Finite Group Databasebeta

← #28265481

Subgroups — #28265481

Order 13568.

1932 conjugacy classes of subgroups.

The subgroup lattice has 1784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288605C211yesmaximal, characteristic, complemented
2#20288568C211yesmaximal, characteristic, complemented
3#20287804C211yesmaximal, characteristic, complemented
4#20287802C211yesmaximal, characteristic, complemented
5#20287789C211yesmaximal, characteristic, complemented
6#20287784C211yesmaximal, characteristic, complemented
7#20287781C211yesmaximal, characteristic, complemented
8#20287780C211yesmaximal, characteristic, complemented
9#20287780C211yesmaximal, characteristic, complemented
10#20287759C211yesmaximal, characteristic, complemented
11#20287752C211yesmaximal, characteristic, complemented
12#20287736C211yesmaximal, characteristic, complemented
13#20287735C211yesmaximal, characteristic, complemented
14#20287725C211yesmaximal, characteristic, complemented
15#20287722C211yesmaximal, characteristic, complemented
16#20287710C211yesmaximal, characteristic, complemented
17#20287708C211yesmaximal, characteristic, complemented
18#20285197C211yesmaximal, characteristic, complemented
19#20285190C211yesmaximal, characteristic, complemented
20#20285178C211yesmaximal, characteristic, complemented
21#20284262C211yesmaximal, characteristic, complemented
22#20284257C211yesmaximal, characteristic, complemented
23#20284234C211yesmaximal, characteristic, complemented
24#20284216C211yesmaximal, characteristic, complemented
25#20284173C211yesmaximal, characteristic, complemented
26#463×D53C211yesmaximal, characteristic, complemented
27#20283660C211yesmaximal, characteristic, complemented
28#20283553C211yesmaximal, characteristic, complemented
29#20283546C211yesmaximal, characteristic, complemented
30#20283520C211yesmaximal, characteristic, complemented
31C53×#3402C211yesmaximal, characteristic, complemented
32C2×#13133249C2211yescharacteristic
33C2×#13133249C2211yescharacteristic
34C2×#13133244C2211yescharacteristic
35C2×#13133244C2211yescharacteristic
36C2×#13133244C2211yescharacteristic
37C2×#13133240C2211yescharacteristic
38C2×#13133240C2211yescharacteristic
39C2×SD16×D53C2211yescharacteristic
40C2×D8×D53C2211yescharacteristic
41#16811358C2211yescharacteristic, complemented
42#16811358C2211yescharacteristic, complemented
43#16811358C2211yescharacteristic, complemented
44#16811358C2211yescharacteristic, complemented
45#16811356C2211yescharacteristic, complemented
46#16811355C2211yescharacteristic, complemented
47#16811355C2211yescharacteristic, complemented
48#16811355C2211yescharacteristic, complemented
49#16811347C2211yescharacteristic, complemented
50#16811347C2211yescharacteristic, complemented
51#16811345C2211yescharacteristic, complemented
52#16811342C2211yescharacteristic, complemented
53#16811336—21no—
54#16811324—21no—
55#16811324—21no—
56#16811300—21no—
57#16811298—21no—
58#16811298—21no—
59#16811297—21no—
60#16811295C2211yescharacteristic, complemented
61#16811294C2211yescharacteristic, complemented
62#16811275—21no—
63#16811243—21no—
64#16811239—21no—
65#16811212—21no—
66#16811212—21no—
67#16811198C2211yescharacteristic
68#16811191C2211yescharacteristic
69#16811191C2211yescharacteristic
70#16811191C2211yescharacteristic
71#16811177C2211yescharacteristic
72#16811174C2211yescharacteristic
73#16811156—21no—
74#16811151—21no—
75#124×D53C2211yescharacteristic
76#16811136—21no—
77#16811135—21no—
78#16811105C2211yescharacteristic
79#16811105C2211yescharacteristic
80#16811099C2211yescharacteristic
81#16811095C2211yescharacteristic
82C4×#11719949C2211yescharacteristic
83C4×D4×D53C2211yescharacteristic
84#16811016C2211yescharacteristic, complemented
85#16811015C2211yescharacteristic, complemented
86#16811013C2211yescharacteristic
87#16811013C2211yescharacteristic
88#16811013C2211yescharacteristic, complemented
89#16811012C2211yescharacteristic, complemented
90#16811012C2211yescharacteristic, complemented
91#16811009C2211yescharacteristic
92#16811009C2211yescharacteristic
93#16811009C2211yescharacteristic, complemented
94#16811008C2211yescharacteristic
95#16811008C2211yescharacteristic, complemented
96#16811008C2211yescharacteristic, complemented
97#16811008C2211yescharacteristic, complemented
98#16811005C2211yescharacteristic, complemented
99#16811004C2211yescharacteristic, complemented
100#16811004C2211yescharacteristic, complemented
101#16811000C2211yescharacteristic
102#16810998C2211yescharacteristic
103#16810997C2211yescharacteristic, complemented
104#16810994C2211yescharacteristic, complemented
105#16810848C2211yescharacteristic, complemented
106#16810847C2211yescharacteristic, complemented
107#16810847C2211yescharacteristic, complemented
108#16810847C2211yescharacteristic, complemented
109#16810847C2211yescharacteristic, complemented
110#16810847C2211yescharacteristic, complemented
111#16810845C2211yescharacteristic, complemented
112#16810842C2211yescharacteristic, complemented
113#16810841C2211yescharacteristic
114#16810841C2211yescharacteristic
115#16810841C2211yescharacteristic, complemented
116#16810841C2211yescharacteristic, complemented
117#16810841C2211yescharacteristic, complemented
118#16810841C2211yescharacteristic, complemented
119#16810840C2211yescharacteristic
120#16810840C2211yescharacteristic
121#16810839C2211yescharacteristic
122#16810839C2211yescharacteristic, complemented
123#16810838C2211yescharacteristic
124#16810837C2211yescharacteristic
125#16810836C2211yescharacteristic
126#16810835C2211yescharacteristic
127#16810835C2211yescharacteristic
128#16810835C2211yescharacteristic, complemented
129#16810831C2211yescharacteristic, complemented
130#16810827C2211yescharacteristic, complemented
131#16810825C2211yescharacteristic, complemented
132#16810825C2211yescharacteristic, complemented
133#16810824C2211yescharacteristic, complemented
134#16810823C2211yescharacteristic, complemented
135#16810823C2211yescharacteristic, complemented
136#16810823C2211yescharacteristic, complemented
137#16810822C2211yescharacteristic, complemented
138#16810821C2211yescharacteristic, complemented
139#16810821C2211yescharacteristic, complemented
140#16810819C2211yescharacteristic
141#16810819C2211yescharacteristic, complemented
142#16810819C2211yescharacteristic, complemented
143#16810818C2211yescharacteristic
144#16810817C2211yescharacteristic
145#16810817C2211yescharacteristic, complemented
146#16810816C2211yescharacteristic
147#16810754C2211yescharacteristic, complemented
148#16810752C2211yescharacteristic, complemented
149#16810752C2211yescharacteristic, complemented
150#16810751C2211yescharacteristic, complemented
151#16810751C2211yescharacteristic, complemented
152C8×Dic106C2211yescharacteristic, complemented
153#16810747C2211yescharacteristic, complemented
154#16810736C2211yescharacteristic, complemented
155#16810736C2211yescharacteristic, complemented
156#16810733C2211yescharacteristic, complemented
157#16810732C2211yescharacteristic, complemented
158#16810730C2211yescharacteristic, complemented
159#16810728C2211yescharacteristic, complemented
160#16810726C2211yescharacteristic, complemented
161#16810722C2211yescharacteristic, complemented
162#16810721C2211yescharacteristic, complemented
163#16810721C2211yescharacteristic, complemented
164#16810715C2211yescharacteristic, complemented
165C4×#11719913C2211yescharacteristic, complemented
166SD16×Dic53C2211yescharacteristic, complemented
167SD16×Dic53C2211yescharacteristic, complemented
168C4×#11719924C2211yescharacteristic, complemented
169#16810708C2211yescharacteristic, complemented
170#16810708C2211yescharacteristic, complemented
171#16810705C2211yescharacteristic, complemented
172#16810705C2211yescharacteristic, complemented
173C4×#11719922C2211yescharacteristic, complemented
174#16810703C2211yescharacteristic, complemented
175#16810664C2211yescharacteristic
176#16810648C2211yescharacteristic
177#16810648C2211yescharacteristic
178C4⋊C8×D53C2211yescharacteristic
179#16810626C2211yescharacteristic
180#16810623C2211yescharacteristic
181#16810618C2211yescharacteristic
182#16810618C2211yescharacteristic
183#103×D53C2211yescharacteristic
184#102×D53C2211yescharacteristic
185#16810580C2211yescharacteristic
186#16810577C2211yescharacteristic
187#16810575C2211yescharacteristic
188C53×#556C2211yescharacteristic, complemented
189C53×#556C2211yescharacteristic, complemented
190C53×#497C2211yescharacteristic, complemented
191C53×#497C2211yescharacteristic, complemented
192C53×#495C2211yescharacteristic
193C53×#464C2211yescharacteristic, complemented
194C53×#464C2211yescharacteristic, complemented
195C53×#463C2211yescharacteristic
196C53×#463C2211yescharacteristic
197C53×#462C2211yescharacteristic, complemented
198C53×#462C2211yescharacteristic, complemented
199C53×#446C2211yescharacteristic, complemented
200C53×#440C2211yescharacteristic, complemented
201C53×#440C2211yescharacteristic, complemented
202C4×Q16×C53C2211yescharacteristic, complemented
203C2×#11719949—21no—
204C2×#11719949C2311yescharacteristic
205C2×#11719949C2311yescharacteristic
206C2×#11719949C2311yescharacteristic
207C2×#11719945—21no—
208C2×Q8×D53C2311yescharacteristic
209C2×D4×D53C2311yescharacteristic
210C2×D4×D53C2311yescharacteristic
211C22×C4×D53—21no—
212#13133249—24no—
213#13133249—42no—
214#13133244—24no—
215#13133244—24no—
216#13133244—42no—
217#13133240—42no—
218#13133240—42no—
219C2×#11719925C2311yescharacteristic
220C2×#11719925C2311yescharacteristic
221C2×#11719913C2311yescharacteristic
222C2×#11719913C2311yescharacteristic
223C2×#11719913C2311yescharacteristic
224C2×#11719923C2311yescharacteristic
225C2×#11719924C2311yescharacteristic
226C2×#11719924C2311yescharacteristic
227C2×#11719924C2311yescharacteristic
228C2×#11719924C2311yescharacteristic
229C2×#11719924C2311yescharacteristic
230C2×#11719924C2311yescharacteristic
231C2×#11719924C2311yescharacteristic
232C2×#11719924C2311yescharacteristic
233C2×#11719924C2311yescharacteristic
234C2×#11719924C2311yescharacteristic
235SD16×D53—42no—
236C2×D424C2311yescharacteristic
237C2×D424C2311yescharacteristic
238C2×D424C2311yescharacteristic
239C2×D424C2311yescharacteristic
240C2×D424C2311yescharacteristic
241C2×D424C2311yescharacteristic
242C2×#11719922C2311yescharacteristic
243C2×#11719922C2311yescharacteristic
244C2×#11719922C2311yescharacteristic
245C2×#11719922C2311yescharacteristic
246C2×#11719922C2311yescharacteristic
247D8×D53—42no—
248C2×#11719912C2311yescharacteristic
249C2×#11719912C2311yescharacteristic
250C2×C8×D53C2311yescharacteristic
251C2×C8×D53C2311yescharacteristic
252#13133216D411yescharacteristic
253#13133215D411yescharacteristic
254#13133215C2311yescharacteristic
255#13133214C2311yescharacteristic
256#13133214C2311yescharacteristic
257#13133214C2311yescharacteristic
258#13133214C2311yescharacteristic
259#13133213C2311yescharacteristic
260#13133213C2311yescharacteristic
261#13133213C2311yescharacteristic
262#13133212—21no—
263#13133212—21no—
264#13133212—21no—
265#13133212—21no—
266#13133212—21no—
267#13133211—21no—
268#13133210—21no—
269#13133210—21no—
270#13133207D411yescharacteristic
271#13133207D411yescharacteristic
272#13133206—21no—
273#13133206C2311yescharacteristic
274#13133206C2311yescharacteristic
275#13133206C2311yescharacteristic
276#13133206C2311yescharacteristic
277#13133206C2311yescharacteristic
278#13133206C2311yescharacteristic
279#13133206C2311yescharacteristic
280#13133205—21no—
281#13133205—21no—
282#13133205—21no—
283#13133205C2311yescharacteristic
284#13133205C2311yescharacteristic
285#13133204C2311yescharacteristic
286#13133203—21no—
287#13133203—21no—
288#13133203—21no—
289#13133203—21no—
290#13133203—21no—
291#13133203—21no—
292#13133202—21no—
293#13133202—21no—
294#13133202—21no—
295#13133202—21no—
296#13133202—21no—
297#13133202—21no—
298#13133202—21no—
299#13133202—21no—
300#13133202—21no—
301#13133202—21no—
302#13133201—21no—
303#13133201—21no—
304#13133201—21no—
305#13133200—21no—
306#13133199—21no—
307#13133199—21no—
308#13133199—21no—
309#13133199—21no—
310#13133197—21no—
311#13133197—21no—
312#13133197D411yescharacteristic
313#13133195—21no—
314#13133195—21no—
315#13133195—21no—
316#13133195D411yescharacteristic
317#13133195D411yescharacteristic
318#13133194—21no—
319#13133193D411yescharacteristic
320#13133192—21no—
321#13133192—21no—
322#13133192—21no—
323#13133192—21no—
324#13133192—21no—
325#13133191—21no—
326#13133190—21no—
327#13133190—21no—
328#13133190—21no—
329#13133190—21no—
330#13133190—21no—
331#13133190—21no—
332#13133190—21no—
333#13133190—21no—
334#13133187—21no—
335#13133187—21no—
336#13133187—21no—
337#13133187—21no—
338#13133187—21no—
339#13133187—21no—
340Q8×Dic53C2311yescharacteristic
341Q8×Dic53C2311yescharacteristic
342Q8×Dic53C2311yescharacteristic
343Q8×Dic53C2311yescharacteristic
344C4×Dic106—21no—
345C4×Dic106C2311yescharacteristic
346C4×Dic106C2311yescharacteristic
347C4×Dic106C2311yescharacteristic
348C4×Dic106C2311yescharacteristic
349#13133182—21no—
350#13133182C2311yescharacteristic
351C4×D212—21no—
352C4×D212—21no—
353C4×D212—21no—
354C4×D212—21no—
355C4×D212—21no—
356C4×D212—21no—
357C4×D212C2311yescharacteristic
358C4×D212C2311yescharacteristic
359C4×D212C2311yescharacteristic
360C4×D212C2311yescharacteristic
361C4×D212C2311yescharacteristic
362D4×Dic53C2311yescharacteristic
363D4×Dic53C2311yescharacteristic
364#13133179—21no—
365#13133179—21no—
366#13133179—21no—
367#13133179—21no—
368#13133179—21no—
369#13133179—21no—
370#13133179C2311yescharacteristic
371#13133179C2311yescharacteristic
372#13133179C2311yescharacteristic
373#13133179C2311yescharacteristic
374#13133179C2311yescharacteristic
375C4×C22⋊D53—21no—
376C4×C22⋊D53—21no—
377C4×C22⋊D53—21no—
378#13133177—21no—
379#13133177—21no—
380#13133177—21no—
381#13133177—21no—
382#13133177—21no—
383#13133175—21no—
384#13133175—21no—
385#13133175—21no—
386#13133175—21no—
387#13133175C2311yescharacteristic
388#13133174—21no—
389#13133174—21no—
390#13133174—21no—
391#13133174—21no—
392#13133174C2311yescharacteristic
393#13133174C2311yescharacteristic
394#13133173—21no—
395C4⋊C4×D53—21no—
396C4⋊C4×D53—21no—
397C4⋊C4×D53C2311yescharacteristic
398C2×#11719921—21no—
399C22⋊C4×D53—21no—
400C22⋊C4×D53—21no—
401C22⋊C4×D53—21no—
402C22⋊C4×D53—21no—
403C42×D53—21no—
404C42×D53C2311yescharacteristic
405#13133150C2311yescharacteristic
406#13133149C2311yescharacteristic
407#13133148C2311yescharacteristic
408C4⋊#88322C2311yescharacteristic
409C4⋊#88322C2311yescharacteristic
410C4⋊#88322C2311yescharacteristic
411#13133146C2311yescharacteristic
412#13133146C2311yescharacteristic
413#13133146C2311yescharacteristic
414#13133146C2311yescharacteristic
415#13133146C2311yescharacteristic
416#13133146C2311yescharacteristic
417#13133142C2311yescharacteristic
418#13133141C2311yescharacteristic
419#13133141C2311yescharacteristic
420#13133141C2311yescharacteristic
421#13133141C2311yescharacteristic
422#13133140C2311yescharacteristic
423#13133139C2311yescharacteristic
424#13133139C2311yescharacteristic
425#13133139C2311yescharacteristic
426#13133139C2311yescharacteristic
427#13133139C2311yescharacteristic
428#13133138C2311yescharacteristic
429#13133138C2311yescharacteristic
430#13133137C2311yescharacteristic
431#13133137C2311yescharacteristic
432#13133137C2311yescharacteristic
433#13133137C2311yescharacteristic
434#13133137C2311yescharacteristic
435#13133128C2311yescharacteristic
436#13133128C2311yescharacteristic
437#13133127C2311yescharacteristic
438#13133127C2311yescharacteristic
439C4×#88322C2311yescharacteristic
440C8×Dic53C2311yescharacteristic
441C8×Dic53C2311yescharacteristic
442C8×Dic53C2311yescharacteristic
443C8×Dic53C2311yescharacteristic
444C2×Q16×C53C2311yescharacteristic
445C2×Q16×C53C2311yescharacteristic
446C2×Q16×C53C2311yescharacteristic
447C2×Q16×C53C2311yescharacteristic
448C2×SD16×C53C2311yescharacteristic
449C2×SD16×C53C2311yescharacteristic
450C2×SD16×C53C2311yescharacteristic
451C2×SD16×C53C2311yescharacteristic
452C2×D8×C53C2311yescharacteristic
453C4⋊Q8×C53C2311yescharacteristic
454C4⋊Q8×C53C2311yescharacteristic
455#126×C53—21no—
456#126×C53—21no—
457#126×C53—21no—
458#126×C53—21no—
459#124×C53C2311yescharacteristic
460#124×C53C2311yescharacteristic
461#124×C53C2311yescharacteristic
462#124×C53C2311yescharacteristic
463C22⋊Q8×C53—21no—
464C22⋊Q8×C53—21no—
465C4×Q8×C53C2311yescharacteristic
466C4×Q8×C53C2311yescharacteristic
467C4×Q8×C53C2311yescharacteristic
468C4×Q8×C53C2311yescharacteristic
469C4×Q8×C53C2311yescharacteristic
470C4×D4×C53C2311yescharacteristic
471C4×D4×C53C2311yescharacteristic
472#117×C53—21no—
473#117×C53—21no—
474#107×C53C2311yescharacteristic
475C4⋊C8×C53C2311yescharacteristic
476C4⋊C8×C53C2311yescharacteristic
477C4⋊C8×C53C2311yescharacteristic
478#103×C53C2311yescharacteristic
479#103×C53C2311yescharacteristic
480#103×C53C2311yescharacteristic
481#103×C53C2311yescharacteristic
482#102×C53C2311yescharacteristic
483#102×C53C2311yescharacteristic
484#97×C53C2311yescharacteristic
485#97×C53C2311yescharacteristic
486C4×C8×C53C2311yescharacteristic
487C23×D53—21no—
488C23×D53—21no—
489C2×Q8×C53C2×D411yescharacteristic
490C2×Q8×C53C2411yescharacteristic
491C2×Q8×C53C2411yescharacteristic
492C2×Q8×C53C2411yescharacteristic
493C2×Q8×C53C2411yescharacteristic
494C2×D4×C53C2411yescharacteristic
495C2×D4×C53C2411yescharacteristic
496C22×C4×C53—21no—
497C22×C4×C53—21no—
498C2×C22⋊D53—21no—
499C2×C22⋊D53—21no—
500C2×C22⋊D53—21no—
501C2×C22⋊D53—21no—
502C2×C22⋊D53—21no—
503C2×C22⋊D53—21no—
504C2×C22⋊D53—21no—
505C2×C22⋊D53—21no—
506C22×Dic53—21no—
507C22×Dic53—21no—
508#11719949—22no—
509#11719949—22no—
510#11719949—22no—
511#11719949—22no—
512#11719949—22no—
513#11719949—22no—
514#11719949—82no—
515Q8×D53—22no—
516Q8×D53—22no—
517D4×D53—22no—
518D4×D53—22no—
519D4×D53—22no—
520D4×D53—22no—
521#11719945—82no—
522C2×D212—21no—
523C2×D212—21no—
524C2×D212—21no—
525C2×D212—21no—
526C2×D212—21no—
527C2×D212—21no—
528C2×D212—21no—
529C2×D212—21no—
530C2×D212—21no—
531C2×D212—21no—
532C2×D212—21no—
533C2×D212C2411yescharacteristic
534C2×D212C2411yescharacteristic
535C2×D212C2411yescharacteristic
536C2×D212C2411yescharacteristic
537C2×D212C2411yescharacteristic
538C2×C4×D53—21no—
539C2×C4×D53—21no—
540C2×C4×D53—21no—
541C2×C4×D53—21no—
542C2×C4×D53—21no—
543C2×C4×D53—21no—
544C2×C4×D53—21no—
545C2×C4×D53—21no—
546C2×C4×D53—21no—
547C2×C4×D53—21no—
548C2×C4×D53—21no—
549C2×C4×D53—21no—
550C2×C4×D53—21no—
551C2×C4×D53—21no—
552C2×C4×D53—21no—
553C2×C4×D53—82no—
554C2×C4×D53C2×D411yescharacteristic
555C2×C4×D53C2×D411yescharacteristic
556C2×C4×D53C2411yescharacteristic
557C2×Dic106—21no—
558C2×Dic106C2×D411yescharacteristic
559C2×Dic106C2×D411yescharacteristic
560C2×Dic106C2×D411yescharacteristic
561C2×Dic106C2411yescharacteristic
562Q16×C53—22no—
563Q16×C53—41no—
564Q16×C53—41no—
565Q16×C53—41no—
566SD16×C53—22no—
567SD16×C53—22no—
568SD16×C53—41no—
569SD16×C53—41no—
570D8×C53—41no—
571C2×C8×C53C2411yescharacteristic
572C2×C8×C53C2411yescharacteristic
573C2×C8×C53C2411yescharacteristic
574C2×C8×C53C2411yescharacteristic
575C4⋊C4×C53—21no—
576C4⋊C4×C53—21no—
577C4⋊C4×C53—21no—
578C4⋊C4×C53—21no—
579C4⋊C4×C53—21no—
580C4⋊C4×C53—21no—
581C4⋊C4×C53—21no—
582C4⋊C4×C53—21no—
583C4⋊C4×C53C2×D411yescharacteristic
584C4⋊C4×C53C2×D411yescharacteristic
585C4⋊C4×C53C2×D411yescharacteristic
586C4⋊C4×C53C2411yescharacteristic
587C4⋊C4×C53C2411yescharacteristic
588C22⋊C4×C53—21no—
589C22⋊C4×C53—21no—
590C22⋊C4×C53—21no—
591C22⋊C4×C53—21no—
592C22⋊C4×C53—21no—
593C22⋊C4×C53—21no—
594C22⋊C4×C53—21no—
595C22⋊C4×C53—21no—
596C22⋊C4×C53—21no—
597C22⋊C4×C53—21no—
598C42×C53—21no—
599C42×C53—21no—
600C42×C53—21no—
601C42×C53—21no—
602C42×C53C2411yescharacteristic
603C42×C53C2411yescharacteristic
604C42×C53C2411yescharacteristic
605C22⋊Dic53—21no—
606C22⋊Dic53—21no—
607C22⋊Dic53—21no—
608C22⋊Dic53—21no—
609#11719925—22no—
610#11719925—41no—
611#11719924—22no—
612#11719924—22no—
613#11719924—22no—
614#11719924—41no—
615#11719924—41no—
616#11719924—41no—
617#11719924—41no—
618#11719924—41no—
619#11719924—41no—
620#11719924—41no—
621#11719923—41no—
622#11719922—22no—
623#11719922—22no—
624#11719922—41no—
625#11719922—41no—
626#11719922—41no—
627#11719921—21no—
628#11719921—21no—
629#11719921—21no—
630#11719921—21no—
631#11719921—21no—
632#11719921—21no—
633#11719921—21no—
634#11719921—21no—
635#11719921—21no—
636#11719921—21no—
637#11719921—21no—
638#11719921—21no—
639#11719921—21no—
640#11719921—21no—
641#11719921—21no—
642#11719921—21no—
643#11719921—21no—
644#11719921—21no—
645#11719921—21no—
646#11719921—21no—
647#11719921—21no—
648#11719921—21no—
649#11719921—21no—
650#11719921—21no—
651#11719921—21no—
652#11719921—21no—
653#11719921—21no—
654#11719921—21no—
655#11719921—21no—
656#11719921C2×D411yescharacteristic
657#11719921C2×D411yescharacteristic
658#11719921C2×D411yescharacteristic
659#11719921C2×D411yescharacteristic
660C4⋊Dic53—21no—
661C4⋊Dic53—21no—
662C4⋊Dic53—21no—
663C4⋊Dic53—21no—
664C4⋊Dic53C2×D411yescharacteristic
665C4⋊Dic53C2×D411yescharacteristic
666C4⋊Dic53C2×D411yescharacteristic
667C4⋊Dic53C2411yescharacteristic
668C4⋊Dic53C2411yescharacteristic
669#11719919—21no—
670#11719919—21no—
671#11719919—21no—
672#11719919—21no—
673#11719919—21no—
674#11719919C2×D411yescharacteristic
675#11719919C2×D411yescharacteristic
676#11719919C2×D411yescharacteristic
677#11719919C2×D411yescharacteristic
678#11719919C2×D411yescharacteristic
679#11719919C2×D411yescharacteristic
680#11719919C2×D411yescharacteristic
681#11719919C2×D411yescharacteristic
682#11719919C2×D411yescharacteristic
683#11719919C2×D411yescharacteristic
684C4×Dic53—21no—
685C4×Dic53—21no—
686C4×Dic53—21no—
687C4×Dic53—21no—
688C4×Dic53—21no—
689C4×Dic53—21no—
690C4×Dic53—21no—
691C4×Dic53C2×D411yescharacteristic
692C4×Dic53C2×D411yescharacteristic
693C4×Dic53C2411yescharacteristic
694C4×Dic53C2411yescharacteristic
695C4×Dic53C2411yescharacteristic
696C2×#88322C2411yescharacteristic
697C2×#88322C2411yescharacteristic
698C2×#88322C2411yescharacteristic
699C2×#88322C2411yescharacteristic
700D424—22no—
701D424—22no—
702D424—41no—
703D424—41no—
704D424—41no—
705D424—41no—
706#11719913—22no—
707#11719913—41no—
708#11719913—41no—
709#11719912—22no—
710#11719912#4114yescomplemented
711C8×D53—22no—
712C8×D53—22no—
713C23×C53—21no—
714C23×C53—21no—
715C22×D53—21no—
716C22×D53—21no—
717C22×D53—21no—
718C22×D53—21no—
719C22×D53—21no—
720C22×D53—42no—
721C22×D53—42no—
722C22×D53—81no—
723C22×D53—81no—
724C22×D53—81no—
725C22×D53—81no—
726C22×D53C22×D411yescharacteristic
727Q8×C53—21no—
728Q8×C53—21no—
729Q8×C53—21no—
730Q8×C53—21no—
731Q8×C53—21no—
732Q8×C53—21no—
733Q8×C53—21no—
734Q8×C53—21no—
735Q8×C53—41no—
736D4×C53—21no—
737D4×C53—21no—
738D4×C53—21no—
739D4×C53—21no—
740C2×C4×C53—21no—
741C2×C4×C53—21no—
742C2×C4×C53—21no—
743C2×C4×C53—21no—
744C2×C4×C53—21no—
745C2×C4×C53—21no—
746C2×C4×C53—42no—
747C2×C4×C53—81no—
748C2×C4×C53C22×D411yescharacteristic
749C2×C4×C53C22×D411yescharacteristic
750C2×C4×C53C22×D411yescharacteristic
751C2×C4×C53C22×D411yescharacteristic
752C2×C4×C53C22×D411yescharacteristic
753C2×C4×C53C22×D411yescharacteristic
754C2×C4×C53C2511yescharacteristic
755C22⋊D53—42no—
756C22⋊D53—42no—
757C22⋊D53—81no—
758C22⋊D53—81no—
759C22⋊D53—81no—
760C22⋊D53—81no—
761C22⋊D53—81no—
762C22⋊D53—81no—
763C2×Dic53—21no—
764C2×Dic53—21no—
765C2×Dic53—21no—
766C2×Dic53—81no—
767C2×Dic53—81no—
768C2×Dic53C22×D411yescharacteristic
769C2×Dic53C22×D411yescharacteristic
770C2×Dic53C22×D411yescharacteristic
771C2×Dic53C22×D411yescharacteristic
772C2×Dic53C22×D411yescharacteristic
773C2×Dic53C22×D411yescharacteristic
774C2×Dic53C22×D411yescharacteristic
775D212—21no—
776D212—21no—
777D212—21no—
778D212—21no—
779D212—21no—
780D212—21no—
781D212—21no—
782D212—21no—
783D212—21no—
784D212—21no—
785D212—42no—
786D212—42no—
787D212—42no—
788D212—42no—
789D212—81no—
790D212—81no—
791D212—81no—
792D212—81no—
793D212—81no—
794D212—81no—
795D212—81no—
796C4×D53—41no—
797C4×D53—41no—
798C4×D53—42no—
799C4×D53—42no—
800C4×D53—42no—
801C4×D53—42no—
802C4×D53—42no—
803C4×D53—81no—
804C4×D53—81no—
805C4×D53—81no—
806C4×D53—81no—
807C4×D53—81no—
808C4×D53—81no—
809C4×D53—81no—
810C4×D53—81no—
811C4×D53—81no—
812C4×D53—81no—
813C4×D53C2×#4112yes—
814C4×D53H(5,𝔽2)12yes—
815Dic106—21no—
816Dic106—21no—
817Dic106—41no—
818Dic106—41no—
819Dic106—41no—
820Dic106—42no—
821C8×C53—21no—
822C8×C53—21no—
823C8×C53—21no—
824C8×C53C2×#4112yes—
825#88322—21no—
826#88322—21no—
827#88322—21no—
828#88322C2×#4112yes—
829#61424—531nomaximal, Sylow
830C22×C53—41no—
831C22×C53—41no—
832C22×C53—41no—
833C22×C53—41no—
834C22×C53—41no—
835C22×C53—41no—
836C22×C53C23×D411yescharacteristic
837C2×D53—21no—
838C2×D53—21no—
839C2×D53—41no—
840C2×D53—41no—
841C2×D53—41no—
842C2×D53—41no—
843C2×D53—41no—
844C2×D53—41no—
845C2×D53—41no—
846C2×D53—41no—
847C2×D53—41no—
848C2×D53—41no—
849C2×D53—41no—
850C2×D53—41no—
851C2×D53—41no—
852C2×D53—41no—
853C2×D53—41no—
854C2×D53—84no—
855C2×D53—162no—
856C2×D53#55012yes—
857C4×C53—21no—
858C4×C53—21no—
859C4×C53—21no—
860C4×C53—21no—
861C4×C53—21no—
862C4×C53—21no—
863C4×C53—41no—
864C4×C53—41no—
865C4×C53—41no—
866C4×C53—41no—
867C4×C53—41no—
868C4×C53—41no—
869C4×C53C22×#4111yescharacteristic
870C4×C53C2×H(5,𝔽2)11yescharacteristic
871Dic53—21no—
872Dic53—21no—
873Dic53—21no—
874Dic53—21no—
875Dic53—21no—
876Dic53—21no—
877Dic53—41no—
878Dic53—41no—
879Dic53—41no—
880Dic53#55012yes—
881#3510—531no—
882#3506—531no—
883#3403—531no—
884#3403—531no—
885#3402—531no—
886#3402D5311yescharacteristic, complemented
887#3401—531no—
888#3401—531no—
889#3401—531no—
890#3401—531no—
891#3399—531no—
892#3399—531no—
893#3397—531no—
894#3397—531no—
895#3396—531no—
896#3396—531no—
897#3394—531no—
898#3394—531no—
899#3155—531no—
900#3154—531no—
901#3153—531no—
902#3046—531no—
903#3045—531no—
904#3043—531no—
905#3041—531no—
906#3035—531no—
907C2×#463—531no—
908#2962—531no—
909#2947—531no—
910#2946—531no—
911C4×AGL(1,ℤ/8)—531no—
912C2×C53—81no—
913C2×C53—81no—
914C2×C53C2×#55011yescharacteristic
915C2×C53#358411yescharacteristic
916C2×C53#358511yescharacteristic
917D53—22no—
918D53—81no—
919D53—81no—
920D53—81no—
921D53—81no—
922D53—81no—
923C2×#137—531no—
924C2×#137—531no—
925C2×AGL(1,ℤ/8)—531no—
926C2×AGL(1,ℤ/8)—531no—
927C2×AGL(1,ℤ/8)—531no—
928C2×#135—531no—
929C2×#135—531no—
930C22×SD16—531no—
931C22×D8—531no—
932#559—531no—
933#559—531no—
934#559—531no—
935#559—531no—
936#559—531no—
937#559—531no—
938#559—531no—
939#559—531no—
940#556—531no—
941#556—531no—
942#556—531no—
943#556—531no—
944#556C2×D5311yescharacteristic, complemented
945#556C2×D5311yescharacteristic, complemented
946#555—1061no—
947#553—1061no—
948#553—1061no—
949#551—1061no—
950#551—1061no—
951#551—1061no—
952#551—1061no—
953#550—531no—
954#550—531no—
955#547—1061no—
956#542—1061no—
957#542—1061no—
958#538—1061no—
959#538—1061no—
960#536—531no—
961#535—531no—
962#535—531no—
963#535—531no—
964#533—531no—
965#532—531no—
966#529—1061no—
967#529—1061no—
968C2×#124—531no—
969#525—1061no—
970#525—1061no—
971#520—531no—
972#520—531no—
973#519—531no—
974#518—531no—
975C4×#41—531no—
976C2×C4×D4—531no—
977#497—531no—
978#497—531no—
979#497C2×D5311yescharacteristic, complemented
980#497C2×D5311yescharacteristic, complemented
981#496—531no—
982#496—531no—
983#496—531no—
984#496—531no—
985#496—531no—
986#496—531no—
987#496—531no—
988#496—531no—
989#495—531no—
990#495—531no—
991#495—531no—
992#495—531no—
993#495—531no—
994#495—531no—
995#495—531no—
996#495C2×D5311yescharacteristic
997#493—531no—
998#493—531no—
999#492—531no—
1000#492—531no—
1001#464—531no—
1002#464—531no—
1003#464—531no—
1004#464—531no—
1005#464—531no—
1006#464—531no—
1007#464—531no—
1008#464—531no—
1009#464C2×D5311yescharacteristic, complemented
1010#464C2×D5311yescharacteristic, complemented
1011#463—531no—
1012#463—531no—
1013#463—531no—
1014#463—531no—
1015#463—531no—
1016#463—531no—
1017#463—531no—
1018#463—531no—
1019#463—531no—
1020#463—531no—
1021#463—531no—
1022#463—531no—
1023#463—531no—
1024#463—531no—
1025#463—531no—
1026#463—531no—
1027#463C2×D5311yescharacteristic
1028#463C2×D5311yescharacteristic
1029#462—531no—
1030#462C2×D5311yescharacteristic, complemented
1031#462C2×D5311yescharacteristic, complemented
1032#461—531no—
1033#461—531no—
1034#461—531no—
1035#460—531no—
1036#460—531no—
1037#460—531no—
1038#460—531no—
1039#460—531no—
1040#460—531no—
1041#460—531no—
1042#459—531no—
1043#459—531no—
1044#459—531no—
1045#459—531no—
1046#459—531no—
1047#459—531no—
1048#459—531no—
1049#446—531no—
1050#446—531no—
1051#446—531no—
1052#446—531no—
1053#446—531no—
1054#446C2×D5311yescharacteristic, complemented
1055C8×Q8—531no—
1056C8×Q8—531no—
1057#442—531no—
1058#442—531no—
1059#442—531no—
1060#442—531no—
1061#441—531no—
1062#441—531no—
1063#440—531no—
1064#440—531no—
1065#440—531no—
1066#440—531no—
1067#440C2×D5311yescharacteristic, complemented
1068#440C2×D5311yescharacteristic, complemented
1069C4×Q16—531no—
1070C4×Q16C2×D5311yescharacteristic, complemented
1071C4×SD16—531no—
1072C4×SD16—531no—
1073C4×SD16—531no—
1074C4×SD16—531no—
1075C4×SD16—531no—
1076C4×SD16—531no—
1077C4×D8—531no—
1078C4×D8—531no—
1079C4×D8—531no—
1080C4×D8—531no—
1081#428—531no—
1082#424—531no—
1083#424—531no—
1084C2×C4⋊C8—531no—
1085#418—531no—
1086#417—531no—
1087#416—531no—
1088#416—531no—
1089C2×#103—531no—
1090C2×#102—531no—
1091#405—531no—
1092#405—531no—
1093C4×M16—531no—
1094C53#6142411yescharacteristic, complemented, Sylow
1095C2×#41—531no—
1096C2×#41—531no—
1097C2×#41—531no—
1098C2×#41—1061no—
1099C2×#41—1061no—
1100C22×Q8—531no—
1101C22×D4—531no—
1102C22×D4—531no—
1103C23×C4—1061no—
1104#137—1064no—
1105#137—2122no—
1106AGL(1,ℤ/8)—1064no—
1107AGL(1,ℤ/8)—1064no—
1108AGL(1,ℤ/8)—2122no—
1109#135—2122no—
1110#135—2122no—
1111C2×Q16—531no—
1112C2×Q16—531no—
1113C2×Q16C22×D5311yescharacteristic
1114C2×Q16C22×D5311yescharacteristic
1115C2×Q16C22×D5311yescharacteristic
1116C2×Q16C22×D5311yescharacteristic
1117C2×SD16—531no—
1118C2×SD16—531no—
1119C2×SD16—531no—
1120C2×SD16—531no—
1121C2×SD16—531no—
1122C2×SD16—531no—
1123C2×SD16—531no—
1124C2×SD16—531no—
1125C2×SD16—531no—
1126C2×SD16—531no—
1127C2×SD16—531no—
1128C2×SD16—531no—
1129C2×SD16—531no—
1130C2×SD16—531no—
1131C2×SD16—2122no—
1132C2×SD16C22×D5311yescharacteristic
1133C2×SD16C22×D5311yescharacteristic
1134C2×SD16C22×D5311yescharacteristic
1135C2×SD16C22×D5311yescharacteristic
1136C2×D8—531no—
1137C2×D8—531no—
1138C2×D8—531no—
1139C2×D8—531no—
1140C2×D8—531no—
1141C2×D8—531no—
1142C2×D8—531no—
1143C2×D8—531no—
1144C2×D8—531no—
1145C2×D8—531no—
1146C2×D8—531no—
1147C2×D8—2122no—
1148C2×D8C22×D5311yescharacteristic
1149C2×M16—531no—
1150C2×M16—531no—
1151C22×C8—531no—
1152C22×C8—531no—
1153C4⋊Q8—531no—
1154C4⋊Q8—531no—
1155C4⋊Q8—531no—
1156C4⋊Q8C22×D5311yescharacteristic
1157C4⋊Q8C22×D5311yescharacteristic
1158#127—531no—
1159#127—531no—
1160#127—531no—
1161#127—531no—
1162#127—531no—
1163#127—531no—
1164#127—531no—
1165#126—21no—
1166#126—21no—
1167#126—21no—
1168#126—21no—
1169#126—1061no—
1170#126—1061no—
1171#126—1061no—
1172#126—1061no—
1173#126—1061no—
1174#126—1061no—
1175#126—1061no—
1176#126—1061no—
1177#125—531no—
1178#125—531no—
1179#124—531no—
1180#124—531no—
1181#124—531no—
1182#124—531no—
1183#124—531no—
1184#124—531no—
1185#124—531no—
1186#124—531no—
1187#124—531no—
1188#124—531no—
1189#124—1061no—
1190#124—1061no—
1191#124—1061no—
1192#124—1061no—
1193#124—1061no—
1194#124—1061no—
1195#124—1061no—
1196#124—1061no—
1197#124—1061no—
1198#124—1061no—
1199#124C22×D5311yescharacteristic
1200#124C22×D5311yescharacteristic
1201#124C22×D5311yescharacteristic
1202#124C22×D5311yescharacteristic
1203#123—1061no—
1204#123—1061no—
1205#123—1061no—
1206#123—1061no—
1207#123—1061no—
1208#123—1061no—
1209#123—1061no—
1210#123—1061no—
1211#123—1061no—
1212#123—1061no—
1213#123—1061no—
1214#123—1061no—
1215#123—1061no—
1216#123—1061no—
1217#123—1061no—
1218#123—1061no—
1219#123—1061no—
1220#123—1061no—
1221C22⋊Q8—21no—
1222C22⋊Q8—21no—
1223C22⋊Q8—531no—
1224C22⋊Q8—531no—
1225C22⋊Q8—531no—
1226C22⋊Q8—531no—
1227C22⋊Q8—1061no—
1228C22⋊Q8—1061no—
1229C22⋊Q8—1061no—
1230C22⋊Q8—1061no—
1231C22⋊Q8—1061no—
1232C22⋊Q8—1061no—
1233#121—1061no—
1234#121—1061no—
1235#121—1061no—
1236#121—1061no—
1237#121—1061no—
1238#121—1061no—
1239#121—1061no—
1240#121—1061no—
1241#121—1061no—
1242#121—1061no—
1243#121—1061no—
1244#121—1061no—
1245#121—1061no—
1246#121—1061no—
1247#120—1061no—
1248#120—1061no—
1249#120—1061no—
1250#120—1061no—
1251#120—1061no—
1252#120—1061no—
1253C4×Q8—531no—
1254C4×Q8—531no—
1255C4×Q8—531no—
1256C4×Q8—531no—
1257C4×Q8—531no—
1258C4×Q8—531no—
1259C4×Q8—531no—
1260C4×Q8—531no—
1261C4×Q8—531no—
1262C4×Q8—1061no—
1263C4×Q8—1061no—
1264C4×Q8C22×D5311yescharacteristic
1265C4×Q8C22×D5311yescharacteristic
1266C4×Q8C22×D5311yescharacteristic
1267C4×Q8C22×D5311yescharacteristic
1268C4×Q8C22×D5311yescharacteristic
1269C4×D4—531no—
1270C4×D4—531no—
1271C4×D4—531no—
1272C4×D4—531no—
1273C4×D4—531no—
1274C4×D4—531no—
1275C4×D4—531no—
1276C4×D4—531no—
1277C4×D4—531no—
1278C4×D4—531no—
1279C4×D4—531no—
1280C4×D4—531no—
1281C4×D4—1061no—
1282C4×D4—1061no—
1283C4×D4—1061no—
1284C4×D4—1061no—
1285C4×D4—1061no—
1286C4×D4—1061no—
1287C4×D4—1061no—
1288C4×D4—1061no—
1289C4×D4—1061no—
1290C4×D4—1061no—
1291C4×D4—1061no—
1292C4×D4—1061no—
1293C4×D4—1061no—
1294C4×D4—1061no—
1295C4×D4—1061no—
1296C4×D4—1061no—
1297C4×D4—1061no—
1298C4×D4—1061no—
1299C4×D4—1061no—
1300C4×D4—1061no—
1301C4×D4C22×D5311yescharacteristic
1302C4×D4C22×D5311yescharacteristic
1303#117—21no—
1304#117—21no—
1305#117—531no—
1306#117—531no—
1307#117—531no—
1308#117—1061no—
1309#117—1061no—
1310#117—1061no—
1311#117—1061no—
1312#117—1061no—
1313#117—1061no—
1314#117—1061no—
1315#117—1061no—
1316#117—1061no—
1317C2×C4⋊C4—531no—
1318C2×C4⋊C4—1061no—
1319C2×C4⋊C4—1061no—
1320C2×C22⋊C4—1061no—
1321C2×C22⋊C4—1061no—
1322C2×C22⋊C4—1061no—
1323C2×C22⋊C4—1061no—
1324C2×C22⋊C4—1061no—
1325C2×C42—531no—
1326C2×C42—1061no—
1327#107—531no—
1328#107C22×D5311yescharacteristic
1329#106—531no—
1330#106—531no—
1331C4⋊C8—531no—
1332C4⋊C8—531no—
1333C4⋊C8—531no—
1334C4⋊C8—531no—
1335C4⋊C8—531no—
1336C4⋊C8—531no—
1337C4⋊C8—531no—
1338C4⋊C8—531no—
1339C4⋊C8—531no—
1340C4⋊C8C22×D5311yescharacteristic
1341C4⋊C8C22×D5311yescharacteristic
1342C4⋊C8C22×D5311yescharacteristic
1343#103—531no—
1344#103—531no—
1345#103—531no—
1346#103—531no—
1347#103—531no—
1348#103—531no—
1349#103C22×D5311yescharacteristic
1350#103C22×D5311yescharacteristic
1351#103C22×D5311yescharacteristic
1352#103C22×D5311yescharacteristic
1353#102—531no—
1354#102—531no—
1355#102—531no—
1356#102—531no—
1357#102—531no—
1358#102—531no—
1359#102—531no—
1360#102—531no—
1361#102—531no—
1362#102—531no—
1363#102—531no—
1364#102—531no—
1365#102C22×D5311yescharacteristic
1366#102C22×D5311yescharacteristic
1367#97—531no—
1368#97—531no—
1369#97—531no—
1370#97—531no—
1371#97C22×D5311yescharacteristic
1372#97C22×D5311yescharacteristic
1373C4×C8—531no—
1374C4×C8—531no—
1375C4×C8—531no—
1376C4×C8—531no—
1377C4×C8—531no—
1378C4×C8C22×D5311yescharacteristic
1379C24—1061no—
1380C24—1061no—
1381#41—1062no—
1382#41—1062no—
1383#41—1062no—
1384#41—1062no—
1385#41—1062no—
1386#41—1062no—
1387#41—4242no—
1388#41—4242no—
1389C2×Q8—531no—
1390C2×Q8—531no—
1391C2×Q8—531no—
1392C2×Q8—531no—
1393C2×Q8—1061no—
1394C2×Q8—1062no—
1395C2×Q8—1062no—
1396C2×Q8D4×D5311yescharacteristic
1397C2×Q8C23×D5311yescharacteristic
1398C2×Q8C23×D5311yescharacteristic
1399C2×Q8C23×D5311yescharacteristic
1400C2×Q8C23×D5311yescharacteristic
1401C2×D4—531no—
1402C2×D4—531no—
1403C2×D4—531no—
1404C2×D4—531no—
1405C2×D4—531no—
1406C2×D4—1061no—
1407C2×D4—1061no—
1408C2×D4—1061no—
1409C2×D4—1062no—
1410C2×D4—1062no—
1411C2×D4—1062no—
1412C2×D4—1062no—
1413C2×D4—1061no—
1414C2×D4—1061no—
1415C2×D4—1061no—
1416C2×D4—1061no—
1417C2×D4—1061no—
1418C2×D4—1061no—
1419C2×D4—1061no—
1420C2×D4—1061no—
1421C2×D4—1061no—
1422C2×D4—1061no—
1423C2×D4—1061no—
1424C2×D4—1061no—
1425C2×D4—1061no—
1426C2×D4—1061no—
1427C2×D4—1061no—
1428C2×D4—1061no—
1429C2×D4C23×D5311yescharacteristic
1430C2×D4C23×D5311yescharacteristic
1431C22×C4—21no—
1432C22×C4—21no—
1433C22×C4—531no—
1434C22×C4—531no—
1435C22×C4—531no—
1436C22×C4—1061no—
1437C22×C4—1061no—
1438C22×C4—1061no—
1439C22×C4—1061no—
1440C22×C4—1061no—
1441C22×C4—1061no—
1442C22×C4—1061no—
1443C22×C4—1061no—
1444C22×C4—1061no—
1445C22×C4—1061no—
1446C22×C4—1061no—
1447C22×C4—1061no—
1448C22×C4—1061no—
1449C22×C4—1061no—
1450C22×C4—1061no—
1451C22×C4—1061no—
1452C22×C4—1061no—
1453C22×C4—4242no—
1454Q16—22no—
1455Q16—41no—
1456Q16—41no—
1457Q16—41no—
1458Q16—1062no—
1459Q16—2121no—
1460SD16—22no—
1461SD16—22no—
1462SD16—41no—
1463SD16—41no—
1464SD16—1062no—
1465SD16—1062no—
1466SD16—1062no—
1467SD16—1062no—
1468SD16—2121no—
1469SD16—2121no—
1470SD16—2121no—
1471SD16—2121no—
1472SD16—2121no—
1473SD16—2121no—
1474SD16—2121no—
1475SD16—2121no—
1476SD16—2121no—
1477SD16—2121no—
1478D8—41no—
1479D8—1062no—
1480D8—1062no—
1481D8—1062no—
1482D8—1062no—
1483D8—2121no—
1484D8—2121no—
1485D8—2121no—
1486D8—2121no—
1487D8—2121no—
1488D8—2121no—
1489D8—2121no—
1490M16—534no—
1491M16—1062no—
1492C2×C8—531no—
1493C2×C8—531no—
1494C2×C8—531no—
1495C2×C8—531no—
1496C2×C8—1062no—
1497C2×C8—1062no—
1498C2×C8C23×D5311yescharacteristic
1499C2×C8C23×D5311yescharacteristic
1500C2×C8C23×D5311yescharacteristic
1501C2×C8C23×D5311yescharacteristic
1502C4⋊C4—21no—
1503C4⋊C4—21no—
1504C4⋊C4—21no—
1505C4⋊C4—21no—
1506C4⋊C4—21no—
1507C4⋊C4—21no—
1508C4⋊C4—21no—
1509C4⋊C4—21no—
1510C4⋊C4—531no—
1511C4⋊C4—531no—
1512C4⋊C4—531no—
1513C4⋊C4—531no—
1514C4⋊C4—531no—
1515C4⋊C4—531no—
1516C4⋊C4—531no—
1517C4⋊C4—531no—
1518C4⋊C4—531no—
1519C4⋊C4—531no—
1520C4⋊C4—531no—
1521C4⋊C4—531no—
1522C4⋊C4—531no—
1523C4⋊C4—531no—
1524C4⋊C4—531no—
1525C4⋊C4—1061no—
1526C4⋊C4—1061no—
1527C4⋊C4—1061no—
1528C4⋊C4—1061no—
1529C4⋊C4—1061no—
1530C4⋊C4—1061no—
1531C4⋊C4—1061no—
1532C4⋊C4—1061no—
1533C4⋊C4—1061no—
1534C4⋊C4D4×D5311yescharacteristic
1535C4⋊C4D4×D5311yescharacteristic
1536C4⋊C4D4×D5311yescharacteristic
1537C4⋊C4C23×D5311yescharacteristic
1538C4⋊C4C23×D5311yescharacteristic
1539C22⋊C4—21no—
1540C22⋊C4—21no—
1541C22⋊C4—21no—
1542C22⋊C4—21no—
1543C22⋊C4—21no—
1544C22⋊C4—21no—
1545C22⋊C4—21no—
1546C22⋊C4—21no—
1547C22⋊C4—21no—
1548C22⋊C4—21no—
1549C22⋊C4—531no—
1550C22⋊C4—531no—
1551C22⋊C4—531no—
1552C22⋊C4—531no—
1553C22⋊C4—1061no—
1554C22⋊C4—1061no—
1555C22⋊C4—1061no—
1556C22⋊C4—1061no—
1557C22⋊C4—1061no—
1558C22⋊C4—1061no—
1559C22⋊C4—1061no—
1560C22⋊C4—1061no—
1561C22⋊C4—1061no—
1562C22⋊C4—1061no—
1563C22⋊C4—1061no—
1564C22⋊C4—1061no—
1565C22⋊C4—1061no—
1566C22⋊C4—1061no—
1567C22⋊C4—1061no—
1568C22⋊C4—1061no—
1569C22⋊C4—1061no—
1570C22⋊C4—1061no—
1571C22⋊C4—1061no—
1572C22⋊C4—1061no—
1573C22⋊C4—1061no—
1574C22⋊C4—1061no—
1575C22⋊C4—1061no—
1576C22⋊C4—1061no—
1577C22⋊C4—1061no—
1578C22⋊C4—1061no—
1579C22⋊C4—1061no—
1580C22⋊C4—1061no—
1581C22⋊C4—1061no—
1582C22⋊C4—1061no—
1583C22⋊C4—1061no—
1584C22⋊C4—1061no—
1585C22⋊C4—1061no—
1586C42—21no—
1587C42—21no—
1588C42—21no—
1589C42—21no—
1590C42—531no—
1591C42—531no—
1592C42—531no—
1593C42—531no—
1594C42—531no—
1595C42—1061no—
1596C42—1061no—
1597C42—1061no—
1598C42—1061no—
1599C42—1061no—
1600C42—1061no—
1601C42—1061no—
1602C42C23×D5311yescharacteristic
1603C42C23×D5311yescharacteristic
1604C42C23×D5311yescharacteristic
1605C23—21no—
1606C23—21no—
1607C23—531no—
1608C23—1061no—
1609C23—1061no—
1610C23—1061no—
1611C23—1061no—
1612C23—1061no—
1613C23—4241no—
1614C23—4241no—
1615C23—4241no—
1616C23—4241no—
1617C23—2122no—
1618C23—2122no—
1619Q8—21no—
1620Q8—21no—
1621Q8—21no—
1622Q8—21no—
1623Q8—21no—
1624Q8—21no—
1625Q8—21no—
1626Q8—21no—
1627Q8—41no—
1628Q8—1061no—
1629Q8—1061no—
1630Q8—2121no—
1631Q8—2121no—
1632Q8—2121no—
1633Q8—2122no—
1634D4—21no—
1635D4—21no—
1636D4—21no—
1637D4—21no—
1638D4—1061no—
1639D4—1061no—
1640D4—1061no—
1641D4—1061no—
1642D4—1061no—
1643D4—1061no—
1644D4—1061no—
1645D4—1061no—
1646D4—1061no—
1647D4—1061no—
1648D4—4241no—
1649D4—4241no—
1650D4—4241no—
1651D4—4241no—
1652D4—4241no—
1653D4—4241no—
1654D4—4241no—
1655D4—4241no—
1656D4—4241no—
1657D4—4241no—
1658D4—4241no—
1659D4—4241no—
1660D4—4241no—
1661D4—2122no—
1662D4—2122no—
1663D4—2122no—
1664D4—2122no—
1665D4—2122no—
1666D4—2122no—
1667C2×C4—21no—
1668C2×C4—21no—
1669C2×C4—21no—
1670C2×C4—21no—
1671C2×C4—21no—
1672C2×C4—21no—
1673C2×C4—42no—
1674C2×C4—81no—
1675C2×C4—531no—
1676C2×C4—532no—
1677C2×C4—532no—
1678C2×C4—531no—
1679C2×C4—531no—
1680C2×C4—531no—
1681C2×C4—531no—
1682C2×C4—531no—
1683C2×C4—531no—
1684C2×C4—1061no—
1685C2×C4—1061no—
1686C2×C4—1061no—
1687C2×C4—4241no—
1688C2×C4—4241no—
1689C2×C4—4241no—
1690C2×C4—4241no—
1691C2×C4—4241no—
1692C2×C4—4241no—
1693C2×C4—4241no—
1694C2×C4—4241no—
1695C2×C4—4241no—
1696C2×C4—4241no—
1697C2×C4—4241no—
1698C2×C4—4241no—
1699C2×C4—2121no—
1700C2×C4—2121no—
1701C2×C4—2122no—
1702C2×C4—2122no—
1703C2×C4—2122no—
1704C2×C4—2122no—
1705C2×C4—2122no—
1706C2×C4C2×D4×D5311yescharacteristic
1707C2×C4C2×D4×D5311yescharacteristic
1708C2×C4C2×D4×D5311yescharacteristic
1709C2×C4C2×D4×D5311yescharacteristic
1710C2×C4C2×D4×D5311yescharacteristic
1711C2×C4C2×D4×D5311yescharacteristic
1712C2×C4C24×D5311yescharacteristic
1713C8—21no—
1714C8—21no—
1715C8—21no—
1716C8—532no—
1717C8—1061no—
1718C8—1061no—
1719C8—1061no—
1720C8#41×D5312yes—
1721C22—41no—
1722C22—41no—
1723C22—41no—
1724C22—41no—
1725C22—41no—
1726C22—41no—
1727C22—532no—
1728C22—8482no—
1729C22—1061no—
1730C22—1061no—
1731C22—4244no—
1732C22—2121no—
1733C22—2121no—
1734C22—2121no—
1735C22—2121no—
1736C22—2121no—
1737C22—2121no—
1738C22—2121no—
1739C22—2121no—
1740C22—2121no—
1741C22—2121no—
1742C22—2121no—
1743C22—2121no—
1744C22—2121no—
1745C22—2121no—
1746C22—2121no—
1747C22C22×D4×D5311yescharacteristic
1748C4—21no—
1749C4—21no—
1750C4—21no—
1751C4—21no—
1752C4—21no—
1753C4—21no—
1754C4—41no—
1755C4—41no—
1756C4—41no—
1757C4—41no—
1758C4—41no—
1759C4—41no—
1760C4—532no—
1761C4—1061no—
1762C4—1061no—
1763C4—1061no—
1764C4—1061no—
1765C4—1061no—
1766C4—1061no—
1767C4—2121no—
1768C4—2121no—
1769C4—2121no—
1770C4C2×#41×D5311yescharacteristic
1771C4H(5,𝔽2)×D5311yescharacteristic
1772C2—81no—
1773C2—81no—
1774C2—1062no—
1775C2—4241no—
1776C2—4241no—
1777C2—4241no—
1778C2—4241no—
1779C2—4241no—
1780C2#550×D5311yescharacteristic
1781C2#2028948511yescharacteristic
1782C2#2028949211yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3402C2
socleC22×C53C23×D4
hypercenter#3402D53
hypocenterC53#61424
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #3402

Complements

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

NH ≅ G/Ntype
1. #20288605C2semidirect
2. #20288568C2semidirect
3. #20287804C2semidirect
4. #20287802C2semidirect
5. #20287789C2semidirect
6. #20287784C2semidirect
7. #20287781C2semidirect
8. #20287780C2semidirect
9. #20287780C2semidirect
10. #20287759C2semidirect
11. #20287752C2semidirect
12. #20287736C2semidirect
13. #20287735C2semidirect
14. #20287725C2semidirect
15. #20287722C2semidirect
16. #20287710C2semidirect
17. #20287708C2semidirect
18. #20285197C2semidirect
19. #20285190C2semidirect
20. #20285178C2semidirect
21. #20284262C2semidirect
22. #20284257C2semidirect
23. #20284234C2semidirect
24. #20284216C2semidirect
25. #20284173C2semidirect
26. #463×D53C2semidirect
27. #20283660C2semidirect
28. #20283553C2semidirect
29. #20283546C2semidirect
30. #20283520C2semidirect
31. C53×#3402C2semidirect
41. #16811358C22semidirect
42. #16811358C22semidirect
43. #16811358C22semidirect
44. #16811358C22semidirect
45. #16811356C22semidirect
46. #16811355C22semidirect
47. #16811355C22semidirect
48. #16811355C22semidirect
49. #16811347C22semidirect
50. #16811347C22semidirect
51. #16811345C22semidirect
52. #16811342C22semidirect
60. #16811295C22semidirect
61. #16811294C22semidirect
84. #16811016C22semidirect
85. #16811015C22semidirect
88. #16811013C22semidirect
89. #16811012C22semidirect
90. #16811012C22semidirect
93. #16811009C22semidirect
95. #16811008C22semidirect
96. #16811008C22semidirect
97. #16811008C22semidirect
98. #16811005C22semidirect
99. #16811004C22semidirect
100. #16811004C22semidirect
103. #16810997C22semidirect
104. #16810994C22semidirect
105. #16810848C22semidirect
106. #16810847C22semidirect
107. #16810847C22semidirect
108. #16810847C22semidirect
109. #16810847C22semidirect
110. #16810847C22semidirect
111. #16810845C22semidirect
112. #16810842C22semidirect
115. #16810841C22semidirect
116. #16810841C22semidirect
117. #16810841C22semidirect
118. #16810841C22semidirect
122. #16810839C22semidirect
128. #16810835C22semidirect
129. #16810831C22semidirect
130. #16810827C22semidirect
131. #16810825C22semidirect
132. #16810825C22semidirect
133. #16810824C22semidirect
134. #16810823C22semidirect
135. #16810823C22semidirect
136. #16810823C22semidirect
137. #16810822C22semidirect
138. #16810821C22semidirect
139. #16810821C22semidirect
141. #16810819C22semidirect
142. #16810819C22semidirect
145. #16810817C22semidirect
147. #16810754C22semidirect
148. #16810752C22semidirect
149. #16810752C22semidirect
150. #16810751C22semidirect
151. #16810751C22semidirect
152. C8×Dic106C22semidirect
153. #16810747C22semidirect
154. #16810736C22semidirect
155. #16810736C22semidirect
156. #16810733C22semidirect
157. #16810732C22semidirect
158. #16810730C22semidirect
159. #16810728C22semidirect
160. #16810726C22semidirect
161. #16810722C22semidirect
162. #16810721C22semidirect
163. #16810721C22semidirect
164. #16810715C22semidirect
165. C4×#11719913C22semidirect
166. SD16×Dic53C22semidirect
167. SD16×Dic53C22semidirect
168. C4×#11719924C22semidirect
169. #16810708C22semidirect
170. #16810708C22semidirect
171. #16810705C22semidirect
172. #16810705C22semidirect
173. C4×#11719922C22semidirect
174. #16810703C22semidirect
188. C53×#556C22semidirect
189. C53×#556C22semidirect
190. C53×#497C22semidirect
191. C53×#497C22semidirect
193. C53×#464C22semidirect
194. C53×#464C22semidirect
197. C53×#462C22semidirect
198. C53×#462C22semidirect
199. C53×#446C22semidirect
200. C53×#440C22semidirect
201. C53×#440C22semidirect
202. C4×Q16×C53C22semidirect
710. #11719912#41semidirect
886. #3402D53semidirect
944. #556C2×D53semidirect
945. #556C2×D53semidirect
979. #497C2×D53semidirect
980. #497C2×D53semidirect
1009. #464C2×D53semidirect
1010. #464C2×D53semidirect
1030. #462C2×D53semidirect
1031. #462C2×D53semidirect
1054. #446C2×D53semidirect
1067. #440C2×D53semidirect
1068. #440C2×D53semidirect
1070. C4×Q16C2×D53semidirect
1094. C53#61424semidirect

Maximal subgroups

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

subgroupindex
#202886052
#202885682
#202878042
#202878022
#202877892
#202877842
#202877812
#202877802
#202877592
#202877522
#202877362
#202877352
#202877252
#202877222
#202877102
#202877082
#202851972
#202851902
#202851782
#202842622
#202842572
#202842342
#202842162
#202841732
#463×D532
#202836602
#202835532
#202835462
#202835202
C53×#34022
#6142453