Finite Group Databasebeta

← #14960620

Subgroups — #14960620

Order 2816.

2422 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66947C211yesmaximal, characteristic
2#13076900C212yesmaximal, complemented
3#13075130C218yesmaximal, complemented
4#13074892C218yesmaximal, complemented
5#13074423C212yesmaximal, complemented
6#13073997C212yesmaximal, complemented
7#13072886C212yesmaximal, complemented
8#13072886C212yesmaximal, complemented
9#13072268C212yesmaximal
10#13071219C211yesmaximal, characteristic, complemented
11C2×C11×#544C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C23×C4×D11C2211yescharacteristic
14C11×#544—28no—
15C2×C11×C4⋊Q8C2214yescomplemented
16C2×C11×#125C2214yescomplemented
17C2×C11×C22⋊Q8C2212yes—
18C2×C11×C22⋊Q8C2212yes—
19C2×C11×#117C2212yes—
20C22×C11×C4⋊C4C2211yescharacteristic
21C2×#67000C2214yes—
22C2×#66999C2214yescomplemented
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C2×#66947—28no—
28C2×#66947C2218yes—
29#10622844C2214yescomplemented
30#10622842C2214yescomplemented
31#10622825C2212yes—
32#10622824C2212yes—
33C4×C22⋊Dic11C2212yes—
34#10622607C2218yescomplemented
35#10622606C2214yescomplemented
36#10622606C2214yescomplemented
37#10622605C2214yescomplemented
38#10622605C2214yescomplemented
39#10622605C2214yescomplemented
40#10622604C2218yes—
41#10622602C2218yescomplemented
42#10622601C2214yes—
43#10622600C2214yescomplemented
44#10622594C2218yescomplemented
45#10622593C2214yescomplemented
46#10622585C2218yescomplemented
47#10622568C2214yes—
48#10622568C2214yes—
49#10622559C2214yes—
50#10622559C2214yes—
51#10622553C2218yescomplemented
52#10622553C2218yescomplemented
53C24×D11C2311yescharacteristic
54C24×D11C2311yescharacteristic
55C22×Q8×C11C2312yes—
56C22×Q8×C11C2312yes—
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×Dic11C2311yescharacteristic
61C23×Dic11C2311yescharacteristic
62C22×D44—24no—
63C22×D44—44no—
64C22×D44C2314yes—
65C22×C4×D11—24no—
66C22×C4×D11—44no—
67C22×C4×D11C2314yes—
68C11×C4⋊Q8—216no—
69C11×#125—216no—
70C11×C22⋊Q8—28no—
71C11×C22⋊Q8—28no—
72C11×#117—28no—
73C2×C11×C4⋊C4D418yes—
74C2×C11×C4⋊C4C2314yes—
75C2×C11×C4⋊C4C2312yes—
76C2×C11×C4⋊C4C2312yes—
77C2×C11×C4⋊C4C2314yes—
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C4⋊C4C2314yes—
81C2×C11×C22⋊C4C2314yes—
82C2×C42×C11C2314yes—
83C2×C22⋊Dic11C2314yes—
84#67000—48no—
85#66999—48no—
86C2×(C2×D11)⋊C4—24no—
87C2×(C2×D11)⋊C4—24no—
88C2×(C2×D11)⋊C4—24no—
89C2×(C2×D11)⋊C4C2314yes—
90C2×(C2×D11)⋊C4C2314yes—
91C2×(C2×D11)⋊C4C2314yes—
92C2×(C2×D11)⋊C4C2318yes—
93C2×(C2×D11)⋊C4C2318yes—
94C2×(C2×D11)⋊C4C2318yes—
95C2×(C2×D11)⋊C4C2318yes—
96C2×C4⋊Dic11C2314yes—
97C2×Dic11⋊C4—24no—
98C2×Dic11⋊C4C2314yes—
99C2×Dic11⋊C4C2318yes—
100C2×Dic11⋊C4C2318yes—
101C2×C4×Dic11C2314yes—
102#66947—232no—
103C11⋊#95C2314yes—
104C11⋊#95C2314yes—
105C11⋊#95C2318yes—
106C11⋊#95C2318yes—
107C11⋊#95C2314yes—
108C11⋊#95C2314yes—
109#36711—111nomaximal, Sylow
110C24×C11C2411yescharacteristic
111C23×D11—22no—
112C23×D11—24no—
113C23×D11—22no—
114C23×D11—24no—
115C23×D11—24no—
116C23×D11—42no—
117C23×D11—42no—
118C23×D11—42no—
119C23×D11C2412yes—
120C23×D11C2412yes—
121C2×Q8×C11—24no—
122C2×Q8×C11—24no—
123C2×Q8×C11—44no—
124C2×Q8×C11—44no—
125C22×C4×C11—24no—
126C22×C4×C11—42no—
127C22×C4×C11—42no—
128C22×C4×C11C2×D414yes—
129C22×C4×C11C2×D414yes—
130C22×C4×C11C2×D414yes—
131C22×C4×C11C2414yes—
132C22×C4×C11C2414yes—
133C22×C4×C11C2412yes—
134C22×C4×C11C2412yes—
135C22×C4×C11C2412yes—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—42no—
139C22×Dic11—42no—
140C22×Dic11C2418yes—
141C22×Dic11C2412yes—
142C22×Dic11C2412yes—
143C2×D44—28no—
144C2×D44—28no—
145C2×D44—44no—
146C2×D44—416no—
147C2×C4×D11—28no—
148C2×C4×D11—28no—
149C2×C4×D11—44no—
150C2×C4×D11—416no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—24no—
155C11×C4⋊C4—28no—
156C11×C4⋊C4—28no—
157C11×C4⋊C4C2×D4116yes—
158C11×C22⋊C4—28no—
159C42×C11—28no—
160C22⋊Dic11—28no—
161(C2×D11)⋊C4—216no—
162(C2×D11)⋊C4—28no—
163(C2×D11)⋊C4—28no—
164(C2×D11)⋊C4—28no—
165(C2×D11)⋊C4—48no—
166(C2×D11)⋊C4—48no—
167(C2×D11)⋊C4—48no—
168C4⋊Dic11—44no—
169Dic11⋊C4—28no—
170Dic11⋊C4—48no—
171Dic11⋊C4—48no—
172C4×Dic11—44no—
173C2×#544D1111yescharacteristic, complemented
174C22×#123—111no—
175#2848—112no—
176#2694—118no—
177#2674—118no—
178#2626—112no—
179#2583—112no—
180#2482—112no—
181#2482—112no—
182#2435—112no—
183#2313—111no—
184C23×C11—22no—
185C23×C11—22no—
186C23×C11C22×D412yes—
187C23×C112−1+414yes—
188C23×C11C2511yescharacteristic
189C22×D11—28no—
190C22×D11—22no—
191C22×D11—22no—
192C22×D11—24no—
193C22×D11—24no—
194C22×D11—22no—
195C22×D11—24no—
196C22×D11—24no—
197C22×D11—24no—
198C22×D11—416no—
199C22×D11—44no—
200C22×D11—44no—
201C22×D11—44no—
202C22×D11—44no—
203C22×D11—44no—
204C22×D11—88no—
205C22×D11H(5,𝔽2)14yes—
206Q8×C11—84no—
207Q8×C11—84no—
208C2×C4×C11—28no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—28no—
215C2×C4×C11—28no—
216C2×C4×C11—44no—
217C2×C4×C11—44no—
218C2×C4×C11C22×D414yes—
219C2×C4×C11C22×D414yes—
220C2×C4×C11C22×D414yes—
221C2×Dic11—22no—
222C2×Dic11—22no—
223C2×Dic11—28no—
224C2×Dic11—24no—
225C2×Dic11—28no—
226C2×Dic11—24no—
227C2×Dic11—28no—
228C2×Dic11—44no—
229C2×Dic11—44no—
230D44—416no—
231C4×D11—416no—
232C23×D4—111no—
233C24×C4—111no—
234#544—28no—
235C2×C4⋊Q8C2×D1114yescomplemented
236C2×#125C2×D1114yescomplemented
237C2×#124—114no—
238C2×#123—118no—
239C2×#123—228no—
240C2×C22⋊Q8—114no—
241C2×C22⋊Q8C2×D1112yes—
242C2×C22⋊Q8C2×D1112yes—
243C2×#117C2×D1112yes—
244C22×C4⋊C4—111no—
245C22×C4⋊C4C2×D1111yescharacteristic
246C22×C22⋊C4—111no—
247C22×C22⋊C4—111no—
248C22×C22⋊C4—111no—
249#399—114no—
250#399—114no—
251#399—114no—
252#398—114no—
253#397—114no—
254#397—114no—
255#396—118no—
256#395—114no—
257#394—118no—
258#393—114no—
259#390—114no—
260#389—118no—
261#388—118no—
262#388—118no—
263#387—118no—
264#385—118no—
265#385—114no—
266#385—114no—
267#381—112no—
268#380—112no—
269#380—114no—
270#379—114no—
271#379—114no—
272C4×C22⋊C4—112no—
273C22×C11—22no—
274C22×C11—22no—
275C22×C11—28no—
276C22×C11#53614yes—
277C22×C11C23×D411yescharacteristic
278C22×C11C2×H(5,𝔽2)12yes—
279C22×C11C2×2−1+412yes—
280C22×C11#58512yes—
281C2×D11—24no—
282C2×D11—28no—
283C2×D11—416no—
284C2×D11—42no—
285C2×D11—42no—
286C2×D11—44no—
287C2×D11—42no—
288C2×D11—42no—
289C2×D11—42no—
290C2×D11—48no—
291C2×D11—88no—
292C4×C11—24no—
293C4×C11—24no—
294C4×C11—24no—
295C4×C11—44no—
296C4×C11—44no—
297Dic11—42no—
298Dic11—42no—
299Dic11—48no—
300C25—111no—
301C25—111no—
302C22×Q8C22×D1112yes—
303C22×Q8C22×D1112yes—
304C22×D4—114no—
305C22×D4—224no—
306C22×D4—444no—
307C23×C4—111no—
308C23×C4—111no—
309C23×C4—114no—
310C23×C4—224no—
311C23×C4—444no—
312C23×C4C22×D1111yescharacteristic
313C23×C4C22×D1111yescharacteristic
314C23×C4C22×D1111yescharacteristic
315C4⋊Q8—216no—
316#125—216no—
317#124—448no—
318#123—2232no—
319C22⋊Q8—28no—
320C22⋊Q8—28no—
321C22⋊Q8—448no—
322#117—28no—
323C2×C4⋊C4—114no—
324C2×C4⋊C4—114no—
325C2×C4⋊C4—118no—
326C2×C4⋊C4—118no—
327C2×C4⋊C4—224no—
328C2×C4⋊C4C22⋊D1118yes—
329C2×C4⋊C4C22×D1112yes—
330C2×C4⋊C4C22×D1112yes—
331C2×C4⋊C4C22×D1112yes—
332C2×C4⋊C4C22×D1112yes—
333C2×C4⋊C4C22×D1114yes—
334C2×C4⋊C4C22×D1114yes—
335C2×C4⋊C4C22×D1114yes—
336C2×C22⋊C4—114no—
337C2×C22⋊C4—114no—
338C2×C22⋊C4—114no—
339C2×C22⋊C4—114no—
340C2×C22⋊C4—118no—
341C2×C22⋊C4—118no—
342C2×C22⋊C4—118no—
343C2×C22⋊C4—118no—
344C2×C22⋊C4—224no—
345C2×C22⋊C4—224no—
346C2×C22⋊C4—224no—
347C2×C22⋊C4C22×D1114yes—
348C2×C42—114no—
349C2×C42C22×D1114yes—
350#95—114no—
351#95—114no—
352#95—118no—
353#95—114no—
354#95—114no—
355#95—118no—
356C2×C11—24no—
357C2×C11C2×#53611yescharacteristic
358C2×C11#348411yescharacteristic
359C2×C11#348711yescharacteristic
360C2×C11#353514yes—
361D11—44no—
362D11—82no—
363C24—112no—
364C24—112no—
365C24—224no—
366C24—222no—
367C24—224no—
368C24—222no—
369C24—224no—
370C24—442no—
371C24—442no—
372C24—442no—
373C24C23×D1111yescharacteristic
374C2×Q8—24no—
375C2×Q8—24no—
376C2×Q8—44no—
377C2×Q8—44no—
378C2×D4—228no—
379C2×D4—228no—
380C2×D4—444no—
381C2×D4—4416no—
382C22×C4—24no—
383C22×C4—42no—
384C22×C4—42no—
385C22×C4—118no—
386C22×C4—112no—
387C22×C4—112no—
388C22×C4—228no—
389C22×C4—222no—
390C22×C4—222no—
391C22×C4—228no—
392C22×C4—444no—
393C22×C4—4416no—
394C22×C4—442no—
395C22×C4—442no—
396C22×C4C2×C22⋊D1114yes—
397C22×C4C2×C22⋊D1114yes—
398C22×C4C2×C22⋊D1114yes—
399C22×C4C23×D1114yes—
400C22×C4C23×D1114yes—
401C22×C4C23×D1112yes—
402C22×C4C23×D1112yes—
403C22×C4C23×D1112yes—
404C4⋊C4—24no—
405C4⋊C4—24no—
406C4⋊C4—24no—
407C4⋊C4—24no—
408C4⋊C4—28no—
409C4⋊C4—28no—
410C4⋊C4—228no—
411C4⋊C4—448no—
412C4⋊C4—444no—
413C4⋊C4—448no—
414C4⋊C4C2×C22⋊D11116yes—
415C22⋊C4—28no—
416C22⋊C4—2216no—
417C22⋊C4—228no—
418C22⋊C4—228no—
419C22⋊C4—228no—
420C22⋊C4—228no—
421C22⋊C4—448no—
422C22⋊C4—448no—
423C22⋊C4—448no—
424C42—28no—
425C42—444no—
426C11#3671111yescharacteristic, complemented, Sylow
427C23—22no—
428C23—22no—
429C23—114no—
430C23—228no—
431C23—224no—
432C23—222no—
433C23—224no—
434C23—222no—
435C23—224no—
436C23—224no—
437C23—224no—
438C23—222no—
439C23—4416no—
440C23—444no—
441C23—444no—
442C23—444no—
443C23—444no—
444C23—444no—
445C23—888no—
446C23#6704014yes—
447C23C22×C22⋊D1112yes—
448C23C24×D1111yescharacteristic
449Q8—84no—
450Q8—84no—
451D4—4416no—
452C2×C4—28no—
453C2×C4—24no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—28no—
457C2×C4—28no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—44no—
461C2×C4—44no—
462C2×C4—228no—
463C2×C4—228no—
464C2×C4—224no—
465C2×C4—228no—
466C2×C4—224no—
467C2×C4—222no—
468C2×C4—222no—
469C2×C4—4416no—
470C2×C4—444no—
471C2×C4—444no—
472C2×C4C22×C22⋊D1114yes—
473C2×C4C22×C22⋊D1114yes—
474C2×C4C22×C22⋊D1114yes—
475C22—22no—
476C22—22no—
477C22—28no—
478C22—224no—
479C22—228no—
480C22—4416no—
481C22—442no—
482C22—442no—
483C22—444no—
484C22—442no—
485C22—442no—
486C22—442no—
487C22—448no—
488C22—888no—
489C22#1062334714yes—
490C22C2×#6704012yes—
491C22D11×H(5,𝔽2)12yes—
492C22#1062345712yes—
493C22C23×C22⋊D1111yescharacteristic
494C4—24no—
495C4—24no—
496C4—24no—
497C4—44no—
498C4—44no—
499C4—442no—
500C4—442no—
501C4—448no—
502C2—24no—
503C2—444no—
504C2—882no—
505C2C2×#1062334711yescharacteristic
506C2#1308224711yescharacteristic
507C2#1308227111yescharacteristic
508C2#1308282614yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC2×C11×#544C2
prime radicalC23×D44C22
hypercenterC2×#544D11
hypocenterC11#36711
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
2. #13076900C2semidirect
3. #13075130C2semidirect
4. #13074892C2semidirect
5. #13074423C2semidirect
6. #13073997C2semidirect
7. #13072886C2semidirect
8. #13072886C2semidirect
10. #13071219C2semidirect
11. C2×C11×#544C2semidirect
15. C2×C11×C4⋊Q8C22semidirect
16. C2×C11×#125C22semidirect
22. C2×#66999C22semidirect
29. #10622844C22semidirect
30. #10622842C22semidirect
34. #10622607C22semidirect
35. #10622606C22semidirect
36. #10622606C22semidirect
37. #10622605C22semidirect
38. #10622605C22semidirect
39. #10622605C22semidirect
41. #10622602C22semidirect
43. #10622600C22semidirect
44. #10622594C22semidirect
45. #10622593C22semidirect
46. #10622585C22semidirect
51. #10622553C22semidirect
52. #10622553C22semidirect
173. C2×#544D11semidirect
235. C2×C4⋊Q8C2×D11semidirect
236. C2×#125C2×D11semidirect
426. C11#36711semidirect

Maximal subgroups

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

subgroupindex
C22×#669472
#130769002
#130751302
#130748922
#130744232
#130739972
#130728862
#130722682
#130712192
C2×C11×#5442
#3671111