Finite Group Databasebeta

← #14651458

Subgroups — #14651458

Order 2816.

468 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 111 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#13077701C211yesmaximal, characteristic
2#13067342C212yesmaximal
3#13066960C211yesmaximal, characteristic
4#13066472C212yesmaximal
5C11×#2546C211yesmaximal, characteristic
6C2×C11×C4⋊Q8C412yes—
7C2×C11×C4⋊Q8C2211yescharacteristic
8C2×C4×Q8×C11C2211yescharacteristic
9C11×#398—21no—
10C11×#398—21no—
11C11×#391C412yes—
12C11×#389—21no—
13C11×#389—21no—
14C4×C11×C4⋊C4C2211yescharacteristic
15#10622637—24no—
16#10622539—21no—
17#10622539C2212yes—
18#10622539C2212yes—
19#10622538—21no—
20#10622184—24no—
21#10622166—21no—
22#10622166—21no—
23C22×Q8×C11C2×C412yes—
24C22×Q8×C11C2×C411yescharacteristic
25C11×C4⋊Q8—22no—
26C11×C4⋊Q8—22no—
27C11×C4⋊Q8—44no—
28C4×Q8×C11—22no—
29C4×Q8×C11—22no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—22no—
32C2×C11×C4⋊C4—22no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4C2×C411yescharacteristic
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C11×C4⋊C4D411yescharacteristic
38C2×C42×C11C2×C412yes—
39C2×C42×C11D411yescharacteristic
40C2×C42×C11D411yescharacteristic
41C2×C42×C11C2311yescharacteristic
42C11×#95—22no—
43C11×#95—22no—
44C11×#95—21no—
45C22⋊(C11⋊C8)—22no—
46C22⋊(C11⋊C8)—22no—
47C4⋊(C11⋊C8)—22no—
48C4⋊(C11⋊C8)—22no—
49C4⋊(C11⋊C8)—22no—
50C4⋊(C11⋊C8)D414yes—
51#66867—22no—
52#66867—22no—
53#66867—22no—
54C4×C11⋊C8—22no—
55#9452—111nomaximal, Sylow
56C2×Q8×C11—22no—
57C2×Q8×C11—22no—
58C2×Q8×C11—24no—
59C2×Q8×C11—41no—
60C2×Q8×C11—42no—
61C2×Q8×C11—42no—
62C22×C4×C11—22no—
63C22×C4×C11—22no—
64C22×C4×C11C22⋊C411yescharacteristic
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22×C411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C11×C4⋊C4—24no—
72C11×C4⋊C4—22no—
73C11×C4⋊C4—22no—
74C11×C4⋊C4—22no—
75C11×C4⋊C4—44no—
76C11×C4⋊C4—44no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—42no—
79C11×C4⋊C4—41no—
80C42×C11—21no—
81C42×C11—21no—
82C42×C11—21no—
83C42×C11—21no—
84C42×C11—42no—
85C42×C11C2×D412yes—
86C42×C11#4112yes—
87C2×C11⋊C8—24no—
88C2×C11⋊C8—42no—
89#2983—111no—
90#2546D1111yescharacteristic
91#1558—112no—
92#1467—111no—
93#1285—112no—
94C23×C11C2×C22⋊C411yescharacteristic
95Q8×C11—44no—
96Q8×C11—84no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—22no—
102C2×C4×C11—24no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—41no—
109C2×C4×C11—42no—
110C2×C4×C11—42no—
111C2×C4×C11—41no—
112C2×C4×C11—41no—
113C2×C4×C11—42no—
114C2×C4×C11—42no—
115C2×C4×C11—42no—
116C2×C4×C11#10012yes—
117C2×C4×C11C4×D412yes—
118C2×C4×C11#12011yescharacteristic
119C2×C4×C11#12112yes—
120C2×C4×C11#12311yescharacteristic
121C11⋊C8—44no—
122C11⋊C8—82no—
123C2×C4⋊Q8Dic1112yes—
124C2×C4⋊Q8C2×D1111yescharacteristic
125C2×C4×Q8C2×D1111yescharacteristic
126#446—224no—
127#432—112no—
128#432—112no—
129#432—221no—
130#431—221no—
131#398—21no—
132#398—21no—
133#391Dic1112yes—
134#389—21no—
135#389—21no—
136C4×C4⋊C4C2×D1111yescharacteristic
137#333—224no—
138#324—221no—
139#324—221no—
140C22×C11—21no—
141C22×C11—21no—
142C22×C11#38611yescharacteristic
143C22×C11C2×#10011yescharacteristic
144C22×C11#41311yescharacteristic
145C4×C11—21no—
146C4×C11—22no—
147C4×C11—22no—
148C4×C11—22no—
149C4×C11—44no—
150C4×C11—41no—
151C4×C11—41no—
152C4×C11—41no—
153C4×C11—82no—
154C4×C11#45612yes—
155C22×Q8C2×Dic1112yes—
156C22×Q8C2×Dic1111yescharacteristic
157C4⋊Q8—22no—
158C4⋊Q8—22no—
159C4⋊Q8—44no—
160C4×Q8—22no—
161C4×Q8—22no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4C2×Dic1111yescharacteristic
168C2×C4⋊C4C22⋊D1111yescharacteristic
169C2×C4⋊C4C22⋊D1111yescharacteristic
170C2×C42C2×Dic1112yes—
171C2×C42C22⋊D1111yescharacteristic
172C2×C42C22⋊D1111yescharacteristic
173C2×C42C22×D1111yescharacteristic
174C4⋊C8—114no—
175C4⋊C8—222no—
176C4⋊C8—222no—
177C4⋊C8—222no—
178C22⋊C8—222no—
179C22⋊C8—222no—
180#97—222no—
181#97—222no—
182#97—222no—
183C4×C8—222no—
184#95—22no—
185#95—22no—
186#95—21no—
187C2×C11—21no—
188C2×C11—21no—
189C2×C11#188611yescharacteristic
190C2×C11#190011yescharacteristic
191C2×C11#190911yescharacteristic
192C2×Q8—22no—
193C2×Q8—22no—
194C2×Q8—24no—
195C2×Q8—41no—
196C2×Q8—42no—
197C2×Q8—42no—
198C22×C4—22no—
199C22×C4—22no—
200C22×C4C22⋊Dic1111yescharacteristic
201C22×C4C22⋊Dic1111yescharacteristic
202C22×C4C22⋊Dic1111yescharacteristic
203C22×C4C22⋊Dic1111yescharacteristic
204C22×C4C22×Dic1111yescharacteristic
205C22×C4C2×C22⋊D1111yescharacteristic
206C22×C4C2×C22⋊D1111yescharacteristic
207C2×C8—224no—
208C2×C8—442no—
209C4⋊C4—24no—
210C4⋊C4—22no—
211C4⋊C4—22no—
212C4⋊C4—22no—
213C4⋊C4—44no—
214C4⋊C4—44no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4—42no—
218C42—21no—
219C42—21no—
220C42—21no—
221C42—21no—
222C42—42no—
223C42D4×D1112yes—
224C42#434112yes—
225C11#945211yescharacteristic, complemented, Sylow
226C23C2×C22⋊Dic1111yescharacteristic
227Q8—44no—
228Q8—84no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—24no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4#6689712yes—
249C2×C4D4×Dic1112yes—
250C2×C4#6698811yescharacteristic
251C2×C4#6699011yescharacteristic
252C2×C4#6699212yes—
253C8—444no—
254C8—882no—
255C22—21no—
256C22—21no—
257C22C2×#6689711yescharacteristic
258C22#1062283311yescharacteristic
259C22#1062285011yescharacteristic
260C4—22no—
261C4—22no—
262C4—22no—
263C4—21no—
264C4—44no—
265C4—41no—
266C4—41no—
267C4—41no—
268C4—82no—
269C4#1062270812yes—
270C2—21no—
271C2—21no—
272C2#1306901011yescharacteristic
273C2#1306908011yescharacteristic
274C2#1306913911yescharacteristic
subgroupG/H
centerC22#10622833
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2546C2
socleC22×C11#386
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#2546D11
hypocenterC11#9452
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2546

Complements

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

NH ≅ G/Ntype
225. C11#9452semidirect

Maximal subgroups

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

subgroupindex
#130777012
#130673422
#130669602
#130664722
C11×#25462
#945211