Finite Group Databasebeta

← #14909714

Subgroups — #14909714

Order 2816.

608 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079184C211yesmaximal, characteristic, complemented
2D11×#495C211yesmaximal, characteristic, complemented
3#13070876C211yesmaximal, characteristic, complemented
4#13070874C211yesmaximal, characteristic, complemented
5#13070849C211yesmaximal, characteristic, complemented
6#13070846C211yesmaximal, characteristic, complemented
7#13070679C211yesmaximal, characteristic, complemented
8#13070675C211yesmaximal, characteristic, complemented
9#13070671C211yesmaximal, characteristic, complemented
10#13070551C211yesmaximal, characteristic, complemented
11#13070546C211yesmaximal, characteristic, complemented
12#13070531C211yesmaximal, characteristic, complemented
13#13070526C211yesmaximal, characteristic
14#13070414C211yesmaximal, characteristic, complemented
15C11×#2210C211yesmaximal, characteristic, complemented
16C2×Q16×D11C2211yescharacteristic
17C2×SD16×D11—21no—
18C2×D8×D11C2211yescharacteristic
19D11×#124—21no—
20#10623088—21no—
21C2×C11×SD32C2211yescharacteristic, complemented
22C2×C11×D16C2211yescharacteristic
23C11×#495C2211yescharacteristic
24C4×C11×D8C2211yescharacteristic, complemented
25#10622804C2211yescharacteristic
26C2×#66893C2211yescharacteristic, complemented
27#10622781—21no—
28#10622770C2211yescharacteristic
29#10622768C2211yescharacteristic
30#10622768C2211yescharacteristic, complemented
31C2×#66891C2211yescharacteristic
32C2×#66891C2211yescharacteristic, complemented
33C2×#66890C2211yescharacteristic
34#10622672—21no—
35C4×#4324—21no—
36C2×Dic88C2211yescharacteristic, complemented
37C2×#66864C2211yescharacteristic
38#10622500C2211yescharacteristic
39#10622491C2211yescharacteristic, complemented
40#10622391—21no—
41#10622381—21no—
42C4×Dic44C2211yescharacteristic, complemented
43#10622309C2211yescharacteristic
44C4×C8×D11C2211yescharacteristic
45C11×C4⋊C16C2211yescharacteristic, complemented
46C11×#358C2211yescharacteristic, complemented
47C11×#357C2211yescharacteristic
48#10622202C2211yescharacteristic, complemented
49#10622200C2211yescharacteristic
50#10622147C2211yescharacteristic
51(C2×D11)⋊C16C2211yescharacteristic
52(C2×D11)⋊C16C2211yescharacteristic
53#10622141C2211yescharacteristic, complemented
54C16×Dic11C2211yescharacteristic, complemented
55C16×Dic11C2211yescharacteristic, complemented
56#10622130C2211yescharacteristic, complemented
57#10622129C2211yescharacteristic
58C4⋊(C11⋊C16)C2211yescharacteristic, complemented
59C2×Q8×D11—21no—
60C2×D4×D11—21no—
61C2×C11×Q16C2311yescharacteristic
62C2×C11×SD16—21no—
63C2×C11×D8C2311yescharacteristic
64C2×C11×D8C2311yescharacteristic
65C11×#124—21no—
66C4×D4×C11—21no—
67#67000—21no—
68C2×#4326—21no—
69C2×#4325—21no—
70#66991—21no—
71#66989—21no—
72#66989—21no—
73C2×#4324—21no—
74C2×#4324—21no—
75C2×#4323—21no—
76C4×C22⋊D11—41no—
77#66979—41no—
78Q16×D11—41no—
79Q16×D11—41no—
80SD16×D11—44no—
81D8×D11—41no—
82D8×D11—41no—
83C2×Dic44C2311yescharacteristic
84C2×Dic44C2311yescharacteristic
85C2×D88C2311yescharacteristic
86C2×#4314—21no—
87C2×C8×D11D411yescharacteristic
88C2×C8×D11C2311yescharacteristic
89#66950—21no—
90#66943—21no—
91#66938—41no—
92#66938—41no—
93#66936—41no—
94C22⋊C4×D11—41no—
95C22⋊C4×D11—41no—
96#66932—41no—
97#66928—21no—
98C42×D11D411yescharacteristic
99C4×Dic22—21no—
100C11×SD32—41no—
101C11×D16—41no—
102C2×C11×C16C2311yescharacteristic
103C2×C11×C16C2311yescharacteristic
104C11×#107C2311yescharacteristic
105C11×#102—21no—
106C4×C8×C11C2311yescharacteristic
107#66896—21no—
108#66893—41no—
109#66891—41no—
110#66891—41no—
111#66890—41no—
112#66882C2311yescharacteristic
113#66880—21no—
114C8×Dic11D411yescharacteristic
115C8×Dic11C2311yescharacteristic
116C2×C11⋊C16C2311yescharacteristic
117C2×C11⋊C16C2311yescharacteristic
118#66874—21no—
119#66872—21no—
120C4×C11⋊C8D411yescharacteristic
121Dic88—41no—
122#66864—41no—
123#33777—111nomaximal, Sylow
124C23×D11—41no—
125C2×Q8×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C22×C4×C11—41no—
129C2×C22⋊D11—41no—
130C2×C22⋊D11—41no—
131Q8×D11—42no—
132Q8×D11—42no—
133D4×D11—42no—
134D4×D11—42no—
135C2×D44—21no—
136C2×C4×D11—41no—
137C2×C4×D11D811yescharacteristic
138C2×C4×D11D811yescharacteristic
139C2×C4×D11C2×D411yescharacteristic
140C2×Dic22—21no—
141C2×Dic22—21no—
142C2×Dic22—41no—
143C11×Q16—21no—
144C11×Q16—21no—
145C11×SD16—42no—
146C11×D8—21no—
147C11×D8—21no—
148C11×D8—21no—
149C11×D8—21no—
150C2×C8×C11C2×D411yescharacteristic
151C2×C8×C11C2411yescharacteristic
152C11×C4⋊C4—21no—
153C11×C22⋊C4—41no—
154C11×C22⋊C4—41no—
155C11×C22⋊C4—41no—
156C42×C11C2×D411yescharacteristic
157C22⋊Dic11—41no—
158C22⋊Dic11—41no—
159C22⋊Dic11—41no—
160C22⋊Dic11—41no—
161C22⋊Dic11—41no—
162#4326—42no—
163#4325—42no—
164#4324—42no—
165#4324—42no—
166#4323—42no—
167(C2×D11)⋊C4—41no—
168(C2×D11)⋊C4—41no—
169(C2×D11)⋊C4—41no—
170(C2×D11)⋊C4—41no—
171(C2×D11)⋊C4—41no—
172C4⋊Dic11—21no—
173C4⋊Dic11—41no—
174C4⋊Dic11—41no—
175Dic11⋊C4—41no—
176Dic11⋊C4—41no—
177C4×Dic11—41no—
178C4×Dic11D811yescharacteristic
179C4×Dic11D811yescharacteristic
180C4×Dic11C2×D411yescharacteristic
181C2×C11⋊C8C2×D411yescharacteristic
182C2×C11⋊C8C2×D411yescharacteristic
183Dic44—21no—
184Dic44—21no—
185Dic44—21no—
186Dic44—21no—
187D88—21no—
188D88—21no—
189#4314—42no—
190C8×D11—21no—
191C8×D11—21no—
192C8×D11—22no—
193C11×C16—21no—
194C11×C16—21no—
195C11⋊C16—21no—
196C11⋊C16—21no—
197#3168—111no—
198C2×#495—111no—
199#2249—111no—
200#2249—111no—
201#2242—111no—
202#2242—111no—
203#2211—111no—
204#2211—111no—
205#2210—111no—
206#2210D1111yescharacteristic, complemented
207#2188—111no—
208#2187—111no—
209#2185—111no—
210#2184—111no—
211#2162—111no—
212C23×C11—41no—
213C23×C11—41no—
214C22×D11—41no—
215C22×D11—82no—
216C22×D11—82no—
217C22×D11—82no—
218C22×D11C2×D811yescharacteristic
219Q8×C11—41no—
220Q8×C11—41no—
221D4×C11—41no—
222D4×C11—41no—
223D4×C11—41no—
224D4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—82no—
228C2×C4×C11C2×D811yescharacteristic
229C2×C4×C11C2×D811yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C22⋊D11—82no—
232C22⋊D11—82no—
233C2×Dic11—41no—
234C2×Dic11—41no—
235C2×Dic11—41no—
236C2×Dic11C2×D811yescharacteristic
237C2×Dic11C2×D811yescharacteristic
238C2×Dic11C2×D811yescharacteristic
239D44—41no—
240D44—41no—
241C4×D11—22no—
242C4×D11—21no—
243C4×D11—21no—
244C4×D11—41no—
245C4×D11—82no—
246Dic22—41no—
247Dic22—41no—
248Dic22—41no—
249Dic22—41no—
250Dic22—82no—
251C8×C11—21no—
252C8×C11H(5,𝔽2)11yescharacteristic
253C8×C11H(5,𝔽2)11yescharacteristic
254C11⋊C8—21no—
255C11⋊C8AGL(1,ℤ/8)12yes—
256C22×Q16—111no—
257C22×SD16—221no—
258C22×D8—111no—
259#529—221no—
260C2×#124—221no—
261C2×Q32—111no—
262C2×Q32—111no—
263C2×SD32—111no—
264C2×SD32—111no—
265C2×SD32—111no—
266C2×SD32C2×D1111yescharacteristic, complemented
267C2×D16—111no—
268C2×D16C2×D1111yescharacteristic
269#499—111no—
270#495—111no—
271#495—111no—
272#495—111no—
273#495—111no—
274#495—221no—
275#495—221no—
276#495C2×D1111yescharacteristic
277#488—221no—
278#467—111no—
279#466—111no—
280#465—221no—
281C4×Q16—111no—
282C4×SD16—221no—
283C4×D8C2×D1111yescharacteristic, complemented
284C2×C4×C8—111no—
285C4⋊C16—111no—
286C4⋊C16C2×D1111yescharacteristic, complemented
287#358—111no—
288#358—111no—
289#358—111no—
290#358C2×D1111yescharacteristic, complemented
291#357—111no—
292#357—111no—
293#357—111no—
294#357C2×D1111yescharacteristic
295C22⋊C16—111no—
296C22⋊C16—111no—
297C4×C16—111no—
298C4×C16—111no—
299C22×C11—81no—
300C22×C11—81no—
301C22×C11—81no—
302C22×C11—81no—
303C22×C11—81no—
304C22×C11—81no—
305C22×C11C22×D811yescharacteristic
306C2×D11—21no—
307C2×D11—21no—
308C2×D11—81no—
309C2×D11—81no—
310C2×D11—81no—
311C2×D11—164no—
312C2×D11#50812yes—
313C4×C11—21no—
314C4×C11—21no—
315C4×C11—81no—
316C4×C11—81no—
317C4×C11#53511yescharacteristic
318C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
319Dic11—21no—
320Dic11—21no—
321Dic11—21no—
322Dic11—81no—
323Dic11—81no—
324Dic11—81no—
325C22×Q8—221no—
326C22×D4—221no—
327C2×Q16—111no—
328C2×Q16—111no—
329C2×Q16—221no—
330C2×Q16—441no—
331C2×Q16—441no—
332C2×Q16C22×D1111yescharacteristic
333C2×SD16—21no—
334C2×SD16—221no—
335C2×SD16—221no—
336C2×SD16—221no—
337C2×SD16—221no—
338C2×SD16—444no—
339C2×D8—111no—
340C2×D8—221no—
341C2×D8—441no—
342C2×D8—441no—
343C2×D8C22×D1111yescharacteristic
344C2×D8C22×D1111yescharacteristic
345C22×C8—111no—
346C22×C8—111no—
347#126—441no—
348#125—221no—
349#124—21no—
350#124—221no—
351#124—221no—
352#124—221no—
353#124—221no—
354#124—441no—
355#124—441no—
356#123—441no—
357C22⋊Q8—221no—
358#121—221no—
359C4×Q8—221no—
360C4×D4—21no—
361C4×D4—441no—
362#117—441no—
363C2×C22⋊C4—441no—
364C2×C22⋊C4—441no—
365C2×C42—111no—
366Q32—441no—
367Q32—441no—
368SD32—41no—
369SD32—441no—
370SD32—441no—
371SD32—441no—
372D16—41no—
373D16—441no—
374C2×C16—111no—
375C2×C16—111no—
376C2×C16C22×D1111yescharacteristic
377C2×C16C22×D1111yescharacteristic
378#107—111no—
379#107C22×D1111yescharacteristic
380#106—221no—
381#103—221no—
382#103—221no—
383#102—21no—
384#102—221no—
385C4×C8—111no—
386C4×C8—111no—
387C4×C8—111no—
388C4×C8C22×D1111yescharacteristic
389C2×C11—161no—
390C2×C11—161no—
391C2×C11#320511yescharacteristic
392C2×C11C2×#50811yescharacteristic
393C2×C11#341411yescharacteristic
394D11—22no—
395D11—161no—
396C24—441no—
397C2×Q8—21no—
398C2×Q8—221no—
399C2×Q8—221no—
400C2×Q8—441no—
401C2×Q8—442no—
402C2×Q8—442no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—221no—
406C2×D4—441no—
407C2×D4—442no—
408C2×D4—442no—
409C2×D4—441no—
410C22×C4—41no—
411C22×C4—111no—
412C22×C4—111no—
413C22×C4—111no—
414C22×C4—441no—
415Q16—21no—
416Q16—21no—
417Q16—221no—
418Q16—221no—
419Q16—221no—
420Q16—221no—
421Q16—442no—
422SD16—42no—
423SD16—442no—
424SD16—442no—
425SD16—442no—
426SD16—442no—
427D8—21no—
428D8—21no—
429D8—21no—
430D8—21no—
431D8—221no—
432D8—221no—
433D8—442no—
434C2×C8—111no—
435C2×C8—111no—
436C2×C8—222no—
437C2×C8—221no—
438C2×C8—221no—
439C2×C8D4×D1111yescharacteristic
440C2×C8C23×D1111yescharacteristic
441C4⋊C4—21no—
442C4⋊C4—221no—
443C4⋊C4—441no—
444C4⋊C4—441no—
445C4⋊C4—441no—
446C4⋊C4—441no—
447C22⋊C4—41no—
448C22⋊C4—41no—
449C22⋊C4—41no—
450C22⋊C4—441no—
451C22⋊C4—441no—
452C22⋊C4—441no—
453C22⋊C4—441no—
454C22⋊C4—441no—
455C22⋊C4—441no—
456C22⋊C4—441no—
457C22⋊C4—441no—
458C22⋊C4—441no—
459C22⋊C4—441no—
460C42—111no—
461C42—111no—
462C42—111no—
463C42—441no—
464C42D4×D1111yescharacteristic
465C16—21no—
466C16—21no—
467C16—221no—
468C16—221no—
469C11#3377711yescharacteristic, complemented, Sylow
470C23—41no—
471C23—41no—
472C23—111no—
473C23—441no—
474C23—882no—
475C23—882no—
476C23—882no—
477Q8—41no—
478Q8—41no—
479Q8—441no—
480Q8—441no—
481Q8—441no—
482Q8—441no—
483Q8—882no—
484D4—41no—
485D4—41no—
486D4—41no—
487D4—41no—
488D4—441no—
489D4—441no—
490D4—882no—
491D4—882no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—82no—
495C2×C4—111no—
496C2×C4—111no—
497C2×C4—111no—
498C2×C4—222no—
499C2×C4—221no—
500C2×C4—221no—
501C2×C4—441no—
502C2×C4—441no—
503C2×C4—441no—
504C2×C4—441no—
505C2×C4—882no—
506C2×C4D8×D1111yescharacteristic
507C2×C4D8×D1111yescharacteristic
508C2×C4C2×D4×D1111yescharacteristic
509C8—21no—
510C8—112no—
511C8—221no—
512C8#6703711yescharacteristic
513C8#6704211yescharacteristic
514C22—81no—
515C22—81no—
516C22—81no—
517C22—81no—
518C22—81no—
519C22—81no—
520C22—112no—
521C22—221no—
522C22—221no—
523C22—881no—
524C22—881no—
525C22—881no—
526C22—1764no—
527C22C2×D8×D1111yescharacteristic
528C4—21no—
529C4—21no—
530C4—81no—
531C4—81no—
532C4—221no—
533C4—221no—
534C4—221no—
535C4—881no—
536C4—881no—
537C4—881no—
538C4#1062313811yescharacteristic
539C4D11×AGL(1,ℤ/8)11yescharacteristic
540C2—161no—
541C2—161no—
542C2—222no—
543C2—1761no—
544C2#1307953311yescharacteristic
545C2D11×#50811yescharacteristic
546C2#1308174811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2210C2
socleC22×C11C22×D8
prime radical#13070526C2
hypercenter#2210D11
hypocenterC11#33777
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2210

Complements

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

NH ≅ G/Ntype
1. #13079184C2semidirect
2. D11×#495C2semidirect
3. #13070876C2semidirect
4. #13070874C2semidirect
5. #13070849C2semidirect
6. #13070846C2semidirect
7. #13070679C2semidirect
8. #13070675C2semidirect
9. #13070671C2semidirect
10. #13070551C2semidirect
11. #13070546C2semidirect
12. #13070531C2semidirect
14. #13070414C2semidirect
15. C11×#2210C2semidirect
21. C2×C11×SD32C22semidirect
24. C4×C11×D8C22semidirect
26. C2×#66893C22semidirect
30. #10622768C22semidirect
32. C2×#66891C22semidirect
36. C2×Dic88C22semidirect
39. #10622491C22semidirect
42. C4×Dic44C22semidirect
45. C11×C4⋊C16C22semidirect
46. C11×#358C22semidirect
48. #10622202C22semidirect
53. #10622141C22semidirect
54. C16×Dic11C22semidirect
55. C16×Dic11C22semidirect
56. #10622130C22semidirect
58. C4⋊(C11⋊C16)C22semidirect
206. #2210D11semidirect
266. C2×SD32C2×D11semidirect
283. C4×D8C2×D11semidirect
286. C4⋊C16C2×D11semidirect
290. #358C2×D11semidirect
469. C11#33777semidirect

Maximal subgroups

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

subgroupindex
#130791842
D11×#4952
#130708762
#130708742
#130708492
#130708462
#130706792
#130706752
#130706712
#130705512
#130705462
#130705312
#130705262
#130704142
C11×#22102
#3377711