Finite Group Databasebeta

← #14664310

Subgroups — #14664310

Order 2816.

304 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 65 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#13079228C211yesmaximal, characteristic
2#13070429C211yesmaximal, characteristic, complemented
3#13068372C211yesmaximal, characteristic, complemented
4#13066609C211yesmaximal, characteristic, complemented
5#13066605C211yesmaximal, characteristic, complemented
6#13066601C211yesmaximal, characteristic
7C11×#1341C211yesmaximal, characteristic
8#10623134—21no—
9C11×#469C2211yescharacteristic
10#10622768C411yescharacteristic, complemented
11#10622765C411yescharacteristic, complemented
12#10622750C2211yescharacteristic
13#10622735—21no—
14#10622735C2211yescharacteristic
15#10622654—21no—
16#10622468C411yescharacteristic, complemented
17#10622466C411yescharacteristic, complemented
18#10622378—21no—
19#10622371—21no—
20C11×#349C2211yescharacteristic
21C11×#338C2211yescharacteristic
22#10622195—21no—
23#10622195C2211yescharacteristic
24#10622191C2211yescharacteristic
25#10622150—21no—
26#10622149—21no—
27C2×C11×D8C2×C411yescharacteristic
28C2×C11×M16—21no—
29C2×C11×M16C2311yescharacteristic
30C11×#121—21no—
31#66989—21no—
32#66989—41no—
33#66988—41no—
34D4×Dic11—21no—
35C2×#4324—21no—
36#66979—21no—
37#66979D411yescharacteristic
38#66977—21no—
39C22×C11⋊C8D411yescharacteristic
40C2×Dic44C2×C411yescharacteristic
41#66941—21no—
42#66940—21no—
43#66932—41no—
44#66931—41no—
45C11×M32—21no—
46C11×#106C2×C411yescharacteristic
47C11×#102—21no—
48#66896—21no—
49#66881C2×C411yescharacteristic
50#66880—21no—
51#66879—22no—
52#66879C2×C411yescharacteristic
53#66879D411yescharacteristic
54C8×Dic11—22no—
55C8×Dic11C2×C411yescharacteristic
56C8×Dic11D411yescharacteristic
57#66876—21no—
58#66874—21no—
59#66872—21no—
60#11769—111nomaximal, Sylow
61C2×D4×C11—21no—
62C2×D4×C11—41no—
63C22×C4×C11C2×D411yescharacteristic
64C22×Dic11—41no—
65C2×Dic22—21no—
66C2×Dic22—41no—
67C11×D8—41no—
68C11×M16—41no—
69C11×M16—41no—
70C11×M16—41no—
71C2×C8×C11—22no—
72C2×C8×C11C22×C411yescharacteristic
73C2×C8×C11C2×D411yescharacteristic
74C11×C4⋊C4—21no—
75C11×C22⋊C4—41no—
76C22⋊Dic11—21no—
77C22⋊Dic11—41no—
78C22⋊Dic11—41no—
79C22⋊Dic11—41no—
80C22⋊Dic11—41no—
81C22⋊Dic11—41no—
82#4324—41no—
83#4324—41no—
84C4⋊Dic11—21no—
85C4⋊Dic11—21no—
86C4⋊Dic11—41no—
87Dic11⋊C4—41no—
88Dic11⋊C4—41no—
89Dic11⋊C4—41no—
90C4×Dic11—22no—
91C4×Dic11—41no—
92C4×Dic11C22⋊C411yescharacteristic
93C4×Dic11C22⋊C411yescharacteristic
94C2×C11⋊C8—21no—
95C2×C11⋊C8—21no—
96C2×C11⋊C8C22⋊C411yescharacteristic
97C2×C11⋊C8C22⋊C411yescharacteristic
98Dic44—41no—
99C11×C16—41no—
100C11⋊C16—41no—
101#3173—111no—
102#2166—111no—
103#1747—111no—
104#1342—111no—
105#1341D1111yescharacteristic
106#1340—111no—
107#1339—111no—
108C23×C11—41no—
109C23×C11AGL(1,ℤ/8)11yescharacteristic
110D4×C11—41no—
111D4×C11—41no—
112D4×C11—161no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—41no—
116C2×C4×C11C2×C22⋊C411yescharacteristic
117C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
118C2×Dic11—21no—
119C2×Dic11—21no—
120C2×Dic11—42no—
121C2×Dic11—41no—
122C2×Dic11—41no—
123C2×Dic11—161no—
124Dic22—41no—
125Dic22—41no—
126Dic22—161no—
127C8×C11—21no—
128C8×C11—21no—
129C8×C11—42no—
130C11⋊C8—21no—
131C11⋊C8#10411yescharacteristic
132C11⋊C8#10411yescharacteristic
133#542—221no—
134#498—111no—
135#495—111no—
136#489—221no—
137#470—111no—
138#469C2×D1111yescharacteristic
139#465—221no—
140#442—111no—
141#441—111no—
142C4×SD16—221no—
143#405—111no—
144#405—221no—
145#364—221no—
146#349—111no—
147#349C2×D1111yescharacteristic
148#347—221no—
149#338C2×D1111yescharacteristic
150H(3,ℤ/4)—111no—
151H(3,ℤ/4)—221no—
152C22×C11—21no—
153C22×C11—41no—
154C22×C11—81no—
155C22×C11—81no—
156C22×C11—81no—
157C22×C11#41811yescharacteristic
158C4×C11—21no—
159C4×C11—81no—
160C4×C11#41011yescharacteristic
161C4×C11C2×#10411yescharacteristic
162Dic11—41no—
163Dic11—41no—
164Dic11—81no—
165Dic11—82no—
166Dic11—81no—
167C2×Q16—111no—
168C2×SD16—221no—
169C2×D8C4×D1111yescharacteristic
170C2×M16—21no—
171C2×M16C22×D1111yescharacteristic
172C22×C8—111no—
173C4⋊Q8—221no—
174#126—441no—
175#124—221no—
176#124—441no—
177#123—441no—
178C22⋊Q8—221no—
179C22⋊Q8—441no—
180#121—21no—
181C4×Q8—221no—
182C4×D4—221no—
183#117—111no—
184#117—221no—
185M32—21no—
186M32—221no—
187#106—111no—
188#106—221no—
189#106C4×D1111yescharacteristic
190#103—221no—
191#103—221no—
192#102—21no—
193#102—221no—
194#97—111no—
195#97—111no—
196#97—222no—
197C4×C8—111no—
198C4×C8—111no—
199C4×C8—222no—
200C2×C11—21no—
201C2×C11—41no—
202C2×C11—161no—
203C2×C11#150511yescharacteristic
204C2×Q8—221no—
205C2×Q8—441no—
206C2×D4—21no—
207C2×D4—41no—
208C22×C4—441no—
209C22×C4D4×D1111yescharacteristic
210Q16—441no—
211SD16—441no—
212SD16—441no—
213D8—41no—
214M16—41no—
215M16—41no—
216M16—41no—
217C2×C8—22no—
218C2×C8—111no—
219C2×C8—111no—
220C2×C8—221no—
221C2×C8—221no—
222C2×C8C2×C4×D1111yescharacteristic
223C2×C8D4×D1111yescharacteristic
224C4⋊C4—21no—
225C4⋊C4—221no—
226C4⋊C4—221no—
227C4⋊C4—441no—
228C4⋊C4—441no—
229C4⋊C4—441no—
230C4⋊C4—441no—
231C22⋊C4—41no—
232C22⋊C4—221no—
233C22⋊C4—441no—
234C22⋊C4—441no—
235C22⋊C4—441no—
236C22⋊C4—441no—
237C22⋊C4—441no—
238C42—111no—
239C42—111no—
240C42—222no—
241C42—441no—
242C16—41no—
243C16—441no—
244C11#1176911yescharacteristic, complemented, Sylow
245C23—41no—
246C23#6696711yescharacteristic
247Q8—441no—
248Q8—441no—
249Q8—1761no—
250D4—41no—
251D4—41no—
252D4—161no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—41no—
256C2×C4—221no—
257C2×C4—221no—
258C2×C4—442no—
259C2×C4—441no—
260C2×C4—441no—
261C2×C4—1761no—
262C2×C4C22⋊C4×D1111yescharacteristic
263C2×C4#6696411yescharacteristic
264C8—21no—
265C8—21no—
266C8—42no—
267C8—111no—
268C8—111no—
269C8—221no—
270C22—21no—
271C22—41no—
272C22—81no—
273C22—81no—
274C22—81no—
275C22#1062238311yescharacteristic
276C4—21no—
277C4—81no—
278C4—441no—
279C4—441no—
280C4—881no—
281C4—882no—
282C4—881no—
283C4#1062235311yescharacteristic
284C4D11×#10411yescharacteristic
285C2—21no—
286C2—41no—
287C2—161no—
288C2#1306712211yescharacteristic
subgroupG/H
centerC2#13067122
commutatorC2×C8×C11C22×C4
FrattiniC2×M16C22×D11
FittingC11×#1341C2
socleC2×C11#1505
prime radicalC11×#469C22
cosocleC2×C11×M16C23
hypercenter#1341D11
hypocenterC11#11769
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #1341

Complements

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

NH ≅ G/Ntype
2. #13070429C2semidirect
3. #13068372C2semidirect
4. #13066609C2semidirect
5. #13066605C2semidirect
10. #10622768C4semidirect
11. #10622765C4semidirect
16. #10622468C4semidirect
17. #10622466C4semidirect
244. C11#11769semidirect

Maximal subgroups

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

subgroupindex
#130792282
#130704292
#130683722
#130666092
#130666052
#130666012
C11×#13412
#1176911