Finite Group Databasebeta

← #14719804

Subgroups — #14719804

Order 2816.

984 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623095C211yesmaximal, characteristic
2#13077645C211yesmaximal, characteristic, complemented
3#13066983C212yesmaximal, complemented
4#13066979C212yesmaximal, complemented
5#13066971C212yesmaximal, complemented
6#13066962C212yesmaximal, complemented
7#13066932C212yesmaximal, complemented
8C2×#10622107C212yesmaximal, complemented
9C11×#2972C211yesmaximal, characteristic, complemented
10C2×C4×D4×C11C2211yescharacteristic
11C2×#66992C411yescharacteristic
12C2×#66988C411yescharacteristic
13C2×#66982C2211yescharacteristic
14C2×C4×C22⋊D11C2211yescharacteristic
15C2×#66977C2211yescharacteristic
16C22×Dic11⋊C4C2211yescharacteristic
17#10623095—24no—
18#10623095—24no—
19C2×#66949C411yescharacteristic
20C2×#66942C411yescharacteristic
21C2×#66939C411yescharacteristic
22C2×#66936C411yescharacteristic
23C2×#66932C411yescharacteristic
24C2×#66931C411yescharacteristic
25C2×#66929C2211yescharacteristic
26C2×#66923C2211yescharacteristic
27C8×D4×C11—24no—
28C11×#431C2212yes—
29C2×C11×C22⋊C8C2212yes—
30C2×C11×C22⋊C8C2212yes—
31#10622820C2212yes—
32C2×C22⋊(C11⋊C8)C2212yes—
33#10622624—24no—
34#10622539C2212yes—
35#10622107C2214yes—
36#10622107C2214yes—
37#10622107C2214yes—
38#10622106C2214yes—
39C22×D4×C11C2×C411yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C22×C22⋊D11C2×C411yescharacteristic
43C22×C22⋊D11C2×C411yescharacteristic
44C23×Dic11C2×C411yescharacteristic
45C23×Dic11C2×C411yescharacteristic
46C22×C4×D11C2×C411yescharacteristic
47C22×Dic22C2×C411yescharacteristic
48C22×C8×C11—22no—
49C22×C8×C11—22no—
50C4×D4×C11D414yes—
51C4×D4×C11D414yes—
52C2×C11×C4⋊C4C2×C411yescharacteristic
53C2×C11×C22⋊C4C2×C411yescharacteristic
54C2×C11×C22⋊C4C2×C411yescharacteristic
55C2×C42×C11C2311yescharacteristic
56C2×C22⋊Dic11C2×C411yescharacteristic
57C2×C22⋊Dic11C2×C411yescharacteristic
58C2×C22⋊Dic11C2×C411yescharacteristic
59C2×C22⋊Dic11C2×C411yescharacteristic
60#66992—24no—
61#66988—24no—
62#66982—22no—
63#66982—22no—
64C4×C22⋊D11—22no—
65C4×C22⋊D11—22no—
66C2×(C2×D11)⋊C4C2×C411yescharacteristic
67C2×(C2×D11)⋊C4C2×C411yescharacteristic
68C2×(C2×D11)⋊C4C2×C411yescharacteristic
69C2×(C2×D11)⋊C4C2311yescharacteristic
70C2×C4⋊Dic11C2×C411yescharacteristic
71C2×C4⋊Dic11C2×C411yescharacteristic
72C2×C4⋊Dic11C2×C411yescharacteristic
73#66977—22no—
74#66977—22no—
75C2×Dic11⋊C4—22no—
76C2×Dic11⋊C4—22no—
77C2×Dic11⋊C4C2×C411yescharacteristic
78C2×Dic11⋊C4C2×C411yescharacteristic
79C2×Dic11⋊C4C2×C411yescharacteristic
80C2×Dic11⋊C4C2×C411yescharacteristic
81C2×Dic11⋊C4C2×C411yescharacteristic
82C2×Dic11⋊C4C2×C411yescharacteristic
83C2×Dic11⋊C4C2×C411yescharacteristic
84C2×Dic11⋊C4C2311yescharacteristic
85C2×Dic11⋊C4C2311yescharacteristic
86C2×Dic11⋊C4C2311yescharacteristic
87C2×C4×Dic11C2×C411yescharacteristic
88C2×#4318—22no—
89C22×C11⋊C8—22no—
90#66949—24no—
91#66942—24no—
92#66939—24no—
93#66936—24no—
94#66932—24no—
95#66931—24no—
96#66929—22no—
97#66929—22no—
98#66923—22no—
99#66923—22no—
100C11×C4⋊C8—22no—
101C11×C22⋊C8—22no—
102C11×C22⋊C8—22no—
103C11×C22⋊C8C2314yes—
104C4×C8×C11—22no—
105C22⋊(C11⋊C8)—22no—
106C22⋊(C11⋊C8)—22no—
107C22⋊(C11⋊C8)C2314yes—
108C4⋊(C11⋊C8)—22no—
109#66867—22no—
110#17387—111nomaximal, Sylow
111C24×C11C22×C411yescharacteristic
112C24×C11C22×C411yescharacteristic
113C23×D11C22×C411yescharacteristic
114C2×D4×C11—24no—
115C2×D4×C11C22⋊C414yes—
116C22×C4×C11—81no—
117C22×C4×C11—81no—
118C22×C4×C11C22×C411yescharacteristic
119C22×C4×C11C22×C411yescharacteristic
120C22×C4×C11C22×C411yescharacteristic
121C22×C4×C11C22×C411yescharacteristic
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2411yescharacteristic
127C2×C22⋊D11—22no—
128C2×C22⋊D11—22no—
129C2×C22⋊D11—24no—
130C2×C22⋊D11—81no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—24no—
134C22×Dic11—81no—
135C22×Dic11C22×C411yescharacteristic
136C22×Dic11C22×C411yescharacteristic
137C22×Dic11C22×C411yescharacteristic
138C22×Dic11C22×C411yescharacteristic
139C22×Dic11C22×C411yescharacteristic
140C22×Dic11C22×C411yescharacteristic
141C22×Dic11C22×C411yescharacteristic
142C2×C4×D11—22no—
143C2×C4×D11—81no—
144C2×Dic22—22no—
145C2×Dic22—81no—
146C2×C8×C11—24no—
147C2×C8×C11—82no—
148C2×C8×C11—82no—
149C11×C4⋊C4C22⋊C414yes—
150C11×C22⋊C4C22⋊C414yes—
151C11×C22⋊C4C22⋊C414yes—
152C42×C11C2×D412yes—
153C42×C11C2×D412yes—
154C22⋊Dic11—22no—
155C22⋊Dic11—22no—
156C22⋊Dic11—22no—
157C22⋊Dic11—22no—
158(C2×D11)⋊C4—22no—
159(C2×D11)⋊C4—22no—
160(C2×D11)⋊C4—22no—
161(C2×D11)⋊C4—21no—
162(C2×D11)⋊C4—21no—
163C4⋊Dic11—22no—
164C4⋊Dic11—22no—
165C4⋊Dic11—22no—
166Dic11⋊C4—22no—
167Dic11⋊C4—22no—
168Dic11⋊C4—22no—
169Dic11⋊C4—22no—
170Dic11⋊C4—22no—
171Dic11⋊C4—22no—
172Dic11⋊C4—22no—
173Dic11⋊C4—21no—
174Dic11⋊C4—21no—
175Dic11⋊C4—21no—
176Dic11⋊C4—21no—
177Dic11⋊C4—21no—
178Dic11⋊C4—21no—
179C4×Dic11—22no—
180#4318—82no—
181C2×C11⋊C8—24no—
182C2×C11⋊C8—82no—
183C2×#539—111no—
184#2973—111no—
185#2972D1111yescharacteristic, complemented
186#1473—112no—
187#1472—112no—
188#1470—112no—
189#1468—112no—
190#1459—112no—
191C2×#324—112no—
192C23×C11—22no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11C2×C22⋊C412yes—
198C23×C11C2×C22⋊C412yes—
199C23×C11#13114yes—
200C23×C11C23×C411yescharacteristic
201C22×D11—21no—
202C22×D11—22no—
203C22×D11—41no—
204C22×D11—41no—
205D4×C11—28no—
206C2×C4×C11—22no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11C2×C22⋊C412yes—
216C2×C4×C11C2×C22⋊C412yes—
217C2×C4×C11C2×C22⋊C412yes—
218C2×C4×C11C2×C22⋊C412yes—
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C22×D411yescharacteristic
221C22⋊D11—44no—
222C22⋊D11—82no—
223C2×Dic11—21no—
224C2×Dic11—21no—
225C2×Dic11—21no—
226C2×Dic11—21no—
227C2×Dic11—21no—
228C2×Dic11—21no—
229C2×Dic11—21no—
230C2×Dic11—22no—
231C2×Dic11—22no—
232C2×Dic11—22no—
233C2×Dic11—44no—
234C2×Dic11—41no—
235C2×Dic11—41no—
236C2×Dic11—41no—
237C2×Dic11—41no—
238C2×Dic11—82no—
239C4×D11—82no—
240Dic22—82no—
241C8×C11—44no—
242C11⋊C8—44no—
243#539—224no—
244#539—224no—
245C2×#126—111no—
246C2×#126—111no—
247C2×#125—111no—
248C2×#125—111no—
249C2×#123—111no—
250C2×#123—111no—
251C2×#123—111no—
252C2×#123—111no—
253C2×C22⋊Q8—111no—
254C2×C22⋊Q8—111no—
255C2×C22⋊Q8—111no—
256C2×#121—111no—
257C2×C4×D4—111no—
258C2×C4×D4C2×D1111yescharacteristic
259C22×C4⋊C4—111no—
260#435—224no—
261C8×D4—24no—
262#432—112no—
263#431C2×D1112yes—
264#407—112no—
265C2×C22⋊C8—112no—
266C2×C22⋊C8C2×D1112yes—
267C2×C22⋊C8C2×D1112yes—
268#324—114no—
269#324—114no—
270#324—114no—
271#323—114no—
272C22×C11—21no—
273C22×C11—22no—
274C22×C11—21no—
275C22×C11—22no—
276C22×C11—22no—
277C22×C11—22no—
278C22×C11—22no—
279C22×C11—44no—
280C22×C11—82no—
281C22×C11#40814yes—
282C22×C11C22×C22⋊C411yescharacteristic
283C22×C11C2×#13112yes—
284C2×D11—41no—
285C2×D11—41no—
286C2×D11—41no—
287C2×D11—82no—
288C4×C11—22no—
289C4×C11—21no—
290C4×C11—21no—
291C4×C11—22no—
292C4×C11—22no—
293C4×C11—22no—
294Dic11—41no—
295Dic11—41no—
296Dic11—41no—
297Dic11—41no—
298Dic11—41no—
299Dic11—41no—
300Dic11—41no—
301C22×Q8—111no—
302C22×D4—111no—
303C22×D4—111no—
304C22×D4C4×D1111yescharacteristic
305C23×C4—111no—
306C23×C4—111no—
307C23×C4—111no—
308C23×C4C22×D1111yescharacteristic
309C23×C4C22×D1111yescharacteristic
310C2×M16—222no—
311C22×C8—22no—
312C22×C8—22no—
313C22×C8—222no—
314#126—224no—
315#126—222no—
316#126—222no—
317#125—224no—
318#125—222no—
319#125—222no—
320#123—224no—
321#123—222no—
322#123—222no—
323#123—224no—
324#123—224no—
325C22⋊Q8—222no—
326C22⋊Q8—222no—
327C22⋊Q8—224no—
328C22⋊Q8—224no—
329#121—224no—
330C4×D4—222no—
331C4×D4—222no—
332C4×D4D4414yes—
333C4×D4C22⋊D1114yes—
334C2×C4⋊C4—111no—
335C2×C4⋊C4—111no—
336C2×C4⋊C4—111no—
337C2×C4⋊C4—111no—
338C2×C4⋊C4—111no—
339C2×C4⋊C4—111no—
340C2×C4⋊C4—111no—
341C2×C4⋊C4—111no—
342C2×C4⋊C4—111no—
343C2×C4⋊C4—111no—
344C2×C4⋊C4—111no—
345C2×C4⋊C4—111no—
346C2×C4⋊C4—111no—
347C2×C4⋊C4—222no—
348C2×C4⋊C4—222no—
349C2×C4⋊C4C4×D1111yescharacteristic
350C2×C22⋊C4—111no—
351C2×C22⋊C4—111no—
352C2×C22⋊C4—111no—
353C2×C22⋊C4—111no—
354C2×C22⋊C4—111no—
355C2×C22⋊C4—111no—
356C2×C22⋊C4—111no—
357C2×C22⋊C4—111no—
358C2×C22⋊C4C4×D1111yescharacteristic
359C2×C22⋊C4C4×D1111yescharacteristic
360C2×C42—111no—
361C2×C42C22×D1111yescharacteristic
362C4⋊C8—22no—
363C4⋊C8—222no—
364C22⋊C8—22no—
365C22⋊C8—22no—
366C22⋊C8—114no—
367C22⋊C8—222no—
368C22⋊C8—222no—
369C22⋊C8C22×D1114yes—
370#97—222no—
371C4×C8—22no—
372C2×C11—22no—
373C2×C11—24no—
374C2×C11—42no—
375C2×C11C2×#40811yescharacteristic
376C2×C11#288311yescharacteristic
377C2×C11#288911yescharacteristic
378D11—81no—
379C24—111no—
380C24C2×C4×D1111yescharacteristic
381C24C2×C4×D1111yescharacteristic
382C2×Q8—222no—
383C2×Q8—881no—
384C2×D4—24no—
385C2×D4—224no—
386C2×D4—222no—
387C2×D4—222no—
388C2×D4—881no—
389C2×D4(C2×D11)⋊C414yes—
390C22×C4—81no—
391C22×C4—81no—
392C22×C4—111no—
393C22×C4—111no—
394C22×C4—111no—
395C22×C4—111no—
396C22×C4—111no—
397C22×C4—111no—
398C22×C4—111no—
399C22×C4—224no—
400C22×C4—222no—
401C22×C4—222no—
402C22×C4—222no—
403C22×C4—881no—
404C22×C4—881no—
405C22×C4C2×C4×D1111yescharacteristic
406C22×C4C2×C4×D1111yescharacteristic
407C22×C4C2×C4×D1111yescharacteristic
408C22×C4C2×C4×D1111yescharacteristic
409C22×C4C2×D4412yes—
410C22×C4C2×D4412yes—
411C22×C4C2×C22⋊D1112yes—
412C22×C4C2×C22⋊D1112yes—
413C22×C4C23×D1111yescharacteristic
414M16—882no—
415C2×C8—24no—
416C2×C8—82no—
417C2×C8—82no—
418C2×C8—224no—
419C2×C8—882no—
420C4⋊C4—222no—
421C4⋊C4—222no—
422C4⋊C4—222no—
423C4⋊C4—222no—
424C4⋊C4—222no—
425C4⋊C4—222no—
426C4⋊C4—222no—
427C4⋊C4—222no—
428C4⋊C4—222no—
429C4⋊C4—222no—
430C4⋊C4—221no—
431C4⋊C4—221no—
432C4⋊C4—221no—
433C4⋊C4—221no—
434C4⋊C4—221no—
435C4⋊C4—221no—
436C4⋊C4(C2×D11)⋊C414yes—
437C22⋊C4—222no—
438C22⋊C4—222no—
439C22⋊C4—222no—
440C22⋊C4—222no—
441C22⋊C4—222no—
442C22⋊C4—222no—
443C22⋊C4—222no—
444C22⋊C4—221no—
445C22⋊C4—221no—
446C22⋊C4(C2×D11)⋊C414yes—
447C22⋊C4(C2×D11)⋊C414yes—
448C42—222no—
449C42C2×D4412yes—
450C42C2×C22⋊D1112yes—
451C11#1738711yescharacteristic, complemented, Sylow
452C23—22no—
453C23—41no—
454C23—41no—
455C23—41no—
456C23—41no—
457C23—221no—
458C23—222no—
459C23—441no—
460C23—441no—
461C23#6695414yes—
462C23C2×(C2×D11)⋊C412yes—
463C23C2×(C2×D11)⋊C412yes—
464C23C22×C4×D1111yescharacteristic
465Q8—882no—
466D4—28no—
467D4—444no—
468D4—882no—
469C2×C4—22no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—222no—
479C2×C4—222no—
480C2×C4—222no—
481C2×C4—221no—
482C2×C4—221no—
483C2×C4—221no—
484C2×C4—221no—
485C2×C4—221no—
486C2×C4—221no—
487C2×C4—221no—
488C2×C4—444no—
489C2×C4—441no—
490C2×C4—441no—
491C2×C4—441no—
492C2×C4—441no—
493C2×C4—882no—
494C2×C4—882no—
495C2×C4C2×(C2×D11)⋊C412yes—
496C2×C4C2×(C2×D11)⋊C412yes—
497C2×C4C2×(C2×D11)⋊C412yes—
498C2×C4C2×(C2×D11)⋊C412yes—
499C2×C4C22×D4411yescharacteristic
500C2×C4C22×C22⋊D1111yescharacteristic
501C8—44no—
502C8—444no—
503C22—21no—
504C22—22no—
505C22—21no—
506C22—22no—
507C22—22no—
508C22—22no—
509C22—22no—
510C22—44no—
511C22—82no—
512C22—441no—
513C22—441no—
514C22—441no—
515C22—882no—
516C22#1062272314yes—
517C22C2×#6695412yes—
518C22C22×(C2×D11)⋊C411yescharacteristic
519C4—22no—
520C4—21no—
521C4—21no—
522C4—22no—
523C4—22no—
524C4—22no—
525C4—441no—
526C4—441no—
527C4—441no—
528C4—441no—
529C4—441no—
530C4—441no—
531C4—441no—
532C2—22no—
533C2—24no—
534C2—42no—
535C2—881no—
536C2C2×#1062272311yescharacteristic
537C2#1307707611yescharacteristic
538C2#1307709811yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2972C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#66992C4
cosocleC22×C4×C11C24
hypercenter#2972D11
hypocenterC11#17387
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2972

Complements

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

NH ≅ G/Ntype
2. #13077645C2semidirect
3. #13066983C2semidirect
4. #13066979C2semidirect
5. #13066971C2semidirect
6. #13066962C2semidirect
7. #13066932C2semidirect
8. C2×#10622107C2semidirect
9. C11×#2972C2semidirect
185. #2972D11semidirect
451. C11#17387semidirect

Maximal subgroups

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

subgroupindex
C2×#106230952
#130776452
#130669832
#130669792
#130669712
#130669622
#130669322
C2×#106221072
C11×#29722
#1738711