Finite Group Databasebeta

← #14665301

Subgroups — #14665301

Order 2816.

280 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 79 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#13079244C211yesmaximal, characteristic
2#13070382C211yesmaximal, characteristic, complemented
3#13066678C212yesmaximal, complemented
4#13066656C212yesmaximal, complemented
5C11×#2166C211yesmaximal, characteristic, complemented
6#10623066C411yescharacteristic
7#10623049C411yescharacteristic
8C11×#405C2211yescharacteristic
9#10622747—21no—
10#10622727—21no—
11C2×#66876—21no—
12#10622326C411yescharacteristic
13#10622323—21no—
14#10622316C411yescharacteristic
15#10622306C2211yescharacteristic
16C4×#4314—21no—
17#10622296C2211yescharacteristic
18C11×#364C2212yes—
19C11×#349—21no—
20C11×#347—21no—
21#10622101—21no—
22#10622101C2212yes—
23C2×C11×M16D411yescharacteristic
24C22×C8×C11D411yescharacteristic
25C11×#117C2×C411yescharacteristic
26#66983—21no—
27#66977—21no—
28C2×#4314—21no—
29C2×#4314—21no—
30#66947—41no—
31#66942—41no—
32#66937—41no—
33#66932—41no—
34#66927C2×C411yescharacteristic
35C4×D44—21no—
36#66923C2×C411yescharacteristic
37#66923C2×C411yescharacteristic
38#66922C2×C411yescharacteristic
39C4×Dic22—21no—
40C11×M32—22no—
41C11×#97C2×C411yescharacteristic
42C11×#97D411yescharacteristic
43C4×C8×C11D411yescharacteristic
44C4×C8×C11C2311yescharacteristic
45#66885—21no—
46#66885—21no—
47#66882—21no—
48#66881—21no—
49#66880—21no—
50#66880—21no—
51#66876—22no—
52#66876—41no—
53C2×C11⋊C16—41no—
54#11991—111nomaximal, Sylow
55C22×C4×C11C22⋊C411yescharacteristic
56C2×C22⋊D11—41no—
57C2×D44—21no—
58C2×D44—41no—
59C2×C4×D11—41no—
60C2×Dic22—21no—
61C11×M16—22no—
62C2×C8×C11—21no—
63C2×C8×C11—21no—
64C2×C8×C11C22⋊C411yescharacteristic
65C2×C8×C11C22⋊C411yescharacteristic
66C2×C8×C11C2×D411yescharacteristic
67C2×C8×C11C2×D411yescharacteristic
68C11×C4⋊C4—21no—
69C11×C22⋊C4—21no—
70C42×C11C22⋊C411yescharacteristic
71C42×C11C22×C411yescharacteristic
72C22⋊Dic11—41no—
73(C2×D11)⋊C4—41no—
74(C2×D11)⋊C4—41no—
75C4⋊Dic11—21no—
76C4⋊Dic11—21no—
77C4⋊Dic11—41no—
78Dic11⋊C4—41no—
79Dic11⋊C4—41no—
80Dic11⋊C4—41no—
81Dic11⋊C4—41no—
82C4×Dic11—41no—
83#4314—42no—
84#4314—41no—
85#4314—41no—
86C11×C16—42no—
87C11⋊C16—42no—
88#3174—111no—
89#2166D1111yescharacteristic, complemented
90#2153—111no—
91#1366—112no—
92#1359—112no—
93C23×C11#10011yescharacteristic
94C22×D11—41no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11#10011yescharacteristic
100C2×C4×C11C2×C22⋊C411yescharacteristic
101C22⋊D11—161no—
102C2×Dic11—41no—
103C2×Dic11—41no—
104C2×Dic11—41no—
105D44—41no—
106D44—41no—
107D44—161no—
108C4×D11—161no—
109Dic22—41no—
110Dic22—41no—
111C8×C11—21no—
112C8×C11—21no—
113C8×C11#13512yes—
114C8×C11AGL(1,ℤ/8)11yescharacteristic
115C8×C11#13711yescharacteristic
116#541—111no—
117#540—111no—
118C2×M32—221no—
119#499—111no—
120#492—111no—
121#491—111no—
122#490—111no—
123#468—221no—
124#465—221no—
125#440—221no—
126C4×SD16—221no—
127#405C2×D1111yescharacteristic
128#364—112no—
129#364—221no—
130#364C2×D1112yes—
131#349—21no—
132#347—21no—
133C22×C11—21no—
134C22×C11—41no—
135C22×C11C2×#10011yescharacteristic
136C2×D11—81no—
137C2×D11—81no—
138C2×D11—81no—
139C4×C11—21no—
140C4×C11—41no—
141C4×C11—41no—
142C4×C11#41611yescharacteristic
143C4×C11#41711yescharacteristic
144Dic11—81no—
145Dic11—81no—
146Dic11—81no—
147C2×SD16—221no—
148C2×SD16—221no—
149C2×M16C22⋊D1111yescharacteristic
150C22×C8D4411yescharacteristic
151C4⋊Q8—111no—
152#127—111no—
153#126—441no—
154#125—111no—
155#125—111no—
156#125—441no—
157#123—441no—
158C22⋊Q8—221no—
159#121—221no—
160#121—441no—
161C4×Q8—221no—
162C4×D4—221no—
163#117C4×D1111yescharacteristic
164M32—22no—
165M32—222no—
166M32—441no—
167C2×C16—441no—
168#107—221no—
169#106—221no—
170#103—221no—
171#103—221no—
172#102—221no—
173#102—221no—
174#97C4×D1111yescharacteristic
175#97C22⋊D1111yescharacteristic
176C4×C8D4411yescharacteristic
177C4×C8C22×D1111yescharacteristic
178C2×C11—21no—
179C2×C11—41no—
180C2×C11#155111yescharacteristic
181D11—161no—
182C2×Q8—221no—
183C2×D4—221no—
184C2×D4—441no—
185C2×D4—441no—
186C22×C4—441no—
187C22×C4(C2×D11)⋊C411yescharacteristic
188SD16—441no—
189SD16—441no—
190SD16—442no—
191M16—22no—
192C2×C8—21no—
193C2×C8—21no—
194C2×C8(C2×D11)⋊C411yescharacteristic
195C2×C8(C2×D11)⋊C411yescharacteristic
196C2×C8C2×D4411yescharacteristic
197C2×C8C2×C22⋊D1111yescharacteristic
198C4⋊C4—21no—
199C4⋊C4—221no—
200C4⋊C4—221no—
201C4⋊C4—441no—
202C4⋊C4—441no—
203C4⋊C4—441no—
204C4⋊C4—441no—
205C4⋊C4—441no—
206C22⋊C4—21no—
207C22⋊C4—441no—
208C22⋊C4—441no—
209C22⋊C4—441no—
210C42—441no—
211C42(C2×D11)⋊C411yescharacteristic
212C42C2×C4×D1111yescharacteristic
213C16—42no—
214C16—442no—
215C11#1199111yescharacteristic, complemented, Sylow
216C23—441no—
217C23#6688711yescharacteristic
218Q8—441no—
219Q8—441no—
220D4—441no—
221D4—441no—
222D4—1761no—
223D4—1761no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—441no—
229C2×C4—441no—
230C2×C4—441no—
231C2×C4—1761no—
232C2×C4#6688711yescharacteristic
233C2×C4C2×(C2×D11)⋊C411yescharacteristic
234C8—21no—
235C8—21no—
236C8#6696111yescharacteristic
237C8#6696211yescharacteristic
238C8#6700312yes—
239C22—21no—
240C22—41no—
241C22—881no—
242C22—881no—
243C22—881no—
244C22C2×#6688711yescharacteristic
245C4—21no—
246C4—41no—
247C4—41no—
248C4—881no—
249C4—881no—
250C4—881no—
251C4#1062261511yescharacteristic
252C4#1062274611yescharacteristic
253C2—21no—
254C2—41no—
255C2—1761no—
256C2#1306731211yescharacteristic
subgroupG/H
centerC2#13067312
commutatorC42×C11C22×C4
FrattiniC4×C8C22×D11
FittingC11×#2166C2
socleC2×C11#1551
prime radical#10623066C4
cosocleC4×C8×C11C23
hypercenter#2166D11
hypocenterC11#11991
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ #405 ◁ #2166

Complements

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

NH ≅ G/Ntype
2. #13070382C2semidirect
3. #13066678C2semidirect
4. #13066656C2semidirect
5. C11×#2166C2semidirect
89. #2166D11semidirect
215. C11#11991semidirect

Maximal subgroups

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

subgroupindex
#130792442
#130703822
#130666782
#130666562
C11×#21662
#1199111