Finite Group Databasebeta

← #28270348

Subgroups — #28270348

Order 13568.

2110 conjugacy classes of subgroups.

The subgroup lattice has 1902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289010C211yesmaximal, characteristic, complemented
2#20288377C211yesmaximal, characteristic, complemented
3#20286857C211yesmaximal, characteristic, complemented
4#20286834C211yesmaximal, characteristic, complemented
5#20286819C211yesmaximal, characteristic, complemented
6#20286752C211yesmaximal, characteristic, complemented
7#20286650C211yesmaximal, characteristic, complemented
8#20286618C211yesmaximal, characteristic, complemented
9#20286554C211yesmaximal, characteristic, complemented
10#20286532C211yesmaximal, characteristic, complemented
11#20286454C211yesmaximal, characteristic, complemented
12#20286438C211yesmaximal, characteristic, complemented
13#20286422C211yesmaximal, characteristic, complemented
14SD16×C22⋊D53C211yesmaximal, characteristic, complemented
15#20286294C211yesmaximal, characteristic, complemented
16#20286279C211yesmaximal, characteristic, complemented
17#20286238C211yesmaximal, characteristic, complemented
18#20286208C211yesmaximal, characteristic, complemented
19#20285813C211yesmaximal, characteristic, complemented
20#20285783C211yesmaximal, characteristic, complemented
21#20285627C211yesmaximal, characteristic, complemented
22#20285597C211yesmaximal, characteristic, complemented
23#20285483C211yesmaximal, characteristic, complemented
24#20285469C211yesmaximal, characteristic, complemented
25#20284985C211yesmaximal, characteristic, complemented
26#20284922C211yesmaximal, characteristic, complemented
27#20284019C211yesmaximal, characteristic, complemented
28#20283936C211yesmaximal, characteristic, complemented
29#452×D53C211yesmaximal, characteristic, complemented
30#20283767C211yesmaximal, characteristic, complemented
31C53×#3009C211yesmaximal, characteristic, complemented
32C2×#41×D53C2211yescharacteristic
33C2×#13133243C2211yescharacteristic, complemented
34C2×#13133240C2211yescharacteristic, complemented
35C2×#13133238C2211yescharacteristic, complemented
36C2×#13133237C2211yescharacteristic, complemented
37C2×Q16×D53C2211yescharacteristic, complemented
38C2×SD16×D53C2211yescharacteristic, complemented
39#16811372—21no—
40#16811370—21no—
41#16811341C2211yescharacteristic, complemented
42#16811334—21no—
43#16811331C2211yescharacteristic, complemented
44#16811318—21no—
45#16811317C2211yescharacteristic, complemented
46#16811315C2211yescharacteristic, complemented
47#16811292C2211yescharacteristic
48#16811292C2211yescharacteristic
49Q8×C22⋊D53C2211yescharacteristic, complemented
50#16811284C2211yescharacteristic, complemented
51#16811283C2211yescharacteristic, complemented
52#16811280C2211yescharacteristic
53#16811280C2211yescharacteristic
54#16811275C2211yescharacteristic, complemented
55#16811267—21no—
56#16811267—21no—
57#16811267C2211yescharacteristic
58#16811267C2211yescharacteristic
59D4×C22⋊D53—21no—
60D4×C22⋊D53—21no—
61D4×C22⋊D53C2211yescharacteristic
62D4×C22⋊D53C2211yescharacteristic
63#16811246C2211yescharacteristic, complemented
64#16811237—21no—
65#16811233C2211yescharacteristic, complemented
66#16811216—21no—
67#16811209—21no—
68#16811207—21no—
69#16811201—21no—
70#16811201C2211yescharacteristic
71#16811201C2211yescharacteristic, complemented
72#16811190—21no—
73#16811190C2211yescharacteristic
74#16811136C2211yescharacteristic, complemented
75#16811130—21no—
76#16811130C2211yescharacteristic
77C22⋊Q8×D53C2211yescharacteristic, complemented
78C2×#13133188—21no—
79C2×#13133188C2211yescharacteristic
80#16811106C2211yescharacteristic
81#16811014C2211yescharacteristic, complemented
82#16811009C2211yescharacteristic, complemented
83#16811004C2211yescharacteristic, complemented
84#16810994C2211yescharacteristic, complemented
85#16810986C2211yescharacteristic, complemented
86#16810981C2211yescharacteristic, complemented
87#16810976C2211yescharacteristic, complemented
88#16810968C2211yescharacteristic, complemented
89#16810964C2211yescharacteristic, complemented
90#16810956C2211yescharacteristic, complemented
91#16810954C2211yescharacteristic, complemented
92#16810954C2211yescharacteristic, complemented
93#16810951C2211yescharacteristic, complemented
94#16810947C2211yescharacteristic, complemented
95#16810946C2211yescharacteristic, complemented
96#16810946C2211yescharacteristic, complemented
97#16810942C2211yescharacteristic, complemented
98#16810942C2211yescharacteristic, complemented
99#16810940C2211yescharacteristic, complemented
100#16810940C2211yescharacteristic, complemented
101#16810928C2211yescharacteristic, complemented
102#16810925C2211yescharacteristic, complemented
103#16810911C2211yescharacteristic, complemented
104#16810906C2211yescharacteristic, complemented
105#16810881C2211yescharacteristic, complemented
106#16810879C2211yescharacteristic, complemented
107#16810876C2211yescharacteristic, complemented
108#16810871C2211yescharacteristic, complemented
109#16810862C2211yescharacteristic, complemented
110#16810858C2211yescharacteristic, complemented
111#16810858C2211yescharacteristic, complemented
112#16810854C2211yescharacteristic, complemented
113#16810852C2211yescharacteristic, complemented
114#16810852C2211yescharacteristic, complemented
115#16810851C2211yescharacteristic, complemented
116#16810851C2211yescharacteristic, complemented
117#16810849C2211yescharacteristic, complemented
118#16810849C2211yescharacteristic, complemented
119#16810849C2211yescharacteristic, complemented
120#16810849C2211yescharacteristic, complemented
121#16810847C2211yescharacteristic, complemented
122#16810844C2211yescharacteristic, complemented
123#16810843C2211yescharacteristic, complemented
124#16810843C2211yescharacteristic, complemented
125#16810840C2211yescharacteristic, complemented
126#16810837C2211yescharacteristic, complemented
127#16810831C2211yescharacteristic, complemented
128#16810826C2211yescharacteristic, complemented
129#16810822C2211yescharacteristic, complemented
130#16810821C2211yescharacteristic, complemented
131#16810821C2211yescharacteristic, complemented
132#16810817C2211yescharacteristic, complemented
133#16810788C2211yescharacteristic, complemented
134#16810787C2211yescharacteristic, complemented
135#16810787C2211yescharacteristic, complemented
136#16810786C2211yescharacteristic, complemented
137#16810785C2211yescharacteristic
138#16810785C2211yescharacteristic, complemented
139#16810784C2211yescharacteristic, complemented
140#16810783C2211yescharacteristic, complemented
141#16810783C2211yescharacteristic, complemented
142#16810782C2211yescharacteristic, complemented
143#16810779C2211yescharacteristic, complemented
144#16810777C2211yescharacteristic, complemented
145#16810774C2211yescharacteristic, complemented
146#16810774C2211yescharacteristic, complemented
147#16810772C2211yescharacteristic, complemented
148#16810770C2211yescharacteristic, complemented
149#16810770C2211yescharacteristic, complemented
150#16810768C2211yescharacteristic
151#16810768C2211yescharacteristic, complemented
152#16810767C2211yescharacteristic, complemented
153#16810767C2211yescharacteristic, complemented
154#16810763C2211yescharacteristic, complemented
155#16810762C2211yescharacteristic, complemented
156#16810760C2211yescharacteristic, complemented
157#16810760C2211yescharacteristic, complemented
158#16810758C2211yescharacteristic, complemented
159#16810757C2211yescharacteristic, complemented
160#16810757C2211yescharacteristic, complemented
161#16810732C2211yescharacteristic, complemented
162#16810730C2211yescharacteristic, complemented
163#16810730C2211yescharacteristic, complemented
164#16810720C2211yescharacteristic, complemented
165#16810715C2211yescharacteristic, complemented
166SD16×Dic53C2211yescharacteristic, complemented
167SD16×Dic53C2211yescharacteristic, complemented
168#16810708C2211yescharacteristic, complemented
169#16810697C2211yescharacteristic, complemented
170#16810697C2211yescharacteristic, complemented
171#16810692C2211yescharacteristic, complemented
172#16810692C2211yescharacteristic, complemented
173C8×C22⋊D53C2211yescharacteristic, complemented
174C8×C22⋊D53C2211yescharacteristic, complemented
175#16810686C2211yescharacteristic, complemented
176#16810686C2211yescharacteristic, complemented
177#16810681C2211yescharacteristic, complemented
178#16810681C2211yescharacteristic, complemented
179#16810624C2211yescharacteristic, complemented
180#16810618C2211yescharacteristic, complemented
181#16810616C2211yescharacteristic, complemented
182#103×D53C2211yescharacteristic, complemented
183C2×#13133138C2211yescharacteristic, complemented
184#102×D53C2211yescharacteristic, complemented
185#16810590C2211yescharacteristic, complemented
186C22⋊C8×D53C2211yescharacteristic, complemented
187C22⋊C8×D53C2211yescharacteristic, complemented
188C2×H(5,𝔽2)×C53C2211yescharacteristic
189C2×#137×C53C2211yescharacteristic, complemented
190C22×SD16×C53C2211yescharacteristic, complemented
191C53×#536C2211yescharacteristic, complemented
192C53×#452C2211yescharacteristic
193C53×#452C2211yescharacteristic
194C53×#452C2211yescharacteristic, complemented
195C53×#452C2211yescharacteristic, complemented
196C53×#450C2211yescharacteristic, complemented
197C53×#450C2211yescharacteristic, complemented
198C53×#450C2211yescharacteristic, complemented
199C53×#450C2211yescharacteristic, complemented
200C53×#418C2211yescharacteristic, complemented
201C53×#416C2211yescharacteristic, complemented
202C53×#408C2211yescharacteristic, complemented
203C2×#11719949C2311yescharacteristic
204C2×#11719949C2311yescharacteristic
205C2×#11719945—21no—
206C2×#11719945C2311yescharacteristic
207C2×#11719945C2311yescharacteristic
208C2×#11719947—21no—
209C2×#11719947C2311yescharacteristic
210#41×D53—42no—
211#41×D53—42no—
212C2×Q8×D53C2311yescharacteristic
213C2×Q8×D53C2311yescharacteristic
214C22×C22⋊D53—21no—
215C22×C22⋊D53—21no—
216C22×C22⋊D53—21no—
217C2×D4×D53—21no—
218C2×D4×D53C2311yescharacteristic
219C22×C4×D53—21no—
220C22×C4×D53C2311yescharacteristic
221#13133243—42no—
222#13133240—42no—
223#13133238—42no—
224#13133237—42no—
225C2×Dic212C2311yescharacteristic
226C2×#11719925C2311yescharacteristic
227C2×#11719925C2311yescharacteristic
228C2×#11719925C2311yescharacteristic
229Q16×D53—42no—
230C2×#11719913C2311yescharacteristic
231C2×#11719913C2311yescharacteristic
232C2×#11719923C2311yescharacteristic
233C2×#11719923C2311yescharacteristic
234C2×#11719923C2311yescharacteristic
235C2×#11719924C2311yescharacteristic
236C2×#11719924C2311yescharacteristic
237C2×#11719924C2311yescharacteristic
238SD16×D53—42no—
239C2×D424C2311yescharacteristic
240C2×#11719922C2311yescharacteristic
241C2×#11719922C2311yescharacteristic
242C2×#11719922C2311yescharacteristic
243C2×#11719917C2311yescharacteristic
244C22×#88322C2311yescharacteristic
245C2×C8×D53C2311yescharacteristic
246C2×C8×D53C2311yescharacteristic
247C2×C8×D53C2311yescharacteristic
248C2×C8×D53C2311yescharacteristic
249#13133216C2311yescharacteristic
250#13133215—21no—
251#13133215C2311yescharacteristic
252#13133213—21no—
253#13133213—21no—
254#13133213C2311yescharacteristic
255#13133213C2311yescharacteristic
256#13133212—21no—
257#13133212—21no—
258#13133211—21no—
259#13133211—21no—
260#13133210—21no—
261#13133210—21no—
262#13133210—21no—
263#13133208—21no—
264#13133208—21no—
265#13133208C2311yescharacteristic
266#13133207—21no—
267#13133207—21no—
268#13133206—21no—
269#13133206C2311yescharacteristic
270#13133204—21no—
271#13133204—21no—
272#13133204C2311yescharacteristic
273#13133204C2311yescharacteristic
274#13133203—21no—
275#13133203—21no—
276#13133203—21no—
277#13133202—21no—
278#13133202—21no—
279#13133201—21no—
280#13133199—21no—
281#13133199—21no—
282#13133199—21no—
283#13133198—21no—
284#13133198—21no—
285#13133198D411yescharacteristic
286#13133198D411yescharacteristic
287#13133197—21no—
288#13133197—21no—
289#13133197C2311yescharacteristic
290#13133196—21no—
291#13133196—21no—
292#13133196—21no—
293#13133196C2311yescharacteristic
294#13133196C2311yescharacteristic
295#13133196C2311yescharacteristic
296#13133196C2311yescharacteristic
297#13133195—21no—
298#13133195—21no—
299#13133194—21no—
300#13133194—21no—
301#13133193—21no—
302#13133193—21no—
303#13133193—21no—
304#13133193—21no—
305#13133193D411yescharacteristic
306#13133193D411yescharacteristic
307#13133193C2311yescharacteristic
308#13133193C2311yescharacteristic
309#13133192C2311yescharacteristic
310#13133191—21no—
311#13133191—21no—
312#13133191—21no—
313#13133191C2311yescharacteristic
314#13133191C2311yescharacteristic
315#13133191C2311yescharacteristic
316#13133191C2311yescharacteristic
317#13133190—21no—
318#13133190—21no—
319#13133190—21no—
320#13133189—21no—
321#13133189—21no—
322#13133189—21no—
323#13133189—21no—
324#13133189—21no—
325#13133189—21no—
326#13133189—21no—
327#13133189—21no—
328#13133188—21no—
329#13133188—21no—
330#13133188—21no—
331#13133188—21no—
332#13133188—21no—
333#13133188—21no—
334#13133188—21no—
335#13133188—21no—
336#13133188—21no—
337#13133188—21no—
338#13133188D411yescharacteristic
339#13133188D411yescharacteristic
340#13133188C2311yescharacteristic
341#13133188C2311yescharacteristic
342#13133188C2311yescharacteristic
343#13133188C2311yescharacteristic
344#13133187—21no—
345#13133186—21no—
346#13133186—21no—
347#13133186—21no—
348#13133186—21no—
349#13133186—21no—
350#13133186—21no—
351#13133185—21no—
352#13133185—21no—
353#13133185D411yescharacteristic
354#13133185D411yescharacteristic
355Q8×Dic53C2311yescharacteristic
356Q8×Dic53C2311yescharacteristic
357Q8×Dic53C2311yescharacteristic
358Q8×Dic53C2311yescharacteristic
359C4×Dic106—21no—
360#13133182C2311yescharacteristic
361C4×D212—21no—
362D4×Dic53—21no—
363D4×Dic53—21no—
364D4×Dic53C2311yescharacteristic
365D4×Dic53C2311yescharacteristic
366#13133179—21no—
367#13133179—21no—
368#13133179C2311yescharacteristic
369C4×C22⋊D53—21no—
370C4×C22⋊D53—21no—
371C4×C22⋊D53—21no—
372C4×C22⋊D53—21no—
373C4×C22⋊D53—21no—
374C4×C22⋊D53—21no—
375C4×C22⋊D53C2311yescharacteristic
376C4×C22⋊D53C2311yescharacteristic
377C4×C22⋊D53C2311yescharacteristic
378C4×C22⋊D53C2311yescharacteristic
379#13133177—21no—
380#13133177—21no—
381#13133176—21no—
382#13133176C2311yescharacteristic
383#13133175C2311yescharacteristic
384#13133173—21no—
385C2×C4⋊Dic53—21no—
386C2×C4⋊Dic53C2311yescharacteristic
387C2×C4⋊Dic53C2311yescharacteristic
388C4⋊C4×D53—21no—
389C4⋊C4×D53—21no—
390C4⋊C4×D53C2311yescharacteristic
391C2×C22⋊Dic53—21no—
392C2×C22⋊Dic53—21no—
393C2×C22⋊Dic53—21no—
394C22⋊C4×D53—21no—
395#13133150C2311yescharacteristic
396#13133150C2311yescharacteristic
397#13133149C2311yescharacteristic
398#13133149C2311yescharacteristic
399#13133149C2311yescharacteristic
400#13133149C2311yescharacteristic
401#13133148C2311yescharacteristic
402#13133148C2311yescharacteristic
403#13133146C2311yescharacteristic
404#13133146C2311yescharacteristic
405#13133146C2311yescharacteristic
406#13133146C2311yescharacteristic
407#13133142C2311yescharacteristic
408#13133142C2311yescharacteristic
409#13133142C2311yescharacteristic
410#13133142C2311yescharacteristic
411#13133141C2311yescharacteristic
412#13133141C2311yescharacteristic
413#13133141C2311yescharacteristic
414#13133141C2311yescharacteristic
415#13133141C2311yescharacteristic
416#13133141C2311yescharacteristic
417#13133140C2311yescharacteristic
418#13133140C2311yescharacteristic
419#13133139C2311yescharacteristic
420#13133139C2311yescharacteristic
421#13133139C2311yescharacteristic
422#13133139C2311yescharacteristic
423#13133138C2311yescharacteristic
424#13133138C2311yescharacteristic
425#13133138C2311yescharacteristic
426#13133138C2311yescharacteristic
427#13133138C2311yescharacteristic
428#13133138C2311yescharacteristic
429#13133137C2311yescharacteristic
430#13133137C2311yescharacteristic
431C22⋊#88322C2311yescharacteristic
432C22⋊#88322C2311yescharacteristic
433C22⋊#88322C2311yescharacteristic
434C22⋊#88322C2311yescharacteristic
435#13133129C2311yescharacteristic
436#13133129C2311yescharacteristic
437#13133129C2311yescharacteristic
438#13133129C2311yescharacteristic
439#13133127C2311yescharacteristic
440#13133127C2311yescharacteristic
441C8×Dic53C2311yescharacteristic
442C8×Dic53C2311yescharacteristic
443H(5,𝔽2)×C53—42no—
444H(5,𝔽2)×C53—42no—
445C2×#41×C53—21no—
446C2×#41×C53C2311yescharacteristic
447C2×#41×C53C2311yescharacteristic
448C2×#41×C53C2311yescharacteristic
449C2×#41×C53C2311yescharacteristic
450C22×Q8×C53C2311yescharacteristic
451C22×D4×C53—21no—
452C22×D4×C53—21no—
453C22×D4×C53—21no—
454C22×D4×C53C2311yescharacteristic
455C22×D4×C53C2311yescharacteristic
456C22×D4×C53C2311yescharacteristic
457#137×C53—42no—
458C2×Q16×C53C2311yescharacteristic
459C2×Q16×C53C2311yescharacteristic
460C2×SD16×C53—42no—
461C2×SD16×C53C2311yescharacteristic
462C2×SD16×C53C2311yescharacteristic
463C2×SD16×C53C2311yescharacteristic
464C2×SD16×C53C2311yescharacteristic
465C2×SD16×C53C2311yescharacteristic
466C2×SD16×C53C2311yescharacteristic
467C2×M16×C53C2311yescharacteristic
468C22×C8×C53C2311yescharacteristic
469C4⋊Q8×C53—21no—
470#124×C53—21no—
471#123×C53—21no—
472#123×C53—21no—
473C22⋊Q8×C53C2311yescharacteristic
474C22⋊Q8×C53C2311yescharacteristic
475C22⋊Q8×C53C2311yescharacteristic
476C22⋊Q8×C53C2311yescharacteristic
477#117×C53C2311yescharacteristic
478#103×C53C2311yescharacteristic
479#103×C53C2311yescharacteristic
480#102×C53C2311yescharacteristic
481#102×C53C2311yescharacteristic
482#102×C53C2311yescharacteristic
483#102×C53C2311yescharacteristic
484#102×C53C2311yescharacteristic
485#102×C53C2311yescharacteristic
486C22⋊C8×C53C2311yescharacteristic
487C22⋊C8×C53C2311yescharacteristic
488C22⋊C8×C53C2311yescharacteristic
489C22⋊C8×C53C2311yescharacteristic
490C24×C53—21no—
491C24×C53—21no—
492C24×C53—21no—
493C23×D53—21no—
494C23×D53C2×D411yescharacteristic
495#41×C53—22no—
496#41×C53—22no—
497#41×C53—22no—
498#41×C53—22no—
499#41×C53—41no—
500#41×C53—41no—
501#41×C53—41no—
502#41×C53—41no—
503#41×C53—44no—
504C2×Q8×C53—21no—
505C2×Q8×C53—41no—
506C2×Q8×C53—41no—
507C2×Q8×C53C2×D411yescharacteristic
508C2×Q8×C53C2411yescharacteristic
509C2×Q8×C53C2411yescharacteristic
510C2×Q8×C53C2411yescharacteristic
511C2×D4×C53—21no—
512C2×D4×C53—22no—
513C2×D4×C53—22no—
514C2×D4×C53—21no—
515C2×D4×C53—21no—
516C2×D4×C53—21no—
517C2×D4×C53—21no—
518C2×D4×C53—21no—
519C2×D4×C53—41no—
520C2×D4×C53—41no—
521C2×D4×C53—41no—
522C2×D4×C53—41no—
523C2×D4×C53—44no—
524C2×D4×C53—44no—
525C2×D4×C53—44no—
526C2×D4×C53C2×D411yescharacteristic
527C2×D4×C53C2×D411yescharacteristic
528C2×D4×C53C2×D411yescharacteristic
529C2×D4×C53C2411yescharacteristic
530C2×D4×C53C2411yescharacteristic
531C2×D4×C53C2411yescharacteristic
532C22×C4×C53—21no—
533C22×C4×C53—21no—
534C22×C4×C53—21no—
535C22×C4×C53—21no—
536C22×C4×C53C2411yescharacteristic
537C22×C4×C53C2411yescharacteristic
538C22×C4×C53C2411yescharacteristic
539C2×C22⋊D53—21no—
540C2×C22⋊D53—21no—
541C2×C22⋊D53—21no—
542C2×C22⋊D53—21no—
543C2×C22⋊D53—21no—
544C2×C22⋊D53—21no—
545C2×C22⋊D53—21no—
546C2×C22⋊D53—21no—
547C2×C22⋊D53—21no—
548C2×C22⋊D53—21no—
549C2×C22⋊D53—21no—
550C2×C22⋊D53—21no—
551C2×C22⋊D53—21no—
552C2×C22⋊D53—21no—
553C2×C22⋊D53—21no—
554C2×C22⋊D53—21no—
555C2×C22⋊D53—82no—
556C2×C22⋊D53—82no—
557C2×C22⋊D53—82no—
558C2×C22⋊D53C2×D411yescharacteristic
559C2×C22⋊D53C2×D411yescharacteristic
560C2×C22⋊D53C2×D411yescharacteristic
561C2×C22⋊D53C2×D411yescharacteristic
562C22×Dic53—21no—
563C22×Dic53—21no—
564C22×Dic53—21no—
565C22×Dic53—21no—
566C22×Dic53—21no—
567C22×Dic53C2×D411yescharacteristic
568#11719949—22no—
569#11719949—41no—
570#11719949—41no—
571#11719949—41no—
572Q8×D53—22no—
573Q8×D53—41no—
574Q8×D53—41no—
575Q8×D53—41no—
576#11719947—22no—
577#11719947—41no—
578#11719947—44no—
579D4×D53—22no—
580D4×D53—41no—
581D4×D53—44no—
582#11719945—41no—
583#11719945—41no—
584#11719945—41no—
585#11719945—41no—
586#11719945—44no—
587C2×D212—21no—
588C2×D212—21no—
589C2×D212—21no—
590C2×D212C2411yescharacteristic
591C2×D212C2411yescharacteristic
592C2×C4×D53—21no—
593C2×C4×D53—21no—
594C2×C4×D53—21no—
595C2×C4×D53—21no—
596C2×C4×D53—21no—
597C2×C4×D53—21no—
598C2×C4×D53—21no—
599C2×C4×D53—21no—
600C2×C4×D53—41no—
601C2×C4×D53—41no—
602C2×C4×D53—44no—
603C2×C4×D53C2×D411yescharacteristic
604C2×C4×D53C2×D411yescharacteristic
605C2×C4×D53C2411yescharacteristic
606C2×C4×D53C2411yescharacteristic
607C2×Dic106—21no—
608C2×Dic106—21no—
609C2×Dic106—21no—
610C2×Dic106C2411yescharacteristic
611C2×Dic106C2411yescharacteristic
612Q16×C53—22no—
613Q16×C53—22no—
614SD16×C53—22no—
615SD16×C53—22no—
616SD16×C53—41no—
617SD16×C53—41no—
618SD16×C53—41no—
619SD16×C53—41no—
620M16×C53—41no—
621C2×C8×C53—41no—
622C2×C8×C53C2411yescharacteristic
623C2×C8×C53C2411yescharacteristic
624C2×C8×C53C2411yescharacteristic
625C2×C8×C53C2411yescharacteristic
626C4⋊C4×C53—21no—
627C4⋊C4×C53—21no—
628C4⋊C4×C53—21no—
629C4⋊C4×C53—21no—
630C4⋊C4×C53C2411yescharacteristic
631C4⋊C4×C53C2411yescharacteristic
632C22⋊C4×C53—21no—
633C22⋊C4×C53—21no—
634C22⋊C4×C53—21no—
635C22⋊C4×C53—21no—
636C22⋊C4×C53—21no—
637C42×C53—21no—
638C22⋊Dic53—21no—
639C22⋊Dic53—21no—
640C22⋊Dic53—21no—
641C22⋊Dic53—21no—
642C22⋊Dic53—21no—
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—
652C22⋊Dic53C2×D411yescharacteristic
653C22⋊Dic53C2×D411yescharacteristic
654C22⋊Dic53C2×D411yescharacteristic
655C22⋊Dic53C2×D411yescharacteristic
656C22⋊Dic53C2×D411yescharacteristic
657C22⋊Dic53C2×D411yescharacteristic
658#11719925—22no—
659#11719925—41no—
660#11719925—41no—
661#11719924—22no—
662#11719924—41no—
663#11719924—41no—
664#11719923—22no—
665#11719923—41no—
666#11719923—41no—
667#11719922—22no—
668#11719922—41no—
669#11719922—41no—
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#11719921C2×D411yescharacteristic
683#11719921C2×D411yescharacteristic
684#11719921C2×D411yescharacteristic
685#11719921C2×D411yescharacteristic
686C4⋊Dic53—21no—
687C4⋊Dic53—21no—
688C4⋊Dic53—21no—
689C4⋊Dic53—21no—
690C4⋊Dic53—21no—
691C4⋊Dic53—21no—
692C4⋊Dic53—21no—
693C4⋊Dic53—21no—
694C4⋊Dic53C2×D411yescharacteristic
695C4⋊Dic53C2×D411yescharacteristic
696C4⋊Dic53C2411yescharacteristic
697C4⋊Dic53C2411yescharacteristic
698C4⋊Dic53C2411yescharacteristic
699C4⋊Dic53C2411yescharacteristic
700#11719919—21no—
701#11719919—21no—
702#11719919—21no—
703#11719919—21no—
704#11719919—21no—
705#11719919—21no—
706#11719919—21no—
707#11719919—21no—
708#11719919—21no—
709#11719919—21no—
710#11719919—21no—
711#11719919—21no—
712#11719919C2×D411yescharacteristic
713#11719919C2×D411yescharacteristic
714#11719919C2×D411yescharacteristic
715#11719919C2×D411yescharacteristic
716C4×Dic53—21no—
717C4×Dic53—21no—
718C4×Dic53—21no—
719C4×Dic53—21no—
720C4×Dic53—21no—
721C4×Dic53—21no—
722C4×Dic53C2411yescharacteristic
723C4×Dic53C2411yescharacteristic
724#11719917—41no—
725C2×#88322—41no—
726C2×#88322C2411yescharacteristic
727C2×#88322C2411yescharacteristic
728C2×#88322C2411yescharacteristic
729C2×#88322C2411yescharacteristic
730Dic212—41no—
731D424—41no—
732#11719913—41no—
733#11719913—41no—
734C8×D53—41no—
735C8×D53—41no—
736C8×D53—41no—
737C8×D53—41no—
738C23×C53—21no—
739C23×C53—21no—
740C23×C53—21no—
741C23×C53—42no—
742C23×C53—42no—
743C23×C53—42no—
744C23×C53—81no—
745C23×C53—81no—
746C23×C53—81no—
747C23×C53—81no—
748C23×C53—81no—
749C23×C53—81no—
750C23×C53C22×D411yescharacteristic
751C23×C53C22×D411yescharacteristic
752C23×C53C22×D411yescharacteristic
753C22×D53—22no—
754C22×D53—21no—
755C22×D53—21no—
756C22×D53—41no—
757C22×D53—41no—
758C22×D53—42no—
759C22×D53—42no—
760C22×D53—81no—
761C22×D53C22×D411yescharacteristic
762C22×D53C22×D411yescharacteristic
763Q8×C53—21no—
764Q8×C53—21no—
765Q8×C53—21no—
766Q8×C53—21no—
767Q8×C53—21no—
768Q8×C53—41no—
769Q8×C53—81no—
770Q8×C53H(5,𝔽2)12yes—
771D4×C53—24no—
772D4×C53—21no—
773D4×C53—21no—
774D4×C53—21no—
775D4×C53—21no—
776D4×C53—21no—
777D4×C53—41no—
778D4×C53—41no—
779D4×C53—41no—
780D4×C53—42no—
781D4×C53—42no—
782D4×C53—42no—
783D4×C53—42no—
784D4×C53—42no—
785D4×C53H(5,𝔽2)12yes—
786C2×C4×C53—24no—
787C2×C4×C53—21no—
788C2×C4×C53—21no—
789C2×C4×C53—21no—
790C2×C4×C53—21no—
791C2×C4×C53—21no—
792C2×C4×C53—21no—
793C2×C4×C53—21no—
794C2×C4×C53—21no—
795C2×C4×C53—21no—
796C2×C4×C53—21no—
797C2×C4×C53—21no—
798C2×C4×C53—42no—
799C2×C4×C53—42no—
800C2×C4×C53—81no—
801C2×C4×C53C22×D411yescharacteristic
802C2×C4×C53C22×D411yescharacteristic
803C2×C4×C53C22×D411yescharacteristic
804C2×C4×C53C2511yescharacteristic
805C22⋊D53—22no—
806C22⋊D53—22no—
807C22⋊D53—41no—
808C22⋊D53—41no—
809C22⋊D53—42no—
810C22⋊D53—42no—
811C22⋊D53—42no—
812C22⋊D53—42no—
813C22⋊D53—42no—
814C22⋊D53—81no—
815C22⋊D53—81no—
816C22⋊D53—81no—
817C22⋊D53—81no—
818C22⋊D53—81no—
819C22⋊D53—81no—
820C22⋊D53—81no—
821C22⋊D53—81no—
822C22⋊D53—81no—
823C22⋊D53—81no—
824C22⋊D53—81no—
825C2×Dic53—21no—
826C2×Dic53—21no—
827C2×Dic53—21no—
828C2×Dic53—21no—
829C2×Dic53—21no—
830C2×Dic53—21no—
831C2×Dic53—41no—
832C2×Dic53—42no—
833C2×Dic53—81no—
834C2×Dic53—81no—
835C2×Dic53—81no—
836C2×Dic53—81no—
837C2×Dic53C22×D411yescharacteristic
838C2×Dic53C22×D411yescharacteristic
839C2×Dic53C22×D411yescharacteristic
840C2×Dic53C22×D411yescharacteristic
841C2×Dic53C22×D411yescharacteristic
842C2×Dic53C22×D411yescharacteristic
843D212—21no—
844D212—21no—
845D212—21no—
846D212—21no—
847D212—42no—
848D212—42no—
849D212—81no—
850C4×D53—21no—
851C4×D53—21no—
852C4×D53—21no—
853C4×D53—21no—
854C4×D53—41no—
855C4×D53—41no—
856C4×D53—42no—
857C4×D53—42no—
858C4×D53—42no—
859C4×D53—81no—
860C4×D53—81no—
861C4×D53—81no—
862C4×D53—81no—
863C4×D53—81no—
864Dic106—21no—
865Dic106—21no—
866Dic106—21no—
867Dic106—21no—
868Dic106—42no—
869Dic106—81no—
870Dic106—81no—
871C8×C53—21no—
872C8×C53—21no—
873C8×C53—21no—
874C8×C53—21no—
875#88322—21no—
876#88322—21no—
877#88322—21no—
878#88322—21no—
879#61640—531nomaximal, Sylow
880C22×C53—21no—
881C22×C53—21no—
882C22×C53—21no—
883C22×C53—21no—
884C22×C53—22no—
885C22×C53—21no—
886C22×C53—21no—
887C22×C53—21no—
888C22×C53—21no—
889C22×C53—21no—
890C22×C53—41no—
891C22×C53—41no—
892C22×C53—41no—
893C22×C53—41no—
894C22×C53—41no—
895C22×C53—41no—
896C22×C53—41no—
897C22×C53—41no—
898C22×C53—162no—
899C22×C53—162no—
900C22×C53—162no—
901C22×C53C23×D411yescharacteristic
902C2×D53—21no—
903C2×D53—21no—
904C2×D53—21no—
905C2×D53—21no—
906C2×D53—21no—
907C2×D53—41no—
908C2×D53—41no—
909C2×D53—41no—
910C2×D53—41no—
911C2×D53—41no—
912C2×D53—41no—
913C2×D53—82no—
914C2×D53—84no—
915C2×D53#57712yes—
916C4×C53—22no—
917C4×C53—21no—
918C4×C53—21no—
919C4×C53—21no—
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—21no—
932Dic53—41no—
933Dic53—41no—
934Dic53—41no—
935Dic53—41no—
936Dic53—41no—
937Dic53—41no—
938#3541—531no—
939#3488—531no—
940#3318—531no—
941#3317—531no—
942#3316—531no—
943#3311—531no—
944#3304—531no—
945#3301—531no—
946#3296—531no—
947#3295—531no—
948#3285—531no—
949#3284—531no—
950#3282—531no—
951D4×SD16—531no—
952#3271—531no—
953#3270—531no—
954#3267—531no—
955#3265—531no—
956#3224—531no—
957#3222—531no—
958#3204—531no—
959#3201—531no—
960#3188—531no—
961#3187—531no—
962#3125—531no—
963#3120—531no—
964#3012—531no—
965#3009D5311yescharacteristic, complemented
966#3002—531no—
967C2×#452—531no—
968#2977—531no—
969C2×C53—41no—
970C2×C53—42no—
971C2×C53—41no—
972C2×C53—41no—
973C2×C53—81no—
974C2×C53—81no—
975C2×C53#348411yescharacteristic
976C2×C53C2×#57711yescharacteristic
977C2×C53#358411yescharacteristic
978D53—22no—
979D53—41no—
980D53—81no—
981D53—81no—
982C2×H(5,𝔽2)C2×D5311yescharacteristic
983C22×#41—531no—
984C2×#137C2×D5311yescharacteristic, complemented
985C2×AGL(1,ℤ/8)—531no—
986C2×#135—531no—
987C2×#135—531no—
988C2×#135—531no—
989C22×Q16—531no—
990C22×SD16—531no—
991C22×SD16C2×D5311yescharacteristic, complemented
992#563—1061no—
993#562—1061no—
994#556—531no—
995#554—531no—
996#554—1061no—
997#553—531no—
998#553—1061no—
999#552—531no—
1000#550—531no—
1001#550—531no—
1002D4×Q8—531no—
1003#548—531no—
1004#548—531no—
1005#548—531no—
1006#548—531no—
1007#547—531no—
1008#546—531no—
1009#546—531no—
1010#546—1061no—
1011#546—1061no—
1012D42—531no—
1013D42—531no—
1014D42—1061no—
1015D42—1061no—
1016#542—531no—
1017#542—1061no—
1018#541—531no—
1019#539—1061no—
1020#538—1061no—
1021#538—1061no—
1022#537—531no—
1023#537—531no—
1024#537—1061no—
1025#536C2×D5311yescharacteristic, complemented
1026#535—531no—
1027#535—1061no—
1028#525—531no—
1029#525—531no—
1030#525—1061no—
1031C2×C22⋊Q8—531no—
1032C2×#121—531no—
1033C2×#121—1061no—
1034#520—531no—
1035#497—531no—
1036#496—531no—
1037#495—531no—
1038#492—531no—
1039#490—531no—
1040#489—531no—
1041#488—531no—
1042#486—531no—
1043#485—531no—
1044#484—531no—
1045#483—531no—
1046#483—531no—
1047#483—531no—
1048#482—531no—
1049#482—531no—
1050#482—531no—
1051#481—531no—
1052#481—531no—
1053#481—531no—
1054#481—531no—
1055#479—531no—
1056#478—531no—
1057#476—531no—
1058#475—531no—
1059#470—531no—
1060#470—531no—
1061#469—531no—
1062#468—531no—
1063#467—531no—
1064#466—531no—
1065#466—531no—
1066#465—531no—
1067#465—531no—
1068#465—531no—
1069#465—531no—
1070#465—531no—
1071#465—531no—
1072#465—531no—
1073#465—531no—
1074#465—531no—
1075#464—531no—
1076#464—531no—
1077#464—531no—
1078#464—531no—
1079#463—531no—
1080#463—531no—
1081#462—531no—
1082#461—531no—
1083#460—531no—
1084#460—531no—
1085#460—531no—
1086#459—531no—
1087#452—531no—
1088#452—531no—
1089#452—531no—
1090#452—531no—
1091#452—531no—
1092#452—531no—
1093#452—531no—
1094#452—531no—
1095#452—531no—
1096#452—531no—
1097#452C2×D5311yescharacteristic
1098#452C2×D5311yescharacteristic
1099#452C2×D5311yescharacteristic, complemented
1100#452C2×D5311yescharacteristic, complemented
1101#451—531no—
1102#451—531no—
1103#450—531no—
1104#450—531no—
1105#450—531no—
1106#450C2×D5311yescharacteristic, complemented
1107#450C2×D5311yescharacteristic, complemented
1108#450C2×D5311yescharacteristic, complemented
1109#450C2×D5311yescharacteristic, complemented
1110#449—531no—
1111#449—531no—
1112#449—531no—
1113#449—531no—
1114#449—531no—
1115#449—531no—
1116#448—531no—
1117#448—531no—
1118#448—531no—
1119#448—531no—
1120#447—531no—
1121#447—531no—
1122#447—531no—
1123#442—531no—
1124#441—531no—
1125#441—531no—
1126#440—531no—
1127C4×Q16—531no—
1128C4×SD16—531no—
1129C4×SD16—531no—
1130C4×SD16—531no—
1131#435—531no—
1132#435—531no—
1133#435—531no—
1134#435—531no—
1135C8×D4—531no—
1136C8×D4—531no—
1137C8×D4—531no—
1138C8×D4—531no—
1139#433—531no—
1140#433—531no—
1141#418C2×D5311yescharacteristic, complemented
1142#417—531no—
1143#416—531no—
1144#416—531no—
1145#416C2×D5311yescharacteristic, complemented
1146C2×#103—531no—
1147C2×#102—531no—
1148C2×#102—531no—
1149#408—531no—
1150#408C2×D5311yescharacteristic, complemented
1151C2×C22⋊C8—531no—
1152C2×C22⋊C8—531no—
1153C53#6164011yescharacteristic, complemented, Sylow
1154H(5,𝔽2)—42no—
1155H(5,𝔽2)—42no—
1156C2×#41—21no—
1157C2×#41—531no—
1158C2×#41—531no—
1159C2×#41—531no—
1160C2×#41—531no—
1161C2×#41—531no—
1162C2×#41—1061no—
1163C2×#41—1061no—
1164C2×#41—2122no—
1165C2×#41—2122no—
1166C2×#41C22×D5311yescharacteristic
1167C2×#41C22×D5311yescharacteristic
1168C2×#41C22×D5311yescharacteristic
1169C2×#41C22×D5311yescharacteristic
1170C22×Q8—531no—
1171C22×Q8—531no—
1172C22×Q8C22×D5311yescharacteristic
1173C22×D4—21no—
1174C22×D4—21no—
1175C22×D4—21no—
1176C22×D4—531no—
1177C22×D4—1061no—
1178C22×D4—1061no—
1179C22×D4—1061no—
1180C22×D4—1061no—
1181C22×D4C22×D5311yescharacteristic
1182C22×D4C22×D5311yescharacteristic
1183C22×D4C22×D5311yescharacteristic
1184C23×C4—531no—
1185C23×C4—1061no—
1186#137—42no—
1187AGL(1,ℤ/8)—2122no—
1188#135—2122no—
1189#135—2122no—
1190#135—2122no—
1191C2×Q16—531no—
1192C2×Q16—531no—
1193C2×Q16—531no—
1194C2×Q16—531no—
1195C2×Q16—2122no—
1196C2×Q16C22×D5311yescharacteristic
1197C2×Q16C22×D5311yescharacteristic
1198C2×SD16—42no—
1199C2×SD16—531no—
1200C2×SD16—531no—
1201C2×SD16—531no—
1202C2×SD16—531no—
1203C2×SD16—531no—
1204C2×SD16—531no—
1205C2×SD16—531no—
1206C2×SD16—531no—
1207C2×SD16—2122no—
1208C2×SD16C22×D5311yescharacteristic
1209C2×SD16C22×D5311yescharacteristic
1210C2×SD16C22×D5311yescharacteristic
1211C2×SD16C22×D5311yescharacteristic
1212C2×SD16C22×D5311yescharacteristic
1213C2×SD16C22×D5311yescharacteristic
1214C2×D8—531no—
1215C2×D8—531no—
1216C2×D8—531no—
1217C2×D8—531no—
1218C2×M16—531no—
1219C2×M16C22×D5311yescharacteristic
1220C22×C8—531no—
1221C22×C8—531no—
1222C22×C8—531no—
1223C22×C8—531no—
1224C22×C8—531no—
1225C22×C8C22×D5311yescharacteristic
1226C4⋊Q8—21no—
1227C4⋊Q8—531no—
1228C4⋊Q8—531no—
1229C4⋊Q8—1061no—
1230#127—531no—
1231#127—531no—
1232#127—1061no—
1233#127—1061no—
1234#126—1061no—
1235#126—1061no—
1236#126—1061no—
1237#126—1061no—
1238#126—1061no—
1239#126—1061no—
1240#126—1061no—
1241#125—531no—
1242#125—1061no—
1243#125—1061no—
1244#125—1061no—
1245#125—1061no—
1246#124—21no—
1247#124—531no—
1248#124—531no—
1249#124—531no—
1250#124—1061no—
1251#124—1061no—
1252#124—1061no—
1253#124—1061no—
1254#124—1061no—
1255#124—1061no—
1256#123—21no—
1257#123—21no—
1258#123—531no—
1259#123—531no—
1260#123—1061no—
1261#123—1061no—
1262#123—1061no—
1263#123—1061no—
1264#123—1061no—
1265#123—1061no—
1266#123—1061no—
1267#123—1061no—
1268C22⋊Q8—531no—
1269C22⋊Q8—531no—
1270C22⋊Q8—531no—
1271C22⋊Q8—531no—
1272C22⋊Q8—531no—
1273C22⋊Q8—531no—
1274C22⋊Q8—531no—
1275C22⋊Q8—531no—
1276C22⋊Q8—531no—
1277C22⋊Q8—1061no—
1278C22⋊Q8—1061no—
1279C22⋊Q8—1061no—
1280C22⋊Q8—1061no—
1281C22⋊Q8—1061no—
1282C22⋊Q8—1061no—
1283C22⋊Q8—1061no—
1284C22⋊Q8—1061no—
1285C22⋊Q8—1061no—
1286C22⋊Q8—1061no—
1287C22⋊Q8—1061no—
1288C22⋊Q8—1061no—
1289C22⋊Q8—1061no—
1290C22⋊Q8C22×D5311yescharacteristic
1291C22⋊Q8C22×D5311yescharacteristic
1292C22⋊Q8C22×D5311yescharacteristic
1293C22⋊Q8C22×D5311yescharacteristic
1294#121—531no—
1295#121—531no—
1296#121—531no—
1297#121—531no—
1298#121—531no—
1299#121—531no—
1300#121—531no—
1301#121—531no—
1302#121—531no—
1303#121—531no—
1304#121—531no—
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#121—1061no—
1323#121—1061no—
1324#121—1061no—
1325#121—1061no—
1326#121—1061no—
1327#121—1061no—
1328#121—1061no—
1329#120—531no—
1330#120—531no—
1331#120—1061no—
1332#120—1061no—
1333#120—1061no—
1334#120—1061no—
1335#120—1061no—
1336#120—1061no—
1337#120—1061no—
1338#120—1061no—
1339#120—1061no—
1340C4×Q8—531no—
1341C4×Q8—531no—
1342C4×Q8—531no—
1343C4×Q8—531no—
1344C4×Q8—531no—
1345C4×Q8—1061no—
1346C4×D4—531no—
1347C4×D4—531no—
1348C4×D4—531no—
1349C4×D4—531no—
1350C4×D4—531no—
1351C4×D4—531no—
1352C4×D4—531no—
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×D4—1061no—
1363C4×D4—1061no—
1364C4×D4—1061no—
1365C4×D4—1061no—
1366#117—531no—
1367#117—531no—
1368#117—1061no—
1369#117—1061no—
1370#117C22×D5311yescharacteristic
1371C2×C4⋊C4—531no—
1372C2×C4⋊C4—531no—
1373C2×C4⋊C4—531no—
1374C2×C4⋊C4—1061no—
1375C2×C4⋊C4—1061no—
1376C2×C4⋊C4—1061no—
1377C2×C22⋊C4—1061no—
1378C2×C22⋊C4—1061no—
1379C2×C22⋊C4—1061no—
1380C2×C22⋊C4—1061no—
1381#107—531no—
1382#107—531no—
1383#106—531no—
1384#106—531no—
1385#106—531no—
1386#106—531no—
1387#106—531no—
1388#106—531no—
1389C4⋊C8—531no—
1390C4⋊C8—531no—
1391C4⋊C8—531no—
1392C4⋊C8—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#103—531no—
1402#103—531no—
1403#103—531no—
1404#103—531no—
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#102C22×D5311yescharacteristic
1420#102C22×D5311yescharacteristic
1421#102C22×D5311yescharacteristic
1422#102C22×D5311yescharacteristic
1423#102C22×D5311yescharacteristic
1424#102C22×D5311yescharacteristic
1425C22⋊C8—531no—
1426C22⋊C8—531no—
1427C22⋊C8—531no—
1428C22⋊C8—531no—
1429C22⋊C8—531no—
1430C22⋊C8—531no—
1431C22⋊C8—531no—
1432C22⋊C8—531no—
1433C22⋊C8C22×D5311yescharacteristic
1434C22⋊C8C22×D5311yescharacteristic
1435C22⋊C8C22×D5311yescharacteristic
1436C22⋊C8C22×D5311yescharacteristic
1437#97—531no—
1438#97—531no—
1439C4×C8—531no—
1440C4×C8—531no—
1441C24—21no—
1442C24—21no—
1443C24—21no—
1444C24—531no—
1445C24—1061no—
1446#41—22no—
1447#41—22no—
1448#41—22no—
1449#41—22no—
1450#41—41no—
1451#41—41no—
1452#41—41no—
1453#41—41no—
1454#41—44no—
1455#41—1062no—
1456#41—1062no—
1457#41—2121no—
1458#41—2121no—
1459#41—2121no—
1460#41—2121no—
1461#41—2124no—
1462#41—2121no—
1463#41—2121no—
1464#41—2121no—
1465#41—2121no—
1466#41—2124no—
1467C2×Q8—21no—
1468C2×Q8—41no—
1469C2×Q8—41no—
1470C2×Q8—531no—
1471C2×Q8—531no—
1472C2×Q8—1061no—
1473C2×Q8—1061no—
1474C2×Q8—1061no—
1475C2×Q8—1062no—
1476C2×Q8—2121no—
1477C2×Q8—2121no—
1478C2×Q8—2121no—
1479C2×Q8D4×D5311yescharacteristic
1480C2×Q8C23×D5311yescharacteristic
1481C2×Q8C23×D5311yescharacteristic
1482C2×Q8C23×D5311yescharacteristic
1483C2×D4—21no—
1484C2×D4—22no—
1485C2×D4—22no—
1486C2×D4—21no—
1487C2×D4—21no—
1488C2×D4—21no—
1489C2×D4—21no—
1490C2×D4—21no—
1491C2×D4—41no—
1492C2×D4—41no—
1493C2×D4—41no—
1494C2×D4—41no—
1495C2×D4—44no—
1496C2×D4—44no—
1497C2×D4—44no—
1498C2×D4—531no—
1499C2×D4—531no—
1500C2×D4—531no—
1501C2×D4—531no—
1502C2×D4—531no—
1503C2×D4—531no—
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—1062no—
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—1061no—
1522C2×D4—1061no—
1523C2×D4—1061no—
1524C2×D4—4242no—
1525C2×D4—4242no—
1526C2×D4—4242no—
1527C2×D4—2121no—
1528C2×D4—2124no—
1529C2×D4D4×D5311yescharacteristic
1530C2×D4D4×D5311yescharacteristic
1531C2×D4D4×D5311yescharacteristic
1532C2×D4C23×D5311yescharacteristic
1533C2×D4C23×D5311yescharacteristic
1534C2×D4C23×D5311yescharacteristic
1535C22×C4—21no—
1536C22×C4—21no—
1537C22×C4—21no—
1538C22×C4—21no—
1539C22×C4—531no—
1540C22×C4—531no—
1541C22×C4—531no—
1542C22×C4—531no—
1543C22×C4—531no—
1544C22×C4—1061no—
1545C22×C4—1061no—
1546C22×C4—1061no—
1547C22×C4—1061no—
1548C22×C4—1061no—
1549C22×C4—1061no—
1550C22×C4—1061no—
1551C22×C4—1061no—
1552C22×C4—1061no—
1553C22×C4—1061no—
1554C22×C4—1061no—
1555C22×C4—1061no—
1556C22×C4—1061no—
1557C22×C4—2121no—
1558C22×C4—2121no—
1559C22×C4—2124no—
1560C22×C4C23×D5311yescharacteristic
1561C22×C4C23×D5311yescharacteristic
1562C22×C4C23×D5311yescharacteristic
1563Q16—22no—
1564Q16—22no—
1565Q16—1062no—
1566Q16—2121no—
1567Q16—2121no—
1568Q16—2121no—
1569SD16—22no—
1570SD16—22no—
1571SD16—41no—
1572SD16—41no—
1573SD16—41no—
1574SD16—41no—
1575SD16—1062no—
1576SD16—1062no—
1577SD16—2121no—
1578SD16—2121no—
1579SD16—2121no—
1580SD16—2121no—
1581SD16—2121no—
1582SD16—2121no—
1583D8—1062no—
1584D8—2121no—
1585D8—2121no—
1586D8—2121no—
1587M16—41no—
1588M16—2121no—
1589C2×C8—41no—
1590C2×C8—531no—
1591C2×C8—531no—
1592C2×C8—531no—
1593C2×C8—531no—
1594C2×C8—2121no—
1595C2×C8—2121no—
1596C2×C8—2121no—
1597C2×C8—2121no—
1598C2×C8—2121no—
1599C2×C8C23×D5311yescharacteristic
1600C2×C8C23×D5311yescharacteristic
1601C2×C8C23×D5311yescharacteristic
1602C2×C8C23×D5311yescharacteristic
1603C4⋊C4—21no—
1604C4⋊C4—21no—
1605C4⋊C4—21no—
1606C4⋊C4—21no—
1607C4⋊C4—531no—
1608C4⋊C4—531no—
1609C4⋊C4—531no—
1610C4⋊C4—531no—
1611C4⋊C4—531no—
1612C4⋊C4—531no—
1613C4⋊C4—531no—
1614C4⋊C4—531no—
1615C4⋊C4—531no—
1616C4⋊C4—531no—
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⋊C4—1061no—
1626C4⋊C4—1061no—
1627C4⋊C4—1061no—
1628C4⋊C4—1061no—
1629C4⋊C4—1061no—
1630C4⋊C4—1061no—
1631C4⋊C4—1061no—
1632C4⋊C4—1061no—
1633C4⋊C4—1061no—
1634C4⋊C4—1061no—
1635C4⋊C4—1061no—
1636C4⋊C4—1061no—
1637C4⋊C4C23×D5311yescharacteristic
1638C4⋊C4C23×D5311yescharacteristic
1639C22⋊C4—21no—
1640C22⋊C4—21no—
1641C22⋊C4—21no—
1642C22⋊C4—21no—
1643C22⋊C4—21no—
1644C22⋊C4—531no—
1645C22⋊C4—531no—
1646C22⋊C4—531no—
1647C22⋊C4—531no—
1648C22⋊C4—531no—
1649C22⋊C4—531no—
1650C22⋊C4—531no—
1651C22⋊C4—531no—
1652C22⋊C4—531no—
1653C22⋊C4—531no—
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⋊C4—1061no—
1673C22⋊C4—1061no—
1674C22⋊C4—1061no—
1675C22⋊C4—1061no—
1676C22⋊C4—1061no—
1677C22⋊C4—1061no—
1678C22⋊C4—1061no—
1679C22⋊C4—1061no—
1680C42—21no—
1681C42—531no—
1682C42—531no—
1683C42—1061no—
1684C42—1061no—
1685C42—1061no—
1686C42—1061no—
1687C42—1061no—
1688C42—1061no—
1689C23—21no—
1690C23—21no—
1691C23—21no—
1692C23—42no—
1693C23—42no—
1694C23—42no—
1695C23—81no—
1696C23—81no—
1697C23—81no—
1698C23—81no—
1699C23—81no—
1700C23—81no—
1701C23—531no—
1702C23—531no—
1703C23—1062no—
1704C23—1061no—
1705C23—1061no—
1706C23—4241no—
1707C23—2121no—
1708C23—2121no—
1709C23—2122no—
1710C23—2122no—
1711C23C2×D4×D5311yescharacteristic
1712C23C2×D4×D5311yescharacteristic
1713C23C2×D4×D5311yescharacteristic
1714Q8—21no—
1715Q8—21no—
1716Q8—21no—
1717Q8—21no—
1718Q8—21no—
1719Q8—41no—
1720Q8—81no—
1721Q8—1061no—
1722Q8—1061no—
1723Q8—1061no—
1724Q8—1061no—
1725Q8—4241no—
1726Q8—4241no—
1727Q8—2122no—
1728Q8#1313326212yes—
1729D4—24no—
1730D4—21no—
1731D4—21no—
1732D4—21no—
1733D4—21no—
1734D4—21no—
1735D4—41no—
1736D4—41no—
1737D4—41no—
1738D4—42no—
1739D4—42no—
1740D4—42no—
1741D4—42no—
1742D4—42no—
1743D4—1062no—
1744D4—1062no—
1745D4—1061no—
1746D4—1061no—
1747D4—1061no—
1748D4—1061no—
1749D4—4241no—
1750D4—4241no—
1751D4—4241no—
1752D4—4241no—
1753D4—4241no—
1754D4—4241no—
1755D4—4241no—
1756D4—4241no—
1757D4—4241no—
1758D4—4241no—
1759D4—4241no—
1760D4—4241no—
1761D4—2122no—
1762D4—2122no—
1763D4—2121no—
1764D4—2121no—
1765D4—2122no—
1766D4—2122no—
1767D4—2122no—
1768D4—2122no—
1769D4—2122no—
1770D4#1313326212yes—
1771C2×C4—24no—
1772C2×C4—21no—
1773C2×C4—21no—
1774C2×C4—21no—
1775C2×C4—21no—
1776C2×C4—21no—
1777C2×C4—21no—
1778C2×C4—21no—
1779C2×C4—21no—
1780C2×C4—21no—
1781C2×C4—21no—
1782C2×C4—21no—
1783C2×C4—42no—
1784C2×C4—42no—
1785C2×C4—81no—
1786C2×C4—531no—
1787C2×C4—531no—
1788C2×C4—531no—
1789C2×C4—531no—
1790C2×C4—531no—
1791C2×C4—531no—
1792C2×C4—1061no—
1793C2×C4—1061no—
1794C2×C4—1061no—
1795C2×C4—1061no—
1796C2×C4—1061no—
1797C2×C4—1061no—
1798C2×C4—1061no—
1799C2×C4—1061no—
1800C2×C4—1061no—
1801C2×C4—1061no—
1802C2×C4—4241no—
1803C2×C4—4241no—
1804C2×C4—4241no—
1805C2×C4—4241no—
1806C2×C4—4241no—
1807C2×C4—4241no—
1808C2×C4—4241no—
1809C2×C4—4241no—
1810C2×C4—4241no—
1811C2×C4—2121no—
1812C2×C4—2121no—
1813C2×C4—2122no—
1814C2×C4—2122no—
1815C2×C4—2122no—
1816C2×C4—2121no—
1817C2×C4—2122no—
1818C2×C4C2×D4×D5311yescharacteristic
1819C2×C4C2×D4×D5311yescharacteristic
1820C2×C4C2×D4×D5311yescharacteristic
1821C2×C4C24×D5311yescharacteristic
1822C8—21no—
1823C8—21no—
1824C8—21no—
1825C8—21no—
1826C8—1061no—
1827C8—1061no—
1828C8—1061no—
1829C8—1061no—
1830C22—21no—
1831C22—21no—
1832C22—22no—
1833C22—21no—
1834C22—21no—
1835C22—21no—
1836C22—21no—
1837C22—21no—
1838C22—21no—
1839C22—21no—
1840C22—41no—
1841C22—41no—
1842C22—41no—
1843C22—41no—
1844C22—41no—
1845C22—41no—
1846C22—41no—
1847C22—41no—
1848C22—162no—
1849C22—162no—
1850C22—162no—
1851C22—532no—
1852C22—1061no—
1853C22—1061no—
1854C22—1061no—
1855C22—1061no—
1856C22—1061no—
1857C22—4244no—
1858C22—4242no—
1859C22—2121no—
1860C22—2121no—
1861C22—2121no—
1862C22—2121no—
1863C22—2121no—
1864C22—2121no—
1865C22C22×D4×D5311yescharacteristic
1866C4—21no—
1867C4—22no—
1868C4—21no—
1869C4—21no—
1870C4—41no—
1871C4—41no—
1872C4—41no—
1873C4—41no—
1874C4—1061no—
1875C4—1061no—
1876C4—1061no—
1877C4—1061no—
1878C4—1061no—
1879C4—1061no—
1880C4—2121no—
1881C4—2121no—
1882C4—2121no—
1883C4—2121no—
1884C4—2121no—
1885C4—2121no—
1886C4C2×#1313326211yescharacteristic
1887C4C2×#1313326211yescharacteristic
1888C2—41no—
1889C2—41no—
1890C2—41no—
1891C2—42no—
1892C2—81no—
1893C2—81no—
1894C2—1062no—
1895C2—4241no—
1896C2—4241no—
1897C2—2121no—
1898C2#2028834411yescharacteristic
1899C2#577×D5311yescharacteristic
1900C2#2028948711yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3009C2
socleC22×C53C23×D4
hypercenter#3009D53
hypocenterC53#61640
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×#41 ◁ #3009

Complements

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

NH ≅ G/Ntype
1. #20289010C2semidirect
2. #20288377C2semidirect
3. #20286857C2semidirect
4. #20286834C2semidirect
5. #20286819C2semidirect
6. #20286752C2semidirect
7. #20286650C2semidirect
8. #20286618C2semidirect
9. #20286554C2semidirect
10. #20286532C2semidirect
11. #20286454C2semidirect
12. #20286438C2semidirect
13. #20286422C2semidirect
14. SD16×C22⋊D53C2semidirect
15. #20286294C2semidirect
16. #20286279C2semidirect
17. #20286238C2semidirect
18. #20286208C2semidirect
19. #20285813C2semidirect
20. #20285783C2semidirect
21. #20285627C2semidirect
22. #20285597C2semidirect
23. #20285483C2semidirect
24. #20285469C2semidirect
25. #20284985C2semidirect
26. #20284922C2semidirect
27. #20284019C2semidirect
28. #20283936C2semidirect
29. #452×D53C2semidirect
30. #20283767C2semidirect
31. C53×#3009C2semidirect
33. C2×#13133243C22semidirect
34. C2×#13133240C22semidirect
35. C2×#13133238C22semidirect
36. C2×#13133237C22semidirect
37. C2×Q16×D53C22semidirect
38. C2×SD16×D53C22semidirect
41. #16811341C22semidirect
43. #16811331C22semidirect
45. #16811317C22semidirect
46. #16811315C22semidirect
49. Q8×C22⋊D53C22semidirect
50. #16811284C22semidirect
51. #16811283C22semidirect
54. #16811275C22semidirect
63. #16811246C22semidirect
65. #16811233C22semidirect
71. #16811201C22semidirect
74. #16811136C22semidirect
77. C22⋊Q8×D53C22semidirect
81. #16811014C22semidirect
82. #16811009C22semidirect
83. #16811004C22semidirect
84. #16810994C22semidirect
85. #16810986C22semidirect
86. #16810981C22semidirect
87. #16810976C22semidirect
88. #16810968C22semidirect
89. #16810964C22semidirect
90. #16810956C22semidirect
91. #16810954C22semidirect
92. #16810954C22semidirect
93. #16810951C22semidirect
94. #16810947C22semidirect
95. #16810946C22semidirect
96. #16810946C22semidirect
97. #16810942C22semidirect
98. #16810942C22semidirect
99. #16810940C22semidirect
100. #16810940C22semidirect
101. #16810928C22semidirect
102. #16810925C22semidirect
103. #16810911C22semidirect
104. #16810906C22semidirect
105. #16810881C22semidirect
106. #16810879C22semidirect
107. #16810876C22semidirect
108. #16810871C22semidirect
109. #16810862C22semidirect
110. #16810858C22semidirect
111. #16810858C22semidirect
112. #16810854C22semidirect
113. #16810852C22semidirect
114. #16810852C22semidirect
115. #16810851C22semidirect
116. #16810851C22semidirect
117. #16810849C22semidirect
118. #16810849C22semidirect
119. #16810849C22semidirect
120. #16810849C22semidirect
121. #16810847C22semidirect
122. #16810844C22semidirect
123. #16810843C22semidirect
124. #16810843C22semidirect
125. #16810840C22semidirect
126. #16810837C22semidirect
127. #16810831C22semidirect
128. #16810826C22semidirect
129. #16810822C22semidirect
130. #16810821C22semidirect
131. #16810821C22semidirect
132. #16810817C22semidirect
133. #16810788C22semidirect
134. #16810787C22semidirect
135. #16810787C22semidirect
136. #16810786C22semidirect
138. #16810785C22semidirect
139. #16810784C22semidirect
140. #16810783C22semidirect
141. #16810783C22semidirect
142. #16810782C22semidirect
143. #16810779C22semidirect
144. #16810777C22semidirect
145. #16810774C22semidirect
146. #16810774C22semidirect
147. #16810772C22semidirect
148. #16810770C22semidirect
149. #16810770C22semidirect
151. #16810768C22semidirect
152. #16810767C22semidirect
153. #16810767C22semidirect
154. #16810763C22semidirect
155. #16810762C22semidirect
156. #16810760C22semidirect
157. #16810760C22semidirect
158. #16810758C22semidirect
159. #16810757C22semidirect
160. #16810757C22semidirect
161. #16810732C22semidirect
162. #16810730C22semidirect
163. #16810730C22semidirect
164. #16810720C22semidirect
165. #16810715C22semidirect
166. SD16×Dic53C22semidirect
167. SD16×Dic53C22semidirect
168. #16810708C22semidirect
169. #16810697C22semidirect
170. #16810697C22semidirect
171. #16810692C22semidirect
172. #16810692C22semidirect
173. C8×C22⋊D53C22semidirect
174. C8×C22⋊D53C22semidirect
175. #16810686C22semidirect
176. #16810686C22semidirect
177. #16810681C22semidirect
178. #16810681C22semidirect
179. #16810624C22semidirect
180. #16810618C22semidirect
181. #16810616C22semidirect
182. #103×D53C22semidirect
183. C2×#13133138C22semidirect
184. #102×D53C22semidirect
185. #16810590C22semidirect
186. C22⋊C8×D53C22semidirect
187. C22⋊C8×D53C22semidirect
189. C2×#137×C53C22semidirect
190. C22×SD16×C53C22semidirect
191. C53×#536C22semidirect
194. C53×#452C22semidirect
195. C53×#452C22semidirect
196. C53×#450C22semidirect
197. C53×#450C22semidirect
198. C53×#450C22semidirect
199. C53×#450C22semidirect
200. C53×#418C22semidirect
201. C53×#416C22semidirect
202. C53×#408C22semidirect
965. #3009D53semidirect
984. C2×#137C2×D53semidirect
991. C22×SD16C2×D53semidirect
1025. #536C2×D53semidirect
1099. #452C2×D53semidirect
1100. #452C2×D53semidirect
1106. #450C2×D53semidirect
1107. #450C2×D53semidirect
1108. #450C2×D53semidirect
1109. #450C2×D53semidirect
1141. #418C2×D53semidirect
1145. #416C2×D53semidirect
1150. #408C2×D53semidirect
1153. C53#61640semidirect

Maximal subgroups

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

subgroupindex
#202890102
#202883772
#202868572
#202868342
#202868192
#202867522
#202866502
#202866182
#202865542
#202865322
#202864542
#202864382
#202864222
SD16×C22⋊D532
#202862942
#202862792
#202862382
#202862082
#202858132
#202857832
#202856272
#202855972
#202854832
#202854692
#202849852
#202849222
#202840192
#202839362
#452×D532
#202837672
C53×#30092
#6164053