Finite Group Databasebeta

← #11771626

Subgroups — #11771626

Order 1152.

206 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 38 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#10590175C211yesmaximal, characteristic
3#10590170C211yesmaximal, 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#1334—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—
41#346—91no—
42#334—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—21no—
58C3⋊Dic3—81no—
59C2×Q16#15711yescharacteristic
60C4×Q8—181no—
61C2×C16—181no—
62#107—91no—
63C4⋊C8—181no—
64#103—181no—
65C4×C8—91no—
66C3×Q8—28no—
67C3×Q8—44no—
68C2×C3×C4—22no—
69C2×C3×C4—44no—
70C2×Dic3—62no—
71C2×Dic3—62no—
72C2×Dic3—124no—
73C3×C8—22no—
74C3×C8—22no—
75C3⋊C8—122no—
76C2×C32D4⋊C811yescharacteristic
77C2×C32#36011yescharacteristic
78C2×C32#36211yescharacteristic
79C2×Q8—21no—
80Q16—21no—
81Q16#62212yescomplemented
82C2×C8—91no—
83C2×C8—361no—
84C2×C8C2×#15711yescharacteristic
85C4⋊C4—181no—
86C4⋊C4—361no—
87C42—91no—
88C42—361no—
89C16—182no—
90C22×C3—22no—
91C3×C4—22no—
92C3×C4—22no—
93C3×C4—48no—
94Dic3—64no—
95Dic3—122no—
96Dic3—244no—
97C32#133411yescharacteristic, complemented, Sylow
98Q8—22no—
99Q8—41no—
100C2×C4—41no—
101C2×C4—91no—
102C2×C4—91no—
103C2×C4—361no—
104C2×C4C22⋊#15711yescharacteristic
105C8—181no—
106C8—721no—
107C8C2×#62211yescharacteristic
108C8#379211yescharacteristic
109C2×C3—22no—
110C2×C3—22no—
111C2×C3—22no—
112C22#6378211yescharacteristic
113C4—42no—
114C4—181no—
115C4—181no—
116C4—721no—
117C4#6378311yescharacteristic
118C4C22⋊#62211yescharacteristic
119C3—22no—
120C2#1059019611yescharacteristic
121C2#1059019911yescharacteristic
122C2D4⋊#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#1334
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
81. Q16#622semidirect
97. C32#1334semidirect

Maximal subgroups

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

subgroupindex
Q16×C3⋊Dic32
#105901752
#105901702
#13349