Finite Group Databasebeta

← #14731645

Subgroups — #14731645

Order 2816.

878 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079843C211yesmaximal, characteristic, complemented
2#13079640C211yesmaximal, characteristic, complemented
3C2×#10622694C211yesmaximal, characteristic, complemented
4#13067844C212yesmaximal, complemented
5#13067837C212yesmaximal, complemented
6#13067830C212yesmaximal, complemented
7#13067823C212yesmaximal, complemented
8#13067342C211yesmaximal, characteristic, complemented
9#13067076C211yesmaximal, characteristic, complemented
10#13067076C211yesmaximal, characteristic, complemented
11C11×#3544C211yesmaximal, characteristic
12C11×#563—22no—
13Q82×C11C2211yescharacteristic
14C11×#555C2211yescharacteristic
15C11×#554C2211yescharacteristic
16C11×#554C2211yescharacteristic
17C11×#552—21no—
18C11×#552—21no—
19C11×#547—21no—
20C11×#547—21no—
21C11×#544—21no—
22C11×#544—21no—
23C11×#542—21no—
24C11×#542—21no—
25C11×#536—22no—
26C2×C11×C4⋊Q8C2211yescharacteristic
27C11×#529C2211yescharacteristic
28C11×#529C2211yescharacteristic
29C2×#66922C2211yescharacteristic
30C2×#66899—22no—
31#10622694—22no—
32#10622694C2212yes—
33#10622694C2212yes—
34#10622682—21no—
35#10622678—21no—
36#10622673—21no—
37#10622668—21no—
38#10622663—21no—
39#10622657—21no—
40#10622653—21no—
41#10622647—21no—
42#10622644C2212yes—
43#10622633C2212yes—
44#10622632C2212yes—
45#10622620C2212yes—
46#10622539C2211yescharacteristic
47#10622539C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622184C2212yes—
50#10622184C2212yes—
51Q8⋊(C11⋊C8)C2212yes—
52Q8⋊(C11⋊C8)C2212yes—
53D4⋊(C11⋊C8)C2212yes—
54D4⋊(C11⋊C8)C2212yes—
55C2×C11×#41—22no—
56C22×Q8×C11D412yes—
57C22×Dic22—21no—
58C11×C4⋊Q8—22no—
59C11×C4⋊Q8—22no—
60C11×C4⋊Q8—21no—
61C11×C4⋊Q8—21no—
62C11×C4⋊Q8—21no—
63C11×C4⋊Q8—21no—
64C11×C4⋊Q8D412yes—
65C11×C4⋊Q8C2311yescharacteristic
66C11×C4⋊Q8C2311yescharacteristic
67C11×#126—22no—
68C11×#126—22no—
69C11×#126—21no—
70C11×#126—21no—
71C11×#125—22no—
72C11×#125—22no—
73C11×#125—21no—
74C11×#125—21no—
75C11×#125D411yescharacteristic
76C11×#125D411yescharacteristic
77C11×#124—22no—
78C11×#124—22no—
79C11×#124D411yescharacteristic
80C11×#124D411yescharacteristic
81C11×#123—22no—
82C11×#123—22no—
83C11×#123—22no—
84C11×#123—22no—
85C11×#123—21no—
86C11×#123—21no—
87C11×C22⋊Q8—22no—
88C11×C22⋊Q8—22no—
89C11×C22⋊Q8—22no—
90C11×C22⋊Q8—22no—
91C11×C22⋊Q8—22no—
92C11×C22⋊Q8—22no—
93C11×C22⋊Q8—21no—
94C11×C22⋊Q8—21no—
95C11×C22⋊Q8D411yescharacteristic
96C11×C22⋊Q8D411yescharacteristic
97C11×#121—21no—
98C11×#121—21no—
99C11×#121D411yescharacteristic
100C11×#121D411yescharacteristic
101C4×Q8×C11—21no—
102C4×Q8×C11—21no—
103C4×Q8×C11C2311yescharacteristic
104C4×Q8×C11C2311yescharacteristic
105C4×D4×C11—21no—
106C4×D4×C11—21no—
107C4×D4×C11—21no—
108C4×D4×C11—21no—
109C4×D4×C11C2311yescharacteristic
110C4×D4×C11C2311yescharacteristic
111C11×#117—22no—
112C11×#117—21no—
113C11×#117—21no—
114C11×#117—21no—
115C11×#117—21no—
116C2×C11×C4⋊C4—21no—
117C2×C11×C4⋊C4—21no—
118C2×C11×C4⋊C4—21no—
119C2×C11×C4⋊C4—21no—
120C2×C42×C11C2311yescharacteristic
121C2×#4326—22no—
122C2×#4324—22no—
123C2×C4⋊Dic11—21no—
124C2×C4⋊Dic11—21no—
125C22×C11⋊C8—21no—
126#66922—21no—
127#66922—21no—
128#66922—21no—
129#66922C2312yes—
130#66899—24no—
131#66899—24no—
132#66899—22no—
133#66896—22no—
134C22⋊(C11⋊C8)—21no—
135C22⋊(C11⋊C8)—21no—
136#66874—22no—
137#66874—22no—
138#66872—22no—
139#66871—22no—
140C4⋊(C11⋊C8)C2312yes—
141C4⋊(C11⋊C8)C2312yes—
142#66867—21no—
143#66867—21no—
144C4×C11⋊C8—21no—
145C4×C11⋊C8C2312yes—
146#18690—111nomaximal, Sylow
147C11×#41—84no—
148C2×Q8×C11—22no—
149C2×Q8×C11—22no—
150C2×Q8×C11—44no—
151C2×Q8×C11C2×D411yescharacteristic
152C2×Q8×C11C2×D411yescharacteristic
153C2×Q8×C11C2×D412yes—
154C2×Q8×C11C2×D412yes—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—22no—
158C2×D4×C11C2×D411yescharacteristic
159C2×D4×C11C2×D411yescharacteristic
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—22no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×Dic11—41no—
169C2×Dic22—22no—
170C2×Dic22—41no—
171C2×Dic22—82no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4C2×D411yescharacteristic
193C11×C4⋊C4C2×D411yescharacteristic
194C11×C4⋊C4C2×D411yescharacteristic
195C11×C4⋊C4C2×D411yescharacteristic
196C11×C22⋊C4—22no—
197C11×C22⋊C4—22no—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—22no—
200C11×C22⋊C4—21no—
201C11×C22⋊C4—21no—
202C11×C22⋊C4—21no—
203C11×C22⋊C4—21no—
204C11×C22⋊C4—21no—
205C11×C22⋊C4—21no—
206C11×C22⋊C4—21no—
207C11×C22⋊C4—21no—
208C11×C22⋊C4—21no—
209C11×C22⋊C4—21no—
210C42×C11—22no—
211C42×C11—22no—
212C42×C11—21no—
213C42×C11—21no—
214C42×C11C2×D411yescharacteristic
215C42×C11C2×D411yescharacteristic
216C42×C11C2×D411yescharacteristic
217C42×C11C2411yescharacteristic
218#4326—82no—
219#4324—82no—
220C4⋊Dic11—22no—
221C4⋊Dic11—22no—
222C4⋊Dic11—41no—
223C4⋊Dic11—41no—
224C2×C11⋊C8—22no—
225C2×C11⋊C8—22no—
226C2×C11⋊C8—22no—
227C2×C11⋊C8—42no—
228#3544D1111yescharacteristic
229#3239—111no—
230#3218—111no—
231C2×#487—111no—
232#1646—112no—
233#1645—112no—
234#1644—112no—
235#1643—112no—
236#1558—111no—
237#1494—111no—
238#1494—111no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11#12011yescharacteristic
242Q8×C11—22no—
243Q8×C11—22no—
244Q8×C11—42no—
245Q8×C11—42no—
246Q8×C11—82no—
247Q8×C11—82no—
248D4×C11—22no—
249D4×C11—22no—
250D4×C11—42no—
251D4×C11—42no—
252D4×C11—82no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—22no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—22no—
264C2×C4×C11—44no—
265C2×C4×C11—42no—
266C2×C4×C11—42no—
267C2×C4×C11—82no—
268C2×C4×C11—82no—
269C2×C4×C11#12011yescharacteristic
270C2×C4×C11#12011yescharacteristic
271C2×C4×C11#12011yescharacteristic
272C2×C4×C11C22×D411yescharacteristic
273C2×C4×C11C22×D411yescharacteristic
274C2×C4×C11C22×D411yescharacteristic
275C2×Dic11—42no—
276C2×Dic11—82no—
277Dic22—42no—
278Dic22—42no—
279Dic22—82no—
280C11⋊C8—42no—
281C11⋊C8—42no—
282C11⋊C8—42no—
283#563—22no—
284Q82C2×D1111yescharacteristic
285#555C2×D1111yescharacteristic
286#554C2×D1111yescharacteristic
287#554C2×D1111yescharacteristic
288#552—21no—
289#552—21no—
290#547—21no—
291#547—21no—
292#544—21no—
293#544—21no—
294#542—21no—
295#542—21no—
296#536—22no—
297C2×C4⋊Q8—111no—
298C2×C4⋊Q8C2×D1111yescharacteristic
299#529C2×D1111yescharacteristic
300#529C2×D1111yescharacteristic
301#501—221no—
302#497—221no—
303#491—221no—
304#489—221no—
305#487—112no—
306#487—112no—
307#487—222no—
308#484—221no—
309#481—221no—
310#475—112no—
311#474—112no—
312#462—112no—
313#461—112no—
314#451—221no—
315#448—221no—
316#432—111no—
317#432—111no—
318C2×#103—222no—
319C2×C4×C8—111no—
320#333—112no—
321#333—112no—
322Q8⋊C8—112no—
323Q8⋊C8—112no—
324D4⋊C8—112no—
325D4⋊C8—112no—
326C22×C11—21no—
327C22×C11—21no—
328C22×C11—41no—
329C22×C11—41no—
330C22×C11—41no—
331C22×C11—41no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11#45512yes—
335C22×C11C2×#12011yescharacteristic
336C4×C11—21no—
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—21no—
340C4×C11—41no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11—41no—
344C4×C11—42no—
345C4×C11—42no—
346C4×C11—41no—
347C4×C11—41no—
348C4×C11#57712yes—
349C4×C11#57812yes—
350Dic11—82no—
351C2×#41—22no—
352C22×Q8—221no—
353C22×Q8C22⋊D1112yes—
354C2×Q16—222no—
355C2×SD16—222no—
356C22×C8—221no—
357C4⋊Q8—22no—
358C4⋊Q8—22no—
359C4⋊Q8—21no—
360C4⋊Q8—21no—
361C4⋊Q8—21no—
362C4⋊Q8—21no—
363C4⋊Q8—112no—
364C4⋊Q8—221no—
365C4⋊Q8—221no—
366C4⋊Q8—221no—
367C4⋊Q8C22⋊D1112yes—
368C4⋊Q8C22×D1111yescharacteristic
369C4⋊Q8C22×D1111yescharacteristic
370#126—22no—
371#126—22no—
372#126—21no—
373#126—21no—
374#125—22no—
375#125—22no—
376#125—21no—
377#125—21no—
378#125C22⋊D1111yescharacteristic
379#125C22⋊D1111yescharacteristic
380#124—22no—
381#124—22no—
382#124C22⋊D1111yescharacteristic
383#124C22⋊D1111yescharacteristic
384#123—22no—
385#123—22no—
386#123—22no—
387#123—22no—
388#123—21no—
389#123—21no—
390C22⋊Q8—22no—
391C22⋊Q8—22no—
392C22⋊Q8—22no—
393C22⋊Q8—22no—
394C22⋊Q8—22no—
395C22⋊Q8—22no—
396C22⋊Q8—21no—
397C22⋊Q8—21no—
398C22⋊Q8C22⋊D1111yescharacteristic
399C22⋊Q8C22⋊D1111yescharacteristic
400#121—21no—
401#121—21no—
402#121C22⋊D1111yescharacteristic
403#121C22⋊D1111yescharacteristic
404C4×Q8—21no—
405C4×Q8—21no—
406C4×Q8C22×D1111yescharacteristic
407C4×Q8C22×D1111yescharacteristic
408C4×D4—21no—
409C4×D4—21no—
410C4×D4—21no—
411C4×D4—21no—
412C4×D4C22×D1111yescharacteristic
413C4×D4C22×D1111yescharacteristic
414#117—22no—
415#117—21no—
416#117—21no—
417#117—21no—
418#117—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4—221no—
425C2×C42C22×D1111yescharacteristic
426#107—222no—
427#106—222no—
428C4⋊C8—112no—
429C4⋊C8—112no—
430#103—224no—
431#103—224no—
432#103—222no—
433#103—222no—
434#103—222no—
435#102—222no—
436C22⋊C8—221no—
437C22⋊C8—221no—
438#97—221no—
439#97—221no—
440C4×C8—112no—
441C4×C8—221no—
442C2×C11—22no—
443C2×C11—81no—
444C2×C11—81no—
445C2×C11#301011yescharacteristic
446C2×C11#301111yescharacteristic
447C2×C11C2×#45511yescharacteristic
448#41—84no—
449C2×Q8—22no—
450C2×Q8—22no—
451C2×Q8—44no—
452C2×Q8—222no—
453C2×Q8—441no—
454C2×Q8—882no—
455C2×Q8C2×C22⋊D1111yescharacteristic
456C2×Q8C2×C22⋊D1111yescharacteristic
457C2×Q8C2×C22⋊D1112yes—
458C2×Q8C2×C22⋊D1112yes—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—22no—
462C2×D4C2×C22⋊D1111yescharacteristic
463C2×D4C2×C22⋊D1111yescharacteristic
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—441no—
470C22×C4C2×C22⋊D1111yescharacteristic
471C22×C4C2×C22⋊D1111yescharacteristic
472C22×C4C2×C22⋊D1111yescharacteristic
473Q16—882no—
474SD16—882no—
475C2×C8—222no—
476C2×C8—222no—
477C2×C8—222no—
478C2×C8—442no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—222no—
500C4⋊C4—222no—
501C4⋊C4—441no—
502C4⋊C4—441no—
503C4⋊C4C2×C22⋊D1111yescharacteristic
504C4⋊C4C2×C22⋊D1111yescharacteristic
505C4⋊C4C2×C22⋊D1111yescharacteristic
506C4⋊C4C2×C22⋊D1111yescharacteristic
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—21no—
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—21no—
516C22⋊C4—21no—
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C42—22no—
522C42—22no—
523C42—21no—
524C42—21no—
525C42C2×C22⋊D1111yescharacteristic
526C42C2×C22⋊D1111yescharacteristic
527C42C2×C22⋊D1111yescharacteristic
528C42C23×D1111yescharacteristic
529C11#1869011yescharacteristic, complemented, Sylow
530C23—21no—
531C23—21no—
532C23#6700611yescharacteristic
533Q8—22no—
534Q8—22no—
535Q8—42no—
536Q8—42no—
537Q8—82no—
538Q8—82no—
539Q8—442no—
540Q8—442no—
541Q8—882no—
542D4—22no—
543D4—22no—
544D4—42no—
545D4—42no—
546D4—82no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—44no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—82no—
562C2×C4—82no—
563C2×C4—442no—
564C2×C4—882no—
565C2×C4#6700611yescharacteristic
566C2×C4#6700611yescharacteristic
567C2×C4#6700611yescharacteristic
568C2×C4C22×C22⋊D1111yescharacteristic
569C2×C4C22×C22⋊D1111yescharacteristic
570C2×C4C22×C22⋊D1111yescharacteristic
571C8—442no—
572C8—442no—
573C8—442no—
574C22—21no—
575C22—21no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22#1062285512yes—
583C22C2×#6700611yescharacteristic
584C4—21no—
585C4—21no—
586C4—21no—
587C4—21no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—42no—
593C4—42no—
594C4—41no—
595C4—41no—
596C4—882no—
597C4#1062336812yes—
598C4#1062336912yes—
599C2—22no—
600C2—81no—
601C2—81no—
602C2#1307790211yescharacteristic
603C2#1307791111yescharacteristic
604C2C2×#1062285511yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3544C2
socleC22×C11C2×#120
hypercenter#3544D11
hypocenterC11#18690
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3544

Complements

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

NH ≅ G/Ntype
1. #13079843C2semidirect
2. #13079640C2semidirect
3. C2×#10622694C2semidirect
4. #13067844C2semidirect
5. #13067837C2semidirect
6. #13067830C2semidirect
7. #13067823C2semidirect
8. #13067342C2semidirect
9. #13067076C2semidirect
10. #13067076C2semidirect
529. C11#18690semidirect

Maximal subgroups

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

subgroupindex
#130798432
#130796402
C2×#106226942
#130678442
#130678372
#130678302
#130678232
#130673422
#130670762
C11×#35442
#1869011