Finite Group Databasebeta

← #28279579

Subgroups — #28279579

Order 13568.

1840 conjugacy classes of subgroups.

The subgroup lattice has 1774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289233C211yesmaximal, characteristic, complemented
2#20288726C211yesmaximal, characteristic, complemented
3#20287785C211yesmaximal, characteristic, complemented
4#20287774C211yesmaximal, characteristic, complemented
5#20287533C211yesmaximal, characteristic, complemented
6#20287524C211yesmaximal, characteristic, complemented
7#20286949C211yesmaximal, characteristic, complemented
8#20286942C211yesmaximal, characteristic, complemented
9#20286872C211yesmaximal, characteristic, complemented
10#20286867C211yesmaximal, characteristic, complemented
11#20286788C211yesmaximal, characteristic, complemented
12#20286777C211yesmaximal, characteristic, complemented
13#20286367C211yesmaximal, characteristic, complemented
14#20286366C211yesmaximal, characteristic, complemented
15#20286225C211yesmaximal, characteristic, complemented
16#20286219C211yesmaximal, characteristic, complemented
17#20286210C211yesmaximal, characteristic, complemented
18#20286205C211yesmaximal, characteristic, complemented
19#20286176C211yesmaximal, characteristic, complemented
20#20286174C211yesmaximal, characteristic, complemented
21#20286100C211yesmaximal, characteristic, complemented
22#20285814C211yesmaximal, characteristic, complemented
23#20285809C211yesmaximal, characteristic, complemented
24#20285716C211yesmaximal, characteristic, complemented
25#20284944C211yesmaximal, characteristic, complemented
26#20284943C211yesmaximal, characteristic, complemented
27#20284865C211yesmaximal, characteristic, complemented
28#20284231C211yesmaximal, characteristic, complemented
29#20284206C211yesmaximal, characteristic, complemented
30#20283883C211yesmaximal, characteristic, complemented
31C53×#3043C211yesmaximal, characteristic, complemented
32C2×#13133249C2211yescharacteristic, complemented
33C2×#13133246C2211yescharacteristic, complemented
34C2×#13133244C2211yescharacteristic
35C2×SD16×D53C2211yescharacteristic, complemented
36#16811368—21no—
37#16811366—21no—
38#16811359C2211yescharacteristic
39#16811355C2211yescharacteristic
40Q8×Dic106C2211yescharacteristic, complemented
41#16811346—21no—
42#16811346C2211yescharacteristic, complemented
43#16811345—21no—
44#16811345C2211yescharacteristic, complemented
45#16811341—21no—
46#16811341C2211yescharacteristic, complemented
47#16811336—21no—
48#16811336C2211yescharacteristic, complemented
49Q8×C22⋊D53C2211yescharacteristic, complemented
50#16811285C2211yescharacteristic, complemented
51#16811284C2211yescharacteristic, complemented
52#16811281C2211yescharacteristic
53#16811280C2211yescharacteristic
54#16811267C2211yescharacteristic
55#16811262—21no—
56#16811261C2211yescharacteristic
57#16811260—21no—
58#16811258C2211yescharacteristic
59D4×C22⋊D53C2211yescharacteristic
60#16811245—21no—
61#16811245C2211yescharacteristic, complemented
62#16811244—21no—
63#16811244C2211yescharacteristic
64#16811244C2211yescharacteristic, complemented
65#16811242C2211yescharacteristic
66#16811210—21no—
67#16811208—21no—
68#16811205—21no—
69#16811186C2211yescharacteristic
70#16811183—21no—
71#16811177—21no—
72#16811177C2211yescharacteristic, complemented
73#16811171C2211yescharacteristic
74#16811151—21no—
75#16811151C2211yescharacteristic
76#124×D53C2211yescharacteristic
77#16811099C2211yescharacteristic, complemented
78C4×#11719949C2211yescharacteristic, complemented
79#16811016C2211yescharacteristic, complemented
80#16811014C2211yescharacteristic, complemented
81#16811010C2211yescharacteristic
82#16811009C2211yescharacteristic
83#16811005C2211yescharacteristic, complemented
84#16811004C2211yescharacteristic, complemented
85#16810984C2211yescharacteristic, complemented
86#16810982C2211yescharacteristic, complemented
87#16810981C2211yescharacteristic, complemented
88#16810981C2211yescharacteristic, complemented
89#16810969C2211yescharacteristic
90#16810968C2211yescharacteristic
91#16810964C2211yescharacteristic, complemented
92#16810963C2211yescharacteristic, complemented
93#16810947C2211yescharacteristic
94#16810945C2211yescharacteristic
95#16810945C2211yescharacteristic, complemented
96#16810945C2211yescharacteristic, complemented
97#16810919C2211yescharacteristic, complemented
98#16810919C2211yescharacteristic, complemented
99#16810918C2211yescharacteristic, complemented
100#16810916C2211yescharacteristic, complemented
101#16810908C2211yescharacteristic, complemented
102#16810904C2211yescharacteristic, complemented
103#16810904C2211yescharacteristic, complemented
104#16810901C2211yescharacteristic, complemented
105#16810901C2211yescharacteristic, complemented
106#16810901C2211yescharacteristic, complemented
107#16810872C2211yescharacteristic, complemented
108#16810869C2211yescharacteristic
109#16810869C2211yescharacteristic, complemented
110#16810868C2211yescharacteristic, complemented
111#16810868C2211yescharacteristic, complemented
112#16810866C2211yescharacteristic
113#16810866C2211yescharacteristic, complemented
114#16810866C2211yescharacteristic, complemented
115#16810864C2211yescharacteristic, complemented
116#16810861C2211yescharacteristic, complemented
117#16810859C2211yescharacteristic
118#16810858C2211yescharacteristic
119#16810847C2211yescharacteristic, complemented
120#16810847C2211yescharacteristic, complemented
121#16810846C2211yescharacteristic, complemented
122#16810846C2211yescharacteristic, complemented
123#16810845C2211yescharacteristic, complemented
124#16810845C2211yescharacteristic, complemented
125#16810844C2211yescharacteristic, complemented
126#16810843C2211yescharacteristic, complemented
127#16810843C2211yescharacteristic, complemented
128#16810842C2211yescharacteristic, complemented
129#16810841C2211yescharacteristic, complemented
130#16810840C2211yescharacteristic, complemented
131#16810839C2211yescharacteristic, complemented
132#16810839C2211yescharacteristic, complemented
133#16810837C2211yescharacteristic, complemented
134#16810835C2211yescharacteristic, complemented
135#16810826C2211yescharacteristic, complemented
136#16810826C2211yescharacteristic, complemented
137#16810822C2211yescharacteristic
138#16810821C2211yescharacteristic
139#16810820C2211yescharacteristic, complemented
140#16810815C2211yescharacteristic, complemented
141#16810785C2211yescharacteristic, complemented
142#16810782C2211yescharacteristic, complemented
143#16810780C2211yescharacteristic, complemented
144#16810779C2211yescharacteristic, complemented
145#16810777C2211yescharacteristic, complemented
146#16810777C2211yescharacteristic, complemented
147#16810775C2211yescharacteristic
148#16810774C2211yescharacteristic, complemented
149#16810772C2211yescharacteristic
150#16810772C2211yescharacteristic, complemented
151#16810769C2211yescharacteristic, complemented
152#16810768C2211yescharacteristic, complemented
153#16810767C2211yescharacteristic, complemented
154#16810767C2211yescharacteristic, complemented
155#16810762C2211yescharacteristic
156#16810760C2211yescharacteristic
157#16810758C2211yescharacteristic, complemented
158#16810757C2211yescharacteristic, complemented
159#16810752C2211yescharacteristic, complemented
160#16810750C2211yescharacteristic, complemented
161#16810732C2211yescharacteristic, complemented
162#16810732C2211yescharacteristic, complemented
163#16810728C2211yescharacteristic, complemented
164#16810727C2211yescharacteristic, complemented
165#16810724C2211yescharacteristic, complemented
166#16810724C2211yescharacteristic, complemented
167#16810724C2211yescharacteristic, complemented
168#16810721C2211yescharacteristic, complemented
169Q16×Dic53C2211yescharacteristic, complemented
170C4×#11719925C2211yescharacteristic, complemented
171#16810714C2211yescharacteristic, complemented
172C4×#11719924C2211yescharacteristic, complemented
173#16810700C2211yescharacteristic, complemented
174#16810699C2211yescharacteristic, complemented
175#16810694C2211yescharacteristic, complemented
176#16810694C2211yescharacteristic, complemented
177#16810693C2211yescharacteristic, complemented
178#16810692C2211yescharacteristic, complemented
179#16810684C2211yescharacteristic, complemented
180#16810683C2211yescharacteristic, complemented
181#16810679C2211yescharacteristic, complemented
182#16810648C2211yescharacteristic, complemented
183#16810645C2211yescharacteristic, complemented
184#16810630C2211yescharacteristic, complemented
185#16810626C2211yescharacteristic
186#16810626C2211yescharacteristic, complemented
187#16810616C2211yescharacteristic, complemented
188C2×#137×C53C2211yescharacteristic, complemented
189C22×SD16×C53C2211yescharacteristic, complemented
190C53×#535C2211yescharacteristic
191C53×#519C2211yescharacteristic, complemented
192C53×#464C2211yescharacteristic, complemented
193C53×#464C2211yescharacteristic, complemented
194C53×#464C2211yescharacteristic, complemented
195C53×#464C2211yescharacteristic, complemented
196C53×#460C2211yescharacteristic
197C53×#460C2211yescharacteristic
198C53×#460C2211yescharacteristic, complemented
199C53×#460C2211yescharacteristic, complemented
200C53×#424C2211yescharacteristic, complemented
201C53×#418C2211yescharacteristic, complemented
202C53×#416C2211yescharacteristic, complemented
203C2×#11719949C2311yescharacteristic
204C2×#11719947—21no—
205C2×#11719947C2311yescharacteristic
206C2×Q8×D53C2311yescharacteristic
207C2×Q8×D53C2311yescharacteristic
208C22×C22⋊D53—21no—
209C2×D4×D53—21no—
210C2×D4×D53C2311yescharacteristic
211C2×D4×D53C2311yescharacteristic
212#13133249—42no—
213#13133246—42no—
214#13133244—42no—
215C2×Dic212C2311yescharacteristic
216C2×#11719925C2311yescharacteristic
217C2×#11719925C2311yescharacteristic
218C2×#11719925C2311yescharacteristic
219C2×#11719913C2311yescharacteristic
220C2×#11719913C2311yescharacteristic
221C2×#11719923C2311yescharacteristic
222C2×#11719923C2311yescharacteristic
223C2×#11719923C2311yescharacteristic
224C2×#11719924C2311yescharacteristic
225C2×#11719924C2311yescharacteristic
226C2×#11719924C2311yescharacteristic
227SD16×D53—42no—
228C2×D424C2311yescharacteristic
229C2×#11719922C2311yescharacteristic
230C2×#11719922C2311yescharacteristic
231C2×#11719922C2311yescharacteristic
232C2×#11719912C2311yescharacteristic
233C2×#11719912C2311yescharacteristic
234C2×#11719912C2311yescharacteristic
235C2×C8×D53C2311yescharacteristic
236#13133217—21no—
237#13133217C2311yescharacteristic
238#13133217C2311yescharacteristic
239#13133216—21no—
240#13133216—21no—
241#13133216C2311yescharacteristic
242#13133216C2311yescharacteristic
243#13133215—21no—
244#13133215C2311yescharacteristic
245#13133213C2311yescharacteristic
246#13133212—21no—
247#13133212—21no—
248#13133212—21no—
249#13133212—21no—
250#13133212—21no—
251#13133212D411yescharacteristic
252#13133211—21no—
253#13133211—21no—
254#13133211—21no—
255#13133210—21no—
256#13133210—21no—
257#13133210D411yescharacteristic
258#13133207—21no—
259#13133207D411yescharacteristic
260#13133206—21no—
261#13133206C2311yescharacteristic
262#13133206C2311yescharacteristic
263#13133205—21no—
264#13133205—21no—
265#13133205—21no—
266#13133205—21no—
267#13133205C2311yescharacteristic
268#13133205C2311yescharacteristic
269#13133204—21no—
270#13133204—21no—
271#13133204—21no—
272#13133204C2311yescharacteristic
273#13133204C2311yescharacteristic
274#13133203—21no—
275#13133203—21no—
276#13133203—21no—
277#13133203—21no—
278#13133203—21no—
279#13133203—21no—
280#13133203—21no—
281#13133203—21no—
282#13133203—21no—
283#13133203D411yescharacteristic
284#13133202—21no—
285#13133202D411yescharacteristic
286#13133201—21no—
287#13133201—21no—
288#13133200—21no—
289#13133199—21no—
290#13133199—21no—
291#13133199—21no—
292#13133199D411yescharacteristic
293#13133198—21no—
294#13133198—21no—
295#13133198—21no—
296#13133197—21no—
297#13133197C2311yescharacteristic
298#13133196—21no—
299#13133196—21no—
300#13133196C2311yescharacteristic
301#13133196C2311yescharacteristic
302#13133195—21no—
303#13133195—21no—
304#13133195—21no—
305#13133195—21no—
306#13133195—21no—
307#13133195D411yescharacteristic
308#13133194—21no—
309#13133194—21no—
310#13133193—21no—
311#13133193—21no—
312#13133193C2311yescharacteristic
313#13133193C2311yescharacteristic
314#13133193C2311yescharacteristic
315#13133192—21no—
316#13133192C2311yescharacteristic
317#13133191—21no—
318#13133191C2311yescharacteristic
319#13133191C2311yescharacteristic
320#13133190—21no—
321#13133190—21no—
322#13133190D411yescharacteristic
323#13133189—21no—
324#13133189—21no—
325#13133189—21no—
326#13133189—21no—
327#13133189—21no—
328#13133188—21no—
329#13133188—21no—
330#13133188—21no—
331#13133188C2311yescharacteristic
332#13133188C2311yescharacteristic
333#13133188C2311yescharacteristic
334#13133186—21no—
335#13133186—21no—
336#13133185—21no—
337#13133185—21no—
338#13133185—21no—
339#13133185—21no—
340#13133185—21no—
341#13133185—21no—
342Q8×Dic53C2311yescharacteristic
343Q8×Dic53C2311yescharacteristic
344Q8×Dic53C2311yescharacteristic
345C4×Dic106—21no—
346C4×Dic106—21no—
347C4×Dic106—21no—
348C4×Dic106—21no—
349C4×Dic106—21no—
350C4×Dic106C2311yescharacteristic
351C4×Dic106C2311yescharacteristic
352C4×Dic106C2311yescharacteristic
353#13133182—21no—
354#13133182C2311yescharacteristic
355C4×D212—21no—
356C4×D212—21no—
357C4×D212C2311yescharacteristic
358C4×D212C2311yescharacteristic
359C4×D212C2311yescharacteristic
360D4×Dic53—21no—
361D4×Dic53—21no—
362D4×Dic53C2311yescharacteristic
363D4×Dic53C2311yescharacteristic
364D4×Dic53C2311yescharacteristic
365#13133179—21no—
366#13133179C2311yescharacteristic
367C4×C22⋊D53—21no—
368C4×C22⋊D53—21no—
369C4×C22⋊D53—21no—
370C4×C22⋊D53C2311yescharacteristic
371C4×C22⋊D53C2311yescharacteristic
372#13133177—21no—
373#13133177—21no—
374#13133175—21no—
375#13133175—21no—
376#13133175C2311yescharacteristic
377#13133175C2311yescharacteristic
378#13133174—21no—
379#13133174—21no—
380#13133174—21no—
381#13133174—21no—
382#13133174C2311yescharacteristic
383C2×C22⋊Dic53—21no—
384C2×#11719921—21no—
385C22⋊C4×D53—21no—
386C22⋊C4×D53—21no—
387C42×D53—21no—
388C42×D53C2311yescharacteristic
389#13133151C2311yescharacteristic
390#13133151C2311yescharacteristic
391#13133151C2311yescharacteristic
392#13133151C2311yescharacteristic
393#13133150C2311yescharacteristic
394#13133150C2311yescharacteristic
395#13133148C2311yescharacteristic
396#13133148C2311yescharacteristic
397C4⋊#88322C2311yescharacteristic
398C4⋊#88322C2311yescharacteristic
399#13133146C2311yescharacteristic
400#13133146C2311yescharacteristic
401#13133146C2311yescharacteristic
402#13133146C2311yescharacteristic
403#13133142C2311yescharacteristic
404#13133142C2311yescharacteristic
405#13133142C2311yescharacteristic
406#13133142C2311yescharacteristic
407#13133141C2311yescharacteristic
408#13133141C2311yescharacteristic
409#13133141C2311yescharacteristic
410#13133141C2311yescharacteristic
411#13133141C2311yescharacteristic
412#13133141C2311yescharacteristic
413#13133140C2311yescharacteristic
414#13133140C2311yescharacteristic
415#13133139C2311yescharacteristic
416#13133139C2311yescharacteristic
417#13133139C2311yescharacteristic
418#13133139C2311yescharacteristic
419#13133138C2311yescharacteristic
420#13133138C2311yescharacteristic
421#13133138C2311yescharacteristic
422#13133138C2311yescharacteristic
423#13133138C2311yescharacteristic
424#13133138C2311yescharacteristic
425#13133137C2311yescharacteristic
426#13133137C2311yescharacteristic
427C22⋊#88322C2311yescharacteristic
428C22⋊#88322C2311yescharacteristic
429#13133129C2311yescharacteristic
430#13133129C2311yescharacteristic
431#13133129C2311yescharacteristic
432#13133129C2311yescharacteristic
433#13133128C2311yescharacteristic
434#13133127C2311yescharacteristic
435#13133127C2311yescharacteristic
436#13133127C2311yescharacteristic
437C4×#88322C2311yescharacteristic
438C8×Dic53C2311yescharacteristic
439C2×#41×C53C2311yescharacteristic
440C22×Q8×C53C2311yescharacteristic
441C22×D4×C53C2311yescharacteristic
442#137×C53—42no—
443C2×Q16×C53C2311yescharacteristic
444C2×Q16×C53C2311yescharacteristic
445C2×SD16×C53—42no—
446C2×SD16×C53C2311yescharacteristic
447C2×SD16×C53C2311yescharacteristic
448C2×SD16×C53C2311yescharacteristic
449C2×SD16×C53C2311yescharacteristic
450C2×SD16×C53C2311yescharacteristic
451C2×SD16×C53C2311yescharacteristic
452C2×M16×C53C2311yescharacteristic
453C22×C8×C53C2311yescharacteristic
454#127×C53C2311yescharacteristic
455#127×C53C2311yescharacteristic
456#124×C53C2311yescharacteristic
457#124×C53C2311yescharacteristic
458#121×C53—21no—
459#121×C53—21no—
460#120×C53—21no—
461#120×C53—21no—
462C4×Q8×C53—21no—
463C4×Q8×C53—21no—
464C4×Q8×C53C2311yescharacteristic
465C4×Q8×C53C2311yescharacteristic
466C4×Q8×C53C2311yescharacteristic
467C4×Q8×C53C2311yescharacteristic
468#117×C53—21no—
469#117×C53—21no—
470#117×C53C2311yescharacteristic
471#117×C53C2311yescharacteristic
472C4⋊C8×C53C2311yescharacteristic
473C4⋊C8×C53C2311yescharacteristic
474C4⋊C8×C53C2311yescharacteristic
475C4⋊C8×C53C2311yescharacteristic
476#103×C53C2311yescharacteristic
477#103×C53C2311yescharacteristic
478#102×C53C2311yescharacteristic
479#102×C53C2311yescharacteristic
480#102×C53C2311yescharacteristic
481#102×C53C2311yescharacteristic
482#102×C53C2311yescharacteristic
483#102×C53C2311yescharacteristic
484C24×C53—21no—
485C23×D53—21no—
486C23×D53—21no—
487#41×C53—41no—
488#41×C53—41no—
489C2×Q8×C53—21no—
490C2×Q8×C53—22no—
491C2×Q8×C53—41no—
492C2×Q8×C53C2411yescharacteristic
493C2×Q8×C53C2411yescharacteristic
494C2×Q8×C53C2411yescharacteristic
495C2×D4×C53—21no—
496C2×D4×C53—21no—
497C2×D4×C53—21no—
498C2×D4×C53—21no—
499C2×D4×C53—21no—
500C2×D4×C53—21no—
501C2×D4×C53—41no—
502C2×D4×C53—41no—
503C2×D4×C53C2411yescharacteristic
504C2×D4×C53C2411yescharacteristic
505C2×D4×C53C2411yescharacteristic
506C22×C4×C53—21no—
507C22×C4×C53—21no—
508C22×C4×C53C2411yescharacteristic
509C2×C22⋊D53—21no—
510C2×C22⋊D53—21no—
511C2×C22⋊D53—21no—
512C2×C22⋊D53—21no—
513C2×C22⋊D53—21no—
514C2×C22⋊D53—21no—
515C2×C22⋊D53—21no—
516C2×C22⋊D53—21no—
517C2×C22⋊D53—21no—
518C2×C22⋊D53—21no—
519C2×C22⋊D53—82no—
520C2×C22⋊D53C2×D411yescharacteristic
521C2×C22⋊D53C2×D411yescharacteristic
522C22×Dic53—21no—
523C22×Dic53—21no—
524C22×Dic53—21no—
525C22×Dic53—21no—
526#11719949—22no—
527#11719949—41no—
528Q8×D53—22no—
529Q8×D53—41no—
530Q8×D53—41no—
531Q8×D53—41no—
532#11719947—41no—
533#11719947—41no—
534#11719947—82no—
535D4×D53—41no—
536D4×D53—41no—
537D4×D53—41no—
538D4×D53—41no—
539D4×D53—82no—
540C2×D212—21no—
541C2×D212—21no—
542C2×D212C2×D411yescharacteristic
543C2×D212C2411yescharacteristic
544C2×D212C2411yescharacteristic
545C2×C4×D53—21no—
546C2×C4×D53—21no—
547C2×C4×D53—21no—
548C2×C4×D53—21no—
549C2×C4×D53—21no—
550C2×C4×D53—21no—
551C2×C4×D53C2×D411yescharacteristic
552C2×C4×D53C2×D411yescharacteristic
553C2×C4×D53C2411yescharacteristic
554C2×C4×D53C2411yescharacteristic
555C2×Dic106—21no—
556C2×Dic106—21no—
557C2×Dic106—21no—
558C2×Dic106—21no—
559C2×Dic106—21no—
560C2×Dic106—21no—
561C2×Dic106C2×D411yescharacteristic
562C2×Dic106C2411yescharacteristic
563C2×Dic106C2411yescharacteristic
564Q16×C53—22no—
565Q16×C53—41no—
566SD16×C53—22no—
567SD16×C53—22no—
568SD16×C53—22no—
569SD16×C53—41no—
570SD16×C53—41no—
571SD16×C53—41no—
572M16×C53—41no—
573C2×C8×C53—41no—
574C2×C8×C53C2411yescharacteristic
575C2×C8×C53C2411yescharacteristic
576C2×C8×C53C2411yescharacteristic
577C2×C8×C53C2411yescharacteristic
578C4⋊C4×C53—21no—
579C4⋊C4×C53—21no—
580C4⋊C4×C53—21no—
581C4⋊C4×C53—21no—
582C4⋊C4×C53C2×D411yescharacteristic
583C4⋊C4×C53C2×D411yescharacteristic
584C4⋊C4×C53C2411yescharacteristic
585C4⋊C4×C53C2411yescharacteristic
586C22⋊C4×C53—21no—
587C22⋊C4×C53—21no—
588C22⋊C4×C53—21no—
589C22⋊C4×C53—21no—
590C22⋊C4×C53—21no—
591C22⋊C4×C53C2×D411yescharacteristic
592C22⋊C4×C53C2×D411yescharacteristic
593C42×C53—21no—
594C42×C53—21no—
595C42×C53—21no—
596C42×C53—21no—
597C42×C53—21no—
598C42×C53C2411yescharacteristic
599C42×C53C2411yescharacteristic
600C22⋊Dic53—21no—
601C22⋊Dic53—21no—
602C22⋊Dic53—21no—
603C22⋊Dic53—21no—
604C22⋊Dic53—21no—
605C22⋊Dic53—21no—
606C22⋊Dic53—21no—
607C22⋊Dic53—21no—
608C22⋊Dic53—21no—
609C22⋊Dic53—21no—
610C22⋊Dic53—21no—
611C22⋊Dic53—21no—
612C22⋊Dic53C2×D411yescharacteristic
613C22⋊Dic53C2×D411yescharacteristic
614#11719925—22no—
615#11719925—41no—
616#11719925—41no—
617#11719924—22no—
618#11719924—41no—
619#11719924—41no—
620#11719923—41no—
621#11719923—41no—
622#11719923—41no—
623#11719922—41no—
624#11719922—41no—
625#11719922—41no—
626#11719921—21no—
627#11719921—21no—
628#11719921—21no—
629#11719921—21no—
630#11719921—21no—
631#11719921—21no—
632#11719921—21no—
633#11719921—21no—
634#11719921—21no—
635#11719921—21no—
636#11719921—21no—
637#11719921—21no—
638#11719921—21no—
639#11719921—21no—
640#11719921—21no—
641#11719921—21no—
642#11719921—21no—
643#11719921—21no—
644#11719921—21no—
645#11719921—21no—
646#11719921C2×D411yescharacteristic
647#11719921C2×D411yescharacteristic
648#11719921C2×D411yescharacteristic
649#11719921C2×D411yescharacteristic
650#11719921C2×D411yescharacteristic
651#11719921C2×D411yescharacteristic
652C4⋊Dic53—21no—
653C4⋊Dic53—21no—
654C4⋊Dic53—21no—
655C4⋊Dic53—21no—
656C4⋊Dic53—21no—
657C4⋊Dic53—21no—
658C4⋊Dic53C2×D411yescharacteristic
659C4⋊Dic53C2×D411yescharacteristic
660C4⋊Dic53C2411yescharacteristic
661C4⋊Dic53C2411yescharacteristic
662C4⋊Dic53C2411yescharacteristic
663C4⋊Dic53C2411yescharacteristic
664#11719919—21no—
665#11719919—21no—
666#11719919—21no—
667#11719919—21no—
668#11719919—21no—
669#11719919—21no—
670#11719919—21no—
671#11719919—21no—
672#11719919—21no—
673#11719919—21no—
674#11719919—21no—
675#11719919—21no—
676#11719919C2×D411yescharacteristic
677#11719919C2×D411yescharacteristic
678#11719919C2×D411yescharacteristic
679#11719919C2×D411yescharacteristic
680#11719919C2×D411yescharacteristic
681#11719919C2×D411yescharacteristic
682C4×Dic53—21no—
683C4×Dic53—21no—
684C4×Dic53—21no—
685C4×Dic53—21no—
686C4×Dic53—21no—
687C4×Dic53—21no—
688C4×Dic53—21no—
689C4×Dic53—21no—
690C4×Dic53C2×D411yescharacteristic
691C4×Dic53C2×D411yescharacteristic
692C4×Dic53C2411yescharacteristic
693C4×Dic53C2411yescharacteristic
694C2×#88322C2411yescharacteristic
695C2×#88322C2411yescharacteristic
696C2×#88322C2411yescharacteristic
697C2×#88322C2411yescharacteristic
698Dic212—41no—
699D424—41no—
700#11719913—41no—
701#11719913—41no—
702#11719912—41no—
703#11719912—41no—
704#11719912—41no—
705C8×D53—41no—
706C23×C53—21no—
707C23×C53—21no—
708C23×C53—21no—
709C23×C53—81no—
710C23×C53—81no—
711C23×C53—81no—
712C23×C53C22×D411yescharacteristic
713C22×D53—21no—
714C22×D53—21no—
715C22×D53—42no—
716C22×D53—81no—
717C22×D53—81no—
718C22×D53—81no—
719C22×D53—81no—
720C22×D53—81no—
721C22×D53C22×D411yescharacteristic
722C22×D53C22×D411yescharacteristic
723Q8×C53—21no—
724Q8×C53—21no—
725Q8×C53—21no—
726Q8×C53—21no—
727Q8×C53—21no—
728Q8×C53—42no—
729Q8×C53H(5,𝔽2)12yes—
730D4×C53—21no—
731D4×C53—21no—
732D4×C53—21no—
733D4×C53—21no—
734D4×C53—21no—
735D4×C53—21no—
736D4×C53—81no—
737D4×C53—81no—
738D4×C53—81no—
739D4×C53—81no—
740D4×C53—81no—
741D4×C53—81no—
742C2×C4×C53—21no—
743C2×C4×C53—21no—
744C2×C4×C53—21no—
745C2×C4×C53—21no—
746C2×C4×C53—21no—
747C2×C4×C53—21no—
748C2×C4×C53—21no—
749C2×C4×C53—42no—
750C2×C4×C53—81no—
751C2×C4×C53C22×D411yescharacteristic
752C2×C4×C53C22×D411yescharacteristic
753C2×C4×C53C22×D411yescharacteristic
754C2×C4×C53C22×D411yescharacteristic
755C2×C4×C53C22×D411yescharacteristic
756C2×C4×C53C2511yescharacteristic
757C22⋊D53—41no—
758C22⋊D53—41no—
759C22⋊D53—42no—
760C22⋊D53—42no—
761C22⋊D53—81no—
762C22⋊D53—81no—
763C22⋊D53—81no—
764C22⋊D53—81no—
765C22⋊D53—81no—
766C22⋊D53—81no—
767C22⋊D53—81no—
768C22⋊D53—81no—
769C2×Dic53—21no—
770C2×Dic53—21no—
771C2×Dic53—21no—
772C2×Dic53—21no—
773C2×Dic53—21no—
774C2×Dic53—21no—
775C2×Dic53—81no—
776C2×Dic53—81no—
777C2×Dic53—81no—
778C2×Dic53—81no—
779C2×Dic53C22×D411yescharacteristic
780C2×Dic53C22×D411yescharacteristic
781C2×Dic53C22×D411yescharacteristic
782C2×Dic53C22×D411yescharacteristic
783C2×Dic53C22×D411yescharacteristic
784C2×Dic53C22×D411yescharacteristic
785D212—21no—
786D212—21no—
787D212—21no—
788D212—21no—
789D212—41no—
790D212—42no—
791D212—81no—
792C4×D53—21no—
793C4×D53—21no—
794C4×D53—21no—
795C4×D53—21no—
796C4×D53—41no—
797C4×D53—41no—
798C4×D53—42no—
799C4×D53—42no—
800C4×D53—42no—
801C4×D53—81no—
802C4×D53—81no—
803C4×D53—81no—
804Dic106—21no—
805Dic106—21no—
806Dic106—21no—
807Dic106—21no—
808Dic106—41no—
809Dic106—42no—
810Dic106—81no—
811Dic106—81no—
812Dic106—81no—
813Dic106—81no—
814Dic106—81no—
815C8×C53—21no—
816C8×C53—21no—
817C8×C53—21no—
818C8×C53—21no—
819#88322—21no—
820#88322—21no—
821#88322—21no—
822#88322—21no—
823#62092—531nomaximal, Sylow
824C22×C53—21no—
825C22×C53—21no—
826C22×C53—21no—
827C22×C53—41no—
828C22×C53—41no—
829C22×C53—41no—
830C22×C53—41no—
831C22×C53—41no—
832C22×C53—41no—
833C22×C53—41no—
834C22×C53—41no—
835C22×C53—41no—
836C22×C53—162no—
837C22×C53C23×D411yescharacteristic
838C2×D53—21no—
839C2×D53—21no—
840C2×D53—21no—
841C2×D53—21no—
842C2×D53—21no—
843C2×D53—21no—
844C2×D53—41no—
845C2×D53—41no—
846C2×D53—41no—
847C2×D53—41no—
848C2×D53—41no—
849C2×D53—41no—
850C2×D53—162no—
851C2×D53—162no—
852C4×C53—21no—
853C4×C53—21no—
854C4×C53—21no—
855C4×C53—21no—
856C4×C53—22no—
857C4×C53—21no—
858C4×C53—41no—
859C4×C53—41no—
860C4×C53—41no—
861C4×C53—41no—
862C4×C53C2×H(5,𝔽2)11yescharacteristic
863C4×C53#58511yescharacteristic
864Dic53—21no—
865Dic53—21no—
866Dic53—21no—
867Dic53—21no—
868Dic53—21no—
869Dic53—21no—
870Dic53—41no—
871Dic53—41no—
872Dic53—41no—
873Dic53—41no—
874Dic53—41no—
875Dic53—41no—
876#3558—531no—
877#3518—531no—
878#3401—531no—
879#3401—531no—
880#3375—531no—
881#3375—531no—
882#3324—531no—
883#3324—531no—
884#3319—531no—
885#3319—531no—
886#3313—531no—
887#3313—531no—
888#3277—531no—
889#3277—531no—
890#3266—531no—
891#3266—531no—
892#3265—531no—
893#3265—531no—
894#3262—531no—
895#3262—531no—
896#3254—531no—
897#3224—531no—
898#3224—531no—
899#3215—531no—
900#3121—531no—
901#3121—531no—
902#3115—531no—
903#3043—531no—
904#3043D5311yescharacteristic, complemented
905#3040—531no—
906#2995—531no—
907C2×C53—41no—
908C2×C53—81no—
909C2×C53—81no—
910C2×C53—81no—
911C2×C53#348811yescharacteristic
912C2×C53#358511yescharacteristic
913C2×C53#358611yescharacteristic
914D53—41no—
915D53—41no—
916D53—81no—
917D53—81no—
918C2×#137—531no—
919C2×#137—531no—
920C2×#137C2×D5311yescharacteristic, complemented
921C2×AGL(1,ℤ/8)—531no—
922C22×SD16—531no—
923C22×SD16C2×D5311yescharacteristic, complemented
924#562—1061no—
925H(3,𝔽4)—1061no—
926#559—531no—
927#559—531no—
928Q82—531no—
929#556—531no—
930#556—531no—
931#556—531no—
932#556—1061no—
933#556—1061no—
934#556—1061no—
935#555—531no—
936#555—1061no—
937D4×Q8—531no—
938#548—531no—
939#548—531no—
940#548—531no—
941#548—531no—
942#546—531no—
943#546—531no—
944#546—1061no—
945#546—1061no—
946D42—531no—
947D42—531no—
948#542—531no—
949#542—531no—
950#542—531no—
951#542—531no—
952#542—1061no—
953#542—1061no—
954#538—1061no—
955#538—1061no—
956#538—1061no—
957#535—531no—
958#535C2×D5311yescharacteristic
959#534—1061no—
960#533—531no—
961#533—1061no—
962#532—531no—
963#529—531no—
964#529—1061no—
965C2×#124—531no—
966#519—531no—
967#519C2×D5311yescharacteristic, complemented
968C4×#41—531no—
969#497—531no—
970#497—531no—
971#496—531no—
972#496—531no—
973#495—531no—
974#495—531no—
975#489—531no—
976#489—531no—
977#489—531no—
978#489—531no—
979#486—531no—
980#486—531no—
981#485—531no—
982#485—531no—
983#482—531no—
984#482—531no—
985#482—531no—
986#482—531no—
987#477—531no—
988#477—531no—
989#477—531no—
990#477—531no—
991#475—531no—
992#474—531no—
993#474—531no—
994#474—531no—
995#474—531no—
996#474—531no—
997#468—531no—
998#468—531no—
999#468—531no—
1000#468—531no—
1001#468—531no—
1002#468—531no—
1003#468—531no—
1004#468—531no—
1005#467—531no—
1006#467—531no—
1007#466—531no—
1008#466—531no—
1009#464—531no—
1010#464—531no—
1011#464—531no—
1012#464—531no—
1013#464—531no—
1014#464—531no—
1015#464—531no—
1016#464—531no—
1017#464—531no—
1018#464—531no—
1019#464C2×D5311yescharacteristic, complemented
1020#464C2×D5311yescharacteristic, complemented
1021#464C2×D5311yescharacteristic, complemented
1022#464C2×D5311yescharacteristic, complemented
1023#463—531no—
1024#463—531no—
1025#463—531no—
1026#463—531no—
1027#463—531no—
1028#463—531no—
1029#461—531no—
1030#461—531no—
1031#460—531no—
1032#460—531no—
1033#460—531no—
1034#460C2×D5311yescharacteristic
1035#460C2×D5311yescharacteristic
1036#460C2×D5311yescharacteristic, complemented
1037#460C2×D5311yescharacteristic, complemented
1038#459—531no—
1039#452—531no—
1040#452—531no—
1041#451—531no—
1042#451—531no—
1043#451—531no—
1044#451—531no—
1045#450—531no—
1046#450—531no—
1047#450—531no—
1048#450—531no—
1049#449—531no—
1050#449—531no—
1051#449—531no—
1052#449—531no—
1053#448—531no—
1054#448—531no—
1055#447—531no—
1056#447—531no—
1057#446—531no—
1058#446—531no—
1059#442—531no—
1060#442—531no—
1061#441—531no—
1062#441—531no—
1063#440—531no—
1064#440—531no—
1065#440—531no—
1066#440—531no—
1067C4×Q16—531no—
1068C4×Q16—531no—
1069C4×SD16—531no—
1070C4×SD16—531no—
1071#436—531no—
1072#436—531no—
1073#435—531no—
1074#435—531no—
1075#435—531no—
1076#435—531no—
1077#433—531no—
1078#433—531no—
1079#432—531no—
1080#424—531no—
1081#424C2×D5311yescharacteristic, complemented
1082#423—531no—
1083#419—531no—
1084#418—531no—
1085#418—531no—
1086#418C2×D5311yescharacteristic, complemented
1087#416—531no—
1088#416C2×D5311yescharacteristic, complemented
1089C53#6209211yescharacteristic, complemented, Sylow
1090C2×#41—531no—
1091C2×#41—531no—
1092C2×#41—1061no—
1093C2×#41C22×D5311yescharacteristic
1094C22×Q8—531no—
1095C22×Q8—531no—
1096C22×Q8C22×D5311yescharacteristic
1097C22×D4—531no—
1098C22×D4—531no—
1099C22×D4—1061no—
1100C22×D4—1061no—
1101C22×D4C22×D5311yescharacteristic
1102#137—42no—
1103#137—2122no—
1104#137—2122no—
1105AGL(1,ℤ/8)—2122no—
1106C2×Q16—531no—
1107C2×Q16—531no—
1108C2×Q16—531no—
1109C2×Q16—531no—
1110C2×Q16C22×D5311yescharacteristic
1111C2×Q16C22×D5311yescharacteristic
1112C2×SD16—42no—
1113C2×SD16—531no—
1114C2×SD16—531no—
1115C2×SD16—531no—
1116C2×SD16—531no—
1117C2×SD16—531no—
1118C2×SD16—531no—
1119C2×SD16—531no—
1120C2×SD16—531no—
1121C2×SD16—2122no—
1122C2×SD16C22×D5311yescharacteristic
1123C2×SD16C22×D5311yescharacteristic
1124C2×SD16C22×D5311yescharacteristic
1125C2×SD16C22×D5311yescharacteristic
1126C2×SD16C22×D5311yescharacteristic
1127C2×SD16C22×D5311yescharacteristic
1128C2×D8—531no—
1129C2×D8—531no—
1130C2×D8—531no—
1131C2×D8—531no—
1132C2×M16—531no—
1133C2×M16—531no—
1134C2×M16—531no—
1135C2×M16C22×D5311yescharacteristic
1136C22×C8—531no—
1137C22×C8C22×D5311yescharacteristic
1138C4⋊Q8—531no—
1139C4⋊Q8—531no—
1140C4⋊Q8—531no—
1141C4⋊Q8—531no—
1142C4⋊Q8—531no—
1143C4⋊Q8—1061no—
1144C4⋊Q8—1061no—
1145C4⋊Q8—1061no—
1146C4⋊Q8—1061no—
1147#127—531no—
1148#127C22×D5311yescharacteristic
1149#127C22×D5311yescharacteristic
1150#126—531no—
1151#126—531no—
1152#126—1061no—
1153#126—1061no—
1154#126—1061no—
1155#126—1061no—
1156#126—1061no—
1157#126—1061no—
1158#126—1061no—
1159#126—1061no—
1160#126—1061no—
1161#126—1061no—
1162#125—531no—
1163#125—1061no—
1164#124—531no—
1165#124—531no—
1166#124—531no—
1167#124—531no—
1168#124—531no—
1169#124—531no—
1170#124—531no—
1171#124—1061no—
1172#124—1061no—
1173#124—1061no—
1174#124—1061no—
1175#124—1061no—
1176#124—1061no—
1177#124—1061no—
1178#124—1061no—
1179#124—1061no—
1180#124—1061no—
1181#124—1061no—
1182#124—1061no—
1183#124—1061no—
1184#124—1061no—
1185#124—1061no—
1186#124—1061no—
1187#124—1061no—
1188#124C22×D5311yescharacteristic
1189#124C22×D5311yescharacteristic
1190#123—531no—
1191#123—531no—
1192#123—1061no—
1193#123—1061no—
1194#123—1061no—
1195#123—1061no—
1196#123—1061no—
1197#123—1061no—
1198#123—1061no—
1199#123—1061no—
1200#123—1061no—
1201#123—1061no—
1202C22⋊Q8—531no—
1203C22⋊Q8—531no—
1204C22⋊Q8—531no—
1205C22⋊Q8—531no—
1206C22⋊Q8—531no—
1207C22⋊Q8—531no—
1208C22⋊Q8—531no—
1209C22⋊Q8—1061no—
1210C22⋊Q8—1061no—
1211C22⋊Q8—1061no—
1212C22⋊Q8—1061no—
1213C22⋊Q8—1061no—
1214C22⋊Q8—1061no—
1215C22⋊Q8—1061no—
1216C22⋊Q8—1061no—
1217C22⋊Q8—1061no—
1218C22⋊Q8—1061no—
1219C22⋊Q8—1061no—
1220C22⋊Q8—1061no—
1221#121—21no—
1222#121—21no—
1223#121—531no—
1224#121—531no—
1225#121—531no—
1226#121—531no—
1227#121—531no—
1228#121—531no—
1229#121—531no—
1230#121—1061no—
1231#121—1061no—
1232#121—1061no—
1233#121—1061no—
1234#121—1061no—
1235#121—1061no—
1236#121—1061no—
1237#121—1061no—
1238#121—1061no—
1239#121—1061no—
1240#121—1061no—
1241#121—1061no—
1242#120—21no—
1243#120—21no—
1244#120—1061no—
1245#120—1061no—
1246#120—1061no—
1247#120—1061no—
1248#120—1061no—
1249#120—1061no—
1250#120—1061no—
1251#120—1061no—
1252C4×Q8—21no—
1253C4×Q8—21no—
1254C4×Q8—531no—
1255C4×Q8—531no—
1256C4×Q8—531no—
1257C4×Q8—531no—
1258C4×Q8—531no—
1259C4×Q8—531no—
1260C4×Q8—531no—
1261C4×Q8—1061no—
1262C4×Q8—1061no—
1263C4×Q8—1061no—
1264C4×Q8—1061no—
1265C4×Q8—1061no—
1266C4×Q8—1061no—
1267C4×Q8C22×D5311yescharacteristic
1268C4×Q8C22×D5311yescharacteristic
1269C4×Q8C22×D5311yescharacteristic
1270C4×Q8C22×D5311yescharacteristic
1271C4×D4—531no—
1272C4×D4—531no—
1273C4×D4—531no—
1274C4×D4—531no—
1275C4×D4—531no—
1276C4×D4—531no—
1277C4×D4—531no—
1278C4×D4—531no—
1279C4×D4—531no—
1280C4×D4—1061no—
1281C4×D4—1061no—
1282C4×D4—1061no—
1283C4×D4—1061no—
1284C4×D4—1061no—
1285C4×D4—1061no—
1286C4×D4—1061no—
1287C4×D4—1061no—
1288C4×D4—1061no—
1289C4×D4—1061no—
1290#117—21no—
1291#117—21no—
1292#117—531no—
1293#117—531no—
1294#117—531no—
1295#117—1061no—
1296#117—1061no—
1297#117—1061no—
1298#117—1061no—
1299#117—1061no—
1300#117—1061no—
1301#117C22×D5311yescharacteristic
1302#117C22×D5311yescharacteristic
1303C2×C22⋊C4—1061no—
1304C2×C22⋊C4—1061no—
1305C2×C22⋊C4—1061no—
1306C2×C22⋊C4—1061no—
1307C2×C42—531no—
1308C2×C42—1061no—
1309#107—531no—
1310#107—531no—
1311#107—531no—
1312#107—531no—
1313#107—531no—
1314#107—531no—
1315#106—531no—
1316#106—531no—
1317C4⋊C8—531no—
1318C4⋊C8—531no—
1319C4⋊C8—531no—
1320C4⋊C8—531no—
1321C4⋊C8—531no—
1322C4⋊C8—531no—
1323C4⋊C8C22×D5311yescharacteristic
1324C4⋊C8C22×D5311yescharacteristic
1325C4⋊C8C22×D5311yescharacteristic
1326C4⋊C8C22×D5311yescharacteristic
1327#103—531no—
1328#103—531no—
1329#103—531no—
1330#103—531no—
1331#103—531no—
1332#103—531no—
1333#103—531no—
1334#103—531no—
1335#103—531no—
1336#103—531no—
1337#103—531no—
1338#103—531no—
1339#103C22×D5311yescharacteristic
1340#103C22×D5311yescharacteristic
1341#102—531no—
1342#102—531no—
1343#102—531no—
1344#102—531no—
1345#102—531no—
1346#102—531no—
1347#102—531no—
1348#102—531no—
1349#102—531no—
1350#102—531no—
1351#102—531no—
1352#102—531no—
1353#102C22×D5311yescharacteristic
1354#102C22×D5311yescharacteristic
1355#102C22×D5311yescharacteristic
1356#102C22×D5311yescharacteristic
1357#102C22×D5311yescharacteristic
1358#102C22×D5311yescharacteristic
1359C22⋊C8—531no—
1360C22⋊C8—531no—
1361C22⋊C8—531no—
1362C22⋊C8—531no—
1363C22⋊C8—531no—
1364C22⋊C8—531no—
1365#97—531no—
1366#97—531no—
1367#97—531no—
1368#97—531no—
1369C4×C8—531no—
1370C4×C8—531no—
1371C24—21no—
1372C24—1061no—
1373C24—1061no—
1374#41—41no—
1375#41—41no—
1376#41—1062no—
1377#41—4242no—
1378#41—2121no—
1379#41—2121no—
1380#41—2121no—
1381C2×Q8—21no—
1382C2×Q8—22no—
1383C2×Q8—41no—
1384C2×Q8—531no—
1385C2×Q8—531no—
1386C2×Q8—531no—
1387C2×Q8—1061no—
1388C2×Q8—1061no—
1389C2×Q8—1061no—
1390C2×Q8—1061no—
1391C2×Q8—1061no—
1392C2×Q8—1061no—
1393C2×Q8—1062no—
1394C2×Q8—2121no—
1395C2×Q8—2121no—
1396C2×Q8—2121no—
1397C2×Q8C23×D5311yescharacteristic
1398C2×Q8C23×D5311yescharacteristic
1399C2×Q8C23×D5311yescharacteristic
1400C2×D4—21no—
1401C2×D4—21no—
1402C2×D4—21no—
1403C2×D4—21no—
1404C2×D4—21no—
1405C2×D4—21no—
1406C2×D4—41no—
1407C2×D4—41no—
1408C2×D4—531no—
1409C2×D4—531no—
1410C2×D4—531no—
1411C2×D4—531no—
1412C2×D4—531no—
1413C2×D4—1061no—
1414C2×D4—1061no—
1415C2×D4—1061no—
1416C2×D4—1061no—
1417C2×D4—1061no—
1418C2×D4—1061no—
1419C2×D4—1061no—
1420C2×D4—1061no—
1421C2×D4—1061no—
1422C2×D4—1061no—
1423C2×D4—1061no—
1424C2×D4—1061no—
1425C2×D4—4242no—
1426C2×D4—4242no—
1427C2×D4—2121no—
1428C2×D4—2121no—
1429C2×D4—2121no—
1430C2×D4—2121no—
1431C2×D4C23×D5311yescharacteristic
1432C2×D4C23×D5311yescharacteristic
1433C2×D4C23×D5311yescharacteristic
1434C22×C4—21no—
1435C22×C4—21no—
1436C22×C4—531no—
1437C22×C4—531no—
1438C22×C4—531no—
1439C22×C4—531no—
1440C22×C4—1061no—
1441C22×C4—1061no—
1442C22×C4—1061no—
1443C22×C4—1061no—
1444C22×C4—1061no—
1445C22×C4—1061no—
1446C22×C4—1061no—
1447C22×C4—1061no—
1448C22×C4—1061no—
1449C22×C4—1061no—
1450C22×C4C23×D5311yescharacteristic
1451Q16—22no—
1452Q16—41no—
1453Q16—1062no—
1454Q16—2121no—
1455Q16—2121no—
1456Q16—2121no—
1457SD16—22no—
1458SD16—22no—
1459SD16—22no—
1460SD16—41no—
1461SD16—41no—
1462SD16—41no—
1463SD16—1062no—
1464SD16—2121no—
1465SD16—2121no—
1466SD16—2121no—
1467SD16—2121no—
1468SD16—2121no—
1469SD16—2121no—
1470SD16—2121no—
1471D8—2121no—
1472D8—2121no—
1473D8—2121no—
1474D8—2121no—
1475M16—41no—
1476M16—2121no—
1477M16—2121no—
1478M16—2121no—
1479C2×C8—41no—
1480C2×C8—531no—
1481C2×C8—531no—
1482C2×C8—531no—
1483C2×C8—531no—
1484C2×C8—2121no—
1485C2×C8C23×D5311yescharacteristic
1486C2×C8C23×D5311yescharacteristic
1487C2×C8C23×D5311yescharacteristic
1488C2×C8C23×D5311yescharacteristic
1489C4⋊C4—21no—
1490C4⋊C4—21no—
1491C4⋊C4—21no—
1492C4⋊C4—21no—
1493C4⋊C4—531no—
1494C4⋊C4—531no—
1495C4⋊C4—531no—
1496C4⋊C4—531no—
1497C4⋊C4—531no—
1498C4⋊C4—531no—
1499C4⋊C4—531no—
1500C4⋊C4—531no—
1501C4⋊C4—531no—
1502C4⋊C4—531no—
1503C4⋊C4—531no—
1504C4⋊C4—531no—
1505C4⋊C4—1061no—
1506C4⋊C4—1061no—
1507C4⋊C4—1061no—
1508C4⋊C4—1061no—
1509C4⋊C4—1061no—
1510C4⋊C4—1061no—
1511C4⋊C4—1061no—
1512C4⋊C4—1061no—
1513C4⋊C4—1061no—
1514C4⋊C4—1061no—
1515C4⋊C4—1061no—
1516C4⋊C4—1061no—
1517C4⋊C4—1061no—
1518C4⋊C4—1061no—
1519C4⋊C4—1061no—
1520C4⋊C4—1061no—
1521C4⋊C4—1061no—
1522C4⋊C4—1061no—
1523C4⋊C4D4×D5311yescharacteristic
1524C4⋊C4D4×D5311yescharacteristic
1525C4⋊C4C23×D5311yescharacteristic
1526C4⋊C4C23×D5311yescharacteristic
1527C22⋊C4—21no—
1528C22⋊C4—21no—
1529C22⋊C4—21no—
1530C22⋊C4—21no—
1531C22⋊C4—21no—
1532C22⋊C4—531no—
1533C22⋊C4—531no—
1534C22⋊C4—531no—
1535C22⋊C4—531no—
1536C22⋊C4—531no—
1537C22⋊C4—531no—
1538C22⋊C4—531no—
1539C22⋊C4—531no—
1540C22⋊C4—1061no—
1541C22⋊C4—1061no—
1542C22⋊C4—1061no—
1543C22⋊C4—1061no—
1544C22⋊C4—1061no—
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—1061no—
1558C22⋊C4—1061no—
1559C22⋊C4—1061no—
1560C22⋊C4—1061no—
1561C22⋊C4—1061no—
1562C22⋊C4—1061no—
1563C22⋊C4—1061no—
1564C22⋊C4—1061no—
1565C22⋊C4—1061no—
1566C22⋊C4—1061no—
1567C22⋊C4—1061no—
1568C22⋊C4—1061no—
1569C22⋊C4—1061no—
1570C22⋊C4—1061no—
1571C22⋊C4—1061no—
1572C22⋊C4D4×D5311yescharacteristic
1573C22⋊C4D4×D5311yescharacteristic
1574C42—21no—
1575C42—21no—
1576C42—21no—
1577C42—21no—
1578C42—21no—
1579C42—531no—
1580C42—531no—
1581C42—531no—
1582C42—531no—
1583C42—1061no—
1584C42—1061no—
1585C42—1061no—
1586C42—1061no—
1587C42—1061no—
1588C42—1061no—
1589C42—1061no—
1590C42—1061no—
1591C42C23×D5311yescharacteristic
1592C42C23×D5311yescharacteristic
1593C23—21no—
1594C23—21no—
1595C23—21no—
1596C23—81no—
1597C23—81no—
1598C23—81no—
1599C23—531no—
1600C23—531no—
1601C23—1061no—
1602C23—1061no—
1603C23—4241no—
1604C23—4241no—
1605C23—4241no—
1606C23—4241no—
1607C23—4241no—
1608C23—2122no—
1609C23C2×D4×D5311yescharacteristic
1610Q8—21no—
1611Q8—21no—
1612Q8—21no—
1613Q8—21no—
1614Q8—21no—
1615Q8—42no—
1616Q8—1061no—
1617Q8—1061no—
1618Q8—1061no—
1619Q8—1061no—
1620Q8—4241no—
1621Q8—4241no—
1622Q8—4241no—
1623Q8—4241no—
1624Q8—4241no—
1625Q8—2121no—
1626Q8—2122no—
1627Q8#1313326212yes—
1628D4—21no—
1629D4—21no—
1630D4—21no—
1631D4—21no—
1632D4—21no—
1633D4—21no—
1634D4—81no—
1635D4—81no—
1636D4—81no—
1637D4—81no—
1638D4—81no—
1639D4—81no—
1640D4—1061no—
1641D4—1061no—
1642D4—1061no—
1643D4—1061no—
1644D4—4241no—
1645D4—4241no—
1646D4—4241no—
1647D4—4241no—
1648D4—4241no—
1649D4—4241no—
1650D4—4241no—
1651D4—4241no—
1652D4—4241no—
1653D4—2121no—
1654D4—2122no—
1655D4—2121no—
1656D4—2121no—
1657D4—2122no—
1658D4—2122no—
1659C2×C4—21no—
1660C2×C4—21no—
1661C2×C4—21no—
1662C2×C4—21no—
1663C2×C4—21no—
1664C2×C4—21no—
1665C2×C4—21no—
1666C2×C4—42no—
1667C2×C4—81no—
1668C2×C4—531no—
1669C2×C4—531no—
1670C2×C4—531no—
1671C2×C4—531no—
1672C2×C4—531no—
1673C2×C4—531no—
1674C2×C4—1061no—
1675C2×C4—1061no—
1676C2×C4—1061no—
1677C2×C4—1061no—
1678C2×C4—1061no—
1679C2×C4—1061no—
1680C2×C4—1061no—
1681C2×C4—1061no—
1682C2×C4—1061no—
1683C2×C4—1061no—
1684C2×C4—4241no—
1685C2×C4—4241no—
1686C2×C4—4241no—
1687C2×C4—4241no—
1688C2×C4—4241no—
1689C2×C4—4241no—
1690C2×C4—4241no—
1691C2×C4—2121no—
1692C2×C4—2121no—
1693C2×C4—2122no—
1694C2×C4—2122no—
1695C2×C4—2122no—
1696C2×C4C2×D4×D5311yescharacteristic
1697C2×C4C2×D4×D5311yescharacteristic
1698C2×C4C2×D4×D5311yescharacteristic
1699C2×C4C2×D4×D5311yescharacteristic
1700C2×C4C2×D4×D5311yescharacteristic
1701C2×C4C24×D5311yescharacteristic
1702C8—21no—
1703C8—21no—
1704C8—21no—
1705C8—21no—
1706C8—1061no—
1707C8—1061no—
1708C8—1061no—
1709C8—1061no—
1710C22—21no—
1711C22—21no—
1712C22—21no—
1713C22—41no—
1714C22—41no—
1715C22—41no—
1716C22—41no—
1717C22—41no—
1718C22—41no—
1719C22—41no—
1720C22—41no—
1721C22—41no—
1722C22—162no—
1723C22—8482no—
1724C22—8482no—
1725C22—1061no—
1726C22—1061no—
1727C22—1061no—
1728C22—1061no—
1729C22—1061no—
1730C22—1061no—
1731C22—2121no—
1732C22—2121no—
1733C22—2121no—
1734C22—2121no—
1735C22—2121no—
1736C22—2121no—
1737C22C22×D4×D5311yescharacteristic
1738C4—21no—
1739C4—22no—
1740C4—21no—
1741C4—21no—
1742C4—21no—
1743C4—21no—
1744C4—41no—
1745C4—41no—
1746C4—41no—
1747C4—41no—
1748C4—1061no—
1749C4—1061no—
1750C4—1061no—
1751C4—1061no—
1752C4—1061no—
1753C4—1061no—
1754C4—2121no—
1755C4—2121no—
1756C4—2121no—
1757C4—2121no—
1758C4—2121no—
1759C4—2121no—
1760C4C2×#1313326211yescharacteristic
1761C4#1681145911yescharacteristic
1762C2—41no—
1763C2—81no—
1764C2—81no—
1765C2—81no—
1766C2—4241no—
1767C2—4241no—
1768C2—2121no—
1769C2—2121no—
1770C2#2028838011yescharacteristic
1771C2#2028949311yescharacteristic
1772C2#2028949711yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3043C2
socleC22×C53C23×D4
hypercenter#3043D53
hypocenterC53#62092
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ #117 ◁ #3043

Complements

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

NH ≅ G/Ntype
1. #20289233C2semidirect
2. #20288726C2semidirect
3. #20287785C2semidirect
4. #20287774C2semidirect
5. #20287533C2semidirect
6. #20287524C2semidirect
7. #20286949C2semidirect
8. #20286942C2semidirect
9. #20286872C2semidirect
10. #20286867C2semidirect
11. #20286788C2semidirect
12. #20286777C2semidirect
13. #20286367C2semidirect
14. #20286366C2semidirect
15. #20286225C2semidirect
16. #20286219C2semidirect
17. #20286210C2semidirect
18. #20286205C2semidirect
19. #20286176C2semidirect
20. #20286174C2semidirect
21. #20286100C2semidirect
22. #20285814C2semidirect
23. #20285809C2semidirect
24. #20285716C2semidirect
25. #20284944C2semidirect
26. #20284943C2semidirect
27. #20284865C2semidirect
28. #20284231C2semidirect
29. #20284206C2semidirect
30. #20283883C2semidirect
31. C53×#3043C2semidirect
32. C2×#13133249C22semidirect
33. C2×#13133246C22semidirect
35. C2×SD16×D53C22semidirect
40. Q8×Dic106C22semidirect
42. #16811346C22semidirect
44. #16811345C22semidirect
46. #16811341C22semidirect
48. #16811336C22semidirect
49. Q8×C22⋊D53C22semidirect
50. #16811285C22semidirect
51. #16811284C22semidirect
61. #16811245C22semidirect
64. #16811244C22semidirect
72. #16811177C22semidirect
77. #16811099C22semidirect
78. C4×#11719949C22semidirect
79. #16811016C22semidirect
80. #16811014C22semidirect
83. #16811005C22semidirect
84. #16811004C22semidirect
85. #16810984C22semidirect
86. #16810982C22semidirect
87. #16810981C22semidirect
88. #16810981C22semidirect
91. #16810964C22semidirect
92. #16810963C22semidirect
95. #16810945C22semidirect
96. #16810945C22semidirect
97. #16810919C22semidirect
98. #16810919C22semidirect
99. #16810918C22semidirect
100. #16810916C22semidirect
101. #16810908C22semidirect
102. #16810904C22semidirect
103. #16810904C22semidirect
104. #16810901C22semidirect
105. #16810901C22semidirect
106. #16810901C22semidirect
107. #16810872C22semidirect
109. #16810869C22semidirect
110. #16810868C22semidirect
111. #16810868C22semidirect
113. #16810866C22semidirect
114. #16810866C22semidirect
115. #16810864C22semidirect
116. #16810861C22semidirect
119. #16810847C22semidirect
120. #16810847C22semidirect
121. #16810846C22semidirect
122. #16810846C22semidirect
123. #16810845C22semidirect
124. #16810845C22semidirect
125. #16810844C22semidirect
126. #16810843C22semidirect
127. #16810843C22semidirect
128. #16810842C22semidirect
129. #16810841C22semidirect
130. #16810840C22semidirect
131. #16810839C22semidirect
132. #16810839C22semidirect
133. #16810837C22semidirect
134. #16810835C22semidirect
135. #16810826C22semidirect
136. #16810826C22semidirect
139. #16810820C22semidirect
140. #16810815C22semidirect
141. #16810785C22semidirect
142. #16810782C22semidirect
143. #16810780C22semidirect
144. #16810779C22semidirect
145. #16810777C22semidirect
146. #16810777C22semidirect
148. #16810774C22semidirect
150. #16810772C22semidirect
151. #16810769C22semidirect
152. #16810768C22semidirect
153. #16810767C22semidirect
154. #16810767C22semidirect
157. #16810758C22semidirect
158. #16810757C22semidirect
159. #16810752C22semidirect
160. #16810750C22semidirect
161. #16810732C22semidirect
162. #16810732C22semidirect
163. #16810728C22semidirect
164. #16810727C22semidirect
165. #16810724C22semidirect
166. #16810724C22semidirect
167. #16810724C22semidirect
168. #16810721C22semidirect
169. Q16×Dic53C22semidirect
170. C4×#11719925C22semidirect
171. #16810714C22semidirect
172. C4×#11719924C22semidirect
173. #16810700C22semidirect
174. #16810699C22semidirect
175. #16810694C22semidirect
176. #16810694C22semidirect
177. #16810693C22semidirect
178. #16810692C22semidirect
179. #16810684C22semidirect
180. #16810683C22semidirect
181. #16810679C22semidirect
182. #16810648C22semidirect
183. #16810645C22semidirect
184. #16810630C22semidirect
186. #16810626C22semidirect
187. #16810616C22semidirect
188. C2×#137×C53C22semidirect
189. C22×SD16×C53C22semidirect
191. C53×#519C22semidirect
192. C53×#464C22semidirect
193. C53×#464C22semidirect
194. C53×#464C22semidirect
195. C53×#464C22semidirect
198. C53×#460C22semidirect
199. C53×#460C22semidirect
200. C53×#424C22semidirect
201. C53×#418C22semidirect
202. C53×#416C22semidirect
904. #3043D53semidirect
920. C2×#137C2×D53semidirect
923. C22×SD16C2×D53semidirect
967. #519C2×D53semidirect
1019. #464C2×D53semidirect
1020. #464C2×D53semidirect
1021. #464C2×D53semidirect
1022. #464C2×D53semidirect
1036. #460C2×D53semidirect
1037. #460C2×D53semidirect
1081. #424C2×D53semidirect
1086. #418C2×D53semidirect
1088. #416C2×D53semidirect
1089. C53#62092semidirect

Maximal subgroups

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

subgroupindex
#202892332
#202887262
#202877852
#202877742
#202875332
#202875242
#202869492
#202869422
#202868722
#202868672
#202867882
#202867772
#202863672
#202863662
#202862252
#202862192
#202862102
#202862052
#202861762
#202861742
#202861002
#202858142
#202858092
#202857162
#202849442
#202849432
#202848652
#202842312
#202842062
#202838832
C53×#30432
#6209253