Finite Group Databasebeta

← #28270328

Subgroups — #28270328

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#20289036C211yesmaximal, characteristic, complemented
2#20288381C211yesmaximal, characteristic, complemented
3#20286866C211yesmaximal, characteristic, complemented
4#20286738C211yesmaximal, characteristic, complemented
5#20286726C211yesmaximal, characteristic, complemented
6#20286710C211yesmaximal, characteristic, complemented
7#20286658C211yesmaximal, characteristic, complemented
8#20286602C211yesmaximal, characteristic, complemented
9#20286572C211yesmaximal, characteristic, complemented
10#20286523C211yesmaximal, characteristic, complemented
11#20286470C211yesmaximal, characteristic, complemented
12#20286422C211yesmaximal, characteristic, complemented
13#20286393C211yesmaximal, characteristic, complemented
14D4×#11719922C211yesmaximal, characteristic, complemented
15#20286254C211yesmaximal, characteristic, complemented
16#20286249C211yesmaximal, characteristic, complemented
17#20286188C211yesmaximal, characteristic, complemented
18#20285808C211yesmaximal, characteristic, complemented
19#20285760C211yesmaximal, characteristic, complemented
20#20285613C211yesmaximal, characteristic, complemented
21#20285571C211yesmaximal, characteristic, complemented
22#20285475C211yesmaximal, characteristic, complemented
23#20285464C211yesmaximal, characteristic, complemented
24#20284975C211yesmaximal, characteristic, complemented
25#20284913C211yesmaximal, characteristic, complemented
26#20284017C211yesmaximal, characteristic, complemented
27#20283982C211yesmaximal, characteristic, complemented
28#20283932C211yesmaximal, characteristic, complemented
29C2×#16810767C211yesmaximal, characteristic, complemented
30#20283766C211yesmaximal, characteristic, complemented
31C53×#3265C211yesmaximal, characteristic, complemented
32C2×#13133263C2211yescharacteristic, complemented
33C22×#11719949C2211yescharacteristic, complemented
34C2×#13133241C2211yescharacteristic, complemented
35C2×#13133238C2211yescharacteristic, complemented
36C2×#13133238C2211yescharacteristic, complemented
37C2×#13133238C2211yescharacteristic, complemented
38C22×#11719922C2211yescharacteristic, complemented
39C22×#11719922C2211yescharacteristic, complemented
40#16811368—21no—
41#16811362—21no—
42#16811337C2211yescharacteristic, complemented
43#16811323C2211yescharacteristic, complemented
44#16811313C2211yescharacteristic, complemented
45#16811304—21no—
46#16811295C2211yescharacteristic, complemented
47#16811293C2211yescharacteristic, complemented
48#16811292C2211yescharacteristic, complemented
49#16811284C2211yescharacteristic, complemented
50#16811273C2211yescharacteristic, complemented
51#16811267—21no—
52#16811267C2211yescharacteristic, complemented
53#16811267C2211yescharacteristic, complemented
54#16811266—21no—
55#16811266C2211yescharacteristic, complemented
56#16811264—21no—
57#16811264C2211yescharacteristic, complemented
58D4×D212—21no—
59D4×D212C2211yescharacteristic
60#16811257—21no—
61#16811257C2211yescharacteristic, complemented
62#16811238C2211yescharacteristic, complemented
63#16811227C2211yescharacteristic, complemented
64#16811223—21no—
65#16811208—21no—
66#16811203—21no—
67#16811203C2211yescharacteristic, complemented
68#16811202C2211yescharacteristic, complemented
69#16811191—21no—
70#16811191C2211yescharacteristic, complemented
71#16811190C2211yescharacteristic, complemented
72#16811188—21no—
73#16811182—21no—
74#16811133C2211yescharacteristic, complemented
75#16811132—21no—
76#16811132C2211yescharacteristic
77C2×#13133188C2211yescharacteristic, complemented
78#121×D53—21no—
79#121×D53C2211yescharacteristic, complemented
80#16811105C2211yescharacteristic, complemented
81#16811011C2211yescharacteristic, complemented
82#16811004C2211yescharacteristic, complemented
83#16810999C2211yescharacteristic, complemented
84#16810988C2211yescharacteristic, complemented
85#16810984C2211yescharacteristic, complemented
86#16810977C2211yescharacteristic, complemented
87#16810968C2211yescharacteristic, complemented
88#16810961C2211yescharacteristic, complemented
89#16810960C2211yescharacteristic, complemented
90#16810957C2211yescharacteristic, complemented
91#16810950C2211yescharacteristic, complemented
92#16810948C2211yescharacteristic, complemented
93#16810946C2211yescharacteristic, complemented
94#16810940C2211yescharacteristic, complemented
95#16810938C2211yescharacteristic, complemented
96#16810937C2211yescharacteristic, complemented
97#16810935C2211yescharacteristic, complemented
98#16810935C2211yescharacteristic, complemented
99#16810934C2211yescharacteristic, complemented
100#16810930C2211yescharacteristic, complemented
101#16810924C2211yescharacteristic, complemented
102#16810916C2211yescharacteristic, complemented
103#16810902C2211yescharacteristic, complemented
104#16810875C2211yescharacteristic, complemented
105#16810869C2211yescharacteristic, complemented
106#16810866C2211yescharacteristic, complemented
107#16810862C2211yescharacteristic, complemented
108#16810858C2211yescharacteristic, complemented
109#16810858C2211yescharacteristic, complemented
110#16810858C2211yescharacteristic, complemented
111#16810857C2211yescharacteristic, complemented
112#16810857C2211yescharacteristic, complemented
113#16810856C2211yescharacteristic, complemented
114#16810856C2211yescharacteristic, complemented
115#16810852C2211yescharacteristic, complemented
116#16810850C2211yescharacteristic, complemented
117#16810849C2211yescharacteristic, complemented
118#16810843C2211yescharacteristic, complemented
119#16810842C2211yescharacteristic, complemented
120#16810840C2211yescharacteristic, complemented
121#16810840C2211yescharacteristic, complemented
122#16810837C2211yescharacteristic, complemented
123#16810824C2211yescharacteristic, complemented
124#16810818C2211yescharacteristic, complemented
125#16810816C2211yescharacteristic, complemented
126#16810816C2211yescharacteristic, complemented
127#16810815C2211yescharacteristic, complemented
128#16810788C2211yescharacteristic, complemented
129#16810788C2211yescharacteristic, complemented
130#16810785C2211yescharacteristic, complemented
131#16810782C2211yescharacteristic, complemented
132#16810779C2211yescharacteristic, complemented
133#16810776C2211yescharacteristic, complemented
134#16810776C2211yescharacteristic, complemented
135#16810775C2211yescharacteristic, complemented
136#16810769C2211yescharacteristic, complemented
137#16810769C2211yescharacteristic, complemented
138#16810767C2211yescharacteristic
139#16810767C2211yescharacteristic, complemented
140#16810767C2211yescharacteristic, complemented
141#16810767C2211yescharacteristic, complemented
142#16810767C2211yescharacteristic, complemented
143#16810767C2211yescharacteristic, complemented
144#16810767C2211yescharacteristic, complemented
145#16810767C2211yescharacteristic, complemented
146#16810767C2211yescharacteristic, complemented
147#16810767C2211yescharacteristic, complemented
148#16810767C2211yescharacteristic, complemented
149#16810767C2211yescharacteristic, complemented
150#16810765C2211yescharacteristic, complemented
151#16810757C2211yescharacteristic, complemented
152#16810757C2211yescharacteristic, complemented
153#16810756C2211yescharacteristic, complemented
154#16810756C2211yescharacteristic, complemented
155#16810755C2211yescharacteristic, complemented
156#16810755C2211yescharacteristic, complemented
157#16810755C2211yescharacteristic, complemented
158#16810755C2211yescharacteristic, complemented
159#16810755C2211yescharacteristic, complemented
160#16810732C2211yescharacteristic, complemented
161#16810725C2211yescharacteristic, complemented
162#16810724C2211yescharacteristic, complemented
163C4×#11719925C2211yescharacteristic, complemented
164SD16×Dic53C2211yescharacteristic, complemented
165C4×#11719922C2211yescharacteristic, complemented
166#16810703C2211yescharacteristic, complemented
167#16810696C2211yescharacteristic, complemented
168#16810692C2211yescharacteristic, complemented
169#16810691C2211yescharacteristic, complemented
170D4×#88322C2211yescharacteristic, complemented
171#16810688C2211yescharacteristic, complemented
172C8×C22⋊D53C2211yescharacteristic, complemented
173#16810686C2211yescharacteristic, complemented
174#16810685C2211yescharacteristic, complemented
175#16810683C2211yescharacteristic, complemented
176#16810629C2211yescharacteristic, complemented
177#16810623C2211yescharacteristic, complemented
178#16810619C2211yescharacteristic, complemented
179#16810618C2211yescharacteristic, complemented
180#16810618C2211yescharacteristic, complemented
181C2×#13133141C2211yescharacteristic, complemented
182C2×#13133139C2211yescharacteristic, complemented
183#102×D53C2211yescharacteristic, complemented
184#16810591C2211yescharacteristic, complemented
185#16810588C2211yescharacteristic, complemented
186C2×#13133129C2211yescharacteristic, complemented
187C22⋊C8×D53C2211yescharacteristic, complemented
188C2×AGL(1,ℤ/8)×C53C2211yescharacteristic, complemented
189C22×SD16×C53C2211yescharacteristic, complemented
190C53×#548C2211yescharacteristic
191D42×C53C2211yescharacteristic, complemented
192C53×#496C2211yescharacteristic, complemented
193C53×#468C2211yescharacteristic, complemented
194C53×#466C2211yescharacteristic, complemented
195C53×#463C2211yescharacteristic, complemented
196C53×#460C2211yescharacteristic, complemented
197C53×#450C2211yescharacteristic, complemented
198C53×#449C2211yescharacteristic, complemented
199C53×#448C2211yescharacteristic, complemented
200C53×#447C2211yescharacteristic, complemented
201C53×#440C2211yescharacteristic, complemented
202C53×#435C2211yescharacteristic, complemented
203#13133263—42no—
204#13133263—42no—
205C2×#11719949—21no—
206C2×#11719949—21no—
207C2×#11719949—42no—
208C2×#11719949—42no—
209C2×#11719949C2311yescharacteristic
210C2×#11719949C2311yescharacteristic
211C2×#11719949C2311yescharacteristic
212C2×#11719949C2311yescharacteristic
213C2×#11719949C2311yescharacteristic
214C2×#11719945—21no—
215C2×#11719945C2311yescharacteristic
216C2×#11719947—21no—
217C2×#11719947C2311yescharacteristic
218C2×#11719947C2311yescharacteristic
219C22×D212—21no—
220C22×D212—21no—
221C22×D212C2311yescharacteristic
222C22×D212C2311yescharacteristic
223C22×C22⋊D53—21no—
224C2×D4×D53—21no—
225C2×D4×D53—21no—
226C2×D4×D53—21no—
227C2×D4×D53—21no—
228C2×D4×D53—21no—
229C2×D4×D53C2311yescharacteristic
230C2×D4×D53C2311yescharacteristic
231C22×C4×D53—21no—
232C22×C4×D53C2311yescharacteristic
233#13133241—42no—
234#13133238—42no—
235#13133238—42no—
236#13133238—42no—
237C2×#11719925C2311yescharacteristic
238C2×#11719925C2311yescharacteristic
239C2×#11719913C2311yescharacteristic
240C2×#11719913C2311yescharacteristic
241C2×#11719913C2311yescharacteristic
242C2×#11719923C2311yescharacteristic
243C2×#11719922—42no—
244C2×#11719922—42no—
245C2×#11719922C2311yescharacteristic
246C2×#11719922C2311yescharacteristic
247C2×#11719922C2311yescharacteristic
248C2×#11719922C2311yescharacteristic
249C2×#11719922C2311yescharacteristic
250C2×#11719922C2311yescharacteristic
251C2×#11719922C2311yescharacteristic
252C2×#11719922C2311yescharacteristic
253C2×#11719922C2311yescharacteristic
254C2×#11719912C2311yescharacteristic
255C22×#88322C2311yescharacteristic
256C22×#88322C2311yescharacteristic
257C2×C8×D53C2311yescharacteristic
258C2×C8×D53C2311yescharacteristic
259C2×C8×D53C2311yescharacteristic
260#13133216C2311yescharacteristic
261#13133214—21no—
262#13133214C2311yescharacteristic
263#13133213—21no—
264#13133213—21no—
265#13133213—21no—
266#13133213C2311yescharacteristic
267#13133210—21no—
268#13133210—21no—
269#13133210—21no—
270#13133209C2311yescharacteristic
271#13133207—21no—
272#13133206—21no—
273#13133206C2311yescharacteristic
274#13133204—21no—
275#13133204—21no—
276#13133204C2311yescharacteristic
277#13133203—21no—
278#13133203—21no—
279#13133202—21no—
280#13133202D411yescharacteristic
281#13133200—21no—
282#13133200—21no—
283#13133199—21no—
284#13133199—21no—
285#13133199—21no—
286#13133199D411yescharacteristic
287#13133198—21no—
288#13133198—21no—
289#13133198—21no—
290#13133198—21no—
291#13133198—21no—
292#13133198—21no—
293#13133197C2311yescharacteristic
294#13133196—21no—
295#13133196C2311yescharacteristic
296#13133196C2311yescharacteristic
297#13133195—21no—
298#13133195D411yescharacteristic
299#13133194—21no—
300#13133194—21no—
301#13133194D411yescharacteristic
302#13133193—21no—
303#13133193C2311yescharacteristic
304#13133192—21no—
305#13133192—21no—
306#13133192—21no—
307#13133192—21no—
308#13133192—21no—
309#13133192C2311yescharacteristic
310#13133192C2311yescharacteristic
311#13133191—21no—
312#13133191—21no—
313#13133191C2311yescharacteristic
314#13133191C2311yescharacteristic
315#13133190—21no—
316#13133190—21no—
317#13133190—21no—
318#13133190—21no—
319#13133190—21no—
320#13133190—21no—
321#13133190—21no—
322#13133190—21no—
323#13133190—21no—
324#13133190D411yescharacteristic
325#13133189—21no—
326#13133189—21no—
327#13133189—21no—
328#13133189—21no—
329#13133189—21no—
330#13133189—21no—
331#13133189—21no—
332#13133189—21no—
333#13133189—21no—
334#13133189D411yescharacteristic
335#13133188—21no—
336#13133188—21no—
337#13133188—21no—
338#13133188—21no—
339#13133188C2311yescharacteristic
340#13133188C2311yescharacteristic
341#13133188C2311yescharacteristic
342#13133188C2311yescharacteristic
343#13133188C2311yescharacteristic
344#13133188C2311yescharacteristic
345#13133188C2311yescharacteristic
346#13133188C2311yescharacteristic
347#13133187—21no—
348#13133187—21no—
349#13133187—21no—
350#13133187—21no—
351#13133187—21no—
352#13133187—21no—
353#13133187—21no—
354#13133187D411yescharacteristic
355#13133186—21no—
356#13133186—21no—
357#13133186—21no—
358#13133186—21no—
359#13133185—21no—
360#13133185—21no—
361#13133185D411yescharacteristic
362Q8×Dic53C2311yescharacteristic
363C4×Dic106C2311yescharacteristic
364C4×D212—21no—
365C4×D212—21no—
366C4×D212C2311yescharacteristic
367C4×D212C2311yescharacteristic
368D4×Dic53—21no—
369D4×Dic53—21no—
370D4×Dic53C2311yescharacteristic
371D4×Dic53C2311yescharacteristic
372#13133179—21no—
373#13133179C2311yescharacteristic
374C4×C22⋊D53—21no—
375C4×C22⋊D53—21no—
376C4×C22⋊D53—21no—
377C4×C22⋊D53C2311yescharacteristic
378C4×C22⋊D53C2311yescharacteristic
379#13133177—21no—
380#13133176C2311yescharacteristic
381#13133175C2311yescharacteristic
382#13133174—21no—
383#13133174C2311yescharacteristic
384#13133173—21no—
385#13133173—21no—
386C2×C4⋊Dic53C2311yescharacteristic
387C4⋊C4×D53—21no—
388C4⋊C4×D53C2311yescharacteristic
389C4⋊C4×D53C2311yescharacteristic
390C2×C22⋊Dic53—21no—
391C2×C22⋊Dic53—21no—
392C2×C22⋊Dic53—21no—
393C22⋊C4×D53—21no—
394C22⋊C4×D53—21no—
395C22⋊C4×D53—21no—
396#13133151C2311yescharacteristic
397#13133151C2311yescharacteristic
398#13133150C2311yescharacteristic
399#13133150C2311yescharacteristic
400#13133150C2311yescharacteristic
401#13133149C2311yescharacteristic
402#13133148C2311yescharacteristic
403C4⋊#88322C2311yescharacteristic
404#13133146C2311yescharacteristic
405#13133146C2311yescharacteristic
406#13133142C2311yescharacteristic
407#13133141C2311yescharacteristic
408#13133141C2311yescharacteristic
409#13133141C2311yescharacteristic
410#13133141C2311yescharacteristic
411#13133141C2311yescharacteristic
412#13133141C2311yescharacteristic
413#13133140C2311yescharacteristic
414#13133139C2311yescharacteristic
415#13133139C2311yescharacteristic
416#13133139C2311yescharacteristic
417#13133139C2311yescharacteristic
418#13133139C2311yescharacteristic
419#13133139C2311yescharacteristic
420#13133139C2311yescharacteristic
421#13133139C2311yescharacteristic
422#13133139C2311yescharacteristic
423#13133138C2311yescharacteristic
424#13133138C2311yescharacteristic
425#13133138C2311yescharacteristic
426#13133138C2311yescharacteristic
427#13133138C2311yescharacteristic
428#13133138C2311yescharacteristic
429#13133137C2311yescharacteristic
430#13133137C2311yescharacteristic
431#13133137C2311yescharacteristic
432C22⋊#88322C2311yescharacteristic
433C22⋊#88322C2311yescharacteristic
434#13133129C2311yescharacteristic
435#13133129C2311yescharacteristic
436#13133129C2311yescharacteristic
437#13133129C2311yescharacteristic
438#13133129C2311yescharacteristic
439#13133129C2311yescharacteristic
440#13133129C2311yescharacteristic
441#13133129C2311yescharacteristic
442#13133127C2311yescharacteristic
443C4×#88322C2311yescharacteristic
444C8×Dic53C2311yescharacteristic
445C2×#41×C53C2311yescharacteristic
446C22×Q8×C53C2311yescharacteristic
447C22×D4×C53—21no—
448C22×D4×C53C2311yescharacteristic
449C22×D4×C53C2311yescharacteristic
450AGL(1,ℤ/8)×C53—42no—
451C2×SD16×C53—42no—
452C2×SD16×C53C2311yescharacteristic
453C2×SD16×C53C2311yescharacteristic
454C2×SD16×C53C2311yescharacteristic
455C2×SD16×C53C2311yescharacteristic
456C2×SD16×C53C2311yescharacteristic
457C2×SD16×C53C2311yescharacteristic
458C2×D8×C53C2311yescharacteristic
459C2×D8×C53C2311yescharacteristic
460C2×D8×C53C2311yescharacteristic
461C2×M16×C53C2311yescharacteristic
462C22×C8×C53C2311yescharacteristic
463#127×C53C2311yescharacteristic
464#124×C53—21no—
465#124×C53C2311yescharacteristic
466C22⋊Q8×C53—21no—
467C22⋊Q8×C53C2311yescharacteristic
468#121×C53—21no—
469#121×C53—21no—
470#121×C53C2311yescharacteristic
471#121×C53C2311yescharacteristic
472#121×C53C2311yescharacteristic
473#120×C53—21no—
474#120×C53—21no—
475C4×Q8×C53C2311yescharacteristic
476C4×D4×C53—21no—
477C4×D4×C53C2311yescharacteristic
478C4×D4×C53C2311yescharacteristic
479#107×C53C2311yescharacteristic
480C4⋊C8×C53C2311yescharacteristic
481#103×C53C2311yescharacteristic
482#103×C53C2311yescharacteristic
483#102×C53C2311yescharacteristic
484#102×C53C2311yescharacteristic
485#102×C53C2311yescharacteristic
486#102×C53C2311yescharacteristic
487C22⋊C8×C53C2311yescharacteristic
488C22⋊C8×C53C2311yescharacteristic
489#97×C53C2311yescharacteristic
490C24×C53—21no—
491C24×C53—21no—
492C23×D53—21no—
493C23×D53—21no—
494C23×D53—21no—
495C23×D53—21no—
496C23×D53C2×D411yescharacteristic
497#41×C53—22no—
498#41×C53—41no—
499C2×Q8×C53—21no—
500C2×Q8×C53—22no—
501C2×Q8×C53—41no—
502C2×Q8×C53C2411yescharacteristic
503C2×Q8×C53C2411yescharacteristic
504C2×D4×C53—21no—
505C2×D4×C53—21no—
506C2×D4×C53—21no—
507C2×D4×C53—21no—
508C2×D4×C53—21no—
509C2×D4×C53—21no—
510C2×D4×C53—21no—
511C2×D4×C53—21no—
512C2×D4×C53—41no—
513C2×D4×C53—41no—
514C2×D4×C53—41no—
515C2×D4×C53—41no—
516C2×D4×C53—82no—
517C2×D4×C53C2×D411yescharacteristic
518C2×D4×C53C2411yescharacteristic
519C2×D4×C53C2411yescharacteristic
520C2×D4×C53C2411yescharacteristic
521C2×D4×C53C2411yescharacteristic
522C22×C4×C53—21no—
523C22×C4×C53—21no—
524C22×C4×C53—21no—
525C22×C4×C53C2411yescharacteristic
526C22×C4×C53C2411yescharacteristic
527C2×C22⋊D53—21no—
528C2×C22⋊D53—21no—
529C2×C22⋊D53—21no—
530C2×C22⋊D53—21no—
531C2×C22⋊D53—21no—
532C2×C22⋊D53—21no—
533C2×C22⋊D53—21no—
534C2×C22⋊D53—21no—
535C2×C22⋊D53—21no—
536C2×C22⋊D53—21no—
537C2×C22⋊D53—21no—
538C2×C22⋊D53—21no—
539C2×C22⋊D53—21no—
540C2×C22⋊D53—21no—
541C2×C22⋊D53—21no—
542C2×C22⋊D53—21no—
543C2×C22⋊D53—82no—
544C2×C22⋊D53C2×D411yescharacteristic
545C2×C22⋊D53C2×D411yescharacteristic
546C2×C22⋊D53C2×D411yescharacteristic
547C2×C22⋊D53C2×D411yescharacteristic
548C22×Dic53—21no—
549C22×Dic53—21no—
550C22×Dic53—21no—
551C22×Dic53—21no—
552C22×Dic53—21no—
553C22×Dic53C2×D411yescharacteristic
554#11719949—22no—
555#11719949—22no—
556#11719949—22no—
557#11719949—22no—
558#11719949—22no—
559#11719949—41no—
560#11719949—41no—
561#11719949—41no—
562#11719949—41no—
563#11719949—41no—
564#11719949—44no—
565#11719949—44no—
566#11719947—41no—
567#11719947—41no—
568#11719947—41no—
569#11719947—41no—
570#11719947—82no—
571D4×D53—22no—
572D4×D53—41no—
573D4×D53—41no—
574D4×D53—41no—
575D4×D53—44no—
576D4×D53—44no—
577D4×D53—82no—
578D4×D53—82no—
579D4×D53—82no—
580#11719945—41no—
581#11719945—41no—
582#11719945—44no—
583C2×D212—21no—
584C2×D212—22no—
585C2×D212—22no—
586C2×D212—21no—
587C2×D212—21no—
588C2×D212—21no—
589C2×D212—21no—
590C2×D212—21no—
591C2×D212—21no—
592C2×D212—21no—
593C2×D212—21no—
594C2×D212—21no—
595C2×D212—21no—
596C2×D212—41no—
597C2×D212—41no—
598C2×D212—44no—
599C2×D212—44no—
600C2×D212C2×D411yescharacteristic
601C2×D212C2×D411yescharacteristic
602C2×D212C2411yescharacteristic
603C2×D212C2411yescharacteristic
604C2×D212C2411yescharacteristic
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—21no—
614C2×C4×D53—41no—
615C2×C4×D53—41no—
616C2×C4×D53—44no—
617C2×C4×D53C2×D411yescharacteristic
618C2×C4×D53C2×D411yescharacteristic
619C2×C4×D53C2411yescharacteristic
620C2×C4×D53C2411yescharacteristic
621C2×C4×D53C2411yescharacteristic
622C2×Dic106—21no—
623C2×Dic106C2×D411yescharacteristic
624C2×Dic106C2411yescharacteristic
625SD16×C53—22no—
626SD16×C53—22no—
627SD16×C53—22no—
628SD16×C53—41no—
629SD16×C53—41no—
630SD16×C53—41no—
631D8×C53—41no—
632D8×C53—41no—
633D8×C53—41no—
634M16×C53—41no—
635C2×C8×C53—41no—
636C2×C8×C53C2411yescharacteristic
637C2×C8×C53C2411yescharacteristic
638C2×C8×C53C2411yescharacteristic
639C2×C8×C53C2411yescharacteristic
640C4⋊C4×C53—21no—
641C4⋊C4×C53—21no—
642C4⋊C4×C53C2×D411yescharacteristic
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×C53C2411yescharacteristic
656C22⋊Dic53—21no—
657C22⋊Dic53—21no—
658C22⋊Dic53—21no—
659C22⋊Dic53—21no—
660C22⋊Dic53—21no—
661C22⋊Dic53—21no—
662C22⋊Dic53—21no—
663C22⋊Dic53—21no—
664C22⋊Dic53—21no—
665C22⋊Dic53—21no—
666C22⋊Dic53—21no—
667C22⋊Dic53—21no—
668C22⋊Dic53—21no—
669C22⋊Dic53—21no—
670C22⋊Dic53—21no—
671C22⋊Dic53C2×D411yescharacteristic
672C22⋊Dic53C2×D411yescharacteristic
673#11719925—22no—
674#11719925—41no—
675#11719923—41no—
676#11719922—22no—
677#11719922—22no—
678#11719922—22no—
679#11719922—41no—
680#11719922—41no—
681#11719922—41no—
682#11719922—41no—
683#11719922—41no—
684#11719922—41no—
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#11719921C2×D411yescharacteristic
697#11719921C2×D411yescharacteristic
698#11719921C2×D411yescharacteristic
699#11719921C2×D411yescharacteristic
700#11719921C2×D411yescharacteristic
701#11719921C2×D411yescharacteristic
702C4⋊Dic53—21no—
703C4⋊Dic53—21no—
704C4⋊Dic53—21no—
705C4⋊Dic53C2×D411yescharacteristic
706C4⋊Dic53C2411yescharacteristic
707C4⋊Dic53C2411yescharacteristic
708C4⋊Dic53C2411yescharacteristic
709C4⋊Dic53C2411yescharacteristic
710#11719919—21no—
711#11719919—21no—
712#11719919—21no—
713#11719919—21no—
714#11719919—21no—
715#11719919—21no—
716#11719919—21no—
717#11719919—21no—
718#11719919—21no—
719#11719919C2×D411yescharacteristic
720#11719919C2×D411yescharacteristic
721#11719919C2×D411yescharacteristic
722#11719919C2×D411yescharacteristic
723C4×Dic53—21no—
724C4×Dic53—21no—
725C4×Dic53—21no—
726C4×Dic53—21no—
727C4×Dic53C2411yescharacteristic
728C2×#88322—41no—
729C2×#88322—41no—
730C2×#88322C2411yescharacteristic
731C2×#88322C2411yescharacteristic
732C2×#88322C2411yescharacteristic
733C2×#88322C2411yescharacteristic
734#11719913—22no—
735#11719913—41no—
736#11719913—41no—
737#11719912—41no—
738C8×D53—41no—
739C8×D53—41no—
740C8×D53—41no—
741C23×C53—21no—
742C23×C53—21no—
743C23×C53—21no—
744C23×C53—21no—
745C23×C53—42no—
746C23×C53—81no—
747C23×C53—81no—
748C23×C53—81no—
749C23×C53—81no—
750C23×C53—81no—
751C23×C53C22×D411yescharacteristic
752C23×C53C22×D411yescharacteristic
753C22×D53—21no—
754C22×D53—22no—
755C22×D53—21no—
756C22×D53—21no—
757C22×D53—41no—
758C22×D53—41no—
759C22×D53—42no—
760C22×D53—42no—
761C22×D53—42no—
762C22×D53—42no—
763C22×D53—42no—
764C22×D53—81no—
765C22×D53—81no—
766C22×D53—81no—
767C22×D53—81no—
768C22×D53—81no—
769C22×D53—81no—
770C22×D53—81no—
771C22×D53C22×D411yescharacteristic
772C22×D53C22×D411yescharacteristic
773C22×D53C22×D411yescharacteristic
774Q8×C53—21no—
775Q8×C53—21no—
776Q8×C53—21no—
777Q8×C53—42no—
778Q8×C53H(5,𝔽2)12yes—
779D4×C53—22no—
780D4×C53—21no—
781D4×C53—21no—
782D4×C53—21no—
783D4×C53—21no—
784D4×C53—21no—
785D4×C53—21no—
786D4×C53—21no—
787D4×C53—21no—
788D4×C53—42no—
789D4×C53—42no—
790D4×C53—42no—
791D4×C53—81no—
792D4×C53—81no—
793D4×C53—81no—
794D4×C53—81no—
795D4×C53—81no—
796C2×C4×C53—21no—
797C2×C4×C53—21no—
798C2×C4×C53—21no—
799C2×C4×C53—21no—
800C2×C4×C53—21no—
801C2×C4×C53—21no—
802C2×C4×C53—21no—
803C2×C4×C53—21no—
804C2×C4×C53—42no—
805C2×C4×C53—42no—
806C2×C4×C53—81no—
807C2×C4×C53C22×D411yescharacteristic
808C2×C4×C53C22×D411yescharacteristic
809C2×C4×C53C22×D411yescharacteristic
810C2×C4×C53C22×D411yescharacteristic
811C2×C4×C53C2511yescharacteristic
812C22⋊D53—22no—
813C22⋊D53—41no—
814C22⋊D53—41no—
815C22⋊D53—41no—
816C22⋊D53—42no—
817C22⋊D53—42no—
818C22⋊D53—42no—
819C22⋊D53—81no—
820C22⋊D53—81no—
821C22⋊D53—81no—
822C22⋊D53—81no—
823C22⋊D53—81no—
824C22⋊D53—81no—
825C22⋊D53—81no—
826C22⋊D53—81no—
827C22⋊D53—81no—
828C22⋊D53—81no—
829C22⋊D53—81no—
830C22⋊D53—81no—
831C22⋊D53—81no—
832C2×Dic53—21no—
833C2×Dic53—21no—
834C2×Dic53—21no—
835C2×Dic53—21no—
836C2×Dic53—21no—
837C2×Dic53—41no—
838C2×Dic53—42no—
839C2×Dic53—81no—
840C2×Dic53—81no—
841C2×Dic53—81no—
842C2×Dic53—81no—
843C2×Dic53C22×D411yescharacteristic
844C2×Dic53C22×D411yescharacteristic
845C2×Dic53C22×D411yescharacteristic
846C2×Dic53C22×D411yescharacteristic
847C2×Dic53C22×D411yescharacteristic
848D212—24no—
849D212—21no—
850D212—21no—
851D212—21no—
852D212—21no—
853D212—21no—
854D212—41no—
855D212—41no—
856D212—42no—
857D212—42no—
858D212—42no—
859D212—42no—
860D212—42no—
861D212—42no—
862D212—81no—
863D212—81no—
864D212—81no—
865D212—81no—
866D212H(5,𝔽2)12yes—
867C4×D53—24no—
868C4×D53—21no—
869C4×D53—21no—
870C4×D53—21no—
871C4×D53—21no—
872C4×D53—21no—
873C4×D53—21no—
874C4×D53—41no—
875C4×D53—41no—
876C4×D53—42no—
877C4×D53—42no—
878C4×D53—42no—
879C4×D53—42no—
880C4×D53—81no—
881C4×D53—81no—
882C4×D53—81no—
883C4×D53—81no—
884Dic106—21no—
885Dic106—21no—
886Dic106—41no—
887Dic106—81no—
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—21no—
900C22×C53—21no—
901C22×C53—21no—
902C22×C53—41no—
903C22×C53—41no—
904C22×C53—41no—
905C22×C53—41no—
906C22×C53—41no—
907C22×C53—41no—
908C22×C53—41no—
909C22×C53—41no—
910C22×C53—41no—
911C22×C53—41no—
912C22×C53—41no—
913C22×C53—41no—
914C22×C53—162no—
915C22×C53—162no—
916C22×C53#57612yes—
917C22×C53C23×D411yescharacteristic
918C2×D53—21no—
919C2×D53—21no—
920C2×D53—21no—
921C2×D53—21no—
922C2×D53—22no—
923C2×D53—21no—
924C2×D53—21no—
925C2×D53—21no—
926C2×D53—21no—
927C2×D53—21no—
928C2×D53—41no—
929C2×D53—41no—
930C2×D53—41no—
931C2×D53—41no—
932C2×D53—41no—
933C2×D53—41no—
934C2×D53—41no—
935C2×D53—41no—
936C2×D53—82no—
937C2×D53—84no—
938C2×D53—162no—
939C2×D53—162no—
940C2×D53—162no—
941C4×C53—21no—
942C4×C53—21no—
943C4×C53—22no—
944C4×C53—21no—
945C4×C53—21no—
946C4×C53—41no—
947C4×C53—41no—
948C4×C53—41no—
949C4×C53C2×H(5,𝔽2)11yescharacteristic
950C4×C53C2×H(5,𝔽2)11yescharacteristic
951Dic53—21no—
952Dic53—21no—
953Dic53—21no—
954Dic53—21no—
955Dic53—21no—
956Dic53—41no—
957Dic53—41no—
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#3265D5311yescharacteristic, complemented
978#3264—531no—
979#3224—531no—
980#3220—531no—
981#3203—531no—
982#3198—531no—
983#3188—531no—
984#3186—531no—
985#3124—531no—
986#3119—531no—
987#3012—531no—
988#3008—531no—
989#3002—531no—
990C2×#449—531no—
991#2977—531no—
992C2×C53—22no—
993C2×C53—41no—
994C2×C53—81no—
995C2×C53—81no—
996C2×C53—81no—
997C2×C53—81no—
998C2×C53#348411yescharacteristic
999C2×C53C2×#57611yescharacteristic
1000C2×C53#358411yescharacteristic
1001D53—41no—
1002D53—41no—
1003D53—41no—
1004D53—42no—
1005D53—81no—
1006D53—81no—
1007C2×H(5,𝔽2)—531no—
1008C22×#41—531no—
1009C2×AGL(1,ℤ/8)—531no—
1010C2×AGL(1,ℤ/8)C2×D5311yescharacteristic, complemented
1011C2×#135—531no—
1012C2×#135—531no—
1013C2×#135—531no—
1014C22×SD16C2×D5311yescharacteristic, complemented
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#548C2×D5311yescharacteristic
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—1061no—
1039D42—1061no—
1040D42C2×D5311yescharacteristic, complemented
1041#542—531no—
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#520—531no—
1060#496—531no—
1061#496C2×D5311yescharacteristic, complemented
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#484—531no—
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#480—531no—
1080#479—531no—
1081#478—531no—
1082#477—531no—
1083#474—531no—
1084#469—531no—
1085#468—531no—
1086#468—531no—
1087#468C2×D5311yescharacteristic, complemented
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#466C2×D5311yescharacteristic, complemented
1097#465—531no—
1098#465—531no—
1099#465—531no—
1100#464—531no—
1101#464—531no—
1102#463—531no—
1103#463—531no—
1104#463—531no—
1105#463C2×D5311yescharacteristic, complemented
1106#460—531no—
1107#460C2×D5311yescharacteristic, complemented
1108#459—531no—
1109#459—531no—
1110#459—531no—
1111#459—531no—
1112#452—531no—
1113#452—531no—
1114#452—531no—
1115#452—531no—
1116#451—531no—
1117#450—531no—
1118#450—531no—
1119#450—531no—
1120#450C2×D5311yescharacteristic, complemented
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, complemented
1137#448C2×D5311yescharacteristic, complemented
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#447C2×D5311yescharacteristic, complemented
1148#442—531no—
1149#440—531no—
1150#440—531no—
1151#440C2×D5311yescharacteristic, complemented
1152C4×Q16—531no—
1153C4×SD16—531no—
1154C4×D8—531no—
1155C4×D8—531no—
1156#435—531no—
1157#435—531no—
1158#435—531no—
1159#435C2×D5311yescharacteristic, complemented
1160C8×D4—531no—
1161C8×D4—531no—
1162C8×D4—531no—
1163C8×D4—531no—
1164#433—531no—
1165#433—531no—
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×Q8C22×D5311yescharacteristic
1197C22×D4—21no—
1198C22×D4—531no—
1199C22×D4—531no—
1200C22×D4—531no—
1201C22×D4—531no—
1202C22×D4—1061no—
1203C22×D4—1061no—
1204C22×D4—1061no—
1205C22×D4—1061no—
1206C22×D4—1061no—
1207C22×D4—1061no—
1208C22×D4—1061no—
1209C22×D4—1061no—
1210C22×D4C22×D5311yescharacteristic
1211C22×D4C22×D5311yescharacteristic
1212C23×C4—531no—
1213C23×C4—1061no—
1214AGL(1,ℤ/8)—42no—
1215AGL(1,ℤ/8)—2122no—
1216#135—2122no—
1217#135—2122no—
1218#135—2122no—
1219C2×Q16—531no—
1220C2×Q16—531no—
1221C2×SD16—42no—
1222C2×SD16—531no—
1223C2×SD16—531no—
1224C2×SD16—531no—
1225C2×SD16—531no—
1226C2×SD16C22×D5311yescharacteristic
1227C2×SD16C22×D5311yescharacteristic
1228C2×SD16C22×D5311yescharacteristic
1229C2×SD16C22×D5311yescharacteristic
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—2122no—
1242C2×D8—2122no—
1243C2×D8C22×D5311yescharacteristic
1244C2×D8C22×D5311yescharacteristic
1245C2×D8C22×D5311yescharacteristic
1246C2×M16—531no—
1247C2×M16C22×D5311yescharacteristic
1248C22×C8—531no—
1249C22×C8—531no—
1250C22×C8—531no—
1251C22×C8—531no—
1252C22×C8—531no—
1253C22×C8C22×D5311yescharacteristic
1254C4⋊Q8—531no—
1255#127—531no—
1256#127—531no—
1257#127—1061no—
1258#127—1061no—
1259#127—1061no—
1260#127—1061no—
1261#127C22×D5311yescharacteristic
1262#126—1061no—
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—531no—
1277#123—531no—
1278#123—1061no—
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—21no—
1304#121—21no—
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#121C22×D5311yescharacteristic
1349#121C22×D5311yescharacteristic
1350#121C22×D5311yescharacteristic
1351#120—21no—
1352#120—21no—
1353#120—531no—
1354#120—531no—
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×Q8—531no—
1369C4×Q8—531no—
1370C4×Q8C22×D5311yescharacteristic
1371C4×D4—21no—
1372C4×D4—531no—
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×D4—1061no—
1388C4×D4C22×D5311yescharacteristic
1389C4×D4C22×D5311yescharacteristic
1390#117—531no—
1391#117—531no—
1392#117—531no—
1393#117—1061no—
1394#117—1061no—
1395#117—1061no—
1396C2×C4⋊C4—531no—
1397C2×C4⋊C4—531no—
1398C2×C4⋊C4—531no—
1399C2×C4⋊C4—1061no—
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#107—531no—
1409#107—531no—
1410#107—531no—
1411#107C22×D5311yescharacteristic
1412#106—531no—
1413#106—531no—
1414C4⋊C8—531no—
1415C4⋊C8—531no—
1416C4⋊C8—531no—
1417C4⋊C8C22×D5311yescharacteristic
1418#103—531no—
1419#103—531no—
1420#103—531no—
1421#103—531no—
1422#103—531no—
1423#103—531no—
1424#103—531no—
1425#103—531no—
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×C8—531no—
1466C24—21no—
1467C24—21no—
1468C24—531no—
1469C24—1061no—
1470C24—1061no—
1471C24—1061no—
1472C24—1061no—
1473#41—22no—
1474#41—41no—
1475#41—1062no—
1476#41—1062no—
1477#41—1062no—
1478#41—1062no—
1479#41—1062no—
1480#41—4242no—
1481#41—2121no—
1482#41—2121no—
1483#41—2124no—
1484#41—2121no—
1485#41—2121no—
1486#41—2121no—
1487#41—2121no—
1488#41—2121no—
1489#41—2121no—
1490#41—2121no—
1491#41—2121no—
1492#41—2121no—
1493#41—2124no—
1494#41—2124no—
1495C2×Q8—21no—
1496C2×Q8—22no—
1497C2×Q8—41no—
1498C2×Q8—531no—
1499C2×Q8—531no—
1500C2×Q8—1061no—
1501C2×Q8C23×D5311yescharacteristic
1502C2×Q8C23×D5311yescharacteristic
1503C2×D4—21no—
1504C2×D4—21no—
1505C2×D4—21no—
1506C2×D4—21no—
1507C2×D4—21no—
1508C2×D4—21no—
1509C2×D4—21no—
1510C2×D4—21no—
1511C2×D4—41no—
1512C2×D4—41no—
1513C2×D4—41no—
1514C2×D4—41no—
1515C2×D4—82no—
1516C2×D4—531no—
1517C2×D4—531no—
1518C2×D4—531no—
1519C2×D4—531no—
1520C2×D4—531no—
1521C2×D4—531no—
1522C2×D4—531no—
1523C2×D4—531no—
1524C2×D4—531no—
1525C2×D4—1062no—
1526C2×D4—1062no—
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—1061no—
1538C2×D4—1062no—
1539C2×D4—1061no—
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—1061no—
1554C2×D4—1061no—
1555C2×D4—4242no—
1556C2×D4—4242no—
1557C2×D4—4242no—
1558C2×D4—4242no—
1559C2×D4—2121no—
1560C2×D4—2121no—
1561C2×D4—2124no—
1562C2×D4—2124no—
1563C2×D4—2121no—
1564C2×D4—2121no—
1565C2×D4—2121no—
1566C2×D4—2124no—
1567C2×D4—2124no—
1568C2×D4D4×D5311yescharacteristic
1569C2×D4C23×D5311yescharacteristic
1570C2×D4C23×D5311yescharacteristic
1571C2×D4C23×D5311yescharacteristic
1572C2×D4C23×D5311yescharacteristic
1573C22×C4—21no—
1574C22×C4—21no—
1575C22×C4—21no—
1576C22×C4—531no—
1577C22×C4—531no—
1578C22×C4—531no—
1579C22×C4—531no—
1580C22×C4—531no—
1581C22×C4—531no—
1582C22×C4—1061no—
1583C22×C4—1061no—
1584C22×C4—1061no—
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—2121no—
1597C22×C4—2121no—
1598C22×C4—2124no—
1599C22×C4C23×D5311yescharacteristic
1600C22×C4C23×D5311yescharacteristic
1601Q16—1062no—
1602Q16—2121no—
1603SD16—22no—
1604SD16—22no—
1605SD16—22no—
1606SD16—41no—
1607SD16—41no—
1608SD16—41no—
1609SD16—1062no—
1610SD16—2121no—
1611SD16—2121no—
1612SD16—2121no—
1613D8—41no—
1614D8—41no—
1615D8—41no—
1616D8—1062no—
1617D8—1062no—
1618D8—1062no—
1619D8—2121no—
1620D8—2121no—
1621D8—2121no—
1622D8—2121no—
1623D8—2121no—
1624D8—2121no—
1625M16—41no—
1626M16—2121no—
1627C2×C8—41no—
1628C2×C8—531no—
1629C2×C8—531no—
1630C2×C8—531no—
1631C2×C8—531no—
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—531no—
1644C4⋊C4—531no—
1645C4⋊C4—531no—
1646C4⋊C4—531no—
1647C4⋊C4—531no—
1648C4⋊C4—531no—
1649C4⋊C4—531no—
1650C4⋊C4—531no—
1651C4⋊C4—531no—
1652C4⋊C4—1061no—
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⋊C4—1061no—
1662C4⋊C4—1061no—
1663C4⋊C4—1061no—
1664C4⋊C4D4×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—531no—
1712C42—1061no—
1713C42—1061no—
1714C42—1061no—
1715C42—1061no—
1716C42C23×D5311yescharacteristic
1717C23—21no—
1718C23—21no—
1719C23—21no—
1720C23—21no—
1721C23—42no—
1722C23—81no—
1723C23—81no—
1724C23—81no—
1725C23—81no—
1726C23—81no—
1727C23—531no—
1728C23—531no—
1729C23—531no—
1730C23—1062no—
1731C23—1061no—
1732C23—1061no—
1733C23—1061no—
1734C23—4241no—
1735C23—4241no—
1736C23—4241no—
1737C23—4241no—
1738C23—4241no—
1739C23—4241no—
1740C23—4241no—
1741C23—2122no—
1742C23—2121no—
1743C23—2121no—
1744C23—2122no—
1745C23—2122no—
1746C23—2122no—
1747C23—2122no—
1748C23C2×D4×D5311yescharacteristic
1749C23C2×D4×D5311yescharacteristic
1750Q8—21no—
1751Q8—21no—
1752Q8—21no—
1753Q8—42no—
1754Q8—1061no—
1755Q8—1061no—
1756Q8—4241no—
1757Q8—2121no—
1758Q8#1313326212yes—
1759D4—22no—
1760D4—21no—
1761D4—21no—
1762D4—21no—
1763D4—21no—
1764D4—21no—
1765D4—21no—
1766D4—21no—
1767D4—21no—
1768D4—42no—
1769D4—42no—
1770D4—42no—
1771D4—81no—
1772D4—81no—
1773D4—81no—
1774D4—81no—
1775D4—81no—
1776D4—532no—
1777D4—1064no—
1778D4—1062no—
1779D4—1061no—
1780D4—1061no—
1781D4—1061no—
1782D4—1061no—
1783D4—1061no—
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—4241no—
1798D4—4241no—
1799D4—4241no—
1800D4—4241no—
1801D4—2121no—
1802D4—2121no—
1803D4—2122no—
1804D4—2122no—
1805D4—2122no—
1806D4—2122no—
1807D4—2122no—
1808D4—2122no—
1809D4—2121no—
1810D4—2121no—
1811D4—2121no—
1812D4—2122no—
1813D4—2122no—
1814D4—2122no—
1815C2×C4—21no—
1816C2×C4—21no—
1817C2×C4—21no—
1818C2×C4—21no—
1819C2×C4—21no—
1820C2×C4—21no—
1821C2×C4—21no—
1822C2×C4—21no—
1823C2×C4—42no—
1824C2×C4—42no—
1825C2×C4—81no—
1826C2×C4—531no—
1827C2×C4—531no—
1828C2×C4—531no—
1829C2×C4—531no—
1830C2×C4—531no—
1831C2×C4—1064no—
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—4241no—
1849C2×C4—4241no—
1850C2×C4—4241no—
1851C2×C4—2121no—
1852C2×C4—2121no—
1853C2×C4—2122no—
1854C2×C4—2122no—
1855C2×C4—2122no—
1856C2×C4—2122no—
1857C2×C4—2121no—
1858C2×C4—2122no—
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—21no—
1874C22—21no—
1875C22—21no—
1876C22—21no—
1877C22—41no—
1878C22—41no—
1879C22—41no—
1880C22—41no—
1881C22—41no—
1882C22—41no—
1883C22—41no—
1884C22—41no—
1885C22—41no—
1886C22—41no—
1887C22—41no—
1888C22—41no—
1889C22—162no—
1890C22—162no—
1891C22—8482no—
1892C22—8482no—
1893C22—8482no—
1894C22—1062no—
1895C22—1061no—
1896C22—1061no—
1897C22—1061no—
1898C22—1061no—
1899C22—1061no—
1900C22—1061no—
1901C22—1061no—
1902C22—1061no—
1903C22—1061no—
1904C22—4244no—
1905C22—4242no—
1906C22—2121no—
1907C22—2121no—
1908C22—2121no—
1909C22—2121no—
1910C22—2121no—
1911C22—2121no—
1912C22—2121no—
1913C22—2121no—
1914C22#1681142712yes—
1915C22C22×D4×D5311yescharacteristic
1916C4—21no—
1917C4—21no—
1918C4—22no—
1919C4—21no—
1920C4—21no—
1921C4—41no—
1922C4—41no—
1923C4—41no—
1924C4—1061no—
1925C4—1061no—
1926C4—1061no—
1927C4—1061no—
1928C4—1061no—
1929C4—2121no—
1930C4—2121no—
1931C4—2121no—
1932C4—2121no—
1933C4—2121no—
1934C4H(5,𝔽2)×D5311yescharacteristic
1935C4C2×#1313326211yescharacteristic
1936C2—22no—
1937C2—41no—
1938C2—81no—
1939C2—81no—
1940C2—81no—
1941C2—81no—
1942C2—4241no—
1943C2—4241no—
1944C2—2121no—
1945C2—2121no—
1946C2—2122no—
1947C2—2121no—
1948C2#2028834311yescharacteristic
1949C2C2×#1681142711yescharacteristic
1950C2#2028948711yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3265C2
socleC22×C53C23×D4
hypercenter#3265D53
hypocenterC53#61639
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3265

Complements

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

NH ≅ G/Ntype
1. #20289036C2semidirect
2. #20288381C2semidirect
3. #20286866C2semidirect
4. #20286738C2semidirect
5. #20286726C2semidirect
6. #20286710C2semidirect
7. #20286658C2semidirect
8. #20286602C2semidirect
9. #20286572C2semidirect
10. #20286523C2semidirect
11. #20286470C2semidirect
12. #20286422C2semidirect
13. #20286393C2semidirect
14. D4×#11719922C2semidirect
15. #20286254C2semidirect
16. #20286249C2semidirect
17. #20286188C2semidirect
18. #20285808C2semidirect
19. #20285760C2semidirect
20. #20285613C2semidirect
21. #20285571C2semidirect
22. #20285475C2semidirect
23. #20285464C2semidirect
24. #20284975C2semidirect
25. #20284913C2semidirect
26. #20284017C2semidirect
27. #20283982C2semidirect
28. #20283932C2semidirect
29. C2×#16810767C2semidirect
30. #20283766C2semidirect
31. C53×#3265C2semidirect
32. C2×#13133263C22semidirect
33. C22×#11719949C22semidirect
34. C2×#13133241C22semidirect
35. C2×#13133238C22semidirect
36. C2×#13133238C22semidirect
37. C2×#13133238C22semidirect
38. C22×#11719922C22semidirect
39. C22×#11719922C22semidirect
42. #16811337C22semidirect
43. #16811323C22semidirect
44. #16811313C22semidirect
46. #16811295C22semidirect
47. #16811293C22semidirect
48. #16811292C22semidirect
49. #16811284C22semidirect
50. #16811273C22semidirect
52. #16811267C22semidirect
53. #16811267C22semidirect
55. #16811266C22semidirect
57. #16811264C22semidirect
61. #16811257C22semidirect
62. #16811238C22semidirect
63. #16811227C22semidirect
67. #16811203C22semidirect
68. #16811202C22semidirect
70. #16811191C22semidirect
71. #16811190C22semidirect
74. #16811133C22semidirect
77. C2×#13133188C22semidirect
79. #121×D53C22semidirect
80. #16811105C22semidirect
81. #16811011C22semidirect
82. #16811004C22semidirect
83. #16810999C22semidirect
84. #16810988C22semidirect
85. #16810984C22semidirect
86. #16810977C22semidirect
87. #16810968C22semidirect
88. #16810961C22semidirect
89. #16810960C22semidirect
90. #16810957C22semidirect
91. #16810950C22semidirect
92. #16810948C22semidirect
93. #16810946C22semidirect
94. #16810940C22semidirect
95. #16810938C22semidirect
96. #16810937C22semidirect
97. #16810935C22semidirect
98. #16810935C22semidirect
99. #16810934C22semidirect
100. #16810930C22semidirect
101. #16810924C22semidirect
102. #16810916C22semidirect
103. #16810902C22semidirect
104. #16810875C22semidirect
105. #16810869C22semidirect
106. #16810866C22semidirect
107. #16810862C22semidirect
108. #16810858C22semidirect
109. #16810858C22semidirect
110. #16810858C22semidirect
111. #16810857C22semidirect
112. #16810857C22semidirect
113. #16810856C22semidirect
114. #16810856C22semidirect
115. #16810852C22semidirect
116. #16810850C22semidirect
117. #16810849C22semidirect
118. #16810843C22semidirect
119. #16810842C22semidirect
120. #16810840C22semidirect
121. #16810840C22semidirect
122. #16810837C22semidirect
123. #16810824C22semidirect
124. #16810818C22semidirect
125. #16810816C22semidirect
126. #16810816C22semidirect
127. #16810815C22semidirect
128. #16810788C22semidirect
129. #16810788C22semidirect
130. #16810785C22semidirect
131. #16810782C22semidirect
132. #16810779C22semidirect
133. #16810776C22semidirect
134. #16810776C22semidirect
135. #16810775C22semidirect
136. #16810769C22semidirect
137. #16810769C22semidirect
139. #16810767C22semidirect
140. #16810767C22semidirect
141. #16810767C22semidirect
142. #16810767C22semidirect
143. #16810767C22semidirect
144. #16810767C22semidirect
145. #16810767C22semidirect
146. #16810767C22semidirect
147. #16810767C22semidirect
148. #16810767C22semidirect
149. #16810767C22semidirect
150. #16810765C22semidirect
151. #16810757C22semidirect
152. #16810757C22semidirect
153. #16810756C22semidirect
154. #16810756C22semidirect
155. #16810755C22semidirect
156. #16810755C22semidirect
157. #16810755C22semidirect
158. #16810755C22semidirect
159. #16810755C22semidirect
160. #16810732C22semidirect
161. #16810725C22semidirect
162. #16810724C22semidirect
163. C4×#11719925C22semidirect
164. SD16×Dic53C22semidirect
165. C4×#11719922C22semidirect
166. #16810703C22semidirect
167. #16810696C22semidirect
168. #16810692C22semidirect
169. #16810691C22semidirect
170. D4×#88322C22semidirect
171. #16810688C22semidirect
172. C8×C22⋊D53C22semidirect
173. #16810686C22semidirect
174. #16810685C22semidirect
175. #16810683C22semidirect
176. #16810629C22semidirect
177. #16810623C22semidirect
178. #16810619C22semidirect
179. #16810618C22semidirect
180. #16810618C22semidirect
181. C2×#13133141C22semidirect
182. C2×#13133139C22semidirect
183. #102×D53C22semidirect
184. #16810591C22semidirect
185. #16810588C22semidirect
186. C2×#13133129C22semidirect
187. C22⋊C8×D53C22semidirect
188. C2×AGL(1,ℤ/8)×C53C22semidirect
189. C22×SD16×C53C22semidirect
191. D42×C53C22semidirect
192. C53×#496C22semidirect
193. C53×#468C22semidirect
194. C53×#466C22semidirect
195. C53×#463C22semidirect
196. C53×#460C22semidirect
197. C53×#450C22semidirect
198. C53×#449C22semidirect
199. C53×#448C22semidirect
200. C53×#447C22semidirect
201. C53×#440C22semidirect
202. C53×#435C22semidirect
977. #3265D53semidirect
1010. C2×AGL(1,ℤ/8)C2×D53semidirect
1014. C22×SD16C2×D53semidirect
1040. D42C2×D53semidirect
1061. #496C2×D53semidirect
1087. #468C2×D53semidirect
1096. #466C2×D53semidirect
1105. #463C2×D53semidirect
1107. #460C2×D53semidirect
1120. #450C2×D53semidirect
1136. #449C2×D53semidirect
1137. #448C2×D53semidirect
1147. #447C2×D53semidirect
1151. #440C2×D53semidirect
1159. #435C2×D53semidirect
1178. C53#61639semidirect

Maximal subgroups

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

subgroupindex
#202890362
#202883812
#202868662
#202867382
#202867262
#202867102
#202866582
#202866022
#202865722
#202865232
#202864702
#202864222
#202863932
D4×#117199222
#202862542
#202862492
#202861882
#202858082
#202857602
#202856132
#202855712
#202854752
#202854642
#202849752
#202849132
#202840172
#202839822
#202839322
C2×#168107672
#202837662
C53×#32652
#6163953