Finite Group Databasebeta

← #14763519

Subgroups — #14763519

Order 2816.

1118 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623111C211yesmaximal, characteristic
2C2×#10622448C211yesmaximal, characteristic, complemented
3#13071022C211yesmaximal, characteristic, complemented
4#13069583C212yesmaximal, complemented
5#13069429C212yesmaximal, complemented
6#13068937C212yesmaximal
7#13068925C212yesmaximal, complemented
8#13068631C211yesmaximal, characteristic, complemented
9#13068627C211yesmaximal, characteristic, complemented
10#13068623C211yesmaximal, characteristic, complemented
11C11×#1805C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×#67000C2211yescharacteristic
14C2×#66999C2211yescharacteristic
15#10623111—24no—
16#10623111C418yescomplemented
17C2×#66951—21no—
18C2×#66948C2211yescharacteristic
19C2×#66947—21no—
20C2×#66945C2212yes—
21C2×#66943C2211yescharacteristic
22C2×C4×D44—21no—
23C2×C4×D44C2211yescharacteristic
24C2×#66925—21no—
25C2×C42×D11C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×#103C2212yes—
28C11×#382C2211yescharacteristic
29C2×#66899C2212yes—
30C2×#66885C2212yes—
31C2×(C2×D11)⋊C8C2212yes—
32C2×#66879C2212yes—
33#10622589C2212yes—
34C2×#66873C2212yes—
35#10622549C2211yescharacteristic
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37#10622448—24no—
38#10622280—21no—
39#10622280—21no—
40#10622262—21no—
41#10622262—21no—
42C11×#340C2212yes—
43#10622189C2212yes—
44#10622167C2212yes—
45#10622167C2212yes—
46C22×Q8×C11C2311yescharacteristic
47C22×D44—21no—
48C22×D44C2311yescharacteristic
49C22×C4×D11—21no—
50C22×C4×D11D411yescharacteristic
51C22×C4×D11D411yescharacteristic
52C22×C4×D11C2311yescharacteristic
53C22×C8×C11C2312yes—
54C4×Q8×C11—22no—
55C4×Q8×C11C2×C414yes—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4C2312yes—
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C42×C11—21no—
60C2×C42×C11C2311yescharacteristic
61#67000—22no—
62#67000C2×C414yes—
63#66999—22no—
64#66999C2×C414yes—
65C2×(C2×D11)⋊C4—21no—
66C2×(C2×D11)⋊C4—21no—
67C2×(C2×D11)⋊C4—21no—
68C2×(C2×D11)⋊C4—21no—
69C2×(C2×D11)⋊C4—21no—
70C2×(C2×D11)⋊C4—22no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11C2312yes—
73C2×C4⋊Dic11C2311yescharacteristic
74C2×Dic11⋊C4—21no—
75C2×Dic11⋊C4—21no—
76C2×Dic11⋊C4—22no—
77C2×Dic11⋊C4—22no—
78C2×C4×Dic11—22no—
79C2×C4×Dic11D411yescharacteristic
80C2×C4×Dic11D411yescharacteristic
81C2×C4×Dic11C2311yescharacteristic
82C22×C11⋊C8C2312yes—
83#66951—28no—
84#66948—22no—
85#66948C2×C414yes—
86#66947—28no—
87#66945—42no—
88#66945—42no—
89#66943—22no—
90#66943C2×C414yes—
91C4×D44—28no—
92C4×D44—22no—
93C4×D44C2×C414yes—
94#66925—28no—
95C42×D11C2×C414yes—
96C42×D11D414yes—
97C11×C4⋊C8—22no—
98C11×#103—42no—
99C11×#95—21no—
100C11×#95—21no—
101#66899—42no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104#66885—42no—
105(C2×D11)⋊C8—24no—
106#66879—24no—
107#66873—42no—
108C4⋊(C11⋊C8)—22no—
109#21868—111nomaximal, Sylow
110C23×D11—21no—
111C23×D11C2×D411yescharacteristic
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11C22×C412yes—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2411yescharacteristic
124C22×Dic11—21no—
125C22×Dic11—22no—
126C22×Dic11C2×D411yescharacteristic
127C22×Dic11C2×D411yescharacteristic
128C22×Dic11C2×D411yescharacteristic
129C2×D44—24no—
130C2×D44—21no—
131C2×D44—21no—
132C2×D44—21no—
133C2×D44—21no—
134C2×D44—21no—
135C2×D44—44no—
136C2×D44C22×C412yes—
137C2×C4×D11—24no—
138C2×C4×D11—21no—
139C2×C4×D11—21no—
140C2×C4×D11—21no—
141C2×C4×D11—21no—
142C2×C4×D11—42no—
143C2×C4×D11—42no—
144C2×C4×D11—44no—
145C2×C4×D11C22⋊C414yes—
146C2×C4×D11C22⋊C414yes—
147C2×C4×D11C22×C412yes—
148C2×C4×D11C2×D412yes—
149C2×C8×C11—22no—
150C2×C8×C11—22no—
151C2×C8×C11—22no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4C22×C412yes—
157C42×C11—24no—
158C42×C11C22×C412yes—
159C42×C11C2×D412yes—
160(C2×D11)⋊C4—24no—
161(C2×D11)⋊C4—24no—
162(C2×D11)⋊C4—24no—
163(C2×D11)⋊C4—24no—
164(C2×D11)⋊C4—24no—
165(C2×D11)⋊C4—44no—
166C4⋊Dic11—24no—
167C4⋊Dic11—21no—
168C4⋊Dic11—22no—
169C4⋊Dic11—22no—
170C4⋊Dic11C22×C412yes—
171Dic11⋊C4—24no—
172Dic11⋊C4—24no—
173Dic11⋊C4—44no—
174Dic11⋊C4—44no—
175C4×Dic11—44no—
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×#432—111no—
185#2285—111no—
186#1992—112no—
187#1959—112no—
188#1875—112no—
189#1873—112no—
190#1805—111no—
191#1805D1111yescharacteristic, complemented
192#1804—111no—
193#1804—111no—
194C23×C11C22×D411yescharacteristic
195C22×D11—21no—
196C22×D11—21no—
197C22×D11—22no—
198C22×D11—22no—
199C22×D11—22no—
200C22×D11—41no—
201C22×D11—41no—
202C22×D11—42no—
203C22×D11—42no—
204C22×D11C2×C22⋊C412yes—
205Q8×C11—22no—
206Q8×C11—22no—
207Q8×C11—41no—
208Q8×C11—41no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11C2×C22⋊C412yes—
220C2×C4×C11C2×C22⋊C412yes—
221C2×C4×C11C23×C411yescharacteristic
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11H(5,𝔽2)11yescharacteristic
224C2×C4×C11H(5,𝔽2)11yescharacteristic
225C2×C4×C112−1+411yescharacteristic
226C2×C4×C112−1+411yescharacteristic
227C2×Dic11—21no—
228C2×Dic11—21no—
229C2×Dic11—22no—
230C2×Dic11—22no—
231C2×Dic11—22no—
232C2×Dic11—42no—
233C2×Dic11—42no—
234C2×Dic11—42no—
235C2×Dic11—42no—
236C2×Dic11C2×C22⋊C412yes—
237C2×Dic11C2×C22⋊C412yes—
238C2×Dic11C2×C22⋊C412yes—
239D44—22no—
240D44—22no—
241D44—48no—
242D44—41no—
243D44—41no—
244C4×D11—22no—
245C4×D11—22no—
246C4×D11—22no—
247C4×D11—22no—
248C4×D11—44no—
249C4×D11—44no—
250C4×D11—48no—
251C8×C11—42no—
252C11⋊C8—42no—
253#529—118no—
254#529—224no—
255C2×#126—221no—
256C2×#125—111no—
257C2×#124—111no—
258C2×#123—221no—
259C2×C22⋊Q8—111no—
260C2×#121—111no—
261C2×C4×Q8C2×D1111yescharacteristic
262C2×C4×D4—111no—
263C2×C4×D4—221no—
264C2×#117—112no—
265C2×#117—221no—
266C22×C42—111no—
267#432—224no—
268C2×C4⋊C8—111no—
269C2×C4⋊C8C2×D1111yescharacteristic
270C2×#103—112no—
271C2×#103C2×D1112yes—
272C2×#102—112no—
273C2×#102—112no—
274C2×C22⋊C8—112no—
275C2×#97—112no—
276#384—112no—
277#382—111no—
278#382C2×D1111yescharacteristic
279#380—221no—
280#380—221no—
281C4×C4⋊C4—221no—
282C4×C4⋊C4—221no—
283#340—112no—
284#340—112no—
285#340—112no—
286#340C2×D1112yes—
287C22×C11C22×C22⋊C411yescharacteristic
288C22×C11#53511yescharacteristic
289C22×C11#53611yescharacteristic
290C22×C11#57512yes—
291C22×C11#57512yes—
292C2×D11—22no—
293C2×D11—22no—
294C2×D11—22no—
295C2×D11—42no—
296C2×D11—42no—
297C2×D11—42no—
298C2×D11—42no—
299C2×D11—42no—
300C2×D11—82no—
301C2×D11—82no—
302C4×C11—22no—
303C4×C11—22no—
304C4×C11—42no—
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—82no—
316C22×Q8C22×D1111yescharacteristic
317C22×D4—111no—
318C22×D4—221no—
319C23×C4—111no—
320C23×C4—111no—
321C23×C4—111no—
322C23×C4—221no—
323C22×C8—112no—
324C22×C8C22×D1112yes—
325#126—228no—
326#125—114no—
327#125—222no—
328#124—114no—
329#124—222no—
330#123—228no—
331C22⋊Q8—114no—
332C22⋊Q8—222no—
333#121—114no—
334#121—222no—
335C4×Q8—22no—
336C4×Q8C4×D1114yes—
337C4×D4—114no—
338C4×D4—228no—
339C4×D4—222no—
340#117—228no—
341#117—442no—
342#117—442no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—111no—
345C2×C4⋊C4—112no—
346C2×C4⋊C4—221no—
347C2×C4⋊C4—221no—
348C2×C4⋊C4—221no—
349C2×C4⋊C4—222no—
350C2×C4⋊C4—222no—
351C2×C4⋊C4C22×D1112yes—
352C2×C4⋊C4C22×D1111yescharacteristic
353C2×C22⋊C4—221no—
354C2×C22⋊C4—221no—
355C2×C22⋊C4—221no—
356C2×C22⋊C4—221no—
357C2×C22⋊C4—221no—
358C2×C22⋊C4—222no—
359C2×C42—21no—
360C2×C42—111no—
361C2×C42—111no—
362C2×C42—111no—
363C2×C42—114no—
364C2×C42—114no—
365C2×C42—222no—
366C2×C42C22×D1111yescharacteristic
367C4⋊C8—22no—
368C4⋊C8—222no—
369#103—42no—
370#103—442no—
371#102—442no—
372#102—442no—
373C22⋊C8—224no—
374#97—224no—
375#95—21no—
376#95—21no—
377#95—221no—
378#95—221no—
379C2×C11#231111yescharacteristic
380C2×C11#289611yescharacteristic
381C2×C11#289611yescharacteristic
382C2×C11#321912yes—
383C2×C11#324012yes—
384D11—42no—
385D11—82no—
386C24—111no—
387C24—221no—
388C2×Q8—21no—
389C2×Q8—21no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—21no—
393C2×Q8C2×C4×D1112yes—
394C2×D4—112no—
395C2×D4—224no—
396C2×D4—221no—
397C2×D4—221no—
398C2×D4—221no—
399C2×D4—221no—
400C2×D4—221no—
401C2×D4—444no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—111no—
406C22×C4—111no—
407C22×C4—111no—
408C22×C4—112no—
409C22×C4—112no—
410C22×C4—114no—
411C22×C4—114no—
412C22×C4—221no—
413C22×C4—221no—
414C22×C4—221no—
415C22×C4—221no—
416C22×C4—221no—
417C22×C4—224no—
418C22×C4—222no—
419C22×C4—442no—
420C22×C4—442no—
421C22×C4—444no—
422C22×C4D4×D1111yescharacteristic
423C22×C4D4×D1111yescharacteristic
424C22×C4C23×D1111yescharacteristic
425C2×C8—22no—
426C2×C8—22no—
427C2×C8—22no—
428C2×C8—222no—
429C2×C8—222no—
430C2×C8—222no—
431C4⋊C4—24no—
432C4⋊C4—21no—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—112no—
436C4⋊C4—224no—
437C4⋊C4—224no—
438C4⋊C4—224no—
439C4⋊C4—221no—
440C4⋊C4—222no—
441C4⋊C4—222no—
442C4⋊C4—444no—
443C4⋊C4—444no—
444C4⋊C4C2×C4×D1112yes—
445C22⋊C4—224no—
446C22⋊C4—224no—
447C22⋊C4—224no—
448C22⋊C4—224no—
449C22⋊C4—224no—
450C22⋊C4—444no—
451C42—24no—
452C42—114no—
453C42—114no—
454C42—112no—
455C42—112no—
456C42—444no—
457C42C2×C4×D1112yes—
458C42D4×D1112yes—
459C11#2186811yescharacteristic, complemented, Sylow
460C23—112no—
461C23—222no—
462C23—222no—
463C23—221no—
464C23—221no—
465C23—222no—
466C23—442no—
467C23—442no—
468C23—441no—
469C23—441no—
470C23C2×D4×D1111yescharacteristic
471Q8—22no—
472Q8—22no—
473Q8—41no—
474Q8—41no—
475D4—222no—
476D4—222no—
477D4—448no—
478D4—441no—
479D4—441no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—42no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—112no—
491C2×C4—112no—
492C2×C4—112no—
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—444no—
503C2×C4—444no—
504C2×C4—448no—
505C2×C4—442no—
506C2×C4—442no—
507C2×C4—442no—
508C2×C4—442no—
509C2×C4C22⋊C4×D1112yes—
510C2×C4C22⋊C4×D1112yes—
511C2×C4C22×C4×D1111yescharacteristic
512C2×C4C2×D4×D1111yescharacteristic
513C2×C4#6703711yescharacteristic
514C2×C4#6704011yescharacteristic
515C2×C4#6704211yescharacteristic
516C2×C4#6704311yescharacteristic
517C8—42no—
518C8—442no—
519C22—222no—
520C22—222no—
521C22—222no—
522C22—442no—
523C22—442no—
524C22—442no—
525C22—442no—
526C22—442no—
527C22—882no—
528C22—882no—
529C22C2×C22⋊C4×D1111yescharacteristic
530C22#1062313811yescharacteristic
531C22#1062315911yescharacteristic
532C22#1062329912yes—
533C22#1062330812yes—
534C4—22no—
535C4—22no—
536C4—42no—
537C4—42no—
538C4—82no—
539C4—222no—
540C4—222no—
541C4—222no—
542C4—442no—
543C4—882no—
544C4#1062303511yescharacteristic
545C4#1062305411yescharacteristic
546C4#1062313911yescharacteristic
547C4#1062316011yescharacteristic
548C2—442no—
549C2—882no—
550C2#1307120511yescharacteristic
551C2#1307713111yescharacteristic
552C2#1307713411yescharacteristic
553C2#1307965812yes—
554C2#1307986112yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1805C2
socleC23×C11C22×D4
prime radicalC2×#66948C22
cosocleC22×C4×C11C24
hypercenter#1805D11
hypocenterC11#21868
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1805

Complements

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

NH ≅ G/Ntype
2. C2×#10622448C2semidirect
3. #13071022C2semidirect
4. #13069583C2semidirect
5. #13069429C2semidirect
7. #13068925C2semidirect
8. #13068631C2semidirect
9. #13068627C2semidirect
10. #13068623C2semidirect
11. C11×#1805C2semidirect
16. #10623111C4semidirect
191. #1805D11semidirect
459. C11#21868semidirect

Maximal subgroups

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

subgroupindex
C2×#106231112
C2×#106224482
#130710222
#130695832
#130694292
#130689372
#130689252
#130686312
#130686272
#130686232
C11×#18052
#2186811