Finite Group Databasebeta

← #13069055

Subgroups — #13069055

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
2C22×#4318C211yesmaximal, 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—
15C2×#4318—22no—
16C2×#4318—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—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—42no—
40C4⋊Dic11—22no—
41C4⋊Dic11—22no—
42#4318—28no—
43C2×C11⋊C8—22no—
44C2×C11⋊C8—22no—
45C2×C11⋊C8D414yescomplemented
46#1895—111nomaximal, Sylow
47C23×C11—22no—
48C23×C11—21no—
49C23×C11—22no—
50C23×C11—21no—
51C23×C11—22no—
52C23×C11—42no—
53C23×C11—42no—
54C23×C11—41no—
55C23×C11—41no—
56C23×C11C22⋊C412yes—
57C23×C11C2×D411yescharacteristic
58D4×C11—24no—
59D4×C11—48no—
60D4×C11—41no—
61D4×C11—41no—
62C2×C4×C11—22no—
63C2×C4×C11—24no—
64C2×C4×C11—22no—
65C2×C4×C11—22no—
66C2×C4×C11—22no—
67C2×C4×C11—42no—
68C2×C4×C11C22⋊C412yes—
69C2×C4×C11C22×C411yescharacteristic
70C2×C4×C11C2×D412yes—
71C2×C4×C11C2×D411yescharacteristic
72C2×C4×C11#4112yes—
73C2×Dic11—42no—
74C2×Dic11—42no—
75C2×Dic11—42no—
76C11⋊C8—24no—
77C22×M16—111no—
78C2×#121D1111yescharacteristic
79C2×#102—112no—
80#380—111no—
81#340—112no—
82C22×C11—22no—
83C22×C11—22no—
84C22×C11—22no—
85C22×C11—42no—
86C22×C11—42no—
87C22×C11—42no—
88C22×C11—42no—
89C22×C11—42no—
90C22×C11—82no—
91C22×C11—82no—
92C22×C11C2×C22⋊C411yescharacteristic
93C22×C11#12112yes—
94C22×C11AGL(1,ℤ/8)12yes—
95C22×C11AGL(1,ℤ/8)11yescharacteristic
96C22×C11#13711yescharacteristic
97C4×C11—22no—
98C4×C11—42no—
99C4×C11C4×D412yes—
100C4×C11#12011yescharacteristic
101C4×C11#12311yescharacteristic
102Dic11—82no—
103C22×D4—21no—
104C22×D4C2×D1111yescharacteristic
105C23×C4C2×D1111yescharacteristic
106C2×M16—224no—
107C2×M16—222no—
108C22×C8—112no—
109#121—22no—
110#121Dic1114yescomplemented
111C2×C4⋊C4—112no—
112C2×C4⋊C4C2×D1111yescharacteristic
113C2×C22⋊C4—21no—
114C2×C22⋊C4—221no—
115#102—224no—
116#95—221no—
117C2×C11—42no—
118C2×C11—82no—
119C2×C11#38611yescharacteristic
120C2×C11#41711yescharacteristic
121C2×C11#41811yescharacteristic
122C2×C11#46812yes—
123C2×C11#46912yes—
124C24—21no—
125C24C22⋊D1111yescharacteristic
126C2×D4—24no—
127C2×D4—22no—
128C2×D4—22no—
129C2×D4—21no—
130C2×D4—44no—
131C2×D4C2×Dic1112yes—
132C22×C4—22no—
133C22×C4—22no—
134C22×C4—21no—
135C22×C4—222no—
136C22×C4C2×Dic1112yes—
137C22×C4C22⋊D1111yescharacteristic
138C22×C4C22⋊D1112yes—
139C22×C4C22×D1111yescharacteristic
140M16—228no—
141C2×C8—114no—
142C2×C8—222no—
143C2×C8—222no—
144C4⋊C4—21no—
145C4⋊C4—222no—
146C4⋊C4—222no—
147C4⋊C4C2×Dic1112yes—
148C22⋊C4—24no—
149C22⋊C4—442no—
150C11#189511yescharacteristic, complemented, Sylow
151C23—22no—
152C23—22no—
153C23—21no—
154C23—21no—
155C23—22no—
156C23—42no—
157C23—42no—
158C23—41no—
159C23—41no—
160C23C22⋊Dic1112yes—
161C23C2×C22⋊D1111yescharacteristic
162D4—24no—
163D4—48no—
164D4—41no—
165D4—41no—
166C2×C4—22no—
167C2×C4—24no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—42no—
172C2×C4—442no—
173C2×C4—442no—
174C2×C4—442no—
175C2×C4C22⋊Dic1112yes—
176C2×C4D4×D1112yes—
177C2×C4#434112yes—
178C2×C4C22×Dic1111yescharacteristic
179C2×C4C2×C22⋊D1111yescharacteristic
180C8—224no—
181C22—22no—
182C22—22no—
183C22—22no—
184C22—42no—
185C22—42no—
186C22—42no—
187C22—42no—
188C22—42no—
189C22—82no—
190C22—82no—
191C22#6698512yes—
192C22#6699212yes—
193C22#6700211yescharacteristic
194C22#6700411yescharacteristic
195C22C2×C22⋊Dic1111yescharacteristic
196C4—22no—
197C4—42no—
198C4—882no—
199C4D4×Dic1112yes—
200C4#6698811yescharacteristic
201C4#6699011yescharacteristic
202C2—42no—
203C2—82no—
204C2#1062265212yes—
205C2#1062265512yes—
206C2#1062282811yescharacteristic
207C2#1062283311yescharacteristic
208C2#1062284511yescharacteristic
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#1895
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. C22×#4318C2semidirect
3. C2×#66896C2semidirect
4. #10622825C2semidirect
5. #10622167C2semidirect
10. C11×#121C4semidirect
45. C2×C11⋊C8D4semidirect
110. #121Dic11semidirect
150. C11#1895semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1212
C22×#43182
C2×#668962
#106228252
#106221672
#189511