Finite Group Databasebeta

← #13070682

Subgroups — #13070682

Order 1408.

154 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 47 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
1C11×#495C211yesmaximal, characteristic, complemented
2#10622792C211yesmaximal, characteristic, complemented
3#10622760C211yesmaximal, characteristic
4#10622313C211yesmaximal, characteristic, complemented
5#10622203C211yesmaximal, characteristic, complemented
6#10622201C211yesmaximal, characteristic, complemented
7#10622101C211yesmaximal, characteristic, complemented
8C2×C11×Q16C2211yescharacteristic
9C2×C11×SD16—21no—
10C2×C11×D8C2211yescharacteristic
11C11×#124—21no—
12#66957C2211yescharacteristic
13#66954—21no—
14C4×C8×C11C2211yescharacteristic
15#66893—21no—
16#66892—21no—
17#66891—21no—
18#66890—21no—
19#66883C2211yescharacteristic
20#66876C2211yescharacteristic
21#66876C2211yescharacteristic
22#66869—21no—
23C2×Q8×C11—21no—
24C2×D4×C11—21no—
25#4339—21no—
26C11×Q16—21no—
27C11×Q16—21no—
28C11×SD16—41no—
29C11×SD16—41no—
30C11×D8—21no—
31C11×D8—21no—
32C2×C8×C11D411yescharacteristic
33C2×C8×C11C2311yescharacteristic
34C11×C22⋊C4—42no—
35C42×C11D411yescharacteristic
36#4318—21no—
37Dic44D411yescharacteristic
38D88D411yescharacteristic
39#4314—21no—
40#4313—41no—
41C8×D11—41no—
42C11⋊C16—21no—
43C11⋊C16—21no—
44#2212—111nomaximal, Sylow
45C23×C11—41no—
46Q8×C11—41no—
47Q8×C11—41no—
48D4×C11—41no—
49D4×C11—41no—
50C2×C4×C11—21no—
51C2×C4×C11—41no—
52C2×C4×C11C2×D411yescharacteristic
53C22⋊D11—41no—
54D44—21no—
55C4×D11—41no—
56Dic22—21no—
57C8×C11D811yescharacteristic
58C8×C11D811yescharacteristic
59C8×C11C2×D411yescharacteristic
60C8×C11#4111yescharacteristic
61C11⋊C8—41no—
62#510—111no—
63#509—111no—
64#495D1111yescharacteristic, complemented
65#443—111no—
66#364—111no—
67#362—111no—
68#361—111no—
69C22×C11—82no—
70C22×C11—81no—
71C22×C11AGL(1,ℤ/8)11yescharacteristic
72C2×D11—41no—
73C4×C11—41no—
74C4×C11—81no—
75C4×C11#12111yescharacteristic
76C4×C11C2×D811yescharacteristic
77Dic11—41no—
78#135—111no—
79C2×Q16C2×D1111yescharacteristic
80C2×SD16—21no—
81C2×D8C2×D1111yescharacteristic
82#131—221no—
83#124—21no—
84Q32—221no—
85SD32—221no—
86SD32—221no—
87D16—221no—
88M32—111no—
89M32—111no—
90#108—111no—
91#104—221no—
92C4×C8C2×D1111yescharacteristic
93C2×C11—21no—
94C2×C11—161no—
95C2×C11#45911yescharacteristic
96D11—81no—
97#41—221no—
98C2×Q8—21no—
99C2×D4—21no—
100Q16—21no—
101Q16—21no—
102Q16—111no—
103SD16—41no—
104SD16—41no—
105SD16—221no—
106D8—21no—
107D8—21no—
108D8—111no—
109M16—221no—
110M16—441no—
111C2×C8—441no—
112C2×C8C22⋊D1111yescharacteristic
113C2×C8C22×D1111yescharacteristic
114C22⋊C4—42no—
115C42C22⋊D1111yescharacteristic
116C16—221no—
117C16—221no—
118C11#221211yescharacteristic, complemented, Sylow
119C23—41no—
120Q8—41no—
121Q8—41no—
122Q8—221no—
123D4—41no—
124D4—41no—
125D4—221no—
126D4—441no—
127C2×C4—21no—
128C2×C4—41no—
129C2×C4—441no—
130C2×C4C2×C22⋊D1111yescharacteristic
131C8—441no—
132C8#432311yescharacteristic
133C8#432311yescharacteristic
134C8D4×D1111yescharacteristic
135C8#434111yescharacteristic
136C22—82no—
137C22—81no—
138C22—441no—
139C22#6698511yescharacteristic
140C4—41no—
141C4—81no—
142C4—441no—
143C4C2×#432311yescharacteristic
144C4#6699111yescharacteristic
145C2—21no—
146C2—161no—
147C2—881no—
148C2#1062268511yescharacteristic
subgroupG/H
centerC2#10622685
commutator, cosocleC2×C8×C11C23
FrattiniC2×C8C22×D11
FittingC11×#495C2
socleC2×C11#459
prime radical#10622760C2
hypercenter#495D11
hypocenterC11#2212
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #495

Complements

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

NH ≅ G/Ntype
1. C11×#495C2semidirect
2. #10622792C2semidirect
4. #10622313C2semidirect
5. #10622203C2semidirect
6. #10622201C2semidirect
7. #10622101C2semidirect
64. #495D11semidirect
118. C11#2212semidirect

Maximal subgroups

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

subgroupindex
C11×#4952
#106227922
#106227602
#106223132
#106222032
#106222012
#106221012
#221211