Finite Group Databasebeta

← #13069039

Subgroups — #13069039

Order 1408.

380 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C23×C8×C11C211yesmaximal, characteristic
2C2×#66977C211yesmaximal, characteristic
3#10622825C211yesmaximal, characteristic
4C2×#66880C212yesmaximal, complemented
5#10622189C212yesmaximal, complemented
6C23×C4×C11C2211yescharacteristic
7C22×Dic22C2211yescharacteristic
8C22×C8×C11—22no—
9C22×C8×C11—24no—
10C22×C8×C11C2212yes—
11C2×C22⋊Dic11—21no—
12C2×C22⋊Dic11—21no—
13C2×C4⋊Dic11C2212yes—
14C2×C4⋊Dic11C2211yescharacteristic
15#66977—22no—
16#66977C414yescomplemented
17C2×Dic11⋊C4—21no—
18C11⋊#95—21no—
19#66880—24no—
20C24×C11D411yescharacteristic
21C22×C4×C11—22no—
22C22×C4×C11—22no—
23C22×C4×C11C2×C412yes—
24C22×C4×C11D411yescharacteristic
25C22×C4×C11D412yes—
26C22×C4×C11C2311yescharacteristic
27C22×Dic11—21no—
28C22×Dic11—21no—
29C22×Dic11—22no—
30C2×Dic22—22no—
31C2×Dic22—21no—
32C2×Dic22—22no—
33C2×Dic22C2×C412yes—
34C2×C8×C11—28no—
35C2×C8×C11—22no—
36C2×C8×C11—22no—
37C2×C8×C11D414yes—
38C22⋊Dic11—24no—
39C22⋊Dic11—42no—
40C4⋊Dic11—21no—
41C4⋊Dic11—22no—
42C4⋊Dic11—22no—
43C4⋊Dic11C2×C412yes—
44Dic11⋊C4—24no—
45#1892—111nomaximal, Sylow
46C23×C11—22no—
47C23×C11—22no—
48C23×C11C22⋊C412yes—
49C23×C11SD1612yes—
50C23×C11Q1612yes—
51C23×C11C2×D411yescharacteristic
52C2×C4×C11—22no—
53C2×C4×C11—24no—
54C2×C4×C11—22no—
55C2×C4×C11—22no—
56C2×C4×C11C22⋊C412yes—
57C2×C4×C11C22×C411yescharacteristic
58C2×C4×C11C2×D412yes—
59C2×C4×C11C2×D411yescharacteristic
60C2×C4×C11#4112yes—
61C2×Dic11—22no—
62C2×Dic11—22no—
63C2×Dic11—42no—
64C2×Dic11—42no—
65C2×Dic11—42no—
66C2×Dic11—42no—
67C2×Dic11—42no—
68Dic22—24no—
69Dic22—41no—
70Dic22—41no—
71C8×C11—24no—
72C23×C8D1111yescharacteristic
73C2×C22⋊Q8—111no—
74C2×#103—112no—
75#380—111no—
76#340—112no—
77C22×C11—22no—
78C22×C11—22no—
79C22×C11—24no—
80C22×C11—24no—
81C22×C11#10314yescomplemented
82C22×C11C2×C22⋊C411yescharacteristic
83C22×C11#12112yes—
84C22×C11C2×SD1611yescharacteristic
85C22×C11C2×Q1611yescharacteristic
86C22×C11#13512yes—
87C4×C11—22no—
88C4×C11C4×D412yes—
89C4×C11#12011yescharacteristic
90C4×C11#12311yescharacteristic
91Dic11—42no—
92Dic11—42no—
93Dic11—82no—
94C22×Q8—111no—
95C23×C4C2×D1111yescharacteristic
96C22×C8—22no—
97C22×C8—24no—
98C22×C8C2×D1112yes—
99C22⋊Q8—114no—
100C22⋊Q8—222no—
101C2×C4⋊C4—111no—
102C2×C4⋊C4—112no—
103C2×C4⋊C4—221no—
104C2×C22⋊C4—221no—
105C2×C22⋊C4—221no—
106#103—224no—
107#95—221no—
108C2×C11—24no—
109C2×C11#38611yescharacteristic
110C2×C11C2×#10311yescharacteristic
111C2×C11#41611yescharacteristic
112C2×C11#46512yes—
113C2×C11#46712yes—
114C24D4411yescharacteristic
115C2×Q8—112no—
116C2×Q8—221no—
117C2×Q8—222no—
118C2×Q8—222no—
119C22×C4—22no—
120C22×C4—22no—
121C22×C4—221no—
122C22×C4—221no—
123C22×C4—222no—
124C22×C4C4×D1112yes—
125C22×C4D4411yescharacteristic
126C22×C4C22⋊D1112yes—
127C22×C4C22×D1111yescharacteristic
128C2×C8—28no—
129C2×C8—22no—
130C2×C8—22no—
131C2×C8C22⋊D1114yes—
132C4⋊C4—112no—
133C4⋊C4—224no—
134C4⋊C4—221no—
135C4⋊C4—222no—
136C4⋊C4—222no—
137C22⋊C4—224no—
138C22⋊C4—442no—
139C11#189211yescharacteristic, complemented, Sylow
140C23—22no—
141C23—22no—
142C23#431412yes—
143C23Dic4412yes—
144C23(C2×D11)⋊C412yes—
145C23C2×D4411yescharacteristic
146Q8—224no—
147Q8—441no—
148Q8—441no—
149C2×C4—22no—
150C2×C4—24no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—222no—
154C2×C4—222no—
155C2×C4—442no—
156C2×C4—442no—
157C2×C4—442no—
158C2×C4—442no—
159C2×C4—442no—
160C2×C4(C2×D11)⋊C412yes—
161C2×C4C2×C4×D1111yescharacteristic
162C2×C4#433912yes—
163C2×C4C2×C22⋊D1112yes—
164C2×C4C2×C22⋊D1111yescharacteristic
165C8—24no—
166C22—22no—
167C22—24no—
168C22—24no—
169C22—22no—
170C22#6688014yescomplemented
171C22C2×#431411yescharacteristic
172C22#6695712yes—
173C22C2×Dic4411yescharacteristic
174C22C2×(C2×D11)⋊C411yescharacteristic
175C22#6698312yes—
176C4—22no—
177C4—442no—
178C4—442no—
179C4—882no—
180C4C4×C22⋊D1112yes—
181C4#6698211yescharacteristic
182C4#6700611yescharacteristic
183C2—24no—
184C2C2×#6688011yescharacteristic
185C2#1062272611yescharacteristic
186C2#1062272712yes—
187C2#1062272912yes—
188C2#1062282611yescharacteristic
subgroupG/H
centerC23C2×D44
commutatorC2×C4×C11C22×C4
FrattiniC22×C4C22×D11
FittingC23×C8×C11C2
socleC23×C11C2×D4
prime radicalC24×C11D4
cosocleC22×C4×C11C23
hypercenterC23×C8D11
hypocenterC11#1892
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8

Complements

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

NH ≅ G/Ntype
4. C2×#66880C2semidirect
5. #10622189C2semidirect
16. #66977C4semidirect
81. C22×C11#103semidirect
139. C11#1892semidirect
170. C22#66880semidirect

Maximal subgroups

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

subgroupindex
C23×C8×C112
C2×#669772
#106228252
C2×#668802
#106221892
#189211