Finite Group Databasebeta

← #14769755

Subgroups — #14769755

Order 2816.

1380 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622810C211yesmaximal, characteristic, complemented
2#13077500C211yesmaximal, characteristic, complemented
3#13077142C212yesmaximal, complemented
4#13069527C211yesmaximal, characteristic, complemented
5#13069493C211yesmaximal, characteristic, complemented
6#13069126C212yesmaximal, complemented
7#13068994C212yesmaximal, complemented
8#13068675C211yesmaximal, characteristic, complemented
9#13068570C212yesmaximal, complemented
10#13068458C211yesmaximal, 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#10622810—24no—
38#10622797—21no—
39SD16×Dic11—22no—
40#10622765—21no—
41C2×#66883C2211yescharacteristic, complemented
42C2×#66881C2211yescharacteristic, complemented
43#10622714C2211yescharacteristic, complemented
44C2×#66879C2211yescharacteristic, 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#66899D412yes—
103#66897—42no—
104#66896—22no—
105#66896—22no—
106#66896—22no—
107#66896—22no—
108#66896—22no—
109#66896—22no—
110#66896D412yes—
111#66883—22no—
112#66881—21no—
113#66881—21no—
114#66879—21no—
115#66879—22no—
116C8×Dic11—21no—
117#22463—111nomaximal, Sylow
118C24×C11—22no—
119C24×C11—42no—
120C11×#41—21no—
121C11×#41—22no—
122C11×#41—22no—
123C11×#41—21no—
124C11×#41—28no—
125C11×#41—28no—
126C11×#41—44no—
127C11×#41—44no—
128C11×#41C22×C414yes—
129C11×#41C22×C412yes—
130C11×#41C2×D414yes—
131C11×#41#4112yes—
132C2×Q8×C11C2×D412yes—
133C2×Q8×C11C2×D411yescharacteristic
134C2×D4×C11—22no—
135C2×D4×C11—21no—
136C2×D4×C11—28no—
137C2×D4×C11—28no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—22no—
142C2×D4×C11—22no—
143C2×D4×C11—44no—
144C2×D4×C11—44no—
145C2×D4×C11—42no—
146C2×D4×C11—42no—
147C2×D4×C11—48no—
148C2×D4×C11—48no—
149C2×D4×C11C22×C414yes—
150C2×D4×C11C2×D412yes—
151C2×D4×C11C2×D411yescharacteristic
152C22×C4×C11—22no—
153C22×C4×C11—21no—
154C22×C4×C11—42no—
155C22×C4×C11C2411yescharacteristic
156C22×Dic11—21no—
157C22×Dic11—22no—
158C22×Dic11—42no—
159C11×Q16C22⋊C414yescomplemented
160C11×SD16—28no—
161C11×SD16C22⋊C418yescomplemented
162C11×D8—24no—
163C11×D8—24no—
164C11×D8—28no—
165C11×D8C22⋊C414yescomplemented
166C11×M16—24no—
167C11×M16—21no—
168C11×M16C22×C412yes—
169C2×C8×C11—24no—
170C2×C8×C11—21no—
171C2×C8×C11C22×C412yes—
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2×D411yescharacteristic
174C2×C8×C11C2×D412yes—
175C22⋊Dic11—21no—
176C22⋊Dic11—42no—
177C22⋊Dic11—84no—
178C4⋊Dic11—22no—
179C4⋊Dic11—22no—
180C4⋊Dic11—42no—
181C4⋊Dic11C2×D412yes—
182C4×Dic11—21no—
183C4×Dic11—21no—
184C4×Dic11—21no—
185C4×Dic11—42no—
186#4318—22no—
187#4318—21no—
188#4318—21no—
189#4318—22no—
190#4318—44no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—44no—
196C2×C11⋊C8C2×D412yes—
197C2×#576D1111yescharacteristic
198C2×#444—111no—
199#2952—111no—
200#2897—112no—
201#1978—111no—
202#1972—111no—
203#1907—112no—
204#1883—112no—
205#1815—111no—
206#1792—112no—
207#1765—111no—
208C23×C11—22no—
209C23×C11—21no—
210C23×C11—24no—
211C23×C11—48no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11—82no—
215C23×C11—82no—
216C23×C11—162no—
217C23×C11—162no—
218C23×C11H(5,𝔽2)11yescharacteristic
219Q8×C11—21no—
220Q8×C11—22no—
221Q8×C11C2×C22⋊C414yes—
222Q8×C11C4×D412yes—
223D4×C11—22no—
224D4×C11—24no—
225D4×C11—22no—
226D4×C11—24no—
227D4×C11—24no—
228D4×C11—24no—
229D4×C11—21no—
230D4×C11—22no—
231D4×C11—48no—
232D4×C11—48no—
233D4×C11—42no—
234D4×C11—42no—
235D4×C11C2×C22⋊C414yes—
236D4×C11C4×D412yes—
237C2×C4×C11—22no—
238C2×C4×C11—21no—
239C2×C4×C11—22no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—22no—
243C2×C4×C11—48no—
244C2×C4×C11C23×C411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11H(5,𝔽2)11yescharacteristic
250C2×Dic11—22no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11—41no—
254C2×Dic11—82no—
255C2×Dic11—162no—
256C8×C11—22no—
257C8×C11C2×C22⋊C412yes—
258C8×C11C2×C22⋊C412yes—
259C11⋊C8—22no—
260C11⋊C8—42no—
261C11⋊C8—41no—
262C2×H(5,𝔽2)C2×D1112yes—
263#576—24no—
264#576Dic1118yescomplemented
265C2×AGL(1,ℤ/8)—22no—
266C2×AGL(1,ℤ/8)C2×D1112yes—
267C2×#135—21no—
268C2×#135C2×D1111yescharacteristic
269C22×D8—21no—
270C22×D8C2×D1111yescharacteristic
271C2×#131—112no—
272C2×#131C2×D1111yescharacteristic
273#520—112no—
274#444—224no—
275#442—221no—
276#441—221no—
277C4×SD16—222no—
278C2×#108—111no—
279C2×#106—111no—
280C2×#104—111no—
281C2×#104—112no—
282#418—112no—
283#418—222no—
284#417—112no—
285#417—112no—
286#417—222no—
287#416—111no—
288#416—222no—
289C2×#102—112no—
290C2×#102—222no—
291C2×#100—112no—
292#405—111no—
293C2×#97—111no—
294#390—112no—
295#343—112no—
296#341—111no—
297#339—111no—
298C22×C11—22no—
299C22×C11—22no—
300C22×C11—24no—
301C22×C11—42no—
302C22×C11—42no—
303C22×C11—42no—
304C22×C11—44no—
305C22×C11—84no—
306C22×C11—82no—
307C22×C11—82no—
308C22×C11—162no—
309C22×C11—168no—
310C22×C11#51811yescharacteristic
311C22×C11D4211yescharacteristic
312C22×C11#54611yescharacteristic
313C4×C11—22no—
314C4×C11—24no—
315C4×C11C22×C22⋊C411yescharacteristic
316C4×C11C2×C4×D411yescharacteristic
317C4×C11D4211yescharacteristic
318C4×C11#54611yescharacteristic
319Dic11—42no—
320Dic11—81no—
321Dic11—82no—
322H(5,𝔽2)—24no—
323H(5,𝔽2)—24no—
324H(5,𝔽2)—42no—
325H(5,𝔽2)C2×Dic1118yescomplemented
326C2×#41—22no—
327C2×#41—22no—
328C2×#41C22×D1111yescharacteristic
329C2×#41C22×D1112yes—
330C22×D4—22no—
331C22×D4—22no—
332C22×D4—42no—
333C22×D4C22×D1112yes—
334AGL(1,ℤ/8)—24no—
335AGL(1,ℤ/8)—216no—
336AGL(1,ℤ/8)C2×Dic1118yescomplemented
337#135—28no—
338#135C2×Dic1114yes—
339#135C22⋊D1114yes—
340C2×Q16C22⋊D1111yescharacteristic
341C2×SD16—22no—
342C2×SD16C22⋊D1112yes—
343C2×D8—22no—
344C2×D8—28no—
345C2×D8—21no—
346C2×D8—21no—
347C2×D8—22no—
348C2×D8C2×Dic1114yescomplemented
349C2×D8C22⋊D1111yescharacteristic
350#131—22no—
351#131—224no—
352#131—442no—
353#131C2×Dic1114yescomplemented
354C2×M16—21no—
355C2×M16—112no—
356C2×M16—111no—
357C2×M16—222no—
358C2×M16C22×D1111yescharacteristic
359C22×C8—21no—
360C22×C8—111no—
361C22×C8—222no—
362C22×C8C22×D1111yescharacteristic
363C4×Q8—222no—
364C4×D4—222no—
365C4×D4—442no—
366#117—111no—
367#117—222no—
368C2×C4⋊C4—112no—
369C2×C4⋊C4—222no—
370C2×C22⋊C4—442no—
371C2×C42—111no—
372#108—222no—
373#106—221no—
374#106—221no—
375#104—222no—
376#104—224no—
377#103—112no—
378#103—222no—
379#103—222no—
380#102—112no—
381#102—222no—
382#102—222no—
383#102—222no—
384#102—222no—
385#102—222no—
386#102—222no—
387#100—442no—
388#97—222no—
389#97—221no—
390C4×C8—221no—
391C2×C11—21no—
392C2×C11—21no—
393C2×C11—44no—
394C2×C11—42no—
395C2×C11—84no—
396C2×C11D4×C22⋊C411yescharacteristic
397C2×C11#328812yes—
398C24—22no—
399C24—42no—
400#41—22no—
401#41—22no—
402#41—21no—
403#41—21no—
404#41—28no—
405#41—28no—
406#41—44no—
407#41—44no—
408#41#434112yes—
409#41C22×Dic1112yes—
410#41C22×Dic1114yes—
411#41C2×C22⋊D1114yes—
412C2×Q8D4×D1111yescharacteristic
413C2×Q8C2×C22⋊D1112yes—
414C2×D4—22no—
415C2×D4—21no—
416C2×D4—28no—
417C2×D4—28no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—44no—
424C2×D4—44no—
425C2×D4—42no—
426C2×D4—42no—
427C2×D4—48no—
428C2×D4—48no—
429C2×D4D4×D1111yescharacteristic
430C2×D4C22×Dic1114yes—
431C2×D4C2×C22⋊D1112yes—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—42no—
435C22×C4—221no—
436C22×C4—222no—
437C22×C4—442no—
438C22×C4C23×D1111yescharacteristic
439Q16C22⋊Dic1114yescomplemented
440SD16—28no—
441SD16C22⋊Dic1118yescomplemented
442D8—28no—
443D8—24no—
444D8—24no—
445D8C22⋊Dic1114yescomplemented
446M16—21no—
447M16—24no—
448M16—221no—
449M16—221no—
450M16—222no—
451M16—222no—
452M16—444no—
453M16C22×Dic1112yes—
454C2×C8—21no—
455C2×C8—24no—
456C2×C8—112no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—222no—
460C2×C8—221no—
461C2×C8—444no—
462C2×C8C22×Dic1112yes—
463C2×C8C2×C22⋊D1111yescharacteristic
464C2×C8C2×C22⋊D1111yescharacteristic
465C2×C8C2×C22⋊D1112yes—
466C4⋊C4—112no—
467C4⋊C4—222no—
468C4⋊C4—222no—
469C4⋊C4—442no—
470C22⋊C4—221no—
471C22⋊C4—442no—
472C22⋊C4—884no—
473C42—221no—
474C42—221no—
475C42—221no—
476C42—442no—
477C11#2246311yescharacteristic, complemented, Sylow
478C23—22no—
479C23—21no—
480C23—24no—
481C23—48no—
482C23—42no—
483C23—42no—
484C23—82no—
485C23—82no—
486C23—162no—
487C23—162no—
488C23#6703711yescharacteristic
489Q8—21no—
490Q8—22no—
491Q8D4×Dic1112yes—
492Q8C2×C22⋊Dic1114yes—
493D4—22no—
494D4—24no—
495D4—22no—
496D4—24no—
497D4—24no—
498D4—21no—
499D4—22no—
500D4—24no—
501D4—48no—
502D4—48no—
503D4—42no—
504D4—42no—
505D4D4×Dic1112yes—
506D4C2×C22⋊Dic1114yes—
507C2×C4—22no—
508C2×C4—21no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—48no—
514C2×C4—222no—
515C2×C4—442no—
516C2×C4—442no—
517C2×C4—441no—
518C2×C4—882no—
519C2×C4—1762no—
520C2×C4C2×D4×D1111yescharacteristic
521C2×C4C2×#434111yescharacteristic
522C2×C4#6703711yescharacteristic
523C2×C4C23×Dic1111yescharacteristic
524C2×C4C22×C22⋊D1111yescharacteristic
525C2×C4C22×C22⋊D1111yescharacteristic
526C8—22no—
527C8—222no—
528C8—442no—
529C8—441no—
530C8C2×C22⋊Dic1112yes—
531C8C2×C22⋊Dic1112yes—
532C22—22no—
533C22—22no—
534C22—24no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—44no—
539C22—84no—
540C22—82no—
541C22—82no—
542C22—162no—
543C22—168no—
544C22#1062332911yescharacteristic
545C22D4×C22⋊D1111yescharacteristic
546C22#1062333711yescharacteristic
547C4—22no—
548C4—24no—
549C4—442no—
550C4—881no—
551C4—882no—
552C4C2×D4×Dic1111yescharacteristic
553C4D4×C22⋊D1111yescharacteristic
554C4#1062333711yescharacteristic
555C4C22×C22⋊Dic1111yescharacteristic
556C2—21no—
557C2—21no—
558C2—42no—
559C2—44no—
560C2—84no—
561C2D4×C22⋊Dic1111yescharacteristic
562C2#1308038012yes—
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#22463
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×#10622810C2semidirect
2. #13077500C2semidirect
3. #13077142C2semidirect
4. #13069527C2semidirect
5. #13069493C2semidirect
6. #13069126C2semidirect
7. #13068994C2semidirect
8. #13068675C2semidirect
9. #13068570C2semidirect
10. #13068458C2semidirect
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×#66881C22semidirect
43. #10622714C22semidirect
44. C2×#66879C22semidirect
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
159. C11×Q16C22⋊C4semidirect
161. C11×SD16C22⋊C4semidirect
165. C11×D8C22⋊C4semidirect
264. #576Dic11semidirect
325. H(5,𝔽2)C2×Dic11semidirect
336. AGL(1,ℤ/8)C2×Dic11semidirect
348. C2×D8C2×Dic11semidirect
353. #131C2×Dic11semidirect
439. Q16C22⋊Dic11semidirect
441. SD16C22⋊Dic11semidirect
445. D8C22⋊Dic11semidirect
477. C11#22463semidirect

Maximal subgroups

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

subgroupindex
C2×#106228102
#130775002
#130771422
#130695272
#130694932
#130691262
#130689942
#130686752
#130685702
#130684582
C2×C11×#5762
#2246311