Finite Group Databasebeta

← #14650752

Subgroups — #14650752

Order 2816.

400 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 95 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#13067321C211yesmaximal, characteristic
3#13067242C211yesmaximal, characteristic, complemented
4#13066973C211yesmaximal, characteristic, complemented
5C11⋊#1308C211yesmaximal, characteristic, complemented
6#13066477C211yesmaximal, characteristic, complemented
7C11×#2980C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×#66923C2211yescharacteristic
10C11×#435—22no—
11C11×#435—22no—
12C11×#432C2211yescharacteristic
13C11×#432C2211yescharacteristic
14C11×#408—22no—
15#10622693—21no—
16#10622684—21no—
17#10622647C412yes—
18#10622646C412yes—
19#10622622—22no—
20#10622539C2211yescharacteristic
21#10622539C2211yescharacteristic
22#10622538C2211yescharacteristic
23#10622185—21no—
24#10622182—21no—
25#10622107—22no—
26#10622103—22no—
27C2×C11×#41—21no—
28C2×C11×M16—22no—
29C22×C8×C11—22no—
30C11×C4⋊Q8D411yescharacteristic
31C11×#127D411yescharacteristic
32C11×#124—21no—
33C11×#121—21no—
34C11×#121C2×C412yes—
35C4×D4×C11—21no—
36C4×D4×C11D412yes—
37C2×C42×C11C2311yescharacteristic
38C2×C4⋊Dic11C2×C411yescharacteristic
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42#66923—21no—
43#66923—21no—
44#66923—21no—
45#66923—21no—
46C11×C4⋊C8—21no—
47C11×C4⋊C8—21no—
48C11×C22⋊C8—24no—
49C11×C22⋊C8—21no—
50C11×C22⋊C8D412yes—
51C11×#97—21no—
52C11×#97D412yes—
53#66896—22no—
54#66896—22no—
55C22⋊(C11⋊C8)—21no—
56C22⋊(C11⋊C8)—21no—
57C22⋊(C11⋊C8)C2×C412yes—
58#66872—22no—
59#66871—22no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63#66867—21no—
64#66867—21no—
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×C11C22×C411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11#4111yescharacteristic
78C22×Dic11—21no—
79C22×Dic11—21no—
80C11×M16—82no—
81C2×C8×C11—22no—
82C2×C8×C11—22no—
83C2×C8×C11—82no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4C22⋊C412yes—
86C11×C22⋊C4—22no—
87C11×C22⋊C4—22no—
88C42×C11C2×D411yescharacteristic
89C42×C11C2×D411yescharacteristic
90C42×C11C2×D411yescharacteristic
91C42×C11#4111yescharacteristic
92C4⋊Dic11—21no—
93C4⋊Dic11—21no—
94C4⋊Dic11—21no—
95C4⋊Dic11—21no—
96Dic11⋊C4—41no—
97Dic11⋊C4—41no—
98Dic11⋊C4—41no—
99Dic11⋊C4—41no—
100C2×C11⋊C8—22no—
101C2×C11⋊C8—41no—
102C2×C11⋊C8—41no—
103#3234—111no—
104#2980D1111yescharacteristic
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×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—42no—
134C8×C11—42no—
135C11⋊C8—42no—
136C11⋊C8—81no—
137C11⋊C8—81no—
138#532C2×D1111yescharacteristic
139C2×#125—111no—
140#501—221no—
141#490—221no—
142#481—112no—
143#480—112no—
144#478—222no—
145#435—22no—
146#435—22no—
147#432—111no—
148#432—111no—
149#432C2×D1111yescharacteristic
150#432C2×D1111yescharacteristic
151#431—111no—
152#408—22no—
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—
171Dic11—81no—
172Dic11—81no—
173C2×#41—21no—
174C2×M16—22no—
175C22×C8—22no—
176C4⋊Q8D4411yescharacteristic
177#127D4411yescharacteristic
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×D4C22⋊D1112yes—
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—24no—
202C22⋊C8—21no—
203C22⋊C8—112no—
204C22⋊C8—221no—
205C22⋊C8—221no—
206C22⋊C8C22⋊D1112yes—
207#97—21no—
208#97—221no—
209#97—221no—
210#97C22⋊D1112yes—
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×D4(C2×D11)⋊C412yes—
224C22×C4—22no—
225C22×C4—221no—
226C22×C4—221no—
227C22×C4C2×C4×D1111yescharacteristic
228C22×C4#433911yescharacteristic
229C22×C4C2×C22⋊D1111yescharacteristic
230M16—82no—
231C2×C8—22no—
232C2×C8—22no—
233C2×C8—82no—
234C2×C8—222no—
235C2×C8—441no—
236C2×C8—441no—
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
250C42#433911yescharacteristic
251C42C2×C22⋊D1111yescharacteristic
252C42C2×C22⋊D1111yescharacteristic
253C11#933511yescharacteristic, complemented, Sylow
254C23—22no—
255C23C4×C22⋊D1111yescharacteristic
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×C4C2×(C2×D11)⋊C411yescharacteristic
272C2×C4C4×C22⋊D1111yescharacteristic
273C2×C4#6698211yescharacteristic
274C2×C4#6698311yescharacteristic
275C2×C4#6698311yescharacteristic
276C2×C4#6700611yescharacteristic
277C8—42no—
278C8—42no—
279C8—442no—
280C8—881no—
281C8—881no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22—42no—
286C22—42no—
287C22—42no—
288C22#1062282611yescharacteristic
289C4—21no—
290C4—21no—
291C4—21no—
292C4—21no—
293C4—21no—
294C4—21no—
295C4—42no—
296C4—881no—
297C4—881no—
298C2—41no—
299C2—82no—
300C2#1306897811yescharacteristic
301C2#1306910311yescharacteristic
302C2#1306916811yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2980C2
socleC22×C11#386
prime radicalC11×#532C22
cosocleC2×C42×C11C23
hypercenter#2980D11
hypocenterC11#9335
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2980

Complements

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

NH ≅ G/Ntype
3. #13067242C2semidirect
4. #13066973C2semidirect
5. C11⋊#1308C2semidirect
6. #13066477C2semidirect
253. C11#9335semidirect

Maximal subgroups

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

subgroupindex
#130798022
#130673212
#130672422
#130669732
C11⋊#13082
#130664772
C11×#29802
#933511