Finite Group Databasebeta

← #13069049

Subgroups — #13069049

Order 1408.

360 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 109 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
1C22×C11×M16C211yesmaximal, characteristic
2C2×#66977C211yesmaximal, characteristic
3#10622825C211yesmaximal, characteristic
4C2×#66880C212yesmaximal, complemented
5#10622189C212yesmaximal, complemented
6C23×C4×C11C2211yescharacteristic
7C22×Dic22C2211yescharacteristic
8C2×C11×M16—22no—
9C2×C11×M16—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—
34C11×M16—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#1894—111nomaximal, Sylow
46C23×C11—22no—
47C23×C11—21no—
48C23×C11—21no—
49C23×C11—22no—
50C23×C11C22⋊C412yes—
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—41no—
65C2×Dic11—41no—
66C2×Dic11—42no—
67C2×Dic11—42no—
68C2×Dic11—42no—
69Dic22—24no—
70Dic22—41no—
71Dic22—41no—
72C8×C11—24no—
73C22×M16D1111yescharacteristic
74C2×C22⋊Q8—111no—
75C2×#103—112no—
76#380—111no—
77#340—112no—
78C22×C11—22no—
79C22×C11—22no—
80C22×C11—22no—
81C22×C11—42no—
82C22×C11—42no—
83C22×C11C2×C22⋊C411yescharacteristic
84C22×C11#12112yes—
85C22×C11AGL(1,ℤ/8)11yescharacteristic
86C22×C11#13711yescharacteristic
87C22×C11#13712yes—
88C4×C11—22no—
89C4×C11C4×D412yes—
90C4×C11#12011yescharacteristic
91C4×C11#12311yescharacteristic
92Dic11—42no—
93Dic11—42no—
94Dic11—82no—
95C22×Q8—111no—
96C23×C4C2×D1111yescharacteristic
97C2×M16—22no—
98C2×M16—24no—
99C22×C8C2×D1112yes—
100C22⋊Q8—114no—
101C22⋊Q8—222no—
102C2×C4⋊C4—111no—
103C2×C4⋊C4—112no—
104C2×C4⋊C4—221no—
105C2×C22⋊C4—221no—
106C2×C22⋊C4—221no—
107#103—224no—
108#95—221no—
109C2×C11—42no—
110C2×C11#38611yescharacteristic
111C2×C11#41711yescharacteristic
112C2×C11#41911yescharacteristic
113C2×C11#46812yes—
114C2×C11#47012yes—
115C24D4411yescharacteristic
116C2×Q8—112no—
117C2×Q8—221no—
118C2×Q8—222no—
119C2×Q8—222no—
120C22×C4—22no—
121C22×C4—22no—
122C22×C4—221no—
123C22×C4—221no—
124C22×C4—222no—
125C22×C4C4×D1112yes—
126C22×C4D4411yescharacteristic
127C22×C4C22⋊D1112yes—
128C22×C4C22×D1111yescharacteristic
129M16—28no—
130C2×C8—22no—
131C2×C8—22no—
132C2×C8C22⋊D1114yes—
133C4⋊C4—112no—
134C4⋊C4—224no—
135C4⋊C4—221no—
136C4⋊C4—222no—
137C4⋊C4—222no—
138C22⋊C4—224no—
139C22⋊C4—442no—
140C11#189411yescharacteristic, complemented, Sylow
141C23—21no—
142C23—22no—
143C23—21no—
144C23—22no—
145C23(C2×D11)⋊C412yes—
146C23C2×D4411yescharacteristic
147Q8—224no—
148Q8—441no—
149Q8—441no—
150C2×C4—22no—
151C2×C4—24no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—222no—
155C2×C4—222no—
156C2×C4—441no—
157C2×C4—441no—
158C2×C4—442no—
159C2×C4—442no—
160C2×C4—442no—
161C2×C4—442no—
162C2×C4(C2×D11)⋊C412yes—
163C2×C4C2×C4×D1111yescharacteristic
164C2×C4#433912yes—
165C2×C4C2×C22⋊D1112yes—
166C2×C4C2×C22⋊D1111yescharacteristic
167C8—24no—
168C22—22no—
169C22—22no—
170C22—22no—
171C22—42no—
172C22—42no—
173C22#6696111yescharacteristic
174C22#6696212yes—
175C22#6696211yescharacteristic
176C22C2×(C2×D11)⋊C411yescharacteristic
177C22#6698312yes—
178C4—22no—
179C4—442no—
180C4—442no—
181C4—882no—
182C4C4×C22⋊D1112yes—
183C4#6698211yescharacteristic
184C4#6700611yescharacteristic
185C2—42no—
186C2#1062273311yescharacteristic
187C2#1062274611yescharacteristic
188C2#1062274712yes—
189C2#1062275012yes—
190C2#1062282611yescharacteristic
subgroupG/H
centerC23C2×D44
commutatorC2×C4×C11C22×C4
FrattiniC22×C4C22×D11
FittingC22×C11×M16C2
socleC23×C11C2×D4
prime radicalC24×C11D4
cosocleC22×C4×C11C23
hypercenterC22×M16D11
hypocenterC11#1894
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
4. C2×#66880C2semidirect
5. #10622189C2semidirect
16. #66977C4semidirect
140. C11#1894semidirect

Maximal subgroups

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

subgroupindex
C22×C11×M162
C2×#669772
#106228252
C2×#668802
#106221892
#189411