Finite Group Databasebeta

← #14650408

Subgroups — #14650408

Order 2816.

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

normal subgroups only

This group has 374 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#13067230C211yesmaximal, characteristic
4#13067230C211yesmaximal, characteristic
5#13067090C211yesmaximal, characteristic
6#13066478C211yesmaximal, characteristic
7C11×#1275C211yesmaximal, characteristic
8#10623001C2211yescharacteristic
9#10623001C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C2×C11×#97C2211yescharacteristic
13#10622539C2211yescharacteristic
14#10622539C2211yescharacteristic
15#10622442—22no—
16#10622441—22no—
17#10622336—22no—
18#10622333—22no—
19#10622295C411yescharacteristic
20#10622294C411yescharacteristic
21#10622294C411yescharacteristic
22#10622293C411yescharacteristic
23#10622292—21no—
24C8×Dic22—21no—
25#10622103—22no—
26#10622103—22no—
27#10622094—21no—
28#10622094—21no—
29C22×C8×C11—21no—
30C2×C42×C11C2311yescharacteristic
31#66979—21no—
32#66979D412yes—
33#66977—21no—
34#66977—21no—
35#66977—21no—
36#66977—21no—
37#66923—21no—
38#66923D412yes—
39#66922C2×C411yescharacteristic
40#66922C2×C411yescharacteristic
41#66922C2×C411yescharacteristic
42#66922C2×C411yescharacteristic
43C4×Dic22—21no—
44C4×Dic22—21no—
45C4×Dic22—21no—
46C4×Dic22—21no—
47C11×C4⋊C8—21no—
48C11×C4⋊C8—21no—
49C11×C22⋊C8—21no—
50C11×C22⋊C8—21no—
51C11×#97—21no—
52C11×#97—21no—
53C4×C8×C11C2×C411yescharacteristic
54C4×C8×C11C2×C411yescharacteristic
55C4×C8×C11D411yescharacteristic
56C4×C8×C11D411yescharacteristic
57C22⋊(C11⋊C8)—21no—
58C22⋊(C11⋊C8)—21no—
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#66867D412yes—
71#9286—111nomaximal, Sylow
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11#4111yescharacteristic
74C22×C4×C11#4111yescharacteristic
75C2×Dic22—21no—
76C2×Dic22—21no—
77C2×Dic22—21no—
78C2×Dic22—21no—
79C2×C8×C11—22no—
80C2×C8×C11—21no—
81C2×C8×C11—21no—
82C2×C8×C11—21no—
83C2×C8×C11—21no—
84C2×C8×C11—41no—
85C2×C8×C11—41no—
86C42×C11C22×C411yescharacteristic
87C42×C11C2×D411yescharacteristic
88C42×C11C2×D411yescharacteristic
89C42×C11C2×D411yescharacteristic
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⋊Dic11C22⋊C412yes—
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#1531—111no—
111#1531—111no—
112#1497—111no—
113#1287—111no—
114#1275D1111yescharacteristic
115C23×C11#12311yescharacteristic
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11C2×C22⋊C411yescharacteristic
121C2×C4×C11C4×D411yescharacteristic
122C2×C4×C11C4×D411yescharacteristic
123C2×C4×C11#12011yescharacteristic
124C2×C4×C11#12111yescharacteristic
125C2×C4×C11#12111yescharacteristic
126C2×Dic11—22no—
127C2×Dic11—22no—
128C2×Dic11—41no—
129C2×Dic11—41no—
130Dic22—41no—
131Dic22—41no—
132Dic22—42no—
133Dic22—41no—
134Dic22—41no—
135Dic22—81no—
136C8×C11—41no—
137C8×C11—41no—
138C8×C11—41no—
139C8×C11—41no—
140C8×C11—42no—
141C11⋊C8—42no—
142C11⋊C8—81no—
143#533—111no—
144#533—111no—
145#500—111no—
146#498—111no—
147#487—111no—
148#487—111no—
149#485—222no—
150#479—222no—
151#446—222no—
152#446—221no—
153C8×Q8—221no—
154#433—222no—
155#432—111no—
156#432—111no—
157#431C2×D1111yescharacteristic
158#431C2×D1111yescharacteristic
159C2×#97C2×D1111yescharacteristic
160#330—222no—
161#330—222no—
162Q8⋊C8—221no—
163Q8⋊C8—221no—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11—21no—
167C22×C11#38611yescharacteristic
168C4×C11—21no—
169C4×C11—21no—
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11#44311yescharacteristic
174C4×C11#44411yescharacteristic
175Dic11—42no—
176Dic11—42no—
177Dic11—81no—
178Dic11—81no—
179C22×C8—21no—
180C4⋊Q8—111no—
181C4⋊Q8—111no—
182C4⋊Q8—111no—
183C4⋊Q8—111no—
184#125—112no—
185#125—221no—
186C22⋊Q8—221no—
187C22⋊Q8—221no—
188C22⋊Q8—221no—
189C22⋊Q8—221no—
190C4×Q8—221no—
191C4×Q8—221no—
192C4×Q8—221no—
193C4×Q8—221no—
194#117—112no—
195#117—221no—
196C2×C42C22×D1111yescharacteristic
197#107—222no—
198#106—222no—
199C4⋊C8—21no—
200C4⋊C8—21no—
201C4⋊C8—222no—
202C4⋊C8—222no—
203C4⋊C8—221no—
204C4⋊C8—221no—
205#103—222no—
206#103—222no—
207C22⋊C8—21no—
208C22⋊C8—21no—
209C22⋊C8—221no—
210C22⋊C8—221no—
211#97—21no—
212#97—21no—
213#97—112no—
214#97—222no—
215#97—221no—
216C4×C8—222no—
217C4×C8C4×D1111yescharacteristic
218C4×C8C4×D1111yescharacteristic
219C4×C8D4411yescharacteristic
220C4×C8D4411yescharacteristic
221C2×C11—41no—
222C2×C11#187611yescharacteristic
223C2×C11#190211yescharacteristic
224C2×C11#191211yescharacteristic
225C2×Q8—221no—
226C2×Q8—221no—
227C2×Q8—221no—
228C2×Q8—221no—
229C22×C4#433911yescharacteristic
230C22×C4D4×D1111yescharacteristic
231C22×C4#434311yescharacteristic
232C2×C8—22no—
233C2×C8—21no—
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—21no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—222no—
240C2×C8—441no—
241C4⋊C4—112no—
242C4⋊C4—112no—
243C4⋊C4—221no—
244C4⋊C4—222no—
245C4⋊C4—221no—
246C4⋊C4—222no—
247C4⋊C4—221no—
248C4⋊C4—221no—
249C4⋊C4—221no—
250C4⋊C4—221no—
251C4⋊C4—441no—
252C4⋊C4—441no—
253C22⋊C4—222no—
254C22⋊C4—441no—
255C42—222no—
256C42—441no—
257C42C2×C4×D1111yescharacteristic
258C42C2×D4411yescharacteristic
259C42D4×D1111yescharacteristic
260C42D4×D1111yescharacteristic
261C11#928611yescharacteristic, complemented, Sylow
262C23#6694711yescharacteristic
263Q8—442no—
264Q8—441no—
265Q8—441no—
266Q8—441no—
267Q8—441no—
268Q8—881no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—222no—
274C2×C4—222no—
275C2×C4—441no—
276C2×C4—441no—
277C2×C4C4×D4411yescharacteristic
278C2×C4C22⋊C4×D1111yescharacteristic
279C2×C4#6693511yescharacteristic
280C2×C4#6693711yescharacteristic
281C2×C4#6694611yescharacteristic
282C2×C4#6694811yescharacteristic
283C8—42no—
284C8—41no—
285C8—41no—
286C8—41no—
287C8—41no—
288C8—442no—
289C8—881no—
290C22—21no—
291C22—21no—
292C22—21no—
293C22#1062227811yescharacteristic
294C4—21no—
295C4—21no—
296C4—21no—
297C4—21no—
298C4—21no—
299C4—442no—
300C4—442no—
301C4—881no—
302C4—881no—
303C4#1062231311yescharacteristic
304C4#1062233011yescharacteristic
305C2—41no—
306C2#1306894211yescharacteristic
307C2#1306909011yescharacteristic
308C2#1306915211yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1275C2
socleC22×C11#386
prime radicalC23×C11#123
cosocleC2×C42×C11C23
hypercenter#1275D11
hypocenterC11#9286
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1275

Complements

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

NH ≅ G/Ntype
261. C11#9286semidirect

Maximal subgroups

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

subgroupindex
#130797772
#130777102
#130672302
#130670902
#130664782
C11×#12752
#928611