Finite Group Databasebeta

← #14647210

Subgroups — #14647210

Order 2816.

514 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 155 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#13068596C212yesmaximal
2#13066499C212yesmaximal, complemented
3#13066499C212yesmaximal, complemented
4C11×#2285C211yesmaximal, characteristic
5C2×C11×#117C412yes—
6C22×C42×C11C2211yescharacteristic
7C11×#384C2211yescharacteristic
8C11×#384C2211yescharacteristic
9C11×#382C412yes—
10C11×#380—22no—
11C4×C11×C4⋊C4—22no—
12C2×C22⋊(C11⋊C8)—22no—
13C2×C4⋊(C11⋊C8)C2214yes—
14#10622162—22no—
15C23×C4×C11C2×C411yescharacteristic
16C23×C4×C11D412yes—
17C11×#117—44no—
18C2×C11×C4⋊C4—22no—
19C2×C11×C4⋊C4—22no—
20C2×C11×C4⋊C4C2×C412yes—
21C2×C11×C4⋊C4C2×C412yes—
22C2×C11×C22⋊C4—22no—
23C2×C42×C11—24no—
24C2×C42×C11—22no—
25C2×C42×C11C2×C411yescharacteristic
26C2×C42×C11D412yes—
27C2×C42×C11C2311yescharacteristic
28C22×C11⋊C8—24no—
29C11×#95—24no—
30C22⋊(C11⋊C8)—44no—
31C4⋊(C11⋊C8)—28no—
32#8728—111nomaximal, Sylow
33C24×C11C22⋊C411yescharacteristic
34C22×C4×C11—22no—
35C22×C4×C11—22no—
36C22×C4×C11—22no—
37C22×C4×C11—24no—
38C22×C4×C11—24no—
39C22×C4×C11—22no—
40C22×C4×C11—22no—
41C22×C4×C11—22no—
42C22×C4×C11—22no—
43C22×C4×C11C22⋊C412yes—
44C22×C4×C11C22⋊C411yescharacteristic
45C22×C4×C11C22×C411yescharacteristic
46C22×C4×C11C2×D412yes—
47C11×C4⋊C4—42no—
48C11×C4⋊C4—42no—
49C11×C4⋊C4—44no—
50C11×C4⋊C4—42no—
51C11×C4⋊C4—42no—
52C11×C22⋊C4—44no—
53C42×C11—22no—
54C42×C11—24no—
55C42×C11—44no—
56C42×C11#4114yes—
57C2×C11⋊C8—44no—
58C2×C11⋊C8—44no—
59C2×C11⋊C8—44no—
60#2285D1111yescharacteristic
61#1797—112no—
62#1296—112no—
63#1296—112no—
64C23×C11—21no—
65C23×C11—21no—
66C23×C11—22no—
67C23×C11—22no—
68C23×C11#10112yes—
69C23×C11C2×C22⋊C411yescharacteristic
70C2×C4×C11—28no—
71C2×C4×C11—21no—
72C2×C4×C11—21no—
73C2×C4×C11—21no—
74C2×C4×C11—21no—
75C2×C4×C11—22no—
76C2×C4×C11—22no—
77C2×C4×C11—22no—
78C2×C4×C11—44no—
79C2×C4×C11—44no—
80C2×C4×C11—42no—
81C2×C4×C11—42no—
82C2×C4×C11—44no—
83C2×C4×C11—44no—
84C2×C4×C11#10012yes—
85C2×C4×C11#11712yes—
86C2×C4×C11#12314yes—
87C2×C4×C11#13514yes—
88C2×C4×C11AGL(1,ℤ/8)12yes—
89C2×C4×C11#13712yes—
90C11⋊C8—84no—
91C2×#117Dic1112yes—
92C22×C42C2×D1111yescharacteristic
93C2×C4⋊C8—114no—
94C2×C22⋊C8—222no—
95#384C2×D1111yescharacteristic
96#384C2×D1111yescharacteristic
97#382Dic1112yes—
98#380—22no—
99C4×C4⋊C4—22no—
100#336—222no—
101C22×C11—24no—
102C22×C11—22no—
103C22×C11—41no—
104C22×C11—41no—
105C22×C11—42no—
106C22×C11#38111yescharacteristic
107C22×C11C2×#10011yescharacteristic
108C22×C11C2×#10111yescharacteristic
109C22×C11#41612yes—
110C22×C11#41712yes—
111C4×C11—22no—
112C4×C11—22no—
113C4×C11—42no—
114C4×C11—82no—
115C4×C11—82no—
116C4×C11#48214yes—
117C4×C11#48514yes—
118C23×C4C2×Dic1111yescharacteristic
119C23×C4C22⋊D1112yes—
120C22×C8—224no—
121#117—44no—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4C2×Dic1112yes—
125C2×C4⋊C4C2×Dic1112yes—
126C2×C22⋊C4—22no—
127C2×C42—24no—
128C2×C42—22no—
129C2×C42C2×Dic1111yescharacteristic
130C2×C42C22⋊D1112yes—
131C2×C42C22×D1111yescharacteristic
132C4⋊C8—228no—
133C22⋊C8—444no—
134#95—24no—
135C2×C11—42no—
136C2×C11#154311yescharacteristic
137C2×C11#155212yes—
138C2×C11#156011yescharacteristic
139C2×C11#182111yescharacteristic
140C2×C11#182512yes—
141C24C22⋊Dic1111yescharacteristic
142C22×C4—22no—
143C22×C4—22no—
144C22×C4—22no—
145C22×C4—24no—
146C22×C4—22no—
147C22×C4—24no—
148C22×C4—22no—
149C22×C4—22no—
150C22×C4—22no—
151C22×C4C22⋊Dic1112yes—
152C22×C4C22⋊Dic1111yescharacteristic
153C22×C4C22×Dic1111yescharacteristic
154C22×C4C2×C22⋊D1112yes—
155C2×C8—444no—
156C2×C8—444no—
157C2×C8—444no—
158C4⋊C4—42no—
159C4⋊C4—42no—
160C4⋊C4—42no—
161C4⋊C4—44no—
162C4⋊C4—42no—
163C22⋊C4—44no—
164C42—22no—
165C42—24no—
166C42—44no—
167C42#433914yes—
168C11#872811yescharacteristic, complemented, Sylow
169C23—21no—
170C23—21no—
171C23—22no—
172C23—22no—
173C23#6690012yes—
174C23C2×C22⋊Dic1111yescharacteristic
175C2×C4—28no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—44no—
184C2×C4—44no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—44no—
188C2×C4—44no—
189C2×C4#6689712yes—
190C2×C4#6697912yes—
191C2×C4#6698214yes—
192C2×C4#6700212yes—
193C2×C4#6700314yes—
194C2×C4#6700412yes—
195C8—884no—
196C22—24no—
197C22—22no—
198C22—41no—
199C22—41no—
200C22—42no—
201C22#1062282411yescharacteristic
202C22C2×#6689711yescharacteristic
203C22C2×#6690011yescharacteristic
204C22#1062284512yes—
205C22#1062284612yes—
206C4—22no—
207C4—22no—
208C4—42no—
209C4—82no—
210C4—82no—
211C4#1062260914yes—
212C4#1062261614yes—
213C2—42no—
214C2#1306727811yescharacteristic
215C2#1306731612yes—
216C2#1306735111yescharacteristic
217C2#1306869611yescharacteristic
218C2#1306871112yes—
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2285C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#2285D11
hypocenterC11#8728
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2285

Complements

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

NH ≅ G/Ntype
2. #13066499C2semidirect
3. #13066499C2semidirect
168. C11#8728semidirect

Maximal subgroups

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

subgroupindex
#130685962
#130664992
C11×#22852
#872811