Finite Group Databasebeta

← #13070517

Subgroups — #13070517

Order 1408.

154 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 51 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#10622765C211yesmaximal, characteristic, complemented
2#10622760C211yesmaximal, characteristic
3#10622507C211yesmaximal, characteristic, complemented
4C11×#361C211yesmaximal, characteristic, complemented
5#10622156C211yesmaximal, characteristic, complemented
6#10622150C211yesmaximal, characteristic, complemented
7#10622132C211yesmaximal, characteristic, complemented
8C2×C11×D8C2211yescharacteristic
9D4×Dic11—21no—
10#66960—21no—
11#66957C2211yescharacteristic
12C11×M32C2211yescharacteristic
13C11×#108C2211yescharacteristic
14#66896—21no—
15#66891C412yescomplemented
16#66890C412yescomplemented
17#66889—21no—
18#66881C2211yescharacteristic
19#66879C2211yescharacteristic
20#66876C2211yescharacteristic
21C2×D4×C11—21no—
22C22×Dic11—41no—
23#4339—21no—
24C11×D8—21no—
25C11×D8C2×C412yes—
26C11×M16—21no—
27C2×C8×C11C2311yescharacteristic
28C22⋊Dic11—41no—
29C4⋊Dic11—21no—
30C4×Dic11D411yescharacteristic
31C2×C11⋊C8D411yescharacteristic
32Dic44C2×C411yescharacteristic, complemented
33D88C2×C411yescharacteristic, complemented
34#4314—21no—
35#4313—41no—
36C8×D11—41no—
37C11×C16—21no—
38C11⋊C16C2×C412yescomplemented
39AGL(1,ℤ/16)—111nomaximal, Sylow
40C23×C11—41no—
41D4×C11—22no—
42D4×C11—41no—
43C2×C4×C11C2×D411yescharacteristic
44C22⋊D11—41no—
45C2×Dic11—21no—
46C2×Dic11—41no—
47C2×Dic11—82no—
48D44—21no—
49C4×D11—41no—
50Dic22—21no—
51C8×C11—41no—
52C8×C11C22×C411yescharacteristic
53C8×C11#4111yescharacteristic
54C11⋊C8—21no—
55#509—111no—
56#444—111no—
57#442—111no—
58#365—111no—
59#361D1111yescharacteristic, complemented
60#360—111no—
61#347—111no—
62C22×C11—42no—
63C22×C11—81no—
64C22×C11—81no—
65C22×C11AGL(1,ℤ/8)11yescharacteristic
66C2×D11—41no—
67C4×C11C4×D411yescharacteristic
68C4×C11AGL(1,ℤ/8)11yescharacteristic
69Dic11—41no—
70Dic11—41no—
71Dic11—81no—
72#135—111no—
73C2×D8C2×D1111yescharacteristic
74#131—221no—
75C4×D4—221no—
76SD32—112no—
77D16—112no—
78M32—111no—
79M32C2×D1111yescharacteristic
80#108C2×D1111yescharacteristic
81#106—111no—
82#104—221no—
83#102—221no—
84#97—111no—
85C2×C11—21no—
86C2×C11—82no—
87C2×C11#44211yescharacteristic
88D11—81no—
89#41—221no—
90C2×D4—21no—
91C22×C4—441no—
92Q16—111no—
93SD16—221no—
94D8—21no—
95D8—111no—
96D8C4×D1112yes—
97M16—21no—
98M16—441no—
99C2×C8—111no—
100C2×C8—441no—
101C2×C8C22×D1111yescharacteristic
102C4⋊C4—221no—
103C22⋊C4—441no—
104C42—111no—
105C16—21no—
106C16—112no—
107C11AGL(1,ℤ/16)11yescharacteristic, complemented, Sylow
108C23—41no—
109Q8—221no—
110D4—22no—
111D4—41no—
112D4—221no—
113D4—441no—
114C2×C4—221no—
115C2×C4—441no—
116C2×C4—441no—
117C2×C4—882no—
118C2×C4D4×D1111yescharacteristic
119C8—41no—
120C8—221no—
121C8C2×C4×D1111yescharacteristic
122C8#434111yescharacteristic
123C22—42no—
124C22—81no—
125C22—81no—
126C22—441no—
127C22#6696711yescharacteristic
128C4—441no—
129C4—441no—
130C4—881no—
131C4(C22⋊D11)⋊C411yescharacteristic
132C4#6696411yescharacteristic
133C2—21no—
134C2—82no—
135C2—881no—
136C2#1062239811yescharacteristic
subgroupG/H
centerC2#10622398
commutatorC8×C11C22×C4
FrattiniC2×C8C22×D11
FittingC11×#361C2
socleC2×C11#442
prime radical#10622760C2
cosocleC2×C8×C11C23
hypercenter#361D11
hypocenterC11AGL(1,ℤ/16)
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #361

Complements

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

NH ≅ G/Ntype
1. #10622765C2semidirect
3. #10622507C2semidirect
4. C11×#361C2semidirect
5. #10622156C2semidirect
6. #10622150C2semidirect
7. #10622132C2semidirect
15. #66891C4semidirect
16. #66890C4semidirect
32. Dic44C2×C4semidirect
33. D88C2×C4semidirect
38. C11⋊C16C2×C4semidirect
59. #361D11semidirect
107. C11AGL(1,ℤ/16)semidirect

Maximal subgroups

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

subgroupindex
#106227652
#106227602
#106225072
C11×#3612
#106221562
#106221502
#106221322
AGL(1,ℤ/16)11