Finite Group Databasebeta

← #14721531

Subgroups — #14721531

Order 2816.

1270 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
1#13082380C211yesmaximal, characteristic
2#13077645C211yesmaximal, characteristic, complemented
3#13067183C212yesmaximal, complemented
4#13067162C212yesmaximal, complemented
5#13067144C212yesmaximal, complemented
6#13067131C212yesmaximal, complemented
7#13067123C212yesmaximal, complemented
8C2×#10622089C212yesmaximal, complemented
9C11×#2353C211yesmaximal, characteristic, complemented
10C2×#67037—21no—
11C2×C4×D4×C11C2211yescharacteristic
12C2×#66983C2212yes—
13C2×#66983C2212yes—
14#10623086C414yescomplemented
15#10623085—24no—
16D4×D44C414yescomplemented
17#10623041—21no—
18#10623024—21no—
19#10623024—21no—
20#10623008C2212yes—
21C11×#388—21no—
22C11×#387—21no—
23C11×#386—21no—
24C11×#383C2211yescharacteristic, complemented
25C11×#381C2211yescharacteristic, complemented
26C11×#380C2211yescharacteristic, complemented
27C4×C11×C22⋊C4—21no—
28C4×C11×C22⋊C4C2211yescharacteristic, complemented
29C11×#376C2211yescharacteristic, complemented
30C2×C11×#95C2211yescharacteristic, complemented
31#10622820C2212yescomplemented
32C2×C22⋊(C11⋊C8)C2212yescomplemented
33#10622624—24no—
34#10622539C2212yescomplemented
35#10622089C2214yescomplemented
36#10622089C2214yescomplemented
37#10622089C2214yescomplemented
38#10622089C2214yescomplemented
39C22×D4×C11D411yescharacteristic
40C23×C4×C11—21no—
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C22×C22⋊D11—22no—
44C22×C22⋊D11—22no—
45#67037—44no—
46#67037—44no—
47C2×#4341—24no—
48C2×D4×D11—24no—
49C2×#4339—22no—
50C22×D44C2×C412yes—
51C22×D44C2×C412yescomplemented
52C4×D4×C11C2×C414yes—
53C4×D4×C11D414yes—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4D411yescharacteristic
56C2×C11×C22⋊C4—21no—
57C2×C11×C22⋊C4—21no—
58C2×C11×C22⋊C4—21no—
59C2×C11×C22⋊C4D411yescharacteristic
60C2×C11×C22⋊C4D411yescharacteristic
61C2×C42×C11—21no—
62C2×C42×C11—21no—
63C2×C42×C11C2311yescharacteristic
64#66983—22no—
65#66983—22no—
66#66983—22no—
67#66983—22no—
68#66983—22no—
69#66983C2×C414yes—
70#66983C2×C414yescomplemented
71#66983C2314yes—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4—22no—
74C2×C4⋊Dic11C2×C412yes—
75C2×C4⋊Dic11C2×C412yescomplemented
76C2×#4318—22no—
77C22×C11⋊C8—22no—
78#66950—24no—
79#66948—24no—
80#66939—24no—
81#66939—24no—
82#66935—24no—
83#66935—24no—
84#66928—22no—
85#66927C2×C412yescomplemented
86C4×D44—22no—
87C4×D44C2×C414yescomplemented
88#66922C2×C412yescomplemented
89C11×#95—21no—
90C11×#95—21no—
91C11×#95—21no—
92C11×#95—21no—
93C11×#95—21no—
94C11×#95C2311yescharacteristic
95C11×#95C2311yescharacteristic
96C11×#95C2311yescharacteristic
97C11×#95C2311yescharacteristic
98C22⋊(C11⋊C8)—22no—
99C22⋊(C11⋊C8)—22no—
100C22⋊(C11⋊C8)C2314yes—
101C4⋊(C11⋊C8)—22no—
102#66867—22no—
103#17620—111nomaximal, Sylow
104C24×C11C2×D411yescharacteristic
105C24×C11C2×D411yescharacteristic
106C23×D11—22no—
107C23×D11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11C22⋊C414yes—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—42no—
116C22×C4×C11—42no—
117C22×C4×C11—81no—
118C22×C4×C11—81no—
119C22×C4×C11—81no—
120C22×C4×C11C22×C412yes—
121C22×C4×C11C22×C412yes—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2411yescharacteristic
129C2×C22⋊D11—24no—
130C2×C22⋊D11—24no—
131C2×C22⋊D11—24no—
132C2×C22⋊D11—44no—
133C2×C22⋊D11—44no—
134C2×C22⋊D11—44no—
135C2×C22⋊D11—44no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138#4341—416no—
139D4×D11—416no—
140#4339—44no—
141#4339—44no—
142C2×D44—22no—
143C2×D44—22no—
144C2×D44—22no—
145C2×D44—22no—
146C2×D44—82no—
147C2×D44—82no—
148C2×D44C22×C414yes—
149C2×C4×D11—24no—
150C2×Dic22—22no—
151C11×C4⋊C4—81no—
152C11×C4⋊C4C22⋊C414yes—
153C11×C22⋊C4—42no—
154C11×C22⋊C4—42no—
155C11×C22⋊C4—81no—
156C11×C22⋊C4C22⋊C414yes—
157C11×C22⋊C4C22⋊C414yes—
158C42×C11—42no—
159C42×C11—81no—
160C42×C11C22×C412yes—
161C42×C11C2×D412yes—
162(C2×D11)⋊C4—24no—
163(C2×D11)⋊C4—24no—
164(C2×D11)⋊C4—24no—
165(C2×D11)⋊C4—24no—
166C4⋊Dic11—22no—
167C4⋊Dic11—22no—
168C4⋊Dic11—22no—
169C4⋊Dic11C22×C414yes—
170#4318—82no—
171C2×C11⋊C8—24no—
172C2×C11⋊C8—82no—
173#3496—111no—
174#2973—111no—
175#2353D1111yescharacteristic, complemented
176#1519—112no—
177#1514—112no—
178#1510—112no—
179#1507—112no—
180#1505—112no—
181C2×#327—112no—
182C23×C11—21no—
183C23×C11—21no—
184C23×C11—41no—
185C23×C11—41no—
186C23×C11—41no—
187C23×C11—41no—
188C23×C11C2×C22⋊C412yes—
189C23×C11C2×C22⋊C412yes—
190C23×C11AGL(1,ℤ/8)12yes—
191C23×C11AGL(1,ℤ/8)12yes—
192C23×C11C22×D411yescharacteristic
193C22×D11—24no—
194C22×D11—44no—
195C22×D11—44no—
196C22×D11—82no—
197C22×D11—82no—
198C22×D11—82no—
199C22×D11—82no—
200D4×C11—28no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—22no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
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×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—84no—
224C2×C4×C11C2×C22⋊C412yes—
225C2×C4×C11C2×C22⋊C412yes—
226C2×C4×C11C2×C22⋊C412yes—
227C2×C4×C11C2×C22⋊C412yes—
228C2×C4×C11C23×C411yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C22⋊D11—48no—
231C22⋊D11—44no—
232C22⋊D11—44no—
233C22⋊D11—48no—
234C2×Dic11—24no—
235C2×Dic11—44no—
236C2×Dic11—44no—
237D44—44no—
238D44—44no—
239D44—82no—
240D44—82no—
241D44—82no—
242C4×D11—48no—
243Dic22—44no—
244C11⋊C8—44no—
245C2×H(5,𝔽2)—221no—
246#547—114no—
247#546—224no—
248D42—114no—
249#537—221no—
250#534—221no—
251#534—221no—
252#532—112no—
253C2×#121—112no—
254C2×#121—112no—
255C2×C4×D4C2×D1111yescharacteristic
256#435—224no—
257#432—112no—
258#407—112no—
259C2×C22⋊C8—112no—
260#388—21no—
261#387—21no—
262#386—21no—
263#383C2×D1111yescharacteristic, complemented
264#381C2×D1111yescharacteristic, complemented
265#380C2×D1111yescharacteristic, complemented
266C4×C22⋊C4—21no—
267C4×C22⋊C4C2×D1111yescharacteristic, complemented
268#376C2×D1111yescharacteristic, complemented
269C2×#95C2×D1111yescharacteristic, complemented
270#327—114no—
271#327—114no—
272#327—114no—
273#327—114no—
274C22×C11—21no—
275C22×C11—22no—
276C22×C11—21no—
277C22×C11—22no—
278C22×C11—22no—
279C22×C11—22no—
280C22×C11—22no—
281C22×C11—42no—
282C22×C11—42no—
283C22×C11—81no—
284C22×C11—81no—
285C22×C11#41814yes—
286C22×C11C22×C22⋊C411yescharacteristic
287C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
288C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
289C2×D11—44no—
290C2×D11—44no—
291C2×D11—44no—
292C2×D11—164no—
293C2×D11—164no—
294C4×C11—21no—
295C4×C11—21no—
296C4×C11—22no—
297C4×C11—22no—
298C4×C11—22no—
299C4×C11—22no—
300C4×C11—42no—
301C4×C11—81no—
302C4×C11—81no—
303C4×C11—81no—
304Dic11—44no—
305H(5,𝔽2)—444no—
306H(5,𝔽2)—444no—
307C2×#41—224no—
308C2×#41—222no—
309C22×D4—112no—
310C22×D4—112no—
311C22×D4—222no—
312C22×D4—222no—
313C22×D4—224no—
314C22×D4C22⋊D1111yescharacteristic
315C23×C4—21no—
316C23×C4C22×D1111yescharacteristic
317C23×C4C22×D1111yescharacteristic
318C2×M16—222no—
319C22×C8—222no—
320C4⋊Q8—112no—
321#127—112no—
322#124—222no—
323#123—224no—
324#123—224no—
325C22⋊Q8—224no—
326#121—114no—
327#121—114no—
328#121—114no—
329#121—222no—
330#121—222no—
331#121—222no—
332#121—222no—
333#121—222no—
334#121—224no—
335#120—224no—
336#120—224no—
337C4×D4—114no—
338C4×D4—222no—
339C4×D4C4×D1114yes—
340C4×D4D4414yes—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—112no—
343C2×C4⋊C4—112no—
344C2×C4⋊C4C22⋊D1111yescharacteristic
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—222no—
349C2×C22⋊C4—222no—
350C2×C22⋊C4C22⋊D1111yescharacteristic
351C2×C22⋊C4C22⋊D1111yescharacteristic
352C2×C42—21no—
353C2×C42—21no—
354C2×C42C22×D1111yescharacteristic
355C4⋊C8—222no—
356C22⋊C8—114no—
357C22⋊C8—222no—
358C22⋊C8—222no—
359#97—222no—
360#95—21no—
361#95—21no—
362#95—21no—
363#95—21no—
364#95—21no—
365#95C22×D1111yescharacteristic
366#95C22×D1111yescharacteristic
367#95C22×D1111yescharacteristic
368#95C22×D1111yescharacteristic
369C2×C11—21no—
370C2×C11—21no—
371C2×C11—24no—
372C2×C11—42no—
373C2×C11#288311yescharacteristic
374C2×C11C2×#41811yescharacteristic
375C2×C11#290111yescharacteristic
376D11—84no—
377C24—222no—
378C24—222no—
379C24C2×C22⋊D1111yescharacteristic
380C24C2×C22⋊D1111yescharacteristic
381#41—444no—
382#41—444no—
383#41—4416no—
384C2×Q8—222no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—114no—
388C2×D4—224no—
389C2×D4—224no—
390C2×D4—224no—
391C2×D4—222no—
392C2×D4—222no—
393C2×D4—222no—
394C2×D4—222no—
395C2×D4—4416no—
396C2×D4—444no—
397C2×D4—444no—
398C2×D4—444no—
399C2×D4—444no—
400C2×D4—882no—
401C2×D4—882no—
402C2×D4(C2×D11)⋊C414yes—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—42no—
408C22×C4—42no—
409C22×C4—81no—
410C22×C4—81no—
411C22×C4—81no—
412C22×C4—222no—
413C22×C4—222no—
414C22×C4—224no—
415C22×C4C2×C4×D1112yes—
416C22×C4C2×C4×D1112yes—
417C22×C4C2×D4412yes—
418C22×C4C2×D4412yes—
419C22×C4C2×C22⋊D1111yescharacteristic
420C22×C4C2×C22⋊D1111yescharacteristic
421C22×C4C2×C22⋊D1111yescharacteristic
422C22×C4C2×C22⋊D1111yescharacteristic
423C22×C4C23×D1111yescharacteristic
424M16—882no—
425C2×C8—224no—
426C2×C8—882no—
427C4⋊C4—81no—
428C4⋊C4—114no—
429C4⋊C4—222no—
430C4⋊C4—222no—
431C4⋊C4—222no—
432C4⋊C4(C2×D11)⋊C414yes—
433C22⋊C4—42no—
434C22⋊C4—42no—
435C22⋊C4—81no—
436C22⋊C4—224no—
437C22⋊C4—224no—
438C22⋊C4—224no—
439C22⋊C4—224no—
440C22⋊C4(C2×D11)⋊C414yes—
441C22⋊C4(C2×D11)⋊C414yes—
442C42—42no—
443C42—81no—
444C42C2×C4×D1112yes—
445C42C2×D4412yes—
446C11#1762011yescharacteristic, complemented, Sylow
447C23—21no—
448C23—21no—
449C23—41no—
450C23—41no—
451C23—41no—
452C23—41no—
453C23—224no—
454C23—444no—
455C23—444no—
456C23—882no—
457C23—882no—
458C23—882no—
459C23—882no—
460C23C2×(C2×D11)⋊C412yes—
461C23C2×(C2×D11)⋊C412yes—
462C23#6700212yes—
463C23#6700212yes—
464C23C22×C22⋊D1111yescharacteristic
465Q8—444no—
466D4—28no—
467D4—444no—
468D4—444no—
469D4—448no—
470D4—444no—
471D4—444no—
472D4—448no—
473D4—882no—
474D4—882no—
475D4—882no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—22no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—84no—
499C2×C4—224no—
500C2×C4—448no—
501C2×C4—444no—
502C2×C4—444no—
503C2×C4C2×(C2×D11)⋊C412yes—
504C2×C4C2×(C2×D11)⋊C412yes—
505C2×C4C2×(C2×D11)⋊C412yes—
506C2×C4C2×(C2×D11)⋊C412yes—
507C2×C4C22×C4×D1111yescharacteristic
508C2×C4C22×D4411yescharacteristic
509C8—444no—
510C22—21no—
511C22—22no—
512C22—21no—
513C22—22no—
514C22—22no—
515C22—22no—
516C22—22no—
517C22—42no—
518C22—42no—
519C22—81no—
520C22—81no—
521C22—444no—
522C22—444no—
523C22—444no—
524C22—1764no—
525C22—1764no—
526C22#1062261414yes—
527C22C22×(C2×D11)⋊C411yescharacteristic
528C22C2×#6700211yescharacteristic
529C22C2×#6700211yescharacteristic
530C4—21no—
531C4—21no—
532C4—22no—
533C4—22no—
534C4—22no—
535C4—22no—
536C4—42no—
537C4—81no—
538C4—81no—
539C4—81no—
540C4—444no—
541C2—21no—
542C2—21no—
543C2—24no—
544C2—42no—
545C2—884no—
546C2#1307707611yescharacteristic
547C2C2×#1062261411yescharacteristic
548C2#1307716411yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2353C2
socleC22×C11C22×C22⋊C4
prime radical#13082380C2
cosocleC22×C4×C11C24
hypercenter#2353D11
hypocenterC11#17620
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2353

Complements

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

NH ≅ G/Ntype
2. #13077645C2semidirect
3. #13067183C2semidirect
4. #13067162C2semidirect
5. #13067144C2semidirect
6. #13067131C2semidirect
7. #13067123C2semidirect
8. C2×#10622089C2semidirect
9. C11×#2353C2semidirect
14. #10623086C4semidirect
16. D4×D44C4semidirect
24. C11×#383C22semidirect
25. C11×#381C22semidirect
26. C11×#380C22semidirect
28. C4×C11×C22⋊C4C22semidirect
29. C11×#376C22semidirect
30. C2×C11×#95C22semidirect
31. #10622820C22semidirect
32. C2×C22⋊(C11⋊C8)C22semidirect
34. #10622539C22semidirect
35. #10622089C22semidirect
36. #10622089C22semidirect
37. #10622089C22semidirect
38. #10622089C22semidirect
51. C22×D44C2×C4semidirect
70. #66983C2×C4semidirect
75. C2×C4⋊Dic11C2×C4semidirect
85. #66927C2×C4semidirect
87. C4×D44C2×C4semidirect
88. #66922C2×C4semidirect
175. #2353D11semidirect
263. #383C2×D11semidirect
264. #381C2×D11semidirect
265. #380C2×D11semidirect
267. C4×C22⋊C4C2×D11semidirect
268. #376C2×D11semidirect
269. C2×#95C2×D11semidirect
446. C11#17620semidirect

Maximal subgroups

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

subgroupindex
#130823802
#130776452
#130671832
#130671622
#130671442
#130671312
#130671232
C2×#106220892
C11×#23532
#1762011