Finite Group Databasebeta

← #14664716

Subgroups — #14664716

Order 2816.

378 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 115 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#13079195C211yesmaximal, characteristic
2#13068744C211yesmaximal, characteristic, complemented
3#13066626C214yesmaximal, complemented
4C11×#2162C211yesmaximal, characteristic, complemented
5#10623008—21no—
6C2×C4×C8×C11C2211yescharacteristic
7#10622728—21no—
8#10622728C2212yes—
9#10622548—21no—
10#10622308C411yescharacteristic, complemented
11#10622307—21no—
12C4×D88—21no—
13C4×D88C412yescomplemented
14#10622295C411yescharacteristic, complemented
15C11×C4⋊C16—21no—
16C11×C22⋊C16C2212yes—
17C4×C11×C16—21no—
18#10622189—21no—
19#10622189C2212yes—
20C2×#4339—41no—
21C22×C8×C11D411yescharacteristic
22C22×C8×C11C2311yescharacteristic
23C2×C42×C11D411yescharacteristic
24#66983—22no—
25#66983—41no—
26C2×C4⋊Dic11—22no—
27C2×C4⋊Dic11—41no—
28C2×C4⋊Dic11—41no—
29C2×D88—21no—
30C2×D88C2×C412yes—
31#66928—41no—
32#66927—21no—
33C4×D44—22no—
34C4×D44—41no—
35#66922—21no—
36C2×C11×C16—22no—
37C4×C8×C11C2×C411yescharacteristic
38C4×C8×C11C2×C411yescharacteristic
39C4×C8×C11D411yescharacteristic
40C4×C8×C11D411yescharacteristic
41#66885—22no—
42#66885—22no—
43#66882—21no—
44#66882C2×C412yes—
45#11856—111nomaximal, Sylow
46C22×C4×C11D811yescharacteristic
47C22×C4×C11D811yescharacteristic
48C22×C4×C11C2×D411yescharacteristic
49C2×C22⋊D11—42no—
50C22×Dic11—42no—
51#4339—82no—
52#4339—82no—
53C2×D44—22no—
54C2×D44—41no—
55C2×D44—41no—
56C2×C4×D11—42no—
57C2×Dic22—41no—
58C2×C8×C11—41no—
59C2×C8×C11—41no—
60C2×C8×C11C22⋊C411yescharacteristic
61C2×C8×C11C22⋊C411yescharacteristic
62C2×C8×C11C22×C411yescharacteristic
63C2×C8×C11C2×D411yescharacteristic
64C42×C11C22⋊C411yescharacteristic
65C42×C11C22⋊C411yescharacteristic
66C42×C11SD1611yescharacteristic
67C42×C11SD1611yescharacteristic
68(C2×D11)⋊C4—42no—
69(C2×D11)⋊C4—42no—
70C4⋊Dic11—22no—
71C4⋊Dic11—42no—
72C4⋊Dic11—42no—
73C4⋊Dic11—41no—
74C4⋊Dic11—82no—
75C4⋊Dic11—82no—
76D88—42no—
77D88—42no—
78C11×C16—42no—
79#3169—111no—
80#2162D1111yescharacteristic, complemented
81#1834—111no—
82#1347—114no—
83C23×C11C2×D811yescharacteristic
84C22×D11—42no—
85C2×C4×C11—22no—
86C2×C4×C11—21no—
87C2×C4×C11—21no—
88C2×C4×C11#10211yescharacteristic
89C2×C4×C11#10211yescharacteristic
90C2×C4×C11#10211yescharacteristic
91C2×C4×C11#10211yescharacteristic
92C2×C4×C11D1612yes—
93C2×C4×C11SD3212yes—
94C2×C4×C11C2×C22⋊C411yescharacteristic
95C2×C4×C11C2×SD1611yescharacteristic
96C22⋊D11—82no—
97C22⋊D11—82no—
98C2×Dic11—42no—
99C2×Dic11—82no—
100C2×Dic11—82no—
101C2×Dic11—82no—
102D44—42no—
103D44—42no—
104D44—82no—
105D44—82no—
106C4×D11—84no—
107Dic22—82no—
108C8×C11—21no—
109C8×C11—21no—
110C8×C11—21no—
111C8×C11—21no—
112#532—221no—
113#500—111no—
114#493—111no—
115#486—221no—
116#466—112no—
117#466—221no—
118C4×D8—112no—
119C4×D8—221no—
120C2×C4×C8C2×D1111yescharacteristic
121#384—221no—
122C4⋊C16—21no—
123C22⋊C16C2×D1112yes—
124C4×C16—21no—
125#340—112no—
126#340—221no—
127C22×C11—21no—
128C22×C11—21no—
129C22×C11C2×#10211yescharacteristic
130C22×C11C2×D1611yescharacteristic
131C22×C11C2×SD3211yescharacteristic
132C2×D11—82no—
133C2×D11—82no—
134C2×D11—82no—
135C4×C11—21no—
136C4×C11—21no—
137C4×C11#35712yes—
138C4×C11#35712yes—
139C4×C11#36012yes—
140C4×C11#41011yescharacteristic
141C4×C11#42111yescharacteristic
142Dic11—82no—
143Dic11—162no—
144C2×#41—441no—
145C2×D8—112no—
146C2×D8—221no—
147C22×C8D4411yescharacteristic
148C22×C8C22×D1111yescharacteristic
149C4⋊Q8—221no—
150#127—221no—
151#124—441no—
152#121—222no—
153#121—441no—
154C4×D4—222no—
155C4×D4—441no—
156C2×C4⋊C4—222no—
157C2×C4⋊C4—441no—
158C2×C4⋊C4—441no—
159C2×C42D4411yescharacteristic
160C2×C16—22no—
161#107—112no—
162#107—221no—
163#102—222no—
164#102—222no—
165C4×C8C4×D1111yescharacteristic
166C4×C8C4×D1111yescharacteristic
167C4×C8C22⋊D1111yescharacteristic
168C4×C8C22⋊D1111yescharacteristic
169C2×C11—21no—
170C2×C11—21no—
171C2×C11#151711yescharacteristic
172C2×C11C2×#35711yescharacteristic
173C2×C11C2×#36011yescharacteristic
174D11—162no—
175#41—882no—
176#41—882no—
177C2×Q8—441no—
178C2×D4—222no—
179C2×D4—442no—
180C2×D4—441no—
181C2×D4—441no—
182C22×C4—442no—
183C22×C4—442no—
184C22×C4D8811yescharacteristic
185C22×C4D8811yescharacteristic
186C22×C4C2×D4411yescharacteristic
187D8—442no—
188D8—442no—
189C2×C8—41no—
190C2×C8—41no—
191C2×C8(C2×D11)⋊C411yescharacteristic
192C2×C8(C2×D11)⋊C411yescharacteristic
193C2×C8C2×C4×D1111yescharacteristic
194C2×C8C2×C22⋊D1111yescharacteristic
195C4⋊C4—222no—
196C4⋊C4—442no—
197C4⋊C4—442no—
198C4⋊C4—441no—
199C4⋊C4—882no—
200C4⋊C4—882no—
201C22⋊C4—442no—
202C22⋊C4—442no—
203C42#431411yescharacteristic
204C42#431411yescharacteristic
205C42(C2×D11)⋊C411yescharacteristic
206C42(C2×D11)⋊C411yescharacteristic
207C16—42no—
208C11#1185611yescharacteristic, complemented, Sylow
209C23—442no—
210C23C2×D8811yescharacteristic
211Q8—882no—
212D4—442no—
213D4—442no—
214D4—882no—
215D4—882no—
216D4—882no—
217D4—882no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—442no—
222C2×C4—884no—
223C2×C4—882no—
224C2×C4—882no—
225C2×C4—882no—
226C2×C4D17612yes—
227C2×C4#6686412yes—
228C2×C4#6688511yescharacteristic
229C2×C4#6688511yescharacteristic
230C2×C4#6688511yescharacteristic
231C2×C4#6688511yescharacteristic
232C2×C4C2×#431411yescharacteristic
233C2×C4C2×(C2×D11)⋊C411yescharacteristic
234C8—21no—
235C8—21no—
236C8—21no—
237C8—21no—
238C22—21no—
239C22—21no—
240C22—882no—
241C22—882no—
242C22—882no—
243C22C2×D17611yescharacteristic
244C22C2×#6686411yescharacteristic
245C22C2×#6688511yescharacteristic
246C4—21no—
247C4—21no—
248C4—882no—
249C4—1762no—
250C4#1062214712yes—
251C4#1062214712yes—
252C4#1062215612yes—
253C4#1062261911yescharacteristic
254C4#1062275211yescharacteristic
255C2—21no—
256C2—21no—
257C2—1762no—
258C2#1306717711yescharacteristic
259C2C2×#1062214711yescharacteristic
260C2C2×#1062215611yescharacteristic
subgroupG/H
centerC22C2×#66885
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#2162C2
socleC22×C11C2×#102
prime radical#13079195C2
cosocleC22×C8×C11C23
hypercenter#2162D11
hypocenterC11#11856
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #2162

Complements

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

NH ≅ G/Ntype
2. #13068744C2semidirect
3. #13066626C2semidirect
4. C11×#2162C2semidirect
10. #10622308C4semidirect
13. C4×D88C4semidirect
14. #10622295C4semidirect
80. #2162D11semidirect
208. C11#11856semidirect

Maximal subgroups

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

subgroupindex
#130791952
#130687442
#130666262
C11×#21622
#1185611