Finite Group Databasebeta

← #14764338

Subgroups — #14764338

Order 2816.

902 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622318C211yesmaximal, characteristic
2D11×#384C211yesmaximal, characteristic
3#13071009C211yesmaximal, characteristic
4#13069378C212yesmaximal, complemented
5#13069373C212yesmaximal, complemented
6#13068810C212yesmaximal
7#13068805C212yesmaximal
8#13068784C211yesmaximal, characteristic, complemented
9#13068782C211yesmaximal, characteristic, complemented
10#13068749C211yesmaximal, characteristic, complemented
11C11×#1836C211yesmaximal, characteristic, complemented
12C2×C4⋊C4×D11—21no—
13C2×C4⋊C4×D11—21no—
14C2×C4⋊C4×D11C2212yes—
15C2×C42×D11C2211yescharacteristic
16C2×C11×#97C2211yescharacteristic
17C11×#384C2211yescharacteristic
18C11×#382C2211yescharacteristic
19C2×(C2×D11)⋊C8C2212yes—
20C2×#66882C2212yes—
21C2×#66881C2212yes—
22C2×Dic11⋊C8C2212yes—
23#10622600C2211yescharacteristic
24#10622600C2211yescharacteristic
25#10622589—21no—
26#10622589—21no—
27#10622589C2212yes—
28C4⋊C4×Dic11C2211yescharacteristic
29C4⋊C4×Dic11C2211yescharacteristic
30C2×#66872C2212yes—
31C2×#66871C2212yes—
32#10622549C2211yescharacteristic
33#10622548C2211yescharacteristic
34C2×#66867C2211yescharacteristic
35#10622318C418yescomplemented
36#10622279—21no—
37#10622277—21no—
38#10622264—21no—
39#10622261—21no—
40C11×#340C2212yes—
41C11×#340C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44C22×C4×D11—22no—
45C22×C4×D11D411yescharacteristic
46C22×C4×D11D411yescharacteristic
47C22×C4×D11C2311yescharacteristic
48C22×C8×C11C2312yes—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4C2312yes—
52C2×C11×C4⋊C4C2311yescharacteristic
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C42×C11C2311yescharacteristic
55C2×(C2×D11)⋊C4—21no—
56C2×(C2×D11)⋊C4—21no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11C2312yes—
60C2×C4⋊Dic11C2311yescharacteristic
61C2×C4⋊Dic11C2311yescharacteristic
62C2×Dic11⋊C4—22no—
63C2×Dic11⋊C4—22no—
64C2×Dic11⋊C4—22no—
65C2×C4×Dic11—21no—
66C2×C4×Dic11—21no—
67C2×C4×Dic11D411yescharacteristic
68C2×C4×Dic11D411yescharacteristic
69C2×C4×Dic11C2311yescharacteristic
70C22×C11⋊C8C2312yes—
71C4⋊C4×D11—42no—
72C4⋊C4×D11—42no—
73C4⋊C4×D11—44no—
74C4⋊C4×D11—44no—
75C42×D11C2×C414yes—
76C42×D11Q814yes—
77C11×#97C2×C414yescomplemented
78C11×#95—21no—
79C11×#95—21no—
80C11⋊#95—21no—
81C11⋊#95—21no—
82C11⋊#95—21no—
83C11⋊#95—21no—
84C11⋊#95—21no—
85C11⋊#95—21no—
86(C2×D11)⋊C8C2×C418yes—
87#66882—42no—
88#66881—42no—
89Dic11⋊C8C2×C418yescomplemented
90#66872—42no—
91#66871—42no—
92#66867C2×C414yescomplemented
93#21987—111nomaximal, Sylow
94C23×D11C2×D411yescharacteristic
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—22no—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2411yescharacteristic
101C22×Dic11—21no—
102C22×Dic11—21no—
103C22×Dic11—22no—
104C22×Dic11C2×D411yescharacteristic
105C22×Dic11C2×D411yescharacteristic
106C22×Dic11C2×D411yescharacteristic
107C2×C4×D11—22no—
108C2×C4×D11—22no—
109C2×C4×D11—22no—
110C2×C4×D11—22no—
111C2×C4×D11—22no—
112C2×C4×D11—22no—
113C2×C4×D11—44no—
114C2×C4×D11—44no—
115C2×C4×D11—44no—
116C2×C4×D11C4⋊C414yes—
117C2×C4×D11C4⋊C414yes—
118C2×C4×D11C22×C412yes—
119C2×C4×D11C2×Q812yes—
120C2×C8×C11—22no—
121C2×C8×C11—22no—
122C2×C8×C11C22×C414yes—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—42no—
128C11×C4⋊C4—42no—
129C42×C11C22×C412yes—
130C42×C11C2×Q812yes—
131(C2×D11)⋊C4—42no—
132(C2×D11)⋊C4—42no—
133C4⋊Dic11—22no—
134C4⋊Dic11—22no—
135C4⋊Dic11—22no—
136C4⋊Dic11—22no—
137C4⋊Dic11—42no—
138C4⋊Dic11—42no—
139Dic11⋊C4—44no—
140Dic11⋊C4—44no—
141Dic11⋊C4—44no—
142C4×Dic11—42no—
143C4×Dic11—42no—
144C4×Dic11C4⋊C414yes—
145C4×Dic11C4⋊C414yes—
146C4×Dic11C22×C412yes—
147C4×Dic11C2×Q812yes—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8C22×C414yes—
151C2×#432—111no—
152C2×#384—111no—
153#2283—111no—
154#1948—112no—
155#1947—112no—
156#1853—112no—
157#1852—112no—
158#1847—111no—
159#1847—111no—
160#1836—111no—
161#1836D1111yescharacteristic, complemented
162C23×C11C22×D411yescharacteristic
163C22×D11—21no—
164C22×D11—21no—
165C22×D11—21no—
166C22×D11—21no—
167C22×D11C2×C4⋊C412yes—
168C22×D11AGL(1,ℤ/8)12yes—
169C22×D11#13712yes—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—42no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11C2×C4⋊C412yes—
184C2×C4×C11C2×C4⋊C412yes—
185C2×C4×C11C23×C411yescharacteristic
186C2×C4×C11C22×Q811yescharacteristic
187C2×C4×C11H(5,𝔽2)12yes—
188C2×C4×C112−1+412yes—
189C2×Dic11—21no—
190C2×Dic11—21no—
191C2×Dic11—21no—
192C2×Dic11—21no—
193C2×Dic11—42no—
194C2×Dic11—41no—
195C2×Dic11—41no—
196C2×Dic11—41no—
197C2×Dic11—42no—
198C2×Dic11—42no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11C2×C4⋊C412yes—
203C2×Dic11C2×C4⋊C412yes—
204C2×Dic11C2×C4⋊C412yes—
205C2×Dic11AGL(1,ℤ/8)12yes—
206C2×Dic11#13712yes—
207C4×D11—28no—
208C4×D11—24no—
209C4×D11—24no—
210C4×D11—28no—
211C4×D11—88no—
212C8×C11—24no—
213C11⋊C8—24no—
214C22×C4⋊C4—112no—
215C22×C4⋊C4—221no—
216C22×C4⋊C4—221no—
217C22×C42—111no—
218#432—118no—
219C2×#107—112no—
220C2×#107—112no—
221C2×#106—112no—
222C2×#106—112no—
223C2×C4⋊C8—112no—
224C2×C22⋊C8—112no—
225C2×#97—111no—
226C2×#97C2×D1111yescharacteristic
227#384—112no—
228#384—111no—
229#384—221no—
230#384—221no—
231#384C2×D1111yescharacteristic
232#383—221no—
233#382—111no—
234#382C2×D1111yescharacteristic
235#381—221no—
236#380—111no—
237#380—111no—
238C4×C4⋊C4—111no—
239C4×C4⋊C4—111no—
240C4×C22⋊C4—221no—
241#376—221no—
242#340—112no—
243#340—112no—
244#340C2×D1112yes—
245#340C2×D1112yes—
246C22×C11C22×C4⋊C411yescharacteristic
247C22×C11#53511yescharacteristic
248C22×C11#53611yescharacteristic
249C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
250C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
251C22×C11C2×#13711yescharacteristic
252C22×C11C2×#13711yescharacteristic
253C2×D11—22no—
254C2×D11—22no—
255C2×D11—22no—
256C2×D11—22no—
257C2×D11—22no—
258C2×D11—22no—
259C2×D11#42814yes—
260C4×C11—22no—
261C4×C11—22no—
262C4×C11—82no—
263C4×C11—81no—
264C4×C11—81no—
265C4×C11#52012yes—
266C4×C11#54412yes—
267Dic11—22no—
268Dic11—22no—
269Dic11—82no—
270Dic11—81no—
271Dic11—81no—
272Dic11#42814yes—
273C23×C4—111no—
274C23×C4—111no—
275C23×C4—111no—
276C23×C4—222no—
277C22×C8—112no—
278C22×C8C22×D1112yes—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—112no—
282C2×C4⋊C4—111no—
283C2×C4⋊C4—111no—
284C2×C4⋊C4—222no—
285C2×C4⋊C4—222no—
286C2×C4⋊C4—222no—
287C2×C4⋊C4—221no—
288C2×C4⋊C4—221no—
289C2×C4⋊C4—442no—
290C2×C4⋊C4—442no—
291C2×C4⋊C4—444no—
292C2×C4⋊C4—444no—
293C2×C4⋊C4C22×D1112yes—
294C2×C4⋊C4C22×D1111yescharacteristic
295C2×C4⋊C4C22×D1111yescharacteristic
296C2×C22⋊C4—221no—
297C2×C22⋊C4—221no—
298C2×C42—111no—
299C2×C42—111no—
300C2×C42—111no—
301C2×C42—114no—
302C2×C42—114no—
303C2×C42—221no—
304C2×C42—221no—
305C2×C42C22×D1111yescharacteristic
306#107—442no—
307#107—442no—
308#106—442no—
309#106—442no—
310C4⋊C8—118no—
311C22⋊C8—118no—
312#97—114no—
313#97C4×D1114yescomplemented
314#95—21no—
315#95—21no—
316#95—221no—
317#95—221no—
318#95—221no—
319#95—221no—
320#95—221no—
321#95—221no—
322C2×C11#231711yescharacteristic
323C2×C11C2×#42811yescharacteristic
324C2×C11C2×#42811yescharacteristic
325C2×C11#321711yescharacteristic
326C2×C11#321811yescharacteristic
327C2×C11#323811yescharacteristic
328C2×C11#323911yescharacteristic
329D11—24no—
330C24—111no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—22no—
334C22×C4—111no—
335C22×C4—111no—
336C22×C4—111no—
337C22×C4—114no—
338C22×C4—114no—
339C22×C4—112no—
340C22×C4—112no—
341C22×C4—222no—
342C22×C4—222no—
343C22×C4—222no—
344C22×C4—222no—
345C22×C4—222no—
346C22×C4—222no—
347C22×C4—221no—
348C22×C4—221no—
349C22×C4—222no—
350C22×C4—444no—
351C22×C4—444no—
352C22×C4—444no—
353C22×C4D4×D1111yescharacteristic
354C22×C4D4×D1111yescharacteristic
355C22×C4C23×D1111yescharacteristic
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—114no—
359C2×C8—222no—
360C2×C8—222no—
361C2×C8C2×C4×D1114yes—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—42no—
367C4⋊C4—42no—
368C4⋊C4—222no—
369C4⋊C4—222no—
370C4⋊C4—222no—
371C4⋊C4—222no—
372C4⋊C4—442no—
373C4⋊C4—442no—
374C4⋊C4—444no—
375C4⋊C4—444no—
376C4⋊C4—444no—
377C22⋊C4—442no—
378C22⋊C4—442no—
379C42—114no—
380C42—114no—
381C42—112no—
382C42—112no—
383C42—442no—
384C42—442no—
385C42C2×C4×D1112yes—
386C42Q8×D1112yes—
387C11#2198711yescharacteristic, complemented, Sylow
388C23—112no—
389C23—112no—
390C23—112no—
391C23—221no—
392C23—221no—
393C23—221no—
394C23—221no—
395C23C2×D4×D1111yescharacteristic
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—42no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—112no—
410C2×C4—112no—
411C2×C4—112no—
412C2×C4—112no—
413C2×C4—112no—
414C2×C4—228no—
415C2×C4—228no—
416C2×C4—221no—
417C2×C4—221no—
418C2×C4—221no—
419C2×C4—221no—
420C2×C4—224no—
421C2×C4—224no—
422C2×C4—441no—
423C2×C4—441no—
424C2×C4—442no—
425C2×C4—442no—
426C2×C4—441no—
427C2×C4—441no—
428C2×C4—442no—
429C2×C4—441no—
430C2×C4—441no—
431C2×C4—888no—
432C2×C4C4⋊C4×D1112yes—
433C2×C4C4⋊C4×D1112yes—
434C2×C4C22×C4×D1111yescharacteristic
435C2×C4C2×Q8×D1111yescharacteristic
436C2×C4#6704212yes—
437C2×C4#6704312yes—
438C8—24no—
439C8—224no—
440C22—114no—
441C22—222no—
442C22—222no—
443C22—222no—
444C22—222no—
445C22—222no—
446C22—222no—
447C22C2×C4⋊C4×D1111yescharacteristic
448C22#1062320511yescharacteristic
449C22#1062320611yescharacteristic
450C22D11×AGL(1,ℤ/8)11yescharacteristic
451C22D11×AGL(1,ℤ/8)11yescharacteristic
452C22D11×#13711yescharacteristic
453C22D11×#13711yescharacteristic
454C4—22no—
455C4—22no—
456C4—81no—
457C4—81no—
458C4—82no—
459C4—114no—
460C4—222no—
461C4—222no—
462C4—882no—
463C4—881no—
464C4—881no—
465C4#1062305412yes—
466C4#1062322012yes—
467C2—224no—
468C2#1307124111yescharacteristic
469C2D11×#42811yescharacteristic
470C2D11×#42811yescharacteristic
471C2#1307963511yescharacteristic
472C2#1307964411yescharacteristic
473C2#1307983311yescharacteristic
474C2#1307984211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1836C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1836D11
hypocenterC11#21987
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1836

Complements

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

NH ≅ G/Ntype
4. #13069378C2semidirect
5. #13069373C2semidirect
8. #13068784C2semidirect
9. #13068782C2semidirect
10. #13068749C2semidirect
11. C11×#1836C2semidirect
35. #10622318C4semidirect
77. C11×#97C2×C4semidirect
89. Dic11⋊C8C2×C4semidirect
92. #66867C2×C4semidirect
161. #1836D11semidirect
313. #97C4×D11semidirect
387. C11#21987semidirect

Maximal subgroups

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

subgroupindex
C2×#106223182
D11×#3842
#130710092
#130693782
#130693732
#130688102
#130688052
#130687842
#130687822
#130687492
C11×#18362
#2198711