Finite Group Databasebeta

← #14647182

Subgroups — #14647182

Order 2816.

526 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 107 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#13071022C211yesmaximal, characteristic
2#13068379C212yesmaximal
3#13066498C212yesmaximal, complemented
4#13066497C211yesmaximal, characteristic, complemented
5C11×#1295C211yesmaximal, characteristic, complemented
6C2×#66945C411yescharacteristic
7C2×#66945C411yescharacteristic
8C2×C42×D11C2211yescharacteristic
9C2×C11×#97C2212yes—
10C11×#382C2211yescharacteristic
11C2×(C2×D11)⋊C8—22no—
12#10622589C411yescharacteristic
13#10622589C411yescharacteristic
14#10622549C2211yescharacteristic
15C2×#66867C2212yes—
16#10622280—22no—
17#10622262—22no—
18#10622188—22no—
19C22×C4×D11C2×C411yescharacteristic
20C22×C4×D11D412yes—
21C22×C8×C11—22no—
22C2×C11×C4⋊C4C2×C411yescharacteristic
23C2×C11×C4⋊C4C2×C411yescharacteristic
24C2×C42×C11C2311yescharacteristic
25C2×(C2×D11)⋊C4—21no—
26C2×(C2×D11)⋊C4—21no—
27C2×C4⋊Dic11C2×C411yescharacteristic
28C2×C4⋊Dic11C2×C411yescharacteristic
29C2×Dic11⋊C4—22no—
30C2×Dic11⋊C4—22no—
31C2×C4×Dic11—21no—
32C2×C4×Dic11—21no—
33C2×C4×Dic11C2×C411yescharacteristic
34C2×C4×Dic11D412yes—
35C22×C11⋊C8—22no—
36#66945—42no—
37#66945—42no—
38C42×D11—22no—
39C42×D11—21no—
40C42×D11—21no—
41C11×#97—22no—
42C11×#97—22no—
43C11×#95—22no—
44C11⋊#95—22no—
45(C2×D11)⋊C8—28no—
46#66867—22no—
47#66867—22no—
48#8721—111nomaximal, Sylow
49C23×D11C22⋊C411yescharacteristic
50C22×C4×C11—21no—
51C22×C4×C11—21no—
52C22×C4×C11C22×C411yescharacteristic
53C22×C4×C11C2×D412yes—
54C22×Dic11—21no—
55C22×Dic11—21no—
56C22×Dic11C22⋊C411yescharacteristic
57C22×Dic11C22⋊C412yes—
58C2×C4×D11—22no—
59C2×C4×D11—24no—
60C2×C4×D11—22no—
61C2×C4×D11—21no—
62C2×C4×D11—21no—
63C2×C4×D11—22no—
64C2×C4×D11—22no—
65C2×C4×D11—42no—
66C2×C8×C11—24no—
67C2×C8×C11—42no—
68C2×C8×C11—42no—
69C11×C4⋊C4—41no—
70C11×C4⋊C4—41no—
71C42×C11#4112yes—
72C42×C11#4111yescharacteristic
73C42×C11#4111yescharacteristic
74(C2×D11)⋊C4—42no—
75(C2×D11)⋊C4—42no—
76C4⋊Dic11—41no—
77C4⋊Dic11—41no—
78Dic11⋊C4—44no—
79Dic11⋊C4—44no—
80C4×Dic11—21no—
81C4×Dic11—21no—
82C4×Dic11—22no—
83C4×Dic11—22no—
84C4×Dic11—42no—
85C4×Dic11—42no—
86C2×C11⋊C8—24no—
87C2×C11⋊C8—42no—
88C2×C11⋊C8—42no—
89#2285—111no—
90#1749—112no—
91#1295—112no—
92#1295—111no—
93#1295D1111yescharacteristic, complemented
94C23×C11C2×C22⋊C411yescharacteristic
95C22×D11—21no—
96C22×D11—21no—
97C22×D11—22no—
98C22×D11—22no—
99C22×D11#10112yes—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—22no—
103C2×C4×C11—22no—
104C2×C4×C11—41no—
105C2×C4×C11—41no—
106C2×C4×C11—42no—
107C2×C4×C11—42no—
108C2×C4×C11#11711yescharacteristic
109C2×C4×C11#11711yescharacteristic
110C2×C4×C11#12312yes—
111C2×C4×C11#12312yes—
112C2×Dic11—21no—
113C2×Dic11—22no—
114C2×Dic11—21no—
115C2×Dic11—22no—
116C2×Dic11—41no—
117C2×Dic11—41no—
118C2×Dic11—42no—
119C2×Dic11—42no—
120C2×Dic11#10012yes—
121C2×Dic11#10414yes—
122C4×D11—24no—
123C4×D11—24no—
124C4×D11—44no—
125C4×D11—44no—
126C8×C11—44no—
127C11⋊C8—44no—
128C2×#117—111no—
129C2×#117—111no—
130C22×C42—111no—
131C2×C22⋊C8—222no—
132C2×#97—112no—
133C2×#97C2×D1112yes—
134#384—111no—
135#384—111no—
136#382—111no—
137#382C2×D1111yescharacteristic
138#380—222no—
139C4×C4⋊C4—222no—
140#336—222no—
141C22×C11#38111yescharacteristic
142C22×C11C2×#10011yescharacteristic
143C22×C11C2×#10111yescharacteristic
144C22×C11C2×#10412yes—
145C22×C11#42112yes—
146C2×D11—22no—
147C2×D11—24no—
148C2×D11—41no—
149C2×D11—42no—
150C2×D11—41no—
151C4×C11—21no—
152C4×C11—21no—
153C4×C11—22no—
154C4×C11—22no—
155C4×C11—81no—
156C4×C11—81no—
157Dic11—22no—
158Dic11—24no—
159Dic11—81no—
160Dic11—81no—
161C23×C4—111no—
162C23×C4—112no—
163C22×C8—22no—
164C22×C8—222no—
165#117—442no—
166#117—442no—
167C2×C4⋊C4—111no—
168C2×C4⋊C4—111no—
169C2×C4⋊C4—222no—
170C2×C4⋊C4—222no—
171C2×C4⋊C4C4×D1111yescharacteristic
172C2×C4⋊C4C4×D1111yescharacteristic
173C2×C22⋊C4—221no—
174C2×C22⋊C4—221no—
175C2×C42—111no—
176C2×C42—112no—
177C2×C42—222no—
178C2×C42—221no—
179C2×C42—221no—
180C2×C42—221no—
181C2×C42—221no—
182C2×C42C22×D1111yescharacteristic
183C22⋊C8—228no—
184#97—22no—
185#97—22no—
186#97—222no—
187#97—222no—
188#95—22no—
189#95—222no—
190C2×C11#152511yescharacteristic
191C2×C11#153112yes—
192C2×C11#153611yescharacteristic
193C2×C11#182111yescharacteristic
194C2×C11#182612yes—
195D11—42no—
196C24—111no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—111no—
200C22×C4—112no—
201C22×C4—222no—
202C22×C4—224no—
203C22×C4—222no—
204C22×C4—221no—
205C22×C4—221no—
206C22×C4—222no—
207C22×C4—222no—
208C22×C4—221no—
209C22×C4—221no—
210C22×C4—442no—
211C22×C4C2×C4×D1111yescharacteristic
212C22×C4D4×D1112yes—
213C2×C8—24no—
214C2×C8—42no—
215C2×C8—42no—
216C2×C8—224no—
217C2×C8—442no—
218C2×C8—442no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—441no—
222C4⋊C4—441no—
223C4⋊C4—444no—
224C4⋊C4—444no—
225C22⋊C4—442no—
226C22⋊C4—442no—
227C42—221no—
228C42—222no—
229C42—221no—
230C42—222no—
231C42—442no—
232C42—442no—
233C42#433912yes—
234C42#434111yescharacteristic
235C42#434311yescharacteristic
236C11#872111yescharacteristic, complemented, Sylow
237C23—112no—
238C23—221no—
239C23—221no—
240C23—222no—
241C23—222no—
242C23C22⋊C4×D1111yescharacteristic
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—112no—
252C2×C4—114no—
253C2×C4—224no—
254C2×C4—224no—
255C2×C4—221no—
256C2×C4—222no—
257C2×C4—221no—
258C2×C4—222no—
259C2×C4—444no—
260C2×C4—444no—
261C2×C4—441no—
262C2×C4—441no—
263C2×C4—442no—
264C2×C4—442no—
265C2×C4#6692511yescharacteristic
266C2×C4#6693612yes—
267C2×C4#6694511yescharacteristic
268C2×C4#6694712yes—
269C8—44no—
270C8—444no—
271C22—222no—
272C22—224no—
273C22—442no—
274C22—441no—
275C22—441no—
276C22#1062227711yescharacteristic
277C22D11×#10011yescharacteristic
278C22D11×#10111yescharacteristic
279C22D11×#10412yes—
280C22#1062243412yes—
281C4—21no—
282C4—21no—
283C4—22no—
284C4—22no—
285C4—81no—
286C4—81no—
287C4—222no—
288C4—224no—
289C4—881no—
290C4—881no—
291C2—442no—
292C2#1306720611yescharacteristic
293C2#1306722912yes—
294C2#1306724911yescharacteristic
295C2#1306869511yescharacteristic
296C2#1306871412yes—
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1295C2
socleC23×C11C2×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1295D11
hypocenterC11#8721
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
3. #13066498C2semidirect
4. #13066497C2semidirect
5. C11×#1295C2semidirect
93. #1295D11semidirect
236. C11#8721semidirect

Maximal subgroups

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

subgroupindex
#130710222
#130683792
#130664982
#130664972
C11×#12952
#872111