Finite Group Databasebeta

← #13068939

Subgroups — #13068939

Order 1408.

412 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 113 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×#121C211yesmaximal, characteristic
2C2×#66979C211yesmaximal, characteristic, complemented
3C2×#66896C212yesmaximal, complemented
4C2×C22⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
5#10622167C212yesmaximal, complemented
6C22×D4×C11—21no—
7C22×D4×C11C2211yescharacteristic
8C23×C4×C11C2211yescharacteristic
9C11×#121—22no—
10C11×#121C414yescomplemented
11C2×C11×C4⋊C4C2211yescharacteristic
12C2×C11×C22⋊C4—21no—
13C2×C22⋊Dic11—21no—
14#66979—24no—
15C2×C4⋊Dic11C2212yes—
16C2×C4×Dic11—21no—
17C22×C11⋊C8C2212yes—
18#66896—24no—
19C22⋊(C11⋊C8)—22no—
20C24×C11—21no—
21C24×C11D411yescharacteristic
22C2×D4×C11—24no—
23C2×D4×C11—22no—
24C2×D4×C11—21no—
25C2×D4×C11—22no—
26C2×D4×C11—44no—
27C2×D4×C11C2×C412yes—
28C22×C4×C11—22no—
29C22×C4×C11—22no—
30C22×C4×C11—21no—
31C22×C4×C11C2×C412yes—
32C22×C4×C11D411yescharacteristic
33C22×C4×C11D412yes—
34C22×C4×C11C2311yescharacteristic
35C22×Dic11—22no—
36C11×C4⋊C4—21no—
37C11×C4⋊C4C2×C412yes—
38C11×C22⋊C4—24no—
39C22⋊Dic11—24no—
40C4⋊Dic11—22no—
41C4⋊Dic11D414yescomplemented
42C4×Dic11—24no—
43C2×C11⋊C8—22no—
44C2×C11⋊C8—22no—
45C2×C11⋊C8—22no—
46#1875—111nomaximal, Sylow
47C23×C11—21no—
48C23×C11—21no—
49C23×C11—22no—
50C23×C11—22no—
51C23×C11—22no—
52C23×C11—41no—
53C23×C11—41no—
54C23×C11—42no—
55C23×C11—42no—
56C23×C11C22⋊C412yes—
57C23×C11C2×D411yescharacteristic
58D4×C11—24no—
59D4×C11—48no—
60D4×C11—42no—
61C2×C4×C11—21no—
62C2×C4×C11—21no—
63C2×C4×C11—24no—
64C2×C4×C11—24no—
65C2×C4×C11—22no—
66C2×C4×C11—42no—
67C2×C4×C11C22⋊C412yes—
68C2×C4×C11C22×C411yescharacteristic
69C2×C4×C11C2×D412yes—
70C2×C4×C11C2×D411yescharacteristic
71C2×C4×C11#4112yes—
72C2×Dic11—24no—
73C2×Dic11—42no—
74C2×Dic11—42no—
75C11⋊C8—42no—
76C2×#121D1111yescharacteristic
77C2×#117—111no—
78C2×#102—112no—
79C2×C22⋊C8—111no—
80#340—112no—
81C22×C11—22no—
82C22×C11—22no—
83C22×C11—22no—
84C22×C11—42no—
85C22×C11—42no—
86C22×C11—42no—
87C22×C11—42no—
88C22×C11—42no—
89C22×C11—82no—
90C22×C11—82no—
91C22×C11C2×C22⋊C411yescharacteristic
92C22×C11#12011yescharacteristic
93C22×C11#12311yescharacteristic
94C22×C11#13512yes—
95C22×C11AGL(1,ℤ/8)12yes—
96C4×C11—22no—
97C4×C11—42no—
98C4×C11C4×D412yes—
99C4×C11#12112yes—
100Dic11—44no—
101C22×D4—21no—
102C22×D4C2×D1111yescharacteristic
103C23×C4C2×D1111yescharacteristic
104C22×C8—112no—
105#121—22no—
106#121Dic1114yescomplemented
107#117—224no—
108C2×C4⋊C4—112no—
109C2×C4⋊C4C2×D1111yescharacteristic
110C2×C22⋊C4—21no—
111C2×C22⋊C4—221no—
112C2×C42—221no—
113#102—224no—
114C22⋊C8—222no—
115C2×C11—42no—
116C2×C11—82no—
117C2×C11#38611yescharacteristic
118C2×C11#41611yescharacteristic
119C2×C11#41811yescharacteristic
120C2×C11#44912yes—
121C2×C11#48212yes—
122C24—21no—
123C24C22⋊D1111yescharacteristic
124C2×D4—24no—
125C2×D4—22no—
126C2×D4—22no—
127C2×D4—21no—
128C2×D4—44no—
129C2×D4C2×Dic1112yes—
130C22×C4—22no—
131C22×C4—22no—
132C22×C4—21no—
133C22×C4—222no—
134C22×C4C2×Dic1112yes—
135C22×C4C22⋊D1111yescharacteristic
136C22×C4C22⋊D1112yes—
137C22×C4C22×D1111yescharacteristic
138C2×C8—222no—
139C2×C8—222no—
140C2×C8—222no—
141C4⋊C4—21no—
142C4⋊C4—114no—
143C4⋊C4—222no—
144C4⋊C4C2×Dic1112yes—
145C22⋊C4—24no—
146C22⋊C4—224no—
147C42—224no—
148C11#187511yescharacteristic, complemented, Sylow
149C23—22no—
150C23—21no—
151C23—21no—
152C23—22no—
153C23—22no—
154C23—42no—
155C23—41no—
156C23—41no—
157C23—42no—
158C23C22⋊Dic1112yes—
159C23C2×C22⋊D1111yescharacteristic
160D4—24no—
161D4—48no—
162D4—42no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—24no—
166C2×C4—24no—
167C2×C4—22no—
168C2×C4—42no—
169C2×C4—224no—
170C2×C4—442no—
171C2×C4—442no—
172C2×C4C22⋊Dic1112yes—
173C2×C4D4×D1112yes—
174C2×C4#434112yes—
175C2×C4C22×Dic1111yescharacteristic
176C2×C4C2×C22⋊D1111yescharacteristic
177C8—442no—
178C22—22no—
179C22—22no—
180C22—22no—
181C22—42no—
182C22—42no—
183C22—42no—
184C22—42no—
185C22—42no—
186C22—82no—
187C22—82no—
188C22#6698512yes—
189C22#6698811yescharacteristic
190C22#6699011yescharacteristic
191C22#6700312yes—
192C22C2×C22⋊Dic1111yescharacteristic
193C4—22no—
194C4—42no—
195C4—444no—
196C4D4×Dic1112yes—
197C4#6699212yes—
198C2—42no—
199C2—82no—
200C2#1062264812yes—
201C2#1062265012yes—
202C2#1062282811yescharacteristic
203C2#1062283311yescharacteristic
204C2#1062284611yescharacteristic
subgroupG/H
centerC23C2×C22⋊D11
commutatorC2×C4×C11C22×C4
FrattiniC22×C4C22×D11
Fitting, prime radicalC2×C11×#121C2
socleC23×C11C2×D4
cosocleC22×C4×C11C23
hypercenterC2×#121D11
hypocenterC11#1875
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
2. C2×#66979C2semidirect
3. C2×#66896C2semidirect
4. C2×C22⋊(C11⋊C8)C2semidirect
5. #10622167C2semidirect
10. C11×#121C4semidirect
41. C4⋊Dic11D4semidirect
106. #121Dic11semidirect
148. C11#1875semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1212
C2×#669792
C2×#668962
C2×C22⋊(C11⋊C8)2
#106221672
#187511