Finite Group Databasebeta

← #14763559

Subgroups — #14763559

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×#10622613C211yesmaximal, characteristic, complemented
2#13071239C211yesmaximal, characteristic, complemented
3#13069586C211yesmaximal, characteristic, complemented
4#13069582C211yesmaximal, characteristic, complemented
5#13069441C211yesmaximal, characteristic, complemented
6#13069423C211yesmaximal, characteristic, complemented
7#13068939C212yesmaximal, complemented
8#13068934C212yesmaximal, complemented
9#13068626C212yesmaximal, complemented
10#13068616C212yesmaximal, complemented
11C2×C11×#540C211yesmaximal, characteristic
12C11×#540—24no—
13C11×#540C418yescomplemented
14C2×C11×#127C2211yescharacteristic
15C2×C11×#125C2211yescharacteristic
16C2×C11×#123—22no—
17C2×C11×#121—22no—
18C2×C11×#121C2212yes—
19C2×C4×D4×C11C2212yes—
20C2×C11×#117C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C2×#66896C2212yes—
24C2×#66896C2212yes—
25C2×#66896C2212yes—
26C2×#66896C2212yes—
27C2×C22⋊(C11⋊C8)C2212yes—
28#10622613—24no—
29#10622598—22no—
30#10622563—22no—
31#10622549C2211yescharacteristic
32#10622549C2211yescharacteristic
33#10622548C2211yescharacteristic
34#10622548C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2212yes—
36C2×#66867C2211yescharacteristic
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42C22×D4×C11—22no—
43C22×D4×C11—22no—
44C22×D4×C11C2312yes—
45C23×C4×C11—22no—
46C23×C4×C11C2311yescharacteristic
47C23×Dic11—21no—
48C11×#127—22no—
49C11×#127C2×C414yescomplemented
50C11×#125—22no—
51C11×#125C2×C414yescomplemented
52C11×#123—216no—
53C11×#121—24no—
54C11×#121—216no—
55C11×#121C2×C418yes—
56C4×D4×C11—24no—
57C4×D4×C11C2×C418yescomplemented
58C11×#117C2×C414yes—
59C11×#117D414yes—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4D412yes—
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4—22no—
65C2×C11×C22⋊C4D412yes—
66C2×C42×C11C2311yescharacteristic
67C2×C42×C11C2311yescharacteristic
68C2×C22⋊Dic11—21no—
69#66979—42no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11—22no—
72C2×C4⋊Dic11—22no—
73C2×C4⋊Dic11—42no—
74C2×C4⋊Dic11C2311yescharacteristic
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4×Dic11—21no—
79C22×C11⋊C8C2312yes—
80C22×C11⋊C8C2312yes—
81#66896—42no—
82#66896—42no—
83#66896—42no—
84#66896—42no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87C22⋊(C11⋊C8)—24no—
88C4⋊(C11⋊C8)—24no—
89#66867—22no—
90C4×C11⋊C8—22no—
91#21872—111nomaximal, Sylow
92C24×C11—22no—
93C24×C11C2×D411yescharacteristic
94C2×D4×C11—28no—
95C2×D4×C11—28no—
96C2×D4×C11—22no—
97C2×D4×C11—22no—
98C2×D4×C11—22no—
99C2×D4×C11—22no—
100C2×D4×C11—22no—
101C2×D4×C11—82no—
102C2×D4×C11—82no—
103C2×D4×C11—82no—
104C2×D4×C11—82no—
105C2×D4×C11C22×C414yes—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—28no—
110C22×C4×C11—82no—
111C22×C4×C11—82no—
112C22×C4×C11C22×C412yes—
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2411yescharacteristic
118C22×Dic11—21no—
119C22×Dic11—21no—
120C22×Dic11—21no—
121C22×Dic11—21no—
122C22×Dic11—42no—
123C22×Dic11—82no—
124C11×C4⋊C4—28no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4C22⋊C418yes—
127C11×C4⋊C4C22×C414yes—
128C11×C22⋊C4—28no—
129C11×C22⋊C4—28no—
130C11×C22⋊C4C22⋊C418yes—
131C42×C11C22×C412yes—
132C42×C11C22×C412yes—
133C42×C11C2×D412yes—
134C42×C11C2×D412yes—
135C22⋊Dic11—42no—
136C4⋊Dic11—22no—
137C4⋊Dic11—22no—
138C4⋊Dic11—22no—
139C4⋊Dic11—22no—
140C4⋊Dic11—42no—
141C4⋊Dic11—82no—
142C4⋊Dic11—82no—
143C4×Dic11—42no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—22no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—22no—
150C2×#540D1111yescharacteristic
151C2×#433—111no—
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×C11—24no—
166C23×C11—42no—
167C23×C11—42no—
168C23×C11—42no—
169C23×C11—42no—
170C23×C11—42no—
171C23×C11—42no—
172C23×C11C2×C22⋊C412yes—
173C23×C11C22×D411yescharacteristic
174D4×C11—24no—
175D4×C11—24no—
176D4×C11—42no—
177D4×C11—42no—
178D4×C11—88no—
179D4×C11—88no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—24no—
187C2×C4×C11—24no—
188C2×C4×C11—24no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—88no—
192C2×C4×C11C2×C22⋊C414yes—
193C2×C4×C11C2×C22⋊C414yes—
194C2×C4×C11C2×C22⋊C412yes—
195C2×C4×C11C23×C411yescharacteristic
196C2×C4×C11C22×D411yescharacteristic
197C2×C4×C11H(5,𝔽2)12yes—
198C2×C4×C112−1+412yes—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11—42no—
207C2×Dic11—84no—
208C11⋊C8—42no—
209C11⋊C8—42no—
210#540—24no—
211#540Dic1118yescomplemented
212C2×#127C2×D1111yescharacteristic
213C2×#125C2×D1111yescharacteristic
214C2×#123—22no—
215C2×#121—22no—
216C2×#121C2×D1112yes—
217C2×C4×D4C2×D1112yes—
218C2×#117—111no—
219C2×#117C2×D1111yescharacteristic
220C22×C4⋊C4—111no—
221#433—224no—
222C2×C4⋊C8—112no—
223C2×#102—112no—
224C2×#102—112no—
225C2×#102—112no—
226C2×#102—112no—
227C2×C22⋊C8—112no—
228C2×#97—111no—
229C2×C4×C8—111no—
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×C11—44no—
246C22×C11—44no—
247C22×C11—44no—
248C22×C11—82no—
249C22×C11—82no—
250C22×C11—82no—
251C22×C11—82no—
252C22×C11C22×C22⋊C411yescharacteristic
253C22×C11#53511yescharacteristic
254C22×C11#53611yescharacteristic
255C22×C11#57612yes—
256C22×C11#57712yes—
257C4×C11—22no—
258C4×C11—24no—
259C4×C11—24no—
260C4×C11—44no—
261C4×C11#52012yes—
262C4×C11#53712yes—
263Dic11—81no—
264Dic11—81no—
265Dic11—81no—
266Dic11—81no—
267C22×D4—22no—
268C22×D4—22no—
269C22×D4C22×D1112yes—
270C23×C4—22no—
271C23×C4—221no—
272C23×C4C22×D1111yescharacteristic
273C22×C8—112no—
274C22×C8—112no—
275#127—22no—
276#127C2×Dic1114yescomplemented
277#125—22no—
278#125C2×Dic1114yescomplemented
279#123—216no—
280#121—24no—
281#121—216no—
282#121C2×Dic1118yes—
283C4×D4—24no—
284C4×D4C2×Dic1118yescomplemented
285#117—442no—
286#117C2×Dic1114yes—
287#117C22⋊D1114yes—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—111no—
290C2×C4⋊C4—111no—
291C2×C4⋊C4—111no—
292C2×C4⋊C4—111no—
293C2×C4⋊C4—221no—
294C2×C4⋊C4—222no—
295C2×C4⋊C4—222no—
296C2×C4⋊C4—442no—
297C2×C4⋊C4C22⋊D1112yes—
298C2×C4⋊C4C22×D1112yes—
299C2×C22⋊C4—22no—
300C2×C22⋊C4—22no—
301C2×C22⋊C4—221no—
302C2×C22⋊C4C22⋊D1112yes—
303C2×C42—221no—
304C2×C42C22×D1111yescharacteristic
305C2×C42C22×D1111yescharacteristic
306C4⋊C8—224no—
307#102—442no—
308#102—442no—
309#102—442no—
310#102—442no—
311C22⋊C8—224no—
312#97—222no—
313C4×C8—222no—
314#95—222no—
315#95—222no—
316C2×C11—42no—
317C2×C11—84no—
318C2×C11#231111yescharacteristic
319C2×C11#289712yes—
320C2×C11#322011yescharacteristic
321C2×C11#322111yescharacteristic
322C2×C11#324112yes—
323C24—22no—
324C24C2×C22⋊D1111yescharacteristic
325C2×D4—28no—
326C2×D4—28no—
327C2×D4—22no—
328C2×D4—22no—
329C2×D4—22no—
330C2×D4—22no—
331C2×D4—22no—
332C2×D4—82no—
333C2×D4—82no—
334C2×D4—82no—
335C2×D4—82no—
336C2×D4C22×Dic1114yes—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—28no—
341C22×C4—82no—
342C22×C4—82no—
343C22×C4—221no—
344C22×C4—221no—
345C22×C4—221no—
346C22×C4—221no—
347C22×C4—442no—
348C22×C4—882no—
349C22×C4C22×Dic1112yes—
350C22×C4C2×C22⋊D1112yes—
351C22×C4C2×C22⋊D1112yes—
352C22×C4C2×C22⋊D1111yescharacteristic
353C22×C4C2×C22⋊D1112yes—
354C22×C4C23×D1111yescharacteristic
355C2×C8—222no—
356C2×C8—222no—
357C2×C8—222no—
358C2×C8—222no—
359C2×C8—222no—
360C2×C8—222no—
361C4⋊C4—28no—
362C4⋊C4—22no—
363C4⋊C4—222no—
364C4⋊C4—222no—
365C4⋊C4—222no—
366C4⋊C4—222no—
367C4⋊C4—442no—
368C4⋊C4—882no—
369C4⋊C4—882no—
370C4⋊C4C22⋊Dic1118yes—
371C4⋊C4C22×Dic1114yes—
372C22⋊C4—28no—
373C22⋊C4—28no—
374C22⋊C4—442no—
375C22⋊C4C22⋊Dic1118yes—
376C42—442no—
377C42C22×Dic1112yes—
378C42C22×Dic1112yes—
379C42C2×C22⋊D1112yes—
380C42C2×C22⋊D1112yes—
381C11#2187211yescharacteristic, complemented, Sylow
382C23—21no—
383C23—21no—
384C23—22no—
385C23—22no—
386C23—24no—
387C23—42no—
388C23—42no—
389C23—42no—
390C23—42no—
391C23—42no—
392C23—42no—
393C23C2×C22⋊Dic1112yes—
394C23C22×C22⋊D1111yescharacteristic
395D4—24no—
396D4—24no—
397D4—42no—
398D4—42no—
399D4—88no—
400D4—88no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—24no—
408C2×C4—24no—
409C2×C4—24no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—88no—
413C2×C4—441no—
414C2×C4—441no—
415C2×C4—441no—
416C2×C4—441no—
417C2×C4—442no—
418C2×C4—442no—
419C2×C4—442no—
420C2×C4—442no—
421C2×C4—884no—
422C2×C4C2×C22⋊Dic1114yes—
423C2×C4C2×C22⋊Dic1114yes—
424C2×C4C2×C22⋊Dic1112yes—
425C2×C4#6704212yes—
426C2×C4#6704312yes—
427C2×C4C23×Dic1111yescharacteristic
428C2×C4C22×C22⋊D1111yescharacteristic
429C8—442no—
430C8—442no—
431C22—22no—
432C22—24no—
433C22—42no—
434C22—41no—
435C22—41no—
436C22—44no—
437C22—44no—
438C22—44no—
439C22—82no—
440C22—82no—
441C22—82no—
442C22—82no—
443C22#1062335611yescharacteristic
444C22#1062336111yescharacteristic
445C22#1062336612yes—
446C22#1062336712yes—
447C22C22×C22⋊Dic1111yescharacteristic
448C4—22no—
449C4—24no—
450C4—24no—
451C4—44no—
452C4—881no—
453C4—881no—
454C4—881no—
455C4—881no—
456C4#1062335812yes—
457C4#1062336412yes—
458C2—42no—
459C2—84no—
460C2#1307120811yescharacteristic
461C2#1307714212yes—
462C2#1307966011yescharacteristic
463C2#1307967111yescharacteristic
464C2#1307986312yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#540C2
socleC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenterC2×#540D11
hypocenterC11#21872
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. C2×#10622613C2semidirect
2. #13071239C2semidirect
3. #13069586C2semidirect
4. #13069582C2semidirect
5. #13069441C2semidirect
6. #13069423C2semidirect
7. #13068939C2semidirect
8. #13068934C2semidirect
9. #13068626C2semidirect
10. #13068616C2semidirect
13. C11×#540C4semidirect
49. C11×#127C2×C4semidirect
51. C11×#125C2×C4semidirect
57. C4×D4×C11C2×C4semidirect
211. #540Dic11semidirect
276. #127C2×Dic11semidirect
278. #125C2×Dic11semidirect
284. C4×D4C2×Dic11semidirect
381. C11#21872semidirect

Maximal subgroups

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

subgroupindex
C2×#106226132
#130712392
#130695862
#130695822
#130694412
#130694232
#130689392
#130689342
#130686262
#130686162
C2×C11×#5402
#2187211