Finite Group Databasebeta

← #14640908

Subgroups — #14640908

Order 2816.

324 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C2×#10622191C211yesmaximal, characteristic
2#13068649C211yesmaximal, characteristic
3C2×C11×#338C211yesmaximal, characteristic
4C22×C11×M16—21no—
5C22×C11×M16C2211yescharacteristic
6#10622825—21no—
7C2×#66882C411yescharacteristic
8C2×#66881C411yescharacteristic
9C2×#66876—21no—
10C11×#338—21no—
11C11×#338C412yescomplemented
12#10622191—21no—
13#10622191C412yescomplemented
14#10622189—21no—
15C23×C4×C11D411yescharacteristic
16C2×C11×M16—22no—
17C2×C11×M16—22no—
18C2×C11×M16—41no—
19C2×C11×M16—41no—
20C2×C11×M16—41no—
21C2×C11×M16—41no—
22C2×C11×M16—41no—
23C2×C11×M16—41no—
24C2×C11×M16C2×C411yescharacteristic
25C2×C11×M16C2×C411yescharacteristic
26C2×C11×M16D411yescharacteristic
27C2×C11×M16Q811yescharacteristic
28C22×C8×C11—22no—
29C22×C8×C11C2×C411yescharacteristic
30C22×C8×C11D411yescharacteristic
31C2×C22⋊Dic11—41no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C11⋊#95—41no—
35#66882—41no—
36#66881—41no—
37#66876—22no—
38#66876—41no—
39C2×C11⋊C16—41no—
40#7255—111nomaximal, Sylow
41C24×C11SD1611yescharacteristic
42C22×C4×C11—21no—
43C22×C4×C11—21no—
44C22×C4×C11—21no—
45C22×C4×C11—21no—
46C22×C4×C11C22⋊C411yescharacteristic
47C22×C4×C11C22⋊C411yescharacteristic
48C22×C4×C11C4⋊C411yescharacteristic
49C22×C4×C11D811yescharacteristic
50C22×C4×C11SD1611yescharacteristic
51C22×C4×C11Q1611yescharacteristic
52C22×Dic11—41no—
53C22×Dic11—41no—
54C11×M16—41no—
55C11×M16—41no—
56C11×M16—41no—
57C11×M16—41no—
58C11×M16—42no—
59C11×M16—42no—
60C11×M16—42no—
61C11×M16—42no—
62C2×C8×C11—24no—
63C2×C8×C11—21no—
64C2×C8×C11—21no—
65C2×C8×C11—21no—
66C2×C8×C11—21no—
67C2×C8×C11—42no—
68C2×C8×C11—42no—
69C2×C8×C11C4211yescharacteristic
70C2×C8×C11C22⋊C411yescharacteristic
71C2×C8×C11C4⋊C411yescharacteristic
72C2×C8×C11C4⋊C411yescharacteristic
73C22⋊Dic11—82no—
74C4⋊Dic11—41no—
75C4⋊Dic11—41no—
76C4⋊Dic11—41no—
77C4⋊Dic11—41no—
78C11⋊C16—42no—
79C2×#349—111no—
80#1809—111no—
81C2×#338D1111yescharacteristic
82C23×C11—21no—
83C23×C11—21no—
84C23×C11—41no—
85C23×C11—41no—
86C23×C11#10211yescharacteristic
87C23×C11#10311yescharacteristic
88C23×C11#10611yescharacteristic
89C2×C4×C11—21no—
90C2×C4×C11—21no—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11#9511yescharacteristic
100C2×C4×C11#9911yescharacteristic
101C2×C4×C11#9911yescharacteristic
102C2×C4×C11#10211yescharacteristic
103C2×C4×C11#10311yescharacteristic
104C2×C4×C11#10411yescharacteristic
105C2×C4×C11#10411yescharacteristic
106C2×C4×C11#10711yescharacteristic
107C2×Dic11—81no—
108C2×Dic11—81no—
109C2×Dic11—81no—
110C2×Dic11—81no—
111C2×Dic11—81no—
112C2×Dic11—81no—
113C8×C11—21no—
114C8×C11—21no—
115C8×C11—21no—
116C8×C11—21no—
117C8×C11—44no—
118C22×M16—21no—
119C22×M16C2×D1111yescharacteristic
120C2×M32—221no—
121C2×#107—111no—
122C2×#106—111no—
123#380—221no—
124#349—112no—
125#349—221no—
126#340—221no—
127#338—21no—
128#338Dic1112yescomplemented
129C22×C11—21no—
130C22×C11—21no—
131C22×C11—21no—
132C22×C11—21no—
133C22×C11—41no—
134C22×C11—41no—
135C22×C11—41no—
136C22×C11—41no—
137C22×C11—81no—
138C22×C11#32711yescharacteristic
139C22×C11#32711yescharacteristic
140C22×C11#34011yescharacteristic
141C4×C11—21no—
142C4×C11—21no—
143C4×C11#32811yescharacteristic
144C4×C11#32811yescharacteristic
145C4×C11#33911yescharacteristic
146C4×C11#34211yescharacteristic
147Dic11—161no—
148Dic11—161no—
149C23×C4C22⋊D1111yescharacteristic
150C2×M16—22no—
151C2×M16—22no—
152C2×M16—41no—
153C2×M16—41no—
154C2×M16—41no—
155C2×M16—41no—
156C2×M16—41no—
157C2×M16—41no—
158C2×M16Dic2211yescharacteristic
159C2×M16C4×D1111yescharacteristic
160C2×M16C2×Dic1111yescharacteristic
161C2×M16C22⋊D1111yescharacteristic
162C22×C8—22no—
163C22×C8C4×D1111yescharacteristic
164C22×C8D4411yescharacteristic
165C2×C4⋊C4—221no—
166C2×C4⋊C4—221no—
167C2×C22⋊C4—441no—
168M32—222no—
169M32—441no—
170C2×C16—441no—
171#107—441no—
172#106—441no—
173#95—441no—
174C2×C11—21no—
175C2×C11—21no—
176C2×C11—41no—
177C2×C11—41no—
178C2×C11#129411yescharacteristic
179C2×C11#134111yescharacteristic
180C2×C11#134211yescharacteristic
181C24#432511yescharacteristic
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—441no—
187C22×C4—441no—
188C22×C4Dic11⋊C411yescharacteristic
189C22×C4(C2×D11)⋊C411yescharacteristic
190C22×C4#432311yescharacteristic
191C22×C4#432411yescharacteristic
192C22×C4#432611yescharacteristic
193C22×C4C22⋊Dic1111yescharacteristic
194M16—41no—
195M16—41no—
196M16—41no—
197M16—41no—
198M16—42no—
199M16—42no—
200M16—42no—
201M16—42no—
202C2×C8—21no—
203C2×C8—21no—
204C2×C8—21no—
205C2×C8—21no—
206C2×C8—24no—
207C2×C8—42no—
208C2×C8—42no—
209C2×C8C4×Dic1111yescharacteristic
210C2×C8Dic11⋊C411yescharacteristic
211C2×C8C4⋊Dic1111yescharacteristic
212C2×C8(C2×D11)⋊C411yescharacteristic
213C4⋊C4—441no—
214C4⋊C4—441no—
215C4⋊C4—441no—
216C4⋊C4—441no—
217C22⋊C4—882no—
218C16—442no—
219C11#725511yescharacteristic, complemented, Sylow
220C23—21no—
221C23—21no—
222C23—41no—
223C23—41no—
224C23#6687211yescharacteristic
225C23#6687311yescharacteristic
226C23#6689911yescharacteristic
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—881no—
238C2×C4—881no—
239C2×C4—881no—
240C2×C4—881no—
241C2×C4—881no—
242C2×C4—881no—
243C2×C4#6686911yescharacteristic
244C2×C4#6686911yescharacteristic
245C2×C4#6687011yescharacteristic
246C2×C4#6687011yescharacteristic
247C2×C4#6687111yescharacteristic
248C2×C4#6687411yescharacteristic
249C2×C4C11⋊#9511yescharacteristic
250C2×C4#6689611yescharacteristic
251C8—21no—
252C8—21no—
253C8—21no—
254C8—21no—
255C8—44no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—41no—
261C22—41no—
262C22—41no—
263C22—41no—
264C22—81no—
265C22#1062208911yescharacteristic
266C22#1062208911yescharacteristic
267C22#1062216711yescharacteristic
268C4—21no—
269C4—21no—
270C4—1761no—
271C4—1761no—
272C4#1062209011yescharacteristic
273C4#1062209011yescharacteristic
274C4#1062216111yescharacteristic
275C4#1062216511yescharacteristic
276C2—21no—
277C2—21no—
278C2—41no—
279C2—41no—
280C2#1306649511yescharacteristic
281C2#1306660611yescharacteristic
282C2#1306660911yescharacteristic
subgroupG/H
centerC22#10622089
commutatorC2×C8×C11C42
FrattiniC22×M16C2×D11
FittingC2×C11×#338C2
socleC22×C11#327
prime radicalC24×C11SD16
cosocleC22×C11×M16C22
hypercenterC2×#338D11
hypocenterC11#7255
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×M16 ◁ C2×#338

Complements

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

NH ≅ G/Ntype
11. C11×#338C4semidirect
13. #10622191C4semidirect
128. #338Dic11semidirect
219. C11#7255semidirect

Maximal subgroups

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

subgroupindex
C2×#106221912
#130686492
C2×C11×#3382
#725511