Finite Group Databasebeta

← #14769792

Subgroups — #14769792

Order 2816.

1384 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622809C211yesmaximal, characteristic, complemented
2#13077492C211yesmaximal, characteristic, complemented
3#13077142C212yesmaximal, complemented
4#13069527C211yesmaximal, characteristic, complemented
5#13069483C211yesmaximal, characteristic, complemented
6#13069126C212yesmaximal, complemented
7#13068994C212yesmaximal, complemented
8#13068680C211yesmaximal, characteristic, complemented
9#13068570C212yesmaximal, complemented
10#13068451C211yesmaximal, characteristic, complemented
11C2×C11×#576C211yesmaximal, characteristic
12C2×C11×H(5,𝔽2)C2212yes—
13C11×#576—24no—
14C11×#576C418yescomplemented
15C2×C11×AGL(1,ℤ/8)—22no—
16C2×C11×AGL(1,ℤ/8)C2212yes—
17C2×C11×#135—21no—
18C2×C11×#135C2211yescharacteristic
19C22×C11×D8—21no—
20C22×C11×D8C2211yescharacteristic
21C2×C11×#131C2211yescharacteristic
22#10623358C2212yescomplemented
23C2×#67001C2212yescomplemented
24C2×#66901C2211yescharacteristic
25C2×#66901C2212yescomplemented
26#10622846—22no—
27#10622846C2211yescharacteristic
28#10622845—22no—
29#10622845C2212yes—
30#10622845C2212yescomplemented
31#10622834C2212yescomplemented
32C2×#66897C2212yescomplemented
33#10622828—22no—
34#10622828C2212yescomplemented
35C2×#66896—22no—
36C2×#66896C2212yescomplemented
37#10622809—24no—
38Q16×Dic11—21no—
39#10622777—22no—
40D8×Dic11—21no—
41C2×#66883C2211yescharacteristic, complemented
42C2×#66882C2211yescharacteristic, complemented
43#10622714C2211yescharacteristic, complemented
44C2×C8×Dic11C2211yescharacteristic, complemented
45#10622196C2211yescharacteristic, complemented
46#10622193C2211yescharacteristic, complemented
47#10622192C2212yescomplemented
48C11×H(5,𝔽2)—24no—
49C11×H(5,𝔽2)—24no—
50C11×H(5,𝔽2)—42no—
51C11×H(5,𝔽2)C2×C418yescomplemented
52C2×C11×#41—22no—
53C2×C11×#41—22no—
54C2×C11×#41C2312yes—
55C2×C11×#41C2311yescharacteristic
56C22×D4×C11—22no—
57C22×D4×C11—22no—
58C22×D4×C11—42no—
59C22×D4×C11C2312yes—
60C11×AGL(1,ℤ/8)—24no—
61C11×AGL(1,ℤ/8)—216no—
62C11×AGL(1,ℤ/8)C2×C418yescomplemented
63C11×#135—28no—
64C11×#135C2×C414yes—
65C11×#135D414yes—
66C2×C11×Q16D411yescharacteristic
67C2×C11×SD16—22no—
68C2×C11×SD16D412yes—
69C2×C11×D8—22no—
70C2×C11×D8—28no—
71C2×C11×D8—21no—
72C2×C11×D8—21no—
73C2×C11×D8—22no—
74C2×C11×D8C2×C414yescomplemented
75C2×C11×D8D411yescharacteristic
76C11×#131—22no—
77C11×#131C2×C414yescomplemented
78C2×C11×M16—21no—
79C2×C11×M16C2311yescharacteristic
80C22×C8×C11—21no—
81C22×C8×C11C2311yescharacteristic
82C2×C22⋊Dic11—42no—
83#67001—24no—
84#67001—42no—
85Q8×Dic11—22no—
86D4×Dic11—22no—
87D4×Dic11—42no—
88#66979—22no—
89#66979C2311yescharacteristic
90C2×C4⋊Dic11—22no—
91C2×C4⋊Dic11C2312yes—
92C2×C4×Dic11C2311yescharacteristic
93C2×#4318—22no—
94C2×#4318C2312yes—
95C2×#4318C2311yescharacteristic
96C22×C11⋊C8—22no—
97C22×C11⋊C8C2311yescharacteristic
98#66901—24no—
99#66901—22no—
100#66899—22no—
101#66899—22no—
102#66899D411yescharacteristic
103#66899D411yescharacteristic
104#66897—42no—
105#66896—22no—
106#66896—22no—
107#66896—22no—
108#66896—22no—
109#66896—22no—
110#66896—22no—
111#66896D411yescharacteristic
112#66896D411yescharacteristic
113#66883—22no—
114#66882—21no—
115#66882—21no—
116#66879—21no—
117C8×Dic11—21no—
118C8×Dic11—22no—
119#22466—111nomaximal, Sylow
120C24×C11—22no—
121C24×C11—42no—
122C11×#41—21no—
123C11×#41—22no—
124C11×#41—22no—
125C11×#41—21no—
126C11×#41—28no—
127C11×#41—28no—
128C11×#41—44no—
129C11×#41—44no—
130C11×#41C22×C414yes—
131C11×#41C22×C412yes—
132C11×#41C2×D414yes—
133C11×#41#4112yes—
134C2×Q8×C11C2×D412yes—
135C2×Q8×C11C2×D411yescharacteristic
136C2×D4×C11—22no—
137C2×D4×C11—21no—
138C2×D4×C11—28no—
139C2×D4×C11—28no—
140C2×D4×C11—22no—
141C2×D4×C11—22no—
142C2×D4×C11—22no—
143C2×D4×C11—22no—
144C2×D4×C11—22no—
145C2×D4×C11—44no—
146C2×D4×C11—44no—
147C2×D4×C11—42no—
148C2×D4×C11—42no—
149C2×D4×C11—48no—
150C2×D4×C11—48no—
151C2×D4×C11C22×C414yes—
152C2×D4×C11C2×D412yes—
153C2×D4×C11C2×D411yescharacteristic
154C22×C4×C11—22no—
155C22×C4×C11—21no—
156C22×C4×C11—42no—
157C22×C4×C11C2411yescharacteristic
158C22×Dic11—21no—
159C22×Dic11—22no—
160C22×Dic11—42no—
161C11×Q16C22⋊C414yescomplemented
162C11×SD16—28no—
163C11×SD16C22⋊C418yescomplemented
164C11×D8—24no—
165C11×D8—24no—
166C11×D8—28no—
167C11×D8C22⋊C414yescomplemented
168C11×M16—24no—
169C11×M16—21no—
170C11×M16C22×C412yes—
171C2×C8×C11—24no—
172C2×C8×C11—21no—
173C2×C8×C11C22×C412yes—
174C2×C8×C11C2×D411yescharacteristic
175C2×C8×C11C2×D412yes—
176C2×C8×C11C2×D411yescharacteristic
177C22⋊Dic11—21no—
178C22⋊Dic11—42no—
179C22⋊Dic11—84no—
180C4⋊Dic11—22no—
181C4⋊Dic11—22no—
182C4⋊Dic11—42no—
183C4⋊Dic11C2×D411yescharacteristic
184C4⋊Dic11C2×D411yescharacteristic
185C4×Dic11—21no—
186C4×Dic11—21no—
187C4×Dic11—21no—
188C4×Dic11—42no—
189#4318—22no—
190#4318—21no—
191#4318—21no—
192#4318—22no—
193#4318—44no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—22no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—44no—
199C2×C11⋊C8C2×D411yescharacteristic
200C2×C11⋊C8C2×D411yescharacteristic
201C2×#576D1111yescharacteristic
202C2×#443—111no—
203#2951—111no—
204#2897—112no—
205#1978—111no—
206#1970—111no—
207#1907—112no—
208#1883—112no—
209#1816—111no—
210#1792—112no—
211#1764—111no—
212C23×C11—22no—
213C23×C11—21no—
214C23×C11—24no—
215C23×C11—48no—
216C23×C11—42no—
217C23×C11—42no—
218C23×C11—82no—
219C23×C11—82no—
220C23×C11—162no—
221C23×C11—162no—
222C23×C11H(5,𝔽2)11yescharacteristic
223Q8×C11—21no—
224Q8×C11—22no—
225Q8×C11C2×C22⋊C414yes—
226Q8×C11C4×D412yes—
227D4×C11—22no—
228D4×C11—24no—
229D4×C11—22no—
230D4×C11—24no—
231D4×C11—24no—
232D4×C11—24no—
233D4×C11—21no—
234D4×C11—22no—
235D4×C11—48no—
236D4×C11—48no—
237D4×C11—42no—
238D4×C11—42no—
239D4×C11C2×C22⋊C414yes—
240D4×C11C4×D412yes—
241C2×C4×C11—22no—
242C2×C4×C11—21no—
243C2×C4×C11—22no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—22no—
247C2×C4×C11—48no—
248C2×C4×C11C23×C411yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11H(5,𝔽2)11yescharacteristic
254C2×Dic11—22no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—42no—
260C2×Dic11—82no—
261C2×Dic11—162no—
262C8×C11—22no—
263C8×C11C2×C22⋊C412yes—
264C8×C11C2×C22⋊C412yes—
265C11⋊C8—21no—
266C11⋊C8—21no—
267C11⋊C8—42no—
268C11⋊C8—41no—
269C2×H(5,𝔽2)C2×D1112yes—
270#576—24no—
271#576Dic1118yescomplemented
272C2×AGL(1,ℤ/8)—22no—
273C2×AGL(1,ℤ/8)C2×D1112yes—
274C2×#135—21no—
275C2×#135C2×D1111yescharacteristic
276C22×D8—21no—
277C22×D8C2×D1111yescharacteristic
278C2×#131—112no—
279C2×#131C2×D1111yescharacteristic
280#520—112no—
281#443—224no—
282#440—222no—
283C4×Q16—221no—
284C4×D8—221no—
285C2×#108—111no—
286C2×#107—111no—
287C2×#104—111no—
288C2×#104—112no—
289#418—112no—
290#418—222no—
291#417—112no—
292#417—112no—
293#417—222no—
294#416—111no—
295#416—222no—
296C2×#102—112no—
297C2×#102—222no—
298C2×#100—112no—
299#405—111no—
300C2×C4×C8—111no—
301#390—112no—
302#343—112no—
303#341—111no—
304#339—111no—
305C22×C11—21no—
306C22×C11—21no—
307C22×C11—22no—
308C22×C11—24no—
309C22×C11—42no—
310C22×C11—41no—
311C22×C11—41no—
312C22×C11—42no—
313C22×C11—44no—
314C22×C11—84no—
315C22×C11—82no—
316C22×C11—82no—
317C22×C11—162no—
318C22×C11—168no—
319C22×C11#51811yescharacteristic
320C22×C11D4211yescharacteristic
321C22×C11#54611yescharacteristic
322C4×C11—22no—
323C4×C11—24no—
324C4×C11C22×C22⋊C411yescharacteristic
325C4×C11C2×C4×D411yescharacteristic
326C4×C11D4211yescharacteristic
327C4×C11#54611yescharacteristic
328Dic11—42no—
329Dic11—41no—
330Dic11—41no—
331Dic11—82no—
332H(5,𝔽2)—24no—
333H(5,𝔽2)—24no—
334H(5,𝔽2)—42no—
335H(5,𝔽2)C2×Dic1118yescomplemented
336C2×#41—22no—
337C2×#41—22no—
338C2×#41C22×D1111yescharacteristic
339C2×#41C22×D1112yes—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—42no—
343C22×D4C22×D1112yes—
344AGL(1,ℤ/8)—24no—
345AGL(1,ℤ/8)—216no—
346AGL(1,ℤ/8)C2×Dic1118yescomplemented
347#135—28no—
348#135C2×Dic1114yes—
349#135C22⋊D1114yes—
350C2×Q16C22⋊D1111yescharacteristic
351C2×SD16—22no—
352C2×SD16C22⋊D1112yes—
353C2×D8—22no—
354C2×D8—28no—
355C2×D8—21no—
356C2×D8—21no—
357C2×D8—22no—
358C2×D8C2×Dic1114yescomplemented
359C2×D8C22⋊D1111yescharacteristic
360#131—22no—
361#131—224no—
362#131—442no—
363#131C2×Dic1114yescomplemented
364C2×M16—21no—
365C2×M16—112no—
366C2×M16—111no—
367C2×M16—222no—
368C2×M16C22×D1111yescharacteristic
369C22×C8—21no—
370C22×C8—111no—
371C22×C8—222no—
372C22×C8C22×D1111yescharacteristic
373C4×Q8—222no—
374C4×D4—222no—
375C4×D4—442no—
376#117—111no—
377#117—222no—
378C2×C4⋊C4—112no—
379C2×C4⋊C4—222no—
380C2×C22⋊C4—442no—
381C2×C42—111no—
382#108—222no—
383#107—221no—
384#107—221no—
385#104—222no—
386#104—224no—
387#103—111no—
388#103—111no—
389#103—222no—
390#103—222no—
391#102—111no—
392#102—111no—
393#102—222no—
394#102—222no—
395#102—222no—
396#102—222no—
397#102—222no—
398#102—222no—
399#100—442no—
400#97—221no—
401C4×C8—222no—
402C4×C8—221no—
403C2×C11—21no—
404C2×C11—21no—
405C2×C11—44no—
406C2×C11—42no—
407C2×C11—84no—
408C2×C11D4×C22⋊C411yescharacteristic
409C2×C11#329011yescharacteristic
410C2×C11#329211yescharacteristic
411C24—22no—
412C24—42no—
413#41—22no—
414#41—22no—
415#41—21no—
416#41—21no—
417#41—28no—
418#41—28no—
419#41—44no—
420#41—44no—
421#41#434112yes—
422#41C22×Dic1112yes—
423#41C22×Dic1114yes—
424#41C2×C22⋊D1114yes—
425C2×Q8D4×D1111yescharacteristic
426C2×Q8C2×C22⋊D1112yes—
427C2×D4—22no—
428C2×D4—21no—
429C2×D4—28no—
430C2×D4—28no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—44no—
437C2×D4—44no—
438C2×D4—42no—
439C2×D4—42no—
440C2×D4—48no—
441C2×D4—48no—
442C2×D4D4×D1111yescharacteristic
443C2×D4C22×Dic1114yes—
444C2×D4C2×C22⋊D1112yes—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—42no—
448C22×C4—221no—
449C22×C4—222no—
450C22×C4—442no—
451C22×C4C23×D1111yescharacteristic
452Q16C22⋊Dic1114yescomplemented
453SD16—28no—
454SD16C22⋊Dic1118yescomplemented
455D8—28no—
456D8—24no—
457D8—24no—
458D8C22⋊Dic1114yescomplemented
459M16—21no—
460M16—24no—
461M16—221no—
462M16—221no—
463M16—222no—
464M16—222no—
465M16—444no—
466M16C22×Dic1112yes—
467C2×C8—21no—
468C2×C8—24no—
469C2×C8—111no—
470C2×C8—111no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—222no—
474C2×C8—221no—
475C2×C8—444no—
476C2×C8C22×Dic1112yes—
477C2×C8C2×C22⋊D1111yescharacteristic
478C2×C8C2×C22⋊D1112yes—
479C2×C8C2×C22⋊D1111yescharacteristic
480C4⋊C4—111no—
481C4⋊C4—111no—
482C4⋊C4—222no—
483C4⋊C4—222no—
484C4⋊C4—442no—
485C22⋊C4—221no—
486C22⋊C4—442no—
487C22⋊C4—884no—
488C42—221no—
489C42—221no—
490C42—221no—
491C42—442no—
492C11#2246611yescharacteristic, complemented, Sylow
493C23—22no—
494C23—21no—
495C23—24no—
496C23—48no—
497C23—42no—
498C23—42no—
499C23—82no—
500C23—82no—
501C23—162no—
502C23—162no—
503C23#6703711yescharacteristic
504Q8—21no—
505Q8—22no—
506Q8D4×Dic1112yes—
507Q8C2×C22⋊Dic1114yes—
508D4—22no—
509D4—24no—
510D4—22no—
511D4—24no—
512D4—24no—
513D4—21no—
514D4—22no—
515D4—24no—
516D4—48no—
517D4—48no—
518D4—42no—
519D4—42no—
520D4D4×Dic1112yes—
521D4C2×C22⋊Dic1114yes—
522C2×C4—22no—
523C2×C4—21no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—48no—
529C2×C4—222no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—442no—
535C2×C4—882no—
536C2×C4—1762no—
537C2×C4C2×D4×D1111yescharacteristic
538C2×C4C2×#434111yescharacteristic
539C2×C4#6703711yescharacteristic
540C2×C4C23×Dic1111yescharacteristic
541C2×C4C22×C22⋊D1111yescharacteristic
542C2×C4C22×C22⋊D1111yescharacteristic
543C8—22no—
544C8—221no—
545C8—221no—
546C8—442no—
547C8—441no—
548C8C2×C22⋊Dic1112yes—
549C8C2×C22⋊Dic1112yes—
550C22—21no—
551C22—21no—
552C22—22no—
553C22—24no—
554C22—41no—
555C22—42no—
556C22—42no—
557C22—41no—
558C22—44no—
559C22—84no—
560C22—82no—
561C22—82no—
562C22—162no—
563C22—168no—
564C22#1062332911yescharacteristic
565C22D4×C22⋊D1111yescharacteristic
566C22#1062333711yescharacteristic
567C4—22no—
568C4—24no—
569C4—442no—
570C4—441no—
571C4—441no—
572C4—882no—
573C4C2×D4×Dic1111yescharacteristic
574C4D4×C22⋊D1111yescharacteristic
575C4#1062333711yescharacteristic
576C4C22×C22⋊Dic1111yescharacteristic
577C2—21no—
578C2—21no—
579C2—42no—
580C2—44no—
581C2—84no—
582C2D4×C22⋊Dic1111yescharacteristic
583C2#1308039811yescharacteristic
584C2#1308041311yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#576C2
socleC22×C11D42
cosocleC22×C4×C11C24
hypercenterC2×#576D11
hypocenterC11#22466
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#576

Complements

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

NH ≅ G/Ntype
1. C2×#10622809C2semidirect
2. #13077492C2semidirect
3. #13077142C2semidirect
4. #13069527C2semidirect
5. #13069483C2semidirect
6. #13069126C2semidirect
7. #13068994C2semidirect
8. #13068680C2semidirect
9. #13068570C2semidirect
10. #13068451C2semidirect
14. C11×#576C4semidirect
22. #10623358C22semidirect
23. C2×#67001C22semidirect
25. C2×#66901C22semidirect
30. #10622845C22semidirect
31. #10622834C22semidirect
32. C2×#66897C22semidirect
34. #10622828C22semidirect
36. C2×#66896C22semidirect
41. C2×#66883C22semidirect
42. C2×#66882C22semidirect
43. #10622714C22semidirect
44. C2×C8×Dic11C22semidirect
45. #10622196C22semidirect
46. #10622193C22semidirect
47. #10622192C22semidirect
51. C11×H(5,𝔽2)C2×C4semidirect
62. C11×AGL(1,ℤ/8)C2×C4semidirect
74. C2×C11×D8C2×C4semidirect
77. C11×#131C2×C4semidirect
161. C11×Q16C22⋊C4semidirect
163. C11×SD16C22⋊C4semidirect
167. C11×D8C22⋊C4semidirect
271. #576Dic11semidirect
335. H(5,𝔽2)C2×Dic11semidirect
346. AGL(1,ℤ/8)C2×Dic11semidirect
358. C2×D8C2×Dic11semidirect
363. #131C2×Dic11semidirect
452. Q16C22⋊Dic11semidirect
454. SD16C22⋊Dic11semidirect
458. D8C22⋊Dic11semidirect
492. C11#22466semidirect

Maximal subgroups

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

subgroupindex
C2×#106228092
#130774922
#130771422
#130695272
#130694832
#130691262
#130689942
#130686802
#130685702
#130684512
C2×C11×#5762
#2246611