Finite Group Databasebeta

← #14736587

Subgroups — #14736587

Order 2816.

758 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078992C211yesmaximal, characteristic, complemented
2C2×#10622628C211yesmaximal, characteristic
3D4×#4318C211yesmaximal, characteristic, complemented
4#13068179C212yesmaximal, complemented
5#13068151C212yesmaximal, complemented
6#13068055C212yesmaximal, complemented
7#13068027C212yesmaximal, complemented
8#13067369C211yesmaximal, characteristic, complemented
9#13067306C211yesmaximal, characteristic, complemented
10#13067283C211yesmaximal, characteristic, complemented
11C11×#3101C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C22×#4323—21no—
15C22×#4318—21no—
16C2×#66927C2211yescharacteristic
17C11×#483—21no—
18C11×#476C2211yescharacteristic, complemented
19C11×#476C2211yescharacteristic, complemented
20C11×#461C2211yescharacteristic, complemented
21C11×#461C2211yescharacteristic, complemented
22C11×#450—21no—
23C4×C11×SD16—21no—
24C4×C11×SD16—21no—
25C11×#431C2211yescharacteristic
26#10622820—21no—
27#10622701C2212yescomplemented
28#10622701C2212yescomplemented
29#10622680—22no—
30#10622628—21no—
31#10622628—21no—
32#10622628C2212yes—
33#10622628C2212yes—
34#10622625C2212yescomplemented
35#10622624—22no—
36D4×C11⋊C8C2212yescomplemented
37#10622614—21no—
38#10622614—21no—
39C2×#66873—21no—
40#10622537C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C4×#4318C2211yescharacteristic
43#10622185C2212yescomplemented
44#10622184C2212yescomplemented
45#10622123C2212yescomplemented
46#10622123C2212yescomplemented
47#10622118C2212yescomplemented
48#10622117C2212yescomplemented
49C22×D4×C11D411yescharacteristic
50C23×C4×C11—21no—
51C22×D44—21no—
52C22×D44—21no—
53C22×D44—21no—
54C2×C11×SD16—21no—
55C2×C11×SD16—21no—
56C11×C4⋊Q8C2311yescharacteristic
57C11×C4⋊Q8C2311yescharacteristic
58C11×#125—21no—
59C11×C22⋊Q8—21no—
60C11×C22⋊Q8—21no—
61C4×Q8×C11—21no—
62C4×Q8×C11—21no—
63C4×D4×C11—21no—
64C4×D4×C11—21no—
65C4×D4×C11D411yescharacteristic
66C4×D4×C11D411yescharacteristic
67C4×D4×C11C2311yescharacteristic
68C4×D4×C11C2311yescharacteristic
69C11×#117—21no—
70C2×C11×C4⋊C4D411yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C42×C11C2311yescharacteristic
73C2×#4323—22no—
74C2×#4323—22no—
75C2×#4323—44no—
76C2×#4318—21no—
77C2×#4318—22no—
78C2×#4318—44no—
79C2×#4318D411yescharacteristic
80C2×#4318D411yescharacteristic
81C22×C11⋊C8—21no—
82C22×C11⋊C8—22no—
83#66927—21no—
84#66927—21no—
85#66927—21no—
86#66927C2312yes—
87C11×#106—21no—
88C11×#106—21no—
89C11×C4⋊C8C2311yescharacteristic
90C11×C4⋊C8C2311yescharacteristic
91C11×#103—21no—
92C11×#103—21no—
93C11×#102—21no—
94C11×#102—21no—
95C11×C22⋊C8—21no—
96C4×C8×C11—21no—
97C22⋊(C11⋊C8)—22no—
98C22⋊(C11⋊C8)—22no—
99#66873—22no—
100#66873—22no—
101#66873—22no—
102#66873—22no—
103#66873—22no—
104#66873—22no—
105C4⋊(C11⋊C8)—21no—
106C4⋊(C11⋊C8)—21no—
107C4⋊(C11⋊C8)C2312yes—
108C4⋊(C11⋊C8)C2312yes—
109#66867D412yes—
110C4×C11⋊C8C2312yes—
111#19166—111nomaximal, Sylow
112C24×C11—21no—
113C23×D11—41no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×D4×C11—22no—
117C2×D4×C11—21no—
118C2×D4×C11—41no—
119C2×D4×C11C2×D411yescharacteristic
120C2×D4×C11C2×D411yescharacteristic
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—42no—
127C22×C4×C11—42no—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11#4111yescharacteristic
131C2×D44—22no—
132C2×D44—22no—
133C2×D44—22no—
134C2×D44—42no—
135C2×D44—42no—
136C2×D44—41no—
137C2×D44—41no—
138C2×D44—41no—
139C2×D44—42no—
140C2×D44—42no—
141C2×D44—82no—
142C11×SD16—42no—
143C11×SD16—42no—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—41no—
152C11×C4⋊C4—41no—
153C11×C4⋊C4C2×D411yescharacteristic
154C11×C4⋊C4C2×D411yescharacteristic
155C11×C22⋊C4—21no—
156C11×C22⋊C4—21no—
157C11×C22⋊C4—21no—
158C11×C22⋊C4—21no—
159C11×C22⋊C4—41no—
160C42×C11—41no—
161C42×C11C2×D411yescharacteristic
162C42×C11C2×D411yescharacteristic
163C42×C11#4111yescharacteristic
164C42×C11C2411yescharacteristic
165#4323—44no—
166#4323—44no—
167#4318—22no—
168#4318—22no—
169#4318—44no—
170#4318—42no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—42no—
174C2×C11⋊C8—44no—
175C2×C11⋊C8C2×D412yes—
176C2×C11⋊C8C2×D412yes—
177#3138—111no—
178#3101D1111yescharacteristic, complemented
179C2×#459—111no—
180D4×M16—111no—
181#1701—112no—
182#1697—112no—
183#1681—112no—
184#1677—112no—
185#1565—111no—
186#1550—111no—
187#1545—111no—
188C23×C11—21no—
189C23×C11—21no—
190C23×C11—42no—
191C23×C11—42no—
192C23×C11—81no—
193C23×C11#12111yescharacteristic
194C22×D11—42no—
195C22×D11—82no—
196C22×D11—82no—
197C22×D11—82no—
198Q8×C11—41no—
199Q8×C11—41no—
200Q8×C11—81no—
201D4×C11—21no—
202D4×C11—21no—
203D4×C11—21no—
204D4×C11—42no—
205D4×C11AGL(1,ℤ/8)12yes—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—41no—
211C2×C4×C11—42no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11#12111yescharacteristic
221C2×C4×C11#12111yescharacteristic
222C2×C4×C11#12111yescharacteristic
223C2×C4×C11#13512yes—
224C2×C4×C11AGL(1,ℤ/8)12yes—
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C2×#4111yescharacteristic
228D44—42no—
229D44—42no—
230D44—42no—
231D44—42no—
232D44—82no—
233D44—82no—
234D44—82no—
235D44—82no—
236C8×C11—41no—
237C8×C11—41no—
238C11⋊C8—22no—
239C11⋊C8—22no—
240C11⋊C8—42no—
241C11⋊C8—42no—
242C22×D8—221no—
243C22×M16—221no—
244#533C2×D1111yescharacteristic
245C2×#127—111no—
246C2×C4×D4C2×D1111yescharacteristic
247#490—222no—
248#486—112no—
249#486—112no—
250#483—21no—
251#476C2×D1111yescharacteristic, complemented
252#476C2×D1111yescharacteristic, complemented
253#461C2×D1111yescharacteristic, complemented
254#461C2×D1111yescharacteristic, complemented
255#459—112no—
256#459—112no—
257#459—221no—
258#459—221no—
259#450—21no—
260C4×SD16—21no—
261C4×SD16—21no—
262#436—112no—
263#435—222no—
264C8×D4—112no—
265#431C2×D1111yescharacteristic
266#423—111no—
267C2×C4⋊C8—111no—
268#418—221no—
269#418—221no—
270C2×#102—221no—
271#407—221no—
272C4×M16—111no—
273#335—112no—
274#334—112no—
275#333—112no—
276#332—112no—
277#331—112no—
278#331—112no—
279C22×C11—21no—
280C22×C11—21no—
281C22×C11—22no—
282C22×C11—41no—
283C22×C11—41no—
284C22×C11—41no—
285C22×C11—41no—
286C22×C11—41no—
287C22×C11—84no—
288C22×C11#46312yes—
289C22×C11C2×#12111yescharacteristic
290C2×D11—82no—
291C2×D11—82no—
292C2×D11—82no—
293C2×D11—164no—
294C4×C11—21no—
295C4×C11—21no—
296C4×C11—21no—
297C4×C11—41no—
298C4×C11—41no—
299C4×C11—81no—
300C4×C11—81no—
301C4×C11#46312yes—
302C4×C11C2×#13511yescharacteristic
303C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
304C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
305C4×C11#57511yescharacteristic
306C22×D4—221no—
307C22×D4—221no—
308C22×D4—221no—
309C22×D4C22⋊D1111yescharacteristic
310C23×C4—21no—
311C2×SD16—21no—
312C2×SD16—21no—
313C2×D8—222no—
314C2×D8—222no—
315C2×D8—444no—
316C2×M16—111no—
317C2×M16—111no—
318C2×M16—222no—
319C2×M16—221no—
320C2×M16—444no—
321C22×C8—222no—
322C22×C8—221no—
323C4⋊Q8C22×D1111yescharacteristic
324C4⋊Q8C22×D1111yescharacteristic
325#127—112no—
326#127—221no—
327#127—221no—
328#127—221no—
329#125—21no—
330C22⋊Q8—21no—
331C22⋊Q8—21no—
332C4×Q8—21no—
333C4×Q8—21no—
334C4×D4—21no—
335C4×D4—21no—
336C4×D4C22⋊D1111yescharacteristic
337C4×D4C22⋊D1111yescharacteristic
338C4×D4C22×D1111yescharacteristic
339C4×D4C22×D1111yescharacteristic
340#117—21no—
341C2×C4⋊C4C22⋊D1111yescharacteristic
342C2×C22⋊C4—21no—
343C2×C42C22×D1111yescharacteristic
344#106—21no—
345#106—21no—
346C4⋊C8—112no—
347C4⋊C8—112no—
348C4⋊C8—221no—
349C4⋊C8—221no—
350C4⋊C8C22×D1111yescharacteristic
351C4⋊C8C22×D1111yescharacteristic
352#103—21no—
353#103—21no—
354#102—21no—
355#102—21no—
356#102—222no—
357#102—222no—
358#102—222no—
359#102—222no—
360#102—222no—
361#102—222no—
362C22⋊C8—21no—
363C22⋊C8—222no—
364C22⋊C8—222no—
365#97—112no—
366C4×C8—21no—
367C4×C8—112no—
368C2×C11—22no—
369C2×C11—42no—
370C2×C11—81no—
371C2×C11C2×#46311yescharacteristic
372C2×C11#305511yescharacteristic
373C2×C11#306811yescharacteristic
374D11—162no—
375C24—21no—
376C24—441no—
377C2×Q8—21no—
378C2×Q8—21no—
379C2×D4—22no—
380C2×D4—21no—
381C2×D4—41no—
382C2×D4—222no—
383C2×D4—222no—
384C2×D4—222no—
385C2×D4—442no—
386C2×D4—442no—
387C2×D4—442no—
388C2×D4—442no—
389C2×D4—441no—
390C2×D4—441no—
391C2×D4—441no—
392C2×D4—882no—
393C2×D4C2×C22⋊D1111yescharacteristic
394C2×D4C2×C22⋊D1111yescharacteristic
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—42no—
401C22×C4—42no—
402C22×C4D4×D1111yescharacteristic
403C22×C4#434111yescharacteristic
404C22×C4C2×C22⋊D1111yescharacteristic
405SD16—42no—
406SD16—42no—
407D8—444no—
408D8—444no—
409M16—222no—
410M16—222no—
411M16—444no—
412M16—442no—
413C2×C8—21no—
414C2×C8—21no—
415C2×C8—112no—
416C2×C8—112no—
417C2×C8—222no—
418C2×C8—222no—
419C2×C8—444no—
420C2×C8—442no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—41no—
427C4⋊C4—41no—
428C4⋊C4C2×C22⋊D1111yescharacteristic
429C4⋊C4C2×C22⋊D1111yescharacteristic
430C22⋊C4—21no—
431C22⋊C4—21no—
432C22⋊C4—21no—
433C22⋊C4—21no—
434C22⋊C4—41no—
435C42—41no—
436C42D4×D1111yescharacteristic
437C42#434111yescharacteristic
438C42C2×C22⋊D1111yescharacteristic
439C42C23×D1111yescharacteristic
440C11#1916611yescharacteristic, complemented, Sylow
441C23—21no—
442C23—21no—
443C23—42no—
444C23—42no—
445C23—81no—
446C23—442no—
447C23—882no—
448C23—882no—
449C23—882no—
450C23#6699211yescharacteristic
451Q8—41no—
452Q8—41no—
453Q8—81no—
454D4—21no—
455D4—21no—
456D4—21no—
457D4—42no—
458D4—442no—
459D4—442no—
460D4—442no—
461D4—442no—
462D4—882no—
463D4—882no—
464D4—882no—
465D4—882no—
466D4#6700212yes—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—41no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4#6696712yes—
482C2×C4#6696912yes—
483C2×C4#6699211yescharacteristic
484C2×C4#6699211yescharacteristic
485C2×C4#6699211yescharacteristic
486C2×C4C2×D4×D1111yescharacteristic
487C2×C4C2×#434111yescharacteristic
488C2×C4C22×C22⋊D1111yescharacteristic
489C8—41no—
490C8—41no—
491C8—222no—
492C8—222no—
493C8—442no—
494C8—442no—
495C22—21no—
496C22—21no—
497C22—22no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—84no—
504C22—882no—
505C22—882no—
506C22—882no—
507C22—1764no—
508C22#1062277812yes—
509C22C2×#6699211yescharacteristic
510C4—21no—
511C4—21no—
512C4—21no—
513C4—41no—
514C4—41no—
515C4—81no—
516C4—81no—
517C4#1062277812yes—
518C4C2×#6696711yescharacteristic
519C4C2×#6696911yescharacteristic
520C4C2×#6700211yescharacteristic
521C4#1062335311yescharacteristic
522C2—22no—
523C2—42no—
524C2—81no—
525C2—1762no—
526C2C2×#1062277811yescharacteristic
527C2#1307823711yescharacteristic
528C2#1307834611yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3101C2
socleC22×C11C2×#121
prime radicalC2×#10622628C2
hypercenter#3101D11
hypocenterC11#19166
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3101

Complements

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

NH ≅ G/Ntype
1. #13078992C2semidirect
3. D4×#4318C2semidirect
4. #13068179C2semidirect
5. #13068151C2semidirect
6. #13068055C2semidirect
7. #13068027C2semidirect
8. #13067369C2semidirect
9. #13067306C2semidirect
10. #13067283C2semidirect
11. C11×#3101C2semidirect
18. C11×#476C22semidirect
19. C11×#476C22semidirect
20. C11×#461C22semidirect
21. C11×#461C22semidirect
27. #10622701C22semidirect
28. #10622701C22semidirect
34. #10622625C22semidirect
36. D4×C11⋊C8C22semidirect
43. #10622185C22semidirect
44. #10622184C22semidirect
45. #10622123C22semidirect
46. #10622123C22semidirect
47. #10622118C22semidirect
48. #10622117C22semidirect
178. #3101D11semidirect
251. #476C2×D11semidirect
252. #476C2×D11semidirect
253. #461C2×D11semidirect
254. #461C2×D11semidirect
440. C11#19166semidirect

Maximal subgroups

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

subgroupindex
#130789922
C2×#106226282
D4×#43182
#130681792
#130681512
#130680552
#130680272
#130673692
#130673062
#130672832
C11×#31012
#1916611