Finite Group Databasebeta

← #28256032

Subgroups — #28256032

Order 13568.

2104 conjugacy classes of subgroups.

The subgroup lattice has 1898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288504C211yesmaximal, characteristic, complemented
2#20288130C211yesmaximal, characteristic, complemented
3#20285824C211yesmaximal, characteristic, complemented
4#20285823C211yesmaximal, characteristic, complemented
5#20285811C211yesmaximal, characteristic, complemented
6#20285808C211yesmaximal, characteristic, complemented
7#20285775C211yesmaximal, characteristic, complemented
8#20285762C211yesmaximal, characteristic, complemented
9#20285759C211yesmaximal, characteristic, complemented
10#20285755C211yesmaximal, characteristic, complemented
11#20285750C211yesmaximal, characteristic, complemented
12#20285701C211yesmaximal, characteristic, complemented
13#20285697C211yesmaximal, characteristic, complemented
14#20285681C211yesmaximal, characteristic, complemented
15#20285679C211yesmaximal, characteristic, complemented
16#20285646C211yesmaximal, characteristic, complemented
17#20285645C211yesmaximal, characteristic, complemented
18#20285199C211yesmaximal, characteristic, complemented
19#20285184C211yesmaximal, characteristic, complemented
20#20285081C211yesmaximal, characteristic, complemented
21#20285068C211yesmaximal, characteristic, complemented
22#20284204C211yesmaximal, characteristic, complemented
23#20284180C211yesmaximal, characteristic, complemented
24#20284171C211yesmaximal, characteristic, complemented
25#463×D53C211yesmaximal, characteristic, complemented
26#20284025C211yesmaximal, characteristic, complemented
27#20284017C211yesmaximal, characteristic, complemented
28#20283996C211yesmaximal, characteristic, complemented
29#20283980C211yesmaximal, characteristic, complemented
30#20283378C211yesmaximal, characteristic, complemented
31C53×#3221C211yesmaximal, characteristic, complemented
32C2×#13133265C2211yescharacteristic
33C2×#13133263C2211yescharacteristic
34C2×#13133246C2211yescharacteristic, complemented
35C2×#13133244C2211yescharacteristic
36C2×#13133244C2211yescharacteristic, complemented
37C2×#13133241C2211yescharacteristic
38C2×#13133238C2211yescharacteristic
39C2×#13133238C2211yescharacteristic, complemented
40C2×SD16×D53C2211yescharacteristic, complemented
41C2×D8×D53C2211yescharacteristic
42#16811283—21no—
43#16811283—21no—
44#16811265—21no—
45#16811265—21no—
46#16811265—21no—
47#16811265—21no—
48#16811264—21no—
49#16811264—21no—
50#16811253C2211yescharacteristic, complemented
51#16811244C2211yescharacteristic, complemented
52#16811241—21no—
53#16811238C2211yescharacteristic, complemented
54#16811224C2211yescharacteristic, complemented
55#16811223—21no—
56#16811209—21no—
57#16811205—21no—
58#16811202C2211yescharacteristic
59#16811198C2211yescharacteristic
60#16811198C2211yescharacteristic, complemented
61#16811192C2211yescharacteristic, complemented
62#16811191C2211yescharacteristic
63#16811191C2211yescharacteristic, complemented
64#16811189C2211yescharacteristic
65#16811186C2211yescharacteristic, complemented
66#16811174C2211yescharacteristic
67#16811174C2211yescharacteristic, complemented
68#16811171C2211yescharacteristic, complemented
69#16811169C2211yescharacteristic, complemented
70#16811168—21no—
71#16811168C2211yescharacteristic, complemented
72#16811158C2211yescharacteristic, complemented
73#16811154C2211yescharacteristic, complemented
74#16811150—21no—
75C2×#13133206C2211yescharacteristic, complemented
76#124×D53C2211yescharacteristic
77#124×D53C2211yescharacteristic, complemented
78#16811133—21no—
79#16811131—21no—
80#16811091C2211yescharacteristic
81C4×#11719947C2211yescharacteristic, complemented
82C4×D4×D53C2211yescharacteristic, complemented
83#16811015C2211yescharacteristic, complemented
84#16811014C2211yescharacteristic, complemented
85#16811012C2211yescharacteristic, complemented
86#16811011C2211yescharacteristic, complemented
87#16811010C2211yescharacteristic, complemented
88#16811009C2211yescharacteristic, complemented
89#16811009C2211yescharacteristic, complemented
90#16811007C2211yescharacteristic, complemented
91#16811005C2211yescharacteristic, complemented
92#16811004C2211yescharacteristic, complemented
93#16811004C2211yescharacteristic, complemented
94#16810999C2211yescharacteristic, complemented
95#16810998C2211yescharacteristic, complemented
96#16810994C2211yescharacteristic, complemented
97#16810990C2211yescharacteristic, complemented
98#16810989C2211yescharacteristic, complemented
99#16810986C2211yescharacteristic, complemented
100#16810984C2211yescharacteristic, complemented
101#16810984C2211yescharacteristic, complemented
102#16810983C2211yescharacteristic, complemented
103#16810982C2211yescharacteristic, complemented
104#16810980C2211yescharacteristic, complemented
105#16810979C2211yescharacteristic, complemented
106#16810979C2211yescharacteristic, complemented
107#16810973C2211yescharacteristic, complemented
108#16810972C2211yescharacteristic, complemented
109#16810970C2211yescharacteristic, complemented
110#16810968C2211yescharacteristic, complemented
111#16810848C2211yescharacteristic, complemented
112#16810848C2211yescharacteristic, complemented
113#16810848C2211yescharacteristic, complemented
114#16810846C2211yescharacteristic, complemented
115#16810844C2211yescharacteristic, complemented
116#16810842C2211yescharacteristic, complemented
117#16810841C2211yescharacteristic, complemented
118#16810841C2211yescharacteristic, complemented
119#16810841C2211yescharacteristic, complemented
120#16810840C2211yescharacteristic, complemented
121#16810840C2211yescharacteristic, complemented
122#16810840C2211yescharacteristic, complemented
123#16810840C2211yescharacteristic, complemented
124#16810840C2211yescharacteristic, complemented
125#16810840C2211yescharacteristic, complemented
126#16810839C2211yescharacteristic, complemented
127#16810838C2211yescharacteristic, complemented
128#16810838C2211yescharacteristic, complemented
129#16810837C2211yescharacteristic, complemented
130#16810836C2211yescharacteristic, complemented
131#16810836C2211yescharacteristic, complemented
132#16810835C2211yescharacteristic, complemented
133#16810830C2211yescharacteristic, complemented
134#16810825C2211yescharacteristic, complemented
135#16810824C2211yescharacteristic, complemented
136#16810819C2211yescharacteristic, complemented
137#16810818C2211yescharacteristic, complemented
138#16810818C2211yescharacteristic, complemented
139#16810788C2211yescharacteristic, complemented
140#16810788C2211yescharacteristic, complemented
141#16810787C2211yescharacteristic, complemented
142#16810785C2211yescharacteristic, complemented
143#16810780C2211yescharacteristic, complemented
144#16810779C2211yescharacteristic, complemented
145#16810776C2211yescharacteristic, complemented
146#16810775C2211yescharacteristic, complemented
147#16810771C2211yescharacteristic
148#16810771C2211yescharacteristic, complemented
149#16810770C2211yescharacteristic, complemented
150#16810768C2211yescharacteristic
151#16810767C2211yescharacteristic
152#16810767C2211yescharacteristic, complemented
153#16810767C2211yescharacteristic, complemented
154#16810767C2211yescharacteristic, complemented
155#16810766C2211yescharacteristic, complemented
156#16810766C2211yescharacteristic, complemented
157#16810763C2211yescharacteristic, complemented
158#16810762C2211yescharacteristic, complemented
159#16810760C2211yescharacteristic, complemented
160#16810760C2211yescharacteristic, complemented
161#16810759C2211yescharacteristic
162#16810758C2211yescharacteristic
163#16810756C2211yescharacteristic
164#16810756C2211yescharacteristic, complemented
165#16810755C2211yescharacteristic
166#16810755C2211yescharacteristic, complemented
167#16810684C2211yescharacteristic, complemented
168#16810683C2211yescharacteristic, complemented
169#16810683C2211yescharacteristic, complemented
170#16810678C2211yescharacteristic, complemented
171#16810677C2211yescharacteristic, complemented
172#16810674C2211yescharacteristic, complemented
173#16810673C2211yescharacteristic, complemented
174#16810645C2211yescharacteristic, complemented
175C4⋊C8×D53C2211yescharacteristic, complemented
176#16810630C2211yescharacteristic, complemented
177#16810626C2211yescharacteristic
178#16810623C2211yescharacteristic
179#16810623C2211yescharacteristic, complemented
180#16810618C2211yescharacteristic
181#16810618C2211yescharacteristic, complemented
182#103×D53C2211yescharacteristic, complemented
183#102×D53C2211yescharacteristic
184#16810588C2211yescharacteristic
185#16810588C2211yescharacteristic
186#16810580C2211yescharacteristic, complemented
187#16810577C2211yescharacteristic, complemented
188C53×#540C2211yescharacteristic, complemented
189C53×#536C2211yescharacteristic, complemented
190C53×#496C2211yescharacteristic, complemented
191C53×#492C2211yescharacteristic, complemented
192C53×#491C2211yescharacteristic, complemented
193C53×#488C2211yescharacteristic, complemented
194C53×#463C2211yescharacteristic, complemented
195C53×#463C2211yescharacteristic, complemented
196C53×#461C2211yescharacteristic, complemented
197C53×#461C2211yescharacteristic, complemented
198C53×#449C2211yescharacteristic
199C53×#449C2211yescharacteristic, complemented
200C53×#448C2211yescharacteristic, complemented
201C53×#448C2211yescharacteristic, complemented
202C53×#433C2211yescharacteristic, complemented
203#13133265—42no—
204#13133265—42no—
205#13133263—42no—
206#13133263—42no—
207C2×#11719949—21no—
208C2×#11719949C2311yescharacteristic
209C2×#11719949C2311yescharacteristic
210C2×#11719949C2311yescharacteristic
211C2×#11719949C2311yescharacteristic
212C2×#11719945—21no—
213C2×#11719945—21no—
214C2×#11719945—21no—
215C2×#11719945C2311yescharacteristic
216C2×#11719945C2311yescharacteristic
217C2×#11719947—21no—
218C2×#11719947—21no—
219C2×#11719947C2311yescharacteristic
220C2×Q8×D53—21no—
221C2×Q8×D53C2311yescharacteristic
222C2×Q8×D53C2311yescharacteristic
223C22×D212—21no—
224C22×D212C2311yescharacteristic
225C2×D4×D53—21no—
226C2×D4×D53—21no—
227C2×D4×D53C2311yescharacteristic
228C2×D4×D53C2311yescharacteristic
229C2×D4×D53C2311yescharacteristic
230C22×C4×D53—21no—
231#13133246—42no—
232#13133244—42no—
233#13133244—42no—
234#13133241—42no—
235#13133238—42no—
236#13133238—42no—
237C2×Dic212C2311yescharacteristic
238C2×#11719925C2311yescharacteristic
239C2×#11719925C2311yescharacteristic
240C2×#11719925C2311yescharacteristic
241C2×#11719913C2311yescharacteristic
242C2×#11719913C2311yescharacteristic
243C2×#11719913C2311yescharacteristic
244C2×#11719913C2311yescharacteristic
245C2×#11719923C2311yescharacteristic
246C2×#11719923C2311yescharacteristic
247C2×#11719923C2311yescharacteristic
248C2×#11719924C2311yescharacteristic
249C2×#11719924C2311yescharacteristic
250C2×#11719924C2311yescharacteristic
251SD16×D53—42no—
252C2×D424C2311yescharacteristic
253C2×D424C2311yescharacteristic
254C2×D424C2311yescharacteristic
255C2×#11719922C2311yescharacteristic
256C2×#11719922C2311yescharacteristic
257C2×#11719922C2311yescharacteristic
258C2×#11719922C2311yescharacteristic
259C2×#11719922C2311yescharacteristic
260C2×#11719922C2311yescharacteristic
261C2×#11719922C2311yescharacteristic
262D8×D53—42no—
263C2×#11719912C2311yescharacteristic
264C2×#11719912C2311yescharacteristic
265C2×C8×D53C2311yescharacteristic
266C2×C8×D53C2311yescharacteristic
267#13133217C2311yescharacteristic
268#13133216—21no—
269#13133216C2311yescharacteristic
270#13133215C2311yescharacteristic
271#13133214C2311yescharacteristic
272#13133214C2311yescharacteristic
273#13133213—21no—
274#13133213C2311yescharacteristic
275#13133213C2311yescharacteristic
276#13133212—21no—
277#13133212—21no—
278#13133210—21no—
279#13133210—21no—
280#13133208C2311yescharacteristic
281#13133207—21no—
282#13133206—21no—
283#13133206—21no—
284#13133206C2311yescharacteristic
285#13133206C2311yescharacteristic
286#13133206C2311yescharacteristic
287#13133206C2311yescharacteristic
288#13133206C2311yescharacteristic
289#13133205C2311yescharacteristic
290#13133205C2311yescharacteristic
291#13133205C2311yescharacteristic
292#13133204—21no—
293#13133204C2311yescharacteristic
294#13133204C2311yescharacteristic
295#13133203—21no—
296#13133203—21no—
297#13133203—21no—
298#13133203—21no—
299#13133203—21no—
300#13133203—21no—
301#13133203—21no—
302#13133203—21no—
303#13133202—21no—
304#13133202—21no—
305#13133202—21no—
306#13133202—21no—
307#13133202—21no—
308#13133200—21no—
309#13133200—21no—
310#13133199—21no—
311#13133199—21no—
312#13133198—21no—
313#13133197—21no—
314#13133197C2311yescharacteristic
315#13133196—21no—
316#13133196C2311yescharacteristic
317#13133195—21no—
318#13133195—21no—
319#13133195—21no—
320#13133195—21no—
321#13133195—21no—
322#13133195—21no—
323#13133194—21no—
324#13133192—21no—
325#13133192—21no—
326#13133192—21no—
327#13133192—21no—
328#13133192—21no—
329#13133192—21no—
330#13133192C2311yescharacteristic
331#13133191—21no—
332#13133191C2311yescharacteristic
333#13133190—21no—
334#13133190—21no—
335#13133190—21no—
336#13133190—21no—
337#13133190—21no—
338#13133190—21no—
339#13133189—21no—
340#13133189—21no—
341#13133189—21no—
342#13133189—21no—
343#13133189—21no—
344#13133189—21no—
345#13133188—21no—
346#13133188—21no—
347#13133188C2311yescharacteristic
348#13133188C2311yescharacteristic
349#13133187—21no—
350#13133187—21no—
351#13133187—21no—
352#13133187—21no—
353#13133187—21no—
354#13133187—21no—
355#13133187—21no—
356#13133185—21no—
357#13133185—21no—
358#13133185—21no—
359C4×Dic106C2311yescharacteristic
360#13133182D411yescharacteristic
361#13133182D411yescharacteristic
362#13133182C2311yescharacteristic
363C4×D212C2311yescharacteristic
364D4×Dic53—21no—
365D4×Dic53—21no—
366D4×Dic53C2311yescharacteristic
367D4×Dic53C2311yescharacteristic
368#13133179—21no—
369#13133179—21no—
370#13133179—21no—
371#13133179—21no—
372#13133179—21no—
373#13133179D411yescharacteristic
374#13133179D411yescharacteristic
375#13133179C2311yescharacteristic
376C4×C22⋊D53—21no—
377C4×C22⋊D53—21no—
378C4×C22⋊D53—21no—
379C4×C22⋊D53—21no—
380#13133177—21no—
381#13133177—21no—
382#13133177—21no—
383#13133177D411yescharacteristic
384#13133177D411yescharacteristic
385#13133177D411yescharacteristic
386#13133177D411yescharacteristic
387#13133175—21no—
388#13133175C2311yescharacteristic
389#13133174C2311yescharacteristic
390#13133174C2311yescharacteristic
391#13133173—21no—
392#13133173—21no—
393C4⋊C4×D53C2311yescharacteristic
394C2×#11719921—21no—
395C2×#11719921—21no—
396C22⋊C4×D53—21no—
397C22⋊C4×D53—21no—
398C22⋊C4×D53—21no—
399C22⋊C4×D53—21no—
400C22⋊C4×D53—21no—
401C2×C4×Dic53—21no—
402C2×C4×Dic53C2311yescharacteristic
403C42×D53C2311yescharacteristic
404C42×D53C2311yescharacteristic
405C4⋊#88322C2311yescharacteristic
406C4⋊#88322C2311yescharacteristic
407#13133146C2311yescharacteristic
408#13133146C2311yescharacteristic
409#13133146C2311yescharacteristic
410#13133146C2311yescharacteristic
411#13133142C2311yescharacteristic
412#13133142C2311yescharacteristic
413#13133141C2311yescharacteristic
414#13133141C2311yescharacteristic
415#13133141C2311yescharacteristic
416#13133141C2311yescharacteristic
417#13133141C2311yescharacteristic
418#13133141C2311yescharacteristic
419#13133140C2311yescharacteristic
420#13133140C2311yescharacteristic
421#13133139C2311yescharacteristic
422#13133139C2311yescharacteristic
423#13133139C2311yescharacteristic
424#13133139C2311yescharacteristic
425#13133139C2311yescharacteristic
426#13133139C2311yescharacteristic
427#13133138C2311yescharacteristic
428#13133138C2311yescharacteristic
429#13133137C2311yescharacteristic
430#13133137C2311yescharacteristic
431#13133137C2311yescharacteristic
432#13133137C2311yescharacteristic
433#13133137C2311yescharacteristic
434#13133137C2311yescharacteristic
435C22⋊#88322C2311yescharacteristic
436C22⋊#88322C2311yescharacteristic
437#13133129C2311yescharacteristic
438#13133129C2311yescharacteristic
439#13133129C2311yescharacteristic
440#13133129C2311yescharacteristic
441#13133128C2311yescharacteristic
442#13133127C2311yescharacteristic
443#13133127C2311yescharacteristic
444C4×#88322C2311yescharacteristic
445C8×Dic53C2311yescharacteristic
446C8×Dic53C2311yescharacteristic
447C2×#41×C53C2311yescharacteristic
448C22×Q8×C53C2311yescharacteristic
449C2×SD16×C53C2311yescharacteristic
450C2×SD16×C53C2311yescharacteristic
451C2×SD16×C53C2311yescharacteristic
452C2×SD16×C53C2311yescharacteristic
453C2×SD16×C53C2311yescharacteristic
454C2×SD16×C53C2311yescharacteristic
455C2×D8×C53C2311yescharacteristic
456C2×D8×C53C2311yescharacteristic
457C4⋊Q8×C53C2311yescharacteristic
458C4⋊Q8×C53C2311yescharacteristic
459#127×C53C2311yescharacteristic
460#125×C53C2311yescharacteristic
461#124×C53C2311yescharacteristic
462#124×C53C2311yescharacteristic
463#123×C53—21no—
464#123×C53—21no—
465#123×C53—21no—
466#123×C53—21no—
467C22⋊Q8×C53—21no—
468C22⋊Q8×C53—21no—
469#121×C53—21no—
470#121×C53—21no—
471#121×C53C2311yescharacteristic
472#121×C53C2311yescharacteristic
473C4×D4×C53C2311yescharacteristic
474C4×D4×C53C2311yescharacteristic
475#117×C53C2311yescharacteristic
476C4⋊C8×C53C2311yescharacteristic
477C4⋊C8×C53C2311yescharacteristic
478#103×C53C2311yescharacteristic
479#103×C53C2311yescharacteristic
480#103×C53C2311yescharacteristic
481#103×C53C2311yescharacteristic
482#103×C53C2311yescharacteristic
483#103×C53C2311yescharacteristic
484#102×C53C2311yescharacteristic
485#102×C53C2311yescharacteristic
486C22⋊C8×C53C2311yescharacteristic
487C22⋊C8×C53C2311yescharacteristic
488#97×C53C2311yescharacteristic
489C4×C8×C53C2311yescharacteristic
490C23×D53—21no—
491C23×D53—21no—
492C23×D53—21no—
493C23×D53—21no—
494#41×C53—41no—
495#41×C53—41no—
496C2×Q8×C53—21no—
497C2×Q8×C53—41no—
498C2×Q8×C53—41no—
499C2×Q8×C53C2411yescharacteristic
500C2×Q8×C53C2411yescharacteristic
501C2×Q8×C53C2411yescharacteristic
502C2×D4×C53—21no—
503C2×D4×C53—21no—
504C2×D4×C53—21no—
505C2×D4×C53—21no—
506C2×D4×C53—21no—
507C2×D4×C53C2411yescharacteristic
508C2×D4×C53C2411yescharacteristic
509C2×D4×C53C2411yescharacteristic
510C22×C4×C53—21no—
511C22×C4×C53—21no—
512C22×C4×C53—21no—
513C22×C4×C53—21no—
514C22×C4×C53C2411yescharacteristic
515C2×C22⋊D53—21no—
516C2×C22⋊D53—21no—
517C2×C22⋊D53—21no—
518C2×C22⋊D53—21no—
519C2×C22⋊D53—21no—
520C2×C22⋊D53—21no—
521C2×C22⋊D53—21no—
522C2×C22⋊D53—21no—
523C2×C22⋊D53—21no—
524C2×C22⋊D53—21no—
525C2×C22⋊D53—21no—
526C2×C22⋊D53—21no—
527C2×C22⋊D53C2×D411yescharacteristic
528C2×C22⋊D53C2×D411yescharacteristic
529C22×Dic53—21no—
530C22×Dic53—21no—
531C22×Dic53—21no—
532C22×Dic53C2×D411yescharacteristic
533C22×Dic53C2×D411yescharacteristic
534#11719949—22no—
535#11719949—22no—
536#11719949—22no—
537#11719949—22no—
538#11719949—41no—
539#11719949—41no—
540#11719949—41no—
541#11719949—41no—
542#11719949—44no—
543Q8×D53—22no—
544Q8×D53—22no—
545Q8×D53—41no—
546Q8×D53—41no—
547Q8×D53—44no—
548#11719947—22no—
549#11719947—22no—
550#11719947—82no—
551#11719947—82no—
552D4×D53—22no—
553D4×D53—22no—
554D4×D53—22no—
555D4×D53—22no—
556D4×D53—41no—
557D4×D53—41no—
558D4×D53—44no—
559D4×D53—44no—
560#11719945—22no—
561#11719945—22no—
562#11719945—41no—
563#11719945—41no—
564#11719945—44no—
565#11719945—44no—
566#11719945—44no—
567C2×D212—21no—
568C2×D212—21no—
569C2×D212—21no—
570C2×D212—21no—
571C2×D212—21no—
572C2×D212—21no—
573C2×D212—21no—
574C2×D212—21no—
575C2×D212—21no—
576C2×D212—21no—
577C2×D212—41no—
578C2×D212—41no—
579C2×D212—44no—
580C2×D212C2×D411yescharacteristic
581C2×D212C2411yescharacteristic
582C2×D212C2411yescharacteristic
583C2×D212C2411yescharacteristic
584C2×D212C2411yescharacteristic
585C2×C4×D53—21no—
586C2×C4×D53—21no—
587C2×C4×D53—21no—
588C2×C4×D53—21no—
589C2×C4×D53—21no—
590C2×C4×D53—21no—
591C2×C4×D53—21no—
592C2×C4×D53—21no—
593C2×C4×D53—21no—
594C2×C4×D53—21no—
595C2×C4×D53—82no—
596C2×C4×D53C2×D411yescharacteristic
597C2×C4×D53C2×D411yescharacteristic
598C2×C4×D53C2×D411yescharacteristic
599C2×C4×D53C2×D411yescharacteristic
600C2×C4×D53C2411yescharacteristic
601C2×C4×D53C2411yescharacteristic
602C2×Dic106—21no—
603C2×Dic106—21no—
604C2×Dic106—21no—
605C2×Dic106—21no—
606C2×Dic106C2×D411yescharacteristic
607C2×Dic106C2411yescharacteristic
608C2×Dic106C2411yescharacteristic
609SD16×C53—41no—
610SD16×C53—41no—
611SD16×C53—41no—
612SD16×C53—41no—
613SD16×C53—41no—
614SD16×C53—41no—
615D8×C53—41no—
616D8×C53—41no—
617C2×C8×C53C2411yescharacteristic
618C2×C8×C53C2411yescharacteristic
619C2×C8×C53C2411yescharacteristic
620C2×C8×C53C2411yescharacteristic
621C4⋊C4×C53—21no—
622C4⋊C4×C53—21no—
623C4⋊C4×C53—21no—
624C4⋊C4×C53—21no—
625C4⋊C4×C53—21no—
626C4⋊C4×C53—21no—
627C4⋊C4×C53C2×D411yescharacteristic
628C4⋊C4×C53C2×D411yescharacteristic
629C4⋊C4×C53C2411yescharacteristic
630C4⋊C4×C53C2411yescharacteristic
631C22⋊C4×C53—21no—
632C22⋊C4×C53—21no—
633C22⋊C4×C53—21no—
634C22⋊C4×C53—21no—
635C22⋊C4×C53—21no—
636C22⋊C4×C53—21no—
637C22⋊C4×C53—21no—
638C22⋊C4×C53—21no—
639C22⋊C4×C53C2×D411yescharacteristic
640C22⋊C4×C53C2×D411yescharacteristic
641C42×C53C2411yescharacteristic
642C42×C53C2411yescharacteristic
643C22⋊Dic53—21no—
644C22⋊Dic53—21no—
645C22⋊Dic53—21no—
646C22⋊Dic53—21no—
647C22⋊Dic53—21no—
648C22⋊Dic53—21no—
649C22⋊Dic53—21no—
650C22⋊Dic53—21no—
651C22⋊Dic53—21no—
652#11719925—41no—
653#11719925—41no—
654#11719925—41no—
655#11719924—41no—
656#11719924—41no—
657#11719924—41no—
658#11719923—41no—
659#11719923—41no—
660#11719923—41no—
661#11719922—41no—
662#11719922—41no—
663#11719922—41no—
664#11719922—41no—
665#11719922—41no—
666#11719922—41no—
667#11719922—41no—
668#11719921—21no—
669#11719921—21no—
670#11719921—21no—
671#11719921—21no—
672#11719921—21no—
673#11719921—21no—
674#11719921—21no—
675#11719921—21no—
676#11719921—21no—
677#11719921—21no—
678#11719921—21no—
679#11719921—21no—
680#11719921—21no—
681#11719921—21no—
682#11719921—21no—
683#11719921—21no—
684#11719921—21no—
685#11719921—21no—
686#11719921—21no—
687#11719921—21no—
688#11719921—21no—
689#11719921—21no—
690#11719921C2×D411yescharacteristic
691#11719921C2×D411yescharacteristic
692#11719921C2×D411yescharacteristic
693#11719921C2×D411yescharacteristic
694C4⋊Dic53—21no—
695C4⋊Dic53—21no—
696C4⋊Dic53—21no—
697C4⋊Dic53C2411yescharacteristic
698C4⋊Dic53C2411yescharacteristic
699#11719919—21no—
700#11719919—21no—
701#11719919—21no—
702#11719919—21no—
703#11719919—21no—
704#11719919—21no—
705#11719919—21no—
706#11719919—21no—
707#11719919C2×D411yescharacteristic
708#11719919C2×D411yescharacteristic
709#11719919C2×D411yescharacteristic
710#11719919C2×D411yescharacteristic
711C4×Dic53—21no—
712C4×Dic53—21no—
713C4×Dic53—21no—
714C4×Dic53C2×D411yescharacteristic
715C4×Dic53C2×D411yescharacteristic
716C4×Dic53C2×D411yescharacteristic
717C4×Dic53C2×D411yescharacteristic
718C4×Dic53C2×D411yescharacteristic
719C4×Dic53C2×D411yescharacteristic
720C4×Dic53C2411yescharacteristic
721C4×Dic53C2411yescharacteristic
722C2×#88322C2411yescharacteristic
723C2×#88322C2411yescharacteristic
724C2×#88322C2411yescharacteristic
725C2×#88322C2411yescharacteristic
726Dic212—41no—
727D424—41no—
728D424—41no—
729D424—41no—
730#11719913—41no—
731#11719913—41no—
732#11719913—41no—
733#11719913—41no—
734#11719912—22no—
735#11719912—22no—
736C8×D53—22no—
737C8×D53—22no—
738C23×C53—21no—
739C23×C53—21no—
740C23×C53—21no—
741C23×C53C22×D411yescharacteristic
742C22×D53—21no—
743C22×D53—21no—
744C22×D53—21no—
745C22×D53—21no—
746C22×D53—42no—
747C22×D53—42no—
748C22×D53—42no—
749C22×D53—42no—
750C22×D53—81no—
751C22×D53—81no—
752C22×D53—81no—
753C22×D53—81no—
754C22×D53—81no—
755C22×D53—81no—
756C22×D53—81no—
757C22×D53—81no—
758C22×D53C22×D411yescharacteristic
759C22×D53C22×D411yescharacteristic
760Q8×C53—21no—
761Q8×C53—21no—
762Q8×C53—21no—
763Q8×C53—21no—
764Q8×C53—21no—
765Q8×C53—21no—
766Q8×C53—42no—
767D4×C53—21no—
768D4×C53—21no—
769D4×C53—21no—
770D4×C53—21no—
771D4×C53—21no—
772D4×C53—21no—
773D4×C53—42no—
774D4×C53—81no—
775D4×C53—81no—
776D4×C53—81no—
777D4×C53—81no—
778C2×C4×C53—21no—
779C2×C4×C53—21no—
780C2×C4×C53—21no—
781C2×C4×C53—21no—
782C2×C4×C53—21no—
783C2×C4×C53—21no—
784C2×C4×C53—21no—
785C2×C4×C53—42no—
786C2×C4×C53—42no—
787C2×C4×C53—81no—
788C2×C4×C53—81no—
789C2×C4×C53C22×D411yescharacteristic
790C2×C4×C53C22×D411yescharacteristic
791C2×C4×C53C22×D411yescharacteristic
792C2×C4×C53C22×D411yescharacteristic
793C2×C4×C53C22×D411yescharacteristic
794C2×C4×C53C2511yescharacteristic
795C22⋊D53—22no—
796C22⋊D53—22no—
797C22⋊D53—42no—
798C22⋊D53—42no—
799C22⋊D53—42no—
800C22⋊D53—42no—
801C22⋊D53—42no—
802C22⋊D53—81no—
803C22⋊D53—81no—
804C22⋊D53—81no—
805C22⋊D53—81no—
806C22⋊D53—81no—
807C22⋊D53—81no—
808C22⋊D53—81no—
809C2×Dic53—21no—
810C2×Dic53—21no—
811C2×Dic53—21no—
812C2×Dic53—21no—
813C2×Dic53—41no—
814C2×Dic53—41no—
815C2×Dic53—42no—
816C2×Dic53—42no—
817C2×Dic53—42no—
818C2×Dic53C22×D411yescharacteristic
819C2×Dic53C22×D411yescharacteristic
820C2×Dic53C22×D411yescharacteristic
821C2×Dic53C22×D411yescharacteristic
822C2×Dic53C22×D411yescharacteristic
823C2×Dic53C22×D411yescharacteristic
824D212—22no—
825D212—21no—
826D212—21no—
827D212—21no—
828D212—21no—
829D212—21no—
830D212—21no—
831D212—21no—
832D212—21no—
833D212—42no—
834D212—42no—
835D212—42no—
836D212—42no—
837D212—42no—
838D212—81no—
839D212—81no—
840D212—81no—
841D212—81no—
842D212—81no—
843C4×D53—21no—
844C4×D53—21no—
845C4×D53—41no—
846C4×D53—41no—
847C4×D53—41no—
848C4×D53—41no—
849C4×D53—42no—
850C4×D53—42no—
851C4×D53—42no—
852C4×D53—42no—
853C4×D53—42no—
854C4×D53—42no—
855C4×D53—42no—
856C4×D53—42no—
857C4×D53—81no—
858C4×D53—81no—
859C4×D53H(5,𝔽2)12yes—
860C4×D53H(5,𝔽2)12yes—
861Dic106—22no—
862Dic106—21no—
863Dic106—21no—
864Dic106—21no—
865Dic106—21no—
866Dic106—42no—
867Dic106—42no—
868Dic106—81no—
869Dic106—81no—
870C8×C53—21no—
871C8×C53—21no—
872C8×C53—21no—
873C8×C53—21no—
874#88322—21no—
875#88322—21no—
876#88322—21no—
877#88322—21no—
878#60834—531nomaximal, Sylow
879C22×C53—21no—
880C22×C53—21no—
881C22×C53—21no—
882C22×C53—41no—
883C22×C53—41no—
884C22×C53—41no—
885C22×C53—41no—
886C22×C53—41no—
887C22×C53—41no—
888C22×C53—41no—
889C22×C53—41no—
890C22×C53—41no—
891C22×C53C23×D411yescharacteristic
892C2×D53—21no—
893C2×D53—21no—
894C2×D53—21no—
895C2×D53—21no—
896C2×D53—21no—
897C2×D53—41no—
898C2×D53—41no—
899C2×D53—41no—
900C2×D53—41no—
901C2×D53—41no—
902C2×D53—41no—
903C2×D53—41no—
904C2×D53—41no—
905C2×D53—41no—
906C2×D53—41no—
907C2×D53—41no—
908C2×D53—41no—
909C2×D53—84no—
910C2×D53—162no—
911C2×D53—162no—
912C2×D53—162no—
913C2×D53#53512yes—
914C4×C53—21no—
915C4×C53—21no—
916C4×C53—21no—
917C4×C53—21no—
918C4×C53—21no—
919C4×C53—41no—
920C4×C53—41no—
921C4×C53—41no—
922C4×C53—41no—
923C4×C53—41no—
924C4×C53C2×H(5,𝔽2)11yescharacteristic
925C4×C53C2×H(5,𝔽2)11yescharacteristic
926Dic53—21no—
927Dic53—21no—
928Dic53—21no—
929Dic53—21no—
930Dic53—21no—
931Dic53—41no—
932Dic53—41no—
933Dic53—41no—
934Dic53—41no—
935Dic53#53512yes—
936#3500—531no—
937#3460—531no—
938#3225—531no—
939#3225—531no—
940#3224—531no—
941#3224—531no—
942#3221—531no—
943#3221D5311yescharacteristic, complemented
944#3220—531no—
945#3220—531no—
946#3219—531no—
947#3219—531no—
948#3213—531no—
949#3213—531no—
950#3211—531no—
951#3211—531no—
952#3207—531no—
953#3207—531no—
954#3155—531no—
955#3154—531no—
956#3137—531no—
957#3136—531no—
958#3040—531no—
959#3036—531no—
960#3035—531no—
961C2×#463—531no—
962#3013—531no—
963#3012—531no—
964#3010—531no—
965#3008—531no—
966#2925—531no—
967C2×C53—41no—
968C2×C53—81no—
969C2×C53—81no—
970C2×C53—81no—
971C2×C53C2×#53511yescharacteristic
972C2×C53#358411yescharacteristic
973C2×C53#358511yescharacteristic
974D53—22no—
975D53—41no—
976D53—81no—
977D53—81no—
978D53—81no—
979D53—81no—
980C2×2−1+4—531no—
981C2×H(5,𝔽2)—531no—
982C2×#137—531no—
983C2×AGL(1,ℤ/8)—531no—
984C2×AGL(1,ℤ/8)—531no—
985C2×AGL(1,ℤ/8)—531no—
986C2×#135—531no—
987C2×#135—531no—
988C22×SD16—531no—
989C22×D8—531no—
990#548—1061no—
991#548—1061no—
992#546—1061no—
993#546—1061no—
994#546—1061no—
995#546—1061no—
996#546—1061no—
997#546—1061no—
998#544—531no—
999#542—531no—
1000#542—531no—
1001#542—1061no—
1002#540—531no—
1003#540—1061no—
1004#540C2×D5311yescharacteristic, complemented
1005#538—1061no—
1006#538—1061no—
1007#537—531no—
1008#536—531no—
1009#536—531no—
1010#536C2×D5311yescharacteristic, complemented
1011#535—531no—
1012#535—531no—
1013#535—531no—
1014#535—531no—
1015#535—531no—
1016#532—531no—
1017#532—531no—
1018#532—531no—
1019#532—531no—
1020#532—531no—
1021#532—1061no—
1022#529—531no—
1023#529—531no—
1024#529—1061no—
1025C2×#124—531no—
1026C2×#124—531no—
1027C2×#124—531no—
1028#525—1061no—
1029#525—1061no—
1030C4×#41—531no—
1031C4×#41—531no—
1032C2×C4×D4—531no—
1033#497—531no—
1034#497—531no—
1035#496—531no—
1036#496—531no—
1037#496—531no—
1038#496—531no—
1039#496—531no—
1040#496C2×D5311yescharacteristic, complemented
1041#495—531no—
1042#495—531no—
1043#495—531no—
1044#495—531no—
1045#493—531no—
1046#493—531no—
1047#492—531no—
1048#492C2×D5311yescharacteristic, complemented
1049#491—531no—
1050#491C2×D5311yescharacteristic, complemented
1051#490—531no—
1052#490—531no—
1053#489—531no—
1054#489—531no—
1055#489—531no—
1056#489—531no—
1057#488—531no—
1058#488—531no—
1059#488—531no—
1060#488C2×D5311yescharacteristic, complemented
1061#487—531no—
1062#487—531no—
1063#486—531no—
1064#486—531no—
1065#464—531no—
1066#464—531no—
1067#464—531no—
1068#464—531no—
1069#464—531no—
1070#464—531no—
1071#463—531no—
1072#463—531no—
1073#463—531no—
1074#463—531no—
1075#463—531no—
1076#463—531no—
1077#463—531no—
1078#463—531no—
1079#463—531no—
1080#463—531no—
1081#463—531no—
1082#463—531no—
1083#463—531no—
1084#463—531no—
1085#463—531no—
1086#463—531no—
1087#463C2×D5311yescharacteristic, complemented
1088#463C2×D5311yescharacteristic, complemented
1089#462—531no—
1090#461—531no—
1091#461C2×D5311yescharacteristic, complemented
1092#461C2×D5311yescharacteristic, complemented
1093#460—531no—
1094#459—531no—
1095#459—531no—
1096#459—531no—
1097#452—531no—
1098#452—531no—
1099#452—531no—
1100#452—531no—
1101#451—531no—
1102#451—531no—
1103#450—531no—
1104#450—531no—
1105#449—531no—
1106#449—531no—
1107#449—531no—
1108#449—531no—
1109#449—531no—
1110#449—531no—
1111#449—531no—
1112#449—531no—
1113#449—531no—
1114#449—531no—
1115#449C2×D5311yescharacteristic
1116#449C2×D5311yescharacteristic, complemented
1117#448—531no—
1118#448—531no—
1119#448—531no—
1120#448—531no—
1121#448C2×D5311yescharacteristic, complemented
1122#448C2×D5311yescharacteristic, complemented
1123#447—531no—
1124#447—531no—
1125#447—531no—
1126#447—531no—
1127#447—531no—
1128#447—531no—
1129#433—531no—
1130#433—531no—
1131#433—531no—
1132#433C2×D5311yescharacteristic, complemented
1133#432—531no—
1134#432—531no—
1135#431—531no—
1136#431—531no—
1137#423—531no—
1138C2×C4⋊C8—531no—
1139#419—531no—
1140#418—531no—
1141#417—531no—
1142#417—531no—
1143#416—531no—
1144#416—531no—
1145C2×#103—531no—
1146C2×#102—531no—
1147#408—531no—
1148#408—531no—
1149#405—531no—
1150#405—531no—
1151C53#6083411yescharacteristic, complemented, Sylow
11522−1+4—2122no—
11532−1+4—2122no—
1154H(5,𝔽2)—2122no—
1155H(5,𝔽2)—2122no—
1156C2×#41—531no—
1157C2×#41—531no—
1158C2×#41—531no—
1159C2×#41—531no—
1160C2×#41—531no—
1161C2×#41—531no—
1162C2×#41—531no—
1163C2×#41—1061no—
1164C2×#41—1061no—
1165C2×#41—1061no—
1166C2×#41—1061no—
1167C2×#41—1061no—
1168C2×#41—1061no—
1169C2×#41C22×D5311yescharacteristic
1170C22×Q8—531no—
1171C22×Q8—531no—
1172C22×Q8—1061no—
1173C22×Q8C22×D5311yescharacteristic
1174C22×D4—531no—
1175C22×D4—531no—
1176C22×D4—531no—
1177C22×D4—531no—
1178C22×D4—1061no—
1179C22×D4—1061no—
1180C22×D4—1061no—
1181C23×C4—1061no—
1182#137—2122no—
1183AGL(1,ℤ/8)—2122no—
1184AGL(1,ℤ/8)—2122no—
1185AGL(1,ℤ/8)—2122no—
1186#135—2122no—
1187#135—2122no—
1188C2×Q16—531no—
1189C2×Q16—531no—
1190C2×Q16—531no—
1191C2×Q16—531no—
1192C2×SD16—531no—
1193C2×SD16—531no—
1194C2×SD16—531no—
1195C2×SD16—531no—
1196C2×SD16—531no—
1197C2×SD16—531no—
1198C2×SD16—531no—
1199C2×SD16—531no—
1200C2×SD16—531no—
1201C2×SD16—531no—
1202C2×SD16—2122no—
1203C2×SD16C22×D5311yescharacteristic
1204C2×SD16C22×D5311yescharacteristic
1205C2×SD16C22×D5311yescharacteristic
1206C2×SD16C22×D5311yescharacteristic
1207C2×SD16C22×D5311yescharacteristic
1208C2×SD16C22×D5311yescharacteristic
1209C2×D8—531no—
1210C2×D8—531no—
1211C2×D8—531no—
1212C2×D8—531no—
1213C2×D8—531no—
1214C2×D8—531no—
1215C2×D8—531no—
1216C2×D8—531no—
1217C2×D8—531no—
1218C2×D8—531no—
1219C2×D8—2122no—
1220C2×D8C22×D5311yescharacteristic
1221C2×D8C22×D5311yescharacteristic
1222C2×M16—531no—
1223C2×M16—531no—
1224C22×C8—531no—
1225C22×C8—531no—
1226C4⋊Q8—531no—
1227C4⋊Q8—531no—
1228C4⋊Q8—531no—
1229C4⋊Q8—1061no—
1230C4⋊Q8C22×D5311yescharacteristic
1231C4⋊Q8C22×D5311yescharacteristic
1232#127—531no—
1233#127—531no—
1234#127—531no—
1235#127—531no—
1236#127—1061no—
1237#127C22×D5311yescharacteristic
1238#126—1061no—
1239#126—1061no—
1240#126—1061no—
1241#126—1061no—
1242#125—531no—
1243#125—1061no—
1244#125C22×D5311yescharacteristic
1245#124—531no—
1246#124—531no—
1247#124—531no—
1248#124—531no—
1249#124—531no—
1250#124—531no—
1251#124—531no—
1252#124—531no—
1253#124—531no—
1254#124—531no—
1255#124—1061no—
1256#124—1061no—
1257#124—1061no—
1258#124—1061no—
1259#124—1061no—
1260#124—1061no—
1261#124—1061no—
1262#124—1061no—
1263#124—1061no—
1264#124—1061no—
1265#124—1061no—
1266#124C22×D5311yescharacteristic
1267#124C22×D5311yescharacteristic
1268#123—21no—
1269#123—21no—
1270#123—21no—
1271#123—21no—
1272#123—1061no—
1273#123—1061no—
1274#123—1061no—
1275#123—1061no—
1276#123—1061no—
1277#123—1061no—
1278#123—1061no—
1279#123—1061no—
1280#123—1061no—
1281#123—1061no—
1282C22⋊Q8—21no—
1283C22⋊Q8—21no—
1284C22⋊Q8—531no—
1285C22⋊Q8—531no—
1286C22⋊Q8—1061no—
1287C22⋊Q8—1061no—
1288C22⋊Q8—1061no—
1289C22⋊Q8—1061no—
1290C22⋊Q8—1061no—
1291C22⋊Q8—1061no—
1292C22⋊Q8—1061no—
1293C22⋊Q8—1061no—
1294C22⋊Q8—1061no—
1295#121—21no—
1296#121—21no—
1297#121—531no—
1298#121—531no—
1299#121—531no—
1300#121—531no—
1301#121—1061no—
1302#121—1061no—
1303#121—1061no—
1304#121—1061no—
1305#121—1061no—
1306#121—1061no—
1307#121—1061no—
1308#121—1061no—
1309#121—1061no—
1310#121—1061no—
1311#121—1061no—
1312#121—1061no—
1313#121—1061no—
1314#121—1061no—
1315#121—1061no—
1316#121—1061no—
1317#121—1061no—
1318#121—1061no—
1319#121—1061no—
1320#121—1061no—
1321#121—1061no—
1322#121C22×D5311yescharacteristic
1323#121C22×D5311yescharacteristic
1324#120—1061no—
1325#120—1061no—
1326#120—1061no—
1327#120—1061no—
1328#120—1061no—
1329#120—1061no—
1330#120—1061no—
1331#120—1061no—
1332#120—1061no—
1333#120—1061no—
1334C4×Q8—531no—
1335C4×Q8—531no—
1336C4×Q8—531no—
1337C4×Q8—531no—
1338C4×D4—531no—
1339C4×D4—531no—
1340C4×D4—531no—
1341C4×D4—531no—
1342C4×D4—531no—
1343C4×D4—531no—
1344C4×D4—531no—
1345C4×D4—531no—
1346C4×D4—531no—
1347C4×D4—531no—
1348C4×D4—1061no—
1349C4×D4—1061no—
1350C4×D4—1061no—
1351C4×D4—1061no—
1352C4×D4—1061no—
1353C4×D4—1061no—
1354C4×D4—1061no—
1355C4×D4—1061no—
1356C4×D4—1061no—
1357C4×D4—1061no—
1358C4×D4—1061no—
1359C4×D4—1061no—
1360C4×D4—1061no—
1361C4×D4—1061no—
1362C4×D4C22×D5311yescharacteristic
1363C4×D4C22×D5311yescharacteristic
1364#117—531no—
1365#117—531no—
1366#117—531no—
1367#117—1061no—
1368#117—1061no—
1369#117—1061no—
1370#117C22×D5311yescharacteristic
1371C2×C4⋊C4—531no—
1372C2×C22⋊C4—1061no—
1373C2×C22⋊C4—1061no—
1374C2×C22⋊C4—1061no—
1375C2×C22⋊C4—1061no—
1376C2×C22⋊C4—1061no—
1377C2×C22⋊C4—1061no—
1378C2×C22⋊C4—1061no—
1379C2×C42—531no—
1380C2×C42—531no—
1381C2×C42—531no—
1382C2×C42—1061no—
1383C4⋊C8—531no—
1384C4⋊C8—531no—
1385C4⋊C8—531no—
1386C4⋊C8—531no—
1387C4⋊C8—531no—
1388C4⋊C8—531no—
1389C4⋊C8C22×D5311yescharacteristic
1390C4⋊C8C22×D5311yescharacteristic
1391#103—531no—
1392#103—531no—
1393#103—531no—
1394#103—531no—
1395#103—531no—
1396#103—531no—
1397#103—531no—
1398#103—531no—
1399#103—531no—
1400#103—531no—
1401#103C22×D5311yescharacteristic
1402#103C22×D5311yescharacteristic
1403#103C22×D5311yescharacteristic
1404#103C22×D5311yescharacteristic
1405#103C22×D5311yescharacteristic
1406#103C22×D5311yescharacteristic
1407#102—531no—
1408#102—531no—
1409#102—531no—
1410#102—531no—
1411#102—531no—
1412#102—531no—
1413#102—531no—
1414#102—531no—
1415#102—531no—
1416#102—531no—
1417#102—531no—
1418#102—531no—
1419#102—531no—
1420#102—531no—
1421#102C22×D5311yescharacteristic
1422#102C22×D5311yescharacteristic
1423C22⋊C8—531no—
1424C22⋊C8—531no—
1425C22⋊C8—531no—
1426C22⋊C8—531no—
1427C22⋊C8—531no—
1428C22⋊C8—531no—
1429C22⋊C8C22×D5311yescharacteristic
1430C22⋊C8C22×D5311yescharacteristic
1431#97—531no—
1432#97—531no—
1433#97—531no—
1434#97C22×D5311yescharacteristic
1435C4×C8—531no—
1436C4×C8—531no—
1437C4×C8—531no—
1438C4×C8C22×D5311yescharacteristic
1439C24—1061no—
1440C24—1061no—
1441C24—1061no—
1442C24—1061no—
1443#41—41no—
1444#41—41no—
1445#41—1062no—
1446#41—1062no—
1447#41—1062no—
1448#41—1062no—
1449#41—1062no—
1450#41—1062no—
1451#41—1062no—
1452#41—1062no—
1453#41—4242no—
1454#41—4242no—
1455#41—2121no—
1456#41—2121no—
1457#41—2124no—
1458#41—2124no—
1459#41—2124no—
1460#41—2121no—
1461#41—2121no—
1462#41—2121no—
1463#41—2121no—
1464#41—2124no—
1465C2×Q8—21no—
1466C2×Q8—41no—
1467C2×Q8—41no—
1468C2×Q8—531no—
1469C2×Q8—531no—
1470C2×Q8—531no—
1471C2×Q8—1061no—
1472C2×Q8—1061no—
1473C2×Q8—1061no—
1474C2×Q8—1062no—
1475C2×Q8—1062no—
1476C2×Q8—1061no—
1477C2×Q8—2121no—
1478C2×Q8—2121no—
1479C2×Q8—2124no—
1480C2×Q8C23×D5311yescharacteristic
1481C2×Q8C23×D5311yescharacteristic
1482C2×Q8C23×D5311yescharacteristic
1483C2×D4—21no—
1484C2×D4—21no—
1485C2×D4—21no—
1486C2×D4—21no—
1487C2×D4—21no—
1488C2×D4—531no—
1489C2×D4—531no—
1490C2×D4—531no—
1491C2×D4—531no—
1492C2×D4—531no—
1493C2×D4—531no—
1494C2×D4—531no—
1495C2×D4—1061no—
1496C2×D4—1061no—
1497C2×D4—1061no—
1498C2×D4—1061no—
1499C2×D4—1061no—
1500C2×D4—1062no—
1501C2×D4—1062no—
1502C2×D4—1062no—
1503C2×D4—1062no—
1504C2×D4—1061no—
1505C2×D4—1061no—
1506C2×D4—1061no—
1507C2×D4—1061no—
1508C2×D4—1061no—
1509C2×D4—1061no—
1510C2×D4—1061no—
1511C2×D4—1061no—
1512C2×D4—1061no—
1513C2×D4—1061no—
1514C2×D4—1061no—
1515C2×D4—1061no—
1516C2×D4—1061no—
1517C2×D4—1061no—
1518C2×D4—1061no—
1519C2×D4—1061no—
1520C2×D4—1061no—
1521C2×D4—2121no—
1522C2×D4—2121no—
1523C2×D4—2124no—
1524C2×D4—2121no—
1525C2×D4—2121no—
1526C2×D4—2124no—
1527C2×D4—2124no—
1528C2×D4C23×D5311yescharacteristic
1529C2×D4C23×D5311yescharacteristic
1530C2×D4C23×D5311yescharacteristic
1531C22×C4—21no—
1532C22×C4—21no—
1533C22×C4—21no—
1534C22×C4—21no—
1535C22×C4—531no—
1536C22×C4—531no—
1537C22×C4—531no—
1538C22×C4—531no—
1539C22×C4—531no—
1540C22×C4—531no—
1541C22×C4—531no—
1542C22×C4—531no—
1543C22×C4—1061no—
1544C22×C4—1061no—
1545C22×C4—1061no—
1546C22×C4—1061no—
1547C22×C4—1061no—
1548C22×C4—1061no—
1549C22×C4—1061no—
1550C22×C4—1061no—
1551C22×C4—1061no—
1552C22×C4—1061no—
1553C22×C4—1061no—
1554C22×C4—1061no—
1555C22×C4—1061no—
1556C22×C4—4242no—
1557C22×C4C23×D5311yescharacteristic
1558Q16—2121no—
1559Q16—2121no—
1560Q16—2121no—
1561Q16—2121no—
1562SD16—41no—
1563SD16—41no—
1564SD16—41no—
1565SD16—41no—
1566SD16—41no—
1567SD16—41no—
1568SD16—2121no—
1569SD16—2121no—
1570SD16—2121no—
1571SD16—2121no—
1572SD16—2121no—
1573SD16—2121no—
1574SD16—2121no—
1575SD16—2121no—
1576SD16—2121no—
1577SD16—2121no—
1578D8—41no—
1579D8—41no—
1580D8—2121no—
1581D8—2121no—
1582D8—2121no—
1583D8—2121no—
1584D8—2121no—
1585D8—2121no—
1586D8—2121no—
1587D8—2121no—
1588D8—2121no—
1589D8—2121no—
1590M16—1062no—
1591M16—1062no—
1592C2×C8—531no—
1593C2×C8—531no—
1594C2×C8—531no—
1595C2×C8—531no—
1596C2×C8—1062no—
1597C2×C8—1062no—
1598C2×C8C23×D5311yescharacteristic
1599C2×C8C23×D5311yescharacteristic
1600C2×C8C23×D5311yescharacteristic
1601C2×C8C23×D5311yescharacteristic
1602C4⋊C4—21no—
1603C4⋊C4—21no—
1604C4⋊C4—21no—
1605C4⋊C4—21no—
1606C4⋊C4—21no—
1607C4⋊C4—21no—
1608C4⋊C4—531no—
1609C4⋊C4—531no—
1610C4⋊C4—531no—
1611C4⋊C4—531no—
1612C4⋊C4—531no—
1613C4⋊C4—531no—
1614C4⋊C4—1061no—
1615C4⋊C4—1061no—
1616C4⋊C4—1061no—
1617C4⋊C4—1061no—
1618C4⋊C4—1061no—
1619C4⋊C4—1061no—
1620C4⋊C4—1061no—
1621C4⋊C4—1061no—
1622C4⋊C4—1061no—
1623C4⋊C4—1061no—
1624C4⋊C4—1061no—
1625C4⋊C4D4×D5311yescharacteristic
1626C4⋊C4D4×D5311yescharacteristic
1627C4⋊C4C23×D5311yescharacteristic
1628C4⋊C4C23×D5311yescharacteristic
1629C22⋊C4—21no—
1630C22⋊C4—21no—
1631C22⋊C4—21no—
1632C22⋊C4—21no—
1633C22⋊C4—21no—
1634C22⋊C4—21no—
1635C22⋊C4—21no—
1636C22⋊C4—21no—
1637C22⋊C4—531no—
1638C22⋊C4—531no—
1639C22⋊C4—531no—
1640C22⋊C4—531no—
1641C22⋊C4—1061no—
1642C22⋊C4—1061no—
1643C22⋊C4—1061no—
1644C22⋊C4—1061no—
1645C22⋊C4—1061no—
1646C22⋊C4—1061no—
1647C22⋊C4—1061no—
1648C22⋊C4—1061no—
1649C22⋊C4—1061no—
1650C22⋊C4—1061no—
1651C22⋊C4—1061no—
1652C22⋊C4—1061no—
1653C22⋊C4—1061no—
1654C22⋊C4—1061no—
1655C22⋊C4—1061no—
1656C22⋊C4—1061no—
1657C22⋊C4—1061no—
1658C22⋊C4—1061no—
1659C22⋊C4—1061no—
1660C22⋊C4—1061no—
1661C22⋊C4—1061no—
1662C22⋊C4—1061no—
1663C22⋊C4—1061no—
1664C22⋊C4—1061no—
1665C22⋊C4—1061no—
1666C22⋊C4—1061no—
1667C22⋊C4—1061no—
1668C22⋊C4—1061no—
1669C22⋊C4—1061no—
1670C22⋊C4—1061no—
1671C22⋊C4—1061no—
1672C22⋊C4D4×D5311yescharacteristic
1673C22⋊C4D4×D5311yescharacteristic
1674C42—531no—
1675C42—531no—
1676C42—531no—
1677C42—531no—
1678C42—531no—
1679C42—531no—
1680C42—531no—
1681C42—531no—
1682C42—1061no—
1683C42—1061no—
1684C42—1061no—
1685C42C23×D5311yescharacteristic
1686C42C23×D5311yescharacteristic
1687C23—21no—
1688C23—21no—
1689C23—21no—
1690C23—531no—
1691C23—531no—
1692C23—1061no—
1693C23—1061no—
1694C23—1061no—
1695C23—1061no—
1696C23—4241no—
1697C23—4241no—
1698C23—4241no—
1699C23—4241no—
1700C23—4241no—
1701C23—4241no—
1702C23—4241no—
1703C23—4241no—
1704C23—2122no—
1705C23—2122no—
1706C23—2122no—
1707C23—2122no—
1708C23C2×D4×D5311yescharacteristic
1709Q8—21no—
1710Q8—21no—
1711Q8—21no—
1712Q8—21no—
1713Q8—21no—
1714Q8—21no—
1715Q8—42no—
1716Q8—1062no—
1717Q8—1061no—
1718Q8—1061no—
1719Q8—1061no—
1720Q8—1061no—
1721Q8—4241no—
1722Q8—4241no—
1723Q8—2122no—
1724Q8—2122no—
1725D4—21no—
1726D4—21no—
1727D4—21no—
1728D4—21no—
1729D4—21no—
1730D4—21no—
1731D4—42no—
1732D4—81no—
1733D4—81no—
1734D4—81no—
1735D4—81no—
1736D4—1062no—
1737D4—1062no—
1738D4—1062no—
1739D4—1061no—
1740D4—1061no—
1741D4—1061no—
1742D4—1061no—
1743D4—1061no—
1744D4—1061no—
1745D4—1061no—
1746D4—1061no—
1747D4—4241no—
1748D4—4241no—
1749D4—4241no—
1750D4—4241no—
1751D4—4241no—
1752D4—4241no—
1753D4—4241no—
1754D4—4241no—
1755D4—4241no—
1756D4—4241no—
1757D4—4241no—
1758D4—4241no—
1759D4—2122no—
1760D4—2122no—
1761D4—2122no—
1762D4—2122no—
1763D4—2122no—
1764D4—2122no—
1765D4—2122no—
1766D4—2122no—
1767D4—2122no—
1768D4—2122no—
1769C2×C4—21no—
1770C2×C4—21no—
1771C2×C4—21no—
1772C2×C4—21no—
1773C2×C4—21no—
1774C2×C4—21no—
1775C2×C4—21no—
1776C2×C4—42no—
1777C2×C4—42no—
1778C2×C4—81no—
1779C2×C4—81no—
1780C2×C4—531no—
1781C2×C4—532no—
1782C2×C4—532no—
1783C2×C4—531no—
1784C2×C4—531no—
1785C2×C4—531no—
1786C2×C4—531no—
1787C2×C4—531no—
1788C2×C4—1061no—
1789C2×C4—1061no—
1790C2×C4—1061no—
1791C2×C4—1061no—
1792C2×C4—1061no—
1793C2×C4—1061no—
1794C2×C4—4241no—
1795C2×C4—4241no—
1796C2×C4—2121no—
1797C2×C4—2121no—
1798C2×C4—2121no—
1799C2×C4—2121no—
1800C2×C4—2122no—
1801C2×C4—2122no—
1802C2×C4—2122no—
1803C2×C4—2122no—
1804C2×C4—2122no—
1805C2×C4—2122no—
1806C2×C4—2122no—
1807C2×C4—2122no—
1808C2×C4—2122no—
1809C2×C4—2121no—
1810C2×C4—2121no—
1811C2×C4—2122no—
1812C2×C4—2122no—
1813C2×C4C2×D4×D5311yescharacteristic
1814C2×C4C2×D4×D5311yescharacteristic
1815C2×C4C2×D4×D5311yescharacteristic
1816C2×C4C2×D4×D5311yescharacteristic
1817C2×C4C2×D4×D5311yescharacteristic
1818C2×C4C24×D5311yescharacteristic
1819C8—21no—
1820C8—21no—
1821C8—21no—
1822C8—21no—
1823C8—1061no—
1824C8—1061no—
1825C8—1061no—
1826C8—1061no—
1827C22—21no—
1828C22—21no—
1829C22—21no—
1830C22—41no—
1831C22—41no—
1832C22—41no—
1833C22—41no—
1834C22—41no—
1835C22—41no—
1836C22—41no—
1837C22—41no—
1838C22—41no—
1839C22—532no—
1840C22—8482no—
1841C22—8482no—
1842C22—8482no—
1843C22—1061no—
1844C22—1061no—
1845C22—1061no—
1846C22—1061no—
1847C22—1061no—
1848C22—4244no—
1849C22—2121no—
1850C22—2121no—
1851C22—2121no—
1852C22—2121no—
1853C22—2121no—
1854C22—2121no—
1855C22—2121no—
1856C22—2121no—
1857C22—2121no—
1858C22—2121no—
1859C22—2121no—
1860C22—2121no—
1861C22C22×D4×D5311yescharacteristic
1862C4—21no—
1863C4—21no—
1864C4—21no—
1865C4—21no—
1866C4—21no—
1867C4—41no—
1868C4—41no—
1869C4—41no—
1870C4—41no—
1871C4—41no—
1872C4—532no—
1873C4—1061no—
1874C4—1061no—
1875C4—1061no—
1876C4—1061no—
1877C4—1061no—
1878C4—2121no—
1879C4—2121no—
1880C4—2121no—
1881C4—2121no—
1882C4H(5,𝔽2)×D5311yescharacteristic
1883C4H(5,𝔽2)×D5311yescharacteristic
1884C2—41no—
1885C2—81no—
1886C2—81no—
1887C2—81no—
1888C2—1062no—
1889C2—4241no—
1890C2—4241no—
1891C2—4241no—
1892C2—4241no—
1893C2—2121no—
1894C2#535×D5311yescharacteristic
1895C2#2028948711yescharacteristic
1896C2#2028949311yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3221C2
socleC22×C53C23×D4
hypercenter#3221D53
hypocenterC53#60834
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ #117 ◁ #3221

Complements

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

NH ≅ G/Ntype
1. #20288504C2semidirect
2. #20288130C2semidirect
3. #20285824C2semidirect
4. #20285823C2semidirect
5. #20285811C2semidirect
6. #20285808C2semidirect
7. #20285775C2semidirect
8. #20285762C2semidirect
9. #20285759C2semidirect
10. #20285755C2semidirect
11. #20285750C2semidirect
12. #20285701C2semidirect
13. #20285697C2semidirect
14. #20285681C2semidirect
15. #20285679C2semidirect
16. #20285646C2semidirect
17. #20285645C2semidirect
18. #20285199C2semidirect
19. #20285184C2semidirect
20. #20285081C2semidirect
21. #20285068C2semidirect
22. #20284204C2semidirect
23. #20284180C2semidirect
24. #20284171C2semidirect
25. #463×D53C2semidirect
26. #20284025C2semidirect
27. #20284017C2semidirect
28. #20283996C2semidirect
29. #20283980C2semidirect
30. #20283378C2semidirect
31. C53×#3221C2semidirect
34. C2×#13133246C22semidirect
36. C2×#13133244C22semidirect
39. C2×#13133238C22semidirect
40. C2×SD16×D53C22semidirect
50. #16811253C22semidirect
51. #16811244C22semidirect
53. #16811238C22semidirect
54. #16811224C22semidirect
60. #16811198C22semidirect
61. #16811192C22semidirect
63. #16811191C22semidirect
65. #16811186C22semidirect
67. #16811174C22semidirect
68. #16811171C22semidirect
69. #16811169C22semidirect
71. #16811168C22semidirect
72. #16811158C22semidirect
73. #16811154C22semidirect
75. C2×#13133206C22semidirect
77. #124×D53C22semidirect
81. C4×#11719947C22semidirect
82. C4×D4×D53C22semidirect
83. #16811015C22semidirect
84. #16811014C22semidirect
85. #16811012C22semidirect
86. #16811011C22semidirect
87. #16811010C22semidirect
88. #16811009C22semidirect
89. #16811009C22semidirect
90. #16811007C22semidirect
91. #16811005C22semidirect
92. #16811004C22semidirect
93. #16811004C22semidirect
94. #16810999C22semidirect
95. #16810998C22semidirect
96. #16810994C22semidirect
97. #16810990C22semidirect
98. #16810989C22semidirect
99. #16810986C22semidirect
100. #16810984C22semidirect
101. #16810984C22semidirect
102. #16810983C22semidirect
103. #16810982C22semidirect
104. #16810980C22semidirect
105. #16810979C22semidirect
106. #16810979C22semidirect
107. #16810973C22semidirect
108. #16810972C22semidirect
109. #16810970C22semidirect
110. #16810968C22semidirect
111. #16810848C22semidirect
112. #16810848C22semidirect
113. #16810848C22semidirect
114. #16810846C22semidirect
115. #16810844C22semidirect
116. #16810842C22semidirect
117. #16810841C22semidirect
118. #16810841C22semidirect
119. #16810841C22semidirect
120. #16810840C22semidirect
121. #16810840C22semidirect
122. #16810840C22semidirect
123. #16810840C22semidirect
124. #16810840C22semidirect
125. #16810840C22semidirect
126. #16810839C22semidirect
127. #16810838C22semidirect
128. #16810838C22semidirect
129. #16810837C22semidirect
130. #16810836C22semidirect
131. #16810836C22semidirect
132. #16810835C22semidirect
133. #16810830C22semidirect
134. #16810825C22semidirect
135. #16810824C22semidirect
136. #16810819C22semidirect
137. #16810818C22semidirect
138. #16810818C22semidirect
139. #16810788C22semidirect
140. #16810788C22semidirect
141. #16810787C22semidirect
142. #16810785C22semidirect
143. #16810780C22semidirect
144. #16810779C22semidirect
145. #16810776C22semidirect
146. #16810775C22semidirect
148. #16810771C22semidirect
149. #16810770C22semidirect
152. #16810767C22semidirect
153. #16810767C22semidirect
154. #16810767C22semidirect
155. #16810766C22semidirect
156. #16810766C22semidirect
157. #16810763C22semidirect
158. #16810762C22semidirect
159. #16810760C22semidirect
160. #16810760C22semidirect
164. #16810756C22semidirect
166. #16810755C22semidirect
167. #16810684C22semidirect
168. #16810683C22semidirect
169. #16810683C22semidirect
170. #16810678C22semidirect
171. #16810677C22semidirect
172. #16810674C22semidirect
173. #16810673C22semidirect
174. #16810645C22semidirect
175. C4⋊C8×D53C22semidirect
176. #16810630C22semidirect
179. #16810623C22semidirect
181. #16810618C22semidirect
182. #103×D53C22semidirect
186. #16810580C22semidirect
187. #16810577C22semidirect
188. C53×#540C22semidirect
189. C53×#536C22semidirect
190. C53×#496C22semidirect
191. C53×#492C22semidirect
192. C53×#491C22semidirect
193. C53×#488C22semidirect
194. C53×#463C22semidirect
195. C53×#463C22semidirect
196. C53×#461C22semidirect
197. C53×#461C22semidirect
199. C53×#449C22semidirect
200. C53×#448C22semidirect
201. C53×#448C22semidirect
202. C53×#433C22semidirect
943. #3221D53semidirect
1004. #540C2×D53semidirect
1010. #536C2×D53semidirect
1040. #496C2×D53semidirect
1048. #492C2×D53semidirect
1050. #491C2×D53semidirect
1060. #488C2×D53semidirect
1087. #463C2×D53semidirect
1088. #463C2×D53semidirect
1091. #461C2×D53semidirect
1092. #461C2×D53semidirect
1116. #449C2×D53semidirect
1121. #448C2×D53semidirect
1122. #448C2×D53semidirect
1132. #433C2×D53semidirect
1151. C53#60834semidirect

Maximal subgroups

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

subgroupindex
#202885042
#202881302
#202858242
#202858232
#202858112
#202858082
#202857752
#202857622
#202857592
#202857552
#202857502
#202857012
#202856972
#202856812
#202856792
#202856462
#202856452
#202851992
#202851842
#202850812
#202850682
#202842042
#202841802
#202841712
#463×D532
#202840252
#202840172
#202839962
#202839802
#202833782
C53×#32212
#6083453