Finite Group Databasebeta

← #14722242

Subgroups — #14722242

Order 2816.

1004 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082490C211yesmaximal, characteristic
2#13077725C211yesmaximal, characteristic, complemented
3#13077281C211yesmaximal, characteristic, complemented
4#13067318C212yesmaximal, complemented
5#13067308C212yesmaximal, complemented
6#13067304C211yesmaximal, characteristic, complemented
7#13067284C211yesmaximal, characteristic, complemented
8#13067275C212yesmaximal, complemented
9#13067274C211yesmaximal, characteristic, complemented
10#13067262C212yesmaximal, complemented
11C2×C11×#331C211yesmaximal, characteristic, complemented
12C2×C11×#127C2211yescharacteristic
13#10623337—22no—
14#10623337C414yes—
15#10623336—21no—
16#10623329—21no—
17#10623250—22no—
18#10623249—21no—
19#10623249C412yes—
20#10623247C2212yes—
21#10623247C2212yes—
22#10623244—21no—
23#10623244C412yes—
24C4×#4339C2211yescharacteristic
25#10623001C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28#10622723—21no—
29C8×C22⋊D11—22no—
30#10622714—21no—
31#10622538C2211yescharacteristic
32#10622537C2211yescharacteristic
33#10622453—22no—
34#10622448C2212yescomplemented
35#10622447—21no—
36#10622446C2212yescomplemented
37#10622446C2212yescomplemented
38D11×C4⋊C8C2212yescomplemented
39#10622443—21no—
40C11×#331C2212yes—
41C11×#331C2212yes—
42#10622182C2212yes—
43#10622182C2212yes—
44#10622124C2211yescharacteristic, complemented
45#10622124C2211yescharacteristic, complemented
46#10622120C2212yescomplemented
47#10622119C2211yescharacteristic, complemented
48#10622119C2211yescharacteristic, complemented
49#10622119C2212yescomplemented
50C22×D4×C11—21no—
51C22×D4×C11—21no—
52C22×D4×C11C2×C412yes—
53C2×#4341—22no—
54C2×#4341C2×C414yes—
55C2×#4339D411yescharacteristic
56C22×C8×C11—21no—
57C22×C8×C11—21no—
58C11×#127—21no—
59C11×#127—21no—
60C11×#127C2×C412yes—
61C11×#127C2312yes—
62C2×C42×C11C2311yescharacteristic
63#67006—24no—
64C2×C22⋊Dic11—24no—
65#66993—22no—
66#66992—24no—
67#66992—24no—
68#66991—22no—
69#66991—22no—
70#66991—22no—
71#66991C2×C414yes—
72#66989—22no—
73#66989—22no—
74#66989C2×C414yes—
75#66988—24no—
76#66988—24no—
77D4×Dic11—22no—
78D4×Dic11—22no—
79D4×Dic11—22no—
80D4×Dic11—22no—
81D4×Dic11—22no—
82D4×Dic11C2×C414yes—
83C4×C22⋊D11C2×C412yes—
84C4×C22⋊D11D412yes—
85#66979—21no—
86#66979D411yescharacteristic
87#66977—21no—
88#66977C2×C412yes—
89C2×#4318—21no—
90C2×C8×D11—22no—
91C4×D44C2×C411yescharacteristic
92C4×D44D411yescharacteristic
93#66925D412yes—
94C42×D11C2312yes—
95#66923—21no—
96#66922C2311yescharacteristic
97#66922C2311yescharacteristic
98C4×Dic22—21no—
99C4×Dic22C2×C412yes—
100C4×Dic22C2×C411yescharacteristic
101C4×Dic22D411yescharacteristic
102C11×C4⋊C8—21no—
103C11×C4⋊C8—21no—
104C11×C4⋊C8C2312yes—
105C11×C4⋊C8C2311yescharacteristic
106C11×C4⋊C8C2311yescharacteristic
107C22⋊(C11⋊C8)—21no—
108(C2×D11)⋊C8—22no—
109(C2×D11)⋊C8—22no—
110(C2×D11)⋊C8—22no—
111#66879—22no—
112Dic11⋊C8—22no—
113C8×Dic11—22no—
114C8×Dic11—22no—
115C4⋊(C11⋊C8)—21no—
116C4⋊(C11⋊C8)C2312yes—
117C4⋊(C11⋊C8)C2311yescharacteristic
118C4⋊(C11⋊C8)C2311yescharacteristic
119C4×C11⋊C8—21no—
120#17724—111nomaximal, Sylow
121C24×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—42no—
128C2×D4×C11—42no—
129C2×D4×C11—81no—
130C2×D4×C11—81no—
131C2×D4×C11—82no—
132C2×D4×C11C22×C414yes—
133C22×C4×C11C22×C411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C2×C22⋊D11—24no—
137C2×C22⋊D11—24no—
138C2×C22⋊D11C22⋊C412yes—
139C22×Dic11—24no—
140C22×Dic11—24no—
141#4341—82no—
142#4341—82no—
143#4341—84no—
144#4339—22no—
145#4339—22no—
146C2×D44C22⋊C411yescharacteristic
147C2×C4×D11C22×C412yes—
148C2×C4×D11C2×D412yes—
149C2×C4×D11C2×D412yes—
150C2×Dic22—21no—
151C2×Dic22C22⋊C411yescharacteristic
152C2×Dic22C22×C412yes—
153C2×C8×C11—21no—
154C2×C8×C11—22no—
155C2×C8×C11—21no—
156C2×C8×C11—42no—
157C2×C8×C11—81no—
158C42×C11C22×C411yescharacteristic
159C42×C11C2×D411yescharacteristic
160C42×C11C2×D411yescharacteristic
161C42×C11C2411yescharacteristic
162C22⋊Dic11—24no—
163C22⋊Dic11—24no—
164C22⋊Dic11—24no—
165C22⋊Dic11—24no—
166C22⋊Dic11—22no—
167C22⋊Dic11C22⋊C412yes—
168(C2×D11)⋊C4C22⋊C412yes—
169(C2×D11)⋊C4C22⋊C412yes—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11C22⋊C411yescharacteristic
174C4⋊Dic11C22⋊C411yescharacteristic
175C4⋊Dic11C22×C412yes—
176Dic11⋊C4—22no—
177Dic11⋊C4—22no—
178Dic11⋊C4C22⋊C412yes—
179Dic11⋊C4C22⋊C412yes—
180C4×Dic11—22no—
181C4×Dic11C22×C412yes—
182C4×Dic11C2×D412yes—
183C4×Dic11C2×D412yes—
184#4318—42no—
185C2×C11⋊C8—21no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—22no—
188C8×D11—82no—
189#3508—111no—
190#2988—111no—
191#2925—111no—
192#1553—112no—
193#1551—112no—
194#1550—111no—
195#1545—111no—
196#1543—112no—
197#1542—111no—
198#1540—112no—
199C2×#331D1111yescharacteristic, complemented
200C23×C11—24no—
201C23×C11—44no—
202C23×C11—82no—
203C23×C11—82no—
204C23×C11C2×C22⋊C411yescharacteristic
205C22×D11C2×C22⋊C412yes—
206D4×C11—44no—
207D4×C11—42no—
208D4×C11—42no—
209D4×C11—42no—
210D4×C11—42no—
211D4×C11—44no—
212D4×C11—82no—
213D4×C11—82no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—41no—
217C2×C4×C11C2×C22⋊C411yescharacteristic
218C2×C4×C11C2×C22⋊C411yescharacteristic
219C2×C4×C11C2×C22⋊C411yescharacteristic
220C2×C4×C11#13512yes—
221C2×C4×C11#13512yes—
222C2×C4×C11C23×C411yescharacteristic
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C22×D411yescharacteristic
225C22⋊D11—24no—
226C22⋊D11—84no—
227C22⋊D11—84no—
228C2×Dic11—22no—
229C2×Dic11—22no—
230C2×Dic11—84no—
231C2×Dic11—84no—
232C2×Dic11C2×C22⋊C412yes—
233C2×Dic11C2×C22⋊C412yes—
234C2×Dic11C2×C22⋊C412yes—
235D44—22no—
236C4×D11—22no—
237C4×D11—22no—
238C4×D11—22no—
239C4×D11—22no—
240C4×D11—42no—
241Dic22—22no—
242Dic22—41no—
243Dic22—41no—
244Dic22—42no—
245C8×C11—41no—
246C8×C11—41no—
247C8×C11—42no—
248C11⋊C8—42no—
249C11⋊C8—41no—
250C11⋊C8—41no—
251#559—112no—
252#559—221no—
253#550—112no—
254#550—221no—
255#546—114no—
256#546—222no—
257#540—222no—
258#535—221no—
259#533—111no—
260#532—112no—
261#532—112no—
262C2×#127C2×D1111yescharacteristic
263#518—221no—
264C4×#41—111no—
265C8×Q8—221no—
266C8×D4—221no—
267C8×D4—222no—
268#433—222no—
269#432—112no—
270#431—111no—
271#431—112no—
272#431—112no—
273#423—111no—
274C2×C4⋊C8—112no—
275C2×C4⋊C8C2×D1111yescharacteristic
276C2×C4⋊C8C2×D1111yescharacteristic
277#408—221no—
278#405—221no—
279#333—111no—
280#333—111no—
281#333—112no—
282#332—111no—
283#332—112no—
284#332—111no—
285#331—112no—
286#331—112no—
287#331C2×D1112yes—
288#331C2×D1112yes—
289C22×C11—21no—
290C22×C11—21no—
291C22×C11—44no—
292C22×C11—44no—
293C22×C11—44no—
294C22×C11—164no—
295C22×C11#41612yes—
296C22×C11C22×C22⋊C411yescharacteristic
297C2×D11—22no—
298C2×D11—22no—
299C2×D11—22no—
300C4×C11—21no—
301C4×C11—21no—
302C4×C11—21no—
303C4×C11#41612yes—
304C4×C11C2×#13511yescharacteristic
305C4×C11C2×#13511yescharacteristic
306C4×C11#57611yescharacteristic
307C4×C11#57711yescharacteristic
308Dic11—22no—
309Dic11—22no—
310Dic11—22no—
311Dic11—42no—
312Dic11—42no—
313C2×#41—111no—
314C2×#41—114no—
315C2×#41—222no—
316C22×D4—21no—
317C22×D4—21no—
318C22×D4C4×D1112yes—
319C2×M16—221no—
320C22×C8—21no—
321C22×C8—21no—
322C22×C8—222no—
323C4⋊Q8—111no—
324C4⋊Q8—111no—
325#127—21no—
326#127—21no—
327#127—222no—
328#127C4×D1112yes—
329#127C22×D1112yes—
330#125—221no—
331#124—114no—
332#124—222no—
333#124—222no—
334#123—224no—
335#123—224no—
336C22⋊Q8—112no—
337C22⋊Q8—221no—
338#121—114no—
339#121—224no—
340#121—224no—
341#121—222no—
342#121—222no—
343#121—222no—
344#120—224no—
345C4×Q8—111no—
346C4×Q8—111no—
347C4×Q8—112no—
348C4×Q8—221no—
349C4×D4—112no—
350C4×D4—112no—
351C4×D4—114no—
352C4×D4—111no—
353C4×D4—111no—
354C4×D4—222no—
355C4×D4—222no—
356C4×D4—222no—
357C4×D4—222no—
358C4×D4—222no—
359#117—111no—
360#117—112no—
361#117—221no—
362C2×C22⋊C4—224no—
363C2×C42—112no—
364C2×C42C22×D1111yescharacteristic
365C4⋊C8—21no—
366C4⋊C8—21no—
367C4⋊C8—111no—
368C4⋊C8—112no—
369C4⋊C8—111no—
370C4⋊C8—222no—
371C4⋊C8—221no—
372C4⋊C8C22×D1112yes—
373C4⋊C8C22×D1111yescharacteristic
374C4⋊C8C22×D1111yescharacteristic
375C22⋊C8—222no—
376C22⋊C8—222no—
377C22⋊C8—222no—
378C22⋊C8—221no—
379#97—222no—
380C4×C8—222no—
381C4×C8—222no—
382C4×C8—221no—
383C2×C11—22no—
384C2×C11—84no—
385C2×C11#288811yescharacteristic
386C2×C11C2×#41611yescharacteristic
387C2×C11#289711yescharacteristic
388D11—42no—
389C24—22no—
390#41—222no—
391#41—222no—
392#41—882no—
393#41—882no—
394#41—884no—
395C2×Q8—111no—
396C2×Q8—112no—
397C2×Q8—221no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—42no—
404C2×D4—42no—
405C2×D4—81no—
406C2×D4—81no—
407C2×D4—82no—
408C2×D4—112no—
409C2×D4—111no—
410C2×D4—224no—
411C2×D4—224no—
412C2×D4C2×C4×D1114yes—
413C22×C4—112no—
414C22×C4—112no—
415C22×C4—112no—
416C22×C4—224no—
417C22×C4—224no—
418C22×C4C2×C4×D1111yescharacteristic
419C22×C4D4×D1111yescharacteristic
420C22×C4D4×D1111yescharacteristic
421M16—442no—
422C2×C8—21no—
423C2×C8—22no—
424C2×C8—21no—
425C2×C8—42no—
426C2×C8—81no—
427C2×C8—221no—
428C2×C8—222no—
429C2×C8—221no—
430C2×C8—882no—
431C4⋊C4—111no—
432C4⋊C4—111no—
433C4⋊C4—112no—
434C4⋊C4—112no—
435C4⋊C4—112no—
436C4⋊C4—222no—
437C4⋊C4—222no—
438C4⋊C4—221no—
439C4⋊C4—221no—
440C4⋊C4—221no—
441C22⋊C4—112no—
442C22⋊C4—112no—
443C22⋊C4—112no—
444C22⋊C4—224no—
445C22⋊C4—224no—
446C22⋊C4—224no—
447C22⋊C4—224no—
448C22⋊C4—222no—
449C42—112no—
450C42—112no—
451C42—112no—
452C42—222no—
453C42C2×C4×D1111yescharacteristic
454C42D4×D1111yescharacteristic
455C42D4×D1111yescharacteristic
456C42C23×D1111yescharacteristic
457C11#1772411yescharacteristic, complemented, Sylow
458C23—24no—
459C23—44no—
460C23—82no—
461C23—82no—
462C23—112no—
463C23C22⋊C4×D1111yescharacteristic
464Q8—222no—
465Q8—442no—
466Q8—441no—
467Q8—441no—
468D4—44no—
469D4—42no—
470D4—42no—
471D4—42no—
472D4—42no—
473D4—44no—
474D4—82no—
475D4—82no—
476D4—224no—
477D4—222no—
478D4—884no—
479D4—884no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—41no—
483C2×C4—112no—
484C2×C4—112no—
485C2×C4—112no—
486C2×C4—222no—
487C2×C4—222no—
488C2×C4—222no—
489C2×C4—222no—
490C2×C4—222no—
491C2×C4—222no—
492C2×C4—442no—
493C2×C4—884no—
494C2×C4—884no—
495C2×C4C22⋊C4×D1111yescharacteristic
496C2×C4C22⋊C4×D1111yescharacteristic
497C2×C4C22⋊C4×D1111yescharacteristic
498C2×C4#6696512yes—
499C2×C4#6696912yes—
500C2×C4C22×C4×D1111yescharacteristic
501C2×C4C2×D4×D1111yescharacteristic
502C2×C4C2×D4×D1111yescharacteristic
503C8—41no—
504C8—41no—
505C8—42no—
506C8—441no—
507C8—442no—
508C8—441no—
509C22—21no—
510C22—21no—
511C22—44no—
512C22—44no—
513C22—44no—
514C22—164no—
515C22—222no—
516C22—222no—
517C22—222no—
518C22#1062238512yes—
519C22C2×C22⋊C4×D1111yescharacteristic
520C4—21no—
521C4—21no—
522C4—21no—
523C4—222no—
524C4—222no—
525C4—222no—
526C4—442no—
527C4—442no—
528C4#1062238512yes—
529C4C2×#6696511yescharacteristic
530C4#1062328811yescharacteristic
531C4C2×#6696911yescharacteristic
532C4#1062329311yescharacteristic
533C2—22no—
534C2—84no—
535C2—442no—
536C2#1307709211yescharacteristic
537C2C2×#1062238511yescharacteristic
538C2#1307713711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC2×C11×#331C2
socleC22×C11C22×C22⋊C4
prime radical#13082490C2
cosocleC42×C11C24
hypercenterC2×#331D11
hypocenterC11#17724
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#331

Complements

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

NH ≅ G/Ntype
2. #13077725C2semidirect
3. #13077281C2semidirect
4. #13067318C2semidirect
5. #13067308C2semidirect
6. #13067304C2semidirect
7. #13067284C2semidirect
8. #13067275C2semidirect
9. #13067274C2semidirect
10. #13067262C2semidirect
11. C2×C11×#331C2semidirect
34. #10622448C22semidirect
36. #10622446C22semidirect
37. #10622446C22semidirect
38. D11×C4⋊C8C22semidirect
44. #10622124C22semidirect
45. #10622124C22semidirect
46. #10622120C22semidirect
47. #10622119C22semidirect
48. #10622119C22semidirect
49. #10622119C22semidirect
199. C2×#331D11semidirect
457. C11#17724semidirect

Maximal subgroups

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

subgroupindex
#130824902
#130777252
#130772812
#130673182
#130673082
#130673042
#130672842
#130672752
#130672742
#130672622
C2×C11×#3312
#1772411