Finite Group Databasebeta

← #14651246

Subgroups — #14651246

Order 2816.

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

normal subgroups only

This group has 420 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#13079330C211yesmaximal, characteristic
2#13077687C211yesmaximal, characteristic
3#13067253C211yesmaximal, characteristic, complemented
4#13067166C211yesmaximal, characteristic, complemented
5#13066487C211yesmaximal, characteristic, complemented
6#13066480C211yesmaximal, characteristic, complemented
7C11×#1514C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9#10623001C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#383C2211yescharacteristic
12#10622847—22no—
13#10622706C411yescharacteristic, complemented
14#10622691C411yescharacteristic, complemented
15#10622689C411yescharacteristic, complemented
16#10622683C411yescharacteristic, complemented
17#10622655—22no—
18#10622631—22no—
19#10622624—22no—
20#10622624—22no—
21#10622539C2211yescharacteristic
22#10622539C2211yescharacteristic
23C4×#4318C2211yescharacteristic
24C11×#327—22no—
25#10622103—22no—
26#10622090—22no—
27C2×C11×#41—21no—
28C11×C4⋊Q8C2×C411yescharacteristic
29C11×#127C2×C411yescharacteristic
30C11×#124—21no—
31C11×#121—21no—
32C11×#121D412yes—
33C4×D4×C11—21no—
34C4×D4×C11D412yes—
35C2×C42×C11C2311yescharacteristic
36C2×#4324—22no—
37#66979—21no—
38#66977—21no—
39#66977—21no—
40C2×#4318—21no—
41C2×#4318—22no—
42C22×C11⋊C8—22no—
43#66923—21no—
44#66922C2×C411yescharacteristic
45#66922C2×C411yescharacteristic
46C4×Dic22—21no—
47C4×Dic22—21no—
48C11×C4⋊C8—21no—
49C11×C22⋊C8—21no—
50C11×#97—21no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95—21no—
54#66896—22no—
55C22⋊(C11⋊C8)—24no—
56C22⋊(C11⋊C8)—21no—
57C22⋊(C11⋊C8)D412yes—
58#66874—22no—
59#66871—22no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62#66867—21no—
63#66867—21no—
64#66867D412yes—
65C4×C11⋊C8C2×C411yescharacteristic
66C4×C11⋊C8C2×C411yescharacteristic
67#9415—111nomaximal, Sylow
68C11×#41—81no—
69C11×#41—81no—
70C2×Q8×C11—21no—
71C2×D4×C11—22no—
72C2×D4×C11—21no—
73C2×D4×C11—21no—
74C2×D4×C11C22⋊C412yes—
75C22×C4×C11—22no—
76C22×C4×C11—41no—
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11#4111yescharacteristic
80C2×Dic22—21no—
81C2×Dic22—21no—
82C2×C8×C11—41no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4C22⋊C412yes—
85C11×C22⋊C4—22no—
86C11×C22⋊C4—22no—
87C42×C11C22×C411yescharacteristic
88C42×C11C2×D411yescharacteristic
89C42×C11C2×D411yescharacteristic
90C42×C11#4111yescharacteristic
91C22⋊Dic11—41no—
92#4324—44no—
93C4⋊Dic11—21no—
94C4⋊Dic11—21no—
95C4⋊Dic11—21no—
96C4⋊Dic11—21no—
97Dic11⋊C4—41no—
98Dic11⋊C4—41no—
99C4×Dic11—41no—
100#4318—42no—
101#4318—82no—
102C2×C11⋊C8—21no—
103C2×C11⋊C8—21no—
104C2×C11⋊C8—22no—
105C2×C11⋊C8—22no—
106C2×C11⋊C8—82no—
107#3182—111no—
108#2980—111no—
109#1537—111no—
110#1515—111no—
111#1514D1111yescharacteristic
112#1291—111no—
113#1288—111no—
114C23×C11—22no—
115C23×C11#12111yescharacteristic
116Q8×C11—81no—
117D4×C11—42no—
118D4×C11—81no—
119D4×C11—81no—
120D4×C11—82no—
121C2×C4×C11—22no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—42no—
126C2×C4×C11—42no—
127C2×C4×C11—81no—
128C2×C4×C11—81no—
129C2×C4×C11—81no—
130C2×C4×C11C2×C22⋊C411yescharacteristic
131C2×C4×C11C4×D411yescharacteristic
132C2×C4×C11C4×D411yescharacteristic
133C2×C4×C11#12011yescharacteristic
134C2×C4×C11#12111yescharacteristic
135C2×C4×C11#12311yescharacteristic
136C2×Dic11—41no—
137C2×Dic11—41no—
138Dic22—42no—
139Dic22—81no—
140C8×C11—81no—
141C11⋊C8—22no—
142C11⋊C8—42no—
143C11⋊C8—42no—
144C11⋊C8—41no—
145#533—111no—
146#532C2×D1111yescharacteristic
147#500—111no—
148#492—111no—
149#487—111no—
150#486—111no—
151#468—222no—
152#440—222no—
153#435—222no—
154#435—222no—
155#432—111no—
156#432—111no—
157#432C2×D1111yescharacteristic
158#408—222no—
159C4×M16—111no—
160#383C2×D1111yescharacteristic
161#330—222no—
162#328—222no—
163#327—22no—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11—21no—
167C22×C11—42no—
168C22×C11—42no—
169C22×C11—42no—
170C22×C11#38611yescharacteristic
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—42no—
178C4×C11—161no—
179Dic11—81no—
180Dic11—81no—
181C2×#41—21no—
182C2×SD16—222no—
183C2×M16—221no—
184C2×M16—222no—
185C22×C8—222no—
186C4⋊Q8—111no—
187C4⋊Q8—111no—
188C4⋊Q8C4×D1111yescharacteristic
189#127C4×D1111yescharacteristic
190#125—221no—
191#124—21no—
192C22⋊Q8—221no—
193C22⋊Q8—221no—
194#121—21no—
195#121C22⋊D1112yes—
196C4×Q8—221no—
197C4×Q8—221no—
198C4×D4—21no—
199C4×D4D4412yes—
200#117—221no—
201C2×C42C22×D1111yescharacteristic
202#107—222no—
203C4⋊C8—21no—
204C4⋊C8—221no—
205C4⋊C8—221no—
206#103—222no—
207#102—222no—
208C22⋊C8—21no—
209C22⋊C8—112no—
210C22⋊C8—224no—
211C22⋊C8—221no—
212#97—21no—
213#97—112no—
214#97—221no—
215#97—221no—
216C4×C8—111no—
217C4×C8—111no—
218#95—21no—
219#95—21no—
220#95—21no—
221C2×C11—41no—
222C2×C11—82no—
223C2×C11#188411yescharacteristic
224C2×C11#190211yescharacteristic
225C2×C11#190411yescharacteristic
226#41—81no—
227#41—81no—
228C2×Q8—21no—
229C2×Q8—221no—
230C2×Q8—221no—
231C2×D4—22no—
232C2×D4—21no—
233C2×D4—21no—
234C2×D4(C2×D11)⋊C412yes—
235C22×C4—22no—
236C22×C4—41no—
237C22×C4D4×D1111yescharacteristic
238C22×C4#434111yescharacteristic
239C22×C4C2×C22⋊D1111yescharacteristic
240SD16—444no—
241M16—442no—
242M16—882no—
243C2×C8—41no—
244C2×C8—221no—
245C2×C8—222no—
246C2×C8—222no—
247C2×C8—221no—
248C2×C8—882no—
249C4⋊C4—21no—
250C4⋊C4—221no—
251C4⋊C4—221no—
252C4⋊C4—221no—
253C4⋊C4—221no—
254C4⋊C4—441no—
255C4⋊C4—441no—
256C4⋊C4(C2×D11)⋊C412yes—
257C22⋊C4—22no—
258C22⋊C4—22no—
259C22⋊C4—441no—
260C42—441no—
261C42C2×C4×D1111yescharacteristic
262C42C2×D4411yescharacteristic
263C42D4×D1111yescharacteristic
264C42#434111yescharacteristic
265C11#941511yescharacteristic, complemented, Sylow
266C23—22no—
267C23#6699211yescharacteristic
268Q8—81no—
269Q8—442no—
270Q8—881no—
271D4—42no—
272D4—81no—
273D4—81no—
274D4—82no—
275C2×C4—22no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—441no—
285C2×C4—441no—
286C2×C4(C22⋊D11)⋊C411yescharacteristic
287C2×C4(C22⋊D11)⋊C411yescharacteristic
288C2×C4#6693511yescharacteristic
289C2×C4#6693911yescharacteristic
290C2×C4C2×(C2×D11)⋊C411yescharacteristic
291C2×C4#6699211yescharacteristic
292C8—81no—
293C8—222no—
294C8—442no—
295C8—442no—
296C8—441no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—42no—
301C22—42no—
302C22—42no—
303C22#1062257111yescharacteristic
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—21no—
309C4—21no—
310C4—42no—
311C4—161no—
312C4—881no—
313C4—881no—
314C2—41no—
315C2—82no—
316C2#1306899711yescharacteristic
317C2#1306908711yescharacteristic
318C2#1306910111yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1514C2
socleC22×C11#386
prime radicalC11×#532C22
cosocleC2×C42×C11C23
hypercenter#1514D11
hypocenterC11#9415
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1514

Complements

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

NH ≅ G/Ntype
3. #13067253C2semidirect
4. #13067166C2semidirect
5. #13066487C2semidirect
6. #13066480C2semidirect
13. #10622706C4semidirect
14. #10622691C4semidirect
15. #10622689C4semidirect
16. #10622683C4semidirect
265. C11#9415semidirect

Maximal subgroups

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

subgroupindex
#130793302
#130776872
#130672532
#130671662
#130664872
#130664802
C11×#15142
#941511