Finite Group Databasebeta

← #14763465

Subgroups — #14763465

Order 2816.

1166 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623222C211yesmaximal, characteristic
2C2×#10622298C211yesmaximal, characteristic, complemented
3D11×#382C211yesmaximal, characteristic, complemented
4#13069582C211yesmaximal, characteristic, complemented
5#13069427C211yesmaximal, characteristic, complemented
6#13069425C211yesmaximal, characteristic, complemented
7#13068932C212yesmaximal
8#13068922C212yesmaximal, complemented
9#13068630C212yesmaximal, complemented
10#13068625C212yesmaximal, complemented
11C11×#1991C211yesmaximal, characteristic, complemented
12C2×C11×#125C2211yescharacteristic
13#10623222—24no—
14#10623222C418yescomplemented
15C2×#66951—21no—
16C2×#66950C2211yescharacteristic
17C2×#66948C2211yescharacteristic
18C2×#66947—21no—
19C2×#66946—21no—
20C2×#66946C2211yescharacteristic
21C2×#66945—21no—
22C2×C4⋊C4×D11C2212yes—
23C2×#66940C2211yescharacteristic
24C2×#66928C2211yescharacteristic
25C2×C42×D11C2211yescharacteristic
26C2×C4×C8×C11C2211yescharacteristic
27C11×#382C2211yescharacteristic
28C2×#66885C2212yes—
29C2×(C2×D11)⋊C8C2212yes—
30C2×#66880C2212yes—
31C2×Dic11⋊C8C2212yes—
32#10622590C2212yes—
33C2×#66874C2212yes—
34C2×#66873C2212yes—
35#10622549C2211yescharacteristic
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622298—24no—
38D11×#95—21no—
39D11×#95—21no—
40#10622263—21no—
41#10622263—21no—
42C11×#340C2212yes—
43C11×#340C2212yes—
44#10622167C2212yes—
45#10622167C2212yes—
46C22×D44—21no—
47C22×D44C2311yescharacteristic
48C22×C4×D11—21no—
49C22×C4×D11—22no—
50C22×C4×D11D411yescharacteristic
51C22×C4×D11D411yescharacteristic
52C22×C4×D11C2311yescharacteristic
53C22×Dic22C2311yescharacteristic
54C22×C8×C11C2312yes—
55C11×#125—22no—
56C11×#125C2×C414yescomplemented
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C42×C11C2311yescharacteristic
63C2×(C2×D11)⋊C4—21no—
64C2×(C2×D11)⋊C4—21no—
65C2×(C2×D11)⋊C4—21no—
66C2×(C2×D11)⋊C4—21no—
67C2×(C2×D11)⋊C4—21no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11C2312yes—
70C2×Dic11⋊C4—21no—
71C2×Dic11⋊C4—22no—
72C2×C4×Dic11—21no—
73C2×C4×Dic11D411yescharacteristic
74C2×C4×Dic11D411yescharacteristic
75C2×C4×Dic11C2311yescharacteristic
76C22×C11⋊C8C2312yes—
77#66951—28no—
78#66950—22no—
79#66950C2×C414yes—
80#66948—22no—
81#66948C2×C414yes—
82#66947—28no—
83#66946—28no—
84#66946—22no—
85#66946C2×C414yescomplemented
86#66945—28no—
87C4⋊C4×D11—42no—
88C4⋊C4×D11—42no—
89#66940—22no—
90#66940C2×C414yescomplemented
91#66928—22no—
92#66928C2×C414yescomplemented
93C42×D11C2×C414yes—
94C42×D11D414yes—
95C4×C8×C11—22no—
96C11×#95—21no—
97C11×#95—21no—
98C11⋊#95—21no—
99C11⋊#95—21no—
100C11⋊#95—22no—
101C11⋊#95—22no—
102#66885—42no—
103(C2×D11)⋊C8—24no—
104#66880—42no—
105Dic11⋊C8—24no—
106#66874—42no—
107#66873—42no—
108C4×C11⋊C8—22no—
109#21861—111nomaximal, Sylow
110C23×D11—21no—
111C23×D11C2×D411yescharacteristic
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—22no—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2411yescharacteristic
118C22×Dic11—21no—
119C22×Dic11—22no—
120C22×Dic11C2×D411yescharacteristic
121C22×Dic11C2×D411yescharacteristic
122C22×Dic11C2×D411yescharacteristic
123C2×D44—24no—
124C2×D44—21no—
125C2×D44—22no—
126C2×D44—22no—
127C2×D44—44no—
128C2×D44C22×C412yes—
129C2×C4×D11—24no—
130C2×C4×D11—24no—
131C2×C4×D11—22no—
132C2×C4×D11—22no—
133C2×C4×D11—42no—
134C2×C4×D11—44no—
135C2×C4×D11—44no—
136C2×C4×D11—44no—
137C2×C4×D11—44no—
138C2×C4×D11C22⋊C414yes—
139C2×C4×D11C22⋊C414yes—
140C2×C4×D11C22×C412yes—
141C2×C4×D11C2×D412yes—
142C2×Dic22—21no—
143C2×Dic22—22no—
144C2×Dic22—22no—
145C2×Dic22C22×C412yes—
146C2×C8×C11—22no—
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C11×C4⋊C4—24no—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4C22×C412yes—
156C11×C4⋊C4C22×C412yes—
157C42×C11C22×C412yes—
158C42×C11C2×D412yes—
159(C2×D11)⋊C4—24no—
160(C2×D11)⋊C4—24no—
161(C2×D11)⋊C4—24no—
162(C2×D11)⋊C4—24no—
163(C2×D11)⋊C4—24no—
164C4⋊Dic11—24no—
165C4⋊Dic11—22no—
166C4⋊Dic11—22no—
167Dic11⋊C4—24no—
168Dic11⋊C4—44no—
169C4×Dic11—24no—
170C4×Dic11C22⋊C414yes—
171C4×Dic11C22⋊C414yes—
172C4×Dic11C22×C412yes—
173C4×Dic11C2×D412yes—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—22no—
177C2×#529—111no—
178C2×#431—111no—
179C2×#382—111no—
180#1991—111no—
181#1991D1111yescharacteristic, complemented
182#1958—111no—
183#1958—111no—
184#1874—112no—
185#1872—112no—
186#1805—112no—
187#1804—112no—
188C23×C11C22×D411yescharacteristic
189C22×D11—21no—
190C22×D11—21no—
191C22×D11—22no—
192C22×D11—22no—
193C22×D11—41no—
194C22×D11—41no—
195C22×D11—42no—
196C22×D11—42no—
197C22×D11C2×C22⋊C412yes—
198C22×D11#13514yes—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11C2×C22⋊C412yes—
209C2×C4×C11C2×C22⋊C412yes—
210C2×C4×C11C23×C411yescharacteristic
211C2×C4×C11C22×D411yescharacteristic
212C2×C4×C11H(5,𝔽2)12yes—
213C2×C4×C112−1+412yes—
214C2×Dic11—21no—
215C2×Dic11—21no—
216C2×Dic11—22no—
217C2×Dic11—22no—
218C2×Dic11—22no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11—42no—
224C2×Dic11C2×C22⋊C412yes—
225C2×Dic11C2×C22⋊C412yes—
226C2×Dic11C2×C22⋊C412yes—
227D44—24no—
228D44—48no—
229D44—42no—
230C4×D11—28no—
231C4×D11—24no—
232C4×D11—24no—
233C4×D11—44no—
234C4×D11—48no—
235C4×D11—88no—
236Dic22—24no—
237Dic22—42no—
238C8×C11—42no—
239C11⋊C8—42no—
240#529—118no—
241#529—224no—
242C2×#126—221no—
243C2×#125C2×D1111yescharacteristic
244C2×#124—111no—
245C2×#123—221no—
246C2×C22⋊Q8—111no—
247C2×#121—111no—
248C2×C4×Q8—111no—
249C2×C4×D4—111no—
250C2×C4×D4—221no—
251C2×#117—221no—
252C22×C4⋊C4—112no—
253C22×C42—111no—
254#431—224no—
255C2×C4⋊C8—112no—
256C2×#103—112no—
257C2×#103—112no—
258C2×#102—112no—
259C2×#102—112no—
260C2×C22⋊C8—112no—
261C2×C4×C8—111no—
262C2×C4×C8C2×D1111yescharacteristic
263#382—112no—
264#382—111no—
265#382—221no—
266#382—221no—
267#382C2×D1111yescharacteristic
268C2×#95—221no—
269C2×#95—221no—
270#340—112no—
271#340—112no—
272#340C2×D1112yes—
273#340C2×D1112yes—
274C22×C11C22×C22⋊C411yescharacteristic
275C22×C11#53511yescharacteristic
276C22×C11#53611yescharacteristic
277C22×C11C2×#13512yes—
278C22×C11#57512yes—
279C2×D11—22no—
280C2×D11—22no—
281C2×D11—24no—
282C2×D11—24no—
283C2×D11—42no—
284C2×D11—42no—
285C2×D11—42no—
286C2×D11—82no—
287C2×D11—82no—
288C2×D11#41614yes—
289C4×C11—22no—
290C4×C11—22no—
291C4×C11—42no—
292C4×C11—42no—
293C4×C11—82no—
294C4×C11#52012yes—
295C4×C11#53712yes—
296Dic11—22no—
297Dic11—22no—
298Dic11—22no—
299Dic11—42no—
300Dic11—82no—
301C22×Q8—111no—
302C22×D4—111no—
303C22×D4—221no—
304C23×C4—111no—
305C23×C4—111no—
306C23×C4—111no—
307C23×C4—221no—
308C23×C4—222no—
309C22×C8—112no—
310C22×C8C22×D1112yes—
311#126—228no—
312#125—22no—
313#125C4×D1114yescomplemented
314#124—114no—
315#124—222no—
316#123—228no—
317C22⋊Q8—114no—
318C22⋊Q8—222no—
319#121—114no—
320#121—222no—
321C4×Q8—114no—
322C4×Q8—222no—
323C4×D4—114no—
324C4×D4—222no—
325C4×D4—228no—
326#117—228no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—112no—
330C2×C4⋊C4—221no—
331C2×C4⋊C4—221no—
332C2×C4⋊C4—222no—
333C2×C4⋊C4—442no—
334C2×C4⋊C4—442no—
335C2×C4⋊C4C22×D1112yes—
336C2×C4⋊C4C22×D1111yescharacteristic
337C2×C4⋊C4C22×D1111yescharacteristic
338C2×C22⋊C4—221no—
339C2×C22⋊C4—221no—
340C2×C22⋊C4—221no—
341C2×C22⋊C4—221no—
342C2×C22⋊C4—221no—
343C2×C42—111no—
344C2×C42—111no—
345C2×C42—111no—
346C2×C42—114no—
347C2×C42—114no—
348C2×C42—221no—
349C2×C42C22×D1111yescharacteristic
350C4⋊C8—224no—
351#103—442no—
352#103—442no—
353#102—442no—
354#102—442no—
355C22⋊C8—224no—
356C4×C8—22no—
357C4×C8—222no—
358#95—21no—
359#95—21no—
360#95—222no—
361#95—222no—
362#95—221no—
363#95—221no—
364C2×C11#231111yescharacteristic
365C2×C11C2×#41611yescharacteristic
366C2×C11#289611yescharacteristic
367C2×C11#321112yes—
368C2×C11#323212yes—
369D11—24no—
370D11—82no—
371C24—111no—
372C24—221no—
373C2×Q8—112no—
374C2×Q8—221no—
375C2×Q8—222no—
376C2×Q8—222no—
377C2×D4—112no—
378C2×D4—224no—
379C2×D4—221no—
380C2×D4—222no—
381C2×D4—222no—
382C2×D4—444no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—22no—
386C22×C4—111no—
387C22×C4—111no—
388C22×C4—111no—
389C22×C4—114no—
390C22×C4—112no—
391C22×C4—112no—
392C22×C4—114no—
393C22×C4—224no—
394C22×C4—224no—
395C22×C4—222no—
396C22×C4—222no—
397C22×C4—221no—
398C22×C4—222no—
399C22×C4—442no—
400C22×C4—444no—
401C22×C4—444no—
402C22×C4—444no—
403C22×C4—444no—
404C22×C4D4×D1111yescharacteristic
405C22×C4D4×D1111yescharacteristic
406C22×C4C23×D1111yescharacteristic
407C2×C8—22no—
408C2×C8—22no—
409C2×C8—22no—
410C2×C8—222no—
411C2×C8—222no—
412C2×C8—222no—
413C4⋊C4—24no—
414C4⋊C4—24no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—224no—
420C4⋊C4—224no—
421C4⋊C4—222no—
422C4⋊C4—222no—
423C4⋊C4—444no—
424C4⋊C4C2×C4×D1112yes—
425C4⋊C4C2×C4×D1112yes—
426C22⋊C4—224no—
427C22⋊C4—224no—
428C22⋊C4—224no—
429C22⋊C4—224no—
430C22⋊C4—224no—
431C42—114no—
432C42—114no—
433C42—112no—
434C42—112no—
435C42—224no—
436C42C2×C4×D1112yes—
437C42D4×D1112yes—
438C11#2186111yescharacteristic, complemented, Sylow
439C23—112no—
440C23—114no—
441C23—221no—
442C23—222no—
443C23—221no—
444C23—222no—
445C23—441no—
446C23—442no—
447C23—442no—
448C23—441no—
449C23C2×D4×D1111yescharacteristic
450Q8—224no—
451Q8—442no—
452D4—224no—
453D4—448no—
454D4—442no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—112no—
465C2×C4—112no—
466C2×C4—112no—
467C2×C4—228no—
468C2×C4—221no—
469C2×C4—222no—
470C2×C4—222no—
471C2×C4—221no—
472C2×C4—224no—
473C2×C4—224no—
474C2×C4—222no—
475C2×C4—444no—
476C2×C4—448no—
477C2×C4—441no—
478C2×C4—441no—
479C2×C4—442no—
480C2×C4—442no—
481C2×C4—442no—
482C2×C4—888no—
483C2×C4C22⋊C4×D1112yes—
484C2×C4C22⋊C4×D1112yes—
485C2×C4C22×C4×D1111yescharacteristic
486C2×C4C2×D4×D1111yescharacteristic
487C2×C4#6704012yes—
488C2×C4#6704212yes—
489C8—42no—
490C8—442no—
491C22—114no—
492C22—224no—
493C22—222no—
494C22—222no—
495C22—224no—
496C22—442no—
497C22—442no—
498C22—442no—
499C22—882no—
500C22—882no—
501C22C2×C22⋊C4×D1111yescharacteristic
502C22#1062320511yescharacteristic
503C22#1062325511yescharacteristic
504C22D11×#13512yes—
505C22#1062329912yes—
506C4—22no—
507C4—22no—
508C4—42no—
509C4—42no—
510C4—82no—
511C4—222no—
512C4—222no—
513C4—222no—
514C4—442no—
515C4—882no—
516C4#1062310512yes—
517C4#1062316012yes—
518C2—224no—
519C2—882no—
520C2#1307120711yescharacteristic
521C2D11×#41611yescharacteristic
522C2#1307713111yescharacteristic
523C2#1307958212yes—
524C2#1307978512yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1991C2
socleC23×C11C22×D4
prime radicalC2×#66948C22
cosocleC22×C4×C11C24
hypercenter#1991D11
hypocenterC11#21861
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1991

Complements

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

NH ≅ G/Ntype
2. C2×#10622298C2semidirect
3. D11×#382C2semidirect
4. #13069582C2semidirect
5. #13069427C2semidirect
6. #13069425C2semidirect
8. #13068922C2semidirect
9. #13068630C2semidirect
10. #13068625C2semidirect
11. C11×#1991C2semidirect
14. #10623222C4semidirect
56. C11×#125C2×C4semidirect
85. #66946C2×C4semidirect
90. #66940C2×C4semidirect
92. #66928C2×C4semidirect
181. #1991D11semidirect
313. #125C4×D11semidirect
438. C11#21861semidirect

Maximal subgroups

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

subgroupindex
C2×#106232222
C2×#106222982
D11×#3822
#130695822
#130694272
#130694252
#130689322
#130689222
#130686302
#130686252
C11×#19912
#2186111