Finite Group Databasebeta

← #14663264

Subgroups — #14663264

Order 2816.

440 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 75 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#13071324C211yesmaximal, characteristic
2#13066953C212yesmaximal
3#13066562C211yesmaximal, characteristic, complemented
4#13066549C212yesmaximal, complemented
5C11×#1325C211yesmaximal, characteristic, complemented
6C2×#66946C2211yescharacteristic
7C2×#66940C411yescharacteristic
8C2×#66928C411yescharacteristic
9C11×#384C2211yescharacteristic
10#10622603—22no—
11#10622602—22no—
12#10622601C411yescharacteristic
13#10622587C2211yescharacteristic
14#10622545C411yescharacteristic
15#10622339—22no—
16C11×#324C2212yes—
17#10622166C2212yes—
18#10622106—22no—
19C22×D44C2×C411yescharacteristic
20C22×C4×D11D412yes—
21C22×Dic22C2×C411yescharacteristic
22C2×C11×C4⋊C4—22no—
23C2×C11×C4⋊C4C2×C411yescharacteristic
24C2×C11×C4⋊C4C2311yescharacteristic
25C2×C42×C11C2×C411yescharacteristic
26C2×(C2×D11)⋊C4—22no—
27C2×(C2×D11)⋊C4—22no—
28C2×(C2×D11)⋊C4D412yes—
29C2×Dic11⋊C4—21no—
30C2×C4×Dic11—21no—
31C2×C4×Dic11C2×C411yescharacteristic
32C2×C4×Dic11C2×C411yescharacteristic
33C2×#4313—42no—
34#66946—42no—
35#66940—42no—
36#66928—22no—
37#66928—22no—
38C11×C22⋊C8—22no—
39C11⋊#95—22no—
40C11⋊#95—21no—
41C11⋊#95—21no—
42C22⋊(C11⋊C8)—22no—
43(C2×D11)⋊C8—42no—
44#11535—111nomaximal, Sylow
45C23×D11C22⋊C412yes—
46C22×C4×C11—21no—
47C22×C4×C11—21no—
48C22×C4×C11C22×C411yescharacteristic
49C22×C4×C11C2×D412yes—
50C22×Dic11—21no—
51C22×Dic11—21no—
52C22×Dic11C22⋊C411yescharacteristic
53C22×Dic11C22⋊C411yescharacteristic
54C2×D44—21no—
55C2×D44—21no—
56C2×D44—41no—
57C2×D44—41no—
58C2×C4×D11—22no—
59C2×C4×D11—22no—
60C2×C4×D11—82no—
61C2×Dic22—21no—
62C2×Dic22—41no—
63C2×Dic22—41no—
64C2×Dic22M1612yescomplemented
65C2×C8×C11—42no—
66C11×C4⋊C4—41no—
67C11×C4⋊C4—41no—
68C11×C4⋊C4—82no—
69C42×C11—21no—
70C42×C11M1612yescomplemented
71(C2×D11)⋊C4—28no—
72(C2×D11)⋊C4—42no—
73(C2×D11)⋊C4—82no—
74Dic11⋊C4—42no—
75C4×Dic11—22no—
76C4×Dic11—41no—
77C4×Dic11—42no—
78C2×C11⋊C8—42no—
79#4313—84no—
80#2326—111no—
81#1465—112no—
82#1325—111no—
83#1325D1111yescharacteristic, complemented
84#1319—112no—
85C23×C11C2×C22⋊C411yescharacteristic
86C22×D11—22no—
87C22×D11—22no—
88C22×D11—22no—
89C22×D11—42no—
90C22×D11—42no—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—22no—
94C2×C4×C11—22no—
95C2×C4×C11—41no—
96C2×C4×C11—41no—
97C2×C4×C11—42no—
98C2×C4×C11—42no—
99C2×C4×C11—41no—
100C2×C4×C11C2×M1611yescharacteristic
101C2×C4×C11C2×M1611yescharacteristic
102C2×Dic11—22no—
103C2×Dic11—21no—
104C2×Dic11—41no—
105C2×Dic11—41no—
106C2×Dic11—41no—
107C2×Dic11—41no—
108C2×Dic11—41no—
109C2×Dic11—41no—
110C2×Dic11—41no—
111C2×Dic11#9912yes—
112D44—42no—
113D44—42no—
114C4×D11—44no—
115C4×D11—82no—
116Dic22—42no—
117Dic22—42no—
118C8×C11—82no—
119C11⋊C8—82no—
120C2×#124—111no—
121C2×C4×Q8—111no—
122C2×C4×D4—111no—
123#407—222no—
124#391—111no—
125#390—111no—
126#388—222no—
127#385—222no—
128#384C2×D1111yescharacteristic
129#376—111no—
130#324—112no—
131#324C2×D1112yes—
132#323—222no—
133C22×C11—21no—
134C22×C11—21no—
135C22×C11#40711yescharacteristic
136C22×C11C2×#9911yescharacteristic
137C22×C11#41311yescharacteristic
138C2×D11—44no—
139C2×D11—42no—
140C2×D11—42no—
141C2×D11—42no—
142C2×D11—82no—
143C4×C11—21no—
144C4×C11—21no—
145C4×C11—42no—
146C4×C11—42no—
147C4×C11—81no—
148Dic11—22no—
149Dic11—41no—
150Dic11—42no—
151Dic11—81no—
152C22×Q8—111no—
153C22×D4—111no—
154C23×C4—112no—
155C2×M16—442no—
156#124—222no—
157#124—222no—
158C4×Q8—442no—
159C4×D4—442no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—221no—
162C2×C4⋊C4C4×D1111yescharacteristic
163C2×C4⋊C4C22×D1111yescharacteristic
164C2×C22⋊C4—112no—
165C2×C22⋊C4—222no—
166C2×C22⋊C4—222no—
167C2×C42—111no—
168C2×C42—111no—
169C2×C42—221no—
170C2×C42C4×D1111yescharacteristic
171C22⋊C8—22no—
172C22⋊C8—222no—
173C22⋊C8—442no—
174#95—221no—
175#95—221no—
176#95—222no—
177C2×C11—21no—
178C2×C11—21no—
179C2×C11#146511yescharacteristic
180C2×C11#212711yescharacteristic
181C2×C11#213511yescharacteristic
182D11—82no—
183C24—112no—
184C2×Q8—112no—
185C2×Q8—221no—
186C2×Q8—441no—
187C2×Q8—441no—
188C2×D4—221no—
189C2×D4—221no—
190C2×D4—441no—
191C2×D4—441no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—111no—
195C22×C4—111no—
196C22×C4—222no—
197C22×C4—222no—
198C22×C4—221no—
199C22×C4—221no—
200C22×C4—882no—
201C22×C4C2×C4×D1111yescharacteristic
202C22×C4D4×D1112yes—
203M16—884no—
204C2×C8—42no—
205C2×C8—442no—
206C4⋊C4—41no—
207C4⋊C4—41no—
208C4⋊C4—82no—
209C4⋊C4—442no—
210C22⋊C4—228no—
211C22⋊C4—442no—
212C22⋊C4—882no—
213C42—21no—
214C42—222no—
215C42—441no—
216C42—442no—
217C42#431312yescomplemented
218C11#1153511yescharacteristic, complemented, Sylow
219C23—222no—
220C23—222no—
221C23—222no—
222C23—442no—
223C23—442no—
224C23C22⋊C4×D1111yescharacteristic
225Q8—442no—
226Q8—442no—
227D4—442no—
228D4—442no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—41no—
238C2×C4—112no—
239C2×C4—222no—
240C2×C4—221no—
241C2×C4—444no—
242C2×C4—441no—
243C2×C4—441no—
244C2×C4—441no—
245C2×C4—441no—
246C2×C4—441no—
247C2×C4—441no—
248C2×C4—441no—
249C2×C4—882no—
250C2×C4C2×#431311yescharacteristic
251C2×C4M16×D1111yescharacteristic
252C8—82no—
253C8—882no—
254C22—21no—
255C22—21no—
256C22—444no—
257C22—442no—
258C22—442no—
259C22—442no—
260C22—882no—
261C22#1062233911yescharacteristic
262C22D11×#9911yescharacteristic
263C22#1062236411yescharacteristic
264C4—21no—
265C4—21no—
266C4—42no—
267C4—42no—
268C4—81no—
269C4—222no—
270C4—442no—
271C4—441no—
272C4—881no—
273C2—21no—
274C2—21no—
275C2—882no—
276C2#1306695311yescharacteristic
277C2#1307028211yescharacteristic
278C2#1307030911yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1325C2
socleC22×C11C2×#99
prime radicalC22×D44C2×C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1325D11
hypocenterC11#11535
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1325

Complements

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

NH ≅ G/Ntype
3. #13066562C2semidirect
4. #13066549C2semidirect
5. C11×#1325C2semidirect
64. C2×Dic22M16semidirect
70. C42×C11M16semidirect
83. #1325D11semidirect
217. C42#4313semidirect
218. C11#11535semidirect

Maximal subgroups

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

subgroupindex
#130713242
#130669532
#130665622
#130665492
C11×#13252
#1153511