Finite Group Databasebeta

← #14651245

Subgroups — #14651245

Order 2816.

420 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 85 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#13077686C211yesmaximal, characteristic
3#13067254C211yesmaximal, characteristic, complemented
4#13067162C211yesmaximal, characteristic
5#13066489C211yesmaximal, 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#10622539C2211yescharacteristic
19#10622539C2211yescharacteristic
20C4×#4318C2211yescharacteristic
21#10622449—22no—
22#10622340—22no—
23#10622319—22no—
24C11×#328—22no—
25#10622181—22no—
26#10622089—22no—
27C2×#4339—21no—
28C11×C4⋊Q8C2×C411yescharacteristic
29C11×C4⋊Q8C2×C411yescharacteristic
30C11×#125—21no—
31C11×C22⋊Q8—21no—
32C11×C22⋊Q8—21no—
33C4×Q8×C11—21no—
34C4×Q8×C11—21no—
35C11×#117—21no—
36C2×C42×C11C2311yescharacteristic
37C2×#4325—22no—
38#66983—21no—
39#66983D412yes—
40C2×#4318—21no—
41C2×#4313—22no—
42C2×C8×D11—22no—
43#66928—21no—
44#66927C2×C411yescharacteristic
45C4×D44—21no—
46C4×D44D412yes—
47#66922C2×C411yescharacteristic
48C11×C4⋊C8—21no—
49C11×C22⋊C8D412yes—
50C11×#97—21no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95—21no—
54#66899—22no—
55C22⋊(C11⋊C8)—21no—
56C22⋊(C11⋊C8)—21no—
57(C2×D11)⋊C8—24no—
58#66873—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
68C2×Q8×C11—21no—
69C2×Q8×C11—21no—
70C22×C4×C11—41no—
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11#4111yescharacteristic
74C2×C22⋊D11—22no—
75#4339—81no—
76#4339—81no—
77C2×D44—21no—
78C2×D44—21no—
79C2×D44C22⋊C412yes—
80C2×C4×D11—22no—
81C2×Dic22—21no—
82C2×C8×C11—22no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C22⋊C4—41no—
90C42×C11—41no—
91C42×C11C22×C411yescharacteristic
92C42×C11C2×D411yescharacteristic
93C42×C11C2×D411yescharacteristic
94C42×C11#4111yescharacteristic
95#4325—44no—
96(C2×D11)⋊C4—22no—
97(C2×D11)⋊C4—22no—
98C4⋊Dic11—21no—
99C4⋊Dic11C22⋊C412yes—
100#4318—42no—
101C2×C11⋊C8—21no—
102C2×C11⋊C8—21no—
103C2×C11⋊C8—22no—
104C2×C11⋊C8—41no—
105#4313—82no—
106C8×D11—82no—
107#3182—111no—
108#2980—111no—
109#1537—111no—
110#1515D1111yescharacteristic, complemented
111#1514—111no—
112#1291—111no—
113#1288—111no—
114C23×C11#12111yescharacteristic
115C22×D11—22no—
116Q8×C11—42no—
117Q8×C11—81no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—81no—
124C2×C4×C11—81no—
125C2×C4×C11—81no—
126C2×C4×C11C2×C22⋊C411yescharacteristic
127C2×C4×C11C4×D411yescharacteristic
128C2×C4×C11C4×D411yescharacteristic
129C2×C4×C11#12011yescharacteristic
130C2×C4×C11#12111yescharacteristic
131C2×C4×C11#12311yescharacteristic
132C22⋊D11—82no—
133C2×Dic11—22no—
134D44—42no—
135D44—81no—
136D44—81no—
137C4×D11—42no—
138C4×D11—42no—
139Dic22—81no—
140C8×C11—42no—
141C11⋊C8—22no—
142C11⋊C8—42no—
143C11⋊C8—41no—
144C11⋊C8—81no—
145#533C2×D1111yescharacteristic
146#532—111no—
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—22no—
163#327—222no—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11—21no—
167C22×C11#38611yescharacteristic
168C2×D11—42no—
169C2×D11—42no—
170C2×D11—42no—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—81no—
178C4×C11—81no—
179C4×C11—161no—
180Dic11—42no—
181C2×#41—221no—
182C2×SD16—222no—
183C2×M16—222no—
184C2×M16—221no—
185C22×C8—222no—
186C4⋊Q8—111no—
187C4⋊Q8C4×D1111yescharacteristic
188C4⋊Q8C4×D1111yescharacteristic
189#127—111no—
190#125—21no—
191#124—221no—
192C22⋊Q8—21no—
193C22⋊Q8—21no—
194#121—112no—
195#121—221no—
196C4×Q8—21no—
197C4×Q8—21no—
198C4×D4—112no—
199C4×D4—221no—
200#117—21no—
201C2×C42C22×D1111yescharacteristic
202#107—222no—
203C4⋊C8—21no—
204C4⋊C8—221no—
205C4⋊C8—221no—
206#103—222no—
207#102—222no—
208C22⋊C8—224no—
209C22⋊C8—221no—
210C22⋊C8—221no—
211C22⋊C8C22⋊D1112yes—
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#188411yescharacteristic
223C2×C11#190211yescharacteristic
224C2×C11#190411yescharacteristic
225D11—82no—
226#41—881no—
227#41—881no—
228C2×Q8—21no—
229C2×Q8—21no—
230C2×Q8—221no—
231C2×D4—112no—
232C2×D4—222no—
233C2×D4—221no—
234C2×D4—221no—
235C22×C4—41no—
236C22×C4—222no—
237C22×C4D4×D1111yescharacteristic
238C22×C4#434111yescharacteristic
239C22×C4C2×C22⋊D1111yescharacteristic
240SD16—444no—
241M16—442no—
242M16—882no—
243C2×C8—22no—
244C2×C8—221no—
245C2×C8—221no—
246C2×C8—222no—
247C2×C8—441no—
248C2×C8—882no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—112no—
256C4⋊C4—221no—
257C22⋊C4—41no—
258C22⋊C4—222no—
259C22⋊C4—222no—
260C42—41no—
261C42C2×C4×D1111yescharacteristic
262C42#433911yescharacteristic
263C42D4×D1111yescharacteristic
264C42D4×D1111yescharacteristic
265C11#941511yescharacteristic, complemented, Sylow
266C23—222no—
267C23#6699111yescharacteristic
268Q8—42no—
269Q8—81no—
270Q8—881no—
271D4—442no—
272D4—881no—
273D4—881no—
274D4—882no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—222no—
284C2×C4—442no—
285C2×C4—442no—
286C2×C4C22⋊C4×D1111yescharacteristic
287C2×C4(C22⋊D11)⋊C411yescharacteristic
288C2×C4#6693611yescharacteristic
289C2×C4#6693711yescharacteristic
290C2×C4C4×C22⋊D1111yescharacteristic
291C2×C4#6699011yescharacteristic
292C8—42no—
293C8—222no—
294C8—442no—
295C8—441no—
296C8—881no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—442no—
301C22—442no—
302C22—442no—
303C22#1062256911yescharacteristic
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—21no—
309C4—21no—
310C4—81no—
311C4—81no—
312C4—161no—
313C4—442no—
314C2—41no—
315C2—882no—
316C2#1306899611yescharacteristic
317C2#1306908611yescharacteristic
318C2#1306910611yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1515C2
socleC22×C11#386
prime radical#10623008C22
cosocleC2×C42×C11C23
hypercenter#1515D11
hypocenterC11#9415
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
3. #13067254C2semidirect
5. #13066489C2semidirect
6. #13066480C2semidirect
7. C11×#1515C2semidirect
12. #10622701C4semidirect
13. #10622698C4semidirect
14. #10622694C4semidirect
15. #10622691C4semidirect
110. #1515D11semidirect
265. C11#9415semidirect

Maximal subgroups

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

subgroupindex
#130793352
#130776862
#130672542
#130671622
#130664892
#130664802
C11×#15152
#941511