Finite Group Databasebeta

← #14651465

Subgroups — #14651465

Order 2816.

448 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 103 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#13073821C211yesmaximal, characteristic
3#13067334C212yesmaximal
4#13066471C212yesmaximal
5C11×#1467C211yesmaximal, characteristic
6C2×C4×Q8×C11C2211yescharacteristic
7C2×#66922C2211yescharacteristic
8C11×#432C2212yes—
9#10622843C412yes—
10#10622637—24no—
11#10622592—21no—
12#10622592—21no—
13#10622589C412yes—
14C4×C4⋊Dic11C2211yescharacteristic
15#10622541—21no—
16#10622541—21no—
17#10622539—21no—
18#10622539C2212yes—
19#10622538—21no—
20C11×#324—21no—
21C11×#324—21no—
22#10622120—24no—
23C22×Q8×C11C2×C411yescharacteristic
24C22×Dic22—21no—
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
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11C2×C412yes—
36C2×Dic11⋊C4—22no—
37C2×Dic11⋊C4—22no—
38C2×C4×Dic11C2×C412yes—
39#66922—22no—
40#66922—22no—
41C11×C4⋊C8—22no—
42C11×C22⋊C8—22no—
43C11×#97—22no—
44C11⋊#95—22no—
45C11⋊#95—22no—
46C11⋊#95—21no—
47C22⋊(C11⋊C8)—22no—
48C4⋊(C11⋊C8)—22no—
49C4⋊(C11⋊C8)—22no—
50C4⋊(C11⋊C8)D414yes—
51#66867—22no—
52#66867—22no—
53C4×C11⋊C8—22no—
54#9454—111nomaximal, Sylow
55C2×Q8×C11—22no—
56C2×Q8×C11—22no—
57C2×Q8×C11—41no—
58C22×C4×C11C22⋊C411yescharacteristic
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C22×C411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C22×Dic11—22no—
66C22×Dic11—22no—
67C2×Dic22—42no—
68C2×Dic22—82no—
69C2×C8×C11—42no—
70C11×C4⋊C4—22no—
71C11×C4⋊C4—22no—
72C11×C4⋊C4—22no—
73C42×C11—21no—
74C42×C11—21no—
75C42×C11—21no—
76C42×C11—21no—
77C42×C11C2×D412yes—
78C42×C11#4112yes—
79C4⋊Dic11—24no—
80C4⋊Dic11—24no—
81C4⋊Dic11—41no—
82C4⋊Dic11—41no—
83Dic11⋊C4—82no—
84Dic11⋊C4—82no—
85C4×Dic11—42no—
86C2×C11⋊C8—24no—
87#2983—111no—
88#2567—111no—
89#1556—112no—
90#1467D1111yescharacteristic
91#1285—112no—
92C23×C11C2×C22⋊C411yescharacteristic
93Q8×C11—44no—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—22no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—41no—
105C2×C4×C11—41no—
106C2×C4×C11—41no—
107C2×C4×C11#10112yes—
108C2×C4×C11C4×D412yes—
109C2×C4×C11#12011yescharacteristic
110C2×C4×C11#12112yes—
111C2×C4×C11#12311yescharacteristic
112C2×Dic11—24no—
113C2×Dic11—42no—
114C2×Dic11—42no—
115C2×Dic11—42no—
116C2×Dic11—42no—
117C2×Dic11—42no—
118Dic22—84no—
119C8×C11—82no—
120C11⋊C8—44no—
121C2×C4⋊Q8—111no—
122C2×C4×Q8C2×D1111yescharacteristic
123#446—224no—
124#432—112no—
125#432—221no—
126#432C2×D1112yes—
127#431—221no—
128#395—221no—
129#395—221no—
130#391—112no—
131#389—221no—
132#389—221no—
133#384—112no—
134C4×C4⋊C4—111no—
135#332—224no—
136#324—21no—
137#324—21no—
138C22×C11—21no—
139C22×C11—21no—
140C22×C11#38611yescharacteristic
141C22×C11C2×#10111yescharacteristic
142C22×C11#41311yescharacteristic
143C4×C11—21no—
144C4×C11—22no—
145C4×C11—22no—
146C4×C11—22no—
147C4×C11—41no—
148C4×C11—41no—
149C4×C11—41no—
150C4×C11#45612yes—
151Dic11—44no—
152Dic11—82no—
153C22×Q8—221no—
154C22×Q8C4×D1111yescharacteristic
155C4⋊Q8—222no—
156C4⋊Q8—222no—
157C4×Q8—22no—
158C4×Q8—22no—
159C2×C4⋊C4—112no—
160C2×C4⋊C4—221no—
161C2×C4⋊C4—221no—
162C2×C4⋊C4—222no—
163C2×C4⋊C4—222no—
164C2×C4⋊C4C4×D1111yescharacteristic
165C2×C4⋊C4C22⋊D1111yescharacteristic
166C2×C4⋊C4C22⋊D1111yescharacteristic
167C2×C42—112no—
168C2×C42D4411yescharacteristic
169C2×C42D4411yescharacteristic
170C2×C42C22×D1111yescharacteristic
171C4⋊C8—22no—
172C4⋊C8—114no—
173C4⋊C8—222no—
174C4⋊C8—222no—
175C22⋊C8—22no—
176C22⋊C8—222no—
177#97—22no—
178#97—222no—
179#97—222no—
180C4×C8—222no—
181#95—222no—
182#95—222no—
183#95—221no—
184C2×C11—21no—
185C2×C11—21no—
186C2×C11#188611yescharacteristic
187C2×C11#190111yescharacteristic
188C2×C11#191011yescharacteristic
189C2×Q8—22no—
190C2×Q8—22no—
191C2×Q8—41no—
192C2×Q8—442no—
193C2×Q8—882no—
194C22×C4—222no—
195C22×C4—222no—
196C22×C4(C2×D11)⋊C411yescharacteristic
197C22×C4(C2×D11)⋊C411yescharacteristic
198C22×C4(C2×D11)⋊C411yescharacteristic
199C22×C4(C2×D11)⋊C411yescharacteristic
200C22×C4C2×C4×D1111yescharacteristic
201C22×C4C2×D4411yescharacteristic
202C22×C4C2×C22⋊D1111yescharacteristic
203C2×C8—42no—
204C2×C8—224no—
205C4⋊C4—22no—
206C4⋊C4—22no—
207C4⋊C4—22no—
208C4⋊C4—224no—
209C4⋊C4—224no—
210C4⋊C4—441no—
211C4⋊C4—441no—
212C4⋊C4—882no—
213C4⋊C4—882no—
214C42—21no—
215C42—21no—
216C42—21no—
217C42—21no—
218C42—442no—
219C42D4×D1112yes—
220C42#434112yes—
221C11#945411yescharacteristic, complemented, Sylow
222C23C2×(C2×D11)⋊C411yescharacteristic
223Q8—44no—
224Q8—884no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—224no—
239C2×C4—442no—
240C2×C4—442no—
241C2×C4—442no—
242C2×C4—442no—
243C2×C4—442no—
244C2×C4#6688812yes—
245C2×C4(C22⋊D11)⋊C412yes—
246C2×C4#6693511yescharacteristic
247C2×C4#6693911yescharacteristic
248C2×C4#6699212yes—
249C8—82no—
250C8—444no—
251C22—21no—
252C22—21no—
253C22#1062257111yescharacteristic
254C22#1062274511yescharacteristic
255C22C2×#6688811yescharacteristic
256C4—22no—
257C4—22no—
258C4—22no—
259C4—21no—
260C4—41no—
261C4—41no—
262C4—41no—
263C4—444no—
264C4—882no—
265C4#1062236512yes—
266C2—21no—
267C2—21no—
268C2#1306900711yescharacteristic
269C2#1306908211yescharacteristic
270C2#1306914111yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1467C2
socleC22×C11#386
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1467D11
hypocenterC11#9454
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1467

Complements

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

NH ≅ G/Ntype
221. C11#9454semidirect

Maximal subgroups

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

subgroupindex
#130777012
#130738212
#130673342
#130664712
C11×#14672
#945411