Finite Group Databasebeta

← #28270325

Subgroups — #28270325

Order 13568.

2174 conjugacy classes of subgroups.

The subgroup lattice has 1952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289027C211yesmaximal, characteristic, complemented
2#20288385C211yesmaximal, characteristic, complemented
3#20286868C211yesmaximal, characteristic, complemented
4#20286741C211yesmaximal, characteristic, complemented
5#20286726C211yesmaximal, characteristic, complemented
6#20286703C211yesmaximal, characteristic, complemented
7#20286662C211yesmaximal, characteristic, complemented
8#20286607C211yesmaximal, characteristic, complemented
9#20286570C211yesmaximal, characteristic, complemented
10#20286525C211yesmaximal, characteristic, complemented
11#20286474C211yesmaximal, characteristic, complemented
12#20286417C211yesmaximal, characteristic, complemented
13#20286395C211yesmaximal, characteristic, complemented
14D8×D212C211yesmaximal, characteristic, complemented
15#20286257C211yesmaximal, characteristic, complemented
16#20286250C211yesmaximal, characteristic, complemented
17#20286212C211yesmaximal, characteristic, complemented
18#20286201C211yesmaximal, characteristic, complemented
19#20285803C211yesmaximal, characteristic, complemented
20#20285767C211yesmaximal, characteristic, complemented
21#20285619C211yesmaximal, characteristic, complemented
22#20285574C211yesmaximal, characteristic, complemented
23#20285485C211yesmaximal, characteristic, complemented
24#20285465C211yesmaximal, characteristic, complemented
25#20284914C211yesmaximal, characteristic, complemented
26#20284023C211yesmaximal, characteristic, complemented
27#20283980C211yesmaximal, characteristic, complemented
28#20283936C211yesmaximal, characteristic, complemented
29#449×D53C211yesmaximal, characteristic, complemented
30#20283770C211yesmaximal, characteristic, complemented
31C53×#3124C211yesmaximal, characteristic, complemented
32C2×#13133263C2211yescharacteristic, complemented
33C2×#41×D53C2211yescharacteristic, complemented
34C2×#13133244C2211yescharacteristic, complemented
35C2×#13133244C2211yescharacteristic, complemented
36C2×#13133240C2211yescharacteristic, complemented
37C2×#13133240C2211yescharacteristic, complemented
38C2×#13133238C2211yescharacteristic, complemented
39C2×SD16×D53C2211yescharacteristic, complemented
40C2×D8×D53C2211yescharacteristic, complemented
41C2×D8×D53C2211yescharacteristic, complemented
42#16811369—21no—
43#16811364—21no—
44#16811339C2211yescharacteristic, complemented
45#16811323C2211yescharacteristic, complemented
46#16811314C2211yescharacteristic, complemented
47#16811298—21no—
48#16811295C2211yescharacteristic, complemented
49#16811295C2211yescharacteristic, complemented
50#16811295C2211yescharacteristic, complemented
51#16811285C2211yescharacteristic
52#16811285C2211yescharacteristic, complemented
53#16811276C2211yescharacteristic, complemented
54#16811268—21no—
55#16811268—21no—
56#16811268C2211yescharacteristic, complemented
57#16811268C2211yescharacteristic, complemented
58#16811266C2211yescharacteristic, complemented
59#16811266C2211yescharacteristic, complemented
60#16811264—21no—
61D4×D212—21no—
62D4×D212—21no—
63D4×D212C2211yescharacteristic
64D4×D212C2211yescharacteristic, complemented
65D4×D212C2211yescharacteristic, complemented
66#16811228C2211yescharacteristic, complemented
67#16811225—21no—
68#16811207—21no—
69#16811204—21no—
70#16811204C2211yescharacteristic, complemented
71#16811203C2211yescharacteristic, complemented
72#16811192—21no—
73#16811192C2211yescharacteristic, complemented
74#16811191—21no—
75#16811189C2211yescharacteristic, complemented
76#16811184—21no—
77#16811136C2211yescharacteristic, complemented
78#16811135—21no—
79#16811135C2211yescharacteristic
80C2×#13133192—21no—
81C2×#13133192C2211yescharacteristic, complemented
82#121×D53C2211yescharacteristic, complemented
83#16811013C2211yescharacteristic, complemented
84#16811012C2211yescharacteristic, complemented
85#16811005C2211yescharacteristic, complemented
86#16811000C2211yescharacteristic, complemented
87#16810988C2211yescharacteristic, complemented
88#16810985C2211yescharacteristic, complemented
89#16810978C2211yescharacteristic, complemented
90#16810971C2211yescharacteristic, complemented
91#16810966C2211yescharacteristic, complemented
92#16810960C2211yescharacteristic, complemented
93#16810950C2211yescharacteristic, complemented
94#16810950C2211yescharacteristic, complemented
95#16810950C2211yescharacteristic, complemented
96#16810941C2211yescharacteristic, complemented
97#16810938C2211yescharacteristic, complemented
98#16810938C2211yescharacteristic, complemented
99#16810938C2211yescharacteristic, complemented
100#16810936C2211yescharacteristic, complemented
101#16810930C2211yescharacteristic, complemented
102#16810923C2211yescharacteristic, complemented
103#16810875C2211yescharacteristic, complemented
104#16810872C2211yescharacteristic, complemented
105#16810870C2211yescharacteristic, complemented
106#16810870C2211yescharacteristic, complemented
107#16810863C2211yescharacteristic, complemented
108#16810860C2211yescharacteristic, complemented
109#16810860C2211yescharacteristic, complemented
110#16810860C2211yescharacteristic, complemented
111#16810860C2211yescharacteristic, complemented
112#16810860C2211yescharacteristic, complemented
113#16810860C2211yescharacteristic, complemented
114#16810858C2211yescharacteristic, complemented
115#16810858C2211yescharacteristic, complemented
116#16810855C2211yescharacteristic, complemented
117#16810855C2211yescharacteristic, complemented
118#16810851C2211yescharacteristic, complemented
119#16810845C2211yescharacteristic, complemented
120#16810839C2211yescharacteristic, complemented
121#16810839C2211yescharacteristic, complemented
122#16810838C2211yescharacteristic, complemented
123#16810823C2211yescharacteristic, complemented
124#16810823C2211yescharacteristic, complemented
125#16810819C2211yescharacteristic, complemented
126#16810819C2211yescharacteristic, complemented
127#16810818C2211yescharacteristic, complemented
128#16810818C2211yescharacteristic, complemented
129#16810788C2211yescharacteristic, complemented
130#16810784C2211yescharacteristic, complemented
131#16810783C2211yescharacteristic, complemented
132#16810777C2211yescharacteristic, complemented
133#16810775C2211yescharacteristic, complemented
134#16810773C2211yescharacteristic, complemented
135#16810772C2211yescharacteristic, complemented
136#16810772C2211yescharacteristic, complemented
137#16810771C2211yescharacteristic, complemented
138#16810771C2211yescharacteristic, complemented
139#16810771C2211yescharacteristic, complemented
140#16810771C2211yescharacteristic, complemented
141#16810771C2211yescharacteristic, complemented
142#16810771C2211yescharacteristic, complemented
143#16810770C2211yescharacteristic, complemented
144#16810770C2211yescharacteristic, complemented
145#16810769C2211yescharacteristic, complemented
146#16810768C2211yescharacteristic, complemented
147#16810768C2211yescharacteristic, complemented
148#16810767C2211yescharacteristic, complemented
149#16810767C2211yescharacteristic, complemented
150#16810766C2211yescharacteristic, complemented
151#16810765C2211yescharacteristic, complemented
152#16810763C2211yescharacteristic, complemented
153#16810759C2211yescharacteristic, complemented
154#16810759C2211yescharacteristic, complemented
155#16810758C2211yescharacteristic, complemented
156#16810758C2211yescharacteristic, complemented
157#16810758C2211yescharacteristic, complemented
158#16810758C2211yescharacteristic, complemented
159#16810758C2211yescharacteristic, complemented
160#16810758C2211yescharacteristic, complemented
161#16810756C2211yescharacteristic, complemented
162#16810755C2211yescharacteristic, complemented
163#16810733C2211yescharacteristic, complemented
164#16810721C2211yescharacteristic, complemented
165C4×#11719924C2211yescharacteristic, complemented
166C4×#11719922C2211yescharacteristic, complemented
167#16810696C2211yescharacteristic, complemented
168#16810696C2211yescharacteristic, complemented
169#16810693C2211yescharacteristic, complemented
170#16810693C2211yescharacteristic, complemented
171C8×D212C2211yescharacteristic, complemented
172C8×D212C2211yescharacteristic, complemented
173#16810688C2211yescharacteristic, complemented
174#16810688C2211yescharacteristic, complemented
175#16810684C2211yescharacteristic, complemented
176#16810626C2211yescharacteristic, complemented
177#16810623C2211yescharacteristic, complemented
178#16810618C2211yescharacteristic, complemented
179#16810618C2211yescharacteristic, complemented
180#16810616C2211yescharacteristic, complemented
181#103×D53C2211yescharacteristic, complemented
182#102×D53C2211yescharacteristic, complemented
183#102×D53C2211yescharacteristic, complemented
184#16810588C2211yescharacteristic, complemented
185#16810588C2211yescharacteristic, complemented
186C22⋊C8×D53C2211yescharacteristic, complemented
187C22⋊C8×D53C2211yescharacteristic, complemented
188C53×#542C2211yescharacteristic, complemented
189C53×#520C2211yescharacteristic, complemented
190C53×#484C2211yescharacteristic, complemented
191C53×#480C2211yescharacteristic, complemented
192C53×#477C2211yescharacteristic, complemented
193C53×#474C2211yescharacteristic, complemented
194C53×#464C2211yescharacteristic, complemented
195C53×#463C2211yescharacteristic, complemented
196C53×#452C2211yescharacteristic, complemented
197C53×#449C2211yescharacteristic
198C53×#440C2211yescharacteristic, complemented
199C53×#440C2211yescharacteristic, complemented
200C4×Q16×C53C2211yescharacteristic, complemented
201C4×D8×C53C2211yescharacteristic, complemented
202C53×#433C2211yescharacteristic, complemented
203#13133263—42no—
204#13133263—42no—
205C2×#11719949—21no—
206C2×#11719949C2311yescharacteristic
207C2×#11719949C2311yescharacteristic
208C2×#11719949C2311yescharacteristic
209C2×#11719949C2311yescharacteristic
210C2×#11719949C2311yescharacteristic
211C2×#11719945—21no—
212C2×#11719945—21no—
213C2×#11719945C2311yescharacteristic
214C2×#11719945C2311yescharacteristic
215C2×#11719947—21no—
216C2×#11719947C2311yescharacteristic
217#41×D53—42no—
218#41×D53—42no—
219C2×Q8×D53C2311yescharacteristic
220C22×D212—21no—
221C22×D212—21no—
222C22×D212—21no—
223C22×D212—21no—
224C22×D212—21no—
225C22×D212C2311yescharacteristic
226C2×D4×D53—21no—
227C2×D4×D53—21no—
228C2×D4×D53—21no—
229C2×D4×D53—21no—
230C2×D4×D53C2311yescharacteristic
231C2×D4×D53C2311yescharacteristic
232C2×D4×D53C2311yescharacteristic
233C2×D4×D53C2311yescharacteristic
234C2×D4×D53C2311yescharacteristic
235C22×C4×D53—21no—
236C22×C4×D53C2311yescharacteristic
237#13133244—42no—
238#13133244—42no—
239#13133240—42no—
240#13133240—42no—
241#13133238—42no—
242C2×#11719925C2311yescharacteristic
243C2×#11719913C2311yescharacteristic
244C2×#11719913C2311yescharacteristic
245C2×#11719923C2311yescharacteristic
246C2×#11719924C2311yescharacteristic
247C2×#11719924C2311yescharacteristic
248C2×#11719924C2311yescharacteristic
249C2×#11719924C2311yescharacteristic
250C2×#11719924C2311yescharacteristic
251SD16×D53—42no—
252C2×D424C2311yescharacteristic
253C2×D424C2311yescharacteristic
254C2×D424C2311yescharacteristic
255C2×D424C2311yescharacteristic
256C2×D424C2311yescharacteristic
257C2×D424C2311yescharacteristic
258C2×#11719922C2311yescharacteristic
259C2×#11719922C2311yescharacteristic
260C2×#11719922C2311yescharacteristic
261C2×#11719922C2311yescharacteristic
262C2×#11719922C2311yescharacteristic
263D8×D53—42no—
264D8×D53—42no—
265C2×#11719912C2311yescharacteristic
266C2×#11719912C2311yescharacteristic
267C2×C8×D53C2311yescharacteristic
268C2×C8×D53C2311yescharacteristic
269C2×C8×D53C2311yescharacteristic
270C2×C8×D53C2311yescharacteristic
271C2×C8×D53C2311yescharacteristic
272C2×C8×D53C2311yescharacteristic
273#13133214—21no—
274#13133214—21no—
275#13133214—21no—
276#13133214C2311yescharacteristic
277#13133214C2311yescharacteristic
278#13133214C2311yescharacteristic
279#13133213—21no—
280#13133211—21no—
281#13133210—21no—
282#13133209C2311yescharacteristic
283#13133207—21no—
284#13133206—21no—
285#13133206—21no—
286#13133205—21no—
287#13133205—21no—
288#13133205C2311yescharacteristic
289#13133205C2311yescharacteristic
290#13133203—21no—
291#13133202—21no—
292#13133202—21no—
293#13133202—21no—
294#13133202—21no—
295#13133202—21no—
296#13133202—21no—
297#13133201—21no—
298#13133201—21no—
299#13133201D411yescharacteristic
300#13133201D411yescharacteristic
301#13133200—21no—
302#13133199—21no—
303#13133199—21no—
304#13133197—21no—
305#13133197—21no—
306#13133197—21no—
307#13133197D411yescharacteristic
308#13133197D411yescharacteristic
309#13133197C2311yescharacteristic
310#13133197C2311yescharacteristic
311#13133195—21no—
312#13133193—21no—
313#13133193C2311yescharacteristic
314#13133193C2311yescharacteristic
315#13133192—21no—
316#13133192—21no—
317#13133192—21no—
318#13133192—21no—
319#13133192—21no—
320#13133192—21no—
321#13133192—21no—
322#13133192—21no—
323#13133192—21no—
324#13133192—21no—
325#13133192—21no—
326#13133192—21no—
327#13133192—21no—
328#13133192—21no—
329#13133192—21no—
330#13133192D411yescharacteristic
331#13133192D411yescharacteristic
332#13133192C2311yescharacteristic
333#13133192C2311yescharacteristic
334#13133192C2311yescharacteristic
335#13133192C2311yescharacteristic
336#13133192C2311yescharacteristic
337#13133192C2311yescharacteristic
338#13133192C2311yescharacteristic
339#13133192C2311yescharacteristic
340#13133192C2311yescharacteristic
341#13133192C2311yescharacteristic
342#13133191—21no—
343#13133191—21no—
344#13133191—21no—
345#13133191—21no—
346#13133191—21no—
347#13133191—21no—
348#13133191—21no—
349#13133191C2311yescharacteristic
350#13133191C2311yescharacteristic
351#13133190—21no—
352#13133190—21no—
353#13133190—21no—
354#13133190—21no—
355#13133190—21no—
356#13133190—21no—
357#13133190—21no—
358#13133190—21no—
359#13133189—21no—
360#13133188C2311yescharacteristic
361#13133188C2311yescharacteristic
362#13133187—21no—
363#13133187—21no—
364#13133187—21no—
365#13133187—21no—
366#13133187—21no—
367#13133187—21no—
368#13133187—21no—
369#13133187—21no—
370#13133187—21no—
371#13133187—21no—
372#13133187—21no—
373#13133187—21no—
374#13133187—21no—
375#13133187—21no—
376#13133187D411yescharacteristic
377#13133187D411yescharacteristic
378#13133185—21no—
379C4×D212—21no—
380C4×D212—21no—
381C4×D212—21no—
382C4×D212—21no—
383C4×D212—21no—
384C4×D212C2311yescharacteristic
385C4×D212C2311yescharacteristic
386C4×D212C2311yescharacteristic
387C4×D212C2311yescharacteristic
388C4×D212C2311yescharacteristic
389C4×D212C2311yescharacteristic
390#13133179—21no—
391C4×C22⋊D53—21no—
392#13133177—21no—
393#13133175—21no—
394#13133175C2311yescharacteristic
395#13133175C2311yescharacteristic
396#13133174—21no—
397C4⋊C4×D53C2311yescharacteristic
398C4⋊C4×D53C2311yescharacteristic
399C2×#11719921—21no—
400C2×#11719921—21no—
401C2×#11719921—21no—
402C22⋊C4×D53—21no—
403C22⋊C4×D53—21no—
404C22⋊C4×D53—21no—
405#13133150C2311yescharacteristic
406#13133150C2311yescharacteristic
407#13133148C2311yescharacteristic
408#13133148C2311yescharacteristic
409C4⋊#88322C2311yescharacteristic
410C4⋊#88322C2311yescharacteristic
411#13133142C2311yescharacteristic
412#13133142C2311yescharacteristic
413#13133141C2311yescharacteristic
414#13133141C2311yescharacteristic
415#13133140C2311yescharacteristic
416#13133140C2311yescharacteristic
417#13133139C2311yescharacteristic
418#13133139C2311yescharacteristic
419#13133139C2311yescharacteristic
420#13133139C2311yescharacteristic
421#13133139C2311yescharacteristic
422#13133139C2311yescharacteristic
423#13133138C2311yescharacteristic
424#13133138C2311yescharacteristic
425#13133137C2311yescharacteristic
426#13133137C2311yescharacteristic
427#13133137C2311yescharacteristic
428#13133137C2311yescharacteristic
429#13133137C2311yescharacteristic
430#13133137C2311yescharacteristic
431#13133137C2311yescharacteristic
432#13133137C2311yescharacteristic
433#13133137C2311yescharacteristic
434#13133137C2311yescharacteristic
435C22⋊#88322C2311yescharacteristic
436C22⋊#88322C2311yescharacteristic
437#13133129C2311yescharacteristic
438#13133129C2311yescharacteristic
439#13133129C2311yescharacteristic
440#13133129C2311yescharacteristic
441#13133129C2311yescharacteristic
442#13133129C2311yescharacteristic
443#13133129C2311yescharacteristic
444#13133129C2311yescharacteristic
445#13133128C2311yescharacteristic
446C4×#88322C2311yescharacteristic
447C2×#41×C53C2311yescharacteristic
448C2×Q16×C53C2311yescharacteristic
449C2×SD16×C53C2311yescharacteristic
450C2×SD16×C53C2311yescharacteristic
451C2×D8×C53C2311yescharacteristic
452C4⋊Q8×C53C2311yescharacteristic
453#126×C53—21no—
454#124×C53—21no—
455#124×C53C2311yescharacteristic
456#123×C53—21no—
457C22⋊Q8×C53—21no—
458C22⋊Q8×C53C2311yescharacteristic
459#121×C53C2311yescharacteristic
460C4×Q8×C53C2311yescharacteristic
461C4×Q8×C53C2311yescharacteristic
462C4×Q8×C53C2311yescharacteristic
463C4×D4×C53—21no—
464C4×D4×C53—21no—
465C4×D4×C53C2311yescharacteristic
466C4×D4×C53C2311yescharacteristic
467C4×D4×C53C2311yescharacteristic
468#117×C53—21no—
469#117×C53C2311yescharacteristic
470C2×C4⋊C4×C53—21no—
471C2×C4⋊C4×C53C2311yescharacteristic
472#107×C53C2311yescharacteristic
473#107×C53C2311yescharacteristic
474#107×C53C2311yescharacteristic
475#107×C53C2311yescharacteristic
476C4⋊C8×C53C2311yescharacteristic
477C4⋊C8×C53C2311yescharacteristic
478#103×C53C2311yescharacteristic
479#103×C53C2311yescharacteristic
480#103×C53C2311yescharacteristic
481#103×C53C2311yescharacteristic
482#102×C53C2311yescharacteristic
483#102×C53C2311yescharacteristic
484#102×C53C2311yescharacteristic
485#102×C53C2311yescharacteristic
486C22⋊C8×C53C2311yescharacteristic
487C22⋊C8×C53C2311yescharacteristic
488#97×C53C2311yescharacteristic
489C4×C8×C53C2311yescharacteristic
490C23×D53—21no—
491C23×D53—21no—
492C23×D53—21no—
493C23×D53—21no—
494C23×D53—21no—
495C23×D53—21no—
496C23×D53C2×D411yescharacteristic
497#41×C53—22no—
498#41×C53—22no—
499C2×Q8×C53—21no—
500C2×Q8×C53C2411yescharacteristic
501C2×Q8×C53C2411yescharacteristic
502C2×D4×C53—21no—
503C2×D4×C53—21no—
504C2×D4×C53C2411yescharacteristic
505C2×D4×C53C2411yescharacteristic
506C22×C4×C53—21no—
507C22×C4×C53—21no—
508C22×C4×C53—21no—
509C22×C4×C53—21no—
510C22×C4×C53—21no—
511C22×C4×C53C2411yescharacteristic
512C2×C22⋊D53—21no—
513C2×C22⋊D53—21no—
514C2×C22⋊D53—21no—
515C2×C22⋊D53—21no—
516C2×C22⋊D53—21no—
517C2×C22⋊D53—21no—
518C2×C22⋊D53—21no—
519C2×C22⋊D53—21no—
520C2×C22⋊D53—21no—
521C2×C22⋊D53—21no—
522C2×C22⋊D53—21no—
523C2×C22⋊D53C2×D411yescharacteristic
524C2×C22⋊D53C2×D411yescharacteristic
525C22×Dic53—21no—
526C22×Dic53C2×D411yescharacteristic
527#11719949—22no—
528#11719949—22no—
529#11719949—22no—
530#11719949—41no—
531#11719949—41no—
532#11719949—41no—
533#11719949—41no—
534#11719949—41no—
535#11719949—41no—
536#11719949—41no—
537#11719949—82no—
538Q8×D53—22no—
539Q8×D53—41no—
540#11719947—22no—
541#11719947—41no—
542#11719947—44no—
543D4×D53—22no—
544D4×D53—22no—
545D4×D53—22no—
546D4×D53—41no—
547D4×D53—41no—
548D4×D53—41no—
549D4×D53—41no—
550D4×D53—41no—
551D4×D53—41no—
552D4×D53—41no—
553D4×D53—44no—
554D4×D53—44no—
555D4×D53—44no—
556D4×D53—82no—
557#11719945—41no—
558#11719945—41no—
559#11719945—41no—
560#11719945—41no—
561#11719945—44no—
562#11719945—44no—
563C2×D212—21no—
564C2×D212—21no—
565C2×D212—21no—
566C2×D212—21no—
567C2×D212—21no—
568C2×D212—21no—
569C2×D212—21no—
570C2×D212—21no—
571C2×D212—21no—
572C2×D212—21no—
573C2×D212—21no—
574C2×D212—21no—
575C2×D212—21no—
576C2×D212—21no—
577C2×D212—21no—
578C2×D212—21no—
579C2×D212—21no—
580C2×D212—21no—
581C2×D212—21no—
582C2×D212—21no—
583C2×D212—21no—
584C2×D212—21no—
585C2×D212—41no—
586C2×D212—41no—
587C2×D212—44no—
588C2×D212—82no—
589C2×D212—82no—
590C2×D212—82no—
591C2×D212—82no—
592C2×D212C2×D411yescharacteristic
593C2×D212C2×D411yescharacteristic
594C2×D212C2×D411yescharacteristic
595C2×D212C2×D411yescharacteristic
596C2×D212C2×D411yescharacteristic
597C2×D212C2411yescharacteristic
598C2×D212C2411yescharacteristic
599C2×D212C2411yescharacteristic
600C2×D212C2411yescharacteristic
601C2×D212C2411yescharacteristic
602C2×C4×D53—21no—
603C2×C4×D53—21no—
604C2×C4×D53—21no—
605C2×C4×D53—21no—
606C2×C4×D53—21no—
607C2×C4×D53—21no—
608C2×C4×D53—21no—
609C2×C4×D53—21no—
610C2×C4×D53—21no—
611C2×C4×D53—21no—
612C2×C4×D53—21no—
613C2×C4×D53—41no—
614C2×C4×D53—41no—
615C2×C4×D53—44no—
616C2×C4×D53C2×D411yescharacteristic
617C2×C4×D53C2×D411yescharacteristic
618C2×C4×D53C2411yescharacteristic
619C2×C4×D53C2411yescharacteristic
620C2×C4×D53C2411yescharacteristic
621C2×C4×D53C2411yescharacteristic
622C2×Dic106—21no—
623C2×Dic106C2×D411yescharacteristic
624C2×Dic106C2411yescharacteristic
625Q16×C53—22no—
626SD16×C53—22no—
627SD16×C53—22no—
628D8×C53—22no—
629C2×C8×C53C2411yescharacteristic
630C2×C8×C53C2411yescharacteristic
631C2×C8×C53C2411yescharacteristic
632C2×C8×C53C2411yescharacteristic
633C4⋊C4×C53—21no—
634C4⋊C4×C53—21no—
635C4⋊C4×C53—21no—
636C4⋊C4×C53—21no—
637C4⋊C4×C53—21no—
638C4⋊C4×C53—21no—
639C4⋊C4×C53C2×D411yescharacteristic
640C4⋊C4×C53C2×D411yescharacteristic
641C4⋊C4×C53C2411yescharacteristic
642C4⋊C4×C53C2411yescharacteristic
643C4⋊C4×C53C2411yescharacteristic
644C4⋊C4×C53C2411yescharacteristic
645C22⋊C4×C53—21no—
646C22⋊C4×C53—21no—
647C22⋊C4×C53—21no—
648C22⋊C4×C53—21no—
649C22⋊C4×C53—21no—
650C22⋊C4×C53—21no—
651C22⋊C4×C53—21no—
652C22⋊C4×C53C2×D411yescharacteristic
653C22⋊C4×C53C2×D411yescharacteristic
654C42×C53—21no—
655C42×C53—21no—
656C42×C53—21no—
657C42×C53C2411yescharacteristic
658C42×C53C2411yescharacteristic
659C22⋊Dic53—21no—
660C22⋊Dic53—21no—
661#11719925—41no—
662#11719924—22no—
663#11719924—22no—
664#11719924—41no—
665#11719924—41no—
666#11719924—41no—
667#11719923—41no—
668#11719922—22no—
669#11719922—22no—
670#11719922—41no—
671#11719922—41no—
672#11719922—41no—
673#11719921—21no—
674#11719921—21no—
675#11719921—21no—
676#11719921—21no—
677#11719921—21no—
678#11719921—21no—
679#11719921—21no—
680#11719921—21no—
681#11719921—21no—
682#11719921—21no—
683#11719921—21no—
684#11719921—21no—
685#11719921—21no—
686#11719921—21no—
687#11719921—21no—
688#11719921—21no—
689#11719921—21no—
690#11719921—21no—
691#11719921—21no—
692#11719921—21no—
693#11719921—21no—
694#11719921—21no—
695#11719921—21no—
696#11719921—21no—
697#11719921C2×D411yescharacteristic
698#11719921C2×D411yescharacteristic
699#11719921C2×D411yescharacteristic
700#11719921C2×D411yescharacteristic
701#11719921C2×D411yescharacteristic
702#11719921C2×D411yescharacteristic
703#11719921C2×D411yescharacteristic
704#11719921C2×D411yescharacteristic
705C4⋊Dic53—21no—
706C4⋊Dic53—21no—
707C4⋊Dic53C2×D411yescharacteristic
708C4⋊Dic53C2×D411yescharacteristic
709C4⋊Dic53C2×D411yescharacteristic
710C4⋊Dic53C2×D411yescharacteristic
711C4⋊Dic53C2411yescharacteristic
712C4⋊Dic53C2411yescharacteristic
713#11719919—21no—
714#11719919—21no—
715#11719919—21no—
716#11719919—21no—
717#11719919—21no—
718#11719919—21no—
719C4×Dic53—21no—
720C4×Dic53—21no—
721C2×#88322C2411yescharacteristic
722C2×#88322C2411yescharacteristic
723C2×#88322C2411yescharacteristic
724C2×#88322C2411yescharacteristic
725D424—41no—
726D424—41no—
727D424—41no—
728D424—41no—
729D424—41no—
730D424—41no—
731#11719913—41no—
732#11719913—41no—
733#11719912—41no—
734#11719912—41no—
735C8×D53—41no—
736C8×D53—41no—
737C8×D53—41no—
738C8×D53—41no—
739C8×D53—41no—
740C8×D53—41no—
741C23×C53—21no—
742C23×C53—21no—
743C23×C53C22×D411yescharacteristic
744C22×D53—22no—
745C22×D53—21no—
746C22×D53—21no—
747C22×D53—21no—
748C22×D53—21no—
749C22×D53—21no—
750C22×D53—41no—
751C22×D53—41no—
752C22×D53—42no—
753C22×D53—42no—
754C22×D53—42no—
755C22×D53—42no—
756C22×D53—42no—
757C22×D53—42no—
758C22×D53—81no—
759C22×D53—81no—
760C22×D53—81no—
761C22×D53—81no—
762C22×D53—81no—
763C22×D53—81no—
764C22×D53—81no—
765C22×D53—81no—
766C22×D53—81no—
767C22×D53—81no—
768C22×D53—81no—
769C22×D53—81no—
770C22×D53C22×D411yescharacteristic
771C22×D53C22×D411yescharacteristic
772C22×D53C22×D411yescharacteristic
773C22×D53C22×D411yescharacteristic
774Q8×C53—21no—
775Q8×C53—21no—
776Q8×C53—21no—
777Q8×C53—81no—
778Q8×C53H(5,𝔽2)12yes—
779D4×C53—24no—
780D4×C53—21no—
781D4×C53—21no—
782D4×C53—21no—
783D4×C53—81no—
784D4×C53H(5,𝔽2)12yes—
785C2×C4×C53—24no—
786C2×C4×C53—21no—
787C2×C4×C53—21no—
788C2×C4×C53—21no—
789C2×C4×C53—21no—
790C2×C4×C53—21no—
791C2×C4×C53—21no—
792C2×C4×C53—21no—
793C2×C4×C53—21no—
794C2×C4×C53—81no—
795C2×C4×C53—81no—
796C2×C4×C53—81no—
797C2×C4×C53—81no—
798C2×C4×C53C22×D411yescharacteristic
799C2×C4×C53C22×D411yescharacteristic
800C2×C4×C53C22×D411yescharacteristic
801C2×C4×C53C22×D411yescharacteristic
802C2×C4×C53C22×D411yescharacteristic
803C2×C4×C53C2511yescharacteristic
804C22⋊D53—41no—
805C22⋊D53—41no—
806C22⋊D53—42no—
807C22⋊D53—42no—
808C22⋊D53—42no—
809C22⋊D53—42no—
810C22⋊D53—42no—
811C22⋊D53—81no—
812C22⋊D53—81no—
813C22⋊D53—81no—
814C22⋊D53—81no—
815C22⋊D53—81no—
816C22⋊D53—81no—
817C2×Dic53—21no—
818C2×Dic53—21no—
819C2×Dic53—21no—
820C2×Dic53—41no—
821C2×Dic53—42no—
822C2×Dic53C22×D411yescharacteristic
823C2×Dic53C22×D411yescharacteristic
824C2×Dic53C22×D411yescharacteristic
825C2×Dic53C22×D411yescharacteristic
826D212—22no—
827D212—22no—
828D212—21no—
829D212—21no—
830D212—21no—
831D212—21no—
832D212—21no—
833D212—21no—
834D212—21no—
835D212—21no—
836D212—21no—
837D212—21no—
838D212—41no—
839D212—41no—
840D212—41no—
841D212—42no—
842D212—42no—
843D212—42no—
844D212—42no—
845D212—42no—
846D212—42no—
847D212—42no—
848D212—81no—
849D212—81no—
850D212—81no—
851D212—81no—
852D212—81no—
853D212—81no—
854D212—81no—
855D212—81no—
856D212—81no—
857D212—81no—
858D212—81no—
859D212—81no—
860D212—81no—
861D212—81no—
862D212—81no—
863C4×D53—21no—
864C4×D53—21no—
865C4×D53—21no—
866C4×D53—21no—
867C4×D53—21no—
868C4×D53—21no—
869C4×D53—21no—
870C4×D53—21no—
871C4×D53—41no—
872C4×D53—41no—
873C4×D53—42no—
874C4×D53—42no—
875C4×D53—42no—
876C4×D53—42no—
877C4×D53—42no—
878C4×D53—42no—
879C4×D53—81no—
880C4×D53—81no—
881C4×D53—81no—
882C4×D53—81no—
883C4×D53—81no—
884Dic106—21no—
885Dic106—21no—
886Dic106—41no—
887Dic106—42no—
888C8×C53—21no—
889C8×C53—21no—
890C8×C53—21no—
891C8×C53—21no—
892#88322—21no—
893#88322—21no—
894#88322—21no—
895#88322—21no—
896#61639—531nomaximal, Sylow
897C22×C53—21no—
898C22×C53—21no—
899C22×C53—22no—
900C22×C53—21no—
901C22×C53—41no—
902C22×C53—41no—
903C22×C53—41no—
904C22×C53—41no—
905C22×C53—41no—
906C22×C53C23×D411yescharacteristic
907C2×D53—21no—
908C2×D53—21no—
909C2×D53—21no—
910C2×D53—21no—
911C2×D53—21no—
912C2×D53—21no—
913C2×D53—21no—
914C2×D53—21no—
915C2×D53—21no—
916C2×D53—21no—
917C2×D53—21no—
918C2×D53—41no—
919C2×D53—41no—
920C2×D53—41no—
921C2×D53—41no—
922C2×D53—41no—
923C2×D53—41no—
924C2×D53—41no—
925C2×D53—41no—
926C2×D53—41no—
927C2×D53—41no—
928C2×D53—41no—
929C2×D53—41no—
930C2×D53—41no—
931C2×D53—41no—
932C2×D53—41no—
933C2×D53—82no—
934C2×D53—84no—
935C2×D53—162no—
936C2×D53—162no—
937C2×D53—162no—
938C2×D53—162no—
939C2×D53—162no—
940C2×D53#57612yes—
941C4×C53—21no—
942C4×C53—21no—
943C4×C53—21no—
944C4×C53—22no—
945C4×C53—21no—
946C4×C53—21no—
947C4×C53—41no—
948C4×C53—41no—
949C4×C53—41no—
950C4×C53—41no—
951C4×C53—41no—
952C4×C53C2×H(5,𝔽2)11yescharacteristic
953C4×C53C2×H(5,𝔽2)11yescharacteristic
954Dic53—21no—
955Dic53—21no—
956Dic53—21no—
957Dic53—21no—
958Dic53—41no—
959Dic53—41no—
960Dic53—41no—
961#3542—531no—
962#3488—531no—
963#3319—531no—
964#3310—531no—
965#3309—531no—
966#3308—531no—
967#3305—531no—
968#3300—531no—
969#3297—531no—
970#3294—531no—
971#3287—531no—
972#3282—531no—
973#3280—531no—
974D4×D8—531no—
975#3268—531no—
976#3268—531no—
977#3265—531no—
978#3264—531no—
979#3224—531no—
980#3220—531no—
981#3203—531no—
982#3198—531no—
983#3188—531no—
984#3186—531no—
985#3124D5311yescharacteristic, complemented
986#3119—531no—
987#3012—531no—
988#3008—531no—
989#3002—531no—
990C2×#449—531no—
991#2977—531no—
992C2×C53—41no—
993C2×C53—42no—
994C2×C53—81no—
995C2×C53#348411yescharacteristic
996C2×C53C2×#57611yescharacteristic
997C2×C53#358411yescharacteristic
998D53—22no—
999D53—41no—
1000D53—41no—
1001D53—41no—
1002D53—81no—
1003D53—81no—
1004D53—81no—
1005D53—81no—
1006D53—81no—
1007C2×H(5,𝔽2)—531no—
1008C22×#41—531no—
1009C2×AGL(1,ℤ/8)—531no—
1010C2×AGL(1,ℤ/8)—531no—
1011C2×#135—531no—
1012C2×#135—531no—
1013C2×#135—531no—
1014C22×SD16—531no—
1015C22×D8—531no—
1016C22×D8—531no—
1017#562—1061no—
1018#560—1061no—
1019#555—531no—
1020#553—531no—
1021#552—531no—
1022#551—1061no—
1023#550—531no—
1024#550—531no—
1025#550—531no—
1026#548—531no—
1027#548—531no—
1028#547—531no—
1029#546—531no—
1030#546—531no—
1031#546—531no—
1032#546—531no—
1033#546—1061no—
1034#546—1061no—
1035#546—1061no—
1036D42—531no—
1037D42—531no—
1038D42—531no—
1039D42—1061no—
1040D42—1061no—
1041#542C2×D5311yescharacteristic, complemented
1042#540—531no—
1043#540—1061no—
1044#538—1061no—
1045#537—531no—
1046#537—531no—
1047#537—1061no—
1048#535—531no—
1049#535—531no—
1050#535—1061no—
1051#535—1061no—
1052#534—1061no—
1053#525—531no—
1054#525—531no—
1055#525—1061no—
1056C2×#121—531no—
1057C2×#121—531no—
1058C2×#121—1061no—
1059#520C2×D5311yescharacteristic, complemented
1060#496—531no—
1061#496—531no—
1062#495—531no—
1063#493—531no—
1064#490—531no—
1065#489—531no—
1066#488—531no—
1067#486—531no—
1068#485—531no—
1069#484—531no—
1070#484C2×D5311yescharacteristic, complemented
1071#482—531no—
1072#482—531no—
1073#482—531no—
1074#481—531no—
1075#480—531no—
1076#480—531no—
1077#480—531no—
1078#480—531no—
1079#480C2×D5311yescharacteristic, complemented
1080#479—531no—
1081#478—531no—
1082#477C2×D5311yescharacteristic, complemented
1083#474C2×D5311yescharacteristic, complemented
1084#469—531no—
1085#468—531no—
1086#468—531no—
1087#468—531no—
1088#467—531no—
1089#466—531no—
1090#466—531no—
1091#466—531no—
1092#466—531no—
1093#466—531no—
1094#466—531no—
1095#466—531no—
1096#466—531no—
1097#465—531no—
1098#465—531no—
1099#465—531no—
1100#464—531no—
1101#464C2×D5311yescharacteristic, complemented
1102#463—531no—
1103#463—531no—
1104#463—531no—
1105#463C2×D5311yescharacteristic, complemented
1106#460—531no—
1107#460—531no—
1108#459—531no—
1109#459—531no—
1110#459—531no—
1111#459—531no—
1112#452—531no—
1113#452—531no—
1114#452—531no—
1115#452C2×D5311yescharacteristic, complemented
1116#451—531no—
1117#450—531no—
1118#450—531no—
1119#450—531no—
1120#450—531no—
1121#449—531no—
1122#449—531no—
1123#449—531no—
1124#449—531no—
1125#449—531no—
1126#449—531no—
1127#449—531no—
1128#449—531no—
1129#449—531no—
1130#449—531no—
1131#449—531no—
1132#449—531no—
1133#449—531no—
1134#449—531no—
1135#449—531no—
1136#449C2×D5311yescharacteristic
1137#448—531no—
1138#447—531no—
1139#447—531no—
1140#447—531no—
1141#447—531no—
1142#447—531no—
1143#447—531no—
1144#447—531no—
1145#447—531no—
1146#447—531no—
1147#447—531no—
1148#442—531no—
1149#440—531no—
1150#440C2×D5311yescharacteristic, complemented
1151#440C2×D5311yescharacteristic, complemented
1152C4×Q16C2×D5311yescharacteristic, complemented
1153C4×SD16—531no—
1154C4×D8—531no—
1155C4×D8C2×D5311yescharacteristic, complemented
1156#435—531no—
1157#435—531no—
1158#435—531no—
1159#435—531no—
1160C8×D4—531no—
1161C8×D4—531no—
1162C8×D4—531no—
1163C8×D4—531no—
1164#433—531no—
1165#433C2×D5311yescharacteristic, complemented
1166#418—531no—
1167#417—531no—
1168#416—531no—
1169#416—531no—
1170#416—531no—
1171C2×#103—531no—
1172C2×#102—531no—
1173C2×#102—531no—
1174#408—531no—
1175#408—531no—
1176C2×C22⋊C8—531no—
1177C2×C22⋊C8—531no—
1178C53#6163911yescharacteristic, complemented, Sylow
1179H(5,𝔽2)—2122no—
1180H(5,𝔽2)—2122no—
1181C2×#41—531no—
1182C2×#41—531no—
1183C2×#41—531no—
1184C2×#41—531no—
1185C2×#41—531no—
1186C2×#41—531no—
1187C2×#41—531no—
1188C2×#41—531no—
1189C2×#41—1061no—
1190C2×#41—1061no—
1191C2×#41—1061no—
1192C2×#41—1061no—
1193C2×#41—2122no—
1194C2×#41—2122no—
1195C2×#41C22×D5311yescharacteristic
1196C22×Q8—531no—
1197C22×D4—531no—
1198C22×D4—531no—
1199C22×D4—531no—
1200C22×D4—531no—
1201C22×D4—531no—
1202C22×D4—531no—
1203C22×D4—1061no—
1204C22×D4—1061no—
1205C22×D4—1061no—
1206C22×D4—1061no—
1207C22×D4—1061no—
1208C22×D4—1061no—
1209C22×D4—1061no—
1210C22×D4—1061no—
1211C22×D4—1061no—
1212C23×C4—531no—
1213C23×C4—1061no—
1214AGL(1,ℤ/8)—2122no—
1215AGL(1,ℤ/8)—2122no—
1216#135—2122no—
1217#135—2122no—
1218#135—2122no—
1219C2×Q16—531no—
1220C2×Q16C22×D5311yescharacteristic
1221C2×SD16—531no—
1222C2×SD16—531no—
1223C2×SD16—531no—
1224C2×SD16—531no—
1225C2×SD16—531no—
1226C2×SD16—531no—
1227C2×SD16—531no—
1228C2×SD16—531no—
1229C2×SD16—2122no—
1230C2×SD16C22×D5311yescharacteristic
1231C2×SD16C22×D5311yescharacteristic
1232C2×D8—531no—
1233C2×D8—531no—
1234C2×D8—531no—
1235C2×D8—531no—
1236C2×D8—531no—
1237C2×D8—531no—
1238C2×D8—531no—
1239C2×D8—531no—
1240C2×D8—531no—
1241C2×D8—531no—
1242C2×D8—531no—
1243C2×D8—2122no—
1244C2×D8—2122no—
1245C2×D8C22×D5311yescharacteristic
1246C2×M16—531no—
1247C2×M16—531no—
1248C22×C8—531no—
1249C22×C8—531no—
1250C22×C8—531no—
1251C22×C8—531no—
1252C22×C8—531no—
1253C22×C8—531no—
1254C4⋊Q8C22×D5311yescharacteristic
1255#127—531no—
1256#127—531no—
1257#127—531no—
1258#127—1061no—
1259#127—1061no—
1260#127—1061no—
1261#127—1061no—
1262#126—21no—
1263#126—1061no—
1264#126—1061no—
1265#125—531no—
1266#125—1061no—
1267#124—21no—
1268#124—531no—
1269#124—531no—
1270#124—1061no—
1271#124—1061no—
1272#124—1061no—
1273#124—1061no—
1274#124—1061no—
1275#124C22×D5311yescharacteristic
1276#123—21no—
1277#123—531no—
1278#123—531no—
1279#123—1061no—
1280#123—1061no—
1281#123—1061no—
1282#123—1061no—
1283#123—1061no—
1284#123—1061no—
1285#123—1061no—
1286#123—1061no—
1287#123—1061no—
1288#123—1061no—
1289#123—1061no—
1290C22⋊Q8—21no—
1291C22⋊Q8—531no—
1292C22⋊Q8—531no—
1293C22⋊Q8—531no—
1294C22⋊Q8—531no—
1295C22⋊Q8—531no—
1296C22⋊Q8—531no—
1297C22⋊Q8—1061no—
1298C22⋊Q8—1061no—
1299C22⋊Q8—1061no—
1300C22⋊Q8—1061no—
1301C22⋊Q8—1061no—
1302C22⋊Q8C22×D5311yescharacteristic
1303#121—531no—
1304#121—531no—
1305#121—531no—
1306#121—531no—
1307#121—531no—
1308#121—531no—
1309#121—531no—
1310#121—531no—
1311#121—531no—
1312#121—531no—
1313#121—531no—
1314#121—531no—
1315#121—531no—
1316#121—531no—
1317#121—531no—
1318#121—531no—
1319#121—1061no—
1320#121—1061no—
1321#121—1061no—
1322#121—1061no—
1323#121—1061no—
1324#121—1061no—
1325#121—1061no—
1326#121—1061no—
1327#121—1061no—
1328#121—1061no—
1329#121—1061no—
1330#121—1061no—
1331#121—1061no—
1332#121—1061no—
1333#121—1061no—
1334#121—1061no—
1335#121—1061no—
1336#121—1061no—
1337#121—1061no—
1338#121—1061no—
1339#121—1061no—
1340#121—1061no—
1341#121—1061no—
1342#121—1061no—
1343#121—1061no—
1344#121—1061no—
1345#121—1061no—
1346#121—1061no—
1347#121—1061no—
1348#121—1061no—
1349#121—1061no—
1350#121C22×D5311yescharacteristic
1351#120—531no—
1352#120—531no—
1353#120—1061no—
1354#120—1061no—
1355#120—1061no—
1356#120—1061no—
1357#120—1061no—
1358#120—1061no—
1359#120—1061no—
1360#120—1061no—
1361#120—1061no—
1362#120—1061no—
1363#120—1061no—
1364#120—1061no—
1365#120—1061no—
1366#120—1061no—
1367#120—1061no—
1368C4×Q8C22×D5311yescharacteristic
1369C4×Q8C22×D5311yescharacteristic
1370C4×Q8C22×D5311yescharacteristic
1371C4×D4—21no—
1372C4×D4—21no—
1373C4×D4—531no—
1374C4×D4—531no—
1375C4×D4—531no—
1376C4×D4—531no—
1377C4×D4—531no—
1378C4×D4—531no—
1379C4×D4—1061no—
1380C4×D4—1061no—
1381C4×D4—1061no—
1382C4×D4—1061no—
1383C4×D4—1061no—
1384C4×D4—1061no—
1385C4×D4—1061no—
1386C4×D4—1061no—
1387C4×D4C22×D5311yescharacteristic
1388C4×D4C22×D5311yescharacteristic
1389C4×D4C22×D5311yescharacteristic
1390#117—21no—
1391#117—531no—
1392#117—531no—
1393#117—1061no—
1394#117—1061no—
1395#117C22×D5311yescharacteristic
1396C2×C4⋊C4—21no—
1397C2×C4⋊C4—531no—
1398C2×C4⋊C4—531no—
1399C2×C4⋊C4C22×D5311yescharacteristic
1400C2×C22⋊C4—1061no—
1401C2×C22⋊C4—1061no—
1402C2×C22⋊C4—1061no—
1403C2×C22⋊C4—1061no—
1404C2×C22⋊C4—1061no—
1405C2×C22⋊C4—1061no—
1406#107—531no—
1407#107—531no—
1408#107C22×D5311yescharacteristic
1409#107C22×D5311yescharacteristic
1410#107C22×D5311yescharacteristic
1411#107C22×D5311yescharacteristic
1412#106—531no—
1413#106—531no—
1414C4⋊C8—531no—
1415C4⋊C8—531no—
1416C4⋊C8C22×D5311yescharacteristic
1417C4⋊C8C22×D5311yescharacteristic
1418#103—531no—
1419#103—531no—
1420#103—531no—
1421#103—531no—
1422#103—531no—
1423#103—531no—
1424#103C22×D5311yescharacteristic
1425#103C22×D5311yescharacteristic
1426#103C22×D5311yescharacteristic
1427#103C22×D5311yescharacteristic
1428#102—531no—
1429#102—531no—
1430#102—531no—
1431#102—531no—
1432#102—531no—
1433#102—531no—
1434#102—531no—
1435#102—531no—
1436#102—531no—
1437#102—531no—
1438#102—531no—
1439#102—531no—
1440#102—531no—
1441#102—531no—
1442#102—531no—
1443#102—531no—
1444#102—531no—
1445#102—531no—
1446#102C22×D5311yescharacteristic
1447#102C22×D5311yescharacteristic
1448#102C22×D5311yescharacteristic
1449#102C22×D5311yescharacteristic
1450C22⋊C8—531no—
1451C22⋊C8—531no—
1452C22⋊C8—531no—
1453C22⋊C8—531no—
1454C22⋊C8—531no—
1455C22⋊C8—531no—
1456C22⋊C8—531no—
1457C22⋊C8—531no—
1458C22⋊C8—531no—
1459C22⋊C8—531no—
1460C22⋊C8C22×D5311yescharacteristic
1461C22⋊C8C22×D5311yescharacteristic
1462#97—531no—
1463#97C22×D5311yescharacteristic
1464C4×C8—531no—
1465C4×C8C22×D5311yescharacteristic
1466C24—531no—
1467C24—1061no—
1468C24—1061no—
1469C24—1061no—
1470C24—1061no—
1471C24—1061no—
1472C24—1061no—
1473#41—22no—
1474#41—22no—
1475#41—1062no—
1476#41—1062no—
1477#41—1062no—
1478#41—1062no—
1479#41—4242no—
1480#41—2121no—
1481#41—2121no—
1482#41—2121no—
1483#41—2121no—
1484#41—2124no—
1485#41—2124no—
1486#41—2121no—
1487#41—2121no—
1488#41—2121no—
1489#41—2121no—
1490#41—2121no—
1491#41—2121no—
1492#41—2121no—
1493#41—2121no—
1494#41—2124no—
1495C2×Q8—21no—
1496C2×Q8—531no—
1497C2×Q8—531no—
1498C2×Q8—1061no—
1499C2×Q8—1062no—
1500C2×Q8—2121no—
1501C2×Q8C23×D5311yescharacteristic
1502C2×Q8C23×D5311yescharacteristic
1503C2×D4—21no—
1504C2×D4—21no—
1505C2×D4—531no—
1506C2×D4—531no—
1507C2×D4—531no—
1508C2×D4—531no—
1509C2×D4—531no—
1510C2×D4—531no—
1511C2×D4—531no—
1512C2×D4—531no—
1513C2×D4—531no—
1514C2×D4—531no—
1515C2×D4—531no—
1516C2×D4—531no—
1517C2×D4—1061no—
1518C2×D4—1061no—
1519C2×D4—1061no—
1520C2×D4—1061no—
1521C2×D4—1061no—
1522C2×D4—1061no—
1523C2×D4—1061no—
1524C2×D4—1061no—
1525C2×D4—1061no—
1526C2×D4—1061no—
1527C2×D4—1061no—
1528C2×D4—1061no—
1529C2×D4—1061no—
1530C2×D4—1061no—
1531C2×D4—1061no—
1532C2×D4—1061no—
1533C2×D4—1061no—
1534C2×D4—1061no—
1535C2×D4—1061no—
1536C2×D4—1061no—
1537C2×D4—1062no—
1538C2×D4—1062no—
1539C2×D4—1062no—
1540C2×D4—1061no—
1541C2×D4—1061no—
1542C2×D4—1061no—
1543C2×D4—1061no—
1544C2×D4—1061no—
1545C2×D4—1061no—
1546C2×D4—1061no—
1547C2×D4—1061no—
1548C2×D4—1061no—
1549C2×D4—1061no—
1550C2×D4—1061no—
1551C2×D4—1061no—
1552C2×D4—1061no—
1553C2×D4—4242no—
1554C2×D4—4242no—
1555C2×D4—4242no—
1556C2×D4—4242no—
1557C2×D4—4242no—
1558C2×D4—2121no—
1559C2×D4—2121no—
1560C2×D4—2124no—
1561C2×D4—2121no—
1562C2×D4—2121no—
1563C2×D4—2121no—
1564C2×D4—2121no—
1565C2×D4—2121no—
1566C2×D4—2121no—
1567C2×D4—2121no—
1568C2×D4—2124no—
1569C2×D4—2124no—
1570C2×D4—2124no—
1571C2×D4C23×D5311yescharacteristic
1572C2×D4C23×D5311yescharacteristic
1573C22×C4—21no—
1574C22×C4—21no—
1575C22×C4—21no—
1576C22×C4—21no—
1577C22×C4—21no—
1578C22×C4—531no—
1579C22×C4—531no—
1580C22×C4—531no—
1581C22×C4—531no—
1582C22×C4—531no—
1583C22×C4—531no—
1584C22×C4—531no—
1585C22×C4—1061no—
1586C22×C4—1061no—
1587C22×C4—1061no—
1588C22×C4—1061no—
1589C22×C4—1061no—
1590C22×C4—1061no—
1591C22×C4—1061no—
1592C22×C4—1061no—
1593C22×C4—1061no—
1594C22×C4—1061no—
1595C22×C4—1061no—
1596C22×C4—1061no—
1597C22×C4—2121no—
1598C22×C4—2121no—
1599C22×C4—2124no—
1600C22×C4C23×D5311yescharacteristic
1601Q16—22no—
1602Q16—2121no—
1603SD16—22no—
1604SD16—22no—
1605SD16—1062no—
1606SD16—1062no—
1607SD16—2121no—
1608SD16—2121no—
1609SD16—2121no—
1610SD16—2121no—
1611SD16—2121no—
1612SD16—2121no—
1613D8—22no—
1614D8—1062no—
1615D8—1062no—
1616D8—2121no—
1617D8—2121no—
1618D8—2121no—
1619D8—2121no—
1620D8—2121no—
1621D8—2121no—
1622D8—2121no—
1623D8—2121no—
1624D8—2121no—
1625M16—2121no—
1626M16—2121no—
1627C2×C8—531no—
1628C2×C8—531no—
1629C2×C8—531no—
1630C2×C8—531no—
1631C2×C8—2121no—
1632C2×C8—2121no—
1633C2×C8—2121no—
1634C2×C8—2121no—
1635C2×C8—2121no—
1636C2×C8—2121no—
1637C2×C8C23×D5311yescharacteristic
1638C2×C8C23×D5311yescharacteristic
1639C2×C8C23×D5311yescharacteristic
1640C2×C8C23×D5311yescharacteristic
1641C4⋊C4—21no—
1642C4⋊C4—21no—
1643C4⋊C4—21no—
1644C4⋊C4—21no—
1645C4⋊C4—21no—
1646C4⋊C4—21no—
1647C4⋊C4—531no—
1648C4⋊C4—531no—
1649C4⋊C4—531no—
1650C4⋊C4—531no—
1651C4⋊C4—531no—
1652C4⋊C4—531no—
1653C4⋊C4—1061no—
1654C4⋊C4—1061no—
1655C4⋊C4—1061no—
1656C4⋊C4—1061no—
1657C4⋊C4—1061no—
1658C4⋊C4—1061no—
1659C4⋊C4—1061no—
1660C4⋊C4—1061no—
1661C4⋊C4D4×D5311yescharacteristic
1662C4⋊C4D4×D5311yescharacteristic
1663C4⋊C4C23×D5311yescharacteristic
1664C4⋊C4C23×D5311yescharacteristic
1665C4⋊C4C23×D5311yescharacteristic
1666C4⋊C4C23×D5311yescharacteristic
1667C22⋊C4—21no—
1668C22⋊C4—21no—
1669C22⋊C4—21no—
1670C22⋊C4—21no—
1671C22⋊C4—21no—
1672C22⋊C4—21no—
1673C22⋊C4—21no—
1674C22⋊C4—531no—
1675C22⋊C4—531no—
1676C22⋊C4—531no—
1677C22⋊C4—531no—
1678C22⋊C4—531no—
1679C22⋊C4—531no—
1680C22⋊C4—531no—
1681C22⋊C4—531no—
1682C22⋊C4—1061no—
1683C22⋊C4—1061no—
1684C22⋊C4—1061no—
1685C22⋊C4—1061no—
1686C22⋊C4—1061no—
1687C22⋊C4—1061no—
1688C22⋊C4—1061no—
1689C22⋊C4—1061no—
1690C22⋊C4—1061no—
1691C22⋊C4—1061no—
1692C22⋊C4—1061no—
1693C22⋊C4—1061no—
1694C22⋊C4—1061no—
1695C22⋊C4—1061no—
1696C22⋊C4—1061no—
1697C22⋊C4—1061no—
1698C22⋊C4—1061no—
1699C22⋊C4—1061no—
1700C22⋊C4—1061no—
1701C22⋊C4—1061no—
1702C22⋊C4—1061no—
1703C22⋊C4—1061no—
1704C22⋊C4—1061no—
1705C22⋊C4—1061no—
1706C22⋊C4—1061no—
1707C22⋊C4—1061no—
1708C22⋊C4D4×D5311yescharacteristic
1709C22⋊C4D4×D5311yescharacteristic
1710C42—21no—
1711C42—21no—
1712C42—21no—
1713C42—1061no—
1714C42—1061no—
1715C42C23×D5311yescharacteristic
1716C42C23×D5311yescharacteristic
1717C23—21no—
1718C23—21no—
1719C23—531no—
1720C23—531no—
1721C23—531no—
1722C23—531no—
1723C23—1062no—
1724C23—1061no—
1725C23—1061no—
1726C23—1061no—
1727C23—1061no—
1728C23—1061no—
1729C23—4241no—
1730C23—4241no—
1731C23—4241no—
1732C23—4241no—
1733C23—4241no—
1734C23—4241no—
1735C23—4241no—
1736C23—4241no—
1737C23—4241no—
1738C23—4241no—
1739C23—4241no—
1740C23—4241no—
1741C23—2122no—
1742C23—2122no—
1743C23—2122no—
1744C23—2121no—
1745C23—2121no—
1746C23—2122no—
1747C23—2122no—
1748C23—2122no—
1749C23C2×D4×D5311yescharacteristic
1750Q8—21no—
1751Q8—21no—
1752Q8—21no—
1753Q8—81no—
1754Q8—1061no—
1755Q8—1061no—
1756Q8—2121no—
1757Q8—2122no—
1758Q8#1313326312yes—
1759D4—24no—
1760D4—21no—
1761D4—21no—
1762D4—21no—
1763D4—81no—
1764D4—1062no—
1765D4—1062no—
1766D4—1061no—
1767D4—1061no—
1768D4—1061no—
1769D4—1061no—
1770D4—1061no—
1771D4—1061no—
1772D4—1061no—
1773D4—1061no—
1774D4—1061no—
1775D4—1061no—
1776D4—4241no—
1777D4—4241no—
1778D4—4241no—
1779D4—4241no—
1780D4—4241no—
1781D4—4241no—
1782D4—4241no—
1783D4—4241no—
1784D4—4241no—
1785D4—4241no—
1786D4—4241no—
1787D4—4241no—
1788D4—4241no—
1789D4—4241no—
1790D4—4241no—
1791D4—4241no—
1792D4—4241no—
1793D4—4241no—
1794D4—4241no—
1795D4—4241no—
1796D4—4241no—
1797D4—2121no—
1798D4—2121no—
1799D4—2121no—
1800D4—2122no—
1801D4—2122no—
1802D4—2122no—
1803D4—2122no—
1804D4—2122no—
1805D4—2122no—
1806D4—2122no—
1807D4—2121no—
1808D4—2121no—
1809D4—2122no—
1810D4—2122no—
1811D4—2122no—
1812D4—2122no—
1813D4—2122no—
1814D4#1313326312yes—
1815C2×C4—24no—
1816C2×C4—21no—
1817C2×C4—21no—
1818C2×C4—21no—
1819C2×C4—21no—
1820C2×C4—21no—
1821C2×C4—21no—
1822C2×C4—21no—
1823C2×C4—21no—
1824C2×C4—81no—
1825C2×C4—81no—
1826C2×C4—81no—
1827C2×C4—81no—
1828C2×C4—531no—
1829C2×C4—531no—
1830C2×C4—531no—
1831C2×C4—531no—
1832C2×C4—1061no—
1833C2×C4—1061no—
1834C2×C4—1061no—
1835C2×C4—1061no—
1836C2×C4—1061no—
1837C2×C4—1061no—
1838C2×C4—1061no—
1839C2×C4—1061no—
1840C2×C4—1061no—
1841C2×C4—1061no—
1842C2×C4—1061no—
1843C2×C4—4241no—
1844C2×C4—4241no—
1845C2×C4—4241no—
1846C2×C4—4241no—
1847C2×C4—4241no—
1848C2×C4—2121no—
1849C2×C4—2121no—
1850C2×C4—2122no—
1851C2×C4—2122no—
1852C2×C4—2122no—
1853C2×C4—2122no—
1854C2×C4—2122no—
1855C2×C4—2122no—
1856C2×C4—2121no—
1857C2×C4—2122no—
1858C2×C4C2×D4×D5311yescharacteristic
1859C2×C4C2×D4×D5311yescharacteristic
1860C2×C4C2×D4×D5311yescharacteristic
1861C2×C4C2×D4×D5311yescharacteristic
1862C2×C4C2×D4×D5311yescharacteristic
1863C2×C4C24×D5311yescharacteristic
1864C8—21no—
1865C8—21no—
1866C8—21no—
1867C8—21no—
1868C8—1061no—
1869C8—1061no—
1870C8—1061no—
1871C8—1061no—
1872C22—21no—
1873C22—22no—
1874C22—21no—
1875C22—21no—
1876C22—41no—
1877C22—41no—
1878C22—41no—
1879C22—41no—
1880C22—41no—
1881C22—532no—
1882C22—8482no—
1883C22—8482no—
1884C22—8482no—
1885C22—8482no—
1886C22—8482no—
1887C22—1061no—
1888C22—1061no—
1889C22—1061no—
1890C22—1061no—
1891C22—1061no—
1892C22—1061no—
1893C22—1061no—
1894C22—1061no—
1895C22—1061no—
1896C22—1061no—
1897C22—1061no—
1898C22—4244no—
1899C22—4242no—
1900C22—2121no—
1901C22—2121no—
1902C22—2121no—
1903C22—2121no—
1904C22—2121no—
1905C22—2121no—
1906C22—2121no—
1907C22—2121no—
1908C22—2121no—
1909C22—2121no—
1910C22—2121no—
1911C22—2121no—
1912C22—2121no—
1913C22—2121no—
1914C22—2121no—
1915C22C22×D4×D5311yescharacteristic
1916C4—21no—
1917C4—22no—
1918C4—21no—
1919C4—21no—
1920C4—21no—
1921C4—21no—
1922C4—41no—
1923C4—41no—
1924C4—41no—
1925C4—41no—
1926C4—41no—
1927C4—1061no—
1928C4—1061no—
1929C4—1061no—
1930C4—1061no—
1931C4—2121no—
1932C4—2121no—
1933C4—2121no—
1934C4C2×#1313326311yescharacteristic
1935C4C2×#1313326311yescharacteristic
1936C2—41no—
1937C2—42no—
1938C2—81no—
1939C2—1062no—
1940C2—4241no—
1941C2—4241no—
1942C2—4241no—
1943C2—4241no—
1944C2—4241no—
1945C2—2121no—
1946C2—2121no—
1947C2—2121no—
1948C2#2028834811yescharacteristic
1949C2#576×D5311yescharacteristic
1950C2#2028948511yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3124C2
socleC22×C53C23×D4
hypercenter#3124D53
hypocenterC53#61639
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ #117 ◁ #3124

Complements

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

NH ≅ G/Ntype
1. #20289027C2semidirect
2. #20288385C2semidirect
3. #20286868C2semidirect
4. #20286741C2semidirect
5. #20286726C2semidirect
6. #20286703C2semidirect
7. #20286662C2semidirect
8. #20286607C2semidirect
9. #20286570C2semidirect
10. #20286525C2semidirect
11. #20286474C2semidirect
12. #20286417C2semidirect
13. #20286395C2semidirect
14. D8×D212C2semidirect
15. #20286257C2semidirect
16. #20286250C2semidirect
17. #20286212C2semidirect
18. #20286201C2semidirect
19. #20285803C2semidirect
20. #20285767C2semidirect
21. #20285619C2semidirect
22. #20285574C2semidirect
23. #20285485C2semidirect
24. #20285465C2semidirect
25. #20284914C2semidirect
26. #20284023C2semidirect
27. #20283980C2semidirect
28. #20283936C2semidirect
29. #449×D53C2semidirect
30. #20283770C2semidirect
31. C53×#3124C2semidirect
32. C2×#13133263C22semidirect
33. C2×#41×D53C22semidirect
34. C2×#13133244C22semidirect
35. C2×#13133244C22semidirect
36. C2×#13133240C22semidirect
37. C2×#13133240C22semidirect
38. C2×#13133238C22semidirect
39. C2×SD16×D53C22semidirect
40. C2×D8×D53C22semidirect
41. C2×D8×D53C22semidirect
44. #16811339C22semidirect
45. #16811323C22semidirect
46. #16811314C22semidirect
48. #16811295C22semidirect
49. #16811295C22semidirect
50. #16811295C22semidirect
52. #16811285C22semidirect
53. #16811276C22semidirect
56. #16811268C22semidirect
57. #16811268C22semidirect
58. #16811266C22semidirect
59. #16811266C22semidirect
64. D4×D212C22semidirect
65. D4×D212C22semidirect
66. #16811228C22semidirect
70. #16811204C22semidirect
71. #16811203C22semidirect
73. #16811192C22semidirect
75. #16811189C22semidirect
77. #16811136C22semidirect
81. C2×#13133192C22semidirect
82. #121×D53C22semidirect
83. #16811013C22semidirect
84. #16811012C22semidirect
85. #16811005C22semidirect
86. #16811000C22semidirect
87. #16810988C22semidirect
88. #16810985C22semidirect
89. #16810978C22semidirect
90. #16810971C22semidirect
91. #16810966C22semidirect
92. #16810960C22semidirect
93. #16810950C22semidirect
94. #16810950C22semidirect
95. #16810950C22semidirect
96. #16810941C22semidirect
97. #16810938C22semidirect
98. #16810938C22semidirect
99. #16810938C22semidirect
100. #16810936C22semidirect
101. #16810930C22semidirect
102. #16810923C22semidirect
103. #16810875C22semidirect
104. #16810872C22semidirect
105. #16810870C22semidirect
106. #16810870C22semidirect
107. #16810863C22semidirect
108. #16810860C22semidirect
109. #16810860C22semidirect
110. #16810860C22semidirect
111. #16810860C22semidirect
112. #16810860C22semidirect
113. #16810860C22semidirect
114. #16810858C22semidirect
115. #16810858C22semidirect
116. #16810855C22semidirect
117. #16810855C22semidirect
118. #16810851C22semidirect
119. #16810845C22semidirect
120. #16810839C22semidirect
121. #16810839C22semidirect
122. #16810838C22semidirect
123. #16810823C22semidirect
124. #16810823C22semidirect
125. #16810819C22semidirect
126. #16810819C22semidirect
127. #16810818C22semidirect
128. #16810818C22semidirect
129. #16810788C22semidirect
130. #16810784C22semidirect
131. #16810783C22semidirect
132. #16810777C22semidirect
133. #16810775C22semidirect
134. #16810773C22semidirect
135. #16810772C22semidirect
136. #16810772C22semidirect
137. #16810771C22semidirect
138. #16810771C22semidirect
139. #16810771C22semidirect
140. #16810771C22semidirect
141. #16810771C22semidirect
142. #16810771C22semidirect
143. #16810770C22semidirect
144. #16810770C22semidirect
145. #16810769C22semidirect
146. #16810768C22semidirect
147. #16810768C22semidirect
148. #16810767C22semidirect
149. #16810767C22semidirect
150. #16810766C22semidirect
151. #16810765C22semidirect
152. #16810763C22semidirect
153. #16810759C22semidirect
154. #16810759C22semidirect
155. #16810758C22semidirect
156. #16810758C22semidirect
157. #16810758C22semidirect
158. #16810758C22semidirect
159. #16810758C22semidirect
160. #16810758C22semidirect
161. #16810756C22semidirect
162. #16810755C22semidirect
163. #16810733C22semidirect
164. #16810721C22semidirect
165. C4×#11719924C22semidirect
166. C4×#11719922C22semidirect
167. #16810696C22semidirect
168. #16810696C22semidirect
169. #16810693C22semidirect
170. #16810693C22semidirect
171. C8×D212C22semidirect
172. C8×D212C22semidirect
173. #16810688C22semidirect
174. #16810688C22semidirect
175. #16810684C22semidirect
176. #16810626C22semidirect
177. #16810623C22semidirect
178. #16810618C22semidirect
179. #16810618C22semidirect
180. #16810616C22semidirect
181. #103×D53C22semidirect
182. #102×D53C22semidirect
183. #102×D53C22semidirect
184. #16810588C22semidirect
185. #16810588C22semidirect
186. C22⋊C8×D53C22semidirect
187. C22⋊C8×D53C22semidirect
188. C53×#542C22semidirect
189. C53×#520C22semidirect
190. C53×#484C22semidirect
191. C53×#480C22semidirect
192. C53×#477C22semidirect
193. C53×#474C22semidirect
194. C53×#464C22semidirect
195. C53×#463C22semidirect
196. C53×#452C22semidirect
198. C53×#440C22semidirect
199. C53×#440C22semidirect
200. C4×Q16×C53C22semidirect
201. C4×D8×C53C22semidirect
202. C53×#433C22semidirect
985. #3124D53semidirect
1041. #542C2×D53semidirect
1059. #520C2×D53semidirect
1070. #484C2×D53semidirect
1079. #480C2×D53semidirect
1082. #477C2×D53semidirect
1083. #474C2×D53semidirect
1101. #464C2×D53semidirect
1105. #463C2×D53semidirect
1115. #452C2×D53semidirect
1150. #440C2×D53semidirect
1151. #440C2×D53semidirect
1152. C4×Q16C2×D53semidirect
1155. C4×D8C2×D53semidirect
1165. #433C2×D53semidirect
1178. C53#61639semidirect

Maximal subgroups

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

subgroupindex
#202890272
#202883852
#202868682
#202867412
#202867262
#202867032
#202866622
#202866072
#202865702
#202865252
#202864742
#202864172
#202863952
D8×D2122
#202862572
#202862502
#202862122
#202862012
#202858032
#202857672
#202856192
#202855742
#202854852
#202854652
#202849142
#202840232
#202839802
#202839362
#449×D532
#202837702
C53×#31242
#6163953