Finite Group Databasebeta

← #14640909

Subgroups — #14640909

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
1#13068649C211yesmaximal, characteristic
2C2×C11⋊#338C211yesmaximal, characteristic
3C2×C11×#349C211yesmaximal, characteristic
4C22×C11×M16C2211yescharacteristic
5C22×#4318—21no—
6C2×C11×M32—21no—
7#10622825—21no—
8C2×#66882C411yescharacteristic
9C2×#66881C411yescharacteristic
10C11×#349—21no—
11C11×#349C412yescomplemented
12C11⋊#338—21no—
13C11⋊#338C412yescomplemented
14#10622189—21no—
15C23×C4×C11D411yescharacteristic
16C2×C11×M16—41no—
17C2×C11×M16—41no—
18C2×C11×M16C2×C411yescharacteristic
19C2×C11×M16C2×C411yescharacteristic
20C2×C11×M16D411yescharacteristic
21C2×C11×M16Q811yescharacteristic
22C22×C8×C11C2×C411yescharacteristic
23C22×C8×C11D411yescharacteristic
24C2×C22⋊Dic11—41no—
25C2×C4⋊Dic11—21no—
26C2×C4⋊Dic11—21no—
27C2×#4318—22no—
28C2×#4318—22no—
29C2×#4318—41no—
30C2×#4318—41no—
31C2×#4318—41no—
32C2×#4318—41no—
33C22×C11⋊C8—22no—
34C11×M32—22no—
35C11×M32—41no—
36C2×C11×C16—41no—
37C11⋊#95—41no—
38#66882—41no—
39#66881—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—
58C2×C8×C11—21no—
59C2×C8×C11—21no—
60C2×C8×C11—21no—
61C2×C8×C11—21no—
62C2×C8×C11C4211yescharacteristic
63C2×C8×C11C22⋊C411yescharacteristic
64C2×C8×C11C4⋊C411yescharacteristic
65C2×C8×C11C4⋊C411yescharacteristic
66C22⋊Dic11—82no—
67C4⋊Dic11—41no—
68C4⋊Dic11—41no—
69C4⋊Dic11—41no—
70C4⋊Dic11—41no—
71#4318—42no—
72#4318—42no—
73#4318—42no—
74#4318—42no—
75C2×C11⋊C8—24no—
76C2×C11⋊C8—42no—
77C2×C11⋊C8—42no—
78C11×C16—42no—
79C2×#349D1111yescharacteristic
80#1809—111no—
81C2×#338—111no—
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—
117C11⋊C8—44no—
118C22×M16—221no—
119C22×M16C2×D1111yescharacteristic
120C2×M32—21no—
121C2×#107—111no—
122C2×#106—111no—
123#380—221no—
124#349—21no—
125#349Dic1112yescomplemented
126#340—221no—
127#338—112no—
128#338—221no—
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×C4D4411yescharacteristic
150C2×M16—41no—
151C2×M16—41no—
152C2×M16—222no—
153C2×M16—222no—
154C2×M16—441no—
155C2×M16—441no—
156C2×M16—441no—
157C2×M16—441no—
158C2×M16Dic2211yescharacteristic
159C2×M16C4×D1111yescharacteristic
160C2×M16C2×Dic1111yescharacteristic
161C2×M16C22⋊D1111yescharacteristic
162C22×C8—222no—
163C22×C8C4×D1111yescharacteristic
164C22×C8C22⋊D1111yescharacteristic
165C2×C4⋊C4—221no—
166C2×C4⋊C4—221no—
167C2×C22⋊C4—441no—
168M32—22no—
169M32—41no—
170C2×C16—41no—
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#431411yescharacteristic
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—441no—
187C22×C4—441no—
188C22×C4#431411yescharacteristic
189C22×C4D8811yescharacteristic
190C22×C4Dic4411yescharacteristic
191C22×C4C4⋊Dic1111yescharacteristic
192C22×C4(C2×D11)⋊C411yescharacteristic
193C22×C4(C2×D11)⋊C411yescharacteristic
194M16—41no—
195M16—41no—
196M16—41no—
197M16—41no—
198M16—442no—
199M16—442no—
200M16—442no—
201M16—442no—
202C2×C8—21no—
203C2×C8—21no—
204C2×C8—21no—
205C2×C8—21no—
206C2×C8—224no—
207C2×C8—442no—
208C2×C8—442no—
209C2×C8C4×Dic1111yescharacteristic
210C2×C8Dic11⋊C411yescharacteristic
211C2×C8Dic11⋊C411yescharacteristic
212C2×C8C22⋊Dic1111yescharacteristic
213C4⋊C4—441no—
214C4⋊C4—441no—
215C4⋊C4—441no—
216C4⋊C4—441no—
217C22⋊C4—882no—
218C16—42no—
219C11#725511yescharacteristic, complemented, Sylow
220C23—21no—
221C23—21no—
222C23—41no—
223C23—41no—
224C23#6688011yescharacteristic
225C23#6688111yescharacteristic
226C23#6688511yescharacteristic
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#6687011yescharacteristic
244C2×C4#6687011yescharacteristic
245C2×C4#6688011yescharacteristic
246C2×C4#6688211yescharacteristic
247C2×C4#6688511yescharacteristic
248C2×C4#6688911yescharacteristic
249C2×C4#6688911yescharacteristic
250C2×C4C11⋊#9511yescharacteristic
251C8—21no—
252C8—21no—
253C8—21no—
254C8—21no—
255C8—444no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—41no—
261C22—41no—
262C22—41no—
263C22—41no—
264C22—81no—
265C22#1062210811yescharacteristic
266C22#1062210811yescharacteristic
267C22#1062218911yescharacteristic
268C4—21no—
269C4—21no—
270C4—1761no—
271C4—1761no—
272C4#1062210511yescharacteristic
273C4#1062210511yescharacteristic
274C4#1062216511yescharacteristic
275C4#1062219311yescharacteristic
276C2—21no—
277C2—21no—
278C2—41no—
279C2—41no—
280C2#1306649611yescharacteristic
281C2#1306660811yescharacteristic
282C2#1306661111yescharacteristic
subgroupG/H
centerC22#10622108
commutatorC2×C8×C11C42
FrattiniC22×M16C2×D11
FittingC2×C11×#349C2
socleC22×C11#327
prime radicalC24×C11SD16
cosocleC22×C11×M16C22
hypercenterC2×#349D11
hypocenterC11#7255
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×M16 ◁ C2×#349

Complements

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

NH ≅ G/Ntype
11. C11×#349C4semidirect
13. C11⋊#338C4semidirect
125. #349Dic11semidirect
219. C11#7255semidirect

Maximal subgroups

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

subgroupindex
#130686492
C2×C11⋊#3382
C2×C11×#3492
#725511