C8×Q8—531no—
993C8×Q8—531no—
994C8×Q8—531no—
995C8×Q8—531no—
996#442—531no—
997#442—531no—
998#442—531no—
999#442—531no—
1000#442—531no—
1001#442—531no—
1002#440—531no—
1003#440—531no—
1004C4×SD16—531no—
1005C4×SD16—531no—
1006C4×SD16—531no—
1007C4×SD16—531no—
1008C4×D8—531no—
1009C4×D8—531no—
1010C4×D8—531no—
1011C4×D8—531no—
1012C4×D8—531no—
1013C4×D8—531no—
1014C4×D8—531no—
1015C4×D8—531no—
1016C4×D8—531no—
1017C4×D8—531no—
1018C4×D8—531no—
1019C4×D8—531no—
1020#433—531no—
1021#433—531no—
1022#433—531no—
1023#433C2×D5311yescharacteristic
1024#431—531no—
1025#431—531no—
1026C53#6186311yescharacteristic, complemented, Sylow
1027C2×#41—1061no—
1028C2×#41—1061no—
1029C22×Q8—1061no—
1030C22×Q8—1061no—
1031C22×Q8—1061no—
1032C22×D4—531no—
1033C23×C4—1061no—
1034C2×SD16—531no—
1035C2×SD16—531no—
1036C2×D8—531no—
1037C2×D8—531no—
1038C2×D8—531no—
1039C2×D8—531no—
1040C2×D8—531no—
1041C2×D8—531no—
1042C4⋊Q8—21no—
1043C4⋊Q8—531no—
1044C4⋊Q8—531no—
1045C4⋊Q8—531no—
1046C4⋊Q8—531no—
1047C4⋊Q8—531no—
1048C4⋊Q8—531no—
1049C4⋊Q8—531no—
1050C4⋊Q8—531no—
1051C4⋊Q8—1061no—
1052C4⋊Q8—1061no—
1053C4⋊Q8C22×D5311yescharacteristic
1054C4⋊Q8C22×D5311yescharacteristic
1055C4⋊Q8C22×D5311yescharacteristic
1056#127—531no—
1057#127—531no—
1058#127—531no—
1059#126—21no—
1060#126—1061no—
1061#126—1061no—
1062#125—21no—
1063#125—531no—
1064#125—531no—
1065#125—531no—
1066#125—531no—
1067#125—531no—
1068#125—531no—
1069#125—531no—
1070#125—531no—
1071#125—531no—
1072#125—1061no—
1073#125—1061no—
1074#125—1061no—
1075#125C22×D5311yescharacteristic
1076#125C22×D5311yescharacteristic
1077#124—21no—
1078#124—531no—
1079#124—531no—
1080#124—1061no—
1081#124—1061no—
1082#124—1061no—
1083#124—1061no—
1084#124—1061no—
1085#124C22×D5311yescharacteristic
1086#123—21no—
1087#123—1061no—
1088#123—1061no—
1089#123—1061no—
1090#123—1061no—
1091#123—1061no—
1092#123—1061no—
1093#123—1061no—
1094#123—1061no—
1095#123—1061no—
1096#123—1061no—
1097#123—1061no—
1098#123—1061no—
1099C22⋊Q8—21no—
1100C22⋊Q8—21no—
1101C22⋊Q8—21no—
1102C22⋊Q8—531no—
1103C22⋊Q8—531no—
1104C22⋊Q8—531no—
1105C22⋊Q8—531no—
1106C22⋊Q8—1061no—
1107C22⋊Q8—1061no—
1108C22⋊Q8—1061no—
1109C22⋊Q8—1061no—
1110C22⋊Q8—1061no—
1111C22⋊Q8—1061no—
1112C22⋊Q8—1061no—
1113C22⋊Q8—1061no—
1114C22⋊Q8—1061no—
1115C22⋊Q8—1061no—
1116C22⋊Q8—1061no—
1117C22⋊Q8—1061no—
1118C22⋊Q8—1061no—
1119C22⋊Q8—1061no—
1120C22⋊Q8—1061no—
1121C22⋊Q8—1061no—
1122C22⋊Q8—1061no—
1123C22⋊Q8—1061no—
1124C22⋊Q8—1061no—
1125C22⋊Q8—1061no—
1126C22⋊Q8—1061no—
1127C22⋊Q8—1061no—
1128C22⋊Q8—1061no—
1129C22⋊Q8—1061no—
1130C22⋊Q8—1061no—
1131C22⋊Q8—1061no—
1132C22⋊Q8—1061no—
1133C22⋊Q8—1061no—
1134C22⋊Q8—1061no—
1135C22⋊Q8—1061no—
1136C22⋊Q8—1061no—
1137C22⋊Q8—1061no—
1138C22⋊Q8—1061no—
1139C22⋊Q8—1061no—
1140C22⋊Q8—1061no—
1141C22⋊Q8—1061no—
1142C22⋊Q8—1061no—
1143C22⋊Q8—1061no—
1144C22⋊Q8C22×D5311yescharacteristic
1145#121—531no—
1146#121—531no—
1147#121—1061no—
1148#121—1061no—
1149#121—1061no—
1150#121—1061no—
1151#121—1061no—
1152#121—1061no—
1153#121—1061no—
1154#121—1061no—
1155#121C22×D5311yescharacteristic
1156C4×Q8—531no—
1157C4×Q8—531no—
1158C4×Q8—531no—
1159C4×Q8—531no—
1160C4×Q8—531no—
1161C4×Q8—531no—
1162C4×Q8—1061no—
1163C4×Q8—1061no—
1164C4×Q8—1061no—
1165C4×Q8C22×D5311yescharacteristic
1166C4×D4—531no—
1167C4×D4—531no—
1168C4×D4—531no—
1169C4×D4—531no—
1170C4×D4—531no—
1171C4×D4—531no—
1172C4×D4—531no—
1173C4×D4—531no—
1174C4×D4—531no—
1175C4×D4—531no—
1176C4×D4—531no—
1177C4×D4—531no—
1178C4×D4—531no—
1179C4×D4—531no—
1180C4×D4—531no—
1181C4×D4—531no—
1182C4×D4—531no—
1183C4×D4—531no—
1184C4×D4—531no—
1185C4×D4—531no—
1186C4×D4—1061no—
1187C4×D4—1061no—
1188C4×D4—1061no—
1189C4×D4—1061no—
1190C4×D4—1061no—
1191C4×D4—1061no—
1192C4×D4—1061no—
1193C4×D4—1061no—
1194C4×D4—1061no—
1195C4×D4—1061no—
1196C4×D4—1061no—
1197C4×D4C22×D5311yescharacteristic
1198#117—531no—
1199#117—531no—
1200#117—1061no—
1201#117C22×D5311yescharacteristic
1202#117C22×D5311yescharacteristic
1203C2×C4⋊C4—1061no—
1204C2×C4⋊C4—1061no—
1205C2×C4⋊C4—1061no—
1206C2×C4⋊C4—1061no—
1207C2×C4⋊C4—1061no—
1208C2×C4⋊C4—1061no—
1209C2×C4⋊C4—1061no—
1210C2×C4⋊C4—1061no—
1211C2×C4⋊C4C22×D5311yescharacteristic
1212C2×C22⋊C4—1061no—
1213C2×C22⋊C4—1061no—
1214C2×C22⋊C4—1061no—
1215C2×C22⋊C4—1061no—
1216C2×C22⋊C4—1061no—
1217C2×C42—531no—
1218#107—531no—
1219#107—531no—
1220#107—531no—
1221#107—531no—
1222#107—531no—
1223#107—531no—
1224#107—531no—
1225#107—531no—
1226#107C22×D5311yescharacteristic
1227#107C22×D5311yescharacteristic
1228#107C22×D5311yescharacteristic
1229#107C22×D5311yescharacteristic
1230#107C22×D5311yescharacteristic
1231#107C22×D5311yescharacteristic
1232#106—531no—
1233#106—531no—
1234#106—531no—
1235#106—531no—
1236#106—531no—
1237#106—531no—
1238#106—531no—
1239#106—531no—
1240#106C22×D5311yescharacteristic
1241#106C22×D5311yescharacteristic
1242C4⋊C8—531no—
1243C4⋊C8—531no—
1244C4⋊C8—531no—
1245C4⋊C8—531no—
1246C4⋊C8—531no—
1247C4⋊C8—531no—
1248C4⋊C8—531no—
1249C4⋊C8—531no—
1250C4⋊C8—531no—
1251C4⋊C8—531no—
1252C4⋊C8C22×D5311yescharacteristic
1253C4⋊C8C22×D5311yescharacteristic
1254#103—531no—
1255#103—531no—
1256#103C22×D5311yescharacteristic
1257#103C22×D5311yescharacteristic
1258#103C22×D5311yescharacteristic
1259#103C22×D5311yescharacteristic
1260#102—531no—
1261#102—531no—
1262#102—531no—
1263#102—531no—
1264#102—531no—
1265#102—531no—
1266#102—531no—
1267#102—531no—
1268#102—531no—
1269#102—531no—
1270#102—531no—
1271#102—531no—
1272#102—531no—
1273#102—531no—
1274#102—531no—
1275#102—531no—
1276#102—531no—
1277#102—531no—
1278#102—531no—
1279#102—531no—
1280#102—531no—
1281#102—531no—
1282#102C22×D5311yescharacteristic
1283#102C22×D5311yescharacteristic
1284#102C22×D5311yescharacteristic
1285#102C22×D5311yescharacteristic
1286C22⋊C8—531no—
1287C22⋊C8—531no—
1288C22⋊C8C22×D5311yescharacteristic
1289C22⋊C8C22×D5311yescharacteristic
1290#97—531no—
1291#97—531no—
1292#97—531no—
1293#97C22×D5311yescharacteristic
1294C4×C8—531no—
1295C4×C8—531no—
1296C4×C8—531no—
1297C4×C8—531no—
1298C4×C8—531no—
1299C4×C8—531no—
1300C4×C8—531no—
1301C4×C8C22×D5311yescharacteristic
1302C24—1061no—
1303#41—4242no—
1304#41—4242no—
1305C2×Q8—21no—
1306C2×Q8—21no—
1307C2×Q8—21no—
1308C2×Q8—531no—
1309C2×Q8—531no—
1310C2×Q8—531no—
1311C2×Q8—531no—
1312C2×Q8—1061no—
1313C2×Q8—1061no—
1314C2×Q8—1061no—
1315C2×Q8—1061no—
1316C2×Q8—1061no—
1317C2×Q8—1061no—
1318C2×Q8—4242no—
1319C2×Q8—4242no—
1320C2×Q8—4242no—
1321C2×Q8C23×D5311yescharacteristic
1322C2×D4—21no—
1323C2×D4—531no—
1324C2×D4—531no—
1325C2×D4—531no—
1326C2×D4—531no—
1327C2×D4—1062no—
1328C2×D4—1062no—
1329C2×D4—1061no—
1330C2×D4—1061no—
1331C2×D4—1061no—
1332C2×D4—1061no—
1333C2×D4—1061no—
1334C2×D4—1061no—
1335C2×D4—1061no—
1336C2×D4—1061no—
1337C2×D4—1061no—
1338C2×D4C23×D5311yescharacteristic
1339C22×C4—21no—
1340C22×C4—21no—
1341C22×C4—531no—
1342C22×C4—531no—
1343C22×C4—1061no—
1344C22×C4—1061no—
1345C22×C4—1061no—
1346C22×C4—1061no—
1347C22×C4—1061no—
1348C22×C4—1061no—
1349C22×C4—1061no—
1350C22×C4—1061no—
1351C22×C4—1061no—
1352C22×C4—1061no—
1353C22×C4—1061no—
1354C22×C4—1061no—
1355C22×C4—1061no—
1356C22×C4—1061no—
1357C22×C4—1061no—
1358C22×C4—1061no—
1359C22×C4—1061no—
1360C22×C4—1061no—
1361C22×C4—1061no—
1362C22×C4—1061no—
1363C22×C4—4242no—
1364C22×C4C23×D5311yescharacteristic
1365SD16—1062no—
1366SD16—1062no—
1367D8—1062no—
1368D8—1062no—
1369D8—1062no—
1370D8—1062no—
1371D8—1062no—
1372D8—1062no—
1373C2×C8—531no—
1374C2×C8—531no—
1375C2×C8—531no—
1376C2×C8—531no—
1377C2×C8C23×D5311yescharacteristic
1378C2×C8C23×D5311yescharacteristic
1379C2×C8C23×D5311yescharacteristic
1380C2×C8C23×D5311yescharacteristic
1381C4⋊C4—21no—
1382C4⋊C4—21no—
1383C4⋊C4—21no—
1384C4⋊C4—21no—
1385C4⋊C4—21no—
1386C4⋊C4—21no—
1387C4⋊C4—21no—
1388C4⋊C4—21no—
1389C4⋊C4—21no—
1390C4⋊C4—21no—
1391C4⋊C4—531no—
1392C4⋊C4—531no—
1393C4⋊C4—531no—
1394C4⋊C4—531no—
1395C4⋊C4—531no—
1396C4⋊C4—531no—
1397C4⋊C4—531no—
1398C4⋊C4—531no—
1399C4⋊C4—531no—
1400C4⋊C4—531no—
1401C4⋊C4—531no—
1402C4⋊C4—531no—
1403C4⋊C4—531no—
1404C4⋊C4—531no—
1405C4⋊C4—531no—
1406C4⋊C4—531no—
1407C4⋊C4—531no—
1408C4⋊C4—531no—
1409C4⋊C4—1061no—
1410C4⋊C4—1061no—
1411C4⋊C4—1061no—
1412C4⋊C4—1061no—
1413C4⋊C4—1061no—
1414C4⋊C4—1061no—
1415C4⋊C4—1061no—
1416C4⋊C4—1061no—
1417C4⋊C4—1061no—
1418C4⋊C4—1061no—
1419C4⋊C4—1061no—
1420C4⋊C4—1061no—
1421C4⋊C4—1061no—
1422C4⋊C4—1061no—
1423C4⋊C4—1061no—
1424C4⋊C4—1061no—
1425C4⋊C4—1061no—
1426C4⋊C4—1061no—
1427C4⋊C4—1061no—
1428C4⋊C4—1061no—
1429C4⋊C4—1061no—
1430C4⋊C4—1061no—
1431C4⋊C4D4×D5311yescharacteristic
1432C4⋊C4D4×D5311yescharacteristic
1433C4⋊C4C23×D5311yescharacteristic
1434C4⋊C4C23×D5311yescharacteristic
1435C4⋊C4C23×D5311yescharacteristic
1436C4⋊C4C23×D5311yescharacteristic
1437C4⋊C4C23×D5311yescharacteristic
1438C4⋊C4C23×D5311yescharacteristic
1439C22⋊C4—21no—
1440C22⋊C4—21no—
1441C22⋊C4—21no—
1442C22⋊C4—21no—
1443C22⋊C4—21no—
1444C22⋊C4—21no—
1445C22⋊C4—531no—
1446C22⋊C4—531no—
1447C22⋊C4—1061no—
1448C22⋊C4—1061no—
1449C22⋊C4—1061no—
1450C22⋊C4—1061no—
1451C22⋊C4—1061no—
1452C22⋊C4—1061no—
1453C22⋊C4—1061no—
1454C22⋊C4—1061no—
1455C22⋊C4—1061no—
1456C22⋊C4—1061no—
1457C22⋊C4—1061no—
1458C22⋊C4—1061no—
1459C22⋊C4—1061no—
1460C22⋊C4—1061no—
1461C22⋊C4—1061no—
1462C22⋊C4—1061no—
1463C22⋊C4—1061no—
1464C22⋊C4—1061no—
1465C22⋊C4—1061no—
1466C22⋊C4—1061no—
1467C22⋊C4—1061no—
1468C22⋊C4—1061no—
1469C22⋊C4—1061no—
1470C22⋊C4—1061no—
1471C22⋊C4—1061no—
1472C22⋊C4—1061no—
1473C22⋊C4—1061no—
1474C22⋊C4D4×D5311yescharacteristic
1475C22⋊C4D4×D5311yescharacteristic
1476C42—21no—
1477C42—21no—
1478C42—531no—
1479C42—531no—
1480C42—531no—
1481C42—531no—
1482C42—531no—
1483C42—531no—
1484C42—1061no—
1485C42—1061no—
1486C42—1061no—
1487C42C23×D5311yescharacteristic
1488C42C23×D5311yescharacteristic
1489C23—21no—
1490C23—1064no—
1491C23—1061no—
1492C23—1061no—
1493C23—1061no—
1494C23—1061no—
1495C23—4241no—
1496C23—4241no—
1497C23C2×D4×D5311yescharacteristic
1498Q8—21no—
1499Q8—21no—
1500Q8—81no—
1501Q8—81no—
1502Q8—81no—
1503Q8—1062no—
1504Q8—1062no—
1505Q8—4241no—
1506Q8—4241no—
1507Q8—4241no—
1508Q8—4241no—
1509Q8—2121no—
1510Q8—2121no—
1511Q8—2122no—
1512Q8—2122no—
1513D4—21no—
1514D4—21no—
1515D4—81no—
1516D4—532no—
1517D4—532no—
1518D4—1064no—
1519D4—1061no—
1520D4—1061no—
1521D4—1061no—
1522D4—1061no—
1523D4—1061no—
1524D4—1061no—
1525D4—4241no—
1526D4—4241no—
1527D4—4241no—
1528D4—4241no—
1529D4—4241no—
1530D4—4241no—
1531D4—4241no—
1532D4—2122no—
1533C2×C4—21no—
1534C2×C4—21no—
1535C2×C4—21no—
1536C2×C4—21no—
1537C2×C4—21no—
1538C2×C4—21no—
1539C2×C4—21no—
1540C2×C4—21no—
1541C2×C4—21no—
1542C2×C4—81no—
1543C2×C4—81no—
1544C2×C4—531no—
1545C2×C4—531no—
1546C2×C4—531no—
1547C2×C4—531no—
1548C2×C4—531no—
1549C2×C4—531no—
1550C2×C4—531no—
1551C2×C4—531no—
1552C2×C4—1062no—
1553C2×C4—1061no—
1554C2×C4—1061no—
1555C2×C4—1061no—
1556C2×C4—1061no—
1557C2×C4—4241no—
1558C2×C4—4241no—
1559C2×C4—4241no—
1560C2×C4—4241no—
1561C2×C4—4241no—
1562C2×C4—4241no—
1563C2×C4—4241no—
1564C2×C4—4241no—
1565C2×C4—4241no—
1566C2×C4—4241no—
1567C2×C4—4241no—
1568C2×C4—4241no—
1569C2×C4—4241no—
1570C2×C4—4241no—
1571C2×C4—4241no—
1572C2×C4—4241no—
1573C2×C4—4241no—
1574C2×C4—2122no—
1575C2×C4—2122no—
1576C2×C4—2122no—
1577C2×C4—2121no—
1578C2×C4C2×D4×D5311yescharacteristic
1579C2×C4C2×D4×D5311yescharacteristic
1580C2×C4C2×D4×D5311yescharacteristic
1581C2×C4C2×D4×D5311yescharacteristic
1582C2×C4C2×D4×D5311yescharacteristic
1583C2×C4C24×D5311yescharacteristic
1584C8—21no—
1585C8—21no—
1586C8—21no—
1587C8—21no—
1588C8—1061no—
1589C8—1061no—
1590C8—1061no—
1591C8—1061no—
1592C22—21no—
1593C22—21no—
1594C22—21no—
1595C22—41no—
1596C22—41no—
1597C22—41no—
1598C22—1062no—
1599C22—1062no—
1600C22—4244no—
1601C22—2121no—
1602C22—2121no—
1603C22—2121no—
1604C22—2121no—
1605C22—2121no—
1606C22—2121no—
1607C22—2121no—
1608C22—2121no—
1609C22—2121no—
1610C22—2121no—
1611C22C22×D4×D5311yescharacteristic
1612C4—21no—
1613C4—21no—
1614C4—21no—
1615C4—21no—
1616C4—21no—
1617C4—41no—
1618C4—41no—
1619C4—41no—
1620C4—41no—
1621C4—41no—
1622C4—41no—
1623C4—41no—
1624C4—532no—
1625C4—1061no—
1626C4—1061no—
1627C4—1061no—
1628C4—1061no—
1629C4—1061no—
1630C4—1061no—
1631C4—1061no—
1632C4—2121no—
1633C4—2121no—
1634C4—2121no—
1635C4—2121no—
1636C42−1+4×D5311yescharacteristic
1637C42−1+4×D5311yescharacteristic
1638C2—41no—
1639C2—81no—
1640C2—4241no—
1641C2—4241no—
1642C2—2122no—
1643C2—2122no—
1644C2#2028836411yescharacteristic
1645C2#576×D5311yescharacteristic
1646C2#2028948511yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3243C2
socleC22×C53C23×D4
hypercenter#3243D53
hypocenterC53#61863
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ #117 ◁ #3243

Complements

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

NH ≅ G/Ntype
1. #20289184C2semidirect
2. #20288517C2semidirect
3. #20287670C2semidirect
4. #20287668C2semidirect
5. #20287639C2semidirect
6. #20287611C2semidirect
7. #20287593C2semidirect
8. #20287584C2semidirect
9. #20287577C2semidirect
10. #20287567C2semidirect
11. #20287504C2semidirect
12. #20287471C2semidirect
13. #20287467C2semidirect
14. #20287425C2semidirect
15. #20287374C2semidirect
16. #20287372C2semidirect
17. #20287372C2semidirect
18. #20287349C2semidirect
19. #20286002C2semidirect
20. #20285968C2semidirect
21. #20285964C2semidirect
22. #20285897C2semidirect
23. #20285849C2semidirect
24. #20284959C2semidirect
25. #20284954C2semidirect
26. #20284902C2semidirect
27. #20284893C2semidirect
28. #20284765C2semidirect
29. #20284712C2semidirect
30. #20283814C2semidirect
31. C53×#3243C2semidirect
34. #16811358C22semidirect
35. #16811355C22semidirect
36. #16811355C22semidirect
37. #16811349C22semidirect
41. #16811334C22semidirect
42. #16811332C22semidirect
49. #16811294C22semidirect
53. #16811288C22semidirect
75. #16811031C22semidirect
76. #16811031C22semidirect
77. #16811029C22semidirect
78. #16811027C22semidirect
79. #16811027C22semidirect
80. #16811024C22semidirect
81. #16811024C22semidirect
82. #16811023C22semidirect
83. #16811022C22semidirect
84. #16811020C22semidirect
85. #16810989C22semidirect
86. #16810986C22semidirect
87. #16810984C22semidirect
88. #16810979C22semidirect
89. #16810979C22semidirect
90. #16810979C22semidirect
91. #16810971C22semidirect
92. #16810968C22semidirect
93. #16810968C22semidirect
94. #16810968C22semidirect
103. #16810928C22semidirect
107. #16810926C22semidirect
108. #16810926C22semidirect
109. #16810926C22semidirect
110. #16810925C22semidirect
114. #16810922C22semidirect
115. #16810921C22semidirect
116. #16810921C22semidirect
117. #16810920C22semidirect
118. #16810920C22semidirect
119. #16810916C22semidirect
120. #16810916C22semidirect
122. #16810912C22semidirect
123. #16810911C22semidirect
125. #16810910C22semidirect
126. #16810906C22semidirect
130. #16810902C22semidirect
131. #16810902C22semidirect
132. #16810902C22semidirect
134. #16810900C22semidirect
151. #16810752C22semidirect
152. #16810752C22semidirect
153. #16810751C22semidirect
154. #16810751C22semidirect
155. C8×Dic106C22semidirect
156. C8×Dic106C22semidirect
157. #16810747C22semidirect
158. #16810747C22semidirect
190. C53×#501C22semidirect
191. C53×#500C22semidirect
192. C53×#489C22semidirect
193. C53×#488C22semidirect
198. C53×#479C22semidirect
199. C53×#478C22semidirect
200. C53×#477C22semidirect
201. C53×#474C22semidirect
834. #3243D53semidirect
903. #501C2×D53semidirect
906. #500C2×D53semidirect
915. #489C2×D53semidirect
919. #488C2×D53semidirect
937. #479C2×D53semidirect
953. #478C2×D53semidirect
956. #477C2×D53semidirect
971. #474C2×D53semidirect
1026. C53#61863semidirect

Maximal subgroups

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

subgroupindex
#202891842
#202885172
#202876702
#202876682
#202876392
#202876112
#202875932
#202875842
#202875772
#202875672
#202875042
#202874712
#202874672
#202874252
#202873742
#202873722
#202873492
#202860022
#202859682
#202859642
#202858972
#202858492
#202849592
#202849542
#202849022
#202848932
#202847652
#202847122
#202838142
C53×#32432
#6186353