Finite Group Databasebeta

← #14736625

Subgroups — #14736625

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#13079066C211yesmaximal, characteristic
2#13078647C211yesmaximal, characteristic, complemented
3Q8×#4318C211yesmaximal, characteristic, complemented
4#13068098C212yesmaximal, complemented
5#13068086C212yesmaximal, complemented
6#13067974C212yesmaximal, complemented
7#13067962C212yesmaximal, complemented
8#13067366C211yesmaximal, characteristic, complemented
9#13067291C211yesmaximal, characteristic, complemented
10#13067284C211yesmaximal, characteristic, complemented
11C2×C11×#460C211yesmaximal, characteristic, complemented
12C22×C11×SD16—21no—
13C2×C11×#127C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×#66985—21no—
16C2×#66985—21no—
17#10623008C2211yescharacteristic
18C11×#460—21no—
19C11×#460—21no—
20C11×#460C2212yes—
21C11×#460C2212yes—
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×#102—21no—
24#10622840—21no—
25#10622689C2212yes—
26#10622687—22no—
27#10622686C2212yes—
28#10622640C2211yescharacteristic, complemented
29#10622640C2211yescharacteristic, complemented
30C4×#4325—21no—
31C4×#4325—21no—
32#10622637—22no—
33#10622637C2212yescomplemented
34Q8×C11⋊C8C2212yescomplemented
35#10622633C2211yescharacteristic, complemented
36#10622633C2211yescharacteristic, complemented
37#10622581—21no—
38#10622538C2211yescharacteristic
39#10622537—21no—
40#10622537C2211yescharacteristic
41C4×#4318—21no—
42C4×#4318C2211yescharacteristic
43#10622182C2212yes—
44#10622182C2212yes—
45#10622124C2212yescomplemented
46#10622123C2212yescomplemented
47#10622118C2212yescomplemented
48#10622117C2212yescomplemented
49C22×Q8×C11D411yescharacteristic
50C22×D4×C11—21no—
51C22×D4×C11—21no—
52C22×D4×C11—21no—
53C2×#4339—21no—
54C2×C11×SD16—22no—
55C2×C11×SD16—22no—
56C2×C11×SD16—44no—
57C22×C8×C11—21no—
58C11×#127—21no—
59C11×#127—21no—
60C11×#127—21no—
61C11×#127C2312yes—
62C4×Q8×C11—21no—
63C4×Q8×C11—21no—
64C4×Q8×C11D411yescharacteristic
65C4×Q8×C11D411yescharacteristic
66C4×Q8×C11C2311yescharacteristic
67C4×Q8×C11C2311yescharacteristic
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4D411yescharacteristic
70C2×C42×C11—21no—
71C2×C42×C11C2311yescharacteristic
72C2×#4325—21no—
73C2×#4325—21no—
74C2×#4324—22no—
75C2×#4324—22no—
76#66985—44no—
77#66985—44no—
78C2×#4323—22no—
79C2×#4323—22no—
80#66983—21no—
81#66983—21no—
82C2×#4318—21no—
83C2×#4318D411yescharacteristic
84C2×#4318D411yescharacteristic
85#66928—21no—
86#66927C2311yescharacteristic
87C4×D44—21no—
88C4×D44—21no—
89#66922C2311yescharacteristic
90C11×C4⋊C8—21no—
91C11×C4⋊C8C2312yes—
92C11×#102—22no—
93C11×#102—22no—
94#66899—21no—
95#66899—21no—
96C22⋊(C11⋊C8)—21no—
97#66873—21no—
98#66873—21no—
99#66872—21no—
100#66872—21no—
101C4⋊(C11⋊C8)—21no—
102C4⋊(C11⋊C8)—22no—
103C4⋊(C11⋊C8)—22no—
104C4⋊(C11⋊C8)C2312yes—
105C4⋊(C11⋊C8)C2311yescharacteristic
106C4⋊(C11⋊C8)C2311yescharacteristic
107#66867—22no—
108#66867D412yes—
109C4×C11⋊C8—21no—
110C4×C11⋊C8—22no—
111C4×C11⋊C8C2312yes—
112#19170—111nomaximal, Sylow
113C24×C11—41no—
114C2×Q8×C11—21no—
115C2×Q8×C11—22no—
116C2×Q8×C11—41no—
117C2×Q8×C11C2×D411yescharacteristic
118C2×Q8×C11C2×D411yescharacteristic
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—42no—
123C2×D4×C11—42no—
124C2×D4×C11—41no—
125C2×D4×C11—41no—
126C2×D4×C11—41no—
127C2×D4×C11—42no—
128C2×D4×C11—42no—
129C2×D4×C11—82no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11#4111yescharacteristic
135C2×C22⋊D11—41no—
136#4339—42no—
137#4339—42no—
138C2×D44—21no—
139C2×D44—21no—
140C2×D44—21no—
141C2×C4×D11—41no—
142C2×Dic22—21no—
143C11×SD16—44no—
144C11×SD16—44no—
145C2×C8×C11—22no—
146C2×C8×C11—42no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4C2×D411yescharacteristic
153C11×C4⋊C4C2×D411yescharacteristic
154C42×C11—21no—
155C42×C11—21no—
156C42×C11—21no—
157C42×C11—21no—
158C42×C11C2×D411yescharacteristic
159C42×C11C2×D411yescharacteristic
160C42×C11#4111yescharacteristic
161C42×C11C2411yescharacteristic
162#4325—42no—
163#4325—42no—
164#4324—44no—
165#4324—44no—
166#4323—44no—
167#4323—44no—
168(C2×D11)⋊C4—41no—
169(C2×D11)⋊C4—41no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172#4318—22no—
173#4318—42no—
174#4318SD1614yescomplemented
175C2×C11⋊C8—22no—
176C2×C11⋊C8—21no—
177C2×C11⋊C8—21no—
178C2×C11⋊C8C2×D412yes—
179C2×C11⋊C8C2×D412yes—
180#3151—111no—
181#3103—111no—
182C2×#460D1111yescharacteristic, complemented
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—42no—
192C23×C11—82no—
193C23×C11—82no—
194C23×C11—82no—
195C23×C11#12111yescharacteristic
196C22×D11—41no—
197Q8×C11—21no—
198Q8×C11—21no—
199Q8×C11—21no—
200Q8×C11—42no—
201Q8×C11AGL(1,ℤ/8)12yescomplemented
202D4×C11—42no—
203D4×C11—42no—
204D4×C11—42no—
205D4×C11—42no—
206D4×C11—82no—
207D4×C11—82no—
208D4×C11—82no—
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—81no—
219C2×C4×C11#12111yescharacteristic
220C2×C4×C11#12111yescharacteristic
221C2×C4×C11#12111yescharacteristic
222C2×C4×C11C2×SD1612yes—
223C2×C4×C11AGL(1,ℤ/8)12yes—
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C2×#4111yescharacteristic
227C22⋊D11—82no—
228C2×Dic11—41no—
229D44—41no—
230D44—41no—
231D44—41no—
232D44—41no—
233D44—81no—
234C4×D11—82no—
235Dic22—41no—
236Dic22—41no—
237C8×C11—42no—
238C11⋊C8—22no—
239C11⋊C8—42no—
240C11⋊C8—41no—
241C11⋊C8—41no—
242C11⋊C8C2×SD1614yescomplemented
243C2×AGL(1,ℤ/8)—221no—
244C2×AGL(1,ℤ/8)—221no—
245C22×SD16—21no—
246#532—111no—
247C2×#127C2×D1111yescharacteristic
248C2×C4×Q8C2×D1111yescharacteristic
249#496—222no—
250#493—112no—
251#492—112no—
252#481—221no—
253#475—111no—
254#475—111no—
255#460—21no—
256#460—21no—
257#460—111no—
258#460—111no—
259#460C2×D1112yes—
260#460C2×D1112yes—
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⋊C8C2×D1111yescharacteristic
271C2×#102—21no—
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—82no—
283C22×C11—82no—
284C22×C11—82no—
285C22×C11—164no—
286C22×C11#46012yes—
287C22×C11C2×#12111yescharacteristic
288C2×D11—81no—
289C2×D11—81no—
290C2×D11—81no—
291C4×C11—21no—
292C4×C11—22no—
293C4×C11—21no—
294C4×C11—21no—
295C4×C11—41no—
296C4×C11—41no—
297C4×C11—41no—
298C4×C11#46012yes—
299C4×C11C22×SD1611yescharacteristic
300C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
301C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
302C4×C11#57511yescharacteristic
303Dic11—81no—
304C2×#41—221no—
305C22×Q8C22⋊D1111yescharacteristic
306C22×D4—21no—
307C22×D4—21no—
308C22×D4—21no—
309AGL(1,ℤ/8)—444no—
310AGL(1,ℤ/8)—444no—
311C2×SD16—22no—
312C2×SD16—22no—
313C2×SD16—44no—
314C2×SD16—222no—
315C2×SD16—222no—
316C2×SD16—221no—
317C2×SD16—221no—
318C2×D8—222no—
319C2×D8—222no—
320C2×M16—111no—
321C2×M16—111no—
322C2×M16—221no—
323C22×C8—21no—
324C4⋊Q8—111no—
325#127—21no—
326#127—21no—
327#127—21no—
328#127—111no—
329#127C22×D1112yes—
330#124—221no—
331#121—221no—
332#121—221no—
333C4×Q8—21no—
334C4×Q8—21no—
335C4×Q8C22⋊D1111yescharacteristic
336C4×Q8C22⋊D1111yescharacteristic
337C4×Q8C22×D1111yescharacteristic
338C4×Q8C22×D1111yescharacteristic
339C4×D4—221no—
340C4×D4—221no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4C22⋊D1111yescharacteristic
343C2×C42—21no—
344C2×C42C22×D1111yescharacteristic
345#106—221no—
346#106—221no—
347C4⋊C8—21no—
348C4⋊C8—112no—
349C4⋊C8—111no—
350C4⋊C8—111no—
351C4⋊C8—222no—
352C4⋊C8—222no—
353C4⋊C8—221no—
354C4⋊C8C22×D1112yes—
355#103—221no—
356#103—221no—
357#102—22no—
358#102—22no—
359#102—221no—
360#102—221no—
361C22⋊C8—221no—
362#97—112no—
363#97—222no—
364C4×C8—112no—
365C4×C8—222no—
366C4×C8—221no—
367C2×C11—22no—
368C2×C11—162no—
369C2×C11C2×#46011yescharacteristic
370C2×C11#305511yescharacteristic
371C2×C11#306811yescharacteristic
372D11—161no—
373C24—41no—
374#41—442no—
375#41—442no—
376C2×Q8—21no—
377C2×Q8—22no—
378C2×Q8—41no—
379C2×Q8—221no—
380C2×Q8C2×C22⋊D1111yescharacteristic
381C2×Q8C2×C22⋊D1111yescharacteristic
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—42no—
386C2×D4—42no—
387C2×D4—42no—
388C2×D4—42no—
389C2×D4—41no—
390C2×D4—41no—
391C2×D4—41no—
392C2×D4—82no—
393C2×D4—221no—
394C2×D4—221no—
395C2×D4—221no—
396C2×D4—441no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—441no—
400C22×C4D4×D1111yescharacteristic
401C22×C4#434111yescharacteristic
402C22×C4C2×C22⋊D1111yescharacteristic
403SD16—44no—
404SD16—44no—
405SD16—444no—
406SD16—444no—
407SD16—442no—
408SD16—442no—
409D8—444no—
410D8—444no—
411M16—114no—
412M16—222no—
413M16—442no—
414C2×C8—22no—
415C2×C8—42no—
416C2×C8—112no—
417C2×C8—112no—
418C2×C8—222no—
419C2×C8—221no—
420C2×C8—221no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—221no—
427C4⋊C4—221no—
428C4⋊C4C2×C22⋊D1111yescharacteristic
429C4⋊C4C2×C22⋊D1111yescharacteristic
430C22⋊C4—441no—
431C22⋊C4—441no—
432C42—21no—
433C42—21no—
434C42—21no—
435C42—21no—
436C42D4×D1111yescharacteristic
437C42#434111yescharacteristic
438C42C2×C22⋊D1111yescharacteristic
439C42C23×D1111yescharacteristic
440C11#1917011yescharacteristic, complemented, Sylow
441C23—42no—
442C23—82no—
443C23—82no—
444C23—82no—
445C23—441no—
446C23#6699211yescharacteristic
447Q8—21no—
448Q8—21no—
449Q8—21no—
450Q8—42no—
451Q8—441no—
452Q8—441no—
453Q8#6698512yescomplemented
454D4—42no—
455D4—42no—
456D4—42no—
457D4—42no—
458D4—82no—
459D4—82no—
460D4—82no—
461D4—82no—
462D4—441no—
463D4—441no—
464D4—441no—
465D4—441no—
466D4—881no—
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—81no—
477C2×C4—441no—
478C2×C4—882no—
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—42no—
488C8—114no—
489C8—222no—
490C8—442no—
491C8—441no—
492C8—441no—
493C22—21no—
494C22—21no—
495C22—82no—
496C22—82no—
497C22—82no—
498C22—164no—
499C22—881no—
500C22—881no—
501C22—881no—
502C22#1062277612yes—
503C22C2×#6699211yescharacteristic
504C4—21no—
505C4—21no—
506C4—21no—
507C4—22no—
508C4—41no—
509C4—41no—
510C4—41no—
511C4—881no—
512C4#1062277612yes—
513C4C2×SD16×D1111yescharacteristic
514C4C2×#6696711yescharacteristic
515C4C2×#6698511yescharacteristic
516C4#1062335311yescharacteristic
517C2—22no—
518C2—162no—
519C2—1761no—
520C2C2×#1062277611yescharacteristic
521C2#1307823111yescharacteristic
522C2#1307834111yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#460C2
socleC22×C11C2×#121
prime radical#13079066C2
hypercenterC2×#460D11
hypocenterC11#19170
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#460

Complements

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

NH ≅ G/Ntype
2. #13078647C2semidirect
3. Q8×#4318C2semidirect
4. #13068098C2semidirect
5. #13068086C2semidirect
6. #13067974C2semidirect
7. #13067962C2semidirect
8. #13067366C2semidirect
9. #13067291C2semidirect
10. #13067284C2semidirect
11. C2×C11×#460C2semidirect
28. #10622640C22semidirect
29. #10622640C22semidirect
33. #10622637C22semidirect
34. Q8×C11⋊C8C22semidirect
35. #10622633C22semidirect
36. #10622633C22semidirect
45. #10622124C22semidirect
46. #10622123C22semidirect
47. #10622118C22semidirect
48. #10622117C22semidirect
174. #4318SD16semidirect
182. C2×#460D11semidirect
201. Q8×C11AGL(1,ℤ/8)semidirect
242. C11⋊C8C2×SD16semidirect
440. C11#19170semidirect
453. Q8#66985semidirect

Maximal subgroups

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

subgroupindex
#130790662
#130786472
Q8×#43182
#130680982
#130680862
#130679742
#130679622
#130673662
#130672912
#130672842
C2×C11×#4602
#1917011