Finite Group Databasebeta

← #14651612

Subgroups — #14651612

Order 2816.

542 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 131 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#13073970C211yesmaximal, characteristic
2#13068608C211yesmaximal, characteristic
3#13067046C212yesmaximal, complemented
4#13066475C212yesmaximal, complemented
5C11×#2972C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C2×C4×Dic22C2211yescharacteristic
8C8×D4×C11—24no—
9C11×#431C2212yes—
10C2×C11×C22⋊C8—22no—
11#10622834—21no—
12C2×#66897—21no—
13#10622823—22no—
14#10622586—21no—
15#10622562C412yes—
16#10622560C412yes—
17#10622549C2211yescharacteristic
18#10622537C2212yes—
19#10622168—21no—
20#10622094—24no—
21C22×D4×C11D411yescharacteristic
22C23×C4×C11D412yes—
23C22×Dic22C2×C411yescharacteristic
24C22×C8×C11—24no—
25C4×D4×C11—22no—
26C4×D4×C11—22no—
27C2×C11×C4⋊C4D411yescharacteristic
28C2×C11×C22⋊C4C2×C412yes—
29C2×C42×C11C2311yescharacteristic
30C2×C22⋊Dic11—22no—
31C2×C22⋊Dic11—22no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11C2×C411yescharacteristic
34C2×Dic11⋊C4—21no—
35C2×Dic11⋊C4—22no—
36C2×C4×Dic11—21no—
37C2×#4318—22no—
38C4×Dic22—22no—
39C4×Dic22—22no—
40C11×C4⋊C8—22no—
41C11×C22⋊C8—24no—
42C11×C22⋊C8—22no—
43C4×C8×C11D414yes—
44#66897—42no—
45C11⋊#95—22no—
46C11⋊#95—21no—
47C11⋊#95C2×C412yes—
48C4⋊(C11⋊C8)—22no—
49C4⋊(C11⋊C8)—22no—
50#9483—111nomaximal, Sylow
51C24×C11C22⋊C412yes—
52C2×D4×C11—22no—
53C2×D4×C11—22no—
54C2×D4×C11SD1612yes—
55C2×D4×C11Q1612yes—
56C22×C4×C11—22no—
57C22×C4×C11—22no—
58C22×C4×C11—82no—
59C22×C4×C11C22⋊C412yes—
60C22×C4×C11C22×C411yescharacteristic
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×Dic11—21no—
64C22×Dic11—22no—
65C22×Dic11—21no—
66C2×Dic22—22no—
67C2×Dic22—42no—
68C2×C8×C11—24no—
69C2×C8×C11—84no—
70C11×C4⋊C4—22no—
71C11×C22⋊C4—24no—
72C42×C11C2×D412yes—
73C42×C11#4112yes—
74C22⋊Dic11—44no—
75C22⋊Dic11—82no—
76C4⋊Dic11—22no—
77C4⋊Dic11—42no—
78Dic11⋊C4—41no—
79Dic11⋊C4—41no—
80Dic11⋊C4—82no—
81C4×Dic11—42no—
82#4318—42no—
83#4318—42no—
84C2×C11⋊C8—42no—
85#2972D1111yescharacteristic
86#2580—111no—
87#1800—111no—
88#1487—112no—
89#1286—112no—
90C23×C11—22no—
91C23×C11—22no—
92C23×C11—42no—
93C23×C11—42no—
94C23×C11#10314yes—
95C23×C11C2×C22⋊C411yescharacteristic
96D4×C11—24no—
97D4×C11—24no—
98C2×C4×C11—22no—
99C2×C4×C11—41no—
100C2×C4×C11—41no—
101C2×C4×C11—44no—
102C2×C4×C11—42no—
103C2×C4×C11—82no—
104C2×C4×C11C4×D412yes—
105C2×C4×C11#12011yescharacteristic
106C2×C4×C11#12112yes—
107C2×C4×C11#12311yescharacteristic
108C2×C4×C11C2×SD1611yescharacteristic
109C2×C4×C11C2×Q1611yescharacteristic
110C2×C4×C11#13512yes—
111C2×Dic11—22no—
112C2×Dic11—41no—
113C2×Dic11—41no—
114C2×Dic11—41no—
115C2×Dic11—42no—
116C2×Dic11—42no—
117C2×Dic11—41no—
118C2×Dic11—41no—
119C2×Dic11—42no—
120Dic22—24no—
121Dic22—42no—
122C8×C11—44no—
123C11⋊C8—82no—
124C2×C4×Q8—111no—
125C2×C4×D4C2×D1111yescharacteristic
126C8×D4—24no—
127#431C2×D1112yes—
128#423—112no—
129C2×#100—221no—
130C2×C22⋊C8—22no—
131#399—112no—
132#393—112no—
133#390—221no—
134#389—221no—
135#385—222no—
136#382—111no—
137#343—221no—
138Q8⋊C8—224no—
139C22×C11—21no—
140C22×C11—21no—
141C22×C11—24no—
142C22×C11—44no—
143C22×C11—42no—
144C22×C11—42no—
145C22×C11—82no—
146C22×C11#38611yescharacteristic
147C22×C11C2×#10311yescharacteristic
148C22×C11#41611yescharacteristic
149C4×C11—22no—
150C4×C11—21no—
151C4×C11—21no—
152C4×C11—42no—
153C4×C11#46512yes—
154C4×C11#46712yes—
155Dic11—42no—
156Dic11—82no—
157Dic11—81no—
158C22×Q8—111no—
159C22×D4D4411yescharacteristic
160C23×C4C22⋊D1112yes—
161C2×M16—222no—
162C22×C8—24no—
163C4×Q8—222no—
164C4×Q8—222no—
165C4×D4—22no—
166C4×D4—22no—
167C2×C4⋊C4—111no—
168C2×C4⋊C4—221no—
169C2×C4⋊C4—221no—
170C2×C4⋊C4—222no—
171C2×C4⋊C4D4411yescharacteristic
172C2×C22⋊C4—222no—
173C2×C22⋊C4—222no—
174C2×C22⋊C4C4×D1112yes—
175C2×C42—221no—
176C2×C42C22×D1111yescharacteristic
177C4⋊C8—22no—
178C4⋊C8—222no—
179C4⋊C8—222no—
180#100—442no—
181C22⋊C8—24no—
182C22⋊C8—22no—
183C4×C8C22⋊D1114yes—
184#95—112no—
185#95—222no—
186#95—221no—
187C2×C11—21no—
188C2×C11—21no—
189C2×C11—44no—
190C2×C11#189111yescharacteristic
191C2×C11#189211yescharacteristic
192C2×C11#191111yescharacteristic
193C24(C2×D11)⋊C412yes—
194C2×Q8—222no—
195C2×Q8—442no—
196C2×D4—22no—
197C2×D4—22no—
198C2×D4#431412yes—
199C2×D4Dic4412yes—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—82no—
203C22×C4—221no—
204C22×C4—222no—
205C22×C4—221no—
206C22×C4(C2×D11)⋊C412yes—
207C22×C4C2×C4×D1111yescharacteristic
208C22×C4C2×D4411yescharacteristic
209C22×C4C2×C22⋊D1111yescharacteristic
210M16—442no—
211M16—442no—
212C2×C8—24no—
213C2×C8—84no—
214C2×C8—442no—
215C4⋊C4—22no—
216C4⋊C4—222no—
217C4⋊C4—442no—
218C4⋊C4—441no—
219C4⋊C4—441no—
220C4⋊C4—882no—
221C22⋊C4—24no—
222C22⋊C4—444no—
223C22⋊C4—882no—
224C42—442no—
225C42#433912yes—
226C42C2×C22⋊D1112yes—
227C11#948311yescharacteristic, complemented, Sylow
228C23—22no—
229C23—22no—
230C23—42no—
231C23—42no—
232C23#6688014yes—
233C23C2×(C2×D11)⋊C411yescharacteristic
234Q8—224no—
235Q8—442no—
236D4—24no—
237D4—24no—
238C2×C4—22no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—44no—
242C2×C4—42no—
243C2×C4—82no—
244C2×C4—222no—
245C2×C4—441no—
246C2×C4—441no—
247C2×C4—442no—
248C2×C4—441no—
249C2×C4—442no—
250C2×C4—441no—
251C2×C4—442no—
252C2×C4—441no—
253C2×C4C2×#431411yescharacteristic
254C2×C4#6695712yes—
255C2×C4C2×Dic4411yescharacteristic
256C2×C4C4×C22⋊D1112yes—
257C2×C4#6698211yescharacteristic
258C2×C4#6698312yes—
259C2×C4#6700611yescharacteristic
260C8—44no—
261C8—882no—
262C22—21no—
263C22—21no—
264C22—24no—
265C22—44no—
266C22—42no—
267C22—42no—
268C22—82no—
269C22C2×#6688011yescharacteristic
270C22#1062272611yescharacteristic
271C22#1062282611yescharacteristic
272C4—21no—
273C4—21no—
274C4—22no—
275C4—42no—
276C4—442no—
277C4—882no—
278C4—881no—
279C4#1062272712yes—
280C4#1062272912yes—
281C2—21no—
282C2—21no—
283C2—44no—
284C2#1306903411yescharacteristic
285C2#1306903911yescharacteristic
286C2#1306914811yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2972C2
socleC22×C11#386
prime radicalC22×D4×C11D4
cosocleC2×C42×C11C23
hypercenter#2972D11
hypocenterC11#9483
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2972

Complements

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

NH ≅ G/Ntype
3. #13067046C2semidirect
4. #13066475C2semidirect
227. C11#9483semidirect

Maximal subgroups

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

subgroupindex
#130739702
#130686082
#130670462
#130664752
C11×#29722
#948311