Finite Group Databasebeta

← #14653871

Subgroups — #14653871

Order 2816.

432 conjugacy classes of subgroups.

The subgroup lattice has 302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077003C211yesmaximal, characteristic
2C4×#66867C211yesmaximal, characteristic
3#13066498C212yesmaximal
4#13066498C212yesmaximal
5C11×#1767C211yesmaximal, characteristic
6C2×C11×C4⋊C8—21no—
7C2×C11×#97C2212yes—
8C43×C11C2211yescharacteristic
9#10622549C2211yescharacteristic
10#10622549C2211yescharacteristic
11#10622546—21no—
12#10622546—21no—
13#10622546—21no—
14#10622546—21no—
15#10622541C411yescharacteristic
16#10622541C411yescharacteristic
17#10622541C411yescharacteristic
18#10622541C411yescharacteristic
19C2×#66867—21no—
20C2×#66867C2212yes—
21C2×C4×C11⋊C8—21no—
22C11×#336—21no—
23C22×C8×C11—22no—
24C2×C42×C11C2×C411yescharacteristic
25C2×C42×C11C2×C411yescharacteristic
26C2×C42×C11D411yescharacteristic
27C2×C42×C11D411yescharacteristic
28C2×C42×C11D411yescharacteristic
29C2×C42×C11D411yescharacteristic
30C2×C42×C11C2311yescharacteristic
31C2×C4⋊Dic11C2×C411yescharacteristic
32C2×C4⋊Dic11C2×C411yescharacteristic
33C2×C4⋊Dic11C2×C411yescharacteristic
34C2×C4⋊Dic11C2×C411yescharacteristic
35C2×Dic11⋊C4—21no—
36C2×Dic11⋊C4—21no—
37C2×Dic11⋊C4—21no—
38C2×Dic11⋊C4—21no—
39C22×C11⋊C8—22no—
40C11×C4⋊C8—24no—
41C11×#97—24no—
42C11⋊#95—21no—
43C11⋊#95—21no—
44C11⋊#95—21no—
45C11⋊#95—21no—
46C11⋊#95—21no—
47C11⋊#95—21no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50#66867—24no—
51#66867—22no—
52#66867Q814yes—
53C4×C11⋊C8—24no—
54#9892—111nomaximal, Sylow
55C22×C4×C11C22⋊C411yescharacteristic
56C22×C4×C11C22⋊C411yescharacteristic
57C22×C4×C11C22⋊C411yescharacteristic
58C22×C4×C11C22⋊C411yescharacteristic
59C22×C4×C11C22×C411yescharacteristic
60C22×C4×C11C2×D411yescharacteristic
61C22×C4×C11C2×D411yescharacteristic
62C22×Dic11—21no—
63C22×Dic11—21no—
64C22×Dic11—21no—
65C22×Dic11—21no—
66C2×C8×C11—24no—
67C2×C8×C11—42no—
68C2×C8×C11—42no—
69C42×C11—22no—
70C42×C11—22no—
71C42×C11—22no—
72C42×C11—41no—
73C42×C11—41no—
74C42×C11—41no—
75C42×C11C2×Q812yes—
76C42×C11#4112yes—
77C4⋊Dic11—41no—
78C4⋊Dic11—41no—
79C4⋊Dic11—41no—
80C4⋊Dic11—41no—
81Dic11⋊C4—42no—
82Dic11⋊C4—42no—
83Dic11⋊C4—42no—
84Dic11⋊C4—42no—
85C2×C11⋊C8—24no—
86C2×C11⋊C8—24no—
87C2×C11⋊C8—24no—
88#2864—111no—
89#1767D1111yescharacteristic
90C4×#97—111no—
91#1295—112no—
92#1295—112no—
93C23×C11C2×C22⋊C411yescharacteristic
94C2×C4×C11—21no—
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—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11#10412yes—
110C2×C4×C11#10412yes—
111C2×C4×C11#10412yes—
112C2×C4×C11C4×Q812yes—
113C2×C4×C11C22⋊Q812yes—
114C2×C4×C11#12411yescharacteristic
115C2×C4×C11C4⋊Q811yescharacteristic
116C2×Dic11—41no—
117C2×Dic11—41no—
118C2×Dic11—41no—
119C2×Dic11—41no—
120C2×Dic11—41no—
121C2×Dic11—41no—
122C2×Dic11—41no—
123C2×Dic11—41no—
124C2×Dic11—41no—
125C2×Dic11—41no—
126C2×Dic11—41no—
127C2×Dic11—41no—
128C8×C11—44no—
129C11⋊C8—28no—
130C2×C4⋊C8—21no—
131C2×#97—112no—
132C2×#97—221no—
133C2×#97C2×D1112yes—
134C2×C4×C8—221no—
135#389—111no—
136#389—111no—
137#389—111no—
138#389—111no—
139#387—221no—
140#387—221no—
141#387—221no—
142#387—221no—
143#382—111no—
144#382—111no—
145C43C2×D1111yescharacteristic
146#336—21no—
147C22×C11#39111yescharacteristic
148C22×C11#41311yescharacteristic
149C22×C11#41311yescharacteristic
150C22×C11C2×#10411yescharacteristic
151C22×C11C2×#10411yescharacteristic
152C22×C11C2×#10411yescharacteristic
153C22×C11#42111yescharacteristic
154C4×C11—21no—
155C4×C11—21no—
156C4×C11—22no—
157C4×C11—22no—
158C4×C11—22no—
159C4×C11—22no—
160C4×C11—22no—
161C4×C11—41no—
162Dic11—81no—
163Dic11—81no—
164Dic11—81no—
165Dic11—81no—
166C22×C8—22no—
167C22×C8—222no—
168C2×C4⋊C4—111no—
169C2×C4⋊C4—111no—
170C2×C4⋊C4—111no—
171C2×C4⋊C4—111no—
172C2×C4⋊C4—221no—
173C2×C4⋊C4—221no—
174C2×C4⋊C4—221no—
175C2×C4⋊C4—221no—
176C2×C42C4×D1111yescharacteristic
177C2×C42C4×D1111yescharacteristic
178C2×C42D4411yescharacteristic
179C2×C42D4411yescharacteristic
180C2×C42C22⋊D1111yescharacteristic
181C2×C42C22⋊D1111yescharacteristic
182C2×C42C22×D1111yescharacteristic
183C4⋊C8—24no—
184#97—24no—
185#97—114no—
186#97—224no—
187#97—222no—
188C4×C8—224no—
189#95—221no—
190#95—221no—
191#95—221no—
192#95—221no—
193#95—221no—
194#95—221no—
195#95—221no—
196#95—221no—
197C2×C11#152411yescharacteristic
198C2×C11#152411yescharacteristic
199C2×C11#152911yescharacteristic
200C2×C11#153211yescharacteristic
201C2×C11#198611yescharacteristic
202C2×C11#199411yescharacteristic
203C2×C11#199811yescharacteristic
204C22×C4—221no—
205C22×C4—221no—
206C22×C4—221no—
207C22×C4—221no—
208C22×C4(C2×D11)⋊C411yescharacteristic
209C22×C4(C2×D11)⋊C411yescharacteristic
210C22×C4(C2×D11)⋊C411yescharacteristic
211C22×C4(C2×D11)⋊C411yescharacteristic
212C22×C4C2×C4×D1111yescharacteristic
213C22×C4C2×D4411yescharacteristic
214C22×C4C2×C22⋊D1111yescharacteristic
215C2×C8—24no—
216C2×C8—42no—
217C2×C8—42no—
218C2×C8—224no—
219C2×C8—224no—
220C2×C8—224no—
221C4⋊C4—441no—
222C4⋊C4—441no—
223C4⋊C4—441no—
224C4⋊C4—441no—
225C4⋊C4—442no—
226C4⋊C4—442no—
227C4⋊C4—442no—
228C4⋊C4—442no—
229C42—22no—
230C42—22no—
231C42—22no—
232C42—41no—
233C42—41no—
234C42—41no—
235C42#434112yes—
236C42Q8×D1112yes—
237C11#989211yescharacteristic, complemented, Sylow
238C23C2×(C2×D11)⋊C411yescharacteristic
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—441no—
255C2×C4—441no—
256C2×C4—441no—
257C2×C4—441no—
258C2×C4—441no—
259C2×C4—441no—
260C2×C4—441no—
261C2×C4—441no—
262C2×C4—441no—
263C2×C4—441no—
264C2×C4—441no—
265C2×C4—441no—
266C2×C4#6686912yes—
267C2×C4#6688912yes—
268C2×C4#6688912yes—
269C2×C4#6694012yes—
270C2×C4#6695012yes—
271C2×C4#6698911yescharacteristic
272C2×C4#6699711yescharacteristic
273C8—44no—
274C8—228no—
275C22C2×#6686911yescharacteristic
276C22#1062258711yescharacteristic
277C22#1062261811yescharacteristic
278C22#1062274511yescharacteristic
279C22#1062274511yescharacteristic
280C22C2×#6688911yescharacteristic
281C22C2×#6688911yescharacteristic
282C4—22no—
283C4—22no—
284C4—22no—
285C4—22no—
286C4—22no—
287C4—21no—
288C4—21no—
289C4—41no—
290C4—881no—
291C4—881no—
292C4—881no—
293C4—881no—
294C2#1306720211yescharacteristic
295C2#1306720511yescharacteristic
296C2#1306722411yescharacteristic
297C2#1306723711yescharacteristic
298C2#1306955911yescharacteristic
299C2#1306959211yescharacteristic
300C2#1306960811yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1767C2
socle, prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1767D11
hypocenterC11#9892
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ #1767

Complements

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

NH ≅ G/Ntype
237. C11#9892semidirect

Maximal subgroups

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

subgroupindex
#130770032
C4×#668672
#130664982
C11×#17672
#989211