Finite Group Databasebeta

← #14651267

Subgroups — #14651267

Order 2816.

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

normal subgroups only

This group has 402 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#13079335C211yesmaximal, characteristic
2#13077722C211yesmaximal, characteristic, complemented
3#13067250C211yesmaximal, characteristic
4#13067162C211yesmaximal, characteristic
5#13066487C211yesmaximal, characteristic, complemented
6#13066480C211yesmaximal, characteristic, complemented
7C11×#1515C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9#10623008C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#383C2211yescharacteristic
12#10622701C411yescharacteristic, complemented
13#10622698C411yescharacteristic, complemented
14#10622694C411yescharacteristic, complemented
15#10622691C411yescharacteristic, complemented
16#10622662—22no—
17#10622639—22no—
18#10622637—22no—
19#10622637—22no—
20#10622613—22no—
21#10622539C2211yescharacteristic
22#10622539C2211yescharacteristic
23C4×#4318C2211yescharacteristic
24C11×#328—22no—
25#10622102—22no—
26#10622089—22no—
27C2×#4339—21no—
28C11×C4⋊Q8C2×C411yescharacteristic
29C11×C4⋊Q8C2×C411yescharacteristic
30C11×#125—21no—
31C11×C22⋊Q8—21no—
32C11×C22⋊Q8D412yes—
33C4×Q8×C11—21no—
34C4×Q8×C11D412yes—
35C11×#117—21no—
36C2×C42×C11C2311yescharacteristic
37C2×#4325—22no—
38#66983—21no—
39#66983—21no—
40C2×#4318—21no—
41#66928—21no—
42#66927C2×C411yescharacteristic
43C4×D44—21no—
44C4×D44—21no—
45#66922C2×C411yescharacteristic
46C11×C4⋊C8—21no—
47C11×C22⋊C8—21no—
48C11×#97—21no—
49C11×#95—21no—
50C11×#95—21no—
51C11×#95—21no—
52#66899—22no—
53C22⋊(C11⋊C8)—21no—
54C22⋊(C11⋊C8)D412yes—
55#66873—22no—
56#66871—22no—
57C4⋊(C11⋊C8)—24no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60#66867—22no—
61#66867—21no—
62#66867—21no—
63#66867D412yes—
64C4×C11⋊C8—22no—
65C4×C11⋊C8C2×C411yescharacteristic
66C4×C11⋊C8C2×C411yescharacteristic
67#9418—111nomaximal, Sylow
68C2×Q8×C11—21no—
69C2×Q8×C11C22⋊C412yes—
70C22×C4×C11—41no—
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11#4111yescharacteristic
74C2×C22⋊D11—41no—
75#4339—82no—
76C2×D44—21no—
77C2×D44—21no—
78C2×D44—21no—
79C2×C4×D11—41no—
80C2×Dic22—21no—
81C2×C8×C11—41no—
82C11×C4⋊C4—21no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—22no—
86C11×C4⋊C4—22no—
87C11×C4⋊C4C22⋊C412yes—
88C11×C22⋊C4—22no—
89C42×C11—22no—
90C42×C11C22×C411yescharacteristic
91C42×C11C2×D411yescharacteristic
92C42×C11C2×D411yescharacteristic
93C42×C11#4111yescharacteristic
94#4325—44no—
95(C2×D11)⋊C4—41no—
96(C2×D11)⋊C4—41no—
97C4⋊Dic11—21no—
98C4⋊Dic11—21no—
99#4318—42no—
100C2×C11⋊C8—21no—
101C2×C11⋊C8—21no—
102C2×C11⋊C8—22no—
103C2×C11⋊C8—22no—
104#3182—111no—
105#2987—111no—
106#1536—111no—
107#1515D1111yescharacteristic, complemented
108#1514—111no—
109#1291—111no—
110#1288—111no—
111C23×C11#12111yescharacteristic
112C22×D11—41no—
113Q8×C11—42no—
114Q8×C11—81no—
115C2×C4×C11—22no—
116C2×C4×C11—22no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—81no—
121C2×C4×C11—81no—
122C2×C4×C11—81no—
123C2×C4×C11C2×C22⋊C411yescharacteristic
124C2×C4×C11C4×D411yescharacteristic
125C2×C4×C11C4×D411yescharacteristic
126C2×C4×C11#12011yescharacteristic
127C2×C4×C11#12111yescharacteristic
128C2×C4×C11#12311yescharacteristic
129C22⋊D11—82no—
130C2×Dic11—41no—
131D44—42no—
132D44—81no—
133D44—81no—
134C4×D11—82no—
135Dic22—81no—
136C8×C11—81no—
137C11⋊C8—22no—
138C11⋊C8—42no—
139C11⋊C8—42no—
140C11⋊C8—41no—
141#533C2×D1111yescharacteristic
142#532—111no—
143#500—111no—
144#492—111no—
145#487—111no—
146#486—111no—
147#468—222no—
148#446—222no—
149#446—222no—
150#440—222no—
151#433—222no—
152#432—111no—
153#432—111no—
154#432C2×D1111yescharacteristic
155C4×M16—111no—
156#383C2×D1111yescharacteristic
157#329—222no—
158#328—22no—
159#327—222no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11—21no—
163C22×C11#38611yescharacteristic
164C2×D11—81no—
165C2×D11—81no—
166C2×D11—81no—
167C4×C11—21no—
168C4×C11—21no—
169C4×C11—21no—
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—42no—
174C4×C11—42no—
175C4×C11—161no—
176Dic11—81no—
177C2×#41—221no—
178C2×SD16—222no—
179C2×M16—221no—
180C4⋊Q8—111no—
181C4⋊Q8C4×D1111yescharacteristic
182C4⋊Q8C4×D1111yescharacteristic
183#127—111no—
184#125—21no—
185#124—221no—
186C22⋊Q8—21no—
187C22⋊Q8C22⋊D1112yes—
188#121—221no—
189#121—221no—
190C4×Q8—21no—
191C4×Q8D4412yes—
192C4×D4—221no—
193C4×D4—221no—
194#117—21no—
195C2×C42C22×D1111yescharacteristic
196#107—222no—
197C4⋊C8—21no—
198C4⋊C8—224no—
199C4⋊C8—221no—
200C4⋊C8—221no—
201#103—222no—
202#102—222no—
203C22⋊C8—21no—
204C22⋊C8—112no—
205C22⋊C8—221no—
206#97—21no—
207#97—112no—
208#97—222no—
209#97—221no—
210#97—221no—
211C4×C8—111no—
212C4×C8—111no—
213C4×C8—222no—
214#95—21no—
215#95—21no—
216#95—21no—
217C2×C11—41no—
218C2×C11#188411yescharacteristic
219C2×C11#190311yescharacteristic
220C2×C11#190511yescharacteristic
221D11—161no—
222#41—882no—
223C2×Q8—21no—
224C2×Q8—221no—
225C2×Q8(C2×D11)⋊C412yes—
226C2×D4—221no—
227C2×D4—221no—
228C2×D4—221no—
229C2×D4—441no—
230C22×C4—41no—
231C22×C4—441no—
232C22×C4D4×D1111yescharacteristic
233C22×C4#434111yescharacteristic
234C22×C4C2×C22⋊D1111yescharacteristic
235SD16—444no—
236M16—442no—
237C2×C8—41no—
238C2×C8—221no—
239C2×C8—222no—
240C2×C8—222no—
241C2×C8—221no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—22no—
246C4⋊C4—22no—
247C4⋊C4—221no—
248C4⋊C4—221no—
249C4⋊C4(C2×D11)⋊C412yes—
250C22⋊C4—22no—
251C22⋊C4—441no—
252C22⋊C4—441no—
253C42—22no—
254C42C2×C4×D1111yescharacteristic
255C42C2×D4411yescharacteristic
256C42D4×D1111yescharacteristic
257C42#434111yescharacteristic
258C11#941811yescharacteristic, complemented, Sylow
259C23—441no—
260C23#6699211yescharacteristic
261Q8—42no—
262Q8—81no—
263Q8—881no—
264D4—442no—
265D4—881no—
266D4—881no—
267D4—882no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—81no—
276C2×C4—441no—
277C2×C4—882no—
278C2×C4(C22⋊D11)⋊C411yescharacteristic
279C2×C4(C22⋊D11)⋊C411yescharacteristic
280C2×C4#6693511yescharacteristic
281C2×C4#6693911yescharacteristic
282C2×C4C2×(C2×D11)⋊C411yescharacteristic
283C2×C4#6699211yescharacteristic
284C8—81no—
285C8—222no—
286C8—441no—
287C8—442no—
288C8—442no—
289C22—21no—
290C22—21no—
291C22—21no—
292C22—881no—
293C22—881no—
294C22—881no—
295C22#1062257111yescharacteristic
296C4—21no—
297C4—21no—
298C4—21no—
299C4—21no—
300C4—21no—
301C4—21no—
302C4—42no—
303C4—42no—
304C4—161no—
305C4—881no—
306C2—41no—
307C2—1761no—
308C2#1306899711yescharacteristic
309C2#1306909411yescharacteristic
310C2#1306910811yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1515C2
socleC22×C11#386
prime radical#10623008C22
cosocleC2×C42×C11C23
hypercenter#1515D11
hypocenterC11#9418
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1515

Complements

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

NH ≅ G/Ntype
2. #13077722C2semidirect
5. #13066487C2semidirect
6. #13066480C2semidirect
7. C11×#1515C2semidirect
12. #10622701C4semidirect
13. #10622698C4semidirect
14. #10622694C4semidirect
15. #10622691C4semidirect
107. #1515D11semidirect
258. C11#9418semidirect

Maximal subgroups

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

subgroupindex
#130793352
#130777222
#130672502
#130671622
#130664872
#130664802
C11×#15152
#941811