Finite Group Databasebeta

← #28267127

Subgroups — #28267127

Order 13568.

1800 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288789C211yesmaximal, characteristic, complemented
2#20288785C211yesmaximal, characteristic, complemented
3#20287789C211yesmaximal, characteristic, complemented
4#20287672C211yesmaximal, characteristic, complemented
5#20287368C211yesmaximal, characteristic, complemented
6#20287367C211yesmaximal, characteristic, complemented
7#20287290C211yesmaximal, characteristic, complemented
8#20287263C211yesmaximal, characteristic, complemented
9#20287257C211yesmaximal, characteristic, complemented
10#20286635C211yesmaximal, characteristic, complemented
11#20286625C211yesmaximal, characteristic, complemented
12#20286563C211yesmaximal, characteristic, complemented
13#20286562C211yesmaximal, characteristic, complemented
14#20286548C211yesmaximal, characteristic, complemented
15#20286543C211yesmaximal, characteristic, complemented
16#20286319C211yesmaximal, characteristic, complemented
17#20286246C211yesmaximal, characteristic, complemented
18#20286243C211yesmaximal, characteristic, complemented
19#20285389C211yesmaximal, characteristic, complemented
20#20285385C211yesmaximal, characteristic, complemented
21#20285288C211yesmaximal, characteristic, complemented
22#20284935C211yesmaximal, characteristic, complemented
23#20284905C211yesmaximal, characteristic, complemented
24#20284901C211yesmaximal, characteristic, complemented
25#20284830C211yesmaximal, characteristic, complemented
26#20284828C211yesmaximal, characteristic, complemented
27#20283688C211yesmaximal, characteristic, complemented
28#20283546C211yesmaximal, characteristic, complemented
29#20283543C211yesmaximal, characteristic, complemented
30C4×#13133238C211yesmaximal, characteristic, complemented
31C53×#3120C211yesmaximal, characteristic, complemented
32C2×#13133244C2211yescharacteristic
33C2×#13133242C2211yescharacteristic
34C2×#13133238C2211yescharacteristic
35#16811347C2211yescharacteristic, complemented
36#16811346C2211yescharacteristic, complemented
37#16811345C2211yescharacteristic, complemented
38#16811344C2211yescharacteristic, complemented
39#16811330C2211yescharacteristic, complemented
40#16811329C2211yescharacteristic, complemented
41#16811326—21no—
42#16811326C2211yescharacteristic
43#16811321C2211yescharacteristic
44#16811319—21no—
45#16811308C2211yescharacteristic
46#16811307C2211yescharacteristic
47#16811306—21no—
48#16811305—21no—
49#16811302—21no—
50#16811298—21no—
51#16811298—21no—
52#16811297—21no—
53#16811276C2211yescharacteristic
54#16811272C2211yescharacteristic
55#16811268C2211yescharacteristic, complemented
56#16811264C2211yescharacteristic
57#16811264C2211yescharacteristic, complemented
58#16811261C2211yescharacteristic
59#16811245C2211yescharacteristic
60#16811244C2211yescharacteristic
61#16811231C2211yescharacteristic, complemented
62#16811221—21no—
63#16811220—21no—
64#16811212—21no—
65#16811206—21no—
66#16811160C2211yescharacteristic, complemented
67#16811160C2211yescharacteristic, complemented
68#16811158—21no—
69#16811153—21no—
70#16811151C2211yescharacteristic
71C2×#13133212—21no—
72#126×D53—21no—
73#16811105C2211yescharacteristic
74#16811097C2211yescharacteristic, complemented
75#16811095C2211yescharacteristic, complemented
76C4×#11719949C2211yescharacteristic, complemented
77C4×#11719947C2211yescharacteristic, complemented
78#16811033C2211yescharacteristic, complemented
79#16811030C2211yescharacteristic, complemented
80#16811024C2211yescharacteristic, complemented
81#16811016C2211yescharacteristic, complemented
82#16811015C2211yescharacteristic, complemented
83#16811008C2211yescharacteristic
84#16810980C2211yescharacteristic, complemented
85#16810979C2211yescharacteristic, complemented
86#16810979C2211yescharacteristic, complemented
87#16810979C2211yescharacteristic, complemented
88#16810973C2211yescharacteristic, complemented
89#16810972C2211yescharacteristic, complemented
90#16810965C2211yescharacteristic, complemented
91#16810963C2211yescharacteristic, complemented
92#16810963C2211yescharacteristic, complemented
93#16810962C2211yescharacteristic, complemented
94#16810960C2211yescharacteristic, complemented
95#16810952C2211yescharacteristic, complemented
96#16810950C2211yescharacteristic, complemented
97#16810949C2211yescharacteristic
98#16810949C2211yescharacteristic, complemented
99#16810948C2211yescharacteristic
100#16810929C2211yescharacteristic, complemented
101#16810928C2211yescharacteristic, complemented
102#16810928C2211yescharacteristic, complemented
103#16810926C2211yescharacteristic, complemented
104#16810922C2211yescharacteristic, complemented
105#16810921C2211yescharacteristic, complemented
106#16810914C2211yescharacteristic, complemented
107#16810912C2211yescharacteristic, complemented
108#16810904C2211yescharacteristic, complemented
109#16810901C2211yescharacteristic, complemented
110#16810880C2211yescharacteristic, complemented
111#16810879C2211yescharacteristic, complemented
112#16810872C2211yescharacteristic
113#16810871C2211yescharacteristic
114#16810862C2211yescharacteristic, complemented
115#16810861C2211yescharacteristic, complemented
116#16810861C2211yescharacteristic, complemented
117#16810860C2211yescharacteristic
118#16810855C2211yescharacteristic, complemented
119#16810855C2211yescharacteristic, complemented
120#16810854C2211yescharacteristic
121#16810853C2211yescharacteristic
122#16810848C2211yescharacteristic, complemented
123#16810847C2211yescharacteristic, complemented
124#16810841C2211yescharacteristic
125#16810841C2211yescharacteristic
126#16810840C2211yescharacteristic
127#16810840C2211yescharacteristic
128#16810839C2211yescharacteristic
129#16810839C2211yescharacteristic
130#16810831C2211yescharacteristic, complemented
131#16810827C2211yescharacteristic, complemented
132#16810788C2211yescharacteristic
133#16810784C2211yescharacteristic
134#16810784C2211yescharacteristic, complemented
135#16810782C2211yescharacteristic, complemented
136#16810776C2211yescharacteristic, complemented
137#16810772C2211yescharacteristic, complemented
138#16810771C2211yescharacteristic
139#16810769C2211yescharacteristic
140#16810759C2211yescharacteristic
141#16810758C2211yescharacteristic
142#16810752C2211yescharacteristic, complemented
143#16810747C2211yescharacteristic, complemented
144#16810736C2211yescharacteristic
145#16810733C2211yescharacteristic
146#16810733C2211yescharacteristic
147#16810732C2211yescharacteristic
148#16810728C2211yescharacteristic, complemented
149#16810726C2211yescharacteristic, complemented
150#16810725C2211yescharacteristic, complemented
151#16810721C2211yescharacteristic, complemented
152#16810721C2211yescharacteristic, complemented
153#16810721C2211yescharacteristic, complemented
154C4×#11719925C2211yescharacteristic, complemented
155#16810715C2211yescharacteristic, complemented
156C4×#11719913C2211yescharacteristic, complemented
157SD16×Dic53C2211yescharacteristic, complemented
158SD16×Dic53C2211yescharacteristic, complemented
159C4×#11719924C2211yescharacteristic, complemented
160C4×#11719924C2211yescharacteristic, complemented
161C4×#11719924C2211yescharacteristic, complemented
162#16810710C2211yescharacteristic, complemented
163C4×D424C2211yescharacteristic
164#16810705C2211yescharacteristic
165C4×#11719922C2211yescharacteristic
166C4×#11719922C2211yescharacteristic
167#16810703C2211yescharacteristic
168#16810698C2211yescharacteristic
169#16810697C2211yescharacteristic, complemented
170#16810693C2211yescharacteristic, complemented
171#16810688C2211yescharacteristic, complemented
172#16810686C2211yescharacteristic
173#16810686C2211yescharacteristic, complemented
174#16810682C2211yescharacteristic, complemented
175#16810678C2211yescharacteristic, complemented
176#16810664C2211yescharacteristic, complemented
177#16810663C2211yescharacteristic, complemented
178#16810658C2211yescharacteristic, complemented
179#16810619C2211yescharacteristic
180#16810618C2211yescharacteristic
181#16810618C2211yescharacteristic, complemented
182#16810616C2211yescharacteristic, complemented
183C2×#13133137C2211yescharacteristic, complemented
184#102×D53C2211yescharacteristic, complemented
185#16810580C2211yescharacteristic, complemented
186#16810579C2211yescharacteristic, complemented
187C4×C8×D53C2211yescharacteristic, complemented
188C53×#541C2211yescharacteristic, complemented
189C53×#520C2211yescharacteristic
190C53×#484C2211yescharacteristic, complemented
191C53×#483C2211yescharacteristic, complemented
192C53×#479C2211yescharacteristic, complemented
193C53×#478C2211yescharacteristic, complemented
194C53×#462C2211yescharacteristic, complemented
195C53×#461C2211yescharacteristic, complemented
196C53×#452C2211yescharacteristic
197C53×#452C2211yescharacteristic
198C53×#441C2211yescharacteristic, complemented
199C53×#440C2211yescharacteristic, complemented
200C4×Q16×C53C2211yescharacteristic, complemented
201C4×SD16×C53C2211yescharacteristic, complemented
202C53×#433C2211yescharacteristic, complemented
203C2×#11719949C2311yescharacteristic
204C2×#11719949C2311yescharacteristic
205C2×#11719947C2311yescharacteristic
206C22×D212C2311yescharacteristic
207C2×D4×D53C2311yescharacteristic
208#13133244—24no—
209#13133242—24no—
210#13133238—24no—
211C2×#11719925C2311yescharacteristic
212C2×#11719925C2311yescharacteristic
213C2×#11719913C2311yescharacteristic
214C2×#11719913C2311yescharacteristic
215C2×#11719924C2311yescharacteristic
216C2×#11719924C2311yescharacteristic
217C2×#11719924C2311yescharacteristic
218C2×#11719924C2311yescharacteristic
219C2×D424C2311yescharacteristic
220C2×D424C2311yescharacteristic
221C2×#11719922C2311yescharacteristic
222C2×#11719922C2311yescharacteristic
223C2×#11719917C2311yescharacteristic
224C2×#11719912C2311yescharacteristic
225C22×#88322C2311yescharacteristic
226C2×C8×D53C2311yescharacteristic
227C2×C8×D53C2311yescharacteristic
228C2×C8×D53C2311yescharacteristic
229#13133217C2311yescharacteristic
230#13133216C2311yescharacteristic
231#13133215C2311yescharacteristic
232#13133212—21no—
233#13133212—21no—
234#13133212—21no—
235#13133212—21no—
236#13133212—21no—
237#13133212—21no—
238#13133212—21no—
239#13133212—21no—
240#13133212—21no—
241#13133212—21no—
242#13133212—21no—
243#13133212—21no—
244#13133212—21no—
245#13133212D411yescharacteristic
246#13133211—21no—
247#13133211—21no—
248#13133211—21no—
249#13133210—21no—
250#13133210—21no—
251#13133210D411yescharacteristic
252#13133209—21no—
253#13133208C2311yescharacteristic
254#13133208C2311yescharacteristic
255#13133208C2311yescharacteristic
256#13133207—21no—
257#13133207—21no—
258#13133207—21no—
259#13133207D411yescharacteristic
260#13133206C2311yescharacteristic
261#13133206C2311yescharacteristic
262#13133206C2311yescharacteristic
263#13133205—21no—
264#13133205—21no—
265#13133205C2311yescharacteristic
266#13133203—21no—
267#13133203—21no—
268#13133203D411yescharacteristic
269#13133202—21no—
270#13133202—21no—
271#13133202—21no—
272#13133202—21no—
273#13133202—21no—
274#13133202—21no—
275#13133202—21no—
276#13133202—21no—
277#13133202—21no—
278#13133202D411yescharacteristic
279#13133201—21no—
280#13133200—21no—
281#13133200—21no—
282#13133200—21no—
283#13133199—21no—
284#13133199—21no—
285#13133199D411yescharacteristic
286#13133198—21no—
287#13133197—21no—
288#13133197—21no—
289#13133197C2311yescharacteristic
290#13133196—21no—
291#13133196C2311yescharacteristic
292#13133195—21no—
293#13133195—21no—
294#13133195—21no—
295#13133195—21no—
296#13133195—21no—
297#13133195D411yescharacteristic
298#13133194—21no—
299#13133194—21no—
300#13133193C2311yescharacteristic
301#13133193C2311yescharacteristic
302#13133193C2311yescharacteristic
303#13133193C2311yescharacteristic
304#13133192—21no—
305#13133192—21no—
306#13133192—21no—
307#13133192—21no—
308#13133192C2311yescharacteristic
309#13133192C2311yescharacteristic
310#13133192C2311yescharacteristic
311#13133191—21no—
312#13133191—21no—
313#13133191C2311yescharacteristic
314#13133190D411yescharacteristic
315#13133189—21no—
316#13133189—21no—
317#13133187—21no—
318#13133187—21no—
319#13133187—21no—
320#13133185—21no—
321Q8×Dic53C2311yescharacteristic
322Q8×Dic53C2311yescharacteristic
323C4×Dic106—21no—
324C4×Dic106C2311yescharacteristic
325C4×Dic106C2311yescharacteristic
326#13133182—21no—
327#13133182C2311yescharacteristic
328C4×D212—21no—
329C4×D212—21no—
330C4×D212—21no—
331C4×D212—21no—
332C4×D212C2311yescharacteristic
333C4×D212C2311yescharacteristic
334C4×D212C2311yescharacteristic
335C4×D212C2311yescharacteristic
336C4×D212C2311yescharacteristic
337C4×D212C2311yescharacteristic
338D4×Dic53C2311yescharacteristic
339D4×Dic53C2311yescharacteristic
340#13133179—21no—
341#13133179—21no—
342#13133179—21no—
343#13133179—21no—
344#13133179—21no—
345#13133179C2311yescharacteristic
346#13133179C2311yescharacteristic
347#13133179C2311yescharacteristic
348C4×C22⋊D53—21no—
349C4×C22⋊D53—21no—
350C4×C22⋊D53—21no—
351C4×C22⋊D53C2311yescharacteristic
352C4×C22⋊D53C2311yescharacteristic
353#13133177—21no—
354#13133177—21no—
355#13133176—21no—
356#13133176C2311yescharacteristic
357#13133175—21no—
358#13133175—21no—
359#13133175—21no—
360#13133175C2311yescharacteristic
361#13133175C2311yescharacteristic
362#13133175C2311yescharacteristic
363#13133174—21no—
364#13133174—21no—
365#13133174—21no—
366#13133174—21no—
367#13133174C2311yescharacteristic
368#13133173—21no—
369C2×C4⋊Dic53—21no—
370C2×#11719919—21no—
371C4⋊C4×D53—21no—
372C4⋊C4×D53—21no—
373C4⋊C4×D53—21no—
374C4⋊C4×D53C2311yescharacteristic
375C2×#11719921—21no—
376C2×#11719921—21no—
377C2×#11719921—21no—
378C22⋊C4×D53—21no—
379C22⋊C4×D53—21no—
380C22⋊C4×D53—21no—
381C22⋊C4×D53—21no—
382C22⋊C4×D53—21no—
383C2×C4×Dic53—21no—
384C42×D53—21no—
385C42×D53C2311yescharacteristic
386#13133151C2311yescharacteristic
387#13133151C2311yescharacteristic
388#13133150C2311yescharacteristic
389#13133150C2311yescharacteristic
390#13133150C2311yescharacteristic
391#13133150C2311yescharacteristic
392#13133149C2311yescharacteristic
393#13133149C2311yescharacteristic
394#13133148C2311yescharacteristic
395#13133148C2311yescharacteristic
396#13133148C2311yescharacteristic
397#13133148C2311yescharacteristic
398#13133146C2311yescharacteristic
399#13133146C2311yescharacteristic
400#13133146C2311yescharacteristic
401#13133146C2311yescharacteristic
402#13133142C2311yescharacteristic
403#13133142C2311yescharacteristic
404#13133141C2311yescharacteristic
405#13133141C2311yescharacteristic
406#13133141C2311yescharacteristic
407#13133141C2311yescharacteristic
408#13133141C2311yescharacteristic
409#13133141C2311yescharacteristic
410#13133140C2311yescharacteristic
411#13133140C2311yescharacteristic
412#13133139C2311yescharacteristic
413#13133139C2311yescharacteristic
414#13133139C2311yescharacteristic
415#13133139C2311yescharacteristic
416#13133139C2311yescharacteristic
417#13133139C2311yescharacteristic
418#13133138C2311yescharacteristic
419#13133138C2311yescharacteristic
420#13133137C2311yescharacteristic
421#13133137C2311yescharacteristic
422#13133137C2311yescharacteristic
423#13133137C2311yescharacteristic
424#13133137C2311yescharacteristic
425#13133137C2311yescharacteristic
426#13133129C2311yescharacteristic
427#13133129C2311yescharacteristic
428#13133129C2311yescharacteristic
429#13133129C2311yescharacteristic
430#13133128C2311yescharacteristic
431#13133128C2311yescharacteristic
432#13133127C2311yescharacteristic
433C4×#88322C2311yescharacteristic
434C4×#88322C2311yescharacteristic
435C8×Dic53C2311yescharacteristic
436C8×Dic53C2311yescharacteristic
437C8×Dic53C2311yescharacteristic
438C2×#41×C53C2311yescharacteristic
439C2×Q16×C53C2311yescharacteristic
440C2×Q16×C53C2311yescharacteristic
441C2×SD16×C53C2311yescharacteristic
442C2×SD16×C53C2311yescharacteristic
443C4⋊Q8×C53C2311yescharacteristic
444#126×C53—21no—
445#126×C53—21no—
446#125×C53—21no—
447#125×C53—21no—
448#125×C53C2311yescharacteristic
449C22⋊Q8×C53C2311yescharacteristic
450C22⋊Q8×C53C2311yescharacteristic
451C4×Q8×C53C2311yescharacteristic
452C4×Q8×C53C2311yescharacteristic
453C4×Q8×C53C2311yescharacteristic
454C4×Q8×C53C2311yescharacteristic
455C4×D4×C53—21no—
456C4×D4×C53—21no—
457C4×D4×C53C2311yescharacteristic
458C4×D4×C53C2311yescharacteristic
459#117×C53—21no—
460#117×C53C2311yescharacteristic
461C2×C4⋊C4×C53—21no—
462C2×C4⋊C4×C53C2311yescharacteristic
463#107×C53C2311yescharacteristic
464#107×C53C2311yescharacteristic
465#106×C53C2311yescharacteristic
466#106×C53C2311yescharacteristic
467C4⋊C8×C53C2311yescharacteristic
468C4⋊C8×C53C2311yescharacteristic
469#103×C53C2311yescharacteristic
470#103×C53C2311yescharacteristic
471#103×C53C2311yescharacteristic
472#103×C53C2311yescharacteristic
473#103×C53C2311yescharacteristic
474#103×C53C2311yescharacteristic
475#102×C53C2311yescharacteristic
476#102×C53C2311yescharacteristic
477C22⋊C8×C53C2311yescharacteristic
478C22⋊C8×C53C2311yescharacteristic
479#97×C53C2311yescharacteristic
480C4×C8×C53C2311yescharacteristic
481C23×D53—21no—
482C23×D53—21no—
483#41×C53—22no—
484#41×C53—41no—
485C2×Q8×C53C2411yescharacteristic
486C2×Q8×C53C2411yescharacteristic
487C2×Q8×C53C2411yescharacteristic
488C2×D4×C53—21no—
489C2×D4×C53C2411yescharacteristic
490C22×C4×C53—21no—
491C22×C4×C53—21no—
492C22×C4×C53—21no—
493C22×C4×C53—21no—
494C22×C4×C53C2411yescharacteristic
495C2×C22⋊D53—21no—
496C2×C22⋊D53—21no—
497C2×C22⋊D53—21no—
498C2×C22⋊D53C2×D411yescharacteristic
499C2×C22⋊D53C2×D411yescharacteristic
500C22×Dic53—21no—
501C22×Dic53—21no—
502C22×Dic53—21no—
503#11719949—22no—
504#11719949—22no—
505#11719949—41no—
506#11719949—41no—
507#11719947—22no—
508#11719947—41no—
509D4×D53—22no—
510D4×D53—41no—
511C2×D212—22no—
512C2×D212—21no—
513C2×D212—21no—
514C2×D212—21no—
515C2×D212—21no—
516C2×D212—21no—
517C2×D212—21no—
518C2×D212—41no—
519C2×D212C2×D411yescharacteristic
520C2×D212C2411yescharacteristic
521C2×D212C2411yescharacteristic
522C2×D212C2411yescharacteristic
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×D53C2×D411yescharacteristic
535C2×C4×D53C2×D411yescharacteristic
536C2×C4×D53C2411yescharacteristic
537C2×C4×D53C2411yescharacteristic
538C2×Dic106—21no—
539C2×Dic106—21no—
540C2×Dic106C2×D411yescharacteristic
541C2×Dic106C2411yescharacteristic
542Q16×C53—41no—
543Q16×C53—41no—
544SD16×C53—22no—
545SD16×C53—22no—
546C2×C8×C53C2411yescharacteristic
547C2×C8×C53C2411yescharacteristic
548C2×C8×C53C2411yescharacteristic
549C2×C8×C53C2411yescharacteristic
550C4⋊C4×C53—21no—
551C4⋊C4×C53—21no—
552C4⋊C4×C53—21no—
553C4⋊C4×C53—21no—
554C4⋊C4×C53—21no—
555C4⋊C4×C53—21no—
556C4⋊C4×C53—21no—
557C4⋊C4×C53—21no—
558C4⋊C4×C53—21no—
559C4⋊C4×C53—21no—
560C4⋊C4×C53—21no—
561C4⋊C4×C53C2×D411yescharacteristic
562C4⋊C4×C53C2×D411yescharacteristic
563C4⋊C4×C53C2411yescharacteristic
564C4⋊C4×C53C2411yescharacteristic
565C4⋊C4×C53C2411yescharacteristic
566C4⋊C4×C53C2411yescharacteristic
567C22⋊C4×C53—21no—
568C22⋊C4×C53—21no—
569C22⋊C4×C53—21no—
570C22⋊C4×C53—21no—
571C22⋊C4×C53C2×D411yescharacteristic
572C22⋊C4×C53C2×D411yescharacteristic
573C42×C53—21no—
574C42×C53—21no—
575C42×C53—21no—
576C42×C53—21no—
577C42×C53C2411yescharacteristic
578C42×C53C2411yescharacteristic
579C22⋊Dic53—21no—
580C22⋊Dic53—21no—
581C22⋊Dic53—21no—
582C22⋊Dic53—21no—
583C22⋊Dic53C2×D411yescharacteristic
584C22⋊Dic53C2×D411yescharacteristic
585#11719925—22no—
586#11719925—41no—
587#11719924—22no—
588#11719924—22no—
589#11719924—22no—
590#11719924—41no—
591#11719922—22no—
592#11719922#4114yes—
593#11719921—21no—
594#11719921—21no—
595#11719921—21no—
596#11719921—21no—
597#11719921—21no—
598#11719921—21no—
599#11719921—21no—
600#11719921—21no—
601#11719921—21no—
602#11719921—21no—
603#11719921—21no—
604#11719921—21no—
605#11719921—21no—
606#11719921—21no—
607#11719921—21no—
608#11719921—21no—
609#11719921—21no—
610#11719921—21no—
611#11719921—21no—
612#11719921—21no—
613#11719921—21no—
614#11719921—21no—
615#11719921—21no—
616#11719921—21no—
617#11719921—21no—
618#11719921—21no—
619#11719921—21no—
620#11719921—21no—
621#11719921C2×D411yescharacteristic
622#11719921C2×D411yescharacteristic
623#11719921C2×D411yescharacteristic
624#11719921C2×D411yescharacteristic
625#11719921C2×D411yescharacteristic
626#11719921C2×D411yescharacteristic
627C4⋊Dic53—21no—
628C4⋊Dic53—21no—
629C4⋊Dic53—21no—
630C4⋊Dic53—21no—
631C4⋊Dic53—21no—
632C4⋊Dic53—21no—
633C4⋊Dic53—21no—
634C4⋊Dic53C2×D411yescharacteristic
635C4⋊Dic53C2×D411yescharacteristic
636C4⋊Dic53C2411yescharacteristic
637C4⋊Dic53C2411yescharacteristic
638C4⋊Dic53C2411yescharacteristic
639C4⋊Dic53C2411yescharacteristic
640#11719919—21no—
641#11719919—21no—
642#11719919—21no—
643#11719919—21no—
644#11719919—21no—
645#11719919—21no—
646#11719919—21no—
647#11719919—21no—
648#11719919—21no—
649#11719919—21no—
650#11719919—21no—
651#11719919—21no—
652#11719919—21no—
653#11719919—21no—
654#11719919C2×D411yescharacteristic
655#11719919C2×D411yescharacteristic
656#11719919C2×D411yescharacteristic
657#11719919C2×D411yescharacteristic
658#11719919C2×D411yescharacteristic
659#11719919C2×D411yescharacteristic
660C4×Dic53—21no—
661C4×Dic53—21no—
662C4×Dic53—21no—
663C4×Dic53—21no—
664C4×Dic53—21no—
665C4×Dic53—21no—
666C4×Dic53—21no—
667C4×Dic53—21no—
668C4×Dic53C2×D411yescharacteristic
669C4×Dic53C2×D411yescharacteristic
670C4×Dic53C2411yescharacteristic
671C4×Dic53C2411yescharacteristic
672#11719917—22no—
673C2×#88322—41no—
674C2×#88322C2411yescharacteristic
675C2×#88322C2411yescharacteristic
676C2×#88322C2411yescharacteristic
677C2×#88322C2411yescharacteristic
678D424—22no—
679D424—41no—
680#11719913—22no—
681#11719913—41no—
682#11719912—22no—
683C8×D53—22no—
684C8×D53—41no—
685C8×D53—41no—
686C23×C53—21no—
687C23×C53C22×D411yescharacteristic
688C22×D53—21no—
689C22×D53—21no—
690C22×D53—21no—
691C22×D53—42no—
692C22×D53—42no—
693C22×D53—81no—
694C22×D53—81no—
695C22×D53—81no—
696C22×D53—81no—
697C22×D53C22×D411yescharacteristic
698C22×D53C22×D411yescharacteristic
699Q8×C53—21no—
700Q8×C53—21no—
701Q8×C53—21no—
702Q8×C53—21no—
703Q8×C53—21no—
704Q8×C53—21no—
705D4×C53—21no—
706D4×C53—42no—
707D4×C53C2×#4112yes—
708C2×C4×C53—21no—
709C2×C4×C53—21no—
710C2×C4×C53—21no—
711C2×C4×C53—21no—
712C2×C4×C53—21no—
713C2×C4×C53—21no—
714C2×C4×C53—21no—
715C2×C4×C53—21no—
716C2×C4×C53—21no—
717C2×C4×C53—42no—
718C2×C4×C53—81no—
719C2×C4×C53—81no—
720C2×C4×C53—81no—
721C2×C4×C53C22×D411yescharacteristic
722C2×C4×C53C22×D411yescharacteristic
723C2×C4×C53C22×D411yescharacteristic
724C2×C4×C53C22×D411yescharacteristic
725C2×C4×C53C22×D411yescharacteristic
726C2×C4×C53C2511yescharacteristic
727C22⋊D53—41no—
728C22⋊D53—41no—
729C22⋊D53—42no—
730C22⋊D53—42no—
731C22⋊D53—81no—
732C2×Dic53—21no—
733C2×Dic53—21no—
734C2×Dic53—21no—
735C2×Dic53—21no—
736C2×Dic53—21no—
737C2×Dic53—42no—
738C2×Dic53—81no—
739C2×Dic53—81no—
740C2×Dic53C22×D411yescharacteristic
741C2×Dic53C22×D411yescharacteristic
742C2×Dic53C22×D411yescharacteristic
743C2×Dic53C22×D411yescharacteristic
744C2×Dic53C22×D411yescharacteristic
745C2×Dic53C22×D411yescharacteristic
746D212—21no—
747D212—21no—
748D212—21no—
749D212—21no—
750D212—21no—
751D212—41no—
752D212—42no—
753D212—42no—
754D212—42no—
755D212—81no—
756D212—81no—
757D212—81no—
758D212C2×#4112yes—
759C4×D53—21no—
760C4×D53—21no—
761C4×D53—21no—
762C4×D53—21no—
763C4×D53—41no—
764C4×D53—41no—
765C4×D53—42no—
766C4×D53—42no—
767C4×D53—81no—
768C4×D53—81no—
769C4×D53—81no—
770C4×D53—81no—
771C4×D53—81no—
772C4×D53—81no—
773C4×D53—81no—
774C4×D53—81no—
775C4×D53—81no—
776Dic106—21no—
777Dic106—21no—
778Dic106—41no—
779Dic106—81no—
780Dic106—81no—
781C8×C53—21no—
782C8×C53—21no—
783C8×C53—21no—
784C8×C53—21no—
785#88322—21no—
786#88322—21no—
787#88322—21no—
788#88322C2×#4112yes—
789#61501—531nomaximal, Sylow
790C22×C53—21no—
791C22×C53—21no—
792C22×C53—22no—
793C22×C53—21no—
794C22×C53—41no—
795C22×C53—41no—
796C22×C53C23×D411yescharacteristic
797C2×D53—21no—
798C2×D53—21no—
799C2×D53—21no—
800C2×D53—21no—
801C2×D53—21no—
802C2×D53—21no—
803C2×D53—22no—
804C2×D53—41no—
805C2×D53—41no—
806C2×D53—41no—
807C2×D53—41no—
808C2×D53—41no—
809C2×D53—41no—
810C2×D53—41no—
811C2×D53—41no—
812C2×D53—162no—
813C2×D53—162no—
814C4×C53—21no—
815C4×C53—21no—
816C4×C53—21no—
817C4×C53—21no—
818C4×C53—21no—
819C4×C53—41no—
820C4×C53—41no—
821C4×C53—41no—
822C4×C53—41no—
823C4×C53—41no—
824C4×C53—41no—
825C4×C53—41no—
826C4×C53C22×#4111yescharacteristic
827C4×C53#58511yescharacteristic
828Dic53—21no—
829Dic53—21no—
830Dic53—21no—
831Dic53—21no—
832Dic53—21no—
833Dic53—21no—
834Dic53—41no—
835Dic53—41no—
836Dic53—41no—
837Dic53—41no—
838Dic53—41no—
839#3521—531no—
840#3521—531no—
841#3402—531no—
842#3389—531no—
843#3360—531no—
844#3360—531no—
845#3352—531no—
846#3350—531no—
847#3350—531no—
848#3302—531no—
849#3302—531no—
850#3297—531no—
851#3297—531no—
852#3296—531no—
853#3296—531no—
854#3273—531no—
855#3267—531no—
856#3267—531no—
857#3178—531no—
858#3178—531no—
859#3168—531no—
860#3120—531no—
861#3120D5311yescharacteristic, complemented
862#3118—531no—
863#3118—531no—
864#3111—531no—
865#3111—531no—
866#2966—531no—
867#2946—531no—
868#2946—531no—
869C4×#135—531no—
870C2×C53—41no—
871C2×C53—42no—
872C2×C53D4×#4111yescharacteristic
873C2×C53#358411yescharacteristic
874C2×C53#358411yescharacteristic
875D53—41no—
876D53—41no—
877D53—42no—
878D53—81no—
879D53—81no—
880C2×AGL(1,ℤ/8)—531no—
881C2×AGL(1,ℤ/8)—531no—
882C2×#135—531no—
883#556—531no—
884#556—531no—
885#556—531no—
886#556—531no—
887#554—531no—
888#554—531no—
889#553—531no—
890#553—531no—
891#553—1061no—
892#553—1061no—
893#552—531no—
894#552—531no—
895#552—1061no—
896#552—1061no—
897#551—1061no—
898#551—1061no—
899#551—1061no—
900#551—1061no—
901#547—531no—
902#547—531no—
903#546—531no—
904#546—531no—
905#546—531no—
906#546—531no—
907#542—531no—
908#542—531no—
909#541—531no—
910#541C2×D5311yescharacteristic, complemented
911#539—1061no—
912#539—1061no—
913#538—1061no—
914#538—1061no—
915#529—531no—
916#529—531no—
917#529—531no—
918#529—1061no—
919#529—1061no—
920C2×#126—1061no—
921C2×#126—1061no—
922#520—531no—
923#520C2×D5311yescharacteristic
924#518—531no—
925#518—531no—
926C4×#41—531no—
927C4×#41—531no—
928#501—531no—
929#501—531no—
930#499—531no—
931#497—531no—
932#497—531no—
933#495—531no—
934#488—531no—
935#488—531no—
936#488—531no—
937#488—531no—
938#487—531no—
939#487—531no—
940#485—531no—
941#485—531no—
942#485—531no—
943#485—531no—
944#484—531no—
945#484C2×D5311yescharacteristic, complemented
946#483—531no—
947#483C2×D5311yescharacteristic, complemented
948#482—531no—
949#482—531no—
950#482—531no—
951#482—531no—
952#479—531no—
953#479—531no—
954#479—531no—
955#479C2×D5311yescharacteristic, complemented
956#478—531no—
957#478—531no—
958#478—531no—
959#478C2×D5311yescharacteristic, complemented
960#476—531no—
961#476—531no—
962#474—531no—
963#474—531no—
964#470—531no—
965#470—531no—
966#468—531no—
967#468—531no—
968#467—531no—
969#467—531no—
970#467—531no—
971#466—531no—
972#465—531no—
973#465—531no—
974#465—531no—
975#465—531no—
976#464—531no—
977#464—531no—
978#463—531no—
979#463—531no—
980#463—531no—
981#463—531no—
982#463—531no—
983#463—531no—
984#462—531no—
985#462C2×D5311yescharacteristic, complemented
986#461—531no—
987#461C2×D5311yescharacteristic, complemented
988#452—531no—
989#452—531no—
990#452—531no—
991#452—531no—
992#452C2×D5311yescharacteristic
993#452C2×D5311yescharacteristic
994#450—531no—
995#450—531no—
996#449—531no—
997#449—531no—
998#447—531no—
999#447—531no—
1000#446—531no—
1001C8×Q8—531no—
1002#442—531no—
1003#442—531no—
1004#442—531no—
1005#442—531no—
1006#441—531no—
1007#441C2×D5311yescharacteristic, complemented
1008#440—531no—
1009#440—531no—
1010#440—531no—
1011#440—531no—
1012#440—531no—
1013#440C2×D5311yescharacteristic, complemented
1014C4×Q16—531no—
1015C4×Q16—531no—
1016C4×Q16C2×D5311yescharacteristic, complemented
1017C4×SD16—531no—
1018C4×SD16—531no—
1019C4×SD16—531no—
1020C4×SD16—531no—
1021C4×SD16—531no—
1022C4×SD16—531no—
1023C4×SD16—531no—
1024C4×SD16C2×D5311yescharacteristic, complemented
1025C4×D8—531no—
1026C4×D8—531no—
1027C4×D8—531no—
1028C4×D8—531no—
1029C4×D8—531no—
1030#436—531no—
1031#435—531no—
1032#435—531no—
1033C8×D4—531no—
1034C8×D4—531no—
1035C8×D4—531no—
1036#433—531no—
1037#433C2×D5311yescharacteristic, complemented
1038#432—531no—
1039#428—531no—
1040#428—531no—
1041#427—531no—
1042#416—531no—
1043#416—531no—
1044#416—531no—
1045#416—531no—
1046C2×#102—531no—
1047C2×#102—531no—
1048#405—531no—
1049#405—531no—
1050C2×C4×C8—531no—
1051C53#6150111yescharacteristic, complemented, Sylow
1052C2×#41—531no—
1053C2×#41—531no—
1054C2×#41—531no—
1055C2×#41C22×D5311yescharacteristic
1056C22×D4—531no—
1057C22×D4—531no—
1058AGL(1,ℤ/8)—1064no—
1059AGL(1,ℤ/8)—1064no—
1060#135—1064no—
1061C2×Q16—531no—
1062C2×Q16—531no—
1063C2×Q16C22×D5311yescharacteristic
1064C2×Q16C22×D5311yescharacteristic
1065C2×SD16—531no—
1066C2×SD16—531no—
1067C2×SD16—531no—
1068C2×SD16—531no—
1069C2×SD16—531no—
1070C2×SD16—531no—
1071C2×SD16C22×D5311yescharacteristic
1072C2×SD16C22×D5311yescharacteristic
1073C2×D8—531no—
1074C2×D8—531no—
1075C2×D8—531no—
1076C2×D8—531no—
1077C2×M16—531no—
1078C2×M16—531no—
1079C22×C8—531no—
1080C22×C8—531no—
1081C22×C8—531no—
1082C22×C8—531no—
1083C4⋊Q8—531no—
1084C4⋊Q8—531no—
1085C4⋊Q8—531no—
1086C4⋊Q8C22×D5311yescharacteristic
1087#126—21no—
1088#126—21no—
1089#126—531no—
1090#126—531no—
1091#126—1061no—
1092#126—1061no—
1093#126—1061no—
1094#126—1061no—
1095#126—1061no—
1096#126—1061no—
1097#126—1061no—
1098#126—1061no—
1099#126—1061no—
1100#126—1061no—
1101#126—1061no—
1102#126—1061no—
1103#126—1061no—
1104#126—1061no—
1105#126—1061no—
1106#126—1061no—
1107#126—1061no—
1108#126—1061no—
1109#125—21no—
1110#125—21no—
1111#125—531no—
1112#125—531no—
1113#125—531no—
1114#125—531no—
1115#125—1061no—
1116#125—1061no—
1117#125—1061no—
1118#125—1061no—
1119#125C22×D5311yescharacteristic
1120#124—531no—
1121#124—531no—
1122#124—531no—
1123#124—531no—
1124#124—531no—
1125#124—1061no—
1126#124—1061no—
1127#124—1061no—
1128#124—1061no—
1129#123—531no—
1130#123—531no—
1131#123—1061no—
1132#123—1061no—
1133#123—1061no—
1134#123—1061no—
1135#123—1061no—
1136#123—1061no—
1137#123—1061no—
1138#123—1061no—
1139#123—1061no—
1140#123—1061no—
1141#123—1061no—
1142#123—1061no—
1143#123—1061no—
1144#123—1061no—
1145#123—1061no—
1146#123—1061no—
1147C22⋊Q8—531no—
1148C22⋊Q8—531no—
1149C22⋊Q8—531no—
1150C22⋊Q8—531no—
1151C22⋊Q8—531no—
1152C22⋊Q8—531no—
1153C22⋊Q8—531no—
1154C22⋊Q8—1061no—
1155C22⋊Q8—1061no—
1156C22⋊Q8—1061no—
1157C22⋊Q8—1061no—
1158C22⋊Q8—1061no—
1159C22⋊Q8—1061no—
1160C22⋊Q8—1061no—
1161C22⋊Q8—1061no—
1162C22⋊Q8—1061no—
1163C22⋊Q8—1061no—
1164C22⋊Q8C22×D5311yescharacteristic
1165C22⋊Q8C22×D5311yescharacteristic
1166#121—531no—
1167#121—531no—
1168#121—531no—
1169#121—531no—
1170#121—531no—
1171#121—1061no—
1172#121—1061no—
1173#121—1061no—
1174#121—1061no—
1175#121—1061no—
1176#121—1061no—
1177#121—1061no—
1178#121—1061no—
1179#120—1061no—
1180#120—1061no—
1181#120—1061no—
1182#120—1061no—
1183C4×Q8—531no—
1184C4×Q8—531no—
1185C4×Q8—531no—
1186C4×Q8—531no—
1187C4×Q8—531no—
1188C4×Q8—1061no—
1189C4×Q8—1061no—
1190C4×Q8C22×D5311yescharacteristic
1191C4×Q8C22×D5311yescharacteristic
1192C4×Q8C22×D5311yescharacteristic
1193C4×Q8C22×D5311yescharacteristic
1194C4×D4—21no—
1195C4×D4—21no—
1196C4×D4—531no—
1197C4×D4—531no—
1198C4×D4—531no—
1199C4×D4—531no—
1200C4×D4—531no—
1201C4×D4—531no—
1202C4×D4—531no—
1203C4×D4—531no—
1204C4×D4—531no—
1205C4×D4—531no—
1206C4×D4—531no—
1207C4×D4—531no—
1208C4×D4—531no—
1209C4×D4—1061no—
1210C4×D4—1061no—
1211C4×D4—1061no—
1212C4×D4—1061no—
1213C4×D4—1061no—
1214C4×D4—1061no—
1215C4×D4—1061no—
1216C4×D4—1061no—
1217C4×D4—1061no—
1218C4×D4—1061no—
1219C4×D4—1061no—
1220C4×D4—1061no—
1221C4×D4—1061no—
1222C4×D4—1061no—
1223C4×D4C22×D5311yescharacteristic
1224C4×D4C22×D5311yescharacteristic
1225#117—21no—
1226#117—531no—
1227#117—531no—
1228#117—531no—
1229#117—531no—
1230#117—531no—
1231#117—1061no—
1232#117—1061no—
1233#117—1061no—
1234#117—1061no—
1235#117—1061no—
1236#117—1061no—
1237#117—1061no—
1238#117—1061no—
1239#117—1061no—
1240#117C22×D5311yescharacteristic
1241C2×C4⋊C4—21no—
1242C2×C4⋊C4—531no—
1243C2×C4⋊C4—1061no—
1244C2×C4⋊C4—1061no—
1245C2×C4⋊C4—1061no—
1246C2×C4⋊C4—1061no—
1247C2×C4⋊C4—1061no—
1248C2×C4⋊C4C22×D5311yescharacteristic
1249C2×C22⋊C4—1061no—
1250C2×C22⋊C4—1061no—
1251C2×C22⋊C4—1061no—
1252C2×C22⋊C4—1061no—
1253C2×C22⋊C4—1061no—
1254C2×C22⋊C4—1061no—
1255C2×C22⋊C4—1061no—
1256C2×C22⋊C4—1061no—
1257C2×C42—531no—
1258C2×C42—1061no—
1259C2×C42—1061no—
1260#107—531no—
1261#107—531no—
1262#107—531no—
1263#107—531no—
1264#107—531no—
1265#107—531no—
1266#107C22×D5311yescharacteristic
1267#107C22×D5311yescharacteristic
1268#106—531no—
1269#106—531no—
1270#106—531no—
1271#106—531no—
1272#106—531no—
1273#106—531no—
1274#106C22×D5311yescharacteristic
1275#106C22×D5311yescharacteristic
1276C4⋊C8—531no—
1277C4⋊C8—531no—
1278C4⋊C8—531no—
1279C4⋊C8—531no—
1280C4⋊C8C22×D5311yescharacteristic
1281C4⋊C8C22×D5311yescharacteristic
1282#103—531no—
1283#103—531no—
1284#103—531no—
1285#103—531no—
1286#103—531no—
1287#103—531no—
1288#103—531no—
1289#103—531no—
1290#103—531no—
1291#103—531no—
1292#103C22×D5311yescharacteristic
1293#103C22×D5311yescharacteristic
1294#103C22×D5311yescharacteristic
1295#103C22×D5311yescharacteristic
1296#103C22×D5311yescharacteristic
1297#103C22×D5311yescharacteristic
1298#102—531no—
1299#102—531no—
1300#102—531no—
1301#102—531no—
1302#102—531no—
1303#102—531no—
1304#102—531no—
1305#102—531no—
1306#102—531no—
1307#102—531no—
1308#102—531no—
1309#102—531no—
1310#102—531no—
1311#102—531no—
1312#102C22×D5311yescharacteristic
1313#102C22×D5311yescharacteristic
1314C22⋊C8—531no—
1315C22⋊C8—531no—
1316C22⋊C8—531no—
1317C22⋊C8—531no—
1318C22⋊C8C22×D5311yescharacteristic
1319C22⋊C8C22×D5311yescharacteristic
1320#97—531no—
1321#97—531no—
1322#97—531no—
1323#97C22×D5311yescharacteristic
1324C4×C8—531no—
1325C4×C8—531no—
1326C4×C8—531no—
1327C4×C8—531no—
1328C4×C8—531no—
1329C4×C8C22×D5311yescharacteristic
1330C24—1061no—
1331C24—1061no—
1332#41—22no—
1333#41—41no—
1334#41—1062no—
1335#41—1062no—
1336#41—1062no—
1337#41—2121no—
1338#41—2121no—
1339#41—2121no—
1340C2×Q8—531no—
1341C2×Q8—531no—
1342C2×Q8—1061no—
1343C2×Q8—1061no—
1344C2×Q8C23×D5311yescharacteristic
1345C2×Q8C23×D5311yescharacteristic
1346C2×Q8C23×D5311yescharacteristic
1347C2×D4—21no—
1348C2×D4—531no—
1349C2×D4—531no—
1350C2×D4—531no—
1351C2×D4—531no—
1352C2×D4—531no—
1353C2×D4—531no—
1354C2×D4—1062no—
1355C2×D4—1061no—
1356C2×D4—1061no—
1357C2×D4—1061no—
1358C2×D4—1061no—
1359C2×D4—1061no—
1360C2×D4—1061no—
1361C2×D4—1062no—
1362C2×D4—1061no—
1363C2×D4—1061no—
1364C2×D4—1061no—
1365C2×D4—2121no—
1366C2×D4—2121no—
1367C2×D4C23×D5311yescharacteristic
1368C22×C4—21no—
1369C22×C4—21no—
1370C22×C4—21no—
1371C22×C4—21no—
1372C22×C4—531no—
1373C22×C4—531no—
1374C22×C4—531no—
1375C22×C4—531no—
1376C22×C4—1061no—
1377C22×C4—1061no—
1378C22×C4—1061no—
1379C22×C4—1061no—
1380C22×C4—1061no—
1381C22×C4—1061no—
1382C22×C4—1061no—
1383C22×C4—1061no—
1384C22×C4—1061no—
1385C22×C4—1061no—
1386C22×C4—1061no—
1387C22×C4—1061no—
1388C22×C4—1061no—
1389C22×C4—1061no—
1390C22×C4C23×D5311yescharacteristic
1391Q16—41no—
1392Q16—41no—
1393Q16—1062no—
1394Q16—2121no—
1395SD16—22no—
1396SD16—22no—
1397SD16—1062no—
1398SD16—1062no—
1399SD16—1062no—
1400SD16—1062no—
1401SD16—2121no—
1402SD16—2121no—
1403D8—534no—
1404D8—1062no—
1405D8—1062no—
1406D8—2121no—
1407M16—1062no—
1408M16—1062no—
1409C2×C8—531no—
1410C2×C8—531no—
1411C2×C8—531no—
1412C2×C8—531no—
1413C2×C8—1062no—
1414C2×C8—2121no—
1415C2×C8—2121no—
1416C2×C8—2121no—
1417C2×C8C23×D5311yescharacteristic
1418C2×C8C23×D5311yescharacteristic
1419C2×C8C23×D5311yescharacteristic
1420C2×C8C23×D5311yescharacteristic
1421C4⋊C4—21no—
1422C4⋊C4—21no—
1423C4⋊C4—21no—
1424C4⋊C4—21no—
1425C4⋊C4—21no—
1426C4⋊C4—21no—
1427C4⋊C4—21no—
1428C4⋊C4—21no—
1429C4⋊C4—21no—
1430C4⋊C4—21no—
1431C4⋊C4—21no—
1432C4⋊C4—531no—
1433C4⋊C4—531no—
1434C4⋊C4—531no—
1435C4⋊C4—531no—
1436C4⋊C4—531no—
1437C4⋊C4—531no—
1438C4⋊C4—531no—
1439C4⋊C4—531no—
1440C4⋊C4—531no—
1441C4⋊C4—531no—
1442C4⋊C4—531no—
1443C4⋊C4—531no—
1444C4⋊C4—1061no—
1445C4⋊C4—1061no—
1446C4⋊C4—1061no—
1447C4⋊C4—1061no—
1448C4⋊C4—1061no—
1449C4⋊C4—1061no—
1450C4⋊C4—1061no—
1451C4⋊C4—1061no—
1452C4⋊C4—1061no—
1453C4⋊C4—1061no—
1454C4⋊C4—1061no—
1455C4⋊C4—1061no—
1456C4⋊C4—1061no—
1457C4⋊C4—1061no—
1458C4⋊C4—1061no—
1459C4⋊C4—1061no—
1460C4⋊C4—1061no—
1461C4⋊C4—1061no—
1462C4⋊C4—1061no—
1463C4⋊C4—1061no—
1464C4⋊C4—1061no—
1465C4⋊C4D4×D5311yescharacteristic
1466C4⋊C4D4×D5311yescharacteristic
1467C4⋊C4C23×D5311yescharacteristic
1468C4⋊C4C23×D5311yescharacteristic
1469C4⋊C4C23×D5311yescharacteristic
1470C4⋊C4C23×D5311yescharacteristic
1471C22⋊C4—21no—
1472C22⋊C4—21no—
1473C22⋊C4—21no—
1474C22⋊C4—21no—
1475C22⋊C4—531no—
1476C22⋊C4—531no—
1477C22⋊C4—531no—
1478C22⋊C4—531no—
1479C22⋊C4—531no—
1480C22⋊C4—531no—
1481C22⋊C4—531no—
1482C22⋊C4—531no—
1483C22⋊C4—1061no—
1484C22⋊C4—1061no—
1485C22⋊C4—1061no—
1486C22⋊C4—1061no—
1487C22⋊C4—1061no—
1488C22⋊C4—1061no—
1489C22⋊C4—1061no—
1490C22⋊C4—1061no—
1491C22⋊C4—1061no—
1492C22⋊C4—1061no—
1493C22⋊C4—1061no—
1494C22⋊C4—1061no—
1495C22⋊C4—1061no—
1496C22⋊C4—1061no—
1497C22⋊C4—1061no—
1498C22⋊C4—1061no—
1499C22⋊C4—1061no—
1500C22⋊C4—1061no—
1501C22⋊C4—1061no—
1502C22⋊C4—1061no—
1503C22⋊C4—1061no—
1504C22⋊C4—1061no—
1505C22⋊C4—1061no—
1506C22⋊C4—1061no—
1507C22⋊C4—1061no—
1508C22⋊C4—1061no—
1509C22⋊C4—1061no—
1510C22⋊C4—1061no—
1511C22⋊C4—1061no—
1512C22⋊C4—1061no—
1513C22⋊C4—1061no—
1514C22⋊C4—1061no—
1515C22⋊C4D4×D5311yescharacteristic
1516C22⋊C4D4×D5311yescharacteristic
1517C42—21no—
1518C42—21no—
1519C42—21no—
1520C42—21no—
1521C42—531no—
1522C42—531no—
1523C42—531no—
1524C42—531no—
1525C42—1061no—
1526C42—1061no—
1527C42—1061no—
1528C42—1061no—
1529C42—1061no—
1530C42—1061no—
1531C42—1061no—
1532C42—1061no—
1533C42C23×D5311yescharacteristic
1534C42C23×D5311yescharacteristic
1535C23—21no—
1536C23—531no—
1537C23—531no—
1538C23—1061no—
1539C23—1061no—
1540C23—1061no—
1541C23—4241no—
1542C23—4241no—
1543C23—4241no—
1544C23—4241no—
1545C23—2122no—
1546C23—2122no—
1547C23C2×D4×D5311yescharacteristic
1548Q8—21no—
1549Q8—21no—
1550Q8—21no—
1551Q8—21no—
1552Q8—21no—
1553Q8—21no—
1554Q8—1061no—
1555Q8—1061no—
1556Q8—4241no—
1557Q8—4241no—
1558Q8—2121no—
1559D4—21no—
1560D4—42no—
1561D4—532no—
1562D4—1061no—
1563D4—1061no—
1564D4—1061no—
1565D4—1061no—
1566D4—1061no—
1567D4—4241no—
1568D4—4241no—
1569D4—4241no—
1570D4—4241no—
1571D4—2121no—
1572D4—2122no—
1573D4—2122no—
1574D4—2122no—
1575D4—2121no—
1576D4—2121no—
1577D4—2122no—
1578D4—2122no—
1579D4#41×D5312yes—
1580C2×C4—21no—
1581C2×C4—21no—
1582C2×C4—21no—
1583C2×C4—21no—
1584C2×C4—21no—
1585C2×C4—21no—
1586C2×C4—21no—
1587C2×C4—21no—
1588C2×C4—21no—
1589C2×C4—42no—
1590C2×C4—81no—
1591C2×C4—81no—
1592C2×C4—81no—
1593C2×C4—531no—
1594C2×C4—531no—
1595C2×C4—531no—
1596C2×C4—531no—
1597C2×C4—531no—
1598C2×C4—531no—
1599C2×C4—1061no—
1600C2×C4—1061no—
1601C2×C4—1061no—
1602C2×C4—1061no—
1603C2×C4—1061no—
1604C2×C4—1061no—
1605C2×C4—1061no—
1606C2×C4—1061no—
1607C2×C4—1061no—
1608C2×C4—4241no—
1609C2×C4—4241no—
1610C2×C4—4241no—
1611C2×C4—4241no—
1612C2×C4—4241no—
1613C2×C4—4241no—
1614C2×C4—4241no—
1615C2×C4—4241no—
1616C2×C4—4241no—
1617C2×C4—4241no—
1618C2×C4—4241no—
1619C2×C4—2121no—
1620C2×C4—2121no—
1621C2×C4—2122no—
1622C2×C4—2122no—
1623C2×C4—2122no—
1624C2×C4C2×D4×D5311yescharacteristic
1625C2×C4C2×D4×D5311yescharacteristic
1626C2×C4C2×D4×D5311yescharacteristic
1627C2×C4C2×D4×D5311yescharacteristic
1628C2×C4C2×D4×D5311yescharacteristic
1629C2×C4C24×D5311yescharacteristic
1630C8—21no—
1631C8—21no—
1632C8—21no—
1633C8—21no—
1634C8—532no—
1635C8—1061no—
1636C8—1061no—
1637C8—1061no—
1638C22—21no—
1639C22—22no—
1640C22—21no—
1641C22—21no—
1642C22—41no—
1643C22—41no—
1644C22—8482no—
1645C22—8482no—
1646C22—1061no—
1647C22—1061no—
1648C22—1062no—
1649C22—1061no—
1650C22—1061no—
1651C22—1061no—
1652C22—1061no—
1653C22—2121no—
1654C22—2121no—
1655C22—2121no—
1656C22—2121no—
1657C22—2121no—
1658C22—2121no—
1659C22—2121no—
1660C22—2121no—
1661C22C22×D4×D5311yescharacteristic
1662C4—21no—
1663C4—21no—
1664C4—21no—
1665C4—21no—
1666C4—21no—
1667C4—41no—
1668C4—41no—
1669C4—41no—
1670C4—41no—
1671C4—41no—
1672C4—41no—
1673C4—41no—
1674C4—1061no—
1675C4—1061no—
1676C4—1061no—
1677C4—1061no—
1678C4—1061no—
1679C4—1061no—
1680C4—2121no—
1681C4—2121no—
1682C4—2121no—
1683C4—2121no—
1684C4—2121no—
1685C4C2×#41×D5311yescharacteristic
1686C4#1681145911yescharacteristic
1687C2—41no—
1688C2—42no—
1689C2—4241no—
1690C2—4241no—
1691C2—2121no—
1692C2—2122no—
1693C2—2121no—
1694C2#2028819811yescharacteristic
1695C2#2028948511yescharacteristic
1696C2#2028948711yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3120C2
socleC22×C53C23×D4
hypercenter#3120D53
hypocenterC53#61501
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ #117 ◁ #3120

Complements

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

NH ≅ G/Ntype
1. #20288789C2semidirect
2. #20288785C2semidirect
3. #20287789C2semidirect
4. #20287672C2semidirect
5. #20287368C2semidirect
6. #20287367C2semidirect
7. #20287290C2semidirect
8. #20287263C2semidirect
9. #20287257C2semidirect
10. #20286635C2semidirect
11. #20286625C2semidirect
12. #20286563C2semidirect
13. #20286562C2semidirect
14. #20286548C2semidirect
15. #20286543C2semidirect
16. #20286319C2semidirect
17. #20286246C2semidirect
18. #20286243C2semidirect
19. #20285389C2semidirect
20. #20285385C2semidirect
21. #20285288C2semidirect
22. #20284935C2semidirect
23. #20284905C2semidirect
24. #20284901C2semidirect
25. #20284830C2semidirect
26. #20284828C2semidirect
27. #20283688C2semidirect
28. #20283546C2semidirect
29. #20283543C2semidirect
30. C4×#13133238C2semidirect
31. C53×#3120C2semidirect
35. #16811347C22semidirect
36. #16811346C22semidirect
37. #16811345C22semidirect
38. #16811344C22semidirect
39. #16811330C22semidirect
40. #16811329C22semidirect
55. #16811268C22semidirect
57. #16811264C22semidirect
61. #16811231C22semidirect
66. #16811160C22semidirect
67. #16811160C22semidirect
74. #16811097C22semidirect
75. #16811095C22semidirect
76. C4×#11719949C22semidirect
77. C4×#11719947C22semidirect
78. #16811033C22semidirect
79. #16811030C22semidirect
80. #16811024C22semidirect
81. #16811016C22semidirect
82. #16811015C22semidirect
84. #16810980C22semidirect
85. #16810979C22semidirect
86. #16810979C22semidirect
87. #16810979C22semidirect
88. #16810973C22semidirect
89. #16810972C22semidirect
90. #16810965C22semidirect
91. #16810963C22semidirect
92. #16810963C22semidirect
93. #16810962C22semidirect
94. #16810960C22semidirect
95. #16810952C22semidirect
96. #16810950C22semidirect
98. #16810949C22semidirect
100. #16810929C22semidirect
101. #16810928C22semidirect
102. #16810928C22semidirect
103. #16810926C22semidirect
104. #16810922C22semidirect
105. #16810921C22semidirect
106. #16810914C22semidirect
107. #16810912C22semidirect
108. #16810904C22semidirect
109. #16810901C22semidirect
110. #16810880C22semidirect
111. #16810879C22semidirect
114. #16810862C22semidirect
115. #16810861C22semidirect
116. #16810861C22semidirect
118. #16810855C22semidirect
119. #16810855C22semidirect
122. #16810848C22semidirect
123. #16810847C22semidirect
130. #16810831C22semidirect
131. #16810827C22semidirect
134. #16810784C22semidirect
135. #16810782C22semidirect
136. #16810776C22semidirect
137. #16810772C22semidirect
142. #16810752C22semidirect
143. #16810747C22semidirect
148. #16810728C22semidirect
149. #16810726C22semidirect
150. #16810725C22semidirect
151. #16810721C22semidirect
152. #16810721C22semidirect
153. #16810721C22semidirect
154. C4×#11719925C22semidirect
155. #16810715C22semidirect
156. C4×#11719913C22semidirect
157. SD16×Dic53C22semidirect
158. SD16×Dic53C22semidirect
159. C4×#11719924C22semidirect
160. C4×#11719924C22semidirect
161. C4×#11719924C22semidirect
162. #16810710C22semidirect
169. #16810697C22semidirect
170. #16810693C22semidirect
171. #16810688C22semidirect
173. #16810686C22semidirect
174. #16810682C22semidirect
175. #16810678C22semidirect
176. #16810664C22semidirect
177. #16810663C22semidirect
178. #16810658C22semidirect
181. #16810618C22semidirect
182. #16810616C22semidirect
183. C2×#13133137C22semidirect
184. #102×D53C22semidirect
185. #16810580C22semidirect
186. #16810579C22semidirect
187. C4×C8×D53C22semidirect
188. C53×#541C22semidirect
190. C53×#484C22semidirect
191. C53×#483C22semidirect
192. C53×#479C22semidirect
193. C53×#478C22semidirect
194. C53×#462C22semidirect
195. C53×#461C22semidirect
198. C53×#441C22semidirect
199. C53×#440C22semidirect
200. C4×Q16×C53C22semidirect
201. C4×SD16×C53C22semidirect
202. C53×#433C22semidirect
861. #3120D53semidirect
910. #541C2×D53semidirect
945. #484C2×D53semidirect
947. #483C2×D53semidirect
955. #479C2×D53semidirect
959. #478C2×D53semidirect
985. #462C2×D53semidirect
987. #461C2×D53semidirect
1007. #441C2×D53semidirect
1013. #440C2×D53semidirect
1016. C4×Q16C2×D53semidirect
1024. C4×SD16C2×D53semidirect
1037. #433C2×D53semidirect
1051. C53#61501semidirect

Maximal subgroups

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

subgroupindex
#202887892
#202887852
#202877892
#202876722
#202873682
#202873672
#202872902
#202872632
#202872572
#202866352
#202866252
#202865632
#202865622
#202865482
#202865432
#202863192
#202862462
#202862432
#202853892
#202853852
#202852882
#202849352
#202849052
#202849012
#202848302
#202848282
#202836882
#202835462
#202835432
C4×#131332382
C53×#31202
#6150153