Finite Group Databasebeta

← #14721525

Subgroups — #14721525

Order 2816.

938 conjugacy classes of subgroups; only the 395 normal subgroups are shown.

normal subgroups only

This group has 938 conjugacy classes of subgroups — too many to draw. Only its 395 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#13077697C211yesmaximal, characteristic
2#13071537C211yesmaximal, characteristic
3#13067180C216yesmaximal
4#13067115C216yesmaximal
5C11×#3502C211yesmaximal, characteristic
6Q82×C11C414yescomplemented
7C11×#557—24no—
8C11×#557C414yescomplemented
9C11×#544—23no—
10C11×#533C2216yes—
11C11×#519—21no—
12C2×C4×Q8×C11C2211yescharacteristic
13C2×Q8×Dic11—21no—
14Q8×C11⋊C8—24no—
15#10622598—23no—
16#10622549C2213yes—
17C4×C4⋊Dic11C2213yes—
18#10622538C2216yes—
19#10622176C2214yes—
20#10622176C22112yes—
21C22×Q8×C11D411yescharacteristic
22C11×C4⋊Q8—212no—
23C11×C4⋊Q8C2×C416yes—
24C11×C4⋊Q8C2×C416yes—
25C11×#125—212no—
26C11×#125—26no—
27C11×C22⋊Q8—26no—
28C11×C22⋊Q8C2314yes—
29C4×Q8×C11—24no—
30C4×Q8×C11—24no—
31C4×Q8×C11—26no—
32C4×Q8×C11C2×C4112yes—
33C4×Q8×C11C2×C414yes—
34C4×Q8×C11D414yes—
35C11×#117—26no—
36C2×C11×C4⋊C4D413yes—
37C2×C42×C11C2313yes—
38Q8×Dic11—44no—
39C2×C4⋊Dic11—23no—
40C2×C4⋊Dic11—23no—
41C2×C4×Dic11—23no—
42C11⋊#95—23no—
43C11⋊#95C2311yescharacteristic
44C11⋊#95C2313yes—
45C22⋊(C11⋊C8)C2314yes—
46C4⋊(C11⋊C8)—26no—
47C4×C11⋊C8—26no—
48#17619—111nomaximal, Sylow
49C2×Q8×C11—26no—
50C2×Q8×C11C22⋊C414yes—
51C2×Q8×C11SD1614yes—
52C2×Q8×C11Q1614yes—
53C2×Q8×C11C22×C414yes—
54C22×C4×C11C2×D413yes—
55C22×C4×C11C2×D413yes—
56C22×C4×C11C2411yescharacteristic
57C22×Dic11—21no—
58C22×Dic11—23no—
59C11×C4⋊C4—26no—
60C11×C4⋊C4—26no—
61C11×C4⋊C4—26no—
62C11×C4⋊C4—212no—
63C11×C4⋊C4—24no—
64C11×C4⋊C4C22⋊C4112yes—
65C11×C4⋊C4C22×C414yes—
66C11×C22⋊C4—24no—
67C42×C11—212no—
68C42×C11C22×C416yes—
69C42×C11C2×D416yes—
70C4⋊Dic11—46no—
71C4⋊Dic11—46no—
72C4×Dic11—46no—
73C2×C11⋊C8—24no—
74#3502D1111yescharacteristic
75#2982—111no—
76#2351—111no—
77#1518—116no—
78#1503—116no—
79C23×C11C22×D411yescharacteristic
80Q8×C11—44no—
81Q8×C11—86no—
82Q8×C11#103116yes—
83C2×C4×C11—24no—
84C2×C4×C11—24no—
85C2×C4×C11—43no—
86C2×C4×C11—41no—
87C2×C4×C11C2×C22⋊C416yes—
88C2×C4×C11C2×C22⋊C416yes—
89C2×C4×C11C2×SD1616yes—
90C2×C4×C11C2×Q1616yes—
91C2×C4×C11C23×C411yescharacteristic
92C2×C4×C11C22×D411yescharacteristic
93C2×Dic11—22no—
94C2×Dic11—41no—
95C2×Dic11—41no—
96C2×Dic11—43no—
97C2×Dic11—43no—
98C2×Dic11—43no—
99C11⋊C8—44no—
100Q82Dic1114yescomplemented
101#557—24no—
102#557Dic1114yescomplemented
103#544—23no—
104#533C2×D1116yes—
105#519—21no—
106C2×C4×Q8—221no—
107C2×C4×Q8C2×D1111yescharacteristic
108C8×Q8—224no—
109#431—116no—
110#389—223no—
111#382—113no—
112C4×C4⋊C4—113no—
113#328—114no—
114#328—1112no—
115C22×C11—21no—
116C22×C11—21no—
117C22×C11C22×C22⋊C411yescharacteristic
118C22×C11C22×SD1611yescharacteristic
119C22×C11C22×Q1611yescharacteristic
120C4×C11—21no—
121C4×C11—21no—
122C4×C11—26no—
123C4×C11—44no—
124C4×C11—44no—
125C4×C11C2×#103112yes—
126Dic11—42no—
127Dic11—83no—
128C22×Q8C22⋊D1111yescharacteristic
129C4⋊Q8—212no—
130C4⋊Q8C2×Dic1116yes—
131C4⋊Q8C2×Dic1116yes—
132#125—212no—
133#125—26no—
134C22⋊Q8—26no—
135C22⋊Q8C22×D1114yes—
136C4×Q8—24no—
137C4×Q8—24no—
138C4×Q8—26no—
139C4×Q8—444no—
140C4×Q8C2×Dic11112yes—
141C4×Q8C2×Dic1114yes—
142C4×Q8C22⋊D1114yes—
143#117—26no—
144C2×C4⋊C4—223no—
145C2×C4⋊C4—223no—
146C2×C4⋊C4C22⋊D1113yes—
147C2×C42—223no—
148C2×C42C22×D1113yes—
149C4⋊C8—226no—
150C22⋊C8—114no—
151C4×C8—226no—
152#95—111no—
153#95—113no—
154#95—223no—
155C2×C11—21no—
156C2×C11—21no—
157C2×C11#288411yescharacteristic
158C2×C11C22×#10311yescharacteristic
159C2×C11#290111yescharacteristic
160C2×Q8—26no—
161C2×Q8#432514yes—
162C2×Q8#432614yes—
163C2×Q8C22⋊Dic1114yes—
164C2×Q8C22×Dic1114yes—
165C22×C4—221no—
166C22×C4—223no—
167C22×C4C2×C22⋊D1113yes—
168C22×C4C2×C22⋊D1113yes—
169C22×C4C23×D1111yescharacteristic
170C2×C8—224no—
171C4⋊C4—26no—
172C4⋊C4—26no—
173C4⋊C4—26no—
174C4⋊C4—212no—
175C4⋊C4—24no—
176C4⋊C4—446no—
177C4⋊C4—446no—
178C4⋊C4C22⋊Dic11112yes—
179C4⋊C4C22×Dic1114yes—
180C22⋊C4—24no—
181C42—212no—
182C42—446no—
183C42C22×Dic1116yes—
184C42C2×C22⋊D1116yes—
185C11#1761911yescharacteristic, complemented, Sylow
186C23C22×C22⋊D1111yescharacteristic
187Q8—44no—
188Q8—86no—
189Q8#66899116yes—
190C2×C4—24no—
191C2×C4—24no—
192C2×C4—43no—
193C2×C4—41no—
194C2×C4—222no—
195C2×C4—441no—
196C2×C4—441no—
197C2×C4—443no—
198C2×C4—443no—
199C2×C4—443no—
200C2×C4C2×#432516yes—
201C2×C4C2×#432616yes—
202C2×C4C2×C22⋊Dic1116yes—
203C2×C4C2×C22⋊Dic1116yes—
204C2×C4C23×Dic1111yescharacteristic
205C2×C4C22×C22⋊D1111yescharacteristic
206C8—444no—
207C22—21no—
208C22—21no—
209C22C22×#432511yescharacteristic
210C22C22×#432611yescharacteristic
211C22C22×C22⋊Dic1111yescharacteristic
212C4—21no—
213C4—21no—
214C4—26no—
215C4—44no—
216C4—44no—
217C4—442no—
218C4—883no—
219C4C2×#66899112yes—
220C2—21no—
221C2—21no—
222C2#1307708011yescharacteristic
223C2C22×#6689911yescharacteristic
224C2#1307716311yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#3502C2
socleC22×C11C22×C22⋊C4
prime radicalC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenter#3502D11
hypocenterC11#17619
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ #3502

Complements

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

NH ≅ G/Ntype
6. Q82×C11C4semidirect
8. C11×#557C4semidirect
100. Q82Dic11semidirect
102. #557Dic11semidirect
185. C11#17619semidirect

Maximal subgroups

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

subgroupindex
#130776972
#130715372
#130671802
#130671152
C11×#35022
#1761911