Finite Group Databasebeta

← #14739012

Subgroups — #14739012

Order 2816.

728 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079734C211yesmaximal, characteristic, complemented
2#13078076C211yesmaximal, characteristic
3C2×#10622454C211yesmaximal, characteristic, complemented
4#13077639C211yesmaximal, characteristic, complemented
5#13068052C214yesmaximal, complemented
6#13068004C214yesmaximal, complemented
7#13067390C211yesmaximal, characteristic, complemented
8#13067287C211yesmaximal, characteristic, complemented
9C11×#1540C211yesmaximal, characteristic, complemented
10C11×#532C2211yescharacteristic
11C2×#67002—21no—
12C22×#4314—21no—
13C2×C4×D44C2211yescharacteristic
14C2×#66922C2211yescharacteristic
15C11×#431C2211yescharacteristic
16C2×C11×C4⋊C8C2211yescharacteristic
17#10622845—21no—
18C2×#66880—21no—
19#10622696C2212yes—
20#10622691C2212yescomplemented
21#10622685C2212yes—
22#10622683C2212yescomplemented
23#10622670—22no—
24#10622646—22no—
25#10622620—22no—
26#10622538C2211yescharacteristic
27#10622537C2211yescharacteristic
28#10622454—22no—
29#10622454C2214yes—
30#10622447C2214yes—
31D11×C22⋊C8—22no—
32C8×D44—22no—
33C11×#332C2212yescomplemented
34C11×#331C2212yescomplemented
35#10622124C2214yescomplemented
36#10622117C2214yescomplemented
37C2×C11×#41—21no—
38C22×D44D411yescharacteristic
39C22×C4×D11—21no—
40C22×Dic22—21no—
41C22×C8×C11—21no—
42C11×C4⋊Q8C2311yescharacteristic
43C11×#127C2311yescharacteristic
44C11×#124—21no—
45C11×#121—21no—
46C11×#121—21no—
47C4×D4×C11—21no—
48C4×D4×C11—21no—
49C2×C42×C11C2311yescharacteristic
50#67002—44no—
51C2×#4325—22no—
52C2×#4323—22no—
53C2×(C2×D11)⋊C4—21no—
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11D411yescharacteristic
57C2×#4318—21no—
58C2×#4314—24no—
59C2×#4314—44no—
60C2×C8×D11—24no—
61C4×D44—21no—
62C4×D44—21no—
63C4×D44D412yes—
64C4×D44C2312yes—
65#66922—21no—
66#66922—21no—
67#66922—21no—
68#66922C2312yes—
69C11×C4⋊C8—21no—
70C11×C4⋊C8C2312yes—
71C11×C4⋊C8C2312yes—
72C11×C22⋊C8—21no—
73C4×C8×C11—21no—
74#66899—22no—
75#66896—22no—
76#66896—24no—
77C22⋊(C11⋊C8)D412yes—
78(C2×D11)⋊C8—24no—
79#66880—24no—
80#66871—24no—
81C4⋊(C11⋊C8)—21no—
82C4⋊(C11⋊C8)D412yes—
83C4⋊(C11⋊C8)C2312yes—
84C4×C11⋊C8C2312yes—
85#19392—111nomaximal, Sylow
86C23×D11—21no—
87C11×#41—42no—
88C11×#41—42no—
89C2×Q8×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11—21no—
93C2×D4×C11—41no—
94C22×C4×C11—41no—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11#4111yescharacteristic
98C22×Dic11—21no—
99C22×Dic11—41no—
100C2×D44—21no—
101C2×D44—22no—
102C2×D44D814yes—
103C2×D44C2×D412yes—
104C2×C4×D11—22no—
105C2×C4×D11—22no—
106C2×C4×D11—82no—
107C2×Dic22—22no—
108C2×Dic22—41no—
109C2×Dic22—42no—
110C2×Dic22—42no—
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C2×C8×C11—42no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—21no—
116C11×C22⋊C4—41no—
117C11×C22⋊C4—41no—
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120C42×C11#4111yescharacteristic
121C42×C11C2411yescharacteristic
122#4325—44no—
123#4323—44no—
124(C2×D11)⋊C4—22no—
125(C2×D11)⋊C4—22no—
126C4⋊Dic11—21no—
127C4⋊Dic11—22no—
128C4⋊Dic11—22no—
129C4⋊Dic11—41no—
130C4⋊Dic11—41no—
131C4⋊Dic11C2×D412yes—
132#4318—42no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8C2×D414yes—
135#4314—48no—
136C8×D11—84no—
137#3226—111no—
138#3036—111no—
139C2×#461—111no—
140#2972—111no—
141#1681—114no—
142#1673—114no—
143#1571—111no—
144#1546—111no—
145#1540D1111yescharacteristic, complemented
146C23×C11—41no—
147C23×C11#12111yescharacteristic
148C22×D11—22no—
149C22×D11—24no—
150C22×D11—81no—
151C22×D11—81no—
152Q8×C11—41no—
153Q8×C11—41no—
154D4×C11—41no—
155D4×C11—41no—
156D4×C11—42no—
157D4×C11—81no—
158D4×C11—82no—
159C2×C4×C11—22no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—82no—
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11#12111yescharacteristic
166C2×C4×C11C2×D812yes—
167C2×C4×C11#13512yes—
168C2×C4×C11C22×D411yescharacteristic
169C2×C4×C11C22×D411yescharacteristic
170C2×C4×C11C2×#4111yescharacteristic
171C2×Dic11—22no—
172C2×Dic11—42no—
173C2×Dic11—81no—
174C2×Dic11—82no—
175D44—22no—
176D44—24no—
177D44C2×D814yes—
178C4×D11—44no—
179C4×D11—82no—
180Dic22—42no—
181Dic22—42no—
182Dic22—82no—
183C8×C11—42no—
184C8×C11—42no—
185C11⋊C8—24no—
186C11⋊C8—42no—
187C2×AGL(1,ℤ/8)—221no—
188C22×SD16—221no—
189#532C2×D1111yescharacteristic
190C2×C4⋊Q8—111no—
191C2×C4×D4—111no—
192#500—112no—
193#486—112no—
194#480—222no—
195#474—222no—
196#463—222no—
197#461—112no—
198#461—114no—
199#461—222no—
200#459—112no—
201C8×D4—114no—
202C8×D4—222no—
203#431—111no—
204#431C2×D1111yescharacteristic
205#423—111no—
206C2×C4⋊C8C2×D1111yescharacteristic
207#417—221no—
208C2×#103—221no—
209C2×C22⋊C8—222no—
210#335—114no—
211#332—114no—
212#332C2×D1112yescomplemented
213#331C2×D1112yescomplemented
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—81no—
217C22×C11—81no—
218C22×C11—81no—
219C22×C11#46612yes—
220C22×C11C2×#12111yescharacteristic
221C2×D11—24no—
222C2×D11—42no—
223C2×D11—42no—
224C2×D11—84no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—81no—
229C4×C11#46612yes—
230C4×C11C22×D811yescharacteristic
231C4×C11C2×#13511yescharacteristic
232C4×C11#57712yes—
233Dic11—42no—
234Dic11—82no—
235C2×#41—21no—
236C22×Q8—221no—
237C22×D4—111no—
238C23×C4—221no—
239AGL(1,ℤ/8)—444no—
240C2×SD16—224no—
241C2×SD16—222no—
242C2×SD16—444no—
243C2×D8—222no—
244C2×M16—221no—
245C22×C8—21no—
246C22×C8—224no—
247C4⋊Q8—112no—
248C4⋊Q8—221no—
249C4⋊Q8—221no—
250C4⋊Q8—221no—
251C4⋊Q8C22×D1111yescharacteristic
252#127C22×D1111yescharacteristic
253#124—21no—
254#121—21no—
255#121—21no—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4—112no—
259C4×D4—112no—
260C4×D4—221no—
261C4×D4—221no—
262C2×C4⋊C4—111no—
263C2×C4⋊C4—221no—
264C2×C4⋊C4—221no—
265C2×C22⋊C4—221no—
266C2×C42C22×D1111yescharacteristic
267#107—224no—
268C4⋊C8—21no—
269C4⋊C8—112no—
270C4⋊C8—112no—
271C4⋊C8—221no—
272C4⋊C8C22×D1112yes—
273C4⋊C8C22×D1112yes—
274#103—224no—
275#103—222no—
276#102—222no—
277#102—224no—
278C22⋊C8—21no—
279C22⋊C8—112no—
280C22⋊C8—224no—
281C4×C8—21no—
282C4×C8—112no—
283C2×C11—22no—
284C2×C11—161no—
285C2×C11#304211yescharacteristic
286C2×C11C2×#46611yescharacteristic
287C2×C11#306911yescharacteristic
288D11—44no—
289C24—221no—
290#41—42no—
291#41—42no—
292C2×Q8—21no—
293C2×Q8—222no—
294C2×Q8—441no—
295C2×Q8—442no—
296C2×Q8—442no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—41no—
301C2×D4—114no—
302C2×D4—112no—
303C2×D4—221no—
304C2×D4—222no—
305C22×C4—41no—
306C22×C4—221no—
307C22×C4—222no—
308C22×C4—222no—
309C22×C4—441no—
310C22×C4—882no—
311C22×C4#433911yescharacteristic
312C22×C4D4×D1111yescharacteristic
313C22×C4D4×D1111yescharacteristic
314SD16—448no—
315SD16—444no—
316D8—444no—
317M16—442no—
318C2×C8—22no—
319C2×C8—22no—
320C2×C8—42no—
321C2×C8—114no—
322C2×C8—222no—
323C2×C8—884no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—112no—
327C4⋊C4—221no—
328C4⋊C4—222no—
329C4⋊C4—222no—
330C4⋊C4—441no—
331C4⋊C4—441no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—222no—
335C22⋊C4—222no—
336C42#433911yescharacteristic
337C42D4×D1111yescharacteristic
338C42D4×D1111yescharacteristic
339C42C23×D1111yescharacteristic
340C11#1939211yescharacteristic, complemented, Sylow
341C23—41no—
342C23—222no—
343C23—224no—
344C23—881no—
345C23—881no—
346C23#6693711yescharacteristic
347Q8—41no—
348Q8—41no—
349Q8—442no—
350Q8—442no—
351Q8—882no—
352D4—41no—
353D4—41no—
354D4—42no—
355D4—81no—
356D4—82no—
357D4—114no—
358D4—222no—
359D4—224no—
360C2×C4—22no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—82no—
364C2×C4—222no—
365C2×C4—444no—
366C2×C4—442no—
367C2×C4—882no—
368C2×C4—881no—
369C2×C4—882no—
370C2×C4#6693711yescharacteristic
371C2×C4#6693711yescharacteristic
372C2×C4#6693711yescharacteristic
373C2×C4D8×D1112yes—
374C2×C4#6696912yes—
375C2×C4C2×#433911yescharacteristic
376C2×C4C2×D4×D1111yescharacteristic
377C2×C4C2×D4×D1111yescharacteristic
378C8—42no—
379C8—42no—
380C8—224no—
381C8—442no—
382C22—21no—
383C22—21no—
384C22—81no—
385C22—81no—
386C22—81no—
387C22—224no—
388C22—442no—
389C22—442no—
390C22—884no—
391C22#1062238812yes—
392C22C2×#6693711yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—81no—
397C4—442no—
398C4—882no—
399C4#1062238812yes—
400C4C2×D8×D1111yescharacteristic
401C4C2×#6696911yescharacteristic
402C4#1062330112yes—
403C2—22no—
404C2—161no—
405C2—444no—
406C2#1307813111yescharacteristic
407C2C2×#1062238811yescharacteristic
408C2#1307835611yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1540C2
socleC22×C11C2×#121
prime radical#13078076C2
hypercenter#1540D11
hypocenterC11#19392
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1540

Complements

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

NH ≅ G/Ntype
1. #13079734C2semidirect
3. C2×#10622454C2semidirect
4. #13077639C2semidirect
5. #13068052C2semidirect
6. #13068004C2semidirect
7. #13067390C2semidirect
8. #13067287C2semidirect
9. C11×#1540C2semidirect
20. #10622691C22semidirect
22. #10622683C22semidirect
33. C11×#332C22semidirect
34. C11×#331C22semidirect
35. #10622124C22semidirect
36. #10622117C22semidirect
145. #1540D11semidirect
212. #332C2×D11semidirect
213. #331C2×D11semidirect
340. C11#19392semidirect

Maximal subgroups

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

subgroupindex
#130797342
#130780762
C2×#106224542
#130776392
#130680522
#130680042
#130673902
#130672872
C11×#15402
#1939211