Finite Group Databasebeta

← #14641258

Subgroups — #14641258

Order 2816.

284 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 37 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#13069747C211yesmaximal, characteristic
2#13066546C211yesmaximal, characteristic, complemented
3C11×#1306C211yesmaximal, characteristic, complemented
4C2×#66982—21no—
5#10623024C411yescharacteristic
6C11×#407—21no—
7C11×#381C2211yescharacteristic
8C2×#66870—21no—
9#10622164C411yescharacteristic
10#10622163—21no—
11C23×C4×C11D411yescharacteristic
12C22×C22⋊D11—21no—
13C2×C11×M16—41no—
14C2×C11×C22⋊C4C2×C411yescharacteristic
15C2×C11×C22⋊C4D411yescharacteristic
16C2×C22⋊Dic11—21no—
17#66983—41no—
18#66982—42no—
19#66982—41no—
20#66982—41no—
21C2×(C2×D11)⋊C4—41no—
22C2×Dic11⋊C4—41no—
23#66939—41no—
24#66935—41no—
25C11×C22⋊C8—22no—
26C11×C22⋊C8—41no—
27C11×#95—41no—
28C22⋊(C11⋊C8)—41no—
29#66870—42no—
30#7395—111nomaximal, Sylow
31C24×C11C22⋊C411yescharacteristic
32C23×D11—21no—
33C22×C4×C11—21no—
34C22×C4×C11—21no—
35C22×C4×C11—21no—
36C22×C4×C11—21no—
37C22×C4×C11—41no—
38C22×C4×C11—41no—
39C22×C4×C11D811yescharacteristic
40C22×C4×C11SD1611yescharacteristic
41C2×C22⋊D11—41no—
42C2×C22⋊D11—41no—
43C2×C22⋊D11—41no—
44C2×C22⋊D11—41no—
45C2×C22⋊D11—41no—
46C2×C22⋊D11—41no—
47C22×Dic11—21no—
48C22×Dic11—41no—
49C2×D44—41no—
50C11×M16—81no—
51C11×M16—81no—
52C2×C8×C11—42no—
53C11×C22⋊C4—41no—
54C11×C22⋊C4—41no—
55C22⋊Dic11—22no—
56C22⋊Dic11—41no—
57(C2×D11)⋊C4—42no—
58(C2×D11)⋊C4—42no—
59(C2×D11)⋊C4—42no—
60C4⋊Dic11—41no—
61Dic11⋊C4—42no—
62Dic11⋊C4—42no—
63C2×C11⋊C8—81no—
64#2022—111no—
65#1317—111no—
66#1306D1111yescharacteristic, complemented
67C23×C11—21no—
68C23×C11—21no—
69C23×C11—81no—
70C23×C11#9911yescharacteristic
71C23×C11#10211yescharacteristic
72C23×C11#10411yescharacteristic
73C22×D11—41no—
74C22×D11—41no—
75C22×D11—41no—
76C22×D11—82no—
77C2×C4×C11—21no—
78C2×C4×C11—21no—
79C2×C4×C11—41no—
80C2×C4×C11—41no—
81C2×C4×C11—41no—
82C2×C4×C11—41no—
83C2×C4×C11—41no—
84C2×C4×C11—41no—
85C2×C4×C11—81no—
86C2×C4×C11—81no—
87C2×C4×C11—81no—
88C22⋊D11—81no—
89C22⋊D11—81no—
90C22⋊D11—81no—
91C22⋊D11—81no—
92C2×Dic11—41no—
93C2×Dic11—42no—
94C2×Dic11—41no—
95C2×Dic11—41no—
96C2×Dic11—82no—
97D44—161no—
98C8×C11—82no—
99C11⋊C8—161no—
100#534—111no—
101C2×#123—221no—
102C2×#99—221no—
103#407—21no—
104#381C2×D1111yescharacteristic
105#342—111no—
106#323—221no—
107C22×C11—21no—
108C22×C11—21no—
109C22×C11—41no—
110C22×C11—41no—
111C22×C11—41no—
112C22×C11—42no—
113C22×C11—81no—
114C22×C11#32711yescharacteristic
115C22×C11AΣL(1,𝔽16)11yescharacteristic
116C22×C11#35311yescharacteristic
117C2×D11—82no—
118C2×D11—82no—
119C2×D11—81no—
120C2×D11—161no—
121C4×C11—41no—
122C4×C11—41no—
123C4×C11—81no—
124C4×C11—81no—
125Dic11—82no—
126Dic11—81no—
127C22×D4—221no—
128C23×C4C22⋊D1111yescharacteristic
129C2×M16—41no—
130#123—441no—
131#123—442no—
132#123—441no—
133#123—441no—
134#121—441no—
135#120—441no—
136C2×C4⋊C4—441no—
137C2×C22⋊C4—221no—
138C2×C22⋊C4—441no—
139C2×C22⋊C4C4×D1111yescharacteristic
140C2×C22⋊C4D4411yescharacteristic
141#99—442no—
142C22⋊C8—22no—
143C22⋊C8—41no—
144C22⋊C8—441no—
145#95—41no—
146C2×C11—21no—
147C2×C11—21no—
148C2×C11—21no—
149C2×C11—41no—
150C2×C11—41no—
151C2×C11#134311yescharacteristic
152D11—161no—
153C24—221no—
154C24(C2×D11)⋊C411yescharacteristic
155C2×D4—441no—
156C2×D4—441no—
157C2×D4—441no—
158C2×D4—441no—
159C2×D4—441no—
160C2×D4—441no—
161C2×D4—441no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—41no—
167C22×C4—41no—
168C22×C4—221no—
169C22×C4—441no—
170C22×C4#432311yescharacteristic
171C22×C4#432511yescharacteristic
172M16—81no—
173M16—81no—
174C2×C8—42no—
175C2×C8—881no—
176C4⋊C4—441no—
177C4⋊C4—442no—
178C4⋊C4—442no—
179C22⋊C4—41no—
180C22⋊C4—41no—
181C22⋊C4—222no—
182C22⋊C4—442no—
183C22⋊C4—442no—
184C22⋊C4—442no—
185C22⋊C4—441no—
186C11#739511yescharacteristic, complemented, Sylow
187C23—21no—
188C23—21no—
189C23—81no—
190C23—441no—
191C23—441no—
192C23—441no—
193C23—882no—
194C23#6686911yescharacteristic
195C23#6687011yescharacteristic
196C23#6687311yescharacteristic
197D4—881no—
198D4—881no—
199D4—881no—
200D4—881no—
201D4—1761no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—81no—
211C2×C4—81no—
212C2×C4—81no—
213C2×C4—442no—
214C2×C4—441no—
215C2×C4—441no—
216C2×C4—441no—
217C2×C4—882no—
218C8—82no—
219C8—1761no—
220C22—21no—
221C22—21no—
222C22—41no—
223C22—41no—
224C22—41no—
225C22—42no—
226C22—81no—
227C22—882no—
228C22—882no—
229C22—881no—
230C22—1761no—
231C22#1062208911yescharacteristic
232C22#1062210911yescharacteristic
233C22#1062211211yescharacteristic
234C4—41no—
235C4—41no—
236C4—81no—
237C4—81no—
238C4—882no—
239C4—881no—
240C2—21no—
241C2—21no—
242C2—21no—
243C2—41no—
244C2—41no—
245C2—1761no—
246C2#1306661211yescharacteristic
subgroupG/H
centerC2#13066612
commutatorC2×C11×C22⋊C4C2×C4
Frattini#381C2×D11
FittingC11×#1306C2
socleC2×C11#1343
prime radical#10623024C4
cosocleC11×#381C22
hypercenter#1306D11
hypocenterC11#7395
LCSG ▷ C2×C11×C22⋊C4 ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C23 ◁ C24 ◁ #381 ◁ #1306

Complements

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

NH ≅ G/Ntype
2. #13066546C2semidirect
3. C11×#1306C2semidirect
66. #1306D11semidirect
186. C11#7395semidirect

Maximal subgroups

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

subgroupindex
#130697472
#130665462
C11×#13062
#739511