Finite Group Databasebeta

← #14648277

Subgroups — #14648277

Order 2816.

412 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077682C211yesmaximal, characteristic
2#13069444C211yesmaximal, characteristic
3#13067405C211yesmaximal, characteristic, complemented
4#13067404C211yesmaximal, characteristic, complemented
5#13067276C211yesmaximal, characteristic
6#13066449C211yesmaximal, characteristic, complemented
7C11×#1276C211yesmaximal, characteristic, complemented
8#10623008C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C43×C11C2211yescharacteristic
12C2×#66869—22no—
13#10622538C2211yescharacteristic
14#10622538C2211yescharacteristic
15#10622537C2211yescharacteristic
16#10622451—21no—
17#10622447—21no—
18#10622340—22no—
19#10622301—21no—
20C8×D44—21no—
21#10622123C411yescharacteristic, complemented
22#10622123C411yescharacteristic, complemented
23#10622119C411yescharacteristic, complemented
24#10622119C411yescharacteristic, complemented
25#10622118—21no—
26#10622117—21no—
27#10622096—21no—
28#10622095—21no—
29C2×#4339D412yes—
30C2×C42×C11—21no—
31C2×C42×C11—21no—
32C2×C42×C11—21no—
33C2×C42×C11C2311yescharacteristic
34#66983—21no—
35#66983—21no—
36C2×#4318—21no—
37C2×#4313—22no—
38C2×C8×D11—22no—
39#66928Q812yes—
40#66927C2×C411yescharacteristic
41C4×D44—21no—
42C4×D44—21no—
43#66922C2×C411yescharacteristic
44C11×C4⋊C8C2×C411yescharacteristic
45C11×C4⋊C8C2×C411yescharacteristic
46C11×C4⋊C8D411yescharacteristic
47C11×C4⋊C8D411yescharacteristic
48C11×C22⋊C8—21no—
49C11×C22⋊C8—21no—
50C4×C8×C11—21no—
51C4×C8×C11—21no—
52C22⋊(C11⋊C8)—21no—
53C22⋊(C11⋊C8)—21no—
54(C2×D11)⋊C8—22no—
55(C2×D11)⋊C8—22no—
56#66869—44no—
57C4⋊(C11⋊C8)—21no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)C2×C411yescharacteristic
60C4⋊(C11⋊C8)C2×C411yescharacteristic
61C4⋊(C11⋊C8)D411yescharacteristic
62C4⋊(C11⋊C8)D411yescharacteristic
63C4×C11⋊C8—21no—
64C4×C11⋊C8—21no—
65#8934—111nomaximal, Sylow
66C22×C4×C11—41no—
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11#4111yescharacteristic
69C22×C4×C11#4111yescharacteristic
70C2×C22⋊D11—22no—
71#4339—42no—
72#4339—42no—
73C2×D44—21no—
74C2×D44—21no—
75C2×D44C4⋊C412yes—
76C2×C4×D11—22no—
77C2×Dic22C4⋊C412yes—
78C2×C8×C11—21no—
79C2×C8×C11—21no—
80C2×C8×C11—21no—
81C2×C8×C11—21no—
82C42×C11—22no—
83C42×C11—22no—
84C42×C11—22no—
85C42×C11—41no—
86C42×C11—41no—
87C42×C11—41no—
88C42×C11C22×C411yescharacteristic
89C42×C11C2×D411yescharacteristic
90C42×C11C2×D411yescharacteristic
91C42×C11C2×Q811yescharacteristic
92(C2×D11)⋊C4—22no—
93(C2×D11)⋊C4—22no—
94C4⋊Dic11—21no—
95C4⋊Dic11—21no—
96#4318—42no—
97C2×C11⋊C8—21no—
98C2×C11⋊C8—21no—
99C2×C11⋊C8—21no—
100C2×C11⋊C8—21no—
101C2×C11⋊C8—41no—
102#4313—82no—
103C8×D11—82no—
104#2979—111no—
105#1962—111no—
106#1574—111no—
107#1574—111no—
108#1543—111no—
109#1276—111no—
110#1276D1111yescharacteristic, complemented
111C23×C11#12311yescharacteristic
112C22×D11—22no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—42no—
122C2×C4×C11C2×C4⋊C411yescharacteristic
123C2×C4×C11C4×D411yescharacteristic
124C2×C4×C11C4×D411yescharacteristic
125C2×C4×C11#12011yescharacteristic
126C2×C4×C11C22⋊Q811yescharacteristic
127C2×C4×C11C22⋊Q811yescharacteristic
128C22⋊D11—82no—
129C2×Dic11—22no—
130D44—42no—
131D44—41no—
132D44—41no—
133D44—41no—
134D44—41no—
135C4×D11—42no—
136C4×D11—42no—
137Dic22—42no—
138C8×C11—41no—
139C8×C11—41no—
140C8×C11—41no—
141C8×C11—41no—
142C11⋊C8—41no—
143C11⋊C8—41no—
144C11⋊C8—41no—
145C11⋊C8—41no—
146C11⋊C8—81no—
147#532—111no—
148#436—221no—
149#436—221no—
150C8×D4—221no—
151C8×D4—221no—
152#431—111no—
153#431—111no—
154#431C2×D1111yescharacteristic
155#431C2×D1111yescharacteristic
156#423—111no—
157C2×#104—222no—
158#408—222no—
159C43C2×D1111yescharacteristic
160#335—221no—
161#335—221no—
162#334—221no—
163#334—221no—
164#333—111no—
165#333—111no—
166#331—111no—
167#331—111no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11#38511yescharacteristic
172C2×D11—42no—
173C2×D11—42no—
174C2×D11—42no—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—21no—
178C4×C11—44no—
179C4×C11#44311yescharacteristic
180C4×C11#44311yescharacteristic
181C4×C11#44411yescharacteristic
182C4×C11#44411yescharacteristic
183C4×C11#45311yescharacteristic
184C4×C11#45511yescharacteristic
185Dic11—42no—
186C2×#41—112no—
187C2×M16—222no—
188C2×M16—221no—
189C22×C8—222no—
190C4⋊Q8—111no—
191#127—111no—
192#124—112no—
193#121—221no—
194#121—221no—
195C4×D4—221no—
196C4×D4—221no—
197C2×C42—21no—
198C2×C42—21no—
199C2×C42—21no—
200C2×C42C22×D1111yescharacteristic
201C4⋊C8—111no—
202C4⋊C8—111no—
203C4⋊C8—111no—
204C4⋊C8—111no—
205C4⋊C8—221no—
206C4⋊C8—221no—
207C4⋊C8C4×D1111yescharacteristic
208C4⋊C8C4×D1111yescharacteristic
209C4⋊C8D4411yescharacteristic
210C4⋊C8D4411yescharacteristic
211#104—444no—
212C22⋊C8—21no—
213C22⋊C8—21no—
214C22⋊C8—222no—
215C22⋊C8—222no—
216C22⋊C8—221no—
217C22⋊C8—221no—
218C4×C8—21no—
219C4×C8—21no—
220C4×C8—221no—
221C4×C8—221no—
222C2×C11—41no—
223C2×C11#185611yescharacteristic
224C2×C11#186611yescharacteristic
225C2×C11#186611yescharacteristic
226D11—82no—
227#41—442no—
228#41—442no—
229C2×Q8—112no—
230C2×D4—112no—
231C2×D4—222no—
232C2×D4—221no—
233C2×D4—221no—
234C22×C4—41no—
235C22×C4—222no—
236C22×C4#433911yescharacteristic
237C22×C4D4×D1111yescharacteristic
238C22×C4#434111yescharacteristic
239M16—442no—
240M16—882no—
241C2×C8—21no—
242C2×C8—21no—
243C2×C8—21no—
244C2×C8—21no—
245C2×C8—221no—
246C2×C8—221no—
247C2×C8—221no—
248C2×C8—221no—
249C2×C8—441no—
250C2×C8—882no—
251C4⋊C4—221no—
252C4⋊C4—221no—
253C22⋊C4—222no—
254C22⋊C4—222no—
255C42—22no—
256C42—22no—
257C42—22no—
258C42—41no—
259C42—41no—
260C42—41no—
261C42C2×C4×D1111yescharacteristic
262C42C2×D4411yescharacteristic
263C42D4×D1111yescharacteristic
264C42Q8×D1111yescharacteristic
265C11#893411yescharacteristic, complemented, Sylow
266C23—222no—
267C23#6693611yescharacteristic
268Q8—442no—
269D4—442no—
270D4—441no—
271D4—441no—
272D4—441no—
273D4—441no—
274D4—882no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—222no—
285C2×C4—442no—
286C2×C4—442no—
287C2×C4C4×D4411yescharacteristic
288C2×C4(C22⋊D11)⋊C411yescharacteristic
289C2×C4#6693511yescharacteristic
290C2×C4C4⋊C4×D1111yescharacteristic
291C2×C4#6694911yescharacteristic
292C2×C4#6695011yescharacteristic
293C8—41no—
294C8—41no—
295C8—41no—
296C8—41no—
297C8—441no—
298C8—441no—
299C8—441no—
300C8—441no—
301C8—881no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—442no—
306C22—442no—
307C22—442no—
308C22#1062228111yescharacteristic
309C4—21no—
310C4—21no—
311C4—21no—
312C4—44no—
313C4—442no—
314C4#1062231311yescharacteristic
315C4#1062233011yescharacteristic
316C4#1062243511yescharacteristic
317C4#1062243611yescharacteristic
318C4#1062243711yescharacteristic
319C4#1062243811yescharacteristic
320C2—41no—
321C2—882no—
322C2#1306882711yescharacteristic
323C2#1306889211yescharacteristic
324C2#1306889411yescharacteristic
subgroupG/H
centerC2×C4#66935
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1276C2
socleC22×C11#385
prime radical#10623008C22
cosocleC2×C42×C11C23
hypercenter#1276D11
hypocenterC11#8934
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1276

Complements

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

NH ≅ G/Ntype
3. #13067405C2semidirect
4. #13067404C2semidirect
6. #13066449C2semidirect
7. C11×#1276C2semidirect
21. #10622123C4semidirect
22. #10622123C4semidirect
23. #10622119C4semidirect
24. #10622119C4semidirect
110. #1276D11semidirect
265. C11#8934semidirect

Maximal subgroups

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

subgroupindex
#130776822
#130694442
#130674052
#130674042
#130672762
#130664492
C11×#12762
#893411