Finite Group Databasebeta

← #14650743

Subgroups — #14650743

Order 2816.

398 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 91 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#13079615C211yesmaximal, characteristic
2#13077722C211yesmaximal, characteristic, complemented
3#13067239C211yesmaximal, characteristic
4#13066967C211yesmaximal, characteristic
5C11⋊#1308C211yesmaximal, characteristic, complemented
6#13066478C211yesmaximal, characteristic, complemented
7C11×#1554C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×#66928C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#431C2211yescharacteristic
12#10622702—21no—
13#10622699—21no—
14#10622663C412yes—
15#10622659C412yes—
16#10622641—22no—
17#10622637—22no—
18#10622637—22no—
19#10622613—22no—
20#10622539C2211yescharacteristic
21#10622539C2211yescharacteristic
22#10622539C2211yescharacteristic
23C11×#333—21no—
24C11×#332—21no—
25#10622106—22no—
26#10622102—22no—
27C22×D44C2×C411yescharacteristic
28C22×Dic22C2×C411yescharacteristic
29C11×C4⋊Q8D411yescharacteristic
30C11×C4⋊Q8D411yescharacteristic
31C11×#125—21no—
32C11×C22⋊Q8—21no—
33C11×C22⋊Q8C2×C412yes—
34C4×Q8×C11—21no—
35C4×Q8×C11D412yes—
36C11×#117—21no—
37C2×C42×C11C2311yescharacteristic
38C2×#4326—22no—
39C2×#4325—22no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42#66928—21no—
43#66928—21no—
44#66928—21no—
45#66928—21no—
46C11×C4⋊C8—21no—
47C11×C4⋊C8—21no—
48C11×C22⋊C8—21no—
49C11×C22⋊C8—21no—
50C11×#97—21no—
51C4×C8×C11—21no—
52C22⋊(C11⋊C8)—21no—
53C22⋊(C11⋊C8)C2×C412yes—
54C22⋊(C11⋊C8)D412yes—
55#66874—22no—
56#66873—22no—
57C4⋊(C11⋊C8)—24no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)—21no—
61#66867—22no—
62#66867—21no—
63#66867—21no—
64#66867D412yes—
65C4×C11⋊C8—22no—
66#9334—111nomaximal, Sylow
67C23×D11—21no—
68C2×Q8×C11—21no—
69C2×Q8×C11C22⋊C412yes—
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11#4111yescharacteristic
73C22×Dic11—21no—
74C2×D44—21no—
75C2×D44—21no—
76C2×D44—81no—
77C2×Dic22—21no—
78C2×Dic22—21no—
79C2×Dic22—81no—
80C2×C8×C11—41no—
81C2×C8×C11—41no—
82C11×C4⋊C4—22no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—22no—
87C11×C4⋊C4C22⋊C412yes—
88C11×C22⋊C4—22no—
89C42×C11—22no—
90C42×C11C2×D411yescharacteristic
91C42×C11C2×D411yescharacteristic
92C42×C11C2×D411yescharacteristic
93C42×C11#4111yescharacteristic
94#4326—82no—
95#4325—82no—
96(C2×D11)⋊C4—41no—
97(C2×D11)⋊C4—41no—
98(C2×D11)⋊C4—41no—
99(C2×D11)⋊C4—41no—
100C2×C11⋊C8—22no—
101C2×C11⋊C8—22no—
102C2×C11⋊C8—22no—
103#3215—111no—
104#2987—111no—
105#1554D1111yescharacteristic, complemented
106#1533—111no—
107#1469—111no—
108#1308—111no—
109#1287—111no—
110C23×C11C4×D411yescharacteristic
111C22×D11—41no—
112C22×D11—42no—
113C22×D11—81no—
114C22×D11—81no—
115Q8×C11—42no—
116Q8×C11—81no—
117C2×C4×C11—22no—
118C2×C4×C11—22no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11C2×C22⋊C411yescharacteristic
123C2×C4×C11C4×D411yescharacteristic
124C2×C4×C11#12011yescharacteristic
125C2×C4×C11#12111yescharacteristic
126C2×C4×C11#12111yescharacteristic
127C2×C4×C11#12311yescharacteristic
128C2×Dic11—41no—
129C2×Dic11—81no—
130D44—42no—
131D44—81no—
132Dic22—42no—
133Dic22—81no—
134C8×C11—81no—
135C8×C11—81no—
136C11⋊C8—42no—
137C11⋊C8—42no—
138C11⋊C8—42no—
139#533C2×D1111yescharacteristic
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#432—111no—
151#432—111no—
152#432C2×D1111yescharacteristic
153#431C2×D1111yescharacteristic
154#333—21no—
155#332—21no—
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—
172C4×C11—42no—
173C4×C11—42no—
174Dic11—81no—
175C22×Q8—111no—
176C22×D4—111no—
177C2×Q16—222no—
178C2×SD16—222no—
179C4⋊Q8C22⋊D1111yescharacteristic
180C4⋊Q8C22⋊D1111yescharacteristic
181#125—21no—
182#124—221no—
183#124—221no—
184#124—221no—
185#124—221no—
186C22⋊Q8—21no—
187C22⋊Q8C4×D1112yes—
188C4×Q8—21no—
189C4×Q8D4412yes—
190#117—21no—
191C2×C22⋊C4—221no—
192C2×C22⋊C4—221no—
193C2×C42C22×D1111yescharacteristic
194C4⋊C8—21no—
195C4⋊C8—21no—
196C4⋊C8—224no—
197C4⋊C8—221no—
198C4⋊C8—221no—
199C4⋊C8—221no—
200#103—222no—
201#102—222no—
202C22⋊C8—21no—
203C22⋊C8—21no—
204C22⋊C8—112no—
205C22⋊C8—112no—
206C22⋊C8—221no—
207#97—21no—
208#97—112no—
209#97—222no—
210#97—221no—
211#97—221no—
212C4×C8—21no—
213C4×C8—222no—
214C2×C11—41no—
215C2×C11#188111yescharacteristic
216C2×C11#190511yescharacteristic
217C2×C11#191411yescharacteristic
218D11—161no—
219C24—221no—
220C2×Q8—21no—
221C2×Q8—221no—
222C2×Q8—221no—
223C2×Q8—881no—
224C2×Q8(C2×D11)⋊C412yes—
225C2×D4—221no—
226C2×D4—221no—
227C2×D4—881no—
228C22×C4—221no—
229C22×C4C2×C4×D1111yescharacteristic
230C22×C4D4×D1111yescharacteristic
231C22×C4#434111yescharacteristic
232Q16—882no—
233SD16—882no—
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—222no—
237C2×C8—222no—
238C2×C8—222no—
239C4⋊C4—22no—
240C4⋊C4—22no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4(C2×D11)⋊C412yes—
245C22⋊C4—22no—
246C22⋊C4—441no—
247C22⋊C4—441no—
248C22⋊C4—441no—
249C22⋊C4—441no—
250C42—22no—
251C42C2×D4411yescharacteristic
252C42D4×D1111yescharacteristic
253C42#434111yescharacteristic
254C42C2×C22⋊D1111yescharacteristic
255C11#933411yescharacteristic, complemented, Sylow
256C23—442no—
257C23—441no—
258C23—881no—
259C23—881no—
260C23(C22⋊D11)⋊C411yescharacteristic
261Q8—42no—
262Q8—81no—
263Q8—442no—
264Q8—881no—
265D4—442no—
266D4—881no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—441no—
273C2×C4—881no—
274C2×C4(C22⋊D11)⋊C411yescharacteristic
275C2×C4#6693511yescharacteristic
276C2×C4#6693911yescharacteristic
277C2×C4C2×(C2×D11)⋊C411yescharacteristic
278C2×C4#6699211yescharacteristic
279C2×C4#6699211yescharacteristic
280C8—81no—
281C8—81no—
282C8—442no—
283C8—442no—
284C8—442no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—881no—
289C22—881no—
290C22—881no—
291C22—1762no—
292C22#1062257111yescharacteristic
293C4—21no—
294C4—21no—
295C4—21no—
296C4—21no—
297C4—21no—
298C4—21no—
299C4—42no—
300C4—42no—
301C4—881no—
302C2—41no—
303C2—1761no—
304C2#1306897611yescharacteristic
305C2#1306910811yescharacteristic
306C2#1306916111yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1554C2
socleC22×C11#386
prime radicalC22×D44C2×C4
cosocleC2×C42×C11C23
hypercenter#1554D11
hypocenterC11#9334
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1554

Complements

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

NH ≅ G/Ntype
2. #13077722C2semidirect
5. C11⋊#1308C2semidirect
6. #13066478C2semidirect
7. C11×#1554C2semidirect
105. #1554D11semidirect
255. C11#9334semidirect

Maximal subgroups

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

subgroupindex
#130796152
#130777222
#130672392
#130669672
C11⋊#13082
#130664782
C11×#15542
#933411