Finite Group Databasebeta

← #14760455

Subgroups — #14760455

Order 2816.

1066 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D8×Dic11C211yesmaximal, characteristic, complemented
2C2×#10622735C211yesmaximal, characteristic, complemented
3#13071311C212yesmaximal, complemented
4#13069493C211yesmaximal, characteristic, complemented
5#13069360C211yesmaximal, characteristic, complemented
6#13069301C212yesmaximal, complemented
7#13069045C212yesmaximal, complemented
8#13068649C211yesmaximal, characteristic, complemented
9#106×Dic11C211yesmaximal, characteristic, complemented
10#13068443C212yesmaximal, complemented
11C2×C11×#469C211yesmaximal, characteristic
12C22×C11×D8C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C2×C11×#121C2212yes—
15C2×D4×Dic11C2212yes—
16C2×#66979C2211yescharacteristic
17C23×C11⋊C8C2211yescharacteristic
18C11×#469C418yescomplemented
19C2×C11×#106C2211yescharacteristic
20C2×C11×#102C2212yes—
21#10622834—22no—
22#10622834C2212yes—
23#10622833—22no—
24C2×#66896C2212yes—
25C2×#66896C2212yes—
26#10622825C2212yes—
27D8×Dic11—24no—
28#10622735—24no—
29C2×#66882C2211yescharacteristic
30C2×#66881C2211yescharacteristic
31C2×#66879C2211yescharacteristic
32C2×#66879C2211yescharacteristic
33C2×C8×Dic11C2211yescharacteristic
34C2×C8×Dic11C2211yescharacteristic
35#10622598C2212yes—
36C4⋊C4×Dic11C2212yes—
37#10622564—22no—
38#10622563—22no—
39#10622189C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42C22×D4×C11—22no—
43C22×D4×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C23×Dic11—22no—
46C2×C11×D8—22no—
47C2×C11×D8—22no—
48C2×C11×D8C2×C414yes—
49C2×C11×M16—22no—
50C2×C11×M16—22no—
51C2×C11×M16C2×C414yescomplemented
52C22×C8×C11C2311yescharacteristic
53C22×C8×C11C2311yescharacteristic
54C11×#121—24no—
55C11×#121C2×C418yescomplemented
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C22⋊C4—22no—
58C2×C22⋊Dic11—22no—
59C2×C22⋊Dic11—22no—
60C2×C22⋊Dic11—22no—
61C2×C22⋊Dic11—22no—
62C2×C22⋊Dic11D411yescharacteristic
63C2×C22⋊Dic11D411yescharacteristic
64D4×Dic11—24no—
65D4×Dic11—24no—
66#66979—22no—
67#66979—22no—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11D411yescharacteristic
70C2×C4⋊Dic11D411yescharacteristic
71C2×C4⋊Dic11C2312yes—
72C2×C4⋊Dic11C2312yes—
73C2×C4×Dic11—22no—
74C2×C4×Dic11C2311yescharacteristic
75C2×C4×Dic11C2311yescharacteristic
76C22×C11⋊C8—22no—
77C22×C11⋊C8—22no—
78C22×C11⋊C8—22no—
79C22×C11⋊C8C2311yescharacteristic
80C22×C11⋊C8C2311yescharacteristic
81C11×#106C2×C414yescomplemented
82C11×#102C2×C418yescomplemented
83#66896—24no—
84#66896—24no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88#66882—22no—
89#66881—22no—
90#66879—22no—
91#66879—22no—
92C8×Dic11—22no—
93C8×Dic11D414yescomplemented
94#21536—111nomaximal, Sylow
95C24×C11—22no—
96C24×C11C2×D411yescharacteristic
97C2×D4×C11—28no—
98C2×D4×C11—22no—
99C2×D4×C11—22no—
100C2×D4×C11—22no—
101C2×D4×C11—22no—
102C2×D4×C11—22no—
103C2×D4×C11—82no—
104C2×D4×C11—82no—
105C2×D4×C11C22×C414yes—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—22no—
111C22×C4×C11C22×C412yes—
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11#4112yes—
114C22×C4×C11C2411yescharacteristic
115C22×Dic11—22no—
116C22×Dic11—22no—
117C22×Dic11—44no—
118C22×Dic11—82no—
119C22×Dic11—82no—
120C22×Dic11C2×D411yescharacteristic
121C22×Dic11C2×D411yescharacteristic
122C22×Dic11C2×D411yescharacteristic
123C22×Dic11C2×D411yescharacteristic
124C11×D8—28no—
125C11×M16—28no—
126C2×C8×C11—21no—
127C2×C8×C11—21no—
128C2×C8×C11C22×C412yes—
129C2×C8×C11C22×C412yes—
130C2×C8×C11C2×D412yes—
131C2×C8×C11#4112yes—
132C11×C4⋊C4—22no—
133C11×C4⋊C4C22×C414yes—
134C11×C22⋊C4—28no—
135C22⋊Dic11—22no—
136C22⋊Dic11—22no—
137C22⋊Dic11—44no—
138C22⋊Dic11—82no—
139C22⋊Dic11—82no—
140C22⋊Dic11—82no—
141C4⋊Dic11—22no—
142C4⋊Dic11—22no—
143C4⋊Dic11—22no—
144C4⋊Dic11—22no—
145C4⋊Dic11—22no—
146C4⋊Dic11—22no—
147C4⋊Dic11—82no—
148C4×Dic11—21no—
149C4×Dic11—21no—
150C4×Dic11—82no—
151C4×Dic11C2×D412yes—
152C4×Dic11#4112yes—
153C2×C11⋊C8—28no—
154C2×C11⋊C8—21no—
155C2×C11⋊C8—21no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8—21no—
158C2×C11⋊C8C2×D412yes—
159C2×C11⋊C8#4112yes—
160C2×#469D1111yescharacteristic
161C2×C4×D8—111no—
162C2×#405—111no—
163#2324—112no—
164#1972—111no—
165#1944—111no—
166#1934—112no—
167#1893—112no—
168#1809—111no—
169C4×#106—111no—
170#1762—112no—
171C23×C11—21no—
172C23×C11—21no—
173C23×C11—22no—
174C23×C11—22no—
175C23×C11—24no—
176C23×C11—42no—
177C23×C11—42no—
178C23×C11—42no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11C4×D412yes—
183C23×C11C22×D411yescharacteristic
184D4×C11—24no—
185D4×C11—24no—
186D4×C11—42no—
187D4×C11—42no—
188D4×C11—88no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—24no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11C4×D412yes—
199C2×C4×C11C23×C411yescharacteristic
200C2×C4×C11C22×D411yescharacteristic
201C2×C4×C11C2×#4111yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×Dic11—22no—
206C2×Dic11—22no—
207C2×Dic11—21no—
208C2×Dic11—21no—
209C2×Dic11—22no—
210C2×Dic11—22no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11—88no—
218C2×Dic11#12112yes—
219C2×Dic11#12112yes—
220C8×C11—22no—
221C8×C11C4×D414yes—
222C11⋊C8—22no—
223C11⋊C8—22no—
224C22×D8C2×D1111yescharacteristic
225C22×M16C2×D1111yescharacteristic
226C23×C8—111no—
227C2×#121C2×D1112yes—
228C2×C4×D4—112no—
229C2×#117—111no—
230#469Dic1118yescomplemented
231C4×D8—224no—
232C2×#107—111no—
233C2×#106—111no—
234C2×#106C2×D1111yescharacteristic
235C2×#102—112no—
236C2×#102—112no—
237C2×#102C2×D1112yes—
238#405—224no—
239C2×#97—111no—
240C2×#97—111no—
241C2×C4×C8—111no—
242C2×C4×C8—111no—
243#390—112no—
244#390—222no—
245#389—112no—
246#388—222no—
247#386—222no—
248#385—222no—
249#380—112no—
250C4×C4⋊C4—112no—
251#340—112no—
252#340—112no—
253#340—112no—
254C22×C11—24no—
255C22×C11—22no—
256C22×C11—42no—
257C22×C11—41no—
258C22×C11—41no—
259C22×C11—44no—
260C22×C11—44no—
261C22×C11—44no—
262C22×C11—82no—
263C22×C11—82no—
264C22×C11—82no—
265C22×C11—82no—
266C22×C11C2×C4×D411yescharacteristic
267C22×C11C2×#12111yescharacteristic
268C22×C11#53211yescharacteristic
269C22×C11#57612yes—
270C22×C11#57712yes—
271C4×C11—22no—
272C4×C11—44no—
273C4×C11C2×C4×D411yescharacteristic
274C4×C11C4×#4111yescharacteristic
275C4×C11#52511yescharacteristic
276C4×C11#52911yescharacteristic
277Dic11—22no—
278Dic11—22no—
279Dic11—41no—
280Dic11—41no—
281Dic11—82no—
282Dic11—82no—
283C22×D4—22no—
284C22×D4C22×D1112yes—
285C23×C4—222no—
286C23×C4C22×D1111yescharacteristic
287C2×D8—22no—
288C2×D8—22no—
289C2×D8C2×Dic1114yes—
290C2×M16—22no—
291C2×M16—22no—
292C2×M16C2×Dic1114yescomplemented
293C22×C8—111no—
294C22×C8—111no—
295C22×C8—222no—
296C22×C8—222no—
297C22×C8—222no—
298C22×C8C22×D1111yescharacteristic
299C22×C8C22×D1111yescharacteristic
300#121—24no—
301#121C2×Dic1118yescomplemented
302C4×D4—224no—
303C4×D4—224no—
304#117—222no—
305#117—222no—
306C2×C4⋊C4—111no—
307C2×C4⋊C4—111no—
308C2×C4⋊C4—112no—
309C2×C4⋊C4—112no—
310C2×C4⋊C4—222no—
311C2×C4⋊C4C22×D1112yes—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—111no—
314C2×C22⋊C4—111no—
315C2×C22⋊C4—222no—
316C2×C22⋊C4—222no—
317C2×C22⋊C4—222no—
318C2×C22⋊C4—222no—
319C2×C42—111no—
320C2×C42—111no—
321C2×C42—222no—
322#107—222no—
323#106—222no—
324#106C2×Dic1114yescomplemented
325#102—224no—
326#102—224no—
327#102C2×Dic1118yescomplemented
328#97—222no—
329#97—222no—
330C4×C8—114no—
331C4×C8—222no—
332#95—222no—
333#95—222no—
334#95—222no—
335C2×C11—42no—
336C2×C11—84no—
337C2×C11C4×#12111yescharacteristic
338C2×C11#294612yes—
339C2×C11#305811yescharacteristic
340C2×C11#306011yescharacteristic
341C2×C11#317912yes—
342C24—22no—
343C24D4×D1111yescharacteristic
344C2×D4—28no—
345C2×D4—22no—
346C2×D4—22no—
347C2×D4—22no—
348C2×D4—22no—
349C2×D4—22no—
350C2×D4—82no—
351C2×D4—82no—
352C2×D4C22×Dic1114yes—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—22no—
358C22×C4—111no—
359C22×C4—111no—
360C22×C4—111no—
361C22×C4—111no—
362C22×C4—222no—
363C22×C4—222no—
364C22×C4—444no—
365C22×C4—882no—
366C22×C4—882no—
367C22×C4D4×D1111yescharacteristic
368C22×C4#434112yes—
369C22×C4C22×Dic1112yes—
370C22×C4C23×D1111yescharacteristic
371D8—28no—
372M16—28no—
373C2×C8—21no—
374C2×C8—21no—
375C2×C8—112no—
376C2×C8—112no—
377C2×C8—228no—
378C2×C8—221no—
379C2×C8—221no—
380C2×C8—221no—
381C2×C8—221no—
382C2×C8D4×D1112yes—
383C2×C8#434112yes—
384C2×C8C22×Dic1112yes—
385C2×C8C22×Dic1112yes—
386C4⋊C4—22no—
387C4⋊C4—222no—
388C4⋊C4—222no—
389C4⋊C4—222no—
390C4⋊C4—222no—
391C4⋊C4—222no—
392C4⋊C4—222no—
393C4⋊C4—882no—
394C4⋊C4C22×Dic1114yes—
395C22⋊C4—28no—
396C22⋊C4—222no—
397C22⋊C4—222no—
398C22⋊C4—444no—
399C22⋊C4—882no—
400C22⋊C4—882no—
401C22⋊C4—882no—
402C42—112no—
403C42—112no—
404C42—221no—
405C42—221no—
406C42—882no—
407C11#2153611yescharacteristic, complemented, Sylow
408C23—22no—
409C23—22no—
410C23—21no—
411C23—21no—
412C23—24no—
413C23—42no—
414C23—42no—
415C23—42no—
416C23—42no—
417C23—42no—
418C23—42no—
419C23D4×Dic1112yes—
420C23C2×D4×D1111yescharacteristic
421D4—24no—
422D4—24no—
423D4—42no—
424D4—42no—
425D4—88no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—24no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—112no—
436C2×C4—112no—
437C2×C4—222no—
438C2×C4—222no—
439C2×C4—222no—
440C2×C4—222no—
441C2×C4—221no—
442C2×C4—221no—
443C2×C4—442no—
444C2×C4—442no—
445C2×C4—442no—
446C2×C4—442no—
447C2×C4—442no—
448C2×C4—442no—
449C2×C4—888no—
450C2×C4D4×Dic1112yes—
451C2×C4C2×D4×D1111yescharacteristic
452C2×C4C2×#434111yescharacteristic
453C2×C4C2×#434111yescharacteristic
454C2×C4#41×D1111yescharacteristic
455C2×C4#41×D1111yescharacteristic
456C2×C4C23×Dic1111yescharacteristic
457C8—22no—
458C8—222no—
459C8—222no—
460C8D4×Dic1114yes—
461C22—22no—
462C22—24no—
463C22—41no—
464C22—42no—
465C22—41no—
466C22—44no—
467C22—44no—
468C22—44no—
469C22—82no—
470C22—82no—
471C22—82no—
472C22—82no—
473C22#1062312711yescharacteristic
474C22D11×#12111yescharacteristic
475C22#1062330512yes—
476C22#1062330612yes—
477C22C2×D4×Dic1111yescharacteristic
478C4—22no—
479C4—44no—
480C4—222no—
481C4—222no—
482C4—441no—
483C4—441no—
484C4—882no—
485C4—882no—
486C4#1062313111yescharacteristic
487C4#1062313711yescharacteristic
488C4C2×D4×Dic1111yescharacteristic
489C4#41×Dic1111yescharacteristic
490C2—42no—
491C2—84no—
492C2#121×Dic1111yescharacteristic
493C2#1307744912yes—
494C2#1307826211yescharacteristic
495C2#1307827611yescharacteristic
496C2#1307930012yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#469C2
socleC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenterC2×#469D11
hypocenterC11#21536
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#469

Complements

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

NH ≅ G/Ntype
1. C2×D8×Dic11C2semidirect
2. C2×#10622735C2semidirect
3. #13071311C2semidirect
4. #13069493C2semidirect
5. #13069360C2semidirect
6. #13069301C2semidirect
7. #13069045C2semidirect
8. #13068649C2semidirect
9. #106×Dic11C2semidirect
10. #13068443C2semidirect
18. C11×#469C4semidirect
51. C2×C11×M16C2×C4semidirect
55. C11×#121C2×C4semidirect
81. C11×#106C2×C4semidirect
82. C11×#102C2×C4semidirect
93. C8×Dic11D4semidirect
230. #469Dic11semidirect
292. C2×M16C2×Dic11semidirect
301. #121C2×Dic11semidirect
324. #106C2×Dic11semidirect
327. #102C2×Dic11semidirect
407. C11#21536semidirect

Maximal subgroups

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

subgroupindex
C2×D8×Dic112
C2×#106227352
#130713112
#130694932
#130693602
#130693012
#130690452
#130686492
#106×Dic112
#130684432
C2×C11×#4692
#2153611