Finite Group Databasebeta

← #14651475

Subgroups — #14651475

Order 2816.

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

normal subgroups only

This group has 432 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#13073828C211yesmaximal, characteristic
3#13067332C212yesmaximal
4#13066471C212yesmaximal
5C11×#1467C211yesmaximal, characteristic
6C2×C4×Q8×C11C2211yescharacteristic
7C2×#66922C2211yescharacteristic
8C11×#432C2212yes—
9#10622843C412yes—
10#10622637—24no—
11#10622599—21no—
12#10622599—21no—
13#10622590C412yes—
14C4×C4⋊Dic11C2211yescharacteristic
15#10622542—21no—
16#10622542—21no—
17#10622539—21no—
18#10622539C2212yes—
19#10622538—21no—
20C11×#324—21no—
21C11×#324—21no—
22#10622124—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×C4×Dic11C2×C412yes—
37#66922—22no—
38#66922—22no—
39C11×C4⋊C8—22no—
40C11×C22⋊C8—22no—
41C11×#97—22no—
42C11⋊#95—22no—
43C11⋊#95—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#9456—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—44no—
68C2×Dic22—41no—
69C2×Dic22—41no—
70C2×C8×C11—42no—
71C11×C4⋊C4—22no—
72C11×C4⋊C4—22no—
73C11×C4⋊C4—22no—
74C42×C11—21no—
75C42×C11—21no—
76C42×C11—21no—
77C42×C11—21no—
78C42×C11C2×D412yes—
79C42×C11#4112yes—
80C4⋊Dic11—24no—
81C4⋊Dic11—42no—
82C4⋊Dic11—42no—
83C4×Dic11—42no—
84C2×C11⋊C8—24no—
85#2983—111no—
86#2568—111no—
87#1556—112no—
88#1467D1111yescharacteristic
89#1285—112no—
90C23×C11C2×C22⋊C411yescharacteristic
91Q8×C11—44no—
92C2×C4×C11—21no—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11—22no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—41no—
103C2×C4×C11—41no—
104C2×C4×C11—41no—
105C2×C4×C11#10112yes—
106C2×C4×C11C4×D412yes—
107C2×C4×C11#12011yescharacteristic
108C2×C4×C11#12112yes—
109C2×C4×C11#12311yescharacteristic
110C2×Dic11—42no—
111C2×Dic11—44no—
112C2×Dic11—42no—
113C2×Dic11—42no—
114C2×Dic11—42no—
115Dic22—82no—
116Dic22—82no—
117C8×C11—82no—
118C11⋊C8—44no—
119C2×C4⋊Q8—111no—
120C2×C4×Q8C2×D1111yescharacteristic
121#446—224no—
122#432—112no—
123#432—221no—
124#432C2×D1112yes—
125#431—221no—
126#400—221no—
127#400—221no—
128#391—112no—
129#391—221no—
130#391—221no—
131#382—112no—
132C4×C4⋊C4—111no—
133#332—224no—
134#324—21no—
135#324—21no—
136C22×C11—21no—
137C22×C11—21no—
138C22×C11#38611yescharacteristic
139C22×C11C2×#10111yescharacteristic
140C22×C11#41311yescharacteristic
141C4×C11—21no—
142C4×C11—22no—
143C4×C11—22no—
144C4×C11—22no—
145C4×C11—41no—
146C4×C11—41no—
147C4×C11—41no—
148C4×C11#45412yes—
149Dic11—82no—
150Dic11—82no—
151C22×Q8—221no—
152C22×Q8C4×D1111yescharacteristic
153C4⋊Q8—222no—
154C4⋊Q8—222no—
155C4×Q8—22no—
156C4×Q8—22no—
157C2×C4⋊C4—112no—
158C2×C4⋊C4—221no—
159C2×C4⋊C4—221no—
160C2×C4⋊C4C4×D1111yescharacteristic
161C2×C4⋊C4C22⋊D1111yescharacteristic
162C2×C4⋊C4C22⋊D1111yescharacteristic
163C2×C42—112no—
164C2×C42D4411yescharacteristic
165C2×C42D4411yescharacteristic
166C2×C42C22×D1111yescharacteristic
167C4⋊C8—22no—
168C4⋊C8—114no—
169C4⋊C8—222no—
170C4⋊C8—222no—
171C22⋊C8—22no—
172C22⋊C8—222no—
173#97—22no—
174#97—222no—
175#97—222no—
176C4×C8—222no—
177#95—222no—
178#95—222no—
179#95—222no—
180#95—222no—
181#95—221no—
182C2×C11—21no—
183C2×C11—21no—
184C2×C11#188811yescharacteristic
185C2×C11#190111yescharacteristic
186C2×C11#190911yescharacteristic
187C2×Q8—22no—
188C2×Q8—22no—
189C2×Q8—41no—
190C2×Q8—444no—
191C2×Q8—441no—
192C2×Q8—441no—
193C22×C4—222no—
194C22×C4—222no—
195C22×C4(C2×D11)⋊C411yescharacteristic
196C22×C4(C2×D11)⋊C411yescharacteristic
197C22×C4(C2×D11)⋊C411yescharacteristic
198C22×C4(C2×D11)⋊C411yescharacteristic
199C22×C4C2×C4×D1111yescharacteristic
200C22×C4C2×D4411yescharacteristic
201C22×C4C2×C22⋊D1111yescharacteristic
202C2×C8—42no—
203C2×C8—224no—
204C4⋊C4—22no—
205C4⋊C4—22no—
206C4⋊C4—22no—
207C4⋊C4—224no—
208C4⋊C4—442no—
209C4⋊C4—442no—
210C42—21no—
211C42—21no—
212C42—21no—
213C42—21no—
214C42—442no—
215C42D4×D1112yes—
216C42#434112yes—
217C11#945611yescharacteristic, complemented, Sylow
218C23C2×(C2×D11)⋊C411yescharacteristic
219Q8—44no—
220Q8—882no—
221Q8—882no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—442no—
236C2×C4—444no—
237C2×C4—442no—
238C2×C4—442no—
239C2×C4—442no—
240C2×C4#6688812yes—
241C2×C4(C22⋊D11)⋊C412yes—
242C2×C4#6693511yescharacteristic
243C2×C4#6693911yescharacteristic
244C2×C4#6699212yes—
245C8—82no—
246C8—444no—
247C22—21no—
248C22—21no—
249C22#1062257111yescharacteristic
250C22#1062274511yescharacteristic
251C22C2×#6688811yescharacteristic
252C4—22no—
253C4—22no—
254C4—22no—
255C4—21no—
256C4—41no—
257C4—41no—
258C4—41no—
259C4—882no—
260C4—882no—
261C4#1062236612yes—
262C2—21no—
263C2—21no—
264C2#1306901711yescharacteristic
265C2#1306908211yescharacteristic
266C2#1306913611yescharacteristic
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#9456
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
217. C11#9456semidirect

Maximal subgroups

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

subgroupindex
#130777012
#130738282
#130673322
#130664712
C11×#14672
#945611