Finite Group Databasebeta

← #14647263

Subgroups — #14647263

Order 2816.

450 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 107 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#13066950C212yesmaximal
2#13066472C214yesmaximal, complemented
3C11×#2296C211yesmaximal, characteristic
4C2×C11×#117C411yescharacteristic
5C2×C11×#117C2211yescharacteristic
6C22×C42×C11C411yescharacteristic
7C11×#389—22no—
8C11×#385—22no—
9C4×C11×C4⋊C4C412yes—
10C4×C11×C4⋊C4C2212yes—
11#10622539C2214yes—
12#10622166—22no—
13#10622163—22no—
14C23×C4×C11—21no—
15C23×C4×C11C2×C411yescharacteristic
16C11×#117—24no—
17C11×#117—42no—
18C2×C11×C4⋊C4—21no—
19C2×C11×C4⋊C4—22no—
20C2×C11×C4⋊C4—22no—
21C2×C11×C4⋊C4D412yes—
22C2×C11×C22⋊C4—21no—
23C2×C11×C22⋊C4D412yes—
24C2×C42×C11—21no—
25C2×C42×C11—42no—
26C2×C42×C11C2×C411yescharacteristic
27C2×C42×C11C2×C412yes—
28C2×C42×C11C2×C412yes—
29C2×C42×C11C2311yescharacteristic
30C11×#95—22no—
31C11×#95—22no—
32C22⋊(C11⋊C8)—24no—
33C4⋊(C11⋊C8)—24no—
34#66867—24no—
35#8743—111nomaximal, Sylow
36C24×C11C22⋊C411yescharacteristic
37C22×C4×C11—22no—
38C22×C4×C11—22no—
39C22×C4×C11—22no—
40C22×C4×C11—22no—
41C22×C4×C11—22no—
42C22×C4×C11—44no—
43C22×C4×C11—42no—
44C22×C4×C11C22⋊C411yescharacteristic
45C22×C4×C11C22⋊C412yes—
46C22×C4×C11C22×C411yescharacteristic
47C22×C4×C11C2×D412yes—
48C11×C4⋊C4—24no—
49C11×C4⋊C4—44no—
50C11×C4⋊C4—44no—
51C11×C4⋊C4—42no—
52C11×C22⋊C4—24no—
53C11×C22⋊C4—42no—
54C42×C11—22no—
55C42×C11—42no—
56C42×C11—42no—
57C42×C11—42no—
58C42×C11#4114yes—
59C2×C11⋊C8—44no—
60#2296D1111yescharacteristic
61#1464—112no—
62#1285—114no—
63C23×C11—21no—
64C23×C11—21no—
65C23×C11—42no—
66C23×C11#10112yes—
67C23×C11C2×C22⋊C411yescharacteristic
68C2×C4×C11—28no—
69C2×C4×C11—21no—
70C2×C4×C11—21no—
71C2×C4×C11—21no—
72C2×C4×C11—21no—
73C2×C4×C11—24no—
74C2×C4×C11—22no—
75C2×C4×C11—42no—
76C2×C4×C11—42no—
77C2×C4×C11—48no—
78C2×C4×C11—42no—
79C2×C4×C11—42no—
80C2×C4×C11—42no—
81C2×C4×C11—42no—
82C2×C4×C11—42no—
83C2×C4×C11#10012yes—
84C2×C4×C11#11712yes—
85C2×C4×C11#12314yes—
86C11⋊C8—84no—
87C2×#117Dic1111yescharacteristic
88C2×#117C2×D1111yescharacteristic
89C22×C42Dic1111yescharacteristic
90#432—114no—
91#389—22no—
92#385—22no—
93C4×C4⋊C4Dic1112yes—
94C4×C4⋊C4C2×D1112yes—
95#324—222no—
96#323—222no—
97C22×C11—22no—
98C22×C11—22no—
99C22×C11—42no—
100C22×C11—42no—
101C22×C11—42no—
102C22×C11#38111yescharacteristic
103C22×C11C2×#10011yescharacteristic
104C22×C11C2×#10111yescharacteristic
105C4×C11—22no—
106C4×C11—22no—
107C4×C11—24no—
108C4×C11—44no—
109C4×C11—42no—
110C4×C11—82no—
111C23×C4—21no—
112C23×C4C2×Dic1111yescharacteristic
113#117—24no—
114#117—42no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—22no—
117C2×C4⋊C4—22no—
118C2×C4⋊C4C22⋊D1112yes—
119C2×C22⋊C4—21no—
120C2×C22⋊C4C22⋊D1112yes—
121C2×C42—21no—
122C2×C42—42no—
123C2×C42C2×Dic1111yescharacteristic
124C2×C42C2×Dic1112yes—
125C2×C42C2×Dic1112yes—
126C2×C42C22×D1111yescharacteristic
127C4⋊C8—224no—
128C22⋊C8—224no—
129#97—224no—
130#95—22no—
131#95—22no—
132C2×C11—21no—
133C2×C11—21no—
134C2×C11—42no—
135C2×C11#182111yescharacteristic
136C2×C11#182712yes—
137C24C22⋊Dic1111yescharacteristic
138C22×C4—22no—
139C22×C4—22no—
140C22×C4—22no—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—44no—
144C22×C4—42no—
145C22×C4C22⋊Dic1111yescharacteristic
146C22×C4C22⋊Dic1112yes—
147C22×C4C22×Dic1111yescharacteristic
148C22×C4C2×C22⋊D1112yes—
149C2×C8—444no—
150C4⋊C4—24no—
151C4⋊C4—44no—
152C4⋊C4—44no—
153C4⋊C4—42no—
154C22⋊C4—24no—
155C22⋊C4—42no—
156C42—22no—
157C42—42no—
158C42—42no—
159C42—42no—
160C42#433914yes—
161C11#874311yescharacteristic, complemented, Sylow
162C23—21no—
163C23—21no—
164C23—42no—
165C23#6690012yes—
166C23C2×C22⋊Dic1111yescharacteristic
167C2×C4—28no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—24no—
173C2×C4—22no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—48no—
177C2×C4—42no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4#6689712yes—
183C2×C4#6697912yes—
184C2×C4#6698214yes—
185C8—884no—
186C22—22no—
187C22—22no—
188C22—42no—
189C22—42no—
190C22—42no—
191C22#1062282411yescharacteristic
192C22C2×#6689711yescharacteristic
193C22C2×#6690011yescharacteristic
194C4—22no—
195C4—22no—
196C4—24no—
197C4—44no—
198C4—42no—
199C4—82no—
200C2—21no—
201C2—21no—
202C2—42no—
203C2#1306869611yescharacteristic
204C2#1306872012yes—
subgroupG/H
centerC22#10622824
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2296C2
socleC22×C11#381
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#2296D11
hypocenterC11#8743
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2296

Complements

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

NH ≅ G/Ntype
2. #13066472C2semidirect
161. C11#8743semidirect

Maximal subgroups

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

subgroupindex
#130669502
#130664722
C11×#22962
#874311