Finite Group Databasebeta

← #14649792

Subgroups — #14649792

Order 2816.

458 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 119 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#13067301C212yesmaximal, complemented
3#13066930C211yesmaximal, characteristic
4#13066474C212yesmaximal, complemented
5C11×#2628C211yesmaximal, characteristic
6C2×C11×C4⋊Q8C2211yescharacteristic
7C2×C11×#117C2211yescharacteristic
8C11×#400C412yes—
9C11×#399C412yes—
10C11×#395—21no—
11C11×#393—21no—
12C11×#389—21no—
13C11×#382C2211yescharacteristic
14C11×#380—21no—
15#10622820—21no—
16#10622613—24no—
17#10622538C2212yes—
18#10622537C2212yes—
19C4×#4318—21no—
20#10622185—24no—
21#10622166—21no—
22#10622163—21no—
23C22×Q8×C11—21no—
24C23×C4×C11D411yescharacteristic
25C11×C4⋊Q8—22no—
26C11×C4⋊Q8—22no—
27C11×#117—22no—
28C11×#117—22no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—22no—
32C2×C11×C4⋊C4C2×C412yes—
33C2×C11×C4⋊C4C2×C411yescharacteristic
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C22⋊C4—22no—
36C2×C11×C22⋊C4C2×C411yescharacteristic
37C2×C11×C22⋊C4D411yescharacteristic
38C2×C42×C11D411yescharacteristic
39C2×C42×C11C2311yescharacteristic
40C2×#4318—22no—
41C11×#95—22no—
42C11×#95—22no—
43C11×#95—21no—
44C11×#95C2×C412yes—
45C22⋊(C11⋊C8)—24no—
46C22⋊(C11⋊C8)—22no—
47C4⋊(C11⋊C8)—22no—
48C4⋊(C11⋊C8)—22no—
49C4⋊(C11⋊C8)D414yes—
50#66867—22no—
51C4×C11⋊C8—22no—
52C4×C11⋊C8—22no—
53#9194—111nomaximal, Sylow
54C24×C11C22⋊C411yescharacteristic
55C2×Q8×C11—42no—
56C2×Q8×C11—82no—
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—22no—
60C22×C4×C11—22no—
61C22×C4×C11—22no—
62C22×C4×C11—22no—
63C22×C4×C11C22⋊C411yescharacteristic
64C22×C4×C11C22⋊C411yescharacteristic
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11C22×C411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C11×C4⋊C4—22no—
70C11×C4⋊C4—22no—
71C11×C4⋊C4—24no—
72C11×C4⋊C4—41no—
73C11×C4⋊C4—41no—
74C11×C4⋊C4—42no—
75C11×C4⋊C4—82no—
76C11×C22⋊C4—22no—
77C11×C22⋊C4—22no—
78C11×C22⋊C4—82no—
79C42×C11—21no—
80C42×C11—21no—
81C42×C11C2×D412yes—
82C42×C11#4112yes—
83#4318—42no—
84#4318—42no—
85C2×C11⋊C8—24no—
86C2×C11⋊C8—42no—
87#2921—111no—
88#2628D1111yescharacteristic
89#1549—112no—
90#1458—111no—
91#1286—112no—
92C23×C11—21no—
93C23×C11—21no—
94C23×C11—21no—
95C23×C11—41no—
96C23×C11—41no—
97C23×C11C2×C22⋊C411yescharacteristic
98Q8×C11—84no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—41no—
105C2×C4×C11—41no—
106C2×C4×C11—42no—
107C2×C4×C11—42no—
108C2×C4×C11—41no—
109C2×C4×C11—41no—
110C2×C4×C11—42no—
111C2×C4×C11—42no—
112C2×C4×C11—42no—
113C2×C4×C11—42no—
114C2×C4×C11—42no—
115C2×C4×C11—42no—
116C2×C4×C11C4×D412yes—
117C2×C4×C11#12011yescharacteristic
118C2×C4×C11#12112yes—
119C2×C4×C11#12311yescharacteristic
120C2×C4×C11#13512yes—
121C2×C4×C11#13712yes—
122C11⋊C8—44no—
123C11⋊C8—82no—
124C2×C4⋊Q8C2×D1111yescharacteristic
125C2×#117C2×D1111yescharacteristic
126#433—224no—
127#431—112no—
128#423—112no—
129#407—221no—
130C4×M16—221no—
131#400Dic1112yes—
132#399Dic1112yes—
133#395—21no—
134#393—21no—
135#389—21no—
136#382C2×D1111yescharacteristic
137#380—21no—
138#332—224no—
139#324—221no—
140#323—221no—
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—82no—
157C4×C11—82no—
158C4×C11#45212yes—
159C4×C11#48512yes—
160C22×Q8—21no—
161C23×C4C22⋊D1111yescharacteristic
162C2×M16—222no—
163C4⋊Q8—22no—
164C4⋊Q8—22no—
165#117—22no—
166#117—22no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4C2×Dic1112yes—
171C2×C4⋊C4C2×Dic1111yescharacteristic
172C2×C4⋊C4C22⋊D1111yescharacteristic
173C2×C22⋊C4—22no—
174C2×C22⋊C4C2×Dic1111yescharacteristic
175C2×C22⋊C4C22⋊D1111yescharacteristic
176C2×C42C22⋊D1111yescharacteristic
177C2×C42C22×D1111yescharacteristic
178C4⋊C8—114no—
179C4⋊C8—222no—
180C4⋊C8—222no—
181C22⋊C8—224no—
182C22⋊C8—222no—
183#97—222no—
184C4×C8—222no—
185C4×C8—222no—
186#95—22no—
187#95—22no—
188#95—21no—
189#95C2×Dic1112yes—
190C2×C11—21no—
191C2×C11—21no—
192C2×C11—81no—
193C2×C11#187311yescharacteristic
194C2×C11#191011yescharacteristic
195C2×C11#191511yescharacteristic
196C24C22⋊Dic1111yescharacteristic
197C2×Q8—42no—
198C2×Q8—82no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4C22⋊Dic1111yescharacteristic
206C22×C4C22⋊Dic1111yescharacteristic
207C22×C4C22⋊Dic1111yescharacteristic
208C22×C4C22×Dic1111yescharacteristic
209C22×C4C2×C22⋊D1111yescharacteristic
210C22×C4C2×C22⋊D1111yescharacteristic
211M16—442no—
212M16—442no—
213C2×C8—224no—
214C2×C8—442no—
215C4⋊C4—22no—
216C4⋊C4—22no—
217C4⋊C4—24no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—42no—
221C4⋊C4—82no—
222C22⋊C4—22no—
223C22⋊C4—22no—
224C22⋊C4—82no—
225C42—21no—
226C42—21no—
227C42D4×D1112yes—
228C42#434112yes—
229C11#919411yescharacteristic, complemented, Sylow
230C23—21no—
231C23—21no—
232C23—21no—
233C23—41no—
234C23—41no—
235C23C2×C22⋊Dic1111yescharacteristic
236Q8—84no—
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—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4D4×Dic1112yes—
255C2×C4#6698811yescharacteristic
256C2×C4#6699011yescharacteristic
257C2×C4#6699212yes—
258C2×C4#6699512yes—
259C2×C4#6700312yes—
260C8—444no—
261C8—882no—
262C22—21no—
263C22—21no—
264C22—42no—
265C22—41no—
266C22—41no—
267C22—41no—
268C22—81no—
269C22#1062283311yescharacteristic
270C22#1062283811yescharacteristic
271C22#1062284611yescharacteristic
272C4—22no—
273C4—22no—
274C4—41no—
275C4—41no—
276C4—41no—
277C4—82no—
278C4—82no—
279C4#1062265812yes—
280C4#1062266012yes—
281C2—21no—
282C2—21no—
283C2—81no—
284C2#1306892911yescharacteristic
285C2#1306914411yescharacteristic
286C2#1306916911yescharacteristic
subgroupG/H
centerC22#10622833
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2628C2
socleC22×C11#386
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#2628D11
hypocenterC11#9194
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2628

Complements

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

NH ≅ G/Ntype
2. #13067301C2semidirect
4. #13066474C2semidirect
229. C11#9194semidirect

Maximal subgroups

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

subgroupindex
#130772542
#130673012
#130669302
#130664742
C11×#26282
#919411