Finite Group Databasebeta

← #14763556

Subgroups — #14763556

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×#10623250C211yesmaximal, characteristic
2C2×#10622303C211yesmaximal, characteristic, complemented
3#13071237C211yesmaximal, characteristic, complemented
4#13069584C211yesmaximal, characteristic, complemented
5#13069581C211yesmaximal, characteristic, complemented
6#13069441C211yesmaximal, characteristic, complemented
7#13068935C212yesmaximal, complemented
8#13068930C212yesmaximal, complemented
9#13068624C212yesmaximal, complemented
10#13068614C212yesmaximal, complemented
11C11×#1957C211yesmaximal, characteristic, complemented
12C2×C11×#127C2211yescharacteristic
13C2×#66992—22no—
14C2×#66991C2212yes—
15C2×#66988—22no—
16C2×D4×Dic11C2212yes—
17#10623250—24no—
18#10623250C418yescomplemented
19C2×#66945C2211yescharacteristic
20C2×C4⋊C4×D11C2211yescharacteristic
21C2×#66925C2211yescharacteristic
22C2×#66923C2211yescharacteristic
23C2×C11×#102C2212yes—
24C2×C11×#102C2212yes—
25C2×C4×C8×C11C2211yescharacteristic
26C11×#384C2211yescharacteristic
27C2×#66896C2212yes—
28C2×#66896C2212yes—
29C2×(C2×D11)⋊C8C2212yes—
30C2×Dic11⋊C8C2212yes—
31#10622602—22no—
32#10622590C2211yescharacteristic
33#10622589C2211yescharacteristic
34#10622585—22no—
35#10622549C2211yescharacteristic
36C2×#66867C2211yescharacteristic
37#10622303—24no—
38#10622189C2212yes—
39#10622189C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42C22×D4×C11—22no—
43C22×D4×C11C2312yes—
44C22×C22⋊D11—22no—
45C23×Dic11—22no—
46C22×C4×D11—21no—
47C22×C4×D11C2311yescharacteristic
48C22×C8×C11C2312yes—
49C11×#127—22no—
50C11×#127C2×C414yescomplemented
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4C2311yescharacteristic
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C42×C11C2311yescharacteristic
55C2×C22⋊Dic11—22no—
56C2×C22⋊Dic11—22no—
57#66992—216no—
58#66991—24no—
59#66991C2×C418yes—
60#66988—216no—
61D4×Dic11—24no—
62D4×Dic11C2×C418yescomplemented
63C2×(C2×D11)⋊C4—21no—
64C2×(C2×D11)⋊C4D412yes—
65C2×C4⋊Dic11C2311yescharacteristic
66C2×C4⋊Dic11C2311yescharacteristic
67C2×C4⋊Dic11C2312yes—
68C2×Dic11⋊C4—22no—
69C2×Dic11⋊C4—21no—
70C2×Dic11⋊C4—22no—
71C2×Dic11⋊C4D412yes—
72C2×C4×Dic11—21no—
73C2×C4×Dic11C2311yescharacteristic
74C22×C11⋊C8C2312yes—
75#66945—42no—
76C4⋊C4×D11—42no—
77#66925C2×C414yes—
78#66925D414yes—
79#66923—22no—
80#66923C2×C414yescomplemented
81C11×#102—42no—
82C11×#102—42no—
83C4×C8×C11—22no—
84#66896—42no—
85#66896—42no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88(C2×D11)⋊C8—24no—
89Dic11⋊C8—24no—
90#66867—22no—
91#21872—111nomaximal, Sylow
92C24×C11—22no—
93C23×D11C2×D411yescharacteristic
94C2×D4×C11—28no—
95C2×D4×C11—22no—
96C2×D4×C11—22no—
97C2×D4×C11—22no—
98C2×D4×C11—22no—
99C2×D4×C11—22no—
100C2×D4×C11—82no—
101C2×D4×C11—82no—
102C2×D4×C11C22×C414yes—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2411yescharacteristic
107C2×C22⋊D11—28no—
108C2×C22⋊D11—82no—
109C2×C22⋊D11—82no—
110C22×Dic11—28no—
111C22×Dic11—22no—
112C22×Dic11—21no—
113C22×Dic11—21no—
114C22×Dic11—82no—
115C22×Dic11—82no—
116C22×Dic11C2×D412yes—
117C22×Dic11C2×D411yescharacteristic
118C2×C4×D11—22no—
119C2×C4×D11—22no—
120C2×C4×D11—42no—
121C2×C4×D11—82no—
122C2×C4×D11C22×C412yes—
123C2×C4×D11C2×D412yes—
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C2×C8×C11—22no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—82no—
130C42×C11C22×C412yes—
131C42×C11C2×D412yes—
132C22⋊Dic11—28no—
133C22⋊Dic11—28no—
134(C2×D11)⋊C4—42no—
135(C2×D11)⋊C4C22⋊C418yes—
136C4⋊Dic11—22no—
137C4⋊Dic11—22no—
138C4⋊Dic11—22no—
139C4⋊Dic11C22×C414yes—
140Dic11⋊C4—28no—
141Dic11⋊C4—42no—
142Dic11⋊C4—82no—
143Dic11⋊C4C22⋊C418yes—
144C4×Dic11—42no—
145C4×Dic11C22×C412yes—
146C4×Dic11C2×D412yes—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—22no—
150C2×#540—111no—
151C2×#433—111no—
152#2317—111no—
153#1992—111no—
154#1991—111no—
155#1961—111no—
156#1957D1111yescharacteristic, complemented
157#1875—112no—
158#1874—112no—
159#1804—112no—
160#1802—112no—
161C23×C11—24no—
162C23×C11—42no—
163C23×C11—42no—
164C23×C11—42no—
165C23×C11—42no—
166C23×C11—42no—
167C23×C11—42no—
168C23×C11C22×D411yescharacteristic
169C22×D11—21no—
170C22×D11—21no—
171C22×D11—22no—
172C22×D11—22no—
173C22×D11C2×C22⋊C412yes—
174D4×C11—24no—
175D4×C11—24no—
176D4×C11—42no—
177D4×C11—42no—
178D4×C11—88no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11C2×C22⋊C414yes—
186C2×C4×C11C23×C411yescharacteristic
187C2×C4×C11C22×D411yescharacteristic
188C2×C4×C11H(5,𝔽2)12yes—
189C2×C4×C112−1+412yes—
190C22⋊D11—88no—
191C2×Dic11—21no—
192C2×Dic11—21no—
193C2×Dic11—22no—
194C2×Dic11—22no—
195C2×Dic11—24no—
196C2×Dic11—42no—
197C2×Dic11—42no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—42no—
201C2×Dic11—42no—
202C2×Dic11—88no—
203C2×Dic11C2×C22⋊C414yes—
204C2×Dic11C2×C22⋊C412yes—
205C4×D11—24no—
206C4×D11—24no—
207C4×D11—84no—
208C8×C11—42no—
209C11⋊C8—42no—
210#540—118no—
211#540—224no—
212C2×#127C2×D1111yescharacteristic
213C2×#125—111no—
214C2×#123—222no—
215C2×#121—112no—
216C2×#121—222no—
217C2×C4×D4—112no—
218C2×#117—111no—
219C2×#117—111no—
220C22×C4⋊C4—111no—
221#433—224no—
222C2×C4⋊C8—112no—
223C2×#102—112no—
224C2×#102—112no—
225C2×#102C2×D1112yes—
226C2×#102C2×D1112yes—
227C2×C22⋊C8—112no—
228C2×#97—111no—
229C2×C4×C8C2×D1111yescharacteristic
230#389—222no—
231#385—222no—
232#384—111no—
233#384C2×D1111yescharacteristic
234#382—111no—
235#382—111no—
236#340—112no—
237#340—112no—
238#340—112no—
239#340—112no—
240C22×C11—44no—
241C22×C11—44no—
242C22×C11—44no—
243C22×C11—82no—
244C22×C11—82no—
245C22×C11—82no—
246C22×C11—82no—
247C22×C11C22×C22⋊C411yescharacteristic
248C22×C11#53511yescharacteristic
249C22×C11#53611yescharacteristic
250C22×C11#57612yes—
251C22×C11#57712yes—
252C2×D11—22no—
253C2×D11—24no—
254C2×D11—41no—
255C2×D11—41no—
256C2×D11—42no—
257C4×C11—24no—
258C4×C11—81no—
259C4×C11—81no—
260C4×C11#52012yes—
261C4×C11#53712yes—
262Dic11—22no—
263Dic11—24no—
264Dic11—44no—
265Dic11—81no—
266Dic11—81no—
267C22×D4—22no—
268C22×D4—222no—
269C22×D4C22×D1112yes—
270C23×C4—111no—
271C23×C4—221no—
272C23×C4—222no—
273C22×C8—112no—
274C22×C8C22×D1112yes—
275#127—22no—
276#127C4×D1114yescomplemented
277#125—114no—
278#125—222no—
279#123—2216no—
280#121—118no—
281#121—2216no—
282#121—224no—
283C4×D4—118no—
284C4×D4—224no—
285#117—114no—
286#117—114no—
287#117—442no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—112no—
290C2×C4⋊C4—112no—
291C2×C4⋊C4—111no—
292C2×C4⋊C4—111no—
293C2×C4⋊C4—222no—
294C2×C4⋊C4—221no—
295C2×C4⋊C4—222no—
296C2×C4⋊C4—442no—
297C2×C4⋊C4C22×D1111yescharacteristic
298C2×C4⋊C4C22×D1111yescharacteristic
299C2×C22⋊C4—112no—
300C2×C22⋊C4—222no—
301C2×C22⋊C4—222no—
302C2×C22⋊C4—221no—
303C2×C42—111no—
304C2×C42—221no—
305C2×C42C22×D1111yescharacteristic
306C4⋊C8—224no—
307#102—42no—
308#102—42no—
309#102—442no—
310#102—442no—
311C22⋊C8—224no—
312#97—222no—
313C4×C8—22no—
314#95—222no—
315#95—222no—
316C2×C11—84no—
317C2×C11#231111yescharacteristic
318C2×C11#289712yes—
319C2×C11#322011yescharacteristic
320C2×C11#322111yescharacteristic
321C2×C11#324112yes—
322D11—42no—
323C24—22no—
324C24—111no—
325C2×D4—28no—
326C2×D4—22no—
327C2×D4—22no—
328C2×D4—22no—
329C2×D4—22no—
330C2×D4—22no—
331C2×D4—82no—
332C2×D4—82no—
333C2×D4—228no—
334C2×D4—882no—
335C2×D4—882no—
336C2×D4C2×C4×D1114yes—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—112no—
340C22×C4—111no—
341C22×C4—112no—
342C22×C4—112no—
343C22×C4—228no—
344C22×C4—222no—
345C22×C4—222no—
346C22×C4—222no—
347C22×C4—221no—
348C22×C4—221no—
349C22×C4—442no—
350C22×C4—882no—
351C22×C4—882no—
352C22×C4—882no—
353C22×C4D4×D1112yes—
354C22×C4C23×D1111yescharacteristic
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—222no—
359C2×C8—222no—
360C2×C8—222no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—82no—
364C4⋊C4—118no—
365C4⋊C4—114no—
366C4⋊C4—228no—
367C4⋊C4—222no—
368C4⋊C4—222no—
369C4⋊C4—222no—
370C4⋊C4—442no—
371C4⋊C4—882no—
372C22⋊C4—118no—
373C22⋊C4—228no—
374C22⋊C4—228no—
375C22⋊C4—442no—
376C42—112no—
377C42—112no—
378C42—442no—
379C42C2×C4×D1112yes—
380C42D4×D1112yes—
381C11#2187211yescharacteristic, complemented, Sylow
382C23—24no—
383C23—42no—
384C23—42no—
385C23—42no—
386C23—42no—
387C23—42no—
388C23—42no—
389C23—112no—
390C23—221no—
391C23—222no—
392C23—222no—
393C23—221no—
394C23C2×D4×D1111yescharacteristic
395D4—24no—
396D4—24no—
397D4—42no—
398D4—42no—
399D4—88no—
400D4—888no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—114no—
408C2×C4—112no—
409C2×C4—221no—
410C2×C4—222no—
411C2×C4—222no—
412C2×C4—221no—
413C2×C4—224no—
414C2×C4—224no—
415C2×C4—224no—
416C2×C4—442no—
417C2×C4—442no—
418C2×C4—441no—
419C2×C4—441no—
420C2×C4—442no—
421C2×C4—442no—
422C2×C4—884no—
423C2×C4—888no—
424C2×C4C22⋊C4×D1114yes—
425C2×C4C22×C4×D1111yescharacteristic
426C2×C4C2×D4×D1111yescharacteristic
427C2×C4#6703712yes—
428C2×C4#6704312yes—
429C8—42no—
430C8—442no—
431C22—44no—
432C22—44no—
433C22—44no—
434C22—82no—
435C22—82no—
436C22—82no—
437C22—82no—
438C22—222no—
439C22—224no—
440C22—442no—
441C22—441no—
442C22—441no—
443C22C2×C22⋊C4×D1111yescharacteristic
444C22#1062320611yescharacteristic
445C22#1062324611yescharacteristic
446C22#1062328812yes—
447C22#1062329312yes—
448C4—24no—
449C4—81no—
450C4—81no—
451C4—222no—
452C4—224no—
453C4—444no—
454C4—881no—
455C4—881no—
456C4#1062307712yes—
457C4#1062313912yes—
458C2—84no—
459C2—442no—
460C2#1307120611yescharacteristic
461C2#1307713712yes—
462C2#1307965911yescharacteristic
463C2#1307967011yescharacteristic
464C2#1307986212yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1957C2
socleC23×C11C22×D4
prime radicalC2×#10623250C2
cosocleC22×C4×C11C24
hypercenter#1957D11
hypocenterC11#21872
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1957

Complements

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

NH ≅ G/Ntype
2. C2×#10622303C2semidirect
3. #13071237C2semidirect
4. #13069584C2semidirect
5. #13069581C2semidirect
6. #13069441C2semidirect
7. #13068935C2semidirect
8. #13068930C2semidirect
9. #13068624C2semidirect
10. #13068614C2semidirect
11. C11×#1957C2semidirect
18. #10623250C4semidirect
50. C11×#127C2×C4semidirect
62. D4×Dic11C2×C4semidirect
80. #66923C2×C4semidirect
156. #1957D11semidirect
276. #127C4×D11semidirect
381. C11#21872semidirect

Maximal subgroups

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

subgroupindex
C2×#106232502
C2×#106223032
#130712372
#130695842
#130695812
#130694412
#130689352
#130689302
#130686242
#130686142
C11×#19572
#2187211