Finite Group Databasebeta

← #28270100

Subgroups — #28270100

Order 13568.

2050 conjugacy classes of subgroups.

The subgroup lattice has 1868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288979C211yesmaximal, characteristic, complemented
2#20288389C211yesmaximal, characteristic, complemented
3#20287012C211yesmaximal, characteristic, complemented
4#20286993C211yesmaximal, characteristic, complemented
5#20286907C211yesmaximal, characteristic, complemented
6#20286876C211yesmaximal, characteristic, complemented
7#20286783C211yesmaximal, characteristic, complemented
8#20286755C211yesmaximal, characteristic, complemented
9#20286636C211yesmaximal, characteristic, complemented
10#20286632C211yesmaximal, characteristic, complemented
11#20286454C211yesmaximal, characteristic, complemented
12#20286418C211yesmaximal, characteristic, complemented
13#20286352C211yesmaximal, characteristic, complemented
14#20286320C211yesmaximal, characteristic, complemented
15#20286284C211yesmaximal, characteristic, complemented
16#20286270C211yesmaximal, characteristic, complemented
17#20286229C211yesmaximal, characteristic, complemented
18#20285823C211yesmaximal, characteristic, complemented
19#20285819C211yesmaximal, characteristic, complemented
20#20285598C211yesmaximal, characteristic, complemented
21#20285571C211yesmaximal, characteristic, complemented
22#20285543C211yesmaximal, characteristic, complemented
23#20285491C211yesmaximal, characteristic, complemented
24#20284996C211yesmaximal, characteristic, complemented
25#20284974C211yesmaximal, characteristic, complemented
26#20284007C211yesmaximal, characteristic, complemented
27#20284000C211yesmaximal, characteristic, complemented
28#20283953C211yesmaximal, characteristic, complemented
29#20283929C211yesmaximal, characteristic, complemented
30#20283764C211yesmaximal, characteristic, complemented
31C53×#3267C211yesmaximal, characteristic, complemented
32C2×#13133264C2211yescharacteristic
33C2×#41×D53C2211yescharacteristic, complemented
34C2×#13133246C2211yescharacteristic
35C2×#13133246C2211yescharacteristic, complemented
36C2×#13133241C2211yescharacteristic
37C2×#13133237C2211yescharacteristic
38C2×Q16×D53C2211yescharacteristic, complemented
39C22×#11719923C2211yescharacteristic, complemented
40#16811366—21no—
41#16811361—21no—
42#16811357—21no—
43#16811344C2211yescharacteristic
44#16811343C2211yescharacteristic, complemented
45#16811338C2211yescharacteristic
46#16811337C2211yescharacteristic, complemented
47#16811299—21no—
48#16811288C2211yescharacteristic, complemented
49#16811286C2211yescharacteristic
50#16811283C2211yescharacteristic, complemented
51#16811282C2211yescharacteristic
52#16811281C2211yescharacteristic
53#16811280C2211yescharacteristic, complemented
54#16811274—21no—
55#16811272C2211yescharacteristic, complemented
56#16811271—21no—
57#16811268C2211yescharacteristic, complemented
58#16811267C2211yescharacteristic
59#16811265—21no—
60#16811262—21no—
61#16811261C2211yescharacteristic
62#16811242C2211yescharacteristic, complemented
63#16811241—21no—
64#16811240—21no—
65#16811238C2211yescharacteristic, complemented
66#16811211—21no—
67#16811208—21no—
68#16811203C2211yescharacteristic
69#16811200—21no—
70#16811198C2211yescharacteristic, complemented
71#16811196C2211yescharacteristic, complemented
72#16811195—21no—
73#16811190C2211yescharacteristic, complemented
74#16811133C2211yescharacteristic
75#16811132C2211yescharacteristic
76#16811131—21no—
77#16811130C2211yescharacteristic
78C2×#13133195—21no—
79C22⋊Q8×D53C2211yescharacteristic, complemented
80#16811102C2211yescharacteristic, complemented
81#16811014C2211yescharacteristic, complemented
82#16811005C2211yescharacteristic, complemented
83#16811004C2211yescharacteristic, complemented
84#16810984C2211yescharacteristic, complemented
85#16810983C2211yescharacteristic, complemented
86#16810973C2211yescharacteristic, complemented
87#16810972C2211yescharacteristic, complemented
88#16810967C2211yescharacteristic, complemented
89#16810965C2211yescharacteristic, complemented
90#16810963C2211yescharacteristic, complemented
91#16810963C2211yescharacteristic, complemented
92#16810961C2211yescharacteristic, complemented
93#16810961C2211yescharacteristic, complemented
94#16810957C2211yescharacteristic, complemented
95#16810955C2211yescharacteristic, complemented
96#16810949C2211yescharacteristic, complemented
97#16810948C2211yescharacteristic, complemented
98#16810940C2211yescharacteristic, complemented
99#16810935C2211yescharacteristic, complemented
100#16810919C2211yescharacteristic, complemented
101#16810911C2211yescharacteristic, complemented
102#16810907C2211yescharacteristic, complemented
103#16810903C2211yescharacteristic, complemented
104#16810880C2211yescharacteristic, complemented
105#16810878C2211yescharacteristic, complemented
106#16810875C2211yescharacteristic, complemented
107#16810869C2211yescharacteristic, complemented
108#16810868C2211yescharacteristic
109#16810866C2211yescharacteristic
110#16810866C2211yescharacteristic, complemented
111#16810864C2211yescharacteristic, complemented
112#16810862C2211yescharacteristic, complemented
113#16810862C2211yescharacteristic, complemented
114#16810858C2211yescharacteristic, complemented
115#16810854C2211yescharacteristic, complemented
116#16810850C2211yescharacteristic, complemented
117#16810849C2211yescharacteristic, complemented
118#16810847C2211yescharacteristic, complemented
119#16810846C2211yescharacteristic, complemented
120#16810844C2211yescharacteristic, complemented
121#16810842C2211yescharacteristic, complemented
122#16810840C2211yescharacteristic, complemented
123#16810838C2211yescharacteristic, complemented
124#16810836C2211yescharacteristic, complemented
125#16810831C2211yescharacteristic, complemented
126#16810830C2211yescharacteristic, complemented
127#16810826C2211yescharacteristic, complemented
128#16810788C2211yescharacteristic, complemented
129#16810787C2211yescharacteristic, complemented
130#16810786C2211yescharacteristic
131#16810786C2211yescharacteristic, complemented
132#16810785C2211yescharacteristic, complemented
133#16810785C2211yescharacteristic, complemented
134#16810785C2211yescharacteristic, complemented
135#16810784C2211yescharacteristic, complemented
136#16810782C2211yescharacteristic
137#16810782C2211yescharacteristic, complemented
138#16810781C2211yescharacteristic, complemented
139#16810780C2211yescharacteristic, complemented
140#16810778C2211yescharacteristic, complemented
141#16810777C2211yescharacteristic, complemented
142#16810777C2211yescharacteristic, complemented
143#16810777C2211yescharacteristic, complemented
144#16810772C2211yescharacteristic, complemented
145#16810767C2211yescharacteristic
146#16810767C2211yescharacteristic
147#16810766C2211yescharacteristic
148#16810765C2211yescharacteristic
149#16810765C2211yescharacteristic
150#16810765C2211yescharacteristic, complemented
151#16810765C2211yescharacteristic, complemented
152#16810763C2211yescharacteristic, complemented
153#16810760C2211yescharacteristic
154#16810760C2211yescharacteristic, complemented
155#16810760C2211yescharacteristic, complemented
156#16810760C2211yescharacteristic, complemented
157#16810760C2211yescharacteristic, complemented
158#16810757C2211yescharacteristic, complemented
159#16810755C2211yescharacteristic
160#16810731C2211yescharacteristic, complemented
161#16810724C2211yescharacteristic, complemented
162#16810720C2211yescharacteristic, complemented
163#16810715C2211yescharacteristic, complemented
164C4×#11719923C2211yescharacteristic, complemented
165C4×#11719923C2211yescharacteristic, complemented
166D8×Dic53C2211yescharacteristic, complemented
167#16810700C2211yescharacteristic, complemented
168#16810699C2211yescharacteristic
169#16810696C2211yescharacteristic, complemented
170#16810694C2211yescharacteristic, complemented
171#16810691C2211yescharacteristic
172D4×#88322C2211yescharacteristic, complemented
173#16810686C2211yescharacteristic, complemented
174#16810685C2211yescharacteristic, complemented
175#16810683C2211yescharacteristic, complemented
176#16810633C2211yescharacteristic, complemented
177#16810630C2211yescharacteristic, complemented
178#16810630C2211yescharacteristic, complemented
179#16810626C2211yescharacteristic, complemented
180#16810620C2211yescharacteristic, complemented
181#16810619C2211yescharacteristic, complemented
182#16810619C2211yescharacteristic, complemented
183#16810616C2211yescharacteristic, complemented
184#16810591C2211yescharacteristic, complemented
185#16810588C2211yescharacteristic, complemented
186#16810585C2211yescharacteristic, complemented
187C2×#13133129C2211yescharacteristic, complemented
188C2×AGL(1,ℤ/8)×C53C2211yescharacteristic, complemented
189C2×#135×C53C2211yescharacteristic
190C53×#547C2211yescharacteristic
191C53×#546C2211yescharacteristic, complemented
192C53×#497C2211yescharacteristic, complemented
193C53×#470C2211yescharacteristic, complemented
194C53×#465C2211yescharacteristic, complemented
195C53×#463C2211yescharacteristic, complemented
196C53×#461C2211yescharacteristic, complemented
197C53×#452C2211yescharacteristic, complemented
198C53×#452C2211yescharacteristic, complemented
199C53×#450C2211yescharacteristic, complemented
200C53×#449C2211yescharacteristic
201C53×#442C2211yescharacteristic, complemented
202C53×#435C2211yescharacteristic, complemented
203#13133264—42no—
204#13133264—42no—
205C2×#11719949C2311yescharacteristic
206C2×#11719945—21no—
207C2×#11719945—21no—
208C2×#11719945C2311yescharacteristic
209C2×#11719945C2311yescharacteristic
210C2×#11719947—21no—
211C2×#11719947—21no—
212C2×#11719947—21no—
213C2×#11719947C2311yescharacteristic
214C2×#11719947C2311yescharacteristic
215C2×#11719947C2311yescharacteristic
216#41×D53—42no—
217#41×D53—42no—
218C22×Dic106—21no—
219C22×Dic106C2311yescharacteristic
220C2×Q8×D53C2311yescharacteristic
221C2×Q8×D53C2311yescharacteristic
222C2×Q8×D53C2311yescharacteristic
223C2×Q8×D53C2311yescharacteristic
224C2×D4×D53—21no—
225C2×D4×D53C2311yescharacteristic
226C22×C4×D53—21no—
227C22×C4×D53C2311yescharacteristic
228#13133246—42no—
229#13133246—42no—
230#13133241—42no—
231#13133237—42no—
232C2×Dic212C2311yescharacteristic
233C2×Dic212C2311yescharacteristic
234C2×#11719925C2311yescharacteristic
235C2×#11719925C2311yescharacteristic
236C2×#11719925C2311yescharacteristic
237C2×#11719925C2311yescharacteristic
238Q16×D53—42no—
239C2×#11719913C2311yescharacteristic
240C2×#11719923—42no—
241C2×#11719923C2311yescharacteristic
242C2×#11719923C2311yescharacteristic
243C2×#11719923C2311yescharacteristic
244C2×#11719923C2311yescharacteristic
245C2×#11719923C2311yescharacteristic
246C2×#11719924C2311yescharacteristic
247C2×#11719922C2311yescharacteristic
248C2×#11719922C2311yescharacteristic
249C2×#11719912C2311yescharacteristic
250C2×#11719912C2311yescharacteristic
251C2×#11719912C2311yescharacteristic
252C22×#88322C2311yescharacteristic
253C22×#88322C2311yescharacteristic
254C2×C8×D53C2311yescharacteristic
255#13133217C2311yescharacteristic
256#13133216—21no—
257#13133216—21no—
258#13133216—21no—
259#13133216C2311yescharacteristic
260#13133215C2311yescharacteristic
261#13133213—21no—
262#13133212—21no—
263#13133210—21no—
264#13133210—21no—
265#13133210—21no—
266#13133210—21no—
267#13133210—21no—
268#13133206C2311yescharacteristic
269#13133205C2311yescharacteristic
270#13133204—21no—
271#13133204—21no—
272#13133204—21no—
273#13133204—21no—
274#13133204C2311yescharacteristic
275#13133203—21no—
276#13133203—21no—
277#13133203—21no—
278#13133203—21no—
279#13133203—21no—
280#13133203—21no—
281#13133203—21no—
282#13133203—21no—
283#13133203—21no—
284#13133203—21no—
285#13133202—21no—
286#13133202—21no—
287#13133202—21no—
288#13133202D411yescharacteristic
289#13133201—21no—
290#13133201—21no—
291#13133200—21no—
292#13133200—21no—
293#13133200—21no—
294#13133199—21no—
295#13133199—21no—
296#13133199D411yescharacteristic
297#13133198—21no—
298#13133198—21no—
299#13133198—21no—
300#13133197C2311yescharacteristic
301#13133197C2311yescharacteristic
302#13133196—21no—
303#13133196—21no—
304#13133196C2311yescharacteristic
305#13133196C2311yescharacteristic
306#13133196C2311yescharacteristic
307#13133195—21no—
308#13133195—21no—
309#13133195—21no—
310#13133195—21no—
311#13133195—21no—
312#13133195—21no—
313#13133195—21no—
314#13133195—21no—
315#13133195—21no—
316#13133195D411yescharacteristic
317#13133194—21no—
318#13133194—21no—
319#13133194—21no—
320#13133194—21no—
321#13133194D411yescharacteristic
322#13133193C2311yescharacteristic
323#13133193C2311yescharacteristic
324#13133193C2311yescharacteristic
325#13133193C2311yescharacteristic
326#13133192—21no—
327#13133192C2311yescharacteristic
328#13133191—21no—
329#13133191—21no—
330#13133191C2311yescharacteristic
331#13133190—21no—
332#13133190—21no—
333#13133190—21no—
334#13133190—21no—
335#13133190D411yescharacteristic
336#13133189—21no—
337#13133189—21no—
338#13133189—21no—
339#13133189—21no—
340#13133189—21no—
341#13133189D411yescharacteristic
342#13133188—21no—
343#13133188C2311yescharacteristic
344#13133188C2311yescharacteristic
345#13133188C2311yescharacteristic
346#13133188C2311yescharacteristic
347#13133188C2311yescharacteristic
348#13133187—21no—
349#13133187D411yescharacteristic
350#13133186—21no—
351#13133186—21no—
352#13133186—21no—
353#13133185—21no—
354#13133185—21no—
355#13133185—21no—
356#13133185D411yescharacteristic
357Q8×Dic53C2311yescharacteristic
358C4×Dic106C2311yescharacteristic
359C4×Dic106C2311yescharacteristic
360#13133182—21no—
361#13133182—21no—
362#13133182C2311yescharacteristic
363C4×D212C2311yescharacteristic
364D4×Dic53—21no—
365D4×Dic53C2311yescharacteristic
366D4×Dic53C2311yescharacteristic
367#13133179—21no—
368#13133179—21no—
369C4×C22⋊D53—21no—
370C4×C22⋊D53—21no—
371C4×C22⋊D53—21no—
372C4×C22⋊D53—21no—
373C4×C22⋊D53C2311yescharacteristic
374C4×C22⋊D53C2311yescharacteristic
375#13133177—21no—
376#13133177—21no—
377#13133177—21no—
378#13133177—21no—
379#13133177—21no—
380#13133176—21no—
381#13133176C2311yescharacteristic
382#13133176C2311yescharacteristic
383#13133175C2311yescharacteristic
384#13133175C2311yescharacteristic
385#13133174C2311yescharacteristic
386#13133173—21no—
387#13133173—21no—
388C2×#11719919—21no—
389C2×#11719919—21no—
390C4⋊C4×D53—21no—
391C4⋊C4×D53C2311yescharacteristic
392C2×C22⋊Dic53—21no—
393C2×#11719921—21no—
394C2×#11719921—21no—
395C22⋊C4×D53—21no—
396#13133151C2311yescharacteristic
397#13133151C2311yescharacteristic
398#13133150C2311yescharacteristic
399#13133150C2311yescharacteristic
400#13133149C2311yescharacteristic
401#13133148C2311yescharacteristic
402#13133148C2311yescharacteristic
403C4⋊#88322C2311yescharacteristic
404#13133146C2311yescharacteristic
405#13133146C2311yescharacteristic
406#13133142C2311yescharacteristic
407#13133142C2311yescharacteristic
408#13133142C2311yescharacteristic
409#13133142C2311yescharacteristic
410#13133142C2311yescharacteristic
411#13133142C2311yescharacteristic
412#13133142C2311yescharacteristic
413#13133141C2311yescharacteristic
414#13133141C2311yescharacteristic
415#13133141C2311yescharacteristic
416#13133141C2311yescharacteristic
417#13133141C2311yescharacteristic
418#13133141C2311yescharacteristic
419#13133141C2311yescharacteristic
420#13133140C2311yescharacteristic
421#13133140C2311yescharacteristic
422#13133140C2311yescharacteristic
423#13133139C2311yescharacteristic
424#13133139C2311yescharacteristic
425#13133139C2311yescharacteristic
426#13133138C2311yescharacteristic
427#13133138C2311yescharacteristic
428#13133138C2311yescharacteristic
429#13133138C2311yescharacteristic
430#13133138C2311yescharacteristic
431#13133137C2311yescharacteristic
432C22⋊#88322C2311yescharacteristic
433C22⋊#88322C2311yescharacteristic
434#13133129C2311yescharacteristic
435#13133129C2311yescharacteristic
436#13133129C2311yescharacteristic
437#13133129C2311yescharacteristic
438#13133129C2311yescharacteristic
439#13133129C2311yescharacteristic
440#13133129C2311yescharacteristic
441#13133129C2311yescharacteristic
442#13133127C2311yescharacteristic
443C4×#88322C2311yescharacteristic
444C8×Dic53C2311yescharacteristic
445C2×#41×C53C2311yescharacteristic
446C2×#41×C53C2311yescharacteristic
447C2×#41×C53C2311yescharacteristic
448C22×D4×C53C2311yescharacteristic
449AGL(1,ℤ/8)×C53—42no—
450#135×C53—42no—
451C2×Q16×C53C2311yescharacteristic
452C2×Q16×C53C2311yescharacteristic
453C2×SD16×C53C2311yescharacteristic
454C2×SD16×C53C2311yescharacteristic
455C2×SD16×C53C2311yescharacteristic
456C2×SD16×C53C2311yescharacteristic
457C2×SD16×C53C2311yescharacteristic
458C2×D8×C53C2311yescharacteristic
459C2×D8×C53C2311yescharacteristic
460C2×M16×C53C2311yescharacteristic
461C22×C8×C53C2311yescharacteristic
462C4⋊Q8×C53C2311yescharacteristic
463#124×C53C2311yescharacteristic
464#123×C53—21no—
465#123×C53—21no—
466#123×C53—21no—
467C22⋊Q8×C53C2311yescharacteristic
468C22⋊Q8×C53C2311yescharacteristic
469C22⋊Q8×C53C2311yescharacteristic
470#121×C53—21no—
471#121×C53—21no—
472#121×C53C2311yescharacteristic
473#120×C53—21no—
474C4×D4×C53C2311yescharacteristic
475C4×D4×C53C2311yescharacteristic
476C4×D4×C53C2311yescharacteristic
477C2×C4⋊C4×C53—21no—
478C2×C22⋊C4×C53—21no—
479#106×C53C2311yescharacteristic
480C4⋊C8×C53C2311yescharacteristic
481#103×C53C2311yescharacteristic
482#103×C53C2311yescharacteristic
483#103×C53C2311yescharacteristic
484#102×C53C2311yescharacteristic
485#102×C53C2311yescharacteristic
486#102×C53C2311yescharacteristic
487C22⋊C8×C53C2311yescharacteristic
488C22⋊C8×C53C2311yescharacteristic
489#97×C53C2311yescharacteristic
490C24×C53—21no—
491C23×D53—21no—
492C23×D53C2×D411yescharacteristic
493#41×C53—22no—
494#41×C53—22no—
495#41×C53—41no—
496#41×C53—41no—
497#41×C53—41no—
498#41×C53—41no—
499C2×Q8×C53C2411yescharacteristic
500C2×Q8×C53C2411yescharacteristic
501C2×Q8×C53C2411yescharacteristic
502C2×D4×C53—21no—
503C2×D4×C53—21no—
504C2×D4×C53—21no—
505C2×D4×C53—21no—
506C2×D4×C53—21no—
507C2×D4×C53—41no—
508C2×D4×C53—41no—
509C2×D4×C53C2×D411yescharacteristic
510C2×D4×C53C2411yescharacteristic
511C2×D4×C53C2411yescharacteristic
512C2×D4×C53C2411yescharacteristic
513C22×C4×C53—21no—
514C22×C4×C53—21no—
515C22×C4×C53—21no—
516C22×C4×C53—21no—
517C22×C4×C53—21no—
518C22×C4×C53C2411yescharacteristic
519C22×C4×C53C2411yescharacteristic
520C2×C22⋊D53—21no—
521C2×C22⋊D53—21no—
522C2×C22⋊D53—21no—
523C2×C22⋊D53—21no—
524C2×C22⋊D53—21no—
525C2×C22⋊D53—21no—
526C2×C22⋊D53—21no—
527C2×C22⋊D53—21no—
528C2×C22⋊D53—21no—
529C2×C22⋊D53—21no—
530C2×C22⋊D53—21no—
531C2×C22⋊D53C2×D411yescharacteristic
532C2×C22⋊D53C2×D411yescharacteristic
533C2×C22⋊D53C2×D411yescharacteristic
534C2×C22⋊D53C2×D411yescharacteristic
535C22×Dic53—21no—
536C22×Dic53—21no—
537C22×Dic53—21no—
538C22×Dic53—21no—
539C22×Dic53—21no—
540C22×Dic53—21no—
541C22×Dic53C2×D411yescharacteristic
542#11719949—41no—
543#11719949—41no—
544Q8×D53—22no—
545Q8×D53—22no—
546Q8×D53—41no—
547Q8×D53—41no—
548Q8×D53—41no—
549Q8×D53—41no—
550Q8×D53—41no—
551Q8×D53—41no—
552#11719947—22no—
553#11719947—22no—
554#11719947—22no—
555#11719947—41no—
556#11719947—41no—
557#11719947—41no—
558#11719947—44no—
559#11719947—44no—
560#11719947—44no—
561D4×D53—22no—
562D4×D53—41no—
563D4×D53—44no—
564#11719945—22no—
565#11719945—41no—
566#11719945—41no—
567#11719945—41no—
568#11719945—44no—
569#11719945—44no—
570C2×D212—21no—
571C2×D212—21no—
572C2×D212C2×D411yescharacteristic
573C2×D212C2×D411yescharacteristic
574C2×D212C2411yescharacteristic
575C2×C4×D53—21no—
576C2×C4×D53—21no—
577C2×C4×D53—21no—
578C2×C4×D53—21no—
579C2×C4×D53—21no—
580C2×C4×D53—21no—
581C2×C4×D53—21no—
582C2×C4×D53—41no—
583C2×C4×D53—41no—
584C2×C4×D53—44no—
585C2×C4×D53C2×D411yescharacteristic
586C2×C4×D53C2×D411yescharacteristic
587C2×C4×D53C2411yescharacteristic
588C2×C4×D53C2411yescharacteristic
589C2×C4×D53C2411yescharacteristic
590C2×Dic106—22no—
591C2×Dic106—21no—
592C2×Dic106—21no—
593C2×Dic106—21no—
594C2×Dic106—21no—
595C2×Dic106—21no—
596C2×Dic106—21no—
597C2×Dic106—21no—
598C2×Dic106—41no—
599C2×Dic106—44no—
600C2×Dic106C2×D411yescharacteristic
601C2×Dic106C2411yescharacteristic
602C2×Dic106C2411yescharacteristic
603C2×Dic106C2411yescharacteristic
604Q16×C53—41no—
605Q16×C53—41no—
606SD16×C53—22no—
607SD16×C53—41no—
608SD16×C53—41no—
609SD16×C53—41no—
610SD16×C53—41no—
611D8×C53—22no—
612D8×C53—22no—
613M16×C53—41no—
614C2×C8×C53—41no—
615C2×C8×C53C2411yescharacteristic
616C2×C8×C53C2411yescharacteristic
617C2×C8×C53C2411yescharacteristic
618C2×C8×C53C2411yescharacteristic
619C4⋊C4×C53—21no—
620C4⋊C4×C53—21no—
621C4⋊C4×C53—21no—
622C4⋊C4×C53—21no—
623C4⋊C4×C53—21no—
624C4⋊C4×C53C2×D411yescharacteristic
625C4⋊C4×C53C2411yescharacteristic
626C4⋊C4×C53C2411yescharacteristic
627C22⋊C4×C53—21no—
628C22⋊C4×C53—21no—
629C22⋊C4×C53—21no—
630C22⋊C4×C53—21no—
631C22⋊C4×C53—21no—
632C22⋊C4×C53—21no—
633C22⋊C4×C53—21no—
634C22⋊C4×C53—21no—
635C22⋊C4×C53C2×D411yescharacteristic
636C22⋊C4×C53C2×D411yescharacteristic
637C42×C53C2411yescharacteristic
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
654#11719925—22no—
655#11719925—41no—
656#11719925—41no—
657#11719925—41no—
658#11719924—41no—
659#11719923—22no—
660#11719923—22no—
661#11719923—22no—
662#11719923—41no—
663#11719923—41no—
664#11719922—41no—
665#11719922—41no—
666#11719921—21no—
667#11719921—21no—
668#11719921—21no—
669#11719921—21no—
670#11719921—21no—
671#11719921—21no—
672#11719921—21no—
673#11719921—21no—
674#11719921—21no—
675#11719921—21no—
676#11719921—21no—
677#11719921—21no—
678#11719921—21no—
679#11719921—21no—
680#11719921C2×D411yescharacteristic
681#11719921C2×D411yescharacteristic
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⋊Dic53C2×D411yescharacteristic
691C4⋊Dic53C2411yescharacteristic
692C4⋊Dic53C2411yescharacteristic
693C4⋊Dic53C2411yescharacteristic
694C4⋊Dic53C2411yescharacteristic
695#11719919—21no—
696#11719919—21no—
697#11719919—21no—
698#11719919—21no—
699#11719919—21no—
700#11719919—21no—
701#11719919—21no—
702#11719919—21no—
703#11719919—21no—
704#11719919—21no—
705#11719919—21no—
706#11719919—21no—
707#11719919—21no—
708#11719919—21no—
709#11719919C2×D411yescharacteristic
710#11719919C2×D411yescharacteristic
711#11719919C2×D411yescharacteristic
712#11719919C2×D411yescharacteristic
713C4×Dic53—21no—
714C4×Dic53—21no—
715C4×Dic53—21no—
716C4×Dic53—21no—
717C4×Dic53—21no—
718C4×Dic53—21no—
719C4×Dic53—21no—
720C4×Dic53—21no—
721C4×Dic53C2411yescharacteristic
722C2×#88322—41no—
723C2×#88322—41no—
724C2×#88322C2411yescharacteristic
725C2×#88322C2411yescharacteristic
726C2×#88322C2411yescharacteristic
727C2×#88322C2411yescharacteristic
728Dic212—22no—
729Dic212—41no—
730#11719913—41no—
731#11719912—41no—
732#11719912—41no—
733#11719912—41no—
734C8×D53—41no—
735C23×C53—21no—
736C23×C53—21no—
737C23×C53—21no—
738C23×C53—81no—
739C23×C53—81no—
740C23×C53—81no—
741C23×C53C22×D411yescharacteristic
742C23×C53C22×D411yescharacteristic
743C22×D53—21no—
744C22×D53—41no—
745C22×D53—41no—
746C22×D53—41no—
747C22×D53—42no—
748C22×D53—42no—
749C22×D53—81no—
750C22×D53C22×D411yescharacteristic
751C22×D53C22×D411yescharacteristic
752C22×D53C22×D411yescharacteristic
753Q8×C53—21no—
754Q8×C53—21no—
755Q8×C53—21no—
756Q8×C53—21no—
757Q8×C53—21no—
758Q8×C53—21no—
759D4×C53—21no—
760D4×C53—21no—
761D4×C53—21no—
762D4×C53—21no—
763D4×C53—21no—
764D4×C53—41no—
765D4×C53—42no—
766D4×C53—42no—
767D4×C53—81no—
768D4×C53—81no—
769D4×C53—81no—
770D4×C53H(5,𝔽2)12yes—
771C2×C4×C53—21no—
772C2×C4×C53—21no—
773C2×C4×C53—21no—
774C2×C4×C53—21no—
775C2×C4×C53—21no—
776C2×C4×C53—21no—
777C2×C4×C53—21no—
778C2×C4×C53—21no—
779C2×C4×C53—21no—
780C2×C4×C53—42no—
781C2×C4×C53—42no—
782C2×C4×C53—81no—
783C2×C4×C53—81no—
784C2×C4×C53—81no—
785C2×C4×C53C22×D411yescharacteristic
786C2×C4×C53C22×D411yescharacteristic
787C2×C4×C53C22×D411yescharacteristic
788C2×C4×C53C22×D411yescharacteristic
789C2×C4×C53C2511yescharacteristic
790C22⋊D53—24no—
791C22⋊D53—41no—
792C22⋊D53—41no—
793C22⋊D53—41no—
794C22⋊D53—41no—
795C22⋊D53—42no—
796C22⋊D53—42no—
797C22⋊D53—42no—
798C22⋊D53—81no—
799C22⋊D53—81no—
800C22⋊D53—81no—
801C22⋊D53—81no—
802C22⋊D53—81no—
803C22⋊D53—81no—
804C22⋊D53—81no—
805C2×Dic53—24no—
806C2×Dic53—21no—
807C2×Dic53—21no—
808C2×Dic53—21no—
809C2×Dic53—21no—
810C2×Dic53—21no—
811C2×Dic53—21no—
812C2×Dic53—21no—
813C2×Dic53—41no—
814C2×Dic53—42no—
815C2×Dic53—42no—
816C2×Dic53—81no—
817C2×Dic53—81no—
818C2×Dic53—81no—
819C2×Dic53C22×D411yescharacteristic
820C2×Dic53C22×D411yescharacteristic
821C2×Dic53C22×D411yescharacteristic
822C2×Dic53C22×D411yescharacteristic
823C2×Dic53C22×D411yescharacteristic
824D212—21no—
825D212—21no—
826D212—41no—
827D212—41no—
828D212—42no—
829D212—81no—
830C4×D53—21no—
831C4×D53—21no—
832C4×D53—21no—
833C4×D53—21no—
834C4×D53—21no—
835C4×D53—21no—
836C4×D53—41no—
837C4×D53—41no—
838C4×D53—42no—
839C4×D53—42no—
840C4×D53—42no—
841C4×D53—42no—
842C4×D53—42no—
843C4×D53—81no—
844C4×D53—81no—
845Dic106—21no—
846Dic106—21no—
847Dic106—21no—
848Dic106—21no—
849Dic106—21no—
850Dic106—41no—
851Dic106—42no—
852Dic106—42no—
853Dic106—42no—
854Dic106—42no—
855Dic106—81no—
856Dic106—81no—
857Dic106—81no—
858Dic106H(5,𝔽2)12yes—
859C8×C53—21no—
860C8×C53—21no—
861C8×C53—21no—
862C8×C53—21no—
863#88322—21no—
864#88322—21no—
865#88322—21no—
866#88322—21no—
867#61627—531nomaximal, Sylow
868C22×C53—21no—
869C22×C53—21no—
870C22×C53—21no—
871C22×C53—21no—
872C22×C53—22no—
873C22×C53—21no—
874C22×C53—21no—
875C22×C53—41no—
876C22×C53—41no—
877C22×C53—41no—
878C22×C53—41no—
879C22×C53—41no—
880C22×C53—41no—
881C22×C53—41no—
882C22×C53—41no—
883C22×C53—162no—
884C22×C53C23×D411yescharacteristic
885C2×D53—21no—
886C2×D53—21no—
887C2×D53—21no—
888C2×D53—21no—
889C2×D53—21no—
890C2×D53—21no—
891C2×D53—21no—
892C2×D53—21no—
893C2×D53—21no—
894C2×D53—41no—
895C2×D53—41no—
896C2×D53—41no—
897C2×D53—82no—
898C2×D53—84no—
899C4×C53—21no—
900C4×C53—21no—
901C4×C53—21no—
902C4×C53—21no—
903C4×C53—41no—
904C4×C53—41no—
905C4×C53—41no—
906C4×C53—41no—
907C4×C53—41no—
908C4×C53C2×H(5,𝔽2)11yescharacteristic
909C4×C53C2×H(5,𝔽2)11yescharacteristic
910Dic53—21no—
911Dic53—21no—
912Dic53—22no—
913Dic53—21no—
914Dic53—21no—
915Dic53—21no—
916Dic53—41no—
917Dic53—41no—
918Dic53—41no—
919Dic53—41no—
920Dic53—41no—
921Dic53—41no—
922#3540—531no—
923#3489—531no—
924#3329—531no—
925#3328—531no—
926#3321—531no—
927#3319—531no—
928#3313—531no—
929#3311—531no—
930#3303—531no—
931#3302—531no—
932#3285—531no—
933#3282—531no—
934#3275—531no—
935#3273—531no—
936#3270—531no—
937#3269—531no—
938#3267D5311yescharacteristic, complemented
939#3266—531no—
940#3225—531no—
941#3225—531no—
942#3201—531no—
943#3198—531no—
944#3196—531no—
945#3190—531no—
946#3125—531no—
947#3124—531no—
948#3011—531no—
949#3010—531no—
950#3005—531no—
951#3002—531no—
952#2976—531no—
953C2×C53—41no—
954C2×C53—42no—
955C2×C53—41no—
956C2×C53—81no—
957C2×C53—81no—
958C2×C53#348411yescharacteristic
959C2×C53#358411yescharacteristic
960C2×C53#358611yescharacteristic
961D53—41no—
962D53—41no—
963D53—41no—
964D53—81no—
965C2×2−1+4—531no—
966C22×#41—531no—
967C2×#137—531no—
968C2×#137—531no—
969C2×AGL(1,ℤ/8)—531no—
970C2×AGL(1,ℤ/8)C2×D5311yescharacteristic, complemented
971C2×#135—531no—
972C2×#135C2×D5311yescharacteristic
973C22×Q16—531no—
974C22×SD16—531no—
975H(3,𝔽4)—1061no—
976#560—1061no—
977#559—1061no—
978#556—531no—
979#556—531no—
980#555—531no—
981#555—531no—
982#551—1061no—
983D4×Q8—531no—
984D4×Q8—531no—
985#548—531no—
986#548—531no—
987#548—531no—
988#548—531no—
989#547—531no—
990#547—1061no—
991#547—1061no—
992#547C2×D5311yescharacteristic
993#546—531no—
994#546—531no—
995#546—531no—
996#546—1061no—
997#546—1061no—
998#546C2×D5311yescharacteristic, complemented
999#542—531no—
1000#542—531no—
1001#542—1061no—
1002#542—1061no—
1003#538—1061no—
1004#538—1061no—
1005#537—531no—
1006#537—1061no—
1007#536—531no—
1008#536—531no—
1009#536—1061no—
1010#535—531no—
1011#525—531no—
1012#525—531no—
1013#525—531no—
1014#525—1061no—
1015C2×C22⋊Q8—531no—
1016C2×C22⋊Q8—1061no—
1017#520—531no—
1018#497—531no—
1019#497C2×D5311yescharacteristic, complemented
1020#495—531no—
1021#495—531no—
1022#489—531no—
1023#489—531no—
1024#487—531no—
1025#487—531no—
1026#485—531no—
1027#485—531no—
1028#485—531no—
1029#485—531no—
1030#485—531no—
1031#485—531no—
1032#484—531no—
1033#483—531no—
1034#482—531no—
1035#482—531no—
1036#481—531no—
1037#480—531no—
1038#477—531no—
1039#476—531no—
1040#475—531no—
1041#474—531no—
1042#470—531no—
1043#470—531no—
1044#470C2×D5311yescharacteristic, complemented
1045#469—531no—
1046#468—531no—
1047#468—531no—
1048#468—531no—
1049#468—531no—
1050#467—531no—
1051#467—531no—
1052#467—531no—
1053#466—531no—
1054#465—531no—
1055#465—531no—
1056#465—531no—
1057#465C2×D5311yescharacteristic, complemented
1058#464—531no—
1059#464—531no—
1060#464—531no—
1061#464—531no—
1062#463—531no—
1063#463—531no—
1064#463—531no—
1065#463C2×D5311yescharacteristic, complemented
1066#462—531no—
1067#462—531no—
1068#461—531no—
1069#461C2×D5311yescharacteristic, complemented
1070#452—531no—
1071#452—531no—
1072#452—531no—
1073#452—531no—
1074#452—531no—
1075#452—531no—
1076#452—531no—
1077#452—531no—
1078#452—531no—
1079#452—531no—
1080#452C2×D5311yescharacteristic, complemented
1081#452C2×D5311yescharacteristic, complemented
1082#451—531no—
1083#451—531no—
1084#451—531no—
1085#451—531no—
1086#451—531no—
1087#451—531no—
1088#450—531no—
1089#450C2×D5311yescharacteristic, complemented
1090#449—531no—
1091#449—531no—
1092#449—531no—
1093#449—531no—
1094#449—531no—
1095#449—531no—
1096#449—531no—
1097#449C2×D5311yescharacteristic
1098#448—531no—
1099#448—531no—
1100#448—531no—
1101#448—531no—
1102#448—531no—
1103#448—531no—
1104#447—531no—
1105#447—531no—
1106#442C2×D5311yescharacteristic, complemented
1107#441—531no—
1108#440—531no—
1109#440—531no—
1110C4×Q16—531no—
1111C4×SD16—531no—
1112C4×SD16—531no—
1113C4×D8—531no—
1114#436—531no—
1115#436—531no—
1116#435—531no—
1117#435—531no—
1118#435—531no—
1119#435C2×D5311yescharacteristic, complemented
1120C8×D4—531no—
1121C8×D4—531no—
1122#433—531no—
1123#433—531no—
1124#419—531no—
1125#419—531no—
1126#419—531no—
1127#418—531no—
1128#416—531no—
1129#416—531no—
1130#416—531no—
1131#416—531no—
1132#408—531no—
1133#408—531no—
1134#407—531no—
1135C2×C22⋊C8—531no—
1136C53#6162711yescharacteristic, complemented, Sylow
11372−1+4—2122no—
11382−1+4—2122no—
1139C2×#41—531no—
1140C2×#41—531no—
1141C2×#41—531no—
1142C2×#41—531no—
1143C2×#41—531no—
1144C2×#41—531no—
1145C2×#41—1061no—
1146C2×#41—1061no—
1147C2×#41—1061no—
1148C2×#41—1061no—
1149C2×#41—1061no—
1150C2×#41—2122no—
1151C2×#41—2122no—
1152C2×#41C22×D5311yescharacteristic
1153C2×#41C22×D5311yescharacteristic
1154C2×#41C22×D5311yescharacteristic
1155C22×Q8—531no—
1156C22×Q8—531no—
1157C22×Q8—531no—
1158C22×Q8—531no—
1159C22×Q8—531no—
1160C22×Q8—1061no—
1161C22×D4—531no—
1162C22×D4—1061no—
1163C22×D4C22×D5311yescharacteristic
1164C23×C4—531no—
1165C23×C4—1061no—
1166#137—2122no—
1167#137—2122no—
1168AGL(1,ℤ/8)—42no—
1169AGL(1,ℤ/8)—2122no—
1170#135—42no—
1171#135—2122no—
1172C2×Q16—531no—
1173C2×Q16—531no—
1174C2×Q16—531no—
1175C2×Q16—531no—
1176C2×Q16—531no—
1177C2×Q16—531no—
1178C2×Q16—2122no—
1179C2×Q16C22×D5311yescharacteristic
1180C2×Q16C22×D5311yescharacteristic
1181C2×SD16—531no—
1182C2×SD16—531no—
1183C2×SD16—531no—
1184C2×SD16—531no—
1185C2×SD16—531no—
1186C2×SD16—531no—
1187C2×SD16—531no—
1188C2×SD16—2122no—
1189C2×SD16C22×D5311yescharacteristic
1190C2×SD16C22×D5311yescharacteristic
1191C2×SD16C22×D5311yescharacteristic
1192C2×SD16C22×D5311yescharacteristic
1193C2×SD16C22×D5311yescharacteristic
1194C2×D8—531no—
1195C2×D8—531no—
1196C2×D8C22×D5311yescharacteristic
1197C2×D8C22×D5311yescharacteristic
1198C2×M16—531no—
1199C2×M16—531no—
1200C2×M16—531no—
1201C2×M16C22×D5311yescharacteristic
1202C22×C8—531no—
1203C22×C8—531no—
1204C22×C8—531no—
1205C22×C8C22×D5311yescharacteristic
1206C4⋊Q8—531no—
1207C4⋊Q8—531no—
1208C4⋊Q8—531no—
1209C4⋊Q8—1061no—
1210C4⋊Q8—1061no—
1211C4⋊Q8—1061no—
1212C4⋊Q8C22×D5311yescharacteristic
1213#127—1061no—
1214#126—1061no—
1215#126—1061no—
1216#126—1061no—
1217#126—1061no—
1218#126—1061no—
1219#126—1061no—
1220#124—531no—
1221#124—531no—
1222#124—531no—
1223#124—1061no—
1224#124—1061no—
1225#124—1061no—
1226#124—1061no—
1227#124—1061no—
1228#124—1061no—
1229#124—1061no—
1230#124—1061no—
1231#124—1061no—
1232#124—1061no—
1233#124—1061no—
1234#124—1061no—
1235#124—1061no—
1236#124—1061no—
1237#124C22×D5311yescharacteristic
1238#123—21no—
1239#123—21no—
1240#123—21no—
1241#123—531no—
1242#123—531no—
1243#123—1061no—
1244#123—1061no—
1245#123—1061no—
1246#123—1061no—
1247#123—1061no—
1248#123—1061no—
1249#123—1061no—
1250#123—1061no—
1251#123—1061no—
1252#123—1061no—
1253#123—1061no—
1254#123—1061no—
1255#123—1061no—
1256C22⋊Q8—531no—
1257C22⋊Q8—531no—
1258C22⋊Q8—531no—
1259C22⋊Q8—531no—
1260C22⋊Q8—531no—
1261C22⋊Q8—531no—
1262C22⋊Q8—531no—
1263C22⋊Q8—531no—
1264C22⋊Q8—531no—
1265C22⋊Q8—531no—
1266C22⋊Q8—531no—
1267C22⋊Q8—1061no—
1268C22⋊Q8—1061no—
1269C22⋊Q8—1061no—
1270C22⋊Q8—1061no—
1271C22⋊Q8—1061no—
1272C22⋊Q8—1061no—
1273C22⋊Q8—1061no—
1274C22⋊Q8—1061no—
1275C22⋊Q8—1061no—
1276C22⋊Q8—1061no—
1277C22⋊Q8—1061no—
1278C22⋊Q8—1061no—
1279C22⋊Q8—1061no—
1280C22⋊Q8—1061no—
1281C22⋊Q8—1061no—
1282C22⋊Q8C22×D5311yescharacteristic
1283C22⋊Q8C22×D5311yescharacteristic
1284C22⋊Q8C22×D5311yescharacteristic
1285#121—21no—
1286#121—21no—
1287#121—531no—
1288#121—531no—
1289#121—531no—
1290#121—531no—
1291#121—531no—
1292#121—531no—
1293#121—531no—
1294#121—531no—
1295#121—531no—
1296#121—1061no—
1297#121—1061no—
1298#121—1061no—
1299#121—1061no—
1300#121—1061no—
1301#121—1061no—
1302#121—1061no—
1303#121—1061no—
1304#121—1061no—
1305#121—1061no—
1306#121—1061no—
1307#121—1061no—
1308#121—1061no—
1309#121C22×D5311yescharacteristic
1310#120—21no—
1311#120—531no—
1312#120—531no—
1313#120—1061no—
1314#120—1061no—
1315#120—1061no—
1316#120—1061no—
1317#120—1061no—
1318#120—1061no—
1319#120—1061no—
1320C4×Q8—531no—
1321C4×Q8—531no—
1322C4×Q8—531no—
1323C4×Q8—531no—
1324C4×Q8—1061no—
1325C4×Q8—1061no—
1326C4×D4—531no—
1327C4×D4—531no—
1328C4×D4—531no—
1329C4×D4—531no—
1330C4×D4—531no—
1331C4×D4—1061no—
1332C4×D4—1061no—
1333C4×D4—1061no—
1334C4×D4—1061no—
1335C4×D4—1061no—
1336C4×D4—1061no—
1337C4×D4—1061no—
1338C4×D4—1061no—
1339C4×D4—1061no—
1340C4×D4—1061no—
1341C4×D4—1061no—
1342C4×D4—1061no—
1343C4×D4C22×D5311yescharacteristic
1344C4×D4C22×D5311yescharacteristic
1345C4×D4C22×D5311yescharacteristic
1346#117—531no—
1347#117—531no—
1348#117—531no—
1349#117—531no—
1350#117—531no—
1351#117—1061no—
1352#117—1061no—
1353#117—1061no—
1354C2×C4⋊C4—21no—
1355C2×C4⋊C4—531no—
1356C2×C4⋊C4—1061no—
1357C2×C4⋊C4—1061no—
1358C2×C4⋊C4—1061no—
1359C2×C22⋊C4—21no—
1360C2×C22⋊C4—1061no—
1361C2×C22⋊C4—1061no—
1362C2×C22⋊C4—1061no—
1363C2×C22⋊C4—1061no—
1364#107—531no—
1365#107—531no—
1366#107—531no—
1367#107—531no—
1368#106—531no—
1369#106—531no—
1370#106—531no—
1371#106C22×D5311yescharacteristic
1372C4⋊C8—531no—
1373C4⋊C8—531no—
1374C4⋊C8—531no—
1375C4⋊C8C22×D5311yescharacteristic
1376#103—531no—
1377#103—531no—
1378#103—531no—
1379#103—531no—
1380#103—531no—
1381#103—531no—
1382#103—531no—
1383#103—531no—
1384#103—531no—
1385#103—531no—
1386#103—531no—
1387#103—531no—
1388#103—531no—
1389#103—531no—
1390#103—531no—
1391#103—531no—
1392#103—531no—
1393#103C22×D5311yescharacteristic
1394#103C22×D5311yescharacteristic
1395#103C22×D5311yescharacteristic
1396#102—531no—
1397#102—531no—
1398#102—531no—
1399#102—531no—
1400#102—531no—
1401#102—531no—
1402#102—531no—
1403#102—531no—
1404#102—531no—
1405#102C22×D5311yescharacteristic
1406#102C22×D5311yescharacteristic
1407#102C22×D5311yescharacteristic
1408C22⋊C8—531no—
1409C22⋊C8—531no—
1410C22⋊C8—531no—
1411C22⋊C8—531no—
1412C22⋊C8—531no—
1413C22⋊C8—531no—
1414C22⋊C8—531no—
1415C22⋊C8—531no—
1416C22⋊C8—531no—
1417C22⋊C8—531no—
1418C22⋊C8C22×D5311yescharacteristic
1419C22⋊C8C22×D5311yescharacteristic
1420#97—531no—
1421#97C22×D5311yescharacteristic
1422C4×C8—531no—
1423C4×C8—531no—
1424C24—21no—
1425C24—531no—
1426C24—1061no—
1427#41—22no—
1428#41—22no—
1429#41—41no—
1430#41—41no—
1431#41—41no—
1432#41—41no—
1433#41—1062no—
1434#41—1062no—
1435#41—1062no—
1436#41—1062no—
1437#41—2121no—
1438#41—2121no—
1439#41—2121no—
1440#41—2124no—
1441#41—2124no—
1442#41—2121no—
1443#41—2121no—
1444#41—2121no—
1445#41—2124no—
1446#41—2124no—
1447#41—2121no—
1448#41—2121no—
1449#41—2124no—
1450C2×Q8—531no—
1451C2×Q8—531no—
1452C2×Q8—531no—
1453C2×Q8—531no—
1454C2×Q8—1061no—
1455C2×Q8—1061no—
1456C2×Q8—1061no—
1457C2×Q8—1061no—
1458C2×Q8—1061no—
1459C2×Q8—1062no—
1460C2×Q8—1061no—
1461C2×Q8—1061no—
1462C2×Q8—1062no—
1463C2×Q8—1062no—
1464C2×Q8—2121no—
1465C2×Q8—2124no—
1466C2×Q8—2121no—
1467C2×Q8—2121no—
1468C2×Q8—2121no—
1469C2×Q8—2121no—
1470C2×Q8—2121no—
1471C2×Q8—2121no—
1472C2×Q8C23×D5311yescharacteristic
1473C2×Q8C23×D5311yescharacteristic
1474C2×Q8C23×D5311yescharacteristic
1475C2×D4—21no—
1476C2×D4—21no—
1477C2×D4—21no—
1478C2×D4—21no—
1479C2×D4—21no—
1480C2×D4—41no—
1481C2×D4—41no—
1482C2×D4—531no—
1483C2×D4—531no—
1484C2×D4—531no—
1485C2×D4—531no—
1486C2×D4—531no—
1487C2×D4—531no—
1488C2×D4—531no—
1489C2×D4—1061no—
1490C2×D4—1061no—
1491C2×D4—1061no—
1492C2×D4—1061no—
1493C2×D4—1062no—
1494C2×D4—1061no—
1495C2×D4—1061no—
1496C2×D4—1061no—
1497C2×D4—1061no—
1498C2×D4—1061no—
1499C2×D4—1061no—
1500C2×D4—1061no—
1501C2×D4—1061no—
1502C2×D4—1061no—
1503C2×D4—2121no—
1504C2×D4—2124no—
1505C2×D4D4×D5311yescharacteristic
1506C2×D4C23×D5311yescharacteristic
1507C2×D4C23×D5311yescharacteristic
1508C2×D4C23×D5311yescharacteristic
1509C22×C4—21no—
1510C22×C4—21no—
1511C22×C4—21no—
1512C22×C4—21no—
1513C22×C4—21no—
1514C22×C4—531no—
1515C22×C4—531no—
1516C22×C4—531no—
1517C22×C4—531no—
1518C22×C4—531no—
1519C22×C4—531no—
1520C22×C4—1061no—
1521C22×C4—1061no—
1522C22×C4—1061no—
1523C22×C4—1061no—
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—2121no—
1534C22×C4—2121no—
1535C22×C4—2124no—
1536C22×C4C23×D5311yescharacteristic
1537C22×C4C23×D5311yescharacteristic
1538Q16—41no—
1539Q16—41no—
1540Q16—1062no—
1541Q16—1062no—
1542Q16—2121no—
1543Q16—2121no—
1544Q16—2121no—
1545Q16—2121no—
1546SD16—22no—
1547SD16—41no—
1548SD16—41no—
1549SD16—41no—
1550SD16—41no—
1551SD16—1062no—
1552SD16—1062no—
1553SD16—1062no—
1554SD16—2121no—
1555SD16—2121no—
1556SD16—2121no—
1557SD16—2121no—
1558D8—22no—
1559D8—22no—
1560D8—2121no—
1561D8—2121no—
1562M16—41no—
1563M16—2121no—
1564M16—2121no—
1565M16—2121no—
1566C2×C8—41no—
1567C2×C8—531no—
1568C2×C8—531no—
1569C2×C8—531no—
1570C2×C8—531no—
1571C2×C8—2121no—
1572C2×C8—2121no—
1573C2×C8—2121no—
1574C2×C8C23×D5311yescharacteristic
1575C2×C8C23×D5311yescharacteristic
1576C2×C8C23×D5311yescharacteristic
1577C2×C8C23×D5311yescharacteristic
1578C4⋊C4—21no—
1579C4⋊C4—21no—
1580C4⋊C4—21no—
1581C4⋊C4—21no—
1582C4⋊C4—21no—
1583C4⋊C4—531no—
1584C4⋊C4—531no—
1585C4⋊C4—531no—
1586C4⋊C4—531no—
1587C4⋊C4—531no—
1588C4⋊C4—531no—
1589C4⋊C4—531no—
1590C4⋊C4—531no—
1591C4⋊C4—531no—
1592C4⋊C4—1061no—
1593C4⋊C4—1061no—
1594C4⋊C4—1061no—
1595C4⋊C4—1061no—
1596C4⋊C4—1061no—
1597C4⋊C4—1061no—
1598C4⋊C4—1061no—
1599C4⋊C4—1061no—
1600C4⋊C4—1061no—
1601C4⋊C4—1061no—
1602C4⋊C4—1061no—
1603C4⋊C4—1061no—
1604C4⋊C4—1061no—
1605C4⋊C4—1061no—
1606C4⋊C4—1061no—
1607C4⋊C4—1061no—
1608C4⋊C4—1061no—
1609C4⋊C4—1061no—
1610C4⋊C4D4×D5311yescharacteristic
1611C4⋊C4C23×D5311yescharacteristic
1612C4⋊C4C23×D5311yescharacteristic
1613C22⋊C4—21no—
1614C22⋊C4—21no—
1615C22⋊C4—21no—
1616C22⋊C4—21no—
1617C22⋊C4—21no—
1618C22⋊C4—21no—
1619C22⋊C4—21no—
1620C22⋊C4—21no—
1621C22⋊C4—531no—
1622C22⋊C4—531no—
1623C22⋊C4—531no—
1624C22⋊C4—531no—
1625C22⋊C4—531no—
1626C22⋊C4—531no—
1627C22⋊C4—531no—
1628C22⋊C4—531no—
1629C22⋊C4—1061no—
1630C22⋊C4—1061no—
1631C22⋊C4—1061no—
1632C22⋊C4—1061no—
1633C22⋊C4—1061no—
1634C22⋊C4—1061no—
1635C22⋊C4—1061no—
1636C22⋊C4—1061no—
1637C22⋊C4—1061no—
1638C22⋊C4—1061no—
1639C22⋊C4—1061no—
1640C22⋊C4—1061no—
1641C22⋊C4—1061no—
1642C22⋊C4—1061no—
1643C22⋊C4—1061no—
1644C22⋊C4—1061no—
1645C22⋊C4—1061no—
1646C22⋊C4—1061no—
1647C22⋊C4—1061no—
1648C22⋊C4—1061no—
1649C22⋊C4—1061no—
1650C22⋊C4—1061no—
1651C22⋊C4—1061no—
1652C22⋊C4—1061no—
1653C22⋊C4—1061no—
1654C22⋊C4—1061no—
1655C22⋊C4—1061no—
1656C22⋊C4—1061no—
1657C22⋊C4D4×D5311yescharacteristic
1658C22⋊C4D4×D5311yescharacteristic
1659C42—531no—
1660C42—1061no—
1661C42—1061no—
1662C42—1061no—
1663C42—1061no—
1664C42—1061no—
1665C42—1061no—
1666C42—1061no—
1667C42—1061no—
1668C42C23×D5311yescharacteristic
1669C23—21no—
1670C23—21no—
1671C23—21no—
1672C23—81no—
1673C23—81no—
1674C23—81no—
1675C23—531no—
1676C23—531no—
1677C23—531no—
1678C23—1061no—
1679C23—4241no—
1680C23—2121no—
1681C23—2121no—
1682C23—2121no—
1683C23—2122no—
1684C23—2122no—
1685C23C2×D4×D5311yescharacteristic
1686C23C2×D4×D5311yescharacteristic
1687Q8—21no—
1688Q8—21no—
1689Q8—21no—
1690Q8—21no—
1691Q8—21no—
1692Q8—21no—
1693Q8—532no—
1694Q8—1061no—
1695Q8—1061no—
1696Q8—1061no—
1697Q8—1061no—
1698Q8—1061no—
1699Q8—4241no—
1700Q8—4241no—
1701Q8—4241no—
1702Q8—2121no—
1703Q8—2122no—
1704Q8—2122no—
1705Q8—2122no—
1706Q8—2122no—
1707D4—21no—
1708D4—21no—
1709D4—21no—
1710D4—21no—
1711D4—21no—
1712D4—41no—
1713D4—42no—
1714D4—42no—
1715D4—81no—
1716D4—81no—
1717D4—81no—
1718D4—1064no—
1719D4—1061no—
1720D4—1061no—
1721D4—4241no—
1722D4—4241no—
1723D4—4241no—
1724D4—4241no—
1725D4—4241no—
1726D4—4241no—
1727D4—4241no—
1728D4—4241no—
1729D4—2121no—
1730D4—2121no—
1731D4—2122no—
1732D4—2121no—
1733D4—2121no—
1734D4—2121no—
1735D4—2121no—
1736D4—2122no—
1737D4—2122no—
1738D4—2122no—
1739D4#1313326212yes—
1740C2×C4—21no—
1741C2×C4—21no—
1742C2×C4—21no—
1743C2×C4—21no—
1744C2×C4—21no—
1745C2×C4—21no—
1746C2×C4—21no—
1747C2×C4—21no—
1748C2×C4—21no—
1749C2×C4—42no—
1750C2×C4—42no—
1751C2×C4—81no—
1752C2×C4—81no—
1753C2×C4—81no—
1754C2×C4—531no—
1755C2×C4—531no—
1756C2×C4—531no—
1757C2×C4—531no—
1758C2×C4—531no—
1759C2×C4—1064no—
1760C2×C4—1061no—
1761C2×C4—1061no—
1762C2×C4—1061no—
1763C2×C4—1061no—
1764C2×C4—1061no—
1765C2×C4—1061no—
1766C2×C4—1061no—
1767C2×C4—1061no—
1768C2×C4—1061no—
1769C2×C4—1061no—
1770C2×C4—1061no—
1771C2×C4—1061no—
1772C2×C4—1061no—
1773C2×C4—4241no—
1774C2×C4—4241no—
1775C2×C4—4241no—
1776C2×C4—4241no—
1777C2×C4—4241no—
1778C2×C4—2121no—
1779C2×C4—2121no—
1780C2×C4—2122no—
1781C2×C4—2122no—
1782C2×C4—2122no—
1783C2×C4—2122no—
1784C2×C4—2122no—
1785C2×C4—2121no—
1786C2×C4—2122no—
1787C2×C4—2122no—
1788C2×C4C2×D4×D5311yescharacteristic
1789C2×C4C2×D4×D5311yescharacteristic
1790C2×C4C2×D4×D5311yescharacteristic
1791C2×C4C2×D4×D5311yescharacteristic
1792C2×C4C24×D5311yescharacteristic
1793C8—21no—
1794C8—21no—
1795C8—21no—
1796C8—21no—
1797C8—1061no—
1798C8—1061no—
1799C8—1061no—
1800C8—1061no—
1801C22—21no—
1802C22—21no—
1803C22—22no—
1804C22—21no—
1805C22—21no—
1806C22—21no—
1807C22—21no—
1808C22—41no—
1809C22—41no—
1810C22—41no—
1811C22—41no—
1812C22—41no—
1813C22—41no—
1814C22—41no—
1815C22—41no—
1816C22—162no—
1817C22—1061no—
1818C22—1061no—
1819C22—1061no—
1820C22—1061no—
1821C22—1061no—
1822C22—1061no—
1823C22—1061no—
1824C22—1061no—
1825C22—1061no—
1826C22—4244no—
1827C22—4242no—
1828C22—2121no—
1829C22—2121no—
1830C22—2121no—
1831C22C22×D4×D5311yescharacteristic
1832C4—21no—
1833C4—21no—
1834C4—21no—
1835C4—21no—
1836C4—41no—
1837C4—41no—
1838C4—41no—
1839C4—41no—
1840C4—41no—
1841C4—1061no—
1842C4—1061no—
1843C4—1061no—
1844C4—1062no—
1845C4—1061no—
1846C4—1061no—
1847C4—2121no—
1848C4—2121no—
1849C4—2121no—
1850C4—2121no—
1851C4—2121no—
1852C4—2121no—
1853C4H(5,𝔽2)×D5311yescharacteristic
1854C4C2×#1313326211yescharacteristic
1855C2—41no—
1856C2—41no—
1857C2—42no—
1858C2—81no—
1859C2—81no—
1860C2—4241no—
1861C2—2121no—
1862C2—2121no—
1863C2—2121no—
1864C2#2028834311yescharacteristic
1865C2#2028948811yescharacteristic
1866C2#2028949711yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3267C2
socleC22×C53C23×D4
hypercenter#3267D53
hypocenterC53#61627
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3267

Complements

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

NH ≅ G/Ntype
1. #20288979C2semidirect
2. #20288389C2semidirect
3. #20287012C2semidirect
4. #20286993C2semidirect
5. #20286907C2semidirect
6. #20286876C2semidirect
7. #20286783C2semidirect
8. #20286755C2semidirect
9. #20286636C2semidirect
10. #20286632C2semidirect
11. #20286454C2semidirect
12. #20286418C2semidirect
13. #20286352C2semidirect
14. #20286320C2semidirect
15. #20286284C2semidirect
16. #20286270C2semidirect
17. #20286229C2semidirect
18. #20285823C2semidirect
19. #20285819C2semidirect
20. #20285598C2semidirect
21. #20285571C2semidirect
22. #20285543C2semidirect
23. #20285491C2semidirect
24. #20284996C2semidirect
25. #20284974C2semidirect
26. #20284007C2semidirect
27. #20284000C2semidirect
28. #20283953C2semidirect
29. #20283929C2semidirect
30. #20283764C2semidirect
31. C53×#3267C2semidirect
33. C2×#41×D53C22semidirect
35. C2×#13133246C22semidirect
38. C2×Q16×D53C22semidirect
39. C22×#11719923C22semidirect
44. #16811343C22semidirect
46. #16811337C22semidirect
48. #16811288C22semidirect
50. #16811283C22semidirect
53. #16811280C22semidirect
55. #16811272C22semidirect
57. #16811268C22semidirect
62. #16811242C22semidirect
65. #16811238C22semidirect
70. #16811198C22semidirect
71. #16811196C22semidirect
73. #16811190C22semidirect
79. C22⋊Q8×D53C22semidirect
80. #16811102C22semidirect
81. #16811014C22semidirect
82. #16811005C22semidirect
83. #16811004C22semidirect
84. #16810984C22semidirect
85. #16810983C22semidirect
86. #16810973C22semidirect
87. #16810972C22semidirect
88. #16810967C22semidirect
89. #16810965C22semidirect
90. #16810963C22semidirect
91. #16810963C22semidirect
92. #16810961C22semidirect
93. #16810961C22semidirect
94. #16810957C22semidirect
95. #16810955C22semidirect
96. #16810949C22semidirect
97. #16810948C22semidirect
98. #16810940C22semidirect
99. #16810935C22semidirect
100. #16810919C22semidirect
101. #16810911C22semidirect
102. #16810907C22semidirect
103. #16810903C22semidirect
104. #16810880C22semidirect
105. #16810878C22semidirect
106. #16810875C22semidirect
107. #16810869C22semidirect
110. #16810866C22semidirect
111. #16810864C22semidirect
112. #16810862C22semidirect
113. #16810862C22semidirect
114. #16810858C22semidirect
115. #16810854C22semidirect
116. #16810850C22semidirect
117. #16810849C22semidirect
118. #16810847C22semidirect
119. #16810846C22semidirect
120. #16810844C22semidirect
121. #16810842C22semidirect
122. #16810840C22semidirect
123. #16810838C22semidirect
124. #16810836C22semidirect
125. #16810831C22semidirect
126. #16810830C22semidirect
127. #16810826C22semidirect
128. #16810788C22semidirect
129. #16810787C22semidirect
131. #16810786C22semidirect
132. #16810785C22semidirect
133. #16810785C22semidirect
134. #16810785C22semidirect
135. #16810784C22semidirect
137. #16810782C22semidirect
138. #16810781C22semidirect
139. #16810780C22semidirect
140. #16810778C22semidirect
141. #16810777C22semidirect
142. #16810777C22semidirect
143. #16810777C22semidirect
144. #16810772C22semidirect
150. #16810765C22semidirect
151. #16810765C22semidirect
152. #16810763C22semidirect
154. #16810760C22semidirect
155. #16810760C22semidirect
156. #16810760C22semidirect
157. #16810760C22semidirect
158. #16810757C22semidirect
160. #16810731C22semidirect
161. #16810724C22semidirect
162. #16810720C22semidirect
163. #16810715C22semidirect
164. C4×#11719923C22semidirect
165. C4×#11719923C22semidirect
166. D8×Dic53C22semidirect
167. #16810700C22semidirect
169. #16810696C22semidirect
170. #16810694C22semidirect
172. D4×#88322C22semidirect
173. #16810686C22semidirect
174. #16810685C22semidirect
175. #16810683C22semidirect
176. #16810633C22semidirect
177. #16810630C22semidirect
178. #16810630C22semidirect
179. #16810626C22semidirect
180. #16810620C22semidirect
181. #16810619C22semidirect
182. #16810619C22semidirect
183. #16810616C22semidirect
184. #16810591C22semidirect
185. #16810588C22semidirect
186. #16810585C22semidirect
187. C2×#13133129C22semidirect
188. C2×AGL(1,ℤ/8)×C53C22semidirect
191. C53×#546C22semidirect
192. C53×#497C22semidirect
193. C53×#470C22semidirect
194. C53×#465C22semidirect
195. C53×#463C22semidirect
196. C53×#461C22semidirect
197. C53×#452C22semidirect
198. C53×#452C22semidirect
199. C53×#450C22semidirect
201. C53×#442C22semidirect
202. C53×#435C22semidirect
938. #3267D53semidirect
970. C2×AGL(1,ℤ/8)C2×D53semidirect
998. #546C2×D53semidirect
1019. #497C2×D53semidirect
1044. #470C2×D53semidirect
1057. #465C2×D53semidirect
1065. #463C2×D53semidirect
1069. #461C2×D53semidirect
1080. #452C2×D53semidirect
1081. #452C2×D53semidirect
1089. #450C2×D53semidirect
1106. #442C2×D53semidirect
1119. #435C2×D53semidirect
1136. C53#61627semidirect

Maximal subgroups

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

subgroupindex
#202889792
#202883892
#202870122
#202869932
#202869072
#202868762
#202867832
#202867552
#202866362
#202866322
#202864542
#202864182
#202863522
#202863202
#202862842
#202862702
#202862292
#202858232
#202858192
#202855982
#202855712
#202855432
#202854912
#202849962
#202849742
#202840072
#202840002
#202839532
#202839292
#202837642
C53×#32672
#6162753