Finite Group Databasebeta

← #14767646

Subgroups — #14767646

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
1C2×#10622671C211yesmaximal, characteristic
2#13071339C211yesmaximal, characteristic, complemented
3#13071329C211yesmaximal, characteristic, complemented
4#13069422C211yesmaximal, characteristic, complemented
5#13068969C212yesmaximal, complemented
6#13068962C212yesmaximal, complemented
7#13068961C212yesmaximal, complemented
8#13068947C212yesmaximal, complemented
9#13068749C211yesmaximal, characteristic, complemented
10#13068367C211yesmaximal, characteristic, complemented
11C11×#1958C211yesmaximal, characteristic, complemented
12C2×C11×#124C2211yescharacteristic
13C2×Q8×Dic11C2211yescharacteristic
14C22×#4325C2212yes—
15C2×D4×Dic11C2211yescharacteristic
16C22×#4323C2212yes—
17C2×#66946C2212yes—
18C2×#66927C2211yescharacteristic
19C2×C11×#103C2212yes—
20C2×C11×#102C2212yes—
21C2×C4×C8×C11C2211yescharacteristic
22C11×#382C2211yescharacteristic
23#10622843C2211yescharacteristic
24#10622834C2211yescharacteristic
25C2×#66885C2212yes—
26C2×#66885C2212yes—
27#10622671C418yescomplemented
28#10622601C2212yes—
29#10622564—22no—
30#10622563—22no—
31#10622548C2211yescharacteristic
32#10622545C2211yescharacteristic
33C2×#66867C2211yescharacteristic
34#10622278—22no—
35#10622278—22no—
36#10622188C2212yes—
37#10622188C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40C22×Q8×C11C2311yescharacteristic
41C22×D4×C11C2311yescharacteristic
42C23×Dic11—21no—
43C22×D44—22no—
44C22×D44C2312yes—
45C22×C4×D11—22no—
46C22×C8×C11C2312yes—
47C11×#124—22no—
48C11×#124C2×C414yescomplemented
49C2×C11×C4⋊C4C2312yes—
50C2×C11×C22⋊C4—22no—
51C2×C42×C11C2311yescharacteristic
52C2×C22⋊Dic11—21no—
53C2×C22⋊Dic11—22no—
54Q8×Dic11—42no—
55C2×#4325—42no—
56C2×#4325—42no—
57C2×#4325C2×C418yescomplemented
58D4×Dic11—42no—
59C2×#4323—42no—
60C2×#4323—42no—
61C2×#4323C2×C418yescomplemented
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4—22no—
64C2×(C2×D11)⋊C4—22no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11—22no—
67C2×C4⋊Dic11C2311yescharacteristic
68C2×C4⋊Dic11C2311yescharacteristic
69C2×C4×Dic11—21no—
70C2×C4×Dic11C2311yescharacteristic
71C2×C4×Dic11C2311yescharacteristic
72C22×C11⋊C8C2312yes—
73#66946—42no—
74#66946—42no—
75#66927—22no—
76#66927C2×C414yescomplemented
77C11×#103—42no—
78C11×#102—42no—
79C4×C8×C11—22no—
80C11×#95—22no—
81C11⋊#95—22no—
82C11⋊#95D412yes—
83C11⋊#95D412yes—
84#66885—42no—
85#66885—42no—
86#66867C2×C414yescomplemented
87#22279—111nomaximal, Sylow
88C24×C11—21no—
89C23×D11—22no—
90C2×Q8×C11—21no—
91C2×Q8×C11—22no—
92C2×Q8×C11—22no—
93C2×Q8×C11C22×C412yes—
94C2×D4×C11—21no—
95C2×D4×C11—22no—
96C2×D4×C11—22no—
97C2×D4×C11C22×C412yes—
98C22×C4×C11—21no—
99C22×C4×C11—22no—
100C22×C4×C11C2×D412yes—
101C22×C4×C11C2411yescharacteristic
102C22×Dic11—21no—
103C22×Dic11—21no—
104C22×Dic11—42no—
105C22×Dic11—82no—
106C22×Dic11C2×D412yes—
107C22×Dic11C2×D411yescharacteristic
108C22×Dic11C2×D411yescharacteristic
109C2×D44—28no—
110C2×D44—22no—
111C2×D44—22no—
112C2×D44—22no—
113C2×D44—22no—
114C2×D44—22no—
115C2×D44—82no—
116C2×D44—82no—
117C2×D44C22×C414yes—
118C2×C4×D11—44no—
119C2×C4×D11—82no—
120C2×C4×D11—82no—
121C2×C8×C11—22no—
122C2×C8×C11—22no—
123C2×C8×C11—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C22⋊C4—28no—
127C42×C11C22×C412yes—
128C42×C11#4112yes—
129C22⋊Dic11—42no—
130C22⋊Dic11—82no—
131#4325—48no—
132#4323—48no—
133(C2×D11)⋊C4—44no—
134(C2×D11)⋊C4—82no—
135(C2×D11)⋊C4—82no—
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⋊C8C22×C414yes—
146C2×#496—111no—
147#2328—111no—
148#2326—111no—
149#1958D1111yescharacteristic, complemented
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—41no—
159C23×C11—41no—
160C23×C11—42no—
161C23×C11—42no—
162C23×C11C22×D411yescharacteristic
163C22×D11—24no—
164C22×D11—42no—
165C22×D11—42no—
166C22×D11—42no—
167C22×D11—42no—
168C22×D11—42no—
169C22×D11—42no—
170Q8×C11—24no—
171Q8×C11—42no—
172D4×C11—24no—
173D4×C11—42no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11C4×D414yes—
183C2×C4×C11C23×C411yescharacteristic
184C2×C4×C11C2×#4111yescharacteristic
185C2×C4×C11H(5,𝔽2)12yes—
186C2×C4×C11H(5,𝔽2)12yes—
187C2×Dic11—21no—
188C2×Dic11—21no—
189C2×Dic11—22no—
190C2×Dic11—22no—
191C2×Dic11—22no—
192C2×Dic11—22no—
193C2×Dic11—22no—
194C2×Dic11—41no—
195C2×Dic11—41no—
196C2×Dic11—42no—
197C2×Dic11—42no—
198C2×Dic11—84no—
199D44—24no—
200D44—24no—
201D44—42no—
202D44—42no—
203D44—88no—
204C4×D11—88no—
205C8×C11—42no—
206C11⋊C8—24no—
207C22×SD16—112no—
208C22×D8—112no—
209C2×#127—111no—
210C2×#124C2×D1111yescharacteristic
211C2×C4×Q8—111no—
212C2×C4×D4—111no—
213C2×C4×D4—112no—
214#496—118no—
215C2×#103C2×D1112yes—
216C2×#102—112no—
217C2×#102—112no—
218C2×#102C2×D1112yes—
219C2×#97—111no—
220C2×C4×C8C2×D1111yescharacteristic
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#382C2×D1111yescharacteristic
230#376—111no—
231#340—112no—
232#340—112no—
233#336—112no—
234#336—112no—
235C22×C11—42no—
236C22×C11—44no—
237C22×C11—81no—
238C22×C11—81no—
239C22×C11—82no—
240C22×C11C2×C4×D411yescharacteristic
241C22×C11#53511yescharacteristic
242C22×C11#53511yescharacteristic
243C22×C11#57612yes—
244C22×C11#57712yes—
245C2×D11—44no—
246C2×D11—44no—
247C2×D11—44no—
248C2×D11—82no—
249C2×D11—82no—
250C2×D11—82no—
251C2×D11—82no—
252C4×C11—24no—
253C4×C11—42no—
254C4×C11—82no—
255C4×C11#51812yes—
256C4×C11#54012yes—
257Dic11—41no—
258Dic11—41no—
259Dic11—42no—
260Dic11—81no—
261Dic11—81no—
262C22×Q8C22×D1111yescharacteristic
263C22×D4—112no—
264C22×D4—222no—
265C22×D4C22×D1111yescharacteristic
266C23×C4—222no—
267C23×C4—221no—
268C2×SD16—118no—
269C2×SD16—442no—
270C2×SD16—442no—
271C2×D8—118no—
272C2×D8—442no—
273C2×D8—442no—
274C22×C8—112no—
275C22×C8C22×D1112yes—
276#127—114no—
277#127—222no—
278#124—22no—
279#124C4×D1114yescomplemented
280C4×Q8—442no—
281C4×D4—442no—
282C4×D4—442no—
283C4×D4—442no—
284C2×C4⋊C4—111no—
285C2×C4⋊C4—111no—
286C2×C4⋊C4—221no—
287C2×C4⋊C4—222no—
288C2×C4⋊C4C22×D1112yes—
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—42no—
300#102—42no—
301#102—442no—
302#102—442no—
303#97—114no—
304C4×C8—22no—
305#95—22no—
306#95—112no—
307#95—112no—
308#95—222no—
309C2×C11—82no—
310C2×C11#232811yescharacteristic
311C2×C11#294612yes—
312C2×C11#322011yescharacteristic
313C2×C11#322111yescharacteristic
314C2×C11#322412yes—
315D11—84no—
316C24—21no—
317C24—222no—
318C2×Q8—21no—
319C2×Q8—22no—
320C2×Q8—22no—
321C2×Q8C2×C4×D1112yes—
322C2×D4—21no—
323C2×D4—22no—
324C2×D4—22no—
325C2×D4—114no—
326C2×D4—228no—
327C2×D4—222no—
328C2×D4—222no—
329C2×D4—222no—
330C2×D4—222no—
331C2×D4—222no—
332C2×D4—882no—
333C2×D4—882no—
334C2×D4C2×C4×D1112yes—
335C22×C4—21no—
336C22×C4—22no—
337C22×C4—112no—
338C22×C4—111no—
339C22×C4—111no—
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—448no—
350D8—448no—
351C2×C8—22no—
352C2×C8—22no—
353C2×C8—22no—
354C2×C8—114no—
355C2×C8—222no—
356C2×C8—222no—
357C4⋊C4—22no—
358C4⋊C4—22no—
359C4⋊C4—222no—
360C4⋊C4—222no—
361C4⋊C4—442no—
362C4⋊C4—882no—
363C22⋊C4—28no—
364C22⋊C4—444no—
365C22⋊C4—442no—
366C22⋊C4—882no—
367C22⋊C4—882no—
368C22⋊C4—882no—
369C42—222no—
370C42—222no—
371C42—442no—
372C42C2×C4×D1112yes—
373C42#434112yes—
374C11#2227911yescharacteristic, complemented, Sylow
375C23—22no—
376C23—41no—
377C23—42no—
378C23—42no—
379C23—41no—
380C23—224no—
381C23—442no—
382C23—442no—
383C23—442no—
384C23—442no—
385C23—442no—
386C23—442no—
387C23C2×D4×D1111yescharacteristic
388Q8—24no—
389Q8—42no—
390D4—24no—
391D4—42no—
392D4—224no—
393D4—224no—
394D4—442no—
395D4—442no—
396D4—888no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—222no—
406C2×C4—222no—
407C2×C4—222no—
408C2×C4—222no—
409C2×C4—222no—
410C2×C4—221no—
411C2×C4—221no—
412C2×C4—442no—
413C2×C4—442no—
414C2×C4—441no—
415C2×C4—441no—
416C2×C4—888no—
417C2×C4—884no—
418C2×C4(C22⋊D11)⋊C414yes—
419C2×C4C22×C4×D1111yescharacteristic
420C2×C4C2×#434111yescharacteristic
421C2×C4#6703712yes—
422C2×C4#6704212yes—
423C8—42no—
424C8—224no—
425C22—44no—
426C22—42no—
427C22—81no—
428C22—81no—
429C22—82no—
430C22—444no—
431C22—444no—
432C22—444no—
433C22—882no—
434C22—882no—
435C22—882no—
436C22—882no—
437C22C2×(C22⋊D11)⋊C411yescharacteristic
438C22#1062320511yescharacteristic
439C22#1062324611yescharacteristic
440C22#1062330012yes—
441C22#1062330112yes—
442C4—24no—
443C4—42no—
444C4—82no—
445C4—441no—
446C4—441no—
447C4—442no—
448C4—881no—
449C4—881no—
450C4#1062307612yes—
451C4#1062315012yes—
452C2—82no—
453C2—884no—
454C2#1307134011yescharacteristic
455C2#1307745112yes—
456C2#1307966911yescharacteristic
457C2#1307968011yescharacteristic
458C2#1307970312yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1958C2
socleC23×C11C22×D4
prime radicalC2×#10622671C2
cosocleC22×C4×C11C24
hypercenter#1958D11
hypocenterC11#22279
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1958

Complements

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

NH ≅ G/Ntype
2. #13071339C2semidirect
3. #13071329C2semidirect
4. #13069422C2semidirect
5. #13068969C2semidirect
6. #13068962C2semidirect
7. #13068961C2semidirect
8. #13068947C2semidirect
9. #13068749C2semidirect
10. #13068367C2semidirect
11. C11×#1958C2semidirect
27. #10622671C4semidirect
48. C11×#124C2×C4semidirect
57. C2×#4325C2×C4semidirect
61. C2×#4323C2×C4semidirect
76. #66927C2×C4semidirect
86. #66867C2×C4semidirect
149. #1958D11semidirect
279. #124C4×D11semidirect
374. C11#22279semidirect

Maximal subgroups

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

subgroupindex
C2×#106226712
#130713392
#130713292
#130694222
#130689692
#130689622
#130689612
#130689472
#130687492
#130683672
C11×#19582
#2227911