Finite Group Databasebeta

← #14770233

Subgroups — #14770233

Order 2816.

1246 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
1C2×#10622625C211yesmaximal, characteristic, complemented
2D4×C4⋊Dic11C211yesmaximal, characteristic, complemented
3#13069578C211yesmaximal, characteristic, complemented
4#13069565C211yesmaximal, characteristic, complemented
5#13069055C212yesmaximal, complemented
6#13068934C212yesmaximal, complemented
7#13068711C212yesmaximal, complemented
8#13068616C211yesmaximal, characteristic, complemented
9C4×#66896C211yesmaximal, characteristic, complemented
10#13068337C212yesmaximal, complemented
11C2×C11×#555C211yesmaximal, characteristic
12C11×#555—24no—
13C11×#555C418yescomplemented
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#124—22no—
16C2×C11×#121—21no—
17C2×C11×#121C2212yes—
18C2×C4×D4×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×C11×#117—21no—
21C2×C11×#117C2212yes—
22C2×D4×Dic11—21no—
23C22×C4⋊Dic11C2212yes—
24C22×#4318C2212yes—
25C2×#66896C2211yescharacteristic
26C2×#66896C2211yescharacteristic
27C2×#66896C2212yes—
28#10622825C2212yes—
29C2×C22⋊(C11⋊C8)C2212yes—
30#10622625—24no—
31#10622598—21no—
32#10622563—22no—
33#10622548C2211yescharacteristic
34C4×C4⋊Dic11C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622167C2212yes—
38#10622167C2212yes—
39#10622167C2211yescharacteristic
40#10622167C2212yes—
41#10622167C2212yes—
42#10622167C2211yescharacteristic
43#10622167C2212yes—
44C22×Q8×C11—21no—
45C22×D4×C11—22no—
46C22×D4×C11D411yescharacteristic
47C22×D4×C11C2311yescharacteristic
48C23×C4×C11—21no—
49C23×C4×C11C2312yes—
50C23×Dic11—22no—
51C11×C4⋊Q8—22no—
52C11×C4⋊Q8C2×C414yescomplemented
53C11×#124—216no—
54C11×#121—28no—
55C11×#121—24no—
56C11×#121C2×C418yescomplemented
57C4×D4×C11—22no—
58C4×D4×C11C2×C414yes—
59C4×D4×C11C2×C414yescomplemented
60C4×D4×C11D414yes—
61C11×#117—24no—
62C11×#117—28no—
63C11×#117C2×C418yescomplemented
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4D411yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4D412yes—
72C2×C42×C11—22no—
73C2×C42×C11C2311yescharacteristic
74C2×C22⋊Dic11—22no—
75D4×Dic11—44no—
76C2×C4⋊Dic11—24no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—22no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11—42no—
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2312yes—
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4×Dic11—21no—
85C2×#4318—24no—
86C2×#4318—24no—
87C2×#4318—42no—
88C22×C11⋊C8C2311yescharacteristic
89C22×C11⋊C8C2312yes—
90C22×C11⋊C8C2311yescharacteristic
91#66896—22no—
92#66896—22no—
93#66896—42no—
94C11⋊#95—21no—
95C11⋊#95—22no—
96C22⋊(C11⋊C8)—24no—
97C4⋊(C11⋊C8)—22no—
98C4×C11⋊C8—22no—
99#22503—111nomaximal, Sylow
100C24×C11—21no—
101C24×C11C2×D412yes—
102C2×Q8×C11—24no—
103C2×Q8×C11—81no—
104C2×Q8×C11—81no—
105C2×D4×C11—28no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—21no—
109C2×D4×C11—21no—
110C2×D4×C11—21no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—82no—
114C2×D4×C11—82no—
115C2×D4×C11C22⋊C414yes—
116C2×D4×C11C22×C412yes—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—21no—
122C22×C4×C11—22no—
123C22×C4×C11—24no—
124C22×C4×C11—42no—
125C22×C4×C11—42no—
126C22×C4×C11C22×C414yes—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D414yes—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2411yescharacteristic
132C22×Dic11—21no—
133C22×Dic11—21no—
134C22×Dic11—22no—
135C22×Dic11—44no—
136C22×Dic11—44no—
137C22×Dic11—82no—
138C11×C4⋊C4—24no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4C22⋊C414yes—
142C11×C4⋊C4C22×C412yes—
143C11×C4⋊C4C22×C414yes—
144C11×C22⋊C4—28no—
145C11×C22⋊C4—28no—
146C11×C22⋊C4—24no—
147C11×C22⋊C4C22⋊C418yes—
148C42×C11—28no—
149C42×C11C22×C412yes—
150C42×C11C2×D412yes—
151C22⋊Dic11—44no—
152C4⋊Dic11—21no—
153C4⋊Dic11—22no—
154C4⋊Dic11—21no—
155C4⋊Dic11—22no—
156C4⋊Dic11—21no—
157C4⋊Dic11—44no—
158C4⋊Dic11—42no—
159C4⋊Dic11—81no—
160C4⋊Dic11#4112yes—
161C4×Dic11—42no—
162#4318—48no—
163C2×C11⋊C8—21no—
164C2×C11⋊C8—21no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—21no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—21no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—21no—
171C2×C11⋊C8#4112yes—
172C2×#555D1111yescharacteristic
173C2×#436—111no—
174D4×C4⋊C4—111no—
175#1990—111no—
176#1987—111no—
177#1895—112no—
178#1874—112no—
179#1825—112no—
180#1802—111no—
181C4×#102—111no—
182#1736—112no—
183C23×C11—22no—
184C23×C11—22no—
185C23×C11—22no—
186C23×C11—22no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—41no—
191C23×C11—41no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11C2×C22⋊C414yes—
197C23×C11C22×D411yescharacteristic
198Q8×C11—84no—
199D4×C11—22no—
200D4×C11—22no—
201D4×C11—28no—
202D4×C11—41no—
203D4×C11—41no—
204D4×C11—88no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11—24no—
213C2×C4×C11—22no—
214C2×C4×C11—24no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—48no—
220C2×C4×C11C2×C22⋊C414yes—
221C2×C4×C11C2×C22⋊C412yes—
222C2×C4×C11C2×C22⋊C412yes—
223C2×C4×C11AGL(1,ℤ/8)12yes—
224C2×C4×C11#13712yes—
225C2×C4×C11C23×C411yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C2×#4111yescharacteristic
228C2×C4×C11C2×#4111yescharacteristic
229C2×C4×C11H(5,𝔽2)11yescharacteristic
230C2×C4×C112−1+411yescharacteristic
231C2×Dic11—22no—
232C2×Dic11—41no—
233C2×Dic11—41no—
234C2×Dic11—42no—
235C2×Dic11—41no—
236C2×Dic11—41no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11—41no—
240C2×Dic11—88no—
241C11⋊C8—22no—
242C11⋊C8—42no—
243C11⋊C8—41no—
244C22×M16—112no—
245#555—24no—
246#555Dic1118yescomplemented
247C2×C4⋊Q8C2×D1111yescharacteristic
248C2×#124—22no—
249C2×#121—21no—
250C2×#121C2×D1112yes—
251C2×C4×D4—221no—
252C2×C4×D4C2×D1111yescharacteristic
253C2×C4×D4C2×D1111yescharacteristic
254C2×#117—21no—
255C2×#117C2×D1112yes—
256C22×C4⋊C4—112no—
257#436—224no—
258C2×C4⋊C8—111no—
259C2×#102—111no—
260C2×#102—111no—
261C2×#102—112no—
262C2×C22⋊C8—112no—
263C2×C4×C8—111no—
264#389—221no—
265#385—222no—
266#384—111no—
267#380—112no—
268C4×C4⋊C4—111no—
269#340—112no—
270#340—111no—
271#340—112no—
272#340—112no—
273#340—112no—
274#340—112no—
275#340—111no—
276C22×C11—24no—
277C22×C11—24no—
278C22×C11—24no—
279C22×C11—42no—
280C22×C11—42no—
281C22×C11—42no—
282C22×C11—42no—
283C22×C11—42no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11—81no—
287C22×C11—81no—
288C22×C11—81no—
289C22×C11—81no—
290C22×C11C22×C22⋊C411yescharacteristic
291C22×C11#54611yescharacteristic
292C22×C11#54711yescharacteristic
293C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
294C22×C11C2×#13711yescharacteristic
295C22×C11#57611yescharacteristic
296C22×C11#57711yescharacteristic
297C4×C11—24no—
298C4×C11—22no—
299C4×C11—42no—
300C4×C11—44no—
301C4×C11#41714yes—
302C4×C11C4×#4111yescharacteristic
303C4×C11#52011yescharacteristic
304C4×C11#54611yescharacteristic
305C4×C11#54711yescharacteristic
306Dic11—42no—
307Dic11—81no—
308Dic11—82no—
309C22×Q8—21no—
310C22×D4—22no—
311C22×D4C22⋊D1111yescharacteristic
312C22×D4C22×D1111yescharacteristic
313C23×C4—21no—
314C23×C4—222no—
315C23×C4C22×D1112yes—
316C2×M16—224no—
317C2×M16—224no—
318C2×M16—442no—
319C22×C8—111no—
320C22×C8—112no—
321C22×C8—111no—
322C4⋊Q8—22no—
323C4⋊Q8C2×Dic1114yescomplemented
324#124—216no—
325#121—28no—
326#121—24no—
327#121C2×Dic1118yescomplemented
328C4×D4—22no—
329C4×D4—444no—
330C4×D4C2×Dic1114yes—
331C4×D4C2×Dic1114yescomplemented
332C4×D4C22⋊D1114yes—
333#117—24no—
334#117—28no—
335#117C2×Dic1118yescomplemented
336C2×C4⋊C4—21no—
337C2×C4⋊C4—111no—
338C2×C4⋊C4—112no—
339C2×C4⋊C4—111no—
340C2×C4⋊C4—224no—
341C2×C4⋊C4—222no—
342C2×C4⋊C4—221no—
343C2×C4⋊C4—221no—
344C2×C4⋊C4—442no—
345C2×C4⋊C4C22⋊D1111yescharacteristic
346C2×C4⋊C4C22×D1111yescharacteristic
347C2×C4⋊C4C22×D1112yes—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—222no—
352C2×C22⋊C4C22⋊D1112yes—
353C2×C42—22no—
354C2×C42—221no—
355C2×C42C22×D1111yescharacteristic
356C4⋊C8—222no—
357#102—222no—
358#102—222no—
359#102—442no—
360C22⋊C8—224no—
361C4×C8—222no—
362#95—221no—
363#95—222no—
364C2×C11—44no—
365C2×C11—82no—
366C2×C11#233911yescharacteristic
367C2×C11C2×#41711yescharacteristic
368C2×C11#289711yescharacteristic
369C2×C11#332511yescharacteristic
370C2×C11#332911yescharacteristic
371C2×C11#335411yescharacteristic
372C2×C11#335711yescharacteristic
373C24—21no—
374C24C2×C22⋊D1112yes—
375C2×Q8—24no—
376C2×Q8—81no—
377C2×Q8—81no—
378C2×D4—28no—
379C2×D4—22no—
380C2×D4—22no—
381C2×D4—21no—
382C2×D4—21no—
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—82no—
387C2×D4—82no—
388C2×D4C22⋊Dic1114yes—
389C2×D4C22×Dic1112yes—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—24no—
397C22×C4—42no—
398C22×C4—42no—
399C22×C4—221no—
400C22×C4—221no—
401C22×C4—222no—
402C22×C4—444no—
403C22×C4—444no—
404C22×C4—882no—
405C22×C4C22×Dic1114yes—
406C22×C4C2×C22⋊D1112yes—
407C22×C4C2×C22⋊D1111yescharacteristic
408C22×C4C2×C22⋊D1114yes—
409C22×C4C2×C22⋊D1111yescharacteristic
410C22×C4C23×D1111yescharacteristic
411M16—448no—
412C2×C8—112no—
413C2×C8—221no—
414C2×C8—221no—
415C2×C8—221no—
416C2×C8—222no—
417C2×C8—222no—
418C2×C8—221no—
419C2×C8—221no—
420C2×C8—222no—
421C4⋊C4—24no—
422C4⋊C4—21no—
423C4⋊C4—22no—
424C4⋊C4—112no—
425C4⋊C4—221no—
426C4⋊C4—221no—
427C4⋊C4—222no—
428C4⋊C4—222no—
429C4⋊C4—221no—
430C4⋊C4—444no—
431C4⋊C4—442no—
432C4⋊C4—881no—
433C4⋊C4C22⋊Dic1114yes—
434C4⋊C4C22×Dic1112yes—
435C4⋊C4C22×Dic1114yes—
436C22⋊C4—28no—
437C22⋊C4—28no—
438C22⋊C4—24no—
439C22⋊C4—444no—
440C22⋊C4C22⋊Dic1118yes—
441C42—28no—
442C42—442no—
443C42C22×Dic1112yes—
444C42C2×C22⋊D1112yes—
445C11#2250311yescharacteristic, complemented, Sylow
446C23—22no—
447C23—22no—
448C23—22no—
449C23—22no—
450C23—22no—
451C23—22no—
452C23—22no—
453C23—41no—
454C23—41no—
455C23—41no—
456C23—41no—
457C23—41no—
458C23—41no—
459C23C2×C22⋊Dic1114yes—
460C23C22×C22⋊D1111yescharacteristic
461Q8—84no—
462D4—28no—
463D4—22no—
464D4—22no—
465D4—41no—
466D4—41no—
467D4—88no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—22no—
477C2×C4—24no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—48no—
483C2×C4—222no—
484C2×C4—441no—
485C2×C4—441no—
486C2×C4—441no—
487C2×C4—442no—
488C2×C4—441no—
489C2×C4—442no—
490C2×C4—442no—
491C2×C4—441no—
492C2×C4—888no—
493C2×C4#6700212yes—
494C2×C4#6700412yes—
495C2×C4C2×C22⋊Dic1114yes—
496C2×C4C2×C22⋊Dic1112yes—
497C2×C4C2×C22⋊Dic1112yes—
498C2×C4#41×D1111yescharacteristic
499C2×C4#41×D1111yescharacteristic
500C2×C4#6704211yescharacteristic
501C2×C4#6704311yescharacteristic
502C2×C4C23×Dic1111yescharacteristic
503C2×C4C22×C22⋊D1111yescharacteristic
504C8—222no—
505C8—441no—
506C8—442no—
507C22—24no—
508C22—24no—
509C22—24no—
510C22—42no—
511C22—42no—
512C22—42no—
513C22—42no—
514C22—42no—
515C22—42no—
516C22—42no—
517C22—81no—
518C22—81no—
519C22—81no—
520C22—81no—
521C22C2×#6700211yescharacteristic
522C22C2×#6700411yescharacteristic
523C22#1062335511yescharacteristic
524C22#1062336011yescharacteristic
525C22#1062336611yescharacteristic
526C22#1062336711yescharacteristic
527C22C22×C22⋊Dic1111yescharacteristic
528C4—24no—
529C4—22no—
530C4—42no—
531C4—44no—
532C4—442no—
533C4—882no—
534C4—881no—
535C4#1062284514yes—
536C4#1062335511yescharacteristic
537C4#41×Dic1111yescharacteristic
538C4#1062335811yescharacteristic
539C4#1062336011yescharacteristic
540C2—44no—
541C2—82no—
542C2#1307144611yescharacteristic
543C2C2×#1062284511yescharacteristic
544C2#1307714211yescharacteristic
545C2#1308085211yescharacteristic
546C2#1308090411yescharacteristic
547C2#1308120511yescharacteristic
548C2#1308123611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#555C2
socleC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenterC2×#555D11
hypocenterC11#22503
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#555

Complements

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

NH ≅ G/Ntype
1. C2×#10622625C2semidirect
2. D4×C4⋊Dic11C2semidirect
3. #13069578C2semidirect
4. #13069565C2semidirect
5. #13069055C2semidirect
6. #13068934C2semidirect
7. #13068711C2semidirect
8. #13068616C2semidirect
9. C4×#66896C2semidirect
10. #13068337C2semidirect
13. C11×#555C4semidirect
52. C11×C4⋊Q8C2×C4semidirect
56. C11×#121C2×C4semidirect
59. C4×D4×C11C2×C4semidirect
63. C11×#117C2×C4semidirect
246. #555Dic11semidirect
323. C4⋊Q8C2×Dic11semidirect
327. #121C2×Dic11semidirect
331. C4×D4C2×Dic11semidirect
335. #117C2×Dic11semidirect
445. C11#22503semidirect

Maximal subgroups

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

subgroupindex
C2×#106226252
D4×C4⋊Dic112
#130695782
#130695652
#130690552
#130689342
#130687112
#130686162
C4×#668962
#130683372
C2×C11×#5552
#2250311