Finite Group Databasebeta

← #14736623

Subgroups — #14736623

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#13078643C211yesmaximal, characteristic, complemented
2C2×#10622688C211yesmaximal, characteristic, complemented
3M16×Dic22C211yesmaximal, characteristic, complemented
4#13068097C212yesmaximal, complemented
5#13068085C212yesmaximal, complemented
6#13067973C212yesmaximal, complemented
7#13067961C212yesmaximal, complemented
8#13067368C211yesmaximal, characteristic, complemented
9#13067293C211yesmaximal, characteristic, complemented
10#13067284C211yesmaximal, characteristic, complemented
11C11×#3151C211yesmaximal, characteristic
12C2×C11×AGL(1,ℤ/8)—21no—
13C2×C11×AGL(1,ℤ/8)—21no—
14C11×#532C2211yescharacteristic
15C2×C11×#127C2211yescharacteristic
16C22×#4324—21no—
17C2×C4×Dic22C2211yescharacteristic
18C11×#496—22no—
19C11×#493C2212yes—
20C11×#492C2212yes—
21C4×C11×M16C2211yescharacteristic
22C2×#66896—21no—
23#10622731—21no—
24M16×Dic11—21no—
25#10622707C2211yescharacteristic, complemented
26#10622707C2211yescharacteristic, complemented
27#10622688—21no—
28#10622688—21no—
29#10622688C2212yes—
30#10622688C2212yes—
31#10622688C2211yescharacteristic, complemented
32#10622688C2211yescharacteristic, complemented
33#10622653—21no—
34#10622647—21no—
35C4×#4324—21no—
36C4×#4324—21no—
37#10622538C2211yescharacteristic
38#10622537C2211yescharacteristic
39C2×C4⋊(C11⋊C8)C2211yescharacteristic
40#10622314—22no—
41#10622292C2212yescomplemented
42C8×Dic22C2212yescomplemented
43#10622185C2212yescomplemented
44#10622182C2212yes—
45#10622182C2212yes—
46#10622182C2212yescomplemented
47#10622096C2212yescomplemented
48#10622095C2212yescomplemented
49C2×C11×#41—21no—
50C22×D4×C11—21no—
51C22×D4×C11—21no—
52C22×D4×C11—21no—
53C22×Dic22D411yescharacteristic
54C11×AGL(1,ℤ/8)—44no—
55C11×AGL(1,ℤ/8)—44no—
56C2×C11×SD16—22no—
57C2×C11×SD16—22no—
58C2×C11×D8—22no—
59C2×C11×D8—22no—
60C2×C11×M16D411yescharacteristic
61C2×C11×M16D411yescharacteristic
62C11×C4⋊Q8C2311yescharacteristic
63C11×#127—21no—
64C11×#127—21no—
65C11×#127—21no—
66C11×#127C2312yes—
67C11×#127C2311yescharacteristic
68C11×#124—21no—
69C11×#121—21no—
70C11×#121—21no—
71C4×D4×C11—21no—
72C4×D4×C11—21no—
73C2×C42×C11C2311yescharacteristic
74C2×#4324—22no—
75C2×#4324—22no—
76C2×#4324—21no—
77C2×#4324—21no—
78C2×#4324—44no—
79C2×C4⋊Dic11D411yescharacteristic
80C2×Dic11⋊C4—21no—
81C2×C4×Dic11—21no—
82C2×#4318—21no—
83C22×C11⋊C8—21no—
84C4×Dic22—21no—
85C4×Dic22—21no—
86C4×Dic22D411yescharacteristic
87C4×Dic22D411yescharacteristic
88C4×Dic22C2311yescharacteristic
89C4×Dic22C2311yescharacteristic
90C11×#97D412yes—
91C4×C8×C11C2312yes—
92#66896—22no—
93#66896—22no—
94#66896—21no—
95#66896—21no—
96C22⋊(C11⋊C8)—21no—
97#66879—22no—
98Dic11⋊C8—22no—
99Dic11⋊C8—22no—
100C8×Dic11—22no—
101#66874—21no—
102#66874—21no—
103#66872—21no—
104#66872—21no—
105C4⋊(C11⋊C8)—21no—
106C4⋊(C11⋊C8)—21no—
107C4⋊(C11⋊C8)C2312yes—
108C4⋊(C11⋊C8)C2312yes—
109C4⋊(C11⋊C8)C2311yescharacteristic
110C4⋊(C11⋊C8)C2311yescharacteristic
111C4×C11⋊C8—21no—
112#19170—111nomaximal, Sylow
113C24×C11—41no—
114C11×#41—42no—
115C11×#41—42no—
116C2×Q8×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—22no—
119C2×D4×C11—21no—
120C2×D4×C11—22no—
121C2×D4×C11—21no—
122C2×D4×C11—22no—
123C2×D4×C11—42no—
124C2×D4×C11—42no—
125C2×D4×C11—41no—
126C2×D4×C11—41no—
127C2×D4×C11—41no—
128C2×D4×C11—41no—
129C2×D4×C11—42no—
130C2×D4×C11—42no—
131C2×D4×C11—82no—
132C22×C4×C11—41no—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11#4111yescharacteristic
136C22×Dic11—21no—
137C22×Dic11—21no—
138C2×Dic22—22no—
139C2×Dic22—21no—
140C2×Dic22—41no—
141C2×Dic22C2×D411yescharacteristic
142C2×Dic22C2×D411yescharacteristic
143C11×SD16—44no—
144C11×SD16—44no—
145C11×D8—44no—
146C11×D8—44no—
147C11×M16—22no—
148C11×M16SD1614yescomplemented
149C2×C8×C11C2×D412yes—
150C2×C8×C11C2×D412yes—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C22⋊C4—41no—
154C11×C22⋊C4—41no—
155C42×C11C2×D411yescharacteristic
156C42×C11C2×D411yescharacteristic
157C42×C11#4111yescharacteristic
158C42×C11C2411yescharacteristic
159#4324—42no—
160#4324—44no—
161#4324—42no—
162#4324—44no—
163C4⋊Dic11—21no—
164C4⋊Dic11C2×D411yescharacteristic
165C4⋊Dic11C2×D411yescharacteristic
166Dic11⋊C4—21no—
167Dic11⋊C4—21no—
168Dic11⋊C4—21no—
169Dic11⋊C4—21no—
170C4×Dic11—21no—
171C4×Dic11—21no—
172C4×Dic11—21no—
173C4×Dic11—21no—
174#4318—42no—
175C2×C11⋊C8—21no—
176C2×C11⋊C8—21no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—42no—
180#3151D1111yescharacteristic
181#3103—111no—
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—42no—
193C23×C11—82no—
194C23×C11—82no—
195C23×C11—82no—
196C23×C11#12111yescharacteristic
197Q8×C11—41no—
198Q8×C11—41no—
199D4×C11—41no—
200D4×C11—42no—
201D4×C11—42no—
202D4×C11—41no—
203D4×C11—41no—
204D4×C11—42no—
205D4×C11—41no—
206D4×C11—42no—
207D4×C11—81no—
208D4×C11—82no—
209D4×C11—82no—
210D4×C11—82no—
211D4×C11—82no—
212D4×C11—82no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—82no—
218C2×C4×C11#12111yescharacteristic
219C2×C4×C11#12111yescharacteristic
220C2×C4×C11#12111yescharacteristic
221C2×C4×C11C2×SD1612yes—
222C2×C4×C11AGL(1,ℤ/8)12yes—
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C2×#4111yescharacteristic
226C2×Dic11—21no—
227C2×Dic11—21no—
228C2×Dic11—21no—
229C2×Dic11—21no—
230C2×Dic11—42no—
231C2×Dic11—81no—
232Dic22—21no—
233Dic22—21no—
234Dic22—21no—
235Dic22—42no—
236Dic22AGL(1,ℤ/8)12yescomplemented
237C8×C11—22no—
238C8×C11C2×SD1614yescomplemented
239C11⋊C8—42no—
240C11⋊C8—42no—
241C11⋊C8—41no—
242C11⋊C8—41no—
243C2×AGL(1,ℤ/8)—21no—
244C2×AGL(1,ℤ/8)—21no—
245C22×SD16—221no—
246#532C2×D1111yescharacteristic
247C2×#127C2×D1111yescharacteristic
248C2×C4×Q8—111no—
249#496—22no—
250#493C2×D1112yes—
251#492C2×D1112yes—
252#481—221no—
253#475—111no—
254#475—111no—
255#460—111no—
256#460—111no—
257#460—112no—
258#460—112no—
259#460—221no—
260#460—221no—
261#448—221no—
262#446—112no—
263#446—222no—
264C8×Q8—112no—
265C4×SD16—221no—
266C4×SD16—221no—
267#431—111no—
268#423—111no—
269#423—221no—
270C2×C4⋊C8—111no—
271C2×#102—221no—
272C4×M16—221no—
273C4×M16C2×D1111yescharacteristic
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—82no—
284C22×C11—82no—
285C22×C11—81no—
286C22×C11—82no—
287C22×C11—81no—
288C22×C11—164no—
289C22×C11#46012yes—
290C22×C11C2×#12111yescharacteristic
291C4×C11—21no—
292C4×C11—21no—
293C4×C11—21no—
294C4×C11—81no—
295C4×C11#46012yes—
296C4×C11C22×SD1611yescharacteristic
297C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
298C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
299C4×C11#57511yescharacteristic
300Dic11—22no—
301Dic11—41no—
302Dic11—41no—
303Dic11—41no—
304C2×#41—21no—
305C22×Q8—111no—
306C22×D4—21no—
307C22×D4—21no—
308C22×D4—21no—
309AGL(1,ℤ/8)—44no—
310AGL(1,ℤ/8)—44no—
311C2×SD16—22no—
312C2×SD16—22no—
313C2×SD16—222no—
314C2×SD16—222no—
315C2×SD16—221no—
316C2×SD16—221no—
317C2×SD16—444no—
318C2×D8—22no—
319C2×D8—22no—
320C2×M16—221no—
321C2×M16C22⋊D1111yescharacteristic
322C2×M16C22⋊D1111yescharacteristic
323C22×C8—221no—
324C4⋊Q8C22×D1111yescharacteristic
325#127—21no—
326#127—21no—
327#127—21no—
328#127C22×D1112yes—
329#127C22×D1111yescharacteristic
330#124—21no—
331#121—21no—
332#121—21no—
333C4×Q8—111no—
334C4×Q8—111no—
335C4×Q8—111no—
336C4×Q8—111no—
337C4×Q8—221no—
338C4×Q8—221no—
339C4×D4—21no—
340C4×D4—21no—
341C2×C4⋊C4—111no—
342C2×C4⋊C4—221no—
343C2×C42—221no—
344C2×C42C22×D1111yescharacteristic
345#106—221no—
346#106—221no—
347C4⋊C8—112no—
348C4⋊C8—111no—
349C4⋊C8—111no—
350C4⋊C8—112no—
351C4⋊C8—222no—
352C4⋊C8—222no—
353C4⋊C8—221no—
354C4⋊C8—221no—
355#103—221no—
356#103—221no—
357#102—222no—
358#102—222no—
359#102—221no—
360#102—221no—
361C22⋊C8—221no—
362#97—222no—
363#97C22⋊D1112yes—
364C4×C8—222no—
365C4×C8—221no—
366C4×C8C22×D1112yes—
367C2×C11—22no—
368C2×C11—161no—
369C2×C11—162no—
370C2×C11C2×#46011yescharacteristic
371C2×C11#305511yescharacteristic
372C2×C11#306811yescharacteristic
373C24—41no—
374#41—42no—
375#41—42no—
376C2×Q8—21no—
377C2×Q8—111no—
378C2×Q8—111no—
379C2×Q8—222no—
380C2×Q8—221no—
381C2×Q8—441no—
382C2×D4—21no—
383C2×D4—22no—
384C2×D4—21no—
385C2×D4—22no—
386C2×D4—21no—
387C2×D4—22no—
388C2×D4—42no—
389C2×D4—42no—
390C2×D4—41no—
391C2×D4—42no—
392C2×D4—42no—
393C2×D4—41no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4—82no—
397C22×C4—41no—
398C22×C4—221no—
399C22×C4—221no—
400C22×C4D4×D1111yescharacteristic
401C22×C4#434111yescharacteristic
402C22×C4C2×C22⋊D1111yescharacteristic
403SD16—44no—
404SD16—44no—
405SD16—444no—
406SD16—442no—
407SD16—444no—
408SD16—442no—
409D8—44no—
410D8—44no—
411M16—22no—
412M16—442no—
413M16#432414yescomplemented
414C2×C8—221no—
415C2×C8—221no—
416C2×C8—222no—
417C2×C8—222no—
418C2×C8—442no—
419C2×C8C2×C22⋊D1112yes—
420C2×C8C2×C22⋊D1112yes—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—111no—
424C4⋊C4—111no—
425C4⋊C4—221no—
426C4⋊C4—221no—
427C4⋊C4—221no—
428C4⋊C4—221no—
429C4⋊C4—221no—
430C22⋊C4—41no—
431C22⋊C4—41no—
432C42—221no—
433C42—221no—
434C42—221no—
435C42—221no—
436C42D4×D1111yescharacteristic
437C42#434111yescharacteristic
438C42C2×C22⋊D1111yescharacteristic
439C42C23×D1111yescharacteristic
440C11#1917011yescharacteristic, complemented, Sylow
441C23—41no—
442C23—42no—
443C23—82no—
444C23—82no—
445C23—82no—
446C23#6699111yescharacteristic
447Q8—41no—
448Q8—41no—
449Q8—112no—
450Q8—221no—
451Q8—221no—
452Q8—221no—
453Q8—442no—
454D4—42no—
455D4—41no—
456D4—41no—
457D4—42no—
458D4—41no—
459D4—42no—
460D4—41no—
461D4—42no—
462D4—81no—
463D4—82no—
464D4—82no—
465D4—82no—
466D4—82no—
467D4—82no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—82no—
473C2×C4—221no—
474C2×C4—221no—
475C2×C4—221no—
476C2×C4—221no—
477C2×C4—442no—
478C2×C4—881no—
479C2×C4#6698512yes—
480C2×C4C2×#432412yes—
481C2×C4#6699111yescharacteristic
482C2×C4#6699111yescharacteristic
483C2×C4#6699111yescharacteristic
484C2×C4C2×D4×D1111yescharacteristic
485C2×C4C2×#434111yescharacteristic
486C2×C4C22×C22⋊D1111yescharacteristic
487C8—22no—
488C8—442no—
489C8—441no—
490C8—441no—
491C8—442no—
492C8C2×#432414yescomplemented
493C22—21no—
494C22—21no—
495C22—81no—
496C22—82no—
497C22—82no—
498C22—81no—
499C22—82no—
500C22—81no—
501C22—164no—
502C22#1062268812yes—
503C22C2×#6699111yescharacteristic
504C4—21no—
505C4—21no—
506C4—21no—
507C4—81no—
508C4—222no—
509C4—441no—
510C4—441no—
511C4—441no—
512C4#1062268812yes—
513C4D11×AGL(1,ℤ/8)11yescharacteristic
514C4#1062330411yescharacteristic
515C4C2×#6698511yescharacteristic
516C4C22×#432411yescharacteristic
517C2—22no—
518C2—162no—
519C2—161no—
520C2C2×#1062268811yescharacteristic
521C2#1307822911yescharacteristic
522C2#1307834011yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3151C2
socleC22×C11C2×#121
hypercenter#3151D11
hypocenterC11#19170
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3151

Complements

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

NH ≅ G/Ntype
1. #13078643C2semidirect
2. C2×#10622688C2semidirect
3. M16×Dic22C2semidirect
4. #13068097C2semidirect
5. #13068085C2semidirect
6. #13067973C2semidirect
7. #13067961C2semidirect
8. #13067368C2semidirect
9. #13067293C2semidirect
10. #13067284C2semidirect
25. #10622707C22semidirect
26. #10622707C22semidirect
31. #10622688C22semidirect
32. #10622688C22semidirect
41. #10622292C22semidirect
42. C8×Dic22C22semidirect
43. #10622185C22semidirect
46. #10622182C22semidirect
47. #10622096C22semidirect
48. #10622095C22semidirect
148. C11×M16SD16semidirect
236. Dic22AGL(1,ℤ/8)semidirect
238. C8×C11C2×SD16semidirect
413. M16#4324semidirect
440. C11#19170semidirect
492. C8C2×#4324semidirect

Maximal subgroups

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

subgroupindex
#130786432
C2×#106226882
M16×Dic222
#130680972
#130680852
#130679732
#130679612
#130673682
#130672932
#130672842
C11×#31512
#1917011