Finite Group Databasebeta

← #14731390

Subgroups — #14731390

Order 2816.

882 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079958C211yesmaximal, characteristic, complemented
2#13079171C211yesmaximal, characteristic
3#13078421C211yesmaximal, characteristic, complemented
4#13067893C212yesmaximal, complemented
5#13067802C212yesmaximal, complemented
6#13067774C212yesmaximal, complemented
7#13067737C212yesmaximal, complemented
8#13067293C211yesmaximal, characteristic
9#13067071C211yesmaximal, characteristic, complemented
10C2×Q8⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
11C11×#3507C211yesmaximal, characteristic
12C11×#559C2212yes—
13C11×#557C2212yes—
14C11×#556—21no—
15C11×#556—22no—
16C11×#554—21no—
17C11×#552—22no—
18C11×#539—22no—
19C11×#536—21no—
20C11×#533C2211yescharacteristic
21C11×#532C2211yescharacteristic
22C11×#529—22no—
23C11×#520—21no—
24C2×C4×Q8×C11C2211yescharacteristic
25#10623001C2211yescharacteristic
26#10622838—21no—
27#10622706C2211yescharacteristic
28#10622704—21no—
29#10622703—21no—
30#10622692C2211yescharacteristic
31#10622689C2211yescharacteristic
32#10622683C2211yescharacteristic
33#10622664—22no—
34#10622654—22no—
35#10622644C2212yes—
36#10622635—22no—
37#10622634C2212yes—
38#10622634C2212yes—
39#10622633C2212yes—
40C4×#4324—22no—
41#10622577—21no—
42#10622537C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44C2×C4×C11⋊C8C2211yescharacteristic
45#10622185C2212yes—
46#10622182C2212yes—
47Q8⋊(C11⋊C8)C2212yes—
48Q8⋊(C11⋊C8)C2212yes—
49Q8⋊(C11⋊C8)C2212yes—
50Q8⋊(C11⋊C8)C2212yes—
51C2×C11×#41—21no—
52C22×Q8×C11D411yescharacteristic
53C11×C4⋊Q8—22no—
54C11×C4⋊Q8D411yescharacteristic
55C11×C4⋊Q8D411yescharacteristic
56C11×C4⋊Q8C2311yescharacteristic
57C11×#127C2311yescharacteristic
58C11×#126—24no—
59C11×#126—24no—
60C11×#125—22no—
61C11×#125—24no—
62C11×#125—21no—
63C11×#124—22no—
64C11×#124—22no—
65C11×#124—21no—
66C11×#123—24no—
67C11×#123—24no—
68C11×C22⋊Q8—22no—
69C11×C22⋊Q8—22no—
70C11×C22⋊Q8—24no—
71C11×C22⋊Q8—21no—
72C11×C22⋊Q8D412yes—
73C11×#121—21no—
74C11×#121D412yes—
75C4×Q8×C11—22no—
76C4×Q8×C11—22no—
77C4×Q8×C11—21no—
78C4×Q8×C11—21no—
79C4×Q8×C11—21no—
80C4×Q8×C11D412yes—
81C4×Q8×C11C2312yes—
82C4×Q8×C11C2312yes—
83C4×D4×C11—24no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C4×D4×C11—21no—
87C4×D4×C11D412yes—
88C11×#117—22no—
89C11×#117—24no—
90C11×#117—21no—
91C2×C11×C4⋊C4—22no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4D411yescharacteristic
94C2×C42×C11—21no—
95C2×C42×C11C2311yescharacteristic
96C2×#4326—22no—
97C2×#4324—22no—
98#66979—21no—
99#66977—21no—
100#66977—21no—
101C2×#4318—21no—
102C22×C11⋊C8—21no—
103C22×C11⋊C8—21no—
104#66923—21no—
105#66922C2311yescharacteristic
106#66922C2311yescharacteristic
107C4×Dic22—21no—
108C4×Dic22—21no—
109#66899—22no—
110#66899—22no—
111#66899—22no—
112#66896—22no—
113#66874—22no—
114#66874—22no—
115#66872—22no—
116#66872—22no—
117#66871—22no—
118#66871—22no—
119C4⋊(C11⋊C8)—21no—
120C4⋊(C11⋊C8)—21no—
121C4⋊(C11⋊C8)C2312yes—
122C4⋊(C11⋊C8)C2312yes—
123C4×C11⋊C8—21no—
124C4×C11⋊C8C2311yescharacteristic
125C4×C11⋊C8C2311yescharacteristic
126#18667—111nomaximal, Sylow
127C11×#41—42no—
128C11×#41—42no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—22no—
133C2×Q8×C11—22no—
134C2×Q8×C11C2×D412yes—
135C2×Q8×C11C2×D412yes—
136C2×D4×C11—22no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11C2×D412yes—
140C22×C4×C11—21no—
141C22×C4×C11—24no—
142C22×C4×C11—21no—
143C22×C4×C11—22no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C2×Dic22—21no—
148C2×Dic22—21no—
149C11×C4⋊C4—24no—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4C2×D412yes—
162C11×C4⋊C4C2×D412yes—
163C11×C4⋊C4C2×D412yes—
164C11×C22⋊C4—24no—
165C11×C22⋊C4—24no—
166C11×C22⋊C4—24no—
167C11×C22⋊C4—22no—
168C11×C22⋊C4—22no—
169C11×C22⋊C4—22no—
170C42×C11—24no—
171C42×C11—22no—
172C42×C11—22no—
173C42×C11—22no—
174C42×C11C2×D411yescharacteristic
175C42×C11C2×D411yescharacteristic
176C42×C11C2×D411yescharacteristic
177C42×C11C2411yescharacteristic
178C22⋊Dic11—41no—
179#4326—82no—
180#4324—44no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185Dic11⋊C4—41no—
186Dic11⋊C4—41no—
187C4×Dic11—41no—
188#4318—42no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—42no—
194C2×C11⋊C8—81no—
195#3507D1111yescharacteristic
196#3249—111no—
197#3167—111no—
198#3078—111no—
199#1653—112no—
200#1640—112no—
201#1636—112no—
202#1630—112no—
203#1547—111no—
204#1493—111no—
205C2×Q8⋊C8—111no—
206C23×C11—22no—
207C23×C11#12011yescharacteristic
208Q8×C11—22no—
209Q8×C11—22no—
210Q8×C11—22no—
211Q8×C11—22no—
212Q8×C11—41no—
213Q8×C11—41no—
214Q8×C11—42no—
215Q8×C11—81no—
216D4×C11—42no—
217D4×C11—44no—
218D4×C11—41no—
219D4×C11—41no—
220D4×C11—41no—
221D4×C11—41no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—41no—
230C2×C4×C11—42no—
231C2×C4×C11—44no—
232C2×C4×C11—81no—
233C2×C4×C11—84no—
234C2×C4×C11#12011yescharacteristic
235C2×C4×C11#12011yescharacteristic
236C2×C4×C11#12011yescharacteristic
237C2×C4×C11#13512yes—
238C2×C4×C11#13712yes—
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C22×D411yescharacteristic
242C2×Dic11—41no—
243C2×Dic11—41no—
244Dic22—42no—
245Dic22—41no—
246Dic22—41no—
247C11⋊C8—22no—
248C11⋊C8—41no—
249C11⋊C8—42no—
250C11⋊C8—42no—
251#559C2×D1112yes—
252#557C2×D1112yes—
253#556—21no—
254#556—22no—
255#554—21no—
256#552—22no—
257#539—22no—
258#536—21no—
259#533—111no—
260#533C2×D1111yescharacteristic
261#532C2×D1111yescharacteristic
262#529—22no—
263#520—21no—
264C2×C4×Q8C2×D1111yescharacteristic
265#498—111no—
266#492—111no—
267#487—111no—
268#486—111no—
269#479—222no—
270#477—112no—
271#477—112no—
272#477—221no—
273#475—112no—
274#467—222no—
275#465—222no—
276#462—112no—
277#462—221no—
278C4×SD16—222no—
279#428—221no—
280#423—111no—
281C2×C4⋊C8—111no—
282#419—221no—
283C2×C4×C8—111no—
284#332—112no—
285#331—112no—
286Q8⋊C8—112no—
287Q8⋊C8—112no—
288Q8⋊C8—112no—
289Q8⋊C8—112no—
290C22×C11—21no—
291C22×C11—21no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11#45212yes—
296C22×C11C2×#12011yescharacteristic
297C4×C11—21no—
298C4×C11—21no—
299C4×C11—21no—
300C4×C11—42no—
301C4×C11—42no—
302C4×C11—42no—
303C4×C11—42no—
304C4×C11—42no—
305C4×C11#45212yes—
306C4×C11C2×#13511yescharacteristic
307C4×C11C2×#13711yescharacteristic
308C4×C11#57711yescharacteristic
309C4×C11#57811yescharacteristic
310Dic11—81no—
311Dic11—81no—
312C2×#41—21no—
313C22×Q8C22⋊D1111yescharacteristic
314C2×Q16—222no—
315C2×SD16—222no—
316C2×M16—221no—
317C22×C8—221no—
318C22×C8—221no—
319C4⋊Q8—22no—
320C4⋊Q8—111no—
321C4⋊Q8—111no—
322C4⋊Q8C22⋊D1111yescharacteristic
323C4⋊Q8C22⋊D1111yescharacteristic
324C4⋊Q8C22×D1111yescharacteristic
325#127C22×D1111yescharacteristic
326#126—24no—
327#126—24no—
328#125—22no—
329#125—24no—
330#125—21no—
331#125—221no—
332#124—22no—
333#124—22no—
334#124—21no—
335#123—24no—
336#123—24no—
337C22⋊Q8—22no—
338C22⋊Q8—22no—
339C22⋊Q8—24no—
340C22⋊Q8—21no—
341C22⋊Q8—221no—
342C22⋊Q8—221no—
343C22⋊Q8C22⋊D1112yes—
344#121—21no—
345#121C22⋊D1112yes—
346C4×Q8—22no—
347C4×Q8—22no—
348C4×Q8—21no—
349C4×Q8—21no—
350C4×Q8—21no—
351C4×Q8—221no—
352C4×Q8—221no—
353C4×Q8C22⋊D1112yes—
354C4×Q8C22×D1112yes—
355C4×Q8C22×D1112yes—
356C4×D4—24no—
357C4×D4—22no—
358C4×D4—22no—
359C4×D4—21no—
360C4×D4C22⋊D1112yes—
361#117—22no—
362#117—24no—
363#117—21no—
364#117—221no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4C22⋊D1111yescharacteristic
368C2×C42—21no—
369C2×C42C22×D1111yescharacteristic
370#107—222no—
371#107—222no—
372#106—222no—
373#106—222no—
374C4⋊C8—112no—
375C4⋊C8—112no—
376C4⋊C8—221no—
377C4⋊C8—221no—
378#103—222no—
379#103—222no—
380#103—222no—
381#103—222no—
382#103—222no—
383#102—222no—
384C4×C8—111no—
385C4×C8—111no—
386C4×C8—221no—
387C2×C11—22no—
388C2×C11—82no—
389C2×C11C2×#45211yescharacteristic
390C2×C11#301311yescharacteristic
391C2×C11#301811yescharacteristic
392#41—42no—
393#41—42no—
394C2×Q8—21no—
395C2×Q8—21no—
396C2×Q8—21no—
397C2×Q8—22no—
398C2×Q8—22no—
399C2×Q8—221no—
400C2×Q8—221no—
401C2×Q8C2×C22⋊D1112yes—
402C2×Q8C2×C22⋊D1112yes—
403C2×D4—22no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4C2×C22⋊D1112yes—
407C22×C4—21no—
408C22×C4—24no—
409C22×C4—21no—
410C22×C4—22no—
411C22×C4C2×C22⋊D1111yescharacteristic
412C22×C4C2×C22⋊D1111yescharacteristic
413C22×C4C2×C22⋊D1111yescharacteristic
414Q16—882no—
415SD16—444no—
416M16—442no—
417C2×C8—221no—
418C2×C8—221no—
419C2×C8—222no—
420C2×C8—222no—
421C2×C8—442no—
422C2×C8—881no—
423C4⋊C4—24no—
424C4⋊C4—24no—
425C4⋊C4—24no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—22no—
429C4⋊C4—21no—
430C4⋊C4—22no—
431C4⋊C4—21no—
432C4⋊C4—22no—
433C4⋊C4—21no—
434C4⋊C4—22no—
435C4⋊C4—221no—
436C4⋊C4—221no—
437C4⋊C4—221no—
438C4⋊C4—221no—
439C4⋊C4—441no—
440C4⋊C4—441no—
441C4⋊C4C2×C22⋊D1112yes—
442C4⋊C4C2×C22⋊D1112yes—
443C4⋊C4C2×C22⋊D1112yes—
444C22⋊C4—24no—
445C22⋊C4—24no—
446C22⋊C4—24no—
447C22⋊C4—22no—
448C22⋊C4—22no—
449C22⋊C4—22no—
450C22⋊C4—441no—
451C42—24no—
452C42—22no—
453C42—22no—
454C42—22no—
455C42—441no—
456C42C2×C22⋊D1111yescharacteristic
457C42C2×C22⋊D1111yescharacteristic
458C42C2×C22⋊D1111yescharacteristic
459C42C23×D1111yescharacteristic
460C11#1866711yescharacteristic, complemented, Sylow
461C23—22no—
462C23#6700611yescharacteristic
463Q8—22no—
464Q8—22no—
465Q8—22no—
466Q8—22no—
467Q8—41no—
468Q8—41no—
469Q8—42no—
470Q8—81no—
471Q8—442no—
472Q8—441no—
473Q8—441no—
474D4—42no—
475D4—44no—
476D4—41no—
477D4—41no—
478D4—41no—
479D4—41no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—41no—
488C2×C4—42no—
489C2×C4—44no—
490C2×C4—81no—
491C2×C4—84no—
492C2×C4—441no—
493C2×C4—441no—
494C2×C4#6700312yes—
495C2×C4#6700412yes—
496C2×C4#6700611yescharacteristic
497C2×C4#6700611yescharacteristic
498C2×C4#6700611yescharacteristic
499C2×C4C22×C22⋊D1111yescharacteristic
500C2×C4C22×C22⋊D1111yescharacteristic
501C2×C4C22×C22⋊D1111yescharacteristic
502C8—222no—
503C8—441no—
504C8—442no—
505C8—442no—
506C22—21no—
507C22—21no—
508C22—42no—
509C22—42no—
510C22—42no—
511C22#1062285212yes—
512C22C2×#6700611yescharacteristic
513C4—21no—
514C4—21no—
515C4—21no—
516C4—42no—
517C4—42no—
518C4—42no—
519C4—42no—
520C4—42no—
521C4—881no—
522C4—881no—
523C4#1062285212yes—
524C4C2×#6700311yescharacteristic
525C4C2×#6700411yescharacteristic
526C4#1062336811yescharacteristic
527C4#1062336911yescharacteristic
528C2—22no—
529C2—82no—
530C2C2×#1062285211yescharacteristic
531C2#1307793111yescharacteristic
532C2#1307796511yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3507C2
socleC22×C11C2×#120
prime radicalC11×#532C22
hypercenter#3507D11
hypocenterC11#18667
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3507

Complements

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

NH ≅ G/Ntype
1. #13079958C2semidirect
3. #13078421C2semidirect
4. #13067893C2semidirect
5. #13067802C2semidirect
6. #13067774C2semidirect
7. #13067737C2semidirect
9. #13067071C2semidirect
10. C2×Q8⋊(C11⋊C8)C2semidirect
460. C11#18667semidirect

Maximal subgroups

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

subgroupindex
#130799582
#130791712
#130784212
#130678932
#130678022
#130677742
#130677372
#130672932
#130670712
C2×Q8⋊(C11⋊C8)2
C11×#35072
#1866711