Finite Group Databasebeta

← #14909212

Subgroups — #14909212

Order 2816.

834 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622531C211yesmaximal, characteristic, complemented
2C2×#10622528C211yesmaximal, characteristic, complemented
3C2×#10622527C211yesmaximal, characteristic, complemented
4C2×#10622524C211yesmaximal, characteristic, complemented
5#13079041C211yesmaximal, characteristic, complemented
6D11×#495C211yesmaximal, characteristic, complemented
7#13070886C211yesmaximal, characteristic, complemented
8#13070884C211yesmaximal, characteristic, complemented
9#13070881C211yesmaximal, characteristic, complemented
10#13070879C211yesmaximal, characteristic, complemented
11#13070877C211yesmaximal, characteristic, complemented
12#13070875C211yesmaximal, characteristic, complemented
13#13070875C211yesmaximal, characteristic, complemented
14C4×#66862C211yesmaximal, characteristic, complemented
15C11×#2249C211yesmaximal, characteristic, complemented
16C2×#66972C2211yescharacteristic
17C2×Q16×D11C2211yescharacteristic
18C2×#66969—21no—
19C2×SD16×D11—21no—
20C2×#66965C2211yescharacteristic
21C2×D8×D11C2211yescharacteristic
22D11×#124—21no—
23#10623199—21no—
24C2×C11×Q32C2211yescharacteristic, complemented
25C2×C11×SD32C2211yescharacteristic
26C2×C11×SD32C2211yescharacteristic, complemented
27C2×C11×D16C2211yescharacteristic
28C11×#495C2211yescharacteristic
29C11×#495C2211yescharacteristic, complemented
30#10622804C2211yescharacteristic
31#10622794C2211yescharacteristic, complemented
32C2×#66893C2211yescharacteristic, complemented
33C2×#66893C2211yescharacteristic, complemented
34C2×#66892C2211yescharacteristic
35C2×#66892C2211yescharacteristic, complemented
36#10622788—21no—
37#10622781—21no—
38#10622768C2211yescharacteristic
39#10622764C2211yescharacteristic, complemented
40C2×#66891C2211yescharacteristic
41C2×#66891C2211yescharacteristic, complemented
42C2×#66890C2211yescharacteristic
43C2×#66890C2211yescharacteristic
44#10622672—21no—
45#10622672—21no—
46#10622531—24no—
47#10622528—24no—
48#10622527—24no—
49#10622524—24no—
50C2×Dic88C2211yescharacteristic, complemented
51C2×#66864C2211yescharacteristic
52C2×#66864C2211yescharacteristic, complemented
53C2×D176C2211yescharacteristic
54C2×#66862C2211yescharacteristic
55C2×#66862C2211yescharacteristic
56#10622309C2211yescharacteristic
57#10622309C2211yescharacteristic, complemented
58C4×C8×D11C2211yescharacteristic
59C4×C11×C16C2211yescharacteristic, complemented
60#10622140C2211yescharacteristic, complemented
61#10622140C2211yescharacteristic, complemented
62C4×C11⋊C16C2211yescharacteristic, complemented
63C2×#4343—21no—
64C2×Q8×D11—21no—
65C2×#4341—21no—
66C2×D4×D11—21no—
67C2×C11×Q16C2311yescharacteristic
68C2×C11×Q16C2311yescharacteristic
69C2×C11×SD16—21no—
70C2×C11×SD16—21no—
71C2×C11×D8C2311yescharacteristic
72C2×C11×D8C2311yescharacteristic
73C11×#124—21no—
74C11×#124—21no—
75#67000—21no—
76#66997—21no—
77C2×#4326—21no—
78C2×#4326—21no—
79C2×#4325—21no—
80C2×#4325—21no—
81#66993—21no—
82#66989—21no—
83C2×#4324—21no—
84C2×#4324—21no—
85C2×#4323—21no—
86C2×#4323—21no—
87#66972—22no—
88#66972—22no—
89Q16×D11—22no—
90Q16×D11—22no—
91#66969—44no—
92SD16×D11—44no—
93#66965—22no—
94#66965—22no—
95D8×D11—22no—
96D8×D11—22no—
97C2×Dic44C2311yescharacteristic
98C2×Dic44C2311yescharacteristic
99C2×D88C2311yescharacteristic
100C2×D88C2311yescharacteristic
101C2×#4314—21no—
102C2×#4314—21no—
103C2×C8×D11D411yescharacteristic
104C2×C8×D11C2311yescharacteristic
105#66938—42no—
106#66937—42no—
107(C22⋊D11)⋊C4—42no—
108C22⋊C4×D11—42no—
109#66928—21no—
110#66928—21no—
111C42×D11D411yescharacteristic
112C11×Q32—22no—
113C11×SD32—22no—
114C11×SD32—22no—
115C11×D16—22no—
116C2×C11×C16C2311yescharacteristic
117C2×C11×C16C2311yescharacteristic
118C4×C8×C11C2311yescharacteristic
119#66893—22no—
120#66893—22no—
121#66892—22no—
122#66892—22no—
123#66891—22no—
124#66891—22no—
125#66890—22no—
126#66890—22no—
127C8×Dic11D411yescharacteristic
128C8×Dic11C2311yescharacteristic
129C2×C11⋊C16C2311yescharacteristic
130C2×C11⋊C16C2311yescharacteristic
131C4×C11⋊C8D411yescharacteristic
132Dic88—22no—
133#66864—22no—
134#66864—22no—
135D176—22no—
136#66862D414yescomplemented
137#66862D414yescomplemented
138#33719—111nomaximal, Sylow
139C23×D11—41no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×C22⋊D11—42no—
145C2×C22⋊D11—41no—
146C2×C22⋊D11—41no—
147C22×Dic11—41no—
148#4343—42no—
149#4343—42no—
150Q8×D11—42no—
151Q8×D11—42no—
152#4341—42no—
153#4341—42no—
154D4×D11—42no—
155D4×D11—42no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—41no—
159C2×C4×D11—41no—
160C2×C4×D11—41no—
161C2×C4×D11D812yes—
162C2×C4×D11C2×D411yescharacteristic
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—41no—
166C11×Q16—21no—
167C11×Q16—21no—
168C11×Q16—21no—
169C11×Q16—21no—
170C11×SD16—42no—
171C11×SD16—42no—
172C11×D8—21no—
173C11×D8—21no—
174C11×D8—21no—
175C11×D8—21no—
176C2×C8×C11C2×D411yescharacteristic
177C2×C8×C11C2411yescharacteristic
178C11×C22⋊C4—42no—
179C11×C22⋊C4—42no—
180C42×C11C2×D411yescharacteristic
181C22⋊Dic11—42no—
182#4326—42no—
183#4326—42no—
184#4325—42no—
185#4325—42no—
186#4324—42no—
187#4324—42no—
188#4323—42no—
189#4323—42no—
190(C2×D11)⋊C4—42no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—42no—
193Dic11⋊C4—42no—
194C4×Dic11D812yes—
195C4×Dic11C2×D411yescharacteristic
196C2×C11⋊C8C2×D411yescharacteristic
197C2×C11⋊C8C2×D411yescharacteristic
198Dic44—21no—
199Dic44—21no—
200Dic44—21no—
201Dic44—21no—
202D88—21no—
203D88—21no—
204D88—21no—
205D88—21no—
206#4314—42no—
207#4314—42no—
208C8×D11D814yes—
209C8×D11C2×D412yes—
210C8×D11C2×D412yes—
211C11×C16C2×D412yes—
212C11×C16C2×D412yes—
213C11⋊C16C2×D412yes—
214C11⋊C16C2×D412yes—
215C2×#510—111no—
216C2×#510—111no—
217C2×#509—111no—
218C2×#509—111no—
219#3147—111no—
220C2×#495—111no—
221#2251—111no—
222#2251—111no—
223#2250—111no—
224#2250—111no—
225#2249—111no—
226#2249—111no—
227#2249—111no—
228#2249D1111yescharacteristic, complemented
229C4×M32—111no—
230C23×C11—41no—
231C23×C11—41no—
232C22×D11—41no—
233C22×D11—41no—
234C22×D11—84no—
235C22×D11—82no—
236C22×D11C2×D811yescharacteristic
237Q8×C11—41no—
238Q8×C11—41no—
239Q8×C11—41no—
240Q8×C11—41no—
241D4×C11—41no—
242D4×C11—41no—
243D4×C11—41no—
244D4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11C2×D812yes—
248C2×C4×C11C22×D411yescharacteristic
249C22⋊D11—84no—
250C22⋊D11—82no—
251C22⋊D11—82no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—82no—
255C2×Dic11C2×D812yes—
256C2×Dic11C2×D811yescharacteristic
257D44—41no—
258D44—41no—
259D44—41no—
260D44—41no—
261D44—82no—
262C4×D11—42no—
263C4×D11—82no—
264C4×D11—82no—
265C4×D11#12712yes—
266C4×D11C2×D812yes—
267Dic22—41no—
268Dic22—41no—
269Dic22—41no—
270Dic22—41no—
271Dic22—82no—
272C8×C11C2×D812yes—
273C8×C11C22×D411yescharacteristic
274C8×C11C22×D411yescharacteristic
275C11⋊C8#12712yes—
276C11⋊C8C2×D812yes—
277C2×#135—111no—
278C2×#135—111no—
279C2×#135—221no—
280C22×Q16—111no—
281C22×SD16—221no—
282C22×D8—111no—
283#532—221no—
284C2×#124—221no—
285#510—224no—
286#510—224no—
287#509—224no—
288#509—224no—
289C2×Q32—111no—
290C2×Q32—111no—
291C2×Q32—111no—
292C2×Q32C2×D1111yescharacteristic, complemented
293C2×SD32—111no—
294C2×SD32—111no—
295C2×SD32—111no—
296C2×SD32—111no—
297C2×SD32—111no—
298C2×SD32—111no—
299C2×SD32C2×D1111yescharacteristic
300C2×SD32C2×D1111yescharacteristic, complemented
301C2×D16—111no—
302C2×D16—111no—
303C2×D16—111no—
304C2×D16C2×D1111yescharacteristic
305C2×M32—111no—
306C2×M32—111no—
307#495—111no—
308#495—111no—
309#495—111no—
310#495—111no—
311#495—221no—
312#495—221no—
313#495—221no—
314#495C2×D1111yescharacteristic
315#495C2×D1111yescharacteristic, complemented
316#494—111no—
317#493—111no—
318#492—221no—
319C2×C4×C8—111no—
320#346—111no—
321#346—111no—
322C4×C16—111no—
323C4×C16C2×D1111yescharacteristic, complemented
324C22×C11—81no—
325C22×C11—81no—
326C22×C11—82no—
327C22×C11—82no—
328C22×C11C22×D811yescharacteristic
329C2×D11—22no—
330C2×D11—81no—
331C2×D11—81no—
332C2×D11—82no—
333C2×D11—82no—
334C2×D11—164no—
335C2×D11#49312yes—
336C4×C11—22no—
337C4×C11—81no—
338C4×C11—81no—
339C4×C11C2×#12711yescharacteristic
340C4×C11C22×D811yescharacteristic
341Dic11—22no—
342Dic11—81no—
343Dic11—81no—
344Dic11#49312yes—
345C2×#41—221no—
346C2×#41—221no—
347C22×Q8—221no—
348C22×D4—221no—
349#135—222no—
350#135—222no—
351#135—222no—
352#135—222no—
353#135—444no—
354C2×Q16—111no—
355C2×Q16—111no—
356C2×Q16—222no—
357C2×Q16—222no—
358C2×Q16—221no—
359C2×Q16—221no—
360C2×Q16C22×D1111yescharacteristic
361C2×Q16C22×D1111yescharacteristic
362C2×SD16—21no—
363C2×SD16—21no—
364C2×SD16—221no—
365C2×SD16—221no—
366C2×SD16—221no—
367C2×SD16—221no—
368C2×SD16—221no—
369C2×SD16—221no—
370C2×SD16—444no—
371C2×D8—111no—
372C2×D8—111no—
373C2×D8—222no—
374C2×D8—222no—
375C2×D8—221no—
376C2×D8—221no—
377C2×D8C22×D1111yescharacteristic
378C2×D8C22×D1111yescharacteristic
379C22×C8—111no—
380C22×C8—111no—
381C4⋊Q8—221no—
382#127—221no—
383#124—21no—
384#124—21no—
385#124—221no—
386#124—221no—
387#124—221no—
388#124—221no—
389#124—442no—
390#121—442no—
391C4×D4—442no—
392C2×C22⋊C4—442no—
393C2×C42—111no—
394Q32—22no—
395Q32—222no—
396Q32—222no—
397Q32—222no—
398SD32—22no—
399SD32—22no—
400SD32—222no—
401SD32—222no—
402SD32—222no—
403SD32—222no—
404SD32—222no—
405SD32—222no—
406D16—22no—
407D16—222no—
408D16—222no—
409D16—222no—
410M32—114no—
411M32—114no—
412C2×C16—111no—
413C2×C16—111no—
414C2×C16C22×D1111yescharacteristic
415C2×C16C22×D1111yescharacteristic
416C4×C8—111no—
417C4×C8—111no—
418C4×C8—111no—
419C4×C8C22×D1111yescharacteristic
420C2×C11—161no—
421C2×C11—161no—
422C2×C11C2×#49311yescharacteristic
423C2×C11#341412yes—
424D11—22no—
425D11—161no—
426D11—161no—
427C24—441no—
428#41—442no—
429#41—442no—
430#41—442no—
431#41—442no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—221no—
435C2×Q8—221no—
436C2×Q8—441no—
437C2×Q8—442no—
438C2×Q8—442no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—221no—
442C2×D4—221no—
443C2×D4—441no—
444C2×D4—442no—
445C2×D4—442no—
446C2×D4—442no—
447C2×D4—441no—
448C2×D4—441no—
449C22×C4—111no—
450C22×C4—112no—
451C22×C4—441no—
452C22×C4—441no—
453C22×C4—441no—
454Q16—21no—
455Q16—21no—
456Q16—21no—
457Q16—21no—
458Q16—221no—
459Q16—221no—
460Q16—221no—
461Q16—221no—
462Q16—442no—
463Q16—442no—
464SD16—42no—
465SD16—42no—
466SD16—442no—
467SD16—442no—
468SD16—442no—
469SD16—442no—
470SD16—442no—
471SD16—442no—
472D8—21no—
473D8—21no—
474D8—21no—
475D8—21no—
476D8—221no—
477D8—221no—
478D8—221no—
479D8—221no—
480D8—442no—
481D8—442no—
482C2×C8—111no—
483C2×C8—111no—
484C2×C8—114no—
485C2×C8—112no—
486C2×C8—112no—
487C2×C8D4×D1111yescharacteristic
488C2×C8C23×D1111yescharacteristic
489C4⋊C4—442no—
490C22⋊C4—42no—
491C22⋊C4—42no—
492C22⋊C4—442no—
493C22⋊C4—442no—
494C22⋊C4—442no—
495C22⋊C4—442no—
496C42—112no—
497C42—111no—
498C42D4×D1111yescharacteristic
499C16—112no—
500C16—112no—
501C16D4×D1112yes—
502C16D4×D1112yes—
503C11#3371911yescharacteristic, complemented, Sylow
504C23—41no—
505C23—41no—
506C23—111no—
507C23—441no—
508C23—441no—
509C23—882no—
510C23—884no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—441no—
516Q8—441no—
517Q8—441no—
518Q8—441no—
519Q8—882no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—441no—
525D4—441no—
526D4—441no—
527D4—441no—
528D4—882no—
529D4—882no—
530D4—884no—
531D4—882no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—111no—
535C2×C4—112no—
536C2×C4—112no—
537C2×C4—112no—
538C2×C4—442no—
539C2×C4—441no—
540C2×C4—441no—
541C2×C4—882no—
542C2×C4—882no—
543C2×C4—882no—
544C2×C4D8×D1112yes—
545C2×C4C2×D4×D1111yescharacteristic
546C8—112no—
547C8—112no—
548C8D8×D1112yes—
549C8C2×D4×D1111yescharacteristic
550C8C2×D4×D1111yescharacteristic
551C22—82no—
552C22—82no—
553C22—81no—
554C22—81no—
555C22—112no—
556C22—222no—
557C22—882no—
558C22—882no—
559C22—881no—
560C22—881no—
561C22—1764no—
562C22C2×D8×D1111yescharacteristic
563C4—22no—
564C4—81no—
565C4—81no—
566C4—112no—
567C4—222no—
568C4—881no—
569C4—881no—
570C4D11×#12711yescharacteristic
571C4C2×D8×D1111yescharacteristic
572C2—161no—
573C2—161no—
574C2—222no—
575C2—1761no—
576C2—1761no—
577C2D11×#49311yescharacteristic
578C2#1308174912yes—
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2249C2
socleC22×C11C22×D8
hypercenter#2249D11
hypocenterC11#33719
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2249

Complements

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

NH ≅ G/Ntype
1. C2×#10622531C2semidirect
2. C2×#10622528C2semidirect
3. C2×#10622527C2semidirect
4. C2×#10622524C2semidirect
5. #13079041C2semidirect
6. D11×#495C2semidirect
7. #13070886C2semidirect
8. #13070884C2semidirect
9. #13070881C2semidirect
10. #13070879C2semidirect
11. #13070877C2semidirect
12. #13070875C2semidirect
13. #13070875C2semidirect
14. C4×#66862C2semidirect
15. C11×#2249C2semidirect
24. C2×C11×Q32C22semidirect
26. C2×C11×SD32C22semidirect
29. C11×#495C22semidirect
31. #10622794C22semidirect
32. C2×#66893C22semidirect
33. C2×#66893C22semidirect
35. C2×#66892C22semidirect
39. #10622764C22semidirect
41. C2×#66891C22semidirect
50. C2×Dic88C22semidirect
52. C2×#66864C22semidirect
57. #10622309C22semidirect
59. C4×C11×C16C22semidirect
60. #10622140C22semidirect
61. #10622140C22semidirect
62. C4×C11⋊C16C22semidirect
136. #66862D4semidirect
137. #66862D4semidirect
228. #2249D11semidirect
292. C2×Q32C2×D11semidirect
300. C2×SD32C2×D11semidirect
315. #495C2×D11semidirect
323. C4×C16C2×D11semidirect
503. C11#33719semidirect

Maximal subgroups

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

subgroupindex
C2×#106225312
C2×#106225282
C2×#106225272
C2×#106225242
#130790412
D11×#4952
#130708862
#130708842
#130708812
#130708792
#130708772
#130708752
C4×#668622
C11×#22492
#3371911