Finite Group Databasebeta

← #14647264

Subgroups — #14647264

Order 2816.

384 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 91 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#13071114C211yesmaximal, characteristic
2#13066950C211yesmaximal, characteristic
3#13066473C212yesmaximal, complemented
4#13066471C212yesmaximal, complemented
5C11×#1464C211yesmaximal, characteristic
6C2×C11×#117C2211yescharacteristic
7C11×#432C2212yes—
8C4×C22⋊Dic11C411yescharacteristic
9C4×C22⋊Dic11C411yescharacteristic
10#10622594—21no—
11#10622594—21no—
12#10622564—21no—
13#10622564—21no—
14C4×C4⋊Dic11C2211yescharacteristic
15C4×C4⋊Dic11C2211yescharacteristic
16#10622545C411yescharacteristic
17C42×Dic11C411yescharacteristic
18#10622539C2212yes—
19C11×#324—21no—
20C11×#323—21no—
21#10622166—21no—
22#10622163—21no—
23C23×C4×C11C2×C411yescharacteristic
24C11×#117—22no—
25C11×#117—22no—
26C2×C11×C4⋊C4D411yescharacteristic
27C2×C11×C4⋊C4D411yescharacteristic
28C2×C11×C22⋊C4D411yescharacteristic
29C2×C11×C22⋊C4D411yescharacteristic
30C2×C42×C11C2×C411yescharacteristic
31C2×C42×C11C2311yescharacteristic
32C2×C22⋊Dic11—21no—
33C2×C22⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C2×C4×Dic11—21no—
37C2×C4×Dic11—21no—
38C2×C4×Dic11C2×C411yescharacteristic
39C2×C4×Dic11C2×C411yescharacteristic
40C2×C4×Dic11C2×C411yescharacteristic
41C2×C4×Dic11C2×C411yescharacteristic
42C11×C4⋊C8—22no—
43C11×C22⋊C8—22no—
44C11×#97—22no—
45C11⋊#95—21no—
46C11⋊#95—21no—
47C11⋊#95—21no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C22⋊(C11⋊C8)—22no—
52C4⋊(C11⋊C8)—22no—
53#66867—22no—
54#8744—111nomaximal, Sylow
55C24×C11C22⋊C411yescharacteristic
56C22×C4×C11—21no—
57C22×C4×C11—21no—
58C22×C4×C11—41no—
59C22×C4×C11—41no—
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11C22×C411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×Dic11—21no—
67C22×Dic11—21no—
68C22×Dic11—21no—
69C22×Dic11—21no—
70C2×C8×C11—42no—
71C11×C4⋊C4—22no—
72C11×C4⋊C4—22no—
73C11×C22⋊C4—22no—
74C11×C22⋊C4—22no—
75C42×C11—21no—
76C42×C11—21no—
77C42×C11#4112yes—
78C42×C11#4112yes—
79C22⋊Dic11—42no—
80C22⋊Dic11—42no—
81C4⋊Dic11—42no—
82C4⋊Dic11—42no—
83C4×Dic11—41no—
84C4×Dic11—41no—
85C4×Dic11—41no—
86C4×Dic11—41no—
87C4×Dic11—42no—
88C4×Dic11—42no—
89C2×C11⋊C8—42no—
90#2298—111no—
91#1464—111no—
92#1464D1111yescharacteristic
93#1285—112no—
94#1285—112no—
95C23×C11—21no—
96C23×C11—21no—
97C23×C11—21no—
98C23×C11—41no—
99C23×C11—41no—
100C23×C11C2×C22⋊C411yescharacteristic
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—41no—
109C2×C4×C11—41no—
110C2×C4×C11—42no—
111C2×C4×C11—42no—
112C2×C4×C11—41no—
113C2×C4×C11—41no—
114C2×C4×C11#11711yescharacteristic
115C2×C4×C11#11711yescharacteristic
116C2×C4×C11#12312yes—
117C2×C4×C11#12312yes—
118C2×Dic11—22no—
119C2×Dic11—22no—
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—
130C8×C11—82no—
131C11⋊C8—82no—
132C2×#117C2×D1111yescharacteristic
133#432—112no—
134#432C2×D1112yes—
135#388—221no—
136#388—221no—
137#387—221no—
138#387—221no—
139C4×C4⋊C4—111no—
140C4×C4⋊C4—111no—
141C4×C22⋊C4—111no—
142C4×C22⋊C4—111no—
143#376—111no—
144C43—111no—
145#324—21no—
146#324—221no—
147#323—21no—
148#323—221no—
149C22×C11—21no—
150C22×C11—21no—
151C22×C11—41no—
152C22×C11—41no—
153C22×C11—41no—
154C22×C11—81no—
155C22×C11—81no—
156C22×C11#38111yescharacteristic
157C22×C11#41311yescharacteristic
158C22×C11#41311yescharacteristic
159C4×C11—21no—
160C4×C11—21no—
161C4×C11—22no—
162C4×C11—22no—
163C4×C11—41no—
164C4×C11—41no—
165C4×C11—41no—
166Dic11—42no—
167Dic11—42no—
168Dic11—81no—
169Dic11—81no—
170C23×C4C4×D1111yescharacteristic
171#117—22no—
172#117—22no—
173C2×C4⋊C4—221no—
174C2×C4⋊C4—221no—
175C2×C4⋊C4D4411yescharacteristic
176C2×C4⋊C4C22⋊D1111yescharacteristic
177C2×C22⋊C4—221no—
178C2×C22⋊C4—221no—
179C2×C22⋊C4D4411yescharacteristic
180C2×C22⋊C4C22⋊D1111yescharacteristic
181C2×C42—111no—
182C2×C42—111no—
183C2×C42—111no—
184C2×C42—111no—
185C2×C42—221no—
186C2×C42—221no—
187C2×C42C4×D1111yescharacteristic
188C2×C42C22×D1111yescharacteristic
189C4⋊C8—22no—
190C4⋊C8—222no—
191C22⋊C8—22no—
192C22⋊C8—222no—
193#97—22no—
194#97—222no—
195#95—221no—
196#95—221no—
197#95—221no—
198#95—221no—
199#95—221no—
200#95—221no—
201C2×C11—21no—
202C2×C11—21no—
203C2×C11—81no—
204C2×C11#182211yescharacteristic
205C2×C11#182711yescharacteristic
206C2×C11#182711yescharacteristic
207C24(C2×D11)⋊C411yescharacteristic
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4—221no—
213C22×C4—221no—
214C22×C4—221no—
215C22×C4—221no—
216C22×C4(C2×D11)⋊C411yescharacteristic
217C22×C4(C2×D11)⋊C411yescharacteristic
218C22×C4(C2×D11)⋊C411yescharacteristic
219C22×C4C2×C4×D1111yescharacteristic
220C22×C4C2×D4411yescharacteristic
221C22×C4C2×C22⋊D1111yescharacteristic
222C2×C8—42no—
223C2×C8—442no—
224C4⋊C4—22no—
225C4⋊C4—22no—
226C4⋊C4—442no—
227C4⋊C4—442no—
228C22⋊C4—22no—
229C22⋊C4—22no—
230C22⋊C4—442no—
231C22⋊C4—442no—
232C42—21no—
233C42—21no—
234C42—441no—
235C42—441no—
236C42—441no—
237C42—441no—
238C42—442no—
239C42—442no—
240C42#434112yes—
241C42#434112yes—
242C11#874411yescharacteristic, complemented, Sylow
243C23—21no—
244C23—21no—
245C23—21no—
246C23—41no—
247C23—41no—
248C23C2×(C2×D11)⋊C411yescharacteristic
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—222no—
263C2×C4—222no—
264C2×C4—441no—
265C2×C4—441no—
266C2×C4—441no—
267C2×C4—441no—
268C2×C4—441no—
269C2×C4—441no—
270C2×C4—441no—
271C2×C4—441no—
272C2×C4—441no—
273C2×C4—441no—
274C2×C4#6693011yescharacteristic
275C2×C4#6693011yescharacteristic
276C2×C4#6693912yes—
277C2×C4#6698812yes—
278C8—82no—
279C8—882no—
280C22—21no—
281C22—21no—
282C22—41no—
283C22—41no—
284C22—41no—
285C22—81no—
286C22—81no—
287C22#1062255611yescharacteristic
288C22#1062274511yescharacteristic
289C22#1062274511yescharacteristic
290C4—21no—
291C4—21no—
292C4—22no—
293C4—22no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—442no—
298C4—442no—
299C4—881no—
300C4—881no—
301C2—21no—
302C2—21no—
303C2—81no—
304C2#1306869711yescharacteristic
305C2#1306871711yescharacteristic
306C2#1306872111yescharacteristic
subgroupG/H
centerC22#10622556
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1464C2
socleC22×C11#381
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1464D11
hypocenterC11#8744
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1464

Complements

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

NH ≅ G/Ntype
3. #13066473C2semidirect
4. #13066471C2semidirect
242. C11#8744semidirect

Maximal subgroups

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

subgroupindex
#130711142
#130669502
#130664732
#130664712
C11×#14642
#874411