Finite Group Databasebeta

← #28277997

Subgroups — #28277997

Order 13568.

1960 conjugacy classes of subgroups.

The subgroup lattice has 1856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289044C211yesmaximal, characteristic, complemented
2#20288666C211yesmaximal, characteristic, complemented
3#20287758C211yesmaximal, characteristic, complemented
4#20287727C211yesmaximal, characteristic, complemented
5#20287508C211yesmaximal, characteristic, complemented
6#20287348C211yesmaximal, characteristic, complemented
7#20286959C211yesmaximal, characteristic, complemented
8#20286955C211yesmaximal, characteristic, complemented
9#20286944C211yesmaximal, characteristic, complemented
10#20286876C211yesmaximal, characteristic, complemented
11#20286869C211yesmaximal, characteristic, complemented
12#20286652C211yesmaximal, characteristic, complemented
13#20286385C211yesmaximal, characteristic, complemented
14#20286333C211yesmaximal, characteristic, complemented
15#20286326C211yesmaximal, characteristic, complemented
16#20286325C211yesmaximal, characteristic, complemented
17#20286197C211yesmaximal, characteristic, complemented
18#20286188C211yesmaximal, characteristic, complemented
19#20286130C211yesmaximal, characteristic, complemented
20#20286120C211yesmaximal, characteristic, complemented
21#20286076C211yesmaximal, characteristic, complemented
22#20285811C211yesmaximal, characteristic, complemented
23#20285806C211yesmaximal, characteristic, complemented
24#20285632C211yesmaximal, characteristic, complemented
25#20284960C211yesmaximal, characteristic, complemented
26#20284738C211yesmaximal, characteristic, complemented
27#20284218C211yesmaximal, characteristic, complemented
28#20284213C211yesmaximal, characteristic, complemented
29#20284190C211yesmaximal, characteristic, complemented
30#20283858C211yesmaximal, characteristic, complemented
31C53×#3122C211yesmaximal, characteristic, complemented
32C2×#13133243C2211yescharacteristic, complemented
33C2×#13133241C2211yescharacteristic, complemented
34C2×#13133241C2211yescharacteristic, complemented
35C2×#13133241C2211yescharacteristic, complemented
36C22×#11719922C2211yescharacteristic, complemented
37C2×D8×D53C2211yescharacteristic, complemented
38#16811363—21no—
39#16811361—21no—
40#16811356C2211yescharacteristic, complemented
41#16811356C2211yescharacteristic, complemented
42#16811341C2211yescharacteristic, complemented
43#16811338C2211yescharacteristic, complemented
44#16811336C2211yescharacteristic, complemented
45#16811302—21no—
46#16811299—21no—
47#16811294C2211yescharacteristic, complemented
48#16811291C2211yescharacteristic
49D4×Dic106C2211yescharacteristic, complemented
50#16811282—21no—
51#16811270C2211yescharacteristic, complemented
52#16811268C2211yescharacteristic, complemented
53#16811268C2211yescharacteristic, complemented
54#16811267C2211yescharacteristic, complemented
55#16811265—21no—
56#16811263—21no—
57D4×D212C2211yescharacteristic, complemented
58#16811257—21no—
59#16811257C2211yescharacteristic
60#16811257C2211yescharacteristic, complemented
61D4×C22⋊D53C2211yescharacteristic, complemented
62#16811244C2211yescharacteristic, complemented
63#16811238C2211yescharacteristic, complemented
64#16811229C2211yescharacteristic, complemented
65#16811225—21no—
66#16811211—21no—
67#16811206—21no—
68#16811192C2211yescharacteristic, complemented
69#16811189—21no—
70#16811186C2211yescharacteristic, complemented
71#16811184—21no—
72#16811181—21no—
73#16811170C2211yescharacteristic, complemented
74#127×D53C2211yescharacteristic, complemented
75#16811158C2211yescharacteristic, complemented
76#16811153—21no—
77#16811151C2211yescharacteristic
78C2×#13133203—21no—
79#16811095C2211yescharacteristic, complemented
80C4×#11719947C2211yescharacteristic, complemented
81#16811012C2211yescharacteristic, complemented
82#16811011C2211yescharacteristic, complemented
83#16811007C2211yescharacteristic, complemented
84#16811006C2211yescharacteristic, complemented
85#16810998C2211yescharacteristic
86#16810998C2211yescharacteristic, complemented
87#16810983C2211yescharacteristic, complemented
88#16810981C2211yescharacteristic, complemented
89#16810970C2211yescharacteristic, complemented
90#16810968C2211yescharacteristic, complemented
91#16810968C2211yescharacteristic, complemented
92#16810968C2211yescharacteristic, complemented
93#16810967C2211yescharacteristic, complemented
94#16810950C2211yescharacteristic, complemented
95#16810950C2211yescharacteristic, complemented
96#16810949C2211yescharacteristic, complemented
97#16810927C2211yescharacteristic, complemented
98#16810920C2211yescharacteristic, complemented
99#16810913C2211yescharacteristic, complemented
100#16810912C2211yescharacteristic, complemented
101#16810907C2211yescharacteristic, complemented
102#16810903C2211yescharacteristic, complemented
103#16810902C2211yescharacteristic, complemented
104#16810902C2211yescharacteristic, complemented
105#16810877C2211yescharacteristic, complemented
106#16810875C2211yescharacteristic, complemented
107#16810875C2211yescharacteristic, complemented
108#16810874C2211yescharacteristic, complemented
109#16810870C2211yescharacteristic, complemented
110#16810870C2211yescharacteristic, complemented
111#16810868C2211yescharacteristic, complemented
112#16810867C2211yescharacteristic, complemented
113#16810858C2211yescharacteristic, complemented
114#16810857C2211yescharacteristic, complemented
115#16810853C2211yescharacteristic, complemented
116#16810850C2211yescharacteristic, complemented
117#16810846C2211yescharacteristic, complemented
118#16810839C2211yescharacteristic, complemented
119#16810838C2211yescharacteristic, complemented
120#16810838C2211yescharacteristic, complemented
121#16810838C2211yescharacteristic, complemented
122#16810838C2211yescharacteristic, complemented
123#16810838C2211yescharacteristic, complemented
124#16810838C2211yescharacteristic, complemented
125#16810837C2211yescharacteristic, complemented
126#16810837C2211yescharacteristic, complemented
127#16810837C2211yescharacteristic, complemented
128#16810836C2211yescharacteristic, complemented
129#16810824C2211yescharacteristic, complemented
130#16810822C2211yescharacteristic, complemented
131#16810822C2211yescharacteristic, complemented
132#16810822C2211yescharacteristic, complemented
133#16810820C2211yescharacteristic, complemented
134#16810819C2211yescharacteristic, complemented
135#16810818C2211yescharacteristic, complemented
136#16810818C2211yescharacteristic, complemented
137#16810818C2211yescharacteristic, complemented
138#16810818C2211yescharacteristic, complemented
139#16810817C2211yescharacteristic, complemented
140#16810817C2211yescharacteristic, complemented
141#16810816C2211yescharacteristic
142#16810816C2211yescharacteristic, complemented
143#16810816C2211yescharacteristic, complemented
144#16810815C2211yescharacteristic, complemented
145#16810787C2211yescharacteristic, complemented
146#16810786C2211yescharacteristic, complemented
147#16810786C2211yescharacteristic, complemented
148#16810776C2211yescharacteristic, complemented
149#16810775C2211yescharacteristic, complemented
150#16810770C2211yescharacteristic, complemented
151#16810769C2211yescharacteristic
152#16810765C2211yescharacteristic, complemented
153#16810759C2211yescharacteristic, complemented
154#16810758C2211yescharacteristic, complemented
155#16810758C2211yescharacteristic, complemented
156#16810758C2211yescharacteristic, complemented
157#16810758C2211yescharacteristic, complemented
158#16810755C2211yescharacteristic, complemented
159#16810755C2211yescharacteristic, complemented
160#16810755C2211yescharacteristic, complemented
161#16810751C2211yescharacteristic, complemented
162C8×Dic106C2211yescharacteristic, complemented
163#16810734C2211yescharacteristic, complemented
164#16810732C2211yescharacteristic, complemented
165#16810717C2211yescharacteristic, complemented
166#16810714C2211yescharacteristic, complemented
167#16810710C2211yescharacteristic, complemented
168#16810705C2211yescharacteristic, complemented
169#16810703C2211yescharacteristic, complemented
170#16810703C2211yescharacteristic, complemented
171#16810702C2211yescharacteristic, complemented
172#16810698C2211yescharacteristic, complemented
173#16810698C2211yescharacteristic, complemented
174#16810696C2211yescharacteristic, complemented
175#16810691C2211yescharacteristic, complemented
176#16810686C2211yescharacteristic, complemented
177#16810683C2211yescharacteristic, complemented
178#16810675C2211yescharacteristic, complemented
179#16810650C2211yescharacteristic, complemented
180#16810648C2211yescharacteristic, complemented
181#16810645C2211yescharacteristic, complemented
182#16810627C2211yescharacteristic, complemented
183#16810626C2211yescharacteristic, complemented
184#16810626C2211yescharacteristic, complemented
185#16810626C2211yescharacteristic, complemented
186#16810617C2211yescharacteristic, complemented
187#16810616C2211yescharacteristic, complemented
188C53×#540C2211yescharacteristic, complemented
189C53×#518C2211yescharacteristic, complemented
190C53×#482C2211yescharacteristic, complemented
191C53×#482C2211yescharacteristic, complemented
192C53×#478C2211yescharacteristic, complemented
193C53×#478C2211yescharacteristic, complemented
194C53×#459C2211yescharacteristic, complemented
195C53×#459C2211yescharacteristic, complemented
196C53×#447C2211yescharacteristic, complemented
197C53×#447C2211yescharacteristic, complemented
198C53×#442C2211yescharacteristic, complemented
199C53×#442C2211yescharacteristic, complemented
200C4×D8×C53C2211yescharacteristic, complemented
201C4×D8×C53C2211yescharacteristic, complemented
202C53×#433C2211yescharacteristic, complemented
203C2×#11719945—21no—
204C2×#11719945—21no—
205C2×#11719945C2311yescharacteristic
206C2×#11719947C2311yescharacteristic
207C2×#11719947C2311yescharacteristic
208C22×Dic106—21no—
209C22×D212—21no—
210C22×D212C2311yescharacteristic
211C22×C22⋊D53—21no—
212C2×D4×D53—21no—
213C2×D4×D53—21no—
214C2×D4×D53—21no—
215C2×D4×D53—21no—
216C2×D4×D53C2311yescharacteristic
217C2×D4×D53C2311yescharacteristic
218C2×D4×D53C2311yescharacteristic
219C2×D4×D53C2311yescharacteristic
220#13133243—42no—
221#13133241—42no—
222#13133241—42no—
223#13133241—42no—
224C2×Dic212C2311yescharacteristic
225C2×#11719913C2311yescharacteristic
226C2×#11719913C2311yescharacteristic
227C2×#11719913C2311yescharacteristic
228C2×#11719913C2311yescharacteristic
229C2×#11719923C2311yescharacteristic
230C2×#11719923C2311yescharacteristic
231C2×#11719923C2311yescharacteristic
232C2×#11719923C2311yescharacteristic
233C2×D424C2311yescharacteristic
234C2×D424C2311yescharacteristic
235C2×D424C2311yescharacteristic
236C2×#11719922—42no—
237C2×#11719922C2311yescharacteristic
238C2×#11719922C2311yescharacteristic
239C2×#11719922C2311yescharacteristic
240C2×#11719922C2311yescharacteristic
241C2×#11719922C2311yescharacteristic
242C2×#11719922C2311yescharacteristic
243C2×#11719922C2311yescharacteristic
244C2×#11719922C2311yescharacteristic
245D8×D53—42no—
246C2×#11719917C2311yescharacteristic
247C2×#11719912C2311yescharacteristic
248C2×#11719912C2311yescharacteristic
249C2×#11719912C2311yescharacteristic
250C22×#88322C2311yescharacteristic
251C2×C8×D53C2311yescharacteristic
252#13133217C2311yescharacteristic
253#13133216C2311yescharacteristic
254#13133216C2311yescharacteristic
255#13133214C2311yescharacteristic
256#13133214C2311yescharacteristic
257#13133213—21no—
258#13133213—21no—
259#13133213—21no—
260#13133213C2311yescharacteristic
261#13133213C2311yescharacteristic
262#13133213C2311yescharacteristic
263#13133213C2311yescharacteristic
264#13133212—21no—
265#13133212—21no—
266#13133212D411yescharacteristic
267#13133211—21no—
268#13133210—21no—
269#13133210—21no—
270#13133210D411yescharacteristic
271#13133207D411yescharacteristic
272#13133205—21no—
273#13133205C2311yescharacteristic
274#13133205C2311yescharacteristic
275#13133205C2311yescharacteristic
276#13133204C2311yescharacteristic
277#13133204C2311yescharacteristic
278#13133203—21no—
279#13133203—21no—
280#13133203—21no—
281#13133203—21no—
282#13133203—21no—
283#13133203—21no—
284#13133203—21no—
285#13133203—21no—
286#13133203—21no—
287#13133203D411yescharacteristic
288#13133202—21no—
289#13133202—21no—
290#13133202—21no—
291#13133202D411yescharacteristic
292#13133201—21no—
293#13133201—21no—
294#13133200—21no—
295#13133200—21no—
296#13133200—21no—
297#13133199—21no—
298#13133199—21no—
299#13133199—21no—
300#13133199—21no—
301#13133199D411yescharacteristic
302#13133198—21no—
303#13133197C2311yescharacteristic
304#13133197C2311yescharacteristic
305#13133196—21no—
306#13133196—21no—
307#13133196C2311yescharacteristic
308#13133195—21no—
309#13133195D411yescharacteristic
310#13133194—21no—
311#13133194—21no—
312#13133192—21no—
313#13133192—21no—
314#13133192—21no—
315#13133192—21no—
316#13133192C2311yescharacteristic
317#13133192C2311yescharacteristic
318#13133192C2311yescharacteristic
319#13133192C2311yescharacteristic
320#13133191—21no—
321#13133191—21no—
322#13133191—21no—
323#13133191—21no—
324#13133191—21no—
325#13133191C2311yescharacteristic
326#13133190—21no—
327#13133190—21no—
328#13133190—21no—
329#13133190—21no—
330#13133190—21no—
331#13133190—21no—
332#13133190—21no—
333#13133190D411yescharacteristic
334#13133189—21no—
335#13133189—21no—
336#13133189—21no—
337#13133189—21no—
338#13133189—21no—
339#13133188—21no—
340#13133188C2311yescharacteristic
341#13133188C2311yescharacteristic
342#13133187—21no—
343#13133187—21no—
344#13133187—21no—
345#13133187—21no—
346#13133187—21no—
347#13133187—21no—
348#13133187—21no—
349#13133187—21no—
350#13133186—21no—
351#13133186—21no—
352#13133185—21no—
353#13133185—21no—
354#13133185—21no—
355#13133185—21no—
356#13133185—21no—
357#13133185—21no—
358C4×Dic106—21no—
359C4×Dic106C2311yescharacteristic
360C4×Dic106C2311yescharacteristic
361#13133182C2311yescharacteristic
362#13133182C2311yescharacteristic
363C4×D212C2311yescharacteristic
364C4×D212C2311yescharacteristic
365D4×Dic53C2311yescharacteristic
366D4×Dic53C2311yescharacteristic
367#13133179—21no—
368#13133179C2311yescharacteristic
369#13133179C2311yescharacteristic
370#13133179C2311yescharacteristic
371#13133179C2311yescharacteristic
372C4×C22⋊D53—21no—
373C4×C22⋊D53—21no—
374C4×C22⋊D53—21no—
375C4×C22⋊D53—21no—
376C4×C22⋊D53—21no—
377C4×C22⋊D53C2311yescharacteristic
378C4×C22⋊D53C2311yescharacteristic
379#13133177—21no—
380#13133177—21no—
381#13133177—21no—
382#13133176—21no—
383#13133175—21no—
384#13133175C2311yescharacteristic
385#13133175C2311yescharacteristic
386#13133174—21no—
387#13133174C2311yescharacteristic
388#13133173—21no—
389C2×C22⋊Dic53—21no—
390C2×#11719921—21no—
391C2×#11719921—21no—
392C2×#11719921—21no—
393C22⋊C4×D53—21no—
394C22⋊C4×D53—21no—
395C2×C4×Dic53—21no—
396C42×D53C2311yescharacteristic
397#13133150C2311yescharacteristic
398#13133150C2311yescharacteristic
399#13133148C2311yescharacteristic
400#13133148C2311yescharacteristic
401C4⋊#88322C2311yescharacteristic
402C4⋊#88322C2311yescharacteristic
403C4⋊#88322C2311yescharacteristic
404C4⋊#88322C2311yescharacteristic
405#13133146C2311yescharacteristic
406#13133146C2311yescharacteristic
407#13133146C2311yescharacteristic
408#13133146C2311yescharacteristic
409#13133142C2311yescharacteristic
410#13133142C2311yescharacteristic
411#13133140C2311yescharacteristic
412#13133140C2311yescharacteristic
413#13133140C2311yescharacteristic
414#13133140C2311yescharacteristic
415#13133139C2311yescharacteristic
416#13133139C2311yescharacteristic
417#13133139C2311yescharacteristic
418#13133139C2311yescharacteristic
419#13133139C2311yescharacteristic
420#13133139C2311yescharacteristic
421#13133138C2311yescharacteristic
422#13133138C2311yescharacteristic
423#13133138C2311yescharacteristic
424#13133138C2311yescharacteristic
425#13133137C2311yescharacteristic
426#13133137C2311yescharacteristic
427#13133137C2311yescharacteristic
428#13133137C2311yescharacteristic
429#13133137C2311yescharacteristic
430#13133137C2311yescharacteristic
431#13133137C2311yescharacteristic
432#13133137C2311yescharacteristic
433#13133129C2311yescharacteristic
434#13133129C2311yescharacteristic
435#13133129C2311yescharacteristic
436#13133129C2311yescharacteristic
437#13133127C2311yescharacteristic
438C8×Dic53C2311yescharacteristic
439C8×Dic53C2311yescharacteristic
440C8×Dic53C2311yescharacteristic
441C22×D4×C53C2311yescharacteristic
442C2×D8×C53C2311yescharacteristic
443C2×D8×C53C2311yescharacteristic
444C2×D8×C53C2311yescharacteristic
445C2×D8×C53C2311yescharacteristic
446#127×C53C2311yescharacteristic
447#125×C53C2311yescharacteristic
448#123×C53—21no—
449#123×C53—21no—
450#121×C53—21no—
451#121×C53—21no—
452#121×C53C2311yescharacteristic
453#121×C53C2311yescharacteristic
454C4×D4×C53—21no—
455C4×D4×C53—21no—
456C4×D4×C53C2311yescharacteristic
457C4×D4×C53C2311yescharacteristic
458C4×D4×C53C2311yescharacteristic
459C4×D4×C53C2311yescharacteristic
460C4×D4×C53C2311yescharacteristic
461C4×D4×C53C2311yescharacteristic
462#117×C53C2311yescharacteristic
463#117×C53C2311yescharacteristic
464C2×C22⋊C4×C53—21no—
465C2×C22⋊C4×C53—21no—
466#107×C53C2311yescharacteristic
467#107×C53C2311yescharacteristic
468#106×C53C2311yescharacteristic
469#106×C53C2311yescharacteristic
470C4⋊C8×C53C2311yescharacteristic
471C4⋊C8×C53C2311yescharacteristic
472#102×C53C2311yescharacteristic
473#102×C53C2311yescharacteristic
474#102×C53C2311yescharacteristic
475#102×C53C2311yescharacteristic
476#102×C53C2311yescharacteristic
477#102×C53C2311yescharacteristic
478#102×C53C2311yescharacteristic
479#102×C53C2311yescharacteristic
480C22⋊C8×C53C2311yescharacteristic
481C22⋊C8×C53C2311yescharacteristic
482#97×C53C2311yescharacteristic
483C4×C8×C53C2311yescharacteristic
484C24×C53—21no—
485C23×D53—21no—
486C23×D53—21no—
487C23×D53—21no—
488C23×D53—21no—
489C23×D53—21no—
490C2×D4×C53—22no—
491C2×D4×C53—21no—
492C2×D4×C53—21no—
493C2×D4×C53—21no—
494C2×D4×C53—21no—
495C2×D4×C53—21no—
496C2×D4×C53—41no—
497C2×D4×C53C2411yescharacteristic
498C2×D4×C53C2411yescharacteristic
499C2×D4×C53C2411yescharacteristic
500C2×D4×C53C2411yescharacteristic
501C22×C4×C53—21no—
502C22×C4×C53—21no—
503C22×C4×C53—21no—
504C22×C4×C53—21no—
505C22×C4×C53—21no—
506C22×C4×C53—21no—
507C22×C4×C53C2411yescharacteristic
508C2×C22⋊D53—21no—
509C2×C22⋊D53—21no—
510C2×C22⋊D53—21no—
511C2×C22⋊D53—21no—
512C2×C22⋊D53—21no—
513C2×C22⋊D53—21no—
514C2×C22⋊D53—21no—
515C2×C22⋊D53—21no—
516C2×C22⋊D53—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⋊D53—21no—
524C2×C22⋊D53—21no—
525C2×C22⋊D53—21no—
526C2×C22⋊D53—82no—
527C2×C22⋊D53C2×D411yescharacteristic
528C2×C22⋊D53C2×D411yescharacteristic
529C22×Dic53—21no—
530C22×Dic53—21no—
531C22×Dic53—21no—
532C22×Dic53—21no—
533#11719947—22no—
534#11719947—41no—
535#11719947—41no—
536#11719947—41no—
537D4×D53—22no—
538D4×D53—41no—
539D4×D53—41no—
540D4×D53—41no—
541D4×D53—41no—
542D4×D53—41no—
543D4×D53—41no—
544D4×D53—41no—
545D4×D53—82no—
546D4×D53—82no—
547D4×D53—82no—
548D4×D53—82no—
549#11719945—41no—
550#11719945—41no—
551#11719945—82no—
552#11719945—82no—
553C2×D212—21no—
554C2×D212—21no—
555C2×D212—21no—
556C2×D212—21no—
557C2×D212—21no—
558C2×D212—21no—
559C2×D212—21no—
560C2×D212—21no—
561C2×D212—21no—
562C2×D212—41no—
563C2×D212—41no—
564C2×D212—82no—
565C2×D212C2×D411yescharacteristic
566C2×D212C2411yescharacteristic
567C2×D212C2411yescharacteristic
568C2×D212C2411yescharacteristic
569C2×D212C2411yescharacteristic
570C2×C4×D53—21no—
571C2×C4×D53—21no—
572C2×C4×D53—21no—
573C2×C4×D53—21no—
574C2×C4×D53—21no—
575C2×C4×D53—21no—
576C2×C4×D53C2×D411yescharacteristic
577C2×C4×D53C2×D411yescharacteristic
578C2×C4×D53C2411yescharacteristic
579C2×C4×D53C2411yescharacteristic
580C2×Dic106—21no—
581C2×Dic106—21no—
582C2×Dic106—21no—
583C2×Dic106—82no—
584C2×Dic106C2×D411yescharacteristic
585C2×Dic106C2411yescharacteristic
586C2×Dic106C2411yescharacteristic
587D8×C53—22no—
588D8×C53—22no—
589D8×C53—41no—
590D8×C53—41no—
591C2×C8×C53C2411yescharacteristic
592C2×C8×C53C2411yescharacteristic
593C2×C8×C53C2411yescharacteristic
594C2×C8×C53C2411yescharacteristic
595C4⋊C4×C53—21no—
596C4⋊C4×C53—21no—
597C4⋊C4×C53C2×D411yescharacteristic
598C4⋊C4×C53C2×D411yescharacteristic
599C4⋊C4×C53C2411yescharacteristic
600C4⋊C4×C53C2411yescharacteristic
601C4⋊C4×C53C2411yescharacteristic
602C4⋊C4×C53C2411yescharacteristic
603C22⋊C4×C53—21no—
604C22⋊C4×C53—21no—
605C22⋊C4×C53—21no—
606C22⋊C4×C53—21no—
607C22⋊C4×C53—21no—
608C22⋊C4×C53—21no—
609C22⋊C4×C53—21no—
610C22⋊C4×C53—21no—
611C22⋊C4×C53—21no—
612C22⋊C4×C53C2×D411yescharacteristic
613C22⋊C4×C53C2×D411yescharacteristic
614C42×C53—21no—
615C42×C53C2411yescharacteristic
616C42×C53C2411yescharacteristic
617C22⋊Dic53—21no—
618C22⋊Dic53—21no—
619C22⋊Dic53—21no—
620C22⋊Dic53—21no—
621C22⋊Dic53—21no—
622C22⋊Dic53—21no—
623C22⋊Dic53—21no—
624C22⋊Dic53—21no—
625C22⋊Dic53—21no—
626C22⋊Dic53C2×D411yescharacteristic
627C22⋊Dic53C2×D411yescharacteristic
628#11719923—22no—
629#11719923—41no—
630#11719923—41no—
631#11719923—41no—
632#11719922—22no—
633#11719922—22no—
634#11719922—22no—
635#11719922—41no—
636#11719922—41no—
637#11719922—41no—
638#11719922—41no—
639#11719922—41no—
640#11719921—21no—
641#11719921—21no—
642#11719921—21no—
643#11719921—21no—
644#11719921—21no—
645#11719921—21no—
646#11719921—21no—
647#11719921—21no—
648#11719921—21no—
649#11719921—21no—
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#11719921C2×D411yescharacteristic
661#11719921C2×D411yescharacteristic
662#11719921C2×D411yescharacteristic
663#11719921C2×D411yescharacteristic
664#11719921C2×D411yescharacteristic
665#11719921C2×D411yescharacteristic
666C4⋊Dic53—21no—
667C4⋊Dic53—21no—
668C4⋊Dic53—21no—
669C4⋊Dic53C2×D411yescharacteristic
670C4⋊Dic53C2×D411yescharacteristic
671C4⋊Dic53C2411yescharacteristic
672C4⋊Dic53C2411yescharacteristic
673#11719919—21no—
674#11719919—21no—
675#11719919—21no—
676#11719919—21no—
677#11719919—21no—
678#11719919—21no—
679#11719919C2×D411yescharacteristic
680#11719919C2×D411yescharacteristic
681#11719919C2×D411yescharacteristic
682#11719919C2×D411yescharacteristic
683#11719919C2×D411yescharacteristic
684#11719919C2×D411yescharacteristic
685C4×Dic53—21no—
686C4×Dic53—21no—
687C4×Dic53—21no—
688C4×Dic53—21no—
689C4×Dic53—21no—
690C4×Dic53C2×D411yescharacteristic
691C4×Dic53C2×D411yescharacteristic
692C4×Dic53C2411yescharacteristic
693C4×Dic53C2411yescharacteristic
694#11719917—41no—
695C2×#88322—41no—
696C2×#88322C2411yescharacteristic
697C2×#88322C2411yescharacteristic
698C2×#88322C2411yescharacteristic
699C2×#88322C2411yescharacteristic
700Dic212—41no—
701D424—41no—
702D424—41no—
703D424—41no—
704#11719913—41no—
705#11719913—41no—
706#11719913—41no—
707#11719913—41no—
708#11719912—41no—
709#11719912—41no—
710#11719912—41no—
711C8×D53—41no—
712C23×C53—21no—
713C23×C53—21no—
714C23×C53—21no—
715C23×C53—21no—
716C23×C53—42no—
717C23×C53—81no—
718C23×C53—81no—
719C23×C53C22×D411yescharacteristic
720C22×D53—21no—
721C22×D53—21no—
722C22×D53—21no—
723C22×D53—21no—
724C22×D53—42no—
725C22×D53—42no—
726C22×D53—42no—
727C22×D53—81no—
728C22×D53—81no—
729C22×D53—81no—
730C22×D53—81no—
731C22×D53—81no—
732C22×D53—81no—
733C22×D53—81no—
734C22×D53—81no—
735C22×D53—81no—
736C22×D53—81no—
737C22×D53—81no—
738C22×D53—81no—
739C22×D53C22×D411yescharacteristic
740C22×D53C22×D411yescharacteristic
741D4×C53—21no—
742D4×C53—21no—
743D4×C53—21no—
744D4×C53—21no—
745D4×C53—21no—
746D4×C53—21no—
747D4×C53—21no—
748D4×C53—42no—
749D4×C53—81no—
750D4×C53—81no—
751D4×C53—81no—
752D4×C53—81no—
753D4×C53H(5,𝔽2)12yes—
754C2×C4×C53—21no—
755C2×C4×C53—21no—
756C2×C4×C53—21no—
757C2×C4×C53—21no—
758C2×C4×C53—21no—
759C2×C4×C53—21no—
760C2×C4×C53—81no—
761C2×C4×C53—81no—
762C2×C4×C53—81no—
763C2×C4×C53—81no—
764C2×C4×C53—81no—
765C2×C4×C53—81no—
766C2×C4×C53C22×D411yescharacteristic
767C2×C4×C53C22×D411yescharacteristic
768C2×C4×C53C22×D411yescharacteristic
769C2×C4×C53C22×D411yescharacteristic
770C2×C4×C53C22×D411yescharacteristic
771C2×C4×C53C2511yescharacteristic
772C22⋊D53—22no—
773C22⋊D53—41no—
774C22⋊D53—42no—
775C22⋊D53—42no—
776C22⋊D53—42no—
777C22⋊D53—42no—
778C22⋊D53—42no—
779C22⋊D53—81no—
780C22⋊D53—81no—
781C22⋊D53—81no—
782C22⋊D53—81no—
783C22⋊D53—81no—
784C22⋊D53—81no—
785C22⋊D53—81no—
786C22⋊D53—81no—
787C22⋊D53—81no—
788C22⋊D53—81no—
789C22⋊D53—81no—
790C22⋊D53—81no—
791C22⋊D53—81no—
792C2×Dic53—21no—
793C2×Dic53—21no—
794C2×Dic53—21no—
795C2×Dic53—21no—
796C2×Dic53—42no—
797C2×Dic53—42no—
798C2×Dic53—81no—
799C2×Dic53—81no—
800C2×Dic53C22×D411yescharacteristic
801C2×Dic53C22×D411yescharacteristic
802C2×Dic53C22×D411yescharacteristic
803C2×Dic53C22×D411yescharacteristic
804C2×Dic53C22×D411yescharacteristic
805C2×Dic53C22×D411yescharacteristic
806D212—21no—
807D212—21no—
808D212—21no—
809D212—21no—
810D212—21no—
811D212—21no—
812D212—21no—
813D212—21no—
814D212—41no—
815D212—42no—
816D212—81no—
817D212—81no—
818D212—81no—
819D212—81no—
820D212—81no—
821D212—81no—
822D212—81no—
823D212—81no—
824C4×D53—21no—
825C4×D53—21no—
826C4×D53—21no—
827C4×D53—21no—
828C4×D53—22no—
829C4×D53—41no—
830C4×D53—42no—
831C4×D53—81no—
832C4×D53—81no—
833C4×D53—81no—
834C4×D53—81no—
835C4×D53—81no—
836Dic106—22no—
837Dic106—21no—
838Dic106—21no—
839Dic106—21no—
840Dic106—21no—
841Dic106—42no—
842Dic106—81no—
843Dic106—81no—
844C8×C53—21no—
845C8×C53—21no—
846C8×C53—21no—
847C8×C53—21no—
848#88322—21no—
849#88322—21no—
850#88322—21no—
851#88322—21no—
852#62031—531nomaximal, Sylow
853C22×C53—21no—
854C22×C53—22no—
855C22×C53—21no—
856C22×C53—21no—
857C22×C53—41no—
858C22×C53—41no—
859C22×C53—41no—
860C22×C53—41no—
861C22×C53—41no—
862C22×C53—41no—
863C22×C53—41no—
864C22×C53—41no—
865C22×C53—41no—
866C22×C53—41no—
867C22×C53—41no—
868C22×C53—162no—
869C22×C53C23×D411yescharacteristic
870C2×D53—21no—
871C2×D53—21no—
872C2×D53—21no—
873C2×D53—21no—
874C2×D53—21no—
875C2×D53—21no—
876C2×D53—41no—
877C2×D53—41no—
878C2×D53—41no—
879C2×D53—41no—
880C2×D53—41no—
881C2×D53—41no—
882C2×D53—41no—
883C2×D53—41no—
884C2×D53—41no—
885C2×D53—41no—
886C2×D53—41no—
887C2×D53—41no—
888C2×D53—162no—
889C2×D53—162no—
890C2×D53—162no—
891C2×D53—162no—
892C2×D53—162no—
893C4×C53—21no—
894C4×C53—21no—
895C4×C53—21no—
896C4×C53—21no—
897C4×C53—21no—
898C4×C53—41no—
899C4×C53—41no—
900C4×C53—41no—
901C4×C53—41no—
902C4×C53C2×H(5,𝔽2)11yescharacteristic
903C4×C53#58511yescharacteristic
904Dic53—21no—
905Dic53—21no—
906Dic53—21no—
907Dic53—21no—
908Dic53—21no—
909Dic53—41no—
910Dic53—41no—
911Dic53—41no—
912Dic53—41no—
913Dic53#57612yes—
914#3543—531no—
915#3514—531no—
916#3399—531no—
917#3396—531no—
918#3373—531no—
919#3358—531no—
920#3325—531no—
921#3325—531no—
922#3324—531no—
923#3319—531no—
924#3319—531no—
925#3304—531no—
926D4×D8—531no—
927#3274—531no—
928#3273—531no—
929#3273—531no—
930#3264—531no—
931#3264—531no—
932#3257—531no—
933#3257—531no—
934#3251—531no—
935#3224—531no—
936#3224—531no—
937#3205—531no—
938#3122—531no—
939#3122D5311yescharacteristic, complemented
940#3102—531no—
941#3041—531no—
942#3041—531no—
943#3038—531no—
944#2993—531no—
945C2×C53—41no—
946C2×C53—42no—
947C2×C53—81no—
948C2×C53—81no—
949C2×C53—81no—
950C2×C53#348811yescharacteristic
951C2×C53C2×#57611yescharacteristic
952C2×C53#358511yescharacteristic
953D53—41no—
954D53—41no—
955D53—81no—
956D53—81no—
957D53—81no—
958D53—81no—
959C2×AGL(1,ℤ/8)—531no—
960C2×AGL(1,ℤ/8)—531no—
961C2×AGL(1,ℤ/8)—531no—
962C2×AGL(1,ℤ/8)—531no—
963C22×D8—531no—
964C22×D8—531no—
965#560—1061no—
966#560—1061no—
967#559—531no—
968#559—531no—
969#556—531no—
970#555—531no—
971#555—531no—
972#551—1061no—
973#551—1061no—
974#550—531no—
975#550—531no—
976D4×Q8—531no—
977#548—1061no—
978#546—531no—
979#546—531no—
980#546—531no—
981#546—531no—
982#546—1061no—
983#546—1061no—
984D42—531no—
985D42—531no—
986D42—531no—
987D42—531no—
988D42—1061no—
989#542—531no—
990#542—531no—
991#540—531no—
992#540—1061no—
993#540C2×D5311yescharacteristic, complemented
994#538—1061no—
995#538—1061no—
996#535—531no—
997#535—531no—
998#535—1061no—
999#534—1061no—
1000#534—1061no—
1001#532—531no—
1002C2×#127—531no—
1003#529—531no—
1004#529—531no—
1005#529—1061no—
1006C2×#124—1061no—
1007#518—531no—
1008#518C2×D5311yescharacteristic, complemented
1009C4×#41—531no—
1010#496—531no—
1011#496—531no—
1012#495—531no—
1013#495—531no—
1014#493—531no—
1015#493—531no—
1016#489—531no—
1017#489—531no—
1018#486—531no—
1019#486—531no—
1020#486—531no—
1021#486—531no—
1022#485—531no—
1023#482—531no—
1024#482—531no—
1025#482—531no—
1026#482C2×D5311yescharacteristic, complemented
1027#482C2×D5311yescharacteristic, complemented
1028#479—531no—
1029#478—531no—
1030#478C2×D5311yescharacteristic, complemented
1031#478C2×D5311yescharacteristic, complemented
1032#476—531no—
1033#476—531no—
1034#475—531no—
1035#474—531no—
1036#474—531no—
1037#474—531no—
1038#469—531no—
1039#469—531no—
1040#469—531no—
1041#469—531no—
1042#468—531no—
1043#468—531no—
1044#468—531no—
1045#468—531no—
1046#466—531no—
1047#466—531no—
1048#465—531no—
1049#465—531no—
1050#464—531no—
1051#463—531no—
1052#463—531no—
1053#463—531no—
1054#463—531no—
1055#463—531no—
1056#463—531no—
1057#463—531no—
1058#463—531no—
1059#463—531no—
1060#463—531no—
1061#463—531no—
1062#460—531no—
1063#460—531no—
1064#460—531no—
1065#460—531no—
1066#460—531no—
1067#459—531no—
1068#459—531no—
1069#459—531no—
1070#459—531no—
1071#459—531no—
1072#459—531no—
1073#459—531no—
1074#459—531no—
1075#459—531no—
1076#459—531no—
1077#459—531no—
1078#459C2×D5311yescharacteristic, complemented
1079#459C2×D5311yescharacteristic, complemented
1080#452—531no—
1081#452—531no—
1082#452—531no—
1083#450—531no—
1084#450—531no—
1085#449—531no—
1086#449—531no—
1087#449—531no—
1088#447—531no—
1089#447—531no—
1090#447—531no—
1091#447—531no—
1092#447—531no—
1093#447—531no—
1094#447—531no—
1095#447—531no—
1096#447C2×D5311yescharacteristic, complemented
1097#447C2×D5311yescharacteristic, complemented
1098#446—531no—
1099C8×Q8—531no—
1100#442—531no—
1101#442—531no—
1102#442C2×D5311yescharacteristic, complemented
1103#442C2×D5311yescharacteristic, complemented
1104C4×Q16—531no—
1105C4×SD16—531no—
1106C4×SD16—531no—
1107C4×D8—531no—
1108C4×D8—531no—
1109C4×D8—531no—
1110C4×D8C2×D5311yescharacteristic, complemented
1111C4×D8C2×D5311yescharacteristic, complemented
1112#436—531no—
1113#436—531no—
1114#436—531no—
1115#435—531no—
1116#435—531no—
1117C8×D4—531no—
1118#433—531no—
1119#433C2×D5311yescharacteristic, complemented
1120#431—531no—
1121#424—531no—
1122#424—531no—
1123#423—531no—
1124#418—531no—
1125#418—531no—
1126#418—531no—
1127#418—531no—
1128#416—531no—
1129#416—531no—
1130C53#6203111yescharacteristic, complemented, Sylow
1131C2×#41—531no—
1132C2×#41—531no—
1133C2×#41—531no—
1134C2×#41—1061no—
1135C2×#41—1061no—
1136C22×Q8—1061no—
1137C22×D4—531no—
1138C22×D4—531no—
1139C22×D4—531no—
1140C22×D4—531no—
1141C22×D4—531no—
1142C22×D4—1061no—
1143C22×D4—1061no—
1144C22×D4—1061no—
1145C22×D4—1061no—
1146C22×D4—1061no—
1147C22×D4—1061no—
1148C22×D4C22×D5311yescharacteristic
1149AGL(1,ℤ/8)—2122no—
1150AGL(1,ℤ/8)—2122no—
1151AGL(1,ℤ/8)—2122no—
1152AGL(1,ℤ/8)—2122no—
1153C2×Q16—531no—
1154C2×SD16—531no—
1155C2×SD16—531no—
1156C2×SD16—531no—
1157C2×SD16—531no—
1158C2×SD16—531no—
1159C2×SD16—531no—
1160C2×SD16—531no—
1161C2×SD16—531no—
1162C2×D8—531no—
1163C2×D8—531no—
1164C2×D8—531no—
1165C2×D8—531no—
1166C2×D8—531no—
1167C2×D8—531no—
1168C2×D8—531no—
1169C2×D8—531no—
1170C2×D8—531no—
1171C2×D8—531no—
1172C2×D8—531no—
1173C2×D8—2122no—
1174C2×D8—2122no—
1175C2×D8C22×D5311yescharacteristic
1176C2×D8C22×D5311yescharacteristic
1177C2×D8C22×D5311yescharacteristic
1178C2×D8C22×D5311yescharacteristic
1179C2×M16—531no—
1180C2×M16—531no—
1181C2×M16—531no—
1182C2×M16—531no—
1183C22×C8—531no—
1184C22×C8—531no—
1185C4⋊Q8—531no—
1186C4⋊Q8—531no—
1187C4⋊Q8—531no—
1188#127—531no—
1189#127—531no—
1190#127—531no—
1191#127—531no—
1192#127—531no—
1193#127—531no—
1194#127—1061no—
1195#127—1061no—
1196#127—1061no—
1197#127C22×D5311yescharacteristic
1198#126—531no—
1199#126—531no—
1200#126—1061no—
1201#126—1061no—
1202#126—1061no—
1203#126—1061no—
1204#126—1061no—
1205#125—531no—
1206#125C22×D5311yescharacteristic
1207#124—531no—
1208#124—531no—
1209#124—531no—
1210#124—531no—
1211#124—531no—
1212#124—531no—
1213#124—1061no—
1214#124—1061no—
1215#124—1061no—
1216#124—1061no—
1217#124—1061no—
1218#124—1061no—
1219#124—1061no—
1220#124—1061no—
1221#124—1061no—
1222#124—1061no—
1223#123—21no—
1224#123—21no—
1225#123—531no—
1226#123—531no—
1227#123—1061no—
1228#123—1061no—
1229#123—1061no—
1230#123—1061no—
1231#123—1061no—
1232#123—1061no—
1233#123—1061no—
1234#123—1061no—
1235#123—1061no—
1236#123—1061no—
1237#123—1061no—
1238#123—1061no—
1239#123—1061no—
1240C22⋊Q8—531no—
1241C22⋊Q8—531no—
1242C22⋊Q8—531no—
1243C22⋊Q8—531no—
1244C22⋊Q8—1061no—
1245C22⋊Q8—1061no—
1246C22⋊Q8—1061no—
1247C22⋊Q8—1061no—
1248C22⋊Q8—1061no—
1249#121—21no—
1250#121—21no—
1251#121—531no—
1252#121—531no—
1253#121—531no—
1254#121—531no—
1255#121—531no—
1256#121—531no—
1257#121—531no—
1258#121—531no—
1259#121—1061no—
1260#121—1061no—
1261#121—1061no—
1262#121—1061no—
1263#121—1061no—
1264#121—1061no—
1265#121—1061no—
1266#121—1061no—
1267#121—1061no—
1268#121—1061no—
1269#121—1061no—
1270#121—1061no—
1271#121—1061no—
1272#121—1061no—
1273#121—1061no—
1274#121—1061no—
1275#121—1061no—
1276#121—1061no—
1277#121—1061no—
1278#121—1061no—
1279#121—1061no—
1280#121—1061no—
1281#121C22×D5311yescharacteristic
1282#121C22×D5311yescharacteristic
1283#120—1061no—
1284#120—1061no—
1285#120—1061no—
1286#120—1061no—
1287#120—1061no—
1288#120—1061no—
1289#120—1061no—
1290#120—1061no—
1291#120—1061no—
1292#120—1061no—
1293#120—1061no—
1294#120—1061no—
1295#120—1061no—
1296#120—1061no—
1297#120—1061no—
1298#120—1061no—
1299C4×Q8—531no—
1300C4×Q8—531no—
1301C4×Q8—531no—
1302C4×Q8—531no—
1303C4×Q8—1061no—
1304C4×D4—21no—
1305C4×D4—21no—
1306C4×D4—531no—
1307C4×D4—531no—
1308C4×D4—531no—
1309C4×D4—531no—
1310C4×D4—531no—
1311C4×D4—531no—
1312C4×D4—531no—
1313C4×D4—531no—
1314C4×D4—531no—
1315C4×D4—531no—
1316C4×D4—1061no—
1317C4×D4—1061no—
1318C4×D4—1061no—
1319C4×D4—1061no—
1320C4×D4—1061no—
1321C4×D4—1061no—
1322C4×D4—1061no—
1323C4×D4—1061no—
1324C4×D4—1061no—
1325C4×D4C22×D5311yescharacteristic
1326C4×D4C22×D5311yescharacteristic
1327C4×D4C22×D5311yescharacteristic
1328C4×D4C22×D5311yescharacteristic
1329C4×D4C22×D5311yescharacteristic
1330C4×D4C22×D5311yescharacteristic
1331#117—531no—
1332#117—531no—
1333#117—531no—
1334#117—1061no—
1335#117—1061no—
1336#117—1061no—
1337#117—1061no—
1338#117C22×D5311yescharacteristic
1339#117C22×D5311yescharacteristic
1340C2×C22⋊C4—21no—
1341C2×C22⋊C4—21no—
1342C2×C22⋊C4—1061no—
1343C2×C22⋊C4—1061no—
1344C2×C22⋊C4—1061no—
1345C2×C22⋊C4—1061no—
1346C2×C22⋊C4—1061no—
1347C2×C22⋊C4—1061no—
1348C2×C42—531no—
1349C2×C42—1061no—
1350#107—531no—
1351#107—531no—
1352#107C22×D5311yescharacteristic
1353#107C22×D5311yescharacteristic
1354#106—531no—
1355#106—531no—
1356#106C22×D5311yescharacteristic
1357#106C22×D5311yescharacteristic
1358C4⋊C8—531no—
1359C4⋊C8—531no—
1360C4⋊C8—531no—
1361C4⋊C8—531no—
1362C4⋊C8—531no—
1363C4⋊C8—531no—
1364C4⋊C8—531no—
1365C4⋊C8—531no—
1366C4⋊C8C22×D5311yescharacteristic
1367C4⋊C8C22×D5311yescharacteristic
1368#103—531no—
1369#103—531no—
1370#103—531no—
1371#103—531no—
1372#103—531no—
1373#103—531no—
1374#102—531no—
1375#102—531no—
1376#102—531no—
1377#102—531no—
1378#102—531no—
1379#102—531no—
1380#102—531no—
1381#102—531no—
1382#102—531no—
1383#102—531no—
1384#102—531no—
1385#102—531no—
1386#102—531no—
1387#102—531no—
1388#102—531no—
1389#102—531no—
1390#102—531no—
1391#102—531no—
1392#102C22×D5311yescharacteristic
1393#102C22×D5311yescharacteristic
1394#102C22×D5311yescharacteristic
1395#102C22×D5311yescharacteristic
1396#102C22×D5311yescharacteristic
1397#102C22×D5311yescharacteristic
1398#102C22×D5311yescharacteristic
1399#102C22×D5311yescharacteristic
1400C22⋊C8—531no—
1401C22⋊C8—531no—
1402C22⋊C8—531no—
1403C22⋊C8—531no—
1404C22⋊C8C22×D5311yescharacteristic
1405C22⋊C8C22×D5311yescharacteristic
1406#97—531no—
1407#97C22×D5311yescharacteristic
1408C4×C8—531no—
1409C4×C8—531no—
1410C4×C8—531no—
1411C4×C8C22×D5311yescharacteristic
1412C24—21no—
1413C24—1061no—
1414C24—1061no—
1415C24—1061no—
1416C24—1061no—
1417C24—1061no—
1418#41—1062no—
1419#41—4242no—
1420#41—4242no—
1421#41—2121no—
1422#41—2121no—
1423#41—2121no—
1424#41—2121no—
1425#41—2121no—
1426C2×Q8—531no—
1427C2×Q8—531no—
1428C2×Q8—531no—
1429C2×Q8—1061no—
1430C2×Q8—1061no—
1431C2×Q8—1061no—
1432C2×Q8—4242no—
1433C2×D4—22no—
1434C2×D4—21no—
1435C2×D4—21no—
1436C2×D4—21no—
1437C2×D4—21no—
1438C2×D4—21no—
1439C2×D4—41no—
1440C2×D4—531no—
1441C2×D4—531no—
1442C2×D4—531no—
1443C2×D4—531no—
1444C2×D4—531no—
1445C2×D4—531no—
1446C2×D4—531no—
1447C2×D4—1061no—
1448C2×D4—1061no—
1449C2×D4—1061no—
1450C2×D4—1061no—
1451C2×D4—1061no—
1452C2×D4—1061no—
1453C2×D4—1061no—
1454C2×D4—1061no—
1455C2×D4—1061no—
1456C2×D4—1061no—
1457C2×D4—1061no—
1458C2×D4—1061no—
1459C2×D4—1061no—
1460C2×D4—1061no—
1461C2×D4—1061no—
1462C2×D4—1061no—
1463C2×D4—1062no—
1464C2×D4—1061no—
1465C2×D4—1061no—
1466C2×D4—1061no—
1467C2×D4—1061no—
1468C2×D4—1061no—
1469C2×D4—1061no—
1470C2×D4—1061no—
1471C2×D4—1061no—
1472C2×D4—1061no—
1473C2×D4—1061no—
1474C2×D4—1061no—
1475C2×D4—4242no—
1476C2×D4—4242no—
1477C2×D4—4242no—
1478C2×D4—4242no—
1479C2×D4—4242no—
1480C2×D4—4242no—
1481C2×D4—2121no—
1482C2×D4—2121no—
1483C2×D4—2121no—
1484C2×D4—2121no—
1485C2×D4—2121no—
1486C2×D4—2121no—
1487C2×D4—2121no—
1488C2×D4—2121no—
1489C2×D4—2121no—
1490C2×D4C23×D5311yescharacteristic
1491C2×D4C23×D5311yescharacteristic
1492C2×D4C23×D5311yescharacteristic
1493C2×D4C23×D5311yescharacteristic
1494C22×C4—21no—
1495C22×C4—21no—
1496C22×C4—21no—
1497C22×C4—21no—
1498C22×C4—21no—
1499C22×C4—21no—
1500C22×C4—531no—
1501C22×C4—531no—
1502C22×C4—531no—
1503C22×C4—531no—
1504C22×C4—1061no—
1505C22×C4—1061no—
1506C22×C4—1061no—
1507C22×C4—1061no—
1508C22×C4—1061no—
1509C22×C4—1061no—
1510C22×C4—1061no—
1511C22×C4—1061no—
1512C22×C4—1061no—
1513C22×C4—1061no—
1514C22×C4C23×D5311yescharacteristic
1515Q16—2121no—
1516SD16—1062no—
1517SD16—2121no—
1518SD16—2121no—
1519SD16—2121no—
1520SD16—2121no—
1521SD16—2121no—
1522SD16—2121no—
1523SD16—2121no—
1524D8—22no—
1525D8—22no—
1526D8—41no—
1527D8—41no—
1528D8—1062no—
1529D8—1062no—
1530D8—1062no—
1531D8—2121no—
1532D8—2121no—
1533D8—2121no—
1534D8—2121no—
1535D8—2121no—
1536D8—2121no—
1537D8—2121no—
1538D8—2121no—
1539M16—2121no—
1540M16—2121no—
1541M16—2121no—
1542M16—2121no—
1543C2×C8—531no—
1544C2×C8—531no—
1545C2×C8—531no—
1546C2×C8—531no—
1547C2×C8—2121no—
1548C2×C8—2121no—
1549C2×C8C23×D5311yescharacteristic
1550C2×C8C23×D5311yescharacteristic
1551C2×C8C23×D5311yescharacteristic
1552C2×C8C23×D5311yescharacteristic
1553C4⋊C4—21no—
1554C4⋊C4—21no—
1555C4⋊C4—531no—
1556C4⋊C4—531no—
1557C4⋊C4—531no—
1558C4⋊C4—531no—
1559C4⋊C4—531no—
1560C4⋊C4—531no—
1561C4⋊C4—531no—
1562C4⋊C4—531no—
1563C4⋊C4—531no—
1564C4⋊C4—531no—
1565C4⋊C4—1061no—
1566C4⋊C4—1061no—
1567C4⋊C4—1061no—
1568C4⋊C4—1061no—
1569C4⋊C4—1061no—
1570C4⋊C4—1061no—
1571C4⋊C4—1061no—
1572C4⋊C4—1061no—
1573C4⋊C4—1061no—
1574C4⋊C4D4×D5311yescharacteristic
1575C4⋊C4D4×D5311yescharacteristic
1576C4⋊C4C23×D5311yescharacteristic
1577C4⋊C4C23×D5311yescharacteristic
1578C4⋊C4C23×D5311yescharacteristic
1579C4⋊C4C23×D5311yescharacteristic
1580C22⋊C4—21no—
1581C22⋊C4—21no—
1582C22⋊C4—21no—
1583C22⋊C4—21no—
1584C22⋊C4—21no—
1585C22⋊C4—21no—
1586C22⋊C4—21no—
1587C22⋊C4—21no—
1588C22⋊C4—21no—
1589C22⋊C4—531no—
1590C22⋊C4—531no—
1591C22⋊C4—531no—
1592C22⋊C4—531no—
1593C22⋊C4—531no—
1594C22⋊C4—531no—
1595C22⋊C4—531no—
1596C22⋊C4—531no—
1597C22⋊C4—1061no—
1598C22⋊C4—1061no—
1599C22⋊C4—1061no—
1600C22⋊C4—1061no—
1601C22⋊C4—1061no—
1602C22⋊C4—1061no—
1603C22⋊C4—1061no—
1604C22⋊C4—1061no—
1605C22⋊C4—1061no—
1606C22⋊C4—1061no—
1607C22⋊C4—1061no—
1608C22⋊C4—1061no—
1609C22⋊C4—1061no—
1610C22⋊C4—1061no—
1611C22⋊C4—1061no—
1612C22⋊C4—1061no—
1613C22⋊C4—1061no—
1614C22⋊C4—1061no—
1615C22⋊C4—1061no—
1616C22⋊C4—1061no—
1617C22⋊C4—1061no—
1618C22⋊C4—1061no—
1619C22⋊C4—1061no—
1620C22⋊C4—1061no—
1621C22⋊C4—1061no—
1622C22⋊C4—1061no—
1623C22⋊C4—1061no—
1624C22⋊C4—1061no—
1625C22⋊C4—1061no—
1626C22⋊C4D4×D5311yescharacteristic
1627C22⋊C4D4×D5311yescharacteristic
1628C42—21no—
1629C42—531no—
1630C42—531no—
1631C42—531no—
1632C42—531no—
1633C42—1061no—
1634C42—1061no—
1635C42—1061no—
1636C42—1061no—
1637C42—1061no—
1638C42C23×D5311yescharacteristic
1639C42C23×D5311yescharacteristic
1640C23—21no—
1641C23—21no—
1642C23—21no—
1643C23—21no—
1644C23—42no—
1645C23—81no—
1646C23—81no—
1647C23—531no—
1648C23—531no—
1649C23—1061no—
1650C23—1061no—
1651C23—1061no—
1652C23—1061no—
1653C23—4241no—
1654C23—4241no—
1655C23—4241no—
1656C23—4241no—
1657C23—4241no—
1658C23—4241no—
1659C23—4241no—
1660C23—4241no—
1661C23—4241no—
1662C23—4241no—
1663C23—4241no—
1664C23—4241no—
1665C23—2122no—
1666C23—2122no—
1667C23—2122no—
1668C23C2×D4×D5311yescharacteristic
1669Q8—1062no—
1670Q8—1061no—
1671Q8—1061no—
1672Q8—1061no—
1673Q8—1061no—
1674Q8—4241no—
1675Q8—4241no—
1676Q8—2122no—
1677D4—21no—
1678D4—21no—
1679D4—21no—
1680D4—21no—
1681D4—21no—
1682D4—21no—
1683D4—21no—
1684D4—42no—
1685D4—81no—
1686D4—81no—
1687D4—81no—
1688D4—81no—
1689D4—1062no—
1690D4—1061no—
1691D4—1061no—
1692D4—1061no—
1693D4—1061no—
1694D4—1061no—
1695D4—1061no—
1696D4—1061no—
1697D4—1061no—
1698D4—4241no—
1699D4—4241no—
1700D4—4241no—
1701D4—4241no—
1702D4—4241no—
1703D4—4241no—
1704D4—4241no—
1705D4—4241no—
1706D4—4241no—
1707D4—4241no—
1708D4—4241no—
1709D4—4241no—
1710D4—4241no—
1711D4—4241no—
1712D4—4241no—
1713D4—4241no—
1714D4—4241no—
1715D4—4241no—
1716D4—4241no—
1717D4—4241no—
1718D4—4241no—
1719D4—2121no—
1720D4—2122no—
1721D4—2122no—
1722D4—2122no—
1723D4—2122no—
1724D4—2121no—
1725D4—2122no—
1726D4—2122no—
1727D4#1313326312yes—
1728C2×C4—21no—
1729C2×C4—21no—
1730C2×C4—21no—
1731C2×C4—21no—
1732C2×C4—21no—
1733C2×C4—21no—
1734C2×C4—81no—
1735C2×C4—81no—
1736C2×C4—81no—
1737C2×C4—81no—
1738C2×C4—81no—
1739C2×C4—81no—
1740C2×C4—531no—
1741C2×C4—531no—
1742C2×C4—531no—
1743C2×C4—531no—
1744C2×C4—531no—
1745C2×C4—531no—
1746C2×C4—1062no—
1747C2×C4—1061no—
1748C2×C4—1061no—
1749C2×C4—1061no—
1750C2×C4—1061no—
1751C2×C4—1061no—
1752C2×C4—1061no—
1753C2×C4—1061no—
1754C2×C4—1061no—
1755C2×C4—4241no—
1756C2×C4—4241no—
1757C2×C4—4241no—
1758C2×C4—4241no—
1759C2×C4—4241no—
1760C2×C4—4241no—
1761C2×C4—4241no—
1762C2×C4—2121no—
1763C2×C4—2122no—
1764C2×C4—2122no—
1765C2×C4—2122no—
1766C2×C4C2×D4×D5311yescharacteristic
1767C2×C4C2×D4×D5311yescharacteristic
1768C2×C4C2×D4×D5311yescharacteristic
1769C2×C4C2×D4×D5311yescharacteristic
1770C2×C4C2×D4×D5311yescharacteristic
1771C2×C4C24×D5311yescharacteristic
1772C8—21no—
1773C8—21no—
1774C8—21no—
1775C8—21no—
1776C8—1061no—
1777C8—1061no—
1778C8—1061no—
1779C8—1061no—
1780C22—21no—
1781C22—22no—
1782C22—21no—
1783C22—21no—
1784C22—41no—
1785C22—41no—
1786C22—41no—
1787C22—41no—
1788C22—41no—
1789C22—41no—
1790C22—41no—
1791C22—41no—
1792C22—41no—
1793C22—41no—
1794C22—41no—
1795C22—162no—
1796C22—8482no—
1797C22—8482no—
1798C22—8482no—
1799C22—8482no—
1800C22—8482no—
1801C22—1061no—
1802C22—1061no—
1803C22—1061no—
1804C22—1061no—
1805C22—1061no—
1806C22—1061no—
1807C22—2121no—
1808C22—2121no—
1809C22—2121no—
1810C22—2121no—
1811C22—2121no—
1812C22—2121no—
1813C22—2121no—
1814C22—2121no—
1815C22—2121no—
1816C22—2121no—
1817C22—2121no—
1818C22—2121no—
1819C22C22×D4×D5311yescharacteristic
1820C4—21no—
1821C4—21no—
1822C4—21no—
1823C4—21no—
1824C4—21no—
1825C4—41no—
1826C4—41no—
1827C4—41no—
1828C4—41no—
1829C4—532no—
1830C4—1061no—
1831C4—1061no—
1832C4—1061no—
1833C4—1061no—
1834C4—1061no—
1835C4—2121no—
1836C4—2121no—
1837C4—2121no—
1838C4—2121no—
1839C4C2×#1313326311yescharacteristic
1840C4#1681145911yescharacteristic
1841C2—41no—
1842C2—42no—
1843C2—81no—
1844C2—81no—
1845C2—81no—
1846C2—4241no—
1847C2—4241no—
1848C2—4241no—
1849C2—4241no—
1850C2—2121no—
1851C2—2121no—
1852C2#2028837611yescharacteristic
1853C2#576×D5311yescharacteristic
1854C2#2028949011yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3122C2
socleC22×C53C23×D4
hypercenter#3122D53
hypocenterC53#62031
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ #117 ◁ #3122

Complements

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

NH ≅ G/Ntype
1. #20289044C2semidirect
2. #20288666C2semidirect
3. #20287758C2semidirect
4. #20287727C2semidirect
5. #20287508C2semidirect
6. #20287348C2semidirect
7. #20286959C2semidirect
8. #20286955C2semidirect
9. #20286944C2semidirect
10. #20286876C2semidirect
11. #20286869C2semidirect
12. #20286652C2semidirect
13. #20286385C2semidirect
14. #20286333C2semidirect
15. #20286326C2semidirect
16. #20286325C2semidirect
17. #20286197C2semidirect
18. #20286188C2semidirect
19. #20286130C2semidirect
20. #20286120C2semidirect
21. #20286076C2semidirect
22. #20285811C2semidirect
23. #20285806C2semidirect
24. #20285632C2semidirect
25. #20284960C2semidirect
26. #20284738C2semidirect
27. #20284218C2semidirect
28. #20284213C2semidirect
29. #20284190C2semidirect
30. #20283858C2semidirect
31. C53×#3122C2semidirect
32. C2×#13133243C22semidirect
33. C2×#13133241C22semidirect
34. C2×#13133241C22semidirect
35. C2×#13133241C22semidirect
36. C22×#11719922C22semidirect
37. C2×D8×D53C22semidirect
40. #16811356C22semidirect
41. #16811356C22semidirect
42. #16811341C22semidirect
43. #16811338C22semidirect
44. #16811336C22semidirect
47. #16811294C22semidirect
49. D4×Dic106C22semidirect
51. #16811270C22semidirect
52. #16811268C22semidirect
53. #16811268C22semidirect
54. #16811267C22semidirect
57. D4×D212C22semidirect
60. #16811257C22semidirect
61. D4×C22⋊D53C22semidirect
62. #16811244C22semidirect
63. #16811238C22semidirect
64. #16811229C22semidirect
68. #16811192C22semidirect
70. #16811186C22semidirect
73. #16811170C22semidirect
74. #127×D53C22semidirect
75. #16811158C22semidirect
79. #16811095C22semidirect
80. C4×#11719947C22semidirect
81. #16811012C22semidirect
82. #16811011C22semidirect
83. #16811007C22semidirect
84. #16811006C22semidirect
86. #16810998C22semidirect
87. #16810983C22semidirect
88. #16810981C22semidirect
89. #16810970C22semidirect
90. #16810968C22semidirect
91. #16810968C22semidirect
92. #16810968C22semidirect
93. #16810967C22semidirect
94. #16810950C22semidirect
95. #16810950C22semidirect
96. #16810949C22semidirect
97. #16810927C22semidirect
98. #16810920C22semidirect
99. #16810913C22semidirect
100. #16810912C22semidirect
101. #16810907C22semidirect
102. #16810903C22semidirect
103. #16810902C22semidirect
104. #16810902C22semidirect
105. #16810877C22semidirect
106. #16810875C22semidirect
107. #16810875C22semidirect
108. #16810874C22semidirect
109. #16810870C22semidirect
110. #16810870C22semidirect
111. #16810868C22semidirect
112. #16810867C22semidirect
113. #16810858C22semidirect
114. #16810857C22semidirect
115. #16810853C22semidirect
116. #16810850C22semidirect
117. #16810846C22semidirect
118. #16810839C22semidirect
119. #16810838C22semidirect
120. #16810838C22semidirect
121. #16810838C22semidirect
122. #16810838C22semidirect
123. #16810838C22semidirect
124. #16810838C22semidirect
125. #16810837C22semidirect
126. #16810837C22semidirect
127. #16810837C22semidirect
128. #16810836C22semidirect
129. #16810824C22semidirect
130. #16810822C22semidirect
131. #16810822C22semidirect
132. #16810822C22semidirect
133. #16810820C22semidirect
134. #16810819C22semidirect
135. #16810818C22semidirect
136. #16810818C22semidirect
137. #16810818C22semidirect
138. #16810818C22semidirect
139. #16810817C22semidirect
140. #16810817C22semidirect
142. #16810816C22semidirect
143. #16810816C22semidirect
144. #16810815C22semidirect
145. #16810787C22semidirect
146. #16810786C22semidirect
147. #16810786C22semidirect
148. #16810776C22semidirect
149. #16810775C22semidirect
150. #16810770C22semidirect
152. #16810765C22semidirect
153. #16810759C22semidirect
154. #16810758C22semidirect
155. #16810758C22semidirect
156. #16810758C22semidirect
157. #16810758C22semidirect
158. #16810755C22semidirect
159. #16810755C22semidirect
160. #16810755C22semidirect
161. #16810751C22semidirect
162. C8×Dic106C22semidirect
163. #16810734C22semidirect
164. #16810732C22semidirect
165. #16810717C22semidirect
166. #16810714C22semidirect
167. #16810710C22semidirect
168. #16810705C22semidirect
169. #16810703C22semidirect
170. #16810703C22semidirect
171. #16810702C22semidirect
172. #16810698C22semidirect
173. #16810698C22semidirect
174. #16810696C22semidirect
175. #16810691C22semidirect
176. #16810686C22semidirect
177. #16810683C22semidirect
178. #16810675C22semidirect
179. #16810650C22semidirect
180. #16810648C22semidirect
181. #16810645C22semidirect
182. #16810627C22semidirect
183. #16810626C22semidirect
184. #16810626C22semidirect
185. #16810626C22semidirect
186. #16810617C22semidirect
187. #16810616C22semidirect
188. C53×#540C22semidirect
189. C53×#518C22semidirect
190. C53×#482C22semidirect
191. C53×#482C22semidirect
192. C53×#478C22semidirect
193. C53×#478C22semidirect
194. C53×#459C22semidirect
195. C53×#459C22semidirect
196. C53×#447C22semidirect
197. C53×#447C22semidirect
198. C53×#442C22semidirect
199. C53×#442C22semidirect
200. C4×D8×C53C22semidirect
201. C4×D8×C53C22semidirect
202. C53×#433C22semidirect
939. #3122D53semidirect
993. #540C2×D53semidirect
1008. #518C2×D53semidirect
1026. #482C2×D53semidirect
1027. #482C2×D53semidirect
1030. #478C2×D53semidirect
1031. #478C2×D53semidirect
1078. #459C2×D53semidirect
1079. #459C2×D53semidirect
1096. #447C2×D53semidirect
1097. #447C2×D53semidirect
1102. #442C2×D53semidirect
1103. #442C2×D53semidirect
1110. C4×D8C2×D53semidirect
1111. C4×D8C2×D53semidirect
1119. #433C2×D53semidirect
1130. C53#62031semidirect

Maximal subgroups

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

subgroupindex
#202890442
#202886662
#202877582
#202877272
#202875082
#202873482
#202869592
#202869552
#202869442
#202868762
#202868692
#202866522
#202863852
#202863332
#202863262
#202863252
#202861972
#202861882
#202861302
#202861202
#202860762
#202858112
#202858062
#202856322
#202849602
#202847382
#202842182
#202842132
#202841902
#202838582
C53×#31222
#6203153