Finite Group Databasebeta

← #28252600

Subgroups — #28252600

Order 13568.

2074 conjugacy classes of subgroups.

The subgroup lattice has 1752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#542×D53C211yesmaximal, characteristic, complemented
2#20287917C211yesmaximal, characteristic, complemented
3#20284999C211yesmaximal, characteristic, complemented
4#20284998C211yesmaximal, characteristic, complemented
5#20284991C211yesmaximal, characteristic, complemented
6#20284990C211yesmaximal, characteristic, complemented
7#20284984C211yesmaximal, characteristic, complemented
8#20284983C211yesmaximal, characteristic, complemented
9#20284976C211yesmaximal, characteristic, complemented
10#20284975C211yesmaximal, characteristic, complemented
11#20284945C211yesmaximal, characteristic, complemented
12#20284944C211yesmaximal, characteristic, complemented
13#20284937C211yesmaximal, characteristic, complemented
14#20284902C211yesmaximal, characteristic, complemented
15#20284901C211yesmaximal, characteristic, complemented
16#20284894C211yesmaximal, characteristic, complemented
17#20284893C211yesmaximal, characteristic, complemented
18#20284662C211yesmaximal, characteristic, complemented
19#20284654C211yesmaximal, characteristic, complemented
20#20284529C211yesmaximal, characteristic, complemented
21#20284525C211yesmaximal, characteristic, complemented
22#20284206C211yesmaximal, characteristic, complemented
23#20284206C211yesmaximal, characteristic, complemented
24#20283974C211yesmaximal, characteristic, complemented
25#20283966C211yesmaximal, characteristic
26C4×#13133249C211yesmaximal, characteristic, complemented
27#20283531C211yesmaximal, characteristic, complemented
28C4×#13133244C211yesmaximal, characteristic, complemented
29#20283520C211yesmaximal, characteristic, complemented
30#20283349C211yesmaximal, characteristic, complemented
31C53×#3121C211yesmaximal, characteristic, complemented
32C22×#11719949C2211yescharacteristic
33C2×#13133249C2211yescharacteristic
34C2×#13133249C2211yescharacteristic
35C2×#13133244C2211yescharacteristic
36C2×#13133244C2211yescharacteristic
37#16811247C2211yescharacteristic, complemented
38#16811246C2211yescharacteristic
39#16811245C2211yescharacteristic, complemented
40#16811244C2211yescharacteristic
41#16811243—21no—
42#16811242C2211yescharacteristic, complemented
43#16811241—21no—
44#16811240C2211yescharacteristic
45#16811239—21no—
46#16811238C2211yescharacteristic, complemented
47#16811237—21no—
48C4⋊Q8×D53C2211yescharacteristic, complemented
49#126×D53—21no—
50#124×D53—21no—
51#124×D53C2211yescharacteristic, complemented
52#123×D53—21no—
53C22⋊Q8×D53—21no—
54C22⋊Q8×D53C2211yescharacteristic
55#121×D53C2211yescharacteristic
56#16811105—21no—
57#16811105—21no—
58#16811105C2211yescharacteristic, complemented
59#16811105C2211yescharacteristic, complemented
60#16811105C2211yescharacteristic, complemented
61#16811105C2211yescharacteristic, complemented
62#16811101C2211yescharacteristic, complemented
63#16811097—21no—
64#16811097—21no—
65#16811097C2211yescharacteristic, complemented
66#16811097C2211yescharacteristic, complemented
67C4×#11719949—21no—
68C4×#11719949—21no—
69C4×#11719949C2211yescharacteristic
70C4×#11719949C2211yescharacteristic
71C4×#11719949C2211yescharacteristic
72C4×#11719949C2211yescharacteristic
73C4×Q8×D53C2211yescharacteristic, complemented
74C4×D4×D53C2211yescharacteristic, complemented
75#117×D53—21no—
76#117×D53—21no—
77#117×D53C2211yescharacteristic
78#117×D53C2211yescharacteristic
79#16810965C2211yescharacteristic, complemented
80#16810964C2211yescharacteristic, complemented
81#16810961C2211yescharacteristic, complemented
82#16810960C2211yescharacteristic, complemented
83#16810957C2211yescharacteristic, complemented
84#16810955C2211yescharacteristic, complemented
85#16810952C2211yescharacteristic, complemented
86#16810948C2211yescharacteristic
87#16810947C2211yescharacteristic
88#16810944C2211yescharacteristic
89#16810943C2211yescharacteristic, complemented
90#16810940C2211yescharacteristic, complemented
91#16810938C2211yescharacteristic, complemented
92#16810935C2211yescharacteristic, complemented
93#16810918C2211yescharacteristic, complemented
94#16810916C2211yescharacteristic, complemented
95#16810916C2211yescharacteristic, complemented
96#16810914C2211yescharacteristic, complemented
97#16810912C2211yescharacteristic, complemented
98#16810912C2211yescharacteristic, complemented
99#16810910C2211yescharacteristic, complemented
100#16810908C2211yescharacteristic, complemented
101#16810906C2211yescharacteristic, complemented
102#16810906C2211yescharacteristic, complemented
103#16810904C2211yescharacteristic, complemented
104#16810902C2211yescharacteristic, complemented
105#16810902C2211yescharacteristic, complemented
106#16810900C2211yescharacteristic, complemented
107#16810847C2211yescharacteristic, complemented
108#16810847C2211yescharacteristic, complemented
109#16810845C2211yescharacteristic, complemented
110#16810845C2211yescharacteristic, complemented
111#16810843C2211yescharacteristic, complemented
112#16810843C2211yescharacteristic, complemented
113#16810841C2211yescharacteristic, complemented
114#16810841C2211yescharacteristic, complemented
115#16810839C2211yescharacteristic, complemented
116#16810839C2211yescharacteristic, complemented
117#16810837C2211yescharacteristic, complemented
118#16810837C2211yescharacteristic, complemented
119#16810835C2211yescharacteristic, complemented
120#16810835C2211yescharacteristic, complemented
121#16810788C2211yescharacteristic, complemented
122#16810788C2211yescharacteristic, complemented
123#16810784C2211yescharacteristic, complemented
124#16810784C2211yescharacteristic, complemented
125#16810779C2211yescharacteristic, complemented
126#16810776C2211yescharacteristic, complemented
127#16810773C2211yescharacteristic, complemented
128#16810771C2211yescharacteristic
129#16810771C2211yescharacteristic
130#16810767C2211yescharacteristic
131#16810767C2211yescharacteristic
132#16810762C2211yescharacteristic
133#16810759C2211yescharacteristic
134#16810756C2211yescharacteristic
135#16810736C2211yescharacteristic, complemented
136#16810734C2211yescharacteristic, complemented
137#16810733C2211yescharacteristic, complemented
138#16810732C2211yescharacteristic, complemented
139#16810730C2211yescharacteristic, complemented
140#16810728C2211yescharacteristic, complemented
141#16810727C2211yescharacteristic, complemented
142#16810726C2211yescharacteristic, complemented
143#16810726C2211yescharacteristic, complemented
144#16810725C2211yescharacteristic, complemented
145#16810724C2211yescharacteristic, complemented
146#16810722C2211yescharacteristic, complemented
147#16810721C2211yescharacteristic, complemented
148#16810721C2211yescharacteristic, complemented
149Q16×Dic53C2211yescharacteristic, complemented
150C4×#11719925C2211yescharacteristic, complemented
151#16810715C2211yescharacteristic, complemented
152C4×#11719913C2211yescharacteristic, complemented
153SD16×Dic53C2211yescharacteristic, complemented
154C4×#11719924C2211yescharacteristic, complemented
155C4×#11719924C2211yescharacteristic, complemented
156#16810710C2211yescharacteristic, complemented
157#16810708C2211yescharacteristic, complemented
158#16810708C2211yescharacteristic, complemented
159C4×D424C2211yescharacteristic, complemented
160#16810705C2211yescharacteristic, complemented
161C4×#11719922C2211yescharacteristic, complemented
162#16810703C2211yescharacteristic, complemented
163#16810685C2211yescharacteristic, complemented
164#16810684C2211yescharacteristic, complemented
165#16810683C2211yescharacteristic, complemented
166#16810683C2211yescharacteristic, complemented
167#16810682C2211yescharacteristic, complemented
168#16810681C2211yescharacteristic, complemented
169#16810681C2211yescharacteristic, complemented
170#16810664C2211yescharacteristic, complemented
171#16810664C2211yescharacteristic, complemented
172#16810662C2211yescharacteristic, complemented
173#16810662C2211yescharacteristic, complemented
174#16810645C2211yescharacteristic, complemented
175#16810645C2211yescharacteristic, complemented
176#16810630C2211yescharacteristic, complemented
177#16810630C2211yescharacteristic, complemented
178#16810626C2211yescharacteristic, complemented
179#16810626C2211yescharacteristic, complemented
180#16810623C2211yescharacteristic
181#16810623C2211yescharacteristic
182#16810623C2211yescharacteristic
183#16810623C2211yescharacteristic
184#16810585C2211yescharacteristic
185#16810585C2211yescharacteristic
186#16810575C2211yescharacteristic, complemented
187C4×#11719912C2211yescharacteristic, complemented
188C53×#542C2211yescharacteristic
189C53×#519C2211yescharacteristic, complemented
190C53×#485C2211yescharacteristic, complemented
191C53×#482C2211yescharacteristic
192C53×#477C2211yescharacteristic, complemented
193C53×#475C2211yescharacteristic, complemented
194C53×#464C2211yescharacteristic, complemented
195C53×#464C2211yescharacteristic, complemented
196C53×#451C2211yescharacteristic, complemented
197C53×#448C2211yescharacteristic
198C53×#441C2211yescharacteristic, complemented
199C53×#440C2211yescharacteristic, complemented
200C4×Q16×C53C2211yescharacteristic, complemented
201C4×SD16×C53C2211yescharacteristic, complemented
202C53×#433C2211yescharacteristic, complemented
203C2×#11719949—24no—
204C2×#11719949—24no—
205C2×#11719949—21no—
206C2×#11719949—21no—
207C2×#11719949C2311yescharacteristic
208C2×#11719949C2311yescharacteristic
209C2×#11719949C2311yescharacteristic
210C2×#11719949C2311yescharacteristic
211C2×Q8×D53—21no—
212C2×Q8×D53C2311yescharacteristic
213C22×D212—21no—
214C22×D212C2311yescharacteristic
215C2×D4×D53—21no—
216C2×D4×D53C2311yescharacteristic
217C22×C4×D53—21no—
218C22×C4×D53—21no—
219C22×C4×D53C2311yescharacteristic
220#13133249—24no—
221#13133249—24no—
222#13133244—24no—
223#13133244—24no—
224C2×#11719925C2311yescharacteristic
225C2×#11719925C2311yescharacteristic
226C2×#11719913C2311yescharacteristic
227C2×#11719913C2311yescharacteristic
228C2×#11719924C2311yescharacteristic
229C2×#11719924C2311yescharacteristic
230C2×#11719924C2311yescharacteristic
231C2×#11719924C2311yescharacteristic
232C2×D424C2311yescharacteristic
233C2×D424C2311yescharacteristic
234C2×#11719922C2311yescharacteristic
235C2×#11719922C2311yescharacteristic
236C2×#11719912C2311yescharacteristic
237C2×#11719912C2311yescharacteristic
238C2×#11719912C2311yescharacteristic
239C2×#11719912C2311yescharacteristic
240#13133217C2311yescharacteristic
241#13133216—21no—
242#13133216C2311yescharacteristic
243#13133216C2311yescharacteristic
244#13133215—21no—
245#13133212—21no—
246#13133212—21no—
247#13133212—21no—
248#13133211—21no—
249#13133210—21no—
250#13133210—21no—
251#13133210—21no—
252#13133206—21no—
253#13133206C2311yescharacteristic
254#13133205—21no—
255#13133205C2311yescharacteristic
256#13133204—21no—
257#13133204C2311yescharacteristic
258#13133203—21no—
259#13133203—21no—
260#13133203—21no—
261#13133203—21no—
262#13133203—21no—
263#13133203—21no—
264#13133202—21no—
265#13133202—21no—
266#13133201—21no—
267#13133200—21no—
268#13133199—21no—
269#13133199—21no—
270#13133198—21no—
271#13133197—21no—
272#13133197C2311yescharacteristic
273#13133196—21no—
274#13133196C2311yescharacteristic
275#13133195—21no—
276#13133195—21no—
277#13133195—21no—
278#13133194—21no—
279#13133194—21no—
280#13133194—21no—
281#13133193—21no—
282#13133193C2311yescharacteristic
283#13133192C2311yescharacteristic
284#13133191C2311yescharacteristic
285#13133190—21no—
286#13133189—21no—
287#13133188C2311yescharacteristic
288Q8×Dic53—21no—
289Q8×Dic53—21no—
290Q8×Dic53C2311yescharacteristic
291Q8×Dic53C2311yescharacteristic
292Q8×Dic53C2311yescharacteristic
293Q8×Dic53C2311yescharacteristic
294Q8×Dic53C2311yescharacteristic
295C4×Dic106—21no—
296C4×Dic106C2311yescharacteristic
297#13133182—21no—
298#13133182C2311yescharacteristic
299C4×D212—21no—
300C4×D212—21no—
301C4×D212—21no—
302C4×D212—21no—
303C4×D212—21no—
304C4×D212—21no—
305C4×D212—21no—
306C4×D212—21no—
307C4×D212—21no—
308C4×D212—21no—
309C4×D212C2311yescharacteristic
310C4×D212C2311yescharacteristic
311C4×D212C2311yescharacteristic
312C4×D212C2311yescharacteristic
313C4×D212C2311yescharacteristic
314D4×Dic53C2311yescharacteristic
315#13133179—21no—
316#13133179—21no—
317#13133179—21no—
318#13133179—21no—
319#13133179—21no—
320#13133179—21no—
321#13133179—21no—
322#13133179—21no—
323#13133179—21no—
324#13133179—21no—
325#13133179C2311yescharacteristic
326#13133179C2311yescharacteristic
327#13133179C2311yescharacteristic
328#13133179C2311yescharacteristic
329#13133179C2311yescharacteristic
330C4×C22⋊D53—21no—
331#13133177—21no—
332#13133176—21no—
333#13133176—21no—
334#13133176C2311yescharacteristic
335#13133176C2311yescharacteristic
336#13133175—21no—
337#13133175—21no—
338#13133175—21no—
339#13133175—21no—
340#13133175D411yescharacteristic
341#13133175D411yescharacteristic
342#13133175C2311yescharacteristic
343#13133175C2311yescharacteristic
344#13133174—21no—
345#13133174—21no—
346#13133174—21no—
347#13133174—21no—
348#13133174—21no—
349#13133174C2311yescharacteristic
350#13133174C2311yescharacteristic
351#13133173—21no—
352#13133173D411yescharacteristic
353#13133173D411yescharacteristic
354C4⋊C4×D53—21no—
355C4⋊C4×D53—21no—
356C4⋊C4×D53—21no—
357C4⋊C4×D53—21no—
358C4⋊C4×D53—21no—
359C4⋊C4×D53—21no—
360C4⋊C4×D53—21no—
361C4⋊C4×D53D411yescharacteristic
362C4⋊C4×D53D411yescharacteristic
363C4⋊C4×D53C2311yescharacteristic
364C4⋊C4×D53C2311yescharacteristic
365C4⋊C4×D53C2311yescharacteristic
366C4⋊C4×D53C2311yescharacteristic
367C22⋊C4×D53—21no—
368C22⋊C4×D53—21no—
369C22⋊C4×D53—21no—
370C22⋊C4×D53—21no—
371C22⋊C4×D53—21no—
372C22⋊C4×D53—21no—
373C22⋊C4×D53—21no—
374C22⋊C4×D53—21no—
375C22⋊C4×D53—21no—
376C22⋊C4×D53—21no—
377C22⋊C4×D53D411yescharacteristic
378C22⋊C4×D53D411yescharacteristic
379C42×D53—21no—
380C42×D53—21no—
381C42×D53—21no—
382C42×D53—21no—
383C42×D53—21no—
384C42×D53—21no—
385C42×D53C2311yescharacteristic
386C42×D53C2311yescharacteristic
387#13133151C2311yescharacteristic
388#13133151C2311yescharacteristic
389#13133150C2311yescharacteristic
390#13133150C2311yescharacteristic
391#13133150C2311yescharacteristic
392#13133150C2311yescharacteristic
393#13133149C2311yescharacteristic
394#13133149C2311yescharacteristic
395#13133148C2311yescharacteristic
396#13133148C2311yescharacteristic
397#13133148C2311yescharacteristic
398#13133148C2311yescharacteristic
399C4⋊#88322C2311yescharacteristic
400C4⋊#88322C2311yescharacteristic
401#13133146C2311yescharacteristic
402#13133146C2311yescharacteristic
403#13133146C2311yescharacteristic
404#13133146C2311yescharacteristic
405#13133142C2311yescharacteristic
406#13133142C2311yescharacteristic
407#13133141C2311yescharacteristic
408#13133141C2311yescharacteristic
409#13133141C2311yescharacteristic
410#13133141C2311yescharacteristic
411#13133141C2311yescharacteristic
412#13133141C2311yescharacteristic
413#13133140C2311yescharacteristic
414#13133140C2311yescharacteristic
415#13133139C2311yescharacteristic
416#13133139C2311yescharacteristic
417#13133139C2311yescharacteristic
418#13133139C2311yescharacteristic
419#13133139C2311yescharacteristic
420#13133139C2311yescharacteristic
421#13133138C2311yescharacteristic
422#13133138C2311yescharacteristic
423#13133137C2311yescharacteristic
424#13133137C2311yescharacteristic
425#13133137C2311yescharacteristic
426#13133137C2311yescharacteristic
427#13133137C2311yescharacteristic
428#13133137C2311yescharacteristic
429C22⋊#88322C2311yescharacteristic
430C22⋊#88322C2311yescharacteristic
431#13133129C2311yescharacteristic
432#13133129C2311yescharacteristic
433#13133129C2311yescharacteristic
434#13133129C2311yescharacteristic
435#13133128C2311yescharacteristic
436#13133127C2311yescharacteristic
437#13133127C2311yescharacteristic
438C4×#88322C2311yescharacteristic
439C8×Dic53C2311yescharacteristic
440C8×Dic53C2311yescharacteristic
441C22×Q8×C53C2311yescharacteristic
442C2×Q16×C53C2311yescharacteristic
443C2×Q16×C53C2311yescharacteristic
444C2×SD16×C53C2311yescharacteristic
445C2×SD16×C53C2311yescharacteristic
446C4⋊Q8×C53C2311yescharacteristic
447#126×C53—21no—
448#124×C53—21no—
449#124×C53C2311yescharacteristic
450#123×C53—21no—
451C22⋊Q8×C53—21no—
452C22⋊Q8×C53C2311yescharacteristic
453#121×C53C2311yescharacteristic
454C4×Q8×C53—21no—
455C4×Q8×C53—21no—
456C4×Q8×C53C2311yescharacteristic
457C4×Q8×C53C2311yescharacteristic
458C4×Q8×C53C2311yescharacteristic
459C4×Q8×C53C2311yescharacteristic
460C4×Q8×C53C2311yescharacteristic
461C4×D4×C53C2311yescharacteristic
462#117×C53—21no—
463#117×C53—21no—
464#117×C53C2311yescharacteristic
465#117×C53C2311yescharacteristic
466#107×C53C2311yescharacteristic
467#107×C53C2311yescharacteristic
468#106×C53C2311yescharacteristic
469#106×C53C2311yescharacteristic
470C4⋊C8×C53C2311yescharacteristic
471C4⋊C8×C53C2311yescharacteristic
472#103×C53C2311yescharacteristic
473#103×C53C2311yescharacteristic
474#103×C53C2311yescharacteristic
475#103×C53C2311yescharacteristic
476#103×C53C2311yescharacteristic
477#103×C53C2311yescharacteristic
478#102×C53C2311yescharacteristic
479#102×C53C2311yescharacteristic
480C22⋊C8×C53C2311yescharacteristic
481C22⋊C8×C53C2311yescharacteristic
482#97×C53C2311yescharacteristic
483C4×C8×C53C2311yescharacteristic
484C23×D53—21no—
485C23×D53—21no—
486C23×D53C2×D411yescharacteristic
487C2×Q8×C53—22no—
488C2×Q8×C53—22no—
489C2×Q8×C53—21no—
490C2×Q8×C53—21no—
491C2×Q8×C53C2411yescharacteristic
492C2×Q8×C53C2411yescharacteristic
493C2×Q8×C53C2411yescharacteristic
494C2×D4×C53—21no—
495C2×D4×C53C2411yescharacteristic
496C22×C4×C53—21no—
497C22×C4×C53—21no—
498C22×C4×C53C2411yescharacteristic
499C2×C22⋊D53—21no—
500C2×C22⋊D53—21no—
501C2×C22⋊D53—21no—
502C22×Dic53—21no—
503C22×Dic53C2×D411yescharacteristic
504#11719949—28no—
505#11719949—28no—
506#11719949—22no—
507#11719949—22no—
508#11719949—22no—
509#11719949—22no—
510#11719949—22no—
511#11719949—22no—
512#11719949#4114yes—
513#11719949#4114yes—
514Q8×D53—22no—
515Q8×D53—22no—
516Q8×D53—82no—
517D4×D53—22no—
518D4×D53—22no—
519D4×D53—82no—
520C2×D212—28no—
521C2×D212—21no—
522C2×D212—21no—
523C2×D212—21no—
524C2×D212—21no—
525C2×D212—21no—
526C2×D212—22no—
527C2×D212—22no—
528C2×D212—21no—
529C2×D212C2411yescharacteristic
530C2×D212C2411yescharacteristic
531C2×D212C2411yescharacteristic
532C2×C4×D53—28no—
533C2×C4×D53—21no—
534C2×C4×D53—21no—
535C2×C4×D53—21no—
536C2×C4×D53—21no—
537C2×C4×D53—22no—
538C2×C4×D53—22no—
539C2×C4×D53—21no—
540C2×C4×D53—21no—
541C2×C4×D53—21no—
542C2×C4×D53—21no—
543C2×C4×D53—21no—
544C2×C4×D53—21no—
545C2×C4×D53—21no—
546C2×C4×D53—21no—
547C2×C4×D53—21no—
548C2×C4×D53—21no—
549C2×C4×D53—21no—
550C2×C4×D53—21no—
551C2×C4×D53—21no—
552C2×C4×D53—21no—
553C2×C4×D53—21no—
554C2×C4×D53—82no—
555C2×C4×D53C2×D411yescharacteristic
556C2×C4×D53C2×D411yescharacteristic
557C2×C4×D53C2×D411yescharacteristic
558C2×C4×D53C2×D411yescharacteristic
559C2×C4×D53C2×D411yescharacteristic
560C2×C4×D53C2×D411yescharacteristic
561C2×C4×D53C2411yescharacteristic
562C2×C4×D53C2411yescharacteristic
563C2×Dic106—21no—
564C2×Dic106—21no—
565C2×Dic106—21no—
566C2×Dic106—21no—
567C2×Dic106C2411yescharacteristic
568Q16×C53—22no—
569Q16×C53—22no—
570SD16×C53—22no—
571SD16×C53—22no—
572C2×C8×C53C2411yescharacteristic
573C2×C8×C53C2411yescharacteristic
574C2×C8×C53C2411yescharacteristic
575C2×C8×C53C2411yescharacteristic
576C4⋊C4×C53—21no—
577C4⋊C4×C53—21no—
578C4⋊C4×C53—21no—
579C4⋊C4×C53—21no—
580C4⋊C4×C53—21no—
581C4⋊C4×C53—21no—
582C4⋊C4×C53—21no—
583C4⋊C4×C53C2×D411yescharacteristic
584C4⋊C4×C53C2×D411yescharacteristic
585C4⋊C4×C53C2411yescharacteristic
586C4⋊C4×C53C2411yescharacteristic
587C4⋊C4×C53C2411yescharacteristic
588C4⋊C4×C53C2411yescharacteristic
589C22⋊C4×C53—21no—
590C22⋊C4×C53—21no—
591C22⋊C4×C53—21no—
592C22⋊C4×C53—21no—
593C22⋊C4×C53—21no—
594C22⋊C4×C53—21no—
595C22⋊C4×C53C2×D411yescharacteristic
596C22⋊C4×C53C2×D411yescharacteristic
597C42×C53—21no—
598C42×C53—21no—
599C42×C53—21no—
600C42×C53—21no—
601C42×C53—21no—
602C42×C53—21no—
603C42×C53C2411yescharacteristic
604C42×C53C2411yescharacteristic
605C22⋊Dic53—21no—
606C22⋊Dic53—21no—
607C22⋊Dic53—21no—
608C22⋊Dic53—21no—
609C22⋊Dic53—21no—
610C22⋊Dic53—21no—
611C22⋊Dic53C2×D411yescharacteristic
612C22⋊Dic53C2×D411yescharacteristic
613#11719925—22no—
614#11719925—22no—
615#11719924—22no—
616#11719924—22no—
617#11719924—22no—
618#11719924—22no—
619#11719922—22no—
620#11719922—22no—
621#11719921—21no—
622#11719921—21no—
623#11719921—21no—
624#11719921—21no—
625#11719921—21no—
626#11719921—21no—
627#11719921—21no—
628#11719921—21no—
629#11719921—21no—
630#11719921—21no—
631#11719921—21no—
632#11719921—21no—
633#11719921—21no—
634#11719921—21no—
635#11719921—21no—
636#11719921—21no—
637#11719921—21no—
638#11719921—21no—
639#11719921—21no—
640#11719921—21no—
641#11719921C2×D411yescharacteristic
642#11719921C2×D411yescharacteristic
643#11719921C2×D411yescharacteristic
644#11719921C2×D411yescharacteristic
645C4⋊Dic53—21no—
646C4⋊Dic53—21no—
647C4⋊Dic53—21no—
648C4⋊Dic53—21no—
649C4⋊Dic53—21no—
650C4⋊Dic53—21no—
651C4⋊Dic53—21no—
652C4⋊Dic53C2×D411yescharacteristic
653C4⋊Dic53C2×D411yescharacteristic
654C4⋊Dic53C2411yescharacteristic
655C4⋊Dic53C2411yescharacteristic
656C4⋊Dic53C2411yescharacteristic
657C4⋊Dic53C2411yescharacteristic
658#11719919—21no—
659#11719919—21no—
660#11719919—21no—
661#11719919—21no—
662#11719919—21no—
663#11719919—21no—
664#11719919—21no—
665#11719919—21no—
666#11719919—21no—
667#11719919—21no—
668#11719919C2×D411yescharacteristic
669#11719919C2×D411yescharacteristic
670#11719919C2×D411yescharacteristic
671#11719919C2×D411yescharacteristic
672C4×Dic53—21no—
673C4×Dic53—21no—
674C4×Dic53—21no—
675C4×Dic53—21no—
676C4×Dic53—21no—
677C4×Dic53—21no—
678C4×Dic53—21no—
679C4×Dic53—21no—
680C4×Dic53—21no—
681C4×Dic53—21no—
682C4×Dic53C2×D411yescharacteristic
683C4×Dic53C2×D411yescharacteristic
684C4×Dic53C2×D411yescharacteristic
685C4×Dic53C2×D411yescharacteristic
686C4×Dic53C2411yescharacteristic
687C4×Dic53C2411yescharacteristic
688C2×#88322C2411yescharacteristic
689C2×#88322C2411yescharacteristic
690C2×#88322C2411yescharacteristic
691C2×#88322C2411yescharacteristic
692D424—22no—
693D424—22no—
694#11719913—22no—
695#11719913—22no—
696#11719912—22no—
697#11719912—22no—
698#11719912—22no—
699#11719912—22no—
700C23×C53—21no—
701C23×C53C22×D411yescharacteristic
702C22×D53—21no—
703C22×D53—21no—
704C22×D53—24no—
705C22×D53—22no—
706C22×D53—21no—
707C22×D53—41no—
708C22×D53—41no—
709C22×D53—42no—
710C22×D53—42no—
711C22×D53—42no—
712C22×D53—81no—
713C22×D53—81no—
714C22×D53C22×D411yescharacteristic
715C22×D53C22×D411yescharacteristic
716Q8×C53—24no—
717Q8×C53—21no—
718Q8×C53—21no—
719Q8×C53—21no—
720Q8×C53—21no—
721Q8×C53—81no—
722Q8×C53C2×#4112yes—
723Q8×C53C2×#4112yes—
724D4×C53—21no—
725D4×C53—21no—
726D4×C53—81no—
727C2×C4×C53—24no—
728C2×C4×C53—21no—
729C2×C4×C53—21no—
730C2×C4×C53—21no—
731C2×C4×C53—21no—
732C2×C4×C53—21no—
733C2×C4×C53—21no—
734C2×C4×C53—21no—
735C2×C4×C53—21no—
736C2×C4×C53—21no—
737C2×C4×C53—81no—
738C2×C4×C53C22×D411yescharacteristic
739C2×C4×C53C22×D411yescharacteristic
740C2×C4×C53C22×D411yescharacteristic
741C2×C4×C53C22×D411yescharacteristic
742C2×C4×C53C22×D411yescharacteristic
743C2×C4×C53C2511yescharacteristic
744C22⋊D53—42no—
745C22⋊D53—81no—
746C22⋊D53—81no—
747C2×Dic53—22no—
748C2×Dic53—21no—
749C2×Dic53—21no—
750C2×Dic53—21no—
751C2×Dic53—21no—
752C2×Dic53—21no—
753C2×Dic53—81no—
754C2×Dic53C22×D411yescharacteristic
755C2×Dic53C22×D411yescharacteristic
756C2×Dic53C22×D411yescharacteristic
757C2×Dic53C22×D411yescharacteristic
758C2×Dic53C22×D411yescharacteristic
759C2×Dic53C22×D411yescharacteristic
760D212—24no—
761D212—24no—
762D212—24no—
763D212—24no—
764D212—24no—
765D212—21no—
766D212—21no—
767D212—21no—
768D212—21no—
769D212—81no—
770D212C2×#4112yes—
771D212C2×#4112yes—
772C4×D53—24no—
773C4×D53—24no—
774C4×D53—22no—
775C4×D53—21no—
776C4×D53—21no—
777C4×D53—24no—
778C4×D53—24no—
779C4×D53—22no—
780C4×D53—41no—
781C4×D53—41no—
782C4×D53—41no—
783C4×D53—41no—
784C4×D53—42no—
785C4×D53—42no—
786C4×D53—42no—
787C4×D53—81no—
788C4×D53—81no—
789C4×D53—81no—
790C4×D53—81no—
791C4×D53—81no—
792C4×D53—81no—
793C4×D53—81no—
794C4×D53—81no—
795C4×D53—81no—
796C4×D53—81no—
797C4×D53—81no—
798C4×D53—81no—
799C4×D53C2×#4112yes—
800C4×D53C2×#4112yes—
801Dic106—21no—
802Dic106—21no—
803Dic106—42no—
804Dic106—81no—
805Dic106—81no—
806Dic106—81no—
807C8×C53—21no—
808C8×C53—21no—
809C8×C53—21no—
810C8×C53—21no—
811#88322—21no—
812#88322—21no—
813#88322—21no—
814#88322—21no—
815#60567—531nomaximal, Sylow
816C22×C53—21no—
817C22×C53—21no—
818C22×C53—21no—
819C22×C53—41no—
820C22×C53—41no—
821C22×C53—41no—
822C22×C53C23×D411yescharacteristic
823C2×D53—21no—
824C2×D53—21no—
825C2×D53—21no—
826C2×D53—21no—
827C2×D53—21no—
828C2×D53—22no—
829C2×D53—22no—
830C2×D53—41no—
831C2×D53—41no—
832C2×D53—41no—
833C2×D53—41no—
834C2×D53—41no—
835C2×D53—41no—
836C2×D53—41no—
837C2×D53—82no—
838C2×D53—84no—
839C2×D53—84no—
840C2×D53#52512yes—
841C4×C53—21no—
842C4×C53—21no—
843C4×C53—21no—
844C4×C53—21no—
845C4×C53—22no—
846C4×C53—22no—
847C4×C53—21no—
848C4×C53—41no—
849C4×C53—41no—
850C4×C53—41no—
851C4×C53—41no—
852C4×C53—41no—
853C4×C53C22×#4111yescharacteristic
854C4×C53C22×#4111yescharacteristic
855Dic53—21no—
856Dic53—21no—
857Dic53—21no—
858Dic53—21no—
859Dic53—21no—
860Dic53—41no—
861Dic53—41no—
862Dic53—41no—
863Dic53—41no—
864Dic53—41no—
865Dic53#52512yes—
866C2×#542—531no—
867#3428—531no—
868#3125—531no—
869#3125—531no—
870#3125—531no—
871#3125—531no—
872#3124—531no—
873#3124—531no—
874#3124—531no—
875#3124—531no—
876#3121—531no—
877#3121—531no—
878#3121—531no—
879#3121D5311yescharacteristic, complemented
880#3118—531no—
881#3118—531no—
882#3118—531no—
883#3118—531no—
884#3095—531no—
885#3094—531no—
886#3079—531no—
887#3079—531no—
888#3040—531no—
889#3040—531no—
890#3007—531no—
891#3006—531no—
892C4×#137—531no—
893C4×#137—531no—
894C4×AGL(1,ℤ/8)—531no—
895C4×AGL(1,ℤ/8)—531no—
896#2921—531no—
897C2×C53—41no—
898C2×C53—81no—
899C2×C53C2×#52511yescharacteristic
900C2×C53#358511yescharacteristic
901C2×C53#358611yescharacteristic
902D53—22no—
903D53—41no—
904D53—42no—
905D53—42no—
906D53—81no—
907C22×#41—531no—
908C2×#137—531no—
909C2×#137—531no—
910C2×AGL(1,ℤ/8)—531no—
911C2×AGL(1,ℤ/8)—531no—
912#542—531no—
913#542—531no—
914#542—531no—
915#542—531no—
916#542—531no—
917#542—531no—
918#542—531no—
919#542—1061no—
920#542—1061no—
921#542—1061no—
922#542—1061no—
923#542C2×D5311yescharacteristic
924C2×C4⋊Q8—531no—
925C2×#126—1061no—
926C2×#124—531no—
927C2×#124—1061no—
928C2×#123—1061no—
929C2×C22⋊Q8—531no—
930C2×C22⋊Q8—1061no—
931C2×#121—531no—
932#520—531no—
933#520—531no—
934#520—531no—
935#520—531no—
936#520—1061no—
937#520—1061no—
938#519—531no—
939#519C2×D5311yescharacteristic, complemented
940#518—531no—
941#518—531no—
942#518—1061no—
943#518—1061no—
944C4×#41—531no—
945C4×#41—531no—
946C4×#41—531no—
947C4×#41—531no—
948C4×#41—1061no—
949C4×#41—1061no—
950C2×C4×Q8—531no—
951C2×C4×D4—531no—
952C2×#117—531no—
953C2×#117—531no—
954C2×#117—1061no—
955C2×#117—1061no—
956#485—531no—
957#485—531no—
958#485—531no—
959#485C2×D5311yescharacteristic, complemented
960#484—531no—
961#484—531no—
962#483—531no—
963#483—531no—
964#482—531no—
965#482—531no—
966#482—531no—
967#482C2×D5311yescharacteristic
968#481—531no—
969#481—531no—
970#480—531no—
971#480—531no—
972#477—531no—
973#477—531no—
974#477—531no—
975#477C2×D5311yescharacteristic, complemented
976#476—531no—
977#476—531no—
978#476—531no—
979#476—531no—
980#475—531no—
981#475—531no—
982#475—531no—
983#475C2×D5311yescharacteristic, complemented
984#474—531no—
985#474—531no—
986#474—531no—
987#474—531no—
988#464—531no—
989#464—531no—
990#464—531no—
991#464—531no—
992#464—531no—
993#464—531no—
994#464C2×D5311yescharacteristic, complemented
995#464C2×D5311yescharacteristic, complemented
996#463—531no—
997#463—531no—
998#463—531no—
999#463—531no—
1000#463—531no—
1001#463—531no—
1002#463—531no—
1003#463—531no—
1004#452—531no—
1005#452—531no—
1006#452—531no—
1007#452—531no—
1008#451—531no—
1009#451C2×D5311yescharacteristic, complemented
1010#450—531no—
1011#450—531no—
1012#449—531no—
1013#449—531no—
1014#449—531no—
1015#449—531no—
1016#448—531no—
1017#448C2×D5311yescharacteristic
1018#447—531no—
1019#447—531no—
1020#442—531no—
1021#442—531no—
1022#442—531no—
1023#442—531no—
1024#441—531no—
1025#441—531no—
1026#441—531no—
1027#441C2×D5311yescharacteristic, complemented
1028#440—531no—
1029#440—531no—
1030#440—531no—
1031#440—531no—
1032#440—531no—
1033#440—531no—
1034#440—531no—
1035#440C2×D5311yescharacteristic, complemented
1036C4×Q16—531no—
1037C4×Q16—531no—
1038C4×Q16—531no—
1039C4×Q16C2×D5311yescharacteristic, complemented
1040C4×SD16—531no—
1041C4×SD16—531no—
1042C4×SD16—531no—
1043C4×SD16—531no—
1044C4×SD16—531no—
1045C4×SD16—531no—
1046C4×SD16—531no—
1047C4×SD16C2×D5311yescharacteristic, complemented
1048C4×D8—531no—
1049C4×D8—531no—
1050C4×D8—531no—
1051C4×D8—531no—
1052#433—531no—
1053#433—531no—
1054#433—531no—
1055#433—531no—
1056#433—531no—
1057#433—531no—
1058#433—531no—
1059#433C2×D5311yescharacteristic, complemented
1060#428—531no—
1061#428—531no—
1062#428—531no—
1063#428—531no—
1064#423—531no—
1065#423—531no—
1066#419—531no—
1067#419—531no—
1068#418—531no—
1069#418—531no—
1070#417—531no—
1071#417—531no—
1072#417—531no—
1073#417—531no—
1074#407—531no—
1075#407—531no—
1076C4×M16—531no—
1077C4×M16—531no—
1078C53#6056711yescharacteristic, complemented, Sylow
1079C2×#41—531no—
1080C2×#41—531no—
1081C2×#41—531no—
1082C2×#41—531no—
1083C2×#41—1061no—
1084C2×#41—1061no—
1085C2×#41—1064no—
1086C2×#41—1064no—
1087C22×Q8—531no—
1088C22×Q8—1061no—
1089C22×Q8C22×D5311yescharacteristic
1090C22×D4—531no—
1091C22×D4—531no—
1092C22×D4—1061no—
1093C22×D4—1061no—
1094C23×C4—531no—
1095C23×C4—1061no—
1096C23×C4—1061no—
1097#137—1064no—
1098#137—1064no—
1099AGL(1,ℤ/8)—1064no—
1100AGL(1,ℤ/8)—1064no—
1101C2×Q16—531no—
1102C2×Q16—531no—
1103C2×Q16C22×D5311yescharacteristic
1104C2×Q16C22×D5311yescharacteristic
1105C2×SD16—531no—
1106C2×SD16—531no—
1107C2×SD16—531no—
1108C2×SD16—531no—
1109C2×SD16—531no—
1110C2×SD16—531no—
1111C2×SD16C22×D5311yescharacteristic
1112C2×SD16C22×D5311yescharacteristic
1113C2×D8—531no—
1114C2×D8—531no—
1115C2×D8—531no—
1116C2×D8—531no—
1117C2×M16—531no—
1118C2×M16—531no—
1119C2×M16—531no—
1120C2×M16—531no—
1121C4⋊Q8—531no—
1122C4⋊Q8—531no—
1123C4⋊Q8—531no—
1124C4⋊Q8—1061no—
1125C4⋊Q8—1061no—
1126C4⋊Q8C22×D5311yescharacteristic
1127#126—21no—
1128#126—1061no—
1129#126—1061no—
1130#126—1061no—
1131#126—1061no—
1132#126—1061no—
1133#126—1061no—
1134#126—1061no—
1135#124—21no—
1136#124—531no—
1137#124—531no—
1138#124—531no—
1139#124—1061no—
1140#124—1061no—
1141#124—1061no—
1142#124—1061no—
1143#124—1061no—
1144#124—1061no—
1145#124—1061no—
1146#124—1061no—
1147#124—1061no—
1148#124C22×D5311yescharacteristic
1149#123—21no—
1150#123—1061no—
1151#123—1061no—
1152#123—1061no—
1153#123—1061no—
1154#123—1061no—
1155#123—1061no—
1156#123—1061no—
1157C22⋊Q8—21no—
1158C22⋊Q8—531no—
1159C22⋊Q8—531no—
1160C22⋊Q8—531no—
1161C22⋊Q8—1061no—
1162C22⋊Q8—1061no—
1163C22⋊Q8—1061no—
1164C22⋊Q8—1061no—
1165C22⋊Q8—1061no—
1166C22⋊Q8—1061no—
1167C22⋊Q8—1061no—
1168C22⋊Q8—1061no—
1169C22⋊Q8—1061no—
1170C22⋊Q8C22×D5311yescharacteristic
1171#121—531no—
1172#121—531no—
1173#121—531no—
1174#121—1061no—
1175#121—1061no—
1176#121C22×D5311yescharacteristic
1177C4×Q8—21no—
1178C4×Q8—21no—
1179C4×Q8—531no—
1180C4×Q8—531no—
1181C4×Q8—531no—
1182C4×Q8—531no—
1183C4×Q8—531no—
1184C4×Q8—531no—
1185C4×Q8—531no—
1186C4×Q8—1061no—
1187C4×Q8—1061no—
1188C4×Q8—1061no—
1189C4×Q8—1061no—
1190C4×Q8C22×D5311yescharacteristic
1191C4×Q8C22×D5311yescharacteristic
1192C4×Q8C22×D5311yescharacteristic
1193C4×Q8C22×D5311yescharacteristic
1194C4×Q8C22×D5311yescharacteristic
1195C4×D4—531no—
1196C4×D4—531no—
1197C4×D4—531no—
1198C4×D4—531no—
1199C4×D4—531no—
1200C4×D4—531no—
1201C4×D4—531no—
1202C4×D4—531no—
1203C4×D4—531no—
1204C4×D4—531no—
1205C4×D4—531no—
1206C4×D4—1061no—
1207C4×D4—1061no—
1208C4×D4—1061no—
1209C4×D4—1061no—
1210C4×D4—1061no—
1211C4×D4—1061no—
1212C4×D4—1061no—
1213C4×D4—1061no—
1214C4×D4—1061no—
1215C4×D4—1061no—
1216C4×D4—1061no—
1217C4×D4—1061no—
1218C4×D4—1061no—
1219C4×D4—1061no—
1220C4×D4—1061no—
1221C4×D4—1061no—
1222C4×D4—1061no—
1223C4×D4—1061no—
1224C4×D4—1061no—
1225C4×D4—1061no—
1226C4×D4—1061no—
1227C4×D4—1061no—
1228C4×D4C22×D5311yescharacteristic
1229#117—21no—
1230#117—21no—
1231#117—531no—
1232#117—531no—
1233#117—531no—
1234#117—531no—
1235#117—531no—
1236#117—531no—
1237#117—531no—
1238#117—531no—
1239#117—531no—
1240#117—531no—
1241#117—1061no—
1242#117—1061no—
1243#117—1061no—
1244#117—1061no—
1245#117—1061no—
1246#117—1061no—
1247#117—1061no—
1248#117—1061no—
1249#117—1061no—
1250#117—1061no—
1251#117—1061no—
1252#117—1061no—
1253#117C22×D5311yescharacteristic
1254#117C22×D5311yescharacteristic
1255C2×C4⋊C4—531no—
1256C2×C4⋊C4—531no—
1257C2×C4⋊C4—531no—
1258C2×C4⋊C4—531no—
1259C2×C4⋊C4—531no—
1260C2×C4⋊C4—531no—
1261C2×C4⋊C4—1061no—
1262C2×C4⋊C4—1061no—
1263C2×C4⋊C4—1061no—
1264C2×C4⋊C4—1061no—
1265C2×C4⋊C4—1061no—
1266C2×C4⋊C4—1061no—
1267C2×C4⋊C4—1061no—
1268C2×C22⋊C4—531no—
1269C2×C22⋊C4—531no—
1270C2×C22⋊C4—1061no—
1271C2×C22⋊C4—1061no—
1272C2×C22⋊C4—1061no—
1273C2×C22⋊C4—1061no—
1274C2×C22⋊C4—1061no—
1275C2×C22⋊C4—1061no—
1276C2×C22⋊C4—1061no—
1277C2×C22⋊C4—1061no—
1278C2×C22⋊C4—1061no—
1279C2×C22⋊C4—1061no—
1280C2×C42—531no—
1281C2×C42—531no—
1282C2×C42—1061no—
1283C2×C42—1061no—
1284C2×C42—1061no—
1285C2×C42—1061no—
1286C2×C42—1061no—
1287C2×C42—1061no—
1288#107—531no—
1289#107—531no—
1290#107—531no—
1291#107—531no—
1292#107—531no—
1293#107—531no—
1294#107C22×D5311yescharacteristic
1295#107C22×D5311yescharacteristic
1296#106—531no—
1297#106—531no—
1298#106—531no—
1299#106—531no—
1300#106—531no—
1301#106—531no—
1302#106C22×D5311yescharacteristic
1303#106C22×D5311yescharacteristic
1304C4⋊C8—531no—
1305C4⋊C8—531no—
1306C4⋊C8—531no—
1307C4⋊C8—531no—
1308C4⋊C8—531no—
1309C4⋊C8—531no—
1310C4⋊C8C22×D5311yescharacteristic
1311C4⋊C8C22×D5311yescharacteristic
1312#103—531no—
1313#103—531no—
1314#103—531no—
1315#103—531no—
1316#103—531no—
1317#103—531no—
1318#103—531no—
1319#103—531no—
1320#103—531no—
1321#103—531no—
1322#103C22×D5311yescharacteristic
1323#103C22×D5311yescharacteristic
1324#103C22×D5311yescharacteristic
1325#103C22×D5311yescharacteristic
1326#103C22×D5311yescharacteristic
1327#103C22×D5311yescharacteristic
1328#102—531no—
1329#102—531no—
1330#102—531no—
1331#102—531no—
1332#102—531no—
1333#102—531no—
1334#102—531no—
1335#102—531no—
1336#102—531no—
1337#102—531no—
1338#102—531no—
1339#102—531no—
1340#102—531no—
1341#102—531no—
1342#102C22×D5311yescharacteristic
1343#102C22×D5311yescharacteristic
1344C22⋊C8—531no—
1345C22⋊C8—531no—
1346C22⋊C8—531no—
1347C22⋊C8—531no—
1348C22⋊C8—531no—
1349C22⋊C8—531no—
1350C22⋊C8C22×D5311yescharacteristic
1351C22⋊C8C22×D5311yescharacteristic
1352#97—531no—
1353#97—531no—
1354#97—531no—
1355#97C22×D5311yescharacteristic
1356C4×C8—531no—
1357C4×C8—531no—
1358C4×C8—531no—
1359C4×C8C22×D5311yescharacteristic
1360C24—531no—
1361C24—1061no—
1362C24—1061no—
1363#41—534no—
1364#41—534no—
1365#41—1062no—
1366#41—1062no—
1367#41—1062no—
1368#41—1062no—
1369#41—1068no—
1370#41—1068no—
1371#41—1062no—
1372#41—1062no—
1373C2×Q8—22no—
1374C2×Q8—22no—
1375C2×Q8—21no—
1376C2×Q8—21no—
1377C2×Q8—531no—
1378C2×Q8—1061no—
1379C2×Q8—1061no—
1380C2×Q8—1061no—
1381C2×Q8—1062no—
1382C2×Q8—1062no—
1383C2×Q8—1061no—
1384C2×Q8—4242no—
1385C2×Q8C23×D5311yescharacteristic
1386C2×Q8C23×D5311yescharacteristic
1387C2×Q8C23×D5311yescharacteristic
1388C2×D4—21no—
1389C2×D4—531no—
1390C2×D4—531no—
1391C2×D4—531no—
1392C2×D4—1062no—
1393C2×D4—1062no—
1394C2×D4—1061no—
1395C2×D4—1061no—
1396C2×D4—1061no—
1397C2×D4—1061no—
1398C2×D4—1068no—
1399C2×D4—1061no—
1400C2×D4—1062no—
1401C2×D4—1062no—
1402C2×D4—1061no—
1403C2×D4—1061no—
1404C2×D4—1061no—
1405C2×D4—1061no—
1406C2×D4—4242no—
1407C2×D4C23×D5311yescharacteristic
1408C22×C4—21no—
1409C22×C4—21no—
1410C22×C4—531no—
1411C22×C4—531no—
1412C22×C4—531no—
1413C22×C4—531no—
1414C22×C4—531no—
1415C22×C4—531no—
1416C22×C4—531no—
1417C22×C4—531no—
1418C22×C4—531no—
1419C22×C4—1061no—
1420C22×C4—1061no—
1421C22×C4—1061no—
1422C22×C4—1061no—
1423C22×C4—1062no—
1424C22×C4—1062no—
1425C22×C4—1061no—
1426C22×C4—1061no—
1427C22×C4—1061no—
1428C22×C4—1061no—
1429C22×C4—1061no—
1430C22×C4—1068no—
1431C22×C4—1061no—
1432C22×C4—1061no—
1433C22×C4—1061no—
1434C22×C4—1061no—
1435C22×C4—1061no—
1436C22×C4—1061no—
1437C22×C4—1061no—
1438C22×C4—1061no—
1439C22×C4—1061no—
1440C22×C4—1061no—
1441C22×C4—1061no—
1442C22×C4—4242no—
1443C22×C4C23×D5311yescharacteristic
1444Q16—22no—
1445Q16—22no—
1446Q16—1062no—
1447Q16—1062no—
1448SD16—22no—
1449SD16—22no—
1450SD16—1062no—
1451SD16—1062no—
1452SD16—1062no—
1453SD16—1062no—
1454SD16—1062no—
1455SD16—1062no—
1456D8—1062no—
1457D8—1062no—
1458D8—1062no—
1459D8—1062no—
1460M16—1062no—
1461M16—1062no—
1462M16—1062no—
1463M16—1062no—
1464C2×C8—531no—
1465C2×C8—531no—
1466C2×C8—531no—
1467C2×C8—531no—
1468C2×C8C23×D5311yescharacteristic
1469C2×C8C23×D5311yescharacteristic
1470C2×C8C23×D5311yescharacteristic
1471C2×C8C23×D5311yescharacteristic
1472C4⋊C4—21no—
1473C4⋊C4—21no—
1474C4⋊C4—21no—
1475C4⋊C4—21no—
1476C4⋊C4—21no—
1477C4⋊C4—21no—
1478C4⋊C4—21no—
1479C4⋊C4—531no—
1480C4⋊C4—531no—
1481C4⋊C4—531no—
1482C4⋊C4—531no—
1483C4⋊C4—531no—
1484C4⋊C4—531no—
1485C4⋊C4—531no—
1486C4⋊C4—531no—
1487C4⋊C4—531no—
1488C4⋊C4—531no—
1489C4⋊C4—1061no—
1490C4⋊C4—1061no—
1491C4⋊C4—1061no—
1492C4⋊C4—1061no—
1493C4⋊C4—1061no—
1494C4⋊C4—1061no—
1495C4⋊C4—1061no—
1496C4⋊C4—1061no—
1497C4⋊C4—1061no—
1498C4⋊C4—1061no—
1499C4⋊C4—1061no—
1500C4⋊C4—1061no—
1501C4⋊C4—1061no—
1502C4⋊C4—1061no—
1503C4⋊C4—1061no—
1504C4⋊C4—1061no—
1505C4⋊C4—1061no—
1506C4⋊C4D4×D5311yescharacteristic
1507C4⋊C4D4×D5311yescharacteristic
1508C4⋊C4C23×D5311yescharacteristic
1509C4⋊C4C23×D5311yescharacteristic
1510C4⋊C4C23×D5311yescharacteristic
1511C4⋊C4C23×D5311yescharacteristic
1512C22⋊C4—21no—
1513C22⋊C4—21no—
1514C22⋊C4—21no—
1515C22⋊C4—21no—
1516C22⋊C4—21no—
1517C22⋊C4—21no—
1518C22⋊C4—531no—
1519C22⋊C4—531no—
1520C22⋊C4—531no—
1521C22⋊C4—531no—
1522C22⋊C4—531no—
1523C22⋊C4—531no—
1524C22⋊C4—1061no—
1525C22⋊C4—1061no—
1526C22⋊C4—1061no—
1527C22⋊C4—1061no—
1528C22⋊C4—1061no—
1529C22⋊C4—1061no—
1530C22⋊C4—1061no—
1531C22⋊C4—1061no—
1532C22⋊C4—1061no—
1533C22⋊C4—1061no—
1534C22⋊C4—1061no—
1535C22⋊C4—1061no—
1536C22⋊C4—1061no—
1537C22⋊C4—1061no—
1538C22⋊C4—1061no—
1539C22⋊C4—1061no—
1540C22⋊C4—1061no—
1541C22⋊C4—1061no—
1542C22⋊C4—1061no—
1543C22⋊C4—1061no—
1544C22⋊C4—1061no—
1545C22⋊C4—1061no—
1546C22⋊C4—1061no—
1547C22⋊C4—1061no—
1548C22⋊C4—1061no—
1549C22⋊C4—1061no—
1550C22⋊C4D4×D5311yescharacteristic
1551C22⋊C4D4×D5311yescharacteristic
1552C42—21no—
1553C42—21no—
1554C42—21no—
1555C42—21no—
1556C42—21no—
1557C42—21no—
1558C42—531no—
1559C42—531no—
1560C42—531no—
1561C42—531no—
1562C42—531no—
1563C42—531no—
1564C42—1061no—
1565C42—1061no—
1566C42—1061no—
1567C42—1061no—
1568C42—1061no—
1569C42—1061no—
1570C42—1061no—
1571C42—1061no—
1572C42—1061no—
1573C42—1061no—
1574C42C23×D5311yescharacteristic
1575C42C23×D5311yescharacteristic
1576C23—21no—
1577C23—531no—
1578C23—531no—
1579C23—1062no—
1580C23—1064no—
1581C23—1061no—
1582C23—1061no—
1583C23—1061no—
1584C23—4241no—
1585C23—4241no—
1586C23—2121no—
1587C23—2121no—
1588C23—2122no—
1589C23—2122no—
1590C23—2122no—
1591C23C2×D4×D5311yescharacteristic
1592Q8—24no—
1593Q8—21no—
1594Q8—21no—
1595Q8—21no—
1596Q8—21no—
1597Q8—81no—
1598Q8—1061no—
1599Q8—1061no—
1600Q8—4241no—
1601Q8—4241no—
1602Q8—4241no—
1603Q8—2122no—
1604Q8#41×D5312yes—
1605Q8#41×D5312yes—
1606D4—21no—
1607D4—21no—
1608D4—81no—
1609D4—532no—
1610D4—532no—
1611D4—1064no—
1612D4—1064no—
1613D4—1064no—
1614D4—1064no—
1615D4—1064no—
1616D4—1061no—
1617D4—1061no—
1618D4—1061no—
1619D4—1061no—
1620D4—4241no—
1621D4—4241no—
1622D4—4241no—
1623D4—2122no—
1624C2×C4—24no—
1625C2×C4—21no—
1626C2×C4—21no—
1627C2×C4—21no—
1628C2×C4—21no—
1629C2×C4—21no—
1630C2×C4—21no—
1631C2×C4—21no—
1632C2×C4—21no—
1633C2×C4—21no—
1634C2×C4—81no—
1635C2×C4—531no—
1636C2×C4—532no—
1637C2×C4—532no—
1638C2×C4—531no—
1639C2×C4—531no—
1640C2×C4—531no—
1641C2×C4—531no—
1642C2×C4—531no—
1643C2×C4—1062no—
1644C2×C4—1064no—
1645C2×C4—1064no—
1646C2×C4—1062no—
1647C2×C4—1064no—
1648C2×C4—1064no—
1649C2×C4—1062no—
1650C2×C4—1061no—
1651C2×C4—1061no—
1652C2×C4—1061no—
1653C2×C4—1061no—
1654C2×C4—1061no—
1655C2×C4—1061no—
1656C2×C4—1061no—
1657C2×C4—4241no—
1658C2×C4—4241no—
1659C2×C4—4241no—
1660C2×C4—4241no—
1661C2×C4—4241no—
1662C2×C4—4241no—
1663C2×C4—4241no—
1664C2×C4—4241no—
1665C2×C4—4241no—
1666C2×C4—4241no—
1667C2×C4—4241no—
1668C2×C4—4241no—
1669C2×C4—4241no—
1670C2×C4—2121no—
1671C2×C4—2121no—
1672C2×C4—2121no—
1673C2×C4—2121no—
1674C2×C4—2122no—
1675C2×C4—2122no—
1676C2×C4—2122no—
1677C2×C4C2×D4×D5311yescharacteristic
1678C2×C4C2×D4×D5311yescharacteristic
1679C2×C4C2×D4×D5311yescharacteristic
1680C2×C4C2×D4×D5311yescharacteristic
1681C2×C4C2×D4×D5311yescharacteristic
1682C2×C4C24×D5311yescharacteristic
1683C8—21no—
1684C8—21no—
1685C8—21no—
1686C8—21no—
1687C8—1061no—
1688C8—1061no—
1689C8—1061no—
1690C8—1061no—
1691C22—21no—
1692C22—21no—
1693C22—21no—
1694C22—41no—
1695C22—41no—
1696C22—41no—
1697C22—532no—
1698C22—1061no—
1699C22—1061no—
1700C22—1062no—
1701C22—1062no—
1702C22—1061no—
1703C22—1061no—
1704C22—1061no—
1705C22—4242no—
1706C22—4244no—
1707C22—4244no—
1708C22—2121no—
1709C22—2121no—
1710C22—2121no—
1711C22—2121no—
1712C22—2121no—
1713C22—2121no—
1714C22—2121no—
1715C22C22×D4×D5311yescharacteristic
1716C4—22no—
1717C4—22no—
1718C4—21no—
1719C4—21no—
1720C4—21no—
1721C4—21no—
1722C4—21no—
1723C4—41no—
1724C4—41no—
1725C4—41no—
1726C4—41no—
1727C4—41no—
1728C4—532no—
1729C4—1061no—
1730C4—1061no—
1731C4—1061no—
1732C4—1061no—
1733C4—1061no—
1734C4—2121no—
1735C4—2121no—
1736C4—2121no—
1737C4—2121no—
1738C4—2121no—
1739C4C2×#41×D5311yescharacteristic
1740C4C2×#41×D5311yescharacteristic
1741C2—41no—
1742C2—81no—
1743C2—1062no—
1744C2—4241no—
1745C2—2121no—
1746C2—2122no—
1747C2—2122no—
1748C2#525×D5311yescharacteristic
1749C2#2028949311yescharacteristic
1750C2#2028950011yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3121C2
socleC22×C53C23×D4
prime radical#20283966C2
hypercenter#3121D53
hypocenterC53#60567
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ #117 ◁ #3121

Complements

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

NH ≅ G/Ntype
1. #542×D53C2semidirect
2. #20287917C2semidirect
3. #20284999C2semidirect
4. #20284998C2semidirect
5. #20284991C2semidirect
6. #20284990C2semidirect
7. #20284984C2semidirect
8. #20284983C2semidirect
9. #20284976C2semidirect
10. #20284975C2semidirect
11. #20284945C2semidirect
12. #20284944C2semidirect
13. #20284937C2semidirect
14. #20284902C2semidirect
15. #20284901C2semidirect
16. #20284894C2semidirect
17. #20284893C2semidirect
18. #20284662C2semidirect
19. #20284654C2semidirect
20. #20284529C2semidirect
21. #20284525C2semidirect
22. #20284206C2semidirect
23. #20284206C2semidirect
24. #20283974C2semidirect
26. C4×#13133249C2semidirect
27. #20283531C2semidirect
28. C4×#13133244C2semidirect
29. #20283520C2semidirect
30. #20283349C2semidirect
31. C53×#3121C2semidirect
37. #16811247C22semidirect
39. #16811245C22semidirect
42. #16811242C22semidirect
46. #16811238C22semidirect
48. C4⋊Q8×D53C22semidirect
51. #124×D53C22semidirect
58. #16811105C22semidirect
59. #16811105C22semidirect
60. #16811105C22semidirect
61. #16811105C22semidirect
62. #16811101C22semidirect
65. #16811097C22semidirect
66. #16811097C22semidirect
73. C4×Q8×D53C22semidirect
74. C4×D4×D53C22semidirect
79. #16810965C22semidirect
80. #16810964C22semidirect
81. #16810961C22semidirect
82. #16810960C22semidirect
83. #16810957C22semidirect
84. #16810955C22semidirect
85. #16810952C22semidirect
89. #16810943C22semidirect
90. #16810940C22semidirect
91. #16810938C22semidirect
92. #16810935C22semidirect
93. #16810918C22semidirect
94. #16810916C22semidirect
95. #16810916C22semidirect
96. #16810914C22semidirect
97. #16810912C22semidirect
98. #16810912C22semidirect
99. #16810910C22semidirect
100. #16810908C22semidirect
101. #16810906C22semidirect
102. #16810906C22semidirect
103. #16810904C22semidirect
104. #16810902C22semidirect
105. #16810902C22semidirect
106. #16810900C22semidirect
107. #16810847C22semidirect
108. #16810847C22semidirect
109. #16810845C22semidirect
110. #16810845C22semidirect
111. #16810843C22semidirect
112. #16810843C22semidirect
113. #16810841C22semidirect
114. #16810841C22semidirect
115. #16810839C22semidirect
116. #16810839C22semidirect
117. #16810837C22semidirect
118. #16810837C22semidirect
119. #16810835C22semidirect
120. #16810835C22semidirect
121. #16810788C22semidirect
122. #16810788C22semidirect
123. #16810784C22semidirect
124. #16810784C22semidirect
125. #16810779C22semidirect
126. #16810776C22semidirect
127. #16810773C22semidirect
135. #16810736C22semidirect
136. #16810734C22semidirect
137. #16810733C22semidirect
138. #16810732C22semidirect
139. #16810730C22semidirect
140. #16810728C22semidirect
141. #16810727C22semidirect
142. #16810726C22semidirect
143. #16810726C22semidirect
144. #16810725C22semidirect
145. #16810724C22semidirect
146. #16810722C22semidirect
147. #16810721C22semidirect
148. #16810721C22semidirect
149. Q16×Dic53C22semidirect
150. C4×#11719925C22semidirect
151. #16810715C22semidirect
152. C4×#11719913C22semidirect
153. SD16×Dic53C22semidirect
154. C4×#11719924C22semidirect
155. C4×#11719924C22semidirect
156. #16810710C22semidirect
157. #16810708C22semidirect
158. #16810708C22semidirect
159. C4×D424C22semidirect
160. #16810705C22semidirect
161. C4×#11719922C22semidirect
162. #16810703C22semidirect
163. #16810685C22semidirect
164. #16810684C22semidirect
165. #16810683C22semidirect
166. #16810683C22semidirect
167. #16810682C22semidirect
168. #16810681C22semidirect
169. #16810681C22semidirect
170. #16810664C22semidirect
171. #16810664C22semidirect
172. #16810662C22semidirect
173. #16810662C22semidirect
174. #16810645C22semidirect
175. #16810645C22semidirect
176. #16810630C22semidirect
177. #16810630C22semidirect
178. #16810626C22semidirect
179. #16810626C22semidirect
186. #16810575C22semidirect
187. C4×#11719912C22semidirect
189. C53×#519C22semidirect
190. C53×#485C22semidirect
192. C53×#477C22semidirect
193. C53×#475C22semidirect
194. C53×#464C22semidirect
195. C53×#464C22semidirect
196. C53×#451C22semidirect
198. C53×#441C22semidirect
199. C53×#440C22semidirect
200. C4×Q16×C53C22semidirect
201. C4×SD16×C53C22semidirect
202. C53×#433C22semidirect
879. #3121D53semidirect
939. #519C2×D53semidirect
959. #485C2×D53semidirect
975. #477C2×D53semidirect
983. #475C2×D53semidirect
994. #464C2×D53semidirect
995. #464C2×D53semidirect
1009. #451C2×D53semidirect
1027. #441C2×D53semidirect
1035. #440C2×D53semidirect
1039. C4×Q16C2×D53semidirect
1047. C4×SD16C2×D53semidirect
1059. #433C2×D53semidirect
1078. C53#60567semidirect

Maximal subgroups

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

subgroupindex
#542×D532
#202879172
#202849992
#202849982
#202849912
#202849902
#202849842
#202849832
#202849762
#202849752
#202849452
#202849442
#202849372
#202849022
#202849012
#202848942
#202848932
#202846622
#202846542
#202845292
#202845252
#202842062
#202839742
#202839662
C4×#131332492
#202835312
C4×#131332442
#202835202
#202833492
C53×#31212
#6056753