Finite Group Databasebeta

← Q32×#64408 #22626326

Subgroups — Q32×#64408 #22626326

Order 9344.

150 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 50 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×#64408C212yesmaximal
2#17989513C211yesmaximal, characteristic
3#17989500C212yesmaximal
4C16×#64408C211yesmaximal, characteristic
5Q32×D73C211yesmaximal, characteristic
6Q8×#64408—22no—
7#14556664C2211yescharacteristic
8#14556660C2212yes—
9#14556654—22no—
10C8×#64408C2211yescharacteristic
11Q16×D73C2212yes—
12Dic584C411yescharacteristic, complemented
13#14556537C412yescomplemented
14C16×D73C2211yescharacteristic
15Q32×C73C411yescharacteristic, complemented
16#11924036D411yescharacteristic
17C4⋊#64408—22no—
18C4⋊#64408—42no—
19C4×#64408—42no—
20C4×#64408D411yescharacteristic
21#11924031—21no—
22Q8×D73—22no—
23Dic292C2×C412yes—
24#11924018—22no—
25C8×D73C2311yescharacteristic
26#11924003C2×C411yescharacteristic
27Q16×C73C2×C412yes—
28C16×C73C2×C411yescharacteristic
29C2×#64408—42no—
30C2×#64408D811yescharacteristic
31C2×#64408D811yescharacteristic
32Q8×C73—22no—
33C4×D73—42no—
34C4×D73C2×D411yescharacteristic
35Dic146—22no—
36Dic146—42no—
37#10596833—21no—
38C8×C73C22×C411yescharacteristic
39#10596831#4111yescharacteristic
40C2×D73C2×D811yescharacteristic
41#64408—21no—
42#64408—82no—
43#64408Q3212yesdirect product factor
44C4×C73—42no—
45C4×C73C4×D411yescharacteristic
46Dic73—42no—
47Dic73#13511yescharacteristic
48C2×C73C4×D811yescharacteristic
49D73C2×Q3211yescharacteristic
50D73#50811yescharacteristic
51C4×Q32—731nomaximal, Sylow
52C73C4×Q3211yescharacteristic, complemented, Sylow
53C2×Q32—731no—
54C4×Q16—732no—
55#366—731no—
56#358—732no—
57C4×C16—731no—
58C2×Q16—732no—
59C4×Q8—1462no—
60Q32—732no—
61Q32—731no—
62Q32#6440811yescharacteristic, direct product factor
63C2×C16—731no—
64C2×C16—731no—
65#107—732no—
66#103—1462no—
67C4×C8—731no—
68C2×Q8—1462no—
69Q16—732no—
70Q16—1462no—
71Q16C2×#6440812yes—
72C2×C8—731no—
73C2×C8—731no—
74C4⋊C4—2922no—
75C4⋊C4—1462no—
76C42—2922no—
77C42—731no—
78C16—731no—
79C16—1461no—
80C16C2×#6440811yescharacteristic
81Q8—22no—
82Q8—2922no—
83Q8—1462no—
84C2×C4—2922no—
85C2×C4—2922no—
86C2×C4—731no—
87C2×C4—731no—
88C2×C4—731no—
89C8—731no—
90C8—1461no—
91C8C22×#6440811yescharacteristic
92C22—731no—
93C4—42no—
94C4—2922no—
95C4—5842no—
96C4—732no—
97C4—731no—
98C4—1461no—
99C4D4×#6440811yescharacteristic
100C2—731no—
101C2—731no—
102C2D8×#6440811yescharacteristic
subgroupG/H
centerC2D8×#64408
commutatorC8×C73C22×C4
FrattiniC8C22×#64408
FittingQ32×C73C4
socleC2×C73C4×D8
hypercenterQ32#64408
hypocenterC73C4×Q32
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ Q32

Complements

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

NH ≅ G/Ntype
12. Dic584C4semidirect
13. #14556537C4semidirect
15. Q32×C73C4semidirect
43. #64408Q32direct (N × H)
52. C73C4×Q32semidirect
62. Q32#64408direct (N × H)