Finite Group Databasebeta

← #14650754

Subgroups — #14650754

Order 2816.

400 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 99 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#13077687C211yesmaximal, characteristic
2#13067321C211yesmaximal, characteristic
3#13067243C211yesmaximal, characteristic, complemented
4#13066972C211yesmaximal, characteristic, complemented
5C11⋊#1308C211yesmaximal, characteristic, complemented
6#13066479C211yesmaximal, characteristic, complemented
7C11×#3234C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×C11×#125C2211yescharacteristic
10C11×#501—21no—
11C11×#490—21no—
12C11×#481C412yes—
13C11×#480C412yes—
14C11×#478—22no—
15C11×#432C2211yescharacteristic
16#10622847—22no—
17#10622624—22no—
18#10622624—22no—
19#10622539C2211yescharacteristic
20#10622539C2211yescharacteristic
21#10622539C2211yescharacteristic
22#10622538C2211yescharacteristic
23#10622185—21no—
24#10622182—21no—
25#10622181—22no—
26#10622166—22no—
27C2×C11×#41—21no—
28C11×C4⋊Q8D411yescharacteristic
29C11×#127D411yescharacteristic
30C11×#125—21no—
31C11×#125—21no—
32C11×#125—21no—
33C11×#125—21no—
34C11×#124—21no—
35C11×#121—21no—
36C11×#121C2×C412yes—
37C4×D4×C11—21no—
38C4×D4×C11D412yes—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4C2×C411yescharacteristic
42C2×C11×C4⋊C4C2×C411yescharacteristic
43C2×C42×C11C2311yescharacteristic
44C2×#4318—22no—
45C22×C11⋊C8—22no—
46C11×#107—22no—
47C11×#106—22no—
48C11×C4⋊C8—21no—
49C11×#102—22no—
50C11×#102—22no—
51C11×C22⋊C8C2×C412yes—
52C11×#97—21no—
53C22⋊(C11⋊C8)—24no—
54C22⋊(C11⋊C8)—21no—
55C22⋊(C11⋊C8)—21no—
56C22⋊(C11⋊C8)—21no—
57C22⋊(C11⋊C8)D412yes—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62#66867—21no—
63#66867—21no—
64#66867D412yes—
65C4×C11⋊C8—21no—
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×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11C22×C411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11#4111yescharacteristic
80C2×C8×C11—22no—
81C11×C4⋊C4—21no—
82C11×C4⋊C4—21no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4C22⋊C412yes—
91C11×C22⋊C4—22no—
92C11×C22⋊C4—22no—
93C42×C11C2×D411yescharacteristic
94C42×C11C2×D411yescharacteristic
95C42×C11C2×D411yescharacteristic
96C42×C11#4111yescharacteristic
97#4318—82no—
98C2×C11⋊C8—22no—
99C2×C11⋊C8—22no—
100C2×C11⋊C8—41no—
101C2×C11⋊C8—41no—
102C2×C11⋊C8—82no—
103#3234D1111yescharacteristic
104#2980—111no—
105#1553—111no—
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×C11—42no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—81no—
127C2×C4×C11C2×C22⋊C411yescharacteristic
128C2×C4×C11C4×D411yescharacteristic
129C2×C4×C11#12011yescharacteristic
130C2×C4×C11#12111yescharacteristic
131C2×C4×C11#12111yescharacteristic
132C2×C4×C11#12311yescharacteristic
133C8×C11—42no—
134C11⋊C8—42no—
135C11⋊C8—42no—
136C11⋊C8—81no—
137C11⋊C8—81no—
138#532C2×D1111yescharacteristic
139C2×#125C2×D1111yescharacteristic
140#501—21no—
141#490—21no—
142#481Dic1112yes—
143#480Dic1112yes—
144#478—22no—
145#435—222no—
146#435—222no—
147#432—111no—
148#432—111no—
149#432—111no—
150#432C2×D1111yescharacteristic
151#431—111no—
152#408—222no—
153#332—221no—
154#331—221no—
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—
171C4×C11—81no—
172C4×C11—81no—
173C2×#41—21no—
174C2×M16—222no—
175C22×C8—222no—
176C4⋊Q8C22⋊D1111yescharacteristic
177#127C22⋊D1111yescharacteristic
178#125—21no—
179#125—21no—
180#125—21no—
181#125—21no—
182#124—21no—
183#121—21no—
184#121C2×Dic1112yes—
185C4×D4—21no—
186C4×D4C22⋊D1112yes—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4C2×Dic1111yescharacteristic
190C2×C4⋊C4C2×Dic1111yescharacteristic
191C2×C42C22×D1111yescharacteristic
192#107—22no—
193#106—22no—
194C4⋊C8—21no—
195C4⋊C8—221no—
196C4⋊C8—221no—
197C4⋊C8—221no—
198C4⋊C8—221no—
199#102—22no—
200#102—22no—
201C22⋊C8—112no—
202C22⋊C8—224no—
203C22⋊C8—221no—
204C22⋊C8—221no—
205C22⋊C8—221no—
206C22⋊C8C2×Dic1112yes—
207#97—21no—
208#97—112no—
209#97—221no—
210#97—221no—
211C4×C8—221no—
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×D4C22⋊Dic1112yes—
224C22×C4—22no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4D4×D1111yescharacteristic
228C22×C4#434111yescharacteristic
229C22×C4C22×Dic1111yescharacteristic
230M16—882no—
231C2×C8—22no—
232C2×C8—222no—
233C2×C8—222no—
234C2×C8—441no—
235C2×C8—441no—
236C2×C8—882no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4C22⋊Dic1112yes—
247C22⋊C4—22no—
248C22⋊C4—22no—
249C42D4×D1111yescharacteristic
250C42#434111yescharacteristic
251C42C2×C22⋊D1111yescharacteristic
252C42C2×C22⋊D1111yescharacteristic
253C11#933511yescharacteristic, complemented, Sylow
254C23—22no—
255C23D4×Dic1111yescharacteristic
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—42no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—81no—
271C2×C4D4×Dic1111yescharacteristic
272C2×C4#6698811yescharacteristic
273C2×C4#6699011yescharacteristic
274C2×C4#6699211yescharacteristic
275C2×C4#6699211yescharacteristic
276C2×C4C2×C22⋊Dic1111yescharacteristic
277C8—42no—
278C8—442no—
279C8—442no—
280C8—881no—
281C8—881no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22—42no—
286C22—42no—
287C22—42no—
288C22#1062283311yescharacteristic
289C4—21no—
290C4—21no—
291C4—21no—
292C4—21no—
293C4—21no—
294C4—21no—
295C4—42no—
296C4—81no—
297C4—81no—
298C2—41no—
299C2—82no—
300C2#1306898011yescharacteristic
301C2#1306910511yescharacteristic
302C2#1306916911yescharacteristic
subgroupG/H
centerC22#10622833
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#3234C2
socleC22×C11#386
prime radicalC11×#532C22
cosocleC2×C42×C11C23
hypercenter#3234D11
hypocenterC11#9335
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3234

Complements

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

NH ≅ G/Ntype
3. #13067243C2semidirect
4. #13066972C2semidirect
5. C11⋊#1308C2semidirect
6. #13066479C2semidirect
253. C11#9335semidirect

Maximal subgroups

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

subgroupindex
#130776872
#130673212
#130672432
#130669722
C11⋊#13082
#130664792
C11×#32342
#933511