Finite Group Databasebeta

← #14651243

Subgroups — #14651243

Order 2816.

552 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 103 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#13074096C211yesmaximal, characteristic
2#13067131C212yesmaximal
3#13066946C211yesmaximal, characteristic, complemented
4#13066502C212yesmaximal, complemented
5C11×#2313C211yesmaximal, characteristic, complemented
6C22×C11×C4⋊C4C2211yescharacteristic
7C2×#66983C2211yescharacteristic
8C11×#387—24no—
9C11×#381—21no—
10C11×#380—21no—
11C4×C11×C22⋊C4C2212yes—
12#10622826—21no—
13#10622826—21no—
14C4×C22⋊Dic11C2211yescharacteristic
15#10622820C2212yes—
16#10622604C412yescomplemented
17#10622603—22no—
18#10622599C412yescomplemented
19#10622166—22no—
20#10622089—24no—
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11C2311yescharacteristic
24C22×C22⋊D11—21no—
25C22×D44C2×C411yescharacteristic
26C2×C11×C4⋊C4—22no—
27C2×C11×C4⋊C4—22no—
28C2×C11×C4⋊C4—22no—
29C2×C11×C4⋊C4C2×C412yes—
30C2×C11×C4⋊C4D412yes—
31C2×C11×C22⋊C4—22no—
32C2×C42×C11—22no—
33C2×C22⋊Dic11—21no—
34#66983—22no—
35#66983—22no—
36C2×(C2×D11)⋊C4—22no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—22no—
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×C4×Dic11—21no—
41C2×#4318—22no—
42C11×#95—22no—
43C11×#95—24no—
44C11×#95D414yes—
45C11⋊#95—22no—
46C11⋊#95—22no—
47C11⋊#95C2×C412yes—
48C22⋊(C11⋊C8)—22no—
49C22⋊(C11⋊C8)—22no—
50#9414—111nomaximal, Sylow
51C24×C11C2×D411yescharacteristic
52C23×D11—21no—
53C22×C4×C11—21no—
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—24no—
58C22×C4×C11—42no—
59C22×C4×C11—81no—
60C22×C4×C11—81no—
61C22×C4×C11C22⋊C412yes—
62C22×C4×C11C22⋊C412yes—
63C22×C4×C11C22×C411yescharacteristic
64C22×C4×C11C2×D412yes—
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11#4112yes—
67C2×C22⋊D11—44no—
68C2×C22⋊D11—41no—
69C2×C22⋊D11—41no—
70C22×Dic11—21no—
71C22×Dic11—22no—
72C2×D44—22no—
73C2×D44—81no—
74C11×C4⋊C4—24no—
75C11×C4⋊C4—24no—
76C11×C4⋊C4—82no—
77C11×C22⋊C4—44no—
78C42×C11—82no—
79C22⋊Dic11—42no—
80(C2×D11)⋊C4—44no—
81(C2×D11)⋊C4—42no—
82(C2×D11)⋊C4—82no—
83C4⋊Dic11—22no—
84C4×Dic11—81no—
85#4318—82no—
86C2×C11⋊C8—42no—
87#2591—111no—
88#2313D1111yescharacteristic, complemented
89#1507—112no—
90#1463—111no—
91#1297—112no—
92C23×C11—22no—
93C23×C11—22no—
94C23×C11—41no—
95C23×C11C2×C22⋊C411yescharacteristic
96C23×C11#12011yescharacteristic
97C23×C11#12311yescharacteristic
98C22×D11—42no—
99C22×D11—42no—
100C22×D11—41no—
101C22×D11—42no—
102C2×C4×C11—22no—
103C2×C4×C11—22no—
104C2×C4×C11—22no—
105C2×C4×C11—22no—
106C2×C4×C11—42no—
107C2×C4×C11—41no—
108C2×C4×C11—42no—
109C2×C4×C11—41no—
110C2×C4×C11—42no—
111C2×C4×C11—42no—
112C2×C4×C11—42no—
113C2×C4×C11—42no—
114C2×C4×C11—44no—
115C2×C4×C11—44no—
116C2×C4×C11—44no—
117C2×C4×C11—81no—
118C2×C4×C11C4×D412yes—
119C2×C4×C11#12112yes—
120C22⋊D11—82no—
121C22⋊D11—82no—
122C2×Dic11—42no—
123C2×Dic11—42no—
124C2×Dic11—42no—
125C2×Dic11—41no—
126C2×Dic11—42no—
127D44—82no—
128C11⋊C8—82no—
129C2×#121—111no—
130C22×C4⋊C4C2×D1111yescharacteristic
131#407—112no—
132#400—112no—
133#394—112no—
134#388—222no—
135#387—24no—
136#386—221no—
137#386—221no—
138#381—21no—
139#380—21no—
140C4×C22⋊C4—111no—
141C4×C22⋊C4C2×D1112yes—
142#327—224no—
143#324—222no—
144C22×C11—21no—
145C22×C11—21no—
146C22×C11—21no—
147C22×C11—21no—
148C22×C11—21no—
149C22×C11—21no—
150C22×C11—21no—
151C22×C11—44no—
152C22×C11#38611yescharacteristic
153C22×C11#42112yes—
154C22×C11#45412yes—
155C2×D11—84no—
156C2×D11—81no—
157C2×D11—81no—
158C2×D11—81no—
159C4×C11—22no—
160C4×C11—22no—
161C4×C11—42no—
162C4×C11—42no—
163C4×C11—84no—
164Dic11—82no—
165Dic11—81no—
166C22×D4—111no—
167C22×D4—221no—
168C23×C4C22⋊D1111yescharacteristic
169C23×C4C22⋊D1111yescharacteristic
170C23×C4C22×D1111yescharacteristic
171C2×M16—222no—
172#121—222no—
173#121—222no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4—111no—
178C2×C4⋊C4C4×D1112yes—
179C2×C4⋊C4D4412yes—
180C2×C22⋊C4—22no—
181C2×C22⋊C4—221no—
182C2×C22⋊C4—222no—
183C2×C22⋊C4—221no—
184C2×C22⋊C4—222no—
185C2×C42—22no—
186C2×C42—221no—
187C22⋊C8—222no—
188C22⋊C8—222no—
189#95—22no—
190#95—24no—
191#95—112no—
192#95—222no—
193#95—222no—
194#95C22⋊D1114yes—
195C2×C11—22no—
196C2×C11—22no—
197C2×C11—41no—
198C2×C11#188811yescharacteristic
199C2×C11#189711yescharacteristic
200C2×C11#191311yescharacteristic
201D11—161no—
202C24—221no—
203C24C2×C22⋊D1111yescharacteristic
204C2×D4—222no—
205C2×D4—444no—
206C2×D4—441no—
207C2×D4—441no—
208C2×D4—881no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—24no—
214C22×C4—42no—
215C22×C4—81no—
216C22×C4—81no—
217C22×C4—222no—
218C22×C4—221no—
219C22×C4(C2×D11)⋊C412yes—
220C22×C4(C2×D11)⋊C412yes—
221C22×C4C2×C4×D1111yescharacteristic
222C22×C4C2×D4411yescharacteristic
223C22×C4#433912yes—
224C22×C4C2×C22⋊D1112yes—
225M16—882no—
226C2×C8—442no—
227C4⋊C4—24no—
228C4⋊C4—24no—
229C4⋊C4—82no—
230C4⋊C4—222no—
231C22⋊C4—44no—
232C22⋊C4—444no—
233C22⋊C4—442no—
234C22⋊C4—442no—
235C22⋊C4—882no—
236C42—82no—
237C42—881no—
238C11#941411yescharacteristic, complemented, Sylow
239C23—22no—
240C23—22no—
241C23—41no—
242C23—442no—
243C23—442no—
244C23—441no—
245C23—442no—
246C23C2×(C2×D11)⋊C411yescharacteristic
247C23#6698211yescharacteristic
248C23#6700611yescharacteristic
249D4—882no—
250D4—882no—
251D4—882no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—42no—
257C2×C4—41no—
258C2×C4—42no—
259C2×C4—41no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—44no—
265C2×C4—44no—
266C2×C4—44no—
267C2×C4—81no—
268C2×C4—442no—
269C2×C4—442no—
270C2×C4—442no—
271C2×C4—441no—
272C2×C4—442no—
273C2×C4C4×C22⋊D1112yes—
274C2×C4#6698312yes—
275C8—882no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—44no—
284C22—884no—
285C22—881no—
286C22—881no—
287C22—881no—
288C22#1062261812yes—
289C22#1062282611yescharacteristic
290C22#1062285812yes—
291C4—22no—
292C4—22no—
293C4—42no—
294C4—42no—
295C4—84no—
296C4—882no—
297C4—881no—
298C2—22no—
299C2—22no—
300C2—41no—
301C2—1761no—
302C2#1306901911yescharacteristic
303C2#1306906411yescharacteristic
304C2#1306915811yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2313C2
socleC22×C11#386
prime radicalC2×#66983C22
cosocleC23×C4×C11C23
hypercenter#2313D11
hypocenterC11#9414
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2313

Complements

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

NH ≅ G/Ntype
3. #13066946C2semidirect
4. #13066502C2semidirect
5. C11×#2313C2semidirect
16. #10622604C4semidirect
18. #10622599C4semidirect
88. #2313D11semidirect
238. C11#9414semidirect

Maximal subgroups

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

subgroupindex
#130740962
#130671312
#130669462
#130665022
C11×#23132
#941411