Finite Group Databasebeta

← #28276434

Subgroups — #28276434

Order 13568.

2178 conjugacy classes of subgroups.

The subgroup lattice has 1892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288583C211yesmaximal, characteristic, complemented
2#20288202C211yesmaximal, characteristic, complemented
3#20287758C211yesmaximal, characteristic, complemented
4#20287752C211yesmaximal, characteristic, complemented
5#20287510C211yesmaximal, characteristic, complemented
6#20287504C211yesmaximal, characteristic, complemented
7#20287040C211yesmaximal, characteristic, complemented
8#20287038C211yesmaximal, characteristic, complemented
9#20286674C211yesmaximal, characteristic, complemented
10#20286672C211yesmaximal, characteristic, complemented
11#20286670C211yesmaximal, characteristic, complemented
12#20286332C211yesmaximal, characteristic, complemented
13#20286328C211yesmaximal, characteristic, complemented
14#20286200C211yesmaximal, characteristic, complemented
15#20286196C211yesmaximal, characteristic, complemented
16#20286192C211yesmaximal, characteristic, complemented
17#20286188C211yesmaximal, characteristic, complemented
18#20286095C211yesmaximal, characteristic, complemented
19#20286092C211yesmaximal, characteristic, complemented
20#20286026C211yesmaximal, characteristic, complemented
21#20285711C211yesmaximal, characteristic, complemented
22#20285707C211yesmaximal, characteristic, complemented
23#20285631C211yesmaximal, characteristic, complemented
24#20284804C211yesmaximal, characteristic, complemented
25#20284803C211yesmaximal, characteristic, complemented
26#20284720C211yesmaximal, characteristic, complemented
27#20284178C211yesmaximal, characteristic, complemented
28#20284177C211yesmaximal, characteristic, complemented
29C2×#16810817C211yesmaximal, characteristic, complemented
30#20283827C211yesmaximal, characteristic, complemented
31C53×#3306C211yesmaximal, characteristic, complemented
32C2×#41×D53—21no—
33C2×#13133245C2211yescharacteristic, complemented
34C2×#13133244C2211yescharacteristic, complemented
35C2×#13133242C2211yescharacteristic, complemented
36C2×#13133241C2211yescharacteristic, complemented
37C22×D424C2211yescharacteristic
38C22×#11719922C2211yescharacteristic
39#16811357—21no—
40#16811356C2211yescharacteristic, complemented
41#16811355C2211yescharacteristic, complemented
42#16811294C2211yescharacteristic, complemented
43#16811292C2211yescharacteristic, complemented
44#16811291—21no—
45#16811291C2211yescharacteristic, complemented
46#16811288C2211yescharacteristic, complemented
47#16811283—21no—
48#16811274C2211yescharacteristic
49#16811274C2211yescharacteristic, complemented
50#16811269C2211yescharacteristic, complemented
51#16811267C2211yescharacteristic, complemented
52#16811265—21no—
53#16811265—21no—
54#16811264C2211yescharacteristic, complemented
55#16811263—21no—
56#16811261—21no—
57#16811260—21no—
58D4×D212C2211yescharacteristic
59#16811257C2211yescharacteristic
60#16811257C2211yescharacteristic, complemented
61#16811225—21no—
62#16811223—21no—
63#16811188—21no—
64#16811175C2211yescharacteristic, complemented
65#16811174C2211yescharacteristic, complemented
66#16811172C2211yescharacteristic, complemented
67#16811170C2211yescharacteristic, complemented
68#16811169C2211yescharacteristic, complemented
69#16811168C2211yescharacteristic
70#16811168C2211yescharacteristic, complemented
71#16811168C2211yescharacteristic, complemented
72C2×#13133213C2211yescharacteristic, complemented
73#16811136—21no—
74#16811131—21no—
75#16811131—21no—
76#16811096—21no—
77C4×#11719947C2211yescharacteristic
78C2×#13133179C2211yescharacteristic
79C2×#13133179C2211yescharacteristic, complemented
80C4×D4×D53C2211yescharacteristic, complemented
81#16811013C2211yescharacteristic, complemented
82#16811012C2211yescharacteristic, complemented
83#16811011C2211yescharacteristic, complemented
84#16811009C2211yescharacteristic, complemented
85#16810998C2211yescharacteristic, complemented
86#16810998C2211yescharacteristic, complemented
87#16810985C2211yescharacteristic, complemented
88#16810984C2211yescharacteristic, complemented
89#16810981C2211yescharacteristic, complemented
90#16810968C2211yescharacteristic, complemented
91#16810968C2211yescharacteristic, complemented
92#16810953C2211yescharacteristic, complemented
93#16810943C2211yescharacteristic, complemented
94#16810941C2211yescharacteristic, complemented
95#16810940C2211yescharacteristic, complemented
96#16810912C2211yescharacteristic, complemented
97#16810912C2211yescharacteristic, complemented
98#16810912C2211yescharacteristic, complemented
99#16810912C2211yescharacteristic, complemented
100#16810911C2211yescharacteristic, complemented
101#16810911C2211yescharacteristic, complemented
102#16810910C2211yescharacteristic, complemented
103#16810907C2211yescharacteristic, complemented
104#16810906C2211yescharacteristic, complemented
105#16810877C2211yescharacteristic, complemented
106#16810877C2211yescharacteristic, complemented
107#16810876C2211yescharacteristic, complemented
108#16810875C2211yescharacteristic, complemented
109#16810875C2211yescharacteristic, complemented
110#16810874C2211yescharacteristic, complemented
111#16810874C2211yescharacteristic, complemented
112#16810854C2211yescharacteristic, complemented
113#16810852C2211yescharacteristic, complemented
114#16810850C2211yescharacteristic, complemented
115#16810841C2211yescharacteristic, complemented
116#16810841C2211yescharacteristic, complemented
117#16810839C2211yescharacteristic, complemented
118#16810838C2211yescharacteristic, complemented
119#16810837C2211yescharacteristic, complemented
120#16810837C2211yescharacteristic, complemented
121#16810835C2211yescharacteristic, complemented
122#16810827C2211yescharacteristic, complemented
123#16810827C2211yescharacteristic, complemented
124#16810827C2211yescharacteristic, complemented
125#16810826C2211yescharacteristic, complemented
126#16810822C2211yescharacteristic, complemented
127#16810821C2211yescharacteristic, complemented
128#16810819C2211yescharacteristic, complemented
129#16810818C2211yescharacteristic, complemented
130#16810817C2211yescharacteristic
131#16810817C2211yescharacteristic
132#16810817C2211yescharacteristic
133#16810817C2211yescharacteristic
134#16810817C2211yescharacteristic, complemented
135#16810817C2211yescharacteristic, complemented
136#16810817C2211yescharacteristic, complemented
137#16810817C2211yescharacteristic, complemented
138#16810817C2211yescharacteristic, complemented
139#16810817C2211yescharacteristic, complemented
140#16810817C2211yescharacteristic, complemented
141#16810816C2211yescharacteristic, complemented
142#16810816C2211yescharacteristic, complemented
143#16810816C2211yescharacteristic, complemented
144#16810776C2211yescharacteristic
145#16810773C2211yescharacteristic
146#16810771C2211yescharacteristic, complemented
147#16810771C2211yescharacteristic, complemented
148#16810770C2211yescharacteristic, complemented
149#16810769C2211yescharacteristic, complemented
150#16810769C2211yescharacteristic, complemented
151#16810768C2211yescharacteristic, complemented
152#16810766C2211yescharacteristic, complemented
153#16810759C2211yescharacteristic, complemented
154#16810759C2211yescharacteristic, complemented
155#16810758C2211yescharacteristic, complemented
156#16810757C2211yescharacteristic, complemented
157#16810756C2211yescharacteristic, complemented
158#16810756C2211yescharacteristic, complemented
159#16810755C2211yescharacteristic, complemented
160#16810752C2211yescharacteristic, complemented
161#16810751C2211yescharacteristic, complemented
162#16810736C2211yescharacteristic, complemented
163#16810734C2211yescharacteristic, complemented
164#16810734C2211yescharacteristic, complemented
165#16810733C2211yescharacteristic, complemented
166#16810733C2211yescharacteristic, complemented
167#16810732C2211yescharacteristic, complemented
168#16810732C2211yescharacteristic, complemented
169#16810710C2211yescharacteristic, complemented
170#16810710C2211yescharacteristic, complemented
171#16810708C2211yescharacteristic, complemented
172#16810708C2211yescharacteristic, complemented
173#16810699C2211yescharacteristic, complemented
174#16810698C2211yescharacteristic, complemented
175#16810695C2211yescharacteristic, complemented
176#16810694C2211yescharacteristic, complemented
177#16810691C2211yescharacteristic, complemented
178#16810678C2211yescharacteristic, complemented
179#16810677C2211yescharacteristic, complemented
180#16810673C2211yescharacteristic, complemented
181#16810646C2211yescharacteristic, complemented
182#16810645C2211yescharacteristic, complemented
183C2×#13133146C2211yescharacteristic, complemented
184#16810623C2211yescharacteristic, complemented
185#16810622C2211yescharacteristic, complemented
186#16810621C2211yescharacteristic, complemented
187C2×#13133137C2211yescharacteristic, complemented
188C53×#547C2211yescharacteristic
189C53×#546C2211yescharacteristic, complemented
190C53×#489C2211yescharacteristic, complemented
191C53×#483C2211yescharacteristic, complemented
192C53×#481C2211yescharacteristic, complemented
193C53×#476C2211yescharacteristic, complemented
194C53×#469C2211yescharacteristic, complemented
195C53×#465C2211yescharacteristic, complemented
196C53×#463C2211yescharacteristic, complemented
197C53×#449C2211yescharacteristic, complemented
198C53×#447C2211yescharacteristic, complemented
199C53×#442C2211yescharacteristic, complemented
200C53×#435C2211yescharacteristic, complemented
201C53×#417C2211yescharacteristic, complemented
202C2×#102×C53C2211yescharacteristic, complemented
203C2×#11719949—21no—
204C2×#11719949C2311yescharacteristic
205C2×#11719945—21no—
206C2×#11719945—21no—
207C2×#11719945—21no—
208C2×#11719945—21no—
209C2×#11719945C2311yescharacteristic
210C2×#11719947—21no—
211C2×#11719947—21no—
212C2×#11719947—21no—
213C2×#11719947D411yescharacteristic
214C2×#11719947C2311yescharacteristic
215#41×D53—48no—
216C2×Q8×D53—21no—
217C22×D212C2311yescharacteristic
218C22×D212C2311yescharacteristic
219C22×D212C2311yescharacteristic
220C22×C22⋊D53—21no—
221C22×C22⋊D53—21no—
222C2×D4×D53—21no—
223C2×D4×D53—21no—
224C2×D4×D53—21no—
225C2×D4×D53C2311yescharacteristic
226C22×C4×D53—21no—
227C22×C4×D53—21no—
228C22×C4×D53—21no—
229#13133245—42no—
230#13133244—42no—
231#13133242—42no—
232#13133241—42no—
233C2×#11719913C2311yescharacteristic
234C2×#11719913C2311yescharacteristic
235C2×#11719913C2311yescharacteristic
236C2×#11719923C2311yescharacteristic
237C2×#11719924C2311yescharacteristic
238C2×#11719924C2311yescharacteristic
239C2×#11719924C2311yescharacteristic
240C2×D424—42no—
241C2×D424C2311yescharacteristic
242C2×D424C2311yescharacteristic
243C2×D424C2311yescharacteristic
244C2×D424C2311yescharacteristic
245C2×D424C2311yescharacteristic
246C2×D424C2311yescharacteristic
247C2×#11719922—42no—
248C2×#11719922C2311yescharacteristic
249C2×#11719922C2311yescharacteristic
250C2×#11719922C2311yescharacteristic
251C2×#11719922C2311yescharacteristic
252C2×#11719922C2311yescharacteristic
253C2×#11719922C2311yescharacteristic
254C2×#11719922C2311yescharacteristic
255C2×#11719922C2311yescharacteristic
256C2×#11719917C2311yescharacteristic
257C2×#11719912C2311yescharacteristic
258C2×#11719912C2311yescharacteristic
259C22×#88322C2311yescharacteristic
260#13133216C2311yescharacteristic
261#13133216C2311yescharacteristic
262#13133216C2311yescharacteristic
263#13133215C2311yescharacteristic
264#13133214C2311yescharacteristic
265#13133213—21no—
266#13133213—21no—
267#13133213—21no—
268#13133213—21no—
269#13133213C2311yescharacteristic
270#13133213C2311yescharacteristic
271#13133213C2311yescharacteristic
272#13133213C2311yescharacteristic
273#13133213C2311yescharacteristic
274#13133213C2311yescharacteristic
275#13133207—21no—
276#13133206—21no—
277#13133206C2311yescharacteristic
278#13133205C2311yescharacteristic
279#13133204C2311yescharacteristic
280#13133203—21no—
281#13133203—21no—
282#13133203—21no—
283#13133203—21no—
284#13133203—21no—
285#13133203—21no—
286#13133202—21no—
287#13133202—21no—
288#13133202—21no—
289#13133202—21no—
290#13133201—21no—
291#13133200—21no—
292#13133200—21no—
293#13133200—21no—
294#13133199—21no—
295#13133199—21no—
296#13133198—21no—
297#13133196C2311yescharacteristic
298#13133195—21no—
299#13133195—21no—
300#13133195—21no—
301#13133195—21no—
302#13133194—21no—
303#13133193—21no—
304#13133192—21no—
305#13133192—21no—
306#13133192—21no—
307#13133192C2311yescharacteristic
308#13133192C2311yescharacteristic
309#13133192C2311yescharacteristic
310#13133191—21no—
311#13133191—21no—
312#13133191C2311yescharacteristic
313#13133191C2311yescharacteristic
314#13133191C2311yescharacteristic
315#13133190—21no—
316#13133190—21no—
317#13133190—21no—
318#13133190—21no—
319#13133190—21no—
320#13133190—21no—
321#13133190—21no—
322#13133190—21no—
323#13133190—21no—
324#13133189—21no—
325#13133189—21no—
326#13133189—21no—
327#13133189—21no—
328#13133189—21no—
329#13133189—21no—
330#13133189—21no—
331#13133188—21no—
332#13133188C2311yescharacteristic
333#13133187—21no—
334#13133187—21no—
335#13133187—21no—
336#13133187—21no—
337#13133187—21no—
338#13133186—21no—
339#13133185—21no—
340#13133185—21no—
341#13133185—21no—
342Q8×Dic53C2311yescharacteristic
343C4×Dic106C2311yescharacteristic
344#13133182—21no—
345#13133182D411yescharacteristic
346#13133182C2311yescharacteristic
347C4×D212C2311yescharacteristic
348C4×D212C2311yescharacteristic
349D4×Dic53D411yescharacteristic
350D4×Dic53C2311yescharacteristic
351D4×Dic53C2311yescharacteristic
352#13133179—21no—
353#13133179—21no—
354#13133179—21no—
355#13133179—21no—
356#13133179—21no—
357#13133179C2311yescharacteristic
358#13133179C2311yescharacteristic
359#13133179C2311yescharacteristic
360#13133179C2311yescharacteristic
361#13133179C2311yescharacteristic
362#13133179C2311yescharacteristic
363#13133179C2311yescharacteristic
364#13133179C2311yescharacteristic
365C4×C22⋊D53—21no—
366C4×C22⋊D53—21no—
367C4×C22⋊D53—21no—
368C4×C22⋊D53—21no—
369C4×C22⋊D53—21no—
370C4×C22⋊D53—21no—
371C4×C22⋊D53C2311yescharacteristic
372C4×C22⋊D53C2311yescharacteristic
373#13133177—21no—
374#13133177—21no—
375#13133177—21no—
376#13133177—21no—
377#13133177—21no—
378#13133177—21no—
379#13133177—21no—
380#13133177—21no—
381#13133177D411yescharacteristic
382#13133177D411yescharacteristic
383#13133175D411yescharacteristic
384#13133173—21no—
385#13133173D411yescharacteristic
386#13133173D411yescharacteristic
387C4⋊C4×D53C2311yescharacteristic
388C2×C22⋊Dic53—21no—
389C2×#11719921—21no—
390C2×#11719921—21no—
391C22⋊C4×D53—21no—
392C22⋊C4×D53—21no—
393C22⋊C4×D53—21no—
394C2×C4×Dic53C2311yescharacteristic
395C2×C4×Dic53C2311yescharacteristic
396C42×D53C2311yescharacteristic
397#13133149C2311yescharacteristic
398#13133148C2311yescharacteristic
399#13133148C2311yescharacteristic
400#13133148C2311yescharacteristic
401#13133148C2311yescharacteristic
402C4⋊#88322C2311yescharacteristic
403#13133146C2311yescharacteristic
404#13133146C2311yescharacteristic
405#13133146C2311yescharacteristic
406#13133146C2311yescharacteristic
407#13133146C2311yescharacteristic
408#13133146C2311yescharacteristic
409#13133146C2311yescharacteristic
410#13133146C2311yescharacteristic
411#13133142C2311yescharacteristic
412#13133141C2311yescharacteristic
413#13133140C2311yescharacteristic
414#13133140C2311yescharacteristic
415#13133140C2311yescharacteristic
416#13133139C2311yescharacteristic
417#13133139C2311yescharacteristic
418#13133139C2311yescharacteristic
419#13133139C2311yescharacteristic
420#13133139C2311yescharacteristic
421#13133138C2311yescharacteristic
422#13133138C2311yescharacteristic
423#13133138C2311yescharacteristic
424#13133137C2311yescharacteristic
425#13133137C2311yescharacteristic
426#13133137C2311yescharacteristic
427#13133137C2311yescharacteristic
428#13133137C2311yescharacteristic
429#13133137C2311yescharacteristic
430#13133137C2311yescharacteristic
431#13133137C2311yescharacteristic
432#13133137C2311yescharacteristic
433C22⋊#88322C2311yescharacteristic
434C22⋊#88322C2311yescharacteristic
435#13133129C2311yescharacteristic
436#13133129C2311yescharacteristic
437#13133128C2311yescharacteristic
438#13133127C2311yescharacteristic
439#13133127C2311yescharacteristic
440C8×Dic53C2311yescharacteristic
441C8×Dic53C2311yescharacteristic
442C2×#41×C53—21no—
443C2×#41×C53C2311yescharacteristic
444C22×D4×C53C2311yescharacteristic
445C2×SD16×C53C2311yescharacteristic
446C2×D8×C53C2311yescharacteristic
447C2×D8×C53C2311yescharacteristic
448C2×M16×C53C2311yescharacteristic
449C22×C8×C53C2311yescharacteristic
450C4⋊Q8×C53C2311yescharacteristic
451#124×C53C2311yescharacteristic
452#123×C53—21no—
453#123×C53—21no—
454#123×C53—21no—
455C22⋊Q8×C53—21no—
456C22⋊Q8×C53C2311yescharacteristic
457#121×C53—21no—
458#121×C53C2311yescharacteristic
459#121×C53C2311yescharacteristic
460#121×C53C2311yescharacteristic
461#120×C53—21no—
462C4×D4×C53C2311yescharacteristic
463C4×D4×C53C2311yescharacteristic
464C4×D4×C53C2311yescharacteristic
465C2×C4⋊C4×C53C2311yescharacteristic
466C2×C4⋊C4×C53C2311yescharacteristic
467C2×C22⋊C4×C53—21no—
468#106×C53C2311yescharacteristic
469#106×C53C2311yescharacteristic
470#106×C53C2311yescharacteristic
471C4⋊C8×C53C2311yescharacteristic
472#103×C53C2311yescharacteristic
473#103×C53C2311yescharacteristic
474#103×C53C2311yescharacteristic
475#102×C53C2311yescharacteristic
476#102×C53C2311yescharacteristic
477#102×C53C2311yescharacteristic
478#102×C53C2311yescharacteristic
479#102×C53C2311yescharacteristic
480#102×C53C2311yescharacteristic
481#102×C53C2311yescharacteristic
482C22⋊C8×C53C2311yescharacteristic
483C22⋊C8×C53C2311yescharacteristic
484#97×C53C2311yescharacteristic
485C24×C53—21no—
486C23×D53—21no—
487C23×D53—21no—
488C23×D53—21no—
489C23×D53—21no—
490#41×C53—41no—
491#41×C53—41no—
492#41×C53—44no—
493C2×Q8×C53—21no—
494C2×Q8×C53C2411yescharacteristic
495C2×D4×C53—21no—
496C2×D4×C53—21no—
497C2×D4×C53—21no—
498C2×D4×C53—21no—
499C2×D4×C53—21no—
500C2×D4×C53—41no—
501C2×D4×C53—41no—
502C2×D4×C53C2×D411yescharacteristic
503C2×D4×C53C2411yescharacteristic
504C2×D4×C53C2411yescharacteristic
505C2×D4×C53C2411yescharacteristic
506C22×C4×C53—21no—
507C22×C4×C53—21no—
508C22×C4×C53—21no—
509C22×C4×C53—21no—
510C22×C4×C53—21no—
511C22×C4×C53C2411yescharacteristic
512C22×C4×C53C2411yescharacteristic
513C2×C22⋊D53—21no—
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⋊D53—21no—
523C2×C22⋊D53—21no—
524C2×C22⋊D53—21no—
525C2×C22⋊D53—21no—
526C2×C22⋊D53—21no—
527C2×C22⋊D53—21no—
528C2×C22⋊D53—21no—
529C2×C22⋊D53—21no—
530C2×C22⋊D53—21no—
531C2×C22⋊D53—21no—
532C2×C22⋊D53—44no—
533C2×C22⋊D53—82no—
534C2×C22⋊D53C2×D411yescharacteristic
535C2×C22⋊D53C2×D411yescharacteristic
536C22×Dic53—21no—
537C22×Dic53—21no—
538C22×Dic53—21no—
539C22×Dic53C2×D411yescharacteristic
540C22×Dic53C2×D411yescharacteristic
541C22×Dic53C2×D411yescharacteristic
542C22×Dic53C2×D411yescharacteristic
543#11719949—44no—
544#11719949—41no—
545#11719949—41no—
546Q8×D53—44no—
547#11719947—24no—
548#11719947—41no—
549#11719947—41no—
550#11719947—44no—
551#11719947—44no—
552#11719947—82no—
553D4×D53—22no—
554D4×D53—41no—
555D4×D53—44no—
556D4×D53—44no—
557D4×D53—44no—
558#11719945—44no—
559#11719945—41no—
560#11719945—41no—
561#11719945—44no—
562#11719945—44no—
563#11719945—82no—
564C2×D212—22no—
565C2×D212—22no—
566C2×D212—21no—
567C2×D212—21no—
568C2×D212—21no—
569C2×D212—21no—
570C2×D212—21no—
571C2×D212—21no—
572C2×D212—21no—
573C2×D212—21no—
574C2×D212—21no—
575C2×D212—41no—
576C2×D212—41no—
577C2×D212—41no—
578C2×D212—41no—
579C2×D212C2411yescharacteristic
580C2×D212C2411yescharacteristic
581C2×D212C2411yescharacteristic
582C2×D212C2411yescharacteristic
583C2×D212C2411yescharacteristic
584C2×C4×D53—21no—
585C2×C4×D53—21no—
586C2×C4×D53—21no—
587C2×C4×D53—21no—
588C2×C4×D53—21no—
589C2×C4×D53—21no—
590C2×C4×D53—21no—
591C2×C4×D53—21no—
592C2×C4×D53—21no—
593C2×C4×D53—21no—
594C2×C4×D53—21no—
595C2×C4×D53—21no—
596C2×C4×D53—21no—
597C2×C4×D53—44no—
598C2×C4×D53—44no—
599C2×C4×D53—44no—
600C2×C4×D53C2×D411yescharacteristic
601C2×C4×D53C2×D411yescharacteristic
602C2×C4×D53C2411yescharacteristic
603C2×Dic106—21no—
604C2×Dic106—21no—
605C2×Dic106—21no—
606C2×Dic106C2×D411yescharacteristic
607C2×Dic106C2411yescharacteristic
608SD16×C53—41no—
609D8×C53—41no—
610D8×C53—41no—
611M16×C53—41no—
612C2×C8×C53—41no—
613C2×C8×C53C2411yescharacteristic
614C2×C8×C53C2411yescharacteristic
615C2×C8×C53C2411yescharacteristic
616C2×C8×C53C2411yescharacteristic
617C4⋊C4×C53—21no—
618C4⋊C4×C53—21no—
619C4⋊C4×C53—21no—
620C4⋊C4×C53—21no—
621C4⋊C4×C53C2×D411yescharacteristic
622C4⋊C4×C53C2411yescharacteristic
623C4⋊C4×C53C2411yescharacteristic
624C4⋊C4×C53C2411yescharacteristic
625C4⋊C4×C53C2411yescharacteristic
626C22⋊C4×C53—21no—
627C22⋊C4×C53—21no—
628C22⋊C4×C53—21no—
629C22⋊C4×C53—21no—
630C22⋊C4×C53—21no—
631C22⋊C4×C53—21no—
632C22⋊C4×C53—21no—
633C22⋊C4×C53—21no—
634C22⋊C4×C53C2×D411yescharacteristic
635C22⋊C4×C53C2×D411yescharacteristic
636C42×C53C2411yescharacteristic
637C22⋊Dic53—21no—
638C22⋊Dic53—21no—
639C22⋊Dic53—21no—
640C22⋊Dic53—21no—
641C22⋊Dic53—21no—
642C22⋊Dic53—21no—
643C22⋊Dic53C2×D411yescharacteristic
644C22⋊Dic53C2×D411yescharacteristic
645#11719924—22no—
646#11719924—41no—
647#11719924—41no—
648#11719923—41no—
649#11719922—22no—
650#11719922—22no—
651#11719922—41no—
652#11719922—41no—
653#11719922—41no—
654#11719922—41no—
655#11719922—41no—
656#11719922—41no—
657#11719921—21no—
658#11719921—21no—
659#11719921—21no—
660#11719921—21no—
661#11719921—21no—
662#11719921—21no—
663#11719921—21no—
664#11719921—21no—
665#11719921—21no—
666#11719921—21no—
667#11719921—21no—
668#11719921—21no—
669#11719921—21no—
670#11719921—21no—
671#11719921—21no—
672#11719921—21no—
673#11719921—21no—
674#11719921—21no—
675#11719921—21no—
676#11719921—21no—
677#11719921C2×D411yescharacteristic
678#11719921C2×D411yescharacteristic
679C4⋊Dic53—21no—
680C4⋊Dic53C2×D411yescharacteristic
681C4⋊Dic53C2411yescharacteristic
682C4⋊Dic53C2411yescharacteristic
683#11719919—21no—
684#11719919—21no—
685#11719919—21no—
686#11719919—21no—
687#11719919—21no—
688#11719919—21no—
689#11719919—21no—
690#11719919—21no—
691#11719919C2×D411yescharacteristic
692#11719919C2×D411yescharacteristic
693#11719919C2×D411yescharacteristic
694#11719919C2×D411yescharacteristic
695C4×Dic53—21no—
696C4×Dic53—21no—
697C4×Dic53C2×D411yescharacteristic
698C4×Dic53C2×D411yescharacteristic
699C4×Dic53C2×D411yescharacteristic
700C4×Dic53C2×D411yescharacteristic
701C4×Dic53C2×D411yescharacteristic
702C4×Dic53C2×D411yescharacteristic
703C4×Dic53C2411yescharacteristic
704C4×Dic53C2411yescharacteristic
705C4×Dic53C2411yescharacteristic
706#11719917—41no—
707C2×#88322—41no—
708C2×#88322C2411yescharacteristic
709C2×#88322C2411yescharacteristic
710C2×#88322C2411yescharacteristic
711C2×#88322C2411yescharacteristic
712D424—22no—
713D424—22no—
714D424—41no—
715D424—41no—
716D424—41no—
717D424—41no—
718#11719913—22no—
719#11719913—41no—
720#11719913—41no—
721#11719912—41no—
722#11719912—41no—
723C23×C53—21no—
724C23×C53—21no—
725C23×C53—21no—
726C23×C53—42no—
727C23×C53—81no—
728C23×C53—81no—
729C23×C53C22×D411yescharacteristic
730C23×C53C22×D411yescharacteristic
731C22×D53—21no—
732C22×D53—21no—
733C22×D53—21no—
734C22×D53—21no—
735C22×D53—21no—
736C22×D53—42no—
737C22×D53—42no—
738C22×D53—42no—
739C22×D53—42no—
740C22×D53—42no—
741C22×D53—42no—
742C22×D53—42no—
743C22×D53—81no—
744C22×D53—81no—
745C22×D53—81no—
746C22×D53—81no—
747C22×D53—81no—
748C22×D53C22×D411yescharacteristic
749Q8×C53—21no—
750Q8×C53—21no—
751Q8×C53—42no—
752D4×C53—22no—
753D4×C53—21no—
754D4×C53—21no—
755D4×C53—21no—
756D4×C53—21no—
757D4×C53—21no—
758D4×C53—21no—
759D4×C53—42no—
760D4×C53—42no—
761D4×C53—81no—
762D4×C53—81no—
763D4×C53—81no—
764C2×C4×C53—21no—
765C2×C4×C53—21no—
766C2×C4×C53—21no—
767C2×C4×C53—21no—
768C2×C4×C53—21no—
769C2×C4×C53—21no—
770C2×C4×C53—21no—
771C2×C4×C53—21no—
772C2×C4×C53—21no—
773C2×C4×C53—42no—
774C2×C4×C53—42no—
775C2×C4×C53—42no—
776C2×C4×C53—81no—
777C2×C4×C53—81no—
778C2×C4×C53C22×D411yescharacteristic
779C2×C4×C53C22×D411yescharacteristic
780C2×C4×C53C22×D411yescharacteristic
781C2×C4×C53C22×D411yescharacteristic
782C2×C4×C53C2511yescharacteristic
783C22⋊D53—22no—
784C22⋊D53—22no—
785C22⋊D53—42no—
786C22⋊D53—42no—
787C22⋊D53—42no—
788C22⋊D53—42no—
789C22⋊D53—42no—
790C22⋊D53—42no—
791C22⋊D53—42no—
792C22⋊D53—42no—
793C22⋊D53—42no—
794C22⋊D53—42no—
795C22⋊D53—42no—
796C22⋊D53—81no—
797C22⋊D53—81no—
798C22⋊D53—81no—
799C22⋊D53—81no—
800C22⋊D53—81no—
801C22⋊D53—81no—
802C22⋊D53—81no—
803C22⋊D53—81no—
804C2×Dic53—22no—
805C2×Dic53—21no—
806C2×Dic53—21no—
807C2×Dic53—21no—
808C2×Dic53—41no—
809C2×Dic53—41no—
810C2×Dic53—42no—
811C2×Dic53—81no—
812C2×Dic53—81no—
813C2×Dic53AGL(1,ℤ/8)14yescomplemented
814C2×Dic53C22×D411yescharacteristic
815C2×Dic53C22×D411yescharacteristic
816C2×Dic53C22×D411yescharacteristic
817C2×Dic53C22×D411yescharacteristic
818C2×Dic53C22×D411yescharacteristic
819C2×Dic53C22×D411yescharacteristic
820C2×Dic53C22×D411yescharacteristic
821D212—21no—
822D212—21no—
823D212—21no—
824D212—21no—
825D212—21no—
826D212—21no—
827D212—21no—
828D212—21no—
829D212—21no—
830D212—42no—
831D212—42no—
832D212—42no—
833D212—42no—
834D212—42no—
835D212—81no—
836D212—81no—
837D212—81no—
838D212—81no—
839D212H(5,𝔽2)12yes—
840C4×D53—21no—
841C4×D53—21no—
842C4×D53—22no—
843C4×D53—41no—
844C4×D53—42no—
845C4×D53—42no—
846C4×D53—42no—
847C4×D53—42no—
848C4×D53—42no—
849C4×D53—42no—
850C4×D53—42no—
851C4×D53—42no—
852C4×D53—42no—
853C4×D53—81no—
854C4×D53—81no—
855C4×D53—81no—
856C4×D53—81no—
857Dic106—22no—
858Dic106—21no—
859Dic106—21no—
860Dic106—42no—
861Dic106—42no—
862Dic106—42no—
863C8×C53—21no—
864C8×C53—21no—
865C8×C53—21no—
866C8×C53—21no—
867#88322—21no—
868#88322—21no—
869#88322—21no—
870#88322—21no—
871#61961—531nomaximal, Sylow
872C22×C53—21no—
873C22×C53—21no—
874C22×C53—21no—
875C22×C53—21no—
876C22×C53—21no—
877C22×C53—41no—
878C22×C53—41no—
879C22×C53—41no—
880C22×C53—41no—
881C22×C53—41no—
882C22×C53—41no—
883C22×C53—41no—
884C22×C53—41no—
885C22×C53—41no—
886C22×C53—162no—
887C22×C53C2×AGL(1,ℤ/8)12yes—
888C22×C53C23×D411yescharacteristic
889C2×D53—21no—
890C2×D53—21no—
891C2×D53—22no—
892C2×D53—21no—
893C2×D53—41no—
894C2×D53—41no—
895C2×D53—41no—
896C2×D53—41no—
897C2×D53—41no—
898C2×D53—41no—
899C2×D53—41no—
900C2×D53—41no—
901C2×D53—41no—
902C2×D53—41no—
903C2×D53—41no—
904C2×D53—41no—
905C2×D53—41no—
906C2×D53—41no—
907C2×D53—84no—
908C2×D53—84no—
909C2×D53—84no—
910C2×D53—162no—
911C4×C53—21no—
912C4×C53—21no—
913C4×C53—21no—
914C4×C53—21no—
915C4×C53—41no—
916C4×C53—41no—
917C4×C53—41no—
918C4×C53—41no—
919C4×C53—41no—
920C4×C53C2×H(5,𝔽2)11yescharacteristic
921C4×C53#58511yescharacteristic
922Dic53—21no—
923Dic53—21no—
924Dic53—21no—
925Dic53—21no—
926Dic53—21no—
927Dic53—41no—
928Dic53—41no—
929Dic53—41no—
930Dic53C2×AGL(1,ℤ/8)12yes—
931Dic53C2×AGL(1,ℤ/8)12yes—
932#3508—531no—
933D4×#41—531no—
934#3399—531no—
935#3399—531no—
936#3373—531no—
937#3373—531no—
938#3332—531no—
939#3332—531no—
940#3306—531no—
941#3306—531no—
942#3306—531no—
943#3306D5311yescharacteristic, complemented
944#3274—531no—
945#3274—531no—
946#3264—531no—
947#3264—531no—
948#3264—531no—
949#3264—531no—
950#3253—531no—
951#3253—531no—
952#3246—531no—
953#3214—531no—
954#3214—531no—
955#3205—531no—
956#3109—531no—
957#3109—531no—
958#3101—531no—
959#3036—531no—
960#3036—531no—
961C2×#459—531no—
962#2989—531no—
963C2×C53—22no—
964C2×C53—41no—
965C2×C53—81no—
966C2×C53—81no—
967C2×C53—81no—
968C2×C53#348811yescharacteristic
969C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
970C2×C53#358511yescharacteristic
971D53—41no—
972D53—42no—
973D53—81no—
974D53—81no—
975D53—81no—
976D53—81no—
977C22×#41—1061no—
978C2×AGL(1,ℤ/8)—531no—
979C2×AGL(1,ℤ/8)—531no—
980C2×AGL(1,ℤ/8)—531no—
981C2×AGL(1,ℤ/8)—531no—
982C22×D8—531no—
983C22×D8—531no—
984#559—531no—
985#559—531no—
986#559—1061no—
987#550—531no—
988#550—531no—
989#550—531no—
990#550—1061no—
991D4×Q8—531no—
992#548—1061no—
993#547—531no—
994#547—531no—
995#547C2×D5311yescharacteristic
996#546—531no—
997#546—531no—
998#546—531no—
999#546—1061no—
1000#546—1061no—
1001#546—1061no—
1002#546—1061no—
1003#546—1061no—
1004#546C2×D5311yescharacteristic, complemented
1005D42—531no—
1006D42—531no—
1007D42—531no—
1008#540—1061no—
1009#540—1061no—
1010#535—1061no—
1011#533—531no—
1012#532—531no—
1013#532—531no—
1014#532—531no—
1015#532—531no—
1016#532—531no—
1017#532—531no—
1018#532—531no—
1019C2×#127—531no—
1020#525—1061no—
1021#525—1061no—
1022#525—1061no—
1023#518—1061no—
1024C4×#41—531no—
1025C2×C4×D4—531no—
1026C2×C4×D4—531no—
1027C2×C4×D4—531no—
1028#496—531no—
1029#496—531no—
1030#496—531no—
1031#496—531no—
1032#493—531no—
1033#493—531no—
1034#489—531no—
1035#489—531no—
1036#489—531no—
1037#489C2×D5311yescharacteristic, complemented
1038#486—531no—
1039#486—531no—
1040#483—531no—
1041#483C2×D5311yescharacteristic, complemented
1042#481—531no—
1043#481—531no—
1044#481—531no—
1045#481C2×D5311yescharacteristic, complemented
1046#476—531no—
1047#476—531no—
1048#476—531no—
1049#476—531no—
1050#476—531no—
1051#476—531no—
1052#476—531no—
1053#476C2×D5311yescharacteristic, complemented
1054#475—531no—
1055#475—531no—
1056#469—531no—
1057#469—531no—
1058#469—531no—
1059#469—531no—
1060#469—531no—
1061#469—531no—
1062#469—531no—
1063#469C2×D5311yescharacteristic, complemented
1064#465—531no—
1065#465—531no—
1066#465—531no—
1067#465C2×D5311yescharacteristic, complemented
1068#463—531no—
1069#463—531no—
1070#463—531no—
1071#463—531no—
1072#463—531no—
1073#463—531no—
1074#463—531no—
1075#463C2×D5311yescharacteristic, complemented
1076#461—531no—
1077#461—531no—
1078#461—531no—
1079#461—531no—
1080#460—531no—
1081#460—531no—
1082#459—531no—
1083#459—531no—
1084#459—531no—
1085#459—531no—
1086#459—531no—
1087#459—531no—
1088#459—531no—
1089#459—531no—
1090#459—531no—
1091#459—531no—
1092#459—531no—
1093#459—531no—
1094#459—531no—
1095#459—531no—
1096#459—531no—
1097#459—531no—
1098#450—531no—
1099#450—531no—
1100#449—531no—
1101#449—531no—
1102#449—531no—
1103#449—531no—
1104#449—531no—
1105#449—531no—
1106#449—531no—
1107#449C2×D5311yescharacteristic, complemented
1108#447—531no—
1109#447—531no—
1110#447—531no—
1111#447—531no—
1112#447—531no—
1113#447—531no—
1114#447—531no—
1115#447C2×D5311yescharacteristic, complemented
1116#446—531no—
1117#446—531no—
1118#442—531no—
1119#442—531no—
1120#442—531no—
1121#442—531no—
1122#442—531no—
1123#442—531no—
1124#442—531no—
1125#442C2×D5311yescharacteristic, complemented
1126C4×SD16—531no—
1127C4×SD16—531no—
1128C4×SD16—531no—
1129C4×SD16—531no—
1130#436—531no—
1131#436—531no—
1132#435—531no—
1133#435—531no—
1134#435—531no—
1135#435C2×D5311yescharacteristic, complemented
1136#432—531no—
1137#432—531no—
1138#431—531no—
1139#423—531no—
1140#423—531no—
1141C2×C4⋊C8—531no—
1142#417—531no—
1143#417—531no—
1144#417—531no—
1145#417C2×D5311yescharacteristic, complemented
1146C2×#102—531no—
1147C2×#102C2×D5311yescharacteristic, complemented
1148C53#6196111yescharacteristic, complemented, Sylow
1149C2×#41—21no—
1150C2×#41—531no—
1151C2×#41—531no—
1152C2×#41—531no—
1153C2×#41—531no—
1154C2×#41—1061no—
1155C2×#41—1061no—
1156C2×#41—1061no—
1157C2×#41—1061no—
1158C2×#41—1061no—
1159C2×#41—1061no—
1160C2×#41—1061no—
1161C2×#41—1061no—
1162C2×#41—2128no—
1163C2×#41C22×D5311yescharacteristic
1164C22×Q8—1061no—
1165C22×D4—531no—
1166C22×D4—531no—
1167C22×D4—531no—
1168C22×D4—531no—
1169C22×D4—1061no—
1170C22×D4—1061no—
1171C22×D4—1061no—
1172C22×D4—1061no—
1173C22×D4—1061no—
1174C22×D4C22×D5311yescharacteristic
1175C23×C4—1061no—
1176C23×C4—1061no—
1177C23×C4—1061no—
1178AGL(1,ℤ/8)—2122no—
1179AGL(1,ℤ/8)—2122no—
1180AGL(1,ℤ/8)—2122no—
1181AGL(1,ℤ/8)—2122no—
1182C2×SD16—531no—
1183C2×SD16—531no—
1184C2×SD16—531no—
1185C2×SD16—531no—
1186C2×SD16—531no—
1187C2×SD16—531no—
1188C2×SD16—531no—
1189C2×SD16C22×D5311yescharacteristic
1190C2×D8—531no—
1191C2×D8—531no—
1192C2×D8—531no—
1193C2×D8—531no—
1194C2×D8—531no—
1195C2×D8—531no—
1196C2×D8—531no—
1197C2×D8—531no—
1198C2×D8—531no—
1199C2×D8—531no—
1200C2×D8—531no—
1201C2×D8—531no—
1202C2×D8—531no—
1203C2×D8—531no—
1204C2×D8—2122no—
1205C2×D8—2122no—
1206C2×D8C22×D5311yescharacteristic
1207C2×D8C22×D5311yescharacteristic
1208C2×M16—531no—
1209C2×M16—531no—
1210C2×M16—531no—
1211C2×M16C22×D5311yescharacteristic
1212C22×C8—531no—
1213C22×C8C22×D5311yescharacteristic
1214C4⋊Q8—531no—
1215C4⋊Q8—531no—
1216C4⋊Q8—531no—
1217C4⋊Q8—531no—
1218C4⋊Q8C22×D5311yescharacteristic
1219#127—531no—
1220#127—531no—
1221#127—531no—
1222#127—531no—
1223#127—531no—
1224#127—531no—
1225#127—531no—
1226#127—1061no—
1227#127—1061no—
1228#127—1061no—
1229#127—1061no—
1230#125—1061no—
1231#124—531no—
1232#124—531no—
1233#124—531no—
1234#124—1061no—
1235#124—1061no—
1236#124—1061no—
1237#124—1061no—
1238#124—1061no—
1239#124—1061no—
1240#124—1061no—
1241#124C22×D5311yescharacteristic
1242#123—21no—
1243#123—21no—
1244#123—21no—
1245#123—1061no—
1246#123—1061no—
1247#123—1061no—
1248#123—1061no—
1249#123—1061no—
1250#123—1061no—
1251#123—1061no—
1252#123—1061no—
1253#123—1061no—
1254#123—1061no—
1255#123—1061no—
1256C22⋊Q8—21no—
1257C22⋊Q8—531no—
1258C22⋊Q8—1061no—
1259C22⋊Q8—1061no—
1260C22⋊Q8—1061no—
1261C22⋊Q8—1061no—
1262C22⋊Q8—1061no—
1263C22⋊Q8—1061no—
1264C22⋊Q8C22×D5311yescharacteristic
1265#121—21no—
1266#121—531no—
1267#121—531no—
1268#121—531no—
1269#121—531no—
1270#121—531no—
1271#121—531no—
1272#121—531no—
1273#121—1061no—
1274#121—1061no—
1275#121—1061no—
1276#121—1061no—
1277#121—1061no—
1278#121—1061no—
1279#121—1061no—
1280#121—1061no—
1281#121—1061no—
1282#121—1061no—
1283#121—1061no—
1284#121—1061no—
1285#121—1061no—
1286#121—1061no—
1287#121—1061no—
1288#121—1061no—
1289#121—1061no—
1290#121—1061no—
1291#121—1061no—
1292#121—1061no—
1293#121—1061no—
1294#121—1061no—
1295#121C22×D5311yescharacteristic
1296#121C22×D5311yescharacteristic
1297#121C22×D5311yescharacteristic
1298#120—21no—
1299#120—1061no—
1300#120—1061no—
1301#120—1061no—
1302#120—1061no—
1303#120—1061no—
1304#120—1061no—
1305#120—1061no—
1306#120—1061no—
1307#120—1061no—
1308C4×Q8—531no—
1309C4×Q8—531no—
1310C4×Q8—531no—
1311C4×Q8—531no—
1312C4×Q8—1061no—
1313C4×D4—531no—
1314C4×D4—531no—
1315C4×D4—531no—
1316C4×D4—531no—
1317C4×D4—531no—
1318C4×D4—531no—
1319C4×D4—531no—
1320C4×D4—531no—
1321C4×D4—531no—
1322C4×D4—531no—
1323C4×D4—531no—
1324C4×D4—531no—
1325C4×D4—531no—
1326C4×D4—531no—
1327C4×D4—531no—
1328C4×D4—531no—
1329C4×D4—531no—
1330C4×D4—1061no—
1331C4×D4—1061no—
1332C4×D4—1061no—
1333C4×D4—1061no—
1334C4×D4—1061no—
1335C4×D4—1061no—
1336C4×D4—1061no—
1337C4×D4—1061no—
1338C4×D4—1061no—
1339C4×D4—1061no—
1340C4×D4—1061no—
1341C4×D4—1061no—
1342C4×D4—1061no—
1343C4×D4—1061no—
1344C4×D4—1061no—
1345C4×D4—1061no—
1346C4×D4—1061no—
1347C4×D4—1061no—
1348C4×D4—1061no—
1349C4×D4C22×D5311yescharacteristic
1350C4×D4C22×D5311yescharacteristic
1351C4×D4C22×D5311yescharacteristic
1352#117—531no—
1353#117—531no—
1354#117—531no—
1355#117—1061no—
1356C2×C4⋊C4—531no—
1357C2×C4⋊C4C22×D5311yescharacteristic
1358C2×C4⋊C4C22×D5311yescharacteristic
1359C2×C22⋊C4—21no—
1360C2×C22⋊C4—1061no—
1361C2×C22⋊C4—1061no—
1362C2×C22⋊C4—1061no—
1363C2×C22⋊C4—1061no—
1364C2×C22⋊C4—1061no—
1365C2×C22⋊C4—1061no—
1366C2×C42—531no—
1367C2×C42—531no—
1368C2×C42—531no—
1369#106—531no—
1370#106—531no—
1371#106—531no—
1372#106—531no—
1373#106—531no—
1374#106C22×D5311yescharacteristic
1375#106C22×D5311yescharacteristic
1376#106C22×D5311yescharacteristic
1377C4⋊C8—531no—
1378C4⋊C8—531no—
1379C4⋊C8—531no—
1380C4⋊C8—531no—
1381C4⋊C8—531no—
1382C4⋊C8—531no—
1383C4⋊C8—531no—
1384C4⋊C8—531no—
1385C4⋊C8—531no—
1386C4⋊C8C22×D5311yescharacteristic
1387#103—531no—
1388#103—531no—
1389#103—531no—
1390#103—531no—
1391#103—531no—
1392#103C22×D5311yescharacteristic
1393#103C22×D5311yescharacteristic
1394#103C22×D5311yescharacteristic
1395#102—531no—
1396#102—531no—
1397#102—531no—
1398#102—531no—
1399#102—531no—
1400#102—531no—
1401#102—531no—
1402#102—531no—
1403#102—531no—
1404#102—531no—
1405#102—531no—
1406#102—531no—
1407#102—531no—
1408#102—531no—
1409#102—531no—
1410#102—531no—
1411#102—531no—
1412#102C22×D5311yescharacteristic
1413#102C22×D5311yescharacteristic
1414#102C22×D5311yescharacteristic
1415#102C22×D5311yescharacteristic
1416#102C22×D5311yescharacteristic
1417#102C22×D5311yescharacteristic
1418#102C22×D5311yescharacteristic
1419C22⋊C8—531no—
1420C22⋊C8—531no—
1421C22⋊C8—531no—
1422C22⋊C8—531no—
1423C22⋊C8C22×D5311yescharacteristic
1424C22⋊C8C22×D5311yescharacteristic
1425#97—531no—
1426#97—531no—
1427#97—531no—
1428#97C22×D5311yescharacteristic
1429C4×C8—531no—
1430C4×C8—531no—
1431C24—21no—
1432C24—1061no—
1433C24—1061no—
1434C24—1061no—
1435C24—1061no—
1436#41—41no—
1437#41—41no—
1438#41—44no—
1439#41—1064no—
1440#41—4242no—
1441#41—4242no—
1442#41—2121no—
1443#41—2121no—
1444#41—2124no—
1445#41—2124no—
1446#41—2124no—
1447#41—2124no—
1448#41—2121no—
1449#41—2121no—
1450#41—2121no—
1451#41—2121no—
1452#41—2124no—
1453#41—2124no—
1454C2×Q8—21no—
1455C2×Q8—531no—
1456C2×Q8—531no—
1457C2×Q8—1061no—
1458C2×Q8—1061no—
1459C2×Q8—1061no—
1460C2×Q8—2124no—
1461C2×Q8C23×D5311yescharacteristic
1462C2×D4—21no—
1463C2×D4—21no—
1464C2×D4—21no—
1465C2×D4—21no—
1466C2×D4—21no—
1467C2×D4—41no—
1468C2×D4—41no—
1469C2×D4—531no—
1470C2×D4—531no—
1471C2×D4—531no—
1472C2×D4—531no—
1473C2×D4—531no—
1474C2×D4—531no—
1475C2×D4—531no—
1476C2×D4—1062no—
1477C2×D4—1062no—
1478C2×D4—1061no—
1479C2×D4—1061no—
1480C2×D4—1061no—
1481C2×D4—1061no—
1482C2×D4—1061no—
1483C2×D4—1061no—
1484C2×D4—1061no—
1485C2×D4—1061no—
1486C2×D4—1061no—
1487C2×D4—1061no—
1488C2×D4—1061no—
1489C2×D4—1061no—
1490C2×D4—1061no—
1491C2×D4—1061no—
1492C2×D4—1061no—
1493C2×D4—1061no—
1494C2×D4—1061no—
1495C2×D4—1062no—
1496C2×D4—1061no—
1497C2×D4—1061no—
1498C2×D4—1061no—
1499C2×D4—1061no—
1500C2×D4—1061no—
1501C2×D4—1061no—
1502C2×D4—1061no—
1503C2×D4—1061no—
1504C2×D4—1061no—
1505C2×D4—1061no—
1506C2×D4—1061no—
1507C2×D4—4242no—
1508C2×D4—2121no—
1509C2×D4—2121no—
1510C2×D4—2121no—
1511C2×D4—2121no—
1512C2×D4—2124no—
1513C2×D4—2121no—
1514C2×D4—2124no—
1515C2×D4—2124no—
1516C2×D4—2124no—
1517C2×D4D4×D5311yescharacteristic
1518C2×D4C23×D5311yescharacteristic
1519C2×D4C23×D5311yescharacteristic
1520C2×D4C23×D5311yescharacteristic
1521C22×C4—21no—
1522C22×C4—21no—
1523C22×C4—21no—
1524C22×C4—21no—
1525C22×C4—21no—
1526C22×C4—531no—
1527C22×C4—531no—
1528C22×C4—531no—
1529C22×C4—531no—
1530C22×C4—531no—
1531C22×C4—531no—
1532C22×C4—531no—
1533C22×C4—1061no—
1534C22×C4—1061no—
1535C22×C4—1061no—
1536C22×C4—1061no—
1537C22×C4—1061no—
1538C22×C4—1061no—
1539C22×C4—1061no—
1540C22×C4—1061no—
1541C22×C4—1061no—
1542C22×C4—1061no—
1543C22×C4—1061no—
1544C22×C4—1061no—
1545C22×C4—1061no—
1546C22×C4—1061no—
1547C22×C4—1061no—
1548C22×C4—1061no—
1549C22×C4—2124no—
1550C22×C4—2124no—
1551C22×C4—2124no—
1552C22×C4C23×D5311yescharacteristic
1553C22×C4C23×D5311yescharacteristic
1554SD16—41no—
1555SD16—1062no—
1556SD16—1062no—
1557SD16—2121no—
1558SD16—2121no—
1559SD16—2121no—
1560SD16—2121no—
1561SD16—2121no—
1562D8—41no—
1563D8—41no—
1564D8—1062no—
1565D8—1062no—
1566D8—1062no—
1567D8—1062no—
1568D8—2121no—
1569D8—2121no—
1570D8—2121no—
1571D8—2121no—
1572D8—2121no—
1573D8—2121no—
1574D8—2121no—
1575D8—2121no—
1576D8—2121no—
1577D8—2121no—
1578M16—41no—
1579M16—2121no—
1580M16—2121no—
1581M16—2121no—
1582C2×C8—41no—
1583C2×C8—531no—
1584C2×C8—531no—
1585C2×C8—531no—
1586C2×C8—531no—
1587C2×C8—2121no—
1588C2×C8C23×D5311yescharacteristic
1589C2×C8C23×D5311yescharacteristic
1590C2×C8C23×D5311yescharacteristic
1591C2×C8C23×D5311yescharacteristic
1592C4⋊C4—21no—
1593C4⋊C4—21no—
1594C4⋊C4—21no—
1595C4⋊C4—21no—
1596C4⋊C4—531no—
1597C4⋊C4—531no—
1598C4⋊C4—531no—
1599C4⋊C4—531no—
1600C4⋊C4—531no—
1601C4⋊C4—531no—
1602C4⋊C4—531no—
1603C4⋊C4—1061no—
1604C4⋊C4—1061no—
1605C4⋊C4—1061no—
1606C4⋊C4—1061no—
1607C4⋊C4—1061no—
1608C4⋊C4—1061no—
1609C4⋊C4—1061no—
1610C4⋊C4—1061no—
1611C4⋊C4—1061no—
1612C4⋊C4D4×D5311yescharacteristic
1613C4⋊C4C23×D5311yescharacteristic
1614C4⋊C4C23×D5311yescharacteristic
1615C4⋊C4C23×D5311yescharacteristic
1616C4⋊C4C23×D5311yescharacteristic
1617C22⋊C4—21no—
1618C22⋊C4—21no—
1619C22⋊C4—21no—
1620C22⋊C4—21no—
1621C22⋊C4—21no—
1622C22⋊C4—21no—
1623C22⋊C4—21no—
1624C22⋊C4—21no—
1625C22⋊C4—531no—
1626C22⋊C4—531no—
1627C22⋊C4—531no—
1628C22⋊C4—531no—
1629C22⋊C4—1061no—
1630C22⋊C4—1061no—
1631C22⋊C4—1061no—
1632C22⋊C4—1061no—
1633C22⋊C4—1061no—
1634C22⋊C4—1061no—
1635C22⋊C4—1061no—
1636C22⋊C4—1061no—
1637C22⋊C4—1061no—
1638C22⋊C4—1061no—
1639C22⋊C4—1061no—
1640C22⋊C4—1061no—
1641C22⋊C4—1061no—
1642C22⋊C4—1061no—
1643C22⋊C4—1061no—
1644C22⋊C4—1061no—
1645C22⋊C4—1061no—
1646C22⋊C4—1061no—
1647C22⋊C4—1061no—
1648C22⋊C4—1061no—
1649C22⋊C4—1061no—
1650C22⋊C4—1061no—
1651C22⋊C4—1061no—
1652C22⋊C4—1061no—
1653C22⋊C4—1061no—
1654C22⋊C4—1061no—
1655C22⋊C4D4×D5311yescharacteristic
1656C22⋊C4D4×D5311yescharacteristic
1657C42—531no—
1658C42—531no—
1659C42—531no—
1660C42—531no—
1661C42—531no—
1662C42—531no—
1663C42—531no—
1664C42—531no—
1665C42—531no—
1666C42—1061no—
1667C42—1061no—
1668C42C23×D5311yescharacteristic
1669C23—21no—
1670C23—21no—
1671C23—21no—
1672C23—42no—
1673C23—81no—
1674C23—81no—
1675C23—531no—
1676C23—1061no—
1677C23—1061no—
1678C23—1061no—
1679C23—1061no—
1680C23—1061no—
1681C23—4241no—
1682C23—4241no—
1683C23—4241no—
1684C23—4241no—
1685C23—4241no—
1686C23—2122no—
1687C23—2122no—
1688C23—2122no—
1689C23—2122no—
1690C23—2122no—
1691C23—2122no—
1692C23—2122no—
1693C23C2×D4×D5311yescharacteristic
1694C23C2×D4×D5311yescharacteristic
1695Q8—21no—
1696Q8—21no—
1697Q8—42no—
1698Q8—1062no—
1699Q8—1061no—
1700Q8—1061no—
1701Q8—2122no—
1702Q8—2122no—
1703Q8—2122no—
1704D4—22no—
1705D4—21no—
1706D4—21no—
1707D4—21no—
1708D4—21no—
1709D4—21no—
1710D4—21no—
1711D4—42no—
1712D4—42no—
1713D4—81no—
1714D4—81no—
1715D4—81no—
1716D4—532no—
1717D4—1062no—
1718D4—1062no—
1719D4—1061no—
1720D4—1061no—
1721D4—1061no—
1722D4—1061no—
1723D4—1061no—
1724D4—1061no—
1725D4—1061no—
1726D4—1061no—
1727D4—1061no—
1728D4—4241no—
1729D4—4241no—
1730D4—4241no—
1731D4—4241no—
1732D4—4241no—
1733D4—4241no—
1734D4—4241no—
1735D4—4241no—
1736D4—4241no—
1737D4—4241no—
1738D4—4241no—
1739D4—4241no—
1740D4—2122no—
1741D4—2122no—
1742D4—2122no—
1743D4—2122no—
1744D4—2122no—
1745D4—2122no—
1746D4—2122no—
1747D4—2122no—
1748D4—2122no—
1749D4—2122no—
1750D4—2122no—
1751D4—2122no—
1752D4—2122no—
1753D4—2122no—
1754D4—2122no—
1755D4—2122no—
1756C2×C4—21no—
1757C2×C4—21no—
1758C2×C4—21no—
1759C2×C4—21no—
1760C2×C4—21no—
1761C2×C4—21no—
1762C2×C4—21no—
1763C2×C4—21no—
1764C2×C4—21no—
1765C2×C4—42no—
1766C2×C4—42no—
1767C2×C4—42no—
1768C2×C4—81no—
1769C2×C4—81no—
1770C2×C4—534no—
1771C2×C4—531no—
1772C2×C4—531no—
1773C2×C4—531no—
1774C2×C4—531no—
1775C2×C4—531no—
1776C2×C4—531no—
1777C2×C4—531no—
1778C2×C4—1062no—
1779C2×C4—1062no—
1780C2×C4—1061no—
1781C2×C4—1061no—
1782C2×C4—1061no—
1783C2×C4—1061no—
1784C2×C4—1061no—
1785C2×C4—4241no—
1786C2×C4—4241no—
1787C2×C4—4241no—
1788C2×C4—4241no—
1789C2×C4—4241no—
1790C2×C4—4241no—
1791C2×C4—2121no—
1792C2×C4—2122no—
1793C2×C4—2122no—
1794C2×C4—2122no—
1795C2×C4—2122no—
1796C2×C4—2122no—
1797C2×C4—2122no—
1798C2×C4—2122no—
1799C2×C4—2122no—
1800C2×C4—2122no—
1801C2×C4—2122no—
1802C2×C4—2121no—
1803C2×C4—2121no—
1804C2×C4C2×D4×D5311yescharacteristic
1805C2×C4C2×D4×D5311yescharacteristic
1806C2×C4C2×D4×D5311yescharacteristic
1807C2×C4C2×D4×D5311yescharacteristic
1808C2×C4C24×D5311yescharacteristic
1809C8—21no—
1810C8—21no—
1811C8—21no—
1812C8—21no—
1813C8—1061no—
1814C8—1061no—
1815C8—1061no—
1816C8—1061no—
1817C22—21no—
1818C22—21no—
1819C22—21no—
1820C22—21no—
1821C22—21no—
1822C22—41no—
1823C22—41no—
1824C22—41no—
1825C22—41no—
1826C22—41no—
1827C22—41no—
1828C22—41no—
1829C22—41no—
1830C22—41no—
1831C22—162no—
1832C22—8482no—
1833C22—1061no—
1834C22—1062no—
1835C22—1061no—
1836C22—1061no—
1837C22—4244no—
1838C22—4244no—
1839C22—4244no—
1840C22—2121no—
1841C22—2121no—
1842C22—2121no—
1843C22—2121no—
1844C22—2121no—
1845C22—2121no—
1846C22—2121no—
1847C22—2121no—
1848C22—2121no—
1849C22—2121no—
1850C22—2121no—
1851C22—2121no—
1852C22—2121no—
1853C22—2121no—
1854C22AGL(1,ℤ/8)×D5312yes—
1855C22C22×D4×D5311yescharacteristic
1856C4—21no—
1857C4—21no—
1858C4—21no—
1859C4—21no—
1860C4—41no—
1861C4—41no—
1862C4—41no—
1863C4—41no—
1864C4—41no—
1865C4—532no—
1866C4—532no—
1867C4—1061no—
1868C4—1061no—
1869C4—1061no—
1870C4—1061no—
1871C4—1061no—
1872C4—2121no—
1873C4—2121no—
1874C4—2121no—
1875C4H(5,𝔽2)×D5311yescharacteristic
1876C4#1681145911yescharacteristic
1877C2—22no—
1878C2—41no—
1879C2—81no—
1880C2—81no—
1881C2—81no—
1882C2—4241no—
1883C2—4241no—
1884C2—4241no—
1885C2—4241no—
1886C2—2121no—
1887C2—2122no—
1888C2#2028837811yescharacteristic
1889C2C2×AGL(1,ℤ/8)×D5311yescharacteristic
1890C2#2028949311yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3306C2
socleC22×C53C23×D4
hypercenter#3306D53
hypocenterC53#61961
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3306

Complements

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

NH ≅ G/Ntype
1. #20288583C2semidirect
2. #20288202C2semidirect
3. #20287758C2semidirect
4. #20287752C2semidirect
5. #20287510C2semidirect
6. #20287504C2semidirect
7. #20287040C2semidirect
8. #20287038C2semidirect
9. #20286674C2semidirect
10. #20286672C2semidirect
11. #20286670C2semidirect
12. #20286332C2semidirect
13. #20286328C2semidirect
14. #20286200C2semidirect
15. #20286196C2semidirect
16. #20286192C2semidirect
17. #20286188C2semidirect
18. #20286095C2semidirect
19. #20286092C2semidirect
20. #20286026C2semidirect
21. #20285711C2semidirect
22. #20285707C2semidirect
23. #20285631C2semidirect
24. #20284804C2semidirect
25. #20284803C2semidirect
26. #20284720C2semidirect
27. #20284178C2semidirect
28. #20284177C2semidirect
29. C2×#16810817C2semidirect
30. #20283827C2semidirect
31. C53×#3306C2semidirect
33. C2×#13133245C22semidirect
34. C2×#13133244C22semidirect
35. C2×#13133242C22semidirect
36. C2×#13133241C22semidirect
40. #16811356C22semidirect
41. #16811355C22semidirect
42. #16811294C22semidirect
43. #16811292C22semidirect
45. #16811291C22semidirect
46. #16811288C22semidirect
49. #16811274C22semidirect
50. #16811269C22semidirect
51. #16811267C22semidirect
54. #16811264C22semidirect
60. #16811257C22semidirect
64. #16811175C22semidirect
65. #16811174C22semidirect
66. #16811172C22semidirect
67. #16811170C22semidirect
68. #16811169C22semidirect
70. #16811168C22semidirect
71. #16811168C22semidirect
72. C2×#13133213C22semidirect
79. C2×#13133179C22semidirect
80. C4×D4×D53C22semidirect
81. #16811013C22semidirect
82. #16811012C22semidirect
83. #16811011C22semidirect
84. #16811009C22semidirect
85. #16810998C22semidirect
86. #16810998C22semidirect
87. #16810985C22semidirect
88. #16810984C22semidirect
89. #16810981C22semidirect
90. #16810968C22semidirect
91. #16810968C22semidirect
92. #16810953C22semidirect
93. #16810943C22semidirect
94. #16810941C22semidirect
95. #16810940C22semidirect
96. #16810912C22semidirect
97. #16810912C22semidirect
98. #16810912C22semidirect
99. #16810912C22semidirect
100. #16810911C22semidirect
101. #16810911C22semidirect
102. #16810910C22semidirect
103. #16810907C22semidirect
104. #16810906C22semidirect
105. #16810877C22semidirect
106. #16810877C22semidirect
107. #16810876C22semidirect
108. #16810875C22semidirect
109. #16810875C22semidirect
110. #16810874C22semidirect
111. #16810874C22semidirect
112. #16810854C22semidirect
113. #16810852C22semidirect
114. #16810850C22semidirect
115. #16810841C22semidirect
116. #16810841C22semidirect
117. #16810839C22semidirect
118. #16810838C22semidirect
119. #16810837C22semidirect
120. #16810837C22semidirect
121. #16810835C22semidirect
122. #16810827C22semidirect
123. #16810827C22semidirect
124. #16810827C22semidirect
125. #16810826C22semidirect
126. #16810822C22semidirect
127. #16810821C22semidirect
128. #16810819C22semidirect
129. #16810818C22semidirect
134. #16810817C22semidirect
135. #16810817C22semidirect
136. #16810817C22semidirect
137. #16810817C22semidirect
138. #16810817C22semidirect
139. #16810817C22semidirect
140. #16810817C22semidirect
141. #16810816C22semidirect
142. #16810816C22semidirect
143. #16810816C22semidirect
146. #16810771C22semidirect
147. #16810771C22semidirect
148. #16810770C22semidirect
149. #16810769C22semidirect
150. #16810769C22semidirect
151. #16810768C22semidirect
152. #16810766C22semidirect
153. #16810759C22semidirect
154. #16810759C22semidirect
155. #16810758C22semidirect
156. #16810757C22semidirect
157. #16810756C22semidirect
158. #16810756C22semidirect
159. #16810755C22semidirect
160. #16810752C22semidirect
161. #16810751C22semidirect
162. #16810736C22semidirect
163. #16810734C22semidirect
164. #16810734C22semidirect
165. #16810733C22semidirect
166. #16810733C22semidirect
167. #16810732C22semidirect
168. #16810732C22semidirect
169. #16810710C22semidirect
170. #16810710C22semidirect
171. #16810708C22semidirect
172. #16810708C22semidirect
173. #16810699C22semidirect
174. #16810698C22semidirect
175. #16810695C22semidirect
176. #16810694C22semidirect
177. #16810691C22semidirect
178. #16810678C22semidirect
179. #16810677C22semidirect
180. #16810673C22semidirect
181. #16810646C22semidirect
182. #16810645C22semidirect
183. C2×#13133146C22semidirect
184. #16810623C22semidirect
185. #16810622C22semidirect
186. #16810621C22semidirect
187. C2×#13133137C22semidirect
189. C53×#546C22semidirect
190. C53×#489C22semidirect
191. C53×#483C22semidirect
192. C53×#481C22semidirect
193. C53×#476C22semidirect
194. C53×#469C22semidirect
195. C53×#465C22semidirect
196. C53×#463C22semidirect
197. C53×#449C22semidirect
198. C53×#447C22semidirect
199. C53×#442C22semidirect
200. C53×#435C22semidirect
201. C53×#417C22semidirect
202. C2×#102×C53C22semidirect
813. C2×Dic53AGL(1,ℤ/8)semidirect
943. #3306D53semidirect
1004. #546C2×D53semidirect
1037. #489C2×D53semidirect
1041. #483C2×D53semidirect
1045. #481C2×D53semidirect
1053. #476C2×D53semidirect
1063. #469C2×D53semidirect
1067. #465C2×D53semidirect
1075. #463C2×D53semidirect
1107. #449C2×D53semidirect
1115. #447C2×D53semidirect
1125. #442C2×D53semidirect
1135. #435C2×D53semidirect
1145. #417C2×D53semidirect
1147. C2×#102C2×D53semidirect
1148. C53#61961semidirect

Maximal subgroups

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

subgroupindex
#202885832
#202882022
#202877582
#202877522
#202875102
#202875042
#202870402
#202870382
#202866742
#202866722
#202866702
#202863322
#202863282
#202862002
#202861962
#202861922
#202861882
#202860952
#202860922
#202860262
#202857112
#202857072
#202856312
#202848042
#202848032
#202847202
#202841782
#202841772
C2×#168108172
#202838272
C53×#33062
#6196153