Finite Group Databasebeta

← #28281305

Subgroups — #28281305

Order 13568.

1716 conjugacy classes of subgroups.

The subgroup lattice has 1668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289356C211yesmaximal, characteristic, complemented
2#20288653C211yesmaximal, characteristic, complemented
3#20287670C211yesmaximal, characteristic, complemented
4#20287587C211yesmaximal, characteristic, complemented
5#20287478C211yesmaximal, characteristic, complemented
6#20287380C211yesmaximal, characteristic, complemented
7#20287308C211yesmaximal, characteristic, complemented
8#20287274C211yesmaximal, characteristic, complemented
9#20287268C211yesmaximal, characteristic, complemented
10#20287244C211yesmaximal, characteristic, complemented
11#20287159C211yesmaximal, characteristic, complemented
12#20287115C211yesmaximal, characteristic, complemented
13#20286945C211yesmaximal, characteristic, complemented
14#20286934C211yesmaximal, characteristic, complemented
15#20286919C211yesmaximal, characteristic, complemented
16#20286869C211yesmaximal, characteristic, complemented
17#20286855C211yesmaximal, characteristic, complemented
18#20286553C211yesmaximal, characteristic, complemented
19#20286175C211yesmaximal, characteristic, complemented
20#20286120C211yesmaximal, characteristic, complemented
21#20286115C211yesmaximal, characteristic, complemented
22#20286012C211yesmaximal, characteristic, complemented
23#20285893C211yesmaximal, characteristic, complemented
24#20284994C211yesmaximal, characteristic, complemented
25#20284904C211yesmaximal, characteristic, complemented
26#20284767C211yesmaximal, characteristic, complemented
27#20284562C211yesmaximal, characteristic, complemented
28#20284545C211yesmaximal, characteristic, complemented
29#20284507C211yesmaximal, characteristic, complemented
30#20283858C211yesmaximal, characteristic, complemented
31C53×#3241C211yesmaximal, characteristic, complemented
32#16811377—21no—
33#16811369—21no—
34#16811359C2211yescharacteristic
35#16811350C2211yescharacteristic, complemented
36#16811347C2211yescharacteristic
37#16811344—21no—
38#16811336C2211yescharacteristic, complemented
39#16811334C2211yescharacteristic, complemented
40#16811329C2211yescharacteristic
41#16811326C2211yescharacteristic
42#16811325C2211yescharacteristic
43#16811321C2211yescharacteristic, complemented
44#16811320—21no—
45#16811312C2211yescharacteristic, complemented
46#16811311C2211yescharacteristic
47#16811308C2211yescharacteristic, complemented
48#16811305—21no—
49#16811301—21no—
50#16811296—21no—
51#16811273C2211yescharacteristic
52#16811270C2211yescharacteristic
53#16811270C2211yescharacteristic
54#16811262—21no—
55#16811258C2211yescharacteristic
56#16811253C2211yescharacteristic, complemented
57#16811247—21no—
58#16811247C2211yescharacteristic, complemented
59#16811246—21no—
60#16811244C2211yescharacteristic, complemented
61#16811238C2211yescharacteristic
62#16811234—21no—
63#16811219—21no—
64#16811216—21no—
65#16811205—21no—
66#16811178C2211yescharacteristic, complemented
67#16811158C2211yescharacteristic, complemented
68#16811155C2211yescharacteristic
69#16811151C2211yescharacteristic
70#16811133—21no—
71#123×D53—21no—
72#16811103C2211yescharacteristic
73#16811095C2211yescharacteristic
74C4×D4×D53C2211yescharacteristic
75#16811031C2211yescharacteristic, complemented
76#16811023C2211yescharacteristic, complemented
77#16811023C2211yescharacteristic, complemented
78#16811020C2211yescharacteristic, complemented
79#16810981C2211yescharacteristic, complemented
80#16810976C2211yescharacteristic, complemented
81#16810976C2211yescharacteristic, complemented
82#16810976C2211yescharacteristic, complemented
83#16810967C2211yescharacteristic, complemented
84#16810967C2211yescharacteristic, complemented
85#16810967C2211yescharacteristic, complemented
86#16810966C2211yescharacteristic, complemented
87#16810960C2211yescharacteristic, complemented
88#16810955C2211yescharacteristic, complemented
89#16810954C2211yescharacteristic, complemented
90#16810949C2211yescharacteristic, complemented
91#16810946C2211yescharacteristic
92#16810946C2211yescharacteristic
93#16810946C2211yescharacteristic
94#16810943C2211yescharacteristic, complemented
95#16810942C2211yescharacteristic, complemented
96#16810940C2211yescharacteristic
97#16810929C2211yescharacteristic, complemented
98#16810927C2211yescharacteristic, complemented
99#16810927C2211yescharacteristic, complemented
100#16810927C2211yescharacteristic, complemented
101#16810926C2211yescharacteristic
102#16810926C2211yescharacteristic
103#16810925C2211yescharacteristic, complemented
104#16810925C2211yescharacteristic, complemented
105#16810925C2211yescharacteristic, complemented
106#16810922C2211yescharacteristic
107#16810922C2211yescharacteristic, complemented
108#16810920C2211yescharacteristic
109#16810920C2211yescharacteristic
110#16810920C2211yescharacteristic, complemented
111#16810917C2211yescharacteristic, complemented
112#16810915C2211yescharacteristic, complemented
113#16810915C2211yescharacteristic, complemented
114#16810914C2211yescharacteristic
115#16810913C2211yescharacteristic, complemented
116#16810911C2211yescharacteristic, complemented
117#16810909C2211yescharacteristic, complemented
118#16810903C2211yescharacteristic, complemented
119#16810902C2211yescharacteristic
120#16810902C2211yescharacteristic, complemented
121#16810900C2211yescharacteristic
122#16810900C2211yescharacteristic
123#16810882C2211yescharacteristic, complemented
124#16810875C2211yescharacteristic
125#16810874C2211yescharacteristic, complemented
126#16810870C2211yescharacteristic, complemented
127#16810870C2211yescharacteristic, complemented
128#16810868C2211yescharacteristic
129#16810868C2211yescharacteristic
130#16810867C2211yescharacteristic, complemented
131#16810865C2211yescharacteristic, complemented
132#16810858C2211yescharacteristic
133#16810857C2211yescharacteristic, complemented
134#16810850C2211yescharacteristic, complemented
135#16810846C2211yescharacteristic, complemented
136#16810844C2211yescharacteristic, complemented
137#16810844C2211yescharacteristic, complemented
138#16810839C2211yescharacteristic
139#16810838C2211yescharacteristic, complemented
140#16810838C2211yescharacteristic, complemented
141#16810837C2211yescharacteristic, complemented
142#16810837C2211yescharacteristic, complemented
143#16810820C2211yescharacteristic
144#16810815C2211yescharacteristic
145#16810787C2211yescharacteristic
146#16810775C2211yescharacteristic
147#16810775C2211yescharacteristic
148#16810770C2211yescharacteristic
149#16810758C2211yescharacteristic
150#16810758C2211yescharacteristic
151#16810751C2211yescharacteristic, complemented
152C8×Dic106C2211yescharacteristic, complemented
153#16810736C2211yescharacteristic
154#16810734C2211yescharacteristic
155#16810731C2211yescharacteristic, complemented
156#16810720C2211yescharacteristic, complemented
157#16810714C2211yescharacteristic, complemented
158C4×#11719913C2211yescharacteristic
159C4×#11719913C2211yescharacteristic, complemented
160#16810710C2211yescharacteristic
161#16810710C2211yescharacteristic
162#16810705C2211yescharacteristic
163#16810703C2211yescharacteristic, complemented
164#16810703C2211yescharacteristic, complemented
165#16810702C2211yescharacteristic
166#16810698C2211yescharacteristic, complemented
167#16810698C2211yescharacteristic, complemented
168#16810696C2211yescharacteristic
169#16810691C2211yescharacteristic, complemented
170#16810686C2211yescharacteristic, complemented
171#16810683C2211yescharacteristic, complemented
172#16810675C2211yescharacteristic, complemented
173#16810666C2211yescharacteristic, complemented
174#16810664C2211yescharacteristic, complemented
175#16810664C2211yescharacteristic, complemented
176#16810664C2211yescharacteristic, complemented
177#16810658C2211yescharacteristic, complemented
178C2×#13133150C2211yescharacteristic, complemented
179#16810650C2211yescharacteristic, complemented
180#16810648C2211yescharacteristic, complemented
181#16810645C2211yescharacteristic, complemented
182#16810626C2211yescharacteristic
183#16810626C2211yescharacteristic
184#16810626C2211yescharacteristic
185#16810622C2211yescharacteristic
186#16810617C2211yescharacteristic
187#102×D53C2211yescharacteristic
188C53×#544C2211yescharacteristic, complemented
189C53×#540C2211yescharacteristic
190C53×#501C2211yescharacteristic, complemented
191C53×#499C2211yescharacteristic, complemented
192C53×#490C2211yescharacteristic
193C53×#486C2211yescharacteristic
194C53×#482C2211yescharacteristic, complemented
195C53×#482C2211yescharacteristic, complemented
196C53×#481C2211yescharacteristic, complemented
197C53×#480C2211yescharacteristic, complemented
198C53×#478C2211yescharacteristic, complemented
199C53×#478C2211yescharacteristic, complemented
200C53×#476C2211yescharacteristic, complemented
201C53×#474C2211yescharacteristic, complemented
202C53×#433C2211yescharacteristic, complemented
203C2×#11719945C2311yescharacteristic
204C2×#11719947—21no—
205C2×D4×D53—21no—
206C2×D4×D53C2311yescharacteristic
207C2×D4×D53C2311yescharacteristic
208C22×C4×D53—21no—
209C2×Dic212C2311yescharacteristic
210C2×#11719913C2311yescharacteristic
211C2×#11719913C2311yescharacteristic
212C2×#11719923C2311yescharacteristic
213C2×#11719923C2311yescharacteristic
214C2×D424C2311yescharacteristic
215C2×#11719922C2311yescharacteristic
216C2×#11719922C2311yescharacteristic
217C2×#11719917C2311yescharacteristic
218C2×#11719912C2311yescharacteristic
219C2×#11719912C2311yescharacteristic
220C2×#11719912C2311yescharacteristic
221C22×#88322C2311yescharacteristic
222C2×C8×D53C2311yescharacteristic
223#13133217C2311yescharacteristic
224#13133216—21no—
225#13133216—21no—
226#13133216C2311yescharacteristic
227#13133216C2311yescharacteristic
228#13133212—21no—
229#13133212—21no—
230#13133212—21no—
231#13133212—21no—
232#13133212—21no—
233#13133212—21no—
234#13133212—21no—
235#13133212—21no—
236#13133212—21no—
237#13133212D411yescharacteristic
238#13133210—21no—
239#13133210—21no—
240#13133210—21no—
241#13133210—21no—
242#13133210D411yescharacteristic
243#13133209—21no—
244#13133208—21no—
245#13133208C2311yescharacteristic
246#13133208C2311yescharacteristic
247#13133208C2311yescharacteristic
248#13133208C2311yescharacteristic
249#13133207—21no—
250#13133207—21no—
251#13133207—21no—
252#13133207—21no—
253#13133207D411yescharacteristic
254#13133206—21no—
255#13133206—21no—
256#13133205—21no—
257#13133205C2311yescharacteristic
258#13133204—21no—
259#13133204C2311yescharacteristic
260#13133204C2311yescharacteristic
261#13133203—21no—
262#13133203—21no—
263#13133203—21no—
264#13133203D411yescharacteristic
265#13133202—21no—
266#13133202—21no—
267#13133202—21no—
268#13133202—21no—
269#13133202—21no—
270#13133202D411yescharacteristic
271#13133201—21no—
272#13133200—21no—
273#13133200—21no—
274#13133199—21no—
275#13133199—21no—
276#13133199—21no—
277#13133199—21no—
278#13133199—21no—
279#13133199—21no—
280#13133199D411yescharacteristic
281#13133198—21no—
282#13133198—21no—
283#13133198—21no—
284#13133197—21no—
285#13133197—21no—
286#13133197—21no—
287#13133197—21no—
288#13133197C2311yescharacteristic
289#13133197C2311yescharacteristic
290#13133197C2311yescharacteristic
291#13133197C2311yescharacteristic
292#13133196—21no—
293#13133196C2311yescharacteristic
294#13133195—21no—
295#13133195—21no—
296#13133195—21no—
297#13133195—21no—
298#13133195D411yescharacteristic
299#13133194—21no—
300#13133193—21no—
301#13133193—21no—
302#13133193—21no—
303#13133193—21no—
304#13133192—21no—
305#13133192C2311yescharacteristic
306#13133192C2311yescharacteristic
307#13133191—21no—
308#13133191C2311yescharacteristic
309#13133190—21no—
310#13133190D411yescharacteristic
311#13133189—21no—
312#13133188—21no—
313#13133188—21no—
314#13133188—21no—
315#13133188C2311yescharacteristic
316#13133188C2311yescharacteristic
317#13133185—21no—
318#13133185—21no—
319#13133185—21no—
320#13133185—21no—
321Q8×Dic53—21no—
322Q8×Dic53—21no—
323C4×Dic106C2311yescharacteristic
324C4×Dic106C2311yescharacteristic
325C4×Dic106C2311yescharacteristic
326C4×Dic106C2311yescharacteristic
327#13133182—21no—
328#13133182—21no—
329#13133182C2311yescharacteristic
330#13133182C2311yescharacteristic
331C4×D212C2311yescharacteristic
332C4×D212C2311yescharacteristic
333C4×D212C2311yescharacteristic
334C4×D212C2311yescharacteristic
335D4×Dic53—21no—
336D4×Dic53—21no—
337D4×Dic53C2311yescharacteristic
338D4×Dic53C2311yescharacteristic
339#13133179—21no—
340#13133179—21no—
341#13133179C2311yescharacteristic
342#13133179C2311yescharacteristic
343#13133179C2311yescharacteristic
344#13133179C2311yescharacteristic
345C4×C22⋊D53—21no—
346C4×C22⋊D53—21no—
347C4×C22⋊D53—21no—
348C4×C22⋊D53—21no—
349C4×C22⋊D53C2311yescharacteristic
350C4×C22⋊D53C2311yescharacteristic
351#13133177—21no—
352#13133177—21no—
353#13133177—21no—
354#13133177—21no—
355#13133176—21no—
356#13133176—21no—
357#13133175—21no—
358#13133175—21no—
359#13133175—21no—
360#13133175C2311yescharacteristic
361#13133175C2311yescharacteristic
362#13133175C2311yescharacteristic
363#13133175C2311yescharacteristic
364#13133174—21no—
365#13133174—21no—
366#13133174C2311yescharacteristic
367C2×C4⋊Dic53C2311yescharacteristic
368C4⋊C4×D53—21no—
369C4⋊C4×D53—21no—
370C4⋊C4×D53—21no—
371C4⋊C4×D53C2311yescharacteristic
372C4⋊C4×D53C2311yescharacteristic
373C2×#11719921—21no—
374C22⋊C4×D53—21no—
375C22⋊C4×D53—21no—
376C22⋊C4×D53—21no—
377C22⋊C4×D53—21no—
378C42×D53C2311yescharacteristic
379#13133150C2311yescharacteristic
380#13133150C2311yescharacteristic
381#13133150C2311yescharacteristic
382#13133150C2311yescharacteristic
383#13133150C2311yescharacteristic
384#13133150C2311yescharacteristic
385#13133150C2311yescharacteristic
386#13133150C2311yescharacteristic
387#13133149C2311yescharacteristic
388#13133149C2311yescharacteristic
389#13133149C2311yescharacteristic
390#13133149C2311yescharacteristic
391#13133148C2311yescharacteristic
392#13133148C2311yescharacteristic
393#13133148C2311yescharacteristic
394#13133148C2311yescharacteristic
395C4⋊#88322C2311yescharacteristic
396C4⋊#88322C2311yescharacteristic
397C4⋊#88322C2311yescharacteristic
398C4⋊#88322C2311yescharacteristic
399#13133146C2311yescharacteristic
400#13133146C2311yescharacteristic
401#13133146C2311yescharacteristic
402#13133146C2311yescharacteristic
403#13133142C2311yescharacteristic
404#13133142C2311yescharacteristic
405#13133142C2311yescharacteristic
406#13133142C2311yescharacteristic
407#13133140C2311yescharacteristic
408#13133140C2311yescharacteristic
409#13133140C2311yescharacteristic
410#13133140C2311yescharacteristic
411#13133140C2311yescharacteristic
412#13133140C2311yescharacteristic
413#13133139C2311yescharacteristic
414#13133139C2311yescharacteristic
415#13133139C2311yescharacteristic
416#13133139C2311yescharacteristic
417#13133138C2311yescharacteristic
418#13133138C2311yescharacteristic
419#13133138C2311yescharacteristic
420#13133138C2311yescharacteristic
421#13133137C2311yescharacteristic
422#13133137C2311yescharacteristic
423#13133137C2311yescharacteristic
424#13133137C2311yescharacteristic
425#13133137C2311yescharacteristic
426#13133137C2311yescharacteristic
427#13133129C2311yescharacteristic
428#13133129C2311yescharacteristic
429#13133129C2311yescharacteristic
430#13133129C2311yescharacteristic
431#13133127C2311yescharacteristic
432C8×Dic53C2311yescharacteristic
433C8×Dic53C2311yescharacteristic
434C8×Dic53C2311yescharacteristic
435C4⋊Q8×C53—21no—
436C4⋊Q8×C53C2311yescharacteristic
437C4⋊Q8×C53C2311yescharacteristic
438#127×C53C2311yescharacteristic
439#125×C53—21no—
440#125×C53C2311yescharacteristic
441#125×C53C2311yescharacteristic
442#125×C53C2311yescharacteristic
443#123×C53—21no—
444#123×C53—21no—
445C22⋊Q8×C53—21no—
446C22⋊Q8×C53—21no—
447#121×C53—21no—
448#121×C53—21no—
449#121×C53C2311yescharacteristic
450#121×C53C2311yescharacteristic
451C4×D4×C53C2311yescharacteristic
452C4×D4×C53C2311yescharacteristic
453#117×C53C2311yescharacteristic
454#117×C53C2311yescharacteristic
455C2×C4⋊C4×C53C2311yescharacteristic
456#107×C53C2311yescharacteristic
457#107×C53C2311yescharacteristic
458#107×C53C2311yescharacteristic
459#107×C53C2311yescharacteristic
460#106×C53C2311yescharacteristic
461#106×C53C2311yescharacteristic
462#106×C53C2311yescharacteristic
463#106×C53C2311yescharacteristic
464C4⋊C8×C53C2311yescharacteristic
465C4⋊C8×C53C2311yescharacteristic
466#102×C53C2311yescharacteristic
467#102×C53C2311yescharacteristic
468#102×C53C2311yescharacteristic
469#102×C53C2311yescharacteristic
470#102×C53C2311yescharacteristic
471#102×C53C2311yescharacteristic
472#102×C53C2311yescharacteristic
473#102×C53C2311yescharacteristic
474C22⋊C8×C53C2311yescharacteristic
475C22⋊C8×C53C2311yescharacteristic
476#97×C53C2311yescharacteristic
477C4×C8×C53C2311yescharacteristic
478C23×D53—21no—
479C23×D53—21no—
480C2×Q8×C53—21no—
481C2×Q8×C53—21no—
482C2×D4×C53—21no—
483C2×D4×C53—21no—
484C2×D4×C53—21no—
485C2×D4×C53—21no—
486C2×D4×C53C2411yescharacteristic
487C2×D4×C53C2411yescharacteristic
488C22×C4×C53—21no—
489C22×C4×C53—21no—
490C22×C4×C53—21no—
491C22×C4×C53C2411yescharacteristic
492C2×C22⋊D53—21no—
493C2×C22⋊D53—21no—
494C2×C22⋊D53—21no—
495C2×C22⋊D53—21no—
496C2×C22⋊D53—21no—
497C2×C22⋊D53—21no—
498C2×C22⋊D53C2×D411yescharacteristic
499C2×C22⋊D53C2×D411yescharacteristic
500C22×Dic53—21no—
501C22×Dic53—21no—
502C22×Dic53—21no—
503#11719947—82no—
504D4×D53—22no—
505D4×D53—22no—
506D4×D53—41no—
507D4×D53—41no—
508D4×D53—82no—
509#11719945—22no—
510#11719945—41no—
511C2×D212—21no—
512C2×D212—21no—
513C2×D212C2×D411yescharacteristic
514C2×D212C2411yescharacteristic
515C2×D212C2411yescharacteristic
516C2×C4×D53—21no—
517C2×C4×D53—21no—
518C2×C4×D53—21no—
519C2×C4×D53—21no—
520C2×C4×D53—21no—
521C2×C4×D53—21no—
522C2×C4×D53—21no—
523C2×C4×D53—21no—
524C2×C4×D53—21no—
525C2×C4×D53—21no—
526C2×C4×D53—82no—
527C2×C4×D53C2×D411yescharacteristic
528C2×C4×D53C2×D411yescharacteristic
529C2×C4×D53C2411yescharacteristic
530C2×C4×D53C2411yescharacteristic
531C2×Dic106—21no—
532C2×Dic106—21no—
533C2×Dic106—21no—
534C2×Dic106C2×D411yescharacteristic
535C2×Dic106C2411yescharacteristic
536C2×Dic106C2411yescharacteristic
537C2×C8×C53C2411yescharacteristic
538C2×C8×C53C2411yescharacteristic
539C2×C8×C53C2411yescharacteristic
540C2×C8×C53C2411yescharacteristic
541C4⋊C4×C53—21no—
542C4⋊C4×C53—21no—
543C4⋊C4×C53—21no—
544C4⋊C4×C53—21no—
545C4⋊C4×C53—21no—
546C4⋊C4×C53—21no—
547C4⋊C4×C53—21no—
548C4⋊C4×C53—21no—
549C4⋊C4×C53—21no—
550C4⋊C4×C53C2×D411yescharacteristic
551C4⋊C4×C53C2×D411yescharacteristic
552C4⋊C4×C53C2411yescharacteristic
553C4⋊C4×C53C2411yescharacteristic
554C4⋊C4×C53C2411yescharacteristic
555C4⋊C4×C53C2411yescharacteristic
556C4⋊C4×C53C2411yescharacteristic
557C4⋊C4×C53C2411yescharacteristic
558C22⋊C4×C53—21no—
559C22⋊C4×C53—21no—
560C22⋊C4×C53—21no—
561C22⋊C4×C53—21no—
562C22⋊C4×C53—21no—
563C22⋊C4×C53C2×D411yescharacteristic
564C22⋊C4×C53C2×D411yescharacteristic
565C42×C53—21no—
566C42×C53C2411yescharacteristic
567C42×C53C2411yescharacteristic
568C22⋊Dic53—21no—
569C22⋊Dic53—21no—
570C22⋊Dic53—21no—
571C22⋊Dic53—21no—
572C22⋊Dic53—21no—
573C22⋊Dic53—21no—
574C22⋊Dic53—21no—
575C22⋊Dic53—21no—
576C22⋊Dic53—21no—
577C22⋊Dic53C2×D411yescharacteristic
578C22⋊Dic53C2×D411yescharacteristic
579#11719923—41no—
580#11719923—41no—
581#11719922—41no—
582#11719922—41no—
583#11719921—21no—
584#11719921—21no—
585#11719921—21no—
586#11719921—21no—
587#11719921—21no—
588#11719921—21no—
589#11719921—21no—
590#11719921—21no—
591#11719921—21no—
592#11719921—21no—
593#11719921—21no—
594#11719921—21no—
595#11719921—21no—
596#11719921—21no—
597#11719921—21no—
598#11719921—21no—
599#11719921—21no—
600#11719921—21no—
601#11719921—21no—
602#11719921—21no—
603#11719921C2×D411yescharacteristic
604#11719921C2×D411yescharacteristic
605#11719921C2×D411yescharacteristic
606#11719921C2×D411yescharacteristic
607#11719921C2×D411yescharacteristic
608#11719921C2×D411yescharacteristic
609C4⋊Dic53—21no—
610C4⋊Dic53—21no—
611C4⋊Dic53—21no—
612C4⋊Dic53—21no—
613C4⋊Dic53—21no—
614C4⋊Dic53—21no—
615C4⋊Dic53—21no—
616C4⋊Dic53—21no—
617C4⋊Dic53—21no—
618C4⋊Dic53—21no—
619C4⋊Dic53C2×D411yescharacteristic
620C4⋊Dic53C2×D411yescharacteristic
621C4⋊Dic53C2411yescharacteristic
622C4⋊Dic53C2411yescharacteristic
623C4⋊Dic53C2411yescharacteristic
624C4⋊Dic53C2411yescharacteristic
625#11719919—21no—
626#11719919—21no—
627#11719919—21no—
628#11719919—21no—
629#11719919—21no—
630#11719919—21no—
631#11719919—21no—
632#11719919—21no—
633#11719919—21no—
634#11719919—21no—
635#11719919—21no—
636#11719919—21no—
637#11719919—21no—
638#11719919—21no—
639#11719919C2×D411yescharacteristic
640#11719919C2×D411yescharacteristic
641#11719919C2×D411yescharacteristic
642#11719919C2×D411yescharacteristic
643#11719919C2×D411yescharacteristic
644#11719919C2×D411yescharacteristic
645C4×Dic53—21no—
646C4×Dic53—21no—
647C4×Dic53—21no—
648C4×Dic53—21no—
649C4×Dic53—21no—
650C4×Dic53—21no—
651C4×Dic53—21no—
652C4×Dic53—21no—
653C4×Dic53—21no—
654C4×Dic53C2×D411yescharacteristic
655C4×Dic53C2×D411yescharacteristic
656C4×Dic53C2411yescharacteristic
657C4×Dic53C2411yescharacteristic
658#11719917—41no—
659C2×#88322—41no—
660C2×#88322C2411yescharacteristic
661C2×#88322C2411yescharacteristic
662C2×#88322C2411yescharacteristic
663C2×#88322C2411yescharacteristic
664Dic212—41no—
665D424—22no—
666#11719913—22no—
667#11719913—41no—
668#11719912—41no—
669#11719912—41no—
670#11719912—41no—
671C8×D53—41no—
672C23×C53—21no—
673C23×C53—21no—
674C23×C53C22×D411yescharacteristic
675C22×D53—21no—
676C22×D53—21no—
677C22×D53—42no—
678C22×D53—42no—
679C22×D53—42no—
680C22×D53—81no—
681C22×D53—81no—
682C22×D53—81no—
683C22×D53C22×D411yescharacteristic
684C22×D53C22×D411yescharacteristic
685Q8×C53—81no—
686Q8×C53—81no—
687D4×C53—21no—
688D4×C53—21no—
689D4×C53—21no—
690D4×C53—21no—
691D4×C53—81no—
692D4×C53—81no—
693D4×C53—81no—
694D4×C53—81no—
695C2×C4×C53—21no—
696C2×C4×C53—21no—
697C2×C4×C53—21no—
698C2×C4×C53—21no—
699C2×C4×C53—21no—
700C2×C4×C53—21no—
701C2×C4×C53—21no—
702C2×C4×C53—21no—
703C2×C4×C53—81no—
704C2×C4×C53—81no—
705C2×C4×C53—81no—
706C2×C4×C53C22×D411yescharacteristic
707C2×C4×C53C22×D411yescharacteristic
708C2×C4×C53C22×D411yescharacteristic
709C2×C4×C53C22×D411yescharacteristic
710C2×C4×C53C22×D411yescharacteristic
711C2×C4×C53C2511yescharacteristic
712C22⋊D53—41no—
713C22⋊D53—41no—
714C22⋊D53—42no—
715C22⋊D53—42no—
716C22⋊D53—42no—
717C22⋊D53—42no—
718C22⋊D53—81no—
719C22⋊D53—81no—
720C2×Dic53—21no—
721C2×Dic53—21no—
722C2×Dic53—21no—
723C2×Dic53—21no—
724C2×Dic53—21no—
725C2×Dic53—21no—
726C2×Dic53—81no—
727C2×Dic53—81no—
728C2×Dic53—81no—
729C2×Dic53C22×D411yescharacteristic
730C2×Dic53C22×D411yescharacteristic
731C2×Dic53C22×D411yescharacteristic
732C2×Dic53C22×D411yescharacteristic
733C2×Dic53C22×D411yescharacteristic
734C2×Dic53C22×D411yescharacteristic
735D212—21no—
736D212—21no—
737D212—21no—
738D212—41no—
739D212—81no—
740D212—81no—
741D2122−1+412yes—
742C4×D53—21no—
743C4×D53—21no—
744C4×D53—21no—
745C4×D53—21no—
746C4×D53—41no—
747C4×D53—41no—
748C4×D53—42no—
749C4×D53—42no—
750C4×D53—81no—
751C4×D53—81no—
752C4×D53—81no—
753C4×D53—81no—
754C4×D53—81no—
755C4×D53—81no—
756C4×D53—81no—
757C4×D53—81no—
758Dic106—21no—
759Dic106—21no—
760Dic106—21no—
761Dic106—21no—
762Dic106—41no—
763Dic106—81no—
764Dic106—81no—
765Dic106—81no—
766C8×C53—21no—
767C8×C53—21no—
768C8×C53—21no—
769C8×C53—21no—
770#88322—21no—
771#88322—21no—
772#88322—21no—
773#88322—21no—
774#62175—531nomaximal, Sylow
775C22×C53—21no—
776C22×C53—21no—
777C22×C53—21no—
778C22×C53—41no—
779C22×C53—41no—
780C22×C53—41no—
781C22×C53—41no—
782C22×C53—41no—
783C22×C53—41no—
784C22×C53C23×D411yescharacteristic
785C2×D53—21no—
786C2×D53—21no—
787C2×D53—21no—
788C2×D53—21no—
789C2×D53—21no—
790C2×D53—21no—
791C2×D53—22no—
792C2×D53—41no—
793C2×D53—41no—
794C2×D53—41no—
795C2×D53—41no—
796C2×D53—41no—
797C2×D53—84no—
798C2×D53—162no—
799C4×C53—21no—
800C4×C53—21no—
801C4×C53—21no—
802C4×C53—21no—
803C4×C53—21no—
804C4×C53—41no—
805C4×C53—41no—
806C4×C53—41no—
807C4×C53—41no—
808C4×C53—41no—
809C4×C53—41no—
810C4×C53C2×2−1+411yescharacteristic
811C4×C53#58511yescharacteristic
812Dic53—21no—
813Dic53—21no—
814Dic53—21no—
815Dic53—21no—
816Dic53—21no—
817Dic53—21no—
818Dic53—41no—
819Dic53—41no—
820Dic53—41no—
821Dic53—41no—
822Dic53—41no—
823Dic53—41no—
824#3565—531no—
825#3513—531no—
826#3389—531no—
827#3381—531no—
828#3371—531no—
829#3361—531no—
830#3354—531no—
831#3351—531no—
832#3351—531no—
833#3349—531no—
834#3343—531no—
835#3339—531no—
836#3324—531no—
837#3323—531no—
838#3322—531no—
839#3319—531no—
840#3318—531no—
841#3296—531no—
842#3262—531no—
843#3257—531no—
844#3256—531no—
845#3244—531no—
846#3241D5311yescharacteristic, complemented
847#3233—531no—
848#3125—531no—
849#3118—531no—
850#3105—531no—
851#3083—531no—
852#3081—531no—
853#3077—531no—
854#2993—531no—
855C2×C53—41no—
856C2×C53—81no—
857C2×C53—81no—
858C2×C53#348911yescharacteristic
859C2×C53#358411yescharacteristic
860C2×C53#358511yescharacteristic
861D53—41no—
862D53—41no—
863D53—42no—
864D53—81no—
865#563—1061no—
866#562—1061no—
867#559—531no—
868#557—531no—
869#556—531no—
870#556—1061no—
871#555—531no—
872#554—531no—
873#554—531no—
874#553—531no—
875#553—531no—
876#553—531no—
877#553—1061no—
878#552—531no—
879#552—531no—
880#552—531no—
881#552—1061no—
882#551—1061no—
883#551—1061no—
884#547—531no—
885#546—531no—
886#546—531no—
887#546—1061no—
888D42—531no—
889#544—531no—
890#544C2×D5311yescharacteristic, complemented
891#542—531no—
892#542—531no—
893#542—531no—
894#542—1061no—
895#542—1061no—
896#541—1061no—
897#540C2×D5311yescharacteristic
898#539—1061no—
899#539—1061no—
900#538—1061no—
901#533—531no—
902#529—531no—
903#529—531no—
904#529—531no—
905#525—1061no—
906C2×#123—1061no—
907#520—531no—
908#518—531no—
909C2×C4×D4—531no—
910#501—531no—
911#501C2×D5311yescharacteristic, complemented
912#499—531no—
913#499—531no—
914#499C2×D5311yescharacteristic, complemented
915#498—531no—
916#490C2×D5311yescharacteristic
917#489—531no—
918#488—531no—
919#488—531no—
920#488—531no—
921#486C2×D5311yescharacteristic
922#485—531no—
923#485—531no—
924#485—531no—
925#485—531no—
926#484—531no—
927#483—531no—
928#483—531no—
929#482—531no—
930#482—531no—
931#482—531no—
932#482—531no—
933#482C2×D5311yescharacteristic, complemented
934#482C2×D5311yescharacteristic, complemented
935#481—531no—
936#481—531no—
937#481—531no—
938#481C2×D5311yescharacteristic, complemented
939#480C2×D5311yescharacteristic, complemented
940#479—531no—
941#479—531no—
942#479—531no—
943#479—531no—
944#478—531no—
945#478—531no—
946#478—531no—
947#478—531no—
948#478—531no—
949#478—531no—
950#478—531no—
951#478—531no—
952#478—531no—
953#478—531no—
954#478C2×D5311yescharacteristic, complemented
955#478C2×D5311yescharacteristic, complemented
956#477—531no—
957#477—531no—
958#477—531no—
959#476—531no—
960#476—531no—
961#476—531no—
962#476C2×D5311yescharacteristic, complemented
963#475—531no—
964#474—531no—
965#474—531no—
966#474—531no—
967#474—531no—
968#474—531no—
969#474C2×D5311yescharacteristic, complemented
970#470—531no—
971#469—531no—
972#469—531no—
973#468—531no—
974#468—531no—
975#468—531no—
976#468—531no—
977#468—531no—
978#467—531no—
979#466—531no—
980#466—531no—
981#465—531no—
982#464—531no—
983#464—531no—
984#464—531no—
985#463—531no—
986#463—531no—
987#463—531no—
988#463—531no—
989#463—531no—
990#460—531no—
991#459—531no—
992#452—531no—
993#450—531no—
994#450—531no—
995#449—531no—
996#447—531no—
997#447—531no—
998#446—531no—
999C8×Q8—531no—
1000#442—531no—
1001#442—531no—
1002#441—531no—
1003#440—531no—
1004C4×SD16—531no—
1005C4×SD16—531no—
1006C4×SD16—531no—
1007C4×SD16—531no—
1008C4×SD16—531no—
1009C4×D8—531no—
1010C4×D8—531no—
1011C4×D8—531no—
1012#436—531no—
1013#436—531no—
1014#436—531no—
1015#435—531no—
1016#435—531no—
1017C8×D4—531no—
1018#433—531no—
1019#433C2×D5311yescharacteristic, complemented
1020#431—531no—
1021#428—531no—
1022#428—531no—
1023#428—531no—
1024#428—531no—
1025#427—531no—
1026C2×#107—531no—
1027#424—531no—
1028#424—531no—
1029#423—531no—
1030#418—531no—
1031#418—531no—
1032#418—531no—
1033#417—531no—
1034#416—531no—
1035C2×#102—531no—
1036C53#6217511yescharacteristic, complemented, Sylow
1037C2×#41—531no—
1038C2×#41—1061no—
1039C22×D4—531no—
1040C22×D4—531no—
1041C22×D4—1061no—
1042C23×C4—1061no—
1043C2×Q16—531no—
1044C2×SD16—531no—
1045C2×SD16—531no—
1046C2×SD16—531no—
1047C2×SD16—531no—
1048C2×D8—531no—
1049C2×D8—531no—
1050C2×D8—531no—
1051C2×M16—531no—
1052C2×M16—531no—
1053C2×M16—531no—
1054C2×M16—531no—
1055C22×C8—531no—
1056C22×C8—531no—
1057C4⋊Q8—21no—
1058C4⋊Q8—531no—
1059C4⋊Q8—531no—
1060C4⋊Q8—531no—
1061C4⋊Q8—1061no—
1062C4⋊Q8—1061no—
1063C4⋊Q8C22×D5311yescharacteristic
1064C4⋊Q8C22×D5311yescharacteristic
1065#127C22×D5311yescharacteristic
1066#126—531no—
1067#126—531no—
1068#126—1061no—
1069#126—1061no—
1070#126—1061no—
1071#126—1061no—
1072#126—1061no—
1073#126—1061no—
1074#126—1061no—
1075#126—1061no—
1076#126—1061no—
1077#126—1061no—
1078#126—1061no—
1079#126—1061no—
1080#126—1061no—
1081#125—21no—
1082#125—531no—
1083#125—531no—
1084#125—531no—
1085#125—531no—
1086#125—531no—
1087#125—1061no—
1088#125—1061no—
1089#125—1061no—
1090#125—1061no—
1091#125—1061no—
1092#125—1061no—
1093#125C22×D5311yescharacteristic
1094#125C22×D5311yescharacteristic
1095#125C22×D5311yescharacteristic
1096#124—531no—
1097#124—531no—
1098#124—531no—
1099#124—531no—
1100#124—1061no—
1101#124—1061no—
1102#124—1061no—
1103#124—1061no—
1104#124—1061no—
1105#124—1061no—
1106#124—1061no—
1107#123—21no—
1108#123—21no—
1109#123—531no—
1110#123—531no—
1111#123—1061no—
1112#123—1061no—
1113#123—1061no—
1114#123—1061no—
1115#123—1061no—
1116#123—1061no—
1117#123—1061no—
1118#123—1061no—
1119#123—1061no—
1120#123—1061no—
1121#123—1061no—
1122#123—1061no—
1123#123—1061no—
1124#123—1061no—
1125#123—1061no—
1126#123—1061no—
1127#123—1061no—
1128C22⋊Q8—21no—
1129C22⋊Q8—21no—
1130C22⋊Q8—531no—
1131C22⋊Q8—531no—
1132C22⋊Q8—531no—
1133C22⋊Q8—531no—
1134C22⋊Q8—531no—
1135C22⋊Q8—531no—
1136C22⋊Q8—1061no—
1137C22⋊Q8—1061no—
1138C22⋊Q8—1061no—
1139C22⋊Q8—1061no—
1140C22⋊Q8—1061no—
1141C22⋊Q8—1061no—
1142C22⋊Q8—1061no—
1143C22⋊Q8—1061no—
1144C22⋊Q8—1061no—
1145C22⋊Q8—1061no—
1146C22⋊Q8—1061no—
1147C22⋊Q8—1061no—
1148C22⋊Q8—1061no—
1149C22⋊Q8—1061no—
1150#121—21no—
1151#121—21no—
1152#121—531no—
1153#121—531no—
1154#121—531no—
1155#121—531no—
1156#121—531no—
1157#121—531no—
1158#121—1061no—
1159#121—1061no—
1160#121—1061no—
1161#121—1061no—
1162#121—1061no—
1163#121—1061no—
1164#121—1061no—
1165#121C22×D5311yescharacteristic
1166#121C22×D5311yescharacteristic
1167#120—1061no—
1168#120—1061no—
1169#120—1061no—
1170#120—1061no—
1171C4×Q8—531no—
1172C4×Q8—531no—
1173C4×Q8—531no—
1174C4×Q8—531no—
1175C4×Q8—531no—
1176C4×Q8—531no—
1177C4×Q8—1061no—
1178C4×Q8—1061no—
1179C4×Q8—1061no—
1180C4×Q8—1061no—
1181C4×D4—531no—
1182C4×D4—531no—
1183C4×D4—531no—
1184C4×D4—531no—
1185C4×D4—531no—
1186C4×D4—531no—
1187C4×D4—531no—
1188C4×D4—531no—
1189C4×D4—531no—
1190C4×D4—531no—
1191C4×D4—531no—
1192C4×D4—531no—
1193C4×D4—1061no—
1194C4×D4—1061no—
1195C4×D4—1061no—
1196C4×D4—1061no—
1197C4×D4—1061no—
1198C4×D4—1061no—
1199C4×D4—1061no—
1200C4×D4—1061no—
1201C4×D4—1061no—
1202C4×D4—1061no—
1203C4×D4—1061no—
1204C4×D4—1061no—
1205C4×D4C22×D5311yescharacteristic
1206C4×D4C22×D5311yescharacteristic
1207#117—531no—
1208#117—531no—
1209#117—531no—
1210#117—531no—
1211#117—531no—
1212#117—1061no—
1213#117—1061no—
1214#117—1061no—
1215#117—1061no—
1216#117—1061no—
1217#117—1061no—
1218#117—1061no—
1219#117C22×D5311yescharacteristic
1220#117C22×D5311yescharacteristic
1221C2×C4⋊C4—531no—
1222C2×C4⋊C4—531no—
1223C2×C4⋊C4—531no—
1224C2×C4⋊C4—1061no—
1225C2×C4⋊C4—1061no—
1226C2×C4⋊C4—1061no—
1227C2×C4⋊C4C22×D5311yescharacteristic
1228C2×C22⋊C4—1061no—
1229C2×C22⋊C4—1061no—
1230C2×C22⋊C4—1061no—
1231C2×C22⋊C4—1061no—
1232C2×C22⋊C4—1061no—
1233C2×C42—531no—
1234#107—531no—
1235#107—531no—
1236#107—531no—
1237#107—531no—
1238#107—531no—
1239#107—531no—
1240#107—531no—
1241#107—531no—
1242#107C22×D5311yescharacteristic
1243#107C22×D5311yescharacteristic
1244#107C22×D5311yescharacteristic
1245#107C22×D5311yescharacteristic
1246#106—531no—
1247#106—531no—
1248#106—531no—
1249#106—531no—
1250#106—531no—
1251#106—531no—
1252#106—531no—
1253#106—531no—
1254#106C22×D5311yescharacteristic
1255#106C22×D5311yescharacteristic
1256#106C22×D5311yescharacteristic
1257#106C22×D5311yescharacteristic
1258C4⋊C8—531no—
1259C4⋊C8—531no—
1260C4⋊C8—531no—
1261C4⋊C8—531no—
1262C4⋊C8—531no—
1263C4⋊C8—531no—
1264C4⋊C8—531no—
1265C4⋊C8—531no—
1266C4⋊C8C22×D5311yescharacteristic
1267C4⋊C8C22×D5311yescharacteristic
1268#103—531no—
1269#103—531no—
1270#103—531no—
1271#103—531no—
1272#103—531no—
1273#103—531no—
1274#103—531no—
1275#103—531no—
1276#103—531no—
1277#103—531no—
1278#102—531no—
1279#102—531no—
1280#102—531no—
1281#102—531no—
1282#102—531no—
1283#102—531no—
1284#102—531no—
1285#102—531no—
1286#102—531no—
1287#102—531no—
1288#102—531no—
1289#102—531no—
1290#102—531no—
1291#102—531no—
1292#102C22×D5311yescharacteristic
1293#102C22×D5311yescharacteristic
1294#102C22×D5311yescharacteristic
1295#102C22×D5311yescharacteristic
1296#102C22×D5311yescharacteristic
1297#102C22×D5311yescharacteristic
1298#102C22×D5311yescharacteristic
1299#102C22×D5311yescharacteristic
1300C22⋊C8—531no—
1301C22⋊C8—531no—
1302C22⋊C8—531no—
1303C22⋊C8—531no—
1304C22⋊C8C22×D5311yescharacteristic
1305C22⋊C8C22×D5311yescharacteristic
1306#97—531no—
1307#97C22×D5311yescharacteristic
1308C4×C8—531no—
1309C4×C8—531no—
1310C4×C8—531no—
1311C4×C8C22×D5311yescharacteristic
1312C24—1061no—
1313C24—1061no—
1314#41—1062no—
1315#41—4242no—
1316#41—2121no—
1317C2×Q8—21no—
1318C2×Q8—21no—
1319C2×Q8—531no—
1320C2×Q8—531no—
1321C2×Q8—531no—
1322C2×Q8—1061no—
1323C2×Q8—1061no—
1324C2×Q8—1061no—
1325C2×D4—21no—
1326C2×D4—21no—
1327C2×D4—21no—
1328C2×D4—21no—
1329C2×D4—531no—
1330C2×D4—531no—
1331C2×D4—531no—
1332C2×D4—531no—
1333C2×D4—531no—
1334C2×D4—1061no—
1335C2×D4—1061no—
1336C2×D4—1061no—
1337C2×D4—1061no—
1338C2×D4—1062no—
1339C2×D4—1062no—
1340C2×D4—1061no—
1341C2×D4—1061no—
1342C2×D4—1061no—
1343C2×D4—1061no—
1344C2×D4—4242no—
1345C2×D4—2121no—
1346C2×D4—2121no—
1347C2×D4C23×D5311yescharacteristic
1348C2×D4C23×D5311yescharacteristic
1349C22×C4—21no—
1350C22×C4—21no—
1351C22×C4—21no—
1352C22×C4—531no—
1353C22×C4—531no—
1354C22×C4—531no—
1355C22×C4—531no—
1356C22×C4—1061no—
1357C22×C4—1061no—
1358C22×C4—1061no—
1359C22×C4—1061no—
1360C22×C4—1061no—
1361C22×C4—1061no—
1362C22×C4—1061no—
1363C22×C4—1061no—
1364C22×C4—1061no—
1365C22×C4—1061no—
1366C22×C4—1061no—
1367C22×C4—1061no—
1368C22×C4—1061no—
1369C22×C4—4242no—
1370C22×C4C23×D5311yescharacteristic
1371Q16—2121no—
1372SD16—1062no—
1373SD16—2121no—
1374SD16—2121no—
1375SD16—2121no—
1376D8—1062no—
1377D8—2121no—
1378D8—2121no—
1379M16—2121no—
1380M16—2121no—
1381M16—2121no—
1382M16—2121no—
1383C2×C8—531no—
1384C2×C8—531no—
1385C2×C8—531no—
1386C2×C8—531no—
1387C2×C8—2121no—
1388C2×C8—2121no—
1389C2×C8C23×D5311yescharacteristic
1390C2×C8C23×D5311yescharacteristic
1391C2×C8C23×D5311yescharacteristic
1392C2×C8C23×D5311yescharacteristic
1393C4⋊C4—21no—
1394C4⋊C4—21no—
1395C4⋊C4—21no—
1396C4⋊C4—21no—
1397C4⋊C4—21no—
1398C4⋊C4—21no—
1399C4⋊C4—21no—
1400C4⋊C4—21no—
1401C4⋊C4—21no—
1402C4⋊C4—531no—
1403C4⋊C4—531no—
1404C4⋊C4—531no—
1405C4⋊C4—531no—
1406C4⋊C4—531no—
1407C4⋊C4—531no—
1408C4⋊C4—531no—
1409C4⋊C4—531no—
1410C4⋊C4—531no—
1411C4⋊C4—531no—
1412C4⋊C4—531no—
1413C4⋊C4—531no—
1414C4⋊C4—1061no—
1415C4⋊C4—1061no—
1416C4⋊C4—1061no—
1417C4⋊C4—1061no—
1418C4⋊C4—1061no—
1419C4⋊C4—1061no—
1420C4⋊C4—1061no—
1421C4⋊C4—1061no—
1422C4⋊C4—1061no—
1423C4⋊C4—1061no—
1424C4⋊C4—1061no—
1425C4⋊C4—1061no—
1426C4⋊C4—1061no—
1427C4⋊C4—1061no—
1428C4⋊C4—1061no—
1429C4⋊C4—1061no—
1430C4⋊C4—1061no—
1431C4⋊C4—1061no—
1432C4⋊C4—1061no—
1433C4⋊C4—1061no—
1434C4⋊C4—1061no—
1435C4⋊C4—1061no—
1436C4⋊C4—1061no—
1437C4⋊C4—1061no—
1438C4⋊C4D4×D5311yescharacteristic
1439C4⋊C4D4×D5311yescharacteristic
1440C4⋊C4C23×D5311yescharacteristic
1441C4⋊C4C23×D5311yescharacteristic
1442C4⋊C4C23×D5311yescharacteristic
1443C4⋊C4C23×D5311yescharacteristic
1444C4⋊C4C23×D5311yescharacteristic
1445C4⋊C4C23×D5311yescharacteristic
1446C22⋊C4—21no—
1447C22⋊C4—21no—
1448C22⋊C4—21no—
1449C22⋊C4—21no—
1450C22⋊C4—21no—
1451C22⋊C4—531no—
1452C22⋊C4—531no—
1453C22⋊C4—531no—
1454C22⋊C4—531no—
1455C22⋊C4—531no—
1456C22⋊C4—531no—
1457C22⋊C4—531no—
1458C22⋊C4—531no—
1459C22⋊C4—1061no—
1460C22⋊C4—1061no—
1461C22⋊C4—1061no—
1462C22⋊C4—1061no—
1463C22⋊C4—1061no—
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—1061no—
1478C22⋊C4—1061no—
1479C22⋊C4—1061no—
1480C22⋊C4—1061no—
1481C22⋊C4—1061no—
1482C22⋊C4—1061no—
1483C22⋊C4—1061no—
1484C22⋊C4—1061no—
1485C22⋊C4—1061no—
1486C22⋊C4—1061no—
1487C22⋊C4—1061no—
1488C22⋊C4D4×D5311yescharacteristic
1489C22⋊C4D4×D5311yescharacteristic
1490C42—21no—
1491C42—531no—
1492C42—531no—
1493C42—531no—
1494C42—531no—
1495C42—1061no—
1496C42—1061no—
1497C42—1061no—
1498C42—1061no—
1499C42—1061no—
1500C42—1061no—
1501C42—1061no—
1502C42—1061no—
1503C42—1061no—
1504C42C23×D5311yescharacteristic
1505C42C23×D5311yescharacteristic
1506C23—21no—
1507C23—21no—
1508C23—531no—
1509C23—531no—
1510C23—1061no—
1511C23—1061no—
1512C23—4241no—
1513C23—4241no—
1514C23—4241no—
1515C23—2122no—
1516C23—2122no—
1517C23—2122no—
1518C23C2×D4×D5311yescharacteristic
1519Q8—81no—
1520Q8—81no—
1521Q8—1061no—
1522Q8—1061no—
1523Q8—1061no—
1524Q8—1061no—
1525Q8—4241no—
1526Q8—4241no—
1527Q8—4241no—
1528Q8—2121no—
1529D4—21no—
1530D4—21no—
1531D4—21no—
1532D4—21no—
1533D4—81no—
1534D4—81no—
1535D4—81no—
1536D4—81no—
1537D4—532no—
1538D4—1061no—
1539D4—1061no—
1540D4—1061no—
1541D4—4241no—
1542D4—4241no—
1543D4—4241no—
1544D4—4241no—
1545D4—2121no—
1546D4—2121no—
1547D4—2121no—
1548D4—2122no—
1549D4—2122no—
1550D4—2122no—
1551D4—2122no—
1552C2×C4—21no—
1553C2×C4—21no—
1554C2×C4—21no—
1555C2×C4—21no—
1556C2×C4—21no—
1557C2×C4—21no—
1558C2×C4—21no—
1559C2×C4—21no—
1560C2×C4—81no—
1561C2×C4—81no—
1562C2×C4—81no—
1563C2×C4—531no—
1564C2×C4—531no—
1565C2×C4—531no—
1566C2×C4—531no—
1567C2×C4—531no—
1568C2×C4—531no—
1569C2×C4—1061no—
1570C2×C4—1061no—
1571C2×C4—1061no—
1572C2×C4—1061no—
1573C2×C4—1061no—
1574C2×C4—1061no—
1575C2×C4—1061no—
1576C2×C4—1061no—
1577C2×C4—1061no—
1578C2×C4—1061no—
1579C2×C4—4241no—
1580C2×C4—4241no—
1581C2×C4—4241no—
1582C2×C4—4241no—
1583C2×C4—4241no—
1584C2×C4—4241no—
1585C2×C4—4241no—
1586C2×C4—4241no—
1587C2×C4—4241no—
1588C2×C4—4241no—
1589C2×C4—4241no—
1590C2×C4—2121no—
1591C2×C4—2121no—
1592C2×C4—2122no—
1593C2×C4—2122no—
1594C2×C4C2×D4×D5311yescharacteristic
1595C2×C4C2×D4×D5311yescharacteristic
1596C2×C4C2×D4×D5311yescharacteristic
1597C2×C4C2×D4×D5311yescharacteristic
1598C2×C4C2×D4×D5311yescharacteristic
1599C2×C4C24×D5311yescharacteristic
1600C8—21no—
1601C8—21no—
1602C8—21no—
1603C8—21no—
1604C8—1061no—
1605C8—1061no—
1606C8—1061no—
1607C8—1061no—
1608C22—21no—
1609C22—21no—
1610C22—21no—
1611C22—41no—
1612C22—41no—
1613C22—41no—
1614C22—41no—
1615C22—41no—
1616C22—41no—
1617C22—8482no—
1618C22—1061no—
1619C22—1061no—
1620C22—1062no—
1621C22—1061no—
1622C22—1061no—
1623C22—1061no—
1624C22—1061no—
1625C22—4244no—
1626C22—2121no—
1627C22—2121no—
1628C22—2121no—
1629C22—2121no—
1630C22—2121no—
1631C22C22×D4×D5311yescharacteristic
1632C4—21no—
1633C4—21no—
1634C4—21no—
1635C4—21no—
1636C4—21no—
1637C4—41no—
1638C4—41no—
1639C4—41no—
1640C4—41no—
1641C4—41no—
1642C4—41no—
1643C4—1061no—
1644C4—1061no—
1645C4—1061no—
1646C4—1061no—
1647C4—1061no—
1648C4—1061no—
1649C4—2121no—
1650C4—2121no—
1651C4—2121no—
1652C4—2121no—
1653C4—2121no—
1654C4—2121no—
1655C42−1+4×D5311yescharacteristic
1656C4#1681146011yescharacteristic
1657C2—41no—
1658C2—81no—
1659C2—81no—
1660C2—4241no—
1661C2—2121no—
1662C2—2122no—
1663C2—2121no—
1664C2#2028839311yescharacteristic
1665C2#2028948711yescharacteristic
1666C2#2028949011yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3241C2
socleC22×C53C23×D4
hypercenter#3241D53
hypocenterC53#62175
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ #117 ◁ #3241

Complements

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

NH ≅ G/Ntype
1. #20289356C2semidirect
2. #20288653C2semidirect
3. #20287670C2semidirect
4. #20287587C2semidirect
5. #20287478C2semidirect
6. #20287380C2semidirect
7. #20287308C2semidirect
8. #20287274C2semidirect
9. #20287268C2semidirect
10. #20287244C2semidirect
11. #20287159C2semidirect
12. #20287115C2semidirect
13. #20286945C2semidirect
14. #20286934C2semidirect
15. #20286919C2semidirect
16. #20286869C2semidirect
17. #20286855C2semidirect
18. #20286553C2semidirect
19. #20286175C2semidirect
20. #20286120C2semidirect
21. #20286115C2semidirect
22. #20286012C2semidirect
23. #20285893C2semidirect
24. #20284994C2semidirect
25. #20284904C2semidirect
26. #20284767C2semidirect
27. #20284562C2semidirect
28. #20284545C2semidirect
29. #20284507C2semidirect
30. #20283858C2semidirect
31. C53×#3241C2semidirect
35. #16811350C22semidirect
38. #16811336C22semidirect
39. #16811334C22semidirect
43. #16811321C22semidirect
45. #16811312C22semidirect
47. #16811308C22semidirect
56. #16811253C22semidirect
58. #16811247C22semidirect
60. #16811244C22semidirect
66. #16811178C22semidirect
67. #16811158C22semidirect
75. #16811031C22semidirect
76. #16811023C22semidirect
77. #16811023C22semidirect
78. #16811020C22semidirect
79. #16810981C22semidirect
80. #16810976C22semidirect
81. #16810976C22semidirect
82. #16810976C22semidirect
83. #16810967C22semidirect
84. #16810967C22semidirect
85. #16810967C22semidirect
86. #16810966C22semidirect
87. #16810960C22semidirect
88. #16810955C22semidirect
89. #16810954C22semidirect
90. #16810949C22semidirect
94. #16810943C22semidirect
95. #16810942C22semidirect
97. #16810929C22semidirect
98. #16810927C22semidirect
99. #16810927C22semidirect
100. #16810927C22semidirect
103. #16810925C22semidirect
104. #16810925C22semidirect
105. #16810925C22semidirect
107. #16810922C22semidirect
110. #16810920C22semidirect
111. #16810917C22semidirect
112. #16810915C22semidirect
113. #16810915C22semidirect
115. #16810913C22semidirect
116. #16810911C22semidirect
117. #16810909C22semidirect
118. #16810903C22semidirect
120. #16810902C22semidirect
123. #16810882C22semidirect
125. #16810874C22semidirect
126. #16810870C22semidirect
127. #16810870C22semidirect
130. #16810867C22semidirect
131. #16810865C22semidirect
133. #16810857C22semidirect
134. #16810850C22semidirect
135. #16810846C22semidirect
136. #16810844C22semidirect
137. #16810844C22semidirect
139. #16810838C22semidirect
140. #16810838C22semidirect
141. #16810837C22semidirect
142. #16810837C22semidirect
151. #16810751C22semidirect
152. C8×Dic106C22semidirect
155. #16810731C22semidirect
156. #16810720C22semidirect
157. #16810714C22semidirect
159. C4×#11719913C22semidirect
163. #16810703C22semidirect
164. #16810703C22semidirect
166. #16810698C22semidirect
167. #16810698C22semidirect
169. #16810691C22semidirect
170. #16810686C22semidirect
171. #16810683C22semidirect
172. #16810675C22semidirect
173. #16810666C22semidirect
174. #16810664C22semidirect
175. #16810664C22semidirect
176. #16810664C22semidirect
177. #16810658C22semidirect
178. C2×#13133150C22semidirect
179. #16810650C22semidirect
180. #16810648C22semidirect
181. #16810645C22semidirect
188. C53×#544C22semidirect
190. C53×#501C22semidirect
191. C53×#499C22semidirect
194. C53×#482C22semidirect
195. C53×#482C22semidirect
196. C53×#481C22semidirect
197. C53×#480C22semidirect
198. C53×#478C22semidirect
199. C53×#478C22semidirect
200. C53×#476C22semidirect
201. C53×#474C22semidirect
202. C53×#433C22semidirect
846. #3241D53semidirect
890. #544C2×D53semidirect
911. #501C2×D53semidirect
914. #499C2×D53semidirect
933. #482C2×D53semidirect
934. #482C2×D53semidirect
938. #481C2×D53semidirect
939. #480C2×D53semidirect
954. #478C2×D53semidirect
955. #478C2×D53semidirect
962. #476C2×D53semidirect
969. #474C2×D53semidirect
1019. #433C2×D53semidirect
1036. C53#62175semidirect

Maximal subgroups

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

subgroupindex
#202893562
#202886532
#202876702
#202875872
#202874782
#202873802
#202873082
#202872742
#202872682
#202872442
#202871592
#202871152
#202869452
#202869342
#202869192
#202868692
#202868552
#202865532
#202861752
#202861202
#202861152
#202860122
#202858932
#202849942
#202849042
#202847672
#202845622
#202845452
#202845072
#202838582
C53×#32412
#6217553