Finite Group Databasebeta

← #14763735

Subgroups — #14763735

Order 2816.

1118 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623211C211yesmaximal, characteristic
2C2×#10622450C211yesmaximal, characteristic, complemented
3#13071012C211yesmaximal, characteristic, complemented
4#13069573C211yesmaximal, characteristic, complemented
5#13069571C211yesmaximal, characteristic, complemented
6#13069549C211yesmaximal, characteristic, complemented
7#13069051C212yesmaximal
8#13069046C212yesmaximal, complemented
9#13068629C212yesmaximal, complemented
10#13068624C212yesmaximal, complemented
11C11×#1983C211yesmaximal, characteristic, complemented
12C2×C11×#124C2211yescharacteristic
13C2×#66999C2211yescharacteristic
14C2×Q8×Dic11C2211yescharacteristic
15C2×#66991C2211yescharacteristic
16C2×D4×Dic11C2211yescharacteristic
17C22×#4313C2212yes—
18#10623211—24no—
19#10623211C418yescomplemented
20C2×#66936—21no—
21C2×(C22⋊D11)⋊C4—21no—
22C2×#66932—21no—
23C2×#66930—21no—
24C2×C42×D11C2211yescharacteristic
25C2×#66923C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×#103C2212yes—
28C2×C11×#102C2212yes—
29C4×C11×C4⋊C4C2211yescharacteristic
30C2×#66899C2212yes—
31C2×#66896C2212yes—
32C2×Dic11⋊C8C2212yes—
33#10622600C2212yes—
34#10622590C2212yes—
35C4×(C2×D11)⋊C4—21no—
36C4×C4⋊Dic11C2211yescharacteristic
37#10622545—21no—
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39#10622450—24no—
40#10622277—21no—
41#10622264—21no—
42#10622189C2212yes—
43#10622189C2212yes—
44#10622167C2212yes—
45#10622167C2212yes—
46C22×Q8×C11C2311yescharacteristic
47C22×D4×C11C2311yescharacteristic
48C22×C22⋊D11—21no—
49C23×Dic11—21no—
50C22×C4×D11D411yescharacteristic
51C22×C4×D11D411yescharacteristic
52C22×C4×D11C2311yescharacteristic
53C22×C8×C11C2312yes—
54C11×#124—22no—
55C11×#124C2×C414yes—
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C22⋊C4—21no—
58C2×C11×C22⋊C4—21no—
59C2×C42×C11—21no—
60C2×C42×C11C2311yescharacteristic
61C2×C22⋊Dic11—21no—
62C2×C22⋊Dic11—21no—
63#66999—22no—
64#66999C2×C414yes—
65Q8×Dic11—22no—
66Q8×Dic11C2×C414yes—
67#66991—22no—
68#66991C2×C414yes—
69D4×Dic11—22no—
70D4×Dic11C2×C414yes—
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—22no—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11C2312yes—
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2311yescharacteristic
77C2×Dic11⋊C4—21no—
78C2×Dic11⋊C4—21no—
79C2×Dic11⋊C4—21no—
80C2×C4×Dic11—21no—
81C2×C4×Dic11—21no—
82C2×C4×Dic11D411yescharacteristic
83C2×C4×Dic11D411yescharacteristic
84C2×C4×Dic11C2311yescharacteristic
85C22×C11⋊C8C2312yes—
86C2×#4313—24no—
87C2×#4313—42no—
88C2×#4313—42no—
89#66936—28no—
90(C22⋊D11)⋊C4—28no—
91#66932—28no—
92#66930—28no—
93C42×D11C2×C414yes—
94C42×D11D414yes—
95#66923—22no—
96#66923C2×C414yes—
97C11×C4⋊C8—22no—
98C11×#103—42no—
99C11×#102—42no—
100C11×#95—21no—
101#66899—42no—
102#66896—42no—
103C11⋊#95—21no—
104C11⋊#95—22no—
105C11⋊#95—22no—
106C11⋊#95—22no—
107Dic11⋊C8—24no—
108C4⋊(C11⋊C8)—22no—
109#21895—111nomaximal, Sylow
110C24×C11—21no—
111C23×D11C2×D411yescharacteristic
112C2×Q8×C11—21no—
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11C22×C412yes—
116C2×D4×C11—21no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11C22×C412yes—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2411yescharacteristic
125C2×C22⋊D11—24no—
126C2×C22⋊D11—42no—
127C2×C22⋊D11—42no—
128C22×Dic11—24no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—22no—
132C22×Dic11—44no—
133C22×Dic11C2×D411yescharacteristic
134C22×Dic11C2×D411yescharacteristic
135C22×Dic11C2×D411yescharacteristic
136C2×C4×D11—22no—
137C2×C4×D11—22no—
138C2×C4×D11—41no—
139C2×C4×D11—41no—
140C2×C4×D11—42no—
141C2×C4×D11C22⋊C414yes—
142C2×C4×D11C22⋊C414yes—
143C2×C4×D11C22×C412yes—
144C2×C4×D11C2×D412yes—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C2×C8×C11—22no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—22no—
150C11×C22⋊C4—24no—
151C11×C22⋊C4—24no—
152C42×C11—42no—
153C42×C11C22×C412yes—
154C42×C11C2×D412yes—
155C22⋊Dic11—24no—
156C22⋊Dic11—24no—
157(C2×D11)⋊C4—24no—
158(C2×D11)⋊C4—44no—
159C4⋊Dic11—24no—
160C4⋊Dic11—21no—
161C4⋊Dic11—21no—
162C4⋊Dic11—22no—
163C4⋊Dic11—22no—
164C4⋊Dic11C22×C412yes—
165C4⋊Dic11C22×C412yes—
166Dic11⋊C4—24no—
167Dic11⋊C4—24no—
168Dic11⋊C4—24no—
169C4×Dic11—24no—
170C4×Dic11—42no—
171C4×Dic11C22⋊C414yes—
172C4×Dic11C22⋊C414yes—
173C4×Dic11C22×C412yes—
174C4×Dic11C2×D412yes—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—22no—
178#4313—48no—
179C2×#529—111no—
180C2×#423—111no—
181#2283—111no—
182#1989—111no—
183#1989—111no—
184#1983—111no—
185#1983D1111yescharacteristic, complemented
186#1895—112no—
187#1894—112no—
188#1805—112no—
189#1804—112no—
190C23×C11—22no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11C22×D411yescharacteristic
196C22×D11—22no—
197C22×D11—22no—
198C22×D11—21no—
199C22×D11—21no—
200C22×D11C2×C22⋊C412yes—
201Q8×C11—24no—
202Q8×C11—41no—
203Q8×C11—41no—
204D4×C11—24no—
205D4×C11—41no—
206D4×C11—41no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11C2×C22⋊C412yes—
216C2×C4×C11C2×C22⋊C412yes—
217C2×C4×C11C23×C411yescharacteristic
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11H(5,𝔽2)12yes—
220C2×C4×C112−1+412yes—
221C22⋊D11—48no—
222C2×Dic11—22no—
223C2×Dic11—22no—
224C2×Dic11—21no—
225C2×Dic11—21no—
226C2×Dic11—22no—
227C2×Dic11—22no—
228C2×Dic11—48no—
229C2×Dic11—42no—
230C2×Dic11—41no—
231C2×Dic11—41no—
232C2×Dic11—42no—
233C2×Dic11—42no—
234C2×Dic11—42no—
235C2×Dic11C2×C22⋊C412yes—
236C2×Dic11C2×C22⋊C412yes—
237C2×Dic11C2×C22⋊C412yes—
238C4×D11—24no—
239C4×D11—22no—
240C4×D11—22no—
241C4×D11—44no—
242C4×D11—44no—
243C8×C11—42no—
244C11⋊C8—42no—
245C22×M16—112no—
246#529—118no—
247#529—224no—
248C2×#126—221no—
249C2×#125—111no—
250C2×#124C2×D1111yescharacteristic
251C2×#123—221no—
252C2×C22⋊Q8—111no—
253C2×#121—111no—
254C2×C4×Q8—111no—
255C2×C4×D4—111no—
256C2×C4×D4—221no—
257C2×#117—221no—
258C22×C42—111no—
259#423—224no—
260C2×C4⋊C8—112no—
261C2×C4⋊C8—111no—
262C2×C4⋊C8C2×D1111yescharacteristic
263C2×#103—112no—
264C2×#103C2×D1112yes—
265C2×#102—112no—
266C2×#102C2×D1112yes—
267#383—221no—
268#382—112no—
269#381—221no—
270#380—112no—
271C4×C4⋊C4—111no—
272C4×C4⋊C4C2×D1111yescharacteristic
273C4×C22⋊C4—221no—
274#376—221no—
275#340—112no—
276#340—112no—
277#340—112no—
278#340—112no—
279C22×C11—42no—
280C22×C11—42no—
281C22×C11—42no—
282C22×C11—82no—
283C22×C11—82no—
284C22×C11C22×C22⋊C411yescharacteristic
285C22×C11#53712yes—
286C22×C11#57512yes—
287C22×C11#57511yescharacteristic
288C22×C11#57511yescharacteristic
289C2×D11—22no—
290C2×D11—22no—
291C2×D11—22no—
292C2×D11—42no—
293C2×D11—42no—
294C4×C11—22no—
295C4×C11—22no—
296C4×C11—42no—
297C4×C11—82no—
298C4×C11#52012yes—
299C4×C11#53511yescharacteristic
300C4×C11#53611yescharacteristic
301Dic11—22no—
302Dic11—22no—
303Dic11—22no—
304Dic11—42no—
305Dic11—42no—
306Dic11—82no—
307C22×Q8C22×D1111yescharacteristic
308C22×D4—221no—
309C22×D4C22×D1111yescharacteristic
310C23×C4—111no—
311C23×C4—111no—
312C23×C4—111no—
313C23×C4—221no—
314C2×M16—224no—
315C2×M16—442no—
316C2×M16—442no—
317C22×C8—112no—
318C22×C8C22×D1112yes—
319#126—228no—
320#125—114no—
321#125—222no—
322#124—22no—
323#124C4×D1114yes—
324#123—228no—
325C22⋊Q8—114no—
326C22⋊Q8—222no—
327#121—114no—
328#121—222no—
329C4×Q8—114no—
330C4×Q8—222no—
331C4×D4—114no—
332C4×D4—222no—
333C4×D4—228no—
334#117—228no—
335C2×C4⋊C4—111no—
336C2×C4⋊C4—111no—
337C2×C4⋊C4—112no—
338C2×C4⋊C4—221no—
339C2×C4⋊C4—221no—
340C2×C4⋊C4—221no—
341C2×C4⋊C4—221no—
342C2×C4⋊C4C22×D1112yes—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—221no—
346C2×C22⋊C4—221no—
347C2×C22⋊C4—221no—
348C2×C22⋊C4—222no—
349C2×C42—21no—
350C2×C42—111no—
351C2×C42—111no—
352C2×C42—111no—
353C2×C42—114no—
354C2×C42—114no—
355C2×C42—221no—
356C2×C42—221no—
357C2×C42C22×D1111yescharacteristic
358C4⋊C8—22no—
359C4⋊C8—224no—
360C4⋊C8—222no—
361#103—42no—
362#103—442no—
363#102—42no—
364#102—442no—
365#95—21no—
366#95—222no—
367#95—222no—
368#95—222no—
369#95—221no—
370C2×C11—82no—
371C2×C11#231111yescharacteristic
372C2×C11#289611yescharacteristic
373C2×C11#289611yescharacteristic
374C2×C11#325612yes—
375C2×C11#325612yes—
376D11—42no—
377C24—21no—
378C24—111no—
379C2×Q8—21no—
380C2×Q8—22no—
381C2×Q8—22no—
382C2×Q8C2×C4×D1112yes—
383C2×D4—21no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—224no—
387C2×D4—442no—
388C2×D4—442no—
389C2×D4C2×C4×D1112yes—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—111no—
393C22×C4—111no—
394C22×C4—111no—
395C22×C4—112no—
396C22×C4—112no—
397C22×C4—114no—
398C22×C4—114no—
399C22×C4—224no—
400C22×C4—222no—
401C22×C4—222no—
402C22×C4—221no—
403C22×C4—221no—
404C22×C4—222no—
405C22×C4—442no—
406C22×C4—441no—
407C22×C4—441no—
408C22×C4—444no—
409C22×C4D4×D1111yescharacteristic
410C22×C4D4×D1111yescharacteristic
411C22×C4C23×D1111yescharacteristic
412M16—448no—
413C2×C8—22no—
414C2×C8—22no—
415C2×C8—22no—
416C2×C8—222no—
417C2×C8—222no—
418C2×C8—222no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—112no—
422C4⋊C4—112no—
423C4⋊C4—224no—
424C4⋊C4—224no—
425C4⋊C4—224no—
426C4⋊C4—224no—
427C4⋊C4—221no—
428C4⋊C4—221no—
429C4⋊C4—222no—
430C4⋊C4—222no—
431C22⋊C4—24no—
432C22⋊C4—24no—
433C22⋊C4—224no—
434C22⋊C4—224no—
435C22⋊C4—224no—
436C22⋊C4—444no—
437C42—42no—
438C42—114no—
439C42—114no—
440C42—112no—
441C42—112no—
442C42—224no—
443C42—442no—
444C42C2×C4×D1112yes—
445C42D4×D1112yes—
446C11#2189511yescharacteristic, complemented, Sylow
447C23—22no—
448C23—42no—
449C23—41no—
450C23—41no—
451C23—42no—
452C23—112no—
453C23—222no—
454C23—221no—
455C23—221no—
456C23—222no—
457C23C2×D4×D1111yescharacteristic
458Q8—24no—
459Q8—41no—
460Q8—41no—
461D4—24no—
462D4—41no—
463D4—41no—
464D4—448no—
465C2×C4—22no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—22no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—112no—
474C2×C4—112no—
475C2×C4—112no—
476C2×C4—222no—
477C2×C4—221no—
478C2×C4—221no—
479C2×C4—222no—
480C2×C4—222no—
481C2×C4—224no—
482C2×C4—222no—
483C2×C4—222no—
484C2×C4—222no—
485C2×C4—444no—
486C2×C4—444no—
487C2×C4—448no—
488C2×C4—442no—
489C2×C4—441no—
490C2×C4—441no—
491C2×C4—442no—
492C2×C4—442no—
493C2×C4—442no—
494C2×C4C22⋊C4×D1112yes—
495C2×C4C22⋊C4×D1112yes—
496C2×C4C22×C4×D1111yescharacteristic
497C2×C4C2×D4×D1111yescharacteristic
498C2×C4#6703712yes—
499C2×C4#6704312yes—
500C8—42no—
501C8—442no—
502C22—42no—
503C22—42no—
504C22—42no—
505C22—82no—
506C22—82no—
507C22—222no—
508C22—222no—
509C22—222no—
510C22—442no—
511C22—442no—
512C22C2×C22⋊C4×D1111yescharacteristic
513C22#1062313912yes—
514C22#1062329912yes—
515C22#1062330411yescharacteristic
516C22#1062330811yescharacteristic
517C4—22no—
518C4—22no—
519C4—42no—
520C4—82no—
521C4—222no—
522C4—222no—
523C4—222no—
524C4—442no—
525C4—442no—
526C4—882no—
527C4#1062307712yes—
528C4#1062320611yescharacteristic
529C4#1062324611yescharacteristic
530C2—82no—
531C2—442no—
532C2#1307120611yescharacteristic
533C2#1307713111yescharacteristic
534C2#1307713211yescharacteristic
535C2#1308001412yes—
536C2#1308001512yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1983C2
socleC23×C11C22×D4
prime radicalC2×#66991C22
cosocleC22×C4×C11C24
hypercenter#1983D11
hypocenterC11#21895
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1983

Complements

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

NH ≅ G/Ntype
2. C2×#10622450C2semidirect
3. #13071012C2semidirect
4. #13069573C2semidirect
5. #13069571C2semidirect
6. #13069549C2semidirect
8. #13069046C2semidirect
9. #13068629C2semidirect
10. #13068624C2semidirect
11. C11×#1983C2semidirect
19. #10623211C4semidirect
185. #1983D11semidirect
446. C11#21895semidirect

Maximal subgroups

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

subgroupindex
C2×#106232112
C2×#106224502
#130710122
#130695732
#130695712
#130695492
#130690512
#130690462
#130686292
#130686242
C11×#19832
#2189511