Finite Group Databasebeta

← #13067142

Subgroups — #13067142

Order 1408.

242 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 73 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
1#10623010C211yesmaximal, characteristic
2C11×#432C211yesmaximal, characteristic, complemented
3C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
4#10622108C212yesmaximal
5#10622105C212yesmaximal, complemented
6C2×C42×C11C2211yescharacteristic
7#66983C2211yescharacteristic
8#66982—21no—
9C4×C22⋊D11—21no—
10C2×C4⋊Dic11—21no—
11#66977C2211yescharacteristic
12C2×C4×Dic11—21no—
13#66929—21no—
14#66928C411yescharacteristic, complemented
15C4×D44C411yescharacteristic, complemented
16#66925—21no—
17#66923C411yescharacteristic, complemented
18C4×Dic22C411yescharacteristic, complemented
19C11×C4⋊C8—21no—
20C11×C22⋊C8C2212yes—
21C11×#97—21no—
22C11⋊#95C2212yes—
23C22×C4×C11D411yescharacteristic
24C22×C4×C11D411yescharacteristic
25C22×C4×C11C2311yescharacteristic
26C2×C22⋊D11—21no—
27C22×Dic11—22no—
28C2×D44C2×C411yescharacteristic
29C2×C4×D11—21no—
30C2×Dic22C2×C411yescharacteristic
31C2×C8×C11—22no—
32C42×C11C2×C411yescharacteristic
33C42×C11C2×C411yescharacteristic
34C42×C11D411yescharacteristic
35C42×C11D411yescharacteristic
36C22⋊Dic11—21no—
37(C2×D11)⋊C4—21no—
38(C2×D11)⋊C4—21no—
39(C2×D11)⋊C4—21no—
40(C2×D11)⋊C4—21no—
41C4⋊Dic11—24no—
42C4⋊Dic11C2×C411yescharacteristic
43C4⋊Dic11C2×C411yescharacteristic
44Dic11⋊C4—21no—
45Dic11⋊C4—21no—
46Dic11⋊C4—21no—
47Dic11⋊C4—21no—
48C4×Dic11—21no—
49C4×Dic11—42no—
50#1509—111nomaximal, Sylow
51C23×C11C2×D411yescharacteristic
52C22×D11—21no—
53C2×C4×C11—21no—
54C2×C4×C11—21no—
55C2×C4×C11—22no—
56C2×C4×C11—41no—
57C2×C4×C11C22⋊C411yescharacteristic
58C2×C4×C11C22⋊C411yescharacteristic
59C2×C4×C11C22⋊C411yescharacteristic
60C2×C4×C11C22⋊C411yescharacteristic
61C2×C4×C11C22×C411yescharacteristic
62C2×C4×C11C2×D411yescharacteristic
63C22⋊D11—41no—
64C22⋊D11—41no—
65C2×Dic11—24no—
66C2×Dic11—21no—
67C2×Dic11—21no—
68C2×Dic11—21no—
69C2×Dic11—42no—
70C2×Dic11—42no—
71D44—41no—
72C4×D11—42no—
73Dic22—41no—
74C8×C11—42no—
75#529—111no—
76#432D1111yescharacteristic, complemented
77C4×C4⋊C4—111no—
78#328—112no—
79#327—112no—
80C22×C11—21no—
81C22×C11—21no—
82C22×C11C2×C22⋊C411yescharacteristic
83C22×C11AGL(1,ℤ/8)11yescharacteristic
84C22×C11#13711yescharacteristic
85C2×D11—41no—
86C2×D11—41no—
87C2×D11—41no—
88C4×C11—21no—
89C4×C11—21no—
90C4×C11—21no—
91C4×C11—21no—
92C4×C11—21no—
93C4×C11#10412yes—
94Dic11—44no—
95Dic11—41no—
96Dic11—41no—
97Dic11—41no—
98#126—221no—
99#125—111no—
100#124—111no—
101#123—221no—
102C22⋊Q8—111no—
103#121—111no—
104C4×Q8—111no—
105C4×D4—111no—
106C4×D4—221no—
107#117—221no—
108C2×C4⋊C4—221no—
109C2×C42—221no—
110C2×C42C2×D1111yescharacteristic
111C4⋊C8—21no—
112C22⋊C8C2×D1112yes—
113#97—21no—
114#95—112no—
115C2×C11—21no—
116C2×C11—21no—
117C2×C11#41011yescharacteristic
118C2×C11#41711yescharacteristic
119C2×C11C2×#10411yescharacteristic
120D11—81no—
121C2×Q8—111no—
122C2×D4—111no—
123C2×D4—221no—
124C22×C4—222no—
125C22×C4—221no—
126C22×C4D4411yescharacteristic
127C22×C4D4411yescharacteristic
128C22×C4C22×D1111yescharacteristic
129C2×C8—22no—
130C4⋊C4—111no—
131C4⋊C4—111no—
132C4⋊C4—224no—
133C4⋊C4—221no—
134C4⋊C4—221no—
135C4⋊C4—221no—
136C4⋊C4—221no—
137C22⋊C4—221no—
138C22⋊C4—221no—
139C22⋊C4—221no—
140C22⋊C4—221no—
141C22⋊C4—221no—
142C42—221no—
143C42—442no—
144C42C4×D1111yescharacteristic
145C42C4×D1111yescharacteristic
146C42C22⋊D1111yescharacteristic
147C42C22⋊D1111yescharacteristic
148C11#150911yescharacteristic, complemented, Sylow
149C23—221no—
150C23C2×D4411yescharacteristic
151Q8—441no—
152D4—441no—
153D4—441no—
154D4—441no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—41no—
159C2×C4—224no—
160C2×C4—221no—
161C2×C4—221no—
162C2×C4—221no—
163C2×C4—442no—
164C2×C4—442no—
165C2×C4—442no—
166C2×C4(C2×D11)⋊C411yescharacteristic
167C2×C4(C2×D11)⋊C411yescharacteristic
168C2×C4(C2×D11)⋊C411yescharacteristic
169C2×C4(C2×D11)⋊C411yescharacteristic
170C2×C4C2×C4×D1111yescharacteristic
171C2×C4C2×C22⋊D1111yescharacteristic
172C8—42no—
173C22—21no—
174C22—21no—
175C22—441no—
176C22—441no—
177C22—441no—
178C22#6696111yescharacteristic
179C22#6696211yescharacteristic
180C22C2×(C2×D11)⋊C411yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—21no—
186C4—444no—
187C4—441no—
188C4—441no—
189C4—441no—
190C4#6688912yes—
191C2—21no—
192C2—21no—
193C2—881no—
194C2#1062261911yescharacteristic
195C2#1062274611yescharacteristic
196C2C2×#6688911yescharacteristic
subgroupG/H
centerC22C2×(C2×D11)⋊C4
commutatorC2×C4×C11C22×C4
FrattiniC22×C4C22×D11
FittingC11×#432C2
socleC22×C11C2×C22⋊C4
prime radical#66983C22
cosocleC22×C4×C11C23
hypercenter#432D11
hypocenterC11#1509
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C11×#432C2semidirect
3. C4×C4⋊Dic11C2semidirect
5. #10622105C2semidirect
14. #66928C4semidirect
15. C4×D44C4semidirect
17. #66923C4semidirect
18. C4×Dic22C4semidirect
76. #432D11semidirect
148. C11#1509semidirect

Maximal subgroups

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

subgroupindex
#106230102
C11×#4322
C4×C4⋊Dic112
#106221082
#106221052
#150911