Finite Group Databasebeta

← #11771590

Subgroups — #11771590

Order 1152.

208 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 40 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
1Q16×C3⋊Dic3C211yesmaximal, characteristic
2#10590174C211yesmaximal, characteristic
3#10590171C211yesmaximal, characteristic
4C2×C32×Q16C411yescharacteristic
5Q8×C3⋊Dic3—21no—
6C4⋊#622—21no—
7C2×#3708—21no—
8#63662—21no—
9#63645C411yescharacteristic
10C8×C3⋊Dic3C2211yescharacteristic
11Dic3×Q16—62no—
12C2×C32×Q8—21no—
13C2×#622—41no—
14C32×Q16—21no—
15C32×Q16C812yescomplemented
16C2×C32×C8C2×C411yescharacteristic
17C4⋊(C3⋊Dic3)—21no—
18C4⋊(C3⋊Dic3)—41no—
19C4×C3⋊Dic3—41no—
20C4×C3⋊Dic3D411yescharacteristic
21C2×C3⋊(C3⋊C8)D411yescharacteristic
22#3708—22no—
23#1332—91nomaximal, Sylow
24C2×C3×Q16—22no—
25Q8×Dic3—64no—
26#835—64no—
27#818—62no—
28C8×Dic3—62no—
29C32×Q8—22no—
30C32×Q8—41no—
31C2×C32×C4—41no—
32C2×C32×C4C22⋊C411yescharacteristic
33C2×C3⋊Dic3—41no—
34C2×C3⋊Dic3D811yescharacteristic
35C2×C3⋊Dic3SD1611yescharacteristic
36#622—81no—
37C32×C8C2×C811yescharacteristic
38C32×C8M1611yescharacteristic
39C3⋊(C3⋊C8)—21no—
40C4×Q16—91no—
41C4×C16—91no—
42#335—91no—
43C2×C3×Q8—24no—
44C3×Q16—24no—
45C3×Q16—24no—
46C2×C3×C8—22no—
47C4⋊Dic3—64no—
48C4⋊Dic3—124no—
49C4×Dic3—62no—
50C4×Dic3—124no—
51C2×C3⋊C8—62no—
52C22×C32#10211yescharacteristic
53C32×C4—42no—
54C32×C4C22⋊C811yescharacteristic
55C32×C4#10411yescharacteristic
56C3⋊Dic3—21no—
57C3⋊Dic3—81no—
58C3⋊Dic3SD3211yescharacteristic
59C3⋊Dic3Q3211yescharacteristic
60C2×Q16#15711yescharacteristic
61C4×Q8—181no—
62C2×C16—181no—
63#107—91no—
64C4⋊C8—181no—
65#103—181no—
66C4×C8—91no—
67C3×Q8—28no—
68C3×Q8—44no—
69C2×C3×C4—22no—
70C2×C3×C4—44no—
71C2×Dic3—62no—
72C2×Dic3—62no—
73C2×Dic3—124no—
74C3×C8—22no—
75C3×C8—22no—
76C3⋊C8—122no—
77C2×C32D4⋊C811yescharacteristic
78C2×C32#35811yescharacteristic
79C2×C32#35911yescharacteristic
80C2×Q8—21no—
81Q16—21no—
82Q16#62212yescomplemented
83C2×C8—91no—
84C2×C8—361no—
85C2×C8C2×#15711yescharacteristic
86C4⋊C4—181no—
87C4⋊C4—361no—
88C42—91no—
89C42—361no—
90C16—182no—
91C22×C3—22no—
92C3×C4—22no—
93C3×C4—22no—
94C3×C4—48no—
95Dic3—62no—
96Dic3—62no—
97Dic3—122no—
98Dic3—244no—
99C32#133211yescharacteristic, complemented, Sylow
100Q8—22no—
101Q8—41no—
102C2×C4—41no—
103C2×C4—91no—
104C2×C4—91no—
105C2×C4—361no—
106C2×C4C22⋊#15711yescharacteristic
107C8—181no—
108C8—721no—
109C8C2×#62211yescharacteristic
110C8#379211yescharacteristic
111C2×C3—22no—
112C2×C3—22no—
113C2×C3—22no—
114C22#6378211yescharacteristic
115C4—42no—
116C4—91no—
117C4—91no—
118C4—181no—
119C4—721no—
120C4#6378311yescharacteristic
121C4C22⋊#62211yescharacteristic
122C3—22no—
123C2#1059019711yescharacteristic
124C2#1059019811yescharacteristic
125C2D4⋊#62211yescharacteristic
subgroupG/H
centerC22#63782
commutatorC32×C8C2×C8
FrattiniC2×C8C2×#157
FittingC2×C32×Q16C4
socle, prime radicalC22×C32#102
cosocleC8×C3⋊Dic3C22
hypercenterC2×Q16#157
hypocenterC32#1332
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
15. C32×Q16C8semidirect
82. Q16#622semidirect
99. C32#1332semidirect

Maximal subgroups

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

subgroupindex
Q16×C3⋊Dic32
#105901742
#105901712
#13329