Finite Group Databasebeta

← #14960996

Subgroups — #14960996

Order 2816.

1770 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076900C212yesmaximal
2#13075777C214yesmaximal, complemented
3#13075700C214yesmaximal, complemented
4#13075197C214yesmaximal, complemented
5#13075066C214yesmaximal, complemented
6#13074586C211yesmaximal, characteristic, complemented
7#13073113C214yesmaximal, complemented
8#13072867C214yesmaximal
9#13071351C212yesmaximal, complemented
10C2×#10622277C211yesmaximal, characteristic
11C11×#2659C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C2×C11×C22⋊Q8C2212yes—
14C2×#66999C2212yes—
15C2×#66999C2212yes—
16C22×(C2×D11)⋊C4C2212yes—
17C2×#66951C2214yes—
18C11×#398C2214yescomplemented
19C11×#395C2214yescomplemented
20C11×#380C2214yes—
21C2×C11×#95C2211yescharacteristic
22#10622843C2214yescomplemented
23#10622825C2212yes—
24#10622823C2214yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2211yescharacteristic
27#10622607C2214yes—
28#10622606C2214yes—
29#10622603C2214yes—
30#10622602C2214yes—
31#10622602C2214yes—
32#10622600C2212yes—
33#10622600C2212yes—
34#10622598C2214yescomplemented
35#10622597C2214yescomplemented
36#10622595C2214yescomplemented
37#10622594C2214yescomplemented
38#10622594C2214yescomplemented
39#10622594C2214yescomplemented
40#10622585C2214yescomplemented
41#10622568C2214yes—
42#10622563C2214yes—
43#10622559C2214yes—
44C22⋊C4×Dic11C2214yes—
45#10622288C2214yes—
46#10622287C2214yes—
47#10622283C2214yes—
48#10622282C2214yes—
49#10622277C2214yes—
50#10622277C2214yes—
51#10622273C2214yescomplemented
52#10622272C2214yescomplemented
53#10622271C2214yescomplemented
54#10622270C2214yescomplemented
55#10622266C2214yescomplemented
56#10622263C2214yescomplemented
57C24×D11C2311yescharacteristic
58C22×Q8×C11C2312yes—
59C23×C4×C11C2312yes—
60C23×C4×C11C2311yescharacteristic
61C23×Dic11C2312yes—
62C23×Dic11C2311yescharacteristic
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⋊C4C2314yes—
88C2×Dic11⋊C4C2314yes—
89C2×Dic11⋊C4C2314yes—
90C2×Dic11⋊C4C2314yes—
91C2×C4×Dic11C2314yes—
92C2×C4×Dic11C2314yes—
93#66951—48no—
94C11×#95C2314yes—
95C11×#95C2314yes—
96C11×#95C2314yes—
97C11⋊#95C2314yes—
98C11⋊#95C2314yes—
99C11⋊#95C2314yes—
100C11⋊#95C2314yes—
101C11⋊#95C2314yes—
102C11⋊#95C2314yes—
103C11⋊#95C2314yes—
104C11⋊#95C2314yes—
105C11⋊#95C2314yes—
106C11⋊#95C2314yes—
107C11⋊#95C2314yes—
108C11⋊#95C2314yes—
109#36732—111nomaximal, Sylow
110C24×C11C2411yescharacteristic
111C23×D11—22no—
112C23×D11—24no—
113C23×D11—24no—
114C23×D11—41no—
115C23×D11—41no—
116C23×D11C2412yes—
117C2×Q8×C11—24no—
118C2×Q8×C11—42no—
119C2×Q8×C11—42no—
120C22×C4×C11—24no—
121C22×C4×C11—42no—
122C22×C4×C11—42no—
123C22×C4×C11—42no—
124C22×C4×C11#4114yes—
125C22×C4×C11C2414yes—
126C22×C4×C11C2414yes—
127C22×C4×C11C2414yes—
128C22×C4×C11C2412yes—
129C22×Dic11—22no—
130C22×Dic11—24no—
131C22×Dic11—42no—
132C22×Dic11—42no—
133C22×Dic11—42no—
134C22×Dic11C2414yes—
135C22×Dic11C2411yescharacteristic
136C22×Dic11C2411yescharacteristic
137C22×Dic11C2414yes—
138C22×Dic11C2414yes—
139C2×C4×D11—24no—
140C2×C4×D11—24no—
141C2×C4×D11—24no—
142C2×C4×D11—24no—
143C2×C4×D11—42no—
144C2×C4×D11—42no—
145C2×C4×D11—416no—
146C11×C4⋊C4—24no—
147C11×C4⋊C4—28no—
148C11×C4⋊C4—44no—
149C11×C4⋊C4—44no—
150C11×C22⋊C4—28no—
151C22⋊Dic11—28no—
152(C2×D11)⋊C4—28no—
153(C2×D11)⋊C4—28no—
154(C2×D11)⋊C4—28no—
155(C2×D11)⋊C4—44no—
156(C2×D11)⋊C4—44no—
157(C2×D11)⋊C4—44no—
158C4⋊Dic11—44no—
159C4⋊Dic11—44no—
160C4⋊Dic11—42no—
161C4⋊Dic11—42no—
162Dic11⋊C4—44no—
163Dic11⋊C4—44no—
164Dic11⋊C4—44no—
165Dic11⋊C4—44no—
166C4×Dic11—44no—
167C4×Dic11—44no—
168#2848—112no—
169#2744—114no—
170#2739—114no—
171#2698—114no—
172#2689—114no—
173#2659D1111yescharacteristic, complemented
174#2646—111no—
175#2505—114no—
176#2480—114no—
177#2329—112no—
178C2×#381—111no—
179C23×C11—22no—
180C23×C11—21no—
181C23×C11—21no—
182C23×C11C2×#4112yes—
183C23×C112−1+414yes—
184C23×C11C2511yescharacteristic
185C22×D11—28no—
186C22×D11—22no—
187C22×D11—22no—
188C22×D11—22no—
189C22×D11—22no—
190C22×D11—22no—
191C22×D11—22no—
192C22×D11—48no—
193C22×D11—48no—
194C22×D11—44no—
195C22×D11—44no—
196C22×D11H(5,𝔽2)14yes—
197Q8×C11—84no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—24no—
201C2×C4×C11—24no—
202C2×C4×C11—24no—
203C2×C4×C11—24no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—44no—
210C2×C4×C11—84no—
211C2×C4×C11C2×#4114yes—
212C2×Dic11—21no—
213C2×Dic11—21no—
214C2×Dic11—24no—
215C2×Dic11—24no—
216C2×Dic11—24no—
217C2×Dic11—22no—
218C2×Dic11—22no—
219C2×Dic11—24no—
220C2×Dic11—24no—
221C2×Dic11—24no—
222C2×Dic11—24no—
223C2×Dic11—24no—
224C2×Dic11—24no—
225C2×Dic11—44no—
226C2×Dic11—84no—
227C4×D11—48no—
228C4×D11—48no—
229C24×C4—111no—
230C2×#126—114no—
231C2×C22⋊Q8—112no—
232C2×C22⋊Q8—112no—
233C2×C22⋊Q8C2×D1112yes—
234C22×C22⋊C4—112no—
235#400—114no—
236#400—114no—
237#400—114no—
238#400—114no—
239#398—114no—
240#398—114no—
241#398C2×D1114yescomplemented
242#397—114no—
243#397—114no—
244#397—114no—
245#396—114no—
246#395C2×D1114yescomplemented
247#391—114no—
248#389—114no—
249#389—114no—
250#388—114no—
251#388—114no—
252#388—114no—
253#387—114no—
254#387—114no—
255#387—114no—
256#387—114no—
257#385—114no—
258#385—114no—
259#385—114no—
260#385—114no—
261#385—114no—
262#382—114no—
263#381—114no—
264#381—114no—
265#380—112no—
266#380—112no—
267#380—112no—
268#380C2×D1114yes—
269#379—114no—
270C4×C22⋊C4—114no—
271C2×#95—111no—
272C2×#95—112no—
273C2×#95C2×D1111yescharacteristic
274C22×C11—22no—
275C22×C11—22no—
276C22×C11—24no—
277C22×C11—24no—
278C22×C11#54114yes—
279C22×C11C22×#4111yescharacteristic
280C22×C11C2×H(5,𝔽2)12yes—
281C22×C11C2×2−1+412yes—
282C22×C11#58511yescharacteristic
283C22×C11#58511yescharacteristic
284C2×D11—24no—
285C2×D11—24no—
286C2×D11—24no—
287C2×D11—416no—
288C2×D11—42no—
289C2×D11—42no—
290C2×D11—42no—
291C2×D11—42no—
292C4×C11—24no—
293C4×C11—44no—
294C4×C11—44no—
295C4×C11—44no—
296Dic11—41no—
297Dic11—41no—
298Dic11—44no—
299Dic11—44no—
300Dic11—44no—
301C25—111no—
302C22×Q8C22×D1112yes—
303C23×C4—112no—
304C23×C4—111no—
305C23×C4—112no—
306C23×C4—112no—
307C23×C4—224no—
308C23×C4—444no—
309C23×C4C22×D1112yes—
310C23×C4C22×D1111yescharacteristic
311#126—448no—
312C22⋊Q8—28no—
313C22⋊Q8—444no—
314C22⋊Q8—444no—
315C2×C4⋊C4—112no—
316C2×C4⋊C4—112no—
317C2×C4⋊C4—114no—
318C2×C4⋊C4—114no—
319C2×C4⋊C4—114no—
320C2×C4⋊C4—114no—
321C2×C4⋊C4—114no—
322C2×C4⋊C4—114no—
323C2×C4⋊C4C22×D1112yes—
324C2×C4⋊C4C22×D1114yes—
325C2×C4⋊C4C22×D1114yes—
326C2×C4⋊C4C22×D1114yes—
327C2×C22⋊C4—114no—
328C2×C22⋊C4—114no—
329C2×C22⋊C4—114no—
330C2×C22⋊C4—114no—
331C2×C22⋊C4—114no—
332C2×C22⋊C4—114no—
333C2×C22⋊C4—114no—
334C2×C22⋊C4—444no—
335C2×C22⋊C4C22×D1114yes—
336C2×C42—114no—
337C2×C42—114no—
338#95—114no—
339#95—114no—
340#95—114no—
341#95—114no—
342#95—114no—
343#95—114no—
344#95—114no—
345#95—114no—
346#95—114no—
347#95—114no—
348#95—114no—
349#95—114no—
350#95C22×D1114yes—
351#95C22×D1114yes—
352#95C22×D1114yes—
353C2×C11—24no—
354C2×C11C2×#54111yescharacteristic
355C2×C11#349011yescharacteristic
356C2×C11#349311yescharacteristic
357C2×C11#353512yes—
358C2×C11#353512yes—
359D11—44no—
360C24—112no—
361C24—224no—
362C24—222no—
363C24—224no—
364C24—441no—
365C24—441no—
366C24C23×D1111yescharacteristic
367C2×Q8—24no—
368C2×Q8—42no—
369C2×Q8—42no—
370C22×C4—24no—
371C22×C4—42no—
372C22×C4—42no—
373C22×C4—42no—
374C22×C4—114no—
375C22×C4—111no—
376C22×C4—111no—
377C22×C4—114no—
378C22×C4—114no—
379C22×C4—224no—
380C22×C4—224no—
381C22×C4—222no—
382C22×C4—224no—
383C22×C4—224no—
384C22×C4—224no—
385C22×C4—442no—
386C22×C4—442no—
387C22×C4—4416no—
388C22×C4—442no—
389C22×C4—442no—
390C22×C4—442no—
391C22×C4#434114yes—
392C22×C4C23×D1114yes—
393C22×C4C23×D1114yes—
394C22×C4C23×D1114yes—
395C22×C4C23×D1112yes—
396C4⋊C4—24no—
397C4⋊C4—28no—
398C4⋊C4—44no—
399C4⋊C4—44no—
400C4⋊C4—444no—
401C4⋊C4—444no—
402C4⋊C4—442no—
403C4⋊C4—442no—
404C4⋊C4—444no—
405C4⋊C4—444no—
406C4⋊C4—444no—
407C4⋊C4—444no—
408C22⋊C4—28no—
409C22⋊C4—228no—
410C22⋊C4—228no—
411C22⋊C4—228no—
412C22⋊C4—228no—
413C22⋊C4—444no—
414C22⋊C4—444no—
415C22⋊C4—444no—
416C42—444no—
417C42—444no—
418C11#3673211yescharacteristic, complemented, Sylow
419C23—22no—
420C23—21no—
421C23—21no—
422C23—114no—
423C23—228no—
424C23—222no—
425C23—222no—
426C23—222no—
427C23—222no—
428C23—222no—
429C23—222no—
430C23—448no—
431C23—448no—
432C23—444no—
433C23—444no—
434C23C2×#434112yes—
435C23#6704014yes—
436C23C24×D1111yescharacteristic
437Q8—84no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—24no—
441C2×C4—24no—
442C2×C4—24no—
443C2×C4—24no—
444C2×C4—24no—
445C2×C4—24no—
446C2×C4—24no—
447C2×C4—24no—
448C2×C4—24no—
449C2×C4—44no—
450C2×C4—84no—
451C2×C4—221no—
452C2×C4—221no—
453C2×C4—224no—
454C2×C4—224no—
455C2×C4—224no—
456C2×C4—224no—
457C2×C4—224no—
458C2×C4—224no—
459C2×C4—222no—
460C2×C4—222no—
461C2×C4—224no—
462C2×C4—224no—
463C2×C4—224no—
464C2×C4—448no—
465C2×C4—448no—
466C2×C4—444no—
467C2×C4—884no—
468C2×C4C2×#434114yes—
469C22—22no—
470C22—24no—
471C22—24no—
472C22—22no—
473C22—224no—
474C22—224no—
475C22—224no—
476C22—4416no—
477C22—442no—
478C22—442no—
479C22—442no—
480C22—442no—
481C22#1062326214yes—
482C22C22×#434111yescharacteristic
483C22C2×#6704012yes—
484C22D11×H(5,𝔽2)12yes—
485C22#1062345511yescharacteristic
486C22#1062345711yescharacteristic
487C4—24no—
488C4—44no—
489C4—44no—
490C4—44no—
491C4—441no—
492C4—441no—
493C4—444no—
494C4—444no—
495C4—444no—
496C2—24no—
497C2—444no—
498C2C2×#1062326211yescharacteristic
499C2#1308230411yescharacteristic
500C2#1308233511yescharacteristic
501C2#1308282612yes—
502C2#1308283012yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2659C2
prime radicalC24×D11C23
hypercenter#2659D11
hypocenterC11#36732
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2659

Complements

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

NH ≅ G/Ntype
2. #13075777C2semidirect
3. #13075700C2semidirect
4. #13075197C2semidirect
5. #13075066C2semidirect
6. #13074586C2semidirect
7. #13073113C2semidirect
9. #13071351C2semidirect
11. C11×#2659C2semidirect
18. C11×#398C22semidirect
19. C11×#395C22semidirect
22. #10622843C22semidirect
34. #10622598C22semidirect
35. #10622597C22semidirect
36. #10622595C22semidirect
37. #10622594C22semidirect
38. #10622594C22semidirect
39. #10622594C22semidirect
40. #10622585C22semidirect
51. #10622273C22semidirect
52. #10622272C22semidirect
53. #10622271C22semidirect
54. #10622270C22semidirect
55. #10622266C22semidirect
56. #10622263C22semidirect
173. #2659D11semidirect
241. #398C2×D11semidirect
246. #395C2×D11semidirect
418. C11#36732semidirect

Maximal subgroups

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

subgroupindex
#130769002
#130757772
#130757002
#130751972
#130750662
#130745862
#130731132
#130728672
#130713512
C2×#106222772
C11×#26592
#3673211