Finite Group Databasebeta

← #22626330

Subgroups — #22626330

Order 9344.

146 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 46 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#17989629C212yesmaximal, complemented
2#17989515C211yesmaximal, characteristic, complemented
3#17989501C212yesmaximal, complemented
4C16×#64408C211yesmaximal, characteristic, complemented
5#17989016C211yesmaximal, characteristic
6#14556678—22no—
7#14556664C2211yescharacteristic
8#14556662C2212yes—
9#14556655—22no—
10C8×#64408C2211yescharacteristic
11#14556610C2212yes—
12Dic584C411yescharacteristic, complemented
13#14556535C412yescomplemented
14C16×D73C2211yescharacteristic
15D16×C73C411yescharacteristic, complemented
16#11924038—22no—
17#11924037—42no—
18#11924036D411yescharacteristic
19C2×#10596833—42no—
20C4×#64408D411yescharacteristic
21#11924031—21no—
22#11924027—22no—
23Dic292C2×C412yes—
24#11924016—22no—
25C8×D73C2311yescharacteristic
26#11924003C2×C411yescharacteristic
27D8×C73C2×C412yes—
28C16×C73C2×C411yescharacteristic
29C2×#64408—21no—
30D4×C73—22no—
31C22⋊D73—42no—
32C2×Dic73—42no—
33C4×D73C2×D411yescharacteristic
34Dic146—22no—
35#10596833—42no—
36#10596833D811yescharacteristic
37#10596833D811yescharacteristic
38C8×C73C22×C411yescharacteristic
39#10596831#4111yescharacteristic
40C22×C73—42no—
41C2×D73#13511yescharacteristic
42#64408—22no—
43C4×C73C4×D411yescharacteristic
44Dic73—42no—
45Dic73C2×D811yescharacteristic
46C2×C73—82no—
47C2×C73C4×D811yescharacteristic
48D73—21no—
49#2178—731nomaximal, Sylow
50C73#217811yescharacteristic, complemented, Sylow
51#508—731no—
52#443—732no—
53#368—731no—
54#359—732no—
55C4×C16—731no—
56#135—732no—
57#131—1462no—
58Q32—731no—
59SD32—732no—
60D16#6440811yescharacteristic, complemented
61C2×C16—731no—
62C2×C16—731no—
63#108—732no—
64#104—1462no—
65C4×C8—731no—
66#41—1462no—
67Q16—732no—
68SD16—1462no—
69D8C2×#6440812yes—
70M16—2922no—
71M16—1462no—
72C2×C8—2922no—
73C2×C8—731no—
74C2×C8—731no—
75C42—731no—
76C16—731no—
77C16—1461no—
78C16C2×#6440811yescharacteristic
79Q8—1462no—
80D4—22no—
81D4—2922no—
82C2×C4—2922no—
83C2×C4—731no—
84C2×C4—1461no—
85C8—2922no—
86C8—731no—
87C8—731no—
88C8—731no—
89C8C22×#6440811yescharacteristic
90C22—42no—
91C22—731no—
92C4—2922no—
93C4—731no—
94C4—1462no—
95C4D4×#6440811yescharacteristic
96C2—82no—
97C2—1461no—
98C2D8×#6440811yescharacteristic
subgroupG/H
centerC2D8×#64408
commutatorC8×C73C22×C4
FrattiniC8C22×#64408
FittingD16×C73C4
socleC2×C73C4×D8
hypercenterD16#64408
hypocenterC73#2178
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ D16

Complements

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

NH ≅ G/Ntype
1. #17989629C2semidirect
2. #17989515C2semidirect
3. #17989501C2semidirect
4. C16×#64408C2semidirect
12. Dic584C4semidirect
13. #14556535C4semidirect
15. D16×C73C4semidirect
50. C73#2178semidirect
60. D16#64408semidirect