Finite Group Databasebeta

← #14767644

Subgroups — #14767644

Order 2816.

986 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071342C211yesmaximal, characteristic, complemented
2#13071329C211yesmaximal, characteristic, complemented
3#13069428C211yesmaximal, characteristic, complemented
4#13069423C211yesmaximal, characteristic, complemented
5#13068973C212yesmaximal, complemented
6#13068966C212yesmaximal, complemented
7#13068966C212yesmaximal, complemented
8#13068952C212yesmaximal, complemented
9#13068750C211yesmaximal, characteristic, complemented
10#13068369C211yesmaximal, characteristic, complemented
11C2×C11×#496C211yesmaximal, characteristic
12C22×C11×SD16C2212yes—
13C22×C11×D8C2212yes—
14C2×C11×#127C2211yescharacteristic
15C2×C11×#124C2211yescharacteristic
16C2×Q8×Dic11C2211yescharacteristic
17C2×D4×Dic11C2212yes—
18C2×D4×Dic11C2211yescharacteristic
19C11×#496C418yescomplemented
20C2×C11×#97C2211yescharacteristic
21#10622843C2211yescharacteristic
22C2×#66899C2212yes—
23#10622834C2211yescharacteristic
24#10622834C2212yes—
25#10622833—22no—
26#10622833—22no—
27C2×#66896C2212yes—
28C2×#66896C2212yes—
29C2×#66896C2212yes—
30#10622564—22no—
31#10622563—22no—
32#10622549C2211yescharacteristic
33#10622548C2211yescharacteristic
34#10622545C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36#10622189C2212yes—
37#10622189C2212yes—
38#10622188C2212yes—
39#10622188C2212yes—
40C22×Q8×C11C2311yescharacteristic
41C22×D4×C11—22no—
42C22×D4×C11C2311yescharacteristic
43C22×D4×C11C2312yes—
44C23×Dic11—21no—
45C23×Dic11—22no—
46C2×C11×SD16—42no—
47C2×C11×SD16—42no—
48C2×C11×SD16C2×C418yescomplemented
49C2×C11×D8—42no—
50C2×C11×D8—42no—
51C2×C11×D8C2×C418yescomplemented
52C22×C8×C11C2312yes—
53C11×#127—22no—
54C11×#127C2×C414yescomplemented
55C11×#124—22no—
56C11×#124C2×C414yescomplemented
57C2×C11×C22⋊C4—22no—
58C2×C42×C11C2311yescharacteristic
59C2×C22⋊Dic11—21no—
60C2×C22⋊Dic11—22no—
61C2×C22⋊Dic11—22no—
62C2×C22⋊Dic11—22no—
63C2×C22⋊Dic11—22no—
64Q8×Dic11—42no—
65D4×Dic11—42no—
66D4×Dic11—42no—
67D4×Dic11—42no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11—22no—
70C2×C4⋊Dic11C2311yescharacteristic
71C2×C4⋊Dic11C2311yescharacteristic
72C2×C4⋊Dic11C2312yes—
73C2×C4×Dic11—21no—
74C2×C4×Dic11C2311yescharacteristic
75C2×C4×Dic11C2311yescharacteristic
76C22×C11⋊C8C2312yes—
77C11×#97C2×C414yescomplemented
78#66899—42no—
79#66896—42no—
80#66896—42no—
81#66896—42no—
82C11⋊#95—22no—
83C11⋊#95—22no—
84C11⋊#95D412yes—
85C11⋊#95D412yes—
86C4×C11⋊C8—22no—
87#22279—111nomaximal, Sylow
88C24×C11—21no—
89C24×C11—22no—
90C2×Q8×C11—21no—
91C2×Q8×C11—22no—
92C2×Q8×C11—22no—
93C2×Q8×C11C22×C412yes—
94C2×D4×C11—28no—
95C2×D4×C11—21no—
96C2×D4×C11—22no—
97C2×D4×C11—22no—
98C2×D4×C11—22no—
99C2×D4×C11—22no—
100C2×D4×C11—22no—
101C2×D4×C11—22no—
102C2×D4×C11—22no—
103C2×D4×C11—82no—
104C2×D4×C11—82no—
105C2×D4×C11C22×C412yes—
106C2×D4×C11C22×C414yes—
107C22×C4×C11—21no—
108C22×C4×C11C2×D412yes—
109C22×C4×C11C2411yescharacteristic
110C22×Dic11—21no—
111C22×Dic11—22no—
112C22×Dic11—21no—
113C22×Dic11—42no—
114C22×Dic11—44no—
115C22×Dic11—82no—
116C22×Dic11—82no—
117C22×Dic11—82no—
118C22×Dic11C2×D412yes—
119C22×Dic11C2×D411yescharacteristic
120C22×Dic11C2×D411yescharacteristic
121C11×SD16—48no—
122C11×D8—48no—
123C2×C8×C11—22no—
124C2×C8×C11—22no—
125C2×C8×C11C22×C414yes—
126C11×C22⋊C4—28no—
127C42×C11C22×C412yes—
128C42×C11#4112yes—
129C22⋊Dic11—42no—
130C22⋊Dic11—44no—
131C22⋊Dic11—82no—
132C22⋊Dic11—82no—
133C22⋊Dic11—82no—
134C4⋊Dic11—22no—
135C4⋊Dic11—22no—
136C4⋊Dic11—22no—
137C4⋊Dic11—22no—
138C4⋊Dic11—42no—
139C4⋊Dic11—82no—
140C4×Dic11—22no—
141C4×Dic11—22no—
142C4×Dic11—42no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—22no—
146C2×#496D1111yescharacteristic
147#2328—111no—
148#2326—111no—
149#1958—111no—
150#1957—111no—
151#1880—112no—
152#1879—112no—
153#1879—112no—
154#1877—112no—
155#1836—111no—
156#1746—111no—
157C23×C11—22no—
158C23×C11—24no—
159C23×C11—41no—
160C23×C11—42no—
161C23×C11—42no—
162C23×C11—41no—
163C23×C11—42no—
164C23×C11—42no—
165C23×C11—42no—
166C23×C11—42no—
167C23×C11—42no—
168C23×C11—42no—
169C23×C11C22×D411yescharacteristic
170Q8×C11—24no—
171Q8×C11—42no—
172D4×C11—24no—
173D4×C11—24no—
174D4×C11—24no—
175D4×C11—42no—
176D4×C11—42no—
177D4×C11—42no—
178D4×C11—88no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11C4×D414yes—
185C2×C4×C11C23×C411yescharacteristic
186C2×C4×C11C2×#4111yescharacteristic
187C2×C4×C11H(5,𝔽2)12yes—
188C2×C4×C11H(5,𝔽2)12yes—
189C2×Dic11—21no—
190C2×Dic11—21no—
191C2×Dic11—22no—
192C2×Dic11—22no—
193C2×Dic11—22no—
194C2×Dic11—22no—
195C2×Dic11—22no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11—42no—
199C2×Dic11—42no—
200C2×Dic11—42no—
201C2×Dic11—42no—
202C2×Dic11—42no—
203C2×Dic11—84no—
204C2×Dic11—88no—
205C8×C11—24no—
206C11⋊C8—42no—
207C22×SD16C2×D1112yes—
208C22×D8C2×D1112yes—
209C2×#127C2×D1111yescharacteristic
210C2×#124C2×D1111yescharacteristic
211C2×C4×Q8—111no—
212C2×C4×D4—111no—
213C2×C4×D4—112no—
214#496Dic1118yescomplemented
215C2×#103—112no—
216C2×#102—112no—
217C2×#102—112no—
218C2×#102—112no—
219C2×#97C2×D1111yescharacteristic
220C2×C4×C8—111no—
221#391—111no—
222#390—111no—
223#390—112no—
224#388—222no—
225#386—222no—
226#386—222no—
227#385—222no—
228#384—111no—
229#382—111no—
230#376—111no—
231#340—112no—
232#340—112no—
233#336—112no—
234#336—112no—
235C22×C11—42no—
236C22×C11—44no—
237C22×C11—44no—
238C22×C11—44no—
239C22×C11—44no—
240C22×C11—82no—
241C22×C11—81no—
242C22×C11—81no—
243C22×C11—82no—
244C22×C11—82no—
245C22×C11—82no—
246C22×C11—82no—
247C22×C11C2×C4×D411yescharacteristic
248C22×C11#53511yescharacteristic
249C22×C11#53511yescharacteristic
250C22×C11#57612yes—
251C22×C11#57712yes—
252C4×C11—24no—
253C4×C11—42no—
254C4×C11#51812yes—
255C4×C11#54012yes—
256Dic11—41no—
257Dic11—41no—
258Dic11—42no—
259Dic11—81no—
260Dic11—81no—
261Dic11—82no—
262C22×Q8C22×D1111yescharacteristic
263C22×D4—22no—
264C22×D4C22×D1111yescharacteristic
265C22×D4C22×D1112yes—
266C23×C4—221no—
267C23×C4—222no—
268C2×SD16—42no—
269C2×SD16—42no—
270C2×SD16C2×Dic1118yescomplemented
271C2×D8—42no—
272C2×D8—42no—
273C2×D8C2×Dic1118yescomplemented
274C22×C8—112no—
275C22×C8C22×D1112yes—
276#127—22no—
277#127C2×Dic1114yescomplemented
278#124—22no—
279#124C2×Dic1114yescomplemented
280C4×Q8—442no—
281C4×D4—442no—
282C4×D4—442no—
283C4×D4—442no—
284C2×C4⋊C4—112no—
285C2×C4⋊C4—111no—
286C2×C4⋊C4—111no—
287C2×C4⋊C4—221no—
288C2×C4⋊C4—222no—
289C2×C22⋊C4—22no—
290C2×C22⋊C4—222no—
291C2×C22⋊C4—221no—
292C2×C22⋊C4—222no—
293C2×C22⋊C4—222no—
294C2×C22⋊C4—222no—
295C2×C42—111no—
296C2×C42—111no—
297C2×C42—221no—
298C2×C42C22×D1111yescharacteristic
299#103—442no—
300#102—442no—
301#102—442no—
302#102—442no—
303#97C2×Dic1114yescomplemented
304C4×C8—222no—
305#95—112no—
306#95—112no—
307#95—222no—
308#95—222no—
309C2×C11—84no—
310C2×C11—82no—
311C2×C11#232811yescharacteristic
312C2×C11#294612yes—
313C2×C11#322011yescharacteristic
314C2×C11#322111yescharacteristic
315C2×C11#322412yes—
316C24—21no—
317C24—22no—
318C2×Q8—21no—
319C2×Q8—22no—
320C2×Q8—22no—
321C2×Q8C22×Dic1112yes—
322C2×D4—28no—
323C2×D4—21no—
324C2×D4—22no—
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—22no—
328C2×D4—22no—
329C2×D4—22no—
330C2×D4—22no—
331C2×D4—82no—
332C2×D4—82no—
333C2×D4C22×Dic1112yes—
334C2×D4C22×Dic1114yes—
335C22×C4—21no—
336C22×C4—112no—
337C22×C4—111no—
338C22×C4—111no—
339C22×C4—222no—
340C22×C4—221no—
341C22×C4—221no—
342C22×C4—444no—
343C22×C4—442no—
344C22×C4—882no—
345C22×C4—882no—
346C22×C4—882no—
347C22×C4D4×D1112yes—
348C22×C4C23×D1111yescharacteristic
349SD16—48no—
350D8—48no—
351C2×C8—22no—
352C2×C8—22no—
353C2×C8—222no—
354C2×C8—222no—
355C2×C8—222no—
356C2×C8C22×Dic1114yes—
357C4⋊C4—222no—
358C4⋊C4—222no—
359C4⋊C4—222no—
360C4⋊C4—222no—
361C4⋊C4—442no—
362C4⋊C4—882no—
363C22⋊C4—28no—
364C22⋊C4—442no—
365C22⋊C4—444no—
366C22⋊C4—882no—
367C22⋊C4—882no—
368C22⋊C4—882no—
369C42—222no—
370C42—222no—
371C42—442no—
372C42#434112yes—
373C42C22×Dic1112yes—
374C11#2227911yescharacteristic, complemented, Sylow
375C23—22no—
376C23—24no—
377C23—41no—
378C23—42no—
379C23—42no—
380C23—41no—
381C23—42no—
382C23—42no—
383C23—42no—
384C23—42no—
385C23—42no—
386C23—42no—
387C23C2×D4×D1111yescharacteristic
388Q8—24no—
389Q8—42no—
390D4—24no—
391D4—24no—
392D4—24no—
393D4—42no—
394D4—42no—
395D4—42no—
396D4—88no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—221no—
403C2×C4—222no—
404C2×C4—221no—
405C2×C4—222no—
406C2×C4—222no—
407C2×C4—222no—
408C2×C4—222no—
409C2×C4—441no—
410C2×C4—441no—
411C2×C4—442no—
412C2×C4—442no—
413C2×C4—442no—
414C2×C4—442no—
415C2×C4—442no—
416C2×C4—884no—
417C2×C4—888no—
418C2×C4D4×Dic1114yes—
419C2×C4C2×#434111yescharacteristic
420C2×C4#6703712yes—
421C2×C4#6703712yes—
422C2×C4C23×Dic1111yescharacteristic
423C8—24no—
424C8—442no—
425C22—44no—
426C22—44no—
427C22—44no—
428C22—42no—
429C22—44no—
430C22—81no—
431C22—82no—
432C22—81no—
433C22—82no—
434C22—82no—
435C22—82no—
436C22—82no—
437C22#1062324611yescharacteristic
438C22#1062324611yescharacteristic
439C22#1062330512yes—
440C22#1062330612yes—
441C22C2×D4×Dic1111yescharacteristic
442C4—24no—
443C4—42no—
444C4—441no—
445C4—441no—
446C4—442no—
447C4—881no—
448C4—881no—
449C4—882no—
450C4#1062325012yes—
451C4#1062332912yes—
452C2—84no—
453C2—82no—
454C2#1307134211yescharacteristic
455C2#1307744912yes—
456C2#1307966111yescharacteristic
457C2#1307967211yescharacteristic
458C2#1307970512yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#496C2
socleC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenterC2×#496D11
hypocenterC11#22279
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#496

Complements

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

NH ≅ G/Ntype
1. #13071342C2semidirect
2. #13071329C2semidirect
3. #13069428C2semidirect
4. #13069423C2semidirect
5. #13068973C2semidirect
6. #13068966C2semidirect
7. #13068966C2semidirect
8. #13068952C2semidirect
9. #13068750C2semidirect
10. #13068369C2semidirect
19. C11×#496C4semidirect
48. C2×C11×SD16C2×C4semidirect
51. C2×C11×D8C2×C4semidirect
54. C11×#127C2×C4semidirect
56. C11×#124C2×C4semidirect
77. C11×#97C2×C4semidirect
214. #496Dic11semidirect
270. C2×SD16C2×Dic11semidirect
273. C2×D8C2×Dic11semidirect
277. #127C2×Dic11semidirect
279. #124C2×Dic11semidirect
303. #97C2×Dic11semidirect
374. C11#22279semidirect

Maximal subgroups

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

subgroupindex
#130713422
#130713292
#130694282
#130694232
#130689732
#130689662
#130689522
#130687502
#130683692
C2×C11×#4962
#2227911