Finite Group Databasebeta

← #13067340

Subgroups — #13067340

Order 1408.

228 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 67 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
1D11×C4⋊Q8C211yesmaximal, characteristic
2#10622448C212yesmaximal
3C11×#333C211yesmaximal, characteristic, complemented
4#10622184C211yesmaximal, characteristic, complemented
5#10622119C212yesmaximal, complemented
6C2×Q8×D11C412yes—
7C11×C4⋊Q8C2211yescharacteristic
8#66997C412yes—
9C4⋊C4×D11—22no—
10#66941—22no—
11C42×D11C2211yescharacteristic
12#66922C2211yescharacteristic
13C11×C4⋊C8C2212yes—
14(C2×D11)⋊C8—22no—
15#66879—22no—
16C4⋊(C11⋊C8)C2212yes—
17C2×Q8×C11C2×C412yes—
18Q8×D11—44no—
19C2×C4×D11—22no—
20C2×C4×D11C2×C411yescharacteristic
21C2×C4×D11D412yes—
22C2×Dic22—22no—
23C2×Dic22C2×C412yes—
24C2×C8×C11—22no—
25C11×C4⋊C4—22no—
26C42×C11C2311yescharacteristic
27C4⋊Dic11—22no—
28Dic11⋊C4—24no—
29C4×Dic11C2×C411yescharacteristic
30C4×Dic11D412yes—
31C2×C11⋊C8—22no—
32#1558—111nomaximal, Sylow
33C22×D11C22⋊C411yescharacteristic
34Q8×C11—42no—
35C2×C4×C11—22no—
36C2×C4×C11C22×C411yescharacteristic
37C2×C4×C11C2×D412yes—
38C2×Dic11—22no—
39C2×Dic11C22⋊C412yes—
40C2×Dic11C22⋊C411yescharacteristic
41C4×D11—22no—
42C4×D11—22no—
43C4×D11—22no—
44C4×D11—44no—
45Dic22—44no—
46Dic22—42no—
47C8×C11—42no—
48C11⋊C8—42no—
49C2×C4⋊Q8—111no—
50#432—112no—
51#333—111no—
52#333—112no—
53#333D1111yescharacteristic, complemented
54C22×C11C2×C22⋊C411yescharacteristic
55C2×D11—22no—
56C2×D11#10012yes—
57C4×C11—21no—
58C4×C11—42no—
59C4×C11#13712yes—
60C4×C11#13712yes—
61Dic11—21no—
62Dic11—22no—
63Dic11—42no—
64C22×Q8—112no—
65C4⋊Q8—112no—
66C4⋊Q8—111no—
67C4⋊Q8—222no—
68C4⋊Q8C2×D1111yescharacteristic
69C2×C4⋊C4—222no—
70C2×C42—111no—
71C4⋊C8—112no—
72C4⋊C8C2×D1112yes—
73C22⋊C8—222no—
74#97—222no—
75C2×C11C2×#10011yescharacteristic
76C2×C11#41912yes—
77D11—22no—
78C2×Q8—112no—
79C2×Q8—222no—
80C2×Q8—444no—
81C2×Q8C4×D1112yes—
82C22×C4—111no—
83C22×C4—112no—
84C22×C4—222no—
85C2×C8—22no—
86C2×C8—222no—
87C4⋊C4—22no—
88C4⋊C4—224no—
89C4⋊C4—222no—
90C42—111no—
91C42—112no—
92C42C22×D1111yescharacteristic
93C11#155811yescharacteristic, complemented, Sylow
94C23—111no—
95Q8—42no—
96Q8—442no—
97Q8—444no—
98C2×C4—22no—
99C2×C4—112no—
100C2×C4—111no—
101C2×C4—222no—
102C2×C4—222no—
103C2×C4—222no—
104C2×C4—222no—
105C2×C4—444no—
106C2×C4C2×C4×D1111yescharacteristic
107C2×C4D4×D1112yes—
108C8—42no—
109C8—442no—
110C22—112no—
111C22—222no—
112C22C22⋊C4×D1111yescharacteristic
113C4—21no—
114C4—42no—
115C4—221no—
116C4—222no—
117C4—442no—
118C4#6696812yes—
119C4#6697112yes—
120C2—222no—
121C2D11×#10011yescharacteristic
122C2#1062241512yes—
subgroupG/H
centerC22C22⋊C4×D11
commutatorC2×C4×C11C22×C4
FrattiniC42C22×D11
FittingC11×#333C2
socleC22×C11C2×C22⋊C4
prime radicalC22×D11C22⋊C4
cosocleC42×C11C23
hypercenter#333D11
hypocenterC11#1558
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
3. C11×#333C2semidirect
4. #10622184C2semidirect
5. #10622119C2semidirect
53. #333D11semidirect
93. C11#1558semidirect

Maximal subgroups

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

subgroupindex
D11×C4⋊Q82
#106224482
C11×#3332
#106221842
#106221192
#155811