Finite Group Databasebeta

← #28279571

Subgroups — #28279571

Order 13568.

1840 conjugacy classes of subgroups.

The subgroup lattice has 1774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289232C211yesmaximal, characteristic, complemented
2#20288723C211yesmaximal, characteristic, complemented
3#20287787C211yesmaximal, characteristic, complemented
4#20287784C211yesmaximal, characteristic, complemented
5#20287527C211yesmaximal, characteristic, complemented
6#20287524C211yesmaximal, characteristic, complemented
7#20286947C211yesmaximal, characteristic, complemented
8#20286941C211yesmaximal, characteristic, complemented
9#20286875C211yesmaximal, characteristic, complemented
10#20286866C211yesmaximal, characteristic, complemented
11#20286781C211yesmaximal, characteristic, complemented
12#20286774C211yesmaximal, characteristic, complemented
13#20286366C211yesmaximal, characteristic, complemented
14#20286219C211yesmaximal, characteristic, complemented
15#20286218C211yesmaximal, characteristic, complemented
16#20286213C211yesmaximal, characteristic, complemented
17#20286211C211yesmaximal, characteristic, complemented
18#20286174C211yesmaximal, characteristic, complemented
19#20286172C211yesmaximal, characteristic, complemented
20#20286097C211yesmaximal, characteristic, complemented
21#20285807C211yesmaximal, characteristic, complemented
22#20285802C211yesmaximal, characteristic, complemented
23#20285717C211yesmaximal, characteristic, complemented
24#20284950C211yesmaximal, characteristic, complemented
25#20284945C211yesmaximal, characteristic, complemented
26#20284859C211yesmaximal, characteristic, complemented
27#20284238C211yesmaximal, characteristic, complemented
28#20284234C211yesmaximal, characteristic, complemented
29#20284211C211yesmaximal, characteristic, complemented
30#20283879C211yesmaximal, characteristic, complemented
31C53×#3277C211yesmaximal, characteristic, complemented
32C2×#13133249C2211yescharacteristic, complemented
33C2×#13133242C2211yescharacteristic
34C22×#11719924C2211yescharacteristic, complemented
35C2×SD16×D53C2211yescharacteristic, complemented
36#16811369—21no—
37#16811365—21no—
38#16811358C2211yescharacteristic
39#16811355C2211yescharacteristic
40Q8×Dic106C2211yescharacteristic, complemented
41#16811344—21no—
42#16811344C2211yescharacteristic, complemented
43#16811343—21no—
44#16811343C2211yescharacteristic, complemented
45#16811342—21no—
46#16811342C2211yescharacteristic, complemented
47#16811337—21no—
48#16811337C2211yescharacteristic, complemented
49Q8×C22⋊D53C2211yescharacteristic, complemented
50#16811284C2211yescharacteristic
51#16811280C2211yescharacteristic, complemented
52#16811268—21no—
53#16811264C2211yescharacteristic
54#16811262—21no—
55#16811261C2211yescharacteristic
56D4×D212C2211yescharacteristic
57#16811257C2211yescharacteristic
58#16811246C2211yescharacteristic
59#16811245C2211yescharacteristic
60#16811242—21no—
61#16811242C2211yescharacteristic, complemented
62#16811240—21no—
63#16811240C2211yescharacteristic, complemented
64#16811213—21no—
65#16811207—21no—
66#16811206—21no—
67#16811191C2211yescharacteristic
68#16811187C2211yescharacteristic
69#16811181—21no—
70#16811175—21no—
71#16811175C2211yescharacteristic, complemented
72#16811168C2211yescharacteristic
73#16811153—21no—
74#16811153C2211yescharacteristic
75C2×#13133206C2211yescharacteristic
76#16811101C2211yescharacteristic, complemented
77#16811099C2211yescharacteristic, complemented
78#41×Dic53C2211yescharacteristic, complemented
79#16811016C2211yescharacteristic, complemented
80#16811016C2211yescharacteristic, complemented
81#16811013C2211yescharacteristic
82#16811011C2211yescharacteristic
83#16811004C2211yescharacteristic, complemented
84#16810984C2211yescharacteristic, complemented
85#16810984C2211yescharacteristic, complemented
86#16810984C2211yescharacteristic, complemented
87#16810982C2211yescharacteristic, complemented
88#16810970C2211yescharacteristic
89#16810968C2211yescharacteristic
90#16810962C2211yescharacteristic, complemented
91#16810961C2211yescharacteristic, complemented
92#16810950C2211yescharacteristic
93#16810948C2211yescharacteristic
94#16810948C2211yescharacteristic, complemented
95#16810944C2211yescharacteristic, complemented
96#16810918C2211yescharacteristic, complemented
97#16810917C2211yescharacteristic, complemented
98#16810916C2211yescharacteristic, complemented
99#16810916C2211yescharacteristic, complemented
100#16810906C2211yescharacteristic, complemented
101#16810904C2211yescharacteristic, complemented
102#16810902C2211yescharacteristic, complemented
103#16810902C2211yescharacteristic, complemented
104#16810901C2211yescharacteristic, complemented
105#16810901C2211yescharacteristic, complemented
106#16810872C2211yescharacteristic
107#16810871C2211yescharacteristic, complemented
108#16810869C2211yescharacteristic
109#16810869C2211yescharacteristic, complemented
110#16810867C2211yescharacteristic, complemented
111#16810866C2211yescharacteristic, complemented
112#16810862C2211yescharacteristic, complemented
113#16810861C2211yescharacteristic, complemented
114#16810858C2211yescharacteristic
115#16810857C2211yescharacteristic
116#16810848C2211yescharacteristic, complemented
117#16810848C2211yescharacteristic, complemented
118#16810847C2211yescharacteristic, complemented
119#16810847C2211yescharacteristic, complemented
120#16810847C2211yescharacteristic, complemented
121#16810847C2211yescharacteristic, complemented
122#16810847C2211yescharacteristic, complemented
123#16810847C2211yescharacteristic, complemented
124#16810847C2211yescharacteristic, complemented
125#16810847C2211yescharacteristic, complemented
126#16810843C2211yescharacteristic, complemented
127#16810842C2211yescharacteristic, complemented
128#16810840C2211yescharacteristic, complemented
129#16810840C2211yescharacteristic, complemented
130#16810840C2211yescharacteristic, complemented
131#16810840C2211yescharacteristic, complemented
132#16810837C2211yescharacteristic, complemented
133#16810835C2211yescharacteristic, complemented
134#16810827C2211yescharacteristic, complemented
135#16810826C2211yescharacteristic, complemented
136#16810824C2211yescharacteristic
137#16810823C2211yescharacteristic
138#16810822C2211yescharacteristic, complemented
139#16810821C2211yescharacteristic
140#16810821C2211yescharacteristic
141#16810821C2211yescharacteristic, complemented
142#16810821C2211yescharacteristic, complemented
143#16810816C2211yescharacteristic, complemented
144#16810785C2211yescharacteristic, complemented
145#16810784C2211yescharacteristic, complemented
146#16810779C2211yescharacteristic, complemented
147#16810777C2211yescharacteristic, complemented
148#16810776C2211yescharacteristic
149#16810776C2211yescharacteristic, complemented
150#16810773C2211yescharacteristic
151#16810772C2211yescharacteristic, complemented
152#16810768C2211yescharacteristic, complemented
153#16810767C2211yescharacteristic, complemented
154#16810763C2211yescharacteristic
155#16810762C2211yescharacteristic
156#16810756C2211yescharacteristic, complemented
157#16810755C2211yescharacteristic, complemented
158#16810753C2211yescharacteristic, complemented
159#16810752C2211yescharacteristic, complemented
160#16810735C2211yescharacteristic, complemented
161#16810732C2211yescharacteristic, complemented
162#16810730C2211yescharacteristic, complemented
163#16810728C2211yescharacteristic, complemented
164#16810726C2211yescharacteristic, complemented
165#16810726C2211yescharacteristic, complemented
166#16810724C2211yescharacteristic, complemented
167#16810721C2211yescharacteristic, complemented
168Q16×Dic53C2211yescharacteristic, complemented
169C4×#11719913C2211yescharacteristic, complemented
170#16810708C2211yescharacteristic, complemented
171#16810699C2211yescharacteristic, complemented
172#16810697C2211yescharacteristic, complemented
173#16810695C2211yescharacteristic, complemented
174#16810692C2211yescharacteristic, complemented
175#16810691C2211yescharacteristic, complemented
176#16810682C2211yescharacteristic, complemented
177#16810681C2211yescharacteristic, complemented
178#16810677C2211yescharacteristic, complemented
179#16810651C2211yescharacteristic, complemented
180#16810648C2211yescharacteristic, complemented
181#16810646C2211yescharacteristic, complemented
182#16810632C2211yescharacteristic, complemented
183#16810629C2211yescharacteristic
184#16810629C2211yescharacteristic, complemented
185#16810626C2211yescharacteristic, complemented
186#16810619C2211yescharacteristic, complemented
187#16810618C2211yescharacteristic, complemented
188C2×#137×C53C2211yescharacteristic, complemented
189C2×#137×C53C2211yescharacteristic, complemented
190C53×#548C2211yescharacteristic
191C53×#548C2211yescharacteristic, complemented
192C53×#495C2211yescharacteristic, complemented
193C53×#468C2211yescharacteristic, complemented
194C53×#468C2211yescharacteristic, complemented
195C53×#464C2211yescharacteristic, complemented
196C53×#464C2211yescharacteristic, complemented
197C53×#451C2211yescharacteristic, complemented
198C53×#451C2211yescharacteristic, complemented
199C53×#449C2211yescharacteristic, complemented
200C53×#449C2211yescharacteristic, complemented
201C4×Q16×C53C2211yescharacteristic, complemented
202C53×#436C2211yescharacteristic, complemented
203C2×#11719949C2311yescharacteristic
204C2×#11719947—21no—
205C2×Q8×D53C2311yescharacteristic
206C22×D212C2311yescharacteristic
207C22×D212C2311yescharacteristic
208C2×D4×D53—21no—
209C2×D4×D53—21no—
210C2×D4×D53C2311yescharacteristic
211#13133249—42no—
212#13133242—42no—
213C2×#11719925C2311yescharacteristic
214C2×#11719925C2311yescharacteristic
215C2×#11719913C2311yescharacteristic
216C2×#11719913C2311yescharacteristic
217C2×#11719913C2311yescharacteristic
218C2×#11719923C2311yescharacteristic
219C2×#11719924—42no—
220C2×#11719924C2311yescharacteristic
221C2×#11719924C2311yescharacteristic
222C2×#11719924C2311yescharacteristic
223C2×#11719924C2311yescharacteristic
224C2×#11719924C2311yescharacteristic
225C2×#11719924C2311yescharacteristic
226SD16×D53—42no—
227C2×#11719922C2311yescharacteristic
228C2×#11719922C2311yescharacteristic
229C2×#11719922C2311yescharacteristic
230C2×#11719917C2311yescharacteristic
231C2×#11719912C2311yescharacteristic
232C22×#88322C2311yescharacteristic
233C2×C8×D53C2311yescharacteristic
234#13133217—21no—
235#13133217C2311yescharacteristic
236#13133216—21no—
237#13133216—21no—
238#13133216C2311yescharacteristic
239#13133216C2311yescharacteristic
240#13133216C2311yescharacteristic
241#13133215—21no—
242#13133215C2311yescharacteristic
243#13133214C2311yescharacteristic
244#13133213C2311yescharacteristic
245#13133213C2311yescharacteristic
246#13133212—21no—
247#13133212—21no—
248#13133212D411yescharacteristic
249#13133211—21no—
250#13133210—21no—
251#13133210—21no—
252#13133210—21no—
253#13133210—21no—
254#13133210—21no—
255#13133210—21no—
256#13133210—21no—
257#13133210D411yescharacteristic
258#13133207—21no—
259#13133207D411yescharacteristic
260#13133206—21no—
261#13133206—21no—
262#13133206—21no—
263#13133206C2311yescharacteristic
264#13133206C2311yescharacteristic
265#13133206C2311yescharacteristic
266#13133206C2311yescharacteristic
267#13133206C2311yescharacteristic
268#13133205—21no—
269#13133205—21no—
270#13133204—21no—
271#13133204—21no—
272#13133204—21no—
273#13133204—21no—
274#13133204C2311yescharacteristic
275#13133203—21no—
276#13133203—21no—
277#13133203—21no—
278#13133203—21no—
279#13133203—21no—
280#13133203—21no—
281#13133203D411yescharacteristic
282#13133202—21no—
283#13133202—21no—
284#13133202—21no—
285#13133202—21no—
286#13133201—21no—
287#13133201—21no—
288#13133201D411yescharacteristic
289#13133200—21no—
290#13133199—21no—
291#13133199—21no—
292#13133198—21no—
293#13133198D411yescharacteristic
294#13133197—21no—
295#13133196—21no—
296#13133196—21no—
297#13133196C2311yescharacteristic
298#13133196C2311yescharacteristic
299#13133195—21no—
300#13133194—21no—
301#13133194—21no—
302#13133194—21no—
303#13133194—21no—
304#13133194D411yescharacteristic
305#13133193—21no—
306#13133193—21no—
307#13133193C2311yescharacteristic
308#13133193C2311yescharacteristic
309#13133192—21no—
310#13133192—21no—
311#13133192C2311yescharacteristic
312#13133191—21no—
313#13133191—21no—
314#13133191—21no—
315#13133191C2311yescharacteristic
316#13133191C2311yescharacteristic
317#13133190—21no—
318#13133190—21no—
319#13133190—21no—
320#13133189—21no—
321#13133189—21no—
322#13133189—21no—
323#13133189D411yescharacteristic
324#13133188—21no—
325#13133188C2311yescharacteristic
326#13133187—21no—
327#13133187—21no—
328#13133187—21no—
329#13133187—21no—
330#13133187—21no—
331#13133187—21no—
332#13133185—21no—
333#13133185—21no—
334#13133185—21no—
335#13133185—21no—
336Q8×Dic53—21no—
337Q8×Dic53—21no—
338Q8×Dic53C2311yescharacteristic
339Q8×Dic53C2311yescharacteristic
340Q8×Dic53C2311yescharacteristic
341Q8×Dic53C2311yescharacteristic
342Q8×Dic53C2311yescharacteristic
343Q8×Dic53C2311yescharacteristic
344C4×Dic106—21no—
345C4×Dic106—21no—
346C4×Dic106C2311yescharacteristic
347C4×Dic106C2311yescharacteristic
348#13133182—21no—
349#13133182—21no—
350#13133182—21no—
351#13133182—21no—
352#13133182C2311yescharacteristic
353C4×D212—21no—
354C4×D212C2311yescharacteristic
355D4×Dic53—21no—
356D4×Dic53—21no—
357D4×Dic53C2311yescharacteristic
358D4×Dic53C2311yescharacteristic
359D4×Dic53C2311yescharacteristic
360#13133179C2311yescharacteristic
361#13133179C2311yescharacteristic
362C4×C22⋊D53—21no—
363C4×C22⋊D53—21no—
364C4×C22⋊D53—21no—
365C4×C22⋊D53C2311yescharacteristic
366C4×C22⋊D53C2311yescharacteristic
367#13133177—21no—
368#13133177—21no—
369#13133176—21no—
370#13133176—21no—
371#13133176—21no—
372#13133176C2311yescharacteristic
373#13133176C2311yescharacteristic
374#13133176C2311yescharacteristic
375#13133175—21no—
376#13133175C2311yescharacteristic
377#13133174—21no—
378#13133174C2311yescharacteristic
379#13133173—21no—
380#13133173—21no—
381#13133173—21no—
382C2×#11719921—21no—
383C2×#11719921—21no—
384C2×#11719921—21no—
385C22⋊C4×D53—21no—
386C2×C4×Dic53—21no—
387C2×C4×Dic53C2311yescharacteristic
388#13133151C2311yescharacteristic
389#13133151C2311yescharacteristic
390#13133150C2311yescharacteristic
391#13133150C2311yescharacteristic
392#13133150C2311yescharacteristic
393#13133149C2311yescharacteristic
394#13133148C2311yescharacteristic
395C4⋊#88322C2311yescharacteristic
396#13133146C2311yescharacteristic
397#13133146C2311yescharacteristic
398#13133146C2311yescharacteristic
399#13133146C2311yescharacteristic
400#13133146C2311yescharacteristic
401#13133146C2311yescharacteristic
402#13133146C2311yescharacteristic
403#13133146C2311yescharacteristic
404#13133142C2311yescharacteristic
405#13133141C2311yescharacteristic
406#13133141C2311yescharacteristic
407#13133141C2311yescharacteristic
408#13133141C2311yescharacteristic
409#13133141C2311yescharacteristic
410#13133141C2311yescharacteristic
411#13133141C2311yescharacteristic
412#13133141C2311yescharacteristic
413#13133140C2311yescharacteristic
414#13133139C2311yescharacteristic
415#13133139C2311yescharacteristic
416#13133139C2311yescharacteristic
417#13133139C2311yescharacteristic
418#13133139C2311yescharacteristic
419#13133139C2311yescharacteristic
420#13133139C2311yescharacteristic
421#13133139C2311yescharacteristic
422#13133139C2311yescharacteristic
423#13133138C2311yescharacteristic
424#13133138C2311yescharacteristic
425#13133138C2311yescharacteristic
426#13133138C2311yescharacteristic
427#13133137C2311yescharacteristic
428#13133137C2311yescharacteristic
429#13133137C2311yescharacteristic
430C22⋊#88322C2311yescharacteristic
431C22⋊#88322C2311yescharacteristic
432#13133129C2311yescharacteristic
433#13133129C2311yescharacteristic
434#13133128C2311yescharacteristic
435#13133127C2311yescharacteristic
436#13133127C2311yescharacteristic
437#13133127C2311yescharacteristic
438C8×Dic53C2311yescharacteristic
439C2×#41×C53C2311yescharacteristic
440C2×#41×C53C2311yescharacteristic
441C22×Q8×C53C2311yescharacteristic
442C22×Q8×C53C2311yescharacteristic
443#137×C53—42no—
444#137×C53—42no—
445C2×Q16×C53C2311yescharacteristic
446C2×Q16×C53C2311yescharacteristic
447C2×Q16×C53C2311yescharacteristic
448C2×Q16×C53C2311yescharacteristic
449C2×SD16×C53C2311yescharacteristic
450C2×SD16×C53C2311yescharacteristic
451C2×SD16×C53C2311yescharacteristic
452C2×SD16×C53C2311yescharacteristic
453C2×D8×C53C2311yescharacteristic
454C2×M16×C53C2311yescharacteristic
455C2×M16×C53C2311yescharacteristic
456#124×C53—21no—
457#124×C53—21no—
458#124×C53C2311yescharacteristic
459#124×C53C2311yescharacteristic
460C22⋊Q8×C53—21no—
461C22⋊Q8×C53—21no—
462C22⋊Q8×C53C2311yescharacteristic
463C22⋊Q8×C53C2311yescharacteristic
464#121×C53—21no—
465#121×C53—21no—
466#121×C53C2311yescharacteristic
467#121×C53C2311yescharacteristic
468C4×Q8×C53C2311yescharacteristic
469C4×Q8×C53C2311yescharacteristic
470C4×D4×C53—21no—
471C4×D4×C53—21no—
472C4×D4×C53C2311yescharacteristic
473#107×C53C2311yescharacteristic
474C4⋊C8×C53C2311yescharacteristic
475#103×C53C2311yescharacteristic
476#103×C53C2311yescharacteristic
477#103×C53C2311yescharacteristic
478#103×C53C2311yescharacteristic
479#102×C53C2311yescharacteristic
480#102×C53C2311yescharacteristic
481C22⋊C8×C53C2311yescharacteristic
482C22⋊C8×C53C2311yescharacteristic
483C4×C8×C53C2311yescharacteristic
484C23×D53—21no—
485C23×D53—21no—
486C23×D53—21no—
487#41×C53—22no—
488#41×C53—41no—
489#41×C53—41no—
490#41×C53—41no—
491C2×Q8×C53—21no—
492C2×Q8×C53—21no—
493C2×Q8×C53—22no—
494C2×Q8×C53—41no—
495C2×Q8×C53—41no—
496C2×Q8×C53—41no—
497C2×Q8×C53C2411yescharacteristic
498C2×Q8×C53C2411yescharacteristic
499C2×Q8×C53C2411yescharacteristic
500C2×Q8×C53C2411yescharacteristic
501C2×D4×C53—21no—
502C2×D4×C53—21no—
503C2×D4×C53—21no—
504C2×D4×C53—21no—
505C2×D4×C53C2×D411yescharacteristic
506C2×D4×C53C2411yescharacteristic
507C2×D4×C53C2411yescharacteristic
508C22×C4×C53—21no—
509C22×C4×C53—21no—
510C22×C4×C53—21no—
511C22×C4×C53—21no—
512C22×C4×C53C2411yescharacteristic
513C22×C4×C53C2411yescharacteristic
514C2×C22⋊D53—21no—
515C2×C22⋊D53—21no—
516C2×C22⋊D53—21no—
517C2×C22⋊D53—21no—
518C2×C22⋊D53—21no—
519C2×C22⋊D53—21no—
520C2×C22⋊D53—21no—
521C2×C22⋊D53—21no—
522C2×C22⋊D53C2×D411yescharacteristic
523C2×C22⋊D53C2×D411yescharacteristic
524C22×Dic53—21no—
525C22×Dic53—21no—
526C22×Dic53—21no—
527C22×Dic53C2×D411yescharacteristic
528C22×Dic53C2×D411yescharacteristic
529#11719949—41no—
530#11719949—41no—
531Q8×D53—22no—
532Q8×D53—41no—
533#11719947—82no—
534D4×D53—41no—
535D4×D53—41no—
536D4×D53—82no—
537D4×D53—82no—
538C2×D212—21no—
539C2×D212—21no—
540C2×D212—21no—
541C2×D212—21no—
542C2×D212—21no—
543C2×D212—21no—
544C2×D212—41no—
545C2×D212—41no—
546C2×D212—41no—
547C2×D212—41no—
548C2×D212C2411yescharacteristic
549C2×D212C2411yescharacteristic
550C2×D212C2411yescharacteristic
551C2×C4×D53—21no—
552C2×C4×D53—21no—
553C2×C4×D53—21no—
554C2×C4×D53—21no—
555C2×C4×D53—21no—
556C2×C4×D53C2411yescharacteristic
557C2×Dic106—21no—
558C2×Dic106—21no—
559C2×Dic106—21no—
560C2×Dic106—21no—
561C2×Dic106—21no—
562C2×Dic106C2×D411yescharacteristic
563C2×Dic106C2411yescharacteristic
564Q16×C53—22no—
565Q16×C53—22no—
566Q16×C53—41no—
567Q16×C53—41no—
568SD16×C53—22no—
569SD16×C53—41no—
570SD16×C53—41no—
571SD16×C53—41no—
572D8×C53—41no—
573M16×C53—41no—
574M16×C53—41no—
575C2×C8×C53C2411yescharacteristic
576C2×C8×C53C2411yescharacteristic
577C2×C8×C53C2411yescharacteristic
578C2×C8×C53C2411yescharacteristic
579C4⋊C4×C53—21no—
580C4⋊C4×C53—21no—
581C4⋊C4×C53—21no—
582C4⋊C4×C53—21no—
583C4⋊C4×C53C2×D411yescharacteristic
584C4⋊C4×C53C2411yescharacteristic
585C4⋊C4×C53C2411yescharacteristic
586C22⋊C4×C53—21no—
587C22⋊C4×C53—21no—
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×C53C2×D411yescharacteristic
595C22⋊C4×C53C2×D411yescharacteristic
596C42×C53—21no—
597C42×C53—21no—
598C42×C53C2411yescharacteristic
599C22⋊Dic53—21no—
600C22⋊Dic53—21no—
601C22⋊Dic53—21no—
602C22⋊Dic53—21no—
603C22⋊Dic53—21no—
604C22⋊Dic53—21no—
605C22⋊Dic53—21no—
606C22⋊Dic53—21no—
607C22⋊Dic53—21no—
608C22⋊Dic53—21no—
609C22⋊Dic53C2×D411yescharacteristic
610C22⋊Dic53C2×D411yescharacteristic
611C22⋊Dic53C2×D411yescharacteristic
612C22⋊Dic53C2×D411yescharacteristic
613#11719925—41no—
614#11719925—41no—
615#11719924—22no—
616#11719924—22no—
617#11719924—22no—
618#11719924—41no—
619#11719924—41no—
620#11719924—41no—
621#11719923—41no—
622#11719922—41no—
623#11719922—41no—
624#11719922—41no—
625#11719921—21no—
626#11719921—21no—
627#11719921—21no—
628#11719921—21no—
629#11719921—21no—
630#11719921—21no—
631#11719921—21no—
632#11719921—21no—
633#11719921—21no—
634#11719921—21no—
635#11719921—21no—
636#11719921—21no—
637#11719921—21no—
638#11719921—21no—
639#11719921—21no—
640#11719921—21no—
641#11719921—21no—
642#11719921—21no—
643#11719921—21no—
644#11719921C2×D411yescharacteristic
645#11719921C2×D411yescharacteristic
646#11719921C2×D411yescharacteristic
647#11719921C2×D411yescharacteristic
648C4⋊Dic53—21no—
649C4⋊Dic53—21no—
650C4⋊Dic53—21no—
651C4⋊Dic53—21no—
652C4⋊Dic53—21no—
653C4⋊Dic53—21no—
654C4⋊Dic53—21no—
655C4⋊Dic53C2×D411yescharacteristic
656C4⋊Dic53C2×D411yescharacteristic
657C4⋊Dic53C2×D411yescharacteristic
658C4⋊Dic53C2411yescharacteristic
659C4⋊Dic53C2411yescharacteristic
660C4⋊Dic53C2411yescharacteristic
661C4⋊Dic53C2411yescharacteristic
662#11719919—21no—
663#11719919—21no—
664#11719919—21no—
665#11719919—21no—
666#11719919—21no—
667#11719919—21no—
668#11719919—21no—
669#11719919—21no—
670#11719919—21no—
671#11719919—21no—
672#11719919—21no—
673#11719919C2×D411yescharacteristic
674#11719919C2×D411yescharacteristic
675#11719919C2×D411yescharacteristic
676#11719919C2×D411yescharacteristic
677#11719919C2×D411yescharacteristic
678#11719919C2×D411yescharacteristic
679C4×Dic53—21no—
680C4×Dic53—21no—
681C4×Dic53—21no—
682C4×Dic53—21no—
683C4×Dic53—21no—
684C4×Dic53—21no—
685C4×Dic53—21no—
686C4×Dic53—21no—
687C4×Dic53—21no—
688C4×Dic53—21no—
689C4×Dic53—21no—
690C4×Dic53C2×D411yescharacteristic
691C4×Dic53C2×D411yescharacteristic
692C4×Dic53C2411yescharacteristic
693C4×Dic53C2411yescharacteristic
694C4×Dic53C2411yescharacteristic
695#11719917—41no—
696C2×#88322—41no—
697C2×#88322C2411yescharacteristic
698C2×#88322C2411yescharacteristic
699C2×#88322C2411yescharacteristic
700C2×#88322C2411yescharacteristic
701#11719913—41no—
702#11719913—41no—
703#11719913—41no—
704#11719912—41no—
705C8×D53—41no—
706C23×C53—21no—
707C23×C53—21no—
708C23×C53C22×D411yescharacteristic
709C23×C53C22×D411yescharacteristic
710C22×D53—21no—
711C22×D53—21no—
712C22×D53—21no—
713C22×D53—42no—
714C22×D53—81no—
715C22×D53—81no—
716C22×D53—81no—
717C22×D53—81no—
718C22×D53—81no—
719C22×D53—81no—
720C22×D53—81no—
721C22×D53—81no—
722C22×D53C22×D411yescharacteristic
723Q8×C53—21no—
724Q8×C53—21no—
725Q8×C53—21no—
726Q8×C53—21no—
727Q8×C53—21no—
728Q8×C53—21no—
729Q8×C53—21no—
730Q8×C53—42no—
731Q8×C53—81no—
732Q8×C53H(5,𝔽2)12yes—
733D4×C53—21no—
734D4×C53—21no—
735D4×C53—21no—
736D4×C53—21no—
737D4×C53—41no—
738D4×C53—42no—
739D4×C53—42no—
740D4×C53—81no—
741D4×C53—81no—
742C2×C4×C53—21no—
743C2×C4×C53—21no—
744C2×C4×C53—21no—
745C2×C4×C53—21no—
746C2×C4×C53—21no—
747C2×C4×C53—21no—
748C2×C4×C53—21no—
749C2×C4×C53—21no—
750C2×C4×C53—21no—
751C2×C4×C53—21no—
752C2×C4×C53—42no—
753C2×C4×C53—42no—
754C2×C4×C53—81no—
755C2×C4×C53—81no—
756C2×C4×C53C22×D411yescharacteristic
757C2×C4×C53C22×D411yescharacteristic
758C2×C4×C53C22×D411yescharacteristic
759C2×C4×C53C22×D411yescharacteristic
760C2×C4×C53C2511yescharacteristic
761C22⋊D53—41no—
762C22⋊D53—41no—
763C22⋊D53—42no—
764C22⋊D53—81no—
765C22⋊D53—81no—
766C22⋊D53—81no—
767C22⋊D53—81no—
768C22⋊D53—81no—
769C22⋊D53—81no—
770C22⋊D53—81no—
771C2×Dic53—21no—
772C2×Dic53—21no—
773C2×Dic53—21no—
774C2×Dic53—21no—
775C2×Dic53—21no—
776C2×Dic53—41no—
777C2×Dic53—41no—
778C2×Dic53—42no—
779C2×Dic53—81no—
780C2×Dic53—81no—
781C2×Dic53C22×D411yescharacteristic
782C2×Dic53C22×D411yescharacteristic
783C2×Dic53C22×D411yescharacteristic
784C2×Dic53C22×D411yescharacteristic
785C2×Dic53C22×D411yescharacteristic
786C2×Dic53C22×D411yescharacteristic
787C2×Dic53C22×D411yescharacteristic
788D212—21no—
789D212—21no—
790D212—21no—
791D212—21no—
792D212—21no—
793D212—21no—
794D212—81no—
795D212—81no—
796D212—81no—
797D212—81no—
798D212—81no—
799D212—81no—
800C4×D53—21no—
801C4×D53—21no—
802C4×D53—42no—
803C4×D53—81no—
804C4×D53—81no—
805C4×D53—81no—
806C4×D53—81no—
807Dic106—21no—
808Dic106—21no—
809Dic106—41no—
810Dic106—42no—
811Dic106—81no—
812Dic106—81no—
813Dic106—81no—
814Dic106—81no—
815C8×C53—21no—
816C8×C53—21no—
817C8×C53—21no—
818C8×C53—21no—
819#88322—21no—
820#88322—21no—
821#88322—21no—
822#88322—21no—
823#62092—531nomaximal, Sylow
824C22×C53—21no—
825C22×C53—21no—
826C22×C53—21no—
827C22×C53—21no—
828C22×C53—21no—
829C22×C53—21no—
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—21no—
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—162no—
850C2×D53—162no—
851C2×D53—162no—
852C4×C53—21no—
853C4×C53—21no—
854C4×C53—22no—
855C4×C53—21no—
856C4×C53—21no—
857C4×C53—41no—
858C4×C53—41no—
859C4×C53—41no—
860C4×C53—41no—
861C4×C53—41no—
862C4×C53C2×H(5,𝔽2)11yescharacteristic
863C4×C53#58511yescharacteristic
864Dic53—21no—
865Dic53—21no—
866Dic53—21no—
867Dic53—21no—
868Dic53—21no—
869Dic53—21no—
870Dic53—21no—
871Dic53—41no—
872Dic53—41no—
873Dic53—41no—
874Dic53—41no—
875Dic53—41no—
876#3558—531no—
877#3518—531no—
878#3401—531no—
879#3401—531no—
880#3375—531no—
881#3375—531no—
882#3324—531no—
883#3324—531no—
884#3319—531no—
885#3319—531no—
886#3313—531no—
887#3313—531no—
888#3277—531no—
889#3277D5311yescharacteristic, complemented
890#3266—531no—
891#3266—531no—
892#3265—531no—
893#3265—531no—
894#3262—531no—
895#3262—531no—
896#3254—531no—
897#3224—531no—
898#3224—531no—
899#3215—531no—
900#3121—531no—
901#3121—531no—
902#3115—531no—
903#3043—531no—
904#3043—531no—
905#3040—531no—
906#2995—531no—
907C2×C53—41no—
908C2×C53—41no—
909C2×C53—81no—
910C2×C53—81no—
911C2×C53#348811yescharacteristic
912C2×C53#358511yescharacteristic
913C2×C53#358611yescharacteristic
914D53—41no—
915D53—81no—
916D53—81no—
917D53—81no—
918C2×#137—531no—
919C2×#137C2×D5311yescharacteristic, complemented
920C2×#137C2×D5311yescharacteristic, complemented
921C2×AGL(1,ℤ/8)—531no—
922C22×SD16—531no—
923C22×SD16—531no—
924#562—1061no—
925H(3,𝔽4)—1061no—
926#559—531no—
927#559—531no—
928Q82—531no—
929#556—531no—
930#556—531no—
931#556—531no—
932#556—1061no—
933#556—1061no—
934#556—1061no—
935#555—531no—
936#555—1061no—
937D4×Q8—531no—
938#548—531no—
939#548—531no—
940#548C2×D5311yescharacteristic
941#548C2×D5311yescharacteristic, complemented
942#546—531no—
943#546—531no—
944#546—1061no—
945#546—1061no—
946D42—531no—
947D42—531no—
948#542—531no—
949#542—531no—
950#542—531no—
951#542—531no—
952#542—1061no—
953#542—1061no—
954#538—1061no—
955#538—1061no—
956#538—1061no—
957#535—531no—
958#535—531no—
959#534—1061no—
960#533—531no—
961#533—1061no—
962#532—531no—
963#529—531no—
964#529—1061no—
965C2×#124—531no—
966#519—531no—
967#519—531no—
968C4×#41—531no—
969#497—531no—
970#497—531no—
971#496—531no—
972#496—531no—
973#495—531no—
974#495C2×D5311yescharacteristic, complemented
975#489—531no—
976#489—531no—
977#489—531no—
978#489—531no—
979#486—531no—
980#486—531no—
981#485—531no—
982#485—531no—
983#482—531no—
984#482—531no—
985#482—531no—
986#482—531no—
987#477—531no—
988#477—531no—
989#477—531no—
990#477—531no—
991#475—531no—
992#474—531no—
993#474—531no—
994#474—531no—
995#474—531no—
996#474—531no—
997#468—531no—
998#468—531no—
999#468—531no—
1000#468—531no—
1001#468—531no—
1002#468—531no—
1003#468C2×D5311yescharacteristic, complemented
1004#468C2×D5311yescharacteristic, complemented
1005#467—531no—
1006#467—531no—
1007#466—531no—
1008#466—531no—
1009#464—531no—
1010#464—531no—
1011#464—531no—
1012#464—531no—
1013#464—531no—
1014#464—531no—
1015#464—531no—
1016#464—531no—
1017#464—531no—
1018#464—531no—
1019#464—531no—
1020#464—531no—
1021#464C2×D5311yescharacteristic, complemented
1022#464C2×D5311yescharacteristic, complemented
1023#463—531no—
1024#463—531no—
1025#463—531no—
1026#463—531no—
1027#463—531no—
1028#463—531no—
1029#461—531no—
1030#461—531no—
1031#460—531no—
1032#460—531no—
1033#460—531no—
1034#460—531no—
1035#460—531no—
1036#460—531no—
1037#460—531no—
1038#459—531no—
1039#452—531no—
1040#452—531no—
1041#451—531no—
1042#451—531no—
1043#451C2×D5311yescharacteristic, complemented
1044#451C2×D5311yescharacteristic, complemented
1045#450—531no—
1046#450—531no—
1047#450—531no—
1048#450—531no—
1049#449—531no—
1050#449—531no—
1051#449C2×D5311yescharacteristic, complemented
1052#449C2×D5311yescharacteristic, complemented
1053#448—531no—
1054#448—531no—
1055#447—531no—
1056#447—531no—
1057#446—531no—
1058#446—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—
1067C4×Q16—531no—
1068C4×Q16C2×D5311yescharacteristic, complemented
1069C4×SD16—531no—
1070C4×SD16—531no—
1071#436—531no—
1072#436C2×D5311yescharacteristic, complemented
1073#435—531no—
1074#435—531no—
1075#435—531no—
1076#435—531no—
1077#433—531no—
1078#433—531no—
1079#432—531no—
1080#424—531no—
1081#424—531no—
1082#423—531no—
1083#419—531no—
1084#418—531no—
1085#418—531no—
1086#418—531no—
1087#416—531no—
1088#416—531no—
1089C53#6209211yescharacteristic, complemented, Sylow
1090C2×#41—531no—
1091C2×#41—1061no—
1092C2×#41C22×D5311yescharacteristic
1093C2×#41C22×D5311yescharacteristic
1094C22×Q8—531no—
1095C22×Q8C22×D5311yescharacteristic
1096C22×Q8C22×D5311yescharacteristic
1097C22×D4—531no—
1098C22×D4—531no—
1099C22×D4—531no—
1100C22×D4—1061no—
1101C22×D4—1061no—
1102#137—42no—
1103#137—42no—
1104#137—2122no—
1105AGL(1,ℤ/8)—2122no—
1106C2×Q16—531no—
1107C2×Q16—531no—
1108C2×Q16C22×D5311yescharacteristic
1109C2×Q16C22×D5311yescharacteristic
1110C2×Q16C22×D5311yescharacteristic
1111C2×Q16C22×D5311yescharacteristic
1112C2×SD16—531no—
1113C2×SD16—531no—
1114C2×SD16—531no—
1115C2×SD16—531no—
1116C2×SD16—531no—
1117C2×SD16—531no—
1118C2×SD16—531no—
1119C2×SD16—531no—
1120C2×SD16—531no—
1121C2×SD16—531no—
1122C2×SD16—2122no—
1123C2×SD16—2122no—
1124C2×SD16C22×D5311yescharacteristic
1125C2×SD16C22×D5311yescharacteristic
1126C2×SD16C22×D5311yescharacteristic
1127C2×SD16C22×D5311yescharacteristic
1128C2×D8—531no—
1129C2×D8—531no—
1130C2×D8—531no—
1131C2×D8C22×D5311yescharacteristic
1132C2×M16—531no—
1133C2×M16—531no—
1134C2×M16C22×D5311yescharacteristic
1135C2×M16C22×D5311yescharacteristic
1136C22×C8—531no—
1137C22×C8—531no—
1138C4⋊Q8—531no—
1139C4⋊Q8—531no—
1140C4⋊Q8—531no—
1141C4⋊Q8—531no—
1142C4⋊Q8—531no—
1143C4⋊Q8—1061no—
1144C4⋊Q8—1061no—
1145C4⋊Q8—1061no—
1146C4⋊Q8—1061no—
1147#127—531no—
1148#127—531no—
1149#127—531no—
1150#126—531no—
1151#126—531no—
1152#126—1061no—
1153#126—1061no—
1154#126—1061no—
1155#126—1061no—
1156#126—1061no—
1157#126—1061no—
1158#126—1061no—
1159#126—1061no—
1160#126—1061no—
1161#126—1061no—
1162#125—531no—
1163#125—1061no—
1164#124—21no—
1165#124—21no—
1166#124—531no—
1167#124—531no—
1168#124—531no—
1169#124—531no—
1170#124—531no—
1171#124—531no—
1172#124—531no—
1173#124—1061no—
1174#124—1061no—
1175#124—1061no—
1176#124—1061no—
1177#124—1061no—
1178#124—1061no—
1179#124—1061no—
1180#124—1061no—
1181#124—1061no—
1182#124—1061no—
1183#124—1061no—
1184#124—1061no—
1185#124—1061no—
1186#124—1061no—
1187#124—1061no—
1188#124C22×D5311yescharacteristic
1189#124C22×D5311yescharacteristic
1190#123—531no—
1191#123—531no—
1192#123—1061no—
1193#123—1061no—
1194#123—1061no—
1195#123—1061no—
1196#123—1061no—
1197#123—1061no—
1198#123—1061no—
1199#123—1061no—
1200#123—1061no—
1201#123—1061no—
1202C22⋊Q8—21no—
1203C22⋊Q8—21no—
1204C22⋊Q8—531no—
1205C22⋊Q8—531no—
1206C22⋊Q8—531no—
1207C22⋊Q8—531no—
1208C22⋊Q8—531no—
1209C22⋊Q8—1061no—
1210C22⋊Q8—1061no—
1211C22⋊Q8—1061no—
1212C22⋊Q8—1061no—
1213C22⋊Q8—1061no—
1214C22⋊Q8—1061no—
1215C22⋊Q8—1061no—
1216C22⋊Q8—1061no—
1217C22⋊Q8—1061no—
1218C22⋊Q8—1061no—
1219C22⋊Q8C22×D5311yescharacteristic
1220C22⋊Q8C22×D5311yescharacteristic
1221#121—21no—
1222#121—21no—
1223#121—531no—
1224#121—531no—
1225#121—531no—
1226#121—531no—
1227#121—531no—
1228#121—1061no—
1229#121—1061no—
1230#121—1061no—
1231#121—1061no—
1232#121—1061no—
1233#121—1061no—
1234#121—1061no—
1235#121—1061no—
1236#121—1061no—
1237#121—1061no—
1238#121—1061no—
1239#121—1061no—
1240#121C22×D5311yescharacteristic
1241#121C22×D5311yescharacteristic
1242#120—1061no—
1243#120—1061no—
1244#120—1061no—
1245#120—1061no—
1246#120—1061no—
1247#120—1061no—
1248#120—1061no—
1249#120—1061no—
1250#120—1061no—
1251#120—1061no—
1252C4×Q8—531no—
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—1061no—
1262C4×Q8—1061no—
1263C4×Q8—1061no—
1264C4×Q8—1061no—
1265C4×Q8—1061no—
1266C4×Q8—1061no—
1267C4×Q8—1061no—
1268C4×Q8—1061no—
1269C4×Q8C22×D5311yescharacteristic
1270C4×Q8C22×D5311yescharacteristic
1271C4×D4—21no—
1272C4×D4—21no—
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×D4C22×D5311yescharacteristic
1290#117—531no—
1291#117—531no—
1292#117—531no—
1293#117—531no—
1294#117—531no—
1295#117—1061no—
1296#117—1061no—
1297#117—1061no—
1298#117—1061no—
1299#117—1061no—
1300#117—1061no—
1301#117—1061no—
1302#117—1061no—
1303C2×C22⋊C4—1061no—
1304C2×C22⋊C4—1061no—
1305C2×C22⋊C4—1061no—
1306C2×C22⋊C4—1061no—
1307C2×C42—531no—
1308C2×C42—1061no—
1309#107—531no—
1310#107—531no—
1311#107—531no—
1312#107—531no—
1313#107—531no—
1314#107C22×D5311yescharacteristic
1315#106—531no—
1316#106—531no—
1317C4⋊C8—531no—
1318C4⋊C8—531no—
1319C4⋊C8—531no—
1320C4⋊C8—531no—
1321C4⋊C8—531no—
1322C4⋊C8—531no—
1323C4⋊C8—531no—
1324C4⋊C8—531no—
1325C4⋊C8—531no—
1326C4⋊C8C22×D5311yescharacteristic
1327#103—531no—
1328#103—531no—
1329#103—531no—
1330#103—531no—
1331#103—531no—
1332#103—531no—
1333#103—531no—
1334#103—531no—
1335#103—531no—
1336#103—531no—
1337#103C22×D5311yescharacteristic
1338#103C22×D5311yescharacteristic
1339#103C22×D5311yescharacteristic
1340#103C22×D5311yescharacteristic
1341#102—531no—
1342#102—531no—
1343#102—531no—
1344#102—531no—
1345#102—531no—
1346#102—531no—
1347#102—531no—
1348#102—531no—
1349#102—531no—
1350#102—531no—
1351#102—531no—
1352#102—531no—
1353#102—531no—
1354#102—531no—
1355#102—531no—
1356#102—531no—
1357#102C22×D5311yescharacteristic
1358#102C22×D5311yescharacteristic
1359C22⋊C8—531no—
1360C22⋊C8—531no—
1361C22⋊C8—531no—
1362C22⋊C8—531no—
1363C22⋊C8C22×D5311yescharacteristic
1364C22⋊C8C22×D5311yescharacteristic
1365#97—531no—
1366#97—531no—
1367#97—531no—
1368#97—531no—
1369C4×C8—531no—
1370C4×C8C22×D5311yescharacteristic
1371C24—1061no—
1372C24—1061no—
1373C24—1061no—
1374#41—22no—
1375#41—41no—
1376#41—41no—
1377#41—41no—
1378#41—4242no—
1379#41—2121no—
1380#41—2121no—
1381C2×Q8—21no—
1382C2×Q8—21no—
1383C2×Q8—22no—
1384C2×Q8—41no—
1385C2×Q8—41no—
1386C2×Q8—41no—
1387C2×Q8—531no—
1388C2×Q8—531no—
1389C2×Q8—1061no—
1390C2×Q8—1061no—
1391C2×Q8—1061no—
1392C2×Q8—1061no—
1393C2×Q8—1061no—
1394C2×Q8—1062no—
1395C2×Q8—2121no—
1396C2×Q8C23×D5311yescharacteristic
1397C2×Q8C23×D5311yescharacteristic
1398C2×Q8C23×D5311yescharacteristic
1399C2×Q8C23×D5311yescharacteristic
1400C2×D4—21no—
1401C2×D4—21no—
1402C2×D4—21no—
1403C2×D4—21no—
1404C2×D4—531no—
1405C2×D4—531no—
1406C2×D4—531no—
1407C2×D4—531no—
1408C2×D4—531no—
1409C2×D4—1061no—
1410C2×D4—1061no—
1411C2×D4—1061no—
1412C2×D4—1061no—
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—4242no—
1424C2×D4—4242no—
1425C2×D4—2121no—
1426C2×D4—2121no—
1427C2×D4—2121no—
1428C2×D4—2121no—
1429C2×D4—2121no—
1430C2×D4—2121no—
1431C2×D4D4×D5311yescharacteristic
1432C2×D4C23×D5311yescharacteristic
1433C2×D4C23×D5311yescharacteristic
1434C22×C4—21no—
1435C22×C4—21no—
1436C22×C4—21no—
1437C22×C4—21no—
1438C22×C4—531no—
1439C22×C4—531no—
1440C22×C4—531no—
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×C4C23×D5311yescharacteristic
1450C22×C4C23×D5311yescharacteristic
1451Q16—22no—
1452Q16—22no—
1453Q16—41no—
1454Q16—41no—
1455Q16—2121no—
1456Q16—2121no—
1457SD16—22no—
1458SD16—41no—
1459SD16—41no—
1460SD16—41no—
1461SD16—1062no—
1462SD16—1062no—
1463SD16—1062no—
1464SD16—2121no—
1465SD16—2121no—
1466SD16—2121no—
1467SD16—2121no—
1468SD16—2121no—
1469SD16—2121no—
1470SD16—2121no—
1471D8—41no—
1472D8—2121no—
1473D8—2121no—
1474D8—2121no—
1475M16—41no—
1476M16—41no—
1477M16—2121no—
1478M16—2121no—
1479C2×C8—531no—
1480C2×C8—531no—
1481C2×C8—531no—
1482C2×C8—531no—
1483C2×C8—2121no—
1484C2×C8—2121no—
1485C2×C8C23×D5311yescharacteristic
1486C2×C8C23×D5311yescharacteristic
1487C2×C8C23×D5311yescharacteristic
1488C2×C8C23×D5311yescharacteristic
1489C4⋊C4—21no—
1490C4⋊C4—21no—
1491C4⋊C4—21no—
1492C4⋊C4—21no—
1493C4⋊C4—531no—
1494C4⋊C4—531no—
1495C4⋊C4—531no—
1496C4⋊C4—531no—
1497C4⋊C4—531no—
1498C4⋊C4—531no—
1499C4⋊C4—531no—
1500C4⋊C4—531no—
1501C4⋊C4—531no—
1502C4⋊C4—531no—
1503C4⋊C4—531no—
1504C4⋊C4—531no—
1505C4⋊C4—531no—
1506C4⋊C4—1061no—
1507C4⋊C4—1061no—
1508C4⋊C4—1061no—
1509C4⋊C4—1061no—
1510C4⋊C4—1061no—
1511C4⋊C4—1061no—
1512C4⋊C4—1061no—
1513C4⋊C4—1061no—
1514C4⋊C4—1061no—
1515C4⋊C4—1061no—
1516C4⋊C4—1061no—
1517C4⋊C4—1061no—
1518C4⋊C4—1061no—
1519C4⋊C4—1061no—
1520C4⋊C4—1061no—
1521C4⋊C4—1061no—
1522C4⋊C4—1061no—
1523C4⋊C4—1061no—
1524C4⋊C4D4×D5311yescharacteristic
1525C4⋊C4C23×D5311yescharacteristic
1526C4⋊C4C23×D5311yescharacteristic
1527C22⋊C4—21no—
1528C22⋊C4—21no—
1529C22⋊C4—21no—
1530C22⋊C4—21no—
1531C22⋊C4—21no—
1532C22⋊C4—21no—
1533C22⋊C4—21no—
1534C22⋊C4—21no—
1535C22⋊C4—531no—
1536C22⋊C4—531no—
1537C22⋊C4—531no—
1538C22⋊C4—531no—
1539C22⋊C4—531no—
1540C22⋊C4—531no—
1541C22⋊C4—531no—
1542C22⋊C4—531no—
1543C22⋊C4—1061no—
1544C22⋊C4—1061no—
1545C22⋊C4—1061no—
1546C22⋊C4—1061no—
1547C22⋊C4—1061no—
1548C22⋊C4—1061no—
1549C22⋊C4—1061no—
1550C22⋊C4—1061no—
1551C22⋊C4—1061no—
1552C22⋊C4—1061no—
1553C22⋊C4—1061no—
1554C22⋊C4—1061no—
1555C22⋊C4—1061no—
1556C22⋊C4—1061no—
1557C22⋊C4—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⋊C4D4×D5311yescharacteristic
1573C22⋊C4D4×D5311yescharacteristic
1574C42—21no—
1575C42—21no—
1576C42—531no—
1577C42—531no—
1578C42—531no—
1579C42—531no—
1580C42—531no—
1581C42—1061no—
1582C42—1061no—
1583C42—1061no—
1584C42—1061no—
1585C42—1061no—
1586C42—1061no—
1587C42—1061no—
1588C42—1061no—
1589C42—1061no—
1590C42—1061no—
1591C42—1061no—
1592C42C23×D5311yescharacteristic
1593C23—21no—
1594C23—21no—
1595C23—531no—
1596C23—1061no—
1597C23—1061no—
1598C23—1061no—
1599C23—4241no—
1600C23—4241no—
1601C23—4241no—
1602C23—4241no—
1603C23—4241no—
1604C23—4241no—
1605C23—4241no—
1606C23—4241no—
1607C23—2122no—
1608C23C2×D4×D5311yescharacteristic
1609C23C2×D4×D5311yescharacteristic
1610Q8—21no—
1611Q8—21no—
1612Q8—21no—
1613Q8—21no—
1614Q8—21no—
1615Q8—21no—
1616Q8—21no—
1617Q8—42no—
1618Q8—81no—
1619Q8—1061no—
1620Q8—1061no—
1621Q8—4241no—
1622Q8—4241no—
1623Q8—4241no—
1624Q8—4241no—
1625Q8—2121no—
1626Q8—2122no—
1627Q8#1313326212yes—
1628D4—21no—
1629D4—21no—
1630D4—21no—
1631D4—21no—
1632D4—41no—
1633D4—42no—
1634D4—42no—
1635D4—81no—
1636D4—81no—
1637D4—1061no—
1638D4—1061no—
1639D4—1061no—
1640D4—1061no—
1641D4—1061no—
1642D4—1061no—
1643D4—4241no—
1644D4—4241no—
1645D4—4241no—
1646D4—4241no—
1647D4—4241no—
1648D4—4241no—
1649D4—4241no—
1650D4—4241no—
1651D4—4241no—
1652D4—4241no—
1653D4—4241no—
1654D4—4241no—
1655D4—4241no—
1656D4—2121no—
1657D4—2121no—
1658D4—2122no—
1659C2×C4—21no—
1660C2×C4—21no—
1661C2×C4—21no—
1662C2×C4—21no—
1663C2×C4—21no—
1664C2×C4—21no—
1665C2×C4—21no—
1666C2×C4—21no—
1667C2×C4—21no—
1668C2×C4—21no—
1669C2×C4—42no—
1670C2×C4—42no—
1671C2×C4—81no—
1672C2×C4—81no—
1673C2×C4—531no—
1674C2×C4—531no—
1675C2×C4—531no—
1676C2×C4—531no—
1677C2×C4—531no—
1678C2×C4—531no—
1679C2×C4—531no—
1680C2×C4—1061no—
1681C2×C4—1061no—
1682C2×C4—1061no—
1683C2×C4—1061no—
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—2122no—
1694C2×C4—2121no—
1695C2×C4—2121no—
1696C2×C4—2122no—
1697C2×C4C2×D4×D5311yescharacteristic
1698C2×C4C2×D4×D5311yescharacteristic
1699C2×C4C2×D4×D5311yescharacteristic
1700C2×C4C2×D4×D5311yescharacteristic
1701C2×C4C24×D5311yescharacteristic
1702C8—21no—
1703C8—21no—
1704C8—21no—
1705C8—21no—
1706C8—1061no—
1707C8—1061no—
1708C8—1061no—
1709C8—1061no—
1710C22—21no—
1711C22—21no—
1712C22—21no—
1713C22—21no—
1714C22—21no—
1715C22—21no—
1716C22—41no—
1717C22—41no—
1718C22—41no—
1719C22—41no—
1720C22—41no—
1721C22—41no—
1722C22—8482no—
1723C22—8482no—
1724C22—8482no—
1725C22—1061no—
1726C22—1061no—
1727C22—1061no—
1728C22—2121no—
1729C22—2121no—
1730C22—2121no—
1731C22—2121no—
1732C22—2121no—
1733C22—2121no—
1734C22—2121no—
1735C22—2121no—
1736C22—2121no—
1737C22C22×D4×D5311yescharacteristic
1738C4—21no—
1739C4—21no—
1740C4—22no—
1741C4—21no—
1742C4—21no—
1743C4—41no—
1744C4—41no—
1745C4—41no—
1746C4—41no—
1747C4—41no—
1748C4—1061no—
1749C4—1061no—
1750C4—1061no—
1751C4—1061no—
1752C4—1061no—
1753C4—1061no—
1754C4—1061no—
1755C4—2121no—
1756C4—2121no—
1757C4—2121no—
1758C4—2121no—
1759C4—2121no—
1760C4C2×#1313326211yescharacteristic
1761C4#1681145811yescharacteristic
1762C2—41no—
1763C2—41no—
1764C2—81no—
1765C2—81no—
1766C2—4241no—
1767C2—4241no—
1768C2—4241no—
1769C2—2121no—
1770C2#2028837511yescharacteristic
1771C2#2028949211yescharacteristic
1772C2#2028950011yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3277C2
socleC22×C53C23×D4
hypercenter#3277D53
hypocenterC53#62092
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3277

Complements

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

NH ≅ G/Ntype
1. #20289232C2semidirect
2. #20288723C2semidirect
3. #20287787C2semidirect
4. #20287784C2semidirect
5. #20287527C2semidirect
6. #20287524C2semidirect
7. #20286947C2semidirect
8. #20286941C2semidirect
9. #20286875C2semidirect
10. #20286866C2semidirect
11. #20286781C2semidirect
12. #20286774C2semidirect
13. #20286366C2semidirect
14. #20286219C2semidirect
15. #20286218C2semidirect
16. #20286213C2semidirect
17. #20286211C2semidirect
18. #20286174C2semidirect
19. #20286172C2semidirect
20. #20286097C2semidirect
21. #20285807C2semidirect
22. #20285802C2semidirect
23. #20285717C2semidirect
24. #20284950C2semidirect
25. #20284945C2semidirect
26. #20284859C2semidirect
27. #20284238C2semidirect
28. #20284234C2semidirect
29. #20284211C2semidirect
30. #20283879C2semidirect
31. C53×#3277C2semidirect
32. C2×#13133249C22semidirect
34. C22×#11719924C22semidirect
35. C2×SD16×D53C22semidirect
40. Q8×Dic106C22semidirect
42. #16811344C22semidirect
44. #16811343C22semidirect
46. #16811342C22semidirect
48. #16811337C22semidirect
49. Q8×C22⋊D53C22semidirect
51. #16811280C22semidirect
61. #16811242C22semidirect
63. #16811240C22semidirect
71. #16811175C22semidirect
76. #16811101C22semidirect
77. #16811099C22semidirect
78. #41×Dic53C22semidirect
79. #16811016C22semidirect
80. #16811016C22semidirect
83. #16811004C22semidirect
84. #16810984C22semidirect
85. #16810984C22semidirect
86. #16810984C22semidirect
87. #16810982C22semidirect
90. #16810962C22semidirect
91. #16810961C22semidirect
94. #16810948C22semidirect
95. #16810944C22semidirect
96. #16810918C22semidirect
97. #16810917C22semidirect
98. #16810916C22semidirect
99. #16810916C22semidirect
100. #16810906C22semidirect
101. #16810904C22semidirect
102. #16810902C22semidirect
103. #16810902C22semidirect
104. #16810901C22semidirect
105. #16810901C22semidirect
107. #16810871C22semidirect
109. #16810869C22semidirect
110. #16810867C22semidirect
111. #16810866C22semidirect
112. #16810862C22semidirect
113. #16810861C22semidirect
116. #16810848C22semidirect
117. #16810848C22semidirect
118. #16810847C22semidirect
119. #16810847C22semidirect
120. #16810847C22semidirect
121. #16810847C22semidirect
122. #16810847C22semidirect
123. #16810847C22semidirect
124. #16810847C22semidirect
125. #16810847C22semidirect
126. #16810843C22semidirect
127. #16810842C22semidirect
128. #16810840C22semidirect
129. #16810840C22semidirect
130. #16810840C22semidirect
131. #16810840C22semidirect
132. #16810837C22semidirect
133. #16810835C22semidirect
134. #16810827C22semidirect
135. #16810826C22semidirect
138. #16810822C22semidirect
141. #16810821C22semidirect
142. #16810821C22semidirect
143. #16810816C22semidirect
144. #16810785C22semidirect
145. #16810784C22semidirect
146. #16810779C22semidirect
147. #16810777C22semidirect
149. #16810776C22semidirect
151. #16810772C22semidirect
152. #16810768C22semidirect
153. #16810767C22semidirect
156. #16810756C22semidirect
157. #16810755C22semidirect
158. #16810753C22semidirect
159. #16810752C22semidirect
160. #16810735C22semidirect
161. #16810732C22semidirect
162. #16810730C22semidirect
163. #16810728C22semidirect
164. #16810726C22semidirect
165. #16810726C22semidirect
166. #16810724C22semidirect
167. #16810721C22semidirect
168. Q16×Dic53C22semidirect
169. C4×#11719913C22semidirect
170. #16810708C22semidirect
171. #16810699C22semidirect
172. #16810697C22semidirect
173. #16810695C22semidirect
174. #16810692C22semidirect
175. #16810691C22semidirect
176. #16810682C22semidirect
177. #16810681C22semidirect
178. #16810677C22semidirect
179. #16810651C22semidirect
180. #16810648C22semidirect
181. #16810646C22semidirect
182. #16810632C22semidirect
184. #16810629C22semidirect
185. #16810626C22semidirect
186. #16810619C22semidirect
187. #16810618C22semidirect
188. C2×#137×C53C22semidirect
189. C2×#137×C53C22semidirect
191. C53×#548C22semidirect
192. C53×#495C22semidirect
193. C53×#468C22semidirect
194. C53×#468C22semidirect
195. C53×#464C22semidirect
196. C53×#464C22semidirect
197. C53×#451C22semidirect
198. C53×#451C22semidirect
199. C53×#449C22semidirect
200. C53×#449C22semidirect
201. C4×Q16×C53C22semidirect
202. C53×#436C22semidirect
889. #3277D53semidirect
919. C2×#137C2×D53semidirect
920. C2×#137C2×D53semidirect
941. #548C2×D53semidirect
974. #495C2×D53semidirect
1003. #468C2×D53semidirect
1004. #468C2×D53semidirect
1021. #464C2×D53semidirect
1022. #464C2×D53semidirect
1043. #451C2×D53semidirect
1044. #451C2×D53semidirect
1051. #449C2×D53semidirect
1052. #449C2×D53semidirect
1068. C4×Q16C2×D53semidirect
1072. #436C2×D53semidirect
1089. C53#62092semidirect

Maximal subgroups

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

subgroupindex
#202892322
#202887232
#202877872
#202877842
#202875272
#202875242
#202869472
#202869412
#202868752
#202868662
#202867812
#202867742
#202863662
#202862192
#202862182
#202862132
#202862112
#202861742
#202861722
#202860972
#202858072
#202858022
#202857172
#202849502
#202849452
#202848592
#202842382
#202842342
#202842112
#202838792
C53×#32772
#6209253