Finite Group Databasebeta

← #14650750

Subgroups — #14650750

Order 2816.

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

normal subgroups only

This group has 400 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#13079802C211yesmaximal, characteristic
2#13077687C211yesmaximal, characteristic
3#13067242C211yesmaximal, characteristic, complemented
4#13066971C211yesmaximal, characteristic, complemented
5C11⋊#1308C211yesmaximal, characteristic, complemented
6#13066478C211yesmaximal, characteristic, complemented
7C11×#1553C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×#66923C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#431C2211yescharacteristic
12#10622847—22no—
13#10622693—21no—
14#10622684—21no—
15#10622647C412yes—
16#10622646C412yes—
17#10622624—22no—
18#10622624—22no—
19#10622622—22no—
20#10622539C2211yescharacteristic
21#10622539C2211yescharacteristic
22#10622539C2211yescharacteristic
23C11×#332—21no—
24C11×#331—21no—
25#10622107—22no—
26#10622103—22no—
27C2×C11×#41—21no—
28C11×C4⋊Q8D411yescharacteristic
29C11×#127D411yescharacteristic
30C11×#124—21no—
31C11×#121—21no—
32C11×#121C2×C412yes—
33C4×D4×C11—21no—
34C4×D4×C11D412yes—
35C2×C42×C11C2311yescharacteristic
36C2×C4⋊Dic11C2×C411yescharacteristic
37C2×C4⋊Dic11C2×C411yescharacteristic
38C2×Dic11⋊C4—21no—
39C2×Dic11⋊C4—21no—
40C2×#4318—22no—
41C22×C11⋊C8—22no—
42#66923—21no—
43#66923—21no—
44#66923—21no—
45#66923—21no—
46C11×C4⋊C8—21no—
47C11×C4⋊C8—21no—
48C11×C22⋊C8—21no—
49C11×C22⋊C8—21no—
50C11×#97—21no—
51C4×C8×C11—21no—
52#66896—22no—
53#66896—22no—
54C22⋊(C11⋊C8)—24no—
55C22⋊(C11⋊C8)—21no—
56C22⋊(C11⋊C8)C2×C412yes—
57C22⋊(C11⋊C8)D412yes—
58#66872—22no—
59#66871—22no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63#66867—21no—
64#66867—21no—
65#66867D412yes—
66#9335—111nomaximal, Sylow
67C11×#41—81no—
68C11×#41—81no—
69C2×Q8×C11—21no—
70C2×D4×C11—22no—
71C2×D4×C11—21no—
72C2×D4×C11—21no—
73C2×D4×C11C22⋊C412yes—
74C22×C4×C11—22no—
75C22×C4×C11C22×C411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11#4111yescharacteristic
78C22×Dic11—21no—
79C22×Dic11—21no—
80C2×C8×C11—41no—
81C2×C8×C11—41no—
82C11×C4⋊C4—21no—
83C11×C4⋊C4C22⋊C412yes—
84C11×C22⋊C4—22no—
85C11×C22⋊C4—22no—
86C42×C11C2×D411yescharacteristic
87C42×C11C2×D411yescharacteristic
88C42×C11C2×D411yescharacteristic
89C42×C11#4111yescharacteristic
90C4⋊Dic11—21no—
91C4⋊Dic11—21no—
92C4⋊Dic11—21no—
93C4⋊Dic11—21no—
94Dic11⋊C4—41no—
95Dic11⋊C4—41no—
96Dic11⋊C4—41no—
97Dic11⋊C4—41no—
98#4318—82no—
99C2×C11⋊C8—22no—
100C2×C11⋊C8—22no—
101C2×C11⋊C8—22no—
102C2×C11⋊C8—82no—
103#3234—111no—
104#2980—111no—
105#1553D1111yescharacteristic
106#1534—111no—
107#1470—111no—
108#1308—111no—
109#1287—111no—
110C23×C11—22no—
111C23×C11C4×D411yescharacteristic
112Q8×C11—81no—
113D4×C11—42no—
114D4×C11—81no—
115D4×C11—81no—
116D4×C11—82no—
117C2×C4×C11—22no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—42no—
122C2×C4×C11—42no—
123C2×C4×C11C2×C22⋊C411yescharacteristic
124C2×C4×C11C4×D411yescharacteristic
125C2×C4×C11#12011yescharacteristic
126C2×C4×C11#12111yescharacteristic
127C2×C4×C11#12111yescharacteristic
128C2×C4×C11#12311yescharacteristic
129C2×Dic11—42no—
130C2×Dic11—41no—
131C2×Dic11—41no—
132C2×Dic11—81no—
133C8×C11—81no—
134C8×C11—81no—
135C11⋊C8—42no—
136C11⋊C8—42no—
137C11⋊C8—42no—
138#532C2×D1111yescharacteristic
139C2×#125—111no—
140#501—221no—
141#490—221no—
142#481—112no—
143#480—112no—
144#478—222no—
145#435—222no—
146#435—222no—
147#432—111no—
148#432—111no—
149#432—111no—
150#432C2×D1111yescharacteristic
151#431C2×D1111yescharacteristic
152#408—222no—
153#332—21no—
154#331—21no—
155#330—222no—
156#324—222no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11—42no—
161C22×C11—42no—
162C22×C11—42no—
163C22×C11#38611yescharacteristic
164C4×C11—21no—
165C4×C11—21no—
166C4×C11—21no—
167C4×C11—21no—
168C4×C11—21no—
169C4×C11—21no—
170C4×C11—42no—
171Dic11—81no—
172Dic11—81no—
173C2×#41—21no—
174C2×M16—222no—
175C22×C8—222no—
176C4⋊Q8C22⋊D1111yescharacteristic
177#127C22⋊D1111yescharacteristic
178#125—221no—
179#125—221no—
180#125—221no—
181#125—221no—
182#124—21no—
183#121—21no—
184#121C4×D1112yes—
185C4×D4—21no—
186C4×D4D4412yes—
187C2×C4⋊C4—111no—
188C2×C4⋊C4—111no—
189C2×C4⋊C4—221no—
190C2×C4⋊C4—221no—
191C2×C42C22×D1111yescharacteristic
192#107—222no—
193#106—222no—
194C4⋊C8—21no—
195C4⋊C8—21no—
196C4⋊C8—221no—
197C4⋊C8—221no—
198C4⋊C8—221no—
199#102—222no—
200#102—222no—
201C22⋊C8—21no—
202C22⋊C8—21no—
203C22⋊C8—112no—
204C22⋊C8—112no—
205C22⋊C8—224no—
206C22⋊C8—221no—
207#97—21no—
208#97—112no—
209#97—221no—
210#97—221no—
211C4×C8—21no—
212C2×C11—41no—
213C2×C11—82no—
214C2×C11#188111yescharacteristic
215C2×C11#190411yescharacteristic
216C2×C11#191511yescharacteristic
217#41—81no—
218#41—81no—
219C2×Q8—21no—
220C2×D4—22no—
221C2×D4—21no—
222C2×D4—21no—
223C2×D4(C2×D11)⋊C412yes—
224C22×C4—22no—
225C22×C4—221no—
226C22×C4—221no—
227C22×C4C2×C4×D1111yescharacteristic
228C22×C4D4×D1111yescharacteristic
229C22×C4#434111yescharacteristic
230M16—882no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—222no—
234C2×C8—222no—
235C2×C8—222no—
236C2×C8—882no—
237C4⋊C4—21no—
238C4⋊C4—221no—
239C4⋊C4—221no—
240C4⋊C4—221no—
241C4⋊C4—221no—
242C4⋊C4—441no—
243C4⋊C4—441no—
244C4⋊C4—441no—
245C4⋊C4—441no—
246C4⋊C4(C2×D11)⋊C412yes—
247C22⋊C4—22no—
248C22⋊C4—22no—
249C42C2×D4411yescharacteristic
250C42D4×D1111yescharacteristic
251C42#434111yescharacteristic
252C42C2×C22⋊D1111yescharacteristic
253C11#933511yescharacteristic, complemented, Sylow
254C23—22no—
255C23(C22⋊D11)⋊C411yescharacteristic
256Q8—81no—
257D4—42no—
258D4—81no—
259D4—81no—
260D4—82no—
261C2×C4—22no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—442no—
268C2×C4—441no—
269C2×C4—441no—
270C2×C4—881no—
271C2×C4(C22⋊D11)⋊C411yescharacteristic
272C2×C4#6693511yescharacteristic
273C2×C4#6693911yescharacteristic
274C2×C4C2×(C2×D11)⋊C411yescharacteristic
275C2×C4#6699211yescharacteristic
276C2×C4#6699211yescharacteristic
277C8—81no—
278C8—81no—
279C8—442no—
280C8—442no—
281C8—442no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22—42no—
286C22—42no—
287C22—42no—
288C22#1062257111yescharacteristic
289C4—21no—
290C4—21no—
291C4—21no—
292C4—21no—
293C4—21no—
294C4—21no—
295C4—42no—
296C4—881no—
297C4—881no—
298C2—41no—
299C2—82no—
300C2#1306897611yescharacteristic
301C2#1306910111yescharacteristic
302C2#1306916611yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1553C2
socleC22×C11#386
prime radicalC11×#532C22
cosocleC2×C42×C11C23
hypercenter#1553D11
hypocenterC11#9335
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1553

Complements

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

NH ≅ G/Ntype
3. #13067242C2semidirect
4. #13066971C2semidirect
5. C11⋊#1308C2semidirect
6. #13066478C2semidirect
253. C11#9335semidirect

Maximal subgroups

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

subgroupindex
#130798022
#130776872
#130672422
#130669712
C11⋊#13082
#130664782
C11×#15532
#933511