Finite Group Databasebeta

← #14662928

Subgroups — #14662928

Order 2816.

462 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 93 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#13066929C212yesmaximal
3#13066561C212yesmaximal, complemented
4#13066560C211yesmaximal, characteristic, complemented
5C11×#1324C211yesmaximal, characteristic, complemented
6C2×#66945C411yescharacteristic
7C2×#66945C2211yescharacteristic
8C2×C42×D11C411yescharacteristic
9C11×#382C2211yescharacteristic
10#10622589C411yescharacteristic
11#10622589C2211yescharacteristic
12#10622549C411yescharacteristic
13#10622331—22no—
14#10622280—22no—
15#10622262—22no—
16C11×#324C2212yes—
17#10622166C2212yes—
18#10622106—22no—
19C22×C4×D11—21no—
20C22×C4×D11C2×C411yescharacteristic
21C2×C11×C4⋊C4C2×C411yescharacteristic
22C2×C11×C4⋊C4C2311yescharacteristic
23C2×C42×C11C2×C411yescharacteristic
24C2×(C2×D11)⋊C4—21no—
25C2×(C2×D11)⋊C4D412yes—
26C2×C4⋊Dic11C2×C411yescharacteristic
27C2×C4⋊Dic11C2×C411yescharacteristic
28C2×Dic11⋊C4—22no—
29C2×Dic11⋊C4—22no—
30C2×C4×Dic11—21no—
31C2×C4×Dic11—21no—
32C2×C4×Dic11C2×C411yescharacteristic
33C2×C4×Dic11D412yes—
34#66945—41no—
35#66945—41no—
36#66945—41no—
37#66945—41no—
38C42×D11—22no—
39C42×D11C814yescomplemented
40C11×C22⋊C8—22no—
41C11×#95—22no—
42C11⋊#95—22no—
43C22⋊(C11⋊C8)—22no—
44Dic11⋊C8—42no—
45C8×Dic11—42no—
46#11447—111nomaximal, Sylow
47C23×D11C22⋊C411yescharacteristic
48C22×C4×C11—21no—
49C22×C4×C11—21no—
50C22×C4×C11C22×C411yescharacteristic
51C22×C4×C11C2×D412yes—
52C22×Dic11—21no—
53C22×Dic11—21no—
54C22×Dic11C22⋊C412yes—
55C22×Dic11C22⋊C411yescharacteristic
56C2×C4×D11—21no—
57C2×C4×D11—21no—
58C2×C4×D11—22no—
59C2×C4×D11—24no—
60C2×C4×D11—42no—
61C2×C4×D11—42no—
62C2×C4×D11C2×C812yes—
63C2×C4×D11M1612yes—
64C2×C8×C11—42no—
65C11×C4⋊C4—41no—
66C11×C4⋊C4—41no—
67C42×C11—21no—
68C42×C11C2×C812yes—
69(C2×D11)⋊C4—42no—
70(C2×D11)⋊C4—42no—
71C4⋊Dic11—41no—
72C4⋊Dic11—41no—
73Dic11⋊C4—44no—
74Dic11⋊C4—44no—
75C4×Dic11—24no—
76C4×Dic11—22no—
77C4×Dic11—22no—
78C4×Dic11—21no—
79C4×Dic11—41no—
80C4×Dic11—41no—
81C4×Dic11C2×C812yes—
82C2×C11⋊C8—42no—
83#2285—111no—
84#1458—112no—
85#1325—112no—
86#1324—111no—
87#1324D1111yescharacteristic, complemented
88C23×C11C2×C22⋊C411yescharacteristic
89C22×D11—21no—
90C22×D11—21no—
91C22×D11—41no—
92C22×D11—41no—
93C22×D11C22⋊C812yes—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11—22no—
97C2×C4×C11—22no—
98C2×C4×C11—41no—
99C2×C4×C11—41no—
100C2×C4×C11—42no—
101C2×C4×C11—42no—
102C2×C4×C11—41no—
103C2×C4×C11C22×C811yescharacteristic
104C2×C4×C11C2×M1611yescharacteristic
105C2×Dic11—22no—
106C2×Dic11—22no—
107C2×Dic11—22no—
108C2×Dic11—22no—
109C2×Dic11—42no—
110C2×Dic11—42no—
111C2×Dic11—41no—
112C2×Dic11C22⋊C812yes—
113C2×Dic11#9911yescharacteristic
114C2×Dic11#9911yescharacteristic
115C2×Dic11#10112yes—
116C4×D11—22no—
117C4×D11—22no—
118C4×D11—22no—
119C4×D11—22no—
120C4×D11—48no—
121C8×C11—82no—
122C11⋊C8—82no—
123C2×#117—111no—
124C2×#117—111no—
125C22×C42—111no—
126#431—222no—
127#384—111no—
128#384—111no—
129#382—111no—
130#382C2×D1111yescharacteristic
131#380—222no—
132C4×C4⋊C4—222no—
133#324—112no—
134#324C2×D1112yes—
135#323—222no—
136C22×C11—21no—
137C22×C11—21no—
138C22×C11C2×C22⋊C811yescharacteristic
139C22×C11C2×#9911yescharacteristic
140C22×C11C2×#10111yescharacteristic
141C2×D11—22no—
142C2×D11—42no—
143C2×D11—41no—
144C2×D11—41no—
145C2×D11—42no—
146C4×C11—21no—
147C4×C11—21no—
148C4×C11—42no—
149C4×C11—42no—
150C4×C11—81no—
151Dic11—24no—
152Dic11—42no—
153Dic11—81no—
154Dic11#32412yes—
155Dic11#32412yes—
156C23×C4—111no—
157C23×C4—221no—
158#117—441no—
159#117—441no—
160#117—441no—
161#117—441no—
162C2×C4⋊C4—111no—
163C2×C4⋊C4—111no—
164C2×C4⋊C4—222no—
165C2×C4⋊C4—222no—
166C2×C4⋊C4C4×D1111yescharacteristic
167C2×C4⋊C4C22×D1111yescharacteristic
168C2×C22⋊C4—112no—
169C2×C22⋊C4—221no—
170C2×C42—111no—
171C2×C42—114no—
172C2×C42—112no—
173C2×C42—222no—
174C2×C42—221no—
175C2×C42—221no—
176C2×C42C4×D1111yescharacteristic
177C4⋊C8—442no—
178C22⋊C8—22no—
179C22⋊C8—222no—
180C4×C8—442no—
181#95—22no—
182#95—222no—
183C2×C11—21no—
184C2×C11—21no—
185C2×C11C2×#32411yescharacteristic
186C2×C11#212611yescharacteristic
187C2×C11#213211yescharacteristic
188D11—42no—
189C24—111no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—111no—
193C22×C4—112no—
194C22×C4—112no—
195C22×C4—112no—
196C22×C4—221no—
197C22×C4—221no—
198C22×C4—222no—
199C22×C4—224no—
200C22×C4—221no—
201C22×C4—221no—
202C22×C4—442no—
203C22×C4—442no—
204C22×C4C2×C4×D1111yescharacteristic
205C22×C4D4×D1112yes—
206C2×C8—42no—
207C2×C8—442no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—441no—
211C4⋊C4—441no—
212C4⋊C4—444no—
213C4⋊C4—444no—
214C22⋊C4—442no—
215C22⋊C4—442no—
216C42—21no—
217C42—112no—
218C42—222no—
219C42—222no—
220C42—224no—
221C42—221no—
222C42—441no—
223C42—441no—
224C42C8×D1112yes—
225C11#1144711yescharacteristic, complemented, Sylow
226C23—112no—
227C23—221no—
228C23—221no—
229C23—441no—
230C23—441no—
231C23C22⋊C4×D1111yescharacteristic
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—41no—
241C2×C4—112no—
242C2×C4—111no—
243C2×C4—111no—
244C2×C4—112no—
245C2×C4—222no—
246C2×C4—222no—
247C2×C4—222no—
248C2×C4—222no—
249C2×C4—222no—
250C2×C4—222no—
251C2×C4—222no—
252C2×C4—222no—
253C2×C4—448no—
254C2×C4—442no—
255C2×C4—442no—
256C2×C4—441no—
257C2×C4C2×C8×D1111yescharacteristic
258C2×C4M16×D1111yescharacteristic
259C8—82no—
260C8—882no—
261C22—21no—
262C22—21no—
263C22—222no—
264C22—442no—
265C22—442no—
266C22—441no—
267C22—441no—
268C22D11×C22⋊C811yescharacteristic
269C22D11×#9911yescharacteristic
270C22D11×#10111yescharacteristic
271C4—21no—
272C4—21no—
273C4—42no—
274C4—42no—
275C4—81no—
276C4—112no—
277C4—112no—
278C4—224no—
279C4—442no—
280C4—881no—
281C2—21no—
282C2—21no—
283C2—442no—
284C2D11×#32411yescharacteristic
285C2#1307028011yescharacteristic
286C2#1307029811yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC2×C4×C11C22×C8
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1324C2
socleC22×C11C2×#99
prime radicalC23×D11C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1324D11
hypocenterC11#11447
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1324

Complements

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

NH ≅ G/Ntype
3. #13066561C2semidirect
4. #13066560C2semidirect
5. C11×#1324C2semidirect
39. C42×D11C8semidirect
87. #1324D11semidirect
225. C11#11447semidirect

Maximal subgroups

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

subgroupindex
#130710222
#130669292
#130665612
#130665602
C11×#13242
#1144711