Finite Group Databasebeta

← #14684787

Subgroups — #14684787

Order 2816.

3274 conjugacy classes of subgroups; only the 371 normal subgroups are shown.

normal subgroups only

This group has 3274 conjugacy classes of subgroups — too many to draw. Only its 371 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
1C22×#67006C211yesmaximal, characteristic
2C2×#10622860C211yesmaximal, characteristic, complemented
3#13066863C216yesmaximal, complemented
4#13066855C216yesmaximal, complemented
5C2×C11×#379C211yesmaximal, characteristic, complemented
6C26×C11C2211yescharacteristic
7C23×C22⋊D11C2213yes—
8C22×C11×C22⋊C4C2216yes—
9C2×#67006—24no—
10C2×#67006—24no—
11C2×#67006C418yescomplemented
12C22×C22⋊Dic11C2213yes—
13C22×C22⋊Dic11C2216yes—
14C22×(C2×D11)⋊C4C2214yescomplemented
15C11×#379—24no—
16#10622860—24no—
17C2×C11⋊#95C22112yescomplemented
18C25×C11—412no—
19C25×C11C2×C414yes—
20C25×C11D414yes—
21C25×C11D414yes—
22C25×C11C2313yes—
23C24×D11C2311yescharacteristic
24C23×C4×C11C2314yes—
25C22×C22⋊D11—26no—
26C22×C22⋊D11—26no—
27C22×C22⋊D11—412no—
28C22×C22⋊D11C2×C4112yes—
29C23×Dic11C2314yes—
30C23×Dic11C2313yes—
31C2×C11×C22⋊C4—212no—
32C2×C11×C22⋊C4—412no—
33#67006—232no—
34C2×C22⋊Dic11—26no—
35C2×C22⋊Dic11—26no—
36C2×C22⋊Dic11—212no—
37C2×C22⋊Dic11—412no—
38C2×C22⋊Dic11C2×C4112yes—
39C2×(C2×D11)⋊C4—412no—
40C11⋊#95—412no—
41#14657—111nomaximal, Sylow
42C24×C11—212no—
43C24×C11—212no—
44C24×C11—212no—
45C24×C11—424no—
46C24×C11—424no—
47C24×C11—424no—
48C24×C11—448no—
49C24×C11—416no—
50C24×C11C22⋊C4116yescomplemented
51C24×C11C22×C416yes—
52C24×C11C2×D416yes—
53C24×C11C2×D416yes—
54C24×C11C2411yescharacteristic
55C23×D11—21no—
56C23×D11—21no—
57C23×D11—212no—
58C23×D11C22×C412yes—
59C22×C4×C11—24no—
60C22×C4×C11—212no—
61C22×C4×C11—212no—
62C2×C22⋊D11—224no—
63C2×C22⋊D11—424no—
64C2×C22⋊D11—424no—
65C2×C22⋊D11—424no—
66C22×Dic11—23no—
67C22×Dic11—23no—
68C22×Dic11—24no—
69C22×Dic11—212no—
70C22×Dic11—212no—
71C22×Dic11—212no—
72C22×Dic11C22×C416yes—
73C11×C22⋊C4—424no—
74C22⋊Dic11—224no—
75C22⋊Dic11—424no—
76(C2×D11)⋊C4—416no—
77C22×#120—111no—
78C2×#379—111no—
79C2×#379D1111yescharacteristic, complemented
80#1440—116no—
81#1438—116no—
82C23×C11—212no—
83C23×C11—212no—
84C23×C11—212no—
85C23×C11—212no—
86C23×C11—212no—
87C23×C11—212no—
88C23×C11—212no—
89C23×C11—212no—
90C23×C11—212no—
91C23×C11—448no—
92C23×C11—464no—
93C23×C11—464no—
94C23×C11—464no—
95C23×C11—436no—
96C23×C11—412no—
97C23×C11C2×C22⋊C4112yes—
98C23×C11C23×C411yescharacteristic
99C23×C11C22×D411yescharacteristic
100C23×C11C22×D411yescharacteristic
101C23×C11H(5,𝔽2)112yes—
102C22×D11—22no—
103C22×D11—212no—
104C22×D11—46no—
105C22×D11—46no—
106C22×D11—412no—
107C22×D11—44no—
108C2×C4×C11—412no—
109C2×C4×C11—412no—
110C2×C4×C11—44no—
111C22⋊D11—448no—
112C2×Dic11—26no—
113C2×Dic11—212no—
114C2×Dic11—46no—
115C2×Dic11—46no—
116C2×Dic11—412no—
117C2×Dic11—412no—
118C2×Dic11—44no—
119C26C2×D1111yescharacteristic
120C23×D4—113no—
121C2×#120—118no—
122C2×#120—224no—
123C2×#120—224no—
124C22×C22⋊C4—113no—
125C22×C22⋊C4—116no—
126C22×C22⋊C4—114no—
127C22×C22⋊C4C2×D1116yes—
128#379—24no—
129#379—224no—
130C2×#95—1112no—
131C22×C11—212no—
132C22×C11—212no—
133C22×C11—212no—
134C22×C11—464no—
135C22×C11—424no—
136C22×C11—424no—
137C22×C11—424no—
138C22×C11C22×C22⋊C411yescharacteristic
139C22×C11#51816yes—
140C22×C11#53416yes—
141C22×C11#53416yes—
142C22×C11#560112yes—
143C22×C11H(3,𝔽4)14yes—
144C2×D11—46no—
145C2×D11—48no—
146C2×D11—84no—
147C2×D11—84no—
148C4×C11—84no—
149Dic11—46no—
150Dic11—84no—
151C25—412no—
152C25—111no—
153C25C4×D1114yes—
154C25D4414yes—
155C25C22⋊D1114yes—
156C25C22×D1113yes—
157C22×D4—1112no—
158C22×D4—226no—
159C22×D4—226no—
160C22×D4—4412no—
161C23×C4—113no—
162C23×C4—114no—
163C23×C4C22×D1114yes—
164#120—2232no—
165C2×C22⋊C4—212no—
166C2×C22⋊C4—412no—
167C2×C22⋊C4—1112no—
168C2×C22⋊C4—226no—
169C2×C22⋊C4—226no—
170C2×C22⋊C4—2212no—
171C2×C22⋊C4—4412no—
172C2×C22⋊C4—4412no—
173#95—4412no—
174C2×C11—412no—
175C2×C11#230813yes—
176C2×C11#237514yes—
177C2×C11#281214yes—
178C2×C11#281214yes—
179D11—82no—
180C24—212no—
181C24—212no—
182C24—212no—
183C24—424no—
184C24—424no—
185C24—424no—
186C24—416no—
187C24—448no—
188C24—112no—
189C24—221no—
190C24—2212no—
191C24—221no—
192C24(C2×D11)⋊C4116yescomplemented
193C24C2×C4×D1116yes—
194C24C2×D4416yes—
195C24C2×C22⋊D1116yes—
196C24C23×D1111yescharacteristic
197C2×D4—2224no—
198C2×D4—4424no—
199C2×D4—4424no—
200C2×D4—4424no—
201C22×C4—212no—
202C22×C4—212no—
203C22×C4—24no—
204C22×C4—116no—
205C22×C4—223no—
206C22×C4—2212no—
207C22×C4—223no—
208C22×C4—224no—
209C22×C4—2212no—
210C22×C4—2212no—
211C22⋊C4—424no—
212C22⋊C4—2224no—
213C22⋊C4—4416no—
214C22⋊C4—4424no—
215C11#1465711yescharacteristic, complemented, Sylow
216C23—212no—
217C23—212no—
218C23—212no—
219C23—212no—
220C23—212no—
221C23—212no—
222C23—212no—
223C23—212no—
224C23—212no—
225C23—448no—
226C23—464no—
227C23—464no—
228C23—464no—
229C23—412no—
230C23—436no—
231C23—2212no—
232C23—222no—
233C23—446no—
234C23—446no—
235C23—444no—
236C23—4412no—
237C23C2×(C2×D11)⋊C4112yes—
238C23C22×C4×D1111yescharacteristic
239C23C22×D4411yescharacteristic
240C23#67037112yes—
241C23C22×C22⋊D1111yescharacteristic
242D4—4448no—
243C2×C4—412no—
244C2×C4—44no—
245C2×C4—412no—
246C2×C4—2212no—
247C2×C4—226no—
248C2×C4—446no—
249C2×C4—446no—
250C2×C4—4412no—
251C2×C4—444no—
252C2×C4—4412no—
253C22—212no—
254C22—212no—
255C22—212no—
256C22—464no—
257C22—424no—
258C22—424no—
259C22—424no—
260C22—446no—
261C22—448no—
262C22—884no—
263C22—884no—
264C22#1062301716yes—
265C22#1062302416yes—
266C22#1062312514yes—
267C22#10623126112yes—
268C22C22×(C2×D11)⋊C411yescharacteristic
269C22#1062333516yes—
270C4—84no—
271C4—446no—
272C4—884no—
273C2—412no—
274C2—882no—
275C2#1307119113yes—
276C2#1307175514yes—
277C2#1307661114yes—
278C2#1307661314yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#379C2
socle, cosocleC24×C11C24
prime radicalC22×#67006C2
hypercenterC2×#379D11
hypocenterC11#14657
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#379

Complements

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

NH ≅ G/Ntype
2. C2×#10622860C2semidirect
3. #13066863C2semidirect
4. #13066855C2semidirect
5. C2×C11×#379C2semidirect
11. C2×#67006C4semidirect
14. C22×(C2×D11)⋊C4C22semidirect
17. C2×C11⋊#95C22semidirect
50. C24×C11C22⋊C4semidirect
79. C2×#379D11semidirect
192. C24(C2×D11)⋊C4semidirect
215. C11#14657semidirect

Maximal subgroups

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

subgroupindex
C22×#670062
C2×#106228602
#130668632
#130668552
C2×C11×#3792
#1465711