Finite Group Databasebeta

← #28257167

Subgroups — #28257167

Order 13568.

1932 conjugacy classes of subgroups.

The subgroup lattice has 1804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288587C211yesmaximal, characteristic, complemented
2#20288135C211yesmaximal, characteristic, complemented
3#20286154C211yesmaximal, characteristic, complemented
4#20286153C211yesmaximal, characteristic, complemented
5#20286152C211yesmaximal, characteristic, complemented
6#20286150C211yesmaximal, characteristic, complemented
7#20286132C211yesmaximal, characteristic, complemented
8#20286126C211yesmaximal, characteristic, complemented
9#20286124C211yesmaximal, characteristic, complemented
10#20286095C211yesmaximal, characteristic, complemented
11#20286092C211yesmaximal, characteristic, complemented
12#20286074C211yesmaximal, characteristic, complemented
13#20286072C211yesmaximal, characteristic, complemented
14#20286038C211yesmaximal, characteristic, complemented
15#20286036C211yesmaximal, characteristic, complemented
16#20286024C211yesmaximal, characteristic, complemented
17#20286021C211yesmaximal, characteristic, complemented
18#20284541C211yesmaximal, characteristic, complemented
19#20284539C211yesmaximal, characteristic, complemented
20#20284510C211yesmaximal, characteristic, complemented
21#20284502C211yesmaximal, characteristic, complemented
22#20284390C211yesmaximal, characteristic, complemented
23#20284388C211yesmaximal, characteristic, complemented
24#20284361C211yesmaximal, characteristic, complemented
25#20284358C211yesmaximal, characteristic, complemented
26#20284216C211yesmaximal, characteristic, complemented
27#20284216C211yesmaximal, characteristic, complemented
28#20284192C211yesmaximal, characteristic, complemented
29#459×D53C211yesmaximal, characteristic, complemented
30#20283282C211yesmaximal, characteristic, complemented
31C53×#3257C211yesmaximal, characteristic, complemented
32C2×#13133244C2211yescharacteristic
33C2×#13133244C2211yescharacteristic
34C2×D8×D53C2211yescharacteristic
35C2×D8×D53C2211yescharacteristic
36C2×#13133225C2211yescharacteristic
37C2×#13133223C2211yescharacteristic
38#16811357—21no—
39#16811357—21no—
40#16811291—21no—
41#16811291—21no—
42#16811265—21no—
43#16811265—21no—
44#16811262—21no—
45#16811262—21no—
46#16811250C2211yescharacteristic
47#16811245C2211yescharacteristic, complemented
48#16811243—21no—
49#16811229C2211yescharacteristic, complemented
50#16811228C2211yescharacteristic, complemented
51#16811228C2211yescharacteristic, complemented
52#16811227C2211yescharacteristic, complemented
53#16811225—21no—
54#16811224C2211yescharacteristic, complemented
55#16811212—21no—
56#16811207—21no—
57#16811203C2211yescharacteristic
58#16811191C2211yescharacteristic
59#16811189C2211yescharacteristic
60#16811189C2211yescharacteristic
61#16811189C2211yescharacteristic
62#16811179C2211yescharacteristic
63#16811174C2211yescharacteristic, complemented
64#16811172—21no—
65#16811170C2211yescharacteristic, complemented
66#16811170C2211yescharacteristic, complemented
67#16811168C2211yescharacteristic, complemented
68#16811168C2211yescharacteristic, complemented
69#16811168C2211yescharacteristic, complemented
70#127×D53C2211yescharacteristic
71#16811159C2211yescharacteristic, complemented
72#16811156—21no—
73#16811152C2211yescharacteristic, complemented
74#16811136—21no—
75#16811131—21no—
76#16811095C2211yescharacteristic
77#16811095C2211yescharacteristic
78C4×#11719949C2211yescharacteristic
79#16811091C2211yescharacteristic
80C4×D4×D53C2211yescharacteristic
81#16810930C2211yescharacteristic, complemented
82#16810926C2211yescharacteristic, complemented
83#16810925C2211yescharacteristic, complemented
84#16810924C2211yescharacteristic, complemented
85#16810924C2211yescharacteristic, complemented
86#16810924C2211yescharacteristic, complemented
87#16810924C2211yescharacteristic, complemented
88#16810923C2211yescharacteristic, complemented
89#16810923C2211yescharacteristic, complemented
90#16810923C2211yescharacteristic, complemented
91#16810922C2211yescharacteristic, complemented
92#16810921C2211yescharacteristic, complemented
93#16810920C2211yescharacteristic, complemented
94#16810920C2211yescharacteristic, complemented
95#16810916C2211yescharacteristic, complemented
96#16810912C2211yescharacteristic, complemented
97#16810912C2211yescharacteristic, complemented
98#16810912C2211yescharacteristic, complemented
99#16810911C2211yescharacteristic, complemented
100#16810911C2211yescharacteristic, complemented
101#16810910C2211yescharacteristic, complemented
102#16810906C2211yescharacteristic, complemented
103#16810902C2211yescharacteristic, complemented
104#16810902C2211yescharacteristic, complemented
105#16810902C2211yescharacteristic, complemented
106#16810901C2211yescharacteristic, complemented
107#16810901C2211yescharacteristic, complemented
108#16810900C2211yescharacteristic, complemented
109#16810877C2211yescharacteristic, complemented
110#16810877C2211yescharacteristic, complemented
111#16810876C2211yescharacteristic, complemented
112#16810876C2211yescharacteristic, complemented
113#16810875C2211yescharacteristic, complemented
114#16810875C2211yescharacteristic, complemented
115#16810875C2211yescharacteristic, complemented
116#16810874C2211yescharacteristic, complemented
117#16810874C2211yescharacteristic, complemented
118#16810874C2211yescharacteristic, complemented
119#16810873C2211yescharacteristic, complemented
120#16810872C2211yescharacteristic, complemented
121#16810871C2211yescharacteristic, complemented
122#16810866C2211yescharacteristic, complemented
123#16810860C2211yescharacteristic, complemented
124#16810860C2211yescharacteristic, complemented
125#16810859C2211yescharacteristic, complemented
126#16810859C2211yescharacteristic, complemented
127#16810858C2211yescharacteristic, complemented
128#16810858C2211yescharacteristic, complemented
129#16810858C2211yescharacteristic, complemented
130#16810857C2211yescharacteristic, complemented
131#16810857C2211yescharacteristic, complemented
132#16810857C2211yescharacteristic, complemented
133#16810856C2211yescharacteristic, complemented
134#16810855C2211yescharacteristic, complemented
135#16810854C2211yescharacteristic, complemented
136#16810849C2211yescharacteristic, complemented
137#16810841C2211yescharacteristic, complemented
138#16810841C2211yescharacteristic, complemented
139#16810840C2211yescharacteristic, complemented
140#16810840C2211yescharacteristic, complemented
141#16810835C2211yescharacteristic, complemented
142#16810835C2211yescharacteristic, complemented
143#16810823C2211yescharacteristic, complemented
144#16810821C2211yescharacteristic, complemented
145#16810821C2211yescharacteristic, complemented
146#16810819C2211yescharacteristic
147#16810819C2211yescharacteristic, complemented
148#16810819C2211yescharacteristic, complemented
149#16810819C2211yescharacteristic, complemented
150#16810818C2211yescharacteristic
151#16810818C2211yescharacteristic, complemented
152#16810818C2211yescharacteristic, complemented
153#16810817C2211yescharacteristic
154#16810817C2211yescharacteristic
155#16810817C2211yescharacteristic, complemented
156#16810817C2211yescharacteristic, complemented
157#16810817C2211yescharacteristic, complemented
158#16810817C2211yescharacteristic, complemented
159#16810816C2211yescharacteristic
160#16810816C2211yescharacteristic
161#16810816C2211yescharacteristic, complemented
162#16810816C2211yescharacteristic, complemented
163#16810815C2211yescharacteristic
164#16810815C2211yescharacteristic, complemented
165#16810664C2211yescharacteristic
166#16810662C2211yescharacteristic
167#16810660C2211yescharacteristic
168#16810658C2211yescharacteristic
169#16810650C2211yescharacteristic, complemented
170#16810648C2211yescharacteristic
171#16810648C2211yescharacteristic
172#16810648C2211yescharacteristic, complemented
173#16810648C2211yescharacteristic, complemented
174#16810646C2211yescharacteristic, complemented
175#16810645C2211yescharacteristic
176#16810645C2211yescharacteristic, complemented
177C2×#13133146C2211yescharacteristic, complemented
178C4⋊C8×D53C2211yescharacteristic
179C4⋊C8×D53C2211yescharacteristic, complemented
180#16810626C2211yescharacteristic
181#16810626C2211yescharacteristic
182#16810626C2211yescharacteristic
183#16810626C2211yescharacteristic
184#16810618C2211yescharacteristic
185#16810618C2211yescharacteristic
186#102×D53C2211yescharacteristic
187#102×D53C2211yescharacteristic
188C53×#542C2211yescharacteristic, complemented
189C53×#540C2211yescharacteristic, complemented
190C53×#479C2211yescharacteristic, complemented
191C53×#478C2211yescharacteristic, complemented
192C53×#476C2211yescharacteristic, complemented
193C53×#474C2211yescharacteristic, complemented
194C53×#469C2211yescharacteristic, complemented
195C53×#468C2211yescharacteristic, complemented
196C53×#466C2211yescharacteristic, complemented
197C53×#465C2211yescharacteristic, complemented
198C53×#463C2211yescharacteristic, complemented
199C53×#463C2211yescharacteristic, complemented
200C53×#460C2211yescharacteristic, complemented
201C53×#459C2211yescharacteristic
202C53×#424C2211yescharacteristic, complemented
203C2×#11719949—21no—
204C2×#11719949C2311yescharacteristic
205C2×#11719945—21no—
206C2×#11719945—21no—
207C2×#11719945C2311yescharacteristic
208C2×#11719947—21no—
209C2×#11719947—21no—
210C2×#11719947—21no—
211C2×D4×D53—21no—
212C2×D4×D53—21no—
213C2×D4×D53C2311yescharacteristic
214C2×D4×D53C2311yescharacteristic
215C2×D4×D53C2311yescharacteristic
216C22×C4×D53—21no—
217#13133244—42no—
218#13133244—42no—
219C2×#11719924C2311yescharacteristic
220C2×#11719924C2311yescharacteristic
221C2×D424C2311yescharacteristic
222C2×D424C2311yescharacteristic
223C2×D424C2311yescharacteristic
224C2×D424C2311yescharacteristic
225C2×#11719922C2311yescharacteristic
226C2×#11719922C2311yescharacteristic
227C2×#11719922C2311yescharacteristic
228C2×#11719922C2311yescharacteristic
229C2×#11719922C2311yescharacteristic
230C2×#11719922C2311yescharacteristic
231D8×D53—42no—
232D8×D53—42no—
233#13133225—42no—
234#13133223—42no—
235C2×#11719917C2311yescharacteristic
236C2×#11719912C2311yescharacteristic
237C2×#11719912C2311yescharacteristic
238C2×#11719912C2311yescharacteristic
239C2×#11719912C2311yescharacteristic
240C22×#88322C2311yescharacteristic
241C2×C8×D53C2311yescharacteristic
242C2×C8×D53C2311yescharacteristic
243C2×C8×D53C2311yescharacteristic
244C2×C8×D53C2311yescharacteristic
245#13133216C2311yescharacteristic
246#13133216C2311yescharacteristic
247#13133216C2311yescharacteristic
248#13133215—21no—
249#13133214C2311yescharacteristic
250#13133214C2311yescharacteristic
251#13133213—21no—
252#13133213—21no—
253#13133213—21no—
254#13133213—21no—
255#13133213—21no—
256#13133213C2311yescharacteristic
257#13133213C2311yescharacteristic
258#13133213C2311yescharacteristic
259#13133212—21no—
260#13133211—21no—
261#13133210—21no—
262#13133209C2311yescharacteristic
263#13133209C2311yescharacteristic
264#13133208C2311yescharacteristic
265#13133207—21no—
266#13133206—21no—
267#13133206C2311yescharacteristic
268#13133205—21no—
269#13133203—21no—
270#13133203—21no—
271#13133203—21no—
272#13133203—21no—
273#13133203—21no—
274#13133203—21no—
275#13133203—21no—
276#13133203—21no—
277#13133202—21no—
278#13133202—21no—
279#13133202—21no—
280#13133202—21no—
281#13133202—21no—
282#13133202—21no—
283#13133202—21no—
284#13133201—21no—
285#13133200—21no—
286#13133199—21no—
287#13133199—21no—
288#13133198—21no—
289#13133198—21no—
290#13133195—21no—
291#13133195—21no—
292#13133195—21no—
293#13133195—21no—
294#13133195—21no—
295#13133193—21no—
296#13133193C2311yescharacteristic
297#13133192—21no—
298#13133192—21no—
299#13133192—21no—
300#13133192—21no—
301#13133192C2311yescharacteristic
302#13133192C2311yescharacteristic
303#13133192C2311yescharacteristic
304#13133192C2311yescharacteristic
305#13133191—21no—
306#13133191C2311yescharacteristic
307#13133191C2311yescharacteristic
308#13133191C2311yescharacteristic
309#13133191C2311yescharacteristic
310#13133190—21no—
311#13133190—21no—
312#13133190—21no—
313#13133190—21no—
314#13133190—21no—
315#13133190—21no—
316#13133190—21no—
317#13133190—21no—
318#13133190—21no—
319#13133190—21no—
320#13133190—21no—
321#13133189—21no—
322#13133189—21no—
323#13133189—21no—
324#13133189—21no—
325#13133189—21no—
326#13133188C2311yescharacteristic
327#13133188C2311yescharacteristic
328#13133188C2311yescharacteristic
329#13133187—21no—
330#13133187—21no—
331#13133187—21no—
332#13133187—21no—
333#13133187—21no—
334#13133185—21no—
335#13133185—21no—
336#13133185—21no—
337Q8×Dic53C2311yescharacteristic
338#13133182—21no—
339#13133182—21no—
340#13133182D411yescharacteristic
341#13133182D411yescharacteristic
342C4×D212—21no—
343C4×D212C2311yescharacteristic
344C4×D212C2311yescharacteristic
345C4×D212C2311yescharacteristic
346C4×D212C2311yescharacteristic
347D4×Dic53C2311yescharacteristic
348D4×Dic53C2311yescharacteristic
349D4×Dic53C2311yescharacteristic
350#13133179—21no—
351#13133179—21no—
352#13133179D411yescharacteristic
353#13133179D411yescharacteristic
354#13133179C2311yescharacteristic
355#13133179C2311yescharacteristic
356#13133179C2311yescharacteristic
357#13133179C2311yescharacteristic
358C4×C22⋊D53—21no—
359C4×C22⋊D53—21no—
360C4×C22⋊D53—21no—
361C4×C22⋊D53—21no—
362C4×C22⋊D53—21no—
363#13133177—21no—
364#13133177—21no—
365#13133177—21no—
366#13133177—21no—
367#13133177—21no—
368#13133177—21no—
369#13133177—21no—
370#13133177—21no—
371#13133177D411yescharacteristic
372#13133177D411yescharacteristic
373#13133177D411yescharacteristic
374#13133177D411yescharacteristic
375#13133175—21no—
376#13133175—21no—
377#13133175C2311yescharacteristic
378#13133175C2311yescharacteristic
379#13133175C2311yescharacteristic
380#13133174C2311yescharacteristic
381#13133174C2311yescharacteristic
382#13133173—21no—
383C4⋊C4×D53C2311yescharacteristic
384C2×#11719921—21no—
385C2×#11719921—21no—
386C22⋊C4×D53—21no—
387C22⋊C4×D53—21no—
388C22⋊C4×D53—21no—
389C2×C4×Dic53C2311yescharacteristic
390C42×D53—21no—
391C42×D53C2311yescharacteristic
392C42×D53C2311yescharacteristic
393#13133151C2311yescharacteristic
394#13133151C2311yescharacteristic
395#13133150C2311yescharacteristic
396#13133150C2311yescharacteristic
397#13133150C2311yescharacteristic
398#13133150C2311yescharacteristic
399#13133149C2311yescharacteristic
400#13133149C2311yescharacteristic
401#13133148C2311yescharacteristic
402#13133148C2311yescharacteristic
403#13133148C2311yescharacteristic
404#13133148C2311yescharacteristic
405C4⋊#88322C2311yescharacteristic
406C4⋊#88322C2311yescharacteristic
407C4⋊#88322C2311yescharacteristic
408C4⋊#88322C2311yescharacteristic
409#13133146C2311yescharacteristic
410#13133146C2311yescharacteristic
411#13133146C2311yescharacteristic
412#13133146C2311yescharacteristic
413#13133146C2311yescharacteristic
414#13133146C2311yescharacteristic
415#13133146C2311yescharacteristic
416#13133146C2311yescharacteristic
417#13133141C2311yescharacteristic
418#13133141C2311yescharacteristic
419#13133139C2311yescharacteristic
420#13133139C2311yescharacteristic
421#13133139C2311yescharacteristic
422#13133139C2311yescharacteristic
423#13133139C2311yescharacteristic
424#13133139C2311yescharacteristic
425#13133139C2311yescharacteristic
426#13133139C2311yescharacteristic
427#13133138C2311yescharacteristic
428#13133138C2311yescharacteristic
429#13133138C2311yescharacteristic
430#13133138C2311yescharacteristic
431#13133138C2311yescharacteristic
432#13133138C2311yescharacteristic
433#13133137C2311yescharacteristic
434#13133137C2311yescharacteristic
435#13133137C2311yescharacteristic
436#13133137C2311yescharacteristic
437#13133137C2311yescharacteristic
438#13133137C2311yescharacteristic
439#13133137C2311yescharacteristic
440#13133137C2311yescharacteristic
441C2×SD16×C53C2311yescharacteristic
442C2×SD16×C53C2311yescharacteristic
443C2×D8×C53C2311yescharacteristic
444C2×D8×C53C2311yescharacteristic
445C2×M16×C53C2311yescharacteristic
446C22×C8×C53C2311yescharacteristic
447C4⋊Q8×C53C2311yescharacteristic
448#127×C53C2311yescharacteristic
449#126×C53—21no—
450#125×C53C2311yescharacteristic
451#124×C53—21no—
452#124×C53C2311yescharacteristic
453#123×C53—21no—
454#123×C53—21no—
455#123×C53—21no—
456C22⋊Q8×C53—21no—
457C22⋊Q8×C53C2311yescharacteristic
458#121×C53—21no—
459#121×C53—21no—
460#121×C53C2311yescharacteristic
461#121×C53C2311yescharacteristic
462#121×C53C2311yescharacteristic
463C4×Q8×C53C2311yescharacteristic
464C4×D4×C53C2311yescharacteristic
465C4×D4×C53C2311yescharacteristic
466C4×D4×C53C2311yescharacteristic
467#117×C53C2311yescharacteristic
468#107×C53C2311yescharacteristic
469#107×C53C2311yescharacteristic
470#106×C53C2311yescharacteristic
471#106×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
484C23×D53—21no—
485C23×D53—21no—
486C23×D53—21no—
487C2×Q8×C53—21no—
488C2×Q8×C53C2411yescharacteristic
489C2×D4×C53—21no—
490C2×D4×C53—21no—
491C2×D4×C53—21no—
492C2×D4×C53—21no—
493C2×D4×C53—21no—
494C2×D4×C53C2411yescharacteristic
495C2×D4×C53C2411yescharacteristic
496C2×D4×C53C2411yescharacteristic
497C22×C4×C53—21no—
498C22×C4×C53—21no—
499C22×C4×C53—21no—
500C22×C4×C53C2411yescharacteristic
501C2×C22⋊D53—21no—
502C2×C22⋊D53—21no—
503C2×C22⋊D53—21no—
504C2×C22⋊D53—21no—
505C2×C22⋊D53—21no—
506C2×C22⋊D53—21no—
507C2×C22⋊D53—21no—
508C2×C22⋊D53—21no—
509C2×C22⋊D53—21no—
510C2×C22⋊D53—21no—
511C2×C22⋊D53—21no—
512C2×C22⋊D53—21no—
513C2×C22⋊D53—21no—
514C2×C22⋊D53—21no—
515C2×C22⋊D53—21no—
516C2×C22⋊D53—21no—
517C2×C22⋊D53C2×D411yescharacteristic
518C2×C22⋊D53C2×D411yescharacteristic
519C22×Dic53—21no—
520C22×Dic53—21no—
521C22×Dic53—21no—
522C22×Dic53C2×D411yescharacteristic
523C22×Dic53C2×D411yescharacteristic
524#11719949—22no—
525#11719949—22no—
526#11719949—82no—
527#11719947—82no—
528#11719947—82no—
529#11719947—82no—
530D4×D53—22no—
531D4×D53—22no—
532D4×D53—22no—
533D4×D53—22no—
534D4×D53—22no—
535D4×D53—22no—
536D4×D53—82no—
537D4×D53—82no—
538#11719945—22no—
539#11719945—22no—
540#11719945—82no—
541#11719945—82no—
542C2×D212—21no—
543C2×D212—21no—
544C2×D212—21no—
545C2×D212—21no—
546C2×D212—21no—
547C2×D212—21no—
548C2×D212—21no—
549C2×D212—21no—
550C2×D212—21no—
551C2×D212C2×D411yescharacteristic
552C2×D212C2411yescharacteristic
553C2×D212C2411yescharacteristic
554C2×D212C2411yescharacteristic
555C2×D212C2411yescharacteristic
556C2×C4×D53—21no—
557C2×C4×D53—21no—
558C2×C4×D53—21no—
559C2×C4×D53—21no—
560C2×C4×D53—21no—
561C2×C4×D53—21no—
562C2×C4×D53—21no—
563C2×C4×D53—21no—
564C2×C4×D53—21no—
565C2×C4×D53—21no—
566C2×C4×D53—82no—
567C2×C4×D53C2×D411yescharacteristic
568C2×C4×D53C2×D411yescharacteristic
569C2×C4×D53C2×D411yescharacteristic
570C2×C4×D53C2×D411yescharacteristic
571C2×C4×D53C2411yescharacteristic
572C2×C4×D53C2411yescharacteristic
573C2×Dic106—21no—
574C2×Dic106—21no—
575C2×Dic106—21no—
576C2×Dic106C2×D411yescharacteristic
577SD16×C53—41no—
578SD16×C53—41no—
579D8×C53—41no—
580D8×C53—41no—
581M16×C53—41no—
582C2×C8×C53—41no—
583C2×C8×C53C2411yescharacteristic
584C2×C8×C53C2411yescharacteristic
585C2×C8×C53C2411yescharacteristic
586C2×C8×C53C2411yescharacteristic
587C4⋊C4×C53—21no—
588C4⋊C4×C53—21no—
589C4⋊C4×C53—21no—
590C4⋊C4×C53—21no—
591C4⋊C4×C53—21no—
592C4⋊C4×C53C2×D411yescharacteristic
593C4⋊C4×C53C2×D411yescharacteristic
594C4⋊C4×C53C2411yescharacteristic
595C4⋊C4×C53C2411yescharacteristic
596C4⋊C4×C53C2411yescharacteristic
597C4⋊C4×C53C2411yescharacteristic
598C22⋊C4×C53—21no—
599C22⋊C4×C53—21no—
600C22⋊C4×C53—21no—
601C22⋊C4×C53—21no—
602C22⋊C4×C53—21no—
603C22⋊C4×C53—21no—
604C22⋊C4×C53—21no—
605C22⋊C4×C53—21no—
606C22⋊C4×C53—21no—
607C22⋊C4×C53C2×D411yescharacteristic
608C22⋊C4×C53C2×D411yescharacteristic
609C42×C53—21no—
610C42×C53C2411yescharacteristic
611C42×C53C2411yescharacteristic
612C22⋊Dic53—21no—
613C22⋊Dic53—21no—
614C22⋊Dic53—21no—
615C22⋊Dic53—21no—
616C22⋊Dic53—21no—
617C22⋊Dic53—21no—
618#11719924—41no—
619#11719924—41no—
620#11719922—41no—
621#11719922—41no—
622#11719922—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#11719921—21no—
647#11719921—21no—
648#11719921C2×D411yescharacteristic
649#11719921C2×D411yescharacteristic
650#11719921C2×D411yescharacteristic
651#11719921C2×D411yescharacteristic
652C4⋊Dic53—21no—
653C4⋊Dic53—21no—
654C4⋊Dic53C2411yescharacteristic
655C4⋊Dic53C2411yescharacteristic
656C4⋊Dic53C2411yescharacteristic
657C4⋊Dic53C2411yescharacteristic
658#11719919—21no—
659#11719919—21no—
660#11719919—21no—
661#11719919—21no—
662#11719919—21no—
663#11719919—21no—
664#11719919—21no—
665#11719919—21no—
666#11719919—21no—
667#11719919—21no—
668#11719919C2×D411yescharacteristic
669#11719919C2×D411yescharacteristic
670#11719919C2×D411yescharacteristic
671#11719919C2×D411yescharacteristic
672C4×Dic53—21no—
673C4×Dic53—21no—
674C4×Dic53—21no—
675C4×Dic53—21no—
676C4×Dic53C2×D411yescharacteristic
677C4×Dic53C2×D411yescharacteristic
678C4×Dic53C2×D411yescharacteristic
679C4×Dic53C2×D411yescharacteristic
680C4×Dic53C2×D411yescharacteristic
681C4×Dic53C2×D411yescharacteristic
682C4×Dic53C2411yescharacteristic
683C4×Dic53C2411yescharacteristic
684#11719917—41no—
685C2×#88322—41no—
686C2×#88322C2411yescharacteristic
687C2×#88322C2411yescharacteristic
688C2×#88322C2411yescharacteristic
689C2×#88322C2411yescharacteristic
690D424—41no—
691D424—41no—
692D424—41no—
693D424—41no—
694#11719912—22no—
695#11719912—22no—
696#11719912—41no—
697#11719912—41no—
698C8×D53—22no—
699C8×D53—22no—
700C8×D53—41no—
701C8×D53—41no—
702C23×C53—21no—
703C23×C53—21no—
704C23×C53—21no—
705C23×C53C22×D411yescharacteristic
706C22×D53—21no—
707C22×D53—21no—
708C22×D53—21no—
709C22×D53—21no—
710C22×D53—42no—
711C22×D53—42no—
712C22×D53—42no—
713C22×D53—81no—
714C22×D53—81no—
715C22×D53—81no—
716C22×D53—81no—
717C22×D53—81no—
718C22×D53—81no—
719C22×D53C22×D411yescharacteristic
720C22×D53C22×D411yescharacteristic
721Q8×C53—21no—
722Q8×C53—21no—
723Q8×C53—81no—
724D4×C53—21no—
725D4×C53—21no—
726D4×C53—21no—
727D4×C53—21no—
728D4×C53—21no—
729D4×C53—21no—
730D4×C53—81no—
731D4×C53—81no—
732D4×C53—81no—
733D4×C53—81no—
734D4×C53—81no—
735C2×C4×C53—21no—
736C2×C4×C53—21no—
737C2×C4×C53—21no—
738C2×C4×C53—21no—
739C2×C4×C53—21no—
740C2×C4×C53—21no—
741C2×C4×C53—21no—
742C2×C4×C53—81no—
743C2×C4×C53—81no—
744C2×C4×C53—81no—
745C2×C4×C53C22×D411yescharacteristic
746C2×C4×C53C22×D411yescharacteristic
747C2×C4×C53C22×D411yescharacteristic
748C2×C4×C53C22×D411yescharacteristic
749C2×C4×C53C22×D411yescharacteristic
750C2×C4×C53C2511yescharacteristic
751C22⋊D53—22no—
752C22⋊D53—22no—
753C22⋊D53—42no—
754C22⋊D53—42no—
755C22⋊D53—42no—
756C22⋊D53—42no—
757C22⋊D53—42no—
758C22⋊D53—42no—
759C22⋊D53—42no—
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—
769C2×Dic53—22no—
770C2×Dic53—21no—
771C2×Dic53—21no—
772C2×Dic53—21no—
773C2×Dic53—21no—
774C2×Dic53—41no—
775C2×Dic53—42no—
776C2×Dic53—81no—
777C2×Dic53—81no—
778C2×Dic53C22×D411yescharacteristic
779C2×Dic53C22×D411yescharacteristic
780C2×Dic53C22×D411yescharacteristic
781C2×Dic53C22×D411yescharacteristic
782C2×Dic53C22×D411yescharacteristic
783C2×Dic53C22×D411yescharacteristic
784D212—22no—
785D212—21no—
786D212—21no—
787D212—21no—
788D212—21no—
789D212—21no—
790D212—21no—
791D212—21no—
792D212—21no—
793D212—42no—
794D212—81no—
795D212—81no—
796D212—81no—
797D212—81no—
798D212—81no—
799D212—81no—
800D212—81no—
801D212—81no—
802C4×D53—21no—
803C4×D53—21no—
804C4×D53—22no—
805C4×D53—22no—
806C4×D53—41no—
807C4×D53—41no—
808C4×D53—42no—
809C4×D53—42no—
810C4×D53—42no—
811C4×D53—81no—
812C4×D53—81no—
813C4×D53—81no—
814C4×D53—81no—
815C4×D53—81no—
816C4×D53—81no—
817C4×D53—81no—
818C4×D53H(5,𝔽2)12yes—
819C4×D532−1+412yes—
820Dic106—22no—
821Dic106—42no—
822Dic106—42no—
823Dic106—81no—
824C8×C53—21no—
825C8×C53—21no—
826C8×C53—21no—
827C8×C53—21no—
828#88322—21no—
829#88322—21no—
830#88322—21no—
831#88322—21no—
832#60922—531nomaximal, Sylow
833C22×C53—21no—
834C22×C53—21no—
835C22×C53—21no—
836C22×C53—41no—
837C22×C53—41no—
838C22×C53—41no—
839C22×C53—41no—
840C22×C53—41no—
841C22×C53—41no—
842C22×C53—41no—
843C22×C53—41no—
844C22×C53—41no—
845C22×C53C23×D411yescharacteristic
846C2×D53—21no—
847C2×D53—21no—
848C2×D53—21no—
849C2×D53—21no—
850C2×D53—21no—
851C2×D53—41no—
852C2×D53—41no—
853C2×D53—41no—
854C2×D53—41no—
855C2×D53—41no—
856C2×D53—41no—
857C2×D53—41no—
858C2×D53—41no—
859C2×D53—41no—
860C2×D53—41no—
861C2×D53—41no—
862C2×D53—41no—
863C2×D53—84no—
864C2×D53—162no—
865C2×D53—162no—
866C2×D53#53712yes—
867C4×C53—21no—
868C4×C53—21no—
869C4×C53—21no—
870C4×C53—21no—
871C4×C53—21no—
872C4×C53—41no—
873C4×C53—41no—
874C4×C53—41no—
875C4×C53—41no—
876C4×C53—41no—
877C4×C53C2×H(5,𝔽2)11yescharacteristic
878C4×C53C2×2−1+411yescharacteristic
879Dic53—21no—
880Dic53—21no—
881Dic53—21no—
882Dic53—21no—
883Dic53—41no—
884Dic53—41no—
885Dic53—41no—
886Dic53—41no—
887Dic53#53712yes—
888Dic53#57612yes—
889#3508—531no—
890#3460—531no—
891#3259—531no—
892#3259—531no—
893#3259—531no—
894#3259—531no—
895#3257—531no—
896#3257—531no—
897#3257—531no—
898#3257D5311yescharacteristic, complemented
899#3253—531no—
900#3253—531no—
901#3251—531no—
902#3251—531no—
903#3247—531no—
904#3247—531no—
905#3245—531no—
906#3245—531no—
907#3081—531no—
908#3081—531no—
909#3077—531no—
910#3076—531no—
911#3062—531no—
912#3062—531no—
913#3058—531no—
914#3058—531no—
915#3041—531no—
916#3041—531no—
917#3038—531no—
918C2×#459—531no—
919#2906—531no—
920C2×C53—41no—
921C2×C53—81no—
922C2×C53—81no—
923C2×C53—81no—
924C2×C53C2×#53711yescharacteristic
925C2×C53C2×#57611yescharacteristic
926C2×C53#358511yescharacteristic
927D53—22no—
928D53—41no—
929D53—81no—
930D53—81no—
931D53—81no—
932D53—81no—
933C2×AGL(1,ℤ/8)—531no—
934C2×AGL(1,ℤ/8)—531no—
935C22×D8—531no—
936C22×D8—531no—
937C2×#131—531no—
938C2×#131—531no—
939#559—1061no—
940#559—1061no—
941#550—1061no—
942#550—1061no—
943#546—1061no—
944#546—1061no—
945#546—1061no—
946#546—1061no—
947#544—531no—
948#542—531no—
949#542—1061no—
950#542C2×D5311yescharacteristic, complemented
951#540—531no—
952#540—531no—
953#540—531no—
954#540—531no—
955#540—531no—
956#540—1061no—
957#540C2×D5311yescharacteristic, complemented
958#538—1061no—
959#538—1061no—
960#537—531no—
961#535—531no—
962#535—531no—
963#535—531no—
964#535—531no—
965#533—531no—
966#532—531no—
967#532—531no—
968#532—531no—
969#532—531no—
970#532—531no—
971#532—531no—
972#532—1061no—
973C2×#127—531no—
974#529—531no—
975#529—531no—
976#529—1061no—
977#525—1061no—
978#525—1061no—
979#518—531no—
980#518—531no—
981C4×#41—531no—
982C4×#41—531no—
983C2×C4×D4—531no—
984#479—531no—
985#479C2×D5311yescharacteristic, complemented
986#478—531no—
987#478—531no—
988#478—531no—
989#478—531no—
990#478—531no—
991#478—531no—
992#478—531no—
993#478—531no—
994#478—531no—
995#478—531no—
996#478—531no—
997#478—531no—
998#478—531no—
999#478C2×D5311yescharacteristic, complemented
1000#477—531no—
1001#476—531no—
1002#476—531no—
1003#476—531no—
1004#476—531no—
1005#476—531no—
1006#476—531no—
1007#476C2×D5311yescharacteristic, complemented
1008#475—531no—
1009#474—531no—
1010#474—531no—
1011#474—531no—
1012#474—531no—
1013#474—531no—
1014#474—531no—
1015#474C2×D5311yescharacteristic, complemented
1016#469—531no—
1017#469—531no—
1018#469—531no—
1019#469—531no—
1020#469—531no—
1021#469—531no—
1022#469—531no—
1023#469—531no—
1024#469—531no—
1025#469—531no—
1026#469—531no—
1027#469C2×D5311yescharacteristic, complemented
1028#468—531no—
1029#468—531no—
1030#468—531no—
1031#468C2×D5311yescharacteristic, complemented
1032#466—531no—
1033#466—531no—
1034#466—531no—
1035#466—531no—
1036#466—531no—
1037#466—531no—
1038#466—531no—
1039#466—531no—
1040#466—531no—
1041#466—531no—
1042#466—531no—
1043#466C2×D5311yescharacteristic, complemented
1044#465—531no—
1045#465—531no—
1046#465—531no—
1047#465C2×D5311yescharacteristic, complemented
1048#463—531no—
1049#463—531no—
1050#463—531no—
1051#463—531no—
1052#463—531no—
1053#463—531no—
1054#463C2×D5311yescharacteristic, complemented
1055#463C2×D5311yescharacteristic, complemented
1056#460—531no—
1057#460—531no—
1058#460—531no—
1059#460C2×D5311yescharacteristic, complemented
1060#459—531no—
1061#459—531no—
1062#459—531no—
1063#459—531no—
1064#459—531no—
1065#459—531no—
1066#459—531no—
1067#459—531no—
1068#459—531no—
1069#459—531no—
1070#459—531no—
1071#459—531no—
1072#459—531no—
1073#459—531no—
1074#459—531no—
1075#459—531no—
1076#459—531no—
1077#459—531no—
1078#459—531no—
1079#459C2×D5311yescharacteristic
1080#428—531no—
1081#428—531no—
1082#427—531no—
1083#427—531no—
1084#424—531no—
1085#424—531no—
1086#424—531no—
1087#424—531no—
1088#424—531no—
1089#424C2×D5311yescharacteristic, complemented
1090#423—531no—
1091#423—531no—
1092#423—531no—
1093C2×C4⋊C8—531no—
1094C2×C4⋊C8—531no—
1095C2×C4⋊C8—531no—
1096#418—531no—
1097#418—531no—
1098#418—531no—
1099#418—531no—
1100#416—531no—
1101#416—531no—
1102C2×#102—531no—
1103C2×#102—531no—
1104C53#6092211yescharacteristic, complemented, Sylow
1105C2×#41—531no—
1106C2×#41—531no—
1107C2×#41—1061no—
1108C2×#41—1061no—
1109C2×#41—1061no—
1110C2×#41—1061no—
1111C2×#41—1061no—
1112C2×#41—1061no—
1113C22×D4—531no—
1114C22×D4—531no—
1115C22×D4—531no—
1116C22×D4—1061no—
1117C22×D4—1061no—
1118C23×C4—1061no—
1119AGL(1,ℤ/8)—2122no—
1120AGL(1,ℤ/8)—2122no—
1121C2×SD16—531no—
1122C2×SD16—531no—
1123C2×SD16C22×D5311yescharacteristic
1124C2×SD16C22×D5311yescharacteristic
1125C2×D8—531no—
1126C2×D8—531no—
1127C2×D8—531no—
1128C2×D8—531no—
1129C2×D8—531no—
1130C2×D8—531no—
1131C2×D8—531no—
1132C2×D8—531no—
1133C2×D8—531no—
1134C2×D8—531no—
1135C2×D8—2122no—
1136C2×D8—2122no—
1137C2×D8C22×D5311yescharacteristic
1138C2×D8C22×D5311yescharacteristic
1139#131—2122no—
1140#131—2122no—
1141C2×M16—531no—
1142C2×M16—531no—
1143C2×M16—531no—
1144C2×M16—531no—
1145C2×M16—531no—
1146C2×M16C22×D5311yescharacteristic
1147C22×C8—531no—
1148C22×C8—531no—
1149C22×C8—531no—
1150C22×C8—531no—
1151C22×C8—531no—
1152C22×C8C22×D5311yescharacteristic
1153C4⋊Q8—531no—
1154C4⋊Q8—531no—
1155C4⋊Q8—531no—
1156C4⋊Q8—1061no—
1157C4⋊Q8C22×D5311yescharacteristic
1158#127—531no—
1159#127—531no—
1160#127—531no—
1161#127—531no—
1162#127—531no—
1163#127—1061no—
1164#127—1061no—
1165#127—1061no—
1166#127—1061no—
1167#127—1061no—
1168#127C22×D5311yescharacteristic
1169#126—21no—
1170#126—1061no—
1171#126—1061no—
1172#126—1061no—
1173#125—531no—
1174#125—531no—
1175#125—531no—
1176#125—1061no—
1177#125C22×D5311yescharacteristic
1178#124—21no—
1179#124—531no—
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#124—1061no—
1189#124—1061no—
1190#124C22×D5311yescharacteristic
1191#123—21no—
1192#123—21no—
1193#123—21no—
1194#123—1061no—
1195#123—1061no—
1196#123—1061no—
1197#123—1061no—
1198#123—1061no—
1199#123—1061no—
1200#123—1061no—
1201#123—1061no—
1202#123—1061no—
1203#123—1061no—
1204#123—1061no—
1205#123—1061no—
1206#123—1061no—
1207C22⋊Q8—21no—
1208C22⋊Q8—531no—
1209C22⋊Q8—1061no—
1210C22⋊Q8—1061no—
1211C22⋊Q8—1061no—
1212C22⋊Q8—1061no—
1213C22⋊Q8—1061no—
1214C22⋊Q8—1061no—
1215C22⋊Q8C22×D5311yescharacteristic
1216#121—21no—
1217#121—21no—
1218#121—531no—
1219#121—531no—
1220#121—531no—
1221#121—531no—
1222#121—531no—
1223#121—531no—
1224#121—531no—
1225#121—531no—
1226#121—531no—
1227#121—531no—
1228#121—531no—
1229#121—1061no—
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#121—1061no—
1243#121—1061no—
1244#121—1061no—
1245#121—1061no—
1246#121—1061no—
1247#121—1061no—
1248#121—1061no—
1249#121—1061no—
1250#121C22×D5311yescharacteristic
1251#121C22×D5311yescharacteristic
1252#121C22×D5311yescharacteristic
1253#120—1061no—
1254#120—1061no—
1255#120—1061no—
1256#120—1061no—
1257#120—1061no—
1258#120—1061no—
1259#120—1061no—
1260#120—1061no—
1261C4×Q8—531no—
1262C4×Q8—531no—
1263C4×Q8—531no—
1264C4×Q8—1061no—
1265C4×Q8—1061no—
1266C4×Q8C22×D5311yescharacteristic
1267C4×D4—531no—
1268C4×D4—531no—
1269C4×D4—531no—
1270C4×D4—531no—
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—531no—
1281C4×D4—531no—
1282C4×D4—531no—
1283C4×D4—531no—
1284C4×D4—1061no—
1285C4×D4—1061no—
1286C4×D4—1061no—
1287C4×D4—1061no—
1288C4×D4—1061no—
1289C4×D4—1061no—
1290C4×D4—1061no—
1291C4×D4—1061no—
1292C4×D4—1061no—
1293C4×D4—1061no—
1294C4×D4—1061no—
1295C4×D4—1061no—
1296C4×D4—1061no—
1297C4×D4—1061no—
1298C4×D4—1061no—
1299C4×D4—1061no—
1300C4×D4C22×D5311yescharacteristic
1301C4×D4C22×D5311yescharacteristic
1302C4×D4C22×D5311yescharacteristic
1303#117—531no—
1304#117—531no—
1305#117—531no—
1306#117—531no—
1307#117—531no—
1308#117—1061no—
1309#117—1061no—
1310#117—1061no—
1311#117C22×D5311yescharacteristic
1312C2×C4⋊C4—531no—
1313C2×C22⋊C4—1061no—
1314C2×C22⋊C4—1061no—
1315C2×C22⋊C4—1061no—
1316C2×C22⋊C4—1061no—
1317C2×C22⋊C4—1061no—
1318C2×C42—531no—
1319C2×C42—531no—
1320C2×C42—531no—
1321C2×C42—1061no—
1322#107—531no—
1323#107—531no—
1324#107—531no—
1325#107—531no—
1326#107—531no—
1327#107—531no—
1328#107C22×D5311yescharacteristic
1329#107C22×D5311yescharacteristic
1330#106—531no—
1331#106—531no—
1332#106—531no—
1333#106—531no—
1334#106—531no—
1335#106—531no—
1336#106C22×D5311yescharacteristic
1337#106C22×D5311yescharacteristic
1338C4⋊C8—531no—
1339C4⋊C8—531no—
1340C4⋊C8—531no—
1341C4⋊C8—531no—
1342C4⋊C8—531no—
1343C4⋊C8—531no—
1344C4⋊C8—531no—
1345C4⋊C8—531no—
1346C4⋊C8—531no—
1347C4⋊C8—531no—
1348C4⋊C8—531no—
1349C4⋊C8—531no—
1350C4⋊C8C22×D5311yescharacteristic
1351C4⋊C8C22×D5311yescharacteristic
1352C4⋊C8C22×D5311yescharacteristic
1353C4⋊C8C22×D5311yescharacteristic
1354#103—531no—
1355#103—531no—
1356#103C22×D5311yescharacteristic
1357#103C22×D5311yescharacteristic
1358#102—531no—
1359#102—531no—
1360#102—531no—
1361#102—531no—
1362#102—531no—
1363#102—531no—
1364#102—531no—
1365#102—531no—
1366#102—531no—
1367#102—531no—
1368#102—531no—
1369#102—531no—
1370#102—531no—
1371#102—531no—
1372#102—531no—
1373#102—531no—
1374#102—531no—
1375#102—531no—
1376#102—531no—
1377#102—531no—
1378#102—531no—
1379#102—531no—
1380#102C22×D5311yescharacteristic
1381#102C22×D5311yescharacteristic
1382#102C22×D5311yescharacteristic
1383#102C22×D5311yescharacteristic
1384#102C22×D5311yescharacteristic
1385#102C22×D5311yescharacteristic
1386C24—1061no—
1387C24—1061no—
1388C24—1061no—
1389#41—1062no—
1390#41—1062no—
1391#41—1062no—
1392#41—1062no—
1393#41—4242no—
1394#41—4242no—
1395#41—4242no—
1396#41—4242no—
1397#41—4242no—
1398#41—4242no—
1399C2×Q8—21no—
1400C2×Q8—531no—
1401C2×Q8—1061no—
1402C2×Q8—1061no—
1403C2×Q8—1061no—
1404C2×Q8C23×D5311yescharacteristic
1405C2×D4—21no—
1406C2×D4—21no—
1407C2×D4—21no—
1408C2×D4—21no—
1409C2×D4—21no—
1410C2×D4—531no—
1411C2×D4—531no—
1412C2×D4—531no—
1413C2×D4—531no—
1414C2×D4—531no—
1415C2×D4—531no—
1416C2×D4—531no—
1417C2×D4—1061no—
1418C2×D4—1061no—
1419C2×D4—1061no—
1420C2×D4—1061no—
1421C2×D4—1061no—
1422C2×D4—1062no—
1423C2×D4—1062no—
1424C2×D4—1062no—
1425C2×D4—1062no—
1426C2×D4—1062no—
1427C2×D4—1062no—
1428C2×D4—1061no—
1429C2×D4—1061no—
1430C2×D4—1061no—
1431C2×D4—1061no—
1432C2×D4—1061no—
1433C2×D4—1061no—
1434C2×D4—1061no—
1435C2×D4—1061no—
1436C2×D4—1061no—
1437C2×D4—1061no—
1438C2×D4—1061no—
1439C2×D4—1061no—
1440C2×D4—1061no—
1441C2×D4—1061no—
1442C2×D4—1061no—
1443C2×D4—1061no—
1444C2×D4—1061no—
1445C2×D4—1061no—
1446C2×D4—1061no—
1447C2×D4—1061no—
1448C2×D4—4242no—
1449C2×D4—4242no—
1450C2×D4C23×D5311yescharacteristic
1451C2×D4C23×D5311yescharacteristic
1452C2×D4C23×D5311yescharacteristic
1453C22×C4—21no—
1454C22×C4—21no—
1455C22×C4—21no—
1456C22×C4—531no—
1457C22×C4—531no—
1458C22×C4—531no—
1459C22×C4—531no—
1460C22×C4—531no—
1461C22×C4—531no—
1462C22×C4—531no—
1463C22×C4—531no—
1464C22×C4—1061no—
1465C22×C4—1061no—
1466C22×C4—1061no—
1467C22×C4—1061no—
1468C22×C4—1061no—
1469C22×C4—1061no—
1470C22×C4—1061no—
1471C22×C4—1061no—
1472C22×C4—1061no—
1473C22×C4—1061no—
1474C22×C4—1061no—
1475C22×C4—1061no—
1476C22×C4—1061no—
1477C22×C4—4242no—
1478C22×C4C23×D5311yescharacteristic
1479SD16—41no—
1480SD16—41no—
1481SD16—2121no—
1482SD16—2121no—
1483D8—41no—
1484D8—41no—
1485D8—2121no—
1486D8—2121no—
1487D8—2121no—
1488D8—2121no—
1489D8—2121no—
1490D8—2121no—
1491D8—2121no—
1492D8—2121no—
1493D8—2121no—
1494D8—2121no—
1495M16—41no—
1496M16—1062no—
1497M16—1062no—
1498M16—2121no—
1499M16—2121no—
1500M16—2121no—
1501C2×C8—41no—
1502C2×C8—531no—
1503C2×C8—531no—
1504C2×C8—531no—
1505C2×C8—531no—
1506C2×C8—1062no—
1507C2×C8—1062no—
1508C2×C8—2121no—
1509C2×C8—2121no—
1510C2×C8—2121no—
1511C2×C8C23×D5311yescharacteristic
1512C2×C8C23×D5311yescharacteristic
1513C2×C8C23×D5311yescharacteristic
1514C2×C8C23×D5311yescharacteristic
1515C4⋊C4—21no—
1516C4⋊C4—21no—
1517C4⋊C4—21no—
1518C4⋊C4—21no—
1519C4⋊C4—21no—
1520C4⋊C4—531no—
1521C4⋊C4—531no—
1522C4⋊C4—531no—
1523C4⋊C4—531no—
1524C4⋊C4—531no—
1525C4⋊C4—531no—
1526C4⋊C4—531no—
1527C4⋊C4—531no—
1528C4⋊C4—1061no—
1529C4⋊C4—1061no—
1530C4⋊C4—1061no—
1531C4⋊C4—1061no—
1532C4⋊C4—1061no—
1533C4⋊C4—1061no—
1534C4⋊C4—1061no—
1535C4⋊C4—1061no—
1536C4⋊C4—1061no—
1537C4⋊C4—1061no—
1538C4⋊C4—1061no—
1539C4⋊C4—1061no—
1540C4⋊C4D4×D5311yescharacteristic
1541C4⋊C4D4×D5311yescharacteristic
1542C4⋊C4C23×D5311yescharacteristic
1543C4⋊C4C23×D5311yescharacteristic
1544C4⋊C4C23×D5311yescharacteristic
1545C4⋊C4C23×D5311yescharacteristic
1546C22⋊C4—21no—
1547C22⋊C4—21no—
1548C22⋊C4—21no—
1549C22⋊C4—21no—
1550C22⋊C4—21no—
1551C22⋊C4—21no—
1552C22⋊C4—21no—
1553C22⋊C4—21no—
1554C22⋊C4—21no—
1555C22⋊C4—531no—
1556C22⋊C4—531no—
1557C22⋊C4—531no—
1558C22⋊C4—531no—
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⋊C4—1061no—
1573C22⋊C4—1061no—
1574C22⋊C4—1061no—
1575C22⋊C4—1061no—
1576C22⋊C4—1061no—
1577C22⋊C4—1061no—
1578C22⋊C4—1061no—
1579C22⋊C4—1061no—
1580C22⋊C4—1061no—
1581C22⋊C4—1061no—
1582C22⋊C4—1061no—
1583C22⋊C4—1061no—
1584C22⋊C4—1061no—
1585C22⋊C4—1061no—
1586C22⋊C4—1061no—
1587C22⋊C4D4×D5311yescharacteristic
1588C22⋊C4D4×D5311yescharacteristic
1589C42—21no—
1590C42—531no—
1591C42—531no—
1592C42—531no—
1593C42—531no—
1594C42—531no—
1595C42—531no—
1596C42—531no—
1597C42—531no—
1598C42—1061no—
1599C42—1061no—
1600C42—1061no—
1601C42—1061no—
1602C42C23×D5311yescharacteristic
1603C42C23×D5311yescharacteristic
1604C23—21no—
1605C23—21no—
1606C23—21no—
1607C23—531no—
1608C23—531no—
1609C23—1061no—
1610C23—1061no—
1611C23—1061no—
1612C23—1061no—
1613C23—4241no—
1614C23—4241no—
1615C23—4241no—
1616C23—4241no—
1617C23—4241no—
1618C23—4241no—
1619C23—2122no—
1620C23—2122no—
1621C23—2122no—
1622C23C2×D4×D5311yescharacteristic
1623Q8—21no—
1624Q8—21no—
1625Q8—81no—
1626Q8—1062no—
1627Q8—4241no—
1628Q8—2122no—
1629Q8—2122no—
1630D4—21no—
1631D4—21no—
1632D4—21no—
1633D4—21no—
1634D4—21no—
1635D4—21no—
1636D4—81no—
1637D4—81no—
1638D4—81no—
1639D4—81no—
1640D4—81no—
1641D4—1062no—
1642D4—1062no—
1643D4—1062no—
1644D4—1061no—
1645D4—1061no—
1646D4—1061no—
1647D4—1061no—
1648D4—1061no—
1649D4—1061no—
1650D4—1061no—
1651D4—1061no—
1652D4—4241no—
1653D4—4241no—
1654D4—4241no—
1655D4—4241no—
1656D4—4241no—
1657D4—4241no—
1658D4—4241no—
1659D4—4241no—
1660D4—4241no—
1661D4—4241no—
1662D4—4241no—
1663D4—4241no—
1664D4—4241no—
1665D4—4241no—
1666D4—4241no—
1667D4—4241no—
1668D4—4241no—
1669D4—2122no—
1670D4—2122no—
1671D4—2122no—
1672D4—2122no—
1673D4—2122no—
1674D4—2122no—
1675D4—2122no—
1676D4—2122no—
1677C2×C4—21no—
1678C2×C4—21no—
1679C2×C4—21no—
1680C2×C4—21no—
1681C2×C4—21no—
1682C2×C4—21no—
1683C2×C4—21no—
1684C2×C4—81no—
1685C2×C4—81no—
1686C2×C4—81no—
1687C2×C4—531no—
1688C2×C4—531no—
1689C2×C4—532no—
1690C2×C4—532no—
1691C2×C4—531no—
1692C2×C4—531no—
1693C2×C4—531no—
1694C2×C4—531no—
1695C2×C4—1062no—
1696C2×C4—1062no—
1697C2×C4—1062no—
1698C2×C4—1061no—
1699C2×C4—1061no—
1700C2×C4—1061no—
1701C2×C4—1061no—
1702C2×C4—1061no—
1703C2×C4—1061no—
1704C2×C4—4241no—
1705C2×C4—4241no—
1706C2×C4—4241no—
1707C2×C4—4241no—
1708C2×C4—4241no—
1709C2×C4—4241no—
1710C2×C4—4241no—
1711C2×C4—4241no—
1712C2×C4—4241no—
1713C2×C4—2121no—
1714C2×C4—2121no—
1715C2×C4—2122no—
1716C2×C4—2122no—
1717C2×C4—2122no—
1718C2×C4—2122no—
1719C2×C4—2121no—
1720C2×C4C2×D4×D5311yescharacteristic
1721C2×C4C2×D4×D5311yescharacteristic
1722C2×C4C2×D4×D5311yescharacteristic
1723C2×C4C2×D4×D5311yescharacteristic
1724C2×C4C2×D4×D5311yescharacteristic
1725C2×C4C24×D5311yescharacteristic
1726C8—21no—
1727C8—21no—
1728C8—21no—
1729C8—21no—
1730C8—1061no—
1731C8—1061no—
1732C8—1061no—
1733C8—1061no—
1734C22—21no—
1735C22—21no—
1736C22—21no—
1737C22—41no—
1738C22—41no—
1739C22—41no—
1740C22—41no—
1741C22—41no—
1742C22—41no—
1743C22—41no—
1744C22—41no—
1745C22—41no—
1746C22—532no—
1747C22—8482no—
1748C22—8482no—
1749C22—1061no—
1750C22—1061no—
1751C22—1061no—
1752C22—1061no—
1753C22—1061no—
1754C22—4244no—
1755C22—2121no—
1756C22—2121no—
1757C22—2121no—
1758C22—2121no—
1759C22—2121no—
1760C22—2121no—
1761C22—2121no—
1762C22—2121no—
1763C22—2121no—
1764C22—2121no—
1765C22—2121no—
1766C22—2121no—
1767C22C22×D4×D5311yescharacteristic
1768C4—21no—
1769C4—21no—
1770C4—21no—
1771C4—21no—
1772C4—21no—
1773C4—41no—
1774C4—41no—
1775C4—41no—
1776C4—41no—
1777C4—41no—
1778C4—532no—
1779C4—532no—
1780C4—1061no—
1781C4—1061no—
1782C4—1061no—
1783C4—1061no—
1784C4—2121no—
1785C4—2121no—
1786C4—2121no—
1787C4—2121no—
1788C4H(5,𝔽2)×D5311yescharacteristic
1789C42−1+4×D5311yescharacteristic
1790C2—41no—
1791C2—81no—
1792C2—81no—
1793C2—81no—
1794C2—1062no—
1795C2—4241no—
1796C2—4241no—
1797C2—4241no—
1798C2—4241no—
1799C2—2121no—
1800C2#537×D5311yescharacteristic
1801C2#576×D5311yescharacteristic
1802C2#2028949311yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3257C2
socleC22×C53C23×D4
hypercenter#3257D53
hypocenterC53#60922
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ #117 ◁ #3257

Complements

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

NH ≅ G/Ntype
1. #20288587C2semidirect
2. #20288135C2semidirect
3. #20286154C2semidirect
4. #20286153C2semidirect
5. #20286152C2semidirect
6. #20286150C2semidirect
7. #20286132C2semidirect
8. #20286126C2semidirect
9. #20286124C2semidirect
10. #20286095C2semidirect
11. #20286092C2semidirect
12. #20286074C2semidirect
13. #20286072C2semidirect
14. #20286038C2semidirect
15. #20286036C2semidirect
16. #20286024C2semidirect
17. #20286021C2semidirect
18. #20284541C2semidirect
19. #20284539C2semidirect
20. #20284510C2semidirect
21. #20284502C2semidirect
22. #20284390C2semidirect
23. #20284388C2semidirect
24. #20284361C2semidirect
25. #20284358C2semidirect
26. #20284216C2semidirect
27. #20284216C2semidirect
28. #20284192C2semidirect
29. #459×D53C2semidirect
30. #20283282C2semidirect
31. C53×#3257C2semidirect
47. #16811245C22semidirect
49. #16811229C22semidirect
50. #16811228C22semidirect
51. #16811228C22semidirect
52. #16811227C22semidirect
54. #16811224C22semidirect
63. #16811174C22semidirect
65. #16811170C22semidirect
66. #16811170C22semidirect
67. #16811168C22semidirect
68. #16811168C22semidirect
69. #16811168C22semidirect
71. #16811159C22semidirect
73. #16811152C22semidirect
81. #16810930C22semidirect
82. #16810926C22semidirect
83. #16810925C22semidirect
84. #16810924C22semidirect
85. #16810924C22semidirect
86. #16810924C22semidirect
87. #16810924C22semidirect
88. #16810923C22semidirect
89. #16810923C22semidirect
90. #16810923C22semidirect
91. #16810922C22semidirect
92. #16810921C22semidirect
93. #16810920C22semidirect
94. #16810920C22semidirect
95. #16810916C22semidirect
96. #16810912C22semidirect
97. #16810912C22semidirect
98. #16810912C22semidirect
99. #16810911C22semidirect
100. #16810911C22semidirect
101. #16810910C22semidirect
102. #16810906C22semidirect
103. #16810902C22semidirect
104. #16810902C22semidirect
105. #16810902C22semidirect
106. #16810901C22semidirect
107. #16810901C22semidirect
108. #16810900C22semidirect
109. #16810877C22semidirect
110. #16810877C22semidirect
111. #16810876C22semidirect
112. #16810876C22semidirect
113. #16810875C22semidirect
114. #16810875C22semidirect
115. #16810875C22semidirect
116. #16810874C22semidirect
117. #16810874C22semidirect
118. #16810874C22semidirect
119. #16810873C22semidirect
120. #16810872C22semidirect
121. #16810871C22semidirect
122. #16810866C22semidirect
123. #16810860C22semidirect
124. #16810860C22semidirect
125. #16810859C22semidirect
126. #16810859C22semidirect
127. #16810858C22semidirect
128. #16810858C22semidirect
129. #16810858C22semidirect
130. #16810857C22semidirect
131. #16810857C22semidirect
132. #16810857C22semidirect
133. #16810856C22semidirect
134. #16810855C22semidirect
135. #16810854C22semidirect
136. #16810849C22semidirect
137. #16810841C22semidirect
138. #16810841C22semidirect
139. #16810840C22semidirect
140. #16810840C22semidirect
141. #16810835C22semidirect
142. #16810835C22semidirect
143. #16810823C22semidirect
144. #16810821C22semidirect
145. #16810821C22semidirect
147. #16810819C22semidirect
148. #16810819C22semidirect
149. #16810819C22semidirect
151. #16810818C22semidirect
152. #16810818C22semidirect
155. #16810817C22semidirect
156. #16810817C22semidirect
157. #16810817C22semidirect
158. #16810817C22semidirect
161. #16810816C22semidirect
162. #16810816C22semidirect
164. #16810815C22semidirect
169. #16810650C22semidirect
172. #16810648C22semidirect
173. #16810648C22semidirect
174. #16810646C22semidirect
176. #16810645C22semidirect
177. C2×#13133146C22semidirect
179. C4⋊C8×D53C22semidirect
188. C53×#542C22semidirect
189. C53×#540C22semidirect
190. C53×#479C22semidirect
191. C53×#478C22semidirect
192. C53×#476C22semidirect
193. C53×#474C22semidirect
194. C53×#469C22semidirect
195. C53×#468C22semidirect
196. C53×#466C22semidirect
197. C53×#465C22semidirect
198. C53×#463C22semidirect
199. C53×#463C22semidirect
200. C53×#460C22semidirect
202. C53×#424C22semidirect
898. #3257D53semidirect
950. #542C2×D53semidirect
957. #540C2×D53semidirect
985. #479C2×D53semidirect
999. #478C2×D53semidirect
1007. #476C2×D53semidirect
1015. #474C2×D53semidirect
1027. #469C2×D53semidirect
1031. #468C2×D53semidirect
1043. #466C2×D53semidirect
1047. #465C2×D53semidirect
1054. #463C2×D53semidirect
1055. #463C2×D53semidirect
1059. #460C2×D53semidirect
1089. #424C2×D53semidirect
1104. C53#60922semidirect

Maximal subgroups

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

subgroupindex
#202885872
#202881352
#202861542
#202861532
#202861522
#202861502
#202861322
#202861262
#202861242
#202860952
#202860922
#202860742
#202860722
#202860382
#202860362
#202860242
#202860212
#202845412
#202845392
#202845102
#202845022
#202843902
#202843882
#202843612
#202843582
#202842162
#202841922
#459×D532
#202832822
C53×#32572
#6092253