Finite Group Databasebeta

← #14665302

Subgroups — #14665302

Order 2816.

412 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 69 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#13079067C211yesmaximal, characteristic
2#13070427C212yesmaximal, complemented
3#13066656C212yesmaximal, complemented
4#13066653C211yesmaximal, characteristic, complemented
5C11×#1357C211yesmaximal, characteristic, complemented
6C2×#66964—22no—
7#10623247C411yescharacteristic
8D11×#127C411yescharacteristic
9C11×#493C2211yescharacteristic
10#10622767—22no—
11#10622689C411yescharacteristic
12#10622686C411yescharacteristic
13#10622306C2211yescharacteristic
14C4×#4313C2211yescharacteristic
15C11×#364C2212yescomplemented
16#10622152—22no—
17#10622150—22no—
18#10622101C2212yescomplemented
19C2×#4341—21no—
20C2×D4×D11—21no—
21C2×D4×D11—41no—
22C2×C11×D8—22no—
23C11×#127C2×C411yescharacteristic
24C11×#127C2×C411yescharacteristic
25#66993—21no—
26#66993—41no—
27#66991—41no—
28#66989—21no—
29D4×Dic11—41no—
30C2×#4324—22no—
31C2×#4323—22no—
32#66964—44no—
33#66964—44no—
34C2×#4314—22no—
35C2×#4313D412yes—
36#66927C2×C411yescharacteristic
37C42×D11C2×C411yescharacteristic
38#66922C2×C411yescharacteristic
39C11×M32—22no—
40C4×C8×C11C2311yescharacteristic
41#66879D412yes—
42#66876—22no—
43C4×C11⋊C8C2×C411yescharacteristic
44#11992—111nomaximal, Sylow
45C23×D11—41no—
46C2×D4×C11—21no—
47C2×D4×C11—21no—
48C2×D4×C11—41no—
49C2×D4×C11—41no—
50C2×C22⋊D11—42no—
51C2×C22⋊D11—41no—
52C2×C22⋊D11—41no—
53C22×Dic11—41no—
54#4341—44no—
55D4×D11—44no—
56D4×D11—84no—
57C2×D44—21no—
58C2×D44—41no—
59C2×C4×D11—21no—
60C2×C4×D11C22⋊C411yescharacteristic
61C2×Dic22—21no—
62C11×D8—42no—
63C11×D8—42no—
64C2×C8×C11C2×D412yes—
65C42×C11C22×C411yescharacteristic
66C22⋊Dic11—42no—
67#4324—44no—
68#4323—44no—
69C4⋊Dic11—41no—
70C4×Dic11—21no—
71C4×Dic11C22⋊C411yescharacteristic
72C2×C11⋊C8C22⋊C412yes—
73#4314—42no—
74#4314—42no—
75#4313—22no—
76#4313—22no—
77C11×C16—42no—
78C11⋊C16—42no—
79#3151—111no—
80#2165—112no—
81#1359—112no—
82#1357—111no—
83#1357D1111yescharacteristic, complemented
84C23×C11—41no—
85C23×C11—41no—
86C22×D11—41no—
87C22×D11—82no—
88C22×D11—84no—
89C22×D11#10011yescharacteristic
90D4×C11—42no—
91D4×C11—42no—
92D4×C11—82no—
93D4×C11—82no—
94C2×C4×C11—21no—
95C2×C4×C11C2×C22⋊C411yescharacteristic
96C22⋊D11—82no—
97C22⋊D11—84no—
98C22⋊D11—82no—
99C2×Dic11—21no—
100C2×Dic11—41no—
101C2×Dic11—82no—
102C2×Dic11#10011yescharacteristic
103D44—42no—
104D44—82no—
105C4×D11—22no—
106C4×D11—42no—
107Dic22—42no—
108C8×C11AGL(1,ℤ/8)12yes—
109C8×C11AGL(1,ℤ/8)12yes—
110C11⋊C8—22no—
111C2×AGL(1,ℤ/8)—222no—
112#532—111no—
113C2×#127—111no—
114#496—222no—
115#493—111no—
116#493C2×D1111yescharacteristic
117#492—111no—
118#492—111no—
119C4×M16—111no—
120#364—112no—
121#364C2×D1112yescomplemented
122#349—222no—
123#347—222no—
124C22×C11—82no—
125C22×C11—82no—
126C22×C11—81no—
127C22×C11—81no—
128C22×C11C2×#10011yescharacteristic
129C2×D11—21no—
130C2×D11—41no—
131C2×D11—82no—
132C2×D11—81no—
133C2×D11—164no—
134C4×C11—22no—
135C4×C11#41812yes—
136Dic11—21no—
137Dic11—41no—
138Dic11—81no—
139C2×#41—221no—
140C22×D4—221no—
141C22×D4—441no—
142AGL(1,ℤ/8)—444no—
143AGL(1,ℤ/8)—444no—
144C2×SD16—222no—
145C2×SD16—222no—
146C2×D8—22no—
147C2×D8—222no—
148C2×M16—112no—
149C4⋊Q8—111no—
150#127—111no—
151#127—221no—
152#127—441no—
153#127C4×D1111yescharacteristic
154#127C4×D1111yescharacteristic
155#124—221no—
156#121—441no—
157C4×D4—441no—
158C2×C42—111no—
159M32—22no—
160M32—222no—
161#97—112no—
162C4×C8—111no—
163C4×C8C22×D1111yescharacteristic
164C2×C11—21no—
165C2×C11—161no—
166C2×C11—161no—
167C2×C11#155511yescharacteristic
168D11—41no—
169D11—161no—
170C24—441no—
171#41—444no—
172C2×Q8—221no—
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—41no—
176C2×D4—41no—
177C2×D4—221no—
178C2×D4—441no—
179C2×D4—441no—
180C2×D4—444no—
181C2×D4—442no—
182C2×D4—441no—
183C2×D4—884no—
184C22×C4—111no—
185C22×C4—221no—
186C22×C4—441no—
187SD16—444no—
188SD16—442no—
189SD16—442no—
190D8—42no—
191D8—42no—
192D8—444no—
193M16—222no—
194M16—222no—
195C2×C8—112no—
196C2×C8D4×D1112yes—
197C4⋊C4—441no—
198C22⋊C4—442no—
199C42—111no—
200C42—221no—
201C42C2×C4×D1111yescharacteristic
202C16—42no—
203C16—442no—
204C11#1199211yescharacteristic, complemented, Sylow
205C23—41no—
206C23—41no—
207C23—111no—
208C23—441no—
209C23—882no—
210C23—884no—
211Q8—442no—
212D4—42no—
213D4—42no—
214D4—82no—
215D4—82no—
216D4—442no—
217D4—882no—
218D4—882no—
219D4—884no—
220D4—882no—
221C2×C4—21no—
222C2×C4—111no—
223C2×C4—222no—
224C2×C4—221no—
225C2×C4—442no—
226C2×C4—441no—
227C2×C4—882no—
228C2×C4C22⋊C4×D1111yescharacteristic
229C8—222no—
230C8#6696412yes—
231C8#6696712yes—
232C22—82no—
233C22—82no—
234C22—81no—
235C22—81no—
236C22—221no—
237C22—441no—
238C22—882no—
239C22—881no—
240C22—1764no—
241C22D11×#10011yescharacteristic
242C4—22no—
243C4—221no—
244C4—441no—
245C4—881no—
246C4#1062238312yes—
247C2—21no—
248C2—161no—
249C2—161no—
250C2—441no—
251C2—1761no—
252C2#1306732811yescharacteristic
subgroupG/H
centerC2#13067328
commutatorC42×C11C22×C4
FrattiniC4×C8C22×D11
FittingC11×#1357C2
socleC2×C11#1555
prime radical#13079067C2
cosocleC4×C8×C11C23
hypercenter#1357D11
hypocenterC11#11992
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1357

Complements

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

NH ≅ G/Ntype
2. #13070427C2semidirect
3. #13066656C2semidirect
4. #13066653C2semidirect
5. C11×#1357C2semidirect
15. C11×#364C22semidirect
18. #10622101C22semidirect
83. #1357D11semidirect
121. #364C2×D11semidirect
204. C11#11992semidirect

Maximal subgroups

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

subgroupindex
#130790672
#130704272
#130666562
#130666532
C11×#13572
#1199211