Finite Group Databasebeta

← #13067697

Subgroups — #13067697

Order 1408.

240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 53 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#10623265C211yesmaximal, characteristic, complemented
2C11×#492C211yesmaximal, characteristic, complemented
3#10622685C212yesmaximal, complemented
4#10622184C211yesmaximal, characteristic, complemented
5#10622097C212yesmaximal, complemented
6C2×C11×SD16—22no—
7C11×C4⋊Q8C2211yescharacteristic
8C11×#127C2211yescharacteristic
9#67000—22no—
10C2×#4323—22no—
11#66948—22no—
12#66945—22no—
13C4×D44C2212yes—
14C4×C8×C11C2211yescharacteristic
15#66896—22no—
16C4⋊(C11⋊C8)C2212yes—
17C2×Q8×C11D412yes—
18C2×D4×C11—22no—
19C2×D4×C11—21no—
20C2×D44—22no—
21C2×D44D412yes—
22C2×C4×D11—22no—
23C11×SD16—44no—
24C2×C8×C11—21no—
25C11×C4⋊C4—22no—
26C42×C11C2311yescharacteristic
27#4323—44no—
28(C2×D11)⋊C4—24no—
29(C2×D11)⋊C4—22no—
30C4⋊Dic11D412yes—
31C4×Dic11—22no—
32C2×C11⋊C8—22no—
33#1624—111nomaximal, Sylow
34C23×C11—41no—
35C22×D11—22no—
36Q8×C11—42no—
37D4×C11—42no—
38D4×C11—42no—
39D4×C11—42no—
40C2×C4×C11—22no—
41C2×C4×C11C2×D412yes—
42C2×C4×C11C2×D411yescharacteristic
43C2×Dic11—22no—
44D44—22no—
45D44—22no—
46D44—82no—
47C4×D11—42no—
48C4×D11—42no—
49C8×C11—22no—
50C11⋊C8—42no—
51#555—111no—
52#492D1111yescharacteristic, complemented
53#459—112no—
54#333—111no—
55D4⋊C8—112no—
56C22×C11—82no—
57C22×C11—81no—
58C22×C11#12011yescharacteristic
59C2×D11—42no—
60C2×D11—42no—
61C2×D11—42no—
62C4×C11—21no—
63C4×C11—42no—
64C4×C11#13512yes—
65C4×C11AGL(1,ℤ/8)12yes—
66Dic11—42no—
67C2×SD16—22no—
68C2×D8—222no—
69C4⋊Q8C2×D1111yescharacteristic
70#127C2×D1111yescharacteristic
71#124—222no—
72#121—222no—
73C4×D4—112no—
74#117—222no—
75C4⋊C8—112no—
76#102—222no—
77C4×C8C2×D1111yescharacteristic
78C2×C11—161no—
79C2×C11#44912yes—
80C2×C11#45311yescharacteristic
81D11—82no—
82C2×Q8C22⋊D1112yes—
83C2×D4—22no—
84C2×D4—21no—
85C2×D4—112no—
86C2×D4—222no—
87C22×C4—222no—
88SD16—44no—
89D8—444no—
90C2×C8—21no—
91C2×C8—222no—
92C4⋊C4—22no—
93C4⋊C4—112no—
94C22⋊C4—224no—
95C22⋊C4—222no—
96C42—222no—
97C42C22×D1111yescharacteristic
98C11#162411yescharacteristic, complemented, Sylow
99C23—41no—
100C23—222no—
101Q8—42no—
102D4—42no—
103D4—42no—
104D4—42no—
105D4—222no—
106D4—222no—
107D4—882no—
108C2×C4—22no—
109C2×C4—222no—
110C2×C4—442no—
111C2×C4—442no—
112C2×C4D4×D1112yes—
113C2×C4C2×C22⋊D1111yescharacteristic
114C8—22no—
115C8—442no—
116C22—82no—
117C22—81no—
118C22—442no—
119C22—442no—
120C22—442no—
121C22#6699011yescharacteristic
122C4—21no—
123C4—42no—
124C4—442no—
125C4#6696712yes—
126C4#6696912yes—
127C2—161no—
128C2—882no—
129C2#1062269011yescharacteristic
130C2#1062278512yes—
subgroupG/H
centerC22#66990
commutator, cosocleC42×C11C23
FrattiniC42C22×D11
FittingC11×#492C2
socleC22×C11#120
hypercenter#492D11
hypocenterC11#1624
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #10623265C2semidirect
2. C11×#492C2semidirect
3. #10622685C2semidirect
4. #10622184C2semidirect
5. #10622097C2semidirect
52. #492D11semidirect
98. C11#1624semidirect

Maximal subgroups

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

subgroupindex
#106232652
C11×#4922
#106226852
#106221842
#106220972
#162411