Finite Group Databasebeta

← #28269963

Subgroups — #28269963

Order 13568.

2156 conjugacy classes of subgroups.

The subgroup lattice has 1226 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288954C211yesmaximal, characteristic, complemented
2#20286968C212yesmaximal, complemented
3#20286886C212yesmaximal, complemented
4#20286691C212yesmaximal, complemented
5#20286565C212yesmaximal, complemented
6D4×#11719924C212yesmaximal, complemented
7#20286315C212yesmaximal, complemented
8#20286211C212yesmaximal, complemented
9#20286196C212yesmaximal, complemented
10#20285776C212yesmaximal, complemented
11#20285561C212yesmaximal, complemented
12#20285517C211yesmaximal, characteristic, complemented
13#20285468C211yesmaximal, characteristic, complemented
14#20284914C212yesmaximal, complemented
15#20284001C212yesmaximal, complemented
16#20283967C211yesmaximal, characteristic, complemented
17C2×#16810768C211yesmaximal, characteristic, complemented
18#20283763C211yesmaximal, characteristic, complemented
19C53×#3489C211yesmaximal, characteristic, complemented
20C2×#13133242C2211yescharacteristic, complemented
21C2×#13133242C2211yescharacteristic, complemented
22C2×#13133242C2212yescomplemented
23C22×#11719924C2212yescomplemented
24C22×#11719924C2211yescharacteristic, complemented
25C22×#11719922C2211yescharacteristic, complemented
26#16811363—22no—
27#16811319C2212yes—
28#16811319C2212yescomplemented
29D4×D212C2212yes—
30D4×D212C2212yescomplemented
31#16811255—22no—
32#16811228C2212yescomplemented
33#16811213—21no—
34#16811213—21no—
35#16811187C2212yescomplemented
36#16811181—21no—
37#16811181—21no—
38C2×#13133191C2211yescharacteristic
39C2×#13133191C2211yescharacteristic
40#16811013C2212yescomplemented
41#16810997C2212yescomplemented
42#16810991C2212yescomplemented
43#16810977C2212yescomplemented
44#16810961C2212yescomplemented
45#16810956C2212yescomplemented
46#16810951C2212yescomplemented
47#16810944C2212yescomplemented
48#16810941C2212yescomplemented
49#16810936C2212yescomplemented
50#16810930C2212yescomplemented
51#16810923C2212yescomplemented
52#16810874C2212yescomplemented
53#16810871C2212yescomplemented
54#16810871C2212yescomplemented
55#16810871C2212yescomplemented
56#16810857C2212yescomplemented
57#16810854C2212yescomplemented
58#16810854C2212yescomplemented
59#16810854C2212yescomplemented
60#16810835C2212yescomplemented
61#16810835C2212yescomplemented
62#16810825C2212yescomplemented
63#16810825C2212yescomplemented
64#16810823C2212yescomplemented
65#16810818C2212yescomplemented
66#16810773C2212yescomplemented
67#16810773C2212yescomplemented
68#16810773C2212yescomplemented
69#16810768C2212yescomplemented
70#16810768C2212yescomplemented
71#16810768C2212yescomplemented
72#16810768C2212yescomplemented
73#16810768C2212yescomplemented
74#16810768C2212yescomplemented
75#16810768C2212yescomplemented
76#16810768C2212yescomplemented
77#16810762C2212yescomplemented
78#16810762C2212yescomplemented
79#16810762C2212yescomplemented
80#16810762C2212yescomplemented
81#16810762C2212yescomplemented
82#16810757C2212yescomplemented
83#16810756C2212yescomplemented
84#16810733C2212yescomplemented
85#16810721C2212yescomplemented
86C4×#11719924C2212yescomplemented
87C4×#11719922C2212yescomplemented
88#16810701C2212yescomplemented
89#16810695C2212yescomplemented
90#16810695C2212yescomplemented
91D4×#88322C2212yescomplemented
92#16810684C2212yescomplemented
93#16810632C2212yescomplemented
94#16810624C2211yescharacteristic, complemented
95#16810624C2211yescharacteristic, complemented
96#16810619C2212yescomplemented
97C2×#13133141C2211yescharacteristic, complemented
98C2×#13133138C2211yescharacteristic, complemented
99#16810590C2212yescomplemented
100#16810587C2211yescharacteristic, complemented
101C2×C22⋊#88322C2211yescharacteristic, complemented
102C2×2−1+4×C53C2211yescharacteristic, complemented
103C22×#41×C53C2211yescharacteristic, complemented
104D4×Q8×C53C2212yescomplemented
105C53×#548C2212yescomplemented
106C53×#547—22no—
107C53×#547C2212yescomplemented
108C53×#546—22no—
109C53×#546C2212yescomplemented
110C53×#537—21no—
111C53×#537C2211yescharacteristic, complemented
112C53×#536—21no—
113C53×#536C2211yescharacteristic, complemented
114C53×#525—21no—
115C53×#525C2211yescharacteristic
116C2×C22⋊Q8×C53—21no—
117C2×C22⋊Q8×C53C2211yescharacteristic, complemented
118C53×#520C2211yescharacteristic, complemented
119C22×D212C2312yes—
120C22×D212C2311yescharacteristic
121C22×D212C2311yescharacteristic
122C22×C22⋊D53—21no—
123C22×C22⋊D53—21no—
124C2×D4×D53—22no—
125C2×D4×D53—22no—
126#13133242—42no—
127#13133242—44no—
128#13133242—42no—
129C2×#11719924—42no—
130C2×#11719924—44no—
131C2×#11719924C2312yes—
132C2×#11719924C2312yes—
133C2×#11719924C2312yes—
134C2×#11719924C2312yes—
135C2×#11719924C2312yes—
136C2×#11719924C2312yes—
137C2×#11719924C2312yes—
138C2×#11719924C2312yes—
139C2×#11719922—42no—
140C2×#11719922C2312yes—
141C2×#11719922C2312yes—
142C2×#11719922C2312yes—
143C2×#11719922C2312yes—
144C2×#11719917C2311yescharacteristic
145C2×#11719917C2311yescharacteristic
146C2×#11719917C2312yes—
147C22×#88322C2311yescharacteristic
148C22×#88322C2311yescharacteristic
149C22×#88322C2312yes—
150#13133214C2312yes—
151#13133213—22no—
152#13133212—22no—
153#13133212—22no—
154#13133209C2312yes—
155#13133206—22no—
156#13133202—22no—
157#13133202—22no—
158#13133199—22no—
159#13133199—22no—
160#13133192—22no—
161#13133192—22no—
162#13133191—21no—
163#13133191—21no—
164#13133191—21no—
165#13133191—21no—
166#13133191C2312yes—
167#13133191C2312yes—
168#13133191C2312yes—
169#13133191C2312yes—
170#13133191C2312yes—
171#13133191C2312yes—
172#13133190—22no—
173#13133190—22no—
174#13133189—22no—
175#13133189—22no—
176#13133187—22no—
177#13133187—22no—
178#13133187—22no—
179#13133187—22no—
180#13133185—22no—
181#13133185—22no—
182C4×D212C2312yes—
183C4×D212C2312yes—
184#13133177—22no—
185#13133177—22no—
186#13133176C2312yes—
187C2×C4⋊Dic53C2311yescharacteristic
188C2×C4⋊Dic53C2311yescharacteristic
189C2×#11719921—21no—
190C2×#11719921—21no—
191#13133150C2312yes—
192#13133150C2312yes—
193#13133148C2312yes—
194#13133148C2312yes—
195C4⋊#88322C2312yes—
196C4⋊#88322C2312yes—
197#13133141C2312yes—
198#13133141C2312yes—
199#13133141C2312yes—
200#13133141C2312yes—
201#13133141C2312yes—
202#13133141C2312yes—
203#13133141C2312yes—
204#13133141C2312yes—
205#13133138C2312yes—
206#13133138C2312yes—
207#13133138C2312yes—
208#13133138C2312yes—
209#13133137C2312yes—
210#13133137C2312yes—
211#13133137C2312yes—
212#13133137C2312yes—
213C22⋊#88322C2312yes—
214C22⋊#88322C2312yes—
215C22⋊#88322C2312yes—
216C22⋊#88322C2312yes—
217C22⋊#88322C2312yes—
218C22⋊#88322C2312yes—
219#13133128C2312yes—
220C4×#88322C2312yes—
2212−1+4×C53—42no—
2222−1+4×C53—42no—
223C2×#41×C53—21no—
224C2×#41×C53—22no—
225C2×#41×C53—21no—
226C2×#41×C53—21no—
227C2×#41×C53—42no—
228C2×#41×C53—42no—
229C2×#41×C53C2311yescharacteristic
230C2×#41×C53C2312yes—
231C2×#41×C53C2311yescharacteristic
232C2×#41×C53C2311yescharacteristic
233C2×#41×C53C2311yescharacteristic
234C2×#41×C53C2311yescharacteristic
235C22×Q8×C53—21no—
236C22×Q8×C53C2312yes—
237C22×Q8×C53C2311yescharacteristic
238C22×Q8×C53C2311yescharacteristic
239C22×D4×C53—21no—
240C22×D4×C53C2311yescharacteristic
241C23×C4×C53—21no—
242C23×C4×C53C2311yescharacteristic
243C4⋊Q8×C53—22no—
244C4⋊Q8×C53C2312yes—
245#124×C53—22no—
246#124×C53C2312yes—
247#123×C53—22no—
248#123×C53—22no—
249#123×C53—22no—
250#123×C53—22no—
251#123×C53D412yes—
252C22⋊Q8×C53—21no—
253C22⋊Q8×C53—22no—
254C22⋊Q8×C53—21no—
255C22⋊Q8×C53—22no—
256C22⋊Q8×C53—22no—
257C22⋊Q8×C53—21no—
258C22⋊Q8×C53—21no—
259C22⋊Q8×C53—21no—
260C22⋊Q8×C53D411yescharacteristic
261C22⋊Q8×C53D411yescharacteristic
262C22⋊Q8×C53C2312yes—
263C22⋊Q8×C53C2312yes—
264C22⋊Q8×C53C2312yes—
265#121×C53—22no—
266#121×C53—21no—
267#121×C53—22no—
268#121×C53—22no—
269#121×C53—22no—
270#121×C53D411yescharacteristic
271#121×C53D411yescharacteristic
272#121×C53C2312yes—
273#120×C53—22no—
274#120×C53D412yes—
275C4×Q8×C53C2312yes—
276C4×D4×C53—22no—
277C4×D4×C53—22no—
278C4×D4×C53—22no—
279C4×D4×C53C2312yes—
280C4×D4×C53C2312yes—
281C4×D4×C53C2312yes—
282#117×C53—21no—
283#117×C53C2311yescharacteristic
284C2×C4⋊C4×C53—21no—
285C2×C4⋊C4×C53—22no—
286C2×C4⋊C4×C53—21no—
287C2×C4⋊C4×C53C2311yescharacteristic
288C2×C22⋊C4×C53—22no—
289C2×C22⋊C4×C53—21no—
290C24×C53—21no—
291C24×C53C2×D411yescharacteristic
292C23×D53—21no—
293C23×D53—21no—
294C23×D53—22no—
295#41×C53—22no—
296#41×C53—22no—
297#41×C53—22no—
298#41×C53—22no—
299#41×C53—24no—
300#41×C53—41no—
301#41×C53—41no—
302#41×C53—41no—
303#41×C53—41no—
304#41×C53—41no—
305#41×C53—41no—
306#41×C53—42no—
307#41×C53—44no—
308#41×C53—44no—
309#41×C53—44no—
310#41×C53—48no—
311C2×Q8×C53—21no—
312C2×Q8×C53—22no—
313C2×Q8×C53—21no—
314C2×Q8×C53—22no—
315C2×Q8×C53—24no—
316C2×Q8×C53—41no—
317C2×Q8×C53—42no—
318C2×Q8×C53—41no—
319C2×Q8×C53—41no—
320C2×Q8×C53—44no—
321C2×Q8×C53C2×D411yescharacteristic
322C2×Q8×C53C2412yes—
323C2×Q8×C53C2411yescharacteristic
324C2×Q8×C53C2411yescharacteristic
325C2×D4×C53—21no—
326C2×D4×C53—22no—
327C2×D4×C53—22no—
328C2×D4×C53—21no—
329C2×D4×C53—21no—
330C2×D4×C53—21no—
331C2×D4×C53—22no—
332C2×D4×C53—21no—
333C2×D4×C53—41no—
334C2×D4×C53—44no—
335C2×D4×C53C2×D412yes—
336C2×D4×C53C2×D412yes—
337C2×D4×C53C2×D412yes—
338C2×D4×C53C2×D411yescharacteristic
339C2×D4×C53C2411yescharacteristic
340C2×D4×C53C2411yescharacteristic
341C22×C4×C53—21no—
342C22×C4×C53—21no—
343C22×C4×C53—22no—
344C22×C4×C53—21no—
345C22×C4×C53—21no—
346C22×C4×C53—22no—
347C22×C4×C53—21no—
348C22×C4×C53—21no—
349C22×C4×C53—21no—
350C22×C4×C53—22no—
351C22×C4×C53—41no—
352C22×C4×C53—41no—
353C22×C4×C53—44no—
354C22×C4×C53C2×D411yescharacteristic
355C22×C4×C53C2×D411yescharacteristic
356C22×C4×C53C2×D411yescharacteristic
357C22×C4×C53C2411yescharacteristic
358C22×C4×C53C2412yes—
359C22×C4×C53C2411yescharacteristic
360C22×C4×C53C2411yescharacteristic
361C2×C22⋊D53—22no—
362C2×C22⋊D53—22no—
363C2×C22⋊D53—22no—
364C2×C22⋊D53—22no—
365C2×C22⋊D53—22no—
366C2×C22⋊D53—22no—
367C2×C22⋊D53—82no—
368C2×C22⋊D53—82no—
369C22×Dic53—21no—
370C22×Dic53—21no—
371D4×D53—84no—
372D4×D53—84no—
373C2×D212—22no—
374C2×D212—22no—
375C2×D212—21no—
376C2×D212—21no—
377C2×D212—22no—
378C2×D212—41no—
379C2×D212—42no—
380C2×D212—41no—
381C2×D212—42no—
382C2×D212—41no—
383C2×D212—41no—
384C2×D212C2412yes—
385C2×D212C2412yes—
386C2×C4×D53—22no—
387C2×C4×D53—22no—
388C4⋊C4×C53—22no—
389C4⋊C4×C53—21no—
390C4⋊C4×C53—22no—
391C4⋊C4×C53—22no—
392C4⋊C4×C53—22no—
393C4⋊C4×C53—22no—
394C4⋊C4×C53—22no—
395C4⋊C4×C53C2×D411yescharacteristic
396C4⋊C4×C53C2×D412yes—
397C4⋊C4×C53C2×D411yescharacteristic
398C4⋊C4×C53C2×D412yes—
399C4⋊C4×C53C2412yes—
400C22⋊C4×C53—22no—
401C22⋊C4×C53—22no—
402C22⋊C4×C53—22no—
403C22⋊C4×C53—22no—
404C22⋊C4×C53—22no—
405C22⋊C4×C53—22no—
406C22⋊C4×C53—22no—
407C22⋊C4×C53C2×D412yes—
408C22⋊C4×C53C2×D412yes—
409C22⋊C4×C53C2×D412yes—
410C22⋊C4×C53C2×D412yes—
411C22⋊C4×C53C2×D412yes—
412C42×C53—22no—
413C42×C53C2412yes—
414C22⋊Dic53—22no—
415#11719924—24no—
416#11719924—24no—
417#11719924—42no—
418#11719924—42no—
419#11719924—42no—
420#11719924—42no—
421#11719924—42no—
422#11719924—42no—
423#11719922—24no—
424#11719922—24no—
425#11719922—42no—
426#11719922—42no—
427#11719921—22no—
428#11719921—22no—
429#11719921—22no—
430#11719921—22no—
431#11719921—22no—
432#11719921—22no—
433#11719921—22no—
434#11719921—22no—
435C4⋊Dic53—21no—
436C4⋊Dic53—21no—
437C4⋊Dic53C2412yes—
438C4⋊Dic53C2412yes—
439#11719919—22no—
440#11719919—22no—
441C4×Dic53—22no—
442#11719917—42no—
443#11719917—41no—
444#11719917—41no—
445C2×#88322—41no—
446C2×#88322—41no—
447C2×#88322—42no—
448C2×#88322C2412yes—
449C2×#88322C2412yes—
450C2×#88322C2412yes—
451C2×#88322C2412yes—
452C23×C53—21no—
453C23×C53—22no—
454C23×C53—21no—
455C23×C53—41no—
456C23×C53—41no—
457C23×C53—42no—
458C23×C53—42no—
459C23×C53—81no—
460C23×C53C22×D411yescharacteristic
461C23×C53C22×D411yescharacteristic
462C23×C53C22×D412yes—
463C23×C53C22×D411yescharacteristic
464C22×D53—22no—
465C22×D53—22no—
466C22×D53—42no—
467C22×D53—42no—
468C22×D53—81no—
469C22×D53—81no—
470C22×D53—82no—
471C22×D53—82no—
472C22×D53—82no—
473C22×D53—81no—
474C22×D53—81no—
475Q8×C53—21no—
476Q8×C53—22no—
477Q8×C53—21no—
478Q8×C53—22no—
479Q8×C53—21no—
480Q8×C53—41no—
481Q8×C53—44no—
482Q8×C53—42no—
483Q8×C53—42no—
484Q8×C53H(5,𝔽2)12yes—
485D4×C53—24no—
486D4×C53—24no—
487D4×C53—21no—
488D4×C53—21no—
489D4×C53—21no—
490D4×C53—42no—
491D4×C53—42no—
492D4×C53—41no—
493D4×C53—42no—
494D4×C53—42no—
495D4×C53—42no—
496D4×C53—44no—
497D4×C53—42no—
498D4×C53—82no—
499D4×C53H(5,𝔽2)12yes—
500C2×C4×C53—24no—
501C2×C4×C53—21no—
502C2×C4×C53—21no—
503C2×C4×C53—21no—
504C2×C4×C53—21no—
505C2×C4×C53—21no—
506C2×C4×C53—22no—
507C2×C4×C53—22no—
508C2×C4×C53—21no—
509C2×C4×C53—21no—
510C2×C4×C53—21no—
511C2×C4×C53—22no—
512C2×C4×C53—22no—
513C2×C4×C53—41no—
514C2×C4×C53—41no—
515C2×C4×C53—41no—
516C2×C4×C53—42no—
517C2×C4×C53—42no—
518C2×C4×C53—42no—
519C2×C4×C53—44no—
520C2×C4×C53—44no—
521C2×C4×C53—42no—
522C2×C4×C53—42no—
523C2×C4×C53—82no—
524C2×C4×C53—81no—
525C2×C4×C53C22×D412yes—
526C2×C4×C53C22×D412yes—
527C2×C4×C53C22×D411yescharacteristic
528C2×C4×C53C22×D412yes—
529C2×C4×C53C22×D411yescharacteristic
530C2×C4×C53C22×D411yescharacteristic
531C2×C4×C53C2511yescharacteristic
532C22⋊D53—44no—
533C22⋊D53—44no—
534C22⋊D53—82no—
535C22⋊D53—82no—
536C22⋊D53—82no—
537C22⋊D53—82no—
538C2×Dic53—22no—
539C2×Dic53—22no—
540C2×Dic53—81no—
541C2×Dic53—81no—
542D212—22no—
543D212—22no—
544D212—22no—
545D212—22no—
546D212—81no—
547D212—81no—
548D212—82no—
549D212—82no—
550D212—82no—
551C4×D53—82no—
552C4×D53—82no—
553#88322—22no—
554#88322—22no—
555#88322—22no—
556#88322—22no—
557#61621—531nomaximal, Sylow
558C22×C53—21no—
559C22×C53—21no—
560C22×C53—21no—
561C22×C53—21no—
562C22×C53—22no—
563C22×C53—21no—
564C22×C53—22no—
565C22×C53—22no—
566C22×C53—21no—
567C22×C53—21no—
568C22×C53—21no—
569C22×C53—22no—
570C22×C53—41no—
571C22×C53—41no—
572C22×C53—41no—
573C22×C53—41no—
574C22×C53—41no—
575C22×C53—82no—
576C22×C53—84no—
577C22×C53#57712yes—
578C22×C53C23×D411yescharacteristic
579C2×D53—42no—
580C2×D53—42no—
581C2×D53—42no—
582C2×D53—42no—
583C2×D53—42no—
584C2×D53—42no—
585C2×D53—162no—
586C2×D53—162no—
587C2×D53—164no—
588C4×C53—22no—
589C4×C53—21no—
590C4×C53—21no—
591C4×C53—22no—
592C4×C53—21no—
593C4×C53—22no—
594C4×C53—22no—
595C4×C53—42no—
596C4×C53—41no—
597C4×C53—42no—
598C4×C53C2×H(5,𝔽2)11yescharacteristic
599C4×C53C2×H(5,𝔽2)11yescharacteristic
600Dic53—42no—
601Dic53—42no—
602#3537—531no—
603#3489D5311yescharacteristic, complemented
604#3326—532no—
605#3320—532no—
606#3307—532no—
607#3297—532no—
608D4×SD16—532no—
609#3272—532no—
610#3265—532no—
611#3264—532no—
612#3221—532no—
613#3198—532no—
614#3193—531no—
615#3187—531no—
616#3119—532no—
617#3010—532no—
618#3006—531no—
619C2×#449—531no—
620#2976—531no—
621C2×C53—22no—
622C2×C53—42no—
623C2×C53—41no—
624C2×C53—41no—
625C2×C53—42no—
626C2×C53—81no—
627C2×C53#348411yescharacteristic
628C2×C53C2×#57711yescharacteristic
629C2×C53#358511yescharacteristic
630D53—82no—
631D53—82no—
632C2×2−1+4C2×D5311yescharacteristic, complemented
633C22×#41C2×D5311yescharacteristic, complemented
634C2×AGL(1,ℤ/8)—531no—
635C2×AGL(1,ℤ/8)—531no—
636C2×AGL(1,ℤ/8)—532no—
637C22×SD16—531no—
638C22×SD16—532no—
639C22×D8—531no—
640#560—1062no—
641#553—532no—
642#553—532no—
643D4×Q8C2×D5312yescomplemented
644#548C2×D5312yescomplemented
645#547—22no—
646#547C2×D5312yescomplemented
647#546—22no—
648#546C2×D5312yescomplemented
649D42—532no—
650D42—532no—
651D42—1062no—
652#540—532no—
653#538—1061no—
654#538—1061no—
655#537—21no—
656#537C2×D5311yescharacteristic, complemented
657#536—21no—
658#536C2×D5311yescharacteristic, complemented
659#535—532no—
660#534—1061no—
661#534—1061no—
662#525—21no—
663#525C2×D5311yescharacteristic
664C2×C22⋊Q8—21no—
665C2×C22⋊Q8C2×D5311yescharacteristic, complemented
666C2×#121—531no—
667C2×#121—531no—
668#520C2×D5311yescharacteristic, complemented
669#496—532no—
670#492—532no—
671#491—532no—
672#488—532no—
673#485—532no—
674#484—532no—
675#483—532no—
676#482—532no—
677#481—532no—
678#480—532no—
679#479—532no—
680#478—532no—
681#469—532no—
682#468—532no—
683#468—532no—
684#468—532no—
685#466—532no—
686#465—532no—
687#465—532no—
688#465—532no—
689#463—532no—
690#463—532no—
691#461—532no—
692#461—532no—
693#460—532no—
694#459—532no—
695#450—532no—
696#450—532no—
697#450—532no—
698#449—532no—
699#449—532no—
700#449—532no—
701#449—532no—
702#449—532no—
703#449—532no—
704#449—532no—
705#449—532no—
706#448—532no—
707#448—532no—
708#448—532no—
709#448—532no—
710#448—532no—
711#447—532no—
712#447—532no—
713#442—532no—
714#440—532no—
715C4×SD16—532no—
716C4×D8—532no—
717#436—532no—
718#435—532no—
719#435—532no—
720C8×D4—532no—
721#433—532no—
722#419—532no—
723#417—531no—
724#417—531no—
725#416—532no—
726C2×#103—531no—
727C2×#102—531no—
728#408—532no—
729#407—531no—
730C2×C22⋊C8—531no—
731C53#6162111yescharacteristic, complemented, Sylow
7322−1+4—42no—
7332−1+4—42no—
734C2×#41—21no—
735C2×#41—22no—
736C2×#41—21no—
737C2×#41—21no—
738C2×#41—42no—
739C2×#41—42no—
740C2×#41C22×D5311yescharacteristic
741C2×#41C22×D5312yes—
742C2×#41C22×D5311yescharacteristic
743C2×#41C22×D5311yescharacteristic
744C2×#41C22×D5311yescharacteristic
745C2×#41C22×D5311yescharacteristic
746C22×Q8—21no—
747C22×Q8C22×D5312yes—
748C22×Q8C22×D5311yescharacteristic
749C22×Q8C22×D5311yescharacteristic
750C22×D4—21no—
751C22×D4—531no—
752C22×D4—531no—
753C22×D4—532no—
754C22×D4—1061no—
755C22×D4—1061no—
756C22×D4—1062no—
757C22×D4—1062no—
758C22×D4C22×D5311yescharacteristic
759C23×C4—21no—
760C23×C4C22×D5311yescharacteristic
761AGL(1,ℤ/8)—2124no—
762AGL(1,ℤ/8)—2122no—
763AGL(1,ℤ/8)—2122no—
764C2×SD16—532no—
765C2×SD16—532no—
766C2×SD16—532no—
767C2×SD16—532no—
768C2×SD16—532no—
769C2×SD16—532no—
770C2×SD16—532no—
771C2×SD16—532no—
772C2×SD16—2122no—
773C2×SD16—2124no—
774C2×D8—532no—
775C2×D8—532no—
776C2×D8—532no—
777C2×D8—532no—
778C2×D8—2122no—
779C2×M16—531no—
780C2×M16—531no—
781C2×M16—532no—
782C22×C8—531no—
783C22×C8—531no—
784C22×C8—532no—
785C4⋊Q8—22no—
786C4⋊Q8C22×D5312yes—
787#127—532no—
788#127—1062no—
789#126—1062no—
790#126—1062no—
791#125—532no—
792#124—22no—
793#124—1062no—
794#124C22×D5312yes—
795#123—22no—
796#123—22no—
797#123—22no—
798#123—22no—
799#123—1062no—
800#123—1062no—
801#123—1062no—
802#123—1062no—
803#123C22⋊D5312yes—
804C22⋊Q8—21no—
805C22⋊Q8—21no—
806C22⋊Q8—21no—
807C22⋊Q8—21no—
808C22⋊Q8—22no—
809C22⋊Q8—21no—
810C22⋊Q8—22no—
811C22⋊Q8—22no—
812C22⋊Q8C22⋊D5311yescharacteristic
813C22⋊Q8C22⋊D5311yescharacteristic
814C22⋊Q8C22×D5312yes—
815C22⋊Q8C22×D5312yes—
816C22⋊Q8C22×D5312yes—
817#121—21no—
818#121—22no—
819#121—22no—
820#121—22no—
821#121—22no—
822#121—532no—
823#121—532no—
824#121—532no—
825#121—532no—
826#121—532no—
827#121—532no—
828#121—1062no—
829#121—1062no—
830#121—1061no—
831#121—1061no—
832#121—1061no—
833#121—1061no—
834#121—1062no—
835#121—1062no—
836#121—1062no—
837#121—1062no—
838#121C22⋊D5311yescharacteristic
839#121C22⋊D5311yescharacteristic
840#121C22×D5312yes—
841#120—22no—
842#120—1062no—
843#120—1062no—
844#120—1062no—
845#120—1062no—
846#120—1062no—
847#120—1062no—
848#120C22⋊D5312yes—
849C4×Q8C22×D5312yes—
850C4×D4—22no—
851C4×D4—22no—
852C4×D4—22no—
853C4×D4—532no—
854C4×D4—532no—
855C4×D4—1062no—
856C4×D4—1062no—
857C4×D4C22×D5312yes—
858C4×D4C22×D5312yes—
859C4×D4C22×D5312yes—
860#117—21no—
861#117—532no—
862#117C22×D5311yescharacteristic
863C2×C4⋊C4—21no—
864C2×C4⋊C4—21no—
865C2×C4⋊C4—22no—
866C2×C4⋊C4—531no—
867C2×C4⋊C4—531no—
868C2×C4⋊C4C22×D5311yescharacteristic
869C2×C22⋊C4—21no—
870C2×C22⋊C4—22no—
871C2×C22⋊C4—1061no—
872C2×C22⋊C4—1061no—
873#107—532no—
874#107—532no—
875#106—532no—
876#106—532no—
877C4⋊C8—532no—
878C4⋊C8—532no—
879#103—532no—
880#103—532no—
881#103—532no—
882#103—532no—
883#103—532no—
884#103—532no—
885#103—532no—
886#103—532no—
887#102—532no—
888#102—532no—
889#102—532no—
890#102—532no—
891#102—532no—
892#102—532no—
893#102—532no—
894#102—532no—
895C22⋊C8—532no—
896C22⋊C8—532no—
897C22⋊C8—532no—
898C22⋊C8—532no—
899C22⋊C8—532no—
900C22⋊C8—532no—
901#97—532no—
902C4×C8—532no—
903C24—21no—
904C24—1062no—
905C24—1061no—
906C24—1061no—
907C24C2×C22⋊D5311yescharacteristic
908#41—22no—
909#41—22no—
910#41—22no—
911#41—22no—
912#41—24no—
913#41—41no—
914#41—41no—
915#41—41no—
916#41—41no—
917#41—41no—
918#41—41no—
919#41—42no—
920#41—44no—
921#41—44no—
922#41—44no—
923#41—48no—
924C2×Q8—21no—
925C2×Q8—22no—
926C2×Q8—21no—
927C2×Q8—22no—
928C2×Q8—24no—
929C2×Q8—41no—
930C2×Q8—42no—
931C2×Q8—41no—
932C2×Q8—41no—
933C2×Q8—44no—
934C2×Q8C2×C22⋊D5311yescharacteristic
935C2×Q8C23×D5312yes—
936C2×Q8C23×D5311yescharacteristic
937C2×Q8C23×D5311yescharacteristic
938C2×D4—21no—
939C2×D4—22no—
940C2×D4—22no—
941C2×D4—21no—
942C2×D4—21no—
943C2×D4—21no—
944C2×D4—22no—
945C2×D4—21no—
946C2×D4—41no—
947C2×D4—44no—
948C2×D4—532no—
949C2×D4—532no—
950C2×D4—1062no—
951C2×D4—1062no—
952C2×D4—1062no—
953C2×D4—1062no—
954C2×D4—1062no—
955C2×D4—1062no—
956C2×D4—1061no—
957C2×D4—1061no—
958C2×D4—1062no—
959C2×D4—1062no—
960C2×D4—1062no—
961C2×D4—4244no—
962C2×D4—4244no—
963C2×D4—4242no—
964C2×D4—4242no—
965C2×D4—2121no—
966C2×D4—2121no—
967C2×D4—2122no—
968C2×D4—2121no—
969C2×D4—2121no—
970C2×D4—2122no—
971C2×D4C2×C22⋊D5312yes—
972C2×D4C2×C22⋊D5312yes—
973C2×D4C2×C22⋊D5311yescharacteristic
974C2×D4C2×C22⋊D5312yes—
975C2×D4C23×D5311yescharacteristic
976C2×D4C23×D5311yescharacteristic
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—22no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—22no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—22no—
987C22×C4—41no—
988C22×C4—41no—
989C22×C4—44no—
990C22×C4—1061no—
991C22×C4—1061no—
992C22×C4—1062no—
993C22×C4—1062no—
994C22×C4C2×C22⋊D5311yescharacteristic
995C22×C4C2×C22⋊D5311yescharacteristic
996C22×C4C2×C22⋊D5311yescharacteristic
997C22×C4C23×D5311yescharacteristic
998C22×C4C23×D5311yescharacteristic
999C22×C4C23×D5311yescharacteristic
1000C22×C4C23×D5312yes—
1001SD16—1064no—
1002SD16—1064no—
1003SD16—2122no—
1004SD16—2122no—
1005SD16—2122no—
1006SD16—2122no—
1007SD16—2122no—
1008SD16—2122no—
1009D8—1064no—
1010D8—1064no—
1011D8—2122no—
1012D8—2122no—
1013M16—2122no—
1014M16—2121no—
1015M16—2121no—
1016C2×C8—532no—
1017C2×C8—532no—
1018C2×C8—532no—
1019C2×C8—532no—
1020C2×C8—2121no—
1021C2×C8—2121no—
1022C2×C8—2122no—
1023C4⋊C4—22no—
1024C4⋊C4—21no—
1025C4⋊C4—22no—
1026C4⋊C4—22no—
1027C4⋊C4—22no—
1028C4⋊C4—22no—
1029C4⋊C4—22no—
1030C4⋊C4—532no—
1031C4⋊C4—532no—
1032C4⋊C4—1061no—
1033C4⋊C4—1061no—
1034C4⋊C4—1062no—
1035C4⋊C4—1062no—
1036C4⋊C4C2×C22⋊D5311yescharacteristic
1037C4⋊C4C2×C22⋊D5312yes—
1038C4⋊C4C2×C22⋊D5311yescharacteristic
1039C4⋊C4C2×C22⋊D5312yes—
1040C4⋊C4C23×D5312yes—
1041C22⋊C4—22no—
1042C22⋊C4—22no—
1043C22⋊C4—22no—
1044C22⋊C4—22no—
1045C22⋊C4—22no—
1046C22⋊C4—22no—
1047C22⋊C4—22no—
1048C22⋊C4—1062no—
1049C22⋊C4—1062no—
1050C22⋊C4—1062no—
1051C22⋊C4—1062no—
1052C22⋊C4—1062no—
1053C22⋊C4—1062no—
1054C22⋊C4—1062no—
1055C22⋊C4—1062no—
1056C22⋊C4—1062no—
1057C22⋊C4C2×C22⋊D5312yes—
1058C22⋊C4C2×C22⋊D5312yes—
1059C22⋊C4C2×C22⋊D5312yes—
1060C22⋊C4C2×C22⋊D5312yes—
1061C22⋊C4C2×C22⋊D5312yes—
1062C42—22no—
1063C42—1062no—
1064C42C23×D5312yes—
1065C23—21no—
1066C23—22no—
1067C23—21no—
1068C23—41no—
1069C23—41no—
1070C23—42no—
1071C23—42no—
1072C23—81no—
1073C23—1062no—
1074C23—1062no—
1075C23—4241no—
1076C23—4241no—
1077C23—4242no—
1078C23—4242no—
1079C23—4241no—
1080C23—4242no—
1081C23—4241no—
1082C23—2122no—
1083C23—2122no—
1084C23C22×C22⋊D5311yescharacteristic
1085C23C22×C22⋊D5312yes—
1086C23C22×C22⋊D5311yescharacteristic
1087C23C22×C22⋊D5311yescharacteristic
1088Q8—21no—
1089Q8—22no—
1090Q8—21no—
1091Q8—22no—
1092Q8—21no—
1093Q8—41no—
1094Q8—44no—
1095Q8—42no—
1096Q8—42no—
1097Q8#1313326212yes—
1098D4—24no—
1099D4—24no—
1100D4—21no—
1101D4—21no—
1102D4—21no—
1103D4—42no—
1104D4—41no—
1105D4—42no—
1106D4—42no—
1107D4—42no—
1108D4—42no—
1109D4—44no—
1110D4—42no—
1111D4—82no—
1112D4—1062no—
1113D4—1062no—
1114D4—1062no—
1115D4—1062no—
1116D4—4242no—
1117D4—4242no—
1118D4—4241no—
1119D4—4241no—
1120D4—4242no—
1121D4—4242no—
1122D4—4242no—
1123D4—4242no—
1124D4—4242no—
1125D4—2124no—
1126D4—2124no—
1127D4#1313326212yes—
1128C2×C4—24no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—22no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—22no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—21no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—42no—
1145C2×C4—42no—
1146C2×C4—42no—
1147C2×C4—44no—
1148C2×C4—44no—
1149C2×C4—42no—
1150C2×C4—42no—
1151C2×C4—82no—
1152C2×C4—81no—
1153C2×C4—1062no—
1154C2×C4—1062no—
1155C2×C4—4242no—
1156C2×C4—4242no—
1157C2×C4—4241no—
1158C2×C4—4241no—
1159C2×C4C22×C22⋊D5312yes—
1160C2×C4C22×C22⋊D5312yes—
1161C2×C4C22×C22⋊D5312yes—
1162C2×C4C22×C22⋊D5311yescharacteristic
1163C2×C4C22×C22⋊D5311yescharacteristic
1164C2×C4C22×C22⋊D5311yescharacteristic
1165C2×C4C24×D5311yescharacteristic
1166C8—1062no—
1167C8—1062no—
1168C8—1062no—
1169C8—1062no—
1170C22—21no—
1171C22—21no—
1172C22—21no—
1173C22—22no—
1174C22—22no—
1175C22—21no—
1176C22—21no—
1177C22—22no—
1178C22—21no—
1179C22—21no—
1180C22—21no—
1181C22—22no—
1182C22—41no—
1183C22—41no—
1184C22—41no—
1185C22—41no—
1186C22—41no—
1187C22—82no—
1188C22—84no—
1189C22—8482no—
1190C22—8484no—
1191C22—8482no—
1192C22—2122no—
1193C22—2122no—
1194C22—2122no—
1195C22—2122no—
1196C22—2122no—
1197C22—2122no—
1198C22#1681143112yes—
1199C22C23×C22⋊D5311yescharacteristic
1200C4—21no—
1201C4—22no—
1202C4—21no—
1203C4—21no—
1204C4—22no—
1205C4—22no—
1206C4—22no—
1207C4—41no—
1208C4—42no—
1209C4—42no—
1210C4—2122no—
1211C4—2122no—
1212C4C2×#1313326211yescharacteristic
1213C4C2×#1313326211yescharacteristic
1214C2—22no—
1215C2—41no—
1216C2—41no—
1217C2—42no—
1218C2—42no—
1219C2—81no—
1220C2—4242no—
1221C2—4242no—
1222C2#2028835011yescharacteristic
1223C2C2×#1681143111yescharacteristic
1224C2#2028949411yescharacteristic
subgroupG/H
centerC22C23×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3489C2
socleC22×C53C23×D4
hypercenter#3489D53
hypocenterC53#61621
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ #525 ◁ #3489

Complements

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

NH ≅ G/Ntype
1. #20288954C2semidirect
2. #20286968C2semidirect
3. #20286886C2semidirect
4. #20286691C2semidirect
5. #20286565C2semidirect
6. D4×#11719924C2semidirect
7. #20286315C2semidirect
8. #20286211C2semidirect
9. #20286196C2semidirect
10. #20285776C2semidirect
11. #20285561C2semidirect
12. #20285517C2semidirect
13. #20285468C2semidirect
14. #20284914C2semidirect
15. #20284001C2semidirect
16. #20283967C2semidirect
17. C2×#16810768C2semidirect
18. #20283763C2semidirect
19. C53×#3489C2semidirect
20. C2×#13133242C22semidirect
21. C2×#13133242C22semidirect
22. C2×#13133242C22semidirect
23. C22×#11719924C22semidirect
24. C22×#11719924C22semidirect
25. C22×#11719922C22semidirect
28. #16811319C22semidirect
30. D4×D212C22semidirect
32. #16811228C22semidirect
35. #16811187C22semidirect
40. #16811013C22semidirect
41. #16810997C22semidirect
42. #16810991C22semidirect
43. #16810977C22semidirect
44. #16810961C22semidirect
45. #16810956C22semidirect
46. #16810951C22semidirect
47. #16810944C22semidirect
48. #16810941C22semidirect
49. #16810936C22semidirect
50. #16810930C22semidirect
51. #16810923C22semidirect
52. #16810874C22semidirect
53. #16810871C22semidirect
54. #16810871C22semidirect
55. #16810871C22semidirect
56. #16810857C22semidirect
57. #16810854C22semidirect
58. #16810854C22semidirect
59. #16810854C22semidirect
60. #16810835C22semidirect
61. #16810835C22semidirect
62. #16810825C22semidirect
63. #16810825C22semidirect
64. #16810823C22semidirect
65. #16810818C22semidirect
66. #16810773C22semidirect
67. #16810773C22semidirect
68. #16810773C22semidirect
69. #16810768C22semidirect
70. #16810768C22semidirect
71. #16810768C22semidirect
72. #16810768C22semidirect
73. #16810768C22semidirect
74. #16810768C22semidirect
75. #16810768C22semidirect
76. #16810768C22semidirect
77. #16810762C22semidirect
78. #16810762C22semidirect
79. #16810762C22semidirect
80. #16810762C22semidirect
81. #16810762C22semidirect
82. #16810757C22semidirect
83. #16810756C22semidirect
84. #16810733C22semidirect
85. #16810721C22semidirect
86. C4×#11719924C22semidirect
87. C4×#11719922C22semidirect
88. #16810701C22semidirect
89. #16810695C22semidirect
90. #16810695C22semidirect
91. D4×#88322C22semidirect
92. #16810684C22semidirect
93. #16810632C22semidirect
94. #16810624C22semidirect
95. #16810624C22semidirect
96. #16810619C22semidirect
97. C2×#13133141C22semidirect
98. C2×#13133138C22semidirect
99. #16810590C22semidirect
100. #16810587C22semidirect
101. C2×C22⋊#88322C22semidirect
102. C2×2−1+4×C53C22semidirect
103. C22×#41×C53C22semidirect
104. D4×Q8×C53C22semidirect
105. C53×#548C22semidirect
107. C53×#547C22semidirect
109. C53×#546C22semidirect
111. C53×#537C22semidirect
113. C53×#536C22semidirect
117. C2×C22⋊Q8×C53C22semidirect
118. C53×#520C22semidirect
603. #3489D53semidirect
632. C2×2−1+4C2×D53semidirect
633. C22×#41C2×D53semidirect
643. D4×Q8C2×D53semidirect
644. #548C2×D53semidirect
646. #547C2×D53semidirect
648. #546C2×D53semidirect
656. #537C2×D53semidirect
658. #536C2×D53semidirect
665. C2×C22⋊Q8C2×D53semidirect
668. #520C2×D53semidirect
731. C53#61621semidirect

Maximal subgroups

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

subgroupindex
#202889542
#202869682
#202868862
#202866912
#202865652
D4×#117199242
#202863152
#202862112
#202861962
#202857762
#202855612
#202855172
#202854682
#202849142
#202840012
#202839672
C2×#168107682
#202837632
C53×#34892
#6162153