Finite Group Databasebeta

← #13069045

Subgroups — #13069045

Order 1408.

432 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 129 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
2C23×C11⋊C8C211yesmaximal, characteristic, complemented
3C2×#66896C212yesmaximal, complemented
4#10622825C211yesmaximal, 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—
14C2×C4⋊Dic11C2212yes—
15C22×C11⋊C8—22no—
16C22×C11⋊C8—24no—
17C22×C11⋊C8C2212yes—
18#66896—24no—
19C11⋊#95—21no—
20C24×C11—21no—
21C24×C11D411yescharacteristic
22C2×D4×C11—24no—
23C2×D4×C11—22no—
24C2×D4×C11—21no—
25C2×D4×C11—22no—
26C2×D4×C11—42no—
27C2×D4×C11—42no—
28C2×D4×C11C2×C412yes—
29C22×C4×C11—22no—
30C22×C4×C11—22no—
31C22×C4×C11—21no—
32C22×C4×C11C2×C412yes—
33C22×C4×C11D411yescharacteristic
34C22×C4×C11D412yes—
35C22×C4×C11C2311yescharacteristic
36C22×Dic11—22no—
37C11×C4⋊C4—21no—
38C11×C4⋊C4C2×C412yes—
39C11×C22⋊C4—24no—
40C22⋊Dic11—42no—
41C4⋊Dic11—22no—
42C4⋊Dic11—22no—
43C2×C11⋊C8—28no—
44C2×C11⋊C8—22no—
45C2×C11⋊C8—22no—
46C2×C11⋊C8D414yescomplemented
47#1893—111nomaximal, Sylow
48C23×C11—22no—
49C23×C11—22no—
50C23×C11—22no—
51C23×C11—42no—
52C23×C11—41no—
53C23×C11—41no—
54C23×C11—42no—
55C23×C11C22⋊C412yes—
56C23×C11D812yes—
57C23×C11SD1612yes—
58C23×C11C2×D411yescharacteristic
59D4×C11—24no—
60D4×C11—48no—
61D4×C11—41no—
62D4×C11—41no—
63C2×C4×C11—22no—
64C2×C4×C11—24no—
65C2×C4×C11—22no—
66C2×C4×C11—22no—
67C2×C4×C11—22no—
68C2×C4×C11—41no—
69C2×C4×C11—41no—
70C2×C4×C11C22⋊C412yes—
71C2×C4×C11C22×C411yescharacteristic
72C2×C4×C11C2×D412yes—
73C2×C4×C11C2×D411yescharacteristic
74C2×C4×C11#4112yes—
75C2×Dic11—42no—
76C2×Dic11—42no—
77C2×Dic11—42no—
78C11⋊C8—24no—
79C23×C8—111no—
80C2×#121D1111yescharacteristic
81C2×#102—112no—
82#380—111no—
83#340—112no—
84C22×C11—22no—
85C22×C11—22no—
86C22×C11—24no—
87C22×C11—24no—
88C22×C11—42no—
89C22×C11—42no—
90C22×C11—42no—
91C22×C11—82no—
92C22×C11—82no—
93C22×C11#10214yescomplemented
94C22×C11C2×C22⋊C411yescharacteristic
95C22×C11#12112yes—
96C22×C11C2×D811yescharacteristic
97C22×C11C2×SD1611yescharacteristic
98C22×C11#13512yes—
99C4×C11—22no—
100C4×C11—42no—
101C4×C11C4×D412yes—
102C4×C11#12011yescharacteristic
103C4×C11#12311yescharacteristic
104Dic11—82no—
105C22×D4—21no—
106C22×D4C2×D1111yescharacteristic
107C23×C4C2×D1111yescharacteristic
108C22×C8—112no—
109C22×C8—224no—
110C22×C8—222no—
111#121—22no—
112#121Dic1114yescomplemented
113C2×C4⋊C4—112no—
114C2×C4⋊C4C2×D1111yescharacteristic
115C2×C22⋊C4—21no—
116C2×C22⋊C4—221no—
117#102—224no—
118#95—221no—
119C2×C11—24no—
120C2×C11—82no—
121C2×C11#38611yescharacteristic
122C2×C11C2×#10211yescharacteristic
123C2×C11#41611yescharacteristic
124C2×C11#46512yes—
125C2×C11#46612yes—
126C24—21no—
127C24C22⋊D1111yescharacteristic
128C2×D4—24no—
129C2×D4—22no—
130C2×D4—22no—
131C2×D4—21no—
132C2×D4—42no—
133C2×D4—42no—
134C2×D4C2×Dic1112yes—
135C22×C4—22no—
136C22×C4—22no—
137C22×C4—21no—
138C22×C4—222no—
139C22×C4C2×Dic1112yes—
140C22×C4C22⋊D1111yescharacteristic
141C22×C4C22⋊D1112yes—
142C22×C4C22×D1111yescharacteristic
143C2×C8—114no—
144C2×C8—228no—
145C2×C8—222no—
146C2×C8—222no—
147C4⋊C4—21no—
148C4⋊C4—222no—
149C4⋊C4—222no—
150C4⋊C4C2×Dic1112yes—
151C22⋊C4—24no—
152C22⋊C4—442no—
153C11#189311yescharacteristic, complemented, Sylow
154C23—22no—
155C23—22no—
156C23—22no—
157C23—41no—
158C23—41no—
159C23—42no—
160C23—42no—
161C23#432312yes—
162C23#432412yes—
163C23C22⋊Dic1112yes—
164C23C2×C22⋊D1111yescharacteristic
165D4—24no—
166D4—48no—
167D4—41no—
168D4—41no—
169C2×C4—22no—
170C2×C4—24no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—442no—
177C2×C4—442no—
178C2×C4—442no—
179C2×C4C22⋊Dic1112yes—
180C2×C4D4×D1112yes—
181C2×C4#434112yes—
182C2×C4C22×Dic1111yescharacteristic
183C2×C4C2×C22⋊D1111yescharacteristic
184C8—224no—
185C22—22no—
186C22—22no—
187C22—24no—
188C22—24no—
189C22—42no—
190C22—42no—
191C22—42no—
192C22—82no—
193C22—82no—
194C22#6689614yescomplemented
195C22C2×#432311yescharacteristic
196C22C2×#432411yescharacteristic
197C22#6699212yes—
198C22#6700312yes—
199C22C2×C22⋊Dic1111yescharacteristic
200C4—22no—
201C4—42no—
202C4—882no—
203C4D4×Dic1112yes—
204C4#6698811yescharacteristic
205C4#6699011yescharacteristic
206C2—24no—
207C2—82no—
208C2#1062265112yes—
209C2#1062265412yes—
210C2C2×#6689611yescharacteristic
211C2#1062283311yescharacteristic
212C2#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#1893
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. C23×C11⋊C8C2semidirect
3. C2×#66896C2semidirect
4. #10622825C2semidirect
5. #10622167C2semidirect
10. C11×#121C4semidirect
46. C2×C11⋊C8D4semidirect
93. C22×C11#102semidirect
112. #121Dic11semidirect
153. C11#1893semidirect
194. C22#66896semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1212
C23×C11⋊C82
C2×#668962
#106228252
#106221672
#189311