Finite Group Databasebeta

← #14736631

Subgroups — #14736631

Order 2816.

766 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079069C211yesmaximal, characteristic
2C2×#10622640C211yesmaximal, characteristic, complemented
3Q8×#4318C211yesmaximal, characteristic, complemented
4#13068098C212yesmaximal, complemented
5#13068090C212yesmaximal, complemented
6#13067974C212yesmaximal, complemented
7#13067966C212yesmaximal, complemented
8#13067369C211yesmaximal, characteristic, complemented
9#13067293C211yesmaximal, characteristic, complemented
10#13067283C211yesmaximal, characteristic, complemented
11C11×#3103C211yesmaximal, characteristic, complemented
12C11×#532C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×#67002—21no—
15C2×#67002—21no—
16C22×#4325—21no—
17C2×#66927C2211yescharacteristic
18C11×#481—21no—
19C11×#475C2211yescharacteristic, complemented
20C11×#475C2211yescharacteristic, complemented
21C11×#460C2211yescharacteristic, complemented
22C11×#460C2211yescharacteristic, complemented
23C11×#448—21no—
24C4×C11×SD16—21no—
25C4×C11×SD16—21no—
26C11×#431C2211yescharacteristic
27#10622698C2212yes—
28#10622686C2212yes—
29#10622671—22no—
30#10622640—21no—
31#10622640—21no—
32#10622640C2212yes—
33#10622640C2212yes—
34#10622637—22no—
35#10622637C2212yescomplemented
36Q8×C11⋊C8C2212yescomplemented
37C2×#66873—21no—
38#10622537—21no—
39#10622537C2211yescharacteristic
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C4×#4318—21no—
42C4×#4318C2211yescharacteristic
43#10622185C2212yescomplemented
44#10622182C2212yescomplemented
45#10622123C2212yes—
46#10622123C2212yes—
47#10622118C2212yescomplemented
48#10622117C2212yescomplemented
49C2×C11×#41—21no—
50C22×Q8×C11D411yescharacteristic
51C22×D44—21no—
52C22×D44—21no—
53C22×D44—21no—
54C2×C11×SD16—21no—
55C2×C11×SD16—21no—
56C11×C4⋊Q8C2311yescharacteristic
57C11×#127C2311yescharacteristic
58C11×#124—21no—
59C11×#121—21no—
60C11×#121—21no—
61C4×Q8×C11—21no—
62C4×Q8×C11—21no—
63C4×Q8×C11D411yescharacteristic
64C4×Q8×C11D411yescharacteristic
65C4×Q8×C11C2311yescharacteristic
66C4×Q8×C11C2311yescharacteristic
67C4×D4×C11—21no—
68C4×D4×C11—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4D411yescharacteristic
71C2×C42×C11—21no—
72C2×C42×C11C2311yescharacteristic
73#67002—44no—
74#67002—44no—
75C2×#4325—22no—
76C2×#4325—22no—
77C2×#4325—22no—
78C2×#4325—22no—
79C2×#4325—44no—
80C2×#4323—22no—
81C2×#4323—22no—
82C2×#4318—21no—
83C2×#4318D411yescharacteristic
84C2×#4318D411yescharacteristic
85C22×C11⋊C8—21no—
86#66927—21no—
87#66927—21no—
88#66927—21no—
89#66927C2312yes—
90C11×#106—21no—
91C11×#106—21no—
92C11×C4⋊C8C2311yescharacteristic
93C11×C4⋊C8C2311yescharacteristic
94C11×#103—21no—
95C11×#103—21no—
96C11×#102—21no—
97C11×#102—21no—
98C11×C22⋊C8—21no—
99C4×C8×C11—21no—
100#66873—22no—
101#66873—22no—
102C4⋊(C11⋊C8)—21no—
103C4⋊(C11⋊C8)—21no—
104C4⋊(C11⋊C8)—22no—
105C4⋊(C11⋊C8)—22no—
106C4⋊(C11⋊C8)C2312yes—
107C4⋊(C11⋊C8)C2312yes—
108#66867—22no—
109#66867D412yes—
110C4×C11⋊C8—22no—
111C4×C11⋊C8C2312yes—
112#19170—111nomaximal, Sylow
113C23×D11—41no—
114C11×#41—42no—
115C11×#41—42no—
116C2×Q8×C11—21no—
117C2×Q8×C11—22no—
118C2×Q8×C11—21no—
119C2×Q8×C11—41no—
120C2×Q8×C11C2×D411yescharacteristic
121C2×Q8×C11C2×D411yescharacteristic
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—41no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—41no—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11#4111yescharacteristic
132C2×D44—22no—
133C2×D44—22no—
134C2×D44—22no—
135C2×D44—42no—
136C2×D44—42no—
137C2×D44—41no—
138C2×D44—41no—
139C2×D44—41no—
140C2×D44—42no—
141C2×D44—42no—
142C2×D44—82no—
143C11×SD16—42no—
144C11×SD16—42no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4C2×D411yescharacteristic
155C11×C4⋊C4C2×D411yescharacteristic
156C11×C22⋊C4—41no—
157C11×C22⋊C4—41no—
158C42×C11—21no—
159C42×C11—21no—
160C42×C11—21no—
161C42×C11—21no—
162C42×C11C2×D411yescharacteristic
163C42×C11C2×D411yescharacteristic
164C42×C11#4111yescharacteristic
165C42×C11C2411yescharacteristic
166#4325—44no—
167#4325—44no—
168#4325—44no—
169#4325—44no—
170#4323—44no—
171#4323—44no—
172#4318—22no—
173#4318—42no—
174#4318SD1614yescomplemented
175C2×C11⋊C8—22no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—42no—
178C2×C11⋊C8C2×D412yes—
179C2×C11⋊C8C2×D412yes—
180#3151—111no—
181#3103D1111yescharacteristic, complemented
182C2×#460—111no—
183Q8×M16—111no—
184#1688—112no—
185#1686—112no—
186#1668—112no—
187#1666—112no—
188#1565—111no—
189#1547—111no—
190#1545—111no—
191C23×C11—41no—
192C23×C11#12111yescharacteristic
193C22×D11—42no—
194C22×D11—82no—
195C22×D11—82no—
196C22×D11—82no—
197Q8×C11—21no—
198Q8×C11—21no—
199Q8×C11—21no—
200Q8×C11—42no—
201Q8×C11—41no—
202Q8×C11—41no—
203Q8×C11AGL(1,ℤ/8)12yescomplemented
204D4×C11—41no—
205D4×C11—41no—
206D4×C11—41no—
207D4×C11—41no—
208D4×C11—81no—
209D4×C11—82no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—41no—
217C2×C4×C11—42no—
218C2×C4×C11—41no—
219C2×C4×C11—81no—
220C2×C4×C11—82no—
221C2×C4×C11#12111yescharacteristic
222C2×C4×C11#12111yescharacteristic
223C2×C4×C11#12111yescharacteristic
224C2×C4×C11C2×SD1612yes—
225C2×C4×C11AGL(1,ℤ/8)12yes—
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C2×#4111yescharacteristic
229D44—42no—
230D44—42no—
231D44—42no—
232D44—42no—
233D44—82no—
234D44—82no—
235D44—82no—
236D44—82no—
237C8×C11—41no—
238C8×C11—41no—
239C11⋊C8—22no—
240C11⋊C8—42no—
241C11⋊C8—42no—
242C11⋊C8C2×SD1614yescomplemented
243C2×AGL(1,ℤ/8)—221no—
244C2×AGL(1,ℤ/8)—221no—
245C22×SD16—221no—
246#532C2×D1111yescharacteristic
247C2×#127—111no—
248C2×C4×Q8C2×D1111yescharacteristic
249#496—222no—
250#493—112no—
251#492—112no—
252#481—21no—
253#475C2×D1111yescharacteristic, complemented
254#475C2×D1111yescharacteristic, complemented
255#460—112no—
256#460—112no—
257#460—221no—
258#460—221no—
259#460C2×D1111yescharacteristic, complemented
260#460C2×D1111yescharacteristic, complemented
261#448—21no—
262#446—112no—
263#446—222no—
264C8×Q8—112no—
265C4×SD16—21no—
266C4×SD16—21no—
267#431C2×D1111yescharacteristic
268#423—111no—
269#423—221no—
270C2×C4⋊C8—111no—
271C2×#102—221no—
272C4×M16—111no—
273C4×M16—221no—
274#335—112no—
275#334—112no—
276#332—112no—
277#331—112no—
278#331—112no—
279#331—112no—
280C22×C11—21no—
281C22×C11—21no—
282C22×C11—81no—
283C22×C11—81no—
284C22×C11—81no—
285C22×C11#46012yes—
286C22×C11C2×#12111yescharacteristic
287C2×D11—82no—
288C2×D11—82no—
289C2×D11—82no—
290C2×D11—164no—
291C4×C11—21no—
292C4×C11—22no—
293C4×C11—21no—
294C4×C11—21no—
295C4×C11—41no—
296C4×C11—41no—
297C4×C11—41no—
298C4×C11—81no—
299C4×C11#46012yes—
300C4×C11C22×SD1611yescharacteristic
301C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
302C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
303C4×C11#57511yescharacteristic
304C2×#41—21no—
305C22×Q8C22⋊D1111yescharacteristic
306C22×D4—221no—
307C22×D4—221no—
308C22×D4—221no—
309AGL(1,ℤ/8)—444no—
310AGL(1,ℤ/8)—444no—
311C2×SD16—21no—
312C2×SD16—21no—
313C2×SD16—222no—
314C2×SD16—222no—
315C2×SD16—222no—
316C2×SD16—222no—
317C2×SD16—444no—
318C2×D8—222no—
319C2×D8—222no—
320C2×M16—111no—
321C2×M16—111no—
322C2×M16—221no—
323C22×C8—221no—
324C4⋊Q8C22×D1111yescharacteristic
325#127—112no—
326#127—221no—
327#127—221no—
328#127—221no—
329#127C22×D1111yescharacteristic
330#124—21no—
331#121—21no—
332#121—21no—
333C4×Q8—21no—
334C4×Q8—21no—
335C4×Q8C22⋊D1111yescharacteristic
336C4×Q8C22⋊D1111yescharacteristic
337C4×Q8C22×D1111yescharacteristic
338C4×Q8C22×D1111yescharacteristic
339C4×D4—21no—
340C4×D4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4C22⋊D1111yescharacteristic
343C2×C42—21no—
344C2×C42C22×D1111yescharacteristic
345#106—21no—
346#106—21no—
347C4⋊C8—112no—
348C4⋊C8—112no—
349C4⋊C8—222no—
350C4⋊C8—222no—
351C4⋊C8—221no—
352C4⋊C8—221no—
353C4⋊C8C22×D1111yescharacteristic
354C4⋊C8C22×D1111yescharacteristic
355#103—21no—
356#103—21no—
357#102—21no—
358#102—21no—
359#102—222no—
360#102—222no—
361C22⋊C8—21no—
362#97—112no—
363#97—222no—
364C4×C8—21no—
365C4×C8—112no—
366C4×C8—222no—
367C2×C11—22no—
368C2×C11—161no—
369C2×C11C2×#46011yescharacteristic
370C2×C11#305511yescharacteristic
371C2×C11#306811yescharacteristic
372D11—162no—
373C24—441no—
374#41—42no—
375#41—42no—
376C2×Q8—21no—
377C2×Q8—22no—
378C2×Q8—21no—
379C2×Q8—41no—
380C2×Q8C2×C22⋊D1111yescharacteristic
381C2×Q8C2×C22⋊D1111yescharacteristic
382C2×D4—21no—
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—41no—
386C2×D4—222no—
387C2×D4—222no—
388C2×D4—222no—
389C2×D4—442no—
390C2×D4—442no—
391C2×D4—442no—
392C2×D4—442no—
393C2×D4—441no—
394C2×D4—441no—
395C2×D4—441no—
396C2×D4—882no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—41no—
400C22×C4D4×D1111yescharacteristic
401C22×C4#434111yescharacteristic
402C22×C4C2×C22⋊D1111yescharacteristic
403SD16—42no—
404SD16—42no—
405SD16—444no—
406SD16—444no—
407SD16—444no—
408SD16—444no—
409D8—444no—
410D8—444no—
411M16—114no—
412M16—222no—
413M16—442no—
414C2×C8—21no—
415C2×C8—21no—
416C2×C8—112no—
417C2×C8—112no—
418C2×C8—222no—
419C2×C8—222no—
420C2×C8—442no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4C2×C22⋊D1111yescharacteristic
429C4⋊C4C2×C22⋊D1111yescharacteristic
430C22⋊C4—41no—
431C22⋊C4—41no—
432C42—21no—
433C42—21no—
434C42—21no—
435C42—21no—
436C42D4×D1111yescharacteristic
437C42#434111yescharacteristic
438C42C2×C22⋊D1111yescharacteristic
439C42C23×D1111yescharacteristic
440C11#1917011yescharacteristic, complemented, Sylow
441C23—41no—
442C23—442no—
443C23—882no—
444C23—882no—
445C23—882no—
446C23#6699211yescharacteristic
447Q8—21no—
448Q8—21no—
449Q8—21no—
450Q8—42no—
451Q8—41no—
452Q8—41no—
453Q8#6700212yescomplemented
454D4—41no—
455D4—41no—
456D4—41no—
457D4—41no—
458D4—81no—
459D4—82no—
460D4—442no—
461D4—442no—
462D4—442no—
463D4—442no—
464D4—882no—
465D4—882no—
466D4—882no—
467D4—882no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—41no—
477C2×C4—81no—
478C2×C4—82no—
479C2×C4SD16×D1112yes—
480C2×C4#6696712yes—
481C2×C4#6699211yescharacteristic
482C2×C4#6699211yescharacteristic
483C2×C4#6699211yescharacteristic
484C2×C4C2×D4×D1111yescharacteristic
485C2×C4C2×#434111yescharacteristic
486C2×C4C22×C22⋊D1111yescharacteristic
487C8—41no—
488C8—41no—
489C8—114no—
490C8—222no—
491C8—442no—
492C8—442no—
493C22—21no—
494C22—21no—
495C22—81no—
496C22—81no—
497C22—81no—
498C22—882no—
499C22—882no—
500C22—882no—
501C22—1764no—
502C22#1062277612yes—
503C22C2×#6699211yescharacteristic
504C4—21no—
505C4—21no—
506C4—21no—
507C4—22no—
508C4—41no—
509C4—41no—
510C4—41no—
511C4—81no—
512C4#1062277612yes—
513C4C2×SD16×D1111yescharacteristic
514C4C2×#6696711yescharacteristic
515C4C2×#6700211yescharacteristic
516C4#1062335311yescharacteristic
517C2—22no—
518C2—161no—
519C2—1762no—
520C2C2×#1062277611yescharacteristic
521C2#1307823711yescharacteristic
522C2#1307834611yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3103C2
socleC22×C11C2×#121
prime radical#13079069C2
hypercenter#3103D11
hypocenterC11#19170
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3103

Complements

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

NH ≅ G/Ntype
2. C2×#10622640C2semidirect
3. Q8×#4318C2semidirect
4. #13068098C2semidirect
5. #13068090C2semidirect
6. #13067974C2semidirect
7. #13067966C2semidirect
8. #13067369C2semidirect
9. #13067293C2semidirect
10. #13067283C2semidirect
11. C11×#3103C2semidirect
19. C11×#475C22semidirect
20. C11×#475C22semidirect
21. C11×#460C22semidirect
22. C11×#460C22semidirect
35. #10622637C22semidirect
36. Q8×C11⋊C8C22semidirect
43. #10622185C22semidirect
44. #10622182C22semidirect
47. #10622118C22semidirect
48. #10622117C22semidirect
174. #4318SD16semidirect
181. #3103D11semidirect
203. Q8×C11AGL(1,ℤ/8)semidirect
242. C11⋊C8C2×SD16semidirect
253. #475C2×D11semidirect
254. #475C2×D11semidirect
259. #460C2×D11semidirect
260. #460C2×D11semidirect
440. C11#19170semidirect
453. Q8#67002semidirect

Maximal subgroups

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

subgroupindex
#130790692
C2×#106226402
Q8×#43182
#130680982
#130680902
#130679742
#130679662
#130673692
#130672932
#130672832
C11×#31032
#1917011