Finite Group Databasebeta

← #28270338

Subgroups — #28270338

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#20289021C211yesmaximal, characteristic, complemented
2#20288383C211yesmaximal, characteristic, complemented
3#20286877C211yesmaximal, characteristic, complemented
4#20286743C211yesmaximal, characteristic, complemented
5#20286721C211yesmaximal, characteristic, complemented
6#20286699C211yesmaximal, characteristic, complemented
7#20286658C211yesmaximal, characteristic, complemented
8#20286607C211yesmaximal, characteristic, complemented
9#20286567C211yesmaximal, characteristic, complemented
10#20286523C211yesmaximal, characteristic, complemented
11#20286416C211yesmaximal, characteristic, complemented
12#20286398C211yesmaximal, characteristic, complemented
13#20286390C211yesmaximal, characteristic, complemented
14#20286256C211yesmaximal, characteristic, complemented
15#20286255C211yesmaximal, characteristic, complemented
16#20286205C211yesmaximal, characteristic, complemented
17#20286198C211yesmaximal, characteristic, complemented
18#20285814C211yesmaximal, characteristic, complemented
19#20285758C211yesmaximal, characteristic, complemented
20#20285614C211yesmaximal, characteristic, complemented
21#20285560C211yesmaximal, characteristic, complemented
22#20285478C211yesmaximal, characteristic, complemented
23#20285462C211yesmaximal, characteristic, complemented
24#20284983C211yesmaximal, characteristic, complemented
25#20284913C211yesmaximal, characteristic, complemented
26#20284015C211yesmaximal, characteristic, complemented
27#20283980C211yesmaximal, characteristic, complemented
28#20283929C211yesmaximal, characteristic, complemented
29#449×D53C211yesmaximal, characteristic, complemented
30#20283768C211yesmaximal, characteristic, complemented
31C53×#3287C211yesmaximal, characteristic, complemented
32C2×#13133263C2211yescharacteristic, complemented
33C2×#41×D53C2211yescharacteristic, complemented
34C2×#13133244C2211yescharacteristic, complemented
35C2×#13133242C2211yescharacteristic, complemented
36C2×#13133237C2211yescharacteristic, complemented
37C2×SD16×D53C2211yescharacteristic, complemented
38C2×D8×D53C2211yescharacteristic, complemented
39C2×D8×D53C2211yescharacteristic, complemented
40#16811368—21no—
41#16811360—21no—
42#16811337C2211yescharacteristic, complemented
43#16811319C2211yescharacteristic, complemented
44#16811314C2211yescharacteristic, complemented
45#16811302—21no—
46#16811292C2211yescharacteristic, complemented
47#16811285C2211yescharacteristic
48#16811280C2211yescharacteristic, complemented
49#16811273C2211yescharacteristic, complemented
50#16811270—21no—
51#16811270C2211yescharacteristic, complemented
52#16811269—21no—
53#16811269C2211yescharacteristic, complemented
54#16811262—21no—
55#16811261C2211yescharacteristic, complemented
56#16811261C2211yescharacteristic, complemented
57#16811258—21no—
58#16811258C2211yescharacteristic
59#16811258C2211yescharacteristic, complemented
60#16811257—21no—
61#16811257C2211yescharacteristic, complemented
62#16811245C2211yescharacteristic, complemented
63#16811227C2211yescharacteristic, complemented
64#16811223—21no—
65#16811206—21no—
66#16811202—21no—
67#16811202C2211yescharacteristic, complemented
68#16811201C2211yescharacteristic, complemented
69#16811189C2211yescharacteristic, complemented
70#16811186—21no—
71#16811186—21no—
72#16811186C2211yescharacteristic, complemented
73#16811181—21no—
74#16811132—21no—
75#16811132C2211yescharacteristic
76#16811130C2211yescharacteristic, complemented
77#121×D53—21no—
78#121×D53C2211yescharacteristic, complemented
79#121×D53C2211yescharacteristic, complemented
80#16811105C2211yescharacteristic, complemented
81#16811010C2211yescharacteristic, complemented
82#16811009C2211yescharacteristic, complemented
83#16811004C2211yescharacteristic, complemented
84#16810987C2211yescharacteristic, complemented
85#16810981C2211yescharacteristic, complemented
86#16810978C2211yescharacteristic, complemented
87#16810968C2211yescharacteristic, complemented
88#16810966C2211yescharacteristic, complemented
89#16810959C2211yescharacteristic, complemented
90#16810957C2211yescharacteristic, complemented
91#16810948C2211yescharacteristic, complemented
92#16810946C2211yescharacteristic, complemented
93#16810944C2211yescharacteristic, complemented
94#16810940C2211yescharacteristic, complemented
95#16810938C2211yescharacteristic, complemented
96#16810938C2211yescharacteristic, complemented
97#16810935C2211yescharacteristic, complemented
98#16810935C2211yescharacteristic, complemented
99#16810934C2211yescharacteristic, complemented
100#16810930C2211yescharacteristic, complemented
101#16810924C2211yescharacteristic, complemented
102#16810916C2211yescharacteristic, complemented
103#16810902C2211yescharacteristic, complemented
104#16810874C2211yescharacteristic, complemented
105#16810868C2211yescharacteristic, complemented
106#16810867C2211yescharacteristic, complemented
107#16810866C2211yescharacteristic, complemented
108#16810863C2211yescharacteristic, complemented
109#16810859C2211yescharacteristic, complemented
110#16810858C2211yescharacteristic, complemented
111#16810857C2211yescharacteristic, complemented
112#16810857C2211yescharacteristic, complemented
113#16810856C2211yescharacteristic, complemented
114#16810856C2211yescharacteristic, complemented
115#16810855C2211yescharacteristic, complemented
116#16810852C2211yescharacteristic, complemented
117#16810849C2211yescharacteristic, complemented
118#16810847C2211yescharacteristic, complemented
119#16810845C2211yescharacteristic, complemented
120#16810841C2211yescharacteristic, complemented
121#16810839C2211yescharacteristic, complemented
122#16810836C2211yescharacteristic, complemented
123#16810836C2211yescharacteristic, complemented
124#16810816C2211yescharacteristic, complemented
125#16810816C2211yescharacteristic, complemented
126#16810815C2211yescharacteristic, complemented
127#16810815C2211yescharacteristic, complemented
128#16810785C2211yescharacteristic, complemented
129#16810784C2211yescharacteristic, complemented
130#16810784C2211yescharacteristic, complemented
131#16810782C2211yescharacteristic, complemented
132#16810777C2211yescharacteristic, complemented
133#16810775C2211yescharacteristic, complemented
134#16810772C2211yescharacteristic, complemented
135#16810772C2211yescharacteristic, complemented
136#16810772C2211yescharacteristic, complemented
137#16810771C2211yescharacteristic
138#16810770C2211yescharacteristic, complemented
139#16810769C2211yescharacteristic, complemented
140#16810768C2211yescharacteristic, complemented
141#16810768C2211yescharacteristic, complemented
142#16810768C2211yescharacteristic, complemented
143#16810767C2211yescharacteristic, complemented
144#16810767C2211yescharacteristic, complemented
145#16810767C2211yescharacteristic, complemented
146#16810766C2211yescharacteristic, complemented
147#16810765C2211yescharacteristic, complemented
148#16810765C2211yescharacteristic, complemented
149#16810760C2211yescharacteristic, complemented
150#16810759C2211yescharacteristic, complemented
151#16810758C2211yescharacteristic, complemented
152#16810758C2211yescharacteristic, complemented
153#16810756C2211yescharacteristic, complemented
154#16810755C2211yescharacteristic, complemented
155#16810755C2211yescharacteristic, complemented
156#16810755C2211yescharacteristic, complemented
157#16810755C2211yescharacteristic, complemented
158#16810755C2211yescharacteristic, complemented
159#16810755C2211yescharacteristic, complemented
160#16810732C2211yescharacteristic, complemented
161#16810724C2211yescharacteristic, complemented
162#16810721C2211yescharacteristic, complemented
163#16810721C2211yescharacteristic, complemented
164SD16×Dic53C2211yescharacteristic, complemented
165C4×D424C2211yescharacteristic, complemented
166#16810703C2211yescharacteristic, complemented
167#16810697C2211yescharacteristic, complemented
168#16810695C2211yescharacteristic, complemented
169#16810694C2211yescharacteristic, complemented
170#16810693C2211yescharacteristic, complemented
171C8×D212C2211yescharacteristic, complemented
172C8×C22⋊D53C2211yescharacteristic, complemented
173#16810686C2211yescharacteristic, complemented
174#16810683C2211yescharacteristic, complemented
175#16810682C2211yescharacteristic, complemented
176#16810626C2211yescharacteristic, complemented
177#16810624C2211yescharacteristic, complemented
178#16810620C2211yescharacteristic, complemented
179#16810619C2211yescharacteristic, complemented
180#16810618C2211yescharacteristic, complemented
181#103×D53C2211yescharacteristic, complemented
182C2×#13133139C2211yescharacteristic, complemented
183#102×D53C2211yescharacteristic, complemented
184#16810589C2211yescharacteristic, complemented
185#16810588C2211yescharacteristic, complemented
186C2×#13133129C2211yescharacteristic, complemented
187C22⋊C8×D53C2211yescharacteristic, complemented
188C2×#135×C53C2211yescharacteristic, complemented
189C2×#135×C53C2211yescharacteristic, complemented
190C53×#550C2211yescharacteristic, complemented
191C53×#550C2211yescharacteristic, complemented
192C53×#493C2211yescharacteristic, complemented
193C53×#466C2211yescharacteristic, complemented
194C53×#466C2211yescharacteristic, complemented
195C53×#460C2211yescharacteristic, complemented
196C53×#460C2211yescharacteristic, complemented
197C53×#449C2211yescharacteristic, complemented
198C53×#449C2211yescharacteristic, complemented
199C53×#449C2211yescharacteristic, complemented
200C53×#449C2211yescharacteristic, complemented
201C4×Q16×C53C2211yescharacteristic, complemented
202C8×D4×C53C2211yescharacteristic, complemented
203#13133263—42no—
204#13133263—42no—
205C2×#11719949C2311yescharacteristic
206C2×#11719949C2311yescharacteristic
207C2×#11719945—21no—
208C2×#11719945—21no—
209C2×#11719945C2311yescharacteristic
210C2×#11719945C2311yescharacteristic
211C2×#11719947—21no—
212C2×#11719947—21no—
213C2×#11719947C2311yescharacteristic
214#41×D53—42no—
215#41×D53—42no—
216C2×Q8×D53C2311yescharacteristic
217C22×D212—21no—
218C22×D212C2311yescharacteristic
219C2×D4×D53—21no—
220C2×D4×D53—21no—
221C2×D4×D53—21no—
222C2×D4×D53—21no—
223C2×D4×D53—21no—
224C2×D4×D53—21no—
225C2×D4×D53—21no—
226C2×D4×D53—21no—
227C2×D4×D53C2311yescharacteristic
228C2×D4×D53C2311yescharacteristic
229C2×D4×D53C2311yescharacteristic
230C2×D4×D53C2311yescharacteristic
231C2×D4×D53C2311yescharacteristic
232C22×C4×D53—21no—
233C22×C4×D53C2311yescharacteristic
234#13133244—42no—
235#13133242—42no—
236#13133237—42no—
237C2×#11719925C2311yescharacteristic
238C2×#11719913C2311yescharacteristic
239C2×#11719923C2311yescharacteristic
240C2×#11719923C2311yescharacteristic
241C2×#11719924C2311yescharacteristic
242C2×#11719924C2311yescharacteristic
243C2×#11719924C2311yescharacteristic
244SD16×D53—42no—
245C2×D424C2311yescharacteristic
246C2×D424C2311yescharacteristic
247C2×#11719922C2311yescharacteristic
248C2×#11719922C2311yescharacteristic
249C2×#11719922C2311yescharacteristic
250C2×#11719922C2311yescharacteristic
251C2×#11719922C2311yescharacteristic
252C2×#11719922C2311yescharacteristic
253D8×D53—42no—
254D8×D53—42no—
255C2×#11719917C2311yescharacteristic
256C2×#11719912C2311yescharacteristic
257C22×#88322C2311yescharacteristic
258C2×C8×D53C2311yescharacteristic
259C2×C8×D53C2311yescharacteristic
260C2×C8×D53C2311yescharacteristic
261#13133216C2311yescharacteristic
262#13133213—21no—
263#13133213—21no—
264#13133213C2311yescharacteristic
265#13133212—21no—
266#13133211—21no—
267#13133211—21no—
268#13133209C2311yescharacteristic
269#13133207—21no—
270#13133206C2311yescharacteristic
271#13133205—21no—
272#13133205—21no—
273#13133205C2311yescharacteristic
274#13133204—21no—
275#13133204—21no—
276#13133204C2311yescharacteristic
277#13133203—21no—
278#13133203—21no—
279#13133202—21no—
280#13133202—21no—
281#13133202—21no—
282#13133202D411yescharacteristic
283#13133200—21no—
284#13133200—21no—
285#13133199—21no—
286#13133199—21no—
287#13133199—21no—
288#13133199D411yescharacteristic
289#13133198—21no—
290#13133198—21no—
291#13133198—21no—
292#13133198—21no—
293#13133197—21no—
294#13133197C2311yescharacteristic
295#13133196—21no—
296#13133196—21no—
297#13133196C2311yescharacteristic
298#13133195—21no—
299#13133195D411yescharacteristic
300#13133194—21no—
301#13133194—21no—
302#13133194D411yescharacteristic
303#13133193C2311yescharacteristic
304#13133193C2311yescharacteristic
305#13133193C2311yescharacteristic
306#13133192—21no—
307#13133192C2311yescharacteristic
308#13133192C2311yescharacteristic
309#13133191—21no—
310#13133191—21no—
311#13133191C2311yescharacteristic
312#13133191C2311yescharacteristic
313#13133191C2311yescharacteristic
314#13133190—21no—
315#13133190—21no—
316#13133190—21no—
317#13133190—21no—
318#13133190—21no—
319#13133190D411yescharacteristic
320#13133189—21no—
321#13133189—21no—
322#13133189—21no—
323#13133189—21no—
324#13133189—21no—
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#13133189D411yescharacteristic
334#13133188—21no—
335#13133188—21no—
336#13133188—21no—
337#13133188—21no—
338#13133188—21no—
339#13133188—21no—
340#13133188C2311yescharacteristic
341#13133188C2311yescharacteristic
342#13133188C2311yescharacteristic
343#13133188C2311yescharacteristic
344#13133188C2311yescharacteristic
345#13133188C2311yescharacteristic
346#13133187—21no—
347#13133187—21no—
348#13133187D411yescharacteristic
349#13133185—21no—
350#13133185—21no—
351#13133185—21no—
352#13133185—21no—
353#13133185—21no—
354#13133185—21no—
355#13133185—21no—
356#13133185—21no—
357#13133185—21no—
358#13133185—21no—
359#13133185—21no—
360#13133185—21no—
361#13133185—21no—
362#13133185D411yescharacteristic
363Q8×Dic53C2311yescharacteristic
364C4×D212—21no—
365C4×D212—21no—
366C4×D212C2311yescharacteristic
367C4×D212C2311yescharacteristic
368C4×D212C2311yescharacteristic
369D4×Dic53C2311yescharacteristic
370D4×Dic53C2311yescharacteristic
371#13133179—21no—
372#13133179C2311yescharacteristic
373C4×C22⋊D53—21no—
374C4×C22⋊D53—21no—
375C4×C22⋊D53—21no—
376C4×C22⋊D53—21no—
377C4×C22⋊D53C2311yescharacteristic
378C4×C22⋊D53C2311yescharacteristic
379#13133177—21no—
380#13133176C2311yescharacteristic
381#13133175C2311yescharacteristic
382#13133174—21no—
383#13133174—21no—
384#13133174C2311yescharacteristic
385#13133173—21no—
386C2×C4⋊Dic53C2311yescharacteristic
387C4⋊C4×D53—21no—
388C4⋊C4×D53C2311yescharacteristic
389C4⋊C4×D53C2311yescharacteristic
390C2×#11719921—21no—
391C2×#11719921—21no—
392C22⋊C4×D53—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#13133142C2311yescharacteristic
408#13133142C2311yescharacteristic
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#13133138C2311yescharacteristic
422#13133138C2311yescharacteristic
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#13133128C2311yescharacteristic
443#13133127C2311yescharacteristic
444C8×Dic53C2311yescharacteristic
445C2×#41×C53C2311yescharacteristic
446C2×#41×C53C2311yescharacteristic
447C2×#41×C53C2311yescharacteristic
448C2×#41×C53C2311yescharacteristic
449#135×C53—42no—
450#135×C53—42no—
451C2×Q16×C53C2311yescharacteristic
452C2×SD16×C53C2311yescharacteristic
453C2×SD16×C53C2311yescharacteristic
454C2×SD16×C53C2311yescharacteristic
455C2×SD16×C53C2311yescharacteristic
456C2×D8×C53C2311yescharacteristic
457C2×D8×C53C2311yescharacteristic
458C2×D8×C53C2311yescharacteristic
459C2×D8×C53C2311yescharacteristic
460C22×C8×C53C2311yescharacteristic
461C22×C8×C53C2311yescharacteristic
462#127×C53—21no—
463#127×C53—21no—
464#127×C53C2311yescharacteristic
465#127×C53C2311yescharacteristic
466#121×C53—21no—
467#121×C53—21no—
468#121×C53—21no—
469#121×C53—21no—
470#121×C53C2311yescharacteristic
471#121×C53C2311yescharacteristic
472#121×C53C2311yescharacteristic
473#121×C53C2311yescharacteristic
474C4×Q8×C53C2311yescharacteristic
475C4×Q8×C53C2311yescharacteristic
476C4×D4×C53—21no—
477C4×D4×C53—21no—
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
489C4×C8×C53C2311yescharacteristic
490C23×D53—21no—
491C23×D53—21no—
492C23×D53—21no—
493C23×D53—21no—
494C23×D53—21no—
495C23×D53—21no—
496C23×D53C2×D411yescharacteristic
497#41×C53—22no—
498#41×C53—22no—
499#41×C53—41no—
500#41×C53—41no—
501#41×C53—41no—
502#41×C53—41no—
503#41×C53—41no—
504#41×C53—41no—
505C2×Q8×C53C2411yescharacteristic
506C2×Q8×C53C2411yescharacteristic
507C2×D4×C53—21no—
508C2×D4×C53—21no—
509C2×D4×C53—21no—
510C2×D4×C53—21no—
511C2×D4×C53—21no—
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×C53C2×D411yescharacteristic
520C2×D4×C53C2411yescharacteristic
521C2×D4×C53C2411yescharacteristic
522C2×D4×C53C2411yescharacteristic
523C2×D4×C53C2411yescharacteristic
524C22×C4×C53—21no—
525C22×C4×C53—21no—
526C22×C4×C53—21no—
527C22×C4×C53—21no—
528C22×C4×C53C2411yescharacteristic
529C22×C4×C53C2411yescharacteristic
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—21no—
544C2×C22⋊D53—21no—
545C2×C22⋊D53—21no—
546C2×C22⋊D53—21no—
547C2×C22⋊D53—21no—
548C2×C22⋊D53C2×D411yescharacteristic
549C2×C22⋊D53C2×D411yescharacteristic
550C2×C22⋊D53C2×D411yescharacteristic
551C2×C22⋊D53C2×D411yescharacteristic
552C22×Dic53—21no—
553C22×Dic53—21no—
554C22×Dic53—21no—
555C22×Dic53—21no—
556C22×Dic53C2×D411yescharacteristic
557#11719949—22no—
558#11719949—22no—
559#11719949—22no—
560#11719949—41no—
561Q8×D53—22no—
562Q8×D53—41no—
563#11719947—41no—
564#11719947—41no—
565#11719947—44no—
566#11719947—82no—
567D4×D53—22no—
568D4×D53—22no—
569D4×D53—41no—
570D4×D53—41no—
571D4×D53—41no—
572D4×D53—41no—
573D4×D53—41no—
574D4×D53—41no—
575D4×D53—41no—
576D4×D53—41no—
577D4×D53—44no—
578D4×D53—44no—
579D4×D53—44no—
580D4×D53—82no—
581D4×D53—82no—
582D4×D53—82no—
583D4×D53—82no—
584D4×D53—82no—
585#11719945—22no—
586#11719945—41no—
587#11719945—41no—
588#11719945—41no—
589#11719945—44no—
590#11719945—44no—
591C2×D212—21no—
592C2×D212—22no—
593C2×D212—21no—
594C2×D212—21no—
595C2×D212—21no—
596C2×D212—21no—
597C2×D212—41no—
598C2×D212—44no—
599C2×D212C2×D411yescharacteristic
600C2×D212C2×D411yescharacteristic
601C2×D212C2411yescharacteristic
602C2×D212C2411yescharacteristic
603C2×D212C2411yescharacteristic
604C2×C4×D53—21no—
605C2×C4×D53—21no—
606C2×C4×D53—21no—
607C2×C4×D53—21no—
608C2×C4×D53—21no—
609C2×C4×D53—21no—
610C2×C4×D53—21no—
611C2×C4×D53—21no—
612C2×C4×D53—21no—
613C2×C4×D53—41no—
614C2×C4×D53—41no—
615C2×C4×D53—44no—
616C2×C4×D53C2×D411yescharacteristic
617C2×C4×D53C2×D411yescharacteristic
618C2×C4×D53C2411yescharacteristic
619C2×C4×D53C2411yescharacteristic
620C2×C4×D53C2411yescharacteristic
621C2×Dic106—21no—
622C2×Dic106—21no—
623C2×Dic106C2×D411yescharacteristic
624C2×Dic106C2411yescharacteristic
625Q16×C53—22no—
626SD16×C53—22no—
627SD16×C53—22no—
628SD16×C53—41no—
629SD16×C53—41no—
630D8×C53—41no—
631D8×C53—41no—
632D8×C53—41no—
633D8×C53—41no—
634C2×C8×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×C53C2×D411yescharacteristic
650C22⋊C4×C53C2×D411yescharacteristic
651C42×C53—21no—
652C42×C53—21no—
653C42×C53C2411yescharacteristic
654C22⋊Dic53—21no—
655C22⋊Dic53—21no—
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⋊Dic53C2×D411yescharacteristic
667C22⋊Dic53C2×D411yescharacteristic
668#11719925—41no—
669#11719924—22no—
670#11719924—22no—
671#11719924—41no—
672#11719923—41no—
673#11719923—41no—
674#11719922—22no—
675#11719922—22no—
676#11719922—41no—
677#11719922—41no—
678#11719922—41no—
679#11719922—41no—
680#11719921—21no—
681#11719921—21no—
682#11719921—21no—
683#11719921—21no—
684#11719921—21no—
685#11719921—21no—
686#11719921—21no—
687#11719921—21no—
688#11719921—21no—
689#11719921—21no—
690#11719921—21no—
691#11719921—21no—
692#11719921—21no—
693#11719921—21no—
694#11719921—21no—
695#11719921—21no—
696#11719921—21no—
697#11719921C2×D411yescharacteristic
698#11719921C2×D411yescharacteristic
699#11719921C2×D411yescharacteristic
700#11719921C2×D411yescharacteristic
701#11719921C2×D411yescharacteristic
702#11719921C2×D411yescharacteristic
703C4⋊Dic53—21no—
704C4⋊Dic53—21no—
705C4⋊Dic53—21no—
706C4⋊Dic53C2×D411yescharacteristic
707C4⋊Dic53C2411yescharacteristic
708C4⋊Dic53C2411yescharacteristic
709C4⋊Dic53C2411yescharacteristic
710C4⋊Dic53C2411yescharacteristic
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#11719919—21no—
720#11719919C2×D411yescharacteristic
721#11719919C2×D411yescharacteristic
722#11719919C2×D411yescharacteristic
723#11719919C2×D411yescharacteristic
724C4×Dic53—21no—
725C4×Dic53—21no—
726C4×Dic53—21no—
727C4×Dic53C2411yescharacteristic
728#11719917—41no—
729C2×#88322—41no—
730C2×#88322C2411yescharacteristic
731C2×#88322C2411yescharacteristic
732C2×#88322C2411yescharacteristic
733C2×#88322C2411yescharacteristic
734D424—22no—
735D424—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×C53C22×D411yescharacteristic
746C23×C53C22×D411yescharacteristic
747C22×D53—21no—
748C22×D53—22no—
749C22×D53—21no—
750C22×D53—21no—
751C22×D53—41no—
752C22×D53—41no—
753C22×D53—42no—
754C22×D53—42no—
755C22×D53—42no—
756C22×D53—42no—
757C22×D53—42no—
758C22×D53—42no—
759C22×D53—81no—
760C22×D53—81no—
761C22×D53—81no—
762C22×D53—81no—
763C22×D53—81no—
764C22×D53—81no—
765C22×D53—81no—
766C22×D53—81no—
767C22×D53—81no—
768C22×D53—81no—
769C22×D53—81no—
770C22×D53—81no—
771C22×D53C22×D411yescharacteristic
772C22×D53C22×D411yescharacteristic
773C22×D53C22×D411yescharacteristic
774Q8×C53—21no—
775Q8×C53—21no—
776Q8×C53—21no—
777Q8×C53H(5,𝔽2)12yes—
778D4×C53—21no—
779D4×C53—21no—
780D4×C53—21no—
781D4×C53—21no—
782D4×C53—21no—
783D4×C53—21no—
784D4×C53—21no—
785D4×C53—21no—
786D4×C53—41no—
787D4×C53—42no—
788D4×C53—42no—
789D4×C53—81no—
790D4×C53—81no—
791D4×C53—81no—
792D4×C53—81no—
793D4×C53—81no—
794D4×C53—81no—
795D4×C53—81no—
796D4×C53—81no—
797D4×C53—81no—
798D4×C53—81no—
799C2×C4×C53—21no—
800C2×C4×C53—21no—
801C2×C4×C53—21no—
802C2×C4×C53—21no—
803C2×C4×C53—21no—
804C2×C4×C53—21no—
805C2×C4×C53—21no—
806C2×C4×C53—21no—
807C2×C4×C53—42no—
808C2×C4×C53—42no—
809C2×C4×C53—81no—
810C2×C4×C53—81no—
811C2×C4×C53C22×D411yescharacteristic
812C2×C4×C53C22×D411yescharacteristic
813C2×C4×C53C22×D411yescharacteristic
814C2×C4×C53C22×D411yescharacteristic
815C2×C4×C53C2511yescharacteristic
816C22⋊D53—22no—
817C22⋊D53—41no—
818C22⋊D53—41no—
819C22⋊D53—41no—
820C22⋊D53—42no—
821C22⋊D53—42no—
822C22⋊D53—42no—
823C22⋊D53—42no—
824C22⋊D53—42no—
825C22⋊D53—42no—
826C22⋊D53—42no—
827C22⋊D53—81no—
828C22⋊D53—81no—
829C22⋊D53—81no—
830C22⋊D53—81no—
831C22⋊D53—81no—
832C22⋊D53—81no—
833C22⋊D53—81no—
834C22⋊D53—81no—
835C22⋊D53—81no—
836C22⋊D53—81no—
837C22⋊D53—81no—
838C2×Dic53—21no—
839C2×Dic53—21no—
840C2×Dic53—21no—
841C2×Dic53—21no—
842C2×Dic53—21no—
843C2×Dic53—41no—
844C2×Dic53—42no—
845C2×Dic53—81no—
846C2×Dic53—81no—
847C2×Dic53—81no—
848C2×Dic53C22×D411yescharacteristic
849C2×Dic53C22×D411yescharacteristic
850C2×Dic53C22×D411yescharacteristic
851C2×Dic53C22×D411yescharacteristic
852C2×Dic53C22×D411yescharacteristic
853D212—24no—
854D212—22no—
855D212—21no—
856D212—21no—
857D212—21no—
858D212—21no—
859D212—21no—
860D212—41no—
861D212—42no—
862D212—42no—
863D212—42no—
864D212—81no—
865D212H(5,𝔽2)12yes—
866C4×D53—24no—
867C4×D53—21no—
868C4×D53—21no—
869C4×D53—21no—
870C4×D53—21no—
871C4×D53—21no—
872C4×D53—21no—
873C4×D53—41no—
874C4×D53—41no—
875C4×D53—42no—
876C4×D53—42no—
877C4×D53—42no—
878C4×D53—42no—
879C4×D53—81no—
880C4×D53—81no—
881C4×D53—81no—
882C4×D53—81no—
883Dic106—21no—
884Dic106—21no—
885Dic106—41no—
886Dic106—42no—
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—21no—
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—41no—
915C22×C53C23×D411yescharacteristic
916C2×D53—21no—
917C2×D53—21no—
918C2×D53—21no—
919C2×D53—21no—
920C2×D53—21no—
921C2×D53—22no—
922C2×D53—21no—
923C2×D53—21no—
924C2×D53—21no—
925C2×D53—41no—
926C2×D53—41no—
927C2×D53—41no—
928C2×D53—41no—
929C2×D53—41no—
930C2×D53—41no—
931C2×D53—41no—
932C2×D53—41no—
933C2×D53—82no—
934C2×D53—84no—
935C2×D53—162no—
936C2×D53—162no—
937C2×D53—162no—
938C2×D53—162no—
939C2×D53—162no—
940C2×D53#57612yes—
941C4×C53—21no—
942C4×C53—22no—
943C4×C53—21no—
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#3287D5311yescharacteristic, complemented
972#3282—531no—
973#3280—531no—
974D4×D8—531no—
975#3268—531no—
976#3268—531no—
977#3265—531no—
978#3264—531no—
979#3224—531no—
980#3220—531no—
981#3203—531no—
982#3198—531no—
983#3188—531no—
984#3186—531no—
985#3124—531no—
986#3119—531no—
987#3012—531no—
988#3008—531no—
989#3002—531no—
990C2×#449—531no—
991#2977—531no—
992C2×C53—41no—
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—22no—
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)—531no—
1011C2×#135—531no—
1012C2×#135C2×D5311yescharacteristic, complemented
1013C2×#135C2×D5311yescharacteristic, complemented
1014C22×SD16—531no—
1015C22×D8—531no—
1016C22×D8—531no—
1017#562—1061no—
1018#560—1061no—
1019#555—531no—
1020#553—531no—
1021#552—531no—
1022#551—1061no—
1023#550—531no—
1024#550C2×D5311yescharacteristic, complemented
1025#550C2×D5311yescharacteristic, complemented
1026#548—531no—
1027#548—531no—
1028#547—531no—
1029#546—531no—
1030#546—531no—
1031#546—531no—
1032#546—531no—
1033#546—1061no—
1034#546—1061no—
1035#546—1061no—
1036D42—531no—
1037D42—531no—
1038D42—531no—
1039D42—1061no—
1040D42—1061no—
1041#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#496—531no—
1062#495—531no—
1063#493C2×D5311yescharacteristic, complemented
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#468—531no—
1088#467—531no—
1089#466—531no—
1090#466—531no—
1091#466—531no—
1092#466—531no—
1093#466—531no—
1094#466—531no—
1095#466C2×D5311yescharacteristic, complemented
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#463—531no—
1106#460C2×D5311yescharacteristic, complemented
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#450—531no—
1121#449—531no—
1122#449—531no—
1123#449—531no—
1124#449—531no—
1125#449—531no—
1126#449—531no—
1127#449—531no—
1128#449—531no—
1129#449—531no—
1130#449—531no—
1131#449—531no—
1132#449—531no—
1133#449C2×D5311yescharacteristic, complemented
1134#449C2×D5311yescharacteristic, complemented
1135#449C2×D5311yescharacteristic, complemented
1136#449C2×D5311yescharacteristic, complemented
1137#448—531no—
1138#447—531no—
1139#447—531no—
1140#447—531no—
1141#447—531no—
1142#447—531no—
1143#447—531no—
1144#447—531no—
1145#447—531no—
1146#447—531no—
1147#447—531no—
1148#442—531no—
1149#440—531no—
1150#440—531no—
1151#440—531no—
1152C4×Q16C2×D5311yescharacteristic, complemented
1153C4×SD16—531no—
1154C4×D8—531no—
1155C4×D8—531no—
1156#435—531no—
1157#435—531no—
1158#435—531no—
1159#435—531no—
1160C8×D4—531no—
1161C8×D4—531no—
1162C8×D4—531no—
1163C8×D4C2×D5311yescharacteristic, complemented
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—1061no—
1187C2×#41—1061no—
1188C2×#41—1061no—
1189C2×#41—1061no—
1190C2×#41—2122no—
1191C2×#41—2122no—
1192C2×#41C22×D5311yescharacteristic
1193C2×#41C22×D5311yescharacteristic
1194C2×#41C22×D5311yescharacteristic
1195C2×#41C22×D5311yescharacteristic
1196C22×Q8—531no—
1197C22×D4—531no—
1198C22×D4—531no—
1199C22×D4—531no—
1200C22×D4—531no—
1201C22×D4—531no—
1202C22×D4—531no—
1203C22×D4—1061no—
1204C22×D4—1061no—
1205C22×D4—1061no—
1206C22×D4—1061no—
1207C22×D4—1061no—
1208C22×D4—1061no—
1209C22×D4—1061no—
1210C22×D4—1061no—
1211C22×D4—1061no—
1212C23×C4—531no—
1213C23×C4—1061no—
1214AGL(1,ℤ/8)—2122no—
1215AGL(1,ℤ/8)—2122no—
1216#135—42no—
1217#135—42no—
1218#135—2122no—
1219C2×Q16—531no—
1220C2×Q16C22×D5311yescharacteristic
1221C2×SD16—531no—
1222C2×SD16—531no—
1223C2×SD16—531no—
1224C2×SD16—531no—
1225C2×SD16—531no—
1226C2×SD16—531no—
1227C2×SD16—2122no—
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—2122no—
1241C2×D8—2122no—
1242C2×D8C22×D5311yescharacteristic
1243C2×D8C22×D5311yescharacteristic
1244C2×D8C22×D5311yescharacteristic
1245C2×D8C22×D5311yescharacteristic
1246C2×M16—531no—
1247C2×M16—531no—
1248C22×C8—531no—
1249C22×C8—531no—
1250C22×C8—531no—
1251C22×C8—531no—
1252C22×C8C22×D5311yescharacteristic
1253C22×C8C22×D5311yescharacteristic
1254C4⋊Q8—531no—
1255#127—21no—
1256#127—21no—
1257#127—531no—
1258#127—1061no—
1259#127—1061no—
1260#127C22×D5311yescharacteristic
1261#127C22×D5311yescharacteristic
1262#126—1061no—
1263#126—1061no—
1264#126—1061no—
1265#125—531no—
1266#125—1061no—
1267#124—531no—
1268#124—531no—
1269#124—531no—
1270#124—1061no—
1271#124—1061no—
1272#124—1061no—
1273#124—1061no—
1274#124—1061no—
1275#124—1061no—
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—531no—
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⋊Q8—1061no—
1303#121—21no—
1304#121—21no—
1305#121—21no—
1306#121—21no—
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—531no—
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#121C22×D5311yescharacteristic
1348#121C22×D5311yescharacteristic
1349#121C22×D5311yescharacteristic
1350#121C22×D5311yescharacteristic
1351#120—531no—
1352#120—531no—
1353#120—1061no—
1354#120—1061no—
1355#120—1061no—
1356#120—1061no—
1357#120—1061no—
1358#120—1061no—
1359#120—1061no—
1360#120—1061no—
1361#120—1061no—
1362#120—1061no—
1363#120—1061no—
1364#120—1061no—
1365#120—1061no—
1366#120—1061no—
1367#120—1061no—
1368C4×Q8—531no—
1369C4×Q8C22×D5311yescharacteristic
1370C4×Q8C22×D5311yescharacteristic
1371C4×D4—21no—
1372C4×D4—21no—
1373C4×D4—531no—
1374C4×D4—531no—
1375C4×D4—531no—
1376C4×D4—531no—
1377C4×D4—531no—
1378C4×D4—531no—
1379C4×D4—531no—
1380C4×D4—531no—
1381C4×D4—1061no—
1382C4×D4—1061no—
1383C4×D4—1061no—
1384C4×D4—1061no—
1385C4×D4—1061no—
1386C4×D4—1061no—
1387C4×D4—1061no—
1388C4×D4—1061no—
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#97—531no—
1464C4×C8—531no—
1465C4×C8C22×D5311yescharacteristic
1466C24—531no—
1467C24—1061no—
1468C24—1061no—
1469C24—1061no—
1470C24—1061no—
1471C24—1061no—
1472C24—1061no—
1473#41—22no—
1474#41—22no—
1475#41—41no—
1476#41—41no—
1477#41—41no—
1478#41—41no—
1479#41—41no—
1480#41—41no—
1481#41—1062no—
1482#41—1062no—
1483#41—1062no—
1484#41—1062no—
1485#41—4242no—
1486#41—2121no—
1487#41—2121no—
1488#41—2121no—
1489#41—2124no—
1490#41—2124no—
1491#41—2121no—
1492#41—2121no—
1493#41—2124no—
1494#41—2121no—
1495C2×Q8—531no—
1496C2×Q8—531no—
1497C2×Q8—1061no—
1498C2×Q8—1061no—
1499C2×Q8—1062no—
1500C2×Q8—2121no—
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—21no—
1512C2×D4—21no—
1513C2×D4—21no—
1514C2×D4—21no—
1515C2×D4—531no—
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—1062no—
1525C2×D4—1061no—
1526C2×D4—1061no—
1527C2×D4—1061no—
1528C2×D4—1061no—
1529C2×D4—1061no—
1530C2×D4—1061no—
1531C2×D4—1061no—
1532C2×D4—1061no—
1533C2×D4—1061no—
1534C2×D4—1061no—
1535C2×D4—1061no—
1536C2×D4—1062no—
1537C2×D4—1062no—
1538C2×D4—1061no—
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—4242no—
1551C2×D4—4242no—
1552C2×D4—4242no—
1553C2×D4—4242no—
1554C2×D4—4242no—
1555C2×D4—2121no—
1556C2×D4—2124no—
1557C2×D4—2121no—
1558C2×D4—2121no—
1559C2×D4—2121no—
1560C2×D4—2121no—
1561C2×D4—2121no—
1562C2×D4—2121no—
1563C2×D4—2121no—
1564C2×D4—2121no—
1565C2×D4—2124no—
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—21no—
1577C22×C4—531no—
1578C22×C4—531no—
1579C22×C4—531no—
1580C22×C4—531no—
1581C22×C4—531no—
1582C22×C4—531no—
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—22no—
1602Q16—2121no—
1603SD16—22no—
1604SD16—22no—
1605SD16—41no—
1606SD16—41no—
1607SD16—1062no—
1608SD16—1062no—
1609SD16—2121no—
1610SD16—2121no—
1611SD16—2121no—
1612SD16—2121no—
1613D8—41no—
1614D8—41no—
1615D8—41no—
1616D8—41no—
1617D8—1062no—
1618D8—1062no—
1619D8—1062no—
1620D8—2121no—
1621D8—2121no—
1622D8—2121no—
1623D8—2121no—
1624D8—2121no—
1625M16—2121no—
1626M16—2121no—
1627C2×C8—41no—
1628C2×C8—41no—
1629C2×C8—531no—
1630C2×C8—531no—
1631C2×C8—531no—
1632C2×C8—531no—
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—531no—
1672C22⋊C4—531no—
1673C22⋊C4—531no—
1674C22⋊C4—531no—
1675C22⋊C4—531no—
1676C22⋊C4—531no—
1677C22⋊C4—531no—
1678C22⋊C4—531no—
1679C22⋊C4—1061no—
1680C22⋊C4—1061no—
1681C22⋊C4—1061no—
1682C22⋊C4—1061no—
1683C22⋊C4—1061no—
1684C22⋊C4—1061no—
1685C22⋊C4—1061no—
1686C22⋊C4—1061no—
1687C22⋊C4—1061no—
1688C22⋊C4—1061no—
1689C22⋊C4—1061no—
1690C22⋊C4—1061no—
1691C22⋊C4—1061no—
1692C22⋊C4—1061no—
1693C22⋊C4—1061no—
1694C22⋊C4—1061no—
1695C22⋊C4—1061no—
1696C22⋊C4—1061no—
1697C22⋊C4—1061no—
1698C22⋊C4—1061no—
1699C22⋊C4—1061no—
1700C22⋊C4—1061no—
1701C22⋊C4—1061no—
1702C22⋊C4—1061no—
1703C22⋊C4—1061no—
1704C22⋊C4—1061no—
1705C22⋊C4—1061no—
1706C22⋊C4—1061no—
1707C22⋊C4—1061no—
1708C22⋊C4D4×D5311yescharacteristic
1709C22⋊C4D4×D5311yescharacteristic
1710C42—21no—
1711C42—21no—
1712C42—531no—
1713C42—1061no—
1714C42—1061no—
1715C42—1061no—
1716C42C23×D5311yescharacteristic
1717C23—21no—
1718C23—21no—
1719C23—21no—
1720C23—21no—
1721C23—531no—
1722C23—531no—
1723C23—531no—
1724C23—1062no—
1725C23—1061no—
1726C23—1061no—
1727C23—1061no—
1728C23—4241no—
1729C23—4241no—
1730C23—4241no—
1731C23—4241no—
1732C23—4241no—
1733C23—4241no—
1734C23—4241no—
1735C23—4241no—
1736C23—4241no—
1737C23—4241no—
1738C23—4241no—
1739C23—4241no—
1740C23—2122no—
1741C23—2121no—
1742C23—2121no—
1743C23—2122no—
1744C23—2122no—
1745C23—2122no—
1746C23—2122no—
1747C23—2122no—
1748C23C2×D4×D5311yescharacteristic
1749C23C2×D4×D5311yescharacteristic
1750Q8—21no—
1751Q8—21no—
1752Q8—21no—
1753Q8—1061no—
1754Q8—1061no—
1755Q8—4241no—
1756Q8—2121no—
1757Q8—2122no—
1758Q8#1313326212yes—
1759D4—21no—
1760D4—21no—
1761D4—21no—
1762D4—21no—
1763D4—21no—
1764D4—21no—
1765D4—21no—
1766D4—21no—
1767D4—41no—
1768D4—42no—
1769D4—42no—
1770D4—81no—
1771D4—81no—
1772D4—81no—
1773D4—81no—
1774D4—81no—
1775D4—81no—
1776D4—81no—
1777D4—81no—
1778D4—81no—
1779D4—81no—
1780D4—532no—
1781D4—1062no—
1782D4—1064no—
1783D4—1062no—
1784D4—1061no—
1785D4—1061no—
1786D4—1061no—
1787D4—1061no—
1788D4—1061no—
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—2122no—
1803D4—2122no—
1804D4—2122no—
1805D4—2121no—
1806D4—2121no—
1807D4—2121no—
1808D4—2122no—
1809D4—2122no—
1810D4—2122no—
1811D4—2122no—
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—81no—
1827C2×C4—531no—
1828C2×C4—531no—
1829C2×C4—531no—
1830C2×C4—531no—
1831C2×C4—531no—
1832C2×C4—1064no—
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—1061no—
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—21no—
1878C22—41no—
1879C22—41no—
1880C22—41no—
1881C22—41no—
1882C22—41no—
1883C22—41no—
1884C22—41no—
1885C22—41no—
1886C22—41no—
1887C22—41no—
1888C22—41no—
1889C22—41no—
1890C22—532no—
1891C22—8482no—
1892C22—8482no—
1893C22—8482no—
1894C22—8482no—
1895C22—8482no—
1896C22—1061no—
1897C22—1061no—
1898C22—1062no—
1899C22—1061no—
1900C22—1061no—
1901C22—1061no—
1902C22—1061no—
1903C22—1061no—
1904C22—1061no—
1905C22—4242no—
1906C22—4244no—
1907C22—2121no—
1908C22—2121no—
1909C22—2121no—
1910C22—2121no—
1911C22—2121no—
1912C22—2121no—
1913C22—2121no—
1914C22—2121no—
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—41no—
1937C2—41no—
1938C2—81no—
1939C2—81no—
1940C2—81no—
1941C2—81no—
1942C2—1062no—
1943C2—4241no—
1944C2—4241no—
1945C2—2121no—
1946C2—2121no—
1947C2—2122no—
1948C2#2028834311yescharacteristic
1949C2#576×D5311yescharacteristic
1950C2#2028948411yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3287C2
socleC22×C53C23×D4
hypercenter#3287D53
hypocenterC53#61639
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3287

Complements

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

NH ≅ G/Ntype
1. #20289021C2semidirect
2. #20288383C2semidirect
3. #20286877C2semidirect
4. #20286743C2semidirect
5. #20286721C2semidirect
6. #20286699C2semidirect
7. #20286658C2semidirect
8. #20286607C2semidirect
9. #20286567C2semidirect
10. #20286523C2semidirect
11. #20286416C2semidirect
12. #20286398C2semidirect
13. #20286390C2semidirect
14. #20286256C2semidirect
15. #20286255C2semidirect
16. #20286205C2semidirect
17. #20286198C2semidirect
18. #20285814C2semidirect
19. #20285758C2semidirect
20. #20285614C2semidirect
21. #20285560C2semidirect
22. #20285478C2semidirect
23. #20285462C2semidirect
24. #20284983C2semidirect
25. #20284913C2semidirect
26. #20284015C2semidirect
27. #20283980C2semidirect
28. #20283929C2semidirect
29. #449×D53C2semidirect
30. #20283768C2semidirect
31. C53×#3287C2semidirect
32. C2×#13133263C22semidirect
33. C2×#41×D53C22semidirect
34. C2×#13133244C22semidirect
35. C2×#13133242C22semidirect
36. C2×#13133237C22semidirect
37. C2×SD16×D53C22semidirect
38. C2×D8×D53C22semidirect
39. C2×D8×D53C22semidirect
42. #16811337C22semidirect
43. #16811319C22semidirect
44. #16811314C22semidirect
46. #16811292C22semidirect
48. #16811280C22semidirect
49. #16811273C22semidirect
51. #16811270C22semidirect
53. #16811269C22semidirect
55. #16811261C22semidirect
56. #16811261C22semidirect
59. #16811258C22semidirect
61. #16811257C22semidirect
62. #16811245C22semidirect
63. #16811227C22semidirect
67. #16811202C22semidirect
68. #16811201C22semidirect
69. #16811189C22semidirect
72. #16811186C22semidirect
76. #16811130C22semidirect
78. #121×D53C22semidirect
79. #121×D53C22semidirect
80. #16811105C22semidirect
81. #16811010C22semidirect
82. #16811009C22semidirect
83. #16811004C22semidirect
84. #16810987C22semidirect
85. #16810981C22semidirect
86. #16810978C22semidirect
87. #16810968C22semidirect
88. #16810966C22semidirect
89. #16810959C22semidirect
90. #16810957C22semidirect
91. #16810948C22semidirect
92. #16810946C22semidirect
93. #16810944C22semidirect
94. #16810940C22semidirect
95. #16810938C22semidirect
96. #16810938C22semidirect
97. #16810935C22semidirect
98. #16810935C22semidirect
99. #16810934C22semidirect
100. #16810930C22semidirect
101. #16810924C22semidirect
102. #16810916C22semidirect
103. #16810902C22semidirect
104. #16810874C22semidirect
105. #16810868C22semidirect
106. #16810867C22semidirect
107. #16810866C22semidirect
108. #16810863C22semidirect
109. #16810859C22semidirect
110. #16810858C22semidirect
111. #16810857C22semidirect
112. #16810857C22semidirect
113. #16810856C22semidirect
114. #16810856C22semidirect
115. #16810855C22semidirect
116. #16810852C22semidirect
117. #16810849C22semidirect
118. #16810847C22semidirect
119. #16810845C22semidirect
120. #16810841C22semidirect
121. #16810839C22semidirect
122. #16810836C22semidirect
123. #16810836C22semidirect
124. #16810816C22semidirect
125. #16810816C22semidirect
126. #16810815C22semidirect
127. #16810815C22semidirect
128. #16810785C22semidirect
129. #16810784C22semidirect
130. #16810784C22semidirect
131. #16810782C22semidirect
132. #16810777C22semidirect
133. #16810775C22semidirect
134. #16810772C22semidirect
135. #16810772C22semidirect
136. #16810772C22semidirect
138. #16810770C22semidirect
139. #16810769C22semidirect
140. #16810768C22semidirect
141. #16810768C22semidirect
142. #16810768C22semidirect
143. #16810767C22semidirect
144. #16810767C22semidirect
145. #16810767C22semidirect
146. #16810766C22semidirect
147. #16810765C22semidirect
148. #16810765C22semidirect
149. #16810760C22semidirect
150. #16810759C22semidirect
151. #16810758C22semidirect
152. #16810758C22semidirect
153. #16810756C22semidirect
154. #16810755C22semidirect
155. #16810755C22semidirect
156. #16810755C22semidirect
157. #16810755C22semidirect
158. #16810755C22semidirect
159. #16810755C22semidirect
160. #16810732C22semidirect
161. #16810724C22semidirect
162. #16810721C22semidirect
163. #16810721C22semidirect
164. SD16×Dic53C22semidirect
165. C4×D424C22semidirect
166. #16810703C22semidirect
167. #16810697C22semidirect
168. #16810695C22semidirect
169. #16810694C22semidirect
170. #16810693C22semidirect
171. C8×D212C22semidirect
172. C8×C22⋊D53C22semidirect
173. #16810686C22semidirect
174. #16810683C22semidirect
175. #16810682C22semidirect
176. #16810626C22semidirect
177. #16810624C22semidirect
178. #16810620C22semidirect
179. #16810619C22semidirect
180. #16810618C22semidirect
181. #103×D53C22semidirect
182. C2×#13133139C22semidirect
183. #102×D53C22semidirect
184. #16810589C22semidirect
185. #16810588C22semidirect
186. C2×#13133129C22semidirect
187. C22⋊C8×D53C22semidirect
188. C2×#135×C53C22semidirect
189. C2×#135×C53C22semidirect
190. C53×#550C22semidirect
191. C53×#550C22semidirect
192. C53×#493C22semidirect
193. C53×#466C22semidirect
194. C53×#466C22semidirect
195. C53×#460C22semidirect
196. C53×#460C22semidirect
197. C53×#449C22semidirect
198. C53×#449C22semidirect
199. C53×#449C22semidirect
200. C53×#449C22semidirect
201. C4×Q16×C53C22semidirect
202. C8×D4×C53C22semidirect
971. #3287D53semidirect
1012. C2×#135C2×D53semidirect
1013. C2×#135C2×D53semidirect
1024. #550C2×D53semidirect
1025. #550C2×D53semidirect
1063. #493C2×D53semidirect
1095. #466C2×D53semidirect
1096. #466C2×D53semidirect
1106. #460C2×D53semidirect
1107. #460C2×D53semidirect
1133. #449C2×D53semidirect
1134. #449C2×D53semidirect
1135. #449C2×D53semidirect
1136. #449C2×D53semidirect
1152. C4×Q16C2×D53semidirect
1163. C8×D4C2×D53semidirect
1178. C53#61639semidirect

Maximal subgroups

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

subgroupindex
#202890212
#202883832
#202868772
#202867432
#202867212
#202866992
#202866582
#202866072
#202865672
#202865232
#202864162
#202863982
#202863902
#202862562
#202862552
#202862052
#202861982
#202858142
#202857582
#202856142
#202855602
#202854782
#202854622
#202849832
#202849132
#202840152
#202839802
#202839292
#449×D532
#202837682
C53×#32872
#6163953