Finite Group Databasebeta

← #14738976

Subgroups — #14738976

Order 2816.

684 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078703C211yesmaximal, characteristic, complemented
2#13078612C211yesmaximal, characteristic, complemented
3#13077639C211yesmaximal, characteristic, complemented
4#13068064C212yesmaximal, complemented
5#13068022C212yesmaximal, complemented
6#13067968C212yesmaximal, complemented
7#13067954C212yesmaximal, complemented
8#13067396C211yesmaximal, characteristic, complemented
9#13067321C211yesmaximal, characteristic, complemented
10#13067278C211yesmaximal, characteristic, complemented
11C11×#3207C211yesmaximal, characteristic, complemented
12C11×#532C2211yescharacteristic
13C11×#532C2211yescharacteristic
14C2×C4×D44C2211yescharacteristic
15C11×#493C2211yescharacteristic, complemented
16C11×#492C2211yescharacteristic, complemented
17C11×#487C2211yescharacteristic, complemented
18C11×#486C2211yescharacteristic, complemented
19C11×#463—22no—
20C11×#449—22no—
21C11×#431C2211yescharacteristic
22#10622700C2212yes—
23#10622697C2212yes—
24#10622685C2212yes—
25#10622685C2212yes—
26#10622649—21no—
27#10622649—21no—
28#10622647—21no—
29#10622646—21no—
30#10622627—22no—
31C4×#4323—22no—
32#10622539C2211yescharacteristic
33#10622538C2211yescharacteristic
34#10622538C2211yescharacteristic
35#10622447—22no—
36D11×C22⋊C8—22no—
37C8×D44C2212yes—
38C8×D44C2212yes—
39#10622185C2212yescomplemented
40#10622184C2212yescomplemented
41#10622182C2212yescomplemented
42#10622182C2212yescomplemented
43#10622096C2212yescomplemented
44#10622095C2212yescomplemented
45C2×C11×#41—21no—
46C2×C11×#41—21no—
47C22×D44D411yescharacteristic
48C22×C4×D11—21no—
49C2×C11×SD16—22no—
50C2×C11×D8—22no—
51C11×C4⋊Q8C2311yescharacteristic
52C11×C4⋊Q8C2311yescharacteristic
53C11×#127C2311yescharacteristic
54C11×#127C2311yescharacteristic
55C11×#124—21no—
56C11×#124—21no—
57C11×#121—21no—
58C11×#121—21no—
59C11×#121—21no—
60C11×#121—21no—
61C4×D4×C11—21no—
62C4×D4×C11—21no—
63C4×D4×C11—21no—
64C4×D4×C11—21no—
65C2×C42×C11C2311yescharacteristic
66C2×#4323—22no—
67C2×#4323—22no—
68C2×(C2×D11)⋊C4—21no—
69C2×C4⋊Dic11D411yescharacteristic
70C2×C8×D11—22no—
71C2×C8×D11—22no—
72C4×D44—21no—
73C4×D44—21no—
74C4×D44D412yes—
75C4×D44C2312yes—
76C11×C4⋊C8D412yes—
77C11×#103—22no—
78C11×#102—22no—
79C11×C22⋊C8D412yes—
80C4×C8×C11C2311yescharacteristic
81C4×C8×C11C2311yescharacteristic
82#66896—22no—
83#66896—22no—
84C22⋊(C11⋊C8)—21no—
85C22⋊(C11⋊C8)—21no—
86C22⋊(C11⋊C8)—21no—
87(C2×D11)⋊C8—22no—
88(C2×D11)⋊C8—22no—
89#66873—22no—
90#66873—22no—
91#66872—22no—
92#66871—22no—
93C4⋊(C11⋊C8)C2312yes—
94C4⋊(C11⋊C8)C2312yes—
95C4⋊(C11⋊C8)C2312yes—
96#66867—21no—
97C4×C11⋊C8—21no—
98C4×C11⋊C8—21no—
99#19389—111nomaximal, Sylow
100C23×D11—21no—
101C11×#41—82no—
102C11×#41—82no—
103C2×Q8×C11—21no—
104C2×Q8×C11—21no—
105C2×D4×C11—21no—
106C2×D4×C11—21no—
107C2×D4×C11—21no—
108C2×D4×C11—21no—
109C2×D4×C11—21no—
110C2×D4×C11—21no—
111C2×D4×C11—41no—
112C2×D4×C11—41no—
113C22×C4×C11—41no—
114C22×C4×C11—41no—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11#4111yescharacteristic
118C22×Dic11—21no—
119C2×D44—24no—
120C2×D44—21no—
121C2×D44C2×D412yes—
122C2×C4×D11—22no—
123C2×C4×D11—22no—
124C2×C4×D11—82no—
125C11×SD16—82no—
126C11×D8—82no—
127C2×C8×C11C2×D412yes—
128C2×C8×C11C2×D412yes—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C22⋊C4—41no—
134C11×C22⋊C4—41no—
135C11×C22⋊C4—41no—
136C11×C22⋊C4—41no—
137C42×C11C2×D411yescharacteristic
138C42×C11C2×D411yescharacteristic
139C42×C11#4111yescharacteristic
140C42×C11C2411yescharacteristic
141#4323—44no—
142#4323—44no—
143(C2×D11)⋊C4—22no—
144(C2×D11)⋊C4—22no—
145C4⋊Dic11—21no—
146C4⋊Dic11C2×D412yes—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—22no—
150C8×D11—82no—
151C8×D11—82no—
152#3207D1111yescharacteristic, complemented
153#3109—111no—
154#3100—111no—
155#2972—111no—
156#1683—112no—
157#1677—112no—
158#1667—112no—
159#1665—112no—
160#1572—111no—
161#1553—111no—
162#1543—111no—
163C23×C11—41no—
164C23×C11—41no—
165C23×C11#12111yescharacteristic
166C22×D11—22no—
167C22×D11—24no—
168C22×D11—81no—
169C22×D11—81no—
170Q8×C11—42no—
171Q8×C11—81no—
172D4×C11—42no—
173D4×C11—42no—
174D4×C11—42no—
175D4×C11—42no—
176D4×C11—81no—
177D4×C11—81no—
178D4×C11—82no—
179D4×C11—82no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—82no—
186C2×C4×C11—82no—
187C2×C4×C11#12111yescharacteristic
188C2×C4×C11#12111yescharacteristic
189C2×C4×C11#12111yescharacteristic
190C2×C4×C11C22×D411yescharacteristic
191C2×C4×C11C22×D411yescharacteristic
192C2×C4×C11C2×#4111yescharacteristic
193C2×Dic11—22no—
194C2×Dic11—81no—
195D44—24no—
196D44—22no—
197D44#13514yes—
198C4×D11—42no—
199C4×D11—42no—
200C4×D11—82no—
201C8×C11—22no—
202C8×C11—22no—
203C11⋊C8—42no—
204C11⋊C8—42no—
205C11⋊C8—42no—
206#532C2×D1111yescharacteristic
207#532C2×D1111yescharacteristic
208C2×C4×D4—111no—
209#493C2×D1111yescharacteristic, complemented
210#492C2×D1111yescharacteristic, complemented
211#487C2×D1111yescharacteristic, complemented
212#486C2×D1111yescharacteristic, complemented
213#481—221no—
214#480—221no—
215#476—112no—
216#474—112no—
217#463—22no—
218#459—112no—
219#459—112no—
220#449—22no—
221#447—221no—
222#447—221no—
223#442—222no—
224C4×D8—222no—
225C8×D4—112no—
226C8×D4—112no—
227C8×D4—222no—
228#432—111no—
229#431—111no—
230#431—111no—
231#431C2×D1111yescharacteristic
232C2×C22⋊C8—222no—
233#335—112no—
234#334—112no—
235#333—112no—
236#332—112no—
237#331—112no—
238#331—112no—
239C22×C11—21no—
240C22×C11—21no—
241C22×C11—21no—
242C22×C11—81no—
243C22×C11—81no—
244C22×C11—81no—
245C22×C11—81no—
246C22×C11—81no—
247C22×C11—81no—
248C22×C11C2×#12111yescharacteristic
249C2×D11—24no—
250C2×D11—42no—
251C2×D11—42no—
252C2×D11—84no—
253C4×C11—21no—
254C4×C11—21no—
255C4×C11—21no—
256C4×C11—21no—
257C4×C11—81no—
258C4×C11—81no—
259C4×C11C2×#13512yes—
260C4×C11#57612yes—
261Dic11—42no—
262C2×#41—21no—
263C2×#41—21no—
264C22×D4—111no—
265C23×C4—221no—
266C2×SD16—22no—
267C2×D8—22no—
268C2×D8—222no—
269C2×D8—222no—
270C22×C8—222no—
271C22×C8—222no—
272C4⋊Q8C22×D1111yescharacteristic
273C4⋊Q8C22×D1111yescharacteristic
274#127C22×D1111yescharacteristic
275#127C22×D1111yescharacteristic
276#124—21no—
277#124—21no—
278#121—21no—
279#121—21no—
280#121—21no—
281#121—21no—
282C4×D4—21no—
283C4×D4—21no—
284C4×D4—21no—
285C4×D4—21no—
286C4×D4—112no—
287C4×D4—112no—
288C4×D4—221no—
289C4×D4—221no—
290C2×C4⋊C4—111no—
291C2×C22⋊C4—221no—
292C2×C42C22×D1111yescharacteristic
293#107—222no—
294#106—222no—
295C4⋊C8—112no—
296C4⋊C8—112no—
297C4⋊C8—112no—
298C4⋊C8C22⋊D1112yes—
299#103—22no—
300#102—22no—
301#102—222no—
302#102—222no—
303#102—222no—
304#102—222no—
305C22⋊C8—221no—
306C22⋊C8—221no—
307C22⋊C8—221no—
308C22⋊C8—222no—
309C22⋊C8—222no—
310C22⋊C8C22⋊D1112yes—
311#97—221no—
312C4×C8—221no—
313C4×C8—221no—
314C4×C8C22×D1111yescharacteristic
315C4×C8C22×D1111yescharacteristic
316C2×C11—41no—
317C2×C11—161no—
318C2×C11—161no—
319C2×C11#304111yescharacteristic
320C2×C11#305011yescharacteristic
321C2×C11#306811yescharacteristic
322D11—44no—
323C24—221no—
324#41—82no—
325#41—82no—
326C2×Q8—21no—
327C2×Q8—21no—
328C2×D4—21no—
329C2×D4—21no—
330C2×D4—21no—
331C2×D4—21no—
332C2×D4—21no—
333C2×D4—21no—
334C2×D4—41no—
335C2×D4—41no—
336C2×D4—112no—
337C2×D4—224no—
338C2×D4—221no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—221no—
342C22×C4—222no—
343C22×C4—222no—
344C22×C4—882no—
345C22×C4D4×D1111yescharacteristic
346C22×C4#434111yescharacteristic
347C22×C4C2×C22⋊D1111yescharacteristic
348SD16—82no—
349D8—82no—
350D8—444no—
351D8—444no—
352C2×C8—222no—
353C2×C8—222no—
354C2×C8—222no—
355C2×C8—882no—
356C2×C8—882no—
357C2×C8C2×C22⋊D1112yes—
358C2×C8C2×C22⋊D1112yes—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—112no—
364C4⋊C4—221no—
365C22⋊C4—41no—
366C22⋊C4—41no—
367C22⋊C4—41no—
368C22⋊C4—41no—
369C22⋊C4—222no—
370C22⋊C4—222no—
371C42D4×D1111yescharacteristic
372C42#434111yescharacteristic
373C42C2×C22⋊D1111yescharacteristic
374C42C23×D1111yescharacteristic
375C11#1938911yescharacteristic, complemented, Sylow
376C23—41no—
377C23—41no—
378C23—224no—
379C23—222no—
380C23—881no—
381C23—881no—
382C23#6699111yescharacteristic
383Q8—42no—
384Q8—81no—
385D4—42no—
386D4—42no—
387D4—42no—
388D4—42no—
389D4—81no—
390D4—81no—
391D4—82no—
392D4—82no—
393D4—114no—
394D4—224no—
395D4—222no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—82no—
402C2×C4—82no—
403C2×C4—222no—
404C2×C4—442no—
405C2×C4—442no—
406C2×C4—882no—
407C2×C4—881no—
408C2×C4#6699111yescharacteristic
409C2×C4#6699111yescharacteristic
410C2×C4#6699111yescharacteristic
411C2×C4C2×D4×D1111yescharacteristic
412C2×C4C2×#434111yescharacteristic
413C2×C4C22×C22⋊D1111yescharacteristic
414C8—22no—
415C8—22no—
416C8—442no—
417C8—442no—
418C8—442no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22—81no—
427C22—81no—
428C22—224no—
429C22—442no—
430C22—442no—
431C22—884no—
432C22C2×#6699111yescharacteristic
433C4—21no—
434C4—21no—
435C4—21no—
436C4—21no—
437C4—81no—
438C4—81no—
439C4—442no—
440C4D11×#13512yes—
441C4#1062336612yes—
442C2—41no—
443C2—161no—
444C2—161no—
445C2—444no—
446C2#1307811511yescharacteristic
447C2#1307819311yescharacteristic
448C2#1307834011yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3207C2
socleC22×C11C2×#121
hypercenter#3207D11
hypocenterC11#19389
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3207

Complements

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

NH ≅ G/Ntype
1. #13078703C2semidirect
2. #13078612C2semidirect
3. #13077639C2semidirect
4. #13068064C2semidirect
5. #13068022C2semidirect
6. #13067968C2semidirect
7. #13067954C2semidirect
8. #13067396C2semidirect
9. #13067321C2semidirect
10. #13067278C2semidirect
11. C11×#3207C2semidirect
15. C11×#493C22semidirect
16. C11×#492C22semidirect
17. C11×#487C22semidirect
18. C11×#486C22semidirect
39. #10622185C22semidirect
40. #10622184C22semidirect
41. #10622182C22semidirect
42. #10622182C22semidirect
43. #10622096C22semidirect
44. #10622095C22semidirect
152. #3207D11semidirect
209. #493C2×D11semidirect
210. #492C2×D11semidirect
211. #487C2×D11semidirect
212. #486C2×D11semidirect
375. C11#19389semidirect

Maximal subgroups

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

subgroupindex
#130787032
#130786122
#130776392
#130680642
#130680222
#130679682
#130679542
#130673962
#130673212
#130672782
C11×#32072
#1938911