Finite Group Databasebeta

← #28267126

Subgroups — #28267126

Order 13568.

1800 conjugacy classes of subgroups.

The subgroup lattice has 1698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288784C211yesmaximal, characteristic, complemented
2#20288768C211yesmaximal, characteristic, complemented
3#20287791C211yesmaximal, characteristic, complemented
4#20287674C211yesmaximal, characteristic, complemented
5#20287368C211yesmaximal, characteristic, complemented
6#20287359C211yesmaximal, characteristic, complemented
7#20287285C211yesmaximal, characteristic, complemented
8#20287266C211yesmaximal, characteristic, complemented
9#20287262C211yesmaximal, characteristic, complemented
10#20286632C211yesmaximal, characteristic, complemented
11#20286625C211yesmaximal, characteristic, complemented
12#20286565C211yesmaximal, characteristic, complemented
13#20286558C211yesmaximal, characteristic, complemented
14#20286554C211yesmaximal, characteristic, complemented
15#20286543C211yesmaximal, characteristic, complemented
16#20286320C211yesmaximal, characteristic, complemented
17#20286240C211yesmaximal, characteristic, complemented
18#20285384C211yesmaximal, characteristic, complemented
19#20285380C211yesmaximal, characteristic, complemented
20#20285278C211yesmaximal, characteristic, complemented
21#20284926C211yesmaximal, characteristic, complemented
22#20284922C211yesmaximal, characteristic, complemented
23#20284900C211yesmaximal, characteristic, complemented
24#20284898C211yesmaximal, characteristic, complemented
25#20284825C211yesmaximal, characteristic, complemented
26#20284817C211yesmaximal, characteristic, complemented
27#20283685C211yesmaximal, characteristic, complemented
28#20283548C211yesmaximal, characteristic, complemented
29#20283544C211yesmaximal, characteristic, complemented
30#135×Dic53C211yesmaximal, characteristic, complemented
31C53×#3267C211yesmaximal, characteristic, complemented
32C2×#13133241C2211yescharacteristic
33#16811347C2211yescharacteristic, complemented
34#16811344C2211yescharacteristic, complemented
35#16811343C2211yescharacteristic, complemented
36#16811342C2211yescharacteristic, complemented
37#16811332C2211yescharacteristic, complemented
38#16811330C2211yescharacteristic, complemented
39#16811325—21no—
40#16811320C2211yescharacteristic
41#16811319C2211yescharacteristic
42#16811316—21no—
43#16811315C2211yescharacteristic
44#16811310—21no—
45#16811308—21no—
46#16811307C2211yescharacteristic
47#16811304—21no—
48#16811299—21no—
49#16811296—21no—
50#16811296—21no—
51#16811272C2211yescharacteristic
52#16811267C2211yescharacteristic
53#16811261C2211yescharacteristic
54#16811261C2211yescharacteristic, complemented
55#16811246C2211yescharacteristic
56#16811242C2211yescharacteristic
57#16811234C2211yescharacteristic, complemented
58#16811233C2211yescharacteristic, complemented
59#16811218—21no—
60#16811217—21no—
61#16811210—21no—
62#16811208—21no—
63#16811159C2211yescharacteristic, complemented
64#16811154C2211yescharacteristic, complemented
65#16811153C2211yescharacteristic
66#16811150—21no—
67#16811150—21no—
68C2×#13133212—21no—
69C2×#13133210—21no—
70#16811106C2211yescharacteristic
71#16811102C2211yescharacteristic
72#16811098C2211yescharacteristic, complemented
73#16811095C2211yescharacteristic, complemented
74#41×Dic53C2211yescharacteristic, complemented
75#41×Dic53C2211yescharacteristic, complemented
76#16811032C2211yescharacteristic, complemented
77#16811030C2211yescharacteristic, complemented
78#16811023C2211yescharacteristic, complemented
79#16811016C2211yescharacteristic, complemented
80#16811004C2211yescharacteristic
81#16810979C2211yescharacteristic, complemented
82#16810979C2211yescharacteristic, complemented
83#16810977C2211yescharacteristic, complemented
84#16810976C2211yescharacteristic, complemented
85#16810973C2211yescharacteristic, complemented
86#16810972C2211yescharacteristic, complemented
87#16810965C2211yescharacteristic, complemented
88#16810962C2211yescharacteristic, complemented
89#16810961C2211yescharacteristic, complemented
90#16810961C2211yescharacteristic, complemented
91#16810957C2211yescharacteristic, complemented
92#16810956C2211yescharacteristic, complemented
93#16810954C2211yescharacteristic, complemented
94#16810952C2211yescharacteristic, complemented
95#16810948C2211yescharacteristic
96#16810948C2211yescharacteristic, complemented
97#16810946C2211yescharacteristic
98#16810944C2211yescharacteristic, complemented
99#16810932C2211yescharacteristic, complemented
100#16810931C2211yescharacteristic, complemented
101#16810928C2211yescharacteristic, complemented
102#16810928C2211yescharacteristic, complemented
103#16810925C2211yescharacteristic, complemented
104#16810925C2211yescharacteristic, complemented
105#16810923C2211yescharacteristic, complemented
106#16810921C2211yescharacteristic, complemented
107#16810914C2211yescharacteristic, complemented
108#16810911C2211yescharacteristic, complemented
109#16810903C2211yescharacteristic, complemented
110#16810901C2211yescharacteristic, complemented
111#16810878C2211yescharacteristic, complemented
112#16810869C2211yescharacteristic
113#16810866C2211yescharacteristic
114#16810862C2211yescharacteristic, complemented
115#16810862C2211yescharacteristic, complemented
116#16810861C2211yescharacteristic, complemented
117#16810857C2211yescharacteristic
118#16810854C2211yescharacteristic
119#16810852C2211yescharacteristic, complemented
120#16810849C2211yescharacteristic
121#16810847C2211yescharacteristic, complemented
122#16810843C2211yescharacteristic, complemented
123#16810840C2211yescharacteristic
124#16810840C2211yescharacteristic
125#16810840C2211yescharacteristic
126#16810836C2211yescharacteristic
127#16810835C2211yescharacteristic
128#16810831C2211yescharacteristic, complemented
129#16810830C2211yescharacteristic, complemented
130#16810826C2211yescharacteristic, complemented
131#16810785C2211yescharacteristic
132#16810785C2211yescharacteristic, complemented
133#16810782C2211yescharacteristic
134#16810782C2211yescharacteristic
135#16810772C2211yescharacteristic, complemented
136#16810768C2211yescharacteristic
137#16810757C2211yescharacteristic
138#16810755C2211yescharacteristic
139#16810751C2211yescharacteristic, complemented
140#16810747C2211yescharacteristic, complemented
141#16810735C2211yescharacteristic
142#16810735C2211yescharacteristic
143#16810732C2211yescharacteristic
144#16810730C2211yescharacteristic, complemented
145#16810727C2211yescharacteristic, complemented
146#16810726C2211yescharacteristic, complemented
147#16810725C2211yescharacteristic, complemented
148#16810724C2211yescharacteristic, complemented
149#16810724C2211yescharacteristic, complemented
150#16810724C2211yescharacteristic, complemented
151#16810720C2211yescharacteristic, complemented
152Q16×Dic53C2211yescharacteristic, complemented
153Q16×Dic53C2211yescharacteristic, complemented
154#16810715C2211yescharacteristic, complemented
155SD16×Dic53C2211yescharacteristic, complemented
156SD16×Dic53C2211yescharacteristic, complemented
157SD16×Dic53C2211yescharacteristic, complemented
158SD16×Dic53C2211yescharacteristic, complemented
159SD16×Dic53C2211yescharacteristic, complemented
160SD16×Dic53C2211yescharacteristic, complemented
161#16810710C2211yescharacteristic, complemented
162C4×#11719923C2211yescharacteristic, complemented
163D8×Dic53C2211yescharacteristic
164D8×Dic53C2211yescharacteristic
165D8×Dic53C2211yescharacteristic
166C4×#11719922C2211yescharacteristic
167#16810703C2211yescharacteristic
168#16810699C2211yescharacteristic
169#16810694C2211yescharacteristic, complemented
170D4×#88322C2211yescharacteristic, complemented
171#16810686C2211yescharacteristic
172#16810686C2211yescharacteristic, complemented
173#16810683C2211yescharacteristic, complemented
174#16810681C2211yescharacteristic, complemented
175#16810677C2211yescharacteristic, complemented
176#16810665C2211yescharacteristic, complemented
177#16810662C2211yescharacteristic, complemented
178#16810661C2211yescharacteristic, complemented
179#16810619C2211yescharacteristic
180#16810619C2211yescharacteristic, complemented
181#16810619C2211yescharacteristic, complemented
182#16810616C2211yescharacteristic
183C2×#13133138C2211yescharacteristic, complemented
184#102×D53C2211yescharacteristic, complemented
185#16810581C2211yescharacteristic, complemented
186#16810580C2211yescharacteristic, complemented
187C2×C8×Dic53C2211yescharacteristic, complemented
188C2×AGL(1,ℤ/8)×C53C2211yescharacteristic
189C2×#135×C53C2211yescharacteristic
190C53×#547C2211yescharacteristic
191C53×#546C2211yescharacteristic, complemented
192C53×#497C2211yescharacteristic, complemented
193C53×#470C2211yescharacteristic, complemented
194C53×#465C2211yescharacteristic, complemented
195C53×#463C2211yescharacteristic
196C53×#461C2211yescharacteristic, complemented
197C53×#452C2211yescharacteristic
198C53×#452C2211yescharacteristic, complemented
199C53×#450C2211yescharacteristic, complemented
200C53×#449C2211yescharacteristic
201C53×#442C2211yescharacteristic
202C53×#435C2211yescharacteristic, complemented
203C2×#11719947C2311yescharacteristic
204C2×D4×D53C2311yescharacteristic
205#13133241—24no—
206C2×#11719925C2311yescharacteristic
207C2×#11719925C2311yescharacteristic
208C2×#11719913C2311yescharacteristic
209C2×#11719923C2311yescharacteristic
210C2×#11719924C2311yescharacteristic
211C2×#11719922C2311yescharacteristic
212C2×#11719922C2311yescharacteristic
213C2×#11719912C2311yescharacteristic
214C22×#88322C2311yescharacteristic
215C22×#88322C2311yescharacteristic
216C2×C8×D53C2311yescharacteristic
217#13133217C2311yescharacteristic
218#13133216C2311yescharacteristic
219#13133215C2311yescharacteristic
220#13133212—21no—
221#13133212—21no—
222#13133212—21no—
223#13133212—21no—
224#13133212—21no—
225#13133212—21no—
226#13133212—21no—
227#13133212—21no—
228#13133212—21no—
229#13133212D411yescharacteristic
230#13133210—21no—
231#13133210—21no—
232#13133210—21no—
233#13133210—21no—
234#13133210—21no—
235#13133210—21no—
236#13133210—21no—
237#13133210—21no—
238#13133210—21no—
239#13133210—21no—
240#13133210—21no—
241#13133210D411yescharacteristic
242#13133209C2311yescharacteristic
243#13133208—21no—
244#13133208—21no—
245#13133208C2311yescharacteristic
246#13133208C2311yescharacteristic
247#13133208C2311yescharacteristic
248#13133207—21no—
249#13133207—21no—
250#13133207—21no—
251#13133207—21no—
252#13133207D411yescharacteristic
253#13133206C2311yescharacteristic
254#13133206C2311yescharacteristic
255#13133204—21no—
256#13133204C2311yescharacteristic
257#13133203—21no—
258#13133203—21no—
259#13133203—21no—
260#13133203D411yescharacteristic
261#13133201—21no—
262#13133201—21no—
263#13133201—21no—
264#13133201D411yescharacteristic
265#13133200—21no—
266#13133200—21no—
267#13133200—21no—
268#13133199—21no—
269#13133199—21no—
270#13133199—21no—
271#13133198—21no—
272#13133198—21no—
273#13133198—21no—
274#13133198—21no—
275#13133198D411yescharacteristic
276#13133197—21no—
277#13133197—21no—
278#13133196—21no—
279#13133196—21no—
280#13133196C2311yescharacteristic
281#13133196C2311yescharacteristic
282#13133194—21no—
283#13133194—21no—
284#13133194—21no—
285#13133194—21no—
286#13133194—21no—
287#13133194—21no—
288#13133194D411yescharacteristic
289#13133193C2311yescharacteristic
290#13133193C2311yescharacteristic
291#13133193C2311yescharacteristic
292#13133191C2311yescharacteristic
293#13133191C2311yescharacteristic
294#13133189—21no—
295#13133189—21no—
296#13133189—21no—
297#13133189—21no—
298#13133189—21no—
299#13133189D411yescharacteristic
300#13133188—21no—
301#13133188C2311yescharacteristic
302#13133186—21no—
303#13133185—21no—
304#13133185—21no—
305Q8×Dic53C2311yescharacteristic
306Q8×Dic53C2311yescharacteristic
307Q8×Dic53C2311yescharacteristic
308Q8×Dic53C2311yescharacteristic
309Q8×Dic53C2311yescharacteristic
310Q8×Dic53C2311yescharacteristic
311C4×Dic106C2311yescharacteristic
312C4×Dic106C2311yescharacteristic
313#13133182—21no—
314#13133182—21no—
315#13133182C2311yescharacteristic
316C4×D212C2311yescharacteristic
317D4×Dic53—21no—
318D4×Dic53—21no—
319D4×Dic53—21no—
320D4×Dic53—21no—
321D4×Dic53—21no—
322D4×Dic53—21no—
323D4×Dic53—21no—
324D4×Dic53—21no—
325D4×Dic53—21no—
326D4×Dic53C2311yescharacteristic
327D4×Dic53C2311yescharacteristic
328D4×Dic53C2311yescharacteristic
329D4×Dic53C2311yescharacteristic
330D4×Dic53C2311yescharacteristic
331D4×Dic53C2311yescharacteristic
332D4×Dic53C2311yescharacteristic
333D4×Dic53C2311yescharacteristic
334#13133179C2311yescharacteristic
335C4×C22⋊D53—21no—
336C4×C22⋊D53—21no—
337C4×C22⋊D53C2311yescharacteristic
338C4×C22⋊D53C2311yescharacteristic
339#13133177—21no—
340#13133177—21no—
341#13133177—21no—
342#13133177—21no—
343#13133177—21no—
344#13133176—21no—
345#13133176—21no—
346#13133176—21no—
347#13133176C2311yescharacteristic
348#13133176C2311yescharacteristic
349#13133176C2311yescharacteristic
350#13133176C2311yescharacteristic
351#13133175—21no—
352#13133175—21no—
353#13133175—21no—
354#13133175C2311yescharacteristic
355#13133174C2311yescharacteristic
356#13133173—21no—
357#13133173—21no—
358#13133173—21no—
359#13133173—21no—
360C2×C4⋊Dic53—21no—
361C2×C4⋊Dic53—21no—
362C2×C4⋊Dic53C2311yescharacteristic
363C2×#11719919—21no—
364C2×#11719919—21no—
365C2×#11719919—21no—
366C4⋊C4×D53C2311yescharacteristic
367C2×C22⋊Dic53—21no—
368C2×C22⋊Dic53—21no—
369C2×C22⋊Dic53—21no—
370C2×#11719921—21no—
371C2×#11719921—21no—
372C2×#11719921—21no—
373C22⋊C4×D53—21no—
374C2×C4×Dic53—21no—
375C2×C4×Dic53—21no—
376C2×C4×Dic53C2311yescharacteristic
377#13133151C2311yescharacteristic
378#13133151C2311yescharacteristic
379#13133151C2311yescharacteristic
380#13133151C2311yescharacteristic
381#13133150C2311yescharacteristic
382#13133150C2311yescharacteristic
383#13133150C2311yescharacteristic
384#13133150C2311yescharacteristic
385#13133149C2311yescharacteristic
386#13133149C2311yescharacteristic
387#13133149C2311yescharacteristic
388#13133149C2311yescharacteristic
389#13133149C2311yescharacteristic
390#13133148C2311yescharacteristic
391#13133148C2311yescharacteristic
392C4⋊#88322C2311yescharacteristic
393#13133146C2311yescharacteristic
394#13133146C2311yescharacteristic
395#13133146C2311yescharacteristic
396#13133146C2311yescharacteristic
397#13133142C2311yescharacteristic
398#13133142C2311yescharacteristic
399#13133142C2311yescharacteristic
400#13133141C2311yescharacteristic
401#13133141C2311yescharacteristic
402#13133141C2311yescharacteristic
403#13133141C2311yescharacteristic
404#13133141C2311yescharacteristic
405#13133141C2311yescharacteristic
406#13133141C2311yescharacteristic
407#13133141C2311yescharacteristic
408#13133141C2311yescharacteristic
409#13133140C2311yescharacteristic
410#13133139C2311yescharacteristic
411#13133139C2311yescharacteristic
412#13133139C2311yescharacteristic
413#13133138C2311yescharacteristic
414#13133138C2311yescharacteristic
415#13133138C2311yescharacteristic
416#13133138C2311yescharacteristic
417#13133138C2311yescharacteristic
418#13133138C2311yescharacteristic
419#13133138C2311yescharacteristic
420#13133138C2311yescharacteristic
421#13133138C2311yescharacteristic
422#13133137C2311yescharacteristic
423C22⋊#88322C2311yescharacteristic
424C22⋊#88322C2311yescharacteristic
425#13133129C2311yescharacteristic
426#13133129C2311yescharacteristic
427#13133127C2311yescharacteristic
428#13133127C2311yescharacteristic
429#13133127C2311yescharacteristic
430C4×#88322C2311yescharacteristic
431C8×Dic53C2311yescharacteristic
432C8×Dic53C2311yescharacteristic
433C8×Dic53C2311yescharacteristic
434C8×Dic53C2311yescharacteristic
435C8×Dic53C2311yescharacteristic
436C2×#41×C53C2311yescharacteristic
437C2×#41×C53C2311yescharacteristic
438C2×#41×C53C2311yescharacteristic
439C22×D4×C53C2311yescharacteristic
440AGL(1,ℤ/8)×C53—24no—
441#135×C53—24no—
442C2×Q16×C53C2311yescharacteristic
443C2×Q16×C53C2311yescharacteristic
444C2×SD16×C53C2311yescharacteristic
445C2×SD16×C53C2311yescharacteristic
446C2×SD16×C53C2311yescharacteristic
447C2×SD16×C53C2311yescharacteristic
448C2×SD16×C53C2311yescharacteristic
449C2×D8×C53C2311yescharacteristic
450C2×D8×C53C2311yescharacteristic
451C2×M16×C53C2311yescharacteristic
452C22×C8×C53C2311yescharacteristic
453C4⋊Q8×C53C2311yescharacteristic
454#124×C53C2311yescharacteristic
455#123×C53—21no—
456#123×C53—21no—
457#123×C53—21no—
458C22⋊Q8×C53C2311yescharacteristic
459C22⋊Q8×C53C2311yescharacteristic
460C22⋊Q8×C53C2311yescharacteristic
461#121×C53—21no—
462#121×C53—21no—
463#121×C53C2311yescharacteristic
464#120×C53—21no—
465C4×D4×C53C2311yescharacteristic
466C4×D4×C53C2311yescharacteristic
467C4×D4×C53C2311yescharacteristic
468C2×C4⋊C4×C53—21no—
469C2×C22⋊C4×C53—21no—
470#106×C53C2311yescharacteristic
471C4⋊C8×C53C2311yescharacteristic
472#103×C53C2311yescharacteristic
473#103×C53C2311yescharacteristic
474#103×C53C2311yescharacteristic
475#102×C53C2311yescharacteristic
476#102×C53C2311yescharacteristic
477#102×C53C2311yescharacteristic
478C22⋊C8×C53C2311yescharacteristic
479C22⋊C8×C53C2311yescharacteristic
480#97×C53C2311yescharacteristic
481C24×C53—21no—
482C23×D53—21no—
483#41×C53—22no—
484#41×C53—22no—
485#41×C53—22no—
486#41×C53—41no—
487#41×C53—41no—
488#41×C53—41no—
489C2×Q8×C53C2411yescharacteristic
490C2×Q8×C53C2411yescharacteristic
491C2×Q8×C53C2411yescharacteristic
492C2×D4×C53—22no—
493C2×D4×C53—21no—
494C2×D4×C53—21no—
495C2×D4×C53—21no—
496C2×D4×C53—21no—
497C2×D4×C53—21no—
498C2×D4×C53—41no—
499C2×D4×C53C2×D411yescharacteristic
500C2×D4×C53C2411yescharacteristic
501C2×D4×C53C2411yescharacteristic
502C2×D4×C53C2411yescharacteristic
503C22×C4×C53—21no—
504C22×C4×C53—21no—
505C22×C4×C53—21no—
506C22×C4×C53—21no—
507C22×C4×C53—21no—
508C22×C4×C53C2411yescharacteristic
509C22×C4×C53C2411yescharacteristic
510C2×C22⋊D53—21no—
511C2×C22⋊D53—21no—
512C2×C22⋊D53—21no—
513C2×C22⋊D53—21no—
514C2×C22⋊D53—21no—
515C2×C22⋊D53C2×D411yescharacteristic
516C2×C22⋊D53C2×D411yescharacteristic
517C22×Dic53—21no—
518C22×Dic53—21no—
519C22×Dic53—21no—
520C22×Dic53—21no—
521C22×Dic53—21no—
522C22×Dic53—21no—
523C22×Dic53—21no—
524C22×Dic53—21no—
525C22×Dic53—21no—
526C22×Dic53—21no—
527C22×Dic53C2×D411yescharacteristic
528C22×Dic53C2×D411yescharacteristic
529#11719947—22no—
530#11719947—41no—
531D4×D53—22no—
532D4×D53—41no—
533C2×D212C2411yescharacteristic
534C2×C4×D53—21no—
535C2×C4×D53—21no—
536C2×C4×D53—21no—
537C2×C4×D53C2411yescharacteristic
538C2×Dic106—21no—
539C2×Dic106—21no—
540C2×Dic106C2×D411yescharacteristic
541C2×Dic106C2411yescharacteristic
542Q16×C53—22no—
543Q16×C53—41no—
544SD16×C53—22no—
545SD16×C53—22no—
546SD16×C53—22no—
547SD16×C53—22no—
548SD16×C53—41no—
549D8×C53—22no—
550D8×C53#4114yes—
551M16×C53—22no—
552C2×C8×C53—22no—
553C2×C8×C53C2411yescharacteristic
554C2×C8×C53C2411yescharacteristic
555C2×C8×C53C2411yescharacteristic
556C2×C8×C53C2411yescharacteristic
557C4⋊C4×C53—21no—
558C4⋊C4×C53—21no—
559C4⋊C4×C53—21no—
560C4⋊C4×C53—21no—
561C4⋊C4×C53—21no—
562C4⋊C4×C53C2×D411yescharacteristic
563C4⋊C4×C53C2411yescharacteristic
564C4⋊C4×C53C2411yescharacteristic
565C22⋊C4×C53—21no—
566C22⋊C4×C53—21no—
567C22⋊C4×C53—21no—
568C22⋊C4×C53—21no—
569C22⋊C4×C53—21no—
570C22⋊C4×C53—21no—
571C22⋊C4×C53—21no—
572C22⋊C4×C53—21no—
573C22⋊C4×C53C2×D411yescharacteristic
574C22⋊C4×C53C2×D411yescharacteristic
575C42×C53C2411yescharacteristic
576C22⋊Dic53—21no—
577C22⋊Dic53—21no—
578C22⋊Dic53—21no—
579C22⋊Dic53—21no—
580C22⋊Dic53—21no—
581C22⋊Dic53—21no—
582C22⋊Dic53—21no—
583C22⋊Dic53—21no—
584C22⋊Dic53—21no—
585C22⋊Dic53—21no—
586C22⋊Dic53—21no—
587C22⋊Dic53—21no—
588C22⋊Dic53—21no—
589C22⋊Dic53—21no—
590C22⋊Dic53—21no—
591C22⋊Dic53—21no—
592C22⋊Dic53C2×D411yescharacteristic
593C22⋊Dic53C2×D411yescharacteristic
594C22⋊Dic53C2×D411yescharacteristic
595C22⋊Dic53C2×D411yescharacteristic
596#11719925—41no—
597#11719925—41no—
598#11719924—41no—
599#11719923—22no—
600#11719922—22no—
601#11719922—41no—
602#11719921—21no—
603#11719921—21no—
604#11719921—21no—
605#11719921—21no—
606#11719921—21no—
607#11719921—21no—
608#11719921—21no—
609#11719921—21no—
610#11719921—21no—
611#11719921—21no—
612#11719921—21no—
613#11719921—21no—
614#11719921C2×D411yescharacteristic
615#11719921C2×D411yescharacteristic
616#11719921C2×D411yescharacteristic
617#11719921C2×D411yescharacteristic
618C4⋊Dic53—21no—
619C4⋊Dic53—21no—
620C4⋊Dic53—21no—
621C4⋊Dic53—21no—
622C4⋊Dic53—21no—
623C4⋊Dic53—21no—
624C4⋊Dic53—21no—
625C4⋊Dic53—21no—
626C4⋊Dic53—21no—
627C4⋊Dic53—21no—
628C4⋊Dic53—21no—
629C4⋊Dic53C2×D411yescharacteristic
630C4⋊Dic53C2×D411yescharacteristic
631C4⋊Dic53C2×D411yescharacteristic
632C4⋊Dic53C2411yescharacteristic
633C4⋊Dic53C2411yescharacteristic
634C4⋊Dic53C2411yescharacteristic
635C4⋊Dic53C2411yescharacteristic
636C4⋊Dic53C2411yescharacteristic
637C4⋊Dic53C2411yescharacteristic
638#11719919—21no—
639#11719919—21no—
640#11719919—21no—
641#11719919—21no—
642#11719919—21no—
643#11719919—21no—
644#11719919—21no—
645#11719919—21no—
646#11719919—21no—
647#11719919—21no—
648#11719919—21no—
649#11719919—21no—
650#11719919—21no—
651#11719919—21no—
652#11719919—21no—
653#11719919—21no—
654#11719919C2×D411yescharacteristic
655#11719919C2×D411yescharacteristic
656#11719919C2×D411yescharacteristic
657#11719919C2×D411yescharacteristic
658#11719919C2×D411yescharacteristic
659#11719919C2×D411yescharacteristic
660C4×Dic53—21no—
661C4×Dic53—21no—
662C4×Dic53—21no—
663C4×Dic53—21no—
664C4×Dic53—21no—
665C4×Dic53—21no—
666C4×Dic53—21no—
667C4×Dic53—21no—
668C4×Dic53—21no—
669C4×Dic53—21no—
670C4×Dic53—21no—
671C4×Dic53—21no—
672C4×Dic53C2×D411yescharacteristic
673C4×Dic53C2×D411yescharacteristic
674C4×Dic53C2411yescharacteristic
675C4×Dic53C2411yescharacteristic
676C4×Dic53C2411yescharacteristic
677C2×#88322—41no—
678C2×#88322—41no—
679C2×#88322C2411yescharacteristic
680C2×#88322C2411yescharacteristic
681C2×#88322C2411yescharacteristic
682C2×#88322C2411yescharacteristic
683#11719913—22no—
684#11719912—22no—
685C8×D53—41no—
686C23×C53—21no—
687C23×C53—21no—
688C23×C53—21no—
689C23×C53—42no—
690C23×C53—81no—
691C23×C53—81no—
692C23×C53C22×D411yescharacteristic
693C23×C53C22×D411yescharacteristic
694C22×D53—21no—
695C22×D53—42no—
696C22×D53—81no—
697C22×D53—81no—
698C22×D53C22×D411yescharacteristic
699Q8×C53—21no—
700Q8×C53—21no—
701Q8×C53—21no—
702Q8×C53—21no—
703Q8×C53—21no—
704Q8×C53—21no—
705D4×C53—21no—
706D4×C53—21no—
707D4×C53—21no—
708D4×C53—21no—
709D4×C53—41no—
710D4×C53—42no—
711D4×C53—42no—
712D4×C53—42no—
713D4×C53—42no—
714D4×C53—81no—
715D4×C53C2×#4112yes—
716D4×C53C2×#4112yes—
717C2×C4×C53—21no—
718C2×C4×C53—21no—
719C2×C4×C53—21no—
720C2×C4×C53—21no—
721C2×C4×C53—21no—
722C2×C4×C53—21no—
723C2×C4×C53—21no—
724C2×C4×C53—21no—
725C2×C4×C53—21no—
726C2×C4×C53—42no—
727C2×C4×C53—42no—
728C2×C4×C53—42no—
729C2×C4×C53—81no—
730C2×C4×C53—81no—
731C2×C4×C53C22×D411yescharacteristic
732C2×C4×C53C22×D411yescharacteristic
733C2×C4×C53C22×D411yescharacteristic
734C2×C4×C53C22×D411yescharacteristic
735C2×C4×C53C2511yescharacteristic
736C22⋊D53—41no—
737C22⋊D53—41no—
738C22⋊D53—42no—
739C22⋊D53—42no—
740C22⋊D53—81no—
741C22⋊D53—81no—
742C22⋊D53—81no—
743C2×Dic53—21no—
744C2×Dic53—21no—
745C2×Dic53—21no—
746C2×Dic53—21no—
747C2×Dic53—21no—
748C2×Dic53—21no—
749C2×Dic53—21no—
750C2×Dic53—41no—
751C2×Dic53—41no—
752C2×Dic53—42no—
753C2×Dic53—81no—
754C2×Dic53—81no—
755C2×Dic53—81no—
756C2×Dic53—81no—
757C2×Dic53—81no—
758C2×Dic53—81no—
759C2×Dic53—81no—
760C2×Dic53—81no—
761C2×Dic53—81no—
762C2×Dic53C22×D411yescharacteristic
763C2×Dic53C22×D411yescharacteristic
764C2×Dic53C22×D411yescharacteristic
765C2×Dic53C22×D411yescharacteristic
766C2×Dic53C22×D411yescharacteristic
767C2×Dic53C22×D411yescharacteristic
768C2×Dic53C22×D411yescharacteristic
769D212—21no—
770D212—21no—
771C4×D53—21no—
772C4×D53—21no—
773C4×D53—81no—
774C4×D53—81no—
775C4×D53—81no—
776Dic106—21no—
777Dic106—21no—
778Dic106—41no—
779Dic106—81no—
780Dic106—81no—
781C8×C53—21no—
782C8×C53—21no—
783C8×C53—21no—
784C8×C53C2×#4112yes—
785#88322—21no—
786#88322—21no—
787#88322—21no—
788#88322—21no—
789#61501—531nomaximal, Sylow
790C22×C53—21no—
791C22×C53—21no—
792C22×C53—21no—
793C22×C53—21no—
794C22×C53—22no—
795C22×C53—22no—
796C22×C53—21no—
797C22×C53—21no—
798C22×C53—41no—
799C22×C53—41no—
800C22×C53—41no—
801C22×C53—41no—
802C22×C53—41no—
803C22×C53—41no—
804C22×C53—41no—
805C22×C53—162no—
806C22×C53C23×D411yescharacteristic
807C2×D53—21no—
808C2×D53—21no—
809C2×D53—21no—
810C2×D53—41no—
811C2×D53—41no—
812C2×D53—41no—
813C2×D53—162no—
814C4×C53—21no—
815C4×C53—21no—
816C4×C53—21no—
817C4×C53—21no—
818C4×C53—41no—
819C4×C53—41no—
820C4×C53—41no—
821C4×C53—41no—
822C4×C53—41no—
823C4×C53C22×#4111yescharacteristic
824C4×C53#58511yescharacteristic
825Dic53—21no—
826Dic53—21no—
827Dic53—21no—
828Dic53—21no—
829Dic53—21no—
830Dic53—21no—
831Dic53—21no—
832Dic53—41no—
833Dic53—41no—
834Dic53—41no—
835Dic53—41no—
836Dic53—41no—
837Dic53—41no—
838Dic53—41no—
839#3521—531no—
840#3521—531no—
841#3402—531no—
842#3389—531no—
843#3360—531no—
844#3360—531no—
845#3352—531no—
846#3350—531no—
847#3350—531no—
848#3302—531no—
849#3302—531no—
850#3297—531no—
851#3297—531no—
852#3296—531no—
853#3296—531no—
854#3273—531no—
855#3267—531no—
856#3267D5311yescharacteristic, complemented
857#3178—531no—
858#3178—531no—
859#3168—531no—
860#3120—531no—
861#3120—531no—
862#3118—531no—
863#3118—531no—
864#3111—531no—
865#3111—531no—
866#2966—531no—
867#2946—531no—
868#2946—531no—
869C4×#135—531no—
870C2×C53—42no—
871C2×C53—41no—
872C2×C53—41no—
873C2×C53—42no—
874C2×C53—81no—
875C2×C53D4×#4111yescharacteristic
876C2×C53#358411yescharacteristic
877C2×C53#358411yescharacteristic
878D53—41no—
879D53—81no—
880C2×AGL(1,ℤ/8)—531no—
881C2×AGL(1,ℤ/8)C2×D5311yescharacteristic
882C2×#135C2×D5311yescharacteristic
883#556—531no—
884#556—531no—
885#556—531no—
886#556—531no—
887#554—531no—
888#554—531no—
889#553—531no—
890#553—531no—
891#553—1061no—
892#553—1061no—
893#552—531no—
894#552—531no—
895#552—1061no—
896#552—1061no—
897#551—1061no—
898#551—1061no—
899#551—1061no—
900#551—1061no—
901#547—531no—
902#547C2×D5311yescharacteristic
903#546—531no—
904#546—531no—
905#546—531no—
906#546C2×D5311yescharacteristic, complemented
907#542—531no—
908#542—531no—
909#541—531no—
910#541—531no—
911#539—1061no—
912#539—1061no—
913#538—1061no—
914#538—1061no—
915#529—531no—
916#529—531no—
917#529—531no—
918#529—1061no—
919#529—1061no—
920C2×#126—1061no—
921C2×#126—1061no—
922#520—531no—
923#520—531no—
924#518—531no—
925#518—531no—
926C4×#41—531no—
927C4×#41—531no—
928#501—531no—
929#501—531no—
930#499—531no—
931#497—531no—
932#497C2×D5311yescharacteristic, complemented
933#495—531no—
934#488—531no—
935#488—531no—
936#488—531no—
937#488—531no—
938#487—531no—
939#487—531no—
940#485—531no—
941#485—531no—
942#485—531no—
943#485—531no—
944#484—531no—
945#484—531no—
946#483—531no—
947#483—531no—
948#482—531no—
949#482—531no—
950#482—531no—
951#482—531no—
952#479—531no—
953#479—531no—
954#479—531no—
955#479—531no—
956#478—531no—
957#478—531no—
958#478—531no—
959#478—531no—
960#476—531no—
961#476—531no—
962#474—531no—
963#474—531no—
964#470—531no—
965#470C2×D5311yescharacteristic, complemented
966#468—531no—
967#468—531no—
968#467—531no—
969#467—531no—
970#467—531no—
971#466—531no—
972#465—531no—
973#465—531no—
974#465—531no—
975#465C2×D5311yescharacteristic, complemented
976#464—531no—
977#464—531no—
978#463—531no—
979#463—531no—
980#463—531no—
981#463—531no—
982#463—531no—
983#463C2×D5311yescharacteristic
984#462—531no—
985#462—531no—
986#461—531no—
987#461C2×D5311yescharacteristic, complemented
988#452—531no—
989#452—531no—
990#452—531no—
991#452—531no—
992#452C2×D5311yescharacteristic
993#452C2×D5311yescharacteristic, complemented
994#450—531no—
995#450C2×D5311yescharacteristic, complemented
996#449—531no—
997#449C2×D5311yescharacteristic
998#447—531no—
999#447—531no—
1000#446—531no—
1001C8×Q8—531no—
1002#442—531no—
1003#442—531no—
1004#442—531no—
1005#442C2×D5311yescharacteristic
1006#441—531no—
1007#441—531no—
1008#440—531no—
1009#440—531no—
1010#440—531no—
1011#440—531no—
1012#440—531no—
1013#440—531no—
1014C4×Q16—531no—
1015C4×Q16—531no—
1016C4×Q16—531no—
1017C4×SD16—531no—
1018C4×SD16—531no—
1019C4×SD16—531no—
1020C4×SD16—531no—
1021C4×SD16—531no—
1022C4×SD16—531no—
1023C4×SD16—531no—
1024C4×SD16—531no—
1025C4×D8—531no—
1026C4×D8—531no—
1027C4×D8—531no—
1028C4×D8—531no—
1029C4×D8—531no—
1030#436—531no—
1031#435—531no—
1032#435C2×D5311yescharacteristic, complemented
1033C8×D4—531no—
1034C8×D4—531no—
1035C8×D4—531no—
1036#433—531no—
1037#433—531no—
1038#432—531no—
1039#428—531no—
1040#428—531no—
1041#427—531no—
1042#416—531no—
1043#416—531no—
1044#416—531no—
1045#416—531no—
1046C2×#102—531no—
1047C2×#102—531no—
1048#405—531no—
1049#405—531no—
1050C2×C4×C8—531no—
1051C53#6150111yescharacteristic, complemented, Sylow
1052C2×#41—531no—
1053C2×#41C22×D5311yescharacteristic
1054C2×#41C22×D5311yescharacteristic
1055C2×#41C22×D5311yescharacteristic
1056C22×D4—531no—
1057C22×D4C22×D5311yescharacteristic
1058AGL(1,ℤ/8)—24no—
1059AGL(1,ℤ/8)—1064no—
1060#135—24no—
1061C2×Q16—531no—
1062C2×Q16—531no—
1063C2×Q16C22×D5311yescharacteristic
1064C2×Q16C22×D5311yescharacteristic
1065C2×SD16—531no—
1066C2×SD16—531no—
1067C2×SD16—531no—
1068C2×SD16C22×D5311yescharacteristic
1069C2×SD16C22×D5311yescharacteristic
1070C2×SD16C22×D5311yescharacteristic
1071C2×SD16C22×D5311yescharacteristic
1072C2×SD16C22×D5311yescharacteristic
1073C2×D8—531no—
1074C2×D8—531no—
1075C2×D8C22×D5311yescharacteristic
1076C2×D8C22×D5311yescharacteristic
1077C2×M16—531no—
1078C2×M16C22×D5311yescharacteristic
1079C22×C8—531no—
1080C22×C8—531no—
1081C22×C8—531no—
1082C22×C8C22×D5311yescharacteristic
1083C4⋊Q8—531no—
1084C4⋊Q8—531no—
1085C4⋊Q8—531no—
1086C4⋊Q8C22×D5311yescharacteristic
1087#126—531no—
1088#126—531no—
1089#126—1061no—
1090#126—1061no—
1091#126—1061no—
1092#126—1061no—
1093#126—1061no—
1094#126—1061no—
1095#126—1061no—
1096#126—1061no—
1097#126—1061no—
1098#126—1061no—
1099#126—1061no—
1100#126—1061no—
1101#126—1061no—
1102#126—1061no—
1103#126—1061no—
1104#126—1061no—
1105#126—1061no—
1106#126—1061no—
1107#126—1061no—
1108#126—1061no—
1109#125—531no—
1110#125—531no—
1111#125—531no—
1112#125—531no—
1113#125—531no—
1114#125—1061no—
1115#125—1061no—
1116#125—1061no—
1117#125—1061no—
1118#125—1061no—
1119#125—1061no—
1120#124—531no—
1121#124—531no—
1122#124—531no—
1123#124—531no—
1124#124—1061no—
1125#124—1061no—
1126#124—1061no—
1127#124—1061no—
1128#124C22×D5311yescharacteristic
1129#123—21no—
1130#123—21no—
1131#123—21no—
1132#123—531no—
1133#123—531no—
1134#123—1061no—
1135#123—1061no—
1136#123—1061no—
1137#123—1061no—
1138#123—1061no—
1139#123—1061no—
1140#123—1061no—
1141#123—1061no—
1142#123—1061no—
1143#123—1061no—
1144#123—1061no—
1145#123—1061no—
1146#123—1061no—
1147C22⋊Q8—531no—
1148C22⋊Q8—531no—
1149C22⋊Q8—531no—
1150C22⋊Q8—531no—
1151C22⋊Q8—531no—
1152C22⋊Q8—531no—
1153C22⋊Q8—1061no—
1154C22⋊Q8—1061no—
1155C22⋊Q8—1061no—
1156C22⋊Q8—1061no—
1157C22⋊Q8—1061no—
1158C22⋊Q8—1061no—
1159C22⋊Q8—1061no—
1160C22⋊Q8—1061no—
1161C22⋊Q8—1061no—
1162C22⋊Q8—1061no—
1163C22⋊Q8C22×D5311yescharacteristic
1164C22⋊Q8C22×D5311yescharacteristic
1165C22⋊Q8C22×D5311yescharacteristic
1166#121—21no—
1167#121—21no—
1168#121—531no—
1169#121—531no—
1170#121—531no—
1171#121—531no—
1172#121—1061no—
1173#121—1061no—
1174#121—1061no—
1175#121—1061no—
1176#121—1061no—
1177#121—1061no—
1178#121C22×D5311yescharacteristic
1179#120—21no—
1180#120—1061no—
1181#120—1061no—
1182#120—1061no—
1183C4×Q8—531no—
1184C4×Q8—531no—
1185C4×Q8—531no—
1186C4×Q8—531no—
1187C4×Q8—531no—
1188C4×Q8—531no—
1189C4×Q8—531no—
1190C4×Q8—531no—
1191C4×Q8—531no—
1192C4×Q8—1061no—
1193C4×Q8—1061no—
1194C4×D4—531no—
1195C4×D4—531no—
1196C4×D4—531no—
1197C4×D4—531no—
1198C4×D4—531no—
1199C4×D4—531no—
1200C4×D4—531no—
1201C4×D4—531no—
1202C4×D4—531no—
1203C4×D4—531no—
1204C4×D4—531no—
1205C4×D4—531no—
1206C4×D4—1061no—
1207C4×D4—1061no—
1208C4×D4—1061no—
1209C4×D4—1061no—
1210C4×D4—1061no—
1211C4×D4—1061no—
1212C4×D4—1061no—
1213C4×D4—1061no—
1214C4×D4—1061no—
1215C4×D4—1061no—
1216C4×D4—1061no—
1217C4×D4—1061no—
1218C4×D4—1061no—
1219C4×D4—1061no—
1220C4×D4—1061no—
1221C4×D4—1061no—
1222C4×D4C22×D5311yescharacteristic
1223C4×D4C22×D5311yescharacteristic
1224C4×D4C22×D5311yescharacteristic
1225#117—531no—
1226#117—531no—
1227#117—531no—
1228#117—531no—
1229#117—531no—
1230#117—531no—
1231#117—1061no—
1232#117—1061no—
1233#117—1061no—
1234#117—1061no—
1235#117—1061no—
1236#117—1061no—
1237#117—1061no—
1238#117—1061no—
1239#117—1061no—
1240#117—1061no—
1241C2×C4⋊C4—21no—
1242C2×C4⋊C4—531no—
1243C2×C4⋊C4—531no—
1244C2×C4⋊C4—1061no—
1245C2×C4⋊C4—1061no—
1246C2×C4⋊C4—1061no—
1247C2×C4⋊C4—1061no—
1248C2×C4⋊C4—1061no—
1249C2×C22⋊C4—21no—
1250C2×C22⋊C4—1061no—
1251C2×C22⋊C4—1061no—
1252C2×C22⋊C4—1061no—
1253C2×C22⋊C4—1061no—
1254C2×C22⋊C4—1061no—
1255C2×C22⋊C4—1061no—
1256C2×C22⋊C4—1061no—
1257C2×C42—531no—
1258C2×C42—1061no—
1259C2×C42—1061no—
1260#107—531no—
1261#107—531no—
1262#107—531no—
1263#107—531no—
1264#107—531no—
1265#107—531no—
1266#107—531no—
1267#107—531no—
1268#106—531no—
1269#106—531no—
1270#106—531no—
1271#106—531no—
1272#106—531no—
1273#106—531no—
1274#106—531no—
1275#106C22×D5311yescharacteristic
1276C4⋊C8—531no—
1277C4⋊C8—531no—
1278C4⋊C8—531no—
1279C4⋊C8—531no—
1280C4⋊C8—531no—
1281C4⋊C8C22×D5311yescharacteristic
1282#103—531no—
1283#103—531no—
1284#103—531no—
1285#103—531no—
1286#103—531no—
1287#103—531no—
1288#103—531no—
1289#103—531no—
1290#103—531no—
1291#103—531no—
1292#103—531no—
1293#103—531no—
1294#103—531no—
1295#103C22×D5311yescharacteristic
1296#103C22×D5311yescharacteristic
1297#103C22×D5311yescharacteristic
1298#102—531no—
1299#102—531no—
1300#102—531no—
1301#102—531no—
1302#102—531no—
1303#102—531no—
1304#102—531no—
1305#102—531no—
1306#102—531no—
1307#102—531no—
1308#102—531no—
1309#102—531no—
1310#102—531no—
1311#102C22×D5311yescharacteristic
1312#102C22×D5311yescharacteristic
1313#102C22×D5311yescharacteristic
1314C22⋊C8—531no—
1315C22⋊C8—531no—
1316C22⋊C8—531no—
1317C22⋊C8—531no—
1318C22⋊C8C22×D5311yescharacteristic
1319C22⋊C8C22×D5311yescharacteristic
1320#97—531no—
1321#97—531no—
1322#97—531no—
1323#97C22×D5311yescharacteristic
1324C4×C8—531no—
1325C4×C8—531no—
1326C4×C8—531no—
1327C4×C8—531no—
1328C4×C8—531no—
1329C4×C8—531no—
1330C24—21no—
1331C24—1061no—
1332#41—22no—
1333#41—22no—
1334#41—22no—
1335#41—41no—
1336#41—41no—
1337#41—41no—
1338#41—1062no—
1339#41—2121no—
1340C2×Q8—531no—
1341C2×Q8—531no—
1342C2×Q8—1061no—
1343C2×Q8—1061no—
1344C2×Q8C23×D5311yescharacteristic
1345C2×Q8C23×D5311yescharacteristic
1346C2×Q8C23×D5311yescharacteristic
1347C2×D4—22no—
1348C2×D4—21no—
1349C2×D4—21no—
1350C2×D4—21no—
1351C2×D4—21no—
1352C2×D4—21no—
1353C2×D4—41no—
1354C2×D4—531no—
1355C2×D4—531no—
1356C2×D4—531no—
1357C2×D4—1061no—
1358C2×D4—1062no—
1359C2×D4—1061no—
1360C2×D4—1061no—
1361C2×D4—1061no—
1362C2×D4—1061no—
1363C2×D4—2121no—
1364C2×D4D4×D5311yescharacteristic
1365C2×D4C23×D5311yescharacteristic
1366C2×D4C23×D5311yescharacteristic
1367C2×D4C23×D5311yescharacteristic
1368C22×C4—21no—
1369C22×C4—21no—
1370C22×C4—21no—
1371C22×C4—21no—
1372C22×C4—21no—
1373C22×C4—531no—
1374C22×C4—531no—
1375C22×C4—531no—
1376C22×C4—1061no—
1377C22×C4—1061no—
1378C22×C4—1061no—
1379C22×C4—1061no—
1380C22×C4—1061no—
1381C22×C4—1061no—
1382C22×C4—1061no—
1383C22×C4—1061no—
1384C22×C4—1061no—
1385C22×C4—1061no—
1386C22×C4—1061no—
1387C22×C4—1061no—
1388C22×C4—1061no—
1389C22×C4C23×D5311yescharacteristic
1390C22×C4C23×D5311yescharacteristic
1391Q16—22no—
1392Q16—41no—
1393Q16—2121no—
1394Q16—2121no—
1395SD16—22no—
1396SD16—22no—
1397SD16—22no—
1398SD16—22no—
1399SD16—41no—
1400SD16—1062no—
1401SD16—1062no—
1402SD16—2121no—
1403D8—22no—
1404D8—1062no—
1405D8—2121no—
1406D8#1171994714yes—
1407M16—22no—
1408M16—1062no—
1409C2×C8—22no—
1410C2×C8—531no—
1411C2×C8—531no—
1412C2×C8—531no—
1413C2×C8—531no—
1414C2×C8—2121no—
1415C2×C8—2121no—
1416C2×C8—2121no—
1417C2×C8C23×D5311yescharacteristic
1418C2×C8C23×D5311yescharacteristic
1419C2×C8C23×D5311yescharacteristic
1420C2×C8C23×D5311yescharacteristic
1421C4⋊C4—21no—
1422C4⋊C4—21no—
1423C4⋊C4—21no—
1424C4⋊C4—21no—
1425C4⋊C4—21no—
1426C4⋊C4—531no—
1427C4⋊C4—531no—
1428C4⋊C4—531no—
1429C4⋊C4—531no—
1430C4⋊C4—531no—
1431C4⋊C4—531no—
1432C4⋊C4—531no—
1433C4⋊C4—531no—
1434C4⋊C4—531no—
1435C4⋊C4—531no—
1436C4⋊C4—531no—
1437C4⋊C4—531no—
1438C4⋊C4—531no—
1439C4⋊C4—531no—
1440C4⋊C4—531no—
1441C4⋊C4—1061no—
1442C4⋊C4—1061no—
1443C4⋊C4—1061no—
1444C4⋊C4—1061no—
1445C4⋊C4—1061no—
1446C4⋊C4—1061no—
1447C4⋊C4—1061no—
1448C4⋊C4—1061no—
1449C4⋊C4—1061no—
1450C4⋊C4—1061no—
1451C4⋊C4—1061no—
1452C4⋊C4—1061no—
1453C4⋊C4—1061no—
1454C4⋊C4—1061no—
1455C4⋊C4—1061no—
1456C4⋊C4—1061no—
1457C4⋊C4—1061no—
1458C4⋊C4—1061no—
1459C4⋊C4—1061no—
1460C4⋊C4—1061no—
1461C4⋊C4—1061no—
1462C4⋊C4—1061no—
1463C4⋊C4—1061no—
1464C4⋊C4—1061no—
1465C4⋊C4—1061no—
1466C4⋊C4—1061no—
1467C4⋊C4—1061no—
1468C4⋊C4D4×D5311yescharacteristic
1469C4⋊C4C23×D5311yescharacteristic
1470C4⋊C4C23×D5311yescharacteristic
1471C22⋊C4—21no—
1472C22⋊C4—21no—
1473C22⋊C4—21no—
1474C22⋊C4—21no—
1475C22⋊C4—21no—
1476C22⋊C4—21no—
1477C22⋊C4—21no—
1478C22⋊C4—21no—
1479C22⋊C4—531no—
1480C22⋊C4—531no—
1481C22⋊C4—531no—
1482C22⋊C4—531no—
1483C22⋊C4—531no—
1484C22⋊C4—531no—
1485C22⋊C4—531no—
1486C22⋊C4—531no—
1487C22⋊C4—1061no—
1488C22⋊C4—1061no—
1489C22⋊C4—1061no—
1490C22⋊C4—1061no—
1491C22⋊C4—1061no—
1492C22⋊C4—1061no—
1493C22⋊C4—1061no—
1494C22⋊C4—1061no—
1495C22⋊C4—1061no—
1496C22⋊C4—1061no—
1497C22⋊C4—1061no—
1498C22⋊C4—1061no—
1499C22⋊C4—1061no—
1500C22⋊C4—1061no—
1501C22⋊C4—1061no—
1502C22⋊C4—1061no—
1503C22⋊C4—1061no—
1504C22⋊C4—1061no—
1505C22⋊C4—1061no—
1506C22⋊C4—1061no—
1507C22⋊C4—1061no—
1508C22⋊C4—1061no—
1509C22⋊C4—1061no—
1510C22⋊C4—1061no—
1511C22⋊C4—1061no—
1512C22⋊C4—1061no—
1513C22⋊C4—1061no—
1514C22⋊C4—1061no—
1515C22⋊C4D4×D5311yescharacteristic
1516C22⋊C4D4×D5311yescharacteristic
1517C42—531no—
1518C42—531no—
1519C42—531no—
1520C42—531no—
1521C42—531no—
1522C42—1061no—
1523C42—1061no—
1524C42—1061no—
1525C42—1061no—
1526C42—1061no—
1527C42—1061no—
1528C42—1061no—
1529C42—1061no—
1530C42—1061no—
1531C42—1061no—
1532C42—1061no—
1533C42—1061no—
1534C42C23×D5311yescharacteristic
1535C23—21no—
1536C23—21no—
1537C23—21no—
1538C23—42no—
1539C23—81no—
1540C23—81no—
1541C23—531no—
1542C23—1061no—
1543C23—4241no—
1544C23—4241no—
1545C23—2122no—
1546C23C2×D4×D5311yescharacteristic
1547C23C2×D4×D5311yescharacteristic
1548Q8—21no—
1549Q8—21no—
1550Q8—21no—
1551Q8—21no—
1552Q8—21no—
1553Q8—21no—
1554Q8—1061no—
1555Q8—1061no—
1556Q8—4241no—
1557Q8—4241no—
1558Q8—2121no—
1559D4—21no—
1560D4—21no—
1561D4—21no—
1562D4—21no—
1563D4—41no—
1564D4—42no—
1565D4—42no—
1566D4—42no—
1567D4—42no—
1568D4—81no—
1569D4—1061no—
1570D4—1061no—
1571D4—4241no—
1572D4—4241no—
1573D4—4241no—
1574D4—2121no—
1575D4—2121no—
1576D4—2122no—
1577D4—2122no—
1578D4C2×#1171994712yes—
1579D4C2×#1171994712yes—
1580C2×C4—21no—
1581C2×C4—21no—
1582C2×C4—21no—
1583C2×C4—21no—
1584C2×C4—21no—
1585C2×C4—21no—
1586C2×C4—21no—
1587C2×C4—21no—
1588C2×C4—21no—
1589C2×C4—42no—
1590C2×C4—42no—
1591C2×C4—42no—
1592C2×C4—81no—
1593C2×C4—81no—
1594C2×C4—531no—
1595C2×C4—531no—
1596C2×C4—531no—
1597C2×C4—531no—
1598C2×C4—531no—
1599C2×C4—531no—
1600C2×C4—531no—
1601C2×C4—1061no—
1602C2×C4—1061no—
1603C2×C4—1061no—
1604C2×C4—1061no—
1605C2×C4—1061no—
1606C2×C4—1061no—
1607C2×C4—1061no—
1608C2×C4—1061no—
1609C2×C4—1061no—
1610C2×C4—4241no—
1611C2×C4—4241no—
1612C2×C4—4241no—
1613C2×C4—4241no—
1614C2×C4—4241no—
1615C2×C4—4241no—
1616C2×C4—4241no—
1617C2×C4—4241no—
1618C2×C4—4241no—
1619C2×C4—4241no—
1620C2×C4—4241no—
1621C2×C4—4241no—
1622C2×C4—2121no—
1623C2×C4—2121no—
1624C2×C4—2122no—
1625C2×C4C2×D4×D5311yescharacteristic
1626C2×C4C2×D4×D5311yescharacteristic
1627C2×C4C2×D4×D5311yescharacteristic
1628C2×C4C2×D4×D5311yescharacteristic
1629C2×C4C24×D5311yescharacteristic
1630C8—21no—
1631C8—21no—
1632C8—21no—
1633C8—1061no—
1634C8—1061no—
1635C8—1061no—
1636C8—1061no—
1637C8C2×#1171994712yes—
1638C22—21no—
1639C22—21no—
1640C22—22no—
1641C22—22no—
1642C22—21no—
1643C22—21no—
1644C22—21no—
1645C22—21no—
1646C22—41no—
1647C22—41no—
1648C22—41no—
1649C22—41no—
1650C22—41no—
1651C22—41no—
1652C22—41no—
1653C22—162no—
1654C22—8482no—
1655C22—1061no—
1656C22—1061no—
1657C22—1061no—
1658C22—2121no—
1659C22—2121no—
1660C22—2121no—
1661C22C22×D4×D5311yescharacteristic
1662C4—21no—
1663C4—21no—
1664C4—21no—
1665C4—21no—
1666C4—41no—
1667C4—41no—
1668C4—41no—
1669C4—41no—
1670C4—41no—
1671C4—1061no—
1672C4—1061no—
1673C4—1061no—
1674C4—1061no—
1675C4—1061no—
1676C4—1061no—
1677C4—1061no—
1678C4—2121no—
1679C4—2121no—
1680C4—2121no—
1681C4—2121no—
1682C4—2121no—
1683C4—2121no—
1684C4—2121no—
1685C4C22×#1171994711yescharacteristic
1686C4#1681145811yescharacteristic
1687C2—41no—
1688C2—41no—
1689C2—42no—
1690C2—42no—
1691C2—81no—
1692C2—4241no—
1693C2—2121no—
1694C2D4×#1171994711yescharacteristic
1695C2#2028948711yescharacteristic
1696C2#2028948811yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3267C2
socleC22×C53C23×D4
hypercenter#3267D53
hypocenterC53#61501
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. #20288784C2semidirect
2. #20288768C2semidirect
3. #20287791C2semidirect
4. #20287674C2semidirect
5. #20287368C2semidirect
6. #20287359C2semidirect
7. #20287285C2semidirect
8. #20287266C2semidirect
9. #20287262C2semidirect
10. #20286632C2semidirect
11. #20286625C2semidirect
12. #20286565C2semidirect
13. #20286558C2semidirect
14. #20286554C2semidirect
15. #20286543C2semidirect
16. #20286320C2semidirect
17. #20286240C2semidirect
18. #20285384C2semidirect
19. #20285380C2semidirect
20. #20285278C2semidirect
21. #20284926C2semidirect
22. #20284922C2semidirect
23. #20284900C2semidirect
24. #20284898C2semidirect
25. #20284825C2semidirect
26. #20284817C2semidirect
27. #20283685C2semidirect
28. #20283548C2semidirect
29. #20283544C2semidirect
30. #135×Dic53C2semidirect
31. C53×#3267C2semidirect
33. #16811347C22semidirect
34. #16811344C22semidirect
35. #16811343C22semidirect
36. #16811342C22semidirect
37. #16811332C22semidirect
38. #16811330C22semidirect
54. #16811261C22semidirect
57. #16811234C22semidirect
58. #16811233C22semidirect
63. #16811159C22semidirect
64. #16811154C22semidirect
72. #16811098C22semidirect
73. #16811095C22semidirect
74. #41×Dic53C22semidirect
75. #41×Dic53C22semidirect
76. #16811032C22semidirect
77. #16811030C22semidirect
78. #16811023C22semidirect
79. #16811016C22semidirect
81. #16810979C22semidirect
82. #16810979C22semidirect
83. #16810977C22semidirect
84. #16810976C22semidirect
85. #16810973C22semidirect
86. #16810972C22semidirect
87. #16810965C22semidirect
88. #16810962C22semidirect
89. #16810961C22semidirect
90. #16810961C22semidirect
91. #16810957C22semidirect
92. #16810956C22semidirect
93. #16810954C22semidirect
94. #16810952C22semidirect
96. #16810948C22semidirect
98. #16810944C22semidirect
99. #16810932C22semidirect
100. #16810931C22semidirect
101. #16810928C22semidirect
102. #16810928C22semidirect
103. #16810925C22semidirect
104. #16810925C22semidirect
105. #16810923C22semidirect
106. #16810921C22semidirect
107. #16810914C22semidirect
108. #16810911C22semidirect
109. #16810903C22semidirect
110. #16810901C22semidirect
111. #16810878C22semidirect
114. #16810862C22semidirect
115. #16810862C22semidirect
116. #16810861C22semidirect
119. #16810852C22semidirect
121. #16810847C22semidirect
122. #16810843C22semidirect
128. #16810831C22semidirect
129. #16810830C22semidirect
130. #16810826C22semidirect
132. #16810785C22semidirect
135. #16810772C22semidirect
139. #16810751C22semidirect
140. #16810747C22semidirect
144. #16810730C22semidirect
145. #16810727C22semidirect
146. #16810726C22semidirect
147. #16810725C22semidirect
148. #16810724C22semidirect
149. #16810724C22semidirect
150. #16810724C22semidirect
151. #16810720C22semidirect
152. Q16×Dic53C22semidirect
153. Q16×Dic53C22semidirect
154. #16810715C22semidirect
155. SD16×Dic53C22semidirect
156. SD16×Dic53C22semidirect
157. SD16×Dic53C22semidirect
158. SD16×Dic53C22semidirect
159. SD16×Dic53C22semidirect
160. SD16×Dic53C22semidirect
161. #16810710C22semidirect
162. C4×#11719923C22semidirect
169. #16810694C22semidirect
170. D4×#88322C22semidirect
172. #16810686C22semidirect
173. #16810683C22semidirect
174. #16810681C22semidirect
175. #16810677C22semidirect
176. #16810665C22semidirect
177. #16810662C22semidirect
178. #16810661C22semidirect
180. #16810619C22semidirect
181. #16810619C22semidirect
183. C2×#13133138C22semidirect
184. #102×D53C22semidirect
185. #16810581C22semidirect
186. #16810580C22semidirect
187. C2×C8×Dic53C22semidirect
191. C53×#546C22semidirect
192. C53×#497C22semidirect
193. C53×#470C22semidirect
194. C53×#465C22semidirect
196. C53×#461C22semidirect
198. C53×#452C22semidirect
199. C53×#450C22semidirect
202. C53×#435C22semidirect
856. #3267D53semidirect
906. #546C2×D53semidirect
932. #497C2×D53semidirect
965. #470C2×D53semidirect
975. #465C2×D53semidirect
987. #461C2×D53semidirect
993. #452C2×D53semidirect
995. #450C2×D53semidirect
1032. #435C2×D53semidirect
1051. C53#61501semidirect

Maximal subgroups

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

subgroupindex
#202887842
#202887682
#202877912
#202876742
#202873682
#202873592
#202872852
#202872662
#202872622
#202866322
#202866252
#202865652
#202865582
#202865542
#202865432
#202863202
#202862402
#202853842
#202853802
#202852782
#202849262
#202849222
#202849002
#202848982
#202848252
#202848172
#202836852
#202835482
#202835442
#135×Dic532
C53×#32672
#6150153