Finite Group Databasebeta

← #14909840

Subgroups — #14909840

Order 2816.

606 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079252C211yesmaximal, characteristic, complemented
2#13079096C211yesmaximal, characteristic, complemented
3#13070875C211yesmaximal, characteristic, complemented
4#13070853C211yesmaximal, characteristic, complemented
5#13070839C211yesmaximal, characteristic, complemented
6#13070676C211yesmaximal, characteristic, complemented
7#13070669C211yesmaximal, characteristic, complemented
8#13070654C211yesmaximal, characteristic, complemented
9#13070649C211yesmaximal, characteristic, complemented
10#13070553C211yesmaximal, characteristic, complemented
11#13070543C211yesmaximal, characteristic, complemented
12#13070536C211yesmaximal, characteristic, complemented
13#13070526C211yesmaximal, characteristic, complemented
14#13070424C211yesmaximal, characteristic, complemented
15C11×#2250C211yesmaximal, characteristic, complemented
16C2×#66965C2211yescharacteristic
17C2×#66964—21no—
18C2×D8×D11C2211yescharacteristic
19#10623246—21no—
20#10623213—21no—
21C2×C11×SD32C2211yescharacteristic
22C2×C11×SD32C2211yescharacteristic, complemented
23C2×C11×D16C2211yescharacteristic
24C2×C11×D16C2211yescharacteristic, complemented
25C11×#495C2211yescharacteristic, complemented
26C11×#493C2211yescharacteristic
27#10622801C2211yescharacteristic
28Q16×Dic11C2211yescharacteristic, complemented
29C2×#66893C2211yescharacteristic, complemented
30C2×#66892C2211yescharacteristic
31#10622787—21no—
32#10622777—21no—
33#10622770C2211yescharacteristic
34#10622768C2211yescharacteristic
35#10622767—21no—
36#10622764C2211yescharacteristic
37D8×Dic11C2211yescharacteristic, complemented
38C2×#66891C2211yescharacteristic, complemented
39C2×#66890C2211yescharacteristic
40#10622687—21no—
41#10622668—21no—
42#10622309C2211yescharacteristic
43#10622302C2211yescharacteristic
44#10622295C2211yescharacteristic, complemented
45C11×#346C2211yescharacteristic, complemented
46#10622200C2211yescharacteristic
47#10622200C2211yescharacteristic
48#10622200C2211yescharacteristic, complemented
49#10622200C2211yescharacteristic, complemented
50#10622147C2211yescharacteristic
51#10622147C2211yescharacteristic
52(C2×D11)⋊C16C2211yescharacteristic
53(C2×D11)⋊C16C2211yescharacteristic
54#10622141C2211yescharacteristic, complemented
55#10622141C2211yescharacteristic, complemented
56Dic11⋊C16C2211yescharacteristic, complemented
57Dic11⋊C16C2211yescharacteristic, complemented
58C4×C11⋊C16C2211yescharacteristic, complemented
59C2×#4341—21no—
60C2×D4×D11—21no—
61C2×C11×Q16C2311yescharacteristic
62C2×C11×SD16—21no—
63C2×C11×D8—21no—
64C2×C11×D8C2311yescharacteristic
65C2×C11×D8C2311yescharacteristic
66C2×C11×D8C2311yescharacteristic
67C11×#127—21no—
68C11×#124—21no—
69#66999—21no—
70Q8×Dic11—21no—
71#66993—21no—
72#66992—41no—
73#66992—41no—
74#66991—21no—
75#66990—41no—
76#66990—41no—
77#66989—21no—
78D4×Dic11—21no—
79C2×#4324—21no—
80C2×#4324—21no—
81C2×#4323—21no—
82C2×#4323—21no—
83#66965—41no—
84#66965—41no—
85#66964—44no—
86D8×D11—41no—
87D8×D11—41no—
88C2×Dic44C2311yescharacteristic
89C2×D88C2311yescharacteristic
90C2×#4314—21no—
91C2×#4313D411yescharacteristic
92C2×C8×D11C2311yescharacteristic
93#66939—41no—
94#66938—41no—
95#66932—41no—
96#66931—41no—
97#66928—21no—
98#66925D411yescharacteristic
99#66922—21no—
100C11×SD32—41no—
101C11×SD32—41no—
102C11×D16—41no—
103C11×D16—41no—
104C2×C11×C16C2311yescharacteristic
105C2×C11×C16C2311yescharacteristic
106C4×C8×C11C2311yescharacteristic
107#66899—21no—
108#66899—21no—
109#66896—21no—
110#66896—21no—
111#66893—41no—
112#66892—41no—
113#66891—41no—
114#66890—41no—
115#66882—21no—
116#66882C2311yescharacteristic
117#66882C2311yescharacteristic
118#66879D411yescharacteristic
119C8×Dic11C2311yescharacteristic
120C2×C11⋊C16C2311yescharacteristic
121C2×C11⋊C16C2311yescharacteristic
122#66867D411yescharacteristic
123#33790—111nomaximal, Sylow
124C23×D11—41no—
125C2×Q8×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—41no—
130C2×D4×C11—41no—
131C2×C22⋊D11—41no—
132C2×C22⋊D11—41no—
133C2×C22⋊D11—41no—
134C2×C22⋊D11—41no—
135C2×C22⋊D11—41no—
136C22×Dic11—41no—
137C22×Dic11—41no—
138#4341—42no—
139#4341—42no—
140D4×D11—42no—
141D4×D11—42no—
142C2×D44—21no—
143C2×C4×D11C2×D411yescharacteristic
144C2×Dic22—21no—
145C2×Dic22—41no—
146C11×Q16—21no—
147C11×Q16—21no—
148C11×SD16—42no—
149C11×D8—21no—
150C11×D8—21no—
151C11×D8—21no—
152C11×D8—21no—
153C11×D8—21no—
154C11×D8—21no—
155C11×D8—42no—
156C2×C8×C11C2×D411yescharacteristic
157C2×C8×C11C2411yescharacteristic
158C11×C22⋊C4—41no—
159C11×C22⋊C4—41no—
160C42×C11C2×D411yescharacteristic
161C22⋊Dic11—41no—
162C22⋊Dic11—41no—
163C22⋊Dic11—41no—
164C22⋊Dic11—41no—
165#4324—42no—
166#4324—42no—
167#4323—42no—
168#4323—42no—
169(C2×D11)⋊C4—41no—
170(C2×D11)⋊C4—41no—
171(C2×D11)⋊C4—41no—
172(C2×D11)⋊C4D811yescharacteristic
173(C2×D11)⋊C4D811yescharacteristic
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—41no—
177C4⋊Dic11—41no—
178Dic11⋊C4—41no—
179Dic11⋊C4D811yescharacteristic
180Dic11⋊C4D811yescharacteristic
181C4×Dic11—41no—
182C4×Dic11C2×D411yescharacteristic
183C2×C11⋊C8C2×D411yescharacteristic
184C2×C11⋊C8C2×D411yescharacteristic
185Dic44—21no—
186Dic44—21no—
187D88—21no—
188D88—21no—
189#4314—42no—
190#4313—22no—
191C8×D11—21no—
192C8×D11—21no—
193C11×C16—21no—
194C11×C16—21no—
195C11⋊C16—21no—
196C11⋊C16—21no—
197#3175—111no—
198#3155—111no—
199#2250D1111yescharacteristic, complemented
200#2249—111no—
201#2243—111no—
202#2240—111no—
203#2211—111no—
204#2210—111no—
205#2207—111no—
206#2206—111no—
207#2189—111no—
208#2187—111no—
209#2186—111no—
210#2184—111no—
211#2164—111no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11—41no—
215C22×D11—41no—
216C22×D11—82no—
217C22×D11—161no—
218C22×D11—161no—
219C22×D11C2×D811yescharacteristic
220Q8×C11—41no—
221Q8×C11—41no—
222D4×C11—41no—
223D4×C11—41no—
224D4×C11—41no—
225D4×C11—41no—
226D4×C11—41no—
227D4×C11—41no—
228D4×C11—161no—
229D4×C11—161no—
230C2×C4×C11—41no—
231C2×C4×C11C2×D811yescharacteristic
232C2×C4×C11C2×D811yescharacteristic
233C2×C4×C11C22×D411yescharacteristic
234C22⋊D11—82no—
235C22⋊D11—82no—
236C22⋊D11—161no—
237C22⋊D11—161no—
238C22⋊D11—161no—
239C2×Dic11—41no—
240C2×Dic11—41no—
241C2×Dic11—41no—
242C2×Dic11—82no—
243C2×Dic11—161no—
244C2×Dic11C2×D811yescharacteristic
245C2×Dic11C2×D811yescharacteristic
246C2×Dic11C2×D811yescharacteristic
247D44—41no—
248D44—41no—
249C4×D11—21no—
250C4×D11—21no—
251Dic22—41no—
252Dic22—41no—
253Dic22—161no—
254C8×C11AGL(1,ℤ/8)12yes—
255C8×C11H(5,𝔽2)11yescharacteristic
256C8×C11H(5,𝔽2)11yescharacteristic
257C11⋊C8—21no—
258C11⋊C8—21no—
259C2×AGL(1,ℤ/8)—221no—
260C2×#135—111no—
261C22×D8—111no—
262#542—221no—
263#535—221no—
264C2×Q32—111no—
265C2×SD32—111no—
266C2×SD32—111no—
267C2×SD32C2×D1111yescharacteristic
268C2×SD32C2×D1111yescharacteristic, complemented
269C2×D16—111no—
270C2×D16C2×D1111yescharacteristic
271C2×D16C2×D1111yescharacteristic, complemented
272#500—111no—
273#496—221no—
274#496—221no—
275#495—111no—
276#495—111no—
277#495C2×D1111yescharacteristic, complemented
278#493—111no—
279#493C2×D1111yescharacteristic
280#489—221no—
281#468—221no—
282#467—111no—
283#466—111no—
284#440—221no—
285C4×Q16—111no—
286C4×D8—111no—
287#405—111no—
288C4⋊C16—111no—
289C4⋊C16—111no—
290#358—111no—
291#358—111no—
292#357—111no—
293#357—111no—
294#357—111no—
295#357—111no—
296#357—111no—
297#357—111no—
298C22⋊C16—111no—
299C22⋊C16—111no—
300#346C2×D1111yescharacteristic, complemented
301C4×C16—111no—
302C22×C11—81no—
303C22×C11—81no—
304C22×C11—81no—
305C22×C11—81no—
306C22×C11—81no—
307C22×C11—81no—
308C22×C11—81no—
309C22×C11—81no—
310C22×C11—81no—
311C22×C11C22×D811yescharacteristic
312C2×D11—21no—
313C2×D11—21no—
314C2×D11—21no—
315C2×D11—81no—
316C2×D11—81no—
317C2×D11—81no—
318C2×D11—164no—
319C4×C11—21no—
320C4×C11—21no—
321C4×C11—81no—
322C4×C11#53511yescharacteristic
323C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
324Dic11—21no—
325Dic11—21no—
326Dic11—21no—
327Dic11—81no—
328Dic11—81no—
329Dic11—81no—
330C2×#41—221no—
331C22×D4—221no—
332AGL(1,ℤ/8)—444no—
333#135—441no—
334#135—441no—
335C2×Q16—111no—
336C2×Q16C22×D1111yescharacteristic
337C2×SD16—21no—
338C2×SD16—221no—
339C2×SD16—221no—
340C2×SD16—221no—
341C2×D8—21no—
342C2×D8—111no—
343C2×D8—221no—
344C2×D8—221no—
345C2×D8—441no—
346C2×D8—441no—
347C2×D8C22×D1111yescharacteristic
348C2×D8C22×D1111yescharacteristic
349C2×D8C22×D1111yescharacteristic
350C2×M16—111no—
351C22×C8—111no—
352C4⋊Q8—221no—
353#127—21no—
354#127—221no—
355#126—441no—
356#124—21no—
357#124—221no—
358#124—221no—
359#124—441no—
360#123—441no—
361C22⋊Q8—221no—
362C22⋊Q8—441no—
363#121—221no—
364#121—441no—
365#121—441no—
366#120—441no—
367#120—441no—
368C4×Q8—221no—
369C4×D4—221no—
370#117—111no—
371Q32—441no—
372SD32—41no—
373SD32—41no—
374SD32—441no—
375SD32—441no—
376D16—41no—
377D16—41no—
378D16—441no—
379C2×C16—111no—
380C2×C16—111no—
381C2×C16C22×D1111yescharacteristic
382C2×C16C22×D1111yescharacteristic
383#107—111no—
384#107—111no—
385#107—221no—
386#103—221no—
387#103—221no—
388#102—221no—
389#102—221no—
390#97—111no—
391#97—111no—
392C4×C8—111no—
393C4×C8C22×D1111yescharacteristic
394C2×C11—161no—
395C2×C11—161no—
396C2×C11—161no—
397C2×C11#320511yescharacteristic
398C2×C11#341511yescharacteristic
399C2×C11#341611yescharacteristic
400D11—41no—
401D11—161no—
402C24—441no—
403#41—442no—
404#41—442no—
405C2×Q8—21no—
406C2×Q8—221no—
407C2×Q8—441no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—41no—
412C2×D4—41no—
413C2×D4—221no—
414C2×D4—441no—
415C2×D4—441no—
416C2×D4—441no—
417C2×D4—442no—
418C2×D4—442no—
419C2×D4—441no—
420C2×D4—441no—
421C22×C4—111no—
422C22×C4—441no—
423C22×C4—441no—
424Q16—21no—
425Q16—21no—
426Q16—221no—
427Q16—221no—
428SD16—42no—
429SD16—442no—
430SD16—442no—
431SD16—442no—
432D8—21no—
433D8—21no—
434D8—21no—
435D8—21no—
436D8—21no—
437D8—21no—
438D8—42no—
439D8—221no—
440D8—221no—
441D8—442no—
442D8—442no—
443M16—222no—
444C2×C8—111no—
445C2×C8—111no—
446C2×C8—221no—
447C2×C8—221no—
448C2×C8D4×D1111yescharacteristic
449C2×C8C23×D1111yescharacteristic
450C4⋊C4—111no—
451C4⋊C4—111no—
452C4⋊C4—221no—
453C4⋊C4—221no—
454C4⋊C4—441no—
455C4⋊C4—441no—
456C4⋊C4—441no—
457C22⋊C4—41no—
458C22⋊C4—41no—
459C22⋊C4—111no—
460C22⋊C4—111no—
461C22⋊C4—441no—
462C22⋊C4—441no—
463C22⋊C4—441no—
464C22⋊C4—441no—
465C22⋊C4—441no—
466C22⋊C4—441no—
467C22⋊C4—441no—
468C42—111no—
469C42—441no—
470C42D4×D1111yescharacteristic
471C16—21no—
472C16—21no—
473C16—221no—
474C16—221no—
475C11#3379011yescharacteristic, complemented, Sylow
476C23—41no—
477C23—41no—
478C23—41no—
479C23—111no—
480C23—441no—
481C23—882no—
482C23—1761no—
483C23—1761no—
484Q8—41no—
485Q8—41no—
486Q8—441no—
487Q8—441no—
488Q8—1761no—
489D4—41no—
490D4—41no—
491D4—41no—
492D4—41no—
493D4—41no—
494D4—41no—
495D4—161no—
496D4—161no—
497D4—441no—
498D4—441no—
499D4—882no—
500D4—882no—
501D4—1761no—
502D4—1761no—
503D4—1761no—
504C2×C4—41no—
505C2×C4—111no—
506C2×C4—111no—
507C2×C4—111no—
508C2×C4—221no—
509C2×C4—221no—
510C2×C4—441no—
511C2×C4—441no—
512C2×C4—441no—
513C2×C4—882no—
514C2×C4—1761no—
515C2×C4D8×D1111yescharacteristic
516C2×C4D8×D1111yescharacteristic
517C2×C4C2×D4×D1111yescharacteristic
518C8—221no—
519C8—221no—
520C8#6696412yes—
521C8#6703711yescharacteristic
522C8#6703711yescharacteristic
523C22—81no—
524C22—81no—
525C22—81no—
526C22—81no—
527C22—81no—
528C22—81no—
529C22—81no—
530C22—81no—
531C22—81no—
532C22—221no—
533C22—221no—
534C22—221no—
535C22—881no—
536C22—881no—
537C22—881no—
538C22—1764no—
539C22C2×D8×D1111yescharacteristic
540C4—21no—
541C4—21no—
542C4—81no—
543C4—221no—
544C4—221no—
545C4—221no—
546C4—881no—
547C4—881no—
548C4—881no—
549C4#1062324611yescharacteristic
550C4C2×#6696411yescharacteristic
551C2—161no—
552C2—161no—
553C2—161no—
554C2—441no—
555C2—1761no—
556C2#1307953011yescharacteristic
557C2#1308175611yescharacteristic
558C2#1308176211yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2250C2
socleC22×C11C22×D8
hypercenter#2250D11
hypocenterC11#33790
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2250

Complements

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

NH ≅ G/Ntype
1. #13079252C2semidirect
2. #13079096C2semidirect
3. #13070875C2semidirect
4. #13070853C2semidirect
5. #13070839C2semidirect
6. #13070676C2semidirect
7. #13070669C2semidirect
8. #13070654C2semidirect
9. #13070649C2semidirect
10. #13070553C2semidirect
11. #13070543C2semidirect
12. #13070536C2semidirect
13. #13070526C2semidirect
14. #13070424C2semidirect
15. C11×#2250C2semidirect
22. C2×C11×SD32C22semidirect
24. C2×C11×D16C22semidirect
25. C11×#495C22semidirect
28. Q16×Dic11C22semidirect
29. C2×#66893C22semidirect
37. D8×Dic11C22semidirect
38. C2×#66891C22semidirect
44. #10622295C22semidirect
45. C11×#346C22semidirect
48. #10622200C22semidirect
49. #10622200C22semidirect
54. #10622141C22semidirect
55. #10622141C22semidirect
56. Dic11⋊C16C22semidirect
57. Dic11⋊C16C22semidirect
58. C4×C11⋊C16C22semidirect
199. #2250D11semidirect
268. C2×SD32C2×D11semidirect
271. C2×D16C2×D11semidirect
277. #495C2×D11semidirect
300. #346C2×D11semidirect
475. C11#33790semidirect

Maximal subgroups

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

subgroupindex
#130792522
#130790962
#130708752
#130708532
#130708392
#130706762
#130706692
#130706542
#130706492
#130705532
#130705432
#130705362
#130705262
#130704242
C11×#22502
#3379011