Finite Group Databasebeta

← #14651457

Subgroups — #14651457

Order 2816.

468 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 107 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#13073601C211yesmaximal, characteristic
2#13067341C212yesmaximal
3#13066960C211yesmaximal, characteristic
4#13066473C212yesmaximal
5C11×#2983C211yesmaximal, characteristic
6C2×C4×Q8×C11C2211yescharacteristic
7C2×#66997C412yes—
8C2×#66922C2211yescharacteristic
9C11×#446—24no—
10C11×#432—21no—
11C11×#432C2212yes—
12C11×#431—21no—
13#10622596—21no—
14#10622596—21no—
15#10622587C412yes—
16C4×C4⋊Dic11C2211yescharacteristic
17#10622541—21no—
18#10622541—21no—
19#10622539C2212yes—
20#10622166—21no—
21#10622166—21no—
22#10622119—24no—
23C22×Q8×C11C2×C411yescharacteristic
24C22×Dic22C2×C412yes—
25C4×Q8×C11—22no—
26C4×Q8×C11—22no—
27C2×C11×C4⋊C4C2×C411yescharacteristic
28C2×C11×C4⋊C4D411yescharacteristic
29C2×C11×C4⋊C4D411yescharacteristic
30C2×C42×C11D411yescharacteristic
31C2×C42×C11D411yescharacteristic
32C2×C42×C11C2311yescharacteristic
33#66997—44no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×Dic11⋊C4—22no—
38C2×Dic11⋊C4—22no—
39C2×C4×Dic11C2×C412yes—
40#66922—22no—
41#66922—22no—
42C11×C4⋊C8—22no—
43C11×C4⋊C8—22no—
44C11×C4⋊C8D414yes—
45C11×C22⋊C8—22no—
46C11×#97—22no—
47C11×#97—22no—
48C4×C8×C11—22no—
49C11⋊#95—22no—
50C11⋊#95—22no—
51C11⋊#95—21no—
52C22⋊(C11⋊C8)—22no—
53C4⋊(C11⋊C8)—22no—
54#66867—22no—
55#9452—111nomaximal, Sylow
56C2×Q8×C11—22no—
57C2×Q8×C11—22no—
58C2×Q8×C11—41no—
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11C22×C411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×Dic11—22no—
67C22×Dic11—22no—
68C2×Dic22—24no—
69C2×Dic22—42no—
70C2×Dic22—42no—
71C2×C8×C11—24no—
72C11×C4⋊C4—22no—
73C11×C4⋊C4—22no—
74C11×C4⋊C4—22no—
75C42×C11—21no—
76C42×C11—21no—
77C42×C11—21no—
78C42×C11—21no—
79C42×C11C2×D412yes—
80C42×C11#4112yes—
81C4⋊Dic11—24no—
82C4⋊Dic11—41no—
83C4⋊Dic11—42no—
84C4⋊Dic11—41no—
85Dic11⋊C4—44no—
86Dic11⋊C4—44no—
87C4×Dic11—42no—
88C2×C11⋊C8—42no—
89#2983D1111yescharacteristic
90#2546—111no—
91#1558—112no—
92#1467—111no—
93#1285—112no—
94C23×C11C2×C22⋊C411yescharacteristic
95Q8×C11—44no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—22no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—41no—
107C2×C4×C11—41no—
108C2×C4×C11—41no—
109C2×C4×C11#10012yes—
110C2×C4×C11C4×D412yes—
111C2×C4×C11#12011yescharacteristic
112C2×C4×C11#12112yes—
113C2×C4×C11#12311yescharacteristic
114C2×Dic11—24no—
115C2×Dic11—42no—
116C2×Dic11—42no—
117C2×Dic11—42no—
118C2×Dic11—42no—
119C2×Dic11—42no—
120Dic22—84no—
121C8×C11—44no—
122C11⋊C8—82no—
123C2×C4⋊Q8—112no—
124C2×C4⋊Q8—111no—
125C2×C4×Q8C2×D1111yescharacteristic
126#446—24no—
127#432—21no—
128#432—112no—
129#432C2×D1112yes—
130#431—21no—
131#398—221no—
132#398—221no—
133#391—112no—
134#389—221no—
135#389—221no—
136C4×C4⋊C4—111no—
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—41no—
150C4×C11—41no—
151C4×C11—41no—
152C4×C11#45612yes—
153Dic11—44no—
154Dic11—82no—
155C22×Q8—112no—
156C22×Q8C4×D1111yescharacteristic
157C4⋊Q8—222no—
158C4⋊Q8—222no—
159C4⋊Q8—444no—
160C4×Q8—22no—
161C4×Q8—22no—
162C2×C4⋊C4—221no—
163C2×C4⋊C4—222no—
164C2×C4⋊C4—222no—
165C2×C4⋊C4—221no—
166C2×C4⋊C4—221no—
167C2×C4⋊C4C4×D1111yescharacteristic
168C2×C4⋊C4D4411yescharacteristic
169C2×C4⋊C4D4411yescharacteristic
170C2×C42—112no—
171C2×C42C22⋊D1111yescharacteristic
172C2×C42C22⋊D1111yescharacteristic
173C2×C42C22×D1111yescharacteristic
174C4⋊C8—22no—
175C4⋊C8—22no—
176C4⋊C8—222no—
177C4⋊C8C22⋊D1114yes—
178C22⋊C8—22no—
179C22⋊C8—222no—
180#97—22no—
181#97—22no—
182#97—222no—
183C4×C8—22no—
184#95—222no—
185#95—222no—
186#95—221no—
187C2×C11—21no—
188C2×C11—21no—
189C2×C11#188611yescharacteristic
190C2×C11#190011yescharacteristic
191C2×C11#190911yescharacteristic
192C2×Q8—22no—
193C2×Q8—22no—
194C2×Q8—41no—
195C2×Q8—224no—
196C2×Q8—442no—
197C2×Q8—442no—
198C22×C4—222no—
199C22×C4—222no—
200C22×C4(C2×D11)⋊C411yescharacteristic
201C22×C4(C2×D11)⋊C411yescharacteristic
202C22×C4(C2×D11)⋊C411yescharacteristic
203C22×C4(C2×D11)⋊C411yescharacteristic
204C22×C4C2×C4×D1111yescharacteristic
205C22×C4C2×D4411yescharacteristic
206C22×C4C2×C22⋊D1111yescharacteristic
207C2×C8—24no—
208C2×C8—442no—
209C4⋊C4—22no—
210C4⋊C4—22no—
211C4⋊C4—22no—
212C4⋊C4—224no—
213C4⋊C4—444no—
214C4⋊C4—444no—
215C4⋊C4—441no—
216C4⋊C4—442no—
217C4⋊C4—441no—
218C42—21no—
219C42—21no—
220C42—21no—
221C42—21no—
222C42—442no—
223C42#433912yes—
224C42C2×C22⋊D1112yes—
225C11#945211yescharacteristic, complemented, Sylow
226C23C2×(C2×D11)⋊C411yescharacteristic
227Q8—44no—
228Q8—884no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—224no—
243C2×C4—442no—
244C2×C4—442no—
245C2×C4—442no—
246C2×C4—442no—
247C2×C4—442no—
248C2×C4#6688712yes—
249C2×C4C4×C22⋊D1112yes—
250C2×C4#6698211yescharacteristic
251C2×C4#6698312yes—
252C2×C4#6700611yescharacteristic
253C8—44no—
254C8—882no—
255C22—21no—
256C22—21no—
257C22C2×#6688711yescharacteristic
258C22#1062274511yescharacteristic
259C22#1062282611yescharacteristic
260C4—22no—
261C4—22no—
262C4—22no—
263C4—21no—
264C4—41no—
265C4—41no—
266C4—41no—
267C4—444no—
268C4—882no—
269C4#1062285912yes—
270C2—21no—
271C2—21no—
272C2#1306900911yescharacteristic
273C2#1306907911yescharacteristic
274C2#1306913811yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2983C2
socleC22×C11#386
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#2983D11
hypocenterC11#9452
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

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
#130736012
#130673412
#130669602
#130664732
C11×#29832
#945211