Finite Group Databasebeta

← #28257139

Subgroups — #28257139

Order 13568.

1822 conjugacy classes of subgroups.

The subgroup lattice has 1726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288106C211yesmaximal, characteristic, complemented
2#542×D53C211yesmaximal, characteristic, complemented
3#20286184C211yesmaximal, characteristic, complemented
4#20286183C211yesmaximal, characteristic, complemented
5#20286181C211yesmaximal, characteristic, complemented
6#20286179C211yesmaximal, characteristic, complemented
7#20286178C211yesmaximal, characteristic, complemented
8#20286177C211yesmaximal, characteristic, complemented
9#20286174C211yesmaximal, characteristic, complemented
10#20286172C211yesmaximal, characteristic, complemented
11#20286139C211yesmaximal, characteristic, complemented
12#20286137C211yesmaximal, characteristic, complemented
13#20286135C211yesmaximal, characteristic, complemented
14#20286132C211yesmaximal, characteristic, complemented
15#20286130C211yesmaximal, characteristic, complemented
16#20286128C211yesmaximal, characteristic, complemented
17#20286126C211yesmaximal, characteristic, complemented
18#20284529C211yesmaximal, characteristic, complemented
19#20284525C211yesmaximal, characteristic, complemented
20#20284518C211yesmaximal, characteristic, complemented
21#20284510C211yesmaximal, characteristic, complemented
22#20284344C211yesmaximal, characteristic, complemented
23#20284342C211yesmaximal, characteristic, complemented
24#20284329C211yesmaximal, characteristic, complemented
25#20284327C211yesmaximal, characteristic, complemented
26#20284206C211yesmaximal, characteristic, complemented
27#20284206C211yesmaximal, characteristic, complemented
28#20284188C211yesmaximal, characteristic, complemented
29#20284180C211yesmaximal, characteristic, complemented
30#20283276C211yesmaximal, characteristic, complemented
31C53×#3258C211yesmaximal, characteristic, complemented
32C2×#13133249C2211yescharacteristic
33C2×#13133249C2211yescharacteristic
34C2×#13133244C2211yescharacteristic
35C2×#13133244C2211yescharacteristic
36C22×#11719912C2211yescharacteristic
37C2×M16×D53C2211yescharacteristic
38#16811247C2211yescharacteristic
39#16811246C2211yescharacteristic
40#16811246C2211yescharacteristic, complemented
41#16811246C2211yescharacteristic, complemented
42#16811245C2211yescharacteristic
43#16811245C2211yescharacteristic, complemented
44#16811245C2211yescharacteristic, complemented
45#16811244C2211yescharacteristic
46#16811243—21no—
47#16811242C2211yescharacteristic
48#16811241—21no—
49#16811240C2211yescharacteristic
50#16811239—21no—
51#16811238C2211yescharacteristic
52#16811237—21no—
53#16811234C2211yescharacteristic, complemented
54#16811229C2211yescharacteristic, complemented
55#16811228C2211yescharacteristic, complemented
56#16811221—21no—
57#16811221—21no—
58#16811212—21no—
59#16811212—21no—
60#16811179C2211yescharacteristic
61#16811174C2211yescharacteristic
62C4⋊Q8×D53C2211yescharacteristic
63#16811158—21no—
64#16811158—21no—
65#16811156—21no—
66#16811156—21no—
67#126×D53—21no—
68#124×D53—21no—
69#124×D53C2211yescharacteristic
70#16811136C2211yescharacteristic
71#16811136C2211yescharacteristic
72#123×D53—21no—
73C22⋊Q8×D53—21no—
74C22⋊Q8×D53C2211yescharacteristic
75#121×D53C2211yescharacteristic
76C4×#11719949C2211yescharacteristic
77C4×#11719949C2211yescharacteristic
78C4×Q8×D53C2211yescharacteristic
79C4×D4×D53C2211yescharacteristic
80#117×D53C2211yescharacteristic
81#16810931C2211yescharacteristic, complemented
82#16810930C2211yescharacteristic, complemented
83#16810927C2211yescharacteristic, complemented
84#16810924C2211yescharacteristic, complemented
85#16810923C2211yescharacteristic, complemented
86#16810920C2211yescharacteristic, complemented
87#16810918C2211yescharacteristic, complemented
88#16810917C2211yescharacteristic, complemented
89#16810916C2211yescharacteristic, complemented
90#16810916C2211yescharacteristic, complemented
91#16810916C2211yescharacteristic, complemented
92#16810914C2211yescharacteristic, complemented
93#16810912C2211yescharacteristic, complemented
94#16810912C2211yescharacteristic, complemented
95#16810912C2211yescharacteristic, complemented
96#16810911C2211yescharacteristic, complemented
97#16810910C2211yescharacteristic, complemented
98#16810908C2211yescharacteristic, complemented
99#16810907C2211yescharacteristic, complemented
100#16810906C2211yescharacteristic, complemented
101#16810906C2211yescharacteristic, complemented
102#16810906C2211yescharacteristic, complemented
103#16810904C2211yescharacteristic, complemented
104#16810902C2211yescharacteristic, complemented
105#16810902C2211yescharacteristic, complemented
106#16810902C2211yescharacteristic, complemented
107#16810901C2211yescharacteristic, complemented
108#16810900C2211yescharacteristic, complemented
109#16810880C2211yescharacteristic, complemented
110#16810879C2211yescharacteristic, complemented
111#16810878C2211yescharacteristic, complemented
112#16810877C2211yescharacteristic
113#16810876C2211yescharacteristic
114#16810875C2211yescharacteristic
115#16810874C2211yescharacteristic
116#16810872C2211yescharacteristic
117#16810872C2211yescharacteristic, complemented
118#16810871C2211yescharacteristic
119#16810871C2211yescharacteristic, complemented
120#16810870C2211yescharacteristic, complemented
121#16810869C2211yescharacteristic, complemented
122#16810866C2211yescharacteristic
123#16810863C2211yescharacteristic, complemented
124#16810862C2211yescharacteristic, complemented
125#16810861C2211yescharacteristic, complemented
126#16810860C2211yescharacteristic
127#16810859C2211yescharacteristic
128#16810858C2211yescharacteristic
129#16810857C2211yescharacteristic
130#16810855C2211yescharacteristic
131#16810855C2211yescharacteristic, complemented
132#16810854C2211yescharacteristic
133#16810854C2211yescharacteristic, complemented
134#16810853C2211yescharacteristic, complemented
135#16810852C2211yescharacteristic, complemented
136#16810849C2211yescharacteristic
137#16810848C2211yescharacteristic, complemented
138#16810848C2211yescharacteristic, complemented
139#16810847C2211yescharacteristic, complemented
140#16810847C2211yescharacteristic, complemented
141#16810847C2211yescharacteristic, complemented
142#16810847C2211yescharacteristic, complemented
143#16810845C2211yescharacteristic, complemented
144#16810845C2211yescharacteristic, complemented
145#16810843C2211yescharacteristic, complemented
146#16810843C2211yescharacteristic, complemented
147#16810841C2211yescharacteristic, complemented
148#16810841C2211yescharacteristic, complemented
149#16810841C2211yescharacteristic, complemented
150#16810841C2211yescharacteristic, complemented
151#16810840C2211yescharacteristic, complemented
152#16810840C2211yescharacteristic, complemented
153#16810839C2211yescharacteristic, complemented
154#16810839C2211yescharacteristic, complemented
155#16810837C2211yescharacteristic, complemented
156#16810837C2211yescharacteristic, complemented
157#16810835C2211yescharacteristic, complemented
158#16810835C2211yescharacteristic, complemented
159#16810830C2211yescharacteristic, complemented
160#16810825C2211yescharacteristic, complemented
161#16810824C2211yescharacteristic, complemented
162#16810823C2211yescharacteristic, complemented
163#16810819C2211yescharacteristic, complemented
164#16810818C2211yescharacteristic, complemented
165#16810664C2211yescharacteristic
166#16810664C2211yescharacteristic
167#16810662C2211yescharacteristic
168#16810662C2211yescharacteristic
169#16810651C2211yescharacteristic, complemented
170#16810650C2211yescharacteristic, complemented
171#16810649C2211yescharacteristic, complemented
172#16810648C2211yescharacteristic, complemented
173#16810648C2211yescharacteristic, complemented
174#16810648C2211yescharacteristic, complemented
175#16810648C2211yescharacteristic, complemented
176#16810645C2211yescharacteristic
177#16810645C2211yescharacteristic
178#16810645C2211yescharacteristic
179#16810645C2211yescharacteristic
180#16810630C2211yescharacteristic
181#16810630C2211yescharacteristic
182#16810626C2211yescharacteristic
183#16810626C2211yescharacteristic
184#16810623C2211yescharacteristic
185#16810623C2211yescharacteristic
186#16810623C2211yescharacteristic
187#16810623C2211yescharacteristic
188C53×#542C2211yescharacteristic
189C53×#541C2211yescharacteristic, complemented
190C53×#479C2211yescharacteristic, complemented
191C53×#478C2211yescharacteristic, complemented
192C53×#477C2211yescharacteristic, complemented
193C53×#475C2211yescharacteristic, complemented
194C53×#470C2211yescharacteristic, complemented
195C53×#468C2211yescharacteristic
196C53×#467C2211yescharacteristic, complemented
197C53×#465C2211yescharacteristic
198C53×#464C2211yescharacteristic, complemented
199C53×#464C2211yescharacteristic, complemented
200C53×#462C2211yescharacteristic, complemented
201C53×#461C2211yescharacteristic, complemented
202C53×#424C2211yescharacteristic, complemented
203C2×#11719949C2311yescharacteristic
204C2×#11719949C2311yescharacteristic
205C2×Q8×D53—21no—
206C2×Q8×D53C2311yescharacteristic
207C2×D4×D53—21no—
208C2×D4×D53C2311yescharacteristic
209C22×C4×D53—21no—
210C22×C4×D53C2311yescharacteristic
211#13133249—42no—
212#13133249—42no—
213#13133244—42no—
214#13133244—42no—
215C2×#11719925C2311yescharacteristic
216C2×#11719925C2311yescharacteristic
217C2×#11719913C2311yescharacteristic
218C2×#11719913C2311yescharacteristic
219C2×#11719924C2311yescharacteristic
220C2×#11719924C2311yescharacteristic
221C2×#11719924C2311yescharacteristic
222C2×#11719924C2311yescharacteristic
223C2×D424C2311yescharacteristic
224C2×D424C2311yescharacteristic
225C2×#11719922C2311yescharacteristic
226C2×#11719922C2311yescharacteristic
227C2×#11719917C2311yescharacteristic
228C2×#11719912—42no—
229C2×#11719912C2311yescharacteristic
230C2×#11719912C2311yescharacteristic
231C2×#11719912C2311yescharacteristic
232C2×#11719912C2311yescharacteristic
233C2×#11719912C2311yescharacteristic
234C2×#11719912C2311yescharacteristic
235M16×D53—42no—
236C22×#88322C2311yescharacteristic
237C2×C8×D53C2311yescharacteristic
238C2×C8×D53C2311yescharacteristic
239#13133217C2311yescharacteristic
240#13133216—21no—
241#13133216C2311yescharacteristic
242#13133216C2311yescharacteristic
243#13133216C2311yescharacteristic
244#13133216C2311yescharacteristic
245#13133215—21no—
246#13133214C2311yescharacteristic
247#13133212—21no—
248#13133212—21no—
249#13133212—21no—
250#13133212—21no—
251#13133212—21no—
252#13133212—21no—
253#13133212—21no—
254#13133211—21no—
255#13133211—21no—
256#13133211—21no—
257#13133210—21no—
258#13133210—21no—
259#13133210—21no—
260#13133209C2311yescharacteristic
261#13133207—21no—
262#13133207—21no—
263#13133206—21no—
264#13133206C2311yescharacteristic
265#13133206C2311yescharacteristic
266#13133206C2311yescharacteristic
267#13133205—21no—
268#13133205—21no—
269#13133205—21no—
270#13133205C2311yescharacteristic
271#13133204—21no—
272#13133204C2311yescharacteristic
273#13133203—21no—
274#13133203—21no—
275#13133203—21no—
276#13133203—21no—
277#13133203—21no—
278#13133203—21no—
279#13133203—21no—
280#13133203—21no—
281#13133202—21no—
282#13133202—21no—
283#13133202—21no—
284#13133202—21no—
285#13133202—21no—
286#13133202—21no—
287#13133202—21no—
288#13133202—21no—
289#13133202—21no—
290#13133202—21no—
291#13133201—21no—
292#13133200—21no—
293#13133199—21no—
294#13133199—21no—
295#13133199—21no—
296#13133199—21no—
297#13133198—21no—
298#13133197—21no—
299#13133197—21no—
300#13133197—21no—
301#13133197C2311yescharacteristic
302#13133196—21no—
303#13133196C2311yescharacteristic
304#13133195—21no—
305#13133195—21no—
306#13133195—21no—
307#13133195—21no—
308#13133195—21no—
309#13133195—21no—
310#13133195—21no—
311#13133194—21no—
312#13133194—21no—
313#13133194—21no—
314#13133193—21no—
315#13133193C2311yescharacteristic
316#13133193C2311yescharacteristic
317#13133193C2311yescharacteristic
318#13133192—21no—
319#13133192—21no—
320#13133192—21no—
321#13133192—21no—
322#13133192C2311yescharacteristic
323#13133192C2311yescharacteristic
324#13133192C2311yescharacteristic
325#13133191C2311yescharacteristic
326#13133191C2311yescharacteristic
327#13133191C2311yescharacteristic
328#13133190—21no—
329#13133190—21no—
330#13133190—21no—
331#13133189—21no—
332#13133188C2311yescharacteristic
333#13133187—21no—
334#13133187—21no—
335Q8×Dic53C2311yescharacteristic
336Q8×Dic53C2311yescharacteristic
337Q8×Dic53C2311yescharacteristic
338C4×Dic106—21no—
339C4×Dic106C2311yescharacteristic
340#13133182—21no—
341#13133182—21no—
342#13133182—21no—
343#13133182C2311yescharacteristic
344C4×D212—21no—
345C4×D212—21no—
346C4×D212C2311yescharacteristic
347C4×D212C2311yescharacteristic
348C4×D212C2311yescharacteristic
349D4×Dic53C2311yescharacteristic
350#13133179—21no—
351#13133179—21no—
352#13133179—21no—
353#13133179—21no—
354#13133179—21no—
355#13133179—21no—
356#13133179C2311yescharacteristic
357#13133179C2311yescharacteristic
358#13133179C2311yescharacteristic
359C4×C22⋊D53—21no—
360#13133177—21no—
361#13133177—21no—
362#13133177—21no—
363#13133176C2311yescharacteristic
364#13133175—21no—
365#13133175—21no—
366#13133175D411yescharacteristic
367#13133175D411yescharacteristic
368#13133175C2311yescharacteristic
369#13133175C2311yescharacteristic
370#13133174C2311yescharacteristic
371#13133174C2311yescharacteristic
372#13133173D411yescharacteristic
373#13133173D411yescharacteristic
374C4⋊C4×D53—21no—
375C4⋊C4×D53—21no—
376C4⋊C4×D53—21no—
377C4⋊C4×D53D411yescharacteristic
378C4⋊C4×D53D411yescharacteristic
379C4⋊C4×D53C2311yescharacteristic
380C4⋊C4×D53C2311yescharacteristic
381C22⋊C4×D53—21no—
382C22⋊C4×D53—21no—
383C22⋊C4×D53—21no—
384C22⋊C4×D53—21no—
385C22⋊C4×D53—21no—
386C22⋊C4×D53D411yescharacteristic
387C22⋊C4×D53D411yescharacteristic
388C42×D53—21no—
389C42×D53—21no—
390C42×D53—21no—
391C42×D53C2311yescharacteristic
392C42×D53C2311yescharacteristic
393#13133151C2311yescharacteristic
394#13133151C2311yescharacteristic
395#13133150C2311yescharacteristic
396#13133150C2311yescharacteristic
397#13133150C2311yescharacteristic
398#13133150C2311yescharacteristic
399#13133149C2311yescharacteristic
400#13133149C2311yescharacteristic
401#13133148C2311yescharacteristic
402#13133148C2311yescharacteristic
403#13133148C2311yescharacteristic
404#13133148C2311yescharacteristic
405C4⋊#88322C2311yescharacteristic
406C4⋊#88322C2311yescharacteristic
407C4⋊#88322C2311yescharacteristic
408C4⋊#88322C2311yescharacteristic
409#13133146C2311yescharacteristic
410#13133146C2311yescharacteristic
411#13133146C2311yescharacteristic
412#13133146C2311yescharacteristic
413#13133146C2311yescharacteristic
414#13133146C2311yescharacteristic
415#13133146C2311yescharacteristic
416#13133146C2311yescharacteristic
417#13133142C2311yescharacteristic
418#13133142C2311yescharacteristic
419#13133141C2311yescharacteristic
420#13133141C2311yescharacteristic
421#13133141C2311yescharacteristic
422#13133141C2311yescharacteristic
423#13133141C2311yescharacteristic
424#13133141C2311yescharacteristic
425#13133140C2311yescharacteristic
426#13133140C2311yescharacteristic
427#13133139C2311yescharacteristic
428#13133139C2311yescharacteristic
429#13133139C2311yescharacteristic
430#13133139C2311yescharacteristic
431#13133139C2311yescharacteristic
432#13133139C2311yescharacteristic
433#13133138C2311yescharacteristic
434#13133138C2311yescharacteristic
435#13133137C2311yescharacteristic
436#13133137C2311yescharacteristic
437#13133137C2311yescharacteristic
438#13133137C2311yescharacteristic
439#13133137C2311yescharacteristic
440#13133137C2311yescharacteristic
441C2×Q16×C53C2311yescharacteristic
442C2×Q16×C53C2311yescharacteristic
443C2×SD16×C53C2311yescharacteristic
444C2×SD16×C53C2311yescharacteristic
445C2×M16×C53C2311yescharacteristic
446C22×C8×C53C2311yescharacteristic
447C4⋊Q8×C53C2311yescharacteristic
448C4⋊Q8×C53C2311yescharacteristic
449#126×C53—21no—
450#126×C53—21no—
451#126×C53—21no—
452#125×C53—21no—
453#125×C53—21no—
454#125×C53C2311yescharacteristic
455#124×C53—21no—
456#124×C53C2311yescharacteristic
457#123×C53—21no—
458C22⋊Q8×C53—21no—
459C22⋊Q8×C53C2311yescharacteristic
460C22⋊Q8×C53C2311yescharacteristic
461C22⋊Q8×C53C2311yescharacteristic
462#121×C53C2311yescharacteristic
463C4×Q8×C53C2311yescharacteristic
464C4×Q8×C53C2311yescharacteristic
465C4×Q8×C53C2311yescharacteristic
466C4×D4×C53C2311yescharacteristic
467#117×C53C2311yescharacteristic
468#107×C53C2311yescharacteristic
469#107×C53C2311yescharacteristic
470#106×C53C2311yescharacteristic
471#106×C53C2311yescharacteristic
472C4⋊C8×C53C2311yescharacteristic
473C4⋊C8×C53C2311yescharacteristic
474C4⋊C8×C53C2311yescharacteristic
475C4⋊C8×C53C2311yescharacteristic
476#103×C53C2311yescharacteristic
477#103×C53C2311yescharacteristic
478#103×C53C2311yescharacteristic
479#103×C53C2311yescharacteristic
480#103×C53C2311yescharacteristic
481#103×C53C2311yescharacteristic
482#102×C53C2311yescharacteristic
483#102×C53C2311yescharacteristic
484C23×D53—21no—
485C23×D53C2×D411yescharacteristic
486C2×Q8×C53—21no—
487C2×Q8×C53C2411yescharacteristic
488C2×Q8×C53C2411yescharacteristic
489C2×Q8×C53C2411yescharacteristic
490C2×D4×C53—21no—
491C2×D4×C53C2411yescharacteristic
492C22×C4×C53—21no—
493C22×C4×C53C2411yescharacteristic
494C2×C22⋊D53—21no—
495C2×C22⋊D53—21no—
496C2×C22⋊D53—21no—
497C2×C22⋊D53—21no—
498C2×C22⋊D53—21no—
499C22×Dic53—21no—
500C22×Dic53C2×D411yescharacteristic
501#11719949—22no—
502#11719949—22no—
503#11719949—22no—
504#11719949—22no—
505Q8×D53—22no—
506Q8×D53—22no—
507Q8×D53—82no—
508D4×D53—22no—
509D4×D53—22no—
510D4×D53—82no—
511C2×D212—21no—
512C2×D212—21no—
513C2×D212—21no—
514C2×D212—21no—
515C2×D212—21no—
516C2×D212—21no—
517C2×D212—21no—
518C2×D212C2411yescharacteristic
519C2×D212C2411yescharacteristic
520C2×D212C2411yescharacteristic
521C2×C4×D53—22no—
522C2×C4×D53—22no—
523C2×C4×D53—21no—
524C2×C4×D53—21no—
525C2×C4×D53—21no—
526C2×C4×D53—21no—
527C2×C4×D53—21no—
528C2×C4×D53—21no—
529C2×C4×D53—21no—
530C2×C4×D53—21no—
531C2×C4×D53—21no—
532C2×C4×D53—21no—
533C2×C4×D53—21no—
534C2×C4×D53—82no—
535C2×C4×D53C2×D411yescharacteristic
536C2×C4×D53C2×D411yescharacteristic
537C2×C4×D53C2×D411yescharacteristic
538C2×C4×D53C2×D411yescharacteristic
539C2×C4×D53C2×D411yescharacteristic
540C2×C4×D53C2×D411yescharacteristic
541C2×C4×D53C2411yescharacteristic
542C2×C4×D53C2411yescharacteristic
543C2×Dic106—21no—
544C2×Dic106—21no—
545C2×Dic106—21no—
546C2×Dic106—21no—
547C2×Dic106—21no—
548C2×Dic106—21no—
549C2×Dic106C2411yescharacteristic
550Q16×C53—41no—
551Q16×C53—41no—
552SD16×C53—41no—
553SD16×C53—41no—
554M16×C53—41no—
555C2×C8×C53—41no—
556C2×C8×C53C2411yescharacteristic
557C2×C8×C53C2411yescharacteristic
558C2×C8×C53C2411yescharacteristic
559C2×C8×C53C2411yescharacteristic
560C4⋊C4×C53—21no—
561C4⋊C4×C53—21no—
562C4⋊C4×C53—21no—
563C4⋊C4×C53—21no—
564C4⋊C4×C53—21no—
565C4⋊C4×C53—21no—
566C4⋊C4×C53—21no—
567C4⋊C4×C53—21no—
568C4⋊C4×C53—21no—
569C4⋊C4×C53—21no—
570C4⋊C4×C53—21no—
571C4⋊C4×C53C2×D411yescharacteristic
572C4⋊C4×C53C2×D411yescharacteristic
573C4⋊C4×C53C2411yescharacteristic
574C4⋊C4×C53C2411yescharacteristic
575C4⋊C4×C53C2411yescharacteristic
576C4⋊C4×C53C2411yescharacteristic
577C22⋊C4×C53—21no—
578C22⋊C4×C53—21no—
579C22⋊C4×C53—21no—
580C22⋊C4×C53—21no—
581C22⋊C4×C53—21no—
582C22⋊C4×C53—21no—
583C22⋊C4×C53—21no—
584C22⋊C4×C53C2×D411yescharacteristic
585C22⋊C4×C53C2×D411yescharacteristic
586C42×C53—21no—
587C42×C53—21no—
588C42×C53—21no—
589C42×C53C2411yescharacteristic
590C42×C53C2411yescharacteristic
591C22⋊Dic53—21no—
592C22⋊Dic53—21no—
593C22⋊Dic53—21no—
594C22⋊Dic53—21no—
595C22⋊Dic53—21no—
596C22⋊Dic53C2×D411yescharacteristic
597C22⋊Dic53C2×D411yescharacteristic
598#11719925—41no—
599#11719925—41no—
600#11719924—41no—
601#11719924—41no—
602#11719924—41no—
603#11719924—41no—
604#11719922—41no—
605#11719922—41no—
606#11719921—21no—
607#11719921—21no—
608#11719921—21no—
609#11719921—21no—
610#11719921—21no—
611#11719921—21no—
612#11719921—21no—
613#11719921—21no—
614#11719921—21no—
615#11719921—21no—
616#11719921—21no—
617#11719921—21no—
618#11719921—21no—
619#11719921—21no—
620#11719921—21no—
621#11719921—21no—
622#11719921—21no—
623#11719921—21no—
624#11719921—21no—
625#11719921—21no—
626#11719921—21no—
627#11719921—21no—
628#11719921—21no—
629#11719921—21no—
630#11719921—21no—
631#11719921—21no—
632#11719921C2×D411yescharacteristic
633#11719921C2×D411yescharacteristic
634#11719921C2×D411yescharacteristic
635#11719921C2×D411yescharacteristic
636C4⋊Dic53—21no—
637C4⋊Dic53—21no—
638C4⋊Dic53—21no—
639C4⋊Dic53—21no—
640C4⋊Dic53—21no—
641C4⋊Dic53C2×D411yescharacteristic
642C4⋊Dic53C2×D411yescharacteristic
643C4⋊Dic53C2411yescharacteristic
644C4⋊Dic53C2411yescharacteristic
645C4⋊Dic53C2411yescharacteristic
646C4⋊Dic53C2411yescharacteristic
647#11719919—21no—
648#11719919—21no—
649#11719919—21no—
650#11719919—21no—
651#11719919—21no—
652#11719919—21no—
653#11719919—21no—
654#11719919—21no—
655#11719919—21no—
656#11719919—21no—
657#11719919—21no—
658#11719919—21no—
659#11719919—21no—
660#11719919—21no—
661#11719919C2×D411yescharacteristic
662#11719919C2×D411yescharacteristic
663#11719919C2×D411yescharacteristic
664#11719919C2×D411yescharacteristic
665C4×Dic53—21no—
666C4×Dic53—21no—
667C4×Dic53—21no—
668C4×Dic53—21no—
669C4×Dic53—21no—
670C4×Dic53—21no—
671C4×Dic53—21no—
672C4×Dic53C2×D411yescharacteristic
673C4×Dic53C2×D411yescharacteristic
674C4×Dic53C2×D411yescharacteristic
675C4×Dic53C2×D411yescharacteristic
676C4×Dic53C2411yescharacteristic
677C4×Dic53C2411yescharacteristic
678#11719917—41no—
679C2×#88322—41no—
680C2×#88322C2411yescharacteristic
681C2×#88322C2411yescharacteristic
682C2×#88322C2411yescharacteristic
683C2×#88322C2411yescharacteristic
684D424—41no—
685D424—41no—
686#11719913—41no—
687#11719913—41no—
688#11719912—22no—
689#11719912—22no—
690#11719912—22no—
691#11719912—22no—
692#11719912—41no—
693#11719912—41no—
694C8×D53—41no—
695C8×D53—41no—
696C23×C53—21no—
697C23×C53C22×D411yescharacteristic
698C22×D53—22no—
699C22×D53—21no—
700C22×D53—21no—
701C22×D53—21no—
702C22×D53—41no—
703C22×D53—41no—
704C22×D53—42no—
705C22×D53—42no—
706C22×D53—42no—
707C22×D53C22×D411yescharacteristic
708C22×D53C22×D411yescharacteristic
709Q8×C53—21no—
710Q8×C53—21no—
711Q8×C53—21no—
712Q8×C53—21no—
713Q8×C53—21no—
714Q8×C53—21no—
715Q8×C53—81no—
716D4×C53—21no—
717D4×C53—21no—
718D4×C53—81no—
719C2×C4×C53—21no—
720C2×C4×C53—21no—
721C2×C4×C53—21no—
722C2×C4×C53—21no—
723C2×C4×C53—21no—
724C2×C4×C53—21no—
725C2×C4×C53—21no—
726C2×C4×C53—21no—
727C2×C4×C53—21no—
728C2×C4×C53—81no—
729C2×C4×C53C22×D411yescharacteristic
730C2×C4×C53C22×D411yescharacteristic
731C2×C4×C53C22×D411yescharacteristic
732C2×C4×C53C22×D411yescharacteristic
733C2×C4×C53C22×D411yescharacteristic
734C2×C4×C53C2511yescharacteristic
735C22⋊D53—42no—
736C22⋊D53—81no—
737C22⋊D53—81no—
738C22⋊D53—81no—
739C22⋊D53—81no—
740C2×Dic53—22no—
741C2×Dic53—21no—
742C2×Dic53—21no—
743C2×Dic53—21no—
744C2×Dic53—21no—
745C2×Dic53—21no—
746C2×Dic53—81no—
747C2×Dic53C22×D411yescharacteristic
748C2×Dic53C22×D411yescharacteristic
749C2×Dic53C22×D411yescharacteristic
750C2×Dic53C22×D411yescharacteristic
751C2×Dic53C22×D411yescharacteristic
752C2×Dic53C22×D411yescharacteristic
753D212—21no—
754D212—21no—
755D212—21no—
756D212—21no—
757D212—21no—
758D212—21no—
759D212—42no—
760D212—42no—
761D212—81no—
762D212—81no—
763D212—81no—
764D212—81no—
765D212—81no—
766C4×D53—22no—
767C4×D53—21no—
768C4×D53—21no—
769C4×D53—22no—
770C4×D53—41no—
771C4×D53—41no—
772C4×D53—41no—
773C4×D53—41no—
774C4×D53—42no—
775C4×D53—42no—
776C4×D53—42no—
777C4×D53—42no—
778C4×D53—42no—
779C4×D53—81no—
780C4×D53—81no—
781C4×D53—81no—
782C4×D53—81no—
783C4×D53—81no—
784C4×D53—81no—
785C4×D53H(5,𝔽2)12yes—
786C4×D532−1+412yes—
787Dic106—21no—
788Dic106—21no—
789Dic106—42no—
790Dic106—81no—
791Dic106—81no—
792Dic106—81no—
793Dic106—81no—
794Dic106—81no—
795C8×C53—21no—
796C8×C53—21no—
797C8×C53—21no—
798C8×C53—21no—
799#88322—21no—
800#88322—21no—
801#88322—21no—
802#88322—21no—
803#60919—531nomaximal, Sylow
804C22×C53—21no—
805C22×C53—21no—
806C22×C53—21no—
807C22×C53—41no—
808C22×C53—41no—
809C22×C53—41no—
810C22×C53C23×D411yescharacteristic
811C2×D53—21no—
812C2×D53—21no—
813C2×D53—21no—
814C2×D53—21no—
815C2×D53—21no—
816C2×D53—41no—
817C2×D53—41no—
818C2×D53—41no—
819C2×D53—41no—
820C2×D53—41no—
821C2×D53—41no—
822C2×D53—41no—
823C2×D53—41no—
824C2×D53—41no—
825C2×D53—82no—
826C2×D53—84no—
827C2×D53#53712yes—
828C4×C53—21no—
829C4×C53—21no—
830C4×C53—21no—
831C4×C53—21no—
832C4×C53—21no—
833C4×C53—41no—
834C4×C53—41no—
835C4×C53—41no—
836C4×C53—41no—
837C4×C53—41no—
838C4×C53—41no—
839C4×C53—41no—
840C4×C53C2×H(5,𝔽2)11yescharacteristic
841C4×C53C2×2−1+411yescharacteristic
842Dic53—21no—
843Dic53—21no—
844Dic53—21no—
845Dic53—21no—
846Dic53—21no—
847Dic53—41no—
848Dic53—41no—
849Dic53—41no—
850Dic53—41no—
851Dic53—41no—
852Dic53#53712yes—
853#3455—531no—
854C2×#542—531no—
855#3263—531no—
856#3263—531no—
857#3263—531no—
858#3263—531no—
859#3262—531no—
860#3262—531no—
861#3262—531no—
862#3262—531no—
863#3258—531no—
864#3258—531no—
865#3258—531no—
866#3258D5311yescharacteristic, complemented
867#3257—531no—
868#3257—531no—
869#3257—531no—
870#3257—531no—
871#3079—531no—
872#3079—531no—
873#3078—531no—
874#3077—531no—
875#3056—531no—
876#3056—531no—
877#3055—531no—
878#3055—531no—
879#3040—531no—
880#3040—531no—
881#3037—531no—
882#3036—531no—
883#2905—531no—
884C2×C53—41no—
885C2×C53—81no—
886C2×C53C2×#53711yescharacteristic
887C2×C53#358511yescharacteristic
888C2×C53#358611yescharacteristic
889D53—22no—
890D53—41no—
891D53—81no—
892D53—81no—
893D53—81no—
894C2×#137—531no—
895C2×#137—531no—
896C2×AGL(1,ℤ/8)—531no—
897C2×AGL(1,ℤ/8)—531no—
898C22×M16—531no—
899C22×M16—531no—
900#542—531no—
901#542—531no—
902#542—531no—
903#542—531no—
904#542—531no—
905#542—531no—
906#542—531no—
907#542—531no—
908#542—531no—
909#542—531no—
910#542—531no—
911#542—1061no—
912#542—1061no—
913#542—1061no—
914#542—1061no—
915#542C2×D5311yescharacteristic
916#541—531no—
917#541C2×D5311yescharacteristic, complemented
918#540—531no—
919#540—531no—
920#539—1061no—
921#539—1061no—
922#538—1061no—
923#538—1061no—
924#533—531no—
925#532—531no—
926C2×C4⋊Q8—531no—
927#529—1061no—
928#529—1061no—
929#529—1061no—
930#529—1061no—
931C2×#126—1061no—
932C2×#124—531no—
933C2×#124—1061no—
934#525—531no—
935#525—531no—
936C2×#123—1061no—
937C2×C22⋊Q8—531no—
938C2×C22⋊Q8—1061no—
939C2×#121—531no—
940C4×#41—531no—
941C4×#41—531no—
942C2×C4×Q8—531no—
943C2×C4×D4—531no—
944C2×#117—531no—
945#479—531no—
946#479—531no—
947#479—531no—
948#479C2×D5311yescharacteristic, complemented
949#478—531no—
950#478—531no—
951#478—531no—
952#478C2×D5311yescharacteristic, complemented
953#477—531no—
954#477—531no—
955#477—531no—
956#477—531no—
957#477—531no—
958#477C2×D5311yescharacteristic, complemented
959#476—531no—
960#476—531no—
961#476—531no—
962#476—531no—
963#476—531no—
964#476—531no—
965#475—531no—
966#475—531no—
967#475—531no—
968#475—531no—
969#475—531no—
970#475C2×D5311yescharacteristic, complemented
971#474—531no—
972#474—531no—
973#474—531no—
974#474—531no—
975#474—531no—
976#474—531no—
977#470—531no—
978#470—531no—
979#470—531no—
980#470C2×D5311yescharacteristic, complemented
981#469—531no—
982#469—531no—
983#469—531no—
984#469—531no—
985#468—531no—
986#468—531no—
987#468—531no—
988#468—531no—
989#468—531no—
990#468—531no—
991#468—531no—
992#468C2×D5311yescharacteristic
993#467—531no—
994#467—531no—
995#467—531no—
996#467C2×D5311yescharacteristic, complemented
997#466—531no—
998#466—531no—
999#466—531no—
1000#466—531no—
1001#465—531no—
1002#465—531no—
1003#465—531no—
1004#465—531no—
1005#465—531no—
1006#465—531no—
1007#465—531no—
1008#465C2×D5311yescharacteristic
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#464C2×D5311yescharacteristic, complemented
1020#464C2×D5311yescharacteristic, complemented
1021#463—531no—
1022#463—531no—
1023#463—531no—
1024#463—531no—
1025#463—531no—
1026#463—531no—
1027#463—531no—
1028#463—531no—
1029#463—531no—
1030#463—531no—
1031#463—531no—
1032#463—531no—
1033#462—531no—
1034#462C2×D5311yescharacteristic, complemented
1035#461—531no—
1036#461C2×D5311yescharacteristic, complemented
1037#460—531no—
1038#460—531no—
1039#459—531no—
1040#459—531no—
1041#428—531no—
1042#428—531no—
1043#428—531no—
1044#428—531no—
1045#424—531no—
1046#424—531no—
1047#424—531no—
1048#424—531no—
1049#424—531no—
1050#424—531no—
1051#424—531no—
1052#424C2×D5311yescharacteristic, complemented
1053#423—531no—
1054#423—531no—
1055#423—531no—
1056#423—531no—
1057#419—531no—
1058#419—531no—
1059#418—531no—
1060#418—531no—
1061#417—531no—
1062#417—531no—
1063#417—531no—
1064#417—531no—
1065C53#6091911yescharacteristic, complemented, Sylow
1066C2×#41—531no—
1067C2×#41—531no—
1068C22×Q8—531no—
1069C22×Q8—1061no—
1070C22×D4—531no—
1071C22×D4—1061no—
1072C23×C4—531no—
1073C23×C4—1061no—
1074#137—2122no—
1075#137—2122no—
1076AGL(1,ℤ/8)—2122no—
1077AGL(1,ℤ/8)—2122no—
1078C2×Q16—531no—
1079C2×Q16—531no—
1080C2×Q16C22×D5311yescharacteristic
1081C2×Q16C22×D5311yescharacteristic
1082C2×SD16—531no—
1083C2×SD16—531no—
1084C2×SD16—531no—
1085C2×SD16—531no—
1086C2×SD16—531no—
1087C2×SD16—531no—
1088C2×SD16C22×D5311yescharacteristic
1089C2×SD16C22×D5311yescharacteristic
1090C2×D8—531no—
1091C2×D8—531no—
1092C2×D8—531no—
1093C2×D8—531no—
1094C2×M16—531no—
1095C2×M16—531no—
1096C2×M16—531no—
1097C2×M16—531no—
1098C2×M16—531no—
1099C2×M16—531no—
1100C2×M16—531no—
1101C2×M16—2122no—
1102C2×M16—2122no—
1103C2×M16C22×D5311yescharacteristic
1104C22×C8—531no—
1105C22×C8—531no—
1106C22×C8—531no—
1107C22×C8C22×D5311yescharacteristic
1108C4⋊Q8—531no—
1109C4⋊Q8—531no—
1110C4⋊Q8—531no—
1111C4⋊Q8—531no—
1112C4⋊Q8—531no—
1113C4⋊Q8—1061no—
1114C4⋊Q8—1061no—
1115C4⋊Q8C22×D5311yescharacteristic
1116C4⋊Q8C22×D5311yescharacteristic
1117#127—531no—
1118#126—21no—
1119#126—21no—
1120#126—21no—
1121#126—1061no—
1122#126—1061no—
1123#126—1061no—
1124#126—1061no—
1125#126—1061no—
1126#126—1061no—
1127#126—1061no—
1128#126—1061no—
1129#126—1061no—
1130#126—1061no—
1131#126—1061no—
1132#126—1061no—
1133#126—1061no—
1134#125—21no—
1135#125—21no—
1136#125—531no—
1137#125—1061no—
1138#125—1061no—
1139#125C22×D5311yescharacteristic
1140#124—21no—
1141#124—531no—
1142#124—531no—
1143#124—531no—
1144#124—531no—
1145#124—531no—
1146#124—1061no—
1147#124—1061no—
1148#124—1061no—
1149#124—1061no—
1150#124—1061no—
1151#124—1061no—
1152#124—1061no—
1153#124—1061no—
1154#124—1061no—
1155#124—1061no—
1156#124—1061no—
1157#124—1061no—
1158#124—1061no—
1159#124C22×D5311yescharacteristic
1160#123—21no—
1161#123—1061no—
1162#123—1061no—
1163#123—1061no—
1164#123—1061no—
1165#123—1061no—
1166#123—1061no—
1167#123—1061no—
1168#123—1061no—
1169#123—1061no—
1170#123—1061no—
1171#123—1061no—
1172#123—1061no—
1173#123—1061no—
1174#123—1061no—
1175#123—1061no—
1176#123—1061no—
1177#123—1061no—
1178C22⋊Q8—21no—
1179C22⋊Q8—531no—
1180C22⋊Q8—531no—
1181C22⋊Q8—531no—
1182C22⋊Q8—531no—
1183C22⋊Q8—531no—
1184C22⋊Q8—1061no—
1185C22⋊Q8—1061no—
1186C22⋊Q8—1061no—
1187C22⋊Q8—1061no—
1188C22⋊Q8—1061no—
1189C22⋊Q8—1061no—
1190C22⋊Q8—1061no—
1191C22⋊Q8—1061no—
1192C22⋊Q8—1061no—
1193C22⋊Q8—1061no—
1194C22⋊Q8—1061no—
1195C22⋊Q8—1061no—
1196C22⋊Q8—1061no—
1197C22⋊Q8—1061no—
1198C22⋊Q8—1061no—
1199C22⋊Q8C22×D5311yescharacteristic
1200C22⋊Q8C22×D5311yescharacteristic
1201C22⋊Q8C22×D5311yescharacteristic
1202#121—531no—
1203#121—531no—
1204#121—531no—
1205#121—531no—
1206#121—531no—
1207#121—531no—
1208#121—531no—
1209#121—1061no—
1210#121—1061no—
1211#121—1061no—
1212#121—1061no—
1213#121—1061no—
1214#121—1061no—
1215#121—1061no—
1216#121—1061no—
1217#121C22×D5311yescharacteristic
1218#120—1061no—
1219#120—1061no—
1220C4×Q8—531no—
1221C4×Q8—531no—
1222C4×Q8—531no—
1223C4×Q8—531no—
1224C4×Q8—531no—
1225C4×Q8—1061no—
1226C4×Q8—1061no—
1227C4×Q8—1061no—
1228C4×Q8—1061no—
1229C4×Q8C22×D5311yescharacteristic
1230C4×Q8C22×D5311yescharacteristic
1231C4×Q8C22×D5311yescharacteristic
1232C4×D4—531no—
1233C4×D4—531no—
1234C4×D4—531no—
1235C4×D4—531no—
1236C4×D4—531no—
1237C4×D4—531no—
1238C4×D4—531no—
1239C4×D4—1061no—
1240C4×D4—1061no—
1241C4×D4—1061no—
1242C4×D4—1061no—
1243C4×D4—1061no—
1244C4×D4—1061no—
1245C4×D4—1061no—
1246C4×D4—1061no—
1247C4×D4—1061no—
1248C4×D4—1061no—
1249C4×D4—1061no—
1250C4×D4—1061no—
1251C4×D4C22×D5311yescharacteristic
1252#117—531no—
1253#117—531no—
1254#117—531no—
1255#117—531no—
1256#117—531no—
1257#117—531no—
1258#117—531no—
1259#117—531no—
1260#117—531no—
1261#117—1061no—
1262#117—1061no—
1263#117C22×D5311yescharacteristic
1264C2×C4⋊C4—531no—
1265C2×C4⋊C4—531no—
1266C2×C4⋊C4—531no—
1267C2×C4⋊C4—531no—
1268C2×C4⋊C4—1061no—
1269C2×C4⋊C4—1061no—
1270C2×C4⋊C4—1061no—
1271C2×C22⋊C4—531no—
1272C2×C22⋊C4—531no—
1273C2×C22⋊C4—1061no—
1274C2×C22⋊C4—1061no—
1275C2×C22⋊C4—1061no—
1276C2×C22⋊C4—1061no—
1277C2×C22⋊C4—1061no—
1278C2×C42—531no—
1279C2×C42—531no—
1280C2×C42—1061no—
1281C2×C42—1061no—
1282C2×C42—1061no—
1283#107—531no—
1284#107—531no—
1285#107—531no—
1286#107—531no—
1287#107—531no—
1288#107—531no—
1289#107C22×D5311yescharacteristic
1290#107C22×D5311yescharacteristic
1291#106—531no—
1292#106—531no—
1293#106—531no—
1294#106—531no—
1295#106—531no—
1296#106—531no—
1297#106C22×D5311yescharacteristic
1298#106C22×D5311yescharacteristic
1299C4⋊C8—531no—
1300C4⋊C8—531no—
1301C4⋊C8—531no—
1302C4⋊C8—531no—
1303C4⋊C8—531no—
1304C4⋊C8—531no—
1305C4⋊C8—531no—
1306C4⋊C8—531no—
1307C4⋊C8—531no—
1308C4⋊C8—531no—
1309C4⋊C8—531no—
1310C4⋊C8—531no—
1311C4⋊C8C22×D5311yescharacteristic
1312C4⋊C8C22×D5311yescharacteristic
1313C4⋊C8C22×D5311yescharacteristic
1314C4⋊C8C22×D5311yescharacteristic
1315#103—531no—
1316#103—531no—
1317#103—531no—
1318#103—531no—
1319#103—531no—
1320#103—531no—
1321#103—531no—
1322#103—531no—
1323#103—531no—
1324#103—531no—
1325#103C22×D5311yescharacteristic
1326#103C22×D5311yescharacteristic
1327#103C22×D5311yescharacteristic
1328#103C22×D5311yescharacteristic
1329#103C22×D5311yescharacteristic
1330#103C22×D5311yescharacteristic
1331#102—531no—
1332#102—531no—
1333#102—531no—
1334#102—531no—
1335#102—531no—
1336#102—531no—
1337#102—531no—
1338#102—531no—
1339#102—531no—
1340#102—531no—
1341#102—531no—
1342#102—531no—
1343#102—531no—
1344#102—531no—
1345#102C22×D5311yescharacteristic
1346#102C22×D5311yescharacteristic
1347C24—531no—
1348C24—1061no—
1349#41—1062no—
1350#41—1062no—
1351#41—1062no—
1352#41—1062no—
1353C2×Q8—21no—
1354C2×Q8—531no—
1355C2×Q8—1061no—
1356C2×Q8—1061no—
1357C2×Q8—1061no—
1358C2×Q8—1061no—
1359C2×Q8—1061no—
1360C2×Q8—1062no—
1361C2×Q8—1062no—
1362C2×Q8—1061no—
1363C2×Q8—4242no—
1364C2×Q8C23×D5311yescharacteristic
1365C2×Q8C23×D5311yescharacteristic
1366C2×Q8C23×D5311yescharacteristic
1367C2×D4—21no—
1368C2×D4—531no—
1369C2×D4—531no—
1370C2×D4—531no—
1371C2×D4—1061no—
1372C2×D4—1061no—
1373C2×D4—1061no—
1374C2×D4—1061no—
1375C2×D4—1061no—
1376C2×D4—1062no—
1377C2×D4—1062no—
1378C2×D4—1061no—
1379C2×D4—1061no—
1380C2×D4—1061no—
1381C2×D4—1061no—
1382C2×D4—1061no—
1383C2×D4—1061no—
1384C2×D4—1061no—
1385C2×D4—4242no—
1386C2×D4C23×D5311yescharacteristic
1387C22×C4—21no—
1388C22×C4—531no—
1389C22×C4—531no—
1390C22×C4—531no—
1391C22×C4—531no—
1392C22×C4—531no—
1393C22×C4—531no—
1394C22×C4—531no—
1395C22×C4—531no—
1396C22×C4—531no—
1397C22×C4—1062no—
1398C22×C4—1062no—
1399C22×C4—1061no—
1400C22×C4—1061no—
1401C22×C4—1061no—
1402C22×C4—1061no—
1403C22×C4—1061no—
1404C22×C4—1061no—
1405C22×C4—1061no—
1406C22×C4—1061no—
1407C22×C4—1061no—
1408C22×C4—1061no—
1409C22×C4—1061no—
1410C22×C4—1061no—
1411C22×C4—4242no—
1412C22×C4C23×D5311yescharacteristic
1413Q16—41no—
1414Q16—41no—
1415Q16—2121no—
1416Q16—2121no—
1417SD16—41no—
1418SD16—41no—
1419SD16—2121no—
1420SD16—2121no—
1421SD16—2121no—
1422SD16—2121no—
1423SD16—2121no—
1424SD16—2121no—
1425D8—2121no—
1426D8—2121no—
1427D8—2121no—
1428D8—2121no—
1429M16—41no—
1430M16—1062no—
1431M16—1062no—
1432M16—1062no—
1433M16—1062no—
1434M16—2121no—
1435M16—2121no—
1436M16—2121no—
1437C2×C8—41no—
1438C2×C8—531no—
1439C2×C8—531no—
1440C2×C8—531no—
1441C2×C8—531no—
1442C2×C8—2121no—
1443C2×C8—2121no—
1444C2×C8—2121no—
1445C2×C8C23×D5311yescharacteristic
1446C2×C8C23×D5311yescharacteristic
1447C2×C8C23×D5311yescharacteristic
1448C2×C8C23×D5311yescharacteristic
1449C4⋊C4—21no—
1450C4⋊C4—21no—
1451C4⋊C4—21no—
1452C4⋊C4—21no—
1453C4⋊C4—21no—
1454C4⋊C4—21no—
1455C4⋊C4—21no—
1456C4⋊C4—21no—
1457C4⋊C4—21no—
1458C4⋊C4—21no—
1459C4⋊C4—21no—
1460C4⋊C4—531no—
1461C4⋊C4—531no—
1462C4⋊C4—531no—
1463C4⋊C4—531no—
1464C4⋊C4—531no—
1465C4⋊C4—531no—
1466C4⋊C4—531no—
1467C4⋊C4—531no—
1468C4⋊C4—531no—
1469C4⋊C4—531no—
1470C4⋊C4—1061no—
1471C4⋊C4—1061no—
1472C4⋊C4—1061no—
1473C4⋊C4—1061no—
1474C4⋊C4—1061no—
1475C4⋊C4—1061no—
1476C4⋊C4—1061no—
1477C4⋊C4—1061no—
1478C4⋊C4—1061no—
1479C4⋊C4—1061no—
1480C4⋊C4—1061no—
1481C4⋊C4—1061no—
1482C4⋊C4—1061no—
1483C4⋊C4—1061no—
1484C4⋊C4—1061no—
1485C4⋊C4—1061no—
1486C4⋊C4—1061no—
1487C4⋊C4—1061no—
1488C4⋊C4—1061no—
1489C4⋊C4D4×D5311yescharacteristic
1490C4⋊C4D4×D5311yescharacteristic
1491C4⋊C4C23×D5311yescharacteristic
1492C4⋊C4C23×D5311yescharacteristic
1493C4⋊C4C23×D5311yescharacteristic
1494C4⋊C4C23×D5311yescharacteristic
1495C22⋊C4—21no—
1496C22⋊C4—21no—
1497C22⋊C4—21no—
1498C22⋊C4—21no—
1499C22⋊C4—21no—
1500C22⋊C4—21no—
1501C22⋊C4—21no—
1502C22⋊C4—531no—
1503C22⋊C4—531no—
1504C22⋊C4—531no—
1505C22⋊C4—531no—
1506C22⋊C4—531no—
1507C22⋊C4—531no—
1508C22⋊C4—1061no—
1509C22⋊C4—1061no—
1510C22⋊C4—1061no—
1511C22⋊C4—1061no—
1512C22⋊C4—1061no—
1513C22⋊C4—1061no—
1514C22⋊C4—1061no—
1515C22⋊C4—1061no—
1516C22⋊C4—1061no—
1517C22⋊C4—1061no—
1518C22⋊C4—1061no—
1519C22⋊C4—1061no—
1520C22⋊C4—1061no—
1521C22⋊C4—1061no—
1522C22⋊C4—1061no—
1523C22⋊C4—1061no—
1524C22⋊C4—1061no—
1525C22⋊C4—1061no—
1526C22⋊C4—1061no—
1527C22⋊C4—1061no—
1528C22⋊C4—1061no—
1529C22⋊C4—1061no—
1530C22⋊C4—1061no—
1531C22⋊C4—1061no—
1532C22⋊C4—1061no—
1533C22⋊C4—1061no—
1534C22⋊C4—1061no—
1535C22⋊C4—1061no—
1536C22⋊C4—1061no—
1537C22⋊C4—1061no—
1538C22⋊C4—1061no—
1539C22⋊C4D4×D5311yescharacteristic
1540C22⋊C4D4×D5311yescharacteristic
1541C42—21no—
1542C42—21no—
1543C42—21no—
1544C42—531no—
1545C42—531no—
1546C42—531no—
1547C42—531no—
1548C42—531no—
1549C42—531no—
1550C42—1061no—
1551C42—1061no—
1552C42—1061no—
1553C42—1061no—
1554C42—1061no—
1555C42—1061no—
1556C42—1061no—
1557C42C23×D5311yescharacteristic
1558C42C23×D5311yescharacteristic
1559C23—21no—
1560C23—531no—
1561C23—531no—
1562C23—1062no—
1563C23—1061no—
1564C23—1061no—
1565C23—1061no—
1566C23—2121no—
1567C23—2121no—
1568C23—2122no—
1569C23—2122no—
1570C23—2122no—
1571C23C2×D4×D5311yescharacteristic
1572Q8—21no—
1573Q8—21no—
1574Q8—21no—
1575Q8—21no—
1576Q8—21no—
1577Q8—21no—
1578Q8—81no—
1579Q8—1061no—
1580Q8—1061no—
1581Q8—4241no—
1582Q8—4241no—
1583Q8—4241no—
1584Q8—4241no—
1585Q8—4241no—
1586Q8—2122no—
1587D4—21no—
1588D4—21no—
1589D4—81no—
1590D4—1061no—
1591D4—1061no—
1592D4—1061no—
1593D4—1061no—
1594D4—1061no—
1595D4—1061no—
1596D4—4241no—
1597D4—4241no—
1598D4—4241no—
1599D4—4241no—
1600D4—4241no—
1601D4—4241no—
1602D4—4241no—
1603D4—4241no—
1604D4—4241no—
1605D4—2122no—
1606D4—2122no—
1607D4—2122no—
1608C2×C4—21no—
1609C2×C4—21no—
1610C2×C4—21no—
1611C2×C4—21no—
1612C2×C4—21no—
1613C2×C4—21no—
1614C2×C4—21no—
1615C2×C4—21no—
1616C2×C4—21no—
1617C2×C4—81no—
1618C2×C4—531no—
1619C2×C4—532no—
1620C2×C4—532no—
1621C2×C4—531no—
1622C2×C4—531no—
1623C2×C4—531no—
1624C2×C4—531no—
1625C2×C4—531no—
1626C2×C4—1062no—
1627C2×C4—1062no—
1628C2×C4—1062no—
1629C2×C4—1061no—
1630C2×C4—1061no—
1631C2×C4—1061no—
1632C2×C4—1061no—
1633C2×C4—1061no—
1634C2×C4—1061no—
1635C2×C4—1061no—
1636C2×C4—4241no—
1637C2×C4—4241no—
1638C2×C4—4241no—
1639C2×C4—4241no—
1640C2×C4—4241no—
1641C2×C4—4241no—
1642C2×C4—4241no—
1643C2×C4—2121no—
1644C2×C4—2121no—
1645C2×C4—2121no—
1646C2×C4—2121no—
1647C2×C4—2122no—
1648C2×C4—2122no—
1649C2×C4—2122no—
1650C2×C4—2122no—
1651C2×C4—2122no—
1652C2×C4C2×D4×D5311yescharacteristic
1653C2×C4C2×D4×D5311yescharacteristic
1654C2×C4C2×D4×D5311yescharacteristic
1655C2×C4C2×D4×D5311yescharacteristic
1656C2×C4C2×D4×D5311yescharacteristic
1657C2×C4C24×D5311yescharacteristic
1658C8—21no—
1659C8—21no—
1660C8—21no—
1661C8—21no—
1662C8—1061no—
1663C8—1061no—
1664C8—1061no—
1665C8—1061no—
1666C22—21no—
1667C22—21no—
1668C22—21no—
1669C22—41no—
1670C22—41no—
1671C22—41no—
1672C22—532no—
1673C22—1061no—
1674C22—1061no—
1675C22—1061no—
1676C22—1061no—
1677C22—1061no—
1678C22—4242no—
1679C22—4244no—
1680C22—2121no—
1681C22—2121no—
1682C22—2121no—
1683C22—2121no—
1684C22—2121no—
1685C22—2121no—
1686C22—2121no—
1687C22—2121no—
1688C22—2121no—
1689C22C22×D4×D5311yescharacteristic
1690C4—21no—
1691C4—21no—
1692C4—21no—
1693C4—21no—
1694C4—21no—
1695C4—41no—
1696C4—41no—
1697C4—41no—
1698C4—41no—
1699C4—41no—
1700C4—41no—
1701C4—41no—
1702C4—532no—
1703C4—1061no—
1704C4—1061no—
1705C4—1061no—
1706C4—1061no—
1707C4—1061no—
1708C4—2121no—
1709C4—2121no—
1710C4—2121no—
1711C4—2121no—
1712C4—2121no—
1713C4H(5,𝔽2)×D5311yescharacteristic
1714C42−1+4×D5311yescharacteristic
1715C2—41no—
1716C2—81no—
1717C2—1062no—
1718C2—4241no—
1719C2—4241no—
1720C2—4241no—
1721C2—2121no—
1722C2#537×D5311yescharacteristic
1723C2#2028949311yescharacteristic
1724C2#2028950011yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3258C2
socleC22×C53C23×D4
hypercenter#3258D53
hypocenterC53#60919
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ #117 ◁ #3258

Complements

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

NH ≅ G/Ntype
1. #20288106C2semidirect
2. #542×D53C2semidirect
3. #20286184C2semidirect
4. #20286183C2semidirect
5. #20286181C2semidirect
6. #20286179C2semidirect
7. #20286178C2semidirect
8. #20286177C2semidirect
9. #20286174C2semidirect
10. #20286172C2semidirect
11. #20286139C2semidirect
12. #20286137C2semidirect
13. #20286135C2semidirect
14. #20286132C2semidirect
15. #20286130C2semidirect
16. #20286128C2semidirect
17. #20286126C2semidirect
18. #20284529C2semidirect
19. #20284525C2semidirect
20. #20284518C2semidirect
21. #20284510C2semidirect
22. #20284344C2semidirect
23. #20284342C2semidirect
24. #20284329C2semidirect
25. #20284327C2semidirect
26. #20284206C2semidirect
27. #20284206C2semidirect
28. #20284188C2semidirect
29. #20284180C2semidirect
30. #20283276C2semidirect
31. C53×#3258C2semidirect
40. #16811246C22semidirect
41. #16811246C22semidirect
43. #16811245C22semidirect
44. #16811245C22semidirect
53. #16811234C22semidirect
54. #16811229C22semidirect
55. #16811228C22semidirect
81. #16810931C22semidirect
82. #16810930C22semidirect
83. #16810927C22semidirect
84. #16810924C22semidirect
85. #16810923C22semidirect
86. #16810920C22semidirect
87. #16810918C22semidirect
88. #16810917C22semidirect
89. #16810916C22semidirect
90. #16810916C22semidirect
91. #16810916C22semidirect
92. #16810914C22semidirect
93. #16810912C22semidirect
94. #16810912C22semidirect
95. #16810912C22semidirect
96. #16810911C22semidirect
97. #16810910C22semidirect
98. #16810908C22semidirect
99. #16810907C22semidirect
100. #16810906C22semidirect
101. #16810906C22semidirect
102. #16810906C22semidirect
103. #16810904C22semidirect
104. #16810902C22semidirect
105. #16810902C22semidirect
106. #16810902C22semidirect
107. #16810901C22semidirect
108. #16810900C22semidirect
109. #16810880C22semidirect
110. #16810879C22semidirect
111. #16810878C22semidirect
117. #16810872C22semidirect
119. #16810871C22semidirect
120. #16810870C22semidirect
121. #16810869C22semidirect
123. #16810863C22semidirect
124. #16810862C22semidirect
125. #16810861C22semidirect
131. #16810855C22semidirect
133. #16810854C22semidirect
134. #16810853C22semidirect
135. #16810852C22semidirect
137. #16810848C22semidirect
138. #16810848C22semidirect
139. #16810847C22semidirect
140. #16810847C22semidirect
141. #16810847C22semidirect
142. #16810847C22semidirect
143. #16810845C22semidirect
144. #16810845C22semidirect
145. #16810843C22semidirect
146. #16810843C22semidirect
147. #16810841C22semidirect
148. #16810841C22semidirect
149. #16810841C22semidirect
150. #16810841C22semidirect
151. #16810840C22semidirect
152. #16810840C22semidirect
153. #16810839C22semidirect
154. #16810839C22semidirect
155. #16810837C22semidirect
156. #16810837C22semidirect
157. #16810835C22semidirect
158. #16810835C22semidirect
159. #16810830C22semidirect
160. #16810825C22semidirect
161. #16810824C22semidirect
162. #16810823C22semidirect
163. #16810819C22semidirect
164. #16810818C22semidirect
169. #16810651C22semidirect
170. #16810650C22semidirect
171. #16810649C22semidirect
172. #16810648C22semidirect
173. #16810648C22semidirect
174. #16810648C22semidirect
175. #16810648C22semidirect
189. C53×#541C22semidirect
190. C53×#479C22semidirect
191. C53×#478C22semidirect
192. C53×#477C22semidirect
193. C53×#475C22semidirect
194. C53×#470C22semidirect
196. C53×#467C22semidirect
198. C53×#464C22semidirect
199. C53×#464C22semidirect
200. C53×#462C22semidirect
201. C53×#461C22semidirect
202. C53×#424C22semidirect
866. #3258D53semidirect
917. #541C2×D53semidirect
948. #479C2×D53semidirect
952. #478C2×D53semidirect
958. #477C2×D53semidirect
970. #475C2×D53semidirect
980. #470C2×D53semidirect
996. #467C2×D53semidirect
1019. #464C2×D53semidirect
1020. #464C2×D53semidirect
1034. #462C2×D53semidirect
1036. #461C2×D53semidirect
1052. #424C2×D53semidirect
1065. C53#60919semidirect

Maximal subgroups

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

subgroupindex
#202881062
#542×D532
#202861842
#202861832
#202861812
#202861792
#202861782
#202861772
#202861742
#202861722
#202861392
#202861372
#202861352
#202861322
#202861302
#202861282
#202861262
#202845292
#202845252
#202845182
#202845102
#202843442
#202843422
#202843292
#202843272
#202842062
#202841882
#202841802
#202832762
C53×#32582
#6091953