Finite Group Databasebeta

← #14647137

Subgroups — #14647137

Order 2816.

540 conjugacy classes of subgroups.

The subgroup lattice has 306 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068596C211yesmaximal, characteristic
2C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic
3#13066457C214yesmaximal, complemented
4C11×#2285C211yesmaximal, characteristic
5C2×C11×#117—21no—
6C22×C42×C11C2211yescharacteristic
7C11×#384C411yescharacteristic
8C11×#384C411yescharacteristic
9C11×#382—21no—
10C11×#380—21no—
11C11×#380C412yes—
12C4×C11×C4⋊C4—21no—
13C4×C11×C4⋊C4C2212yes—
14C2×C22⋊(C11⋊C8)—21no—
15C2×C22⋊(C11⋊C8)—21no—
16C2×C4⋊(C11⋊C8)C2212yes—
17C2×C4×C11⋊C8C2212yes—
18#10622162—21no—
19#10622162—21no—
20C23×C4×C11C2×C411yescharacteristic
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C11×#117—44no—
24C2×C11×C4⋊C4—21no—
25C2×C11×C4⋊C4—21no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4C2×C412yes—
29C2×C11×C4⋊C4C2×C412yes—
30C2×C11×C22⋊C4—22no—
31C2×C42×C11—24no—
32C2×C42×C11—22no—
33C2×C42×C11C2×C411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×C42×C11C2311yescharacteristic
37C22×C11⋊C8—22no—
38C22×C11⋊C8—22no—
39C11×#95—22no—
40C11×#95—22no—
41C22⋊(C11⋊C8)—24no—
42C22⋊(C11⋊C8)—42no—
43C4⋊(C11⋊C8)—24no—
44C4×C11⋊C8—24no—
45#8710—111nomaximal, Sylow
46C24×C11C22⋊C411yescharacteristic
47C22×C4×C11—22no—
48C22×C4×C11—22no—
49C22×C4×C11—22no—
50C22×C4×C11—22no—
51C22×C4×C11—22no—
52C22×C4×C11—22no—
53C22×C4×C11—22no—
54C22×C4×C11—22no—
55C22×C4×C11—22no—
56C22×C4×C11—41no—
57C22×C4×C11C22⋊C411yescharacteristic
58C22×C4×C11C22⋊C411yescharacteristic
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11SD1612yes—
61C22×C4×C11Q1612yes—
62C22×C4×C11C22×C411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C11×C4⋊C4—24no—
66C11×C4⋊C4—24no—
67C11×C4⋊C4—42no—
68C11×C4⋊C4—42no—
69C11×C4⋊C4—42no—
70C11×C4⋊C4—42no—
71C11×C22⋊C4—44no—
72C42×C11—22no—
73C42×C11—22no—
74C42×C11—22no—
75C42×C11—44no—
76C42×C11#4114yes—
77C2×C11⋊C8—24no—
78C2×C11⋊C8—42no—
79C2×C11⋊C8—42no—
80C2×C11⋊C8—42no—
81C2×C11⋊C8—42no—
82C2×C11⋊C8—42no—
83#2285D1111yescharacteristic
84#1797—111no—
85C4×C22⋊C8—111no—
86#1279—114no—
87C23×C11—21no—
88C23×C11—21no—
89C23×C11—21no—
90C23×C11—21no—
91C23×C11—21no—
92C23×C11—21no—
93C23×C11#10312yes—
94C23×C11C2×C22⋊C411yescharacteristic
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—24no—
102C2×C4×C11—24no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—44no—
107C2×C4×C11—44no—
108C2×C4×C11—42no—
109C2×C4×C11—42no—
110C2×C4×C11—42no—
111C2×C4×C11—42no—
112C2×C4×C11—42no—
113C2×C4×C11—42no—
114C2×C4×C11#10312yes—
115C2×C4×C11#10412yes—
116C2×C4×C11#11712yes—
117C2×C4×C11#12312yes—
118C2×C4×C11#12312yes—
119C2×C4×C11#13112yes—
120C2×C4×C11#13112yes—
121C2×C4×C11C2×SD1611yescharacteristic
122C2×C4×C11C2×Q1611yescharacteristic
123C2×C4×C11AGL(1,ℤ/8)12yes—
124C11⋊C8—44no—
125C11⋊C8—82no—
126C2×#117—21no—
127C22×C42C2×D1111yescharacteristic
128C2×C4⋊C8—112no—
129C2×C22⋊C8—221no—
130C2×C22⋊C8—221no—
131C2×C4×C8—112no—
132#384Dic1111yescharacteristic
133#384Dic1111yescharacteristic
134#382—21no—
135#380—21no—
136#380Dic1112yes—
137C4×C4⋊C4—21no—
138C4×C4⋊C4C2×D1112yes—
139#336—221no—
140#336—221no—
141C22×C11—22no—
142C22×C11—22no—
143C22×C11—22no—
144C22×C11—41no—
145C22×C11—41no—
146C22×C11—41no—
147C22×C11—41no—
148C22×C11#38111yescharacteristic
149C22×C11#40811yescharacteristic
150C22×C11#40811yescharacteristic
151C22×C11C2×#10311yescharacteristic
152C22×C11#41811yescharacteristic
153C22×C11C2×#10411yescharacteristic
154C22×C11#42111yescharacteristic
155C4×C11—22no—
156C4×C11—22no—
157C4×C11—22no—
158C4×C11—41no—
159C4×C11—82no—
160C4×C11—82no—
161C4×C11#43314yes—
162C4×C11#48112yes—
163C4×C11#48412yes—
164C23×C4C2×Dic1111yescharacteristic
165C23×C4C22⋊D1111yescharacteristic
166C23×C4C22⋊D1111yescharacteristic
167C22×C8—222no—
168C22×C8—222no—
169#117—44no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4C2×Dic1112yes—
175C2×C4⋊C4C2×Dic1112yes—
176C2×C22⋊C4—22no—
177C2×C42—24no—
178C2×C42—22no—
179C2×C42C2×Dic1111yescharacteristic
180C2×C42C22⋊D1111yescharacteristic
181C2×C42C22⋊D1111yescharacteristic
182C2×C42C22×D1111yescharacteristic
183C4⋊C8—224no—
184C22⋊C8—224no—
185C22⋊C8—442no—
186C4×C8—224no—
187#95—22no—
188#95—22no—
189C2×C11—42no—
190C2×C11#148111yescharacteristic
191C2×C11#148411yescharacteristic
192C2×C11#149311yescharacteristic
193C2×C11#149611yescharacteristic
194C2×C11#181811yescharacteristic
195C2×C11#182411yescharacteristic
196C2×C11#182611yescharacteristic
197C24C22⋊Dic1111yescharacteristic
198C22×C4—22no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—41no—
208C22×C4#432512yes—
209C22×C4#432612yes—
210C22×C4C22⋊Dic1111yescharacteristic
211C22×C4C22⋊Dic1111yescharacteristic
212C22×C4C22⋊Dic1111yescharacteristic
213C22×C4C22×Dic1111yescharacteristic
214C22×C4C2×C22⋊D1111yescharacteristic
215C22×C4C2×C22⋊D1111yescharacteristic
216C2×C8—224no—
217C2×C8—442no—
218C2×C8—442no—
219C2×C8—442no—
220C2×C8—442no—
221C2×C8—442no—
222C4⋊C4—24no—
223C4⋊C4—24no—
224C4⋊C4—42no—
225C4⋊C4—42no—
226C4⋊C4—42no—
227C4⋊C4—42no—
228C22⋊C4—44no—
229C42—22no—
230C42—22no—
231C42—22no—
232C42—44no—
233C42#433914yes—
234C11#871011yescharacteristic, complemented, Sylow
235C23—21no—
236C23—21no—
237C23—21no—
238C23—21no—
239C23—21no—
240C23—21no—
241C23#6689912yes—
242C23C2×C22⋊Dic1111yescharacteristic
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—24no—
250C2×C4—24no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—44no—
255C2×C4—44no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4#6689912yes—
263C2×C4#6690112yes—
264C2×C4#6697912yes—
265C2×C4#6698212yes—
266C2×C4#6698212yes—
267C2×C4#6698512yes—
268C2×C4C2×#432511yescharacteristic
269C2×C4C2×#432611yescharacteristic
270C2×C4#6700112yes—
271C2×C4#6700112yes—
272C8—444no—
273C8—882no—
274C22—22no—
275C22—22no—
276C22—22no—
277C22—41no—
278C22—41no—
279C22—41no—
280C22—41no—
281C22#1062282411yescharacteristic
282C22#1062282811yescharacteristic
283C22C2×#6689911yescharacteristic
284C22#1062284711yescharacteristic
285C22#1062284711yescharacteristic
286C22C2×#6690111yescharacteristic
287C22#1062284911yescharacteristic
288C4—22no—
289C4—22no—
290C4—22no—
291C4—41no—
292C4—82no—
293C4—82no—
294C4#1062258112yes—
295C4#1062258312yes—
296C4#1062261314yes—
297C2—42no—
298C2#1306701911yescharacteristic
299C2#1306703311yescharacteristic
300C2#1306707111yescharacteristic
301C2#1306708511yescharacteristic
302C2#1306868711yescharacteristic
303C2#1306870611yescharacteristic
304C2#1306871511yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2285C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#2285D11
hypocenterC11#8710
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ #2285

Complements

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

NH ≅ G/Ntype
3. #13066457C2semidirect
234. C11#8710semidirect

Maximal subgroups

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

subgroupindex
#130685962
C4×C22⋊(C11⋊C8)2
#130664572
C11×#22852
#871011