Finite Group Databasebeta

← #14730942

Subgroups — #14730942

Order 2816.

1056 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#13079764C211yesmaximal, characteristic, complemented
2C2×#10622689C211yesmaximal, characteristic, complemented
3#13078431C211yesmaximal, characteristic, complemented
4#13067743C214yesmaximal, complemented
5#13067737C214yesmaximal, complemented
6#13067284C211yesmaximal, characteristic, complemented
7#13067071C211yesmaximal, characteristic, complemented
8#13066998C211yesmaximal, characteristic, complemented
9C11×#3508C211yesmaximal, characteristic
10C11×#559—21no—
11C11×#559C2212yes—
12C11×#550—21no—
13C11×#550C2212yes—
14C11×#546—22no—
15C11×#546—22no—
16C11×#540—22no—
17C11×#535—21no—
18C11×#533C2211yescharacteristic
19C11×#532—21no—
20C11×#532—21no—
21C2×C11×#127C2211yescharacteristic
22C11×#518—21no—
23C4×C11×#41C2211yescharacteristic
24C22×#4324—22no—
25C2×#66922C2211yescharacteristic
26#10622845—21no—
27#10622694—21no—
28#10622691—21no—
29#10622689—22no—
30#10622689C2214yes—
31#10622657—22no—
32#10622634C2212yescomplemented
33#10622634C2214yescomplemented
34#10622633—21no—
35#10622621C2212yescomplemented
36#10622620—21no—
37#10622608—21no—
38#10622538C2211yescharacteristic
39#10622537C2211yescharacteristic
40C2×C4×C11⋊C8C2211yescharacteristic
41#10622182C2214yes—
42Q8⋊(C11⋊C8)C2214yescomplemented
43Q8⋊(C11⋊C8)C2212yescomplemented
44D4⋊(C11⋊C8)C2212yescomplemented
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41D411yescharacteristic
48C22×D4×C11—21no—
49C22×D4×C11—21no—
50C22×D4×C11D412yes—
51C22×Dic22—21no—
52C11×C4⋊Q8D411yescharacteristic
53C11×C4⋊Q8D411yescharacteristic
54C11×#127—22no—
55C11×#127—21no—
56C11×#127—21no—
57C11×#127D412yes—
58C11×#127C2312yes—
59C11×#125—21no—
60C11×#124—22no—
61C11×#124—22no—
62C11×#124—22no—
63C11×#123—24no—
64C11×#123—24no—
65C11×C22⋊Q8—21no—
66C11×C22⋊Q8D412yes—
67C11×#121—22no—
68C11×#121—22no—
69C11×#121—22no—
70C11×#121—24no—
71C11×#121—24no—
72C11×#121—22no—
73C11×#120—24no—
74C4×Q8×C11—21no—
75C4×Q8×C11D411yescharacteristic
76C4×Q8×C11C2311yescharacteristic
77C4×Q8×C11C2312yes—
78C4×D4×C11—22no—
79C4×D4×C11—22no—
80C4×D4×C11—22no—
81C4×D4×C11—21no—
82C4×D4×C11—21no—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C4×D4×C11D411yescharacteristic
87C4×D4×C11C2311yescharacteristic
88C11×#117—21no—
89C11×#117—21no—
90C11×#117D411yescharacteristic
91C2×C11×C22⋊C4—24no—
92C2×C42×C11—21no—
93C2×C42×C11C2311yescharacteristic
94C2×#4324—28no—
95C2×#4324—48no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11—21no—
98C2×#4318—21no—
99C22×C11⋊C8—21no—
100#66922—21no—
101#66922—21no—
102#66922—21no—
103#66922C2312yes—
104#66899—22no—
105#66899—24no—
106#66896—22no—
107C22⋊(C11⋊C8)—21no—
108#66872—22no—
109#66871—22no—
110#66871—24no—
111C4⋊(C11⋊C8)—21no—
112C4⋊(C11⋊C8)C2312yes—
113C4⋊(C11⋊C8)C2312yes—
114C4×C11⋊C8—21no—
115C4×C11⋊C8—21no—
116C4×C11⋊C8C2312yes—
117#18625—111nomaximal, Sylow
118C24×C11—22no—
119C11×#41—22no—
120C11×#41—22no—
121C11×#41—84no—
122C11×#41—84no—
123C2×Q8×C11—21no—
124C2×Q8×C11C2×D411yescharacteristic
125C2×Q8×C11C2×D412yes—
126C2×D4×C11—21no—
127C2×D4×C11—24no—
128C2×D4×C11—24no—
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11—22no—
133C2×D4×C11—22no—
134C2×D4×C11—44no—
135C2×D4×C11—42no—
136C2×D4×C11—42no—
137C2×D4×C11—82no—
138C2×D4×C11C2×D411yescharacteristic
139C2×D4×C11C2×D414yes—
140C22×C4×C11—24no—
141C22×C4×C11—24no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×Dic11—41no—
149C2×Dic22—22no—
150C2×Dic22—44no—
151C2×Dic22—41no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4C2×D411yescharacteristic
160C11×C4⋊C4C2×D412yes—
161C11×C4⋊C4C2×D411yescharacteristic
162C11×C22⋊C4—24no—
163C11×C22⋊C4—24no—
164C11×C22⋊C4—24no—
165C11×C22⋊C4—24no—
166C11×C22⋊C4—21no—
167C11×C22⋊C4—22no—
168C11×C22⋊C4—21no—
169C11×C22⋊C4—21no—
170C42×C11—21no—
171C42×C11—21no—
172C42×C11—21no—
173C42×C11—22no—
174C42×C11C2×D411yescharacteristic
175C42×C11C2×D411yescharacteristic
176C42×C11C2×D411yescharacteristic
177C42×C11C2411yescharacteristic
178#4324—416no—
179C4⋊Dic11—22no—
180C4⋊Dic11—22no—
181C4⋊Dic11—41no—
182C4⋊Dic11—41no—
183#4318—42no—
184C2×C11⋊C8—24no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8—22no—
188#3508D1111yescharacteristic
189#3230—111no—
190C2×#492—111no—
191#3079—111no—
192#1631—114no—
193#1630—114no—
194#1545—111no—
195#1493—111no—
196#1476—111no—
197C23×C11—24no—
198C23×C11—21no—
199C23×C11—44no—
200C23×C11—82no—
201C23×C11—82no—
202C23×C11#12011yescharacteristic
203Q8×C11—21no—
204Q8×C11—21no—
205Q8×C11—24no—
206Q8×C11—42no—
207D4×C11—21no—
208D4×C11—21no—
209D4×C11—44no—
210D4×C11—42no—
211D4×C11—42no—
212D4×C11—42no—
213D4×C11—44no—
214D4×C11—44no—
215D4×C11—44no—
216D4×C11—82no—
217D4×C11—84no—
218D4×C11—84no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—84no—
230C2×C4×C11—84no—
231C2×C4×C11#12011yescharacteristic
232C2×C4×C11#12011yescharacteristic
233C2×C4×C11#12011yescharacteristic
234C2×C4×C11#13512yes—
235C2×C4×C11#13712yes—
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C2×Dic11—42no—
240C2×Dic11—82no—
241Dic22—44no—
242Dic22—82no—
243C11⋊C8—24no—
244C11⋊C8—42no—
245C11⋊C8—42no—
246C22×SD16—222no—
247#559—21no—
248#559C2×D1112yes—
249#550—21no—
250#550C2×D1112yes—
251#546—22no—
252#546—22no—
253#540—22no—
254#535—21no—
255#533C2×D1111yescharacteristic
256#532—21no—
257#532—21no—
258C2×C4⋊Q8—111no—
259C2×#127C2×D1111yescharacteristic
260#518—21no—
261C4×#41C2×D1111yescharacteristic
262#500—221no—
263#492—114no—
264#492—222no—
265#487—221no—
266#484—222no—
267#477—112no—
268#477—114no—
269#476—112no—
270#475—221no—
271#474—221no—
272#431—111no—
273#428—221no—
274#423—111no—
275#417—221no—
276C2×C4×C8—111no—
277#331—114no—
278Q8⋊C8—112no—
279Q8⋊C8—114no—
280D4⋊C8—112no—
281C22×C11—21no—
282C22×C11—21no—
283C22×C11—41no—
284C22×C11—44no—
285C22×C11—41no—
286C22×C11—44no—
287C22×C11—41no—
288C22×C11—44no—
289C22×C11—164no—
290C22×C11#45212yes—
291C22×C11C2×#12011yescharacteristic
292C4×C11—21no—
293C4×C11—21no—
294C4×C11—41no—
295C4×C11—41no—
296C4×C11—42no—
297C4×C11—41no—
298C4×C11—42no—
299C4×C11#45212yes—
300C4×C11#45312yes—
301C4×C11C2×#13511yescharacteristic
302C4×C11C2×#13711yescharacteristic
303C4×C11#57712yes—
304Dic11—82no—
305C2×#41—22no—
306C2×#41—22no—
307C2×#41C22⋊D1111yescharacteristic
308C22×Q8—221no—
309C22×D4—21no—
310C22×D4—21no—
311C22×D4C22⋊D1112yes—
312C2×SD16—228no—
313C2×SD16—448no—
314C2×M16—221no—
315C22×C8—221no—
316C4⋊Q8—112no—
317C4⋊Q8—221no—
318C4⋊Q8—221no—
319C4⋊Q8—221no—
320C4⋊Q8C22⋊D1111yescharacteristic
321C4⋊Q8C22⋊D1111yescharacteristic
322#127—22no—
323#127—21no—
324#127—21no—
325#127C22⋊D1112yes—
326#127C22×D1112yes—
327#125—21no—
328#124—22no—
329#124—22no—
330#124—22no—
331#123—24no—
332#123—24no—
333C22⋊Q8—21no—
334C22⋊Q8C22⋊D1112yes—
335#121—22no—
336#121—22no—
337#121—22no—
338#121—24no—
339#121—24no—
340#121—22no—
341#120—24no—
342C4×Q8—21no—
343C4×Q8C22⋊D1111yescharacteristic
344C4×Q8C22×D1111yescharacteristic
345C4×Q8C22×D1112yes—
346C4×D4—22no—
347C4×D4—22no—
348C4×D4—22no—
349C4×D4—21no—
350C4×D4—21no—
351C4×D4—22no—
352C4×D4—22no—
353C4×D4—22no—
354C4×D4C22⋊D1111yescharacteristic
355C4×D4C22×D1111yescharacteristic
356#117—21no—
357#117—21no—
358#117C22⋊D1111yescharacteristic
359C2×C4⋊C4—221no—
360C2×C4⋊C4—221no—
361C2×C22⋊C4—24no—
362C2×C42—21no—
363C2×C42C22×D1111yescharacteristic
364#107—222no—
365#107—224no—
366#106—222no—
367C4⋊C8—112no—
368C4⋊C8—112no—
369C4⋊C8—221no—
370#103—222no—
371#103—224no—
372#102—222no—
373C22⋊C8—221no—
374C4×C8—112no—
375C4×C8—221no—
376C4×C8—221no—
377C2×C11—22no—
378C2×C11—81no—
379C2×C11—84no—
380C2×C11C2×#45211yescharacteristic
381C2×C11#300911yescharacteristic
382C2×C11C2×#45311yescharacteristic
383C24—22no—
384#41—22no—
385#41—22no—
386#41—84no—
387#41—84no—
388C2×Q8—21no—
389C2×Q8—222no—
390C2×Q8—444no—
391C2×Q8—441no—
392C2×Q8C2×C22⋊D1111yescharacteristic
393C2×Q8C2×C22⋊D1112yes—
394C2×D4—21no—
395C2×D4—24no—
396C2×D4—24no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—44no—
403C2×D4—42no—
404C2×D4—42no—
405C2×D4—82no—
406C2×D4C2×C22⋊D1111yescharacteristic
407C2×D4C2×C22⋊D1114yes—
408C22×C4—24no—
409C22×C4—24no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—441no—
414C22×C4C2×C22⋊D1111yescharacteristic
415C22×C4C2×C22⋊D1111yescharacteristic
416C22×C4C2×C22⋊D1111yescharacteristic
417SD16—4416no—
418M16—442no—
419C2×C8—224no—
420C2×C8—222no—
421C2×C8—222no—
422C2×C8—222no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—22no—
428C4⋊C4—21no—
429C4⋊C4—22no—
430C4⋊C4—222no—
431C4⋊C4—222no—
432C4⋊C4—441no—
433C4⋊C4—441no—
434C4⋊C4C2×C22⋊D1111yescharacteristic
435C4⋊C4C2×C22⋊D1111yescharacteristic
436C4⋊C4C2×C22⋊D1112yes—
437C22⋊C4—24no—
438C22⋊C4—24no—
439C22⋊C4—24no—
440C22⋊C4—24no—
441C22⋊C4—21no—
442C22⋊C4—22no—
443C22⋊C4—21no—
444C22⋊C4—21no—
445C42—21no—
446C42—21no—
447C42—21no—
448C42—22no—
449C42C2×C22⋊D1111yescharacteristic
450C42C2×C22⋊D1111yescharacteristic
451C42C2×C22⋊D1111yescharacteristic
452C42C23×D1111yescharacteristic
453C11#1862511yescharacteristic, complemented, Sylow
454C23—24no—
455C23—21no—
456C23—44no—
457C23—82no—
458C23—82no—
459C23#6700611yescharacteristic
460Q8—21no—
461Q8—21no—
462Q8—24no—
463Q8—42no—
464Q8—444no—
465Q8—882no—
466D4—21no—
467D4—21no—
468D4—44no—
469D4—42no—
470D4—42no—
471D4—42no—
472D4—44no—
473D4—44no—
474D4—44no—
475D4—82no—
476D4—84no—
477D4—84no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—84no—
489C2×C4—84no—
490C2×C4—442no—
491C2×C4—882no—
492C2×C4#6700312yes—
493C2×C4#6700412yes—
494C2×C4#6700611yescharacteristic
495C2×C4#6700611yescharacteristic
496C2×C4#6700611yescharacteristic
497C2×C4C22×C22⋊D1111yescharacteristic
498C2×C4C22×C22⋊D1111yescharacteristic
499C2×C4C22×C22⋊D1111yescharacteristic
500C8—224no—
501C8—442no—
502C8—442no—
503C22—21no—
504C22—21no—
505C22—41no—
506C22—44no—
507C22—41no—
508C22—44no—
509C22—41no—
510C22—44no—
511C22—164no—
512C22#1062285212yes—
513C22C2×#6700611yescharacteristic
514C4—21no—
515C4—21no—
516C4—41no—
517C4—41no—
518C4—42no—
519C4—41no—
520C4—42no—
521C4—882no—
522C4#1062285212yes—
523C4#1062285412yes—
524C4C2×#6700311yescharacteristic
525C4C2×#6700411yescharacteristic
526C4#1062336712yes—
527C2—22no—
528C2—84no—
529C2—81no—
530C2C2×#1062285211yescharacteristic
531C2#1307789311yescharacteristic
532C2C2×#1062285411yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3508C2
socleC22×C11C2×#120
hypercenter#3508D11
hypocenterC11#18625
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3508

Complements

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

NH ≅ G/Ntype
1. #13079764C2semidirect
2. C2×#10622689C2semidirect
3. #13078431C2semidirect
4. #13067743C2semidirect
5. #13067737C2semidirect
6. #13067284C2semidirect
7. #13067071C2semidirect
8. #13066998C2semidirect
32. #10622634C22semidirect
33. #10622634C22semidirect
35. #10622621C22semidirect
42. Q8⋊(C11⋊C8)C22semidirect
43. Q8⋊(C11⋊C8)C22semidirect
44. D4⋊(C11⋊C8)C22semidirect
453. C11#18625semidirect

Maximal subgroups

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

subgroupindex
#130797642
C2×#106226892
#130784312
#130677432
#130677372
#130672842
#130670712
#130669982
C11×#35082
#1862511