Finite Group Databasebeta

← #14721524

Subgroups — #14721524

Order 2816.

938 conjugacy classes of subgroups; only the 355 normal subgroups are shown.

normal subgroups only

This group has 938 conjugacy classes of subgroups — too many to draw. Only its 355 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#13082426C211yesmaximal, characteristic
2#13077697C211yesmaximal, characteristic
3#13067179C216yesmaximal
4#13067114C216yesmaximal
5C11×#2351C211yesmaximal, characteristic
6C2×C4×Q8×C11—21no—
7C2×C4×Q8×C11C2211yescharacteristic
8#10623343—21no—
9#10623101C414yescomplemented
10#10623100—24no—
11Q8×Dic22C414yescomplemented
12#10623031—23no—
13#10623001C2216yes—
14C11×#389—23no—
15C11×#382C2213yes—
16C4×C11×C4⋊C4C2213yes—
17Q8×C11⋊C8—24no—
18#10622538C2216yes—
19#10622090C2214yes—
20#10622090C22112yes—
21C22×Q8×C11D411yescharacteristic
22C4×Q8×C11—44no—
23C4×Q8×C11C2×C414yes—
24C4×Q8×C11D414yes—
25C2×C11×C4⋊C4—23no—
26C2×C11×C4⋊C4—23no—
27C2×C11×C4⋊C4D413yes—
28C2×C42×C11—23no—
29C2×C42×C11C2313yes—
30Q8×Dic11—24no—
31Q8×Dic11—24no—
32#66979—26no—
33#66977—26no—
34#66977C2314yes—
35#66943—212no—
36#66941—212no—
37#66923—26no—
38#66922C2×C416yes—
39#66922C2×C416yes—
40C4×Dic22—26no—
41C4×Dic22C2×C4112yes—
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×C11C22⋊C414yes—
50C2×Q8×C11SD1614yes—
51C2×Q8×C11Q1614yes—
52C22×C4×C11—21no—
53C22×C4×C11—23no—
54C22×C4×C11C2×D413yes—
55C22×C4×C11C2×D413yes—
56C22×C4×C11C2411yescharacteristic
57C2×Dic22—26no—
58C2×Dic22C22×C414yes—
59C11×C4⋊C4—46no—
60C11×C4⋊C4—46no—
61C11×C4⋊C4C22⋊C4112yes—
62C42×C11—46no—
63C42×C11C22×C416yes—
64C42×C11C2×D416yes—
65C22⋊Dic11—24no—
66C4⋊Dic11—26no—
67C4⋊Dic11—26no—
68C4⋊Dic11—26no—
69C4⋊Dic11C22×C414yes—
70Dic11⋊C4—212no—
71Dic11⋊C4—24no—
72C4×Dic11—212no—
73C2×C11⋊C8—24no—
74#3502—111no—
75#2982—111no—
76#2351D1111yescharacteristic
77#1518—116no—
78#1503—116no—
79C23×C11C22×D411yescharacteristic
80Q8×C11#103116yes—
81C2×C4×C11—22no—
82C2×C4×C11—43no—
83C2×C4×C11—41no—
84C2×C4×C11—41no—
85C2×C4×C11—41no—
86C2×C4×C11—43no—
87C2×C4×C11—43no—
88C2×C4×C11—43no—
89C2×C4×C11C2×C22⋊C416yes—
90C2×C4×C11C2×C22⋊C416yes—
91C2×C4×C11C2×SD1616yes—
92C2×C4×C11C2×Q1616yes—
93C2×C4×C11C23×C411yescharacteristic
94C2×C4×C11C22×D411yescharacteristic
95C2×Dic11—24no—
96C2×Dic11—24no—
97Dic22—44no—
98Dic22—86no—
99C11⋊C8—44no—
100Q82—114no—
101#557—114no—
102#557—224no—
103#544—223no—
104#533—116no—
105#519—221no—
106C2×C4×Q8—21no—
107C2×C4×Q8C2×D1111yescharacteristic
108C8×Q8—224no—
109#431—116no—
110#389—23no—
111#382C2×D1113yes—
112C4×C4⋊C4C2×D1113yes—
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—42no—
124C4×C11—83no—
125C4×C11C2×#103112yes—
126Dic11—44no—
127Dic11—44no—
128C22×Q8C22⋊D1111yescharacteristic
129C4⋊Q8—116no—
130C4⋊Q8—116no—
131C4⋊Q8—2212no—
132#125—2212no—
133#125—226no—
134C22⋊Q8—114no—
135C22⋊Q8—226no—
136C4×Q8—44no—
137C4×Q8—1112no—
138C4×Q8—224no—
139C4×Q8—224no—
140C4×Q8—226no—
141C4×Q8C4×D1114yes—
142C4×Q8D4414yes—
143#117—226no—
144C2×C4⋊C4—23no—
145C2×C4⋊C4—23no—
146C2×C4⋊C4C22⋊D1113yes—
147C2×C42—23no—
148C2×C42C22×D1113yes—
149C4⋊C8—226no—
150C22⋊C8—114no—
151C4×C8—226no—
152#95—23no—
153#95C22×D1111yescharacteristic
154#95C22×D1113yes—
155C2×C11—21no—
156C2×C11—21no—
157C2×C11#288411yescharacteristic
158C2×C11C22×#10311yescharacteristic
159C2×C11#290111yescharacteristic
160C2×Q8—114no—
161C2×Q8—226no—
162C2×Q8(C2×D11)⋊C414yes—
163C2×Q8#432414yes—
164C2×Q8#432614yes—
165C22×C4—21no—
166C22×C4—23no—
167C22×C4C2×C22⋊D1113yes—
168C22×C4C2×C22⋊D1113yes—
169C22×C4C23×D1111yescharacteristic
170C2×C8—224no—
171C4⋊C4—46no—
172C4⋊C4—46no—
173C4⋊C4—114no—
174C4⋊C4—226no—
175C4⋊C4—226no—
176C4⋊C4—2212no—
177C4⋊C4—226no—
178C4⋊C4—224no—
179C4⋊C4(C2×D11)⋊C4112yes—
180C22⋊C4—224no—
181C42—46no—
182C42—2212no—
183C42C2×C4×D1116yes—
184C42C2×D4416yes—
185C11#1761911yescharacteristic, complemented, Sylow
186C23C22×C22⋊D1111yescharacteristic
187Q8—444no—
188Q8—886no—
189Q8#66874116yes—
190C2×C4—22no—
191C2×C4—43no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—43no—
196C2×C4—43no—
197C2×C4—43no—
198C2×C4—224no—
199C2×C4—224no—
200C2×C4C2×(C2×D11)⋊C416yes—
201C2×C4C2×(C2×D11)⋊C416yes—
202C2×C4C2×#432416yes—
203C2×C4C2×#432616yes—
204C2×C4C22×C4×D1111yescharacteristic
205C2×C4C22×D4411yescharacteristic
206C8—444no—
207C22—21no—
208C22—21no—
209C22C22×(C2×D11)⋊C411yescharacteristic
210C22C22×#432411yescharacteristic
211C22C22×#432611yescharacteristic
212C4—21no—
213C4—21no—
214C4—26no—
215C4—42no—
216C4—83no—
217C4—444no—
218C4—444no—
219C4C2×#66874112yes—
220C2—21no—
221C2—21no—
222C2#1307707911yescharacteristic
223C2C22×#6687411yescharacteristic
224C2#1307716411yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2351C2
socleC22×C11C22×C22⋊C4
prime radicalC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenter#2351D11
hypocenterC11#17619
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ #2351

Complements

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

NH ≅ G/Ntype
9. #10623101C4semidirect
11. Q8×Dic22C4semidirect
185. C11#17619semidirect

Maximal subgroups

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

subgroupindex
#130824262
#130776972
#130671792
#130671142
C11×#23512
#1761911