Finite Group Databasebeta

← #14763553

Subgroups — #14763553

Order 2816.

1150 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623066C211yesmaximal, characteristic
2#13071239C211yesmaximal, characteristic, complemented
3#13069585C211yesmaximal, characteristic, complemented
4#13069581C211yesmaximal, characteristic, complemented
5#13069440C211yesmaximal, characteristic, complemented
6#13069422C211yesmaximal, characteristic, complemented
7#13068936C212yesmaximal, complemented
8#13068931C212yesmaximal, complemented
9#13068627C212yesmaximal, complemented
10#13068617C212yesmaximal, complemented
11C2×C11×#433C211yesmaximal, characteristic, complemented
12C2×C11×#117C2211yescharacteristic
13C2×#66983C2212yes—
14C2×#66979C2211yescharacteristic
15C22×C4⋊Dic11C2211yescharacteristic
16#10623066—24no—
17#10623066C418yescomplemented
18C2×#66947—22no—
19C2×#66937—22no—
20C2×#66927C2211yescharacteristic
21C2×C4×D44C2212yes—
22C2×#66923C2211yescharacteristic
23C11×#433—24no—
24C2×C11×C4⋊C8C2212yes—
25C2×C11×C22⋊C8C2212yes—
26C2×C11×#97C2211yescharacteristic
27C2×C4×C8×C11C2211yescharacteristic
28C2×#66885C2212yes—
29C2×#66885C2212yes—
30C2×#66885C2212yes—
31C2×#66885C2212yes—
32#10622598—22no—
33#10622563—22no—
34#10622549C2211yescharacteristic
35#10622549C2211yescharacteristic
36#10622548C2211yescharacteristic
37#10622548C2211yescharacteristic
38#10622189C2212yes—
39#10622189C2212yes—
40#10622189C2212yes—
41#10622189C2212yes—
42C23×C4×C11C2311yescharacteristic
43C22×C22⋊D11—22no—
44C23×Dic11—21no—
45C22×D44—22no—
46C22×D44C2312yes—
47C22×C4×D11—22no—
48C22×C8×C11C2312yes—
49C22×C8×C11C2312yes—
50C11×#117C2×C414yes—
51C11×#117D414yes—
52C2×C11×C4⋊C4D412yes—
53C2×C11×C22⋊C4D412yes—
54C2×C42×C11C2311yescharacteristic
55C2×C42×C11C2311yescharacteristic
56C2×C22⋊Dic11—21no—
57#66983—24no—
58#66983C2×C418yes—
59C2×(C2×D11)⋊C4—22no—
60C2×(C2×D11)⋊C4—22no—
61#66979—42no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—22no—
64C2×C4⋊Dic11—22no—
65C2×C4⋊Dic11—42no—
66C2×C4⋊Dic11C2311yescharacteristic
67C2×C4⋊Dic11C2311yescharacteristic
68C2×C4⋊Dic11C2311yescharacteristic
69C2×C4⋊Dic11C2311yescharacteristic
70C2×C4⋊Dic11C2312yes—
71C2×Dic11⋊C4—22no—
72C2×C4×Dic11—21no—
73#66947—216no—
74#66937—216no—
75#66927—22no—
76#66927C2×C414yescomplemented
77C4×D44—24no—
78C4×D44C2×C418yescomplemented
79#66923—22no—
80#66923C2×C414yescomplemented
81C11×C4⋊C8—24no—
82C11×C22⋊C8—24no—
83C11×#97—22no—
84C4×C8×C11—22no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87#66885—42no—
88#66885—42no—
89#66885—42no—
90#66885—42no—
91#21872—111nomaximal, Sylow
92C24×C11C2×D411yescharacteristic
93C23×D11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11C22×C412yes—
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2×D412yes—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D412yes—
101C22×C4×C11C2411yescharacteristic
102C2×C22⋊D11—28no—
103C2×C22⋊D11—82no—
104C2×C22⋊D11—82no—
105C22×Dic11—22no—
106C22×Dic11—21no—
107C22×Dic11—21no—
108C22×Dic11—21no—
109C22×Dic11—21no—
110C22×Dic11—42no—
111C22×Dic11—82no—
112C2×D44—28no—
113C2×D44—22no—
114C2×D44—22no—
115C2×D44—22no—
116C2×D44—22no—
117C2×D44—22no—
118C2×D44—82no—
119C2×D44—82no—
120C2×D44C22×C414yes—
121C2×C4×D11—28no—
122C2×C4×D11—82no—
123C2×C4×D11—82no—
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C2×C8×C11—22no—
127C2×C8×C11—22no—
128C2×C8×C11—22no—
129C2×C8×C11—22no—
130C11×C4⋊C4C22⋊C418yes—
131C11×C22⋊C4C22⋊C418yes—
132C42×C11C22×C412yes—
133C42×C11C22×C412yes—
134C42×C11C2×D412yes—
135C42×C11C2×D412yes—
136C22⋊Dic11—42no—
137(C2×D11)⋊C4—28no—
138(C2×D11)⋊C4—28no—
139C4⋊Dic11—22no—
140C4⋊Dic11—22no—
141C4⋊Dic11—22no—
142C4⋊Dic11—22no—
143C4⋊Dic11—22no—
144C4⋊Dic11—42no—
145C4⋊Dic11—82no—
146C4⋊Dic11—82no—
147C4⋊Dic11C22×C414yes—
148Dic11⋊C4—28no—
149C4×Dic11—42no—
150C2×#540—111no—
151C2×#433D1111yescharacteristic, complemented
152#2317—111no—
153#1992—111no—
154#1991—111no—
155#1961—111no—
156#1957—111no—
157#1875—112no—
158#1874—112no—
159#1804—112no—
160#1802—112no—
161C23×C11—21no—
162C23×C11—21no—
163C23×C11—22no—
164C23×C11—22no—
165C23×C11C2×C22⋊C412yes—
166C23×C11C22×D411yescharacteristic
167C22×D11—24no—
168C22×D11—42no—
169C22×D11—42no—
170C22×D11—42no—
171C22×D11—42no—
172C22×D11—42no—
173C22×D11—42no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—24no—
181C2×C4×C11—24no—
182C2×C4×C11C2×C22⋊C414yes—
183C2×C4×C11C2×C22⋊C412yes—
184C2×C4×C11C2×C22⋊C414yes—
185C2×C4×C11C23×C411yescharacteristic
186C2×C4×C11C22×D411yescharacteristic
187C2×C4×C11H(5,𝔽2)12yes—
188C2×C4×C112−1+412yes—
189C22⋊D11—88no—
190C2×Dic11—24no—
191C2×Dic11—42no—
192C2×Dic11—42no—
193C2×Dic11—41no—
194C2×Dic11—41no—
195C2×Dic11—41no—
196C2×Dic11—41no—
197C2×Dic11—42no—
198C2×Dic11—42no—
199C2×Dic11—42no—
200C2×Dic11—42no—
201C2×Dic11—84no—
202D44—24no—
203D44—24no—
204D44—42no—
205D44—42no—
206D44—88no—
207C4×D11—88no—
208C8×C11—42no—
209C8×C11—42no—
210#540—118no—
211#540—224no—
212C2×#127—111no—
213C2×#125—111no—
214C2×#123—222no—
215C2×#121—112no—
216C2×#121—222no—
217C2×C4×D4—112no—
218C2×#117—111no—
219C2×#117C2×D1111yescharacteristic
220C22×C4⋊C4—111no—
221#433—24no—
222C2×C4⋊C8C2×D1112yes—
223C2×#102—112no—
224C2×#102—112no—
225C2×#102—112no—
226C2×#102—112no—
227C2×C22⋊C8C2×D1112yes—
228C2×#97C2×D1111yescharacteristic
229C2×C4×C8C2×D1111yescharacteristic
230#389—222no—
231#385—222no—
232#384—111no—
233#384—111no—
234#382—111no—
235#382—111no—
236#340—112no—
237#340—112no—
238#340—112no—
239#340—112no—
240C22×C11—22no—
241C22×C11—24no—
242C22×C11—41no—
243C22×C11—41no—
244C22×C11—42no—
245C22×C11C22×C22⋊C411yescharacteristic
246C22×C11#53511yescharacteristic
247C22×C11#53611yescharacteristic
248C22×C11#57612yes—
249C22×C11#57712yes—
250C2×D11—44no—
251C2×D11—44no—
252C2×D11—44no—
253C2×D11—82no—
254C2×D11—82no—
255C2×D11—82no—
256C2×D11—82no—
257C4×C11—22no—
258C4×C11—24no—
259C4×C11—24no—
260C4×C11#52012yes—
261C4×C11#53712yes—
262Dic11—44no—
263Dic11—81no—
264Dic11—81no—
265Dic11—81no—
266Dic11—81no—
267C22×D4—112no—
268C22×D4—222no—
269C22×D4—222no—
270C23×C4—222no—
271C23×C4—221no—
272C23×C4C22×D1111yescharacteristic
273C22×C8C22×D1112yes—
274C22×C8C22×D1112yes—
275#127—114no—
276#127—222no—
277#125—114no—
278#125—222no—
279#123—2216no—
280#121—118no—
281#121—224no—
282#121—2216no—
283C4×D4—118no—
284C4×D4—224no—
285#117—442no—
286#117C4×D1114yes—
287#117C22⋊D1114yes—
288C2×C4⋊C4—112no—
289C2×C4⋊C4—111no—
290C2×C4⋊C4—111no—
291C2×C4⋊C4—111no—
292C2×C4⋊C4—111no—
293C2×C4⋊C4—222no—
294C2×C4⋊C4—221no—
295C2×C4⋊C4—222no—
296C2×C4⋊C4—222no—
297C2×C4⋊C4—442no—
298C2×C4⋊C4D4412yes—
299C2×C22⋊C4—222no—
300C2×C22⋊C4—222no—
301C2×C22⋊C4—221no—
302C2×C22⋊C4D4412yes—
303C2×C42—221no—
304C2×C42C22×D1111yescharacteristic
305C2×C42C22×D1111yescharacteristic
306C4⋊C8—24no—
307#102—442no—
308#102—442no—
309#102—442no—
310#102—442no—
311C22⋊C8—24no—
312#97—22no—
313C4×C8—22no—
314#95—222no—
315#95—222no—
316C2×C11—42no—
317C2×C11#231111yescharacteristic
318C2×C11#289712yes—
319C2×C11#322011yescharacteristic
320C2×C11#322111yescharacteristic
321C2×C11#324112yes—
322D11—84no—
323C24—222no—
324C24C2×D4411yescharacteristic
325C2×D4—114no—
326C2×D4—228no—
327C2×D4—228no—
328C2×D4—222no—
329C2×D4—222no—
330C2×D4—222no—
331C2×D4—222no—
332C2×D4—222no—
333C2×D4—882no—
334C2×D4—882no—
335C2×D4—882no—
336C2×D4—882no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—222no—
340C22×C4—228no—
341C22×C4—221no—
342C22×C4—221no—
343C22×C4—221no—
344C22×C4—221no—
345C22×C4—442no—
346C22×C4—882no—
347C22×C4—882no—
348C22×C4—882no—
349C22×C4C2×C4×D1112yes—
350C22×C4C2×D4412yes—
351C22×C4C2×D4412yes—
352C22×C4C2×D4411yescharacteristic
353C22×C4C2×C22⋊D1112yes—
354C22×C4C23×D1111yescharacteristic
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—22no—
359C2×C8—22no—
360C2×C8—22no—
361C4⋊C4—114no—
362C4⋊C4—228no—
363C4⋊C4—222no—
364C4⋊C4—222no—
365C4⋊C4—222no—
366C4⋊C4—222no—
367C4⋊C4—222no—
368C4⋊C4—442no—
369C4⋊C4—882no—
370C4⋊C4—882no—
371C4⋊C4(C2×D11)⋊C418yes—
372C22⋊C4—228no—
373C22⋊C4—228no—
374C22⋊C4—442no—
375C22⋊C4(C2×D11)⋊C418yes—
376C42—442no—
377C42C2×C4×D1112yes—
378C42C2×C4×D1112yes—
379C42C2×C22⋊D1112yes—
380C42C2×C22⋊D1112yes—
381C11#2187211yescharacteristic, complemented, Sylow
382C23—22no—
383C23—22no—
384C23—21no—
385C23—21no—
386C23—224no—
387C23—442no—
388C23—442no—
389C23—442no—
390C23—442no—
391C23—442no—
392C23—442no—
393C23C2×(C2×D11)⋊C412yes—
394C23C22×D4411yescharacteristic
395D4—224no—
396D4—224no—
397D4—442no—
398D4—442no—
399D4—888no—
400D4—888no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—24no—
408C2×C4—24no—
409C2×C4—224no—
410C2×C4—442no—
411C2×C4—442no—
412C2×C4—442no—
413C2×C4—442no—
414C2×C4—442no—
415C2×C4—442no—
416C2×C4—441no—
417C2×C4—441no—
418C2×C4—441no—
419C2×C4—441no—
420C2×C4—888no—
421C2×C4—884no—
422C2×C4C2×(C2×D11)⋊C414yes—
423C2×C4C2×(C2×D11)⋊C414yes—
424C2×C4C2×(C2×D11)⋊C412yes—
425C2×C4C22×C4×D1111yescharacteristic
426C2×C4#6704212yes—
427C2×C4#6704312yes—
428C2×C4C22×C22⋊D1111yescharacteristic
429C8—42no—
430C8—42no—
431C22—22no—
432C22—24no—
433C22—42no—
434C22—41no—
435C22—41no—
436C22—444no—
437C22—444no—
438C22—444no—
439C22—882no—
440C22—882no—
441C22—882no—
442C22—882no—
443C22#1062305611yescharacteristic
444C22#1062305711yescharacteristic
445C22#1062328212yes—
446C22#1062328312yes—
447C22C22×(C2×D11)⋊C411yescharacteristic
448C4—22no—
449C4—24no—
450C4—24no—
451C4—444no—
452C4—881no—
453C4—881no—
454C4—881no—
455C4—881no—
456C4#1062305412yes—
457C4#1062336412yes—
458C2—42no—
459C2—884no—
460C2#1307120411yescharacteristic
461C2#1307714312yes—
462C2#1307966811yescharacteristic
463C2#1307967911yescharacteristic
464C2#1307987112yes—
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#433C2
socleC23×C11C22×D4
prime radicalC2×#10623066C2
cosocleC22×C4×C11C24
hypercenterC2×#433D11
hypocenterC11#21872
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
2. #13071239C2semidirect
3. #13069585C2semidirect
4. #13069581C2semidirect
5. #13069440C2semidirect
6. #13069422C2semidirect
7. #13068936C2semidirect
8. #13068931C2semidirect
9. #13068627C2semidirect
10. #13068617C2semidirect
11. C2×C11×#433C2semidirect
17. #10623066C4semidirect
76. #66927C2×C4semidirect
78. C4×D44C2×C4semidirect
80. #66923C2×C4semidirect
151. C2×#433D11semidirect
381. C11#21872semidirect

Maximal subgroups

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

subgroupindex
C2×#106230662
#130712392
#130695852
#130695812
#130694402
#130694222
#130689362
#130689312
#130686272
#130686172
C2×C11×#4332
#2187211