Finite Group Databasebeta

← #14960936

Subgroups — #14960936

Order 2816.

1854 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076900C212yesmaximal
2#13075817C214yesmaximal, complemented
3#13075527C214yesmaximal, complemented
4#13075281C214yesmaximal, complemented
5#13075081C214yesmaximal, complemented
6#13074586C211yesmaximal, characteristic, complemented
7#13072867C214yesmaximal
8#13072762C214yesmaximal, complemented
9#13071351C212yesmaximal, complemented
10C2×#10622280C211yesmaximal, characteristic
11C11×#2659C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C2×C11×C22⋊Q8C2212yes—
14C2×#66999C2212yes—
15C2×#66999C2212yes—
16C22×(C2×D11)⋊C4C2212yes—
17C22×Dic11⋊C4C2212yes—
18C2×#66951C2214yes—
19C2×#66942C2214yescomplemented
20C11×#398C2214yescomplemented
21C11×#395C2214yescomplemented
22C11×#380C2214yes—
23C2×C11×#95C2211yescharacteristic
24#10622843C2214yescomplemented
25#10622825C2212yes—
26#10622823C2214yes—
27C2×C11⋊#95C2211yescharacteristic
28#10622607C2214yes—
29#10622606C2214yes—
30#10622603C2214yes—
31#10622602C2214yes—
32#10622602C2214yes—
33#10622600C2212yes—
34#10622600C2212yes—
35#10622598C2214yescomplemented
36#10622596C2214yescomplemented
37#10622594C2214yescomplemented
38#10622594C2214yescomplemented
39#10622593C2214yescomplemented
40#10622591C2214yescomplemented
41#10622568C2214yes—
42#10622563C2214yes—
43#10622559C2214yes—
44C22⋊C4×Dic11C2214yes—
45#10622288C2214yes—
46#10622287C2214yes—
47#10622283C2214yes—
48#10622282C2214yes—
49#10622280C2214yes—
50#10622280C2214yes—
51#10622273C2214yescomplemented
52#10622271C2214yescomplemented
53#10622270C2214yescomplemented
54#10622270C2214yescomplemented
55#10622265C2214yescomplemented
56#10622260C2214yescomplemented
57C24×D11C2311yescharacteristic
58C22×Q8×C11C2312yes—
59C23×C4×C11C2312yes—
60C23×C4×C11C2311yescharacteristic
61C23×Dic11C2311yescharacteristic
62C23×Dic11C2312yes—
63C22×C4×D11—24no—
64C22×C4×D11—44no—
65C22×C4×D11C2312yes—
66C22×C4×D11C2312yes—
67C11×C22⋊Q8—28no—
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C4⋊C4C2314yes—
70C2×C11×C4⋊C4C2314yes—
71C2×C11×C4⋊C4C2314yes—
72C2×C11×C22⋊C4C2314yes—
73C2×C22⋊Dic11C2314yes—
74#66999—44no—
75#66999—44no—
76C2×(C2×D11)⋊C4—44no—
77C2×(C2×D11)⋊C4C2314yes—
78C2×(C2×D11)⋊C4C2314yes—
79C2×(C2×D11)⋊C4C2314yes—
80C2×(C2×D11)⋊C4C2314yes—
81C2×(C2×D11)⋊C4C2314yes—
82C2×(C2×D11)⋊C4C2314yes—
83C2×C4⋊Dic11C2314yes—
84C2×C4⋊Dic11C2312yes—
85C2×C4⋊Dic11C2314yes—
86C2×C4⋊Dic11C2312yes—
87C2×Dic11⋊C4—44no—
88C2×Dic11⋊C4C2314yes—
89C2×Dic11⋊C4C2314yes—
90C2×Dic11⋊C4C2314yes—
91C2×Dic11⋊C4C2314yes—
92C2×Dic11⋊C4C2314yes—
93C2×Dic11⋊C4C2314yes—
94C2×C4×Dic11C2314yes—
95C2×C4×Dic11C2314yes—
96#66951—48no—
97#66942—48no—
98C11×#95C2314yes—
99C11×#95C2314yes—
100C11×#95C2314yes—
101C11⋊#95C2314yes—
102C11⋊#95C2314yes—
103C11⋊#95C2314yes—
104C11⋊#95C2314yes—
105C11⋊#95C2314yes—
106C11⋊#95C2314yes—
107C11⋊#95C2314yes—
108C11⋊#95C2314yes—
109C11⋊#95C2314yes—
110C11⋊#95C2314yes—
111#36728—111nomaximal, Sylow
112C24×C11C2411yescharacteristic
113C23×D11—22no—
114C23×D11—22no—
115C23×D11—22no—
116C23×D11—24no—
117C23×D11—42no—
118C23×D11C2411yescharacteristic
119C23×D11C2411yescharacteristic
120C2×Q8×C11—24no—
121C2×Q8×C11—42no—
122C2×Q8×C11—42no—
123C22×C4×C11—24no—
124C22×C4×C11—42no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11#4114yes—
128C22×C4×C11C2414yes—
129C22×C4×C11C2414yes—
130C22×C4×C11C2414yes—
131C22×C4×C11C2412yes—
132C22×Dic11—24no—
133C22×Dic11—22no—
134C22×Dic11—24no—
135C22×Dic11—42no—
136C22×Dic11—42no—
137C22×Dic11C2414yes—
138C22×Dic11C2414yes—
139C22×Dic11C2414yes—
140C22×Dic11C2412yes—
141C2×C4×D11—24no—
142C2×C4×D11—24no—
143C2×C4×D11—24no—
144C2×C4×D11—24no—
145C2×C4×D11—42no—
146C2×C4×D11—42no—
147C2×C4×D11—416no—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—28no—
150C11×C4⋊C4—44no—
151C11×C4⋊C4—44no—
152C11×C22⋊C4—28no—
153C22⋊Dic11—28no—
154(C2×D11)⋊C4—28no—
155(C2×D11)⋊C4—28no—
156(C2×D11)⋊C4—28no—
157(C2×D11)⋊C4—44no—
158(C2×D11)⋊C4—44no—
159(C2×D11)⋊C4—44no—
160C4⋊Dic11—44no—
161C4⋊Dic11—44no—
162C4⋊Dic11—42no—
163C4⋊Dic11—42no—
164Dic11⋊C4—28no—
165Dic11⋊C4—28no—
166Dic11⋊C4—28no—
167Dic11⋊C4—44no—
168Dic11⋊C4—44no—
169Dic11⋊C4—44no—
170C4×Dic11—44no—
171C4×Dic11—44no—
172#2848—112no—
173#2747—114no—
174#2722—114no—
175#2704—114no—
176#2690—114no—
177#2659D1111yescharacteristic, complemented
178#2646—111no—
179#2480—114no—
180#2473—114no—
181#2329—112no—
182C2×#380—111no—
183C23×C11—22no—
184C23×C11—21no—
185C23×C11—21no—
186C23×C11C2×#4112yes—
187C23×C112−1+414yes—
188C23×C11C2511yescharacteristic
189C22×D11—28no—
190C22×D11—21no—
191C22×D11—21no—
192C22×D11—21no—
193C22×D11—22no—
194C22×D11—22no—
195C22×D11—22no—
196C22×D11—22no—
197C22×D11—21no—
198C22×D11—48no—
199C22×D11—48no—
200C22×D11—44no—
201C22×D11—44no—
202C22×D11H(5,𝔽2)12yes—
203C22×D112−1+412yes—
204Q8×C11—84no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—44no—
217C2×C4×C11—84no—
218C2×C4×C11C2×#4114yes—
219C2×Dic11—28no—
220C2×Dic11—22no—
221C2×Dic11—22no—
222C2×Dic11—24no—
223C2×Dic11—24no—
224C2×Dic11—24no—
225C2×Dic11—24no—
226C2×Dic11—24no—
227C2×Dic11—24no—
228C2×Dic11—24no—
229C2×Dic11—24no—
230C2×Dic11—24no—
231C2×Dic11—84no—
232C2×Dic11H(5,𝔽2)14yes—
233C4×D11—48no—
234C4×D11—48no—
235C24×C4—111no—
236C2×#126—114no—
237C2×#125—114no—
238C2×C22⋊Q8—112no—
239C2×C22⋊Q8—112no—
240C2×C22⋊Q8C2×D1112yes—
241C22×C4⋊C4—112no—
242C22×C22⋊C4—112no—
243#400—114no—
244#400—114no—
245#398—114no—
246#398—114no—
247#398—114no—
248#398—114no—
249#398C2×D1114yescomplemented
250#397—114no—
251#397—114no—
252#397—114no—
253#396—114no—
254#395C2×D1114yescomplemented
255#391—114no—
256#389—114no—
257#389—114no—
258#388—114no—
259#388—114no—
260#388—114no—
261#387—114no—
262#387—114no—
263#387—114no—
264#387—114no—
265#385—114no—
266#385—114no—
267#385—114no—
268#385—114no—
269#385—114no—
270#380—112no—
271#380—112no—
272#380—112no—
273#380—114no—
274#380—114no—
275#380C2×D1114yes—
276#379—114no—
277C4×C22⋊C4—114no—
278C2×#95—111no—
279C2×#95C2×D1111yescharacteristic
280C22×C11—22no—
281C22×C11—22no—
282C22×C11—24no—
283C22×C11—24no—
284C22×C11#54114yes—
285C22×C11C22×#4111yescharacteristic
286C22×C11C2×H(5,𝔽2)12yes—
287C22×C11C2×H(5,𝔽2)11yescharacteristic
288C22×C11C2×2−1+412yes—
289C22×C11C2×2−1+411yescharacteristic
290C2×D11—22no—
291C2×D11—22no—
292C2×D11—24no—
293C2×D11—24no—
294C2×D11—416no—
295C2×D11—41no—
296C2×D11—41no—
297C2×D11—41no—
298C2×D11—41no—
299C2×D11—42no—
300C2×D11—42no—
301C4×C11—24no—
302C4×C11—44no—
303C4×C11—44no—
304C4×C11—44no—
305Dic11—24no—
306Dic11—44no—
307Dic11—44no—
308Dic11—44no—
309C25—111no—
310C22×Q8C22×D1112yes—
311C23×C4—111no—
312C23×C4—112no—
313C23×C4—112no—
314C23×C4—112no—
315C23×C4—224no—
316C23×C4—444no—
317C23×C4C22×D1112yes—
318C23×C4C22×D1111yescharacteristic
319#126—448no—
320#125—448no—
321C22⋊Q8—28no—
322C22⋊Q8—444no—
323C22⋊Q8—444no—
324C2×C4⋊C4—114no—
325C2×C4⋊C4—114no—
326C2×C4⋊C4—114no—
327C2×C4⋊C4—114no—
328C2×C4⋊C4—112no—
329C2×C4⋊C4—112no—
330C2×C4⋊C4—114no—
331C2×C4⋊C4—114no—
332C2×C4⋊C4—114no—
333C2×C4⋊C4—114no—
334C2×C4⋊C4—444no—
335C2×C4⋊C4C22×D1112yes—
336C2×C4⋊C4C22×D1114yes—
337C2×C4⋊C4C22×D1114yes—
338C2×C4⋊C4C22×D1114yes—
339C2×C22⋊C4—114no—
340C2×C22⋊C4—114no—
341C2×C22⋊C4—114no—
342C2×C22⋊C4—114no—
343C2×C22⋊C4—114no—
344C2×C22⋊C4—114no—
345C2×C22⋊C4—114no—
346C2×C22⋊C4—444no—
347C2×C22⋊C4C22×D1114yes—
348C2×C42—114no—
349C2×C42—114no—
350#95—114no—
351#95—114no—
352#95—114no—
353#95—114no—
354#95—114no—
355#95—114no—
356#95—114no—
357#95—114no—
358#95—114no—
359#95—114no—
360#95C22×D1114yes—
361#95C22×D1114yes—
362#95C22×D1114yes—
363C2×C11—24no—
364C2×C11C2×#54111yescharacteristic
365C2×C11#349011yescharacteristic
366C2×C11#349211yescharacteristic
367C2×C11#353612yes—
368C2×C11#353812yes—
369D11—42no—
370D11—42no—
371C24—111no—
372C24—111no—
373C24—222no—
374C24—222no—
375C24—222no—
376C24—224no—
377C24—442no—
378C24C23×D1111yescharacteristic
379C2×Q8—24no—
380C2×Q8—42no—
381C2×Q8—42no—
382C22×C4—24no—
383C22×C4—42no—
384C22×C4—42no—
385C22×C4—42no—
386C22×C4—112no—
387C22×C4—114no—
388C22×C4—114no—
389C22×C4—114no—
390C22×C4—224no—
391C22×C4—224no—
392C22×C4—224no—
393C22×C4—222no—
394C22×C4—224no—
395C22×C4—224no—
396C22×C4—224no—
397C22×C4—442no—
398C22×C4—442no—
399C22×C4—4416no—
400C22×C4—442no—
401C22×C4—442no—
402C22×C4#434114yes—
403C22×C4C23×D1114yes—
404C22×C4C23×D1114yes—
405C22×C4C23×D1114yes—
406C22×C4C23×D1112yes—
407C4⋊C4—24no—
408C4⋊C4—28no—
409C4⋊C4—44no—
410C4⋊C4—44no—
411C4⋊C4—228no—
412C4⋊C4—228no—
413C4⋊C4—228no—
414C4⋊C4—444no—
415C4⋊C4—442no—
416C4⋊C4—442no—
417C4⋊C4—444no—
418C4⋊C4—444no—
419C4⋊C4—444no—
420C4⋊C4—444no—
421C22⋊C4—28no—
422C22⋊C4—228no—
423C22⋊C4—228no—
424C22⋊C4—228no—
425C22⋊C4—228no—
426C22⋊C4—444no—
427C22⋊C4—444no—
428C22⋊C4—444no—
429C42—444no—
430C42—444no—
431C11#3672811yescharacteristic, complemented, Sylow
432C23—22no—
433C23—21no—
434C23—21no—
435C23—112no—
436C23—112no—
437C23—228no—
438C23—221no—
439C23—221no—
440C23—222no—
441C23—222no—
442C23—221no—
443C23—222no—
444C23—222no—
445C23—221no—
446C23—448no—
447C23—448no—
448C23—444no—
449C23—444no—
450C23C2×#434112yes—
451C23#6704014yes—
452C23C24×D1111yescharacteristic
453Q8—84no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—44no—
466C2×C4—84no—
467C2×C4—114no—
468C2×C4—228no—
469C2×C4—222no—
470C2×C4—222no—
471C2×C4—224no—
472C2×C4—224no—
473C2×C4—224no—
474C2×C4—224no—
475C2×C4—224no—
476C2×C4—224no—
477C2×C4—224no—
478C2×C4—224no—
479C2×C4—224no—
480C2×C4—448no—
481C2×C4—448no—
482C2×C4—884no—
483C2×C4C2×#434114yes—
484C22—22no—
485C22—22no—
486C22—24no—
487C22—24no—
488C22—222no—
489C22—222no—
490C22—224no—
491C22—224no—
492C22—4416no—
493C22—441no—
494C22—441no—
495C22—441no—
496C22—441no—
497C22—442no—
498C22—442no—
499C22#1062326214yes—
500C22C22×#434111yescharacteristic
501C22C2×#6704012yes—
502C22D11×H(5,𝔽2)12yes—
503C22D11×H(5,𝔽2)11yescharacteristic
504C22D11×2−1+411yescharacteristic
505C4—24no—
506C4—44no—
507C4—44no—
508C4—44no—
509C4—224no—
510C4—444no—
511C4—444no—
512C4—444no—
513C2—24no—
514C2—442no—
515C2—442no—
516C2C2×#1062326211yescharacteristic
517C2#1308230411yescharacteristic
518C2#1308232311yescharacteristic
519C2#1308284212yes—
520C2#1308285812yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2659C2
prime radicalC24×D11C23
hypercenter#2659D11
hypocenterC11#36728
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2659

Complements

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

NH ≅ G/Ntype
2. #13075817C2semidirect
3. #13075527C2semidirect
4. #13075281C2semidirect
5. #13075081C2semidirect
6. #13074586C2semidirect
8. #13072762C2semidirect
9. #13071351C2semidirect
11. C11×#2659C2semidirect
19. C2×#66942C22semidirect
20. C11×#398C22semidirect
21. C11×#395C22semidirect
24. #10622843C22semidirect
35. #10622598C22semidirect
36. #10622596C22semidirect
37. #10622594C22semidirect
38. #10622594C22semidirect
39. #10622593C22semidirect
40. #10622591C22semidirect
51. #10622273C22semidirect
52. #10622271C22semidirect
53. #10622270C22semidirect
54. #10622270C22semidirect
55. #10622265C22semidirect
56. #10622260C22semidirect
177. #2659D11semidirect
249. #398C2×D11semidirect
254. #395C2×D11semidirect
431. C11#36728semidirect

Maximal subgroups

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

subgroupindex
#130769002
#130758172
#130755272
#130752812
#130750812
#130745862
#130728672
#130727622
#130713512
C2×#106222802
C11×#26592
#3672811