Finite Group Databasebeta

← #14719821

Subgroups — #14719821

Order 2816.

1040 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623093C211yesmaximal, characteristic
2#13077656C211yesmaximal, characteristic, complemented
3#13077639C211yesmaximal, characteristic, complemented
4#13066974C214yesmaximal, complemented
5#13066961C214yesmaximal, complemented
6#13066937C211yesmaximal, characteristic, complemented
7#13066928C211yesmaximal, characteristic, complemented
8#13066928C211yesmaximal, characteristic, complemented
9C11×#1460C211yesmaximal, characteristic, complemented
10C2×C4×D4×C11C2211yescharacteristic
11C2×#66993C411yescharacteristic
12C2×#66991C411yescharacteristic
13C2×#66983C412yes—
14C2×#66982C412yes—
15#10623093—22no—
16#10623093—22no—
17#10623093—22no—
18#10623093—22no—
19C2×#66948C411yescharacteristic
20C2×#66943C411yescharacteristic
21C2×#66937C2212yes—
22C2×#66936C2212yes—
23C2×C4×D44C2211yescharacteristic
24C2×#66925C2211yescharacteristic
25C11×#431C2211yescharacteristic
26C11×#431C2211yescharacteristic
27#10622538C2211yescharacteristic
28#10622538C2211yescharacteristic
29#10622451—22no—
30#10622447—22no—
31#10622339C2214yes—
32D11×C22⋊C8C2214yes—
33#10622301—22no—
34C8×D44—22no—
35C11×#323C2214yes—
36#10622163C2214yes—
37#10622107C2212yes—
38#10622107C2212yes—
39#10622106C2212yes—
40#10622106C2212yes—
41C22×D4×C11C2×C411yescharacteristic
42C23×C4×C11C2×C412yes—
43C22×C22⋊D11C2×C412yes—
44C22×C22⋊D11C2×C412yes—
45C22×C22⋊D11C2×C412yes—
46C22×D44C2×C411yescharacteristic
47C22×D44C2×C412yes—
48C22×C4×D11C2×C411yescharacteristic
49C22×C4×D11C2312yes—
50C4×D4×C11—21no—
51C4×D4×C11—21no—
52C4×D4×C11—21no—
53C4×D4×C11—21no—
54C2×C11×C4⋊C4C2×C411yescharacteristic
55C2×C11×C22⋊C4C2312yes—
56C2×C42×C11C2311yescharacteristic
57C2×C22⋊Dic11C2×C412yes—
58#66993—22no—
59#66993—22no—
60#66991—22no—
61#66991—22no—
62#66983—24no—
63#66983—24no—
64#66982—24no—
65#66982—24no—
66C2×(C2×D11)⋊C4C2×C411yescharacteristic
67C2×(C2×D11)⋊C4C2×C412yes—
68C2×(C2×D11)⋊C4C2×C412yes—
69C2×(C2×D11)⋊C4C2311yescharacteristic
70C2×C4⋊Dic11C2×C412yes—
71C2×C4⋊Dic11C2×C411yescharacteristic
72C2×Dic11⋊C4C2×C411yescharacteristic
73C2×Dic11⋊C4C2×C412yes—
74C2×Dic11⋊C4C2311yescharacteristic
75C2×C4×Dic11C2×C411yescharacteristic
76C2×#4313—24no—
77C2×C8×D11—24no—
78#66948—22no—
79#66948—22no—
80#66943—22no—
81#66943—22no—
82#66937—24no—
83#66937—24no—
84#66936—24no—
85#66936—24no—
86C4×D44D412yes—
87C4×D44D412yes—
88C4×D44D412yes—
89C4×D44D412yes—
90#66925—21no—
91#66925—21no—
92#66925—21no—
93#66925—21no—
94C11×C4⋊C8—21no—
95C11×C4⋊C8—21no—
96C11×C22⋊C8C2312yes—
97C11×C22⋊C8C2312yes—
98C4×C8×C11—21no—
99C4×C8×C11—21no—
100C22⋊(C11⋊C8)C2312yes—
101C22⋊(C11⋊C8)C2312yes—
102(C2×D11)⋊C8—24no—
103(C2×D11)⋊C8—24no—
104C4⋊(C11⋊C8)—21no—
105C4⋊(C11⋊C8)—21no—
106C4×C11⋊C8—21no—
107C4×C11⋊C8—21no—
108#17389—111nomaximal, Sylow
109C24×C11C22×C412yes—
110C23×D11C22×C411yescharacteristic
111C23×D11C22×C412yes—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—82no—
119C22×C4×C11C22×C412yes—
120C22×C4×C11C22×C411yescharacteristic
121C22×C4×C11C22×C411yescharacteristic
122C22×C4×C11C2411yescharacteristic
123C2×C22⋊D11—24no—
124C2×C22⋊D11—24no—
125C2×C22⋊D11—24no—
126C2×C22⋊D11—82no—
127C2×C22⋊D11—82no—
128C2×C22⋊D11—82no—
129C22×Dic11C22×C411yescharacteristic
130C22×Dic11C22×C411yescharacteristic
131C22×Dic11C22×C411yescharacteristic
132C22×Dic11C22×C412yes—
133C2×D44—24no—
134C2×D44—22no—
135C2×D44—22no—
136C2×D44—82no—
137C2×D44C22⋊C412yes—
138C2×D44C22⋊C412yes—
139C2×C4×D11—21no—
140C2×C4×D11—21no—
141C2×C4×D11—22no—
142C2×C4×D11—22no—
143C2×C4×D11—82no—
144C2×C4×D11C2×D414yes—
145C2×C4×D11C2×D414yes—
146C2×C8×C11—22no—
147C2×C8×C11—22no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C22⋊C4—22no—
151C11×C22⋊C4—22no—
152C42×C11C2×D411yescharacteristic
153C42×C11C2×D411yescharacteristic
154C42×C11C2×D411yescharacteristic
155C42×C11C2×D411yescharacteristic
156C22⋊Dic11—24no—
157(C2×D11)⋊C4—24no—
158(C2×D11)⋊C4—21no—
159(C2×D11)⋊C4—21no—
160(C2×D11)⋊C4—21no—
161(C2×D11)⋊C4—21no—
162(C2×D11)⋊C4C22⋊C414yes—
163(C2×D11)⋊C4C22⋊C414yes—
164C4⋊Dic11—24no—
165C4⋊Dic11C22⋊C412yes—
166C4⋊Dic11C22⋊C412yes—
167Dic11⋊C4—24no—
168Dic11⋊C4—21no—
169Dic11⋊C4—21no—
170Dic11⋊C4—21no—
171Dic11⋊C4—21no—
172C4×Dic11—21no—
173C4×Dic11—21no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—22no—
176#4313—84no—
177C8×D11—84no—
178C2×#540—111no—
179#2975—111no—
180#2972—111no—
181#1471—114no—
182#1468—114no—
183#1460—111no—
184#1460D1111yescharacteristic, complemented
185#1458—111no—
186#1458—111no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—42no—
191C23×C11—42no—
192C23×C11C23×C411yescharacteristic
193C22×D11—22no—
194C22×D11—22no—
195C22×D11—21no—
196C22×D11—21no—
197C22×D11—21no—
198C22×D11—42no—
199C22×D11—42no—
200C22×D11—41no—
201C22×D11—41no—
202C22×D11C2×C22⋊C414yes—
203D4×C11—42no—
204D4×C11—42no—
205C2×C4×C11—22no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—42no—
209C2×C4×C11—82no—
210C2×C4×C11—82no—
211C2×C4×C11C2×C22⋊C411yescharacteristic
212C2×C4×C11C2×C22⋊C411yescharacteristic
213C2×C4×C11C2×C22⋊C411yescharacteristic
214C2×C4×C11C2×C22⋊C411yescharacteristic
215C2×C4×C11#13112yes—
216C2×C4×C11#13112yes—
217C2×C4×C11C22×D411yescharacteristic
218C2×C4×C11C22×D411yescharacteristic
219C22⋊D11—84no—
220C22⋊D11—84no—
221C22⋊D11—84no—
222C2×Dic11—21no—
223C2×Dic11—21no—
224C2×Dic11—21no—
225C2×Dic11—21no—
226C2×Dic11—21no—
227C2×Dic11—42no—
228C2×Dic11—41no—
229C2×Dic11—41no—
230C2×Dic11C2×C22⋊C414yes—
231D44—24no—
232D44—24no—
233D44—84no—
234C4×D11—44no—
235C4×D11—44no—
236C4×D11—42no—
237C4×D11—42no—
238C8×C11—42no—
239C8×C11—42no—
240C11⋊C8—42no—
241C11⋊C8—42no—
242#540—222no—
243#540—222no—
244#540—222no—
245#540—222no—
246C2×#127—111no—
247C2×#125—111no—
248C2×#123—112no—
249C2×#123—112no—
250C2×#121—111no—
251C2×#121—112no—
252C2×#121—111no—
253C2×#121—112no—
254C2×C4×D4—111no—
255C2×C4×D4C2×D1111yescharacteristic
256C2×#117—111no—
257#436—222no—
258#436—222no—
259C8×D4—222no—
260C8×D4—222no—
261#431—111no—
262#431—111no—
263#431C2×D1111yescharacteristic
264#431C2×D1111yescharacteristic
265#407—114no—
266C2×C22⋊C8—114no—
267#324—112no—
268#324—112no—
269#323—114no—
270#323—112no—
271#323—112no—
272#323C2×D1114yes—
273C22×C11—21no—
274C22×C11—21no—
275C22×C11—42no—
276C22×C11—42no—
277C22×C11—42no—
278C22×C11—82no—
279C22×C11—82no—
280C22×C11C22×C22⋊C411yescharacteristic
281C22×C11C2×#13111yescharacteristic
282C22×C11C2×#13111yescharacteristic
283C2×D11—24no—
284C2×D11—24no—
285C2×D11—24no—
286C2×D11—41no—
287C2×D11—41no—
288C2×D11—41no—
289C2×D11—82no—
290C2×D11—82no—
291C2×D11—81no—
292C2×D11—81no—
293C4×C11—21no—
294C4×C11—21no—
295C4×C11—21no—
296C4×C11—21no—
297C4×C11—42no—
298C4×C11#40812yes—
299C4×C11#40812yes—
300Dic11—24no—
301Dic11—41no—
302Dic11—41no—
303Dic11—41no—
304C22×D4—112no—
305C22×D4—112no—
306C22×D4—112no—
307C22×D4—111no—
308C22×D4—112no—
309C22×D4C4×D1111yescharacteristic
310C23×C4—112no—
311C23×C4—111no—
312C23×C4C4×D1112yes—
313C2×M16—224no—
314C22×C8—224no—
315#127—222no—
316#127—222no—
317#125—222no—
318#125—222no—
319#123—224no—
320#123—224no—
321#123—224no—
322#123—224no—
323#121—224no—
324#121—224no—
325#121—224no—
326#121—224no—
327#121—222no—
328#121—222no—
329#121—222no—
330#121—222no—
331C4×D4—21no—
332C4×D4—21no—
333C4×D4—21no—
334C4×D4—21no—
335C4×D4—112no—
336C4×D4—112no—
337C4×D4—112no—
338C4×D4—112no—
339#117—221no—
340#117—221no—
341#117—221no—
342#117—221no—
343C2×C4⋊C4—111no—
344C2×C4⋊C4—111no—
345C2×C4⋊C4—112no—
346C2×C4⋊C4—112no—
347C2×C4⋊C4—111no—
348C2×C4⋊C4C4×D1111yescharacteristic
349C2×C22⋊C4—112no—
350C2×C22⋊C4—112no—
351C2×C22⋊C4—111no—
352C2×C22⋊C4—112no—
353C2×C22⋊C4—111no—
354C2×C22⋊C4C22×D1112yes—
355C2×C42—111no—
356C2×C42C22×D1111yescharacteristic
357C4⋊C8—21no—
358C4⋊C8—21no—
359C4⋊C8—221no—
360C4⋊C8—221no—
361C22⋊C8—112no—
362C22⋊C8—112no—
363C22⋊C8—224no—
364C22⋊C8—224no—
365C22⋊C8C22×D1112yes—
366C22⋊C8C22×D1112yes—
367C4×C8—21no—
368C4×C8—21no—
369C4×C8—221no—
370C4×C8—221no—
371C2×C11—21no—
372C2×C11—21no—
373C2×C11—82no—
374C2×C11C2×#40811yescharacteristic
375C2×C11#288311yescharacteristic
376C2×C11#288811yescharacteristic
377D11—44no—
378D11—81no—
379C24—112no—
380C24—111no—
381C24C2×C4×D1112yes—
382C2×D4—21no—
383C2×D4—21no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—112no—
387C2×D4—112no—
388C2×D4—224no—
389C2×D4—224no—
390C2×D4—224no—
391C2×D4—224no—
392C2×D4—222no—
393C2×D4—222no—
394C2×D4—882no—
395C2×D4—882no—
396C2×D4—882no—
397C2×D4—882no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—82no—
401C22×C4—112no—
402C22×C4—114no—
403C22×C4—114no—
404C22×C4—111no—
405C22×C4—111no—
406C22×C4—111no—
407C22×C4—221no—
408C22×C4—221no—
409C22×C4—222no—
410C22×C4—222no—
411C22×C4—882no—
412C22×C4C2×C4×D1112yes—
413C22×C4C2×C4×D1111yescharacteristic
414C22×C4C2×C4×D1111yescharacteristic
415C22×C4C23×D1111yescharacteristic
416M16—884no—
417C2×C8—22no—
418C2×C8—22no—
419C2×C8—222no—
420C2×C8—222no—
421C2×C8—884no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—112no—
425C4⋊C4—112no—
426C4⋊C4—224no—
427C4⋊C4—224no—
428C4⋊C4—221no—
429C4⋊C4—221no—
430C4⋊C4—221no—
431C4⋊C4—221no—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—114no—
435C22⋊C4—114no—
436C22⋊C4—224no—
437C22⋊C4—224no—
438C22⋊C4—221no—
439C22⋊C4—221no—
440C22⋊C4—221no—
441C22⋊C4—221no—
442C42—221no—
443C42—221no—
444C42D4×D1111yescharacteristic
445C42D4×D1111yescharacteristic
446C42D4×D1111yescharacteristic
447C42D4×D1111yescharacteristic
448C11#1738911yescharacteristic, complemented, Sylow
449C23—22no—
450C23—22no—
451C23—22no—
452C23—42no—
453C23—42no—
454C23—114no—
455C23—222no—
456C23—222no—
457C23—221no—
458C23—221no—
459C23—221no—
460C23—442no—
461C23—442no—
462C23—441no—
463C23—441no—
464C23C22×C4×D1111yescharacteristic
465D4—42no—
466D4—42no—
467D4—224no—
468D4—224no—
469D4—884no—
470D4—884no—
471D4—884no—
472D4—884no—
473C2×C4—22no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—42no—
477C2×C4—82no—
478C2×C4—82no—
479C2×C4—114no—
480C2×C4—221no—
481C2×C4—221no—
482C2×C4—221no—
483C2×C4—221no—
484C2×C4—221no—
485C2×C4—444no—
486C2×C4—444no—
487C2×C4—442no—
488C2×C4—442no—
489C2×C4—442no—
490C2×C4—441no—
491C2×C4—441no—
492C2×C4C22⋊C4×D1111yescharacteristic
493C2×C4C22⋊C4×D1111yescharacteristic
494C2×C4C22⋊C4×D1111yescharacteristic
495C2×C4C22⋊C4×D1111yescharacteristic
496C2×C4#6695412yes—
497C2×C4#6696012yes—
498C2×C4C2×D4×D1111yescharacteristic
499C2×C4C2×D4×D1111yescharacteristic
500C8—42no—
501C8—42no—
502C8—442no—
503C8—442no—
504C22—21no—
505C22—21no—
506C22—42no—
507C22—42no—
508C22—42no—
509C22—82no—
510C22—82no—
511C22—224no—
512C22—224no—
513C22—224no—
514C22—441no—
515C22—441no—
516C22—441no—
517C22—882no—
518C22—882no—
519C22—881no—
520C22—881no—
521C22C2×C22⋊C4×D1111yescharacteristic
522C22C2×#6695411yescharacteristic
523C22C2×#6696011yescharacteristic
524C4—21no—
525C4—21no—
526C4—21no—
527C4—21no—
528C4—42no—
529C4—224no—
530C4—441no—
531C4—441no—
532C4—441no—
533C4#1062234012yes—
534C4#1062234012yes—
535C2—21no—
536C2—21no—
537C2—82no—
538C2—444no—
539C2—881no—
540C2C2×#1062234011yescharacteristic
541C2#1307707511yescharacteristic
542C2#1307709211yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1460C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623093C2
cosocleC22×C4×C11C24
hypercenter#1460D11
hypocenterC11#17389
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1460

Complements

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

NH ≅ G/Ntype
2. #13077656C2semidirect
3. #13077639C2semidirect
4. #13066974C2semidirect
5. #13066961C2semidirect
6. #13066937C2semidirect
7. #13066928C2semidirect
8. #13066928C2semidirect
9. C11×#1460C2semidirect
184. #1460D11semidirect
448. C11#17389semidirect

Maximal subgroups

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

subgroupindex
C2×#106230932
#130776562
#130776392
#130669742
#130669612
#130669372
#130669282
C11×#14602
#1738911