Finite Group Databasebeta

← #28261488

Subgroups — #28261488

Order 13568.

2230 conjugacy classes of subgroups.

The subgroup lattice has 1898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288429C211yesmaximal, characteristic, complemented
2#20288343C211yesmaximal, characteristic, complemented
3#20286956C211yesmaximal, characteristic, complemented
4#20286953C211yesmaximal, characteristic, complemented
5#20286941C211yesmaximal, characteristic, complemented
6#20286936C211yesmaximal, characteristic, complemented
7#20286926C211yesmaximal, characteristic, complemented
8#20286918C211yesmaximal, characteristic, complemented
9#20286912C211yesmaximal, characteristic, complemented
10#20286869C211yesmaximal, characteristic, complemented
11#20286868C211yesmaximal, characteristic, complemented
12#20286859C211yesmaximal, characteristic, complemented
13#20286856C211yesmaximal, characteristic, complemented
14#20286745C211yesmaximal, characteristic, complemented
15#20286744C211yesmaximal, characteristic, complemented
16#20286743C211yesmaximal, characteristic, complemented
17#20286740C211yesmaximal, characteristic, complemented
18#20285064C211yesmaximal, characteristic, complemented
19#20284670C211yesmaximal, characteristic, complemented
20#20284643C211yesmaximal, characteristic, complemented
21#20284539C211yesmaximal, characteristic, complemented
22#20284390C211yesmaximal, characteristic, complemented
23#20284319C211yesmaximal, characteristic, complemented
24#20284251C211yesmaximal, characteristic, complemented
25#20284020C211yesmaximal, characteristic, complemented
26#20283943C211yesmaximal, characteristic, complemented
27#20283542C211yesmaximal, characteristic, complemented
28#20283415C211yesmaximal, characteristic, complemented
29#20283240C211yesmaximal, characteristic, complemented
30#418×D53C211yesmaximal, characteristic, complemented
31C53×#3324C211yesmaximal, characteristic, complemented
32C2×#13133262C2211yescharacteristic
33C22×D4×D53C2211yescharacteristic
34C2×#13133244C2211yescharacteristic
35C2×#13133244C2211yescharacteristic, complemented
36C2×#13133238C2211yescharacteristic, complemented
37C2×#13133225C2211yescharacteristic, complemented
38C2×M16×D53C2211yescharacteristic, complemented
39#16811345—21no—
40#16811344C2211yescharacteristic, complemented
41#16811339C2211yescharacteristic, complemented
42#16811336C2211yescharacteristic, complemented
43#16811335—21no—
44#16811324—21no—
45#16811319C2211yescharacteristic, complemented
46#16811317C2211yescharacteristic, complemented
47#16811315C2211yescharacteristic, complemented
48#16811314C2211yescharacteristic, complemented
49#16811309—21no—
50#16811270C2211yescharacteristic
51#16811269C2211yescharacteristic
52#16811268C2211yescharacteristic
53#16811267C2211yescharacteristic
54#16811262—21no—
55#16811260—21no—
56#16811258C2211yescharacteristic
57#16811257C2211yescharacteristic
58D4×C22⋊D53—21no—
59D4×C22⋊D53C2211yescharacteristic
60#16811255—21no—
61#16811250C2211yescharacteristic, complemented
62#16811212—21no—
63#16811207—21no—
64#16811203C2211yescharacteristic, complemented
65#16811189C2211yescharacteristic
66#16811186C2211yescharacteristic
67#16811183—21no—
68#16811181—21no—
69#16811160—21no—
70#16811156—21no—
71#16811136C2211yescharacteristic, complemented
72#16811133C2211yescharacteristic
73#16811132C2211yescharacteristic
74C2×#13133185—21no—
75#120×D53—21no—
76#16811105C2211yescharacteristic, complemented
77#16811103C2211yescharacteristic, complemented
78#16811095C2211yescharacteristic
79#117×D53C2211yescharacteristic, complemented
80#16810987C2211yescharacteristic, complemented
81#16810986C2211yescharacteristic, complemented
82#16810985C2211yescharacteristic, complemented
83#16810981C2211yescharacteristic, complemented
84#16810978C2211yescharacteristic, complemented
85#16810976C2211yescharacteristic, complemented
86#16810968C2211yescharacteristic, complemented
87#16810967C2211yescharacteristic, complemented
88#16810966C2211yescharacteristic, complemented
89#16810965C2211yescharacteristic, complemented
90#16810964C2211yescharacteristic, complemented
91#16810950C2211yescharacteristic, complemented
92#16810947C2211yescharacteristic, complemented
93#16810946C2211yescharacteristic, complemented
94#16810945C2211yescharacteristic, complemented
95#16810945C2211yescharacteristic, complemented
96#16810944C2211yescharacteristic, complemented
97#16810943C2211yescharacteristic, complemented
98#16810939C2211yescharacteristic, complemented
99#16810937C2211yescharacteristic, complemented
100#16810935C2211yescharacteristic, complemented
101#16810926C2211yescharacteristic, complemented
102#16810924C2211yescharacteristic, complemented
103#16810923C2211yescharacteristic, complemented
104#16810921C2211yescharacteristic, complemented
105#16810911C2211yescharacteristic, complemented
106#16810910C2211yescharacteristic, complemented
107#16810902C2211yescharacteristic, complemented
108#16810880C2211yescharacteristic, complemented
109#16810879C2211yescharacteristic, complemented
110#16810876C2211yescharacteristic, complemented
111#16810875C2211yescharacteristic, complemented
112#16810875C2211yescharacteristic, complemented
113#16810874C2211yescharacteristic, complemented
114#16810872C2211yescharacteristic, complemented
115#16810870C2211yescharacteristic, complemented
116#16810869C2211yescharacteristic, complemented
117#16810866C2211yescharacteristic, complemented
118#16810860C2211yescharacteristic, complemented
119#16810857C2211yescharacteristic, complemented
120#16810854C2211yescharacteristic, complemented
121#16810849C2211yescharacteristic, complemented
122#16810845C2211yescharacteristic, complemented
123#16810843C2211yescharacteristic, complemented
124#16810839C2211yescharacteristic, complemented
125#16810837C2211yescharacteristic, complemented
126#16810821C2211yescharacteristic, complemented
127#16810817C2211yescharacteristic, complemented
128#16810815C2211yescharacteristic, complemented
129#16810783C2211yescharacteristic, complemented
130#16810782C2211yescharacteristic, complemented
131#16810773C2211yescharacteristic, complemented
132#16810772C2211yescharacteristic, complemented
133#16810772C2211yescharacteristic, complemented
134#16810772C2211yescharacteristic, complemented
135#16810770C2211yescharacteristic, complemented
136#16810769C2211yescharacteristic, complemented
137#16810759C2211yescharacteristic, complemented
138#16810758C2211yescharacteristic, complemented
139#16810758C2211yescharacteristic, complemented
140#16810758C2211yescharacteristic, complemented
141#16810757C2211yescharacteristic, complemented
142#16810757C2211yescharacteristic, complemented
143#16810734C2211yescharacteristic, complemented
144#16810733C2211yescharacteristic, complemented
145#16810724C2211yescharacteristic, complemented
146#16810721C2211yescharacteristic, complemented
147#16810708C2211yescharacteristic, complemented
148C4×D424C2211yescharacteristic, complemented
149#16810703C2211yescharacteristic, complemented
150#16810702C2211yescharacteristic, complemented
151#16810699C2211yescharacteristic, complemented
152#16810699C2211yescharacteristic, complemented
153#16810697C2211yescharacteristic, complemented
154#16810695C2211yescharacteristic, complemented
155#16810693C2211yescharacteristic, complemented
156#16810691C2211yescharacteristic, complemented
157#16810664C2211yescharacteristic, complemented
158#16810662C2211yescharacteristic, complemented
159#16810660C2211yescharacteristic, complemented
160#16810648C2211yescharacteristic, complemented
161#16810629C2211yescharacteristic, complemented
162#16810628C2211yescharacteristic, complemented
163#16810627C2211yescharacteristic, complemented
164#16810626C2211yescharacteristic
165#16810626C2211yescharacteristic, complemented
166#16810626C2211yescharacteristic, complemented
167#16810626C2211yescharacteristic, complemented
168#16810626C2211yescharacteristic, complemented
169#16810626C2211yescharacteristic, complemented
170#16810626C2211yescharacteristic, complemented
171#16810625C2211yescharacteristic, complemented
172#16810621C2211yescharacteristic, complemented
173#16810621C2211yescharacteristic, complemented
174#16810621C2211yescharacteristic, complemented
175#16810618C2211yescharacteristic, complemented
176#16810617C2211yescharacteristic, complemented
177#16810616C2211yescharacteristic, complemented
178#16810616C2211yescharacteristic, complemented
179C2×#13133138C2211yescharacteristic, complemented
180#102×D53C2211yescharacteristic
181#102×D53C2211yescharacteristic
182#102×D53C2211yescharacteristic, complemented
183#102×D53C2211yescharacteristic, complemented
184#102×D53C2211yescharacteristic, complemented
185#16810588C2211yescharacteristic, complemented
186#16810585C2211yescharacteristic, complemented
187#16810577C2211yescharacteristic, complemented
188C53×#556C2211yescharacteristic, complemented
189D42×C53C2211yescharacteristic
190C53×#486C2211yescharacteristic, complemented
191C53×#482C2211yescharacteristic, complemented
192C53×#482C2211yescharacteristic, complemented
193C53×#474C2211yescharacteristic, complemented
194C53×#468C2211yescharacteristic, complemented
195C53×#468C2211yescharacteristic, complemented
196C53×#460C2211yescharacteristic, complemented
197C53×#450C2211yescharacteristic, complemented
198C53×#450C2211yescharacteristic, complemented
199C4×SD16×C53C2211yescharacteristic, complemented
200C53×#436C2211yescharacteristic, complemented
201C53×#418C2211yescharacteristic, complemented
202C53×#418C2211yescharacteristic, complemented
203C24×D53—21no—
204#13133262—24no—
205#13133262—42no—
206C2×#11719949C2311yescharacteristic
207C2×#11719945C2311yescharacteristic
208C2×#11719945C2311yescharacteristic
209C2×#11719947—21no—
210C2×#11719947C2311yescharacteristic
211C2×#11719947C2311yescharacteristic
212C22×D212C2311yescharacteristic
213C22×C22⋊D53—21no—
214C22×C22⋊D53—21no—
215C22×C22⋊D53—21no—
216C22×C22⋊D53—21no—
217C2×D4×D53—24no—
218C2×D4×D53—21no—
219C2×D4×D53—21no—
220C2×D4×D53—21no—
221C2×D4×D53—21no—
222C2×D4×D53—21no—
223C2×D4×D53—42no—
224C2×D4×D53C2311yescharacteristic
225C2×D4×D53C2311yescharacteristic
226C2×D4×D53C2311yescharacteristic
227C2×D4×D53C2311yescharacteristic
228C2×D4×D53C2311yescharacteristic
229C22×C4×D53C2311yescharacteristic
230#13133244—24no—
231#13133244—42no—
232#13133238—42no—
233C2×#11719925C2311yescharacteristic, complemented
234C2×#11719913C2311yescharacteristic, complemented
235C2×#11719924C2311yescharacteristic
236C2×#11719924C2311yescharacteristic
237C2×D424C2311yescharacteristic
238C2×D424C2311yescharacteristic
239C2×#11719922C2311yescharacteristic
240C2×#11719922C2311yescharacteristic
241C2×#11719922C2311yescharacteristic, complemented
242#13133225—42no—
243C2×#11719917C2311yescharacteristic
244C2×#11719912C2311yescharacteristic
245C2×#11719912C2311yescharacteristic
246C2×#11719912C2311yescharacteristic
247C2×#11719912C2311yescharacteristic
248C2×#11719912C2311yescharacteristic, complemented
249M16×D53—42no—
250C22×#88322C2311yescharacteristic, complemented
251C2×C8×D53C2311yescharacteristic
252C2×C8×D53C2311yescharacteristic
253C2×C8×D53C2311yescharacteristic, complemented
254#13133216C2311yescharacteristic, complemented
255#13133215—21no—
256#13133213—21no—
257#13133213C2311yescharacteristic
258#13133212—21no—
259#13133212—21no—
260#13133212—21no—
261#13133211—21no—
262#13133211—21no—
263#13133210—21no—
264#13133209C2311yescharacteristic, complemented
265#13133208—21no—
266#13133208C2311yescharacteristic, complemented
267#13133207—21no—
268#13133207—21no—
269#13133206—21no—
270#13133206—21no—
271#13133205—21no—
272#13133205C2311yescharacteristic
273#13133204C2311yescharacteristic
274#13133203—21no—
275#13133203—21no—
276#13133203—21no—
277#13133202—21no—
278#13133202—21no—
279#13133202—21no—
280#13133202D411yescharacteristic
281#13133201—21no—
282#13133201—21no—
283#13133199—21no—
284#13133199—21no—
285#13133199—21no—
286#13133199—21no—
287#13133199D411yescharacteristic
288#13133198—21no—
289#13133197C2311yescharacteristic
290#13133196C2311yescharacteristic
291#13133195—21no—
292#13133195—21no—
293#13133195D411yescharacteristic
294#13133194D411yescharacteristic
295#13133193—21no—
296#13133193C2311yescharacteristic
297#13133193C2311yescharacteristic, complemented
298#13133192—21no—
299#13133192—21no—
300#13133192C2311yescharacteristic
301#13133192C2311yescharacteristic
302#13133192C2311yescharacteristic, complemented
303#13133191—21no—
304#13133191C2311yescharacteristic
305#13133191C2311yescharacteristic
306#13133191C2311yescharacteristic, complemented
307#13133190—21no—
308#13133190—21no—
309#13133190—21no—
310#13133190—21no—
311#13133190—21no—
312#13133190—21no—
313#13133190D411yescharacteristic
314#13133189—21no—
315#13133189—21no—
316#13133189—21no—
317#13133189—21no—
318#13133189—21no—
319#13133189D411yescharacteristic
320#13133188—21no—
321#13133188—21no—
322#13133188C2311yescharacteristic
323#13133188C2311yescharacteristic
324#13133187—21no—
325#13133187—21no—
326#13133187—21no—
327#13133187—21no—
328#13133187D411yescharacteristic
329#13133186—21no—
330#13133186—21no—
331#13133185—21no—
332#13133185—21no—
333#13133185—21no—
334#13133185—21no—
335#13133185—21no—
336#13133185—21no—
337#13133185—21no—
338#13133185—21no—
339#13133185—21no—
340#13133185—21no—
341#13133185D411yescharacteristic
342Q8×Dic53C2311yescharacteristic, complemented
343C4×Dic106—21no—
344#13133182—21no—
345C4×D212—21no—
346C4×D212—21no—
347C4×D212—21no—
348C4×D212C2311yescharacteristic
349C4×D212C2311yescharacteristic
350C4×D212C2311yescharacteristic, complemented
351D4×Dic53—21no—
352D4×Dic53C2311yescharacteristic
353#13133179—21no—
354#13133179—21no—
355#13133179C2311yescharacteristic
356#13133179C2311yescharacteristic, complemented
357C4×C22⋊D53—21no—
358C4×C22⋊D53C2311yescharacteristic
359C4×C22⋊D53C2311yescharacteristic
360#13133177—21no—
361#13133177—21no—
362#13133177—21no—
363#13133177—21no—
364#13133177—21no—
365#13133177—21no—
366#13133176C2311yescharacteristic
367#13133175—21no—
368#13133175C2311yescharacteristic
369#13133175C2311yescharacteristic
370#13133175C2311yescharacteristic
371#13133175C2311yescharacteristic
372#13133175C2311yescharacteristic, complemented
373#13133174—21no—
374#13133174—21no—
375#13133174—21no—
376#13133174—21no—
377#13133174C2311yescharacteristic
378#13133173—21no—
379#13133173—21no—
380C2×C4⋊Dic53C2311yescharacteristic, complemented
381C4⋊C4×D53—21no—
382C4⋊C4×D53C2311yescharacteristic
383C4⋊C4×D53C2311yescharacteristic
384C4⋊C4×D53C2311yescharacteristic, complemented
385C2×C22⋊Dic53—21no—
386C2×#11719921—21no—
387C2×#11719921—21no—
388C22⋊C4×D53—21no—
389C22⋊C4×D53—21no—
390C22⋊C4×D53—21no—
391C22⋊C4×D53—21no—
392C42×D53—21no—
393#13133151C2311yescharacteristic, complemented
394#13133151C2311yescharacteristic, complemented
395#13133150C2311yescharacteristic, complemented
396#13133150C2311yescharacteristic, complemented
397#13133149C2311yescharacteristic, complemented
398#13133148C2311yescharacteristic, complemented
399#13133148C2311yescharacteristic, complemented
400#13133148C2311yescharacteristic, complemented
401#13133148C2311yescharacteristic, complemented
402C4⋊#88322C2311yescharacteristic, complemented
403#13133146C2311yescharacteristic, complemented
404#13133146C2311yescharacteristic, complemented
405#13133142C2311yescharacteristic, complemented
406#13133142C2311yescharacteristic, complemented
407#13133142C2311yescharacteristic, complemented
408#13133141C2311yescharacteristic, complemented
409#13133140C2311yescharacteristic, complemented
410#13133140C2311yescharacteristic, complemented
411#13133140C2311yescharacteristic, complemented
412#13133139C2311yescharacteristic
413#13133139C2311yescharacteristic
414#13133139C2311yescharacteristic
415#13133139C2311yescharacteristic
416#13133139C2311yescharacteristic
417#13133139C2311yescharacteristic
418#13133139C2311yescharacteristic, complemented
419#13133138C2311yescharacteristic
420#13133138C2311yescharacteristic
421#13133138C2311yescharacteristic
422#13133138C2311yescharacteristic
423#13133138C2311yescharacteristic
424#13133138C2311yescharacteristic
425#13133138C2311yescharacteristic, complemented
426#13133138C2311yescharacteristic, complemented
427#13133138C2311yescharacteristic, complemented
428#13133137C2311yescharacteristic
429#13133137C2311yescharacteristic
430#13133137C2311yescharacteristic
431#13133137C2311yescharacteristic
432#13133137C2311yescharacteristic
433#13133137C2311yescharacteristic
434#13133137C2311yescharacteristic, complemented
435C22⋊#88322C2311yescharacteristic
436C22⋊#88322C2311yescharacteristic, complemented
437#13133129C2311yescharacteristic
438#13133129C2311yescharacteristic
439#13133129C2311yescharacteristic, complemented
440#13133129C2311yescharacteristic, complemented
441#13133128C2311yescharacteristic, complemented
442#13133127C2311yescharacteristic, complemented
443C8×Dic53C2311yescharacteristic, complemented
444C22×D4×C53—21no—
445C22×D4×C53C2311yescharacteristic
446C22×D4×C53C2311yescharacteristic
447C2×SD16×C53C2311yescharacteristic
448C2×SD16×C53C2311yescharacteristic
449C2×SD16×C53C2311yescharacteristic, complemented
450C2×M16×C53C2311yescharacteristic
451C2×M16×C53C2311yescharacteristic, complemented
452C4⋊Q8×C53C2311yescharacteristic, complemented
453#127×C53C2311yescharacteristic
454#126×C53—21no—
455#126×C53—21no—
456#124×C53—21no—
457C22⋊Q8×C53C2311yescharacteristic
458C22⋊Q8×C53C2311yescharacteristic, complemented
459#121×C53—21no—
460#121×C53C2311yescharacteristic
461#121×C53C2311yescharacteristic
462#120×C53—21no—
463#120×C53—21no—
464C4×Q8×C53—21no—
465C4×Q8×C53C2311yescharacteristic, complemented
466C4×D4×C53C2311yescharacteristic
467C4×D4×C53C2311yescharacteristic
468#117×C53C2311yescharacteristic
469#117×C53C2311yescharacteristic, complemented
470#107×C53C2311yescharacteristic, complemented
471#107×C53C2311yescharacteristic, complemented
472#106×C53C2311yescharacteristic, complemented
473C4⋊C8×C53C2311yescharacteristic, complemented
474#103×C53C2311yescharacteristic, complemented
475#102×C53C2311yescharacteristic
476#102×C53C2311yescharacteristic
477#102×C53C2311yescharacteristic
478#102×C53C2311yescharacteristic
479#102×C53C2311yescharacteristic
480#102×C53C2311yescharacteristic
481#102×C53C2311yescharacteristic, complemented
482#102×C53C2311yescharacteristic, complemented
483#102×C53C2311yescharacteristic, complemented
484C22⋊C8×C53C2311yescharacteristic
485C22⋊C8×C53C2311yescharacteristic, complemented
486C4×C8×C53C2311yescharacteristic, complemented
487C24×C53—21no—
488C24×C53—21no—
489C23×D53—21no—
490C23×D53—21no—
491C23×D53—21no—
492C23×D53—21no—
493C23×D53—21no—
494C23×D53—21no—
495C23×D53—44no—
496C23×D53—82no—
497C23×D53—82no—
498C23×D53C2×D411yescharacteristic
499C2×Q8×C53—21no—
500C2×Q8×C53C2411yescharacteristic
501C2×D4×C53—22no—
502C2×D4×C53—22no—
503C2×D4×C53—21no—
504C2×D4×C53—21no—
505C2×D4×C53—21no—
506C2×D4×C53—21no—
507C2×D4×C53—21no—
508C2×D4×C53—21no—
509C2×D4×C53—41no—
510C2×D4×C53—41no—
511C2×D4×C53—82no—
512C2×D4×C53C2×D411yescharacteristic
513C2×D4×C53C2411yescharacteristic
514C2×D4×C53C2411yescharacteristic
515C2×D4×C53C2411yescharacteristic
516C22×C4×C53—21no—
517C22×C4×C53C2411yescharacteristic
518C22×C4×C53C2411yescharacteristic
519C2×C22⋊D53—21no—
520C2×C22⋊D53—21no—
521C2×C22⋊D53—21no—
522C2×C22⋊D53—21no—
523C2×C22⋊D53—21no—
524C2×C22⋊D53—21no—
525C2×C22⋊D53—21no—
526C2×C22⋊D53—21no—
527C2×C22⋊D53—21no—
528C2×C22⋊D53—21no—
529C2×C22⋊D53—21no—
530C2×C22⋊D53—21no—
531C2×C22⋊D53—21no—
532C2×C22⋊D53—21no—
533C2×C22⋊D53—21no—
534C2×C22⋊D53—44no—
535C2×C22⋊D53—44no—
536C2×C22⋊D53—44no—
537C2×C22⋊D53—82no—
538C2×C22⋊D53C2×D411yescharacteristic
539C2×C22⋊D53C2×D411yescharacteristic
540C2×C22⋊D53C2×D411yescharacteristic
541C2×C22⋊D53C2×D411yescharacteristic
542C22×Dic53—21no—
543C22×Dic53—21no—
544C22×Dic53—21no—
545C22×Dic53—21no—
546C22×Dic53C2×D411yescharacteristic
547#11719949—22no—
548#11719949—22no—
549#11719947—22no—
550#11719947—22no—
551#11719947—22no—
552#11719947—41no—
553#11719947—44no—
554D4×D53—22no—
555D4×D53—22no—
556D4×D53—22no—
557D4×D53—22no—
558D4×D53—22no—
559D4×D53—22no—
560D4×D53—41no—
561D4×D53—41no—
562D4×D53—41no—
563D4×D53—44no—
564D4×D53—44no—
565D4×D53—44no—
566D4×D53—82no—
567D4×D53—82no—
568D4×D53#4114yes—
569#11719945—22no—
570#11719945—22no—
571#11719945—22no—
572#11719945—41no—
573C2×D212—22no—
574C2×D212—21no—
575C2×D212—21no—
576C2×D212—21no—
577C2×D212—21no—
578C2×D212—21no—
579C2×D212—41no—
580C2×D212C2×D411yescharacteristic
581C2×D212C2×D411yescharacteristic
582C2×D212C2411yescharacteristic
583C2×D212C2411yescharacteristic
584C2×D212C2411yescharacteristic
585C2×C4×D53—22no—
586C2×C4×D53—22no—
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—21no—
596C2×C4×D53C2×D411yescharacteristic
597C2×C4×D53C2×D411yescharacteristic
598C2×C4×D53C2411yescharacteristic
599C2×C4×D53C2411yescharacteristic
600C2×C4×D53C2411yescharacteristic
601C2×Dic106—21no—
602C2×Dic106C2×D411yescharacteristic
603C2×Dic106C2411yescharacteristic
604SD16×C53—22no—
605SD16×C53—41no—
606SD16×C53—41no—
607M16×C53—41no—
608M16×C53—41no—
609C2×C8×C53C2411yescharacteristic
610C2×C8×C53C2411yescharacteristic
611C2×C8×C53C2411yescharacteristic
612C2×C8×C53C2411yescharacteristic
613C4⋊C4×C53—21no—
614C4⋊C4×C53—21no—
615C4⋊C4×C53—21no—
616C4⋊C4×C53—21no—
617C4⋊C4×C53C2×D411yescharacteristic
618C4⋊C4×C53C2411yescharacteristic
619C4⋊C4×C53C2411yescharacteristic
620C4⋊C4×C53C2411yescharacteristic
621C4⋊C4×C53C2411yescharacteristic
622C22⋊C4×C53—21no—
623C22⋊C4×C53—21no—
624C22⋊C4×C53—21no—
625C22⋊C4×C53—21no—
626C22⋊C4×C53—21no—
627C22⋊C4×C53—21no—
628C22⋊C4×C53—21no—
629C22⋊C4×C53C2×D411yescharacteristic
630C22⋊C4×C53C2×D411yescharacteristic
631C42×C53—21no—
632C42×C53—21no—
633C42×C53—21no—
634C42×C53C2411yescharacteristic
635C22⋊Dic53—21no—
636C22⋊Dic53—21no—
637C22⋊Dic53—21no—
638C22⋊Dic53—21no—
639C22⋊Dic53—21no—
640C22⋊Dic53—21no—
641C22⋊Dic53—21no—
642C22⋊Dic53C2×D411yescharacteristic
643C22⋊Dic53C2×D411yescharacteristic
644#11719925—41no—
645#11719924—22no—
646#11719924—41no—
647#11719922—22no—
648#11719922—41no—
649#11719922—41no—
650#11719921—21no—
651#11719921—21no—
652#11719921—21no—
653#11719921—21no—
654#11719921—21no—
655#11719921—21no—
656#11719921—21no—
657#11719921—21no—
658#11719921—21no—
659#11719921—21no—
660#11719921—21no—
661#11719921—21no—
662#11719921—21no—
663#11719921—21no—
664#11719921—21no—
665#11719921—21no—
666#11719921—21no—
667#11719921—21no—
668#11719921—21no—
669#11719921—21no—
670#11719921C2×D411yescharacteristic
671#11719921C2×D411yescharacteristic
672#11719921C2×D411yescharacteristic
673#11719921C2×D411yescharacteristic
674#11719921C2×D411yescharacteristic
675#11719921C2×D411yescharacteristic
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#11719919C2×D411yescharacteristic
696#11719919C2×D411yescharacteristic
697#11719919C2×D411yescharacteristic
698#11719919C2×D411yescharacteristic
699C4×Dic53—21no—
700C4×Dic53—21no—
701C4×Dic53—21no—
702C4×Dic53—21no—
703C4×Dic53—21no—
704C4×Dic53—21no—
705C4×Dic53—21no—
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—
720#11719912—41no—
721C8×D53—22no—
722C8×D53—22no—
723C8×D53—41no—
724C23×C53—21no—
725C23×C53—21no—
726C23×C53—21no—
727C23×C53—42no—
728C23×C53—42no—
729C23×C53—42no—
730C23×C53—81no—
731C23×C53—81no—
732C23×C53—81no—
733C23×C53C22×D411yescharacteristic
734C23×C53C22×D411yescharacteristic
735C22×D53—21no—
736C22×D53—22no—
737C22×D53—24no—
738C22×D53—21no—
739C22×D53—21no—
740C22×D53—41no—
741C22×D53—41no—
742C22×D53—42no—
743C22×D53—42no—
744C22×D53—42no—
745C22×D53—42no—
746C22×D53—42no—
747C22×D53—42no—
748C22×D53—42no—
749C22×D53—42no—
750C22×D53—81no—
751C22×D53—81no—
752C22×D53—81no—
753C22×D53—81no—
754C22×D53—81no—
755C22×D53—81no—
756C22×D53—81no—
757C22×D53—81no—
758C22×D53—81no—
759C22×D53—816no—
760C22×D53C22×D411yescharacteristic
761C22×D53C22×D411yescharacteristic
762C22×D53C22×D411yescharacteristic
763Q8×C53—21no—
764Q8×C53—21no—
765Q8×C53—81no—
766D4×C53—21no—
767D4×C53—21no—
768D4×C53—21no—
769D4×C53—21no—
770D4×C53—21no—
771D4×C53—41no—
772D4×C53—42no—
773D4×C53—42no—
774D4×C53—42no—
775D4×C53—81no—
776D4×C53—81no—
777D4×C53—81no—
778D4×C53C2×#4112yes—
779C2×C4×C53—21no—
780C2×C4×C53—21no—
781C2×C4×C53—21no—
782C2×C4×C53—21no—
783C2×C4×C53—21no—
784C2×C4×C53—21no—
785C2×C4×C53—21no—
786C2×C4×C53—21no—
787C2×C4×C53—21no—
788C2×C4×C53—81no—
789C2×C4×C53C22×D411yescharacteristic
790C2×C4×C53C22×D411yescharacteristic
791C2×C4×C53C22×D411yescharacteristic
792C2×C4×C53C22×D411yescharacteristic
793C2×C4×C53C2511yescharacteristic
794C22⋊D53—22no—
795C22⋊D53—22no—
796C22⋊D53—24no—
797C22⋊D53—41no—
798C22⋊D53—41no—
799C22⋊D53—42no—
800C22⋊D53—42no—
801C22⋊D53—42no—
802C22⋊D53—42no—
803C22⋊D53—42no—
804C22⋊D53—42no—
805C22⋊D53—42no—
806C22⋊D53—42no—
807C22⋊D53—81no—
808C22⋊D53—81no—
809C22⋊D53—81no—
810C22⋊D53—81no—
811C22⋊D53—81no—
812C22⋊D53—81no—
813C2×Dic53—22no—
814C2×Dic53—21no—
815C2×Dic53—21no—
816C2×Dic53—21no—
817C2×Dic53—21no—
818C2×Dic53—21no—
819C2×Dic53—42no—
820C2×Dic53—42no—
821C2×Dic53—81no—
822C2×Dic53—81no—
823C2×Dic53C22×D411yescharacteristic
824C2×Dic53C22×D411yescharacteristic
825C2×Dic53C22×D411yescharacteristic
826C2×Dic53C22×D411yescharacteristic
827C2×Dic53C22×D411yescharacteristic
828D212—22no—
829D212—21no—
830D212—21no—
831D212—21no—
832D212—21no—
833D212—21no—
834D212—41no—
835D212—42no—
836D212—42no—
837D212—81no—
838D212—81no—
839D212—81no—
840D212C2×#4112yes—
841C4×D53—22no—
842C4×D53—21no—
843C4×D53—21no—
844C4×D53—21no—
845C4×D53—21no—
846C4×D53—22no—
847C4×D53—42no—
848C4×D53—42no—
849C4×D53—81no—
850C4×D53—81no—
851C4×D53—81no—
852C4×D53—81no—
853C4×D53—81no—
854C4×D53—81no—
855C4×D53—81no—
856C4×D53C2×#4112yes—
857C4×D53H(5,𝔽2)12yes—
858Dic106—22no—
859Dic106—21no—
860Dic106—21no—
861Dic106—81no—
862C8×C53—21no—
863C8×C53—21no—
864C8×C53—21no—
865C8×C53—21no—
866#88322—21no—
867#88322—21no—
868#88322—21no—
869#88322—21no—
870#61175—531nomaximal, Sylow
871C22×C53—21no—
872C22×C53—21no—
873C22×C53—21no—
874C22×C53—21no—
875C22×C53—21no—
876C22×C53—22no—
877C22×C53—21no—
878C22×C53—41no—
879C22×C53—41no—
880C22×C53—41no—
881C22×C53—41no—
882C22×C53—41no—
883C22×C53—41no—
884C22×C53—41no—
885C22×C53—41no—
886C22×C53—84no—
887C22×C53—162no—
888C22×C53C23×D411yescharacteristic
889C2×D53—21no—
890C2×D53—21no—
891C2×D53—21no—
892C2×D53—21no—
893C2×D53—21no—
894C2×D53—21no—
895C2×D53—21no—
896C2×D53—21no—
897C2×D53—22no—
898C2×D53—44no—
899C2×D53—41no—
900C2×D53—41no—
901C2×D53—41no—
902C2×D53—41no—
903C2×D53—41no—
904C2×D53—41no—
905C2×D53—41no—
906C2×D53—41no—
907C2×D53—84no—
908C2×D53—84no—
909C2×D53—84no—
910C2×D53—84no—
911C2×D53—84no—
912C2×D53—162no—
913C2×D53#54612yes—
914C4×C53—21no—
915C4×C53—21no—
916C4×C53—21no—
917C4×C53—21no—
918C4×C53—41no—
919C4×C53—41no—
920C4×C53—41no—
921C4×C53—41no—
922C4×C53—41no—
923C4×C53C22×#4111yescharacteristic
924C4×C53C2×H(5,𝔽2)11yescharacteristic
925Dic53—21no—
926Dic53—21no—
927Dic53—21no—
928Dic53—21no—
929Dic53—41no—
930Dic53—41no—
931Dic53—41no—
932Dic53—41no—
933Dic53—41no—
934Dic53#54612yes—
935#3493—531no—
936#3484—531no—
937#3325—531no—
938#3325—531no—
939#3324—531no—
940#3324D5311yescharacteristic, complemented
941#3323—531no—
942#3323—531no—
943#3322—531no—
944#3322—531no—
945#3319—531no—
946#3319—531no—
947#3318—531no—
948#3318—531no—
949#3311—531no—
950#3311—531no—
951#3310—531no—
952#3310—531no—
953#3136—531no—
954#3096—531no—
955#3093—531no—
956#3081—531no—
957#3062—531no—
958#3054—531no—
959#3045—531no—
960#3012—531no—
961#3003—531no—
962#2946—531no—
963#2930—531no—
964#2897—531no—
965C2×#418—531no—
966C2×C53—41no—
967C2×C53—42no—
968C2×C53—41no—
969C2×C53—81no—
970C2×C53—81no—
971C2×C53C2×#54611yescharacteristic
972C2×C53#358511yescharacteristic
973C2×C53#358511yescharacteristic
974D53—22no—
975D53—41no—
976D53—41no—
977D53—42no—
978D53—81no—
979D53—81no—
980C2×H(5,𝔽2)—531no—
981C23×D4—531no—
982C2×AGL(1,ℤ/8)—531no—
983C2×AGL(1,ℤ/8)—531no—
984C2×#135—531no—
985C2×#131—531no—
986C22×M16—531no—
987#556—531no—
988#556—1061no—
989#556C2×D5311yescharacteristic, complemented
990#555—531no—
991#555—531no—
992#555—1061no—
993#553—531no—
994#553—531no—
995#553—1061no—
996#552—531no—
997#552—531no—
998#552—1061no—
999#546—531no—
1000#546—531no—
1001#546—531no—
1002#546—531no—
1003#546—1061no—
1004#546—1061no—
1005D42—531no—
1006D42—531no—
1007D42—531no—
1008D42—1061no—
1009D42—1061no—
1010D42C2×D5311yescharacteristic
1011#544—531no—
1012#538—1061no—
1013#538—1061no—
1014#537—531no—
1015#535—531no—
1016#535—531no—
1017#534—1061no—
1018#534—1061no—
1019#529—1061no—
1020#529—1061no—
1021#525—531no—
1022#525—531no—
1023#525—531no—
1024C2×#120—1061no—
1025C2×#120—1061no—
1026#520—531no—
1027#520—531no—
1028#518—531no—
1029C2×#117—531no—
1030#490—531no—
1031#490—531no—
1032#489—531no—
1033#489—531no—
1034#488—531no—
1035#488—531no—
1036#486—531no—
1037#486C2×D5311yescharacteristic, complemented
1038#485—531no—
1039#485—531no—
1040#485—531no—
1041#485—531no—
1042#482—531no—
1043#482—531no—
1044#482—531no—
1045#482—531no—
1046#482—531no—
1047#482—531no—
1048#482C2×D5311yescharacteristic, complemented
1049#482C2×D5311yescharacteristic, complemented
1050#481—531no—
1051#481—531no—
1052#480—531no—
1053#480—531no—
1054#478—531no—
1055#478—531no—
1056#478—531no—
1057#478—531no—
1058#476—531no—
1059#476—531no—
1060#474—531no—
1061#474C2×D5311yescharacteristic, complemented
1062#470—531no—
1063#470—531no—
1064#469—531no—
1065#469—531no—
1066#469—531no—
1067#469—531no—
1068#468—531no—
1069#468—531no—
1070#468—531no—
1071#468—531no—
1072#468C2×D5311yescharacteristic, complemented
1073#468C2×D5311yescharacteristic, complemented
1074#466—531no—
1075#466—531no—
1076#465—531no—
1077#465—531no—
1078#464—531no—
1079#464—531no—
1080#463—531no—
1081#463—531no—
1082#460—531no—
1083#460C2×D5311yescharacteristic, complemented
1084#459—531no—
1085#459—531no—
1086#452—531no—
1087#452—531no—
1088#450—531no—
1089#450—531no—
1090#450—531no—
1091#450—531no—
1092#450C2×D5311yescharacteristic, complemented
1093#450C2×D5311yescharacteristic, complemented
1094#449—531no—
1095#449—531no—
1096#447—531no—
1097#447—531no—
1098#447—531no—
1099#447—531no—
1100#447—531no—
1101#447—531no—
1102#442—531no—
1103#442—531no—
1104#440—531no—
1105#440—531no—
1106C4×SD16—531no—
1107C4×SD16C2×D5311yescharacteristic, complemented
1108C4×D8—531no—
1109C4×D8—531no—
1110#436—531no—
1111#436—531no—
1112#436—531no—
1113#436C2×D5311yescharacteristic, complemented
1114#435—531no—
1115#435—531no—
1116#435—531no—
1117#435—531no—
1118#428—531no—
1119#428—531no—
1120#427—531no—
1121#424—531no—
1122#418—531no—
1123#418—531no—
1124#418—531no—
1125#418—531no—
1126#418—531no—
1127#418—531no—
1128#418—531no—
1129#418—531no—
1130#418—531no—
1131#418—531no—
1132#418C2×D5311yescharacteristic, complemented
1133#418C2×D5311yescharacteristic, complemented
1134#417—531no—
1135#417—531no—
1136#417—531no—
1137#417—531no—
1138#416—531no—
1139#416—531no—
1140#416—531no—
1141#416—531no—
1142C2×#102—531no—
1143C2×#102—531no—
1144C2×#102—531no—
1145C2×#102—531no—
1146C2×#102—531no—
1147C2×#102—531no—
1148#408—531no—
1149#407—531no—
1150#405—531no—
1151C53#6117511yescharacteristic, complemented, Sylow
1152C25—1061no—
1153H(5,𝔽2)—1064no—
1154H(5,𝔽2)—2122no—
1155C2×#41—531no—
1156C2×#41—531no—
1157C2×#41—531no—
1158C2×#41—531no—
1159C2×#41—531no—
1160C2×#41—1061no—
1161C22×D4—21no—
1162C22×D4—531no—
1163C22×D4—531no—
1164C22×D4—531no—
1165C22×D4—531no—
1166C22×D4—531no—
1167C22×D4—531no—
1168C22×D4—1061no—
1169C22×D4—1061no—
1170C22×D4—1061no—
1171C22×D4—1064no—
1172C22×D4—1061no—
1173C22×D4—1061no—
1174C22×D4—1061no—
1175C22×D4—1061no—
1176C22×D4—1061no—
1177C22×D4—1061no—
1178C22×D4—2122no—
1179C22×D4C22×D5311yescharacteristic
1180C22×D4C22×D5311yescharacteristic
1181C23×C4—531no—
1182AGL(1,ℤ/8)—1064no—
1183AGL(1,ℤ/8)—2122no—
1184#135—2122no—
1185C2×Q16—531no—
1186C2×SD16—531no—
1187C2×SD16—531no—
1188C2×SD16—531no—
1189C2×SD16C22×D5311yescharacteristic
1190C2×SD16C22×D5311yescharacteristic
1191C2×SD16C22×D5311yescharacteristic, complemented
1192C2×D8—531no—
1193C2×D8—531no—
1194C2×D8—531no—
1195C2×D8—531no—
1196C2×D8—531no—
1197#131—2122no—
1198C2×M16—531no—
1199C2×M16—531no—
1200C2×M16—531no—
1201C2×M16—531no—
1202C2×M16—531no—
1203C2×M16—531no—
1204C2×M16—2122no—
1205C2×M16C22×D5311yescharacteristic
1206C2×M16C22×D5311yescharacteristic, complemented
1207C22×C8—531no—
1208C22×C8—531no—
1209C22×C8—531no—
1210C22×C8—531no—
1211C4⋊Q8—531no—
1212C4⋊Q8—1061no—
1213C4⋊Q8C22×D5311yescharacteristic, complemented
1214#127—531no—
1215#127—1061no—
1216#127C22×D5311yescharacteristic
1217#126—21no—
1218#126—21no—
1219#126—1061no—
1220#126—1061no—
1221#126—1061no—
1222#126—1061no—
1223#126—1061no—
1224#126—1061no—
1225#125—531no—
1226#125—531no—
1227#125—1061no—
1228#125—1061no—
1229#125—1061no—
1230#124—21no—
1231#124—531no—
1232#124—531no—
1233#124—1061no—
1234#124—1061no—
1235#124—1061no—
1236#124—1061no—
1237#124—1061no—
1238#124—1061no—
1239#123—531no—
1240#123—531no—
1241#123—1061no—
1242#123—1061no—
1243#123—1061no—
1244#123—1061no—
1245#123—1061no—
1246#123—1061no—
1247#123—1061no—
1248#123—1061no—
1249#123—1061no—
1250#123—1061no—
1251C22⋊Q8—531no—
1252C22⋊Q8—531no—
1253C22⋊Q8—531no—
1254C22⋊Q8—531no—
1255C22⋊Q8—531no—
1256C22⋊Q8—531no—
1257C22⋊Q8—1061no—
1258C22⋊Q8—1061no—
1259C22⋊Q8—1061no—
1260C22⋊Q8C22×D5311yescharacteristic
1261C22⋊Q8C22×D5311yescharacteristic, complemented
1262#121—21no—
1263#121—531no—
1264#121—531no—
1265#121—531no—
1266#121—531no—
1267#121—531no—
1268#121—531no—
1269#121—531no—
1270#121—531no—
1271#121—531no—
1272#121—531no—
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#121C22×D5311yescharacteristic
1290#121C22×D5311yescharacteristic
1291#120—21no—
1292#120—21no—
1293#120—531no—
1294#120—531no—
1295#120—1061no—
1296#120—1061no—
1297#120—1061no—
1298#120—1061no—
1299#120—1061no—
1300#120—1061no—
1301#120—1061no—
1302#120—1061no—
1303#120—1061no—
1304#120—1061no—
1305#120—1061no—
1306#120—1061no—
1307#120—1061no—
1308#120—1061no—
1309#120—1061no—
1310#120—1061no—
1311C4×Q8—21no—
1312C4×Q8—531no—
1313C4×Q8—1061no—
1314C4×Q8—1061no—
1315C4×Q8C22×D5311yescharacteristic, complemented
1316C4×D4—531no—
1317C4×D4—531no—
1318C4×D4—531no—
1319C4×D4—531no—
1320C4×D4—531no—
1321C4×D4—531no—
1322C4×D4—531no—
1323C4×D4—531no—
1324C4×D4—1061no—
1325C4×D4—1061no—
1326C4×D4—1061no—
1327C4×D4—1061no—
1328C4×D4—1061no—
1329C4×D4—1061no—
1330C4×D4—1061no—
1331C4×D4—1061no—
1332C4×D4—1061no—
1333C4×D4—1061no—
1334C4×D4—1061no—
1335C4×D4—1061no—
1336C4×D4—1061no—
1337C4×D4C22×D5311yescharacteristic
1338C4×D4C22×D5311yescharacteristic
1339#117—531no—
1340#117—531no—
1341#117—531no—
1342#117—531no—
1343#117—531no—
1344#117—531no—
1345#117—531no—
1346#117—1061no—
1347#117—1061no—
1348#117—1061no—
1349#117—1061no—
1350#117—1061no—
1351#117—1061no—
1352#117—1061no—
1353#117C22×D5311yescharacteristic
1354#117C22×D5311yescharacteristic, complemented
1355C2×C4⋊C4—531no—
1356C2×C4⋊C4—531no—
1357C2×C4⋊C4—531no—
1358C2×C4⋊C4—531no—
1359C2×C4⋊C4—1061no—
1360C2×C22⋊C4—1061no—
1361C2×C22⋊C4—1061no—
1362C2×C22⋊C4—1061no—
1363C2×C22⋊C4—1061no—
1364C2×C22⋊C4—1061no—
1365C2×C22⋊C4—1061no—
1366C2×C22⋊C4—1061no—
1367C2×C42—1061no—
1368#107—531no—
1369#107—531no—
1370#107—531no—
1371#107—531no—
1372#107C22×D5311yescharacteristic, complemented
1373#107C22×D5311yescharacteristic, complemented
1374#106—531no—
1375#106—531no—
1376#106—531no—
1377#106—531no—
1378#106—531no—
1379#106C22×D5311yescharacteristic, complemented
1380C4⋊C8—531no—
1381C4⋊C8—531no—
1382C4⋊C8—531no—
1383C4⋊C8C22×D5311yescharacteristic, complemented
1384#103—531no—
1385#103—531no—
1386#103—531no—
1387#103—531no—
1388#103—531no—
1389#103—531no—
1390#103—531no—
1391#103C22×D5311yescharacteristic, complemented
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#102—531no—
1406#102—531no—
1407#102—531no—
1408#102—531no—
1409#102—531no—
1410#102—531no—
1411#102—531no—
1412#102—531no—
1413#102—531no—
1414#102—531no—
1415#102C22×D5311yescharacteristic
1416#102C22×D5311yescharacteristic
1417#102C22×D5311yescharacteristic
1418#102C22×D5311yescharacteristic
1419#102C22×D5311yescharacteristic
1420#102C22×D5311yescharacteristic
1421#102C22×D5311yescharacteristic, complemented
1422#102C22×D5311yescharacteristic, complemented
1423#102C22×D5311yescharacteristic, complemented
1424C22⋊C8—531no—
1425C22⋊C8—531no—
1426C22⋊C8—531no—
1427C22⋊C8—531no—
1428C22⋊C8—531no—
1429C22⋊C8—531no—
1430C22⋊C8C22×D5311yescharacteristic
1431C22⋊C8C22×D5311yescharacteristic, complemented
1432#97—531no—
1433#97—531no—
1434C4×C8—531no—
1435C4×C8C22×D5311yescharacteristic, complemented
1436C24—21no—
1437C24—21no—
1438C24—531no—
1439C24—1061no—
1440C24—1061no—
1441C24—1061no—
1442C24—1061no—
1443C24—1061no—
1444C24—1061no—
1445C24—4242no—
1446C24—4242no—
1447C24—2124no—
1448#41—1062no—
1449#41—1062no—
1450#41—1062no—
1451#41—1062no—
1452#41—1062no—
1453#41—1062no—
1454#41—1062no—
1455#41—1062no—
1456#41—2121no—
1457#41—2121no—
1458#41—2124no—
1459C2×Q8—21no—
1460C2×Q8—531no—
1461C2×Q8—531no—
1462C2×Q8—1061no—
1463C2×Q8C23×D5311yescharacteristic
1464C2×D4—22no—
1465C2×D4—22no—
1466C2×D4—21no—
1467C2×D4—21no—
1468C2×D4—21no—
1469C2×D4—21no—
1470C2×D4—21no—
1471C2×D4—21no—
1472C2×D4—41no—
1473C2×D4—41no—
1474C2×D4—82no—
1475C2×D4—534no—
1476C2×D4—531no—
1477C2×D4—531no—
1478C2×D4—531no—
1479C2×D4—531no—
1480C2×D4—531no—
1481C2×D4—531no—
1482C2×D4—531no—
1483C2×D4—531no—
1484C2×D4—531no—
1485C2×D4—1062no—
1486C2×D4—1061no—
1487C2×D4—1061no—
1488C2×D4—1061no—
1489C2×D4—1061no—
1490C2×D4—1062no—
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—1062no—
1501C2×D4—1062no—
1502C2×D4—1062no—
1503C2×D4—1061no—
1504C2×D4—1061no—
1505C2×D4—1061no—
1506C2×D4—1061no—
1507C2×D4—1061no—
1508C2×D4—1061no—
1509C2×D4—1061no—
1510C2×D4—1061no—
1511C2×D4—1061no—
1512C2×D4—4242no—
1513C2×D4—4242no—
1514C2×D4—4242no—
1515C2×D4—2121no—
1516C2×D4—2121no—
1517C2×D4—2121no—
1518C2×D4—2121no—
1519C2×D4—2124no—
1520C2×D4—2124no—
1521C2×D4—2124no—
1522C2×D4—2124no—
1523C2×D4—2124no—
1524C2×D4—2124no—
1525C2×D4D4×D5311yescharacteristic
1526C2×D4C23×D5311yescharacteristic
1527C2×D4C23×D5311yescharacteristic
1528C2×D4C23×D5311yescharacteristic
1529C22×C4—21no—
1530C22×C4—531no—
1531C22×C4—531no—
1532C22×C4—531no—
1533C22×C4—531no—
1534C22×C4—531no—
1535C22×C4—531no—
1536C22×C4—1062no—
1537C22×C4—1062no—
1538C22×C4—1061no—
1539C22×C4—1061no—
1540C22×C4—1061no—
1541C22×C4—1061no—
1542C22×C4—1061no—
1543C22×C4—1061no—
1544C22×C4—1061no—
1545C22×C4—1061no—
1546C22×C4—1061no—
1547C22×C4—1061no—
1548C22×C4—1061no—
1549C22×C4—1061no—
1550C22×C4—1061no—
1551C22×C4C23×D5311yescharacteristic
1552C22×C4C23×D5311yescharacteristic
1553Q16—2121no—
1554SD16—22no—
1555SD16—41no—
1556SD16—41no—
1557SD16—1062no—
1558SD16—2121no—
1559SD16—2121no—
1560D8—1062no—
1561D8—1062no—
1562D8—2121no—
1563D8—2121no—
1564D8—2121no—
1565M16—41no—
1566M16—41no—
1567M16—1062no—
1568M16—1062no—
1569M16—2121no—
1570M16—2121no—
1571M16—2121no—
1572M16—2121no—
1573C2×C8—531no—
1574C2×C8—531no—
1575C2×C8—531no—
1576C2×C8—531no—
1577C2×C8—1062no—
1578C2×C8—1062no—
1579C2×C8—2121no—
1580C2×C8—2121no—
1581C2×C8C23×D5311yescharacteristic
1582C2×C8C23×D5311yescharacteristic
1583C2×C8C23×D5311yescharacteristic
1584C2×C8C23×D5311yescharacteristic
1585C4⋊C4—21no—
1586C4⋊C4—21no—
1587C4⋊C4—21no—
1588C4⋊C4—21no—
1589C4⋊C4—531no—
1590C4⋊C4—531no—
1591C4⋊C4—531no—
1592C4⋊C4—531no—
1593C4⋊C4—531no—
1594C4⋊C4—531no—
1595C4⋊C4—531no—
1596C4⋊C4—531no—
1597C4⋊C4—531no—
1598C4⋊C4—1061no—
1599C4⋊C4—1061no—
1600C4⋊C4—1061no—
1601C4⋊C4—1061no—
1602C4⋊C4—1061no—
1603C4⋊C4—1061no—
1604C4⋊C4—1061no—
1605C4⋊C4—1061no—
1606C4⋊C4—1061no—
1607C4⋊C4—1061no—
1608C4⋊C4—1061no—
1609C4⋊C4—1061no—
1610C4⋊C4—1061no—
1611C4⋊C4—1061no—
1612C4⋊C4D4×D5311yescharacteristic
1613C4⋊C4C23×D5311yescharacteristic
1614C4⋊C4C23×D5311yescharacteristic
1615C4⋊C4C23×D5311yescharacteristic
1616C4⋊C4C23×D5311yescharacteristic
1617C22⋊C4—21no—
1618C22⋊C4—21no—
1619C22⋊C4—21no—
1620C22⋊C4—21no—
1621C22⋊C4—21no—
1622C22⋊C4—21no—
1623C22⋊C4—21no—
1624C22⋊C4—531no—
1625C22⋊C4—531no—
1626C22⋊C4—531no—
1627C22⋊C4—531no—
1628C22⋊C4—531no—
1629C22⋊C4—531no—
1630C22⋊C4—531no—
1631C22⋊C4—531no—
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⋊C4—1061no—
1648C22⋊C4—1061no—
1649C22⋊C4—1061no—
1650C22⋊C4—1061no—
1651C22⋊C4—1061no—
1652C22⋊C4—1061no—
1653C22⋊C4—1061no—
1654C22⋊C4—1061no—
1655C22⋊C4—1061no—
1656C22⋊C4—1061no—
1657C22⋊C4—1061no—
1658C22⋊C4—1061no—
1659C22⋊C4D4×D5311yescharacteristic
1660C22⋊C4D4×D5311yescharacteristic
1661C42—21no—
1662C42—21no—
1663C42—21no—
1664C42—531no—
1665C42—1061no—
1666C42—1061no—
1667C42—1061no—
1668C42—1061no—
1669C42—1061no—
1670C42—1061no—
1671C42—1061no—
1672C42C23×D5311yescharacteristic
1673C23—21no—
1674C23—21no—
1675C23—21no—
1676C23—42no—
1677C23—42no—
1678C23—42no—
1679C23—81no—
1680C23—81no—
1681C23—81no—
1682C23—531no—
1683C23—531no—
1684C23—531no—
1685C23—1064no—
1686C23—1062no—
1687C23—1061no—
1688C23—1061no—
1689C23—1061no—
1690C23—4241no—
1691C23—4241no—
1692C23—4241no—
1693C23—4241no—
1694C23—4241no—
1695C23—4241no—
1696C23—4241no—
1697C23—4241no—
1698C23—4241no—
1699C23—42416no—
1700C23—2121no—
1701C23—2121no—
1702C23—2122no—
1703C23—2122no—
1704C23—2122no—
1705C23—2122no—
1706C23—2122no—
1707C23—2122no—
1708C23—2122no—
1709C23—2122no—
1710C23C2×D4×D5311yescharacteristic
1711C23C2×D4×D5311yescharacteristic
1712Q8—21no—
1713Q8—21no—
1714Q8—81no—
1715Q8—1062no—
1716Q8—1061no—
1717Q8—1061no—
1718Q8—4241no—
1719D4—21no—
1720D4—21no—
1721D4—21no—
1722D4—21no—
1723D4—21no—
1724D4—41no—
1725D4—42no—
1726D4—42no—
1727D4—42no—
1728D4—81no—
1729D4—81no—
1730D4—81no—
1731D4—532no—
1732D4—1062no—
1733D4—1064no—
1734D4—1062no—
1735D4—1062no—
1736D4—1061no—
1737D4—1061no—
1738D4—1061no—
1739D4—1061no—
1740D4—1061no—
1741D4—4241no—
1742D4—4241no—
1743D4—4241no—
1744D4—4241no—
1745D4—4241no—
1746D4—4241no—
1747D4—4241no—
1748D4—4241no—
1749D4—4241no—
1750D4—2121no—
1751D4—2122no—
1752D4—2122no—
1753D4—2122no—
1754D4—2121no—
1755D4—2121no—
1756D4—2122no—
1757D4—2122no—
1758D4—2122no—
1759D4—2122no—
1760D4—2122no—
1761D4—2122no—
1762D4—2122no—
1763D4#41×D5312yes—
1764C2×C4—21no—
1765C2×C4—21no—
1766C2×C4—21no—
1767C2×C4—21no—
1768C2×C4—21no—
1769C2×C4—21no—
1770C2×C4—21no—
1771C2×C4—21no—
1772C2×C4—21no—
1773C2×C4—81no—
1774C2×C4—531no—
1775C2×C4—532no—
1776C2×C4—532no—
1777C2×C4—531no—
1778C2×C4—531no—
1779C2×C4—531no—
1780C2×C4—531no—
1781C2×C4—1062no—
1782C2×C4—1062no—
1783C2×C4—1062no—
1784C2×C4—1061no—
1785C2×C4—1061no—
1786C2×C4—1061no—
1787C2×C4—1061no—
1788C2×C4—1061no—
1789C2×C4—1061no—
1790C2×C4—1061no—
1791C2×C4—1061no—
1792C2×C4—1061no—
1793C2×C4—4241no—
1794C2×C4—4241no—
1795C2×C4—4241no—
1796C2×C4—4241no—
1797C2×C4—4241no—
1798C2×C4—4241no—
1799C2×C4—4241no—
1800C2×C4—4241no—
1801C2×C4—4241no—
1802C2×C4—2122no—
1803C2×C4—2122no—
1804C2×C4—2122no—
1805C2×C4—2122no—
1806C2×C4C2×D4×D5311yescharacteristic
1807C2×C4C2×D4×D5311yescharacteristic
1808C2×C4C2×D4×D5311yescharacteristic
1809C2×C4C2×D4×D5311yescharacteristic
1810C2×C4C24×D5311yescharacteristic
1811C8—21no—
1812C8—21no—
1813C8—21no—
1814C8—21no—
1815C8—1061no—
1816C8—1061no—
1817C8—1061no—
1818C8—1061no—
1819C22—21no—
1820C22—21no—
1821C22—22no—
1822C22—21no—
1823C22—21no—
1824C22—21no—
1825C22—21no—
1826C22—41no—
1827C22—41no—
1828C22—41no—
1829C22—41no—
1830C22—41no—
1831C22—41no—
1832C22—41no—
1833C22—41no—
1834C22—84no—
1835C22—162no—
1836C22—532no—
1837C22—8482no—
1838C22—1061no—
1839C22—1061no—
1840C22—1061no—
1841C22—1061no—
1842C22—1062no—
1843C22—1061no—
1844C22—1061no—
1845C22—1061no—
1846C22—1061no—
1847C22—4244no—
1848C22—4244no—
1849C22—4244no—
1850C22—4244no—
1851C22—4244no—
1852C22—2124no—
1853C22—2121no—
1854C22—2121no—
1855C22—2121no—
1856C22—2121no—
1857C22—2121no—
1858C22—2121no—
1859C22—2121no—
1860C22—2121no—
1861C22C22×D4×D5311yescharacteristic
1862C4—21no—
1863C4—21no—
1864C4—21no—
1865C4—21no—
1866C4—41no—
1867C4—41no—
1868C4—41no—
1869C4—41no—
1870C4—41no—
1871C4—532no—
1872C4—1061no—
1873C4—1061no—
1874C4—1061no—
1875C4—1061no—
1876C4—2121no—
1877C4—2121no—
1878C4—2121no—
1879C4—2121no—
1880C4—2121no—
1881C4C2×#41×D5311yescharacteristic
1882C4H(5,𝔽2)×D5311yescharacteristic
1883C2—41no—
1884C2—41no—
1885C2—42no—
1886C2—81no—
1887C2—81no—
1888C2—1062no—
1889C2—4241no—
1890C2—4241no—
1891C2—2121no—
1892C2—2122no—
1893C2—2121no—
1894C2#546×D5311yescharacteristic
1895C2#2028949111yescharacteristic
1896C2#2028949311yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3324C2
socleC22×C53C23×D4
hypercenter#3324D53
hypocenterC53#61175
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3324

Complements

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

NH ≅ G/Ntype
1. #20288429C2semidirect
2. #20288343C2semidirect
3. #20286956C2semidirect
4. #20286953C2semidirect
5. #20286941C2semidirect
6. #20286936C2semidirect
7. #20286926C2semidirect
8. #20286918C2semidirect
9. #20286912C2semidirect
10. #20286869C2semidirect
11. #20286868C2semidirect
12. #20286859C2semidirect
13. #20286856C2semidirect
14. #20286745C2semidirect
15. #20286744C2semidirect
16. #20286743C2semidirect
17. #20286740C2semidirect
18. #20285064C2semidirect
19. #20284670C2semidirect
20. #20284643C2semidirect
21. #20284539C2semidirect
22. #20284390C2semidirect
23. #20284319C2semidirect
24. #20284251C2semidirect
25. #20284020C2semidirect
26. #20283943C2semidirect
27. #20283542C2semidirect
28. #20283415C2semidirect
29. #20283240C2semidirect
30. #418×D53C2semidirect
31. C53×#3324C2semidirect
35. C2×#13133244C22semidirect
36. C2×#13133238C22semidirect
37. C2×#13133225C22semidirect
38. C2×M16×D53C22semidirect
40. #16811344C22semidirect
41. #16811339C22semidirect
42. #16811336C22semidirect
45. #16811319C22semidirect
46. #16811317C22semidirect
47. #16811315C22semidirect
48. #16811314C22semidirect
61. #16811250C22semidirect
64. #16811203C22semidirect
71. #16811136C22semidirect
76. #16811105C22semidirect
77. #16811103C22semidirect
79. #117×D53C22semidirect
80. #16810987C22semidirect
81. #16810986C22semidirect
82. #16810985C22semidirect
83. #16810981C22semidirect
84. #16810978C22semidirect
85. #16810976C22semidirect
86. #16810968C22semidirect
87. #16810967C22semidirect
88. #16810966C22semidirect
89. #16810965C22semidirect
90. #16810964C22semidirect
91. #16810950C22semidirect
92. #16810947C22semidirect
93. #16810946C22semidirect
94. #16810945C22semidirect
95. #16810945C22semidirect
96. #16810944C22semidirect
97. #16810943C22semidirect
98. #16810939C22semidirect
99. #16810937C22semidirect
100. #16810935C22semidirect
101. #16810926C22semidirect
102. #16810924C22semidirect
103. #16810923C22semidirect
104. #16810921C22semidirect
105. #16810911C22semidirect
106. #16810910C22semidirect
107. #16810902C22semidirect
108. #16810880C22semidirect
109. #16810879C22semidirect
110. #16810876C22semidirect
111. #16810875C22semidirect
112. #16810875C22semidirect
113. #16810874C22semidirect
114. #16810872C22semidirect
115. #16810870C22semidirect
116. #16810869C22semidirect
117. #16810866C22semidirect
118. #16810860C22semidirect
119. #16810857C22semidirect
120. #16810854C22semidirect
121. #16810849C22semidirect
122. #16810845C22semidirect
123. #16810843C22semidirect
124. #16810839C22semidirect
125. #16810837C22semidirect
126. #16810821C22semidirect
127. #16810817C22semidirect
128. #16810815C22semidirect
129. #16810783C22semidirect
130. #16810782C22semidirect
131. #16810773C22semidirect
132. #16810772C22semidirect
133. #16810772C22semidirect
134. #16810772C22semidirect
135. #16810770C22semidirect
136. #16810769C22semidirect
137. #16810759C22semidirect
138. #16810758C22semidirect
139. #16810758C22semidirect
140. #16810758C22semidirect
141. #16810757C22semidirect
142. #16810757C22semidirect
143. #16810734C22semidirect
144. #16810733C22semidirect
145. #16810724C22semidirect
146. #16810721C22semidirect
147. #16810708C22semidirect
148. C4×D424C22semidirect
149. #16810703C22semidirect
150. #16810702C22semidirect
151. #16810699C22semidirect
152. #16810699C22semidirect
153. #16810697C22semidirect
154. #16810695C22semidirect
155. #16810693C22semidirect
156. #16810691C22semidirect
157. #16810664C22semidirect
158. #16810662C22semidirect
159. #16810660C22semidirect
160. #16810648C22semidirect
161. #16810629C22semidirect
162. #16810628C22semidirect
163. #16810627C22semidirect
165. #16810626C22semidirect
166. #16810626C22semidirect
167. #16810626C22semidirect
168. #16810626C22semidirect
169. #16810626C22semidirect
170. #16810626C22semidirect
171. #16810625C22semidirect
172. #16810621C22semidirect
173. #16810621C22semidirect
174. #16810621C22semidirect
175. #16810618C22semidirect
176. #16810617C22semidirect
177. #16810616C22semidirect
178. #16810616C22semidirect
179. C2×#13133138C22semidirect
182. #102×D53C22semidirect
183. #102×D53C22semidirect
184. #102×D53C22semidirect
185. #16810588C22semidirect
186. #16810585C22semidirect
187. #16810577C22semidirect
188. C53×#556C22semidirect
190. C53×#486C22semidirect
191. C53×#482C22semidirect
192. C53×#482C22semidirect
193. C53×#474C22semidirect
194. C53×#468C22semidirect
195. C53×#468C22semidirect
196. C53×#460C22semidirect
197. C53×#450C22semidirect
198. C53×#450C22semidirect
199. C4×SD16×C53C22semidirect
200. C53×#436C22semidirect
201. C53×#418C22semidirect
202. C53×#418C22semidirect
233. C2×#11719925C23semidirect
234. C2×#11719913C23semidirect
241. C2×#11719922C23semidirect
248. C2×#11719912C23semidirect
250. C22×#88322C23semidirect
253. C2×C8×D53C23semidirect
254. #13133216C23semidirect
264. #13133209C23semidirect
266. #13133208C23semidirect
297. #13133193C23semidirect
302. #13133192C23semidirect
306. #13133191C23semidirect
342. Q8×Dic53C23semidirect
350. C4×D212C23semidirect
356. #13133179C23semidirect
372. #13133175C23semidirect
380. C2×C4⋊Dic53C23semidirect
384. C4⋊C4×D53C23semidirect
393. #13133151C23semidirect
394. #13133151C23semidirect
395. #13133150C23semidirect
396. #13133150C23semidirect
397. #13133149C23semidirect
398. #13133148C23semidirect
399. #13133148C23semidirect
400. #13133148C23semidirect
401. #13133148C23semidirect
402. C4⋊#88322C23semidirect
403. #13133146C23semidirect
404. #13133146C23semidirect
405. #13133142C23semidirect
406. #13133142C23semidirect
407. #13133142C23semidirect
408. #13133141C23semidirect
409. #13133140C23semidirect
410. #13133140C23semidirect
411. #13133140C23semidirect
418. #13133139C23semidirect
425. #13133138C23semidirect
426. #13133138C23semidirect
427. #13133138C23semidirect
434. #13133137C23semidirect
436. C22⋊#88322C23semidirect
439. #13133129C23semidirect
440. #13133129C23semidirect
441. #13133128C23semidirect
442. #13133127C23semidirect
443. C8×Dic53C23semidirect
449. C2×SD16×C53C23semidirect
451. C2×M16×C53C23semidirect
452. C4⋊Q8×C53C23semidirect
458. C22⋊Q8×C53C23semidirect
465. C4×Q8×C53C23semidirect
469. #117×C53C23semidirect
470. #107×C53C23semidirect
471. #107×C53C23semidirect
472. #106×C53C23semidirect
473. C4⋊C8×C53C23semidirect
474. #103×C53C23semidirect
481. #102×C53C23semidirect
482. #102×C53C23semidirect
483. #102×C53C23semidirect
485. C22⋊C8×C53C23semidirect
486. C4×C8×C53C23semidirect
940. #3324D53semidirect
989. #556C2×D53semidirect
1037. #486C2×D53semidirect
1048. #482C2×D53semidirect
1049. #482C2×D53semidirect
1061. #474C2×D53semidirect
1072. #468C2×D53semidirect
1073. #468C2×D53semidirect
1083. #460C2×D53semidirect
1092. #450C2×D53semidirect
1093. #450C2×D53semidirect
1107. C4×SD16C2×D53semidirect
1113. #436C2×D53semidirect
1132. #418C2×D53semidirect
1133. #418C2×D53semidirect
1151. C53#61175semidirect
1191. C2×SD16C22×D53semidirect
1206. C2×M16C22×D53semidirect
1213. C4⋊Q8C22×D53semidirect
1261. C22⋊Q8C22×D53semidirect
1315. C4×Q8C22×D53semidirect
1354. #117C22×D53semidirect
1372. #107C22×D53semidirect
1373. #107C22×D53semidirect
1379. #106C22×D53semidirect
1383. C4⋊C8C22×D53semidirect
1391. #103C22×D53semidirect
1421. #102C22×D53semidirect
1422. #102C22×D53semidirect
1423. #102C22×D53semidirect
1431. C22⋊C8C22×D53semidirect
1435. C4×C8C22×D53semidirect

Maximal subgroups

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

subgroupindex
#202884292
#202883432
#202869562
#202869532
#202869412
#202869362
#202869262
#202869182
#202869122
#202868692
#202868682
#202868592
#202868562
#202867452
#202867442
#202867432
#202867402
#202850642
#202846702
#202846432
#202845392
#202843902
#202843192
#202842512
#202840202
#202839432
#202835422
#202834152
#202832402
#418×D532
C53×#33242
#6117553