Finite Group Databasebeta

← #14721532

Subgroups — #14721532

Order 2816.

1270 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077645C211yesmaximal, characteristic, complemented
2#13071556C211yesmaximal, characteristic, complemented
3#13067184C212yesmaximal, complemented
4#13067163C212yesmaximal, complemented
5#13067145C212yesmaximal, complemented
6#13067132C212yesmaximal, complemented
7#13067124C212yesmaximal, complemented
8C2×#10622175C212yesmaximal, complemented
9C11×#3496C211yesmaximal, characteristic
10C2×C11×H(5,𝔽2)—21no—
11C11×#547C414yescomplemented
12C11×#546—24no—
13D42×C11C414yescomplemented
14C11×#537—21no—
15C11×#534—21no—
16C11×#534—21no—
17C11×#532C2212yes—
18C2×C11×#121C2212yes—
19C2×C11×#121C2212yes—
20C2×C4×D4×C11C2211yescharacteristic
21#10622833—21no—
22#10622825C2211yescharacteristic, complemented
23#10622824C2211yescharacteristic, complemented
24C4×C22⋊Dic11C2211yescharacteristic, complemented
25C2×C11⋊#95C2211yescharacteristic, complemented
26#10622820C2212yescomplemented
27C2×C22⋊(C11⋊C8)C2212yescomplemented
28#10622624—24no—
29#10622594—21no—
30#10622564—21no—
31C22⋊C4×Dic11—21no—
32#10622550C2211yescharacteristic, complemented
33#10622545C2211yescharacteristic, complemented
34#10622539C2212yescomplemented
35#10622175C2214yescomplemented
36#10622175C2214yescomplemented
37#10622175C2214yescomplemented
38#10622175C2214yescomplemented
39C11×H(5,𝔽2)—44no—
40C11×H(5,𝔽2)—44no—
41C2×C11×#41—24no—
42C2×C11×#41—22no—
43C22×D4×C11—22no—
44C22×D4×C11—22no—
45C22×D4×C11—24no—
46C22×D4×C11C2×C412yes—
47C22×D4×C11C2×C412yescomplemented
48C22×D4×C11D411yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C23×Dic11—21no—
52C11×C4⋊Q8C2×C412yescomplemented
53C11×#127C2×C412yescomplemented
54C11×#124—22no—
55C11×#123—24no—
56C11×#123—24no—
57C11×C22⋊Q8—24no—
58C11×#121—22no—
59C11×#121—22no—
60C11×#121—22no—
61C11×#121—22no—
62C11×#121—22no—
63C11×#121—24no—
64C11×#121C2×C414yes—
65C11×#121C2×C414yescomplemented
66C11×#121C2314yes—
67C11×#120—24no—
68C11×#120—24no—
69C4×D4×C11—22no—
70C4×D4×C11C2×C414yes—
71C4×D4×C11C2×C414yescomplemented
72C4×D4×C11D414yes—
73C2×C11×C4⋊C4C2×C412yes—
74C2×C11×C4⋊C4C2×C412yescomplemented
75C2×C11×C4⋊C4D411yescharacteristic
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4D411yescharacteristic
79C2×C11×C22⋊C4D411yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4×Dic11—21no—
86C2×C4×Dic11—21no—
87C2×#4318—22no—
88C22×C11⋊C8—22no—
89C11⋊#95—21no—
90C11⋊#95—21no—
91C11⋊#95—21no—
92C11⋊#95—21no—
93C11⋊#95—21no—
94C11⋊#95C2311yescharacteristic
95C11⋊#95C2311yescharacteristic
96C11⋊#95C2311yescharacteristic
97C11⋊#95C2311yescharacteristic
98C22⋊(C11⋊C8)—22no—
99C22⋊(C11⋊C8)—22no—
100C22⋊(C11⋊C8)C2314yes—
101C4⋊(C11⋊C8)—22no—
102#66867—22no—
103#17620—111nomaximal, Sylow
104C24×C11—22no—
105C24×C11—22no—
106C24×C11C2×D411yescharacteristic
107C24×C11C2×D411yescharacteristic
108C11×#41—44no—
109C11×#41—44no—
110C11×#41—416no—
111C2×Q8×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—24no—
115C2×D4×C11—24no—
116C2×D4×C11—24no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—416no—
122C2×D4×C11—44no—
123C2×D4×C11—44no—
124C2×D4×C11—44no—
125C2×D4×C11—44no—
126C2×D4×C11—82no—
127C2×D4×C11—82no—
128C2×D4×C11C22⋊C414yes—
129C2×D4×C11C22×C414yes—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—24no—
133C22×C4×C11—81no—
134C22×C4×C11—81no—
135C22×C4×C11C22×C412yes—
136C22×C4×C11C22×C412yes—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2411yescharacteristic
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—42no—
149C22×Dic11—42no—
150C22×Dic11—81no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4C22⋊C414yes—
155C11×C4⋊C4C22×C414yes—
156C11×C22⋊C4—24no—
157C11×C22⋊C4—24no—
158C11×C22⋊C4—24no—
159C11×C22⋊C4—24no—
160C11×C22⋊C4C22⋊C414yes—
161C11×C22⋊C4C22⋊C414yes—
162C42×C11C22×C412yes—
163C42×C11C2×D412yes—
164C22⋊Dic11—42no—
165C22⋊Dic11—42no—
166C22⋊Dic11—81no—
167C4⋊Dic11—81no—
168C4×Dic11—42no—
169C4×Dic11—81no—
170#4318—82no—
171C2×C11⋊C8—24no—
172C2×C11⋊C8—82no—
173#3496D1111yescharacteristic
174#2973—111no—
175#2353—111no—
176#1519—112no—
177#1514—112no—
178#1510—112no—
179#1507—112no—
180#1505—112no—
181C2×#327—112no—
182C23×C11—21no—
183C23×C11—21no—
184C23×C11—24no—
185C23×C11—41no—
186C23×C11—41no—
187C23×C11—41no—
188C23×C11—41no—
189C23×C11—44no—
190C23×C11—44no—
191C23×C11—82no—
192C23×C11—82no—
193C23×C11—82no—
194C23×C11—82no—
195C23×C11C2×C22⋊C412yes—
196C23×C11C2×C22⋊C412yes—
197C23×C11AGL(1,ℤ/8)12yes—
198C23×C11AGL(1,ℤ/8)12yes—
199C23×C11C22×D411yescharacteristic
200Q8×C11—44no—
201D4×C11—28no—
202D4×C11—44no—
203D4×C11—44no—
204D4×C11—48no—
205D4×C11—44no—
206D4×C11—44no—
207D4×C11—48no—
208D4×C11—82no—
209D4×C11—82no—
210D4×C11—82no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—24no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—48no—
223C2×C4×C11—44no—
224C2×C4×C11—44no—
225C2×C4×C11C2×C22⋊C412yes—
226C2×C4×C11C2×C22⋊C412yes—
227C2×C4×C11C2×C22⋊C412yes—
228C2×C4×C11C2×C22⋊C412yes—
229C2×C4×C11C23×C411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×Dic11—22no—
232C2×Dic11—41no—
233C2×Dic11—41no—
234C2×Dic11—41no—
235C2×Dic11—41no—
236C2×Dic11—41no—
237C2×Dic11—41no—
238C2×Dic11—41no—
239C2×Dic11—41no—
240C2×Dic11—41no—
241C2×Dic11—41no—
242C2×Dic11—41no—
243C2×Dic11—84no—
244C11⋊C8—44no—
245C2×H(5,𝔽2)—21no—
246#547Dic1114yescomplemented
247#546—24no—
248D42Dic1114yescomplemented
249#537—21no—
250#534—21no—
251#534—21no—
252#532C2×D1112yes—
253C2×#121C2×D1112yes—
254C2×#121C2×D1112yes—
255C2×C4×D4C2×D1111yescharacteristic
256#435—224no—
257#432—112no—
258#407—112no—
259C2×C22⋊C8—112no—
260#388—221no—
261#387—221no—
262#386—221no—
263#383—111no—
264#381—111no—
265#380—111no—
266C4×C22⋊C4—111no—
267C4×C22⋊C4—221no—
268#376—111no—
269C2×#95—111no—
270#327—114no—
271#327—114no—
272#327—114no—
273#327—114no—
274C22×C11—21no—
275C22×C11—22no—
276C22×C11—21no—
277C22×C11—22no—
278C22×C11—22no—
279C22×C11—22no—
280C22×C11—22no—
281C22×C11—42no—
282C22×C11—42no—
283C22×C11—44no—
284C22×C11—44no—
285C22×C11—44no—
286C22×C11—81no—
287C22×C11—81no—
288C22×C11—164no—
289C22×C11—164no—
290C22×C11#41814yes—
291C22×C11C22×C22⋊C411yescharacteristic
292C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
293C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
294C4×C11—21no—
295C4×C11—21no—
296C4×C11—22no—
297C4×C11—22no—
298C4×C11—22no—
299C4×C11—22no—
300C4×C11—44no—
301Dic11—42no—
302Dic11—81no—
303Dic11—81no—
304Dic11—81no—
305H(5,𝔽2)—44no—
306H(5,𝔽2)—44no—
307C2×#41—24no—
308C2×#41—22no—
309C22×D4—22no—
310C22×D4—22no—
311C22×D4—24no—
312C22×D4C2×Dic1112yes—
313C22×D4C2×Dic1112yescomplemented
314C22×D4C22⋊D1111yescharacteristic
315C23×C4—221no—
316C23×C4C22×D1111yescharacteristic
317C23×C4C22×D1111yescharacteristic
318C2×M16—222no—
319C22×C8—222no—
320C4⋊Q8C2×Dic1112yescomplemented
321#127C2×Dic1112yescomplemented
322#124—22no—
323#123—24no—
324#123—24no—
325C22⋊Q8—24no—
326#121—22no—
327#121—22no—
328#121—22no—
329#121—22no—
330#121—22no—
331#121—24no—
332#121C2×Dic1114yes—
333#121C2×Dic1114yescomplemented
334#121C22×D1114yes—
335#120—24no—
336#120—24no—
337C4×D4—22no—
338C4×D4C2×Dic1114yes—
339C4×D4C2×Dic1114yescomplemented
340C4×D4C22⋊D1114yes—
341C2×C4⋊C4—221no—
342C2×C4⋊C4C2×Dic1112yes—
343C2×C4⋊C4C2×Dic1112yescomplemented
344C2×C4⋊C4C22⋊D1111yescharacteristic
345C2×C22⋊C4—22no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—221no—
348C2×C22⋊C4—221no—
349C2×C22⋊C4—221no—
350C2×C22⋊C4C22⋊D1111yescharacteristic
351C2×C22⋊C4C22⋊D1111yescharacteristic
352C2×C42—221no—
353C2×C42—221no—
354C2×C42C22×D1111yescharacteristic
355C4⋊C8—222no—
356C22⋊C8—114no—
357C22⋊C8—222no—
358C22⋊C8—222no—
359#97—222no—
360#95—111no—
361#95—111no—
362#95—111no—
363#95—111no—
364#95—221no—
365#95—221no—
366#95—221no—
367#95—221no—
368#95—221no—
369C2×C11—21no—
370C2×C11—21no—
371C2×C11—24no—
372C2×C11—42no—
373C2×C11—84no—
374C2×C11#288311yescharacteristic
375C2×C11C2×#41811yescharacteristic
376C2×C11#290111yescharacteristic
377C24—22no—
378C24—22no—
379C24C2×C22⋊D1111yescharacteristic
380C24C2×C22⋊D1111yescharacteristic
381#41—44no—
382#41—44no—
383#41—416no—
384C2×Q8—22no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—24no—
388C2×D4—24no—
389C2×D4—24no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—416no—
395C2×D4—44no—
396C2×D4—44no—
397C2×D4—44no—
398C2×D4—44no—
399C2×D4—82no—
400C2×D4—82no—
401C2×D4C22⋊Dic1114yes—
402C2×D4C22×Dic1114yes—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—24no—
406C22×C4—81no—
407C22×C4—81no—
408C22×C4—221no—
409C22×C4—221no—
410C22×C4—221no—
411C22×C4—221no—
412C22×C4—442no—
413C22×C4—442no—
414C22×C4—881no—
415C22×C4C22×Dic1112yes—
416C22×C4C22×Dic1112yes—
417C22×C4C2×C22⋊D1111yescharacteristic
418C22×C4C2×C22⋊D1111yescharacteristic
419C22×C4C2×C22⋊D1111yescharacteristic
420C22×C4C2×C22⋊D1111yescharacteristic
421C22×C4C2×C22⋊D1112yes—
422C22×C4C2×C22⋊D1112yes—
423C22×C4C23×D1111yescharacteristic
424M16—882no—
425C2×C8—224no—
426C2×C8—882no—
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—881no—
431C4⋊C4C22⋊Dic1114yes—
432C4⋊C4C22×Dic1114yes—
433C22⋊C4—24no—
434C22⋊C4—24no—
435C22⋊C4—24no—
436C22⋊C4—24no—
437C22⋊C4—442no—
438C22⋊C4—442no—
439C22⋊C4—881no—
440C22⋊C4C22⋊Dic1114yes—
441C22⋊C4C22⋊Dic1114yes—
442C42—442no—
443C42—881no—
444C42C22×Dic1112yes—
445C42C2×C22⋊D1112yes—
446C11#1762011yescharacteristic, complemented, Sylow
447C23—21no—
448C23—21no—
449C23—24no—
450C23—41no—
451C23—41no—
452C23—41no—
453C23—41no—
454C23—44no—
455C23—44no—
456C23—82no—
457C23—82no—
458C23—82no—
459C23—82no—
460C23#6698512yes—
461C23#6698512yes—
462C23C2×C22⋊Dic1112yes—
463C23C2×C22⋊Dic1112yes—
464C23C22×C22⋊D1111yescharacteristic
465Q8—44no—
466D4—28no—
467D4—44no—
468D4—44no—
469D4—48no—
470D4—44no—
471D4—44no—
472D4—48no—
473D4—82no—
474D4—82no—
475D4—82no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—24no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—48no—
488C2×C4—44no—
489C2×C4—44no—
490C2×C4—222no—
491C2×C4—441no—
492C2×C4—441no—
493C2×C4—441no—
494C2×C4—441no—
495C2×C4—441no—
496C2×C4—441no—
497C2×C4—441no—
498C2×C4—441no—
499C2×C4—441no—
500C2×C4—441no—
501C2×C4—441no—
502C2×C4—884no—
503C2×C4C2×C22⋊Dic1112yes—
504C2×C4C2×C22⋊Dic1112yes—
505C2×C4C2×C22⋊Dic1112yes—
506C2×C4C2×C22⋊Dic1112yes—
507C2×C4C23×Dic1111yescharacteristic
508C2×C4C22×C22⋊D1111yescharacteristic
509C8—444no—
510C22—21no—
511C22—22no—
512C22—21no—
513C22—22no—
514C22—22no—
515C22—22no—
516C22—22no—
517C22—42no—
518C22—42no—
519C22—44no—
520C22—44no—
521C22—44no—
522C22—81no—
523C22—81no—
524C22—164no—
525C22—164no—
526C22#1062282814yes—
527C22C2×#6698511yescharacteristic
528C22C2×#6698511yescharacteristic
529C22C22×C22⋊Dic1111yescharacteristic
530C4—21no—
531C4—21no—
532C4—22no—
533C4—22no—
534C4—22no—
535C4—22no—
536C4—44no—
537C4—442no—
538C4—881no—
539C4—881no—
540C4—881no—
541C2—21no—
542C2—21no—
543C2—24no—
544C2—42no—
545C2—84no—
546C2#1307707711yescharacteristic
547C2C2×#1062282811yescharacteristic
548C2#1307716311yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3496C2
socleC22×C11C22×C22⋊C4
cosocleC22×C4×C11C24
hypercenter#3496D11
hypocenterC11#17620
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #3496

Complements

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

NH ≅ G/Ntype
1. #13077645C2semidirect
2. #13071556C2semidirect
3. #13067184C2semidirect
4. #13067163C2semidirect
5. #13067145C2semidirect
6. #13067132C2semidirect
7. #13067124C2semidirect
8. C2×#10622175C2semidirect
11. C11×#547C4semidirect
13. D42×C11C4semidirect
22. #10622825C22semidirect
23. #10622824C22semidirect
24. C4×C22⋊Dic11C22semidirect
25. C2×C11⋊#95C22semidirect
26. #10622820C22semidirect
27. C2×C22⋊(C11⋊C8)C22semidirect
32. #10622550C22semidirect
33. #10622545C22semidirect
34. #10622539C22semidirect
35. #10622175C22semidirect
36. #10622175C22semidirect
37. #10622175C22semidirect
38. #10622175C22semidirect
47. C22×D4×C11C2×C4semidirect
52. C11×C4⋊Q8C2×C4semidirect
53. C11×#127C2×C4semidirect
65. C11×#121C2×C4semidirect
71. C4×D4×C11C2×C4semidirect
74. C2×C11×C4⋊C4C2×C4semidirect
246. #547Dic11semidirect
248. D42Dic11semidirect
313. C22×D4C2×Dic11semidirect
320. C4⋊Q8C2×Dic11semidirect
321. #127C2×Dic11semidirect
333. #121C2×Dic11semidirect
339. C4×D4C2×Dic11semidirect
343. C2×C4⋊C4C2×Dic11semidirect
446. C11#17620semidirect

Maximal subgroups

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

subgroupindex
#130776452
#130715562
#130671842
#130671632
#130671452
#130671322
#130671242
C2×#106221752
C11×#34962
#1762011