Finite Group Databasebeta

← #14649779

Subgroups — #14649779

Order 2816.

458 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 111 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#13077254C211yesmaximal, characteristic
2#13074437C211yesmaximal, characteristic
3#13067296C212yesmaximal, complemented
4#13066475C212yesmaximal, complemented
5C11×#1458C211yesmaximal, characteristic
6C2×C11×#117C2211yescharacteristic
7C2×#66922C2211yescharacteristic
8C11×#431C2212yes—
9#10622825—21no—
10#10622820—21no—
11#10622613—24no—
12#10622599—21no—
13#10622592C412yes—
14#10622562—21no—
15#10622560C412yes—
16#10622549C2211yescharacteristic
17#10622541—21no—
18#10622537C2212yes—
19C4×#4318—21no—
20C11×#324—21no—
21C11×#323—21no—
22#10622119—24no—
23C23×C4×C11D411yescharacteristic
24C22×Dic22C2×C412yes—
25C11×#117—22no—
26C11×#117—22no—
27C2×C11×C4⋊C4C2×C411yescharacteristic
28C2×C11×C4⋊C4D411yescharacteristic
29C2×C11×C22⋊C4C2×C411yescharacteristic
30C2×C11×C22⋊C4D411yescharacteristic
31C2×C42×C11D411yescharacteristic
32C2×C42×C11C2311yescharacteristic
33C2×C22⋊Dic11—22no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×Dic11⋊C4—22no—
38C2×#4318—22no—
39#66922—22no—
40#66922—22no—
41C11×C4⋊C8—22no—
42C11×C22⋊C8—22no—
43C4×C8×C11—22no—
44C11⋊#95—22no—
45C11⋊#95—22no—
46C11⋊#95—21no—
47C11⋊#95C2×C412yes—
48C22⋊(C11⋊C8)—24no—
49C4⋊(C11⋊C8)—22no—
50C4⋊(C11⋊C8)D414yes—
51#66867—22no—
52C4×C11⋊C8—22no—
53#9192—111nomaximal, Sylow
54C24×C11C22⋊C411yescharacteristic
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—22no—
58C22×C4×C11—22no—
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C22×C411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C22×Dic11—22no—
66C22×Dic11—22no—
67C2×Dic22—24no—
68C2×Dic22—82no—
69C2×C8×C11—42no—
70C11×C4⋊C4—22no—
71C11×C4⋊C4—22no—
72C11×C22⋊C4—22no—
73C11×C22⋊C4—22no—
74C42×C11—21no—
75C42×C11—21no—
76C42×C11C2×D412yes—
77C42×C11#4112yes—
78C22⋊Dic11—82no—
79C4⋊Dic11—41no—
80C4⋊Dic11—42no—
81C4⋊Dic11—41no—
82C4⋊Dic11—42no—
83Dic11⋊C4—82no—
84#4318—42no—
85#4318—42no—
86C2×C11⋊C8—24no—
87#2921—111no—
88#2628—111no—
89#1548—112no—
90#1458D1111yescharacteristic
91#1286—112no—
92C23×C11—21no—
93C23×C11—21no—
94C23×C11—21no—
95C23×C11—41no—
96C23×C11—41no—
97C23×C11C2×C22⋊C411yescharacteristic
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—41no—
104C2×C4×C11—41no—
105C2×C4×C11—42no—
106C2×C4×C11—42no—
107C2×C4×C11—41no—
108C2×C4×C11—41no—
109C2×C4×C11C4×D412yes—
110C2×C4×C11#12011yescharacteristic
111C2×C4×C11#12112yes—
112C2×C4×C11#12311yescharacteristic
113C2×C4×C11#13512yes—
114C2×C4×C11#13712yes—
115C2×Dic11—42no—
116C2×Dic11—42no—
117C2×Dic11—42no—
118C2×Dic11—42no—
119C2×Dic11—42no—
120C2×Dic11—42no—
121Dic22—84no—
122C8×C11—82no—
123C11⋊C8—44no—
124C2×C4⋊Q8—111no—
125C2×#117C2×D1111yescharacteristic
126#433—224no—
127#431C2×D1112yes—
128#423—112no—
129#407—221no—
130C4×M16—221no—
131#400—221no—
132#399—221no—
133#395—112no—
134#393—112no—
135#389—221no—
136#382—111no—
137#380—221no—
138#333—224no—
139#324—21no—
140#323—21no—
141C22×C11—21no—
142C22×C11—21no—
143C22×C11—42no—
144C22×C11—41no—
145C22×C11—41no—
146C22×C11—41no—
147C22×C11—81no—
148C22×C11#38611yescharacteristic
149C22×C11#41611yescharacteristic
150C22×C11#41911yescharacteristic
151C4×C11—22no—
152C4×C11—22no—
153C4×C11—41no—
154C4×C11—41no—
155C4×C11—41no—
156C4×C11#45212yes—
157C4×C11#48512yes—
158Dic11—82no—
159Dic11—82no—
160C22×Q8—112no—
161C23×C4D4411yescharacteristic
162C2×M16—222no—
163C4⋊Q8—222no—
164C4⋊Q8—222no—
165#117—22no—
166#117—22no—
167C2×C4⋊C4—221no—
168C2×C4⋊C4—221no—
169C2×C4⋊C4—221no—
170C2×C4⋊C4—222no—
171C2×C4⋊C4C4×D1111yescharacteristic
172C2×C4⋊C4C22⋊D1111yescharacteristic
173C2×C22⋊C4—222no—
174C2×C22⋊C4C4×D1111yescharacteristic
175C2×C22⋊C4C22⋊D1111yescharacteristic
176C2×C42D4411yescharacteristic
177C2×C42C22×D1111yescharacteristic
178C4⋊C8—22no—
179C4⋊C8—114no—
180C4⋊C8—222no—
181C22⋊C8—22no—
182C22⋊C8—224no—
183#97—222no—
184C4×C8—22no—
185C4×C8—222no—
186#95—112no—
187#95—222no—
188#95—222no—
189#95—221no—
190C2×C11—21no—
191C2×C11—21no—
192C2×C11—81no—
193C2×C11#187311yescharacteristic
194C2×C11#190911yescharacteristic
195C2×C11#191411yescharacteristic
196C24(C2×D11)⋊C411yescharacteristic
197C2×Q8—224no—
198C2×Q8—882no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—222no—
204C22×C4—222no—
205C22×C4(C2×D11)⋊C411yescharacteristic
206C22×C4(C2×D11)⋊C411yescharacteristic
207C22×C4(C2×D11)⋊C411yescharacteristic
208C22×C4C2×C4×D1111yescharacteristic
209C22×C4C2×D4411yescharacteristic
210C22×C4C2×C22⋊D1111yescharacteristic
211M16—442no—
212M16—442no—
213C2×C8—42no—
214C2×C8—224no—
215C4⋊C4—22no—
216C4⋊C4—22no—
217C4⋊C4—441no—
218C4⋊C4—441no—
219C4⋊C4—442no—
220C4⋊C4—442no—
221C4⋊C4—882no—
222C22⋊C4—22no—
223C22⋊C4—22no—
224C22⋊C4—882no—
225C42—21no—
226C42—21no—
227C42D4×D1112yes—
228C42#434112yes—
229C11#919211yescharacteristic, complemented, Sylow
230C23—21no—
231C23—21no—
232C23—21no—
233C23—41no—
234C23—41no—
235C23C2×(C2×D11)⋊C411yescharacteristic
236Q8—884no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—442no—
249C2×C4—442no—
250C2×C4—442no—
251C2×C4—442no—
252C2×C4—442no—
253C2×C4—442no—
254C2×C4(C22⋊D11)⋊C412yes—
255C2×C4#6693511yescharacteristic
256C2×C4#6693911yescharacteristic
257C2×C4#6695712yes—
258C2×C4#6696212yes—
259C2×C4#6699212yes—
260C8—82no—
261C8—444no—
262C22—21no—
263C22—21no—
264C22—42no—
265C22—41no—
266C22—41no—
267C22—41no—
268C22—81no—
269C22#1062257111yescharacteristic
270C22#1062272611yescharacteristic
271C22#1062273311yescharacteristic
272C4—22no—
273C4—22no—
274C4—41no—
275C4—41no—
276C4—41no—
277C4—882no—
278C4—882no—
279C4#1062233612yes—
280C4#1062234612yes—
281C2—21no—
282C2—21no—
283C2—81no—
284C2#1306892611yescharacteristic
285C2#1306913611yescharacteristic
286C2#1306916111yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1458C2
socleC22×C11#386
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1458D11
hypocenterC11#9192
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1458

Complements

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

NH ≅ G/Ntype
3. #13067296C2semidirect
4. #13066475C2semidirect
229. C11#9192semidirect

Maximal subgroups

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

subgroupindex
#130772542
#130744372
#130672962
#130664752
C11×#14582
#919211