Finite Group Databasebeta

← #14650744

Subgroups — #14650744

Order 2816.

398 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 85 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#13079621C211yesmaximal, characteristic
2#13077721C211yesmaximal, characteristic, complemented
3#13067327C211yesmaximal, characteristic, complemented
4#13067239C211yesmaximal, characteristic
5#13066969C211yesmaximal, characteristic
6#13066479C211yesmaximal, characteristic, complemented
7C11×#1308C211yesmaximal, characteristic, complemented
8C2×#66928C2211yescharacteristic
9#10623001C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#432C2211yescharacteristic
12C11×#432C2211yescharacteristic
13#10622539C2211yescharacteristic
14#10622538C2211yescharacteristic
15#10622458—22no—
16#10622441—22no—
17#10622352C412yes—
18#10622344C412yes—
19#10622333—22no—
20#10622328—21no—
21#10622327—21no—
22#10622314—22no—
23#10622120—21no—
24#10622119—21no—
25#10622106—22no—
26#10622102—22no—
27C22×D44C2×C411yescharacteristic
28C22×Dic22C2×C411yescharacteristic
29C2×C42×C11C2311yescharacteristic
30C2×(C2×D11)⋊C4—21no—
31C2×(C2×D11)⋊C4—21no—
32#66979—21no—
33#66977—21no—
34#66977C2×C412yes—
35C2×Dic44—22no—
36C2×#4314—22no—
37#66928—21no—
38#66928—21no—
39#66928—21no—
40#66928—21no—
41#66923—21no—
42#66922D411yescharacteristic
43#66922D411yescharacteristic
44C4×Dic22—21no—
45C4×Dic22D412yes—
46C11×C4⋊C8—21no—
47C11×C4⋊C8—21no—
48C11×C4⋊C8—21no—
49C11×C22⋊C8—21no—
50C11×C22⋊C8C2×C412yes—
51C11×C22⋊C8D412yes—
52C11×#97—21no—
53C11×#97—21no—
54C11×#97—21no—
55C22⋊(C11⋊C8)—21no—
56C22⋊(C11⋊C8)—21no—
57#66885—22no—
58#66880—22no—
59#66879—22no—
60Dic11⋊C8—24no—
61C8×Dic11—22no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64#66867D412yes—
65C4×C11⋊C8—21no—
66#9334—111nomaximal, Sylow
67C23×D11—21no—
68C22×C4×C11C22×C411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11#4111yescharacteristic
71C22×Dic11—21no—
72C2×D44—21no—
73C2×D44—21no—
74C2×D44—81no—
75C2×Dic22—21no—
76C2×Dic22—21no—
77C2×Dic22—21no—
78C2×Dic22—81no—
79C2×Dic22C22⋊C412yes—
80C2×C8×C11—22no—
81C2×C8×C11—22no—
82C2×C8×C11—41no—
83C42×C11C2×D411yescharacteristic
84C42×C11C2×D411yescharacteristic
85C42×C11C2×D411yescharacteristic
86C42×C11#4111yescharacteristic
87C22⋊Dic11—22no—
88(C2×D11)⋊C4—41no—
89(C2×D11)⋊C4—41no—
90(C2×D11)⋊C4—41no—
91(C2×D11)⋊C4—41no—
92C4⋊Dic11—21no—
93C4⋊Dic11—21no—
94C4⋊Dic11—21no—
95C4⋊Dic11C22⋊C412yes—
96Dic11⋊C4—22no—
97Dic11⋊C4—22no—
98C4×Dic11—22no—
99C2×C11⋊C8—22no—
100C2×C11⋊C8—41no—
101Dic44—82no—
102#4314—82no—
103#3215—111no—
104#2987—111no—
105#1554—111no—
106#1533—111no—
107#1469—111no—
108#1308D1111yescharacteristic, complemented
109#1287—111no—
110C23×C11C4×D411yescharacteristic
111C22×D11—41no—
112C22×D11—42no—
113C22×D11—81no—
114C22×D11—81no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11C2×C22⋊C411yescharacteristic
119C2×C4×C11C4×D411yescharacteristic
120C2×C4×C11#12011yescharacteristic
121C2×C4×C11#12111yescharacteristic
122C2×C4×C11#12111yescharacteristic
123C2×C4×C11#12311yescharacteristic
124C2×Dic11—22no—
125C2×Dic11—22no—
126C2×Dic11—41no—
127C2×Dic11—81no—
128D44—42no—
129D44—81no—
130Dic22—42no—
131Dic22—42no—
132Dic22—81no—
133Dic22—81no—
134C8×C11—42no—
135C8×C11—42no—
136C8×C11—81no—
137C11⋊C8—42no—
138C11⋊C8—81no—
139#533—111no—
140C2×#124—111no—
141#497—221no—
142#489—221no—
143#464—222no—
144#451—112no—
145#450—112no—
146#446—222no—
147#446—222no—
148#433—222no—
149#432—111no—
150#432C2×D1111yescharacteristic
151#432C2×D1111yescharacteristic
152#432C2×D1111yescharacteristic
153#431—111no—
154#333—221no—
155#332—221no—
156#329—222no—
157#323—222no—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11#38611yescharacteristic
162C2×D11—81no—
163C2×D11—81no—
164C2×D11—81no—
165C2×D11—162no—
166C4×C11—21no—
167C4×C11—21no—
168C4×C11—21no—
169C4×C11—21no—
170C4×C11—21no—
171C4×C11—21no—
172Dic11—42no—
173Dic11—42no—
174Dic11—81no—
175C22×Q8—111no—
176C22×D4—111no—
177C2×Q16—222no—
178C2×SD16—222no—
179C4⋊Q8—111no—
180C4⋊Q8—111no—
181#125—221no—
182#124—221no—
183#124—221no—
184#124—221no—
185#124—221no—
186C22⋊Q8—112no—
187C22⋊Q8—221no—
188C4×Q8—112no—
189C4×Q8—221no—
190#117—221no—
191C2×C22⋊C4—221no—
192C2×C22⋊C4—221no—
193C2×C42C22×D1111yescharacteristic
194C4⋊C8—21no—
195C4⋊C8—21no—
196C4⋊C8—21no—
197C4⋊C8—224no—
198C4⋊C8—221no—
199C4⋊C8—221no—
200#103—222no—
201#102—222no—
202C22⋊C8—21no—
203C22⋊C8—221no—
204C22⋊C8—221no—
205C22⋊C8C4×D1112yes—
206C22⋊C8D4412yes—
207#97—21no—
208#97—21no—
209#97—21no—
210#97—112no—
211#97—222no—
212C4×C8—222no—
213C4×C8—221no—
214C2×C11—41no—
215C2×C11#188111yescharacteristic
216C2×C11#190511yescharacteristic
217C2×C11#191411yescharacteristic
218D11—161no—
219C24—221no—
220C2×Q8—112no—
221C2×Q8—221no—
222C2×Q8—221no—
223C2×Q8—221no—
224C2×Q8—881no—
225C2×D4—221no—
226C2×D4—221no—
227C2×D4—881no—
228C22×C4—221no—
229C22×C4C2×C4×D1111yescharacteristic
230C22×C4C2×D4411yescharacteristic
231C22×C4#433911yescharacteristic
232Q16—882no—
233SD16—882no—
234C2×C8—22no—
235C2×C8—22no—
236C2×C8—41no—
237C2×C8—222no—
238C2×C8—441no—
239C4⋊C4—112no—
240C4⋊C4—221no—
241C4⋊C4—222no—
242C4⋊C4—222no—
243C4⋊C4—221no—
244C4⋊C4—221no—
245C22⋊C4—222no—
246C22⋊C4—441no—
247C22⋊C4—441no—
248C22⋊C4—441no—
249C22⋊C4—441no—
250C42—222no—
251C42D4×D1111yescharacteristic
252C42D4×D1111yescharacteristic
253C42D4×D1111yescharacteristic
254C42#434311yescharacteristic
255C11#933411yescharacteristic, complemented, Sylow
256C23—442no—
257C23—441no—
258C23—881no—
259C23—881no—
260C23C4×D4411yescharacteristic
261Q8—442no—
262Q8—442no—
263Q8—881no—
264Q8—881no—
265D4—442no—
266D4—881no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—222no—
271C2×C4—222no—
272C2×C4—441no—
273C2×C4—881no—
274C2×C4C22⋊C4×D1111yescharacteristic
275C2×C4#6693511yescharacteristic
276C2×C4#6693711yescharacteristic
277C2×C4#6694611yescharacteristic
278C2×C4#6694711yescharacteristic
279C2×C4#6694811yescharacteristic
280C8—42no—
281C8—42no—
282C8—81no—
283C8—442no—
284C8—881no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—881no—
289C22—881no—
290C22—881no—
291C22—1762no—
292C22#1062227811yescharacteristic
293C4—21no—
294C4—21no—
295C4—21no—
296C4—21no—
297C4—21no—
298C4—21no—
299C4—442no—
300C4—442no—
301C4—881no—
302C2—41no—
303C2—1761no—
304C2#1306897711yescharacteristic
305C2#1306910911yescharacteristic
306C2#1306916211yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1308C2
socleC22×C11#386
prime radicalC22×D44C2×C4
cosocleC2×C42×C11C23
hypercenter#1308D11
hypocenterC11#9334
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1308

Complements

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

NH ≅ G/Ntype
2. #13077721C2semidirect
3. #13067327C2semidirect
6. #13066479C2semidirect
7. C11×#1308C2semidirect
108. #1308D11semidirect
255. C11#9334semidirect

Maximal subgroups

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

subgroupindex
#130796212
#130777212
#130673272
#130672392
#130669692
#130664792
C11×#13082
#933411