Finite Group Databasebeta

← #14651224

Subgroups — #14651224

Order 2816.

644 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 115 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#13070973C211yesmaximal, characteristic, complemented
2#13067132C212yesmaximal
3#13066946C211yesmaximal, characteristic, complemented
4#13066502C212yesmaximal, complemented
5C11×#2591C211yesmaximal, characteristic
6C2×C11×#121C2211yescharacteristic
7C22×C11×C4⋊C4C2211yescharacteristic
8C2×#66979—21no—
9C11×#400C412yescomplemented
10C11×#394C412yescomplemented
11C11×#388—22no—
12C11×#386—21no—
13C11×#386—21no—
14C4×C11×C22⋊C4C2211yescharacteristic
15C4×C22⋊Dic11—21no—
16C4×C22⋊Dic11C2212yes—
17#10622820C2212yes—
18C4⋊C4×Dic11—24no—
19#10622175—24no—
20#10622166—22no—
21C22×D4×C11—21no—
22C22×D4×C11C2×C411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11C2311yescharacteristic
26C11×#121—22no—
27C11×#121—22no—
28C2×C11×C4⋊C4—22no—
29C2×C11×C4⋊C4—22no—
30C2×C11×C4⋊C4C2×C411yescharacteristic
31C2×C11×C4⋊C4C2×C412yes—
32C2×C11×C4⋊C4D412yes—
33C2×C11×C22⋊C4—21no—
34C2×C11×C22⋊C4—22no—
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—22no—
37C2×C42×C11—21no—
38C2×C22⋊Dic11—22no—
39#66979—28no—
40C2×C4⋊Dic11—22no—
41C2×C4×Dic11—22no—
42C2×C4×Dic11—22no—
43C2×C4×Dic11—22no—
44C2×#4318—22no—
45C11×#95—22no—
46C11×#95—22no—
47C11×#95C2×C412yes—
48C11⋊#95—22no—
49C11⋊#95D414yes—
50C22⋊(C11⋊C8)—22no—
51C22⋊(C11⋊C8)—22no—
52#9410—111nomaximal, Sylow
53C24×C11—21no—
54C24×C11C2×D411yescharacteristic
55C2×D4×C11—22no—
56C2×D4×C11—44no—
57C2×D4×C11—41no—
58C2×D4×C11—41no—
59C2×D4×C11—81no—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—24no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—22no—
67C22×C4×C11—81no—
68C22×C4×C11—81no—
69C22×C4×C11C22⋊C412yes—
70C22×C4×C11C22⋊C412yes—
71C22×C4×C11C22×C411yescharacteristic
72C22×C4×C11C2×D412yes—
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11#4112yes—
75C22×Dic11—24no—
76C11×C4⋊C4—24no—
77C11×C4⋊C4—24no—
78C11×C4⋊C4—22no—
79C11×C22⋊C4—42no—
80C11×C22⋊C4—44no—
81C11×C22⋊C4—42no—
82C11×C22⋊C4—82no—
83C42×C11—81no—
84C22⋊Dic11—28no—
85C4⋊Dic11—28no—
86C4×Dic11—28no—
87C4×Dic11—82no—
88C4×Dic11—82no—
89#4318—82no—
90C2×C11⋊C8—42no—
91#2591D1111yescharacteristic
92#2274—111no—
93#1507—112no—
94#1463—111no—
95#1297—112no—
96C23×C11—22no—
97C23×C11—22no—
98C23×C11—41no—
99C23×C11—42no—
100C23×C11—42no—
101C23×C11—41no—
102C23×C11—42no—
103C23×C11C2×C22⋊C411yescharacteristic
104C23×C11#12011yescharacteristic
105C23×C11#12311yescharacteristic
106D4×C11—82no—
107D4×C11—82no—
108D4×C11—82no—
109C2×C4×C11—22no—
110C2×C4×C11—22no—
111C2×C4×C11—24no—
112C2×C4×C11—22no—
113C2×C4×C11—22no—
114C2×C4×C11—22no—
115C2×C4×C11—42no—
116C2×C4×C11—42no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—42no—
122C2×C4×C11—42no—
123C2×C4×C11—42no—
124C2×C4×C11—41no—
125C2×C4×C11—42no—
126C2×C4×C11—81no—
127C2×C4×C11#10414yes—
128C2×C4×C11C4×D412yes—
129C2×C4×C11#12112yes—
130C2×Dic11—28no—
131C2×Dic11—44no—
132C2×Dic11—44no—
133C11⋊C8—82no—
134C2×#121C2×D1111yescharacteristic
135C2×#117—221no—
136C22×C4⋊C4C2×D1111yescharacteristic
137#407—112no—
138#400Dic1112yescomplemented
139#394Dic1112yescomplemented
140#388—22no—
141#386—21no—
142#386—21no—
143C4×C4⋊C4—224no—
144C4×C22⋊C4—112no—
145C4×C22⋊C4—221no—
146C4×C22⋊C4C2×D1111yescharacteristic
147#327—224no—
148#324—222no—
149C22×C11—21no—
150C22×C11—21no—
151C22×C11—21no—
152C22×C11—21no—
153C22×C11—21no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11—44no—
157C22×C11—84no—
158C22×C11—81no—
159C22×C11—81no—
160C22×C11—81no—
161C22×C11#38611yescharacteristic
162C22×C11C2×#10412yes—
163C22×C11#45412yes—
164C4×C11—24no—
165C4×C11—22no—
166C4×C11—22no—
167C4×C11—42no—
168C4×C11—82no—
169C4×C11—81no—
170Dic11—48no—
171C22×D4—21no—
172C22×D4C2×Dic1111yescharacteristic
173C23×C4C22⋊D1111yescharacteristic
174C23×C4C22⋊D1111yescharacteristic
175C23×C4C22×D1111yescharacteristic
176C2×M16—222no—
177#121—22no—
178#121—22no—
179#117—228no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—222no—
183C2×C4⋊C4C2×Dic1111yescharacteristic
184C2×C4⋊C4C2×Dic1112yes—
185C2×C4⋊C4C22⋊D1112yes—
186C2×C22⋊C4—21no—
187C2×C22⋊C4—22no—
188C2×C22⋊C4—21no—
189C2×C22⋊C4—22no—
190C2×C22⋊C4—222no—
191C2×C42—21no—
192C2×C42—222no—
193C2×C42—222no—
194C2×C42—222no—
195C22⋊C8—222no—
196C22⋊C8—222no—
197#95—22no—
198#95—22no—
199#95—114no—
200#95—222no—
201#95C2×Dic1112yes—
202C2×C11—22no—
203C2×C11—22no—
204C2×C11—41no—
205C2×C11—161no—
206C2×C11#188811yescharacteristic
207C2×C11#189611yescharacteristic
208C2×C11#191311yescharacteristic
209C24—21no—
210C24C2×C22⋊D1111yescharacteristic
211C2×D4—22no—
212C2×D4—44no—
213C2×D4—41no—
214C2×D4—41no—
215C2×D4—81no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—24no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—22no—
223C22×C4—81no—
224C22×C4—81no—
225C22×C4—224no—
226C22×C4C22⋊Dic1112yes—
227C22×C4C22⋊Dic1112yes—
228C22×C4D4×D1112yes—
229C22×C4#434112yes—
230C22×C4C22×Dic1111yescharacteristic
231C22×C4C2×C22⋊D1111yescharacteristic
232M16—882no—
233C2×C8—442no—
234C4⋊C4—24no—
235C4⋊C4—24no—
236C4⋊C4—22no—
237C4⋊C4—228no—
238C22⋊C4—42no—
239C22⋊C4—44no—
240C22⋊C4—42no—
241C22⋊C4—82no—
242C22⋊C4—228no—
243C42—81no—
244C42—228no—
245C42—882no—
246C42—882no—
247C11#941011yescharacteristic, complemented, Sylow
248C23—22no—
249C23—22no—
250C23—41no—
251C23—42no—
252C23—42no—
253C23—41no—
254C23—42no—
255C23#6698811yescharacteristic
256C23#6699011yescharacteristic
257C23C2×C22⋊Dic1111yescharacteristic
258D4—82no—
259D4—82no—
260D4—82no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—24no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—41no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—41no—
277C2×C4—42no—
278C2×C4—81no—
279C2×C4—228no—
280C2×C4—444no—
281C2×C4—444no—
282C2×C4#6690114yes—
283C2×C4D4×Dic1112yes—
284C2×C4#6699212yes—
285C8—882no—
286C22—21no—
287C22—21no—
288C22—21no—
289C22—21no—
290C22—21no—
291C22—21no—
292C22—21no—
293C22—44no—
294C22—84no—
295C22—81no—
296C22—81no—
297C22—81no—
298C22#1062267512yes—
299C22#1062283311yescharacteristic
300C22C2×#6690112yes—
301C4—24no—
302C4—22no—
303C4—22no—
304C4—42no—
305C4—82no—
306C4—81no—
307C4—448no—
308C2—22no—
309C2—22no—
310C2—41no—
311C2—161no—
312C2#1306902011yescharacteristic
313C2#1306906011yescharacteristic
314C2#1306915911yescharacteristic
subgroupG/H
centerC22#10622833
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2591C2
socleC22×C11#386
prime radicalC2×C11×#121C22
cosocleC23×C4×C11C23
hypercenter#2591D11
hypocenterC11#9410
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2591

Complements

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

NH ≅ G/Ntype
1. #13070973C2semidirect
3. #13066946C2semidirect
4. #13066502C2semidirect
9. C11×#400C4semidirect
10. C11×#394C4semidirect
138. #400Dic11semidirect
139. #394Dic11semidirect
247. C11#9410semidirect

Maximal subgroups

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

subgroupindex
#130709732
#130671322
#130669462
#130665022
C11×#25912
#941011