Finite Group Databasebeta

← #14647189

Subgroups — #14647189

Order 2816.

630 conjugacy classes of subgroups; only the 195 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 195 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#13066499C214yesmaximal, complemented
3C2×C11×#384C211yesmaximal, characteristic
4C22×C11×C4⋊C4—22no—
5C22×C11×C4⋊C4C412yes—
6C22×C42×C11C2211yescharacteristic
7C11×#384—22no—
8C11×#384C412yes—
9C11×#384C2212yes—
10C2×C22⋊(C11⋊C8)—22no—
11C2×C4⋊(C11⋊C8)C2214yes—
12#10622162—22no—
13C23×C4×C11—22no—
14C23×C4×C11C2×C411yescharacteristic
15C23×C4×C11D412yes—
16C2×C11×C4⋊C4—24no—
17C2×C11×C4⋊C4—22no—
18C2×C11×C4⋊C4—24no—
19C2×C11×C4⋊C4—44no—
20C2×C11×C4⋊C4—44no—
21C2×C11×C4⋊C4—44no—
22C2×C11×C4⋊C4C2×C414yes—
23C2×C42×C11—24no—
24C2×C42×C11C2×C411yescharacteristic
25C2×C42×C11D412yes—
26C2×C42×C11C2311yescharacteristic
27C22×C11⋊C8—24no—
28C22⋊(C11⋊C8)—44no—
29C4⋊(C11⋊C8)—28no—
30#8723—111nomaximal, Sylow
31C24×C11C22⋊C411yescharacteristic
32C22×C4×C11—22no—
33C22×C4×C11—22no—
34C22×C4×C11—22no—
35C22×C4×C11—24no—
36C22×C4×C11—24no—
37C22×C4×C11—24no—
38C22×C4×C11—44no—
39C22×C4×C11—48no—
40C22×C4×C11C22⋊C411yescharacteristic
41C22×C4×C11C22⋊C412yes—
42C22×C4×C11D814yes—
43C22×C4×C11SD1614yes—
44C22×C4×C11C22×C411yescharacteristic
45C22×C4×C11C2×D412yes—
46C11×C4⋊C4—44no—
47C11×C4⋊C4—44no—
48C11×C4⋊C4—48no—
49C11×C4⋊C4—44no—
50C11×C4⋊C4—44no—
51C42×C11—22no—
52C42×C11—24no—
53C42×C11#4114yes—
54C2×C11⋊C8—44no—
55C2×C11⋊C8—44no—
56C2×C11⋊C8—44no—
57C2×#384D1111yescharacteristic
58#1797—112no—
59#1296—114no—
60C23×C11—21no—
61C23×C11—21no—
62C23×C11—22no—
63C23×C11#10012yes—
64C23×C11#10214yes—
65C23×C11C2×C22⋊C411yescharacteristic
66C2×C4×C11—28no—
67C2×C4×C11—21no—
68C2×C4×C11—22no—
69C2×C4×C11—21no—
70C2×C4×C11—21no—
71C2×C4×C11—21no—
72C2×C4×C11—22no—
73C2×C4×C11—28no—
74C2×C4×C11—28no—
75C2×C4×C11—44no—
76C2×C4×C11—48no—
77C2×C4×C11—88no—
78C2×C4×C11#10112yes—
79C2×C4×C11#10214yes—
80C2×C4×C11#11712yes—
81C2×C4×C11#12314yes—
82C2×C4×C11C2×D812yes—
83C2×C4×C11C2×SD1612yes—
84C2×C4×C11#13714yes—
85C11⋊C8—84no—
86C22×C4⋊C4—22no—
87C22×C4⋊C4Dic1112yes—
88C22×C42C2×D1111yescharacteristic
89C2×C4⋊C8—114no—
90C2×C22⋊C8—222no—
91#384—22no—
92#384Dic1112yes—
93#384C2×D1112yes—
94#336—222no—
95C22×C11—24no—
96C22×C11—22no—
97C22×C11—22no—
98C22×C11—24no—
99C22×C11#33114yes—
100C22×C11#38111yescharacteristic
101C22×C11C2×#10011yescharacteristic
102C22×C11C2×#10111yescharacteristic
103C22×C11C2×#10212yes—
104C22×C11#41912yes—
105C4×C11—22no—
106C4×C11—22no—
107C4×C11—24no—
108C4×C11—84no—
109C4×C11#48014yes—
110C4×C11#48314yes—
111C23×C4—22no—
112C23×C4C2×Dic1111yescharacteristic
113C23×C4C22⋊D1112yes—
114C22×C8—224no—
115C2×C4⋊C4—24no—
116C2×C4⋊C4—22no—
117C2×C4⋊C4—24no—
118C2×C4⋊C4—44no—
119C2×C4⋊C4—44no—
120C2×C4⋊C4—44no—
121C2×C4⋊C4C2×Dic1114yes—
122C2×C42—24no—
123C2×C42C2×Dic1111yescharacteristic
124C2×C42C22⋊D1112yes—
125C2×C42C22×D1111yescharacteristic
126C4⋊C8—228no—
127C22⋊C8—444no—
128C2×C11—24no—
129C2×C11C2×#33111yescharacteristic
130C2×C11#154612yes—
131C2×C11#155811yescharacteristic
132C2×C11#182111yescharacteristic
133C2×C11#182312yes—
134C24C22⋊Dic1111yescharacteristic
135C22×C4—22no—
136C22×C4—22no—
137C22×C4—22no—
138C22×C4—24no—
139C22×C4—24no—
140C22×C4—24no—
141C22×C4—48no—
142C22×C4—44no—
143C22×C4#432314yes—
144C22×C4#432414yes—
145C22×C4C22⋊Dic1112yes—
146C22×C4C22⋊Dic1111yescharacteristic
147C22×C4C22×Dic1111yescharacteristic
148C22×C4C2×C22⋊D1112yes—
149C2×C8—444no—
150C2×C8—444no—
151C2×C8—444no—
152C4⋊C4—44no—
153C4⋊C4—44no—
154C4⋊C4—48no—
155C4⋊C4—44no—
156C4⋊C4—44no—
157C42—22no—
158C42—24no—
159C42#433914yes—
160C11#872311yescharacteristic, complemented, Sylow
161C23—21no—
162C23—22no—
163C23—21no—
164C23#6689614yes—
165C23#6689712yes—
166C23C2×C22⋊Dic1111yescharacteristic
167C2×C4—28no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—22no—
173C2×C4—21no—
174C2×C4—28no—
175C2×C4—28no—
176C2×C4—48no—
177C2×C4—44no—
178C2×C4—88no—
179C2×C4#6689614yes—
180C2×C4#6690012yes—
181C2×C4#6697912yes—
182C2×C4#6698214yes—
183C2×C4C2×#432312yes—
184C2×C4C2×#432412yes—
185C2×C4#6699514yes—
186C8—884no—
187C22—24no—
188C22—22no—
189C22—22no—
190C22—24no—
191C22#1062218214yes—
192C22#1062282411yescharacteristic
193C22C2×#6689612yes—
194C22C2×#6689711yescharacteristic
195C22#1062283812yes—
196C22C2×#6690011yescharacteristic
197C4—22no—
198C4—22no—
199C4—24no—
200C4—84no—
201C4#1062258014yes—
202C4#1062258414yes—
203C2—24no—
204C2C2×#1062218211yescharacteristic
205C2#1306728812yes—
206C2#1306734211yescharacteristic
207C2#1306869611yescharacteristic
208C2#1306870212yes—
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#384C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenterC2×#384D11
hypocenterC11#8723
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#384

Complements

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

NH ≅ G/Ntype
2. #13066499C2semidirect
160. C11#8723semidirect

Maximal subgroups

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

subgroupindex
#130685962
#130664992
C2×C11×#3842
#872311