Finite Group Databasebeta

← #14763071

Subgroups — #14763071

Order 2816.

1194 conjugacy classes of subgroups; only the 235 normal subgroups are shown.

normal subgroups only

This group has 1194 conjugacy classes of subgroups — too many to draw. Only its 235 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×#10623347C211yesmaximal, characteristic
2#13077251C212yesmaximal, complemented
3#13069464C214yesmaximal, complemented
4#13069458C214yesmaximal, complemented
5#13068542C212yesmaximal
6#13068540C211yesmaximal, characteristic, complemented
7C11×#1784C211yesmaximal, characteristic, complemented
8C23×Q8×C11C2211yescharacteristic
9C22×#4339C2211yescharacteristic
10#10623347—28no—
11C2×#67000C2212yes—
12C2×#66999C414yes—
13C2×#66997C2212yes—
14C2×#66982C414yes—
15C2×#66979C2211yescharacteristic
16C2×C11×#101C2214yes—
17C11×#407C2212yes—
18C2×#66900C2214yes—
19#10622820C2212yes—
20C2×#66888C2214yes—
21C2×#66887C2214yes—
22#10622731C2214yes—
23M16×Dic11C2214yes—
24#10622333—28no—
25C22×Q8×C11—24no—
26C22×Q8×C11—44no—
27C22×Q8×C11C2×C412yes—
28C22×Q8×C11C2312yes—
29C23×C4×C11C2×C412yes—
30C23×C4×C11C2311yescharacteristic
31C22×C22⋊D11C2×C412yes—
32C2×#4339—24no—
33C2×#4339—44no—
34C22×D44C2311yescharacteristic
35C22×C4×D11C2×C412yes—
36C22×Dic22C2311yescharacteristic
37C2×C11×M16C2314yes—
38C2×C22⋊Dic11C2×C412yes—
39#67000—24no—
40#67000—24no—
41#66999—216no—
42#66997—24no—
43#66997—24no—
44#66982—216no—
45C2×(C2×D11)⋊C4C2×C418yes—
46#66979D418yes—
47C2×C4⋊Dic11C2×C412yes—
48C2×Dic11⋊C4C2×C418yes—
49C2×C4×Dic11C2312yes—
50C2×#4318C2314yes—
51C11×#101—44no—
52C11×C22⋊C8—24no—
53#66900—44no—
54C22⋊(C11⋊C8)—24no—
55#66888—44no—
56#66887—44no—
57#66879—24no—
58Dic11⋊C8—28no—
59C8×Dic11—24no—
60#21802—111nomaximal, Sylow
61C24×C11C22×C411yescharacteristic
62C23×D11C22×C412yes—
63C2×Q8×C11—24no—
64C2×Q8×C11—22no—
65C2×Q8×C11—22no—
66C2×Q8×C11—24no—
67C2×Q8×C11—24no—
68C2×Q8×C11—44no—
69C2×Q8×C11—416no—
70C22×C4×C11—24no—
71C22×C4×C11—24no—
72C22×C4×C11—44no—
73C22×C4×C11C22×C414yes—
74C22×C4×C11C22×C411yescharacteristic
75C22×C4×C11C2×D414yes—
76C22×C4×C11C2411yescharacteristic
77C2×C22⋊D11—24no—
78C2×C22⋊D11—44no—
79C22×Dic11C22×C412yes—
80C22×Dic11C22×C414yes—
81#4339—416no—
82C2×D44—22no—
83C2×D44—24no—
84C2×C4×D11—24no—
85C2×C4×D11—44no—
86C2×Dic22—22no—
87C2×Dic22—24no—
88C11×M16—24no—
89C11×M16—24no—
90C2×C8×C11—24no—
91C22⋊Dic11C22⋊C418yes—
92(C2×D11)⋊C4—216no—
93C4⋊Dic11C22⋊C418yes—
94Dic11⋊C4—216no—
95C4×Dic11C2×D414yes—
96C4×Dic11C2×D414yes—
97#4318—24no—
98#4318—24no—
99C2×C11⋊C8—24no—
100C2×#536—111no—
101#2921—112no—
102#1967—114no—
103#1966—114no—
104#1785—112no—
105#1784—111no—
106#1784D1111yescharacteristic, complemented
107C23×C11—22no—
108C23×C11—42no—
109C23×C11C2×C22⋊C412yes—
110C23×C11C23×C411yescharacteristic
111C22×D11—22no—
112C22×D11—24no—
113C22×D11—44no—
114Q8×C11—48no—
115Q8×C11—44no—
116Q8×C11—44no—
117C2×C4×C11—22no—
118C2×C4×C11—28no—
119C2×C4×C11—24no—
120C2×C4×C11—24no—
121C2×C4×C11—24no—
122C2×C4×C11—48no—
123C2×C4×C11C2×C22⋊C412yes—
124C2×C4×C11C22×D412yes—
125C2×C4×C11H(5,𝔽2)14yes—
126C22⋊D11—48no—
127C2×Dic11—22no—
128C2×Dic11—24no—
129C2×Dic11—44no—
130C2×Dic11C2×C22⋊C418yes—
131D44—44no—
132C4×D11—48no—
133Dic22—44no—
134C8×C11—44no—
135C11⋊C8—44no—
136C22×#41—111no—
137C23×Q8C2×D1111yescharacteristic
138#536—228no—
139C2×C4⋊Q8—112no—
140C2×#124—112no—
141C2×#123—114no—
142C2×C22⋊Q8—114no—
143C2×#117—111no—
144#433—228no—
145#423—114no—
146C2×#101—114no—
147C2×#101—114no—
148C2×#101C2×D1114yes—
149C2×#100—114no—
150#407—112no—
151#407C2×D1112yes—
152C4×M16—114no—
153C22×C11—22no—
154C22×C11—22no—
155C22×C11—24no—
156C22×C11—44no—
157C22×C11C22×C22⋊C411yescharacteristic
158C22×C11#51812yes—
159C2×D11—42no—
160C2×D11—44no—
161C2×D11—84no—
162C4×C11—22no—
163C4×C11—44no—
164C4×C11#53514yes—
165Dic11—28no—
166Dic11—42no—
167C2×#41—224no—
168C2×#41—444no—
169C22×Q8—24no—
170C22×Q8—44no—
171C22×Q8—111no—
172C22×Q8C4×D1112yes—
173C22×Q8C22×D1112yes—
174C22×D4—112no—
175C22×D4—111no—
176C23×C4—112no—
177C23×C4C4×D1112yes—
178C23×C4C22×D1111yescharacteristic
179C2×M16—114no—
180C2×M16C22×D1114yes—
181C4⋊Q8—224no—
182C4⋊Q8—224no—
183#124—224no—
184#124—224no—
185#123—2216no—
186C22⋊Q8—2216no—
187#117—118no—
188C2×C4⋊C4—112no—
189C2×C4⋊C4—118no—
190C2×C22⋊C4—112no—
191C2×C22⋊C4—118no—
192C2×C42—112no—
193C4⋊C8—228no—
194#101—44no—
195#101—444no—
196#101—444no—
197#100—444no—
198C22⋊C8—24no—
199C22⋊C8—224no—
200#97—224no—
201C4×C8—224no—
202C2×C11—22no—
203C2×C11—42no—
204C2×C11#230911yescharacteristic
205C2×C11#288912yes—
206D11—82no—
207C24—112no—
208C24C2×C4×D1111yescharacteristic
209#41—4416no—
210C2×Q8—24no—
211C2×Q8—22no—
212C2×Q8—22no—
213C2×Q8—24no—
214C2×Q8—24no—
215C2×Q8—44no—
216C2×Q8—416no—
217C2×Q8—222no—
218C2×Q8—224no—
219C2×D4—224no—
220C2×D4—222no—
221C2×D4—224no—
222C2×D4—444no—
223C22×C4—24no—
224C22×C4—24no—
225C22×C4—44no—
226C22×C4—114no—
227C22×C4—112no—
228C22×C4—224no—
229C22×C4—444no—
230C22×C4C2×C4×D1114yes—
231C22×C4C2×C4×D1111yescharacteristic
232C22×C4D4×D1114yes—
233C22×C4C23×D1111yescharacteristic
234M16—24no—
235M16—24no—
236M16—224no—
237M16—224no—
238C2×C8—24no—
239C2×C8—224no—
240C4⋊C4—118no—
241C4⋊C4—2216no—
242C22⋊C4—118no—
243C22⋊C4—2216no—
244C42—114no—
245C42—114no—
246C11#2180211yescharacteristic, complemented, Sylow
247C23—22no—
248C23—42no—
249C23—222no—
250C23—224no—
251C23—444no—
252C23C22⋊C4×D1112yes—
253C23C22×C4×D1111yescharacteristic
254Q8—48no—
255Q8—44no—
256Q8—44no—
257Q8—444no—
258D4—448no—
259D4—444no—
260C2×C4—22no—
261C2×C4—28no—
262C2×C4—24no—
263C2×C4—24no—
264C2×C4—24no—
265C2×C4—48no—
266C2×C4—118no—
267C2×C4—222no—
268C2×C4—224no—
269C2×C4—448no—
270C2×C4—444no—
271C2×C4C22⋊C4×D1112yes—
272C2×C4C2×D4×D1112yes—
273C2×C4#6703714yes—
274C8—44no—
275C8—444no—
276C22—22no—
277C22—22no—
278C22—24no—
279C22—44no—
280C22—442no—
281C22—444no—
282C22—884no—
283C22C2×C22⋊C4×D1111yescharacteristic
284C22#1062301712yes—
285C4—22no—
286C4—44no—
287C4—228no—
288C4—442no—
289C4#1062312314yes—
290C2—22no—
291C2—42no—
292C2—882no—
293C2#1307119711yescharacteristic
294C2#1307709612yes—
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1784C2
socleC22×C11C22×C22⋊C4
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenter#1784D11
hypocenterC11#21802
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1784

Complements

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

NH ≅ G/Ntype
2. #13077251C2semidirect
3. #13069464C2semidirect
4. #13069458C2semidirect
6. #13068540C2semidirect
7. C11×#1784C2semidirect
106. #1784D11semidirect
246. C11#21802semidirect

Maximal subgroups

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

subgroupindex
C2×#106233472
#130772512
#130694642
#130694582
#130685422
#130685402
C11×#17842
#2180211