Finite Group Databasebeta

← #14642262

Subgroups — #14642262

Order 2816.

410 conjugacy classes of subgroups.

The subgroup lattice has 310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076998C211yesmaximal, characteristic
2#13068469C211yesmaximal, characteristic
3#13066441C212yesmaximal
4#13066440C212yesmaximal
5C4×C11×C4⋊C8C211yesmaximal, characteristic
6C2×C11×C4⋊C8—21no—
7C2×C4×C8×C11—21no—
8C43×C11C2211yescharacteristic
9#10622550—21no—
10#10622546—21no—
11#10622546—21no—
12#10622546—21no—
13#10622542C411yescharacteristic
14#10622542C411yescharacteristic
15#10622542C2211yescharacteristic
16#10622541C411yescharacteristic
17#10622541C411yescharacteristic
18#10622541C2211yescharacteristic
19C2×C4⋊(C11⋊C8)—21no—
20C2×#66867—21no—
21C11×#336C2212yes—
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—
39C11×C4⋊C8—24no—
40C4×C8×C11—42no—
41C11⋊#95—21no—
42C11⋊#95—21no—
43C11⋊#95—21no—
44C11⋊#95—21no—
45C11⋊#95—21no—
46C11⋊#95—21no—
47C11⋊#95—21no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50C4⋊(C11⋊C8)—24no—
51#66867—42no—
52#7689—111nomaximal, Sylow
53C22×C4×C11C22⋊C411yescharacteristic
54C22×C4×C11C22⋊C411yescharacteristic
55C22×C4×C11C22⋊C411yescharacteristic
56C22×C4×C11C22⋊C411yescharacteristic
57C22×C4×C11C22×C411yescharacteristic
58C22×C4×C11C2×D411yescharacteristic
59C22×C4×C11C2×D411yescharacteristic
60C22×Dic11—21no—
61C22×Dic11—21no—
62C22×Dic11—21no—
63C22×Dic11—21no—
64C2×Dic22—22no—
65C2×Dic22—41no—
66C2×Dic22—41no—
67C2×C8×C11—24no—
68C2×C8×C11—42no—
69C2×C8×C11—42no—
70C42×C11—22no—
71C42×C11—22no—
72C42×C11—22no—
73C42×C11—21no—
74C42×C11—21no—
75C42×C11—41no—
76C42×C11—41no—
77C42×C11SD1612yes—
78C42×C11Q1612yes—
79C4⋊Dic11—22no—
80C4⋊Dic11—41no—
81C4⋊Dic11—41no—
82Dic11⋊C4—42no—
83Dic11⋊C4—42no—
84Dic11⋊C4—41no—
85Dic11⋊C4—41no—
86C2×C11⋊C8—24no—
87C2×C11⋊C8—42no—
88C2×C11⋊C8—42no—
89#2863—111no—
90#1767—111no—
91C4×C4⋊C8D1111yescharacteristic
92#1272—112no—
93#1271—112no—
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—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#10312yes—
110C2×C4×C11#10312yes—
111C2×C4×C11#10412yes—
112C2×C4×C11#10412yes—
113C2×C4×C11#13112yes—
114C2×C4×C11C2×SD1611yescharacteristic
115C2×C4×C11C2×Q1611yescharacteristic
116C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
117C2×C4×C11#13711yescharacteristic
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—
128C2×Dic11—41no—
129C2×Dic11—41no—
130Dic22—82no—
131C8×C11—44no—
132C11⋊C8—44no—
133C2×C4⋊C8—21no—
134C2×C4⋊C8—221no—
135C2×#97—221no—
136C2×C4×C8—21no—
137#391—111no—
138#391—111no—
139#391—111no—
140#389—111no—
141#389—111no—
142#389—111no—
143#387—221no—
144#387—221no—
145#387—221no—
146#383—221no—
147C43C2×D1111yescharacteristic
148#336—112no—
149#336C2×D1112yes—
150C22×C11#40811yescharacteristic
151C22×C11#41011yescharacteristic
152C22×C11#41311yescharacteristic
153C22×C11C2×#10311yescharacteristic
154C22×C11#41711yescharacteristic
155C22×C11C2×#10411yescharacteristic
156C22×C11C2×#10411yescharacteristic
157C4×C11—22no—
158C4×C11—22no—
159C4×C11—22no—
160C4×C11—22no—
161C4×C11—21no—
162C4×C11—21no—
163C4×C11—21no—
164C4×C11—21no—
165C4×C11—22no—
166Dic11—81no—
167Dic11—81no—
168Dic11—81no—
169Dic11—81no—
170C22×Q8—111no—
171C22×C8—22no—
172C22×C8—222no—
173C2×C4⋊C4—111no—
174C2×C4⋊C4—111no—
175C2×C4⋊C4—111no—
176C2×C4⋊C4—221no—
177C2×C4⋊C4—221no—
178C2×C4⋊C4—221no—
179C2×C42C4×D1111yescharacteristic
180C2×C42C4×D1111yescharacteristic
181C2×C42D4411yescharacteristic
182C2×C42D4411yescharacteristic
183C2×C42C22⋊D1111yescharacteristic
184C2×C42C22⋊D1111yescharacteristic
185C2×C42C22×D1111yescharacteristic
186C4⋊C8—24no—
187C4⋊C8—224no—
188#97—442no—
189C4×C8—42no—
190#95—221no—
191#95—221no—
192#95—221no—
193#95—221no—
194#95—221no—
195#95—221no—
196#95—221no—
197#95—221no—
198#95—221no—
199C2×C11#147311yescharacteristic
200C2×C11#148311yescharacteristic
201C2×C11#149311yescharacteristic
202C2×C11#150311yescharacteristic
203C2×C11#150911yescharacteristic
204C2×C11#152411yescharacteristic
205C2×C11#155011yescharacteristic
206C2×Q8—222no—
207C2×Q8—441no—
208C2×Q8—441no—
209C22×C4—221no—
210C22×C4—221no—
211C22×C4—221no—
212C22×C4—221no—
213C22×C4(C2×D11)⋊C411yescharacteristic
214C22×C4(C2×D11)⋊C411yescharacteristic
215C22×C4(C2×D11)⋊C411yescharacteristic
216C22×C4(C2×D11)⋊C411yescharacteristic
217C22×C4C2×C4×D1111yescharacteristic
218C22×C4C2×D4411yescharacteristic
219C22×C4C2×C22⋊D1111yescharacteristic
220C2×C8—24no—
221C2×C8—42no—
222C2×C8—42no—
223C2×C8—224no—
224C2×C8—442no—
225C2×C8—442no—
226C4⋊C4—222no—
227C4⋊C4—441no—
228C4⋊C4—441no—
229C4⋊C4—442no—
230C4⋊C4—442no—
231C4⋊C4—441no—
232C4⋊C4—441no—
233C42—22no—
234C42—22no—
235C42—22no—
236C42—21no—
237C42—21no—
238C42—41no—
239C42—41no—
240C42#431412yes—
241C42Dic4412yes—
242C11#768911yescharacteristic, complemented, Sylow
243C23C2×(C2×D11)⋊C411yescharacteristic
244Q8—882no—
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—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—441no—
260C2×C4—441no—
261C2×C4—441no—
262C2×C4—441no—
263C2×C4—441no—
264C2×C4—441no—
265C2×C4—441no—
266C2×C4—441no—
267C2×C4—441no—
268C2×C4—441no—
269C2×C4—441no—
270C2×C4—441no—
271C2×C4#6686912yes—
272C2×C4#6688012yes—
273C2×C4#6688012yes—
274C2×C4#6688912yes—
275C2×C4#6695412yes—
276C2×C4C2×#431411yescharacteristic
277C2×C4C2×Dic4411yescharacteristic
278C2×C4#6698511yescharacteristic
279C2×C4#6699511yescharacteristic
280C8—44no—
281C8—444no—
282C22C2×#6686911yescharacteristic
283C22#1062257911yescharacteristic
284C22#1062261911yescharacteristic
285C22C2×#6688011yescharacteristic
286C22#1062272311yescharacteristic
287C22#1062274511yescharacteristic
288C22C2×#6688911yescharacteristic
289C4—22no—
290C4—22no—
291C4—22no—
292C4—21no—
293C4—21no—
294C4—21no—
295C4—21no—
296C4—22no—
297C4—22no—
298C4—881no—
299C4—881no—
300C4—881no—
301C4—881no—
302C2#1306698311yescharacteristic
303C2#1306702711yescharacteristic
304C2#1306707211yescharacteristic
305C2#1306711611yescharacteristic
306C2#1306713911yescharacteristic
307C2#1306720511yescharacteristic
308C2#1306730411yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC4×C11×C4⋊C8C2
socle, prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenterC4×C4⋊C8D11
hypocenterC11#7689
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ C4×C4⋊C8

Complements

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

NH ≅ G/Ntype
242. C11#7689semidirect

Maximal subgroups

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

subgroupindex
#130769982
#130684692
#130664412
#130664402
C4×C11×C4⋊C82
#768911