Finite Group Databasebeta

← #14650366

Subgroups — #14650366

Order 2816.

382 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 89 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#13079777C211yesmaximal, characteristic
2#13077710C211yesmaximal, characteristic
3#13067127C211yesmaximal, characteristic
4#13067127C211yesmaximal, characteristic
5#13067090C211yesmaximal, characteristic
6#13066478C211yesmaximal, characteristic
7C11×#1274C211yesmaximal, characteristic
8#10623001C2211yescharacteristic
9#10623001C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#376C2211yescharacteristic
13#10622539C2211yescharacteristic
14#10622539C2211yescharacteristic
15#10622442—22no—
16#10622441—22no—
17#10622336—22no—
18#10622333—22no—
19#10622295C411yescharacteristic, complemented
20#10622294C411yescharacteristic, complemented
21#10622294C411yescharacteristic, complemented
22#10622293C411yescharacteristic, complemented
23#10622292—21no—
24C8×Dic22—21no—
25#10622094—21no—
26#10622094—21no—
27#10622090—22no—
28#10622090—22no—
29C2×C42×C11—21no—
30C2×C42×C11C2311yescharacteristic
31#66979—21no—
32#66979—21no—
33#66977—21no—
34#66977—21no—
35#66977—21no—
36#66977D412yes—
37#66923—21no—
38#66923—21no—
39#66922C2×C411yescharacteristic
40#66922C2×C411yescharacteristic
41#66922C2×C411yescharacteristic
42#66922C2×C411yescharacteristic
43C4×Dic22—21no—
44C4×Dic22—21no—
45C4×Dic22—21no—
46C4×Dic22D412yes—
47C11×C4⋊C8—21no—
48C11×C4⋊C8—21no—
49C11×C22⋊C8—21no—
50C11×C22⋊C8—21no—
51C4×C8×C11C2×C411yescharacteristic
52C4×C8×C11C2×C411yescharacteristic
53C4×C8×C11D411yescharacteristic
54C4×C8×C11D411yescharacteristic
55C11×#95—21no—
56C11×#95—21no—
57C22⋊(C11⋊C8)—21no—
58C22⋊(C11⋊C8)D412yes—
59#66882—22no—
60#66881—22no—
61#66880—22no—
62#66880—22no—
63#66879—22no—
64Dic11⋊C8—22no—
65Dic11⋊C8—22no—
66C8×Dic11—22no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)—21no—
69#66867—21no—
70#66867—21no—
71#9280—111nomaximal, Sylow
72C22×C4×C11—41no—
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11#4111yescharacteristic
76C2×Dic22—21no—
77C2×Dic22—21no—
78C2×Dic22—21no—
79C2×Dic22C22⋊C412yes—
80C2×C8×C11—21no—
81C2×C8×C11—21no—
82C2×C8×C11—21no—
83C2×C8×C11—21no—
84C42×C11—22no—
85C42×C11—41no—
86C42×C11C22×C411yescharacteristic
87C42×C11C2×D411yescharacteristic
88C42×C11C2×D411yescharacteristic
89C42×C11#4111yescharacteristic
90C22⋊Dic11—22no—
91C22⋊Dic11—41no—
92C4⋊Dic11—21no—
93C4⋊Dic11—21no—
94C4⋊Dic11—21no—
95C4⋊Dic11—21no—
96C4⋊Dic11—21no—
97C4⋊Dic11—21no—
98C4⋊Dic11—21no—
99C4⋊Dic11C22⋊C412yes—
100Dic11⋊C4—22no—
101Dic11⋊C4—22no—
102Dic11⋊C4—41no—
103Dic11⋊C4—41no—
104C4×Dic11—22no—
105C4×Dic11—41no—
106C2×C11⋊C8—22no—
107C2×C11⋊C8—41no—
108#3231—111no—
109#2985—111no—
110#1506—111no—
111#1506—111no—
112#1497—111no—
113#1287—111no—
114#1274D1111yescharacteristic
115C23×C11#12111yescharacteristic
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—42no—
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
129C2×Dic11—22no—
130C2×Dic11—22no—
131C2×Dic11—41no—
132C2×Dic11—41no—
133Dic22—41no—
134Dic22—41no—
135Dic22—42no—
136Dic22—41no—
137Dic22—41no—
138Dic22—81no—
139C8×C11—41no—
140C8×C11—41no—
141C8×C11—41no—
142C8×C11—41no—
143C11⋊C8—42no—
144C11⋊C8—81no—
145#533—111no—
146#533—111no—
147#500—111no—
148#498—111no—
149#487—111no—
150#487—111no—
151#485—222no—
152#479—222no—
153#446—222no—
154#446—221no—
155C8×Q8—221no—
156#433—222no—
157#432—111no—
158#432—111no—
159#431C2×D1111yescharacteristic
160#431C2×D1111yescharacteristic
161#376C2×D1111yescharacteristic
162#328—222no—
163#328—222no—
164Q8⋊C8—221no—
165Q8⋊C8—221no—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11#38611yescharacteristic
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—82no—
176C4×C11#44311yescharacteristic
177C4×C11#44411yescharacteristic
178Dic11—42no—
179Dic11—42no—
180Dic11—81no—
181Dic11—81no—
182C4⋊Q8—111no—
183C4⋊Q8—111no—
184C4⋊Q8—111no—
185C4⋊Q8—111no—
186#125—221no—
187#125—221no—
188C22⋊Q8—112no—
189C22⋊Q8—221no—
190C22⋊Q8—221no—
191C22⋊Q8—221no—
192C4×Q8—112no—
193C4×Q8—221no—
194C4×Q8—221no—
195C4×Q8—221no—
196#117—221no—
197#117—221no—
198C2×C42—21no—
199C2×C42C22×D1111yescharacteristic
200#107—222no—
201#106—222no—
202C4⋊C8—21no—
203C4⋊C8—21no—
204C4⋊C8—222no—
205C4⋊C8—222no—
206C4⋊C8—221no—
207C4⋊C8—221no—
208#103—222no—
209#103—222no—
210C22⋊C8—21no—
211C22⋊C8—21no—
212C22⋊C8—112no—
213C22⋊C8—221no—
214#97—222no—
215#97—221no—
216#97—221no—
217C4×C8—222no—
218C4×C8C4×D1111yescharacteristic
219C4×C8C4×D1111yescharacteristic
220C4×C8D4411yescharacteristic
221C4×C8D4411yescharacteristic
222#95—21no—
223#95—21no—
224C2×C11—41no—
225C2×C11#187611yescharacteristic
226C2×C11#190511yescharacteristic
227C2×C11#190911yescharacteristic
228C2×Q8—112no—
229C2×Q8—221no—
230C2×Q8—221no—
231C2×Q8—221no—
232C22×C4—41no—
233C22×C4#433911yescharacteristic
234C22×C4D4×D1111yescharacteristic
235C22×C4D4×D1111yescharacteristic
236C2×C8—21no—
237C2×C8—21no—
238C2×C8—21no—
239C2×C8—21no—
240C2×C8—222no—
241C2×C8—441no—
242C4⋊C4—112no—
243C4⋊C4—221no—
244C4⋊C4—221no—
245C4⋊C4—221no—
246C4⋊C4—222no—
247C4⋊C4—222no—
248C4⋊C4—221no—
249C4⋊C4—221no—
250C4⋊C4—221no—
251C4⋊C4—221no—
252C4⋊C4—441no—
253C4⋊C4—441no—
254C22⋊C4—222no—
255C22⋊C4—441no—
256C42—22no—
257C42—41no—
258C42—222no—
259C42—441no—
260C42C2×C4×D1111yescharacteristic
261C42C2×D4411yescharacteristic
262C42D4×D1111yescharacteristic
263C42#434311yescharacteristic
264C11#928011yescharacteristic, complemented, Sylow
265C23#6693711yescharacteristic
266Q8—442no—
267Q8—441no—
268Q8—441no—
269Q8—441no—
270Q8—441no—
271Q8—881no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—42no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—222no—
280C2×C4—222no—
281C2×C4—441no—
282C2×C4—441no—
283C2×C4C4×D4411yescharacteristic
284C2×C4C22⋊C4×D1111yescharacteristic
285C2×C4#6693511yescharacteristic
286C2×C4#6694611yescharacteristic
287C2×C4#6694711yescharacteristic
288C2×C4#6694811yescharacteristic
289C8—41no—
290C8—41no—
291C8—41no—
292C8—41no—
293C8—442no—
294C8—881no—
295C22—21no—
296C22—21no—
297C22—21no—
298C22#1062227811yescharacteristic
299C4—21no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—82no—
305C4—442no—
306C4—442no—
307C4—881no—
308C4—881no—
309C4#1062231311yescharacteristic
310C4#1062233011yescharacteristic
311C2—41no—
312C2#1306894211yescharacteristic
313C2#1306911111yescharacteristic
314C2#1306913711yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1274C2
socleC22×C11#386
prime radicalC23×C11#121
cosocleC2×C42×C11C23
hypercenter#1274D11
hypocenterC11#9280
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1274

Complements

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

NH ≅ G/Ntype
19. #10622295C4semidirect
20. #10622294C4semidirect
21. #10622294C4semidirect
22. #10622293C4semidirect
264. C11#9280semidirect

Maximal subgroups

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

subgroupindex
#130797772
#130777102
#130671272
#130670902
#130664782
C11×#12742
#928011