Finite Group Databasebeta

← #14763462

Subgroups — #14763462

Order 2816.

1166 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623088C211yesmaximal, characteristic
2C2×#10622446C211yesmaximal, characteristic, complemented
3D11×#382C211yesmaximal, characteristic, complemented
4#13069579C212yesmaximal, complemented
5#13069426C212yesmaximal, complemented
6#13068930C212yesmaximal
7#13068922C212yesmaximal, complemented
8#13068632C211yesmaximal, characteristic, complemented
9#13068628C211yesmaximal, characteristic, complemented
10#13068626C211yesmaximal, characteristic, complemented
11C11×#1804C211yesmaximal, characteristic, complemented
12C2×C4×D4×C11C2211yescharacteristic
13C2×#66991C2211yescharacteristic
14C2×#66989C2211yescharacteristic
15C2×C4×C22⋊D11—21no—
16C2×#66979—21no—
17#10623088—24no—
18#10623088C418yescomplemented
19C2×#66950C2211yescharacteristic
20C2×C4⋊C4×D11C2212yes—
21C2×#66943C2211yescharacteristic
22C2×#66936—21no—
23C2×#66932—21no—
24C2×C42×D11C2211yescharacteristic
25C2×C4×Dic22C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×#102C2212yes—
28C11×#382C2211yescharacteristic
29C2×#66896C2212yes—
30C2×(C2×D11)⋊C8C2212yes—
31C2×#66880C2212yes—
32C2×C8×Dic11C2212yes—
33#10622590C2212yes—
34C2×#66874C2212yes—
35#10622549C2211yescharacteristic
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37#10622446—24no—
38D11×#95—21no—
39D11×#95—21no—
40#10622263—21no—
41#10622263—21no—
42C11×#340C2212yes—
43#10622189C2212yes—
44#10622167C2212yes—
45#10622167C2212yes—
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C22×C22⋊D11—21no—
49C22×C4×D11—22no—
50C22×C4×D11D411yescharacteristic
51C22×C4×D11D411yescharacteristic
52C22×C4×D11C2311yescharacteristic
53C22×Dic22C2311yescharacteristic
54C22×C8×C11C2312yes—
55C4×D4×C11—22no—
56C4×D4×C11C2×C414yescomplemented
57C2×C11×C4⋊C4C2312yes—
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C22⋊C4—21no—
60C2×C42×C11C2311yescharacteristic
61C2×C22⋊Dic11—21no—
62C2×C22⋊Dic11—21no—
63C2×C22⋊Dic11—21no—
64#66991—22no—
65#66991C2×C414yes—
66#66989—22no—
67#66989C2×C414yescomplemented
68C4×C22⋊D11—28no—
69C2×(C2×D11)⋊C4—21no—
70#66979—28no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11C2312yes—
74C2×C4⋊Dic11C2311yescharacteristic
75C2×Dic11⋊C4—21no—
76C2×Dic11⋊C4—21no—
77C2×Dic11⋊C4—22no—
78C2×C4×Dic11—21no—
79C2×C4×Dic11D411yescharacteristic
80C2×C4×Dic11D411yescharacteristic
81C2×C4×Dic11C2311yescharacteristic
82C22×C11⋊C8C2312yes—
83#66950—22no—
84#66950C2×C414yes—
85C4⋊C4×D11—42no—
86C4⋊C4×D11—42no—
87#66943—22no—
88#66943C2×C414yescomplemented
89#66936—28no—
90#66932—28no—
91C42×D11C2×C414yes—
92C42×D11D414yes—
93C4×Dic22—22no—
94C4×Dic22C2×C414yescomplemented
95C11×C4⋊C8—22no—
96C11×#102—42no—
97C11×#95—21no—
98C11×#95—21no—
99#66896—42no—
100C11⋊#95—21no—
101C11⋊#95—21no—
102C11⋊#95—22no—
103C11⋊#95—22no—
104(C2×D11)⋊C8—24no—
105#66880—42no—
106C8×Dic11—24no—
107#66874—42no—
108C4⋊(C11⋊C8)—22no—
109#21861—111nomaximal, Sylow
110C24×C11—21no—
111C23×D11C2×D411yescharacteristic
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11C22×C412yes—
118C22×C4×C11—21no—
119C22×C4×C11—24no—
120C22×C4×C11—22no—
121C22×C4×C11—44no—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2411yescharacteristic
125C2×C22⋊D11—24no—
126C2×C22⋊D11—44no—
127C22×Dic11—21no—
128C22×Dic11—21no—
129C22×Dic11—22no—
130C22×Dic11C2×D411yescharacteristic
131C22×Dic11C2×D411yescharacteristic
132C22×Dic11C2×D411yescharacteristic
133C2×C4×D11—24no—
134C2×C4×D11—21no—
135C2×C4×D11—21no—
136C2×C4×D11—21no—
137C2×C4×D11—21no—
138C2×C4×D11—42no—
139C2×C4×D11—44no—
140C2×C4×D11—44no—
141C2×C4×D11—44no—
142C2×C4×D11C22⋊C414yes—
143C2×C4×D11C22⋊C414yes—
144C2×C4×D11C22×C412yes—
145C2×C4×D11C2×D412yes—
146C2×Dic22—21no—
147C2×Dic22—21no—
148C2×Dic22—21no—
149C2×Dic22—21no—
150C2×Dic22—21no—
151C2×Dic22C22×C412yes—
152C2×C8×C11—22no—
153C2×C8×C11—22no—
154C2×C8×C11—22no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4C22×C412yes—
159C11×C22⋊C4—24no—
160C42×C11C22×C412yes—
161C42×C11C2×D412yes—
162C22⋊Dic11—24no—
163C22⋊Dic11—24no—
164C22⋊Dic11—24no—
165(C2×D11)⋊C4—24no—
166C4⋊Dic11—24no—
167C4⋊Dic11—24no—
168C4⋊Dic11—21no—
169C4⋊Dic11—22no—
170C4⋊Dic11—22no—
171C4⋊Dic11C22×C412yes—
172Dic11⋊C4—24no—
173Dic11⋊C4—24no—
174Dic11⋊C4—44no—
175C4×Dic11—24no—
176C4×Dic11C22⋊C414yes—
177C4×Dic11C22⋊C414yes—
178C4×Dic11C22×C412yes—
179C4×Dic11C2×D412yes—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8—22no—
183C2×#529—111no—
184C2×#431—111no—
185C2×#382—111no—
186#1991—112no—
187#1958—112no—
188#1874—112no—
189#1872—112no—
190#1805—111no—
191#1805—111no—
192#1804—111no—
193#1804D1111yescharacteristic, complemented
194C23×C11—22no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11C22×D411yescharacteristic
200C22×D11—21no—
201C22×D11—21no—
202C22×D11—22no—
203C22×D11C2×C22⋊C412yes—
204C22×D11#13514yes—
205D4×C11—22no—
206D4×C11—22no—
207D4×C11—41no—
208D4×C11—41no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—48no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11C2×C22⋊C412yes—
218C2×C4×C11C2×C22⋊C412yes—
219C2×C4×C11C23×C411yescharacteristic
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11H(5,𝔽2)11yescharacteristic
222C2×C4×C11H(5,𝔽2)11yescharacteristic
223C2×C4×C112−1+411yescharacteristic
224C2×C4×C112−1+411yescharacteristic
225C22⋊D11—48no—
226C2×Dic11—21no—
227C2×Dic11—21no—
228C2×Dic11—22no—
229C2×Dic11—22no—
230C2×Dic11—22no—
231C2×Dic11—22no—
232C2×Dic11—41no—
233C2×Dic11—41no—
234C2×Dic11—42no—
235C2×Dic11—42no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11C2×C22⋊C412yes—
239C2×Dic11C2×C22⋊C412yes—
240C2×Dic11C2×C22⋊C412yes—
241C4×D11—28no—
242C4×D11—22no—
243C4×D11—22no—
244C4×D11—22no—
245C4×D11—22no—
246C4×D11—44no—
247C4×D11—88no—
248Dic22—22no—
249Dic22—22no—
250Dic22—41no—
251Dic22—41no—
252C8×C11—42no—
253C11⋊C8—42no—
254#529—118no—
255#529—224no—
256C2×#126—221no—
257C2×#125—111no—
258C2×#124—111no—
259C2×#123—221no—
260C2×C22⋊Q8—111no—
261C2×#121—111no—
262C2×C4×Q8—111no—
263C2×C4×D4—221no—
264C2×C4×D4C2×D1111yescharacteristic
265C2×#117—221no—
266C22×C4⋊C4—112no—
267C22×C42—111no—
268#431—224no—
269C2×C4⋊C8—111no—
270C2×C4⋊C8C2×D1111yescharacteristic
271C2×#103—112no—
272C2×#103—112no—
273C2×#102—112no—
274C2×#102C2×D1112yes—
275C2×C22⋊C8—112no—
276C2×C4×C8—112no—
277#382—112no—
278#382—111no—
279#382—221no—
280#382—221no—
281#382C2×D1111yescharacteristic
282C2×#95—221no—
283C2×#95—221no—
284#340—112no—
285#340—112no—
286#340—112no—
287#340C2×D1112yes—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11—82no—
292C22×C11—82no—
293C22×C11C22×C22⋊C411yescharacteristic
294C22×C11#53511yescharacteristic
295C22×C11#53611yescharacteristic
296C22×C11C2×#13512yes—
297C22×C11#57512yes—
298C2×D11—22no—
299C2×D11—22no—
300C2×D11—24no—
301C2×D11—24no—
302C2×D11#41614yes—
303C4×C11—22no—
304C4×C11—22no—
305C4×C11—42no—
306C4×C11—82no—
307C4×C11#52011yescharacteristic
308C4×C11#52011yescharacteristic
309C4×C11#53711yescharacteristic
310C4×C11#53711yescharacteristic
311Dic11—22no—
312Dic11—22no—
313Dic11—22no—
314Dic11—42no—
315Dic11—42no—
316Dic11—82no—
317C22×Q8—111no—
318C22×D4—221no—
319C22×D4C22×D1111yescharacteristic
320C23×C4—21no—
321C23×C4—111no—
322C23×C4—111no—
323C23×C4—111no—
324C23×C4—222no—
325C22×C8—112no—
326C22×C8C22×D1112yes—
327#126—228no—
328#125—114no—
329#125—222no—
330#124—114no—
331#124—222no—
332#123—228no—
333C22⋊Q8—114no—
334C22⋊Q8—222no—
335#121—114no—
336#121—222no—
337C4×Q8—114no—
338C4×Q8—222no—
339C4×D4—22no—
340C4×D4—228no—
341C4×D4C4×D1114yescomplemented
342#117—228no—
343C2×C4⋊C4—111no—
344C2×C4⋊C4—112no—
345C2×C4⋊C4—221no—
346C2×C4⋊C4—221no—
347C2×C4⋊C4—221no—
348C2×C4⋊C4—221no—
349C2×C4⋊C4—222no—
350C2×C4⋊C4—442no—
351C2×C4⋊C4—442no—
352C2×C4⋊C4C22×D1112yes—
353C2×C4⋊C4C22×D1111yescharacteristic
354C2×C22⋊C4—21no—
355C2×C22⋊C4—221no—
356C2×C22⋊C4—221no—
357C2×C22⋊C4—221no—
358C2×C22⋊C4—221no—
359C2×C42—111no—
360C2×C42—111no—
361C2×C42—111no—
362C2×C42—114no—
363C2×C42—114no—
364C2×C42—221no—
365C2×C42C22×D1111yescharacteristic
366C4⋊C8—22no—
367C4⋊C8—222no—
368#103—442no—
369#103—442no—
370#102—42no—
371#102—442no—
372C22⋊C8—224no—
373C4×C8—224no—
374#95—21no—
375#95—21no—
376#95—222no—
377#95—222no—
378#95—221no—
379#95—221no—
380C2×C11—82no—
381C2×C11#231111yescharacteristic
382C2×C11C2×#41611yescharacteristic
383C2×C11#289611yescharacteristic
384C2×C11#321112yes—
385C2×C11#323212yes—
386D11—24no—
387C24—21no—
388C24—111no—
389C2×Q8—112no—
390C2×Q8—221no—
391C2×Q8—221no—
392C2×Q8—221no—
393C2×Q8—221no—
394C2×Q8—221no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—21no—
398C2×D4—21no—
399C2×D4—21no—
400C2×D4—224no—
401C2×D4—444no—
402C2×D4C2×C4×D1112yes—
403C22×C4—21no—
404C22×C4—24no—
405C22×C4—22no—
406C22×C4—44no—
407C22×C4—111no—
408C22×C4—111no—
409C22×C4—111no—
410C22×C4—114no—
411C22×C4—112no—
412C22×C4—112no—
413C22×C4—114no—
414C22×C4—224no—
415C22×C4—221no—
416C22×C4—221no—
417C22×C4—221no—
418C22×C4—221no—
419C22×C4—221no—
420C22×C4—221no—
421C22×C4—222no—
422C22×C4—442no—
423C22×C4—444no—
424C22×C4—444no—
425C22×C4—444no—
426C22×C4D4×D1111yescharacteristic
427C22×C4D4×D1111yescharacteristic
428C22×C4C23×D1111yescharacteristic
429C2×C8—22no—
430C2×C8—22no—
431C2×C8—22no—
432C2×C8—222no—
433C2×C8—222no—
434C2×C8—222no—
435C4⋊C4—21no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—112no—
439C4⋊C4—224no—
440C4⋊C4—224no—
441C4⋊C4—224no—
442C4⋊C4—224no—
443C4⋊C4—221no—
444C4⋊C4—222no—
445C4⋊C4—222no—
446C4⋊C4—444no—
447C4⋊C4C2×C4×D1112yes—
448C22⋊C4—24no—
449C22⋊C4—224no—
450C22⋊C4—224no—
451C22⋊C4—224no—
452C22⋊C4—224no—
453C42—114no—
454C42—114no—
455C42—112no—
456C42—112no—
457C42—224no—
458C42C2×C4×D1112yes—
459C42D4×D1112yes—
460C11#2186111yescharacteristic, complemented, Sylow
461C23—22no—
462C23—42no—
463C23—42no—
464C23—41no—
465C23—41no—
466C23—112no—
467C23—114no—
468C23—222no—
469C23—221no—
470C23—221no—
471C23C2×D4×D1111yescharacteristic
472Q8—222no—
473Q8—222no—
474Q8—441no—
475Q8—441no—
476D4—22no—
477D4—22no—
478D4—41no—
479D4—41no—
480D4—448no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—48no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—112no—
490C2×C4—112no—
491C2×C4—112no—
492C2×C4—228no—
493C2×C4—222no—
494C2×C4—222no—
495C2×C4—221no—
496C2×C4—221no—
497C2×C4—222no—
498C2×C4—222no—
499C2×C4—222no—
500C2×C4—222no—
501C2×C4—222no—
502C2×C4—222no—
503C2×C4—444no—
504C2×C4—442no—
505C2×C4—441no—
506C2×C4—441no—
507C2×C4—442no—
508C2×C4—442no—
509C2×C4—442no—
510C2×C4—888no—
511C2×C4C22⋊C4×D1112yes—
512C2×C4C22⋊C4×D1112yes—
513C2×C4C22×C4×D1111yescharacteristic
514C2×C4C2×D4×D1111yescharacteristic
515C2×C4#6703711yescharacteristic
516C2×C4#6704011yescharacteristic
517C2×C4#6704211yescharacteristic
518C2×C4#6704311yescharacteristic
519C8—42no—
520C8—442no—
521C22—42no—
522C22—42no—
523C22—42no—
524C22—82no—
525C22—82no—
526C22—114no—
527C22—224no—
528C22—222no—
529C22—222no—
530C22—224no—
531C22C2×C22⋊C4×D1111yescharacteristic
532C22#1062313811yescharacteristic
533C22#1062315911yescharacteristic
534C22D11×#13512yes—
535C22#1062330412yes—
536C4—22no—
537C4—22no—
538C4—42no—
539C4—82no—
540C4—222no—
541C4—222no—
542C4—222no—
543C4—442no—
544C4—442no—
545C4—882no—
546C4#1062303511yescharacteristic
547C4#1062305411yescharacteristic
548C4#1062313911yescharacteristic
549C4#1062316011yescharacteristic
550C2—82no—
551C2—224no—
552C2#1307120511yescharacteristic
553C2D11×#41611yescharacteristic
554C2#1307713011yescharacteristic
555C2#1307957912yes—
556C2#1307978212yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1804C2
socleC23×C11C22×D4
prime radicalC2×#66991C22
cosocleC22×C4×C11C24
hypercenter#1804D11
hypocenterC11#21861
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1804

Complements

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

NH ≅ G/Ntype
2. C2×#10622446C2semidirect
3. D11×#382C2semidirect
4. #13069579C2semidirect
5. #13069426C2semidirect
7. #13068922C2semidirect
8. #13068632C2semidirect
9. #13068628C2semidirect
10. #13068626C2semidirect
11. C11×#1804C2semidirect
18. #10623088C4semidirect
56. C4×D4×C11C2×C4semidirect
67. #66989C2×C4semidirect
88. #66943C2×C4semidirect
94. C4×Dic22C2×C4semidirect
193. #1804D11semidirect
341. C4×D4C4×D11semidirect
460. C11#21861semidirect

Maximal subgroups

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

subgroupindex
C2×#106230882
C2×#106224462
D11×#3822
#130695792
#130694262
#130689302
#130689222
#130686322
#130686282
#130686262
C11×#18042
#2186111