Finite Group Databasebeta

← #13079760

Subgroups — #13079760

Order 1408.

360 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C2×C11×C4⋊Q8C211yesmaximal, characteristic
2#10623001C211yesmaximal, characteristic
3#10622707C214yesmaximal, complemented
4#10622706C212yesmaximal, complemented
5#10622692C212yesmaximal, complemented
6#10622584C214yesmaximal
7#10622538C211yesmaximal, characteristic
8C22×Q8×C11—21no—
9C11×C4⋊Q8—21no—
10C11×C4⋊Q8—21no—
11C11×C4⋊Q8C2212yes—
12C11×C4⋊Q8C2212yes—
13C2×C11×C4⋊C4—21no—
14C2×C11×C4⋊C4C2212yes—
15C2×C42×C11C2211yescharacteristic
16#66979—21no—
17#66977—21no—
18#66977C2212yes—
19#66923—21no—
20#66922C2211yescharacteristic
21#66922C2211yescharacteristic
22C4×Dic22—21no—
23C4×Dic22C2212yes—
24C22⋊(C11⋊C8)C2212yes—
25#66874C2218yes—
26#66872C2218yes—
27C4⋊(C11⋊C8)C2212yes—
28C4×C11⋊C8C2212yes—
29C2×Q8×C11—22no—
30C2×Q8×C11—22no—
31C2×Q8×C11—44no—
32C22×C4×C11—22no—
33C22×C4×C11D411yescharacteristic
34C22×C4×C11D411yescharacteristic
35C22×C4×C11C2311yescharacteristic
36C2×Dic22—21no—
37C2×Dic22C2312yes—
38C11×C4⋊C4—22no—
39C11×C4⋊C4—22no—
40C11×C4⋊C4—22no—
41C11×C4⋊C4C2314yes—
42C42×C11D411yescharacteristic
43C42×C11D411yescharacteristic
44C42×C11C2311yescharacteristic
45C42×C11C2311yescharacteristic
46C22⋊Dic11—22no—
47C4⋊Dic11—21no—
48C4⋊Dic11—21no—
49C4⋊Dic11—21no—
50C4⋊Dic11C2312yes—
51Dic11⋊C4—22no—
52Dic11⋊C4—22no—
53C4×Dic11—22no—
54C2×C11⋊C8C2314yes—
55#3229—111nomaximal, Sylow
56C23×C11C2×D411yescharacteristic
57Q8×C11—44no—
58Q8×C11—44no—
59C2×C4×C11—22no—
60C2×C4×C11—22no—
61C2×C4×C11—24no—
62C2×C4×C11—44no—
63C2×C4×C11SD1614yes—
64C2×C4×C11C2×D411yescharacteristic
65C2×C4×C11C2×D411yescharacteristic
66C2×C4×C11C2×D411yescharacteristic
67C2×C4×C11C2×D411yescharacteristic
68C2×C4×C11C2×D411yescharacteristic
69C2×C4×C11C2411yescharacteristic
70C2×Dic11—22no—
71C2×Dic11—22no—
72Dic22—24no—
73Dic22—42no—
74C11⋊C8—24no—
75#533—111no—
76C2×C4⋊Q8D1111yescharacteristic
77#498—112no—
78#487—112no—
79#483—114no—
80#475—114no—
81#431—111no—
82C22×C11—21no—
83C22×C11—21no—
84C22×C11C2×SD1612yes—
85C22×C11C22×D411yescharacteristic
86C4×C11—21no—
87C4×C11—21no—
88C4×C11—44no—
89C4×C11C2×SD1612yes—
90C4×C11C2×SD1612yes—
91C4×C11#13712yes—
92C4×C112−1+412yes—
93Dic11—42no—
94Dic11—42no—
95C22×Q8—21no—
96C4⋊Q8—21no—
97C4⋊Q8—21no—
98C4⋊Q8—111no—
99C4⋊Q8—111no—
100C4⋊Q8C2×D1112yes—
101C4⋊Q8C2×D1112yes—
102#125—221no—
103C22⋊Q8—112no—
104C22⋊Q8—221no—
105C4×Q8—112no—
106C4×Q8—221no—
107#117—221no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4C2×D1112yes—
110C2×C42C2×D1111yescharacteristic
111#106—118no—
112C4⋊C8—112no—
113#103—118no—
114C22⋊C8—112no—
115C4×C8—112no—
116C2×C11—22no—
117C2×C11#53611yescharacteristic
118C2×C11C22×SD1611yescharacteristic
119C2×C11C2×#13711yescharacteristic
120C2×Q8—22no—
121C2×Q8—22no—
122C2×Q8—44no—
123C2×Q8—112no—
124C2×Q8—221no—
125C22×C4—22no—
126C22×C4C22⋊D1111yescharacteristic
127C22×C4C22⋊D1111yescharacteristic
128C22×C4C22×D1111yescharacteristic
129C2×C8—114no—
130C4⋊C4—22no—
131C4⋊C4—22no—
132C4⋊C4—22no—
133C4⋊C4—112no—
134C4⋊C4—221no—
135C4⋊C4—221no—
136C4⋊C4—222no—
137C4⋊C4—222no—
138C4⋊C4—221no—
139C4⋊C4C22×D1114yes—
140C22⋊C4—222no—
141C42—222no—
142C42C22⋊D1111yescharacteristic
143C42C22⋊D1111yescharacteristic
144C42C22×D1111yescharacteristic
145C42C22×D1111yescharacteristic
146C11#322911yescharacteristic, complemented, Sylow
147C23C2×C22⋊D1111yescharacteristic
148Q8—44no—
149Q8—44no—
150Q8—224no—
151Q8—442no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—24no—
155C2×C4—44no—
156C2×C4—222no—
157C2×C4—222no—
158C2×C4#432414yes—
159C2×C4C2×C22⋊D1111yescharacteristic
160C2×C4C2×C22⋊D1111yescharacteristic
161C2×C4C2×C22⋊D1111yescharacteristic
162C2×C4C2×C22⋊D1111yescharacteristic
163C2×C4C2×C22⋊D1111yescharacteristic
164C2×C4C23×D1111yescharacteristic
165C8—224no—
166C22—21no—
167C22—21no—
168C22C2×#432412yes—
169C22C22×C22⋊D1111yescharacteristic
170C4—21no—
171C4—21no—
172C4—44no—
173C4—442no—
174C4—442no—
175C4C2×#432412yes—
176C4C2×#432412yes—
177C4#6699512yes—
178C4#6704012yes—
179C2—22no—
180C2C22×#432411yescharacteristic
181C2C2×#6699511yescharacteristic
182C2#1062334711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC2×C11×C4⋊Q8C2
socleC22×C11C22×D4
prime radicalC23×C11C2×D4
hypercenterC2×C4⋊Q8D11
hypocenterC11#3229
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #10622707C2semidirect
4. #10622706C2semidirect
5. #10622692C2semidirect
146. C11#3229semidirect

Maximal subgroups

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

subgroupindex
C2×C11×C4⋊Q82
#106230012
#106227072
#106227062
#106226922
#106225842
#106225382
#322911