Finite Group Databasebeta

← #14909619

Subgroups — #14909619

Order 2816.

584 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078266C211yesmaximal, characteristic, complemented
2#13078259C211yesmaximal, characteristic
3#13070826C211yesmaximal, characteristic, complemented
4#13070823C211yesmaximal, characteristic, complemented
5#13070810C211yesmaximal, characteristic, complemented
6#13070805C211yesmaximal, characteristic, complemented
7#13070729C211yesmaximal, characteristic, complemented
8#13070714C211yesmaximal, characteristic, complemented
9#13070710C211yesmaximal, characteristic, complemented
10#13070546C211yesmaximal, characteristic, complemented
11#13070543C211yesmaximal, characteristic, complemented
12#13070534C211yesmaximal, characteristic, complemented
13#13070531C211yesmaximal, characteristic, complemented
14#13070231C211yesmaximal, characteristic, complemented
15C11×#2220C211yesmaximal, characteristic, complemented
16C2×Q16×D11C2211yescharacteristic, complemented
17C2×D8×D11C2211yescharacteristic
18C2×#66954C2211yescharacteristic
19#10623159—21no—
20#10623138—21no—
21C2×C11×SD32C2211yescharacteristic
22C2×C11×M32C2211yescharacteristic, complemented
23C11×#467C2211yescharacteristic, complemented
24C11×#466C2211yescharacteristic
25#10622801C2211yescharacteristic
26C2×#66892C2211yescharacteristic
27#10622770C2211yescharacteristic
28C2×#66891C2211yescharacteristic
29#10622729C2211yescharacteristic, complemented
30#10622728C2211yescharacteristic
31C22×C11⋊C16C2211yescharacteristic, complemented
32#10622665—21no—
33#10622652—21no—
34C2×#66864C2211yescharacteristic
35#10622500C2211yescharacteristic
36#10622496C2211yescharacteristic
37#10622493C2211yescharacteristic
38#10622493C2211yescharacteristic, complemented
39#10622429—21no—
40#10622415—21no—
41#10622395—21no—
42#10622383—21no—
43C11×#366C2211yescharacteristic, complemented
44C11×#358C2211yescharacteristic, complemented
45C11×#357C2211yescharacteristic
46#10622202C2211yescharacteristic, complemented
47#10622200C2211yescharacteristic
48#10622147C2211yescharacteristic
49(C2×D11)⋊C16C2211yescharacteristic
50(C2×D11)⋊C16C2211yescharacteristic
51(C2×D11)⋊C16C2211yescharacteristic, complemented
52(C2×D11)⋊C16C2211yescharacteristic, complemented
53#10622142C2211yescharacteristic, complemented
54#10622141C2211yescharacteristic, complemented
55#10622130C2211yescharacteristic, complemented
56#10622129C2211yescharacteristic
57#10622128C2211yescharacteristic, complemented
58#10622128C2211yescharacteristic, complemented
59C2×Q8×D11—21no—
60C2×D4×D11—21no—
61C2×#4339D411yescharacteristic
62C2×C11×Q16C2311yescharacteristic
63C2×C11×D8C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C11×C22⋊Q8—21no—
66C11×#121—21no—
67#66999—21no—
68C2×#4326—21no—
69#66993—41no—
70#66991—21no—
71#66990—41no—
72C2×#4323—21no—
73#66983—21no—
74#66977—21no—
75C2×#4318D411yescharacteristic
76Q16×D11—41no—
77Q16×D11—41no—
78D8×D11—41no—
79D8×D11—41no—
80C2×Dic44C2311yescharacteristic
81C2×D88C2311yescharacteristic
82#66954—41no—
83#66954—41no—
84C2×#4313D411yescharacteristic
85C2×#4313D411yescharacteristic
86C2×C8×D11C2311yescharacteristic
87C2×C8×D11C2311yescharacteristic
88#66950—21no—
89#66948—21no—
90#66947—41no—
91#66945—21no—
92#66945—21no—
93#66941—41no—
94#66938—41no—
95#66938—41no—
96#66936—41no—
97#66935—41no—
98C11×SD32—41no—
99C11×M32—41no—
100C2×C11×C16C2311yescharacteristic
101C2×C11×C16C2311yescharacteristic
102C11×#107C2311yescharacteristic
103C11×#107C2311yescharacteristic
104C11×#103—21no—
105C11×#102—21no—
106#66899—21no—
107#66896—21no—
108#66892—41no—
109#66891—41no—
110#66885—21no—
111#66882C2311yescharacteristic
112#66882C2311yescharacteristic
113#66880—21no—
114C2×C11⋊C16—41no—
115C2×C11⋊C16C2311yescharacteristic
116C2×C11⋊C16C2311yescharacteristic
117#66874—21no—
118#66873—21no—
119#66872—21no—
120#66872—21no—
121#66864—41no—
122#33766—111nomaximal, Sylow
123C23×D11—41no—
124C2×Q8×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—41no—
127C22×C4×C11C2×D411yescharacteristic
128C2×C22⋊D11—41no—
129C2×C22⋊D11—41no—
130C2×C22⋊D11—41no—
131C2×C22⋊D11D811yescharacteristic
132C2×C22⋊D11D811yescharacteristic
133Q8×D11—42no—
134Q8×D11—42no—
135D4×D11—42no—
136D4×D11—42no—
137#4339—41no—
138#4339—41no—
139C2×D44—21no—
140C2×D44—41no—
141C2×D44D811yescharacteristic
142C2×C4×D11—41no—
143C2×C4×D11C2×D411yescharacteristic
144C2×C4×D11C2×D411yescharacteristic
145C2×Dic22—21no—
146C2×Dic22—41no—
147C2×Dic22D811yescharacteristic
148C11×Q16—21no—
149C11×Q16—21no—
150C11×D8—21no—
151C11×D8—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11C2×D411yescharacteristic
155C2×C8×C11C2411yescharacteristic
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—41no—
159C11×C22⋊C4—41no—
160C11×C22⋊C4—41no—
161C22⋊Dic11—41no—
162C22⋊Dic11—41no—
163#4326—42no—
164#4323—42no—
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—
170(C2×D11)⋊C4—41no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—41no—
174Dic11⋊C4—41no—
175Dic11⋊C4—41no—
176C4×Dic11—41no—
177C4×Dic11—41no—
178#4318—41no—
179C2×C11⋊C8C2×D411yescharacteristic
180C2×C11⋊C8C2×D411yescharacteristic
181Dic44—21no—
182Dic44—21no—
183D88—21no—
184D88—21no—
185#4313—41no—
186#4313—41no—
187C8×D11—21no—
188C8×D11—21no—
189C8×D11—21no—
190C8×D11—21no—
191C11×C16—21no—
192C11×C16—21no—
193C11⋊C16—21no—
194C11⋊C16—21no—
195#3059—111no—
196#3058—111no—
197#2237—111no—
198#2237—111no—
199#2234—111no—
200#2234—111no—
201#2220—111no—
202#2220D1111yescharacteristic, complemented
203#2217—111no—
204#2217—111no—
205#2187—111no—
206#2187—111no—
207#2185—111no—
208#2185—111no—
209#2113—111no—
210C23×C11—41no—
211C23×C11C2×D811yescharacteristic
212C22×D11—41no—
213C22×D11—82no—
214C22×D11—161no—
215C22×D11—161no—
216C22×D11C2×D811yescharacteristic
217C22×D11C2×D811yescharacteristic
218Q8×C11—41no—
219Q8×C11—41no—
220D4×C11—41no—
221D4×C11—41no—
222D4×C11—161no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11C2×D811yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C22⋊D11—41no—
231C22⋊D11—41no—
232C22⋊D11—82no—
233C22⋊D11—161no—
234C22⋊D11—161no—
235C2×Dic11—41no—
236C2×Dic11—41no—
237C2×Dic11—41no—
238C2×Dic11C2×D811yescharacteristic
239C2×Dic11C2×D811yescharacteristic
240D44—41no—
241D44—41no—
242D44—41no—
243D44—161no—
244C4×D11—21no—
245C4×D11—21no—
246C4×D11—21no—
247C4×D11—21no—
248C4×D11—82no—
249Dic22—41no—
250Dic22—41no—
251Dic22—41no—
252Dic22—82no—
253C8×C11—21no—
254C8×C11H(5,𝔽2)11yescharacteristic
255C8×C11H(5,𝔽2)11yescharacteristic
256C11⋊C8—21no—
257C11⋊C8—21no—
258C22×Q16—111no—
259C22×D8—111no—
260C2×#131—111no—
261#536—221no—
262#535—221no—
263C2×SD32—111no—
264C2×SD32—111no—
265C2×SD32—111no—
266C2×SD32C2×D1111yescharacteristic
267C2×M32C2×D1111yescharacteristic, complemented
268C22×C16—111no—
269#470—221no—
270#470—221no—
271#469—221no—
272#469—221no—
273#467—111no—
274#467—111no—
275#467—111no—
276#467C2×D1111yescharacteristic, complemented
277#466—111no—
278#466—111no—
279#466—111no—
280#466C2×D1111yescharacteristic
281#427—111no—
282#427—111no—
283#419—221no—
284#418—221no—
285#367—111no—
286#367—111no—
287#366—111no—
288#366C2×D1111yescharacteristic, complemented
289#358—111no—
290#358—111no—
291#358—111no—
292#358C2×D1111yescharacteristic, complemented
293#357—111no—
294#357—111no—
295#357—111no—
296#357C2×D1111yescharacteristic
297C22⋊C16—111no—
298C22⋊C16—111no—
299C22⋊C16—111no—
300C22⋊C16—111no—
301C22×C11—21no—
302C22×C11—21no—
303C22×C11—21no—
304C22×C11—81no—
305C22×C11—81no—
306C22×C11—81no—
307C22×C11C22×D811yescharacteristic
308C2×D11—21no—
309C2×D11—21no—
310C2×D11—21no—
311C2×D11—21no—
312C2×D11—21no—
313C2×D11—21no—
314C2×D11—81no—
315C2×D11—81no—
316C2×D11—81no—
317C2×D11—164no—
318C4×C11—21no—
319C4×C11—81no—
320C4×C11—81no—
321C4×C11—81no—
322C4×C11#53411yescharacteristic
323C4×C11#57511yescharacteristic
324Dic11—21no—
325Dic11—21no—
326Dic11—81no—
327Dic11—81no—
328Dic11—81no—
329C2×#41—111no—
330C22×Q8—221no—
331C22×D4—221no—
332C2×Q16—111no—
333C2×Q16—221no—
334C2×Q16—441no—
335C2×Q16—441no—
336C2×Q16C22×D1111yescharacteristic
337C2×D8—111no—
338C2×D8—221no—
339C2×D8—441no—
340C2×D8—441no—
341C2×D8C22×D1111yescharacteristic
342#131—441no—
343#131—441no—
344C2×M16—111no—
345C2×M16—111no—
346C2×M16—111no—
347C22×C8—111no—
348C22×C8—111no—
349C22×C8C22×D1111yescharacteristic
350C4⋊Q8—441no—
351#127—441no—
352#124—441no—
353#124—441no—
354#123—441no—
355#123—441no—
356C22⋊Q8—21no—
357C22⋊Q8—221no—
358C22⋊Q8—221no—
359C22⋊Q8—221no—
360#121—21no—
361#121—221no—
362#121—221no—
363#121—221no—
364#120—441no—
365#120—441no—
366#117—221no—
367#117—221no—
368SD32—41no—
369SD32—441no—
370SD32—441no—
371SD32—441no—
372M32—41no—
373C2×C16—111no—
374C2×C16—111no—
375C2×C16—441no—
376C2×C16C22×D1111yescharacteristic
377C2×C16C22×D1111yescharacteristic
378#107—111no—
379#107—111no—
380#107C22×D1111yescharacteristic
381#107C22×D1111yescharacteristic
382#106—221no—
383#106—221no—
384#103—21no—
385#103—221no—
386#103—221no—
387#103—221no—
388#102—21no—
389#102—221no—
390#102—221no—
391#102—221no—
392C2×C11—41no—
393C2×C11—161no—
394C2×C11#318611yescharacteristic
395C2×C11#341611yescharacteristic
396C2×C11#341611yescharacteristic
397D11—41no—
398D11—41no—
399D11—161no—
400C24—441no—
401#41—441no—
402#41—441no—
403C2×Q8—21no—
404C2×Q8—111no—
405C2×Q8—221no—
406C2×Q8—441no—
407C2×Q8—442no—
408C2×Q8—442no—
409C2×D4—21no—
410C2×D4—41no—
411C2×D4—111no—
412C2×D4—111no—
413C2×D4—111no—
414C2×D4—221no—
415C2×D4—441no—
416C2×D4—441no—
417C2×D4—442no—
418C2×D4—442no—
419C2×D4—441no—
420C2×D4—441no—
421C22×C4—111no—
422C22×C4—111no—
423C22×C4—441no—
424C22×C4D4×D1111yescharacteristic
425Q16—21no—
426Q16—21no—
427Q16—221no—
428Q16—221no—
429Q16—442no—
430D8—21no—
431D8—21no—
432D8—221no—
433D8—221no—
434D8—442no—
435M16—441no—
436M16—441no—
437M16—441no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—111no—
441C2×C8—111no—
442C2×C8—221no—
443C2×C8—221no—
444C2×C8—221no—
445C2×C8—221no—
446C2×C8D4×D1111yescharacteristic
447C2×C8C23×D1111yescharacteristic
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—41no—
451C4⋊C4—221no—
452C4⋊C4—221no—
453C4⋊C4—441no—
454C4⋊C4—441no—
455C4⋊C4—441no—
456C22⋊C4—41no—
457C22⋊C4—41no—
458C22⋊C4—441no—
459C22⋊C4—441no—
460C22⋊C4—441no—
461C22⋊C4—441no—
462C22⋊C4—441no—
463C22⋊C4—441no—
464C22⋊C4—441no—
465C22⋊C4—441no—
466C42—441no—
467C42—441no—
468C16—21no—
469C16—21no—
470C16—221no—
471C16—221no—
472C11#3376611yescharacteristic, complemented, Sylow
473C23—41no—
474C23—111no—
475C23—111no—
476C23—441no—
477C23—882no—
478C23—1761no—
479C23—1761no—
480C23D8×D1111yescharacteristic
481Q8—41no—
482Q8—41no—
483Q8—441no—
484Q8—441no—
485Q8—441no—
486Q8—882no—
487D4—41no—
488D4—41no—
489D4—161no—
490D4—441no—
491D4—441no—
492D4—441no—
493D4—441no—
494D4—441no—
495D4—882no—
496D4—1761no—
497D4—1761no—
498D4—1761no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—111no—
505C2×C4—111no—
506C2×C4—221no—
507C2×C4—221no—
508C2×C4—221no—
509C2×C4—221no—
510C2×C4—441no—
511C2×C4—441no—
512C2×C4—441no—
513C2×C4—882no—
514C2×C4D8×D1111yescharacteristic
515C2×C4C2×D4×D1111yescharacteristic
516C8—21no—
517C8—221no—
518C8—221no—
519C8#6703711yescharacteristic
520C8#6704211yescharacteristic
521C22—21no—
522C22—21no—
523C22—21no—
524C22—81no—
525C22—81no—
526C22—81no—
527C22—221no—
528C22—221no—
529C22—221no—
530C22—221no—
531C22—221no—
532C22—221no—
533C22—881no—
534C22—881no—
535C22—881no—
536C22—1764no—
537C22C2×D8×D1111yescharacteristic
538C4—21no—
539C4—81no—
540C4—81no—
541C4—81no—
542C4—221no—
543C4—221no—
544C4—881no—
545C4—881no—
546C4—881no—
547C4#1062313611yescharacteristic
548C4#1062329911yescharacteristic
549C2—41no—
550C2—161no—
551C2—441no—
552C2—441no—
553C2—1761no—
554C2#1307936311yescharacteristic
555C2#1308176111yescharacteristic
556C2#1308176211yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2220C2
socleC22×C11C22×D8
prime radical#13078259C2
hypercenter#2220D11
hypocenterC11#33766
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2220

Complements

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

NH ≅ G/Ntype
1. #13078266C2semidirect
3. #13070826C2semidirect
4. #13070823C2semidirect
5. #13070810C2semidirect
6. #13070805C2semidirect
7. #13070729C2semidirect
8. #13070714C2semidirect
9. #13070710C2semidirect
10. #13070546C2semidirect
11. #13070543C2semidirect
12. #13070534C2semidirect
13. #13070531C2semidirect
14. #13070231C2semidirect
15. C11×#2220C2semidirect
16. C2×Q16×D11C22semidirect
22. C2×C11×M32C22semidirect
23. C11×#467C22semidirect
29. #10622729C22semidirect
31. C22×C11⋊C16C22semidirect
38. #10622493C22semidirect
43. C11×#366C22semidirect
44. C11×#358C22semidirect
46. #10622202C22semidirect
51. (C2×D11)⋊C16C22semidirect
52. (C2×D11)⋊C16C22semidirect
53. #10622142C22semidirect
54. #10622141C22semidirect
55. #10622130C22semidirect
57. #10622128C22semidirect
58. #10622128C22semidirect
202. #2220D11semidirect
267. C2×M32C2×D11semidirect
276. #467C2×D11semidirect
288. #366C2×D11semidirect
292. #358C2×D11semidirect
472. C11#33766semidirect

Maximal subgroups

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

subgroupindex
#130782662
#130782592
#130708262
#130708232
#130708102
#130708052
#130707292
#130707142
#130707102
#130705462
#130705432
#130705342
#130705312
#130702312
C11×#22202
#3376611