Finite Group Databasebeta

← #28270654

Subgroups — #28270654

Order 13568.

2100 conjugacy classes of subgroups.

The subgroup lattice has 1902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288996C211yesmaximal, characteristic, complemented
2#20288377C211yesmaximal, characteristic, complemented
3#20287049C211yesmaximal, characteristic, complemented
4#20286984C211yesmaximal, characteristic, complemented
5#20286939C211yesmaximal, characteristic, complemented
6#20286920C211yesmaximal, characteristic, complemented
7#20286792C211yesmaximal, characteristic, complemented
8#20286785C211yesmaximal, characteristic, complemented
9#20286732C211yesmaximal, characteristic, complemented
10#20286725C211yesmaximal, characteristic, complemented
11#20286374C211yesmaximal, characteristic, complemented
12#20286365C211yesmaximal, characteristic, complemented
13#20286346C211yesmaximal, characteristic, complemented
14#20286309C211yesmaximal, characteristic, complemented
15#20286300C211yesmaximal, characteristic, complemented
16#20286270C211yesmaximal, characteristic, complemented
17#20286229C211yesmaximal, characteristic, complemented
18#20286214C211yesmaximal, characteristic, complemented
19#20285805C211yesmaximal, characteristic, complemented
20#20285783C211yesmaximal, characteristic, complemented
21#20285612C211yesmaximal, characteristic, complemented
22#20285599C211yesmaximal, characteristic, complemented
23#20285526C211yesmaximal, characteristic, complemented
24#20285518C211yesmaximal, characteristic, complemented
25#20284970C211yesmaximal, characteristic, complemented
26#20284922C211yesmaximal, characteristic, complemented
27#20283992C211yesmaximal, characteristic, complemented
28#20283972C211yesmaximal, characteristic, complemented
29#20283953C211yesmaximal, characteristic, complemented
30#20283773C211yesmaximal, characteristic, complemented
31C53×#3012C211yesmaximal, characteristic, complemented
32C2×#41×D53C2211yescharacteristic
33C2×#13133249C2211yescharacteristic, complemented
34C2×#13133247C2211yescharacteristic, complemented
35C2×#13133246C2211yescharacteristic, complemented
36C2×#13133246C2211yescharacteristic, complemented
37C2×#13133241C2211yescharacteristic, complemented
38C22×#11719923C2211yescharacteristic, complemented
39#16811374—21no—
40#16811368—21no—
41#16811344C2211yescharacteristic, complemented
42#16811328C2211yescharacteristic, complemented
43#16811327—21no—
44#16811320—21no—
45#16811320C2211yescharacteristic, complemented
46#16811308C2211yescharacteristic, complemented
47#16811292C2211yescharacteristic
48#16811292C2211yescharacteristic
49#16811286C2211yescharacteristic, complemented
50#16811280C2211yescharacteristic
51#16811280C2211yescharacteristic
52#16811280C2211yescharacteristic, complemented
53#16811279C2211yescharacteristic, complemented
54#16811272C2211yescharacteristic, complemented
55#16811267—21no—
56#16811267—21no—
57#16811267C2211yescharacteristic
58#16811267C2211yescharacteristic
59D4×C22⋊D53—21no—
60D4×C22⋊D53—21no—
61D4×C22⋊D53C2211yescharacteristic
62D4×C22⋊D53C2211yescharacteristic
63#16811240—21no—
64#16811240C2211yescharacteristic, complemented
65#16811233C2211yescharacteristic, complemented
66#16811218—21no—
67#16811205—21no—
68#16811205—21no—
69#16811201—21no—
70#16811201C2211yescharacteristic
71#16811194C2211yescharacteristic, complemented
72#16811190—21no—
73#16811190C2211yescharacteristic
74#16811133C2211yescharacteristic, complemented
75#16811130—21no—
76#16811130C2211yescharacteristic
77C22⋊Q8×D53C2211yescharacteristic, complemented
78C2×#13133188—21no—
79C2×#13133188C2211yescharacteristic
80#16811106C2211yescharacteristic
81#16811014C2211yescharacteristic, complemented
82#16811011C2211yescharacteristic, complemented
83#16811006C2211yescharacteristic, complemented
84#16810994C2211yescharacteristic, complemented
85#16810986C2211yescharacteristic, complemented
86#16810981C2211yescharacteristic, complemented
87#16810976C2211yescharacteristic, complemented
88#16810968C2211yescharacteristic, complemented
89#16810965C2211yescharacteristic, complemented
90#16810959C2211yescharacteristic, complemented
91#16810958C2211yescharacteristic, complemented
92#16810956C2211yescharacteristic, complemented
93#16810954C2211yescharacteristic, complemented
94#16810948C2211yescharacteristic, complemented
95#16810946C2211yescharacteristic, complemented
96#16810946C2211yescharacteristic, complemented
97#16810936C2211yescharacteristic, complemented
98#16810935C2211yescharacteristic, complemented
99#16810935C2211yescharacteristic, complemented
100#16810934C2211yescharacteristic, complemented
101#16810928C2211yescharacteristic, complemented
102#16810925C2211yescharacteristic, complemented
103#16810916C2211yescharacteristic, complemented
104#16810901C2211yescharacteristic, complemented
105#16810881C2211yescharacteristic, complemented
106#16810873C2211yescharacteristic, complemented
107#16810873C2211yescharacteristic, complemented
108#16810871C2211yescharacteristic, complemented
109#16810869C2211yescharacteristic, complemented
110#16810868C2211yescharacteristic, complemented
111#16810868C2211yescharacteristic, complemented
112#16810868C2211yescharacteristic, complemented
113#16810868C2211yescharacteristic, complemented
114#16810867C2211yescharacteristic, complemented
115#16810866C2211yescharacteristic, complemented
116#16810866C2211yescharacteristic, complemented
117#16810864C2211yescharacteristic, complemented
118#16810862C2211yescharacteristic, complemented
119#16810857C2211yescharacteristic, complemented
120#16810852C2211yescharacteristic, complemented
121#16810844C2211yescharacteristic, complemented
122#16810844C2211yescharacteristic, complemented
123#16810843C2211yescharacteristic, complemented
124#16810843C2211yescharacteristic, complemented
125#16810836C2211yescharacteristic, complemented
126#16810836C2211yescharacteristic, complemented
127#16810831C2211yescharacteristic, complemented
128#16810826C2211yescharacteristic, complemented
129#16810822C2211yescharacteristic, complemented
130#16810822C2211yescharacteristic, complemented
131#16810821C2211yescharacteristic, complemented
132#16810816C2211yescharacteristic, complemented
133#16810788C2211yescharacteristic, complemented
134#16810787C2211yescharacteristic, complemented
135#16810787C2211yescharacteristic, complemented
136#16810786C2211yescharacteristic, complemented
137#16810785C2211yescharacteristic
138#16810785C2211yescharacteristic
139#16810785C2211yescharacteristic, complemented
140#16810785C2211yescharacteristic, complemented
141#16810785C2211yescharacteristic, complemented
142#16810783C2211yescharacteristic, complemented
143#16810781C2211yescharacteristic, complemented
144#16810780C2211yescharacteristic, complemented
145#16810777C2211yescharacteristic, complemented
146#16810775C2211yescharacteristic, complemented
147#16810774C2211yescharacteristic, complemented
148#16810774C2211yescharacteristic, complemented
149#16810774C2211yescharacteristic, complemented
150#16810774C2211yescharacteristic, complemented
151#16810772C2211yescharacteristic, complemented
152#16810768C2211yescharacteristic, complemented
153#16810767C2211yescharacteristic, complemented
154#16810766C2211yescharacteristic, complemented
155#16810765C2211yescharacteristic, complemented
156#16810765C2211yescharacteristic, complemented
157#16810765C2211yescharacteristic, complemented
158#16810764C2211yescharacteristic, complemented
159#16810760C2211yescharacteristic, complemented
160#16810760C2211yescharacteristic, complemented
161#16810730C2211yescharacteristic, complemented
162#16810724C2211yescharacteristic, complemented
163#16810720C2211yescharacteristic, complemented
164#16810720C2211yescharacteristic, complemented
165#16810715C2211yescharacteristic, complemented
166#16810715C2211yescharacteristic, complemented
167SD16×Dic53C2211yescharacteristic, complemented
168D8×Dic53C2211yescharacteristic, complemented
169#16810699C2211yescharacteristic, complemented
170#16810699C2211yescharacteristic, complemented
171#16810698C2211yescharacteristic, complemented
172#16810698C2211yescharacteristic, complemented
173#16810694C2211yescharacteristic, complemented
174#16810694C2211yescharacteristic, complemented
175#16810691C2211yescharacteristic, complemented
176#16810691C2211yescharacteristic, complemented
177#16810681C2211yescharacteristic, complemented
178#16810681C2211yescharacteristic, complemented
179#16810630C2211yescharacteristic, complemented
180#16810628C2211yescharacteristic, complemented
181#16810626C2211yescharacteristic, complemented
182#16810623C2211yescharacteristic, complemented
183#16810621C2211yescharacteristic, complemented
184#16810619C2211yescharacteristic, complemented
185#16810590C2211yescharacteristic, complemented
186#16810585C2211yescharacteristic, complemented
187#16810585C2211yescharacteristic, complemented
188C2×H(5,𝔽2)×C53C2211yescharacteristic
189C2×AGL(1,ℤ/8)×C53C2211yescharacteristic, complemented
190C2×#135×C53C2211yescharacteristic, complemented
191C53×#537C2211yescharacteristic, complemented
192C53×#452C2211yescharacteristic
193C53×#452C2211yescharacteristic, complemented
194C53×#450C2211yescharacteristic, complemented
195C53×#450C2211yescharacteristic, complemented
196C53×#449C2211yescharacteristic
197C53×#449C2211yescharacteristic, complemented
198C53×#447C2211yescharacteristic, complemented
199C53×#447C2211yescharacteristic, complemented
200C53×#417C2211yescharacteristic, complemented
201C2×#102×C53C2211yescharacteristic, complemented
202C53×#408C2211yescharacteristic, complemented
203C2×#11719949C2311yescharacteristic
204C2×#11719945—21no—
205C2×#11719945C2311yescharacteristic
206C2×#11719947—21no—
207C2×#11719947C2311yescharacteristic
208C2×#11719947C2311yescharacteristic
209#41×D53—42no—
210#41×D53—42no—
211C22×Dic106C2311yescharacteristic
212C2×Q8×D53C2311yescharacteristic
213C2×Q8×D53C2311yescharacteristic
214C22×C22⋊D53—21no—
215C22×C22⋊D53—21no—
216C22×C22⋊D53—21no—
217C2×D4×D53—21no—
218C2×D4×D53C2311yescharacteristic
219C22×C4×D53—21no—
220C22×C4×D53C2311yescharacteristic
221#13133249—42no—
222#13133247—42no—
223#13133246—42no—
224#13133246—42no—
225#13133241—42no—
226C2×Dic212C2311yescharacteristic
227C2×Dic212C2311yescharacteristic
228C2×#11719925C2311yescharacteristic
229C2×#11719925C2311yescharacteristic
230C2×#11719925C2311yescharacteristic
231C2×#11719913C2311yescharacteristic
232C2×#11719913C2311yescharacteristic
233C2×#11719923—42no—
234C2×#11719923C2311yescharacteristic
235C2×#11719923C2311yescharacteristic
236C2×#11719923C2311yescharacteristic
237C2×#11719923C2311yescharacteristic
238C2×#11719923C2311yescharacteristic
239C2×#11719923C2311yescharacteristic
240C2×#11719923C2311yescharacteristic
241C2×#11719924C2311yescharacteristic
242C2×#11719922C2311yescharacteristic
243C2×#11719917C2311yescharacteristic
244C2×#11719912C2311yescharacteristic
245C2×#11719912C2311yescharacteristic
246C2×#11719912C2311yescharacteristic
247C2×#11719912C2311yescharacteristic
248C22×#88322C2311yescharacteristic
249#13133216—21no—
250#13133216C2311yescharacteristic
251#13133215—21no—
252#13133215C2311yescharacteristic
253#13133213—21no—
254#13133213—21no—
255#13133213C2311yescharacteristic
256#13133213C2311yescharacteristic
257#13133212—21no—
258#13133212—21no—
259#13133210—21no—
260#13133210—21no—
261#13133210—21no—
262#13133210—21no—
263#13133210—21no—
264#13133208—21no—
265#13133208C2311yescharacteristic
266#13133207—21no—
267#13133207—21no—
268#13133207—21no—
269#13133204—21no—
270#13133204—21no—
271#13133204—21no—
272#13133204—21no—
273#13133204—21no—
274#13133204C2311yescharacteristic
275#13133204C2311yescharacteristic
276#13133204C2311yescharacteristic
277#13133203—21no—
278#13133203—21no—
279#13133200—21no—
280#13133200—21no—
281#13133199—21no—
282#13133198—21no—
283#13133198—21no—
284#13133198—21no—
285#13133198—21no—
286#13133198—21no—
287#13133198—21no—
288#13133198—21no—
289#13133198D411yescharacteristic
290#13133198D411yescharacteristic
291#13133197C2311yescharacteristic
292#13133197C2311yescharacteristic
293#13133196—21no—
294#13133196—21no—
295#13133196—21no—
296#13133196—21no—
297#13133196C2311yescharacteristic
298#13133196C2311yescharacteristic
299#13133196C2311yescharacteristic
300#13133196C2311yescharacteristic
301#13133196C2311yescharacteristic
302#13133196C2311yescharacteristic
303#13133195—21no—
304#13133195—21no—
305#13133195—21no—
306#13133194—21no—
307#13133194—21no—
308#13133194—21no—
309#13133194—21no—
310#13133193—21no—
311#13133193D411yescharacteristic
312#13133193D411yescharacteristic
313#13133193C2311yescharacteristic
314#13133191—21no—
315#13133191—21no—
316#13133191C2311yescharacteristic
317#13133191C2311yescharacteristic
318#13133189—21no—
319#13133189—21no—
320#13133189—21no—
321#13133189—21no—
322#13133189—21no—
323#13133189—21no—
324#13133189—21no—
325#13133189—21no—
326#13133188—21no—
327#13133188—21no—
328#13133188—21no—
329#13133188—21no—
330#13133188—21no—
331#13133188—21no—
332#13133188—21no—
333#13133188—21no—
334#13133188—21no—
335#13133188—21no—
336#13133188—21no—
337#13133188D411yescharacteristic
338#13133188D411yescharacteristic
339#13133188C2311yescharacteristic
340#13133188C2311yescharacteristic
341#13133188C2311yescharacteristic
342#13133188C2311yescharacteristic
343#13133188C2311yescharacteristic
344#13133186—21no—
345#13133186—21no—
346#13133186—21no—
347#13133186—21no—
348#13133186—21no—
349#13133186—21no—
350#13133185—21no—
351#13133185—21no—
352#13133185—21no—
353#13133185D411yescharacteristic
354#13133185D411yescharacteristic
355Q8×Dic53C2311yescharacteristic
356Q8×Dic53C2311yescharacteristic
357Q8×Dic53C2311yescharacteristic
358#13133182—21no—
359#13133182C2311yescharacteristic
360#13133182C2311yescharacteristic
361D4×Dic53—21no—
362D4×Dic53—21no—
363D4×Dic53—21no—
364D4×Dic53—21no—
365D4×Dic53C2311yescharacteristic
366D4×Dic53C2311yescharacteristic
367D4×Dic53C2311yescharacteristic
368C4×C22⋊D53—21no—
369C4×C22⋊D53—21no—
370C4×C22⋊D53—21no—
371C4×C22⋊D53—21no—
372C4×C22⋊D53—21no—
373C4×C22⋊D53—21no—
374C4×C22⋊D53C2311yescharacteristic
375C4×C22⋊D53C2311yescharacteristic
376C4×C22⋊D53C2311yescharacteristic
377C4×C22⋊D53C2311yescharacteristic
378#13133177—21no—
379#13133177—21no—
380#13133177—21no—
381#13133176—21no—
382#13133176—21no—
383#13133176C2311yescharacteristic
384#13133176C2311yescharacteristic
385#13133175C2311yescharacteristic
386C2×C4⋊Dic53—21no—
387C2×C4⋊Dic53C2311yescharacteristic
388C2×#11719919—21no—
389C4⋊C4×D53—21no—
390C4⋊C4×D53C2311yescharacteristic
391C2×C22⋊Dic53—21no—
392C2×C22⋊Dic53—21no—
393C2×C22⋊Dic53—21no—
394C22⋊C4×D53—21no—
395#13133151C2311yescharacteristic
396#13133151C2311yescharacteristic
397#13133150C2311yescharacteristic
398#13133150C2311yescharacteristic
399#13133150C2311yescharacteristic
400#13133150C2311yescharacteristic
401#13133149C2311yescharacteristic
402#13133149C2311yescharacteristic
403#13133146C2311yescharacteristic
404#13133146C2311yescharacteristic
405#13133146C2311yescharacteristic
406#13133146C2311yescharacteristic
407#13133142C2311yescharacteristic
408#13133142C2311yescharacteristic
409#13133142C2311yescharacteristic
410#13133142C2311yescharacteristic
411#13133142C2311yescharacteristic
412#13133142C2311yescharacteristic
413#13133141C2311yescharacteristic
414#13133141C2311yescharacteristic
415#13133141C2311yescharacteristic
416#13133141C2311yescharacteristic
417#13133140C2311yescharacteristic
418#13133140C2311yescharacteristic
419#13133139C2311yescharacteristic
420#13133139C2311yescharacteristic
421#13133138C2311yescharacteristic
422#13133138C2311yescharacteristic
423#13133138C2311yescharacteristic
424#13133138C2311yescharacteristic
425#13133138C2311yescharacteristic
426#13133138C2311yescharacteristic
427#13133138C2311yescharacteristic
428#13133138C2311yescharacteristic
429#13133137C2311yescharacteristic
430#13133137C2311yescharacteristic
431C22⋊#88322C2311yescharacteristic
432C22⋊#88322C2311yescharacteristic
433C22⋊#88322C2311yescharacteristic
434C22⋊#88322C2311yescharacteristic
435#13133129C2311yescharacteristic
436#13133129C2311yescharacteristic
437#13133129C2311yescharacteristic
438#13133129C2311yescharacteristic
439#13133127C2311yescharacteristic
440#13133127C2311yescharacteristic
441C8×Dic53C2311yescharacteristic
442C8×Dic53C2311yescharacteristic
443H(5,𝔽2)×C53—42no—
444H(5,𝔽2)×C53—42no—
445C2×#41×C53—21no—
446C2×#41×C53C2311yescharacteristic
447C2×#41×C53C2311yescharacteristic
448C2×#41×C53C2311yescharacteristic
449C2×#41×C53C2311yescharacteristic
450C2×#41×C53C2311yescharacteristic
451C22×D4×C53—21no—
452C22×D4×C53—21no—
453C22×D4×C53—21no—
454C22×D4×C53C2311yescharacteristic
455C22×D4×C53C2311yescharacteristic
456C22×D4×C53C2311yescharacteristic
457AGL(1,ℤ/8)×C53—42no—
458#135×C53—42no—
459C2×Q16×C53C2311yescharacteristic
460C2×SD16×C53C2311yescharacteristic
461C2×SD16×C53C2311yescharacteristic
462C2×SD16×C53C2311yescharacteristic
463C2×SD16×C53C2311yescharacteristic
464C2×D8×C53C2311yescharacteristic
465C2×D8×C53C2311yescharacteristic
466C2×D8×C53C2311yescharacteristic
467C2×M16×C53C2311yescharacteristic
468C22×C8×C53C2311yescharacteristic
469C22⋊Q8×C53—21no—
470C22⋊Q8×C53C2311yescharacteristic
471C22⋊Q8×C53C2311yescharacteristic
472#121×C53—21no—
473#121×C53—21no—
474#121×C53—21no—
475#121×C53C2311yescharacteristic
476#121×C53C2311yescharacteristic
477C2×C4⋊C4×C53C2311yescharacteristic
478#103×C53C2311yescharacteristic
479#103×C53C2311yescharacteristic
480#102×C53C2311yescharacteristic
481#102×C53C2311yescharacteristic
482#102×C53C2311yescharacteristic
483#102×C53C2311yescharacteristic
484#102×C53C2311yescharacteristic
485#102×C53C2311yescharacteristic
486C22⋊C8×C53C2311yescharacteristic
487C22⋊C8×C53C2311yescharacteristic
488C22⋊C8×C53C2311yescharacteristic
489C22⋊C8×C53C2311yescharacteristic
490C24×C53—21no—
491C24×C53—21no—
492C24×C53—21no—
493C23×D53—21no—
494C23×D53C2×D411yescharacteristic
495#41×C53—22no—
496#41×C53—22no—
497#41×C53—22no—
498#41×C53—22no—
499#41×C53—41no—
500#41×C53—41no—
501#41×C53—41no—
502#41×C53—41no—
503#41×C53—44no—
504#41×C53—41no—
505#41×C53—41no—
506C2×Q8×C53C2×D411yescharacteristic
507C2×Q8×C53C2411yescharacteristic
508C2×Q8×C53C2411yescharacteristic
509C2×D4×C53—21no—
510C2×D4×C53—22no—
511C2×D4×C53—22no—
512C2×D4×C53—21no—
513C2×D4×C53—21no—
514C2×D4×C53—21no—
515C2×D4×C53—21no—
516C2×D4×C53—21no—
517C2×D4×C53—21no—
518C2×D4×C53—21no—
519C2×D4×C53—21no—
520C2×D4×C53—41no—
521C2×D4×C53—41no—
522C2×D4×C53—41no—
523C2×D4×C53—41no—
524C2×D4×C53—44no—
525C2×D4×C53—44no—
526C2×D4×C53—44no—
527C2×D4×C53C2×D411yescharacteristic
528C2×D4×C53C2×D411yescharacteristic
529C2×D4×C53C2×D411yescharacteristic
530C2×D4×C53C2411yescharacteristic
531C2×D4×C53C2411yescharacteristic
532C2×D4×C53C2411yescharacteristic
533C2×D4×C53C2411yescharacteristic
534C22×C4×C53—21no—
535C22×C4×C53—21no—
536C22×C4×C53—21no—
537C22×C4×C53—21no—
538C22×C4×C53—21no—
539C22×C4×C53C2411yescharacteristic
540C22×C4×C53C2411yescharacteristic
541C22×C4×C53C2411yescharacteristic
542C2×C22⋊D53—21no—
543C2×C22⋊D53—21no—
544C2×C22⋊D53—21no—
545C2×C22⋊D53—21no—
546C2×C22⋊D53—21no—
547C2×C22⋊D53—21no—
548C2×C22⋊D53—21no—
549C2×C22⋊D53—21no—
550C2×C22⋊D53—21no—
551C2×C22⋊D53—21no—
552C2×C22⋊D53—21no—
553C2×C22⋊D53—21no—
554C2×C22⋊D53—21no—
555C2×C22⋊D53—21no—
556C2×C22⋊D53—21no—
557C2×C22⋊D53—82no—
558C2×C22⋊D53—82no—
559C2×C22⋊D53—82no—
560C2×C22⋊D53C2×D411yescharacteristic
561C2×C22⋊D53C2×D411yescharacteristic
562C2×C22⋊D53C2×D411yescharacteristic
563C2×C22⋊D53C2×D411yescharacteristic
564C22×Dic53—21no—
565C22×Dic53—21no—
566C22×Dic53—21no—
567C22×Dic53—21no—
568C22×Dic53—21no—
569C22×Dic53—21no—
570C22×Dic53—21no—
571C22×Dic53C2×D411yescharacteristic
572#11719949—22no—
573#11719949—41no—
574Q8×D53—22no—
575Q8×D53—41no—
576Q8×D53—41no—
577Q8×D53—41no—
578#11719947—22no—
579#11719947—41no—
580#11719947—41no—
581#11719947—41no—
582#11719947—44no—
583D4×D53—22no—
584D4×D53—41no—
585D4×D53—44no—
586#11719945—41no—
587#11719945—41no—
588#11719945—44no—
589C2×D212—21no—
590C2×D212C2411yescharacteristic
591C2×C4×D53—21no—
592C2×C4×D53—21no—
593C2×C4×D53—21no—
594C2×C4×D53—21no—
595C2×C4×D53—21no—
596C2×C4×D53—41no—
597C2×C4×D53—41no—
598C2×C4×D53—44no—
599C2×C4×D53C2×D411yescharacteristic
600C2×C4×D53C2×D411yescharacteristic
601C2×C4×D53C2411yescharacteristic
602C2×C4×D53C2411yescharacteristic
603C2×Dic106—21no—
604C2×Dic106—21no—
605C2×Dic106—21no—
606C2×Dic106—21no—
607C2×Dic106—41no—
608C2×Dic106—41no—
609C2×Dic106C2411yescharacteristic
610C2×Dic106C2411yescharacteristic
611C2×Dic106C2411yescharacteristic
612Q16×C53—22no—
613SD16×C53—22no—
614SD16×C53—22no—
615SD16×C53—41no—
616SD16×C53—41no—
617D8×C53—22no—
618D8×C53—41no—
619D8×C53—41no—
620M16×C53—41no—
621C2×C8×C53—41no—
622C2×C8×C53C2411yescharacteristic
623C2×C8×C53C2411yescharacteristic
624C2×C8×C53C2411yescharacteristic
625C2×C8×C53C2411yescharacteristic
626C4⋊C4×C53—21no—
627C4⋊C4×C53—21no—
628C4⋊C4×C53—21no—
629C4⋊C4×C53C2411yescharacteristic
630C4⋊C4×C53C2411yescharacteristic
631C22⋊C4×C53—21no—
632C22⋊C4×C53—21no—
633C22⋊C4×C53—21no—
634C22⋊C4×C53—21no—
635C22⋊Dic53—21no—
636C22⋊Dic53—21no—
637C22⋊Dic53—21no—
638C22⋊Dic53—21no—
639C22⋊Dic53—21no—
640C22⋊Dic53—21no—
641C22⋊Dic53—21no—
642C22⋊Dic53—21no—
643C22⋊Dic53—21no—
644C22⋊Dic53—21no—
645C22⋊Dic53—21no—
646C22⋊Dic53—21no—
647C22⋊Dic53—21no—
648C22⋊Dic53—21no—
649C22⋊Dic53—21no—
650C22⋊Dic53—21no—
651C22⋊Dic53—21no—
652C22⋊Dic53—21no—
653C22⋊Dic53—21no—
654C22⋊Dic53—21no—
655C22⋊Dic53—21no—
656C22⋊Dic53C2×D411yescharacteristic
657C22⋊Dic53C2×D411yescharacteristic
658C22⋊Dic53C2×D411yescharacteristic
659C22⋊Dic53C2×D411yescharacteristic
660C22⋊Dic53C2×D411yescharacteristic
661C22⋊Dic53C2×D411yescharacteristic
662#11719925—22no—
663#11719925—22no—
664#11719925—41no—
665#11719924—41no—
666#11719923—22no—
667#11719923—22no—
668#11719923—41no—
669#11719923—41no—
670#11719923—41no—
671#11719923—41no—
672#11719923—41no—
673#11719922—41no—
674#11719921—21no—
675#11719921—21no—
676#11719921—21no—
677#11719921—21no—
678#11719921—21no—
679#11719921—21no—
680#11719921C2×D411yescharacteristic
681#11719921C2×D411yescharacteristic
682#11719921C2×D411yescharacteristic
683#11719921C2×D411yescharacteristic
684C4⋊Dic53—21no—
685C4⋊Dic53—21no—
686C4⋊Dic53—21no—
687C4⋊Dic53—21no—
688C4⋊Dic53—21no—
689C4⋊Dic53—21no—
690C4⋊Dic53—21no—
691C4⋊Dic53C2×D411yescharacteristic
692C4⋊Dic53C2×D411yescharacteristic
693C4⋊Dic53C2411yescharacteristic
694C4⋊Dic53C2411yescharacteristic
695C4⋊Dic53C2411yescharacteristic
696C4⋊Dic53C2411yescharacteristic
697#11719919—21no—
698#11719919—21no—
699#11719919—21no—
700#11719919—21no—
701#11719919—21no—
702#11719919—21no—
703#11719919—21no—
704#11719919—21no—
705#11719919—21no—
706#11719919—21no—
707#11719919—21no—
708#11719919—21no—
709#11719919—21no—
710#11719919—21no—
711#11719919C2×D411yescharacteristic
712#11719919C2×D411yescharacteristic
713#11719919C2×D411yescharacteristic
714#11719919C2×D411yescharacteristic
715C4×Dic53—21no—
716C4×Dic53—21no—
717C4×Dic53—21no—
718C4×Dic53—21no—
719C4×Dic53—21no—
720C4×Dic53—21no—
721C4×Dic53—21no—
722C4×Dic53C2411yescharacteristic
723C4×Dic53C2411yescharacteristic
724#11719917—41no—
725C2×#88322—41no—
726C2×#88322C2411yescharacteristic
727C2×#88322C2411yescharacteristic
728C2×#88322C2411yescharacteristic
729C2×#88322C2411yescharacteristic
730Dic212—41no—
731Dic212—41no—
732#11719913—41no—
733#11719913—41no—
734#11719912—41no—
735#11719912—41no—
736#11719912—41no—
737#11719912—41no—
738C23×C53—21no—
739C23×C53—21no—
740C23×C53—21no—
741C23×C53—21no—
742C23×C53—42no—
743C23×C53—42no—
744C23×C53—42no—
745C23×C53—81no—
746C23×C53—81no—
747C23×C53—81no—
748C23×C53—81no—
749C23×C53—81no—
750C23×C53—81no—
751C23×C53C22×D411yescharacteristic
752C23×C53C22×D411yescharacteristic
753C23×C53C22×D411yescharacteristic
754C22×D53—21no—
755C22×D53—41no—
756C22×D53—41no—
757C22×D53—41no—
758C22×D53—42no—
759C22×D53—42no—
760C22×D53—81no—
761C22×D53C22×D411yescharacteristic
762C22×D53C22×D411yescharacteristic
763Q8×C53—21no—
764Q8×C53—21no—
765Q8×C53—21no—
766Q8×C53—41no—
767Q8×C53H(5,𝔽2)12yes—
768D4×C53—24no—
769D4×C53—21no—
770D4×C53—21no—
771D4×C53—21no—
772D4×C53—21no—
773D4×C53—21no—
774D4×C53—21no—
775D4×C53—21no—
776D4×C53—41no—
777D4×C53—41no—
778D4×C53—41no—
779D4×C53—42no—
780D4×C53—42no—
781D4×C53—42no—
782D4×C53—42no—
783D4×C53—42no—
784D4×C53—81no—
785D4×C53—81no—
786D4×C53—81no—
787D4×C53H(5,𝔽2)12yes—
788C2×C4×C53—24no—
789C2×C4×C53—21no—
790C2×C4×C53—21no—
791C2×C4×C53—21no—
792C2×C4×C53—21no—
793C2×C4×C53—21no—
794C2×C4×C53—21no—
795C2×C4×C53—21no—
796C2×C4×C53—21no—
797C2×C4×C53—21no—
798C2×C4×C53—21no—
799C2×C4×C53—42no—
800C2×C4×C53—42no—
801C2×C4×C53—81no—
802C2×C4×C53—81no—
803C2×C4×C53C22×D411yescharacteristic
804C2×C4×C53C22×D411yescharacteristic
805C2×C4×C53C22×D411yescharacteristic
806C2×C4×C53C2511yescharacteristic
807C22⋊D53—41no—
808C22⋊D53—41no—
809C22⋊D53—41no—
810C22⋊D53—41no—
811C22⋊D53—42no—
812C22⋊D53—42no—
813C22⋊D53—42no—
814C22⋊D53—42no—
815C22⋊D53—42no—
816C22⋊D53—42no—
817C22⋊D53—81no—
818C22⋊D53—81no—
819C22⋊D53—81no—
820C22⋊D53—81no—
821C22⋊D53—81no—
822C22⋊D53—81no—
823C22⋊D53—81no—
824C22⋊D53—81no—
825C22⋊D53—81no—
826C2×Dic53—21no—
827C2×Dic53—21no—
828C2×Dic53—21no—
829C2×Dic53—21no—
830C2×Dic53—21no—
831C2×Dic53—21no—
832C2×Dic53—21no—
833C2×Dic53—41no—
834C2×Dic53—42no—
835C2×Dic53—81no—
836C2×Dic53—81no—
837C2×Dic53—81no—
838C2×Dic53—81no—
839C2×Dic53—81no—
840C2×Dic53—81no—
841C2×Dic53C22×D411yescharacteristic
842C2×Dic53C22×D411yescharacteristic
843C2×Dic53C22×D411yescharacteristic
844C2×Dic53C22×D411yescharacteristic
845C2×Dic53C22×D411yescharacteristic
846C2×Dic53C22×D411yescharacteristic
847D212—21no—
848D212—21no—
849D212—42no—
850C4×D53—21no—
851C4×D53—21no—
852C4×D53—21no—
853C4×D53—21no—
854C4×D53—41no—
855C4×D53—41no—
856C4×D53—42no—
857C4×D53—42no—
858C4×D53—42no—
859C4×D53—81no—
860C4×D53—81no—
861Dic106—21no—
862Dic106—21no—
863Dic106—21no—
864Dic106—21no—
865Dic106—21no—
866Dic106—21no—
867Dic106—42no—
868Dic106—81no—
869Dic106—81no—
870Dic106—81no—
871C8×C53—21no—
872C8×C53—21no—
873C8×C53—21no—
874C8×C53—21no—
875#88322—21no—
876#88322—21no—
877#88322—21no—
878#88322—21no—
879#61654—531nomaximal, Sylow
880C22×C53—21no—
881C22×C53—21no—
882C22×C53—21no—
883C22×C53—21no—
884C22×C53—21no—
885C22×C53—21no—
886C22×C53—21no—
887C22×C53—22no—
888C22×C53—21no—
889C22×C53—21no—
890C22×C53—41no—
891C22×C53—41no—
892C22×C53—41no—
893C22×C53—41no—
894C22×C53—41no—
895C22×C53—41no—
896C22×C53—41no—
897C22×C53—41no—
898C22×C53—41no—
899C22×C53—41no—
900C22×C53—41no—
901C22×C53—162no—
902C22×C53—162no—
903C22×C53—162no—
904C22×C53C23×D411yescharacteristic
905C2×D53—21no—
906C2×D53—21no—
907C2×D53—21no—
908C2×D53—21no—
909C2×D53—21no—
910C2×D53—21no—
911C2×D53—41no—
912C2×D53—41no—
913C2×D53—41no—
914C2×D53—82no—
915C2×D53—84no—
916C4×C53—22no—
917C4×C53—21no—
918C4×C53—21no—
919C4×C53—21no—
920C4×C53—41no—
921C4×C53—41no—
922C4×C53—41no—
923C4×C53C2×H(5,𝔽2)11yescharacteristic
924C4×C53C2×H(5,𝔽2)11yescharacteristic
925Dic53—21no—
926Dic53—21no—
927Dic53—21no—
928Dic53—21no—
929Dic53—21no—
930Dic53—21no—
931Dic53—41no—
932Dic53—41no—
933Dic53—41no—
934Dic53—41no—
935Dic53—41no—
936Dic53—41no—
937Dic53—41no—
938#3541—531no—
939#3488—531no—
940#3333—531no—
941#3327—531no—
942#3324—531no—
943#3322—531no—
944#3314—531no—
945#3313—531no—
946#3310—531no—
947#3309—531no—
948#3278—531no—
949#3277—531no—
950#3275—531no—
951#3272—531no—
952#3271—531no—
953#3269—531no—
954#3266—531no—
955#3265—531no—
956#3224—531no—
957#3222—531no—
958#3203—531no—
959#3201—531no—
960#3194—531no—
961#3193—531no—
962#3124—531no—
963#3120—531no—
964#3012D5311yescharacteristic, complemented
965#3009—531no—
966#3007—531no—
967#3005—531no—
968#2978—531no—
969C2×C53—41no—
970C2×C53—42no—
971C2×C53—41no—
972C2×C53—41no—
973C2×C53—81no—
974C2×C53—81no—
975C2×C53—81no—
976C2×C53#348411yescharacteristic
977C2×C53#358511yescharacteristic
978C2×C53#358611yescharacteristic
979D53—41no—
980D53—41no—
981D53—81no—
982C2×H(5,𝔽2)C2×D5311yescharacteristic
983C22×#41—531no—
984C2×#137—531no—
985C2×#137—531no—
986C2×#137—531no—
987C2×#137—531no—
988C2×AGL(1,ℤ/8)—531no—
989C2×AGL(1,ℤ/8)C2×D5311yescharacteristic, complemented
990C2×#135C2×D5311yescharacteristic, complemented
991C22×SD16—531no—
992#563—1061no—
993#562—1061no—
994#556—531no—
995#554—531no—
996#554—1061no—
997#553—531no—
998#553—1061no—
999#552—531no—
1000#550—531no—
1001#550—531no—
1002D4×Q8—531no—
1003#548—531no—
1004#548—531no—
1005#548—531no—
1006#548—531no—
1007#547—531no—
1008#546—531no—
1009#546—531no—
1010#546—1061no—
1011#546—1061no—
1012D42—531no—
1013D42—531no—
1014D42—1061no—
1015D42—1061no—
1016#542—531no—
1017#542—1061no—
1018#541—531no—
1019#539—1061no—
1020#538—1061no—
1021#538—1061no—
1022#537—531no—
1023#537—1061no—
1024#537C2×D5311yescharacteristic, complemented
1025#536—531no—
1026#535—531no—
1027#535—1061no—
1028#525—531no—
1029#525—531no—
1030#525—1061no—
1031C2×C22⋊Q8—531no—
1032C2×#121—531no—
1033C2×#121—1061no—
1034#520—531no—
1035#497—531no—
1036#496—531no—
1037#495—531no—
1038#492—531no—
1039#490—531no—
1040#489—531no—
1041#488—531no—
1042#486—531no—
1043#485—531no—
1044#484—531no—
1045#484—531no—
1046#484—531no—
1047#483—531no—
1048#482—531no—
1049#482—531no—
1050#482—531no—
1051#480—531no—
1052#480—531no—
1053#480—531no—
1054#480—531no—
1055#479—531no—
1056#478—531no—
1057#477—531no—
1058#474—531no—
1059#470—531no—
1060#469—531no—
1061#469—531no—
1062#468—531no—
1063#468—531no—
1064#468—531no—
1065#468—531no—
1066#468—531no—
1067#468—531no—
1068#468—531no—
1069#468—531no—
1070#468—531no—
1071#467—531no—
1072#467—531no—
1073#466—531no—
1074#465—531no—
1075#464—531no—
1076#464—531no—
1077#464—531no—
1078#464—531no—
1079#463—531no—
1080#463—531no—
1081#462—531no—
1082#461—531no—
1083#460—531no—
1084#460—531no—
1085#460—531no—
1086#459—531no—
1087#452—531no—
1088#452—531no—
1089#452—531no—
1090#452—531no—
1091#452—531no—
1092#452—531no—
1093#452—531no—
1094#452—531no—
1095#452—531no—
1096#452—531no—
1097#452C2×D5311yescharacteristic
1098#452C2×D5311yescharacteristic, complemented
1099#451—531no—
1100#451—531no—
1101#451—531no—
1102#450—531no—
1103#450—531no—
1104#450—531no—
1105#450—531no—
1106#450—531no—
1107#450—531no—
1108#450C2×D5311yescharacteristic, complemented
1109#450C2×D5311yescharacteristic, complemented
1110#449—531no—
1111#449—531no—
1112#449—531no—
1113#449—531no—
1114#449—531no—
1115#449—531no—
1116#449C2×D5311yescharacteristic
1117#449C2×D5311yescharacteristic, complemented
1118#448—531no—
1119#448—531no—
1120#448—531no—
1121#447C2×D5311yescharacteristic, complemented
1122#447C2×D5311yescharacteristic, complemented
1123#441—531no—
1124#440—531no—
1125#440—531no—
1126#440—531no—
1127C4×Q16—531no—
1128C4×Q16—531no—
1129C4×SD16—531no—
1130C4×D8—531no—
1131#436—531no—
1132#436—531no—
1133#436—531no—
1134#436—531no—
1135#435—531no—
1136#435—531no—
1137#435—531no—
1138#435—531no—
1139#433—531no—
1140#433—531no—
1141#419—531no—
1142#418—531no—
1143#418—531no—
1144#417—531no—
1145#417—531no—
1146#417C2×D5311yescharacteristic, complemented
1147#416—531no—
1148C2×#102C2×D5311yescharacteristic, complemented
1149#408—531no—
1150#408C2×D5311yescharacteristic, complemented
1151#407—531no—
1152#407—531no—
1153C53#6165411yescharacteristic, complemented, Sylow
1154H(5,𝔽2)—42no—
1155H(5,𝔽2)—42no—
1156C2×#41—21no—
1157C2×#41—531no—
1158C2×#41—531no—
1159C2×#41—531no—
1160C2×#41—531no—
1161C2×#41—1061no—
1162C2×#41—1061no—
1163C2×#41—2122no—
1164C2×#41—2122no—
1165C2×#41C22×D5311yescharacteristic
1166C2×#41C22×D5311yescharacteristic
1167C2×#41C22×D5311yescharacteristic
1168C2×#41C22×D5311yescharacteristic
1169C2×#41C22×D5311yescharacteristic
1170C22×Q8—531no—
1171C22×Q8—531no—
1172C22×Q8—531no—
1173C22×D4—21no—
1174C22×D4—21no—
1175C22×D4—21no—
1176C22×D4—531no—
1177C22×D4—1061no—
1178C22×D4—1061no—
1179C22×D4—1061no—
1180C22×D4—1061no—
1181C22×D4C22×D5311yescharacteristic
1182C22×D4C22×D5311yescharacteristic
1183C22×D4C22×D5311yescharacteristic
1184C23×C4—531no—
1185C23×C4—1061no—
1186#137—2122no—
1187#137—2122no—
1188#137—2122no—
1189#137—2122no—
1190AGL(1,ℤ/8)—42no—
1191AGL(1,ℤ/8)—2122no—
1192#135—42no—
1193C2×Q16—531no—
1194C2×Q16—531no—
1195C2×Q16—531no—
1196C2×Q16—531no—
1197C2×Q16—531no—
1198C2×Q16C22×D5311yescharacteristic
1199C2×SD16—531no—
1200C2×SD16—531no—
1201C2×SD16—531no—
1202C2×SD16—531no—
1203C2×SD16—531no—
1204C2×SD16—531no—
1205C2×SD16—531no—
1206C2×SD16—531no—
1207C2×SD16—531no—
1208C2×SD16—531no—
1209C2×SD16—2122no—
1210C2×SD16C22×D5311yescharacteristic
1211C2×SD16C22×D5311yescharacteristic
1212C2×SD16C22×D5311yescharacteristic
1213C2×SD16C22×D5311yescharacteristic
1214C2×D8—531no—
1215C2×D8C22×D5311yescharacteristic
1216C2×D8C22×D5311yescharacteristic
1217C2×D8C22×D5311yescharacteristic
1218C2×M16—531no—
1219C2×M16—531no—
1220C2×M16—531no—
1221C2×M16—531no—
1222C2×M16—531no—
1223C2×M16C22×D5311yescharacteristic
1224C22×C8—531no—
1225C22×C8C22×D5311yescharacteristic
1226C4⋊Q8—531no—
1227C4⋊Q8—531no—
1228C4⋊Q8—1061no—
1229C4⋊Q8—1061no—
1230#127—531no—
1231#127—531no—
1232#127—1061no—
1233#127—1061no—
1234#126—1061no—
1235#126—1061no—
1236#126—1061no—
1237#126—1061no—
1238#126—1061no—
1239#126—1061no—
1240#126—1061no—
1241#125—531no—
1242#125—1061no—
1243#125—1061no—
1244#125—1061no—
1245#125—1061no—
1246#124—531no—
1247#124—531no—
1248#124—531no—
1249#124—1061no—
1250#124—1061no—
1251#124—1061no—
1252#124—1061no—
1253#124—1061no—
1254#124—1061no—
1255#124—1061no—
1256#123—531no—
1257#123—531no—
1258#123—1061no—
1259#123—1061no—
1260#123—1061no—
1261#123—1061no—
1262#123—1061no—
1263#123—1061no—
1264#123—1061no—
1265#123—1061no—
1266#123—1061no—
1267#123—1061no—
1268C22⋊Q8—21no—
1269C22⋊Q8—531no—
1270C22⋊Q8—531no—
1271C22⋊Q8—531no—
1272C22⋊Q8—531no—
1273C22⋊Q8—531no—
1274C22⋊Q8—531no—
1275C22⋊Q8—531no—
1276C22⋊Q8—531no—
1277C22⋊Q8—531no—
1278C22⋊Q8—531no—
1279C22⋊Q8—531no—
1280C22⋊Q8—1061no—
1281C22⋊Q8—1061no—
1282C22⋊Q8—1061no—
1283C22⋊Q8—1061no—
1284C22⋊Q8—1061no—
1285C22⋊Q8—1061no—
1286C22⋊Q8—1061no—
1287C22⋊Q8—1061no—
1288C22⋊Q8—1061no—
1289C22⋊Q8—1061no—
1290C22⋊Q8—1061no—
1291C22⋊Q8—1061no—
1292C22⋊Q8C22×D5311yescharacteristic
1293C22⋊Q8C22×D5311yescharacteristic
1294#121—21no—
1295#121—21no—
1296#121—21no—
1297#121—531no—
1298#121—531no—
1299#121—531no—
1300#121—531no—
1301#121—531no—
1302#121—531no—
1303#121—531no—
1304#121—531no—
1305#121—531no—
1306#121—1061no—
1307#121—1061no—
1308#121—1061no—
1309#121—1061no—
1310#121—1061no—
1311#121—1061no—
1312#121—1061no—
1313#121—1061no—
1314#121—1061no—
1315#121—1061no—
1316#121—1061no—
1317#121—1061no—
1318#121—1061no—
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#121C22×D5311yescharacteristic
1328#121C22×D5311yescharacteristic
1329#120—531no—
1330#120—531no—
1331#120—1061no—
1332#120—1061no—
1333#120—1061no—
1334#120—1061no—
1335#120—1061no—
1336#120—1061no—
1337#120—1061no—
1338#120—1061no—
1339#120—1061no—
1340C4×Q8—531no—
1341C4×Q8—531no—
1342C4×Q8—531no—
1343C4×Q8—531no—
1344C4×Q8—531no—
1345C4×Q8—1061no—
1346C4×D4—531no—
1347C4×D4—531no—
1348C4×D4—531no—
1349C4×D4—531no—
1350C4×D4—531no—
1351C4×D4—531no—
1352C4×D4—531no—
1353C4×D4—1061no—
1354C4×D4—1061no—
1355C4×D4—1061no—
1356C4×D4—1061no—
1357C4×D4—1061no—
1358C4×D4—1061no—
1359C4×D4—1061no—
1360C4×D4—1061no—
1361C4×D4—1061no—
1362C4×D4—1061no—
1363C4×D4—1061no—
1364C4×D4—1061no—
1365C4×D4—1061no—
1366#117—531no—
1367#117—531no—
1368#117—531no—
1369#117—1061no—
1370#117—1061no—
1371C2×C4⋊C4—531no—
1372C2×C4⋊C4—531no—
1373C2×C4⋊C4—1061no—
1374C2×C4⋊C4—1061no—
1375C2×C4⋊C4—1061no—
1376C2×C4⋊C4C22×D5311yescharacteristic
1377C2×C22⋊C4—1061no—
1378C2×C22⋊C4—1061no—
1379C2×C22⋊C4—1061no—
1380C2×C22⋊C4—1061no—
1381#107—531no—
1382#107—531no—
1383#107—531no—
1384#107—531no—
1385#107—531no—
1386#107—531no—
1387#106—531no—
1388#106—531no—
1389C4⋊C8—531no—
1390C4⋊C8—531no—
1391C4⋊C8—531no—
1392C4⋊C8—531no—
1393#103—531no—
1394#103—531no—
1395#103—531no—
1396#103—531no—
1397#103—531no—
1398#103—531no—
1399#103—531no—
1400#103—531no—
1401#103—531no—
1402#103—531no—
1403#103—531no—
1404#103—531no—
1405#103C22×D5311yescharacteristic
1406#103C22×D5311yescharacteristic
1407#102—531no—
1408#102—531no—
1409#102—531no—
1410#102—531no—
1411#102—531no—
1412#102—531no—
1413#102—531no—
1414#102—531no—
1415#102—531no—
1416#102—531no—
1417#102—531no—
1418#102—531no—
1419#102C22×D5311yescharacteristic
1420#102C22×D5311yescharacteristic
1421#102C22×D5311yescharacteristic
1422#102C22×D5311yescharacteristic
1423#102C22×D5311yescharacteristic
1424#102C22×D5311yescharacteristic
1425C22⋊C8—531no—
1426C22⋊C8—531no—
1427C22⋊C8—531no—
1428C22⋊C8—531no—
1429C22⋊C8—531no—
1430C22⋊C8—531no—
1431C22⋊C8—531no—
1432C22⋊C8—531no—
1433C22⋊C8C22×D5311yescharacteristic
1434C22⋊C8C22×D5311yescharacteristic
1435C22⋊C8C22×D5311yescharacteristic
1436C22⋊C8C22×D5311yescharacteristic
1437#97—531no—
1438#97—531no—
1439C4×C8—531no—
1440C4×C8—531no—
1441C24—21no—
1442C24—21no—
1443C24—21no—
1444C24—531no—
1445C24—1061no—
1446#41—22no—
1447#41—22no—
1448#41—22no—
1449#41—22no—
1450#41—41no—
1451#41—41no—
1452#41—41no—
1453#41—41no—
1454#41—44no—
1455#41—41no—
1456#41—41no—
1457#41—1062no—
1458#41—1062no—
1459#41—2121no—
1460#41—2121no—
1461#41—2124no—
1462#41—2121no—
1463#41—2121no—
1464#41—2121no—
1465#41—2121no—
1466#41—2124no—
1467C2×Q8—531no—
1468C2×Q8—531no—
1469C2×Q8—531no—
1470C2×Q8—1061no—
1471C2×Q8—1061no—
1472C2×Q8—1061no—
1473C2×Q8—1061no—
1474C2×Q8—1062no—
1475C2×Q8—2121no—
1476C2×Q8—2121no—
1477C2×Q8—2121no—
1478C2×Q8—2121no—
1479C2×Q8—2121no—
1480C2×Q8D4×D5311yescharacteristic
1481C2×Q8C23×D5311yescharacteristic
1482C2×Q8C23×D5311yescharacteristic
1483C2×D4—21no—
1484C2×D4—22no—
1485C2×D4—22no—
1486C2×D4—21no—
1487C2×D4—21no—
1488C2×D4—21no—
1489C2×D4—21no—
1490C2×D4—21no—
1491C2×D4—21no—
1492C2×D4—21no—
1493C2×D4—21no—
1494C2×D4—41no—
1495C2×D4—41no—
1496C2×D4—41no—
1497C2×D4—41no—
1498C2×D4—44no—
1499C2×D4—44no—
1500C2×D4—44no—
1501C2×D4—531no—
1502C2×D4—531no—
1503C2×D4—531no—
1504C2×D4—531no—
1505C2×D4—531no—
1506C2×D4—1061no—
1507C2×D4—1061no—
1508C2×D4—1061no—
1509C2×D4—1061no—
1510C2×D4—1061no—
1511C2×D4—1061no—
1512C2×D4—1062no—
1513C2×D4—1061no—
1514C2×D4—1061no—
1515C2×D4—1061no—
1516C2×D4—1061no—
1517C2×D4—1061no—
1518C2×D4—1061no—
1519C2×D4—1061no—
1520C2×D4—1061no—
1521C2×D4—1061no—
1522C2×D4—1061no—
1523C2×D4—4242no—
1524C2×D4—4242no—
1525C2×D4—4242no—
1526C2×D4—2121no—
1527C2×D4—2124no—
1528C2×D4D4×D5311yescharacteristic
1529C2×D4D4×D5311yescharacteristic
1530C2×D4D4×D5311yescharacteristic
1531C2×D4C23×D5311yescharacteristic
1532C2×D4C23×D5311yescharacteristic
1533C2×D4C23×D5311yescharacteristic
1534C2×D4C23×D5311yescharacteristic
1535C22×C4—21no—
1536C22×C4—21no—
1537C22×C4—21no—
1538C22×C4—21no—
1539C22×C4—21no—
1540C22×C4—531no—
1541C22×C4—531no—
1542C22×C4—531no—
1543C22×C4—531no—
1544C22×C4—531no—
1545C22×C4—1061no—
1546C22×C4—1061no—
1547C22×C4—1061no—
1548C22×C4—1061no—
1549C22×C4—1061no—
1550C22×C4—1061no—
1551C22×C4—1061no—
1552C22×C4—1061no—
1553C22×C4—1061no—
1554C22×C4—1061no—
1555C22×C4—1061no—
1556C22×C4—1061no—
1557C22×C4—2121no—
1558C22×C4—2121no—
1559C22×C4—2124no—
1560C22×C4C23×D5311yescharacteristic
1561C22×C4C23×D5311yescharacteristic
1562C22×C4C23×D5311yescharacteristic
1563Q16—22no—
1564Q16—1062no—
1565Q16—1062no—
1566Q16—2121no—
1567Q16—2121no—
1568Q16—2121no—
1569SD16—22no—
1570SD16—22no—
1571SD16—41no—
1572SD16—41no—
1573SD16—1062no—
1574SD16—1062no—
1575SD16—2121no—
1576SD16—2121no—
1577SD16—2121no—
1578SD16—2121no—
1579SD16—2121no—
1580SD16—2121no—
1581SD16—2121no—
1582SD16—2121no—
1583D8—22no—
1584D8—41no—
1585D8—41no—
1586D8—2121no—
1587M16—41no—
1588M16—2121no—
1589M16—2121no—
1590M16—2121no—
1591M16—2121no—
1592M16—2121no—
1593C2×C8—41no—
1594C2×C8—531no—
1595C2×C8—531no—
1596C2×C8—531no—
1597C2×C8—531no—
1598C2×C8—2121no—
1599C2×C8C23×D5311yescharacteristic
1600C2×C8C23×D5311yescharacteristic
1601C2×C8C23×D5311yescharacteristic
1602C2×C8C23×D5311yescharacteristic
1603C4⋊C4—21no—
1604C4⋊C4—21no—
1605C4⋊C4—21no—
1606C4⋊C4—531no—
1607C4⋊C4—531no—
1608C4⋊C4—531no—
1609C4⋊C4—531no—
1610C4⋊C4—531no—
1611C4⋊C4—531no—
1612C4⋊C4—531no—
1613C4⋊C4—531no—
1614C4⋊C4—531no—
1615C4⋊C4—531no—
1616C4⋊C4—1061no—
1617C4⋊C4—1061no—
1618C4⋊C4—1061no—
1619C4⋊C4—1061no—
1620C4⋊C4—1061no—
1621C4⋊C4—1061no—
1622C4⋊C4—1061no—
1623C4⋊C4—1061no—
1624C4⋊C4—1061no—
1625C4⋊C4—1061no—
1626C4⋊C4—1061no—
1627C4⋊C4—1061no—
1628C4⋊C4—1061no—
1629C4⋊C4—1061no—
1630C4⋊C4—1061no—
1631C4⋊C4—1061no—
1632C4⋊C4—1061no—
1633C4⋊C4—1061no—
1634C4⋊C4—1061no—
1635C4⋊C4—1061no—
1636C4⋊C4—1061no—
1637C4⋊C4C23×D5311yescharacteristic
1638C4⋊C4C23×D5311yescharacteristic
1639C22⋊C4—21no—
1640C22⋊C4—21no—
1641C22⋊C4—21no—
1642C22⋊C4—21no—
1643C22⋊C4—531no—
1644C22⋊C4—531no—
1645C22⋊C4—531no—
1646C22⋊C4—531no—
1647C22⋊C4—531no—
1648C22⋊C4—531no—
1649C22⋊C4—531no—
1650C22⋊C4—531no—
1651C22⋊C4—531no—
1652C22⋊C4—531no—
1653C22⋊C4—1061no—
1654C22⋊C4—1061no—
1655C22⋊C4—1061no—
1656C22⋊C4—1061no—
1657C22⋊C4—1061no—
1658C22⋊C4—1061no—
1659C22⋊C4—1061no—
1660C22⋊C4—1061no—
1661C22⋊C4—1061no—
1662C22⋊C4—1061no—
1663C22⋊C4—1061no—
1664C22⋊C4—1061no—
1665C22⋊C4—1061no—
1666C22⋊C4—1061no—
1667C22⋊C4—1061no—
1668C22⋊C4—1061no—
1669C22⋊C4—1061no—
1670C22⋊C4—1061no—
1671C22⋊C4—1061no—
1672C22⋊C4—1061no—
1673C22⋊C4—1061no—
1674C22⋊C4—1061no—
1675C22⋊C4—1061no—
1676C22⋊C4—1061no—
1677C22⋊C4—1061no—
1678C22⋊C4—1061no—
1679C22⋊C4—1061no—
1680C42—531no—
1681C42—531no—
1682C42—1061no—
1683C42—1061no—
1684C42—1061no—
1685C42—1061no—
1686C42—1061no—
1687C42—1061no—
1688C42—1061no—
1689C23—21no—
1690C23—21no—
1691C23—21no—
1692C23—21no—
1693C23—42no—
1694C23—42no—
1695C23—42no—
1696C23—81no—
1697C23—81no—
1698C23—81no—
1699C23—81no—
1700C23—81no—
1701C23—81no—
1702C23—531no—
1703C23—531no—
1704C23—1061no—
1705C23—4241no—
1706C23—2121no—
1707C23—2121no—
1708C23—2121no—
1709C23—2122no—
1710C23—2122no—
1711C23C2×D4×D5311yescharacteristic
1712C23C2×D4×D5311yescharacteristic
1713C23C2×D4×D5311yescharacteristic
1714Q8—21no—
1715Q8—21no—
1716Q8—21no—
1717Q8—41no—
1718Q8—1061no—
1719Q8—1061no—
1720Q8—1061no—
1721Q8—1061no—
1722Q8—1061no—
1723Q8—1061no—
1724Q8—4241no—
1725Q8—4241no—
1726Q8—4241no—
1727Q8—2122no—
1728Q8#1313326212yes—
1729D4—24no—
1730D4—21no—
1731D4—21no—
1732D4—21no—
1733D4—21no—
1734D4—21no—
1735D4—21no—
1736D4—21no—
1737D4—41no—
1738D4—41no—
1739D4—41no—
1740D4—42no—
1741D4—42no—
1742D4—42no—
1743D4—42no—
1744D4—42no—
1745D4—81no—
1746D4—81no—
1747D4—81no—
1748D4—1061no—
1749D4—1061no—
1750D4—4241no—
1751D4—4241no—
1752D4—4241no—
1753D4—4241no—
1754D4—4241no—
1755D4—4241no—
1756D4—4241no—
1757D4—4241no—
1758D4—4241no—
1759D4—2122no—
1760D4—2121no—
1761D4—2121no—
1762D4—2121no—
1763D4—2121no—
1764D4—2122no—
1765D4—2122no—
1766D4—2122no—
1767D4—2122no—
1768D4—2122no—
1769D4—2122no—
1770D4#1313326212yes—
1771C2×C4—24no—
1772C2×C4—21no—
1773C2×C4—21no—
1774C2×C4—21no—
1775C2×C4—21no—
1776C2×C4—21no—
1777C2×C4—21no—
1778C2×C4—21no—
1779C2×C4—21no—
1780C2×C4—21no—
1781C2×C4—21no—
1782C2×C4—42no—
1783C2×C4—42no—
1784C2×C4—81no—
1785C2×C4—81no—
1786C2×C4—531no—
1787C2×C4—531no—
1788C2×C4—531no—
1789C2×C4—531no—
1790C2×C4—531no—
1791C2×C4—531no—
1792C2×C4—1061no—
1793C2×C4—1061no—
1794C2×C4—1061no—
1795C2×C4—1061no—
1796C2×C4—1061no—
1797C2×C4—1061no—
1798C2×C4—1061no—
1799C2×C4—1061no—
1800C2×C4—1061no—
1801C2×C4—1061no—
1802C2×C4—1061no—
1803C2×C4—4241no—
1804C2×C4—4241no—
1805C2×C4—4241no—
1806C2×C4—4241no—
1807C2×C4—4241no—
1808C2×C4—4241no—
1809C2×C4—4241no—
1810C2×C4—4241no—
1811C2×C4—2121no—
1812C2×C4—2121no—
1813C2×C4—2122no—
1814C2×C4—2122no—
1815C2×C4—2122no—
1816C2×C4—2121no—
1817C2×C4—2122no—
1818C2×C4C2×D4×D5311yescharacteristic
1819C2×C4C2×D4×D5311yescharacteristic
1820C2×C4C2×D4×D5311yescharacteristic
1821C2×C4C24×D5311yescharacteristic
1822C8—21no—
1823C8—21no—
1824C8—21no—
1825C8—21no—
1826C8—1061no—
1827C8—1061no—
1828C8—1061no—
1829C8—1061no—
1830C22—21no—
1831C22—21no—
1832C22—22no—
1833C22—21no—
1834C22—21no—
1835C22—21no—
1836C22—21no—
1837C22—21no—
1838C22—21no—
1839C22—21no—
1840C22—41no—
1841C22—41no—
1842C22—41no—
1843C22—41no—
1844C22—41no—
1845C22—41no—
1846C22—41no—
1847C22—41no—
1848C22—41no—
1849C22—41no—
1850C22—41no—
1851C22—162no—
1852C22—162no—
1853C22—162no—
1854C22—1061no—
1855C22—1061no—
1856C22—1061no—
1857C22—1061no—
1858C22—1061no—
1859C22—1061no—
1860C22—4244no—
1861C22—4242no—
1862C22—2121no—
1863C22—2121no—
1864C22—2121no—
1865C22C22×D4×D5311yescharacteristic
1866C4—21no—
1867C4—22no—
1868C4—21no—
1869C4—21no—
1870C4—41no—
1871C4—41no—
1872C4—41no—
1873C4—1061no—
1874C4—1061no—
1875C4—1061no—
1876C4—1061no—
1877C4—1061no—
1878C4—1061no—
1879C4—2121no—
1880C4—2121no—
1881C4—2121no—
1882C4—2121no—
1883C4—2121no—
1884C4—2121no—
1885C4—2121no—
1886C4C2×#1313326211yescharacteristic
1887C4C2×#1313326211yescharacteristic
1888C2—41no—
1889C2—41no—
1890C2—41no—
1891C2—42no—
1892C2—81no—
1893C2—81no—
1894C2—81no—
1895C2—4241no—
1896C2—2121no—
1897C2—2121no—
1898C2#2028834411yescharacteristic
1899C2#2028949011yescharacteristic
1900C2#2028949711yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3012C2
socleC22×C53C23×D4
hypercenter#3012D53
hypocenterC53#61654
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×#41 ◁ #3012

Complements

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

NH ≅ G/Ntype
1. #20288996C2semidirect
2. #20288377C2semidirect
3. #20287049C2semidirect
4. #20286984C2semidirect
5. #20286939C2semidirect
6. #20286920C2semidirect
7. #20286792C2semidirect
8. #20286785C2semidirect
9. #20286732C2semidirect
10. #20286725C2semidirect
11. #20286374C2semidirect
12. #20286365C2semidirect
13. #20286346C2semidirect
14. #20286309C2semidirect
15. #20286300C2semidirect
16. #20286270C2semidirect
17. #20286229C2semidirect
18. #20286214C2semidirect
19. #20285805C2semidirect
20. #20285783C2semidirect
21. #20285612C2semidirect
22. #20285599C2semidirect
23. #20285526C2semidirect
24. #20285518C2semidirect
25. #20284970C2semidirect
26. #20284922C2semidirect
27. #20283992C2semidirect
28. #20283972C2semidirect
29. #20283953C2semidirect
30. #20283773C2semidirect
31. C53×#3012C2semidirect
33. C2×#13133249C22semidirect
34. C2×#13133247C22semidirect
35. C2×#13133246C22semidirect
36. C2×#13133246C22semidirect
37. C2×#13133241C22semidirect
38. C22×#11719923C22semidirect
41. #16811344C22semidirect
42. #16811328C22semidirect
45. #16811320C22semidirect
46. #16811308C22semidirect
49. #16811286C22semidirect
52. #16811280C22semidirect
53. #16811279C22semidirect
54. #16811272C22semidirect
64. #16811240C22semidirect
65. #16811233C22semidirect
71. #16811194C22semidirect
74. #16811133C22semidirect
77. C22⋊Q8×D53C22semidirect
81. #16811014C22semidirect
82. #16811011C22semidirect
83. #16811006C22semidirect
84. #16810994C22semidirect
85. #16810986C22semidirect
86. #16810981C22semidirect
87. #16810976C22semidirect
88. #16810968C22semidirect
89. #16810965C22semidirect
90. #16810959C22semidirect
91. #16810958C22semidirect
92. #16810956C22semidirect
93. #16810954C22semidirect
94. #16810948C22semidirect
95. #16810946C22semidirect
96. #16810946C22semidirect
97. #16810936C22semidirect
98. #16810935C22semidirect
99. #16810935C22semidirect
100. #16810934C22semidirect
101. #16810928C22semidirect
102. #16810925C22semidirect
103. #16810916C22semidirect
104. #16810901C22semidirect
105. #16810881C22semidirect
106. #16810873C22semidirect
107. #16810873C22semidirect
108. #16810871C22semidirect
109. #16810869C22semidirect
110. #16810868C22semidirect
111. #16810868C22semidirect
112. #16810868C22semidirect
113. #16810868C22semidirect
114. #16810867C22semidirect
115. #16810866C22semidirect
116. #16810866C22semidirect
117. #16810864C22semidirect
118. #16810862C22semidirect
119. #16810857C22semidirect
120. #16810852C22semidirect
121. #16810844C22semidirect
122. #16810844C22semidirect
123. #16810843C22semidirect
124. #16810843C22semidirect
125. #16810836C22semidirect
126. #16810836C22semidirect
127. #16810831C22semidirect
128. #16810826C22semidirect
129. #16810822C22semidirect
130. #16810822C22semidirect
131. #16810821C22semidirect
132. #16810816C22semidirect
133. #16810788C22semidirect
134. #16810787C22semidirect
135. #16810787C22semidirect
136. #16810786C22semidirect
139. #16810785C22semidirect
140. #16810785C22semidirect
141. #16810785C22semidirect
142. #16810783C22semidirect
143. #16810781C22semidirect
144. #16810780C22semidirect
145. #16810777C22semidirect
146. #16810775C22semidirect
147. #16810774C22semidirect
148. #16810774C22semidirect
149. #16810774C22semidirect
150. #16810774C22semidirect
151. #16810772C22semidirect
152. #16810768C22semidirect
153. #16810767C22semidirect
154. #16810766C22semidirect
155. #16810765C22semidirect
156. #16810765C22semidirect
157. #16810765C22semidirect
158. #16810764C22semidirect
159. #16810760C22semidirect
160. #16810760C22semidirect
161. #16810730C22semidirect
162. #16810724C22semidirect
163. #16810720C22semidirect
164. #16810720C22semidirect
165. #16810715C22semidirect
166. #16810715C22semidirect
167. SD16×Dic53C22semidirect
168. D8×Dic53C22semidirect
169. #16810699C22semidirect
170. #16810699C22semidirect
171. #16810698C22semidirect
172. #16810698C22semidirect
173. #16810694C22semidirect
174. #16810694C22semidirect
175. #16810691C22semidirect
176. #16810691C22semidirect
177. #16810681C22semidirect
178. #16810681C22semidirect
179. #16810630C22semidirect
180. #16810628C22semidirect
181. #16810626C22semidirect
182. #16810623C22semidirect
183. #16810621C22semidirect
184. #16810619C22semidirect
185. #16810590C22semidirect
186. #16810585C22semidirect
187. #16810585C22semidirect
189. C2×AGL(1,ℤ/8)×C53C22semidirect
190. C2×#135×C53C22semidirect
191. C53×#537C22semidirect
193. C53×#452C22semidirect
194. C53×#450C22semidirect
195. C53×#450C22semidirect
197. C53×#449C22semidirect
198. C53×#447C22semidirect
199. C53×#447C22semidirect
200. C53×#417C22semidirect
201. C2×#102×C53C22semidirect
202. C53×#408C22semidirect
964. #3012D53semidirect
989. C2×AGL(1,ℤ/8)C2×D53semidirect
990. C2×#135C2×D53semidirect
1024. #537C2×D53semidirect
1098. #452C2×D53semidirect
1108. #450C2×D53semidirect
1109. #450C2×D53semidirect
1117. #449C2×D53semidirect
1121. #447C2×D53semidirect
1122. #447C2×D53semidirect
1146. #417C2×D53semidirect
1148. C2×#102C2×D53semidirect
1150. #408C2×D53semidirect
1153. C53#61654semidirect

Maximal subgroups

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

subgroupindex
#202889962
#202883772
#202870492
#202869842
#202869392
#202869202
#202867922
#202867852
#202867322
#202867252
#202863742
#202863652
#202863462
#202863092
#202863002
#202862702
#202862292
#202862142
#202858052
#202857832
#202856122
#202855992
#202855262
#202855182
#202849702
#202849222
#202839922
#202839722
#202839532
#202837732
C53×#30122
#6165453