Finite Group Databasebeta

← #14664622

Subgroups — #14664622

Order 2816.

324 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 71 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#13079354C211yesmaximal, characteristic
2#13068765C211yesmaximal, characteristic, complemented
3#13066608C212yesmaximal, complemented
4#13066602C212yesmaximal, complemented
5C11×#2165C211yesmaximal, characteristic, complemented
6#10623008—21no—
7C4×C11×M16C2211yescharacteristic
8#10622748—21no—
9#10622748C2212yes—
10#10622324—21no—
11#10622324C412yescomplemented
12#10622308C411yescharacteristic, complemented
13#10622307—21no—
14#10622293C411yescharacteristic, complemented
15C11×#364—21no—
16C11×#349C2212yes—
17C11×#347—21no—
18C11⋊#338C2211yescharacteristic
19#10622195C2211yescharacteristic
20#10622194—21no—
21#10622161—21no—
22C2×#4339—41no—
23C2×C11×M16D411yescharacteristic
24C2×C11×M16C2311yescharacteristic
25C2×C42×C11D411yescharacteristic
26#66983—22no—
27#66983—41no—
28#66979—21no—
29C2×#4318—21no—
30C2×D88—21no—
31C2×D88C2×C412yes—
32#66928—41no—
33#66927—21no—
34C4×D44—22no—
35C4×D44—41no—
36#66922—21no—
37C11×M32—22no—
38C11×#97C2×C411yescharacteristic
39C11×#97D411yescharacteristic
40C4×C8×C11C2×C411yescharacteristic
41C4×C8×C11D411yescharacteristic
42#66885—22no—
43#66885—22no—
44#66881—21no—
45#66881C2×C412yes—
46#11837—111nomaximal, Sylow
47C22×C4×C11—21no—
48C22×C4×C11C2×D411yescharacteristic
49C2×C22⋊D11—42no—
50#4339—84no—
51C2×D44—22no—
52C2×D44—41no—
53C2×D44—41no—
54C2×C4×D11—42no—
55C2×Dic22—41no—
56C11×M16—41no—
57C11×M16—41no—
58C2×C8×C11C22⋊C411yescharacteristic
59C2×C8×C11C22⋊C411yescharacteristic
60C2×C8×C11C22×C411yescharacteristic
61C2×C8×C11C2×D411yescharacteristic
62C42×C11—21no—
63C42×C11C22⋊C411yescharacteristic
64C42×C11C22⋊C411yescharacteristic
65C22⋊Dic11—41no—
66(C2×D11)⋊C4—42no—
67(C2×D11)⋊C4—42no—
68C4⋊Dic11—22no—
69C4⋊Dic11—41no—
70C4⋊Dic11—41no—
71C4×Dic11—41no—
72#4318—41no—
73#4318—41no—
74C2×C11⋊C8—41no—
75D88—42no—
76D88—42no—
77C11×C16—42no—
78#3184—111no—
79#2165D1111yescharacteristic, complemented
80#1841—111no—
81#1341—112no—
82#1339—112no—
83C23×C11AGL(1,ℤ/8)11yescharacteristic
84C22×D11—42no—
85C2×C4×C11—21no—
86C2×C4×C11—21no—
87C2×C4×C11—21no—
88C2×C4×C11—21no—
89C2×C4×C11—42no—
90C2×C4×C11C2×C22⋊C411yescharacteristic
91C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
92C22⋊D11—84no—
93C2×Dic11—42no—
94C2×Dic11—81no—
95D44—42no—
96D44—42no—
97D44—82no—
98D44—82no—
99C4×D11—84no—
100Dic22—82no—
101C8×C11—21no—
102C8×C11—21no—
103C8×C11—21no—
104C8×C11—21no—
105C11⋊C8—81no—
106#532—221no—
107#498—111no—
108#493—111no—
109#486—221no—
110#469—112no—
111#469—221no—
112#442—112no—
113#442—221no—
114C4×M16C2×D1111yescharacteristic
115#364—21no—
116#349C2×D1112yes—
117#347—21no—
118#344—221no—
119#339—221no—
120#338—111no—
121H(3,ℤ/4)—111no—
122C22×C11—21no—
123C22×C11—41no—
124C22×C11#41811yescharacteristic
125C2×D11—82no—
126C2×D11—82no—
127C2×D11—82no—
128C4×C11—22no—
129C4×C11—21no—
130C4×C11—41no—
131C4×C11#41011yescharacteristic
132C4×C11#42111yescharacteristic
133Dic11—82no—
134Dic11—161no—
135C2×#41—441no—
136C2×D8—112no—
137C2×D8—221no—
138C2×M16—221no—
139C2×M16D4411yescharacteristic
140C2×M16C22×D1111yescharacteristic
141C4⋊Q8—221no—
142#127—221no—
143#124—441no—
144#121—222no—
145#121—441no—
146C4×D4—222no—
147C4×D4—441no—
148#117—221no—
149C2×C42D4411yescharacteristic
150M32—22no—
151#106—112no—
152#106—221no—
153#102—222no—
154#102—222no—
155#97C4×D1111yescharacteristic
156#97C22⋊D1111yescharacteristic
157C4×C8C4×D1111yescharacteristic
158C4×C8C22⋊D1111yescharacteristic
159C2×C11—21no—
160C2×C11—41no—
161C2×C11#151411yescharacteristic
162D11—162no—
163#41—884no—
164C2×Q8—441no—
165C2×D4—222no—
166C2×D4—441no—
167C2×D4—441no—
168C2×D4—442no—
169C22×C4—21no—
170C22×C4—442no—
171C22×C4C2×D4411yescharacteristic
172D8—442no—
173D8—442no—
174M16—41no—
175M16—41no—
176M16—441no—
177M16—441no—
178C2×C8—441no—
179C2×C8(C2×D11)⋊C411yescharacteristic
180C2×C8(C2×D11)⋊C411yescharacteristic
181C2×C8C2×C4×D1111yescharacteristic
182C2×C8C2×C22⋊D1111yescharacteristic
183C4⋊C4—222no—
184C4⋊C4—441no—
185C4⋊C4—441no—
186C22⋊C4—442no—
187C22⋊C4—442no—
188C22⋊C4—441no—
189C42—21no—
190C42—441no—
191C42(C2×D11)⋊C411yescharacteristic
192C42(C2×D11)⋊C411yescharacteristic
193C16—42no—
194C11#1183711yescharacteristic, complemented, Sylow
195C23—442no—
196C23#6696111yescharacteristic
197Q8—882no—
198D4—442no—
199D4—442no—
200D4—882no—
201D4—882no—
202D4—884no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—42no—
208C2×C4—442no—
209C2×C4—884no—
210C2×C4—881no—
211C2×C4#6696111yescharacteristic
212C2×C4C2×(C2×D11)⋊C411yescharacteristic
213C8—21no—
214C8—21no—
215C8—21no—
216C8—21no—
217C8—881no—
218C22—21no—
219C22—41no—
220C22—882no—
221C22—882no—
222C22—882no—
223C22#1062274411yescharacteristic
224C4—22no—
225C4—21no—
226C4—41no—
227C4—882no—
228C4—1761no—
229C4#1062261911yescharacteristic
230C4#1062275211yescharacteristic
231C2—21no—
232C2—41no—
233C2—1762no—
234C2#1306716411yescharacteristic
subgroupG/H
centerC2#13067164
commutatorC2×C8×C11C22×C4
FrattiniC2×M16C22×D11
FittingC11×#2165C2
socleC2×C11#1514
prime radical#13079354C2
cosocleC2×C11×M16C23
hypercenter#2165D11
hypocenterC11#11837
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×M16 ◁ #2165

Complements

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

NH ≅ G/Ntype
2. #13068765C2semidirect
3. #13066608C2semidirect
4. #13066602C2semidirect
5. C11×#2165C2semidirect
11. #10622324C4semidirect
12. #10622308C4semidirect
14. #10622293C4semidirect
79. #2165D11semidirect
194. C11#11837semidirect

Maximal subgroups

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

subgroupindex
#130793542
#130687652
#130666082
#130666022
C11×#21652
#1183711