Finite Group Databasebeta

← #14909582

Subgroups — #14909582

Order 2816.

588 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078199C211yesmaximal, characteristic
2D11×#467C211yesmaximal, characteristic, complemented
3#13070827C211yesmaximal, characteristic, complemented
4#13070823C211yesmaximal, characteristic, complemented
5#13070817C211yesmaximal, characteristic, complemented
6#13070803C211yesmaximal, characteristic, complemented
7#13070731C211yesmaximal, characteristic, complemented
8#13070729C211yesmaximal, characteristic, complemented
9#13070722C211yesmaximal, characteristic, complemented
10#13070559C211yesmaximal, characteristic, complemented
11#13070555C211yesmaximal, characteristic, complemented
12#13070548C211yesmaximal, characteristic, complemented
13#13070534C211yesmaximal, characteristic, complemented
14#13070226C211yesmaximal, characteristic, complemented
15C11×#2219C211yesmaximal, characteristic, complemented
16C2×#66972C2211yescharacteristic
17C2×Q16×D11C2211yescharacteristic
18C22×C8×D11C2211yescharacteristic
19#10623158—21no—
20D11×C22⋊Q8—21no—
21C2×C11×Q32C2211yescharacteristic, complemented
22C2×C11×M32C2211yescharacteristic
23C11×#467C2211yescharacteristic
24C11×#467C2211yescharacteristic
25#10622801C2211yescharacteristic
26#10622801C2211yescharacteristic
27C2×#66893C2211yescharacteristic, complemented
28C2×#66892C2211yescharacteristic, complemented
29#10622729C2211yescharacteristic
30#10622728C2211yescharacteristic
31C2×#66876C2211yescharacteristic
32#10622664—21no—
33#10622661—21no—
34C2×#66864C2211yescharacteristic, complemented
35#10622500C2211yescharacteristic
36#10622496C2211yescharacteristic
37#10622493C2211yescharacteristic
38D11×#107C2211yescharacteristic
39#10622426—21no—
40#10622420—21no—
41#10622417—21no—
42D11×#103—21no—
43C11×#367C2211yescharacteristic, complemented
44C11×#358C2211yescharacteristic, complemented
45C11×#358C2211yescharacteristic, complemented
46#10622202C2211yescharacteristic, complemented
47#10622202C2211yescharacteristic, complemented
48#10622147C2211yescharacteristic, complemented
49(C2×D11)⋊C16C2211yescharacteristic
50(C2×D11)⋊C16C2211yescharacteristic
51(C2×D11)⋊C16C2211yescharacteristic
52(C2×D11)⋊C16C2211yescharacteristic
53#10622142C2211yescharacteristic, complemented
54#10622141C2211yescharacteristic, complemented
55#10622130C2211yescharacteristic, complemented
56#10622129C2211yescharacteristic, complemented
57#10622128C2211yescharacteristic, complemented
58#10622127C2211yescharacteristic, complemented
59C2×#4343—21no—
60C2×Q8×D11—21no—
61C22×C4×D11D411yescharacteristic
62C2×C11×Q16C2311yescharacteristic
63C2×C11×Q16C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C11×C22⋊Q8—21no—
66C11×C22⋊Q8—21no—
67#66999—21no—
68#66999—21no—
69C2×#4326—21no—
70C2×#4325—21no—
71#66983—21no—
72#66977—21no—
73C22×C11⋊C8D411yescharacteristic
74#66972—41no—
75#66972—41no—
76Q16×D11—41no—
77Q16×D11—41no—
78C2×Dic44C2311yescharacteristic
79C2×D88C2311yescharacteristic
80C2×C8×D11—41no—
81C2×C8×D11—41no—
82C2×C8×D11D411yescharacteristic
83C2×C8×D11D411yescharacteristic
84C2×C8×D11C2311yescharacteristic
85C2×C8×D11C2311yescharacteristic
86#66950—21no—
87#66949—41no—
88#66948—21no—
89#66947—41no—
90#66946—41no—
91#66945—21no—
92C4⋊C4×D11—21no—
93C4⋊C4×D11—41no—
94#66935—41no—
95(C22⋊D11)⋊C4—41no—
96C22⋊C4×D11—41no—
97#66931—41no—
98C11×Q32—41no—
99C11×M32—41no—
100C2×C11×C16C2311yescharacteristic
101C2×C11×C16C2311yescharacteristic
102C11×#107C2311yescharacteristic
103C11×#107C2311yescharacteristic
104C11×#103—21no—
105C11×#103—21no—
106#66899—21no—
107#66899—21no—
108#66893—41no—
109#66892—41no—
110#66885—21no—
111#66882C2311yescharacteristic
112#66882C2311yescharacteristic
113#66880—21no—
114#66876—41no—
115C2×C11⋊C16C2311yescharacteristic
116C2×C11⋊C16C2311yescharacteristic
117#66874—21no—
118#66873—21no—
119#66872—21no—
120#66871—21no—
121#66864—41no—
122#33762—111nomaximal, Sylow
123C23×D11D811yescharacteristic
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C22×C4×C11C2×D411yescharacteristic
127C2×C22⋊D11—41no—
128C22×Dic11D811yescharacteristic
129#4343—42no—
130#4343—42no—
131Q8×D11—42no—
132Q8×D11—42no—
133C2×D44—21no—
134C2×D44—41no—
135C2×D44—41no—
136C2×C4×D11—41no—
137C2×C4×D11—41no—
138C2×C4×D11—41no—
139C2×C4×D11—41no—
140C2×C4×D11—41no—
141C2×C4×D11D811yescharacteristic
142C2×C4×D11D811yescharacteristic
143C2×C4×D11C2×D411yescharacteristic
144C2×C4×D11C2×D411yescharacteristic
145C2×Dic22—21no—
146C2×Dic22—41no—
147C11×Q16—21no—
148C11×Q16—21no—
149C11×Q16—21no—
150C11×Q16—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11C2×D411yescharacteristic
154C2×C8×C11C2411yescharacteristic
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—41no—
158C11×C4⋊C4—41no—
159C11×C22⋊C4—41no—
160C11×C22⋊C4—41no—
161C22⋊Dic11—41no—
162#4326—42no—
163#4325—42no—
164(C2×D11)⋊C4—41no—
165(C2×D11)⋊C4—41no—
166(C2×D11)⋊C4—41no—
167(C2×D11)⋊C4—41no—
168(C2×D11)⋊C4—41no—
169(C2×D11)⋊C4—41no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—41no—
173Dic11⋊C4—41no—
174Dic11⋊C4—41no—
175Dic11⋊C4—41no—
176Dic11⋊C4—41no—
177C4×Dic11—41no—
178C2×C11⋊C8—41no—
179C2×C11⋊C8C2×D411yescharacteristic
180C2×C11⋊C8C2×D411yescharacteristic
181Dic44—21no—
182Dic44—21no—
183D88—21no—
184D88—21no—
185C8×D11—21no—
186C8×D11—21no—
187C8×D11—21no—
188C8×D11—21no—
189C8×D11—41no—
190C8×D11—41no—
191C11×C16—21no—
192C11×C16—21no—
193C11⋊C16—21no—
194C11⋊C16—21no—
195#3050—111no—
196C2×#467—111no—
197#2237—111no—
198#2237—111no—
199#2236—111no—
200#2233—111no—
201#2220—111no—
202#2220—111no—
203#2219—111no—
204#2219D1111yescharacteristic, complemented
205#2189—111no—
206#2189—111no—
207#2188—111no—
208#2185—111no—
209#2112—111no—
210C23×C11C2×D811yescharacteristic
211C22×D11—22no—
212C22×D11—41no—
213C22×D11—41no—
214C22×D11—41no—
215C22×D11C2×D811yescharacteristic
216C22×D11C2×D811yescharacteristic
217Q8×C11—41no—
218Q8×C11—41no—
219Q8×C11—41no—
220Q8×C11—41no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11C2×D811yescharacteristic
228C2×C4×C11C22×D411yescharacteristic
229C22⋊D11—82no—
230C2×Dic11—41no—
231C2×Dic11—41no—
232C2×Dic11—41no—
233C2×Dic11—41no—
234C2×Dic11C2×D811yescharacteristic
235C2×Dic11C2×D811yescharacteristic
236D44—41no—
237D44—41no—
238D44—82no—
239D44—82no—
240C4×D11—21no—
241C4×D11—21no—
242C4×D11—21no—
243C4×D11—21no—
244C4×D11—41no—
245C4×D11—41no—
246C4×D11—82no—
247C4×D11—82no—
248C4×D11—82no—
249Dic22—41no—
250Dic22—41no—
251Dic22—82no—
252C8×C11—21no—
253C8×C11H(5,𝔽2)11yescharacteristic
254C8×C11H(5,𝔽2)11yescharacteristic
255C11⋊C8—21no—
256C11⋊C8—21no—
257C2×#135—111no—
258C22×Q16—111no—
259C23×C8—111no—
260#525—221no—
261C2×C22⋊Q8—221no—
262C2×Q32—111no—
263C2×Q32C2×D1111yescharacteristic, complemented
264C2×SD32—111no—
265C2×SD32—111no—
266C2×M32—111no—
267C2×M32C2×D1111yescharacteristic
268#467—111no—
269#467—111no—
270#467—111no—
271#467—111no—
272#467—221no—
273#467—221no—
274#467C2×D1111yescharacteristic
275#467C2×D1111yescharacteristic
276#466—111no—
277#466—111no—
278#465—221no—
279#465—221no—
280#427—111no—
281C2×#107—111no—
282#416—221no—
283C2×#103—221no—
284#367—111no—
285#367C2×D1111yescharacteristic, complemented
286#366—111no—
287#366—111no—
288#358—111no—
289#358—111no—
290#358—111no—
291#358—111no—
292#358C2×D1111yescharacteristic, complemented
293#358C2×D1111yescharacteristic, complemented
294#357—111no—
295#357—111no—
296C22⋊C16—111no—
297C22⋊C16—111no—
298C22⋊C16—111no—
299C22⋊C16—111no—
300C22×C11—21no—
301C22×C11—21no—
302C22×C11—21no—
303C22×C11C22×D811yescharacteristic
304C2×D11—21no—
305C2×D11—21no—
306C2×D11—21no—
307C2×D11—21no—
308C2×D11—21no—
309C2×D11—44no—
310C2×D11—81no—
311C2×D11—81no—
312C2×D11—81no—
313C2×D11#51012yes—
314C4×C11—21no—
315C4×C11—81no—
316C4×C11—81no—
317C4×C11—81no—
318C4×C11—81no—
319C4×C11#53411yescharacteristic
320C4×C11#57511yescharacteristic
321Dic11—21no—
322Dic11—21no—
323Dic11—81no—
324Dic11—81no—
325Dic11—81no—
326C2×#41—221no—
327C22×Q8—221no—
328C23×C4—111no—
329#135—441no—
330#135—441no—
331C2×Q16—111no—
332C2×Q16—221no—
333C2×Q16—441no—
334C2×Q16—441no—
335C2×Q16C22×D1111yescharacteristic
336C2×Q16C22×D1111yescharacteristic
337C2×SD16—221no—
338C2×D8—111no—
339C22×C8—111no—
340C22×C8—111no—
341C22×C8—111no—
342C22×C8—111no—
343C22×C8—111no—
344C22×C8—441no—
345C22×C8—441no—
346C22×C8C22×D1111yescharacteristic
347#123—441no—
348C22⋊Q8—21no—
349C22⋊Q8—21no—
350C22⋊Q8—221no—
351C22⋊Q8—221no—
352C22⋊Q8—221no—
353C22⋊Q8—221no—
354C22⋊Q8—441no—
355C22⋊Q8—441no—
356#121—221no—
357#121—221no—
358#120—441no—
359C4×D4—441no—
360C4×D4—441no—
361#117—221no—
362C2×C4⋊C4—221no—
363C2×C4⋊C4—441no—
364C2×C22⋊C4—441no—
365Q32—41no—
366Q32—441no—
367SD32—441no—
368SD32—441no—
369M32—41no—
370M32—441no—
371C2×C16—111no—
372C2×C16—111no—
373C2×C16C22×D1111yescharacteristic
374C2×C16C22×D1111yescharacteristic
375#107—111no—
376#107—111no—
377#107—221no—
378#107C22×D1111yescharacteristic
379#107C22×D1111yescharacteristic
380#106—221no—
381#103—21no—
382#103—21no—
383#103—221no—
384#103—221no—
385#103—221no—
386#103—221no—
387#102—221no—
388#102—221no—
389C2×C11—41no—
390C2×C11#318611yescharacteristic
391C2×C11C2×#51011yescharacteristic
392C2×C11#341411yescharacteristic
393D11—22no—
394D11—41no—
395D11—161no—
396C24—111no—
397#41—442no—
398#41—442no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—221no—
402C2×Q8—441no—
403C2×Q8—442no—
404C2×Q8—442no—
405C2×D4—221no—
406C2×D4—441no—
407C2×D4—441no—
408C2×D4—441no—
409C22×C4—111no—
410C22×C4—111no—
411C22×C4—111no—
412C22×C4—111no—
413C22×C4—111no—
414C22×C4—441no—
415C22×C4—441no—
416C22×C4—441no—
417C22×C4—441no—
418C22×C4—441no—
419C22×C4D4×D1111yescharacteristic
420Q16—21no—
421Q16—21no—
422Q16—21no—
423Q16—21no—
424Q16—221no—
425Q16—221no—
426Q16—442no—
427SD16—442no—
428D8—221no—
429D8—221no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—111no—
433C2×C8—111no—
434C2×C8—221no—
435C2×C8—221no—
436C2×C8—221no—
437C2×C8—221no—
438C2×C8—441no—
439C2×C8—441no—
440C2×C8—441no—
441C2×C8D4×D1111yescharacteristic
442C2×C8C23×D1111yescharacteristic
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—41no—
446C4⋊C4—41no—
447C4⋊C4—221no—
448C4⋊C4—221no—
449C4⋊C4—441no—
450C4⋊C4—441no—
451C4⋊C4—441no—
452C4⋊C4—441no—
453C4⋊C4—441no—
454C22⋊C4—41no—
455C22⋊C4—41no—
456C22⋊C4—441no—
457C22⋊C4—441no—
458C22⋊C4—441no—
459C22⋊C4—441no—
460C22⋊C4—441no—
461C22⋊C4—441no—
462C22⋊C4—441no—
463C42—441no—
464C16—21no—
465C16—21no—
466C16—221no—
467C16—221no—
468C11#3376211yescharacteristic, complemented, Sylow
469C23—111no—
470C23—111no—
471C23—222no—
472C23—441no—
473C23—441no—
474C23—441no—
475C23D8×D1111yescharacteristic
476Q8—41no—
477Q8—41no—
478Q8—41no—
479Q8—41no—
480Q8—441no—
481Q8—441no—
482Q8—882no—
483D4—441no—
484D4—441no—
485D4—882no—
486D4—882no—
487D4—882no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—111no—
495C2×C4—111no—
496C2×C4—221no—
497C2×C4—221no—
498C2×C4—221no—
499C2×C4—221no—
500C2×C4—441no—
501C2×C4—441no—
502C2×C4—441no—
503C2×C4—441no—
504C2×C4—441no—
505C2×C4—441no—
506C2×C4—882no—
507C2×C4—882no—
508C2×C4—882no—
509C2×C4D8×D1111yescharacteristic
510C2×C4C2×D4×D1111yescharacteristic
511C8—21no—
512C8—221no—
513C8—221no—
514C8#6703711yescharacteristic
515C8#6704211yescharacteristic
516C22—21no—
517C22—21no—
518C22—21no—
519C22—112no—
520C22—221no—
521C22—221no—
522C22—221no—
523C22—221no—
524C22—221no—
525C22—444no—
526C22—881no—
527C22—881no—
528C22—881no—
529C22C2×D8×D1111yescharacteristic
530C4—21no—
531C4—81no—
532C4—81no—
533C4—81no—
534C4—81no—
535C4—221no—
536C4—221no—
537C4—881no—
538C4—881no—
539C4—881no—
540C4#1062313611yescharacteristic
541C4#1062329911yescharacteristic
542C2—41no—
543C2—222no—
544C2—441no—
545C2—1761no—
546C2#1307936311yescharacteristic
547C2D11×#51011yescharacteristic
548C2#1308175111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2219C2
socleC22×C11C22×D8
prime radical#13078199C2
hypercenter#2219D11
hypocenterC11#33762
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2219

Complements

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

NH ≅ G/Ntype
2. D11×#467C2semidirect
3. #13070827C2semidirect
4. #13070823C2semidirect
5. #13070817C2semidirect
6. #13070803C2semidirect
7. #13070731C2semidirect
8. #13070729C2semidirect
9. #13070722C2semidirect
10. #13070559C2semidirect
11. #13070555C2semidirect
12. #13070548C2semidirect
13. #13070534C2semidirect
14. #13070226C2semidirect
15. C11×#2219C2semidirect
21. C2×C11×Q32C22semidirect
27. C2×#66893C22semidirect
28. C2×#66892C22semidirect
34. C2×#66864C22semidirect
43. C11×#367C22semidirect
44. C11×#358C22semidirect
45. C11×#358C22semidirect
46. #10622202C22semidirect
47. #10622202C22semidirect
48. #10622147C22semidirect
53. #10622142C22semidirect
54. #10622141C22semidirect
55. #10622130C22semidirect
56. #10622129C22semidirect
57. #10622128C22semidirect
58. #10622127C22semidirect
204. #2219D11semidirect
263. C2×Q32C2×D11semidirect
285. #367C2×D11semidirect
292. #358C2×D11semidirect
293. #358C2×D11semidirect
468. C11#33762semidirect

Maximal subgroups

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

subgroupindex
#130781992
D11×#4672
#130708272
#130708232
#130708172
#130708032
#130707312
#130707292
#130707222
#130705592
#130705552
#130705482
#130705342
#130702262
C11×#22192
#3376211