Finite Group Databasebeta

← #14642170

Subgroups — #14642170

Order 2816.

384 conjugacy classes of subgroups.

The subgroup lattice has 298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076998C211yesmaximal, characteristic
2#13068733C211yesmaximal, characteristic
3#13066441C212yesmaximal
4#13066440C212yesmaximal
5C11×#1744C211yesmaximal, characteristic
6C2×C4×C8×C11—21no—
7C43×C11C2211yescharacteristic
8#10622550—21no—
9#10622546—21no—
10#10622546—21no—
11#10622546—21no—
12#10622542C411yescharacteristic
13#10622542C411yescharacteristic
14#10622542C2211yescharacteristic
15#10622541C411yescharacteristic
16#10622541C411yescharacteristic
17#10622541C2211yescharacteristic
18C2×C4⋊(C11⋊C8)—21no—
19C11×#336—21no—
20C11×#336C2212yes—
21#10622162—21no—
22#10622162C2212yes—
23C22×Dic22C2×C411yescharacteristic
24C22×C8×C11—22no—
25C2×C42×C11C2×C411yescharacteristic
26C2×C42×C11C2×C411yescharacteristic
27C2×C42×C11D411yescharacteristic
28C2×C42×C11D411yescharacteristic
29C2×C42×C11D411yescharacteristic
30C2×C42×C11D411yescharacteristic
31C2×C42×C11C2311yescharacteristic
32C2×C4⋊Dic11C2×C411yescharacteristic
33C2×C4⋊Dic11C2×C411yescharacteristic
34C2×C4⋊Dic11C2×C411yescharacteristic
35C2×Dic11⋊C4—21no—
36C2×Dic11⋊C4—21no—
37C2×Dic11⋊C4—21no—
38C22×C11⋊C8—22no—
39C4×C8×C11—24no—
40C11⋊#95—21no—
41C11⋊#95—21no—
42C11⋊#95—21no—
43C11⋊#95—21no—
44C11⋊#95—21no—
45C11⋊#95—21no—
46C11⋊#95—21no—
47C11⋊#95—21no—
48C11⋊#95—21no—
49C4⋊(C11⋊C8)—42no—
50#7669—111nomaximal, Sylow
51C22×C4×C11C22⋊C411yescharacteristic
52C22×C4×C11C22⋊C411yescharacteristic
53C22×C4×C11C22⋊C411yescharacteristic
54C22×C4×C11C22⋊C411yescharacteristic
55C22×C4×C11C22×C411yescharacteristic
56C22×C4×C11C2×D411yescharacteristic
57C22×C4×C11C2×D411yescharacteristic
58C22×Dic11—21no—
59C22×Dic11—21no—
60C22×Dic11—21no—
61C22×Dic11—21no—
62C2×Dic22—22no—
63C2×Dic22—41no—
64C2×Dic22—41no—
65C2×C8×C11—24no—
66C2×C8×C11—42no—
67C2×C8×C11—42no—
68C42×C11—22no—
69C42×C11—22no—
70C42×C11—22no—
71C42×C11—41no—
72C42×C11—41no—
73C42×C11—41no—
74C42×C11SD1612yes—
75C42×C11Q1612yes—
76C4⋊Dic11—22no—
77C4⋊Dic11—41no—
78C4⋊Dic11—41no—
79Dic11⋊C4—42no—
80Dic11⋊C4—42no—
81Dic11⋊C4—42no—
82C2×C11⋊C8—42no—
83C2×C11⋊C8—42no—
84C2×C11⋊C8—42no—
85#2863—111no—
86#1831—111no—
87#1744D1111yescharacteristic
88#1272—112no—
89#1271—112no—
90C23×C11C2×C22⋊C411yescharacteristic
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—21no—
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#10312yes—
107C2×C4×C11#10312yes—
108C2×C4×C11#10412yes—
109C2×C4×C11#13112yes—
110C2×C4×C11C2×SD1611yescharacteristic
111C2×C4×C11C2×Q1611yescharacteristic
112C2×C4×C11#13512yes—
113C2×Dic11—41no—
114C2×Dic11—41no—
115C2×Dic11—41no—
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—
125Dic22—82no—
126C8×C11—44no—
127C11⋊C8—82no—
128C2×C4⋊C8—221no—
129C2×C4×C8—21no—
130#391—111no—
131#391—111no—
132#391—111no—
133#389—111no—
134#389—111no—
135#389—111no—
136#387—221no—
137#387—221no—
138#387—221no—
139#383—221no—
140C43C2×D1111yescharacteristic
141#336—21no—
142#336—112no—
143#336—221no—
144#336C2×D1112yes—
145C22×C11#40811yescharacteristic
146C22×C11#41011yescharacteristic
147C22×C11#41311yescharacteristic
148C22×C11C2×#10311yescharacteristic
149C22×C11#41611yescharacteristic
150C22×C11C2×#10411yescharacteristic
151C22×C11#42111yescharacteristic
152C4×C11—22no—
153C4×C11—22no—
154C4×C11—22no—
155C4×C11—22no—
156C4×C11—21no—
157C4×C11—21no—
158C4×C11—22no—
159C4×C11—41no—
160Dic11—81no—
161Dic11—81no—
162Dic11—81no—
163Dic11—81no—
164C22×Q8—111no—
165C22×C8—22no—
166C22×C8—222no—
167C2×C4⋊C4—111no—
168C2×C4⋊C4—111no—
169C2×C4⋊C4—111no—
170C2×C4⋊C4—221no—
171C2×C4⋊C4—221no—
172C2×C4⋊C4—221no—
173C2×C42C4×D1111yescharacteristic
174C2×C42C4×D1111yescharacteristic
175C2×C42D4411yescharacteristic
176C2×C42D4411yescharacteristic
177C2×C42C22⋊D1111yescharacteristic
178C2×C42C22⋊D1111yescharacteristic
179C2×C42C22×D1111yescharacteristic
180C4⋊C8—442no—
181C4×C8—24no—
182#95—221no—
183#95—221no—
184#95—221no—
185#95—221no—
186#95—221no—
187#95—221no—
188#95—221no—
189#95—221no—
190#95—221no—
191C2×C11#147311yescharacteristic
192C2×C11#148211yescharacteristic
193C2×C11#149311yescharacteristic
194C2×C11#150011yescharacteristic
195C2×C11#151811yescharacteristic
196C2×C11#153211yescharacteristic
197C2×C11#154211yescharacteristic
198C2×Q8—222no—
199C2×Q8—441no—
200C2×Q8—441no—
201C22×C4—221no—
202C22×C4—221no—
203C22×C4—221no—
204C22×C4—221no—
205C22×C4(C2×D11)⋊C411yescharacteristic
206C22×C4(C2×D11)⋊C411yescharacteristic
207C22×C4(C2×D11)⋊C411yescharacteristic
208C22×C4(C2×D11)⋊C411yescharacteristic
209C22×C4C2×C4×D1111yescharacteristic
210C22×C4C2×D4411yescharacteristic
211C22×C4C2×C22⋊D1111yescharacteristic
212C2×C8—24no—
213C2×C8—42no—
214C2×C8—42no—
215C2×C8—442no—
216C2×C8—442no—
217C2×C8—442no—
218C4⋊C4—222no—
219C4⋊C4—441no—
220C4⋊C4—441no—
221C4⋊C4—442no—
222C4⋊C4—442no—
223C4⋊C4—442no—
224C42—22no—
225C42—22no—
226C42—22no—
227C42—41no—
228C42—41no—
229C42—41no—
230C42#431412yes—
231C42Dic4412yes—
232C11#766911yescharacteristic, complemented, Sylow
233C23C2×(C2×D11)⋊C411yescharacteristic
234Q8—882no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
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—441no—
251C2×C4—441no—
252C2×C4—441no—
253C2×C4—441no—
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#6686912yes—
263C2×C4#6688012yes—
264C2×C4#6688012yes—
265C2×C4#6695412yes—
266C2×C4C2×#431411yescharacteristic
267C2×C4C2×Dic4411yescharacteristic
268C2×C4#6700312yes—
269C8—44no—
270C8—882no—
271C22C2×#6686911yescharacteristic
272C22#1062261511yescharacteristic
273C22#1062261911yescharacteristic
274C22C2×#6688011yescharacteristic
275C22#1062272311yescharacteristic
276C22#1062274511yescharacteristic
277C22#1062275211yescharacteristic
278C4—22no—
279C4—22no—
280C4—22no—
281C4—21no—
282C4—21no—
283C4—22no—
284C4—22no—
285C4—41no—
286C4—881no—
287C4—881no—
288C4—881no—
289C4—881no—
290C2#1306698311yescharacteristic
291C2#1306702211yescharacteristic
292C2#1306707211yescharacteristic
293C2#1306710011yescharacteristic
294C2#1306718111yescharacteristic
295C2#1306723411yescharacteristic
296C2#1306727111yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1744C2
socle, prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1744D11
hypocenterC11#7669
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ #1744

Complements

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

NH ≅ G/Ntype
232. C11#7669semidirect

Maximal subgroups

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

subgroupindex
#130769982
#130687332
#130664412
#130664402
C11×#17442
#766911