Finite Group Databasebeta

← #14795052

Subgroups — #14795052

Order 2816.

784 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622409C211yesmaximal, characteristic, complemented
2C2×#10622332C211yesmaximal, characteristic
3#13076924C211yesmaximal, characteristic
4C22⋊Q8×Dic11C211yesmaximal, characteristic
5#13070052C211yesmaximal, characteristic
6#13070044C211yesmaximal, characteristic
7#13069816C211yesmaximal, characteristic
8#13069570C211yesmaximal, characteristic, complemented
9#13069385C211yesmaximal, characteristic, complemented
10#13069360C211yesmaximal, characteristic, complemented
11#13069353C211yesmaximal, characteristic, complemented
12#13069308C211yesmaximal, characteristic, complemented
13#13069303C211yesmaximal, characteristic, complemented
14#13068629C211yesmaximal, characteristic, complemented
15C11×#2035C211yesmaximal, characteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×Q8×Dic11C2211yescharacteristic
18C22×C4×Dic11C2211yescharacteristic
19C2×#66943C2211yescharacteristic
20C2×C11×#106C2211yescharacteristic
21C2×C11×#103C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C11×C22⋊C8C2211yescharacteristic
24C11×#380C2211yescharacteristic
25#10622843C2211yescharacteristic
26C2×#66899C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28#10622825C2211yescharacteristic
29#10622825C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31C2×#66882C2211yescharacteristic
32C2×#66879C2211yescharacteristic
33C2×#66879C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36#10622598C2211yescharacteristic
37#10622598C2211yescharacteristic
38#10622594—21no—
39#10622590C2211yescharacteristic
40C4⋊C4×Dic11—21no—
41C4⋊C4×Dic11C2211yescharacteristic
42#10622586C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45#10622563—21no—
46#10622563—21no—
47#10622559—21no—
48C22⋊C4×Dic11—21no—
49#10622409—24no—
50#10622332—24no—
51#10622268—21no—
52#10622267—21no—
53C11×#340C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×Dic11D411yescharacteristic
64C23×Dic11D411yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×C22⋊Q8—22no—
68C11×C22⋊Q8—22no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—21no—
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—21no—
77Q8×Dic11—22no—
78Q8×Dic11—22no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×C4×Dic11—22no—
90C2×C4×Dic11—22no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11D411yescharacteristic
94C2×C4×Dic11D411yescharacteristic
95C2×C4×Dic11C2311yescharacteristic
96C2×C4×Dic11C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99#66943—22no—
100#66943—22no—
101C11×#106—22no—
102C11×#103—22no—
103C11×#103—22no—
104C11×C22⋊C8—22no—
105C11×#95—21no—
106#66899—22no—
107#66899—22no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C22⋊(C11⋊C8)—22no—
119#66882—22no—
120#66879—22no—
121#66879—22no—
122Dic11⋊C8—22no—
123Dic11⋊C8D414yes—
124#66872—22no—
125#66871—22no—
126#24707—111nomaximal, Sylow
127C24×C11C2×D411yescharacteristic
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11#4112yes—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2411yescharacteristic
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—41no—
154C22×Dic11—41no—
155C22×Dic11—41no—
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11C2×D412yes—
166C11×C4⋊C4—24no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4#4112yes—
173C11×C22⋊C4—24no—
174C11×C22⋊C4—42no—
175C22⋊Dic11—42no—
176C22⋊Dic11—42no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—42no—
186C4⋊Dic11—42no—
187C4⋊Dic11—42no—
188C4⋊Dic11—42no—
189Dic11⋊C4—42no—
190Dic11⋊C4—42no—
191C4×Dic11—22no—
192C4×Dic11—22no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—42no—
196C4×Dic11—42no—
197C4×Dic11C2×D412yes—
198C4×Dic11#4112yes—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8C2×D412yes—
205C2×#479—111no—
206C2×#432—111no—
207#2851—111no—
208C4×C22⋊Q8—111no—
209#2077—111no—
210#2076—111no—
211#2036—111no—
212#2035D1111yescharacteristic
213#1989—111no—
214#1949—111no—
215#1944—111no—
216#1943—111no—
217#1935—111no—
218#1935—111no—
219#1805—111no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11#13712yes—
227C23×C11C22×D411yescharacteristic
228Q8×C11—22no—
229Q8×C11—22no—
230Q8×C11—41no—
231Q8×C11—41no—
232C2×C4×C11—21no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C112−1+411yescharacteristic
256C2×C4×C112−1+411yescharacteristic
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—44no—
268C2×Dic11—44no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11#12112yes—
282C2×Dic11#12112yes—
283C8×C11—22no—
284C8×C11—41no—
285C11⋊C8—22no—
286C11⋊C8—41no—
287C2×#125—111no—
288C2×C22⋊Q8C2×D1111yescharacteristic
289C2×C4×Q8—111no—
290C22×C42—111no—
291#479—224no—
292#432—224no—
293C2×#107—111no—
294C2×#107—111no—
295C2×#106—111no—
296C2×#106C2×D1111yescharacteristic
297C2×C4⋊C8—111no—
298C2×C4⋊C8—111no—
299C2×#103—111no—
300C2×#103—111no—
301C2×#103C2×D1111yescharacteristic
302C2×#103C2×D1111yescharacteristic
303C2×C22⋊C8—111no—
304C2×C22⋊C8C2×D1111yescharacteristic
305C2×#97—111no—
306C2×#97—111no—
307#391—111no—
308#389—111no—
309#389—111no—
310#389—111no—
311#387—221no—
312#387—221no—
313#387—221no—
314#385—221no—
315#385—221no—
316#385—221no—
317#382—111no—
318#380—111no—
319#380—111no—
320#380C2×D1111yescharacteristic
321C4×C4⋊C4—111no—
322C4×C4⋊C4—221no—
323C4×C22⋊C4—221no—
324#340—111no—
325#340—111no—
326#340—111no—
327#340—111no—
328#340—111no—
329#340—111no—
330#340—111no—
331#340C2×D1111yescharacteristic
332C22×C11—22no—
333C22×C11—22no—
334C22×C11—22no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11C2×#12111yescharacteristic
340C22×C11#52511yescharacteristic
341C22×C11#53611yescharacteristic
342C22×C11C2×#13711yescharacteristic
343C22×C11#57511yescharacteristic
344C22×C11#57511yescharacteristic
345C22×C11#57511yescharacteristic
346C4×C11—42no—
347C4×C11—41no—
348C4×C11—42no—
349C4×C11—81no—
350C4×C11—81no—
351C4×C11#54711yescharacteristic
352C4×C11#54811yescharacteristic
353C4×C11#55211yescharacteristic
354C4×C11#55611yescharacteristic
355Dic11—22no—
356Dic11—22no—
357Dic11—41no—
358Dic11—41no—
359Dic11—81no—
360Dic11—81no—
361Dic11—81no—
362Dic11—81no—
363C22×Q8C22×D1111yescharacteristic
364C23×C4—111no—
365C23×C4—111no—
366C23×C4C22×D1111yescharacteristic
367C22×C8—111no—
368C22×C8—111no—
369C22×C8C22×D1111yescharacteristic
370C22×C8C22×D1111yescharacteristic
371#125—222no—
372#125—222no—
373C22⋊Q8—22no—
374C22⋊Q8—22no—
375C4×Q8—222no—
376C4×Q8—222no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4C22×D1111yescharacteristic
389C2×C4⋊C4C22×D1111yescharacteristic
390C2×C4⋊C4C22×D1111yescharacteristic
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—221no—
394C2×C22⋊C4—221no—
395C2×C42—111no—
396C2×C42—111no—
397C2×C42—111no—
398C2×C42—111no—
399C2×C42—222no—
400C2×C42—222no—
401C2×C42—221no—
402C2×C42—221no—
403#107—222no—
404#107—222no—
405#106—22no—
406#106—222no—
407C4⋊C8—114no—
408C4⋊C8—222no—
409#103—22no—
410#103—22no—
411#103—222no—
412#103—222no—
413C22⋊C8—22no—
414C22⋊C8—222no—
415#97—222no—
416#97—222no—
417#95—21no—
418#95—221no—
419#95—221no—
420#95—221no—
421#95—221no—
422#95—221no—
423#95—221no—
424#95—221no—
425#95—221no—
426#95—221no—
427#95—221no—
428C2×C11—42no—
429C2×C11#241511yescharacteristic
430C2×C11#305411yescharacteristic
431C2×C11#305611yescharacteristic
432C2×C11#311111yescharacteristic
433C2×C11#311711yescharacteristic
434C2×C11#323611yescharacteristic
435C2×C11#324011yescharacteristic
436C24D4×D1111yescharacteristic
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8#434112yes—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—111no—
454C22×C4—111no—
455C22×C4—111no—
456C22×C4—111no—
457C22×C4—222no—
458C22×C4—222no—
459C22×C4—222no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—441no—
465C22×C4—441no—
466C22×C4—441no—
467C22×C4D4×D1111yescharacteristic
468C22×C4C23×D1111yescharacteristic
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—112no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8D4×D1112yes—
481C4⋊C4—24no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—442no—
496C4⋊C4—442no—
497C4⋊C4—442no—
498C4⋊C4—442no—
499C4⋊C4—442no—
500C4⋊C4—442no—
501C4⋊C4#434112yes—
502C22⋊C4—24no—
503C22⋊C4—42no—
504C22⋊C4—442no—
505C22⋊C4—442no—
506C42—112no—
507C42—112no—
508C42—222no—
509C42—222no—
510C42—221no—
511C42—221no—
512C42—442no—
513C42—442no—
514C11#2470711yescharacteristic, complemented, Sylow
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23#6696812yes—
522C23C2×D4×D1111yescharacteristic
523Q8—22no—
524Q8—22no—
525Q8—41no—
526Q8—41no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—112no—
547C2×C4—112no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—444no—
559C2×C4—444no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4C2×D4×D1111yescharacteristic
573C2×C4C2×#434111yescharacteristic
574C2×C4C2×#434111yescharacteristic
575C2×C4#41×D1111yescharacteristic
576C2×C4#6704311yescharacteristic
577C2×C4#6704311yescharacteristic
578C8—22no—
579C8—41no—
580C8—222no—
581C8—441no—
582C22—22no—
583C22—22no—
584C22—22no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22#1062311711yescharacteristic
590C22D11×#12111yescharacteristic
591C22#1062317911yescharacteristic
592C22C2×#6696811yescharacteristic
593C22#1062329911yescharacteristic
594C22#1062330811yescharacteristic
595C22#1062330811yescharacteristic
596C4—41no—
597C4—42no—
598C4—42no—
599C4—81no—
600C4—81no—
601C4—222no—
602C4—222no—
603C4—441no—
604C4—441no—
605C4—881no—
606C4—881no—
607C4—881no—
608C4—881no—
609C4#1062312911yescharacteristic
610C4#1062314211yescharacteristic
611C4#1062318111yescharacteristic
612C4#1062320211yescharacteristic
613C2—42no—
614C2#1307203811yescharacteristic
615C2#1307822711yescharacteristic
616C2#1307823911yescharacteristic
617C2#1307872611yescharacteristic
618C2#1307878211yescharacteristic
619C2#1307981911yescharacteristic
620C2#1307986011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2035C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#2035D11
hypocenterC11#24707
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2035

Complements

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

NH ≅ G/Ntype
1. C2×#10622409C2semidirect
8. #13069570C2semidirect
9. #13069385C2semidirect
10. #13069360C2semidirect
11. #13069353C2semidirect
12. #13069308C2semidirect
13. #13069303C2semidirect
14. #13068629C2semidirect
514. C11#24707semidirect

Maximal subgroups

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

subgroupindex
C2×#106224092
C2×#106223322
#130769242
C22⋊Q8×Dic112
#130700522
#130700442
#130698162
#130695702
#130693852
#130693602
#130693532
#130693082
#130693032
#130686292
C11×#20352
#2470711